LMFDB - Embedded newform 799.2.a.d.1.3

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			1.3
Root			$-1.49338$ 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)

$f(q)$	$=$	$q-1.39501 q^{2} -2.49338 q^{3} -0.0539349 q^{4} -3.75291 q^{5} +3.47830 q^{6} -3.19565 q^{7} +2.86527 q^{8} +3.21694 q^{9} +O(q^{10})$	\(q-1.39501 q^{2} -2.49338 q^{3} -0.0539349 q^{4} -3.75291 q^{5} +3.47830 q^{6} -3.19565 q^{7} +2.86527 q^{8} +3.21694 q^{9} +5.23536 q^{10} +3.83195 q^{11} +0.134480 q^{12} +4.68138 q^{13} +4.45797 q^{14} +9.35742 q^{15} -3.88922 q^{16} +1.00000 q^{17} -4.48767 q^{18} -4.04399 q^{19} +0.202413 q^{20} +7.96795 q^{21} -5.34563 q^{22} +2.89033 q^{23} -7.14420 q^{24} +9.08431 q^{25} -6.53060 q^{26} -0.540903 q^{27} +0.172357 q^{28} -9.80094 q^{29} -13.0537 q^{30} +3.81322 q^{31} -0.305018 q^{32} -9.55450 q^{33} -1.39501 q^{34} +11.9930 q^{35} -0.173505 q^{36} -4.11724 q^{37} +5.64142 q^{38} -11.6725 q^{39} -10.7531 q^{40} -11.2409 q^{41} -11.1154 q^{42} +10.6389 q^{43} -0.206676 q^{44} -12.0729 q^{45} -4.03205 q^{46} +1.00000 q^{47} +9.69730 q^{48} +3.21215 q^{49} -12.6727 q^{50} -2.49338 q^{51} -0.252490 q^{52} +14.1269 q^{53} +0.754568 q^{54} -14.3810 q^{55} -9.15638 q^{56} +10.0832 q^{57} +13.6724 q^{58} +1.11089 q^{59} -0.504691 q^{60} +12.5018 q^{61} -5.31950 q^{62} -10.2802 q^{63} +8.20395 q^{64} -17.5688 q^{65} +13.3287 q^{66} +0.882542 q^{67} -0.0539349 q^{68} -7.20668 q^{69} -16.7304 q^{70} -2.76950 q^{71} +9.21739 q^{72} +10.8280 q^{73} +5.74361 q^{74} -22.6506 q^{75} +0.218112 q^{76} -12.2456 q^{77} +16.2833 q^{78} +8.70130 q^{79} +14.5959 q^{80} -8.30213 q^{81} +15.6812 q^{82} -10.8020 q^{83} -0.429751 q^{84} -3.75291 q^{85} -14.8415 q^{86} +24.4374 q^{87} +10.9796 q^{88} -18.2239 q^{89} +16.8418 q^{90} -14.9600 q^{91} -0.155889 q^{92} -9.50781 q^{93} -1.39501 q^{94} +15.1767 q^{95} +0.760525 q^{96} -12.7257 q^{97} -4.48100 q^{98} +12.3271 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.39501	−0.986424	−0.493212	−	0.869909i	$-0.664177\pi$
$2$	−1.39501	−0.986424	−0.493212	+	0.869909i	$0.664177\pi$
$3$	−2.49338	−1.43955	−0.719776	−	0.694206i	$-0.755756\pi$
$3$	−2.49338	−1.43955	−0.719776	+	0.694206i	$0.755756\pi$
$4$	−0.0539349	−0.0269674
$5$	−3.75291	−1.67835	−0.839176	−	0.543861i	$-0.816962\pi$
$5$	−3.75291	−1.67835	−0.839176	+	0.543861i	$0.816962\pi$
$6$	3.47830	1.42001
$7$	−3.19565	−1.20784	−0.603920	−	0.797045i	$-0.706396\pi$
$7$	−3.19565	−1.20784	−0.603920	+	0.797045i	$0.706396\pi$
$8$	2.86527	1.01303
$9$	3.21694	1.07231
$10$	5.23536	1.65557
$11$	3.83195	1.15538	0.577688	−	0.816257i	$-0.303955\pi$
$11$	3.83195	1.15538	0.577688	+	0.816257i	$0.303955\pi$
$12$	0.134480	0.0388210
$13$	4.68138	1.29838	0.649191	−	0.760625i	$-0.275107\pi$
$13$	4.68138	1.29838	0.649191	+	0.760625i	$0.275107\pi$
$14$	4.45797	1.19144
$15$	9.35742	2.41607
$16$	−3.88922	−0.972305
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−4.48767	−1.05775
$19$	−4.04399	−0.927754	−0.463877	−	0.885900i	$-0.653542\pi$
$19$	−4.04399	−0.927754	−0.463877	+	0.885900i	$0.653542\pi$
$20$	0.202413	0.0452608
$21$	7.96795	1.73875
$22$	−5.34563	−1.13969
$23$	2.89033	0.602675	0.301337	−	0.953518i	$-0.402567\pi$
$23$	2.89033	0.602675	0.301337	+	0.953518i	$0.402567\pi$
$24$	−7.14420	−1.45830
$25$	9.08431	1.81686
$26$	−6.53060	−1.28076
$27$	−0.540903	−0.104097
$28$	0.172357	0.0325724
$29$	−9.80094	−1.81999	−0.909994	−	0.414621i	$-0.863914\pi$
$29$	−9.80094	−1.81999	−0.909994	+	0.414621i	$0.863914\pi$
$30$	−13.0537	−2.38327
$31$	3.81322	0.684875	0.342437	−	0.939541i	$-0.388748\pi$
$31$	3.81322	0.684875	0.342437	+	0.939541i	$0.388748\pi$
$32$	−0.305018	−0.0539200
$33$	−9.55450	−1.66323
$34$	−1.39501	−0.239243
$35$	11.9930	2.02718
$36$	−0.173505	−0.0289175
$37$	−4.11724	−0.676871	−0.338435	−	0.940990i	$-0.609898\pi$
$37$	−4.11724	−0.676871	−0.338435	+	0.940990i	$0.609898\pi$
$38$	5.64142	0.915159
$39$	−11.6725	−1.86909
$40$	−10.7531	−1.70021
$41$	−11.2409	−1.75554	−0.877768	−	0.479087i	$-0.840968\pi$
$41$	−11.2409	−1.75554	−0.877768	+	0.479087i	$0.840968\pi$
$42$	−11.1154	−1.71515
$43$	10.6389	1.62242	0.811212	−	0.584753i	$-0.198808\pi$
$43$	10.6389	1.62242	0.811212	+	0.584753i	$0.198808\pi$
$44$	−0.206676	−0.0311575
$45$	−12.0729	−1.79972
$46$	−4.03205	−0.594493
$47$	1.00000	0.145865
$47$	1.00000	0.145865
$48$	9.69730	1.39968
$49$	3.21215	0.458879
$50$	−12.6727	−1.79220
$51$	−2.49338	−0.349143
$52$	−0.252490	−0.0350140
$53$	14.1269	1.94048	0.970239	−	0.242151i	$-0.0778530\pi$
$53$	14.1269	1.94048	0.970239	+	0.242151i	$0.0778530\pi$
$54$	0.754568	0.102684
$55$	−14.3810	−1.93913
$56$	−9.15638	−1.22357
$57$	10.0832	1.33555
$58$	13.6724	1.79528
$59$	1.11089	0.144626	0.0723128	−	0.997382i	$-0.476962\pi$
$59$	1.11089	0.144626	0.0723128	+	0.997382i	$0.476962\pi$
$60$	−0.504691	−0.0651553
$61$	12.5018	1.60069	0.800347	−	0.599537i	$-0.204648\pi$
$61$	12.5018	1.60069	0.800347	+	0.599537i	$0.204648\pi$
$62$	−5.31950	−0.675577
$63$	−10.2802	−1.29518
$64$	8.20395	1.02549
$65$	−17.5688	−2.17914
$66$	13.3287	1.64065
$67$	0.882542	0.107820	0.0539098	−	0.998546i	$-0.482832\pi$
$67$	0.882542	0.107820	0.0539098	+	0.998546i	$0.482832\pi$
$68$	−0.0539349	−0.00654056
$69$	−7.20668	−0.867582
$70$	−16.7304	−1.99966
$71$	−2.76950	−0.328679	−0.164339	−	0.986404i	$-0.552549\pi$
$71$	−2.76950	−0.328679	−0.164339	+	0.986404i	$0.552549\pi$
$72$	9.21739	1.08628
$73$	10.8280	1.26732	0.633660	−	0.773612i	$-0.281552\pi$
$73$	10.8280	1.26732	0.633660	+	0.773612i	$0.281552\pi$
$74$	5.74361	0.667681
$75$	−22.6506	−2.61547
$76$	0.218112	0.0250192
