LMFDB - Embedded newform 8041.2.a.h.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8041,2,Mod(1,8041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.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:	$64.2077082653$
Analytic rank:	$1$
Dimension:	$74$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.89916 q^{2} -0.231765 q^{3} +1.60683 q^{4} +2.27252 q^{5} +0.440160 q^{6} +0.501161 q^{7} +0.746704 q^{8} -2.94628 q^{9} +O(q^{10})$	\(q-1.89916 q^{2} -0.231765 q^{3} +1.60683 q^{4} +2.27252 q^{5} +0.440160 q^{6} +0.501161 q^{7} +0.746704 q^{8} -2.94628 q^{9} -4.31590 q^{10} -1.00000 q^{11} -0.372406 q^{12} -1.48512 q^{13} -0.951787 q^{14} -0.526692 q^{15} -4.63176 q^{16} -1.00000 q^{17} +5.59548 q^{18} -2.10272 q^{19} +3.65155 q^{20} -0.116152 q^{21} +1.89916 q^{22} -0.822329 q^{23} -0.173060 q^{24} +0.164368 q^{25} +2.82049 q^{26} +1.37814 q^{27} +0.805278 q^{28} +7.80413 q^{29} +1.00028 q^{30} -0.476950 q^{31} +7.30307 q^{32} +0.231765 q^{33} +1.89916 q^{34} +1.13890 q^{35} -4.73416 q^{36} -11.0192 q^{37} +3.99342 q^{38} +0.344200 q^{39} +1.69690 q^{40} +4.53868 q^{41} +0.220591 q^{42} -1.00000 q^{43} -1.60683 q^{44} -6.69550 q^{45} +1.56174 q^{46} +13.5123 q^{47} +1.07348 q^{48} -6.74884 q^{49} -0.312162 q^{50} +0.231765 q^{51} -2.38633 q^{52} +5.80353 q^{53} -2.61732 q^{54} -2.27252 q^{55} +0.374219 q^{56} +0.487338 q^{57} -14.8213 q^{58} +1.54926 q^{59} -0.846302 q^{60} +2.70930 q^{61} +0.905806 q^{62} -1.47656 q^{63} -4.60621 q^{64} -3.37498 q^{65} -0.440160 q^{66} +3.26338 q^{67} -1.60683 q^{68} +0.190587 q^{69} -2.16296 q^{70} -6.18175 q^{71} -2.20000 q^{72} +11.1273 q^{73} +20.9273 q^{74} -0.0380948 q^{75} -3.37871 q^{76} -0.501161 q^{77} -0.653692 q^{78} +15.2882 q^{79} -10.5258 q^{80} +8.51945 q^{81} -8.61970 q^{82} +14.7444 q^{83} -0.186636 q^{84} -2.27252 q^{85} +1.89916 q^{86} -1.80873 q^{87} -0.746704 q^{88} +11.1598 q^{89} +12.7159 q^{90} -0.744286 q^{91} -1.32134 q^{92} +0.110540 q^{93} -25.6621 q^{94} -4.77849 q^{95} -1.69260 q^{96} +15.8136 q^{97} +12.8172 q^{98} +2.94628 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9}+O(q^{10}) $ 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9	\( 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9} - 9 q^{10} - 74 q^{11} - 3 q^{12} + 4 q^{13} - 5 q^{14} - 17 q^{15} + 85 q^{16} - 74 q^{17} - 23 q^{18} - 21 q^{20} - 22 q^{21} + 7 q^{22} - 23 q^{23} - 51 q^{24} + 90 q^{25} - 46 q^{26} - 27 q^{27} - 61 q^{28} - 63 q^{29} - 22 q^{30} - 31 q^{31} - 69 q^{32} + 3 q^{33} + 7 q^{34} - 20 q^{35} + 51 q^{36} + 8 q^{37} - 2 q^{38} - 77 q^{39} - 37 q^{40} - 64 q^{41} + 13 q^{42} - 74 q^{43} - 79 q^{44} - 12 q^{45} - 53 q^{46} - 32 q^{47} + 2 q^{48} + 78 q^{49} - 104 q^{50} + 3 q^{51} + 13 q^{52} + 25 q^{53} - 110 q^{54} + 6 q^{55} - 29 q^{56} - 29 q^{57} - 14 q^{58} - 61 q^{59} - 82 q^{60} - 36 q^{61} - 63 q^{62} - 104 q^{63} + 107 q^{64} - 65 q^{65} + 12 q^{66} + 33 q^{67} - 79 q^{68} - 34 q^{69} - 3 q^{70} - 168 q^{71} - 67 q^{72} - 47 q^{73} - 54 q^{74} - 53 q^{75} - 4 q^{76} + 16 q^{77} - 3 q^{78} - 79 q^{79} - 59 q^{80} + 70 q^{81} - 18 q^{82} - 36 q^{83} - 118 q^{84} + 6 q^{85} + 7 q^{86} - 24 q^{87} + 21 q^{88} - 24 q^{89} + 25 q^{90} - 14 q^{91} - 18 q^{92} - 13 q^{93} + 9 q^{94} - 155 q^{95} - 50 q^{96} + q^{97} - 60 q^{98} - 75 q^{99}+O(q^{100}) \) 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9 - 9 * q^10 - 74 * q^11 - 3 * q^12 + 4 * q^13 - 5 * q^14 - 17 * q^15 + 85 * q^16 - 74 * q^17 - 23 * q^18 - 21 * q^20 - 22 * q^21 + 7 * q^22 - 23 * q^23 - 51 * q^24 + 90 * q^25 - 46 * q^26 - 27 * q^27 - 61 * q^28 - 63 * q^29 - 22 * q^30 - 31 * q^31 - 69 * q^32 + 3 * q^33 + 7 * q^34 - 20 * q^35 + 51 * q^36 + 8 * q^37 - 2 * q^38 - 77 * q^39 - 37 * q^40 - 64 * q^41 + 13 * q^42 - 74 * q^43 - 79 * q^44 - 12 * q^45 - 53 * q^46 - 32 * q^47 + 2 * q^48 + 78 * q^49 - 104 * q^50 + 3 * q^51 + 13 * q^52 + 25 * q^53 - 110 * q^54 + 6 * q^55 - 29 * q^56 - 29 * q^57 - 14 * q^58 - 61 * q^59 - 82 * q^60 - 36 * q^61 - 63 * q^62 - 104 * q^63 + 107 * q^64 - 65 * q^65 + 12 * q^66 + 33 * q^67 - 79 * q^68 - 34 * q^69 - 3 * q^70 - 168 * q^71 - 67 * q^72 - 47 * q^73 - 54 * q^74 - 53 * q^75 - 4 * q^76 + 16 * q^77 - 3 * q^78 - 79 * q^79 - 59 * q^80 + 70 * q^81 - 18 * q^82 - 36 * q^83 - 118 * q^84 + 6 * q^85 + 7 * q^86 - 24 * q^87 + 21 * q^88 - 24 * q^89 + 25 * q^90 - 14 * q^91 - 18 * q^92 - 13 * q^93 + 9 * q^94 - 155 * q^95 - 50 * q^96 + q^97 - 60 * q^98 - 75 * 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 $

$2$	−1.89916	−1.34291	−0.671456	−	0.741044i	$-0.734331\pi$
$2$	−1.89916	−1.34291	−0.671456	+	0.741044i	$0.734331\pi$
$3$	−0.231765	−0.133810	−0.0669049	−	0.997759i	$-0.521312\pi$
$3$	−0.231765	−0.133810	−0.0669049	+	0.997759i	$0.521312\pi$
$4$	1.60683	0.803413
$5$	2.27252	1.01630	0.508152	−	0.861267i	$-0.330329\pi$
$5$	2.27252	1.01630	0.508152	+	0.861267i	$0.330329\pi$
$6$	0.440160	0.179695
$7$	0.501161	0.189421	0.0947105	−	0.995505i	$-0.469807\pi$
$7$	0.501161	0.189421	0.0947105	+	0.995505i	$0.469807\pi$
$8$	0.746704	0.264000
$9$	−2.94628	−0.982095
$10$	−4.31590	−1.36481
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−0.372406	−0.107504
$13$	−1.48512	−0.411899	−0.205950	−	0.978563i	$-0.566028\pi$
$13$	−1.48512	−0.411899	−0.205950	+	0.978563i	$0.566028\pi$
$14$	−0.951787	−0.254376
$15$	−0.526692	−0.135991
$16$	−4.63176	−1.15794
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	5.59548	1.31887
$19$	−2.10272	−0.482398	−0.241199	−	0.970476i	$-0.577541\pi$
$19$	−2.10272	−0.482398	−0.241199	+	0.970476i	$0.577541\pi$
$20$	3.65155	0.816511
$21$	−0.116152	−0.0253464
$22$	1.89916	0.404903
$23$	−0.822329	−0.171468	−0.0857338	−	0.996318i	$-0.527323\pi$
$23$	−0.822329	−0.171468	−0.0857338	+	0.996318i	$0.527323\pi$
$24$	−0.173060	−0.0353257
$25$	0.164368	0.0328736
$26$	2.82049	0.553144
$27$	1.37814	0.265224
$28$	0.805278	0.152183
$29$	7.80413	1.44919	0.724596	−	0.689174i	$-0.242027\pi$
$29$	7.80413	1.44919	0.724596	+	0.689174i	$0.242027\pi$
$30$	1.00028	0.182624
$31$	−0.476950	−0.0856627	−0.0428314	−	0.999082i	$-0.513638\pi$
$31$	−0.476950	−0.0856627	−0.0428314	+	0.999082i	$0.513638\pi$
$32$	7.30307	1.29101
$33$	0.231765	0.0403452
