LMFDB - Embedded newform 6014.2.a.i.1.6

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:	$28$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
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)

$f(q)$	$=$	$q+1.00000 q^{2} -2.00278 q^{3} +1.00000 q^{4} +3.09460 q^{5} -2.00278 q^{6} -1.28060 q^{7} +1.00000 q^{8} +1.01112 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.00278 q^{3} +1.00000 q^{4} +3.09460 q^{5} -2.00278 q^{6} -1.28060 q^{7} +1.00000 q^{8} +1.01112 q^{9} +3.09460 q^{10} +3.84352 q^{11} -2.00278 q^{12} -2.84929 q^{13} -1.28060 q^{14} -6.19780 q^{15} +1.00000 q^{16} -2.89095 q^{17} +1.01112 q^{18} +5.36061 q^{19} +3.09460 q^{20} +2.56475 q^{21} +3.84352 q^{22} -0.595195 q^{23} -2.00278 q^{24} +4.57657 q^{25} -2.84929 q^{26} +3.98329 q^{27} -1.28060 q^{28} +1.19706 q^{29} -6.19780 q^{30} -1.00000 q^{31} +1.00000 q^{32} -7.69772 q^{33} -2.89095 q^{34} -3.96294 q^{35} +1.01112 q^{36} +6.21621 q^{37} +5.36061 q^{38} +5.70649 q^{39} +3.09460 q^{40} +6.98982 q^{41} +2.56475 q^{42} -2.89767 q^{43} +3.84352 q^{44} +3.12901 q^{45} -0.595195 q^{46} -10.4604 q^{47} -2.00278 q^{48} -5.36007 q^{49} +4.57657 q^{50} +5.78993 q^{51} -2.84929 q^{52} +1.55070 q^{53} +3.98329 q^{54} +11.8942 q^{55} -1.28060 q^{56} -10.7361 q^{57} +1.19706 q^{58} -3.92939 q^{59} -6.19780 q^{60} +4.00026 q^{61} -1.00000 q^{62} -1.29483 q^{63} +1.00000 q^{64} -8.81742 q^{65} -7.69772 q^{66} +11.8934 q^{67} -2.89095 q^{68} +1.19204 q^{69} -3.96294 q^{70} -3.79131 q^{71} +1.01112 q^{72} +11.8532 q^{73} +6.21621 q^{74} -9.16586 q^{75} +5.36061 q^{76} -4.92201 q^{77} +5.70649 q^{78} +13.3914 q^{79} +3.09460 q^{80} -11.0110 q^{81} +6.98982 q^{82} +8.29747 q^{83} +2.56475 q^{84} -8.94635 q^{85} -2.89767 q^{86} -2.39745 q^{87} +3.84352 q^{88} +14.7202 q^{89} +3.12901 q^{90} +3.64879 q^{91} -0.595195 q^{92} +2.00278 q^{93} -10.4604 q^{94} +16.5890 q^{95} -2.00278 q^{96} -1.00000 q^{97} -5.36007 q^{98} +3.88625 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 28 q^{2} + 12 q^{3} + 28 q^{4} + 10 q^{5} + 12 q^{6} + 13 q^{7} + 28 q^{8} + 38 q^{9}+O(q^{10}) $ 28 * q + 28 * q^2 + 12 * q^3 + 28 * q^4 + 10 * q^5 + 12 * q^6 + 13 * q^7 + 28 * q^8 + 38 * q^9	\( 28 q + 28 q^{2} + 12 q^{3} + 28 q^{4} + 10 q^{5} + 12 q^{6} + 13 q^{7} + 28 q^{8} + 38 q^{9} + 10 q^{10} + 12 q^{11} + 12 q^{12} + 20 q^{13} + 13 q^{14} + 19 q^{15} + 28 q^{16} - 4 q^{17} + 38 q^{18} + 35 q^{19} + 10 q^{20} + 30 q^{21} + 12 q^{22} + 20 q^{23} + 12 q^{24} + 46 q^{25} + 20 q^{26} + 39 q^{27} + 13 q^{28} + 5 q^{29} + 19 q^{30} - 28 q^{31} + 28 q^{32} + 12 q^{33} - 4 q^{34} + 36 q^{35} + 38 q^{36} + 11 q^{37} + 35 q^{38} - 4 q^{39} + 10 q^{40} - 5 q^{41} + 30 q^{42} + 43 q^{43} + 12 q^{44} + 11 q^{45} + 20 q^{46} + 18 q^{47} + 12 q^{48} + 99 q^{49} + 46 q^{50} - 43 q^{51} + 20 q^{52} + 11 q^{53} + 39 q^{54} + 66 q^{55} + 13 q^{56} - 15 q^{57} + 5 q^{58} + 34 q^{59} + 19 q^{60} + 66 q^{61} - 28 q^{62} + 65 q^{63} + 28 q^{64} - 16 q^{65} + 12 q^{66} + 5 q^{67} - 4 q^{68} - 33 q^{69} + 36 q^{70} + 25 q^{71} + 38 q^{72} - 9 q^{73} + 11 q^{74} + 92 q^{75} + 35 q^{76} + 4 q^{77} - 4 q^{78} + 15 q^{79} + 10 q^{80} - 5 q^{82} - 12 q^{83} + 30 q^{84} + 88 q^{85} + 43 q^{86} + 31 q^{87} + 12 q^{88} + 8 q^{89} + 11 q^{90} + 34 q^{91} + 20 q^{92} - 12 q^{93} + 18 q^{94} + 32 q^{95} + 12 q^{96} - 28 q^{97} + 99 q^{98} + 51 q^{99}+O(q^{100}) \) 28 * q + 28 * q^2 + 12 * q^3 + 28 * q^4 + 10 * q^5 + 12 * q^6 + 13 * q^7 + 28 * q^8 + 38 * q^9 + 10 * q^10 + 12 * q^11 + 12 * q^12 + 20 * q^13 + 13 * q^14 + 19 * q^15 + 28 * q^16 - 4 * q^17 + 38 * q^18 + 35 * q^19 + 10 * q^20 + 30 * q^21 + 12 * q^22 + 20 * q^23 + 12 * q^24 + 46 * q^25 + 20 * q^26 + 39 * q^27 + 13 * q^28 + 5 * q^29 + 19 * q^30 - 28 * q^31 + 28 * q^32 + 12 * q^33 - 4 * q^34 + 36 * q^35 + 38 * q^36 + 11 * q^37 + 35 * q^38 - 4 * q^39 + 10 * q^40 - 5 * q^41 + 30 * q^42 + 43 * q^43 + 12 * q^44 + 11 * q^45 + 20 * q^46 + 18 * q^47 + 12 * q^48 + 99 * q^49 + 46 * q^50 - 43 * q^51 + 20 * q^52 + 11 * q^53 + 39 * q^54 + 66 * q^55 + 13 * q^56 - 15 * q^57 + 5 * q^58 + 34 * q^59 + 19 * q^60 + 66 * q^61 - 28 * q^62 + 65 * q^63 + 28 * q^64 - 16 * q^65 + 12 * q^66 + 5 * q^67 - 4 * q^68 - 33 * q^69 + 36 * q^70 + 25 * q^71 + 38 * q^72 - 9 * q^73 + 11 * q^74 + 92 * q^75 + 35 * q^76 + 4 * q^77 - 4 * q^78 + 15 * q^79 + 10 * q^80 - 5 * q^82 - 12 * q^83 + 30 * q^84 + 88 * q^85 + 43 * q^86 + 31 * q^87 + 12 * q^88 + 8 * q^89 + 11 * q^90 + 34 * q^91 + 20 * q^92 - 12 * q^93 + 18 * q^94 + 32 * q^95 + 12 * q^96 - 28 * q^97 + 99 * q^98 + 51 * 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
$3$	−2.00278	−1.15630	−0.578152	−	0.815929i	$-0.696226\pi$
$3$	−2.00278	−1.15630	−0.578152	+	0.815929i	$0.696226\pi$
$4$	1.00000	0.500000
$5$	3.09460	1.38395	0.691974	−	0.721922i	$-0.256741\pi$
$5$	3.09460	1.38395	0.691974	+	0.721922i	$0.256741\pi$
$6$	−2.00278	−0.817630
$7$	−1.28060	−0.484021	−0.242010	−	0.970274i	$-0.577807\pi$
$7$	−1.28060	−0.484021	−0.242010	+	0.970274i	$0.577807\pi$
$8$	1.00000	0.353553
$9$	1.01112	0.337039
$10$	3.09460	0.978600
$11$	3.84352	1.15887	0.579433	−	0.815020i	$-0.303274\pi$
$11$	3.84352	1.15887	0.579433	+	0.815020i	$0.303274\pi$
$12$	−2.00278	−0.578152
$13$	−2.84929	−0.790251	−0.395125	−	0.918627i	$-0.629299\pi$
$13$	−2.84929	−0.790251	−0.395125	+	0.918627i	$0.629299\pi$
$14$	−1.28060	−0.342254
$15$	−6.19780	−1.60027
$16$	1.00000	0.250000
$17$	−2.89095	−0.701159	−0.350579	−	0.936533i	$-0.614015\pi$
$17$	−2.89095	−0.701159	−0.350579	+	0.936533i	$0.614015\pi$
$18$	1.01112	0.238322
$19$	5.36061	1.22981	0.614905	−	0.788601i	$-0.289194\pi$
$19$	5.36061	1.22981	0.614905	+	0.788601i	$0.289194\pi$
$20$	3.09460	0.691974
$21$	2.56475	0.559675
$22$	3.84352	0.819442
$23$	−0.595195	−0.124107	−0.0620534	−	0.998073i	$-0.519765\pi$
$23$	−0.595195	−0.124107	−0.0620534	+	0.998073i	$0.519765\pi$
$24$	−2.00278	−0.408815
$25$	4.57657	0.915315
$26$	−2.84929	−0.558792
$27$	3.98329	0.766585
$28$	−1.28060	−0.242010
$29$	1.19706	0.222289	0.111144	−	0.993804i	$-0.464548\pi$
$29$	1.19706	0.222289	0.111144	+	0.993804i	$0.464548\pi$
$30$	−6.19780	−1.13156
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	1.00000	0.176777
