LMFDB - Embedded newform 847.2.a.o.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(1,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, 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("847.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.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:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 11x^{6} + 10x^{5} + 35x^{4} - 30x^{3} - 30x^{2} + 30x - 5 $ x^8 - x^7 - 11x^6 + 10x^5 + 35x^4 - 30x^3 - 30x^2 + 30x - 5
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 77)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-2.43045$ of defining polynomial
Character	$\chi$	$=$	847.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.43045 q^{2} +1.43421 q^{3} +3.90710 q^{4} +1.25863 q^{5} +3.48577 q^{6} -1.00000 q^{7} +4.63512 q^{8} -0.943053 q^{9} +O(q^{10})$	\(q+2.43045 q^{2} +1.43421 q^{3} +3.90710 q^{4} +1.25863 q^{5} +3.48577 q^{6} -1.00000 q^{7} +4.63512 q^{8} -0.943053 q^{9} +3.05904 q^{10} +5.60359 q^{12} +3.17831 q^{13} -2.43045 q^{14} +1.80514 q^{15} +3.45123 q^{16} -5.92418 q^{17} -2.29204 q^{18} -2.86222 q^{19} +4.91760 q^{20} -1.43421 q^{21} +6.76343 q^{23} +6.64771 q^{24} -3.41585 q^{25} +7.72473 q^{26} -5.65515 q^{27} -3.90710 q^{28} -4.49549 q^{29} +4.38730 q^{30} +9.72751 q^{31} -0.882184 q^{32} -14.3984 q^{34} -1.25863 q^{35} -3.68460 q^{36} -5.45495 q^{37} -6.95648 q^{38} +4.55835 q^{39} +5.83390 q^{40} +0.314484 q^{41} -3.48577 q^{42} +0.132562 q^{43} -1.18696 q^{45} +16.4382 q^{46} +9.37505 q^{47} +4.94977 q^{48} +1.00000 q^{49} -8.30206 q^{50} -8.49650 q^{51} +12.4180 q^{52} +4.35192 q^{53} -13.7446 q^{54} -4.63512 q^{56} -4.10501 q^{57} -10.9261 q^{58} -6.94685 q^{59} +7.05285 q^{60} +2.45215 q^{61} +23.6423 q^{62} +0.943053 q^{63} -9.04656 q^{64} +4.00032 q^{65} -9.41987 q^{67} -23.1464 q^{68} +9.70015 q^{69} -3.05904 q^{70} -0.116610 q^{71} -4.37116 q^{72} -0.615032 q^{73} -13.2580 q^{74} -4.89903 q^{75} -11.1830 q^{76} +11.0789 q^{78} -8.52928 q^{79} +4.34382 q^{80} -5.28149 q^{81} +0.764339 q^{82} -0.950532 q^{83} -5.60359 q^{84} -7.45636 q^{85} +0.322186 q^{86} -6.44746 q^{87} +10.0552 q^{89} -2.88484 q^{90} -3.17831 q^{91} +26.4254 q^{92} +13.9513 q^{93} +22.7856 q^{94} -3.60248 q^{95} -1.26523 q^{96} +17.5770 q^{97} +2.43045 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} + 4 q^{3} + 7 q^{4} + 10 q^{5} + q^{6} - 8 q^{7} + 14 q^{9}+O(q^{10}) $ 8 * q - q^2 + 4 * q^3 + 7 * q^4 + 10 * q^5 + q^6 - 8 * q^7 + 14 * q^9	$ 8 q - q^{2} + 4 q^{3} + 7 q^{4} + 10 q^{5} + q^{6} - 8 q^{7} + 14 q^{9} - 6 q^{10} + 9 q^{12} + 6 q^{13} + q^{14} + 11 q^{15} + q^{16} + 5 q^{17} - 8 q^{18} + 13 q^{19} + 23 q^{20} - 4 q^{21} + 16 q^{23} + 10 q^{24} + 16 q^{25} - 6 q^{26} + 10 q^{27} - 7 q^{28} - 9 q^{29} + 36 q^{30} + 9 q^{31} - 16 q^{32} - 12 q^{34} - 10 q^{35} - 14 q^{36} + 7 q^{37} - 10 q^{38} - 13 q^{39} - 5 q^{40} + 10 q^{41} - q^{42} + 4 q^{43} + 35 q^{45} - 4 q^{46} + 16 q^{47} - 3 q^{48} + 8 q^{49} - 6 q^{50} - 13 q^{51} + 41 q^{52} + 37 q^{53} - 30 q^{54} - 2 q^{57} - 15 q^{58} + q^{59} + 5 q^{60} - 19 q^{61} + 18 q^{62} - 14 q^{63} - 4 q^{64} + 4 q^{65} - 19 q^{67} - 9 q^{68} + 20 q^{69} + 6 q^{70} + 13 q^{71} + 35 q^{72} + 25 q^{73} - 33 q^{74} - 13 q^{75} - 26 q^{76} - 29 q^{78} + 4 q^{80} + 8 q^{81} - 13 q^{82} + 25 q^{83} - 9 q^{84} - 3 q^{85} + 4 q^{86} + 36 q^{87} + 37 q^{89} + 2 q^{90} - 6 q^{91} + 35 q^{92} + 21 q^{93} + 42 q^{94} - 21 q^{95} + 6 q^{96} + 15 q^{97} - q^{98}+O(q^{100}) $ 8 * q - q^2 + 4 * q^3 + 7 * q^4 + 10 * q^5 + q^6 - 8 * q^7 + 14 * q^9 - 6 * q^10 + 9 * q^12 + 6 * q^13 + q^14 + 11 * q^15 + q^16 + 5 * q^17 - 8 * q^18 + 13 * q^19 + 23 * q^20 - 4 * q^21 + 16 * q^23 + 10 * q^24 + 16 * q^25 - 6 * q^26 + 10 * q^27 - 7 * q^28 - 9 * q^29 + 36 * q^30 + 9 * q^31 - 16 * q^32 - 12 * q^34 - 10 * q^35 - 14 * q^36 + 7 * q^37 - 10 * q^38 - 13 * q^39 - 5 * q^40 + 10 * q^41 - q^42 + 4 * q^43 + 35 * q^45 - 4 * q^46 + 16 * q^47 - 3 * q^48 + 8 * q^49 - 6 * q^50 - 13 * q^51 + 41 * q^52 + 37 * q^53 - 30 * q^54 - 2 * q^57 - 15 * q^58 + q^59 + 5 * q^60 - 19 * q^61 + 18 * q^62 - 14 * q^63 - 4 * q^64 + 4 * q^65 - 19 * q^67 - 9 * q^68 + 20 * q^69 + 6 * q^70 + 13 * q^71 + 35 * q^72 + 25 * q^73 - 33 * q^74 - 13 * q^75 - 26 * q^76 - 29 * q^78 + 4 * q^80 + 8 * q^81 - 13 * q^82 + 25 * q^83 - 9 * q^84 - 3 * q^85 + 4 * q^86 + 36 * q^87 + 37 * q^89 + 2 * q^90 - 6 * q^91 + 35 * q^92 + 21 * q^93 + 42 * q^94 - 21 * q^95 + 6 * q^96 + 15 * q^97 - q^98

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 $

$2$	2.43045	1.71859	0.859295	−	0.511481i	$-0.170903\pi$
$2$	2.43045	1.71859	0.859295	+	0.511481i	$0.170903\pi$
$3$	1.43421	0.828039	0.414020	−	0.910268i	$-0.364124\pi$
$3$	1.43421	0.828039	0.414020	+	0.910268i	$0.364124\pi$
$4$	3.90710	1.95355
$5$	1.25863	0.562877	0.281438	−	0.959579i	$-0.409188\pi$
$5$	1.25863	0.562877	0.281438	+	0.959579i	$0.409188\pi$
$6$	3.48577	1.42306
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	4.63512	1.63876
$9$	−0.943053	−0.314351
$10$	3.05904	0.967354
$11$	0	0
$11$	0	0
$12$	5.60359	1.61762
$13$	3.17831	0.881504	0.440752	−	0.897629i	$-0.354712\pi$
$13$	3.17831	0.881504	0.440752	+	0.897629i	$0.354712\pi$
$14$	−2.43045	−0.649566
$15$	1.80514	0.466084
$16$	3.45123	0.862807
$17$	−5.92418	−1.43682	−0.718412	−	0.695617i	$-0.755131\pi$
$17$	−5.92418	−1.43682	−0.718412	+	0.695617i	$0.755131\pi$
$18$	−2.29204	−0.540240
$19$	−2.86222	−0.656638	−0.328319	−	0.944567i	$-0.606482\pi$
$19$	−2.86222	−0.656638	−0.328319	+	0.944567i	$0.606482\pi$
$20$	4.91760	1.09961
$21$	−1.43421	−0.312969
$22$	0	0
$23$	6.76343	1.41027	0.705136	−	0.709072i	$-0.250886\pi$
$23$	6.76343	1.41027	0.705136	+	0.709072i	$0.250886\pi$
$24$	6.64771	1.35696
$25$	−3.41585	−0.683170
$26$	7.72473	1.51494
$27$	−5.65515	−1.08833
$28$	−3.90710	−0.738372
$29$	−4.49549	−0.834792	−0.417396	−	0.908725i	$-0.637057\pi$
$29$	−4.49549	−0.834792	−0.417396	+	0.908725i	$0.637057\pi$
$30$	4.38730	0.801008
$31$	9.72751	1.74711	0.873556	−	0.486723i	$-0.161808\pi$
$31$	9.72751	1.74711	0.873556	+	0.486723i	$0.161808\pi$
$32$	−0.882184	−0.155950
$33$	0	0
$34$	−14.3984	−2.46931
$35$	−1.25863	−0.212747
