LMFDB - Embedded newform 966.2.a.n.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(1,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, 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("966.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{41}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 10 $ x^2 - x - 10
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			1.2
Root			$3.70156$ of defining polynomial
Character	$\chi$	$=$	966.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.70156 q^{5} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.70156 q^{5} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.70156 q^{10} -4.00000 q^{11} +1.00000 q^{12} +5.70156 q^{13} -1.00000 q^{14} +3.70156 q^{15} +1.00000 q^{16} +4.00000 q^{17} -1.00000 q^{18} -5.40312 q^{19} +3.70156 q^{20} +1.00000 q^{21} +4.00000 q^{22} +1.00000 q^{23} -1.00000 q^{24} +8.70156 q^{25} -5.70156 q^{26} +1.00000 q^{27} +1.00000 q^{28} +0.298438 q^{29} -3.70156 q^{30} -2.00000 q^{31} -1.00000 q^{32} -4.00000 q^{33} -4.00000 q^{34} +3.70156 q^{35} +1.00000 q^{36} +4.29844 q^{37} +5.40312 q^{38} +5.70156 q^{39} -3.70156 q^{40} -0.298438 q^{41} -1.00000 q^{42} -1.70156 q^{43} -4.00000 q^{44} +3.70156 q^{45} -1.00000 q^{46} -11.1047 q^{47} +1.00000 q^{48} +1.00000 q^{49} -8.70156 q^{50} +4.00000 q^{51} +5.70156 q^{52} -9.40312 q^{53} -1.00000 q^{54} -14.8062 q^{55} -1.00000 q^{56} -5.40312 q^{57} -0.298438 q^{58} -7.40312 q^{59} +3.70156 q^{60} -2.00000 q^{61} +2.00000 q^{62} +1.00000 q^{63} +1.00000 q^{64} +21.1047 q^{65} +4.00000 q^{66} +14.8062 q^{67} +4.00000 q^{68} +1.00000 q^{69} -3.70156 q^{70} -7.40312 q^{71} -1.00000 q^{72} +1.40312 q^{73} -4.29844 q^{74} +8.70156 q^{75} -5.40312 q^{76} -4.00000 q^{77} -5.70156 q^{78} +8.00000 q^{79} +3.70156 q^{80} +1.00000 q^{81} +0.298438 q^{82} +13.4031 q^{83} +1.00000 q^{84} +14.8062 q^{85} +1.70156 q^{86} +0.298438 q^{87} +4.00000 q^{88} -11.4031 q^{89} -3.70156 q^{90} +5.70156 q^{91} +1.00000 q^{92} -2.00000 q^{93} +11.1047 q^{94} -20.0000 q^{95} -1.00000 q^{96} +6.29844 q^{97} -1.00000 q^{98} -4.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} + q^{5} - 2 q^{6} + 2 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 + q^5 - 2 * q^6 + 2 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} + q^{5} - 2 q^{6} + 2 q^{7} - 2 q^{8} + 2 q^{9} - q^{10} - 8 q^{11} + 2 q^{12} + 5 q^{13} - 2 q^{14} + q^{15} + 2 q^{16} + 8 q^{17} - 2 q^{18} + 2 q^{19} + q^{20} + 2 q^{21} + 8 q^{22} + 2 q^{23} - 2 q^{24} + 11 q^{25} - 5 q^{26} + 2 q^{27} + 2 q^{28} + 7 q^{29} - q^{30} - 4 q^{31} - 2 q^{32} - 8 q^{33} - 8 q^{34} + q^{35} + 2 q^{36} + 15 q^{37} - 2 q^{38} + 5 q^{39} - q^{40} - 7 q^{41} - 2 q^{42} + 3 q^{43} - 8 q^{44} + q^{45} - 2 q^{46} - 3 q^{47} + 2 q^{48} + 2 q^{49} - 11 q^{50} + 8 q^{51} + 5 q^{52} - 6 q^{53} - 2 q^{54} - 4 q^{55} - 2 q^{56} + 2 q^{57} - 7 q^{58} - 2 q^{59} + q^{60} - 4 q^{61} + 4 q^{62} + 2 q^{63} + 2 q^{64} + 23 q^{65} + 8 q^{66} + 4 q^{67} + 8 q^{68} + 2 q^{69} - q^{70} - 2 q^{71} - 2 q^{72} - 10 q^{73} - 15 q^{74} + 11 q^{75} + 2 q^{76} - 8 q^{77} - 5 q^{78} + 16 q^{79} + q^{80} + 2 q^{81} + 7 q^{82} + 14 q^{83} + 2 q^{84} + 4 q^{85} - 3 q^{86} + 7 q^{87} + 8 q^{88} - 10 q^{89} - q^{90} + 5 q^{91} + 2 q^{92} - 4 q^{93} + 3 q^{94} - 40 q^{95} - 2 q^{96} + 19 q^{97} - 2 q^{98} - 8 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 + q^5 - 2 * q^6 + 2 * q^7 - 2 * q^8 + 2 * q^9 - q^10 - 8 * q^11 + 2 * q^12 + 5 * q^13 - 2 * q^14 + q^15 + 2 * q^16 + 8 * q^17 - 2 * q^18 + 2 * q^19 + q^20 + 2 * q^21 + 8 * q^22 + 2 * q^23 - 2 * q^24 + 11 * q^25 - 5 * q^26 + 2 * q^27 + 2 * q^28 + 7 * q^29 - q^30 - 4 * q^31 - 2 * q^32 - 8 * q^33 - 8 * q^34 + q^35 + 2 * q^36 + 15 * q^37 - 2 * q^38 + 5 * q^39 - q^40 - 7 * q^41 - 2 * q^42 + 3 * q^43 - 8 * q^44 + q^45 - 2 * q^46 - 3 * q^47 + 2 * q^48 + 2 * q^49 - 11 * q^50 + 8 * q^51 + 5 * q^52 - 6 * q^53 - 2 * q^54 - 4 * q^55 - 2 * q^56 + 2 * q^57 - 7 * q^58 - 2 * q^59 + q^60 - 4 * q^61 + 4 * q^62 + 2 * q^63 + 2 * q^64 + 23 * q^65 + 8 * q^66 + 4 * q^67 + 8 * q^68 + 2 * q^69 - q^70 - 2 * q^71 - 2 * q^72 - 10 * q^73 - 15 * q^74 + 11 * q^75 + 2 * q^76 - 8 * q^77 - 5 * q^78 + 16 * q^79 + q^80 + 2 * q^81 + 7 * q^82 + 14 * q^83 + 2 * q^84 + 4 * q^85 - 3 * q^86 + 7 * q^87 + 8 * q^88 - 10 * q^89 - q^90 + 5 * q^91 + 2 * q^92 - 4 * q^93 + 3 * q^94 - 40 * q^95 - 2 * q^96 + 19 * q^97 - 2 * q^98 - 8 * 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
$5$	3.70156	1.65539	0.827694	−	0.561179i	$-0.189652\pi$
$5$	3.70156	1.65539	0.827694	+	0.561179i	$0.189652\pi$
$6$	−1.00000	−0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−3.70156	−1.17054
$11$	−4.00000	−1.20605	−0.603023	−	0.797724i	$-0.706037\pi$
$11$	−4.00000	−1.20605	−0.603023	+	0.797724i	$0.706037\pi$
$12$	1.00000	0.288675
$13$	5.70156	1.58133	0.790664	−	0.612250i	$-0.209735\pi$
$13$	5.70156	1.58133	0.790664	+	0.612250i	$0.209735\pi$
$14$	−1.00000	−0.267261
$15$	3.70156	0.955739
$16$	1.00000	0.250000
$17$	4.00000	0.970143	0.485071	−	0.874475i	$-0.338794\pi$
$17$	4.00000	0.970143	0.485071	+	0.874475i	$0.338794\pi$
$18$	−1.00000	−0.235702
$19$	−5.40312	−1.23956	−0.619781	−	0.784775i	$-0.712779\pi$
$19$	−5.40312	−1.23956	−0.619781	+	0.784775i	$0.712779\pi$
$20$	3.70156	0.827694
$21$	1.00000	0.218218
$22$	4.00000	0.852803
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−1.00000	−0.204124
$25$	8.70156	1.74031
$26$	−5.70156	−1.11817
$27$	1.00000	0.192450
$28$	1.00000	0.188982
$29$	0.298438	0.0554185	0.0277093	−	0.999616i	$-0.491179\pi$
$29$	0.298438	0.0554185	0.0277093	+	0.999616i	$0.491179\pi$
$30$	−3.70156	−0.675810
$31$	−2.00000	−0.359211	−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000	−0.359211	−0.179605	+	0.983739i	$0.557482\pi$
$32$	−1.00000	−0.176777
$33$	−4.00000	−0.696311
$34$	−4.00000	−0.685994
$35$	3.70156	0.625678
$36$	1.00000	0.166667
$37$	4.29844	0.706659	0.353329	−	0.935499i	$-0.385049\pi$
$37$	4.29844	0.706659	0.353329	+	0.935499i	$0.385049\pi$
$38$	5.40312	0.876502
$39$	5.70156	0.912981
$40$	−3.70156	−0.585268
$41$	−0.298438	−0.0466082	−0.0233041	−	0.999728i	$-0.507419\pi$
