LMFDB - Embedded newform 4026.2.a.y.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4026,2,Mod(1,4026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4026, 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("4026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4026 = 2 \cdot 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4026.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:	$32.1477718538$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 2x^{6} - 21x^{5} + 39x^{4} + 89x^{3} - 100x^{2} - 96x + 8 $ x^7 - 2x^6 - 21x^5 + 39x^4 + 89x^3 - 100x^2 - 96x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-4.00088$ of defining polynomial
Character	$\chi$	$=$	4026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +4.00088 q^{5} +1.00000 q^{6} -0.723236 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +4.00088 q^{5} +1.00000 q^{6} -0.723236 q^{7} -1.00000 q^{8} +1.00000 q^{9} -4.00088 q^{10} -1.00000 q^{11} -1.00000 q^{12} -5.63742 q^{13} +0.723236 q^{14} -4.00088 q^{15} +1.00000 q^{16} +3.87268 q^{17} -1.00000 q^{18} -6.95201 q^{19} +4.00088 q^{20} +0.723236 q^{21} +1.00000 q^{22} +1.76473 q^{23} +1.00000 q^{24} +11.0070 q^{25} +5.63742 q^{26} -1.00000 q^{27} -0.723236 q^{28} +2.17957 q^{29} +4.00088 q^{30} -5.07315 q^{31} -1.00000 q^{32} +1.00000 q^{33} -3.87268 q^{34} -2.89358 q^{35} +1.00000 q^{36} -1.08212 q^{37} +6.95201 q^{38} +5.63742 q^{39} -4.00088 q^{40} +6.24231 q^{41} -0.723236 q^{42} -2.74993 q^{43} -1.00000 q^{44} +4.00088 q^{45} -1.76473 q^{46} -2.44441 q^{47} -1.00000 q^{48} -6.47693 q^{49} -11.0070 q^{50} -3.87268 q^{51} -5.63742 q^{52} -7.11956 q^{53} +1.00000 q^{54} -4.00088 q^{55} +0.723236 q^{56} +6.95201 q^{57} -2.17957 q^{58} -1.47229 q^{59} -4.00088 q^{60} -1.00000 q^{61} +5.07315 q^{62} -0.723236 q^{63} +1.00000 q^{64} -22.5546 q^{65} -1.00000 q^{66} +2.22180 q^{67} +3.87268 q^{68} -1.76473 q^{69} +2.89358 q^{70} -4.50520 q^{71} -1.00000 q^{72} -2.52732 q^{73} +1.08212 q^{74} -11.0070 q^{75} -6.95201 q^{76} +0.723236 q^{77} -5.63742 q^{78} -2.24689 q^{79} +4.00088 q^{80} +1.00000 q^{81} -6.24231 q^{82} -9.99351 q^{83} +0.723236 q^{84} +15.4941 q^{85} +2.74993 q^{86} -2.17957 q^{87} +1.00000 q^{88} -15.4941 q^{89} -4.00088 q^{90} +4.07718 q^{91} +1.76473 q^{92} +5.07315 q^{93} +2.44441 q^{94} -27.8142 q^{95} +1.00000 q^{96} +4.25307 q^{97} +6.47693 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} - 2 q^{5} + 7 q^{6} + q^{7} - 7 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 - 2 * q^5 + 7 * q^6 + q^7 - 7 * q^8 + 7 * q^9	$ 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} - 2 q^{5} + 7 q^{6} + q^{7} - 7 q^{8} + 7 q^{9} + 2 q^{10} - 7 q^{11} - 7 q^{12} - q^{14} + 2 q^{15} + 7 q^{16} + 3 q^{17} - 7 q^{18} - 5 q^{19} - 2 q^{20} - q^{21} + 7 q^{22} - 3 q^{23} + 7 q^{24} + 11 q^{25} - 7 q^{27} + q^{28} - 14 q^{29} - 2 q^{30} + 5 q^{31} - 7 q^{32} + 7 q^{33} - 3 q^{34} - 9 q^{35} + 7 q^{36} + 14 q^{37} + 5 q^{38} + 2 q^{40} - 7 q^{41} + q^{42} + q^{43} - 7 q^{44} - 2 q^{45} + 3 q^{46} - 7 q^{48} - 11 q^{50} - 3 q^{51} - 3 q^{53} + 7 q^{54} + 2 q^{55} - q^{56} + 5 q^{57} + 14 q^{58} - 14 q^{59} + 2 q^{60} - 7 q^{61} - 5 q^{62} + q^{63} + 7 q^{64} - 10 q^{65} - 7 q^{66} + 3 q^{68} + 3 q^{69} + 9 q^{70} - 22 q^{71} - 7 q^{72} + q^{73} - 14 q^{74} - 11 q^{75} - 5 q^{76} - q^{77} + 10 q^{79} - 2 q^{80} + 7 q^{81} + 7 q^{82} - 17 q^{83} - q^{84} + 18 q^{85} - q^{86} + 14 q^{87} + 7 q^{88} - 18 q^{89} + 2 q^{90} + 21 q^{91} - 3 q^{92} - 5 q^{93} - 41 q^{95} + 7 q^{96} + 25 q^{97} - 7 q^{99}+O(q^{100}) $ 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 - 2 * q^5 + 7 * q^6 + q^7 - 7 * q^8 + 7 * q^9 + 2 * q^10 - 7 * q^11 - 7 * q^12 - q^14 + 2 * q^15 + 7 * q^16 + 3 * q^17 - 7 * q^18 - 5 * q^19 - 2 * q^20 - q^21 + 7 * q^22 - 3 * q^23 + 7 * q^24 + 11 * q^25 - 7 * q^27 + q^28 - 14 * q^29 - 2 * q^30 + 5 * q^31 - 7 * q^32 + 7 * q^33 - 3 * q^34 - 9 * q^35 + 7 * q^36 + 14 * q^37 + 5 * q^38 + 2 * q^40 - 7 * q^41 + q^42 + q^43 - 7 * q^44 - 2 * q^45 + 3 * q^46 - 7 * q^48 - 11 * q^50 - 3 * q^51 - 3 * q^53 + 7 * q^54 + 2 * q^55 - q^56 + 5 * q^57 + 14 * q^58 - 14 * q^59 + 2 * q^60 - 7 * q^61 - 5 * q^62 + q^63 + 7 * q^64 - 10 * q^65 - 7 * q^66 + 3 * q^68 + 3 * q^69 + 9 * q^70 - 22 * q^71 - 7 * q^72 + q^73 - 14 * q^74 - 11 * q^75 - 5 * q^76 - q^77 + 10 * q^79 - 2 * q^80 + 7 * q^81 + 7 * q^82 - 17 * q^83 - q^84 + 18 * q^85 - q^86 + 14 * q^87 + 7 * q^88 - 18 * q^89 + 2 * q^90 + 21 * q^91 - 3 * q^92 - 5 * q^93 - 41 * q^95 + 7 * q^96 + 25 * q^97 - 7 * 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
$5$	4.00088	1.78925	0.894624	−	0.446820i	$-0.147443\pi$
$5$	4.00088	1.78925	0.894624	+	0.446820i	$0.147443\pi$
$6$	1.00000	0.408248
$7$	−0.723236	−0.273357	−0.136679	−	0.990615i	$-0.543643\pi$
$7$	−0.723236	−0.273357	−0.136679	+	0.990615i	$0.543643\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−4.00088	−1.26519
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−1.00000	−0.288675
$13$	−5.63742	−1.56354	−0.781769	−	0.623568i	$-0.785682\pi$
$13$	−5.63742	−1.56354	−0.781769	+	0.623568i	$0.785682\pi$
$14$	0.723236	0.193293
$15$	−4.00088	−1.03302
$16$	1.00000	0.250000
$17$	3.87268	0.939264	0.469632	−	0.882862i	$-0.344387\pi$
$17$	3.87268	0.939264	0.469632	+	0.882862i	$0.344387\pi$
$18$	−1.00000	−0.235702
$19$	−6.95201	−1.59490	−0.797450	−	0.603385i	$-0.793818\pi$
$19$	−6.95201	−1.59490	−0.797450	+	0.603385i	$0.793818\pi$
$20$	4.00088	0.894624
$21$	0.723236	0.157823
$22$	1.00000	0.213201
$23$	1.76473	0.367972	0.183986	−	0.982929i	$-0.441100\pi$
$23$	1.76473	0.367972	0.183986	+	0.982929i	$0.441100\pi$
$24$	1.00000	0.204124
$25$	11.0070	2.20141
$26$	5.63742	1.10559
$27$	−1.00000	−0.192450
$28$	−0.723236	−0.136679
$29$	2.17957	0.404735	0.202368	−	0.979310i	$-0.435136\pi$
$29$	2.17957	0.404735	0.202368	+	0.979310i	$0.435136\pi$
$30$	4.00088	0.730458
$31$	−5.07315	−0.911164	−0.455582	−	0.890194i	$-0.650569\pi$
$31$	−5.07315	−0.911164	−0.455582	+	0.890194i	$0.650569\pi$
$32$	−1.00000	−0.176777
$33$	1.00000	0.174078
$34$	−3.87268	−0.664160
$35$	−2.89358	−0.489104