$34$	1.89916	0.325704
$35$	1.13890	0.192509
$36$	−4.73416	−0.789027
$37$	−11.0192	−1.81155	−0.905775	−	0.423759i	$-0.860710\pi$
$37$	−11.0192	−1.81155	−0.905775	+	0.423759i	$0.860710\pi$
$38$	3.99342	0.647818
$39$	0.344200	0.0551161
$40$	1.69690	0.268304
$41$	4.53868	0.708823	0.354411	−	0.935090i	$-0.384681\pi$
$41$	4.53868	0.708823	0.354411	+	0.935090i	$0.384681\pi$
$42$	0.220591	0.0340380
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−1.60683	−0.242238
$45$	−6.69550	−0.998107
$46$	1.56174	0.230266
$47$	13.5123	1.97097	0.985486	−	0.169756i	$-0.0542981\pi$
$47$	13.5123	1.97097	0.985486	+	0.169756i	$0.0542981\pi$
$48$	1.07348	0.154944
$49$	−6.74884	−0.964120
$50$	−0.312162	−0.0441463
$51$	0.231765	0.0324536
$52$	−2.38633	−0.330925
$53$	5.80353	0.797176	0.398588	−	0.917130i	$-0.369500\pi$
$53$	5.80353	0.797176	0.398588	+	0.917130i	$0.369500\pi$
$54$	−2.61732	−0.356172
$55$	−2.27252	−0.306427
$56$	0.374219	0.0500071
$57$	0.487338	0.0645496
$58$	−14.8213	−1.94614
$59$	1.54926	0.201697	0.100849	−	0.994902i	$-0.467844\pi$
$59$	1.54926	0.201697	0.100849	+	0.994902i	$0.467844\pi$
$60$	−0.846302	−0.109257
$61$	2.70930	0.346891	0.173445	−	0.984843i	$-0.444510\pi$
$61$	2.70930	0.346891	0.173445	+	0.984843i	$0.444510\pi$
$62$	0.905806	0.115038
$63$	−1.47656	−0.186029
$64$	−4.60621	−0.575776
$65$	−3.37498	−0.418615
$66$	−0.440160	−0.0541800
$67$	3.26338	0.398686	0.199343	−	0.979930i	$-0.436119\pi$
$67$	3.26338	0.398686	0.199343	+	0.979930i	$0.436119\pi$
$68$	−1.60683	−0.194856
$69$	0.190587	0.0229440
$70$	−2.16296	−0.258523
$71$	−6.18175	−0.733639	−0.366819	−	0.930292i	$-0.619553\pi$
$71$	−6.18175	−0.733639	−0.366819	+	0.930292i	$0.619553\pi$
$72$	−2.20000	−0.259273
$73$	11.1273	1.30236	0.651179	−	0.758924i	$-0.274275\pi$
$73$	11.1273	1.30236	0.651179	+	0.758924i	$0.274275\pi$
$74$	20.9273	2.43275
$75$	−0.0380948	−0.00439881
$76$	−3.37871	−0.387565
$77$	−0.501161	−0.0571126
$78$	−0.653692	−0.0740161
$79$	15.2882	1.72005	0.860027	−	0.510248i	$-0.170446\pi$
$79$	15.2882	1.72005	0.860027	+	0.510248i	$0.170446\pi$
$80$	−10.5258	−1.17682
$81$	8.51945	0.946605
$82$	−8.61970	−0.951887
$83$	14.7444	1.61840	0.809201	−	0.587531i	$-0.199900\pi$
$83$	14.7444	1.61840	0.809201	+	0.587531i	$0.199900\pi$
$84$	−0.186636	−0.0203636
$85$	−2.27252	−0.246490
$86$	1.89916	0.204792
$87$	−1.80873	−0.193916
$88$	−0.746704	−0.0795989
$89$	11.1598	1.18293	0.591466	−	0.806330i	$-0.298549\pi$
$89$	11.1598	1.18293	0.591466	+	0.806330i	$0.298549\pi$
$90$	12.7159	1.34037
$91$	−0.744286	−0.0780224
$92$	−1.32134	−0.137759
$93$	0.110540	0.0114625
$94$	−25.6621	−2.64684
$95$	−4.77849	−0.490263
$96$	−1.69260	−0.172750
$97$	15.8136	1.60563	0.802816	−	0.596227i	$-0.203334\pi$
$97$	15.8136	1.60563	0.802816	+	0.596227i	$0.203334\pi$
$98$	12.8172	1.29473
$99$	2.94628	0.296113
$100$	0.264111	0.0264111
$101$	−10.4990	−1.04469	−0.522346	−	0.852733i	$-0.674943\pi$
$101$	−10.4990	−1.04469	−0.522346	+	0.852733i	$0.674943\pi$
$102$	−0.440160	−0.0435824
$103$	−11.0744	−1.09119	−0.545597	−	0.838048i	$-0.683697\pi$
$103$	−11.0744	−1.09119	−0.545597	+	0.838048i	$0.683697\pi$
$104$	−1.10895	−0.108741
$105$	−0.263958	−0.0257596
$106$	−11.0219	−1.07054
$107$	−20.4791	−1.97979	−0.989896	−	0.141796i	$-0.954712\pi$
$107$	−20.4791	−1.97979	−0.989896	+	0.141796i	$0.954712\pi$
$108$	2.21443	0.213084
$109$	−19.3234	−1.85085	−0.925423	−	0.378935i	$-0.876290\pi$
$109$	−19.3234	−1.85085	−0.925423	+	0.378935i	$0.876290\pi$
$110$	4.31590	0.411505
$111$	2.55387	0.242403
$112$	−2.32126	−0.219338
$113$	−17.4684	−1.64329	−0.821643	−	0.570003i	$-0.806942\pi$
$113$	−17.4684	−1.64329	−0.821643	+	0.570003i	$0.806942\pi$
$114$	−0.925536	−0.0866844
$115$	−1.86876	−0.174263
$116$	12.5399	1.16430
$117$	4.37560	0.404524
$118$	−2.94231	−0.270861
$119$	−0.501161	−0.0459414
$120$	−0.393283	−0.0359017
$121$	1.00000	0.0909091
$122$	−5.14541	−0.465844
$123$	−1.05191	−0.0948474
$124$	−0.766375	−0.0688225
$125$	−10.9891	−0.982894
$126$	2.80424	0.249821
$127$	−12.3410	−1.09509	−0.547544	−	0.836777i	$-0.684437\pi$
$127$	−12.3410	−1.09509	−0.547544	+	0.836777i	$0.684437\pi$
$128$	−5.85820	−0.517797
$129$	0.231765	0.0204058
$130$	6.40964	0.562163
$131$	1.80545	0.157743	0.0788713	−	0.996885i	$-0.474868\pi$
$131$	1.80545	0.157743	0.0788713	+	0.996885i	$0.474868\pi$
$132$	0.372406	0.0324138
$133$	−1.05380	−0.0913763
$134$	−6.19770	−0.535400
$135$	3.13186	0.269548
$136$	−0.746704	−0.0640293
$137$	4.49073	0.383669	0.191834	−	0.981427i	$-0.438556\pi$
$137$	4.49073	0.383669	0.191834	+	0.981427i	$0.438556\pi$
$138$	−0.361957	−0.0308118
$139$	−13.3026	−1.12831	−0.564156	−	0.825668i	$-0.690798\pi$
$139$	−13.3026	−1.12831	−0.564156	+	0.825668i	$0.690798\pi$
$140$	1.83001	0.154664
$141$	−3.13168	−0.263735
$142$	11.7402	0.985212
$143$	1.48512	0.124192
$144$	13.6465	1.13721
$145$	17.7351	1.47282
$146$	−21.1327	−1.74895
$147$	1.56415	0.129009
$148$	−17.7060	−1.45542
$149$	23.0829	1.89103	0.945513	−	0.325584i	$-0.105561\pi$
$149$	23.0829	1.89103	0.945513	+	0.325584i	$0.105561\pi$
$150$	0.0723483	0.00590721
$151$	−20.1551	−1.64020	−0.820100	−	0.572220i	$-0.806082\pi$
$151$	−20.1551	−1.64020	−0.820100	+	0.572220i	$0.806082\pi$
$152$	−1.57011	−0.127353
$153$	2.94628	0.238193
$154$	0.951787	0.0766972
$155$	−1.08388	−0.0870594
$156$	0.553069	0.0442810
$157$	−17.6011	−1.40472	−0.702362	−	0.711820i	$-0.747871\pi$
$157$	−17.6011	−1.40472	−0.702362	+	0.711820i	$0.747871\pi$
$158$	−29.0348	−2.30988
$159$	−1.34506	−0.106670
$160$	16.5964	1.31206
$161$	−0.412119	−0.0324796
$162$	−16.1798	−1.27121
$163$	3.68871	0.288922	0.144461	−	0.989510i	$-0.453855\pi$
$163$	3.68871	0.288922	0.144461	+	0.989510i	$0.453855\pi$
$164$	7.29287	0.569477
$165$	0.526692	0.0410029
$166$	−28.0019	−2.17337
$167$	−22.5771	−1.74707	−0.873533	−	0.486765i	$-0.838177\pi$
$167$	−22.5771	−1.74707	−0.873533	+	0.486765i	$0.838177\pi$
$168$	−0.0867309	−0.00669144
$169$	−10.7944	−0.830339
$170$	4.31590	0.331014
$171$	6.19522	0.473761
$172$	−1.60683	−0.122519
$173$	−7.33151	−0.557404	−0.278702	−	0.960378i	$-0.589904\pi$
$173$	−7.33151	−0.557404	−0.278702	+	0.960378i	$0.589904\pi$
$174$	3.43507	0.260412
$175$	0.0823748	0.00622695
$176$	4.63176	0.349132
