LMFDB - Embedded newform 861.2.a.k.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [861,2,Mod(1,861)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(861, 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("861.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 861 = 3 \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	861.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$6.87511961403$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.1197392.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 8x^{3} + 6x^{2} + 14x - 2 $ x^5 - 2x^4 - 8x^3 + 6x^2 + 14x - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.54585$ of defining polynomial
Character	$\chi$	$=$	861.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.54585 q^{2} -1.00000 q^{3} +4.48134 q^{4} -2.36161 q^{5} -2.54585 q^{6} +1.00000 q^{7} +6.31711 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.54585 q^{2} -1.00000 q^{3} +4.48134 q^{4} -2.36161 q^{5} -2.54585 q^{6} +1.00000 q^{7} +6.31711 q^{8} +1.00000 q^{9} -6.01230 q^{10} +2.84295 q^{11} -4.48134 q^{12} +3.22788 q^{13} +2.54585 q^{14} +2.36161 q^{15} +7.11973 q^{16} +3.62736 q^{17} +2.54585 q^{18} +1.65154 q^{19} -10.5832 q^{20} -1.00000 q^{21} +7.23772 q^{22} +6.36076 q^{23} -6.31711 q^{24} +0.577197 q^{25} +8.21770 q^{26} -1.00000 q^{27} +4.48134 q^{28} -2.75041 q^{29} +6.01230 q^{30} -7.33743 q^{31} +5.49152 q^{32} -2.84295 q^{33} +9.23471 q^{34} -2.36161 q^{35} +4.48134 q^{36} +2.24188 q^{37} +4.20456 q^{38} -3.22788 q^{39} -14.9186 q^{40} -1.00000 q^{41} -2.54585 q^{42} +0.638391 q^{43} +12.7402 q^{44} -2.36161 q^{45} +16.1935 q^{46} -13.6312 q^{47} -7.11973 q^{48} +1.00000 q^{49} +1.46946 q^{50} -3.62736 q^{51} +14.4653 q^{52} -12.4563 q^{53} -2.54585 q^{54} -6.71394 q^{55} +6.31711 q^{56} -1.65154 q^{57} -7.00212 q^{58} -3.75638 q^{59} +10.5832 q^{60} +10.8426 q^{61} -18.6800 q^{62} +1.00000 q^{63} -0.258884 q^{64} -7.62300 q^{65} -7.23772 q^{66} +5.35112 q^{67} +16.2554 q^{68} -6.36076 q^{69} -6.01230 q^{70} -7.48346 q^{71} +6.31711 q^{72} +2.79930 q^{73} +5.70748 q^{74} -0.577197 q^{75} +7.40109 q^{76} +2.84295 q^{77} -8.21770 q^{78} +7.82559 q^{79} -16.8140 q^{80} +1.00000 q^{81} -2.54585 q^{82} +3.76826 q^{83} -4.48134 q^{84} -8.56641 q^{85} +1.62525 q^{86} +2.75041 q^{87} +17.9592 q^{88} -11.2114 q^{89} -6.01230 q^{90} +3.22788 q^{91} +28.5047 q^{92} +7.33743 q^{93} -34.7030 q^{94} -3.90028 q^{95} -5.49152 q^{96} +9.84210 q^{97} +2.54585 q^{98} +2.84295 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 3 q^{2} - 5 q^{3} + 11 q^{4} - 9 q^{5} - 3 q^{6} + 5 q^{7} + 9 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q + 3 * q^2 - 5 * q^3 + 11 * q^4 - 9 * q^5 - 3 * q^6 + 5 * q^7 + 9 * q^8 + 5 * q^9	\( 5 q + 3 q^{2} - 5 q^{3} + 11 q^{4} - 9 q^{5} - 3 q^{6} + 5 q^{7} + 9 q^{8} + 5 q^{9} + 9 q^{10} - 11 q^{12} - 3 q^{13} + 3 q^{14} + 9 q^{15} + 27 q^{16} - 16 q^{17} + 3 q^{18} + 4 q^{19} - 7 q^{20} - 5 q^{21} - 6 q^{22} - 3 q^{23} - 9 q^{24} + 20 q^{25} + 17 q^{26} - 5 q^{27} + 11 q^{28} + 13 q^{29} - 9 q^{30} - 4 q^{31} + 21 q^{32} - 4 q^{34} - 9 q^{35} + 11 q^{36} + 17 q^{37} + 4 q^{38} + 3 q^{39} + 37 q^{40} - 5 q^{41} - 3 q^{42} + 6 q^{43} + 32 q^{44} - 9 q^{45} + 27 q^{46} - 15 q^{47} - 27 q^{48} + 5 q^{49} - 14 q^{50} + 16 q^{51} - 17 q^{52} + 11 q^{53} - 3 q^{54} - 16 q^{55} + 9 q^{56} - 4 q^{57} + 9 q^{58} + 12 q^{59} + 7 q^{60} + 12 q^{61} + 8 q^{62} + 5 q^{63} + 19 q^{64} - 19 q^{65} + 6 q^{66} + 11 q^{67} - 28 q^{68} + 3 q^{69} + 9 q^{70} + 18 q^{71} + 9 q^{72} + 12 q^{73} - 27 q^{74} - 20 q^{75} - 26 q^{76} - 17 q^{78} + 23 q^{79} - 7 q^{80} + 5 q^{81} - 3 q^{82} - 2 q^{83} - 11 q^{84} + 20 q^{85} + 18 q^{86} - 13 q^{87} - 22 q^{88} - 28 q^{89} + 9 q^{90} - 3 q^{91} - 7 q^{92} + 4 q^{93} - 3 q^{94} - 10 q^{95} - 21 q^{96} + 3 q^{97} + 3 q^{98}+O(q^{100}) \) 5 * q + 3 * q^2 - 5 * q^3 + 11 * q^4 - 9 * q^5 - 3 * q^6 + 5 * q^7 + 9 * q^8 + 5 * q^9 + 9 * q^10 - 11 * q^12 - 3 * q^13 + 3 * q^14 + 9 * q^15 + 27 * q^16 - 16 * q^17 + 3 * q^18 + 4 * q^19 - 7 * q^20 - 5 * q^21 - 6 * q^22 - 3 * q^23 - 9 * q^24 + 20 * q^25 + 17 * q^26 - 5 * q^27 + 11 * q^28 + 13 * q^29 - 9 * q^30 - 4 * q^31 + 21 * q^32 - 4 * q^34 - 9 * q^35 + 11 * q^36 + 17 * q^37 + 4 * q^38 + 3 * q^39 + 37 * q^40 - 5 * q^41 - 3 * q^42 + 6 * q^43 + 32 * q^44 - 9 * q^45 + 27 * q^46 - 15 * q^47 - 27 * q^48 + 5 * q^49 - 14 * q^50 + 16 * q^51 - 17 * q^52 + 11 * q^53 - 3 * q^54 - 16 * q^55 + 9 * q^56 - 4 * q^57 + 9 * q^58 + 12 * q^59 + 7 * q^60 + 12 * q^61 + 8 * q^62 + 5 * q^63 + 19 * q^64 - 19 * q^65 + 6 * q^66 + 11 * q^67 - 28 * q^68 + 3 * q^69 + 9 * q^70 + 18 * q^71 + 9 * q^72 + 12 * q^73 - 27 * q^74 - 20 * q^75 - 26 * q^76 - 17 * q^78 + 23 * q^79 - 7 * q^80 + 5 * q^81 - 3 * q^82 - 2 * q^83 - 11 * q^84 + 20 * q^85 + 18 * q^86 - 13 * q^87 - 22 * q^88 - 28 * q^89 + 9 * q^90 - 3 * q^91 - 7 * q^92 + 4 * q^93 - 3 * q^94 - 10 * q^95 - 21 * q^96 + 3 * q^97 + 3 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.54585	1.80019	0.900093	−	0.435698i	$-0.143498\pi$
$2$	2.54585	1.80019	0.900093	+	0.435698i	$0.143498\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.48134	2.24067
$5$	−2.36161	−1.05614	−0.528072	−	0.849200i	$-0.677085\pi$
$5$	−2.36161	−1.05614	−0.528072	+	0.849200i	$0.677085\pi$
$6$	−2.54585	−1.03934
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	6.31711	2.23344
$9$	1.00000	0.333333
$10$	−6.01230	−1.90126
$11$	2.84295	0.857182	0.428591	−	0.903499i	$-0.359010\pi$
$11$	2.84295	0.857182	0.428591	+	0.903499i	$0.359010\pi$
$12$	−4.48134	−1.29365
$13$	3.22788	0.895254	0.447627	−	0.894220i	$-0.352269\pi$
$13$	3.22788	0.895254	0.447627	+	0.894220i	$0.352269\pi$
$14$	2.54585	0.680406
$15$	2.36161	0.609765
$16$	7.11973	1.77993
$17$	3.62736	0.879764	0.439882	−	0.898055i	$-0.355020\pi$
$17$	3.62736	0.879764	0.439882	+	0.898055i	$0.355020\pi$
$18$	2.54585	0.600062
$19$	1.65154	0.378888	0.189444	−	0.981891i	$-0.439331\pi$
$19$	1.65154	0.378888	0.189444	+	0.981891i	$0.439331\pi$
$20$	−10.5832	−2.36647
$21$	−1.00000	−0.218218
$22$	7.23772	1.54309
$23$	6.36076	1.32631	0.663155	−	0.748482i	$-0.269217\pi$
$23$	6.36076	1.32631	0.663155	+	0.748482i	$0.269217\pi$
$24$	−6.31711	−1.28948
