LMFDB - Embedded newform 6014.2.a.f.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6014, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6014 = 2 \cdot 31 \cdot 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6014.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.0220317756$
Analytic rank:	$1$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
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)

$f(q)$	$=$	$q-1.00000 q^{2} -2.80047 q^{3} +1.00000 q^{4} +0.364133 q^{5} +2.80047 q^{6} +1.53058 q^{7} -1.00000 q^{8} +4.84261 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.80047 q^{3} +1.00000 q^{4} +0.364133 q^{5} +2.80047 q^{6} +1.53058 q^{7} -1.00000 q^{8} +4.84261 q^{9} -0.364133 q^{10} +1.43885 q^{11} -2.80047 q^{12} +3.76553 q^{13} -1.53058 q^{14} -1.01974 q^{15} +1.00000 q^{16} +3.34216 q^{17} -4.84261 q^{18} +0.670158 q^{19} +0.364133 q^{20} -4.28634 q^{21} -1.43885 q^{22} +2.07296 q^{23} +2.80047 q^{24} -4.86741 q^{25} -3.76553 q^{26} -5.16017 q^{27} +1.53058 q^{28} -4.52160 q^{29} +1.01974 q^{30} +1.00000 q^{31} -1.00000 q^{32} -4.02945 q^{33} -3.34216 q^{34} +0.557335 q^{35} +4.84261 q^{36} -8.71171 q^{37} -0.670158 q^{38} -10.5452 q^{39} -0.364133 q^{40} +2.82229 q^{41} +4.28634 q^{42} -3.57774 q^{43} +1.43885 q^{44} +1.76336 q^{45} -2.07296 q^{46} -13.0879 q^{47} -2.80047 q^{48} -4.65732 q^{49} +4.86741 q^{50} -9.35962 q^{51} +3.76553 q^{52} +1.76064 q^{53} +5.16017 q^{54} +0.523933 q^{55} -1.53058 q^{56} -1.87676 q^{57} +4.52160 q^{58} +1.87670 q^{59} -1.01974 q^{60} -10.0127 q^{61} -1.00000 q^{62} +7.41201 q^{63} +1.00000 q^{64} +1.37115 q^{65} +4.02945 q^{66} +13.4531 q^{67} +3.34216 q^{68} -5.80524 q^{69} -0.557335 q^{70} -1.91017 q^{71} -4.84261 q^{72} -1.06852 q^{73} +8.71171 q^{74} +13.6310 q^{75} +0.670158 q^{76} +2.20228 q^{77} +10.5452 q^{78} -4.25502 q^{79} +0.364133 q^{80} -0.0769468 q^{81} -2.82229 q^{82} -2.19851 q^{83} -4.28634 q^{84} +1.21699 q^{85} +3.57774 q^{86} +12.6626 q^{87} -1.43885 q^{88} -5.06946 q^{89} -1.76336 q^{90} +5.76344 q^{91} +2.07296 q^{92} -2.80047 q^{93} +13.0879 q^{94} +0.244027 q^{95} +2.80047 q^{96} +1.00000 q^{97} +4.65732 q^{98} +6.96780 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 22 q^{2} + 22 q^{4} - 11 q^{7} - 22 q^{8} + 8 q^{9}+O(q^{10}) $ 22 * q - 22 * q^2 + 22 * q^4 - 11 * q^7 - 22 * q^8 + 8 * q^9	$ 22 q - 22 q^{2} + 22 q^{4} - 11 q^{7} - 22 q^{8} + 8 q^{9} - 8 q^{13} + 11 q^{14} + q^{15} + 22 q^{16} - 4 q^{17} - 8 q^{18} - 23 q^{19} - 12 q^{21} + 2 q^{23} - 12 q^{25} + 8 q^{26} + 3 q^{27} - 11 q^{28} + 9 q^{29} - q^{30} + 22 q^{31} - 22 q^{32} + 4 q^{34} + 4 q^{35} + 8 q^{36} - 17 q^{37} + 23 q^{38} + 8 q^{39} - 21 q^{41} + 12 q^{42} - 7 q^{43} + 9 q^{45} - 2 q^{46} - 10 q^{47} - 27 q^{49} + 12 q^{50} - q^{51} - 8 q^{52} + 9 q^{53} - 3 q^{54} - 6 q^{55} + 11 q^{56} - q^{57} - 9 q^{58} - 12 q^{59} + q^{60} - 34 q^{61} - 22 q^{62} - 5 q^{63} + 22 q^{64} + 4 q^{65} - 31 q^{67} - 4 q^{68} - 51 q^{69} - 4 q^{70} - 15 q^{71} - 8 q^{72} + 3 q^{73} + 17 q^{74} - 24 q^{75} - 23 q^{76} + 24 q^{77} - 8 q^{78} - 23 q^{79} - 26 q^{81} + 21 q^{82} + 22 q^{83} - 12 q^{84} - 42 q^{85} + 7 q^{86} - 9 q^{87} - 36 q^{89} - 9 q^{90} - 6 q^{91} + 2 q^{92} + 10 q^{94} + 2 q^{95} + 22 q^{97} + 27 q^{98} - 25 q^{99}+O(q^{100}) $ 22 * q - 22 * q^2 + 22 * q^4 - 11 * q^7 - 22 * q^8 + 8 * q^9 - 8 * q^13 + 11 * q^14 + q^15 + 22 * q^16 - 4 * q^17 - 8 * q^18 - 23 * q^19 - 12 * q^21 + 2 * q^23 - 12 * q^25 + 8 * q^26 + 3 * q^27 - 11 * q^28 + 9 * q^29 - q^30 + 22 * q^31 - 22 * q^32 + 4 * q^34 + 4 * q^35 + 8 * q^36 - 17 * q^37 + 23 * q^38 + 8 * q^39 - 21 * q^41 + 12 * q^42 - 7 * q^43 + 9 * q^45 - 2 * q^46 - 10 * q^47 - 27 * q^49 + 12 * q^50 - q^51 - 8 * q^52 + 9 * q^53 - 3 * q^54 - 6 * q^55 + 11 * q^56 - q^57 - 9 * q^58 - 12 * q^59 + q^60 - 34 * q^61 - 22 * q^62 - 5 * q^63 + 22 * q^64 + 4 * q^65 - 31 * q^67 - 4 * q^68 - 51 * q^69 - 4 * q^70 - 15 * q^71 - 8 * q^72 + 3 * q^73 + 17 * q^74 - 24 * q^75 - 23 * q^76 + 24 * q^77 - 8 * q^78 - 23 * q^79 - 26 * q^81 + 21 * q^82 + 22 * q^83 - 12 * q^84 - 42 * q^85 + 7 * q^86 - 9 * q^87 - 36 * q^89 - 9 * q^90 - 6 * q^91 + 2 * q^92 + 10 * q^94 + 2 * q^95 + 22 * q^97 + 27 * q^98 - 25 * 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
$3$	−2.80047	−1.61685	−0.808425	−	0.588599i	$-0.799680\pi$
$3$	−2.80047	−1.61685	−0.808425	+	0.588599i	$0.799680\pi$
$4$	1.00000	0.500000
$5$	0.364133	0.162845	0.0814227	−	0.996680i	$-0.474054\pi$
$5$	0.364133	0.162845	0.0814227	+	0.996680i	$0.474054\pi$
$6$	2.80047	1.14329
$7$	1.53058	0.578505	0.289253	−	0.957253i	$-0.406593\pi$
$7$	1.53058	0.578505	0.289253	+	0.957253i	$0.406593\pi$
$8$	−1.00000	−0.353553
$9$	4.84261	1.61420
$10$	−0.364133	−0.115149
$11$	1.43885	0.433830	0.216915	−	0.976191i	$-0.430401\pi$
$11$	1.43885	0.433830	0.216915	+	0.976191i	$0.430401\pi$
$12$	−2.80047	−0.808425
$13$	3.76553	1.04437	0.522185	−	0.852832i	$-0.325117\pi$
$13$	3.76553	1.04437	0.522185	+	0.852832i	$0.325117\pi$
$14$	−1.53058	−0.409065
$15$	−1.01974	−0.263296
$16$	1.00000	0.250000
$17$	3.34216	0.810594	0.405297	−	0.914185i	$-0.367168\pi$
$17$	3.34216	0.810594	0.405297	+	0.914185i	$0.367168\pi$
$18$	−4.84261	−1.14141
$19$	0.670158	0.153745	0.0768724	−	0.997041i	$-0.475507\pi$
$19$	0.670158	0.153745	0.0768724	+	0.997041i	$0.475507\pi$
$20$	0.364133	0.0814227
$21$	−4.28634	−0.935356
$22$	−1.43885	−0.306764
$23$	2.07296	0.432241	0.216121	−	0.976367i	$-0.430660\pi$
$23$	2.07296	0.432241	0.216121	+	0.976367i	$0.430660\pi$
$24$	2.80047	0.571643
$25$	−4.86741	−0.973481
$26$	−3.76553	−0.738481
$27$	−5.16017	−0.993076
$28$	1.53058	0.289253
$29$	−4.52160	−0.839640	−0.419820	−	0.907607i	$-0.637907\pi$
$29$	−4.52160	−0.839640	−0.419820	+	0.907607i	$0.637907\pi$
$30$	1.01974	0.186179
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−1.00000	−0.176777
$33$	−4.02945	−0.701438
$34$	−3.34216	−0.573176
$35$	0.557335	0.0942068
$36$	4.84261	0.807102
$37$	−8.71171	−1.43220	−0.716098	−	0.698000i	$-0.754074\pi$
$37$	−8.71171	−1.43220	−0.716098	+	0.698000i	$0.754074\pi$
