LMFDB - Embedded newform 6014.2.a.e.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6014,2,Mod(1,6014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6014, 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("6014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6014 = 2 \cdot 31 \cdot 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6014.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:	$48.0220317756$
Analytic rank:	$1$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	6014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.74046 q^{3} +1.00000 q^{4} +0.258024 q^{5} +1.74046 q^{6} -2.13023 q^{7} +1.00000 q^{8} +0.0291912 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.74046 q^{3} +1.00000 q^{4} +0.258024 q^{5} +1.74046 q^{6} -2.13023 q^{7} +1.00000 q^{8} +0.0291912 q^{9} +0.258024 q^{10} +1.46211 q^{11} +1.74046 q^{12} -6.38517 q^{13} -2.13023 q^{14} +0.449080 q^{15} +1.00000 q^{16} -0.785672 q^{17} +0.0291912 q^{18} -1.66991 q^{19} +0.258024 q^{20} -3.70757 q^{21} +1.46211 q^{22} +6.44230 q^{23} +1.74046 q^{24} -4.93342 q^{25} -6.38517 q^{26} -5.17057 q^{27} -2.13023 q^{28} -4.13748 q^{29} +0.449080 q^{30} +1.00000 q^{31} +1.00000 q^{32} +2.54475 q^{33} -0.785672 q^{34} -0.549650 q^{35} +0.0291912 q^{36} -1.48178 q^{37} -1.66991 q^{38} -11.1131 q^{39} +0.258024 q^{40} -6.43885 q^{41} -3.70757 q^{42} +0.972831 q^{43} +1.46211 q^{44} +0.00753203 q^{45} +6.44230 q^{46} -9.94139 q^{47} +1.74046 q^{48} -2.46212 q^{49} -4.93342 q^{50} -1.36743 q^{51} -6.38517 q^{52} +1.91410 q^{53} -5.17057 q^{54} +0.377260 q^{55} -2.13023 q^{56} -2.90641 q^{57} -4.13748 q^{58} +2.02158 q^{59} +0.449080 q^{60} +2.52864 q^{61} +1.00000 q^{62} -0.0621840 q^{63} +1.00000 q^{64} -1.64753 q^{65} +2.54475 q^{66} +3.24991 q^{67} -0.785672 q^{68} +11.2125 q^{69} -0.549650 q^{70} -0.963411 q^{71} +0.0291912 q^{72} +6.89950 q^{73} -1.48178 q^{74} -8.58641 q^{75} -1.66991 q^{76} -3.11464 q^{77} -11.1131 q^{78} -16.3050 q^{79} +0.258024 q^{80} -9.08672 q^{81} -6.43885 q^{82} +2.31414 q^{83} -3.70757 q^{84} -0.202722 q^{85} +0.972831 q^{86} -7.20110 q^{87} +1.46211 q^{88} -10.8406 q^{89} +0.00753203 q^{90} +13.6019 q^{91} +6.44230 q^{92} +1.74046 q^{93} -9.94139 q^{94} -0.430877 q^{95} +1.74046 q^{96} -1.00000 q^{97} -2.46212 q^{98} +0.0426809 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 21 q^{2} - 10 q^{3} + 21 q^{4} - 10 q^{5} - 10 q^{6} - 11 q^{7} + 21 q^{8} + 7 q^{9}+O(q^{10}) $ 21 * q + 21 * q^2 - 10 * q^3 + 21 * q^4 - 10 * q^5 - 10 * q^6 - 11 * q^7 + 21 * q^8 + 7 * q^9	\( 21 q + 21 q^{2} - 10 q^{3} + 21 q^{4} - 10 q^{5} - 10 q^{6} - 11 q^{7} + 21 q^{8} + 7 q^{9} - 10 q^{10} - 12 q^{11} - 10 q^{12} - 14 q^{13} - 11 q^{14} + q^{15} + 21 q^{16} + 7 q^{18} - 27 q^{19} - 10 q^{20} - 6 q^{21} - 12 q^{22} - 4 q^{23} - 10 q^{24} + q^{25} - 14 q^{26} - 19 q^{27} - 11 q^{28} - 13 q^{29} + q^{30} + 21 q^{31} + 21 q^{32} - 20 q^{33} - 20 q^{35} + 7 q^{36} - 13 q^{37} - 27 q^{38} - 4 q^{39} - 10 q^{40} - 19 q^{41} - 6 q^{42} - 19 q^{43} - 12 q^{44} + 13 q^{45} - 4 q^{46} - 18 q^{47} - 10 q^{48} - 20 q^{49} + q^{50} - 33 q^{51} - 14 q^{52} - 15 q^{53} - 19 q^{54} - 26 q^{55} - 11 q^{56} + 9 q^{57} - 13 q^{58} - 32 q^{59} + q^{60} - 36 q^{61} + 21 q^{62} - 27 q^{63} + 21 q^{64} - 20 q^{65} - 20 q^{66} - 43 q^{67} - 11 q^{69} - 20 q^{70} - 31 q^{71} + 7 q^{72} - 11 q^{73} - 13 q^{74} - 22 q^{75} - 27 q^{76} + 12 q^{77} - 4 q^{78} - 31 q^{79} - 10 q^{80} - 39 q^{81} - 19 q^{82} - 26 q^{83} - 6 q^{84} - 12 q^{85} - 19 q^{86} + 19 q^{87} - 12 q^{88} - 14 q^{89} + 13 q^{90} - 30 q^{91} - 4 q^{92} - 10 q^{93} - 18 q^{94} - 40 q^{95} - 10 q^{96} - 21 q^{97} - 20 q^{98} - 17 q^{99}+O(q^{100}) \) 21 * q + 21 * q^2 - 10 * q^3 + 21 * q^4 - 10 * q^5 - 10 * q^6 - 11 * q^7 + 21 * q^8 + 7 * q^9 - 10 * q^10 - 12 * q^11 - 10 * q^12 - 14 * q^13 - 11 * q^14 + q^15 + 21 * q^16 + 7 * q^18 - 27 * q^19 - 10 * q^20 - 6 * q^21 - 12 * q^22 - 4 * q^23 - 10 * q^24 + q^25 - 14 * q^26 - 19 * q^27 - 11 * q^28 - 13 * q^29 + q^30 + 21 * q^31 + 21 * q^32 - 20 * q^33 - 20 * q^35 + 7 * q^36 - 13 * q^37 - 27 * q^38 - 4 * q^39 - 10 * q^40 - 19 * q^41 - 6 * q^42 - 19 * q^43 - 12 * q^44 + 13 * q^45 - 4 * q^46 - 18 * q^47 - 10 * q^48 - 20 * q^49 + q^50 - 33 * q^51 - 14 * q^52 - 15 * q^53 - 19 * q^54 - 26 * q^55 - 11 * q^56 + 9 * q^57 - 13 * q^58 - 32 * q^59 + q^60 - 36 * q^61 + 21 * q^62 - 27 * q^63 + 21 * q^64 - 20 * q^65 - 20 * q^66 - 43 * q^67 - 11 * q^69 - 20 * q^70 - 31 * q^71 + 7 * q^72 - 11 * q^73 - 13 * q^74 - 22 * q^75 - 27 * q^76 + 12 * q^77 - 4 * q^78 - 31 * q^79 - 10 * q^80 - 39 * q^81 - 19 * q^82 - 26 * q^83 - 6 * q^84 - 12 * q^85 - 19 * q^86 + 19 * q^87 - 12 * q^88 - 14 * q^89 + 13 * q^90 - 30 * q^91 - 4 * q^92 - 10 * q^93 - 18 * q^94 - 40 * q^95 - 10 * q^96 - 21 * q^97 - 20 * q^98 - 17 * 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
$3$	1.74046	1.00485	0.502427	−	0.864620i	$-0.332441\pi$
$3$	1.74046	1.00485	0.502427	+	0.864620i	$0.332441\pi$
$4$	1.00000	0.500000
$5$	0.258024	0.115392	0.0576959	−	0.998334i	$-0.481625\pi$
$5$	0.258024	0.115392	0.0576959	+	0.998334i	$0.481625\pi$
$6$	1.74046	0.710539
$7$	−2.13023	−0.805151	−0.402576	−	0.915387i	$-0.631885\pi$
$7$	−2.13023	−0.805151	−0.402576	+	0.915387i	$0.631885\pi$
$8$	1.00000	0.353553
$9$	0.0291912	0.00973040
$10$	0.258024	0.0815943
$11$	1.46211	0.440844	0.220422	−	0.975405i	$-0.429257\pi$
$11$	1.46211	0.440844	0.220422	+	0.975405i	$0.429257\pi$
$12$	1.74046	0.502427
$13$	−6.38517	−1.77093	−0.885464	−	0.464707i	$-0.846160\pi$
$13$	−6.38517	−1.77093	−0.885464	+	0.464707i	$0.846160\pi$
$14$	−2.13023	−0.569328
$15$	0.449080	0.115952
$16$	1.00000	0.250000
$17$	−0.785672	−0.190553	−0.0952767	−	0.995451i	$-0.530374\pi$
$17$	−0.785672	−0.190553	−0.0952767	+	0.995451i	$0.530374\pi$
$18$	0.0291912	0.00688043
$19$	−1.66991	−0.383104	−0.191552	−	0.981482i	$-0.561352\pi$
$19$	−1.66991	−0.383104	−0.191552	+	0.981482i	$0.561352\pi$
$20$	0.258024	0.0576959
$21$	−3.70757	−0.809059
$22$	1.46211	0.311724
$23$	6.44230	1.34331	0.671656	−	0.740863i	$-0.265583\pi$
$23$	6.44230	1.34331	0.671656	+	0.740863i	$0.265583\pi$
$24$	1.74046	0.355269
$25$	−4.93342	−0.986685
$26$	−6.38517	−1.25224
$27$	−5.17057	−0.995076
$28$	−2.13023	−0.402576
$29$	−4.13748	−0.768310	−0.384155	−	0.923269i	$-0.625507\pi$
