LMFDB - Embedded newform 6022.2.a.b.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6022,2,Mod(1,6022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6022, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6022 = 2 \cdot 3011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6022.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:	$48.0859120972$
Analytic rank:	$1$
Dimension:	$54$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	6022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.92077 q^{3} +1.00000 q^{4} +3.09656 q^{5} -1.92077 q^{6} -3.07737 q^{7} +1.00000 q^{8} +0.689347 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.92077 q^{3} +1.00000 q^{4} +3.09656 q^{5} -1.92077 q^{6} -3.07737 q^{7} +1.00000 q^{8} +0.689347 q^{9} +3.09656 q^{10} -0.0868382 q^{11} -1.92077 q^{12} +1.23108 q^{13} -3.07737 q^{14} -5.94777 q^{15} +1.00000 q^{16} +5.46364 q^{17} +0.689347 q^{18} -3.74953 q^{19} +3.09656 q^{20} +5.91090 q^{21} -0.0868382 q^{22} -6.57027 q^{23} -1.92077 q^{24} +4.58869 q^{25} +1.23108 q^{26} +4.43823 q^{27} -3.07737 q^{28} -7.64556 q^{29} -5.94777 q^{30} -0.596870 q^{31} +1.00000 q^{32} +0.166796 q^{33} +5.46364 q^{34} -9.52925 q^{35} +0.689347 q^{36} -0.702711 q^{37} -3.74953 q^{38} -2.36462 q^{39} +3.09656 q^{40} +4.85857 q^{41} +5.91090 q^{42} -6.26112 q^{43} -0.0868382 q^{44} +2.13460 q^{45} -6.57027 q^{46} -5.40358 q^{47} -1.92077 q^{48} +2.47018 q^{49} +4.58869 q^{50} -10.4944 q^{51} +1.23108 q^{52} +13.4051 q^{53} +4.43823 q^{54} -0.268900 q^{55} -3.07737 q^{56} +7.20198 q^{57} -7.64556 q^{58} -5.15049 q^{59} -5.94777 q^{60} -4.14673 q^{61} -0.596870 q^{62} -2.12137 q^{63} +1.00000 q^{64} +3.81212 q^{65} +0.166796 q^{66} -8.70756 q^{67} +5.46364 q^{68} +12.6200 q^{69} -9.52925 q^{70} -1.88332 q^{71} +0.689347 q^{72} +11.3462 q^{73} -0.702711 q^{74} -8.81381 q^{75} -3.74953 q^{76} +0.267233 q^{77} -2.36462 q^{78} -7.21356 q^{79} +3.09656 q^{80} -10.5928 q^{81} +4.85857 q^{82} +2.30311 q^{83} +5.91090 q^{84} +16.9185 q^{85} -6.26112 q^{86} +14.6853 q^{87} -0.0868382 q^{88} -6.30610 q^{89} +2.13460 q^{90} -3.78848 q^{91} -6.57027 q^{92} +1.14645 q^{93} -5.40358 q^{94} -11.6107 q^{95} -1.92077 q^{96} +7.66801 q^{97} +2.47018 q^{98} -0.0598616 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q + 54 q^{2} - 22 q^{3} + 54 q^{4} - 14 q^{5} - 22 q^{6} - 20 q^{7} + 54 q^{8} + 32 q^{9}+O(q^{10}) $ 54 * q + 54 * q^2 - 22 * q^3 + 54 * q^4 - 14 * q^5 - 22 * q^6 - 20 * q^7 + 54 * q^8 + 32 * q^9	\( 54 q + 54 q^{2} - 22 q^{3} + 54 q^{4} - 14 q^{5} - 22 q^{6} - 20 q^{7} + 54 q^{8} + 32 q^{9} - 14 q^{10} - 22 q^{11} - 22 q^{12} - 24 q^{13} - 20 q^{14} - 32 q^{15} + 54 q^{16} - 67 q^{17} + 32 q^{18} - 54 q^{19} - 14 q^{20} - 18 q^{21} - 22 q^{22} - 52 q^{23} - 22 q^{24} + 20 q^{25} - 24 q^{26} - 82 q^{27} - 20 q^{28} - 30 q^{29} - 32 q^{30} - 78 q^{31} + 54 q^{32} - 48 q^{33} - 67 q^{34} - 71 q^{35} + 32 q^{36} - 15 q^{37} - 54 q^{38} - 39 q^{39} - 14 q^{40} - 61 q^{41} - 18 q^{42} - 53 q^{43} - 22 q^{44} - 14 q^{45} - 52 q^{46} - 96 q^{47} - 22 q^{48} + 6 q^{49} + 20 q^{50} - 13 q^{51} - 24 q^{52} - 39 q^{53} - 82 q^{54} - 75 q^{55} - 20 q^{56} - 17 q^{57} - 30 q^{58} - 78 q^{59} - 32 q^{60} - 23 q^{61} - 78 q^{62} - 52 q^{63} + 54 q^{64} - 43 q^{65} - 48 q^{66} - 54 q^{67} - 67 q^{68} + 7 q^{69} - 71 q^{70} - 41 q^{71} + 32 q^{72} - 62 q^{73} - 15 q^{74} - 81 q^{75} - 54 q^{76} - 85 q^{77} - 39 q^{78} - 45 q^{79} - 14 q^{80} + 22 q^{81} - 61 q^{82} - 117 q^{83} - 18 q^{84} - 53 q^{86} - 84 q^{87} - 22 q^{88} - 60 q^{89} - 14 q^{90} - 60 q^{91} - 52 q^{92} + 26 q^{93} - 96 q^{94} - 44 q^{95} - 22 q^{96} - 48 q^{97} + 6 q^{98} + 7 q^{99}+O(q^{100}) \) 54 * q + 54 * q^2 - 22 * q^3 + 54 * q^4 - 14 * q^5 - 22 * q^6 - 20 * q^7 + 54 * q^8 + 32 * q^9 - 14 * q^10 - 22 * q^11 - 22 * q^12 - 24 * q^13 - 20 * q^14 - 32 * q^15 + 54 * q^16 - 67 * q^17 + 32 * q^18 - 54 * q^19 - 14 * q^20 - 18 * q^21 - 22 * q^22 - 52 * q^23 - 22 * q^24 + 20 * q^25 - 24 * q^26 - 82 * q^27 - 20 * q^28 - 30 * q^29 - 32 * q^30 - 78 * q^31 + 54 * q^32 - 48 * q^33 - 67 * q^34 - 71 * q^35 + 32 * q^36 - 15 * q^37 - 54 * q^38 - 39 * q^39 - 14 * q^40 - 61 * q^41 - 18 * q^42 - 53 * q^43 - 22 * q^44 - 14 * q^45 - 52 * q^46 - 96 * q^47 - 22 * q^48 + 6 * q^49 + 20 * q^50 - 13 * q^51 - 24 * q^52 - 39 * q^53 - 82 * q^54 - 75 * q^55 - 20 * q^56 - 17 * q^57 - 30 * q^58 - 78 * q^59 - 32 * q^60 - 23 * q^61 - 78 * q^62 - 52 * q^63 + 54 * q^64 - 43 * q^65 - 48 * q^66 - 54 * q^67 - 67 * q^68 + 7 * q^69 - 71 * q^70 - 41 * q^71 + 32 * q^72 - 62 * q^73 - 15 * q^74 - 81 * q^75 - 54 * q^76 - 85 * q^77 - 39 * q^78 - 45 * q^79 - 14 * q^80 + 22 * q^81 - 61 * q^82 - 117 * q^83 - 18 * q^84 - 53 * q^86 - 84 * q^87 - 22 * q^88 - 60 * q^89 - 14 * q^90 - 60 * q^91 - 52 * q^92 + 26 * q^93 - 96 * q^94 - 44 * q^95 - 22 * q^96 - 48 * q^97 + 6 * q^98 + 7 * 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
$3$	−1.92077	−1.10896	−0.554478	−	0.832199i	$-0.687082\pi$
$3$	−1.92077	−1.10896	−0.554478	+	0.832199i	$0.687082\pi$
$4$	1.00000	0.500000
$5$	3.09656	1.38482	0.692412	−	0.721502i	$-0.256548\pi$
$5$	3.09656	1.38482	0.692412	+	0.721502i	$0.256548\pi$
$6$	−1.92077	−0.784150
$7$	−3.07737	−1.16313	−0.581567	−	0.813498i	$-0.697560\pi$
$7$	−3.07737	−1.16313	−0.581567	+	0.813498i	$0.697560\pi$
$8$	1.00000	0.353553
$9$	0.689347	0.229782
$10$	3.09656	0.979219
$11$	−0.0868382	−0.0261827	−0.0130914	−	0.999914i	$-0.504167\pi$
$11$	−0.0868382	−0.0261827	−0.0130914	+	0.999914i	$0.504167\pi$
$12$	−1.92077	−0.554478
$13$	1.23108	0.341440	0.170720	−	0.985320i	$-0.445391\pi$
$13$	1.23108	0.341440	0.170720	+	0.985320i	$0.445391\pi$
$14$	−3.07737	−0.822461
$15$	−5.94777	−1.53571
$16$	1.00000	0.250000
$17$	5.46364	1.32513	0.662564	−	0.749005i	$-0.269468\pi$
$17$	5.46364	1.32513	0.662564	+	0.749005i	$0.269468\pi$
$18$	0.689347	0.162481
$19$	−3.74953	−0.860201	−0.430101	−	0.902781i	$-0.641522\pi$
$19$	−3.74953	−0.860201	−0.430101	+	0.902781i	$0.641522\pi$
$20$	3.09656	0.692412
$21$	5.91090	1.28986
$22$	−0.0868382	−0.0185140
$23$	−6.57027	−1.37000	−0.684998	−	0.728545i	$-0.740197\pi$
$23$	−6.57027	−1.37000	−0.684998	+	0.728545i	$0.740197\pi$
$24$	−1.92077	−0.392075
$25$	4.58869	0.917739
$26$	1.23108	0.241435
$27$	4.43823	0.854137
