LMFDB - Embedded newform 9282.2.a.bs.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9282,2,Mod(1,9282)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9282, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("9282.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9282 = 2 \cdot 3 \cdot 7 \cdot 13 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9282.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:	$74.1171431562$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.1462249.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 7x^{3} + 7x^{2} + 15x + 2 $ x^5 - 2x^4 - 7x^3 + 7x^2 + 15x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.144408$ of defining polynomial
Character	$\chi$	$=$	9282.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.855592 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.855592 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.855592 q^{10} +4.22324 q^{11} -1.00000 q^{12} +1.00000 q^{13} +1.00000 q^{14} +0.855592 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} -7.42425 q^{19} -0.855592 q^{20} -1.00000 q^{21} +4.22324 q^{22} +3.03574 q^{23} -1.00000 q^{24} -4.26796 q^{25} +1.00000 q^{26} -1.00000 q^{27} +1.00000 q^{28} -2.59064 q^{29} +0.855592 q^{30} -6.12978 q^{31} +1.00000 q^{32} -4.22324 q^{33} +1.00000 q^{34} -0.855592 q^{35} +1.00000 q^{36} +0.647234 q^{37} -7.42425 q^{38} -1.00000 q^{39} -0.855592 q^{40} -10.1671 q^{41} -1.00000 q^{42} -12.2449 q^{43} +4.22324 q^{44} -0.855592 q^{45} +3.03574 q^{46} -2.38802 q^{47} -1.00000 q^{48} +1.00000 q^{49} -4.26796 q^{50} -1.00000 q^{51} +1.00000 q^{52} -0.591130 q^{53} -1.00000 q^{54} -3.61337 q^{55} +1.00000 q^{56} +7.42425 q^{57} -2.59064 q^{58} -9.76294 q^{59} +0.855592 q^{60} -1.31540 q^{61} -6.12978 q^{62} +1.00000 q^{63} +1.00000 q^{64} -0.855592 q^{65} -4.22324 q^{66} +3.84775 q^{67} +1.00000 q^{68} -3.03574 q^{69} -0.855592 q^{70} +14.9352 q^{71} +1.00000 q^{72} -0.0934659 q^{73} +0.647234 q^{74} +4.26796 q^{75} -7.42425 q^{76} +4.22324 q^{77} -1.00000 q^{78} -4.16714 q^{79} -0.855592 q^{80} +1.00000 q^{81} -10.1671 q^{82} +2.37281 q^{83} -1.00000 q^{84} -0.855592 q^{85} -12.2449 q^{86} +2.59064 q^{87} +4.22324 q^{88} -6.79002 q^{89} -0.855592 q^{90} +1.00000 q^{91} +3.03574 q^{92} +6.12978 q^{93} -2.38802 q^{94} +6.35212 q^{95} -1.00000 q^{96} +9.00753 q^{97} +1.00000 q^{98} +4.22324 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} - 7 q^{5} - 5 q^{6} + 5 q^{7} + 5 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 - 7 * q^5 - 5 * q^6 + 5 * q^7 + 5 * q^8 + 5 * q^9	\( 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} - 7 q^{5} - 5 q^{6} + 5 q^{7} + 5 q^{8} + 5 q^{9} - 7 q^{10} - 9 q^{11} - 5 q^{12} + 5 q^{13} + 5 q^{14} + 7 q^{15} + 5 q^{16} + 5 q^{17} + 5 q^{18} - q^{19} - 7 q^{20} - 5 q^{21} - 9 q^{22} - 6 q^{23} - 5 q^{24} + 2 q^{25} + 5 q^{26} - 5 q^{27} + 5 q^{28} - 10 q^{29} + 7 q^{30} - 7 q^{31} + 5 q^{32} + 9 q^{33} + 5 q^{34} - 7 q^{35} + 5 q^{36} - 3 q^{37} - q^{38} - 5 q^{39} - 7 q^{40} - 19 q^{41} - 5 q^{42} - 3 q^{43} - 9 q^{44} - 7 q^{45} - 6 q^{46} - 2 q^{47} - 5 q^{48} + 5 q^{49} + 2 q^{50} - 5 q^{51} + 5 q^{52} + 5 q^{53} - 5 q^{54} + 14 q^{55} + 5 q^{56} + q^{57} - 10 q^{58} - 12 q^{59} + 7 q^{60} - 21 q^{61} - 7 q^{62} + 5 q^{63} + 5 q^{64} - 7 q^{65} + 9 q^{66} + 12 q^{67} + 5 q^{68} + 6 q^{69} - 7 q^{70} + 4 q^{71} + 5 q^{72} + 6 q^{73} - 3 q^{74} - 2 q^{75} - q^{76} - 9 q^{77} - 5 q^{78} + 11 q^{79} - 7 q^{80} + 5 q^{81} - 19 q^{82} - 23 q^{83} - 5 q^{84} - 7 q^{85} - 3 q^{86} + 10 q^{87} - 9 q^{88} - 12 q^{89} - 7 q^{90} + 5 q^{91} - 6 q^{92} + 7 q^{93} - 2 q^{94} + 15 q^{95} - 5 q^{96} - 9 q^{97} + 5 q^{98} - 9 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 - 7 * q^5 - 5 * q^6 + 5 * q^7 + 5 * q^8 + 5 * q^9 - 7 * q^10 - 9 * q^11 - 5 * q^12 + 5 * q^13 + 5 * q^14 + 7 * q^15 + 5 * q^16 + 5 * q^17 + 5 * q^18 - q^19 - 7 * q^20 - 5 * q^21 - 9 * q^22 - 6 * q^23 - 5 * q^24 + 2 * q^25 + 5 * q^26 - 5 * q^27 + 5 * q^28 - 10 * q^29 + 7 * q^30 - 7 * q^31 + 5 * q^32 + 9 * q^33 + 5 * q^34 - 7 * q^35 + 5 * q^36 - 3 * q^37 - q^38 - 5 * q^39 - 7 * q^40 - 19 * q^41 - 5 * q^42 - 3 * q^43 - 9 * q^44 - 7 * q^45 - 6 * q^46 - 2 * q^47 - 5 * q^48 + 5 * q^49 + 2 * q^50 - 5 * q^51 + 5 * q^52 + 5 * q^53 - 5 * q^54 + 14 * q^55 + 5 * q^56 + q^57 - 10 * q^58 - 12 * q^59 + 7 * q^60 - 21 * q^61 - 7 * q^62 + 5 * q^63 + 5 * q^64 - 7 * q^65 + 9 * q^66 + 12 * q^67 + 5 * q^68 + 6 * q^69 - 7 * q^70 + 4 * q^71 + 5 * q^72 + 6 * q^73 - 3 * q^74 - 2 * q^75 - q^76 - 9 * q^77 - 5 * q^78 + 11 * q^79 - 7 * q^80 + 5 * q^81 - 19 * q^82 - 23 * q^83 - 5 * q^84 - 7 * q^85 - 3 * q^86 + 10 * q^87 - 9 * q^88 - 12 * q^89 - 7 * q^90 + 5 * q^91 - 6 * q^92 + 7 * q^93 - 2 * q^94 + 15 * q^95 - 5 * q^96 - 9 * q^97 + 5 * q^98 - 9 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−0.855592	−0.382632	−0.191316	−	0.981528i	$-0.561276\pi$
$5$	−0.855592	−0.382632	−0.191316	+	0.981528i	$0.561276\pi$
$6$	−1.00000	−0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−0.855592	−0.270562
$11$	4.22324	1.27336	0.636678	−	0.771130i	$-0.280308\pi$
$11$	4.22324	1.27336	0.636678	+	0.771130i	$0.280308\pi$
$12$	−1.00000	−0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	1.00000	0.267261
$15$	0.855592	0.220913
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.00000	0.235702
$19$	−7.42425	−1.70324	−0.851619	−	0.524161i	$-0.824379\pi$
$19$	−7.42425	−1.70324	−0.851619	+	0.524161i	$0.824379\pi$
$20$	−0.855592	−0.191316
$21$	−1.00000	−0.218218
$22$	4.22324	0.900399
$23$	3.03574	0.632995	0.316498	−	0.948593i	$-0.397493\pi$
$23$	3.03574	0.632995	0.316498	+	0.948593i	$0.397493\pi$
$24$	−1.00000	−0.204124
$25$	−4.26796	−0.853593
$26$	1.00000	0.196116
$27$	−1.00000	−0.192450
$28$	1.00000	0.188982
$29$	−2.59064	−0.481070	−0.240535	−	0.970640i	$-0.577323\pi$
$29$	−2.59064	−0.481070	−0.240535	+	0.970640i	$0.577323\pi$
$30$	0.855592	0.156209
$31$	−6.12978	−1.10094	−0.550470	−	0.834855i	$-0.685552\pi$
$31$	−6.12978	−1.10094	−0.550470	+	0.834855i	$0.685552\pi$
$32$	1.00000	0.176777
$33$	−4.22324	−0.735172
$34$	1.00000	0.171499
$35$	−0.855592	−0.144621
$36$	1.00000	0.166667
$37$	0.647234	0.106405	0.0532023	−	0.998584i	$-0.483057\pi$