$77$	−12.2456	−1.39551
$78$	16.2833	1.84372
$79$	8.70130	0.978973	0.489486	−	0.872011i	$-0.337184\pi$
$79$	8.70130	0.978973	0.489486	+	0.872011i	$0.337184\pi$
$80$	14.5959	1.63187
$81$	−8.30213	−0.922459
$82$	15.6812	1.73170
$83$	−10.8020	−1.18567	−0.592836	−	0.805323i	$-0.701992\pi$
$83$	−10.8020	−1.18567	−0.592836	+	0.805323i	$0.701992\pi$
$84$	−0.429751	−0.0468896
$85$	−3.75291	−0.407060
$86$	−14.8415	−1.60040
$87$	24.4374	2.61997
$88$	10.9796	1.17043
$89$	−18.2239	−1.93173	−0.965867	−	0.259039i	$-0.916594\pi$
$89$	−18.2239	−1.93173	−0.965867	+	0.259039i	$0.916594\pi$
$90$	16.8418	1.77528
$91$	−14.9600	−1.56824
$92$	−0.155889	−0.0162526
$93$	−9.50781	−0.985914
$94$	−1.39501	−0.143885
$95$	15.1767	1.55710
$96$	0.760525	0.0776207
$97$	−12.7257	−1.29210	−0.646052	−	0.763294i	$-0.723581\pi$
$97$	−12.7257	−1.29210	−0.646052	+	0.763294i	$0.723581\pi$
$98$	−4.48100	−0.452649
$99$	12.3271	1.23892
$100$	−0.489961	−0.0489961
$101$	−0.662557	−0.0659269	−0.0329634	−	0.999457i	$-0.510494\pi$
$101$	−0.662557	−0.0659269	−0.0329634	+	0.999457i	$0.510494\pi$
$102$	3.47830	0.344403
$103$	−8.98688	−0.885504	−0.442752	−	0.896644i	$-0.645998\pi$
$103$	−8.98688	−0.885504	−0.442752	+	0.896644i	$0.645998\pi$
$104$	13.4134	1.31529
$105$	−29.9030	−2.91823
$106$	−19.7072	−1.91413
$107$	3.42735	0.331335	0.165667	−	0.986182i	$-0.447022\pi$
$107$	3.42735	0.331335	0.165667	+	0.986182i	$0.447022\pi$
$108$	0.0291736	0.00280723
$109$	−5.48617	−0.525480	−0.262740	−	0.964867i	$-0.584626\pi$
$109$	−5.48617	−0.525480	−0.262740	+	0.964867i	$0.584626\pi$
$110$	20.0616	1.91280
$111$	10.2658	0.974391
$112$	12.4286	1.17439
$113$	−11.5580	−1.08729	−0.543643	−	0.839316i	$-0.682956\pi$
$113$	−11.5580	−1.08729	−0.543643	+	0.839316i	$0.682956\pi$
$114$	−14.0662	−1.31742
$115$	−10.8471	−1.01150
$116$	0.528612	0.0490804
$117$	15.0597	1.39227
$118$	−1.54971	−0.142662
$119$	−3.19565	−0.292944
$120$	26.8115	2.44755
$121$	3.68384	0.334895
$122$	−17.4402	−1.57896
$123$	28.0278	2.52719
$124$	−0.205666	−0.0184693
$125$	−15.3280	−1.37098
$126$	14.3410	1.27760
$127$	16.3733	1.45290	0.726449	−	0.687221i	$-0.241169\pi$
$127$	16.3733	1.45290	0.726449	+	0.687221i	$0.241169\pi$
$128$	−10.8346	−0.957651
$129$	−26.5269	−2.33556
$130$	24.5087	2.14956
$131$	−4.20444	−0.367343	−0.183672	−	0.982988i	$-0.558798\pi$
$131$	−4.20444	−0.367343	−0.183672	+	0.982988i	$0.558798\pi$
$132$	0.515321	0.0448529
$133$	12.9232	1.12058
$134$	−1.23116	−0.106356
$135$	2.02996	0.174711
$136$	2.86527	0.245695
$137$	9.44299	0.806769	0.403385	−	0.915031i	$-0.367834\pi$
$137$	9.44299	0.806769	0.403385	+	0.915031i	$0.367834\pi$
$138$	10.0534	0.855804
$139$	10.0949	0.856241	0.428120	−	0.903722i	$-0.359176\pi$
$139$	10.0949	0.856241	0.428120	+	0.903722i	$0.359176\pi$
$140$	−0.646839	−0.0546679
$141$	−2.49338	−0.209980
$142$	3.86349	0.324217
$143$	17.9388	1.50012
$144$	−12.5114	−1.04261
$145$	36.7820	3.05458
$146$	−15.1052	−1.25011
$147$	−8.00911	−0.660581
$148$	0.222063	0.0182535
$149$	−5.56291	−0.455732	−0.227866	−	0.973693i	$-0.573175\pi$
$149$	−5.56291	−0.455732	−0.227866	+	0.973693i	$0.573175\pi$
$150$	31.5979	2.57996
$151$	−10.5843	−0.861339	−0.430670	−	0.902510i	$-0.641723\pi$
$151$	−10.5843	−0.861339	−0.430670	+	0.902510i	$0.641723\pi$
$152$	−11.5871	−0.939839
$153$	3.21694	0.260074
$154$	17.0827	1.37657
$155$	−14.3107	−1.14946
$156$	0.629553	0.0504046
$157$	−0.124652	−0.00994830	−0.00497415	−	0.999988i	$-0.501583\pi$
$157$	−0.124652	−0.00994830	−0.00497415	+	0.999988i	$0.501583\pi$
$158$	−12.1384	−0.965683
$159$	−35.2237	−2.79342
$160$	1.14470	0.0904967
$161$	−9.23646	−0.727935
$162$	11.5816	0.909936
$163$	−6.67853	−0.523103	−0.261551	−	0.965190i	$-0.584234\pi$
$163$	−6.67853	−0.523103	−0.261551	+	0.965190i	$0.584234\pi$
$164$	0.606277	0.0473423
$165$	35.8572	2.79148
$166$	15.0689	1.16958
$167$	−6.73738	−0.521354	−0.260677	−	0.965426i	$-0.583946\pi$
$167$	−6.73738	−0.521354	−0.260677	+	0.965426i	$0.583946\pi$
$168$	22.8303	1.76140
$169$	8.91536	0.685797
$170$	5.23536	0.401534
$171$	−13.0092	−0.994842
$172$	−0.573810	−0.0437526
$173$	−8.65044	−0.657680	−0.328840	−	0.944386i	$-0.606658\pi$
$173$	−8.65044	−0.657680	−0.328840	+	0.944386i	$0.606658\pi$
$174$	−34.0906	−2.58440
$175$	−29.0302	−2.19448
$176$	−14.9033	−1.12338
$177$	−2.76987	−0.208196
$178$	25.4227	1.90551
$179$	−3.16147	−0.236299	−0.118150	−	0.992996i	$-0.537696\pi$
$179$	−3.16147	−0.236299	−0.118150	+	0.992996i	$0.537696\pi$
$180$	0.651148	0.0485337
$181$	−5.68143	−0.422297	−0.211149	−	0.977454i	$-0.567720\pi$
$181$	−5.68143	−0.422297	−0.211149	+	0.977454i	$0.567720\pi$
$182$	20.8695	1.54695
$183$	−31.1718	−2.30428
$184$	8.28156	0.610525
$185$	15.4516	1.13603
$186$	13.2635	0.972529
$187$	3.83195	0.280220
$188$	−0.0539349	−0.00393360
$189$	1.72854	0.125732
$190$	−21.1717	−1.53596
$191$	13.8693	1.00355	0.501775	−	0.864998i	$-0.332680\pi$
$191$	13.8693	1.00355	0.501775	+	0.864998i	$0.332680\pi$
$192$	−20.4555	−1.47625
$193$	−8.99503	−0.647476	−0.323738	−	0.946147i	$-0.604940\pi$
$193$	−8.99503	−0.647476	−0.323738	+	0.946147i	$0.604940\pi$
$194$	17.7526	1.27456
$195$	43.8057	3.13699
$196$	−0.173247	−0.0123748
$197$	16.2928	1.16081	0.580405	−	0.814328i	$-0.302894\pi$
$197$	16.2928	1.16081	0.580405	+	0.814328i	$0.302894\pi$
$198$	−17.1965	−1.22210
$199$	7.64146	0.541689	0.270844	−	0.962623i	$-0.412697\pi$
$199$	7.64146	0.541689	0.270844	+	0.962623i	$0.412697\pi$
$200$	26.0290	1.84053
$201$	−2.20051	−0.155212
$202$	0.924276	0.0650319
$203$	31.3203	2.19826
$204$	0.134480	0.00941549
$205$	42.1861	2.94640
$206$	12.5368	0.873482