$25$	0.577197	0.115439
$26$	8.21770	1.61162
$27$	−1.00000	−0.192450
$28$	4.48134	0.846894
$29$	−2.75041	−0.510738	−0.255369	−	0.966844i	$-0.582197\pi$
$29$	−2.75041	−0.510738	−0.255369	+	0.966844i	$0.582197\pi$
$30$	6.01230	1.09769
$31$	−7.33743	−1.31784	−0.658921	−	0.752212i	$-0.728987\pi$
$31$	−7.33743	−1.31784	−0.658921	+	0.752212i	$0.728987\pi$
$32$	5.49152	0.970773
$33$	−2.84295	−0.494894
$34$	9.23471	1.58374
$35$	−2.36161	−0.399185
$36$	4.48134	0.746890
$37$	2.24188	0.368562	0.184281	−	0.982874i	$-0.441004\pi$
$37$	2.24188	0.368562	0.184281	+	0.982874i	$0.441004\pi$
$38$	4.20456	0.682069
$39$	−3.22788	−0.516875
$40$	−14.9186	−2.35883
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	−2.54585	−0.392833
$43$	0.638391	0.0973537	0.0486769	−	0.998815i	$-0.484500\pi$
$43$	0.638391	0.0973537	0.0486769	+	0.998815i	$0.484500\pi$
$44$	12.7402	1.92066
$45$	−2.36161	−0.352048
$46$	16.1935	2.38761
$47$	−13.6312	−1.98832	−0.994159	−	0.107924i	$-0.965580\pi$
$47$	−13.6312	−1.98832	−0.994159	+	0.107924i	$0.965580\pi$
$48$	−7.11973	−1.02764
$49$	1.00000	0.142857
$50$	1.46946	0.207812
$51$	−3.62736	−0.507932
$52$	14.4653	2.00597
$53$	−12.4563	−1.71101	−0.855503	−	0.517797i	$-0.826752\pi$
$53$	−12.4563	−1.71101	−0.855503	+	0.517797i	$0.826752\pi$
$54$	−2.54585	−0.346446
$55$	−6.71394	−0.905307
$56$	6.31711	0.844160
$57$	−1.65154	−0.218751
$58$	−7.00212	−0.919423
$59$	−3.75638	−0.489038	−0.244519	−	0.969644i	$-0.578630\pi$
$59$	−3.75638	−0.489038	−0.244519	+	0.969644i	$0.578630\pi$
$60$	10.5832	1.36628
$61$	10.8426	1.38825	0.694126	−	0.719853i	$-0.255791\pi$
$61$	10.8426	1.38825	0.694126	+	0.719853i	$0.255791\pi$
$62$	−18.6800	−2.37236
$63$	1.00000	0.125988
$64$	−0.258884	−0.0323605
$65$	−7.62300	−0.945517
$66$	−7.23772	−0.890901
$67$	5.35112	0.653743	0.326872	−	0.945069i	$-0.394005\pi$
$67$	5.35112	0.653743	0.326872	+	0.945069i	$0.394005\pi$
$68$	16.2554	1.97126
$69$	−6.36076	−0.765746
$70$	−6.01230	−0.718607
$71$	−7.48346	−0.888123	−0.444061	−	0.895996i	$-0.646463\pi$
$71$	−7.48346	−0.888123	−0.444061	+	0.895996i	$0.646463\pi$
$72$	6.31711	0.744479
$73$	2.79930	0.327634	0.163817	−	0.986491i	$-0.447619\pi$
$73$	2.79930	0.327634	0.163817	+	0.986491i	$0.447619\pi$
$74$	5.70748	0.663481
$75$	−0.577197	−0.0666490
$76$	7.40109	0.848964
$77$	2.84295	0.323984
$78$	−8.21770	−0.930472
$79$	7.82559	0.880448	0.440224	−	0.897888i	$-0.354899\pi$
$79$	7.82559	0.880448	0.440224	+	0.897888i	$0.354899\pi$
$80$	−16.8140	−1.87986
$81$	1.00000	0.111111
$82$	−2.54585	−0.281142
$83$	3.76826	0.413620	0.206810	−	0.978381i	$-0.433692\pi$
$83$	3.76826	0.413620	0.206810	+	0.978381i	$0.433692\pi$
$84$	−4.48134	−0.488954
$85$	−8.56641	−0.929158
$86$	1.62525	0.175255
$87$	2.75041	0.294874
$88$	17.9592	1.91446
$89$	−11.2114	−1.18841	−0.594204	−	0.804314i	$-0.702533\pi$
$89$	−11.2114	−1.18841	−0.594204	+	0.804314i	$0.702533\pi$
$90$	−6.01230	−0.633752
$91$	3.22788	0.338374
$92$	28.5047	2.97182
$93$	7.33743	0.760857
$94$	−34.7030	−3.57934
$95$	−3.90028	−0.400160
$96$	−5.49152	−0.560476
$97$	9.84210	0.999314	0.499657	−	0.866223i	$-0.333459\pi$
$97$	9.84210	0.999314	0.499657	+	0.866223i	$0.333459\pi$
$98$	2.54585	0.257169
$99$	2.84295	0.285727
$100$	2.58662	0.258662
$101$	−3.44909	−0.343198	−0.171599	−	0.985167i	$-0.554893\pi$
$101$	−3.44909	−0.343198	−0.171599	+	0.985167i	$0.554893\pi$
$102$	−9.23471	−0.914373
$103$	−9.08699	−0.895367	−0.447684	−	0.894192i	$-0.647751\pi$
$103$	−9.08699	−0.895367	−0.447684	+	0.894192i	$0.647751\pi$
$104$	20.3909	1.99949
$105$	2.36161	0.230469
$106$	−31.7119	−3.08013
$107$	−9.01670	−0.871677	−0.435839	−	0.900025i	$-0.643548\pi$
$107$	−9.01670	−0.871677	−0.435839	+	0.900025i	$0.643548\pi$
$108$	−4.48134	−0.431217
$109$	−6.01454	−0.576089	−0.288044	−	0.957617i	$-0.593005\pi$
$109$	−6.01454	−0.576089	−0.288044	+	0.957617i	$0.593005\pi$
$110$	−17.0927	−1.62972
$111$	−2.24188	−0.212790
$112$	7.11973	0.672751
$113$	4.39211	0.413175	0.206587	−	0.978428i	$-0.433764\pi$
$113$	4.39211	0.413175	0.206587	+	0.978428i	$0.433764\pi$
$114$	−4.20456	−0.393793
$115$	−15.0216	−1.40077
$116$	−12.3255	−1.14439
$117$	3.22788	0.298418
$118$	−9.56316	−0.880360
$119$	3.62736	0.332520
$120$	14.9186	1.36187
$121$	−2.91764	−0.265240
$122$	27.6036	2.49911
$123$	1.00000	0.0901670
$124$	−32.8815	−2.95285
$125$	10.4449	0.934223
$126$	2.54585	0.226802
$127$	6.51450	0.578068	0.289034	−	0.957319i	$-0.406666\pi$
$127$	6.51450	0.578068	0.289034	+	0.957319i	$0.406666\pi$
$128$	−11.6421	−1.02903
$129$	−0.638391	−0.0562072
$130$	−19.4070	−1.70211
$131$	14.0051	1.22363	0.611817	−	0.791000i	$-0.290439\pi$
$131$	14.0051	1.22363	0.611817	+	0.791000i	$0.290439\pi$
$132$	−12.7402	−1.10889
$133$	1.65154	0.143206
$134$	13.6231	1.17686
$135$	2.36161	0.203255
$136$	22.9145	1.96490
$137$	−11.0254	−0.941967	−0.470984	−	0.882142i	$-0.656101\pi$
$137$	−11.0254	−0.941967	−0.470984	+	0.882142i	$0.656101\pi$
$138$	−16.1935	−1.37848
$139$	3.30813	0.280592	0.140296	−	0.990110i	$-0.455195\pi$
$139$	3.30813	0.280592	0.140296	+	0.990110i	$0.455195\pi$
$140$	−10.5832	−0.894441
$141$	13.6312	1.14796
$142$	−19.0517	−1.59879
$143$	9.17671	0.767395
$144$	7.11973	0.593311
$145$	6.49538	0.539412
$146$	7.12660	0.589802
$147$	−1.00000	−0.0824786
$148$	10.0466	0.825827
$149$	−20.4071	−1.67181	−0.835906	−	0.548872i	$-0.815057\pi$
$149$	−20.4071	−1.67181	−0.835906	+	0.548872i	$0.815057\pi$
$150$	−1.46946	−0.119981
$151$	−5.69518	−0.463467	−0.231734	−	0.972779i	$-0.574440\pi$
$151$	−5.69518	−0.463467	−0.231734	+	0.972779i	$0.574440\pi$
$152$	10.4329	0.846223
$153$	3.62736	0.293255
$154$	7.23772	0.583232
$155$	17.3282	1.39183
$156$	−14.4653	−1.15815
$157$	3.54881	0.283226	0.141613	−	0.989922i	$-0.454771\pi$
$157$	3.54881	0.283226	0.141613	+	0.989922i	$0.454771\pi$
$158$	19.9228	1.58497
$159$	12.4563	0.987850
$160$	−12.9688	−1.02528
$161$	6.36076	0.501298
$162$	2.54585	0.200021
$163$	15.6366	1.22476	0.612378	−	0.790565i	$-0.290213\pi$
$163$	15.6366	1.22476	0.612378	+	0.790565i	$0.290213\pi$
$164$	−4.48134	−0.349934
$165$	6.71394	0.522679
$166$	9.59342	0.744594
$167$	23.1005	1.78757	0.893785	−	0.448496i	$-0.148040\pi$
$167$	23.1005	1.78757	0.893785	+	0.448496i	$0.148040\pi$
$168$	−6.31711	−0.487376