$37$	0.647234	0.106405	0.0532023	+	0.998584i	$0.483057\pi$
$38$	−7.42425	−1.20437
$39$	−1.00000	−0.160128
$40$	−0.855592	−0.135281
$41$	−10.1671	−1.58784	−0.793920	−	0.608022i	$-0.791963\pi$
$41$	−10.1671	−1.58784	−0.793920	+	0.608022i	$0.791963\pi$
$42$	−1.00000	−0.154303
$43$	−12.2449	−1.86733	−0.933666	−	0.358145i	$-0.883409\pi$
$43$	−12.2449	−1.86733	−0.933666	+	0.358145i	$0.883409\pi$
$44$	4.22324	0.636678
$45$	−0.855592	−0.127544
$46$	3.03574	0.447595
$47$	−2.38802	−0.348328	−0.174164	−	0.984717i	$-0.555722\pi$
$47$	−2.38802	−0.348328	−0.174164	+	0.984717i	$0.555722\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	−4.26796	−0.603581
$51$	−1.00000	−0.140028
$52$	1.00000	0.138675
$53$	−0.591130	−0.0811980	−0.0405990	−	0.999176i	$-0.512927\pi$
$53$	−0.591130	−0.0811980	−0.0405990	+	0.999176i	$0.512927\pi$
$54$	−1.00000	−0.136083
$55$	−3.61337	−0.487227
$56$	1.00000	0.133631
$57$	7.42425	0.983365
$58$	−2.59064	−0.340168
$59$	−9.76294	−1.27103	−0.635513	−	0.772090i	$-0.719212\pi$
$59$	−9.76294	−1.27103	−0.635513	+	0.772090i	$0.719212\pi$
$60$	0.855592	0.110456
$61$	−1.31540	−0.168420	−0.0842101	−	0.996448i	$-0.526837\pi$
$61$	−1.31540	−0.168420	−0.0842101	+	0.996448i	$0.526837\pi$
$62$	−6.12978	−0.778483
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	−0.855592	−0.106123
$66$	−4.22324	−0.519845
$67$	3.84775	0.470077	0.235038	−	0.971986i	$-0.424478\pi$
$67$	3.84775	0.470077	0.235038	+	0.971986i	$0.424478\pi$
$68$	1.00000	0.121268
$69$	−3.03574	−0.365460
$70$	−0.855592	−0.102263
$71$	14.9352	1.77249	0.886244	−	0.463219i	$-0.153306\pi$
$71$	14.9352	1.77249	0.886244	+	0.463219i	$0.153306\pi$
$72$	1.00000	0.117851
$73$	−0.0934659	−0.0109394	−0.00546968	−	0.999985i	$-0.501741\pi$
$73$	−0.0934659	−0.0109394	−0.00546968	+	0.999985i	$0.501741\pi$
$74$	0.647234	0.0752394
$75$	4.26796	0.492822
$76$	−7.42425	−0.851619
$77$	4.22324	0.481283
$78$	−1.00000	−0.113228
$79$	−4.16714	−0.468840	−0.234420	−	0.972135i	$-0.575319\pi$
$79$	−4.16714	−0.468840	−0.234420	+	0.972135i	$0.575319\pi$
$80$	−0.855592	−0.0956581
$81$	1.00000	0.111111
$82$	−10.1671	−1.12277
$83$	2.37281	0.260450	0.130225	−	0.991484i	$-0.458430\pi$
$83$	2.37281	0.260450	0.130225	+	0.991484i	$0.458430\pi$
$84$	−1.00000	−0.109109
$85$	−0.855592	−0.0928020
$86$	−12.2449	−1.32040
$87$	2.59064	0.277746
$88$	4.22324	0.450199
$89$	−6.79002	−0.719741	−0.359870	−	0.933002i	$-0.617179\pi$
$89$	−6.79002	−0.719741	−0.359870	+	0.933002i	$0.617179\pi$
$90$	−0.855592	−0.0901873
$91$	1.00000	0.104828
$92$	3.03574	0.316498
$93$	6.12978	0.635628
$94$	−2.38802	−0.246305
$95$	6.35212	0.651714
$96$	−1.00000	−0.102062
$97$	9.00753	0.914576	0.457288	−	0.889319i	$-0.348821\pi$
$97$	9.00753	0.914576	0.457288	+	0.889319i	$0.348821\pi$
$98$	1.00000	0.101015
$99$	4.22324	0.424452
$100$	−4.26796	−0.426796
$101$	−5.84152	−0.581253	−0.290627	−	0.956837i	$-0.593864\pi$
$101$	−5.84152	−0.581253	−0.290627	+	0.956837i	$0.593864\pi$
$102$	−1.00000	−0.0990148
$103$	5.77136	0.568669	0.284335	−	0.958725i	$-0.408227\pi$
$103$	5.77136	0.568669	0.284335	+	0.958725i	$0.408227\pi$
$104$	1.00000	0.0980581
$105$	0.855592	0.0834972
$106$	−0.591130	−0.0574156
$107$	13.4755	1.30273	0.651364	−	0.758766i	$-0.274197\pi$
$107$	13.4755	1.30273	0.651364	+	0.758766i	$0.274197\pi$
$108$	−1.00000	−0.0962250
$109$	−9.53340	−0.913134	−0.456567	−	0.889689i	$-0.650921\pi$
$109$	−9.53340	−0.913134	−0.456567	+	0.889689i	$0.650921\pi$
$110$	−3.61337	−0.344522
$111$	−0.647234	−0.0614327
$112$	1.00000	0.0944911
$113$	−6.55157	−0.616320	−0.308160	−	0.951335i	$-0.599713\pi$
$113$	−6.55157	−0.616320	−0.308160	+	0.951335i	$0.599713\pi$
$114$	7.42425	0.695344
$115$	−2.59735	−0.242204
$116$	−2.59064	−0.240535
$117$	1.00000	0.0924500
$118$	−9.76294	−0.898752
$119$	1.00000	0.0916698
$120$	0.855592	0.0781045
$121$	6.83579	0.621435
$122$	−1.31540	−0.119091
$123$	10.1671	0.916740
$124$	−6.12978	−0.550470
$125$	7.92959	0.709244
$126$	1.00000	0.0890871
$127$	−13.4194	−1.19078	−0.595390	−	0.803437i	$-0.703002\pi$
$127$	−13.4194	−1.19078	−0.595390	+	0.803437i	$0.703002\pi$
$128$	1.00000	0.0883883
$129$	12.2449	1.07810
$130$	−0.855592	−0.0750404
$131$	−0.0520754	−0.00454985	−0.00227493	−	0.999997i	$-0.500724\pi$
$131$	−0.0520754	−0.00454985	−0.00227493	+	0.999997i	$0.500724\pi$
$132$	−4.22324	−0.367586
$133$	−7.42425	−0.643764
$134$	3.84775	0.332395
$135$	0.855592	0.0736376
$136$	1.00000	0.0857493
$137$	15.9062	1.35896	0.679480	−	0.733694i	$-0.262205\pi$
$137$	15.9062	1.35896	0.679480	+	0.733694i	$0.262205\pi$
$138$	−3.03574	−0.258419
$139$	0.639960	0.0542807	0.0271403	−	0.999632i	$-0.491360\pi$
$139$	0.639960	0.0542807	0.0271403	+	0.999632i	$0.491360\pi$
$140$	−0.855592	−0.0723107
$141$	2.38802	0.201107
$142$	14.9352	1.25334
$143$	4.22324	0.353165
$144$	1.00000	0.0833333
$145$	2.21653	0.184073
$146$	−0.0934659	−0.00773529
$147$	−1.00000	−0.0824786
$148$	0.647234	0.0532023
$149$	−6.50848	−0.533195	−0.266598	−	0.963808i	$-0.585899\pi$
$149$	−6.50848	−0.533195	−0.266598	+	0.963808i	$0.585899\pi$
$150$	4.26796	0.348478
$151$	3.94390	0.320950	0.160475	−	0.987040i	$-0.448697\pi$
$151$	3.94390	0.320950	0.160475	+	0.987040i	$0.448697\pi$
$152$	−7.42425	−0.602186
$153$	1.00000	0.0808452
$154$	4.22324	0.340319
$155$	5.24459	0.421255
$156$	−1.00000	−0.0800641
$157$	−2.75156	−0.219598	−0.109799	−	0.993954i	$-0.535021\pi$
$157$	−2.75156	−0.219598	−0.109799	+	0.993954i	$0.535021\pi$
$158$	−4.16714	−0.331520
$159$	0.591130	0.0468797
$160$	−0.855592	−0.0676405
$161$	3.03574	0.239250
$162$	1.00000	0.0785674
$163$	−19.3606	−1.51644	−0.758220	−	0.651998i	$-0.773931\pi$
$163$	−19.3606	−1.51644	−0.758220	+	0.651998i	$0.773931\pi$
$164$	−10.1671	−0.793920
$165$	3.61337	0.281301
$166$	2.37281	0.184166
$167$	−5.04423	−0.390334	−0.195167	−	0.980770i	$-0.562525\pi$
$167$	−5.04423	−0.390334	−0.195167	+	0.980770i	$0.562525\pi$
$168$	−1.00000	−0.0771517
$169$	1.00000	0.0769231
$170$	−0.855592	−0.0656209
$171$	−7.42425	−0.567746
$172$	−12.2449	−0.933666
$173$	−20.6469	−1.56976	−0.784878	−	0.619650i	$-0.787274\pi$
$173$	−20.6469	−1.56976	−0.784878	+	0.619650i	$0.787274\pi$
$174$	2.59064	0.196396
$175$	−4.26796	−0.322628
$176$	4.22324	0.318339
$177$	9.76294	0.733828
