LMFDB - Embedded newform 453.2.a.e.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [453,2,Mod(1,453)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(453, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("453.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 453 = 3 \cdot 151 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	453.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:	$3.61722321156$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$0.445042$ of defining polynomial
Character	$\chi$	$=$	453.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.445042 q^{2} -1.00000 q^{3} -1.80194 q^{4} +2.04892 q^{5} +0.445042 q^{6} -2.49396 q^{7} +1.69202 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.445042 q^{2} -1.00000 q^{3} -1.80194 q^{4} +2.04892 q^{5} +0.445042 q^{6} -2.49396 q^{7} +1.69202 q^{8} +1.00000 q^{9} -0.911854 q^{10} +2.13706 q^{11} +1.80194 q^{12} -1.10992 q^{13} +1.10992 q^{14} -2.04892 q^{15} +2.85086 q^{16} -4.75302 q^{17} -0.445042 q^{18} -5.89977 q^{19} -3.69202 q^{20} +2.49396 q^{21} -0.951083 q^{22} -8.49396 q^{23} -1.69202 q^{24} -0.801938 q^{25} +0.493959 q^{26} -1.00000 q^{27} +4.49396 q^{28} -1.08815 q^{29} +0.911854 q^{30} +4.26875 q^{31} -4.65279 q^{32} -2.13706 q^{33} +2.11529 q^{34} -5.10992 q^{35} -1.80194 q^{36} +3.02715 q^{37} +2.62565 q^{38} +1.10992 q^{39} +3.46681 q^{40} -0.493959 q^{41} -1.10992 q^{42} -5.95108 q^{43} -3.85086 q^{44} +2.04892 q^{45} +3.78017 q^{46} -10.6136 q^{47} -2.85086 q^{48} -0.780167 q^{49} +0.356896 q^{50} +4.75302 q^{51} +2.00000 q^{52} -1.56033 q^{53} +0.445042 q^{54} +4.37867 q^{55} -4.21983 q^{56} +5.89977 q^{57} +0.484271 q^{58} +0.884707 q^{59} +3.69202 q^{60} -0.615957 q^{61} -1.89977 q^{62} -2.49396 q^{63} -3.63102 q^{64} -2.27413 q^{65} +0.951083 q^{66} +3.42758 q^{67} +8.56465 q^{68} +8.49396 q^{69} +2.27413 q^{70} -1.32975 q^{71} +1.69202 q^{72} +14.1414 q^{73} -1.34721 q^{74} +0.801938 q^{75} +10.6310 q^{76} -5.32975 q^{77} -0.493959 q^{78} -7.20775 q^{79} +5.84117 q^{80} +1.00000 q^{81} +0.219833 q^{82} +8.59179 q^{83} -4.49396 q^{84} -9.73855 q^{85} +2.64848 q^{86} +1.08815 q^{87} +3.61596 q^{88} -4.31767 q^{89} -0.911854 q^{90} +2.76809 q^{91} +15.3056 q^{92} -4.26875 q^{93} +4.72348 q^{94} -12.0881 q^{95} +4.65279 q^{96} +18.3937 q^{97} +0.347207 q^{98} +2.13706 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - q^{2} - 3 q^{3} - q^{4} - 3 q^{5} + q^{6} + 2 q^{7} + 3 q^{9}+O(q^{10}) $ 3 * q - q^2 - 3 * q^3 - q^4 - 3 * q^5 + q^6 + 2 * q^7 + 3 * q^9	\( 3 q - q^{2} - 3 q^{3} - q^{4} - 3 q^{5} + q^{6} + 2 q^{7} + 3 q^{9} + q^{10} + q^{11} + q^{12} - 4 q^{13} + 4 q^{14} + 3 q^{15} - 5 q^{16} - 19 q^{17} - q^{18} + 5 q^{19} - 6 q^{20} - 2 q^{21} - 12 q^{22} - 16 q^{23} + 2 q^{25} - 8 q^{26} - 3 q^{27} + 4 q^{28} - 7 q^{29} - q^{30} + 5 q^{31} + 4 q^{32} - q^{33} + 4 q^{34} - 16 q^{35} - q^{36} + 3 q^{37} - 4 q^{38} + 4 q^{39} + 7 q^{40} + 8 q^{41} - 4 q^{42} - 27 q^{43} + 2 q^{44} - 3 q^{45} + 10 q^{46} - q^{47} + 5 q^{48} - q^{49} - 3 q^{50} + 19 q^{51} + 6 q^{52} - 2 q^{53} + q^{54} + 6 q^{55} - 14 q^{56} - 5 q^{57} + 14 q^{58} + 5 q^{59} + 6 q^{60} - 12 q^{61} + 17 q^{62} + 2 q^{63} + 4 q^{64} + 4 q^{65} + 12 q^{66} - 6 q^{67} + 4 q^{68} + 16 q^{69} - 4 q^{70} - 6 q^{71} + 18 q^{73} - 22 q^{74} - 2 q^{75} + 17 q^{76} - 18 q^{77} + 8 q^{78} - 4 q^{79} + 26 q^{80} + 3 q^{81} + 2 q^{82} - 2 q^{83} - 4 q^{84} + 26 q^{85} + 9 q^{86} + 7 q^{87} + 21 q^{88} + 4 q^{89} + q^{90} - 12 q^{91} + 10 q^{92} - 5 q^{93} - 16 q^{94} - 40 q^{95} - 4 q^{96} + 23 q^{97} + 19 q^{98} + q^{99}+O(q^{100}) \) 3 * q - q^2 - 3 * q^3 - q^4 - 3 * q^5 + q^6 + 2 * q^7 + 3 * q^9 + q^10 + q^11 + q^12 - 4 * q^13 + 4 * q^14 + 3 * q^15 - 5 * q^16 - 19 * q^17 - q^18 + 5 * q^19 - 6 * q^20 - 2 * q^21 - 12 * q^22 - 16 * q^23 + 2 * q^25 - 8 * q^26 - 3 * q^27 + 4 * q^28 - 7 * q^29 - q^30 + 5 * q^31 + 4 * q^32 - q^33 + 4 * q^34 - 16 * q^35 - q^36 + 3 * q^37 - 4 * q^38 + 4 * q^39 + 7 * q^40 + 8 * q^41 - 4 * q^42 - 27 * q^43 + 2 * q^44 - 3 * q^45 + 10 * q^46 - q^47 + 5 * q^48 - q^49 - 3 * q^50 + 19 * q^51 + 6 * q^52 - 2 * q^53 + q^54 + 6 * q^55 - 14 * q^56 - 5 * q^57 + 14 * q^58 + 5 * q^59 + 6 * q^60 - 12 * q^61 + 17 * q^62 + 2 * q^63 + 4 * q^64 + 4 * q^65 + 12 * q^66 - 6 * q^67 + 4 * q^68 + 16 * q^69 - 4 * q^70 - 6 * q^71 + 18 * q^73 - 22 * q^74 - 2 * q^75 + 17 * q^76 - 18 * q^77 + 8 * q^78 - 4 * q^79 + 26 * q^80 + 3 * q^81 + 2 * q^82 - 2 * q^83 - 4 * q^84 + 26 * q^85 + 9 * q^86 + 7 * q^87 + 21 * q^88 + 4 * q^89 + q^90 - 12 * q^91 + 10 * q^92 - 5 * q^93 - 16 * q^94 - 40 * q^95 - 4 * q^96 + 23 * q^97 + 19 * q^98 + 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 $

$2$	−0.445042	−0.314692	−0.157346	−	0.987544i	$-0.550294\pi$
$2$	−0.445042	−0.314692	−0.157346	+	0.987544i	$0.550294\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.80194	−0.900969
$5$	2.04892	0.916304	0.458152	−	0.888874i	$-0.348512\pi$
$5$	2.04892	0.916304	0.458152	+	0.888874i	$0.348512\pi$
$6$	0.445042	0.181688
$7$	−2.49396	−0.942628	−0.471314	−	0.881965i	$-0.656220\pi$
$7$	−2.49396	−0.942628	−0.471314	+	0.881965i	$0.656220\pi$
$8$	1.69202	0.598220
$9$	1.00000	0.333333
$10$	−0.911854	−0.288354
$11$	2.13706	0.644349	0.322174	−	0.946680i	$-0.395586\pi$
$11$	2.13706	0.644349	0.322174	+	0.946680i	$0.395586\pi$
$12$	1.80194	0.520175
$13$	−1.10992	−0.307835	−0.153918	−	0.988084i	$-0.549189\pi$
$13$	−1.10992	−0.307835	−0.153918	+	0.988084i	$0.549189\pi$
$14$	1.10992	0.296638
$15$	−2.04892	−0.529028
$16$	2.85086	0.712714
$17$	−4.75302	−1.15278	−0.576388	−	0.817176i	$-0.695538\pi$
$17$	−4.75302	−1.15278	−0.576388	+	0.817176i	$0.695538\pi$
$18$	−0.445042	−0.104897
$19$	−5.89977	−1.35350	−0.676750	−	0.736213i	$-0.736612\pi$
$19$	−5.89977	−1.35350	−0.676750	+	0.736213i	$0.736612\pi$
$20$	−3.69202	−0.825561
$21$	2.49396	0.544227
$22$	−0.951083	−0.202772
$23$	−8.49396	−1.77111	−0.885556	−	0.464532i	$-0.846223\pi$
$23$	−8.49396	−1.77111	−0.885556	+	0.464532i	$0.846223\pi$
$24$	−1.69202	−0.345382
$25$	−0.801938	−0.160388
$26$	0.493959	0.0968734
$27$	−1.00000	−0.192450
$28$	4.49396	0.849278
$29$	−1.08815	−0.202064	−0.101032	−	0.994883i	$-0.532214\pi$
$29$	−1.08815	−0.202064	−0.101032	+	0.994883i	$0.532214\pi$
