LMFDB - Embedded newform 799.2.a.g.1.14

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:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} - 24 x^{18} + 108 x^{17} + 221 x^{16} - 1200 x^{15} - 931 x^{14} + 7128 x^{13} + \cdots + 63 $ x^20 - 4x^19 - 24x^18 + 108x^17 + 221x^16 - 1200x^15 - 931x^14 + 7128x^13 + 1280x^12 - 24559x^11 + 3411x^10 + 49829x^9 - 15132x^8 - 58070x^7 + 20659x^6 + 36738x^5 - 11129x^4 - 11299x^3 + 1589x^2 + 1289*x + 63
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Root			$1.22248$ 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)

$f(q)$	$=$	$q+1.22248 q^{2} +1.90981 q^{3} -0.505532 q^{4} +1.00510 q^{5} +2.33471 q^{6} +1.73367 q^{7} -3.06297 q^{8} +0.647363 q^{9} +O(q^{10})$	\(q+1.22248 q^{2} +1.90981 q^{3} -0.505532 q^{4} +1.00510 q^{5} +2.33471 q^{6} +1.73367 q^{7} -3.06297 q^{8} +0.647363 q^{9} +1.22872 q^{10} +3.84830 q^{11} -0.965468 q^{12} +6.27896 q^{13} +2.11939 q^{14} +1.91954 q^{15} -2.73337 q^{16} -1.00000 q^{17} +0.791391 q^{18} -4.53158 q^{19} -0.508109 q^{20} +3.31098 q^{21} +4.70449 q^{22} -6.54056 q^{23} -5.84969 q^{24} -3.98978 q^{25} +7.67593 q^{26} -4.49308 q^{27} -0.876427 q^{28} +8.30336 q^{29} +2.34661 q^{30} +7.38823 q^{31} +2.78444 q^{32} +7.34951 q^{33} -1.22248 q^{34} +1.74251 q^{35} -0.327263 q^{36} +6.01049 q^{37} -5.53979 q^{38} +11.9916 q^{39} -3.07859 q^{40} +5.13833 q^{41} +4.04763 q^{42} -8.84264 q^{43} -1.94544 q^{44} +0.650664 q^{45} -7.99573 q^{46} +1.00000 q^{47} -5.22022 q^{48} -3.99437 q^{49} -4.87744 q^{50} -1.90981 q^{51} -3.17421 q^{52} -7.48214 q^{53} -5.49272 q^{54} +3.86792 q^{55} -5.31020 q^{56} -8.65445 q^{57} +10.1507 q^{58} -1.25271 q^{59} -0.970390 q^{60} -4.60400 q^{61} +9.03200 q^{62} +1.12232 q^{63} +8.87068 q^{64} +6.31097 q^{65} +8.98466 q^{66} -6.91456 q^{67} +0.505532 q^{68} -12.4912 q^{69} +2.13019 q^{70} -0.406485 q^{71} -1.98286 q^{72} -13.6037 q^{73} +7.34773 q^{74} -7.61971 q^{75} +2.29086 q^{76} +6.67170 q^{77} +14.6595 q^{78} +4.25780 q^{79} -2.74731 q^{80} -10.5230 q^{81} +6.28153 q^{82} -11.3054 q^{83} -1.67381 q^{84} -1.00510 q^{85} -10.8100 q^{86} +15.8578 q^{87} -11.7872 q^{88} -1.69968 q^{89} +0.795426 q^{90} +10.8857 q^{91} +3.30646 q^{92} +14.1101 q^{93} +1.22248 q^{94} -4.55469 q^{95} +5.31774 q^{96} +4.78101 q^{97} -4.88306 q^{98} +2.49125 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{2} + 3 q^{3} + 24 q^{4} + 13 q^{5} + 11 q^{6} - 3 q^{7} + 12 q^{8} + 37 q^{9}+O(q^{10}) $ 20 * q + 4 * q^2 + 3 * q^3 + 24 * q^4 + 13 * q^5 + 11 * q^6 - 3 * q^7 + 12 * q^8 + 37 * q^9	\( 20 q + 4 q^{2} + 3 q^{3} + 24 q^{4} + 13 q^{5} + 11 q^{6} - 3 q^{7} + 12 q^{8} + 37 q^{9} - 2 q^{10} + 10 q^{11} + 8 q^{12} + q^{13} + 13 q^{14} + q^{15} + 28 q^{16} - 20 q^{17} + 15 q^{18} + 5 q^{19} + 37 q^{20} + 6 q^{21} - 19 q^{22} + 4 q^{23} + 30 q^{24} + 41 q^{25} - 9 q^{26} + 6 q^{27} - 25 q^{28} + 26 q^{29} - 25 q^{30} + 6 q^{31} + 28 q^{32} + 29 q^{33} - 4 q^{34} + 21 q^{35} - 5 q^{36} - 8 q^{37} - 21 q^{38} - 19 q^{39} - 25 q^{40} + 69 q^{41} + 3 q^{42} - 7 q^{43} + 16 q^{44} + 39 q^{45} - 24 q^{46} + 20 q^{47} + 26 q^{48} + 53 q^{49} + 16 q^{50} - 3 q^{51} + 18 q^{52} + 29 q^{53} + 23 q^{54} + 5 q^{55} - 22 q^{56} - 36 q^{57} - q^{58} + 55 q^{59} - 103 q^{60} - 17 q^{61} - 7 q^{62} - 9 q^{63} + 58 q^{64} + 40 q^{65} + 50 q^{66} - 6 q^{67} - 24 q^{68} + 17 q^{69} - 15 q^{70} + 47 q^{71} + 7 q^{72} - 32 q^{73} - 67 q^{74} - 22 q^{75} - 5 q^{76} + 4 q^{77} - 60 q^{78} - 26 q^{79} + 108 q^{80} + 68 q^{81} + 25 q^{82} + 3 q^{83} + 24 q^{84} - 13 q^{85} + 8 q^{86} - 41 q^{87} - 47 q^{88} + 119 q^{89} - 54 q^{90} - 35 q^{91} - 15 q^{93} + 4 q^{94} - 48 q^{95} - 84 q^{96} - 13 q^{97} + q^{98} - 5 q^{99}+O(q^{100}) \) 20 * q + 4 * q^2 + 3 * q^3 + 24 * q^4 + 13 * q^5 + 11 * q^6 - 3 * q^7 + 12 * q^8 + 37 * q^9 - 2 * q^10 + 10 * q^11 + 8 * q^12 + q^13 + 13 * q^14 + q^15 + 28 * q^16 - 20 * q^17 + 15 * q^18 + 5 * q^19 + 37 * q^20 + 6 * q^21 - 19 * q^22 + 4 * q^23 + 30 * q^24 + 41 * q^25 - 9 * q^26 + 6 * q^27 - 25 * q^28 + 26 * q^29 - 25 * q^30 + 6 * q^31 + 28 * q^32 + 29 * q^33 - 4 * q^34 + 21 * q^35 - 5 * q^36 - 8 * q^37 - 21 * q^38 - 19 * q^39 - 25 * q^40 + 69 * q^41 + 3 * q^42 - 7 * q^43 + 16 * q^44 + 39 * q^45 - 24 * q^46 + 20 * q^47 + 26 * q^48 + 53 * q^49 + 16 * q^50 - 3 * q^51 + 18 * q^52 + 29 * q^53 + 23 * q^54 + 5 * q^55 - 22 * q^56 - 36 * q^57 - q^58 + 55 * q^59 - 103 * q^60 - 17 * q^61 - 7 * q^62 - 9 * q^63 + 58 * q^64 + 40 * q^65 + 50 * q^66 - 6 * q^67 - 24 * q^68 + 17 * q^69 - 15 * q^70 + 47 * q^71 + 7 * q^72 - 32 * q^73 - 67 * q^74 - 22 * q^75 - 5 * q^76 + 4 * q^77 - 60 * q^78 - 26 * q^79 + 108 * q^80 + 68 * q^81 + 25 * q^82 + 3 * q^83 + 24 * q^84 - 13 * q^85 + 8 * q^86 - 41 * q^87 - 47 * q^88 + 119 * q^89 - 54 * q^90 - 35 * q^91 - 15 * q^93 + 4 * q^94 - 48 * q^95 - 84 * q^96 - 13 * q^97 + q^98 - 5 * 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 $

$2$	1.22248	0.864427	0.432214	−	0.901771i	$-0.357733\pi$
$2$	1.22248	0.864427	0.432214	+	0.901771i	$0.357733\pi$
$3$	1.90981	1.10263	0.551314	−	0.834298i	$-0.314127\pi$
$3$	1.90981	1.10263	0.551314	+	0.834298i	$0.314127\pi$
$4$	−0.505532	−0.252766
$5$	1.00510	0.449494	0.224747	−	0.974417i	$-0.427845\pi$
$5$	1.00510	0.449494	0.224747	+	0.974417i	$0.427845\pi$
$6$	2.33471	0.953141
$7$	1.73367	0.655267	0.327634	−	0.944805i	$-0.393749\pi$
$7$	1.73367	0.655267	0.327634	+	0.944805i	$0.393749\pi$
$8$	−3.06297	−1.08292
$9$	0.647363	0.215788
$10$	1.22872	0.388554
$11$	3.84830	1.16031	0.580153	−	0.814507i	$-0.302993\pi$
$11$	3.84830	1.16031	0.580153	+	0.814507i	$0.302993\pi$
$12$	−0.965468	−0.278707
$13$	6.27896	1.74147	0.870735	−	0.491753i	$-0.163644\pi$
$13$	6.27896	1.74147	0.870735	+	0.491753i	$0.163644\pi$
$14$	2.11939	0.566431
$15$	1.91954	0.495624
$16$	−2.73337	−0.683344
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	0.791391	0.186533
$19$	−4.53158	−1.03962	−0.519808	−	0.854283i	$-0.673997\pi$
$19$	−4.53158	−1.03962	−0.519808	+	0.854283i	$0.673997\pi$
$20$	−0.508109	−0.113617
$21$	3.31098	0.722516
$22$	4.70449	1.00300
$23$	−6.54056	−1.36380	−0.681900	−	0.731445i	$-0.738846\pi$
$23$	−6.54056	−1.36380	−0.681900	+	0.731445i	$0.738846\pi$
$24$	−5.84969	−1.19406