$33$	−7.69772	−1.34000
$34$	−2.89095	−0.495794
$35$	−3.96294	−0.669860
$36$	1.01112	0.168519
$37$	6.21621	1.02194	0.510969	−	0.859599i	$-0.329287\pi$
$37$	6.21621	1.02194	0.510969	+	0.859599i	$0.329287\pi$
$38$	5.36061	0.869607
$39$	5.70649	0.913770
$40$	3.09460	0.489300
$41$	6.98982	1.09163	0.545813	−	0.837907i	$-0.316221\pi$
$41$	6.98982	1.09163	0.545813	+	0.837907i	$0.316221\pi$
$42$	2.56475	0.395750
$43$	−2.89767	−0.441891	−0.220945	−	0.975286i	$-0.570914\pi$
$43$	−2.89767	−0.441891	−0.220945	+	0.975286i	$0.570914\pi$
$44$	3.84352	0.579433
$45$	3.12901	0.466445
$46$	−0.595195	−0.0877568
$47$	−10.4604	−1.52581	−0.762906	−	0.646510i	$-0.776228\pi$
$47$	−10.4604	−1.52581	−0.762906	+	0.646510i	$0.776228\pi$
$48$	−2.00278	−0.289076
$49$	−5.36007	−0.765724
$50$	4.57657	0.647225
$51$	5.78993	0.810752
$52$	−2.84929	−0.395125
$53$	1.55070	0.213005	0.106503	−	0.994312i	$-0.466035\pi$
$53$	1.55070	0.213005	0.106503	+	0.994312i	$0.466035\pi$
$54$	3.98329	0.542057
$55$	11.8942	1.60381
$56$	−1.28060	−0.171127
$57$	−10.7361	−1.42203
$58$	1.19706	0.157182
$59$	−3.92939	−0.511562	−0.255781	−	0.966735i	$-0.582333\pi$
$59$	−3.92939	−0.511562	−0.255781	+	0.966735i	$0.582333\pi$
$60$	−6.19780	−0.800133
$61$	4.00026	0.512181	0.256091	−	0.966653i	$-0.417565\pi$
$61$	4.00026	0.512181	0.256091	+	0.966653i	$0.417565\pi$
$62$	−1.00000	−0.127000
$63$	−1.29483	−0.163134
$64$	1.00000	0.125000
$65$	−8.81742	−1.09367
$66$	−7.69772	−0.947524
$67$	11.8934	1.45302	0.726508	−	0.687158i	$-0.241142\pi$
$67$	11.8934	1.45302	0.726508	+	0.687158i	$0.241142\pi$
$68$	−2.89095	−0.350579
$69$	1.19204	0.143505
$70$	−3.96294	−0.473662
$71$	−3.79131	−0.449946	−0.224973	−	0.974365i	$-0.572229\pi$
$71$	−3.79131	−0.449946	−0.224973	+	0.974365i	$0.572229\pi$
$72$	1.01112	0.119161
$73$	11.8532	1.38732	0.693659	−	0.720304i	$-0.255998\pi$
$73$	11.8532	1.38732	0.693659	+	0.720304i	$0.255998\pi$
$74$	6.21621	0.722620
$75$	−9.16586	−1.05838
$76$	5.36061	0.614905
$77$	−4.92201	−0.560915
$78$	5.70649	0.646133
$79$	13.3914	1.50665	0.753323	−	0.657651i	$-0.228450\pi$
$79$	13.3914	1.50665	0.753323	+	0.657651i	$0.228450\pi$
$80$	3.09460	0.345987
$81$	−11.0110	−1.22344
$82$	6.98982	0.771896
$83$	8.29747	0.910766	0.455383	−	0.890296i	$-0.349502\pi$
$83$	8.29747	0.910766	0.455383	+	0.890296i	$0.349502\pi$
$84$	2.56475	0.279837
$85$	−8.94635	−0.970368
$86$	−2.89767	−0.312464
$87$	−2.39745	−0.257033
$88$	3.84352	0.409721
$89$	14.7202	1.56034	0.780168	−	0.625570i	$-0.215134\pi$
$89$	14.7202	1.56034	0.780168	+	0.625570i	$0.215134\pi$
$90$	3.12901	0.329826
$91$	3.64879	0.382498
$92$	−0.595195	−0.0620534
$93$	2.00278	0.207678
$94$	−10.4604	−1.07891
$95$	16.5890	1.70199
$96$	−2.00278	−0.204408
$97$	−1.00000	−0.101535
$97$	−1.00000	−0.101535
$98$	−5.36007	−0.541449
$99$	3.88625	0.390583
$100$	4.57657	0.457657
$101$	−2.56784	−0.255509	−0.127755	−	0.991806i	$-0.540777\pi$
$101$	−2.56784	−0.255509	−0.127755	+	0.991806i	$0.540777\pi$
$102$	5.78993	0.573289
$103$	3.48003	0.342898	0.171449	−	0.985193i	$-0.445155\pi$
$103$	3.48003	0.342898	0.171449	+	0.985193i	$0.445155\pi$
$104$	−2.84929	−0.279396
$105$	7.93689	0.774561
$106$	1.55070	0.150618
$107$	−8.94080	−0.864340	−0.432170	−	0.901792i	$-0.642252\pi$
$107$	−8.94080	−0.864340	−0.432170	+	0.901792i	$0.642252\pi$
$108$	3.98329	0.383292
$109$	−6.69192	−0.640969	−0.320485	−	0.947254i	$-0.603846\pi$
$109$	−6.69192	−0.640969	−0.320485	+	0.947254i	$0.603846\pi$
$110$	11.8942	1.13407
$111$	−12.4497	−1.18167
$112$	−1.28060	−0.121005
$113$	7.80010	0.733772	0.366886	−	0.930266i	$-0.380424\pi$
$113$	7.80010	0.733772	0.366886	+	0.930266i	$0.380424\pi$
$114$	−10.7361	−1.00553
$115$	−1.84189	−0.171757
$116$	1.19706	0.111144
$117$	−2.88096	−0.266345
$118$	−3.92939	−0.361729
$119$	3.70215	0.339375
$120$	−6.19780	−0.565779
$121$	3.77266	0.342969
$122$	4.00026	0.362167
$123$	−13.9990	−1.26225
$124$	−1.00000	−0.0898027
$125$	−1.31034	−0.117200
$126$	−1.29483	−0.115353
$127$	17.1311	1.52014	0.760068	−	0.649844i	$-0.225166\pi$
$127$	17.1311	1.52014	0.760068	+	0.649844i	$0.225166\pi$
$128$	1.00000	0.0883883
$129$	5.80339	0.510960
$130$	−8.81742	−0.773339
$131$	14.7945	1.29260	0.646302	−	0.763082i	$-0.276315\pi$
$131$	14.7945	1.29260	0.646302	+	0.763082i	$0.276315\pi$
$132$	−7.69772	−0.670000
$133$	−6.86479	−0.595253
$134$	11.8934	1.02744
$135$	12.3267	1.06091
$136$	−2.89095	−0.247897
$137$	−14.5184	−1.24039	−0.620197	−	0.784446i	$-0.712947\pi$
$137$	−14.5184	−1.24039	−0.620197	+	0.784446i	$0.712947\pi$
$138$	1.19204	0.101473
$139$	4.30845	0.365438	0.182719	−	0.983165i	$-0.441510\pi$
$139$	4.30845	0.365438	0.182719	+	0.983165i	$0.441510\pi$
$140$	−3.96294	−0.334930
$141$	20.9499	1.76430
$142$	−3.79131	−0.318160
$143$	−10.9513	−0.915794
$144$	1.01112	0.0842597
$145$	3.70443	0.307636
$146$	11.8532	0.980982
$147$	10.7350	0.885410
$148$	6.21621	0.510969
$149$	−16.7816	−1.37480	−0.687402	−	0.726277i	$-0.741249\pi$
$149$	−16.7816	−1.37480	−0.687402	+	0.726277i	$0.741249\pi$
$150$	−9.16586	−0.748389
$151$	7.94117	0.646243	0.323122	−	0.946357i	$-0.395268\pi$
$151$	7.94117	0.646243	0.323122	+	0.946357i	$0.395268\pi$
$152$	5.36061	0.434803
$153$	−2.92309	−0.236318
$154$	−4.92201	−0.396627
$155$	−3.09460	−0.248565
$156$	5.70649	0.456885
$157$	−17.9543	−1.43291	−0.716455	−	0.697634i	$-0.754236\pi$
$157$	−17.9543	−1.43291	−0.716455	+	0.697634i	$0.754236\pi$
$158$	13.3914	1.06536
$159$	−3.10571	−0.246299
$160$	3.09460	0.244650
$161$	0.762206	0.0600702
$162$	−11.0110	−0.865105
$163$	−17.8497	−1.39810	−0.699049	−	0.715074i	$-0.746393\pi$
$163$	−17.8497	−1.39810	−0.699049	+	0.715074i	$0.746393\pi$
$164$	6.98982	0.545813
$165$	−23.8214	−1.85449
$166$	8.29747	0.644009
$167$	6.15773	0.476499	0.238250	−	0.971204i	$-0.423426\pi$
$167$	6.15773	0.476499	0.238250	+	0.971204i	$0.423426\pi$
$168$	2.56475	0.197875
$169$	−4.88155	−0.375504
$170$	−8.94635	−0.686153
$171$	5.42021	0.414494
$172$	−2.89767	−0.220945
$173$	10.2639	0.780353	0.390176	−	0.920740i	$-0.372414\pi$
$173$	10.2639	0.780353	0.390176	+	0.920740i	$0.372414\pi$
$174$	−2.39745	−0.181750
$175$	−5.86075	−0.443031
$176$	3.84352	0.289716
