LMFDB - Embedded newform 1859.2.a.o.1.7

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			1.7
Root			$-0.920076$ 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)

$f(q)$	$=$	$q+0.920076 q^{2} +0.898842 q^{3} -1.15346 q^{4} +2.76396 q^{5} +0.827003 q^{6} -3.49246 q^{7} -2.90142 q^{8} -2.19208 q^{9} +O(q^{10})$	\(q+0.920076 q^{2} +0.898842 q^{3} -1.15346 q^{4} +2.76396 q^{5} +0.827003 q^{6} -3.49246 q^{7} -2.90142 q^{8} -2.19208 q^{9} +2.54305 q^{10} +1.00000 q^{11} -1.03678 q^{12} -3.21333 q^{14} +2.48436 q^{15} -0.362608 q^{16} -2.81068 q^{17} -2.01688 q^{18} -0.317766 q^{19} -3.18812 q^{20} -3.13917 q^{21} +0.920076 q^{22} -1.29701 q^{23} -2.60792 q^{24} +2.63948 q^{25} -4.66686 q^{27} +4.02841 q^{28} +2.92413 q^{29} +2.28580 q^{30} -5.06660 q^{31} +5.46922 q^{32} +0.898842 q^{33} -2.58604 q^{34} -9.65303 q^{35} +2.52848 q^{36} -10.9591 q^{37} -0.292368 q^{38} -8.01942 q^{40} -4.96960 q^{41} -2.88827 q^{42} -0.952128 q^{43} -1.15346 q^{44} -6.05883 q^{45} -1.19335 q^{46} +5.36849 q^{47} -0.325928 q^{48} +5.19728 q^{49} +2.42853 q^{50} -2.52636 q^{51} -6.51071 q^{53} -4.29387 q^{54} +2.76396 q^{55} +10.1331 q^{56} -0.285621 q^{57} +2.69043 q^{58} -7.99471 q^{59} -2.86562 q^{60} -7.39024 q^{61} -4.66166 q^{62} +7.65576 q^{63} +5.75731 q^{64} +0.827003 q^{66} -11.2955 q^{67} +3.24201 q^{68} -1.16581 q^{69} -8.88152 q^{70} +10.3886 q^{71} +6.36016 q^{72} +14.3245 q^{73} -10.0832 q^{74} +2.37248 q^{75} +0.366530 q^{76} -3.49246 q^{77} +7.74098 q^{79} -1.00224 q^{80} +2.38148 q^{81} -4.57241 q^{82} -10.1740 q^{83} +3.62091 q^{84} -7.76861 q^{85} -0.876030 q^{86} +2.62833 q^{87} -2.90142 q^{88} -16.8188 q^{89} -5.57459 q^{90} +1.49605 q^{92} -4.55408 q^{93} +4.93942 q^{94} -0.878292 q^{95} +4.91596 q^{96} -12.2495 q^{97} +4.78189 q^{98} -2.19208 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.920076	0.650592	0.325296	−	0.945612i	$-0.394536\pi$
$2$	0.920076	0.650592	0.325296	+	0.945612i	$0.394536\pi$
$3$	0.898842	0.518947	0.259473	−	0.965750i	$-0.416451\pi$
$3$	0.898842	0.518947	0.259473	+	0.965750i	$0.416451\pi$
$4$	−1.15346	−0.576730
$5$	2.76396	1.23608	0.618041	−	0.786146i	$-0.287927\pi$
$5$	2.76396	1.23608	0.618041	+	0.786146i	$0.287927\pi$
$6$	0.827003	0.337622
$7$	−3.49246	−1.32003	−0.660013	−	0.751254i	$-0.729449\pi$
$7$	−3.49246	−1.32003	−0.660013	+	0.751254i	$0.729449\pi$
$8$	−2.90142	−1.02581
$9$	−2.19208	−0.730694
$10$	2.54305	0.804184
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.03678	−0.299292
$13$	0	0
$13$	0	0
$14$	−3.21333	−0.858798
$15$	2.48436	0.641460
$16$	−0.362608	−0.0906521
$17$	−2.81068	−0.681690	−0.340845	−	0.940119i	$-0.610713\pi$
$17$	−2.81068	−0.681690	−0.340845	+	0.940119i	$0.610713\pi$
$18$	−2.01688	−0.475384
$19$	−0.317766	−0.0729004	−0.0364502	−	0.999335i	$-0.511605\pi$
$19$	−0.317766	−0.0729004	−0.0364502	+	0.999335i	$0.511605\pi$
$20$	−3.18812	−0.712885
$21$	−3.13917	−0.685023
$22$	0.920076	0.196161
$23$	−1.29701	−0.270445	−0.135223	−	0.990815i	$-0.543175\pi$
$23$	−1.29701	−0.270445	−0.135223	+	0.990815i	$0.543175\pi$
$24$	−2.60792	−0.532339
$25$	2.63948	0.527897
$26$	0	0
$27$	−4.66686	−0.898138
$28$	4.02841	0.761299
$29$	2.92413	0.542998	0.271499	−	0.962439i	$-0.412481\pi$
$29$	2.92413	0.542998	0.271499	+	0.962439i	$0.412481\pi$
$30$	2.28580	0.417329
$31$	−5.06660	−0.909989	−0.454994	−	0.890494i	$-0.650359\pi$
$31$	−5.06660	−0.909989	−0.454994	+	0.890494i	$0.650359\pi$
$32$	5.46922	0.966830
$33$	0.898842	0.156468
$34$	−2.58604	−0.443502
$35$	−9.65303	−1.63166
$36$	2.52848	0.421414
$37$	−10.9591	−1.80167	−0.900836	−	0.434160i	$-0.857045\pi$
$37$	−10.9591	−1.80167	−0.900836	+	0.434160i	$0.857045\pi$
$38$	−0.292368	−0.0474284
$39$	0	0
$40$	−8.01942	−1.26798
$41$	−4.96960	−0.776122	−0.388061	−	0.921634i	$-0.626855\pi$
$41$	−4.96960	−0.776122	−0.388061	+	0.921634i	$0.626855\pi$
$42$	−2.88827	−0.445670
$43$	−0.952128	−0.145198	−0.0725991	−	0.997361i	$-0.523129\pi$
$43$	−0.952128	−0.145198	−0.0725991	+	0.997361i	$0.523129\pi$
$44$	−1.15346	−0.173891
$45$	−6.05883	−0.903198
$46$	−1.19335	−0.175949
$47$	5.36849	0.783075	0.391538	−	0.920162i	$-0.371943\pi$
$47$	5.36849	0.783075	0.391538	+	0.920162i	$0.371943\pi$
$48$	−0.325928	−0.0470436
$49$	5.19728	0.742468
$50$	2.42853	0.343445
$51$	−2.52636	−0.353761
$52$	0	0
$53$	−6.51071	−0.894315	−0.447158	−	0.894455i	$-0.647564\pi$
$53$	−6.51071	−0.894315	−0.447158	+	0.894455i	$0.647564\pi$
$54$	−4.29387	−0.584321
$55$	2.76396	0.372693
$56$	10.1331	1.35409
$57$	−0.285621	−0.0378314
$58$	2.69043	0.353270
$59$	−7.99471	−1.04082	−0.520411	−	0.853916i	$-0.674221\pi$
$59$	−7.99471	−1.04082	−0.520411	+	0.853916i	$0.674221\pi$
$60$	−2.86562	−0.369949
$61$	−7.39024	−0.946224	−0.473112	−	0.881002i	$-0.656869\pi$
$61$	−7.39024	−0.946224	−0.473112	+	0.881002i	$0.656869\pi$
$62$	−4.66166	−0.592031
$63$	7.65576	0.964536
$64$	5.75731	0.719664
$65$	0	0
$66$	0.827003	0.101797
$67$	−11.2955	−1.37996	−0.689982	−	0.723827i	$-0.742382\pi$
$67$	−11.2955	−1.37996	−0.689982	+	0.723827i	$0.742382\pi$
$68$	3.24201	0.393151
$69$	−1.16581	−0.140347
$70$	−8.88152	−1.06154
$71$	10.3886	1.23290	0.616451	−	0.787393i	$-0.288570\pi$
$71$	10.3886	1.23290	0.616451	+	0.787393i	$0.288570\pi$
$72$	6.36016	0.749552
$73$	14.3245	1.67656	0.838279	−	0.545241i	$-0.183562\pi$
$73$	14.3245	1.67656	0.838279	+	0.545241i	$0.183562\pi$
$74$	−10.0832	−1.17215
$75$	2.37248	0.273950
$76$	0.366530	0.0420439
$77$	−3.49246	−0.398003
