LMFDB - Embedded newform 799.2.a.d.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [799,2,Mod(1,799)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(799, 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("799.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 799 = 17 \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	799.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:	$6.38004712150$
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} - x^{7} - 8x^{6} + 3x^{5} + 18x^{4} - 10x^{2} - x + 1 $ x^8 - x^7 - 8x^6 + 3x^5 + 18x^4 - 10x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-1.74404$ of defining polynomial
Character	$\chi$	$=$	799.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.887509 q^{2} -2.74404 q^{3} -1.21233 q^{4} -0.0255318 q^{5} -2.43536 q^{6} +2.42435 q^{7} -2.85097 q^{8} +4.52975 q^{9} +O(q^{10})$	\(q+0.887509 q^{2} -2.74404 q^{3} -1.21233 q^{4} -0.0255318 q^{5} -2.43536 q^{6} +2.42435 q^{7} -2.85097 q^{8} +4.52975 q^{9} -0.0226597 q^{10} +4.74840 q^{11} +3.32667 q^{12} -2.26200 q^{13} +2.15163 q^{14} +0.0700602 q^{15} -0.105606 q^{16} +1.00000 q^{17} +4.02019 q^{18} -4.71881 q^{19} +0.0309529 q^{20} -6.65251 q^{21} +4.21424 q^{22} -6.32601 q^{23} +7.82317 q^{24} -4.99935 q^{25} -2.00755 q^{26} -4.19769 q^{27} -2.93911 q^{28} -2.93491 q^{29} +0.0621790 q^{30} -8.12315 q^{31} +5.60821 q^{32} -13.0298 q^{33} +0.887509 q^{34} -0.0618980 q^{35} -5.49154 q^{36} -3.83982 q^{37} -4.18799 q^{38} +6.20701 q^{39} +0.0727903 q^{40} +1.63274 q^{41} -5.90417 q^{42} +2.12182 q^{43} -5.75661 q^{44} -0.115653 q^{45} -5.61439 q^{46} +1.00000 q^{47} +0.289786 q^{48} -1.12252 q^{49} -4.43697 q^{50} -2.74404 q^{51} +2.74229 q^{52} +0.584174 q^{53} -3.72549 q^{54} -0.121235 q^{55} -6.91175 q^{56} +12.9486 q^{57} -2.60476 q^{58} -9.86120 q^{59} -0.0849359 q^{60} +2.80795 q^{61} -7.20937 q^{62} +10.9817 q^{63} +5.18855 q^{64} +0.0577529 q^{65} -11.5640 q^{66} +14.2473 q^{67} -1.21233 q^{68} +17.3588 q^{69} -0.0549350 q^{70} -8.56752 q^{71} -12.9142 q^{72} -8.05904 q^{73} -3.40788 q^{74} +13.7184 q^{75} +5.72075 q^{76} +11.5118 q^{77} +5.50878 q^{78} -2.78329 q^{79} +0.00269630 q^{80} -2.07063 q^{81} +1.44907 q^{82} +5.34512 q^{83} +8.06503 q^{84} -0.0255318 q^{85} +1.88313 q^{86} +8.05352 q^{87} -13.5375 q^{88} -12.8562 q^{89} -0.102643 q^{90} -5.48388 q^{91} +7.66920 q^{92} +22.2902 q^{93} +0.887509 q^{94} +0.120480 q^{95} -15.3892 q^{96} -13.3570 q^{97} -0.996246 q^{98} +21.5090 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} - 7 q^{3} + 7 q^{4} - 10 q^{5} + 2 q^{6} - 9 q^{7} - q^{9}+O(q^{10}) $ 8 * q + q^2 - 7 * q^3 + 7 * q^4 - 10 * q^5 + 2 * q^6 - 9 * q^7 - q^9	\( 8 q + q^{2} - 7 q^{3} + 7 q^{4} - 10 q^{5} + 2 q^{6} - 9 q^{7} - q^{9} + 2 q^{10} - 2 q^{11} - 11 q^{12} - 3 q^{13} - 9 q^{14} + 14 q^{15} - 7 q^{16} + 8 q^{17} - 5 q^{18} - 8 q^{19} - 20 q^{20} + 4 q^{21} - 20 q^{22} - 9 q^{23} - 4 q^{24} + 14 q^{25} - 20 q^{26} + 2 q^{27} - 21 q^{28} - 2 q^{29} - 27 q^{30} - 7 q^{31} + 21 q^{32} - 23 q^{33} + q^{34} + 7 q^{35} - 17 q^{36} - 13 q^{37} - 7 q^{38} + 9 q^{39} - 16 q^{40} - 39 q^{41} + 11 q^{42} + 35 q^{43} - 17 q^{44} - 13 q^{45} + 19 q^{46} + 8 q^{47} + 9 q^{48} + q^{49} - 30 q^{50} - 7 q^{51} - 17 q^{52} - 6 q^{53} - 4 q^{54} + 22 q^{55} - 48 q^{56} + 5 q^{57} + 3 q^{58} - 19 q^{59} + 32 q^{60} - 15 q^{61} + 15 q^{62} + 17 q^{63} - 8 q^{64} - 29 q^{65} - 5 q^{66} + 15 q^{67} + 7 q^{68} - 12 q^{69} + 35 q^{70} - 7 q^{71} + q^{72} - 22 q^{73} - 43 q^{74} - 29 q^{75} + 52 q^{76} + 2 q^{77} + 43 q^{78} - 43 q^{79} + 6 q^{80} - 16 q^{81} + 19 q^{82} - 3 q^{83} + 34 q^{84} - 10 q^{85} - 19 q^{86} + q^{87} + 5 q^{88} - 53 q^{89} + 42 q^{90} + 5 q^{91} + 28 q^{92} + 44 q^{93} + q^{94} - 53 q^{95} - 41 q^{96} - 40 q^{97} + 30 q^{98} + 45 q^{99}+O(q^{100}) \) 8 * q + q^2 - 7 * q^3 + 7 * q^4 - 10 * q^5 + 2 * q^6 - 9 * q^7 - q^9 + 2 * q^10 - 2 * q^11 - 11 * q^12 - 3 * q^13 - 9 * q^14 + 14 * q^15 - 7 * q^16 + 8 * q^17 - 5 * q^18 - 8 * q^19 - 20 * q^20 + 4 * q^21 - 20 * q^22 - 9 * q^23 - 4 * q^24 + 14 * q^25 - 20 * q^26 + 2 * q^27 - 21 * q^28 - 2 * q^29 - 27 * q^30 - 7 * q^31 + 21 * q^32 - 23 * q^33 + q^34 + 7 * q^35 - 17 * q^36 - 13 * q^37 - 7 * q^38 + 9 * q^39 - 16 * q^40 - 39 * q^41 + 11 * q^42 + 35 * q^43 - 17 * q^44 - 13 * q^45 + 19 * q^46 + 8 * q^47 + 9 * q^48 + q^49 - 30 * q^50 - 7 * q^51 - 17 * q^52 - 6 * q^53 - 4 * q^54 + 22 * q^55 - 48 * q^56 + 5 * q^57 + 3 * q^58 - 19 * q^59 + 32 * q^60 - 15 * q^61 + 15 * q^62 + 17 * q^63 - 8 * q^64 - 29 * q^65 - 5 * q^66 + 15 * q^67 + 7 * q^68 - 12 * q^69 + 35 * q^70 - 7 * q^71 + q^72 - 22 * q^73 - 43 * q^74 - 29 * q^75 + 52 * q^76 + 2 * q^77 + 43 * q^78 - 43 * q^79 + 6 * q^80 - 16 * q^81 + 19 * q^82 - 3 * q^83 + 34 * q^84 - 10 * q^85 - 19 * q^86 + q^87 + 5 * q^88 - 53 * q^89 + 42 * q^90 + 5 * q^91 + 28 * q^92 + 44 * q^93 + q^94 - 53 * q^95 - 41 * q^96 - 40 * q^97 + 30 * q^98 + 45 * 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 $

$2$	0.887509	0.627564	0.313782	−	0.949495i	$-0.398404\pi$
$2$	0.887509	0.627564	0.313782	+	0.949495i	$0.398404\pi$
$3$	−2.74404	−1.58427	−0.792136	−	0.610345i	$-0.791031\pi$
$3$	−2.74404	−1.58427	−0.792136	+	0.610345i	$0.791031\pi$
$4$	−1.21233	−0.606164
$5$	−0.0255318	−0.0114182	−0.00570908	−	0.999984i	$-0.501817\pi$
$5$	−0.0255318	−0.0114182	−0.00570908	+	0.999984i	$0.501817\pi$
$6$	−2.43536	−0.994231
$7$	2.42435	0.916319	0.458159	−	0.888870i	$-0.348509\pi$
$7$	2.42435	0.916319	0.458159	+	0.888870i	$0.348509\pi$
$8$	−2.85097	−1.00797
$9$	4.52975	1.50992
$10$	−0.0226597	−0.00716562
$11$	4.74840	1.43170	0.715848	−	0.698257i	$-0.246041\pi$
$11$	4.74840	1.43170	0.715848	+	0.698257i	$0.246041\pi$
$12$	3.32667	0.960328
$13$	−2.26200	−0.627366	−0.313683	−	0.949528i	$-0.601563\pi$
$13$	−2.26200	−0.627366	−0.313683	+	0.949528i	$0.601563\pi$
$14$	2.15163	0.575048
$15$	0.0700602	0.0180895
$16$	−0.105606	−0.0264014
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	4.02019	0.947568
$19$	−4.71881	−1.08257	−0.541285	−	0.840839i	$-0.682062\pi$
$19$	−4.71881	−1.08257	−0.541285	+	0.840839i	$0.682062\pi$
$20$	0.0309529	0.00692127
$21$	−6.65251	−1.45170
$22$	4.21424	0.898480
$23$	−6.32601	−1.31907	−0.659533	−	0.751676i	$-0.729246\pi$
$23$	−6.32601	−1.31907	−0.659533	+	0.751676i	$0.729246\pi$