$25$	−3.98978	−0.797956
$26$	7.67593	1.50537
$27$	−4.49308	−0.864694
$28$	−0.876427	−0.165629
$29$	8.30336	1.54190	0.770948	−	0.636898i	$-0.219783\pi$
$29$	8.30336	1.54190	0.770948	+	0.636898i	$0.219783\pi$
$30$	2.34661	0.428431
$31$	7.38823	1.32697	0.663483	−	0.748191i	$-0.269077\pi$
$31$	7.38823	1.32697	0.663483	+	0.748191i	$0.269077\pi$
$32$	2.78444	0.492224
$33$	7.34951	1.27939
$34$	−1.22248	−0.209654
$35$	1.74251	0.294538
$36$	−0.327263	−0.0545438
$37$	6.01049	0.988119	0.494060	−	0.869428i	$-0.335512\pi$
$37$	6.01049	0.988119	0.494060	+	0.869428i	$0.335512\pi$
$38$	−5.53979	−0.898673
$39$	11.9916	1.92019
$40$	−3.07859	−0.486768
$41$	5.13833	0.802473	0.401236	−	0.915975i	$-0.368581\pi$
$41$	5.13833	0.802473	0.401236	+	0.915975i	$0.368581\pi$
$42$	4.04763	0.624562
$43$	−8.84264	−1.34849	−0.674245	−	0.738507i	$-0.735531\pi$
$43$	−8.84264	−1.34849	−0.674245	+	0.738507i	$0.735531\pi$
$44$	−1.94544	−0.293286
$45$	0.650664	0.0969952
$46$	−7.99573	−1.17891
$47$	1.00000	0.145865
$47$	1.00000	0.145865
$48$	−5.22022	−0.753473
$49$	−3.99437	−0.570625
$50$	−4.87744	−0.689774
$51$	−1.90981	−0.267426
$52$	−3.17421	−0.440184
$53$	−7.48214	−1.02775	−0.513875	−	0.857865i	$-0.671791\pi$
$53$	−7.48214	−1.02775	−0.513875	+	0.857865i	$0.671791\pi$
$54$	−5.49272	−0.747465
$55$	3.86792	0.521550
$56$	−5.31020	−0.709605
$57$	−8.65445	−1.14631
$58$	10.1507	1.33286
$59$	−1.25271	−0.163088	−0.0815442	−	0.996670i	$-0.525985\pi$
$59$	−1.25271	−0.163088	−0.0815442	+	0.996670i	$0.525985\pi$
$60$	−0.970390	−0.125277
$61$	−4.60400	−0.589482	−0.294741	−	0.955577i	$-0.595233\pi$
$61$	−4.60400	−0.589482	−0.294741	+	0.955577i	$0.595233\pi$
$62$	9.03200	1.14707
$63$	1.12232	0.141399
$64$	8.87068	1.10884
$65$	6.31097	0.782779
$66$	8.98466	1.10594
$67$	−6.91456	−0.844748	−0.422374	−	0.906422i	$-0.638803\pi$
$67$	−6.91456	−0.844748	−0.422374	+	0.906422i	$0.638803\pi$
$68$	0.505532	0.0613047
$69$	−12.4912	−1.50376
$70$	2.13019	0.254607
$71$	−0.406485	−0.0482409	−0.0241205	−	0.999709i	$-0.507679\pi$
$71$	−0.406485	−0.0482409	−0.0241205	+	0.999709i	$0.507679\pi$
$72$	−1.98286	−0.233682
$73$	−13.6037	−1.59219	−0.796097	−	0.605170i	$-0.793105\pi$
$73$	−13.6037	−1.59219	−0.796097	+	0.605170i	$0.793105\pi$
$74$	7.34773	0.854157
$75$	−7.61971	−0.879848
$76$	2.29086	0.262780
$77$	6.67170	0.760311
$78$	14.6595	1.65987
$79$	4.25780	0.479040	0.239520	−	0.970891i	$-0.423010\pi$
$79$	4.25780	0.479040	0.239520	+	0.970891i	$0.423010\pi$
$80$	−2.74731	−0.307158
$81$	−10.5230	−1.16922
$82$	6.28153	0.693679
$83$	−11.3054	−1.24092	−0.620462	−	0.784236i	$-0.713055\pi$
$83$	−11.3054	−1.24092	−0.620462	+	0.784236i	$0.713055\pi$
$84$	−1.67381	−0.182627
$85$	−1.00510	−0.109018
$86$	−10.8100	−1.16567
$87$	15.8578	1.70014
$88$	−11.7872	−1.25652
$89$	−1.69968	−0.180166	−0.0900830	−	0.995934i	$-0.528713\pi$
$89$	−1.69968	−0.180166	−0.0900830	+	0.995934i	$0.528713\pi$
$90$	0.795426	0.0838453
$91$	10.8857	1.14113
$92$	3.30646	0.344722
$93$	14.1101	1.46315
$94$	1.22248	0.126090
$95$	−4.55469	−0.467301
$96$	5.31774	0.542740
$97$	4.78101	0.485438	0.242719	−	0.970097i	$-0.421961\pi$
$97$	4.78101	0.485438	0.242719	+	0.970097i	$0.421961\pi$
$98$	−4.88306	−0.493264
$99$	2.49125	0.250380
$100$	2.01696	0.201696
$101$	0.0797415	0.00793457	0.00396729	−	0.999992i	$-0.498737\pi$
$101$	0.0797415	0.00793457	0.00396729	+	0.999992i	$0.498737\pi$
$102$	−2.33471	−0.231171
$103$	−15.5023	−1.52749	−0.763745	−	0.645518i	$-0.776642\pi$
$103$	−15.5023	−1.52749	−0.763745	+	0.645518i	$0.776642\pi$
$104$	−19.2323	−1.88588
$105$	3.32786	0.324766
$106$	−9.14680	−0.888416
$107$	11.5439	1.11599	0.557997	−	0.829843i	$-0.311570\pi$
$107$	11.5439	1.11599	0.557997	+	0.829843i	$0.311570\pi$
$108$	2.27140	0.218565
$109$	2.31825	0.222048	0.111024	−	0.993818i	$-0.464587\pi$
$109$	2.31825	0.222048	0.111024	+	0.993818i	$0.464587\pi$
$110$	4.72847	0.450842
$111$	11.4789	1.08953
$112$	−4.73878	−0.447773
$113$	−5.38113	−0.506214	−0.253107	−	0.967438i	$-0.581453\pi$
$113$	−5.38113	−0.506214	−0.253107	+	0.967438i	$0.581453\pi$
$114$	−10.5799	−0.990901
$115$	−6.57390	−0.613020
$116$	−4.19761	−0.389739
$117$	4.06477	0.375788
$118$	−1.53141	−0.140978
$119$	−1.73367	−0.158926
$120$	−5.87951	−0.536723
$121$	3.80942	0.346311
$122$	−5.62832	−0.509564
$123$	9.81323	0.884829
$124$	−3.73499	−0.335412
$125$	−9.03561	−0.808169
$126$	1.37201	0.122229
$127$	6.21569	0.551553	0.275776	−	0.961222i	$-0.411065\pi$
$127$	6.21569	0.551553	0.275776	+	0.961222i	$0.411065\pi$
$128$	5.27539	0.466283
$129$	−16.8877	−1.48688
$130$	7.71506	0.676656
$131$	16.9531	1.48120	0.740598	−	0.671948i	$-0.234542\pi$
$131$	16.9531	1.48120	0.740598	+	0.671948i	$0.234542\pi$
$132$	−3.71541	−0.323385
$133$	−7.85629	−0.681227
$134$	−8.45294	−0.730223
$135$	−4.51599	−0.388674
$136$	3.06297	0.262648
$137$	−17.3736	−1.48433	−0.742164	−	0.670219i	$-0.766200\pi$
$137$	−17.3736	−1.48433	−0.742164	+	0.670219i	$0.766200\pi$
$138$	−15.2703	−1.29989
$139$	13.6892	1.16110	0.580550	−	0.814225i	$-0.302838\pi$
$139$	13.6892	1.16110	0.580550	+	0.814225i	$0.302838\pi$
$140$	−0.880895	−0.0744493
$141$	1.90981	0.160835
$142$	−0.496922	−0.0417007
$143$	24.1633	2.02064
$144$	−1.76949	−0.147457
$145$	8.34569	0.693072
$146$	−16.6303	−1.37633
$147$	−7.62848	−0.629187
$148$	−3.03850	−0.249763
$149$	−5.30730	−0.434791	−0.217395	−	0.976084i	$-0.569756\pi$
$149$	−5.30730	−0.434791	−0.217395	+	0.976084i	$0.569756\pi$
$150$	−9.31497	−0.760564
$151$	−20.6481	−1.68032	−0.840161	−	0.542337i	$-0.817540\pi$
$151$	−20.6481	−1.68032	−0.840161	+	0.542337i	$0.817540\pi$
$152$	13.8801	1.12583
$153$	−0.647363	−0.0523362
$154$	8.15605	0.657233
$155$	7.42590	0.596463
$156$	−6.06214	−0.485359
$157$	−4.48268	−0.357757	−0.178878	−	0.983871i	$-0.557247\pi$
$157$	−4.48268	−0.357757	−0.178878	+	0.983871i	$0.557247\pi$
$158$	5.20510	0.414095
$159$	−14.2894	−1.13323
$160$	2.79864	0.221252
$161$	−11.3392	−0.893654
$162$	−12.8642	−1.01071
$163$	16.2009	1.26895	0.634476	−	0.772942i	$-0.281216\pi$
$163$	16.2009	1.26895	0.634476	+	0.772942i	$0.281216\pi$
$164$	−2.59759	−0.202838
$165$	7.38698	0.575076
$166$	−13.8206	−1.07269
$167$	−15.9203	−1.23195	−0.615976	−	0.787765i	$-0.711238\pi$
$167$	−15.9203	−1.23195	−0.615976	+	0.787765i	$0.711238\pi$