$30$	0.911854	0.166481
$31$	4.26875	0.766690	0.383345	−	0.923605i	$-0.374772\pi$
$31$	4.26875	0.766690	0.383345	+	0.923605i	$0.374772\pi$
$32$	−4.65279	−0.822505
$33$	−2.13706	−0.372015
$34$	2.11529	0.362770
$35$	−5.10992	−0.863733
$36$	−1.80194	−0.300323
$37$	3.02715	0.497660	0.248830	−	0.968547i	$-0.419954\pi$
$37$	3.02715	0.497660	0.248830	+	0.968547i	$0.419954\pi$
$38$	2.62565	0.425936
$39$	1.10992	0.177729
$40$	3.46681	0.548151
$41$	−0.493959	−0.0771435	−0.0385717	−	0.999256i	$-0.512281\pi$
$41$	−0.493959	−0.0771435	−0.0385717	+	0.999256i	$0.512281\pi$
$42$	−1.10992	−0.171264
$43$	−5.95108	−0.907532	−0.453766	−	0.891121i	$-0.649920\pi$
$43$	−5.95108	−0.907532	−0.453766	+	0.891121i	$0.649920\pi$
$44$	−3.85086	−0.580538
$45$	2.04892	0.305435
$46$	3.78017	0.557355
$47$	−10.6136	−1.54815	−0.774074	−	0.633095i	$-0.781784\pi$
$47$	−10.6136	−1.54815	−0.774074	+	0.633095i	$0.781784\pi$
$48$	−2.85086	−0.411485
$49$	−0.780167	−0.111452
$50$	0.356896	0.0504727
$51$	4.75302	0.665556
$52$	2.00000	0.277350
$53$	−1.56033	−0.214328	−0.107164	−	0.994241i	$-0.534177\pi$
$53$	−1.56033	−0.214328	−0.107164	+	0.994241i	$0.534177\pi$
$54$	0.445042	0.0605625
$55$	4.37867	0.590419
$56$	−4.21983	−0.563899
$57$	5.89977	0.781444
$58$	0.484271	0.0635878
$59$	0.884707	0.115179	0.0575895	−	0.998340i	$-0.481659\pi$
$59$	0.884707	0.115179	0.0575895	+	0.998340i	$0.481659\pi$
$60$	3.69202	0.476638
$61$	−0.615957	−0.0788652	−0.0394326	−	0.999222i	$-0.512555\pi$
$61$	−0.615957	−0.0788652	−0.0394326	+	0.999222i	$0.512555\pi$
$62$	−1.89977	−0.241271
$63$	−2.49396	−0.314209
$64$	−3.63102	−0.453878
$65$	−2.27413	−0.282071
$66$	0.951083	0.117070
$67$	3.42758	0.418746	0.209373	−	0.977836i	$-0.432858\pi$
$67$	3.42758	0.418746	0.209373	+	0.977836i	$0.432858\pi$
$68$	8.56465	1.03862
$69$	8.49396	1.02255
$70$	2.27413	0.271810
$71$	−1.32975	−0.157812	−0.0789061	−	0.996882i	$-0.525143\pi$
$71$	−1.32975	−0.157812	−0.0789061	+	0.996882i	$0.525143\pi$
$72$	1.69202	0.199407
$73$	14.1414	1.65512	0.827561	−	0.561375i	$-0.189728\pi$
$73$	14.1414	1.65512	0.827561	+	0.561375i	$0.189728\pi$
$74$	−1.34721	−0.156610
$75$	0.801938	0.0925998
$76$	10.6310	1.21946
$77$	−5.32975	−0.607381
$78$	−0.493959	−0.0559299
$79$	−7.20775	−0.810935	−0.405468	−	0.914109i	$-0.632891\pi$
$79$	−7.20775	−0.810935	−0.405468	+	0.914109i	$0.632891\pi$
$80$	5.84117	0.653062
$81$	1.00000	0.111111
$82$	0.219833	0.0242764
$83$	8.59179	0.943072	0.471536	−	0.881847i	$-0.343700\pi$
$83$	8.59179	0.943072	0.471536	+	0.881847i	$0.343700\pi$
$84$	−4.49396	−0.490331
$85$	−9.73855	−1.05629
$86$	2.64848	0.285593
$87$	1.08815	0.116661
$88$	3.61596	0.385462
$89$	−4.31767	−0.457672	−0.228836	−	0.973465i	$-0.573492\pi$
$89$	−4.31767	−0.457672	−0.228836	+	0.973465i	$0.573492\pi$
$90$	−0.911854	−0.0961179
$91$	2.76809	0.290174
$92$	15.3056	1.59572
$93$	−4.26875	−0.442649
$94$	4.72348	0.487190
$95$	−12.0881	−1.24022
$96$	4.65279	0.474874
$97$	18.3937	1.86760	0.933800	−	0.357795i	$-0.116471\pi$
$97$	18.3937	1.86760	0.933800	+	0.357795i	$0.116471\pi$
$98$	0.347207	0.0350732
$99$	2.13706	0.214783
$100$	1.44504	0.144504
$101$	17.7560	1.76679	0.883394	−	0.468631i	$-0.155252\pi$
$101$	17.7560	1.76679	0.883394	+	0.468631i	$0.155252\pi$
$102$	−2.11529	−0.209445
$103$	−13.5646	−1.33656	−0.668282	−	0.743908i	$-0.732970\pi$
$103$	−13.5646	−1.33656	−0.668282	+	0.743908i	$0.732970\pi$
$104$	−1.87800	−0.184153
$105$	5.10992	0.498677
$106$	0.694414	0.0674475
$107$	0.591794	0.0572109	0.0286054	−	0.999591i	$-0.490893\pi$
$107$	0.591794	0.0572109	0.0286054	+	0.999591i	$0.490893\pi$
$108$	1.80194	0.173392
$109$	17.0858	1.63652	0.818259	−	0.574849i	$-0.194939\pi$
$109$	17.0858	1.63652	0.818259	+	0.574849i	$0.194939\pi$
$110$	−1.94869	−0.185800
$111$	−3.02715	−0.287324
$112$	−7.10992	−0.671824
$113$	−11.9215	−1.12148	−0.560742	−	0.827990i	$-0.689484\pi$
$113$	−11.9215	−1.12148	−0.560742	+	0.827990i	$0.689484\pi$
$114$	−2.62565	−0.245914
$115$	−17.4034	−1.62288
$116$	1.96077	0.182053
$117$	−1.10992	−0.102612
$118$	−0.393732	−0.0362459
$119$	11.8538	1.08664
$120$	−3.46681	−0.316475
$121$	−6.43296	−0.584815
$122$	0.274127	0.0248183
$123$	0.493959	0.0445388
$124$	−7.69202	−0.690764
$125$	−11.8877	−1.06327
$126$	1.10992	0.0988792
$127$	9.25667	0.821396	0.410698	−	0.911771i	$-0.365285\pi$
$127$	9.25667	0.821396	0.410698	+	0.911771i	$0.365285\pi$
$128$	10.9215	0.965337
$129$	5.95108	0.523964
$130$	1.01208	0.0887654
$131$	−9.65817	−0.843838	−0.421919	−	0.906633i	$-0.638643\pi$
$131$	−9.65817	−0.843838	−0.421919	+	0.906633i	$0.638643\pi$
$132$	3.85086	0.335174
$133$	14.7138	1.27585
$134$	−1.52542	−0.131776
$135$	−2.04892	−0.176343
$136$	−8.04221	−0.689614
$137$	−14.0489	−1.20028	−0.600140	−	0.799895i	$-0.704888\pi$
$137$	−14.0489	−1.20028	−0.600140	+	0.799895i	$0.704888\pi$
$138$	−3.78017	−0.321789
$139$	−2.10023	−0.178139	−0.0890695	−	0.996025i	$-0.528389\pi$
$139$	−2.10023	−0.178139	−0.0890695	+	0.996025i	$0.528389\pi$
$140$	9.20775	0.778197
$141$	10.6136	0.893823
$142$	0.591794	0.0496622
$143$	−2.37196	−0.198353
$144$	2.85086	0.237571
$145$	−2.22952	−0.185152
$146$	−6.29350	−0.520854
$147$	0.780167	0.0643471
$148$	−5.45473	−0.448376
$149$	8.27413	0.677843	0.338921	−	0.940815i	$-0.389938\pi$
$149$	8.27413	0.677843	0.338921	+	0.940815i	$0.389938\pi$
$150$	−0.356896	−0.0291404
$151$	−1.00000	−0.0813788
$151$	−1.00000	−0.0813788
$152$	−9.98254	−0.809691
$153$	−4.75302	−0.384259
$154$	2.37196	0.191138
$155$	8.74632	0.702521
$156$	−2.00000	−0.160128
$157$	−19.3056	−1.54075	−0.770377	−	0.637589i	$-0.779932\pi$
$157$	−19.3056	−1.54075	−0.770377	+	0.637589i	$0.779932\pi$
$158$	3.20775	0.255195
$159$	1.56033	0.123743
$160$	−9.53319	−0.753665
$161$	21.1836	1.66950
$162$	−0.445042	−0.0349658
$163$	−7.72587	−0.605137	−0.302569	−	0.953128i	$-0.597844\pi$
$163$	−7.72587	−0.605137	−0.302569	+	0.953128i	$0.597844\pi$
$164$	0.890084	0.0695039
$165$	−4.37867	−0.340879
$166$	−3.82371	−0.296777
$167$	−2.76809	−0.214201	−0.107100	−	0.994248i	$-0.534157\pi$
$167$	−2.76809	−0.214201	−0.107100	+	0.994248i	$0.534157\pi$
$168$	4.21983	0.325567
$169$	−11.7681	−0.905237
$170$	4.33406	0.332407
$171$	−5.89977	−0.451167
$172$	10.7235	0.817658
