LMFDB - Embedded newform 4026.2.a.bc.1.6

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:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - x^{8} - 30x^{7} + 7x^{6} + 284x^{5} + 100x^{4} - 777x^{3} - 250x^{2} + 574x - 68 $ x^9 - x^8 - 30x^7 + 7x^6 + 284x^5 + 100x^4 - 777x^3 - 250x^2 + 574*x - 68
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-1.48002$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.48002 q^{5} +1.00000 q^{6} +3.05465 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.48002 q^{5} +1.00000 q^{6} +3.05465 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.48002 q^{10} +1.00000 q^{11} +1.00000 q^{12} -0.563179 q^{13} +3.05465 q^{14} +2.48002 q^{15} +1.00000 q^{16} -7.92722 q^{17} +1.00000 q^{18} +2.52127 q^{19} +2.48002 q^{20} +3.05465 q^{21} +1.00000 q^{22} +5.23607 q^{23} +1.00000 q^{24} +1.15051 q^{25} -0.563179 q^{26} +1.00000 q^{27} +3.05465 q^{28} -6.06505 q^{29} +2.48002 q^{30} +9.71609 q^{31} +1.00000 q^{32} +1.00000 q^{33} -7.92722 q^{34} +7.57560 q^{35} +1.00000 q^{36} -0.209636 q^{37} +2.52127 q^{38} -0.563179 q^{39} +2.48002 q^{40} -8.94907 q^{41} +3.05465 q^{42} +11.5248 q^{43} +1.00000 q^{44} +2.48002 q^{45} +5.23607 q^{46} -11.1915 q^{47} +1.00000 q^{48} +2.33089 q^{49} +1.15051 q^{50} -7.92722 q^{51} -0.563179 q^{52} +10.0107 q^{53} +1.00000 q^{54} +2.48002 q^{55} +3.05465 q^{56} +2.52127 q^{57} -6.06505 q^{58} +6.44123 q^{59} +2.48002 q^{60} -1.00000 q^{61} +9.71609 q^{62} +3.05465 q^{63} +1.00000 q^{64} -1.39670 q^{65} +1.00000 q^{66} +0.884771 q^{67} -7.92722 q^{68} +5.23607 q^{69} +7.57560 q^{70} -0.510840 q^{71} +1.00000 q^{72} -9.15175 q^{73} -0.209636 q^{74} +1.15051 q^{75} +2.52127 q^{76} +3.05465 q^{77} -0.563179 q^{78} -11.7545 q^{79} +2.48002 q^{80} +1.00000 q^{81} -8.94907 q^{82} +9.91345 q^{83} +3.05465 q^{84} -19.6597 q^{85} +11.5248 q^{86} -6.06505 q^{87} +1.00000 q^{88} -6.04252 q^{89} +2.48002 q^{90} -1.72031 q^{91} +5.23607 q^{92} +9.71609 q^{93} -11.1915 q^{94} +6.25281 q^{95} +1.00000 q^{96} -1.64385 q^{97} +2.33089 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 9 q^{2} + 9 q^{3} + 9 q^{4} + 8 q^{5} + 9 q^{6} + 9 q^{7} + 9 q^{8} + 9 q^{9}+O(q^{10}) $ 9 * q + 9 * q^2 + 9 * q^3 + 9 * q^4 + 8 * q^5 + 9 * q^6 + 9 * q^7 + 9 * q^8 + 9 * q^9	\( 9 q + 9 q^{2} + 9 q^{3} + 9 q^{4} + 8 q^{5} + 9 q^{6} + 9 q^{7} + 9 q^{8} + 9 q^{9} + 8 q^{10} + 9 q^{11} + 9 q^{12} + 8 q^{13} + 9 q^{14} + 8 q^{15} + 9 q^{16} + q^{17} + 9 q^{18} + 5 q^{19} + 8 q^{20} + 9 q^{21} + 9 q^{22} - q^{23} + 9 q^{24} + 23 q^{25} + 8 q^{26} + 9 q^{27} + 9 q^{28} - 14 q^{29} + 8 q^{30} + 25 q^{31} + 9 q^{32} + 9 q^{33} + q^{34} + 5 q^{35} + 9 q^{36} + 16 q^{37} + 5 q^{38} + 8 q^{39} + 8 q^{40} + 5 q^{41} + 9 q^{42} + 5 q^{43} + 9 q^{44} + 8 q^{45} - q^{46} + 8 q^{47} + 9 q^{48} + 30 q^{49} + 23 q^{50} + q^{51} + 8 q^{52} + q^{53} + 9 q^{54} + 8 q^{55} + 9 q^{56} + 5 q^{57} - 14 q^{58} + 4 q^{59} + 8 q^{60} - 9 q^{61} + 25 q^{62} + 9 q^{63} + 9 q^{64} - 14 q^{65} + 9 q^{66} - 4 q^{67} + q^{68} - q^{69} + 5 q^{70} + 20 q^{71} + 9 q^{72} + 15 q^{73} + 16 q^{74} + 23 q^{75} + 5 q^{76} + 9 q^{77} + 8 q^{78} - 2 q^{79} + 8 q^{80} + 9 q^{81} + 5 q^{82} + 21 q^{83} + 9 q^{84} - 16 q^{85} + 5 q^{86} - 14 q^{87} + 9 q^{88} + 10 q^{89} + 8 q^{90} - 19 q^{91} - q^{92} + 25 q^{93} + 8 q^{94} - 7 q^{95} + 9 q^{96} + 3 q^{97} + 30 q^{98} + 9 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 + 9 * q^3 + 9 * q^4 + 8 * q^5 + 9 * q^6 + 9 * q^7 + 9 * q^8 + 9 * q^9 + 8 * q^10 + 9 * q^11 + 9 * q^12 + 8 * q^13 + 9 * q^14 + 8 * q^15 + 9 * q^16 + q^17 + 9 * q^18 + 5 * q^19 + 8 * q^20 + 9 * q^21 + 9 * q^22 - q^23 + 9 * q^24 + 23 * q^25 + 8 * q^26 + 9 * q^27 + 9 * q^28 - 14 * q^29 + 8 * q^30 + 25 * q^31 + 9 * q^32 + 9 * q^33 + q^34 + 5 * q^35 + 9 * q^36 + 16 * q^37 + 5 * q^38 + 8 * q^39 + 8 * q^40 + 5 * q^41 + 9 * q^42 + 5 * q^43 + 9 * q^44 + 8 * q^45 - q^46 + 8 * q^47 + 9 * q^48 + 30 * q^49 + 23 * q^50 + q^51 + 8 * q^52 + q^53 + 9 * q^54 + 8 * q^55 + 9 * q^56 + 5 * q^57 - 14 * q^58 + 4 * q^59 + 8 * q^60 - 9 * q^61 + 25 * q^62 + 9 * q^63 + 9 * q^64 - 14 * q^65 + 9 * q^66 - 4 * q^67 + q^68 - q^69 + 5 * q^70 + 20 * q^71 + 9 * q^72 + 15 * q^73 + 16 * q^74 + 23 * q^75 + 5 * q^76 + 9 * q^77 + 8 * q^78 - 2 * q^79 + 8 * q^80 + 9 * q^81 + 5 * q^82 + 21 * q^83 + 9 * q^84 - 16 * q^85 + 5 * q^86 - 14 * q^87 + 9 * q^88 + 10 * q^89 + 8 * q^90 - 19 * q^91 - q^92 + 25 * q^93 + 8 * q^94 - 7 * q^95 + 9 * q^96 + 3 * q^97 + 30 * q^98 + 9 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	2.48002	1.10910	0.554550	−	0.832151i	$-0.312890\pi$
$5$	2.48002	1.10910	0.554550	+	0.832151i	$0.312890\pi$
$6$	1.00000	0.408248
$7$	3.05465	1.15455	0.577275	−	0.816550i	$-0.304116\pi$
$7$	3.05465	1.15455	0.577275	+	0.816550i	$0.304116\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	2.48002	0.784252
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.00000	0.288675
$13$	−0.563179	−0.156198	−0.0780989	−	0.996946i	$-0.524885\pi$
$13$	−0.563179	−0.156198	−0.0780989	+	0.996946i	$0.524885\pi$
$14$	3.05465	0.816390
$15$	2.48002	0.640339
$16$	1.00000	0.250000
$17$	−7.92722	−1.92263	−0.961317	−	0.275446i	$-0.911174\pi$
$17$	−7.92722	−1.92263	−0.961317	+	0.275446i	$0.911174\pi$
$18$	1.00000	0.235702
$19$	2.52127	0.578419	0.289210	−	0.957266i	$-0.406607\pi$
$19$	2.52127	0.578419	0.289210	+	0.957266i	$0.406607\pi$
$20$	2.48002	0.554550
$21$	3.05465	0.666579
$22$	1.00000	0.213201
$23$	5.23607	1.09180	0.545898	−	0.837852i	$-0.316189\pi$
$23$	5.23607	1.09180	0.545898	+	0.837852i	$0.316189\pi$
$24$	1.00000	0.204124
$25$	1.15051	0.230102
$26$	−0.563179	−0.110448
$27$	1.00000	0.192450
$28$	3.05465	0.577275
$29$	−6.06505	−1.12625	−0.563126	−	0.826371i	$-0.690401\pi$
$29$	−6.06505	−1.12625	−0.563126	+	0.826371i	$0.690401\pi$
$30$	2.48002	0.452788
$31$	9.71609	1.74506	0.872531	−	0.488559i	$-0.162477\pi$
$31$	9.71609	1.74506	0.872531	+	0.488559i	$0.162477\pi$
$32$	1.00000	0.176777
$33$	1.00000	0.174078
$34$	−7.92722	−1.35951
$35$	7.57560	1.28051
$36$	1.00000	0.166667
$37$	−0.209636	−0.0344640	−0.0172320	−	0.999852i	$-0.505485\pi$