$169$	−2.58076	−0.198520
$170$	−21.8088	−1.67266
$171$	1.65154	0.126296
$172$	2.86085	0.218138
$173$	−14.6419	−1.11320	−0.556602	−	0.830780i	$-0.687895\pi$
$173$	−14.6419	−1.11320	−0.556602	+	0.830780i	$0.687895\pi$
$174$	7.00212	0.530829
$175$	0.577197	0.0436320
$176$	20.2410	1.52573
$177$	3.75638	0.282346
$178$	−28.5426	−2.13936
$179$	12.5378	0.937118	0.468559	−	0.883432i	$-0.344773\pi$
$179$	12.5378	0.937118	0.468559	+	0.883432i	$0.344773\pi$
$180$	−10.5832	−0.788823
$181$	11.8230	0.878796	0.439398	−	0.898293i	$-0.355192\pi$
$181$	11.8230	0.878796	0.439398	+	0.898293i	$0.355192\pi$
$182$	8.21770	0.609137
$183$	−10.8426	−0.801508
$184$	40.1817	2.96223
$185$	−5.29444	−0.389255
$186$	18.6800	1.36968
$187$	10.3124	0.754118
$188$	−61.0862	−4.45517
$189$	−1.00000	−0.0727393
$190$	−9.92952	−0.720363
$191$	−11.7883	−0.852970	−0.426485	−	0.904495i	$-0.640248\pi$
$191$	−11.7883	−0.852970	−0.426485	+	0.904495i	$0.640248\pi$
$192$	0.258884	0.0186833
$193$	−17.7641	−1.27869	−0.639344	−	0.768921i	$-0.720794\pi$
$193$	−17.7641	−1.27869	−0.639344	+	0.768921i	$0.720794\pi$
$194$	25.0565	1.79895
$195$	7.62300	0.545895
$196$	4.48134	0.320096
$197$	−2.00000	−0.142494	−0.0712470	−	0.997459i	$-0.522698\pi$
$197$	−2.00000	−0.142494	−0.0712470	+	0.997459i	$0.522698\pi$
$198$	7.23772	0.514362
$199$	−12.9233	−0.916106	−0.458053	−	0.888925i	$-0.651453\pi$
$199$	−12.9233	−0.916106	−0.458053	+	0.888925i	$0.651453\pi$
$200$	3.64622	0.257827
$201$	−5.35112	−0.377439
$202$	−8.78086	−0.617819
$203$	−2.75041	−0.193041
$204$	−16.2554	−1.13811
$205$	2.36161	0.164942
$206$	−23.1341	−1.61183
$207$	6.36076	0.442103
$208$	22.9817	1.59349
$209$	4.69523	0.324776
$210$	6.01230	0.414888
$211$	−0.520825	−0.0358551	−0.0179276	−	0.999839i	$-0.505707\pi$
$211$	−0.520825	−0.0358551	−0.0179276	+	0.999839i	$0.505707\pi$
$212$	−55.8210	−3.83380
$213$	7.48346	0.512758
$214$	−22.9551	−1.56918
$215$	−1.50763	−0.102820
$216$	−6.31711	−0.429825
$217$	−7.33743	−0.498098
$218$	−15.3121	−1.03707
$219$	−2.79930	−0.189159
$220$	−30.0874	−2.02849
$221$	11.7087	0.787613
$222$	−5.70748	−0.383061
$223$	5.91427	0.396049	0.198025	−	0.980197i	$-0.436547\pi$
$223$	5.91427	0.396049	0.198025	+	0.980197i	$0.436547\pi$
$224$	5.49152	0.366918
$225$	0.577197	0.0384798
$226$	11.1816	0.743792
$227$	−24.0039	−1.59320	−0.796598	−	0.604509i	$-0.793369\pi$
$227$	−24.0039	−1.59320	−0.796598	+	0.604509i	$0.793369\pi$
$228$	−7.40109	−0.490149
$229$	10.0908	0.666822	0.333411	−	0.942782i	$-0.391800\pi$
$229$	10.0908	0.666822	0.333411	+	0.942782i	$0.391800\pi$
$230$	−38.2428	−2.52165
$231$	−2.84295	−0.187052
$232$	−17.3746	−1.14070
$233$	−29.4265	−1.92780	−0.963898	−	0.266272i	$-0.914208\pi$
$233$	−29.4265	−1.92780	−0.963898	+	0.266272i	$0.914208\pi$
$234$	8.21770	0.537208
$235$	32.1916	2.09995
$236$	−16.8336	−1.09577
$237$	−7.82559	−0.508327
$238$	9.23471	0.598597
$239$	1.79128	0.115868	0.0579341	−	0.998320i	$-0.481549\pi$
$239$	1.79128	0.115868	0.0579341	+	0.998320i	$0.481549\pi$
$240$	16.8140	1.08534
$241$	−20.6044	−1.32725	−0.663625	−	0.748066i	$-0.730983\pi$
$241$	−20.6044	−1.32725	−0.663625	+	0.748066i	$0.730983\pi$
$242$	−7.42786	−0.477481
$243$	−1.00000	−0.0641500
$244$	48.5894	3.11062
$245$	−2.36161	−0.150878
$246$	2.54585	0.162317
$247$	5.33097	0.339201
$248$	−46.3514	−2.94332
$249$	−3.76826	−0.238804
$250$	26.5912	1.68178
$251$	8.55021	0.539684	0.269842	−	0.962905i	$-0.413028\pi$
$251$	8.55021	0.539684	0.269842	+	0.962905i	$0.413028\pi$
$252$	4.48134	0.282298
$253$	18.0833	1.13689
$254$	16.5849	1.04063
$255$	8.56641	0.536449
$256$	−29.1213	−1.82008
$257$	30.4618	1.90015	0.950077	−	0.312014i	$-0.101004\pi$
$257$	30.4618	1.90015	0.950077	+	0.312014i	$0.101004\pi$
$258$	−1.62525	−0.101183
$259$	2.24188	0.139303
$260$	−34.1613	−2.11859
$261$	−2.75041	−0.170246
$262$	35.6549	2.20277
$263$	−17.9280	−1.10549	−0.552744	−	0.833351i	$-0.686419\pi$
$263$	−17.9280	−1.10549	−0.552744	+	0.833351i	$0.686419\pi$
$264$	−17.9592	−1.10531
$265$	29.4170	1.80707
$266$	4.20456	0.257798
$267$	11.2114	0.686128
$268$	23.9802	1.46482
$269$	27.8285	1.69673	0.848366	−	0.529410i	$-0.177587\pi$
$269$	27.8285	1.69673	0.848366	+	0.529410i	$0.177587\pi$
$270$	6.01230	0.365897
$271$	8.92374	0.542079	0.271039	−	0.962568i	$-0.412633\pi$
$271$	8.92374	0.542079	0.271039	+	0.962568i	$0.412633\pi$
$272$	25.8258	1.56592
$273$	−3.22788	−0.195360
$274$	−28.0691	−1.69572
$275$	1.64094	0.0989525
$276$	−28.5047	−1.71578
$277$	29.5205	1.77372	0.886858	−	0.462042i	$-0.152883\pi$
$277$	29.5205	1.77372	0.886858	+	0.462042i	$0.152883\pi$
$278$	8.42200	0.505118
$279$	−7.33743	−0.439281
$280$	−14.9186	−0.891554
$281$	30.7307	1.83324	0.916619	−	0.399763i	$-0.130908\pi$
$281$	30.7307	1.83324	0.916619	+	0.399763i	$0.130908\pi$
$282$	34.7030	2.06653
$283$	−2.36377	−0.140512	−0.0702559	−	0.997529i	$-0.522382\pi$
$283$	−2.36377	−0.140512	−0.0702559	+	0.997529i	$0.522382\pi$
$284$	−33.5359	−1.98999
$285$	3.90028	0.231033
$286$	23.3625	1.38145
$287$	−1.00000	−0.0590281
$288$	5.49152	0.323591
$289$	−3.84225	−0.226015
$290$	16.5363	0.971043
$291$	−9.84210	−0.576954
$292$	12.5446	0.734119
$293$	−24.8201	−1.45000	−0.725002	−	0.688746i	$-0.758161\pi$
$293$	−24.8201	−1.45000	−0.725002	+	0.688746i	$0.758161\pi$
$294$	−2.54585	−0.148477
$295$	8.87109	0.516495
$296$	14.1622	0.823161
$297$	−2.84295	−0.164965
$298$	−51.9533	−3.00957
$299$	20.5318	1.18738
$300$	−2.58662	−0.149338
$301$	0.638391	0.0367962
$302$	−14.4991	−0.834327
$303$	3.44909	0.198145
$304$	11.7585	0.674396
$305$	−25.6060	−1.46619
$306$	9.23471	0.527913
$307$	12.9953	0.741683	0.370842	−	0.928696i	$-0.379069\pi$
$307$	12.9953	0.741683	0.370842	+	0.928696i	$0.379069\pi$
$308$	12.7402	0.725942
$309$	9.08699	0.516941
$310$	44.1148	2.50555
$311$	−11.7636	−0.667052	−0.333526	−	0.942741i	$-0.608239\pi$
$311$	−11.7636	−0.667052	−0.333526	+	0.942741i	$0.608239\pi$
$312$	−20.3909	−1.15441
$313$	−25.2228	−1.42568	−0.712839	−	0.701327i	$-0.752591\pi$
$313$	−25.2228	−1.42568	−0.712839	+	0.701327i	$0.752591\pi$
$314$	9.03473	0.509859
$315$	−2.36161	−0.133062
$316$	35.0691	1.97279
$317$	−15.0037	−0.842694	−0.421347	−	0.906900i	$-0.638442\pi$
$317$	−15.0037	−0.842694	−0.421347	+	0.906900i	$0.638442\pi$