$41$	−0.298438	−0.0466082	−0.0233041	+	0.999728i	$0.507419\pi$
$42$	−1.00000	−0.154303
$43$	−1.70156	−0.259486	−0.129743	−	0.991548i	$-0.541415\pi$
$43$	−1.70156	−0.259486	−0.129743	+	0.991548i	$0.541415\pi$
$44$	−4.00000	−0.603023
$45$	3.70156	0.551796
$46$	−1.00000	−0.147442
$47$	−11.1047	−1.61978	−0.809892	−	0.586578i	$-0.800475\pi$
$47$	−11.1047	−1.61978	−0.809892	+	0.586578i	$0.800475\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	−8.70156	−1.23059
$51$	4.00000	0.560112
$52$	5.70156	0.790664
$53$	−9.40312	−1.29162	−0.645809	−	0.763499i	$-0.723480\pi$
$53$	−9.40312	−1.29162	−0.645809	+	0.763499i	$0.723480\pi$
$54$	−1.00000	−0.136083
$55$	−14.8062	−1.99647
$56$	−1.00000	−0.133631
$57$	−5.40312	−0.715661
$58$	−0.298438	−0.0391868
$59$	−7.40312	−0.963805	−0.481902	−	0.876225i	$-0.660054\pi$
$59$	−7.40312	−0.963805	−0.481902	+	0.876225i	$0.660054\pi$
$60$	3.70156	0.477870
$61$	−2.00000	−0.256074	−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000	−0.256074	−0.128037	+	0.991769i	$0.540868\pi$
$62$	2.00000	0.254000
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	21.1047	2.61771
$66$	4.00000	0.492366
$67$	14.8062	1.80887	0.904436	−	0.426610i	$-0.140292\pi$
$67$	14.8062	1.80887	0.904436	+	0.426610i	$0.140292\pi$
$68$	4.00000	0.485071
$69$	1.00000	0.120386
$70$	−3.70156	−0.442421
$71$	−7.40312	−0.878589	−0.439295	−	0.898343i	$-0.644772\pi$
$71$	−7.40312	−0.878589	−0.439295	+	0.898343i	$0.644772\pi$
$72$	−1.00000	−0.117851
$73$	1.40312	0.164223	0.0821116	−	0.996623i	$-0.473834\pi$
$73$	1.40312	0.164223	0.0821116	+	0.996623i	$0.473834\pi$
$74$	−4.29844	−0.499683
$75$	8.70156	1.00477
$76$	−5.40312	−0.619781
$77$	−4.00000	−0.455842
$78$	−5.70156	−0.645575
$79$	8.00000	0.900070	0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000	0.900070	0.450035	+	0.893011i	$0.351411\pi$
$80$	3.70156	0.413847
$81$	1.00000	0.111111
$82$	0.298438	0.0329570
$83$	13.4031	1.47118	0.735592	−	0.677425i	$-0.236904\pi$
$83$	13.4031	1.47118	0.735592	+	0.677425i	$0.236904\pi$
$84$	1.00000	0.109109
$85$	14.8062	1.60596
$86$	1.70156	0.183484
$87$	0.298438	0.0319959
$88$	4.00000	0.426401
$89$	−11.4031	−1.20873	−0.604364	−	0.796708i	$-0.706573\pi$
$89$	−11.4031	−1.20873	−0.604364	+	0.796708i	$0.706573\pi$
$90$	−3.70156	−0.390179
$91$	5.70156	0.597686
$92$	1.00000	0.104257
$93$	−2.00000	−0.207390
$94$	11.1047	1.14536
$95$	−20.0000	−2.05196
$96$	−1.00000	−0.102062
$97$	6.29844	0.639509	0.319755	−	0.947500i	$-0.396399\pi$
$97$	6.29844	0.639509	0.319755	+	0.947500i	$0.396399\pi$
$98$	−1.00000	−0.101015
$99$	−4.00000	−0.402015
$100$	8.70156	0.870156
$101$	−3.40312	−0.338624	−0.169312	−	0.985563i	$-0.554154\pi$
$101$	−3.40312	−0.338624	−0.169312	+	0.985563i	$0.554154\pi$
$102$	−4.00000	−0.396059
$103$	2.29844	0.226472	0.113236	−	0.993568i	$-0.463878\pi$
$103$	2.29844	0.226472	0.113236	+	0.993568i	$0.463878\pi$
$104$	−5.70156	−0.559084
$105$	3.70156	0.361235
$106$	9.40312	0.913312
$107$	18.8062	1.81807	0.909034	−	0.416721i	$-0.136821\pi$
$107$	18.8062	1.81807	0.909034	+	0.416721i	$0.136821\pi$
$108$	1.00000	0.0962250
$109$	−7.70156	−0.737676	−0.368838	−	0.929494i	$-0.620244\pi$
$109$	−7.70156	−0.737676	−0.368838	+	0.929494i	$0.620244\pi$
$110$	14.8062	1.41172
$111$	4.29844	0.407990
$112$	1.00000	0.0944911
$113$	7.10469	0.668353	0.334176	−	0.942511i	$-0.391542\pi$
$113$	7.10469	0.668353	0.334176	+	0.942511i	$0.391542\pi$
$114$	5.40312	0.506049
$115$	3.70156	0.345172
$116$	0.298438	0.0277093
$117$	5.70156	0.527110
$118$	7.40312	0.681513
$119$	4.00000	0.366679
$120$	−3.70156	−0.337905
$121$	5.00000	0.454545
$122$	2.00000	0.181071
$123$	−0.298438	−0.0269092
$124$	−2.00000	−0.179605
$125$	13.7016	1.22550
$126$	−1.00000	−0.0890871
$127$	−5.70156	−0.505932	−0.252966	−	0.967475i	$-0.581406\pi$
$127$	−5.70156	−0.505932	−0.252966	+	0.967475i	$0.581406\pi$
$128$	−1.00000	−0.0883883
$129$	−1.70156	−0.149814
$130$	−21.1047	−1.85100
$131$	−7.40312	−0.646814	−0.323407	−	0.946260i	$-0.604828\pi$
$131$	−7.40312	−0.646814	−0.323407	+	0.946260i	$0.604828\pi$
$132$	−4.00000	−0.348155
$133$	−5.40312	−0.468510
$134$	−14.8062	−1.27907
$135$	3.70156	0.318580
$136$	−4.00000	−0.342997
$137$	−19.7016	−1.68322	−0.841609	−	0.540087i	$-0.818391\pi$
$137$	−19.7016	−1.68322	−0.841609	+	0.540087i	$0.818391\pi$
$138$	−1.00000	−0.0851257
$139$	17.7016	1.50143	0.750713	−	0.660628i	$-0.229710\pi$
$139$	17.7016	1.50143	0.750713	+	0.660628i	$0.229710\pi$
$140$	3.70156	0.312839
$141$	−11.1047	−0.935183
$142$	7.40312	0.621256
$143$	−22.8062	−1.90715
$144$	1.00000	0.0833333
$145$	1.10469	0.0917392
$146$	−1.40312	−0.116123
$147$	1.00000	0.0824786
$148$	4.29844	0.353329
$149$	−20.2094	−1.65562	−0.827808	−	0.561011i	$-0.810412\pi$
$149$	−20.2094	−1.65562	−0.827808	+	0.561011i	$0.810412\pi$
$150$	−8.70156	−0.710480
$151$	23.9109	1.94584	0.972922	−	0.231133i	$-0.0742433\pi$
$151$	23.9109	1.94584	0.972922	+	0.231133i	$0.0742433\pi$
$152$	5.40312	0.438251
$153$	4.00000	0.323381
$154$	4.00000	0.322329
$155$	−7.40312	−0.594633
$156$	5.70156	0.456490
$157$	−1.40312	−0.111982	−0.0559908	−	0.998431i	$-0.517832\pi$
$157$	−1.40312	−0.111982	−0.0559908	+	0.998431i	$0.517832\pi$
$158$	−8.00000	−0.636446
$159$	−9.40312	−0.745716
$160$	−3.70156	−0.292634
$161$	1.00000	0.0788110
$162$	−1.00000	−0.0785674
$163$	−10.8062	−0.846411	−0.423205	−	0.906034i	$-0.639095\pi$
$163$	−10.8062	−0.846411	−0.423205	+	0.906034i	$0.639095\pi$
$164$	−0.298438	−0.0233041
$165$	−14.8062	−1.15266
$166$	−13.4031	−1.04028
$167$	−13.4031	−1.03716	−0.518582	−	0.855028i	$-0.673540\pi$
$167$	−13.4031	−1.03716	−0.518582	+	0.855028i	$0.673540\pi$
$168$	−1.00000	−0.0771517
$169$	19.5078	1.50060
$170$	−14.8062	−1.13559
$171$	−5.40312	−0.413187
$172$	−1.70156	−0.129743
$173$	19.4031	1.47519	0.737596	−	0.675242i	$-0.235961\pi$
$173$	19.4031	1.47519	0.737596	+	0.675242i	$0.235961\pi$
$174$	−0.298438	−0.0226245
$175$	8.70156	0.657776
$176$	−4.00000	−0.301511
$177$	−7.40312	−0.556453
$178$	11.4031	0.854700
$179$	−25.1047	−1.87641	−0.938206	−	0.346077i	$-0.887514\pi$
$179$	−25.1047	−1.87641	−0.938206	+	0.346077i	$0.887514\pi$