$36$	1.00000	0.166667
$37$	−1.08212	−0.177900	−0.0889499	−	0.996036i	$-0.528351\pi$
$37$	−1.08212	−0.177900	−0.0889499	+	0.996036i	$0.528351\pi$
$38$	6.95201	1.12777
$39$	5.63742	0.902709
$40$	−4.00088	−0.632595
$41$	6.24231	0.974885	0.487443	−	0.873155i	$-0.337930\pi$
$41$	6.24231	0.974885	0.487443	+	0.873155i	$0.337930\pi$
$42$	−0.723236	−0.111598
$43$	−2.74993	−0.419361	−0.209680	−	0.977770i	$-0.567242\pi$
$43$	−2.74993	−0.419361	−0.209680	+	0.977770i	$0.567242\pi$
$44$	−1.00000	−0.150756
$45$	4.00088	0.596416
$46$	−1.76473	−0.260196
$47$	−2.44441	−0.356554	−0.178277	−	0.983980i	$-0.557052\pi$
$47$	−2.44441	−0.356554	−0.178277	+	0.983980i	$0.557052\pi$
$48$	−1.00000	−0.144338
$49$	−6.47693	−0.925276
$50$	−11.0070	−1.55663
$51$	−3.87268	−0.542284
$52$	−5.63742	−0.781769
$53$	−7.11956	−0.977947	−0.488973	−	0.872299i	$-0.662629\pi$
$53$	−7.11956	−0.977947	−0.488973	+	0.872299i	$0.662629\pi$
$54$	1.00000	0.136083
$55$	−4.00088	−0.539479
$56$	0.723236	0.0966465
$57$	6.95201	0.920816
$58$	−2.17957	−0.286191
$59$	−1.47229	−0.191675	−0.0958377	−	0.995397i	$-0.530553\pi$
$59$	−1.47229	−0.191675	−0.0958377	+	0.995397i	$0.530553\pi$
$60$	−4.00088	−0.516511
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	5.07315	0.644290
$63$	−0.723236	−0.0911192
$64$	1.00000	0.125000
$65$	−22.5546	−2.79756
$66$	−1.00000	−0.123091
$67$	2.22180	0.271436	0.135718	−	0.990748i	$-0.456666\pi$
$67$	2.22180	0.271436	0.135718	+	0.990748i	$0.456666\pi$
$68$	3.87268	0.469632
$69$	−1.76473	−0.212449
$70$	2.89358	0.345849
$71$	−4.50520	−0.534669	−0.267334	−	0.963604i	$-0.586143\pi$
$71$	−4.50520	−0.534669	−0.267334	+	0.963604i	$0.586143\pi$
$72$	−1.00000	−0.117851
$73$	−2.52732	−0.295801	−0.147900	−	0.989002i	$-0.547251\pi$
$73$	−2.52732	−0.295801	−0.147900	+	0.989002i	$0.547251\pi$
$74$	1.08212	0.125794
$75$	−11.0070	−1.27098
$76$	−6.95201	−0.797450
$77$	0.723236	0.0824204
$78$	−5.63742	−0.638312
$79$	−2.24689	−0.252795	−0.126397	−	0.991980i	$-0.540341\pi$
$79$	−2.24689	−0.252795	−0.126397	+	0.991980i	$0.540341\pi$
$80$	4.00088	0.447312
$81$	1.00000	0.111111
$82$	−6.24231	−0.689348
$83$	−9.99351	−1.09693	−0.548465	−	0.836173i	$-0.684788\pi$
$83$	−9.99351	−1.09693	−0.548465	+	0.836173i	$0.684788\pi$
$84$	0.723236	0.0789115
$85$	15.4941	1.68058
$86$	2.74993	0.296533
$87$	−2.17957	−0.233674
$88$	1.00000	0.106600
$89$	−15.4941	−1.64238	−0.821188	−	0.570658i	$-0.806688\pi$
$89$	−15.4941	−1.64238	−0.821188	+	0.570658i	$0.806688\pi$
$90$	−4.00088	−0.421730
$91$	4.07718	0.427405
$92$	1.76473	0.183986
$93$	5.07315	0.526061
$94$	2.44441	0.252122
$95$	−27.8142	−2.85367
$96$	1.00000	0.102062
$97$	4.25307	0.431834	0.215917	−	0.976412i	$-0.430726\pi$
$97$	4.25307	0.431834	0.215917	+	0.976412i	$0.430726\pi$
$98$	6.47693	0.654269
$99$	−1.00000	−0.100504
$100$	11.0070	1.10070
$101$	1.07556	0.107023	0.0535113	−	0.998567i	$-0.482959\pi$
$101$	1.07556	0.107023	0.0535113	+	0.998567i	$0.482959\pi$
$102$	3.87268	0.383453
$103$	−2.22917	−0.219646	−0.109823	−	0.993951i	$-0.535028\pi$
$103$	−2.22917	−0.219646	−0.109823	+	0.993951i	$0.535028\pi$
$104$	5.63742	0.552794
$105$	2.89358	0.282385
$106$	7.11956	0.691513
$107$	−4.37700	−0.423141	−0.211570	−	0.977363i	$-0.567858\pi$
$107$	−4.37700	−0.423141	−0.211570	+	0.977363i	$0.567858\pi$
$108$	−1.00000	−0.0962250
$109$	−13.0736	−1.25223	−0.626114	−	0.779732i	$-0.715355\pi$
$109$	−13.0736	−1.25223	−0.626114	+	0.779732i	$0.715355\pi$
$110$	4.00088	0.381469
$111$	1.08212	0.102711
$112$	−0.723236	−0.0683394
$113$	12.3139	1.15840	0.579198	−	0.815187i	$-0.303366\pi$
$113$	12.3139	1.15840	0.579198	+	0.815187i	$0.303366\pi$
$114$	−6.95201	−0.651115
$115$	7.06049	0.658394
$116$	2.17957	0.202368
$117$	−5.63742	−0.521179
$118$	1.47229	0.135535
$119$	−2.80086	−0.256755
$120$	4.00088	0.365229
$121$	1.00000	0.0909091
$122$	1.00000	0.0905357
$123$	−6.24231	−0.562850
$124$	−5.07315	−0.455582
$125$	24.0335	2.14962
$126$	0.723236	0.0644310
$127$	−4.42513	−0.392667	−0.196334	−	0.980537i	$-0.562904\pi$
$127$	−4.42513	−0.392667	−0.196334	+	0.980537i	$0.562904\pi$
$128$	−1.00000	−0.0883883
$129$	2.74993	0.242118
$130$	22.5546	1.97817
$131$	−3.00672	−0.262699	−0.131349	−	0.991336i	$-0.541931\pi$
$131$	−3.00672	−0.262699	−0.131349	+	0.991336i	$0.541931\pi$
$132$	1.00000	0.0870388
$133$	5.02794	0.435978
$134$	−2.22180	−0.191934
$135$	−4.00088	−0.344341
$136$	−3.87268	−0.332080
$137$	22.7938	1.94741	0.973703	−	0.227822i	$-0.0731605\pi$
$137$	22.7938	1.94741	0.973703	+	0.227822i	$0.0731605\pi$
$138$	1.76473	0.150224
$139$	−17.5742	−1.49062	−0.745312	−	0.666715i	$-0.767700\pi$
$139$	−17.5742	−1.49062	−0.745312	+	0.666715i	$0.767700\pi$
$140$	−2.89358	−0.244552
$141$	2.44441	0.205856
$142$	4.50520	0.378068
$143$	5.63742	0.471424
$144$	1.00000	0.0833333
$145$	8.72018	0.724172
$146$	2.52732	0.209163
$147$	6.47693	0.534208
$148$	−1.08212	−0.0889499
$149$	−14.8953	−1.22027	−0.610137	−	0.792296i	$-0.708886\pi$
$149$	−14.8953	−1.22027	−0.610137	+	0.792296i	$0.708886\pi$
$150$	11.0070	0.898722
$151$	9.47315	0.770914	0.385457	−	0.922726i	$-0.374044\pi$
$151$	9.47315	0.770914	0.385457	+	0.922726i	$0.374044\pi$
$152$	6.95201	0.563883
$153$	3.87268	0.313088
$154$	−0.723236	−0.0582800
$155$	−20.2971	−1.63030
$156$	5.63742	0.451355
$157$	5.33271	0.425597	0.212798	−	0.977096i	$-0.431742\pi$
$157$	5.33271	0.425597	0.212798	+	0.977096i	$0.431742\pi$
$158$	2.24689	0.178753
$159$	7.11956	0.564618
$160$	−4.00088	−0.316297
$161$	−1.27632	−0.100588
$162$	−1.00000	−0.0785674
$163$	1.79925	0.140928	0.0704639	−	0.997514i	$-0.477552\pi$
$163$	1.79925	0.140928	0.0704639	+	0.997514i	$0.477552\pi$
$164$	6.24231	0.487443
$165$	4.00088	0.311468
$166$	9.99351	0.775647
$167$	17.4854	1.35306	0.676529	−	0.736416i	$-0.263483\pi$
$167$	17.4854	1.35306	0.676529	+	0.736416i	$0.263483\pi$
$168$	−0.723236	−0.0557989
$169$	18.7805	1.44465
$170$	−15.4941	−1.18835
$171$	−6.95201	−0.531634
$172$	−2.74993	−0.209680
$173$	−3.38760	−0.257554	−0.128777	−	0.991674i	$-0.541105\pi$
$173$	−3.38760	−0.257554	−0.128777	+	0.991674i	$0.541105\pi$
$174$	2.17957	0.165232
$175$	−7.96069	−0.601772