$318$	31.7119	1.77831
$319$	−7.81927	−0.437795
$320$	0.611383	0.0341773
$321$	9.01670	0.503263
$322$	16.1935	0.902430
$323$	5.99072	0.333332
$324$	4.48134	0.248963
$325$	1.86313	0.103348
$326$	39.8085	2.20479
$327$	6.01454	0.332605
$328$	−6.31711	−0.348804
$329$	−13.6312	−0.751514
$330$	17.0927	0.940920
$331$	−4.23560	−0.232810	−0.116405	−	0.993202i	$-0.537137\pi$
$331$	−4.23560	−0.232810	−0.116405	+	0.993202i	$0.537137\pi$
$332$	16.8869	0.926787
$333$	2.24188	0.122854
$334$	58.8103	3.21796
$335$	−12.6373	−0.690447
$336$	−7.11973	−0.388413
$337$	29.3846	1.60068	0.800340	−	0.599546i	$-0.204652\pi$
$337$	29.3846	1.60068	0.800340	+	0.599546i	$0.204652\pi$
$338$	−6.57022	−0.357373
$339$	−4.39211	−0.238547
$340$	−38.3890	−2.08194
$341$	−20.8600	−1.12963
$342$	4.20456	0.227356
$343$	1.00000	0.0539949
$344$	4.03279	0.217433
$345$	15.0216	0.808737
$346$	−37.2761	−2.00397
$347$	16.2391	0.871761	0.435881	−	0.900004i	$-0.356437\pi$
$347$	16.2391	0.871761	0.435881	+	0.900004i	$0.356437\pi$
$348$	12.3255	0.660716
$349$	−15.9562	−0.854118	−0.427059	−	0.904224i	$-0.640450\pi$
$349$	−15.9562	−0.854118	−0.427059	+	0.904224i	$0.640450\pi$
$350$	1.46946	0.0785457
$351$	−3.22788	−0.172292
$352$	15.6121	0.832129
$353$	−15.9872	−0.850914	−0.425457	−	0.904979i	$-0.639887\pi$
$353$	−15.9872	−0.850914	−0.425457	+	0.904979i	$0.639887\pi$
$354$	9.56316	0.508276
$355$	17.6730	0.937985
$356$	−50.2422	−2.66283
$357$	−3.62736	−0.191980
$358$	31.9193	1.68699
$359$	31.5683	1.66611	0.833057	−	0.553188i	$-0.186589\pi$
$359$	31.5683	1.66611	0.833057	+	0.553188i	$0.186589\pi$
$360$	−14.9186	−0.786277
$361$	−16.2724	−0.856444
$362$	30.0995	1.58200
$363$	2.91764	0.153136
$364$	14.4653	0.758185
$365$	−6.61086	−0.346028
$366$	−27.6036	−1.44286
$367$	0.978471	0.0510758	0.0255379	−	0.999674i	$-0.491870\pi$
$367$	0.978471	0.0510758	0.0255379	+	0.999674i	$0.491870\pi$
$368$	45.2869	2.36074
$369$	−1.00000	−0.0520579
$370$	−13.4788	−0.700731
$371$	−12.4563	−0.646700
$372$	32.8815	1.70483
$373$	12.3974	0.641914	0.320957	−	0.947094i	$-0.395995\pi$
$373$	12.3974	0.641914	0.320957	+	0.947094i	$0.395995\pi$
$374$	26.2538	1.35755
$375$	−10.4449	−0.539374
$376$	−86.1100	−4.44078
$377$	−8.87799	−0.457240
$378$	−2.54585	−0.130944
$379$	19.4591	0.999549	0.499775	−	0.866156i	$-0.333416\pi$
$379$	19.4591	0.999549	0.499775	+	0.866156i	$0.333416\pi$
$380$	−17.4785	−0.896628
$381$	−6.51450	−0.333748
$382$	−30.0111	−1.53550
$383$	14.2187	0.726540	0.363270	−	0.931684i	$-0.381660\pi$
$383$	14.2187	0.726540	0.363270	+	0.931684i	$0.381660\pi$
$384$	11.6421	0.594110
$385$	−6.71394	−0.342174
$386$	−45.2247	−2.30188
$387$	0.638391	0.0324512
$388$	44.1058	2.23913
$389$	−24.4555	−1.23994	−0.619972	−	0.784624i	$-0.712856\pi$
$389$	−24.4555	−1.23994	−0.619972	+	0.784624i	$0.712856\pi$
$390$	19.4070	0.982712
$391$	23.0728	1.16684
$392$	6.31711	0.319062
$393$	−14.0051	−0.706465
$394$	−5.09170	−0.256516
$395$	−18.4810	−0.929880
$396$	12.7402	0.640220
$397$	−2.10900	−0.105848	−0.0529239	−	0.998599i	$-0.516854\pi$
$397$	−2.10900	−0.105848	−0.0529239	+	0.998599i	$0.516854\pi$
$398$	−32.9007	−1.64916
$399$	−1.65154	−0.0826802
$400$	4.10949	0.205474
$401$	−12.5959	−0.629007	−0.314504	−	0.949256i	$-0.601838\pi$
$401$	−12.5959	−0.629007	−0.314504	+	0.949256i	$0.601838\pi$
$402$	−13.6231	−0.679460
$403$	−23.6844	−1.17980
$404$	−15.4566	−0.768992
$405$	−2.36161	−0.117349
$406$	−7.00212	−0.347509
$407$	6.37354	0.315925
$408$	−22.9145	−1.13443
$409$	5.86763	0.290136	0.145068	−	0.989422i	$-0.453660\pi$
$409$	5.86763	0.290136	0.145068	+	0.989422i	$0.453660\pi$
$410$	6.01230	0.296926
$411$	11.0254	0.543845
$412$	−40.7219	−2.00622
$413$	−3.75638	−0.184839
$414$	16.1935	0.795869
$415$	−8.89916	−0.436842
$416$	17.7260	0.869089
$417$	−3.30813	−0.162000
$418$	11.9533	0.584657
$419$	−2.93886	−0.143573	−0.0717863	−	0.997420i	$-0.522870\pi$
$419$	−2.93886	−0.143573	−0.0717863	+	0.997420i	$0.522870\pi$
$420$	10.5832	0.516406
$421$	30.3022	1.47684	0.738420	−	0.674341i	$-0.235572\pi$
$421$	30.3022	1.47684	0.738420	+	0.674341i	$0.235572\pi$
$422$	−1.32594	−0.0645459
$423$	−13.6312	−0.662773
$424$	−78.6880	−3.82143
$425$	2.09370	0.101559
$426$	19.0517	0.923060
$427$	10.8426	0.524710
$428$	−40.4069	−1.95314
$429$	−9.17671	−0.443056
$430$	−3.83820	−0.185094
$431$	16.3808	0.789034	0.394517	−	0.918889i	$-0.370912\pi$
$431$	16.3808	0.789034	0.394517	+	0.918889i	$0.370912\pi$
$432$	−7.11973	−0.342548
$433$	−16.2707	−0.781919	−0.390960	−	0.920408i	$-0.627857\pi$
$433$	−16.2707	−0.781919	−0.390960	+	0.920408i	$0.627857\pi$
$434$	−18.6800	−0.896668
$435$	−6.49538	−0.311430
$436$	−26.9532	−1.29082
$437$	10.5050	0.502523
$438$	−7.12660	−0.340522
$439$	1.20912	0.0577082	0.0288541	−	0.999584i	$-0.490814\pi$
$439$	1.20912	0.0577082	0.0288541	+	0.999584i	$0.490814\pi$
$440$	−42.4127	−2.02195
$441$	1.00000	0.0476190
$442$	29.8086	1.41785
$443$	30.4284	1.44570	0.722849	−	0.691006i	$-0.242832\pi$
$443$	30.4284	1.44570	0.722849	+	0.691006i	$0.242832\pi$
$444$	−10.0466	−0.476791
$445$	26.4770	1.25513
$446$	15.0568	0.712962
$447$	20.4071	0.965221
$448$	−0.258884	−0.0122311
$449$	35.1897	1.66071	0.830353	−	0.557238i	$-0.188139\pi$
$449$	35.1897	1.66071	0.830353	+	0.557238i	$0.188139\pi$
$450$	1.46946	0.0692708
$451$	−2.84295	−0.133869
$452$	19.6825	0.925789
$453$	5.69518	0.267583
$454$	−61.1104	−2.86805
$455$	−7.62300	−0.357372
$456$	−10.4329	−0.488567
$457$	−20.7825	−0.972166	−0.486083	−	0.873913i	$-0.661575\pi$
$457$	−20.7825	−0.972166	−0.486083	+	0.873913i	$0.661575\pi$
$458$	25.6898	1.20040
$459$	−3.62736	−0.169311
$460$	−67.3170	−3.13867
$461$	−39.4892	−1.83919	−0.919597	−	0.392862i	$-0.871485\pi$
$461$	−39.4892	−1.83919	−0.919597	+	0.392862i	$0.871485\pi$
$462$	−7.23772	−0.336729
$463$	−40.6119	−1.88739	−0.943697	−	0.330811i	$-0.892678\pi$
$463$	−40.6119	−1.88739	−0.943697	+	0.330811i	$0.892678\pi$
$464$	−19.5822	−0.909079
$465$	−17.3282	−0.803574
$466$	−74.9154	−3.47039
$467$	−9.95015	−0.460438	−0.230219	−	0.973139i	$-0.573944\pi$
$467$	−9.95015	−0.460438	−0.230219	+	0.973139i	$0.573944\pi$
$468$	14.4653	0.668656
$469$	5.35112	0.247092
$470$	81.9550	3.78030
$471$	−3.54881	−0.163521
$472$	−23.7295	−1.09224
$473$	1.81491	0.0834498