$78$	0	0
$79$	7.74098	0.870928	0.435464	−	0.900206i	$-0.356584\pi$
$79$	7.74098	0.870928	0.435464	+	0.900206i	$0.356584\pi$
$80$	−1.00224	−0.112053
$81$	2.38148	0.264609
$82$	−4.57241	−0.504939
$83$	−10.1740	−1.11674	−0.558372	−	0.829591i	$-0.688574\pi$
$83$	−10.1740	−1.11674	−0.558372	+	0.829591i	$0.688574\pi$
$84$	3.62091	0.395073
$85$	−7.76861	−0.842624
$86$	−0.876030	−0.0944648
$87$	2.62833	0.281787
$88$	−2.90142	−0.309293
$89$	−16.8188	−1.78279	−0.891397	−	0.453224i	$-0.850274\pi$
$89$	−16.8188	−1.78279	−0.891397	+	0.453224i	$0.850274\pi$
$90$	−5.57459	−0.587613
$91$	0	0
$92$	1.49605	0.155974
$93$	−4.55408	−0.472236
$94$	4.93942	0.509462
$95$	−0.878292	−0.0901108
$96$	4.91596	0.501733
$97$	−12.2495	−1.24375	−0.621876	−	0.783115i	$-0.713629\pi$
$97$	−12.2495	−1.24375	−0.621876	+	0.783115i	$0.713629\pi$
$98$	4.78189	0.483044
$99$	−2.19208	−0.220313
$100$	−3.04454	−0.304454
$101$	−0.478436	−0.0476061	−0.0238031	−	0.999717i	$-0.507577\pi$
$101$	−0.478436	−0.0476061	−0.0238031	+	0.999717i	$0.507577\pi$
$102$	−2.32444	−0.230154
$103$	14.5230	1.43099	0.715496	−	0.698616i	$-0.246201\pi$
$103$	14.5230	1.43099	0.715496	+	0.698616i	$0.246201\pi$
$104$	0	0
$105$	−8.67654	−0.846744
$106$	−5.99035	−0.581834
$107$	19.4033	1.87579	0.937894	−	0.346921i	$-0.112773\pi$
$107$	19.4033	1.87579	0.937894	+	0.346921i	$0.112773\pi$
$108$	5.38304	0.517983
$109$	3.06474	0.293549	0.146774	−	0.989170i	$-0.453111\pi$
$109$	3.06474	0.293549	0.146774	+	0.989170i	$0.453111\pi$
$110$	2.54305	0.242471
$111$	−9.85054	−0.934971
$112$	1.26640	0.119663
$113$	13.0229	1.22509	0.612545	−	0.790436i	$-0.290146\pi$
$113$	13.0229	1.22509	0.612545	+	0.790436i	$0.290146\pi$
$114$	−0.262793	−0.0246128
$115$	−3.58489	−0.334292
$116$	−3.37287	−0.313163
$117$	0	0
$118$	−7.35574	−0.677151
$119$	9.81619	0.899849
$120$	−7.20819	−0.658015
$121$	1.00000	0.0909091
$122$	−6.79959	−0.615606
$123$	−4.46689	−0.402766
$124$	5.84413	0.524818
$125$	−6.52438	−0.583558
$126$	7.04388	0.627519
$127$	18.2918	1.62314	0.811568	−	0.584258i	$-0.198614\pi$
$127$	18.2918	1.62314	0.811568	+	0.584258i	$0.198614\pi$
$128$	−5.64127	−0.498623
$129$	−0.855813	−0.0753501
$130$	0	0
$131$	−2.69291	−0.235280	−0.117640	−	0.993056i	$-0.537533\pi$
$131$	−2.69291	−0.235280	−0.117640	+	0.993056i	$0.537533\pi$
$132$	−1.03678	−0.0902400
$133$	1.10978	0.0962304
$134$	−10.3927	−0.897793
$135$	−12.8990	−1.11017
$136$	8.15497	0.699283
$137$	3.60773	0.308229	0.154114	−	0.988053i	$-0.450748\pi$
$137$	3.60773	0.308229	0.154114	+	0.988053i	$0.450748\pi$
$138$	−1.07263	−0.0913084
$139$	19.1140	1.62123	0.810613	−	0.585583i	$-0.199134\pi$
$139$	19.1140	1.62123	0.810613	+	0.585583i	$0.199134\pi$
$140$	11.1344	0.941027
$141$	4.82543	0.406374
$142$	9.55832	0.802117
$143$	0	0
$144$	0.794868	0.0662390
$145$	8.08219	0.671190
$146$	13.1796	1.09076
$147$	4.67153	0.385301
$148$	12.6409	1.03908
$149$	17.6824	1.44860	0.724298	−	0.689487i	$-0.242164\pi$
$149$	17.6824	1.44860	0.724298	+	0.689487i	$0.242164\pi$
$150$	2.18286	0.178230
$151$	−14.6794	−1.19459	−0.597297	−	0.802020i	$-0.703759\pi$
$151$	−14.6794	−1.19459	−0.597297	+	0.802020i	$0.703759\pi$
$152$	0.921972	0.0747818
$153$	6.16125	0.498107
$154$	−3.21333	−0.258937
$155$	−14.0039	−1.12482
$156$	0	0
$157$	5.77063	0.460546	0.230273	−	0.973126i	$-0.426038\pi$
$157$	5.77063	0.460546	0.230273	+	0.973126i	$0.426038\pi$
$158$	7.12229	0.566619
$159$	−5.85210	−0.464102
$160$	15.1167	1.19508
$161$	4.52976	0.356995
$162$	2.19114	0.172152
$163$	−6.36270	−0.498365	−0.249183	−	0.968457i	$-0.580162\pi$
$163$	−6.36270	−0.498365	−0.249183	+	0.968457i	$0.580162\pi$
$164$	5.73224	0.447613
$165$	2.48436	0.193407
$166$	−9.36086	−0.726544
$167$	−11.2501	−0.870561	−0.435281	−	0.900295i	$-0.643351\pi$
$167$	−11.2501	−0.870561	−0.435281	+	0.900295i	$0.643351\pi$
$168$	9.10806	0.702702
$169$	0	0
$170$	−7.14771	−0.548205
$171$	0.696569	0.0532679
$172$	1.09824	0.0837402
$173$	−12.4319	−0.945177	−0.472588	−	0.881283i	$-0.656680\pi$
$173$	−12.4319	−0.945177	−0.472588	+	0.881283i	$0.656680\pi$
$174$	2.41827	0.183328
$175$	−9.21829	−0.696837
$176$	−0.362608	−0.0273326
$177$	−7.18598	−0.540132
$178$	−15.4746	−1.15987
$179$	−11.1239	−0.831438	−0.415719	−	0.909493i	$-0.636470\pi$
$179$	−11.1239	−0.831438	−0.415719	+	0.909493i	$0.636470\pi$
$180$	6.98863	0.520901
$181$	−10.9348	−0.812778	−0.406389	−	0.913700i	$-0.633212\pi$
$181$	−10.9348	−0.812778	−0.406389	+	0.913700i	$0.633212\pi$
$182$	0	0
$183$	−6.64266	−0.491040
$184$	3.76317	0.277425
$185$	−30.2906	−2.22701
$186$	−4.19010	−0.307233
$187$	−2.81068	−0.205537
$188$	−6.19234	−0.451623
$189$	16.2988	1.18557
$190$	−0.808095	−0.0586254
$191$	−7.36082	−0.532611	−0.266305	−	0.963889i	$-0.585803\pi$
$191$	−7.36082	−0.532611	−0.266305	+	0.963889i	$0.585803\pi$
$192$	5.17491	0.373467
$193$	24.7381	1.78069	0.890344	−	0.455287i	$-0.150464\pi$
$193$	24.7381	1.78069	0.890344	+	0.455287i	$0.150464\pi$
$194$	−11.2705	−0.809175
$195$	0	0
$196$	−5.99485	−0.428204
$197$	−13.8178	−0.984479	−0.492239	−	0.870460i	$-0.663822\pi$
$197$	−13.8178	−0.984479	−0.492239	+	0.870460i	$0.663822\pi$
$198$	−2.01688	−0.143334
$199$	9.78062	0.693330	0.346665	−	0.937989i	$-0.387314\pi$
$199$	9.78062	0.693330	0.346665	+	0.937989i	$0.387314\pi$
$200$	−7.65826	−0.541521
$201$	−10.1529	−0.716128
$202$	−0.440197	−0.0309722
$203$	−10.2124	−0.716771
$204$	2.91405	0.204024
$205$	−13.7358	−0.959350
$206$	13.3623	0.930992
$207$	2.84315	0.197613