$29$	−4.13748	−0.768310	−0.384155	+	0.923269i	$0.625507\pi$
$30$	0.449080	0.0819903
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	1.00000	0.176777
$33$	2.54475	0.442983
$34$	−0.785672	−0.134742
$35$	−0.549650	−0.0929078
$36$	0.0291912	0.00486520
$37$	−1.48178	−0.243603	−0.121801	−	0.992554i	$-0.538867\pi$
$37$	−1.48178	−0.243603	−0.121801	+	0.992554i	$0.538867\pi$
$38$	−1.66991	−0.270895
$39$	−11.1131	−1.77952
$40$	0.258024	0.0407972
$41$	−6.43885	−1.00558	−0.502789	−	0.864409i	$-0.667693\pi$
$41$	−6.43885	−1.00558	−0.502789	+	0.864409i	$0.667693\pi$
$42$	−3.70757	−0.572091
$43$	0.972831	0.148355	0.0741777	−	0.997245i	$-0.476367\pi$
$43$	0.972831	0.148355	0.0741777	+	0.997245i	$0.476367\pi$
$44$	1.46211	0.220422
$45$	0.00753203	0.00112281
$46$	6.44230	0.949865
$47$	−9.94139	−1.45010	−0.725050	−	0.688696i	$-0.758183\pi$
$47$	−9.94139	−1.45010	−0.725050	+	0.688696i	$0.758183\pi$
$48$	1.74046	0.251213
$49$	−2.46212	−0.351732
$50$	−4.93342	−0.697691
$51$	−1.36743	−0.191478
$52$	−6.38517	−0.885464
$53$	1.91410	0.262922	0.131461	−	0.991321i	$-0.458033\pi$
$53$	1.91410	0.262922	0.131461	+	0.991321i	$0.458033\pi$
$54$	−5.17057	−0.703625
$55$	0.377260	0.0508698
$56$	−2.13023	−0.284664
$57$	−2.90641	−0.384963
$58$	−4.13748	−0.543278
$59$	2.02158	0.263188	0.131594	−	0.991304i	$-0.457990\pi$
$59$	2.02158	0.263188	0.131594	+	0.991304i	$0.457990\pi$
$60$	0.449080	0.0579759
$61$	2.52864	0.323759	0.161879	−	0.986811i	$-0.448244\pi$
$61$	2.52864	0.323759	0.161879	+	0.986811i	$0.448244\pi$
$62$	1.00000	0.127000
$63$	−0.0621840	−0.00783444
$64$	1.00000	0.125000
$65$	−1.64753	−0.204351
$66$	2.54475	0.313237
$67$	3.24991	0.397039	0.198520	−	0.980097i	$-0.436387\pi$
$67$	3.24991	0.397039	0.198520	+	0.980097i	$0.436387\pi$
$68$	−0.785672	−0.0952767
$69$	11.2125	1.34983
$70$	−0.549650	−0.0656957
$71$	−0.963411	−0.114336	−0.0571680	−	0.998365i	$-0.518207\pi$
$71$	−0.963411	−0.114336	−0.0571680	+	0.998365i	$0.518207\pi$
$72$	0.0291912	0.00344022
$73$	6.89950	0.807526	0.403763	−	0.914864i	$-0.367702\pi$
$73$	6.89950	0.807526	0.403763	+	0.914864i	$0.367702\pi$
$74$	−1.48178	−0.172253
$75$	−8.58641	−0.991474
$76$	−1.66991	−0.191552
$77$	−3.11464	−0.354946
$78$	−11.1131	−1.25831
$79$	−16.3050	−1.83446	−0.917230	−	0.398359i	$-0.869580\pi$
$79$	−16.3050	−1.83446	−0.917230	+	0.398359i	$0.869580\pi$
$80$	0.258024	0.0288479
$81$	−9.08672	−1.00964
$82$	−6.43885	−0.711051
$83$	2.31414	0.254010	0.127005	−	0.991902i	$-0.459464\pi$
$83$	2.31414	0.254010	0.127005	+	0.991902i	$0.459464\pi$
$84$	−3.70757	−0.404529
$85$	−0.202722	−0.0219883
$86$	0.972831	0.104903
$87$	−7.20110	−0.772039
$88$	1.46211	0.155862
$89$	−10.8406	−1.14910	−0.574550	−	0.818470i	$-0.694823\pi$
$89$	−10.8406	−1.14910	−0.574550	+	0.818470i	$0.694823\pi$
$90$	0.00753203	0.000793946 0
$91$	13.6019	1.42587
$92$	6.44230	0.671656
$93$	1.74046	0.180477
$94$	−9.94139	−1.02538
$95$	−0.430877	−0.0442070
$96$	1.74046	0.177635
$97$	−1.00000	−0.101535
$97$	−1.00000	−0.101535
$98$	−2.46212	−0.248712
$99$	0.0426809	0.00428959
$100$	−4.93342	−0.493342
$101$	0.204333	0.0203319	0.0101659	−	0.999948i	$-0.496764\pi$
$101$	0.204333	0.0203319	0.0101659	+	0.999948i	$0.496764\pi$
$102$	−1.36743	−0.135396
$103$	17.0213	1.67716	0.838579	−	0.544780i	$-0.183387\pi$
$103$	17.0213	1.67716	0.838579	+	0.544780i	$0.183387\pi$
$104$	−6.38517	−0.626118
$105$	−0.956642	−0.0933587
$106$	1.91410	0.185914
$107$	11.8542	1.14599	0.572995	−	0.819559i	$-0.305781\pi$
$107$	11.8542	1.14599	0.572995	+	0.819559i	$0.305781\pi$
$108$	−5.17057	−0.497538
$109$	−1.37638	−0.131833	−0.0659167	−	0.997825i	$-0.520997\pi$
$109$	−1.37638	−0.131833	−0.0659167	+	0.997825i	$0.520997\pi$
$110$	0.377260	0.0359703
$111$	−2.57897	−0.244785
$112$	−2.13023	−0.201288
$113$	−7.74079	−0.728192	−0.364096	−	0.931361i	$-0.618622\pi$
$113$	−7.74079	−0.728192	−0.364096	+	0.931361i	$0.618622\pi$
$114$	−2.90641	−0.272210
$115$	1.66227	0.155007
$116$	−4.13748	−0.384155
$117$	−0.186391	−0.0172318
$118$	2.02158	0.186102
$119$	1.67366	0.153424
$120$	0.449080	0.0409952
$121$	−8.86222	−0.805657
$122$	2.52864	0.228932
$123$	−11.2065	−1.01046
$124$	1.00000	0.0898027
$125$	−2.56306	−0.229247
$126$	−0.0621840	−0.00553979
$127$	−7.98330	−0.708403	−0.354201	−	0.935169i	$-0.615247\pi$
$127$	−7.98330	−0.708403	−0.354201	+	0.935169i	$0.615247\pi$
$128$	1.00000	0.0883883
$129$	1.69317	0.149075
$130$	−1.64753	−0.144498
$131$	9.98745	0.872608	0.436304	−	0.899799i	$-0.356287\pi$
$131$	9.98745	0.872608	0.436304	+	0.899799i	$0.356287\pi$
$132$	2.54475	0.221492
$133$	3.55729	0.308456
$134$	3.24991	0.280749
$135$	−1.33413	−0.114824
$136$	−0.785672	−0.0673708
$137$	−20.1362	−1.72035	−0.860175	−	0.510000i	$-0.829646\pi$
$137$	−20.1362	−1.72035	−0.860175	+	0.510000i	$0.829646\pi$
$138$	11.2125	0.954475
$139$	12.2359	1.03784	0.518919	−	0.854824i	$-0.326335\pi$
$139$	12.2359	1.03784	0.518919	+	0.854824i	$0.326335\pi$
$140$	−0.549650	−0.0464539
$141$	−17.3026	−1.45714
$142$	−0.963411	−0.0808477
$143$	−9.33585	−0.780703
$144$	0.0291912	0.00243260
$145$	−1.06757	−0.0886567
$146$	6.89950	0.571007
$147$	−4.28522	−0.353439
$148$	−1.48178	−0.121801
$149$	−5.34594	−0.437957	−0.218978	−	0.975730i	$-0.570272\pi$
$149$	−5.34594	−0.437957	−0.218978	+	0.975730i	$0.570272\pi$
$150$	−8.58641	−0.701078
$151$	1.18419	0.0963678	0.0481839	−	0.998838i	$-0.484657\pi$
$151$	1.18419	0.0963678	0.0481839	+	0.998838i	$0.484657\pi$
$152$	−1.66991	−0.135448
$153$	−0.0229347	−0.00185416
$154$	−3.11464	−0.250985
$155$	0.258024	0.0207250
$156$	−11.1131	−0.889762
$157$	−13.9758	−1.11539	−0.557694	−	0.830047i	$-0.688314\pi$
$157$	−13.9758	−1.11539	−0.557694	+	0.830047i	$0.688314\pi$
$158$	−16.3050	−1.29716
$159$	3.33141	0.264198
$160$	0.258024	0.0203986
$161$	−13.7236	−1.08157
$162$	−9.08672	−0.713920
$163$	−3.39084	−0.265591	−0.132795	−	0.991143i	$-0.542395\pi$
$163$	−3.39084	−0.265591	−0.132795	+	0.991143i	$0.542395\pi$
$164$	−6.43885	−0.502789
$165$	0.656605	0.0511166
$166$	2.31414	0.179612
$167$	−20.9528	−1.62138	−0.810689	−	0.585476i	$-0.800907\pi$
$167$	−20.9528	−1.62138	−0.810689	+	0.585476i	$0.800907\pi$
$168$	−3.70757	−0.286045
$169$	27.7704	2.13619
$170$	−0.202722	−0.0155481
$171$	−0.0487467	−0.00372775
$172$	0.972831	0.0741777
$173$	9.19344	0.698964	0.349482	−	0.936943i	$-0.386358\pi$