$474$	−19.9228	−0.915083
$475$	0.953262	0.0437386
$476$	16.2554	0.745067
$477$	−12.4563	−0.570336
$478$	4.56033	0.208585
$479$	20.6264	0.942444	0.471222	−	0.882015i	$-0.343813\pi$
$479$	20.6264	0.942444	0.471222	+	0.882015i	$0.343813\pi$
$480$	12.9688	0.591943
$481$	7.23652	0.329957
$482$	−52.4558	−2.38930
$483$	−6.36076	−0.289425
$484$	−13.0749	−0.594315
$485$	−23.2432	−1.05542
$486$	−2.54585	−0.115482
$487$	−18.0289	−0.816970	−0.408485	−	0.912765i	$-0.633943\pi$
$487$	−18.0289	−0.816970	−0.408485	+	0.912765i	$0.633943\pi$
$488$	68.4939	3.10058
$489$	−15.6366	−0.707114
$490$	−6.01230	−0.271608
$491$	9.53853	0.430468	0.215234	−	0.976563i	$-0.430949\pi$
$491$	9.53853	0.430468	0.215234	+	0.976563i	$0.430949\pi$
$492$	4.48134	0.202034
$493$	−9.97672	−0.449329
$494$	13.5718	0.610626
$495$	−6.71394	−0.301769
$496$	−52.2406	−2.34567
$497$	−7.48346	−0.335679
$498$	−9.59342	−0.429891
$499$	30.2250	1.35306	0.676528	−	0.736417i	$-0.263484\pi$
$499$	30.2250	1.35306	0.676528	+	0.736417i	$0.263484\pi$
$500$	46.8073	2.09329
$501$	−23.1005	−1.03205
$502$	21.7675	0.971532
$503$	−23.3866	−1.04276	−0.521379	−	0.853325i	$-0.674582\pi$
$503$	−23.3866	−1.04276	−0.521379	+	0.853325i	$0.674582\pi$
$504$	6.31711	0.281387
$505$	8.14541	0.362466
$506$	46.0374	2.04661
$507$	2.58076	0.114616
$508$	29.1937	1.29526
$509$	2.45103	0.108640	0.0543200	−	0.998524i	$-0.482701\pi$
$509$	2.45103	0.108640	0.0543200	+	0.998524i	$0.482701\pi$
$510$	21.8088	0.965709
$511$	2.79930	0.123834
$512$	−50.8542	−2.24746
$513$	−1.65154	−0.0729171
$514$	77.5511	3.42063
$515$	21.4599	0.945636
$516$	−2.86085	−0.125942
$517$	−38.7529	−1.70435
$518$	5.70748	0.250772
$519$	14.6419	0.642708
$520$	−48.1554	−2.11175
$521$	40.1307	1.75816	0.879079	−	0.476677i	$-0.158159\pi$
$521$	40.1307	1.75816	0.879079	+	0.476677i	$0.158159\pi$
$522$	−7.00212	−0.306474
$523$	21.8493	0.955402	0.477701	−	0.878522i	$-0.341470\pi$
$523$	21.8493	0.955402	0.477701	+	0.878522i	$0.341470\pi$
$524$	62.7617	2.74176
$525$	−0.577197	−0.0251909
$526$	−45.6420	−1.99009
$527$	−26.6155	−1.15939
$528$	−20.2410	−0.880878
$529$	17.4593	0.759099
$530$	74.8911	3.25306
$531$	−3.75638	−0.163013
$532$	7.40109	0.320878
$533$	−3.22788	−0.139815
$534$	28.5426	1.23516
$535$	21.2939	0.920616
$536$	33.8036	1.46010
$537$	−12.5378	−0.541045
$538$	70.8471	3.05443
$539$	2.84295	0.122455
$540$	10.5832	0.455427
$541$	−7.30235	−0.313953	−0.156976	−	0.987602i	$-0.550175\pi$
$541$	−7.30235	−0.313953	−0.156976	+	0.987602i	$0.550175\pi$
$542$	22.7185	0.975843
$543$	−11.8230	−0.507373
$544$	19.9197	0.854052
$545$	14.2040	0.608432
$546$	−8.21770	−0.351685
$547$	34.5622	1.47777	0.738887	−	0.673829i	$-0.235352\pi$
$547$	34.5622	1.47777	0.738887	+	0.673829i	$0.235352\pi$
$548$	−49.4088	−2.11064
$549$	10.8426	0.462751
$550$	4.17759	0.178133
$551$	−4.54239	−0.193512
$552$	−40.1817	−1.71024
$553$	7.82559	0.332778
$554$	75.1548	3.19302
$555$	5.29444	0.224736
$556$	14.8249	0.628714
$557$	−22.5641	−0.956070	−0.478035	−	0.878341i	$-0.658651\pi$
$557$	−22.5641	−0.956070	−0.478035	+	0.878341i	$0.658651\pi$
$558$	−18.6800	−0.790787
$559$	2.06065	0.0871563
$560$	−16.8140	−0.710522
$561$	−10.3124	−0.435390
$562$	78.2356	3.30017
$563$	4.31892	0.182021	0.0910105	−	0.995850i	$-0.470990\pi$
$563$	4.31892	0.182021	0.0910105	+	0.995850i	$0.470990\pi$
$564$	61.0862	2.57219
$565$	−10.3724	−0.436372
$566$	−6.01781	−0.252947
$567$	1.00000	0.0419961
$568$	−47.2738	−1.98357
$569$	−22.0896	−0.926044	−0.463022	−	0.886347i	$-0.653235\pi$
$569$	−22.0896	−0.926044	−0.463022	+	0.886347i	$0.653235\pi$
$570$	9.92952	0.415902
$571$	18.3048	0.766033	0.383016	−	0.923742i	$-0.374885\pi$
$571$	18.3048	0.766033	0.383016	+	0.923742i	$0.374885\pi$
$572$	41.1240	1.71948
$573$	11.7883	0.492462
$574$	−2.54585	−0.106262
$575$	3.67141	0.153108
$576$	−0.258884	−0.0107868
$577$	−11.9103	−0.495831	−0.247916	−	0.968782i	$-0.579746\pi$
$577$	−11.9103	−0.495831	−0.247916	+	0.968782i	$0.579746\pi$
$578$	−9.78178	−0.406868
$579$	17.7641	0.738251
$580$	29.1080	1.20865
$581$	3.76826	0.156334
$582$	−25.0565	−1.03862
$583$	−35.4127	−1.46664
$584$	17.6835	0.731749
$585$	−7.62300	−0.315172
$586$	−63.1882	−2.61028
$587$	32.8165	1.35448	0.677242	−	0.735761i	$-0.263175\pi$
$587$	32.8165	1.35448	0.677242	+	0.735761i	$0.263175\pi$
$588$	−4.48134	−0.184807
$589$	−12.1180	−0.499315
$590$	22.5844	0.929787
$591$	2.00000	0.0822690
$592$	15.9616	0.656016
$593$	−9.18879	−0.377338	−0.188669	−	0.982041i	$-0.560417\pi$
$593$	−9.18879	−0.377338	−0.188669	+	0.982041i	$0.560417\pi$
$594$	−7.23772	−0.296967
$595$	−8.56641	−0.351189
$596$	−91.4510	−3.74598
$597$	12.9233	0.528914
$598$	52.2708	2.13751
$599$	38.7022	1.58133	0.790666	−	0.612248i	$-0.209735\pi$
$599$	38.7022	1.58133	0.790666	+	0.612248i	$0.209735\pi$
$600$	−3.64622	−0.148856
$601$	23.2479	0.948302	0.474151	−	0.880444i	$-0.342755\pi$
$601$	23.2479	0.948302	0.474151	+	0.880444i	$0.342755\pi$
$602$	1.62525	0.0662401
$603$	5.35112	0.217914
$604$	−25.5220	−1.03848
$605$	6.89032	0.280131
$606$	8.78086	0.356698
$607$	42.2806	1.71612	0.858058	−	0.513553i	$-0.171671\pi$
$607$	42.2806	1.71612	0.858058	+	0.513553i	$0.171671\pi$
$608$	9.06945	0.367815
$609$	2.75041	0.111452
$610$	−65.1889	−2.63942
$611$	−44.0000	−1.78005
$612$	16.2554	0.657087
$613$	12.2758	0.495814	0.247907	−	0.968784i	$-0.420257\pi$
$613$	12.2758	0.495814	0.247907	+	0.968784i	$0.420257\pi$
$614$	33.0842	1.33517
$615$	−2.36161	−0.0952293
$616$	17.9592	0.723598
$617$	−25.0296	−1.00765	−0.503827	−	0.863805i	$-0.668075\pi$
$617$	−25.0296	−1.00765	−0.503827	+	0.863805i	$0.668075\pi$
$618$	23.1341	0.930589
$619$	−31.0046	−1.24618	−0.623091	−	0.782149i	$-0.714123\pi$
$619$	−31.0046	−1.24618	−0.623091	+	0.782149i	$0.714123\pi$
$620$	77.6533	3.11863
$621$	−6.36076	−0.255249
$622$	−29.9483	−1.20082
$623$	−11.2114	−0.449176
$624$	−22.9817	−0.920003
$625$	−27.5528	−1.10211
$626$	−64.2135	−2.56649
$627$	−4.69523	−0.187510
$628$	15.9034	0.634616
$629$	8.13210	0.324248
$630$	−6.01230	−0.239536
$631$	15.2964	0.608942	0.304471	−	0.952522i	$-0.401520\pi$
$631$	15.2964	0.608942	0.304471	+	0.952522i	$0.401520\pi$
$632$	49.4352	1.96643
$633$	0.520825	0.0207010
$634$	−38.1972	−1.51701
$635$	−15.3847	−0.610523
