LMFDB - Embedded newform 799.2.a.c.1.1

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:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.61803$ 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)

$f(q)$	$=$	$q-2.61803 q^{2} +2.23607 q^{3} +4.85410 q^{4} -1.61803 q^{5} -5.85410 q^{6} -3.23607 q^{7} -7.47214 q^{8} +2.00000 q^{9} +O(q^{10})$	\(q-2.61803 q^{2} +2.23607 q^{3} +4.85410 q^{4} -1.61803 q^{5} -5.85410 q^{6} -3.23607 q^{7} -7.47214 q^{8} +2.00000 q^{9} +4.23607 q^{10} -3.00000 q^{11} +10.8541 q^{12} +6.23607 q^{13} +8.47214 q^{14} -3.61803 q^{15} +9.85410 q^{16} +1.00000 q^{17} -5.23607 q^{18} +1.14590 q^{19} -7.85410 q^{20} -7.23607 q^{21} +7.85410 q^{22} -1.38197 q^{23} -16.7082 q^{24} -2.38197 q^{25} -16.3262 q^{26} -2.23607 q^{27} -15.7082 q^{28} -2.76393 q^{29} +9.47214 q^{30} -2.85410 q^{31} -10.8541 q^{32} -6.70820 q^{33} -2.61803 q^{34} +5.23607 q^{35} +9.70820 q^{36} -4.38197 q^{37} -3.00000 q^{38} +13.9443 q^{39} +12.0902 q^{40} -9.23607 q^{41} +18.9443 q^{42} -5.00000 q^{43} -14.5623 q^{44} -3.23607 q^{45} +3.61803 q^{46} +1.00000 q^{47} +22.0344 q^{48} +3.47214 q^{49} +6.23607 q^{50} +2.23607 q^{51} +30.2705 q^{52} -10.0902 q^{53} +5.85410 q^{54} +4.85410 q^{55} +24.1803 q^{56} +2.56231 q^{57} +7.23607 q^{58} +0.763932 q^{59} -17.5623 q^{60} +2.47214 q^{61} +7.47214 q^{62} -6.47214 q^{63} +8.70820 q^{64} -10.0902 q^{65} +17.5623 q^{66} -7.14590 q^{67} +4.85410 q^{68} -3.09017 q^{69} -13.7082 q^{70} -9.76393 q^{71} -14.9443 q^{72} -7.00000 q^{73} +11.4721 q^{74} -5.32624 q^{75} +5.56231 q^{76} +9.70820 q^{77} -36.5066 q^{78} +15.8541 q^{79} -15.9443 q^{80} -11.0000 q^{81} +24.1803 q^{82} +13.4721 q^{83} -35.1246 q^{84} -1.61803 q^{85} +13.0902 q^{86} -6.18034 q^{87} +22.4164 q^{88} -10.4721 q^{89} +8.47214 q^{90} -20.1803 q^{91} -6.70820 q^{92} -6.38197 q^{93} -2.61803 q^{94} -1.85410 q^{95} -24.2705 q^{96} -5.32624 q^{97} -9.09017 q^{98} -6.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{2} + 3 q^{4} - q^{5} - 5 q^{6} - 2 q^{7} - 6 q^{8} + 4 q^{9}+O(q^{10}) $ 2 * q - 3 * q^2 + 3 * q^4 - q^5 - 5 * q^6 - 2 * q^7 - 6 * q^8 + 4 * q^9	\( 2 q - 3 q^{2} + 3 q^{4} - q^{5} - 5 q^{6} - 2 q^{7} - 6 q^{8} + 4 q^{9} + 4 q^{10} - 6 q^{11} + 15 q^{12} + 8 q^{13} + 8 q^{14} - 5 q^{15} + 13 q^{16} + 2 q^{17} - 6 q^{18} + 9 q^{19} - 9 q^{20} - 10 q^{21} + 9 q^{22} - 5 q^{23} - 20 q^{24} - 7 q^{25} - 17 q^{26} - 18 q^{28} - 10 q^{29} + 10 q^{30} + q^{31} - 15 q^{32} - 3 q^{34} + 6 q^{35} + 6 q^{36} - 11 q^{37} - 6 q^{38} + 10 q^{39} + 13 q^{40} - 14 q^{41} + 20 q^{42} - 10 q^{43} - 9 q^{44} - 2 q^{45} + 5 q^{46} + 2 q^{47} + 15 q^{48} - 2 q^{49} + 8 q^{50} + 27 q^{52} - 9 q^{53} + 5 q^{54} + 3 q^{55} + 26 q^{56} - 15 q^{57} + 10 q^{58} + 6 q^{59} - 15 q^{60} - 4 q^{61} + 6 q^{62} - 4 q^{63} + 4 q^{64} - 9 q^{65} + 15 q^{66} - 21 q^{67} + 3 q^{68} + 5 q^{69} - 14 q^{70} - 24 q^{71} - 12 q^{72} - 14 q^{73} + 14 q^{74} + 5 q^{75} - 9 q^{76} + 6 q^{77} - 35 q^{78} + 25 q^{79} - 14 q^{80} - 22 q^{81} + 26 q^{82} + 18 q^{83} - 30 q^{84} - q^{85} + 15 q^{86} + 10 q^{87} + 18 q^{88} - 12 q^{89} + 8 q^{90} - 18 q^{91} - 15 q^{93} - 3 q^{94} + 3 q^{95} - 15 q^{96} + 5 q^{97} - 7 q^{98} - 12 q^{99}+O(q^{100}) \) 2 * q - 3 * q^2 + 3 * q^4 - q^5 - 5 * q^6 - 2 * q^7 - 6 * q^8 + 4 * q^9 + 4 * q^10 - 6 * q^11 + 15 * q^12 + 8 * q^13 + 8 * q^14 - 5 * q^15 + 13 * q^16 + 2 * q^17 - 6 * q^18 + 9 * q^19 - 9 * q^20 - 10 * q^21 + 9 * q^22 - 5 * q^23 - 20 * q^24 - 7 * q^25 - 17 * q^26 - 18 * q^28 - 10 * q^29 + 10 * q^30 + q^31 - 15 * q^32 - 3 * q^34 + 6 * q^35 + 6 * q^36 - 11 * q^37 - 6 * q^38 + 10 * q^39 + 13 * q^40 - 14 * q^41 + 20 * q^42 - 10 * q^43 - 9 * q^44 - 2 * q^45 + 5 * q^46 + 2 * q^47 + 15 * q^48 - 2 * q^49 + 8 * q^50 + 27 * q^52 - 9 * q^53 + 5 * q^54 + 3 * q^55 + 26 * q^56 - 15 * q^57 + 10 * q^58 + 6 * q^59 - 15 * q^60 - 4 * q^61 + 6 * q^62 - 4 * q^63 + 4 * q^64 - 9 * q^65 + 15 * q^66 - 21 * q^67 + 3 * q^68 + 5 * q^69 - 14 * q^70 - 24 * q^71 - 12 * q^72 - 14 * q^73 + 14 * q^74 + 5 * q^75 - 9 * q^76 + 6 * q^77 - 35 * q^78 + 25 * q^79 - 14 * q^80 - 22 * q^81 + 26 * q^82 + 18 * q^83 - 30 * q^84 - q^85 + 15 * q^86 + 10 * q^87 + 18 * q^88 - 12 * q^89 + 8 * q^90 - 18 * q^91 - 15 * q^93 - 3 * q^94 + 3 * q^95 - 15 * q^96 + 5 * q^97 - 7 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.61803	−1.85123	−0.925615	−	0.378467i	$-0.876451\pi$
$2$	−2.61803	−1.85123	−0.925615	+	0.378467i	$0.876451\pi$
$3$	2.23607	1.29099	0.645497	−	0.763763i	$-0.276650\pi$
$3$	2.23607	1.29099	0.645497	+	0.763763i	$0.276650\pi$
$4$	4.85410	2.42705
$5$	−1.61803	−0.723607	−0.361803	−	0.932254i	$-0.617839\pi$
$5$	−1.61803	−0.723607	−0.361803	+	0.932254i	$0.617839\pi$
$6$	−5.85410	−2.38993
$7$	−3.23607	−1.22312	−0.611559	−	0.791199i	$-0.709457\pi$
$7$	−3.23607	−1.22312	−0.611559	+	0.791199i	$0.709457\pi$
$8$	−7.47214	−2.64180
$9$	2.00000	0.666667
$10$	4.23607	1.33956
$11$	−3.00000	−0.904534	−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−3.00000	−0.904534	−0.452267	+	0.891883i	$0.649385\pi$
$12$	10.8541	3.13331
$13$	6.23607	1.72957	0.864787	−	0.502139i	$-0.167453\pi$
$13$	6.23607	1.72957	0.864787	+	0.502139i	$0.167453\pi$
$14$	8.47214	2.26427
$15$	−3.61803	−0.934172
$16$	9.85410	2.46353
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−5.23607	−1.23415
$19$	1.14590	0.262887	0.131444	−	0.991324i	$-0.458039\pi$
$19$	1.14590	0.262887	0.131444	+	0.991324i	$0.458039\pi$
$20$	−7.85410	−1.75623
$21$	−7.23607	−1.57904
$22$	7.85410	1.67450
$23$	−1.38197	−0.288160	−0.144080	−	0.989566i	$-0.546022\pi$
$23$	−1.38197	−0.288160	−0.144080	+	0.989566i	$0.546022\pi$
$24$	−16.7082	−3.41055
$25$	−2.38197	−0.476393
$26$	−16.3262	−3.20184
$27$	−2.23607	−0.430331
$28$	−15.7082	−2.96857
$29$	−2.76393	−0.513249	−0.256625	−	0.966511i	$-0.582610\pi$
$29$	−2.76393	−0.513249	−0.256625	+	0.966511i	$0.582610\pi$
$30$	9.47214	1.72937
$31$	−2.85410	−0.512612	−0.256306	−	0.966596i	$-0.582505\pi$
$31$	−2.85410	−0.512612	−0.256306	+	0.966596i	$0.582505\pi$
$32$	−10.8541	−1.91875
$33$	−6.70820	−1.16775
$34$	−2.61803	−0.448989