$173$	9.19344	0.698964	0.349482	+	0.936943i	$0.386358\pi$
$174$	−7.20110	−0.545914
$175$	10.5093	0.794430
$176$	1.46211	0.110211
$177$	3.51848	0.264465
$178$	−10.8406	−0.812536
$179$	24.2534	1.81278	0.906390	−	0.422441i	$-0.138827\pi$
$179$	24.2534	1.81278	0.906390	+	0.422441i	$0.138827\pi$
$180$	0.00753203	0.000561404 0
$181$	−4.62508	−0.343779	−0.171890	−	0.985116i	$-0.554987\pi$
$181$	−4.62508	−0.343779	−0.171890	+	0.985116i	$0.554987\pi$
$182$	13.6019	1.00824
$183$	4.40099	0.325330
$184$	6.44230	0.474932
$185$	−0.382334	−0.0281098
$186$	1.74046	0.127617
$187$	−1.14874	−0.0840043
$188$	−9.94139	−0.725050
$189$	11.0145	0.801186
$190$	−0.430877	−0.0312591
$191$	4.66864	0.337811	0.168905	−	0.985632i	$-0.445977\pi$
$191$	4.66864	0.337811	0.168905	+	0.985632i	$0.445977\pi$
$192$	1.74046	0.125607
$193$	−10.2541	−0.738108	−0.369054	−	0.929408i	$-0.620318\pi$
$193$	−10.2541	−0.738108	−0.369054	+	0.929408i	$0.620318\pi$
$194$	−1.00000	−0.0717958
$195$	−2.86745	−0.205342
$196$	−2.46212	−0.175866
$197$	−7.12720	−0.507792	−0.253896	−	0.967232i	$-0.581712\pi$
$197$	−7.12720	−0.507792	−0.253896	+	0.967232i	$0.581712\pi$
$198$	0.0426809	0.00303320
$199$	3.57195	0.253209	0.126604	−	0.991953i	$-0.459592\pi$
$199$	3.57195	0.253209	0.126604	+	0.991953i	$0.459592\pi$
$200$	−4.93342	−0.348846
$201$	5.65632	0.398966
$202$	0.204333	0.0143768
$203$	8.81378	0.618606
$204$	−1.36743	−0.0957391
$205$	−1.66138	−0.116036
$206$	17.0213	1.18593
$207$	0.188058	0.0130710
$208$	−6.38517	−0.442732
$209$	−2.44160	−0.168889
$210$	−0.956642	−0.0660146
$211$	19.2818	1.32742	0.663708	−	0.747992i	$-0.268982\pi$
$211$	19.2818	1.32742	0.663708	+	0.747992i	$0.268982\pi$
$212$	1.91410	0.131461
$213$	−1.67678	−0.114891
$214$	11.8542	0.810338
$215$	0.251014	0.0171190
$216$	−5.17057	−0.351812
$217$	−2.13023	−0.144609
$218$	−1.37638	−0.0932204
$219$	12.0083	0.811445
$220$	0.377260	0.0254349
$221$	5.01665	0.337456
$222$	−2.57897	−0.173089
$223$	20.9785	1.40482	0.702412	−	0.711770i	$-0.252106\pi$
$223$	20.9785	1.40482	0.702412	+	0.711770i	$0.252106\pi$
$224$	−2.13023	−0.142332
$225$	−0.144013	−0.00960084
$226$	−7.74079	−0.514910
$227$	−1.08654	−0.0721164	−0.0360582	−	0.999350i	$-0.511480\pi$
$227$	−1.08654	−0.0721164	−0.0360582	+	0.999350i	$0.511480\pi$
$228$	−2.90641	−0.192482
$229$	−8.97184	−0.592876	−0.296438	−	0.955052i	$-0.595799\pi$
$229$	−8.97184	−0.592876	−0.296438	+	0.955052i	$0.595799\pi$
$230$	1.66227	0.109607
$231$	−5.42089	−0.356669
$232$	−4.13748	−0.271639
$233$	2.78284	0.182310	0.0911551	−	0.995837i	$-0.470944\pi$
$233$	2.78284	0.182310	0.0911551	+	0.995837i	$0.470944\pi$
$234$	−0.186391	−0.0121848
$235$	−2.56512	−0.167330
$236$	2.02158	0.131594
$237$	−28.3782	−1.84336
$238$	1.67366	0.108487
$239$	−23.9822	−1.55128	−0.775641	−	0.631175i	$-0.782573\pi$
$239$	−23.9822	−1.55128	−0.775641	+	0.631175i	$0.782573\pi$
$240$	0.449080	0.0289880
$241$	4.87502	0.314027	0.157014	−	0.987596i	$-0.449813\pi$
$241$	4.87502	0.314027	0.157014	+	0.987596i	$0.449813\pi$
$242$	−8.86222	−0.569685
$243$	−0.303353	−0.0194601
$244$	2.52864	0.161879
$245$	−0.635286	−0.0405870
$246$	−11.2065	−0.714503
$247$	10.6627	0.678449
$248$	1.00000	0.0635001
$249$	4.02767	0.255243
$250$	−2.56306	−0.162102
$251$	−24.2913	−1.53326	−0.766628	−	0.642091i	$-0.778067\pi$
$251$	−24.2913	−1.53326	−0.766628	+	0.642091i	$0.778067\pi$
$252$	−0.0621840	−0.00391722
$253$	9.41937	0.592191
$254$	−7.98330	−0.500917
$255$	−0.352829	−0.0220950
$256$	1.00000	0.0625000
$257$	−3.11574	−0.194355	−0.0971774	−	0.995267i	$-0.530981\pi$
$257$	−3.11574	−0.194355	−0.0971774	+	0.995267i	$0.530981\pi$
$258$	1.69317	0.105412
$259$	3.15653	0.196137
$260$	−1.64753	−0.102175
$261$	−0.120778	−0.00747597
$262$	9.98745	0.617027
$263$	16.6927	1.02931	0.514657	−	0.857396i	$-0.327919\pi$
$263$	16.6927	1.02931	0.514657	+	0.857396i	$0.327919\pi$
$264$	2.54475	0.156618
$265$	0.493884	0.0303390
$266$	3.55729	0.218112
$267$	−18.8676	−1.15468
$268$	3.24991	0.198520
$269$	6.47587	0.394841	0.197420	−	0.980319i	$-0.436744\pi$
$269$	6.47587	0.394841	0.197420	+	0.980319i	$0.436744\pi$
$270$	−1.33413	−0.0811925
$271$	21.3615	1.29762	0.648811	−	0.760950i	$-0.275267\pi$
$271$	21.3615	1.29762	0.648811	+	0.760950i	$0.275267\pi$
$272$	−0.785672	−0.0476383
$273$	23.6735	1.43279
$274$	−20.1362	−1.21647
$275$	−7.21323	−0.434974
$276$	11.2125	0.674916
$277$	3.20914	0.192819	0.0964094	−	0.995342i	$-0.469264\pi$
$277$	3.20914	0.192819	0.0964094	+	0.995342i	$0.469264\pi$
$278$	12.2359	0.733862
$279$	0.0291912	0.00174763
$280$	−0.549650	−0.0328479
$281$	21.5375	1.28482	0.642410	−	0.766361i	$-0.277935\pi$
$281$	21.5375	1.28482	0.642410	+	0.766361i	$0.277935\pi$
$282$	−17.3026	−1.03035
$283$	5.05308	0.300375	0.150187	−	0.988658i	$-0.452012\pi$
$283$	5.05308	0.300375	0.150187	+	0.988658i	$0.452012\pi$
$284$	−0.963411	−0.0571680
$285$	−0.749923	−0.0444216
$286$	−9.33585	−0.552040
$287$	13.7162	0.809643
$288$	0.0291912	0.00172011
$289$	−16.3827	−0.963689
$290$	−1.06757	−0.0626898
$291$	−1.74046	−0.102027
$292$	6.89950	0.403763
$293$	−18.5514	−1.08378	−0.541892	−	0.840448i	$-0.682292\pi$
$293$	−18.5514	−1.08378	−0.541892	+	0.840448i	$0.682292\pi$
$294$	−4.28522	−0.249919
$295$	0.521617	0.0303697
$296$	−1.48178	−0.0861266
$297$	−7.55995	−0.438673
$298$	−5.34594	−0.309682
$299$	−41.1352	−2.37891
$300$	−8.58641	−0.495737
$301$	−2.07235	−0.119448
$302$	1.18419	0.0681423
$303$	0.355633	0.0204306
$304$	−1.66991	−0.0957759
$305$	0.652449	0.0373591
$306$	−0.0229347	−0.00131109
$307$	27.9369	1.59444	0.797221	−	0.603688i	$-0.206303\pi$
$307$	27.9369	1.59444	0.797221	+	0.603688i	$0.206303\pi$
$308$	−3.11464	−0.177473
$309$	29.6248	1.68530
$310$	0.258024	0.0146548
$311$	−0.969149	−0.0549554	−0.0274777	−	0.999622i	$-0.508748\pi$
$311$	−0.969149	−0.0549554	−0.0274777	+	0.999622i	$0.508748\pi$
$312$	−11.1131	−0.629157
$313$	−31.8147	−1.79827	−0.899137	−	0.437666i	$-0.855805\pi$
$313$	−31.8147	−1.79827	−0.899137	+	0.437666i	$0.855805\pi$
$314$	−13.9758	−0.788698
$315$	−0.0160450	−0.000904031 0
$316$	−16.3050	−0.917230
$317$	−15.2778	−0.858089	−0.429045	−	0.903283i	$-0.641150\pi$
$317$	−15.2778	−0.858089	−0.429045	+	0.903283i	$0.641150\pi$
$318$	3.33141	0.186816
$319$	−6.04946	−0.338705
$320$	0.258024	0.0144240
$321$	20.6318	1.15155