$28$	−3.07737	−0.581567
$29$	−7.64556	−1.41974	−0.709872	−	0.704331i	$-0.751247\pi$
$29$	−7.64556	−1.41974	−0.709872	+	0.704331i	$0.751247\pi$
$30$	−5.94777	−1.08591
$31$	−0.596870	−0.107201	−0.0536005	−	0.998562i	$-0.517070\pi$
$31$	−0.596870	−0.107201	−0.0536005	+	0.998562i	$0.517070\pi$
$32$	1.00000	0.176777
$33$	0.166796	0.0290355
$34$	5.46364	0.937007
$35$	−9.52925	−1.61074
$36$	0.689347	0.114891
$37$	−0.702711	−0.115525	−0.0577625	−	0.998330i	$-0.518397\pi$
$37$	−0.702711	−0.115525	−0.0577625	+	0.998330i	$0.518397\pi$
$38$	−3.74953	−0.608254
$39$	−2.36462	−0.378642
$40$	3.09656	0.489609
$41$	4.85857	0.758782	0.379391	−	0.925237i	$-0.376134\pi$
$41$	4.85857	0.758782	0.379391	+	0.925237i	$0.376134\pi$
$42$	5.91090	0.912072
$43$	−6.26112	−0.954812	−0.477406	−	0.878683i	$-0.658423\pi$
$43$	−6.26112	−0.954812	−0.477406	+	0.878683i	$0.658423\pi$
$44$	−0.0868382	−0.0130914
$45$	2.13460	0.318208
$46$	−6.57027	−0.968734
$47$	−5.40358	−0.788193	−0.394097	−	0.919069i	$-0.628942\pi$
$47$	−5.40358	−0.788193	−0.394097	+	0.919069i	$0.628942\pi$
$48$	−1.92077	−0.277239
$49$	2.47018	0.352883
$50$	4.58869	0.648939
$51$	−10.4944	−1.46951
$52$	1.23108	0.170720
$53$	13.4051	1.84134	0.920668	−	0.390346i	$-0.127645\pi$
$53$	13.4051	1.84134	0.920668	+	0.390346i	$0.127645\pi$
$54$	4.43823	0.603966
$55$	−0.268900	−0.0362585
$56$	−3.07737	−0.411230
$57$	7.20198	0.953925
$58$	−7.64556	−1.00391
$59$	−5.15049	−0.670536	−0.335268	−	0.942123i	$-0.608827\pi$
$59$	−5.15049	−0.670536	−0.335268	+	0.942123i	$0.608827\pi$
$60$	−5.94777	−0.767854
$61$	−4.14673	−0.530934	−0.265467	−	0.964120i	$-0.585526\pi$
$61$	−4.14673	−0.530934	−0.265467	+	0.964120i	$0.585526\pi$
$62$	−0.596870	−0.0758025
$63$	−2.12137	−0.267268
$64$	1.00000	0.125000
$65$	3.81212	0.472835
$66$	0.166796	0.0205312
$67$	−8.70756	−1.06380	−0.531899	−	0.846808i	$-0.678521\pi$
$67$	−8.70756	−1.06380	−0.531899	+	0.846808i	$0.678521\pi$
$68$	5.46364	0.662564
$69$	12.6200	1.51927
$70$	−9.52925	−1.13896
$71$	−1.88332	−0.223509	−0.111754	−	0.993736i	$-0.535647\pi$
$71$	−1.88332	−0.223509	−0.111754	+	0.993736i	$0.535647\pi$
$72$	0.689347	0.0812403
$73$	11.3462	1.32797	0.663987	−	0.747744i	$-0.268863\pi$
$73$	11.3462	1.32797	0.663987	+	0.747744i	$0.268863\pi$
$74$	−0.702711	−0.0816885
$75$	−8.81381	−1.01773
$76$	−3.74953	−0.430101
$77$	0.267233	0.0304540
$78$	−2.36462	−0.267740
$79$	−7.21356	−0.811589	−0.405794	−	0.913964i	$-0.633005\pi$
$79$	−7.21356	−0.811589	−0.405794	+	0.913964i	$0.633005\pi$
$80$	3.09656	0.346206
$81$	−10.5928	−1.17698
$82$	4.85857	0.536540
$83$	2.30311	0.252799	0.126400	−	0.991979i	$-0.459658\pi$
$83$	2.30311	0.252799	0.126400	+	0.991979i	$0.459658\pi$
$84$	5.91090	0.644932
$85$	16.9185	1.83507
$86$	−6.26112	−0.675154
$87$	14.6853	1.57443
$88$	−0.0868382	−0.00925699
$89$	−6.30610	−0.668446	−0.334223	−	0.942494i	$-0.608474\pi$
$89$	−6.30610	−0.668446	−0.334223	+	0.942494i	$0.608474\pi$
$90$	2.13460	0.225007
$91$	−3.78848	−0.397141
$92$	−6.57027	−0.684998
$93$	1.14645	0.118881
$94$	−5.40358	−0.557337
$95$	−11.6107	−1.19123
$96$	−1.92077	−0.196037
$97$	7.66801	0.778568	0.389284	−	0.921118i	$-0.372722\pi$
$97$	7.66801	0.778568	0.389284	+	0.921118i	$0.372722\pi$
$98$	2.47018	0.249526
$99$	−0.0598616	−0.00601632
$100$	4.58869	0.458869
$101$	5.85604	0.582698	0.291349	−	0.956617i	$-0.405896\pi$
$101$	5.85604	0.582698	0.291349	+	0.956617i	$0.405896\pi$
$102$	−10.4944	−1.03910
$103$	−19.4504	−1.91650	−0.958251	−	0.285930i	$-0.907698\pi$
$103$	−19.4504	−1.91650	−0.958251	+	0.285930i	$0.907698\pi$
$104$	1.23108	0.120717
$105$	18.3035	1.78624
$106$	13.4051	1.30202
$107$	18.2950	1.76865	0.884325	−	0.466873i	$-0.154619\pi$
$107$	18.2950	1.76865	0.884325	+	0.466873i	$0.154619\pi$
$108$	4.43823	0.427069
$109$	−20.1991	−1.93472	−0.967361	−	0.253401i	$-0.918451\pi$
$109$	−20.1991	−1.93472	−0.967361	+	0.253401i	$0.918451\pi$
$110$	−0.268900	−0.0256386
$111$	1.34974	0.128112
$112$	−3.07737	−0.290784
$113$	−15.4086	−1.44952	−0.724760	−	0.689002i	$-0.758049\pi$
$113$	−15.4086	−1.44952	−0.724760	+	0.689002i	$0.758049\pi$
$114$	7.20198	0.674527
$115$	−20.3453	−1.89720
$116$	−7.64556	−0.709872
$117$	0.848641	0.0784569
$118$	−5.15049	−0.474141
$119$	−16.8136	−1.54130
$120$	−5.94777	−0.542955
$121$	−10.9925	−0.999314
$122$	−4.14673	−0.375427
$123$	−9.33219	−0.841455
$124$	−0.596870	−0.0536005
$125$	−1.27364	−0.113917
$126$	−2.12137	−0.188987
$127$	19.7872	1.75583	0.877914	−	0.478819i	$-0.158935\pi$
$127$	19.7872	1.75583	0.877914	+	0.478819i	$0.158935\pi$
$128$	1.00000	0.0883883
$129$	12.0262	1.05884
$130$	3.81212	0.334345
$131$	−4.76810	−0.416591	−0.208296	−	0.978066i	$-0.566792\pi$
$131$	−4.76810	−0.416591	−0.208296	+	0.978066i	$0.566792\pi$
$132$	0.166796	0.0145177
$133$	11.5387	1.00053
$134$	−8.70756	−0.752218
$135$	13.7432	1.18283
$136$	5.46364	0.468504
$137$	−15.3109	−1.30810	−0.654049	−	0.756453i	$-0.726931\pi$
$137$	−15.3109	−1.30810	−0.654049	+	0.756453i	$0.726931\pi$
$138$	12.6200	1.07428
$139$	18.4532	1.56518	0.782589	−	0.622539i	$-0.213899\pi$
$139$	18.4532	1.56518	0.782589	+	0.622539i	$0.213899\pi$
$140$	−9.52925	−0.805369
$141$	10.3790	0.874071
$142$	−1.88332	−0.158045
$143$	−0.106905	−0.00893983
$144$	0.689347	0.0574456
$145$	−23.6749	−1.96610
$146$	11.3462	0.939019
$147$	−4.74464	−0.391332
$148$	−0.702711	−0.0577625
$149$	−2.12820	−0.174349	−0.0871745	−	0.996193i	$-0.527784\pi$
$149$	−2.12820	−0.174349	−0.0871745	+	0.996193i	$0.527784\pi$
$150$	−8.81381	−0.719645
$151$	−4.69400	−0.381992	−0.190996	−	0.981591i	$-0.561172\pi$
$151$	−4.69400	−0.381992	−0.190996	+	0.981591i	$0.561172\pi$
$152$	−3.74953	−0.304127
$153$	3.76634	0.304491
$154$	0.267233	0.0215343
$155$	−1.84824	−0.148455
$156$	−2.36462	−0.189321
$157$	−4.24205	−0.338552	−0.169276	−	0.985569i	$-0.554143\pi$
$157$	−4.24205	−0.338552	−0.169276	+	0.985569i	$0.554143\pi$
$158$	−7.21356	−0.573880
$159$	−25.7481	−2.04196
$160$	3.09656	0.244805
$161$	20.2191	1.59349
$162$	−10.5928	−0.832252
$163$	0.946145	0.0741078	0.0370539	−	0.999313i	$-0.488203\pi$
$163$	0.946145	0.0741078	0.0370539	+	0.999313i	$0.488203\pi$
$164$	4.85857	0.379391
$165$	0.516494	0.0402090
$166$	2.30311	0.178756
$167$	16.2744	1.25935	0.629674	−	0.776860i	$-0.283189\pi$
$167$	16.2744	1.25935	0.629674	+	0.776860i	$0.283189\pi$