$36$	−3.68460	−0.614100
$37$	−5.45495	−0.896789	−0.448394	−	0.893836i	$-0.648004\pi$
$37$	−5.45495	−0.896789	−0.448394	+	0.893836i	$0.648004\pi$
$38$	−6.95648	−1.12849
$39$	4.55835	0.729920
$40$	5.83390	0.922421
$41$	0.314484	0.0491142	0.0245571	−	0.999698i	$-0.492182\pi$
$41$	0.314484	0.0491142	0.0245571	+	0.999698i	$0.492182\pi$
$42$	−3.48577	−0.537866
$43$	0.132562	0.0202155	0.0101078	−	0.999949i	$-0.496783\pi$
$43$	0.132562	0.0202155	0.0101078	+	0.999949i	$0.496783\pi$
$44$	0	0
$45$	−1.18696	−0.176941
$46$	16.4382	2.42368
$47$	9.37505	1.36749	0.683746	−	0.729720i	$-0.260350\pi$
$47$	9.37505	1.36749	0.683746	+	0.729720i	$0.260350\pi$
$48$	4.94977	0.714438
$49$	1.00000	0.142857
$50$	−8.30206	−1.17409
$51$	−8.49650	−1.18975
$52$	12.4180	1.72206
$53$	4.35192	0.597783	0.298891	−	0.954287i	$-0.403383\pi$
$53$	4.35192	0.597783	0.298891	+	0.954287i	$0.403383\pi$
$54$	−13.7446	−1.87040
$55$	0	0
$56$	−4.63512	−0.619393
$57$	−4.10501	−0.543722
$58$	−10.9261	−1.43466
$59$	−6.94685	−0.904403	−0.452202	−	0.891916i	$-0.649361\pi$
$59$	−6.94685	−0.904403	−0.452202	+	0.891916i	$0.649361\pi$
$60$	7.05285	0.910519
$61$	2.45215	0.313966	0.156983	−	0.987601i	$-0.449823\pi$
$61$	2.45215	0.313966	0.156983	+	0.987601i	$0.449823\pi$
$62$	23.6423	3.00257
$63$	0.943053	0.118813
$64$	−9.04656	−1.13082
$65$	4.00032	0.496179
$66$	0	0
$67$	−9.41987	−1.15082	−0.575410	−	0.817865i	$-0.695158\pi$
$67$	−9.41987	−1.15082	−0.575410	+	0.817865i	$0.695158\pi$
$68$	−23.1464	−2.80691
$69$	9.70015	1.16776
$70$	−3.05904	−0.365626
$71$	−0.116610	−0.0138391	−0.00691954	−	0.999976i	$-0.502203\pi$
$71$	−0.116610	−0.0138391	−0.00691954	+	0.999976i	$0.502203\pi$
$72$	−4.37116	−0.515146
$73$	−0.615032	−0.0719840	−0.0359920	−	0.999352i	$-0.511459\pi$
$73$	−0.615032	−0.0719840	−0.0359920	+	0.999352i	$0.511459\pi$
$74$	−13.2580	−1.54121
$75$	−4.89903	−0.565691
$76$	−11.1830	−1.28277
$77$	0	0
$78$	11.0789	1.25443
$79$	−8.52928	−0.959619	−0.479810	−	0.877373i	$-0.659294\pi$
$79$	−8.52928	−0.959619	−0.479810	+	0.877373i	$0.659294\pi$
$80$	4.34382	0.485654
$81$	−5.28149	−0.586833
$82$	0.764339	0.0844072
$83$	−0.950532	−0.104334	−0.0521672	−	0.998638i	$-0.516613\pi$
$83$	−0.950532	−0.104334	−0.0521672	+	0.998638i	$0.516613\pi$
$84$	−5.60359	−0.611401
$85$	−7.45636	−0.808756
$86$	0.322186	0.0347422
$87$	−6.44746	−0.691241
$88$	0	0
$89$	10.0552	1.06585	0.532923	−	0.846164i	$-0.321094\pi$
$89$	10.0552	1.06585	0.532923	+	0.846164i	$0.321094\pi$
$90$	−2.88484	−0.304089
$91$	−3.17831	−0.333177
$92$	26.4254	2.75504
$93$	13.9513	1.44668
$94$	22.7856	2.35016
$95$	−3.60248	−0.369606
$96$	−1.26523	−0.129132
$97$	17.5770	1.78467	0.892337	−	0.451369i	$-0.149064\pi$
$97$	17.5770	1.78467	0.892337	+	0.451369i	$0.149064\pi$
$98$	2.43045	0.245513
$99$	0	0
$100$	−13.3461	−1.33461
$101$	12.4761	1.24142	0.620711	−	0.784039i	$-0.286844\pi$
$101$	12.4761	1.24142	0.620711	+	0.784039i	$0.286844\pi$
$102$	−20.6503	−2.04469
$103$	8.21802	0.809746	0.404873	−	0.914373i	$-0.367316\pi$
$103$	8.21802	0.809746	0.404873	+	0.914373i	$0.367316\pi$
$104$	14.7318	1.44457
$105$	−1.80514	−0.176163
$106$	10.5771	1.02734
$107$	−12.1885	−1.17831	−0.589154	−	0.808020i	$-0.700539\pi$
$107$	−12.1885	−1.17831	−0.589154	+	0.808020i	$0.700539\pi$
$108$	−22.0952	−2.12612
$109$	−0.886088	−0.0848718	−0.0424359	−	0.999099i	$-0.513512\pi$
$109$	−0.886088	−0.0848718	−0.0424359	+	0.999099i	$0.513512\pi$
$110$	0	0
$111$	−7.82353	−0.742577
$112$	−3.45123	−0.326110
$113$	4.54502	0.427559	0.213780	−	0.976882i	$-0.431423\pi$
$113$	4.54502	0.427559	0.213780	+	0.976882i	$0.431423\pi$
$114$	−9.97703	−0.934435
$115$	8.51266	0.793810
$116$	−17.5643	−1.63081
$117$	−2.99731	−0.277102
$118$	−16.8840	−1.55430
$119$	5.92418	0.543069
$120$	8.36702	0.763801
$121$	0	0
$122$	5.95984	0.539579
$123$	0.451035	0.0406685
$124$	38.0064	3.41307
$125$	−10.5924	−0.947417
$126$	2.29204	0.204192
$127$	8.02779	0.712351	0.356175	−	0.934419i	$-0.384081\pi$
$127$	8.02779	0.712351	0.356175	+	0.934419i	$0.384081\pi$
$128$	−20.2229	−1.78747
$129$	0.190121	0.0167392
$130$	9.72259	0.852727
$131$	−0.101461	−0.00886466	−0.00443233	−	0.999990i	$-0.501411\pi$
$131$	−0.101461	−0.00886466	−0.00443233	+	0.999990i	$0.501411\pi$
$132$	0	0
$133$	2.86222	0.248186
$134$	−22.8945	−1.97779
$135$	−7.11775	−0.612598
$136$	−27.4593	−2.35461
$137$	−4.56409	−0.389937	−0.194968	−	0.980810i	$-0.562460\pi$
$137$	−4.56409	−0.389937	−0.194968	+	0.980810i	$0.562460\pi$
$138$	23.5758	2.00690
$139$	3.82533	0.324460	0.162230	−	0.986753i	$-0.448131\pi$
$139$	3.82533	0.324460	0.162230	+	0.986753i	$0.448131\pi$
$140$	−4.91760	−0.415613
$141$	13.4458	1.13234
$142$	−0.283415	−0.0237837
$143$	0	0
$144$	−3.25469	−0.271224
$145$	−5.65817	−0.469885
$146$	−1.49480	−0.123711
$147$	1.43421	0.118291
$148$	−21.3130	−1.75192
$149$	4.87223	0.399149	0.199574	−	0.979883i	$-0.436044\pi$
$149$	4.87223	0.399149	0.199574	+	0.979883i	$0.436044\pi$
$150$	−11.9069	−0.972191
$151$	16.9739	1.38131	0.690657	−	0.723183i	$-0.257322\pi$
$151$	16.9739	1.38131	0.690657	+	0.723183i	$0.257322\pi$
$152$	−13.2667	−1.07607
$153$	5.58681	0.451667
$154$	0	0
$155$	12.2434	0.983410
$156$	17.8099	1.42594
$157$	2.24483	0.179157	0.0895785	−	0.995980i	$-0.471448\pi$
$157$	2.24483	0.179157	0.0895785	+	0.995980i	$0.471448\pi$
$158$	−20.7300	−1.64919
$159$	6.24156	0.494988
$160$	−1.11034	−0.0877804
$161$	−6.76343	−0.533033
$162$	−12.8364	−1.00852
$163$	−15.8372	−1.24047	−0.620235	−	0.784416i	$-0.712963\pi$
$163$	−15.8372	−1.24047	−0.620235	+	0.784416i	$0.712963\pi$
$164$	1.22872	0.0959470
$165$	0	0
$166$	−2.31022	−0.179308
$167$	−20.7416	−1.60503	−0.802515	−	0.596632i	$-0.796505\pi$
$167$	−20.7416	−1.60503	−0.802515	+	0.596632i	$0.796505\pi$
$168$	−6.64771	−0.512882
$169$	−2.89835	−0.222950
$170$	−18.1223	−1.38992
$171$	2.69922	0.206415
$172$	0.517933	0.0394920
$173$	21.5554	1.63883	0.819414	−	0.573202i	$-0.194299\pi$
$173$	21.5554	1.63883	0.819414	+	0.573202i	$0.194299\pi$
$174$	−15.6703	−1.18796
$175$	3.41585	0.258214
$176$	0	0
$177$	−9.96322	−0.748881
$178$	24.4386	1.83175
$179$	4.78161	0.357394	0.178697	−	0.983904i	$-0.442812\pi$
$179$	4.78161	0.357394	0.178697	+	0.983904i	$0.442812\pi$