$207$	9.29799	0.646255
$208$	−18.2069	−1.26242
$209$	−15.4964	−1.07191
$210$	41.7151	2.87862
$211$	2.90812	0.200203	0.100102	−	0.994977i	$-0.468083\pi$
$211$	2.90812	0.200203	0.100102	+	0.994977i	$0.468083\pi$
$212$	−0.761932	−0.0523297
$213$	6.90540	0.473150
$214$	−4.78121	−0.326836
$215$	−39.9270	−2.72300
$216$	−1.54983	−0.105453
$217$	−12.1857	−0.827220
$218$	7.65329	0.518346
$219$	−26.9983	−1.82437
$220$	0.775635	0.0522933
$221$	4.68138	0.314904
$222$	−14.3210	−0.961163
$223$	8.89000	0.595318	0.297659	−	0.954672i	$-0.403794\pi$
$223$	8.89000	0.595318	0.297659	+	0.954672i	$0.403794\pi$
$224$	0.974729	0.0651268
$225$	29.2236	1.94824
$226$	16.1236	1.07253
$227$	−4.17081	−0.276826	−0.138413	−	0.990375i	$-0.544200\pi$
$227$	−4.17081	−0.276826	−0.138413	+	0.990375i	$0.544200\pi$
$228$	−0.543836	−0.0360164
$229$	−13.6493	−0.901970	−0.450985	−	0.892531i	$-0.648927\pi$
$229$	−13.6493	−0.901970	−0.450985	+	0.892531i	$0.648927\pi$
$230$	15.1319	0.997768
$231$	30.5328	2.00891
$232$	−28.0823	−1.84369
$233$	−15.1905	−0.995163	−0.497581	−	0.867417i	$-0.665778\pi$
$233$	−15.1905	−0.995163	−0.497581	+	0.867417i	$0.665778\pi$
$234$	−21.0085	−1.37337
$235$	−3.75291	−0.244813
$236$	−0.0599157	−0.00390018
$237$	−21.6956	−1.40928
$238$	4.45797	0.288967
$239$	1.03889	0.0672002	0.0336001	−	0.999435i	$-0.489303\pi$
$239$	1.03889	0.0672002	0.0336001	+	0.999435i	$0.489303\pi$
$240$	−36.3931	−2.34916
$241$	6.38258	0.411138	0.205569	−	0.978643i	$-0.434096\pi$
$241$	6.38258	0.411138	0.205569	+	0.978643i	$0.434096\pi$
$242$	−5.13901	−0.330348
$243$	22.3231	1.43203
$244$	−0.674284	−0.0431666
$245$	−12.0549	−0.770160
$246$	−39.0992	−2.49288
$247$	−18.9315	−1.20458
$248$	10.9259	0.693796
$249$	26.9334	1.70684
$250$	21.3828	1.35237
$251$	−2.77673	−0.175266	−0.0876329	−	0.996153i	$-0.527930\pi$
$251$	−2.77673	−0.175266	−0.0876329	+	0.996153i	$0.527930\pi$
$252$	0.554461	0.0349277
$253$	11.0756	0.696316
$254$	−22.8410	−1.43317
$255$	9.35742	0.585984
$256$	−1.29349	−0.0808429
$257$	−17.5164	−1.09264	−0.546321	−	0.837576i	$-0.683972\pi$
$257$	−17.5164	−1.09264	−0.546321	+	0.837576i	$0.683972\pi$
$258$	37.0054	2.30386
$259$	13.1573	0.817552
$260$	0.947571	0.0587659
$261$	−31.5290	−1.95159
$262$	5.86525	0.362356
$263$	−16.9602	−1.04581	−0.522907	−	0.852390i	$-0.675152\pi$
$263$	−16.9602	−1.04581	−0.522907	+	0.852390i	$0.675152\pi$
$264$	−27.3762	−1.68489
$265$	−53.0169	−3.25680
$266$	−18.0280	−1.10537
$267$	45.4392	2.78083
$268$	−0.0475998	−0.00290762
$269$	25.9800	1.58403	0.792014	−	0.610503i	$-0.209032\pi$
$269$	25.9800	1.58403	0.792014	+	0.610503i	$0.209032\pi$
$270$	−2.83182	−0.172339
$271$	3.49048	0.212032	0.106016	−	0.994364i	$-0.466191\pi$
$271$	3.49048	0.212032	0.106016	+	0.994364i	$0.466191\pi$
$272$	−3.88922	−0.235819
$273$	37.3011	2.25756
$274$	−13.1731	−0.795816
$275$	34.8106	2.09916
$276$	0.388691	0.0233965
$277$	−9.31079	−0.559431	−0.279716	−	0.960083i	$-0.590240\pi$
$277$	−9.31079	−0.559431	−0.279716	+	0.960083i	$0.590240\pi$
$278$	−14.0826	−0.844617
$279$	12.2669	0.734400
$280$	34.3631	2.05359
$281$	−9.99508	−0.596256	−0.298128	−	0.954526i	$-0.596362\pi$
$281$	−9.99508	−0.596256	−0.298128	+	0.954526i	$0.596362\pi$
$282$	3.47830	0.207130
$283$	−25.9221	−1.54091	−0.770454	−	0.637495i	$-0.779971\pi$
$283$	−25.9221	−1.54091	−0.770454	+	0.637495i	$0.779971\pi$
$284$	0.149372	0.00886362
$285$	−37.8413	−2.24152
$286$	−25.0249	−1.47976
$287$	35.9220	2.12041
$288$	−0.981223	−0.0578191
$289$	1.00000	0.0588235
$290$	−51.3114	−3.01311
$291$	31.7301	1.86005
$292$	−0.584006	−0.0341764
$293$	−9.72299	−0.568023	−0.284012	−	0.958821i	$-0.591665\pi$
$293$	−9.72299	−0.568023	−0.284012	+	0.958821i	$0.591665\pi$
$294$	11.1728	0.651613
$295$	−4.16907	−0.242732
$296$	−11.7970	−0.685687
$297$	−2.07271	−0.120271
$298$	7.76034	0.449545
$299$	13.5307	0.782502
$300$	1.22166	0.0705325
$301$	−33.9983	−1.95963
$302$	14.7653	0.849646
$303$	1.65200	0.0949052
$304$	15.7280	0.902060
$305$	−46.9182	−2.68653
$306$	−4.48767	−0.256543
$307$	−10.3843	−0.592662	−0.296331	−	0.955085i	$-0.595763\pi$
$307$	−10.3843	−0.592662	−0.296331	+	0.955085i	$0.595763\pi$
$308$	0.660463	0.0376333
$309$	22.4077	1.27473
$310$	19.9636	1.13386
$311$	−33.3144	−1.88909	−0.944544	−	0.328384i	$-0.893496\pi$
$311$	−33.3144	−1.88909	−0.944544	+	0.328384i	$0.893496\pi$
$312$	−33.4447	−1.89344
$313$	−3.83717	−0.216890	−0.108445	−	0.994102i	$-0.534587\pi$
$313$	−3.83717	−0.216890	−0.108445	+	0.994102i	$0.534587\pi$
$314$	0.173891	0.00981324
$315$	38.5806	2.17377
$316$	−0.469304	−0.0264004
$317$	24.4030	1.37061	0.685305	−	0.728256i	$-0.259669\pi$
$317$	24.4030	1.37061	0.685305	+	0.728256i	$0.259669\pi$
$318$	49.1375	2.75550
$319$	−37.5567	−2.10277
$320$	−30.7886	−1.72114
$321$	−8.54569	−0.476974
$322$	12.8850	0.718053
$323$	−4.04399	−0.225013
$324$	0.447774	0.0248764
$325$	42.5272	2.35898
$326$	9.31665	0.516001
$327$	13.6791	0.756456
$328$	−32.2082	−1.77840
$329$	−3.19565	−0.176182
$330$	−50.0213	−2.75358
$331$	12.4166	0.682477	0.341239	−	0.939977i	$-0.389154\pi$
$331$	12.4166	0.682477	0.341239	+	0.939977i	$0.389154\pi$
$332$	0.582604	0.0319745
$333$	−13.2449	−0.725816
$334$	9.39874	0.514276
$335$	−3.31210	−0.180959
$336$	−30.9891	−1.69060
$337$	−24.8575	−1.35407	−0.677037	−	0.735949i	$-0.736736\pi$
$337$	−24.8575	−1.35407	−0.677037	+	0.735949i	$0.736736\pi$
$338$	−12.4371	−0.676487
$339$	28.8185	1.56521
$340$	0.202413	0.0109774
$341$	14.6121	0.791288
$342$	18.1481	0.981336
$343$	12.1046	0.653588
$344$	30.4834	1.64356
$345$	27.0460	1.45611
$346$	12.0675	0.648752