$37$	−0.209636	−0.0344640	−0.0172320	+	0.999852i	$0.505485\pi$
$38$	2.52127	0.409004
$39$	−0.563179	−0.0901808
$40$	2.48002	0.392126
$41$	−8.94907	−1.39761	−0.698805	−	0.715312i	$-0.746285\pi$
$41$	−8.94907	−1.39761	−0.698805	+	0.715312i	$0.746285\pi$
$42$	3.05465	0.471343
$43$	11.5248	1.75752	0.878761	−	0.477262i	$-0.158371\pi$
$43$	11.5248	1.75752	0.878761	+	0.477262i	$0.158371\pi$
$44$	1.00000	0.150756
$45$	2.48002	0.369700
$46$	5.23607	0.772016
$47$	−11.1915	−1.63245	−0.816224	−	0.577735i	$-0.803937\pi$
$47$	−11.1915	−1.63245	−0.816224	+	0.577735i	$0.803937\pi$
$48$	1.00000	0.144338
$49$	2.33089	0.332984
$50$	1.15051	0.162707
$51$	−7.92722	−1.11003
$52$	−0.563179	−0.0780989
$53$	10.0107	1.37508	0.687539	−	0.726147i	$-0.258691\pi$
$53$	10.0107	1.37508	0.687539	+	0.726147i	$0.258691\pi$
$54$	1.00000	0.136083
$55$	2.48002	0.334406
$56$	3.05465	0.408195
$57$	2.52127	0.333951
$58$	−6.06505	−0.796381
$59$	6.44123	0.838577	0.419288	−	0.907853i	$-0.362280\pi$
$59$	6.44123	0.838577	0.419288	+	0.907853i	$0.362280\pi$
$60$	2.48002	0.320170
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	9.71609	1.23394
$63$	3.05465	0.384850
$64$	1.00000	0.125000
$65$	−1.39670	−0.173239
$66$	1.00000	0.123091
$67$	0.884771	0.108092	0.0540460	−	0.998538i	$-0.482788\pi$
$67$	0.884771	0.108092	0.0540460	+	0.998538i	$0.482788\pi$
$68$	−7.92722	−0.961317
$69$	5.23607	0.630348
$70$	7.57560	0.905458
$71$	−0.510840	−0.0606256	−0.0303128	−	0.999540i	$-0.509650\pi$
$71$	−0.510840	−0.0606256	−0.0303128	+	0.999540i	$0.509650\pi$
$72$	1.00000	0.117851
$73$	−9.15175	−1.07113	−0.535566	−	0.844494i	$-0.679902\pi$
$73$	−9.15175	−1.07113	−0.535566	+	0.844494i	$0.679902\pi$
$74$	−0.209636	−0.0243697
$75$	1.15051	0.132850
$76$	2.52127	0.289210
$77$	3.05465	0.348110
$78$	−0.563179	−0.0637675
$79$	−11.7545	−1.32248	−0.661242	−	0.750172i	$-0.729971\pi$
$79$	−11.7545	−1.32248	−0.661242	+	0.750172i	$0.729971\pi$
$80$	2.48002	0.277275
$81$	1.00000	0.111111
$82$	−8.94907	−0.988260
$83$	9.91345	1.08814	0.544071	−	0.839039i	$-0.316882\pi$
$83$	9.91345	1.08814	0.544071	+	0.839039i	$0.316882\pi$
$84$	3.05465	0.333290
$85$	−19.6597	−2.13239
$86$	11.5248	1.24276
$87$	−6.06505	−0.650242
$88$	1.00000	0.106600
$89$	−6.04252	−0.640505	−0.320253	−	0.947332i	$-0.603768\pi$
$89$	−6.04252	−0.640505	−0.320253	+	0.947332i	$0.603768\pi$
$90$	2.48002	0.261417
$91$	−1.72031	−0.180338
$92$	5.23607	0.545898
$93$	9.71609	1.00751
$94$	−11.1915	−1.15432
$95$	6.25281	0.641525
$96$	1.00000	0.102062
$97$	−1.64385	−0.166908	−0.0834539	−	0.996512i	$-0.526595\pi$
$97$	−1.64385	−0.166908	−0.0834539	+	0.996512i	$0.526595\pi$
$98$	2.33089	0.235455
$99$	1.00000	0.100504
$100$	1.15051	0.115051
$101$	1.83614	0.182703	0.0913515	−	0.995819i	$-0.470881\pi$
$101$	1.83614	0.182703	0.0913515	+	0.995819i	$0.470881\pi$
$102$	−7.92722	−0.784912
$103$	14.7996	1.45824	0.729122	−	0.684384i	$-0.239929\pi$
$103$	14.7996	1.45824	0.729122	+	0.684384i	$0.239929\pi$
$104$	−0.563179	−0.0552242
$105$	7.57560	0.739303
$106$	10.0107	0.972327
$107$	8.98865	0.868965	0.434483	−	0.900680i	$-0.356931\pi$
$107$	8.98865	0.868965	0.434483	+	0.900680i	$0.356931\pi$
$108$	1.00000	0.0962250
$109$	−3.15550	−0.302242	−0.151121	−	0.988515i	$-0.548288\pi$
$109$	−3.15550	−0.302242	−0.151121	+	0.988515i	$0.548288\pi$
$110$	2.48002	0.236461
$111$	−0.209636	−0.0198978
$112$	3.05465	0.288637
$113$	−18.7992	−1.76848	−0.884238	−	0.467036i	$-0.845322\pi$
$113$	−18.7992	−1.76848	−0.884238	+	0.467036i	$0.845322\pi$
$114$	2.52127	0.236139
$115$	12.9856	1.21091
$116$	−6.06505	−0.563126
$117$	−0.563179	−0.0520659
$118$	6.44123	0.592963
$119$	−24.2149	−2.21977
$120$	2.48002	0.226394
$121$	1.00000	0.0909091
$122$	−1.00000	−0.0905357
$123$	−8.94907	−0.806911
$124$	9.71609	0.872531
$125$	−9.54682	−0.853893
$126$	3.05465	0.272130
$127$	−8.93785	−0.793106	−0.396553	−	0.918012i	$-0.629794\pi$
$127$	−8.93785	−0.793106	−0.396553	+	0.918012i	$0.629794\pi$
$128$	1.00000	0.0883883
$129$	11.5248	1.01471
$130$	−1.39670	−0.122498
$131$	−1.23327	−0.107751	−0.0538755	−	0.998548i	$-0.517157\pi$
$131$	−1.23327	−0.107751	−0.0538755	+	0.998548i	$0.517157\pi$
$132$	1.00000	0.0870388
$133$	7.70161	0.667814
$134$	0.884771	0.0764326
$135$	2.48002	0.213446
$136$	−7.92722	−0.679753
$137$	−12.5567	−1.07279	−0.536397	−	0.843966i	$-0.680215\pi$
$137$	−12.5567	−1.07279	−0.536397	+	0.843966i	$0.680215\pi$
$138$	5.23607	0.445724
$139$	1.69681	0.143922	0.0719608	−	0.997407i	$-0.477074\pi$
$139$	1.69681	0.143922	0.0719608	+	0.997407i	$0.477074\pi$
$140$	7.57560	0.640255
$141$	−11.1915	−0.942495
$142$	−0.510840	−0.0428688
$143$	−0.563179	−0.0470954
$144$	1.00000	0.0833333
$145$	−15.0415	−1.24913
$146$	−9.15175	−0.757404
$147$	2.33089	0.192249
$148$	−0.209636	−0.0172320
$149$	−11.1537	−0.913750	−0.456875	−	0.889531i	$-0.651031\pi$
$149$	−11.1537	−0.913750	−0.456875	+	0.889531i	$0.651031\pi$
$150$	1.15051	0.0939388
$151$	−24.0110	−1.95399	−0.976993	−	0.213272i	$-0.931588\pi$
$151$	−24.0110	−1.95399	−0.976993	+	0.213272i	$0.931588\pi$
$152$	2.52127	0.204502
$153$	−7.92722	−0.640878
$154$	3.05465	0.246151
$155$	24.0961	1.93545
$156$	−0.563179	−0.0450904
$157$	2.98169	0.237965	0.118982	−	0.992896i	$-0.462037\pi$
$157$	2.98169	0.237965	0.118982	+	0.992896i	$0.462037\pi$
$158$	−11.7545	−0.935138
$159$	10.0107	0.793902
$160$	2.48002	0.196063
$161$	15.9944	1.26053
$162$	1.00000	0.0785674
$163$	0.137462	0.0107668	0.00538341	−	0.999986i	$-0.498286\pi$
$163$	0.137462	0.0107668	0.00538341	+	0.999986i	$0.498286\pi$
$164$	−8.94907	−0.698805
$165$	2.48002	0.193069
$166$	9.91345	0.769433
$167$	−23.8724	−1.84730	−0.923651	−	0.383235i	$-0.874810\pi$
$167$	−23.8724	−1.84730	−0.923651	+	0.383235i	$0.874810\pi$
$168$	3.05465	0.235671
$169$	−12.6828	−0.975602
$170$	−19.6597	−1.50783
$171$	2.52127	0.192806
$172$	11.5248	0.878761
$173$	23.1350	1.75892	0.879462	−	0.475969i	$-0.157903\pi$
$173$	23.1350	1.75892	0.879462	+	0.475969i	$0.157903\pi$
$174$	−6.06505	−0.459791
$175$	3.51441	0.265664
$176$	1.00000	0.0753778
$177$	6.44123	0.484152
$178$	−6.04252	−0.452906
$179$	5.52363	0.412856	0.206428	−	0.978462i	$-0.433816\pi$