$168$	5.91090	0.456036
$169$	−11.4844	−0.883419
$170$	16.9185	1.29759
$171$	−2.58473	−0.197659
$172$	−6.26112	−0.477406
$173$	−21.7471	−1.65340	−0.826700	−	0.562643i	$-0.809785\pi$
$173$	−21.7471	−1.65340	−0.826700	+	0.562643i	$0.809785\pi$
$174$	14.6853	1.11329
$175$	−14.1211	−1.06745
$176$	−0.0868382	−0.00654568
$177$	9.89288	0.743595
$178$	−6.30610	−0.472663
$179$	−8.96135	−0.669803	−0.334901	−	0.942253i	$-0.608703\pi$
$179$	−8.96135	−0.669803	−0.334901	+	0.942253i	$0.608703\pi$
$180$	2.13460	0.159104
$181$	7.93227	0.589601	0.294800	−	0.955559i	$-0.404747\pi$
$181$	7.93227	0.589601	0.294800	+	0.955559i	$0.404747\pi$
$182$	−3.78848	−0.280821
$183$	7.96489	0.588782
$184$	−6.57027	−0.484367
$185$	−2.17599	−0.159982
$186$	1.14645	0.0840616
$187$	−0.474453	−0.0346955
$188$	−5.40358	−0.394097
$189$	−13.6580	−0.993477
$190$	−11.6107	−0.842325
$191$	−10.8672	−0.786322	−0.393161	−	0.919470i	$-0.628619\pi$
$191$	−10.8672	−0.786322	−0.393161	+	0.919470i	$0.628619\pi$
$192$	−1.92077	−0.138619
$193$	−13.4725	−0.969775	−0.484888	−	0.874576i	$-0.661139\pi$
$193$	−13.4725	−0.969775	−0.484888	+	0.874576i	$0.661139\pi$
$194$	7.66801	0.550531
$195$	−7.32219	−0.524353
$196$	2.47018	0.176442
$197$	−22.3555	−1.59276	−0.796381	−	0.604796i	$-0.793255\pi$
$197$	−22.3555	−1.59276	−0.796381	+	0.604796i	$0.793255\pi$
$198$	−0.0598616	−0.00425418
$199$	−15.6192	−1.10721	−0.553607	−	0.832778i	$-0.686749\pi$
$199$	−15.6192	−1.10721	−0.553607	+	0.832778i	$0.686749\pi$
$200$	4.58869	0.324470
$201$	16.7252	1.17970
$202$	5.85604	0.412030
$203$	23.5282	1.65135
$204$	−10.4944	−0.734754
$205$	15.0449	1.05078
$206$	−19.4504	−1.35517
$207$	−4.52920	−0.314801
$208$	1.23108	0.0853600
$209$	0.325603	0.0225224
$210$	18.3035	1.26306
$211$	14.8399	1.02162	0.510812	−	0.859692i	$-0.329345\pi$
$211$	14.8399	1.02162	0.510812	+	0.859692i	$0.329345\pi$
$212$	13.4051	0.920668
$213$	3.61742	0.247861
$214$	18.2950	1.25062
$215$	−19.3879	−1.32225
$216$	4.43823	0.301983
$217$	1.83679	0.124689
$218$	−20.1991	−1.36806
$219$	−21.7934	−1.47266
$220$	−0.268900	−0.0181292
$221$	6.72618	0.452452
$222$	1.34974	0.0905889
$223$	19.6674	1.31702	0.658512	−	0.752570i	$-0.271186\pi$
$223$	19.6674	1.31702	0.658512	+	0.752570i	$0.271186\pi$
$224$	−3.07737	−0.205615
$225$	3.16320	0.210880
$226$	−15.4086	−1.02496
$227$	4.86018	0.322582	0.161291	−	0.986907i	$-0.448434\pi$
$227$	4.86018	0.322582	0.161291	+	0.986907i	$0.448434\pi$
$228$	7.20198	0.476963
$229$	−6.78352	−0.448267	−0.224134	−	0.974558i	$-0.571955\pi$
$229$	−6.78352	−0.448267	−0.224134	+	0.974558i	$0.571955\pi$
$230$	−20.3453	−1.34153
$231$	−0.513292	−0.0337722
$232$	−7.64556	−0.501955
$233$	−27.2439	−1.78481	−0.892405	−	0.451236i	$-0.850983\pi$
$233$	−27.2439	−1.78481	−0.892405	+	0.451236i	$0.850983\pi$
$234$	0.848641	0.0554774
$235$	−16.7325	−1.09151
$236$	−5.15049	−0.335268
$237$	13.8556	0.900016
$238$	−16.8136	−1.08987
$239$	12.1334	0.784846	0.392423	−	0.919785i	$-0.371637\pi$
$239$	12.1334	0.784846	0.392423	+	0.919785i	$0.371637\pi$
$240$	−5.94777	−0.383927
$241$	8.41981	0.542368	0.271184	−	0.962528i	$-0.412585\pi$
$241$	8.41981	0.542368	0.271184	+	0.962528i	$0.412585\pi$
$242$	−10.9925	−0.706622
$243$	7.03170	0.451084
$244$	−4.14673	−0.265467
$245$	7.64907	0.488681
$246$	−9.33219	−0.594999
$247$	−4.61597	−0.293707
$248$	−0.596870	−0.0379013
$249$	−4.42374	−0.280343
$250$	−1.27364	−0.0805518
$251$	18.1704	1.14690	0.573452	−	0.819239i	$-0.305604\pi$
$251$	18.1704	1.14690	0.573452	+	0.819239i	$0.305604\pi$
$252$	−2.12137	−0.133634
$253$	0.570551	0.0358702
$254$	19.7872	1.24156
$255$	−32.4965	−2.03501
$256$	1.00000	0.0625000
$257$	25.6006	1.59692	0.798461	−	0.602046i	$-0.205648\pi$
$257$	25.6006	1.59692	0.798461	+	0.602046i	$0.205648\pi$
$258$	12.0262	0.748716
$259$	2.16250	0.134371
$260$	3.81212	0.236417
$261$	−5.27044	−0.326232
$262$	−4.76810	−0.294574
$263$	15.0802	0.929882	0.464941	−	0.885342i	$-0.346076\pi$
$263$	15.0802	0.929882	0.464941	+	0.885342i	$0.346076\pi$
$264$	0.166796	0.0102656
$265$	41.5098	2.54993
$266$	11.5387	0.707482
$267$	12.1126	0.741277
$268$	−8.70756	−0.531899
$269$	24.3510	1.48471	0.742355	−	0.670007i	$-0.233709\pi$
$269$	24.3510	1.48471	0.742355	+	0.670007i	$0.233709\pi$
$270$	13.7432	0.836387
$271$	−0.982042	−0.0596548	−0.0298274	−	0.999555i	$-0.509496\pi$
$271$	−0.982042	−0.0596548	−0.0298274	+	0.999555i	$0.509496\pi$
$272$	5.46364	0.331282
$273$	7.27680	0.440412
$274$	−15.3109	−0.924964
$275$	−0.398474	−0.0240289
$276$	12.6200	0.759633
$277$	−3.94284	−0.236902	−0.118451	−	0.992960i	$-0.537793\pi$
$277$	−3.94284	−0.236902	−0.118451	+	0.992960i	$0.537793\pi$
$278$	18.4532	1.10675
$279$	−0.411450	−0.0246329
$280$	−9.52925	−0.569482
$281$	2.11191	0.125986	0.0629930	−	0.998014i	$-0.479935\pi$
$281$	2.11191	0.125986	0.0629930	+	0.998014i	$0.479935\pi$
$282$	10.3790	0.618062
$283$	1.00358	0.0596565	0.0298283	−	0.999555i	$-0.490504\pi$
$283$	1.00358	0.0596565	0.0298283	+	0.999555i	$0.490504\pi$
$284$	−1.88332	−0.111754
$285$	22.3014	1.32102
$286$	−0.106905	−0.00632141
$287$	−14.9516	−0.882566
$288$	0.689347	0.0406201
$289$	12.8514	0.755965
$290$	−23.6749	−1.39024
$291$	−14.7285	−0.863398
$292$	11.3462	0.663987
$293$	−29.2786	−1.71047	−0.855236	−	0.518239i	$-0.826588\pi$
$293$	−29.2786	−1.71047	−0.855236	+	0.518239i	$0.826588\pi$
$294$	−4.74464	−0.276713
$295$	−15.9488	−0.928575
$296$	−0.702711	−0.0408443
$297$	−0.385408	−0.0223636
$298$	−2.12820	−0.123283
$299$	−8.08853	−0.467772
$300$	−8.81381	−0.508866
$301$	19.2678	1.11058
$302$	−4.69400	−0.270109
$303$	−11.2481	−0.646186
$304$	−3.74953	−0.215050
$305$	−12.8406	−0.735250
$306$	3.76634	0.215308
$307$	−30.0391	−1.71442	−0.857210	−	0.514966i	$-0.827804\pi$
$307$	−30.0391	−1.71442	−0.857210	+	0.514966i	$0.827804\pi$
$308$	0.267233	0.0152270
$309$	37.3596	2.12531
$310$	−1.84824	−0.104973
$311$	−0.838753	−0.0475613	−0.0237806	−	0.999717i	$-0.507570\pi$
$311$	−0.838753	−0.0475613	−0.0237806	+	0.999717i	$0.507570\pi$
$312$	−2.36462	−0.133870
$313$	−25.1099	−1.41929	−0.709647	−	0.704558i	$-0.751145\pi$
$313$	−25.1099	−1.41929	−0.709647	+	0.704558i	$0.751145\pi$
$314$	−4.24205	−0.239393
$315$	−6.56896	−0.370119
$316$	−7.21356	−0.405794
$317$	−23.5696	−1.32380	−0.661901	−	0.749592i	$-0.730250\pi$