$178$	−6.79002	−0.508933
$179$	14.4839	1.08257	0.541287	−	0.840838i	$-0.317937\pi$
$179$	14.4839	1.08257	0.541287	+	0.840838i	$0.317937\pi$
$180$	−0.855592	−0.0637720
$181$	25.0103	1.85900	0.929501	−	0.368820i	$-0.120238\pi$
$181$	25.0103	1.85900	0.929501	+	0.368820i	$0.120238\pi$
$182$	1.00000	0.0741249
$183$	1.31540	0.0972375
$184$	3.03574	0.223798
$185$	−0.553768	−0.0407138
$186$	6.12978	0.449457
$187$	4.22324	0.308834
$188$	−2.38802	−0.174164
$189$	−1.00000	−0.0727393
$190$	6.35212	0.460831
$191$	−12.3535	−0.893869	−0.446934	−	0.894567i	$-0.647484\pi$
$191$	−12.3535	−0.893869	−0.446934	+	0.894567i	$0.647484\pi$
$192$	−1.00000	−0.0721688
$193$	−12.0814	−0.869635	−0.434818	−	0.900519i	$-0.643187\pi$
$193$	−12.0814	−0.869635	−0.434818	+	0.900519i	$0.643187\pi$
$194$	9.00753	0.646703
$195$	0.855592	0.0612702
$196$	1.00000	0.0714286
$197$	−10.4809	−0.746735	−0.373367	−	0.927684i	$-0.621797\pi$
$197$	−10.4809	−0.746735	−0.373367	+	0.927684i	$0.621797\pi$
$198$	4.22324	0.300133
$199$	−9.82003	−0.696123	−0.348062	−	0.937472i	$-0.613160\pi$
$199$	−9.82003	−0.696123	−0.348062	+	0.937472i	$0.613160\pi$
$200$	−4.26796	−0.301791
$201$	−3.84775	−0.271399
$202$	−5.84152	−0.411008
$203$	−2.59064	−0.181827
$204$	−1.00000	−0.0700140
$205$	8.69892	0.607559
$206$	5.77136	0.402110
$207$	3.03574	0.210998
$208$	1.00000	0.0693375
$209$	−31.3544	−2.16883
$210$	0.855592	0.0590414
$211$	1.08830	0.0749220	0.0374610	−	0.999298i	$-0.488073\pi$
$211$	1.08830	0.0749220	0.0374610	+	0.999298i	$0.488073\pi$
$212$	−0.591130	−0.0405990
$213$	−14.9352	−1.02335
$214$	13.4755	0.921167
$215$	10.4766	0.714501
$216$	−1.00000	−0.0680414
$217$	−6.12978	−0.416116
$218$	−9.53340	−0.645684
$219$	0.0934659	0.00631584
$220$	−3.61337	−0.243614
$221$	1.00000	0.0672673
$222$	−0.647234	−0.0434395
$223$	1.76514	0.118202	0.0591012	−	0.998252i	$-0.481177\pi$
$223$	1.76514	0.118202	0.0591012	+	0.998252i	$0.481177\pi$
$224$	1.00000	0.0668153
$225$	−4.26796	−0.284531
$226$	−6.55157	−0.435804
$227$	−0.549694	−0.0364845	−0.0182422	−	0.999834i	$-0.505807\pi$
$227$	−0.549694	−0.0364845	−0.0182422	+	0.999834i	$0.505807\pi$
$228$	7.42425	0.491683
$229$	−3.00057	−0.198283	−0.0991417	−	0.995073i	$-0.531610\pi$
$229$	−3.00057	−0.198283	−0.0991417	+	0.995073i	$0.531610\pi$
$230$	−2.59735	−0.171264
$231$	−4.22324	−0.277869
$232$	−2.59064	−0.170084
$233$	2.81332	0.184307	0.0921535	−	0.995745i	$-0.470625\pi$
$233$	2.81332	0.184307	0.0921535	+	0.995745i	$0.470625\pi$
$234$	1.00000	0.0653720
$235$	2.04317	0.133282
$236$	−9.76294	−0.635513
$237$	4.16714	0.270685
$238$	1.00000	0.0648204
$239$	−8.68894	−0.562041	−0.281020	−	0.959702i	$-0.590673\pi$
$239$	−8.68894	−0.562041	−0.281020	+	0.959702i	$0.590673\pi$
$240$	0.855592	0.0552282
$241$	−10.4892	−0.675672	−0.337836	−	0.941205i	$-0.609695\pi$
$241$	−10.4892	−0.675672	−0.337836	+	0.941205i	$0.609695\pi$
$242$	6.83579	0.439421
$243$	−1.00000	−0.0641500
$244$	−1.31540	−0.0842101
$245$	−0.855592	−0.0546618
$246$	10.1671	0.648233
$247$	−7.42425	−0.472393
$248$	−6.12978	−0.389241
$249$	−2.37281	−0.150371
$250$	7.92959	0.501511
$251$	−6.73343	−0.425010	−0.212505	−	0.977160i	$-0.568162\pi$
$251$	−6.73343	−0.425010	−0.212505	+	0.977160i	$0.568162\pi$
$252$	1.00000	0.0629941
$253$	12.8207	0.806029
$254$	−13.4194	−0.842009
$255$	0.855592	0.0535792
$256$	1.00000	0.0625000
$257$	5.19348	0.323960	0.161980	−	0.986794i	$-0.448212\pi$
$257$	5.19348	0.323960	0.161980	+	0.986794i	$0.448212\pi$
$258$	12.2449	0.762335
$259$	0.647234	0.0402171
$260$	−0.855592	−0.0530615
$261$	−2.59064	−0.160357
$262$	−0.0520754	−0.00321723
$263$	−0.101078	−0.00623273	−0.00311636	−	0.999995i	$-0.500992\pi$
$263$	−0.101078	−0.00623273	−0.00311636	+	0.999995i	$0.500992\pi$
$264$	−4.22324	−0.259923
$265$	0.505766	0.0310690
$266$	−7.42425	−0.455210
$267$	6.79002	0.415542
$268$	3.84775	0.235038
$269$	−30.1730	−1.83968	−0.919842	−	0.392290i	$-0.871683\pi$
$269$	−30.1730	−1.83968	−0.919842	+	0.392290i	$0.871683\pi$
$270$	0.855592	0.0520697
$271$	−12.0741	−0.733448	−0.366724	−	0.930330i	$-0.619521\pi$
$271$	−12.0741	−0.733448	−0.366724	+	0.930330i	$0.619521\pi$
$272$	1.00000	0.0606339
$273$	−1.00000	−0.0605228
$274$	15.9062	0.960930
$275$	−18.0246	−1.08693
$276$	−3.03574	−0.182730
$277$	2.42701	0.145825	0.0729125	−	0.997338i	$-0.476771\pi$
$277$	2.42701	0.145825	0.0729125	+	0.997338i	$0.476771\pi$
$278$	0.639960	0.0383822
$279$	−6.12978	−0.366980
$280$	−0.855592	−0.0511314
$281$	−1.23763	−0.0738309	−0.0369154	−	0.999318i	$-0.511753\pi$
$281$	−1.23763	−0.0738309	−0.0369154	+	0.999318i	$0.511753\pi$
$282$	2.38802	0.142204
$283$	−6.12355	−0.364008	−0.182004	−	0.983298i	$-0.558258\pi$
$283$	−6.12355	−0.364008	−0.182004	+	0.983298i	$0.558258\pi$
$284$	14.9352	0.886244
$285$	−6.35212	−0.376267
$286$	4.22324	0.249726
$287$	−10.1671	−0.600147
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	2.21653	0.130159
$291$	−9.00753	−0.528031
$292$	−0.0934659	−0.00546968
$293$	24.5895	1.43653	0.718267	−	0.695767i	$-0.244935\pi$
$293$	24.5895	1.43653	0.718267	+	0.695767i	$0.244935\pi$
$294$	−1.00000	−0.0583212
$295$	8.35309	0.486336
$296$	0.647234	0.0376197
$297$	−4.22324	−0.245057
$298$	−6.50848	−0.377026
$299$	3.03574	0.175561
$300$	4.26796	0.246411
$301$	−12.2449	−0.705785
$302$	3.94390	0.226946
$303$	5.84152	0.335587
$304$	−7.42425	−0.425810
$305$	1.12545	0.0644430
$306$	1.00000	0.0571662
$307$	29.3841	1.67704	0.838520	−	0.544871i	$-0.183422\pi$
$307$	29.3841	1.67704	0.838520	+	0.544871i	$0.183422\pi$
$308$	4.22324	0.240642
$309$	−5.77136	−0.328321
$310$	5.24459	0.297873
$311$	18.9496	1.07453	0.537266	−	0.843413i	$-0.319457\pi$
$311$	18.9496	1.07453	0.537266	+	0.843413i	$0.319457\pi$
$312$	−1.00000	−0.0566139
$313$	8.43766	0.476925	0.238462	−	0.971152i	$-0.423357\pi$
$313$	8.43766	0.476925	0.238462	+	0.971152i	$0.423357\pi$
$314$	−2.75156	−0.155279
$315$	−0.855592	−0.0482071
$316$	−4.16714	−0.234420
$317$	−17.8971	−1.00520	−0.502600	−	0.864519i	$-0.667623\pi$
$317$	−17.8971	−1.00520	−0.502600	+	0.864519i	$0.667623\pi$
$318$	0.591130	0.0331489
$319$	−10.9409	−0.612573
$320$	−0.855592	−0.0478290
$321$	−13.4755	−0.752130
$322$	3.03574	0.169175
$323$	−7.42425	−0.413096
$324$	1.00000	0.0555556