$177$	7.86968	0.591522
$178$	14.7202	1.10332
$179$	−4.80948	−0.359478	−0.179739	−	0.983714i	$-0.557525\pi$
$179$	−4.80948	−0.359478	−0.179739	+	0.983714i	$0.557525\pi$
$180$	3.12901	0.233222
$181$	−11.5243	−0.856596	−0.428298	−	0.903638i	$-0.640887\pi$
$181$	−11.5243	−0.856596	−0.428298	+	0.903638i	$0.640887\pi$
$182$	3.64879	0.270467
$183$	−8.01164	−0.592237
$184$	−0.595195	−0.0438784
$185$	19.2367	1.41431
$186$	2.00278	0.146851
$187$	−11.1114	−0.812548
$188$	−10.4604	−0.762906
$189$	−5.10099	−0.371043
$190$	16.5890	1.20349
$191$	9.35955	0.677233	0.338616	−	0.940924i	$-0.390041\pi$
$191$	9.35955	0.677233	0.338616	+	0.940924i	$0.390041\pi$
$192$	−2.00278	−0.144538
$193$	−9.29429	−0.669017	−0.334509	−	0.942393i	$-0.608570\pi$
$193$	−9.29429	−0.669017	−0.334509	+	0.942393i	$0.608570\pi$
$194$	−1.00000	−0.0717958
$195$	17.6593	1.26461
$196$	−5.36007	−0.382862
$197$	5.87426	0.418524	0.209262	−	0.977860i	$-0.432894\pi$
$197$	5.87426	0.418524	0.209262	+	0.977860i	$0.432894\pi$
$198$	3.88625	0.276184
$199$	22.4506	1.59148	0.795742	−	0.605636i	$-0.207081\pi$
$199$	22.4506	1.59148	0.795742	+	0.605636i	$0.207081\pi$
$200$	4.57657	0.323613
$201$	−23.8199	−1.68013
$202$	−2.56784	−0.180672
$203$	−1.53295	−0.107592
$204$	5.78993	0.405376
$205$	21.6307	1.51075
$206$	3.48003	0.242465
$207$	−0.601812	−0.0418288
$208$	−2.84929	−0.197563
$209$	20.6036	1.42518
$210$	7.93689	0.547698
$211$	10.5513	0.726380	0.363190	−	0.931715i	$-0.381688\pi$
$211$	10.5513	0.726380	0.363190	+	0.931715i	$0.381688\pi$
$212$	1.55070	0.106503
$213$	7.59315	0.520274
$214$	−8.94080	−0.611180
$215$	−8.96715	−0.611554
$216$	3.98329	0.271029
$217$	1.28060	0.0869327
$218$	−6.69192	−0.453234
$219$	−23.7394	−1.60416
$220$	11.8942	0.801905
$221$	8.23716	0.554091
$222$	−12.4497	−0.835568
$223$	14.7675	0.988906	0.494453	−	0.869204i	$-0.335368\pi$
$223$	14.7675	0.988906	0.494453	+	0.869204i	$0.335368\pi$
$224$	−1.28060	−0.0855635
$225$	4.62745	0.308497
$226$	7.80010	0.518855
$227$	25.0709	1.66401	0.832006	−	0.554766i	$-0.187192\pi$
$227$	25.0709	1.66401	0.832006	+	0.554766i	$0.187192\pi$
$228$	−10.7361	−0.711017
$229$	−4.40158	−0.290864	−0.145432	−	0.989368i	$-0.546457\pi$
$229$	−4.40158	−0.290864	−0.145432	+	0.989368i	$0.546457\pi$
$230$	−1.84189	−0.121451
$231$	9.85768	0.648588
$232$	1.19706	0.0785909
$233$	29.8961	1.95856	0.979279	−	0.202515i	$-0.0649116\pi$
$233$	29.8961	1.95856	0.979279	+	0.202515i	$0.0649116\pi$
$234$	−2.88096	−0.188335
$235$	−32.3709	−2.11164
$236$	−3.92939	−0.255781
$237$	−26.8199	−1.74214
$238$	3.70215	0.239974
$239$	28.8972	1.86921	0.934603	−	0.355692i	$-0.115755\pi$
$239$	28.8972	1.86921	0.934603	+	0.355692i	$0.115755\pi$
$240$	−6.19780	−0.400066
$241$	−5.00435	−0.322359	−0.161179	−	0.986925i	$-0.551530\pi$
$241$	−5.00435	−0.322359	−0.161179	+	0.986925i	$0.551530\pi$
$242$	3.77266	0.242516
$243$	10.1027	0.648088
$244$	4.00026	0.256091
$245$	−16.5873	−1.05972
$246$	−13.9990	−0.892547
$247$	−15.2739	−0.971858
$248$	−1.00000	−0.0635001
$249$	−16.6180	−1.05312
$250$	−1.31034	−0.0828731
$251$	−15.8080	−0.997791	−0.498896	−	0.866662i	$-0.666261\pi$
$251$	−15.8080	−0.997791	−0.498896	+	0.866662i	$0.666261\pi$
$252$	−1.29483	−0.0815669
$253$	−2.28765	−0.143823
$254$	17.1311	1.07490
$255$	17.9175	1.12204
$256$	1.00000	0.0625000
$257$	−18.8385	−1.17511	−0.587555	−	0.809184i	$-0.699910\pi$
$257$	−18.8385	−1.17511	−0.587555	+	0.809184i	$0.699910\pi$
$258$	5.80339	0.361303
$259$	−7.96046	−0.494639
$260$	−8.81742	−0.546833
$261$	1.21037	0.0749199
$262$	14.7945	0.914009
$263$	−27.6187	−1.70304	−0.851520	−	0.524322i	$-0.824319\pi$
$263$	−27.6187	−1.70304	−0.851520	+	0.524322i	$0.824319\pi$
$264$	−7.69772	−0.473762
$265$	4.79881	0.294789
$266$	−6.86479	−0.420907
$267$	−29.4812	−1.80422
$268$	11.8934	0.726508
$269$	16.4353	1.00208	0.501038	−	0.865425i	$-0.332952\pi$
$269$	16.4353	1.00208	0.501038	+	0.865425i	$0.332952\pi$
$270$	12.3267	0.750179
$271$	15.3469	0.932260	0.466130	−	0.884716i	$-0.345648\pi$
$271$	15.3469	0.932260	0.466130	+	0.884716i	$0.345648\pi$
$272$	−2.89095	−0.175290
$273$	−7.30772	−0.442283
$274$	−14.5184	−0.877092
$275$	17.5902	1.06073
$276$	1.19204	0.0717526
$277$	−17.8269	−1.07111	−0.535556	−	0.844500i	$-0.679898\pi$
$277$	−17.8269	−1.07111	−0.535556	+	0.844500i	$0.679898\pi$
$278$	4.30845	0.258404
$279$	−1.01112	−0.0605340
$280$	−3.96294	−0.236831
$281$	−6.14458	−0.366555	−0.183278	−	0.983061i	$-0.558671\pi$
$281$	−6.14458	−0.366555	−0.183278	+	0.983061i	$0.558671\pi$
$282$	20.9499	1.24755
$283$	11.1810	0.664639	0.332320	−	0.943167i	$-0.392169\pi$
$283$	11.1810	0.664639	0.332320	+	0.943167i	$0.392169\pi$
$284$	−3.79131	−0.224973
$285$	−33.2240	−1.96802
$286$	−10.9513	−0.647564
$287$	−8.95115	−0.528369
$288$	1.01112	0.0595806
$289$	−8.64240	−0.508377
$290$	3.70443	0.217531
$291$	2.00278	0.117405
$292$	11.8532	0.693659
$293$	−27.0431	−1.57987	−0.789936	−	0.613189i	$-0.789886\pi$
$293$	−27.0431	−1.57987	−0.789936	+	0.613189i	$0.789886\pi$
$294$	10.7350	0.626079
$295$	−12.1599	−0.707976
$296$	6.21621	0.361310
$297$	15.3099	0.888368
$298$	−16.7816	−0.972134
$299$	1.69588	0.0980755
$300$	−9.16586	−0.529191
$301$	3.71075	0.213884
$302$	7.94117	0.456963
$303$	5.14280	0.295446
$304$	5.36061	0.307452
$305$	12.3792	0.708833
$306$	−2.92309	−0.167102
$307$	2.27927	0.130085	0.0650423	−	0.997883i	$-0.479282\pi$
$307$	2.27927	0.130085	0.0650423	+	0.997883i	$0.479282\pi$
$308$	−4.92201	−0.280457
$309$	−6.96973	−0.396494
$310$	−3.09460	−0.175762
$311$	24.7637	1.40422	0.702110	−	0.712068i	$-0.252241\pi$
$311$	24.7637	1.40422	0.702110	+	0.712068i	$0.252241\pi$
$312$	5.70649	0.323067
$313$	22.2836	1.25954	0.629772	−	0.776780i	$-0.283148\pi$
$313$	22.2836	1.25954	0.629772	+	0.776780i	$0.283148\pi$
$314$	−17.9543	−1.01322
$315$	−4.00700	−0.225769
$316$	13.3914	0.753323
$317$	15.9913	0.898162	0.449081	−	0.893491i	$-0.351751\pi$
$317$	15.9913	0.898162	0.449081	+	0.893491i	$0.351751\pi$
$318$	−3.10571	−0.174160
$319$	4.60093	0.257603
$320$	3.09460	0.172994
$321$	17.9064	0.999439
$322$	0.762206	0.0424761
$323$	−15.4973	−0.862291
$324$	−11.0110	−0.611722
$325$	−13.0400	−0.723328
$326$	−17.8497	−0.988604
$327$	13.4024	0.741155