$347$	18.1301	0.973273	0.486637	−	0.873604i	$-0.338224\pi$
$347$	18.1301	0.973273	0.486637	+	0.873604i	$0.338224\pi$
$348$	−1.31803	−0.0706538
$349$	4.85937	0.260116	0.130058	−	0.991506i	$-0.458484\pi$
$349$	4.85937	0.260116	0.130058	+	0.991506i	$0.458484\pi$
$350$	40.4976	2.16469
$351$	−2.53218	−0.135158
$352$	−1.16881	−0.0622979
$353$	−10.1028	−0.537720	−0.268860	−	0.963179i	$-0.586647\pi$
$353$	−10.1028	−0.537720	−0.268860	+	0.963179i	$0.586647\pi$
$354$	3.86401	0.205370
$355$	10.3937	0.551638
$356$	0.982906	0.0520939
$357$	7.96795	0.421709
$358$	4.41029	0.233091
$359$	−2.14936	−0.113439	−0.0567194	−	0.998390i	$-0.518064\pi$
$359$	−2.14936	−0.113439	−0.0567194	+	0.998390i	$0.518064\pi$
$360$	−34.5920	−1.82316
$361$	−2.64617	−0.139272
$362$	7.92568	0.416564
$363$	−9.18521	−0.482099
$364$	0.806868	0.0422914
$365$	−40.6364	−2.12701
$366$	43.4851	2.27300
$367$	−32.6733	−1.70553	−0.852765	−	0.522295i	$-0.825076\pi$
$367$	−32.6733	−1.70553	−0.852765	+	0.522295i	$0.825076\pi$
$368$	−11.2411	−0.585984
$369$	−36.1613	−1.88248
$370$	−21.5552	−1.12060
$371$	−45.1445	−2.34379
$372$	0.512802	0.0265876
$373$	−9.18273	−0.475464	−0.237732	−	0.971331i	$-0.576404\pi$
$373$	−9.18273	−0.475464	−0.237732	+	0.971331i	$0.576404\pi$
$374$	−5.34563	−0.276416
$375$	38.2186	1.97360
$376$	2.86527	0.147765
$377$	−45.8819	−2.36304
$378$	−2.41133	−0.124026
$379$	22.9551	1.17913	0.589563	−	0.807723i	$-0.299300\pi$
$379$	22.9551	1.17913	0.589563	+	0.807723i	$0.299300\pi$
$380$	−0.818554	−0.0419909
$381$	−40.8249	−2.09152
$382$	−19.3479	−0.989926
$383$	27.9969	1.43058	0.715288	−	0.698830i	$-0.246296\pi$
$383$	27.9969	1.43058	0.715288	+	0.698830i	$0.246296\pi$
$384$	27.0147	1.37859
$385$	45.9564	2.34216
$386$	12.5482	0.638686
$387$	34.2248	1.73974
$388$	0.686361	0.0348447
$389$	−7.32999	−0.371645	−0.185823	−	0.982583i	$-0.559495\pi$
$389$	−7.32999	−0.371645	−0.185823	+	0.982583i	$0.559495\pi$
$390$	−61.1095	−3.09440
$391$	2.89033	0.146170
$392$	9.20368	0.464856
$393$	10.4833	0.528810
$394$	−22.7286	−1.14505
$395$	−32.6552	−1.64306
$396$	−0.664863	−0.0334106
$397$	−10.4681	−0.525380	−0.262690	−	0.964880i	$-0.584610\pi$
$397$	−10.4681	−0.525380	−0.262690	+	0.964880i	$0.584610\pi$
$398$	−10.6599	−0.534335
$399$	−32.2223	−1.61313
$400$	−35.3309	−1.76654
$401$	−34.4387	−1.71979	−0.859894	−	0.510472i	$-0.829471\pi$
$401$	−34.4387	−1.71979	−0.859894	+	0.510472i	$0.829471\pi$
$402$	3.06974	0.153105
$403$	17.8512	0.889230
$404$	0.0357349	0.00177788
$405$	31.1571	1.54821
$406$	−43.6923	−2.16841
$407$	−15.7771	−0.782040
$408$	−7.14420	−0.353691
$409$	−3.33542	−0.164926	−0.0824630	−	0.996594i	$-0.526279\pi$
$409$	−3.33542	−0.164926	−0.0824630	+	0.996594i	$0.526279\pi$
$410$	−58.8502	−2.90640
$411$	−23.5449	−1.16139
$412$	0.484706	0.0238798
$413$	−3.55001	−0.174685
$414$	−12.9708	−0.637482
$415$	40.5389	1.98997
$416$	−1.42791	−0.0700088
$417$	−25.1705	−1.23260
$418$	21.6176	1.05735
$419$	25.2019	1.23119	0.615597	−	0.788061i	$-0.288915\pi$
$419$	25.2019	1.23119	0.615597	+	0.788061i	$0.288915\pi$
$420$	1.61281	0.0786973
$421$	21.0548	1.02615	0.513074	−	0.858344i	$-0.328507\pi$
$421$	21.0548	1.02615	0.513074	+	0.858344i	$0.328507\pi$
$422$	−4.05687	−0.197485
$423$	3.21694	0.156413
$424$	40.4773	1.96575
$425$	9.08431	0.440654
$426$	−9.63313	−0.466727
$427$	−39.9514	−1.93338
$428$	−0.184854	−0.00893524
$429$	−44.7283	−2.15950
$430$	55.6987	2.68603
$431$	10.6688	0.513899	0.256949	−	0.966425i	$-0.417283\pi$
$431$	10.6688	0.513899	0.256949	+	0.966425i	$0.417283\pi$
$432$	2.10369	0.101214
$433$	3.30960	0.159049	0.0795245	−	0.996833i	$-0.474660\pi$
$433$	3.30960	0.159049	0.0795245	+	0.996833i	$0.474660\pi$
$434$	16.9992	0.815990
$435$	−91.7114	−4.39723
$436$	0.295896	0.0141708
$437$	−11.6884	−0.559134
$438$	37.6630	1.79961
$439$	5.69706	0.271906	0.135953	−	0.990715i	$-0.456590\pi$
$439$	5.69706	0.271906	0.135953	+	0.990715i	$0.456590\pi$
$440$	−41.2053	−1.96439
$441$	10.3333	0.492062
$442$	−6.53060	−0.310629
$443$	20.2797	0.963516	0.481758	−	0.876304i	$-0.339998\pi$
$443$	20.2797	0.963516	0.481758	+	0.876304i	$0.339998\pi$
$444$	−0.553687	−0.0262768
$445$	68.3928	3.24213
$446$	−12.4017	−0.587236
$447$	13.8704	0.656050
$448$	−26.2169	−1.23863
$449$	−35.6467	−1.68227	−0.841137	−	0.540822i	$-0.818113\pi$
$449$	−35.6467	−1.68227	−0.841137	+	0.540822i	$0.818113\pi$
$450$	−40.7674	−1.92179
$451$	−43.0746	−2.02830
$452$	0.623380	0.0293213
$453$	26.3907	1.23994
$454$	5.81833	0.273068
$455$	56.1437	2.63206
$456$	28.8910	1.35295
$457$	21.2355	0.993356	0.496678	−	0.867935i	$-0.334553\pi$
$457$	21.2355	0.993356	0.496678	+	0.867935i	$0.334553\pi$
$458$	19.0410	0.889725
$459$	−0.540903	−0.0252472
$460$	0.585038	0.0272776
$461$	−4.40426	−0.205127	−0.102564	−	0.994726i	$-0.532704\pi$
$461$	−4.40426	−0.205127	−0.102564	+	0.994726i	$0.532704\pi$
$462$	−42.5937	−1.98164
$463$	1.68644	0.0783757	0.0391879	−	0.999232i	$-0.487523\pi$
$463$	1.68644	0.0783757	0.0391879	+	0.999232i	$0.487523\pi$
$464$	38.1180	1.76958
$465$	35.6819	1.65471
$466$	21.1910	0.981652
$467$	−17.0303	−0.788066	−0.394033	−	0.919096i	$-0.628921\pi$
$467$	−17.0303	−0.788066	−0.394033	+	0.919096i	$0.628921\pi$
$468$	−0.812244	−0.0375460
$469$	−2.82029	−0.130229
$470$	5.23536	0.241489
$471$	0.310804	0.0143211
$472$	3.18300	0.146509
$473$	40.7679	1.87451
$474$	30.2657	1.39015
$475$	−36.7368	−1.68560
$476$	0.172357	0.00789996
$477$	45.4453	2.08080
$478$	−1.44927	−0.0662879
$479$	−18.2256	−0.832749	−0.416375	−	0.909193i	$-0.636700\pi$
$479$	−18.2256	−0.832749	−0.416375	+	0.909193i	$0.636700\pi$
$480$	−2.85418	−0.130275