$180$	−4.63755	−0.345663
$181$	−7.85284	−0.583697	−0.291849	−	0.956465i	$-0.594270\pi$
$181$	−7.85284	−0.583697	−0.291849	+	0.956465i	$0.594270\pi$
$182$	−7.72473	−0.572595
$183$	3.51689	0.259976
$184$	31.3493	2.31110
$185$	−6.86578	−0.504782
$186$	33.9079	2.48625
$187$	0	0
$188$	36.6293	2.67146
$189$	5.65515	0.411352
$190$	−8.75565	−0.635201
$191$	−8.83029	−0.638937	−0.319469	−	0.947597i	$-0.603504\pi$
$191$	−8.83029	−0.638937	−0.319469	+	0.947597i	$0.603504\pi$
$192$	−12.9746	−0.936364
$193$	−25.6023	−1.84289	−0.921446	−	0.388507i	$-0.872991\pi$
$193$	−25.6023	−1.84289	−0.921446	+	0.388507i	$0.872991\pi$
$194$	42.7201	3.06712
$195$	5.73728	0.410855
$196$	3.90710	0.279079
$197$	11.1977	0.797802	0.398901	−	0.916994i	$-0.369392\pi$
$197$	11.1977	0.797802	0.398901	+	0.916994i	$0.369392\pi$
$198$	0	0
$199$	−12.2503	−0.868400	−0.434200	−	0.900817i	$-0.642969\pi$
$199$	−12.2503	−0.868400	−0.434200	+	0.900817i	$0.642969\pi$
$200$	−15.8328	−1.11955
$201$	−13.5100	−0.952924
$202$	30.3227	2.13350
$203$	4.49549	0.315522
$204$	−33.1967	−2.32423
$205$	0.395820	0.0276453
$206$	19.9735	1.39162
$207$	−6.37827	−0.443320
$208$	10.9691	0.760568
$209$	0	0
$210$	−4.38730	−0.302752
$211$	14.2636	0.981946	0.490973	−	0.871175i	$-0.336641\pi$
$211$	14.2636	0.981946	0.490973	+	0.871175i	$0.336641\pi$
$212$	17.0034	1.16780
$213$	−0.167243	−0.0114593
$214$	−29.6236	−2.02503
$215$	0.166847	0.0113788
$216$	−26.2123	−1.78352
$217$	−9.72751	−0.660347
$218$	−2.15359	−0.145860
$219$	−0.882082	−0.0596056
$220$	0	0
$221$	−18.8289	−1.26657
$222$	−19.0147	−1.27618
$223$	−2.96400	−0.198484	−0.0992421	−	0.995063i	$-0.531642\pi$
$223$	−2.96400	−0.198484	−0.0992421	+	0.995063i	$0.531642\pi$
$224$	0.882184	0.0589434
$225$	3.22132	0.214755
$226$	11.0465	0.734799
$227$	−8.25605	−0.547974	−0.273987	−	0.961733i	$-0.588342\pi$
$227$	−8.25605	−0.547974	−0.273987	+	0.961733i	$0.588342\pi$
$228$	−16.0387	−1.06219
$229$	13.1081	0.866208	0.433104	−	0.901344i	$-0.357418\pi$
$229$	13.1081	0.866208	0.433104	+	0.901344i	$0.357418\pi$
$230$	20.6896	1.36423
$231$	0	0
$232$	−20.8371	−1.36802
$233$	12.8277	0.840369	0.420185	−	0.907439i	$-0.361965\pi$
$233$	12.8277	0.840369	0.420185	+	0.907439i	$0.361965\pi$
$234$	−7.28483	−0.476224
$235$	11.7997	0.769730
$236$	−27.1420	−1.76680
$237$	−12.2328	−0.794603
$238$	14.3984	0.933312
$239$	4.98109	0.322200	0.161100	−	0.986938i	$-0.448496\pi$
$239$	4.98109	0.322200	0.161100	+	0.986938i	$0.448496\pi$
$240$	6.22994	0.402141
$241$	2.62686	0.169211	0.0846053	−	0.996415i	$-0.473037\pi$
$241$	2.62686	0.169211	0.0846053	+	0.996415i	$0.473037\pi$
$242$	0	0
$243$	9.39070	0.602414
$244$	9.58081	0.613349
$245$	1.25863	0.0804110
$246$	1.09622	0.0698924
$247$	−9.09701	−0.578829
$248$	45.0881	2.86310
$249$	−1.36326	−0.0863930
$250$	−25.7444	−1.62822
$251$	−26.2229	−1.65518	−0.827588	−	0.561337i	$-0.810287\pi$
$251$	−26.2229	−1.65518	−0.827588	+	0.561337i	$0.810287\pi$
$252$	3.68460	0.232108
$253$	0	0
$254$	19.5112	1.22424
$255$	−10.6940	−0.669681
$256$	−31.0576	−1.94110
$257$	29.9518	1.86834	0.934170	−	0.356827i	$-0.116141\pi$
$257$	29.9518	1.86834	0.934170	+	0.356827i	$0.116141\pi$
$258$	0.462081	0.0287679
$259$	5.45495	0.338954
$260$	15.6296	0.969309
$261$	4.23949	0.262418
$262$	−0.246595	−0.0152347
$263$	−3.33709	−0.205774	−0.102887	−	0.994693i	$-0.532808\pi$
$263$	−3.33709	−0.205774	−0.102887	+	0.994693i	$0.532808\pi$
$264$	0	0
$265$	5.47747	0.336478
$266$	6.95648	0.426529
$267$	14.4212	0.882562
$268$	−36.8044	−2.24818
$269$	−1.73581	−0.105834	−0.0529172	−	0.998599i	$-0.516852\pi$
$269$	−1.73581	−0.105834	−0.0529172	+	0.998599i	$0.516852\pi$
$270$	−17.2994	−1.05280
$271$	2.47596	0.150404	0.0752019	−	0.997168i	$-0.476040\pi$
$271$	2.47596	0.150404	0.0752019	+	0.997168i	$0.476040\pi$
$272$	−20.4457	−1.23970
$273$	−4.55835	−0.275884
$274$	−11.0928	−0.670141
$275$	0	0
$276$	37.8995	2.28128
$277$	−5.15571	−0.309776	−0.154888	−	0.987932i	$-0.549502\pi$
$277$	−5.15571	−0.309776	−0.154888	+	0.987932i	$0.549502\pi$
$278$	9.29728	0.557614
$279$	−9.17356	−0.549206
$280$	−5.83390	−0.348642
$281$	22.5705	1.34644	0.673222	−	0.739441i	$-0.264910\pi$
$281$	22.5705	1.34644	0.673222	+	0.739441i	$0.264910\pi$
$282$	32.6793	1.94602
$283$	8.48757	0.504534	0.252267	−	0.967658i	$-0.418824\pi$
$283$	8.48757	0.504534	0.252267	+	0.967658i	$0.418824\pi$
$284$	−0.455608	−0.0270353
$285$	−5.16669	−0.306049
$286$	0	0
$287$	−0.314484	−0.0185634
$288$	0.831946	0.0490229
$289$	18.0959	1.06447
$290$	−13.7519	−0.807540
$291$	25.2090	1.47778
$292$	−2.40299	−0.140624
$293$	−24.6261	−1.43867	−0.719336	−	0.694662i	$-0.755554\pi$
$293$	−24.6261	−1.43867	−0.719336	+	0.694662i	$0.755554\pi$
$294$	3.48577	0.203294
$295$	−8.74353	−0.509068
$296$	−25.2843	−1.46962
$297$	0	0
$298$	11.8417	0.685973
$299$	21.4963	1.24316
$300$	−19.1410	−1.10511
$301$	−0.132562	−0.00764075
$302$	41.2542	2.37391
$303$	17.8934	1.02795
$304$	−9.87817	−0.566552
$305$	3.08636	0.176724
$306$	13.5785	0.776230
$307$	−4.59391	−0.262188	−0.131094	−	0.991370i	$-0.541849\pi$
$307$	−4.59391	−0.262188	−0.131094	+	0.991370i	$0.541849\pi$
$308$	0	0
$309$	11.7863	0.670502
$310$	29.7569	1.69008
$311$	−2.21073	−0.125359	−0.0626796	−	0.998034i	$-0.519965\pi$
$311$	−2.21073	−0.125359	−0.0626796	+	0.998034i	$0.519965\pi$
$312$	21.1285	1.19616
$313$	−9.69928	−0.548236	−0.274118	−	0.961696i	$-0.588386\pi$
$313$	−9.69928	−0.548236	−0.274118	+	0.961696i	$0.588386\pi$
$314$	5.45595	0.307897
$315$	1.18696	0.0668774
$316$	−33.3248	−1.87466
$317$	6.45539	0.362571	0.181286	−	0.983431i	$-0.441974\pi$
$317$	6.45539	0.362571	0.181286	+	0.983431i	$0.441974\pi$
$318$	15.1698	0.850680
$319$	0	0
$320$	−11.3863	−0.636513
$321$	−17.4809	−0.975686
$322$	−16.4382	−0.916065
$323$	16.9563	0.943474
$324$	−20.6353	−1.14641
$325$	−10.8566	−0.602217
$326$	−38.4917	−2.13186
$327$	−1.27083	−0.0702772
$328$	1.45767	0.0804864
$329$	−9.37505	−0.516863
$330$	0	0
$331$	3.62076	0.199015	0.0995075	−	0.995037i	$-0.468273\pi$
$331$	3.62076	0.199015	0.0995075	+	0.995037i	$0.468273\pi$
$332$	−3.71382	−0.203823
$333$	5.14431	0.281906
$334$	−50.4114	−2.75839
$335$	−11.8561	−0.647770
$336$	−4.94977	−0.270032