$328$	6.98982	0.385948
$329$	13.3956	0.738524
$330$	−23.8214	−1.31132
$331$	20.8250	1.14465	0.572324	−	0.820028i	$-0.306042\pi$
$331$	20.8250	1.14465	0.572324	+	0.820028i	$0.306042\pi$
$332$	8.29747	0.455383
$333$	6.28531	0.344433
$334$	6.15773	0.336936
$335$	36.8055	2.01090
$336$	2.56475	0.139919
$337$	−23.0262	−1.25432	−0.627158	−	0.778892i	$-0.715782\pi$
$337$	−23.0262	−1.25432	−0.627158	+	0.778892i	$0.715782\pi$
$338$	−4.88155	−0.265521
$339$	−15.6219	−0.848464
$340$	−8.94635	−0.485184
$341$	−3.84352	−0.208138
$342$	5.42021	0.293091
$343$	15.8283	0.854647
$344$	−2.89767	−0.156232
$345$	3.68890	0.198604
$346$	10.2639	0.551793
$347$	25.0089	1.34255	0.671274	−	0.741209i	$-0.265747\pi$
$347$	25.0089	1.34255	0.671274	+	0.741209i	$0.265747\pi$
$348$	−2.39745	−0.128517
$349$	20.3914	1.09153	0.545764	−	0.837939i	$-0.316240\pi$
$349$	20.3914	1.09153	0.545764	+	0.837939i	$0.316240\pi$
$350$	−5.86075	−0.313270
$351$	−11.3495	−0.605794
$352$	3.84352	0.204860
$353$	21.1592	1.12619	0.563095	−	0.826392i	$-0.309611\pi$
$353$	21.1592	1.12619	0.563095	+	0.826392i	$0.309611\pi$
$354$	7.86968	0.418269
$355$	−11.7326	−0.622702
$356$	14.7202	0.780168
$357$	−7.41457	−0.392421
$358$	−4.80948	−0.254189
$359$	−23.0873	−1.21850	−0.609251	−	0.792977i	$-0.708530\pi$
$359$	−23.0873	−1.21850	−0.609251	+	0.792977i	$0.708530\pi$
$360$	3.12901	0.164913
$361$	9.73619	0.512431
$362$	−11.5243	−0.605705
$363$	−7.55580	−0.396577
$364$	3.64879	0.191249
$365$	36.6811	1.91998
$366$	−8.01164	−0.418775
$367$	0.653977	0.0341373	0.0170687	−	0.999854i	$-0.494567\pi$
$367$	0.653977	0.0341373	0.0170687	+	0.999854i	$0.494567\pi$
$368$	−0.595195	−0.0310267
$369$	7.06752	0.367921
$370$	19.2367	1.00007
$371$	−1.98583	−0.103099
$372$	2.00278	0.103839
$373$	27.8710	1.44310	0.721552	−	0.692360i	$-0.243429\pi$
$373$	27.8710	1.44310	0.721552	+	0.692360i	$0.243429\pi$
$374$	−11.1114	−0.574559
$375$	2.62432	0.135519
$376$	−10.4604	−0.539456
$377$	−3.41077	−0.175664
$378$	−5.10099	−0.262367
$379$	24.0882	1.23733	0.618665	−	0.785655i	$-0.287674\pi$
$379$	24.0882	1.23733	0.618665	+	0.785655i	$0.287674\pi$
$380$	16.5890	0.850997
$381$	−34.3097	−1.75774
$382$	9.35955	0.478876
$383$	−8.50130	−0.434396	−0.217198	−	0.976128i	$-0.569692\pi$
$383$	−8.50130	−0.434396	−0.217198	+	0.976128i	$0.569692\pi$
$384$	−2.00278	−0.102204
$385$	−15.2317	−0.776277
$386$	−9.29429	−0.473067
$387$	−2.92988	−0.148934
$388$	−1.00000	−0.0507673
$389$	11.1811	0.566902	0.283451	−	0.958987i	$-0.408521\pi$
$389$	11.1811	0.566902	0.283451	+	0.958987i	$0.408521\pi$
$390$	17.6593	0.894215
$391$	1.72068	0.0870185
$392$	−5.36007	−0.270724
$393$	−29.6301	−1.49464
$394$	5.87426	0.295941
$395$	41.4410	2.08512
$396$	3.88625	0.195291
$397$	−9.10950	−0.457193	−0.228596	−	0.973521i	$-0.573414\pi$
$397$	−9.10950	−0.457193	−0.228596	+	0.973521i	$0.573414\pi$
$398$	22.4506	1.12535
$399$	13.7486	0.688293
$400$	4.57657	0.228829
$401$	32.5351	1.62472	0.812362	−	0.583154i	$-0.198182\pi$
$401$	32.5351	1.62472	0.812362	+	0.583154i	$0.198182\pi$
$402$	−23.8199	−1.18803
$403$	2.84929	0.141933
$404$	−2.56784	−0.127755
$405$	−34.0747	−1.69318
$406$	−1.53295	−0.0760792
$407$	23.8921	1.18429
$408$	5.78993	0.286644
$409$	35.8619	1.77326	0.886628	−	0.462483i	$-0.153041\pi$
$409$	35.8619	1.77326	0.886628	+	0.462483i	$0.153041\pi$
$410$	21.6307	1.06827
$411$	29.0772	1.43427
$412$	3.48003	0.171449
$413$	5.03196	0.247607
$414$	−0.601812	−0.0295774
$415$	25.6774	1.26045
$416$	−2.84929	−0.139698
$417$	−8.62887	−0.422557
$418$	20.6036	1.00776
$419$	−14.0666	−0.687200	−0.343600	−	0.939116i	$-0.611647\pi$
$419$	−14.0666	−0.687200	−0.343600	+	0.939116i	$0.611647\pi$
$420$	7.93689	0.387281
$421$	0.812485	0.0395981	0.0197990	−	0.999804i	$-0.493697\pi$
$421$	0.812485	0.0395981	0.0197990	+	0.999804i	$0.493697\pi$
$422$	10.5513	0.513628
$423$	−10.5767	−0.514258
$424$	1.55070	0.0753088
$425$	−13.2306	−0.641781
$426$	7.59315	0.367889
$427$	−5.12273	−0.247906
$428$	−8.94080	−0.432170
$429$	21.9330	1.05894
$430$	−8.96715	−0.432434
$431$	26.5201	1.27743	0.638714	−	0.769445i	$-0.279467\pi$
$431$	26.5201	1.27743	0.638714	+	0.769445i	$0.279467\pi$
$432$	3.98329	0.191646
$433$	−32.5209	−1.56285	−0.781427	−	0.623997i	$-0.785508\pi$
$433$	−32.5209	−1.56285	−0.781427	+	0.623997i	$0.785508\pi$
$434$	1.28060	0.0614707
$435$	−7.41914	−0.355721
$436$	−6.69192	−0.320485
$437$	−3.19061	−0.152628
$438$	−23.7394	−1.13431
$439$	4.58412	0.218788	0.109394	−	0.993998i	$-0.465109\pi$
$439$	4.58412	0.218788	0.109394	+	0.993998i	$0.465109\pi$
$440$	11.8942	0.567033
$441$	−5.41966	−0.258079
$442$	8.23716	0.391802
$443$	−28.6307	−1.36028	−0.680142	−	0.733081i	$-0.738082\pi$
$443$	−28.6307	−1.36028	−0.680142	+	0.733081i	$0.738082\pi$
$444$	−12.4497	−0.590836
$445$	45.5531	2.15943
$446$	14.7675	0.699262
$447$	33.6099	1.58969
$448$	−1.28060	−0.0605026
$449$	−33.7104	−1.59089	−0.795446	−	0.606024i	$-0.792763\pi$
$449$	−33.7104	−1.59089	−0.795446	+	0.606024i	$0.792763\pi$
$450$	4.62745	0.218140
$451$	26.8655	1.26505
$452$	7.80010	0.366886
$453$	−15.9044	−0.747253
$454$	25.0709	1.17663
$455$	11.2916	0.529357
$456$	−10.7361	−0.502765
$457$	1.68154	0.0786591	0.0393296	−	0.999226i	$-0.487478\pi$
$457$	1.68154	0.0786591	0.0393296	+	0.999226i	$0.487478\pi$
$458$	−4.40158	−0.205672
$459$	−11.5155	−0.537497
$460$	−1.84189	−0.0858787
$461$	35.3005	1.64411	0.822053	−	0.569410i	$-0.192828\pi$
$461$	35.3005	1.64411	0.822053	+	0.569410i	$0.192828\pi$
$462$	9.85768	0.458621
$463$	−10.2108	−0.474535	−0.237267	−	0.971444i	$-0.576252\pi$
$463$	−10.2108	−0.474535	−0.237267	+	0.971444i	$0.576252\pi$
$464$	1.19706	0.0555721
$465$	6.19780	0.287416
$466$	29.8961	1.38491
$467$	−35.9111	−1.66177	−0.830883	−	0.556447i	$-0.812164\pi$
$467$	−35.9111	−1.66177	−0.830883	+	0.556447i	$0.812164\pi$
$468$	−2.88096	−0.133173
$469$	−15.2307	−0.703289
$470$	−32.3709	−1.49316
$471$	35.9585	1.65688
$472$	−3.92939	−0.180865
$473$	−11.1373	−0.512092
$474$	−26.8199	−1.23188
$475$	24.5332	1.12566
$476$	3.70215	0.169688
$477$	1.56794	0.0717911
$478$	28.8972	1.32173
$479$	34.1802	1.56173	0.780867	−	0.624697i	$-0.214777\pi$
$479$	34.1802	1.56173	0.780867	+	0.624697i	$0.214777\pi$