$177$	−0.359066	−0.0269890
$178$	−21.1942	−1.58857
$179$	9.10234	0.680341	0.340171	−	0.940364i	$-0.389515\pi$
$179$	9.10234	0.680341	0.340171	+	0.940364i	$0.389515\pi$
$180$	−10.7585	−0.801892
$181$	9.13426	0.678945	0.339472	−	0.940616i	$-0.389752\pi$
$181$	9.13426	0.678945	0.339472	+	0.940616i	$0.389752\pi$
$182$	1.41352	0.104777
$183$	−0.627923	−0.0464174
$184$	−0.614036	−0.0452674
$185$	−25.0415	−1.84109
$186$	−0.209934	−0.0153931
$187$	1.00000	0.0731272
$188$	21.7119	1.58350
$189$	0.690671	0.0502389
$190$	9.07514	0.658380
$191$	3.62089	0.261999	0.130999	−	0.991382i	$-0.458181\pi$
$191$	3.62089	0.261999	0.130999	+	0.991382i	$0.458181\pi$
$192$	1.06756	0.0770444
$193$	0.920528	0.0662610	0.0331305	−	0.999451i	$-0.489452\pi$
$193$	0.920528	0.0662610	0.0331305	+	0.999451i	$0.489452\pi$
$194$	−30.0327	−2.15622
$195$	0.782203	0.0560147
$196$	−10.8442	−0.774586
$197$	−16.2274	−1.15616	−0.578078	−	0.815981i	$-0.696197\pi$
$197$	−16.2274	−1.15616	−0.578078	+	0.815981i	$0.696197\pi$
$198$	−5.59548	−0.397653
$199$	−2.65117	−0.187937	−0.0939683	−	0.995575i	$-0.529955\pi$
$199$	−2.65117	−0.187937	−0.0939683	+	0.995575i	$0.529955\pi$
$200$	0.122734	0.00867862
$201$	−0.756339	−0.0533481
$202$	19.9394	1.40293
$203$	3.91113	0.274507
$204$	0.372406	0.0260737
$205$	10.3143	0.720380
$206$	21.0321	1.46538
$207$	2.42282	0.168397
$208$	6.87874	0.476955
$209$	2.10272	0.145448
$210$	0.501299	0.0345929
$211$	3.71962	0.256069	0.128034	−	0.991770i	$-0.459133\pi$
$211$	3.71962	0.256069	0.128034	+	0.991770i	$0.459133\pi$
$212$	9.32526	0.640461
$213$	1.43272	0.0981680
$214$	38.8932	2.65869
$215$	−2.27252	−0.154985
$216$	1.02906	0.0700190
$217$	−0.239029	−0.0162263
$218$	36.6983	2.48552
$219$	−2.57893	−0.174268
$220$	−3.65155	−0.246187
$221$	1.48512	0.0999002
$222$	−4.85023	−0.325526
$223$	15.9030	1.06494	0.532470	−	0.846449i	$-0.321264\pi$
$223$	15.9030	1.06494	0.532470	+	0.846449i	$0.321264\pi$
$224$	3.66001	0.244545
$225$	−0.484275	−0.0322850
$226$	33.1753	2.20679
$227$	11.8776	0.788344	0.394172	−	0.919037i	$-0.371031\pi$
$227$	11.8776	0.788344	0.394172	+	0.919037i	$0.371031\pi$
$228$	0.783068	0.0518599
$229$	−15.1404	−1.00051	−0.500254	−	0.865879i	$-0.666760\pi$
$229$	−15.1404	−1.00051	−0.500254	+	0.865879i	$0.666760\pi$
$230$	3.54909	0.234020
$231$	0.116152	0.00764222
$232$	5.82738	0.382586
$233$	−0.989124	−0.0647997	−0.0323998	−	0.999475i	$-0.510315\pi$
$233$	−0.989124	−0.0647997	−0.0323998	+	0.999475i	$0.510315\pi$
$234$	−8.30998	−0.543240
$235$	30.7070	2.00311
$236$	2.48940	0.162046
$237$	−3.54327	−0.230160
$238$	0.951787	0.0616952
$239$	−21.5759	−1.39563	−0.697815	−	0.716278i	$-0.745844\pi$
$239$	−21.5759	−1.39563	−0.697815	+	0.716278i	$0.745844\pi$
$240$	2.43951	0.157470
$241$	−16.1667	−1.04139	−0.520694	−	0.853744i	$-0.674327\pi$
$241$	−16.1667	−1.04139	−0.520694	+	0.853744i	$0.674327\pi$
$242$	−1.89916	−0.122083
$243$	−6.10894	−0.391889
$244$	4.35338	0.278696
$245$	−15.3369	−0.979839
$246$	1.99775	0.127372
$247$	3.12280	0.198699
$248$	−0.356140	−0.0226149
$249$	−3.41723	−0.216558
$250$	20.8701	1.31994
$251$	16.2349	1.02474	0.512370	−	0.858765i	$-0.328768\pi$
$251$	16.2349	1.02474	0.512370	+	0.858765i	$0.328768\pi$
$252$	−2.37258	−0.149458
$253$	0.822329	0.0516994
$254$	23.4376	1.47061
$255$	0.526692	0.0329828
$256$	20.3381	1.27113
$257$	−24.7656	−1.54483	−0.772417	−	0.635116i	$-0.780952\pi$
$257$	−24.7656	−1.54483	−0.772417	+	0.635116i	$0.780952\pi$
$258$	−0.440160	−0.0274032
$259$	−5.52241	−0.343146
$260$	−5.42300	−0.336320
$261$	−22.9932	−1.42324
$262$	−3.42884	−0.211835
$263$	−16.7005	−1.02979	−0.514897	−	0.857252i	$-0.672170\pi$
$263$	−16.7005	−1.02979	−0.514897	+	0.857252i	$0.672170\pi$
$264$	0.173060	0.0106511
$265$	13.1887	0.810173
$266$	2.00135	0.122710
$267$	−2.58645	−0.158288
$268$	5.24369	0.320309
$269$	−2.15258	−0.131245	−0.0656226	−	0.997845i	$-0.520903\pi$
$269$	−2.15258	−0.131245	−0.0656226	+	0.997845i	$0.520903\pi$
$270$	−5.94792	−0.361979
$271$	5.61495	0.341084	0.170542	−	0.985350i	$-0.445448\pi$
$271$	5.61495	0.341084	0.170542	+	0.985350i	$0.445448\pi$
$272$	4.63176	0.280842
$273$	0.172500	0.0104402
$274$	−8.52862	−0.515233
$275$	−0.164368	−0.00991176
$276$	0.306241	0.0184335
$277$	−7.77852	−0.467366	−0.233683	−	0.972313i	$-0.575078\pi$
$277$	−7.77852	−0.467366	−0.233683	+	0.972313i	$0.575078\pi$
$278$	25.2638	1.51522
$279$	1.40523	0.0841289
$280$	0.850422	0.0508224
$281$	−5.34728	−0.318992	−0.159496	−	0.987199i	$-0.550987\pi$
$281$	−5.34728	−0.318992	−0.159496	+	0.987199i	$0.550987\pi$
$282$	5.94758	0.354173
$283$	−16.2723	−0.967289	−0.483644	−	0.875265i	$-0.660687\pi$
$283$	−16.2723	−0.967289	−0.483644	+	0.875265i	$0.660687\pi$
$284$	−9.93299	−0.589415
$285$	1.10749	0.0656020
$286$	−2.82049	−0.166779
$287$	2.27461	0.134266
$288$	−21.5169	−1.26790
$289$	1.00000	0.0588235
$290$	−33.6818	−1.97787
$291$	−3.66505	−0.214849
$292$	17.8797	1.04633
$293$	11.5350	0.673881	0.336940	−	0.941526i	$-0.390608\pi$
$293$	11.5350	0.673881	0.336940	+	0.941526i	$0.390608\pi$
$294$	−2.97057	−0.173247
$295$	3.52074	0.204986
$296$	−8.22810	−0.478249
$297$	−1.37814	−0.0799679
$298$	−43.8383	−2.53948
$299$	1.22126	0.0706273
$300$	−0.0612117	−0.00353406
$301$	−0.501161	−0.0288864
$302$	38.2779	2.20264
$303$	2.43331	0.139790
$304$	9.73932	0.558588
$305$	6.15696	0.352547
$306$	−5.59548	−0.319872
$307$	−6.65250	−0.379678	−0.189839	−	0.981815i	$-0.560797\pi$
$307$	−6.65250	−0.379678	−0.189839	+	0.981815i	$0.560797\pi$
$308$	−0.805278	−0.0458850
$309$	2.56666	0.146012
$310$	2.05847	0.116913
$311$	−24.0457	−1.36351	−0.681753	−	0.731582i	$-0.738782\pi$
$311$	−24.0457	−1.36351	−0.681753	+	0.731582i	$0.738782\pi$
$312$	0.257015	0.0145506
$313$	−7.41718	−0.419244	−0.209622	−	0.977783i	$-0.567223\pi$
$313$	−7.41718	−0.419244	−0.209622	+	0.977783i	$0.567223\pi$
$314$	33.4275	1.88642
$315$	−3.35553	−0.189062
$316$	24.5654	1.38191
$317$	12.8978	0.724415	0.362207	−	0.932098i	$-0.382023\pi$
$317$	12.8978	0.724415	0.362207	+	0.932098i	$0.382023\pi$
$318$	2.55448	0.143248
$319$	−7.80413	−0.436948
$320$	−10.4677	−0.585163
$321$	4.74635	0.264915
$322$	0.782682	0.0436172
$323$	2.10272	0.116999
$324$	13.6893	0.760515
$325$	−0.244107	−0.0135406
