LMFDB - Embedded newform 6014.2.a.e.1.7

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			1.7
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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.32252 q^{3} +1.00000 q^{4} -0.257676 q^{5} -1.32252 q^{6} -2.07296 q^{7} +1.00000 q^{8} -1.25095 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.32252 q^{3} +1.00000 q^{4} -0.257676 q^{5} -1.32252 q^{6} -2.07296 q^{7} +1.00000 q^{8} -1.25095 q^{9} -0.257676 q^{10} +2.10111 q^{11} -1.32252 q^{12} -2.55769 q^{13} -2.07296 q^{14} +0.340780 q^{15} +1.00000 q^{16} +5.81241 q^{17} -1.25095 q^{18} +5.99828 q^{19} -0.257676 q^{20} +2.74153 q^{21} +2.10111 q^{22} -6.71969 q^{23} -1.32252 q^{24} -4.93360 q^{25} -2.55769 q^{26} +5.62195 q^{27} -2.07296 q^{28} -1.24263 q^{29} +0.340780 q^{30} +1.00000 q^{31} +1.00000 q^{32} -2.77875 q^{33} +5.81241 q^{34} +0.534152 q^{35} -1.25095 q^{36} -7.69956 q^{37} +5.99828 q^{38} +3.38259 q^{39} -0.257676 q^{40} +6.40932 q^{41} +2.74153 q^{42} +1.78748 q^{43} +2.10111 q^{44} +0.322340 q^{45} -6.71969 q^{46} -2.26104 q^{47} -1.32252 q^{48} -2.70282 q^{49} -4.93360 q^{50} -7.68700 q^{51} -2.55769 q^{52} +1.88726 q^{53} +5.62195 q^{54} -0.541405 q^{55} -2.07296 q^{56} -7.93282 q^{57} -1.24263 q^{58} +3.71893 q^{59} +0.340780 q^{60} +2.98549 q^{61} +1.00000 q^{62} +2.59318 q^{63} +1.00000 q^{64} +0.659055 q^{65} -2.77875 q^{66} -1.02100 q^{67} +5.81241 q^{68} +8.88689 q^{69} +0.534152 q^{70} -8.75635 q^{71} -1.25095 q^{72} +14.2024 q^{73} -7.69956 q^{74} +6.52477 q^{75} +5.99828 q^{76} -4.35553 q^{77} +3.38259 q^{78} -12.6284 q^{79} -0.257676 q^{80} -3.68226 q^{81} +6.40932 q^{82} +3.08853 q^{83} +2.74153 q^{84} -1.49772 q^{85} +1.78748 q^{86} +1.64340 q^{87} +2.10111 q^{88} -9.67769 q^{89} +0.322340 q^{90} +5.30201 q^{91} -6.71969 q^{92} -1.32252 q^{93} -2.26104 q^{94} -1.54561 q^{95} -1.32252 q^{96} -1.00000 q^{97} -2.70282 q^{98} -2.62839 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.32252	−0.763555	−0.381777	−	0.924254i	$-0.624688\pi$
$3$	−1.32252	−0.763555	−0.381777	+	0.924254i	$0.624688\pi$
$4$	1.00000	0.500000
$5$	−0.257676	−0.115236	−0.0576180	−	0.998339i	$-0.518351\pi$
$5$	−0.257676	−0.115236	−0.0576180	+	0.998339i	$0.518351\pi$
$6$	−1.32252	−0.539915
$7$	−2.07296	−0.783507	−0.391753	−	0.920070i	$-0.628131\pi$
$7$	−2.07296	−0.783507	−0.391753	+	0.920070i	$0.628131\pi$
$8$	1.00000	0.353553
$9$	−1.25095	−0.416984
$10$	−0.257676	−0.0814842
$11$	2.10111	0.633509	0.316755	−	0.948508i	$-0.397407\pi$
$11$	2.10111	0.633509	0.316755	+	0.948508i	$0.397407\pi$
$12$	−1.32252	−0.381777
$13$	−2.55769	−0.709377	−0.354688	−	0.934985i	$-0.615413\pi$
$13$	−2.55769	−0.709377	−0.354688	+	0.934985i	$0.615413\pi$
$14$	−2.07296	−0.554023
$15$	0.340780	0.0879890
$16$	1.00000	0.250000
$17$	5.81241	1.40972	0.704858	−	0.709348i	$-0.251011\pi$
$17$	5.81241	1.40972	0.704858	+	0.709348i	$0.251011\pi$
$18$	−1.25095	−0.294852
$19$	5.99828	1.37610	0.688050	−	0.725664i	$-0.258467\pi$
$19$	5.99828	1.37610	0.688050	+	0.725664i	$0.258467\pi$
$20$	−0.257676	−0.0576180
$21$	2.74153	0.598250
$22$	2.10111	0.447959
$23$	−6.71969	−1.40115	−0.700576	−	0.713578i	$-0.747074\pi$
$23$	−6.71969	−1.40115	−0.700576	+	0.713578i	$0.747074\pi$
$24$	−1.32252	−0.269957
$25$	−4.93360	−0.986721
$26$	−2.55769	−0.501605
$27$	5.62195	1.08194
$28$	−2.07296	−0.391753
$29$	−1.24263	−0.230751	−0.115376	−	0.993322i	$-0.536807\pi$
$29$	−1.24263	−0.230751	−0.115376	+	0.993322i	$0.536807\pi$
$30$	0.340780	0.0622176
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	1.00000	0.176777
$33$	−2.77875	−0.483719
$34$	5.81241	0.996820
$35$	0.534152	0.0902882
$36$	−1.25095	−0.208492
$37$	−7.69956	−1.26580	−0.632900	−	0.774234i	$-0.718136\pi$
$37$	−7.69956	−1.26580	−0.632900	+	0.774234i	$0.718136\pi$
$38$	5.99828	0.973049
$39$	3.38259	0.541648
$40$	−0.257676	−0.0407421
$41$	6.40932	1.00097	0.500484	−	0.865746i	$-0.333156\pi$
$41$	6.40932	1.00097	0.500484	+	0.865746i	$0.333156\pi$
$42$	2.74153	0.423027
$43$	1.78748	0.272589	0.136294	−	0.990668i	$-0.456481\pi$
$43$	1.78748	0.272589	0.136294	+	0.990668i	$0.456481\pi$
$44$	2.10111	0.316755
$45$	0.322340	0.0480516
$46$	−6.71969	−0.990764
$47$	−2.26104	−0.329806	−0.164903	−	0.986310i	$-0.552731\pi$
$47$	−2.26104	−0.329806	−0.164903	+	0.986310i	$0.552731\pi$
$48$	−1.32252	−0.190889
$49$	−2.70282	−0.386118
$50$	−4.93360	−0.697717
$51$	−7.68700	−1.07640
$52$	−2.55769	−0.354688
$53$	1.88726	0.259234	0.129617	−	0.991564i	$-0.458625\pi$
$53$	1.88726	0.259234	0.129617	+	0.991564i	$0.458625\pi$
$54$	5.62195	0.765051
$55$	−0.541405	−0.0730031
$56$	−2.07296	−0.277011
$57$	−7.93282	−1.05073
$58$	−1.24263	−0.163166
$59$	3.71893	0.484163	0.242081	−	0.970256i	$-0.422170\pi$
$59$	3.71893	0.484163	0.242081	+	0.970256i	$0.422170\pi$
$60$	0.340780	0.0439945
$61$	2.98549	0.382252	0.191126	−	0.981565i	$-0.438786\pi$
$61$	2.98549	0.382252	0.191126	+	0.981565i	$0.438786\pi$
$62$	1.00000	0.127000
$63$	2.59318	0.326710
$64$	1.00000	0.125000
$65$	0.659055	0.0817458
$66$	−2.77875	−0.342041
$67$	−1.02100	−0.124735	−0.0623675	−	0.998053i	$-0.519865\pi$
$67$	−1.02100	−0.124735	−0.0623675	+	0.998053i	$0.519865\pi$
$68$	5.81241	0.704858
$69$	8.88689	1.06986
$70$	0.534152	0.0638434
$71$	−8.75635	−1.03919	−0.519594	−	0.854413i	$-0.673917\pi$
$71$	−8.75635	−1.03919	−0.519594	+	0.854413i	$0.673917\pi$
$72$	−1.25095	−0.147426
$73$	14.2024	1.66226	0.831131	−	0.556076i	$-0.187694\pi$
$73$	14.2024	1.66226	0.831131	+	0.556076i	$0.187694\pi$
$74$	−7.69956	−0.895056
$75$	6.52477	0.753415
$76$	5.99828	0.688050