$168$	−10.1415	−0.782430
$169$	26.4253	2.03272
$170$	−1.22872	−0.0942383
$171$	−2.93358	−0.224337
$172$	4.47024	0.340852
$173$	16.7894	1.27647	0.638237	−	0.769840i	$-0.279664\pi$
$173$	16.7894	1.27647	0.638237	+	0.769840i	$0.279664\pi$
$174$	19.3859	1.46964
$175$	−6.91697	−0.522874
$176$	−10.5188	−0.792888
$177$	−2.39243	−0.179826
$178$	−2.07784	−0.155740
$179$	3.53647	0.264328	0.132164	−	0.991228i	$-0.457807\pi$
$179$	3.53647	0.264328	0.132164	+	0.991228i	$0.457807\pi$
$180$	−0.328931	−0.0245171
$181$	11.5055	0.855196	0.427598	−	0.903969i	$-0.359360\pi$
$181$	11.5055	0.855196	0.427598	+	0.903969i	$0.359360\pi$
$182$	13.3076	0.986422
$183$	−8.79276	−0.649980
$184$	20.0336	1.47689
$185$	6.04114	0.444153
$186$	17.2494	1.26479
$187$	−3.84830	−0.281416
$188$	−0.505532	−0.0368697
$189$	−7.78954	−0.566606
$190$	−5.56803	−0.403948
$191$	11.3611	0.822061	0.411030	−	0.911622i	$-0.365169\pi$
$191$	11.3611	0.822061	0.411030	+	0.911622i	$0.365169\pi$
$192$	16.9413	1.22263
$193$	3.58307	0.257915	0.128958	−	0.991650i	$-0.458837\pi$
$193$	3.58307	0.257915	0.128958	+	0.991650i	$0.458837\pi$
$194$	5.84472	0.419626
$195$	12.0527	0.863114
$196$	2.01928	0.144235
$197$	10.6363	0.757808	0.378904	−	0.925436i	$-0.376301\pi$
$197$	10.6363	0.757808	0.378904	+	0.925436i	$0.376301\pi$
$198$	3.04551	0.216435
$199$	−24.8580	−1.76213	−0.881067	−	0.472991i	$-0.843174\pi$
$199$	−24.8580	−1.76213	−0.881067	+	0.472991i	$0.843174\pi$
$200$	12.2206	0.864126
$201$	−13.2055	−0.931442
$202$	0.0974827	0.00685886
$203$	14.3953	1.01035
$204$	0.965468	0.0675963
$205$	5.16453	0.360706
$206$	−18.9514	−1.32040
$207$	−4.23412	−0.294291
$208$	−17.1627	−1.19002
$209$	−17.4389	−1.20627
$210$	4.06826	0.280737
$211$	18.4879	1.27276	0.636381	−	0.771375i	$-0.280431\pi$
$211$	18.4879	1.27276	0.636381	+	0.771375i	$0.280431\pi$
$212$	3.78246	0.259780
$213$	−0.776308	−0.0531918
$214$	14.1123	0.964695
$215$	−8.88773	−0.606138
$216$	13.7622	0.936399
$217$	12.8088	0.869517
$218$	2.83402	0.191944
$219$	−25.9805	−1.75560
$220$	−1.95536	−0.131830
$221$	−6.27896	−0.422369
$222$	14.0328	0.941817
$223$	−22.6429	−1.51628	−0.758141	−	0.652090i	$-0.773892\pi$
$223$	−22.6429	−1.51628	−0.758141	+	0.652090i	$0.773892\pi$
$224$	4.82731	0.322538
$225$	−2.58284	−0.172189
$226$	−6.57835	−0.437585
$227$	−24.7288	−1.64131	−0.820653	−	0.571426i	$-0.806390\pi$
$227$	−24.7288	−1.64131	−0.820653	+	0.571426i	$0.806390\pi$
$228$	4.37510	0.289748
$229$	22.5085	1.48741	0.743703	−	0.668510i	$-0.233068\pi$
$229$	22.5085	1.48741	0.743703	+	0.668510i	$0.233068\pi$
$230$	−8.03649	−0.529911
$231$	12.7417	0.838340
$232$	−25.4330	−1.66976
$233$	20.5627	1.34711	0.673554	−	0.739138i	$-0.264767\pi$
$233$	20.5627	1.34711	0.673554	+	0.739138i	$0.264767\pi$
$234$	4.96911	0.324841
$235$	1.00510	0.0655654
$236$	0.633283	0.0412232
$237$	8.13158	0.528203
$238$	−2.11939	−0.137380
$239$	−7.18998	−0.465081	−0.232541	−	0.972587i	$-0.574704\pi$
$239$	−7.18998	−0.465081	−0.232541	+	0.972587i	$0.574704\pi$
$240$	−5.24683	−0.338681
$241$	−14.6085	−0.941015	−0.470507	−	0.882396i	$-0.655929\pi$
$241$	−14.6085	−0.941015	−0.470507	+	0.882396i	$0.655929\pi$
$242$	4.65695	0.299360
$243$	−6.61767	−0.424524
$244$	2.32747	0.149001
$245$	−4.01474	−0.256492
$246$	11.9965	0.764870
$247$	−28.4536	−1.81046
$248$	−22.6300	−1.43700
$249$	−21.5911	−1.36828
$250$	−11.0459	−0.698603
$251$	14.8670	0.938397	0.469199	−	0.883093i	$-0.344543\pi$
$251$	14.8670	0.938397	0.469199	+	0.883093i	$0.344543\pi$
$252$	−0.567367	−0.0357407
$253$	−25.1700	−1.58243
$254$	7.59858	0.476777
$255$	−1.91954	−0.120206
$256$	−11.2923	−0.705768
$257$	12.1483	0.757788	0.378894	−	0.925440i	$-0.376304\pi$
$257$	12.1483	0.757788	0.378894	+	0.925440i	$0.376304\pi$
$258$	−20.6450	−1.28530
$259$	10.4202	0.647482
$260$	−3.19040	−0.197860
$261$	5.37529	0.332722
$262$	20.7249	1.28039
$263$	7.53877	0.464861	0.232430	−	0.972613i	$-0.425332\pi$
$263$	7.53877	0.464861	0.232430	+	0.972613i	$0.425332\pi$
$264$	−22.5114	−1.38548
$265$	−7.52028	−0.461967
$266$	−9.60419	−0.588871
$267$	−3.24607	−0.198656
$268$	3.49553	0.213523
$269$	−1.56095	−0.0951729	−0.0475865	−	0.998867i	$-0.515153\pi$
$269$	−1.56095	−0.0951729	−0.0475865	+	0.998867i	$0.515153\pi$
$270$	−5.52073	−0.335981
$271$	23.5556	1.43090	0.715452	−	0.698662i	$-0.246221\pi$
$271$	23.5556	1.43090	0.715452	+	0.698662i	$0.246221\pi$
$272$	2.73337	0.165735
$273$	20.7895	1.25824
$274$	−21.2390	−1.28309
$275$	−15.3539	−0.925873
$276$	6.31470	0.380100
$277$	19.3757	1.16417	0.582087	−	0.813126i	$-0.302236\pi$
$277$	19.3757	1.16417	0.582087	+	0.813126i	$0.302236\pi$
$278$	16.7348	1.00369
$279$	4.78287	0.286343
$280$	−5.33727	−0.318963
$281$	21.5251	1.28408	0.642039	−	0.766672i	$-0.278089\pi$
$281$	21.5251	1.28408	0.642039	+	0.766672i	$0.278089\pi$
$282$	2.33471	0.139030
$283$	10.5318	0.626050	0.313025	−	0.949745i	$-0.398658\pi$
$283$	10.5318	0.626050	0.313025	+	0.949745i	$0.398658\pi$
$284$	0.205491	0.0121937
$285$	−8.69857	−0.515259
$286$	29.5393	1.74669
$287$	8.90820	0.525834
$288$	1.80254	0.106216
$289$	1.00000	0.0588235
$290$	10.2025	0.599110
$291$	9.13081	0.535258
$292$	6.87710	0.402452
$293$	10.4034	0.607771	0.303886	−	0.952708i	$-0.401716\pi$
$293$	10.4034	0.607771	0.303886	+	0.952708i	$0.401716\pi$
$294$	−9.32570	−0.543886
$295$	−1.25909	−0.0733072
$296$	−18.4100	−1.07006
$297$	−17.2907	−1.00331
$298$	−6.48809	−0.375845
$299$	−41.0679	−2.37502
$300$	3.85200	0.222396
$301$	−15.3303	−0.883622
$302$	−25.2420	−1.45252
$303$	0.152291	0.00874888
$304$	12.3865	0.710415
$305$	−4.62748	−0.264968
$306$	−0.791391	−0.0452408
$307$	12.8651	0.734248	0.367124	−	0.930172i	$-0.380342\pi$
$307$	12.8651	0.734248	0.367124	+	0.930172i	$0.380342\pi$
$308$	−3.37276	−0.192181
$309$	−29.6065	−1.68425
$310$	9.07805	0.515598
$311$	−8.97067	−0.508680	−0.254340	−	0.967115i	$-0.581858\pi$
$311$	−8.97067	−0.508680	−0.254340	+	0.967115i	$0.581858\pi$
$312$	−36.7300	−2.07942
$313$	−21.7671	−1.23035	−0.615173	−	0.788392i	$-0.710914\pi$
$313$	−21.7671	−1.23035	−0.615173	+	0.788392i	$0.710914\pi$
$314$	−5.48001	−0.309255
$315$	1.12804	0.0635578
$316$	−2.15245	−0.121085
$317$	21.4202	1.20308	0.601539	−	0.798843i	$-0.294554\pi$
$317$	21.4202	1.20308	0.601539	+	0.798843i	$0.294554\pi$