$317$	−23.5696	−1.32380	−0.661901	+	0.749592i	$0.730250\pi$
$318$	−25.7481	−1.44388
$319$	0.663927	0.0371727
$320$	3.09656	0.173103
$321$	−35.1405	−1.96135
$322$	20.2191	1.12677
$323$	−20.4861	−1.13988
$324$	−10.5928	−0.588491
$325$	5.64905	0.313353
$326$	0.946145	0.0524021
$327$	38.7978	2.14552
$328$	4.85857	0.268270
$329$	16.6288	0.916775
$330$	0.516494	0.0284321
$331$	−31.8993	−1.75334	−0.876672	−	0.481089i	$-0.840242\pi$
$331$	−31.8993	−1.75334	−0.876672	+	0.481089i	$0.840242\pi$
$332$	2.30311	0.126400
$333$	−0.484412	−0.0265456
$334$	16.2744	0.890493
$335$	−26.9635	−1.47317
$336$	5.91090	0.322466
$337$	−26.2190	−1.42824	−0.714120	−	0.700024i	$-0.753173\pi$
$337$	−26.2190	−1.42824	−0.714120	+	0.700024i	$0.753173\pi$
$338$	−11.4844	−0.624671
$339$	29.5963	1.60745
$340$	16.9185	0.917535
$341$	0.0518311	0.00280681
$342$	−2.58473	−0.139766
$343$	13.9399	0.752684
$344$	−6.26112	−0.337577
$345$	39.0785	2.10392
$346$	−21.7471	−1.16913
$347$	7.46521	0.400753	0.200377	−	0.979719i	$-0.435783\pi$
$347$	7.46521	0.400753	0.200377	+	0.979719i	$0.435783\pi$
$348$	14.6853	0.787216
$349$	−2.51923	−0.134851	−0.0674256	−	0.997724i	$-0.521479\pi$
$349$	−2.51923	−0.134851	−0.0674256	+	0.997724i	$0.521479\pi$
$350$	−14.1211	−0.754804
$351$	5.46381	0.291637
$352$	−0.0868382	−0.00462849
$353$	17.3573	0.923833	0.461917	−	0.886923i	$-0.347162\pi$
$353$	17.3573	0.923833	0.461917	+	0.886923i	$0.347162\pi$
$354$	9.89288	0.525801
$355$	−5.83181	−0.309520
$356$	−6.30610	−0.334223
$357$	32.2951	1.70924
$358$	−8.96135	−0.473622
$359$	36.4948	1.92612	0.963060	−	0.269286i	$-0.0867876\pi$
$359$	36.4948	1.92612	0.963060	+	0.269286i	$0.0867876\pi$
$360$	2.13460	0.112504
$361$	−4.94102	−0.260054
$362$	7.93227	0.416911
$363$	21.1140	1.10820
$364$	−3.78848	−0.198571
$365$	35.1342	1.83901
$366$	7.96489	0.416332
$367$	−10.9063	−0.569304	−0.284652	−	0.958631i	$-0.591878\pi$
$367$	−10.9063	−0.569304	−0.284652	+	0.958631i	$0.591878\pi$
$368$	−6.57027	−0.342499
$369$	3.34924	0.174355
$370$	−2.17599	−0.113124
$371$	−41.2525	−2.14172
$372$	1.14645	0.0594405
$373$	−34.0149	−1.76122	−0.880611	−	0.473839i	$-0.842868\pi$
$373$	−34.0149	−1.76122	−0.880611	+	0.473839i	$0.842868\pi$
$374$	−0.474453	−0.0245334
$375$	2.44636	0.126329
$376$	−5.40358	−0.278668
$377$	−9.41229	−0.484758
$378$	−13.6580	−0.702494
$379$	−31.7579	−1.63129	−0.815646	−	0.578551i	$-0.803618\pi$
$379$	−31.7579	−1.63129	−0.815646	+	0.578551i	$0.803618\pi$
$380$	−11.6107	−0.595614
$381$	−38.0065	−1.94713
$382$	−10.8672	−0.556014
$383$	16.1480	0.825122	0.412561	−	0.910930i	$-0.364634\pi$
$383$	16.1480	0.825122	0.412561	+	0.910930i	$0.364634\pi$
$384$	−1.92077	−0.0980187
$385$	0.827504	0.0421735
$386$	−13.4725	−0.685735
$387$	−4.31608	−0.219399
$388$	7.66801	0.389284
$389$	34.3674	1.74249	0.871247	−	0.490845i	$-0.163312\pi$
$389$	34.3674	1.74249	0.871247	+	0.490845i	$0.163312\pi$
$390$	−7.32219	−0.370773
$391$	−35.8976	−1.81542
$392$	2.47018	0.124763
$393$	9.15842	0.461981
$394$	−22.3555	−1.12625
$395$	−22.3372	−1.12391
$396$	−0.0598616	−0.00300816
$397$	−3.64407	−0.182891	−0.0914453	−	0.995810i	$-0.529149\pi$
$397$	−3.64407	−0.182891	−0.0914453	+	0.995810i	$0.529149\pi$
$398$	−15.6192	−0.782919
$399$	−22.1631	−1.10954
$400$	4.58869	0.229435
$401$	23.4469	1.17088	0.585442	−	0.810714i	$-0.300921\pi$
$401$	23.4469	1.17088	0.585442	+	0.810714i	$0.300921\pi$
$402$	16.7252	0.834177
$403$	−0.734794	−0.0366027
$404$	5.85604	0.291349
$405$	−32.8014	−1.62991
$406$	23.5282	1.16768
$407$	0.0610222	0.00302476
$408$	−10.4944	−0.519550
$409$	−15.8618	−0.784316	−0.392158	−	0.919898i	$-0.628271\pi$
$409$	−15.8618	−0.784316	−0.392158	+	0.919898i	$0.628271\pi$
$410$	15.0449	0.743013
$411$	29.4086	1.45062
$412$	−19.4504	−0.958251
$413$	15.8499	0.779924
$414$	−4.52920	−0.222598
$415$	7.13172	0.350082
$416$	1.23108	0.0603587
$417$	−35.4442	−1.73571
$418$	0.325603	0.0159257
$419$	−38.3568	−1.87385	−0.936927	−	0.349526i	$-0.886343\pi$
$419$	−38.3568	−1.87385	−0.936927	+	0.349526i	$0.886343\pi$
$420$	18.3035	0.893118
$421$	32.5351	1.58566	0.792831	−	0.609442i	$-0.208606\pi$
$421$	32.5351	1.58566	0.792831	+	0.609442i	$0.208606\pi$
$422$	14.8399	0.722397
$423$	−3.72494	−0.181113
$424$	13.4051	0.651011
$425$	25.0710	1.21612
$426$	3.61742	0.175264
$427$	12.7610	0.617548
$428$	18.2950	0.884325
$429$	0.205339	0.00991387
$430$	−19.3879	−0.934970
$431$	−10.8875	−0.524431	−0.262215	−	0.965009i	$-0.584453\pi$
$431$	−10.8875	−0.524431	−0.262215	+	0.965009i	$0.584453\pi$
$432$	4.43823	0.213534
$433$	−15.7157	−0.755251	−0.377625	−	0.925958i	$-0.623259\pi$
$433$	−15.7157	−0.755251	−0.377625	+	0.925958i	$0.623259\pi$
$434$	1.83679	0.0881686
$435$	45.4740	2.18031
$436$	−20.1991	−0.967361
$437$	24.6354	1.17847
$438$	−21.7934	−1.04133
$439$	13.7872	0.658025	0.329013	−	0.944326i	$-0.393284\pi$
$439$	13.7872	0.658025	0.329013	+	0.944326i	$0.393284\pi$
$440$	−0.268900	−0.0128193
$441$	1.70281	0.0810862
$442$	6.72618	0.319932
$443$	−27.8742	−1.32434	−0.662172	−	0.749352i	$-0.730365\pi$
$443$	−27.8742	−1.32434	−0.662172	+	0.749352i	$0.730365\pi$
$444$	1.34974	0.0640561
$445$	−19.5272	−0.925680
$446$	19.6674	0.931277
$447$	4.08778	0.193345
$448$	−3.07737	−0.145392
$449$	−14.2230	−0.671223	−0.335611	−	0.942001i	$-0.608943\pi$
$449$	−14.2230	−0.671223	−0.335611	+	0.942001i	$0.608943\pi$
$450$	3.16320	0.149115
$451$	−0.421910	−0.0198670
$452$	−15.4086	−0.724760
$453$	9.01608	0.423613
$454$	4.86018	0.228100
$455$	−11.7313	−0.549971
$456$	7.20198	0.337263
$457$	−40.0549	−1.87369	−0.936844	−	0.349747i	$-0.886268\pi$
$457$	−40.0549	−1.87369	−0.936844	+	0.349747i	$0.886268\pi$
$458$	−6.78352	−0.316973
$459$	24.2489	1.13184
$460$	−20.3453	−0.948602
$461$	25.7487	1.19923	0.599617	−	0.800287i	$-0.295320\pi$
$461$	25.7487	1.19923	0.599617	+	0.800287i	$0.295320\pi$
$462$	−0.513292	−0.0238805
$463$	−29.3136	−1.36232	−0.681159	−	0.732136i	$-0.738524\pi$
$463$	−29.3136	−1.36232	−0.681159	+	0.732136i	$0.738524\pi$
$464$	−7.64556	−0.354936
$465$	3.55005	0.164629
$466$	−27.2439	−1.26205
$467$	−23.9427	−1.10793	−0.553967	−	0.832539i	$-0.686887\pi$
$467$	−23.9427	−1.10793	−0.553967	+	0.832539i	$0.686887\pi$
$468$	0.848641	0.0392284
$469$	26.7963	1.23734
$470$	−16.7325	−0.771813
$471$	8.14798	0.375439
$472$	−5.15049	−0.237070