$24$	7.82317	1.59690
$25$	−4.99935	−0.999870
$26$	−2.00755	−0.393712
$27$	−4.19769	−0.807845
$28$	−2.93911	−0.555439
$29$	−2.93491	−0.545000	−0.272500	−	0.962156i	$-0.587850\pi$
$29$	−2.93491	−0.545000	−0.272500	+	0.962156i	$0.587850\pi$
$30$	0.0621790	0.0113523
$31$	−8.12315	−1.45896	−0.729480	−	0.684002i	$-0.760238\pi$
$31$	−8.12315	−1.45896	−0.729480	+	0.684002i	$0.760238\pi$
$32$	5.60821	0.991401
$33$	−13.0298	−2.26819
$34$	0.887509	0.152207
$35$	−0.0618980	−0.0104627
$36$	−5.49154	−0.915257
$37$	−3.83982	−0.631263	−0.315631	−	0.948882i	$-0.602216\pi$
$37$	−3.83982	−0.631263	−0.315631	+	0.948882i	$0.602216\pi$
$38$	−4.18799	−0.679381
$39$	6.20701	0.993918
$40$	0.0727903	0.0115092
$41$	1.63274	0.254992	0.127496	−	0.991839i	$-0.459306\pi$
$41$	1.63274	0.254992	0.127496	+	0.991839i	$0.459306\pi$
$42$	−5.90417	−0.911033
$43$	2.12182	0.323574	0.161787	−	0.986826i	$-0.448274\pi$
$43$	2.12182	0.323574	0.161787	+	0.986826i	$0.448274\pi$
$44$	−5.75661	−0.867842
$45$	−0.115653	−0.0172405
$46$	−5.61439	−0.827797
$47$	1.00000	0.145865
$47$	1.00000	0.145865
$48$	0.289786	0.0418270
$49$	−1.12252	−0.160360
$50$	−4.43697	−0.627482
$51$	−2.74404	−0.384242
$52$	2.74229	0.380287
$53$	0.584174	0.0802425	0.0401212	−	0.999195i	$-0.487226\pi$
$53$	0.584174	0.0802425	0.0401212	+	0.999195i	$0.487226\pi$
$54$	−3.72549	−0.506974
$55$	−0.121235	−0.0163473
$56$	−6.91175	−0.923622
$57$	12.9486	1.71508
$58$	−2.60476	−0.342022
$59$	−9.86120	−1.28382	−0.641910	−	0.766780i	$-0.721858\pi$
$59$	−9.86120	−1.28382	−0.641910	+	0.766780i	$0.721858\pi$
$60$	−0.0849359	−0.0109652
$61$	2.80795	0.359522	0.179761	−	0.983710i	$-0.442468\pi$
$61$	2.80795	0.359522	0.179761	+	0.983710i	$0.442468\pi$
$62$	−7.20937	−0.915591
$63$	10.9817	1.38356
$64$	5.18855	0.648569
$65$	0.0577529	0.00716336
$66$	−11.5640	−1.42344
$67$	14.2473	1.74058	0.870290	−	0.492539i	$-0.163931\pi$
$67$	14.2473	1.74058	0.870290	+	0.492539i	$0.163931\pi$
$68$	−1.21233	−0.147016
$69$	17.3588	2.08976
$70$	−0.0549350	−0.00656599
$71$	−8.56752	−1.01678	−0.508389	−	0.861128i	$-0.669759\pi$
$71$	−8.56752	−1.01678	−0.508389	+	0.861128i	$0.669759\pi$
$72$	−12.9142	−1.52195
$73$	−8.05904	−0.943240	−0.471620	−	0.881802i	$-0.656331\pi$
$73$	−8.05904	−0.943240	−0.471620	+	0.881802i	$0.656331\pi$
$74$	−3.40788	−0.396158
$75$	13.7184	1.58406
$76$	5.72075	0.656215
$77$	11.5118	1.31189
$78$	5.50878	0.623747
$79$	−2.78329	−0.313144	−0.156572	−	0.987667i	$-0.550044\pi$
$79$	−2.78329	−0.313144	−0.156572	+	0.987667i	$0.550044\pi$
$80$	0.00269630	0.000301456 0
$81$	−2.07063	−0.230070
$82$	1.44907	0.160023
$83$	5.34512	0.586703	0.293352	−	0.956005i	$-0.405229\pi$
$83$	5.34512	0.586703	0.293352	+	0.956005i	$0.405229\pi$
$84$	8.06503	0.879967
$85$	−0.0255318	−0.00276931
$86$	1.88313	0.203063
$87$	8.05352	0.863428
$88$	−13.5375	−1.44311
$89$	−12.8562	−1.36276	−0.681378	−	0.731932i	$-0.738619\pi$
$89$	−12.8562	−1.36276	−0.681378	+	0.731932i	$0.738619\pi$
$90$	−0.102643	−0.0108195
$91$	−5.48388	−0.574867
$92$	7.66920	0.799570
$93$	22.2902	2.31139
$94$	0.887509	0.0915396
$95$	0.120480	0.0123609
$96$	−15.3892	−1.57065
$97$	−13.3570	−1.35620	−0.678098	−	0.734971i	$-0.737196\pi$
$97$	−13.3570	−1.35620	−0.678098	+	0.734971i	$0.737196\pi$
$98$	−0.996246	−0.100636
$99$	21.5090	2.16174
$100$	6.06085	0.606085
$101$	−16.3631	−1.62819	−0.814095	−	0.580732i	$-0.802766\pi$
$101$	−16.3631	−1.62819	−0.814095	+	0.580732i	$0.802766\pi$
$102$	−2.43536	−0.241136
$103$	7.34666	0.723887	0.361944	−	0.932200i	$-0.382113\pi$
$103$	7.34666	0.723887	0.361944	+	0.932200i	$0.382113\pi$
$104$	6.44889	0.632366
$105$	0.169850	0.0165757
$106$	0.518460	0.0503573
$107$	2.65161	0.256340	0.128170	−	0.991752i	$-0.459090\pi$
$107$	2.65161	0.256340	0.128170	+	0.991752i	$0.459090\pi$
$108$	5.08897	0.489687
$109$	−9.50240	−0.910165	−0.455082	−	0.890449i	$-0.650390\pi$
$109$	−9.50240	−0.910165	−0.455082	+	0.890449i	$0.650390\pi$
$110$	−0.107597	−0.0102590
$111$	10.5366	1.00009
$112$	−0.256026	−0.0241921
$113$	−2.07634	−0.195326	−0.0976629	−	0.995220i	$-0.531137\pi$
$113$	−2.07634	−0.195326	−0.0976629	+	0.995220i	$0.531137\pi$
$114$	11.4920	1.07632
$115$	0.161514	0.0150613
$116$	3.55808	0.330359
$117$	−10.2463	−0.947270
$118$	−8.75191	−0.805678
$119$	2.42435	0.222240
$120$	−0.199739	−0.0182336
$121$	11.5473	1.04975
$122$	2.49208	0.225623
$123$	−4.48031	−0.403976
$124$	9.84792	0.884369
$125$	0.255301	0.0228348
$126$	9.74636	0.868275
$127$	15.7281	1.39564	0.697820	−	0.716273i	$-0.254154\pi$
$127$	15.7281	1.39564	0.697820	+	0.716273i	$0.254154\pi$
$128$	−6.61154	−0.584383
$129$	−5.82235	−0.512629
$130$	0.0512562	0.00449546
$131$	15.3326	1.33961	0.669807	−	0.742535i	$-0.266377\pi$
$131$	15.3326	1.33961	0.669807	+	0.742535i	$0.266377\pi$
$132$	15.7964	1.37490
$133$	−11.4401	−0.991979
$134$	12.6446	1.09233
$135$	0.107174	0.00922411
$136$	−2.85097	−0.244469
$137$	−15.3984	−1.31557	−0.657786	−	0.753205i	$-0.728507\pi$
$137$	−15.3984	−1.31557	−0.657786	+	0.753205i	$0.728507\pi$
$138$	15.4061	1.31146
$139$	−20.1858	−1.71214	−0.856069	−	0.516862i	$-0.827100\pi$
$139$	−20.1858	−1.71214	−0.856069	+	0.516862i	$0.827100\pi$
$140$	0.0750407	0.00634209
$141$	−2.74404	−0.231090
$142$	−7.60375	−0.638093
$143$	−10.7409	−0.898197
$144$	−0.478368	−0.0398640
$145$	0.0749336	0.00622289
$146$	−7.15247	−0.591943
$147$	3.08024	0.254054
$148$	4.65512	0.382649
$149$	17.7726	1.45599	0.727995	−	0.685582i	$-0.240452\pi$
$149$	17.7726	1.45599	0.727995	+	0.685582i	$0.240452\pi$
$150$	12.1752	0.994102
$151$	6.89764	0.561322	0.280661	−	0.959807i	$-0.409446\pi$
$151$	6.89764	0.561322	0.280661	+	0.959807i	$0.409446\pi$
$152$	13.4532	1.09120
$153$	4.52975	0.366208
$154$	10.2168	0.823294
$155$	0.207398	0.0166586
$156$	−7.52494	−0.602477
$157$	15.1168	1.20645	0.603227	−	0.797570i	$-0.293881\pi$
$157$	15.1168	1.20645	0.603227	+	0.797570i	$0.293881\pi$
$158$	−2.47019	−0.196518
$159$	−1.60300	−0.127126
$160$	−0.143188	−0.0113200
$161$	−15.3365	−1.20868
$162$	−1.83770	−0.144383
$163$	15.8476	1.24128	0.620642	−	0.784094i	$-0.286872\pi$
$163$	15.8476	1.24128	0.620642	+	0.784094i	$0.286872\pi$
$164$	−1.97942	−0.154567
$165$	0.332673	0.0258986
$166$	4.74384	0.368194
$167$	−20.0997	−1.55536	−0.777682	−	0.628658i	$-0.783605\pi$
$167$	−20.0997	−1.55536	−0.777682	+	0.628658i	$0.783605\pi$