$318$	−17.4686	−0.979592
$319$	31.9538	1.78907
$320$	8.91591	0.498414
$321$	22.0467	1.23053
$322$	−13.8620	−0.772499
$323$	4.53158	0.252144
$324$	5.31972	0.295540
$325$	−25.0517	−1.38962
$326$	19.8053	1.09692
$327$	4.42740	0.244836
$328$	−15.7386	−0.869018
$329$	1.73367	0.0955805
$330$	9.03047	0.497111
$331$	12.1612	0.668439	0.334219	−	0.942495i	$-0.391527\pi$
$331$	12.1612	0.668439	0.334219	+	0.942495i	$0.391527\pi$
$332$	5.71522	0.313663
$333$	3.89097	0.213224
$334$	−19.4623	−1.06493
$335$	−6.94981	−0.379709
$336$	−9.05016	−0.493726
$337$	−7.98077	−0.434740	−0.217370	−	0.976089i	$-0.569748\pi$
$337$	−7.98077	−0.434740	−0.217370	+	0.976089i	$0.569748\pi$
$338$	32.3046	1.75714
$339$	−10.2769	−0.558166
$340$	0.508109	0.0275561
$341$	28.4321	1.53969
$342$	−3.58626	−0.193923
$343$	−19.0607	−1.02918
$344$	27.0848	1.46031
$345$	−12.5549	−0.675932
$346$	20.5248	1.10342
$347$	9.13030	0.490140	0.245070	−	0.969505i	$-0.421189\pi$
$347$	9.13030	0.490140	0.245070	+	0.969505i	$0.421189\pi$
$348$	−8.01663	−0.429737
$349$	25.9786	1.39060	0.695300	−	0.718719i	$-0.255271\pi$
$349$	25.9786	1.39060	0.695300	+	0.718719i	$0.255271\pi$
$350$	−8.45589	−0.451987
$351$	−28.2119	−1.50584
$352$	10.7154	0.571131
$353$	19.0409	1.01344	0.506722	−	0.862110i	$-0.330857\pi$
$353$	19.0409	1.01344	0.506722	+	0.862110i	$0.330857\pi$
$354$	−2.92470	−0.155446
$355$	−0.408557	−0.0216840
$356$	0.859243	0.0455398
$357$	−3.31098	−0.175236
$358$	4.32328	0.228493
$359$	−19.2868	−1.01792	−0.508958	−	0.860791i	$-0.669969\pi$
$359$	−19.2868	−1.01792	−0.508958	+	0.860791i	$0.669969\pi$
$360$	−1.99297	−0.105038
$361$	1.53525	0.0808028
$362$	14.0653	0.739255
$363$	7.27525	0.381852
$364$	−5.50305	−0.288438
$365$	−13.6731	−0.715681
$366$	−10.7490	−0.561860
$367$	−10.3124	−0.538303	−0.269151	−	0.963098i	$-0.586743\pi$
$367$	−10.3124	−0.538303	−0.269151	+	0.963098i	$0.586743\pi$
$368$	17.8778	0.931944
$369$	3.32637	0.173164
$370$	7.38519	0.383938
$371$	−12.9716	−0.673451
$372$	−7.13311	−0.369834
$373$	18.9203	0.979655	0.489827	−	0.871819i	$-0.337060\pi$
$373$	18.9203	0.979655	0.489827	+	0.871819i	$0.337060\pi$
$374$	−4.70449	−0.243263
$375$	−17.2563	−0.891110
$376$	−3.06297	−0.157961
$377$	52.1365	2.68517
$378$	−9.52259	−0.489789
$379$	9.53027	0.489537	0.244769	−	0.969582i	$-0.421288\pi$
$379$	9.53027	0.489537	0.244769	+	0.969582i	$0.421288\pi$
$380$	2.30254	0.118118
$381$	11.8708	0.608157
$382$	13.8888	0.710612
$383$	14.2414	0.727701	0.363851	−	0.931457i	$-0.381462\pi$
$383$	14.2414	0.727701	0.363851	+	0.931457i	$0.381462\pi$
$384$	10.0750	0.514137
$385$	6.70571	0.341755
$386$	4.38025	0.222949
$387$	−5.72440	−0.290988
$388$	−2.41695	−0.122702
$389$	37.7077	1.91186	0.955929	−	0.293599i	$-0.0948531\pi$
$389$	37.7077	1.91186	0.955929	+	0.293599i	$0.0948531\pi$
$390$	14.7343	0.746099
$391$	6.54056	0.330770
$392$	12.2347	0.617944
$393$	32.3771	1.63321
$394$	13.0028	0.655070
$395$	4.27951	0.215325
$396$	−1.25941	−0.0632875
$397$	−31.0364	−1.55767	−0.778835	−	0.627228i	$-0.784189\pi$
$397$	−31.0364	−1.55767	−0.778835	+	0.627228i	$0.784189\pi$
$398$	−30.3885	−1.52324
$399$	−15.0040	−0.751139
$400$	10.9056	0.545278
$401$	−0.186645	−0.00932060	−0.00466030	−	0.999989i	$-0.501483\pi$
$401$	−0.186645	−0.00932060	−0.00466030	+	0.999989i	$0.501483\pi$
$402$	−16.1435	−0.805164
$403$	46.3904	2.31087
$404$	−0.0403118	−0.00200559
$405$	−10.5767	−0.525558
$406$	17.5981	0.873377
$407$	23.1302	1.14652
$408$	5.84969	0.289603
$409$	−25.4570	−1.25877	−0.629384	−	0.777095i	$-0.716693\pi$
$409$	−25.4570	−1.25877	−0.629384	+	0.777095i	$0.716693\pi$
$410$	6.31356	0.311804
$411$	−33.1802	−1.63666
$412$	7.83692	0.386097
$413$	−2.17178	−0.106866
$414$	−5.17614	−0.254394
$415$	−11.3630	−0.557787
$416$	17.4834	0.857193
$417$	26.1437	1.28026
$418$	−21.3188	−1.04274
$419$	11.6596	0.569608	0.284804	−	0.958586i	$-0.408072\pi$
$419$	11.6596	0.569608	0.284804	+	0.958586i	$0.408072\pi$
$420$	−1.68234	−0.0820898
$421$	−40.7023	−1.98371	−0.991853	−	0.127386i	$-0.959341\pi$
$421$	−40.7023	−1.98371	−0.991853	+	0.127386i	$0.959341\pi$
$422$	22.6012	1.10021
$423$	0.647363	0.0314759
$424$	22.9176	1.11298
$425$	3.98978	0.193533
$426$	−0.949025	−0.0459804
$427$	−7.98184	−0.386268
$428$	−5.83582	−0.282085
$429$	46.1473	2.22801
$430$	−10.8651	−0.523962
$431$	37.5071	1.80665	0.903326	−	0.428954i	$-0.141118\pi$
$431$	37.5071	1.80665	0.903326	+	0.428954i	$0.141118\pi$
$432$	12.2813	0.590883
$433$	−16.6063	−0.798048	−0.399024	−	0.916941i	$-0.630651\pi$
$433$	−16.6063	−0.798048	−0.399024	+	0.916941i	$0.630651\pi$
$434$	15.6585	0.751634
$435$	15.9387	0.764201
$436$	−1.17195	−0.0561261
$437$	29.6391	1.41783
$438$	−31.7607	−1.51758
$439$	−3.20397	−0.152917	−0.0764587	−	0.997073i	$-0.524361\pi$
$439$	−3.20397	−0.152917	−0.0764587	+	0.997073i	$0.524361\pi$
$440$	−11.8473	−0.564800
$441$	−2.58581	−0.123134
$442$	−7.67593	−0.365107
$443$	−15.4790	−0.735431	−0.367715	−	0.929938i	$-0.619860\pi$
$443$	−15.4790	−0.735431	−0.367715	+	0.929938i	$0.619860\pi$
$444$	−5.80294	−0.275395
$445$	−1.70835	−0.0809834
$446$	−27.6806	−1.31072
$447$	−10.1359	−0.479412
$448$	15.3789	0.726583
$449$	2.21359	0.104466	0.0522328	−	0.998635i	$-0.483366\pi$
$449$	2.21359	0.104466	0.0522328	+	0.998635i	$0.483366\pi$
$450$	−3.15748	−0.148845
$451$	19.7739	0.931114
$452$	2.72033	0.127954
$453$	−39.4340	−1.85277
$454$	−30.2306	−1.41879
$455$	10.9412	0.512930
$456$	26.5084	1.24137
$457$	11.0925	0.518885	0.259442	−	0.965759i	$-0.416461\pi$
$457$	11.0925	0.518885	0.259442	+	0.965759i	$0.416461\pi$
$458$	27.5163	1.28575
$459$	4.49308	0.209719
$460$	3.32332	0.154950
$461$	−7.58700	−0.353362	−0.176681	−	0.984268i	$-0.556536\pi$
$461$	−7.58700	−0.353362	−0.176681	+	0.984268i	$0.556536\pi$
$462$	15.5765	0.724683
$463$	−32.0481	−1.48940	−0.744701	−	0.667398i	$-0.767408\pi$
$463$	−32.0481	−1.48940	−0.744701	+	0.667398i	$0.767408\pi$
$464$	−22.6962	−1.05364
$465$	14.1820	0.657676
$466$	25.1376	1.16448
$467$	9.72443	0.449993	0.224996	−	0.974360i	$-0.427763\pi$
$467$	9.72443	0.449993	0.224996	+	0.974360i	$0.427763\pi$
$468$	−2.05487	−0.0949864
$469$	−11.9876	−0.553536
$470$	1.22872	0.0566765
$471$	−8.56106	−0.394473
$472$	3.83700	0.176612
$473$	−34.0292	−1.56466