$179$	5.52363	0.412856	0.206428	+	0.978462i	$0.433816\pi$
$180$	2.48002	0.184850
$181$	13.7332	1.02078	0.510391	−	0.859943i	$-0.329501\pi$
$181$	13.7332	1.02078	0.510391	+	0.859943i	$0.329501\pi$
$182$	−1.72031	−0.127518
$183$	−1.00000	−0.0739221
$184$	5.23607	0.386008
$185$	−0.519903	−0.0382240
$186$	9.71609	0.712418
$187$	−7.92722	−0.579696
$188$	−11.1915	−0.816224
$189$	3.05465	0.222193
$190$	6.25281	0.453627
$191$	3.16971	0.229352	0.114676	−	0.993403i	$-0.463417\pi$
$191$	3.16971	0.229352	0.114676	+	0.993403i	$0.463417\pi$
$192$	1.00000	0.0721688
$193$	12.5415	0.902758	0.451379	−	0.892332i	$-0.350932\pi$
$193$	12.5415	0.902758	0.451379	+	0.892332i	$0.350932\pi$
$194$	−1.64385	−0.118022
$195$	−1.39670	−0.100020
$196$	2.33089	0.166492
$197$	−6.86021	−0.488769	−0.244385	−	0.969678i	$-0.578586\pi$
$197$	−6.86021	−0.488769	−0.244385	+	0.969678i	$0.578586\pi$
$198$	1.00000	0.0710669
$199$	15.1849	1.07643	0.538213	−	0.842809i	$-0.319100\pi$
$199$	15.1849	1.07643	0.538213	+	0.842809i	$0.319100\pi$
$200$	1.15051	0.0813534
$201$	0.884771	0.0624069
$202$	1.83614	0.129191
$203$	−18.5266	−1.30031
$204$	−7.92722	−0.555016
$205$	−22.1939	−1.55009
$206$	14.7996	1.03113
$207$	5.23607	0.363932
$208$	−0.563179	−0.0390494
$209$	2.52127	0.174400
$210$	7.57560	0.522766
$211$	−12.8366	−0.883708	−0.441854	−	0.897087i	$-0.645679\pi$
$211$	−12.8366	−0.883708	−0.441854	+	0.897087i	$0.645679\pi$
$212$	10.0107	0.687539
$213$	−0.510840	−0.0350022
$214$	8.98865	0.614451
$215$	28.5819	1.94927
$216$	1.00000	0.0680414
$217$	29.6793	2.01476
$218$	−3.15550	−0.213717
$219$	−9.15175	−0.618418
$220$	2.48002	0.167203
$221$	4.46444	0.300311
$222$	−0.209636	−0.0140699
$223$	−9.17245	−0.614233	−0.307116	−	0.951672i	$-0.599364\pi$
$223$	−9.17245	−0.614233	−0.307116	+	0.951672i	$0.599364\pi$
$224$	3.05465	0.204097
$225$	1.15051	0.0767007
$226$	−18.7992	−1.25050
$227$	−18.1194	−1.20263	−0.601314	−	0.799013i	$-0.705356\pi$
$227$	−18.1194	−1.20263	−0.601314	+	0.799013i	$0.705356\pi$
$228$	2.52127	0.166975
$229$	−2.69696	−0.178220	−0.0891101	−	0.996022i	$-0.528402\pi$
$229$	−2.69696	−0.178220	−0.0891101	+	0.996022i	$0.528402\pi$
$230$	12.9856	0.856243
$231$	3.05465	0.200981
$232$	−6.06505	−0.398190
$233$	23.2176	1.52104	0.760519	−	0.649315i	$-0.224945\pi$
$233$	23.2176	1.52104	0.760519	+	0.649315i	$0.224945\pi$
$234$	−0.563179	−0.0368162
$235$	−27.7552	−1.81055
$236$	6.44123	0.419288
$237$	−11.7545	−0.763537
$238$	−24.2149	−1.56962
$239$	1.27199	0.0822784	0.0411392	−	0.999153i	$-0.486901\pi$
$239$	1.27199	0.0822784	0.0411392	+	0.999153i	$0.486901\pi$
$240$	2.48002	0.160085
$241$	−3.69603	−0.238082	−0.119041	−	0.992889i	$-0.537982\pi$
$241$	−3.69603	−0.238082	−0.119041	+	0.992889i	$0.537982\pi$
$242$	1.00000	0.0642824
$243$	1.00000	0.0641500
$244$	−1.00000	−0.0640184
$245$	5.78066	0.369313
$246$	−8.94907	−0.570572
$247$	−1.41993	−0.0903478
$248$	9.71609	0.616972
$249$	9.91345	0.628239
$250$	−9.54682	−0.603794
$251$	14.6841	0.926855	0.463428	−	0.886135i	$-0.346619\pi$
$251$	14.6841	0.926855	0.463428	+	0.886135i	$0.346619\pi$
$252$	3.05465	0.192425
$253$	5.23607	0.329189
$254$	−8.93785	−0.560811
$255$	−19.6597	−1.23114
$256$	1.00000	0.0625000
$257$	14.5769	0.909284	0.454642	−	0.890674i	$-0.349767\pi$
$257$	14.5769	0.909284	0.454642	+	0.890674i	$0.349767\pi$
$258$	11.5248	0.717505
$259$	−0.640365	−0.0397904
$260$	−1.39670	−0.0866194
$261$	−6.06505	−0.375417
$262$	−1.23327	−0.0761915
$263$	5.61536	0.346258	0.173129	−	0.984899i	$-0.444612\pi$
$263$	5.61536	0.346258	0.173129	+	0.984899i	$0.444612\pi$
$264$	1.00000	0.0615457
$265$	24.8268	1.52510
$266$	7.70161	0.472216
$267$	−6.04252	−0.369796
$268$	0.884771	0.0540460
$269$	2.38580	0.145465	0.0727324	−	0.997351i	$-0.476828\pi$
$269$	2.38580	0.145465	0.0727324	+	0.997351i	$0.476828\pi$
$270$	2.48002	0.150929
$271$	9.99441	0.607117	0.303559	−	0.952813i	$-0.401825\pi$
$271$	9.99441	0.607117	0.303559	+	0.952813i	$0.401825\pi$
$272$	−7.92722	−0.480658
$273$	−1.72031	−0.104118
$274$	−12.5567	−0.758580
$275$	1.15051	0.0693784
$276$	5.23607	0.315174
$277$	−23.6176	−1.41905	−0.709523	−	0.704682i	$-0.751090\pi$
$277$	−23.6176	−1.41905	−0.709523	+	0.704682i	$0.751090\pi$
$278$	1.69681	0.101768
$279$	9.71609	0.581687
$280$	7.57560	0.452729
$281$	−3.30201	−0.196982	−0.0984908	−	0.995138i	$-0.531401\pi$
$281$	−3.30201	−0.196982	−0.0984908	+	0.995138i	$0.531401\pi$
$282$	−11.1915	−0.666444
$283$	8.84256	0.525636	0.262818	−	0.964845i	$-0.415348\pi$
$283$	8.84256	0.525636	0.262818	+	0.964845i	$0.415348\pi$
$284$	−0.510840	−0.0303128
$285$	6.25281	0.370385
$286$	−0.563179	−0.0333015
$287$	−27.3363	−1.61361
$288$	1.00000	0.0589256
$289$	45.8408	2.69652
$290$	−15.0415	−0.883265
$291$	−1.64385	−0.0963643
$292$	−9.15175	−0.535566
$293$	−9.08141	−0.530542	−0.265271	−	0.964174i	$-0.585461\pi$
$293$	−9.08141	−0.530542	−0.265271	+	0.964174i	$0.585461\pi$
$294$	2.33089	0.135940
$295$	15.9744	0.930065
$296$	−0.209636	−0.0121849
$297$	1.00000	0.0580259
$298$	−11.1537	−0.646119
$299$	−2.94884	−0.170536
$300$	1.15051	0.0664248
$301$	35.2044	2.02915
$302$	−24.0110	−1.38168
$303$	1.83614	0.105484
$304$	2.52127	0.144605
$305$	−2.48002	−0.142006
$306$	−7.92722	−0.453169
$307$	27.4504	1.56668	0.783338	−	0.621596i	$-0.213516\pi$
$307$	27.4504	1.56668	0.783338	+	0.621596i	$0.213516\pi$
$308$	3.05465	0.174055
$309$	14.7996	0.841918
$310$	24.0961	1.36857
$311$	−18.8187	−1.06711	−0.533557	−	0.845764i	$-0.679145\pi$
$311$	−18.8187	−1.06711	−0.533557	+	0.845764i	$0.679145\pi$
$312$	−0.563179	−0.0318837
$313$	3.52222	0.199087	0.0995437	−	0.995033i	$-0.468262\pi$
$313$	3.52222	0.199087	0.0995437	+	0.995033i	$0.468262\pi$
$314$	2.98169	0.168267
$315$	7.57560	0.426837
$316$	−11.7545	−0.661242
$317$	5.11337	0.287196	0.143598	−	0.989636i	$-0.454133\pi$
$317$	5.11337	0.287196	0.143598	+	0.989636i	$0.454133\pi$
$318$	10.0107	0.561373
$319$	−6.06505	−0.339578
$320$	2.48002	0.138637
$321$	8.98865	0.501697
$322$	15.9944	0.891331
$323$	−19.9867	−1.11209
$324$	1.00000	0.0555556
$325$	−0.647943	−0.0359414
$326$	0.137462	0.00761329
$327$	−3.15550	−0.174500
$328$	−8.94907	−0.494130