$35$	5.23607	0.885057
$36$	9.70820	1.61803
$37$	−4.38197	−0.720391	−0.360195	−	0.932877i	$-0.617290\pi$
$37$	−4.38197	−0.720391	−0.360195	+	0.932877i	$0.617290\pi$
$38$	−3.00000	−0.486664
$39$	13.9443	2.23287
$40$	12.0902	1.91162
$41$	−9.23607	−1.44243	−0.721216	−	0.692711i	$-0.756416\pi$
$41$	−9.23607	−1.44243	−0.721216	+	0.692711i	$0.756416\pi$
$42$	18.9443	2.92316
$43$	−5.00000	−0.762493	−0.381246	−	0.924473i	$-0.624505\pi$
$43$	−5.00000	−0.762493	−0.381246	+	0.924473i	$0.624505\pi$
$44$	−14.5623	−2.19535
$45$	−3.23607	−0.482405
$46$	3.61803	0.533450
$47$	1.00000	0.145865
$47$	1.00000	0.145865
$48$	22.0344	3.18040
$49$	3.47214	0.496019
$50$	6.23607	0.881913
$51$	2.23607	0.313112
$52$	30.2705	4.19776
$53$	−10.0902	−1.38599	−0.692996	−	0.720942i	$-0.743710\pi$
$53$	−10.0902	−1.38599	−0.692996	+	0.720942i	$0.743710\pi$
$54$	5.85410	0.796642
$55$	4.85410	0.654527
$56$	24.1803	3.23123
$57$	2.56231	0.339386
$58$	7.23607	0.950142
$59$	0.763932	0.0994555	0.0497277	−	0.998763i	$-0.484165\pi$
$59$	0.763932	0.0994555	0.0497277	+	0.998763i	$0.484165\pi$
$60$	−17.5623	−2.26728
$61$	2.47214	0.316525	0.158262	−	0.987397i	$-0.449411\pi$
$61$	2.47214	0.316525	0.158262	+	0.987397i	$0.449411\pi$
$62$	7.47214	0.948962
$63$	−6.47214	−0.815412
$64$	8.70820	1.08853
$65$	−10.0902	−1.25153
$66$	17.5623	2.16177
$67$	−7.14590	−0.873010	−0.436505	−	0.899702i	$-0.643784\pi$
$67$	−7.14590	−0.873010	−0.436505	+	0.899702i	$0.643784\pi$
$68$	4.85410	0.588646
$69$	−3.09017	−0.372013
$70$	−13.7082	−1.63844
$71$	−9.76393	−1.15877	−0.579383	−	0.815056i	$-0.696706\pi$
$71$	−9.76393	−1.15877	−0.579383	+	0.815056i	$0.696706\pi$
$72$	−14.9443	−1.76120
$73$	−7.00000	−0.819288	−0.409644	−	0.912245i	$-0.634347\pi$
$73$	−7.00000	−0.819288	−0.409644	+	0.912245i	$0.634347\pi$
$74$	11.4721	1.33361
$75$	−5.32624	−0.615021
$76$	5.56231	0.638040
$77$	9.70820	1.10635
$78$	−36.5066	−4.13356
$79$	15.8541	1.78373	0.891863	−	0.452306i	$-0.149398\pi$
$79$	15.8541	1.78373	0.891863	+	0.452306i	$0.149398\pi$
$80$	−15.9443	−1.78262
$81$	−11.0000	−1.22222
$82$	24.1803	2.67027
$83$	13.4721	1.47876	0.739380	−	0.673289i	$-0.235119\pi$
$83$	13.4721	1.47876	0.739380	+	0.673289i	$0.235119\pi$
$84$	−35.1246	−3.83241
$85$	−1.61803	−0.175500
$86$	13.0902	1.41155
$87$	−6.18034	−0.662602
$88$	22.4164	2.38960
$89$	−10.4721	−1.11004	−0.555022	−	0.831836i	$-0.687290\pi$
$89$	−10.4721	−1.11004	−0.555022	+	0.831836i	$0.687290\pi$
$90$	8.47214	0.893042
$91$	−20.1803	−2.11547
$92$	−6.70820	−0.699379
$93$	−6.38197	−0.661779
$94$	−2.61803	−0.270030
$95$	−1.85410	−0.190227
$96$	−24.2705	−2.47710
$97$	−5.32624	−0.540798	−0.270399	−	0.962748i	$-0.587156\pi$
$97$	−5.32624	−0.540798	−0.270399	+	0.962748i	$0.587156\pi$
$98$	−9.09017	−0.918246
$99$	−6.00000	−0.603023
$100$	−11.5623	−1.15623
$101$	−14.3262	−1.42551	−0.712757	−	0.701411i	$-0.752554\pi$
$101$	−14.3262	−1.42551	−0.712757	+	0.701411i	$0.752554\pi$
$102$	−5.85410	−0.579642
$103$	12.6180	1.24329	0.621646	−	0.783298i	$-0.286464\pi$
$103$	12.6180	1.24329	0.621646	+	0.783298i	$0.286464\pi$
$104$	−46.5967	−4.56919
$105$	11.7082	1.14260
$106$	26.4164	2.56579
$107$	15.4721	1.49575	0.747874	−	0.663841i	$-0.231075\pi$
$107$	15.4721	1.49575	0.747874	+	0.663841i	$0.231075\pi$
$108$	−10.8541	−1.04444
$109$	−10.5623	−1.01169	−0.505843	−	0.862626i	$-0.668818\pi$
$109$	−10.5623	−1.01169	−0.505843	+	0.862626i	$0.668818\pi$
$110$	−12.7082	−1.21168
$111$	−9.79837	−0.930020
$112$	−31.8885	−3.01318
$113$	−2.05573	−0.193387	−0.0966933	−	0.995314i	$-0.530827\pi$
$113$	−2.05573	−0.193387	−0.0966933	+	0.995314i	$0.530827\pi$
$114$	−6.70820	−0.628281
$115$	2.23607	0.208514
$116$	−13.4164	−1.24568
$117$	12.4721	1.15305
$118$	−2.00000	−0.184115
$119$	−3.23607	−0.296650
$120$	27.0344	2.46790
$121$	−2.00000	−0.181818
$122$	−6.47214	−0.585960
$123$	−20.6525	−1.86217
$124$	−13.8541	−1.24414
$125$	11.9443	1.06833
$126$	16.9443	1.50952
$127$	18.4164	1.63419	0.817096	−	0.576502i	$-0.195583\pi$
$127$	18.4164	1.63419	0.817096	+	0.576502i	$0.195583\pi$
$128$	−1.09017	−0.0963583
$129$	−11.1803	−0.984374
$130$	26.4164	2.31687
$131$	11.6525	1.01808	0.509041	−	0.860742i	$-0.330000\pi$
$131$	11.6525	1.01808	0.509041	+	0.860742i	$0.330000\pi$
$132$	−32.5623	−2.83418
$133$	−3.70820	−0.321542
$134$	18.7082	1.61614
$135$	3.61803	0.311391
$136$	−7.47214	−0.640730
$137$	0.763932	0.0652671	0.0326336	−	0.999467i	$-0.489611\pi$
$137$	0.763932	0.0652671	0.0326336	+	0.999467i	$0.489611\pi$
$138$	8.09017	0.688681
$139$	−17.7984	−1.50964	−0.754819	−	0.655933i	$-0.772275\pi$
$139$	−17.7984	−1.50964	−0.754819	+	0.655933i	$0.772275\pi$
$140$	25.4164	2.14808
$141$	2.23607	0.188311
$142$	25.5623	2.14514
$143$	−18.7082	−1.56446
$144$	19.7082	1.64235
$145$	4.47214	0.371391
$146$	18.3262	1.51669
$147$	7.76393	0.640358
$148$	−21.2705	−1.74843
$149$	10.7984	0.884637	0.442319	−	0.896858i	$-0.354156\pi$
$149$	10.7984	0.884637	0.442319	+	0.896858i	$0.354156\pi$
$150$	13.9443	1.13855
$151$	2.43769	0.198377	0.0991884	−	0.995069i	$-0.468375\pi$
$151$	2.43769	0.198377	0.0991884	+	0.995069i	$0.468375\pi$
$152$	−8.56231	−0.694495
$153$	2.00000	0.161690
$154$	−25.4164	−2.04811
$155$	4.61803	0.370929
$156$	67.6869	5.41929
$157$	6.70820	0.535373	0.267686	−	0.963506i	$-0.413741\pi$
$157$	6.70820	0.535373	0.267686	+	0.963506i	$0.413741\pi$
$158$	−41.5066	−3.30209
$159$	−22.5623	−1.78931
$160$	17.5623	1.38842
$161$	4.47214	0.352454
$162$	28.7984	2.26261
$163$	−11.6525	−0.912692	−0.456346	−	0.889802i	$-0.650842\pi$
$163$	−11.6525	−0.912692	−0.456346	+	0.889802i	$0.650842\pi$
$164$	−44.8328	−3.50085
$165$	10.8541	0.844991
$166$	−35.2705	−2.73752
$167$	13.3262	1.03122	0.515608	−	0.856825i	$-0.327566\pi$
$167$	13.3262	1.03122	0.515608	+	0.856825i	$0.327566\pi$
$168$	54.0689	4.17150
$169$	25.8885	1.99143
$170$	4.23607	0.324892
$171$	2.29180	0.175258
$172$	−24.2705	−1.85061
$173$	18.7082	1.42236	0.711179	−	0.703011i	$-0.248161\pi$
$173$	18.7082	1.42236	0.711179	+	0.703011i	$0.248161\pi$
$174$	16.1803	1.22663
$175$	7.70820	0.582685
$176$	−29.5623	−2.22834
$177$	1.70820	0.128396