$480$	−6.19780	−0.282890
$481$	−17.7118	−0.807588
$482$	−5.00435	−0.227942
$483$	−1.52653	−0.0694594
$484$	3.77266	0.171485
$485$	−3.09460	−0.140519
$486$	10.1027	0.458268
$487$	−26.6951	−1.20967	−0.604834	−	0.796351i	$-0.706761\pi$
$487$	−26.6951	−1.20967	−0.604834	+	0.796351i	$0.706761\pi$
$488$	4.00026	0.181083
$489$	35.7490	1.61663
$490$	−16.5873	−0.749337
$491$	37.1012	1.67436	0.837178	−	0.546931i	$-0.184204\pi$
$491$	37.1012	1.67436	0.837178	+	0.546931i	$0.184204\pi$
$492$	−13.9990	−0.631126
$493$	−3.46064	−0.155859
$494$	−15.2739	−0.687207
$495$	12.0264	0.540547
$496$	−1.00000	−0.0449013
$497$	4.85515	0.217783
$498$	−16.6180	−0.744670
$499$	−17.4597	−0.781603	−0.390801	−	0.920475i	$-0.627802\pi$
$499$	−17.4597	−0.781603	−0.390801	+	0.920475i	$0.627802\pi$
$500$	−1.31034	−0.0586002
$501$	−12.3326	−0.550978
$502$	−15.8080	−0.705545
$503$	−16.1850	−0.721653	−0.360827	−	0.932633i	$-0.617505\pi$
$503$	−16.1850	−0.721653	−0.360827	+	0.932633i	$0.617505\pi$
$504$	−1.29483	−0.0576765
$505$	−7.94643	−0.353612
$506$	−2.28765	−0.101698
$507$	9.77665	0.434196
$508$	17.1311	0.760068
$509$	−9.35854	−0.414810	−0.207405	−	0.978255i	$-0.566502\pi$
$509$	−9.35854	−0.414810	−0.207405	+	0.978255i	$0.566502\pi$
$510$	17.9175	0.793402
$511$	−15.1792	−0.671490
$512$	1.00000	0.0441942
$513$	21.3529	0.942753
$514$	−18.8385	−0.830929
$515$	10.7693	0.474553
$516$	5.80339	0.255480
$517$	−40.2049	−1.76821
$518$	−7.96046	−0.349763
$519$	−20.5564	−0.902325
$520$	−8.81742	−0.386670
$521$	23.6320	1.03534	0.517668	−	0.855581i	$-0.326800\pi$
$521$	23.6320	1.03534	0.517668	+	0.855581i	$0.326800\pi$
$522$	1.21037	0.0529764
$523$	−11.5117	−0.503372	−0.251686	−	0.967809i	$-0.580985\pi$
$523$	−11.5117	−0.503372	−0.251686	+	0.967809i	$0.580985\pi$
$524$	14.7945	0.646302
$525$	11.7378	0.512279
$526$	−27.6187	−1.20423
$527$	2.89095	0.125932
$528$	−7.69772	−0.335000
$529$	−22.6457	−0.984598
$530$	4.79881	0.208447
$531$	−3.97307	−0.172416
$532$	−6.86479	−0.297626
$533$	−19.9160	−0.862658
$534$	−29.4812	−1.27578
$535$	−27.6682	−1.19620
$536$	11.8934	0.513719
$537$	9.63232	0.415665
$538$	16.4353	0.708574
$539$	−20.6015	−0.887371
$540$	12.3267	0.530457
$541$	−12.8315	−0.551667	−0.275834	−	0.961205i	$-0.588954\pi$
$541$	−12.8315	−0.551667	−0.275834	+	0.961205i	$0.588954\pi$
$542$	15.3469	0.659208
$543$	23.0807	0.990486
$544$	−2.89095	−0.123948
$545$	−20.7088	−0.887069
$546$	−7.30772	−0.312742
$547$	−18.4362	−0.788277	−0.394138	−	0.919051i	$-0.628957\pi$
$547$	−18.4362	−0.788277	−0.394138	+	0.919051i	$0.628957\pi$
$548$	−14.5184	−0.620197
$549$	4.04473	0.172625
$550$	17.5902	0.750047
$551$	6.41698	0.273373
$552$	1.19204	0.0507367
$553$	−17.1490	−0.729248
$554$	−17.8269	−0.757391
$555$	−38.5268	−1.63537
$556$	4.30845	0.182719
$557$	−16.3340	−0.692095	−0.346047	−	0.938217i	$-0.612476\pi$
$557$	−16.3340	−0.692095	−0.346047	+	0.938217i	$0.612476\pi$
$558$	−1.01112	−0.0428040
$559$	8.25631	0.349205
$560$	−3.96294	−0.167465
$561$	22.2537	0.939553
$562$	−6.14458	−0.259194
$563$	−4.85371	−0.204559	−0.102280	−	0.994756i	$-0.532614\pi$
$563$	−4.85371	−0.204559	−0.102280	+	0.994756i	$0.532614\pi$
$564$	20.9499	0.882151
$565$	24.1382	1.01550
$566$	11.1810	0.469971
$567$	14.1007	0.592172
$568$	−3.79131	−0.159080
$569$	−37.1180	−1.55607	−0.778034	−	0.628222i	$-0.783783\pi$
$569$	−37.1180	−1.55607	−0.778034	+	0.628222i	$0.783783\pi$
$570$	−33.2240	−1.39160
$571$	−8.79677	−0.368133	−0.184067	−	0.982914i	$-0.558926\pi$
$571$	−8.79677	−0.368133	−0.184067	+	0.982914i	$0.558926\pi$
$572$	−10.9513	−0.457897
$573$	−18.7451	−0.783087
$574$	−8.95115	−0.373614
$575$	−2.72395	−0.113597
$576$	1.01112	0.0421299
$577$	31.3754	1.30617	0.653087	−	0.757283i	$-0.273474\pi$
$577$	31.3754	1.30617	0.653087	+	0.757283i	$0.273474\pi$
$578$	−8.64240	−0.359477
$579$	18.6144	0.773587
$580$	3.70443	0.153818
$581$	−10.6257	−0.440829
$582$	2.00278	0.0830178
$583$	5.96016	0.246845
$584$	11.8532	0.490491
$585$	−8.91544	−0.368608
$586$	−27.0431	−1.11714
$587$	−11.8896	−0.490738	−0.245369	−	0.969430i	$-0.578909\pi$
$587$	−11.8896	−0.490738	−0.245369	+	0.969430i	$0.578909\pi$
$588$	10.7350	0.442705
$589$	−5.36061	−0.220880
$590$	−12.1599	−0.500615
$591$	−11.7648	−0.483941
$592$	6.21621	0.255485
$593$	−10.7012	−0.439444	−0.219722	−	0.975563i	$-0.570515\pi$
$593$	−10.7012	−0.439444	−0.219722	+	0.975563i	$0.570515\pi$
$594$	15.3099	0.628171
$595$	11.4567	0.469678
$596$	−16.7816	−0.687402
$597$	−44.9636	−1.84024
$598$	1.69588	0.0693498
$599$	32.2345	1.31707	0.658533	−	0.752552i	$-0.271177\pi$
$599$	32.2345	1.31707	0.658533	+	0.752552i	$0.271177\pi$
$600$	−9.16586	−0.374195
$601$	−45.0031	−1.83572	−0.917858	−	0.396909i	$-0.870083\pi$
$601$	−45.0031	−1.83572	−0.917858	+	0.396909i	$0.870083\pi$
$602$	3.71075	0.151239
$603$	12.0257	0.489723
$604$	7.94117	0.323122
$605$	11.6749	0.474652
$606$	5.14280	0.208912
$607$	16.5524	0.671840	0.335920	−	0.941890i	$-0.390953\pi$
$607$	16.5524	0.671840	0.335920	+	0.941890i	$0.390953\pi$
$608$	5.36061	0.217402
$609$	3.07016	0.124409
$610$	12.3792	0.501221
$611$	29.8048	1.20577
$612$	−2.92309	−0.118159
$613$	−31.5445	−1.27407	−0.637034	−	0.770836i	$-0.719839\pi$
$613$	−31.5445	−1.27407	−0.637034	+	0.770836i	$0.719839\pi$
$614$	2.27927	0.0919837
$615$	−43.3215	−1.74689
$616$	−4.92201	−0.198313
$617$	−25.7422	−1.03634	−0.518171	−	0.855277i	$-0.673387\pi$
$617$	−25.7422	−1.03634	−0.518171	+	0.855277i	$0.673387\pi$
$618$	−6.96973	−0.280364
$619$	4.36973	0.175634	0.0878171	−	0.996137i	$-0.472011\pi$
$619$	4.36973	0.175634	0.0878171	+	0.996137i	$0.472011\pi$
$620$	−3.09460	−0.124282
$621$	−2.37084	−0.0951383
$622$	24.7637	0.992934
$623$	−18.8506	−0.755235
$624$	5.70649	0.228443
$625$	−26.9378	−1.07751
$626$	22.2836	0.890633
$627$	−41.2645	−1.64795
$628$	−17.9543	−0.716455
$629$	−17.9708	−0.716541
$630$	−4.00700	−0.159643
$631$	−15.8550	−0.631176	−0.315588	−	0.948896i	$-0.602202\pi$
$631$	−15.8550	−0.631176	−0.315588	+	0.948896i	$0.602202\pi$
$632$	13.3914	0.532680
$633$	−21.1319	−0.839916
$634$	15.9913	0.635097
$635$	53.0139	2.10379
$636$	−3.10571	−0.123150
$637$	15.2724	0.605114
$638$	4.60093	0.182152