$329$	−34.1861	−1.88474
$330$	2.48002	0.136521
$331$	−3.31658	−0.182296	−0.0911478	−	0.995837i	$-0.529054\pi$
$331$	−3.31658	−0.182296	−0.0911478	+	0.995837i	$0.529054\pi$
$332$	9.91345	0.544071
$333$	−0.209636	−0.0114880
$334$	−23.8724	−1.30624
$335$	2.19425	0.119885
$336$	3.05465	0.166645
$337$	25.8047	1.40567	0.702836	−	0.711352i	$-0.251917\pi$
$337$	25.8047	1.40567	0.702836	+	0.711352i	$0.251917\pi$
$338$	−12.6828	−0.689855
$339$	−18.7992	−1.02103
$340$	−19.6597	−1.06620
$341$	9.71609	0.526156
$342$	2.52127	0.136335
$343$	−14.2625	−0.770103
$344$	11.5248	0.621378
$345$	12.9856	0.699119
$346$	23.1350	1.24375
$347$	10.6264	0.570454	0.285227	−	0.958460i	$-0.407931\pi$
$347$	10.6264	0.570454	0.285227	+	0.958460i	$0.407931\pi$
$348$	−6.06505	−0.325121
$349$	−8.05418	−0.431131	−0.215565	−	0.976489i	$-0.569159\pi$
$349$	−8.05418	−0.431131	−0.215565	+	0.976489i	$0.569159\pi$
$350$	3.51441	0.187853
$351$	−0.563179	−0.0300603
$352$	1.00000	0.0533002
$353$	15.8575	0.844008	0.422004	−	0.906594i	$-0.361327\pi$
$353$	15.8575	0.844008	0.422004	+	0.906594i	$0.361327\pi$
$354$	6.44123	0.342347
$355$	−1.26690	−0.0672398
$356$	−6.04252	−0.320253
$357$	−24.2149	−1.28159
$358$	5.52363	0.291933
$359$	−22.9502	−1.21127	−0.605633	−	0.795744i	$-0.707080\pi$
$359$	−22.9502	−1.21127	−0.605633	+	0.795744i	$0.707080\pi$
$360$	2.48002	0.130709
$361$	−12.6432	−0.665431
$362$	13.7332	0.721802
$363$	1.00000	0.0524864
$364$	−1.72031	−0.0901690
$365$	−22.6965	−1.18799
$366$	−1.00000	−0.0522708
$367$	−1.88699	−0.0985003	−0.0492501	−	0.998786i	$-0.515683\pi$
$367$	−1.88699	−0.0985003	−0.0492501	+	0.998786i	$0.515683\pi$
$368$	5.23607	0.272949
$369$	−8.94907	−0.465870
$370$	−0.519903	−0.0270284
$371$	30.5792	1.58760
$372$	9.71609	0.503756
$373$	−28.7332	−1.48775	−0.743875	−	0.668318i	$-0.767014\pi$
$373$	−28.7332	−1.48775	−0.743875	+	0.668318i	$0.767014\pi$
$374$	−7.92722	−0.409907
$375$	−9.54682	−0.492996
$376$	−11.1915	−0.577158
$377$	3.41571	0.175918
$378$	3.05465	0.157114
$379$	−20.4724	−1.05160	−0.525799	−	0.850609i	$-0.676234\pi$
$379$	−20.4724	−1.05160	−0.525799	+	0.850609i	$0.676234\pi$
$380$	6.25281	0.320762
$381$	−8.93785	−0.457900
$382$	3.16971	0.162177
$383$	−9.30271	−0.475346	−0.237673	−	0.971345i	$-0.576385\pi$
$383$	−9.30271	−0.475346	−0.237673	+	0.971345i	$0.576385\pi$
$384$	1.00000	0.0510310
$385$	7.57560	0.386088
$386$	12.5415	0.638346
$387$	11.5248	0.585841
$388$	−1.64385	−0.0834539
$389$	18.7260	0.949446	0.474723	−	0.880135i	$-0.342548\pi$
$389$	18.7260	0.949446	0.474723	+	0.880135i	$0.342548\pi$
$390$	−1.39670	−0.0707245
$391$	−41.5075	−2.09912
$392$	2.33089	0.117728
$393$	−1.23327	−0.0622101
$394$	−6.86021	−0.345612
$395$	−29.1514	−1.46677
$396$	1.00000	0.0502519
$397$	9.81052	0.492376	0.246188	−	0.969222i	$-0.420822\pi$
$397$	9.81052	0.492376	0.246188	+	0.969222i	$0.420822\pi$
$398$	15.1849	0.761148
$399$	7.70161	0.385563
$400$	1.15051	0.0575255
$401$	−28.6037	−1.42840	−0.714199	−	0.699942i	$-0.753209\pi$
$401$	−28.6037	−1.42840	−0.714199	+	0.699942i	$0.753209\pi$
$402$	0.884771	0.0441284
$403$	−5.47190	−0.272575
$404$	1.83614	0.0913515
$405$	2.48002	0.123233
$406$	−18.5266	−0.919461
$407$	−0.209636	−0.0103913
$408$	−7.92722	−0.392456
$409$	22.5803	1.11652	0.558262	−	0.829665i	$-0.311468\pi$
$409$	22.5803	1.11652	0.558262	+	0.829665i	$0.311468\pi$
$410$	−22.1939	−1.09608
$411$	−12.5567	−0.619378
$412$	14.7996	0.729122
$413$	19.6757	0.968178
$414$	5.23607	0.257339
$415$	24.5856	1.20686
$416$	−0.563179	−0.0276121
$417$	1.69681	0.0830931
$418$	2.52127	0.123319
$419$	10.5038	0.513142	0.256571	−	0.966525i	$-0.417407\pi$
$419$	10.5038	0.513142	0.256571	+	0.966525i	$0.417407\pi$
$420$	7.57560	0.369651
$421$	9.57254	0.466537	0.233269	−	0.972412i	$-0.425058\pi$
$421$	9.57254	0.466537	0.233269	+	0.972412i	$0.425058\pi$
$422$	−12.8366	−0.624876
$423$	−11.1915	−0.544150
$424$	10.0107	0.486164
$425$	−9.12035	−0.442402
$426$	−0.510840	−0.0247503
$427$	−3.05465	−0.147825
$428$	8.98865	0.434483
$429$	−0.563179	−0.0271905
$430$	28.5819	1.37834
$431$	22.8634	1.10129	0.550645	−	0.834740i	$-0.314382\pi$
$431$	22.8634	1.10129	0.550645	+	0.834740i	$0.314382\pi$
$432$	1.00000	0.0481125
$433$	−24.8870	−1.19599	−0.597996	−	0.801499i	$-0.704036\pi$
$433$	−24.8870	−1.19599	−0.597996	+	0.801499i	$0.704036\pi$
$434$	29.6793	1.42465
$435$	−15.0415	−0.721183
$436$	−3.15550	−0.151121
$437$	13.2016	0.631516
$438$	−9.15175	−0.437287
$439$	37.4005	1.78503	0.892514	−	0.451021i	$-0.148940\pi$
$439$	37.4005	1.78503	0.892514	+	0.451021i	$0.148940\pi$
$440$	2.48002	0.118230
$441$	2.33089	0.110995
$442$	4.46444	0.212352
$443$	4.65294	0.221068	0.110534	−	0.993872i	$-0.464744\pi$
$443$	4.65294	0.221068	0.110534	+	0.993872i	$0.464744\pi$
$444$	−0.209636	−0.00994890
$445$	−14.9856	−0.710384
$446$	−9.17245	−0.434328
$447$	−11.1537	−0.527554
$448$	3.05465	0.144319
$449$	7.34048	0.346419	0.173209	−	0.984885i	$-0.444586\pi$
$449$	7.34048	0.346419	0.173209	+	0.984885i	$0.444586\pi$
$450$	1.15051	0.0542356
$451$	−8.94907	−0.421395
$452$	−18.7992	−0.884238
$453$	−24.0110	−1.12813
$454$	−18.1194	−0.850387
$455$	−4.26642	−0.200013
$456$	2.52127	0.118069
$457$	−22.9286	−1.07256	−0.536278	−	0.844041i	$-0.680170\pi$
$457$	−22.9286	−1.07256	−0.536278	+	0.844041i	$0.680170\pi$
$458$	−2.69696	−0.126021
$459$	−7.92722	−0.370011
$460$	12.9856	0.605455
$461$	−30.3009	−1.41125	−0.705627	−	0.708584i	$-0.749334\pi$
$461$	−30.3009	−1.41125	−0.705627	+	0.708584i	$0.749334\pi$
$462$	3.05465	0.142115
$463$	−13.1614	−0.611661	−0.305831	−	0.952086i	$-0.598934\pi$
$463$	−13.1614	−0.611661	−0.305831	+	0.952086i	$0.598934\pi$
$464$	−6.06505	−0.281563
$465$	24.0961	1.11743
$466$	23.2176	1.07554
$467$	−39.2863	−1.81796	−0.908978	−	0.416845i	$-0.863136\pi$
$467$	−39.2863	−1.81796	−0.908978	+	0.416845i	$0.863136\pi$
$468$	−0.563179	−0.0260330
$469$	2.70267	0.124798
$470$	−27.7552	−1.28025
$471$	2.98169	0.137389
$472$	6.44123	0.296482
$473$	11.5248	0.529913
$474$	−11.7545	−0.539902
$475$	2.90075	0.133096
$476$	−24.2149	−1.10989
$477$	10.0107	0.458359
$478$	1.27199	0.0581796
$479$	27.5371	1.25820	0.629102	−	0.777323i	$-0.283423\pi$