$173$	1.13169	0.0860405	0.0430203	−	0.999074i	$-0.486302\pi$
$173$	1.13169	0.0860405	0.0430203	+	0.999074i	$0.486302\pi$
$174$	−0.484271	−0.0367125
$175$	2.00000	0.151186
$176$	6.09246	0.459236
$177$	−0.884707	−0.0664986
$178$	1.92154	0.144026
$179$	−4.39612	−0.328582	−0.164291	−	0.986412i	$-0.552534\pi$
$179$	−4.39612	−0.328582	−0.164291	+	0.986412i	$0.552534\pi$
$180$	−3.69202	−0.275187
$181$	25.6340	1.90536	0.952680	−	0.303974i	$-0.0983136\pi$
$181$	25.6340	1.90536	0.952680	+	0.303974i	$0.0983136\pi$
$182$	−1.23191	−0.0913155
$183$	0.615957	0.0455329
$184$	−14.3720	−1.05952
$185$	6.20237	0.456008
$186$	1.89977	0.139298
$187$	−10.1575	−0.742790
$188$	19.1250	1.39483
$189$	2.49396	0.181409
$190$	5.37973	0.390287
$191$	−5.22952	−0.378395	−0.189197	−	0.981939i	$-0.560589\pi$
$191$	−5.22952	−0.378395	−0.189197	+	0.981939i	$0.560589\pi$
$192$	3.63102	0.262046
$193$	3.45712	0.248849	0.124425	−	0.992229i	$-0.460292\pi$
$193$	3.45712	0.248849	0.124425	+	0.992229i	$0.460292\pi$
$194$	−8.18598	−0.587719
$195$	2.27413	0.162854
$196$	1.40581	0.100415
$197$	6.63533	0.472748	0.236374	−	0.971662i	$-0.424041\pi$
$197$	6.63533	0.472748	0.236374	+	0.971662i	$0.424041\pi$
$198$	−0.951083	−0.0675905
$199$	16.5133	1.17060	0.585300	−	0.810817i	$-0.300977\pi$
$199$	16.5133	1.17060	0.585300	+	0.810817i	$0.300977\pi$
$200$	−1.35690	−0.0959470
$201$	−3.42758	−0.241763
$202$	−7.90217	−0.555994
$203$	2.71379	0.190471
$204$	−8.56465	−0.599645
$205$	−1.01208	−0.0706868
$206$	6.03684	0.420606
$207$	−8.49396	−0.590371
$208$	−3.16421	−0.219399
$209$	−12.6082	−0.872127
$210$	−2.27413	−0.156930
$211$	−2.05429	−0.141423	−0.0707117	−	0.997497i	$-0.522527\pi$
$211$	−2.05429	−0.141423	−0.0707117	+	0.997497i	$0.522527\pi$
$212$	2.81163	0.193103
$213$	1.32975	0.0911129
$214$	−0.263373	−0.0180038
$215$	−12.1933	−0.831575
$216$	−1.69202	−0.115127
$217$	−10.6461	−0.722704
$218$	−7.60388	−0.514999
$219$	−14.1414	−0.955586
$220$	−7.89008	−0.531949
$221$	5.27545	0.354865
$222$	1.34721	0.0904186
$223$	−1.64310	−0.110030	−0.0550152	−	0.998486i	$-0.517521\pi$
$223$	−1.64310	−0.110030	−0.0550152	+	0.998486i	$0.517521\pi$
$224$	11.6039	0.775317
$225$	−0.801938	−0.0534625
$226$	5.30559	0.352922
$227$	8.19136	0.543679	0.271840	−	0.962343i	$-0.412368\pi$
$227$	8.19136	0.543679	0.271840	+	0.962343i	$0.412368\pi$
$228$	−10.6310	−0.704057
$229$	−2.55065	−0.168551	−0.0842757	−	0.996442i	$-0.526858\pi$
$229$	−2.55065	−0.168551	−0.0842757	+	0.996442i	$0.526858\pi$
$230$	7.74525	0.510707
$231$	5.32975	0.350672
$232$	−1.84117	−0.120878
$233$	−2.12200	−0.139017	−0.0695084	−	0.997581i	$-0.522143\pi$
$233$	−2.12200	−0.139017	−0.0695084	+	0.997581i	$0.522143\pi$
$234$	0.493959	0.0322911
$235$	−21.7463	−1.41857
$236$	−1.59419	−0.103773
$237$	7.20775	0.468194
$238$	−5.27545	−0.341957
$239$	−15.3991	−0.996086	−0.498043	−	0.867152i	$-0.665948\pi$
$239$	−15.3991	−0.996086	−0.498043	+	0.867152i	$0.665948\pi$
$240$	−5.84117	−0.377046
$241$	3.27114	0.210713	0.105356	−	0.994435i	$-0.466402\pi$
$241$	3.27114	0.210713	0.105356	+	0.994435i	$0.466402\pi$
$242$	2.86294	0.184037
$243$	−1.00000	−0.0641500
$244$	1.10992	0.0710551
$245$	−1.59850	−0.102124
$246$	−0.219833	−0.0140160
$247$	6.54825	0.416655
$248$	7.22282	0.458649
$249$	−8.59179	−0.544483
$250$	5.29052	0.334602
$251$	−23.8431	−1.50496	−0.752481	−	0.658614i	$-0.771143\pi$
$251$	−23.8431	−1.50496	−0.752481	+	0.658614i	$0.771143\pi$
$252$	4.49396	0.283093
$253$	−18.1521	−1.14121
$254$	−4.11960	−0.258487
$255$	9.73855	0.609851
$256$	2.40150	0.150094
$257$	−28.3913	−1.77100	−0.885502	−	0.464636i	$-0.846185\pi$
$257$	−28.3913	−1.77100	−0.885502	+	0.464636i	$0.846185\pi$
$258$	−2.64848	−0.164887
$259$	−7.54958	−0.469108
$260$	4.09783	0.254137
$261$	−1.08815	−0.0673545
$262$	4.29829	0.265549
$263$	24.7875	1.52846	0.764230	−	0.644944i	$-0.223119\pi$
$263$	24.7875	1.52846	0.764230	+	0.644944i	$0.223119\pi$
$264$	−3.61596	−0.222547
$265$	−3.19700	−0.196390
$266$	−6.54825	−0.401499
$267$	4.31767	0.264237
$268$	−6.17629	−0.377277
$269$	−7.44265	−0.453786	−0.226893	−	0.973920i	$-0.572857\pi$
$269$	−7.44265	−0.453786	−0.226893	+	0.973920i	$0.572857\pi$
$270$	0.911854	0.0554937
$271$	11.2862	0.685588	0.342794	−	0.939411i	$-0.388627\pi$
$271$	11.2862	0.685588	0.342794	+	0.939411i	$0.388627\pi$
$272$	−13.5502	−0.821600
$273$	−2.76809	−0.167532
$274$	6.25236	0.377719
$275$	−1.71379	−0.103346
$276$	−15.3056	−0.921288
$277$	−25.6233	−1.53955	−0.769776	−	0.638314i	$-0.779632\pi$
$277$	−25.6233	−1.53955	−0.769776	+	0.638314i	$0.779632\pi$
$278$	0.934689	0.0560589
$279$	4.26875	0.255563
$280$	−8.64609	−0.516703
$281$	13.2862	0.792589	0.396294	−	0.918124i	$-0.370296\pi$
$281$	13.2862	0.792589	0.396294	+	0.918124i	$0.370296\pi$
$282$	−4.72348	−0.281279
$283$	11.4034	0.677863	0.338931	−	0.940811i	$-0.389935\pi$
$283$	11.4034	0.677863	0.338931	+	0.940811i	$0.389935\pi$
$284$	2.39612	0.142184
$285$	12.0881	0.716040
$286$	1.05562	0.0624202
$287$	1.23191	0.0727176
$288$	−4.65279	−0.274168
$289$	5.59120	0.328894
$290$	0.992230	0.0582658
$291$	−18.3937	−1.07826
$292$	−25.4819	−1.49121
$293$	−17.7995	−1.03986	−0.519930	−	0.854209i	$-0.674042\pi$
$293$	−17.7995	−1.03986	−0.519930	+	0.854209i	$0.674042\pi$
$294$	−0.347207	−0.0202495
$295$	1.81269	0.105539
$296$	5.12200	0.297710
$297$	−2.13706	−0.124005
$298$	−3.68233	−0.213312
$299$	9.42758	0.545211
$300$	−1.44504	−0.0834295
$301$	14.8418	0.855465
$302$	0.445042	0.0256093
$303$	−17.7560	−1.02006
$304$	−16.8194	−0.964659
$305$	−1.26205	−0.0722645
$306$	2.11529	0.120923
$307$	22.3870	1.27770	0.638848	−	0.769333i	$-0.279411\pi$
$307$	22.3870	1.27770	0.638848	+	0.769333i	$0.279411\pi$
$308$	9.60388	0.547232
$309$	13.5646	0.771666
$310$	−3.89248	−0.221078
$311$	8.89546	0.504415	0.252208	−	0.967673i	$-0.418843\pi$
$311$	8.89546	0.504415	0.252208	+	0.967673i	$0.418843\pi$
$312$	1.87800	0.106321
$313$	17.1890	0.971578	0.485789	−	0.874076i	$-0.338532\pi$
$313$	17.1890	0.971578	0.485789	+	0.874076i	$0.338532\pi$
$314$	8.59179	0.484863
$315$	−5.10992	−0.287911
$316$	12.9879	0.730627
$317$	−14.4940	−0.814062	−0.407031	−	0.913414i	$-0.633436\pi$
$317$	−14.4940	−0.814062	−0.407031	+	0.913414i	$0.633436\pi$
$318$	−0.694414	−0.0389408
$319$	−2.32544	−0.130199