$481$	−19.2744	−0.878837
$482$	−8.90379	−0.405556
$483$	23.0300	1.04790
$484$	−0.198688	−0.00903125
$485$	47.7585	2.16860
$486$	−31.1410	−1.41258
$487$	25.4958	1.15532	0.577662	−	0.816276i	$-0.303965\pi$
$487$	25.4958	1.15532	0.577662	+	0.816276i	$0.303965\pi$
$488$	35.8211	1.62154
$489$	16.6521	0.753034
$490$	16.8168	0.759705
$491$	−22.0465	−0.994946	−0.497473	−	0.867479i	$-0.665739\pi$
$491$	−22.0465	−0.994946	−0.497473	+	0.867479i	$0.665739\pi$
$492$	−1.51168	−0.0681517
$493$	−9.80094	−0.441412
$494$	26.4097	1.18823
$495$	−46.2626	−2.07935
$496$	−14.8305	−0.665908
$497$	8.85033	0.396991
$498$	−37.5725	−1.68367
$499$	−4.95351	−0.221750	−0.110875	−	0.993834i	$-0.535365\pi$
$499$	−4.95351	−0.221750	−0.110875	+	0.993834i	$0.535365\pi$
$500$	0.826716	0.0369719
$501$	16.7988	0.750517
$502$	3.87358	0.172886
$503$	31.8115	1.41840	0.709202	−	0.705006i	$-0.249056\pi$
$503$	31.8115	1.41840	0.709202	+	0.705006i	$0.249056\pi$
$504$	−29.4555	−1.31205
$505$	2.48651	0.110648
$506$	−15.4506	−0.686863
$507$	−22.2294	−0.987241
$508$	−0.883093	−0.0391809
$509$	−5.27920	−0.233996	−0.116998	−	0.993132i	$-0.537327\pi$
$509$	−5.27920	−0.233996	−0.116998	+	0.993132i	$0.537327\pi$
$510$	−13.0537	−0.578029
$511$	−34.6024	−1.53072
$512$	23.4736	1.03740
$513$	2.18741	0.0965763
$514$	24.4356	1.07781
$515$	33.7269	1.48619
$516$	1.43073	0.0629842
$517$	3.83195	0.168529
$518$	−18.3546	−0.806453
$519$	21.5688	0.946766
$520$	−50.3393	−2.20753
$521$	−18.6839	−0.818556	−0.409278	−	0.912410i	$-0.634219\pi$
$521$	−18.6839	−0.818556	−0.409278	+	0.912410i	$0.634219\pi$
$522$	43.9834	1.92510
$523$	−11.6517	−0.509494	−0.254747	−	0.967008i	$-0.581992\pi$
$523$	−11.6517	−0.509494	−0.254747	+	0.967008i	$0.581992\pi$
$524$	0.226766	0.00990631
$525$	72.3834	3.15907
$526$	23.6598	1.03162
$527$	3.81322	0.166107
$528$	37.1596	1.61716
$529$	−14.6460	−0.636783
$530$	73.9593	3.21259
$531$	3.57366	0.155084
$532$	−0.697009	−0.0302192
$533$	−52.6230	−2.27936
$534$	−63.3883	−2.74308
$535$	−12.8625	−0.556096
$536$	2.52872	0.109224
$537$	7.88274	0.340165
$538$	−36.2425	−1.56252
$539$	12.3088	0.530178
$540$	−0.109486	−0.00471151
$541$	−31.7416	−1.36468	−0.682338	−	0.731037i	$-0.739037\pi$
$541$	−31.7416	−1.36468	−0.682338	+	0.731037i	$0.739037\pi$
$542$	−4.86927	−0.209153
$543$	14.1660	0.607919
$544$	−0.305018	−0.0130775
$545$	20.5891	0.881940
$546$	−52.0355	−2.22691
$547$	−11.4081	−0.487775	−0.243887	−	0.969804i	$-0.578423\pi$
$547$	−11.4081	−0.487775	−0.243887	+	0.969804i	$0.578423\pi$
$548$	−0.509306	−0.0217565
$549$	40.2176	1.71644
$550$	−48.5613	−2.07066
$551$	39.6349	1.68850
$552$	−20.6491	−0.878883
$553$	−27.8063	−1.18244
$554$	12.9887	0.551837
$555$	−38.5268	−1.63537
$556$	−0.544469	−0.0230906
$557$	24.9496	1.05715	0.528575	−	0.848887i	$-0.322727\pi$
$557$	24.9496	1.05715	0.528575	+	0.848887i	$0.322727\pi$
$558$	−17.1125	−0.724429
$559$	49.8050	2.10653
$560$	−46.6433	−1.97104
$561$	−9.55450	−0.403391
$562$	13.9433	0.588162
$563$	−34.1865	−1.44079	−0.720395	−	0.693564i	$-0.756040\pi$
$563$	−34.1865	−1.44079	−0.720395	+	0.693564i	$0.756040\pi$
$564$	0.134480	0.00566263
$565$	43.3762	1.82485
$566$	36.1617	1.51999
$567$	26.5307	1.11418
$568$	−7.93535	−0.332960
$569$	−34.5749	−1.44945	−0.724727	−	0.689036i	$-0.758034\pi$
$569$	−34.5749	−1.44945	−0.724727	+	0.689036i	$0.758034\pi$
$570$	52.7891	2.21109
$571$	30.7981	1.28886	0.644431	−	0.764663i	$-0.277094\pi$
$571$	30.7981	1.28886	0.644431	+	0.764663i	$0.277094\pi$
$572$	−0.967529	−0.0404544
$573$	−34.5815	−1.44466
$574$	−50.1117	−2.09162
$575$	26.2566	1.09498
$576$	26.3916	1.09965
$577$	−4.53880	−0.188953	−0.0944763	−	0.995527i	$-0.530118\pi$
$577$	−4.53880	−0.188953	−0.0944763	+	0.995527i	$0.530118\pi$
$578$	−1.39501	−0.0580249
$579$	22.4280	0.932076
$580$	−1.98383	−0.0823742
$581$	34.5193	1.43210
$582$	−44.2639	−1.83480
$583$	54.1335	2.24198
$584$	31.0251	1.28383
$585$	−56.5177	−2.33672
$586$	13.5637	0.560312
$587$	−23.3416	−0.963412	−0.481706	−	0.876333i	$-0.659983\pi$
$587$	−23.3416	−0.963412	−0.481706	+	0.876333i	$0.659983\pi$
$588$	0.431971	0.0178142
$589$	−15.4206	−0.635396
$590$	5.81591	0.239437
$591$	−40.6240	−1.67105
$592$	16.0129	0.658125
$593$	9.55561	0.392402	0.196201	−	0.980564i	$-0.437140\pi$
$593$	9.55561	0.392402	0.196201	+	0.980564i	$0.437140\pi$
$594$	2.89147	0.118638
$595$	11.9930	0.491664
$596$	0.300035	0.0122899
$597$	−19.0531	−0.779790
$598$	−18.8756	−0.771879
$599$	−22.1207	−0.903827	−0.451914	−	0.892062i	$-0.649258\pi$
$599$	−22.1207	−0.903827	−0.451914	+	0.892062i	$0.649258\pi$
$600$	−64.9001	−2.64954
$601$	35.1223	1.43267	0.716335	−	0.697756i	$-0.245818\pi$
$601$	35.1223	1.43267	0.716335	+	0.697756i	$0.245818\pi$
$602$	47.4281	1.93302
$603$	2.83908	0.115616
$604$	0.570864	0.0232281
$605$	−13.8251	−0.562071
$606$	−2.30457	−0.0936168
$607$	−46.6072	−1.89173	−0.945865	−	0.324561i	$-0.894783\pi$
$607$	−46.6072	−1.89173	−0.945865	+	0.324561i	$0.894783\pi$
$608$	1.23349	0.0500245
$609$	−78.0934	−3.16450
$610$	65.4515	2.65006
$611$	4.68138	0.189389
$612$	−0.173505	−0.00701353
$613$	−5.18398	−0.209379	−0.104689	−	0.994505i	$-0.533385\pi$
$613$	−5.18398	−0.209379	−0.104689	+	0.994505i	$0.533385\pi$
$614$	14.4862	0.584616
$615$	−105.186	−4.24150
$616$	−35.0868	−1.41369
$617$	−24.7428	−0.996108	−0.498054	−	0.867146i	$-0.665952\pi$
$617$	−24.7428	−0.996108	−0.498054	+	0.867146i	$0.665952\pi$
$618$	−31.2591	−1.25742
$619$	7.40544	0.297650	0.148825	−	0.988864i	$-0.452451\pi$
$619$	7.40544	0.297650	0.148825	+	0.988864i	$0.452451\pi$
$620$	0.771844	0.0309980
$621$	−1.56339	−0.0627366