$77$	−4.35553	−0.496359
$78$	3.38259	0.383003
$79$	−12.6284	−1.42081	−0.710404	−	0.703794i	$-0.751488\pi$
$79$	−12.6284	−1.42081	−0.710404	+	0.703794i	$0.751488\pi$
$80$	−0.257676	−0.0288090
$81$	−3.68226	−0.409140
$82$	6.40932	0.707791
$83$	3.08853	0.339010	0.169505	−	0.985529i	$-0.445783\pi$
$83$	3.08853	0.339010	0.169505	+	0.985529i	$0.445783\pi$
$84$	2.74153	0.299125
$85$	−1.49772	−0.162450
$86$	1.78748	0.192749
$87$	1.64340	0.176191
$88$	2.10111	0.223979
$89$	−9.67769	−1.02583	−0.512916	−	0.858439i	$-0.671435\pi$
$89$	−9.67769	−1.02583	−0.512916	+	0.858439i	$0.671435\pi$
$90$	0.322340	0.0339776
$91$	5.30201	0.555801
$92$	−6.71969	−0.700576
$93$	−1.32252	−0.137138
$94$	−2.26104	−0.233208
$95$	−1.54561	−0.158576
$96$	−1.32252	−0.134979
$97$	−1.00000	−0.101535
$97$	−1.00000	−0.101535
$98$	−2.70282	−0.273026
$99$	−2.62839	−0.264163
$100$	−4.93360	−0.493360
$101$	−14.4032	−1.43317	−0.716585	−	0.697500i	$-0.754296\pi$
$101$	−14.4032	−1.43317	−0.716585	+	0.697500i	$0.754296\pi$
$102$	−7.68700	−0.761126
$103$	−1.72604	−0.170072	−0.0850361	−	0.996378i	$-0.527101\pi$
$103$	−1.72604	−0.170072	−0.0850361	+	0.996378i	$0.527101\pi$
$104$	−2.55769	−0.250803
$105$	−0.706424	−0.0689400
$106$	1.88726	0.183306
$107$	4.07277	0.393730	0.196865	−	0.980431i	$-0.436924\pi$
$107$	4.07277	0.393730	0.196865	+	0.980431i	$0.436924\pi$
$108$	5.62195	0.540972
$109$	10.9595	1.04973	0.524865	−	0.851186i	$-0.324116\pi$
$109$	10.9595	1.04973	0.524865	+	0.851186i	$0.324116\pi$
$110$	−0.541405	−0.0516210
$111$	10.1828	0.966507
$112$	−2.07296	−0.195877
$113$	−9.88249	−0.929667	−0.464833	−	0.885398i	$-0.653886\pi$
$113$	−9.88249	−0.929667	−0.464833	+	0.885398i	$0.653886\pi$
$114$	−7.93282	−0.742976
$115$	1.73150	0.161463
$116$	−1.24263	−0.115376
$117$	3.19956	0.295799
$118$	3.71893	0.342355
$119$	−12.0489	−1.10452
$120$	0.340780	0.0311088
$121$	−6.58533	−0.598666
$122$	2.98549	0.270293
$123$	−8.47642	−0.764293
$124$	1.00000	0.0898027
$125$	2.55965	0.228942
$126$	2.59318	0.231019
$127$	−3.96695	−0.352010	−0.176005	−	0.984389i	$-0.556317\pi$
$127$	−3.96695	−0.352010	−0.176005	+	0.984389i	$0.556317\pi$
$128$	1.00000	0.0883883
$129$	−2.36397	−0.208136
$130$	0.659055	0.0578030
$131$	−12.7684	−1.11558	−0.557788	−	0.829983i	$-0.688350\pi$
$131$	−12.7684	−1.11558	−0.557788	+	0.829983i	$0.688350\pi$
$132$	−2.77875	−0.241859
$133$	−12.4342	−1.07818
$134$	−1.02100	−0.0882010
$135$	−1.44864	−0.124679
$136$	5.81241	0.498410
$137$	−7.85316	−0.670941	−0.335470	−	0.942051i	$-0.608895\pi$
$137$	−7.85316	−0.670941	−0.335470	+	0.942051i	$0.608895\pi$
$138$	8.88689	0.756503
$139$	−17.6482	−1.49690	−0.748448	−	0.663193i	$-0.769201\pi$
$139$	−17.6482	−1.49690	−0.748448	+	0.663193i	$0.769201\pi$
$140$	0.534152	0.0451441
$141$	2.99026	0.251825
$142$	−8.75635	−0.734817
$143$	−5.37400	−0.449397
$144$	−1.25095	−0.104246
$145$	0.320196	0.0265909
$146$	14.2024	1.17540
$147$	3.57452	0.294822
$148$	−7.69956	−0.632900
$149$	−14.0734	−1.15294	−0.576469	−	0.817119i	$-0.695570\pi$
$149$	−14.0734	−1.15294	−0.576469	+	0.817119i	$0.695570\pi$
$150$	6.52477	0.532745
$151$	2.99129	0.243428	0.121714	−	0.992565i	$-0.461161\pi$
$151$	2.99129	0.243428	0.121714	+	0.992565i	$0.461161\pi$
$152$	5.99828	0.486525
$153$	−7.27105	−0.587830
$154$	−4.35553	−0.350979
$155$	−0.257676	−0.0206970
$156$	3.38259	0.270824
$157$	19.6122	1.56522	0.782611	−	0.622511i	$-0.213887\pi$
$157$	19.6122	1.56522	0.782611	+	0.622511i	$0.213887\pi$
$158$	−12.6284	−1.00466
$159$	−2.49592	−0.197940
$160$	−0.257676	−0.0203710
$161$	13.9297	1.09781
$162$	−3.68226	−0.289305
$163$	2.23568	0.175112	0.0875561	−	0.996160i	$-0.472094\pi$
$163$	2.23568	0.175112	0.0875561	+	0.996160i	$0.472094\pi$
$164$	6.40932	0.500484
$165$	0.716017	0.0557418
$166$	3.08853	0.239716
$167$	5.35094	0.414068	0.207034	−	0.978334i	$-0.433619\pi$
$167$	5.35094	0.414068	0.207034	+	0.978334i	$0.433619\pi$
$168$	2.74153	0.211513
$169$	−6.45820	−0.496785
$170$	−1.49772	−0.114870
$171$	−7.50356	−0.573812
$172$	1.78748	0.136294
$173$	−16.2914	−1.23861	−0.619305	−	0.785151i	$-0.712585\pi$
$173$	−16.2914	−1.23861	−0.619305	+	0.785151i	$0.712585\pi$
$174$	1.64340	0.124586
$175$	10.2272	0.773102
$176$	2.10111	0.158377
$177$	−4.91834	−0.369685
$178$	−9.67769	−0.725373
$179$	3.50564	0.262024	0.131012	−	0.991381i	$-0.458177\pi$
$179$	3.50564	0.262024	0.131012	+	0.991381i	$0.458177\pi$
$180$	0.322340	0.0240258
$181$	−9.38760	−0.697775	−0.348888	−	0.937165i	$-0.613440\pi$
$181$	−9.38760	−0.697775	−0.348888	+	0.937165i	$0.613440\pi$
$182$	5.30201	0.393011
$183$	−3.94835	−0.291871
$184$	−6.71969	−0.495382
$185$	1.98399	0.145866
$186$	−1.32252	−0.0969715
$187$	12.2125	0.893068
$188$	−2.26104	−0.164903
$189$	−11.6541	−0.847711
$190$	−1.54561	−0.112130
$191$	−19.0016	−1.37491	−0.687453	−	0.726229i	$-0.741271\pi$
$191$	−19.0016	−1.37491	−0.687453	+	0.726229i	$0.741271\pi$
$192$	−1.32252	−0.0954443
$193$	5.53588	0.398481	0.199241	−	0.979951i	$-0.436152\pi$
$193$	5.53588	0.398481	0.199241	+	0.979951i	$0.436152\pi$
$194$	−1.00000	−0.0717958
$195$	−0.871611	−0.0624174
$196$	−2.70282	−0.193059
$197$	−26.0139	−1.85341	−0.926707	−	0.375785i	$-0.877373\pi$
$197$	−26.0139	−1.85341	−0.926707	+	0.375785i	$0.877373\pi$
$198$	−2.62839	−0.186792
$199$	−8.32118	−0.589873	−0.294936	−	0.955517i	$-0.595298\pi$
$199$	−8.32118	−0.589873	−0.294936	+	0.955517i	$0.595298\pi$
$200$	−4.93360	−0.348858
$201$	1.35029	0.0952420
$202$	−14.4032	−1.01340
$203$	2.57593	0.180795
$204$	−7.68700	−0.538198
$205$	−1.65153	−0.115348
$206$	−1.72604	−0.120259
$207$	8.40602	0.584259
