LMFDB - Embedded newform 6034.2.a.p.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, 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("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.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:	$48.1817325796$
Analytic rank:	$0$
Dimension:	$27$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.81149 q^{3} +1.00000 q^{4} -1.26479 q^{5} +1.81149 q^{6} +1.00000 q^{7} -1.00000 q^{8} +0.281479 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.81149 q^{3} +1.00000 q^{4} -1.26479 q^{5} +1.81149 q^{6} +1.00000 q^{7} -1.00000 q^{8} +0.281479 q^{9} +1.26479 q^{10} -3.69998 q^{11} -1.81149 q^{12} -1.60916 q^{13} -1.00000 q^{14} +2.29115 q^{15} +1.00000 q^{16} +1.22557 q^{17} -0.281479 q^{18} -8.48264 q^{19} -1.26479 q^{20} -1.81149 q^{21} +3.69998 q^{22} +2.94922 q^{23} +1.81149 q^{24} -3.40030 q^{25} +1.60916 q^{26} +4.92456 q^{27} +1.00000 q^{28} -5.38169 q^{29} -2.29115 q^{30} +1.88362 q^{31} -1.00000 q^{32} +6.70245 q^{33} -1.22557 q^{34} -1.26479 q^{35} +0.281479 q^{36} -5.44694 q^{37} +8.48264 q^{38} +2.91497 q^{39} +1.26479 q^{40} -3.98088 q^{41} +1.81149 q^{42} -12.2128 q^{43} -3.69998 q^{44} -0.356012 q^{45} -2.94922 q^{46} +0.841801 q^{47} -1.81149 q^{48} +1.00000 q^{49} +3.40030 q^{50} -2.22010 q^{51} -1.60916 q^{52} +1.85550 q^{53} -4.92456 q^{54} +4.67971 q^{55} -1.00000 q^{56} +15.3662 q^{57} +5.38169 q^{58} -9.72023 q^{59} +2.29115 q^{60} -5.36202 q^{61} -1.88362 q^{62} +0.281479 q^{63} +1.00000 q^{64} +2.03525 q^{65} -6.70245 q^{66} -1.54318 q^{67} +1.22557 q^{68} -5.34246 q^{69} +1.26479 q^{70} +0.705663 q^{71} -0.281479 q^{72} +15.3830 q^{73} +5.44694 q^{74} +6.15959 q^{75} -8.48264 q^{76} -3.69998 q^{77} -2.91497 q^{78} +3.15953 q^{79} -1.26479 q^{80} -9.76521 q^{81} +3.98088 q^{82} -1.30049 q^{83} -1.81149 q^{84} -1.55009 q^{85} +12.2128 q^{86} +9.74885 q^{87} +3.69998 q^{88} -9.94355 q^{89} +0.356012 q^{90} -1.60916 q^{91} +2.94922 q^{92} -3.41215 q^{93} -0.841801 q^{94} +10.7288 q^{95} +1.81149 q^{96} -3.24220 q^{97} -1.00000 q^{98} -1.04146 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q - 27 q^{2} + 4 q^{3} + 27 q^{4} + 9 q^{5} - 4 q^{6} + 27 q^{7} - 27 q^{8} + 35 q^{9}+O(q^{10}) $ 27 * q - 27 * q^2 + 4 * q^3 + 27 * q^4 + 9 * q^5 - 4 * q^6 + 27 * q^7 - 27 * q^8 + 35 * q^9	\( 27 q - 27 q^{2} + 4 q^{3} + 27 q^{4} + 9 q^{5} - 4 q^{6} + 27 q^{7} - 27 q^{8} + 35 q^{9} - 9 q^{10} + 24 q^{11} + 4 q^{12} - 13 q^{13} - 27 q^{14} + 16 q^{15} + 27 q^{16} - 5 q^{17} - 35 q^{18} + q^{19} + 9 q^{20} + 4 q^{21} - 24 q^{22} + 32 q^{23} - 4 q^{24} + 30 q^{25} + 13 q^{26} + q^{27} + 27 q^{28} + 26 q^{29} - 16 q^{30} + 21 q^{31} - 27 q^{32} + 7 q^{33} + 5 q^{34} + 9 q^{35} + 35 q^{36} + 4 q^{37} - q^{38} + 13 q^{39} - 9 q^{40} + 31 q^{41} - 4 q^{42} - 13 q^{43} + 24 q^{44} + 19 q^{45} - 32 q^{46} + 41 q^{47} + 4 q^{48} + 27 q^{49} - 30 q^{50} + 21 q^{51} - 13 q^{52} + 29 q^{53} - q^{54} + 9 q^{55} - 27 q^{56} - 26 q^{58} + 36 q^{59} + 16 q^{60} + q^{61} - 21 q^{62} + 35 q^{63} + 27 q^{64} + 46 q^{65} - 7 q^{66} - 2 q^{67} - 5 q^{68} + 43 q^{69} - 9 q^{70} + 70 q^{71} - 35 q^{72} - 21 q^{73} - 4 q^{74} + 37 q^{75} + q^{76} + 24 q^{77} - 13 q^{78} + 19 q^{79} + 9 q^{80} + 67 q^{81} - 31 q^{82} + 25 q^{83} + 4 q^{84} - 6 q^{85} + 13 q^{86} - 9 q^{87} - 24 q^{88} + 85 q^{89} - 19 q^{90} - 13 q^{91} + 32 q^{92} + 23 q^{93} - 41 q^{94} + 77 q^{95} - 4 q^{96} - 2 q^{97} - 27 q^{98} + 38 q^{99}+O(q^{100}) \) 27 * q - 27 * q^2 + 4 * q^3 + 27 * q^4 + 9 * q^5 - 4 * q^6 + 27 * q^7 - 27 * q^8 + 35 * q^9 - 9 * q^10 + 24 * q^11 + 4 * q^12 - 13 * q^13 - 27 * q^14 + 16 * q^15 + 27 * q^16 - 5 * q^17 - 35 * q^18 + q^19 + 9 * q^20 + 4 * q^21 - 24 * q^22 + 32 * q^23 - 4 * q^24 + 30 * q^25 + 13 * q^26 + q^27 + 27 * q^28 + 26 * q^29 - 16 * q^30 + 21 * q^31 - 27 * q^32 + 7 * q^33 + 5 * q^34 + 9 * q^35 + 35 * q^36 + 4 * q^37 - q^38 + 13 * q^39 - 9 * q^40 + 31 * q^41 - 4 * q^42 - 13 * q^43 + 24 * q^44 + 19 * q^45 - 32 * q^46 + 41 * q^47 + 4 * q^48 + 27 * q^49 - 30 * q^50 + 21 * q^51 - 13 * q^52 + 29 * q^53 - q^54 + 9 * q^55 - 27 * q^56 - 26 * q^58 + 36 * q^59 + 16 * q^60 + q^61 - 21 * q^62 + 35 * q^63 + 27 * q^64 + 46 * q^65 - 7 * q^66 - 2 * q^67 - 5 * q^68 + 43 * q^69 - 9 * q^70 + 70 * q^71 - 35 * q^72 - 21 * q^73 - 4 * q^74 + 37 * q^75 + q^76 + 24 * q^77 - 13 * q^78 + 19 * q^79 + 9 * q^80 + 67 * q^81 - 31 * q^82 + 25 * q^83 + 4 * q^84 - 6 * q^85 + 13 * q^86 - 9 * q^87 - 24 * q^88 + 85 * q^89 - 19 * q^90 - 13 * q^91 + 32 * q^92 + 23 * q^93 - 41 * q^94 + 77 * q^95 - 4 * q^96 - 2 * q^97 - 27 * q^98 + 38 * 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
$3$	−1.81149	−1.04586	−0.522931	−	0.852375i	$-0.675161\pi$
$3$	−1.81149	−1.04586	−0.522931	+	0.852375i	$0.675161\pi$
$4$	1.00000	0.500000
$5$	−1.26479	−0.565633	−0.282816	−	0.959174i	$-0.591269\pi$
$5$	−1.26479	−0.565633	−0.282816	+	0.959174i	$0.591269\pi$
$6$	1.81149	0.739536
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	0.281479	0.0938262
$10$	1.26479	0.399963
$11$	−3.69998	−1.11559	−0.557793	−	0.829980i	$-0.688352\pi$
$11$	−3.69998	−1.11559	−0.557793	+	0.829980i	$0.688352\pi$
$12$	−1.81149	−0.522931
$13$	−1.60916	−0.446300	−0.223150	−	0.974784i	$-0.571634\pi$
$13$	−1.60916	−0.446300	−0.223150	+	0.974784i	$0.571634\pi$
$14$	−1.00000	−0.267261
$15$	2.29115	0.591574
$16$	1.00000	0.250000
$17$	1.22557	0.297244	0.148622	−	0.988894i	$-0.452516\pi$
$17$	1.22557	0.297244	0.148622	+	0.988894i	$0.452516\pi$
$18$	−0.281479	−0.0663452
$19$	−8.48264	−1.94605	−0.973026	−	0.230696i	$-0.925900\pi$
$19$	−8.48264	−1.94605	−0.973026	+	0.230696i	$0.925900\pi$
$20$	−1.26479	−0.282816
$21$	−1.81149	−0.395298
$22$	3.69998	0.788838
$23$	2.94922	0.614954	0.307477	−	0.951555i	$-0.400515\pi$
$23$	2.94922	0.614954	0.307477	+	0.951555i	$0.400515\pi$
$24$	1.81149	0.369768
$25$	−3.40030	−0.680060
$26$	1.60916	0.315582
$27$	4.92456	0.947732
$28$	1.00000	0.188982
$29$	−5.38169	−0.999355	−0.499677	−	0.866212i	$-0.666548\pi$
$29$	−5.38169	−0.999355	−0.499677	+	0.866212i	$0.666548\pi$
$30$	−2.29115	−0.418306
$31$	1.88362	0.338309	0.169154	−	0.985590i	$-0.445896\pi$
$31$	1.88362	0.338309	0.169154	+	0.985590i	$0.445896\pi$