$320$	−7.43967	−0.415890
$321$	−0.591794	−0.0330307
$322$	−9.42758	−0.525379
$323$	28.0417	1.56028
$324$	−1.80194	−0.100108
$325$	0.890084	0.0493730
$326$	3.43834	0.190432
$327$	−17.0858	−0.944844
$328$	−0.835790	−0.0461488
$329$	26.4698	1.45933
$330$	1.94869	0.107272
$331$	29.5163	1.62236	0.811182	−	0.584794i	$-0.198825\pi$
$331$	29.5163	1.62236	0.811182	+	0.584794i	$0.198825\pi$
$332$	−15.4819	−0.849678
$333$	3.02715	0.165887
$334$	1.23191	0.0674073
$335$	7.02284	0.383698
$336$	7.10992	0.387878
$337$	11.4034	0.621184	0.310592	−	0.950543i	$-0.399473\pi$
$337$	11.4034	0.621184	0.310592	+	0.950543i	$0.399473\pi$
$338$	5.23729	0.284871
$339$	11.9215	0.647489
$340$	17.5483	0.951688
$341$	9.12259	0.494016
$342$	2.62565	0.141979
$343$	19.4034	1.04769
$344$	−10.0694	−0.542903
$345$	17.4034	0.936969
$346$	−0.503648	−0.0270763
$347$	1.42758	0.0766367	0.0383183	−	0.999266i	$-0.487800\pi$
$347$	1.42758	0.0766367	0.0383183	+	0.999266i	$0.487800\pi$
$348$	−1.96077	−0.105108
$349$	−27.4185	−1.46768	−0.733839	−	0.679323i	$-0.762273\pi$
$349$	−27.4185	−1.46768	−0.733839	+	0.679323i	$0.762273\pi$
$350$	−0.890084	−0.0475770
$351$	1.10992	0.0592429
$352$	−9.94331	−0.529980
$353$	32.9530	1.75391	0.876956	−	0.480571i	$-0.159571\pi$
$353$	32.9530	1.75391	0.876956	+	0.480571i	$0.159571\pi$
$354$	0.393732	0.0209266
$355$	−2.72455	−0.144604
$356$	7.78017	0.412348
$357$	−11.8538	−0.627372
$358$	1.95646	0.103402
$359$	37.2573	1.96636	0.983181	−	0.182631i	$-0.0584615\pi$
$359$	37.2573	1.96636	0.983181	+	0.182631i	$0.0584615\pi$
$360$	3.46681	0.182717
$361$	15.8073	0.831964
$362$	−11.4082	−0.599602
$363$	6.43296	0.337643
$364$	−4.98792	−0.261438
$365$	28.9745	1.51660
$366$	−0.274127	−0.0143288
$367$	−34.7525	−1.81407	−0.907034	−	0.421057i	$-0.861659\pi$
$367$	−34.7525	−1.81407	−0.907034	+	0.421057i	$0.861659\pi$
$368$	−24.2150	−1.26230
$369$	−0.493959	−0.0257145
$370$	−2.76032	−0.143502
$371$	3.89141	0.202032
$372$	7.69202	0.398813
$373$	7.82371	0.405096	0.202548	−	0.979272i	$-0.435078\pi$
$373$	7.82371	0.405096	0.202548	+	0.979272i	$0.435078\pi$
$374$	4.52052	0.233750
$375$	11.8877	0.613878
$376$	−17.9584	−0.926133
$377$	1.20775	0.0622023
$378$	−1.10992	−0.0570879
$379$	23.7995	1.22250	0.611250	−	0.791437i	$-0.290667\pi$
$379$	23.7995	1.22250	0.611250	+	0.791437i	$0.290667\pi$
$380$	21.7821	1.11740
$381$	−9.25667	−0.474233
$382$	2.32736	0.119078
$383$	−11.6635	−0.595979	−0.297990	−	0.954569i	$-0.596316\pi$
$383$	−11.6635	−0.595979	−0.297990	+	0.954569i	$0.596316\pi$
$384$	−10.9215	−0.557338
$385$	−10.9202	−0.556546
$386$	−1.53856	−0.0783109
$387$	−5.95108	−0.302511
$388$	−33.1444	−1.68265
$389$	−22.6353	−1.14766	−0.573829	−	0.818975i	$-0.694542\pi$
$389$	−22.6353	−1.14766	−0.573829	+	0.818975i	$0.694542\pi$
$390$	−1.01208	−0.0512487
$391$	40.3720	2.04170
$392$	−1.32006	−0.0666731
$393$	9.65817	0.487190
$394$	−2.95300	−0.148770
$395$	−14.7681	−0.743063
$396$	−3.85086	−0.193513
$397$	−15.5773	−0.781803	−0.390902	−	0.920432i	$-0.627837\pi$
$397$	−15.5773	−0.781803	−0.390902	+	0.920432i	$0.627837\pi$
$398$	−7.34913	−0.368378
$399$	−14.7138	−0.736611
$400$	−2.28621	−0.114310
$401$	−30.4239	−1.51930	−0.759648	−	0.650335i	$-0.774629\pi$
$401$	−30.4239	−1.51930	−0.759648	+	0.650335i	$0.774629\pi$
$402$	1.52542	0.0760809
$403$	−4.73795	−0.236014
$404$	−31.9952	−1.59182
$405$	2.04892	0.101812
$406$	−1.20775	−0.0599397
$407$	6.46921	0.320667
$408$	8.04221	0.398149
$409$	29.6582	1.46650	0.733251	−	0.679958i	$-0.238002\pi$
$409$	29.6582	1.46650	0.733251	+	0.679958i	$0.238002\pi$
$410$	0.450419	0.0222446
$411$	14.0489	0.692982
$412$	24.4426	1.20420
$413$	−2.20642	−0.108571
$414$	3.78017	0.185785
$415$	17.6039	0.864140
$416$	5.16421	0.253196
$417$	2.10023	0.102849
$418$	5.61117	0.274451
$419$	−2.51812	−0.123018	−0.0615092	−	0.998107i	$-0.519591\pi$
$419$	−2.51812	−0.123018	−0.0615092	+	0.998107i	$0.519591\pi$
$420$	−9.20775	−0.449292
$421$	11.8479	0.577430	0.288715	−	0.957415i	$-0.406772\pi$
$421$	11.8479	0.577430	0.288715	+	0.957415i	$0.406772\pi$
$422$	0.914247	0.0445048
$423$	−10.6136	−0.516049
$424$	−2.64012	−0.128216
$425$	3.81163	0.184891
$426$	−0.591794	−0.0286725
$427$	1.53617	0.0743406
$428$	−1.06638	−0.0515452
$429$	2.37196	0.114519
$430$	5.42652	0.261690
$431$	8.93362	0.430318	0.215159	−	0.976579i	$-0.430973\pi$
$431$	8.93362	0.430318	0.215159	+	0.976579i	$0.430973\pi$
$432$	−2.85086	−0.137162
$433$	−5.92154	−0.284571	−0.142286	−	0.989826i	$-0.545445\pi$
$433$	−5.92154	−0.284571	−0.142286	+	0.989826i	$0.545445\pi$
$434$	4.73795	0.227429
$435$	2.22952	0.106897
$436$	−30.7875	−1.47445
$437$	50.1124	2.39720
$438$	6.29350	0.300715
$439$	−18.0344	−0.860737	−0.430368	−	0.902653i	$-0.641616\pi$
$439$	−18.0344	−0.860737	−0.430368	+	0.902653i	$0.641616\pi$
$440$	7.40880	0.353201
$441$	−0.780167	−0.0371508
$442$	−2.34780	−0.111673
$443$	−22.9288	−1.08938	−0.544691	−	0.838637i	$-0.683353\pi$
$443$	−22.9288	−1.08938	−0.544691	+	0.838637i	$0.683353\pi$
$444$	5.45473	0.258870
$445$	−8.84654	−0.419366
$446$	0.731250	0.0346257
$447$	−8.27413	−0.391353
$448$	9.05562	0.427838
$449$	−11.3491	−0.535598	−0.267799	−	0.963475i	$-0.586296\pi$
$449$	−11.3491	−0.535598	−0.267799	+	0.963475i	$0.586296\pi$
$450$	0.356896	0.0168242
$451$	−1.05562	−0.0497073
$452$	21.4819	1.01042
$453$	1.00000	0.0469841
$454$	−3.64550	−0.171092
$455$	5.67158	0.265888
$456$	9.98254	0.467475
$457$	17.4330	0.815479	0.407740	−	0.913098i	$-0.366317\pi$
$457$	17.4330	0.815479	0.407740	+	0.913098i	$0.366317\pi$
$458$	1.13514	0.0530418
$459$	4.75302	0.221852
$460$	31.3599	1.46216
$461$	−9.66248	−0.450027	−0.225013	−	0.974356i	$-0.572243\pi$
$461$	−9.66248	−0.450027	−0.225013	+	0.974356i	$0.572243\pi$
$462$	−2.37196	−0.110354
$463$	−23.4319	−1.08897	−0.544486	−	0.838770i	$-0.683275\pi$
$463$	−23.4319	−1.08897	−0.544486	+	0.838770i	$0.683275\pi$
$464$	−3.10215	−0.144014
$465$	−8.74632	−0.405601
$466$	0.944378	0.0437475
$467$	−12.7138	−0.588324	−0.294162	−	0.955756i	$-0.595041\pi$
$467$	−12.7138	−0.588324	−0.294162	+	0.955756i	$0.595041\pi$
$468$	2.00000	0.0924500
$469$	−8.54825	−0.394722
$470$	9.67802	0.446414
$471$	19.3056	0.889554
$472$	1.49694	0.0689024
$473$	−12.7178	−0.584767
$474$	−3.20775	−0.147337