$38$	−0.670158	−0.108714
$39$	−10.5452	−1.68859
$40$	−0.364133	−0.0575745
$41$	2.82229	0.440768	0.220384	−	0.975413i	$-0.429269\pi$
$41$	2.82229	0.440768	0.220384	+	0.975413i	$0.429269\pi$
$42$	4.28634	0.661396
$43$	−3.57774	−0.545600	−0.272800	−	0.962071i	$-0.587950\pi$
$43$	−3.57774	−0.545600	−0.272800	+	0.962071i	$0.587950\pi$
$44$	1.43885	0.216915
$45$	1.76336	0.262866
$46$	−2.07296	−0.305641
$47$	−13.0879	−1.90907	−0.954534	−	0.298103i	$-0.903646\pi$
$47$	−13.0879	−1.90907	−0.954534	+	0.298103i	$0.903646\pi$
$48$	−2.80047	−0.404212
$49$	−4.65732	−0.665332
$50$	4.86741	0.688355
$51$	−9.35962	−1.31061
$52$	3.76553	0.522185
$53$	1.76064	0.241842	0.120921	−	0.992662i	$-0.461415\pi$
$53$	1.76064	0.241842	0.120921	+	0.992662i	$0.461415\pi$
$54$	5.16017	0.702210
$55$	0.523933	0.0706472
$56$	−1.53058	−0.204532
$57$	−1.87676	−0.248582
$58$	4.52160	0.593715
$59$	1.87670	0.244326	0.122163	−	0.992510i	$-0.461017\pi$
$59$	1.87670	0.244326	0.122163	+	0.992510i	$0.461017\pi$
$60$	−1.01974	−0.131648
$61$	−10.0127	−1.28200	−0.640999	−	0.767542i	$-0.721480\pi$
$61$	−10.0127	−1.28200	−0.640999	+	0.767542i	$0.721480\pi$
$62$	−1.00000	−0.127000
$63$	7.41201	0.933825
$64$	1.00000	0.125000
$65$	1.37115	0.170071
$66$	4.02945	0.495991
$67$	13.4531	1.64356	0.821780	−	0.569805i	$-0.192981\pi$
$67$	13.4531	1.64356	0.821780	+	0.569805i	$0.192981\pi$
$68$	3.34216	0.405297
$69$	−5.80524	−0.698869
$70$	−0.557335	−0.0666143
$71$	−1.91017	−0.226696	−0.113348	−	0.993555i	$-0.536157\pi$
$71$	−1.91017	−0.226696	−0.113348	+	0.993555i	$0.536157\pi$
$72$	−4.84261	−0.570707
$73$	−1.06852	−0.125061	−0.0625307	−	0.998043i	$-0.519917\pi$
$73$	−1.06852	−0.125061	−0.0625307	+	0.998043i	$0.519917\pi$
$74$	8.71171	1.01272
$75$	13.6310	1.57397
$76$	0.670158	0.0768724
$77$	2.20228	0.250973
$78$	10.5452	1.19401
$79$	−4.25502	−0.478728	−0.239364	−	0.970930i	$-0.576939\pi$
$79$	−4.25502	−0.478728	−0.239364	+	0.970930i	$0.576939\pi$
$80$	0.364133	0.0407113
$81$	−0.0769468	−0.00854964
$82$	−2.82229	−0.311670
$83$	−2.19851	−0.241317	−0.120659	−	0.992694i	$-0.538501\pi$
$83$	−2.19851	−0.241317	−0.120659	+	0.992694i	$0.538501\pi$
$84$	−4.28634	−0.467678
$85$	1.21699	0.132001
$86$	3.57774	0.385798
$87$	12.6626	1.35757
$88$	−1.43885	−0.153382
$89$	−5.06946	−0.537361	−0.268681	−	0.963229i	$-0.586588\pi$
$89$	−5.06946	−0.537361	−0.268681	+	0.963229i	$0.586588\pi$
$90$	−1.76336	−0.185874
$91$	5.76344	0.604173
$92$	2.07296	0.216121
$93$	−2.80047	−0.290395
$94$	13.0879	1.34991
$95$	0.244027	0.0250366
$96$	2.80047	0.285821
$97$	1.00000	0.101535
$97$	1.00000	0.101535
$98$	4.65732	0.470461
$99$	6.96780	0.700290
$100$	−4.86741	−0.486741
$101$	0.935457	0.0930815	0.0465407	−	0.998916i	$-0.485180\pi$
$101$	0.935457	0.0930815	0.0465407	+	0.998916i	$0.485180\pi$
$102$	9.35962	0.926740
$103$	3.55335	0.350122	0.175061	−	0.984558i	$-0.443988\pi$
$103$	3.55335	0.350122	0.175061	+	0.984558i	$0.443988\pi$
$104$	−3.76553	−0.369240
$105$	−1.56080	−0.152318
$106$	−1.76064	−0.171008
$107$	−14.2310	−1.37576	−0.687882	−	0.725822i	$-0.741459\pi$
$107$	−14.2310	−1.37576	−0.687882	+	0.725822i	$0.741459\pi$
$108$	−5.16017	−0.496538
$109$	−13.9694	−1.33803	−0.669015	−	0.743249i	$-0.733284\pi$
$109$	−13.9694	−1.33803	−0.669015	+	0.743249i	$0.733284\pi$
$110$	−0.523933	−0.0499551
$111$	24.3968	2.31565
$112$	1.53058	0.144626
$113$	−10.1081	−0.950889	−0.475445	−	0.879746i	$-0.657713\pi$
$113$	−10.1081	−0.950889	−0.475445	+	0.879746i	$0.657713\pi$
$114$	1.87676	0.175774
$115$	0.754832	0.0703885
$116$	−4.52160	−0.419820
$117$	18.2350	1.68583
$118$	−1.87670	−0.172765
$119$	5.11545	0.468932
$120$	1.01974	0.0930894
$121$	−8.92971	−0.811792
$122$	10.0127	0.906510
$123$	−7.90373	−0.712656
$124$	1.00000	0.0898027
$125$	−3.59305	−0.321372
$126$	−7.41201	−0.660314
$127$	−17.7322	−1.57348	−0.786741	−	0.617283i	$-0.788233\pi$
$127$	−17.7322	−1.57348	−0.786741	+	0.617283i	$0.788233\pi$
$128$	−1.00000	−0.0883883
$129$	10.0193	0.882154
$130$	−1.37115	−0.120258
$131$	3.71215	0.324332	0.162166	−	0.986763i	$-0.448152\pi$
$131$	3.71215	0.324332	0.162166	+	0.986763i	$0.448152\pi$
$132$	−4.02945	−0.350719
$133$	1.02573	0.0889422
$134$	−13.4531	−1.16217
$135$	−1.87899	−0.161718
$136$	−3.34216	−0.286588
$137$	−8.30760	−0.709766	−0.354883	−	0.934911i	$-0.615479\pi$
$137$	−8.30760	−0.709766	−0.354883	+	0.934911i	$0.615479\pi$
$138$	5.80524	0.494175
$139$	17.6888	1.50035	0.750173	−	0.661241i	$-0.229970\pi$
$139$	17.6888	1.50035	0.750173	+	0.661241i	$0.229970\pi$
$140$	0.557335	0.0471034
$141$	36.6522	3.08668
$142$	1.91017	0.160298
$143$	5.41803	0.453079
$144$	4.84261	0.403551
$145$	−1.64646	−0.136731
$146$	1.06852	0.0884317
$147$	13.0427	1.07574
$148$	−8.71171	−0.716098
$149$	12.1570	0.995939	0.497969	−	0.867195i	$-0.334079\pi$
$149$	12.1570	0.995939	0.497969	+	0.867195i	$0.334079\pi$
$150$	−13.6310	−1.11297
$151$	−4.97550	−0.404900	−0.202450	−	0.979293i	$-0.564890\pi$
$151$	−4.97550	−0.404900	−0.202450	+	0.979293i	$0.564890\pi$
$152$	−0.670158	−0.0543570
$153$	16.1848	1.30846
$154$	−2.20228	−0.177465
$155$	0.364133	0.0292479
$156$	−10.5452	−0.844294
$157$	−4.92292	−0.392892	−0.196446	−	0.980515i	$-0.562940\pi$
$157$	−4.92292	−0.392892	−0.196446	+	0.980515i	$0.562940\pi$
$158$	4.25502	0.338512
$159$	−4.93060	−0.391022
$160$	−0.364133	−0.0287873
$161$	3.17283	0.250054
$162$	0.0769468	0.00604551
$163$	19.8430	1.55422	0.777110	−	0.629365i	$-0.216685\pi$
$163$	19.8430	1.55422	0.777110	+	0.629365i	$0.216685\pi$
$164$	2.82229	0.220384
$165$	−1.46726	−0.114226
$166$	2.19851	0.170637
$167$	16.0420	1.24136	0.620682	−	0.784062i	$-0.286856\pi$
$167$	16.0420	1.24136	0.620682	+	0.784062i	$0.286856\pi$
$168$	4.28634	0.330698
$169$	1.17920	0.0907079
$170$	−1.21699	−0.0933391
$171$	3.24532	0.248176
$172$	−3.57774	−0.272800
$173$	6.66014	0.506361	0.253181	−	0.967419i	$-0.418523\pi$
$173$	6.66014	0.506361	0.253181	+	0.967419i	$0.418523\pi$
$174$	−12.6626	−0.959948
$175$	−7.44996	−0.563164
$176$	1.43885	0.108457
$177$	−5.25565	−0.395039
$178$	5.06946	0.379972
$179$	−10.3405	−0.772886	−0.386443	−	0.922313i	$-0.626296\pi$