$32$	−1.00000	−0.176777
$33$	6.70245	1.16675
$34$	−1.22557	−0.210184
$35$	−1.26479	−0.213789
$36$	0.281479	0.0469131
$37$	−5.44694	−0.895471	−0.447735	−	0.894166i	$-0.647769\pi$
$37$	−5.44694	−0.895471	−0.447735	+	0.894166i	$0.647769\pi$
$38$	8.48264	1.37607
$39$	2.91497	0.466768
$40$	1.26479	0.199981
$41$	−3.98088	−0.621709	−0.310854	−	0.950458i	$-0.600615\pi$
$41$	−3.98088	−0.621709	−0.310854	+	0.950458i	$0.600615\pi$
$42$	1.81149	0.279518
$43$	−12.2128	−1.86244	−0.931220	−	0.364457i	$-0.881255\pi$
$43$	−12.2128	−1.86244	−0.931220	+	0.364457i	$0.881255\pi$
$44$	−3.69998	−0.557793
$45$	−0.356012	−0.0530712
$46$	−2.94922	−0.434838
$47$	0.841801	0.122789	0.0613946	−	0.998114i	$-0.480445\pi$
$47$	0.841801	0.122789	0.0613946	+	0.998114i	$0.480445\pi$
$48$	−1.81149	−0.261465
$49$	1.00000	0.142857
$50$	3.40030	0.480875
$51$	−2.22010	−0.310876
$52$	−1.60916	−0.223150
$53$	1.85550	0.254873	0.127436	−	0.991847i	$-0.459325\pi$
$53$	1.85550	0.254873	0.127436	+	0.991847i	$0.459325\pi$
$54$	−4.92456	−0.670148
$55$	4.67971	0.631012
$56$	−1.00000	−0.133631
$57$	15.3662	2.03530
$58$	5.38169	0.706651
$59$	−9.72023	−1.26547	−0.632733	−	0.774370i	$-0.718067\pi$
$59$	−9.72023	−1.26547	−0.632733	+	0.774370i	$0.718067\pi$
$60$	2.29115	0.295787
$61$	−5.36202	−0.686536	−0.343268	−	0.939237i	$-0.611534\pi$
$61$	−5.36202	−0.686536	−0.343268	+	0.939237i	$0.611534\pi$
$62$	−1.88362	−0.239220
$63$	0.281479	0.0354630
$64$	1.00000	0.125000
$65$	2.03525	0.252442
$66$	−6.70245	−0.825015
$67$	−1.54318	−0.188529	−0.0942646	−	0.995547i	$-0.530050\pi$
$67$	−1.54318	−0.188529	−0.0942646	+	0.995547i	$0.530050\pi$
$68$	1.22557	0.148622
$69$	−5.34246	−0.643157
$70$	1.26479	0.151172
$71$	0.705663	0.0837468	0.0418734	−	0.999123i	$-0.486667\pi$
$71$	0.705663	0.0837468	0.0418734	+	0.999123i	$0.486667\pi$
$72$	−0.281479	−0.0331726
$73$	15.3830	1.80044	0.900220	−	0.435435i	$-0.143405\pi$
$73$	15.3830	1.80044	0.900220	+	0.435435i	$0.143405\pi$
$74$	5.44694	0.633193
$75$	6.15959	0.711248
$76$	−8.48264	−0.973026
$77$	−3.69998	−0.421652
$78$	−2.91497	−0.330055
$79$	3.15953	0.355475	0.177738	−	0.984078i	$-0.443122\pi$
$79$	3.15953	0.355475	0.177738	+	0.984078i	$0.443122\pi$
$80$	−1.26479	−0.141408
$81$	−9.76521	−1.08502
$82$	3.98088	0.439615
$83$	−1.30049	−0.142747	−0.0713735	−	0.997450i	$-0.522738\pi$
$83$	−1.30049	−0.142747	−0.0713735	+	0.997450i	$0.522738\pi$
$84$	−1.81149	−0.197649
$85$	−1.55009	−0.168131
$86$	12.2128	1.31694
$87$	9.74885	1.04519
$88$	3.69998	0.394419
$89$	−9.94355	−1.05401	−0.527007	−	0.849861i	$-0.676686\pi$
$89$	−9.94355	−1.05401	−0.527007	+	0.849861i	$0.676686\pi$
$90$	0.356012	0.0375270
$91$	−1.60916	−0.168686
$92$	2.94922	0.307477
$93$	−3.41215	−0.353824
$94$	−0.841801	−0.0868251
$95$	10.7288	1.10075
$96$	1.81149	0.184884
$97$	−3.24220	−0.329196	−0.164598	−	0.986361i	$-0.552633\pi$
$97$	−3.24220	−0.329196	−0.164598	+	0.986361i	$0.552633\pi$
$98$	−1.00000	−0.101015
$99$	−1.04146	−0.104671
$100$	−3.40030	−0.340030
$101$	1.22958	0.122348	0.0611740	−	0.998127i	$-0.480516\pi$
$101$	1.22958	0.122348	0.0611740	+	0.998127i	$0.480516\pi$
$102$	2.22010	0.219823
$103$	−11.5690	−1.13993	−0.569963	−	0.821671i	$-0.693042\pi$
$103$	−11.5690	−1.13993	−0.569963	+	0.821671i	$0.693042\pi$
$104$	1.60916	0.157791
$105$	2.29115	0.223594
$106$	−1.85550	−0.180222
$107$	0.619641	0.0599029	0.0299515	−	0.999551i	$-0.490465\pi$
$107$	0.619641	0.0599029	0.0299515	+	0.999551i	$0.490465\pi$
$108$	4.92456	0.473866
$109$	−9.85275	−0.943722	−0.471861	−	0.881673i	$-0.656418\pi$
$109$	−9.85275	−0.943722	−0.471861	+	0.881673i	$0.656418\pi$
$110$	−4.67971	−0.446193
$111$	9.86704	0.936538
$112$	1.00000	0.0944911
$113$	−3.40332	−0.320158	−0.160079	−	0.987104i	$-0.551175\pi$
$113$	−3.40332	−0.320158	−0.160079	+	0.987104i	$0.551175\pi$
$114$	−15.3662	−1.43917
$115$	−3.73015	−0.347838
$116$	−5.38169	−0.499677
$117$	−0.452944	−0.0418747
$118$	9.72023	0.894820
$119$	1.22557	0.112348
$120$	−2.29115	−0.209153
$121$	2.68984	0.244530
$122$	5.36202	0.485454
$123$	7.21131	0.650221
$124$	1.88362	0.169154
$125$	10.6246	0.950297
$126$	−0.281479	−0.0250761
$127$	17.4409	1.54763	0.773817	−	0.633410i	$-0.218345\pi$
$127$	17.4409	1.54763	0.773817	+	0.633410i	$0.218345\pi$
$128$	−1.00000	−0.0883883
$129$	22.1234	1.94785
$130$	−2.03525	−0.178503
$131$	3.14802	0.275044	0.137522	−	0.990499i	$-0.456086\pi$
$131$	3.14802	0.275044	0.137522	+	0.990499i	$0.456086\pi$
$132$	6.70245	0.583374
$133$	−8.48264	−0.735538
$134$	1.54318	0.133310
$135$	−6.22855	−0.536068
$136$	−1.22557	−0.105092
$137$	−2.98165	−0.254740	−0.127370	−	0.991855i	$-0.540654\pi$
$137$	−2.98165	−0.254740	−0.127370	+	0.991855i	$0.540654\pi$
$138$	5.34246	0.454781
$139$	−6.82476	−0.578868	−0.289434	−	0.957198i	$-0.593467\pi$
$139$	−6.82476	−0.578868	−0.289434	+	0.957198i	$0.593467\pi$
$140$	−1.26479	−0.106895
$141$	−1.52491	−0.128421
$142$	−0.705663	−0.0592179
$143$	5.95385	0.497886
$144$	0.281479	0.0234566
$145$	6.80673	0.565268
$146$	−15.3830	−1.27310
$147$	−1.81149	−0.149409
$148$	−5.44694	−0.447735
$149$	1.70491	0.139672	0.0698358	−	0.997558i	$-0.477752\pi$
$149$	1.70491	0.139672	0.0698358	+	0.997558i	$0.477752\pi$
$150$	−6.15959	−0.502928
$151$	19.2929	1.57004	0.785019	−	0.619472i	$-0.212653\pi$
$151$	19.2929	1.57004	0.785019	+	0.619472i	$0.212653\pi$
$152$	8.48264	0.688033
$153$	0.344972	0.0278893
$154$	3.69998	0.298153
$155$	−2.38239	−0.191358
$156$	2.91497	0.233384
$157$	−10.4163	−0.831309	−0.415655	−	0.909523i	$-0.636447\pi$
$157$	−10.4163	−0.831309	−0.415655	+	0.909523i	$0.636447\pi$
$158$	−3.15953	−0.251359
$159$	−3.36122	−0.266562
$160$	1.26479	0.0999907
$161$	2.94922	0.232431
$162$	9.76521	0.767227
$163$	−6.39508	−0.500901	−0.250451	−	0.968129i	$-0.580579\pi$
$163$	−6.39508	−0.500901	−0.250451	+	0.968129i	$0.580579\pi$
$164$	−3.98088	−0.310854
$165$	−8.47722	−0.659951
$166$	1.30049	0.100937
$167$	−20.1081	−1.55601	−0.778005	−	0.628258i	$-0.783768\pi$
$167$	−20.1081	−1.55601	−0.778005	+	0.628258i	$0.783768\pi$
$168$	1.81149	0.139759
$169$	−10.4106	−0.800816
$170$	1.55009	0.118887
$171$	−2.38768	−0.182591
$172$	−12.2128	−0.931220
$173$	−15.9922	−1.21586	−0.607931	−	0.793990i	$-0.708000\pi$