$326$	−7.00547	−0.387997
$327$	4.47849	0.247661
$328$	3.38905	0.187129
$329$	6.77184	0.373344
$330$	−1.00028	−0.0550633
$331$	23.5125	1.29236	0.646181	−	0.763184i	$-0.276365\pi$
$331$	23.5125	1.29236	0.646181	+	0.763184i	$0.276365\pi$
$332$	23.6916	1.30025
$333$	32.4658	1.77911
$334$	42.8775	2.34616
$335$	7.41612	0.405186
$336$	0.537987	0.0293496
$337$	−7.16135	−0.390104	−0.195052	−	0.980793i	$-0.562488\pi$
$337$	−7.16135	−0.390104	−0.195052	+	0.980793i	$0.562488\pi$
$338$	20.5004	1.11507
$339$	4.04856	0.219888
$340$	−3.65155	−0.198033
$341$	0.476950	0.0258283
$342$	−11.7657	−0.636219
$343$	−6.89038	−0.372046
$344$	−0.746704	−0.0402596
$345$	0.433115	0.0233181
$346$	13.9237	0.748545
$347$	19.3920	1.04102	0.520510	−	0.853856i	$-0.325742\pi$
$347$	19.3920	1.04102	0.520510	+	0.853856i	$0.325742\pi$
$348$	−2.90631	−0.155794
$349$	−19.7037	−1.05472	−0.527358	−	0.849643i	$-0.676817\pi$
$349$	−19.7037	−1.05472	−0.527358	+	0.849643i	$0.676817\pi$
$350$	−0.156443	−0.00836225
$351$	−2.04671	−0.109245
$352$	−7.30307	−0.389255
$353$	−23.1014	−1.22957	−0.614783	−	0.788697i	$-0.710756\pi$
$353$	−23.1014	−1.22957	−0.614783	+	0.788697i	$0.710756\pi$
$354$	0.681925	0.0362439
$355$	−14.0482	−0.745600
$356$	17.9318	0.950383
$357$	0.116152	0.00614740
$358$	−17.2868	−0.913638
$359$	6.68015	0.352565	0.176282	−	0.984340i	$-0.443593\pi$
$359$	6.68015	0.352565	0.176282	+	0.984340i	$0.443593\pi$
$360$	−4.99956	−0.263500
$361$	−14.5786	−0.767292
$362$	−17.3475	−0.911763
$363$	−0.231765	−0.0121645
$364$	−1.19594	−0.0626841
$365$	25.2872	1.32359
$366$	1.19253	0.0623345
$367$	1.76364	0.0920612	0.0460306	−	0.998940i	$-0.485343\pi$
$367$	1.76364	0.0920612	0.0460306	+	0.998940i	$0.485343\pi$
$368$	3.80883	0.198549
$369$	−13.3722	−0.696131
$370$	47.5579	2.47242
$371$	2.90850	0.151002
$372$	0.177619	0.00920912
$373$	25.8311	1.33748	0.668742	−	0.743495i	$-0.266833\pi$
$373$	25.8311	1.33748	0.668742	+	0.743495i	$0.266833\pi$
$374$	−1.89916	−0.0982034
$375$	2.54689	0.131521
$376$	10.0897	0.520336
$377$	−11.5901	−0.596920
$378$	−1.31170	−0.0674665
$379$	−16.4563	−0.845304	−0.422652	−	0.906292i	$-0.638901\pi$
$379$	−16.4563	−0.845304	−0.422652	+	0.906292i	$0.638901\pi$
$380$	−7.67820	−0.393883
$381$	2.86022	0.146533
$382$	−6.87667	−0.351841
$383$	−14.0962	−0.720280	−0.360140	−	0.932898i	$-0.617271\pi$
$383$	−14.0962	−0.720280	−0.360140	+	0.932898i	$0.617271\pi$
$384$	1.35773	0.0692862
$385$	−1.13890	−0.0580438
$386$	−1.74823	−0.0889827
$387$	2.94628	0.149768
$388$	25.4098	1.28998
$389$	4.27817	0.216912	0.108456	−	0.994101i	$-0.465409\pi$
$389$	4.27817	0.216912	0.108456	+	0.994101i	$0.465409\pi$
$390$	−1.48553	−0.0752228
$391$	0.822329	0.0415870
$392$	−5.03938	−0.254527
$393$	−0.418440	−0.0211075
$394$	30.8186	1.55262
$395$	34.7428	1.74810
$396$	4.73416	0.237901
$397$	11.1545	0.559828	0.279914	−	0.960025i	$-0.409694\pi$
$397$	11.1545	0.559828	0.279914	+	0.960025i	$0.409694\pi$
$398$	5.03501	0.252382
$399$	0.244235	0.0122270
$400$	−0.761314	−0.0380657
$401$	21.0381	1.05059	0.525295	−	0.850920i	$-0.323955\pi$
$401$	21.0381	1.05059	0.525295	+	0.850920i	$0.323955\pi$
$402$	1.43641	0.0716417
$403$	0.708329	0.0352844
$404$	−16.8701	−0.839319
$405$	19.3607	0.962039
$406$	−7.42787	−0.368639
$407$	11.0192	0.546203
$408$	0.173060	0.00856775
$409$	−1.31161	−0.0648550	−0.0324275	−	0.999474i	$-0.510324\pi$
$409$	−1.31161	−0.0648550	−0.0324275	+	0.999474i	$0.510324\pi$
$410$	−19.5885	−0.967406
$411$	−1.04079	−0.0513386
$412$	−17.7946	−0.876679
$413$	0.776431	0.0382057
$414$	−4.60133	−0.226143
$415$	33.5069	1.64479
$416$	−10.8460	−0.531767
$417$	3.08308	0.150979
$418$	−3.99342	−0.195324
$419$	20.2383	0.988704	0.494352	−	0.869262i	$-0.335405\pi$
$419$	20.2383	0.988704	0.494352	+	0.869262i	$0.335405\pi$
$420$	−0.424134	−0.0206956
$421$	24.0901	1.17408	0.587041	−	0.809557i	$-0.300293\pi$
$421$	24.0901	1.17408	0.587041	+	0.809557i	$0.300293\pi$
$422$	−7.06416	−0.343878
$423$	−39.8111	−1.93568
$424$	4.33352	0.210454
$425$	−0.164368	−0.00797302
$426$	−2.72096	−0.131831
$427$	1.35780	0.0657084
$428$	−32.9064	−1.59059
$429$	−0.344200	−0.0166181
$430$	4.31590	0.208131
$431$	−33.5728	−1.61714	−0.808572	−	0.588397i	$-0.799759\pi$
$431$	−33.5728	−1.61714	−0.808572	+	0.588397i	$0.799759\pi$
$432$	−6.38323	−0.307113
$433$	6.39816	0.307476	0.153738	−	0.988112i	$-0.450869\pi$
$433$	6.39816	0.307476	0.153738	+	0.988112i	$0.450869\pi$
$434$	0.453955	0.0217905
$435$	−4.11038	−0.197077
$436$	−31.0493	−1.48699
$437$	1.72913	0.0827156
$438$	4.89782	0.234027
$439$	−8.73526	−0.416911	−0.208456	−	0.978032i	$-0.566844\pi$
$439$	−8.73526	−0.416911	−0.208456	+	0.978032i	$0.566844\pi$
$440$	−1.69690	−0.0808967
$441$	19.8840	0.946857
$442$	−2.82049	−0.134157
$443$	−38.8291	−1.84483	−0.922414	−	0.386202i	$-0.873787\pi$
$443$	−38.8291	−1.84483	−0.922414	+	0.386202i	$0.873787\pi$
$444$	4.10363	0.194750
$445$	25.3608	1.20222
$446$	−30.2023	−1.43012
$447$	−5.34982	−0.253038
$448$	−2.30845	−0.109064
$449$	6.56424	0.309786	0.154893	−	0.987931i	$-0.450497\pi$
$449$	6.56424	0.309786	0.154893	+	0.987931i	$0.450497\pi$
$450$	0.919718	0.0433559
$451$	−4.53868	−0.213718
$452$	−28.0686	−1.32024
$453$	4.67126	0.219475
$454$	−22.5575	−1.05868
$455$	−1.69141	−0.0792944
$456$	0.363898	0.0170411
$457$	−9.36448	−0.438052	−0.219026	−	0.975719i	$-0.570288\pi$
$457$	−9.36448	−0.438052	−0.219026	+	0.975719i	$0.570288\pi$
$458$	28.7542	1.34359
$459$	−1.37814	−0.0643262
$460$	−3.00278	−0.140005
$461$	−5.76512	−0.268508	−0.134254	−	0.990947i	$-0.542864\pi$
$461$	−5.76512	−0.268508	−0.134254	+	0.990947i	$0.542864\pi$
$462$	−0.220591	−0.0102628
$463$	7.20063	0.334641	0.167321	−	0.985903i	$-0.446488\pi$
$463$	7.20063	0.334641	0.167321	+	0.985903i	$0.446488\pi$
$464$	−36.1469	−1.67808
$465$	0.251206	0.0116494
$466$	1.87851	0.0870203
$467$	22.4473	1.03874	0.519370	−	0.854550i	$-0.326167\pi$
$467$	22.4473	1.03874	0.519370	+	0.854550i	$0.326167\pi$
$468$	7.03082	0.325000
$469$	1.63548	0.0755195
$470$	−58.3177	−2.69000
$471$	4.07933	0.187966
$472$	1.15684	0.0532480
$473$	1.00000	0.0459800
$474$	6.72925	0.309085
$475$	−0.345621	−0.0158582
$476$	−0.805278	−0.0369099
$477$	−17.0989	−0.782903