$337$	6.40510	0.348908	0.174454	−	0.984665i	$-0.444184\pi$
$337$	6.40510	0.348908	0.174454	+	0.984665i	$0.444184\pi$
$338$	−7.04430	−0.383159
$339$	6.51849	0.354036
$340$	−29.1327	−1.57994
$341$	0	0
$342$	6.56033	0.354742
$343$	−1.00000	−0.0539949
$344$	0.614440	0.0331284
$345$	12.2089	0.657306
$346$	52.3894	2.81647
$347$	17.4600	0.937302	0.468651	−	0.883383i	$-0.344740\pi$
$347$	17.4600	0.937302	0.468651	+	0.883383i	$0.344740\pi$
$348$	−25.1909	−1.35037
$349$	21.6249	1.15755	0.578777	−	0.815486i	$-0.303530\pi$
$349$	21.6249	1.15755	0.578777	+	0.815486i	$0.303530\pi$
$350$	8.30206	0.443764
$351$	−17.9738	−0.959371
$352$	0	0
$353$	4.40150	0.234268	0.117134	−	0.993116i	$-0.462629\pi$
$353$	4.40150	0.234268	0.117134	+	0.993116i	$0.462629\pi$
$354$	−24.2151	−1.28702
$355$	−0.146769	−0.00778970
$356$	39.2865	2.08218
$357$	8.49650	0.449682
$358$	11.6215	0.614214
$359$	10.6817	0.563760	0.281880	−	0.959450i	$-0.409042\pi$
$359$	10.6817	0.563760	0.281880	+	0.959450i	$0.409042\pi$
$360$	−5.50167	−0.289964
$361$	−10.8077	−0.568827
$362$	−19.0860	−1.00314
$363$	0	0
$364$	−12.4180	−0.650879
$365$	−0.774098	−0.0405181
$366$	8.54765	0.446793
$367$	10.2167	0.533309	0.266655	−	0.963792i	$-0.414082\pi$
$367$	10.2167	0.533309	0.266655	+	0.963792i	$0.414082\pi$
$368$	23.3421	1.21679
$369$	−0.296575	−0.0154391
$370$	−16.6869	−0.867513
$371$	−4.35192	−0.225941
$372$	54.5090	2.82616
$373$	27.8851	1.44383	0.721917	−	0.691980i	$-0.243261\pi$
$373$	27.8851	1.44383	0.721917	+	0.691980i	$0.243261\pi$
$374$	0	0
$375$	−15.1918	−0.784499
$376$	43.4544	2.24099
$377$	−14.2881	−0.735873
$378$	13.7446	0.706945
$379$	1.14803	0.0589703	0.0294852	−	0.999565i	$-0.490613\pi$
$379$	1.14803	0.0589703	0.0294852	+	0.999565i	$0.490613\pi$
$380$	−14.0752	−0.722044
$381$	11.5135	0.589855
$382$	−21.4616	−1.09807
$383$	−19.9516	−1.01948	−0.509740	−	0.860328i	$-0.670258\pi$
$383$	−19.9516	−1.01948	−0.509740	+	0.860328i	$0.670258\pi$
$384$	−29.0038	−1.48009
$385$	0	0
$386$	−62.2251	−3.16717
$387$	−0.125013	−0.00635476
$388$	68.6751	3.48645
$389$	2.60000	0.131825	0.0659127	−	0.997825i	$-0.479004\pi$
$389$	2.60000	0.131825	0.0659127	+	0.997825i	$0.479004\pi$
$390$	13.9442	0.706092
$391$	−40.0678	−2.02631
$392$	4.63512	0.234109
$393$	−0.145516	−0.00734029
$394$	27.2154	1.37109
$395$	−10.7352	−0.540148
$396$	0	0
$397$	8.77237	0.440272	0.220136	−	0.975469i	$-0.429350\pi$
$397$	8.77237	0.440272	0.220136	+	0.975469i	$0.429350\pi$
$398$	−29.7737	−1.49242
$399$	4.10501	0.205508
$400$	−11.7889	−0.589444
$401$	28.3535	1.41591	0.707953	−	0.706260i	$-0.249619\pi$
$401$	28.3535	1.41591	0.707953	+	0.706260i	$0.249619\pi$
$402$	−32.8355	−1.63769
$403$	30.9170	1.54009
$404$	48.7455	2.42518
$405$	−6.64745	−0.330315
$406$	10.9261	0.542252
$407$	0	0
$408$	−39.3822	−1.94971
$409$	−19.9055	−0.984264	−0.492132	−	0.870521i	$-0.663782\pi$
$409$	−19.9055	−0.984264	−0.492132	+	0.870521i	$0.663782\pi$
$410$	0.962021	0.0475108
$411$	−6.54585	−0.322883
$412$	32.1086	1.58188
$413$	6.94685	0.341832
$414$	−15.5021	−0.761886
$415$	−1.19637	−0.0587275
$416$	−2.80385	−0.137470
$417$	5.48631	0.268666
$418$	0	0
$419$	−30.8957	−1.50935	−0.754676	−	0.656097i	$-0.772206\pi$
$419$	−30.8957	−1.50935	−0.754676	+	0.656097i	$0.772206\pi$
$420$	−7.05285	−0.344144
$421$	−24.1931	−1.17910	−0.589551	−	0.807732i	$-0.700695\pi$
$421$	−24.1931	−1.17910	−0.589551	+	0.807732i	$0.700695\pi$
$422$	34.6670	1.68756
$423$	−8.84117	−0.429872
$424$	20.1717	0.979623
$425$	20.2361	0.981595
$426$	−0.406476	−0.0196938
$427$	−2.45215	−0.118668
$428$	−47.6218	−2.30188
$429$	0	0
$430$	0.405513	0.0195556
$431$	−19.4001	−0.934468	−0.467234	−	0.884134i	$-0.654749\pi$
$431$	−19.4001	−0.934468	−0.467234	+	0.884134i	$0.654749\pi$
$432$	−19.5172	−0.939022
$433$	−21.3877	−1.02783	−0.513914	−	0.857842i	$-0.671805\pi$
$433$	−21.3877	−1.02783	−0.513914	+	0.857842i	$0.671805\pi$
$434$	−23.6423	−1.13486
$435$	−8.11498	−0.389083
$436$	−3.46203	−0.165801
$437$	−19.3584	−0.926038
$438$	−2.14386	−0.102438
$439$	31.7315	1.51446	0.757232	−	0.653146i	$-0.226551\pi$
$439$	31.7315	1.51446	0.757232	+	0.653146i	$0.226551\pi$
$440$	0	0
$441$	−0.943053	−0.0449073
$442$	−45.7627	−2.17671
$443$	−1.66610	−0.0791590	−0.0395795	−	0.999216i	$-0.512602\pi$
$443$	−1.66610	−0.0791590	−0.0395795	+	0.999216i	$0.512602\pi$
$444$	−30.5673	−1.45066
$445$	12.6557	0.599940
$446$	−7.20386	−0.341113
$447$	6.98779	0.330511
$448$	9.04656	0.427410
$449$	−17.1858	−0.811047	−0.405524	−	0.914085i	$-0.632911\pi$
$449$	−17.1858	−0.811047	−0.405524	+	0.914085i	$0.632911\pi$
$450$	7.82927	0.369076
$451$	0	0
$452$	17.7578	0.835258
$453$	24.3440	1.14378
$454$	−20.0659	−0.941742
$455$	−4.00032	−0.187538
$456$	−19.0272	−0.891030
$457$	−10.2206	−0.478101	−0.239051	−	0.971007i	$-0.576836\pi$
$457$	−10.2206	−0.478101	−0.239051	+	0.971007i	$0.576836\pi$
$458$	31.8586	1.48866
$459$	33.5021	1.56375
$460$	33.2598	1.55075
$461$	22.1160	1.03004	0.515022	−	0.857177i	$-0.327784\pi$
$461$	22.1160	1.03004	0.515022	+	0.857177i	$0.327784\pi$
$462$	0	0
$463$	−30.3717	−1.41149	−0.705747	−	0.708464i	$-0.749389\pi$
$463$	−30.3717	−1.41149	−0.705747	+	0.708464i	$0.749389\pi$
$464$	−15.5150	−0.720265
$465$	17.5595	0.814302
$466$	31.1771	1.44425
$467$	25.1909	1.16570	0.582848	−	0.812581i	$-0.301938\pi$
$467$	25.1909	1.16570	0.582848	+	0.812581i	$0.301938\pi$
$468$	−11.7108	−0.541332
$469$	9.41987	0.434969
$470$	28.6787	1.32285
$471$	3.21955	0.148349
$472$	−32.1995	−1.48210
$473$	0	0
$474$	−29.7311	−1.36560
$475$	9.77690	0.448595
$476$	23.1464	1.06091
$477$	−4.10409	−0.187913
$478$	12.1063	0.553729
$479$	21.2040	0.968835	0.484417	−	0.874837i	$-0.339032\pi$
$479$	21.2040	0.968835	0.484417	+	0.874837i	$0.339032\pi$
$480$	−1.59246	−0.0726856
$481$	−17.3375	−0.790523
$482$	6.38445	0.290804
$483$	−9.70015	−0.441372
$484$	0	0
$485$	22.1230	1.00455
$486$	22.8237	1.03530
$487$	−16.8198	−0.762176	−0.381088	−	0.924539i	$-0.624451\pi$
$487$	−16.8198	−0.762176	−0.381088	+	0.924539i	$0.624451\pi$
$488$	11.3660	0.514515
$489$	−22.7139	−1.02716
$490$	3.05904	0.138193
$491$	−4.83804	−0.218338	−0.109169	−	0.994023i	$-0.534819\pi$
$491$	−4.83804	−0.218338	−0.109169	+	0.994023i	$0.534819\pi$