$176$	−1.00000	−0.0753778
$177$	1.47229	0.110664
$178$	15.4941	1.16134
$179$	3.74878	0.280197	0.140098	−	0.990138i	$-0.455258\pi$
$179$	3.74878	0.280197	0.140098	+	0.990138i	$0.455258\pi$
$180$	4.00088	0.298208
$181$	−4.35484	−0.323693	−0.161846	−	0.986816i	$-0.551745\pi$
$181$	−4.35484	−0.323693	−0.161846	+	0.986816i	$0.551745\pi$
$182$	−4.07718	−0.302221
$183$	1.00000	0.0739221
$184$	−1.76473	−0.130098
$185$	−4.32944	−0.318307
$186$	−5.07315	−0.371981
$187$	−3.87268	−0.283199
$188$	−2.44441	−0.178277
$189$	0.723236	0.0526077
$190$	27.8142	2.01785
$191$	1.21893	0.0881983	0.0440992	−	0.999027i	$-0.485958\pi$
$191$	1.21893	0.0881983	0.0440992	+	0.999027i	$0.485958\pi$
$192$	−1.00000	−0.0721688
$193$	−15.6810	−1.12874	−0.564370	−	0.825522i	$-0.690881\pi$
$193$	−15.6810	−1.12874	−0.564370	+	0.825522i	$0.690881\pi$
$194$	−4.25307	−0.305353
$195$	22.5546	1.61517
$196$	−6.47693	−0.462638
$197$	−15.3813	−1.09587	−0.547935	−	0.836521i	$-0.684586\pi$
$197$	−15.3813	−1.09587	−0.547935	+	0.836521i	$0.684586\pi$
$198$	1.00000	0.0710669
$199$	−1.46575	−0.103904	−0.0519522	−	0.998650i	$-0.516544\pi$
$199$	−1.46575	−0.103904	−0.0519522	+	0.998650i	$0.516544\pi$
$200$	−11.0070	−0.778316
$201$	−2.22180	−0.156714
$202$	−1.07556	−0.0756765
$203$	−1.57634	−0.110637
$204$	−3.87268	−0.271142
$205$	24.9747	1.74431
$206$	2.22917	0.155313
$207$	1.76473	0.122657
$208$	−5.63742	−0.390885
$209$	6.95201	0.480881
$210$	−2.89358	−0.199676
$211$	−4.57433	−0.314910	−0.157455	−	0.987526i	$-0.550329\pi$
$211$	−4.57433	−0.314910	−0.157455	+	0.987526i	$0.550329\pi$
$212$	−7.11956	−0.488973
$213$	4.50520	0.308691
$214$	4.37700	0.299206
$215$	−11.0021	−0.750340
$216$	1.00000	0.0680414
$217$	3.66908	0.249073
$218$	13.0736	0.885458
$219$	2.52732	0.170781
$220$	−4.00088	−0.269739
$221$	−21.8319	−1.46857
$222$	−1.08212	−0.0726273
$223$	26.9557	1.80509	0.902543	−	0.430601i	$-0.141698\pi$
$223$	26.9557	1.80509	0.902543	+	0.430601i	$0.141698\pi$
$224$	0.723236	0.0483232
$225$	11.0070	0.733803
$226$	−12.3139	−0.819110
$227$	−21.4962	−1.42675	−0.713376	−	0.700781i	$-0.752835\pi$
$227$	−21.4962	−1.42675	−0.713376	+	0.700781i	$0.752835\pi$
$228$	6.95201	0.460408
$229$	17.1684	1.13452	0.567260	−	0.823539i	$-0.308004\pi$
$229$	17.1684	1.13452	0.567260	+	0.823539i	$0.308004\pi$
$230$	−7.06049	−0.465555
$231$	−0.723236	−0.0475854
$232$	−2.17957	−0.143095
$233$	10.3451	0.677733	0.338867	−	0.940834i	$-0.389956\pi$
$233$	10.3451	0.677733	0.338867	+	0.940834i	$0.389956\pi$
$234$	5.63742	0.368529
$235$	−9.77979	−0.637963
$236$	−1.47229	−0.0958377
$237$	2.24689	0.145951
$238$	2.80086	0.181553
$239$	−7.09783	−0.459121	−0.229560	−	0.973294i	$-0.573729\pi$
$239$	−7.09783	−0.459121	−0.229560	+	0.973294i	$0.573729\pi$
$240$	−4.00088	−0.258256
$241$	−27.8766	−1.79569	−0.897844	−	0.440313i	$-0.854867\pi$
$241$	−27.8766	−1.79569	−0.897844	+	0.440313i	$0.854867\pi$
$242$	−1.00000	−0.0642824
$243$	−1.00000	−0.0641500
$244$	−1.00000	−0.0640184
$245$	−25.9134	−1.65555
$246$	6.24231	0.397995
$247$	39.1914	2.49369
$248$	5.07315	0.322145
$249$	9.99351	0.633313
$250$	−24.0335	−1.52001
$251$	4.85751	0.306603	0.153302	−	0.988179i	$-0.451009\pi$
$251$	4.85751	0.306603	0.153302	+	0.988179i	$0.451009\pi$
$252$	−0.723236	−0.0455596
$253$	−1.76473	−0.110948
$254$	4.42513	0.277658
$255$	−15.4941	−0.970281
$256$	1.00000	0.0625000
$257$	−14.4855	−0.903584	−0.451792	−	0.892123i	$-0.649215\pi$
$257$	−14.4855	−0.903584	−0.451792	+	0.892123i	$0.649215\pi$
$258$	−2.74993	−0.171203
$259$	0.782630	0.0486303
$260$	−22.5546	−1.39878
$261$	2.17957	0.134912
$262$	3.00672	0.185756
$263$	−8.45551	−0.521389	−0.260695	−	0.965421i	$-0.583952\pi$
$263$	−8.45551	−0.521389	−0.260695	+	0.965421i	$0.583952\pi$
$264$	−1.00000	−0.0615457
$265$	−28.4845	−1.74979
$266$	−5.02794	−0.308283
$267$	15.4941	0.948226
$268$	2.22180	0.135718
$269$	−14.8968	−0.908275	−0.454137	−	0.890932i	$-0.650052\pi$
$269$	−14.8968	−0.908275	−0.454137	+	0.890932i	$0.650052\pi$
$270$	4.00088	0.243486
$271$	3.40432	0.206798	0.103399	−	0.994640i	$-0.467028\pi$
$271$	3.40432	0.206798	0.103399	+	0.994640i	$0.467028\pi$
$272$	3.87268	0.234816
$273$	−4.07718	−0.246762
$274$	−22.7938	−1.37702
$275$	−11.0070	−0.663750
$276$	−1.76473	−0.106224
$277$	2.48377	0.149235	0.0746175	−	0.997212i	$-0.476226\pi$
$277$	2.48377	0.149235	0.0746175	+	0.997212i	$0.476226\pi$
$278$	17.5742	1.05403
$279$	−5.07315	−0.303721
$280$	2.89358	0.172925
$281$	5.65561	0.337385	0.168693	−	0.985669i	$-0.446045\pi$
$281$	5.65561	0.337385	0.168693	+	0.985669i	$0.446045\pi$
$282$	−2.44441	−0.145562
$283$	−7.98313	−0.474548	−0.237274	−	0.971443i	$-0.576254\pi$
$283$	−7.98313	−0.474548	−0.237274	+	0.971443i	$0.576254\pi$
$284$	−4.50520	−0.267334
$285$	27.8142	1.64757
$286$	−5.63742	−0.333347
$287$	−4.51466	−0.266492
$288$	−1.00000	−0.0589256
$289$	−2.00233	−0.117784
$290$	−8.72018	−0.512067
$291$	−4.25307	−0.249319
$292$	−2.52732	−0.147900
$293$	−11.4367	−0.668137	−0.334068	−	0.942549i	$-0.608422\pi$
$293$	−11.4367	−0.668137	−0.334068	+	0.942549i	$0.608422\pi$
$294$	−6.47693	−0.377742
$295$	−5.89044	−0.342955
$296$	1.08212	0.0628971
$297$	1.00000	0.0580259
$298$	14.8953	0.862864
$299$	−9.94854	−0.575339
$300$	−11.0070	−0.635492
$301$	1.98885	0.114635
$302$	−9.47315	−0.545119
$303$	−1.07556	−0.0617896
$304$	−6.95201	−0.398725
$305$	−4.00088	−0.229090
$306$	−3.87268	−0.221387
$307$	−33.1891	−1.89420	−0.947101	−	0.320936i	$-0.896002\pi$
$307$	−33.1891	−1.89420	−0.947101	+	0.320936i	$0.896002\pi$
$308$	0.723236	0.0412102
$309$	2.22917	0.126813
$310$	20.2971	1.15280
$311$	−1.35439	−0.0768002	−0.0384001	−	0.999262i	$-0.512226\pi$
$311$	−1.35439	−0.0768002	−0.0384001	+	0.999262i	$0.512226\pi$
$312$	−5.63742	−0.319156
$313$	8.32711	0.470676	0.235338	−	0.971914i	$-0.424380\pi$
$313$	8.32711	0.470676	0.235338	+	0.971914i	$0.424380\pi$
$314$	−5.33271	−0.300942
$315$	−2.89358	−0.163035
$316$	−2.24689	−0.126397
$317$	−32.0470	−1.79994	−0.899970	−	0.435952i	$-0.856412\pi$
$317$	−32.0470	−1.79994	−0.899970	+	0.435952i	$0.856412\pi$
$318$	−7.11956	−0.399245
$319$	−2.17957	−0.122032
$320$	4.00088	0.223656