$178$	27.4164	2.05495
$179$	−21.1803	−1.58309	−0.791546	−	0.611109i	$-0.790724\pi$
$179$	−21.1803	−1.58309	−0.791546	+	0.611109i	$0.790724\pi$
$180$	−15.7082	−1.17082
$181$	7.18034	0.533710	0.266855	−	0.963737i	$-0.414015\pi$
$181$	7.18034	0.533710	0.266855	+	0.963737i	$0.414015\pi$
$182$	52.8328	3.91623
$183$	5.52786	0.408631
$184$	10.3262	0.761260
$185$	7.09017	0.521280
$186$	16.7082	1.22510
$187$	−3.00000	−0.219382
$188$	4.85410	0.354022
$189$	7.23607	0.526346
$190$	4.85410	0.352154
$191$	−0.819660	−0.0593085	−0.0296543	−	0.999560i	$-0.509441\pi$
$191$	−0.819660	−0.0593085	−0.0296543	+	0.999560i	$0.509441\pi$
$192$	19.4721	1.40528
$193$	15.2705	1.09920	0.549598	−	0.835429i	$-0.314781\pi$
$193$	15.2705	1.09920	0.549598	+	0.835429i	$0.314781\pi$
$194$	13.9443	1.00114
$195$	−22.5623	−1.61572
$196$	16.8541	1.20386
$197$	−16.0344	−1.14241	−0.571203	−	0.820809i	$-0.693523\pi$
$197$	−16.0344	−1.14241	−0.571203	+	0.820809i	$0.693523\pi$
$198$	15.7082	1.11633
$199$	−7.70820	−0.546420	−0.273210	−	0.961954i	$-0.588085\pi$
$199$	−7.70820	−0.546420	−0.273210	+	0.961954i	$0.588085\pi$
$200$	17.7984	1.25854
$201$	−15.9787	−1.12705
$202$	37.5066	2.63895
$203$	8.94427	0.627765
$204$	10.8541	0.759939
$205$	14.9443	1.04375
$206$	−33.0344	−2.30162
$207$	−2.76393	−0.192107
$208$	61.4508	4.26085
$209$	−3.43769	−0.237790
$210$	−30.6525	−2.11522
$211$	−25.8541	−1.77987	−0.889935	−	0.456088i	$-0.849250\pi$
$211$	−25.8541	−1.77987	−0.889935	+	0.456088i	$0.849250\pi$
$212$	−48.9787	−3.36387
$213$	−21.8328	−1.49596
$214$	−40.5066	−2.76897
$215$	8.09017	0.551745
$216$	16.7082	1.13685
$217$	9.23607	0.626985
$218$	27.6525	1.87286
$219$	−15.6525	−1.05770
$220$	23.5623	1.58857
$221$	6.23607	0.419483
$222$	25.6525	1.72168
$223$	14.0344	0.939816	0.469908	−	0.882715i	$-0.344287\pi$
$223$	14.0344	0.939816	0.469908	+	0.882715i	$0.344287\pi$
$224$	35.1246	2.34686
$225$	−4.76393	−0.317595
$226$	5.38197	0.358003
$227$	15.8885	1.05456	0.527280	−	0.849692i	$-0.323212\pi$
$227$	15.8885	1.05456	0.527280	+	0.849692i	$0.323212\pi$
$228$	12.4377	0.823706
$229$	22.1459	1.46344	0.731721	−	0.681604i	$-0.238717\pi$
$229$	22.1459	1.46344	0.731721	+	0.681604i	$0.238717\pi$
$230$	−5.85410	−0.386008
$231$	21.7082	1.42829
$232$	20.6525	1.35590
$233$	−17.8885	−1.17192	−0.585959	−	0.810341i	$-0.699282\pi$
$233$	−17.8885	−1.17192	−0.585959	+	0.810341i	$0.699282\pi$
$234$	−32.6525	−2.13456
$235$	−1.61803	−0.105549
$236$	3.70820	0.241384
$237$	35.4508	2.30278
$238$	8.47214	0.549167
$239$	−29.6180	−1.91583	−0.957916	−	0.287050i	$-0.907325\pi$
$239$	−29.6180	−1.91583	−0.957916	+	0.287050i	$0.907325\pi$
$240$	−35.6525	−2.30136
$241$	−8.14590	−0.524723	−0.262362	−	0.964970i	$-0.584501\pi$
$241$	−8.14590	−0.524723	−0.262362	+	0.964970i	$0.584501\pi$
$242$	5.23607	0.336587
$243$	−17.8885	−1.14755
$244$	12.0000	0.768221
$245$	−5.61803	−0.358923
$246$	54.0689	3.44731
$247$	7.14590	0.454683
$248$	21.3262	1.35422
$249$	30.1246	1.90907
$250$	−31.2705	−1.97772
$251$	17.5623	1.10852	0.554261	−	0.832343i	$-0.313001\pi$
$251$	17.5623	1.10852	0.554261	+	0.832343i	$0.313001\pi$
$252$	−31.4164	−1.97905
$253$	4.14590	0.260650
$254$	−48.2148	−3.02526
$255$	−3.61803	−0.226570
$256$	−14.5623	−0.910144
$257$	17.7984	1.11023	0.555116	−	0.831773i	$-0.312674\pi$
$257$	17.7984	1.11023	0.555116	+	0.831773i	$0.312674\pi$
$258$	29.2705	1.82230
$259$	14.1803	0.881123
$260$	−48.9787	−3.03753
$261$	−5.52786	−0.342166
$262$	−30.5066	−1.88470
$263$	7.47214	0.460752	0.230376	−	0.973102i	$-0.426004\pi$
$263$	7.47214	0.460752	0.230376	+	0.973102i	$0.426004\pi$
$264$	50.1246	3.08496
$265$	16.3262	1.00291
$266$	9.70820	0.595248
$267$	−23.4164	−1.43306
$268$	−34.6869	−2.11884
$269$	−30.1803	−1.84013	−0.920064	−	0.391768i	$-0.871863\pi$
$269$	−30.1803	−1.84013	−0.920064	+	0.391768i	$0.871863\pi$
$270$	−9.47214	−0.576456
$271$	8.41641	0.511260	0.255630	−	0.966775i	$-0.417717\pi$
$271$	8.41641	0.511260	0.255630	+	0.966775i	$0.417717\pi$
$272$	9.85410	0.597493
$273$	−45.1246	−2.73107
$274$	−2.00000	−0.120824
$275$	7.14590	0.430914
$276$	−15.0000	−0.902894
$277$	−14.1459	−0.849945	−0.424972	−	0.905206i	$-0.639716\pi$
$277$	−14.1459	−0.849945	−0.424972	+	0.905206i	$0.639716\pi$
$278$	46.5967	2.79469
$279$	−5.70820	−0.341741
$280$	−39.1246	−2.33814
$281$	−1.94427	−0.115986	−0.0579928	−	0.998317i	$-0.518470\pi$
$281$	−1.94427	−0.115986	−0.0579928	+	0.998317i	$0.518470\pi$
$282$	−5.85410	−0.348607
$283$	−32.8328	−1.95171	−0.975854	−	0.218423i	$-0.929909\pi$
$283$	−32.8328	−1.95171	−0.975854	+	0.218423i	$0.929909\pi$
$284$	−47.3951	−2.81238
$285$	−4.14590	−0.245582
$286$	48.9787	2.89617
$287$	29.8885	1.76426
$288$	−21.7082	−1.27917
$289$	1.00000	0.0588235
$290$	−11.7082	−0.687529
$291$	−11.9098	−0.698167
$292$	−33.9787	−1.98845
$293$	−0.708204	−0.0413737	−0.0206869	−	0.999786i	$-0.506585\pi$
$293$	−0.708204	−0.0413737	−0.0206869	+	0.999786i	$0.506585\pi$
$294$	−20.3262	−1.18545
$295$	−1.23607	−0.0719667
$296$	32.7426	1.90313
$297$	6.70820	0.389249
$298$	−28.2705	−1.63767
$299$	−8.61803	−0.498394
$300$	−25.8541	−1.49269
$301$	16.1803	0.932619
$302$	−6.38197	−0.367241
$303$	−32.0344	−1.84033
$304$	11.2918	0.647629
$305$	−4.00000	−0.229039
$306$	−5.23607	−0.299326
$307$	24.8541	1.41850	0.709249	−	0.704958i	$-0.249034\pi$
$307$	24.8541	1.41850	0.709249	+	0.704958i	$0.249034\pi$
$308$	47.1246	2.68517
$309$	28.2148	1.60508
$310$	−12.0902	−0.686676
$311$	24.5967	1.39475	0.697377	−	0.716705i	$-0.254350\pi$
$311$	24.5967	1.39475	0.697377	+	0.716705i	$0.254350\pi$
$312$	−104.193	−5.89880
$313$	−9.00000	−0.508710	−0.254355	−	0.967111i	$-0.581863\pi$
$313$	−9.00000	−0.508710	−0.254355	+	0.967111i	$0.581863\pi$
$314$	−17.5623	−0.991098
$315$	10.4721	0.590038
$316$	76.9574	4.32919
$317$	−1.76393	−0.0990723	−0.0495361	−	0.998772i	$-0.515774\pi$
$317$	−1.76393	−0.0990723	−0.0495361	+	0.998772i	$0.515774\pi$
$318$	59.0689	3.31242
$319$	8.29180	0.464251
$320$	−14.0902	−0.787664
$321$	34.5967	1.93100
$322$	−11.7082	−0.652473
$323$	1.14590	0.0637595
$324$	−53.3951	−2.96640
$325$	−14.8541	−0.823957
$326$	30.5066	1.68960