$473$	0.543705	0.0249996
$474$	13.8556	0.636407
$475$	−17.2054	−0.789440
$476$	−16.8136	−0.770652
$477$	9.24078	0.423106
$478$	12.1334	0.554970
$479$	31.2124	1.42613	0.713065	−	0.701098i	$-0.247306\pi$
$479$	31.2124	1.42613	0.713065	+	0.701098i	$0.247306\pi$
$480$	−5.94777	−0.271477
$481$	−0.865094	−0.0394449
$482$	8.41981	0.383512
$483$	−38.8363	−1.76711
$484$	−10.9925	−0.499657
$485$	23.7445	1.07818
$486$	7.03170	0.318964
$487$	−33.3702	−1.51215	−0.756074	−	0.654486i	$-0.772885\pi$
$487$	−33.3702	−1.51215	−0.756074	+	0.654486i	$0.772885\pi$
$488$	−4.14673	−0.187713
$489$	−1.81732	−0.0821823
$490$	7.64907	0.345550
$491$	3.48110	0.157100	0.0785499	−	0.996910i	$-0.474971\pi$
$491$	3.48110	0.157100	0.0785499	+	0.996910i	$0.474971\pi$
$492$	−9.33219	−0.420728
$493$	−41.7726	−1.88134
$494$	−4.61597	−0.207682
$495$	−0.185365	−0.00833155
$496$	−0.596870	−0.0268002
$497$	5.79566	0.259971
$498$	−4.42374	−0.198232
$499$	20.2119	0.904810	0.452405	−	0.891813i	$-0.350566\pi$
$499$	20.2119	0.904810	0.452405	+	0.891813i	$0.350566\pi$
$500$	−1.27364	−0.0569587
$501$	−31.2592	−1.39656
$502$	18.1704	0.810984
$503$	4.68984	0.209110	0.104555	−	0.994519i	$-0.466658\pi$
$503$	4.68984	0.209110	0.104555	+	0.994519i	$0.466658\pi$
$504$	−2.12137	−0.0944934
$505$	18.1336	0.806934
$506$	0.570551	0.0253641
$507$	22.0589	0.979672
$508$	19.7872	0.877914
$509$	22.8872	1.01446	0.507228	−	0.861812i	$-0.330670\pi$
$509$	22.8872	1.01446	0.507228	+	0.861812i	$0.330670\pi$
$510$	−32.4965	−1.43897
$511$	−34.9164	−1.54461
$512$	1.00000	0.0441942
$513$	−16.6413	−0.734730
$514$	25.6006	1.12919
$515$	−60.2292	−2.65402
$516$	12.0262	0.529422
$517$	0.469237	0.0206370
$518$	2.16250	0.0950148
$519$	41.7711	1.83355
$520$	3.81212	0.167172
$521$	−9.53723	−0.417834	−0.208917	−	0.977933i	$-0.566994\pi$
$521$	−9.53723	−0.417834	−0.208917	+	0.977933i	$0.566994\pi$
$522$	−5.27044	−0.230681
$523$	−5.79916	−0.253580	−0.126790	−	0.991930i	$-0.540467\pi$
$523$	−5.79916	−0.253580	−0.126790	+	0.991930i	$0.540467\pi$
$524$	−4.76810	−0.208296
$525$	27.1233	1.18376
$526$	15.0802	0.657526
$527$	−3.26108	−0.142055
$528$	0.166796	0.00725887
$529$	20.1685	0.876891
$530$	41.5098	1.80307
$531$	−3.55047	−0.154077
$532$	11.5387	0.500265
$533$	5.98129	0.259079
$534$	12.1126	0.524162
$535$	56.6517	2.44927
$536$	−8.70756	−0.376109
$537$	17.2127	0.742782
$538$	24.3510	1.04985
$539$	−0.214506	−0.00923943
$540$	13.7432	0.591415
$541$	−16.7935	−0.722010	−0.361005	−	0.932564i	$-0.617566\pi$
$541$	−16.7935	−0.722010	−0.361005	+	0.932564i	$0.617566\pi$
$542$	−0.982042	−0.0421823
$543$	−15.2360	−0.653841
$544$	5.46364	0.234252
$545$	−62.5477	−2.67925
$546$	7.27680	0.311418
$547$	−39.0011	−1.66756	−0.833782	−	0.552093i	$-0.813829\pi$
$547$	−39.0011	−1.66756	−0.833782	+	0.552093i	$0.813829\pi$
$548$	−15.3109	−0.654049
$549$	−2.85853	−0.121999
$550$	−0.398474	−0.0169910
$551$	28.6672	1.22127
$552$	12.6200	0.537141
$553$	22.1988	0.943987
$554$	−3.94284	−0.167515
$555$	4.17957	0.177413
$556$	18.4532	0.782589
$557$	33.9443	1.43827	0.719133	−	0.694872i	$-0.244539\pi$
$557$	33.9443	1.43827	0.719133	+	0.694872i	$0.244539\pi$
$558$	−0.411450	−0.0174181
$559$	−7.70794	−0.326011
$560$	−9.52925	−0.402684
$561$	0.911314	0.0384757
$562$	2.11191	0.0890856
$563$	−28.8983	−1.21792	−0.608959	−	0.793202i	$-0.708412\pi$
$563$	−28.8983	−1.21792	−0.608959	+	0.793202i	$0.708412\pi$
$564$	10.3790	0.437036
$565$	−47.7137	−2.00733
$566$	1.00358	0.0421835
$567$	32.5980	1.36899
$568$	−1.88332	−0.0790223
$569$	39.5839	1.65944	0.829721	−	0.558178i	$-0.188500\pi$
$569$	39.5839	1.65944	0.829721	+	0.558178i	$0.188500\pi$
$570$	22.3014	0.934101
$571$	33.9517	1.42084	0.710418	−	0.703780i	$-0.248506\pi$
$571$	33.9517	1.42084	0.710418	+	0.703780i	$0.248506\pi$
$572$	−0.106905	−0.00446992
$573$	20.8733	0.871996
$574$	−14.9516	−0.624068
$575$	−30.1490	−1.25730
$576$	0.689347	0.0287228
$577$	4.12321	0.171651	0.0858257	−	0.996310i	$-0.472647\pi$
$577$	4.12321	0.171651	0.0858257	+	0.996310i	$0.472647\pi$
$578$	12.8514	0.534548
$579$	25.8776	1.07544
$580$	−23.6749	−0.983048
$581$	−7.08751	−0.294040
$582$	−14.7285	−0.610514
$583$	−1.16408	−0.0482112
$584$	11.3462	0.469510
$585$	2.62787	0.108649
$586$	−29.2786	−1.20949
$587$	20.5507	0.848217	0.424109	−	0.905611i	$-0.360587\pi$
$587$	20.5507	0.848217	0.424109	+	0.905611i	$0.360587\pi$
$588$	−4.74464	−0.195666
$589$	2.23798	0.0922144
$590$	−15.9488	−0.656601
$591$	42.9396	1.76630
$592$	−0.702711	−0.0288813
$593$	31.7929	1.30558	0.652789	−	0.757540i	$-0.273599\pi$
$593$	31.7929	1.30558	0.652789	+	0.757540i	$0.273599\pi$
$594$	−0.385408	−0.0158135
$595$	−52.0644	−2.13443
$596$	−2.12820	−0.0871745
$597$	30.0008	1.22785
$598$	−8.08853	−0.330765
$599$	23.0785	0.942964	0.471482	−	0.881876i	$-0.343719\pi$
$599$	23.0785	0.942964	0.471482	+	0.881876i	$0.343719\pi$
$600$	−8.81381	−0.359822
$601$	25.6563	1.04654	0.523271	−	0.852166i	$-0.324711\pi$
$601$	25.6563	1.04654	0.523271	+	0.852166i	$0.324711\pi$
$602$	19.2678	0.785295
$603$	−6.00253	−0.244442
$604$	−4.69400	−0.190996
$605$	−34.0388	−1.38388
$606$	−11.2481	−0.456923
$607$	23.0522	0.935660	0.467830	−	0.883818i	$-0.345036\pi$
$607$	23.0522	0.935660	0.467830	+	0.883818i	$0.345036\pi$
$608$	−3.74953	−0.152064
$609$	−45.1921	−1.83128
$610$	−12.8406	−0.519900
$611$	−6.65224	−0.269121
$612$	3.76634	0.152245
$613$	18.2475	0.737011	0.368506	−	0.929626i	$-0.379870\pi$
$613$	18.2475	0.737011	0.368506	+	0.929626i	$0.379870\pi$
$614$	−30.0391	−1.21228
$615$	−28.8977	−1.16527
$616$	0.267233	0.0107671
$617$	15.8961	0.639954	0.319977	−	0.947425i	$-0.396325\pi$
$617$	15.8961	0.639954	0.319977	+	0.947425i	$0.396325\pi$
$618$	37.3596	1.50282
$619$	6.90958	0.277720	0.138860	−	0.990312i	$-0.455656\pi$
$619$	6.90958	0.277720	0.138860	+	0.990312i	$0.455656\pi$
$620$	−1.84824	−0.0742273
$621$	−29.1604	−1.17017
$622$	−0.838753	−0.0336309
$623$	19.4062	0.777493
$624$	−2.36462	−0.0946605
$625$	−26.8874	−1.07549
$626$	−25.1099	−1.00359
$627$	−0.625407	−0.0249763
$628$	−4.24205	−0.169276
$629$	−3.83936	−0.153085
$630$	−6.56896	−0.261714
$631$	−16.1979	−0.644828	−0.322414	−	0.946599i	$-0.604494\pi$
$631$	−16.1979	−0.644828	−0.322414	+	0.946599i	$0.604494\pi$
$632$	−7.21356	−0.286940
$633$	−28.5041	−1.13294
$634$	−23.5696	−0.936069