$325$	−4.26796	−0.236744
$326$	−19.3606	−1.07229
$327$	9.53340	0.527198
$328$	−10.1671	−0.561386
$329$	−2.38802	−0.131656
$330$	3.61337	0.198910
$331$	−12.3253	−0.677460	−0.338730	−	0.940884i	$-0.609997\pi$
$331$	−12.3253	−0.677460	−0.338730	+	0.940884i	$0.609997\pi$
$332$	2.37281	0.130225
$333$	0.647234	0.0354682
$334$	−5.04423	−0.276008
$335$	−3.29210	−0.179867
$336$	−1.00000	−0.0545545
$337$	11.7556	0.640368	0.320184	−	0.947355i	$-0.396255\pi$
$337$	11.7556	0.640368	0.320184	+	0.947355i	$0.396255\pi$
$338$	1.00000	0.0543928
$339$	6.55157	0.355833
$340$	−0.855592	−0.0464010
$341$	−25.8875	−1.40189
$342$	−7.42425	−0.401457
$343$	1.00000	0.0539949
$344$	−12.2449	−0.660201
$345$	2.59735	0.139837
$346$	−20.6469	−1.10999
$347$	−24.4942	−1.31492	−0.657458	−	0.753491i	$-0.728368\pi$
$347$	−24.4942	−1.31492	−0.657458	+	0.753491i	$0.728368\pi$
$348$	2.59064	0.138873
$349$	−13.6852	−0.732554	−0.366277	−	0.930506i	$-0.619368\pi$
$349$	−13.6852	−0.732554	−0.366277	+	0.930506i	$0.619368\pi$
$350$	−4.26796	−0.228132
$351$	−1.00000	−0.0533761
$352$	4.22324	0.225100
$353$	−0.490391	−0.0261009	−0.0130504	−	0.999915i	$-0.504154\pi$
$353$	−0.490391	−0.0261009	−0.0130504	+	0.999915i	$0.504154\pi$
$354$	9.76294	0.518895
$355$	−12.7785	−0.678211
$356$	−6.79002	−0.359870
$357$	−1.00000	−0.0529256
$358$	14.4839	0.765495
$359$	−17.0926	−0.902112	−0.451056	−	0.892496i	$-0.648952\pi$
$359$	−17.0926	−0.902112	−0.451056	+	0.892496i	$0.648952\pi$
$360$	−0.855592	−0.0450936
$361$	36.1194	1.90102
$362$	25.0103	1.31451
$363$	−6.83579	−0.358786
$364$	1.00000	0.0524142
$365$	0.0799686	0.00418575
$366$	1.31540	0.0687573
$367$	16.0520	0.837908	0.418954	−	0.908008i	$-0.362397\pi$
$367$	16.0520	0.837908	0.418954	+	0.908008i	$0.362397\pi$
$368$	3.03574	0.158249
$369$	−10.1671	−0.529280
$370$	−0.553768	−0.0287890
$371$	−0.591130	−0.0306900
$372$	6.12978	0.317814
$373$	18.7559	0.971145	0.485572	−	0.874196i	$-0.338611\pi$
$373$	18.7559	0.971145	0.485572	+	0.874196i	$0.338611\pi$
$374$	4.22324	0.218379
$375$	−7.92959	−0.409482
$376$	−2.38802	−0.123153
$377$	−2.59064	−0.133425
$378$	−1.00000	−0.0514344
$379$	9.78461	0.502602	0.251301	−	0.967909i	$-0.419142\pi$
$379$	9.78461	0.502602	0.251301	+	0.967909i	$0.419142\pi$
$380$	6.35212	0.325857
$381$	13.4194	0.687497
$382$	−12.3535	−0.632061
$383$	−33.8916	−1.73178	−0.865890	−	0.500235i	$-0.833247\pi$
$383$	−33.8916	−1.73178	−0.865890	+	0.500235i	$0.833247\pi$
$384$	−1.00000	−0.0510310
$385$	−3.61337	−0.184155
$386$	−12.0814	−0.614925
$387$	−12.2449	−0.622444
$388$	9.00753	0.457288
$389$	9.61423	0.487461	0.243730	−	0.969843i	$-0.421629\pi$
$389$	9.61423	0.487461	0.243730	+	0.969843i	$0.421629\pi$
$390$	0.855592	0.0433246
$391$	3.03574	0.153524
$392$	1.00000	0.0505076
$393$	0.0520754	0.00262686
$394$	−10.4809	−0.528021
$395$	3.56537	0.179393
$396$	4.22324	0.212226
$397$	−21.4366	−1.07587	−0.537936	−	0.842986i	$-0.680796\pi$
$397$	−21.4366	−1.07587	−0.537936	+	0.842986i	$0.680796\pi$
$398$	−9.82003	−0.492233
$399$	7.42425	0.371677
$400$	−4.26796	−0.213398
$401$	29.9863	1.49744	0.748722	−	0.662885i	$-0.230668\pi$
$401$	29.9863	1.49744	0.748722	+	0.662885i	$0.230668\pi$
$402$	−3.84775	−0.191908
$403$	−6.12978	−0.305346
$404$	−5.84152	−0.290627
$405$	−0.855592	−0.0425147
$406$	−2.59064	−0.128571
$407$	2.73343	0.135491
$408$	−1.00000	−0.0495074
$409$	34.3168	1.69686	0.848428	−	0.529310i	$-0.177549\pi$
$409$	34.3168	1.69686	0.848428	+	0.529310i	$0.177549\pi$
$410$	8.69892	0.429609
$411$	−15.9062	−0.784596
$412$	5.77136	0.284335
$413$	−9.76294	−0.480403
$414$	3.03574	0.149198
$415$	−2.03016	−0.0996566
$416$	1.00000	0.0490290
$417$	−0.639960	−0.0313390
$418$	−31.3544	−1.53359
$419$	−31.0438	−1.51659	−0.758293	−	0.651913i	$-0.773967\pi$
$419$	−31.0438	−1.51659	−0.758293	+	0.651913i	$0.773967\pi$
$420$	0.855592	0.0417486
$421$	−22.0936	−1.07677	−0.538387	−	0.842698i	$-0.680966\pi$
$421$	−22.0936	−1.07677	−0.538387	+	0.842698i	$0.680966\pi$
$422$	1.08830	0.0529778
$423$	−2.38802	−0.116109
$424$	−0.591130	−0.0287078
$425$	−4.26796	−0.207027
$426$	−14.9352	−0.723615
$427$	−1.31540	−0.0636569
$428$	13.4755	0.651364
$429$	−4.22324	−0.203900
$430$	10.4766	0.505229
$431$	−4.32965	−0.208552	−0.104276	−	0.994548i	$-0.533252\pi$
$431$	−4.32965	−0.208552	−0.104276	+	0.994548i	$0.533252\pi$
$432$	−1.00000	−0.0481125
$433$	20.1139	0.966613	0.483307	−	0.875451i	$-0.339436\pi$
$433$	20.1139	0.966613	0.483307	+	0.875451i	$0.339436\pi$
$434$	−6.12978	−0.294239
$435$	−2.21653	−0.106275
$436$	−9.53340	−0.456567
$437$	−22.5381	−1.07814
$438$	0.0934659	0.00446597
$439$	−15.4475	−0.737267	−0.368633	−	0.929575i	$-0.620174\pi$
$439$	−15.4475	−0.737267	−0.368633	+	0.929575i	$0.620174\pi$
$440$	−3.61337	−0.172261
$441$	1.00000	0.0476190
$442$	1.00000	0.0475651
$443$	29.7250	1.41228	0.706139	−	0.708073i	$-0.250435\pi$
$443$	29.7250	1.41228	0.706139	+	0.708073i	$0.250435\pi$
$444$	−0.647234	−0.0307164
$445$	5.80948	0.275396
$446$	1.76514	0.0835817
$447$	6.50848	0.307840
$448$	1.00000	0.0472456
$449$	−9.28719	−0.438290	−0.219145	−	0.975692i	$-0.570327\pi$
$449$	−9.28719	−0.438290	−0.219145	+	0.975692i	$0.570327\pi$
$450$	−4.26796	−0.201194
$451$	−42.9383	−2.02189
$452$	−6.55157	−0.308160
$453$	−3.94390	−0.185300
$454$	−0.549694	−0.0257984
$455$	−0.855592	−0.0401108
$456$	7.42425	0.347672
$457$	7.57569	0.354376	0.177188	−	0.984177i	$-0.443300\pi$
$457$	7.57569	0.354376	0.177188	+	0.984177i	$0.443300\pi$
$458$	−3.00057	−0.140208
$459$	−1.00000	−0.0466760
$460$	−2.59735	−0.121102
$461$	−23.2077	−1.08089	−0.540446	−	0.841379i	$-0.681744\pi$
$461$	−23.2077	−1.08089	−0.540446	+	0.841379i	$0.681744\pi$
$462$	−4.22324	−0.196483
$463$	31.1737	1.44876	0.724382	−	0.689399i	$-0.242125\pi$
$463$	31.1737	1.44876	0.724382	+	0.689399i	$0.242125\pi$
$464$	−2.59064	−0.120267
$465$	−5.24459	−0.243212
$466$	2.81332	0.130325
$467$	22.3379	1.03367	0.516837	−	0.856084i	$-0.327109\pi$
$467$	22.3379	1.03367	0.516837	+	0.856084i	$0.327109\pi$
$468$	1.00000	0.0462250
$469$	3.84775	0.177672
$470$	2.04317	0.0942443
$471$	2.75156	0.126785
$472$	−9.76294	−0.449376
$473$	−51.7133	−2.37778
$474$	4.16714	0.191403
$475$	31.6864	1.45387
$476$	1.00000	0.0458349
$477$	−0.591130	−0.0270660