$321$	4.37700	0.244300
$322$	1.27632	0.0711265
$323$	−26.9229	−1.49803
$324$	1.00000	0.0555556
$325$	−62.0513	−3.44199
$326$	−1.79925	−0.0996510
$327$	13.0736	0.722974
$328$	−6.24231	−0.344674
$329$	1.76788	0.0974666
$330$	−4.00088	−0.220241
$331$	22.7888	1.25258	0.626292	−	0.779588i	$-0.284572\pi$
$331$	22.7888	1.25258	0.626292	+	0.779588i	$0.284572\pi$
$332$	−9.99351	−0.548465
$333$	−1.08212	−0.0593000
$334$	−17.4854	−0.956756
$335$	8.88916	0.485666
$336$	0.723236	0.0394558
$337$	23.5611	1.28346	0.641729	−	0.766932i	$-0.278218\pi$
$337$	23.5611	1.28346	0.641729	+	0.766932i	$0.278218\pi$
$338$	−18.7805	−1.02152
$339$	−12.3139	−0.668801
$340$	15.4941	0.840288
$341$	5.07315	0.274726
$342$	6.95201	0.375922
$343$	9.74700	0.526288
$344$	2.74993	0.148266
$345$	−7.06049	−0.380124
$346$	3.38760	0.182118
$347$	27.3053	1.46582	0.732911	−	0.680324i	$-0.238161\pi$
$347$	27.3053	1.46582	0.732911	+	0.680324i	$0.238161\pi$
$348$	−2.17957	−0.116837
$349$	21.4464	1.14800	0.574001	−	0.818855i	$-0.305391\pi$
$349$	21.4464	1.14800	0.574001	+	0.818855i	$0.305391\pi$
$350$	7.96069	0.425517
$351$	5.63742	0.300903
$352$	1.00000	0.0533002
$353$	−7.40805	−0.394291	−0.197145	−	0.980374i	$-0.563167\pi$
$353$	−7.40805	−0.394291	−0.197145	+	0.980374i	$0.563167\pi$
$354$	−1.47229	−0.0782511
$355$	−18.0248	−0.956655
$356$	−15.4941	−0.821188
$357$	2.80086	0.148237
$358$	−3.74878	−0.198129
$359$	1.53680	0.0811092	0.0405546	−	0.999177i	$-0.487088\pi$
$359$	1.53680	0.0811092	0.0405546	+	0.999177i	$0.487088\pi$
$360$	−4.00088	−0.210865
$361$	29.3305	1.54371
$362$	4.35484	0.228885
$363$	−1.00000	−0.0524864
$364$	4.07718	0.213702
$365$	−10.1115	−0.529261
$366$	−1.00000	−0.0522708
$367$	−21.5514	−1.12497	−0.562487	−	0.826806i	$-0.690155\pi$
$367$	−21.5514	−1.12497	−0.562487	+	0.826806i	$0.690155\pi$
$368$	1.76473	0.0919931
$369$	6.24231	0.324962
$370$	4.32944	0.225077
$371$	5.14912	0.267329
$372$	5.07315	0.263030
$373$	7.60487	0.393765	0.196883	−	0.980427i	$-0.436918\pi$
$373$	7.60487	0.393765	0.196883	+	0.980427i	$0.436918\pi$
$374$	3.87268	0.200252
$375$	−24.0335	−1.24108
$376$	2.44441	0.126061
$377$	−12.2871	−0.632819
$378$	−0.723236	−0.0371992
$379$	−20.6628	−1.06138	−0.530688	−	0.847567i	$-0.678066\pi$
$379$	−20.6628	−1.06138	−0.530688	+	0.847567i	$0.678066\pi$
$380$	−27.8142	−1.42684
$381$	4.42513	0.226707
$382$	−1.21893	−0.0623656
$383$	17.7922	0.909139	0.454569	−	0.890711i	$-0.349793\pi$
$383$	17.7922	0.909139	0.454569	+	0.890711i	$0.349793\pi$
$384$	1.00000	0.0510310
$385$	2.89358	0.147471
$386$	15.6810	0.798140
$387$	−2.74993	−0.139787
$388$	4.25307	0.215917
$389$	−25.4808	−1.29193	−0.645963	−	0.763369i	$-0.723544\pi$
$389$	−25.4808	−1.29193	−0.645963	+	0.763369i	$0.723544\pi$
$390$	−22.5546	−1.14210
$391$	6.83425	0.345623
$392$	6.47693	0.327134
$393$	3.00672	0.151669
$394$	15.3813	0.774897
$395$	−8.98954	−0.452313
$396$	−1.00000	−0.0502519
$397$	36.2443	1.81905	0.909523	−	0.415653i	$-0.136447\pi$
$397$	36.2443	1.81905	0.909523	+	0.415653i	$0.136447\pi$
$398$	1.46575	0.0734715
$399$	−5.02794	−0.251712
$400$	11.0070	0.550352
$401$	13.8033	0.689306	0.344653	−	0.938730i	$-0.387997\pi$
$401$	13.8033	0.689306	0.344653	+	0.938730i	$0.387997\pi$
$402$	2.22180	0.110813
$403$	28.5994	1.42464
$404$	1.07556	0.0535113
$405$	4.00088	0.198805
$406$	1.57634	0.0782324
$407$	1.08212	0.0536388
$408$	3.87268	0.191726
$409$	−29.4414	−1.45578	−0.727891	−	0.685693i	$-0.759499\pi$
$409$	−29.4414	−1.45578	−0.727891	+	0.685693i	$0.759499\pi$
$410$	−24.9747	−1.23341
$411$	−22.7938	−1.12434
$412$	−2.22917	−0.109823
$413$	1.06481	0.0523959
$414$	−1.76473	−0.0867319
$415$	−39.9828	−1.96268
$416$	5.63742	0.276397
$417$	17.5742	0.860613
$418$	−6.95201	−0.340034
$419$	−37.9741	−1.85516	−0.927578	−	0.373630i	$-0.878113\pi$
$419$	−37.9741	−1.85516	−0.927578	+	0.373630i	$0.878113\pi$
$420$	2.89358	0.141192
$421$	32.2009	1.56938	0.784688	−	0.619891i	$-0.212823\pi$
$421$	32.2009	1.56938	0.784688	+	0.619891i	$0.212823\pi$
$422$	4.57433	0.222675
$423$	−2.44441	−0.118851
$424$	7.11956	0.345756
$425$	42.6268	2.06770
$426$	−4.50520	−0.218278
$427$	0.723236	0.0349998
$428$	−4.37700	−0.211570
$429$	−5.63742	−0.272177
$430$	11.0021	0.530571
$431$	10.0535	0.484260	0.242130	−	0.970244i	$-0.422154\pi$
$431$	10.0535	0.484260	0.242130	+	0.970244i	$0.422154\pi$
$432$	−1.00000	−0.0481125
$433$	−25.9517	−1.24716	−0.623581	−	0.781759i	$-0.714323\pi$
$433$	−25.9517	−1.24716	−0.623581	+	0.781759i	$0.714323\pi$
$434$	−3.66908	−0.176122
$435$	−8.72018	−0.418101
$436$	−13.0736	−0.626114
$437$	−12.2684	−0.586879
$438$	−2.52732	−0.120760
$439$	5.03718	0.240412	0.120206	−	0.992749i	$-0.461645\pi$
$439$	5.03718	0.240412	0.120206	+	0.992749i	$0.461645\pi$
$440$	4.00088	0.190735
$441$	−6.47693	−0.308425
$442$	21.8319	1.03844
$443$	−10.7967	−0.512967	−0.256484	−	0.966549i	$-0.582564\pi$
$443$	−10.7967	−0.512967	−0.256484	+	0.966549i	$0.582564\pi$
$444$	1.08212	0.0513553
$445$	−61.9902	−2.93862
$446$	−26.9557	−1.27639
$447$	14.8953	0.704525
$448$	−0.723236	−0.0341697
$449$	−8.61724	−0.406673	−0.203336	−	0.979109i	$-0.565178\pi$
$449$	−8.61724	−0.406673	−0.203336	+	0.979109i	$0.565178\pi$
$450$	−11.0070	−0.518877
$451$	−6.24231	−0.293939
$452$	12.3139	0.579198
$453$	−9.47315	−0.445087
$454$	21.4962	1.00887
$455$	16.3123	0.764733
$456$	−6.95201	−0.325558
$457$	−16.1462	−0.755285	−0.377643	−	0.925951i	$-0.623265\pi$
$457$	−16.1462	−0.755285	−0.377643	+	0.925951i	$0.623265\pi$
$458$	−17.1684	−0.802226
$459$	−3.87268	−0.180761
$460$	7.06049	0.329197
$461$	−13.2398	−0.616638	−0.308319	−	0.951283i	$-0.599766\pi$
$461$	−13.2398	−0.616638	−0.308319	+	0.951283i	$0.599766\pi$
$462$	0.723236	0.0336480
$463$	−23.5517	−1.09454	−0.547271	−	0.836956i	$-0.684333\pi$
$463$	−23.5517	−1.09454	−0.547271	+	0.836956i	$0.684333\pi$
$464$	2.17957	0.101184
$465$	20.2971	0.941253
$466$	−10.3451	−0.479230
$467$	24.9320	1.15372	0.576858	−	0.816845i	$-0.304279\pi$
$467$	24.9320	1.15372	0.576858	+	0.816845i	$0.304279\pi$
$468$	−5.63742	−0.260590
$469$	−1.60689	−0.0741991
$470$	9.77979	0.451108
$471$	−5.33271	−0.245718
$472$	1.47229	0.0677675