$479$	27.5371	1.25820	0.629102	+	0.777323i	$0.283423\pi$
$480$	2.48002	0.113197
$481$	0.118063	0.00538320
$482$	−3.69603	−0.168350
$483$	15.9944	0.727768
$484$	1.00000	0.0454545
$485$	−4.07679	−0.185117
$486$	1.00000	0.0453609
$487$	−23.3045	−1.05603	−0.528014	−	0.849236i	$-0.677063\pi$
$487$	−23.3045	−1.05603	−0.528014	+	0.849236i	$0.677063\pi$
$488$	−1.00000	−0.0452679
$489$	0.137462	0.00621622
$490$	5.78066	0.261144
$491$	26.6058	1.20070	0.600352	−	0.799736i	$-0.295027\pi$
$491$	26.6058	1.20070	0.600352	+	0.799736i	$0.295027\pi$
$492$	−8.94907	−0.403455
$493$	48.0790	2.16537
$494$	−1.41993	−0.0638856
$495$	2.48002	0.111469
$496$	9.71609	0.436265
$497$	−1.56044	−0.0699952
$498$	9.91345	0.444232
$499$	19.4279	0.869710	0.434855	−	0.900500i	$-0.356800\pi$
$499$	19.4279	0.869710	0.434855	+	0.900500i	$0.356800\pi$
$500$	−9.54682	−0.426947
$501$	−23.8724	−1.06654
$502$	14.6841	0.655386
$503$	−1.34412	−0.0599315	−0.0299657	−	0.999551i	$-0.509540\pi$
$503$	−1.34412	−0.0599315	−0.0299657	+	0.999551i	$0.509540\pi$
$504$	3.05465	0.136065
$505$	4.55368	0.202636
$506$	5.23607	0.232772
$507$	−12.6828	−0.563264
$508$	−8.93785	−0.396553
$509$	−1.53645	−0.0681019	−0.0340509	−	0.999420i	$-0.510841\pi$
$509$	−1.53645	−0.0681019	−0.0340509	+	0.999420i	$0.510841\pi$
$510$	−19.6597	−0.870545
$511$	−27.9554	−1.23667
$512$	1.00000	0.0441942
$513$	2.52127	0.111317
$514$	14.5769	0.642961
$515$	36.7032	1.61734
$516$	11.5248	0.507353
$517$	−11.1915	−0.492202
$518$	−0.640365	−0.0281360
$519$	23.1350	1.01552
$520$	−1.39670	−0.0612492
$521$	−8.24810	−0.361356	−0.180678	−	0.983542i	$-0.557829\pi$
$521$	−8.24810	−0.361356	−0.180678	+	0.983542i	$0.557829\pi$
$522$	−6.06505	−0.265460
$523$	23.6098	1.03239	0.516193	−	0.856472i	$-0.327349\pi$
$523$	23.6098	1.03239	0.516193	+	0.856472i	$0.327349\pi$
$524$	−1.23327	−0.0538755
$525$	3.51441	0.153381
$526$	5.61536	0.244841
$527$	−77.0216	−3.35511
$528$	1.00000	0.0435194
$529$	4.41640	0.192018
$530$	24.8268	1.07841
$531$	6.44123	0.279526
$532$	7.70161	0.333907
$533$	5.03993	0.218304
$534$	−6.04252	−0.261485
$535$	22.2920	0.963769
$536$	0.884771	0.0382163
$537$	5.52363	0.238362
$538$	2.38580	0.102859
$539$	2.33089	0.100399
$540$	2.48002	0.106723
$541$	−6.18059	−0.265724	−0.132862	−	0.991135i	$-0.542417\pi$
$541$	−6.18059	−0.265724	−0.132862	+	0.991135i	$0.542417\pi$
$542$	9.99441	0.429297
$543$	13.7332	0.589349
$544$	−7.92722	−0.339877
$545$	−7.82571	−0.335217
$546$	−1.72031	−0.0736227
$547$	31.9594	1.36649	0.683243	−	0.730191i	$-0.260569\pi$
$547$	31.9594	1.36649	0.683243	+	0.730191i	$0.260569\pi$
$548$	−12.5567	−0.536397
$549$	−1.00000	−0.0426790
$550$	1.15051	0.0490579
$551$	−15.2917	−0.651446
$552$	5.23607	0.222862
$553$	−35.9059	−1.52687
$554$	−23.6176	−1.00342
$555$	−0.519903	−0.0220686
$556$	1.69681	0.0719608
$557$	20.0481	0.849465	0.424732	−	0.905319i	$-0.360368\pi$
$557$	20.0481	0.849465	0.424732	+	0.905319i	$0.360368\pi$
$558$	9.71609	0.411315
$559$	−6.49055	−0.274521
$560$	7.57560	0.320128
$561$	−7.92722	−0.334687
$562$	−3.30201	−0.139287
$563$	−28.3156	−1.19336	−0.596681	−	0.802479i	$-0.703514\pi$
$563$	−28.3156	−1.19336	−0.596681	+	0.802479i	$0.703514\pi$
$564$	−11.1915	−0.471247
$565$	−46.6223	−1.96142
$566$	8.84256	0.371681
$567$	3.05465	0.128283
$568$	−0.510840	−0.0214344
$569$	−24.2313	−1.01583	−0.507915	−	0.861407i	$-0.669584\pi$
$569$	−24.2313	−1.01583	−0.507915	+	0.861407i	$0.669584\pi$
$570$	6.25281	0.261901
$571$	31.8198	1.33162	0.665809	−	0.746122i	$-0.268087\pi$
$571$	31.8198	1.33162	0.665809	+	0.746122i	$0.268087\pi$
$572$	−0.563179	−0.0235477
$573$	3.16971	0.132417
$574$	−27.3363	−1.14099
$575$	6.02415	0.251224
$576$	1.00000	0.0416667
$577$	26.1956	1.09054	0.545268	−	0.838262i	$-0.316428\pi$
$577$	26.1956	1.09054	0.545268	+	0.838262i	$0.316428\pi$
$578$	45.8408	1.90673
$579$	12.5415	0.521207
$580$	−15.0415	−0.624563
$581$	30.2821	1.25631
$582$	−1.64385	−0.0681399
$583$	10.0107	0.414602
$584$	−9.15175	−0.378702
$585$	−1.39670	−0.0577463
$586$	−9.08141	−0.375150
$587$	−30.5834	−1.26231	−0.631156	−	0.775656i	$-0.717419\pi$
$587$	−30.5834	−1.26231	−0.631156	+	0.775656i	$0.717419\pi$
$588$	2.33089	0.0961243
$589$	24.4969	1.00938
$590$	15.9744	0.657655
$591$	−6.86021	−0.282191
$592$	−0.209636	−0.00861600
$593$	−28.1893	−1.15760	−0.578798	−	0.815471i	$-0.696478\pi$
$593$	−28.1893	−1.15760	−0.578798	+	0.815471i	$0.696478\pi$
$594$	1.00000	0.0410305
$595$	−60.0535	−2.46195
$596$	−11.1537	−0.456875
$597$	15.1849	0.621475
$598$	−2.94884	−0.120587
$599$	−12.5385	−0.512308	−0.256154	−	0.966636i	$-0.582455\pi$
$599$	−12.5385	−0.512308	−0.256154	+	0.966636i	$0.582455\pi$
$600$	1.15051	0.0469694
$601$	16.9268	0.690458	0.345229	−	0.938518i	$-0.387801\pi$
$601$	16.9268	0.690458	0.345229	+	0.938518i	$0.387801\pi$
$602$	35.2044	1.43482
$603$	0.884771	0.0360307
$604$	−24.0110	−0.976993
$605$	2.48002	0.100827
$606$	1.83614	0.0745882
$607$	37.6087	1.52649	0.763245	−	0.646109i	$-0.223605\pi$
$607$	37.6087	1.52649	0.763245	+	0.646109i	$0.223605\pi$
$608$	2.52127	0.102251
$609$	−18.5266	−0.750737
$610$	−2.48002	−0.100413
$611$	6.30282	0.254985
$612$	−7.92722	−0.320439
$613$	−39.6419	−1.60112	−0.800561	−	0.599251i	$-0.795465\pi$
$613$	−39.6419	−1.60112	−0.800561	+	0.599251i	$0.795465\pi$
$614$	27.4504	1.10781
$615$	−22.1939	−0.894944
$616$	3.05465	0.123075
$617$	−43.0664	−1.73379	−0.866894	−	0.498493i	$-0.833887\pi$
$617$	−43.0664	−1.73379	−0.866894	+	0.498493i	$0.833887\pi$
$618$	14.7996	0.595326
$619$	−14.0636	−0.565264	−0.282632	−	0.959228i	$-0.591208\pi$
$619$	−14.0636	−0.565264	−0.282632	+	0.959228i	$0.591208\pi$
$620$	24.0961	0.967723
$621$	5.23607	0.210116
$622$	−18.8187	−0.754563
$623$	−18.4578	−0.739495
$624$	−0.563179	−0.0225452
$625$	−29.4289	−1.17716
$626$	3.52222	0.140776
$627$	2.52127	0.100690
$628$	2.98169	0.118982
$629$	1.66183	0.0662616
$630$	7.57560	0.301819
$631$	−2.98845	−0.118968	−0.0594841	−	0.998229i	$-0.518946\pi$
$631$	−2.98845	−0.118968	−0.0594841	+	0.998229i	$0.518946\pi$
$632$	−11.7545	−0.467569
$633$	−12.8366	−0.510209
$634$	5.11337	0.203078
$635$	−22.1661	−0.879634