$475$	4.73125	0.217085
$476$	−21.3599	−0.979028
$477$	−1.56033	−0.0714428
$478$	6.85325	0.313460
$479$	−1.83446	−0.0838187	−0.0419093	−	0.999121i	$-0.513344\pi$
$479$	−1.83446	−0.0838187	−0.0419093	+	0.999121i	$0.513344\pi$
$480$	9.53319	0.435129
$481$	−3.35988	−0.153197
$482$	−1.45580	−0.0663097
$483$	−21.1836	−0.963887
$484$	11.5918	0.526900
$485$	37.6872	1.71129
$486$	0.445042	0.0201875
$487$	−12.9554	−0.587065	−0.293532	−	0.955949i	$-0.594831\pi$
$487$	−12.9554	−0.587065	−0.293532	+	0.955949i	$0.594831\pi$
$488$	−1.04221	−0.0471787
$489$	7.72587	0.349376
$490$	0.711399	0.0321377
$491$	5.17821	0.233689	0.116845	−	0.993150i	$-0.462722\pi$
$491$	5.17821	0.233689	0.116845	+	0.993150i	$0.462722\pi$
$492$	−0.890084	−0.0401281
$493$	5.17198	0.232934
$494$	−2.91425	−0.131118
$495$	4.37867	0.196806
$496$	12.1696	0.546431
$497$	3.31634	0.148758
$498$	3.82371	0.171344
$499$	−21.3163	−0.954250	−0.477125	−	0.878835i	$-0.658321\pi$
$499$	−21.3163	−0.954250	−0.477125	+	0.878835i	$0.658321\pi$
$500$	21.4209	0.957971
$501$	2.76809	0.123669
$502$	10.6112	0.473600
$503$	36.0441	1.60713	0.803564	−	0.595218i	$-0.202934\pi$
$503$	36.0441	1.60713	0.803564	+	0.595218i	$0.202934\pi$
$504$	−4.21983	−0.187966
$505$	36.3806	1.61891
$506$	8.07846	0.359131
$507$	11.7681	0.522639
$508$	−16.6799	−0.740053
$509$	28.4349	1.26035	0.630177	−	0.776452i	$-0.282982\pi$
$509$	28.4349	1.26035	0.630177	+	0.776452i	$0.282982\pi$
$510$	−4.33406	−0.191915
$511$	−35.2680	−1.56017
$512$	−22.9119	−1.01257
$513$	5.89977	0.260481
$514$	12.6353	0.557321
$515$	−27.7928	−1.22470
$516$	−10.7235	−0.472075
$517$	−22.6819	−0.997547
$518$	3.35988	0.147625
$519$	−1.13169	−0.0496755
$520$	−3.84787	−0.168740
$521$	−3.06877	−0.134445	−0.0672226	−	0.997738i	$-0.521414\pi$
$521$	−3.06877	−0.134445	−0.0672226	+	0.997738i	$0.521414\pi$
$522$	0.484271	0.0211959
$523$	−41.4577	−1.81282	−0.906410	−	0.422400i	$-0.861188\pi$
$523$	−41.4577	−1.81282	−0.906410	+	0.422400i	$0.861188\pi$
$524$	17.4034	0.760272
$525$	−2.00000	−0.0872872
$526$	−11.0315	−0.480994
$527$	−20.2895	−0.883823
$528$	−6.09246	−0.265140
$529$	49.1473	2.13684
$530$	1.42280	0.0618024
$531$	0.884707	0.0383930
$532$	−26.5133	−1.14950
$533$	0.548253	0.0237475
$534$	−1.92154	−0.0831533
$535$	1.21254	0.0524225
$536$	5.79954	0.250502
$537$	4.39612	0.189707
$538$	3.31229	0.142803
$539$	−1.66727	−0.0718143
$540$	3.69202	0.158879
$541$	32.5924	1.40126	0.700628	−	0.713527i	$-0.252903\pi$
$541$	32.5924	1.40126	0.700628	+	0.713527i	$0.252903\pi$
$542$	−5.02284	−0.215749
$543$	−25.6340	−1.10006
$544$	22.1148	0.948165
$545$	35.0073	1.49955
$546$	1.23191	0.0527211
$547$	−13.4166	−0.573651	−0.286825	−	0.957983i	$-0.592600\pi$
$547$	−13.4166	−0.573651	−0.286825	+	0.957983i	$0.592600\pi$
$548$	25.3153	1.08141
$549$	−0.615957	−0.0262884
$550$	0.762709	0.0325220
$551$	6.41981	0.273493
$552$	14.3720	0.611711
$553$	17.9758	0.764410
$554$	11.4034	0.484485
$555$	−6.20237	−0.263276
$556$	3.78448	0.160498
$557$	−8.43488	−0.357397	−0.178699	−	0.983904i	$-0.557189\pi$
$557$	−8.43488	−0.357397	−0.178699	+	0.983904i	$0.557189\pi$
$558$	−1.89977	−0.0804238
$559$	6.60520	0.279370
$560$	−14.5676	−0.615595
$561$	10.1575	0.428850
$562$	−5.91292	−0.249421
$563$	−40.1885	−1.69374	−0.846871	−	0.531798i	$-0.821517\pi$
$563$	−40.1885	−1.69374	−0.846871	+	0.531798i	$0.821517\pi$
$564$	−19.1250	−0.805307
$565$	−24.4263	−1.02762
$566$	−5.07500	−0.213318
$567$	−2.49396	−0.104736
$568$	−2.24996	−0.0944064
$569$	−31.4513	−1.31851	−0.659253	−	0.751921i	$-0.729127\pi$
$569$	−31.4513	−1.31851	−0.659253	+	0.751921i	$0.729127\pi$
$570$	−5.37973	−0.225332
$571$	−44.6493	−1.86852	−0.934258	−	0.356597i	$-0.883937\pi$
$571$	−44.6493	−1.86852	−0.934258	+	0.356597i	$0.883937\pi$
$572$	4.27413	0.178710
$573$	5.22952	0.218466
$574$	−0.548253	−0.0228837
$575$	6.81163	0.284064
$576$	−3.63102	−0.151293
$577$	5.31873	0.221422	0.110711	−	0.993853i	$-0.464687\pi$
$577$	5.31873	0.221422	0.110711	+	0.993853i	$0.464687\pi$
$578$	−2.48832	−0.103500
$579$	−3.45712	−0.143673
$580$	4.01746	0.166816
$581$	−21.4276	−0.888966
$582$	8.18598	0.339320
$583$	−3.33453	−0.138102
$584$	23.9275	0.990127
$585$	−2.27413	−0.0940236
$586$	7.92154	0.327236
$587$	−2.14138	−0.0883840	−0.0441920	−	0.999023i	$-0.514071\pi$
$587$	−2.14138	−0.0883840	−0.0441920	+	0.999023i	$0.514071\pi$
$588$	−1.40581	−0.0579748
$589$	−25.1847	−1.03772
$590$	−0.806724	−0.0332123
$591$	−6.63533	−0.272941
$592$	8.62996	0.354689
$593$	−36.9095	−1.51569	−0.757845	−	0.652435i	$-0.773748\pi$
$593$	−36.9095	−1.51569	−0.757845	+	0.652435i	$0.773748\pi$
$594$	0.951083	0.0390234
$595$	24.2875	0.995692
$596$	−14.9095	−0.610715
$597$	−16.5133	−0.675846
$598$	−4.19567	−0.171574
$599$	−5.12067	−0.209225	−0.104612	−	0.994513i	$-0.533360\pi$
$599$	−5.12067	−0.209225	−0.104612	+	0.994513i	$0.533360\pi$
$600$	1.35690	0.0553950
$601$	4.38596	0.178907	0.0894536	−	0.995991i	$-0.471488\pi$
$601$	4.38596	0.178907	0.0894536	+	0.995991i	$0.471488\pi$
$602$	−6.60520	−0.269208
$603$	3.42758	0.139582
$604$	1.80194	0.0733198
$605$	−13.1806	−0.535868
$606$	7.90217	0.321004
$607$	44.0737	1.78890	0.894448	−	0.447173i	$-0.147569\pi$
$607$	44.0737	1.78890	0.894448	+	0.447173i	$0.147569\pi$
$608$	27.4504	1.11326
$609$	−2.71379	−0.109968
$610$	0.561663	0.0227411
$611$	11.7802	0.476575
$612$	8.56465	0.346205
$613$	−26.8310	−1.08369	−0.541847	−	0.840477i	$-0.682275\pi$
$613$	−26.8310	−1.08369	−0.541847	+	0.840477i	$0.682275\pi$
$614$	−9.96316	−0.402081
$615$	1.01208	0.0408111
$616$	−9.01805	−0.363348
$617$	−43.1487	−1.73710	−0.868550	−	0.495601i	$-0.834948\pi$
$617$	−43.1487	−1.73710	−0.868550	+	0.495601i	$0.834948\pi$
$618$	−6.03684	−0.242837
$619$	−12.8224	−0.515375	−0.257687	−	0.966228i	$-0.582960\pi$
$619$	−12.8224	−0.515375	−0.257687	+	0.966228i	$0.582960\pi$
$620$	−15.7603	−0.632950
$621$	8.49396	0.340851
$622$	−3.95885	−0.158736
$623$	10.7681	0.431414
$624$	3.16421	0.126670
$625$	−20.3472	−0.813888
$626$	−7.64981	−0.305748
$627$	12.6082	0.503523
$628$	34.7875	1.38817
$629$	−14.3881	−0.573691
$630$	2.27413	0.0906034
$631$	13.6340	0.542761	0.271381	−	0.962472i	$-0.412520\pi$
$631$	13.6340	0.542761	0.271381	+	0.962472i	$0.412520\pi$
$632$	−12.1957	−0.485118