$322$	−13.7236	−0.764785
$323$	1.31200	0.0730017
$324$	−9.08672	−0.504818
$325$	31.5008	1.74735
$326$	−3.39084	−0.187801
$327$	−2.39553	−0.132473
$328$	−6.43885	−0.355526
$329$	21.1774	1.16755
$330$	0.656605	0.0361449
$331$	9.23442	0.507570	0.253785	−	0.967261i	$-0.418324\pi$
$331$	9.23442	0.507570	0.253785	+	0.967261i	$0.418324\pi$
$332$	2.31414	0.127005
$333$	−0.0432549	−0.00237035
$334$	−20.9528	−1.14649
$335$	0.838553	0.0458151
$336$	−3.70757	−0.202265
$337$	30.4705	1.65984	0.829918	−	0.557886i	$-0.188387\pi$
$337$	30.4705	1.65984	0.829918	+	0.557886i	$0.188387\pi$
$338$	27.7704	1.51051
$339$	−13.4725	−0.731727
$340$	−0.202722	−0.0109941
$341$	1.46211	0.0791779
$342$	−0.0487467	−0.00263592
$343$	20.1565	1.08835
$344$	0.972831	0.0524515
$345$	2.89310	0.155759
$346$	9.19344	0.494242
$347$	−4.89179	−0.262605	−0.131303	−	0.991342i	$-0.541916\pi$
$347$	−4.89179	−0.262605	−0.131303	+	0.991342i	$0.541916\pi$
$348$	−7.20110	−0.386020
$349$	2.81866	0.150879	0.0754397	−	0.997150i	$-0.475964\pi$
$349$	2.81866	0.150879	0.0754397	+	0.997150i	$0.475964\pi$
$350$	10.5093	0.561747
$351$	33.0150	1.76221
$352$	1.46211	0.0779309
$353$	−8.33664	−0.443715	−0.221857	−	0.975079i	$-0.571212\pi$
$353$	−8.33664	−0.443715	−0.221857	+	0.975079i	$0.571212\pi$
$354$	3.51848	0.187005
$355$	−0.248583	−0.0131934
$356$	−10.8406	−0.574550
$357$	2.91294	0.154169
$358$	24.2534	1.28183
$359$	19.8229	1.04621	0.523107	−	0.852267i	$-0.324773\pi$
$359$	19.8229	1.04621	0.523107	+	0.852267i	$0.324773\pi$
$360$	0.00753203	0.000396973 0
$361$	−16.2114	−0.853232
$362$	−4.62508	−0.243089
$363$	−15.4243	−0.809567
$364$	13.6019	0.712933
$365$	1.78024	0.0931818
$366$	4.40099	0.230043
$367$	3.13340	0.163562	0.0817811	−	0.996650i	$-0.473939\pi$
$367$	3.13340	0.163562	0.0817811	+	0.996650i	$0.473939\pi$
$368$	6.44230	0.335828
$369$	−0.187958	−0.00978469
$370$	−0.382334	−0.0198766
$371$	−4.07747	−0.211692
$372$	1.74046	0.0902385
$373$	3.88925	0.201378	0.100689	−	0.994918i	$-0.467895\pi$
$373$	3.88925	0.201378	0.100689	+	0.994918i	$0.467895\pi$
$374$	−1.14874	−0.0594000
$375$	−4.46090	−0.230360
$376$	−9.94139	−0.512688
$377$	26.4185	1.36062
$378$	11.0145	0.566524
$379$	6.52210	0.335018	0.167509	−	0.985871i	$-0.446428\pi$
$379$	6.52210	0.335018	0.167509	+	0.985871i	$0.446428\pi$
$380$	−0.430877	−0.0221035
$381$	−13.8946	−0.711841
$382$	4.66864	0.238868
$383$	−36.5308	−1.86664	−0.933318	−	0.359052i	$-0.883100\pi$
$383$	−36.5308	−1.86664	−0.933318	+	0.359052i	$0.883100\pi$
$384$	1.74046	0.0888173
$385$	−0.803651	−0.0409578
$386$	−10.2541	−0.521921
$387$	0.0283981	0.00144356
$388$	−1.00000	−0.0507673
$389$	0.168335	0.00853490	0.00426745	−	0.999991i	$-0.498642\pi$
$389$	0.168335	0.00853490	0.00426745	+	0.999991i	$0.498642\pi$
$390$	−2.86745	−0.145199
$391$	−5.06153	−0.255973
$392$	−2.46212	−0.124356
$393$	17.3827	0.876843
$394$	−7.12720	−0.359063
$395$	−4.20709	−0.211682
$396$	0.0426809	0.00214479
$397$	25.4635	1.27798	0.638989	−	0.769216i	$-0.279353\pi$
$397$	25.4635	1.27798	0.638989	+	0.769216i	$0.279353\pi$
$398$	3.57195	0.179046
$399$	6.19131	0.309953
$400$	−4.93342	−0.246671
$401$	16.4477	0.821360	0.410680	−	0.911780i	$-0.365291\pi$
$401$	16.4477	0.821360	0.410680	+	0.911780i	$0.365291\pi$
$402$	5.65632	0.282112
$403$	−6.38517	−0.318068
$404$	0.204333	0.0101659
$405$	−2.34459	−0.116504
$406$	8.81378	0.437420
$407$	−2.16653	−0.107391
$408$	−1.36743	−0.0676978
$409$	0.616136	0.0304660	0.0152330	−	0.999884i	$-0.495151\pi$
$409$	0.616136	0.0304660	0.0152330	+	0.999884i	$0.495151\pi$
$410$	−1.66138	−0.0820495
$411$	−35.0461	−1.72870
$412$	17.0213	0.838579
$413$	−4.30644	−0.211906
$414$	0.188058	0.00924257
$415$	0.597104	0.0293107
$416$	−6.38517	−0.313059
$417$	21.2961	1.04287
$418$	−2.44160	−0.119422
$419$	−4.73388	−0.231265	−0.115633	−	0.993292i	$-0.536889\pi$
$419$	−4.73388	−0.231265	−0.115633	+	0.993292i	$0.536889\pi$
$420$	−0.956642	−0.0466794
$421$	−6.92736	−0.337619	−0.168809	−	0.985649i	$-0.553992\pi$
$421$	−6.92736	−0.337619	−0.168809	+	0.985649i	$0.553992\pi$
$422$	19.2818	0.938625
$423$	−0.290201	−0.0141101
$424$	1.91410	0.0929569
$425$	3.87605	0.188016
$426$	−1.67678	−0.0812401
$427$	−5.38658	−0.260675
$428$	11.8542	0.572995
$429$	−16.2486	−0.784492
$430$	0.251014	0.0121050
$431$	−11.9357	−0.574923	−0.287461	−	0.957792i	$-0.592811\pi$
$431$	−11.9357	−0.574923	−0.287461	+	0.957792i	$0.592811\pi$
$432$	−5.17057	−0.248769
$433$	−25.7850	−1.23915	−0.619575	−	0.784937i	$-0.712695\pi$
$433$	−25.7850	−1.23915	−0.619575	+	0.784937i	$0.712695\pi$
$434$	−2.13023	−0.102254
$435$	−1.85806	−0.0890870
$436$	−1.37638	−0.0659167
$437$	−10.7581	−0.514628
$438$	12.0083	0.573778
$439$	−9.89087	−0.472065	−0.236033	−	0.971745i	$-0.575847\pi$
$439$	−9.89087	−0.472065	−0.236033	+	0.971745i	$0.575847\pi$
$440$	0.377260	0.0179852
$441$	−0.0718723	−0.00342249
$442$	5.01665	0.238618
$443$	−18.0581	−0.857965	−0.428982	−	0.903313i	$-0.641128\pi$
$443$	−18.0581	−0.857965	−0.428982	+	0.903313i	$0.641128\pi$
$444$	−2.57897	−0.122393
$445$	−2.79713	−0.132597
$446$	20.9785	0.993361
$447$	−9.30438	−0.440082
$448$	−2.13023	−0.100644
$449$	22.0032	1.03839	0.519197	−	0.854654i	$-0.326231\pi$
$449$	22.0032	1.03839	0.519197	+	0.854654i	$0.326231\pi$
$450$	−0.144013	−0.00678882
$451$	−9.41432	−0.443303
$452$	−7.74079	−0.364096
$453$	2.06103	0.0968355
$454$	−1.08654	−0.0509940
$455$	3.50961	0.164533
$456$	−2.90641	−0.136105
$457$	19.6747	0.920345	0.460173	−	0.887829i	$-0.347788\pi$
$457$	19.6747	0.920345	0.460173	+	0.887829i	$0.347788\pi$
$458$	−8.97184	−0.419227
$459$	4.06237	0.189615
$460$	1.66227	0.0775036
$461$	−10.3139	−0.480367	−0.240184	−	0.970727i	$-0.577208\pi$
$461$	−10.3139	−0.480367	−0.240184	+	0.970727i	$0.577208\pi$
$462$	−5.42089	−0.252203
$463$	−11.2353	−0.522148	−0.261074	−	0.965319i	$-0.584077\pi$
$463$	−11.2353	−0.522148	−0.261074	+	0.965319i	$0.584077\pi$
$464$	−4.13748	−0.192078
$465$	0.449080	0.0208256
$466$	2.78284	0.128913
$467$	−28.3868	−1.31359	−0.656793	−	0.754071i	$-0.728087\pi$
$467$	−28.3868	−1.31359	−0.656793	+	0.754071i	$0.728087\pi$
$468$	−0.186391	−0.00861592
$469$	−6.92305	−0.319677
$470$	−2.56512	−0.118320
$471$	−24.3242	−1.12080
$472$	2.02158	0.0930510
$473$	1.42239	0.0654015
$474$	−28.3782	−1.30345
$475$	8.23838	0.378003