$208$	0	0
$209$	−0.317766	−0.0219803
$210$	−7.98308	−0.550885
$211$	−7.84922	−0.540363	−0.270181	−	0.962809i	$-0.587084\pi$
$211$	−7.84922	−0.540363	−0.270181	+	0.962809i	$0.587084\pi$
$212$	7.50985	0.515779
$213$	9.33773	0.639811
$214$	17.8525	1.22037
$215$	−2.63165	−0.179477
$216$	13.5405	0.921317
$217$	17.6949	1.20121
$218$	2.81979	0.190980
$219$	12.8755	0.870044
$220$	−3.18812	−0.214943
$221$	0	0
$222$	−9.06324	−0.608285
$223$	9.88993	0.662279	0.331140	−	0.943582i	$-0.392567\pi$
$223$	9.88993	0.662279	0.331140	+	0.943582i	$0.392567\pi$
$224$	−19.1010	−1.27624
$225$	−5.78597	−0.385731
$226$	11.9820	0.797033
$227$	−6.00459	−0.398539	−0.199269	−	0.979945i	$-0.563857\pi$
$227$	−6.00459	−0.398539	−0.199269	+	0.979945i	$0.563857\pi$
$228$	0.329452	0.0218185
$229$	−23.8186	−1.57398	−0.786990	−	0.616966i	$-0.788361\pi$
$229$	−23.8186	−1.57398	−0.786990	+	0.616966i	$0.788361\pi$
$230$	−3.29837	−0.217488
$231$	−3.13917	−0.206542
$232$	−8.48415	−0.557012
$233$	−0.975770	−0.0639248	−0.0319624	−	0.999489i	$-0.510176\pi$
$233$	−0.975770	−0.0639248	−0.0319624	+	0.999489i	$0.510176\pi$
$234$	0	0
$235$	14.8383	0.967945
$236$	9.22158	0.600274
$237$	6.95791	0.451965
$238$	9.03164	0.585434
$239$	−13.2120	−0.854615	−0.427308	−	0.904106i	$-0.640538\pi$
$239$	−13.2120	−0.854615	−0.427308	+	0.904106i	$0.640538\pi$
$240$	−0.900851	−0.0581497
$241$	6.19919	0.399325	0.199662	−	0.979865i	$-0.436015\pi$
$241$	6.19919	0.399325	0.199662	+	0.979865i	$0.436015\pi$
$242$	0.920076	0.0591447
$243$	16.1412	1.03546
$244$	8.52435	0.545716
$245$	14.3651	0.917751
$246$	−4.10988	−0.262036
$247$	0	0
$248$	14.7004	0.933474
$249$	−9.14483	−0.579530
$250$	−6.00292	−0.379658
$251$	−11.1748	−0.705346	−0.352673	−	0.935747i	$-0.614727\pi$
$251$	−11.1748	−0.705346	−0.352673	+	0.935747i	$0.614727\pi$
$252$	−8.83062	−0.556277
$253$	−1.29701	−0.0815423
$254$	16.8299	1.05600
$255$	−6.98275	−0.437277
$256$	−16.7050	−1.04406
$257$	−27.6872	−1.72708	−0.863539	−	0.504282i	$-0.831757\pi$
$257$	−27.6872	−1.72708	−0.863539	+	0.504282i	$0.831757\pi$
$258$	−0.787413	−0.0490222
$259$	38.2744	2.37825
$260$	0	0
$261$	−6.40995	−0.396766
$262$	−2.47768	−0.153071
$263$	13.9811	0.862111	0.431055	−	0.902325i	$-0.358141\pi$
$263$	13.9811	0.862111	0.431055	+	0.902325i	$0.358141\pi$
$264$	−2.60792	−0.160506
$265$	−17.9954	−1.10545
$266$	1.02108	0.0626067
$267$	−15.1175	−0.925174
$268$	13.0289	0.795867
$269$	−7.01168	−0.427510	−0.213755	−	0.976887i	$-0.568569\pi$
$269$	−7.01168	−0.427510	−0.213755	+	0.976887i	$0.568569\pi$
$270$	−11.8681	−0.722269
$271$	18.3961	1.11748	0.558742	−	0.829341i	$-0.311284\pi$
$271$	18.3961	1.11748	0.558742	+	0.829341i	$0.311284\pi$
$272$	1.01918	0.0617966
$273$	0	0
$274$	3.31938	0.200531
$275$	2.63948	0.159167
$276$	1.34471	0.0809421
$277$	−17.5215	−1.05276	−0.526381	−	0.850249i	$-0.676452\pi$
$277$	−17.5215	−1.05276	−0.526381	+	0.850249i	$0.676452\pi$
$278$	17.5863	1.05476
$279$	11.1064	0.664924
$280$	28.0075	1.67377
$281$	2.88328	0.172002	0.0860010	−	0.996295i	$-0.472591\pi$
$281$	2.88328	0.172002	0.0860010	+	0.996295i	$0.472591\pi$
$282$	4.43976	0.264384
$283$	14.0396	0.834569	0.417284	−	0.908776i	$-0.362982\pi$
$283$	14.0396	0.834569	0.417284	+	0.908776i	$0.362982\pi$
$284$	−11.9829	−0.711052
$285$	−0.789445	−0.0467627
$286$	0	0
$287$	17.3561	1.02450
$288$	−11.9890	−0.706458
$289$	−9.10008	−0.535299
$290$	7.43623	0.436671
$291$	−11.0104	−0.645441
$292$	−16.5228	−0.966922
$293$	−18.8256	−1.09980	−0.549901	−	0.835230i	$-0.685334\pi$
$293$	−18.8256	−1.09980	−0.549901	+	0.835230i	$0.685334\pi$
$294$	4.29816	0.250674
$295$	−22.0971	−1.28654
$296$	31.7971	1.84817
$297$	−4.66686	−0.270799
$298$	16.2691	0.942445
$299$	0	0
$300$	−2.73656	−0.157995
$301$	3.32527	0.191665
$302$	−13.5062	−0.777193
$303$	−0.430038	−0.0247050
$304$	0.115224	0.00660857
$305$	−20.4264	−1.16961
$306$	5.66881	0.324064
$307$	9.79069	0.558784	0.279392	−	0.960177i	$-0.409867\pi$
$307$	9.79069	0.558784	0.279392	+	0.960177i	$0.409867\pi$
$308$	4.02841	0.229540
$309$	13.0539	0.742609
$310$	−12.8846	−0.731799
$311$	−5.02318	−0.284838	−0.142419	−	0.989806i	$-0.545488\pi$
$311$	−5.02318	−0.284838	−0.142419	+	0.989806i	$0.545488\pi$
$312$	0	0
$313$	24.3202	1.37466	0.687329	−	0.726346i	$-0.258783\pi$
$313$	24.3202	1.37466	0.687329	+	0.726346i	$0.258783\pi$
$314$	5.30942	0.299628
$315$	21.1602	1.19224
$316$	−8.92891	−0.502291
$317$	23.8080	1.33719	0.668594	−	0.743627i	$-0.266896\pi$
$317$	23.8080	1.33719	0.668594	+	0.743627i	$0.266896\pi$
$318$	−5.38438	−0.301941
$319$	2.92413	0.163720
$320$	15.9130	0.889563
$321$	17.4405	0.973434
$322$	4.16772	0.232258
$323$	0.893137	0.0496955
$324$	−2.74694	−0.152608
$325$	0	0
$326$	−5.85417	−0.324232
$327$	2.75471	0.152336
$328$	14.4189	0.796152
$329$	−18.7492	−1.03368
$330$	2.28580	0.125829
$331$	−13.9917	−0.769052	−0.384526	−	0.923114i	$-0.625635\pi$
$331$	−13.9917	−0.769052	−0.384526	+	0.923114i	$0.625635\pi$
$332$	11.7353	0.644059
$333$	24.0234	1.31647
$334$	−10.3510	−0.566380
$335$	−31.2203	−1.70575
$336$	1.13829	0.0620988
$337$	12.1376	0.661176	0.330588	−	0.943775i	$-0.392753\pi$
$337$	12.1376	0.661176	0.330588	+	0.943775i	$0.392753\pi$
$338$	0	0
$339$	11.7055	0.635756
$340$	8.96079	0.485967
$341$	−5.06660	−0.274372
$342$	0.640896	0.0346557
$343$	6.29594	0.339949
$344$	2.76253	0.148945
$345$	−3.22224	−0.173480
$346$	−11.4383	−0.614924
$347$	4.21569	0.226310	0.113155	−	0.993577i	$-0.463904\pi$