$473$	2.74993	0.126442
$474$	−2.24689	−0.103203
$475$	−76.5211	−3.51103
$476$	−2.80086	−0.128377
$477$	−7.11956	−0.325982
$478$	7.09783	0.324647
$479$	−23.5250	−1.07488	−0.537442	−	0.843301i	$-0.680609\pi$
$479$	−23.5250	−1.07488	−0.537442	+	0.843301i	$0.680609\pi$
$480$	4.00088	0.182614
$481$	6.10038	0.278153
$482$	27.8766	1.26974
$483$	1.27632	0.0580745
$484$	1.00000	0.0454545
$485$	17.0160	0.772658
$486$	1.00000	0.0453609
$487$	12.8278	0.581282	0.290641	−	0.956832i	$-0.406132\pi$
$487$	12.8278	0.581282	0.290641	+	0.956832i	$0.406132\pi$
$488$	1.00000	0.0452679
$489$	−1.79925	−0.0813647
$490$	25.9134	1.17065
$491$	−32.3200	−1.45858	−0.729290	−	0.684205i	$-0.760150\pi$
$491$	−32.3200	−1.45858	−0.729290	+	0.684205i	$0.760150\pi$
$492$	−6.24231	−0.281425
$493$	8.44077	0.380153
$494$	−39.1914	−1.76330
$495$	−4.00088	−0.179826
$496$	−5.07315	−0.227791
$497$	3.25832	0.146156
$498$	−9.99351	−0.447820
$499$	−24.8170	−1.11096	−0.555480	−	0.831530i	$-0.687465\pi$
$499$	−24.8170	−1.11096	−0.555480	+	0.831530i	$0.687465\pi$
$500$	24.0335	1.07481
$501$	−17.4854	−0.781188
$502$	−4.85751	−0.216801
$503$	17.8661	0.796610	0.398305	−	0.917253i	$-0.369599\pi$
$503$	17.8661	0.796610	0.398305	+	0.917253i	$0.369599\pi$
$504$	0.723236	0.0322155
$505$	4.30321	0.191490
$506$	1.76473	0.0784520
$507$	−18.7805	−0.834070
$508$	−4.42513	−0.196334
$509$	12.5156	0.554743	0.277372	−	0.960763i	$-0.410537\pi$
$509$	12.5156	0.554743	0.277372	+	0.960763i	$0.410537\pi$
$510$	15.4941	0.686092
$511$	1.82785	0.0808593
$512$	−1.00000	−0.0441942
$513$	6.95201	0.306939
$514$	14.4855	0.638930
$515$	−8.91863	−0.393002
$516$	2.74993	0.121059
$517$	2.44441	0.107505
$518$	−0.782630	−0.0343868
$519$	3.38760	0.148699
$520$	22.5546	0.989086
$521$	−14.0592	−0.615943	−0.307972	−	0.951396i	$-0.599650\pi$
$521$	−14.0592	−0.615943	−0.307972	+	0.951396i	$0.599650\pi$
$522$	−2.17957	−0.0953970
$523$	−44.8151	−1.95963	−0.979814	−	0.199912i	$-0.935934\pi$
$523$	−44.8151	−1.95963	−0.979814	+	0.199912i	$0.935934\pi$
$524$	−3.00672	−0.131349
$525$	7.96069	0.347433
$526$	8.45551	0.368678
$527$	−19.6467	−0.855823
$528$	1.00000	0.0435194
$529$	−19.8857	−0.864596
$530$	28.4845	1.23729
$531$	−1.47229	−0.0638918
$532$	5.02794	0.217989
$533$	−35.1905	−1.52427
$534$	−15.4941	−0.670497
$535$	−17.5119	−0.757104
$536$	−2.22180	−0.0959671
$537$	−3.74878	−0.161772
$538$	14.8968	0.642247
$539$	6.47693	0.278981
$540$	−4.00088	−0.172170
$541$	40.3896	1.73648	0.868242	−	0.496142i	$-0.165250\pi$
$541$	40.3896	1.73648	0.868242	+	0.496142i	$0.165250\pi$
$542$	−3.40432	−0.146228
$543$	4.35484	0.186884
$544$	−3.87268	−0.166040
$545$	−52.3061	−2.24055
$546$	4.07718	0.174487
$547$	7.84469	0.335415	0.167707	−	0.985837i	$-0.446364\pi$
$547$	7.84469	0.335415	0.167707	+	0.985837i	$0.446364\pi$
$548$	22.7938	0.973703
$549$	−1.00000	−0.0426790
$550$	11.0070	0.469342
$551$	−15.1524	−0.645512
$552$	1.76473	0.0751121
$553$	1.62503	0.0691034
$554$	−2.48377	−0.105525
$555$	4.32944	0.183775
$556$	−17.5742	−0.745312
$557$	33.6361	1.42521	0.712603	−	0.701567i	$-0.247516\pi$
$557$	33.6361	1.42521	0.712603	+	0.701567i	$0.247516\pi$
$558$	5.07315	0.214763
$559$	15.5025	0.655686
$560$	−2.89358	−0.122276
$561$	3.87268	0.163505
$562$	−5.65561	−0.238568
$563$	41.6593	1.75573	0.877866	−	0.478907i	$-0.158967\pi$
$563$	41.6593	1.75573	0.877866	+	0.478907i	$0.158967\pi$
$564$	2.44441	0.102928
$565$	49.2666	2.07266
$566$	7.98313	0.335556
$567$	−0.723236	−0.0303731
$568$	4.50520	0.189034
$569$	−10.4660	−0.438757	−0.219378	−	0.975640i	$-0.570403\pi$
$569$	−10.4660	−0.438757	−0.219378	+	0.975640i	$0.570403\pi$
$570$	−27.8142	−1.16501
$571$	19.8356	0.830095	0.415047	−	0.909800i	$-0.363765\pi$
$571$	19.8356	0.830095	0.415047	+	0.909800i	$0.363765\pi$
$572$	5.63742	0.235712
$573$	−1.21893	−0.0509213
$574$	4.51466	0.188438
$575$	19.4245	0.810058
$576$	1.00000	0.0416667
$577$	43.4835	1.81024	0.905120	−	0.425156i	$-0.139781\pi$
$577$	43.4835	1.81024	0.905120	+	0.425156i	$0.139781\pi$
$578$	2.00233	0.0832858
$579$	15.6810	0.651679
$580$	8.72018	0.362086
$581$	7.22766	0.299854
$582$	4.25307	0.176295
$583$	7.11956	0.294862
$584$	2.52732	0.104581
$585$	−22.5546	−0.932519
$586$	11.4367	0.472444
$587$	−28.0639	−1.15832	−0.579161	−	0.815213i	$-0.696620\pi$
$587$	−28.0639	−1.15832	−0.579161	+	0.815213i	$0.696620\pi$
$588$	6.47693	0.267104
$589$	35.2686	1.45322
$590$	5.89044	0.242506
$591$	15.3813	0.632701
$592$	−1.08212	−0.0444750
$593$	23.2842	0.956169	0.478085	−	0.878314i	$-0.341331\pi$
$593$	23.2842	0.956169	0.478085	+	0.878314i	$0.341331\pi$
$594$	−1.00000	−0.0410305
$595$	−11.2059	−0.459398
$596$	−14.8953	−0.610137
$597$	1.46575	0.0599892
$598$	9.94854	0.406826
$599$	−1.23000	−0.0502563	−0.0251281	−	0.999684i	$-0.507999\pi$
$599$	−1.23000	−0.0502563	−0.0251281	+	0.999684i	$0.507999\pi$
$600$	11.0070	0.449361
$601$	16.2093	0.661192	0.330596	−	0.943772i	$-0.392750\pi$
$601$	16.2093	0.661192	0.330596	+	0.943772i	$0.392750\pi$
$602$	−1.98885	−0.0810594
$603$	2.22180	0.0904787
$604$	9.47315	0.385457
$605$	4.00088	0.162659
$606$	1.07556	0.0436918
$607$	−35.2866	−1.43224	−0.716119	−	0.697978i	$-0.754083\pi$
$607$	−35.2866	−1.43224	−0.716119	+	0.697978i	$0.754083\pi$
$608$	6.95201	0.281941
$609$	1.57634	0.0638765
$610$	4.00088	0.161991
$611$	13.7802	0.557485
$612$	3.87268	0.156544
$613$	19.5297	0.788798	0.394399	−	0.918939i	$-0.370953\pi$
$613$	19.5297	0.788798	0.394399	+	0.918939i	$0.370953\pi$
$614$	33.1891	1.33940
$615$	−24.9747	−1.00708
$616$	−0.723236	−0.0291400
$617$	13.3602	0.537861	0.268931	−	0.963160i	$-0.413330\pi$
$617$	13.3602	0.537861	0.268931	+	0.963160i	$0.413330\pi$
$618$	−2.22917	−0.0896703
$619$	14.4224	0.579684	0.289842	−	0.957075i	$-0.406397\pi$
$619$	14.4224	0.579684	0.289842	+	0.957075i	$0.406397\pi$
$620$	−20.2971	−0.815149
$621$	−1.76473	−0.0708163
$622$	1.35439	0.0543059
$623$	11.2059	0.448956
$624$	5.63742	0.225677
$625$	41.1198	1.64479
$626$	−8.32711	−0.332818
$627$	−6.95201	−0.277637
$628$	5.33271	0.212798
$629$	−4.19072	−0.167095
$630$	2.89358	0.115283
$631$	46.6899	1.85869	0.929347	−	0.369206i	$-0.120370\pi$