$476$	1.67366	0.0767121
$477$	0.0558749	0.00255834
$478$	−23.9822	−1.09692
$479$	19.3886	0.885889	0.442945	−	0.896549i	$-0.353934\pi$
$479$	19.3886	0.885889	0.442945	+	0.896549i	$0.353934\pi$
$480$	0.449080	0.0204976
$481$	9.46141	0.431403
$482$	4.87502	0.222051
$483$	−23.8853	−1.08682
$484$	−8.86222	−0.402828
$485$	−0.258024	−0.0117163
$486$	−0.303353	−0.0137604
$487$	−32.0881	−1.45405	−0.727024	−	0.686612i	$-0.759097\pi$
$487$	−32.0881	−1.45405	−0.727024	+	0.686612i	$0.759097\pi$
$488$	2.52864	0.114466
$489$	−5.90161	−0.266880
$490$	−0.635286	−0.0286993
$491$	35.0844	1.58334	0.791669	−	0.610950i	$-0.209212\pi$
$491$	35.0844	1.58334	0.791669	+	0.610950i	$0.209212\pi$
$492$	−11.2065	−0.505230
$493$	3.25070	0.146404
$494$	10.6627	0.479736
$495$	0.0110127	0.000494983 0
$496$	1.00000	0.0449013
$497$	2.05229	0.0920577
$498$	4.02767	0.180484
$499$	1.90743	0.0853883	0.0426941	−	0.999088i	$-0.486406\pi$
$499$	1.90743	0.0853883	0.0426941	+	0.999088i	$0.486406\pi$
$500$	−2.56306	−0.114624
$501$	−36.4675	−1.62925
$502$	−24.2913	−1.08418
$503$	6.78491	0.302524	0.151262	−	0.988494i	$-0.451666\pi$
$503$	6.78491	0.302524	0.151262	+	0.988494i	$0.451666\pi$
$504$	−0.0621840	−0.00276989
$505$	0.0527228	0.00234613
$506$	9.41937	0.418742
$507$	48.3333	2.14656
$508$	−7.98330	−0.354201
$509$	−31.1573	−1.38102	−0.690512	−	0.723321i	$-0.742615\pi$
$509$	−31.1573	−1.38102	−0.690512	+	0.723321i	$0.742615\pi$
$510$	−0.352829	−0.0156235
$511$	−14.6975	−0.650180
$512$	1.00000	0.0441942
$513$	8.63438	0.381217
$514$	−3.11574	−0.137430
$515$	4.39190	0.193530
$516$	1.69317	0.0745377
$517$	−14.5354	−0.639268
$518$	3.15653	0.138690
$519$	16.0008	0.702357
$520$	−1.64753	−0.0722489
$521$	−1.71178	−0.0749943	−0.0374971	−	0.999297i	$-0.511939\pi$
$521$	−1.71178	−0.0749943	−0.0374971	+	0.999297i	$0.511939\pi$
$522$	−0.120778	−0.00528631
$523$	34.9250	1.52716	0.763582	−	0.645710i	$-0.223439\pi$
$523$	34.9250	1.52716	0.763582	+	0.645710i	$0.223439\pi$
$524$	9.98745	0.436304
$525$	18.2910	0.798286
$526$	16.6927	0.727835
$527$	−0.785672	−0.0342244
$528$	2.54475	0.110746
$529$	18.5032	0.804487
$530$	0.493884	0.0214529
$531$	0.0590125	0.00256092
$532$	3.55729	0.154228
$533$	41.1131	1.78081
$534$	−18.8676	−0.816479
$535$	3.05867	0.132238
$536$	3.24991	0.140375
$537$	42.2119	1.82158
$538$	6.47587	0.279195
$539$	−3.59990	−0.155059
$540$	−1.33413	−0.0574118
$541$	30.8045	1.32439	0.662194	−	0.749332i	$-0.269625\pi$
$541$	30.8045	1.32439	0.662194	+	0.749332i	$0.269625\pi$
$542$	21.3615	0.917557
$543$	−8.04975	−0.345448
$544$	−0.785672	−0.0336854
$545$	−0.355139	−0.0152125
$546$	23.6735	1.01313
$547$	43.4041	1.85583	0.927914	−	0.372795i	$-0.121601\pi$
$547$	43.4041	1.85583	0.927914	+	0.372795i	$0.121601\pi$
$548$	−20.1362	−0.860175
$549$	0.0738140	0.00315030
$550$	−7.21323	−0.307573
$551$	6.90922	0.294343
$552$	11.2125	0.477237
$553$	34.7335	1.47702
$554$	3.20914	0.136343
$555$	−0.665436	−0.0282462
$556$	12.2359	0.518919
$557$	23.3091	0.987640	0.493820	−	0.869564i	$-0.335600\pi$
$557$	23.3091	0.987640	0.493820	+	0.869564i	$0.335600\pi$
$558$	0.0291912	0.00123576
$559$	−6.21169	−0.262727
$560$	−0.549650	−0.0232270
$561$	−1.99933	−0.0844120
$562$	21.5375	0.908505
$563$	−20.7221	−0.873333	−0.436666	−	0.899624i	$-0.643841\pi$
$563$	−20.7221	−0.873333	−0.436666	+	0.899624i	$0.643841\pi$
$564$	−17.3026	−0.728569
$565$	−1.99731	−0.0840274
$566$	5.05308	0.212397
$567$	19.3568	0.812909
$568$	−0.963411	−0.0404238
$569$	41.5749	1.74291	0.871456	−	0.490474i	$-0.163176\pi$
$569$	41.5749	1.74291	0.871456	+	0.490474i	$0.163176\pi$
$570$	−0.749923	−0.0314108
$571$	−35.5452	−1.48752	−0.743759	−	0.668447i	$-0.766959\pi$
$571$	−35.5452	−1.48752	−0.743759	+	0.668447i	$0.766959\pi$
$572$	−9.33585	−0.390351
$573$	8.12556	0.339450
$574$	13.7162	0.572504
$575$	−31.7826	−1.32543
$576$	0.0291912	0.00121630
$577$	−9.94726	−0.414110	−0.207055	−	0.978329i	$-0.566388\pi$
$577$	−9.94726	−0.414110	−0.207055	+	0.978329i	$0.566388\pi$
$578$	−16.3827	−0.681431
$579$	−17.8469	−0.741691
$580$	−1.06757	−0.0443284
$581$	−4.92966	−0.204517
$582$	−1.74046	−0.0721443
$583$	2.79863	0.115907
$584$	6.89950	0.285503
$585$	−0.0480933	−0.00198841
$586$	−18.5514	−0.766351
$587$	20.0908	0.829237	0.414619	−	0.909995i	$-0.363915\pi$
$587$	20.0908	0.829237	0.414619	+	0.909995i	$0.363915\pi$
$588$	−4.28522	−0.176719
$589$	−1.66991	−0.0688075
$590$	0.521617	0.0214746
$591$	−12.4046	−0.510256
$592$	−1.48178	−0.0609007
$593$	7.67288	0.315087	0.157544	−	0.987512i	$-0.449642\pi$
$593$	7.67288	0.315087	0.157544	+	0.987512i	$0.449642\pi$
$594$	−7.55995	−0.310189
$595$	0.431844	0.0177039
$596$	−5.34594	−0.218978
$597$	6.21683	0.254438
$598$	−41.1352	−1.68214
$599$	16.4815	0.673415	0.336708	−	0.941609i	$-0.390687\pi$
$599$	16.4815	0.673415	0.336708	+	0.941609i	$0.390687\pi$
$600$	−8.58641	−0.350539
$601$	−10.7269	−0.437557	−0.218779	−	0.975774i	$-0.570207\pi$
$601$	−10.7269	−0.437557	−0.218779	+	0.975774i	$0.570207\pi$
$602$	−2.07235	−0.0844628
$603$	0.0948687	0.00386335
$604$	1.18419	0.0481839
$605$	−2.28667	−0.0929662
$606$	0.355633	0.0144466
$607$	−20.6059	−0.836367	−0.418183	−	0.908363i	$-0.637333\pi$
$607$	−20.6059	−0.836367	−0.418183	+	0.908363i	$0.637333\pi$
$608$	−1.66991	−0.0677238
$609$	15.3400	0.621608
$610$	0.652449	0.0264169
$611$	63.4775	2.56802
$612$	−0.0229347	−0.000927081 0
$613$	−35.9007	−1.45002	−0.725008	−	0.688741i	$-0.758164\pi$
$613$	−35.9007	−1.45002	−0.725008	+	0.688741i	$0.758164\pi$
$614$	27.9369	1.12744
$615$	−2.89155	−0.116599
$616$	−3.11464	−0.125492
$617$	−14.7708	−0.594648	−0.297324	−	0.954777i	$-0.596094\pi$
$617$	−14.7708	−0.594648	−0.297324	+	0.954777i	$0.596094\pi$
$618$	29.6248	1.19169
$619$	−32.9160	−1.32301	−0.661503	−	0.749943i	$-0.730081\pi$
$619$	−32.9160	−1.32301	−0.661503	+	0.749943i	$0.730081\pi$
$620$	0.258024	0.0103625
$621$	−33.3103	−1.33670
$622$	−0.969149	−0.0388593
$623$	23.0929	0.925198
$624$	−11.1131	−0.444881
$625$	24.0058	0.960232
$626$	−31.8147	−1.27157
$627$	−4.24950	−0.169709
$628$	−13.9758	−0.557694
$629$	1.16419	0.0464194
$630$	−0.0160450	−0.000639246 0
$631$	−1.18477	−0.0471648	−0.0235824	−	0.999722i	$-0.507507\pi$
$631$	−1.18477	−0.0471648	−0.0235824	+	0.999722i	$0.507507\pi$
$632$	−16.3050	−0.648579
$633$	33.5592	1.33386
$634$	−15.2778	−0.606761