$492$	1.76224	0.0794479
$493$	26.6321	1.19945
$494$	−22.1099	−0.994770
$495$	0	0
$496$	33.5719	1.50742
$497$	0.116610	0.00523068
$498$	−3.31334	−0.148474
$499$	30.5836	1.36911	0.684554	−	0.728962i	$-0.259997\pi$
$499$	30.5836	1.36911	0.684554	+	0.728962i	$0.259997\pi$
$500$	−41.3858	−1.85083
$501$	−29.7477	−1.32903
$502$	−63.7335	−2.84457
$503$	28.2407	1.25919	0.629594	−	0.776924i	$-0.283221\pi$
$503$	28.2407	1.25919	0.629594	+	0.776924i	$0.283221\pi$
$504$	4.37116	0.194707
$505$	15.7029	0.698768
$506$	0	0
$507$	−4.15683	−0.184611
$508$	31.3654	1.39161
$509$	−4.20065	−0.186190	−0.0930952	−	0.995657i	$-0.529676\pi$
$509$	−4.20065	−0.186190	−0.0930952	+	0.995657i	$0.529676\pi$
$510$	−25.9912	−1.15091
$511$	0.615032	0.0272074
$512$	−35.0383	−1.54849
$513$	16.1863	0.714641
$514$	72.7964	3.21091
$515$	10.3435	0.455787
$516$	0.742823	0.0327009
$517$	0	0
$518$	13.2580	0.582523
$519$	30.9149	1.35701
$520$	18.5419	0.813118
$521$	−20.6470	−0.904560	−0.452280	−	0.891876i	$-0.649389\pi$
$521$	−20.6470	−0.904560	−0.452280	+	0.891876i	$0.649389\pi$
$522$	10.3039	0.450988
$523$	22.6341	0.989719	0.494859	−	0.868973i	$-0.335220\pi$
$523$	22.6341	0.989719	0.494859	+	0.868973i	$0.335220\pi$
$524$	−0.396417	−0.0173176
$525$	4.89903	0.213811
$526$	−8.11063	−0.353640
$527$	−57.6275	−2.51030
$528$	0	0
$529$	22.7440	0.988869
$530$	13.3127	0.578268
$531$	6.55125	0.284300
$532$	11.1830	0.484843
$533$	0.999529	0.0432944
$534$	35.0500	1.51676
$535$	−15.3409	−0.663243
$536$	−43.6622	−1.88592
$537$	6.85781	0.295936
$538$	−4.21881	−0.181886
$539$	0	0
$540$	−27.8098	−1.19674
$541$	−42.7163	−1.83652	−0.918258	−	0.395982i	$-0.870404\pi$
$541$	−42.7163	−1.83652	−0.918258	+	0.395982i	$0.870404\pi$
$542$	6.01770	0.258482
$543$	−11.2626	−0.483324
$544$	5.22622	0.224072
$545$	−1.11526	−0.0477724
$546$	−11.0789	−0.474131
$547$	−44.4827	−1.90194	−0.950972	−	0.309278i	$-0.899913\pi$
$547$	−44.4827	−1.90194	−0.950972	+	0.309278i	$0.899913\pi$
$548$	−17.8324	−0.761761
$549$	−2.31251	−0.0986955
$550$	0	0
$551$	12.8671	0.548156
$552$	44.9613	1.91368
$553$	8.52928	0.362702
$554$	−12.5307	−0.532379
$555$	−9.84694	−0.417979
$556$	14.9459	0.633849
$557$	24.9911	1.05891	0.529454	−	0.848339i	$-0.322397\pi$
$557$	24.9911	1.05891	0.529454	+	0.848339i	$0.322397\pi$
$558$	−22.2959	−0.943860
$559$	0.421323	0.0178201
$560$	−4.34382	−0.183560
$561$	0	0
$562$	54.8565	2.31398
$563$	−9.01005	−0.379729	−0.189864	−	0.981810i	$-0.560805\pi$
$563$	−9.01005	−0.379729	−0.189864	+	0.981810i	$0.560805\pi$
$564$	52.5339	2.21208
$565$	5.72050	0.240663
$566$	20.6286	0.867086
$567$	5.28149	0.221802
$568$	−0.540502	−0.0226789
$569$	−29.1738	−1.22303	−0.611516	−	0.791232i	$-0.709440\pi$
$569$	−29.1738	−1.22303	−0.611516	+	0.791232i	$0.709440\pi$
$570$	−12.5574	−0.525972
$571$	−1.78994	−0.0749067	−0.0374533	−	0.999298i	$-0.511925\pi$
$571$	−1.78994	−0.0749067	−0.0374533	+	0.999298i	$0.511925\pi$
$572$	0	0
$573$	−12.6645	−0.529065
$574$	−0.764339	−0.0319029
$575$	−23.1028	−0.963455
$576$	8.53138	0.355474
$577$	−21.5850	−0.898594	−0.449297	−	0.893382i	$-0.648325\pi$
$577$	−21.5850	−0.898594	−0.449297	+	0.893382i	$0.648325\pi$
$578$	43.9813	1.82938
$579$	−36.7189	−1.52599
$580$	−22.1070	−0.917944
$581$	0.950532	0.0394347
$582$	61.2694	2.53970
$583$	0	0
$584$	−2.85074	−0.117965
$585$	−3.77251	−0.155974
$586$	−59.8526	−2.47249
$587$	5.52355	0.227981	0.113991	−	0.993482i	$-0.463637\pi$
$587$	5.52355	0.227981	0.113991	+	0.993482i	$0.463637\pi$
$588$	5.60359	0.231088
$589$	−27.8423	−1.14722
$590$	−21.2507	−0.874879
$591$	16.0598	0.660611
$592$	−18.8263	−0.773756
$593$	40.7867	1.67491	0.837454	−	0.546508i	$-0.184043\pi$
$593$	40.7867	1.67491	0.837454	+	0.546508i	$0.184043\pi$
$594$	0	0
$595$	7.45636	0.305681
$596$	19.0363	0.779757
$597$	−17.5694	−0.719069
$598$	52.2457	2.13648
$599$	−26.5149	−1.08337	−0.541685	−	0.840582i	$-0.682213\pi$
$599$	−26.5149	−1.08337	−0.541685	+	0.840582i	$0.682213\pi$
$600$	−22.7076	−0.927033
$601$	37.7699	1.54067	0.770333	−	0.637641i	$-0.220090\pi$
$601$	37.7699	1.54067	0.770333	+	0.637641i	$0.220090\pi$
$602$	−0.322186	−0.0131313
$603$	8.88343	0.361761
$604$	66.3186	2.69847
$605$	0	0
$606$	43.4890	1.76662
$607$	27.7244	1.12530	0.562649	−	0.826696i	$-0.309782\pi$
$607$	27.7244	1.12530	0.562649	+	0.826696i	$0.309782\pi$
$608$	2.52500	0.102402
$609$	6.44746	0.261264
$610$	7.50125	0.303717
$611$	29.7968	1.20545
$612$	21.8282	0.882354
$613$	−36.2264	−1.46317	−0.731586	−	0.681749i	$-0.761220\pi$
$613$	−36.2264	−1.46317	−0.731586	+	0.681749i	$0.761220\pi$
$614$	−11.1653	−0.450594
$615$	0.567687	0.0228914
$616$	0	0
$617$	41.1920	1.65833	0.829163	−	0.559007i	$-0.188817\pi$
$617$	41.1920	1.65833	0.829163	+	0.559007i	$0.188817\pi$
$618$	28.6461	1.15232
$619$	−35.7395	−1.43649	−0.718247	−	0.695789i	$-0.755055\pi$
$619$	−35.7395	−1.43649	−0.718247	+	0.695789i	$0.755055\pi$
$620$	47.8360	1.92114
$621$	−38.2482	−1.53485
$622$	−5.37308	−0.215441
$623$	−10.0552	−0.402852
$624$	15.7319	0.629780
$625$	3.74725	0.149890
$626$	−23.5736	−0.942192
$627$	0	0
$628$	8.77077	0.349992
$629$	32.3161	1.28853
$630$	2.88484	0.114935
$631$	2.76508	0.110076	0.0550380	−	0.998484i	$-0.482472\pi$
$631$	2.76508	0.110076	0.0550380	+	0.998484i	$0.482472\pi$
$632$	−39.5342	−1.57259
$633$	20.4569	0.813090
$634$	15.6895	0.623111
$635$	10.1040	0.400966
$636$	24.3864	0.966983
$637$	3.17831	0.125929
$638$	0	0
$639$	0.109970	0.00435033
$640$	−25.4531	−1.00612
$641$	38.4864	1.52012	0.760061	−	0.649851i	$-0.225169\pi$
$641$	38.4864	1.52012	0.760061	+	0.649851i	$0.225169\pi$
$642$	−42.4864	−1.67680
$643$	−26.3781	−1.04025	−0.520126	−	0.854089i	$-0.674115\pi$
$643$	−26.3781	−1.04025	−0.520126	+	0.854089i	$0.674115\pi$
$644$	−26.4254	−1.04131
$645$	0.239293	0.00942213
$646$	41.2115	1.62144
$647$	−27.3211	−1.07410	−0.537051	−	0.843549i	$-0.680462\pi$
$647$	−27.3211	−1.07410	−0.537051	+	0.843549i	$0.680462\pi$
$648$	−24.4803	−0.961678
$649$	0	0
$650$	−26.3865	−1.03496
$651$	−13.9513	−0.546793
$652$	−61.8777	−2.42332
$653$	−8.46165	−0.331130	−0.165565	−	0.986199i	$-0.552945\pi$
$653$	−8.46165	−0.331130	−0.165565	+	0.986199i	$0.552945\pi$
