LMFDB - Embedded newform 6014.2.a.j.1.12

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:	$0$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
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)

$f(q)$	$=$	$q-1.00000 q^{2} -0.848161 q^{3} +1.00000 q^{4} +4.13342 q^{5} +0.848161 q^{6} +1.58594 q^{7} -1.00000 q^{8} -2.28062 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.848161 q^{3} +1.00000 q^{4} +4.13342 q^{5} +0.848161 q^{6} +1.58594 q^{7} -1.00000 q^{8} -2.28062 q^{9} -4.13342 q^{10} +5.98433 q^{11} -0.848161 q^{12} +0.0719775 q^{13} -1.58594 q^{14} -3.50580 q^{15} +1.00000 q^{16} +4.53899 q^{17} +2.28062 q^{18} +5.29995 q^{19} +4.13342 q^{20} -1.34514 q^{21} -5.98433 q^{22} +2.66042 q^{23} +0.848161 q^{24} +12.0851 q^{25} -0.0719775 q^{26} +4.47882 q^{27} +1.58594 q^{28} +7.48980 q^{29} +3.50580 q^{30} -1.00000 q^{31} -1.00000 q^{32} -5.07568 q^{33} -4.53899 q^{34} +6.55537 q^{35} -2.28062 q^{36} -5.22661 q^{37} -5.29995 q^{38} -0.0610485 q^{39} -4.13342 q^{40} +11.5851 q^{41} +1.34514 q^{42} -6.07160 q^{43} +5.98433 q^{44} -9.42677 q^{45} -2.66042 q^{46} +0.00414143 q^{47} -0.848161 q^{48} -4.48478 q^{49} -12.0851 q^{50} -3.84979 q^{51} +0.0719775 q^{52} -0.527092 q^{53} -4.47882 q^{54} +24.7358 q^{55} -1.58594 q^{56} -4.49521 q^{57} -7.48980 q^{58} -8.17090 q^{59} -3.50580 q^{60} -2.13023 q^{61} +1.00000 q^{62} -3.61694 q^{63} +1.00000 q^{64} +0.297513 q^{65} +5.07568 q^{66} -8.75308 q^{67} +4.53899 q^{68} -2.25646 q^{69} -6.55537 q^{70} +10.7912 q^{71} +2.28062 q^{72} -13.8762 q^{73} +5.22661 q^{74} -10.2502 q^{75} +5.29995 q^{76} +9.49082 q^{77} +0.0610485 q^{78} +13.0554 q^{79} +4.13342 q^{80} +3.04311 q^{81} -11.5851 q^{82} -4.79927 q^{83} -1.34514 q^{84} +18.7615 q^{85} +6.07160 q^{86} -6.35255 q^{87} -5.98433 q^{88} -6.54419 q^{89} +9.42677 q^{90} +0.114152 q^{91} +2.66042 q^{92} +0.848161 q^{93} -0.00414143 q^{94} +21.9069 q^{95} +0.848161 q^{96} +1.00000 q^{97} +4.48478 q^{98} -13.6480 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 32 q^{2} - 2 q^{3} + 32 q^{4} + 2 q^{6} + 5 q^{7} - 32 q^{8} + 30 q^{9}+O(q^{10}) $ 32 * q - 32 * q^2 - 2 * q^3 + 32 * q^4 + 2 * q^6 + 5 * q^7 - 32 * q^8 + 30 * q^9	\( 32 q - 32 q^{2} - 2 q^{3} + 32 q^{4} + 2 q^{6} + 5 q^{7} - 32 q^{8} + 30 q^{9} - 4 q^{11} - 2 q^{12} + 10 q^{13} - 5 q^{14} - q^{15} + 32 q^{16} + 14 q^{17} - 30 q^{18} + 33 q^{19} + 4 q^{22} - 2 q^{23} + 2 q^{24} + 46 q^{25} - 10 q^{26} - 5 q^{27} + 5 q^{28} - q^{29} + q^{30} - 32 q^{31} - 32 q^{32} + 32 q^{33} - 14 q^{34} + 8 q^{35} + 30 q^{36} + 31 q^{37} - 33 q^{38} + 4 q^{39} + 31 q^{41} + 15 q^{43} - 4 q^{44} + q^{45} + 2 q^{46} - 14 q^{47} - 2 q^{48} + 75 q^{49} - 46 q^{50} + 27 q^{51} + 10 q^{52} - 31 q^{53} + 5 q^{54} + 14 q^{55} - 5 q^{56} + 51 q^{57} + q^{58} - 8 q^{59} - q^{60} + 24 q^{61} + 32 q^{62} + 23 q^{63} + 32 q^{64} + 20 q^{65} - 32 q^{66} + 17 q^{67} + 14 q^{68} - 31 q^{69} - 8 q^{70} - 31 q^{71} - 30 q^{72} + 19 q^{73} - 31 q^{74} - 40 q^{75} + 33 q^{76} + 8 q^{77} - 4 q^{78} + 39 q^{79} + 116 q^{81} - 31 q^{82} - 6 q^{83} + 56 q^{85} - 15 q^{86} - 17 q^{87} + 4 q^{88} + 8 q^{89} - q^{90} + 34 q^{91} - 2 q^{92} + 2 q^{93} + 14 q^{94} - 22 q^{95} + 2 q^{96} + 32 q^{97} - 75 q^{98} - 27 q^{99}+O(q^{100}) \) 32 * q - 32 * q^2 - 2 * q^3 + 32 * q^4 + 2 * q^6 + 5 * q^7 - 32 * q^8 + 30 * q^9 - 4 * q^11 - 2 * q^12 + 10 * q^13 - 5 * q^14 - q^15 + 32 * q^16 + 14 * q^17 - 30 * q^18 + 33 * q^19 + 4 * q^22 - 2 * q^23 + 2 * q^24 + 46 * q^25 - 10 * q^26 - 5 * q^27 + 5 * q^28 - q^29 + q^30 - 32 * q^31 - 32 * q^32 + 32 * q^33 - 14 * q^34 + 8 * q^35 + 30 * q^36 + 31 * q^37 - 33 * q^38 + 4 * q^39 + 31 * q^41 + 15 * q^43 - 4 * q^44 + q^45 + 2 * q^46 - 14 * q^47 - 2 * q^48 + 75 * q^49 - 46 * q^50 + 27 * q^51 + 10 * q^52 - 31 * q^53 + 5 * q^54 + 14 * q^55 - 5 * q^56 + 51 * q^57 + q^58 - 8 * q^59 - q^60 + 24 * q^61 + 32 * q^62 + 23 * q^63 + 32 * q^64 + 20 * q^65 - 32 * q^66 + 17 * q^67 + 14 * q^68 - 31 * q^69 - 8 * q^70 - 31 * q^71 - 30 * q^72 + 19 * q^73 - 31 * q^74 - 40 * q^75 + 33 * q^76 + 8 * q^77 - 4 * q^78 + 39 * q^79 + 116 * q^81 - 31 * q^82 - 6 * q^83 + 56 * q^85 - 15 * q^86 - 17 * q^87 + 4 * q^88 + 8 * q^89 - q^90 + 34 * q^91 - 2 * q^92 + 2 * q^93 + 14 * q^94 - 22 * q^95 + 2 * q^96 + 32 * q^97 - 75 * q^98 - 27 * 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
$3$	−0.848161	−0.489686	−0.244843	−	0.969563i	$-0.578736\pi$
$3$	−0.848161	−0.489686	−0.244843	+	0.969563i	$0.578736\pi$
$4$	1.00000	0.500000
$5$	4.13342	1.84852	0.924260	−	0.381762i	$-0.124683\pi$
$5$	4.13342	1.84852	0.924260	+	0.381762i	$0.124683\pi$
$6$	0.848161	0.346260
$7$	1.58594	0.599430	0.299715	−	0.954029i	$-0.403108\pi$
$7$	1.58594	0.599430	0.299715	+	0.954029i	$0.403108\pi$
$8$	−1.00000	−0.353553
$9$	−2.28062	−0.760208
$10$	−4.13342	−1.30710
$11$	5.98433	1.80434	0.902172	−	0.431376i	$-0.141972\pi$
$11$	5.98433	1.80434	0.902172	+	0.431376i	$0.141972\pi$
$12$	−0.848161	−0.244843
$13$	0.0719775	0.0199630	0.00998148	−	0.999950i	$-0.496823\pi$
$13$	0.0719775	0.0199630	0.00998148	+	0.999950i	$0.496823\pi$
$14$	−1.58594	−0.423861
$15$	−3.50580	−0.905195
$16$	1.00000	0.250000
$17$	4.53899	1.10087	0.550433	−	0.834879i	$-0.314463\pi$
$17$	4.53899	1.10087	0.550433	+	0.834879i	$0.314463\pi$
$18$	2.28062	0.537548
$19$	5.29995	1.21589	0.607946	−	0.793979i	$-0.291994\pi$
$19$	5.29995	1.21589	0.607946	+	0.793979i	$0.291994\pi$
$20$	4.13342	0.924260
$21$	−1.34514	−0.293533
$22$	−5.98433	−1.27586
$23$	2.66042	0.554735	0.277367	−	0.960764i	$-0.410538\pi$
$23$	2.66042	0.554735	0.277367	+	0.960764i	$0.410538\pi$
$24$	0.848161	0.173130
$25$	12.0851	2.41703
$26$	−0.0719775	−0.0141159
$27$	4.47882	0.861949
$28$	1.58594	0.299715
$29$	7.48980	1.39082	0.695410	−	0.718613i	$-0.255223\pi$
$29$	7.48980	1.39082	0.695410	+	0.718613i	$0.255223\pi$
$30$	3.50580	0.640069
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−1.00000	−0.176777
$33$	−5.07568	−0.883562
$34$	−4.53899	−0.778430
$35$	6.55537	1.10806
$36$	−2.28062	−0.380104
$37$	−5.22661	−0.859249	−0.429625	−	0.903008i	$-0.641354\pi$
$37$	−5.22661	−0.859249	−0.429625	+	0.903008i	$0.641354\pi$