$478$	40.9762	1.87421
$479$	−22.4949	−1.02782	−0.513909	−	0.857845i	$-0.671803\pi$
$479$	−22.4949	−1.02782	−0.513909	+	0.857845i	$0.671803\pi$
$480$	−3.84647	−0.175567
$481$	16.3649	0.746176
$482$	30.7032	1.39849
$483$	0.0955150	0.00434608
$484$	1.60683	0.0730375
$485$	35.9369	1.63181
$486$	11.6019	0.526272
$487$	−11.7125	−0.530743	−0.265372	−	0.964146i	$-0.585495\pi$
$487$	−11.7125	−0.530743	−0.265372	+	0.964146i	$0.585495\pi$
$488$	2.02305	0.0915791
$489$	−0.854916	−0.0386606
$490$	29.1273	1.31584
$491$	−14.4225	−0.650877	−0.325439	−	0.945563i	$-0.605512\pi$
$491$	−14.4225	−0.650877	−0.325439	+	0.945563i	$0.605512\pi$
$492$	−1.69023	−0.0762016
$493$	−7.80413	−0.351480
$494$	−5.93072	−0.266836
$495$	6.69550	0.300941
$496$	2.20912	0.0991924
$497$	−3.09805	−0.138967
$498$	6.48988	0.290818
$499$	29.6941	1.32929	0.664644	−	0.747160i	$-0.268583\pi$
$499$	29.6941	1.32929	0.664644	+	0.747160i	$0.268583\pi$
$500$	−17.6575	−0.789670
$501$	5.23258	0.233774
$502$	−30.8328	−1.37614
$503$	−16.2079	−0.722676	−0.361338	−	0.932435i	$-0.617680\pi$
$503$	−16.2079	−0.722676	−0.361338	+	0.932435i	$0.617680\pi$
$504$	−1.10256	−0.0491117
$505$	−23.8593	−1.06173
$506$	−1.56174	−0.0694277
$507$	2.50177	0.111107
$508$	−19.8298	−0.879807
$509$	−25.3902	−1.12540	−0.562700	−	0.826661i	$-0.690238\pi$
$509$	−25.3902	−1.12540	−0.562700	+	0.826661i	$0.690238\pi$
$510$	−1.00028	−0.0442929
$511$	5.57659	0.246694
$512$	−26.9090	−1.18922
$513$	−2.89785	−0.127943
$514$	47.0339	2.07458
$515$	−25.1669	−1.10899
$516$	0.372406	0.0163943
$517$	−13.5123	−0.594270
$518$	10.4880	0.460814
$519$	1.69919	0.0745862
$520$	−2.52011	−0.110514
$521$	−17.9443	−0.786154	−0.393077	−	0.919506i	$-0.628589\pi$
$521$	−17.9443	−0.786154	−0.393077	+	0.919506i	$0.628589\pi$
$522$	43.6679	1.91129
$523$	−9.82093	−0.429439	−0.214720	−	0.976676i	$-0.568884\pi$
$523$	−9.82093	−0.429439	−0.214720	+	0.976676i	$0.568884\pi$
$524$	2.90104	0.126732
$525$	−0.0190916	−0.000833227 0
$526$	31.7169	1.38292
$527$	0.476950	0.0207763
$528$	−1.07348	−0.0467173
$529$	−22.3238	−0.970599
$530$	−25.0474	−1.08799
$531$	−4.56458	−0.198086
$532$	−1.69328	−0.0734129
$533$	−6.74050	−0.291963
$534$	4.91209	0.212567
$535$	−46.5393	−2.01207
$536$	2.43678	0.105253
$537$	−2.10961	−0.0910363
$538$	4.08810	0.176251
$539$	6.74884	0.290693
$540$	5.03236	0.216558
$541$	22.0019	0.945934	0.472967	−	0.881080i	$-0.343183\pi$
$541$	22.0019	0.945934	0.472967	+	0.881080i	$0.343183\pi$
$542$	−10.6637	−0.458046
$543$	−2.11701	−0.0908494
$544$	−7.30307	−0.313117
$545$	−43.9129	−1.88102
$546$	−0.327605	−0.0140202
$547$	−23.7472	−1.01535	−0.507677	−	0.861547i	$-0.669496\pi$
$547$	−23.7472	−1.01535	−0.507677	+	0.861547i	$0.669496\pi$
$548$	7.21581	0.308244
$549$	−7.98238	−0.340680
$550$	0.312162	0.0133106
$551$	−16.4099	−0.699087
$552$	0.142312	0.00605722
$553$	7.66184	0.325815
$554$	14.7727	0.627631
$555$	5.80374	0.246355
$556$	−21.3750	−0.906500
$557$	10.3331	0.437829	0.218914	−	0.975744i	$-0.429748\pi$
$557$	10.3331	0.437829	0.218914	+	0.975744i	$0.429748\pi$
$558$	−2.66876	−0.112978
$559$	1.48512	0.0628140
$560$	−5.27512	−0.222914
$561$	−0.231765	−0.00978514
$562$	10.1554	0.428378
$563$	−42.1979	−1.77843	−0.889215	−	0.457490i	$-0.848748\pi$
$563$	−42.1979	−1.77843	−0.889215	+	0.457490i	$0.848748\pi$
$564$	−5.03207	−0.211888
$565$	−39.6973	−1.67008
$566$	30.9038	1.29898
$567$	4.26962	0.179307
$568$	−4.61594	−0.193680
$569$	31.8485	1.33516	0.667578	−	0.744540i	$-0.267331\pi$
$569$	31.8485	1.33516	0.667578	+	0.744540i	$0.267331\pi$
$570$	−2.10330	−0.0880977
$571$	−34.7941	−1.45609	−0.728044	−	0.685530i	$-0.759570\pi$
$571$	−34.7941	−1.45609	−0.728044	+	0.685530i	$0.759570\pi$
$572$	2.38633	0.0997776
$573$	−0.839197	−0.0350580
$574$	−4.31986	−0.180307
$575$	−0.135165	−0.00563675
$576$	13.5712	0.565467
$577$	34.8301	1.45000	0.724999	−	0.688750i	$-0.241840\pi$
$577$	34.8301	1.45000	0.724999	+	0.688750i	$0.241840\pi$
$578$	−1.89916	−0.0789948
$579$	−0.213346	−0.00886637
$580$	28.4972	1.18328
$581$	7.38929	0.306560
$582$	6.96054	0.288524
$583$	−5.80353	−0.240358
$584$	8.30883	0.343822
$585$	9.94365	0.411119
$586$	−21.9068	−0.904962
$587$	−19.4760	−0.803859	−0.401930	−	0.915671i	$-0.631660\pi$
$587$	−19.4760	−0.803859	−0.401930	+	0.915671i	$0.631660\pi$
$588$	2.51331	0.103647
$589$	1.00289	0.0413235
$590$	−6.68647	−0.275278
$591$	3.76096	0.154705
$592$	51.0385	2.09767
$593$	7.90236	0.324511	0.162256	−	0.986749i	$-0.448123\pi$
$593$	7.90236	0.324511	0.162256	+	0.986749i	$0.448123\pi$
$594$	2.61732	0.107390
$595$	−1.13890	−0.0466904
$596$	37.0902	1.51927
$597$	0.614450	0.0251477
$598$	−2.31937	−0.0948463
$599$	−1.36488	−0.0557675	−0.0278837	−	0.999611i	$-0.508877\pi$
$599$	−1.36488	−0.0557675	−0.0278837	+	0.999611i	$0.508877\pi$
$600$	−0.0284455	−0.00116128
$601$	−11.1871	−0.456333	−0.228166	−	0.973622i	$-0.573273\pi$
$601$	−11.1871	−0.456333	−0.228166	+	0.973622i	$0.573273\pi$
$602$	0.951787	0.0387919
$603$	−9.61486	−0.391547
$604$	−32.3858	−1.31776
$605$	2.27252	0.0923913
$606$	−4.62126	−0.187726
$607$	6.40398	0.259930	0.129965	−	0.991519i	$-0.458514\pi$
$607$	6.40398	0.259930	0.129965	+	0.991519i	$0.458514\pi$
$608$	−15.3563	−0.622782
$609$	−0.906463	−0.0367318
$610$	−11.6931	−0.473439
$611$	−20.0674	−0.811842
$612$	4.73416	0.191367
$613$	1.45911	0.0589328	0.0294664	−	0.999566i	$-0.490619\pi$
$613$	1.45911	0.0589328	0.0294664	+	0.999566i	$0.490619\pi$
$614$	12.6342	0.509874
$615$	−2.39049	−0.0963938
$616$	−0.374219	−0.0150777
$617$	44.7134	1.80009	0.900046	−	0.435794i	$-0.143532\pi$
$617$	44.7134	1.80009	0.900046	+	0.435794i	$0.143532\pi$
$618$	−4.87452	−0.196082
$619$	−44.5714	−1.79148	−0.895738	−	0.444583i	$-0.853352\pi$
$619$	−44.5714	−1.79148	−0.895738	+	0.444583i	$0.853352\pi$
$620$	−1.74161	−0.0699446
$621$	−1.13329	−0.0454772
$622$	45.6667	1.83107
$623$	5.59284	0.224072
$624$	−1.59425	−0.0638212
$625$	−25.7948	−1.03179
$626$	14.0864	0.563007
$627$	−0.487338	−0.0194624
$628$	−28.2820	−1.12857
$629$	11.0192	0.439365
$630$	6.37269	0.253894
$631$	6.04211	0.240533	0.120266	−	0.992742i	$-0.461625\pi$
$631$	6.04211	0.240533	0.120266	+	0.992742i	$0.461625\pi$
$632$	11.4157	0.454094
$633$	−0.862078	−0.0342645