$327$	−23.6180	−1.30608
$328$	69.0132	3.81061
$329$	−3.23607	−0.178410
$330$	−28.4164	−1.56427
$331$	−7.32624	−0.402686	−0.201343	−	0.979521i	$-0.564531\pi$
$331$	−7.32624	−0.402686	−0.201343	+	0.979521i	$0.564531\pi$
$332$	65.3951	3.58902
$333$	−8.76393	−0.480261
$334$	−34.8885	−1.90902
$335$	11.5623	0.631716
$336$	−71.3050	−3.89000
$337$	−29.7426	−1.62019	−0.810093	−	0.586302i	$-0.800583\pi$
$337$	−29.7426	−1.62019	−0.810093	+	0.586302i	$0.800583\pi$
$338$	−67.7771	−3.68659
$339$	−4.59675	−0.249661
$340$	−7.85410	−0.425948
$341$	8.56231	0.463675
$342$	−6.00000	−0.324443
$343$	11.4164	0.616428
$344$	37.3607	2.01435
$345$	5.00000	0.269191
$346$	−48.9787	−2.63311
$347$	22.3262	1.19854	0.599268	−	0.800549i	$-0.295459\pi$
$347$	22.3262	1.19854	0.599268	+	0.800549i	$0.295459\pi$
$348$	−30.0000	−1.60817
$349$	1.14590	0.0613385	0.0306693	−	0.999530i	$-0.490236\pi$
$349$	1.14590	0.0613385	0.0306693	+	0.999530i	$0.490236\pi$
$350$	−20.1803	−1.07868
$351$	−13.9443	−0.744290
$352$	32.5623	1.73558
$353$	14.6738	0.781006	0.390503	−	0.920602i	$-0.372301\pi$
$353$	14.6738	0.781006	0.390503	+	0.920602i	$0.372301\pi$
$354$	−4.47214	−0.237691
$355$	15.7984	0.838491
$356$	−50.8328	−2.69413
$357$	−7.23607	−0.382973
$358$	55.4508	2.93067
$359$	−5.20163	−0.274531	−0.137266	−	0.990534i	$-0.543831\pi$
$359$	−5.20163	−0.274531	−0.137266	+	0.990534i	$0.543831\pi$
$360$	24.1803	1.27442
$361$	−17.6869	−0.930890
$362$	−18.7984	−0.988021
$363$	−4.47214	−0.234726
$364$	−97.9574	−5.13436
$365$	11.3262	0.592842
$366$	−14.4721	−0.756471
$367$	21.2705	1.11031	0.555156	−	0.831746i	$-0.312659\pi$
$367$	21.2705	1.11031	0.555156	+	0.831746i	$0.312659\pi$
$368$	−13.6180	−0.709889
$369$	−18.4721	−0.961621
$370$	−18.5623	−0.965008
$371$	32.6525	1.69523
$372$	−30.9787	−1.60617
$373$	−14.6525	−0.758676	−0.379338	−	0.925258i	$-0.623848\pi$
$373$	−14.6525	−0.758676	−0.379338	+	0.925258i	$0.623848\pi$
$374$	7.85410	0.406126
$375$	26.7082	1.37921
$376$	−7.47214	−0.385346
$377$	−17.2361	−0.887703
$378$	−18.9443	−0.974388
$379$	−5.74265	−0.294980	−0.147490	−	0.989064i	$-0.547119\pi$
$379$	−5.74265	−0.294980	−0.147490	+	0.989064i	$0.547119\pi$
$380$	−9.00000	−0.461690
$381$	41.1803	2.10973
$382$	2.14590	0.109794
$383$	4.67376	0.238818	0.119409	−	0.992845i	$-0.461900\pi$
$383$	4.67376	0.238818	0.119409	+	0.992845i	$0.461900\pi$
$384$	−2.43769	−0.124398
$385$	−15.7082	−0.800564
$386$	−39.9787	−2.03486
$387$	−10.0000	−0.508329
$388$	−25.8541	−1.31254
$389$	18.4721	0.936574	0.468287	−	0.883576i	$-0.344871\pi$
$389$	18.4721	0.936574	0.468287	+	0.883576i	$0.344871\pi$
$390$	59.0689	2.99107
$391$	−1.38197	−0.0698890
$392$	−25.9443	−1.31038
$393$	26.0557	1.31434
$394$	41.9787	2.11486
$395$	−25.6525	−1.29072
$396$	−29.1246	−1.46357
$397$	−14.7082	−0.738184	−0.369092	−	0.929393i	$-0.620331\pi$
$397$	−14.7082	−0.738184	−0.369092	+	0.929393i	$0.620331\pi$
$398$	20.1803	1.01155
$399$	−8.29180	−0.415109
$400$	−23.4721	−1.17361
$401$	23.1803	1.15757	0.578785	−	0.815480i	$-0.303527\pi$
$401$	23.1803	1.15757	0.578785	+	0.815480i	$0.303527\pi$
$402$	41.8328	2.08643
$403$	−17.7984	−0.886600
$404$	−69.5410	−3.45980
$405$	17.7984	0.884408
$406$	−23.4164	−1.16214
$407$	13.1459	0.651618
$408$	−16.7082	−0.827179
$409$	21.9787	1.08678	0.543389	−	0.839481i	$-0.317141\pi$
$409$	21.9787	1.08678	0.543389	+	0.839481i	$0.317141\pi$
$410$	−39.1246	−1.93223
$411$	1.70820	0.0842595
$412$	61.2492	3.01753
$413$	−2.47214	−0.121646
$414$	7.23607	0.355633
$415$	−21.7984	−1.07004
$416$	−67.6869	−3.31862
$417$	−39.7984	−1.94893
$418$	9.00000	0.440204
$419$	24.5967	1.20163	0.600815	−	0.799388i	$-0.294843\pi$
$419$	24.5967	1.20163	0.600815	+	0.799388i	$0.294843\pi$
$420$	56.8328	2.77316
$421$	−32.8541	−1.60121	−0.800605	−	0.599192i	$-0.795489\pi$
$421$	−32.8541	−1.60121	−0.800605	+	0.599192i	$0.795489\pi$
$422$	67.6869	3.29495
$423$	2.00000	0.0972433
$424$	75.3951	3.66151
$425$	−2.38197	−0.115542
$426$	57.1591	2.76937
$427$	−8.00000	−0.387147
$428$	75.1033	3.63026
$429$	−41.8328	−2.01971
$430$	−21.1803	−1.02141
$431$	20.0344	0.965025	0.482513	−	0.875889i	$-0.339724\pi$
$431$	20.0344	0.965025	0.482513	+	0.875889i	$0.339724\pi$
$432$	−22.0344	−1.06013
$433$	39.5623	1.90124	0.950622	−	0.310353i	$-0.100447\pi$
$433$	39.5623	1.90124	0.950622	+	0.310353i	$0.100447\pi$
$434$	−24.1803	−1.16069
$435$	10.0000	0.479463
$436$	−51.2705	−2.45541
$437$	−1.58359	−0.0757535
$438$	40.9787	1.95804
$439$	16.7082	0.797439	0.398720	−	0.917073i	$-0.369455\pi$
$439$	16.7082	0.797439	0.398720	+	0.917073i	$0.369455\pi$
$440$	−36.2705	−1.72913
$441$	6.94427	0.330680
$442$	−16.3262	−0.776560
$443$	12.9443	0.615001	0.307500	−	0.951548i	$-0.400507\pi$
$443$	12.9443	0.615001	0.307500	+	0.951548i	$0.400507\pi$
$444$	−47.5623	−2.25721
$445$	16.9443	0.803236
$446$	−36.7426	−1.73981
$447$	24.1459	1.14206
$448$	−28.1803	−1.33140
$449$	3.32624	0.156975	0.0784874	−	0.996915i	$-0.474991\pi$
$449$	3.32624	0.156975	0.0784874	+	0.996915i	$0.474991\pi$
$450$	12.4721	0.587942
$451$	27.7082	1.30473
$452$	−9.97871	−0.469359
$453$	5.45085	0.256103
$454$	−41.5967	−1.95223
$455$	32.6525	1.53077
$456$	−19.1459	−0.896589
$457$	−24.2361	−1.13372	−0.566858	−	0.823816i	$-0.691841\pi$
$457$	−24.2361	−1.13372	−0.566858	+	0.823816i	$0.691841\pi$
$458$	−57.9787	−2.70917
$459$	−2.23607	−0.104371
$460$	10.8541	0.506075
$461$	13.3820	0.623260	0.311630	−	0.950203i	$-0.399125\pi$
$461$	13.3820	0.623260	0.311630	+	0.950203i	$0.399125\pi$
$462$	−56.8328	−2.64410
$463$	−17.7426	−0.824571	−0.412285	−	0.911055i	$-0.635269\pi$
$463$	−17.7426	−0.824571	−0.412285	+	0.911055i	$0.635269\pi$
$464$	−27.2361	−1.26440
$465$	10.3262	0.478868
$466$	46.8328	2.16949
$467$	−38.3951	−1.77671	−0.888357	−	0.459153i	$-0.848153\pi$
$467$	−38.3951	−1.77671	−0.888357	+	0.459153i	$0.848153\pi$
$468$	60.5410	2.79851
$469$	23.1246	1.06780
$470$	4.23607	0.195395
$471$	15.0000	0.691164
$472$	−5.70820	−0.262741
$473$	15.0000	0.689701
$474$	−92.8115	−4.26297
$475$	−2.72949	−0.125238
$476$	−15.7082	−0.719984
$477$	−20.1803	−0.923994
$478$	77.5410	3.54664