$635$	61.2722	2.43151
$636$	−25.7481	−1.02098
$637$	3.04099	0.120488
$638$	0.663927	0.0262851
$639$	−1.29826	−0.0513583
$640$	3.09656	0.122402
$641$	−24.8644	−0.982083	−0.491042	−	0.871136i	$-0.663384\pi$
$641$	−24.8644	−0.982083	−0.491042	+	0.871136i	$0.663384\pi$
$642$	−35.1405	−1.38689
$643$	−33.3717	−1.31605	−0.658025	−	0.752996i	$-0.728608\pi$
$643$	−33.3717	−1.31605	−0.658025	+	0.752996i	$0.728608\pi$
$644$	20.2191	0.796746
$645$	37.2397	1.46631
$646$	−20.4861	−0.806015
$647$	5.99364	0.235634	0.117817	−	0.993035i	$-0.462410\pi$
$647$	5.99364	0.235634	0.117817	+	0.993035i	$0.462410\pi$
$648$	−10.5928	−0.416126
$649$	0.447259	0.0175565
$650$	5.64905	0.221574
$651$	−3.52804	−0.138275
$652$	0.946145	0.0370539
$653$	47.7885	1.87011	0.935055	−	0.354503i	$-0.115350\pi$
$653$	47.7885	1.87011	0.935055	+	0.354503i	$0.115350\pi$
$654$	38.7978	1.51711
$655$	−14.7647	−0.576906
$656$	4.85857	0.189695
$657$	7.82147	0.305145
$658$	16.6288	0.648258
$659$	−15.7904	−0.615108	−0.307554	−	0.951531i	$-0.599510\pi$
$659$	−15.7904	−0.615108	−0.307554	+	0.951531i	$0.599510\pi$
$660$	0.516494	0.0201045
$661$	38.9596	1.51535	0.757677	−	0.652629i	$-0.226334\pi$
$661$	38.9596	1.51535	0.757677	+	0.652629i	$0.226334\pi$
$662$	−31.8993	−1.23980
$663$	−12.9194	−0.501749
$664$	2.30311	0.0893780
$665$	35.7302	1.38556
$666$	−0.484412	−0.0187706
$667$	50.2334	1.94504
$668$	16.2744	0.629674
$669$	−37.7764	−1.46052
$670$	−26.9635	−1.04169
$671$	0.360094	0.0139013
$672$	5.91090	0.228018
$673$	38.5825	1.48725	0.743623	−	0.668600i	$-0.233106\pi$
$673$	38.5825	1.48725	0.743623	+	0.668600i	$0.233106\pi$
$674$	−26.2190	−1.00992
$675$	20.3657	0.783875
$676$	−11.4844	−0.441709
$677$	−46.2289	−1.77672	−0.888361	−	0.459146i	$-0.848156\pi$
$677$	−46.2289	−1.77672	−0.888361	+	0.459146i	$0.848156\pi$
$678$	29.5963	1.13664
$679$	−23.5973	−0.905580
$680$	16.9185	0.648795
$681$	−9.33528	−0.357729
$682$	0.0518311	0.00198472
$683$	−22.0882	−0.845180	−0.422590	−	0.906321i	$-0.638879\pi$
$683$	−22.0882	−0.845180	−0.422590	+	0.906321i	$0.638879\pi$
$684$	−2.58473	−0.0988295
$685$	−47.4111	−1.81148
$686$	13.9399	0.532228
$687$	13.0296	0.497109
$688$	−6.26112	−0.238703
$689$	16.5028	0.628706
$690$	39.0785	1.48769
$691$	42.5120	1.61723	0.808617	−	0.588336i	$-0.200217\pi$
$691$	42.5120	1.61723	0.808617	+	0.588336i	$0.200217\pi$
$692$	−21.7471	−0.826700
$693$	0.184216	0.00699779
$694$	7.46521	0.283375
$695$	57.1414	2.16750
$696$	14.6853	0.556646
$697$	26.5455	1.00548
$698$	−2.51923	−0.0953543
$699$	52.3293	1.97927
$700$	−14.1211	−0.533727
$701$	35.6036	1.34473	0.672364	−	0.740221i	$-0.265279\pi$
$701$	35.6036	1.34473	0.672364	+	0.740221i	$0.265279\pi$
$702$	5.46381	0.206218
$703$	2.63484	0.0993748
$704$	−0.0868382	−0.00327284
$705$	32.1393	1.21043
$706$	17.3573	0.653249
$707$	−18.0212	−0.677756
$708$	9.89288	0.371797
$709$	−26.1287	−0.981285	−0.490643	−	0.871361i	$-0.663238\pi$
$709$	−26.1287	−0.981285	−0.490643	+	0.871361i	$0.663238\pi$
$710$	−5.83181	−0.218864
$711$	−4.97264	−0.186489
$712$	−6.30610	−0.236331
$713$	3.92160	0.146865
$714$	32.2951	1.20861
$715$	−0.331037	−0.0123801
$716$	−8.96135	−0.334901
$717$	−23.3055	−0.870359
$718$	36.4948	1.36197
$719$	37.2498	1.38918	0.694592	−	0.719404i	$-0.255585\pi$
$719$	37.2498	1.38918	0.694592	+	0.719404i	$0.255585\pi$
$720$	2.13460	0.0795520
$721$	59.8559	2.22915
$722$	−4.94102	−0.183886
$723$	−16.1725	−0.601462
$724$	7.93227	0.294800
$725$	−35.0831	−1.30295
$726$	21.1140	0.783612
$727$	21.5124	0.797852	0.398926	−	0.916983i	$-0.369383\pi$
$727$	21.5124	0.797852	0.398926	+	0.916983i	$0.369383\pi$
$728$	−3.78848	−0.140411
$729$	18.2723	0.676751
$730$	35.1342	1.30038
$731$	−34.2085	−1.26525
$732$	7.96489	0.294391
$733$	−5.05277	−0.186628	−0.0933142	−	0.995637i	$-0.529746\pi$
$733$	−5.05277	−0.186628	−0.0933142	+	0.995637i	$0.529746\pi$
$734$	−10.9063	−0.402559
$735$	−14.6921	−0.541925
$736$	−6.57027	−0.242183
$737$	0.756149	0.0278531
$738$	3.34924	0.123287
$739$	−7.82744	−0.287937	−0.143969	−	0.989582i	$-0.545986\pi$
$739$	−7.82744	−0.287937	−0.143969	+	0.989582i	$0.545986\pi$
$740$	−2.17599	−0.0799909
$741$	8.86621	0.325708
$742$	−41.2525	−1.51443
$743$	−6.42215	−0.235606	−0.117803	−	0.993037i	$-0.537585\pi$
$743$	−6.42215	−0.235606	−0.117803	+	0.993037i	$0.537585\pi$
$744$	1.14645	0.0420308
$745$	−6.59011	−0.241443
$746$	−34.0149	−1.24537
$747$	1.58764	0.0580887
$748$	−0.474453	−0.0173477
$749$	−56.3006	−2.05718
$750$	2.44636	0.0893284
$751$	37.0950	1.35362	0.676808	−	0.736159i	$-0.263363\pi$
$751$	37.0950	1.35362	0.676808	+	0.736159i	$0.263363\pi$
$752$	−5.40358	−0.197048
$753$	−34.9011	−1.27187
$754$	−9.41229	−0.342775
$755$	−14.5353	−0.528992
$756$	−13.6580	−0.496738
$757$	−15.3017	−0.556148	−0.278074	−	0.960560i	$-0.589696\pi$
$757$	−15.3017	−0.556148	−0.278074	+	0.960560i	$0.589696\pi$
$758$	−31.7579	−1.15350
$759$	−1.09590	−0.0397785
$760$	−11.6107	−0.421163
$761$	−4.34317	−0.157440	−0.0787199	−	0.996897i	$-0.525083\pi$
$761$	−4.34317	−0.157440	−0.0787199	+	0.996897i	$0.525083\pi$
$762$	−38.0065	−1.37683
$763$	62.1600	2.25034
$764$	−10.8672	−0.393161
$765$	11.6627	0.421666
$766$	16.1480	0.583450
$767$	−6.34066	−0.228948
$768$	−1.92077	−0.0693097
$769$	−18.4962	−0.666989	−0.333494	−	0.942752i	$-0.608228\pi$
$769$	−18.4962	−0.666989	−0.333494	+	0.942752i	$0.608228\pi$
$770$	0.827504	0.0298212
$771$	−49.1728	−1.77092
$772$	−13.4725	−0.484888
$773$	37.0953	1.33423	0.667113	−	0.744956i	$-0.267530\pi$
$773$	37.0953	1.33423	0.667113	+	0.744956i	$0.267530\pi$
$774$	−4.31608	−0.155138
$775$	−2.73885	−0.0983825
$776$	7.66801	0.275265
$777$	−4.15366	−0.149012
$778$	34.3674	1.23213
$779$	−18.2174	−0.652705
$780$	−7.32219	−0.262176
$781$	0.163544	0.00585207
$782$	−35.8976	−1.28370
$783$	−33.9327	−1.21266
$784$	2.47018	0.0882208
$785$	−13.1358	−0.468835
$786$	9.15842	0.326670
$787$	16.9449	0.604021	0.302010	−	0.953305i	$-0.402342\pi$
$787$	16.9449	0.604021	0.302010	+	0.953305i	$0.402342\pi$
$788$	−22.3555	−0.796381
$789$	−28.9655	−1.03120
$790$	−22.3372	−0.794723
$791$	47.4179	1.68599
$792$	−0.0598616	−0.00212709
$793$	−5.10495	−0.181282
$794$	−3.64407	−0.129323
$795$	−79.7307	−2.82776
$796$	−15.6192	−0.553607
$797$	8.92472	0.316130	0.158065	−	0.987429i	$-0.449474\pi$