$636$	10.0107	0.396951
$637$	−1.31271	−0.0520114
$638$	−6.06505	−0.240118
$639$	−0.510840	−0.0202085
$640$	2.48002	0.0980315
$641$	3.37291	0.133222	0.0666110	−	0.997779i	$-0.478781\pi$
$641$	3.37291	0.133222	0.0666110	+	0.997779i	$0.478781\pi$
$642$	8.98865	0.354754
$643$	−32.4451	−1.27951	−0.639755	−	0.768579i	$-0.720964\pi$
$643$	−32.4451	−1.27951	−0.639755	+	0.768579i	$0.720964\pi$
$644$	15.9944	0.630266
$645$	28.5819	1.12541
$646$	−19.9867	−0.786365
$647$	12.8345	0.504575	0.252288	−	0.967652i	$-0.418817\pi$
$647$	12.8345	0.504575	0.252288	+	0.967652i	$0.418817\pi$
$648$	1.00000	0.0392837
$649$	6.44123	0.252840
$650$	−0.647943	−0.0254144
$651$	29.6793	1.16322
$652$	0.137462	0.00538341
$653$	−27.5362	−1.07757	−0.538787	−	0.842442i	$-0.681117\pi$
$653$	−27.5362	−1.07757	−0.538787	+	0.842442i	$0.681117\pi$
$654$	−3.15550	−0.123390
$655$	−3.05853	−0.119507
$656$	−8.94907	−0.349403
$657$	−9.15175	−0.357044
$658$	−34.1861	−1.33271
$659$	11.5977	0.451781	0.225891	−	0.974153i	$-0.427471\pi$
$659$	11.5977	0.451781	0.225891	+	0.974153i	$0.427471\pi$
$660$	2.48002	0.0965347
$661$	9.16858	0.356616	0.178308	−	0.983975i	$-0.442938\pi$
$661$	9.16858	0.356616	0.178308	+	0.983975i	$0.442938\pi$
$662$	−3.31658	−0.128902
$663$	4.46444	0.173385
$664$	9.91345	0.384716
$665$	19.1002	0.740672
$666$	−0.209636	−0.00812324
$667$	−31.7570	−1.22964
$668$	−23.8724	−0.923651
$669$	−9.17245	−0.354627
$670$	2.19425	0.0847713
$671$	−1.00000	−0.0386046
$672$	3.05465	0.117836
$673$	−9.77653	−0.376857	−0.188429	−	0.982087i	$-0.560339\pi$
$673$	−9.77653	−0.376857	−0.188429	+	0.982087i	$0.560339\pi$
$674$	25.8047	0.993960
$675$	1.15051	0.0442832
$676$	−12.6828	−0.487801
$677$	−23.6193	−0.907764	−0.453882	−	0.891062i	$-0.649961\pi$
$677$	−23.6193	−0.907764	−0.453882	+	0.891062i	$0.649961\pi$
$678$	−18.7992	−0.721978
$679$	−5.02139	−0.192703
$680$	−19.6597	−0.753914
$681$	−18.1194	−0.694338
$682$	9.71609	0.372048
$683$	8.49649	0.325109	0.162554	−	0.986700i	$-0.448027\pi$
$683$	8.49649	0.325109	0.162554	+	0.986700i	$0.448027\pi$
$684$	2.52127	0.0964032
$685$	−31.1410	−1.18983
$686$	−14.2625	−0.544545
$687$	−2.69696	−0.102895
$688$	11.5248	0.439381
$689$	−5.63783	−0.214784
$690$	12.9856	0.494352
$691$	37.9056	1.44200	0.720999	−	0.692937i	$-0.243683\pi$
$691$	37.9056	1.44200	0.720999	+	0.692937i	$0.243683\pi$
$692$	23.1350	0.879462
$693$	3.05465	0.116037
$694$	10.6264	0.403372
$695$	4.20813	0.159623
$696$	−6.06505	−0.229895
$697$	70.9413	2.68709
$698$	−8.05418	−0.304855
$699$	23.2176	0.878172
$700$	3.51441	0.132832
$701$	17.5404	0.662491	0.331245	−	0.943545i	$-0.392531\pi$
$701$	17.5404	0.662491	0.331245	+	0.943545i	$0.392531\pi$
$702$	−0.563179	−0.0212558
$703$	−0.528550	−0.0199346
$704$	1.00000	0.0376889
$705$	−27.7552	−1.04532
$706$	15.8575	0.596804
$707$	5.60877	0.210940
$708$	6.44123	0.242076
$709$	3.19203	0.119879	0.0599396	−	0.998202i	$-0.480909\pi$
$709$	3.19203	0.119879	0.0599396	+	0.998202i	$0.480909\pi$
$710$	−1.26690	−0.0475457
$711$	−11.7545	−0.440828
$712$	−6.04252	−0.226453
$713$	50.8741	1.90525
$714$	−24.2149	−0.906219
$715$	−1.39670	−0.0522335
$716$	5.52363	0.206428
$717$	1.27199	0.0475035
$718$	−22.9502	−0.856494
$719$	−8.35794	−0.311699	−0.155849	−	0.987781i	$-0.549811\pi$
$719$	−8.35794	−0.311699	−0.155849	+	0.987781i	$0.549811\pi$
$720$	2.48002	0.0924250
$721$	45.2075	1.68361
$722$	−12.6432	−0.470531
$723$	−3.69603	−0.137457
$724$	13.7332	0.510391
$725$	−6.97791	−0.259153
$726$	1.00000	0.0371135
$727$	9.05645	0.335885	0.167943	−	0.985797i	$-0.446288\pi$
$727$	9.05645	0.335885	0.167943	+	0.985797i	$0.446288\pi$
$728$	−1.72031	−0.0637591
$729$	1.00000	0.0370370
$730$	−22.6965	−0.840037
$731$	−91.3600	−3.37907
$732$	−1.00000	−0.0369611
$733$	−42.4251	−1.56701	−0.783503	−	0.621388i	$-0.786569\pi$
$733$	−42.4251	−1.56701	−0.783503	+	0.621388i	$0.786569\pi$
$734$	−1.88699	−0.0696502
$735$	5.78066	0.213223
$736$	5.23607	0.193004
$737$	0.884771	0.0325910
$738$	−8.94907	−0.329420
$739$	1.48944	0.0547898	0.0273949	−	0.999625i	$-0.491279\pi$
$739$	1.48944	0.0547898	0.0273949	+	0.999625i	$0.491279\pi$
$740$	−0.519903	−0.0191120
$741$	−1.41993	−0.0521623
$742$	30.5792	1.12260
$743$	2.22990	0.0818072	0.0409036	−	0.999163i	$-0.486976\pi$
$743$	2.22990	0.0818072	0.0409036	+	0.999163i	$0.486976\pi$
$744$	9.71609	0.356209
$745$	−27.6615	−1.01344
$746$	−28.7332	−1.05200
$747$	9.91345	0.362714
$748$	−7.92722	−0.289848
$749$	27.4572	1.00326
$750$	−9.54682	−0.348601
$751$	−39.7426	−1.45023	−0.725114	−	0.688629i	$-0.758213\pi$
$751$	−39.7426	−1.45023	−0.725114	+	0.688629i	$0.758213\pi$
$752$	−11.1915	−0.408112
$753$	14.6841	0.535120
$754$	3.41571	0.124393
$755$	−59.5478	−2.16716
$756$	3.05465	0.111097
$757$	−4.74560	−0.172482	−0.0862409	−	0.996274i	$-0.527485\pi$
$757$	−4.74560	−0.172482	−0.0862409	+	0.996274i	$0.527485\pi$
$758$	−20.4724	−0.743592
$759$	5.23607	0.190057
$760$	6.25281	0.226813
$761$	−43.2710	−1.56857	−0.784285	−	0.620400i	$-0.786970\pi$
$761$	−43.2710	−1.56857	−0.784285	+	0.620400i	$0.786970\pi$
$762$	−8.93785	−0.323784
$763$	−9.63895	−0.348953
$764$	3.16971	0.114676
$765$	−19.6597	−0.710797
$766$	−9.30271	−0.336121
$767$	−3.62756	−0.130984
$768$	1.00000	0.0360844
$769$	−8.05143	−0.290342	−0.145171	−	0.989407i	$-0.546373\pi$
$769$	−8.05143	−0.290342	−0.145171	+	0.989407i	$0.546373\pi$
$770$	7.57560	0.273006
$771$	14.5769	0.524975
$772$	12.5415	0.451379
$773$	16.4522	0.591743	0.295871	−	0.955228i	$-0.404390\pi$
$773$	16.4522	0.591743	0.295871	+	0.955228i	$0.404390\pi$
$774$	11.5248	0.414252
$775$	11.1785	0.401542
$776$	−1.64385	−0.0590108
$777$	−0.640365	−0.0229730
$778$	18.7260	0.671359
$779$	−22.5630	−0.808405
$780$	−1.39670	−0.0500098
$781$	−0.510840	−0.0182793
$782$	−41.5075	−1.48430
$783$	−6.06505	−0.216747
$784$	2.33089	0.0832461
$785$	7.39466	0.263927
$786$	−1.23327	−0.0439892
$787$	7.94206	0.283104	0.141552	−	0.989931i	$-0.454791\pi$
$787$	7.94206	0.283104	0.141552	+	0.989931i	$0.454791\pi$
$788$	−6.86021	−0.244385
$789$	5.61536	0.199912
$790$	−29.1514	−1.03716
$791$	−57.4249	−2.04179
$792$	1.00000	0.0355335
$793$	0.563179	0.0199991