$38$	−5.29995	−0.859765
$39$	−0.0610485	−0.00977558
$40$	−4.13342	−0.653551
$41$	11.5851	1.80929	0.904647	−	0.426161i	$-0.140134\pi$
$41$	11.5851	1.80929	0.904647	+	0.426161i	$0.140134\pi$
$42$	1.34514	0.207559
$43$	−6.07160	−0.925910	−0.462955	−	0.886382i	$-0.653211\pi$
$43$	−6.07160	−0.925910	−0.462955	+	0.886382i	$0.653211\pi$
$44$	5.98433	0.902172
$45$	−9.42677	−1.40526
$46$	−2.66042	−0.392257
$47$	0.00414143	0.000604090 0	0.000302045	−	1.00000i	$-0.499904\pi$
$47$	0.00414143	0.000604090 0	0.000302045		1.00000i	$0.499904\pi$
$48$	−0.848161	−0.122421
$49$	−4.48478	−0.640683
$50$	−12.0851	−1.70910
$51$	−3.84979	−0.539079
$52$	0.0719775	0.00998148
$53$	−0.527092	−0.0724016	−0.0362008	−	0.999345i	$-0.511526\pi$
$53$	−0.527092	−0.0724016	−0.0362008	+	0.999345i	$0.511526\pi$
$54$	−4.47882	−0.609490
$55$	24.7358	3.33537
$56$	−1.58594	−0.211931
$57$	−4.49521	−0.595405
$58$	−7.48980	−0.983459
$59$	−8.17090	−1.06376	−0.531880	−	0.846820i	$-0.678514\pi$
$59$	−8.17090	−1.06376	−0.531880	+	0.846820i	$0.678514\pi$
$60$	−3.50580	−0.452597
$61$	−2.13023	−0.272749	−0.136374	−	0.990657i	$-0.543545\pi$
$61$	−2.13023	−0.272749	−0.136374	+	0.990657i	$0.543545\pi$
$62$	1.00000	0.127000
$63$	−3.61694	−0.455692
$64$	1.00000	0.125000
$65$	0.297513	0.0369019
$66$	5.07568	0.624773
$67$	−8.75308	−1.06936	−0.534680	−	0.845055i	$-0.679568\pi$
$67$	−8.75308	−1.06936	−0.534680	+	0.845055i	$0.679568\pi$
$68$	4.53899	0.550433
$69$	−2.25646	−0.271646
$70$	−6.55537	−0.783516
$71$	10.7912	1.28068	0.640340	−	0.768092i	$-0.278794\pi$
$71$	10.7912	1.28068	0.640340	+	0.768092i	$0.278794\pi$
$72$	2.28062	0.268774
$73$	−13.8762	−1.62409	−0.812044	−	0.583596i	$-0.801645\pi$
$73$	−13.8762	−1.62409	−0.812044	+	0.583596i	$0.801645\pi$
$74$	5.22661	0.607581
$75$	−10.2502	−1.18359
$76$	5.29995	0.607946
$77$	9.49082	1.08158
$78$	0.0610485	0.00691238
$79$	13.0554	1.46884	0.734422	−	0.678694i	$-0.237454\pi$
$79$	13.0554	1.46884	0.734422	+	0.678694i	$0.237454\pi$
$80$	4.13342	0.462130
$81$	3.04311	0.338123
$82$	−11.5851	−1.27936
$83$	−4.79927	−0.526789	−0.263394	−	0.964688i	$-0.584842\pi$
$83$	−4.79927	−0.526789	−0.263394	+	0.964688i	$0.584842\pi$
$84$	−1.34514	−0.146766
$85$	18.7615	2.03497
$86$	6.07160	0.654717
$87$	−6.35255	−0.681065
$88$	−5.98433	−0.637932
$89$	−6.54419	−0.693683	−0.346842	−	0.937924i	$-0.612746\pi$
$89$	−6.54419	−0.693683	−0.346842	+	0.937924i	$0.612746\pi$
$90$	9.42677	0.993669
$91$	0.114152	0.0119664
$92$	2.66042	0.277367
$93$	0.848161	0.0879502
$94$	−0.00414143	−0.000427156 0
$95$	21.9069	2.24760
$96$	0.848161	0.0865651
$97$	1.00000	0.101535
$97$	1.00000	0.101535
$98$	4.48478	0.453031
$99$	−13.6480	−1.37168
$100$	12.0851	1.20851
$101$	14.6973	1.46243	0.731216	−	0.682146i	$-0.238953\pi$
$101$	14.6973	1.46243	0.731216	+	0.682146i	$0.238953\pi$
$102$	3.84979	0.381186
$103$	−14.7637	−1.45471	−0.727356	−	0.686261i	$-0.759251\pi$
$103$	−14.7637	−1.45471	−0.727356	+	0.686261i	$0.759251\pi$
$104$	−0.0719775	−0.00705797
$105$	−5.56001	−0.542601
$106$	0.527092	0.0511957
$107$	7.56826	0.731652	0.365826	−	0.930683i	$-0.380787\pi$
$107$	7.56826	0.731652	0.365826	+	0.930683i	$0.380787\pi$
$108$	4.47882	0.430974
$109$	−18.7671	−1.79756	−0.898781	−	0.438398i	$-0.855546\pi$
$109$	−18.7671	−1.79756	−0.898781	+	0.438398i	$0.855546\pi$
$110$	−24.7358	−2.35846
$111$	4.43301	0.420762
$112$	1.58594	0.149858
$113$	−17.9926	−1.69260	−0.846301	−	0.532705i	$-0.821176\pi$
$113$	−17.9926	−1.69260	−0.846301	+	0.532705i	$0.821176\pi$
$114$	4.49521	0.421015
$115$	10.9966	1.02544
$116$	7.48980	0.695410
$117$	−0.164153	−0.0151760
$118$	8.17090	0.752192
$119$	7.19858	0.659893
$120$	3.50580	0.320035
$121$	24.8122	2.25566
$122$	2.13023	0.192862
$123$	−9.82606	−0.885986
$124$	−1.00000	−0.0898027
$125$	29.2859	2.61941
$126$	3.61694	0.322223
$127$	−2.23409	−0.198243	−0.0991216	−	0.995075i	$-0.531603\pi$
$127$	−2.23409	−0.198243	−0.0991216	+	0.995075i	$0.531603\pi$
$128$	−1.00000	−0.0883883
$129$	5.14969	0.453405
$130$	−0.297513	−0.0260936
$131$	−9.57707	−0.836753	−0.418376	−	0.908274i	$-0.637401\pi$
$131$	−9.57707	−0.836753	−0.418376	+	0.908274i	$0.637401\pi$
$132$	−5.07568	−0.441781
$133$	8.40542	0.728842
$134$	8.75308	0.756151
$135$	18.5128	1.59333
$136$	−4.53899	−0.389215
$137$	3.96331	0.338608	0.169304	−	0.985564i	$-0.445848\pi$
$137$	3.96331	0.338608	0.169304	+	0.985564i	$0.445848\pi$
$138$	2.25646	0.192083
$139$	9.82275	0.833154	0.416577	−	0.909100i	$-0.363230\pi$
$139$	9.82275	0.833154	0.416577	+	0.909100i	$0.363230\pi$
$140$	6.55537	0.554030
$141$	−0.00351260	−0.000295814 0
$142$	−10.7912	−0.905577
$143$	0.430737	0.0360200
$144$	−2.28062	−0.190052
$145$	30.9585	2.57096
$146$	13.8762	1.14840
$147$	3.80382	0.313734
$148$	−5.22661	−0.429625
$149$	−9.47469	−0.776197	−0.388099	−	0.921618i	$-0.626868\pi$
$149$	−9.47469	−0.776197	−0.388099	+	0.921618i	$0.626868\pi$
$150$	10.2502	0.836921
$151$	−5.40567	−0.439907	−0.219953	−	0.975510i	$-0.570591\pi$
$151$	−5.40567	−0.439907	−0.219953	+	0.975510i	$0.570591\pi$
$152$	−5.29995	−0.429882
$153$	−10.3517	−0.836887
$154$	−9.49082	−0.764792
$155$	−4.13342	−0.332004
$156$	−0.0610485	−0.00488779
$157$	−3.18543	−0.254225	−0.127112	−	0.991888i	$-0.540571\pi$
$157$	−3.18543	−0.254225	−0.127112	+	0.991888i	$0.540571\pi$
$158$	−13.0554	−1.03863
$159$	0.447059	0.0354540
$160$	−4.13342	−0.326775
$161$	4.21927	0.332525
$162$	−3.04311	−0.239089
$163$	−10.5913	−0.829572	−0.414786	−	0.909919i	$-0.636144\pi$
$163$	−10.5913	−0.829572	−0.414786	+	0.909919i	$0.636144\pi$
$164$	11.5851	0.904647
$165$	−20.9799	−1.63328
$166$	4.79927	0.372496
$167$	−7.33832	−0.567856	−0.283928	−	0.958846i	$-0.591638\pi$
$167$	−7.33832	−0.567856	−0.283928	+	0.958846i	$0.591638\pi$
$168$	1.34514	0.103779
$169$	−12.9948	−0.999601
$170$	−18.7615	−1.43894
$171$	−12.0872	−0.924330
$172$	−6.07160	−0.462955
$173$	3.27946	0.249333	0.124666	−	0.992199i	$-0.460214\pi$
$173$	3.27946	0.249333	0.124666	+	0.992199i	$0.460214\pi$
$174$	6.35255	0.481586
$175$	19.1664	1.44884
$176$	5.98433	0.451086
$177$	6.93024	0.520908
$178$	6.54419	0.490508
$179$	−20.0943	−1.50192	−0.750959	−	0.660349i	$-0.770408\pi$