$173$	−15.9922	−1.21586	−0.607931	+	0.793990i	$0.708000\pi$
$174$	−9.74885	−0.739059
$175$	−3.40030	−0.257038
$176$	−3.69998	−0.278896
$177$	17.6080	1.32350
$178$	9.94355	0.745301
$179$	15.7842	1.17977	0.589885	−	0.807487i	$-0.299173\pi$
$179$	15.7842	1.17977	0.589885	+	0.807487i	$0.299173\pi$
$180$	−0.356012	−0.0265356
$181$	−17.5280	−1.30285	−0.651424	−	0.758714i	$-0.725828\pi$
$181$	−17.5280	−1.30285	−0.651424	+	0.758714i	$0.725828\pi$
$182$	1.60916	0.119279
$183$	9.71322	0.718022
$184$	−2.94922	−0.217419
$185$	6.88925	0.506508
$186$	3.41215	0.250191
$187$	−4.53458	−0.331601
$188$	0.841801	0.0613946
$189$	4.92456	0.358209
$190$	−10.7288	−0.778348
$191$	−25.0315	−1.81122	−0.905608	−	0.424116i	$-0.860585\pi$
$191$	−25.0315	−1.81122	−0.905608	+	0.424116i	$0.860585\pi$
$192$	−1.81149	−0.130733
$193$	1.36102	0.0979682	0.0489841	−	0.998800i	$-0.484402\pi$
$193$	1.36102	0.0979682	0.0489841	+	0.998800i	$0.484402\pi$
$194$	3.24220	0.232777
$195$	−3.68683	−0.264019
$196$	1.00000	0.0714286
$197$	−7.39068	−0.526564	−0.263282	−	0.964719i	$-0.584805\pi$
$197$	−7.39068	−0.526564	−0.263282	+	0.964719i	$0.584805\pi$
$198$	1.04146	0.0740137
$199$	−15.7798	−1.11860	−0.559300	−	0.828965i	$-0.688930\pi$
$199$	−15.7798	−1.11860	−0.559300	+	0.828965i	$0.688930\pi$
$200$	3.40030	0.240437
$201$	2.79545	0.197176
$202$	−1.22958	−0.0865131
$203$	−5.38169	−0.377721
$204$	−2.22010	−0.155438
$205$	5.03499	0.351659
$206$	11.5690	0.806049
$207$	0.830142	0.0576988
$208$	−1.60916	−0.111575
$209$	31.3856	2.17099
$210$	−2.29115	−0.158105
$211$	3.39957	0.234036	0.117018	−	0.993130i	$-0.462666\pi$
$211$	3.39957	0.234036	0.117018	+	0.993130i	$0.462666\pi$
$212$	1.85550	0.127436
$213$	−1.27830	−0.0875875
$214$	−0.619641	−0.0423578
$215$	15.4467	1.05346
$216$	−4.92456	−0.335074
$217$	1.88362	0.127869
$218$	9.85275	0.667312
$219$	−27.8660	−1.88301
$220$	4.67971	0.315506
$221$	−1.97214	−0.132660
$222$	−9.86704	−0.662233
$223$	−19.6925	−1.31870	−0.659352	−	0.751834i	$-0.729169\pi$
$223$	−19.6925	−1.31870	−0.659352	+	0.751834i	$0.729169\pi$
$224$	−1.00000	−0.0668153
$225$	−0.957111	−0.0638074
$226$	3.40332	0.226386
$227$	21.0869	1.39959	0.699794	−	0.714345i	$-0.253275\pi$
$227$	21.0869	1.39959	0.699794	+	0.714345i	$0.253275\pi$
$228$	15.3662	1.01765
$229$	−15.9648	−1.05498	−0.527492	−	0.849560i	$-0.676867\pi$
$229$	−15.9648	−1.05498	−0.527492	+	0.849560i	$0.676867\pi$
$230$	3.73015	0.245959
$231$	6.70245	0.440989
$232$	5.38169	0.353325
$233$	16.9445	1.11007	0.555036	−	0.831826i	$-0.312704\pi$
$233$	16.9445	1.11007	0.555036	+	0.831826i	$0.312704\pi$
$234$	0.452944	0.0296099
$235$	−1.06470	−0.0694536
$236$	−9.72023	−0.632733
$237$	−5.72345	−0.371778
$238$	−1.22557	−0.0794419
$239$	10.9737	0.709828	0.354914	−	0.934899i	$-0.384510\pi$
$239$	10.9737	0.709828	0.354914	+	0.934899i	$0.384510\pi$
$240$	2.29115	0.147893
$241$	14.2772	0.919677	0.459839	−	0.888003i	$-0.347907\pi$
$241$	14.2772	0.919677	0.459839	+	0.888003i	$0.347907\pi$
$242$	−2.68984	−0.172909
$243$	2.91584	0.187051
$244$	−5.36202	−0.343268
$245$	−1.26479	−0.0808047
$246$	−7.21131	−0.459776
$247$	13.6499	0.868523
$248$	−1.88362	−0.119610
$249$	2.35581	0.149294
$250$	−10.6246	−0.671961
$251$	−2.05705	−0.129840	−0.0649198	−	0.997890i	$-0.520679\pi$
$251$	−2.05705	−0.129840	−0.0649198	+	0.997890i	$0.520679\pi$
$252$	0.281479	0.0177315
$253$	−10.9120	−0.686034
$254$	−17.4409	−1.09434
$255$	2.80797	0.175842
$256$	1.00000	0.0625000
$257$	−21.6689	−1.35167	−0.675835	−	0.737053i	$-0.736217\pi$
$257$	−21.6689	−1.35167	−0.675835	+	0.737053i	$0.736217\pi$
$258$	−22.1234	−1.37734
$259$	−5.44694	−0.338456
$260$	2.03525	0.126221
$261$	−1.51483	−0.0937657
$262$	−3.14802	−0.194485
$263$	11.9621	0.737612	0.368806	−	0.929506i	$-0.379767\pi$
$263$	11.9621	0.737612	0.368806	+	0.929506i	$0.379767\pi$
$264$	−6.70245	−0.412508
$265$	−2.34683	−0.144164
$266$	8.48264	0.520104
$267$	18.0126	1.10235
$268$	−1.54318	−0.0942646
$269$	8.82775	0.538238	0.269119	−	0.963107i	$-0.413268\pi$
$269$	8.82775	0.538238	0.269119	+	0.963107i	$0.413268\pi$
$270$	6.22855	0.379058
$271$	5.09600	0.309560	0.154780	−	0.987949i	$-0.450533\pi$
$271$	5.09600	0.309560	0.154780	+	0.987949i	$0.450533\pi$
$272$	1.22557	0.0743111
$273$	2.91497	0.176422
$274$	2.98165	0.180128
$275$	12.5810	0.758664
$276$	−5.34246	−0.321578
$277$	13.3444	0.801786	0.400893	−	0.916125i	$-0.368700\pi$
$277$	13.3444	0.801786	0.400893	+	0.916125i	$0.368700\pi$
$278$	6.82476	0.409322
$279$	0.530200	0.0317422
$280$	1.26479	0.0755859
$281$	24.0353	1.43382	0.716912	−	0.697163i	$-0.245555\pi$
$281$	24.0353	1.43382	0.716912	+	0.697163i	$0.245555\pi$
$282$	1.52491	0.0908070
$283$	−6.07700	−0.361240	−0.180620	−	0.983553i	$-0.557810\pi$
$283$	−6.07700	−0.361240	−0.180620	+	0.983553i	$0.557810\pi$
$284$	0.705663	0.0418734
$285$	−19.4350	−1.15123
$286$	−5.95385	−0.352058
$287$	−3.98088	−0.234984
$288$	−0.281479	−0.0165863
$289$	−15.4980	−0.911646
$290$	−6.80673	−0.399705
$291$	5.87320	0.344293
$292$	15.3830	0.900220
$293$	28.1074	1.64205	0.821025	−	0.570892i	$-0.193403\pi$
$293$	28.1074	1.64205	0.821025	+	0.570892i	$0.193403\pi$
$294$	1.81149	0.105648
$295$	12.2941	0.715789
$296$	5.44694	0.316597
$297$	−18.2208	−1.05728
$298$	−1.70491	−0.0987628
$299$	−4.74576	−0.274454
$300$	6.15959	0.355624
$301$	−12.2128	−0.703936
$302$	−19.2929	−1.11018
$303$	−2.22737	−0.127959
$304$	−8.48264	−0.486513
$305$	6.78185	0.388327
$306$	−0.344972	−0.0197207
$307$	−19.3194	−1.10261	−0.551307	−	0.834302i	$-0.685871\pi$
$307$	−19.3194	−1.10261	−0.551307	+	0.834302i	$0.685871\pi$
$308$	−3.69998	−0.210826
$309$	20.9570	1.19220
$310$	2.38239	0.135311
$311$	−2.74556	−0.155686	−0.0778432	−	0.996966i	$-0.524803\pi$
$311$	−2.74556	−0.155686	−0.0778432	+	0.996966i	$0.524803\pi$
$312$	−2.91497	−0.165027
$313$	10.0581	0.568515	0.284257	−	0.958748i	$-0.408253\pi$
$313$	10.0581	0.568515	0.284257	+	0.958748i	$0.408253\pi$
$314$	10.4163	0.587824
$315$	−0.356012	−0.0200590
$316$	3.15953	0.177738
$317$	35.4943	1.99356	0.996780	−	0.0801895i	$-0.0255525\pi$
$317$	35.4943	1.99356	0.996780	+	0.0801895i	$0.0255525\pi$
$318$	3.36122	0.188488
$319$	19.9121	1.11487
$320$	−1.26479	−0.0707041
$321$	−1.12247	−0.0626502
$322$	−2.94922	−0.164353