$634$	−24.4951	−0.972825
$635$	−28.0452	−1.11294
$636$	−2.16127	−0.0857000
$637$	10.0229	0.397120
$638$	14.8213	0.586782
$639$	18.2132	0.720503
$640$	−13.3129	−0.526239
$641$	17.2182	0.680076	0.340038	−	0.940412i	$-0.389560\pi$
$641$	17.2182	0.680076	0.340038	+	0.940412i	$0.389560\pi$
$642$	−9.01410	−0.355758
$643$	20.7144	0.816897	0.408449	−	0.912781i	$-0.366070\pi$
$643$	20.7144	0.816897	0.408449	+	0.912781i	$0.366070\pi$
$644$	−0.662204	−0.0260945
$645$	0.526692	0.0207385
$646$	−3.99342	−0.157119
$647$	−12.3523	−0.485621	−0.242810	−	0.970074i	$-0.578069\pi$
$647$	−12.3523	−0.485621	−0.242810	+	0.970074i	$0.578069\pi$
$648$	6.36151	0.249904
$649$	−1.54926	−0.0608140
$650$	0.463599	0.0181838
$651$	0.0553986	0.00217124
$652$	5.92712	0.232124
$653$	0.826443	0.0323412	0.0161706	−	0.999869i	$-0.494853\pi$
$653$	0.826443	0.0323412	0.0161706	+	0.999869i	$0.494853\pi$
$654$	−8.50540	−0.332587
$655$	4.10292	0.160315
$656$	−21.0221	−0.820775
$657$	−32.7843	−1.27904
$658$	−12.8608	−0.501368
$659$	13.5325	0.527152	0.263576	−	0.964639i	$-0.415098\pi$
$659$	13.5325	0.527152	0.263576	+	0.964639i	$0.415098\pi$
$660$	0.846302	0.0329423
$661$	−48.9005	−1.90201	−0.951004	−	0.309179i	$-0.899946\pi$
$661$	−48.9005	−1.90201	−0.951004	+	0.309179i	$0.899946\pi$
$662$	−44.6540	−1.73553
$663$	−0.344200	−0.0133676
$664$	11.0097	0.427258
$665$	−2.39479	−0.0928661
$666$	−61.6579	−2.38919
$667$	−6.41757	−0.248489
$668$	−36.2774	−1.40361
$669$	−3.68575	−0.142499
$670$	−14.0844	−0.544129
$671$	−2.70930	−0.104592
$672$	−0.848264	−0.0327225
$673$	17.0226	0.656174	0.328087	−	0.944647i	$-0.393596\pi$
$673$	17.0226	0.656174	0.328087	+	0.944647i	$0.393596\pi$
$674$	13.6006	0.523875
$675$	0.226523	0.00871886
$676$	−17.3447	−0.667105
$677$	−39.9986	−1.53727	−0.768636	−	0.639687i	$-0.779064\pi$
$677$	−39.9986	−1.53727	−0.768636	+	0.639687i	$0.779064\pi$
$678$	−7.68888	−0.295290
$679$	7.92518	0.304140
$680$	−1.69690	−0.0650733
$681$	−2.75282	−0.105488
$682$	−0.905806	−0.0346851
$683$	−21.8880	−0.837520	−0.418760	−	0.908097i	$-0.637535\pi$
$683$	−21.8880	−0.837520	−0.418760	+	0.908097i	$0.637535\pi$
$684$	9.95464	0.380625
$685$	10.2053	0.389924
$686$	13.0860	0.499624
$687$	3.50903	0.133878
$688$	4.63176	0.176584
$689$	−8.61896	−0.328356
$690$	−0.822556	−0.0313142
$691$	20.8566	0.793421	0.396710	−	0.917944i	$-0.370152\pi$
$691$	20.8566	0.793421	0.396710	+	0.917944i	$0.370152\pi$
$692$	−11.7805	−0.447826
$693$	1.47656	0.0560900
$694$	−36.8287	−1.39800
$695$	−30.2305	−1.14671
$696$	−1.35058	−0.0511937
$697$	−4.53868	−0.171915
$698$	37.4206	1.41639
$699$	0.229245	0.00867083
$700$	0.132362	0.00500281
$701$	−14.1197	−0.533294	−0.266647	−	0.963794i	$-0.585916\pi$
$701$	−14.1197	−0.533294	−0.266647	+	0.963794i	$0.585916\pi$
$702$	3.88704	0.146707
$703$	23.1704	0.873888
$704$	4.60621	0.173603
$705$	−7.11683	−0.268035
$706$	43.8734	1.65120
$707$	−5.26171	−0.197887
$708$	−0.576956	−0.0216833
$709$	14.8662	0.558313	0.279156	−	0.960246i	$-0.409945\pi$
$709$	14.8662	0.558313	0.279156	+	0.960246i	$0.409945\pi$
$710$	26.6798	1.00128
$711$	−45.0433	−1.68926
$712$	8.33304	0.312294
$713$	0.392210	0.0146884
$714$	−0.220591	−0.00825542
$715$	3.37498	0.126217
$716$	14.6259	0.546594
$717$	5.00055	0.186749
$718$	−12.6867	−0.473464
$719$	29.8944	1.11487	0.557436	−	0.830220i	$-0.311785\pi$
$719$	29.8944	1.11487	0.557436	+	0.830220i	$0.311785\pi$
$720$	31.0120	1.15575
$721$	−5.55006	−0.206695
$722$	27.6871	1.03041
$723$	3.74687	0.139348
$724$	14.6772	0.545473
$725$	1.28275	0.0476401
$726$	0.440160	0.0163359
$727$	18.0969	0.671178	0.335589	−	0.942008i	$-0.391065\pi$
$727$	18.0969	0.671178	0.335589	+	0.942008i	$0.391065\pi$
$728$	−0.555761	−0.0205979
$729$	−24.1425	−0.894167
$730$	−48.0245	−1.77747
$731$	1.00000	0.0369863
$732$	−1.00896	−0.0372923
$733$	−0.535484	−0.0197786	−0.00988928	−	0.999951i	$-0.503148\pi$
$733$	−0.535484	−0.0197786	−0.00988928	+	0.999951i	$0.503148\pi$
$734$	−3.34944	−0.123630
$735$	3.55456	0.131112
$736$	−6.00553	−0.221367
$737$	−3.26338	−0.120208
$738$	25.3961	0.934843
$739$	−19.1220	−0.703413	−0.351706	−	0.936110i	$-0.614398\pi$
$739$	−19.1220	−0.703413	−0.351706	+	0.936110i	$0.614398\pi$
$740$	−40.2373	−1.47915
$741$	−0.723758	−0.0265879
$742$	−5.52373	−0.202782
$743$	49.1960	1.80483	0.902414	−	0.430871i	$-0.141794\pi$
$743$	49.1960	1.80483	0.902414	+	0.430871i	$0.141794\pi$
$744$	0.0825410	0.00302610
$745$	52.4565	1.92186
$746$	−49.0575	−1.79612
$747$	−43.4411	−1.58943
$748$	1.60683	0.0587513
$749$	−10.2633	−0.375014
$750$	−4.83696	−0.176621
$751$	−25.7458	−0.939477	−0.469738	−	0.882806i	$-0.655652\pi$
$751$	−25.7458	−0.939477	−0.469738	+	0.882806i	$0.655652\pi$
$752$	−62.5858	−2.28227
$753$	−3.76269	−0.137120
$754$	22.0115	0.801612
$755$	−45.8030	−1.66694
$756$	1.10979	0.0403626
$757$	−42.0251	−1.52743	−0.763714	−	0.645555i	$-0.776626\pi$
$757$	−42.0251	−1.52743	−0.763714	+	0.645555i	$0.776626\pi$
$758$	31.2533	1.13517
$759$	−0.190587	−0.00691788
$760$	−3.56812	−0.129429
$761$	−25.4996	−0.924361	−0.462180	−	0.886786i	$-0.652933\pi$
$761$	−25.4996	−0.924361	−0.462180	+	0.886786i	$0.652933\pi$
$762$	−5.43202	−0.196781
$763$	−9.68414	−0.350589
$764$	5.81814	0.210493
$765$	6.69550	0.242076
$766$	26.7709	0.967272
$767$	−2.30085	−0.0830788
$768$	−4.71367	−0.170090
$769$	39.8656	1.43759	0.718796	−	0.695221i	$-0.244694\pi$
$769$	39.8656	1.43759	0.718796	+	0.695221i	$0.244694\pi$
$770$	2.16296	0.0779476
$771$	5.73980	0.206714
$772$	1.47913	0.0532349
$773$	−27.6784	−0.995522	−0.497761	−	0.867314i	$-0.665844\pi$
$773$	−27.6784	−0.995522	−0.497761	+	0.867314i	$0.665844\pi$
$774$	−5.59548	−0.201125
$775$	−0.0783953	−0.00281604
$776$	11.8081	0.423886
$777$	1.27990	0.0459162
$778$	−8.12494	−0.291293
$779$	−9.54359	−0.341935
$780$	1.25686	0.0450029
$781$	6.18175	0.221200
$782$	−1.56174	−0.0558477
$783$	10.7552	0.384360
$784$	31.2590	1.11639
$785$	−39.9990	−1.42763
$786$	0.794687	0.0283455
$787$	1.98579	0.0707857	0.0353928	−	0.999373i	$-0.488732\pi$
$787$	1.98579	0.0707857	0.0353928	+	0.999373i	$0.488732\pi$
$788$	−26.0746	−0.928871
$789$	3.87058	0.137796
$790$	−65.9822	−2.34754
$791$	−8.75446	−0.311273
$792$	2.20000	0.0781737
$793$	−4.02365	−0.142884