$168$	18.9661	1.46327
$169$	−7.88336	−0.606412
$170$	−0.0226597	−0.00173792
$171$	−21.3750	−1.63459
$172$	−2.57234	−0.196139
$173$	2.11364	0.160697	0.0803484	−	0.996767i	$-0.474397\pi$
$173$	2.11364	0.160697	0.0803484	+	0.996767i	$0.474397\pi$
$174$	7.14757	0.541856
$175$	−12.1202	−0.916199
$176$	−0.501458	−0.0377988
$177$	27.0595	2.03392
$178$	−11.4100	−0.855216
$179$	12.7997	0.956697	0.478348	−	0.878170i	$-0.341236\pi$
$179$	12.7997	0.956697	0.478348	+	0.878170i	$0.341236\pi$
$180$	0.140209	0.0104505
$181$	7.80454	0.580107	0.290054	−	0.957010i	$-0.406327\pi$
$181$	7.80454	0.580107	0.290054	+	0.957010i	$0.406327\pi$
$182$	−4.86700	−0.360766
$183$	−7.70513	−0.569580
$184$	18.0353	1.32958
$185$	0.0980375	0.00720786
$186$	19.7828	1.45054
$187$	4.74840	0.347237
$188$	−1.21233	−0.0884181
$189$	−10.1767	−0.740244
$190$	0.106927	0.00775728
$191$	7.51632	0.543862	0.271931	−	0.962317i	$-0.412338\pi$
$191$	7.51632	0.543862	0.271931	+	0.962317i	$0.412338\pi$
$192$	−14.2376	−1.02751
$193$	4.45590	0.320743	0.160371	−	0.987057i	$-0.448731\pi$
$193$	4.45590	0.320743	0.160371	+	0.987057i	$0.448731\pi$
$194$	−11.8544	−0.851100
$195$	−0.158476	−0.0113487
$196$	1.36086	0.0972044
$197$	0.859154	0.0612122	0.0306061	−	0.999532i	$-0.490256\pi$
$197$	0.859154	0.0612122	0.0306061	+	0.999532i	$0.490256\pi$
$198$	19.0895	1.35663
$199$	25.0562	1.77618	0.888092	−	0.459665i	$-0.152030\pi$
$199$	25.0562	1.77618	0.888092	+	0.459665i	$0.152030\pi$
$200$	14.2530	1.00784
$201$	−39.0951	−2.75755
$202$	−14.5224	−1.02179
$203$	−7.11526	−0.499394
$204$	3.32667	0.232914
$205$	−0.0416868	−0.00291153
$206$	6.52022	0.454285
$207$	−28.6553	−1.99168
$208$	0.238880	0.0165634
$209$	−22.4068	−1.54991
$210$	0.150744	0.0104023
$211$	−13.8969	−0.956701	−0.478350	−	0.878169i	$-0.658765\pi$
$211$	−13.8969	−0.956701	−0.478350	+	0.878169i	$0.658765\pi$
$212$	−0.708210	−0.0486401
$213$	23.5096	1.61085
$214$	2.35332	0.160870
$215$	−0.0541738	−0.00369462
$216$	11.9675	0.814284
$217$	−19.6934	−1.33687
$218$	−8.43347	−0.571186
$219$	22.1143	1.49435
$220$	0.146977	0.00990915
$221$	−2.26200	−0.152159
$222$	9.35135	0.627621
$223$	−3.01432	−0.201854	−0.100927	−	0.994894i	$-0.532181\pi$
$223$	−3.01432	−0.201854	−0.100927	+	0.994894i	$0.532181\pi$
$224$	13.5963	0.908440
$225$	−22.6458	−1.50972
$226$	−1.84277	−0.122579
$227$	−6.59790	−0.437918	−0.218959	−	0.975734i	$-0.570266\pi$
$227$	−6.59790	−0.437918	−0.218959	+	0.975734i	$0.570266\pi$
$228$	−15.6979	−1.03962
$229$	−6.47482	−0.427868	−0.213934	−	0.976848i	$-0.568628\pi$
$229$	−6.47482	−0.427868	−0.213934	+	0.976848i	$0.568628\pi$
$230$	0.143345	0.00945192
$231$	−31.5888	−2.07839
$232$	8.36735	0.549344
$233$	−21.7407	−1.42428	−0.712139	−	0.702039i	$-0.752273\pi$
$233$	−21.7407	−1.42428	−0.712139	+	0.702039i	$0.752273\pi$
$234$	−9.09367	−0.594472
$235$	−0.0255318	−0.00166551
$236$	11.9550	0.778205
$237$	7.63744	0.496105
$238$	2.15163	0.139470
$239$	11.0873	0.717180	0.358590	−	0.933495i	$-0.383258\pi$
$239$	11.0873	0.717180	0.358590	+	0.933495i	$0.383258\pi$
$240$	−0.00739876	−0.000477588 0
$241$	−23.9945	−1.54562	−0.772812	−	0.634636i	$-0.781150\pi$
$241$	−23.9945	−1.54562	−0.772812	+	0.634636i	$0.781150\pi$
$242$	10.2483	0.658786
$243$	18.2749	1.17234
$244$	−3.40416	−0.217929
$245$	0.0286599	0.00183101
$246$	−3.97632	−0.253521
$247$	10.6739	0.679167
$248$	23.1588	1.47059
$249$	−14.6672	−0.929497
$250$	0.226582	0.0143303
$251$	−4.76560	−0.300802	−0.150401	−	0.988625i	$-0.548056\pi$
$251$	−4.76560	−0.300802	−0.150401	+	0.988625i	$0.548056\pi$
$252$	−13.3134	−0.838667
$253$	−30.0384	−1.88850
$254$	13.9588	0.875853
$255$	0.0700602	0.00438734
$256$	−16.2449	−1.01531
$257$	12.9175	0.805773	0.402887	−	0.915250i	$-0.368007\pi$
$257$	12.9175	0.805773	0.402887	+	0.915250i	$0.368007\pi$
$258$	−5.16739	−0.321707
$259$	−9.30908	−0.578438
$260$	−0.0700154	−0.00434217
$261$	−13.2944	−0.822904
$262$	13.6078	0.840693
$263$	8.37994	0.516729	0.258365	−	0.966047i	$-0.416816\pi$
$263$	8.37994	0.516729	0.258365	+	0.966047i	$0.416816\pi$
$264$	37.1475	2.28627
$265$	−0.0149150	−0.000916221 0
$266$	−10.1532	−0.622530
$267$	35.2780	2.15898
$268$	−17.2724	−1.05508
$269$	−25.5055	−1.55510	−0.777549	−	0.628823i	$-0.783537\pi$
$269$	−25.5055	−1.55510	−0.777549	+	0.628823i	$0.783537\pi$
$270$	0.0951183	0.00578871
$271$	8.45862	0.513824	0.256912	−	0.966435i	$-0.417295\pi$
$271$	8.45862	0.513824	0.256912	+	0.966435i	$0.417295\pi$
$272$	−0.105606	−0.00640329
$273$	15.0480	0.910746
$274$	−13.6662	−0.825605
$275$	−23.7389	−1.43151
$276$	−21.0446	−1.26674
$277$	11.6872	0.702215	0.351107	−	0.936335i	$-0.385805\pi$
$277$	11.6872	0.702215	0.351107	+	0.936335i	$0.385805\pi$
$278$	−17.9151	−1.07448
$279$	−36.7958	−2.20291
$280$	0.176469	0.0105461
$281$	−3.71891	−0.221851	−0.110926	−	0.993829i	$-0.535382\pi$
$281$	−3.71891	−0.221851	−0.110926	+	0.993829i	$0.535382\pi$
$282$	−2.43536	−0.145024
$283$	−9.73676	−0.578790	−0.289395	−	0.957210i	$-0.593454\pi$
$283$	−9.73676	−0.578790	−0.289395	+	0.957210i	$0.593454\pi$
$284$	10.3866	0.616334
$285$	−0.330601	−0.0195831
$286$	−9.53262	−0.563676
$287$	3.95834	0.233654
$288$	25.4038	1.49693
$289$	1.00000	0.0588235
$290$	0.0665042	0.00390526
$291$	36.6521	2.14858
$292$	9.77020	0.571758
$293$	27.0477	1.58014	0.790072	−	0.613014i	$-0.210043\pi$
$293$	27.0477	1.58014	0.790072	+	0.613014i	$0.210043\pi$
$294$	2.73374	0.159435
$295$	0.251774	0.0146589
$296$	10.9472	0.636294
$297$	−19.9323	−1.15659
$298$	15.7734	0.913727
$299$	14.3094	0.827536
$300$	−16.6312	−0.960203
$301$	5.14403	0.296497
$302$	6.12172	0.352265
$303$	44.9010	2.57949
$304$	0.498334	0.0285814
$305$	−0.0716920	−0.00410507
$306$	4.02019	0.229819
$307$	−9.65437	−0.551004	−0.275502	−	0.961301i	$-0.588844\pi$
$307$	−9.65437	−0.551004	−0.275502	+	0.961301i	$0.588844\pi$
$308$	−13.9561	−0.795220
$309$	−20.1595	−1.14683
$310$	0.184068	0.0104544
$311$	−0.139732	−0.00792346	−0.00396173	−	0.999992i	$-0.501261\pi$
$311$	−0.139732	−0.00792346	−0.00396173	+	0.999992i	$0.501261\pi$
$312$	−17.6960	−1.00184
$313$	14.6583	0.828535	0.414267	−	0.910155i	$-0.364038\pi$
$313$	14.6583	0.828535	0.414267	+	0.910155i	$0.364038\pi$
$314$	13.4163	0.757126
$315$	−0.280382	−0.0157978
$316$	3.37425	0.189817
$317$	−23.4685	−1.31812	−0.659062	−	0.752089i	$-0.729046\pi$