$208$	−2.55769	−0.177344
$209$	12.6031	0.871772
$210$	−0.706424	−0.0487479
$211$	1.99573	0.137392	0.0686958	−	0.997638i	$-0.478116\pi$
$211$	1.99573	0.137392	0.0686958	+	0.997638i	$0.478116\pi$
$212$	1.88726	0.129617
$213$	11.5804	0.793476
$214$	4.07277	0.278409
$215$	−0.460591	−0.0314120
$216$	5.62195	0.382525
$217$	−2.07296	−0.140722
$218$	10.9595	0.742271
$219$	−18.7829	−1.26923
$220$	−0.541405	−0.0365015
$221$	−14.8664	−1.00002
$222$	10.1828	0.683424
$223$	−17.3671	−1.16299	−0.581494	−	0.813551i	$-0.697532\pi$
$223$	−17.3671	−1.16299	−0.581494	+	0.813551i	$0.697532\pi$
$224$	−2.07296	−0.138506
$225$	6.17171	0.411447
$226$	−9.88249	−0.657374
$227$	4.29800	0.285269	0.142634	−	0.989775i	$-0.454443\pi$
$227$	4.29800	0.285269	0.142634	+	0.989775i	$0.454443\pi$
$228$	−7.93282	−0.525364
$229$	−3.08583	−0.203918	−0.101959	−	0.994789i	$-0.532511\pi$
$229$	−3.08583	−0.203918	−0.101959	+	0.994789i	$0.532511\pi$
$230$	1.73150	0.114172
$231$	5.76025	0.378997
$232$	−1.24263	−0.0815829
$233$	13.9399	0.913233	0.456617	−	0.889664i	$-0.349061\pi$
$233$	13.9399	0.913233	0.456617	+	0.889664i	$0.349061\pi$
$234$	3.19956	0.209161
$235$	0.582615	0.0380056
$236$	3.71893	0.242081
$237$	16.7013	1.08486
$238$	−12.0489	−0.781015
$239$	−2.52720	−0.163471	−0.0817354	−	0.996654i	$-0.526046\pi$
$239$	−2.52720	−0.163471	−0.0817354	+	0.996654i	$0.526046\pi$
$240$	0.340780	0.0219973
$241$	−19.2119	−1.23755	−0.618775	−	0.785568i	$-0.712371\pi$
$241$	−19.2119	−1.23755	−0.618775	+	0.785568i	$0.712371\pi$
$242$	−6.58533	−0.423321
$243$	−11.9960	−0.769544
$244$	2.98549	0.191126
$245$	0.696452	0.0444947
$246$	−8.47642	−0.540437
$247$	−15.3418	−0.976173
$248$	1.00000	0.0635001
$249$	−4.08463	−0.258853
$250$	2.55965	0.161886
$251$	2.13697	0.134885	0.0674423	−	0.997723i	$-0.478516\pi$
$251$	2.13697	0.134885	0.0674423	+	0.997723i	$0.478516\pi$
$252$	2.59318	0.163355
$253$	−14.1188	−0.887643
$254$	−3.96695	−0.248908
$255$	1.98075	0.124040
$256$	1.00000	0.0625000
$257$	−3.26010	−0.203359	−0.101680	−	0.994817i	$-0.532422\pi$
$257$	−3.26010	−0.203359	−0.101680	+	0.994817i	$0.532422\pi$
$258$	−2.36397	−0.147175
$259$	15.9609	0.991762
$260$	0.659055	0.0408729
$261$	1.55448	0.0962197
$262$	−12.7684	−0.788832
$263$	−31.4200	−1.93744	−0.968720	−	0.248158i	$-0.920175\pi$
$263$	−31.4200	−1.93744	−0.968720	+	0.248158i	$0.920175\pi$
$264$	−2.77875	−0.171020
$265$	−0.486300	−0.0298732
$266$	−12.4342	−0.762390
$267$	12.7989	0.783279
$268$	−1.02100	−0.0623675
$269$	6.79846	0.414509	0.207255	−	0.978287i	$-0.433547\pi$
$269$	6.79846	0.414509	0.207255	+	0.978287i	$0.433547\pi$
$270$	−1.44864	−0.0881614
$271$	−24.0712	−1.46222	−0.731110	−	0.682260i	$-0.760997\pi$
$271$	−24.0712	−1.46222	−0.731110	+	0.682260i	$0.760997\pi$
$272$	5.81241	0.352429
$273$	−7.01199	−0.424385
$274$	−7.85316	−0.474427
$275$	−10.3661	−0.625097
$276$	8.88689	0.534928
$277$	29.8520	1.79363	0.896817	−	0.442402i	$-0.145874\pi$
$277$	29.8520	1.79363	0.896817	+	0.442402i	$0.145874\pi$
$278$	−17.6482	−1.05847
$279$	−1.25095	−0.0748926
$280$	0.534152	0.0319217
$281$	0.375419	0.0223956	0.0111978	−	0.999937i	$-0.496436\pi$
$281$	0.375419	0.0223956	0.0111978	+	0.999937i	$0.496436\pi$
$282$	2.99026	0.178067
$283$	−17.8464	−1.06086	−0.530428	−	0.847730i	$-0.677969\pi$
$283$	−17.8464	−1.06086	−0.530428	+	0.847730i	$0.677969\pi$
$284$	−8.75635	−0.519594
$285$	2.04409	0.121082
$286$	−5.37400	−0.317771
$287$	−13.2863	−0.784264
$288$	−1.25095	−0.0737131
$289$	16.7841	0.987300
$290$	0.320196	0.0188026
$291$	1.32252	0.0775272
$292$	14.2024	0.831131
$293$	15.0351	0.878358	0.439179	−	0.898400i	$-0.355269\pi$
$293$	15.0351	0.878358	0.439179	+	0.898400i	$0.355269\pi$
$294$	3.57452	0.208471
$295$	−0.958277	−0.0557930
$296$	−7.69956	−0.447528
$297$	11.8123	0.685422
$298$	−14.0734	−0.815250
$299$	17.1869	0.993945
$300$	6.52477	0.376708
$301$	−3.70539	−0.213575
$302$	2.99129	0.172130
$303$	19.0484	1.09430
$304$	5.99828	0.344025
$305$	−0.769287	−0.0440493
$306$	−7.27105	−0.415658
$307$	6.20579	0.354183	0.177091	−	0.984194i	$-0.443331\pi$
$307$	6.20579	0.354183	0.177091	+	0.984194i	$0.443331\pi$
$308$	−4.35553	−0.248179
$309$	2.28272	0.129859
$310$	−0.257676	−0.0146350
$311$	−10.4649	−0.593410	−0.296705	−	0.954969i	$-0.595888\pi$
$311$	−10.4649	−0.593410	−0.296705	+	0.954969i	$0.595888\pi$
$312$	3.38259	0.191501
$313$	3.18145	0.179826	0.0899132	−	0.995950i	$-0.471341\pi$
$313$	3.18145	0.179826	0.0899132	+	0.995950i	$0.471341\pi$
$314$	19.6122	1.10678
$315$	−0.668199	−0.0376488
$316$	−12.6284	−0.710404
$317$	26.2671	1.47531	0.737654	−	0.675179i	$-0.235934\pi$
$317$	26.2671	1.47531	0.737654	+	0.675179i	$0.235934\pi$
$318$	−2.49592	−0.139964
$319$	−2.61091	−0.146183
$320$	−0.257676	−0.0144045
$321$	−5.38630	−0.300634
$322$	13.9297	0.776270
$323$	34.8644	1.93991
$324$	−3.68226	−0.204570
$325$	12.6186	0.699957
$326$	2.23568	0.123823
$327$	−14.4941	−0.801526
$328$	6.40932	0.353895
$329$	4.68705	0.258405
$330$	0.716017	0.0394154
$331$	8.66944	0.476516	0.238258	−	0.971202i	$-0.423424\pi$
$331$	8.66944	0.476516	0.238258	+	0.971202i	$0.423424\pi$
$332$	3.08853	0.169505
$333$	9.63179	0.527819
$334$	5.35094	0.292790
$335$	0.263087	0.0143740
$336$	2.74153	0.149563
$337$	19.3844	1.05593	0.527966	−	0.849265i	$-0.322955\pi$
$337$	19.3844	1.05593	0.527966	+	0.849265i	$0.322955\pi$
$338$	−6.45820	−0.351280
$339$	13.0697	0.709851
$340$	−1.49772	−0.0812251
$341$	2.10111	0.113782
$342$	−7.50356	−0.405746
$343$	20.1136	1.08603
$344$	1.78748	0.0963746
$345$	−2.28994	−0.123286
$346$	−16.2914	−0.875829