$622$	46.4741	1.86344
$623$	58.2373	2.33323
$624$	45.3968	1.81733
$625$	12.1032	0.484126
$626$	5.35291	0.213945
$627$	38.6383	1.54306
$628$	0.00672308	0.000268280 0
$629$	−4.11724	−0.164165
$630$	−53.8205	−2.14426
$631$	22.4997	0.895700	0.447850	−	0.894109i	$-0.352190\pi$
$631$	22.4997	0.895700	0.447850	+	0.894109i	$0.352190\pi$
$632$	24.9316	0.991724
$633$	−7.25105	−0.288203
$634$	−34.0426	−1.35200
$635$	−61.4476	−2.43847
$636$	1.89978	0.0753313
$637$	15.0373	0.595801
$638$	52.3921	2.07422
$639$	−8.90929	−0.352446
$640$	40.6612	1.60728
$641$	11.4113	0.450720	0.225360	−	0.974276i	$-0.427644\pi$
$641$	11.4113	0.450720	0.225360	+	0.974276i	$0.427644\pi$
$642$	11.9214	0.470498
$643$	22.8917	0.902762	0.451381	−	0.892331i	$-0.350932\pi$
$643$	22.8917	0.902762	0.451381	+	0.892331i	$0.350932\pi$
$644$	0.498167	0.0196305
$645$	99.5530	3.91990
$646$	5.64142	0.221959
$647$	0.990297	0.0389326	0.0194663	−	0.999811i	$-0.493803\pi$
$647$	0.990297	0.0389326	0.0194663	+	0.999811i	$0.493803\pi$
$648$	−23.7878	−0.934474
$649$	4.25688	0.167097
$650$	−59.3260	−2.32696
$651$	30.3836	1.19083
$652$	0.360206	0.0141067
$653$	−7.04823	−0.275819	−0.137909	−	0.990445i	$-0.544038\pi$
$653$	−7.04823	−0.275819	−0.137909	+	0.990445i	$0.544038\pi$
$654$	−19.0825	−0.746187
$655$	15.7789	0.616531
$656$	43.7184	1.70692
$657$	34.8329	1.35896
$658$	4.45797	0.173790
$659$	−16.6601	−0.648985	−0.324492	−	0.945888i	$-0.605193\pi$
$659$	−16.6601	−0.648985	−0.324492	+	0.945888i	$0.605193\pi$
$660$	−1.93395	−0.0752789
$661$	−29.6762	−1.15427	−0.577135	−	0.816649i	$-0.695829\pi$
$661$	−29.6762	−1.15427	−0.577135	+	0.816649i	$0.695829\pi$
$662$	−17.3213	−0.673212
$663$	−11.6725	−0.453321
$664$	−30.9506	−1.20112
$665$	−48.4994	−1.88073
$666$	18.4768	0.715963
$667$	−28.3279	−1.09686
$668$	0.363380	0.0140596
$669$	−22.1661	−0.856992
$670$	4.62042	0.178503
$671$	47.9064	1.84940
$672$	−2.43037	−0.0937535
$673$	−20.6252	−0.795043	−0.397522	−	0.917593i	$-0.630130\pi$
$673$	−20.6252	−0.795043	−0.397522	+	0.917593i	$0.630130\pi$
$674$	34.6765	1.33569
$675$	−4.91373	−0.189130
$676$	−0.480849	−0.0184942
$677$	9.35670	0.359607	0.179804	−	0.983703i	$-0.442454\pi$
$677$	9.35670	0.359607	0.179804	+	0.983703i	$0.442454\pi$
$678$	−40.2022	−1.54396
$679$	40.6670	1.56066
$680$	−10.7531	−0.412362
$681$	10.3994	0.398506
$682$	−20.3841	−0.780546
$683$	40.3273	1.54308	0.771541	−	0.636179i	$-0.219486\pi$
$683$	40.3273	1.54308	0.771541	+	0.636179i	$0.219486\pi$
$684$	0.701652	0.0268283
$685$	−35.4387	−1.35404
$686$	−16.8861	−0.644715
$687$	34.0328	1.29843
$688$	−41.3772	−1.57749
$689$	66.1334	2.51948
$690$	−37.7295	−1.43634
$691$	−46.7566	−1.77871	−0.889353	−	0.457221i	$-0.848845\pi$
$691$	−46.7566	−1.77871	−0.889353	+	0.457221i	$0.848845\pi$
$692$	0.466560	0.0177360
$693$	−39.3932	−1.49642
$694$	−25.2917	−0.960060
$695$	−37.8853	−1.43707
$696$	70.0198	2.65409
$697$	−11.2409	−0.425780
$698$	−6.77889	−0.256585
$699$	37.8757	1.43259
$700$	1.56574	0.0591795
$701$	7.91016	0.298763	0.149381	−	0.988780i	$-0.452272\pi$
$701$	7.91016	0.298763	0.149381	+	0.988780i	$0.452272\pi$
$702$	3.53242	0.133323
$703$	16.6501	0.627970
$704$	31.4371	1.18483
$705$	9.35742	0.352421
$706$	14.0936	0.530420
$707$	2.11730	0.0796292
$708$	0.149393	0.00561452
$709$	−19.0138	−0.714077	−0.357039	−	0.934090i	$-0.616214\pi$
$709$	−19.0138	−0.714077	−0.357039	+	0.934090i	$0.616214\pi$
$710$	−14.4993	−0.544149
$711$	27.9915	1.04976
$712$	−52.2165	−1.95690
$713$	11.0215	0.412757
$714$	−11.1154	−0.415984
$715$	−67.3228	−2.51773
$716$	0.170513	0.00637238
$717$	−2.59035	−0.0967382
$718$	2.99838	0.111899
$719$	12.4677	0.464965	0.232483	−	0.972601i	$-0.425315\pi$
$719$	12.4677	0.464965	0.232483	+	0.972601i	$0.425315\pi$
$720$	46.9540	1.74987
$721$	28.7189	1.06955
$722$	3.69144	0.137381
$723$	−15.9142	−0.591855
$724$	0.306427	0.0113883
$725$	−89.0347	−3.30667
$726$	12.8135	0.475554
$727$	9.32312	0.345775	0.172888	−	0.984942i	$-0.444690\pi$
$727$	9.32312	0.345775	0.172888	+	0.984942i	$0.444690\pi$
$728$	−42.8646	−1.58867
$729$	−30.7535	−1.13902
$730$	56.6884	2.09813
$731$	10.6389	0.393495
$732$	1.68125	0.0621406
$733$	22.9391	0.847276	0.423638	−	0.905832i	$-0.360753\pi$
$733$	22.9391	0.847276	0.423638	+	0.905832i	$0.360753\pi$
$734$	45.5797	1.68238
$735$	30.0575	1.10869
$736$	−0.881601	−0.0324962
$737$	3.38186	0.124572
$738$	50.4455	1.85693
$739$	10.1115	0.371956	0.185978	−	0.982554i	$-0.440455\pi$
$739$	10.1115	0.371956	0.185978	+	0.982554i	$0.440455\pi$
$740$	−0.833382	−0.0306357
$741$	47.2033	1.73406
$742$	62.9773	2.31197
$743$	2.31377	0.0848839	0.0424420	−	0.999099i	$-0.486486\pi$
$743$	2.31377	0.0848839	0.0424420	+	0.999099i	$0.486486\pi$
$744$	−27.2424	−0.998756
$745$	20.8771	0.764877
$746$	12.8100	0.469009
$747$	−34.7493	−1.27141
$748$	−0.206676	−0.00755681
$749$	−10.9526	−0.400199
$750$	−53.3155	−1.94681
$751$	−5.22473	−0.190653	−0.0953265	−	0.995446i	$-0.530390\pi$
$751$	−5.22473	−0.190653	−0.0953265	+	0.995446i	$0.530390\pi$
$752$	−3.88922	−0.141825
$753$	6.92345	0.252304
$754$	64.0060	2.33096
$755$	39.7219	1.44563
$756$	−0.0932284	−0.00339068
$757$	42.7740	1.55465	0.777323	−	0.629102i	$-0.216577\pi$
$757$	42.7740	1.55465	0.777323	+	0.629102i	$0.216577\pi$
$758$	−32.0227	−1.16312
$759$	−27.6156	−1.00238
$760$	43.4853	1.57738
$761$	−35.2599	−1.27817	−0.639085	−	0.769136i	$-0.720687\pi$
$761$	−35.2599	−1.27817	−0.639085	+	0.769136i	$0.720687\pi$
$762$	56.9513	2.06313
$763$	17.5319	0.634696
$764$	−0.748041	−0.0270632
$765$	−12.0729	−0.436495
$766$	−39.0561	−1.41115
$767$	5.20050	0.187779
$768$	3.22515	0.116378