$633$	2.05429	0.0816509
$634$	6.45042	0.256179
$635$	18.9661	0.752649
$636$	−2.81163	−0.111488
$637$	0.865921	0.0343090
$638$	1.03492	0.0409727
$639$	−1.32975	−0.0526040
$640$	22.3773	0.884542
$641$	−19.2808	−0.761547	−0.380774	−	0.924668i	$-0.624342\pi$
$641$	−19.2808	−0.761547	−0.380774	+	0.924668i	$0.624342\pi$
$642$	0.263373	0.0103945
$643$	41.8950	1.65218	0.826088	−	0.563540i	$-0.190561\pi$
$643$	41.8950	1.65218	0.826088	+	0.563540i	$0.190561\pi$
$644$	−38.1715	−1.50417
$645$	12.1933	0.480110
$646$	−12.4797	−0.491009
$647$	0.679349	0.0267080	0.0133540	−	0.999911i	$-0.495749\pi$
$647$	0.679349	0.0267080	0.0133540	+	0.999911i	$0.495749\pi$
$648$	1.69202	0.0664689
$649$	1.89067	0.0742155
$650$	−0.396125	−0.0155373
$651$	10.6461	0.417253
$652$	13.9215	0.545210
$653$	0.328421	0.0128521	0.00642605	−	0.999979i	$-0.497955\pi$
$653$	0.328421	0.0128521	0.00642605	+	0.999979i	$0.497955\pi$
$654$	7.60388	0.297335
$655$	−19.7888	−0.773212
$656$	−1.40821	−0.0549812
$657$	14.1414	0.551708
$658$	−11.7802	−0.459239
$659$	−31.3217	−1.22012	−0.610060	−	0.792355i	$-0.708855\pi$
$659$	−31.3217	−1.22012	−0.610060	+	0.792355i	$0.708855\pi$
$660$	7.89008	0.307121
$661$	16.0000	0.622328	0.311164	−	0.950356i	$-0.399281\pi$
$661$	16.0000	0.622328	0.311164	+	0.950356i	$0.399281\pi$
$662$	−13.1360	−0.510545
$663$	−5.27545	−0.204882
$664$	14.5375	0.564164
$665$	30.1473	1.16906
$666$	−1.34721	−0.0522032
$667$	9.24267	0.357878
$668$	4.98792	0.192988
$669$	1.64310	0.0635261
$670$	−3.12546	−0.120747
$671$	−1.31634	−0.0508167
$672$	−11.6039	−0.447629
$673$	−26.5090	−1.02185	−0.510924	−	0.859626i	$-0.670697\pi$
$673$	−26.5090	−1.02185	−0.510924	+	0.859626i	$0.670697\pi$
$674$	−5.07500	−0.195482
$675$	0.801938	0.0308666
$676$	21.2054	0.815591
$677$	−33.8345	−1.30036	−0.650182	−	0.759779i	$-0.725307\pi$
$677$	−33.8345	−1.30036	−0.650182	+	0.759779i	$0.725307\pi$
$678$	−5.30559	−0.203760
$679$	−45.8732	−1.76045
$680$	−16.4778	−0.631896
$681$	−8.19136	−0.313894
$682$	−4.05993	−0.155463
$683$	−1.88876	−0.0722712	−0.0361356	−	0.999347i	$-0.511505\pi$
$683$	−1.88876	−0.0722712	−0.0361356	+	0.999347i	$0.511505\pi$
$684$	10.6310	0.406487
$685$	−28.7851	−1.09982
$686$	−8.63533	−0.329699
$687$	2.55065	0.0973132
$688$	−16.9657	−0.646810
$689$	1.73184	0.0659779
$690$	−7.74525	−0.294857
$691$	12.8418	0.488523	0.244262	−	0.969709i	$-0.421454\pi$
$691$	12.8418	0.488523	0.244262	+	0.969709i	$0.421454\pi$
$692$	−2.03923	−0.0775198
$693$	−5.32975	−0.202460
$694$	−0.635334	−0.0241170
$695$	−4.30319	−0.163229
$696$	1.84117	0.0697892
$697$	2.34780	0.0889292
$698$	12.2024	0.461867
$699$	2.12200	0.0802613
$700$	−3.60388	−0.136214
$701$	−3.38942	−0.128017	−0.0640083	−	0.997949i	$-0.520388\pi$
$701$	−3.38942	−0.128017	−0.0640083	+	0.997949i	$0.520388\pi$
$702$	−0.493959	−0.0186433
$703$	−17.8595	−0.673583
$704$	−7.75973	−0.292456
$705$	21.7463	0.819014
$706$	−14.6655	−0.551942
$707$	−44.2828	−1.66542
$708$	1.59419	0.0599132
$709$	24.6504	0.925765	0.462883	−	0.886420i	$-0.346815\pi$
$709$	24.6504	0.925765	0.462883	+	0.886420i	$0.346815\pi$
$710$	1.21254	0.0455057
$711$	−7.20775	−0.270312
$712$	−7.30559	−0.273788
$713$	−36.2586	−1.35789
$714$	5.27545	0.197429
$715$	−4.85995	−0.181752
$716$	7.92154	0.296042
$717$	15.3991	0.575090
$718$	−16.5810	−0.618799
$719$	32.7982	1.22317	0.611584	−	0.791180i	$-0.290533\pi$
$719$	32.7982	1.22317	0.611584	+	0.791180i	$0.290533\pi$
$720$	5.84117	0.217687
$721$	33.8297	1.25988
$722$	−7.03492	−0.261812
$723$	−3.27114	−0.121655
$724$	−46.1909	−1.71667
$725$	0.872625	0.0324085
$726$	−2.86294	−0.106254
$727$	36.8310	1.36599	0.682993	−	0.730425i	$-0.260678\pi$
$727$	36.8310	1.36599	0.682993	+	0.730425i	$0.260678\pi$
$728$	4.68366	0.173588
$729$	1.00000	0.0370370
$730$	−12.8949	−0.477261
$731$	28.2856	1.04618
$732$	−1.10992	−0.0410237
$733$	−28.7875	−1.06329	−0.531645	−	0.846968i	$-0.678426\pi$
$733$	−28.7875	−1.06329	−0.531645	+	0.846968i	$0.678426\pi$
$734$	15.4663	0.570873
$735$	1.59850	0.0589615
$736$	39.5206	1.45675
$737$	7.32496	0.269818
$738$	0.219833	0.00809215
$739$	−15.1051	−0.555651	−0.277826	−	0.960632i	$-0.589614\pi$
$739$	−15.1051	−0.555651	−0.277826	+	0.960632i	$0.589614\pi$
$740$	−11.1763	−0.410849
$741$	−6.54825	−0.240556
$742$	−1.73184	−0.0635779
$743$	−40.6698	−1.49203	−0.746015	−	0.665929i	$-0.768035\pi$
$743$	−40.6698	−1.49203	−0.746015	+	0.665929i	$0.768035\pi$
$744$	−7.22282	−0.264801
$745$	16.9530	0.621110
$746$	−3.48188	−0.127481
$747$	8.59179	0.314357
$748$	18.3032	0.669231
$749$	−1.47591	−0.0539286
$750$	−5.29052	−0.193182
$751$	−29.2922	−1.06889	−0.534443	−	0.845204i	$-0.679479\pi$
$751$	−29.2922	−1.06889	−0.534443	+	0.845204i	$0.679479\pi$
$752$	−30.2577	−1.10339
$753$	23.8431	0.868890
$754$	−0.537500	−0.0195746
$755$	−2.04892	−0.0745677
$756$	−4.49396	−0.163444
$757$	50.1554	1.82293	0.911464	−	0.411380i	$-0.134953\pi$
$757$	50.1554	1.82293	0.911464	+	0.411380i	$0.134953\pi$
$758$	−10.5918	−0.384711
$759$	18.1521	0.658881
$760$	−20.4534	−0.741923
$761$	32.6762	1.18451	0.592256	−	0.805750i	$-0.298237\pi$
$761$	32.6762	1.18451	0.592256	+	0.805750i	$0.298237\pi$
$762$	4.11960	0.149238
$763$	−42.6112	−1.54263
$764$	9.42327	0.340922
$765$	−9.73855	−0.352098
$766$	5.19077	0.187550
$767$	−0.981951	−0.0354562
$768$	−2.40150	−0.0866567
$769$	−16.4784	−0.594227	−0.297114	−	0.954842i	$-0.596024\pi$
$769$	−16.4784	−0.594227	−0.297114	+	0.954842i	$0.596024\pi$
$770$	4.85995	0.175141
$771$	28.3913	1.02249
$772$	−6.22952	−0.224205
$773$	6.08708	0.218937	0.109469	−	0.993990i	$-0.465085\pi$
$773$	6.08708	0.218937	0.109469	+	0.993990i	$0.465085\pi$
$774$	2.64848	0.0951977
$775$	−3.42327	−0.122968
$776$	31.1226	1.11724
$777$	7.54958	0.270840
$778$	10.0737	0.361159
$779$	2.91425	0.104414
$780$	−4.09783	−0.146726
$781$	−2.84176	−0.101686
$782$	−17.9672	−0.642506
$783$	1.08815	0.0388872
$784$	−2.22414	−0.0794337
$785$	−39.5555	−1.41180
$786$	−4.29829	−0.153315
$787$	6.30857	0.224876	0.112438	−	0.993659i	$-0.464134\pi$
$787$	6.30857	0.224876	0.112438	+	0.993659i	$0.464134\pi$
$788$	−11.9565	−0.425931
$789$	−24.7875	−0.882457
$790$	6.57242	0.233836
$791$	29.7318	1.05714
$792$	3.61596	0.128487
$793$	0.683661	0.0242775
$794$	6.93256	0.246027