$797$	8.92472	0.316130	0.158065	+	0.987429i	$0.449474\pi$
$798$	−22.1631	−0.784566
$799$	−29.5232	−1.04446
$800$	4.58869	0.162235
$801$	−4.34709	−0.153597
$802$	23.4469	0.827940
$803$	−0.985285	−0.0347700
$804$	16.7252	0.589852
$805$	62.6098	2.20671
$806$	−0.734794	−0.0258820
$807$	−46.7727	−1.64648
$808$	5.85604	0.206015
$809$	−25.8858	−0.910095	−0.455047	−	0.890467i	$-0.650378\pi$
$809$	−25.8858	−0.910095	−0.455047	+	0.890467i	$0.650378\pi$
$810$	−32.8014	−1.15252
$811$	−36.4203	−1.27889	−0.639445	−	0.768837i	$-0.720836\pi$
$811$	−36.4203	−1.27889	−0.639445	+	0.768837i	$0.720836\pi$
$812$	23.5282	0.825677
$813$	1.88627	0.0661546
$814$	0.0610222	0.00213883
$815$	2.92980	0.102626
$816$	−10.4944	−0.367377
$817$	23.4763	0.821331
$818$	−15.8618	−0.554595
$819$	−2.61158	−0.0912559
$820$	15.0449	0.525390
$821$	26.7190	0.932499	0.466250	−	0.884653i	$-0.345605\pi$
$821$	26.7190	0.932499	0.466250	+	0.884653i	$0.345605\pi$
$822$	29.4086	1.02574
$823$	−16.3123	−0.568611	−0.284306	−	0.958734i	$-0.591763\pi$
$823$	−16.3123	−0.568611	−0.284306	+	0.958734i	$0.591763\pi$
$824$	−19.4504	−0.677586
$825$	0.765376	0.0266470
$826$	15.8499	0.551489
$827$	23.9166	0.831663	0.415831	−	0.909442i	$-0.363491\pi$
$827$	23.9166	0.831663	0.415831	+	0.909442i	$0.363491\pi$
$828$	−4.52920	−0.157400
$829$	−44.0013	−1.52823	−0.764114	−	0.645082i	$-0.776823\pi$
$829$	−44.0013	−1.52823	−0.764114	+	0.645082i	$0.776823\pi$
$830$	7.13172	0.247546
$831$	7.57328	0.262714
$832$	1.23108	0.0426800
$833$	13.4962	0.467615
$834$	−35.4442	−1.22733
$835$	50.3945	1.74397
$836$	0.325603	0.0112612
$837$	−2.64904	−0.0915643
$838$	−38.3568	−1.32501
$839$	23.5514	0.813085	0.406542	−	0.913632i	$-0.366734\pi$
$839$	23.5514	0.813085	0.406542	+	0.913632i	$0.366734\pi$
$840$	18.3035	0.631530
$841$	29.4545	1.01567
$842$	32.5351	1.12123
$843$	−4.05649	−0.139713
$844$	14.8399	0.510812
$845$	−35.5623	−1.22338
$846$	−3.72494	−0.128066
$847$	33.8278	1.16234
$848$	13.4051	0.460334
$849$	−1.92764	−0.0661564
$850$	25.0710	0.859928
$851$	4.61701	0.158269
$852$	3.61742	0.123931
$853$	29.0352	0.994146	0.497073	−	0.867709i	$-0.334408\pi$
$853$	29.0352	0.994146	0.497073	+	0.867709i	$0.334408\pi$
$854$	12.7610	0.436672
$855$	−8.00376	−0.273723
$856$	18.2950	0.625312
$857$	−42.4326	−1.44947	−0.724735	−	0.689028i	$-0.758038\pi$
$857$	−42.4326	−1.44947	−0.724735	+	0.689028i	$0.758038\pi$
$858$	0.205339	0.00701017
$859$	−10.8638	−0.370667	−0.185333	−	0.982676i	$-0.559337\pi$
$859$	−10.8638	−0.370667	−0.185333	+	0.982676i	$0.559337\pi$
$860$	−19.3879	−0.661123
$861$	28.7186	0.978726
$862$	−10.8875	−0.370828
$863$	−46.6455	−1.58783	−0.793915	−	0.608028i	$-0.791961\pi$
$863$	−46.6455	−1.58783	−0.793915	+	0.608028i	$0.791961\pi$
$864$	4.43823	0.150992
$865$	−67.3412	−2.28967
$866$	−15.7157	−0.534043
$867$	−24.6846	−0.838331
$868$	1.83679	0.0623446
$869$	0.626413	0.0212496
$870$	45.4740	1.54171
$871$	−10.7197	−0.363223
$872$	−20.1991	−0.684028
$873$	5.28592	0.178901
$874$	24.6354	0.833306
$875$	3.91945	0.132501
$876$	−21.7934	−0.736332
$877$	−3.68041	−0.124279	−0.0621393	−	0.998067i	$-0.519792\pi$
$877$	−3.68041	−0.124279	−0.0621393	+	0.998067i	$0.519792\pi$
$878$	13.7872	0.465294
$879$	56.2373	1.89684
$880$	−0.268900	−0.00906462
$881$	14.5066	0.488741	0.244370	−	0.969682i	$-0.421419\pi$
$881$	14.5066	0.488741	0.244370	+	0.969682i	$0.421419\pi$
$882$	1.70281	0.0573366
$883$	−4.31157	−0.145096	−0.0725479	−	0.997365i	$-0.523113\pi$
$883$	−4.31157	−0.145096	−0.0725479	+	0.997365i	$0.523113\pi$
$884$	6.72618	0.226226
$885$	30.6339	1.02975
$886$	−27.8742	−0.936452
$887$	7.69966	0.258529	0.129265	−	0.991610i	$-0.458738\pi$
$887$	7.69966	0.258529	0.129265	+	0.991610i	$0.458738\pi$
$888$	1.34974	0.0452945
$889$	−60.8923	−2.04226
$890$	−19.5272	−0.654555
$891$	0.919864	0.0308166
$892$	19.6674	0.658512
$893$	20.2609	0.678005
$894$	4.08778	0.136716
$895$	−27.7494	−0.927559
$896$	−3.07737	−0.102808
$897$	15.5362	0.518738
$898$	−14.2230	−0.474626
$899$	4.56340	0.152198
$900$	3.16320	0.105440
$901$	73.2409	2.44001
$902$	−0.421910	−0.0140481
$903$	−37.0089	−1.23158
$904$	−15.4086	−0.512482
$905$	24.5627	0.816493
$906$	9.01608	0.299539
$907$	37.1909	1.23490	0.617452	−	0.786609i	$-0.288165\pi$
$907$	37.1909	1.23490	0.617452	+	0.786609i	$0.288165\pi$
$908$	4.86018	0.161291
$909$	4.03684	0.133894
$910$	−11.7313	−0.388888
$911$	24.0237	0.795939	0.397970	−	0.917399i	$-0.369715\pi$
$911$	24.0237	0.795939	0.397970	+	0.917399i	$0.369715\pi$
$912$	7.20198	0.238481
$913$	−0.199998	−0.00661897
$914$	−40.0549	−1.32490
$915$	24.6638	0.815360
$916$	−6.78352	−0.224134
$917$	14.6732	0.484552
$918$	24.2489	0.800333
$919$	8.16935	0.269482	0.134741	−	0.990881i	$-0.456980\pi$
$919$	8.16935	0.269482	0.134741	+	0.990881i	$0.456980\pi$
$920$	−20.3453	−0.670763
$921$	57.6981	1.90122
$922$	25.7487	0.847987
$923$	−2.31852	−0.0763149
$924$	−0.513292	−0.0168861
$925$	−3.22453	−0.106022
$926$	−29.3136	−0.963304
$927$	−13.4080	−0.440378
$928$	−7.64556	−0.250978
$929$	24.8952	0.816786	0.408393	−	0.912806i	$-0.366089\pi$
$929$	24.8952	0.816786	0.408393	+	0.912806i	$0.366089\pi$
$930$	3.55005	0.116411
$931$	−9.26202	−0.303550
$932$	−27.2439	−0.892405
$933$	1.61105	0.0527434
$934$	−23.9427	−0.783428
$935$	−1.46917	−0.0480471
$936$	0.848641	0.0277387
$937$	36.2269	1.18348	0.591740	−	0.806129i	$-0.298441\pi$
$937$	36.2269	1.18348	0.591740	+	0.806129i	$0.298441\pi$
$938$	26.7963	0.874931
$939$	48.2302	1.57393
$940$	−16.7325	−0.545755
$941$	−39.7401	−1.29549	−0.647744	−	0.761858i	$-0.724288\pi$
$941$	−39.7401	−1.29549	−0.647744	+	0.761858i	$0.724288\pi$
$942$	8.14798	0.265476
$943$	−31.9222	−1.03953
$944$	−5.15049	−0.167634
$945$	−42.2930	−1.37579
$946$	0.543705	0.0176774
$947$	38.1539	1.23983	0.619917	−	0.784667i	$-0.287166\pi$
$947$	38.1539	1.23983	0.619917	+	0.784667i	$0.287166\pi$
$948$	13.8556	0.450008
$949$	13.9681	0.453424
$950$	−17.2054	−0.558218
$951$	45.2717	1.46804
$952$	−16.8136	−0.544933
$953$	4.49069	0.145468	0.0727339	−	0.997351i	$-0.476828\pi$
$953$	4.49069	0.145468	0.0727339	+	0.997351i	$0.476828\pi$
$954$	9.24078	0.299181
$955$	−33.6509	−1.08892
$956$	12.1334	0.392423
$957$	−1.27525	−0.0412229
$958$	31.2124	1.00843
$959$	47.1172	1.52149
$960$	−5.94777	−0.191964
$961$	−30.6437	−0.988508