$317$	−23.4685	−1.31812	−0.659062	+	0.752089i	$0.729046\pi$
$318$	−1.42267	−0.0797796
$319$	−13.9361	−0.780274
$320$	−0.132473	−0.00740546
$321$	−7.27611	−0.406113
$322$	−13.6113	−0.758526
$323$	−4.71881	−0.262562
$324$	2.51028	0.139460
$325$	11.3085	0.627284
$326$	14.0649	0.778984
$327$	26.0750	1.44195
$328$	−4.65490	−0.257024
$329$	2.42435	0.133659
$330$	0.295251	0.0162530
$331$	19.4967	1.07164	0.535818	−	0.844334i	$-0.320003\pi$
$331$	19.4967	1.07164	0.535818	+	0.844334i	$0.320003\pi$
$332$	−6.48004	−0.355638
$333$	−17.3934	−0.953154
$334$	−17.8387	−0.976090
$335$	−0.363758	−0.0198742
$336$	0.702544	0.0383269
$337$	20.1670	1.09857	0.549284	−	0.835636i	$-0.314900\pi$
$337$	20.1670	1.09857	0.549284	+	0.835636i	$0.314900\pi$
$338$	−6.99655	−0.380562
$339$	5.69756	0.309449
$340$	0.0309529	0.00167866
$341$	−38.5719	−2.08879
$342$	−18.9705	−1.02581
$343$	−19.6918	−1.06326
$344$	−6.04924	−0.326153
$345$	−0.443202	−0.0238612
$346$	1.87587	0.100847
$347$	−1.43006	−0.0767695	−0.0383848	−	0.999263i	$-0.512221\pi$
$347$	−1.43006	−0.0767695	−0.0383848	+	0.999263i	$0.512221\pi$
$348$	−9.76350	−0.523379
$349$	−3.82546	−0.204772	−0.102386	−	0.994745i	$-0.532648\pi$
$349$	−3.82546	−0.204772	−0.102386	+	0.994745i	$0.532648\pi$
$350$	−10.7568	−0.574973
$351$	9.49517	0.506815
$352$	26.6300	1.41938
$353$	−24.5629	−1.30735	−0.653675	−	0.756775i	$-0.726774\pi$
$353$	−24.5629	−1.30735	−0.653675	+	0.756775i	$0.726774\pi$
$354$	24.0156	1.27641
$355$	0.218744	0.0116097
$356$	15.5859	0.826054
$357$	−6.65251	−0.352088
$358$	11.3599	0.600388
$359$	6.79451	0.358601	0.179300	−	0.983794i	$-0.442617\pi$
$359$	6.79451	0.358601	0.179300	+	0.983794i	$0.442617\pi$
$360$	0.329722	0.0173779
$361$	3.26718	0.171957
$362$	6.92660	0.364054
$363$	−31.6861	−1.66309
$364$	6.64826	0.348464
$365$	0.205762	0.0107701
$366$	−6.83837	−0.357448
$367$	23.0424	1.20280	0.601402	−	0.798947i	$-0.294609\pi$
$367$	23.0424	1.20280	0.601402	+	0.798947i	$0.294609\pi$
$368$	0.668064	0.0348252
$369$	7.39592	0.385016
$370$	0.0870091	0.00452339
$371$	1.41624	0.0735277
$372$	−27.0231	−1.40108
$373$	17.0288	0.881720	0.440860	−	0.897576i	$-0.354673\pi$
$373$	17.0288	0.881720	0.440860	+	0.897576i	$0.354673\pi$
$374$	4.21424	0.217913
$375$	−0.700556	−0.0361766
$376$	−2.85097	−0.147028
$377$	6.63877	0.341914
$378$	−9.03189	−0.464550
$379$	−11.4764	−0.589504	−0.294752	−	0.955574i	$-0.595237\pi$
$379$	−11.4764	−0.589504	−0.294752	+	0.955574i	$0.595237\pi$
$380$	−0.146061	−0.00749276
$381$	−43.1584	−2.21107
$382$	6.67080	0.341308
$383$	−7.66114	−0.391466	−0.195733	−	0.980657i	$-0.562709\pi$
$383$	−7.66114	−0.391466	−0.195733	+	0.980657i	$0.562709\pi$
$384$	18.1423	0.925822
$385$	−0.293916	−0.0149794
$386$	3.95465	0.201286
$387$	9.61130	0.488570
$388$	16.1930	0.822077
$389$	29.2830	1.48471	0.742353	−	0.670009i	$-0.233710\pi$
$389$	29.2830	1.48471	0.742353	+	0.670009i	$0.233710\pi$
$390$	−0.140649	−0.00712204
$391$	−6.32601	−0.319920
$392$	3.20027	0.161638
$393$	−42.0732	−2.12231
$394$	0.762507	0.0384145
$395$	0.0710622	0.00357553
$396$	−26.0760	−1.31037
$397$	35.8457	1.79904	0.899521	−	0.436878i	$-0.143916\pi$
$397$	35.8457	1.79904	0.899521	+	0.436878i	$0.143916\pi$
$398$	22.2376	1.11467
$399$	31.3920	1.57156
$400$	0.527960	0.0263980
$401$	23.3232	1.16470	0.582352	−	0.812936i	$-0.302132\pi$
$401$	23.3232	1.16470	0.582352	+	0.812936i	$0.302132\pi$
$402$	−34.6972	−1.73054
$403$	18.3746	0.915302
$404$	19.8374	0.986950
$405$	0.0528667	0.00262697
$406$	−6.31486	−0.313401
$407$	−18.2330	−0.903776
$408$	7.82317	0.387305
$409$	−16.0144	−0.791861	−0.395931	−	0.918280i	$-0.629578\pi$
$409$	−16.0144	−0.791861	−0.395931	+	0.918280i	$0.629578\pi$
$410$	−0.0369974	−0.00182717
$411$	42.2537	2.08422
$412$	−8.90655	−0.438794
$413$	−23.9070	−1.17639
$414$	−25.4318	−1.24990
$415$	−0.136470	−0.00669907
$416$	−12.6858	−0.621971
$417$	55.3906	2.71249
$418$	−19.8862	−0.972667
$419$	24.4853	1.19619	0.598093	−	0.801427i	$-0.295925\pi$
$419$	24.4853	1.19619	0.598093	+	0.801427i	$0.295925\pi$
$420$	−0.205914	−0.0100476
$421$	−9.05622	−0.441373	−0.220687	−	0.975345i	$-0.570830\pi$
$421$	−9.05622	−0.441373	−0.220687	+	0.975345i	$0.570830\pi$
$422$	−12.3336	−0.600390
$423$	4.52975	0.220244
$424$	−1.66546	−0.0808820
$425$	−4.99935	−0.242504
$426$	20.8650	1.01091
$427$	6.80747	0.329436
$428$	−3.21462	−0.155384
$429$	29.4734	1.42299
$430$	−0.0480797	−0.00231861
$431$	−14.4175	−0.694467	−0.347234	−	0.937779i	$-0.612879\pi$
$431$	−14.4175	−0.694467	−0.347234	+	0.937779i	$0.612879\pi$
$432$	0.443300	0.0213283
$433$	23.3515	1.12220	0.561101	−	0.827748i	$-0.310378\pi$
$433$	23.3515	1.12220	0.561101	+	0.827748i	$0.310378\pi$
$434$	−17.4780	−0.838973
$435$	−0.205621	−0.00985875
$436$	11.5200	0.551709
$437$	29.8513	1.42798
$438$	19.6267	0.937798
$439$	30.5993	1.46043	0.730213	−	0.683219i	$-0.239421\pi$
$439$	30.5993	1.46043	0.730213	+	0.683219i	$0.239421\pi$
$440$	0.345637	0.0164776
$441$	−5.08473	−0.242130
$442$	−2.00755	−0.0954892
$443$	−11.5579	−0.549130	−0.274565	−	0.961569i	$-0.588534\pi$
$443$	−11.5579	−0.549130	−0.274565	+	0.961569i	$0.588534\pi$
$444$	−12.7738	−0.606220
$445$	0.328242	0.0155602
$446$	−2.67524	−0.126676
$447$	−48.7688	−2.30668
$448$	12.5789	0.594296
$449$	−24.8765	−1.17399	−0.586996	−	0.809590i	$-0.699690\pi$
$449$	−24.8765	−1.17399	−0.586996	+	0.809590i	$0.699690\pi$
$450$	−20.0983	−0.947445
$451$	7.75291	0.365070
$452$	2.51721	0.118399
$453$	−18.9274	−0.889287
$454$	−5.85570	−0.274822
$455$	0.140013	0.00656392
$456$	−36.9161	−1.72875
$457$	−4.09533	−0.191571	−0.0957857	−	0.995402i	$-0.530536\pi$
$457$	−4.09533	−0.191571	−0.0957857	+	0.995402i	$0.530536\pi$
$458$	−5.74646	−0.268515
$459$	−4.19769	−0.195931
$460$	−0.195808	−0.00912961
$461$	−22.5164	−1.04869	−0.524346	−	0.851505i	$-0.675690\pi$
$461$	−22.5164	−1.04869	−0.524346	+	0.851505i	$0.675690\pi$
$462$	−28.0353	−1.30432
$463$	37.3557	1.73606	0.868032	−	0.496508i	$-0.165384\pi$
$463$	37.3557	1.73606	0.868032	+	0.496508i	$0.165384\pi$
$464$	0.309944	0.0143888
$465$	−0.569109	−0.0263918
$466$	−19.2950	−0.893825
$467$	−31.2352	−1.44539	−0.722695	−	0.691167i	$-0.757097\pi$
$467$	−31.2352	−1.44539	−0.722695	+	0.691167i	$0.757097\pi$
$468$	12.4219	0.574201
$469$	34.5404	1.59493
$470$	−0.0226597	−0.00104521
$471$	−41.4811	−1.91135