$179$	−20.0943	−1.50192	−0.750959	+	0.660349i	$0.770408\pi$
$180$	−9.42677	−0.702630
$181$	0.706111	0.0524848	0.0262424	−	0.999656i	$-0.491646\pi$
$181$	0.706111	0.0524848	0.0262424	+	0.999656i	$0.491646\pi$
$182$	−0.114152	−0.00846152
$183$	1.80678	0.133561
$184$	−2.66042	−0.196128
$185$	−21.6038	−1.58834
$186$	−0.848161	−0.0621902
$187$	27.1628	1.98634
$188$	0.00414143	0.000302045 0
$189$	7.10315	0.516678
$190$	−21.9069	−1.58929
$191$	−14.2225	−1.02911	−0.514553	−	0.857458i	$-0.672042\pi$
$191$	−14.2225	−1.02911	−0.514553	+	0.857458i	$0.672042\pi$
$192$	−0.848161	−0.0612107
$193$	−6.10206	−0.439236	−0.219618	−	0.975586i	$-0.570481\pi$
$193$	−6.10206	−0.439236	−0.219618	+	0.975586i	$0.570481\pi$
$194$	−1.00000	−0.0717958
$195$	−0.252339	−0.0180704
$196$	−4.48478	−0.320342
$197$	−17.7015	−1.26118	−0.630591	−	0.776115i	$-0.717187\pi$
$197$	−17.7015	−1.26118	−0.630591	+	0.776115i	$0.717187\pi$
$198$	13.6480	0.969922
$199$	−16.8972	−1.19781	−0.598905	−	0.800820i	$-0.704397\pi$
$199$	−16.8972	−1.19781	−0.598905	+	0.800820i	$0.704397\pi$
$200$	−12.0851	−0.854549
$201$	7.42402	0.523650
$202$	−14.6973	−1.03410
$203$	11.8784	0.833700
$204$	−3.84979	−0.269539
$205$	47.8862	3.34452
$206$	14.7637	1.02864
$207$	−6.06740	−0.421714
$208$	0.0719775	0.00499074
$209$	31.7167	2.19389
$210$	5.56001	0.383677
$211$	−19.5432	−1.34541	−0.672703	−	0.739912i	$-0.734867\pi$
$211$	−19.5432	−1.34541	−0.672703	+	0.739912i	$0.734867\pi$
$212$	−0.527092	−0.0362008
$213$	−9.15267	−0.627131
$214$	−7.56826	−0.517356
$215$	−25.0964	−1.71156
$216$	−4.47882	−0.304745
$217$	−1.58594	−0.107661
$218$	18.7671	1.27107
$219$	11.7693	0.795293
$220$	24.7358	1.66768
$221$	0.326705	0.0219765
$222$	−4.43301	−0.297524
$223$	5.12265	0.343038	0.171519	−	0.985181i	$-0.445133\pi$
$223$	5.12265	0.343038	0.171519	+	0.985181i	$0.445133\pi$
$224$	−1.58594	−0.105965
$225$	−27.5617	−1.83744
$226$	17.9926	1.19685
$227$	13.5936	0.902239	0.451119	−	0.892464i	$-0.351025\pi$
$227$	13.5936	0.902239	0.451119	+	0.892464i	$0.351025\pi$
$228$	−4.49521	−0.297702
$229$	9.69085	0.640390	0.320195	−	0.947352i	$-0.396252\pi$
$229$	9.69085	0.640390	0.320195	+	0.947352i	$0.396252\pi$
$230$	−10.9966	−0.725095
$231$	−8.04974	−0.529634
$232$	−7.48980	−0.491729
$233$	24.4054	1.59885	0.799424	−	0.600767i	$-0.205138\pi$
$233$	24.4054	1.59885	0.799424	+	0.600767i	$0.205138\pi$
$234$	0.164153	0.0107310
$235$	0.0171183	0.00111667
$236$	−8.17090	−0.531880
$237$	−11.0730	−0.719272
$238$	−7.19858	−0.466614
$239$	8.89550	0.575402	0.287701	−	0.957720i	$-0.407109\pi$
$239$	8.89550	0.575402	0.287701	+	0.957720i	$0.407109\pi$
$240$	−3.50580	−0.226299
$241$	−4.68067	−0.301508	−0.150754	−	0.988571i	$-0.548170\pi$
$241$	−4.68067	−0.301508	−0.150754	+	0.988571i	$0.548170\pi$
$242$	−24.8122	−1.59499
$243$	−16.0175	−1.02752
$244$	−2.13023	−0.136374
$245$	−18.5375	−1.18432
$246$	9.82606	0.626487
$247$	0.381477	0.0242728
$248$	1.00000	0.0635001
$249$	4.07056	0.257961
$250$	−29.2859	−1.85220
$251$	−17.3890	−1.09759	−0.548793	−	0.835958i	$-0.684913\pi$
$251$	−17.3890	−1.09759	−0.548793	+	0.835958i	$0.684913\pi$
$252$	−3.61694	−0.227846
$253$	15.9208	1.00093
$254$	2.23409	0.140179
$255$	−15.9128	−0.996498
$256$	1.00000	0.0625000
$257$	4.12818	0.257509	0.128754	−	0.991677i	$-0.458902\pi$
$257$	4.12818	0.257509	0.128754	+	0.991677i	$0.458902\pi$
$258$	−5.14969	−0.320606
$259$	−8.28911	−0.515060
$260$	0.297513	0.0184510
$261$	−17.0814	−1.05731
$262$	9.57707	0.591673
$263$	10.9821	0.677186	0.338593	−	0.940933i	$-0.390049\pi$
$263$	10.9821	0.677186	0.338593	+	0.940933i	$0.390049\pi$
$264$	5.07568	0.312386
$265$	−2.17869	−0.133836
$266$	−8.40542	−0.515369
$267$	5.55053	0.339687
$268$	−8.75308	−0.534680
$269$	−27.2655	−1.66240	−0.831202	−	0.555970i	$-0.812347\pi$
$269$	−27.2655	−1.66240	−0.831202	+	0.555970i	$0.812347\pi$
$270$	−18.5128	−1.12665
$271$	−16.9871	−1.03189	−0.515947	−	0.856621i	$-0.672560\pi$
$271$	−16.9871	−1.03189	−0.515947	+	0.856621i	$0.672560\pi$
$272$	4.53899	0.275217
$273$	−0.0968194	−0.00585978
$274$	−3.96331	−0.239432
$275$	72.3216	4.36115
$276$	−2.25646	−0.135823
$277$	−6.11158	−0.367209	−0.183605	−	0.983000i	$-0.558777\pi$
$277$	−6.11158	−0.367209	−0.183605	+	0.983000i	$0.558777\pi$
$278$	−9.82275	−0.589129
$279$	2.28062	0.136537
$280$	−6.55537	−0.391758
$281$	5.70101	0.340094	0.170047	−	0.985436i	$-0.445608\pi$
$281$	5.70101	0.340094	0.170047	+	0.985436i	$0.445608\pi$
$282$	0.00351260	0.000209172 0
$283$	−8.77944	−0.521883	−0.260942	−	0.965355i	$-0.584033\pi$
$283$	−8.77944	−0.521883	−0.260942	+	0.965355i	$0.584033\pi$
$284$	10.7912	0.640340
$285$	−18.5806	−1.10062
$286$	−0.430737	−0.0254700
$287$	18.3734	1.08455
$288$	2.28062	0.134387
$289$	3.60240	0.211906
$290$	−30.9585	−1.81794
$291$	−0.848161	−0.0497201
$292$	−13.8762	−0.812044
$293$	19.6833	1.14991	0.574956	−	0.818184i	$-0.305019\pi$
$293$	19.6833	1.14991	0.574956	+	0.818184i	$0.305019\pi$
$294$	−3.80382	−0.221843
$295$	−33.7737	−1.96638
$296$	5.22661	0.303790
$297$	26.8027	1.55525
$298$	9.47469	0.548854
$299$	0.191490	0.0110741
$300$	−10.2502	−0.591793
$301$	−9.62921	−0.555018
$302$	5.40567	0.311061
$303$	−12.4656	−0.716132
$304$	5.29995	0.303973
$305$	−8.80515	−0.504181
$306$	10.3517	0.591768
$307$	−32.7842	−1.87110	−0.935548	−	0.353201i	$-0.885093\pi$
$307$	−32.7842	−1.87110	−0.935548	+	0.353201i	$0.885093\pi$
$308$	9.49082	0.540789
$309$	12.5220	0.712352
$310$	4.13342	0.234762
$311$	−2.91516	−0.165303	−0.0826517	−	0.996578i	$-0.526339\pi$
$311$	−2.91516	−0.165303	−0.0826517	+	0.996578i	$0.526339\pi$
$312$	0.0610485	0.00345619
$313$	−10.8471	−0.613117	−0.306558	−	0.951852i	$-0.599177\pi$
$313$	−10.8471	−0.613117	−0.306558	+	0.951852i	$0.599177\pi$
$314$	3.18543	0.179764
$315$	−14.9503	−0.842355
$316$	13.0554	0.734422
$317$	7.77676	0.436786	0.218393	−	0.975861i	$-0.429918\pi$
$317$	7.77676	0.436786	0.218393	+	0.975861i	$0.429918\pi$
$318$	−0.447059	−0.0250698
$319$	44.8215	2.50952
$320$	4.13342	0.231065
$321$	−6.41911	−0.358280
$322$	−4.21927	−0.235131
$323$	24.0564	1.33853
$324$	3.04311	0.169062
$325$	0.869858	0.0482511
$326$	10.5913	0.586596
$327$	15.9175	0.880241
$328$	−11.5851	−0.639682