$636$	55.8210	2.21345
$637$	3.22788	0.127893
$638$	−19.9067	−0.788112
$639$	−7.48346	−0.296041
$640$	27.4941	1.08680
$641$	19.8773	0.785105	0.392552	−	0.919730i	$-0.371592\pi$
$641$	19.8773	0.785105	0.392552	+	0.919730i	$0.371592\pi$
$642$	22.9551	0.905967
$643$	−22.1447	−0.873301	−0.436650	−	0.899631i	$-0.643835\pi$
$643$	−22.1447	−0.873301	−0.436650	+	0.899631i	$0.643835\pi$
$644$	28.5047	1.12324
$645$	1.50763	0.0593629
$646$	15.2515	0.600060
$647$	20.0770	0.789308	0.394654	−	0.918830i	$-0.370865\pi$
$647$	20.0770	0.789308	0.394654	+	0.918830i	$0.370865\pi$
$648$	6.31711	0.248160
$649$	−10.6792	−0.419195
$650$	4.74323	0.186045
$651$	7.33743	0.287577
$652$	70.0731	2.74428
$653$	26.0336	1.01877	0.509387	−	0.860537i	$-0.329872\pi$
$653$	26.0336	1.01877	0.509387	+	0.860537i	$0.329872\pi$
$654$	15.3121	0.598751
$655$	−33.0746	−1.29233
$656$	−7.11973	−0.277979
$657$	2.79930	0.109211
$658$	−34.7030	−1.35286
$659$	41.2486	1.60682	0.803408	−	0.595429i	$-0.203018\pi$
$659$	41.2486	1.60682	0.803408	+	0.595429i	$0.203018\pi$
$660$	30.0874	1.17115
$661$	−16.0223	−0.623196	−0.311598	−	0.950214i	$-0.600864\pi$
$661$	−16.0223	−0.623196	−0.311598	+	0.950214i	$0.600864\pi$
$662$	−10.7832	−0.419101
$663$	−11.7087	−0.454728
$664$	23.8045	0.923795
$665$	−3.90028	−0.151246
$666$	5.70748	0.221160
$667$	−17.4947	−0.677397
$668$	103.521	4.00535
$669$	−5.91427	−0.228659
$670$	−32.1725	−1.24293
$671$	30.8250	1.18998
$672$	−5.49152	−0.211840
$673$	−43.9924	−1.69578	−0.847892	−	0.530169i	$-0.822129\pi$
$673$	−43.9924	−1.69578	−0.847892	+	0.530169i	$0.822129\pi$
$674$	74.8087	2.88152
$675$	−0.577197	−0.0222163
$676$	−11.5653	−0.444818
$677$	−30.4118	−1.16882	−0.584410	−	0.811459i	$-0.698674\pi$
$677$	−30.4118	−1.16882	−0.584410	+	0.811459i	$0.698674\pi$
$678$	−11.1816	−0.429428
$679$	9.84210	0.377705
$680$	−54.1150	−2.07522
$681$	24.0039	0.919833
$682$	−53.1063	−2.03354
$683$	24.4552	0.935752	0.467876	−	0.883794i	$-0.345019\pi$
$683$	24.4552	0.935752	0.467876	+	0.883794i	$0.345019\pi$
$684$	7.40109	0.282988
$685$	26.0378	0.994853
$686$	2.54585	0.0972009
$687$	−10.0908	−0.384990
$688$	4.54517	0.173283
$689$	−40.2076	−1.53179
$690$	38.2428	1.45588
$691$	−8.95340	−0.340603	−0.170302	−	0.985392i	$-0.554474\pi$
$691$	−8.95340	−0.340603	−0.170302	+	0.985392i	$0.554474\pi$
$692$	−65.6154	−2.49432
$693$	2.84295	0.107995
$694$	41.3423	1.56933
$695$	−7.81251	−0.296346
$696$	17.3746	0.658584
$697$	−3.62736	−0.137396
$698$	−40.6221	−1.53757
$699$	29.4265	1.11301
$700$	2.58662	0.0977649
$701$	−7.75968	−0.293079	−0.146539	−	0.989205i	$-0.546814\pi$
$701$	−7.75968	−0.293079	−0.146539	+	0.989205i	$0.546814\pi$
$702$	−8.21770	−0.310157
$703$	3.70254	0.139644
$704$	−0.735994	−0.0277388
$705$	−32.1916	−1.21241
$706$	−40.7010	−1.53180
$707$	−3.44909	−0.129716
$708$	16.8336	0.632645
$709$	−41.9099	−1.57396	−0.786980	−	0.616979i	$-0.788356\pi$
$709$	−41.9099	−1.57396	−0.786980	+	0.616979i	$0.788356\pi$
$710$	44.9928	1.68855
$711$	7.82559	0.293483
$712$	−70.8239	−2.65424
$713$	−46.6717	−1.74787
$714$	−9.23471	−0.345600
$715$	−21.6718	−0.810480
$716$	56.1861	2.09977
$717$	−1.79128	−0.0668966
$718$	80.3682	2.99931
$719$	−2.07621	−0.0774296	−0.0387148	−	0.999250i	$-0.512326\pi$
$719$	−2.07621	−0.0774296	−0.0387148	+	0.999250i	$0.512326\pi$
$720$	−16.8140	−0.626622
$721$	−9.08699	−0.338417
$722$	−41.4271	−1.54176
$723$	20.6044	0.766288
$724$	52.9828	1.96909
$725$	−1.58753	−0.0589592
$726$	7.42786	0.275674
$727$	5.93830	0.220239	0.110120	−	0.993918i	$-0.464877\pi$
$727$	5.93830	0.220239	0.110120	+	0.993918i	$0.464877\pi$
$728$	20.3909	0.755738
$729$	1.00000	0.0370370
$730$	−16.8302	−0.622915
$731$	2.31567	0.0856483
$732$	−48.5894	−1.79592
$733$	15.3185	0.565802	0.282901	−	0.959149i	$-0.408703\pi$
$733$	15.3185	0.565802	0.282901	+	0.959149i	$0.408703\pi$
$734$	2.49104	0.0919459
$735$	2.36161	0.0871093
$736$	34.9303	1.28755
$737$	15.2130	0.560377
$738$	−2.54585	−0.0937139
$739$	19.4423	0.715196	0.357598	−	0.933876i	$-0.383596\pi$
$739$	19.4423	0.715196	0.357598	+	0.933876i	$0.383596\pi$
$740$	−23.7262	−0.872192
$741$	−5.33097	−0.195838
$742$	−31.7119	−1.16418
$743$	−49.8095	−1.82733	−0.913666	−	0.406465i	$-0.866761\pi$
$743$	−49.8095	−1.82733	−0.913666	+	0.406465i	$0.866761\pi$
$744$	46.3514	1.69933
$745$	48.1935	1.76567
$746$	31.5619	1.15556
$747$	3.76826	0.137873
$748$	46.2134	1.68973
$749$	−9.01670	−0.329463
$750$	−26.5912	−0.970973
$751$	9.23153	0.336863	0.168432	−	0.985713i	$-0.446130\pi$
$751$	9.23153	0.336863	0.168432	+	0.985713i	$0.446130\pi$
$752$	−97.0506	−3.53907
$753$	−8.55021	−0.311587
$754$	−22.6020	−0.823117
$755$	13.4498	0.489488
$756$	−4.48134	−0.162985
$757$	23.1248	0.840487	0.420243	−	0.907411i	$-0.361945\pi$
$757$	23.1248	0.840487	0.420243	+	0.907411i	$0.361945\pi$
$758$	49.5400	1.79937
$759$	−18.0833	−0.656383
$760$	−24.6385	−0.893733
$761$	27.9227	1.01220	0.506098	−	0.862476i	$-0.331087\pi$
$761$	27.9227	1.01220	0.506098	+	0.862476i	$0.331087\pi$
$762$	−16.5849	−0.600808
$763$	−6.01454	−0.217741
$764$	−52.8273	−1.91122
$765$	−8.56641	−0.309719
$766$	36.1986	1.30791
$767$	−12.1251	−0.437814
$768$	29.1213	1.05082
$769$	0.685712	0.0247274	0.0123637	−	0.999924i	$-0.496064\pi$
$769$	0.685712	0.0247274	0.0123637	+	0.999924i	$0.496064\pi$
$770$	−17.0927	−0.615977
$771$	−30.4618	−1.09705
$772$	−79.6070	−2.86512
$773$	1.55461	0.0559154	0.0279577	−	0.999609i	$-0.491100\pi$
$773$	1.55461	0.0559154	0.0279577	+	0.999609i	$0.491100\pi$
$774$	1.62525	0.0584183
$775$	−4.23515	−0.152131
$776$	62.1737	2.23191
$777$	−2.24188	−0.0804269
$778$	−62.2600	−2.23213
$779$	−1.65154	−0.0591724
$780$	34.1613	1.22317
$781$	−21.2751	−0.761282
$782$	58.7398	2.10053
$783$	2.75041	0.0982915
$784$	7.11973	0.254276
$785$	−8.38090	−0.299127
$786$	−35.6549	−1.27177
$787$	−39.3541	−1.40282	−0.701410	−	0.712758i	$-0.747446\pi$
$787$	−39.3541	−1.40282	−0.701410	+	0.712758i	$0.747446\pi$
$788$	−8.96268	−0.319282
$789$	17.9280	0.638254
$790$	−47.0498	−1.67396
$791$	4.39211	0.156165
$792$	17.9592	0.638154
$793$	34.9987	1.24284
$794$	−5.36920	−0.190546
$795$	−29.4170	−1.04331
$796$	−57.9136	−2.05269
$797$	13.9152	0.492903	0.246452	−	0.969155i	$-0.420735\pi$
$797$	13.9152	0.492903	0.246452	+	0.969155i	$0.420735\pi$