$472$	28.1140	1.29405
$473$	10.0752	0.463259
$474$	6.77830	0.311338
$475$	23.5910	1.08243
$476$	−2.93911	−0.134714
$477$	2.64616	0.121159
$478$	9.84011	0.450076
$479$	−30.2164	−1.38062	−0.690311	−	0.723513i	$-0.742526\pi$
$479$	−30.2164	−1.38062	−0.690311	+	0.723513i	$0.742526\pi$
$480$	0.392912	0.0179339
$481$	8.68568	0.396033
$482$	−21.2954	−0.969977
$483$	42.0839	1.91488
$484$	−13.9991	−0.636321
$485$	0.341028	0.0154853
$486$	16.2192	0.735717
$487$	−40.0531	−1.81498	−0.907489	−	0.420075i	$-0.862004\pi$
$487$	−40.0531	−1.81498	−0.907489	+	0.420075i	$0.862004\pi$
$488$	−8.00539	−0.362387
$489$	−43.4865	−1.96653
$490$	0.0254359	0.00114908
$491$	23.7377	1.07127	0.535633	−	0.844451i	$-0.320073\pi$
$491$	23.7377	1.07127	0.535633	+	0.844451i	$0.320073\pi$
$492$	5.43161	0.244876
$493$	−2.93491	−0.132182
$494$	9.47323	0.426221
$495$	−0.549164	−0.0246831
$496$	0.857851	0.0385187
$497$	−20.7707	−0.931692
$498$	−13.0173	−0.583319
$499$	6.13143	0.274481	0.137240	−	0.990538i	$-0.456177\pi$
$499$	6.13143	0.274481	0.137240	+	0.990538i	$0.456177\pi$
$500$	−0.309509	−0.0138416
$501$	55.1544	2.46412
$502$	−4.22951	−0.188772
$503$	13.1744	0.587418	0.293709	−	0.955895i	$-0.405110\pi$
$503$	13.1744	0.587418	0.293709	+	0.955895i	$0.405110\pi$
$504$	−31.3085	−1.39459
$505$	0.417779	0.0185909
$506$	−26.6594	−1.18515
$507$	21.6322	0.960721
$508$	−19.0676	−0.845986
$509$	−25.1811	−1.11613	−0.558067	−	0.829796i	$-0.688457\pi$
$509$	−25.1811	−1.11613	−0.558067	+	0.829796i	$0.688457\pi$
$510$	0.0621790	0.00275333
$511$	−19.5380	−0.864308
$512$	−1.19442	−0.0527863
$513$	19.8081	0.874549
$514$	11.4644	0.505674
$515$	−0.187573	−0.00826546
$516$	7.05859	0.310737
$517$	4.74840	0.208834
$518$	−8.26189	−0.363007
$519$	−5.79990	−0.254587
$520$	−0.164652	−0.00722045
$521$	−13.7619	−0.602920	−0.301460	−	0.953479i	$-0.597474\pi$
$521$	−13.7619	−0.602920	−0.301460	+	0.953479i	$0.597474\pi$
$522$	−11.7989	−0.516425
$523$	23.1133	1.01068	0.505338	−	0.862922i	$-0.331368\pi$
$523$	23.1133	1.01068	0.505338	+	0.862922i	$0.331368\pi$
$524$	−18.5881	−0.812026
$525$	33.2582	1.45151
$526$	7.43727	0.324280
$527$	−8.12315	−0.353850
$528$	1.37602	0.0598836
$529$	17.0185	0.739933
$530$	−0.0132372	−0.000574987 0
$531$	−44.6688	−1.93846
$532$	13.8691	0.601302
$533$	−3.69327	−0.159973
$534$	31.3095	1.35489
$535$	−0.0677002	−0.00292693
$536$	−40.6185	−1.75445
$537$	−35.1229	−1.51567
$538$	−22.6364	−0.975922
$539$	−5.33017	−0.229587
$540$	−0.129931	−0.00559132
$541$	38.4690	1.65391	0.826956	−	0.562266i	$-0.190070\pi$
$541$	38.4690	1.65391	0.826956	+	0.562266i	$0.190070\pi$
$542$	7.50710	0.322458
$543$	−21.4160	−0.919047
$544$	5.60821	0.240450
$545$	0.242613	0.0103924
$546$	13.3552	0.571551
$547$	−19.4797	−0.832891	−0.416446	−	0.909161i	$-0.636724\pi$
$547$	−19.4797	−0.832891	−0.416446	+	0.909161i	$0.636724\pi$
$548$	18.6679	0.797452
$549$	12.7193	0.542847
$550$	−21.0685	−0.898363
$551$	13.8493	0.590000
$552$	−49.4895	−2.10641
$553$	−6.74766	−0.286940
$554$	10.3725	0.440684
$555$	−0.269019	−0.0114192
$556$	24.4718	1.03784
$557$	−36.3059	−1.53833	−0.769164	−	0.639051i	$-0.779327\pi$
$557$	−36.3059	−1.53833	−0.769164	+	0.639051i	$0.779327\pi$
$558$	−32.6566	−1.38246
$559$	−4.79955	−0.202999
$560$	0.00653679	0.000276230 0
$561$	−13.0298	−0.550118
$562$	−3.30056	−0.139226
$563$	−20.2734	−0.854424	−0.427212	−	0.904152i	$-0.640504\pi$
$563$	−20.2734	−0.854424	−0.427212	+	0.904152i	$0.640504\pi$
$564$	3.32667	0.140078
$565$	0.0530127	0.00223026
$566$	−8.64146	−0.363228
$567$	−5.01992	−0.210817
$568$	24.4257	1.02488
$569$	−2.91746	−0.122306	−0.0611532	−	0.998128i	$-0.519478\pi$
$569$	−2.91746	−0.122306	−0.0611532	+	0.998128i	$0.519478\pi$
$570$	−0.293411	−0.0122896
$571$	−24.8507	−1.03997	−0.519984	−	0.854176i	$-0.674062\pi$
$571$	−24.8507	−1.03997	−0.519984	+	0.854176i	$0.674062\pi$
$572$	13.0215	0.544454
$573$	−20.6251	−0.861625
$574$	3.51307	0.146633
$575$	31.6259	1.31889
$576$	23.5028	0.979285
$577$	13.8981	0.578585	0.289293	−	0.957241i	$-0.406580\pi$
$577$	13.8981	0.578585	0.289293	+	0.957241i	$0.406580\pi$
$578$	0.887509	0.0369155
$579$	−12.2272	−0.508143
$580$	−0.0908440	−0.00377209
$581$	12.9585	0.537607
$582$	32.5291	1.34837
$583$	2.77389	0.114883
$584$	22.9761	0.950757
$585$	0.261606	0.0108161
$586$	24.0051	0.991641
$587$	−35.7603	−1.47599	−0.737993	−	0.674808i	$-0.764226\pi$
$587$	−35.7603	−1.47599	−0.737993	+	0.674808i	$0.764226\pi$
$588$	−3.73426	−0.153998
$589$	38.3316	1.57943
$590$	0.223452	0.00919936
$591$	−2.35755	−0.0969767
$592$	0.405507	0.0166662
$593$	−38.5022	−1.58110	−0.790549	−	0.612399i	$-0.790205\pi$
$593$	−38.5022	−1.58110	−0.790549	+	0.612399i	$0.790205\pi$
$594$	−17.6901	−0.725833
$595$	−0.0618980	−0.00253757
$596$	−21.5462	−0.882569
$597$	−68.7551	−2.81396
$598$	12.6998	0.519332
$599$	10.7739	0.440208	0.220104	−	0.975476i	$-0.429360\pi$
$599$	10.7739	0.440208	0.220104	+	0.975476i	$0.429360\pi$
$600$	−39.1108	−1.59669
$601$	−21.5525	−0.879145	−0.439573	−	0.898207i	$-0.644870\pi$
$601$	−21.5525	−0.879145	−0.439573	+	0.898207i	$0.644870\pi$
$602$	4.56537	0.186071
$603$	64.5365	2.62813
$604$	−8.36220	−0.340253
$605$	−0.294822	−0.0119862
$606$	39.8500	1.61880
$607$	−3.98588	−0.161782	−0.0808910	−	0.996723i	$-0.525777\pi$
$607$	−3.98588	−0.161782	−0.0808910	+	0.996723i	$0.525777\pi$
$608$	−26.4641	−1.07326
$609$	19.5246	0.791175
$610$	−0.0636273	−0.00257619
$611$	−2.26200	−0.0915107
$612$	−5.49154	−0.221982
$613$	14.8422	0.599472	0.299736	−	0.954022i	$-0.403101\pi$
$613$	14.8422	0.599472	0.299736	+	0.954022i	$0.403101\pi$
$614$	−8.56834	−0.345790
$615$	0.114390	0.00461266
$616$	−32.8197	−1.32235
$617$	−8.08208	−0.325372	−0.162686	−	0.986678i	$-0.552016\pi$
$617$	−8.08208	−0.325372	−0.162686	+	0.986678i	$0.552016\pi$
$618$	−17.8917	−0.719711
$619$	−30.8284	−1.23910	−0.619550	−	0.784957i	$-0.712685\pi$
$619$	−30.8284	−1.23910	−0.619550	+	0.784957i	$0.712685\pi$
$620$	−0.251435	−0.0100979
$621$	26.5546	1.06560
$622$	−0.124013	−0.00497247
$623$	−31.1680	−1.24872
$624$	−0.655497	−0.0262409
$625$	24.9902	0.999609
$626$	13.0093	0.519958
$627$	61.4851	2.45548
$628$	−18.3265	−0.731309
$629$	−3.83982	−0.153104
$630$	−0.248842	−0.00991410
$631$	−15.6567	−0.623284	−0.311642	−	0.950200i	$-0.600879\pi$
$631$	−15.6567	−0.623284	−0.311642	+	0.950200i	$0.600879\pi$