$794$	−21.1842	−0.751800
$795$	−3.05667	−0.108409
$796$	−4.25997	−0.150991
$797$	45.0994	1.59750	0.798751	−	0.601661i	$-0.205494\pi$
$797$	45.0994	1.59750	0.798751	+	0.601661i	$0.205494\pi$
$798$	−0.463842	−0.0164198
$799$	−13.5123	−0.478031
$800$	1.20039	0.0424402
$801$	−32.8799	−1.16175
$802$	−39.9547	−1.41085
$803$	−11.1273	−0.392675
$804$	−1.21530	−0.0428605
$805$	−0.936551	−0.0330091
$806$	−1.34523	−0.0473838
$807$	0.498893	0.0175619
$808$	−7.83967	−0.275799
$809$	−47.5234	−1.67084	−0.835418	−	0.549616i	$-0.814774\pi$
$809$	−47.5234	−1.67084	−0.835418	+	0.549616i	$0.814774\pi$
$810$	−36.7691	−1.29193
$811$	−39.7544	−1.39597	−0.697983	−	0.716114i	$-0.745919\pi$
$811$	−39.7544	−1.39597	−0.697983	+	0.716114i	$0.745919\pi$
$812$	6.28450	0.220543
$813$	−1.30135	−0.0456404
$814$	−20.9273	−0.733502
$815$	8.38269	0.293633
$816$	−1.07348	−0.0375794
$817$	2.10272	0.0735650
$818$	2.49096	0.0870945
$819$	2.19288	0.0766254
$820$	16.5732	0.578762
$821$	14.1450	0.493664	0.246832	−	0.969058i	$-0.420610\pi$
$821$	14.1450	0.493664	0.246832	+	0.969058i	$0.420610\pi$
$822$	1.97664	0.0689432
$823$	12.7394	0.444067	0.222034	−	0.975039i	$-0.428731\pi$
$823$	12.7394	0.444067	0.222034	+	0.975039i	$0.428731\pi$
$824$	−8.26931	−0.288075
$825$	0.0380948	0.00132629
$826$	−1.47457	−0.0513069
$827$	35.8607	1.24700	0.623499	−	0.781824i	$-0.285710\pi$
$827$	35.8607	1.24700	0.623499	+	0.781824i	$0.285710\pi$
$828$	3.89304	0.135293
$829$	−24.4209	−0.848173	−0.424086	−	0.905622i	$-0.639405\pi$
$829$	−24.4209	−0.848173	−0.424086	+	0.905622i	$0.639405\pi$
$830$	−63.6351	−2.20881
$831$	1.80279	0.0625381
$832$	6.84078	0.237162
$833$	6.74884	0.233833
$834$	−5.85528	−0.202752
$835$	−51.3069	−1.77555
$836$	3.37871	0.116855
$837$	−0.657305	−0.0227198
$838$	−38.4358	−1.32774
$839$	43.2330	1.49257	0.746284	−	0.665628i	$-0.231836\pi$
$839$	43.2330	1.49257	0.746284	+	0.665628i	$0.231836\pi$
$840$	−0.197098	−0.00680053
$841$	31.9045	1.10015
$842$	−45.7511	−1.57669
$843$	1.23931	0.0426842
$844$	5.97677	0.205729
$845$	−24.5306	−0.843877
$846$	75.6078	2.59945
$847$	0.501161	0.0172201
$848$	−26.8806	−0.923083
$849$	3.77136	0.129433
$850$	0.312162	0.0107071
$851$	9.06143	0.310622
$852$	2.30212	0.0788694
$853$	5.88407	0.201467	0.100733	−	0.994913i	$-0.467881\pi$
$853$	5.88407	0.201467	0.100733	+	0.994913i	$0.467881\pi$
$854$	−2.57868	−0.0882406
$855$	14.0788	0.481485
$856$	−15.2918	−0.522664
$857$	4.59657	0.157016	0.0785080	−	0.996913i	$-0.474984\pi$
$857$	4.59657	0.157016	0.0785080	+	0.996913i	$0.474984\pi$
$858$	0.653692	0.0223167
$859$	−49.9343	−1.70374	−0.851869	−	0.523755i	$-0.824531\pi$
$859$	−49.9343	−1.70374	−0.851869	+	0.523755i	$0.824531\pi$
$860$	−3.65155	−0.124517
$861$	−0.527176	−0.0179661
$862$	63.7602	2.17168
$863$	−6.49019	−0.220929	−0.110464	−	0.993880i	$-0.535234\pi$
$863$	−6.49019	−0.220929	−0.110464	+	0.993880i	$0.535234\pi$
$864$	10.0647	0.342407
$865$	−16.6610	−0.566492
$866$	−12.1512	−0.412913
$867$	−0.231765	−0.00787116
$868$	−0.384077	−0.0130364
$869$	−15.2882	−0.518616
$870$	7.80628	0.264658
$871$	−4.84653	−0.164218
$872$	−14.4289	−0.488623
$873$	−46.5915	−1.57688
$874$	−3.28391	−0.111080
$875$	−5.50730	−0.186181
$876$	−4.14389	−0.140009
$877$	29.8182	1.00689	0.503445	−	0.864027i	$-0.332066\pi$
$877$	29.8182	1.00689	0.503445	+	0.864027i	$0.332066\pi$
$878$	16.5897	0.559875
$879$	−2.67341	−0.0901718
$880$	10.5258	0.354825
$881$	−23.4859	−0.791262	−0.395631	−	0.918410i	$-0.629474\pi$
$881$	−23.4859	−0.791262	−0.395631	+	0.918410i	$0.629474\pi$
$882$	−37.7630	−1.27155
$883$	7.27245	0.244737	0.122369	−	0.992485i	$-0.460951\pi$
$883$	7.27245	0.244737	0.122369	+	0.992485i	$0.460951\pi$
$884$	2.38633	0.0802611
$885$	−0.815986	−0.0274291
$886$	73.7429	2.47744
$887$	47.1265	1.58235	0.791177	−	0.611588i	$-0.209469\pi$
$887$	47.1265	1.58235	0.791177	+	0.611588i	$0.209469\pi$
$888$	1.90699	0.0639943
$889$	−6.18483	−0.207433
$890$	−48.1644	−1.61447
$891$	−8.51945	−0.285412
$892$	25.5533	0.855587
$893$	−28.4126	−0.950793
$894$	10.1602	0.339807
$895$	20.6853	0.691433
$896$	−2.93590	−0.0980816
$897$	−0.283046	−0.00945062
$898$	−12.4666	−0.416015
$899$	−3.72218	−0.124142
$900$	−0.778145	−0.0259382
$901$	−5.80353	−0.193344
$902$	8.61970	0.287005
$903$	0.116152	0.00386529
$904$	−13.0437	−0.433827
$905$	20.7578	0.690014
$906$	−8.87149	−0.294735
$907$	14.3442	0.476290	0.238145	−	0.971230i	$-0.423461\pi$
$907$	14.3442	0.476290	0.238145	+	0.971230i	$0.423461\pi$
$908$	19.0852	0.633366
$909$	30.9331	1.02599
$910$	3.21226	0.106485
$911$	−45.3982	−1.50411	−0.752055	−	0.659101i	$-0.770937\pi$
$911$	−45.3982	−1.50411	−0.752055	+	0.659101i	$0.770937\pi$
$912$	−2.25724	−0.0747446
$913$	−14.7444	−0.487967
$914$	17.7847	0.588265
$915$	−1.42697	−0.0471742
$916$	−24.3280	−0.803821
$917$	0.904820	0.0298798
$918$	2.61732	0.0863844
$919$	−9.43209	−0.311136	−0.155568	−	0.987825i	$-0.549721\pi$
$919$	−9.43209	−0.311136	−0.155568	+	0.987825i	$0.549721\pi$
$920$	−1.39541	−0.0460054
$921$	1.54182	0.0508046
$922$	10.9489	0.360583
$923$	9.18066	0.302185
$924$	0.186636	0.00613986
$925$	−1.81121	−0.0595522
$926$	−13.6752	−0.449394
$927$	32.6284	1.07166
$928$	56.9941	1.87092
$929$	26.8592	0.881221	0.440611	−	0.897698i	$-0.354762\pi$
$929$	26.8592	0.881221	0.440611	+	0.897698i	$0.354762\pi$
$930$	−0.477081	−0.0156441
$931$	14.1909	0.465089
$932$	−1.58935	−0.0520609
$933$	5.57296	0.182450
$934$	−42.6312	−1.39494
$935$	2.27252	0.0743195
$936$	3.26727	0.106794
$937$	−22.2168	−0.725791	−0.362895	−	0.931830i	$-0.618212\pi$
$937$	−22.2168	−0.725791	−0.362895	+	0.931830i	$0.618212\pi$
$938$	−3.10605	−0.101416
$939$	1.71904	0.0560989
$940$	49.3408	1.60932
$941$	−12.8859	−0.420068	−0.210034	−	0.977694i	$-0.567357\pi$
$941$	−12.8859	−0.420068	−0.210034	+	0.977694i	$0.567357\pi$
$942$	−7.74733	−0.252422
$943$	−3.73229	−0.121540
$944$	−7.17583	−0.233553
$945$	1.56957	0.0510580
$946$	−1.89916	−0.0617472
$947$	−53.2529	−1.73049	−0.865243	−	0.501353i	$-0.832836\pi$
$947$	−53.2529	−1.73049	−0.865243	+	0.501353i	$0.832836\pi$
$948$	−5.69341	−0.184914
$949$	−16.5255	−0.536440
$950$	0.656390	0.0212961
$951$	−2.98927	−0.0969338
$952$	−0.374219	−0.0121285