$474$	9.94073	0.456593
$475$	18.0800	0.829568
$476$	0.876427	0.0401710
$477$	−4.84366	−0.221776
$478$	−8.78964	−0.402029
$479$	−13.9737	−0.638477	−0.319238	−	0.947674i	$-0.603427\pi$
$479$	−13.9737	−0.638477	−0.319238	+	0.947674i	$0.603427\pi$
$480$	5.34485	0.243958
$481$	37.7396	1.72078
$482$	−17.8586	−0.813439
$483$	−21.6557	−0.985368
$484$	−1.92578	−0.0875356
$485$	4.80539	0.218201
$486$	−8.09000	−0.366970
$487$	22.2239	1.00706	0.503529	−	0.863978i	$-0.332035\pi$
$487$	22.2239	1.00706	0.503529	+	0.863978i	$0.332035\pi$
$488$	14.1019	0.638365
$489$	30.9406	1.39918
$490$	−4.90795	−0.221719
$491$	−2.71216	−0.122398	−0.0611990	−	0.998126i	$-0.519492\pi$
$491$	−2.71216	−0.122398	−0.0611990	+	0.998126i	$0.519492\pi$
$492$	−4.96090	−0.223655
$493$	−8.30336	−0.373965
$494$	−34.7841	−1.56501
$495$	2.50395	0.112544
$496$	−20.1948	−0.906774
$497$	−0.704713	−0.0316107
$498$	−26.3947	−1.18278
$499$	−28.3916	−1.27098	−0.635491	−	0.772108i	$-0.719202\pi$
$499$	−28.3916	−1.27098	−0.635491	+	0.772108i	$0.719202\pi$
$500$	4.56779	0.204278
$501$	−30.4047	−1.35838
$502$	18.1747	0.811176
$503$	36.2845	1.61785	0.808923	−	0.587914i	$-0.200051\pi$
$503$	36.2845	1.61785	0.808923	+	0.587914i	$0.200051\pi$
$504$	−3.43763	−0.153124
$505$	0.0801480	0.00356654
$506$	−30.7700	−1.36789
$507$	50.4673	2.24133
$508$	−3.14223	−0.139414
$509$	−32.6836	−1.44867	−0.724337	−	0.689446i	$-0.757854\pi$
$509$	−32.6836	−1.44867	−0.724337	+	0.689446i	$0.757854\pi$
$510$	−2.34661	−0.103910
$511$	−23.5844	−1.04331
$512$	−24.3554	−1.07637
$513$	20.3608	0.898950
$514$	14.8511	0.655053
$515$	−15.5814	−0.686597
$516$	8.53729	0.375833
$517$	3.84830	0.169248
$518$	12.7386	0.559701
$519$	32.0645	1.40748
$520$	−19.3303	−0.847691
$521$	−11.6085	−0.508578	−0.254289	−	0.967128i	$-0.581842\pi$
$521$	−11.6085	−0.508578	−0.254289	+	0.967128i	$0.581842\pi$
$522$	6.57121	0.287614
$523$	−22.5662	−0.986749	−0.493375	−	0.869817i	$-0.664237\pi$
$523$	−22.5662	−0.986749	−0.493375	+	0.869817i	$0.664237\pi$
$524$	−8.57032	−0.374396
$525$	−13.2101	−0.576535
$526$	9.21603	0.401838
$527$	−7.38823	−0.321837
$528$	−20.0890	−0.874260
$529$	19.7789	0.859953
$530$	−9.19343	−0.399337
$531$	−0.810956	−0.0351925
$532$	3.97160	0.172191
$533$	32.2634	1.39748
$534$	−3.96826	−0.171724
$535$	11.6028	0.501632
$536$	21.1791	0.914798
$537$	6.75398	0.291456
$538$	−1.90824	−0.0822700
$539$	−15.3716	−0.662100
$540$	2.28298	0.0982436
$541$	−16.7265	−0.719128	−0.359564	−	0.933120i	$-0.617075\pi$
$541$	−16.7265	−0.719128	−0.359564	+	0.933120i	$0.617075\pi$
$542$	28.7964	1.23691
$543$	21.9733	0.942963
$544$	−2.78444	−0.119382
$545$	2.33006	0.0998090
$546$	25.4149	1.08766
$547$	−8.35361	−0.357174	−0.178587	−	0.983924i	$-0.557153\pi$
$547$	−8.35361	−0.357174	−0.178587	+	0.983924i	$0.557153\pi$
$548$	8.78291	0.375187
$549$	−2.98046	−0.127203
$550$	−18.7699	−0.800350
$551$	−37.6274	−1.60298
$552$	38.2602	1.62846
$553$	7.38164	0.313899
$554$	23.6865	1.00634
$555$	11.5374	0.489736
$556$	−6.92031	−0.293486
$557$	38.4888	1.63082	0.815412	−	0.578880i	$-0.196510\pi$
$557$	38.4888	1.63082	0.815412	+	0.578880i	$0.196510\pi$
$558$	5.84699	0.247523
$559$	−55.5226	−2.34836
$560$	−4.76294	−0.201271
$561$	−7.34951	−0.310297
$562$	26.3141	1.10999
$563$	−16.6170	−0.700323	−0.350161	−	0.936689i	$-0.613873\pi$
$563$	−16.6170	−0.700323	−0.350161	+	0.936689i	$0.613873\pi$
$564$	−0.965468	−0.0406535
$565$	−5.40857	−0.227540
$566$	12.8749	0.541174
$567$	−18.2435	−0.766154
$568$	1.24505	0.0522413
$569$	−16.8090	−0.704670	−0.352335	−	0.935874i	$-0.614612\pi$
$569$	−16.8090	−0.704670	−0.352335	+	0.935874i	$0.614612\pi$
$570$	−10.6339	−0.445404
$571$	−30.1445	−1.26151	−0.630754	−	0.775983i	$-0.717254\pi$
$571$	−30.1445	−1.26151	−0.630754	+	0.775983i	$0.717254\pi$
$572$	−12.2153	−0.510749
$573$	21.6975	0.906427
$574$	10.8901	0.454545
$575$	26.0954	1.08825
$576$	5.74255	0.239273
$577$	−23.5711	−0.981276	−0.490638	−	0.871363i	$-0.663236\pi$
$577$	−23.5711	−0.981276	−0.490638	+	0.871363i	$0.663236\pi$
$578$	1.22248	0.0508486
$579$	6.84297	0.284384
$580$	−4.21901	−0.175185
$581$	−19.5998	−0.813137
$582$	11.1623	0.462691
$583$	−28.7935	−1.19251
$584$	41.6678	1.72423
$585$	4.08549	0.168914
$586$	12.7180	0.525374
$587$	−9.08720	−0.375069	−0.187534	−	0.982258i	$-0.560050\pi$
$587$	−9.08720	−0.375069	−0.187534	+	0.982258i	$0.560050\pi$
$588$	3.85644	0.159037
$589$	−33.4804	−1.37954
$590$	−1.53922	−0.0633687
$591$	20.3134	0.835580
$592$	−16.4289	−0.675225
$593$	37.5430	1.54171	0.770853	−	0.637013i	$-0.219830\pi$
$593$	37.5430	1.54171	0.770853	+	0.637013i	$0.219830\pi$
$594$	−21.1377	−0.867288
$595$	−1.74251	−0.0714360
$596$	2.68301	0.109900
$597$	−47.4739	−1.94298
$598$	−50.2049	−2.05303
$599$	24.7008	1.00925	0.504623	−	0.863340i	$-0.331631\pi$
$599$	24.7008	1.00925	0.504623	+	0.863340i	$0.331631\pi$
$600$	23.3390	0.952809
$601$	10.9127	0.445138	0.222569	−	0.974917i	$-0.428556\pi$
$601$	10.9127	0.445138	0.222569	+	0.974917i	$0.428556\pi$
$602$	−18.7410	−0.763827
$603$	−4.47623	−0.182286
$604$	10.4383	0.424728
$605$	3.82884	0.155664
$606$	0.186173	0.00756277
$607$	−25.3359	−1.02835	−0.514177	−	0.857684i	$-0.671903\pi$
$607$	−25.3359	−1.02835	−0.514177	+	0.857684i	$0.671903\pi$
$608$	−12.6179	−0.511724
$609$	27.4923	1.11404
$610$	−5.65702	−0.229046
$611$	6.27896	0.254020
$612$	0.327263	0.0132288
$613$	31.1943	1.25993	0.629964	−	0.776625i	$-0.283070\pi$
$613$	31.1943	1.25993	0.629964	+	0.776625i	$0.283070\pi$
$614$	15.7274	0.634704
$615$	9.86326	0.397725
$616$	−20.4352	−0.823359
$617$	35.5096	1.42956	0.714781	−	0.699348i	$-0.246526\pi$
$617$	35.5096	1.42956	0.714781	+	0.699348i	$0.246526\pi$
$618$	−36.1934	−1.45591
$619$	3.19385	0.128371	0.0641857	−	0.997938i	$-0.479555\pi$
$619$	3.19385	0.128371	0.0641857	+	0.997938i	$0.479555\pi$
$620$	−3.75403	−0.150765
$621$	29.3873	1.17927
$622$	−10.9665	−0.439717
$623$	−2.94670	−0.118057
$624$	−32.7775	−1.31215
$625$	10.8672	0.434689
$626$	−26.6099	−1.06354
$627$	−33.3049	−1.33007
$628$	2.26614	0.0904288
$629$	−6.01049	−0.239654
$630$	1.37901	0.0549411
$631$	−34.4955	−1.37324	−0.686622	−	0.727015i	$-0.740907\pi$
$631$	−34.4955	−1.37324	−0.686622	+	0.727015i	$0.740907\pi$
$632$	−13.0415	−0.518764
$633$	35.3084	1.40338