$769$	−0.309969	−0.0111778	−0.00558888	−	0.999984i	$-0.501779\pi$
$769$	−0.309969	−0.0111778	−0.00558888	+	0.999984i	$0.501779\pi$
$770$	−64.1099	−2.31036
$771$	43.6750	1.57292
$772$	0.485146	0.0174608
$773$	−0.478689	−0.0172172	−0.00860862	−	0.999963i	$-0.502740\pi$
$773$	−0.478689	−0.0172172	−0.00860862	+	0.999963i	$0.502740\pi$
$774$	−47.7441	−1.71613
$775$	34.6405	1.24432
$776$	−36.4627	−1.30893
$777$	−32.8060	−1.17691
$778$	10.2254	0.366600
$779$	45.4581	1.62871
$780$	−2.36265	−0.0845966
$781$	−10.6126	−0.379748
$782$	−4.03205	−0.144186
$783$	5.30136	0.189455
$784$	−12.4928	−0.446171
$785$	0.467807	0.0166967
$786$	−14.6243	−0.521631
$787$	12.1621	0.433532	0.216766	−	0.976224i	$-0.430449\pi$
$787$	12.1621	0.433532	0.216766	+	0.976224i	$0.430449\pi$
$788$	−0.878748	−0.0313041
$789$	42.2883	1.50550
$790$	45.5544	1.62075
$791$	36.9353	1.31327
$792$	35.3206	1.25506
$793$	58.5259	2.07831
$794$	14.6032	0.518247
$795$	132.191	4.68834
$796$	−0.412141	−0.0146080
$797$	22.0657	0.781608	0.390804	−	0.920474i	$-0.372197\pi$
$797$	22.0657	0.781608	0.390804	+	0.920474i	$0.372197\pi$
$798$	44.9506	1.59123
$799$	1.00000	0.0353775
$800$	−2.77088	−0.0979653
$801$	−58.6253	−2.07142
$802$	48.0425	1.69644
$803$	41.4923	1.46423
$804$	0.118684	0.00418567
$805$	34.6636	1.22173
$806$	−24.9026	−0.877158
$807$	−64.7780	−2.28029
$808$	−1.89840	−0.0667856
$809$	−11.5553	−0.406263	−0.203132	−	0.979151i	$-0.565112\pi$
$809$	−11.5553	−0.406263	−0.203132	+	0.979151i	$0.565112\pi$
$810$	−43.4646	−1.52719
$811$	−2.64496	−0.0928772	−0.0464386	−	0.998921i	$-0.514787\pi$
$811$	−2.64496	−0.0928772	−0.0464386	+	0.998921i	$0.514787\pi$
$812$	−1.68926	−0.0592813
$813$	−8.70309	−0.305231
$814$	22.0092	0.771423
$815$	25.0639	0.877950
$816$	9.69730	0.339473
$817$	−43.0237	−1.50521
$818$	4.65296	0.162687
$819$	−48.1255	−1.68164
$820$	−2.27530	−0.0794570
$821$	20.5152	0.715985	0.357992	−	0.933724i	$-0.383461\pi$
$821$	20.5152	0.715985	0.357992	+	0.933724i	$0.383461\pi$
$822$	32.8455	1.14562
$823$	24.6019	0.857568	0.428784	−	0.903407i	$-0.358942\pi$
$823$	24.6019	0.857568	0.428784	+	0.903407i	$0.358942\pi$
$824$	−25.7498	−0.897038
$825$	−86.7961	−3.02185
$826$	4.95232	0.172313
$827$	−3.67085	−0.127648	−0.0638239	−	0.997961i	$-0.520330\pi$
$827$	−3.67085	−0.127648	−0.0638239	+	0.997961i	$0.520330\pi$
$828$	−0.501486	−0.0174278
$829$	−20.1127	−0.698542	−0.349271	−	0.937022i	$-0.613571\pi$
$829$	−20.1127	−0.698542	−0.349271	+	0.937022i	$0.613571\pi$
$830$	−56.5523	−1.96296
$831$	23.2153	0.805331
$832$	38.4058	1.33148
$833$	3.21215	0.111295
$834$	35.1132	1.21587
$835$	25.2848	0.875015
$836$	0.835794	0.0289065
$837$	−2.06258	−0.0712934
$838$	−35.1570	−1.21448
$839$	−41.5764	−1.43538	−0.717688	−	0.696364i	$-0.754800\pi$
$839$	−41.5764	−1.43538	−0.717688	+	0.696364i	$0.754800\pi$
$840$	−85.6801	−2.95624
$841$	67.0583	2.31236
$842$	−29.3718	−1.01222
$843$	24.9215	0.858342
$844$	−0.156849	−0.00539897
$845$	−33.4585	−1.15101
$846$	−4.48767	−0.154289
$847$	−11.7723	−0.404500
$848$	−54.9426	−1.88674
$849$	64.6336	2.21822
$850$	−12.6727	−0.434672
$851$	−11.9002	−0.407933
$852$	−0.372442	−0.0127597
$853$	−13.2865	−0.454922	−0.227461	−	0.973787i	$-0.573042\pi$
$853$	−13.2865	−0.454922	−0.227461	+	0.973787i	$0.573042\pi$
$854$	55.7328	1.90714
$855$	48.8225	1.66969
$856$	9.82028	0.335650
$857$	−0.592991	−0.0202562	−0.0101281	−	0.999949i	$-0.503224\pi$
$857$	−0.592991	−0.0202562	−0.0101281	+	0.999949i	$0.503224\pi$
$858$	62.3966	2.13019
$859$	−45.1884	−1.54181	−0.770904	−	0.636951i	$-0.780195\pi$
$859$	−45.1884	−1.54181	−0.770904	+	0.636951i	$0.780195\pi$
$860$	2.15346	0.0734322
$861$	−89.5671	−3.05244
$862$	−14.8832	−0.506922
$863$	−27.3346	−0.930481	−0.465241	−	0.885184i	$-0.654032\pi$
$863$	−27.3346	−0.930481	−0.465241	+	0.885184i	$0.654032\pi$
$864$	0.164985	0.00561291
$865$	32.4643	1.10382
$866$	−4.61693	−0.156890
$867$	−2.49338	−0.0846796
$868$	0.657235	0.0223080
$869$	33.3430	1.13108
$870$	127.939	4.33753
$871$	4.13152	0.139991
$872$	−15.7194	−0.532325
$873$	−40.9379	−1.38554
$874$	16.3055	0.551543
$875$	48.9830	1.65593
$876$	1.45615	0.0491987
$877$	25.4298	0.858704	0.429352	−	0.903137i	$-0.358742\pi$
$877$	25.4298	0.858704	0.429352	+	0.903137i	$0.358742\pi$
$878$	−7.94748	−0.268214
$879$	24.2431	0.817699
$880$	55.9307	1.88542
$881$	45.9036	1.54653	0.773266	−	0.634082i	$-0.218622\pi$
$881$	45.9036	1.54653	0.773266	+	0.634082i	$0.218622\pi$
$882$	−14.4151	−0.485381
$883$	19.3653	0.651693	0.325846	−	0.945423i	$-0.394351\pi$
$883$	19.3653	0.651693	0.325846	+	0.945423i	$0.394351\pi$
$884$	−0.252490	−0.00849215
$885$	10.3951	0.349426
$886$	−28.2904	−0.950435
$887$	−28.8806	−0.969715	−0.484857	−	0.874593i	$-0.661129\pi$
$887$	−28.8806	−0.969715	−0.484857	+	0.874593i	$0.661129\pi$
$888$	29.4144	0.987083
$889$	−52.3234	−1.75487
$890$	−95.4089	−3.19811
$891$	−31.8134	−1.06579
$892$	−0.479481	−0.0160542
$893$	−4.04399	−0.135327
$894$	−19.3495	−0.647143
$895$	11.8647	0.396593
$896$	34.6235	1.15669
$897$	−33.7372	−1.12645
$898$	49.7277	1.65944
$899$	−37.3731	−1.24646
$900$	−1.57617	−0.0525391
$901$	14.1269	0.470635
$902$	60.0897	2.00077
$903$	84.7706	2.82099
$904$	−33.1168	−1.10145
$905$	21.3219	0.708763
$906$	−36.8154	−1.22311
$907$	45.5286	1.51175	0.755875	−	0.654716i	$-0.227212\pi$
$907$	45.5286	1.51175	0.755875	+	0.654716i	$0.227212\pi$
$908$	0.224952	0.00746529
$909$	−2.13140	−0.0706942
$910$	−78.3212	−2.59632
$911$	−45.1521	−1.49596	−0.747978	−	0.663724i	$-0.768975\pi$
$911$	−45.1521	−1.49596	−0.747978	+	0.663724i	$0.768975\pi$
$912$	−39.2158	−1.29856