$329$	0.00656808	0.000362110 0
$330$	20.9799	1.15491
$331$	−11.5526	−0.634988	−0.317494	−	0.948260i	$-0.602841\pi$
$331$	−11.5526	−0.634988	−0.317494	+	0.948260i	$0.602841\pi$
$332$	−4.79927	−0.263394
$333$	11.9199	0.653208
$334$	7.33832	0.401535
$335$	−36.1802	−1.97673
$336$	−1.34514	−0.0733832
$337$	30.0092	1.63470	0.817352	−	0.576138i	$-0.195441\pi$
$337$	30.0092	1.63470	0.817352	+	0.576138i	$0.195441\pi$
$338$	12.9948	0.706825
$339$	15.2606	0.828844
$340$	18.7615	1.01749
$341$	−5.98433	−0.324070
$342$	12.0872	0.653600
$343$	−18.2142	−0.983475
$344$	6.07160	0.327359
$345$	−9.32690	−0.502143
$346$	−3.27946	−0.176305
$347$	18.1887	0.976422	0.488211	−	0.872726i	$-0.337650\pi$
$347$	18.1887	0.976422	0.488211	+	0.872726i	$0.337650\pi$
$348$	−6.35255	−0.340533
$349$	13.1443	0.703596	0.351798	−	0.936076i	$-0.385570\pi$
$349$	13.1443	0.703596	0.351798	+	0.936076i	$0.385570\pi$
$350$	−19.1664	−1.02449
$351$	0.322374	0.0172070
$352$	−5.98433	−0.318966
$353$	32.1286	1.71003	0.855017	−	0.518599i	$-0.173546\pi$
$353$	32.1286	1.71003	0.855017	+	0.518599i	$0.173546\pi$
$354$	−6.93024	−0.368338
$355$	44.6045	2.36736
$356$	−6.54419	−0.346842
$357$	−6.10555	−0.323140
$358$	20.0943	1.06202
$359$	−20.6094	−1.08772	−0.543861	−	0.839175i	$-0.683038\pi$
$359$	−20.6094	−1.08772	−0.543861	+	0.839175i	$0.683038\pi$
$360$	9.42677	0.496834
$361$	9.08944	0.478391
$362$	−0.706111	−0.0371124
$363$	−21.0448	−1.10456
$364$	0.114152	0.00598320
$365$	−57.3562	−3.00216
$366$	−1.80678	−0.0944420
$367$	−16.7069	−0.872092	−0.436046	−	0.899924i	$-0.643622\pi$
$367$	−16.7069	−0.872092	−0.436046	+	0.899924i	$0.643622\pi$
$368$	2.66042	0.138684
$369$	−26.4213	−1.37544
$370$	21.6038	1.12313
$371$	−0.835938	−0.0433997
$372$	0.848161	0.0439751
$373$	7.29599	0.377772	0.188886	−	0.981999i	$-0.439512\pi$
$373$	7.29599	0.377772	0.188886	+	0.981999i	$0.439512\pi$
$374$	−27.1628	−1.40456
$375$	−24.8391	−1.28269
$376$	−0.00414143	−0.000213578 0
$377$	0.539097	0.0277649
$378$	−7.10315	−0.365347
$379$	−17.5506	−0.901512	−0.450756	−	0.892647i	$-0.648846\pi$
$379$	−17.5506	−0.901512	−0.450756	+	0.892647i	$0.648846\pi$
$380$	21.9069	1.12380
$381$	1.89487	0.0970770
$382$	14.2225	0.727688
$383$	25.2230	1.28884	0.644418	−	0.764674i	$-0.277100\pi$
$383$	25.2230	1.28884	0.644418	+	0.764674i	$0.277100\pi$
$384$	0.848161	0.0432825
$385$	39.2295	1.99932
$386$	6.10206	0.310586
$387$	13.8470	0.703884
$388$	1.00000	0.0507673
$389$	7.34490	0.372401	0.186201	−	0.982512i	$-0.440383\pi$
$389$	7.34490	0.372401	0.186201	+	0.982512i	$0.440383\pi$
$390$	0.252339	0.0127777
$391$	12.0756	0.610689
$392$	4.48478	0.226516
$393$	8.12290	0.409746
$394$	17.7015	0.891790
$395$	53.9633	2.71519
$396$	−13.6480	−0.685838
$397$	5.95616	0.298931	0.149466	−	0.988767i	$-0.452245\pi$
$397$	5.95616	0.298931	0.149466	+	0.988767i	$0.452245\pi$
$398$	16.8972	0.846980
$399$	−7.12915	−0.356904
$400$	12.0851	0.604257
$401$	−30.7075	−1.53346	−0.766730	−	0.641970i	$-0.778118\pi$
$401$	−30.7075	−1.53346	−0.766730	+	0.641970i	$0.778118\pi$
$402$	−7.42402	−0.370277
$403$	−0.0719775	−0.00358545
$404$	14.6973	0.731216
$405$	12.5784	0.625028
$406$	−11.8784	−0.589515
$407$	−31.2778	−1.55038
$408$	3.84979	0.190593
$409$	−12.5330	−0.619717	−0.309859	−	0.950783i	$-0.600282\pi$
$409$	−12.5330	−0.619717	−0.309859	+	0.950783i	$0.600282\pi$
$410$	−47.8862	−2.36493
$411$	−3.36152	−0.165812
$412$	−14.7637	−0.727356
$413$	−12.9586	−0.637650
$414$	6.06740	0.298197
$415$	−19.8374	−0.973780
$416$	−0.0719775	−0.00352899
$417$	−8.33127	−0.407984
$418$	−31.7167	−1.55131
$419$	13.0487	0.637471	0.318736	−	0.947844i	$-0.396742\pi$
$419$	13.0487	0.637471	0.318736	+	0.947844i	$0.396742\pi$
$420$	−5.56001	−0.271301
$421$	28.1589	1.37238	0.686192	−	0.727421i	$-0.259281\pi$
$421$	28.1589	1.37238	0.686192	+	0.727421i	$0.259281\pi$
$422$	19.5432	0.951346
$423$	−0.00944504	−0.000459234 0
$424$	0.527092	0.0255978
$425$	54.8543	2.66083
$426$	9.15267	0.443448
$427$	−3.37843	−0.163494
$428$	7.56826	0.365826
$429$	−0.365334	−0.0176385
$430$	25.0964	1.21026
$431$	−10.6955	−0.515183	−0.257591	−	0.966254i	$-0.582929\pi$
$431$	−10.6955	−0.515183	−0.257591	+	0.966254i	$0.582929\pi$
$432$	4.47882	0.215487
$433$	−34.6660	−1.66594	−0.832970	−	0.553318i	$-0.813362\pi$
$433$	−34.6660	−1.66594	−0.832970	+	0.553318i	$0.813362\pi$
$434$	1.58594	0.0761277
$435$	−26.2578	−1.25896
$436$	−18.7671	−0.898781
$437$	14.1001	0.674497
$438$	−11.7693	−0.562357
$439$	17.2154	0.821647	0.410824	−	0.911715i	$-0.365241\pi$
$439$	17.2154	0.821647	0.410824	+	0.911715i	$0.365241\pi$
$440$	−24.7358	−1.17923
$441$	10.2281	0.487052
$442$	−0.326705	−0.0155398
$443$	−4.56699	−0.216984	−0.108492	−	0.994097i	$-0.534602\pi$
$443$	−4.56699	−0.216984	−0.108492	+	0.994097i	$0.534602\pi$
$444$	4.43301	0.210381
$445$	−27.0499	−1.28229
$446$	−5.12265	−0.242564
$447$	8.03606	0.380093
$448$	1.58594	0.0749288
$449$	−0.0929875	−0.00438835	−0.00219418	−	0.999998i	$-0.500698\pi$
$449$	−0.0929875	−0.00438835	−0.00219418	+	0.999998i	$0.500698\pi$
$450$	27.5617	1.29927
$451$	69.3293	3.26459
$452$	−17.9926	−0.846301
$453$	4.58487	0.215416
$454$	−13.5936	−0.637979
$455$	0.471839	0.0221201
$456$	4.49521	0.210507
$457$	10.7958	0.505008	0.252504	−	0.967596i	$-0.418746\pi$
$457$	10.7958	0.505008	0.252504	+	0.967596i	$0.418746\pi$
$458$	−9.69085	−0.452824
$459$	20.3293	0.948890
$460$	10.9966	0.512720
$461$	−10.1861	−0.474416	−0.237208	−	0.971459i	$-0.576232\pi$
$461$	−10.1861	−0.474416	−0.237208	+	0.971459i	$0.576232\pi$
$462$	8.04974	0.374508
$463$	−16.3607	−0.760345	−0.380172	−	0.924916i	$-0.624135\pi$
$463$	−16.3607	−0.760345	−0.380172	+	0.924916i	$0.624135\pi$
$464$	7.48980	0.347705
$465$	3.50580	0.162578
$466$	−24.4054	−1.13056
$467$	3.07291	0.142197	0.0710985	−	0.997469i	$-0.477350\pi$
$467$	3.07291	0.142197	0.0710985	+	0.997469i	$0.477350\pi$
$468$	−0.164153	−0.00758800
$469$	−13.8819	−0.641006
$470$	−0.0171183	−0.000789607 0
$471$	2.70176	0.124490
$472$	8.17090	0.376096
$473$	−36.3345	−1.67066
$474$	11.0730	0.508602
$475$	64.0506	2.93885
$476$	7.19858	0.329946
$477$	1.20210	0.0550402
$478$	−8.89550	−0.406871