$639$	−3.83346	−0.151649
$640$	3.09460	0.122325
$641$	−35.6963	−1.40992	−0.704960	−	0.709247i	$-0.749035\pi$
$641$	−35.6963	−1.40992	−0.704960	+	0.709247i	$0.749035\pi$
$642$	17.9064	0.706710
$643$	−21.6943	−0.855539	−0.427770	−	0.903888i	$-0.640701\pi$
$643$	−21.6943	−0.855539	−0.427770	+	0.903888i	$0.640701\pi$
$644$	0.762206	0.0300351
$645$	17.9592	0.707143
$646$	−15.4973	−0.609732
$647$	−5.29617	−0.208214	−0.104107	−	0.994566i	$-0.533198\pi$
$647$	−5.29617	−0.208214	−0.104107	+	0.994566i	$0.533198\pi$
$648$	−11.0110	−0.432553
$649$	−15.1027	−0.592832
$650$	−13.0400	−0.511470
$651$	−2.56475	−0.100521
$652$	−17.8497	−0.699049
$653$	36.2694	1.41933	0.709666	−	0.704538i	$-0.248846\pi$
$653$	36.2694	1.41933	0.709666	+	0.704538i	$0.248846\pi$
$654$	13.4024	0.524076
$655$	45.7832	1.78890
$656$	6.98982	0.272907
$657$	11.9850	0.467580
$658$	13.3956	0.522215
$659$	−24.1323	−0.940061	−0.470030	−	0.882650i	$-0.655757\pi$
$659$	−24.1323	−0.940061	−0.470030	+	0.882650i	$0.655757\pi$
$660$	−23.8214	−0.927246
$661$	−40.1094	−1.56007	−0.780037	−	0.625734i	$-0.784800\pi$
$661$	−40.1094	−1.56007	−0.780037	+	0.625734i	$0.784800\pi$
$662$	20.8250	0.809388
$663$	−16.4972	−0.640698
$664$	8.29747	0.322004
$665$	−21.2438	−0.823800
$666$	6.28531	0.243551
$667$	−0.712485	−0.0275875
$668$	6.15773	0.238250
$669$	−29.5760	−1.14348
$670$	36.8055	1.42192
$671$	15.3751	0.593549
$672$	2.56475	0.0989375
$673$	−32.4508	−1.25089	−0.625443	−	0.780270i	$-0.715082\pi$
$673$	−32.4508	−1.25089	−0.625443	+	0.780270i	$0.715082\pi$
$674$	−23.0262	−0.886935
$675$	18.2298	0.701666
$676$	−4.88155	−0.187752
$677$	−32.6873	−1.25628	−0.628138	−	0.778102i	$-0.716183\pi$
$677$	−32.6873	−1.25628	−0.628138	+	0.778102i	$0.716183\pi$
$678$	−15.6219	−0.599954
$679$	1.28060	0.0491448
$680$	−8.94635	−0.343077
$681$	−50.2114	−1.92410
$682$	−3.84352	−0.147176
$683$	39.6501	1.51717	0.758585	−	0.651575i	$-0.225891\pi$
$683$	39.6501	1.51717	0.758585	+	0.651575i	$0.225891\pi$
$684$	5.42021	0.207247
$685$	−44.9288	−1.71664
$686$	15.8283	0.604326
$687$	8.81538	0.336328
$688$	−2.89767	−0.110473
$689$	−4.41840	−0.168328
$690$	3.68890	0.140434
$691$	28.3201	1.07735	0.538673	−	0.842515i	$-0.318926\pi$
$691$	28.3201	1.07735	0.538673	+	0.842515i	$0.318926\pi$
$692$	10.2639	0.390176
$693$	−4.97672	−0.189050
$694$	25.0089	0.949325
$695$	13.3329	0.505748
$696$	−2.39745	−0.0908749
$697$	−20.2072	−0.765403
$698$	20.3914	0.771827
$699$	−59.8752	−2.26469
$700$	−5.86075	−0.221516
$701$	−0.499961	−0.0188833	−0.00944163	−	0.999955i	$-0.503005\pi$
$701$	−0.499961	−0.0188833	−0.00944163	+	0.999955i	$0.503005\pi$
$702$	−11.3495	−0.428361
$703$	33.3227	1.25679
$704$	3.84352	0.144858
$705$	64.8317	2.44170
$706$	21.1592	0.796336
$707$	3.28837	0.123672
$708$	7.86968	0.295761
$709$	3.95453	0.148516	0.0742578	−	0.997239i	$-0.476341\pi$
$709$	3.95453	0.148516	0.0742578	+	0.997239i	$0.476341\pi$
$710$	−11.7326	−0.440317
$711$	13.5402	0.507798
$712$	14.7202	0.551662
$713$	0.595195	0.0222902
$714$	−7.41457	−0.277483
$715$	−33.8900	−1.26741
$716$	−4.80948	−0.179739
$717$	−57.8747	−2.16137
$718$	−23.0873	−0.861611
$719$	−39.1121	−1.45864	−0.729318	−	0.684175i	$-0.760163\pi$
$719$	−39.1121	−1.45864	−0.729318	+	0.684175i	$0.760163\pi$
$720$	3.12901	0.116611
$721$	−4.45652	−0.165969
$722$	9.73619	0.362343
$723$	10.0226	0.372745
$724$	−11.5243	−0.428298
$725$	5.47843	0.203464
$726$	−7.55580	−0.280422
$727$	−3.06286	−0.113595	−0.0567975	−	0.998386i	$-0.518089\pi$
$727$	−3.06286	−0.113595	−0.0567975	+	0.998386i	$0.518089\pi$
$728$	3.64879	0.135233
$729$	12.7995	0.474057
$730$	36.6811	1.35763
$731$	8.37703	0.309836
$732$	−8.01164	−0.296119
$733$	−36.0641	−1.33206	−0.666029	−	0.745926i	$-0.732007\pi$
$733$	−36.0641	−1.33206	−0.666029	+	0.745926i	$0.732007\pi$
$734$	0.653977	0.0241387
$735$	33.2206	1.22536
$736$	−0.595195	−0.0219392
$737$	45.7127	1.68385
$738$	7.06752	0.260159
$739$	−29.0242	−1.06767	−0.533837	−	0.845587i	$-0.679250\pi$
$739$	−29.0242	−1.06767	−0.533837	+	0.845587i	$0.679250\pi$
$740$	19.2367	0.707155
$741$	30.5903	1.12376
$742$	−1.98583	−0.0729020
$743$	36.5671	1.34152	0.670758	−	0.741676i	$-0.265969\pi$
$743$	36.5671	1.34152	0.670758	+	0.741676i	$0.265969\pi$
$744$	2.00278	0.0734254
$745$	−51.9325	−1.90266
$746$	27.8710	1.02043
$747$	8.38971	0.306964
$748$	−11.1114	−0.406274
$749$	11.4496	0.418358
$750$	2.62432	0.0958265
$751$	22.5650	0.823408	0.411704	−	0.911318i	$-0.364934\pi$
$751$	22.5650	0.823408	0.411704	+	0.911318i	$0.364934\pi$
$752$	−10.4604	−0.381453
$753$	31.6599	1.15375
$754$	−3.41077	−0.124213
$755$	24.5748	0.894367
$756$	−5.10099	−0.185521
$757$	27.6621	1.00540	0.502698	−	0.864462i	$-0.332341\pi$
$757$	27.6621	1.00540	0.502698	+	0.864462i	$0.332341\pi$
$758$	24.0882	0.874924
$759$	4.58165	0.166303
$760$	16.5890	0.601745
$761$	−5.54487	−0.201002	−0.100501	−	0.994937i	$-0.532044\pi$
$761$	−5.54487	−0.201002	−0.100501	+	0.994937i	$0.532044\pi$
$762$	−34.3097	−1.24291
$763$	8.56965	0.310242
$764$	9.35955	0.338616
$765$	−9.04580	−0.327052
$766$	−8.50130	−0.307165
$767$	11.1960	0.404263
$768$	−2.00278	−0.0722690
$769$	5.36412	0.193435	0.0967175	−	0.995312i	$-0.469166\pi$
$769$	5.36412	0.193435	0.0967175	+	0.995312i	$0.469166\pi$
$770$	−15.2317	−0.548911
$771$	37.7292	1.35879
$772$	−9.29429	−0.334509
$773$	28.4375	1.02283	0.511414	−	0.859335i	$-0.329122\pi$
$773$	28.4375	1.02283	0.511414	+	0.859335i	$0.329122\pi$
$774$	−2.92988	−0.105313
$775$	−4.57657	−0.164395
$776$	−1.00000	−0.0358979
$777$	15.9430	0.571953
$778$	11.1811	0.400860
$779$	37.4697	1.34249
$780$	17.6593	0.632306
$781$	−14.5720	−0.521427
$782$	1.72068	0.0615314
$783$	4.76824	0.170403
$784$	−5.36007	−0.191431
$785$	−55.5615	−1.98307
$786$	−29.6301	−1.05687
$787$	−28.5564	−1.01793	−0.508964	−	0.860788i	$-0.669971\pi$
$787$	−28.5564	−1.01793	−0.508964	+	0.860788i	$0.669971\pi$
$788$	5.87426	0.209262
$789$	55.3141	1.96923
$790$	41.4410	1.47440
$791$	−9.98880	−0.355161
$792$	3.88625	0.138092
$793$	−11.3979	−0.404752
$794$	−9.10950	−0.323284
$795$	−9.61095	−0.340865
$796$	22.4506	0.795742
$797$	11.6405	0.412329	0.206165	−	0.978517i	$-0.433902\pi$