$654$	−3.08870	−0.120778
$655$	−0.127702	−0.00498971
$656$	1.08536	0.0423761
$657$	0.580007	0.0226282
$658$	−22.7856	−0.888276
$659$	5.29247	0.206165	0.103083	−	0.994673i	$-0.467129\pi$
$659$	5.29247	0.206165	0.103083	+	0.994673i	$0.467129\pi$
$660$	0	0
$661$	−19.2700	−0.749517	−0.374759	−	0.927122i	$-0.622274\pi$
$661$	−19.2700	−0.749517	−0.374759	+	0.927122i	$0.622274\pi$
$662$	8.80008	0.342025
$663$	−27.0045	−1.04877
$664$	−4.40583	−0.170979
$665$	3.60248	0.139698
$666$	12.5030	0.484481
$667$	−30.4050	−1.17728
$668$	−81.0393	−3.13551
$669$	−4.25099	−0.164353
$670$	−28.8158	−1.11325
$671$	0	0
$672$	1.26523	0.0488074
$673$	18.9922	0.732096	0.366048	−	0.930596i	$-0.380711\pi$
$673$	18.9922	0.732096	0.366048	+	0.930596i	$0.380711\pi$
$674$	15.5673	0.599629
$675$	19.3171	0.743517
$676$	−11.3241	−0.435544
$677$	−32.4219	−1.24607	−0.623037	−	0.782192i	$-0.714101\pi$
$677$	−32.4219	−1.24607	−0.623037	+	0.782192i	$0.714101\pi$
$678$	15.8429	0.608442
$679$	−17.5770	−0.674544
$680$	−34.5611	−1.32536
$681$	−11.8409	−0.453744
$682$	0	0
$683$	15.1260	0.578779	0.289389	−	0.957211i	$-0.406548\pi$
$683$	15.1260	0.578779	0.289389	+	0.957211i	$0.406548\pi$
$684$	10.5461	0.403241
$685$	−5.74451	−0.219486
$686$	−2.43045	−0.0927951
$687$	18.7997	0.717255
$688$	0.457502	0.0174421
$689$	13.8318	0.526948
$690$	29.6732	1.12964
$691$	−31.4108	−1.19492	−0.597461	−	0.801898i	$-0.703824\pi$
$691$	−31.4108	−1.19492	−0.597461	+	0.801898i	$0.703824\pi$
$692$	84.2192	3.20153
$693$	0	0
$694$	42.4357	1.61084
$695$	4.81468	0.182631
$696$	−29.8847	−1.13278
$697$	−1.86306	−0.0705685
$698$	52.5583	1.98936
$699$	18.3975	0.695859
$700$	13.3461	0.504434
$701$	16.0647	0.606755	0.303377	−	0.952870i	$-0.401886\pi$
$701$	16.0647	0.606755	0.303377	+	0.952870i	$0.401886\pi$
$702$	−43.6845	−1.64877
$703$	15.6133	0.588865
$704$	0	0
$705$	16.9232	0.637366
$706$	10.6976	0.402611
$707$	−12.4761	−0.469214
$708$	−38.9273	−1.46298
$709$	39.6978	1.49088	0.745441	−	0.666572i	$-0.232239\pi$
$709$	39.6978	1.49088	0.745441	+	0.666572i	$0.232239\pi$
$710$	−0.356716	−0.0133873
$711$	8.04356	0.301657
$712$	46.6069	1.74667
$713$	65.7913	2.46391
$714$	20.6503	0.772819
$715$	0	0
$716$	18.6822	0.698187
$717$	7.14391	0.266794
$718$	25.9614	0.968873
$719$	−9.86241	−0.367806	−0.183903	−	0.982944i	$-0.558873\pi$
$719$	−9.86241	−0.367806	−0.183903	+	0.982944i	$0.558873\pi$
$720$	−4.09645	−0.152666
$721$	−8.21802	−0.306055
$722$	−26.2676	−0.977580
$723$	3.76745	0.140113
$724$	−30.6818	−1.14028
$725$	15.3559	0.570305
$726$	0	0
$727$	−31.5764	−1.17111	−0.585553	−	0.810634i	$-0.699122\pi$
$727$	−31.5764	−1.17111	−0.585553	+	0.810634i	$0.699122\pi$
$728$	−14.7318	−0.545998
$729$	29.3127	1.08565
$730$	−1.88141	−0.0696340
$731$	−0.785321	−0.0290462
$732$	13.7409	0.507877
$733$	−41.2926	−1.52518	−0.762588	−	0.646885i	$-0.776072\pi$
$733$	−41.2926	−1.52518	−0.762588	+	0.646885i	$0.776072\pi$
$734$	24.8313	0.916540
$735$	1.80514	0.0665835
$736$	−5.96659	−0.219931
$737$	0	0
$738$	−0.720812	−0.0265335
$739$	−35.4095	−1.30256	−0.651281	−	0.758837i	$-0.725768\pi$
$739$	−35.4095	−1.30256	−0.651281	+	0.758837i	$0.725768\pi$
$740$	−26.8253	−0.986116
$741$	−13.0470	−0.479293
$742$	−10.5771	−0.388299
$743$	4.02408	0.147629	0.0738146	−	0.997272i	$-0.476483\pi$
$743$	4.02408	0.147629	0.0738146	+	0.997272i	$0.476483\pi$
$744$	64.6657	2.37076
$745$	6.13235	0.224672
$746$	67.7733	2.48136
$747$	0.896402	0.0327976
$748$	0	0
$749$	12.1885	0.445359
$750$	−36.9228	−1.34823
$751$	24.4190	0.891062	0.445531	−	0.895267i	$-0.353015\pi$
$751$	24.4190	0.891062	0.445531	+	0.895267i	$0.353015\pi$
$752$	32.3554	1.17988
$753$	−37.6091	−1.37055
$754$	−34.7265	−1.26466
$755$	21.3638	0.777510
$756$	22.0952	0.803596
$757$	−1.31723	−0.0478755	−0.0239377	−	0.999713i	$-0.507620\pi$
$757$	−1.31723	−0.0478755	−0.0239377	+	0.999713i	$0.507620\pi$
$758$	2.79023	0.101346
$759$	0	0
$760$	−16.6979	−0.605696
$761$	7.24404	0.262596	0.131298	−	0.991343i	$-0.458085\pi$
$761$	7.24404	0.262596	0.131298	+	0.991343i	$0.458085\pi$
$762$	27.9830	1.01372
$763$	0.886088	0.0320785
$764$	−34.5008	−1.24820
$765$	7.03174	0.254233
$766$	−48.4915	−1.75207
$767$	−22.0792	−0.797235
$768$	−44.5430	−1.60731
$769$	−44.3139	−1.59800	−0.798999	−	0.601332i	$-0.794637\pi$
$769$	−44.3139	−1.59800	−0.798999	+	0.601332i	$0.794637\pi$
$770$	0	0
$771$	42.9570	1.54706
$772$	−100.031	−3.60018
$773$	19.0559	0.685395	0.342697	−	0.939446i	$-0.388659\pi$
$773$	19.0559	0.685395	0.342697	+	0.939446i	$0.388659\pi$
$774$	−0.303838	−0.0109212
$775$	−33.2277	−1.19357
$776$	81.4714	2.92465
$777$	7.82353	0.280668
$778$	6.31918	0.226554
$779$	−0.900123	−0.0322502
$780$	22.4161	0.802626
$781$	0	0
$782$	−97.3828	−3.48240
$783$	25.4227	0.908533
$784$	3.45123	0.123258
$785$	2.82541	0.100843
$786$	−0.353669	−0.0126149
$787$	−31.4600	−1.12143	−0.560714	−	0.828009i	$-0.689473\pi$
$787$	−31.4600	−1.12143	−0.560714	+	0.828009i	$0.689473\pi$
$788$	43.7505	1.55855
$789$	−4.78607	−0.170389
$790$	−26.0914	−0.928292
$791$	−4.54502	−0.161602
$792$	0	0
$793$	7.79370	0.276763
$794$	21.3208	0.756648
$795$	7.85582	0.278617
$796$	−47.8631	−1.69646
$797$	−12.5453	−0.444376	−0.222188	−	0.975004i	$-0.571320\pi$
$797$	−12.5453	−0.444376	−0.222188	+	0.975004i	$0.571320\pi$
$798$	9.97703	0.353183
$799$	−55.5395	−1.96485
$800$	3.01340	0.106540
$801$	−9.48255	−0.335049
$802$	68.9118	2.43336
$803$	0	0
$804$	−52.7850	−1.86159
$805$	−8.51266	−0.300032
$806$	75.1424	2.64678
$807$	−2.48951	−0.0876350
$808$	57.8284	2.03440
$809$	5.38024	0.189159	0.0945796	−	0.995517i	$-0.469849\pi$
$809$	5.38024	0.189159	0.0945796	+	0.995517i	$0.469849\pi$
$810$	−16.1563	−0.567675
$811$	−13.6999	−0.481070	−0.240535	−	0.970641i	$-0.577323\pi$
$811$	−13.6999	−0.481070	−0.240535	+	0.970641i	$0.577323\pi$
$812$	17.5643	0.616387
$813$	3.55103	0.124540
$814$	0	0
$815$	−19.9333	−0.698231
$816$	−29.3234	−1.02652
$817$	−0.379421	−0.0132743
$818$	−48.3794	−1.69155
$819$	2.99731	0.104735
$820$	1.54651	0.0540064
$821$	9.23116	0.322170	0.161085	−	0.986941i	$-0.448501\pi$
$821$	9.23116	0.322170	0.161085	+	0.986941i	$0.448501\pi$
$822$	−15.9094	−0.554903
$823$	−12.4427	−0.433724	−0.216862	−	0.976202i	$-0.569582\pi$