$479$	17.4167	0.795791	0.397896	−	0.917431i	$-0.369741\pi$
$479$	17.4167	0.795791	0.397896	+	0.917431i	$0.369741\pi$
$480$	3.50580	0.160017
$481$	−0.376198	−0.0171532
$482$	4.68067	0.213199
$483$	−3.57862	−0.162833
$484$	24.8122	1.12783
$485$	4.13342	0.187689
$486$	16.0175	0.726569
$487$	−28.5620	−1.29427	−0.647134	−	0.762376i	$-0.724033\pi$
$487$	−28.5620	−1.29427	−0.647134	+	0.762376i	$0.724033\pi$
$488$	2.13023	0.0964312
$489$	8.98310	0.406230
$490$	18.5375	0.837438
$491$	6.25830	0.282433	0.141216	−	0.989979i	$-0.454899\pi$
$491$	6.25830	0.282433	0.141216	+	0.989979i	$0.454899\pi$
$492$	−9.82606	−0.442993
$493$	33.9961	1.53111
$494$	−0.381477	−0.0171634
$495$	−56.4129	−2.53557
$496$	−1.00000	−0.0449013
$497$	17.1142	0.767678
$498$	−4.07056	−0.182406
$499$	28.6732	1.28359	0.641794	−	0.766877i	$-0.278191\pi$
$499$	28.6732	1.28359	0.641794	+	0.766877i	$0.278191\pi$
$500$	29.2859	1.30970
$501$	6.22408	0.278071
$502$	17.3890	0.776111
$503$	8.19275	0.365297	0.182648	−	0.983178i	$-0.441533\pi$
$503$	8.19275	0.365297	0.182648	+	0.983178i	$0.441533\pi$
$504$	3.61694	0.161111
$505$	60.7499	2.70334
$506$	−15.9208	−0.707767
$507$	11.0217	0.489491
$508$	−2.23409	−0.0991216
$509$	0.911351	0.0403949	0.0201975	−	0.999796i	$-0.493571\pi$
$509$	0.911351	0.0403949	0.0201975	+	0.999796i	$0.493571\pi$
$510$	15.9128	0.704631
$511$	−22.0069	−0.973528
$512$	−1.00000	−0.0441942
$513$	23.7375	1.04804
$514$	−4.12818	−0.182086
$515$	−61.0246	−2.68906
$516$	5.14969	0.226703
$517$	0.0247837	0.00108999
$518$	8.28911	0.364202
$519$	−2.78151	−0.122095
$520$	−0.297513	−0.0130468
$521$	14.1945	0.621871	0.310935	−	0.950431i	$-0.399358\pi$
$521$	14.1945	0.621871	0.310935	+	0.950431i	$0.399358\pi$
$522$	17.0814	0.747633
$523$	−24.1329	−1.05526	−0.527628	−	0.849476i	$-0.676918\pi$
$523$	−24.1329	−1.05526	−0.527628	+	0.849476i	$0.676918\pi$
$524$	−9.57707	−0.418376
$525$	−16.2562	−0.709477
$526$	−10.9821	−0.478843
$527$	−4.53899	−0.197721
$528$	−5.07568	−0.220891
$529$	−15.9222	−0.692269
$530$	2.17869	0.0946363
$531$	18.6347	0.808679
$532$	8.40542	0.364421
$533$	0.833869	0.0361189
$534$	−5.55053	−0.240195
$535$	31.2828	1.35247
$536$	8.75308	0.378076
$537$	17.0432	0.735468
$538$	27.2655	1.17550
$539$	−26.8384	−1.15601
$540$	18.5128	0.796665
$541$	1.05823	0.0454971	0.0227485	−	0.999741i	$-0.492758\pi$
$541$	1.05823	0.0454971	0.0227485	+	0.999741i	$0.492758\pi$
$542$	16.9871	0.729659
$543$	−0.598896	−0.0257011
$544$	−4.53899	−0.194607
$545$	−77.5723	−3.32283
$546$	0.0968194	0.00414349
$547$	−33.9145	−1.45008	−0.725041	−	0.688706i	$-0.758179\pi$
$547$	−33.9145	−1.45008	−0.725041	+	0.688706i	$0.758179\pi$
$548$	3.96331	0.169304
$549$	4.85826	0.207346
$550$	−72.3216	−3.08380
$551$	39.6955	1.69109
$552$	2.25646	0.0960413
$553$	20.7051	0.880469
$554$	6.11158	0.259656
$555$	18.3235	0.777788
$556$	9.82275	0.416577
$557$	−20.4231	−0.865356	−0.432678	−	0.901549i	$-0.642431\pi$
$557$	−20.4231	−0.865356	−0.432678	+	0.901549i	$0.642431\pi$
$558$	−2.28062	−0.0965465
$559$	−0.437018	−0.0184839
$560$	6.55537	0.277015
$561$	−23.0384	−0.972684
$562$	−5.70101	−0.240483
$563$	−16.4980	−0.695308	−0.347654	−	0.937623i	$-0.613022\pi$
$563$	−16.4980	−0.695308	−0.347654	+	0.937623i	$0.613022\pi$
$564$	−0.00351260	−0.000147907 0
$565$	−74.3710	−3.12881
$566$	8.77944	0.369027
$567$	4.82620	0.202681
$568$	−10.7912	−0.452788
$569$	28.3109	1.18685	0.593427	−	0.804888i	$-0.297775\pi$
$569$	28.3109	1.18685	0.593427	+	0.804888i	$0.297775\pi$
$570$	18.5806	0.778255
$571$	41.6971	1.74497	0.872484	−	0.488642i	$-0.162508\pi$
$571$	41.6971	1.74497	0.872484	+	0.488642i	$0.162508\pi$
$572$	0.430737	0.0180100
$573$	12.0630	0.503939
$574$	−18.3734	−0.766890
$575$	32.1515	1.34081
$576$	−2.28062	−0.0950260
$577$	27.8953	1.16130	0.580649	−	0.814154i	$-0.302799\pi$
$577$	27.8953	1.16130	0.580649	+	0.814154i	$0.302799\pi$
$578$	−3.60240	−0.149840
$579$	5.17553	0.215087
$580$	30.9585	1.28548
$581$	−7.61137	−0.315773
$582$	0.848161	0.0351574
$583$	−3.15429	−0.130637
$584$	13.8762	0.574202
$585$	−0.678515	−0.0280531
$586$	−19.6833	−0.813111
$587$	−13.5690	−0.560054	−0.280027	−	0.959992i	$-0.590343\pi$
$587$	−13.5690	−0.560054	−0.280027	+	0.959992i	$0.590343\pi$
$588$	3.80382	0.156867
$589$	−5.29995	−0.218381
$590$	33.7737	1.39044
$591$	15.0137	0.617583
$592$	−5.22661	−0.214812
$593$	−5.65790	−0.232342	−0.116171	−	0.993229i	$-0.537062\pi$
$593$	−5.65790	−0.232342	−0.116171	+	0.993229i	$0.537062\pi$
$594$	−26.8027	−1.09973
$595$	29.7547	1.21983
$596$	−9.47469	−0.388099
$597$	14.3315	0.586551
$598$	−0.191490	−0.00783061
$599$	5.69453	0.232672	0.116336	−	0.993210i	$-0.462885\pi$
$599$	5.69453	0.232672	0.116336	+	0.993210i	$0.462885\pi$
$600$	10.2502	0.418461
$601$	21.2986	0.868787	0.434393	−	0.900723i	$-0.356963\pi$
$601$	21.2986	0.868787	0.434393	+	0.900723i	$0.356963\pi$
$602$	9.62921	0.392457
$603$	19.9625	0.812935
$604$	−5.40567	−0.219953
$605$	102.559	4.16963
$606$	12.4656	0.506382
$607$	−12.7518	−0.517579	−0.258790	−	0.965934i	$-0.583324\pi$
$607$	−12.7518	−0.517579	−0.258790	+	0.965934i	$0.583324\pi$
$608$	−5.29995	−0.214941
$609$	−10.0748	−0.408251
$610$	8.80515	0.356510
$611$	0.000298090 0	1.20594e−5 0
$612$	−10.3517	−0.418443
$613$	38.9849	1.57459	0.787293	−	0.616579i	$-0.211482\pi$
$613$	38.9849	1.57459	0.787293	+	0.616579i	$0.211482\pi$
$614$	32.7842	1.32306
$615$	−40.6152	−1.63776
$616$	−9.49082	−0.382396
$617$	6.44955	0.259649	0.129825	−	0.991537i	$-0.458559\pi$
$617$	6.44955	0.259649	0.129825	+	0.991537i	$0.458559\pi$
$618$	−12.5220	−0.503709
$619$	31.8136	1.27870	0.639348	−	0.768917i	$-0.279204\pi$
$619$	31.8136	1.27870	0.639348	+	0.768917i	$0.279204\pi$
$620$	−4.13342	−0.166002
$621$	11.9155	0.478153
$622$	2.91516	0.116887
$623$	−10.3787	−0.415815
$624$	−0.0610485	−0.00244389
$625$	60.6251	2.42500
$626$	10.8471	0.433539
$627$	−26.9008	−1.07432
$628$	−3.18543	−0.127112
$629$	−23.7235	−0.945918
$630$	14.9503	0.595635
$631$	23.9593	0.953805	0.476903	−	0.878956i	$-0.341759\pi$
$631$	23.9593	0.953805	0.476903	+	0.878956i	$0.341759\pi$
$632$	−13.0554	−0.519314
$633$	16.5757	0.658827
$634$	−7.77676	−0.308855
$635$	−9.23442	−0.366457