$479$	−12.3820	−0.565746	−0.282873	−	0.959157i	$-0.591288\pi$
$479$	−12.3820	−0.565746	−0.282873	+	0.959157i	$0.591288\pi$
$480$	39.2705	1.79245
$481$	−27.3262	−1.24597
$482$	21.3262	0.971384
$483$	10.0000	0.455016
$484$	−9.70820	−0.441282
$485$	8.61803	0.391325
$486$	46.8328	2.12438
$487$	−11.2705	−0.510716	−0.255358	−	0.966847i	$-0.582193\pi$
$487$	−11.2705	−0.510716	−0.255358	+	0.966847i	$0.582193\pi$
$488$	−18.4721	−0.836194
$489$	−26.0557	−1.17828
$490$	14.7082	0.664449
$491$	−24.3262	−1.09783	−0.548914	−	0.835879i	$-0.684959\pi$
$491$	−24.3262	−1.09783	−0.548914	+	0.835879i	$0.684959\pi$
$492$	−100.249	−4.51958
$493$	−2.76393	−0.124481
$494$	−18.7082	−0.841722
$495$	9.70820	0.436351
$496$	−28.1246	−1.26283
$497$	31.5967	1.41731
$498$	−78.8673	−3.53413
$499$	6.70820	0.300300	0.150150	−	0.988663i	$-0.452024\pi$
$499$	6.70820	0.300300	0.150150	+	0.988663i	$0.452024\pi$
$500$	57.9787	2.59289
$501$	29.7984	1.33129
$502$	−45.9787	−2.05213
$503$	5.65248	0.252031	0.126016	−	0.992028i	$-0.459781\pi$
$503$	5.65248	0.252031	0.126016	+	0.992028i	$0.459781\pi$
$504$	48.3607	2.15416
$505$	23.1803	1.03151
$506$	−10.8541	−0.482524
$507$	57.8885	2.57092
$508$	89.3951	3.96627
$509$	38.5967	1.71077	0.855385	−	0.517992i	$-0.173320\pi$
$509$	38.5967	1.71077	0.855385	+	0.517992i	$0.173320\pi$
$510$	9.47214	0.419433
$511$	22.6525	1.00209
$512$	40.3050	1.78124
$513$	−2.56231	−0.113129
$514$	−46.5967	−2.05529
$515$	−20.4164	−0.899654
$516$	−54.2705	−2.38913
$517$	−3.00000	−0.131940
$518$	−37.1246	−1.63116
$519$	41.8328	1.83626
$520$	75.3951	3.30629
$521$	−35.6180	−1.56045	−0.780227	−	0.625496i	$-0.784897\pi$
$521$	−35.6180	−1.56045	−0.780227	+	0.625496i	$0.784897\pi$
$522$	14.4721	0.633428
$523$	1.58359	0.0692456	0.0346228	−	0.999400i	$-0.488977\pi$
$523$	1.58359	0.0692456	0.0346228	+	0.999400i	$0.488977\pi$
$524$	56.5623	2.47094
$525$	17.2361	0.752244
$526$	−19.5623	−0.852957
$527$	−2.85410	−0.124327
$528$	−66.1033	−2.87678
$529$	−21.0902	−0.916964
$530$	−42.7426	−1.85662
$531$	1.52786	0.0663037
$532$	−18.0000	−0.780399
$533$	−57.5967	−2.49479
$534$	61.3050	2.65292
$535$	−25.0344	−1.08233
$536$	53.3951	2.30632
$537$	−47.3607	−2.04376
$538$	79.0132	3.40650
$539$	−10.4164	−0.448666
$540$	17.5623	0.755761
$541$	−20.6869	−0.889400	−0.444700	−	0.895680i	$-0.646690\pi$
$541$	−20.6869	−0.889400	−0.444700	+	0.895680i	$0.646690\pi$
$542$	−22.0344	−0.946460
$543$	16.0557	0.689017
$544$	−10.8541	−0.465366
$545$	17.0902	0.732062
$546$	118.138	5.05583
$547$	−15.2361	−0.651447	−0.325724	−	0.945465i	$-0.605608\pi$
$547$	−15.2361	−0.651447	−0.325724	+	0.945465i	$0.605608\pi$
$548$	3.70820	0.158407
$549$	4.94427	0.211016
$550$	−18.7082	−0.797720
$551$	−3.16718	−0.134927
$552$	23.0902	0.982783
$553$	−51.3050	−2.18171
$554$	37.0344	1.57344
$555$	15.8541	0.672969
$556$	−86.3951	−3.66397
$557$	6.27051	0.265690	0.132845	−	0.991137i	$-0.457589\pi$
$557$	6.27051	0.265690	0.132845	+	0.991137i	$0.457589\pi$
$558$	14.9443	0.632641
$559$	−31.1803	−1.31879
$560$	51.5967	2.18036
$561$	−6.70820	−0.283221
$562$	5.09017	0.214716
$563$	27.6738	1.16631	0.583155	−	0.812361i	$-0.301818\pi$
$563$	27.6738	1.16631	0.583155	+	0.812361i	$0.301818\pi$
$564$	10.8541	0.457040
$565$	3.32624	0.139936
$566$	85.9574	3.61306
$567$	35.5967	1.49492
$568$	72.9574	3.06123
$569$	−35.5967	−1.49229	−0.746147	−	0.665782i	$-0.768098\pi$
$569$	−35.5967	−1.49229	−0.746147	+	0.665782i	$0.768098\pi$
$570$	10.8541	0.454628
$571$	16.8885	0.706764	0.353382	−	0.935479i	$-0.385032\pi$
$571$	16.8885	0.706764	0.353382	+	0.935479i	$0.385032\pi$
$572$	−90.8115	−3.79702
$573$	−1.83282	−0.0765670
$574$	−78.2492	−3.26606
$575$	3.29180	0.137277
$576$	17.4164	0.725684
$577$	−13.1803	−0.548705	−0.274352	−	0.961629i	$-0.588463\pi$
$577$	−13.1803	−0.548705	−0.274352	+	0.961629i	$0.588463\pi$
$578$	−2.61803	−0.108896
$579$	34.1459	1.41906
$580$	21.7082	0.901384
$581$	−43.5967	−1.80870
$582$	31.1803	1.29247
$583$	30.2705	1.25368
$584$	52.3050	2.16439
$585$	−20.1803	−0.834354
$586$	1.85410	0.0765922
$587$	−24.5410	−1.01292	−0.506458	−	0.862265i	$-0.669046\pi$
$587$	−24.5410	−1.01292	−0.506458	+	0.862265i	$0.669046\pi$
$588$	37.6869	1.55418
$589$	−3.27051	−0.134759
$590$	3.23607	0.133227
$591$	−35.8541	−1.47484
$592$	−43.1803	−1.77470
$593$	−12.7082	−0.521863	−0.260932	−	0.965357i	$-0.584030\pi$
$593$	−12.7082	−0.521863	−0.260932	+	0.965357i	$0.584030\pi$
$594$	−17.5623	−0.720590
$595$	5.23607	0.214658
$596$	52.4164	2.14706
$597$	−17.2361	−0.705425
$598$	22.5623	0.922641
$599$	26.7639	1.09354	0.546772	−	0.837281i	$-0.315856\pi$
$599$	26.7639	1.09354	0.546772	+	0.837281i	$0.315856\pi$
$600$	39.7984	1.62476
$601$	26.5967	1.08490	0.542452	−	0.840087i	$-0.317496\pi$
$601$	26.5967	1.08490	0.542452	+	0.840087i	$0.317496\pi$
$602$	−42.3607	−1.72649
$603$	−14.2918	−0.582007
$604$	11.8328	0.481470
$605$	3.23607	0.131565
$606$	83.8673	3.40687
$607$	−9.88854	−0.401364	−0.200682	−	0.979656i	$-0.564316\pi$
$607$	−9.88854	−0.401364	−0.200682	+	0.979656i	$0.564316\pi$
$608$	−12.4377	−0.504415
$609$	20.0000	0.810441
$610$	10.4721	0.424004
$611$	6.23607	0.252284
$612$	9.70820	0.392431
$613$	−39.8328	−1.60883	−0.804416	−	0.594066i	$-0.797522\pi$
$613$	−39.8328	−1.60883	−0.804416	+	0.594066i	$0.797522\pi$
$614$	−65.0689	−2.62597
$615$	33.4164	1.34748
$616$	−72.5410	−2.92276
$617$	26.4508	1.06487	0.532436	−	0.846471i	$-0.321277\pi$
$617$	26.4508	1.06487	0.532436	+	0.846471i	$0.321277\pi$
$618$	−73.8673	−2.97138
$619$	5.72949	0.230288	0.115144	−	0.993349i	$-0.463267\pi$
$619$	5.72949	0.230288	0.115144	+	0.993349i	$0.463267\pi$
$620$	22.4164	0.900265
$621$	3.09017	0.124004
$622$	−64.3951	−2.58201
$623$	33.8885	1.35772
$624$	137.408	5.50073
$625$	−7.41641	−0.296656
$626$	23.5623	0.941739
$627$	−7.68692	−0.306986
$628$	32.5623	1.29938
$629$	−4.38197	−0.174720
$630$	−27.4164	−1.09230
$631$	−39.1803	−1.55974	−0.779872	−	0.625939i	$-0.784716\pi$
$631$	−39.1803	−1.55974	−0.779872	+	0.625939i	$0.784716\pi$
$632$	−118.464	−4.71225
$633$	−57.8115	−2.29780
$634$	4.61803	0.183406
$635$	−29.7984	−1.18251