$823$	−12.4427	−0.433724	−0.216862	+	0.976202i	$0.569582\pi$
$824$	38.0915	1.32698
$825$	0	0
$826$	16.8840	0.587469
$827$	4.48387	0.155919	0.0779597	−	0.996957i	$-0.475159\pi$
$827$	4.48387	0.155919	0.0779597	+	0.996957i	$0.475159\pi$
$828$	−24.9205	−0.866048
$829$	−36.8776	−1.28081	−0.640405	−	0.768037i	$-0.721234\pi$
$829$	−36.8776	−1.28081	−0.640405	+	0.768037i	$0.721234\pi$
$830$	−2.90772	−0.100928
$831$	−7.39435	−0.256507
$832$	−28.7528	−0.996823
$833$	−5.92418	−0.205261
$834$	13.3342	0.461726
$835$	−26.1060	−0.903435
$836$	0	0
$837$	−55.0105	−1.90144
$838$	−75.0905	−2.59396
$839$	9.16407	0.316379	0.158189	−	0.987409i	$-0.449434\pi$
$839$	9.16407	0.316379	0.158189	+	0.987409i	$0.449434\pi$
$840$	−8.36702	−0.288689
$841$	−8.79054	−0.303122
$842$	−58.8003	−2.02639
$843$	32.3708	1.11491
$844$	55.7293	1.91828
$845$	−3.64795	−0.125493
$846$	−21.4880	−0.738774
$847$	0	0
$848$	15.0195	0.515771
$849$	12.1729	0.417774
$850$	49.1829	1.68696
$851$	−36.8942	−1.26472
$852$	−0.653435	−0.0223863
$853$	−6.52049	−0.223257	−0.111629	−	0.993750i	$-0.535607\pi$
$853$	−6.52049	−0.223257	−0.111629	+	0.993750i	$0.535607\pi$
$854$	−5.95984	−0.203942
$855$	3.39732	0.116186
$856$	−56.4952	−1.93097
$857$	−48.0736	−1.64216	−0.821082	−	0.570810i	$-0.806629\pi$
$857$	−48.0736	−1.64216	−0.821082	+	0.570810i	$0.806629\pi$
$858$	0	0
$859$	−0.316298	−0.0107920	−0.00539598	−	0.999985i	$-0.501718\pi$
$859$	−0.316298	−0.0107920	−0.00539598	+	0.999985i	$0.501718\pi$
$860$	0.651887	0.0222291
$861$	−0.451035	−0.0153712
$862$	−47.1509	−1.60597
$863$	3.62693	0.123462	0.0617311	−	0.998093i	$-0.480338\pi$
$863$	3.62693	0.123462	0.0617311	+	0.998093i	$0.480338\pi$
$864$	4.98888	0.169725
$865$	27.1303	0.922458
$866$	−51.9818	−1.76641
$867$	25.9533	0.881420
$868$	−38.0064	−1.29002
$869$	0	0
$870$	−19.7231	−0.668675
$871$	−29.9393	−1.01445
$872$	−4.10712	−0.139085
$873$	−16.5760	−0.561014
$874$	−47.0497	−1.59148
$875$	10.5924	0.358090
$876$	−3.44638	−0.116442
$877$	−26.7076	−0.901852	−0.450926	−	0.892561i	$-0.648906\pi$
$877$	−26.7076	−0.901852	−0.450926	+	0.892561i	$0.648906\pi$
$878$	77.1220	2.60274
$879$	−35.3189	−1.19128
$880$	0	0
$881$	2.91937	0.0983560	0.0491780	−	0.998790i	$-0.484340\pi$
$881$	2.91937	0.0983560	0.0491780	+	0.998790i	$0.484340\pi$
$882$	−2.29204	−0.0771772
$883$	−45.1574	−1.51967	−0.759834	−	0.650117i	$-0.774720\pi$
$883$	−45.1574	−1.51967	−0.759834	+	0.650117i	$0.774720\pi$
$884$	−73.5663	−2.47430
$885$	−12.5400	−0.421528
$886$	−4.04939	−0.136042
$887$	24.0249	0.806676	0.403338	−	0.915051i	$-0.367850\pi$
$887$	24.0249	0.806676	0.403338	+	0.915051i	$0.367850\pi$
$888$	−36.2630	−1.21691
$889$	−8.02779	−0.269243
$890$	30.7592	1.03105
$891$	0	0
$892$	−11.5806	−0.387749
$893$	−26.8334	−0.897947
$894$	16.9835	0.568013
$895$	6.01828	0.201169
$896$	20.2229	0.675599
$897$	30.8301	1.02939
$898$	−41.7692	−1.39386
$899$	−43.7300	−1.45848
$900$	12.5860	0.419534
$901$	−25.7816	−0.858909
$902$	0	0
$903$	−0.190121	−0.00632684
$904$	21.0667	0.700667
$905$	−9.88384	−0.328550
$906$	59.1670	1.96569
$907$	−16.0270	−0.532166	−0.266083	−	0.963950i	$-0.585730\pi$
$907$	−16.0270	−0.532166	−0.266083	+	0.963950i	$0.585730\pi$
$908$	−32.2572	−1.07049
$909$	−11.7657	−0.390242
$910$	−9.72259	−0.322301
$911$	−16.4043	−0.543500	−0.271750	−	0.962368i	$-0.587602\pi$
$911$	−16.4043	−0.543500	−0.271750	+	0.962368i	$0.587602\pi$
$912$	−14.1673	−0.469127
$913$	0	0
$914$	−24.8408	−0.821660
$915$	4.42647	0.146335
$916$	51.2147	1.69218
$917$	0.101461	0.00335053
$918$	81.4253	2.68744
$919$	−32.3201	−1.06614	−0.533071	−	0.846070i	$-0.678962\pi$
$919$	−32.3201	−1.06614	−0.533071	+	0.846070i	$0.678962\pi$
$920$	39.4572	1.30086
$921$	−6.58861	−0.217102
$922$	53.7518	1.77022
$923$	−0.370623	−0.0121992
$924$	0	0
$925$	18.6333	0.612659
$926$	−73.8171	−2.42578
$927$	−7.75003	−0.254544
$928$	3.96585	0.130185
$929$	−8.19531	−0.268879	−0.134440	−	0.990922i	$-0.542923\pi$
$929$	−8.19531	−0.268879	−0.134440	+	0.990922i	$0.542923\pi$
$930$	42.6775	1.39945
$931$	−2.86222	−0.0938054
$932$	50.1190	1.64170
$933$	−3.17065	−0.103802
$934$	61.2253	2.00335
$935$	0	0
$936$	−13.8929	−0.454103
$937$	−34.1374	−1.11522	−0.557610	−	0.830103i	$-0.688282\pi$
$937$	−34.1374	−1.11522	−0.557610	+	0.830103i	$0.688282\pi$
$938$	22.8945	0.747533
$939$	−13.9108	−0.453961
$940$	46.1027	1.50371
$941$	−0.979371	−0.0319266	−0.0159633	−	0.999873i	$-0.505081\pi$
$941$	−0.979371	−0.0319266	−0.0159633	+	0.999873i	$0.505081\pi$
$942$	7.82496	0.254951
$943$	2.12699	0.0692644
$944$	−23.9752	−0.780326
$945$	7.11775	0.231540
$946$	0	0
$947$	0.935599	0.0304029	0.0152014	−	0.999884i	$-0.495161\pi$
$947$	0.935599	0.0304029	0.0152014	+	0.999884i	$0.495161\pi$
$948$	−47.7946	−1.55230
$949$	−1.95476	−0.0634542
$950$	23.7623	0.770950
$951$	9.25837	0.300223
$952$	27.4593	0.889960
$953$	−16.7321	−0.542004	−0.271002	−	0.962579i	$-0.587355\pi$
$953$	−16.7321	−0.542004	−0.271002	+	0.962579i	$0.587355\pi$
$954$	−9.97480	−0.322946
$955$	−11.1141	−0.359643
$956$	19.4616	0.629434
$957$	0	0
$958$	51.5353	1.66503
$959$	4.56409	0.147382
$960$	−16.3303	−0.527058
$961$	63.6245	2.05240
$962$	−42.1380	−1.35859
$963$	11.4944	0.370402
$964$	10.2634	0.330561
$965$	−32.2238	−1.03732
$966$	−23.5758	−0.758538
$967$	−36.4439	−1.17196	−0.585978	−	0.810327i	$-0.699290\pi$
$967$	−36.4439	−1.17196	−0.585978	+	0.810327i	$0.699290\pi$
$968$	0	0
$969$	24.3188	0.781233
$970$	53.7688	1.72641
$971$	−33.2417	−1.06678	−0.533389	−	0.845870i	$-0.679082\pi$
$971$	−33.2417	−1.06678	−0.533389	+	0.845870i	$0.679082\pi$
$972$	36.6904	1.17685
$973$	−3.82533	−0.122634
$974$	−40.8796	−1.30987
$975$	−15.5706	−0.498659
$976$	8.46294	0.270892
$977$	22.5666	0.721970	0.360985	−	0.932572i	$-0.382441\pi$
$977$	22.5666	0.721970	0.360985	+	0.932572i	$0.382441\pi$
$978$	−55.2050	−1.76526
$979$	0	0
$980$	4.91760	0.157087
$981$	0.835628	0.0266795
$982$	−11.7586	−0.375233
$983$	−15.1048	−0.481767	−0.240884	−	0.970554i	$-0.577437\pi$
$983$	−15.1048	−0.481767	−0.240884	+	0.970554i	$0.577437\pi$
$984$	2.09060	0.0666459
$985$	14.0938	0.449064
$986$	64.7281	2.06136
$987$	−13.4458	−0.427983
$988$	−35.5429	−1.13077