$180$	3.70156	0.275898
$181$	−16.8062	−1.24920	−0.624599	−	0.780945i	$-0.714738\pi$
$181$	−16.8062	−1.24920	−0.624599	+	0.780945i	$0.714738\pi$
$182$	−5.70156	−0.422628
$183$	−2.00000	−0.147844
$184$	−1.00000	−0.0737210
$185$	15.9109	1.16980
$186$	2.00000	0.146647
$187$	−16.0000	−1.17004
$188$	−11.1047	−0.809892
$189$	1.00000	0.0727393
$190$	20.0000	1.45095
$191$	22.8062	1.65020	0.825101	−	0.564985i	$-0.191118\pi$
$191$	22.8062	1.65020	0.825101	+	0.564985i	$0.191118\pi$
$192$	1.00000	0.0721688
$193$	−23.1047	−1.66311	−0.831556	−	0.555441i	$-0.812549\pi$
$193$	−23.1047	−1.66311	−0.831556	+	0.555441i	$0.812549\pi$
$194$	−6.29844	−0.452201
$195$	21.1047	1.51134
$196$	1.00000	0.0714286
$197$	22.5078	1.60362	0.801808	−	0.597582i	$-0.203872\pi$
$197$	22.5078	1.60362	0.801808	+	0.597582i	$0.203872\pi$
$198$	4.00000	0.284268
$199$	−2.29844	−0.162932	−0.0814660	−	0.996676i	$-0.525960\pi$
$199$	−2.29844	−0.162932	−0.0814660	+	0.996676i	$0.525960\pi$
$200$	−8.70156	−0.615293
$201$	14.8062	1.04435
$202$	3.40312	0.239443
$203$	0.298438	0.0209462
$204$	4.00000	0.280056
$205$	−1.10469	−0.0771546
$206$	−2.29844	−0.160140
$207$	1.00000	0.0695048
$208$	5.70156	0.395332
$209$	21.6125	1.49497
$210$	−3.70156	−0.255432
$211$	10.8062	0.743933	0.371966	−	0.928246i	$-0.378684\pi$
$211$	10.8062	0.743933	0.371966	+	0.928246i	$0.378684\pi$
$212$	−9.40312	−0.645809
$213$	−7.40312	−0.507254
$214$	−18.8062	−1.28557
$215$	−6.29844	−0.429550
$216$	−1.00000	−0.0680414
$217$	−2.00000	−0.135769
$218$	7.70156	0.521616
$219$	1.40312	0.0948143
$220$	−14.8062	−0.998237
$221$	22.8062	1.53411
$222$	−4.29844	−0.288492
$223$	−22.0000	−1.47323	−0.736614	−	0.676313i	$-0.763577\pi$
$223$	−22.0000	−1.47323	−0.736614	+	0.676313i	$0.763577\pi$
$224$	−1.00000	−0.0668153
$225$	8.70156	0.580104
$226$	−7.10469	−0.472597
$227$	−23.1047	−1.53351	−0.766756	−	0.641939i	$-0.778130\pi$
$227$	−23.1047	−1.53351	−0.766756	+	0.641939i	$0.778130\pi$
$228$	−5.40312	−0.357831
$229$	−14.5969	−0.964589	−0.482294	−	0.876009i	$-0.660196\pi$
$229$	−14.5969	−0.964589	−0.482294	+	0.876009i	$0.660196\pi$
$230$	−3.70156	−0.244074
$231$	−4.00000	−0.263181
$232$	−0.298438	−0.0195934
$233$	−26.0000	−1.70332	−0.851658	−	0.524097i	$-0.824403\pi$
$233$	−26.0000	−1.70332	−0.851658	+	0.524097i	$0.824403\pi$
$234$	−5.70156	−0.372723
$235$	−41.1047	−2.68137
$236$	−7.40312	−0.481902
$237$	8.00000	0.519656
$238$	−4.00000	−0.259281
$239$	10.8062	0.698998	0.349499	−	0.936937i	$-0.386352\pi$
$239$	10.8062	0.698998	0.349499	+	0.936937i	$0.386352\pi$
$240$	3.70156	0.238935
$241$	−15.9109	−1.02491	−0.512457	−	0.858713i	$-0.671264\pi$
$241$	−15.9109	−1.02491	−0.512457	+	0.858713i	$0.671264\pi$
$242$	−5.00000	−0.321412
$243$	1.00000	0.0641500
$244$	−2.00000	−0.128037
$245$	3.70156	0.236484
$246$	0.298438	0.0190277
$247$	−30.8062	−1.96015
$248$	2.00000	0.127000
$249$	13.4031	0.849388
$250$	−13.7016	−0.866563
$251$	19.7016	1.24355	0.621776	−	0.783195i	$-0.286412\pi$
$251$	19.7016	1.24355	0.621776	+	0.783195i	$0.286412\pi$
$252$	1.00000	0.0629941
$253$	−4.00000	−0.251478
$254$	5.70156	0.357748
$255$	14.8062	0.927203
$256$	1.00000	0.0625000
$257$	2.00000	0.124757	0.0623783	−	0.998053i	$-0.480131\pi$
$257$	2.00000	0.124757	0.0623783	+	0.998053i	$0.480131\pi$
$258$	1.70156	0.105935
$259$	4.29844	0.267092
$260$	21.1047	1.30886
$261$	0.298438	0.0184728
$262$	7.40312	0.457367
$263$	9.70156	0.598224	0.299112	−	0.954218i	$-0.403310\pi$
$263$	9.70156	0.598224	0.299112	+	0.954218i	$0.403310\pi$
$264$	4.00000	0.246183
$265$	−34.8062	−2.13813
$266$	5.40312	0.331287
$267$	−11.4031	−0.697860
$268$	14.8062	0.904436
$269$	−10.2094	−0.622476	−0.311238	−	0.950332i	$-0.600744\pi$
$269$	−10.2094	−0.622476	−0.311238	+	0.950332i	$0.600744\pi$
$270$	−3.70156	−0.225270
$271$	1.40312	0.0852337	0.0426169	−	0.999091i	$-0.486431\pi$
$271$	1.40312	0.0852337	0.0426169	+	0.999091i	$0.486431\pi$
$272$	4.00000	0.242536
$273$	5.70156	0.345074
$274$	19.7016	1.19021
$275$	−34.8062	−2.09890
$276$	1.00000	0.0601929
$277$	−21.4031	−1.28599	−0.642995	−	0.765871i	$-0.722308\pi$
$277$	−21.4031	−1.28599	−0.642995	+	0.765871i	$0.722308\pi$
$278$	−17.7016	−1.06167
$279$	−2.00000	−0.119737
$280$	−3.70156	−0.221211
$281$	14.5078	0.865463	0.432732	−	0.901523i	$-0.357550\pi$
$281$	14.5078	0.865463	0.432732	+	0.901523i	$0.357550\pi$
$282$	11.1047	0.661274
$283$	4.80625	0.285702	0.142851	−	0.989744i	$-0.454373\pi$
$283$	4.80625	0.285702	0.142851	+	0.989744i	$0.454373\pi$
$284$	−7.40312	−0.439295
$285$	−20.0000	−1.18470
$286$	22.8062	1.34856
$287$	−0.298438	−0.0176162
$288$	−1.00000	−0.0589256
$289$	−1.00000	−0.0588235
$290$	−1.10469	−0.0648694
$291$	6.29844	0.369221
$292$	1.40312	0.0821116
$293$	−20.8062	−1.21551	−0.607757	−	0.794123i	$-0.707931\pi$
$293$	−20.8062	−1.21551	−0.607757	+	0.794123i	$0.707931\pi$
$294$	−1.00000	−0.0583212
$295$	−27.4031	−1.59547
$296$	−4.29844	−0.249842
$297$	−4.00000	−0.232104
$298$	20.2094	1.17070
$299$	5.70156	0.329730
$300$	8.70156	0.502385
$301$	−1.70156	−0.0980764
$302$	−23.9109	−1.37592
$303$	−3.40312	−0.195504
$304$	−5.40312	−0.309890
$305$	−7.40312	−0.423902
$306$	−4.00000	−0.228665
$307$	11.9109	0.679793	0.339896	−	0.940463i	$-0.389608\pi$
$307$	11.9109	0.679793	0.339896	+	0.940463i	$0.389608\pi$
$308$	−4.00000	−0.227921
$309$	2.29844	0.130754
$310$	7.40312	0.420469
$311$	13.4031	0.760021	0.380011	−	0.924982i	$-0.375920\pi$
$311$	13.4031	0.760021	0.380011	+	0.924982i	$0.375920\pi$
$312$	−5.70156	−0.322787
$313$	−6.20937	−0.350974	−0.175487	−	0.984482i	$-0.556150\pi$
$313$	−6.20937	−0.350974	−0.175487	+	0.984482i	$0.556150\pi$
$314$	1.40312	0.0791829
$315$	3.70156	0.208559
$316$	8.00000	0.450035
$317$	−8.29844	−0.466087	−0.233043	−	0.972466i	$-0.574868\pi$
$317$	−8.29844	−0.466087	−0.233043	+	0.972466i	$0.574868\pi$
$318$	9.40312	0.527301
$319$	−1.19375	−0.0668373
$320$	3.70156	0.206924
$321$	18.8062	1.04966
$322$	−1.00000	−0.0557278
$323$	−21.6125	−1.20255
$324$	1.00000	0.0555556
$325$	49.6125	2.75201
$326$	10.8062	0.598503
$327$	−7.70156	−0.425897
$328$	0.298438	0.0164785
$329$	−11.1047	−0.612221
$330$	14.8062	0.815057