$478$	−8.68894	−0.397423
$479$	−26.4017	−1.20632	−0.603162	−	0.797619i	$-0.706093\pi$
$479$	−26.4017	−1.20632	−0.603162	+	0.797619i	$0.706093\pi$
$480$	0.855592	0.0390522
$481$	0.647234	0.0295113
$482$	−10.4892	−0.477772
$483$	−3.03574	−0.138131
$484$	6.83579	0.310718
$485$	−7.70677	−0.349946
$486$	−1.00000	−0.0453609
$487$	−1.36734	−0.0619599	−0.0309799	−	0.999520i	$-0.509863\pi$
$487$	−1.36734	−0.0619599	−0.0309799	+	0.999520i	$0.509863\pi$
$488$	−1.31540	−0.0595455
$489$	19.3606	0.875518
$490$	−0.855592	−0.0386517
$491$	−4.96641	−0.224131	−0.112065	−	0.993701i	$-0.535747\pi$
$491$	−4.96641	−0.224131	−0.112065	+	0.993701i	$0.535747\pi$
$492$	10.1671	0.458370
$493$	−2.59064	−0.116677
$494$	−7.42425	−0.334033
$495$	−3.61337	−0.162409
$496$	−6.12978	−0.275235
$497$	14.9352	0.669937
$498$	−2.37281	−0.106328
$499$	−26.5805	−1.18991	−0.594954	−	0.803760i	$-0.702830\pi$
$499$	−26.5805	−1.18991	−0.594954	+	0.803760i	$0.702830\pi$
$500$	7.92959	0.354622
$501$	5.04423	0.225360
$502$	−6.73343	−0.300528
$503$	−25.1739	−1.12245	−0.561224	−	0.827664i	$-0.689669\pi$
$503$	−25.1739	−1.12245	−0.561224	+	0.827664i	$0.689669\pi$
$504$	1.00000	0.0445435
$505$	4.99796	0.222406
$506$	12.8207	0.569948
$507$	−1.00000	−0.0444116
$508$	−13.4194	−0.595390
$509$	−18.1627	−0.805050	−0.402525	−	0.915409i	$-0.631867\pi$
$509$	−18.1627	−0.805050	−0.402525	+	0.915409i	$0.631867\pi$
$510$	0.855592	0.0378862
$511$	−0.0934659	−0.00413469
$512$	1.00000	0.0441942
$513$	7.42425	0.327788
$514$	5.19348	0.229075
$515$	−4.93793	−0.217591
$516$	12.2449	0.539052
$517$	−10.0852	−0.443545
$518$	0.647234	0.0284378
$519$	20.6469	0.906299
$520$	−0.855592	−0.0375202
$521$	11.4508	0.501668	0.250834	−	0.968030i	$-0.419295\pi$
$521$	11.4508	0.501668	0.250834	+	0.968030i	$0.419295\pi$
$522$	−2.59064	−0.113389
$523$	−16.7420	−0.732075	−0.366038	−	0.930600i	$-0.619286\pi$
$523$	−16.7420	−0.732075	−0.366038	+	0.930600i	$0.619286\pi$
$524$	−0.0520754	−0.00227493
$525$	4.26796	0.186269
$526$	−0.101078	−0.00440720
$527$	−6.12978	−0.267017
$528$	−4.22324	−0.183793
$529$	−13.7843	−0.599317
$530$	0.505766	0.0219691
$531$	−9.76294	−0.423676
$532$	−7.42425	−0.321882
$533$	−10.1671	−0.440388
$534$	6.79002	0.293833
$535$	−11.5295	−0.498465
$536$	3.84775	0.166197
$537$	−14.4839	−0.625024
$538$	−30.1730	−1.30085
$539$	4.22324	0.181908
$540$	0.855592	0.0368188
$541$	3.76733	0.161970	0.0809851	−	0.996715i	$-0.474193\pi$
$541$	3.76733	0.161970	0.0809851	+	0.996715i	$0.474193\pi$
$542$	−12.0741	−0.518626
$543$	−25.0103	−1.07329
$544$	1.00000	0.0428746
$545$	8.15670	0.349395
$546$	−1.00000	−0.0427960
$547$	0.156600	0.00669572	0.00334786	−	0.999994i	$-0.498934\pi$
$547$	0.156600	0.00669572	0.00334786	+	0.999994i	$0.498934\pi$
$548$	15.9062	0.679480
$549$	−1.31540	−0.0561401
$550$	−18.0246	−0.768574
$551$	19.2336	0.819377
$552$	−3.03574	−0.129210
$553$	−4.16714	−0.177205
$554$	2.42701	0.103114
$555$	0.553768	0.0235061
$556$	0.639960	0.0271403
$557$	0.413178	0.0175069	0.00875345	−	0.999962i	$-0.497214\pi$
$557$	0.413178	0.0175069	0.00875345	+	0.999962i	$0.497214\pi$
$558$	−6.12978	−0.259494
$559$	−12.2449	−0.517905
$560$	−0.855592	−0.0361554
$561$	−4.22324	−0.178305
$562$	−1.23763	−0.0522063
$563$	20.9066	0.881109	0.440555	−	0.897726i	$-0.354782\pi$
$563$	20.9066	0.881109	0.440555	+	0.897726i	$0.354782\pi$
$564$	2.38802	0.100554
$565$	5.60547	0.235824
$566$	−6.12355	−0.257392
$567$	1.00000	0.0419961
$568$	14.9352	0.626669
$569$	12.0055	0.503295	0.251648	−	0.967819i	$-0.419028\pi$
$569$	12.0055	0.503295	0.251648	+	0.967819i	$0.419028\pi$
$570$	−6.35212	−0.266061
$571$	15.5811	0.652048	0.326024	−	0.945361i	$-0.394291\pi$
$571$	15.5811	0.652048	0.326024	+	0.945361i	$0.394291\pi$
$572$	4.22324	0.176583
$573$	12.3535	0.516075
$574$	−10.1671	−0.424368
$575$	−12.9564	−0.540320
$576$	1.00000	0.0416667
$577$	12.5945	0.524315	0.262157	−	0.965025i	$-0.415566\pi$
$577$	12.5945	0.524315	0.262157	+	0.965025i	$0.415566\pi$
$578$	1.00000	0.0415945
$579$	12.0814	0.502084
$580$	2.21653	0.0920364
$581$	2.37281	0.0984409
$582$	−9.00753	−0.373374
$583$	−2.49649	−0.103394
$584$	−0.0934659	−0.00386765
$585$	−0.855592	−0.0353744
$586$	24.5895	1.01578
$587$	1.69686	0.0700368	0.0350184	−	0.999387i	$-0.488851\pi$
$587$	1.69686	0.0700368	0.0350184	+	0.999387i	$0.488851\pi$
$588$	−1.00000	−0.0412393
$589$	45.5090	1.87516
$590$	8.35309	0.343891
$591$	10.4809	0.431127
$592$	0.647234	0.0266011
$593$	−32.0042	−1.31425	−0.657127	−	0.753780i	$-0.728228\pi$
$593$	−32.0042	−1.31425	−0.657127	+	0.753780i	$0.728228\pi$
$594$	−4.22324	−0.173282
$595$	−0.855592	−0.0350758
$596$	−6.50848	−0.266598
$597$	9.82003	0.401907
$598$	3.03574	0.124141
$599$	0.553524	0.0226164	0.0113082	−	0.999936i	$-0.496400\pi$
$599$	0.553524	0.0226164	0.0113082	+	0.999936i	$0.496400\pi$
$600$	4.26796	0.174239
$601$	−15.7242	−0.641405	−0.320702	−	0.947180i	$-0.603919\pi$
$601$	−15.7242	−0.641405	−0.320702	+	0.947180i	$0.603919\pi$
$602$	−12.2449	−0.499065
$603$	3.84775	0.156692
$604$	3.94390	0.160475
$605$	−5.84864	−0.237781
$606$	5.84152	0.237296
$607$	−37.1038	−1.50600	−0.752999	−	0.658022i	$-0.771393\pi$
$607$	−37.1038	−1.50600	−0.752999	+	0.658022i	$0.771393\pi$
$608$	−7.42425	−0.301093
$609$	2.59064	0.104978
$610$	1.12545	0.0455681
$611$	−2.38802	−0.0966088
$612$	1.00000	0.0404226
$613$	20.2685	0.818636	0.409318	−	0.912392i	$-0.365767\pi$
$613$	20.2685	0.818636	0.409318	+	0.912392i	$0.365767\pi$
$614$	29.3841	1.18585
$615$	−8.69892	−0.350774
$616$	4.22324	0.170159
$617$	−7.37851	−0.297048	−0.148524	−	0.988909i	$-0.547452\pi$
$617$	−7.37851	−0.297048	−0.148524	+	0.988909i	$0.547452\pi$
$618$	−5.77136	−0.232158
$619$	41.4436	1.66576	0.832880	−	0.553454i	$-0.186690\pi$
$619$	41.4436	1.66576	0.832880	+	0.553454i	$0.186690\pi$
$620$	5.24459	0.210628
$621$	−3.03574	−0.121820
$622$	18.9496	0.759808
$623$	−6.79002	−0.272036
$624$	−1.00000	−0.0400320
$625$	14.5553	0.582213
$626$	8.43766	0.337237
$627$	31.3544	1.25217
$628$	−2.75156	−0.109799
$629$	0.647234	0.0258069
$630$	−0.855592	−0.0340876
$631$	−8.46416	−0.336953	−0.168477	−	0.985706i	$-0.553885\pi$
$631$	−8.46416	−0.336953	−0.168477	+	0.985706i	$0.553885\pi$
$632$	−4.16714	−0.165760
$633$	−1.08830	−0.0432562