$634$	26.1859	1.03997
$635$	6.24737	0.247919
$636$	7.22377	0.286441
$637$	−25.0805	−0.993726
$638$	39.0631	1.54652
$639$	−0.263144	−0.0104098
$640$	5.30229	0.209591
$641$	16.7935	0.663305	0.331652	−	0.943402i	$-0.392394\pi$
$641$	16.7935	0.663305	0.331652	+	0.943402i	$0.392394\pi$
$642$	26.9517	1.06370
$643$	47.1250	1.85843	0.929214	−	0.369543i	$-0.120486\pi$
$643$	47.1250	1.85843	0.929214	+	0.369543i	$0.120486\pi$
$644$	5.73232	0.225885
$645$	−16.9738	−0.668344
$646$	5.53979	0.217960
$647$	3.20519	0.126009	0.0630045	−	0.998013i	$-0.479932\pi$
$647$	3.20519	0.126009	0.0630045	+	0.998013i	$0.479932\pi$
$648$	32.2317	1.26618
$649$	−4.82079	−0.189232
$650$	−30.6253	−1.20122
$651$	24.4623	0.958754
$652$	−8.19007	−0.320748
$653$	3.44303	0.134736	0.0673682	−	0.997728i	$-0.478540\pi$
$653$	3.44303	0.134736	0.0673682	+	0.997728i	$0.478540\pi$
$654$	5.41243	0.211643
$655$	17.0395	0.665788
$656$	−14.0450	−0.548365
$657$	−8.80654	−0.343576
$658$	2.11939	0.0826224
$659$	−42.1027	−1.64009	−0.820045	−	0.572299i	$-0.806051\pi$
$659$	−42.1027	−1.64009	−0.820045	+	0.572299i	$0.806051\pi$
$660$	−3.73435	−0.145360
$661$	−14.6727	−0.570701	−0.285350	−	0.958423i	$-0.592110\pi$
$661$	−14.6727	−0.570701	−0.285350	+	0.958423i	$0.592110\pi$
$662$	14.8669	0.577817
$663$	−11.9916	−0.465715
$664$	34.6280	1.34383
$665$	−7.89634	−0.306207
$666$	4.75665	0.184317
$667$	−54.3086	−2.10284
$668$	8.04823	0.311395
$669$	−43.2436	−1.67190
$670$	−8.49604	−0.328231
$671$	−17.7176	−0.683980
$672$	9.21923	0.355640
$673$	6.10773	0.235436	0.117718	−	0.993047i	$-0.462442\pi$
$673$	6.10773	0.235436	0.117718	+	0.993047i	$0.462442\pi$
$674$	−9.75637	−0.375801
$675$	17.9264	0.689987
$676$	−13.3588	−0.513802
$677$	41.4009	1.59117	0.795583	−	0.605845i	$-0.207165\pi$
$677$	41.4009	1.59117	0.795583	+	0.605845i	$0.207165\pi$
$678$	−12.5634	−0.482494
$679$	8.28872	0.318092
$680$	3.07859	0.118058
$681$	−47.2272	−1.80975
$682$	34.7579	1.33095
$683$	−0.632389	−0.0241977	−0.0120989	−	0.999927i	$-0.503851\pi$
$683$	−0.632389	−0.0241977	−0.0120989	+	0.999927i	$0.503851\pi$
$684$	1.48302	0.0567046
$685$	−17.4622	−0.667195
$686$	−23.3014	−0.889650
$687$	42.9870	1.64005
$688$	24.1703	0.921482
$689$	−46.9800	−1.78980
$690$	−15.3482	−0.584294
$691$	43.2116	1.64385	0.821924	−	0.569597i	$-0.192901\pi$
$691$	43.2116	1.64385	0.821924	+	0.569597i	$0.192901\pi$
$692$	−8.48757	−0.322649
$693$	4.31901	0.164066
$694$	11.1616	0.423690
$695$	13.7589	0.521907
$696$	−48.5721	−1.84112
$697$	−5.13833	−0.194628
$698$	31.7584	1.20207
$699$	39.2708	1.48536
$700$	3.49675	0.132165
$701$	8.63941	0.326306	0.163153	−	0.986601i	$-0.447834\pi$
$701$	8.63941	0.326306	0.163153	+	0.986601i	$0.447834\pi$
$702$	−34.4886	−1.30169
$703$	−27.2371	−1.02726
$704$	34.1371	1.28659
$705$	1.91954	0.0722942
$706$	23.2772	0.876048
$707$	0.138246	0.00519926
$708$	1.20945	0.0454538
$709$	−0.933519	−0.0350591	−0.0175295	−	0.999846i	$-0.505580\pi$
$709$	−0.933519	−0.0350591	−0.0175295	+	0.999846i	$0.505580\pi$
$710$	−0.499455	−0.0187442
$711$	2.75634	0.103371
$712$	5.20608	0.195106
$713$	−48.3232	−1.80972
$714$	−4.04763	−0.151479
$715$	24.2865	0.908264
$716$	−1.78780	−0.0668132
$717$	−13.7315	−0.512811
$718$	−23.5778	−0.879915
$719$	−30.8166	−1.14927	−0.574633	−	0.818411i	$-0.694855\pi$
$719$	−30.8166	−1.14927	−0.574633	+	0.818411i	$0.694855\pi$
$720$	−1.77851	−0.0662810
$721$	−26.8760	−1.00091
$722$	1.87682	0.0698481
$723$	−27.8994	−1.03759
$724$	−5.81639	−0.216164
$725$	−33.1286	−1.23036
$726$	8.89389	0.330083
$727$	22.1987	0.823303	0.411652	−	0.911341i	$-0.364952\pi$
$727$	22.1987	0.823303	0.411652	+	0.911341i	$0.364952\pi$
$728$	−33.3425	−1.23576
$729$	18.9306	0.701132
$730$	−16.7151	−0.618654
$731$	8.84264	0.327057
$732$	4.44502	0.164293
$733$	37.1985	1.37396	0.686980	−	0.726677i	$-0.258936\pi$
$733$	37.1985	1.37396	0.686980	+	0.726677i	$0.258936\pi$
$734$	−12.6067	−0.465324
$735$	−7.66738	−0.282815
$736$	−18.2118	−0.671296
$737$	−26.6093	−0.980166
$738$	4.06643	0.149687
$739$	−35.9519	−1.32251	−0.661257	−	0.750160i	$-0.729977\pi$
$739$	−35.9519	−1.32251	−0.661257	+	0.750160i	$0.729977\pi$
$740$	−3.05399	−0.112267
$741$	−54.3409	−1.99626
$742$	−15.8576	−0.582150
$743$	−0.442012	−0.0162158	−0.00810792	−	0.999967i	$-0.502581\pi$
$743$	−0.442012	−0.0162158	−0.00810792	+	0.999967i	$0.502581\pi$
$744$	−43.2189	−1.58448
$745$	−5.33435	−0.195436
$746$	23.1297	0.846840
$747$	−7.31867	−0.267776
$748$	1.94544	0.0711323
$749$	20.0134	0.731274
$750$	−21.0955	−0.770300
$751$	−26.5856	−0.970123	−0.485062	−	0.874480i	$-0.661203\pi$
$751$	−26.5856	−0.970123	−0.485062	+	0.874480i	$0.661203\pi$
$752$	−2.73337	−0.0996759
$753$	28.3931	1.03470
$754$	63.7360	2.32113
$755$	−20.7534	−0.755294
$756$	3.93786	0.143219
$757$	12.6628	0.460236	0.230118	−	0.973163i	$-0.426089\pi$
$757$	12.6628	0.460236	0.230118	+	0.973163i	$0.426089\pi$
$758$	11.6506	0.423169
$759$	−48.0699	−1.74483
$760$	13.9509	0.506052
$761$	40.6545	1.47373	0.736863	−	0.676042i	$-0.236306\pi$
$761$	40.6545	1.47373	0.736863	+	0.676042i	$0.236306\pi$
$762$	14.5118	0.525708
$763$	4.01908	0.145501
$764$	−5.74340	−0.207789
$765$	−0.650664	−0.0235248
$766$	17.4099	0.629045
$767$	−7.86569	−0.284014
$768$	−21.5661	−0.778199
$769$	20.2709	0.730988	0.365494	−	0.930814i	$-0.380900\pi$
$769$	20.2709	0.730988	0.365494	+	0.930814i	$0.380900\pi$
$770$	8.19763	0.295422
$771$	23.2009	0.835558
$772$	−1.81136	−0.0651921
$773$	21.1001	0.758917	0.379458	−	0.925209i	$-0.376110\pi$
$773$	21.1001	0.758917	0.379458	+	0.925209i	$0.376110\pi$
$774$	−6.99799	−0.251538
$775$	−29.4774	−1.05886
$776$	−14.6441	−0.525693
$777$	19.9006	0.713932
$778$	46.0971	1.65266
$779$	−23.2848	−0.834264
$780$	−6.09304	−0.218166
$781$	−1.56428	−0.0559742
$782$	7.99573	0.285927
$783$	−37.3077	−1.33327
$784$	10.9181	0.389933
$785$	−4.50554	−0.160809
$786$	39.5805	1.41179
$787$	−22.0411	−0.785681	−0.392841	−	0.919607i	$-0.628508\pi$
$787$	−22.0411	−0.785681	−0.392841	+	0.919607i	$0.628508\pi$
$788$	−5.37701	−0.191548
$789$	14.3976	0.512568
$790$	5.23163	0.186133
$791$	−9.32913	−0.331706
$792$	−7.63063	−0.271143
$793$	−28.9084	−1.02657
$794$	−37.9415	−1.34649
$795$	−14.3623	−0.509378
$796$	12.5665	0.445407