$331$	−20.0000	−1.09930	−0.549650	−	0.835395i	$-0.685239\pi$
$331$	−20.0000	−1.09930	−0.549650	+	0.835395i	$0.685239\pi$
$332$	13.4031	0.735592
$333$	4.29844	0.235553
$334$	13.4031	0.733386
$335$	54.8062	2.99439
$336$	1.00000	0.0545545
$337$	−4.20937	−0.229299	−0.114650	−	0.993406i	$-0.536575\pi$
$337$	−4.20937	−0.229299	−0.114650	+	0.993406i	$0.536575\pi$
$338$	−19.5078	−1.06109
$339$	7.10469	0.385874
$340$	14.8062	0.802982
$341$	8.00000	0.433224
$342$	5.40312	0.292167
$343$	1.00000	0.0539949
$344$	1.70156	0.0917421
$345$	3.70156	0.199285
$346$	−19.4031	−1.04312
$347$	−10.2984	−0.552849	−0.276425	−	0.961036i	$-0.589150\pi$
$347$	−10.2984	−0.552849	−0.276425	+	0.961036i	$0.589150\pi$
$348$	0.298438	0.0159979
$349$	12.5969	0.674295	0.337148	−	0.941452i	$-0.390538\pi$
$349$	12.5969	0.674295	0.337148	+	0.941452i	$0.390538\pi$
$350$	−8.70156	−0.465118
$351$	5.70156	0.304327
$352$	4.00000	0.213201
$353$	4.29844	0.228783	0.114391	−	0.993436i	$-0.463508\pi$
$353$	4.29844	0.228783	0.114391	+	0.993436i	$0.463508\pi$
$354$	7.40312	0.393472
$355$	−27.4031	−1.45441
$356$	−11.4031	−0.604364
$357$	4.00000	0.211702
$358$	25.1047	1.32682
$359$	−2.89531	−0.152809	−0.0764044	−	0.997077i	$-0.524344\pi$
$359$	−2.89531	−0.152809	−0.0764044	+	0.997077i	$0.524344\pi$
$360$	−3.70156	−0.195089
$361$	10.1938	0.536513
$362$	16.8062	0.883317
$363$	5.00000	0.262432
$364$	5.70156	0.298843
$365$	5.19375	0.271853
$366$	2.00000	0.104542
$367$	−17.1047	−0.892857	−0.446429	−	0.894819i	$-0.647304\pi$
$367$	−17.1047	−0.892857	−0.446429	+	0.894819i	$0.647304\pi$
$368$	1.00000	0.0521286
$369$	−0.298438	−0.0155361
$370$	−15.9109	−0.827170
$371$	−9.40312	−0.488186
$372$	−2.00000	−0.103695
$373$	−0.806248	−0.0417460	−0.0208730	−	0.999782i	$-0.506645\pi$
$373$	−0.806248	−0.0417460	−0.0208730	+	0.999782i	$0.506645\pi$
$374$	16.0000	0.827340
$375$	13.7016	0.707546
$376$	11.1047	0.572680
$377$	1.70156	0.0876349
$378$	−1.00000	−0.0514344
$379$	13.7016	0.703802	0.351901	−	0.936037i	$-0.385535\pi$
$379$	13.7016	0.703802	0.351901	+	0.936037i	$0.385535\pi$
$380$	−20.0000	−1.02598
$381$	−5.70156	−0.292100
$382$	−22.8062	−1.16687
$383$	29.6125	1.51313	0.756564	−	0.653920i	$-0.226877\pi$
$383$	29.6125	1.51313	0.756564	+	0.653920i	$0.226877\pi$
$384$	−1.00000	−0.0510310
$385$	−14.8062	−0.754596
$386$	23.1047	1.17600
$387$	−1.70156	−0.0864953
$388$	6.29844	0.319755
$389$	−6.00000	−0.304212	−0.152106	−	0.988364i	$-0.548606\pi$
$389$	−6.00000	−0.304212	−0.152106	+	0.988364i	$0.548606\pi$
$390$	−21.1047	−1.06868
$391$	4.00000	0.202289
$392$	−1.00000	−0.0505076
$393$	−7.40312	−0.373438
$394$	−22.5078	−1.13393
$395$	29.6125	1.48997
$396$	−4.00000	−0.201008
$397$	8.59688	0.431465	0.215732	−	0.976453i	$-0.430786\pi$
$397$	8.59688	0.431465	0.215732	+	0.976453i	$0.430786\pi$
$398$	2.29844	0.115210
$399$	−5.40312	−0.270495
$400$	8.70156	0.435078
$401$	30.0000	1.49813	0.749064	−	0.662497i	$-0.230503\pi$
$401$	30.0000	1.49813	0.749064	+	0.662497i	$0.230503\pi$
$402$	−14.8062	−0.738469
$403$	−11.4031	−0.568030
$404$	−3.40312	−0.169312
$405$	3.70156	0.183932
$406$	−0.298438	−0.0148112
$407$	−17.1938	−0.852263
$408$	−4.00000	−0.198030
$409$	5.40312	0.267167	0.133584	−	0.991038i	$-0.457352\pi$
$409$	5.40312	0.267167	0.133584	+	0.991038i	$0.457352\pi$
$410$	1.10469	0.0545566
$411$	−19.7016	−0.971806
$412$	2.29844	0.113236
$413$	−7.40312	−0.364284
$414$	−1.00000	−0.0491473
$415$	49.6125	2.43538
$416$	−5.70156	−0.279542
$417$	17.7016	0.866849
$418$	−21.6125	−1.05710
$419$	−0.209373	−0.0102285	−0.00511426	−	0.999987i	$-0.501628\pi$
$419$	−0.209373	−0.0102285	−0.00511426	+	0.999987i	$0.501628\pi$
$420$	3.70156	0.180618
$421$	−15.7016	−0.765247	−0.382624	−	0.923904i	$-0.624979\pi$
$421$	−15.7016	−0.765247	−0.382624	+	0.923904i	$0.624979\pi$
$422$	−10.8062	−0.526040
$423$	−11.1047	−0.539928
$424$	9.40312	0.456656
$425$	34.8062	1.68835
$426$	7.40312	0.358683
$427$	−2.00000	−0.0967868
$428$	18.8062	0.909034
$429$	−22.8062	−1.10110
$430$	6.29844	0.303738
$431$	−3.91093	−0.188383	−0.0941916	−	0.995554i	$-0.530027\pi$
$431$	−3.91093	−0.188383	−0.0941916	+	0.995554i	$0.530027\pi$
$432$	1.00000	0.0481125
$433$	31.3141	1.50486	0.752429	−	0.658674i	$-0.228882\pi$
$433$	31.3141	1.50486	0.752429	+	0.658674i	$0.228882\pi$
$434$	2.00000	0.0960031
$435$	1.10469	0.0529657
$436$	−7.70156	−0.368838
$437$	−5.40312	−0.258466
$438$	−1.40312	−0.0670439
$439$	−22.0000	−1.05000	−0.525001	−	0.851101i	$-0.675935\pi$
$439$	−22.0000	−1.05000	−0.525001	+	0.851101i	$0.675935\pi$
$440$	14.8062	0.705860
$441$	1.00000	0.0476190
$442$	−22.8062	−1.08478
$443$	−13.7016	−0.650981	−0.325490	−	0.945545i	$-0.605529\pi$
$443$	−13.7016	−0.650981	−0.325490	+	0.945545i	$0.605529\pi$
$444$	4.29844	0.203995
$445$	−42.2094	−2.00092
$446$	22.0000	1.04173
$447$	−20.2094	−0.955871
$448$	1.00000	0.0472456
$449$	−38.4187	−1.81309	−0.906546	−	0.422106i	$-0.861291\pi$
$449$	−38.4187	−1.81309	−0.906546	+	0.422106i	$0.861291\pi$
$450$	−8.70156	−0.410196
$451$	1.19375	0.0562116
$452$	7.10469	0.334176
$453$	23.9109	1.12343
$454$	23.1047	1.08436
$455$	21.1047	0.989403
$456$	5.40312	0.253024
$457$	28.2094	1.31958	0.659789	−	0.751451i	$-0.270645\pi$
$457$	28.2094	1.31958	0.659789	+	0.751451i	$0.270645\pi$
$458$	14.5969	0.682067
$459$	4.00000	0.186704
$460$	3.70156	0.172586
$461$	−2.20937	−0.102901	−0.0514504	−	0.998676i	$-0.516384\pi$
$461$	−2.20937	−0.102901	−0.0514504	+	0.998676i	$0.516384\pi$
$462$	4.00000	0.186097
$463$	−22.2984	−1.03630	−0.518148	−	0.855291i	$-0.673378\pi$
$463$	−22.2984	−1.03630	−0.518148	+	0.855291i	$0.673378\pi$
$464$	0.298438	0.0138546
$465$	−7.40312	−0.343312
$466$	26.0000	1.20443
$467$	−3.70156	−0.171288	−0.0856439	−	0.996326i	$-0.527295\pi$
$467$	−3.70156	−0.171288	−0.0856439	+	0.996326i	$0.527295\pi$
$468$	5.70156	0.263555
$469$	14.8062	0.683689
$470$	41.1047	1.89602
$471$	−1.40312	−0.0646526
$472$	7.40312	0.340756
$473$	6.80625	0.312952
$474$	−8.00000	−0.367452
$475$	−47.0156	−2.15722
$476$	4.00000	0.183340
$477$	−9.40312	−0.430539
$478$	−10.8062	−0.494266
$479$	16.5969	0.758331	0.379165	−	0.925329i	$-0.376211\pi$