$634$	−17.8971	−0.710783
$635$	11.4815	0.455631
$636$	0.591130	0.0234398
$637$	1.00000	0.0396214
$638$	−10.9409	−0.433155
$639$	14.9352	0.590829
$640$	−0.855592	−0.0338202
$641$	25.8808	1.02223	0.511115	−	0.859512i	$-0.329233\pi$
$641$	25.8808	1.02223	0.511115	+	0.859512i	$0.329233\pi$
$642$	−13.4755	−0.531836
$643$	14.1013	0.556102	0.278051	−	0.960566i	$-0.410312\pi$
$643$	14.1013	0.556102	0.278051	+	0.960566i	$0.410312\pi$
$644$	3.03574	0.119625
$645$	−10.4766	−0.412518
$646$	−7.42425	−0.292103
$647$	40.1912	1.58008	0.790040	−	0.613055i	$-0.210060\pi$
$647$	40.1912	1.58008	0.790040	+	0.613055i	$0.210060\pi$
$648$	1.00000	0.0392837
$649$	−41.2313	−1.61847
$650$	−4.26796	−0.167403
$651$	6.12978	0.240245
$652$	−19.3606	−0.758220
$653$	−37.0670	−1.45054	−0.725272	−	0.688462i	$-0.758286\pi$
$653$	−37.0670	−1.45054	−0.725272	+	0.688462i	$0.758286\pi$
$654$	9.53340	0.372786
$655$	0.0445553	0.00174092
$656$	−10.1671	−0.396960
$657$	−0.0934659	−0.00364645
$658$	−2.38802	−0.0930946
$659$	12.9442	0.504233	0.252116	−	0.967697i	$-0.418873\pi$
$659$	12.9442	0.504233	0.252116	+	0.967697i	$0.418873\pi$
$660$	3.61337	0.140650
$661$	−33.7975	−1.31457	−0.657286	−	0.753642i	$-0.728295\pi$
$661$	−33.7975	−1.31457	−0.657286	+	0.753642i	$0.728295\pi$
$662$	−12.3253	−0.479036
$663$	−1.00000	−0.0388368
$664$	2.37281	0.0920830
$665$	6.35212	0.246325
$666$	0.647234	0.0250798
$667$	−7.86451	−0.304515
$668$	−5.04423	−0.195167
$669$	−1.76514	−0.0682442
$670$	−3.29210	−0.127185
$671$	−5.55527	−0.214459
$672$	−1.00000	−0.0385758
$673$	−37.9743	−1.46380	−0.731901	−	0.681411i	$-0.761367\pi$
$673$	−37.9743	−1.46380	−0.731901	+	0.681411i	$0.761367\pi$
$674$	11.7556	0.452809
$675$	4.26796	0.164274
$676$	1.00000	0.0384615
$677$	−25.8149	−0.992146	−0.496073	−	0.868281i	$-0.665225\pi$
$677$	−25.8149	−0.992146	−0.496073	+	0.868281i	$0.665225\pi$
$678$	6.55157	0.251612
$679$	9.00753	0.345677
$680$	−0.855592	−0.0328104
$681$	0.549694	0.0210643
$682$	−25.8875	−0.991285
$683$	−0.957815	−0.0366498	−0.0183249	−	0.999832i	$-0.505833\pi$
$683$	−0.957815	−0.0366498	−0.0183249	+	0.999832i	$0.505833\pi$
$684$	−7.42425	−0.283873
$685$	−13.6092	−0.519982
$686$	1.00000	0.0381802
$687$	3.00057	0.114479
$688$	−12.2449	−0.466833
$689$	−0.591130	−0.0225203
$690$	2.59735	0.0988796
$691$	46.4172	1.76579	0.882897	−	0.469567i	$-0.155590\pi$
$691$	46.4172	1.76579	0.882897	+	0.469567i	$0.155590\pi$
$692$	−20.6469	−0.784878
$693$	4.22324	0.160428
$694$	−24.4942	−0.929786
$695$	−0.547544	−0.0207695
$696$	2.59064	0.0981980
$697$	−10.1671	−0.385108
$698$	−13.6852	−0.517994
$699$	−2.81332	−0.106410
$700$	−4.26796	−0.161314
$701$	−6.19284	−0.233900	−0.116950	−	0.993138i	$-0.537312\pi$
$701$	−6.19284	−0.233900	−0.116950	+	0.993138i	$0.537312\pi$
$702$	−1.00000	−0.0377426
$703$	−4.80522	−0.181232
$704$	4.22324	0.159169
$705$	−2.04317	−0.0769501
$706$	−0.490391	−0.0184561
$707$	−5.84152	−0.219693
$708$	9.76294	0.366914
$709$	4.29065	0.161139	0.0805694	−	0.996749i	$-0.474326\pi$
$709$	4.29065	0.161139	0.0805694	+	0.996749i	$0.474326\pi$
$710$	−12.7785	−0.479567
$711$	−4.16714	−0.156280
$712$	−6.79002	−0.254467
$713$	−18.6084	−0.696890
$714$	−1.00000	−0.0374241
$715$	−3.61337	−0.135132
$716$	14.4839	0.541287
$717$	8.68894	0.324494
$718$	−17.0926	−0.637889
$719$	50.4078	1.87989	0.939946	−	0.341323i	$-0.110875\pi$
$719$	50.4078	1.87989	0.939946	+	0.341323i	$0.110875\pi$
$720$	−0.855592	−0.0318860
$721$	5.77136	0.214937
$722$	36.1194	1.34423
$723$	10.4892	0.390099
$724$	25.0103	0.929501
$725$	11.0568	0.410638
$726$	−6.83579	−0.253700
$727$	−8.48092	−0.314540	−0.157270	−	0.987556i	$-0.550269\pi$
$727$	−8.48092	−0.314540	−0.157270	+	0.987556i	$0.550269\pi$
$728$	1.00000	0.0370625
$729$	1.00000	0.0370370
$730$	0.0799686	0.00295977
$731$	−12.2449	−0.452894
$732$	1.31540	0.0486187
$733$	22.4334	0.828597	0.414298	−	0.910141i	$-0.364027\pi$
$733$	22.4334	0.828597	0.414298	+	0.910141i	$0.364027\pi$
$734$	16.0520	0.592490
$735$	0.855592	0.0315590
$736$	3.03574	0.111899
$737$	16.2500	0.598575
$738$	−10.1671	−0.374258
$739$	−6.88353	−0.253215	−0.126607	−	0.991953i	$-0.540409\pi$
$739$	−6.88353	−0.253215	−0.126607	+	0.991953i	$0.540409\pi$
$740$	−0.553768	−0.0203569
$741$	7.42425	0.272736
$742$	−0.591130	−0.0217011
$743$	−21.7590	−0.798261	−0.399130	−	0.916894i	$-0.630688\pi$
$743$	−21.7590	−0.798261	−0.399130	+	0.916894i	$0.630688\pi$
$744$	6.12978	0.224729
$745$	5.56860	0.204018
$746$	18.7559	0.686703
$747$	2.37281	0.0868167
$748$	4.22324	0.154417
$749$	13.4755	0.492385
$750$	−7.92959	−0.289548
$751$	30.8121	1.12435	0.562176	−	0.827018i	$-0.309965\pi$
$751$	30.8121	1.12435	0.562176	+	0.827018i	$0.309965\pi$
$752$	−2.38802	−0.0870820
$753$	6.73343	0.245380
$754$	−2.59064	−0.0943456
$755$	−3.37437	−0.122806
$756$	−1.00000	−0.0363696
$757$	21.3617	0.776404	0.388202	−	0.921574i	$-0.373096\pi$
$757$	21.3617	0.776404	0.388202	+	0.921574i	$0.373096\pi$
$758$	9.78461	0.355393
$759$	−12.8207	−0.465361
$760$	6.35212	0.230416
$761$	−24.2683	−0.879726	−0.439863	−	0.898065i	$-0.644973\pi$
$761$	−24.2683	−0.879726	−0.439863	+	0.898065i	$0.644973\pi$
$762$	13.4194	0.486134
$763$	−9.53340	−0.345132
$764$	−12.3535	−0.446934
$765$	−0.855592	−0.0309340
$766$	−33.8916	−1.22455
$767$	−9.76294	−0.352519
$768$	−1.00000	−0.0360844
$769$	25.1682	0.907588	0.453794	−	0.891107i	$-0.350070\pi$
$769$	25.1682	0.907588	0.453794	+	0.891107i	$0.350070\pi$
$770$	−3.61337	−0.130217
$771$	−5.19348	−0.187039
$772$	−12.0814	−0.434818
$773$	5.24376	0.188605	0.0943025	−	0.995544i	$-0.469938\pi$
$773$	5.24376	0.188605	0.0943025	+	0.995544i	$0.469938\pi$
$774$	−12.2449	−0.440134
$775$	26.1617	0.939755
$776$	9.00753	0.323351
$777$	−0.647234	−0.0232194
$778$	9.61423	0.344687
$779$	75.4833	2.70447
$780$	0.855592	0.0306351
$781$	63.0752	2.25701
$782$	3.03574	0.108558
$783$	2.59064	0.0925819
$784$	1.00000	0.0357143
$785$	2.35421	0.0840254
$786$	0.0520754	0.00185747
$787$	52.5562	1.87343	0.936714	−	0.350096i	$-0.113851\pi$
$787$	52.5562	1.87343	0.936714	+	0.350096i	$0.113851\pi$
$788$	−10.4809	−0.373367
$789$	0.101078	0.00359847
$790$	3.56537	0.126850
$791$	−6.55157	−0.232947
$792$	4.22324	0.150066
$793$	−1.31540	−0.0467114
$794$	−21.4366	−0.760756