$323$	−10.3961	−0.578453
$324$	−9.76521	−0.542511
$325$	5.47162	0.303511
$326$	6.39508	0.354191
$327$	17.8481	0.987002
$328$	3.98088	0.219807
$329$	0.841801	0.0464100
$330$	8.47722	0.466656
$331$	11.8033	0.648768	0.324384	−	0.945925i	$-0.394843\pi$
$331$	11.8033	0.648768	0.324384	+	0.945925i	$0.394843\pi$
$332$	−1.30049	−0.0713735
$333$	−1.53320	−0.0840186
$334$	20.1081	1.10027
$335$	1.95180	0.106638
$336$	−1.81149	−0.0988246
$337$	−20.4124	−1.11193	−0.555967	−	0.831205i	$-0.687652\pi$
$337$	−20.4124	−1.11193	−0.555967	+	0.831205i	$0.687652\pi$
$338$	10.4106	0.566263
$339$	6.16507	0.334841
$340$	−1.55009	−0.0840656
$341$	−6.96936	−0.377412
$342$	2.38768	0.129111
$343$	1.00000	0.0539949
$344$	12.2128	0.658472
$345$	6.75711	0.363791
$346$	15.9922	0.859744
$347$	22.9837	1.23383	0.616914	−	0.787030i	$-0.288383\pi$
$347$	22.9837	1.23383	0.616914	+	0.787030i	$0.288383\pi$
$348$	9.74885	0.522593
$349$	−18.7096	−1.00150	−0.500752	−	0.865591i	$-0.666943\pi$
$349$	−18.7096	−1.00150	−0.500752	+	0.865591i	$0.666943\pi$
$350$	3.40030	0.181754
$351$	−7.92440	−0.422973
$352$	3.69998	0.197209
$353$	−27.0394	−1.43916	−0.719582	−	0.694408i	$-0.755666\pi$
$353$	−27.0394	−1.43916	−0.719582	+	0.694408i	$0.755666\pi$
$354$	−17.6080	−0.935857
$355$	−0.892518	−0.0473699
$356$	−9.94355	−0.527007
$357$	−2.22010	−0.117500
$358$	−15.7842	−0.834223
$359$	29.9526	1.58084	0.790418	−	0.612568i	$-0.209863\pi$
$359$	29.9526	1.58084	0.790418	+	0.612568i	$0.209863\pi$
$360$	0.356012	0.0187635
$361$	52.9552	2.78712
$362$	17.5280	0.921252
$363$	−4.87260	−0.255745
$364$	−1.60916	−0.0843428
$365$	−19.4563	−1.01839
$366$	−9.71322	−0.507718
$367$	13.0823	0.682893	0.341446	−	0.939901i	$-0.389083\pi$
$367$	13.0823	0.682893	0.341446	+	0.939901i	$0.389083\pi$
$368$	2.94922	0.153739
$369$	−1.12053	−0.0583326
$370$	−6.88925	−0.358155
$371$	1.85550	0.0963329
$372$	−3.41215	−0.176912
$373$	−15.2780	−0.791065	−0.395533	−	0.918452i	$-0.629440\pi$
$373$	−15.2780	−0.791065	−0.395533	+	0.918452i	$0.629440\pi$
$374$	4.53458	0.234478
$375$	−19.2464	−0.993879
$376$	−0.841801	−0.0434126
$377$	8.65999	0.446012
$378$	−4.92456	−0.253292
$379$	24.4251	1.25463	0.627315	−	0.778765i	$-0.284154\pi$
$379$	24.4251	1.25463	0.627315	+	0.778765i	$0.284154\pi$
$380$	10.7288	0.550375
$381$	−31.5940	−1.61861
$382$	25.0315	1.28072
$383$	2.42731	0.124030	0.0620149	−	0.998075i	$-0.480247\pi$
$383$	2.42731	0.124030	0.0620149	+	0.998075i	$0.480247\pi$
$384$	1.81149	0.0924420
$385$	4.67971	0.238500
$386$	−1.36102	−0.0692740
$387$	−3.43765	−0.174746
$388$	−3.24220	−0.164598
$389$	11.3762	0.576794	0.288397	−	0.957511i	$-0.406878\pi$
$389$	11.3762	0.576794	0.288397	+	0.957511i	$0.406878\pi$
$390$	3.68683	0.186690
$391$	3.61447	0.182792
$392$	−1.00000	−0.0505076
$393$	−5.70259	−0.287657
$394$	7.39068	0.372337
$395$	−3.99616	−0.201069
$396$	−1.04146	−0.0523356
$397$	−14.7057	−0.738056	−0.369028	−	0.929418i	$-0.620309\pi$
$397$	−14.7057	−0.738056	−0.369028	+	0.929418i	$0.620309\pi$
$398$	15.7798	0.790970
$399$	15.3662	0.769271
$400$	−3.40030	−0.170015
$401$	16.3247	0.815219	0.407609	−	0.913156i	$-0.366363\pi$
$401$	16.3247	0.815219	0.407609	+	0.913156i	$0.366363\pi$
$402$	−2.79545	−0.139424
$403$	−3.03105	−0.150987
$404$	1.22958	0.0611740
$405$	12.3510	0.613725
$406$	5.38169	0.267089
$407$	20.1535	0.998974
$408$	2.22010	0.109911
$409$	−31.4450	−1.55486	−0.777429	−	0.628971i	$-0.783476\pi$
$409$	−31.4450	−1.55486	−0.777429	+	0.628971i	$0.783476\pi$
$410$	−5.03499	−0.248660
$411$	5.40122	0.266422
$412$	−11.5690	−0.569963
$413$	−9.72023	−0.478301
$414$	−0.830142	−0.0407992
$415$	1.64485	0.0807424
$416$	1.60916	0.0788955
$417$	12.3629	0.605416
$418$	−31.3856	−1.53512
$419$	25.4766	1.24461	0.622307	−	0.782773i	$-0.286195\pi$
$419$	25.4766	1.24461	0.622307	+	0.782773i	$0.286195\pi$
$420$	2.29115	0.111797
$421$	−31.6146	−1.54080	−0.770400	−	0.637561i	$-0.779943\pi$
$421$	−31.6146	−1.54080	−0.770400	+	0.637561i	$0.779943\pi$
$422$	−3.39957	−0.165488
$423$	0.236949	0.0115209
$424$	−1.85550	−0.0901112
$425$	−4.16730	−0.202144
$426$	1.27830	0.0619337
$427$	−5.36202	−0.259486
$428$	0.619641	0.0299515
$429$	−10.7853	−0.520720
$430$	−15.4467	−0.744907
$431$	−1.00000	−0.0481683
$431$	−1.00000	−0.0481683
$432$	4.92456	0.236933
$433$	34.8395	1.67428	0.837139	−	0.546990i	$-0.184226\pi$
$433$	34.8395	1.67428	0.837139	+	0.546990i	$0.184226\pi$
$434$	−1.88362	−0.0904168
$435$	−12.3303	−0.591192
$436$	−9.85275	−0.471861
$437$	−25.0172	−1.19673
$438$	27.8660	1.33149
$439$	11.0042	0.525201	0.262601	−	0.964905i	$-0.415420\pi$
$439$	11.0042	0.525201	0.262601	+	0.964905i	$0.415420\pi$
$440$	−4.67971	−0.223096
$441$	0.281479	0.0134037
$442$	1.97214	0.0938049
$443$	4.80323	0.228208	0.114104	−	0.993469i	$-0.463600\pi$
$443$	4.80323	0.228208	0.114104	+	0.993469i	$0.463600\pi$
$444$	9.86704	0.468269
$445$	12.5765	0.596185
$446$	19.6925	0.932465
$447$	−3.08842	−0.146077
$448$	1.00000	0.0472456
$449$	0.0286033	0.00134987	0.000674936	−	1.00000i	$-0.499785\pi$
$449$	0.0286033	0.00134987	0.000674936		1.00000i	$0.499785\pi$
$450$	0.957111	0.0451187
$451$	14.7292	0.693569
$452$	−3.40332	−0.160079
$453$	−34.9489	−1.64204
$454$	−21.0869	−0.989658
$455$	2.03525	0.0954141
$456$	−15.3662	−0.719587
$457$	−9.61452	−0.449748	−0.224874	−	0.974388i	$-0.572197\pi$
$457$	−9.61452	−0.449748	−0.224874	+	0.974388i	$0.572197\pi$
$458$	15.9648	0.745986
$459$	6.03539	0.281708
$460$	−3.73015	−0.173919
$461$	34.0608	1.58637	0.793186	−	0.608980i	$-0.208421\pi$
$461$	34.0608	1.58637	0.793186	+	0.608980i	$0.208421\pi$
$462$	−6.70245	−0.311826
$463$	−22.6241	−1.05143	−0.525715	−	0.850661i	$-0.676202\pi$
$463$	−22.6241	−1.05143	−0.525715	+	0.850661i	$0.676202\pi$
$464$	−5.38169	−0.249839
$465$	4.31567	0.200134
$466$	−16.9445	−0.784940
$467$	26.5106	1.22676	0.613381	−	0.789787i	$-0.289809\pi$
$467$	26.5106	1.22676	0.613381	+	0.789787i	$0.289809\pi$
$468$	−0.452944	−0.0209373
$469$	−1.54318	−0.0712574
$470$	1.06470	0.0491111
$471$	18.8689	0.869434
$472$	9.72023	0.447410
$473$	45.1872	2.07771
$474$	5.72345	0.262887
$475$	28.8435	1.32343
$476$	1.22557	0.0561739
$477$	0.522284	0.0239138
$478$	−10.9737	−0.501924
$479$	20.3244	0.928644	0.464322	−	0.885667i	$-0.346298\pi$