$479$	16.5969	0.758331	0.379165	+	0.925329i	$0.376211\pi$
$480$	−3.70156	−0.168952
$481$	24.5078	1.11746
$482$	15.9109	0.724723
$483$	1.00000	0.0455016
$484$	5.00000	0.227273
$485$	23.3141	1.05864
$486$	−1.00000	−0.0453609
$487$	−6.29844	−0.285409	−0.142705	−	0.989765i	$-0.545580\pi$
$487$	−6.29844	−0.285409	−0.142705	+	0.989765i	$0.545580\pi$
$488$	2.00000	0.0905357
$489$	−10.8062	−0.488675
$490$	−3.70156	−0.167220
$491$	−9.61250	−0.433806	−0.216903	−	0.976193i	$-0.569596\pi$
$491$	−9.61250	−0.433806	−0.216903	+	0.976193i	$0.569596\pi$
$492$	−0.298438	−0.0134546
$493$	1.19375	0.0537639
$494$	30.8062	1.38604
$495$	−14.8062	−0.665491
$496$	−2.00000	−0.0898027
$497$	−7.40312	−0.332076
$498$	−13.4031	−0.600608
$499$	−23.4031	−1.04767	−0.523834	−	0.851820i	$-0.675499\pi$
$499$	−23.4031	−1.04767	−0.523834	+	0.851820i	$0.675499\pi$
$500$	13.7016	0.612752
$501$	−13.4031	−0.598807
$502$	−19.7016	−0.879324
$503$	4.59688	0.204965	0.102482	−	0.994735i	$-0.467322\pi$
$503$	4.59688	0.204965	0.102482	+	0.994735i	$0.467322\pi$
$504$	−1.00000	−0.0445435
$505$	−12.5969	−0.560554
$506$	4.00000	0.177822
$507$	19.5078	0.866372
$508$	−5.70156	−0.252966
$509$	37.6125	1.66714	0.833572	−	0.552410i	$-0.186292\pi$
$509$	37.6125	1.66714	0.833572	+	0.552410i	$0.186292\pi$
$510$	−14.8062	−0.655632
$511$	1.40312	0.0620706
$512$	−1.00000	−0.0441942
$513$	−5.40312	−0.238554
$514$	−2.00000	−0.0882162
$515$	8.50781	0.374899
$516$	−1.70156	−0.0749071
$517$	44.4187	1.95353
$518$	−4.29844	−0.188863
$519$	19.4031	0.851703
$520$	−21.1047	−0.925502
$521$	−20.5969	−0.902366	−0.451183	−	0.892432i	$-0.648998\pi$
$521$	−20.5969	−0.902366	−0.451183	+	0.892432i	$0.648998\pi$
$522$	−0.298438	−0.0130623
$523$	20.8062	0.909794	0.454897	−	0.890544i	$-0.349676\pi$
$523$	20.8062	0.909794	0.454897	+	0.890544i	$0.349676\pi$
$524$	−7.40312	−0.323407
$525$	8.70156	0.379767
$526$	−9.70156	−0.423008
$527$	−8.00000	−0.348485
$528$	−4.00000	−0.174078
$529$	1.00000	0.0434783
$530$	34.8062	1.51189
$531$	−7.40312	−0.321268
$532$	−5.40312	−0.234255
$533$	−1.70156	−0.0737028
$534$	11.4031	0.493461
$535$	69.6125	3.00961
$536$	−14.8062	−0.639533
$537$	−25.1047	−1.08335
$538$	10.2094	0.440157
$539$	−4.00000	−0.172292
$540$	3.70156	0.159290
$541$	33.4031	1.43611	0.718056	−	0.695985i	$-0.245032\pi$
$541$	33.4031	1.43611	0.718056	+	0.695985i	$0.245032\pi$
$542$	−1.40312	−0.0602693
$543$	−16.8062	−0.721225
$544$	−4.00000	−0.171499
$545$	−28.5078	−1.22114
$546$	−5.70156	−0.244004
$547$	29.0156	1.24062	0.620309	−	0.784357i	$-0.287007\pi$
$547$	29.0156	1.24062	0.620309	+	0.784357i	$0.287007\pi$
$548$	−19.7016	−0.841609
$549$	−2.00000	−0.0853579
$550$	34.8062	1.48414
$551$	−1.61250	−0.0686947
$552$	−1.00000	−0.0425628
$553$	8.00000	0.340195
$554$	21.4031	0.909332
$555$	15.9109	0.675382
$556$	17.7016	0.750713
$557$	−37.4031	−1.58482	−0.792411	−	0.609988i	$-0.791174\pi$
$557$	−37.4031	−1.58482	−0.792411	+	0.609988i	$0.791174\pi$
$558$	2.00000	0.0846668
$559$	−9.70156	−0.410332
$560$	3.70156	0.156420
$561$	−16.0000	−0.675521
$562$	−14.5078	−0.611975
$563$	−3.10469	−0.130847	−0.0654235	−	0.997858i	$-0.520840\pi$
$563$	−3.10469	−0.130847	−0.0654235	+	0.997858i	$0.520840\pi$
$564$	−11.1047	−0.467592
$565$	26.2984	1.10638
$566$	−4.80625	−0.202022
$567$	1.00000	0.0419961
$568$	7.40312	0.310628
$569$	31.7016	1.32900	0.664499	−	0.747289i	$-0.268645\pi$
$569$	31.7016	1.32900	0.664499	+	0.747289i	$0.268645\pi$
$570$	20.0000	0.837708
$571$	−14.8062	−0.619622	−0.309811	−	0.950798i	$-0.600266\pi$
$571$	−14.8062	−0.619622	−0.309811	+	0.950798i	$0.600266\pi$
$572$	−22.8062	−0.953577
$573$	22.8062	0.952745
$574$	0.298438	0.0124566
$575$	8.70156	0.362880
$576$	1.00000	0.0416667
$577$	−10.0000	−0.416305	−0.208153	−	0.978096i	$-0.566745\pi$
$577$	−10.0000	−0.416305	−0.208153	+	0.978096i	$0.566745\pi$
$578$	1.00000	0.0415945
$579$	−23.1047	−0.960198
$580$	1.10469	0.0458696
$581$	13.4031	0.556055
$582$	−6.29844	−0.261079
$583$	37.6125	1.55775
$584$	−1.40312	−0.0580617
$585$	21.1047	0.872571
$586$	20.8062	0.859498
$587$	14.8062	0.611119	0.305560	−	0.952173i	$-0.401156\pi$
$587$	14.8062	0.611119	0.305560	+	0.952173i	$0.401156\pi$
$588$	1.00000	0.0412393
$589$	10.8062	0.445264
$590$	27.4031	1.12817
$591$	22.5078	0.925848
$592$	4.29844	0.176665
$593$	43.7016	1.79461	0.897304	−	0.441413i	$-0.145523\pi$
$593$	43.7016	1.79461	0.897304	+	0.441413i	$0.145523\pi$
$594$	4.00000	0.164122
$595$	14.8062	0.606997
$596$	−20.2094	−0.827808
$597$	−2.29844	−0.0940688
$598$	−5.70156	−0.233154
$599$	13.6125	0.556192	0.278096	−	0.960553i	$-0.410297\pi$
$599$	13.6125	0.556192	0.278096	+	0.960553i	$0.410297\pi$
$600$	−8.70156	−0.355240
$601$	−13.4031	−0.546725	−0.273362	−	0.961911i	$-0.588136\pi$
$601$	−13.4031	−0.546725	−0.273362	+	0.961911i	$0.588136\pi$
$602$	1.70156	0.0693505
$603$	14.8062	0.602957
$604$	23.9109	0.972922
$605$	18.5078	0.752450
$606$	3.40312	0.138242
$607$	−39.6125	−1.60782	−0.803911	−	0.594750i	$-0.797251\pi$
$607$	−39.6125	−1.60782	−0.803911	+	0.594750i	$0.797251\pi$
$608$	5.40312	0.219126
$609$	0.298438	0.0120933
$610$	7.40312	0.299744
$611$	−63.3141	−2.56141
$612$	4.00000	0.161690
$613$	3.70156	0.149505	0.0747523	−	0.997202i	$-0.476183\pi$
$613$	3.70156	0.149505	0.0747523	+	0.997202i	$0.476183\pi$
$614$	−11.9109	−0.480686
$615$	−1.10469	−0.0445453
$616$	4.00000	0.161165
$617$	−19.1938	−0.772711	−0.386356	−	0.922350i	$-0.626266\pi$
$617$	−19.1938	−0.772711	−0.386356	+	0.922350i	$0.626266\pi$
$618$	−2.29844	−0.0924567
$619$	−7.19375	−0.289141	−0.144571	−	0.989494i	$-0.546180\pi$
$619$	−7.19375	−0.289141	−0.144571	+	0.989494i	$0.546180\pi$
$620$	−7.40312	−0.297317
$621$	1.00000	0.0401286
$622$	−13.4031	−0.537416
$623$	−11.4031	−0.456857
$624$	5.70156	0.228245
$625$	7.20937	0.288375
$626$	6.20937	0.248176
$627$	21.6125	0.863120
$628$	−1.40312	−0.0559908
$629$	17.1938	0.685560
$630$	−3.70156	−0.147474
$631$	−29.6125	−1.17885	−0.589427	−	0.807821i	$-0.700647\pi$
$631$	−29.6125	−1.17885	−0.589427	+	0.807821i	$0.700647\pi$
$632$	−8.00000	−0.318223
$633$	10.8062	0.429510
$634$	8.29844	0.329573
$635$	−21.1047	−0.837514
$636$	−9.40312	−0.372858