$347$	4.21569	0.226310	0.113155	+	0.993577i	$0.463904\pi$
$348$	−3.03168	−0.162515
$349$	2.79896	0.149825	0.0749125	−	0.997190i	$-0.476132\pi$
$349$	2.79896	0.149825	0.0749125	+	0.997190i	$0.476132\pi$
$350$	−8.48153	−0.453357
$351$	0	0
$352$	5.46922	0.291510
$353$	17.1664	0.913676	0.456838	−	0.889550i	$-0.348982\pi$
$353$	17.1664	0.913676	0.456838	+	0.889550i	$0.348982\pi$
$354$	−6.61165	−0.351405
$355$	28.7138	1.52397
$356$	19.3999	1.02819
$357$	8.82320	0.466973
$358$	−10.2348	−0.540927
$359$	0.258832	0.0136606	0.00683031	−	0.999977i	$-0.497826\pi$
$359$	0.258832	0.0136606	0.00683031	+	0.999977i	$0.497826\pi$
$360$	17.5792	0.926507
$361$	−18.8990	−0.994686
$362$	−10.0609	−0.528787
$363$	0.898842	0.0471770
$364$	0	0
$365$	39.5924	2.07236
$366$	−6.11175	−0.319466
$367$	0.818779	0.0427399	0.0213700	−	0.999772i	$-0.493197\pi$
$367$	0.818779	0.0427399	0.0213700	+	0.999772i	$0.493197\pi$
$368$	0.470307	0.0245164
$369$	10.8938	0.567108
$370$	−27.8697	−1.44888
$371$	22.7384	1.18052
$372$	5.25295	0.272353
$373$	−16.3987	−0.849091	−0.424545	−	0.905407i	$-0.639566\pi$
$373$	−16.3987	−0.849091	−0.424545	+	0.905407i	$0.639566\pi$
$374$	−2.58604	−0.133721
$375$	−5.86438	−0.302835
$376$	−15.5763	−0.803285
$377$	0	0
$378$	14.9962	0.771319
$379$	25.6855	1.31938	0.659689	−	0.751539i	$-0.270688\pi$
$379$	25.6855	1.31938	0.659689	+	0.751539i	$0.270688\pi$
$380$	1.01307	0.0519696
$381$	16.4414	0.842321
$382$	−6.77252	−0.346512
$383$	26.3618	1.34702	0.673511	−	0.739177i	$-0.264785\pi$
$383$	26.3618	1.34702	0.673511	+	0.739177i	$0.264785\pi$
$384$	−5.07061	−0.258759
$385$	−9.65303	−0.491964
$386$	22.7609	1.15850
$387$	2.08714	0.106096
$388$	14.1294	0.717310
$389$	12.7576	0.646835	0.323418	−	0.946256i	$-0.395168\pi$
$389$	12.7576	0.646835	0.323418	+	0.946256i	$0.395168\pi$
$390$	0	0
$391$	3.64548	0.184360
$392$	−15.0795	−0.761630
$393$	−2.42050	−0.122098
$394$	−12.7134	−0.640494
$395$	21.3958	1.07654
$396$	2.52848	0.127061
$397$	−12.8228	−0.643559	−0.321780	−	0.946815i	$-0.604281\pi$
$397$	−12.8228	−0.643559	−0.321780	+	0.946815i	$0.604281\pi$
$398$	8.99891	0.451075
$399$	0.997520	0.0499385
$400$	−0.957099	−0.0478549
$401$	−31.2159	−1.55885	−0.779424	−	0.626497i	$-0.784488\pi$
$401$	−31.2159	−1.55885	−0.779424	+	0.626497i	$0.784488\pi$
$402$	−9.34140	−0.465907
$403$	0	0
$404$	0.551857	0.0274559
$405$	6.58232	0.327078
$406$	−9.39620	−0.466326
$407$	−10.9591	−0.543225
$408$	7.33003	0.362891
$409$	−6.98947	−0.345607	−0.172804	−	0.984956i	$-0.555283\pi$
$409$	−6.98947	−0.345607	−0.172804	+	0.984956i	$0.555283\pi$
$410$	−12.6380	−0.624145
$411$	3.24278	0.159954
$412$	−16.7517	−0.825297
$413$	27.9212	1.37391
$414$	2.61592	0.128565
$415$	−28.1206	−1.38039
$416$	0	0
$417$	17.1804	0.841329
$418$	−0.292368	−0.0143002
$419$	36.3080	1.77376	0.886881	−	0.461998i	$-0.152867\pi$
$419$	36.3080	1.77376	0.886881	+	0.461998i	$0.152867\pi$
$420$	10.0080	0.488343
$421$	9.98294	0.486539	0.243269	−	0.969959i	$-0.421780\pi$
$421$	9.98294	0.486539	0.243269	+	0.969959i	$0.421780\pi$
$422$	−7.22188	−0.351556
$423$	−11.7682	−0.572189
$424$	18.8903	0.917396
$425$	−7.41874	−0.359862
$426$	8.59142	0.416256
$427$	25.8101	1.24904
$428$	−22.3809	−1.08182
$429$	0	0
$430$	−2.42131	−0.116766
$431$	−24.4172	−1.17614	−0.588068	−	0.808812i	$-0.700111\pi$
$431$	−24.4172	−1.17614	−0.588068	+	0.808812i	$0.700111\pi$
$432$	1.69224	0.0814181
$433$	21.6079	1.03841	0.519205	−	0.854650i	$-0.326228\pi$
$433$	21.6079	1.03841	0.519205	+	0.854650i	$0.326228\pi$
$434$	16.2807	0.781497
$435$	7.26461	0.348312
$436$	−3.53505	−0.169298
$437$	0.412145	0.0197156
$438$	11.8464	0.566044
$439$	−35.0649	−1.67355	−0.836777	−	0.547543i	$-0.815563\pi$
$439$	−35.0649	−1.67355	−0.836777	+	0.547543i	$0.815563\pi$
$440$	−8.01942	−0.382311
$441$	−11.3929	−0.542517
$442$	0	0
$443$	−21.5193	−1.02241	−0.511206	−	0.859458i	$-0.670801\pi$
$443$	−21.5193	−1.02241	−0.511206	+	0.859458i	$0.670801\pi$
$444$	11.3622	0.539226
$445$	−46.4866	−2.20368
$446$	9.09949	0.430873
$447$	15.8936	0.751744
$448$	−20.1072	−0.949975
$449$	−3.75661	−0.177285	−0.0886426	−	0.996063i	$-0.528253\pi$
$449$	−3.75661	−0.177285	−0.0886426	+	0.996063i	$0.528253\pi$
$450$	−5.32353	−0.250954
$451$	−4.96960	−0.234010
$452$	−15.0214	−0.706546
$453$	−13.1945	−0.619930
$454$	−5.52468	−0.259286
$455$	0	0
$456$	0.828707	0.0388078
$457$	−7.02271	−0.328509	−0.164254	−	0.986418i	$-0.552522\pi$
$457$	−7.02271	−0.328509	−0.164254	+	0.986418i	$0.552522\pi$
$458$	−21.9149	−1.02402
$459$	13.1171	0.612252
$460$	4.13502	0.192796
$461$	−9.36293	−0.436075	−0.218038	−	0.975940i	$-0.569966\pi$
$461$	−9.36293	−0.436075	−0.218038	+	0.975940i	$0.569966\pi$
$462$	−2.88827	−0.134375
$463$	19.0225	0.884051	0.442026	−	0.897002i	$-0.354260\pi$
$463$	19.0225	0.884051	0.442026	+	0.897002i	$0.354260\pi$
$464$	−1.06032	−0.0492239
$465$	−12.5873	−0.583722
$466$	−0.897782	−0.0415890
$467$	−0.590106	−0.0273069	−0.0136534	−	0.999907i	$-0.504346\pi$
$467$	−0.590106	−0.0273069	−0.0136534	+	0.999907i	$0.504346\pi$
$468$	0	0
$469$	39.4491	1.82159
$470$	13.6524	0.629737
$471$	5.18688	0.238999
$472$	23.1960	1.06768
$473$	−0.952128	−0.0437789
$474$	6.40181	0.294045
$475$	−0.838737	−0.0384839
$476$	−11.3226	−0.518970
$477$	14.2720	0.653471
$478$	−12.1561	−0.556006
$479$	−1.71629	−0.0784193	−0.0392096	−	0.999231i	$-0.512484\pi$
$479$	−1.71629	−0.0784193	−0.0392096	+	0.999231i	$0.512484\pi$
$480$	13.5875	0.620183
$481$	0	0
$482$	5.70373	0.259798