$795$	3.19700	0.113386
$796$	−29.7560	−1.05467
$797$	−34.3105	−1.21534	−0.607670	−	0.794190i	$-0.707896\pi$
$797$	−34.3105	−1.21534	−0.607670	+	0.794190i	$0.707896\pi$
$798$	6.54825	0.231806
$799$	50.4465	1.78467
$800$	3.73125	0.131920
$801$	−4.31767	−0.152557
$802$	13.5399	0.478110
$803$	30.2210	1.06648
$804$	6.17629	0.217821
$805$	43.4034	1.52977
$806$	2.10859	0.0742719
$807$	7.44265	0.261994
$808$	30.0435	1.05693
$809$	16.5870	0.583168	0.291584	−	0.956545i	$-0.405818\pi$
$809$	16.5870	0.583168	0.291584	+	0.956545i	$0.405818\pi$
$810$	−0.911854	−0.0320393
$811$	8.25475	0.289863	0.144932	−	0.989442i	$-0.453704\pi$
$811$	8.25475	0.289863	0.144932	+	0.989442i	$0.453704\pi$
$812$	−4.89008	−0.171608
$813$	−11.2862	−0.395825
$814$	−2.87907	−0.100911
$815$	−15.8297	−0.554489
$816$	13.5502	0.474351
$817$	35.1100	1.22834
$818$	−13.1991	−0.461497
$819$	2.76809	0.0967247
$820$	1.82371	0.0636866
$821$	−29.1400	−1.01699	−0.508497	−	0.861064i	$-0.669799\pi$
$821$	−29.1400	−1.01699	−0.508497	+	0.861064i	$0.669799\pi$
$822$	−6.25236	−0.218076
$823$	−46.0519	−1.60527	−0.802634	−	0.596472i	$-0.796569\pi$
$823$	−46.0519	−1.60527	−0.802634	+	0.596472i	$0.796569\pi$
$824$	−22.9517	−0.799559
$825$	1.71379	0.0596666
$826$	0.981951	0.0341664
$827$	−21.2707	−0.739654	−0.369827	−	0.929101i	$-0.620583\pi$
$827$	−21.2707	−0.739654	−0.369827	+	0.929101i	$0.620583\pi$
$828$	15.3056	0.531906
$829$	7.31900	0.254199	0.127100	−	0.991890i	$-0.459433\pi$
$829$	7.31900	0.254199	0.127100	+	0.991890i	$0.459433\pi$
$830$	−7.83446	−0.271938
$831$	25.6233	0.888861
$832$	4.03013	0.139720
$833$	3.70815	0.128480
$834$	−0.934689	−0.0323656
$835$	−5.67158	−0.196273
$836$	22.7192	0.785759
$837$	−4.26875	−0.147550
$838$	1.12067	0.0387129
$839$	4.54586	0.156941	0.0784703	−	0.996916i	$-0.474996\pi$
$839$	4.54586	0.156941	0.0784703	+	0.996916i	$0.474996\pi$
$840$	8.64609	0.298318
$841$	−27.8159	−0.959170
$842$	−5.27280	−0.181713
$843$	−13.2862	−0.457601
$844$	3.70171	0.127418
$845$	−24.1118	−0.829472
$846$	4.72348	0.162397
$847$	16.0435	0.551263
$848$	−4.44829	−0.152755
$849$	−11.4034	−0.391364
$850$	−1.69633	−0.0581838
$851$	−25.7125	−0.881412
$852$	−2.39612	−0.0820899
$853$	19.3110	0.661195	0.330597	−	0.943772i	$-0.392750\pi$
$853$	19.3110	0.661195	0.330597	+	0.943772i	$0.392750\pi$
$854$	−0.683661	−0.0233944
$855$	−12.0881	−0.413406
$856$	1.00133	0.0342247
$857$	−7.88876	−0.269475	−0.134737	−	0.990881i	$-0.543019\pi$
$857$	−7.88876	−0.269475	−0.134737	+	0.990881i	$0.543019\pi$
$858$	−1.05562	−0.0360383
$859$	40.0086	1.36508	0.682538	−	0.730850i	$-0.260876\pi$
$859$	40.0086	1.36508	0.682538	+	0.730850i	$0.260876\pi$
$860$	21.9715	0.749223
$861$	−1.23191	−0.0419835
$862$	−3.97584	−0.135418
$863$	44.3866	1.51094	0.755468	−	0.655186i	$-0.227410\pi$
$863$	44.3866	1.51094	0.755468	+	0.655186i	$0.227410\pi$
$864$	4.65279	0.158291
$865$	2.31873	0.0788393
$866$	2.63533	0.0895523
$867$	−5.59120	−0.189887
$868$	19.1836	0.651133
$869$	−15.4034	−0.522525
$870$	−0.992230	−0.0336398
$871$	−3.80433	−0.128905
$872$	28.9095	0.978998
$873$	18.3937	0.622533
$874$	−22.3021	−0.754381
$875$	29.6474	1.00227
$876$	25.4819	0.860953
$877$	−2.18492	−0.0737794	−0.0368897	−	0.999319i	$-0.511745\pi$
$877$	−2.18492	−0.0737794	−0.0368897	+	0.999319i	$0.511745\pi$
$878$	8.02608	0.270867
$879$	17.7995	0.600364
$880$	12.4829	0.420800
$881$	−51.7948	−1.74501	−0.872505	−	0.488605i	$-0.837506\pi$
$881$	−51.7948	−1.74501	−0.872505	+	0.488605i	$0.837506\pi$
$882$	0.347207	0.0116911
$883$	−25.2422	−0.849467	−0.424734	−	0.905318i	$-0.639632\pi$
$883$	−25.2422	−0.849467	−0.424734	+	0.905318i	$0.639632\pi$
$884$	−9.50604	−0.319723
$885$	−1.81269	−0.0609330
$886$	10.2043	0.342820
$887$	54.4564	1.82847	0.914233	−	0.405188i	$-0.132794\pi$
$887$	54.4564	1.82847	0.914233	+	0.405188i	$0.132794\pi$
$888$	−5.12200	−0.171883
$889$	−23.0858	−0.774271
$890$	3.93708	0.131971
$891$	2.13706	0.0715943
$892$	2.96077	0.0991340
$893$	62.6176	2.09542
$894$	3.68233	0.123156
$895$	−9.00730	−0.301081
$896$	−27.2379	−0.909954
$897$	−9.42758	−0.314778
$898$	5.05084	0.168549
$899$	−4.64502	−0.154920
$900$	1.44504	0.0481681
$901$	7.41630	0.247073
$902$	0.469796	0.0156425
$903$	−14.8418	−0.493903
$904$	−20.1715	−0.670894
$905$	52.5220	1.74589
$906$	−0.445042	−0.0147855
$907$	−42.2476	−1.40281	−0.701404	−	0.712764i	$-0.747443\pi$
$907$	−42.2476	−1.40281	−0.701404	+	0.712764i	$0.747443\pi$
$908$	−14.7603	−0.489838
$909$	17.7560	0.588929
$910$	−2.52409	−0.0836728
$911$	47.6402	1.57839	0.789196	−	0.614142i	$-0.210498\pi$
$911$	47.6402	1.57839	0.789196	+	0.614142i	$0.210498\pi$
$912$	16.8194	0.556946
$913$	18.3612	0.607667
$914$	−7.75840	−0.256625
$915$	1.26205	0.0417219
$916$	4.59611	0.151860
$917$	24.0871	0.795425
$918$	−2.11529	−0.0698151
$919$	−45.2573	−1.49290	−0.746450	−	0.665442i	$-0.768243\pi$
$919$	−45.2573	−1.49290	−0.746450	+	0.665442i	$0.768243\pi$
$920$	−29.4470	−0.970838
$921$	−22.3870	−0.737678
$922$	4.30021	0.141620
$923$	1.47591	0.0485802
$924$	−9.60388	−0.315944
$925$	−2.42758	−0.0798185
$926$	10.4282	0.342691
$927$	−13.5646	−0.445521
$928$	5.06292	0.166198
$929$	−27.5555	−0.904068	−0.452034	−	0.892001i	$-0.649301\pi$
$929$	−27.5555	−0.904068	−0.452034	+	0.892001i	$0.649301\pi$
$930$	3.89248	0.127639
$931$	4.60281	0.150851
$932$	3.82371	0.125250
$933$	−8.89546	−0.291224
$934$	5.65817	0.185141
$935$	−20.8119	−0.680622
$936$	−1.87800	−0.0613844
$937$	9.80194	0.320215	0.160108	−	0.987100i	$-0.448816\pi$
$937$	9.80194	0.320215	0.160108	+	0.987100i	$0.448816\pi$
$938$	3.80433	0.124216
$939$	−17.1890	−0.560941
$940$	39.1855	1.27809
$941$	−56.3720	−1.83767	−0.918837	−	0.394638i	$-0.870870\pi$
$941$	−56.3720	−1.83767	−0.918837	+	0.394638i	$0.870870\pi$
$942$	−8.59179	−0.279936
$943$	4.19567	0.136630
$944$	2.52217	0.0820897
$945$	5.10992	0.166226
$946$	5.65997	0.184022
$947$	−12.9336	−0.420286	−0.210143	−	0.977671i	$-0.567393\pi$
$947$	−12.9336	−0.420286	−0.210143	+	0.977671i	$0.567393\pi$
$948$	−12.9879	−0.421828
$949$	−15.6957	−0.509505
$950$	−2.10560	−0.0683148
$951$	14.4940	0.469999
$952$	20.0570	0.650049
$953$	−53.3226	−1.72729	−0.863644	−	0.504103i	$-0.831823\pi$
$953$	−53.3226	−1.72729	−0.863644	+	0.504103i	$0.831823\pi$
$954$	0.694414	0.0224825