$347$	22.5946	1.21294	0.606472	−	0.795105i	$-0.292584\pi$
$347$	22.5946	1.21294	0.606472	+	0.795105i	$0.292584\pi$
$348$	1.64340	0.0880956
$349$	−28.5125	−1.52624	−0.763121	−	0.646256i	$-0.776334\pi$
$349$	−28.5125	−1.52624	−0.763121	+	0.646256i	$0.776334\pi$
$350$	10.2272	0.546666
$351$	−14.3792	−0.767507
$352$	2.10111	0.111990
$353$	4.19049	0.223037	0.111519	−	0.993762i	$-0.464429\pi$
$353$	4.19049	0.223037	0.111519	+	0.993762i	$0.464429\pi$
$354$	−4.91834	−0.261407
$355$	2.25630	0.119752
$356$	−9.67769	−0.512916
$357$	15.9349	0.843363
$358$	3.50564	0.185279
$359$	18.4415	0.973307	0.486654	−	0.873595i	$-0.338217\pi$
$359$	18.4415	0.973307	0.486654	+	0.873595i	$0.338217\pi$
$360$	0.322340	0.0169888
$361$	16.9793	0.893650
$362$	−9.38760	−0.493402
$363$	8.70920	0.457114
$364$	5.30201	0.277901
$365$	−3.65961	−0.191553
$366$	−3.94835	−0.206384
$367$	−17.4255	−0.909605	−0.454802	−	0.890592i	$-0.650290\pi$
$367$	−17.4255	−0.909605	−0.454802	+	0.890592i	$0.650290\pi$
$368$	−6.71969	−0.350288
$369$	−8.01776	−0.417388
$370$	1.98399	0.103143
$371$	−3.91221	−0.203112
$372$	−1.32252	−0.0685692
$373$	−16.7349	−0.866500	−0.433250	−	0.901274i	$-0.642633\pi$
$373$	−16.7349	−0.866500	−0.433250	+	0.901274i	$0.642633\pi$
$374$	12.2125	0.631495
$375$	−3.38517	−0.174810
$376$	−2.26104	−0.116604
$377$	3.17828	0.163690
$378$	−11.6541	−0.599422
$379$	−19.1344	−0.982866	−0.491433	−	0.870915i	$-0.663527\pi$
$379$	−19.1344	−0.982866	−0.491433	+	0.870915i	$0.663527\pi$
$380$	−1.54561	−0.0792881
$381$	5.24635	0.268779
$382$	−19.0016	−0.972205
$383$	17.3251	0.885272	0.442636	−	0.896701i	$-0.354043\pi$
$383$	17.3251	0.885272	0.442636	+	0.896701i	$0.354043\pi$
$384$	−1.32252	−0.0674893
$385$	1.12231	0.0571984
$386$	5.53588	0.281769
$387$	−2.23606	−0.113665
$388$	−1.00000	−0.0507673
$389$	24.3576	1.23498	0.617490	−	0.786578i	$-0.288149\pi$
$389$	24.3576	1.23498	0.617490	+	0.786578i	$0.288149\pi$
$390$	−0.871611	−0.0441357
$391$	−39.0576	−1.97523
$392$	−2.70282	−0.136513
$393$	16.8864	0.851804
$394$	−26.0139	−1.31056
$395$	3.25404	0.163728
$396$	−2.62839	−0.132082
$397$	10.4066	0.522291	0.261145	−	0.965300i	$-0.415900\pi$
$397$	10.4066	0.522291	0.261145	+	0.965300i	$0.415900\pi$
$398$	−8.32118	−0.417103
$399$	16.4444	0.823251
$400$	−4.93360	−0.246680
$401$	−36.2160	−1.80854	−0.904270	−	0.426961i	$-0.859584\pi$
$401$	−36.2160	−1.80854	−0.904270	+	0.426961i	$0.859584\pi$
$402$	1.35029	0.0673463
$403$	−2.55769	−0.127408
$404$	−14.4032	−0.716585
$405$	0.948828	0.0471476
$406$	2.57593	0.127841
$407$	−16.1776	−0.801896
$408$	−7.68700	−0.380563
$409$	16.9519	0.838218	0.419109	−	0.907936i	$-0.362343\pi$
$409$	16.9519	0.838218	0.419109	+	0.907936i	$0.362343\pi$
$410$	−1.65153	−0.0815630
$411$	10.3859	0.512300
$412$	−1.72604	−0.0850361
$413$	−7.70920	−0.379345
$414$	8.40602	0.413133
$415$	−0.795839	−0.0390662
$416$	−2.55769	−0.125401
$417$	23.3400	1.14296
$418$	12.6031	0.616436
$419$	14.2785	0.697551	0.348776	−	0.937206i	$-0.386598\pi$
$419$	14.2785	0.697551	0.348776	+	0.937206i	$0.386598\pi$
$420$	−0.706424	−0.0344700
$421$	−12.0871	−0.589090	−0.294545	−	0.955638i	$-0.595168\pi$
$421$	−12.0871	−0.589090	−0.294545	+	0.955638i	$0.595168\pi$
$422$	1.99573	0.0971505
$423$	2.82845	0.137524
$424$	1.88726	0.0916532
$425$	−28.6761	−1.39100
$426$	11.5804	0.561073
$427$	−6.18880	−0.299497
$428$	4.07277	0.196865
$429$	7.10720	0.343139
$430$	−0.460591	−0.0222117
$431$	−20.4728	−0.986142	−0.493071	−	0.869989i	$-0.664126\pi$
$431$	−20.4728	−0.986142	−0.493071	+	0.869989i	$0.664126\pi$
$432$	5.62195	0.270486
$433$	18.8439	0.905580	0.452790	−	0.891617i	$-0.350429\pi$
$433$	18.8439	0.905580	0.452790	+	0.891617i	$0.350429\pi$
$434$	−2.07296	−0.0995054
$435$	−0.423465	−0.0203036
$436$	10.9595	0.524865
$437$	−40.3066	−1.92812
$438$	−18.7829	−0.897480
$439$	−16.7609	−0.799956	−0.399978	−	0.916525i	$-0.630982\pi$
$439$	−16.7609	−0.799956	−0.399978	+	0.916525i	$0.630982\pi$
$440$	−0.541405	−0.0258105
$441$	3.38110	0.161005
$442$	−14.8664	−0.707121
$443$	−27.2739	−1.29582	−0.647911	−	0.761716i	$-0.724357\pi$
$443$	−27.2739	−1.29582	−0.647911	+	0.761716i	$0.724357\pi$
$444$	10.1828	0.483254
$445$	2.49370	0.118213
$446$	−17.3671	−0.822357
$447$	18.6123	0.880330
$448$	−2.07296	−0.0979383
$449$	−40.0321	−1.88923	−0.944615	−	0.328179i	$-0.893565\pi$
$449$	−40.0321	−1.88923	−0.944615	+	0.328179i	$0.893565\pi$
$450$	6.17171	0.290937
$451$	13.4667	0.634122
$452$	−9.88249	−0.464833
$453$	−3.95603	−0.185871
$454$	4.29800	0.201715
$455$	−1.36620	−0.0640483
$456$	−7.93282	−0.371488
$457$	41.1383	1.92437	0.962183	−	0.272402i	$-0.0878182\pi$
$457$	41.1383	1.92437	0.962183	+	0.272402i	$0.0878182\pi$
$458$	−3.08583	−0.144192
$459$	32.6771	1.52524
$460$	1.73150	0.0807316
$461$	27.3686	1.27468	0.637342	−	0.770581i	$-0.280034\pi$
$461$	27.3686	1.27468	0.637342	+	0.770581i	$0.280034\pi$
$462$	5.76025	0.267991
$463$	22.8321	1.06110	0.530548	−	0.847655i	$-0.321986\pi$
$463$	22.8321	1.06110	0.530548	+	0.847655i	$0.321986\pi$
$464$	−1.24263	−0.0576878
$465$	0.340780	0.0158033
$466$	13.9399	0.645753
$467$	−36.9273	−1.70879	−0.854396	−	0.519622i	$-0.826073\pi$
$467$	−36.9273	−1.70879	−0.854396	+	0.519622i	$0.826073\pi$
$468$	3.19956	0.147899
$469$	2.11650	0.0977307
$470$	0.582615	0.0268740
$471$	−25.9374	−1.19513
$472$	3.71893	0.171177
$473$	3.75570	0.172687
$474$	16.7013	0.767115
$475$	−29.5931	−1.35783
$476$	−12.0489	−0.552261
$477$	−2.36087	−0.108097
$478$	−2.52720	−0.115591
$479$	18.2930	0.835829	0.417914	−	0.908486i	$-0.362761\pi$
$479$	18.2930	0.835829	0.417914	+	0.908486i	$0.362761\pi$