$635$	−2.05988	−0.0817439
$636$	3.33141	0.132099
$637$	15.7211	0.622892
$638$	−6.04946	−0.239501
$639$	−0.0281231	−0.00111253
$640$	0.258024	0.0101993
$641$	−6.97736	−0.275589	−0.137795	−	0.990461i	$-0.544001\pi$
$641$	−6.97736	−0.275589	−0.137795	+	0.990461i	$0.544001\pi$
$642$	20.6318	0.814271
$643$	14.8520	0.585705	0.292853	−	0.956158i	$-0.405395\pi$
$643$	14.8520	0.585705	0.292853	+	0.956158i	$0.405395\pi$
$644$	−13.7236	−0.540784
$645$	0.436878	0.0172021
$646$	1.31200	0.0516200
$647$	5.98951	0.235472	0.117736	−	0.993045i	$-0.462436\pi$
$647$	5.98951	0.235472	0.117736	+	0.993045i	$0.462436\pi$
$648$	−9.08672	−0.356960
$649$	2.95579	0.116025
$650$	31.5008	1.23556
$651$	−3.70757	−0.145311
$652$	−3.39084	−0.132795
$653$	−44.3682	−1.73626	−0.868132	−	0.496334i	$-0.834679\pi$
$653$	−44.3682	−1.73626	−0.868132	+	0.496334i	$0.834679\pi$
$654$	−2.39553	−0.0936728
$655$	2.57700	0.100692
$656$	−6.43885	−0.251395
$657$	0.201405	0.00785755
$658$	21.1774	0.825582
$659$	17.7778	0.692524	0.346262	−	0.938138i	$-0.387451\pi$
$659$	17.7778	0.692524	0.346262	+	0.938138i	$0.387451\pi$
$660$	0.656605	0.0255583
$661$	−46.6371	−1.81397	−0.906986	−	0.421161i	$-0.861623\pi$
$661$	−46.6371	−1.81397	−0.906986	+	0.421161i	$0.861623\pi$
$662$	9.23442	0.358906
$663$	8.73126	0.339094
$664$	2.31414	0.0898062
$665$	0.917866	0.0355933
$666$	−0.0432549	−0.00167609
$667$	−26.6549	−1.03208
$668$	−20.9528	−0.810689
$669$	36.5122	1.41164
$670$	0.838553	0.0323961
$671$	3.69716	0.142727
$672$	−3.70757	−0.143023
$673$	19.8587	0.765498	0.382749	−	0.923852i	$-0.374977\pi$
$673$	19.8587	0.765498	0.382749	+	0.923852i	$0.374977\pi$
$674$	30.4705	1.17368
$675$	25.5086	0.981826
$676$	27.7704	1.06809
$677$	−7.69021	−0.295559	−0.147779	−	0.989020i	$-0.547213\pi$
$677$	−7.69021	−0.295559	−0.147779	+	0.989020i	$0.547213\pi$
$678$	−13.4725	−0.517409
$679$	2.13023	0.0817507
$680$	−0.202722	−0.00777404
$681$	−1.89108	−0.0724664
$682$	1.46211	0.0559872
$683$	−5.05057	−0.193255	−0.0966274	−	0.995321i	$-0.530806\pi$
$683$	−5.05057	−0.193255	−0.0966274	+	0.995321i	$0.530806\pi$
$684$	−0.0487467	−0.00186388
$685$	−5.19561	−0.198514
$686$	20.1565	0.769578
$687$	−15.6151	−0.595754
$688$	0.972831	0.0370888
$689$	−12.2219	−0.465616
$690$	2.89310	0.110139
$691$	21.8803	0.832367	0.416183	−	0.909281i	$-0.363367\pi$
$691$	21.8803	0.832367	0.416183	+	0.909281i	$0.363367\pi$
$692$	9.19344	0.349482
$693$	−0.0909200	−0.00345377
$694$	−4.89179	−0.185690
$695$	3.15716	0.119758
$696$	−7.20110	−0.272957
$697$	5.05882	0.191616
$698$	2.81866	0.106688
$699$	4.84342	0.183195
$700$	10.5093	0.397215
$701$	2.23620	0.0844600	0.0422300	−	0.999108i	$-0.486554\pi$
$701$	2.23620	0.0844600	0.0422300	+	0.999108i	$0.486554\pi$
$702$	33.0150	1.24607
$703$	2.47444	0.0933252
$704$	1.46211	0.0551055
$705$	−4.46447	−0.168142
$706$	−8.33664	−0.313754
$707$	−0.435276	−0.0163702
$708$	3.51848	0.132233
$709$	30.1064	1.13067	0.565335	−	0.824862i	$-0.308747\pi$
$709$	30.1064	1.13067	0.565335	+	0.824862i	$0.308747\pi$
$710$	−0.248583	−0.00932916
$711$	−0.475964	−0.0178500
$712$	−10.8406	−0.406268
$713$	6.44230	0.241266
$714$	2.91294	0.109014
$715$	−2.40887	−0.0900867
$716$	24.2534	0.906390
$717$	−41.7400	−1.55881
$718$	19.8229	0.739786
$719$	33.6347	1.25436	0.627182	−	0.778873i	$-0.284208\pi$
$719$	33.6347	1.25436	0.627182	+	0.778873i	$0.284208\pi$
$720$	0.00753203	0.000280702 0
$721$	−36.2593	−1.35037
$722$	−16.2114	−0.603326
$723$	8.48476	0.315552
$724$	−4.62508	−0.171890
$725$	20.4119	0.758080
$726$	−15.4243	−0.572450
$727$	−37.8415	−1.40346	−0.701731	−	0.712442i	$-0.747589\pi$
$727$	−37.8415	−1.40346	−0.701731	+	0.712442i	$0.747589\pi$
$728$	13.6019	0.504119
$729$	26.7322	0.990081
$730$	1.78024	0.0658895
$731$	−0.764326	−0.0282696
$732$	4.40099	0.162665
$733$	8.09784	0.299100	0.149550	−	0.988754i	$-0.452217\pi$
$733$	8.09784	0.299100	0.149550	+	0.988754i	$0.452217\pi$
$734$	3.13340	0.115656
$735$	−1.10569	−0.0407839
$736$	6.44230	0.237466
$737$	4.75173	0.175032
$738$	−0.187958	−0.00691882
$739$	−46.3638	−1.70552	−0.852760	−	0.522303i	$-0.825073\pi$
$739$	−46.3638	−1.70552	−0.852760	+	0.522303i	$0.825073\pi$
$740$	−0.382334	−0.0140549
$741$	18.5579	0.681742
$742$	−4.07747	−0.149689
$743$	−2.13149	−0.0781968	−0.0390984	−	0.999235i	$-0.512449\pi$
$743$	−2.13149	−0.0781968	−0.0390984	+	0.999235i	$0.512449\pi$
$744$	1.74046	0.0638083
$745$	−1.37938	−0.0505366
$746$	3.88925	0.142396
$747$	0.0675527	0.00247162
$748$	−1.14874	−0.0420021
$749$	−25.2522	−0.922695
$750$	−4.46090	−0.162889
$751$	5.88753	0.214839	0.107419	−	0.994214i	$-0.465741\pi$
$751$	5.88753	0.214839	0.107419	+	0.994214i	$0.465741\pi$
$752$	−9.94139	−0.362525
$753$	−42.2780	−1.54070
$754$	26.4185	0.962106
$755$	0.305549	0.0111201
$756$	11.0145	0.400593
$757$	23.0489	0.837728	0.418864	−	0.908049i	$-0.362428\pi$
$757$	23.0489	0.837728	0.418864	+	0.908049i	$0.362428\pi$
$758$	6.52210	0.236894
$759$	16.3940	0.595065
$760$	−0.430877	−0.0156295
$761$	−5.45767	−0.197840	−0.0989201	−	0.995095i	$-0.531539\pi$
$761$	−5.45767	−0.197840	−0.0989201	+	0.995095i	$0.531539\pi$
$762$	−13.8946	−0.503348
$763$	2.93201	0.106146
$764$	4.66864	0.168905
$765$	−0.00591770	−0.000213955 0
$766$	−36.5308	−1.31991
$767$	−12.9082	−0.466087
$768$	1.74046	0.0628033
$769$	−3.00283	−0.108285	−0.0541424	−	0.998533i	$-0.517242\pi$
$769$	−3.00283	−0.108285	−0.0541424	+	0.998533i	$0.517242\pi$
$770$	−0.803651	−0.0289616
$771$	−5.42282	−0.195298
$772$	−10.2541	−0.369054
$773$	−5.50084	−0.197851	−0.0989257	−	0.995095i	$-0.531541\pi$
$773$	−5.50084	−0.197851	−0.0989257	+	0.995095i	$0.531541\pi$
$774$	0.0283981	0.00102075
$775$	−4.93342	−0.177214
$776$	−1.00000	−0.0358979
$777$	5.49380	0.197089
$778$	0.168335	0.00603509
$779$	10.7523	0.385241
$780$	−2.86745	−0.102671
$781$	−1.40862	−0.0504043
$782$	−5.06153	−0.181000
$783$	21.3931	0.764527
$784$	−2.46212	−0.0879329
$785$	−3.60608	−0.128707
$786$	17.3827	0.620022
$787$	−12.1384	−0.432688	−0.216344	−	0.976317i	$-0.569413\pi$
$787$	−12.1384	−0.432688	−0.216344	+	0.976317i	$0.569413\pi$
$788$	−7.12720	−0.253896
$789$	29.0529	1.03431
$790$	−4.20709	−0.149681
$791$	16.4897	0.586305
$792$	0.0426809	0.00151660
$793$	−16.1458	−0.573354
$794$	25.4635	0.903667
$795$	0.859583	0.0304863
$796$	3.57195	0.126604