$795$	−0.505766	−0.0179377
$796$	−9.82003	−0.348062
$797$	−27.0368	−0.957693	−0.478846	−	0.877899i	$-0.658945\pi$
$797$	−27.0368	−0.957693	−0.478846	+	0.877899i	$0.658945\pi$
$798$	7.42425	0.262815
$799$	−2.38802	−0.0844819
$800$	−4.26796	−0.150895
$801$	−6.79002	−0.239914
$802$	29.9863	1.05885
$803$	−0.394729	−0.0139297
$804$	−3.84775	−0.135700
$805$	−2.59735	−0.0915447
$806$	−6.12978	−0.215912
$807$	30.1730	1.06214
$808$	−5.84152	−0.205504
$809$	−20.4732	−0.719801	−0.359900	−	0.932991i	$-0.617189\pi$
$809$	−20.4732	−0.719801	−0.359900	+	0.932991i	$0.617189\pi$
$810$	−0.855592	−0.0300624
$811$	−16.0629	−0.564044	−0.282022	−	0.959408i	$-0.591005\pi$
$811$	−16.0629	−0.564044	−0.282022	+	0.959408i	$0.591005\pi$
$812$	−2.59064	−0.0909137
$813$	12.0741	0.423457
$814$	2.73343	0.0958065
$815$	16.5648	0.580239
$816$	−1.00000	−0.0350070
$817$	90.9092	3.18051
$818$	34.3168	1.19986
$819$	1.00000	0.0349428
$820$	8.69892	0.303780
$821$	−11.1044	−0.387545	−0.193772	−	0.981047i	$-0.562072\pi$
$821$	−11.1044	−0.387545	−0.193772	+	0.981047i	$0.562072\pi$
$822$	−15.9062	−0.554793
$823$	15.2234	0.530655	0.265328	−	0.964158i	$-0.414520\pi$
$823$	15.2234	0.530655	0.265328	+	0.964158i	$0.414520\pi$
$824$	5.77136	0.201055
$825$	18.0246	0.627538
$826$	−9.76294	−0.339696
$827$	−20.4858	−0.712359	−0.356180	−	0.934417i	$-0.615921\pi$
$827$	−20.4858	−0.712359	−0.356180	+	0.934417i	$0.615921\pi$
$828$	3.03574	0.105499
$829$	−17.9907	−0.624842	−0.312421	−	0.949944i	$-0.601140\pi$
$829$	−17.9907	−0.624842	−0.312421	+	0.949944i	$0.601140\pi$
$830$	−2.03016	−0.0704679
$831$	−2.42701	−0.0841922
$832$	1.00000	0.0346688
$833$	1.00000	0.0346479
$834$	−0.639960	−0.0221600
$835$	4.31580	0.149354
$836$	−31.3544	−1.08441
$837$	6.12978	0.211876
$838$	−31.0438	−1.07239
$839$	−29.6745	−1.02448	−0.512239	−	0.858843i	$-0.671184\pi$
$839$	−29.6745	−1.02448	−0.512239	+	0.858843i	$0.671184\pi$
$840$	0.855592	0.0295207
$841$	−22.2886	−0.768572
$842$	−22.0936	−0.761394
$843$	1.23763	0.0426263
$844$	1.08830	0.0374610
$845$	−0.855592	−0.0294333
$846$	−2.38802	−0.0821017
$847$	6.83579	0.234880
$848$	−0.591130	−0.0202995
$849$	6.12355	0.210160
$850$	−4.26796	−0.146390
$851$	1.96483	0.0673536
$852$	−14.9352	−0.511673
$853$	−7.34283	−0.251414	−0.125707	−	0.992067i	$-0.540120\pi$
$853$	−7.34283	−0.251414	−0.125707	+	0.992067i	$0.540120\pi$
$854$	−1.31540	−0.0450122
$855$	6.35212	0.217238
$856$	13.4755	0.460584
$857$	−32.2420	−1.10136	−0.550682	−	0.834715i	$-0.685632\pi$
$857$	−32.2420	−1.10136	−0.550682	+	0.834715i	$0.685632\pi$
$858$	−4.22324	−0.144179
$859$	22.1499	0.755743	0.377872	−	0.925858i	$-0.376656\pi$
$859$	22.1499	0.755743	0.377872	+	0.925858i	$0.376656\pi$
$860$	10.4766	0.357251
$861$	10.1671	0.346495
$862$	−4.32965	−0.147468
$863$	45.1469	1.53682	0.768410	−	0.639958i	$-0.221048\pi$
$863$	45.1469	1.53682	0.768410	+	0.639958i	$0.221048\pi$
$864$	−1.00000	−0.0340207
$865$	17.6653	0.600639
$866$	20.1139	0.683499
$867$	−1.00000	−0.0339618
$868$	−6.12978	−0.208058
$869$	−17.5988	−0.597000
$870$	−2.21653	−0.0751474
$871$	3.84775	0.130376
$872$	−9.53340	−0.322842
$873$	9.00753	0.304859
$874$	−22.5381	−0.762362
$875$	7.92959	0.268069
$876$	0.0934659	0.00315792
$877$	−5.55320	−0.187518	−0.0937590	−	0.995595i	$-0.529888\pi$
$877$	−5.55320	−0.187518	−0.0937590	+	0.995595i	$0.529888\pi$
$878$	−15.4475	−0.521326
$879$	−24.5895	−0.829384
$880$	−3.61337	−0.121807
$881$	−7.58313	−0.255482	−0.127741	−	0.991808i	$-0.540773\pi$
$881$	−7.58313	−0.255482	−0.127741	+	0.991808i	$0.540773\pi$
$882$	1.00000	0.0336718
$883$	−15.0355	−0.505985	−0.252993	−	0.967468i	$-0.581415\pi$
$883$	−15.0355	−0.505985	−0.252993	+	0.967468i	$0.581415\pi$
$884$	1.00000	0.0336336
$885$	−8.35309	−0.280786
$886$	29.7250	0.998631
$887$	26.6918	0.896224	0.448112	−	0.893977i	$-0.352096\pi$
$887$	26.6918	0.896224	0.448112	+	0.893977i	$0.352096\pi$
$888$	−0.647234	−0.0217197
$889$	−13.4194	−0.450073
$890$	5.80948	0.194734
$891$	4.22324	0.141484
$892$	1.76514	0.0591012
$893$	17.7292	0.593286
$894$	6.50848	0.217676
$895$	−12.3923	−0.414228
$896$	1.00000	0.0334077
$897$	−3.03574	−0.101360
$898$	−9.28719	−0.309918
$899$	15.8801	0.529629
$900$	−4.26796	−0.142265
$901$	−0.591130	−0.0196934
$902$	−42.9383	−1.42969
$903$	12.2449	0.407485
$904$	−6.55157	−0.217902
$905$	−21.3986	−0.711314
$906$	−3.94390	−0.131027
$907$	37.2241	1.23601	0.618003	−	0.786176i	$-0.287942\pi$
$907$	37.2241	1.23601	0.618003	+	0.786176i	$0.287942\pi$
$908$	−0.549694	−0.0182422
$909$	−5.84152	−0.193751
$910$	−0.855592	−0.0283626
$911$	−5.62262	−0.186286	−0.0931428	−	0.995653i	$-0.529691\pi$
$911$	−5.62262	−0.186286	−0.0931428	+	0.995653i	$0.529691\pi$
$912$	7.42425	0.245841
$913$	10.0210	0.331646
$914$	7.57569	0.250582
$915$	−1.12545	−0.0372062
$916$	−3.00057	−0.0991417
$917$	−0.0520754	−0.00171968
$918$	−1.00000	−0.0330049
$919$	16.6227	0.548332	0.274166	−	0.961682i	$-0.411598\pi$
$919$	16.6227	0.548332	0.274166	+	0.961682i	$0.411598\pi$
$920$	−2.59735	−0.0856322
$921$	−29.3841	−0.968239
$922$	−23.2077	−0.764306
$923$	14.9352	0.491600
$924$	−4.22324	−0.138935
$925$	−2.76237	−0.0908261
$926$	31.1737	1.02443
$927$	5.77136	0.189556
$928$	−2.59064	−0.0850419
$929$	26.2419	0.860968	0.430484	−	0.902598i	$-0.358343\pi$
$929$	26.2419	0.860968	0.430484	+	0.902598i	$0.358343\pi$
$930$	−5.24459	−0.171977
$931$	−7.42425	−0.243320
$932$	2.81332	0.0921535
$933$	−18.9496	−0.620381
$934$	22.3379	0.730917
$935$	−3.61337	−0.118170
$936$	1.00000	0.0326860
$937$	−54.9344	−1.79463	−0.897315	−	0.441391i	$-0.854485\pi$
$937$	−54.9344	−1.79463	−0.897315	+	0.441391i	$0.854485\pi$
$938$	3.84775	0.125633
$939$	−8.43766	−0.275353
$940$	2.04317	0.0666408
$941$	54.2040	1.76700	0.883500	−	0.468432i	$-0.155181\pi$
$941$	54.2040	1.76700	0.883500	+	0.468432i	$0.155181\pi$
$942$	2.75156	0.0896506
$943$	−30.8648	−1.00510
$944$	−9.76294	−0.317757
$945$	0.855592	0.0278324
$946$	−51.7133	−1.68134
$947$	−57.4215	−1.86595	−0.932973	−	0.359946i	$-0.882795\pi$
$947$	−57.4215	−1.86595	−0.932973	+	0.359946i	$0.882795\pi$
$948$	4.16714	0.135342
$949$	−0.0934659	−0.00303403
$950$	31.6864	1.02804
$951$	17.8971	0.580352
$952$	1.00000	0.0324102
$953$	−36.8581	−1.19395	−0.596975	−	0.802260i	$-0.703631\pi$