$637$	5.70156	0.225904
$638$	1.19375	0.0472611
$639$	−7.40312	−0.292863
$640$	−3.70156	−0.146317
$641$	−20.7172	−0.818280	−0.409140	−	0.912472i	$-0.634171\pi$
$641$	−20.7172	−0.818280	−0.409140	+	0.912472i	$0.634171\pi$
$642$	−18.8062	−0.742223
$643$	0.806248	0.0317953	0.0158977	−	0.999874i	$-0.494939\pi$
$643$	0.806248	0.0317953	0.0158977	+	0.999874i	$0.494939\pi$
$644$	1.00000	0.0394055
$645$	−6.29844	−0.248001
$646$	21.6125	0.850332
$647$	−6.59688	−0.259350	−0.129675	−	0.991557i	$-0.541393\pi$
$647$	−6.59688	−0.259350	−0.129675	+	0.991557i	$0.541393\pi$
$648$	−1.00000	−0.0392837
$649$	29.6125	1.16239
$650$	−49.6125	−1.94596
$651$	−2.00000	−0.0783862
$652$	−10.8062	−0.423205
$653$	7.10469	0.278028	0.139014	−	0.990290i	$-0.455607\pi$
$653$	7.10469	0.278028	0.139014	+	0.990290i	$0.455607\pi$
$654$	7.70156	0.301155
$655$	−27.4031	−1.07073
$656$	−0.298438	−0.0116520
$657$	1.40312	0.0547411
$658$	11.1047	0.432906
$659$	8.00000	0.311636	0.155818	−	0.987786i	$-0.450199\pi$
$659$	8.00000	0.311636	0.155818	+	0.987786i	$0.450199\pi$
$660$	−14.8062	−0.576332
$661$	42.4187	1.64990	0.824949	−	0.565207i	$-0.191204\pi$
$661$	42.4187	1.64990	0.824949	+	0.565207i	$0.191204\pi$
$662$	20.0000	0.777322
$663$	22.8062	0.885721
$664$	−13.4031	−0.520142
$665$	−20.0000	−0.775567
$666$	−4.29844	−0.166561
$667$	0.298438	0.0115556
$668$	−13.4031	−0.518582
$669$	−22.0000	−0.850569
$670$	−54.8062	−2.11735
$671$	8.00000	0.308837
$672$	−1.00000	−0.0385758
$673$	7.70156	0.296873	0.148437	−	0.988922i	$-0.452576\pi$
$673$	7.70156	0.296873	0.148437	+	0.988922i	$0.452576\pi$
$674$	4.20937	0.162139
$675$	8.70156	0.334923
$676$	19.5078	0.750300
$677$	−50.4187	−1.93775	−0.968875	−	0.247551i	$-0.920374\pi$
$677$	−50.4187	−1.93775	−0.968875	+	0.247551i	$0.920374\pi$
$678$	−7.10469	−0.272854
$679$	6.29844	0.241712
$680$	−14.8062	−0.567794
$681$	−23.1047	−0.885374
$682$	−8.00000	−0.306336
$683$	33.6125	1.28615	0.643073	−	0.765805i	$-0.277659\pi$
$683$	33.6125	1.28615	0.643073	+	0.765805i	$0.277659\pi$
$684$	−5.40312	−0.206594
$685$	−72.9266	−2.78638
$686$	−1.00000	−0.0381802
$687$	−14.5969	−0.556906
$688$	−1.70156	−0.0648714
$689$	−53.6125	−2.04247
$690$	−3.70156	−0.140916
$691$	−0.507811	−0.0193180	−0.00965901	−	0.999953i	$-0.503075\pi$
$691$	−0.507811	−0.0193180	−0.00965901	+	0.999953i	$0.503075\pi$
$692$	19.4031	0.737596
$693$	−4.00000	−0.151947
$694$	10.2984	0.390923
$695$	65.5234	2.48545
$696$	−0.298438	−0.0113123
$697$	−1.19375	−0.0452166
$698$	−12.5969	−0.476799
$699$	−26.0000	−0.983410
$700$	8.70156	0.328888
$701$	47.0156	1.77576	0.887878	−	0.460079i	$-0.152179\pi$
$701$	47.0156	1.77576	0.887878	+	0.460079i	$0.152179\pi$
$702$	−5.70156	−0.215192
$703$	−23.2250	−0.875947
$704$	−4.00000	−0.150756
$705$	−41.1047	−1.54809
$706$	−4.29844	−0.161774
$707$	−3.40312	−0.127988
$708$	−7.40312	−0.278226
$709$	23.1938	0.871060	0.435530	−	0.900174i	$-0.356561\pi$
$709$	23.1938	0.871060	0.435530	+	0.900174i	$0.356561\pi$
$710$	27.4031	1.02842
$711$	8.00000	0.300023
$712$	11.4031	0.427350
$713$	−2.00000	−0.0749006
$714$	−4.00000	−0.149696
$715$	−84.4187	−3.15708
$716$	−25.1047	−0.938206
$717$	10.8062	0.403567
$718$	2.89531	0.108052
$719$	−5.91093	−0.220441	−0.110220	−	0.993907i	$-0.535156\pi$
$719$	−5.91093	−0.220441	−0.110220	+	0.993907i	$0.535156\pi$
$720$	3.70156	0.137949
$721$	2.29844	0.0855983
$722$	−10.1938	−0.379372
$723$	−15.9109	−0.591734
$724$	−16.8062	−0.624599
$725$	2.59688	0.0964455
$726$	−5.00000	−0.185567
$727$	−12.0000	−0.445055	−0.222528	−	0.974926i	$-0.571431\pi$
$727$	−12.0000	−0.445055	−0.222528	+	0.974926i	$0.571431\pi$
$728$	−5.70156	−0.211314
$729$	1.00000	0.0370370
$730$	−5.19375	−0.192229
$731$	−6.80625	−0.251738
$732$	−2.00000	−0.0739221
$733$	52.2094	1.92840	0.964199	−	0.265181i	$-0.0854318\pi$
$733$	52.2094	1.92840	0.964199	+	0.265181i	$0.0854318\pi$
$734$	17.1047	0.631345
$735$	3.70156	0.136534
$736$	−1.00000	−0.0368605
$737$	−59.2250	−2.18158
$738$	0.298438	0.0109857
$739$	−29.0156	−1.06736	−0.533678	−	0.845687i	$-0.679191\pi$
$739$	−29.0156	−1.06736	−0.533678	+	0.845687i	$0.679191\pi$
$740$	15.9109	0.584898
$741$	−30.8062	−1.13170
$742$	9.40312	0.345200
$743$	32.0000	1.17397	0.586983	−	0.809599i	$-0.300316\pi$
$743$	32.0000	1.17397	0.586983	+	0.809599i	$0.300316\pi$
$744$	2.00000	0.0733236
$745$	−74.8062	−2.74069
$746$	0.806248	0.0295189
$747$	13.4031	0.490395
$748$	−16.0000	−0.585018
$749$	18.8062	0.687165
$750$	−13.7016	−0.500310
$751$	29.6125	1.08058	0.540288	−	0.841480i	$-0.318315\pi$
$751$	29.6125	1.08058	0.540288	+	0.841480i	$0.318315\pi$
$752$	−11.1047	−0.404946
$753$	19.7016	0.717965
$754$	−1.70156	−0.0619672
$755$	88.5078	3.22113
$756$	1.00000	0.0363696
$757$	−26.4187	−0.960206	−0.480103	−	0.877212i	$-0.659401\pi$
$757$	−26.4187	−0.960206	−0.480103	+	0.877212i	$0.659401\pi$
$758$	−13.7016	−0.497663
$759$	−4.00000	−0.145191
$760$	20.0000	0.725476
$761$	−35.6125	−1.29095	−0.645476	−	0.763781i	$-0.723341\pi$
$761$	−35.6125	−1.29095	−0.645476	+	0.763781i	$0.723341\pi$
$762$	5.70156	0.206546
$763$	−7.70156	−0.278815
$764$	22.8062	0.825101
$765$	14.8062	0.535321
$766$	−29.6125	−1.06994
$767$	−42.2094	−1.52409
$768$	1.00000	0.0360844
$769$	15.9109	0.573763	0.286881	−	0.957966i	$-0.407381\pi$
$769$	15.9109	0.573763	0.286881	+	0.957966i	$0.407381\pi$
$770$	14.8062	0.533580
$771$	2.00000	0.0720282
$772$	−23.1047	−0.831556
$773$	−7.10469	−0.255538	−0.127769	−	0.991804i	$-0.540782\pi$
$773$	−7.10469	−0.255538	−0.127769	+	0.991804i	$0.540782\pi$
$774$	1.70156	0.0611614
$775$	−17.4031	−0.625139
$776$	−6.29844	−0.226101
$777$	4.29844	0.154206
$778$	6.00000	0.215110
$779$	1.61250	0.0577737
$780$	21.1047	0.755669
$781$	29.6125	1.05962
$782$	−4.00000	−0.143040
$783$	0.298438	0.0106653
$784$	1.00000	0.0357143
$785$	−5.19375	−0.185373
$786$	7.40312	0.264061
$787$	−18.5969	−0.662907	−0.331454	−	0.943472i	$-0.607539\pi$
$787$	−18.5969	−0.662907	−0.331454	+	0.943472i	$0.607539\pi$
$788$	22.5078	0.801808
$789$	9.70156	0.345385
$790$	−29.6125	−1.05357
$791$	7.10469	0.252614
$792$	4.00000	0.142134
$793$	−11.4031	−0.404937
$794$	−8.59688	−0.305092