$798$	−4.20456	−0.148840
$799$	−49.4454	−1.74925
$800$	3.16969	0.112065
$801$	−11.2114	−0.396136
$802$	−32.0672	−1.13233
$803$	7.95828	0.280842
$804$	−23.9802	−0.845716
$805$	−15.0216	−0.529443
$806$	−60.2969	−2.12387
$807$	−27.8285	−0.979609
$808$	−21.7883	−0.766510
$809$	8.87641	0.312078	0.156039	−	0.987751i	$-0.450127\pi$
$809$	8.87641	0.312078	0.156039	+	0.987751i	$0.450127\pi$
$810$	−6.01230	−0.211251
$811$	38.9536	1.36785	0.683923	−	0.729554i	$-0.260272\pi$
$811$	38.9536	1.36785	0.683923	+	0.729554i	$0.260272\pi$
$812$	−12.3255	−0.432540
$813$	−8.92374	−0.312969
$814$	16.2261	0.568724
$815$	−36.9276	−1.29352
$816$	−25.8258	−0.904085
$817$	1.05433	0.0368862
$818$	14.9381	0.522298
$819$	3.22788	0.112791
$820$	10.5832	0.369580
$821$	−1.83217	−0.0639431	−0.0319716	−	0.999489i	$-0.510179\pi$
$821$	−1.83217	−0.0639431	−0.0319716	+	0.999489i	$0.510179\pi$
$822$	28.0691	0.979022
$823$	26.8386	0.935535	0.467767	−	0.883852i	$-0.345059\pi$
$823$	26.8386	0.935535	0.467767	+	0.883852i	$0.345059\pi$
$824$	−57.4035	−1.99975
$825$	−1.64094	−0.0571303
$826$	−9.56316	−0.332745
$827$	28.1422	0.978599	0.489299	−	0.872116i	$-0.337253\pi$
$827$	28.1422	0.978599	0.489299	+	0.872116i	$0.337253\pi$
$828$	28.5047	0.990608
$829$	14.1103	0.490071	0.245036	−	0.969514i	$-0.421200\pi$
$829$	14.1103	0.490071	0.245036	+	0.969514i	$0.421200\pi$
$830$	−22.6559	−0.786398
$831$	−29.5205	−1.02406
$832$	−0.835648	−0.0289709
$833$	3.62736	0.125681
$834$	−8.42200	−0.291630
$835$	−54.5543	−1.88793
$836$	21.0409	0.727716
$837$	7.33743	0.253619
$838$	−7.48188	−0.258457
$839$	−21.7863	−0.752148	−0.376074	−	0.926590i	$-0.622726\pi$
$839$	−21.7863	−0.752148	−0.376074	+	0.926590i	$0.622726\pi$
$840$	14.9186	0.514739
$841$	−21.4353	−0.739147
$842$	77.1449	2.65859
$843$	−30.7307	−1.05842
$844$	−2.33400	−0.0803395
$845$	6.09474	0.209666
$846$	−34.7030	−1.19311
$847$	−2.91764	−0.100251
$848$	−88.6856	−3.04548
$849$	2.36377	0.0811245
$850$	5.33025	0.182826
$851$	14.2600	0.488828
$852$	33.5359	1.14892
$853$	−42.8533	−1.46727	−0.733635	−	0.679544i	$-0.762178\pi$
$853$	−42.8533	−1.46727	−0.733635	+	0.679544i	$0.762178\pi$
$854$	27.6036	0.944576
$855$	−3.90028	−0.133387
$856$	−56.9595	−1.94684
$857$	−10.1494	−0.346696	−0.173348	−	0.984861i	$-0.555459\pi$
$857$	−10.1494	−0.346696	−0.173348	+	0.984861i	$0.555459\pi$
$858$	−23.3625	−0.797583
$859$	35.3853	1.20733	0.603665	−	0.797238i	$-0.293706\pi$
$859$	35.3853	1.20733	0.603665	+	0.797238i	$0.293706\pi$
$860$	−6.75620	−0.230385
$861$	1.00000	0.0340799
$862$	41.7029	1.42041
$863$	15.1524	0.515792	0.257896	−	0.966173i	$-0.416971\pi$
$863$	15.1524	0.515792	0.257896	+	0.966173i	$0.416971\pi$
$864$	−5.49152	−0.186825
$865$	34.5784	1.17570
$866$	−41.4227	−1.40760
$867$	3.84225	0.130490
$868$	−32.8815	−1.11607
$869$	22.2478	0.754704
$870$	−16.5363	−0.560632
$871$	17.2728	0.585267
$872$	−37.9945	−1.28666
$873$	9.84210	0.333105
$874$	26.7442	0.904636
$875$	10.4449	0.353103
$876$	−12.5446	−0.423844
$877$	−0.212473	−0.00717471	−0.00358735	−	0.999994i	$-0.501142\pi$
$877$	−0.212473	−0.00717471	−0.00358735	+	0.999994i	$0.501142\pi$
$878$	3.07824	0.103885
$879$	24.8201	0.837161
$880$	−47.8014	−1.61139
$881$	−2.92517	−0.0985515	−0.0492758	−	0.998785i	$-0.515691\pi$
$881$	−2.92517	−0.0985515	−0.0492758	+	0.998785i	$0.515691\pi$
$882$	2.54585	0.0857232
$883$	−8.48098	−0.285408	−0.142704	−	0.989765i	$-0.545580\pi$
$883$	−8.48098	−0.285408	−0.142704	+	0.989765i	$0.545580\pi$
$884$	52.4707	1.76478
$885$	−8.87109	−0.298198
$886$	77.4661	2.60253
$887$	−10.5513	−0.354277	−0.177139	−	0.984186i	$-0.556684\pi$
$887$	−10.5513	−0.354277	−0.177139	+	0.984186i	$0.556684\pi$
$888$	−14.1622	−0.475252
$889$	6.51450	0.218489
$890$	67.4064	2.25947
$891$	2.84295	0.0952424
$892$	26.5039	0.887415
$893$	−22.5125	−0.753350
$894$	51.9533	1.73758
$895$	−29.6093	−0.989731
$896$	−11.6421	−0.388936
$897$	−20.5318	−0.685537
$898$	89.5877	2.98958
$899$	20.1809	0.673072
$900$	2.58662	0.0862205
$901$	−45.1836	−1.50528
$902$	−7.23772	−0.240990
$903$	−0.638391	−0.0212443
$904$	27.7455	0.922800
$905$	−27.9213	−0.928135
$906$	14.4991	0.481699
$907$	−53.6891	−1.78272	−0.891359	−	0.453297i	$-0.850248\pi$
$907$	−53.6891	−1.78272	−0.891359	+	0.453297i	$0.850248\pi$
$908$	−107.570	−3.56983
$909$	−3.44909	−0.114399
$910$	−19.4070	−0.643336
$911$	32.2807	1.06951	0.534754	−	0.845008i	$-0.320404\pi$
$911$	32.2807	1.06951	0.534754	+	0.845008i	$0.320404\pi$
$912$	−11.7585	−0.389363
$913$	10.7130	0.354548
$914$	−52.9091	−1.75008
$915$	25.6060	0.846508
$916$	45.2205	1.49413
$917$	14.0051	0.462490
$918$	−9.23471	−0.304791
$919$	−34.7950	−1.14778	−0.573890	−	0.818932i	$-0.694566\pi$
$919$	−34.7950	−1.14778	−0.573890	+	0.818932i	$0.694566\pi$
$920$	−94.8934	−3.12854
$921$	−12.9953	−0.428211
$922$	−100.533	−3.31089
$923$	−24.1557	−0.795096
$924$	−12.7402	−0.419123
$925$	1.29401	0.0425466
$926$	−103.392	−3.39766
$927$	−9.08699	−0.298456
$928$	−15.1039	−0.495810
$929$	−36.8642	−1.20948	−0.604738	−	0.796425i	$-0.706722\pi$
$929$	−36.8642	−1.20948	−0.604738	+	0.796425i	$0.706722\pi$
$930$	−44.1148	−1.44658
$931$	1.65154	0.0541269
$932$	−131.870	−4.31955
$933$	11.7636	0.385123
$934$	−25.3316	−0.828874
$935$	−24.3539	−0.796457
$936$	20.3909	0.666498
$937$	−60.2648	−1.96877	−0.984383	−	0.176042i	$-0.943671\pi$
$937$	−60.2648	−1.96877	−0.984383	+	0.176042i	$0.943671\pi$
$938$	13.6231	0.444811
$939$	25.2228	0.823116
$940$	144.262	4.70529
$941$	−0.580503	−0.0189239	−0.00946193	−	0.999955i	$-0.503012\pi$
$941$	−0.580503	−0.0189239	−0.00946193	+	0.999955i	$0.503012\pi$
$942$	−9.03473	−0.294367
$943$	−6.36076	−0.207135
$944$	−26.7444	−0.870456
$945$	2.36161	0.0768231
$946$	4.62049	0.150225
$947$	19.8393	0.644690	0.322345	−	0.946622i	$-0.395529\pi$
$947$	19.8393	0.644690	0.322345	+	0.946622i	$0.395529\pi$
$948$	−35.0691	−1.13899
$949$	9.03583	0.293315
$950$	2.42686	0.0787377
$951$	15.0037	0.486529
$952$	22.9145	0.742662
$953$	−37.2517	−1.20670	−0.603350	−	0.797476i	$-0.706168\pi$
$953$	−37.2517	−1.20670	−0.603350	+	0.797476i	$0.706168\pi$
$954$	−31.7119	−1.02671
$955$	27.8393	0.900858
$956$	8.02734	0.259623
$957$	7.81927	0.252761
$958$	52.5116	1.69657
$959$	−11.0254	−0.356030