$479$	20.3244	0.928644	0.464322	+	0.885667i	$0.346298\pi$
$480$	−2.29115	−0.104576
$481$	8.76498	0.399649
$482$	−14.2772	−0.650310
$483$	−5.34246	−0.243090
$484$	2.68984	0.122265
$485$	4.10072	0.186204
$486$	−2.91584	−0.132265
$487$	24.8261	1.12498	0.562489	−	0.826805i	$-0.309844\pi$
$487$	24.8261	1.12498	0.562489	+	0.826805i	$0.309844\pi$
$488$	5.36202	0.242727
$489$	11.5846	0.523873
$490$	1.26479	0.0571375
$491$	10.4468	0.471459	0.235729	−	0.971819i	$-0.424252\pi$
$491$	10.4468	0.471459	0.235729	+	0.971819i	$0.424252\pi$
$492$	7.21131	0.325111
$493$	−6.59564	−0.297053
$494$	−13.6499	−0.614139
$495$	1.31724	0.0592054
$496$	1.88362	0.0845771
$497$	0.705663	0.0316533
$498$	−2.35581	−0.105566
$499$	−35.0560	−1.56932	−0.784660	−	0.619926i	$-0.787163\pi$
$499$	−35.0560	−1.56932	−0.784660	+	0.619926i	$0.787163\pi$
$500$	10.6246	0.475148
$501$	36.4255	1.62737
$502$	2.05705	0.0918104
$503$	−25.9380	−1.15652	−0.578260	−	0.815852i	$-0.696268\pi$
$503$	−25.9380	−1.15652	−0.578260	+	0.815852i	$0.696268\pi$
$504$	−0.281479	−0.0125381
$505$	−1.55517	−0.0692040
$506$	10.9120	0.485099
$507$	18.8587	0.837543
$508$	17.4409	0.773817
$509$	16.2577	0.720610	0.360305	−	0.932835i	$-0.382673\pi$
$509$	16.2577	0.720610	0.360305	+	0.932835i	$0.382673\pi$
$510$	−2.80797	−0.124339
$511$	15.3830	0.680502
$512$	−1.00000	−0.0441942
$513$	−41.7733	−1.84434
$514$	21.6689	0.955776
$515$	14.6324	0.644779
$516$	22.1234	0.973927
$517$	−3.11464	−0.136982
$518$	5.44694	0.239325
$519$	28.9696	1.27162
$520$	−2.03525	−0.0892517
$521$	26.5759	1.16431	0.582155	−	0.813078i	$-0.302210\pi$
$521$	26.5759	1.16431	0.582155	+	0.813078i	$0.302210\pi$
$522$	1.51483	0.0663024
$523$	−4.51580	−0.197462	−0.0987312	−	0.995114i	$-0.531478\pi$
$523$	−4.51580	−0.197462	−0.0987312	+	0.995114i	$0.531478\pi$
$524$	3.14802	0.137522
$525$	6.15959	0.268826
$526$	−11.9621	−0.521570
$527$	2.30851	0.100560
$528$	6.70245	0.291687
$529$	−14.3021	−0.621831
$530$	2.34683	0.101940
$531$	−2.73604	−0.118734
$532$	−8.48264	−0.367769
$533$	6.40587	0.277469
$534$	−18.0126	−0.779481
$535$	−0.783717	−0.0338831
$536$	1.54318	0.0666552
$537$	−28.5929	−1.23388
$538$	−8.82775	−0.380592
$539$	−3.69998	−0.159369
$540$	−6.22855	−0.268034
$541$	10.9554	0.471011	0.235505	−	0.971873i	$-0.424325\pi$
$541$	10.9554	0.471011	0.235505	+	0.971873i	$0.424325\pi$
$542$	−5.09600	−0.218892
$543$	31.7517	1.36260
$544$	−1.22557	−0.0525459
$545$	12.4617	0.533800
$546$	−2.91497	−0.124749
$547$	−3.64746	−0.155954	−0.0779770	−	0.996955i	$-0.524846\pi$
$547$	−3.64746	−0.155954	−0.0779770	+	0.996955i	$0.524846\pi$
$548$	−2.98165	−0.127370
$549$	−1.50929	−0.0644151
$550$	−12.5810	−0.536457
$551$	45.6510	1.94480
$552$	5.34246	0.227390
$553$	3.15953	0.134357
$554$	−13.3444	−0.566948
$555$	−12.4798	−0.529737
$556$	−6.82476	−0.289434
$557$	−30.2262	−1.28072	−0.640362	−	0.768073i	$-0.721216\pi$
$557$	−30.2262	−1.28072	−0.640362	+	0.768073i	$0.721216\pi$
$558$	−0.530200	−0.0224451
$559$	19.6524	0.831208
$560$	−1.26479	−0.0534473
$561$	8.21433	0.346809
$562$	−24.0353	−1.01387
$563$	−2.76600	−0.116573	−0.0582864	−	0.998300i	$-0.518564\pi$
$563$	−2.76600	−0.116573	−0.0582864	+	0.998300i	$0.518564\pi$
$564$	−1.52491	−0.0642103
$565$	4.30450	0.181092
$566$	6.07700	0.255435
$567$	−9.76521	−0.410100
$568$	−0.705663	−0.0296090
$569$	−28.5638	−1.19746	−0.598728	−	0.800952i	$-0.704327\pi$
$569$	−28.5638	−1.19746	−0.598728	+	0.800952i	$0.704327\pi$
$570$	19.4350	0.814045
$571$	15.5867	0.652283	0.326142	−	0.945321i	$-0.394251\pi$
$571$	15.5867	0.652283	0.326142	+	0.945321i	$0.394251\pi$
$572$	5.95385	0.248943
$573$	45.3442	1.89428
$574$	3.98088	0.166159
$575$	−10.0282	−0.418205
$576$	0.281479	0.0117283
$577$	−36.1615	−1.50542	−0.752712	−	0.658350i	$-0.771255\pi$
$577$	−36.1615	−1.50542	−0.752712	+	0.658350i	$0.771255\pi$
$578$	15.4980	0.644631
$579$	−2.46546	−0.102461
$580$	6.80673	0.282634
$581$	−1.30049	−0.0539533
$582$	−5.87320	−0.243452
$583$	−6.86532	−0.284332
$584$	−15.3830	−0.636552
$585$	0.572880	0.0236857
$586$	−28.1074	−1.16110
$587$	40.4034	1.66763	0.833813	−	0.552048i	$-0.186153\pi$
$587$	40.4034	1.66763	0.833813	+	0.552048i	$0.186153\pi$
$588$	−1.81149	−0.0747044
$589$	−15.9781	−0.658366
$590$	−12.2941	−0.506139
$591$	13.3881	0.550713
$592$	−5.44694	−0.223868
$593$	9.29155	0.381558	0.190779	−	0.981633i	$-0.438899\pi$
$593$	9.29155	0.381558	0.190779	+	0.981633i	$0.438899\pi$
$594$	18.2208	0.747607
$595$	−1.55009	−0.0635476
$596$	1.70491	0.0698358
$597$	28.5849	1.16990
$598$	4.74576	0.194068
$599$	21.6832	0.885950	0.442975	−	0.896534i	$-0.353923\pi$
$599$	21.6832	0.885950	0.442975	+	0.896534i	$0.353923\pi$
$600$	−6.15959	−0.251464
$601$	7.90326	0.322381	0.161190	−	0.986923i	$-0.448467\pi$
$601$	7.90326	0.322381	0.161190	+	0.986923i	$0.448467\pi$
$602$	12.2128	0.497758
$603$	−0.434372	−0.0176890
$604$	19.2929	0.785019
$605$	−3.40209	−0.138314
$606$	2.22737	0.0904807
$607$	−1.56999	−0.0637241	−0.0318620	−	0.999492i	$-0.510144\pi$
$607$	−1.56999	−0.0637241	−0.0318620	+	0.999492i	$0.510144\pi$
$608$	8.48264	0.344017
$609$	9.74885	0.395044
$610$	−6.78185	−0.274589
$611$	−1.35459	−0.0548009
$612$	0.344972	0.0139447
$613$	1.33177	0.0537898	0.0268949	−	0.999638i	$-0.491438\pi$
$613$	1.33177	0.0537898	0.0268949	+	0.999638i	$0.491438\pi$
$614$	19.3194	0.779667
$615$	−9.12081	−0.367787
$616$	3.69998	0.149076
$617$	38.8458	1.56387	0.781936	−	0.623358i	$-0.214232\pi$
$617$	38.8458	1.56387	0.781936	+	0.623358i	$0.214232\pi$
$618$	−20.9570	−0.843016
$619$	15.8900	0.638671	0.319336	−	0.947642i	$-0.396540\pi$
$619$	15.8900	0.638671	0.319336	+	0.947642i	$0.396540\pi$
$620$	−2.38239	−0.0956792
$621$	14.5236	0.582812
$622$	2.74556	0.110087
$623$	−9.94355	−0.398380
$624$	2.91497	0.116692
$625$	3.56351	0.142540
$626$	−10.0581	−0.402001
$627$	−56.8545	−2.27055
$628$	−10.4163	−0.415655
$629$	−6.67560	−0.266174
$630$	0.356012	0.0141839
$631$	−7.42086	−0.295420	−0.147710	−	0.989031i	$-0.547190\pi$
$631$	−7.42086	−0.295420	−0.147710	+	0.989031i	$0.547190\pi$
$632$	−3.15953	−0.125680
$633$	−6.15827	−0.244769
$634$	−35.4943	−1.40966
$635$	−22.0592	−0.875392
$636$	−3.36122	−0.133281
$637$	−1.60916	−0.0637572