$953$	16.1455	0.523004	0.261502	−	0.965203i	$-0.415782\pi$
$953$	16.1455	0.523004	0.261502	+	0.965203i	$0.415782\pi$
$954$	32.4735	1.05137
$955$	8.22857	0.266270
$956$	−34.6687	−1.12127
$957$	1.80873	0.0584678
$958$	42.7215	1.38027
$959$	2.25058	0.0726749
$960$	2.42605	0.0783006
$961$	−30.7725	−0.992662
$962$	−31.0797	−1.00205
$963$	60.3373	1.94434
$964$	−25.9770	−0.836663
$965$	2.09192	0.0673413
$966$	−0.181399	−0.00583641
$967$	−45.5056	−1.46336	−0.731681	−	0.681648i	$-0.761264\pi$
$967$	−45.5056	−1.46336	−0.731681	+	0.681648i	$0.761264\pi$
$968$	0.746704	0.0240000
$969$	−0.487338	−0.0156556
$970$	−68.2500	−2.19138
$971$	19.7269	0.633068	0.316534	−	0.948581i	$-0.397481\pi$
$971$	19.7269	0.633068	0.316534	+	0.948581i	$0.397481\pi$
$972$	−9.81600	−0.314848
$973$	−6.66675	−0.213726
$974$	22.2439	0.712742
$975$	0.0565755	0.00181186
$976$	−12.5489	−0.401679
$977$	26.4194	0.845232	0.422616	−	0.906309i	$-0.361112\pi$
$977$	26.4194	0.845232	0.422616	+	0.906309i	$0.361112\pi$
$978$	1.62363	0.0519178
$979$	−11.1598	−0.356668
$980$	−24.6437	−0.787215
$981$	56.9322	1.81771
$982$	27.3906	0.874071
$983$	−21.7534	−0.693827	−0.346913	−	0.937897i	$-0.612770\pi$
$983$	−21.7534	−0.693827	−0.346913	+	0.937897i	$0.612770\pi$
$984$	−0.785464	−0.0250397
$985$	−36.8772	−1.17501
$986$	14.8213	0.472007
$987$	−1.56948	−0.0499570
$988$	5.01780	0.159637
$989$	0.822329	0.0261486
$990$	−12.7159	−0.404137
$991$	26.1466	0.830574	0.415287	−	0.909690i	$-0.363681\pi$
$991$	26.1466	0.830574	0.415287	+	0.909690i	$0.363681\pi$
$992$	−3.48320	−0.110592
$993$	−5.44937	−0.172931
$994$	5.88371	0.186620
$995$	−6.02485	−0.191001
$996$	−5.49089	−0.173985
$997$	−42.1696	−1.33553	−0.667763	−	0.744374i	$-0.732748\pi$
$997$	−42.1696	−1.33553	−0.667763	+	0.744374i	$0.732748\pi$
$998$	−56.3939	−1.78512
$999$	−15.1861	−0.480466

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.h.1.16	✓	74

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.h.1.16	✓	74	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-1.89916 q^{2} -0.231765 q^{3} +1.60683 q^{4} +2.27252 q^{5} +0.440160 q^{6} +0.501161 q^{7} +0.746704 q^{8} -2.94628 q^{9} +O(q^{10})\)	\(q-1.89916 q^{2} -0.231765 q^{3} +1.60683 q^{4} +2.27252 q^{5} +0.440160 q^{6} +0.501161 q^{7} +0.746704 q^{8} -2.94628 q^{9} -4.31590 q^{10} -1.00000 q^{11} -0.372406 q^{12} -1.48512 q^{13} -0.951787 q^{14} -0.526692 q^{15} -4.63176 q^{16} -1.00000 q^{17} +5.59548 q^{18} -2.10272 q^{19} +3.65155 q^{20} -0.116152 q^{21} +1.89916 q^{22} -0.822329 q^{23} -0.173060 q^{24} +0.164368 q^{25} +2.82049 q^{26} +1.37814 q^{27} +0.805278 q^{28} +7.80413 q^{29} +1.00028 q^{30} -0.476950 q^{31} +7.30307 q^{32} +0.231765 q^{33} +1.89916 q^{34} +1.13890 q^{35} -4.73416 q^{36} -11.0192 q^{37} +3.99342 q^{38} +0.344200 q^{39} +1.69690 q^{40} +4.53868 q^{41} +0.220591 q^{42} -1.00000 q^{43} -1.60683 q^{44} -6.69550 q^{45} +1.56174 q^{46} +13.5123 q^{47} +1.07348 q^{48} -6.74884 q^{49} -0.312162 q^{50} +0.231765 q^{51} -2.38633 q^{52} +5.80353 q^{53} -2.61732 q^{54} -2.27252 q^{55} +0.374219 q^{56} +0.487338 q^{57} -14.8213 q^{58} +1.54926 q^{59} -0.846302 q^{60} +2.70930 q^{61} +0.905806 q^{62} -1.47656 q^{63} -4.60621 q^{64} -3.37498 q^{65} -0.440160 q^{66} +3.26338 q^{67} -1.60683 q^{68} +0.190587 q^{69} -2.16296 q^{70} -6.18175 q^{71} -2.20000 q^{72} +11.1273 q^{73} +20.9273 q^{74} -0.0380948 q^{75} -3.37871 q^{76} -0.501161 q^{77} -0.653692 q^{78} +15.2882 q^{79} -10.5258 q^{80} +8.51945 q^{81} -8.61970 q^{82} +14.7444 q^{83} -0.186636 q^{84} -2.27252 q^{85} +1.89916 q^{86} -1.80873 q^{87} -0.746704 q^{88} +11.1598 q^{89} +12.7159 q^{90} -0.744286 q^{91} -1.32134 q^{92} +0.110540 q^{93} -25.6621 q^{94} -4.77849 q^{95} -1.69260 q^{96} +15.8136 q^{97} +12.8172 q^{98} +2.94628 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9}+O(q^{10}) \) 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9	\( 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9} - 9 q^{10} - 74 q^{11} - 3 q^{12} + 4 q^{13} - 5 q^{14} - 17 q^{15} + 85 q^{16} - 74 q^{17} - 23 q^{18} - 21 q^{20} - 22 q^{21} + 7 q^{22} - 23 q^{23} - 51 q^{24} + 90 q^{25} - 46 q^{26} - 27 q^{27} - 61 q^{28} - 63 q^{29} - 22 q^{30} - 31 q^{31} - 69 q^{32} + 3 q^{33} + 7 q^{34} - 20 q^{35} + 51 q^{36} + 8 q^{37} - 2 q^{38} - 77 q^{39} - 37 q^{40} - 64 q^{41} + 13 q^{42} - 74 q^{43} - 79 q^{44} - 12 q^{45} - 53 q^{46} - 32 q^{47} + 2 q^{48} + 78 q^{49} - 104 q^{50} + 3 q^{51} + 13 q^{52} + 25 q^{53} - 110 q^{54} + 6 q^{55} - 29 q^{56} - 29 q^{57} - 14 q^{58} - 61 q^{59} - 82 q^{60} - 36 q^{61} - 63 q^{62} - 104 q^{63} + 107 q^{64} - 65 q^{65} + 12 q^{66} + 33 q^{67} - 79 q^{68} - 34 q^{69} - 3 q^{70} - 168 q^{71} - 67 q^{72} - 47 q^{73} - 54 q^{74} - 53 q^{75} - 4 q^{76} + 16 q^{77} - 3 q^{78} - 79 q^{79} - 59 q^{80} + 70 q^{81} - 18 q^{82} - 36 q^{83} - 118 q^{84} + 6 q^{85} + 7 q^{86} - 24 q^{87} + 21 q^{88} - 24 q^{89} + 25 q^{90} - 14 q^{91} - 18 q^{92} - 13 q^{93} + 9 q^{94} - 155 q^{95} - 50 q^{96} + q^{97} - 60 q^{98} - 75 q^{99}+O(q^{100}) \) 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9 - 9 * q^10 - 74 * q^11 - 3 * q^12 + 4 * q^13 - 5 * q^14 - 17 * q^15 + 85 * q^16 - 74 * q^17 - 23 * q^18 - 21 * q^20 - 22 * q^21 + 7 * q^22 - 23 * q^23 - 51 * q^24 + 90 * q^25 - 46 * q^26 - 27 * q^27 - 61 * q^28 - 63 * q^29 - 22 * q^30 - 31 * q^31 - 69 * q^32 + 3 * q^33 + 7 * q^34 - 20 * q^35 + 51 * q^36 + 8 * q^37 - 2 * q^38 - 77 * q^39 - 37 * q^40 - 64 * q^41 + 13 * q^42 - 74 * q^43 - 79 * q^44 - 12 * q^45 - 53 * q^46 - 32 * q^47 + 2 * q^48 + 78 * q^49 - 104 * q^50 + 3 * q^51 + 13 * q^52 + 25 * q^53 - 110 * q^54 + 6 * q^55 - 29 * q^56 - 29 * q^57 - 14 * q^58 - 61 * q^59 - 82 * q^60 - 36 * q^61 - 63 * q^62 - 104 * q^63 + 107 * q^64 - 65 * q^65 + 12 * q^66 + 33 * q^67 - 79 * q^68 - 34 * q^69 - 3 * q^70 - 168 * q^71 - 67 * q^72 - 47 * q^73 - 54 * q^74 - 53 * q^75 - 4 * q^76 + 16 * q^77 - 3 * q^78 - 79 * q^79 - 59 * q^80 + 70 * q^81 - 18 * q^82 - 36 * q^83 - 118 * q^84 + 6 * q^85 + 7 * q^86 - 24 * q^87 + 21 * q^88 - 24 * q^89 + 25 * q^90 - 14 * q^91 - 18 * q^92 - 13 * q^93 + 9 * q^94 - 155 * q^95 - 50 * q^96 + q^97 - 60 * q^98 - 75 * q^99

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