$632$	7.93506	0.315640
$633$	38.1336	1.51567
$634$	−20.8285	−0.827206
$635$	−0.401565	−0.0159356
$636$	1.94336	0.0770591
$637$	2.53914	0.100604
$638$	−12.3684	−0.489671
$639$	−38.8087	−1.53525
$640$	0.168804	0.00667258
$641$	13.7084	0.541451	0.270726	−	0.962657i	$-0.412736\pi$
$641$	13.7084	0.541451	0.270726	+	0.962657i	$0.412736\pi$
$642$	−6.45761	−0.254862
$643$	32.3653	1.27636	0.638181	−	0.769886i	$-0.279687\pi$
$643$	32.3653	1.27636	0.638181	+	0.769886i	$0.279687\pi$
$644$	18.5928	0.732661
$645$	0.148655	0.00585328
$646$	−4.18799	−0.164774
$647$	−22.6233	−0.889415	−0.444708	−	0.895676i	$-0.646692\pi$
$647$	−22.6233	−0.889415	−0.444708	+	0.895676i	$0.646692\pi$
$648$	5.90329	0.231903
$649$	−46.8249	−1.83804
$650$	10.0364	0.393661
$651$	54.0394	2.11797
$652$	−19.2125	−0.752421
$653$	2.09867	0.0821274	0.0410637	−	0.999157i	$-0.486925\pi$
$653$	2.09867	0.0821274	0.0410637	+	0.999157i	$0.486925\pi$
$654$	23.1418	0.904914
$655$	−0.391468	−0.0152959
$656$	−0.172427	−0.00673215
$657$	−36.5054	−1.42421
$658$	2.15163	0.0838794
$659$	29.5297	1.15031	0.575157	−	0.818043i	$-0.304941\pi$
$659$	29.5297	1.15031	0.575157	+	0.818043i	$0.304941\pi$
$660$	−0.403309	−0.0156988
$661$	−1.69485	−0.0659220	−0.0329610	−	0.999457i	$-0.510494\pi$
$661$	−1.69485	−0.0659220	−0.0329610	+	0.999457i	$0.510494\pi$
$662$	17.3035	0.672519
$663$	6.20701	0.241060
$664$	−15.2388	−0.591379
$665$	0.292085	0.0113266
$666$	−15.4368	−0.598165
$667$	18.5663	0.718890
$668$	24.3675	0.942806
$669$	8.27142	0.319792
$670$	−0.322839	−0.0124723
$671$	13.3333	0.514725
$672$	−37.3087	−1.43922
$673$	33.4044	1.28764	0.643822	−	0.765176i	$-0.277348\pi$
$673$	33.4044	1.28764	0.643822	+	0.765176i	$0.277348\pi$
$674$	17.8984	0.689422
$675$	20.9857	0.807740
$676$	9.55721	0.367585
$677$	17.7629	0.682682	0.341341	−	0.939939i	$-0.389119\pi$
$677$	17.7629	0.682682	0.341341	+	0.939939i	$0.389119\pi$
$678$	5.05664	0.194199
$679$	−32.3820	−1.24271
$680$	0.0727903	0.00279138
$681$	18.1049	0.693781
$682$	−34.2329	−1.31085
$683$	8.06220	0.308492	0.154246	−	0.988033i	$-0.450705\pi$
$683$	8.06220	0.308492	0.154246	+	0.988033i	$0.450705\pi$
$684$	25.9135	0.990829
$685$	0.393148	0.0150214
$686$	−17.4767	−0.667263
$687$	17.7672	0.677860
$688$	−0.224076	−0.00854282
$689$	−1.32140	−0.0503414
$690$	−0.393345	−0.0149744
$691$	11.9771	0.455630	0.227815	−	0.973704i	$-0.426842\pi$
$691$	11.9771	0.455630	0.227815	+	0.973704i	$0.426842\pi$
$692$	−2.56242	−0.0974086
$693$	52.1455	1.98084
$694$	−1.26919	−0.0481778
$695$	0.515379	0.0195495
$696$	−22.9603	−0.870309
$697$	1.63274	0.0618446
$698$	−3.39513	−0.128508
$699$	59.6572	2.25644
$700$	14.6936	0.555367
$701$	28.9904	1.09495	0.547476	−	0.836821i	$-0.315589\pi$
$701$	28.9904	1.09495	0.547476	+	0.836821i	$0.315589\pi$
$702$	8.42705	0.318058
$703$	18.1194	0.683386
$704$	24.6373	0.928553
$705$	0.0700602	0.00263862
$706$	−21.7998	−0.820446
$707$	−39.6699	−1.49194
$708$	−32.8050	−1.23289
$709$	−14.7389	−0.553532	−0.276766	−	0.960937i	$-0.589263\pi$
$709$	−14.7389	−0.553532	−0.276766	+	0.960937i	$0.589263\pi$
$710$	0.194137	0.00728584
$711$	−12.6076	−0.472821
$712$	36.6527	1.37362
$713$	51.3872	1.92446
$714$	−5.90417	−0.220958
$715$	0.274233	0.0102558
$716$	−15.5175	−0.579915
$717$	−30.4241	−1.13621
$718$	6.03019	0.225045
$719$	−23.3362	−0.870292	−0.435146	−	0.900360i	$-0.643303\pi$
$719$	−23.3362	−0.870292	−0.435146	+	0.900360i	$0.643303\pi$
$720$	0.0122136	0.000455173 0
$721$	17.8109	0.663312
$722$	2.89965	0.107914
$723$	65.8419	2.44869
$724$	−9.46166	−0.351640
$725$	14.6727	0.544929
$726$	−28.1217	−1.04370
$727$	−33.3919	−1.23844	−0.619218	−	0.785219i	$-0.712550\pi$
$727$	−33.3919	−1.23844	−0.619218	+	0.785219i	$0.712550\pi$
$728$	15.6344	0.579449
$729$	−43.9353	−1.62723
$730$	0.182615	0.00675890
$731$	2.12182	0.0784782
$732$	9.34115	0.345259
$733$	38.2138	1.41146	0.705729	−	0.708482i	$-0.250620\pi$
$733$	38.2138	1.41146	0.705729	+	0.708482i	$0.250620\pi$
$734$	20.4503	0.754836
$735$	−0.0786439	−0.00290082
$736$	−35.4776	−1.30772
$737$	67.6517	2.49198
$738$	6.56394	0.241622
$739$	17.3798	0.639325	0.319662	−	0.947532i	$-0.396431\pi$
$739$	17.3798	0.639325	0.319662	+	0.947532i	$0.396431\pi$
$740$	−0.118854	−0.00436914
$741$	−29.2897	−1.07599
$742$	1.25693	0.0461433
$743$	−13.4630	−0.493908	−0.246954	−	0.969027i	$-0.579430\pi$
$743$	−13.4630	−0.493908	−0.246954	+	0.969027i	$0.579430\pi$
$744$	−63.5488	−2.32981
$745$	−0.453767	−0.0166247
$746$	15.1133	0.553336
$747$	24.2120	0.885873
$748$	−5.75661	−0.210483
$749$	6.42842	0.234890
$750$	−0.621750	−0.0227031
$751$	32.0294	1.16877	0.584384	−	0.811477i	$-0.301336\pi$
$751$	32.0294	1.16877	0.584384	+	0.811477i	$0.301336\pi$
$752$	−0.105606	−0.00385105
$753$	13.0770	0.476552
$754$	5.89197	0.214573
$755$	−0.176109	−0.00640927
$756$	12.3375	0.448709
$757$	−24.3500	−0.885016	−0.442508	−	0.896765i	$-0.645911\pi$
$757$	−24.3500	−0.885016	−0.442508	+	0.896765i	$0.645911\pi$
$758$	−10.1854	−0.369951
$759$	82.4266	2.99190
$760$	−0.343484	−0.0124595
$761$	27.2405	0.987469	0.493734	−	0.869613i	$-0.335632\pi$
$761$	27.2405	0.987469	0.493734	+	0.869613i	$0.335632\pi$
$762$	−38.3035	−1.38759
$763$	−23.0372	−0.834001
$764$	−9.11224	−0.329669
$765$	−0.115653	−0.00418143
$766$	−6.79933	−0.245670
$767$	22.3060	0.805425
$768$	44.5766	1.60852
$769$	6.21695	0.224189	0.112094	−	0.993698i	$-0.464244\pi$
$769$	6.21695	0.224189	0.112094	+	0.993698i	$0.464244\pi$
$770$	−0.260853	−0.00940050
$771$	−35.4462	−1.27656
$772$	−5.40201	−0.194423
$773$	−24.3975	−0.877518	−0.438759	−	0.898605i	$-0.644582\pi$
$773$	−24.3975	−0.877518	−0.438759	+	0.898605i	$0.644582\pi$
$774$	8.53011	0.306609
$775$	40.6104	1.45877
$776$	38.0804	1.36701
$777$	25.5445	0.916403
$778$	25.9889	0.931747
$779$	−7.70461	−0.276046
$780$	0.192125	0.00687918
$781$	−40.6820	−1.45572
$782$	−5.61439	−0.200770
$783$	12.3199	0.440276
$784$	0.118545	0.00423373
$785$	−0.385959	−0.0137755
$786$	−37.3404	−1.33189
$787$	41.5817	1.48223	0.741114	−	0.671379i	$-0.234298\pi$
$787$	41.5817	1.48223	0.741114	+	0.671379i	$0.234298\pi$
$788$	−1.04158	−0.0371046
$789$	−22.9949	−0.818639
$790$	0.0630684	0.00224387
$791$	−5.03378	−0.178981
$792$	−61.3216	−2.17897
$793$	−6.35159	−0.225552
$794$	31.8133	1.12901
$795$	0.0409273	0.00145154
$796$	−30.3763	−1.07666