$483$	4.07153	0.185261
$484$	−1.15346	−0.0524300
$485$	−33.8573	−1.53738
$486$	14.8511	0.673659
$487$	−27.6315	−1.25210	−0.626051	−	0.779782i	$-0.715330\pi$
$487$	−27.6315	−1.25210	−0.626051	+	0.779782i	$0.715330\pi$
$488$	21.4422	0.970644
$489$	−5.71906	−0.258625
$490$	13.2170	0.597081
$491$	15.0698	0.680092	0.340046	−	0.940409i	$-0.389557\pi$
$491$	15.0698	0.680092	0.340046	+	0.940409i	$0.389557\pi$
$492$	5.15238	0.232287
$493$	−8.21881	−0.370156
$494$	0	0
$495$	−6.05883	−0.272324
$496$	1.83719	0.0824924
$497$	−36.2819	−1.62746
$498$	−8.41394	−0.377038
$499$	−26.9347	−1.20576	−0.602881	−	0.797831i	$-0.705981\pi$
$499$	−26.9347	−1.20576	−0.602881	+	0.797831i	$0.705981\pi$
$500$	7.52561	0.336556
$501$	−10.1121	−0.451775
$502$	−10.2816	−0.458892
$503$	13.3962	0.597309	0.298654	−	0.954361i	$-0.403462\pi$
$503$	13.3962	0.597309	0.298654	+	0.954361i	$0.403462\pi$
$504$	−22.2126	−0.989428
$505$	−1.32238	−0.0588451
$506$	−1.19335	−0.0530508
$507$	0	0
$508$	−21.0989	−0.936111
$509$	−11.7260	−0.519745	−0.259872	−	0.965643i	$-0.583680\pi$
$509$	−11.7260	−0.519745	−0.259872	+	0.965643i	$0.583680\pi$
$510$	−6.42466	−0.284489
$511$	−50.0278	−2.21310
$512$	−4.08734	−0.180637
$513$	1.48297	0.0654746
$514$	−25.4743	−1.12362
$515$	40.1410	1.76882
$516$	0.987146	0.0434567
$517$	5.36849	0.236106
$518$	35.2153	1.54727
$519$	−11.1743	−0.490496
$520$	0	0
$521$	−40.9088	−1.79225	−0.896125	−	0.443803i	$-0.853629\pi$
$521$	−40.9088	−1.79225	−0.896125	+	0.443803i	$0.853629\pi$
$522$	−5.89764	−0.258133
$523$	17.9946	0.786847	0.393423	−	0.919357i	$-0.371291\pi$
$523$	17.9946	0.786847	0.393423	+	0.919357i	$0.371291\pi$
$524$	3.10616	0.135693
$525$	−8.28579	−0.361621
$526$	12.8637	0.560882
$527$	14.2406	0.620330
$528$	−0.325928	−0.0141842
$529$	−21.3178	−0.926859
$530$	−16.5571	−0.719194
$531$	17.5251	0.760524
$532$	−1.28009	−0.0554990
$533$	0	0
$534$	−13.9092	−0.601911
$535$	53.6300	2.31863
$536$	32.7730	1.41558
$537$	−9.99861	−0.431472
$538$	−6.45128	−0.278135
$539$	5.19728	0.223863
$540$	14.8785	0.640269
$541$	−25.5658	−1.09916	−0.549579	−	0.835442i	$-0.685212\pi$
$541$	−25.5658	−1.09916	−0.549579	+	0.835442i	$0.685212\pi$
$542$	16.9258	0.727026
$543$	−9.82867	−0.421789
$544$	−15.3722	−0.659079
$545$	8.47082	0.362850
$546$	0	0
$547$	−15.2924	−0.653856	−0.326928	−	0.945049i	$-0.606013\pi$
$547$	−15.2924	−0.653856	−0.326928	+	0.945049i	$0.606013\pi$
$548$	−4.16137	−0.177765
$549$	16.2000	0.691400
$550$	2.42853	0.103553
$551$	−0.929189	−0.0395848
$552$	3.38250	0.143969
$553$	−27.0351	−1.14965
$554$	−16.1211	−0.684919
$555$	−27.2265	−1.15570
$556$	−22.0472	−0.935010
$557$	30.4136	1.28866	0.644332	−	0.764746i	$-0.277135\pi$
$557$	30.4136	1.28866	0.644332	+	0.764746i	$0.277135\pi$
$558$	10.2187	0.432594
$559$	0	0
$560$	3.50027	0.147913
$561$	−2.52636	−0.106663
$562$	2.65283	0.111903
$563$	−28.2468	−1.19046	−0.595231	−	0.803555i	$-0.702939\pi$
$563$	−28.2468	−1.19046	−0.595231	+	0.803555i	$0.702939\pi$
$564$	−5.56594	−0.234368
$565$	35.9947	1.51431
$566$	12.9175	0.542964
$567$	−8.31722	−0.349291
$568$	−30.1418	−1.26472
$569$	−29.2112	−1.22460	−0.612299	−	0.790626i	$-0.709755\pi$
$569$	−29.2112	−1.22460	−0.612299	+	0.790626i	$0.709755\pi$
$570$	−0.726350	−0.0304234
$571$	5.27540	0.220768	0.110384	−	0.993889i	$-0.464792\pi$
$571$	5.27540	0.220768	0.110384	+	0.993889i	$0.464792\pi$
$572$	0	0
$573$	−6.61622	−0.276396
$574$	15.9690	0.666532
$575$	−3.42344	−0.142767
$576$	−12.6205	−0.525855
$577$	−17.5199	−0.729364	−0.364682	−	0.931132i	$-0.618822\pi$
$577$	−17.5199	−0.729364	−0.364682	+	0.931132i	$0.618822\pi$
$578$	−8.37276	−0.348261
$579$	22.2357	0.924082
$580$	−9.32249	−0.387095
$581$	35.5323	1.47413
$582$	−10.1304	−0.419919
$583$	−6.51071	−0.269646
$584$	−41.5615	−1.71983
$585$	0	0
$586$	−17.3210	−0.715522
$587$	−25.7262	−1.06183	−0.530917	−	0.847424i	$-0.678152\pi$
$587$	−25.7262	−1.06183	−0.530917	+	0.847424i	$0.678152\pi$
$588$	−5.38842	−0.222215
$589$	1.60999	0.0663386
$590$	−20.3310	−0.837014
$591$	−12.4200	−0.510892
$592$	3.97388	0.163325
$593$	27.0225	1.10968	0.554840	−	0.831957i	$-0.312779\pi$
$593$	27.0225	1.10968	0.554840	+	0.831957i	$0.312779\pi$
$594$	−4.29387	−0.176179
$595$	27.1316	1.11229
$596$	−20.3959	−0.835449
$597$	8.79123	0.359801
$598$	0	0
$599$	31.0171	1.26732	0.633662	−	0.773610i	$-0.281551\pi$
$599$	31.0171	1.26732	0.633662	+	0.773610i	$0.281551\pi$
$600$	−6.88356	−0.281020
$601$	−11.2191	−0.457638	−0.228819	−	0.973469i	$-0.573486\pi$
$601$	−11.2191	−0.457638	−0.228819	+	0.973469i	$0.573486\pi$
$602$	3.05950	0.124696
$603$	24.7607	1.00833
$604$	16.9321	0.688958
$605$	2.76396	0.112371
$606$	−0.395668	−0.0160729
$607$	15.5706	0.631990	0.315995	−	0.948761i	$-0.397662\pi$
$607$	15.5706	0.631990	0.315995	+	0.948761i	$0.397662\pi$
$608$	−1.73793	−0.0704823
$609$	−9.17935	−0.371966
$610$	−18.7938	−0.760938
$611$	0	0
$612$	−7.10675	−0.287273
$613$	−44.0765	−1.78023	−0.890116	−	0.455734i	$-0.849377\pi$
$613$	−44.0765	−1.78023	−0.890116	+	0.455734i	$0.849377\pi$
$614$	9.00818	0.363540
$615$	−12.3463	−0.497851
$616$	10.1331	0.408274
$617$	21.0956	0.849276	0.424638	−	0.905363i	$-0.360401\pi$
$617$	21.0956	0.849276	0.424638	+	0.905363i	$0.360401\pi$
$618$	12.0106	0.483135
$619$	27.5309	1.10656	0.553280	−	0.832995i	$-0.313376\pi$
$619$	27.5309	1.10656	0.553280	+	0.832995i	$0.313376\pi$
$620$	16.1529	0.648718
$621$	6.05297	0.242897
$622$	−4.62171	−0.185314
$623$	58.7391	2.35333