$636$	0.447059	0.0177270
$637$	−0.322803	−0.0127899
$638$	−44.8215	−1.77450
$639$	−24.6106	−0.973582
$640$	−4.13342	−0.163388
$641$	35.9271	1.41904	0.709518	−	0.704687i	$-0.248913\pi$
$641$	35.9271	1.41904	0.709518	+	0.704687i	$0.248913\pi$
$642$	6.41911	0.253342
$643$	−12.9340	−0.510069	−0.255034	−	0.966932i	$-0.582087\pi$
$643$	−12.9340	−0.510069	−0.255034	+	0.966932i	$0.582087\pi$
$644$	4.21927	0.166262
$645$	21.2858	0.838129
$646$	−24.0564	−0.946486
$647$	22.5454	0.886350	0.443175	−	0.896435i	$-0.353852\pi$
$647$	22.5454	0.886350	0.443175	+	0.896435i	$0.353852\pi$
$648$	−3.04311	−0.119545
$649$	−48.8974	−1.91939
$650$	−0.869858	−0.0341186
$651$	1.34514	0.0527200
$652$	−10.5913	−0.414786
$653$	−25.8249	−1.01061	−0.505303	−	0.862942i	$-0.668619\pi$
$653$	−25.8249	−1.01061	−0.505303	+	0.862942i	$0.668619\pi$
$654$	−15.9175	−0.622424
$655$	−39.5860	−1.54675
$656$	11.5851	0.452324
$657$	31.6464	1.23464
$658$	−0.00656808	−0.000256050 0
$659$	1.34348	0.0523344	0.0261672	−	0.999658i	$-0.491670\pi$
$659$	1.34348	0.0523344	0.0261672	+	0.999658i	$0.491670\pi$
$660$	−20.9799	−0.816642
$661$	44.7861	1.74198	0.870990	−	0.491302i	$-0.163479\pi$
$661$	44.7861	1.74198	0.870990	+	0.491302i	$0.163479\pi$
$662$	11.5526	0.449004
$663$	−0.277098	−0.0107616
$664$	4.79927	0.186248
$665$	34.7431	1.34728
$666$	−11.9199	−0.461888
$667$	19.9260	0.771537
$668$	−7.33832	−0.283928
$669$	−4.34483	−0.167981
$670$	36.1802	1.39776
$671$	−12.7480	−0.492132
$672$	1.34514	0.0518897
$673$	20.4210	0.787172	0.393586	−	0.919288i	$-0.371234\pi$
$673$	20.4210	0.787172	0.393586	+	0.919288i	$0.371234\pi$
$674$	−30.0092	−1.15591
$675$	54.1272	2.08336
$676$	−12.9948	−0.499801
$677$	−0.0444172	−0.00170709	−0.000853546	−	1.00000i	$-0.500272\pi$
$677$	−0.0444172	−0.00170709	−0.000853546		1.00000i	$0.500272\pi$
$678$	−15.2606	−0.586081
$679$	1.58594	0.0608629
$680$	−18.7615	−0.719472
$681$	−11.5296	−0.441814
$682$	5.98433	0.229152
$683$	27.8371	1.06516	0.532578	−	0.846381i	$-0.321223\pi$
$683$	27.8371	1.06516	0.532578	+	0.846381i	$0.321223\pi$
$684$	−12.0872	−0.462165
$685$	16.3820	0.625924
$686$	18.2142	0.695422
$687$	−8.21940	−0.313590
$688$	−6.07160	−0.231477
$689$	−0.0379387	−0.00144535
$690$	9.32690	0.355069
$691$	40.9453	1.55763	0.778817	−	0.627251i	$-0.215820\pi$
$691$	40.9453	1.55763	0.778817	+	0.627251i	$0.215820\pi$
$692$	3.27946	0.124666
$693$	−21.6450	−0.822224
$694$	−18.1887	−0.690435
$695$	40.6015	1.54010
$696$	6.35255	0.240793
$697$	52.5848	1.99179
$698$	−13.1443	−0.497517
$699$	−20.6997	−0.782934
$700$	19.1664	0.724420
$701$	22.0231	0.831801	0.415901	−	0.909410i	$-0.363466\pi$
$701$	22.0231	0.831801	0.415901	+	0.909410i	$0.363466\pi$
$702$	−0.322374	−0.0121672
$703$	−27.7008	−1.04475
$704$	5.98433	0.225543
$705$	−0.0145190	−0.000546819 0
$706$	−32.1286	−1.20918
$707$	23.3090	0.876626
$708$	6.93024	0.260454
$709$	39.3166	1.47657	0.738284	−	0.674490i	$-0.235637\pi$
$709$	39.3166	1.47657	0.738284	+	0.674490i	$0.235637\pi$
$710$	−44.6045	−1.67398
$711$	−29.7744	−1.11663
$712$	6.54419	0.245254
$713$	−2.66042	−0.0996333
$714$	6.10555	0.228495
$715$	1.78042	0.0665838
$716$	−20.0943	−0.750959
$717$	−7.54482	−0.281766
$718$	20.6094	0.769136
$719$	−42.3234	−1.57840	−0.789198	−	0.614139i	$-0.789504\pi$
$719$	−42.3234	−1.57840	−0.789198	+	0.614139i	$0.789504\pi$
$720$	−9.42677	−0.351315
$721$	−23.4144	−0.871998
$722$	−9.08944	−0.338274
$723$	3.96996	0.147644
$724$	0.706111	0.0262424
$725$	90.5153	3.36165
$726$	21.0448	0.781045
$727$	−33.6968	−1.24975	−0.624873	−	0.780726i	$-0.714849\pi$
$727$	−33.6968	−1.24975	−0.624873	+	0.780726i	$0.714849\pi$
$728$	−0.114152	−0.00423076
$729$	4.45609	0.165040
$730$	57.3562	2.12285
$731$	−27.5589	−1.01930
$732$	1.80678	0.0667806
$733$	−10.1613	−0.375318	−0.187659	−	0.982234i	$-0.560090\pi$
$733$	−10.1613	−0.375318	−0.187659	+	0.982234i	$0.560090\pi$
$734$	16.7069	0.616662
$735$	15.7228	0.579943
$736$	−2.66042	−0.0980642
$737$	−52.3814	−1.92949
$738$	26.4213	0.972582
$739$	43.6572	1.60596	0.802978	−	0.596009i	$-0.203248\pi$
$739$	43.6572	1.60596	0.802978	+	0.596009i	$0.203248\pi$
$740$	−21.6038	−0.794170
$741$	−0.323554	−0.0118860
$742$	0.835938	0.0306882
$743$	−27.8312	−1.02103	−0.510513	−	0.859870i	$-0.670545\pi$
$743$	−27.8312	−1.02103	−0.510513	+	0.859870i	$0.670545\pi$
$744$	−0.848161	−0.0310951
$745$	−39.1629	−1.43482
$746$	−7.29599	−0.267125
$747$	10.9453	0.400469
$748$	27.1628	0.993171
$749$	12.0028	0.438574
$750$	24.8391	0.906997
$751$	−25.6579	−0.936270	−0.468135	−	0.883657i	$-0.655074\pi$
$751$	−25.6579	−0.936270	−0.468135	+	0.883657i	$0.655074\pi$
$752$	0.00414143	0.000151022 0
$753$	14.7487	0.537473
$754$	−0.539097	−0.0196327
$755$	−22.3439	−0.813177
$756$	7.10315	0.258339
$757$	47.4313	1.72392	0.861960	−	0.506976i	$-0.169237\pi$
$757$	47.4313	1.72392	0.861960	+	0.506976i	$0.169237\pi$
$758$	17.5506	0.637465
$759$	−13.5034	−0.490143
$760$	−21.9069	−0.794647
$761$	28.7836	1.04340	0.521702	−	0.853128i	$-0.325297\pi$
$761$	28.7836	1.04340	0.521702	+	0.853128i	$0.325297\pi$
$762$	−1.89487	−0.0686438
$763$	−29.7636	−1.07751
$764$	−14.2225	−0.514553
$765$	−42.7880	−1.54700
$766$	−25.2230	−0.911344
$767$	−0.588120	−0.0212358
$768$	−0.848161	−0.0306054
$769$	−31.7775	−1.14593	−0.572963	−	0.819582i	$-0.694206\pi$
$769$	−31.7775	−1.14593	−0.572963	+	0.819582i	$0.694206\pi$
$770$	−39.2295	−1.41373
$771$	−3.50136	−0.126098
$772$	−6.10206	−0.219618
$773$	−41.2933	−1.48522	−0.742608	−	0.669726i	$-0.766411\pi$
$773$	−41.2933	−1.48522	−0.742608	+	0.669726i	$0.766411\pi$
$774$	−13.8470	−0.497721
$775$	−12.0851	−0.434111
$776$	−1.00000	−0.0358979
$777$	7.03050	0.252218
$778$	−7.34490	−0.263328
$779$	61.4006	2.19990
$780$	−0.252339	−0.00903518
$781$	64.5781	2.31079
$782$	−12.0756	−0.431822
$783$	33.5454	1.19882
$784$	−4.48478	−0.160171
$785$	−13.1667	−0.469940
$786$	−8.12290	−0.289734
$787$	33.6795	1.20055	0.600273	−	0.799795i	$-0.295059\pi$
$787$	33.6795	1.20055	0.600273	+	0.799795i	$0.295059\pi$
$788$	−17.7015	−0.630591
$789$	−9.31460	−0.331608
$790$	−53.9633	−1.91993
$791$	−28.5353	−1.01460
$792$	13.6480	0.484961
$793$	−0.153329	−0.00544487