$989$	0.896574	0.0285094
$990$	0	0
$991$	−55.1534	−1.75201	−0.876003	−	0.482305i	$-0.839800\pi$
$991$	−55.1534	−1.75201	−0.876003	+	0.482305i	$0.839800\pi$
$992$	−8.58145	−0.272461
$993$	5.19292	0.164792
$994$	0.283415	0.00898939
$995$	−15.4186	−0.488802
$996$	−5.32639	−0.168773
$997$	−49.7048	−1.57417	−0.787083	−	0.616847i	$-0.788410\pi$
$997$	−49.7048	−1.57417	−0.787083	+	0.616847i	$0.788410\pi$
$998$	74.3319	2.35293
$999$	30.8486	0.976006

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.a.o.1.8		8
3.2	odd	2		7623.2.a.cw.1.1		8
7.6	odd	2		5929.2.a.bs.1.8		8
11.2	odd	10		847.2.f.w.323.4		16
11.3	even	5		847.2.f.x.372.4		16
11.4	even	5		847.2.f.x.148.4		16
11.5	even	5		847.2.f.v.729.1		16
11.6	odd	10		847.2.f.w.729.4		16
11.7	odd	10		77.2.f.b.71.1	yes	16
11.8	odd	10		77.2.f.b.64.1	✓	16
11.9	even	5		847.2.f.v.323.1		16
11.10	odd	2		847.2.a.p.1.1		8
33.8	even	10		693.2.m.i.64.4		16
33.29	even	10		693.2.m.i.379.4		16
33.32	even	2		7623.2.a.ct.1.8		8
77.18	odd	30		539.2.q.g.324.4		32
77.19	even	30		539.2.q.f.361.4		32
77.30	odd	30		539.2.q.g.361.4		32
77.40	even	30		539.2.q.f.214.1		32
77.41	even	10		539.2.f.e.295.1		16
77.51	odd	30		539.2.q.g.214.1		32
77.52	even	30		539.2.q.f.471.1		32
77.62	even	10		539.2.f.e.148.1		16
77.73	even	30		539.2.q.f.324.4		32
77.74	odd	30		539.2.q.g.471.1		32
77.76	even	2		5929.2.a.bt.1.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.b.64.1	✓	16	11.8	odd	10
77.2.f.b.71.1	yes	16	11.7	odd	10
539.2.f.e.148.1		16	77.62	even	10
539.2.f.e.295.1		16	77.41	even	10
539.2.q.f.214.1		32	77.40	even	30
539.2.q.f.324.4		32	77.73	even	30
539.2.q.f.361.4		32	77.19	even	30
539.2.q.f.471.1		32	77.52	even	30
539.2.q.g.214.1		32	77.51	odd	30
539.2.q.g.324.4		32	77.18	odd	30
539.2.q.g.361.4		32	77.30	odd	30
539.2.q.g.471.1		32	77.74	odd	30
693.2.m.i.64.4		16	33.8	even	10
693.2.m.i.379.4		16	33.29	even	10
847.2.a.o.1.8		8	1.1	even	1	trivial
847.2.a.p.1.1		8	11.10	odd	2
847.2.f.v.323.1		16	11.9	even	5
847.2.f.v.729.1		16	11.5	even	5
847.2.f.w.323.4		16	11.2	odd	10
847.2.f.w.729.4		16	11.6	odd	10
847.2.f.x.148.4		16	11.4	even	5
847.2.f.x.372.4		16	11.3	even	5
5929.2.a.bs.1.8		8	7.6	odd	2
5929.2.a.bt.1.1		8	77.76	even	2
7623.2.a.ct.1.8		8	33.32	even	2
7623.2.a.cw.1.1		8	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.a (trivial)

\(f(q)\)	\(=\)	\(q+2.43045 q^{2} +1.43421 q^{3} +3.90710 q^{4} +1.25863 q^{5} +3.48577 q^{6} -1.00000 q^{7} +4.63512 q^{8} -0.943053 q^{9} +O(q^{10})\)	\(q+2.43045 q^{2} +1.43421 q^{3} +3.90710 q^{4} +1.25863 q^{5} +3.48577 q^{6} -1.00000 q^{7} +4.63512 q^{8} -0.943053 q^{9} +3.05904 q^{10} +5.60359 q^{12} +3.17831 q^{13} -2.43045 q^{14} +1.80514 q^{15} +3.45123 q^{16} -5.92418 q^{17} -2.29204 q^{18} -2.86222 q^{19} +4.91760 q^{20} -1.43421 q^{21} +6.76343 q^{23} +6.64771 q^{24} -3.41585 q^{25} +7.72473 q^{26} -5.65515 q^{27} -3.90710 q^{28} -4.49549 q^{29} +4.38730 q^{30} +9.72751 q^{31} -0.882184 q^{32} -14.3984 q^{34} -1.25863 q^{35} -3.68460 q^{36} -5.45495 q^{37} -6.95648 q^{38} +4.55835 q^{39} +5.83390 q^{40} +0.314484 q^{41} -3.48577 q^{42} +0.132562 q^{43} -1.18696 q^{45} +16.4382 q^{46} +9.37505 q^{47} +4.94977 q^{48} +1.00000 q^{49} -8.30206 q^{50} -8.49650 q^{51} +12.4180 q^{52} +4.35192 q^{53} -13.7446 q^{54} -4.63512 q^{56} -4.10501 q^{57} -10.9261 q^{58} -6.94685 q^{59} +7.05285 q^{60} +2.45215 q^{61} +23.6423 q^{62} +0.943053 q^{63} -9.04656 q^{64} +4.00032 q^{65} -9.41987 q^{67} -23.1464 q^{68} +9.70015 q^{69} -3.05904 q^{70} -0.116610 q^{71} -4.37116 q^{72} -0.615032 q^{73} -13.2580 q^{74} -4.89903 q^{75} -11.1830 q^{76} +11.0789 q^{78} -8.52928 q^{79} +4.34382 q^{80} -5.28149 q^{81} +0.764339 q^{82} -0.950532 q^{83} -5.60359 q^{84} -7.45636 q^{85} +0.322186 q^{86} -6.44746 q^{87} +10.0552 q^{89} -2.88484 q^{90} -3.17831 q^{91} +26.4254 q^{92} +13.9513 q^{93} +22.7856 q^{94} -3.60248 q^{95} -1.26523 q^{96} +17.5770 q^{97} +2.43045 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} + 4 q^{3} + 7 q^{4} + 10 q^{5} + q^{6} - 8 q^{7} + 14 q^{9}+O(q^{10}) \) 8 * q - q^2 + 4 * q^3 + 7 * q^4 + 10 * q^5 + q^6 - 8 * q^7 + 14 * q^9	\( 8 q - q^{2} + 4 q^{3} + 7 q^{4} + 10 q^{5} + q^{6} - 8 q^{7} + 14 q^{9} - 6 q^{10} + 9 q^{12} + 6 q^{13} + q^{14} + 11 q^{15} + q^{16} + 5 q^{17} - 8 q^{18} + 13 q^{19} + 23 q^{20} - 4 q^{21} + 16 q^{23} + 10 q^{24} + 16 q^{25} - 6 q^{26} + 10 q^{27} - 7 q^{28} - 9 q^{29} + 36 q^{30} + 9 q^{31} - 16 q^{32} - 12 q^{34} - 10 q^{35} - 14 q^{36} + 7 q^{37} - 10 q^{38} - 13 q^{39} - 5 q^{40} + 10 q^{41} - q^{42} + 4 q^{43} + 35 q^{45} - 4 q^{46} + 16 q^{47} - 3 q^{48} + 8 q^{49} - 6 q^{50} - 13 q^{51} + 41 q^{52} + 37 q^{53} - 30 q^{54} - 2 q^{57} - 15 q^{58} + q^{59} + 5 q^{60} - 19 q^{61} + 18 q^{62} - 14 q^{63} - 4 q^{64} + 4 q^{65} - 19 q^{67} - 9 q^{68} + 20 q^{69} + 6 q^{70} + 13 q^{71} + 35 q^{72} + 25 q^{73} - 33 q^{74} - 13 q^{75} - 26 q^{76} - 29 q^{78} + 4 q^{80} + 8 q^{81} - 13 q^{82} + 25 q^{83} - 9 q^{84} - 3 q^{85} + 4 q^{86} + 36 q^{87} + 37 q^{89} + 2 q^{90} - 6 q^{91} + 35 q^{92} + 21 q^{93} + 42 q^{94} - 21 q^{95} + 6 q^{96} + 15 q^{97} - q^{98}+O(q^{100}) \) 8 * q - q^2 + 4 * q^3 + 7 * q^4 + 10 * q^5 + q^6 - 8 * q^7 + 14 * q^9 - 6 * q^10 + 9 * q^12 + 6 * q^13 + q^14 + 11 * q^15 + q^16 + 5 * q^17 - 8 * q^18 + 13 * q^19 + 23 * q^20 - 4 * q^21 + 16 * q^23 + 10 * q^24 + 16 * q^25 - 6 * q^26 + 10 * q^27 - 7 * q^28 - 9 * q^29 + 36 * q^30 + 9 * q^31 - 16 * q^32 - 12 * q^34 - 10 * q^35 - 14 * q^36 + 7 * q^37 - 10 * q^38 - 13 * q^39 - 5 * q^40 + 10 * q^41 - q^42 + 4 * q^43 + 35 * q^45 - 4 * q^46 + 16 * q^47 - 3 * q^48 + 8 * q^49 - 6 * q^50 - 13 * q^51 + 41 * q^52 + 37 * q^53 - 30 * q^54 - 2 * q^57 - 15 * q^58 + q^59 + 5 * q^60 - 19 * q^61 + 18 * q^62 - 14 * q^63 - 4 * q^64 + 4 * q^65 - 19 * q^67 - 9 * q^68 + 20 * q^69 + 6 * q^70 + 13 * q^71 + 35 * q^72 + 25 * q^73 - 33 * q^74 - 13 * q^75 - 26 * q^76 - 29 * q^78 + 4 * q^80 + 8 * q^81 - 13 * q^82 + 25 * q^83 - 9 * q^84 - 3 * q^85 + 4 * q^86 + 36 * q^87 + 37 * q^89 + 2 * q^90 - 6 * q^91 + 35 * q^92 + 21 * q^93 + 42 * q^94 - 21 * q^95 + 6 * q^96 + 15 * q^97 - q^98

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