$624$	0	0
$625$	−31.2305	−1.24922
$626$	22.3764	0.894341
$627$	−0.285621	−0.0114066
$628$	−6.65619	−0.265611
$629$	30.8026	1.22818
$630$	19.4690	0.775664
$631$	5.55027	0.220953	0.110476	−	0.993879i	$-0.464762\pi$
$631$	5.55027	0.220953	0.110476	+	0.993879i	$0.464762\pi$
$632$	−22.4599	−0.893405
$633$	−7.05521	−0.280419
$634$	21.9051	0.869964
$635$	50.5579	2.00633
$636$	6.75017	0.267662
$637$	0	0
$638$	2.69043	0.106515
$639$	−22.7727	−0.900875
$640$	−15.5923	−0.616338
$641$	9.88802	0.390553	0.195277	−	0.980748i	$-0.437440\pi$
$641$	9.88802	0.390553	0.195277	+	0.980748i	$0.437440\pi$
$642$	16.0466	0.633308
$643$	−36.3030	−1.43165	−0.715826	−	0.698279i	$-0.753950\pi$
$643$	−36.3030	−1.43165	−0.715826	+	0.698279i	$0.753950\pi$
$644$	−5.22489	−0.205890
$645$	−2.36543	−0.0931389
$646$	0.821754	0.0323315
$647$	−2.42343	−0.0952748	−0.0476374	−	0.998865i	$-0.515169\pi$
$647$	−2.42343	−0.0952748	−0.0476374	+	0.998865i	$0.515169\pi$
$648$	−6.90968	−0.271438
$649$	−7.99471	−0.313820
$650$	0	0
$651$	15.9049	0.623363
$652$	7.33912	0.287422
$653$	−35.1794	−1.37668	−0.688338	−	0.725391i	$-0.741659\pi$
$653$	−35.1794	−1.37668	−0.688338	+	0.725391i	$0.741659\pi$
$654$	2.53455	0.0991086
$655$	−7.44309	−0.290826
$656$	1.80202	0.0703571
$657$	−31.4005	−1.22505
$658$	−17.2507	−0.672503
$659$	−2.75830	−0.107448	−0.0537240	−	0.998556i	$-0.517109\pi$
$659$	−2.75830	−0.107448	−0.0537240	+	0.998556i	$0.517109\pi$
$660$	−2.86562	−0.111544
$661$	−2.47968	−0.0964482	−0.0482241	−	0.998837i	$-0.515356\pi$
$661$	−2.47968	−0.0964482	−0.0482241	+	0.998837i	$0.515356\pi$
$662$	−12.8734	−0.500339
$663$	0	0
$664$	29.5191	1.14556
$665$	3.06740	0.118949
$666$	22.1033	0.856486
$667$	−3.79263	−0.146851
$668$	12.9766	0.502079
$669$	8.88949	0.343687
$670$	−28.7250	−1.10975
$671$	−7.39024	−0.285297
$672$	−17.1688	−0.662301
$673$	−10.3924	−0.400596	−0.200298	−	0.979735i	$-0.564191\pi$
$673$	−10.3924	−0.400596	−0.200298	+	0.979735i	$0.564191\pi$
$674$	11.1675	0.430156
$675$	−12.3181	−0.474124
$676$	0	0
$677$	−5.05328	−0.194213	−0.0971067	−	0.995274i	$-0.530959\pi$
$677$	−5.05328	−0.194213	−0.0971067	+	0.995274i	$0.530959\pi$
$678$	10.7700	0.413618
$679$	42.7810	1.64179
$680$	22.5400	0.864371
$681$	−5.39718	−0.206820
$682$	−4.66166	−0.178504
$683$	20.3385	0.778233	0.389116	−	0.921189i	$-0.372780\pi$
$683$	20.3385	0.778233	0.389116	+	0.921189i	$0.372780\pi$
$684$	−0.803464	−0.0307212
$685$	9.97162	0.380996
$686$	5.79274	0.221168
$687$	−21.4092	−0.816811
$688$	0.345250	0.0131625
$689$	0	0
$690$	−2.96471	−0.112865
$691$	11.5821	0.440602	0.220301	−	0.975432i	$-0.429296\pi$
$691$	11.5821	0.440602	0.220301	+	0.975432i	$0.429296\pi$
$692$	14.3397	0.545112
$693$	7.65576	0.290818
$694$	3.87875	0.147235
$695$	52.8303	2.00397
$696$	−7.62591	−0.289059
$697$	13.9680	0.529075
$698$	2.57526	0.0974749
$699$	−0.877063	−0.0331736
$700$	10.6329	0.401887
$701$	−3.86964	−0.146154	−0.0730772	−	0.997326i	$-0.523282\pi$
$701$	−3.86964	−0.146154	−0.0730772	+	0.997326i	$0.523282\pi$
$702$	0	0
$703$	3.48244	0.131343
$704$	5.75731	0.216987
$705$	13.3373	0.502312
$706$	15.7944	0.594430
$707$	1.67092	0.0628413
$708$	8.28875	0.311510
$709$	5.65488	0.212373	0.106187	−	0.994346i	$-0.466136\pi$
$709$	5.65488	0.212373	0.106187	+	0.994346i	$0.466136\pi$
$710$	26.4188	0.991481
$711$	−16.9689	−0.636382
$712$	48.7986	1.82880
$713$	6.57144	0.246102
$714$	8.11801	0.303809
$715$	0	0
$716$	12.8310	0.479515
$717$	−11.8755	−0.443500
$718$	0.238145	0.00888749
$719$	−15.5329	−0.579278	−0.289639	−	0.957136i	$-0.593535\pi$
$719$	−15.5329	−0.579278	−0.289639	+	0.957136i	$0.593535\pi$
$720$	2.19698	0.0818768
$721$	−50.7210	−1.88895
$722$	−17.3885	−0.647134
$723$	5.57209	0.207228
$724$	12.6129	0.468754
$725$	7.71820	0.286647
$726$	0.827003	0.0306929
$727$	5.42062	0.201040	0.100520	−	0.994935i	$-0.467949\pi$
$727$	5.42062	0.201040	0.100520	+	0.994935i	$0.467949\pi$
$728$	0	0
$729$	7.36391	0.272737
$730$	36.4280	1.34826
$731$	2.67613	0.0989802
$732$	7.66205	0.283197
$733$	−2.65158	−0.0979384	−0.0489692	−	0.998800i	$-0.515594\pi$
$733$	−2.65158	−0.0979384	−0.0489692	+	0.998800i	$0.515594\pi$
$734$	0.753339	0.0278063
$735$	12.9119	0.476264
$736$	−7.09363	−0.261475
$737$	−11.2955	−0.416075
$738$	10.0231	0.368956
$739$	−30.8423	−1.13455	−0.567276	−	0.823528i	$-0.692003\pi$
$739$	−30.8423	−1.13455	−0.567276	+	0.823528i	$0.692003\pi$
$740$	34.9391	1.28439
$741$	0	0
$742$	20.9211	0.768036
$743$	−33.3376	−1.22304	−0.611519	−	0.791229i	$-0.709441\pi$
$743$	−33.3376	−1.22304	−0.611519	+	0.791229i	$0.709441\pi$
$744$	13.2133	0.484423
$745$	48.8734	1.79058
$746$	−15.0880	−0.552412
$747$	22.3023	0.815998
$748$	3.24201	0.118540
$749$	−67.7653	−2.47609
$750$	−5.39568	−0.197022
$751$	36.4584	1.33039	0.665194	−	0.746671i	$-0.268349\pi$
$751$	36.4584	1.33039	0.665194	+	0.746671i	$0.268349\pi$
$752$	−1.94666	−0.0709874
$753$	−10.0444	−0.366037
$754$	0	0
$755$	−40.5733	−1.47661
$756$	−18.8001	−0.683751
$757$	13.6628	0.496583	0.248291	−	0.968685i	$-0.420131\pi$
$757$	13.6628	0.496583	0.248291	+	0.968685i	$0.420131\pi$
$758$	23.6327	0.858377
$759$	−1.16581	−0.0423161
$760$	2.54830	0.0924364
$761$	38.6347	1.40051	0.700253	−	0.713895i	$-0.253070\pi$
$761$	38.6347	1.40051	0.700253	+	0.713895i	$0.253070\pi$
$762$	15.1274	0.548007
$763$	−10.7035	−0.387492
$764$	8.49042	0.307173
$765$	17.0294	0.615701
$766$	24.2548	0.876362
$767$	0	0
$768$	−15.0152	−0.541813