$795$	−34.8062	−1.23445
$796$	−2.29844	−0.0814660
$797$	15.7016	0.556178	0.278089	−	0.960555i	$-0.410299\pi$
$797$	15.7016	0.556178	0.278089	+	0.960555i	$0.410299\pi$
$798$	5.40312	0.191269
$799$	−44.4187	−1.57142
$800$	−8.70156	−0.307647
$801$	−11.4031	−0.402910
$802$	−30.0000	−1.05934
$803$	−5.61250	−0.198061
$804$	14.8062	0.522176
$805$	3.70156	0.130463
$806$	11.4031	0.401658
$807$	−10.2094	−0.359387
$808$	3.40312	0.119721
$809$	31.0156	1.09045	0.545226	−	0.838289i	$-0.316444\pi$
$809$	31.0156	1.09045	0.545226	+	0.838289i	$0.316444\pi$
$810$	−3.70156	−0.130060
$811$	52.5078	1.84380	0.921899	−	0.387430i	$-0.126637\pi$
$811$	52.5078	1.84380	0.921899	+	0.387430i	$0.126637\pi$
$812$	0.298438	0.0104731
$813$	1.40312	0.0492097
$814$	17.1938	0.602641
$815$	−40.0000	−1.40114
$816$	4.00000	0.140028
$817$	9.19375	0.321649
$818$	−5.40312	−0.188916
$819$	5.70156	0.199229
$820$	−1.10469	−0.0385773
$821$	27.6125	0.963683	0.481841	−	0.876258i	$-0.339968\pi$
$821$	27.6125	0.963683	0.481841	+	0.876258i	$0.339968\pi$
$822$	19.7016	0.687171
$823$	−13.7016	−0.477606	−0.238803	−	0.971068i	$-0.576755\pi$
$823$	−13.7016	−0.477606	−0.238803	+	0.971068i	$0.576755\pi$
$824$	−2.29844	−0.0800699
$825$	−34.8062	−1.21180
$826$	7.40312	0.257588
$827$	−47.4031	−1.64837	−0.824184	−	0.566322i	$-0.808366\pi$
$827$	−47.4031	−1.64837	−0.824184	+	0.566322i	$0.808366\pi$
$828$	1.00000	0.0347524
$829$	55.4031	1.92423	0.962115	−	0.272644i	$-0.0878981\pi$
$829$	55.4031	1.92423	0.962115	+	0.272644i	$0.0878981\pi$
$830$	−49.6125	−1.72207
$831$	−21.4031	−0.742466
$832$	5.70156	0.197666
$833$	4.00000	0.138592
$834$	−17.7016	−0.612955
$835$	−49.6125	−1.71691
$836$	21.6125	0.747484
$837$	−2.00000	−0.0691301
$838$	0.209373	0.00723266
$839$	42.2094	1.45723	0.728615	−	0.684924i	$-0.240165\pi$
$839$	42.2094	1.45723	0.728615	+	0.684924i	$0.240165\pi$
$840$	−3.70156	−0.127716
$841$	−28.9109	−0.996929
$842$	15.7016	0.541112
$843$	14.5078	0.499676
$844$	10.8062	0.371966
$845$	72.2094	2.48408
$846$	11.1047	0.381787
$847$	5.00000	0.171802
$848$	−9.40312	−0.322905
$849$	4.80625	0.164950
$850$	−34.8062	−1.19384
$851$	4.29844	0.147349
$852$	−7.40312	−0.253627
$853$	9.10469	0.311739	0.155869	−	0.987778i	$-0.450182\pi$
$853$	9.10469	0.311739	0.155869	+	0.987778i	$0.450182\pi$
$854$	2.00000	0.0684386
$855$	−20.0000	−0.683986
$856$	−18.8062	−0.642784
$857$	−0.298438	−0.0101944	−0.00509722	−	0.999987i	$-0.501623\pi$
$857$	−0.298438	−0.0101944	−0.00509722	+	0.999987i	$0.501623\pi$
$858$	22.8062	0.778592
$859$	−15.4922	−0.528587	−0.264293	−	0.964442i	$-0.585139\pi$
$859$	−15.4922	−0.528587	−0.264293	+	0.964442i	$0.585139\pi$
$860$	−6.29844	−0.214775
$861$	−0.298438	−0.0101707
$862$	3.91093	0.133207
$863$	−6.38750	−0.217433	−0.108717	−	0.994073i	$-0.534674\pi$
$863$	−6.38750	−0.217433	−0.108717	+	0.994073i	$0.534674\pi$
$864$	−1.00000	−0.0340207
$865$	71.8219	2.44202
$866$	−31.3141	−1.06410
$867$	−1.00000	−0.0339618
$868$	−2.00000	−0.0678844
$869$	−32.0000	−1.08553
$870$	−1.10469	−0.0374524
$871$	84.4187	2.86042
$872$	7.70156	0.260808
$873$	6.29844	0.213170
$874$	5.40312	0.182763
$875$	13.7016	0.463197
$876$	1.40312	0.0474072
$877$	−17.4031	−0.587662	−0.293831	−	0.955857i	$-0.594930\pi$
$877$	−17.4031	−0.587662	−0.293831	+	0.955857i	$0.594930\pi$
$878$	22.0000	0.742464
$879$	−20.8062	−0.701777
$880$	−14.8062	−0.499119
$881$	6.20937	0.209199	0.104600	−	0.994514i	$-0.466644\pi$
$881$	6.20937	0.209199	0.104600	+	0.994514i	$0.466644\pi$
$882$	−1.00000	−0.0336718
$883$	−24.5969	−0.827751	−0.413875	−	0.910334i	$-0.635825\pi$
$883$	−24.5969	−0.827751	−0.413875	+	0.910334i	$0.635825\pi$
$884$	22.8062	0.767057
$885$	−27.4031	−0.921146
$886$	13.7016	0.460313
$887$	−28.2094	−0.947178	−0.473589	−	0.880746i	$-0.657042\pi$
$887$	−28.2094	−0.947178	−0.473589	+	0.880746i	$0.657042\pi$
$888$	−4.29844	−0.144246
$889$	−5.70156	−0.191224
$890$	42.2094	1.41486
$891$	−4.00000	−0.134005
$892$	−22.0000	−0.736614
$893$	60.0000	2.00782
$894$	20.2094	0.675903
$895$	−92.9266	−3.10619
$896$	−1.00000	−0.0334077
$897$	5.70156	0.190370
$898$	38.4187	1.28205
$899$	−0.596876	−0.0199069
$900$	8.70156	0.290052
$901$	−37.6125	−1.25305
$902$	−1.19375	−0.0397476
$903$	−1.70156	−0.0566244
$904$	−7.10469	−0.236298
$905$	−62.2094	−2.06791
$906$	−23.9109	−0.794388
$907$	20.5078	0.680951	0.340475	−	0.940253i	$-0.389412\pi$
$907$	20.5078	0.680951	0.340475	+	0.940253i	$0.389412\pi$
$908$	−23.1047	−0.766756
$909$	−3.40312	−0.112875
$910$	−21.1047	−0.699614
$911$	53.1047	1.75944	0.879718	−	0.475495i	$-0.157731\pi$
$911$	53.1047	1.75944	0.879718	+	0.475495i	$0.157731\pi$
$912$	−5.40312	−0.178915
$913$	−53.6125	−1.77431
$914$	−28.2094	−0.933083
$915$	−7.40312	−0.244740
$916$	−14.5969	−0.482294
$917$	−7.40312	−0.244473
$918$	−4.00000	−0.132020
$919$	−52.4187	−1.72913	−0.864567	−	0.502517i	$-0.832407\pi$
$919$	−52.4187	−1.72913	−0.864567	+	0.502517i	$0.832407\pi$
$920$	−3.70156	−0.122037
$921$	11.9109	0.392479
$922$	2.20937	0.0727618
$923$	−42.2094	−1.38934
$924$	−4.00000	−0.131590
$925$	37.4031	1.22981
$926$	22.2984	0.732772
$927$	2.29844	0.0754906
$928$	−0.298438	−0.00979670
$929$	−45.9109	−1.50629	−0.753144	−	0.657855i	$-0.771464\pi$
$929$	−45.9109	−1.50629	−0.753144	+	0.657855i	$0.771464\pi$
$930$	7.40312	0.242758
$931$	−5.40312	−0.177080
$932$	−26.0000	−0.851658
$933$	13.4031	0.438799
$934$	3.70156	0.121119
$935$	−59.2250	−1.93686
$936$	−5.70156	−0.186361
$937$	25.1047	0.820134	0.410067	−	0.912055i	$-0.365505\pi$
$937$	25.1047	0.820134	0.410067	+	0.912055i	$0.365505\pi$
$938$	−14.8062	−0.483441
$939$	−6.20937	−0.202635
$940$	−41.1047	−1.34069
$941$	25.3141	0.825215	0.412607	−	0.910909i	$-0.364618\pi$
$941$	25.3141	0.825215	0.412607	+	0.910909i	$0.364618\pi$
$942$	1.40312	0.0457163
$943$	−0.298438	−0.00971847
$944$	−7.40312	−0.240951
$945$	3.70156	0.120412
$946$	−6.80625	−0.221290
$947$	15.9109	0.517036	0.258518	−	0.966006i	$-0.416766\pi$
$947$	15.9109	0.517036	0.258518	+	0.966006i	$0.416766\pi$
$948$	8.00000	0.259828
$949$	8.00000	0.259691
$950$	47.0156	1.52539
$951$	−8.29844	−0.269095
$952$	−4.00000	−0.129641