$797$	30.7531	1.08933	0.544665	−	0.838654i	$-0.316657\pi$
$797$	30.7531	1.08933	0.544665	+	0.838654i	$0.316657\pi$
$798$	27.8606	0.986256
$799$	1.00000	0.0353775
$800$	−28.0374	−0.991272
$801$	−58.2354	−2.05765
$802$	20.6995	0.730926
$803$	−38.2675	−1.35043
$804$	47.3960	1.67153
$805$	0.391568	0.0138009
$806$	16.3076	0.574410
$807$	69.9881	2.46370
$808$	46.6507	1.64117
$809$	−43.7679	−1.53880	−0.769398	−	0.638770i	$-0.779444\pi$
$809$	−43.7679	−1.53880	−0.769398	+	0.638770i	$0.779444\pi$
$810$	0.0469197	0.00164859
$811$	−52.4513	−1.84182	−0.920908	−	0.389780i	$-0.872551\pi$
$811$	−52.4513	−1.84182	−0.920908	+	0.389780i	$0.872551\pi$
$812$	8.62603	0.302714
$813$	−23.2108	−0.814037
$814$	−16.1819	−0.567177
$815$	−0.404618	−0.0141732
$816$	0.289786	0.0101445
$817$	−10.0125	−0.350291
$818$	−14.2129	−0.496943
$819$	−24.8406	−0.868001
$820$	0.0505381	0.00176487
$821$	−10.6276	−0.370905	−0.185452	−	0.982653i	$-0.559375\pi$
$821$	−10.6276	−0.370905	−0.185452	+	0.982653i	$0.559375\pi$
$822$	37.5006	1.30798
$823$	51.7671	1.80449	0.902243	−	0.431228i	$-0.141920\pi$
$823$	51.7671	1.80449	0.902243	+	0.431228i	$0.141920\pi$
$824$	−20.9451	−0.729657
$825$	65.1404	2.26790
$826$	−21.2177	−0.738258
$827$	0.125202	0.00435369	0.00217684	−	0.999998i	$-0.499307\pi$
$827$	0.125202	0.00435369	0.00217684	+	0.999998i	$0.499307\pi$
$828$	34.7396	1.20728
$829$	28.6755	0.995942	0.497971	−	0.867194i	$-0.334079\pi$
$829$	28.6755	0.995942	0.497971	+	0.867194i	$0.334079\pi$
$830$	−0.121119	−0.00420409
$831$	−32.0701	−1.11250
$832$	−11.7365	−0.406890
$833$	−1.12252	−0.0388930
$834$	49.1597	1.70226
$835$	0.513182	0.0177594
$836$	27.1644	0.939499
$837$	34.0984	1.17861
$838$	21.7309	0.750683
$839$	−22.8536	−0.788993	−0.394496	−	0.918898i	$-0.629081\pi$
$839$	−22.8536	−0.788993	−0.394496	+	0.918898i	$0.629081\pi$
$840$	−0.484239	−0.0167078
$841$	−20.3863	−0.702975
$842$	−8.03748	−0.276990
$843$	10.2048	0.351473
$844$	16.8476	0.579917
$845$	0.201276	0.00692411
$846$	4.02019	0.138217
$847$	27.9946	0.961907
$848$	−0.0616921	−0.00211852
$849$	26.7180	0.916961
$850$	−4.43697	−0.152187
$851$	24.2908	0.832677
$852$	−28.5013	−0.976440
$853$	33.1843	1.13621	0.568105	−	0.822956i	$-0.307677\pi$
$853$	33.1843	1.13621	0.568105	+	0.822956i	$0.307677\pi$
$854$	6.04169	0.206742
$855$	0.545742	0.0186640
$856$	−7.55965	−0.258383
$857$	54.1025	1.84811	0.924053	−	0.382263i	$-0.124855\pi$
$857$	54.1025	1.84811	0.924053	+	0.382263i	$0.124855\pi$
$858$	26.1579	0.893015
$859$	−7.38665	−0.252029	−0.126015	−	0.992028i	$-0.540219\pi$
$859$	−7.38665	−0.252029	−0.126015	+	0.992028i	$0.540219\pi$
$860$	0.0656763	0.00223954
$861$	−10.8618	−0.370171
$862$	−12.7957	−0.435822
$863$	−18.6921	−0.636288	−0.318144	−	0.948042i	$-0.603060\pi$
$863$	−18.6921	−0.636288	−0.318144	+	0.948042i	$0.603060\pi$
$864$	−23.5415	−0.800899
$865$	−0.0539649	−0.00183486
$866$	20.7247	0.704253
$867$	−2.74404	−0.0931924
$868$	23.8748	0.810364
$869$	−13.2161	−0.448327
$870$	−0.182490	−0.00618699
$871$	−32.2273	−1.09198
$872$	27.0911	0.917419
$873$	−60.5038	−2.04774
$874$	26.4933	0.896148
$875$	0.618940	0.0209240
$876$	−26.8098	−0.905820
$877$	−21.9567	−0.741425	−0.370713	−	0.928748i	$-0.620887\pi$
$877$	−21.9567	−0.741425	−0.370713	+	0.928748i	$0.620887\pi$
$878$	27.1572	0.916511
$879$	−74.2200	−2.50338
$880$	0.0128031	0.000431593 0
$881$	53.4860	1.80199	0.900995	−	0.433830i	$-0.142838\pi$
$881$	53.4860	1.80199	0.900995	+	0.433830i	$0.142838\pi$
$882$	−4.51274	−0.151952
$883$	−6.32344	−0.212801	−0.106400	−	0.994323i	$-0.533933\pi$
$883$	−6.32344	−0.212801	−0.106400	+	0.994323i	$0.533933\pi$
$884$	2.74229	0.0922330
$885$	−0.690878	−0.0232236
$886$	−10.2577	−0.344614
$887$	−26.4348	−0.887593	−0.443797	−	0.896128i	$-0.646369\pi$
$887$	−26.4348	−0.887593	−0.443797	+	0.896128i	$0.646369\pi$
$888$	−30.0396	−1.00806
$889$	38.1303	1.27885
$890$	0.291318	0.00976499
$891$	−9.83215	−0.329389
$892$	3.65435	0.122357
$893$	−4.71881	−0.157909
$894$	−43.2827	−1.44759
$895$	−0.326800	−0.0109237
$896$	−16.0287	−0.535481
$897$	−39.2657	−1.31104
$898$	−22.0781	−0.736755
$899$	23.8407	0.795133
$900$	27.4541	0.915137
$901$	0.584174	0.0194617
$902$	6.88078	0.229105
$903$	−14.1154	−0.469732
$904$	5.91959	0.196883
$905$	−0.199264	−0.00662375
$906$	−16.7982	−0.558084
$907$	−11.7721	−0.390886	−0.195443	−	0.980715i	$-0.562615\pi$
$907$	−11.7721	−0.390886	−0.195443	+	0.980715i	$0.562615\pi$
$908$	7.99882	0.265450
$909$	−74.1207	−2.45843
$910$	0.124263	0.00411928
$911$	−20.1339	−0.667067	−0.333534	−	0.942738i	$-0.608241\pi$
$911$	−20.1339	−0.667067	−0.333534	+	0.942738i	$0.608241\pi$
$912$	−1.36745	−0.0452807
$913$	25.3807	0.839980
$914$	−3.63464	−0.120223
$915$	0.196726	0.00650355
$916$	7.84961	0.259358
$917$	37.1716	1.22751
$918$	−3.72549	−0.122959
$919$	−22.3147	−0.736094	−0.368047	−	0.929807i	$-0.619974\pi$
$919$	−22.3147	−0.736094	−0.368047	+	0.929807i	$0.619974\pi$
$920$	−0.460473	−0.0151813
$921$	26.4920	0.872939
$922$	−19.9835	−0.658121
$923$	19.3797	0.637892
$924$	38.2959	1.25984
$925$	19.1966	0.631181
$926$	33.1535	1.08949
$927$	33.2785	1.09301
$928$	−16.4596	−0.540314
$929$	−40.6901	−1.33500	−0.667499	−	0.744610i	$-0.732635\pi$
$929$	−40.6901	−1.33500	−0.667499	+	0.744610i	$0.732635\pi$
$930$	−0.505089	−0.0165625
$931$	5.29696	0.173601
$932$	26.3568	0.863346
$933$	0.383429	0.0125529
$934$	−27.7215	−0.907075
$935$	−0.121235	−0.00396481
$936$	29.2119	0.954820
$937$	−4.03961	−0.131968	−0.0659842	−	0.997821i	$-0.521019\pi$
$937$	−4.03961	−0.131968	−0.0659842	+	0.997821i	$0.521019\pi$
$938$	30.6549	1.00092
$939$	−40.2229	−1.31262
$940$	0.0309529	0.00100957
$941$	−34.5274	−1.12556	−0.562781	−	0.826606i	$-0.690269\pi$
$941$	−34.5274	−1.12556	−0.562781	+	0.826606i	$0.690269\pi$
$942$	−36.8149	−1.19949
$943$	−10.3288	−0.336351
$944$	1.04140	0.0338947
$945$	0.259828	0.00845222
$946$	8.94186	0.290725
$947$	44.4997	1.44605	0.723023	−	0.690824i	$-0.242752\pi$
$947$	44.4997	1.44605	0.723023	+	0.690824i	$0.242752\pi$
$948$	−9.25908	−0.300721
$949$	18.2296	0.591756
$950$	20.9372	0.679293
$951$	64.3985	2.08826
$952$	−6.91175	−0.224011
$953$	45.7617	1.48237	0.741184	−	0.671302i	$-0.234265\pi$
$953$	45.7617	1.48237	0.741184	+	0.671302i	$0.234265\pi$
$954$	2.34849	0.0760352
$955$	−0.191905	−0.00620990
$956$	−13.4415	−0.434729