$769$	−11.8982	−0.429061	−0.214531	−	0.976717i	$-0.568822\pi$
$769$	−11.8982	−0.429061	−0.214531	+	0.976717i	$0.568822\pi$
$770$	−8.88152	−0.320068
$771$	−24.8864	−0.896261
$772$	−28.5344	−1.02698
$773$	−33.4728	−1.20393	−0.601967	−	0.798521i	$-0.705616\pi$
$773$	−33.4728	−1.20393	−0.601967	+	0.798521i	$0.705616\pi$
$774$	1.92033	0.0690249
$775$	−13.3732	−0.480380
$776$	35.5411	1.27585
$777$	34.4026	1.23419
$778$	11.7379	0.420826
$779$	1.57917	0.0565796
$780$	0	0
$781$	10.3886	0.371734
$782$	3.35412	0.119943
$783$	−13.6465	−0.487687
$784$	−1.88458	−0.0673063
$785$	15.9498	0.569273
$786$	−2.22704	−0.0794359
$787$	−11.5947	−0.413305	−0.206653	−	0.978414i	$-0.566257\pi$
$787$	−11.5947	−0.413305	−0.206653	+	0.978414i	$0.566257\pi$
$788$	15.9383	0.567779
$789$	12.5668	0.447389
$790$	19.6857	0.700387
$791$	−45.4819	−1.61715
$792$	6.36016	0.225998
$793$	0	0
$794$	−11.7980	−0.418694
$795$	−16.1750	−0.573668
$796$	−11.2816	−0.399864
$797$	21.7613	0.770826	0.385413	−	0.922744i	$-0.374059\pi$
$797$	21.7613	0.770826	0.385413	+	0.922744i	$0.374059\pi$
$798$	0.917794	0.0324896
$799$	−15.0891	−0.533815
$800$	14.4359	0.510387
$801$	36.8683	1.30268
$802$	−28.7210	−1.01417
$803$	14.3245	0.505501
$804$	11.7109	0.413012
$805$	12.5201	0.441274
$806$	0	0
$807$	−6.30240	−0.221855
$808$	1.38814	0.0488348
$809$	−10.2071	−0.358863	−0.179432	−	0.983770i	$-0.557426\pi$
$809$	−10.2071	−0.358863	−0.179432	+	0.983770i	$0.557426\pi$
$810$	6.05623	0.212794
$811$	−34.2961	−1.20430	−0.602149	−	0.798384i	$-0.705689\pi$
$811$	−34.2961	−1.20430	−0.602149	+	0.798384i	$0.705689\pi$
$812$	11.7796	0.413384
$813$	16.5352	0.579915
$814$	−10.0832	−0.353417
$815$	−17.5863	−0.616020
$816$	0.916078	0.0320691
$817$	0.302554	0.0105850
$818$	−6.43084	−0.224849
$819$	0	0
$820$	15.8437	0.553286
$821$	−9.32959	−0.325605	−0.162803	−	0.986659i	$-0.552053\pi$
$821$	−9.32959	−0.325605	−0.162803	+	0.986659i	$0.552053\pi$
$822$	2.98360	0.104065
$823$	−13.5465	−0.472202	−0.236101	−	0.971729i	$-0.575870\pi$
$823$	−13.5465	−0.472202	−0.236101	+	0.971729i	$0.575870\pi$
$824$	−42.1373	−1.46792
$825$	2.37248	0.0825991
$826$	25.6896	0.893857
$827$	−35.4704	−1.23343	−0.616714	−	0.787188i	$-0.711536\pi$
$827$	−35.4704	−1.23343	−0.616714	+	0.787188i	$0.711536\pi$
$828$	−3.27947	−0.113969
$829$	19.9934	0.694399	0.347199	−	0.937791i	$-0.387133\pi$
$829$	19.9934	0.694399	0.347199	+	0.937791i	$0.387133\pi$
$830$	−25.8731	−0.898067
$831$	−15.7490	−0.546328
$832$	0	0
$833$	−14.6079	−0.506133
$834$	15.8073	0.547362
$835$	−31.0949	−1.07608
$836$	0.366530	0.0126767
$837$	23.6451	0.817296
$838$	33.4061	1.15400
$839$	2.21129	0.0763421	0.0381711	−	0.999271i	$-0.487847\pi$
$839$	2.21129	0.0763421	0.0381711	+	0.999271i	$0.487847\pi$
$840$	25.1743	0.868597
$841$	−20.4494	−0.705153
$842$	9.18506	0.316538
$843$	2.59161	0.0892598
$844$	9.05377	0.311644
$845$	0	0
$846$	−10.8276	−0.372261
$847$	−3.49246	−0.120002
$848$	2.36084	0.0810716
$849$	12.6194	0.433097
$850$	−6.82581	−0.234123
$851$	14.2141	0.487254
$852$	−10.7707	−0.368998
$853$	−9.63602	−0.329931	−0.164965	−	0.986299i	$-0.552751\pi$
$853$	−9.63602	−0.329931	−0.164965	+	0.986299i	$0.552751\pi$
$854$	23.7473	0.812615
$855$	1.92529	0.0658435
$856$	−56.2972	−1.92420
$857$	−3.05995	−0.104526	−0.0522629	−	0.998633i	$-0.516643\pi$
$857$	−3.05995	−0.104526	−0.0522629	+	0.998633i	$0.516643\pi$
$858$	0	0
$859$	−3.96603	−0.135319	−0.0676595	−	0.997708i	$-0.521553\pi$
$859$	−3.96603	−0.135319	−0.0676595	+	0.997708i	$0.521553\pi$
$860$	3.03550	0.103510
$861$	15.6004	0.531661
$862$	−22.4657	−0.765184
$863$	−28.2148	−0.960444	−0.480222	−	0.877147i	$-0.659444\pi$
$863$	−28.2148	−0.960444	−0.480222	+	0.877147i	$0.659444\pi$
$864$	−25.5241	−0.868347
$865$	−34.3612	−1.16832
$866$	19.8809	0.675581
$867$	−8.17953	−0.277791
$868$	−20.4104	−0.692773
$869$	7.74098	0.262595
$870$	6.68400	0.226609
$871$	0	0
$872$	−8.89210	−0.301124
$873$	26.8520	0.908803
$874$	0.379205	0.0128268
$875$	22.7861	0.770312
$876$	−14.8514	−0.501781
$877$	−48.5999	−1.64110	−0.820551	−	0.571573i	$-0.806333\pi$
$877$	−48.5999	−1.64110	−0.820551	+	0.571573i	$0.806333\pi$
$878$	−32.2623	−1.08880
$879$	−16.9212	−0.570738
$880$	−1.00224	−0.0337854
$881$	23.5618	0.793816	0.396908	−	0.917858i	$-0.370083\pi$
$881$	23.5618	0.793816	0.396908	+	0.917858i	$0.370083\pi$
$882$	−10.4823	−0.352957
$883$	34.0788	1.14684	0.573422	−	0.819260i	$-0.305615\pi$
$883$	34.0788	1.14684	0.573422	+	0.819260i	$0.305615\pi$
$884$	0	0
$885$	−19.8618	−0.667646
$886$	−19.7994	−0.665173
$887$	−5.80013	−0.194749	−0.0973747	−	0.995248i	$-0.531045\pi$
$887$	−5.80013	−0.194749	−0.0973747	+	0.995248i	$0.531045\pi$
$888$	28.5806	0.959101
$889$	−63.8834	−2.14258
$890$	−42.7712	−1.43369
$891$	2.38148	0.0797826
$892$	−11.4076	−0.381956
$893$	−1.70592	−0.0570865
$894$	14.6234	0.489078
$895$	−30.7460	−1.02772
$896$	19.7019	0.658195
$897$	0	0
$898$	−3.45636	−0.115340
$899$	−14.8154	−0.494122
$900$	6.67388	0.222463
$901$	18.2995	0.609646
$902$	−4.57241	−0.152245
$903$	2.98889	0.0994641
$904$	−37.7849	−1.25671
$905$	−30.2234	−1.00466
$906$	−12.1399	−0.403322
$907$	−51.0513	−1.69513	−0.847565	−	0.530692i	$-0.821932\pi$
$907$	−51.0513	−1.69513	−0.847565	+	0.530692i	$0.821932\pi$
$908$	6.92606	0.229849
$909$	1.04877	0.0347855
$910$	0	0
$911$	16.9183	0.560528	0.280264	−	0.959923i	$-0.409578\pi$
$911$	16.9183	0.560528	0.280264	+	0.959923i	$0.409578\pi$
$912$	0.103569	0.00342950
$913$	−10.1740	−0.336711
$914$	−6.46143	−0.213725