$638$	−19.9121	−0.788329
$639$	0.198629	0.00785764
$640$	1.26479	0.0499954
$641$	8.61857	0.340413	0.170206	−	0.985408i	$-0.445557\pi$
$641$	8.61857	0.340413	0.170206	+	0.985408i	$0.445557\pi$
$642$	1.12247	0.0443004
$643$	32.5802	1.28484	0.642420	−	0.766353i	$-0.277931\pi$
$643$	32.5802	1.28484	0.642420	+	0.766353i	$0.277931\pi$
$644$	2.94922	0.116215
$645$	−27.9815	−1.10177
$646$	10.3961	0.409028
$647$	−27.6517	−1.08710	−0.543550	−	0.839377i	$-0.682920\pi$
$647$	−27.6517	−1.08710	−0.543550	+	0.839377i	$0.682920\pi$
$648$	9.76521	0.383614
$649$	35.9646	1.41174
$650$	−5.47162	−0.214614
$651$	−3.41215	−0.133733
$652$	−6.39508	−0.250451
$653$	−10.4012	−0.407030	−0.203515	−	0.979072i	$-0.565237\pi$
$653$	−10.4012	−0.407030	−0.203515	+	0.979072i	$0.565237\pi$
$654$	−17.8481	−0.697916
$655$	−3.98159	−0.155574
$656$	−3.98088	−0.155427
$657$	4.32998	0.168929
$658$	−0.841801	−0.0328168
$659$	−9.48292	−0.369402	−0.184701	−	0.982795i	$-0.559132\pi$
$659$	−9.48292	−0.369402	−0.184701	+	0.982795i	$0.559132\pi$
$660$	−8.47722	−0.329975
$661$	26.3470	1.02478	0.512389	−	0.858754i	$-0.328761\pi$
$661$	26.3470	1.02478	0.512389	+	0.858754i	$0.328761\pi$
$662$	−11.8033	−0.458748
$663$	3.57250	0.138744
$664$	1.30049	0.0504687
$665$	10.7288	0.416045
$666$	1.53320	0.0594101
$667$	−15.8718	−0.614558
$668$	−20.1081	−0.778005
$669$	35.6726	1.37918
$670$	−1.95180	−0.0754047
$671$	19.8394	0.765890
$672$	1.81149	0.0698796
$673$	9.72527	0.374882	0.187441	−	0.982276i	$-0.439981\pi$
$673$	9.72527	0.374882	0.187441	+	0.982276i	$0.439981\pi$
$674$	20.4124	0.786255
$675$	−16.7450	−0.644514
$676$	−10.4106	−0.400408
$677$	11.8866	0.456840	0.228420	−	0.973563i	$-0.426644\pi$
$677$	11.8866	0.456840	0.228420	+	0.973563i	$0.426644\pi$
$678$	−6.16507	−0.236768
$679$	−3.24220	−0.124424
$680$	1.55009	0.0594433
$681$	−38.1986	−1.46377
$682$	6.96936	0.266871
$683$	44.2105	1.69167	0.845835	−	0.533445i	$-0.179103\pi$
$683$	44.2105	1.69167	0.845835	+	0.533445i	$0.179103\pi$
$684$	−2.38768	−0.0912954
$685$	3.77117	0.144089
$686$	−1.00000	−0.0381802
$687$	28.9200	1.10337
$688$	−12.2128	−0.465610
$689$	−2.98580	−0.113750
$690$	−6.75711	−0.257239
$691$	23.9389	0.910677	0.455339	−	0.890318i	$-0.349518\pi$
$691$	23.9389	0.910677	0.455339	+	0.890318i	$0.349518\pi$
$692$	−15.9922	−0.607931
$693$	−1.04146	−0.0395620
$694$	−22.9837	−0.872448
$695$	8.63191	0.327427
$696$	−9.74885	−0.369529
$697$	−4.87885	−0.184800
$698$	18.7096	0.708170
$699$	−30.6947	−1.16098
$700$	−3.40030	−0.128519
$701$	15.9629	0.602910	0.301455	−	0.953480i	$-0.402528\pi$
$701$	15.9629	0.602910	0.301455	+	0.953480i	$0.402528\pi$
$702$	7.92440	0.299087
$703$	46.2044	1.74263
$704$	−3.69998	−0.139448
$705$	1.92870	0.0726389
$706$	27.0394	1.01764
$707$	1.22958	0.0462432
$708$	17.6080	0.661751
$709$	1.43886	0.0540375	0.0270187	−	0.999635i	$-0.491399\pi$
$709$	1.43886	0.0540375	0.0270187	+	0.999635i	$0.491399\pi$
$710$	0.892518	0.0334956
$711$	0.889342	0.0333529
$712$	9.94355	0.372650
$713$	5.55521	0.208044
$714$	2.22010	0.0830852
$715$	−7.53039	−0.281621
$716$	15.7842	0.589885
$717$	−19.8787	−0.742382
$718$	−29.9526	−1.11782
$719$	2.49023	0.0928699	0.0464349	−	0.998921i	$-0.485214\pi$
$719$	2.49023	0.0928699	0.0464349	+	0.998921i	$0.485214\pi$
$720$	−0.356012	−0.0132678
$721$	−11.5690	−0.430851
$722$	−52.9552	−1.97079
$723$	−25.8630	−0.961855
$724$	−17.5280	−0.651424
$725$	18.2994	0.679621
$726$	4.87260	0.180839
$727$	−21.6123	−0.801558	−0.400779	−	0.916175i	$-0.631260\pi$
$727$	−21.6123	−0.801558	−0.400779	+	0.916175i	$0.631260\pi$
$728$	1.60916	0.0596394
$729$	24.0136	0.889393
$730$	19.4563	0.720109
$731$	−14.9677	−0.553600
$732$	9.71322	0.359011
$733$	−38.2633	−1.41329	−0.706644	−	0.707569i	$-0.749792\pi$
$733$	−38.2633	−1.41329	−0.706644	+	0.707569i	$0.749792\pi$
$734$	−13.0823	−0.482878
$735$	2.29115	0.0845105
$736$	−2.94922	−0.108710
$737$	5.70973	0.210321
$738$	1.12053	0.0412474
$739$	37.8254	1.39143	0.695715	−	0.718318i	$-0.255088\pi$
$739$	37.8254	1.39143	0.695715	+	0.718318i	$0.255088\pi$
$740$	6.88925	0.253254
$741$	−24.7266	−0.908355
$742$	−1.85550	−0.0681176
$743$	−28.0878	−1.03044	−0.515222	−	0.857057i	$-0.672290\pi$
$743$	−28.0878	−1.03044	−0.515222	+	0.857057i	$0.672290\pi$
$744$	3.41215	0.125096
$745$	−2.15636	−0.0790029
$746$	15.2780	0.559368
$747$	−0.366059	−0.0133934
$748$	−4.53458	−0.165801
$749$	0.619641	0.0226412
$750$	19.2464	0.702778
$751$	26.0289	0.949810	0.474905	−	0.880037i	$-0.342482\pi$
$751$	26.0289	0.949810	0.474905	+	0.880037i	$0.342482\pi$
$752$	0.841801	0.0306973
$753$	3.72631	0.135794
$754$	−8.65999	−0.315378
$755$	−24.4016	−0.888065
$756$	4.92456	0.179105
$757$	−33.3381	−1.21170	−0.605848	−	0.795581i	$-0.707166\pi$
$757$	−33.3381	−1.21170	−0.605848	+	0.795581i	$0.707166\pi$
$758$	−24.4251	−0.887158
$759$	19.7670	0.717496
$760$	−10.7288	−0.389174
$761$	−27.6007	−1.00052	−0.500262	−	0.865874i	$-0.666763\pi$
$761$	−27.6007	−1.00052	−0.500262	+	0.865874i	$0.666763\pi$
$762$	31.5940	1.14453
$763$	−9.85275	−0.356693
$764$	−25.0315	−0.905608
$765$	−0.436318	−0.0157751
$766$	−2.42731	−0.0877023
$767$	15.6414	0.564778
$768$	−1.81149	−0.0653663
$769$	6.25353	0.225508	0.112754	−	0.993623i	$-0.464033\pi$
$769$	6.25353	0.225508	0.112754	+	0.993623i	$0.464033\pi$
$770$	−4.67971	−0.168645
$771$	39.2529	1.41366
$772$	1.36102	0.0489841
$773$	−33.9778	−1.22210	−0.611049	−	0.791593i	$-0.709252\pi$
$773$	−33.9778	−1.22210	−0.611049	+	0.791593i	$0.709252\pi$
$774$	3.43765	0.123564
$775$	−6.40488	−0.230070
$776$	3.24220	0.116388
$777$	9.86704	0.353978
$778$	−11.3762	−0.407855
$779$	33.7684	1.20988
$780$	−3.68683	−0.132010
$781$	−2.61094	−0.0934267
$782$	−3.61447	−0.129253
$783$	−26.5025	−0.947121
$784$	1.00000	0.0357143
$785$	13.1744	0.470216
$786$	5.70259	0.203404
$787$	−55.8348	−1.99030	−0.995148	−	0.0983889i	$-0.968631\pi$
$787$	−55.8348	−1.99030	−0.995148	+	0.0983889i	$0.968631\pi$
$788$	−7.39068	−0.263282
$789$	−21.6691	−0.771440
$790$	3.99616	0.142177
$791$	−3.40332	−0.121008
$792$	1.04146	0.0370068
$793$	8.62834	0.306401
$794$	14.7057	0.521885
$795$	4.25124	0.150776
$796$	−15.7798	−0.559300
$797$	−18.4166	−0.652349	−0.326175	−	0.945310i	$-0.605760\pi$