$179$	−10.3405	−0.772886	−0.386443	+	0.922313i	$0.626296\pi$
$180$	1.76336	0.131433
$181$	−17.0760	−1.26925	−0.634623	−	0.772822i	$-0.718845\pi$
$181$	−17.0760	−1.26925	−0.634623	+	0.772822i	$0.718845\pi$
$182$	−5.76344	−0.427215
$183$	28.0403	2.07280
$184$	−2.07296	−0.152820
$185$	−3.17222	−0.233226
$186$	2.80047	0.205340
$187$	4.80887	0.351660
$188$	−13.0879	−0.954534
$189$	−7.89806	−0.574499
$190$	−0.244027	−0.0177036
$191$	27.3748	1.98077	0.990386	−	0.138332i	$-0.0441742\pi$
$191$	27.3748	1.98077	0.990386	+	0.138332i	$0.0441742\pi$
$192$	−2.80047	−0.202106
$193$	−6.13879	−0.441880	−0.220940	−	0.975287i	$-0.570912\pi$
$193$	−6.13879	−0.441880	−0.220940	+	0.975287i	$0.570912\pi$
$194$	−1.00000	−0.0717958
$195$	−3.83987	−0.274979
$196$	−4.65732	−0.332666
$197$	19.5580	1.39345	0.696724	−	0.717339i	$-0.254640\pi$
$197$	19.5580	1.39345	0.696724	+	0.717339i	$0.254640\pi$
$198$	−6.96780	−0.495180
$199$	18.1166	1.28425	0.642125	−	0.766600i	$-0.278053\pi$
$199$	18.1166	1.28425	0.642125	+	0.766600i	$0.278053\pi$
$200$	4.86741	0.344178
$201$	−37.6750	−2.65739
$202$	−0.935457	−0.0658185
$203$	−6.92067	−0.485736
$204$	−9.35962	−0.655304
$205$	1.02769	0.0717770
$206$	−3.55335	−0.247574
$207$	10.0385	0.697725
$208$	3.76553	0.261092
$209$	0.964258	0.0666991
$210$	1.56080	0.107705
$211$	−25.6339	−1.76471	−0.882355	−	0.470585i	$-0.844043\pi$
$211$	−25.6339	−1.76471	−0.882355	+	0.470585i	$0.844043\pi$
$212$	1.76064	0.120921
$213$	5.34937	0.366533
$214$	14.2310	0.972812
$215$	−1.30277	−0.0888485
$216$	5.16017	0.351105
$217$	1.53058	0.103903
$218$	13.9694	0.946131
$219$	2.99237	0.202205
$220$	0.523933	0.0353236
$221$	12.5850	0.846559
$222$	−24.3968	−1.63741
$223$	19.5468	1.30895	0.654476	−	0.756083i	$-0.272889\pi$
$223$	19.5468	1.30895	0.654476	+	0.756083i	$0.272889\pi$
$224$	−1.53058	−0.102266
$225$	−23.5710	−1.57140
$226$	10.1081	0.672380
$227$	17.5275	1.16334	0.581671	−	0.813424i	$-0.302399\pi$
$227$	17.5275	1.16334	0.581671	+	0.813424i	$0.302399\pi$
$228$	−1.87676	−0.124291
$229$	−24.6544	−1.62921	−0.814606	−	0.580015i	$-0.803047\pi$
$229$	−24.6544	−1.62921	−0.814606	+	0.580015i	$0.803047\pi$
$230$	−0.754832	−0.0497722
$231$	−6.16740	−0.405785
$232$	4.52160	0.296857
$233$	−2.26438	−0.148344	−0.0741722	−	0.997245i	$-0.523631\pi$
$233$	−2.26438	−0.148344	−0.0741722	+	0.997245i	$0.523631\pi$
$234$	−18.2350	−1.19206
$235$	−4.76574	−0.310883
$236$	1.87670	0.122163
$237$	11.9161	0.774031
$238$	−5.11545	−0.331585
$239$	−15.0808	−0.975494	−0.487747	−	0.872985i	$-0.662181\pi$
$239$	−15.0808	−0.975494	−0.487747	+	0.872985i	$0.662181\pi$
$240$	−1.01974	−0.0658241
$241$	25.1895	1.62260	0.811299	−	0.584632i	$-0.198761\pi$
$241$	25.1895	1.62260	0.811299	+	0.584632i	$0.198761\pi$
$242$	8.92971	0.574023
$243$	15.6960	1.00690
$244$	−10.0127	−0.640999
$245$	−1.69589	−0.108346
$246$	7.90373	0.503924
$247$	2.52350	0.160566
$248$	−1.00000	−0.0635001
$249$	6.15684	0.390174
$250$	3.59305	0.227244
$251$	−13.2492	−0.836280	−0.418140	−	0.908382i	$-0.637318\pi$
$251$	−13.2492	−0.836280	−0.418140	+	0.908382i	$0.637318\pi$
$252$	7.41201	0.466913
$253$	2.98267	0.187519
$254$	17.7322	1.11262
$255$	−3.40815	−0.213426
$256$	1.00000	0.0625000
$257$	−18.5817	−1.15910	−0.579548	−	0.814938i	$-0.696771\pi$
$257$	−18.5817	−1.15910	−0.579548	+	0.814938i	$0.696771\pi$
$258$	−10.0193	−0.623777
$259$	−13.3340	−0.828533
$260$	1.37115	0.0850354
$261$	−21.8963	−1.35535
$262$	−3.71215	−0.229337
$263$	−2.78229	−0.171563	−0.0857816	−	0.996314i	$-0.527339\pi$
$263$	−2.78229	−0.171563	−0.0857816	+	0.996314i	$0.527339\pi$
$264$	4.02945	0.247996
$265$	0.641106	0.0393828
$266$	−1.02573	−0.0628916
$267$	14.1968	0.868833
$268$	13.4531	0.821780
$269$	5.74062	0.350012	0.175006	−	0.984567i	$-0.444006\pi$
$269$	5.74062	0.350012	0.175006	+	0.984567i	$0.444006\pi$
$270$	1.87899	0.114352
$271$	−18.5064	−1.12418	−0.562092	−	0.827075i	$-0.690003\pi$
$271$	−18.5064	−1.12418	−0.562092	+	0.827075i	$0.690003\pi$
$272$	3.34216	0.202648
$273$	−16.1403	−0.976857
$274$	8.30760	0.501880
$275$	−7.00347	−0.422325
$276$	−5.80524	−0.349435
$277$	−3.92282	−0.235699	−0.117850	−	0.993031i	$-0.537600\pi$
$277$	−3.92282	−0.235699	−0.117850	+	0.993031i	$0.537600\pi$
$278$	−17.6888	−1.06091
$279$	4.84261	0.289920
$280$	−0.557335	−0.0333071
$281$	19.6067	1.16964	0.584819	−	0.811164i	$-0.301166\pi$
$281$	19.6067	1.16964	0.584819	+	0.811164i	$0.301166\pi$
$282$	−36.6522	−2.18261
$283$	−15.1441	−0.900226	−0.450113	−	0.892972i	$-0.648616\pi$
$283$	−15.1441	−0.900226	−0.450113	+	0.892972i	$0.648616\pi$
$284$	−1.91017	−0.113348
$285$	−0.683389	−0.0404805
$286$	−5.41803	−0.320375
$287$	4.31975	0.254986
$288$	−4.84261	−0.285354
$289$	−5.82994	−0.342938
$290$	1.64646	0.0966837
$291$	−2.80047	−0.164166
$292$	−1.06852	−0.0625307
$293$	21.9990	1.28520	0.642598	−	0.766204i	$-0.277857\pi$
$293$	21.9990	1.28520	0.642598	+	0.766204i	$0.277857\pi$
$294$	−13.0427	−0.760664
$295$	0.683371	0.0397874
$296$	8.71171	0.506358
$297$	−7.42472	−0.430826
$298$	−12.1570	−0.704235
$299$	7.80577	0.451420
$300$	13.6310	0.786987
$301$	−5.47602	−0.315632
$302$	4.97550	0.286308
$303$	−2.61972	−0.150499
$304$	0.670158	0.0384362
$305$	−3.64597	−0.208767
$306$	−16.1848	−0.925223
$307$	−15.1754	−0.866103	−0.433052	−	0.901369i	$-0.642563\pi$
$307$	−15.1754	−0.866103	−0.433052	+	0.901369i	$0.642563\pi$
$308$	2.20228	0.125486
$309$	−9.95104	−0.566095
$310$	−0.364133	−0.0206814
$311$	−31.8151	−1.80407	−0.902034	−	0.431666i	$-0.857926\pi$
$311$	−31.8151	−1.80407	−0.902034	+	0.431666i	$0.857926\pi$
$312$	10.5452	0.597006
$313$	−20.9498	−1.18415	−0.592077	−	0.805881i	$-0.701692\pi$
$313$	−20.9498	−1.18415	−0.592077	+	0.805881i	$0.701692\pi$
$314$	4.92292	0.277816
$315$	2.69896	0.152069
$316$	−4.25502	−0.239364
$317$	32.8482	1.84494	0.922468	−	0.386073i	$-0.126169\pi$
$317$	32.8482	1.84494	0.922468	+	0.386073i	$0.126169\pi$
$318$	4.93060	0.276494
$319$	−6.50590	−0.364261
$320$	0.364133	0.0203557
$321$	39.8535	2.22440
$322$	−3.17283	−0.176815
$323$	2.23978	0.124625
$324$	−0.0769468	−0.00427482
$325$	−18.3284	−1.01667