$636$	−109.520	−4.34274
$637$	21.6525	0.857902
$638$	−21.7082	−0.859436
$639$	−19.5279	−0.772510
$640$	1.76393	0.0697255
$641$	−28.5279	−1.12678	−0.563391	−	0.826190i	$-0.690504\pi$
$641$	−28.5279	−1.12678	−0.563391	+	0.826190i	$0.690504\pi$
$642$	−90.5755	−3.57473
$643$	4.81966	0.190069	0.0950344	−	0.995474i	$-0.469704\pi$
$643$	4.81966	0.190069	0.0950344	+	0.995474i	$0.469704\pi$
$644$	21.7082	0.855423
$645$	18.0902	0.712300
$646$	−3.00000	−0.118033
$647$	−29.4508	−1.15783	−0.578916	−	0.815387i	$-0.696524\pi$
$647$	−29.4508	−1.15783	−0.578916	+	0.815387i	$0.696524\pi$
$648$	82.1935	3.22887
$649$	−2.29180	−0.0899609
$650$	38.8885	1.52533
$651$	20.6525	0.809434
$652$	−56.5623	−2.21515
$653$	−12.4721	−0.488072	−0.244036	−	0.969766i	$-0.578472\pi$
$653$	−12.4721	−0.488072	−0.244036	+	0.969766i	$0.578472\pi$
$654$	61.8328	2.41785
$655$	−18.8541	−0.736691
$656$	−91.0132	−3.55347
$657$	−14.0000	−0.546192
$658$	8.47214	0.330278
$659$	10.6869	0.416303	0.208152	−	0.978097i	$-0.433255\pi$
$659$	10.6869	0.416303	0.208152	+	0.978097i	$0.433255\pi$
$660$	52.6869	2.05084
$661$	1.14590	0.0445703	0.0222851	−	0.999752i	$-0.492906\pi$
$661$	1.14590	0.0445703	0.0222851	+	0.999752i	$0.492906\pi$
$662$	19.1803	0.745465
$663$	13.9443	0.541551
$664$	−100.666	−3.90658
$665$	6.00000	0.232670
$666$	22.9443	0.889072
$667$	3.81966	0.147898
$668$	64.6869	2.50281
$669$	31.3820	1.21330
$670$	−30.2705	−1.16945
$671$	−7.41641	−0.286307
$672$	78.5410	3.02979
$673$	−19.0000	−0.732396	−0.366198	−	0.930537i	$-0.619341\pi$
$673$	−19.0000	−0.732396	−0.366198	+	0.930537i	$0.619341\pi$
$674$	77.8673	2.99933
$675$	5.32624	0.205007
$676$	125.666	4.83329
$677$	46.5967	1.79086	0.895429	−	0.445204i	$-0.146869\pi$
$677$	46.5967	1.79086	0.895429	+	0.445204i	$0.146869\pi$
$678$	12.0344	0.462180
$679$	17.2361	0.661460
$680$	12.0902	0.463637
$681$	35.5279	1.36143
$682$	−22.4164	−0.858369
$683$	−8.65248	−0.331078	−0.165539	−	0.986203i	$-0.552936\pi$
$683$	−8.65248	−0.331078	−0.165539	+	0.986203i	$0.552936\pi$
$684$	11.1246	0.425360
$685$	−1.23607	−0.0472277
$686$	−29.8885	−1.14115
$687$	49.5197	1.88930
$688$	−49.2705	−1.87842
$689$	−62.9230	−2.39717
$690$	−13.0902	−0.498334
$691$	15.4164	0.586468	0.293234	−	0.956041i	$-0.405269\pi$
$691$	15.4164	0.586468	0.293234	+	0.956041i	$0.405269\pi$
$692$	90.8115	3.45214
$693$	19.4164	0.737568
$694$	−58.4508	−2.21876
$695$	28.7984	1.09238
$696$	46.1803	1.75046
$697$	−9.23607	−0.349841
$698$	−3.00000	−0.113552
$699$	−40.0000	−1.51294
$700$	37.4164	1.41421
$701$	−45.2705	−1.70984	−0.854922	−	0.518757i	$-0.826395\pi$
$701$	−45.2705	−1.70984	−0.854922	+	0.518757i	$0.826395\pi$
$702$	36.5066	1.37785
$703$	−5.02129	−0.189381
$704$	−26.1246	−0.984608
$705$	−3.61803	−0.136263
$706$	−38.4164	−1.44582
$707$	46.3607	1.74357
$708$	8.29180	0.311625
$709$	−0.854102	−0.0320765	−0.0160382	−	0.999871i	$-0.505105\pi$
$709$	−0.854102	−0.0320765	−0.0160382	+	0.999871i	$0.505105\pi$
$710$	−41.3607	−1.55224
$711$	31.7082	1.18915
$712$	78.2492	2.93251
$713$	3.94427	0.147714
$714$	18.9443	0.708972
$715$	30.2705	1.13205
$716$	−102.812	−3.84225
$717$	−66.2279	−2.47333
$718$	13.6180	0.508221
$719$	30.0000	1.11881	0.559406	−	0.828894i	$-0.311029\pi$
$719$	30.0000	1.11881	0.559406	+	0.828894i	$0.311029\pi$
$720$	−31.8885	−1.18842
$721$	−40.8328	−1.52069
$722$	46.3050	1.72329
$723$	−18.2148	−0.677415
$724$	34.8541	1.29534
$725$	6.58359	0.244508
$726$	11.7082	0.434532
$727$	−37.2492	−1.38150	−0.690749	−	0.723095i	$-0.742719\pi$
$727$	−37.2492	−1.38150	−0.690749	+	0.723095i	$0.742719\pi$
$728$	150.790	5.58866
$729$	−7.00000	−0.259259
$730$	−29.6525	−1.09749
$731$	−5.00000	−0.184932
$732$	26.8328	0.991769
$733$	9.12461	0.337025	0.168513	−	0.985699i	$-0.446104\pi$
$733$	9.12461	0.337025	0.168513	+	0.985699i	$0.446104\pi$
$734$	−55.6869	−2.05544
$735$	−12.5623	−0.463368
$736$	15.0000	0.552907
$737$	21.4377	0.789668
$738$	48.3607	1.78018
$739$	−20.6869	−0.760981	−0.380490	−	0.924785i	$-0.624245\pi$
$739$	−20.6869	−0.760981	−0.380490	+	0.924785i	$0.624245\pi$
$740$	34.4164	1.26517
$741$	15.9787	0.586993
$742$	−85.4853	−3.13826
$743$	26.8885	0.986445	0.493223	−	0.869903i	$-0.335819\pi$
$743$	26.8885	0.986445	0.493223	+	0.869903i	$0.335819\pi$
$744$	47.6869	1.74829
$745$	−17.4721	−0.640130
$746$	38.3607	1.40448
$747$	26.9443	0.985839
$748$	−14.5623	−0.532451
$749$	−50.0689	−1.82948
$750$	−69.9230	−2.55323
$751$	5.70820	0.208295	0.104148	−	0.994562i	$-0.466789\pi$
$751$	5.70820	0.208295	0.104148	+	0.994562i	$0.466789\pi$
$752$	9.85410	0.359342
$753$	39.2705	1.43110
$754$	45.1246	1.64334
$755$	−3.94427	−0.143547
$756$	35.1246	1.27747
$757$	20.0902	0.730190	0.365095	−	0.930970i	$-0.381037\pi$
$757$	20.0902	0.730190	0.365095	+	0.930970i	$0.381037\pi$
$758$	15.0344	0.546076
$759$	9.27051	0.336498
$760$	13.8541	0.502541
$761$	−17.3607	−0.629324	−0.314662	−	0.949204i	$-0.601891\pi$
$761$	−17.3607	−0.629324	−0.314662	+	0.949204i	$0.601891\pi$
$762$	−107.812	−3.90560
$763$	34.1803	1.23741
$764$	−3.97871	−0.143945
$765$	−3.23607	−0.117000
$766$	−12.2361	−0.442107
$767$	4.76393	0.172016
$768$	−32.5623	−1.17499
$769$	15.6180	0.563201	0.281600	−	0.959532i	$-0.409135\pi$
$769$	15.6180	0.563201	0.281600	+	0.959532i	$0.409135\pi$
$770$	41.1246	1.48203
$771$	39.7984	1.43330
$772$	74.1246	2.66780
$773$	−39.3050	−1.41370	−0.706850	−	0.707363i	$-0.749885\pi$
$773$	−39.3050	−1.41370	−0.706850	+	0.707363i	$0.749885\pi$
$774$	26.1803	0.941033
$775$	6.79837	0.244205
$776$	39.7984	1.42868
$777$	31.7082	1.13753
$778$	−48.3607	−1.73381
$779$	−10.5836	−0.379197
$780$	−109.520	−3.92144
$781$	29.2918	1.04814
$782$	3.61803	0.129381
$783$	6.18034	0.220867
$784$	34.2148	1.22196
$785$	−10.8541	−0.387400
$786$	−68.2148	−2.43314
$787$	−24.6180	−0.877538	−0.438769	−	0.898600i	$-0.644585\pi$
$787$	−24.6180	−0.877538	−0.438769	+	0.898600i	$0.644585\pi$
$788$	−77.8328	−2.77268
$789$	16.7082	0.594828
$790$	67.1591	2.38941
$791$	6.65248	0.236535
$792$	44.8328	1.59306
$793$	15.4164	0.547453
$794$	38.5066	1.36655
$795$	36.5066	1.29475
$796$	−37.4164	−1.32619