$797$	−18.4166	−0.652349	−0.326175	+	0.945310i	$0.605760\pi$
$798$	−15.3662	−0.543957
$799$	1.03169	0.0364984
$800$	3.40030	0.120219
$801$	−2.79890	−0.0988942
$802$	−16.3247	−0.576447
$803$	−56.9166	−2.00854
$804$	2.79545	0.0985878
$805$	−3.73015	−0.131471
$806$	3.03105	0.106764
$807$	−15.9913	−0.562922
$808$	−1.22958	−0.0432565
$809$	−47.5677	−1.67239	−0.836196	−	0.548431i	$-0.815225\pi$
$809$	−47.5677	−1.67239	−0.836196	+	0.548431i	$0.815225\pi$
$810$	−12.3510	−0.433969
$811$	−0.655007	−0.0230004	−0.0115002	−	0.999934i	$-0.503661\pi$
$811$	−0.655007	−0.0230004	−0.0115002	+	0.999934i	$0.503661\pi$
$812$	−5.38169	−0.188860
$813$	−9.23132	−0.323757
$814$	−20.1535	−0.706381
$815$	8.08846	0.283326
$816$	−2.22010	−0.0777191
$817$	103.597	3.62441
$818$	31.4450	1.09945
$819$	−0.452944	−0.0158271
$820$	5.03499	0.175830
$821$	32.6022	1.13783	0.568913	−	0.822398i	$-0.307364\pi$
$821$	32.6022	1.13783	0.568913	+	0.822398i	$0.307364\pi$
$822$	−5.40122	−0.188389
$823$	50.4042	1.75698	0.878491	−	0.477759i	$-0.158551\pi$
$823$	50.4042	1.75698	0.878491	+	0.477759i	$0.158551\pi$
$824$	11.5690	0.403024
$825$	−22.7903	−0.793458
$826$	9.72023	0.338210
$827$	48.3992	1.68300	0.841502	−	0.540253i	$-0.181672\pi$
$827$	48.3992	1.68300	0.841502	+	0.540253i	$0.181672\pi$
$828$	0.830142	0.0288494
$829$	−7.08727	−0.246151	−0.123076	−	0.992397i	$-0.539276\pi$
$829$	−7.08727	−0.246151	−0.123076	+	0.992397i	$0.539276\pi$
$830$	−1.64485	−0.0570935
$831$	−24.1731	−0.838557
$832$	−1.60916	−0.0557875
$833$	1.22557	0.0424635
$834$	−12.3629	−0.428094
$835$	25.4326	0.880130
$836$	31.3856	1.08549
$837$	9.27601	0.320626
$838$	−25.4766	−0.880075
$839$	−1.15223	−0.0397792	−0.0198896	−	0.999802i	$-0.506331\pi$
$839$	−1.15223	−0.0397792	−0.0198896	+	0.999802i	$0.506331\pi$
$840$	−2.29115	−0.0790523
$841$	−0.0373990	−0.00128962
$842$	31.6146	1.08951
$843$	−43.5396	−1.49958
$844$	3.39957	0.117018
$845$	13.1673	0.452968
$846$	−0.236949	−0.00814647
$847$	2.68984	0.0924238
$848$	1.85550	0.0637182
$849$	11.0084	0.377807
$850$	4.16730	0.142937
$851$	−16.0642	−0.550673
$852$	−1.27830	−0.0437938
$853$	31.3149	1.07220	0.536100	−	0.844154i	$-0.319897\pi$
$853$	31.3149	1.07220	0.536100	+	0.844154i	$0.319897\pi$
$854$	5.36202	0.183485
$855$	3.01993	0.103279
$856$	−0.619641	−0.0211789
$857$	5.45441	0.186319	0.0931595	−	0.995651i	$-0.470303\pi$
$857$	5.45441	0.186319	0.0931595	+	0.995651i	$0.470303\pi$
$858$	10.7853	0.368204
$859$	−19.4755	−0.664495	−0.332248	−	0.943192i	$-0.607807\pi$
$859$	−19.4755	−0.664495	−0.332248	+	0.943192i	$0.607807\pi$
$860$	15.4467	0.526729
$861$	7.21131	0.245761
$862$	1.00000	0.0340601
$863$	−20.7381	−0.705933	−0.352966	−	0.935636i	$-0.614827\pi$
$863$	−20.7381	−0.705933	−0.352966	+	0.935636i	$0.614827\pi$
$864$	−4.92456	−0.167537
$865$	20.2268	0.687731
$866$	−34.8395	−1.18389
$867$	28.0744	0.953455
$868$	1.88362	0.0639343
$869$	−11.6902	−0.396563
$870$	12.3303	0.418036
$871$	2.48322	0.0841407
$872$	9.85275	0.333656
$873$	−0.912611	−0.0308872
$874$	25.0172	0.846218
$875$	10.6246	0.359178
$876$	−27.8660	−0.941506
$877$	6.27229	0.211800	0.105900	−	0.994377i	$-0.466228\pi$
$877$	6.27229	0.211800	0.105900	+	0.994377i	$0.466228\pi$
$878$	−11.0042	−0.371373
$879$	−50.9161	−1.71736
$880$	4.67971	0.157753
$881$	−13.3039	−0.448219	−0.224109	−	0.974564i	$-0.571947\pi$
$881$	−13.3039	−0.448219	−0.224109	+	0.974564i	$0.571947\pi$
$882$	−0.281479	−0.00947788
$883$	−27.1088	−0.912282	−0.456141	−	0.889907i	$-0.650769\pi$
$883$	−27.1088	−0.912282	−0.456141	+	0.889907i	$0.650769\pi$
$884$	−1.97214	−0.0663301
$885$	−22.2705	−0.748616
$886$	−4.80323	−0.161368
$887$	−45.6506	−1.53280	−0.766399	−	0.642365i	$-0.777953\pi$
$887$	−45.6506	−1.53280	−0.766399	+	0.642365i	$0.777953\pi$
$888$	−9.86704	−0.331116
$889$	17.4409	0.584950
$890$	−12.5765	−0.421566
$891$	36.1310	1.21044
$892$	−19.6925	−0.659352
$893$	−7.14070	−0.238954
$894$	3.08842	0.103292
$895$	−19.9638	−0.667316
$896$	−1.00000	−0.0334077
$897$	8.59687	0.287041
$898$	−0.0286033	−0.000954503 0
$899$	−10.1371	−0.338090
$900$	−0.957111	−0.0319037
$901$	2.27405	0.0757595
$902$	−14.7292	−0.490428
$903$	22.1234	0.736220
$904$	3.40332	0.113193
$905$	22.1693	0.736933
$906$	34.9489	1.16110
$907$	−27.2585	−0.905103	−0.452552	−	0.891738i	$-0.649486\pi$
$907$	−27.2585	−0.905103	−0.452552	+	0.891738i	$0.649486\pi$
$908$	21.0869	0.699794
$909$	0.346101	0.0114794
$910$	−2.03525	−0.0674680
$911$	−50.4963	−1.67302	−0.836509	−	0.547954i	$-0.815407\pi$
$911$	−50.4963	−1.67302	−0.836509	+	0.547954i	$0.815407\pi$
$912$	15.3662	0.508825
$913$	4.81177	0.159246
$914$	9.61452	0.318020
$915$	−12.2852	−0.406137
$916$	−15.9648	−0.527492
$917$	3.14802	0.103957
$918$	−6.03539	−0.199198
$919$	−58.4139	−1.92690	−0.963449	−	0.267892i	$-0.913673\pi$
$919$	−58.4139	−1.92690	−0.963449	+	0.267892i	$0.913673\pi$
$920$	3.73015	0.122979
$921$	34.9968	1.15318
$922$	−34.0608	−1.12173
$923$	−1.13552	−0.0373762
$924$	6.70245	0.220495
$925$	18.5212	0.608973
$926$	22.6241	0.743473
$927$	−3.25642	−0.106955
$928$	5.38169	0.176663
$929$	−27.4308	−0.899974	−0.449987	−	0.893035i	$-0.648571\pi$
$929$	−27.4308	−0.899974	−0.449987	+	0.893035i	$0.648571\pi$
$930$	−4.31567	−0.141516
$931$	−8.48264	−0.278007
$932$	16.9445	0.555036
$933$	4.97354	0.162826
$934$	−26.5106	−0.867452
$935$	5.73531	0.187565
$936$	0.452944	0.0148049
$937$	−29.2519	−0.955619	−0.477809	−	0.878464i	$-0.658569\pi$
$937$	−29.2519	−0.955619	−0.477809	+	0.878464i	$0.658569\pi$
$938$	1.54318	0.0503866
$939$	−18.2200	−0.594588
$940$	−1.06470	−0.0347268
$941$	15.4059	0.502217	0.251108	−	0.967959i	$-0.419205\pi$
$941$	15.4059	0.502217	0.251108	+	0.967959i	$0.419205\pi$
$942$	−18.8689	−0.614783
$943$	−11.7405	−0.382323
$944$	−9.72023	−0.316366
$945$	−6.22855	−0.202615
$946$	−45.1872	−1.46916
$947$	−27.6419	−0.898242	−0.449121	−	0.893471i	$-0.648263\pi$
$947$	−27.6419	−0.898242	−0.449121	+	0.893471i	$0.648263\pi$
$948$	−5.72345	−0.185889
$949$	−24.7536	−0.803537
$950$	−28.8435	−0.935807
$951$	−64.2974	−2.08499
$952$	−1.22557	−0.0397210
$953$	4.41701	0.143081	0.0715405	−	0.997438i	$-0.477208\pi$
$953$	4.41701	0.143081	0.0715405	+	0.997438i	$0.477208\pi$
$954$	−0.522284	−0.0169096
$955$	31.6597	1.02448