$797$	−19.5643	−0.693002	−0.346501	−	0.938050i	$-0.612630\pi$
$797$	−19.5643	−0.693002	−0.346501	+	0.938050i	$0.612630\pi$
$798$	6.19131	0.219170
$799$	7.81067	0.276321
$800$	−4.93342	−0.174423
$801$	−0.316450	−0.0111812
$802$	16.4477	0.580789
$803$	10.0879	0.355993
$804$	5.65632	0.199483
$805$	−3.54101	−0.124804
$806$	−6.38517	−0.224908
$807$	11.2710	0.396757
$808$	0.204333	0.00718841
$809$	16.0308	0.563613	0.281806	−	0.959471i	$-0.409066\pi$
$809$	16.0308	0.563613	0.281806	+	0.959471i	$0.409066\pi$
$810$	−2.34459	−0.0823805
$811$	10.3510	0.363473	0.181736	−	0.983347i	$-0.441828\pi$
$811$	10.3510	0.363473	0.181736	+	0.983347i	$0.441828\pi$
$812$	8.81378	0.309303
$813$	37.1788	1.30392
$814$	−2.16653	−0.0759368
$815$	−0.874917	−0.0306470
$816$	−1.36743	−0.0478696
$817$	−1.62454	−0.0568355
$818$	0.616136	0.0215427
$819$	0.397055	0.0138742
$820$	−1.66138	−0.0580178
$821$	−13.1245	−0.458047	−0.229024	−	0.973421i	$-0.573553\pi$
$821$	−13.1245	−0.458047	−0.229024	+	0.973421i	$0.573553\pi$
$822$	−35.0461	−1.22237
$823$	−31.3719	−1.09356	−0.546778	−	0.837278i	$-0.684146\pi$
$823$	−31.3719	−1.09356	−0.546778	+	0.837278i	$0.684146\pi$
$824$	17.0213	0.592965
$825$	−12.5543	−0.437085
$826$	−4.30644	−0.149840
$827$	−46.7818	−1.62676	−0.813382	−	0.581731i	$-0.802376\pi$
$827$	−46.7818	−1.62676	−0.813382	+	0.581731i	$0.802376\pi$
$828$	0.188058	0.00653548
$829$	53.6721	1.86411	0.932054	−	0.362320i	$-0.118015\pi$
$829$	53.6721	1.86411	0.932054	+	0.362320i	$0.118015\pi$
$830$	0.597104	0.0207258
$831$	5.58538	0.193755
$832$	−6.38517	−0.221366
$833$	1.93442	0.0670237
$834$	21.2961	0.737423
$835$	−5.40633	−0.187094
$836$	−2.44160	−0.0844445
$837$	−5.17057	−0.178721
$838$	−4.73388	−0.163529
$839$	−46.2628	−1.59717	−0.798584	−	0.601883i	$-0.794417\pi$
$839$	−46.2628	−1.59717	−0.798584	+	0.601883i	$0.794417\pi$
$840$	−0.956642	−0.0330073
$841$	−11.8813	−0.409699
$842$	−6.92736	−0.238733
$843$	37.4851	1.29106
$844$	19.2818	0.663708
$845$	7.16544	0.246499
$846$	−0.290201	−0.00997732
$847$	18.8786	0.648675
$848$	1.91410	0.0657305
$849$	8.79467	0.301832
$850$	3.87605	0.132947
$851$	−9.54606	−0.327235
$852$	−1.67678	−0.0574454
$853$	36.8025	1.26009	0.630046	−	0.776557i	$-0.283036\pi$
$853$	36.8025	1.26009	0.630046	+	0.776557i	$0.283036\pi$
$854$	−5.38658	−0.184325
$855$	−0.0125778	−0.000430152 0
$856$	11.8542	0.405169
$857$	0.718411	0.0245404	0.0122702	−	0.999925i	$-0.496094\pi$
$857$	0.718411	0.0245404	0.0122702	+	0.999925i	$0.496094\pi$
$858$	−16.2486	−0.554720
$859$	−26.6901	−0.910654	−0.455327	−	0.890324i	$-0.650478\pi$
$859$	−26.6901	−0.910654	−0.455327	+	0.890324i	$0.650478\pi$
$860$	0.251014	0.00855949
$861$	23.8725	0.813572
$862$	−11.9357	−0.406532
$863$	50.7652	1.72807	0.864034	−	0.503433i	$-0.167930\pi$
$863$	50.7652	1.72807	0.864034	+	0.503433i	$0.167930\pi$
$864$	−5.17057	−0.175906
$865$	2.37213	0.0806547
$866$	−25.7850	−0.876212
$867$	−28.5134	−0.968367
$868$	−2.13023	−0.0723047
$869$	−23.8398	−0.808710
$870$	−1.85806	−0.0629940
$871$	−20.7512	−0.703128
$872$	−1.37638	−0.0466102
$873$	−0.0291912	−0.000987973 0
$874$	−10.7581	−0.363897
$875$	5.45991	0.184579
$876$	12.0083	0.405722
$877$	−50.1514	−1.69349	−0.846746	−	0.531997i	$-0.821442\pi$
$877$	−50.1514	−1.69349	−0.846746	+	0.531997i	$0.821442\pi$
$878$	−9.89087	−0.333801
$879$	−32.2879	−1.08904
$880$	0.377260	0.0127174
$881$	12.6032	0.424612	0.212306	−	0.977203i	$-0.431903\pi$
$881$	12.6032	0.424612	0.212306	+	0.977203i	$0.431903\pi$
$882$	−0.0718723	−0.00242007
$883$	7.69183	0.258851	0.129425	−	0.991589i	$-0.458687\pi$
$883$	7.69183	0.258851	0.129425	+	0.991589i	$0.458687\pi$
$884$	5.01665	0.168728
$885$	0.907852	0.0305171
$886$	−18.0581	−0.606673
$887$	−58.0946	−1.95062	−0.975312	−	0.220831i	$-0.929123\pi$
$887$	−58.0946	−1.95062	−0.975312	+	0.220831i	$0.929123\pi$
$888$	−2.57897	−0.0865446
$889$	17.0063	0.570371
$890$	−2.79713	−0.0937599
$891$	−13.2858	−0.445092
$892$	20.9785	0.702412
$893$	16.6012	0.555539
$894$	−9.30438	−0.311185
$895$	6.25794	0.209180
$896$	−2.13023	−0.0711660
$897$	−71.5940	−2.39046
$898$	22.0032	0.734256
$899$	−4.13748	−0.137993
$900$	−0.144013	−0.00480042
$901$	−1.50385	−0.0501006
$902$	−9.41432	−0.313463
$903$	−3.60684	−0.120028
$904$	−7.74079	−0.257455
$905$	−1.19338	−0.0396693
$906$	2.06103	0.0684731
$907$	−25.6409	−0.851391	−0.425696	−	0.904866i	$-0.639971\pi$
$907$	−25.6409	−0.851391	−0.425696	+	0.904866i	$0.639971\pi$
$908$	−1.08654	−0.0360582
$909$	0.00596472	0.000197837 0
$910$	3.50961	0.116342
$911$	−32.0334	−1.06131	−0.530656	−	0.847587i	$-0.678055\pi$
$911$	−32.0334	−1.06131	−0.530656	+	0.847587i	$0.678055\pi$
$912$	−2.90641	−0.0962408
$913$	3.38354	0.111979
$914$	19.6747	0.650782
$915$	1.13556	0.0375404
$916$	−8.97184	−0.296438
$917$	−21.2756	−0.702581
$918$	4.06237	0.134078
$919$	−38.4716	−1.26906	−0.634530	−	0.772898i	$-0.718806\pi$
$919$	−38.4716	−1.26906	−0.634530	+	0.772898i	$0.718806\pi$
$920$	1.66227	0.0548033
$921$	48.6229	1.60218
$922$	−10.3139	−0.339671
$923$	6.15155	0.202481
$924$	−5.42089	−0.178334
$925$	7.31024	0.240359
$926$	−11.2353	−0.369215
$927$	0.496872	0.0163194
$928$	−4.13748	−0.135819
$929$	12.6799	0.416013	0.208006	−	0.978127i	$-0.433302\pi$
$929$	12.6799	0.416013	0.208006	+	0.978127i	$0.433302\pi$
$930$	0.449080	0.0147259
$931$	4.11152	0.134750
$932$	2.78284	0.0911551
$933$	−1.68676	−0.0552221
$934$	−28.3868	−0.928845
$935$	−0.296403	−0.00969340
$936$	−0.186391	−0.00609238
$937$	13.5628	0.443078	0.221539	−	0.975151i	$-0.428892\pi$
$937$	13.5628	0.443078	0.221539	+	0.975151i	$0.428892\pi$
$938$	−6.92305	−0.226045
$939$	−55.3722	−1.80700
$940$	−2.56512	−0.0836648
$941$	−26.2700	−0.856376	−0.428188	−	0.903690i	$-0.640848\pi$
$941$	−26.2700	−0.856376	−0.428188	+	0.903690i	$0.640848\pi$
$942$	−24.3242	−0.792526
$943$	−41.4810	−1.35081
$944$	2.02158	0.0657970
$945$	2.84200	0.0924503
$946$	1.42239	0.0462459
$947$	14.3191	0.465307	0.232653	−	0.972560i	$-0.425259\pi$
$947$	14.3191	0.465307	0.232653	+	0.972560i	$0.425259\pi$
$948$	−28.3782	−0.921681
$949$	−44.0545	−1.43007
$950$	8.23838	0.267288
$951$	−26.5904	−0.862254
$952$	1.67366	0.0542437
$953$	27.4838	0.890286	0.445143	−	0.895459i	$-0.353153\pi$
$953$	27.4838	0.890286	0.445143	+	0.895459i	$0.353153\pi$
$954$	0.0558749	0.00180902
$955$	1.20462	0.0389806
$956$	−23.9822	−0.775641