$631$	46.6899	1.85869	0.929347	+	0.369206i	$0.120370\pi$
$632$	2.24689	0.0893765
$633$	4.57433	0.181813
$634$	32.0470	1.27275
$635$	−17.7044	−0.702579
$636$	7.11956	0.282309
$637$	36.5132	1.44670
$638$	2.17957	0.0862898
$639$	−4.50520	−0.178223
$640$	−4.00088	−0.158149
$641$	−21.9953	−0.868764	−0.434382	−	0.900729i	$-0.643033\pi$
$641$	−21.9953	−0.868764	−0.434382	+	0.900729i	$0.643033\pi$
$642$	−4.37700	−0.172746
$643$	38.7138	1.52672	0.763362	−	0.645971i	$-0.223547\pi$
$643$	38.7138	1.52672	0.763362	+	0.645971i	$0.223547\pi$
$644$	−1.27632	−0.0502940
$645$	11.0021	0.433209
$646$	26.9229	1.05927
$647$	−33.3036	−1.30930	−0.654649	−	0.755933i	$-0.727184\pi$
$647$	−33.3036	−1.30930	−0.654649	+	0.755933i	$0.727184\pi$
$648$	−1.00000	−0.0392837
$649$	1.47229	0.0577923
$650$	62.0513	2.43385
$651$	−3.66908	−0.143803
$652$	1.79925	0.0704639
$653$	0.812702	0.0318035	0.0159018	−	0.999874i	$-0.494938\pi$
$653$	0.812702	0.0318035	0.0159018	+	0.999874i	$0.494938\pi$
$654$	−13.0736	−0.511220
$655$	−12.0295	−0.470033
$656$	6.24231	0.243721
$657$	−2.52732	−0.0986002
$658$	−1.76788	−0.0689193
$659$	−2.79982	−0.109065	−0.0545327	−	0.998512i	$-0.517367\pi$
$659$	−2.79982	−0.109065	−0.0545327	+	0.998512i	$0.517367\pi$
$660$	4.00088	0.155734
$661$	−46.6766	−1.81551	−0.907754	−	0.419502i	$-0.862205\pi$
$661$	−46.6766	−1.81551	−0.907754	+	0.419502i	$0.862205\pi$
$662$	−22.7888	−0.885711
$663$	21.8319	0.847882
$664$	9.99351	0.387823
$665$	20.1162	0.780073
$666$	1.08212	0.0419314
$667$	3.84635	0.148931
$668$	17.4854	0.676529
$669$	−26.9557	−1.04217
$670$	−8.88916	−0.343418
$671$	1.00000	0.0386046
$672$	−0.723236	−0.0278994
$673$	−39.5600	−1.52492	−0.762462	−	0.647033i	$-0.776010\pi$
$673$	−39.5600	−1.52492	−0.762462	+	0.647033i	$0.776010\pi$
$674$	−23.5611	−0.907541
$675$	−11.0070	−0.423661
$676$	18.7805	0.722326
$677$	−6.74221	−0.259124	−0.129562	−	0.991571i	$-0.541357\pi$
$677$	−6.74221	−0.259124	−0.129562	+	0.991571i	$0.541357\pi$
$678$	12.3139	0.472914
$679$	−3.07597	−0.118045
$680$	−15.4941	−0.594173
$681$	21.4962	0.823736
$682$	−5.07315	−0.194261
$683$	43.2051	1.65320	0.826598	−	0.562792i	$-0.190273\pi$
$683$	43.2051	1.65320	0.826598	+	0.562792i	$0.190273\pi$
$684$	−6.95201	−0.265817
$685$	91.1953	3.48439
$686$	−9.74700	−0.372142
$687$	−17.1684	−0.655015
$688$	−2.74993	−0.104840
$689$	40.1359	1.52906
$690$	7.06049	0.268788
$691$	−24.0179	−0.913684	−0.456842	−	0.889548i	$-0.651020\pi$
$691$	−24.0179	−0.913684	−0.456842	+	0.889548i	$0.651020\pi$
$692$	−3.38760	−0.128777
$693$	0.723236	0.0274735
$694$	−27.3053	−1.03649
$695$	−70.3123	−2.66710
$696$	2.17957	0.0826162
$697$	24.1745	0.915674
$698$	−21.4464	−0.811760
$699$	−10.3451	−0.391289
$700$	−7.96069	−0.300886
$701$	−32.1873	−1.21570	−0.607849	−	0.794052i	$-0.707968\pi$
$701$	−32.1873	−1.21570	−0.607849	+	0.794052i	$0.707968\pi$
$702$	−5.63742	−0.212771
$703$	7.52293	0.283733
$704$	−1.00000	−0.0376889
$705$	9.77979	0.368328
$706$	7.40805	0.278806
$707$	−0.777887	−0.0292555
$708$	1.47229	0.0553319
$709$	−25.1621	−0.944983	−0.472491	−	0.881335i	$-0.656645\pi$
$709$	−25.1621	−0.944983	−0.472491	+	0.881335i	$0.656645\pi$
$710$	18.0248	0.676457
$711$	−2.24689	−0.0842650
$712$	15.4941	0.580668
$713$	−8.95275	−0.335283
$714$	−2.80086	−0.104820
$715$	22.5546	0.843495
$716$	3.74878	0.140098
$717$	7.09783	0.265073
$718$	−1.53680	−0.0573528
$719$	9.87833	0.368400	0.184200	−	0.982889i	$-0.441031\pi$
$719$	9.87833	0.368400	0.184200	+	0.982889i	$0.441031\pi$
$720$	4.00088	0.149104
$721$	1.61221	0.0600420
$722$	−29.3305	−1.09157
$723$	27.8766	1.03674
$724$	−4.35484	−0.161846
$725$	23.9906	0.890988
$726$	1.00000	0.0371135
$727$	−16.5205	−0.612712	−0.306356	−	0.951917i	$-0.599110\pi$
$727$	−16.5205	−0.612712	−0.306356	+	0.951917i	$0.599110\pi$
$728$	−4.07718	−0.151110
$729$	1.00000	0.0370370
$730$	10.1115	0.374244
$731$	−10.6496	−0.393890
$732$	1.00000	0.0369611
$733$	−10.6881	−0.394775	−0.197388	−	0.980326i	$-0.563246\pi$
$733$	−10.6881	−0.394775	−0.197388	+	0.980326i	$0.563246\pi$
$734$	21.5514	0.795476
$735$	25.9134	0.955831
$736$	−1.76473	−0.0650489
$737$	−2.22180	−0.0818410
$738$	−6.24231	−0.229783
$739$	18.7259	0.688843	0.344422	−	0.938815i	$-0.388075\pi$
$739$	18.7259	0.688843	0.344422	+	0.938815i	$0.388075\pi$
$740$	−4.32944	−0.159154
$741$	−39.1914	−1.43973
$742$	−5.14912	−0.189030
$743$	−12.0826	−0.443266	−0.221633	−	0.975130i	$-0.571139\pi$
$743$	−12.0826	−0.443266	−0.221633	+	0.975130i	$0.571139\pi$
$744$	−5.07315	−0.185991
$745$	−59.5945	−2.18337
$746$	−7.60487	−0.278434
$747$	−9.99351	−0.365643
$748$	−3.87268	−0.141599
$749$	3.16560	0.115669
$750$	24.0335	0.877578
$751$	−26.1042	−0.952557	−0.476279	−	0.879294i	$-0.658015\pi$
$751$	−26.1042	−0.952557	−0.476279	+	0.879294i	$0.658015\pi$
$752$	−2.44441	−0.0891384
$753$	−4.85751	−0.177018
$754$	12.2871	0.447470
$755$	37.9009	1.37936
$756$	0.723236	0.0263038
$757$	25.0299	0.909726	0.454863	−	0.890561i	$-0.349688\pi$
$757$	25.0299	0.909726	0.454863	+	0.890561i	$0.349688\pi$
$758$	20.6628	0.750506
$759$	1.76473	0.0640558
$760$	27.8142	1.00893
$761$	12.4688	0.451995	0.225997	−	0.974128i	$-0.427436\pi$
$761$	12.4688	0.451995	0.225997	+	0.974128i	$0.427436\pi$
$762$	−4.42513	−0.160306
$763$	9.45532	0.342306
$764$	1.21893	0.0440992
$765$	15.4941	0.560192
$766$	−17.7922	−0.642858
$767$	8.29989	0.299692
$768$	−1.00000	−0.0360844
$769$	18.6101	0.671098	0.335549	−	0.942023i	$-0.391078\pi$
$769$	18.6101	0.671098	0.335549	+	0.942023i	$0.391078\pi$
$770$	−2.89358	−0.104277
$771$	14.4855	0.521684
$772$	−15.6810	−0.564370
$773$	50.9361	1.83204	0.916022	−	0.401128i	$-0.131382\pi$
$773$	50.9361	1.83204	0.916022	+	0.401128i	$0.131382\pi$
$774$	2.74993	0.0988442
$775$	−55.8404	−2.00584
$776$	−4.25307	−0.152676
$777$	−0.782630	−0.0280767
$778$	25.4808	0.913530
$779$	−43.3966	−1.55485
$780$	22.5546	0.807585
$781$	4.50520	0.161209
$782$	−6.83425	−0.244392
$783$	−2.17957	−0.0778913
$784$	−6.47693	−0.231319
$785$	21.3355	0.761498
$786$	−3.00672	−0.107246
$787$	54.1966	1.93190	0.965949	−	0.258731i	$-0.0833042\pi$