$326$	−19.8430	−1.09900
$327$	39.1210	2.16339
$328$	−2.82229	−0.155835
$329$	−20.0321	−1.10441
$330$	1.46726	0.0807699
$331$	20.7246	1.13913	0.569564	−	0.821947i	$-0.307112\pi$
$331$	20.7246	1.13913	0.569564	+	0.821947i	$0.307112\pi$
$332$	−2.19851	−0.120659
$333$	−42.1874	−2.31186
$334$	−16.0420	−0.877777
$335$	4.89873	0.267646
$336$	−4.28634	−0.233839
$337$	−2.32309	−0.126547	−0.0632734	−	0.997996i	$-0.520154\pi$
$337$	−2.32309	−0.126547	−0.0632734	+	0.997996i	$0.520154\pi$
$338$	−1.17920	−0.0641402
$339$	28.3074	1.53744
$340$	1.21699	0.0660007
$341$	1.43885	0.0779181
$342$	−3.24532	−0.175487
$343$	−17.8425	−0.963403
$344$	3.57774	0.192899
$345$	−2.11388	−0.113808
$346$	−6.66014	−0.358051
$347$	−17.2884	−0.928088	−0.464044	−	0.885812i	$-0.653602\pi$
$347$	−17.2884	−0.928088	−0.464044	+	0.885812i	$0.653602\pi$
$348$	12.6626	0.678786
$349$	−1.89157	−0.101253	−0.0506267	−	0.998718i	$-0.516122\pi$
$349$	−1.89157	−0.101253	−0.0506267	+	0.998718i	$0.516122\pi$
$350$	7.44996	0.398217
$351$	−19.4308	−1.03714
$352$	−1.43885	−0.0766910
$353$	−3.91314	−0.208275	−0.104138	−	0.994563i	$-0.533208\pi$
$353$	−3.91314	−0.208275	−0.104138	+	0.994563i	$0.533208\pi$
$354$	5.25565	0.279335
$355$	−0.695557	−0.0369164
$356$	−5.06946	−0.268681
$357$	−14.3256	−0.758194
$358$	10.3405	0.546513
$359$	−27.1126	−1.43095	−0.715475	−	0.698638i	$-0.753790\pi$
$359$	−27.1126	−1.43095	−0.715475	+	0.698638i	$0.753790\pi$
$360$	−1.76336	−0.0929370
$361$	−18.5509	−0.976363
$362$	17.0760	0.897493
$363$	25.0073	1.31255
$364$	5.76344	0.302087
$365$	−0.389085	−0.0203657
$366$	−28.0403	−1.46569
$367$	−19.9093	−1.03926	−0.519629	−	0.854392i	$-0.673930\pi$
$367$	−19.9093	−1.03926	−0.519629	+	0.854392i	$0.673930\pi$
$368$	2.07296	0.108060
$369$	13.6673	0.711489
$370$	3.17222	0.164916
$371$	2.69480	0.139907
$372$	−2.80047	−0.145197
$373$	−10.0669	−0.521243	−0.260622	−	0.965441i	$-0.583927\pi$
$373$	−10.0669	−0.521243	−0.260622	+	0.965441i	$0.583927\pi$
$374$	−4.80887	−0.248661
$375$	10.0622	0.519611
$376$	13.0879	0.674957
$377$	−17.0262	−0.876894
$378$	7.89806	0.406232
$379$	−20.5321	−1.05466	−0.527331	−	0.849660i	$-0.676807\pi$
$379$	−20.5321	−1.05466	−0.527331	+	0.849660i	$0.676807\pi$
$380$	0.244027	0.0125183
$381$	49.6585	2.54408
$382$	−27.3748	−1.40062
$383$	29.8868	1.52714	0.763572	−	0.645723i	$-0.223444\pi$
$383$	29.8868	1.52714	0.763572	+	0.645723i	$0.223444\pi$
$384$	2.80047	0.142911
$385$	0.801922	0.0408697
$386$	6.13879	0.312456
$387$	−17.3256	−0.880710
$388$	1.00000	0.0507673
$389$	25.5269	1.29426	0.647132	−	0.762378i	$-0.275968\pi$
$389$	25.5269	1.29426	0.647132	+	0.762378i	$0.275968\pi$
$390$	3.83987	0.194439
$391$	6.92816	0.350372
$392$	4.65732	0.235230
$393$	−10.3957	−0.524396
$394$	−19.5580	−0.985316
$395$	−1.54940	−0.0779586
$396$	6.96780	0.350145
$397$	−21.5616	−1.08214	−0.541072	−	0.840977i	$-0.681981\pi$
$397$	−21.5616	−1.08214	−0.541072	+	0.840977i	$0.681981\pi$
$398$	−18.1166	−0.908102
$399$	−2.87253	−0.143806
$400$	−4.86741	−0.243370
$401$	−31.3875	−1.56742	−0.783709	−	0.621128i	$-0.786675\pi$
$401$	−31.3875	−1.56742	−0.783709	+	0.621128i	$0.786675\pi$
$402$	37.6750	1.87906
$403$	3.76553	0.187574
$404$	0.935457	0.0465407
$405$	−0.0280189	−0.00139227
$406$	6.92067	0.343467
$407$	−12.5348	−0.621329
$408$	9.35962	0.463370
$409$	22.6512	1.12003	0.560015	−	0.828483i	$-0.310796\pi$
$409$	22.6512	1.12003	0.560015	+	0.828483i	$0.310796\pi$
$410$	−1.02769	−0.0507540
$411$	23.2652	1.14759
$412$	3.55335	0.175061
$413$	2.87245	0.141344
$414$	−10.0385	−0.493366
$415$	−0.800549	−0.0392974
$416$	−3.76553	−0.184620
$417$	−49.5370	−2.42584
$418$	−0.964258	−0.0471634
$419$	−35.5722	−1.73782	−0.868908	−	0.494974i	$-0.835178\pi$
$419$	−35.5722	−1.73782	−0.868908	+	0.494974i	$0.835178\pi$
$420$	−1.56080	−0.0761592
$421$	−25.7513	−1.25504	−0.627520	−	0.778600i	$-0.715930\pi$
$421$	−25.7513	−1.25504	−0.627520	+	0.778600i	$0.715930\pi$
$422$	25.6339	1.24784
$423$	−63.3797	−3.08162
$424$	−1.76064	−0.0855041
$425$	−16.2677	−0.789098
$426$	−5.34937	−0.259178
$427$	−15.3253	−0.741642
$428$	−14.2310	−0.687882
$429$	−15.1730	−0.732560
$430$	1.30277	0.0628253
$431$	11.6626	0.561767	0.280883	−	0.959742i	$-0.409373\pi$
$431$	11.6626	0.561767	0.280883	+	0.959742i	$0.409373\pi$
$432$	−5.16017	−0.248269
$433$	−19.8514	−0.953997	−0.476999	−	0.878904i	$-0.658275\pi$
$433$	−19.8514	−0.953997	−0.476999	+	0.878904i	$0.658275\pi$
$434$	−1.53058	−0.0734702
$435$	4.61087	0.221074
$436$	−13.9694	−0.669015
$437$	1.38921	0.0664549
$438$	−2.99237	−0.142981
$439$	13.8206	0.659621	0.329810	−	0.944047i	$-0.393015\pi$
$439$	13.8206	0.659621	0.329810	+	0.944047i	$0.393015\pi$
$440$	−0.523933	−0.0249775
$441$	−22.5536	−1.07398
$442$	−12.5850	−0.598608
$443$	20.9391	0.994845	0.497422	−	0.867509i	$-0.334280\pi$
$443$	20.9391	0.994845	0.497422	+	0.867509i	$0.334280\pi$
$444$	24.3968	1.15782
$445$	−1.84596	−0.0875068
$446$	−19.5468	−0.925568
$447$	−34.0452	−1.61028
$448$	1.53058	0.0723131
$449$	−14.7050	−0.693971	−0.346985	−	0.937871i	$-0.612795\pi$
$449$	−14.7050	−0.693971	−0.346985	+	0.937871i	$0.612795\pi$
$450$	23.5710	1.11115
$451$	4.06086	0.191218
$452$	−10.1081	−0.475445
$453$	13.9337	0.654663
$454$	−17.5275	−0.822606
$455$	2.09866	0.0983868
$456$	1.87676	0.0878871
$457$	18.8320	0.880926	0.440463	−	0.897771i	$-0.354814\pi$
$457$	18.8320	0.880926	0.440463	+	0.897771i	$0.354814\pi$
$458$	24.6544	1.15203
$459$	−17.2461	−0.804981
$460$	0.754832	0.0351942
$461$	−17.5292	−0.816418	−0.408209	−	0.912889i	$-0.633846\pi$
$461$	−17.5292	−0.816418	−0.408209	+	0.912889i	$0.633846\pi$
$462$	6.16740	0.286933
$463$	5.67588	0.263780	0.131890	−	0.991264i	$-0.457895\pi$
$463$	5.67588	0.263780	0.131890	+	0.991264i	$0.457895\pi$
$464$	−4.52160	−0.209910
$465$	−1.01974	−0.0472894
$466$	2.26438	0.104895
$467$	24.1576	1.11788	0.558941	−	0.829208i	$-0.311208\pi$
$467$	24.1576	1.11788	0.558941	+	0.829208i	$0.311208\pi$
$468$	18.2350	0.842913
$469$	20.5911	0.950808
$470$	4.76574	0.219827
$471$	13.7865	0.635247
$472$	−1.87670	−0.0863823
$473$	−5.14783	−0.236698