$794$	9.81052	0.348162
$795$	24.8268	0.880516
$796$	15.1849	0.538213
$797$	15.9814	0.566089	0.283045	−	0.959107i	$-0.408656\pi$
$797$	15.9814	0.566089	0.283045	+	0.959107i	$0.408656\pi$
$798$	7.70161	0.272634
$799$	88.7175	3.13860
$800$	1.15051	0.0406767
$801$	−6.04252	−0.213502
$802$	−28.6037	−1.01003
$803$	−9.15175	−0.322958
$804$	0.884771	0.0312035
$805$	39.6664	1.39806
$806$	−5.47190	−0.192739
$807$	2.38580	0.0839841
$808$	1.83614	0.0645953
$809$	−14.8680	−0.522730	−0.261365	−	0.965240i	$-0.584173\pi$
$809$	−14.8680	−0.522730	−0.261365	+	0.965240i	$0.584173\pi$
$810$	2.48002	0.0871391
$811$	−2.72880	−0.0958212	−0.0479106	−	0.998852i	$-0.515256\pi$
$811$	−2.72880	−0.0958212	−0.0479106	+	0.998852i	$0.515256\pi$
$812$	−18.5266	−0.650157
$813$	9.99441	0.350519
$814$	−0.209636	−0.00734775
$815$	0.340908	0.0119415
$816$	−7.92722	−0.277508
$817$	29.0573	1.01659
$818$	22.5803	0.789502
$819$	−1.72031	−0.0601127
$820$	−22.1939	−0.775045
$821$	−52.2326	−1.82293	−0.911465	−	0.411378i	$-0.865048\pi$
$821$	−52.2326	−1.82293	−0.911465	+	0.411378i	$0.865048\pi$
$822$	−12.5567	−0.437966
$823$	−16.5978	−0.578563	−0.289282	−	0.957244i	$-0.593416\pi$
$823$	−16.5978	−0.578563	−0.289282	+	0.957244i	$0.593416\pi$
$824$	14.7996	0.515567
$825$	1.15051	0.0400556
$826$	19.6757	0.684605
$827$	−23.7169	−0.824718	−0.412359	−	0.911021i	$-0.635295\pi$
$827$	−23.7169	−0.824718	−0.412359	+	0.911021i	$0.635295\pi$
$828$	5.23607	0.181966
$829$	29.9201	1.03917	0.519585	−	0.854419i	$-0.326087\pi$
$829$	29.9201	1.03917	0.519585	+	0.854419i	$0.326087\pi$
$830$	24.5856	0.853378
$831$	−23.6176	−0.819286
$832$	−0.563179	−0.0195247
$833$	−18.4775	−0.640206
$834$	1.69681	0.0587557
$835$	−59.2041	−2.04884
$836$	2.52127	0.0872000
$837$	9.71609	0.335837
$838$	10.5038	0.362846
$839$	31.8873	1.10087	0.550435	−	0.834878i	$-0.314462\pi$
$839$	31.8873	1.10087	0.550435	+	0.834878i	$0.314462\pi$
$840$	7.57560	0.261383
$841$	7.78488	0.268444
$842$	9.57254	0.329892
$843$	−3.30201	−0.113727
$844$	−12.8366	−0.441854
$845$	−31.4537	−1.08204
$846$	−11.1915	−0.384772
$847$	3.05465	0.104959
$848$	10.0107	0.343770
$849$	8.84256	0.303476
$850$	−9.12035	−0.312825
$851$	−1.09767	−0.0376276
$852$	−0.510840	−0.0175011
$853$	6.82860	0.233807	0.116903	−	0.993143i	$-0.462703\pi$
$853$	6.82860	0.233807	0.116903	+	0.993143i	$0.462703\pi$
$854$	−3.05465	−0.104528
$855$	6.25281	0.213842
$856$	8.98865	0.307226
$857$	55.5248	1.89669	0.948345	−	0.317241i	$-0.102756\pi$
$857$	55.5248	1.89669	0.948345	+	0.317241i	$0.102756\pi$
$858$	−0.563179	−0.0192266
$859$	40.5582	1.38383	0.691914	−	0.721980i	$-0.256768\pi$
$859$	40.5582	1.38383	0.691914	+	0.721980i	$0.256768\pi$
$860$	28.5819	0.974634
$861$	−27.3363	−0.931618
$862$	22.8634	0.778729
$863$	−37.9939	−1.29333	−0.646664	−	0.762775i	$-0.723836\pi$
$863$	−37.9939	−1.29333	−0.646664	+	0.762775i	$0.723836\pi$
$864$	1.00000	0.0340207
$865$	57.3754	1.95082
$866$	−24.8870	−0.845694
$867$	45.8408	1.55684
$868$	29.6793	1.00738
$869$	−11.7545	−0.398744
$870$	−15.0415	−0.509954
$871$	−0.498284	−0.0168837
$872$	−3.15550	−0.106859
$873$	−1.64385	−0.0556360
$874$	13.2016	0.446549
$875$	−29.1622	−0.985862
$876$	−9.15175	−0.309209
$877$	−21.1864	−0.715415	−0.357708	−	0.933834i	$-0.616442\pi$
$877$	−21.1864	−0.715415	−0.357708	+	0.933834i	$0.616442\pi$
$878$	37.4005	1.26220
$879$	−9.08141	−0.306308
$880$	2.48002	0.0836015
$881$	47.6282	1.60464	0.802318	−	0.596897i	$-0.203600\pi$
$881$	47.6282	1.60464	0.802318	+	0.596897i	$0.203600\pi$
$882$	2.33089	0.0784851
$883$	20.3471	0.684735	0.342367	−	0.939566i	$-0.388771\pi$
$883$	20.3471	0.684735	0.342367	+	0.939566i	$0.388771\pi$
$884$	4.46444	0.150155
$885$	15.9744	0.536973
$886$	4.65294	0.156319
$887$	10.3078	0.346101	0.173050	−	0.984913i	$-0.444638\pi$
$887$	10.3078	0.346101	0.173050	+	0.984913i	$0.444638\pi$
$888$	−0.209636	−0.00703493
$889$	−27.3020	−0.915680
$890$	−14.9856	−0.502318
$891$	1.00000	0.0335013
$892$	−9.17245	−0.307116
$893$	−28.2168	−0.944240
$894$	−11.1537	−0.373037
$895$	13.6987	0.457898
$896$	3.05465	0.102049
$897$	−2.94884	−0.0984590
$898$	7.34048	0.244955
$899$	−58.9286	−1.96538
$900$	1.15051	0.0383504
$901$	−79.3572	−2.64377
$902$	−8.94907	−0.297971
$903$	35.2044	1.17153
$904$	−18.7992	−0.625251
$905$	34.0587	1.13215
$906$	−24.0110	−0.797711
$907$	−5.06282	−0.168108	−0.0840541	−	0.996461i	$-0.526787\pi$
$907$	−5.06282	−0.168108	−0.0840541	+	0.996461i	$0.526787\pi$
$908$	−18.1194	−0.601314
$909$	1.83614	0.0609010
$910$	−4.26642	−0.141430
$911$	−25.5720	−0.847238	−0.423619	−	0.905840i	$-0.639240\pi$
$911$	−25.5720	−0.847238	−0.423619	+	0.905840i	$0.639240\pi$
$912$	2.52127	0.0834877
$913$	9.91345	0.328087
$914$	−22.9286	−0.758412
$915$	−2.48002	−0.0819870
$916$	−2.69696	−0.0891101
$917$	−3.76720	−0.124404
$918$	−7.92722	−0.261637
$919$	31.4159	1.03631	0.518157	−	0.855285i	$-0.326618\pi$
$919$	31.4159	1.03631	0.518157	+	0.855285i	$0.326618\pi$
$920$	12.9856	0.428121
$921$	27.4504	0.904521
$922$	−30.3009	−0.997907
$923$	0.287695	0.00946958
$924$	3.05465	0.100491
$925$	−0.241189	−0.00793024
$926$	−13.1614	−0.432510
$927$	14.7996	0.486081
$928$	−6.06505	−0.199095
$929$	29.5591	0.969802	0.484901	−	0.874569i	$-0.338856\pi$
$929$	29.5591	0.969802	0.484901	+	0.874569i	$0.338856\pi$
$930$	24.0961	0.790143
$931$	5.87681	0.192605
$932$	23.2176	0.760519
$933$	−18.8187	−0.616098
$934$	−39.2863	−1.28549
$935$	−19.6597	−0.642940
$936$	−0.563179	−0.0184081
$937$	48.8881	1.59711	0.798553	−	0.601925i	$-0.205599\pi$
$937$	48.8881	1.59711	0.798553	+	0.601925i	$0.205599\pi$
$938$	2.70267	0.0882452
$939$	3.52222	0.114943
$940$	−27.7552	−0.905274
$941$	47.8671	1.56042	0.780211	−	0.625516i	$-0.215111\pi$
$941$	47.8671	1.56042	0.780211	+	0.625516i	$0.215111\pi$
$942$	2.98169	0.0971488
$943$	−46.8579	−1.52590
$944$	6.44123	0.209644
$945$	7.57560	0.246434
$946$	11.5248	0.374705
$947$	48.4058	1.57298	0.786489	−	0.617604i	$-0.211897\pi$
$947$	48.4058	1.57298	0.786489	+	0.617604i	$0.211897\pi$
$948$	−11.7545	−0.381769
$949$	5.15407	0.167308
$950$	2.90075	0.0941128
$951$	5.11337	0.165813
$952$	−24.2149	−0.784809