$957$	38.2413	1.23617
$958$	−26.8173	−0.866428
$959$	−37.3311	−1.20548
$960$	0.363511	0.0117323
$961$	34.9855	1.12857
$962$	7.70862	0.248536
$963$	12.0111	0.387052
$964$	29.0892	0.936901
$965$	−0.113767	−0.00366229
$966$	37.3498	1.20171
$967$	−59.0209	−1.89798	−0.948992	−	0.315300i	$-0.897895\pi$
$967$	−59.0209	−1.89798	−0.948992	+	0.315300i	$0.897895\pi$
$968$	−32.9209	−1.05812
$969$	12.9486	0.415969
$970$	0.302665	0.00971799
$971$	−23.6836	−0.760044	−0.380022	−	0.924977i	$-0.624084\pi$
$971$	−23.6836	−0.760044	−0.380022	+	0.924977i	$0.624084\pi$
$972$	−22.1552	−0.710629
$973$	−48.9375	−1.56886
$974$	−35.5475	−1.13901
$975$	−31.0310	−0.993788
$976$	−0.296536	−0.00949189
$977$	38.3764	1.22777	0.613885	−	0.789395i	$-0.289606\pi$
$977$	38.3764	1.22777	0.613885	+	0.789395i	$0.289606\pi$
$978$	−38.5947	−1.23412
$979$	−61.0464	−1.95105
$980$	−0.0347452	−0.00110989
$981$	−43.0435	−1.37427
$982$	21.0674	0.672288
$983$	24.2215	0.772546	0.386273	−	0.922384i	$-0.373762\pi$
$983$	24.2215	0.772546	0.386273	+	0.922384i	$0.373762\pi$
$984$	12.7732	0.407196
$985$	−0.0219357	−0.000698930 0
$986$	−2.60476	−0.0829525
$987$	−6.65251	−0.211752
$988$	−12.9403	−0.411687
$989$	−13.4226	−0.426815
$990$	−0.487388	−0.0154902
$991$	20.1007	0.638520	0.319260	−	0.947667i	$-0.396566\pi$
$991$	20.1007	0.638520	0.319260	+	0.947667i	$0.396566\pi$
$992$	−45.5563	−1.44642
$993$	−53.4997	−1.69776
$994$	−18.4342	−0.584696
$995$	−0.639728	−0.0202808
$996$	17.7815	0.563428
$997$	1.82993	0.0579545	0.0289772	−	0.999580i	$-0.490775\pi$
$997$	1.82993	0.0579545	0.0289772	+	0.999580i	$0.490775\pi$
$998$	5.44170	0.172254
$999$	16.1184	0.509963

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	799.2.a.d.1.5	✓	8
3.2	odd	2		7191.2.a.u.1.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
799.2.a.d.1.5	✓	8	1.1	even	1	trivial
7191.2.a.u.1.4		8	3.2	odd	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:	\( N \)	\(=\)	\( 799 = 17 \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	799.a (trivial)

\(f(q)\)	\(=\)	\(q+0.887509 q^{2} -2.74404 q^{3} -1.21233 q^{4} -0.0255318 q^{5} -2.43536 q^{6} +2.42435 q^{7} -2.85097 q^{8} +4.52975 q^{9} +O(q^{10})\)	\(q+0.887509 q^{2} -2.74404 q^{3} -1.21233 q^{4} -0.0255318 q^{5} -2.43536 q^{6} +2.42435 q^{7} -2.85097 q^{8} +4.52975 q^{9} -0.0226597 q^{10} +4.74840 q^{11} +3.32667 q^{12} -2.26200 q^{13} +2.15163 q^{14} +0.0700602 q^{15} -0.105606 q^{16} +1.00000 q^{17} +4.02019 q^{18} -4.71881 q^{19} +0.0309529 q^{20} -6.65251 q^{21} +4.21424 q^{22} -6.32601 q^{23} +7.82317 q^{24} -4.99935 q^{25} -2.00755 q^{26} -4.19769 q^{27} -2.93911 q^{28} -2.93491 q^{29} +0.0621790 q^{30} -8.12315 q^{31} +5.60821 q^{32} -13.0298 q^{33} +0.887509 q^{34} -0.0618980 q^{35} -5.49154 q^{36} -3.83982 q^{37} -4.18799 q^{38} +6.20701 q^{39} +0.0727903 q^{40} +1.63274 q^{41} -5.90417 q^{42} +2.12182 q^{43} -5.75661 q^{44} -0.115653 q^{45} -5.61439 q^{46} +1.00000 q^{47} +0.289786 q^{48} -1.12252 q^{49} -4.43697 q^{50} -2.74404 q^{51} +2.74229 q^{52} +0.584174 q^{53} -3.72549 q^{54} -0.121235 q^{55} -6.91175 q^{56} +12.9486 q^{57} -2.60476 q^{58} -9.86120 q^{59} -0.0849359 q^{60} +2.80795 q^{61} -7.20937 q^{62} +10.9817 q^{63} +5.18855 q^{64} +0.0577529 q^{65} -11.5640 q^{66} +14.2473 q^{67} -1.21233 q^{68} +17.3588 q^{69} -0.0549350 q^{70} -8.56752 q^{71} -12.9142 q^{72} -8.05904 q^{73} -3.40788 q^{74} +13.7184 q^{75} +5.72075 q^{76} +11.5118 q^{77} +5.50878 q^{78} -2.78329 q^{79} +0.00269630 q^{80} -2.07063 q^{81} +1.44907 q^{82} +5.34512 q^{83} +8.06503 q^{84} -0.0255318 q^{85} +1.88313 q^{86} +8.05352 q^{87} -13.5375 q^{88} -12.8562 q^{89} -0.102643 q^{90} -5.48388 q^{91} +7.66920 q^{92} +22.2902 q^{93} +0.887509 q^{94} +0.120480 q^{95} -15.3892 q^{96} -13.3570 q^{97} -0.996246 q^{98} +21.5090 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} - 7 q^{3} + 7 q^{4} - 10 q^{5} + 2 q^{6} - 9 q^{7} - q^{9}+O(q^{10}) \) 8 * q + q^2 - 7 * q^3 + 7 * q^4 - 10 * q^5 + 2 * q^6 - 9 * q^7 - q^9	\( 8 q + q^{2} - 7 q^{3} + 7 q^{4} - 10 q^{5} + 2 q^{6} - 9 q^{7} - q^{9} + 2 q^{10} - 2 q^{11} - 11 q^{12} - 3 q^{13} - 9 q^{14} + 14 q^{15} - 7 q^{16} + 8 q^{17} - 5 q^{18} - 8 q^{19} - 20 q^{20} + 4 q^{21} - 20 q^{22} - 9 q^{23} - 4 q^{24} + 14 q^{25} - 20 q^{26} + 2 q^{27} - 21 q^{28} - 2 q^{29} - 27 q^{30} - 7 q^{31} + 21 q^{32} - 23 q^{33} + q^{34} + 7 q^{35} - 17 q^{36} - 13 q^{37} - 7 q^{38} + 9 q^{39} - 16 q^{40} - 39 q^{41} + 11 q^{42} + 35 q^{43} - 17 q^{44} - 13 q^{45} + 19 q^{46} + 8 q^{47} + 9 q^{48} + q^{49} - 30 q^{50} - 7 q^{51} - 17 q^{52} - 6 q^{53} - 4 q^{54} + 22 q^{55} - 48 q^{56} + 5 q^{57} + 3 q^{58} - 19 q^{59} + 32 q^{60} - 15 q^{61} + 15 q^{62} + 17 q^{63} - 8 q^{64} - 29 q^{65} - 5 q^{66} + 15 q^{67} + 7 q^{68} - 12 q^{69} + 35 q^{70} - 7 q^{71} + q^{72} - 22 q^{73} - 43 q^{74} - 29 q^{75} + 52 q^{76} + 2 q^{77} + 43 q^{78} - 43 q^{79} + 6 q^{80} - 16 q^{81} + 19 q^{82} - 3 q^{83} + 34 q^{84} - 10 q^{85} - 19 q^{86} + q^{87} + 5 q^{88} - 53 q^{89} + 42 q^{90} + 5 q^{91} + 28 q^{92} + 44 q^{93} + q^{94} - 53 q^{95} - 41 q^{96} - 40 q^{97} + 30 q^{98} + 45 q^{99}+O(q^{100}) \) 8 * q + q^2 - 7 * q^3 + 7 * q^4 - 10 * q^5 + 2 * q^6 - 9 * q^7 - q^9 + 2 * q^10 - 2 * q^11 - 11 * q^12 - 3 * q^13 - 9 * q^14 + 14 * q^15 - 7 * q^16 + 8 * q^17 - 5 * q^18 - 8 * q^19 - 20 * q^20 + 4 * q^21 - 20 * q^22 - 9 * q^23 - 4 * q^24 + 14 * q^25 - 20 * q^26 + 2 * q^27 - 21 * q^28 - 2 * q^29 - 27 * q^30 - 7 * q^31 + 21 * q^32 - 23 * q^33 + q^34 + 7 * q^35 - 17 * q^36 - 13 * q^37 - 7 * q^38 + 9 * q^39 - 16 * q^40 - 39 * q^41 + 11 * q^42 + 35 * q^43 - 17 * q^44 - 13 * q^45 + 19 * q^46 + 8 * q^47 + 9 * q^48 + q^49 - 30 * q^50 - 7 * q^51 - 17 * q^52 - 6 * q^53 - 4 * q^54 + 22 * q^55 - 48 * q^56 + 5 * q^57 + 3 * q^58 - 19 * q^59 + 32 * q^60 - 15 * q^61 + 15 * q^62 + 17 * q^63 - 8 * q^64 - 29 * q^65 - 5 * q^66 + 15 * q^67 + 7 * q^68 - 12 * q^69 + 35 * q^70 - 7 * q^71 + q^72 - 22 * q^73 - 43 * q^74 - 29 * q^75 + 52 * q^76 + 2 * q^77 + 43 * q^78 - 43 * q^79 + 6 * q^80 - 16 * q^81 + 19 * q^82 - 3 * q^83 + 34 * q^84 - 10 * q^85 - 19 * q^86 + q^87 + 5 * q^88 - 53 * q^89 + 42 * q^90 + 5 * q^91 + 28 * q^92 + 44 * q^93 + q^94 - 53 * q^95 - 41 * q^96 - 40 * q^97 + 30 * q^98 + 45 * q^99

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