$474$	−11.9161	−0.547322
$475$	−3.26193	−0.149668
$476$	5.11545	0.234466
$477$	8.52608	0.390382
$478$	15.0808	0.689779
$479$	−1.34048	−0.0612483	−0.0306242	−	0.999531i	$-0.509749\pi$
$479$	−1.34048	−0.0612483	−0.0306242	+	0.999531i	$0.509749\pi$
$480$	1.01974	0.0465447
$481$	−32.8042	−1.49574
$482$	−25.1895	−1.14735
$483$	−8.88539	−0.404299
$484$	−8.92971	−0.405896
$485$	0.364133	0.0165344
$486$	−15.6960	−0.711985
$487$	16.8959	0.765628	0.382814	−	0.923826i	$-0.374955\pi$
$487$	16.8959	0.765628	0.382814	+	0.923826i	$0.374955\pi$
$488$	10.0127	0.453255
$489$	−55.5695	−2.51294
$490$	1.69589	0.0766123
$491$	34.0805	1.53803	0.769015	−	0.639231i	$-0.220747\pi$
$491$	34.0805	1.53803	0.769015	+	0.639231i	$0.220747\pi$
$492$	−7.90373	−0.356328
$493$	−15.1119	−0.680607
$494$	−2.52350	−0.113538
$495$	2.53721	0.114039
$496$	1.00000	0.0449013
$497$	−2.92367	−0.131145
$498$	−6.15684	−0.275895
$499$	8.34283	0.373476	0.186738	−	0.982410i	$-0.440208\pi$
$499$	8.34283	0.373476	0.186738	+	0.982410i	$0.440208\pi$
$500$	−3.59305	−0.160686
$501$	−44.9250	−2.00710
$502$	13.2492	0.591340
$503$	−25.4233	−1.13357	−0.566785	−	0.823866i	$-0.691813\pi$
$503$	−25.4233	−1.13357	−0.566785	+	0.823866i	$0.691813\pi$
$504$	−7.41201	−0.330157
$505$	0.340631	0.0151579
$506$	−2.98267	−0.132596
$507$	−3.30232	−0.146661
$508$	−17.7322	−0.786741
$509$	−30.3133	−1.34361	−0.671807	−	0.740726i	$-0.734482\pi$
$509$	−30.3133	−1.34361	−0.671807	+	0.740726i	$0.734482\pi$
$510$	3.40815	0.150915
$511$	−1.63546	−0.0723486
$512$	−1.00000	−0.0441942
$513$	−3.45813	−0.152680
$514$	18.5817	0.819605
$515$	1.29389	0.0570157
$516$	10.0193	0.441077
$517$	−18.8315	−0.828210
$518$	13.3340	0.585861
$519$	−18.6515	−0.818710
$520$	−1.37115	−0.0601291
$521$	−35.0464	−1.53541	−0.767704	−	0.640804i	$-0.778601\pi$
$521$	−35.0464	−1.53541	−0.767704	+	0.640804i	$0.778601\pi$
$522$	21.8963	0.958377
$523$	10.6166	0.464229	0.232115	−	0.972688i	$-0.425436\pi$
$523$	10.6166	0.464229	0.232115	+	0.972688i	$0.425436\pi$
$524$	3.71215	0.162166
$525$	20.8634	0.910551
$526$	2.78229	0.121313
$527$	3.34216	0.145587
$528$	−4.02945	−0.175359
$529$	−18.7029	−0.813168
$530$	−0.641106	−0.0278479
$531$	9.08815	0.394392
$532$	1.02573	0.0444711
$533$	10.6274	0.460325
$534$	−14.1968	−0.614357
$535$	−5.18199	−0.224037
$536$	−13.4531	−0.581086
$537$	28.9583	1.24964
$538$	−5.74062	−0.247496
$539$	−6.70119	−0.288641
$540$	−1.87899	−0.0808589
$541$	−22.2839	−0.958059	−0.479030	−	0.877799i	$-0.659011\pi$
$541$	−22.2839	−0.958059	−0.479030	+	0.877799i	$0.659011\pi$
$542$	18.5064	0.794918
$543$	47.8206	2.05218
$544$	−3.34216	−0.143294
$545$	−5.08674	−0.217892
$546$	16.1403	0.690742
$547$	35.9391	1.53664	0.768322	−	0.640064i	$-0.221092\pi$
$547$	35.9391	1.53664	0.768322	+	0.640064i	$0.221092\pi$
$548$	−8.30760	−0.354883
$549$	−48.4877	−2.06941
$550$	7.00347	0.298629
$551$	−3.03019	−0.129090
$552$	5.80524	0.247088
$553$	−6.51266	−0.276946
$554$	3.92282	0.166665
$555$	8.88370	0.377092
$556$	17.6888	0.750173
$557$	16.2781	0.689726	0.344863	−	0.938653i	$-0.387925\pi$
$557$	16.2781	0.689726	0.344863	+	0.938653i	$0.387925\pi$
$558$	−4.84261	−0.205004
$559$	−13.4721	−0.569808
$560$	0.557335	0.0235517
$561$	−13.4671	−0.568581
$562$	−19.6067	−0.827059
$563$	22.7253	0.957755	0.478878	−	0.877882i	$-0.341044\pi$
$563$	22.7253	0.957755	0.478878	+	0.877882i	$0.341044\pi$
$564$	36.6522	1.54334
$565$	−3.68069	−0.154848
$566$	15.1441	0.636556
$567$	−0.117773	−0.00494601
$568$	1.91017	0.0801491
$569$	−8.51529	−0.356980	−0.178490	−	0.983942i	$-0.557121\pi$
$569$	−8.51529	−0.356980	−0.178490	+	0.983942i	$0.557121\pi$
$570$	0.683389	0.0286240
$571$	−36.1386	−1.51235	−0.756177	−	0.654367i	$-0.772935\pi$
$571$	−36.1386	−1.51235	−0.756177	+	0.654367i	$0.772935\pi$
$572$	5.41803	0.226539
$573$	−76.6622	−3.20261
$574$	−4.31975	−0.180303
$575$	−10.0899	−0.420779
$576$	4.84261	0.201775
$577$	8.27183	0.344361	0.172180	−	0.985065i	$-0.444919\pi$
$577$	8.27183	0.344361	0.172180	+	0.985065i	$0.444919\pi$
$578$	5.82994	0.242494
$579$	17.1915	0.714453
$580$	−1.64646	−0.0683657
$581$	−3.36499	−0.139603
$582$	2.80047	0.116083
$583$	2.53329	0.104918
$584$	1.06852	0.0442159
$585$	6.63997	0.274529
$586$	−21.9990	−0.908770
$587$	−11.2526	−0.464443	−0.232222	−	0.972663i	$-0.574599\pi$
$587$	−11.2526	−0.464443	−0.232222	+	0.972663i	$0.574599\pi$
$588$	13.0427	0.537871
$589$	0.670158	0.0276134
$590$	−0.683371	−0.0281339
$591$	−54.7714	−2.25300
$592$	−8.71171	−0.358049
$593$	−45.2424	−1.85788	−0.928941	−	0.370228i	$-0.879280\pi$
$593$	−45.2424	−1.85788	−0.928941	+	0.370228i	$0.879280\pi$
$594$	7.42472	0.304640
$595$	1.86271	0.0763635
$596$	12.1570	0.497969
$597$	−50.7349	−2.07644
$598$	−7.80577	−0.319202
$599$	43.4783	1.77648	0.888238	−	0.459384i	$-0.151930\pi$
$599$	43.4783	1.77648	0.888238	+	0.459384i	$0.151930\pi$
$600$	−13.6310	−0.556484
$601$	−42.5879	−1.73720	−0.868598	−	0.495517i	$-0.834979\pi$
$601$	−42.5879	−1.73720	−0.868598	+	0.495517i	$0.834979\pi$
$602$	5.47602	0.223186
$603$	65.1482	2.65304
$604$	−4.97550	−0.202450
$605$	−3.25160	−0.132196
$606$	2.61972	0.106419
$607$	−8.97528	−0.364296	−0.182148	−	0.983271i	$-0.558305\pi$
$607$	−8.97528	−0.364296	−0.182148	+	0.983271i	$0.558305\pi$
$608$	−0.670158	−0.0271785
$609$	19.3811	0.785362
$610$	3.64597	0.147621
$611$	−49.2829	−1.99377
$612$	16.1848	0.654232
$613$	40.3862	1.63118	0.815592	−	0.578627i	$-0.196411\pi$
$613$	40.3862	1.63118	0.815592	+	0.578627i	$0.196411\pi$
$614$	15.1754	0.612427
$615$	−2.87801	−0.116053
$616$	−2.20228	−0.0887323
$617$	14.8134	0.596367	0.298183	−	0.954509i	$-0.403619\pi$
$617$	14.8134	0.596367	0.298183	+	0.954509i	$0.403619\pi$
$618$	9.95104	0.400289
$619$	27.6227	1.11025	0.555125	−	0.831767i	$-0.312671\pi$
$619$	27.6227	1.11025	0.555125	+	0.831767i	$0.312671\pi$
$620$	0.364133	0.0146239
$621$	−10.6968	−0.429248
$622$	31.8151	1.27567
$623$	−7.75921	−0.310866
$624$	−10.5452	−0.422147
$625$	23.0287	0.921147
$626$	20.9498	0.837324
$627$	−2.70037	−0.107842
$628$	−4.92292	−0.196446
$629$	−29.1160	−1.16093
$630$	−2.69896	−0.107529