$962$	−0.865094	−0.0278917
$963$	12.6116	0.406404
$964$	8.41981	0.271184
$965$	−41.7186	−1.34297
$966$	−38.8363	−1.24954
$967$	−35.7548	−1.14980	−0.574898	−	0.818225i	$-0.694958\pi$
$967$	−35.7548	−1.14980	−0.574898	+	0.818225i	$0.694958\pi$
$968$	−10.9925	−0.353311
$969$	39.3490	1.26407
$970$	23.7445	0.762389
$971$	15.2131	0.488213	0.244106	−	0.969748i	$-0.421505\pi$
$971$	15.2131	0.488213	0.244106	+	0.969748i	$0.421505\pi$
$972$	7.03170	0.225542
$973$	−56.7871	−1.82051
$974$	−33.3702	−1.06925
$975$	−10.8505	−0.347494
$976$	−4.14673	−0.132733
$977$	−19.3840	−0.620150	−0.310075	−	0.950712i	$-0.600354\pi$
$977$	−19.3840	−0.620150	−0.310075	+	0.950712i	$0.600354\pi$
$978$	−1.81732	−0.0581116
$979$	0.547611	0.0175017
$980$	7.64907	0.244341
$981$	−13.9242	−0.444565
$982$	3.48110	0.111086
$983$	6.79339	0.216676	0.108338	−	0.994114i	$-0.465447\pi$
$983$	6.79339	0.216676	0.108338	+	0.994114i	$0.465447\pi$
$984$	−9.33219	−0.297499
$985$	−69.2251	−2.20569
$986$	−41.7726	−1.33031
$987$	−31.9400	−1.01666
$988$	−4.61597	−0.146854
$989$	41.1373	1.30809
$990$	−0.185365	−0.00589129
$991$	7.86384	0.249803	0.124902	−	0.992169i	$-0.460138\pi$
$991$	7.86384	0.249803	0.124902	+	0.992169i	$0.460138\pi$
$992$	−0.596870	−0.0189506
$993$	61.2711	1.94438
$994$	5.79566	0.183827
$995$	−48.3658	−1.53330
$996$	−4.42374	−0.140171
$997$	20.3390	0.644141	0.322071	−	0.946716i	$-0.395621\pi$
$997$	20.3390	0.644141	0.322071	+	0.946716i	$0.395621\pi$
$998$	20.2119	0.639797
$999$	−3.11879	−0.0986742

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6022.2.a.b.1.13	✓	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6022.2.a.b.1.13	✓	54	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:	\( N \)	\(=\)	\( 6022 = 2 \cdot 3011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6022.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.92077 q^{3} +1.00000 q^{4} +3.09656 q^{5} -1.92077 q^{6} -3.07737 q^{7} +1.00000 q^{8} +0.689347 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.92077 q^{3} +1.00000 q^{4} +3.09656 q^{5} -1.92077 q^{6} -3.07737 q^{7} +1.00000 q^{8} +0.689347 q^{9} +3.09656 q^{10} -0.0868382 q^{11} -1.92077 q^{12} +1.23108 q^{13} -3.07737 q^{14} -5.94777 q^{15} +1.00000 q^{16} +5.46364 q^{17} +0.689347 q^{18} -3.74953 q^{19} +3.09656 q^{20} +5.91090 q^{21} -0.0868382 q^{22} -6.57027 q^{23} -1.92077 q^{24} +4.58869 q^{25} +1.23108 q^{26} +4.43823 q^{27} -3.07737 q^{28} -7.64556 q^{29} -5.94777 q^{30} -0.596870 q^{31} +1.00000 q^{32} +0.166796 q^{33} +5.46364 q^{34} -9.52925 q^{35} +0.689347 q^{36} -0.702711 q^{37} -3.74953 q^{38} -2.36462 q^{39} +3.09656 q^{40} +4.85857 q^{41} +5.91090 q^{42} -6.26112 q^{43} -0.0868382 q^{44} +2.13460 q^{45} -6.57027 q^{46} -5.40358 q^{47} -1.92077 q^{48} +2.47018 q^{49} +4.58869 q^{50} -10.4944 q^{51} +1.23108 q^{52} +13.4051 q^{53} +4.43823 q^{54} -0.268900 q^{55} -3.07737 q^{56} +7.20198 q^{57} -7.64556 q^{58} -5.15049 q^{59} -5.94777 q^{60} -4.14673 q^{61} -0.596870 q^{62} -2.12137 q^{63} +1.00000 q^{64} +3.81212 q^{65} +0.166796 q^{66} -8.70756 q^{67} +5.46364 q^{68} +12.6200 q^{69} -9.52925 q^{70} -1.88332 q^{71} +0.689347 q^{72} +11.3462 q^{73} -0.702711 q^{74} -8.81381 q^{75} -3.74953 q^{76} +0.267233 q^{77} -2.36462 q^{78} -7.21356 q^{79} +3.09656 q^{80} -10.5928 q^{81} +4.85857 q^{82} +2.30311 q^{83} +5.91090 q^{84} +16.9185 q^{85} -6.26112 q^{86} +14.6853 q^{87} -0.0868382 q^{88} -6.30610 q^{89} +2.13460 q^{90} -3.78848 q^{91} -6.57027 q^{92} +1.14645 q^{93} -5.40358 q^{94} -11.6107 q^{95} -1.92077 q^{96} +7.66801 q^{97} +2.47018 q^{98} -0.0598616 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 54 q^{2} - 22 q^{3} + 54 q^{4} - 14 q^{5} - 22 q^{6} - 20 q^{7} + 54 q^{8} + 32 q^{9}+O(q^{10}) \) 54 * q + 54 * q^2 - 22 * q^3 + 54 * q^4 - 14 * q^5 - 22 * q^6 - 20 * q^7 + 54 * q^8 + 32 * q^9	\( 54 q + 54 q^{2} - 22 q^{3} + 54 q^{4} - 14 q^{5} - 22 q^{6} - 20 q^{7} + 54 q^{8} + 32 q^{9} - 14 q^{10} - 22 q^{11} - 22 q^{12} - 24 q^{13} - 20 q^{14} - 32 q^{15} + 54 q^{16} - 67 q^{17} + 32 q^{18} - 54 q^{19} - 14 q^{20} - 18 q^{21} - 22 q^{22} - 52 q^{23} - 22 q^{24} + 20 q^{25} - 24 q^{26} - 82 q^{27} - 20 q^{28} - 30 q^{29} - 32 q^{30} - 78 q^{31} + 54 q^{32} - 48 q^{33} - 67 q^{34} - 71 q^{35} + 32 q^{36} - 15 q^{37} - 54 q^{38} - 39 q^{39} - 14 q^{40} - 61 q^{41} - 18 q^{42} - 53 q^{43} - 22 q^{44} - 14 q^{45} - 52 q^{46} - 96 q^{47} - 22 q^{48} + 6 q^{49} + 20 q^{50} - 13 q^{51} - 24 q^{52} - 39 q^{53} - 82 q^{54} - 75 q^{55} - 20 q^{56} - 17 q^{57} - 30 q^{58} - 78 q^{59} - 32 q^{60} - 23 q^{61} - 78 q^{62} - 52 q^{63} + 54 q^{64} - 43 q^{65} - 48 q^{66} - 54 q^{67} - 67 q^{68} + 7 q^{69} - 71 q^{70} - 41 q^{71} + 32 q^{72} - 62 q^{73} - 15 q^{74} - 81 q^{75} - 54 q^{76} - 85 q^{77} - 39 q^{78} - 45 q^{79} - 14 q^{80} + 22 q^{81} - 61 q^{82} - 117 q^{83} - 18 q^{84} - 53 q^{86} - 84 q^{87} - 22 q^{88} - 60 q^{89} - 14 q^{90} - 60 q^{91} - 52 q^{92} + 26 q^{93} - 96 q^{94} - 44 q^{95} - 22 q^{96} - 48 q^{97} + 6 q^{98} + 7 q^{99}+O(q^{100}) \) 54 * q + 54 * q^2 - 22 * q^3 + 54 * q^4 - 14 * q^5 - 22 * q^6 - 20 * q^7 + 54 * q^8 + 32 * q^9 - 14 * q^10 - 22 * q^11 - 22 * q^12 - 24 * q^13 - 20 * q^14 - 32 * q^15 + 54 * q^16 - 67 * q^17 + 32 * q^18 - 54 * q^19 - 14 * q^20 - 18 * q^21 - 22 * q^22 - 52 * q^23 - 22 * q^24 + 20 * q^25 - 24 * q^26 - 82 * q^27 - 20 * q^28 - 30 * q^29 - 32 * q^30 - 78 * q^31 + 54 * q^32 - 48 * q^33 - 67 * q^34 - 71 * q^35 + 32 * q^36 - 15 * q^37 - 54 * q^38 - 39 * q^39 - 14 * q^40 - 61 * q^41 - 18 * q^42 - 53 * q^43 - 22 * q^44 - 14 * q^45 - 52 * q^46 - 96 * q^47 - 22 * q^48 + 6 * q^49 + 20 * q^50 - 13 * q^51 - 24 * q^52 - 39 * q^53 - 82 * q^54 - 75 * q^55 - 20 * q^56 - 17 * q^57 - 30 * q^58 - 78 * q^59 - 32 * q^60 - 23 * q^61 - 78 * q^62 - 52 * q^63 + 54 * q^64 - 43 * q^65 - 48 * q^66 - 54 * q^67 - 67 * q^68 + 7 * q^69 - 71 * q^70 - 41 * q^71 + 32 * q^72 - 62 * q^73 - 15 * q^74 - 81 * q^75 - 54 * q^76 - 85 * q^77 - 39 * q^78 - 45 * q^79 - 14 * q^80 + 22 * q^81 - 61 * q^82 - 117 * q^83 - 18 * q^84 - 53 * q^86 - 84 * q^87 - 22 * q^88 - 60 * q^89 - 14 * q^90 - 60 * q^91 - 52 * q^92 + 26 * q^93 - 96 * q^94 - 44 * q^95 - 22 * q^96 - 48 * q^97 + 6 * q^98 + 7 * q^99

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