$956$	10.9737	0.354914
$957$	−36.0705	−1.16600
$958$	−20.3244	−0.656650
$959$	−2.98165	−0.0962826
$960$	2.29115	0.0739467
$961$	−27.4520	−0.885547
$962$	−8.76498	−0.282594
$963$	0.174416	0.00562047
$964$	14.2772	0.459839
$965$	−1.72141	−0.0554140
$966$	5.34246	0.171891
$967$	−9.02948	−0.290368	−0.145184	−	0.989405i	$-0.546377\pi$
$967$	−9.02948	−0.290368	−0.145184	+	0.989405i	$0.546377\pi$
$968$	−2.68984	−0.0864546
$969$	18.8323	0.604982
$970$	−4.10072	−0.131666
$971$	52.2268	1.67604	0.838018	−	0.545642i	$-0.183714\pi$
$971$	52.2268	1.67604	0.838018	+	0.545642i	$0.183714\pi$
$972$	2.91584	0.0935257
$973$	−6.82476	−0.218792
$974$	−24.8261	−0.795479
$975$	−9.91175	−0.317430
$976$	−5.36202	−0.171634
$977$	−9.07541	−0.290348	−0.145174	−	0.989406i	$-0.546374\pi$
$977$	−9.07541	−0.290348	−0.145174	+	0.989406i	$0.546374\pi$
$978$	−11.5846	−0.370434
$979$	36.7909	1.17584
$980$	−1.26479	−0.0404023
$981$	−2.77334	−0.0885459
$982$	−10.4468	−0.333372
$983$	−55.4641	−1.76903	−0.884516	−	0.466510i	$-0.845511\pi$
$983$	−55.4641	−1.76903	−0.884516	+	0.466510i	$0.845511\pi$
$984$	−7.21131	−0.229888
$985$	9.34768	0.297842
$986$	6.59564	0.210048
$987$	−1.52491	−0.0485384
$988$	13.6499	0.434262
$989$	−36.0183	−1.14532
$990$	−1.31724	−0.0418646
$991$	10.5969	0.336623	0.168311	−	0.985734i	$-0.446169\pi$
$991$	10.5969	0.336623	0.168311	+	0.985734i	$0.446169\pi$
$992$	−1.88362	−0.0598051
$993$	−21.3815	−0.678522
$994$	−0.705663	−0.0223823
$995$	19.9582	0.632717
$996$	2.35581	0.0746468
$997$	25.9340	0.821339	0.410669	−	0.911784i	$-0.365295\pi$
$997$	25.9340	0.821339	0.410669	+	0.911784i	$0.365295\pi$
$998$	35.0560	1.10968
$999$	−26.8238	−0.848666

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.p.1.7	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.p.1.7	✓	27	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:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.81149 q^{3} +1.00000 q^{4} -1.26479 q^{5} +1.81149 q^{6} +1.00000 q^{7} -1.00000 q^{8} +0.281479 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.81149 q^{3} +1.00000 q^{4} -1.26479 q^{5} +1.81149 q^{6} +1.00000 q^{7} -1.00000 q^{8} +0.281479 q^{9} +1.26479 q^{10} -3.69998 q^{11} -1.81149 q^{12} -1.60916 q^{13} -1.00000 q^{14} +2.29115 q^{15} +1.00000 q^{16} +1.22557 q^{17} -0.281479 q^{18} -8.48264 q^{19} -1.26479 q^{20} -1.81149 q^{21} +3.69998 q^{22} +2.94922 q^{23} +1.81149 q^{24} -3.40030 q^{25} +1.60916 q^{26} +4.92456 q^{27} +1.00000 q^{28} -5.38169 q^{29} -2.29115 q^{30} +1.88362 q^{31} -1.00000 q^{32} +6.70245 q^{33} -1.22557 q^{34} -1.26479 q^{35} +0.281479 q^{36} -5.44694 q^{37} +8.48264 q^{38} +2.91497 q^{39} +1.26479 q^{40} -3.98088 q^{41} +1.81149 q^{42} -12.2128 q^{43} -3.69998 q^{44} -0.356012 q^{45} -2.94922 q^{46} +0.841801 q^{47} -1.81149 q^{48} +1.00000 q^{49} +3.40030 q^{50} -2.22010 q^{51} -1.60916 q^{52} +1.85550 q^{53} -4.92456 q^{54} +4.67971 q^{55} -1.00000 q^{56} +15.3662 q^{57} +5.38169 q^{58} -9.72023 q^{59} +2.29115 q^{60} -5.36202 q^{61} -1.88362 q^{62} +0.281479 q^{63} +1.00000 q^{64} +2.03525 q^{65} -6.70245 q^{66} -1.54318 q^{67} +1.22557 q^{68} -5.34246 q^{69} +1.26479 q^{70} +0.705663 q^{71} -0.281479 q^{72} +15.3830 q^{73} +5.44694 q^{74} +6.15959 q^{75} -8.48264 q^{76} -3.69998 q^{77} -2.91497 q^{78} +3.15953 q^{79} -1.26479 q^{80} -9.76521 q^{81} +3.98088 q^{82} -1.30049 q^{83} -1.81149 q^{84} -1.55009 q^{85} +12.2128 q^{86} +9.74885 q^{87} +3.69998 q^{88} -9.94355 q^{89} +0.356012 q^{90} -1.60916 q^{91} +2.94922 q^{92} -3.41215 q^{93} -0.841801 q^{94} +10.7288 q^{95} +1.81149 q^{96} -3.24220 q^{97} -1.00000 q^{98} -1.04146 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 27 q^{2} + 4 q^{3} + 27 q^{4} + 9 q^{5} - 4 q^{6} + 27 q^{7} - 27 q^{8} + 35 q^{9}+O(q^{10}) \) 27 * q - 27 * q^2 + 4 * q^3 + 27 * q^4 + 9 * q^5 - 4 * q^6 + 27 * q^7 - 27 * q^8 + 35 * q^9	\( 27 q - 27 q^{2} + 4 q^{3} + 27 q^{4} + 9 q^{5} - 4 q^{6} + 27 q^{7} - 27 q^{8} + 35 q^{9} - 9 q^{10} + 24 q^{11} + 4 q^{12} - 13 q^{13} - 27 q^{14} + 16 q^{15} + 27 q^{16} - 5 q^{17} - 35 q^{18} + q^{19} + 9 q^{20} + 4 q^{21} - 24 q^{22} + 32 q^{23} - 4 q^{24} + 30 q^{25} + 13 q^{26} + q^{27} + 27 q^{28} + 26 q^{29} - 16 q^{30} + 21 q^{31} - 27 q^{32} + 7 q^{33} + 5 q^{34} + 9 q^{35} + 35 q^{36} + 4 q^{37} - q^{38} + 13 q^{39} - 9 q^{40} + 31 q^{41} - 4 q^{42} - 13 q^{43} + 24 q^{44} + 19 q^{45} - 32 q^{46} + 41 q^{47} + 4 q^{48} + 27 q^{49} - 30 q^{50} + 21 q^{51} - 13 q^{52} + 29 q^{53} - q^{54} + 9 q^{55} - 27 q^{56} - 26 q^{58} + 36 q^{59} + 16 q^{60} + q^{61} - 21 q^{62} + 35 q^{63} + 27 q^{64} + 46 q^{65} - 7 q^{66} - 2 q^{67} - 5 q^{68} + 43 q^{69} - 9 q^{70} + 70 q^{71} - 35 q^{72} - 21 q^{73} - 4 q^{74} + 37 q^{75} + q^{76} + 24 q^{77} - 13 q^{78} + 19 q^{79} + 9 q^{80} + 67 q^{81} - 31 q^{82} + 25 q^{83} + 4 q^{84} - 6 q^{85} + 13 q^{86} - 9 q^{87} - 24 q^{88} + 85 q^{89} - 19 q^{90} - 13 q^{91} + 32 q^{92} + 23 q^{93} - 41 q^{94} + 77 q^{95} - 4 q^{96} - 2 q^{97} - 27 q^{98} + 38 q^{99}+O(q^{100}) \) 27 * q - 27 * q^2 + 4 * q^3 + 27 * q^4 + 9 * q^5 - 4 * q^6 + 27 * q^7 - 27 * q^8 + 35 * q^9 - 9 * q^10 + 24 * q^11 + 4 * q^12 - 13 * q^13 - 27 * q^14 + 16 * q^15 + 27 * q^16 - 5 * q^17 - 35 * q^18 + q^19 + 9 * q^20 + 4 * q^21 - 24 * q^22 + 32 * q^23 - 4 * q^24 + 30 * q^25 + 13 * q^26 + q^27 + 27 * q^28 + 26 * q^29 - 16 * q^30 + 21 * q^31 - 27 * q^32 + 7 * q^33 + 5 * q^34 + 9 * q^35 + 35 * q^36 + 4 * q^37 - q^38 + 13 * q^39 - 9 * q^40 + 31 * q^41 - 4 * q^42 - 13 * q^43 + 24 * q^44 + 19 * q^45 - 32 * q^46 + 41 * q^47 + 4 * q^48 + 27 * q^49 - 30 * q^50 + 21 * q^51 - 13 * q^52 + 29 * q^53 - q^54 + 9 * q^55 - 27 * q^56 - 26 * q^58 + 36 * q^59 + 16 * q^60 + q^61 - 21 * q^62 + 35 * q^63 + 27 * q^64 + 46 * q^65 - 7 * q^66 - 2 * q^67 - 5 * q^68 + 43 * q^69 - 9 * q^70 + 70 * q^71 - 35 * q^72 - 21 * q^73 - 4 * q^74 + 37 * q^75 + q^76 + 24 * q^77 - 13 * q^78 + 19 * q^79 + 9 * q^80 + 67 * q^81 - 31 * q^82 + 25 * q^83 + 4 * q^84 - 6 * q^85 + 13 * q^86 - 9 * q^87 - 24 * q^88 + 85 * q^89 - 19 * q^90 - 13 * q^91 + 32 * q^92 + 23 * q^93 - 41 * q^94 + 77 * q^95 - 4 * q^96 - 2 * q^97 - 27 * q^98 + 38 * q^99

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