$913$	−41.3927	−1.36990
$914$	−29.6239	−0.979870
$915$	116.985	3.86740
$916$	0.736173	0.0243238
$917$	13.4359	0.443692
$918$	0.754568	0.0249045
$919$	−31.2323	−1.03026	−0.515130	−	0.857112i	$-0.672256\pi$
$919$	−31.2323	−1.03026	−0.515130	+	0.857112i	$0.672256\pi$
$920$	−31.0799	−1.02467
$921$	25.8919	0.853167
$922$	6.14401	0.202342
$923$	−12.9651	−0.426751
$924$	−1.64678	−0.0541752
$925$	−37.4023	−1.22978
$926$	−2.35261	−0.0773117
$927$	−28.9102	−0.949536
$928$	2.98946	0.0981338
$929$	−4.18902	−0.137437	−0.0687186	−	0.997636i	$-0.521891\pi$
$929$	−4.18902	−0.137437	−0.0687186	+	0.997636i	$0.521891\pi$
$930$	−49.7768	−1.63224
$931$	−12.9899	−0.425727
$932$	0.819297	0.0268370
$933$	83.0655	2.71944
$934$	23.7575	0.777368
$935$	−14.3810	−0.470307
$936$	43.1501	1.41041
$937$	−37.4138	−1.22225	−0.611127	−	0.791532i	$-0.709284\pi$
$937$	−37.4138	−1.22225	−0.611127	+	0.791532i	$0.709284\pi$
$938$	3.93435	0.128461
$939$	9.56751	0.312224
$940$	0.202413	0.00660197
$941$	−39.4110	−1.28476	−0.642382	−	0.766385i	$-0.722054\pi$
$941$	−39.4110	−1.28476	−0.642382	+	0.766385i	$0.722054\pi$
$942$	−0.433576	−0.0141267
$943$	−32.4899	−1.05802
$944$	−4.32050	−0.140620
$945$	−6.48703	−0.211023
$946$	−56.8718	−1.84906
$947$	−35.8864	−1.16615	−0.583075	−	0.812418i	$-0.698151\pi$
$947$	−35.8864	−1.16615	−0.583075	+	0.812418i	$0.698151\pi$
$948$	1.17015	0.0380048
$949$	50.6900	1.64547
$950$	51.2484	1.66272
$951$	−60.8460	−1.97307
$952$	−9.15638	−0.296760
$953$	2.46624	0.0798895	0.0399447	−	0.999202i	$-0.487282\pi$
$953$	2.46624	0.0798895	0.0399447	+	0.999202i	$0.487282\pi$
$954$	−63.3968	−2.05255
$955$	−52.0504	−1.68431
$956$	−0.0560324	−0.00181222
$957$	93.6431	3.02705
$958$	25.4250	0.821444
$959$	−30.1765	−0.974449
$960$	76.7678	2.47767
$961$	−16.4593	−0.530946
$962$	26.8881	0.866906
$963$	11.0256	0.355294
$964$	−0.344244	−0.0110873
$965$	33.7575	1.08669
$966$	−32.1272	−1.03367
$967$	−7.16053	−0.230267	−0.115133	−	0.993350i	$-0.536730\pi$
$967$	−7.16053	−0.230267	−0.115133	+	0.993350i	$0.536730\pi$
$968$	10.5552	0.339257
$969$	10.0832	0.323919
$970$	−66.6238	−2.13916
$971$	45.2298	1.45149	0.725747	−	0.687962i	$-0.241494\pi$
$971$	45.2298	1.45149	0.725747	+	0.687962i	$0.241494\pi$
$972$	−1.20399	−0.0386180
$973$	−32.2598	−1.03420
$974$	−35.5670	−1.13964
$975$	−106.036	−3.39588
$976$	−48.6224	−1.55636
$977$	−22.1494	−0.708623	−0.354311	−	0.935127i	$-0.615285\pi$
$977$	−22.1494	−0.708623	−0.354311	+	0.935127i	$0.615285\pi$
$978$	−23.2299	−0.742811
$979$	−69.8332	−2.23188
$980$	0.650180	0.0207692
$981$	−17.6487	−0.563478
$982$	30.7552	0.981439
$983$	−38.4925	−1.22772	−0.613860	−	0.789415i	$-0.710384\pi$
$983$	−38.4925	−1.22772	−0.613860	+	0.789415i	$0.710384\pi$
$984$	80.3073	2.56010
$985$	−61.1452	−1.94825
$986$	13.6724	0.435419
$987$	7.96795	0.253623
$988$	1.02107	0.0324844
$989$	30.7500	0.977793
$990$	64.5370	2.05112
$991$	−13.0508	−0.414572	−0.207286	−	0.978280i	$-0.566463\pi$
$991$	−13.0508	−0.414572	−0.207286	+	0.978280i	$0.566463\pi$
$992$	−1.16310	−0.0369285
$993$	−30.9592	−0.982462
$994$	−12.3463	−0.391602
$995$	−28.6777	−0.909144
$996$	−1.45265	−0.0460290
$997$	0.0150166	0.000475581 0	0.000237791	−	1.00000i	$-0.499924\pi$
$997$	0.0150166	0.000475581 0	0.000237791		1.00000i	$0.499924\pi$
$998$	6.91022	0.218739
$999$	2.22703	0.0704601

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	799.2.a.d.1.3	✓	8
3.2	odd	2		7191.2.a.u.1.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
799.2.a.d.1.3	✓	8	1.1	even	1	trivial
7191.2.a.u.1.6		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)

\(f(q)\)	\(=\)	\(q-1.39501 q^{2} -2.49338 q^{3} -0.0539349 q^{4} -3.75291 q^{5} +3.47830 q^{6} -3.19565 q^{7} +2.86527 q^{8} +3.21694 q^{9} +O(q^{10})\)	\(q-1.39501 q^{2} -2.49338 q^{3} -0.0539349 q^{4} -3.75291 q^{5} +3.47830 q^{6} -3.19565 q^{7} +2.86527 q^{8} +3.21694 q^{9} +5.23536 q^{10} +3.83195 q^{11} +0.134480 q^{12} +4.68138 q^{13} +4.45797 q^{14} +9.35742 q^{15} -3.88922 q^{16} +1.00000 q^{17} -4.48767 q^{18} -4.04399 q^{19} +0.202413 q^{20} +7.96795 q^{21} -5.34563 q^{22} +2.89033 q^{23} -7.14420 q^{24} +9.08431 q^{25} -6.53060 q^{26} -0.540903 q^{27} +0.172357 q^{28} -9.80094 q^{29} -13.0537 q^{30} +3.81322 q^{31} -0.305018 q^{32} -9.55450 q^{33} -1.39501 q^{34} +11.9930 q^{35} -0.173505 q^{36} -4.11724 q^{37} +5.64142 q^{38} -11.6725 q^{39} -10.7531 q^{40} -11.2409 q^{41} -11.1154 q^{42} +10.6389 q^{43} -0.206676 q^{44} -12.0729 q^{45} -4.03205 q^{46} +1.00000 q^{47} +9.69730 q^{48} +3.21215 q^{49} -12.6727 q^{50} -2.49338 q^{51} -0.252490 q^{52} +14.1269 q^{53} +0.754568 q^{54} -14.3810 q^{55} -9.15638 q^{56} +10.0832 q^{57} +13.6724 q^{58} +1.11089 q^{59} -0.504691 q^{60} +12.5018 q^{61} -5.31950 q^{62} -10.2802 q^{63} +8.20395 q^{64} -17.5688 q^{65} +13.3287 q^{66} +0.882542 q^{67} -0.0539349 q^{68} -7.20668 q^{69} -16.7304 q^{70} -2.76950 q^{71} +9.21739 q^{72} +10.8280 q^{73} +5.74361 q^{74} -22.6506 q^{75} +0.218112 q^{76} -12.2456 q^{77} +16.2833 q^{78} +8.70130 q^{79} +14.5959 q^{80} -8.30213 q^{81} +15.6812 q^{82} -10.8020 q^{83} -0.429751 q^{84} -3.75291 q^{85} -14.8415 q^{86} +24.4374 q^{87} +10.9796 q^{88} -18.2239 q^{89} +16.8418 q^{90} -14.9600 q^{91} -0.155889 q^{92} -9.50781 q^{93} -1.39501 q^{94} +15.1767 q^{95} +0.760525 q^{96} -12.7257 q^{97} -4.48100 q^{98} +12.3271 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} - 7 q^{3} + 7 q^{4} - 10 q^{5} + 2 q^{6} - 9 q^{7} - q^{9}+O(q^{10}) \) 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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