$797$	11.6405	0.412329	0.206165	+	0.978517i	$0.433902\pi$
$798$	13.7486	0.486697
$799$	30.2406	1.06984
$800$	4.57657	0.161806
$801$	14.8838	0.525894
$802$	32.5351	1.14885
$803$	45.5582	1.60771
$804$	−23.8199	−0.840064
$805$	2.35873	0.0831341
$806$	2.84929	0.100362
$807$	−32.9162	−1.15870
$808$	−2.56784	−0.0903361
$809$	0.878768	0.0308958	0.0154479	−	0.999881i	$-0.495083\pi$
$809$	0.878768	0.0308958	0.0154479	+	0.999881i	$0.495083\pi$
$810$	−34.0747	−1.19726
$811$	−51.7016	−1.81549	−0.907744	−	0.419525i	$-0.862197\pi$
$811$	−51.7016	−1.81549	−0.907744	+	0.419525i	$0.862197\pi$
$812$	−1.53295	−0.0537961
$813$	−30.7365	−1.07798
$814$	23.8921	0.837419
$815$	−55.2378	−1.93490
$816$	5.78993	0.202688
$817$	−15.5333	−0.543441
$818$	35.8619	1.25388
$819$	3.68936	0.128917
$820$	21.6307	0.755377
$821$	45.5997	1.59144	0.795721	−	0.605664i	$-0.207092\pi$
$821$	45.5997	1.59144	0.795721	+	0.605664i	$0.207092\pi$
$822$	29.0772	1.01418
$823$	24.2107	0.843933	0.421967	−	0.906611i	$-0.361340\pi$
$823$	24.2107	0.843933	0.421967	+	0.906611i	$0.361340\pi$
$824$	3.48003	0.121233
$825$	−35.2292	−1.22652
$826$	5.03196	0.175084
$827$	−37.0723	−1.28913	−0.644565	−	0.764549i	$-0.722962\pi$
$827$	−37.0723	−1.28913	−0.644565	+	0.764549i	$0.722962\pi$
$828$	−0.601812	−0.0209144
$829$	−7.40350	−0.257134	−0.128567	−	0.991701i	$-0.541038\pi$
$829$	−7.40350	−0.257134	−0.128567	+	0.991701i	$0.541038\pi$
$830$	25.6774	0.891275
$831$	35.7032	1.23853
$832$	−2.84929	−0.0987813
$833$	15.4957	0.536894
$834$	−8.62887	−0.298793
$835$	19.0557	0.659451
$836$	20.6036	0.712592
$837$	−3.98329	−0.137683
$838$	−14.0666	−0.485924
$839$	27.7090	0.956621	0.478311	−	0.878191i	$-0.341249\pi$
$839$	27.7090	0.956621	0.478311	+	0.878191i	$0.341249\pi$
$840$	7.93689	0.273849
$841$	−27.5670	−0.950588
$842$	0.812485	0.0280001
$843$	12.3062	0.423849
$844$	10.5513	0.363190
$845$	−15.1065	−0.519678
$846$	−10.5767	−0.363635
$847$	−4.83127	−0.166004
$848$	1.55070	0.0532514
$849$	−22.3930	−0.768525
$850$	−13.2306	−0.453807
$851$	−3.69986	−0.126829
$852$	7.59315	0.260137
$853$	28.9763	0.992128	0.496064	−	0.868286i	$-0.334778\pi$
$853$	28.9763	0.992128	0.496064	+	0.868286i	$0.334778\pi$
$854$	−5.12273	−0.175296
$855$	16.7734	0.573638
$856$	−8.94080	−0.305590
$857$	−36.6106	−1.25059	−0.625297	−	0.780387i	$-0.715022\pi$
$857$	−36.6106	−1.25059	−0.625297	+	0.780387i	$0.715022\pi$
$858$	21.9330	0.748781
$859$	−12.4025	−0.423168	−0.211584	−	0.977360i	$-0.567862\pi$
$859$	−12.4025	−0.423168	−0.211584	+	0.977360i	$0.567862\pi$
$860$	−8.96715	−0.305777
$861$	17.9272	0.610956
$862$	26.5201	0.903277
$863$	−23.4757	−0.799121	−0.399560	−	0.916707i	$-0.630837\pi$
$863$	−23.4757	−0.799121	−0.399560	+	0.916707i	$0.630837\pi$
$864$	3.98329	0.135514
$865$	31.7628	1.07997
$866$	−32.5209	−1.10510
$867$	17.3088	0.587838
$868$	1.28060	0.0434663
$869$	51.4700	1.74600
$870$	−7.41914	−0.251533
$871$	−33.8879	−1.14825
$872$	−6.69192	−0.226617
$873$	−1.01112	−0.0342211
$874$	−3.19061	−0.107924
$875$	1.67802	0.0567274
$876$	−23.7394	−0.802080
$877$	50.5670	1.70752	0.853762	−	0.520663i	$-0.174315\pi$
$877$	50.5670	1.70752	0.853762	+	0.520663i	$0.174315\pi$
$878$	4.58412	0.154706
$879$	54.1612	1.82681
$880$	11.8942	0.400953
$881$	8.95097	0.301566	0.150783	−	0.988567i	$-0.451821\pi$
$881$	8.95097	0.301566	0.150783	+	0.988567i	$0.451821\pi$
$882$	−5.41966	−0.182489
$883$	25.9227	0.872368	0.436184	−	0.899857i	$-0.356330\pi$
$883$	25.9227	0.872368	0.436184	+	0.899857i	$0.356330\pi$
$884$	8.23716	0.277046
$885$	24.3536	0.818636
$886$	−28.6307	−0.961866
$887$	−17.8160	−0.598204	−0.299102	−	0.954221i	$-0.596687\pi$
$887$	−17.8160	−0.598204	−0.299102	+	0.954221i	$0.596687\pi$
$888$	−12.4497	−0.417784
$889$	−21.9380	−0.735777
$890$	45.5531	1.52694
$891$	−42.3210	−1.41781
$892$	14.7675	0.494453
$893$	−56.0744	−1.87646
$894$	33.6099	1.12408
$895$	−14.8834	−0.497499
$896$	−1.28060	−0.0427818
$897$	−3.39648	−0.113405
$898$	−33.7104	−1.12493
$899$	−1.19706	−0.0399242
$900$	4.62745	0.154248
$901$	−4.48301	−0.149351
$902$	26.8655	0.894524
$903$	−7.43181	−0.247315
$904$	7.80010	0.259428
$905$	−35.6632	−1.18549
$906$	−15.9044	−0.528388
$907$	−39.6820	−1.31762	−0.658809	−	0.752310i	$-0.728939\pi$
$907$	−39.6820	−1.31762	−0.658809	+	0.752310i	$0.728939\pi$
$908$	25.0709	0.832006
$909$	−2.59638	−0.0861165
$910$	11.2916	0.374312
$911$	−16.7362	−0.554496	−0.277248	−	0.960798i	$-0.589422\pi$
$911$	−16.7362	−0.554496	−0.277248	+	0.960798i	$0.589422\pi$
$912$	−10.7361	−0.355508
$913$	31.8915	1.05546
$914$	1.68154	0.0556204
$915$	−24.7928	−0.819626
$916$	−4.40158	−0.145432
$917$	−18.9458	−0.625647
$918$	−11.5155	−0.380068
$919$	27.7210	0.914432	0.457216	−	0.889356i	$-0.348847\pi$
$919$	27.7210	0.914432	0.457216	+	0.889356i	$0.348847\pi$
$920$	−1.84189	−0.0607254
$921$	−4.56486	−0.150417
$922$	35.3005	1.16256
$923$	10.8025	0.355570
$924$	9.85768	0.324294
$925$	28.4489	0.935395
$926$	−10.2108	−0.335547
$927$	3.51872	0.115570
$928$	1.19706	0.0392954
$929$	10.5121	0.344892	0.172446	−	0.985019i	$-0.444833\pi$
$929$	10.5121	0.344892	0.172446	+	0.985019i	$0.444833\pi$
$930$	6.19780	0.203234
$931$	−28.7333	−0.941695
$932$	29.8961	0.979279
$933$	−49.5962	−1.62371
$934$	−35.9111	−1.17505
$935$	−34.3855	−1.12453
$936$	−2.88096	−0.0941673
$937$	−35.1983	−1.14988	−0.574939	−	0.818196i	$-0.694974\pi$
$937$	−35.1983	−1.14988	−0.574939	+	0.818196i	$0.694974\pi$
$938$	−15.2307	−0.497301
$939$	−44.6291	−1.45642
$940$	−32.3709	−1.05582
$941$	31.3824	1.02304	0.511519	−	0.859272i	$-0.329083\pi$
$941$	31.3824	1.02304	0.511519	+	0.859272i	$0.329083\pi$
$942$	35.9585	1.17159
$943$	−4.16031	−0.135478
$944$	−3.92939	−0.127891
$945$	−15.7856	−0.513504
$946$	−11.1373	−0.362104
$947$	−31.8252	−1.03418	−0.517089	−	0.855931i	$-0.672985\pi$
$947$	−31.8252	−1.03418	−0.517089	+	0.855931i	$0.672985\pi$
$948$	−26.8199	−0.871071
$949$	−33.7733	−1.09633
$950$	24.5332	0.795964
$951$	−32.0271	−1.03855
$952$	3.70215	0.119987
$953$	−48.2542	−1.56311	−0.781553	−	0.623838i	$-0.785572\pi$
$953$	−48.2542	−1.56311	−0.781553	+	0.623838i	$0.785572\pi$
$954$	1.56794	0.0507640
$955$	28.9641	0.937256
$956$	28.8972	0.934603
$957$	−9.21463	−0.297867