$953$	61.2250	1.98327	0.991636	−	0.129066i	$-0.0411978\pi$
$953$	61.2250	1.98327	0.991636	+	0.129066i	$0.0411978\pi$
$954$	9.40312	0.304437
$955$	84.4187	2.73173
$956$	10.8062	0.349499
$957$	−1.19375	−0.0385885
$958$	−16.5969	−0.536221
$959$	−19.7016	−0.636197
$960$	3.70156	0.119467
$961$	−27.0000	−0.870968
$962$	−24.5078	−0.790164
$963$	18.8062	0.606023
$964$	−15.9109	−0.512457
$965$	−85.5234	−2.75310
$966$	−1.00000	−0.0321745
$967$	−14.8062	−0.476137	−0.238068	−	0.971248i	$-0.576514\pi$
$967$	−14.8062	−0.476137	−0.238068	+	0.971248i	$0.576514\pi$
$968$	−5.00000	−0.160706
$969$	−21.6125	−0.694293
$970$	−23.3141	−0.748569
$971$	49.8219	1.59886	0.799430	−	0.600759i	$-0.205135\pi$
$971$	49.8219	1.59886	0.799430	+	0.600759i	$0.205135\pi$
$972$	1.00000	0.0320750
$973$	17.7016	0.567486
$974$	6.29844	0.201815
$975$	49.6125	1.58887
$976$	−2.00000	−0.0640184
$977$	16.7172	0.534830	0.267415	−	0.963581i	$-0.413831\pi$
$977$	16.7172	0.534830	0.267415	+	0.963581i	$0.413831\pi$
$978$	10.8062	0.345546
$979$	45.6125	1.45778
$980$	3.70156	0.118242
$981$	−7.70156	−0.245892
$982$	9.61250	0.306747
$983$	42.2094	1.34627	0.673135	−	0.739520i	$-0.264947\pi$
$983$	42.2094	1.34627	0.673135	+	0.739520i	$0.264947\pi$
$984$	0.298438	0.00951385
$985$	83.3141	2.65461
$986$	−1.19375	−0.0380168
$987$	−11.1047	−0.353466
$988$	−30.8062	−0.980077
$989$	−1.70156	−0.0541065
$990$	14.8062	0.470573
$991$	28.0000	0.889449	0.444725	−	0.895667i	$-0.353302\pi$
$991$	28.0000	0.889449	0.444725	+	0.895667i	$0.353302\pi$
$992$	2.00000	0.0635001
$993$	−20.0000	−0.634681
$994$	7.40312	0.234813
$995$	−8.50781	−0.269716
$996$	13.4031	0.424694
$997$	−23.4031	−0.741184	−0.370592	−	0.928796i	$-0.620845\pi$
$997$	−23.4031	−0.741184	−0.370592	+	0.928796i	$0.620845\pi$
$998$	23.4031	0.740813
$999$	4.29844	0.135997

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.a.n.1.2	✓	2
3.2	odd	2		2898.2.a.bb.1.1		2
4.3	odd	2		7728.2.a.bc.1.2		2
7.6	odd	2		6762.2.a.bo.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.a.n.1.2	✓	2	1.1	even	1	trivial
2898.2.a.bb.1.1		2	3.2	odd	2
6762.2.a.bo.1.1		2	7.6	odd	2
7728.2.a.bc.1.2		2	4.3	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.70156 q^{5} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.70156 q^{5} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.70156 q^{10} -4.00000 q^{11} +1.00000 q^{12} +5.70156 q^{13} -1.00000 q^{14} +3.70156 q^{15} +1.00000 q^{16} +4.00000 q^{17} -1.00000 q^{18} -5.40312 q^{19} +3.70156 q^{20} +1.00000 q^{21} +4.00000 q^{22} +1.00000 q^{23} -1.00000 q^{24} +8.70156 q^{25} -5.70156 q^{26} +1.00000 q^{27} +1.00000 q^{28} +0.298438 q^{29} -3.70156 q^{30} -2.00000 q^{31} -1.00000 q^{32} -4.00000 q^{33} -4.00000 q^{34} +3.70156 q^{35} +1.00000 q^{36} +4.29844 q^{37} +5.40312 q^{38} +5.70156 q^{39} -3.70156 q^{40} -0.298438 q^{41} -1.00000 q^{42} -1.70156 q^{43} -4.00000 q^{44} +3.70156 q^{45} -1.00000 q^{46} -11.1047 q^{47} +1.00000 q^{48} +1.00000 q^{49} -8.70156 q^{50} +4.00000 q^{51} +5.70156 q^{52} -9.40312 q^{53} -1.00000 q^{54} -14.8062 q^{55} -1.00000 q^{56} -5.40312 q^{57} -0.298438 q^{58} -7.40312 q^{59} +3.70156 q^{60} -2.00000 q^{61} +2.00000 q^{62} +1.00000 q^{63} +1.00000 q^{64} +21.1047 q^{65} +4.00000 q^{66} +14.8062 q^{67} +4.00000 q^{68} +1.00000 q^{69} -3.70156 q^{70} -7.40312 q^{71} -1.00000 q^{72} +1.40312 q^{73} -4.29844 q^{74} +8.70156 q^{75} -5.40312 q^{76} -4.00000 q^{77} -5.70156 q^{78} +8.00000 q^{79} +3.70156 q^{80} +1.00000 q^{81} +0.298438 q^{82} +13.4031 q^{83} +1.00000 q^{84} +14.8062 q^{85} +1.70156 q^{86} +0.298438 q^{87} +4.00000 q^{88} -11.4031 q^{89} -3.70156 q^{90} +5.70156 q^{91} +1.00000 q^{92} -2.00000 q^{93} +11.1047 q^{94} -20.0000 q^{95} -1.00000 q^{96} +6.29844 q^{97} -1.00000 q^{98} -4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} + q^{5} - 2 q^{6} + 2 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 + q^5 - 2 * q^6 + 2 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} + q^{5} - 2 q^{6} + 2 q^{7} - 2 q^{8} + 2 q^{9} - q^{10} - 8 q^{11} + 2 q^{12} + 5 q^{13} - 2 q^{14} + q^{15} + 2 q^{16} + 8 q^{17} - 2 q^{18} + 2 q^{19} + q^{20} + 2 q^{21} + 8 q^{22} + 2 q^{23} - 2 q^{24} + 11 q^{25} - 5 q^{26} + 2 q^{27} + 2 q^{28} + 7 q^{29} - q^{30} - 4 q^{31} - 2 q^{32} - 8 q^{33} - 8 q^{34} + q^{35} + 2 q^{36} + 15 q^{37} - 2 q^{38} + 5 q^{39} - q^{40} - 7 q^{41} - 2 q^{42} + 3 q^{43} - 8 q^{44} + q^{45} - 2 q^{46} - 3 q^{47} + 2 q^{48} + 2 q^{49} - 11 q^{50} + 8 q^{51} + 5 q^{52} - 6 q^{53} - 2 q^{54} - 4 q^{55} - 2 q^{56} + 2 q^{57} - 7 q^{58} - 2 q^{59} + q^{60} - 4 q^{61} + 4 q^{62} + 2 q^{63} + 2 q^{64} + 23 q^{65} + 8 q^{66} + 4 q^{67} + 8 q^{68} + 2 q^{69} - q^{70} - 2 q^{71} - 2 q^{72} - 10 q^{73} - 15 q^{74} + 11 q^{75} + 2 q^{76} - 8 q^{77} - 5 q^{78} + 16 q^{79} + q^{80} + 2 q^{81} + 7 q^{82} + 14 q^{83} + 2 q^{84} + 4 q^{85} - 3 q^{86} + 7 q^{87} + 8 q^{88} - 10 q^{89} - q^{90} + 5 q^{91} + 2 q^{92} - 4 q^{93} + 3 q^{94} - 40 q^{95} - 2 q^{96} + 19 q^{97} - 2 q^{98} - 8 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 + q^5 - 2 * q^6 + 2 * q^7 - 2 * q^8 + 2 * q^9 - q^10 - 8 * q^11 + 2 * q^12 + 5 * q^13 - 2 * q^14 + q^15 + 2 * q^16 + 8 * q^17 - 2 * q^18 + 2 * q^19 + q^20 + 2 * q^21 + 8 * q^22 + 2 * q^23 - 2 * q^24 + 11 * q^25 - 5 * q^26 + 2 * q^27 + 2 * q^28 + 7 * q^29 - q^30 - 4 * q^31 - 2 * q^32 - 8 * q^33 - 8 * q^34 + q^35 + 2 * q^36 + 15 * q^37 - 2 * q^38 + 5 * q^39 - q^40 - 7 * q^41 - 2 * q^42 + 3 * q^43 - 8 * q^44 + q^45 - 2 * q^46 - 3 * q^47 + 2 * q^48 + 2 * q^49 - 11 * q^50 + 8 * q^51 + 5 * q^52 - 6 * q^53 - 2 * q^54 - 4 * q^55 - 2 * q^56 + 2 * q^57 - 7 * q^58 - 2 * q^59 + q^60 - 4 * q^61 + 4 * q^62 + 2 * q^63 + 2 * q^64 + 23 * q^65 + 8 * q^66 + 4 * q^67 + 8 * q^68 + 2 * q^69 - q^70 - 2 * q^71 - 2 * q^72 - 10 * q^73 - 15 * q^74 + 11 * q^75 + 2 * q^76 - 8 * q^77 - 5 * q^78 + 16 * q^79 + q^80 + 2 * q^81 + 7 * q^82 + 14 * q^83 + 2 * q^84 + 4 * q^85 - 3 * q^86 + 7 * q^87 + 8 * q^88 - 10 * q^89 - q^90 + 5 * q^91 + 2 * q^92 - 4 * q^93 + 3 * q^94 - 40 * q^95 - 2 * q^96 + 19 * q^97 - 2 * q^98 - 8 * q^99

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