$480$	0.340780	0.0155544
$481$	19.6931	0.897929
$482$	−19.2119	−0.875080
$483$	−18.4222	−0.838239
$484$	−6.58533	−0.299333
$485$	0.257676	0.0117004
$486$	−11.9960	−0.544150
$487$	−36.2684	−1.64348	−0.821739	−	0.569865i	$-0.806996\pi$
$487$	−36.2684	−1.64348	−0.821739	+	0.569865i	$0.806996\pi$
$488$	2.98549	0.135147
$489$	−2.95672	−0.133708
$490$	0.696452	0.0314625
$491$	−24.9369	−1.12539	−0.562694	−	0.826665i	$-0.690235\pi$
$491$	−24.9369	−1.12539	−0.562694	+	0.826665i	$0.690235\pi$
$492$	−8.47642	−0.382147
$493$	−7.22269	−0.325294
$494$	−15.3418	−0.690258
$495$	0.677273	0.0304411
$496$	1.00000	0.0449013
$497$	18.1516	0.814210
$498$	−4.08463	−0.183037
$499$	−12.5385	−0.561299	−0.280649	−	0.959810i	$-0.590550\pi$
$499$	−12.5385	−0.561299	−0.280649	+	0.959810i	$0.590550\pi$
$500$	2.55965	0.114471
$501$	−7.07670	−0.316164
$502$	2.13697	0.0953778
$503$	−3.48341	−0.155318	−0.0776589	−	0.996980i	$-0.524744\pi$
$503$	−3.48341	−0.155318	−0.0776589	+	0.996980i	$0.524744\pi$
$504$	2.59318	0.115509
$505$	3.71135	0.165153
$506$	−14.1188	−0.627658
$507$	8.54107	0.379322
$508$	−3.96695	−0.176005
$509$	−6.63176	−0.293948	−0.146974	−	0.989140i	$-0.546953\pi$
$509$	−6.63176	−0.293948	−0.146974	+	0.989140i	$0.546953\pi$
$510$	1.98075	0.0877092
$511$	−29.4410	−1.30239
$512$	1.00000	0.0441942
$513$	33.7220	1.48886
$514$	−3.26010	−0.143797
$515$	0.444760	0.0195985
$516$	−2.36397	−0.104068
$517$	−4.75070	−0.208935
$518$	15.9609	0.701282
$519$	21.5456	0.945746
$520$	0.659055	0.0289015
$521$	29.2728	1.28247	0.641233	−	0.767346i	$-0.278423\pi$
$521$	29.2728	1.28247	0.641233	+	0.767346i	$0.278423\pi$
$522$	1.55448	0.0680376
$523$	25.4585	1.11322	0.556610	−	0.830774i	$-0.312102\pi$
$523$	25.4585	1.11322	0.556610	+	0.830774i	$0.312102\pi$
$524$	−12.7684	−0.557788
$525$	−13.5256	−0.590306
$526$	−31.4200	−1.36998
$527$	5.81241	0.253193
$528$	−2.77875	−0.120930
$529$	22.1542	0.963228
$530$	−0.486300	−0.0211235
$531$	−4.65220	−0.201888
$532$	−12.4342	−0.539091
$533$	−16.3931	−0.710063
$534$	12.7989	0.553862
$535$	−1.04945	−0.0453719
$536$	−1.02100	−0.0441005
$537$	−4.63626	−0.200069
$538$	6.79846	0.293102
$539$	−5.67893	−0.244609
$540$	−1.44864	−0.0623395
$541$	−37.1232	−1.59605	−0.798026	−	0.602623i	$-0.794122\pi$
$541$	−37.1232	−1.59605	−0.798026	+	0.602623i	$0.794122\pi$
$542$	−24.0712	−1.03395
$543$	12.4153	0.532789
$544$	5.81241	0.249205
$545$	−2.82400	−0.120967
$546$	−7.01199	−0.300085
$547$	36.5775	1.56394	0.781971	−	0.623315i	$-0.214215\pi$
$547$	36.5775	1.56394	0.781971	+	0.623315i	$0.214215\pi$
$548$	−7.85316	−0.335470
$549$	−3.73470	−0.159393
$550$	−10.3661	−0.442010
$551$	−7.45366	−0.317537
$552$	8.88689	0.378251
$553$	26.1782	1.11321
$554$	29.8520	1.26829
$555$	−2.62386	−0.111376
$556$	−17.6482	−0.748448
$557$	38.6410	1.63727	0.818635	−	0.574314i	$-0.194731\pi$
$557$	38.6410	1.63727	0.818635	+	0.574314i	$0.194731\pi$
$558$	−1.25095	−0.0529571
$559$	−4.57184	−0.193368
$560$	0.534152	0.0225720
$561$	−16.1512	−0.681906
$562$	0.375419	0.0158361
$563$	−34.9373	−1.47243	−0.736215	−	0.676748i	$-0.763389\pi$
$563$	−34.9373	−1.47243	−0.736215	+	0.676748i	$0.763389\pi$
$564$	2.99026	0.125913
$565$	2.54648	0.107131
$566$	−17.8464	−0.750138
$567$	7.63319	0.320564
$568$	−8.75635	−0.367408
$569$	23.5566	0.987542	0.493771	−	0.869592i	$-0.335618\pi$
$569$	23.5566	0.987542	0.493771	+	0.869592i	$0.335618\pi$
$570$	2.04409	0.0856176
$571$	−25.3998	−1.06295	−0.531474	−	0.847074i	$-0.678362\pi$
$571$	−25.3998	−1.06295	−0.531474	+	0.847074i	$0.678362\pi$
$572$	−5.37400	−0.224698
$573$	25.1299	1.04982
$574$	−13.2863	−0.554559
$575$	33.1523	1.38255
$576$	−1.25095	−0.0521230
$577$	17.9432	0.746985	0.373493	−	0.927633i	$-0.378160\pi$
$577$	17.9432	0.746985	0.373493	+	0.927633i	$0.378160\pi$
$578$	16.7841	0.698126
$579$	−7.32128	−0.304262
$580$	0.320196	0.0132954
$581$	−6.40241	−0.265617
$582$	1.32252	0.0548200
$583$	3.96534	0.164227
$584$	14.2024	0.587698
$585$	−0.824447	−0.0340867
$586$	15.0351	0.621093
$587$	−7.94951	−0.328111	−0.164056	−	0.986451i	$-0.552458\pi$
$587$	−7.94951	−0.328111	−0.164056	+	0.986451i	$0.552458\pi$
$588$	3.57452	0.147411
$589$	5.99828	0.247155
$590$	−0.958277	−0.0394516
$591$	34.4038	1.41518
$592$	−7.69956	−0.316450
$593$	5.00804	0.205656	0.102828	−	0.994699i	$-0.467211\pi$
$593$	5.00804	0.205656	0.102828	+	0.994699i	$0.467211\pi$
$594$	11.8123	0.484667
$595$	3.10471	0.127281
$596$	−14.0734	−0.576469
$597$	11.0049	0.450400
$598$	17.1869	0.702825
$599$	−28.0608	−1.14653	−0.573267	−	0.819369i	$-0.694324\pi$
$599$	−28.0608	−1.14653	−0.573267	+	0.819369i	$0.694324\pi$
$600$	6.52477	0.266372
$601$	−21.2246	−0.865771	−0.432886	−	0.901449i	$-0.642505\pi$
$601$	−21.2246	−0.865771	−0.432886	+	0.901449i	$0.642505\pi$
$602$	−3.70539	−0.151020
$603$	1.27722	0.0520126
$604$	2.99129	0.121714
$605$	1.69688	0.0689879
$606$	19.0484	0.773789
$607$	−35.1897	−1.42830	−0.714152	−	0.699991i	$-0.753188\pi$
$607$	−35.1897	−1.42830	−0.714152	+	0.699991i	$0.753188\pi$
$608$	5.99828	0.243262
$609$	−3.40671	−0.138047
$610$	−0.769287	−0.0311475
$611$	5.78305	0.233957
$612$	−7.27105	−0.293915
$613$	22.4770	0.907839	0.453919	−	0.891043i	$-0.350025\pi$
$613$	22.4770	0.907839	0.453919	+	0.891043i	$0.350025\pi$
$614$	6.20579	0.250445
$615$	2.18417	0.0880741
$616$	−4.35553	−0.175489
$617$	21.2042	0.853649	0.426825	−	0.904334i	$-0.359632\pi$
$617$	21.2042	0.853649	0.426825	+	0.904334i	$0.359632\pi$
$618$	2.28272	0.0918245
$619$	46.2918	1.86063	0.930313	−	0.366767i	$-0.119536\pi$
$619$	46.2918	1.86063	0.930313	+	0.366767i	$0.119536\pi$