$955$	−10.7149	−0.346725
$956$	27.7482	0.897442
$957$	2.32544	0.0751707
$958$	0.816412	0.0263771
$959$	35.0374	1.13142
$960$	7.43967	0.240114
$961$	−12.7778	−0.412186
$962$	1.49529	0.0482100
$963$	0.591794	0.0190703
$964$	−5.89440	−0.189846
$965$	7.08336	0.228021
$966$	9.42758	0.303328
$967$	−25.4120	−0.817196	−0.408598	−	0.912714i	$-0.633982\pi$
$967$	−25.4120	−0.817196	−0.408598	+	0.912714i	$0.633982\pi$
$968$	−10.8847	−0.349848
$969$	−28.0417	−0.900830
$970$	−16.7724	−0.538529
$971$	−41.5362	−1.33296	−0.666480	−	0.745523i	$-0.732200\pi$
$971$	−41.5362	−1.33296	−0.666480	+	0.745523i	$0.732200\pi$
$972$	1.80194	0.0577972
$973$	5.23788	0.167919
$974$	5.76569	0.184745
$975$	−0.890084	−0.0285055
$976$	−1.75600	−0.0562083
$977$	55.7211	1.78268	0.891338	−	0.453340i	$-0.149768\pi$
$977$	55.7211	1.78268	0.891338	+	0.453340i	$0.149768\pi$
$978$	−3.43834	−0.109946
$979$	−9.22713	−0.294900
$980$	2.88040	0.0920108
$981$	17.0858	0.545506
$982$	−2.30452	−0.0735402
$983$	17.6125	0.561751	0.280876	−	0.959744i	$-0.409375\pi$
$983$	17.6125	0.561751	0.280876	+	0.959744i	$0.409375\pi$
$984$	0.835790	0.0266440
$985$	13.5953	0.433181
$986$	−2.30175	−0.0733026
$987$	−26.4698	−0.842543
$988$	−11.7995	−0.375394
$989$	50.5483	1.60734
$990$	−1.94869	−0.0619334
$991$	−35.7885	−1.13686	−0.568430	−	0.822732i	$-0.692449\pi$
$991$	−35.7885	−1.13686	−0.568430	+	0.822732i	$0.692449\pi$
$992$	−19.8616	−0.630607
$993$	−29.5163	−0.936672
$994$	−1.47591	−0.0468130
$995$	33.8345	1.07262
$996$	15.4819	0.490562
$997$	25.1202	0.795565	0.397782	−	0.917480i	$-0.369780\pi$
$997$	25.1202	0.795565	0.397782	+	0.917480i	$0.369780\pi$
$998$	9.48666	0.300295
$999$	−3.02715	−0.0957747

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	453.2.a.e.1.2	✓	3
3.2	odd	2		1359.2.a.f.1.2		3
4.3	odd	2		7248.2.a.v.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
453.2.a.e.1.2	✓	3	1.1	even	1	trivial
1359.2.a.f.1.2		3	3.2	odd	2
7248.2.a.v.1.3		3	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 453 = 3 \cdot 151 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	453.a (trivial)

\(f(q)\)	\(=\)	\(q-0.445042 q^{2} -1.00000 q^{3} -1.80194 q^{4} +2.04892 q^{5} +0.445042 q^{6} -2.49396 q^{7} +1.69202 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.445042 q^{2} -1.00000 q^{3} -1.80194 q^{4} +2.04892 q^{5} +0.445042 q^{6} -2.49396 q^{7} +1.69202 q^{8} +1.00000 q^{9} -0.911854 q^{10} +2.13706 q^{11} +1.80194 q^{12} -1.10992 q^{13} +1.10992 q^{14} -2.04892 q^{15} +2.85086 q^{16} -4.75302 q^{17} -0.445042 q^{18} -5.89977 q^{19} -3.69202 q^{20} +2.49396 q^{21} -0.951083 q^{22} -8.49396 q^{23} -1.69202 q^{24} -0.801938 q^{25} +0.493959 q^{26} -1.00000 q^{27} +4.49396 q^{28} -1.08815 q^{29} +0.911854 q^{30} +4.26875 q^{31} -4.65279 q^{32} -2.13706 q^{33} +2.11529 q^{34} -5.10992 q^{35} -1.80194 q^{36} +3.02715 q^{37} +2.62565 q^{38} +1.10992 q^{39} +3.46681 q^{40} -0.493959 q^{41} -1.10992 q^{42} -5.95108 q^{43} -3.85086 q^{44} +2.04892 q^{45} +3.78017 q^{46} -10.6136 q^{47} -2.85086 q^{48} -0.780167 q^{49} +0.356896 q^{50} +4.75302 q^{51} +2.00000 q^{52} -1.56033 q^{53} +0.445042 q^{54} +4.37867 q^{55} -4.21983 q^{56} +5.89977 q^{57} +0.484271 q^{58} +0.884707 q^{59} +3.69202 q^{60} -0.615957 q^{61} -1.89977 q^{62} -2.49396 q^{63} -3.63102 q^{64} -2.27413 q^{65} +0.951083 q^{66} +3.42758 q^{67} +8.56465 q^{68} +8.49396 q^{69} +2.27413 q^{70} -1.32975 q^{71} +1.69202 q^{72} +14.1414 q^{73} -1.34721 q^{74} +0.801938 q^{75} +10.6310 q^{76} -5.32975 q^{77} -0.493959 q^{78} -7.20775 q^{79} +5.84117 q^{80} +1.00000 q^{81} +0.219833 q^{82} +8.59179 q^{83} -4.49396 q^{84} -9.73855 q^{85} +2.64848 q^{86} +1.08815 q^{87} +3.61596 q^{88} -4.31767 q^{89} -0.911854 q^{90} +2.76809 q^{91} +15.3056 q^{92} -4.26875 q^{93} +4.72348 q^{94} -12.0881 q^{95} +4.65279 q^{96} +18.3937 q^{97} +0.347207 q^{98} +2.13706 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - q^{2} - 3 q^{3} - q^{4} - 3 q^{5} + q^{6} + 2 q^{7} + 3 q^{9}+O(q^{10}) \) 3 * q - q^2 - 3 * q^3 - q^4 - 3 * q^5 + q^6 + 2 * q^7 + 3 * q^9	\( 3 q - q^{2} - 3 q^{3} - q^{4} - 3 q^{5} + q^{6} + 2 q^{7} + 3 q^{9} + q^{10} + q^{11} + q^{12} - 4 q^{13} + 4 q^{14} + 3 q^{15} - 5 q^{16} - 19 q^{17} - q^{18} + 5 q^{19} - 6 q^{20} - 2 q^{21} - 12 q^{22} - 16 q^{23} + 2 q^{25} - 8 q^{26} - 3 q^{27} + 4 q^{28} - 7 q^{29} - q^{30} + 5 q^{31} + 4 q^{32} - q^{33} + 4 q^{34} - 16 q^{35} - q^{36} + 3 q^{37} - 4 q^{38} + 4 q^{39} + 7 q^{40} + 8 q^{41} - 4 q^{42} - 27 q^{43} + 2 q^{44} - 3 q^{45} + 10 q^{46} - q^{47} + 5 q^{48} - q^{49} - 3 q^{50} + 19 q^{51} + 6 q^{52} - 2 q^{53} + q^{54} + 6 q^{55} - 14 q^{56} - 5 q^{57} + 14 q^{58} + 5 q^{59} + 6 q^{60} - 12 q^{61} + 17 q^{62} + 2 q^{63} + 4 q^{64} + 4 q^{65} + 12 q^{66} - 6 q^{67} + 4 q^{68} + 16 q^{69} - 4 q^{70} - 6 q^{71} + 18 q^{73} - 22 q^{74} - 2 q^{75} + 17 q^{76} - 18 q^{77} + 8 q^{78} - 4 q^{79} + 26 q^{80} + 3 q^{81} + 2 q^{82} - 2 q^{83} - 4 q^{84} + 26 q^{85} + 9 q^{86} + 7 q^{87} + 21 q^{88} + 4 q^{89} + q^{90} - 12 q^{91} + 10 q^{92} - 5 q^{93} - 16 q^{94} - 40 q^{95} - 4 q^{96} + 23 q^{97} + 19 q^{98} + q^{99}+O(q^{100}) \) 3 * q - q^2 - 3 * q^3 - q^4 - 3 * q^5 + q^6 + 2 * q^7 + 3 * q^9 + q^10 + q^11 + q^12 - 4 * q^13 + 4 * q^14 + 3 * q^15 - 5 * q^16 - 19 * q^17 - q^18 + 5 * q^19 - 6 * q^20 - 2 * q^21 - 12 * q^22 - 16 * q^23 + 2 * q^25 - 8 * q^26 - 3 * q^27 + 4 * q^28 - 7 * q^29 - q^30 + 5 * q^31 + 4 * q^32 - q^33 + 4 * q^34 - 16 * q^35 - q^36 + 3 * q^37 - 4 * q^38 + 4 * q^39 + 7 * q^40 + 8 * q^41 - 4 * q^42 - 27 * q^43 + 2 * q^44 - 3 * q^45 + 10 * q^46 - q^47 + 5 * q^48 - q^49 - 3 * q^50 + 19 * q^51 + 6 * q^52 - 2 * q^53 + q^54 + 6 * q^55 - 14 * q^56 - 5 * q^57 + 14 * q^58 + 5 * q^59 + 6 * q^60 - 12 * q^61 + 17 * q^62 + 2 * q^63 + 4 * q^64 + 4 * q^65 + 12 * q^66 - 6 * q^67 + 4 * q^68 + 16 * q^69 - 4 * q^70 - 6 * q^71 + 18 * q^73 - 22 * q^74 - 2 * q^75 + 17 * q^76 - 18 * q^77 + 8 * q^78 - 4 * q^79 + 26 * q^80 + 3 * q^81 + 2 * q^82 - 2 * q^83 - 4 * q^84 + 26 * q^85 + 9 * q^86 + 7 * q^87 + 21 * q^88 + 4 * q^89 + q^90 - 12 * q^91 + 10 * q^92 - 5 * q^93 - 16 * q^94 - 40 * q^95 - 4 * q^96 + 23 * q^97 + 19 * q^98 + q^99

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