$797$	38.1803	1.35242	0.676209	−	0.736710i	$-0.263622\pi$
$797$	38.1803	1.35242	0.676209	+	0.736710i	$0.263622\pi$
$798$	21.7082	0.768462
$799$	1.00000	0.0353775
$800$	25.8541	0.914081
$801$	−20.9443	−0.740029
$802$	−60.6869	−2.14293
$803$	21.0000	0.741074
$804$	−77.5623	−2.73541
$805$	−7.23607	−0.255038
$806$	46.5967	1.64130
$807$	−67.4853	−2.37559
$808$	107.048	3.76592
$809$	21.2705	0.747831	0.373916	−	0.927463i	$-0.378015\pi$
$809$	21.2705	0.747831	0.373916	+	0.927463i	$0.378015\pi$
$810$	−46.5967	−1.63724
$811$	9.47214	0.332612	0.166306	−	0.986074i	$-0.446816\pi$
$811$	9.47214	0.332612	0.166306	+	0.986074i	$0.446816\pi$
$812$	43.4164	1.52362
$813$	18.8197	0.660034
$814$	−34.4164	−1.20629
$815$	18.8541	0.660430
$816$	22.0344	0.771360
$817$	−5.72949	−0.200449
$818$	−57.5410	−2.01187
$819$	−40.3607	−1.41032
$820$	72.5410	2.53324
$821$	−9.92299	−0.346315	−0.173157	−	0.984894i	$-0.555397\pi$
$821$	−9.92299	−0.346315	−0.173157	+	0.984894i	$0.555397\pi$
$822$	−4.47214	−0.155984
$823$	1.12461	0.0392015	0.0196008	−	0.999808i	$-0.493760\pi$
$823$	1.12461	0.0392015	0.0196008	+	0.999808i	$0.493760\pi$
$824$	−94.2837	−3.28453
$825$	15.9787	0.556307
$826$	6.47214	0.225194
$827$	10.9656	0.381310	0.190655	−	0.981657i	$-0.438939\pi$
$827$	10.9656	0.381310	0.190655	+	0.981657i	$0.438939\pi$
$828$	−13.4164	−0.466252
$829$	−2.43769	−0.0846646	−0.0423323	−	0.999104i	$-0.513479\pi$
$829$	−2.43769	−0.0846646	−0.0423323	+	0.999104i	$0.513479\pi$
$830$	57.0689	1.98089
$831$	−31.6312	−1.09727
$832$	54.3050	1.88269
$833$	3.47214	0.120302
$834$	104.193	3.60793
$835$	−21.5623	−0.746194
$836$	−16.6869	−0.577129
$837$	6.38197	0.220593
$838$	−64.3951	−2.22449
$839$	−40.3050	−1.39148	−0.695741	−	0.718293i	$-0.744924\pi$
$839$	−40.3050	−1.39148	−0.695741	+	0.718293i	$0.744924\pi$
$840$	−87.4853	−3.01853
$841$	−21.3607	−0.736575
$842$	86.0132	2.96421
$843$	−4.34752	−0.149737
$844$	−125.498	−4.31983
$845$	−41.8885	−1.44101
$846$	−5.23607	−0.180020
$847$	6.47214	0.222385
$848$	−99.4296	−3.41443
$849$	−73.4164	−2.51964
$850$	6.23607	0.213895
$851$	6.05573	0.207588
$852$	−105.979	−3.63077
$853$	9.14590	0.313150	0.156575	−	0.987666i	$-0.449955\pi$
$853$	9.14590	0.313150	0.156575	+	0.987666i	$0.449955\pi$
$854$	20.9443	0.716698
$855$	−3.70820	−0.126818
$856$	−115.610	−3.95147
$857$	−15.7639	−0.538486	−0.269243	−	0.963072i	$-0.586773\pi$
$857$	−15.7639	−0.538486	−0.269243	+	0.963072i	$0.586773\pi$
$858$	109.520	3.73894
$859$	−7.18034	−0.244990	−0.122495	−	0.992469i	$-0.539090\pi$
$859$	−7.18034	−0.244990	−0.122495	+	0.992469i	$0.539090\pi$
$860$	39.2705	1.33911
$861$	66.8328	2.27766
$862$	−52.4508	−1.78648
$863$	55.7214	1.89678	0.948389	−	0.317111i	$-0.102713\pi$
$863$	55.7214	1.89678	0.948389	+	0.317111i	$0.102713\pi$
$864$	24.2705	0.825700
$865$	−30.2705	−1.02923
$866$	−103.575	−3.51964
$867$	2.23607	0.0759408
$868$	44.8328	1.52172
$869$	−47.5623	−1.61344
$870$	−26.1803	−0.887597
$871$	−44.5623	−1.50994
$872$	78.9230	2.67267
$873$	−10.6525	−0.360532
$874$	4.14590	0.140237
$875$	−38.6525	−1.30669
$876$	−75.9787	−2.56708
$877$	20.5623	0.694340	0.347170	−	0.937802i	$-0.387143\pi$
$877$	20.5623	0.694340	0.347170	+	0.937802i	$0.387143\pi$
$878$	−43.7426	−1.47624
$879$	−1.58359	−0.0534132
$880$	47.8328	1.61244
$881$	−33.0132	−1.11224	−0.556121	−	0.831102i	$-0.687711\pi$
$881$	−33.0132	−1.11224	−0.556121	+	0.831102i	$0.687711\pi$
$882$	−18.1803	−0.612164
$883$	−42.7426	−1.43840	−0.719202	−	0.694801i	$-0.755493\pi$
$883$	−42.7426	−1.43840	−0.719202	+	0.694801i	$0.755493\pi$
$884$	30.2705	1.01811
$885$	−2.76393	−0.0929086
$886$	−33.8885	−1.13851
$887$	−24.0000	−0.805841	−0.402921	−	0.915235i	$-0.632005\pi$
$887$	−24.0000	−0.805841	−0.402921	+	0.915235i	$0.632005\pi$
$888$	73.2148	2.45693
$889$	−59.5967	−1.99881
$890$	−44.3607	−1.48697
$891$	33.0000	1.10554
$892$	68.1246	2.28098
$893$	1.14590	0.0383460
$894$	−63.2148	−2.11422
$895$	34.2705	1.14554
$896$	3.52786	0.117858
$897$	−19.2705	−0.643424
$898$	−8.70820	−0.290597
$899$	7.88854	0.263098
$900$	−23.1246	−0.770820
$901$	−10.0902	−0.336152
$902$	−72.5410	−2.41535
$903$	36.1803	1.20401
$904$	15.3607	0.510889
$905$	−11.6180	−0.386197
$906$	−14.2705	−0.474106
$907$	−56.4164	−1.87328	−0.936638	−	0.350299i	$-0.886080\pi$
$907$	−56.4164	−1.87328	−0.936638	+	0.350299i	$0.886080\pi$
$908$	77.1246	2.55947
$909$	−28.6525	−0.950343
$910$	−85.4853	−2.83381
$911$	−37.3607	−1.23781	−0.618907	−	0.785464i	$-0.712424\pi$
$911$	−37.3607	−1.23781	−0.618907	+	0.785464i	$0.712424\pi$
$912$	25.2492	0.836085
$913$	−40.4164	−1.33759
$914$	63.4508	2.09877
$915$	−8.94427	−0.295689
$916$	107.498	3.55185
$917$	−37.7082	−1.24523
$918$	5.85410	0.193214
$919$	5.27051	0.173858	0.0869290	−	0.996215i	$-0.472295\pi$
$919$	5.27051	0.173858	0.0869290	+	0.996215i	$0.472295\pi$
$920$	−16.7082	−0.550853
$921$	55.5755	1.83127
$922$	−35.0344	−1.15380
$923$	−60.8885	−2.00417
$924$	105.374	3.46654
$925$	10.4377	0.343189
$926$	46.4508	1.52647
$927$	25.2361	0.828861
$928$	30.0000	0.984798
$929$	−35.3607	−1.16015	−0.580073	−	0.814564i	$-0.696976\pi$
$929$	−35.3607	−1.16015	−0.580073	+	0.814564i	$0.696976\pi$
$930$	−27.0344	−0.886494
$931$	3.97871	0.130397
$932$	−86.8328	−2.84430
$933$	55.0000	1.80062
$934$	100.520	3.28911
$935$	4.85410	0.158746
$936$	−93.1935	−3.04612
$937$	60.7771	1.98550	0.992750	−	0.120194i	$-0.0383516\pi$
$937$	60.7771	1.98550	0.992750	+	0.120194i	$0.0383516\pi$
$938$	−60.5410	−1.97673
$939$	−20.1246	−0.656742
$940$	−7.85410	−0.256173
$941$	11.0344	0.359713	0.179856	−	0.983693i	$-0.442437\pi$
$941$	11.0344	0.359713	0.179856	+	0.983693i	$0.442437\pi$
$942$	−39.2705	−1.27950
$943$	12.7639	0.415651
$944$	7.52786	0.245011
$945$	−11.7082	−0.380868
$946$	−39.2705	−1.27679
$947$	−36.9443	−1.20053	−0.600264	−	0.799802i	$-0.704938\pi$
$947$	−36.9443	−1.20053	−0.600264	+	0.799802i	$0.704938\pi$
$948$	172.082	5.58896
$949$	−43.6525	−1.41702
$950$	7.14590	0.231844
$951$	−3.94427	−0.127902
$952$	24.1803	0.783689
$953$	1.36068	0.0440767	0.0220384	−	0.999757i	$-0.492984\pi$
$953$	1.36068	0.0440767	0.0220384	+	0.999757i	$0.492984\pi$