$631$	−20.6464	−0.821920	−0.410960	−	0.911653i	$-0.634806\pi$
$631$	−20.6464	−0.821920	−0.410960	+	0.911653i	$0.634806\pi$
$632$	4.25502	0.169256
$633$	71.7868	2.85327
$634$	−32.8482	−1.30457
$635$	−6.45690	−0.256234
$636$	−4.93060	−0.195511
$637$	−17.5373	−0.694852
$638$	6.50590	0.257571
$639$	−9.25023	−0.365933
$640$	−0.364133	−0.0143936
$641$	27.5407	1.08779	0.543896	−	0.839153i	$-0.316949\pi$
$641$	27.5407	1.08779	0.543896	+	0.839153i	$0.316949\pi$
$642$	−39.8535	−1.57289
$643$	4.84670	0.191135	0.0955676	−	0.995423i	$-0.469533\pi$
$643$	4.84670	0.191135	0.0955676	+	0.995423i	$0.469533\pi$
$644$	3.17283	0.125027
$645$	3.64838	0.143655
$646$	−2.23978	−0.0881229
$647$	10.6987	0.420607	0.210304	−	0.977636i	$-0.432555\pi$
$647$	10.6987	0.420607	0.210304	+	0.977636i	$0.432555\pi$
$648$	0.0769468	0.00302275
$649$	2.70030	0.105996
$650$	18.3284	0.718897
$651$	−4.28634	−0.167995
$652$	19.8430	0.777110
$653$	29.3014	1.14665	0.573327	−	0.819327i	$-0.305652\pi$
$653$	29.3014	1.14665	0.573327	+	0.819327i	$0.305652\pi$
$654$	−39.1210	−1.52975
$655$	1.35172	0.0528159
$656$	2.82229	0.110192
$657$	−5.17445	−0.201875
$658$	20.0321	0.780932
$659$	−7.19287	−0.280195	−0.140097	−	0.990138i	$-0.544742\pi$
$659$	−7.19287	−0.280195	−0.140097	+	0.990138i	$0.544742\pi$
$660$	−1.46726	−0.0571129
$661$	−23.7883	−0.925257	−0.462628	−	0.886552i	$-0.653094\pi$
$661$	−23.7883	−0.925257	−0.462628	+	0.886552i	$0.653094\pi$
$662$	−20.7246	−0.805486
$663$	−35.2439	−1.36876
$664$	2.19851	0.0853186
$665$	0.373503	0.0144838
$666$	42.1874	1.63473
$667$	−9.37307	−0.362927
$668$	16.0420	0.620682
$669$	−54.7402	−2.11638
$670$	−4.89873	−0.189254
$671$	−14.4068	−0.556169
$672$	4.28634	0.165349
$673$	−7.44408	−0.286948	−0.143474	−	0.989654i	$-0.545827\pi$
$673$	−7.44408	−0.286948	−0.143474	+	0.989654i	$0.545827\pi$
$674$	2.32309	0.0894820
$675$	25.1167	0.966741
$676$	1.17920	0.0453539
$677$	14.1348	0.543244	0.271622	−	0.962404i	$-0.412440\pi$
$677$	14.1348	0.543244	0.271622	+	0.962404i	$0.412440\pi$
$678$	−28.3074	−1.08714
$679$	1.53058	0.0587383
$680$	−1.21699	−0.0466695
$681$	−49.0852	−1.88095
$682$	−1.43885	−0.0550964
$683$	−7.85158	−0.300432	−0.150216	−	0.988653i	$-0.547997\pi$
$683$	−7.85158	−0.300432	−0.150216	+	0.988653i	$0.547997\pi$
$684$	3.24532	0.124088
$685$	−3.02507	−0.115582
$686$	17.8425	0.681229
$687$	69.0439	2.63419
$688$	−3.57774	−0.136400
$689$	6.62973	0.252572
$690$	2.11388	0.0804741
$691$	−22.7493	−0.865423	−0.432712	−	0.901532i	$-0.642443\pi$
$691$	−22.7493	−0.865423	−0.432712	+	0.901532i	$0.642443\pi$
$692$	6.66014	0.253181
$693$	10.6648	0.405121
$694$	17.2884	0.656257
$695$	6.44109	0.244324
$696$	−12.6626	−0.479974
$697$	9.43256	0.357284
$698$	1.89157	0.0715969
$699$	6.34132	0.239851
$700$	−7.44996	−0.281582
$701$	−3.51518	−0.132766	−0.0663832	−	0.997794i	$-0.521146\pi$
$701$	−3.51518	−0.132766	−0.0663832	+	0.997794i	$0.521146\pi$
$702$	19.4308	0.733367
$703$	−5.83822	−0.220193
$704$	1.43885	0.0542287
$705$	13.3463	0.502651
$706$	3.91314	0.147273
$707$	1.43179	0.0538481
$708$	−5.25565	−0.197519
$709$	37.8472	1.42138	0.710691	−	0.703504i	$-0.248382\pi$
$709$	37.8472	1.42138	0.710691	+	0.703504i	$0.248382\pi$
$710$	0.695557	0.0261038
$711$	−20.6054	−0.772764
$712$	5.06946	0.189986
$713$	2.07296	0.0776328
$714$	14.3256	0.536124
$715$	1.97289	0.0737817
$716$	−10.3405	−0.386443
$717$	42.2332	1.57723
$718$	27.1126	1.01184
$719$	−16.0295	−0.597798	−0.298899	−	0.954285i	$-0.596619\pi$
$719$	−16.0295	−0.597798	−0.298899	+	0.954285i	$0.596619\pi$
$720$	1.76336	0.0657164
$721$	5.43869	0.202547
$722$	18.5509	0.690393
$723$	−70.5423	−2.62350
$724$	−17.0760	−0.634623
$725$	22.0085	0.817374
$726$	−25.0073	−0.928110
$727$	−17.8259	−0.661126	−0.330563	−	0.943784i	$-0.607239\pi$
$727$	−17.8259	−0.661126	−0.330563	+	0.943784i	$0.607239\pi$
$728$	−5.76344	−0.213607
$729$	−43.7253	−1.61946
$730$	0.389085	0.0144007
$731$	−11.9574	−0.442260
$732$	28.0403	1.03640
$733$	−3.24648	−0.119911	−0.0599556	−	0.998201i	$-0.519096\pi$
$733$	−3.24648	−0.119911	−0.0599556	+	0.998201i	$0.519096\pi$
$734$	19.9093	0.734867
$735$	4.74927	0.175180
$736$	−2.07296	−0.0764102
$737$	19.3570	0.713025
$738$	−13.6673	−0.503099
$739$	24.1261	0.887494	0.443747	−	0.896152i	$-0.353649\pi$
$739$	24.1261	0.887494	0.443747	+	0.896152i	$0.353649\pi$
$740$	−3.17222	−0.116613
$741$	−7.06698	−0.259612
$742$	−2.69480	−0.0989291
$743$	−5.88641	−0.215951	−0.107976	−	0.994154i	$-0.534437\pi$
$743$	−5.88641	−0.215951	−0.107976	+	0.994154i	$0.534437\pi$
$744$	2.80047	0.102670
$745$	4.42676	0.162184
$746$	10.0669	0.368574
$747$	−10.6465	−0.389535
$748$	4.80887	0.175830
$749$	−21.7817	−0.795887
$750$	−10.0622	−0.367420
$751$	8.11628	0.296167	0.148084	−	0.988975i	$-0.452690\pi$
$751$	8.11628	0.296167	0.148084	+	0.988975i	$0.452690\pi$
$752$	−13.0879	−0.477267
$753$	37.1039	1.35214
$754$	17.0262	0.620058
$755$	−1.81174	−0.0659361
$756$	−7.89806	−0.287250
$757$	29.4492	1.07035	0.535175	−	0.844741i	$-0.320246\pi$
$757$	29.4492	1.07035	0.535175	+	0.844741i	$0.320246\pi$
$758$	20.5321	0.745759
$759$	−8.35288	−0.303190
$760$	−0.244027	−0.00885179
$761$	3.52785	0.127885	0.0639423	−	0.997954i	$-0.479633\pi$
$761$	3.52785	0.127885	0.0639423	+	0.997954i	$0.479633\pi$
$762$	−49.6585	−1.79894
$763$	−21.3814	−0.774057
$764$	27.3748	0.990386
$765$	5.89342	0.213077
$766$	−29.8868	−1.07985
$767$	7.06678	0.255167
$768$	−2.80047	−0.101053
$769$	−34.3465	−1.23857	−0.619283	−	0.785168i	$-0.712576\pi$
$769$	−34.3465	−1.23857	−0.619283	+	0.785168i	$0.712576\pi$
$770$	−0.801922	−0.0288993
$771$	52.0375	1.87408
$772$	−6.13879	−0.220940
$773$	18.7035	0.672718	0.336359	−	0.941734i	$-0.390804\pi$
$773$	18.7035	0.672718	0.336359	+	0.941734i	$0.390804\pi$
$774$	17.3256	0.622756
$775$	−4.86741	−0.174842
$776$	−1.00000	−0.0358979
$777$	37.3413	1.33961
$778$	−25.5269	−0.915182
$779$	1.89138	0.0677658
$780$	−3.83987	−0.137489
$781$	−2.74845	−0.0983474
$782$	−6.92816	−0.247750
$783$	23.3322	0.833826
$784$	−4.65732	−0.166333
$785$	−1.79260	−0.0639806
$786$	10.3957	0.370804
$787$	48.6019	1.73247	0.866235	−	0.499637i	$-0.166533\pi$