$797$	0.0594544	0.00210598	0.00105299	−	0.999999i	$-0.499665\pi$
$797$	0.0594544	0.00210598	0.00105299	+	0.999999i	$0.499665\pi$
$798$	−18.3422	−0.649305
$799$	−1.00000	−0.0353775
$800$	−11.1093	−0.392773
$801$	−1.10031	−0.0388776
$802$	−0.228170	−0.00805698
$803$	−52.3511	−1.84743
$804$	6.67579	0.235437
$805$	−11.3970	−0.401692
$806$	56.7116	1.99758
$807$	−2.98112	−0.104940
$808$	−0.244246	−0.00859254
$809$	−2.67049	−0.0938895	−0.0469448	−	0.998897i	$-0.514948\pi$
$809$	−2.67049	−0.0938895	−0.0469448	+	0.998897i	$0.514948\pi$
$810$	−12.9298	−0.454307
$811$	26.2724	0.922549	0.461274	−	0.887258i	$-0.347392\pi$
$811$	26.2724	0.922549	0.461274	+	0.887258i	$0.347392\pi$
$812$	−7.27729	−0.255383
$813$	44.9867	1.57775
$814$	28.2763	0.991084
$815$	16.2835	0.570386
$816$	5.22022	0.182744
$817$	40.0712	1.40191
$818$	−31.1208	−1.08811
$819$	7.04698	0.246241
$820$	−2.61083	−0.0911743
$821$	−29.7536	−1.03841	−0.519203	−	0.854651i	$-0.673771\pi$
$821$	−29.7536	−1.03841	−0.519203	+	0.854651i	$0.673771\pi$
$822$	−40.5623	−1.41477
$823$	11.3404	0.395301	0.197650	−	0.980273i	$-0.436669\pi$
$823$	11.3404	0.395301	0.197650	+	0.980273i	$0.436669\pi$
$824$	47.4832	1.65416
$825$	−29.3229	−1.02089
$826$	−2.65497	−0.0923783
$827$	3.08784	0.107375	0.0536873	−	0.998558i	$-0.482903\pi$
$827$	3.08784	0.107375	0.0536873	+	0.998558i	$0.482903\pi$
$828$	2.14048	0.0743869
$829$	20.1242	0.698941	0.349471	−	0.936947i	$-0.386361\pi$
$829$	20.1242	0.698941	0.349471	+	0.936947i	$0.386361\pi$
$830$	−13.8911	−0.482167
$831$	37.0039	1.28365
$832$	55.6987	1.93100
$833$	3.99437	0.138397
$834$	31.9602	1.10669
$835$	−16.0015	−0.553754
$836$	8.81592	0.304905
$837$	−33.1959	−1.14742
$838$	14.2537	0.492384
$839$	29.8409	1.03022	0.515111	−	0.857123i	$-0.327751\pi$
$839$	29.8409	1.03022	0.515111	+	0.857123i	$0.327751\pi$
$840$	−10.1932	−0.351697
$841$	39.9458	1.37744
$842$	−49.7579	−1.71477
$843$	41.1087	1.41586
$844$	−9.34624	−0.321711
$845$	26.5600	0.913693
$846$	0.791391	0.0272086
$847$	6.60429	0.226926
$848$	20.4515	0.702307
$849$	20.1137	0.690300
$850$	4.87744	0.167295
$851$	−39.3120	−1.34760
$852$	0.392448	0.0134451
$853$	−49.8632	−1.70728	−0.853642	−	0.520861i	$-0.825611\pi$
$853$	−49.8632	−1.70728	−0.853642	+	0.520861i	$0.825611\pi$
$854$	−9.75768	−0.333901
$855$	−2.94854	−0.100838
$856$	−35.3587	−1.20854
$857$	−14.3939	−0.491687	−0.245844	−	0.969310i	$-0.579065\pi$
$857$	−14.3939	−0.491687	−0.245844	+	0.969310i	$0.579065\pi$
$858$	56.4143	1.92595
$859$	5.68484	0.193964	0.0969821	−	0.995286i	$-0.469081\pi$
$859$	5.68484	0.193964	0.0969821	+	0.995286i	$0.469081\pi$
$860$	4.49303	0.153211
$861$	17.0129	0.579799
$862$	45.8518	1.56172
$863$	−23.5098	−0.800283	−0.400141	−	0.916453i	$-0.631039\pi$
$863$	−23.5098	−0.800283	−0.400141	+	0.916453i	$0.631039\pi$
$864$	−12.5107	−0.425623
$865$	16.8750	0.573767
$866$	−20.3009	−0.689854
$867$	1.90981	0.0648605
$868$	−6.47525	−0.219784
$869$	16.3853	0.555833
$870$	19.4848	0.660596
$871$	−43.4162	−1.47110
$872$	−7.10073	−0.240461
$873$	3.09505	0.104752
$874$	36.2333	1.22561
$875$	−15.6648	−0.529567
$876$	13.1339	0.443755
$877$	−41.3451	−1.39612	−0.698062	−	0.716037i	$-0.745954\pi$
$877$	−41.3451	−1.39612	−0.698062	+	0.716037i	$0.745954\pi$
$878$	−3.91681	−0.132186
$879$	19.8684	0.670146
$880$	−10.5725	−0.356398
$881$	5.23910	0.176510	0.0882548	−	0.996098i	$-0.471871\pi$
$881$	5.23910	0.176510	0.0882548	+	0.996098i	$0.471871\pi$
$882$	−3.16111	−0.106440
$883$	−56.6195	−1.90540	−0.952698	−	0.303918i	$-0.901705\pi$
$883$	−56.6195	−1.90540	−0.952698	+	0.303918i	$0.901705\pi$
$884$	3.17421	0.106760
$885$	−2.40462	−0.0808305
$886$	−18.9229	−0.635726
$887$	−30.6309	−1.02849	−0.514243	−	0.857645i	$-0.671927\pi$
$887$	−30.6309	−1.02849	−0.514243	+	0.857645i	$0.671927\pi$
$888$	−35.1595	−1.17988
$889$	10.7760	0.361415
$890$	−2.08843	−0.0700043
$891$	−40.4957	−1.35666
$892$	11.4467	0.383265
$893$	−4.53158	−0.151644
$894$	−12.3910	−0.414417
$895$	3.55450	0.118814
$896$	9.14581	0.305540
$897$	−78.4318	−2.61876
$898$	2.70608	0.0903029
$899$	61.3472	2.04604
$900$	1.30571	0.0435235
$901$	7.48214	0.249266
$902$	24.1732	0.804880
$903$	−29.2778	−0.974306
$904$	16.4823	0.548192
$905$	11.5641	0.384405
$906$	−48.2074	−1.60158
$907$	−49.5742	−1.64608	−0.823042	−	0.567981i	$-0.807725\pi$
$907$	−49.5742	−1.64608	−0.823042	+	0.567981i	$0.807725\pi$
$908$	12.5012	0.414866
$909$	0.0516217	0.00171218
$910$	13.3754	0.443390
$911$	30.0568	0.995825	0.497912	−	0.867227i	$-0.334100\pi$
$911$	30.0568	0.995825	0.497912	+	0.867227i	$0.334100\pi$
$912$	23.6559	0.783324
$913$	−43.5064	−1.43985
$914$	13.5604	0.448538
$915$	−8.83759	−0.292162
$916$	−11.3788	−0.375965
$917$	29.3911	0.970580
$918$	5.49272	0.181287
$919$	−23.9339	−0.789507	−0.394754	−	0.918787i	$-0.629170\pi$
$919$	−23.9339	−0.789507	−0.394754	+	0.918787i	$0.629170\pi$
$920$	20.1357	0.663854
$921$	24.5698	0.809603
$922$	−9.27500	−0.305456
$923$	−2.55230	−0.0840101
$924$	−6.44131	−0.211904
$925$	−23.9805	−0.788475
$926$	−39.1783	−1.28748
$927$	−10.0356	−0.329614
$928$	23.1202	0.758958
$929$	35.3970	1.16134	0.580669	−	0.814140i	$-0.302791\pi$
$929$	35.3970	1.16134	0.580669	+	0.814140i	$0.302791\pi$
$930$	17.3373	0.568513
$931$	18.1008	0.593231
$932$	−10.3951	−0.340503
$933$	−17.1322	−0.560885
$934$	11.8880	0.388986
$935$	−3.86792	−0.126495
$936$	−12.4503	−0.406950
$937$	−12.5775	−0.410888	−0.205444	−	0.978669i	$-0.565864\pi$
$937$	−12.5775	−0.410888	−0.205444	+	0.978669i	$0.565864\pi$
$938$	−14.6546	−0.478491
$939$	−41.5709	−1.35661
$940$	−0.508109	−0.0165727
$941$	−44.9868	−1.46653	−0.733263	−	0.679945i	$-0.762004\pi$
$941$	−44.9868	−1.46653	−0.733263	+	0.679945i	$0.762004\pi$
$942$	−10.4658	−0.340993
$943$	−33.6076	−1.09441
$944$	3.42411	0.111445
$945$	−7.82925	−0.254686
$946$	−41.6001	−1.35254
$947$	12.1181	0.393785	0.196892	−	0.980425i	$-0.436915\pi$
$947$	12.1181	0.393785	0.196892	+	0.980425i	$0.436915\pi$
$948$	−4.11077	−0.133512
$949$	−85.4171	−2.77276
$950$	22.1025	0.717101
$951$	40.9084	1.32655
$952$	5.31020	0.172105
$953$	−59.4269	−1.92503	−0.962514	−	0.271233i	$-0.912568\pi$
$953$	−59.4269	−1.92503	−0.962514	+	0.271233i	$0.912568\pi$
$954$	−5.92130	−0.191709
$955$	11.4190	0.369511
$956$	3.63476	0.117557