$957$	−10.5288	−0.340349
$958$	19.3886	0.626418
$959$	42.8947	1.38514
$960$	0.449080	0.0144940
$961$	1.00000	0.0322581
$962$	9.46141	0.305048
$963$	0.346039	0.0111509
$964$	4.87502	0.157014
$965$	−2.64581	−0.0851716
$966$	−23.8853	−0.768497
$967$	53.8114	1.73046	0.865229	−	0.501377i	$-0.167173\pi$
$967$	53.8114	1.73046	0.865229	+	0.501377i	$0.167173\pi$
$968$	−8.86222	−0.284843
$969$	2.28348	0.0733560
$970$	−0.258024	−0.00828465
$971$	−28.4341	−0.912495	−0.456248	−	0.889853i	$-0.650807\pi$
$971$	−28.4341	−0.912495	−0.456248	+	0.889853i	$0.650807\pi$
$972$	−0.303353	−0.00973006
$973$	−26.0653	−0.835616
$974$	−32.0881	−1.02817
$975$	54.8257	1.75583
$976$	2.52864	0.0809397
$977$	53.7620	1.72000	0.860000	−	0.510295i	$-0.170464\pi$
$977$	53.7620	1.72000	0.860000	+	0.510295i	$0.170464\pi$
$978$	−5.90161	−0.188713
$979$	−15.8502	−0.506573
$980$	−0.635286	−0.0202935
$981$	−0.0401783	−0.00128279
$982$	35.0844	1.11959
$983$	21.0837	0.672465	0.336233	−	0.941779i	$-0.390847\pi$
$983$	21.0837	0.672465	0.336233	+	0.941779i	$0.390847\pi$
$984$	−11.2065	−0.357251
$985$	−1.83899	−0.0585950
$986$	3.25070	0.103523
$987$	36.8584	1.17322
$988$	10.6627	0.339225
$989$	6.26727	0.199287
$990$	0.0110127	0.000350006 0
$991$	−23.7822	−0.755467	−0.377733	−	0.925914i	$-0.623296\pi$
$991$	−23.7822	−0.755467	−0.377733	+	0.925914i	$0.623296\pi$
$992$	1.00000	0.0317500
$993$	16.0721	0.510033
$994$	2.05229	0.0650946
$995$	0.921648	0.0292182
$996$	4.02767	0.127622
$997$	−38.1971	−1.20971	−0.604857	−	0.796334i	$-0.706770\pi$
$997$	−38.1971	−1.20971	−0.604857	+	0.796334i	$0.706770\pi$
$998$	1.90743	0.0603786
$999$	7.66163	0.242403

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.e.1.19	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.e.1.19	✓	21	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:	\( N \)	\(=\)	\( 6014 = 2 \cdot 31 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6014.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.74046 q^{3} +1.00000 q^{4} +0.258024 q^{5} +1.74046 q^{6} -2.13023 q^{7} +1.00000 q^{8} +0.0291912 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.74046 q^{3} +1.00000 q^{4} +0.258024 q^{5} +1.74046 q^{6} -2.13023 q^{7} +1.00000 q^{8} +0.0291912 q^{9} +0.258024 q^{10} +1.46211 q^{11} +1.74046 q^{12} -6.38517 q^{13} -2.13023 q^{14} +0.449080 q^{15} +1.00000 q^{16} -0.785672 q^{17} +0.0291912 q^{18} -1.66991 q^{19} +0.258024 q^{20} -3.70757 q^{21} +1.46211 q^{22} +6.44230 q^{23} +1.74046 q^{24} -4.93342 q^{25} -6.38517 q^{26} -5.17057 q^{27} -2.13023 q^{28} -4.13748 q^{29} +0.449080 q^{30} +1.00000 q^{31} +1.00000 q^{32} +2.54475 q^{33} -0.785672 q^{34} -0.549650 q^{35} +0.0291912 q^{36} -1.48178 q^{37} -1.66991 q^{38} -11.1131 q^{39} +0.258024 q^{40} -6.43885 q^{41} -3.70757 q^{42} +0.972831 q^{43} +1.46211 q^{44} +0.00753203 q^{45} +6.44230 q^{46} -9.94139 q^{47} +1.74046 q^{48} -2.46212 q^{49} -4.93342 q^{50} -1.36743 q^{51} -6.38517 q^{52} +1.91410 q^{53} -5.17057 q^{54} +0.377260 q^{55} -2.13023 q^{56} -2.90641 q^{57} -4.13748 q^{58} +2.02158 q^{59} +0.449080 q^{60} +2.52864 q^{61} +1.00000 q^{62} -0.0621840 q^{63} +1.00000 q^{64} -1.64753 q^{65} +2.54475 q^{66} +3.24991 q^{67} -0.785672 q^{68} +11.2125 q^{69} -0.549650 q^{70} -0.963411 q^{71} +0.0291912 q^{72} +6.89950 q^{73} -1.48178 q^{74} -8.58641 q^{75} -1.66991 q^{76} -3.11464 q^{77} -11.1131 q^{78} -16.3050 q^{79} +0.258024 q^{80} -9.08672 q^{81} -6.43885 q^{82} +2.31414 q^{83} -3.70757 q^{84} -0.202722 q^{85} +0.972831 q^{86} -7.20110 q^{87} +1.46211 q^{88} -10.8406 q^{89} +0.00753203 q^{90} +13.6019 q^{91} +6.44230 q^{92} +1.74046 q^{93} -9.94139 q^{94} -0.430877 q^{95} +1.74046 q^{96} -1.00000 q^{97} -2.46212 q^{98} +0.0426809 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 21 q^{2} - 10 q^{3} + 21 q^{4} - 10 q^{5} - 10 q^{6} - 11 q^{7} + 21 q^{8} + 7 q^{9}+O(q^{10}) \) 21 * q + 21 * q^2 - 10 * q^3 + 21 * q^4 - 10 * q^5 - 10 * q^6 - 11 * q^7 + 21 * q^8 + 7 * q^9	\( 21 q + 21 q^{2} - 10 q^{3} + 21 q^{4} - 10 q^{5} - 10 q^{6} - 11 q^{7} + 21 q^{8} + 7 q^{9} - 10 q^{10} - 12 q^{11} - 10 q^{12} - 14 q^{13} - 11 q^{14} + q^{15} + 21 q^{16} + 7 q^{18} - 27 q^{19} - 10 q^{20} - 6 q^{21} - 12 q^{22} - 4 q^{23} - 10 q^{24} + q^{25} - 14 q^{26} - 19 q^{27} - 11 q^{28} - 13 q^{29} + q^{30} + 21 q^{31} + 21 q^{32} - 20 q^{33} - 20 q^{35} + 7 q^{36} - 13 q^{37} - 27 q^{38} - 4 q^{39} - 10 q^{40} - 19 q^{41} - 6 q^{42} - 19 q^{43} - 12 q^{44} + 13 q^{45} - 4 q^{46} - 18 q^{47} - 10 q^{48} - 20 q^{49} + q^{50} - 33 q^{51} - 14 q^{52} - 15 q^{53} - 19 q^{54} - 26 q^{55} - 11 q^{56} + 9 q^{57} - 13 q^{58} - 32 q^{59} + q^{60} - 36 q^{61} + 21 q^{62} - 27 q^{63} + 21 q^{64} - 20 q^{65} - 20 q^{66} - 43 q^{67} - 11 q^{69} - 20 q^{70} - 31 q^{71} + 7 q^{72} - 11 q^{73} - 13 q^{74} - 22 q^{75} - 27 q^{76} + 12 q^{77} - 4 q^{78} - 31 q^{79} - 10 q^{80} - 39 q^{81} - 19 q^{82} - 26 q^{83} - 6 q^{84} - 12 q^{85} - 19 q^{86} + 19 q^{87} - 12 q^{88} - 14 q^{89} + 13 q^{90} - 30 q^{91} - 4 q^{92} - 10 q^{93} - 18 q^{94} - 40 q^{95} - 10 q^{96} - 21 q^{97} - 20 q^{98} - 17 q^{99}+O(q^{100}) \) 21 * q + 21 * q^2 - 10 * q^3 + 21 * q^4 - 10 * q^5 - 10 * q^6 - 11 * q^7 + 21 * q^8 + 7 * q^9 - 10 * q^10 - 12 * q^11 - 10 * q^12 - 14 * q^13 - 11 * q^14 + q^15 + 21 * q^16 + 7 * q^18 - 27 * q^19 - 10 * q^20 - 6 * q^21 - 12 * q^22 - 4 * q^23 - 10 * q^24 + q^25 - 14 * q^26 - 19 * q^27 - 11 * q^28 - 13 * q^29 + q^30 + 21 * q^31 + 21 * q^32 - 20 * q^33 - 20 * q^35 + 7 * q^36 - 13 * q^37 - 27 * q^38 - 4 * q^39 - 10 * q^40 - 19 * q^41 - 6 * q^42 - 19 * q^43 - 12 * q^44 + 13 * q^45 - 4 * q^46 - 18 * q^47 - 10 * q^48 - 20 * q^49 + q^50 - 33 * q^51 - 14 * q^52 - 15 * q^53 - 19 * q^54 - 26 * q^55 - 11 * q^56 + 9 * q^57 - 13 * q^58 - 32 * q^59 + q^60 - 36 * q^61 + 21 * q^62 - 27 * q^63 + 21 * q^64 - 20 * q^65 - 20 * q^66 - 43 * q^67 - 11 * q^69 - 20 * q^70 - 31 * q^71 + 7 * q^72 - 11 * q^73 - 13 * q^74 - 22 * q^75 - 27 * q^76 + 12 * q^77 - 4 * q^78 - 31 * q^79 - 10 * q^80 - 39 * q^81 - 19 * q^82 - 26 * q^83 - 6 * q^84 - 12 * q^85 - 19 * q^86 + 19 * q^87 - 12 * q^88 - 14 * q^89 + 13 * q^90 - 30 * q^91 - 4 * q^92 - 10 * q^93 - 18 * q^94 - 40 * q^95 - 10 * q^96 - 21 * q^97 - 20 * q^98 - 17 * q^99

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