$620$	−0.257676	−0.0103485
$621$	−37.7778	−1.51597
$622$	−10.4649	−0.419604
$623$	20.0615	0.803747
$624$	3.38259	0.135412
$625$	24.0085	0.960338
$626$	3.18145	0.127156
$627$	−16.6677	−0.665645
$628$	19.6122	0.782611
$629$	−44.7530	−1.78442
$630$	−0.668199	−0.0266217
$631$	32.6722	1.30066	0.650330	−	0.759652i	$-0.274631\pi$
$631$	32.6722	1.30066	0.650330	+	0.759652i	$0.274631\pi$
$632$	−12.6284	−0.502331
$633$	−2.63938	−0.104906
$634$	26.2671	1.04320
$635$	1.02219	0.0405642
$636$	−2.49592	−0.0989698
$637$	6.91299	0.273903
$638$	−2.61091	−0.103367
$639$	10.9538	0.433325
$640$	−0.257676	−0.0101855
$641$	−23.3060	−0.920530	−0.460265	−	0.887782i	$-0.652246\pi$
$641$	−23.3060	−0.920530	−0.460265	+	0.887782i	$0.652246\pi$
$642$	−5.38630	−0.212580
$643$	21.5458	0.849682	0.424841	−	0.905268i	$-0.360330\pi$
$643$	21.5458	0.849682	0.424841	+	0.905268i	$0.360330\pi$
$644$	13.9297	0.548906
$645$	0.609138	0.0239848
$646$	34.8644	1.37172
$647$	8.67533	0.341063	0.170531	−	0.985352i	$-0.445452\pi$
$647$	8.67533	0.341063	0.170531	+	0.985352i	$0.445452\pi$
$648$	−3.68226	−0.144653
$649$	7.81388	0.306722
$650$	12.6186	0.494944
$651$	2.74153	0.107449
$652$	2.23568	0.0875561
$653$	30.9467	1.21104	0.605518	−	0.795832i	$-0.292966\pi$
$653$	30.9467	1.21104	0.605518	+	0.795832i	$0.292966\pi$
$654$	−14.4941	−0.566764
$655$	3.29009	0.128555
$656$	6.40932	0.250242
$657$	−17.7665	−0.693137
$658$	4.68705	0.182720
$659$	−30.6747	−1.19492	−0.597458	−	0.801900i	$-0.703823\pi$
$659$	−30.6747	−1.19492	−0.597458	+	0.801900i	$0.703823\pi$
$660$	0.716017	0.0278709
$661$	−20.2152	−0.786279	−0.393139	−	0.919479i	$-0.628611\pi$
$661$	−20.2152	−0.786279	−0.393139	+	0.919479i	$0.628611\pi$
$662$	8.66944	0.336948
$663$	19.6610	0.763570
$664$	3.08853	0.119858
$665$	3.20399	0.124246
$666$	9.63179	0.373224
$667$	8.35011	0.323318
$668$	5.35094	0.207034
$669$	22.9683	0.888005
$670$	0.263087	0.0101639
$671$	6.27284	0.242160
$672$	2.74153	0.105757
$673$	−38.3186	−1.47707	−0.738537	−	0.674213i	$-0.764483\pi$
$673$	−38.3186	−1.47707	−0.738537	+	0.674213i	$0.764483\pi$
$674$	19.3844	0.746657
$675$	−27.7365	−1.06758
$676$	−6.45820	−0.248392
$677$	−37.1444	−1.42758	−0.713788	−	0.700362i	$-0.753022\pi$
$677$	−37.1444	−1.42758	−0.713788	+	0.700362i	$0.753022\pi$
$678$	13.0697	0.501941
$679$	2.07296	0.0795530
$680$	−1.49772	−0.0574348
$681$	−5.68418	−0.217818
$682$	2.10111	0.0804557
$683$	11.1685	0.427353	0.213676	−	0.976905i	$-0.431456\pi$
$683$	11.1685	0.427353	0.213676	+	0.976905i	$0.431456\pi$
$684$	−7.50356	−0.286906
$685$	2.02357	0.0773166
$686$	20.1136	0.767941
$687$	4.08106	0.155702
$688$	1.78748	0.0681472
$689$	−4.82702	−0.183895
$690$	−2.28994	−0.0871764
$691$	−24.6389	−0.937307	−0.468654	−	0.883382i	$-0.655261\pi$
$691$	−24.6389	−0.937307	−0.468654	+	0.883382i	$0.655261\pi$
$692$	−16.2914	−0.619305
$693$	5.44856	0.206974
$694$	22.5946	0.857681
$695$	4.54750	0.172496
$696$	1.64340	0.0622930
$697$	37.2536	1.41108
$698$	−28.5125	−1.07922
$699$	−18.4357	−0.697303
$700$	10.2272	0.386551
$701$	37.7465	1.42567	0.712833	−	0.701334i	$-0.247412\pi$
$701$	37.7465	1.42567	0.712833	+	0.701334i	$0.247412\pi$
$702$	−14.3792	−0.542709
$703$	−46.1841	−1.74187
$704$	2.10111	0.0791886
$705$	−0.770517	−0.0290193
$706$	4.19049	0.157711
$707$	29.8572	1.12290
$708$	−4.91834	−0.184842
$709$	−20.9255	−0.785874	−0.392937	−	0.919565i	$-0.628541\pi$
$709$	−20.9255	−0.785874	−0.392937	+	0.919565i	$0.628541\pi$
$710$	2.25630	0.0846773
$711$	15.7976	0.592455
$712$	−9.67769	−0.362687
$713$	−6.71969	−0.251654
$714$	15.9349	0.596348
$715$	1.38475	0.0517867
$716$	3.50564	0.131012
$717$	3.34226	0.124819
$718$	18.4415	0.688232
$719$	−21.3364	−0.795715	−0.397858	−	0.917447i	$-0.630246\pi$
$719$	−21.3364	−0.795715	−0.397858	+	0.917447i	$0.630246\pi$
$720$	0.322340	0.0120129
$721$	3.57803	0.133253
$722$	16.9793	0.631906
$723$	25.4081	0.944937
$724$	−9.38760	−0.348888
$725$	6.13066	0.227687
$726$	8.70920	0.323229
$727$	−2.15842	−0.0800515	−0.0400257	−	0.999199i	$-0.512744\pi$
$727$	−2.15842	−0.0800515	−0.0400257	+	0.999199i	$0.512744\pi$
$728$	5.30201	0.196505
$729$	26.9117	0.996729
$730$	−3.65961	−0.135448
$731$	10.3896	0.384273
$732$	−3.94835	−0.145935
$733$	−25.9547	−0.958660	−0.479330	−	0.877635i	$-0.659120\pi$
$733$	−25.9547	−0.958660	−0.479330	+	0.877635i	$0.659120\pi$
$734$	−17.4255	−0.643188
$735$	−0.921068	−0.0339741
$736$	−6.71969	−0.247691
$737$	−2.14524	−0.0790208
$738$	−8.01776	−0.295138
$739$	45.3100	1.66676	0.833378	−	0.552704i	$-0.186404\pi$
$739$	45.3100	1.66676	0.833378	+	0.552704i	$0.186404\pi$
$740$	1.98399	0.0729329
$741$	20.2897	0.745361
$742$	−3.91221	−0.143622
$743$	−28.5365	−1.04690	−0.523452	−	0.852055i	$-0.675356\pi$
$743$	−28.5365	−1.04690	−0.523452	+	0.852055i	$0.675356\pi$
$744$	−1.32252	−0.0484858
$745$	3.62637	0.132860
$746$	−16.7349	−0.612708
$747$	−3.86361	−0.141362
$748$	12.2125	0.446534
$749$	−8.44271	−0.308490
$750$	−3.38517	−0.123609
$751$	7.65136	0.279202	0.139601	−	0.990208i	$-0.455418\pi$
$751$	7.65136	0.279202	0.139601	+	0.990208i	$0.455418\pi$
$752$	−2.26104	−0.0824516
$753$	−2.82618	−0.102992
$754$	3.17828	0.115746
$755$	−0.770783	−0.0280517
$756$	−11.6541	−0.423855
$757$	27.1238	0.985833	0.492916	−	0.870077i	$-0.335931\pi$
$757$	27.1238	0.985833	0.492916	+	0.870077i	$0.335931\pi$
$758$	−19.1344	−0.694991
$759$	18.6724	0.677764
$760$	−1.54561	−0.0560652
$761$	−16.9087	−0.612941	−0.306470	−	0.951880i	$-0.599148\pi$
$761$	−16.9087	−0.612941	−0.306470	+	0.951880i	$0.599148\pi$
$762$	5.24635	0.190055
$763$	−22.7186	−0.822470
$764$	−19.0016	−0.687453