$957$	61.0257	1.97268
$958$	−17.0827	−0.551916
$959$	−30.1202	−0.972631
$960$	17.0277	0.549565
$961$	23.5860	0.760839
$962$	46.1361	1.48749
$963$	7.47311	0.240818
$964$	7.38505	0.237856
$965$	3.60134	0.115931
$966$	−26.4737	−0.851778
$967$	−9.91157	−0.318735	−0.159367	−	0.987219i	$-0.550945\pi$
$967$	−9.91157	−0.318735	−0.159367	+	0.987219i	$0.550945\pi$
$968$	−11.6681	−0.375028
$969$	8.65445	0.278021
$970$	5.87451	0.188619
$971$	−7.28239	−0.233703	−0.116851	−	0.993149i	$-0.537280\pi$
$971$	−7.28239	−0.233703	−0.116851	+	0.993149i	$0.537280\pi$
$972$	3.34544	0.107305
$973$	23.7325	0.760830
$974$	27.1683	0.870529
$975$	−47.8438	−1.53223
$976$	12.5845	0.402819
$977$	−29.7300	−0.951148	−0.475574	−	0.879676i	$-0.657760\pi$
$977$	−29.7300	−0.951148	−0.475574	+	0.879676i	$0.657760\pi$
$978$	37.8244	1.20949
$979$	−6.54089	−0.209048
$980$	2.02958	0.0648325
$981$	1.50075	0.0479152
$982$	−3.31557	−0.105804
$983$	1.89993	0.0605985	0.0302992	−	0.999541i	$-0.490354\pi$
$983$	1.89993	0.0605985	0.0302992	+	0.999541i	$0.490354\pi$
$984$	−30.0577	−0.958203
$985$	10.6906	0.340630
$986$	−10.1507	−0.323265
$987$	3.31098	0.105390
$988$	14.3842	0.457623
$989$	57.8358	1.83907
$990$	3.06104	0.0972862
$991$	−53.2814	−1.69254	−0.846270	−	0.532755i	$-0.821157\pi$
$991$	−53.2814	−1.69254	−0.846270	+	0.532755i	$0.821157\pi$
$992$	20.5721	0.653165
$993$	23.2255	0.737039
$994$	−0.861500	−0.0273251
$995$	−24.9847	−0.792068
$996$	10.9150	0.345854
$997$	34.3073	1.08652	0.543261	−	0.839564i	$-0.317189\pi$
$997$	34.3073	1.08652	0.543261	+	0.839564i	$0.317189\pi$
$998$	−34.7083	−1.09867
$999$	−27.0056	−0.854421

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	799.2.a.g.1.14	✓	20
3.2	odd	2		7191.2.a.bb.1.7		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
799.2.a.g.1.14	✓	20	1.1	even	1	trivial
7191.2.a.bb.1.7		20	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)

\(f(q)\)	\(=\)	\(q+1.22248 q^{2} +1.90981 q^{3} -0.505532 q^{4} +1.00510 q^{5} +2.33471 q^{6} +1.73367 q^{7} -3.06297 q^{8} +0.647363 q^{9} +O(q^{10})\)	\(q+1.22248 q^{2} +1.90981 q^{3} -0.505532 q^{4} +1.00510 q^{5} +2.33471 q^{6} +1.73367 q^{7} -3.06297 q^{8} +0.647363 q^{9} +1.22872 q^{10} +3.84830 q^{11} -0.965468 q^{12} +6.27896 q^{13} +2.11939 q^{14} +1.91954 q^{15} -2.73337 q^{16} -1.00000 q^{17} +0.791391 q^{18} -4.53158 q^{19} -0.508109 q^{20} +3.31098 q^{21} +4.70449 q^{22} -6.54056 q^{23} -5.84969 q^{24} -3.98978 q^{25} +7.67593 q^{26} -4.49308 q^{27} -0.876427 q^{28} +8.30336 q^{29} +2.34661 q^{30} +7.38823 q^{31} +2.78444 q^{32} +7.34951 q^{33} -1.22248 q^{34} +1.74251 q^{35} -0.327263 q^{36} +6.01049 q^{37} -5.53979 q^{38} +11.9916 q^{39} -3.07859 q^{40} +5.13833 q^{41} +4.04763 q^{42} -8.84264 q^{43} -1.94544 q^{44} +0.650664 q^{45} -7.99573 q^{46} +1.00000 q^{47} -5.22022 q^{48} -3.99437 q^{49} -4.87744 q^{50} -1.90981 q^{51} -3.17421 q^{52} -7.48214 q^{53} -5.49272 q^{54} +3.86792 q^{55} -5.31020 q^{56} -8.65445 q^{57} +10.1507 q^{58} -1.25271 q^{59} -0.970390 q^{60} -4.60400 q^{61} +9.03200 q^{62} +1.12232 q^{63} +8.87068 q^{64} +6.31097 q^{65} +8.98466 q^{66} -6.91456 q^{67} +0.505532 q^{68} -12.4912 q^{69} +2.13019 q^{70} -0.406485 q^{71} -1.98286 q^{72} -13.6037 q^{73} +7.34773 q^{74} -7.61971 q^{75} +2.29086 q^{76} +6.67170 q^{77} +14.6595 q^{78} +4.25780 q^{79} -2.74731 q^{80} -10.5230 q^{81} +6.28153 q^{82} -11.3054 q^{83} -1.67381 q^{84} -1.00510 q^{85} -10.8100 q^{86} +15.8578 q^{87} -11.7872 q^{88} -1.69968 q^{89} +0.795426 q^{90} +10.8857 q^{91} +3.30646 q^{92} +14.1101 q^{93} +1.22248 q^{94} -4.55469 q^{95} +5.31774 q^{96} +4.78101 q^{97} -4.88306 q^{98} +2.49125 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{2} + 3 q^{3} + 24 q^{4} + 13 q^{5} + 11 q^{6} - 3 q^{7} + 12 q^{8} + 37 q^{9}+O(q^{10}) \) 20 * q + 4 * q^2 + 3 * q^3 + 24 * q^4 + 13 * q^5 + 11 * q^6 - 3 * q^7 + 12 * q^8 + 37 * q^9	\( 20 q + 4 q^{2} + 3 q^{3} + 24 q^{4} + 13 q^{5} + 11 q^{6} - 3 q^{7} + 12 q^{8} + 37 q^{9} - 2 q^{10} + 10 q^{11} + 8 q^{12} + q^{13} + 13 q^{14} + q^{15} + 28 q^{16} - 20 q^{17} + 15 q^{18} + 5 q^{19} + 37 q^{20} + 6 q^{21} - 19 q^{22} + 4 q^{23} + 30 q^{24} + 41 q^{25} - 9 q^{26} + 6 q^{27} - 25 q^{28} + 26 q^{29} - 25 q^{30} + 6 q^{31} + 28 q^{32} + 29 q^{33} - 4 q^{34} + 21 q^{35} - 5 q^{36} - 8 q^{37} - 21 q^{38} - 19 q^{39} - 25 q^{40} + 69 q^{41} + 3 q^{42} - 7 q^{43} + 16 q^{44} + 39 q^{45} - 24 q^{46} + 20 q^{47} + 26 q^{48} + 53 q^{49} + 16 q^{50} - 3 q^{51} + 18 q^{52} + 29 q^{53} + 23 q^{54} + 5 q^{55} - 22 q^{56} - 36 q^{57} - q^{58} + 55 q^{59} - 103 q^{60} - 17 q^{61} - 7 q^{62} - 9 q^{63} + 58 q^{64} + 40 q^{65} + 50 q^{66} - 6 q^{67} - 24 q^{68} + 17 q^{69} - 15 q^{70} + 47 q^{71} + 7 q^{72} - 32 q^{73} - 67 q^{74} - 22 q^{75} - 5 q^{76} + 4 q^{77} - 60 q^{78} - 26 q^{79} + 108 q^{80} + 68 q^{81} + 25 q^{82} + 3 q^{83} + 24 q^{84} - 13 q^{85} + 8 q^{86} - 41 q^{87} - 47 q^{88} + 119 q^{89} - 54 q^{90} - 35 q^{91} - 15 q^{93} + 4 q^{94} - 48 q^{95} - 84 q^{96} - 13 q^{97} + q^{98} - 5 q^{99}+O(q^{100}) \) 20 * q + 4 * q^2 + 3 * q^3 + 24 * q^4 + 13 * q^5 + 11 * q^6 - 3 * q^7 + 12 * q^8 + 37 * q^9 - 2 * q^10 + 10 * q^11 + 8 * q^12 + q^13 + 13 * q^14 + q^15 + 28 * q^16 - 20 * q^17 + 15 * q^18 + 5 * q^19 + 37 * q^20 + 6 * q^21 - 19 * q^22 + 4 * q^23 + 30 * q^24 + 41 * q^25 - 9 * q^26 + 6 * q^27 - 25 * q^28 + 26 * q^29 - 25 * q^30 + 6 * q^31 + 28 * q^32 + 29 * q^33 - 4 * q^34 + 21 * q^35 - 5 * q^36 - 8 * q^37 - 21 * q^38 - 19 * q^39 - 25 * q^40 + 69 * q^41 + 3 * q^42 - 7 * q^43 + 16 * q^44 + 39 * q^45 - 24 * q^46 + 20 * q^47 + 26 * q^48 + 53 * q^49 + 16 * q^50 - 3 * q^51 + 18 * q^52 + 29 * q^53 + 23 * q^54 + 5 * q^55 - 22 * q^56 - 36 * q^57 - q^58 + 55 * q^59 - 103 * q^60 - 17 * q^61 - 7 * q^62 - 9 * q^63 + 58 * q^64 + 40 * q^65 + 50 * q^66 - 6 * q^67 - 24 * q^68 + 17 * q^69 - 15 * q^70 + 47 * q^71 + 7 * q^72 - 32 * q^73 - 67 * q^74 - 22 * q^75 - 5 * q^76 + 4 * q^77 - 60 * q^78 - 26 * q^79 + 108 * q^80 + 68 * q^81 + 25 * q^82 + 3 * q^83 + 24 * q^84 - 13 * q^85 + 8 * q^86 - 41 * q^87 - 47 * q^88 + 119 * q^89 - 54 * q^90 - 35 * q^91 - 15 * q^93 + 4 * q^94 - 48 * q^95 - 84 * q^96 - 13 * q^97 + q^98 - 5 * q^99

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