$960$	−0.611383	−0.0197323
$961$	22.8379	0.736708
$962$	18.4231	0.593984
$963$	−9.01670	−0.290559
$964$	−92.3355	−2.97393
$965$	41.9519	1.35048
$966$	−16.1935	−0.521018
$967$	−5.76885	−0.185514	−0.0927569	−	0.995689i	$-0.529568\pi$
$967$	−5.76885	−0.185514	−0.0927569	+	0.995689i	$0.529568\pi$
$968$	−18.4311	−0.592397
$969$	−5.99072	−0.192450
$970$	−59.1736	−1.89995
$971$	18.5893	0.596559	0.298280	−	0.954478i	$-0.403587\pi$
$971$	18.5893	0.596559	0.298280	+	0.954478i	$0.403587\pi$
$972$	−4.48134	−0.143739
$973$	3.30813	0.106054
$974$	−45.8990	−1.47070
$975$	−1.86313	−0.0596678
$976$	77.1964	2.47100
$977$	22.9468	0.734133	0.367067	−	0.930195i	$-0.380362\pi$
$977$	22.9468	0.734133	0.367067	+	0.930195i	$0.380362\pi$
$978$	−39.8085	−1.27294
$979$	−31.8735	−1.01868
$980$	−10.5832	−0.338067
$981$	−6.01454	−0.192030
$982$	24.2837	0.774922
$983$	−5.65800	−0.180462	−0.0902311	−	0.995921i	$-0.528761\pi$
$983$	−5.65800	−0.180462	−0.0902311	+	0.995921i	$0.528761\pi$
$984$	6.31711	0.201382
$985$	4.72322	0.150494
$986$	−25.3992	−0.808875
$987$	13.6312	0.433887
$988$	23.8899	0.760038
$989$	4.06065	0.129121
$990$	−17.0927	−0.543240
$991$	34.9103	1.10896	0.554482	−	0.832196i	$-0.312916\pi$
$991$	34.9103	1.10896	0.554482	+	0.832196i	$0.312916\pi$
$992$	−40.2937	−1.27933
$993$	4.23560	0.134413
$994$	−19.0517	−0.604284
$995$	30.5197	0.967540
$996$	−16.8869	−0.535081
$997$	−20.5673	−0.651372	−0.325686	−	0.945478i	$-0.605595\pi$
$997$	−20.5673	−0.651372	−0.325686	+	0.945478i	$0.605595\pi$
$998$	76.9482	2.43575
$999$	−2.24188	−0.0709299

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	861.2.a.k.1.4	✓	5
3.2	odd	2		2583.2.a.q.1.2		5
7.6	odd	2		6027.2.a.x.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.a.k.1.4	✓	5	1.1	even	1	trivial
2583.2.a.q.1.2		5	3.2	odd	2
6027.2.a.x.1.4		5	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 861 = 3 \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	861.a (trivial)

\(f(q)\)	\(=\)	\(q+2.54585 q^{2} -1.00000 q^{3} +4.48134 q^{4} -2.36161 q^{5} -2.54585 q^{6} +1.00000 q^{7} +6.31711 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.54585 q^{2} -1.00000 q^{3} +4.48134 q^{4} -2.36161 q^{5} -2.54585 q^{6} +1.00000 q^{7} +6.31711 q^{8} +1.00000 q^{9} -6.01230 q^{10} +2.84295 q^{11} -4.48134 q^{12} +3.22788 q^{13} +2.54585 q^{14} +2.36161 q^{15} +7.11973 q^{16} +3.62736 q^{17} +2.54585 q^{18} +1.65154 q^{19} -10.5832 q^{20} -1.00000 q^{21} +7.23772 q^{22} +6.36076 q^{23} -6.31711 q^{24} +0.577197 q^{25} +8.21770 q^{26} -1.00000 q^{27} +4.48134 q^{28} -2.75041 q^{29} +6.01230 q^{30} -7.33743 q^{31} +5.49152 q^{32} -2.84295 q^{33} +9.23471 q^{34} -2.36161 q^{35} +4.48134 q^{36} +2.24188 q^{37} +4.20456 q^{38} -3.22788 q^{39} -14.9186 q^{40} -1.00000 q^{41} -2.54585 q^{42} +0.638391 q^{43} +12.7402 q^{44} -2.36161 q^{45} +16.1935 q^{46} -13.6312 q^{47} -7.11973 q^{48} +1.00000 q^{49} +1.46946 q^{50} -3.62736 q^{51} +14.4653 q^{52} -12.4563 q^{53} -2.54585 q^{54} -6.71394 q^{55} +6.31711 q^{56} -1.65154 q^{57} -7.00212 q^{58} -3.75638 q^{59} +10.5832 q^{60} +10.8426 q^{61} -18.6800 q^{62} +1.00000 q^{63} -0.258884 q^{64} -7.62300 q^{65} -7.23772 q^{66} +5.35112 q^{67} +16.2554 q^{68} -6.36076 q^{69} -6.01230 q^{70} -7.48346 q^{71} +6.31711 q^{72} +2.79930 q^{73} +5.70748 q^{74} -0.577197 q^{75} +7.40109 q^{76} +2.84295 q^{77} -8.21770 q^{78} +7.82559 q^{79} -16.8140 q^{80} +1.00000 q^{81} -2.54585 q^{82} +3.76826 q^{83} -4.48134 q^{84} -8.56641 q^{85} +1.62525 q^{86} +2.75041 q^{87} +17.9592 q^{88} -11.2114 q^{89} -6.01230 q^{90} +3.22788 q^{91} +28.5047 q^{92} +7.33743 q^{93} -34.7030 q^{94} -3.90028 q^{95} -5.49152 q^{96} +9.84210 q^{97} +2.54585 q^{98} +2.84295 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 3 q^{2} - 5 q^{3} + 11 q^{4} - 9 q^{5} - 3 q^{6} + 5 q^{7} + 9 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q + 3 * q^2 - 5 * q^3 + 11 * q^4 - 9 * q^5 - 3 * q^6 + 5 * q^7 + 9 * q^8 + 5 * q^9	\( 5 q + 3 q^{2} - 5 q^{3} + 11 q^{4} - 9 q^{5} - 3 q^{6} + 5 q^{7} + 9 q^{8} + 5 q^{9} + 9 q^{10} - 11 q^{12} - 3 q^{13} + 3 q^{14} + 9 q^{15} + 27 q^{16} - 16 q^{17} + 3 q^{18} + 4 q^{19} - 7 q^{20} - 5 q^{21} - 6 q^{22} - 3 q^{23} - 9 q^{24} + 20 q^{25} + 17 q^{26} - 5 q^{27} + 11 q^{28} + 13 q^{29} - 9 q^{30} - 4 q^{31} + 21 q^{32} - 4 q^{34} - 9 q^{35} + 11 q^{36} + 17 q^{37} + 4 q^{38} + 3 q^{39} + 37 q^{40} - 5 q^{41} - 3 q^{42} + 6 q^{43} + 32 q^{44} - 9 q^{45} + 27 q^{46} - 15 q^{47} - 27 q^{48} + 5 q^{49} - 14 q^{50} + 16 q^{51} - 17 q^{52} + 11 q^{53} - 3 q^{54} - 16 q^{55} + 9 q^{56} - 4 q^{57} + 9 q^{58} + 12 q^{59} + 7 q^{60} + 12 q^{61} + 8 q^{62} + 5 q^{63} + 19 q^{64} - 19 q^{65} + 6 q^{66} + 11 q^{67} - 28 q^{68} + 3 q^{69} + 9 q^{70} + 18 q^{71} + 9 q^{72} + 12 q^{73} - 27 q^{74} - 20 q^{75} - 26 q^{76} - 17 q^{78} + 23 q^{79} - 7 q^{80} + 5 q^{81} - 3 q^{82} - 2 q^{83} - 11 q^{84} + 20 q^{85} + 18 q^{86} - 13 q^{87} - 22 q^{88} - 28 q^{89} + 9 q^{90} - 3 q^{91} - 7 q^{92} + 4 q^{93} - 3 q^{94} - 10 q^{95} - 21 q^{96} + 3 q^{97} + 3 q^{98}+O(q^{100}) \) 5 * q + 3 * q^2 - 5 * q^3 + 11 * q^4 - 9 * q^5 - 3 * q^6 + 5 * q^7 + 9 * q^8 + 5 * q^9 + 9 * q^10 - 11 * q^12 - 3 * q^13 + 3 * q^14 + 9 * q^15 + 27 * q^16 - 16 * q^17 + 3 * q^18 + 4 * q^19 - 7 * q^20 - 5 * q^21 - 6 * q^22 - 3 * q^23 - 9 * q^24 + 20 * q^25 + 17 * q^26 - 5 * q^27 + 11 * q^28 + 13 * q^29 - 9 * q^30 - 4 * q^31 + 21 * q^32 - 4 * q^34 - 9 * q^35 + 11 * q^36 + 17 * q^37 + 4 * q^38 + 3 * q^39 + 37 * q^40 - 5 * q^41 - 3 * q^42 + 6 * q^43 + 32 * q^44 - 9 * q^45 + 27 * q^46 - 15 * q^47 - 27 * q^48 + 5 * q^49 - 14 * q^50 + 16 * q^51 - 17 * q^52 + 11 * q^53 - 3 * q^54 - 16 * q^55 + 9 * q^56 - 4 * q^57 + 9 * q^58 + 12 * q^59 + 7 * q^60 + 12 * q^61 + 8 * q^62 + 5 * q^63 + 19 * q^64 - 19 * q^65 + 6 * q^66 + 11 * q^67 - 28 * q^68 + 3 * q^69 + 9 * q^70 + 18 * q^71 + 9 * q^72 + 12 * q^73 - 27 * q^74 - 20 * q^75 - 26 * q^76 - 17 * q^78 + 23 * q^79 - 7 * q^80 + 5 * q^81 - 3 * q^82 - 2 * q^83 - 11 * q^84 + 20 * q^85 + 18 * q^86 - 13 * q^87 - 22 * q^88 - 28 * q^89 + 9 * q^90 - 3 * q^91 - 7 * q^92 + 4 * q^93 - 3 * q^94 - 10 * q^95 - 21 * q^96 + 3 * q^97 + 3 * q^98

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