$787$	48.6019	1.73247	0.866235	+	0.499637i	$0.166533\pi$
$788$	19.5580	0.696724
$789$	7.79170	0.277392
$790$	1.54940	0.0551250
$791$	−15.4712	−0.550094
$792$	−6.96780	−0.247590
$793$	−37.7032	−1.33888
$794$	21.5616	0.765191
$795$	−1.79540	−0.0636761
$796$	18.1166	0.642125
$797$	−7.55245	−0.267521	−0.133761	−	0.991014i	$-0.542705\pi$
$797$	−7.55245	−0.267521	−0.133761	+	0.991014i	$0.542705\pi$
$798$	2.87253	0.101686
$799$	−43.7419	−1.54748
$800$	4.86741	0.172089
$801$	−24.5494	−0.867411
$802$	31.3875	1.10833
$803$	−1.53745	−0.0542553
$804$	−37.6750	−1.32870
$805$	1.15533	0.0407201
$806$	−3.76553	−0.132635
$807$	−16.0764	−0.565916
$808$	−0.935457	−0.0329093
$809$	39.8892	1.40243	0.701215	−	0.712950i	$-0.252641\pi$
$809$	39.8892	1.40243	0.701215	+	0.712950i	$0.252641\pi$
$810$	0.0280189	0.000984483 0
$811$	34.5213	1.21221	0.606104	−	0.795385i	$-0.292732\pi$
$811$	34.5213	1.21221	0.606104	+	0.795385i	$0.292732\pi$
$812$	−6.92067	−0.242868
$813$	51.8266	1.81764
$814$	12.5348	0.439346
$815$	7.22548	0.253098
$816$	−9.35962	−0.327652
$817$	−2.39765	−0.0838832
$818$	−22.6512	−0.791980
$819$	27.9101	0.975258
$820$	1.02769	0.0358885
$821$	−54.4344	−1.89977	−0.949887	−	0.312595i	$-0.898802\pi$
$821$	−54.4344	−1.89977	−0.949887	+	0.312595i	$0.898802\pi$
$822$	−23.2652	−0.811465
$823$	−48.6789	−1.69684	−0.848421	−	0.529323i	$-0.822446\pi$
$823$	−48.6789	−1.69684	−0.848421	+	0.529323i	$0.822446\pi$
$824$	−3.55335	−0.123787
$825$	19.6130	0.682837
$826$	−2.87245	−0.0999452
$827$	−25.5046	−0.886883	−0.443441	−	0.896303i	$-0.646243\pi$
$827$	−25.5046	−0.886883	−0.443441	+	0.896303i	$0.646243\pi$
$828$	10.0385	0.348863
$829$	10.3132	0.358193	0.179096	−	0.983832i	$-0.442683\pi$
$829$	10.3132	0.358193	0.179096	+	0.983832i	$0.442683\pi$
$830$	0.800549	0.0277875
$831$	10.9857	0.381091
$832$	3.76553	0.130546
$833$	−15.5655	−0.539314
$834$	49.5370	1.71532
$835$	5.84141	0.202150
$836$	0.964258	0.0333495
$837$	−5.16017	−0.178362
$838$	35.5722	1.22882
$839$	27.1673	0.937920	0.468960	−	0.883220i	$-0.344629\pi$
$839$	27.1673	0.937920	0.468960	+	0.883220i	$0.344629\pi$
$840$	1.56080	0.0538527
$841$	−8.55515	−0.295005
$842$	25.7513	0.887448
$843$	−54.9079	−1.89113
$844$	−25.6339	−0.882355
$845$	0.429387	0.0147714
$846$	63.3797	2.17904
$847$	−13.6676	−0.469626
$848$	1.76064	0.0604605
$849$	42.4107	1.45553
$850$	16.2677	0.557976
$851$	−18.0590	−0.619054
$852$	5.34937	0.183267
$853$	−32.9812	−1.12925	−0.564627	−	0.825346i	$-0.690980\pi$
$853$	−32.9812	−1.12925	−0.564627	+	0.825346i	$0.690980\pi$
$854$	15.3253	0.524420
$855$	1.18173	0.0404142
$856$	14.2310	0.486406
$857$	19.1437	0.653935	0.326967	−	0.945036i	$-0.393973\pi$
$857$	19.1437	0.653935	0.326967	+	0.945036i	$0.393973\pi$
$858$	15.1730	0.517998
$859$	15.4562	0.527359	0.263679	−	0.964610i	$-0.415064\pi$
$859$	15.4562	0.527359	0.263679	+	0.964610i	$0.415064\pi$
$860$	−1.30277	−0.0444242
$861$	−12.0973	−0.412275
$862$	−11.6626	−0.397229
$863$	51.7744	1.76242	0.881211	−	0.472723i	$-0.156729\pi$
$863$	51.7744	1.76242	0.881211	+	0.472723i	$0.156729\pi$
$864$	5.16017	0.175553
$865$	2.42518	0.0824586
$866$	19.8514	0.674578
$867$	16.3266	0.554479
$868$	1.53058	0.0519513
$869$	−6.12234	−0.207686
$870$	−4.61087	−0.156323
$871$	50.6581	1.71648
$872$	13.9694	0.473065
$873$	4.84261	0.163898
$874$	−1.38921	−0.0469907
$875$	−5.49945	−0.185915
$876$	2.99237	0.101103
$877$	19.7422	0.666648	0.333324	−	0.942812i	$-0.391830\pi$
$877$	19.7422	0.666648	0.333324	+	0.942812i	$0.391830\pi$
$878$	−13.8206	−0.466422
$879$	−61.6075	−2.07797
$880$	0.523933	0.0176618
$881$	−47.1938	−1.59000	−0.794999	−	0.606611i	$-0.792529\pi$
$881$	−47.1938	−1.59000	−0.794999	+	0.606611i	$0.792529\pi$
$882$	22.5536	0.759420
$883$	−42.7932	−1.44011	−0.720054	−	0.693918i	$-0.755883\pi$
$883$	−42.7932	−1.44011	−0.720054	+	0.693918i	$0.755883\pi$
$884$	12.5850	0.423280
$885$	−1.91376	−0.0643302
$886$	−20.9391	−0.703461
$887$	17.7948	0.597490	0.298745	−	0.954333i	$-0.403432\pi$
$887$	17.7948	0.597490	0.298745	+	0.954333i	$0.403432\pi$
$888$	−24.3968	−0.818705
$889$	−27.1406	−0.910267
$890$	1.84596	0.0618766
$891$	−0.110715	−0.00370909
$892$	19.5468	0.654476
$893$	−8.77097	−0.293509
$894$	34.0452	1.13864
$895$	−3.76533	−0.125861
$896$	−1.53058	−0.0511331
$897$	−21.8598	−0.729878
$898$	14.7050	0.490711
$899$	−4.52160	−0.150804
$900$	−23.5710	−0.785699
$901$	5.88433	0.196036
$902$	−4.06086	−0.135212
$903$	15.3354	0.510330
$904$	10.1081	0.336190
$905$	−6.21792	−0.206691
$906$	−13.9337	−0.462916
$907$	−17.9926	−0.597434	−0.298717	−	0.954342i	$-0.596559\pi$
$907$	−17.9926	−0.597434	−0.298717	+	0.954342i	$0.596559\pi$
$908$	17.5275	0.581671
$909$	4.53006	0.150252
$910$	−2.09866	−0.0695699
$911$	−55.2910	−1.83187	−0.915935	−	0.401326i	$-0.868550\pi$
$911$	−55.2910	−1.83187	−0.915935	+	0.401326i	$0.868550\pi$
$912$	−1.87676	−0.0621456
$913$	−3.16332	−0.104691
$914$	−18.8320	−0.622909
$915$	10.2104	0.337546
$916$	−24.6544	−0.814606
$917$	5.68174	0.187628
$918$	17.2461	0.569207
$919$	25.9195	0.855005	0.427502	−	0.904014i	$-0.359394\pi$
$919$	25.9195	0.855005	0.427502	+	0.904014i	$0.359394\pi$
$920$	−0.754832	−0.0248861
$921$	42.4981	1.40036
$922$	17.5292	0.577294
$923$	−7.19281	−0.236754
$924$	−6.16740	−0.202893
$925$	42.4034	1.39422
$926$	−5.67588	−0.186521
$927$	17.2075	0.565168
$928$	4.52160	0.148429
$929$	31.6058	1.03695	0.518477	−	0.855092i	$-0.326499\pi$
$929$	31.6058	1.03695	0.518477	+	0.855092i	$0.326499\pi$
$930$	1.01974	0.0334387
$931$	−3.12114	−0.102291
$932$	−2.26438	−0.0741722
$933$	89.0970	2.91691
$934$	−24.1576	−0.790461
$935$	1.75107	0.0572661
$936$	−18.2350	−0.596029
$937$	−53.5717	−1.75011	−0.875055	−	0.484023i	$-0.839175\pi$
$937$	−53.5717	−1.75011	−0.875055	+	0.484023i	$0.839175\pi$
$938$	−20.5911	−0.672323
$939$	58.6693	1.91460
$940$	−4.76574	−0.155441
$941$	−21.5069	−0.701104	−0.350552	−	0.936543i	$-0.614006\pi$
$941$	−21.5069	−0.701104	−0.350552	+	0.936543i	$0.614006\pi$
$942$	−13.7865	−0.449187
$943$	5.85049	0.190518
$944$	1.87670	0.0610815
$945$	−2.87595	−0.0935545