$953$	−36.8581	−1.19395	−0.596975	+	0.802260i	$0.703631\pi$
$954$	−0.591130	−0.0191385
$955$	10.5696	0.342023
$956$	−8.68894	−0.281020
$957$	10.9409	0.353669
$958$	−26.4017	−0.853000
$959$	15.9062	0.513639
$960$	0.855592	0.0276141
$961$	6.57418	0.212070
$962$	0.647234	0.0208677
$963$	13.4755	0.434242
$964$	−10.4892	−0.337836
$965$	10.3367	0.332750
$966$	−3.03574	−0.0976733
$967$	35.1045	1.12888	0.564442	−	0.825472i	$-0.309091\pi$
$967$	35.1045	1.12888	0.564442	+	0.825472i	$0.309091\pi$
$968$	6.83579	0.219711
$969$	7.42425	0.238501
$970$	−7.70677	−0.247449
$971$	−24.1821	−0.776040	−0.388020	−	0.921651i	$-0.626841\pi$
$971$	−24.1821	−0.776040	−0.388020	+	0.921651i	$0.626841\pi$
$972$	−1.00000	−0.0320750
$973$	0.639960	0.0205162
$974$	−1.36734	−0.0438122
$975$	4.26796	0.136684
$976$	−1.31540	−0.0421051
$977$	−3.34408	−0.106986	−0.0534932	−	0.998568i	$-0.517036\pi$
$977$	−3.34408	−0.106986	−0.0534932	+	0.998568i	$0.517036\pi$
$978$	19.3606	0.619084
$979$	−28.6759	−0.916486
$980$	−0.855592	−0.0273309
$981$	−9.53340	−0.304378
$982$	−4.96641	−0.158485
$983$	43.5956	1.39048	0.695242	−	0.718776i	$-0.255297\pi$
$983$	43.5956	1.39048	0.695242	+	0.718776i	$0.255297\pi$
$984$	10.1671	0.324117
$985$	8.96739	0.285725
$986$	−2.59064	−0.0825028
$987$	2.38802	0.0760114
$988$	−7.42425	−0.236197
$989$	−37.1724	−1.18201
$990$	−3.61337	−0.114841
$991$	10.0429	0.319024	0.159512	−	0.987196i	$-0.449008\pi$
$991$	10.0429	0.319024	0.159512	+	0.987196i	$0.449008\pi$
$992$	−6.12978	−0.194621
$993$	12.3253	0.391132
$994$	14.9352	0.473717
$995$	8.40193	0.266359
$996$	−2.37281	−0.0751855
$997$	−21.4227	−0.678464	−0.339232	−	0.940703i	$-0.610167\pi$
$997$	−21.4227	−0.678464	−0.339232	+	0.940703i	$0.610167\pi$
$998$	−26.5805	−0.841392
$999$	−0.647234	−0.0204776

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9282.2.a.bs.1.3	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9282.2.a.bs.1.3	✓	5	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:	\( N \)	\(=\)	\( 9282 = 2 \cdot 3 \cdot 7 \cdot 13 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9282.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.855592 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.855592 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.855592 q^{10} +4.22324 q^{11} -1.00000 q^{12} +1.00000 q^{13} +1.00000 q^{14} +0.855592 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} -7.42425 q^{19} -0.855592 q^{20} -1.00000 q^{21} +4.22324 q^{22} +3.03574 q^{23} -1.00000 q^{24} -4.26796 q^{25} +1.00000 q^{26} -1.00000 q^{27} +1.00000 q^{28} -2.59064 q^{29} +0.855592 q^{30} -6.12978 q^{31} +1.00000 q^{32} -4.22324 q^{33} +1.00000 q^{34} -0.855592 q^{35} +1.00000 q^{36} +0.647234 q^{37} -7.42425 q^{38} -1.00000 q^{39} -0.855592 q^{40} -10.1671 q^{41} -1.00000 q^{42} -12.2449 q^{43} +4.22324 q^{44} -0.855592 q^{45} +3.03574 q^{46} -2.38802 q^{47} -1.00000 q^{48} +1.00000 q^{49} -4.26796 q^{50} -1.00000 q^{51} +1.00000 q^{52} -0.591130 q^{53} -1.00000 q^{54} -3.61337 q^{55} +1.00000 q^{56} +7.42425 q^{57} -2.59064 q^{58} -9.76294 q^{59} +0.855592 q^{60} -1.31540 q^{61} -6.12978 q^{62} +1.00000 q^{63} +1.00000 q^{64} -0.855592 q^{65} -4.22324 q^{66} +3.84775 q^{67} +1.00000 q^{68} -3.03574 q^{69} -0.855592 q^{70} +14.9352 q^{71} +1.00000 q^{72} -0.0934659 q^{73} +0.647234 q^{74} +4.26796 q^{75} -7.42425 q^{76} +4.22324 q^{77} -1.00000 q^{78} -4.16714 q^{79} -0.855592 q^{80} +1.00000 q^{81} -10.1671 q^{82} +2.37281 q^{83} -1.00000 q^{84} -0.855592 q^{85} -12.2449 q^{86} +2.59064 q^{87} +4.22324 q^{88} -6.79002 q^{89} -0.855592 q^{90} +1.00000 q^{91} +3.03574 q^{92} +6.12978 q^{93} -2.38802 q^{94} +6.35212 q^{95} -1.00000 q^{96} +9.00753 q^{97} +1.00000 q^{98} +4.22324 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} - 7 q^{5} - 5 q^{6} + 5 q^{7} + 5 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 - 7 * q^5 - 5 * q^6 + 5 * q^7 + 5 * q^8 + 5 * q^9	\( 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} - 7 q^{5} - 5 q^{6} + 5 q^{7} + 5 q^{8} + 5 q^{9} - 7 q^{10} - 9 q^{11} - 5 q^{12} + 5 q^{13} + 5 q^{14} + 7 q^{15} + 5 q^{16} + 5 q^{17} + 5 q^{18} - q^{19} - 7 q^{20} - 5 q^{21} - 9 q^{22} - 6 q^{23} - 5 q^{24} + 2 q^{25} + 5 q^{26} - 5 q^{27} + 5 q^{28} - 10 q^{29} + 7 q^{30} - 7 q^{31} + 5 q^{32} + 9 q^{33} + 5 q^{34} - 7 q^{35} + 5 q^{36} - 3 q^{37} - q^{38} - 5 q^{39} - 7 q^{40} - 19 q^{41} - 5 q^{42} - 3 q^{43} - 9 q^{44} - 7 q^{45} - 6 q^{46} - 2 q^{47} - 5 q^{48} + 5 q^{49} + 2 q^{50} - 5 q^{51} + 5 q^{52} + 5 q^{53} - 5 q^{54} + 14 q^{55} + 5 q^{56} + q^{57} - 10 q^{58} - 12 q^{59} + 7 q^{60} - 21 q^{61} - 7 q^{62} + 5 q^{63} + 5 q^{64} - 7 q^{65} + 9 q^{66} + 12 q^{67} + 5 q^{68} + 6 q^{69} - 7 q^{70} + 4 q^{71} + 5 q^{72} + 6 q^{73} - 3 q^{74} - 2 q^{75} - q^{76} - 9 q^{77} - 5 q^{78} + 11 q^{79} - 7 q^{80} + 5 q^{81} - 19 q^{82} - 23 q^{83} - 5 q^{84} - 7 q^{85} - 3 q^{86} + 10 q^{87} - 9 q^{88} - 12 q^{89} - 7 q^{90} + 5 q^{91} - 6 q^{92} + 7 q^{93} - 2 q^{94} + 15 q^{95} - 5 q^{96} - 9 q^{97} + 5 q^{98} - 9 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 - 7 * q^5 - 5 * q^6 + 5 * q^7 + 5 * q^8 + 5 * q^9 - 7 * q^10 - 9 * q^11 - 5 * q^12 + 5 * q^13 + 5 * q^14 + 7 * q^15 + 5 * q^16 + 5 * q^17 + 5 * q^18 - q^19 - 7 * q^20 - 5 * q^21 - 9 * q^22 - 6 * q^23 - 5 * q^24 + 2 * q^25 + 5 * q^26 - 5 * q^27 + 5 * q^28 - 10 * q^29 + 7 * q^30 - 7 * q^31 + 5 * q^32 + 9 * q^33 + 5 * q^34 - 7 * q^35 + 5 * q^36 - 3 * q^37 - q^38 - 5 * q^39 - 7 * q^40 - 19 * q^41 - 5 * q^42 - 3 * q^43 - 9 * q^44 - 7 * q^45 - 6 * q^46 - 2 * q^47 - 5 * q^48 + 5 * q^49 + 2 * q^50 - 5 * q^51 + 5 * q^52 + 5 * q^53 - 5 * q^54 + 14 * q^55 + 5 * q^56 + q^57 - 10 * q^58 - 12 * q^59 + 7 * q^60 - 21 * q^61 - 7 * q^62 + 5 * q^63 + 5 * q^64 - 7 * q^65 + 9 * q^66 + 12 * q^67 + 5 * q^68 + 6 * q^69 - 7 * q^70 + 4 * q^71 + 5 * q^72 + 6 * q^73 - 3 * q^74 - 2 * q^75 - q^76 - 9 * q^77 - 5 * q^78 + 11 * q^79 - 7 * q^80 + 5 * q^81 - 19 * q^82 - 23 * q^83 - 5 * q^84 - 7 * q^85 - 3 * q^86 + 10 * q^87 - 9 * q^88 - 12 * q^89 - 7 * q^90 + 5 * q^91 - 6 * q^92 + 7 * q^93 - 2 * q^94 + 15 * q^95 - 5 * q^96 - 9 * q^97 + 5 * q^98 - 9 * q^99

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