$958$	34.1802	1.10431
$959$	18.5923	0.600377
$960$	−6.19780	−0.200033
$961$	1.00000	0.0322581
$962$	−17.7118	−0.571051
$963$	−9.04019	−0.291316
$964$	−5.00435	−0.161179
$965$	−28.7621	−0.925886
$966$	−1.52653	−0.0491152
$967$	−3.46376	−0.111387	−0.0556936	−	0.998448i	$-0.517737\pi$
$967$	−3.46376	−0.111387	−0.0556936	+	0.998448i	$0.517737\pi$
$968$	3.77266	0.121258
$969$	31.0376	0.997071
$970$	−3.09460	−0.0993617
$971$	−51.1913	−1.64281	−0.821403	−	0.570348i	$-0.806808\pi$
$971$	−51.1913	−1.64281	−0.821403	+	0.570348i	$0.806808\pi$
$972$	10.1027	0.324044
$973$	−5.51739	−0.176880
$974$	−26.6951	−0.855365
$975$	26.1162	0.836387
$976$	4.00026	0.128045
$977$	−54.6391	−1.74806	−0.874030	−	0.485872i	$-0.838502\pi$
$977$	−54.6391	−1.74806	−0.874030	+	0.485872i	$0.838502\pi$
$978$	35.7490	1.14313
$979$	56.5773	1.80822
$980$	−16.5873	−0.529862
$981$	−6.76631	−0.216032
$982$	37.1012	1.18395
$983$	3.54137	0.112952	0.0564761	−	0.998404i	$-0.482014\pi$
$983$	3.54137	0.112952	0.0564761	+	0.998404i	$0.482014\pi$
$984$	−13.9990	−0.446273
$985$	18.1785	0.579216
$986$	−3.46064	−0.110209
$987$	−26.8284	−0.853958
$988$	−15.2739	−0.485929
$989$	1.72468	0.0548417
$990$	12.0264	0.382224
$991$	−22.6599	−0.719814	−0.359907	−	0.932988i	$-0.617192\pi$
$991$	−22.6599	−0.719814	−0.359907	+	0.932988i	$0.617192\pi$
$992$	−1.00000	−0.0317500
$993$	−41.7079	−1.32356
$994$	4.85515	0.153996
$995$	69.4758	2.20253
$996$	−16.6180	−0.526561
$997$	23.8452	0.755185	0.377593	−	0.925972i	$-0.376752\pi$
$997$	23.8452	0.755185	0.377593	+	0.925972i	$0.376752\pi$
$998$	−17.4597	−0.552676
$999$	24.7610	0.783402

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.i.1.6	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.i.1.6	✓	28	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.00278 q^{3} +1.00000 q^{4} +3.09460 q^{5} -2.00278 q^{6} -1.28060 q^{7} +1.00000 q^{8} +1.01112 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.00278 q^{3} +1.00000 q^{4} +3.09460 q^{5} -2.00278 q^{6} -1.28060 q^{7} +1.00000 q^{8} +1.01112 q^{9} +3.09460 q^{10} +3.84352 q^{11} -2.00278 q^{12} -2.84929 q^{13} -1.28060 q^{14} -6.19780 q^{15} +1.00000 q^{16} -2.89095 q^{17} +1.01112 q^{18} +5.36061 q^{19} +3.09460 q^{20} +2.56475 q^{21} +3.84352 q^{22} -0.595195 q^{23} -2.00278 q^{24} +4.57657 q^{25} -2.84929 q^{26} +3.98329 q^{27} -1.28060 q^{28} +1.19706 q^{29} -6.19780 q^{30} -1.00000 q^{31} +1.00000 q^{32} -7.69772 q^{33} -2.89095 q^{34} -3.96294 q^{35} +1.01112 q^{36} +6.21621 q^{37} +5.36061 q^{38} +5.70649 q^{39} +3.09460 q^{40} +6.98982 q^{41} +2.56475 q^{42} -2.89767 q^{43} +3.84352 q^{44} +3.12901 q^{45} -0.595195 q^{46} -10.4604 q^{47} -2.00278 q^{48} -5.36007 q^{49} +4.57657 q^{50} +5.78993 q^{51} -2.84929 q^{52} +1.55070 q^{53} +3.98329 q^{54} +11.8942 q^{55} -1.28060 q^{56} -10.7361 q^{57} +1.19706 q^{58} -3.92939 q^{59} -6.19780 q^{60} +4.00026 q^{61} -1.00000 q^{62} -1.29483 q^{63} +1.00000 q^{64} -8.81742 q^{65} -7.69772 q^{66} +11.8934 q^{67} -2.89095 q^{68} +1.19204 q^{69} -3.96294 q^{70} -3.79131 q^{71} +1.01112 q^{72} +11.8532 q^{73} +6.21621 q^{74} -9.16586 q^{75} +5.36061 q^{76} -4.92201 q^{77} +5.70649 q^{78} +13.3914 q^{79} +3.09460 q^{80} -11.0110 q^{81} +6.98982 q^{82} +8.29747 q^{83} +2.56475 q^{84} -8.94635 q^{85} -2.89767 q^{86} -2.39745 q^{87} +3.84352 q^{88} +14.7202 q^{89} +3.12901 q^{90} +3.64879 q^{91} -0.595195 q^{92} +2.00278 q^{93} -10.4604 q^{94} +16.5890 q^{95} -2.00278 q^{96} -1.00000 q^{97} -5.36007 q^{98} +3.88625 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 28 q^{2} + 12 q^{3} + 28 q^{4} + 10 q^{5} + 12 q^{6} + 13 q^{7} + 28 q^{8} + 38 q^{9}+O(q^{10}) \) 28 * q + 28 * q^2 + 12 * q^3 + 28 * q^4 + 10 * q^5 + 12 * q^6 + 13 * q^7 + 28 * q^8 + 38 * q^9	\( 28 q + 28 q^{2} + 12 q^{3} + 28 q^{4} + 10 q^{5} + 12 q^{6} + 13 q^{7} + 28 q^{8} + 38 q^{9} + 10 q^{10} + 12 q^{11} + 12 q^{12} + 20 q^{13} + 13 q^{14} + 19 q^{15} + 28 q^{16} - 4 q^{17} + 38 q^{18} + 35 q^{19} + 10 q^{20} + 30 q^{21} + 12 q^{22} + 20 q^{23} + 12 q^{24} + 46 q^{25} + 20 q^{26} + 39 q^{27} + 13 q^{28} + 5 q^{29} + 19 q^{30} - 28 q^{31} + 28 q^{32} + 12 q^{33} - 4 q^{34} + 36 q^{35} + 38 q^{36} + 11 q^{37} + 35 q^{38} - 4 q^{39} + 10 q^{40} - 5 q^{41} + 30 q^{42} + 43 q^{43} + 12 q^{44} + 11 q^{45} + 20 q^{46} + 18 q^{47} + 12 q^{48} + 99 q^{49} + 46 q^{50} - 43 q^{51} + 20 q^{52} + 11 q^{53} + 39 q^{54} + 66 q^{55} + 13 q^{56} - 15 q^{57} + 5 q^{58} + 34 q^{59} + 19 q^{60} + 66 q^{61} - 28 q^{62} + 65 q^{63} + 28 q^{64} - 16 q^{65} + 12 q^{66} + 5 q^{67} - 4 q^{68} - 33 q^{69} + 36 q^{70} + 25 q^{71} + 38 q^{72} - 9 q^{73} + 11 q^{74} + 92 q^{75} + 35 q^{76} + 4 q^{77} - 4 q^{78} + 15 q^{79} + 10 q^{80} - 5 q^{82} - 12 q^{83} + 30 q^{84} + 88 q^{85} + 43 q^{86} + 31 q^{87} + 12 q^{88} + 8 q^{89} + 11 q^{90} + 34 q^{91} + 20 q^{92} - 12 q^{93} + 18 q^{94} + 32 q^{95} + 12 q^{96} - 28 q^{97} + 99 q^{98} + 51 q^{99}+O(q^{100}) \) 28 * q + 28 * q^2 + 12 * q^3 + 28 * q^4 + 10 * q^5 + 12 * q^6 + 13 * q^7 + 28 * q^8 + 38 * q^9 + 10 * q^10 + 12 * q^11 + 12 * q^12 + 20 * q^13 + 13 * q^14 + 19 * q^15 + 28 * q^16 - 4 * q^17 + 38 * q^18 + 35 * q^19 + 10 * q^20 + 30 * q^21 + 12 * q^22 + 20 * q^23 + 12 * q^24 + 46 * q^25 + 20 * q^26 + 39 * q^27 + 13 * q^28 + 5 * q^29 + 19 * q^30 - 28 * q^31 + 28 * q^32 + 12 * q^33 - 4 * q^34 + 36 * q^35 + 38 * q^36 + 11 * q^37 + 35 * q^38 - 4 * q^39 + 10 * q^40 - 5 * q^41 + 30 * q^42 + 43 * q^43 + 12 * q^44 + 11 * q^45 + 20 * q^46 + 18 * q^47 + 12 * q^48 + 99 * q^49 + 46 * q^50 - 43 * q^51 + 20 * q^52 + 11 * q^53 + 39 * q^54 + 66 * q^55 + 13 * q^56 - 15 * q^57 + 5 * q^58 + 34 * q^59 + 19 * q^60 + 66 * q^61 - 28 * q^62 + 65 * q^63 + 28 * q^64 - 16 * q^65 + 12 * q^66 + 5 * q^67 - 4 * q^68 - 33 * q^69 + 36 * q^70 + 25 * q^71 + 38 * q^72 - 9 * q^73 + 11 * q^74 + 92 * q^75 + 35 * q^76 + 4 * q^77 - 4 * q^78 + 15 * q^79 + 10 * q^80 - 5 * q^82 - 12 * q^83 + 30 * q^84 + 88 * q^85 + 43 * q^86 + 31 * q^87 + 12 * q^88 + 8 * q^89 + 11 * q^90 + 34 * q^91 + 20 * q^92 - 12 * q^93 + 18 * q^94 + 32 * q^95 + 12 * q^96 - 28 * q^97 + 99 * q^98 + 51 * q^99

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