$953$	−36.5601	−1.18430	−0.592149	−	0.805828i	$-0.701720\pi$
$953$	−36.5601	−1.18430	−0.592149	+	0.805828i	$0.701720\pi$
$954$	10.0107	0.324109
$955$	7.86095	0.254374
$956$	1.27199	0.0411392
$957$	−6.06505	−0.196055
$958$	27.5371	0.889684
$959$	−38.3564	−1.23859
$960$	2.48002	0.0800424
$961$	63.4024	2.04524
$962$	0.118063	0.00380650
$963$	8.98865	0.289655
$964$	−3.69603	−0.119041
$965$	31.1032	1.00125
$966$	15.9944	0.514610
$967$	27.2489	0.876267	0.438133	−	0.898910i	$-0.355640\pi$
$967$	27.2489	0.876267	0.438133	+	0.898910i	$0.355640\pi$
$968$	1.00000	0.0321412
$969$	−19.9867	−0.642065
$970$	−4.07679	−0.130898
$971$	−1.38132	−0.0443285	−0.0221643	−	0.999754i	$-0.507056\pi$
$971$	−1.38132	−0.0443285	−0.0221643	+	0.999754i	$0.507056\pi$
$972$	1.00000	0.0320750
$973$	5.18316	0.166164
$974$	−23.3045	−0.746724
$975$	−0.647943	−0.0207508
$976$	−1.00000	−0.0320092
$977$	9.30511	0.297697	0.148848	−	0.988860i	$-0.452443\pi$
$977$	9.30511	0.297697	0.148848	+	0.988860i	$0.452443\pi$
$978$	0.137462	0.00439553
$979$	−6.04252	−0.193120
$980$	5.78066	0.184656
$981$	−3.15550	−0.100747
$982$	26.6058	0.849025
$983$	−10.3254	−0.329330	−0.164665	−	0.986350i	$-0.552654\pi$
$983$	−10.3254	−0.329330	−0.164665	+	0.986350i	$0.552654\pi$
$984$	−8.94907	−0.285286
$985$	−17.0135	−0.542094
$986$	48.0790	1.53115
$987$	−34.1861	−1.08816
$988$	−1.41993	−0.0451739
$989$	60.3449	1.91885
$990$	2.48002	0.0788203
$991$	49.4368	1.57041	0.785206	−	0.619234i	$-0.212557\pi$
$991$	49.4368	1.57041	0.785206	+	0.619234i	$0.212557\pi$
$992$	9.71609	0.308486
$993$	−3.31658	−0.105248
$994$	−1.56044	−0.0494941
$995$	37.6588	1.19386
$996$	9.91345	0.314120
$997$	12.9086	0.408820	0.204410	−	0.978885i	$-0.434472\pi$
$997$	12.9086	0.408820	0.204410	+	0.978885i	$0.434472\pi$
$998$	19.4279	0.614978
$999$	−0.209636	−0.00663260

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4026.2.a.bc.1.6	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4026.2.a.bc.1.6	✓	9	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.48002 q^{5} +1.00000 q^{6} +3.05465 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.48002 q^{5} +1.00000 q^{6} +3.05465 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.48002 q^{10} +1.00000 q^{11} +1.00000 q^{12} -0.563179 q^{13} +3.05465 q^{14} +2.48002 q^{15} +1.00000 q^{16} -7.92722 q^{17} +1.00000 q^{18} +2.52127 q^{19} +2.48002 q^{20} +3.05465 q^{21} +1.00000 q^{22} +5.23607 q^{23} +1.00000 q^{24} +1.15051 q^{25} -0.563179 q^{26} +1.00000 q^{27} +3.05465 q^{28} -6.06505 q^{29} +2.48002 q^{30} +9.71609 q^{31} +1.00000 q^{32} +1.00000 q^{33} -7.92722 q^{34} +7.57560 q^{35} +1.00000 q^{36} -0.209636 q^{37} +2.52127 q^{38} -0.563179 q^{39} +2.48002 q^{40} -8.94907 q^{41} +3.05465 q^{42} +11.5248 q^{43} +1.00000 q^{44} +2.48002 q^{45} +5.23607 q^{46} -11.1915 q^{47} +1.00000 q^{48} +2.33089 q^{49} +1.15051 q^{50} -7.92722 q^{51} -0.563179 q^{52} +10.0107 q^{53} +1.00000 q^{54} +2.48002 q^{55} +3.05465 q^{56} +2.52127 q^{57} -6.06505 q^{58} +6.44123 q^{59} +2.48002 q^{60} -1.00000 q^{61} +9.71609 q^{62} +3.05465 q^{63} +1.00000 q^{64} -1.39670 q^{65} +1.00000 q^{66} +0.884771 q^{67} -7.92722 q^{68} +5.23607 q^{69} +7.57560 q^{70} -0.510840 q^{71} +1.00000 q^{72} -9.15175 q^{73} -0.209636 q^{74} +1.15051 q^{75} +2.52127 q^{76} +3.05465 q^{77} -0.563179 q^{78} -11.7545 q^{79} +2.48002 q^{80} +1.00000 q^{81} -8.94907 q^{82} +9.91345 q^{83} +3.05465 q^{84} -19.6597 q^{85} +11.5248 q^{86} -6.06505 q^{87} +1.00000 q^{88} -6.04252 q^{89} +2.48002 q^{90} -1.72031 q^{91} +5.23607 q^{92} +9.71609 q^{93} -11.1915 q^{94} +6.25281 q^{95} +1.00000 q^{96} -1.64385 q^{97} +2.33089 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 9 q^{2} + 9 q^{3} + 9 q^{4} + 8 q^{5} + 9 q^{6} + 9 q^{7} + 9 q^{8} + 9 q^{9}+O(q^{10}) \) 9 * q + 9 * q^2 + 9 * q^3 + 9 * q^4 + 8 * q^5 + 9 * q^6 + 9 * q^7 + 9 * q^8 + 9 * q^9	\( 9 q + 9 q^{2} + 9 q^{3} + 9 q^{4} + 8 q^{5} + 9 q^{6} + 9 q^{7} + 9 q^{8} + 9 q^{9} + 8 q^{10} + 9 q^{11} + 9 q^{12} + 8 q^{13} + 9 q^{14} + 8 q^{15} + 9 q^{16} + q^{17} + 9 q^{18} + 5 q^{19} + 8 q^{20} + 9 q^{21} + 9 q^{22} - q^{23} + 9 q^{24} + 23 q^{25} + 8 q^{26} + 9 q^{27} + 9 q^{28} - 14 q^{29} + 8 q^{30} + 25 q^{31} + 9 q^{32} + 9 q^{33} + q^{34} + 5 q^{35} + 9 q^{36} + 16 q^{37} + 5 q^{38} + 8 q^{39} + 8 q^{40} + 5 q^{41} + 9 q^{42} + 5 q^{43} + 9 q^{44} + 8 q^{45} - q^{46} + 8 q^{47} + 9 q^{48} + 30 q^{49} + 23 q^{50} + q^{51} + 8 q^{52} + q^{53} + 9 q^{54} + 8 q^{55} + 9 q^{56} + 5 q^{57} - 14 q^{58} + 4 q^{59} + 8 q^{60} - 9 q^{61} + 25 q^{62} + 9 q^{63} + 9 q^{64} - 14 q^{65} + 9 q^{66} - 4 q^{67} + q^{68} - q^{69} + 5 q^{70} + 20 q^{71} + 9 q^{72} + 15 q^{73} + 16 q^{74} + 23 q^{75} + 5 q^{76} + 9 q^{77} + 8 q^{78} - 2 q^{79} + 8 q^{80} + 9 q^{81} + 5 q^{82} + 21 q^{83} + 9 q^{84} - 16 q^{85} + 5 q^{86} - 14 q^{87} + 9 q^{88} + 10 q^{89} + 8 q^{90} - 19 q^{91} - q^{92} + 25 q^{93} + 8 q^{94} - 7 q^{95} + 9 q^{96} + 3 q^{97} + 30 q^{98} + 9 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 + 9 * q^3 + 9 * q^4 + 8 * q^5 + 9 * q^6 + 9 * q^7 + 9 * q^8 + 9 * q^9 + 8 * q^10 + 9 * q^11 + 9 * q^12 + 8 * q^13 + 9 * q^14 + 8 * q^15 + 9 * q^16 + q^17 + 9 * q^18 + 5 * q^19 + 8 * q^20 + 9 * q^21 + 9 * q^22 - q^23 + 9 * q^24 + 23 * q^25 + 8 * q^26 + 9 * q^27 + 9 * q^28 - 14 * q^29 + 8 * q^30 + 25 * q^31 + 9 * q^32 + 9 * q^33 + q^34 + 5 * q^35 + 9 * q^36 + 16 * q^37 + 5 * q^38 + 8 * q^39 + 8 * q^40 + 5 * q^41 + 9 * q^42 + 5 * q^43 + 9 * q^44 + 8 * q^45 - q^46 + 8 * q^47 + 9 * q^48 + 30 * q^49 + 23 * q^50 + q^51 + 8 * q^52 + q^53 + 9 * q^54 + 8 * q^55 + 9 * q^56 + 5 * q^57 - 14 * q^58 + 4 * q^59 + 8 * q^60 - 9 * q^61 + 25 * q^62 + 9 * q^63 + 9 * q^64 - 14 * q^65 + 9 * q^66 - 4 * q^67 + q^68 - q^69 + 5 * q^70 + 20 * q^71 + 9 * q^72 + 15 * q^73 + 16 * q^74 + 23 * q^75 + 5 * q^76 + 9 * q^77 + 8 * q^78 - 2 * q^79 + 8 * q^80 + 9 * q^81 + 5 * q^82 + 21 * q^83 + 9 * q^84 - 16 * q^85 + 5 * q^86 - 14 * q^87 + 9 * q^88 + 10 * q^89 + 8 * q^90 - 19 * q^91 - q^92 + 25 * q^93 + 8 * q^94 - 7 * q^95 + 9 * q^96 + 3 * q^97 + 30 * q^98 + 9 * q^99

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