$915$	−18.3601	−0.606965
$916$	27.4738	0.907761
$917$	9.40487	0.310576
$918$	12.0687	0.398326
$919$	−20.3558	−0.671477	−0.335738	−	0.941955i	$-0.608986\pi$
$919$	−20.3558	−0.671477	−0.335738	+	0.941955i	$0.608986\pi$
$920$	10.4013	0.342920
$921$	8.80028	0.289979
$922$	−8.61461	−0.283707
$923$	0	0
$924$	3.62091	0.119119
$925$	−28.9265	−0.951097
$926$	17.5022	0.575157
$927$	−31.8356	−1.04562
$928$	15.9927	0.524987
$929$	40.4424	1.32687	0.663435	−	0.748234i	$-0.269098\pi$
$929$	40.4424	1.32687	0.663435	+	0.748234i	$0.269098\pi$
$930$	−11.5813	−0.379765
$931$	−1.65152	−0.0541262
$932$	1.12551	0.0368674
$933$	−4.51504	−0.147816
$934$	−0.542943	−0.0177656
$935$	−7.76861	−0.254061
$936$	0	0
$937$	0.769181	0.0251280	0.0125640	−	0.999921i	$-0.496001\pi$
$937$	0.769181	0.0251280	0.0125640	+	0.999921i	$0.496001\pi$
$938$	36.2961	1.18511
$939$	21.8600	0.713374
$940$	−17.1154	−0.558243
$941$	−43.6328	−1.42239	−0.711195	−	0.702995i	$-0.751846\pi$
$941$	−43.6328	−1.42239	−0.711195	+	0.702995i	$0.751846\pi$
$942$	4.77233	0.155491
$943$	6.44563	0.209898
$944$	2.89895	0.0943528
$945$	45.0493	1.46545
$946$	−0.876030	−0.0284822
$947$	51.0576	1.65915	0.829575	−	0.558396i	$-0.188583\pi$
$947$	51.0576	1.65915	0.829575	+	0.558396i	$0.188583\pi$
$948$	−8.02568	−0.260662
$949$	0	0
$950$	−0.771702	−0.0250373
$951$	21.3996	0.693929
$952$	−28.4809	−0.923072
$953$	8.02753	0.260037	0.130019	−	0.991512i	$-0.458496\pi$
$953$	8.02753	0.260037	0.130019	+	0.991512i	$0.458496\pi$
$954$	13.1313	0.425143
$955$	−20.3450	−0.658350
$956$	15.2396	0.492883
$957$	2.62833	0.0849620
$958$	−1.57912	−0.0510189
$959$	−12.5998	−0.406870
$960$	14.3033	0.461636
$961$	−5.32952	−0.171920
$962$	0	0
$963$	−42.5337	−1.37063
$964$	−7.15052	−0.230303
$965$	68.3752	2.20108
$966$	3.74612	0.120529
$967$	24.5015	0.787916	0.393958	−	0.919128i	$-0.371106\pi$
$967$	24.5015	0.787916	0.393958	+	0.919128i	$0.371106\pi$
$968$	−2.90142	−0.0932553
$969$	0.802789	0.0257893
$970$	−31.1513	−1.00021
$971$	−37.6631	−1.20867	−0.604334	−	0.796731i	$-0.706561\pi$
$971$	−37.6631	−1.20867	−0.604334	+	0.796731i	$0.706561\pi$
$972$	−18.6182	−0.597179
$973$	−66.7548	−2.14006
$974$	−25.4231	−0.814607
$975$	0	0
$976$	2.67976	0.0857772
$977$	0.922382	0.0295096	0.0147548	−	0.999891i	$-0.495303\pi$
$977$	0.922382	0.0295096	0.0147548	+	0.999891i	$0.495303\pi$
$978$	−5.26197	−0.168259
$979$	−16.8188	−0.537532
$980$	−16.5695	−0.529295
$981$	−6.71816	−0.214494
$982$	13.8654	0.442462
$983$	16.7820	0.535263	0.267631	−	0.963521i	$-0.413759\pi$
$983$	16.7820	0.535263	0.267631	+	0.963521i	$0.413759\pi$
$984$	12.9603	0.413160
$985$	−38.1919	−1.21690
$986$	−7.56193	−0.240821
$987$	−16.8526	−0.536424
$988$	0	0
$989$	1.23492	0.0392682
$990$	−5.57459	−0.177172
$991$	−25.8981	−0.822679	−0.411340	−	0.911482i	$-0.634939\pi$
$991$	−25.8981	−0.822679	−0.411340	+	0.911482i	$0.634939\pi$
$992$	−27.7104	−0.879805
$993$	−12.5763	−0.399097
$994$	−33.3821	−1.05881
$995$	27.0333	0.857012
$996$	10.5482	0.334232
$997$	−12.0133	−0.380464	−0.190232	−	0.981739i	$-0.560924\pi$
$997$	−12.0133	−0.380464	−0.190232	+	0.981739i	$0.560924\pi$
$998$	−24.7820	−0.784460
$999$	51.1448	1.61815

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.2.a.o.1.7		8
13.6	odd	12		143.2.j.b.23.4	✓	16
13.11	odd	12		143.2.j.b.56.4	yes	16
13.12	even	2		1859.2.a.p.1.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.2.j.b.23.4	✓	16	13.6	odd	12
143.2.j.b.56.4	yes	16	13.11	odd	12
1859.2.a.o.1.7		8	1.1	even	1	trivial
1859.2.a.p.1.2		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)

\(f(q)\)	\(=\)	\(q+0.920076 q^{2} +0.898842 q^{3} -1.15346 q^{4} +2.76396 q^{5} +0.827003 q^{6} -3.49246 q^{7} -2.90142 q^{8} -2.19208 q^{9} +O(q^{10})\)	\(q+0.920076 q^{2} +0.898842 q^{3} -1.15346 q^{4} +2.76396 q^{5} +0.827003 q^{6} -3.49246 q^{7} -2.90142 q^{8} -2.19208 q^{9} +2.54305 q^{10} +1.00000 q^{11} -1.03678 q^{12} -3.21333 q^{14} +2.48436 q^{15} -0.362608 q^{16} -2.81068 q^{17} -2.01688 q^{18} -0.317766 q^{19} -3.18812 q^{20} -3.13917 q^{21} +0.920076 q^{22} -1.29701 q^{23} -2.60792 q^{24} +2.63948 q^{25} -4.66686 q^{27} +4.02841 q^{28} +2.92413 q^{29} +2.28580 q^{30} -5.06660 q^{31} +5.46922 q^{32} +0.898842 q^{33} -2.58604 q^{34} -9.65303 q^{35} +2.52848 q^{36} -10.9591 q^{37} -0.292368 q^{38} -8.01942 q^{40} -4.96960 q^{41} -2.88827 q^{42} -0.952128 q^{43} -1.15346 q^{44} -6.05883 q^{45} -1.19335 q^{46} +5.36849 q^{47} -0.325928 q^{48} +5.19728 q^{49} +2.42853 q^{50} -2.52636 q^{51} -6.51071 q^{53} -4.29387 q^{54} +2.76396 q^{55} +10.1331 q^{56} -0.285621 q^{57} +2.69043 q^{58} -7.99471 q^{59} -2.86562 q^{60} -7.39024 q^{61} -4.66166 q^{62} +7.65576 q^{63} +5.75731 q^{64} +0.827003 q^{66} -11.2955 q^{67} +3.24201 q^{68} -1.16581 q^{69} -8.88152 q^{70} +10.3886 q^{71} +6.36016 q^{72} +14.3245 q^{73} -10.0832 q^{74} +2.37248 q^{75} +0.366530 q^{76} -3.49246 q^{77} +7.74098 q^{79} -1.00224 q^{80} +2.38148 q^{81} -4.57241 q^{82} -10.1740 q^{83} +3.62091 q^{84} -7.76861 q^{85} -0.876030 q^{86} +2.62833 q^{87} -2.90142 q^{88} -16.8188 q^{89} -5.57459 q^{90} +1.49605 q^{92} -4.55408 q^{93} +4.93942 q^{94} -0.878292 q^{95} +4.91596 q^{96} -12.2495 q^{97} +4.78189 q^{98} -2.19208 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 4 q^{4} - 8 q^{5} - 4 q^{6} - 14 q^{7} + 6 q^{8} + 2 q^{9}+O(q^{10}) \) 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

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