$787$	54.1966	1.93190	0.965949	+	0.258731i	$0.0833042\pi$
$788$	−15.3813	−0.547935
$789$	8.45551	0.301024
$790$	8.98954	0.319833
$791$	−8.90588	−0.316656
$792$	1.00000	0.0355335
$793$	5.63742	0.200191
$794$	−36.2443	−1.28626
$795$	28.4845	1.01024
$796$	−1.46575	−0.0519522
$797$	2.25967	0.0800415	0.0400207	−	0.999199i	$-0.487258\pi$
$797$	2.25967	0.0800415	0.0400207	+	0.999199i	$0.487258\pi$
$798$	5.02794	0.177987
$799$	−9.46642	−0.334898
$800$	−11.0070	−0.389158
$801$	−15.4941	−0.547459
$802$	−13.8033	−0.487413
$803$	2.52732	0.0891872
$804$	−2.22180	−0.0783568
$805$	−5.10640	−0.179977
$806$	−28.5994	−1.00737
$807$	14.8968	0.524393
$808$	−1.07556	−0.0378382
$809$	32.5258	1.14355	0.571773	−	0.820412i	$-0.306256\pi$
$809$	32.5258	1.14355	0.571773	+	0.820412i	$0.306256\pi$
$810$	−4.00088	−0.140577
$811$	−37.7092	−1.32415	−0.662075	−	0.749438i	$-0.730324\pi$
$811$	−37.7092	−1.32415	−0.662075	+	0.749438i	$0.730324\pi$
$812$	−1.57634	−0.0553187
$813$	−3.40432	−0.119395
$814$	−1.08212	−0.0379284
$815$	7.19857	0.252155
$816$	−3.87268	−0.135571
$817$	19.1176	0.668838
$818$	29.4414	1.02939
$819$	4.07718	0.142468
$820$	24.9747	0.872156
$821$	25.2230	0.880287	0.440144	−	0.897927i	$-0.354928\pi$
$821$	25.2230	0.880287	0.440144	+	0.897927i	$0.354928\pi$
$822$	22.7938	0.795025
$823$	18.6280	0.649331	0.324665	−	0.945829i	$-0.394748\pi$
$823$	18.6280	0.649331	0.324665	+	0.945829i	$0.394748\pi$
$824$	2.22917	0.0776567
$825$	11.0070	0.383216
$826$	−1.06481	−0.0370495
$827$	45.1800	1.57106	0.785532	−	0.618821i	$-0.212389\pi$
$827$	45.1800	1.57106	0.785532	+	0.618821i	$0.212389\pi$
$828$	1.76473	0.0613287
$829$	−39.6836	−1.37827	−0.689133	−	0.724634i	$-0.742009\pi$
$829$	−39.6836	−1.37827	−0.689133	+	0.724634i	$0.742009\pi$
$830$	39.9828	1.38782
$831$	−2.48377	−0.0861609
$832$	−5.63742	−0.195442
$833$	−25.0831	−0.869078
$834$	−17.5742	−0.608545
$835$	69.9568	2.42096
$836$	6.95201	0.240440
$837$	5.07315	0.175354
$838$	37.9741	1.31179
$839$	−7.53769	−0.260230	−0.130115	−	0.991499i	$-0.541535\pi$
$839$	−7.53769	−0.260230	−0.130115	+	0.991499i	$0.541535\pi$
$840$	−2.89358	−0.0998380
$841$	−24.2495	−0.836189
$842$	−32.2009	−1.10972
$843$	−5.65561	−0.194790
$844$	−4.57433	−0.157455
$845$	75.1384	2.58484
$846$	2.44441	0.0840405
$847$	−0.723236	−0.0248507
$848$	−7.11956	−0.244487
$849$	7.98313	0.273980
$850$	−42.6268	−1.46209
$851$	−1.90966	−0.0654623
$852$	4.50520	0.154346
$853$	−7.46285	−0.255523	−0.127762	−	0.991805i	$-0.540779\pi$
$853$	−7.46285	−0.255523	−0.127762	+	0.991805i	$0.540779\pi$
$854$	−0.723236	−0.0247486
$855$	−27.8142	−0.951224
$856$	4.37700	0.149603
$857$	−11.7903	−0.402748	−0.201374	−	0.979514i	$-0.564541\pi$
$857$	−11.7903	−0.402748	−0.201374	+	0.979514i	$0.564541\pi$
$858$	5.63742	0.192458
$859$	9.09164	0.310203	0.155101	−	0.987899i	$-0.450430\pi$
$859$	9.09164	0.310203	0.155101	+	0.987899i	$0.450430\pi$
$860$	−11.0021	−0.375170
$861$	4.51466	0.153859
$862$	−10.0535	−0.342423
$863$	18.3886	0.625955	0.312977	−	0.949761i	$-0.398674\pi$
$863$	18.3886	0.625955	0.312977	+	0.949761i	$0.398674\pi$
$864$	1.00000	0.0340207
$865$	−13.5534	−0.460828
$866$	25.9517	0.881876
$867$	2.00233	0.0680025
$868$	3.66908	0.124537
$869$	2.24689	0.0762205
$870$	8.72018	0.295642
$871$	−12.5252	−0.424401
$872$	13.0736	0.442729
$873$	4.25307	0.143945
$874$	12.2684	0.414986
$875$	−17.3819	−0.587615
$876$	2.52732	0.0853903
$877$	42.2387	1.42630	0.713150	−	0.701012i	$-0.247268\pi$
$877$	42.2387	1.42630	0.713150	+	0.701012i	$0.247268\pi$
$878$	−5.03718	−0.169997
$879$	11.4367	0.385749
$880$	−4.00088	−0.134870
$881$	−24.6611	−0.830852	−0.415426	−	0.909627i	$-0.636367\pi$
$881$	−24.6611	−0.830852	−0.415426	+	0.909627i	$0.636367\pi$
$882$	6.47693	0.218090
$883$	37.2347	1.25305	0.626524	−	0.779402i	$-0.284477\pi$
$883$	37.2347	1.25305	0.626524	+	0.779402i	$0.284477\pi$
$884$	−21.8319	−0.734287
$885$	5.89044	0.198005
$886$	10.7967	0.362723
$887$	−10.0933	−0.338899	−0.169449	−	0.985539i	$-0.554199\pi$
$887$	−10.0933	−0.338899	−0.169449	+	0.985539i	$0.554199\pi$
$888$	−1.08212	−0.0363137
$889$	3.20042	0.107339
$890$	61.9902	2.07792
$891$	−1.00000	−0.0335013
$892$	26.9557	0.902543
$893$	16.9936	0.568668
$894$	−14.8953	−0.498175
$895$	14.9984	0.501342
$896$	0.723236	0.0241616
$897$	9.94854	0.332172
$898$	8.61724	0.287561
$899$	−11.0573	−0.368780
$900$	11.0070	0.366902
$901$	−27.5718	−0.918550
$902$	6.24231	0.207846
$903$	−1.98885	−0.0661847
$904$	−12.3139	−0.409555
$905$	−17.4232	−0.579167
$906$	9.47315	0.314724
$907$	−14.5884	−0.484399	−0.242199	−	0.970227i	$-0.577869\pi$
$907$	−14.5884	−0.484399	−0.242199	+	0.970227i	$0.577869\pi$
$908$	−21.4962	−0.713376
$909$	1.07556	0.0356742
$910$	−16.3123	−0.540748
$911$	13.2383	0.438605	0.219302	−	0.975657i	$-0.429622\pi$
$911$	13.2383	0.438605	0.219302	+	0.975657i	$0.429622\pi$
$912$	6.95201	0.230204
$913$	9.99351	0.330737
$914$	16.1462	0.534067
$915$	4.00088	0.132265
$916$	17.1684	0.567260
$917$	2.17457	0.0718106
$918$	3.87268	0.127818
$919$	−13.3687	−0.440991	−0.220496	−	0.975388i	$-0.570767\pi$
$919$	−13.3687	−0.440991	−0.220496	+	0.975388i	$0.570767\pi$
$920$	−7.06049	−0.232777
$921$	33.1891	1.09362
$922$	13.2398	0.436029
$923$	25.3977	0.835975
$924$	−0.723236	−0.0237927
$925$	−11.9110	−0.391630
$926$	23.5517	0.773958
$927$	−2.22917	−0.0732155
$928$	−2.17957	−0.0715477
$929$	40.2008	1.31894	0.659472	−	0.751729i	$-0.270780\pi$
$929$	40.2008	1.31894	0.659472	+	0.751729i	$0.270780\pi$
$930$	−20.2971	−0.665567
$931$	45.0277	1.47572
$932$	10.3451	0.338867
$933$	1.35439	0.0443406
$934$	−24.9320	−0.815800
$935$	−15.4941	−0.506713
$936$	5.63742	0.184265
$937$	10.4401	0.341064	0.170532	−	0.985352i	$-0.445451\pi$
$937$	10.4401	0.341064	0.170532	+	0.985352i	$0.445451\pi$
$938$	1.60689	0.0524667
$939$	−8.32711	−0.271745
$940$	−9.77979	−0.318982
$941$	23.0933	0.752819	0.376410	−	0.926453i	$-0.377159\pi$
$941$	23.0933	0.752819	0.376410	+	0.926453i	$0.377159\pi$
$942$	5.33271	0.173749
$943$	11.0160	0.358731
$944$	−1.47229	−0.0479188
$945$	2.89358	0.0941282
$946$	−2.74993	−0.0894080
$947$	27.1613	0.882622	0.441311	−	0.897354i	$-0.354513\pi$