$765$	1.87357	0.0677392
$766$	17.3251	0.625982
$767$	−9.51188	−0.343454
$768$	−1.32252	−0.0477222
$769$	25.0208	0.902272	0.451136	−	0.892455i	$-0.351019\pi$
$769$	25.0208	0.902272	0.451136	+	0.892455i	$0.351019\pi$
$770$	1.12231	0.0404454
$771$	4.31153	0.155276
$772$	5.53588	0.199241
$773$	−52.2416	−1.87900	−0.939500	−	0.342549i	$-0.888710\pi$
$773$	−52.2416	−1.87900	−0.939500	+	0.342549i	$0.888710\pi$
$774$	−2.23606	−0.0803734
$775$	−4.93360	−0.177220
$776$	−1.00000	−0.0358979
$777$	−21.1085	−0.757265
$778$	24.3576	0.873263
$779$	38.4449	1.37743
$780$	−0.871611	−0.0312087
$781$	−18.3981	−0.658335
$782$	−39.0576	−1.39670
$783$	−6.98602	−0.249660
$784$	−2.70282	−0.0965294
$785$	−5.05358	−0.180370
$786$	16.8864	0.602316
$787$	22.2318	0.792478	0.396239	−	0.918147i	$-0.370315\pi$
$787$	22.2318	0.792478	0.396239	+	0.918147i	$0.370315\pi$
$788$	−26.0139	−0.926707
$789$	41.5534	1.47934
$790$	3.25404	0.115773
$791$	20.4860	0.728400
$792$	−2.62839	−0.0933959
$793$	−7.63596	−0.271161
$794$	10.4066	0.369315
$795$	0.643139	0.0228098
$796$	−8.32118	−0.294936
$797$	19.0878	0.676124	0.338062	−	0.941124i	$-0.390229\pi$
$797$	19.0878	0.676124	0.338062	+	0.941124i	$0.390229\pi$
$798$	16.4444	0.582127
$799$	−13.1421	−0.464933
$800$	−4.93360	−0.174429
$801$	12.1063	0.427756
$802$	−36.2160	−1.27883
$803$	29.8408	1.05306
$804$	1.35029	0.0476210
$805$	−3.58934	−0.126508
$806$	−2.55769	−0.0900909
$807$	−8.99107	−0.316501
$808$	−14.4032	−0.506702
$809$	−25.8953	−0.910432	−0.455216	−	0.890381i	$-0.650438\pi$
$809$	−25.8953	−0.910432	−0.455216	+	0.890381i	$0.650438\pi$
$810$	0.948828	0.0333384
$811$	9.59344	0.336871	0.168436	−	0.985713i	$-0.446128\pi$
$811$	9.59344	0.336871	0.168436	+	0.985713i	$0.446128\pi$
$812$	2.57593	0.0903976
$813$	31.8345	1.11648
$814$	−16.1776	−0.567026
$815$	−0.576081	−0.0201792
$816$	−7.68700	−0.269099
$817$	10.7218	0.375109
$818$	16.9519	0.592710
$819$	−6.63256	−0.231760
$820$	−1.65153	−0.0576738
$821$	24.8531	0.867379	0.433690	−	0.901062i	$-0.357211\pi$
$821$	24.8531	0.867379	0.433690	+	0.901062i	$0.357211\pi$
$822$	10.3859	0.362251
$823$	33.1668	1.15612	0.578062	−	0.815993i	$-0.303809\pi$
$823$	33.1668	1.15612	0.578062	+	0.815993i	$0.303809\pi$
$824$	−1.72604	−0.0601296
$825$	13.7093	0.477295
$826$	−7.70920	−0.268237
$827$	20.2856	0.705400	0.352700	−	0.935736i	$-0.385264\pi$
$827$	20.2856	0.705400	0.352700	+	0.935736i	$0.385264\pi$
$828$	8.40602	0.292129
$829$	11.1144	0.386020	0.193010	−	0.981197i	$-0.438175\pi$
$829$	11.1144	0.386020	0.193010	+	0.981197i	$0.438175\pi$
$830$	−0.795839	−0.0276240
$831$	−39.4797	−1.36954
$832$	−2.55769	−0.0886721
$833$	−15.7099	−0.544316
$834$	23.3400	0.808197
$835$	−1.37881	−0.0477156
$836$	12.6031	0.435886
$837$	5.62195	0.194323
$838$	14.2785	0.493243
$839$	56.0174	1.93393	0.966967	−	0.254902i	$-0.0820432\pi$
$839$	56.0174	1.93393	0.966967	+	0.254902i	$0.0820432\pi$
$840$	−0.706424	−0.0243740
$841$	−27.4559	−0.946754
$842$	−12.0871	−0.416550
$843$	−0.496497	−0.0171003
$844$	1.99573	0.0686958
$845$	1.66412	0.0572475
$846$	2.82845	0.0972442
$847$	13.6511	0.469059
$848$	1.88726	0.0648086
$849$	23.6021	0.810022
$850$	−28.6761	−0.983583
$851$	51.7387	1.77358
$852$	11.5804	0.396738
$853$	−3.62513	−0.124122	−0.0620610	−	0.998072i	$-0.519767\pi$
$853$	−3.62513	−0.124122	−0.0620610	+	0.998072i	$0.519767\pi$
$854$	−6.18880	−0.211777
$855$	1.93349	0.0661238
$856$	4.07277	0.139204
$857$	−3.60294	−0.123074	−0.0615371	−	0.998105i	$-0.519600\pi$
$857$	−3.60294	−0.123074	−0.0615371	+	0.998105i	$0.519600\pi$
$858$	7.10720	0.242636
$859$	−19.1623	−0.653809	−0.326904	−	0.945057i	$-0.606006\pi$
$859$	−19.1623	−0.653809	−0.326904	+	0.945057i	$0.606006\pi$
$860$	−0.460591	−0.0157060
$861$	17.5713	0.598829
$862$	−20.4728	−0.697307
$863$	20.0677	0.683112	0.341556	−	0.939861i	$-0.389046\pi$
$863$	20.0677	0.683112	0.341556	+	0.939861i	$0.389046\pi$
$864$	5.62195	0.191263
$865$	4.19789	0.142732
$866$	18.8439	0.640341
$867$	−22.1972	−0.753857
$868$	−2.07296	−0.0703610
$869$	−26.5337	−0.900095
$870$	−0.423465	−0.0143568
$871$	2.61141	0.0884842
$872$	10.9595	0.371135
$873$	1.25095	0.0423383
$874$	−40.3066	−1.36339
$875$	−5.30606	−0.179377
$876$	−18.7829	−0.634614
$877$	16.7308	0.564960	0.282480	−	0.959273i	$-0.408843\pi$
$877$	16.7308	0.564960	0.282480	+	0.959273i	$0.408843\pi$
$878$	−16.7609	−0.565654
$879$	−19.8841	−0.670674
$880$	−0.541405	−0.0182508
$881$	39.0211	1.31465	0.657327	−	0.753605i	$-0.271687\pi$
$881$	39.0211	1.31465	0.657327	+	0.753605i	$0.271687\pi$
$882$	3.38110	0.113848
$883$	−39.1492	−1.31748	−0.658739	−	0.752372i	$-0.728910\pi$
$883$	−39.1492	−1.31748	−0.658739	+	0.752372i	$0.728910\pi$
$884$	−14.8664	−0.500010
$885$	1.26734	0.0426010
$886$	−27.2739	−0.916284
$887$	22.3751	0.751284	0.375642	−	0.926765i	$-0.377422\pi$
$887$	22.3751	0.751284	0.375642	+	0.926765i	$0.377422\pi$
$888$	10.1828	0.341712
$889$	8.22334	0.275802
$890$	2.49370	0.0835891
$891$	−7.73684	−0.259194
$892$	−17.3671	−0.581494
$893$	−13.5623	−0.453846
$894$	18.6123	0.622488
$895$	−0.903317	−0.0301946
$896$	−2.07296	−0.0692528
$897$	−22.7300	−0.758931
$898$	−40.0321	−1.33589
$899$	−1.24263	−0.0414441
$900$	6.17171	0.205724
$901$	10.9695	0.365447
$902$	13.4667	0.448392
$903$	4.90043	0.163076
$904$	−9.88249	−0.328687
$905$	2.41896	0.0804088
$906$	−3.95603	−0.131430
$907$	−57.4453	−1.90744	−0.953719	−	0.300699i	$-0.902780\pi$
$907$	−57.4453	−1.90744	−0.953719	+	0.300699i	$0.902780\pi$
$908$	4.29800	0.142634
$909$	18.0177	0.597609
$910$	−1.36620	−0.0452890
$911$	−13.8753	−0.459710	−0.229855	−	0.973225i	$-0.573825\pi$