$946$	5.14783	0.167371
$947$	50.7004	1.64754	0.823770	−	0.566924i	$-0.191867\pi$
$947$	50.7004	1.64754	0.823770	+	0.566924i	$0.191867\pi$
$948$	11.9161	0.387015
$949$	−4.02356	−0.130610
$950$	3.26193	0.105831
$951$	−91.9902	−2.98299
$952$	−5.11545	−0.165793
$953$	23.4901	0.760918	0.380459	−	0.924798i	$-0.375766\pi$
$953$	23.4901	0.760918	0.380459	+	0.924798i	$0.375766\pi$
$954$	−8.52608	−0.276042
$955$	9.96808	0.322559
$956$	−15.0808	−0.487747
$957$	18.2196	0.588955
$958$	1.34048	0.0433091
$959$	−12.7155	−0.410603
$960$	−1.01974	−0.0329121
$961$	1.00000	0.0322581
$962$	32.8042	1.05765
$963$	−68.9153	−2.22076
$964$	25.1895	0.811299
$965$	−2.23534	−0.0719581
$966$	8.88539	0.285883
$967$	8.59208	0.276303	0.138151	−	0.990411i	$-0.455884\pi$
$967$	8.59208	0.276303	0.138151	+	0.990411i	$0.455884\pi$
$968$	8.92971	0.287012
$969$	−6.27242	−0.201499
$970$	−0.364133	−0.0116916
$971$	−14.4137	−0.462557	−0.231279	−	0.972888i	$-0.574291\pi$
$971$	−14.4137	−0.462557	−0.231279	+	0.972888i	$0.574291\pi$
$972$	15.6960	0.503450
$973$	27.0742	0.867958
$974$	−16.8959	−0.541380
$975$	51.3279	1.64381
$976$	−10.0127	−0.320500
$977$	6.80528	0.217720	0.108860	−	0.994057i	$-0.465280\pi$
$977$	6.80528	0.217720	0.108860	+	0.994057i	$0.465280\pi$
$978$	55.5695	1.77692
$979$	−7.29419	−0.233123
$980$	−1.69589	−0.0541731
$981$	−67.6486	−2.15985
$982$	−34.0805	−1.08755
$983$	8.28545	0.264265	0.132132	−	0.991232i	$-0.457818\pi$
$983$	8.28545	0.264265	0.132132	+	0.991232i	$0.457818\pi$
$984$	7.90373	0.251962
$985$	7.12171	0.226916
$986$	15.1119	0.481262
$987$	56.0992	1.78566
$988$	2.52350	0.0802832
$989$	−7.41650	−0.235831
$990$	−2.53721	−0.0806377
$991$	39.5472	1.25626	0.628129	−	0.778109i	$-0.283821\pi$
$991$	39.5472	1.25626	0.628129	+	0.778109i	$0.283821\pi$
$992$	−1.00000	−0.0317500
$993$	−58.0386	−1.84180
$994$	2.92367	0.0927333
$995$	6.59685	0.209134
$996$	6.15684	0.195087
$997$	−31.2521	−0.989763	−0.494881	−	0.868960i	$-0.664789\pi$
$997$	−31.2521	−0.989763	−0.494881	+	0.868960i	$0.664789\pi$
$998$	−8.34283	−0.264088
$999$	44.9539	1.42228

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.f.1.2	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.f.1.2	✓	22	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.80047 q^{3} +1.00000 q^{4} +0.364133 q^{5} +2.80047 q^{6} +1.53058 q^{7} -1.00000 q^{8} +4.84261 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.80047 q^{3} +1.00000 q^{4} +0.364133 q^{5} +2.80047 q^{6} +1.53058 q^{7} -1.00000 q^{8} +4.84261 q^{9} -0.364133 q^{10} +1.43885 q^{11} -2.80047 q^{12} +3.76553 q^{13} -1.53058 q^{14} -1.01974 q^{15} +1.00000 q^{16} +3.34216 q^{17} -4.84261 q^{18} +0.670158 q^{19} +0.364133 q^{20} -4.28634 q^{21} -1.43885 q^{22} +2.07296 q^{23} +2.80047 q^{24} -4.86741 q^{25} -3.76553 q^{26} -5.16017 q^{27} +1.53058 q^{28} -4.52160 q^{29} +1.01974 q^{30} +1.00000 q^{31} -1.00000 q^{32} -4.02945 q^{33} -3.34216 q^{34} +0.557335 q^{35} +4.84261 q^{36} -8.71171 q^{37} -0.670158 q^{38} -10.5452 q^{39} -0.364133 q^{40} +2.82229 q^{41} +4.28634 q^{42} -3.57774 q^{43} +1.43885 q^{44} +1.76336 q^{45} -2.07296 q^{46} -13.0879 q^{47} -2.80047 q^{48} -4.65732 q^{49} +4.86741 q^{50} -9.35962 q^{51} +3.76553 q^{52} +1.76064 q^{53} +5.16017 q^{54} +0.523933 q^{55} -1.53058 q^{56} -1.87676 q^{57} +4.52160 q^{58} +1.87670 q^{59} -1.01974 q^{60} -10.0127 q^{61} -1.00000 q^{62} +7.41201 q^{63} +1.00000 q^{64} +1.37115 q^{65} +4.02945 q^{66} +13.4531 q^{67} +3.34216 q^{68} -5.80524 q^{69} -0.557335 q^{70} -1.91017 q^{71} -4.84261 q^{72} -1.06852 q^{73} +8.71171 q^{74} +13.6310 q^{75} +0.670158 q^{76} +2.20228 q^{77} +10.5452 q^{78} -4.25502 q^{79} +0.364133 q^{80} -0.0769468 q^{81} -2.82229 q^{82} -2.19851 q^{83} -4.28634 q^{84} +1.21699 q^{85} +3.57774 q^{86} +12.6626 q^{87} -1.43885 q^{88} -5.06946 q^{89} -1.76336 q^{90} +5.76344 q^{91} +2.07296 q^{92} -2.80047 q^{93} +13.0879 q^{94} +0.244027 q^{95} +2.80047 q^{96} +1.00000 q^{97} +4.65732 q^{98} +6.96780 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 22 q^{2} + 22 q^{4} - 11 q^{7} - 22 q^{8} + 8 q^{9}+O(q^{10}) \) 22 * q - 22 * q^2 + 22 * q^4 - 11 * q^7 - 22 * q^8 + 8 * q^9	\( 22 q - 22 q^{2} + 22 q^{4} - 11 q^{7} - 22 q^{8} + 8 q^{9} - 8 q^{13} + 11 q^{14} + q^{15} + 22 q^{16} - 4 q^{17} - 8 q^{18} - 23 q^{19} - 12 q^{21} + 2 q^{23} - 12 q^{25} + 8 q^{26} + 3 q^{27} - 11 q^{28} + 9 q^{29} - q^{30} + 22 q^{31} - 22 q^{32} + 4 q^{34} + 4 q^{35} + 8 q^{36} - 17 q^{37} + 23 q^{38} + 8 q^{39} - 21 q^{41} + 12 q^{42} - 7 q^{43} + 9 q^{45} - 2 q^{46} - 10 q^{47} - 27 q^{49} + 12 q^{50} - q^{51} - 8 q^{52} + 9 q^{53} - 3 q^{54} - 6 q^{55} + 11 q^{56} - q^{57} - 9 q^{58} - 12 q^{59} + q^{60} - 34 q^{61} - 22 q^{62} - 5 q^{63} + 22 q^{64} + 4 q^{65} - 31 q^{67} - 4 q^{68} - 51 q^{69} - 4 q^{70} - 15 q^{71} - 8 q^{72} + 3 q^{73} + 17 q^{74} - 24 q^{75} - 23 q^{76} + 24 q^{77} - 8 q^{78} - 23 q^{79} - 26 q^{81} + 21 q^{82} + 22 q^{83} - 12 q^{84} - 42 q^{85} + 7 q^{86} - 9 q^{87} - 36 q^{89} - 9 q^{90} - 6 q^{91} + 2 q^{92} + 10 q^{94} + 2 q^{95} + 22 q^{97} + 27 q^{98} - 25 q^{99}+O(q^{100}) \) 22 * q - 22 * q^2 + 22 * q^4 - 11 * q^7 - 22 * q^8 + 8 * q^9 - 8 * q^13 + 11 * q^14 + q^15 + 22 * q^16 - 4 * q^17 - 8 * q^18 - 23 * q^19 - 12 * q^21 + 2 * q^23 - 12 * q^25 + 8 * q^26 + 3 * q^27 - 11 * q^28 + 9 * q^29 - q^30 + 22 * q^31 - 22 * q^32 + 4 * q^34 + 4 * q^35 + 8 * q^36 - 17 * q^37 + 23 * q^38 + 8 * q^39 - 21 * q^41 + 12 * q^42 - 7 * q^43 + 9 * q^45 - 2 * q^46 - 10 * q^47 - 27 * q^49 + 12 * q^50 - q^51 - 8 * q^52 + 9 * q^53 - 3 * q^54 - 6 * q^55 + 11 * q^56 - q^57 - 9 * q^58 - 12 * q^59 + q^60 - 34 * q^61 - 22 * q^62 - 5 * q^63 + 22 * q^64 + 4 * q^65 - 31 * q^67 - 4 * q^68 - 51 * q^69 - 4 * q^70 - 15 * q^71 - 8 * q^72 + 3 * q^73 + 17 * q^74 - 24 * q^75 - 23 * q^76 + 24 * q^77 - 8 * q^78 - 23 * q^79 - 26 * q^81 + 21 * q^82 + 22 * q^83 - 12 * q^84 - 42 * q^85 + 7 * q^86 - 9 * q^87 - 36 * q^89 - 9 * q^90 - 6 * q^91 + 2 * q^92 + 10 * q^94 + 2 * q^95 + 22 * q^97 + 27 * q^98 - 25 * q^99

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