$954$	52.8328	1.71053
$955$	1.32624	0.0429161
$956$	−143.769	−4.64982
$957$	18.5410	0.599346
$958$	32.4164	1.04733
$959$	−2.47214	−0.0798294
$960$	−31.5066	−1.01687
$961$	−22.8541	−0.737229
$962$	71.5410	2.30658
$963$	30.9443	0.997165
$964$	−39.5410	−1.27353
$965$	−24.7082	−0.795385
$966$	−26.1803	−0.842339
$967$	−26.1246	−0.840111	−0.420055	−	0.907498i	$-0.637989\pi$
$967$	−26.1246	−0.840111	−0.420055	+	0.907498i	$0.637989\pi$
$968$	14.9443	0.480327
$969$	2.56231	0.0823131
$970$	−22.5623	−0.724432
$971$	33.5967	1.07817	0.539085	−	0.842251i	$-0.318770\pi$
$971$	33.5967	1.07817	0.539085	+	0.842251i	$0.318770\pi$
$972$	−86.8328	−2.78516
$973$	57.5967	1.84647
$974$	29.5066	0.945452
$975$	−33.2148	−1.06372
$976$	24.3607	0.779766
$977$	6.97871	0.223269	0.111634	−	0.993749i	$-0.464391\pi$
$977$	6.97871	0.223269	0.111634	+	0.993749i	$0.464391\pi$
$978$	68.2148	2.18127
$979$	31.4164	1.00407
$980$	−27.2705	−0.871124
$981$	−21.1246	−0.674457
$982$	63.6869	2.03233
$983$	26.5279	0.846107	0.423054	−	0.906105i	$-0.360958\pi$
$983$	26.5279	0.846107	0.423054	+	0.906105i	$0.360958\pi$
$984$	154.318	4.91948
$985$	25.9443	0.826653
$986$	7.23607	0.230443
$987$	−7.23607	−0.230327
$988$	34.6869	1.10354
$989$	6.90983	0.219720
$990$	−25.4164	−0.807786
$991$	12.4721	0.396190	0.198095	−	0.980183i	$-0.436524\pi$
$991$	12.4721	0.396190	0.198095	+	0.980183i	$0.436524\pi$
$992$	30.9787	0.983575
$993$	−16.3820	−0.519866
$994$	−82.7214	−2.62376
$995$	12.4721	0.395393
$996$	146.228	4.63341
$997$	28.7082	0.909198	0.454599	−	0.890696i	$-0.349783\pi$
$997$	28.7082	0.909198	0.454599	+	0.890696i	$0.349783\pi$
$998$	−17.5623	−0.555925
$999$	9.79837	0.310007

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	799.2.a.c.1.1	✓	2
3.2	odd	2		7191.2.a.o.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
799.2.a.c.1.1	✓	2	1.1	even	1	trivial
7191.2.a.o.1.2		2	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)

\(f(q)\)	\(=\)	\(q-2.61803 q^{2} +2.23607 q^{3} +4.85410 q^{4} -1.61803 q^{5} -5.85410 q^{6} -3.23607 q^{7} -7.47214 q^{8} +2.00000 q^{9} +O(q^{10})\)	\(q-2.61803 q^{2} +2.23607 q^{3} +4.85410 q^{4} -1.61803 q^{5} -5.85410 q^{6} -3.23607 q^{7} -7.47214 q^{8} +2.00000 q^{9} +4.23607 q^{10} -3.00000 q^{11} +10.8541 q^{12} +6.23607 q^{13} +8.47214 q^{14} -3.61803 q^{15} +9.85410 q^{16} +1.00000 q^{17} -5.23607 q^{18} +1.14590 q^{19} -7.85410 q^{20} -7.23607 q^{21} +7.85410 q^{22} -1.38197 q^{23} -16.7082 q^{24} -2.38197 q^{25} -16.3262 q^{26} -2.23607 q^{27} -15.7082 q^{28} -2.76393 q^{29} +9.47214 q^{30} -2.85410 q^{31} -10.8541 q^{32} -6.70820 q^{33} -2.61803 q^{34} +5.23607 q^{35} +9.70820 q^{36} -4.38197 q^{37} -3.00000 q^{38} +13.9443 q^{39} +12.0902 q^{40} -9.23607 q^{41} +18.9443 q^{42} -5.00000 q^{43} -14.5623 q^{44} -3.23607 q^{45} +3.61803 q^{46} +1.00000 q^{47} +22.0344 q^{48} +3.47214 q^{49} +6.23607 q^{50} +2.23607 q^{51} +30.2705 q^{52} -10.0902 q^{53} +5.85410 q^{54} +4.85410 q^{55} +24.1803 q^{56} +2.56231 q^{57} +7.23607 q^{58} +0.763932 q^{59} -17.5623 q^{60} +2.47214 q^{61} +7.47214 q^{62} -6.47214 q^{63} +8.70820 q^{64} -10.0902 q^{65} +17.5623 q^{66} -7.14590 q^{67} +4.85410 q^{68} -3.09017 q^{69} -13.7082 q^{70} -9.76393 q^{71} -14.9443 q^{72} -7.00000 q^{73} +11.4721 q^{74} -5.32624 q^{75} +5.56231 q^{76} +9.70820 q^{77} -36.5066 q^{78} +15.8541 q^{79} -15.9443 q^{80} -11.0000 q^{81} +24.1803 q^{82} +13.4721 q^{83} -35.1246 q^{84} -1.61803 q^{85} +13.0902 q^{86} -6.18034 q^{87} +22.4164 q^{88} -10.4721 q^{89} +8.47214 q^{90} -20.1803 q^{91} -6.70820 q^{92} -6.38197 q^{93} -2.61803 q^{94} -1.85410 q^{95} -24.2705 q^{96} -5.32624 q^{97} -9.09017 q^{98} -6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{2} + 3 q^{4} - q^{5} - 5 q^{6} - 2 q^{7} - 6 q^{8} + 4 q^{9}+O(q^{10}) \) 2 * q - 3 * q^2 + 3 * q^4 - q^5 - 5 * q^6 - 2 * q^7 - 6 * q^8 + 4 * q^9	\( 2 q - 3 q^{2} + 3 q^{4} - q^{5} - 5 q^{6} - 2 q^{7} - 6 q^{8} + 4 q^{9} + 4 q^{10} - 6 q^{11} + 15 q^{12} + 8 q^{13} + 8 q^{14} - 5 q^{15} + 13 q^{16} + 2 q^{17} - 6 q^{18} + 9 q^{19} - 9 q^{20} - 10 q^{21} + 9 q^{22} - 5 q^{23} - 20 q^{24} - 7 q^{25} - 17 q^{26} - 18 q^{28} - 10 q^{29} + 10 q^{30} + q^{31} - 15 q^{32} - 3 q^{34} + 6 q^{35} + 6 q^{36} - 11 q^{37} - 6 q^{38} + 10 q^{39} + 13 q^{40} - 14 q^{41} + 20 q^{42} - 10 q^{43} - 9 q^{44} - 2 q^{45} + 5 q^{46} + 2 q^{47} + 15 q^{48} - 2 q^{49} + 8 q^{50} + 27 q^{52} - 9 q^{53} + 5 q^{54} + 3 q^{55} + 26 q^{56} - 15 q^{57} + 10 q^{58} + 6 q^{59} - 15 q^{60} - 4 q^{61} + 6 q^{62} - 4 q^{63} + 4 q^{64} - 9 q^{65} + 15 q^{66} - 21 q^{67} + 3 q^{68} + 5 q^{69} - 14 q^{70} - 24 q^{71} - 12 q^{72} - 14 q^{73} + 14 q^{74} + 5 q^{75} - 9 q^{76} + 6 q^{77} - 35 q^{78} + 25 q^{79} - 14 q^{80} - 22 q^{81} + 26 q^{82} + 18 q^{83} - 30 q^{84} - q^{85} + 15 q^{86} + 10 q^{87} + 18 q^{88} - 12 q^{89} + 8 q^{90} - 18 q^{91} - 15 q^{93} - 3 q^{94} + 3 q^{95} - 15 q^{96} + 5 q^{97} - 7 q^{98} - 12 q^{99}+O(q^{100}) \) 2 * q - 3 * q^2 + 3 * q^4 - q^5 - 5 * q^6 - 2 * q^7 - 6 * q^8 + 4 * q^9 + 4 * q^10 - 6 * q^11 + 15 * q^12 + 8 * q^13 + 8 * q^14 - 5 * q^15 + 13 * q^16 + 2 * q^17 - 6 * q^18 + 9 * q^19 - 9 * q^20 - 10 * q^21 + 9 * q^22 - 5 * q^23 - 20 * q^24 - 7 * q^25 - 17 * q^26 - 18 * q^28 - 10 * q^29 + 10 * q^30 + q^31 - 15 * q^32 - 3 * q^34 + 6 * q^35 + 6 * q^36 - 11 * q^37 - 6 * q^38 + 10 * q^39 + 13 * q^40 - 14 * q^41 + 20 * q^42 - 10 * q^43 - 9 * q^44 - 2 * q^45 + 5 * q^46 + 2 * q^47 + 15 * q^48 - 2 * q^49 + 8 * q^50 + 27 * q^52 - 9 * q^53 + 5 * q^54 + 3 * q^55 + 26 * q^56 - 15 * q^57 + 10 * q^58 + 6 * q^59 - 15 * q^60 - 4 * q^61 + 6 * q^62 - 4 * q^63 + 4 * q^64 - 9 * q^65 + 15 * q^66 - 21 * q^67 + 3 * q^68 + 5 * q^69 - 14 * q^70 - 24 * q^71 - 12 * q^72 - 14 * q^73 + 14 * q^74 + 5 * q^75 - 9 * q^76 + 6 * q^77 - 35 * q^78 + 25 * q^79 - 14 * q^80 - 22 * q^81 + 26 * q^82 + 18 * q^83 - 30 * q^84 - q^85 + 15 * q^86 + 10 * q^87 + 18 * q^88 - 12 * q^89 + 8 * q^90 - 18 * q^91 - 15 * q^93 - 3 * q^94 + 3 * q^95 - 15 * q^96 + 5 * q^97 - 7 * q^98 - 12 * q^99

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