$911$	−13.8753	−0.459710	−0.229855	+	0.973225i	$0.573825\pi$
$912$	−7.93282	−0.262682
$913$	6.48935	0.214766
$914$	41.1383	1.36073
$915$	1.01739	0.0336340
$916$	−3.08583	−0.101959
$917$	26.4683	0.874062
$918$	32.6771	1.07850
$919$	−47.1402	−1.55501	−0.777505	−	0.628876i	$-0.783515\pi$
$919$	−47.1402	−1.55501	−0.777505	+	0.628876i	$0.783515\pi$
$920$	1.73150	0.0570859
$921$	−8.20725	−0.270438
$922$	27.3686	0.901338
$923$	22.3961	0.737175
$924$	5.76025	0.189498
$925$	37.9866	1.24899
$926$	22.8321	0.750308
$927$	2.15920	0.0709175
$928$	−1.24263	−0.0407914
$929$	7.23029	0.237218	0.118609	−	0.992941i	$-0.462156\pi$
$929$	7.23029	0.237218	0.118609	+	0.992941i	$0.462156\pi$
$930$	0.340780	0.0111746
$931$	−16.2123	−0.531336
$932$	13.9399	0.456617
$933$	13.8400	0.453101
$934$	−36.9273	−1.20830
$935$	−3.14687	−0.102914
$936$	3.19956	0.104581
$937$	6.64592	0.217113	0.108556	−	0.994090i	$-0.465377\pi$
$937$	6.64592	0.217113	0.108556	+	0.994090i	$0.465377\pi$
$938$	2.11650	0.0691061
$939$	−4.20752	−0.137307
$940$	0.582615	0.0190028
$941$	39.2736	1.28028	0.640142	−	0.768257i	$-0.278875\pi$
$941$	39.2736	1.28028	0.640142	+	0.768257i	$0.278875\pi$
$942$	−25.9374	−0.845086
$943$	−43.0686	−1.40251
$944$	3.71893	0.121041
$945$	3.00298	0.0976868
$946$	3.75570	0.122108
$947$	2.01848	0.0655917	0.0327958	−	0.999462i	$-0.489559\pi$
$947$	2.01848	0.0655917	0.0327958	+	0.999462i	$0.489559\pi$
$948$	16.7013	0.542432
$949$	−36.3253	−1.17917
$950$	−29.5931	−0.960128
$951$	−34.7386	−1.12648
$952$	−12.0489	−0.390507
$953$	−30.9355	−1.00210	−0.501050	−	0.865418i	$-0.667053\pi$
$953$	−30.9355	−1.00210	−0.501050	+	0.865418i	$0.667053\pi$
$954$	−2.36087	−0.0764359
$955$	4.89624	0.158439
$956$	−2.52720	−0.0817354
$957$	3.45297	0.111619
$958$	18.2930	0.591020
$959$	16.2793	0.525687
$960$	0.340780	0.0109986
$961$	1.00000	0.0322581
$962$	19.6931	0.634932
$963$	−5.09485	−0.164179
$964$	−19.2119	−0.618775
$965$	−1.42646	−0.0459194
$966$	−18.4222	−0.592725
$967$	−14.4468	−0.464579	−0.232290	−	0.972647i	$-0.574622\pi$
$967$	−14.4468	−0.464579	−0.232290	+	0.972647i	$0.574622\pi$
$968$	−6.58533	−0.211660
$969$	−46.1088	−1.48123
$970$	0.257676	0.00827347
$971$	4.11524	0.132064	0.0660321	−	0.997817i	$-0.478966\pi$
$971$	4.11524	0.132064	0.0660321	+	0.997817i	$0.478966\pi$
$972$	−11.9960	−0.384772
$973$	36.5840	1.17283
$974$	−36.2684	−1.16211
$975$	−16.6884	−0.534455
$976$	2.98549	0.0955631
$977$	52.8133	1.68965	0.844824	−	0.535045i	$-0.179705\pi$
$977$	52.8133	1.68965	0.844824	+	0.535045i	$0.179705\pi$
$978$	−2.95672	−0.0945456
$979$	−20.3339	−0.649874
$980$	0.696452	0.0222473
$981$	−13.7098	−0.437721
$982$	−24.9369	−0.795770
$983$	17.6003	0.561362	0.280681	−	0.959801i	$-0.409440\pi$
$983$	17.6003	0.561362	0.280681	+	0.959801i	$0.409440\pi$
$984$	−8.47642	−0.270218
$985$	6.70315	0.213580
$986$	−7.22269	−0.230017
$987$	−6.19870	−0.197307
$988$	−15.3418	−0.488086
$989$	−12.0113	−0.381938
$990$	0.677273	0.0215251
$991$	−2.35049	−0.0746658	−0.0373329	−	0.999303i	$-0.511886\pi$
$991$	−2.35049	−0.0746658	−0.0373329	+	0.999303i	$0.511886\pi$
$992$	1.00000	0.0317500
$993$	−11.4655	−0.363846
$994$	18.1516	0.575734
$995$	2.14417	0.0679746
$996$	−4.08463	−0.129426
$997$	−15.3436	−0.485938	−0.242969	−	0.970034i	$-0.578121\pi$
$997$	−15.3436	−0.485938	−0.242969	+	0.970034i	$0.578121\pi$
$998$	−12.5385	−0.396898
$999$	−43.2865	−1.36953

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.e.1.7	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.e.1.7	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.32252 q^{3} +1.00000 q^{4} -0.257676 q^{5} -1.32252 q^{6} -2.07296 q^{7} +1.00000 q^{8} -1.25095 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.32252 q^{3} +1.00000 q^{4} -0.257676 q^{5} -1.32252 q^{6} -2.07296 q^{7} +1.00000 q^{8} -1.25095 q^{9} -0.257676 q^{10} +2.10111 q^{11} -1.32252 q^{12} -2.55769 q^{13} -2.07296 q^{14} +0.340780 q^{15} +1.00000 q^{16} +5.81241 q^{17} -1.25095 q^{18} +5.99828 q^{19} -0.257676 q^{20} +2.74153 q^{21} +2.10111 q^{22} -6.71969 q^{23} -1.32252 q^{24} -4.93360 q^{25} -2.55769 q^{26} +5.62195 q^{27} -2.07296 q^{28} -1.24263 q^{29} +0.340780 q^{30} +1.00000 q^{31} +1.00000 q^{32} -2.77875 q^{33} +5.81241 q^{34} +0.534152 q^{35} -1.25095 q^{36} -7.69956 q^{37} +5.99828 q^{38} +3.38259 q^{39} -0.257676 q^{40} +6.40932 q^{41} +2.74153 q^{42} +1.78748 q^{43} +2.10111 q^{44} +0.322340 q^{45} -6.71969 q^{46} -2.26104 q^{47} -1.32252 q^{48} -2.70282 q^{49} -4.93360 q^{50} -7.68700 q^{51} -2.55769 q^{52} +1.88726 q^{53} +5.62195 q^{54} -0.541405 q^{55} -2.07296 q^{56} -7.93282 q^{57} -1.24263 q^{58} +3.71893 q^{59} +0.340780 q^{60} +2.98549 q^{61} +1.00000 q^{62} +2.59318 q^{63} +1.00000 q^{64} +0.659055 q^{65} -2.77875 q^{66} -1.02100 q^{67} +5.81241 q^{68} +8.88689 q^{69} +0.534152 q^{70} -8.75635 q^{71} -1.25095 q^{72} +14.2024 q^{73} -7.69956 q^{74} +6.52477 q^{75} +5.99828 q^{76} -4.35553 q^{77} +3.38259 q^{78} -12.6284 q^{79} -0.257676 q^{80} -3.68226 q^{81} +6.40932 q^{82} +3.08853 q^{83} +2.74153 q^{84} -1.49772 q^{85} +1.78748 q^{86} +1.64340 q^{87} +2.10111 q^{88} -9.67769 q^{89} +0.322340 q^{90} +5.30201 q^{91} -6.71969 q^{92} -1.32252 q^{93} -2.26104 q^{94} -1.54561 q^{95} -1.32252 q^{96} -1.00000 q^{97} -2.70282 q^{98} -2.62839 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 21 q^{2} - 10 q^{3} + 21 q^{4} - 10 q^{5} - 10 q^{6} - 11 q^{7} + 21 q^{8} + 7 q^{9}+O(q^{10}) \) 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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