$947$	27.1613	0.882622	0.441311	+	0.897354i	$0.354513\pi$
$948$	2.24689	0.0729756
$949$	14.2476	0.462496
$950$	76.5211	2.48267
$951$	32.0470	1.03920
$952$	2.80086	0.0907765
$953$	−15.8804	−0.514418	−0.257209	−	0.966356i	$-0.582803\pi$
$953$	−15.8804	−0.514418	−0.257209	+	0.966356i	$0.582803\pi$
$954$	7.11956	0.230504
$955$	4.87678	0.157809
$956$	−7.09783	−0.229560
$957$	2.17957	0.0704553
$958$	23.5250	0.760058
$959$	−16.4853	−0.532338
$960$	−4.00088	−0.129128
$961$	−5.26319	−0.169780
$962$	−6.10038	−0.196684
$963$	−4.37700	−0.141047
$964$	−27.8766	−0.897844
$965$	−62.7377	−2.01960
$966$	−1.27632	−0.0410649
$967$	−49.6529	−1.59673	−0.798364	−	0.602175i	$-0.794301\pi$
$967$	−49.6529	−1.59673	−0.798364	+	0.602175i	$0.794301\pi$
$968$	−1.00000	−0.0321412
$969$	26.9229	0.864889
$970$	−17.0160	−0.546352
$971$	24.2703	0.778870	0.389435	−	0.921054i	$-0.372670\pi$
$971$	24.2703	0.778870	0.389435	+	0.921054i	$0.372670\pi$
$972$	−1.00000	−0.0320750
$973$	12.7103	0.407473
$974$	−12.8278	−0.411028
$975$	62.0513	1.98723
$976$	−1.00000	−0.0320092
$977$	−45.8884	−1.46810	−0.734050	−	0.679095i	$-0.762372\pi$
$977$	−45.8884	−1.46810	−0.734050	+	0.679095i	$0.762372\pi$
$978$	1.79925	0.0575335
$979$	15.4941	0.495195
$980$	−25.9134	−0.827774
$981$	−13.0736	−0.417409
$982$	32.3200	1.03137
$983$	−12.1094	−0.386229	−0.193114	−	0.981176i	$-0.561859\pi$
$983$	−12.1094	−0.386229	−0.193114	+	0.981176i	$0.561859\pi$
$984$	6.24231	0.198998
$985$	−61.5386	−1.96078
$986$	−8.44077	−0.268809
$987$	−1.76788	−0.0562724
$988$	39.1914	1.24684
$989$	−4.85290	−0.154313
$990$	4.00088	0.127156
$991$	16.3700	0.520011	0.260006	−	0.965607i	$-0.416276\pi$
$991$	16.3700	0.520011	0.260006	+	0.965607i	$0.416276\pi$
$992$	5.07315	0.161073
$993$	−22.7888	−0.723180
$994$	−3.25832	−0.103348
$995$	−5.86430	−0.185911
$996$	9.99351	0.316656
$997$	−8.90683	−0.282082	−0.141041	−	0.990004i	$-0.545045\pi$
$997$	−8.90683	−0.282082	−0.141041	+	0.990004i	$0.545045\pi$
$998$	24.8170	0.785567
$999$	1.08212	0.0342369

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4026.2.a.y.1.7	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4026.2.a.y.1.7	✓	7	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4026.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +4.00088 q^{5} +1.00000 q^{6} -0.723236 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +4.00088 q^{5} +1.00000 q^{6} -0.723236 q^{7} -1.00000 q^{8} +1.00000 q^{9} -4.00088 q^{10} -1.00000 q^{11} -1.00000 q^{12} -5.63742 q^{13} +0.723236 q^{14} -4.00088 q^{15} +1.00000 q^{16} +3.87268 q^{17} -1.00000 q^{18} -6.95201 q^{19} +4.00088 q^{20} +0.723236 q^{21} +1.00000 q^{22} +1.76473 q^{23} +1.00000 q^{24} +11.0070 q^{25} +5.63742 q^{26} -1.00000 q^{27} -0.723236 q^{28} +2.17957 q^{29} +4.00088 q^{30} -5.07315 q^{31} -1.00000 q^{32} +1.00000 q^{33} -3.87268 q^{34} -2.89358 q^{35} +1.00000 q^{36} -1.08212 q^{37} +6.95201 q^{38} +5.63742 q^{39} -4.00088 q^{40} +6.24231 q^{41} -0.723236 q^{42} -2.74993 q^{43} -1.00000 q^{44} +4.00088 q^{45} -1.76473 q^{46} -2.44441 q^{47} -1.00000 q^{48} -6.47693 q^{49} -11.0070 q^{50} -3.87268 q^{51} -5.63742 q^{52} -7.11956 q^{53} +1.00000 q^{54} -4.00088 q^{55} +0.723236 q^{56} +6.95201 q^{57} -2.17957 q^{58} -1.47229 q^{59} -4.00088 q^{60} -1.00000 q^{61} +5.07315 q^{62} -0.723236 q^{63} +1.00000 q^{64} -22.5546 q^{65} -1.00000 q^{66} +2.22180 q^{67} +3.87268 q^{68} -1.76473 q^{69} +2.89358 q^{70} -4.50520 q^{71} -1.00000 q^{72} -2.52732 q^{73} +1.08212 q^{74} -11.0070 q^{75} -6.95201 q^{76} +0.723236 q^{77} -5.63742 q^{78} -2.24689 q^{79} +4.00088 q^{80} +1.00000 q^{81} -6.24231 q^{82} -9.99351 q^{83} +0.723236 q^{84} +15.4941 q^{85} +2.74993 q^{86} -2.17957 q^{87} +1.00000 q^{88} -15.4941 q^{89} -4.00088 q^{90} +4.07718 q^{91} +1.76473 q^{92} +5.07315 q^{93} +2.44441 q^{94} -27.8142 q^{95} +1.00000 q^{96} +4.25307 q^{97} +6.47693 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} - 2 q^{5} + 7 q^{6} + q^{7} - 7 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 - 2 * q^5 + 7 * q^6 + q^7 - 7 * q^8 + 7 * q^9	\( 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} - 2 q^{5} + 7 q^{6} + q^{7} - 7 q^{8} + 7 q^{9} + 2 q^{10} - 7 q^{11} - 7 q^{12} - q^{14} + 2 q^{15} + 7 q^{16} + 3 q^{17} - 7 q^{18} - 5 q^{19} - 2 q^{20} - q^{21} + 7 q^{22} - 3 q^{23} + 7 q^{24} + 11 q^{25} - 7 q^{27} + q^{28} - 14 q^{29} - 2 q^{30} + 5 q^{31} - 7 q^{32} + 7 q^{33} - 3 q^{34} - 9 q^{35} + 7 q^{36} + 14 q^{37} + 5 q^{38} + 2 q^{40} - 7 q^{41} + q^{42} + q^{43} - 7 q^{44} - 2 q^{45} + 3 q^{46} - 7 q^{48} - 11 q^{50} - 3 q^{51} - 3 q^{53} + 7 q^{54} + 2 q^{55} - q^{56} + 5 q^{57} + 14 q^{58} - 14 q^{59} + 2 q^{60} - 7 q^{61} - 5 q^{62} + q^{63} + 7 q^{64} - 10 q^{65} - 7 q^{66} + 3 q^{68} + 3 q^{69} + 9 q^{70} - 22 q^{71} - 7 q^{72} + q^{73} - 14 q^{74} - 11 q^{75} - 5 q^{76} - q^{77} + 10 q^{79} - 2 q^{80} + 7 q^{81} + 7 q^{82} - 17 q^{83} - q^{84} + 18 q^{85} - q^{86} + 14 q^{87} + 7 q^{88} - 18 q^{89} + 2 q^{90} + 21 q^{91} - 3 q^{92} - 5 q^{93} - 41 q^{95} + 7 q^{96} + 25 q^{97} - 7 q^{99}+O(q^{100}) \) 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 - 2 * q^5 + 7 * q^6 + q^7 - 7 * q^8 + 7 * q^9 + 2 * q^10 - 7 * q^11 - 7 * q^12 - q^14 + 2 * q^15 + 7 * q^16 + 3 * q^17 - 7 * q^18 - 5 * q^19 - 2 * q^20 - q^21 + 7 * q^22 - 3 * q^23 + 7 * q^24 + 11 * q^25 - 7 * q^27 + q^28 - 14 * q^29 - 2 * q^30 + 5 * q^31 - 7 * q^32 + 7 * q^33 - 3 * q^34 - 9 * q^35 + 7 * q^36 + 14 * q^37 + 5 * q^38 + 2 * q^40 - 7 * q^41 + q^42 + q^43 - 7 * q^44 - 2 * q^45 + 3 * q^46 - 7 * q^48 - 11 * q^50 - 3 * q^51 - 3 * q^53 + 7 * q^54 + 2 * q^55 - q^56 + 5 * q^57 + 14 * q^58 - 14 * q^59 + 2 * q^60 - 7 * q^61 - 5 * q^62 + q^63 + 7 * q^64 - 10 * q^65 - 7 * q^66 + 3 * q^68 + 3 * q^69 + 9 * q^70 - 22 * q^71 - 7 * q^72 + q^73 - 14 * q^74 - 11 * q^75 - 5 * q^76 - q^77 + 10 * q^79 - 2 * q^80 + 7 * q^81 + 7 * q^82 - 17 * q^83 - q^84 + 18 * q^85 - q^86 + 14 * q^87 + 7 * q^88 - 18 * q^89 + 2 * q^90 + 21 * q^91 - 3 * q^92 - 5 * q^93 - 41 * q^95 + 7 * q^96 + 25 * q^97 - 7 * q^99

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