$794$	−5.95616	−0.211376
$795$	1.84788	0.0655375
$796$	−16.8972	−0.598905
$797$	44.3785	1.57197	0.785983	−	0.618248i	$-0.212157\pi$
$797$	44.3785	1.57197	0.785983	+	0.618248i	$0.212157\pi$
$798$	7.12915	0.252369
$799$	0.0187979	0.000665022 0
$800$	−12.0851	−0.427275
$801$	14.9248	0.527343
$802$	30.7075	1.08432
$803$	−83.0399	−2.93041
$804$	7.42402	0.261825
$805$	17.4400	0.614679
$806$	0.0719775	0.00253530
$807$	23.1255	0.814056
$808$	−14.6973	−0.517048
$809$	14.9987	0.527328	0.263664	−	0.964615i	$-0.415069\pi$
$809$	14.9987	0.527328	0.263664	+	0.964615i	$0.415069\pi$
$810$	−12.5784	−0.441962
$811$	15.2905	0.536921	0.268460	−	0.963291i	$-0.413485\pi$
$811$	15.2905	0.536921	0.268460	+	0.963291i	$0.413485\pi$
$812$	11.8784	0.416850
$813$	14.4078	0.505304
$814$	31.2778	1.09629
$815$	−43.7781	−1.53348
$816$	−3.84979	−0.134770
$817$	−32.1791	−1.12581
$818$	12.5330	0.438206
$819$	−0.260338	−0.00909695
$820$	47.8862	1.67226
$821$	15.1942	0.530282	0.265141	−	0.964210i	$-0.414581\pi$
$821$	15.1942	0.530282	0.265141	+	0.964210i	$0.414581\pi$
$822$	3.36152	0.117247
$823$	−3.40399	−0.118656	−0.0593278	−	0.998239i	$-0.518896\pi$
$823$	−3.40399	−0.118656	−0.0593278	+	0.998239i	$0.518896\pi$
$824$	14.7637	0.514318
$825$	−61.3403	−2.13560
$826$	12.9586	0.450887
$827$	−33.1989	−1.15444	−0.577220	−	0.816589i	$-0.695863\pi$
$827$	−33.1989	−1.15444	−0.577220	+	0.816589i	$0.695863\pi$
$828$	−6.06740	−0.210857
$829$	−30.9107	−1.07357	−0.536786	−	0.843718i	$-0.680362\pi$
$829$	−30.9107	−1.07357	−0.536786	+	0.843718i	$0.680362\pi$
$830$	19.8374	0.688566
$831$	5.18360	0.179817
$832$	0.0719775	0.00249537
$833$	−20.3564	−0.705306
$834$	8.33127	0.288488
$835$	−30.3324	−1.04969
$836$	31.7167	1.09694
$837$	−4.47882	−0.154811
$838$	−13.0487	−0.450760
$839$	18.8723	0.651546	0.325773	−	0.945448i	$-0.394376\pi$
$839$	18.8723	0.651546	0.325773	+	0.945448i	$0.394376\pi$
$840$	5.56001	0.191838
$841$	27.0971	0.934382
$842$	−28.1589	−0.970421
$843$	−4.83537	−0.166539
$844$	−19.5432	−0.672703
$845$	−53.7130	−1.84778
$846$	0.00944504	0.000324727 0
$847$	39.3508	1.35211
$848$	−0.527092	−0.0181004
$849$	7.44637	0.255559
$850$	−54.8543	−1.88149
$851$	−13.9050	−0.476656
$852$	−9.15267	−0.313565
$853$	27.7812	0.951210	0.475605	−	0.879659i	$-0.342229\pi$
$853$	27.7812	0.951210	0.475605	+	0.879659i	$0.342229\pi$
$854$	3.37843	0.115608
$855$	−49.9614	−1.70864
$856$	−7.56826	−0.258678
$857$	−43.1148	−1.47277	−0.736386	−	0.676562i	$-0.763469\pi$
$857$	−43.1148	−1.47277	−0.736386	+	0.676562i	$0.763469\pi$
$858$	0.365334	0.0124723
$859$	−31.4731	−1.07385	−0.536925	−	0.843630i	$-0.680414\pi$
$859$	−31.4731	−1.07385	−0.536925	+	0.843630i	$0.680414\pi$
$860$	−25.0964	−0.855782
$861$	−15.5836	−0.531087
$862$	10.6955	0.364289
$863$	−44.5774	−1.51743	−0.758715	−	0.651422i	$-0.774173\pi$
$863$	−44.5774	−1.51743	−0.758715	+	0.651422i	$0.774173\pi$
$864$	−4.47882	−0.152372
$865$	13.5554	0.460897
$866$	34.6660	1.17800
$867$	−3.05542	−0.103767
$868$	−1.58594	−0.0538304
$869$	78.1277	2.65030
$870$	26.2578	0.890222
$871$	−0.630025	−0.0213476
$872$	18.7671	0.635534
$873$	−2.28062	−0.0771874
$874$	−14.1001	−0.476942
$875$	46.4458	1.57015
$876$	11.7693	0.397647
$877$	−42.3803	−1.43108	−0.715541	−	0.698571i	$-0.753820\pi$
$877$	−42.3803	−1.43108	−0.715541	+	0.698571i	$0.753820\pi$
$878$	−17.2154	−0.580993
$879$	−16.6946	−0.563096
$880$	24.7358	0.833842
$881$	13.4687	0.453773	0.226887	−	0.973921i	$-0.427145\pi$
$881$	13.4687	0.453773	0.226887	+	0.973921i	$0.427145\pi$
$882$	−10.2281	−0.344398
$883$	23.8121	0.801340	0.400670	−	0.916223i	$-0.368777\pi$
$883$	23.8121	0.801340	0.400670	+	0.916223i	$0.368777\pi$
$884$	0.326705	0.0109883
$885$	28.6456	0.962910
$886$	4.56699	0.153431
$887$	−7.36272	−0.247216	−0.123608	−	0.992331i	$-0.539447\pi$
$887$	−7.36272	−0.247216	−0.123608	+	0.992331i	$0.539447\pi$
$888$	−4.43301	−0.148762
$889$	−3.54314	−0.118833
$890$	27.0499	0.906714
$891$	18.2110	0.610091
$892$	5.12265	0.171519
$893$	0.0219494	0.000734508 0
$894$	−8.03606	−0.268766
$895$	−83.0581	−2.77633
$896$	−1.58594	−0.0529827
$897$	−0.162414	−0.00542286
$898$	0.0929875	0.00310303
$899$	−7.48980	−0.249799
$900$	−27.5617	−0.918722
$901$	−2.39246	−0.0797045
$902$	−69.3293	−2.30841
$903$	8.16712	0.271785
$904$	17.9926	0.598425
$905$	2.91865	0.0970193
$906$	−4.58487	−0.152322
$907$	−19.6868	−0.653690	−0.326845	−	0.945078i	$-0.605986\pi$
$907$	−19.6868	−0.653690	−0.326845	+	0.945078i	$0.605986\pi$
$908$	13.5936	0.451119
$909$	−33.5189	−1.11175
$910$	−0.471839	−0.0156413
$911$	−15.5092	−0.513844	−0.256922	−	0.966432i	$-0.582708\pi$
$911$	−15.5092	−0.513844	−0.256922	+	0.966432i	$0.582708\pi$
$912$	−4.49521	−0.148851
$913$	−28.7204	−0.950508
$914$	−10.7958	−0.357094
$915$	7.46818	0.246891
$916$	9.69085	0.320195
$917$	−15.1887	−0.501575
$918$	−20.3293	−0.670967
$919$	−8.98169	−0.296279	−0.148139	−	0.988967i	$-0.547328\pi$
$919$	−8.98169	−0.296279	−0.148139	+	0.988967i	$0.547328\pi$
$920$	−10.9966	−0.362548
$921$	27.8063	0.916249
$922$	10.1861	0.335463
$923$	0.776723	0.0255661
$924$	−8.04974	−0.264817
$925$	−63.1643	−2.07683
$926$	16.3607	0.537645
$927$	33.6704	1.10588
$928$	−7.48980	−0.245865
$929$	45.3505	1.48790	0.743951	−	0.668234i	$-0.232949\pi$
$929$	45.3505	1.48790	0.743951	+	0.668234i	$0.232949\pi$
$930$	−3.50580	−0.114960
$931$	−23.7691	−0.779001
$932$	24.4054	0.799424
$933$	2.47252	0.0809467
$934$	−3.07291	−0.100549
$935$	112.275	3.67179
$936$	0.164153	0.00536552
$937$	27.6530	0.903383	0.451692	−	0.892174i	$-0.350821\pi$
$937$	27.6530	0.903383	0.451692	+	0.892174i	$0.350821\pi$
$938$	13.8819	0.453260
$939$	9.20012	0.300235
$940$	0.0171183	0.000558336 0
$941$	34.5179	1.12525	0.562625	−	0.826712i	$-0.309791\pi$
$941$	34.5179	1.12525	0.562625	+	0.826712i	$0.309791\pi$
$942$	−2.70176	−0.0880280
$943$	30.8213	1.00368
$944$	−8.17090	−0.265940
$945$	29.3603	0.955091
$946$	36.3345	1.18134
$947$	13.2723	0.431292	0.215646	−	0.976472i	$-0.430814\pi$
$947$	13.2723	0.431292	0.215646	+	0.976472i	$0.430814\pi$
$948$	−11.0730	−0.359636
$949$	−0.998775	−0.0324216
$950$	−64.0506	−2.07808
$951$	−6.59595	−0.213888
$952$	−7.19858	−0.233307
$953$	−20.1253	−0.651921	−0.325961	−	0.945383i	$-0.605688\pi$
$953$	−20.1253	−0.651921	−0.325961	+	0.945383i	$0.605688\pi$
$954$	−1.20210	−0.0389193
$955$	−58.7877	−1.90233
$956$	8.89550	0.287701
$957$	−38.0158	−1.22888
$958$	−17.4167	−0.562709
$959$	6.28558	0.202972
$960$	−3.50580	−0.113149
$961$	1.00000	0.0322581
$962$	0.376198	0.0121291
$963$	−17.2604	−0.556207
$964$	−4.68067	−0.150754
$965$	−25.2223	−0.811936
$966$	3.57862	0.115140
$967$	10.2967	0.331121	0.165560	−	0.986200i	$-0.447057\pi$
$967$	10.2967	0.331121	0.165560	+	0.986200i	$0.447057\pi$
$968$	−24.8122	−0.797496
$969$	−20.4037	−0.655461
$970$	−4.13342	−0.132716
$971$	−59.3610	−1.90499	−0.952493	−	0.304561i	$-0.901490\pi$
$971$	−59.3610	−1.90499	−0.952493	+	0.304561i	$0.901490\pi$
$972$	−16.0175	−0.513762
$973$	15.5783	0.499418
$974$	28.5620	0.915186
$975$	−0.737780	−0.0236279
$976$	−2.13023	−0.0681871
$977$	−42.9542	−1.37423	−0.687114	−	0.726550i	$-0.741123\pi$
$977$	−42.9542	−1.37423	−0.687114	+	0.726550i	$0.741123\pi$
$978$	−8.98310	−0.287248
$979$	−39.1626	−1.25164
$980$	−18.5375	−0.592158
$981$	42.8007	1.36652
$982$	−6.25830	−0.199710
$983$	−13.4434	−0.428779	−0.214389	−	0.976748i	$-0.568776\pi$
$983$	−13.4434	−0.428779	−0.214389	+	0.976748i	$0.568776\pi$
$984$	9.82606	0.313243
$985$	−73.1678	−2.33132
$986$	−33.9961	−1.08266
$987$	−0.00557079	−0.000177320 0
$988$	0.381477	0.0121364
$989$	−16.1530	−0.513635
$990$	56.4129	1.79292
$991$	−25.9565	−0.824534	−0.412267	−	0.911063i	$-0.635263\pi$
$991$	−25.9565	−0.824534	−0.412267	+	0.911063i	$0.635263\pi$
$992$	1.00000	0.0317500
$993$	9.79845	0.310945
$994$	−17.1142	−0.542830
$995$	−69.8432	−2.21418
$996$	4.07056	0.128980
$997$	−33.1552	−1.05004	−0.525018	−	0.851091i	$-0.675941\pi$
$997$	−33.1552	−1.05004	−0.525018	+	0.851091i	$0.675941\pi$
$998$	−28.6732	−0.907633
$999$	−23.4090	−0.740629

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.j.1.12	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.j.1.12	✓	32	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.848161 q^{3} +1.00000 q^{4} +4.13342 q^{5} +0.848161 q^{6} +1.58594 q^{7} -1.00000 q^{8} -2.28062 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.848161 q^{3} +1.00000 q^{4} +4.13342 q^{5} +0.848161 q^{6} +1.58594 q^{7} -1.00000 q^{8} -2.28062 q^{9} -4.13342 q^{10} +5.98433 q^{11} -0.848161 q^{12} +0.0719775 q^{13} -1.58594 q^{14} -3.50580 q^{15} +1.00000 q^{16} +4.53899 q^{17} +2.28062 q^{18} +5.29995 q^{19} +4.13342 q^{20} -1.34514 q^{21} -5.98433 q^{22} +2.66042 q^{23} +0.848161 q^{24} +12.0851 q^{25} -0.0719775 q^{26} +4.47882 q^{27} +1.58594 q^{28} +7.48980 q^{29} +3.50580 q^{30} -1.00000 q^{31} -1.00000 q^{32} -5.07568 q^{33} -4.53899 q^{34} +6.55537 q^{35} -2.28062 q^{36} -5.22661 q^{37} -5.29995 q^{38} -0.0610485 q^{39} -4.13342 q^{40} +11.5851 q^{41} +1.34514 q^{42} -6.07160 q^{43} +5.98433 q^{44} -9.42677 q^{45} -2.66042 q^{46} +0.00414143 q^{47} -0.848161 q^{48} -4.48478 q^{49} -12.0851 q^{50} -3.84979 q^{51} +0.0719775 q^{52} -0.527092 q^{53} -4.47882 q^{54} +24.7358 q^{55} -1.58594 q^{56} -4.49521 q^{57} -7.48980 q^{58} -8.17090 q^{59} -3.50580 q^{60} -2.13023 q^{61} +1.00000 q^{62} -3.61694 q^{63} +1.00000 q^{64} +0.297513 q^{65} +5.07568 q^{66} -8.75308 q^{67} +4.53899 q^{68} -2.25646 q^{69} -6.55537 q^{70} +10.7912 q^{71} +2.28062 q^{72} -13.8762 q^{73} +5.22661 q^{74} -10.2502 q^{75} +5.29995 q^{76} +9.49082 q^{77} +0.0610485 q^{78} +13.0554 q^{79} +4.13342 q^{80} +3.04311 q^{81} -11.5851 q^{82} -4.79927 q^{83} -1.34514 q^{84} +18.7615 q^{85} +6.07160 q^{86} -6.35255 q^{87} -5.98433 q^{88} -6.54419 q^{89} +9.42677 q^{90} +0.114152 q^{91} +2.66042 q^{92} +0.848161 q^{93} -0.00414143 q^{94} +21.9069 q^{95} +0.848161 q^{96} +1.00000 q^{97} +4.48478 q^{98} -13.6480 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{2} - 2 q^{3} + 32 q^{4} + 2 q^{6} + 5 q^{7} - 32 q^{8} + 30 q^{9}+O(q^{10}) \) 32 * q - 32 * q^2 - 2 * q^3 + 32 * q^4 + 2 * q^6 + 5 * q^7 - 32 * q^8 + 30 * q^9	\( 32 q - 32 q^{2} - 2 q^{3} + 32 q^{4} + 2 q^{6} + 5 q^{7} - 32 q^{8} + 30 q^{9} - 4 q^{11} - 2 q^{12} + 10 q^{13} - 5 q^{14} - q^{15} + 32 q^{16} + 14 q^{17} - 30 q^{18} + 33 q^{19} + 4 q^{22} - 2 q^{23} + 2 q^{24} + 46 q^{25} - 10 q^{26} - 5 q^{27} + 5 q^{28} - q^{29} + q^{30} - 32 q^{31} - 32 q^{32} + 32 q^{33} - 14 q^{34} + 8 q^{35} + 30 q^{36} + 31 q^{37} - 33 q^{38} + 4 q^{39} + 31 q^{41} + 15 q^{43} - 4 q^{44} + q^{45} + 2 q^{46} - 14 q^{47} - 2 q^{48} + 75 q^{49} - 46 q^{50} + 27 q^{51} + 10 q^{52} - 31 q^{53} + 5 q^{54} + 14 q^{55} - 5 q^{56} + 51 q^{57} + q^{58} - 8 q^{59} - q^{60} + 24 q^{61} + 32 q^{62} + 23 q^{63} + 32 q^{64} + 20 q^{65} - 32 q^{66} + 17 q^{67} + 14 q^{68} - 31 q^{69} - 8 q^{70} - 31 q^{71} - 30 q^{72} + 19 q^{73} - 31 q^{74} - 40 q^{75} + 33 q^{76} + 8 q^{77} - 4 q^{78} + 39 q^{79} + 116 q^{81} - 31 q^{82} - 6 q^{83} + 56 q^{85} - 15 q^{86} - 17 q^{87} + 4 q^{88} + 8 q^{89} - q^{90} + 34 q^{91} - 2 q^{92} + 2 q^{93} + 14 q^{94} - 22 q^{95} + 2 q^{96} + 32 q^{97} - 75 q^{98} - 27 q^{99}+O(q^{100}) \) 32 * q - 32 * q^2 - 2 * q^3 + 32 * q^4 + 2 * q^6 + 5 * q^7 - 32 * q^8 + 30 * q^9 - 4 * q^11 - 2 * q^12 + 10 * q^13 - 5 * q^14 - q^15 + 32 * q^16 + 14 * q^17 - 30 * q^18 + 33 * q^19 + 4 * q^22 - 2 * q^23 + 2 * q^24 + 46 * q^25 - 10 * q^26 - 5 * q^27 + 5 * q^28 - q^29 + q^30 - 32 * q^31 - 32 * q^32 + 32 * q^33 - 14 * q^34 + 8 * q^35 + 30 * q^36 + 31 * q^37 - 33 * q^38 + 4 * q^39 + 31 * q^41 + 15 * q^43 - 4 * q^44 + q^45 + 2 * q^46 - 14 * q^47 - 2 * q^48 + 75 * q^49 - 46 * q^50 + 27 * q^51 + 10 * q^52 - 31 * q^53 + 5 * q^54 + 14 * q^55 - 5 * q^56 + 51 * q^57 + q^58 - 8 * q^59 - q^60 + 24 * q^61 + 32 * q^62 + 23 * q^63 + 32 * q^64 + 20 * q^65 - 32 * q^66 + 17 * q^67 + 14 * q^68 - 31 * q^69 - 8 * q^70 - 31 * q^71 - 30 * q^72 + 19 * q^73 - 31 * q^74 - 40 * q^75 + 33 * q^76 + 8 * q^77 - 4 * q^78 + 39 * q^79 + 116 * q^81 - 31 * q^82 - 6 * q^83 + 56 * q^85 - 15 * q^86 - 17 * q^87 + 4 * q^88 + 8 * q^89 - q^90 + 34 * q^91 - 2 * q^92 + 2 * q^93 + 14 * q^94 - 22 * q^95 + 2 * q^96 + 32 * q^97 - 75 * q^98 - 27 * q^99

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