LMFDB - Embedded newform 6005.2.a.c.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6005,2,Mod(1,6005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6005, 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("6005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6005 = 5 \cdot 1201 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6005.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:	$47.9501664138$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.2777.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} + x + 2 $ x^4 - x^3 - 4*x^2 + x + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.50848$ of defining polynomial
Character	$\chi$	$=$	6005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.18264 q^{2} -2.96664 q^{3} -0.601352 q^{4} -1.00000 q^{5} -3.50848 q^{6} -3.50848 q^{7} -3.07647 q^{8} +5.80096 q^{9} +O(q^{10})$	\(q+1.18264 q^{2} -2.96664 q^{3} -0.601352 q^{4} -1.00000 q^{5} -3.50848 q^{6} -3.50848 q^{7} -3.07647 q^{8} +5.80096 q^{9} -1.18264 q^{10} -5.93328 q^{11} +1.78400 q^{12} -0.182644 q^{13} -4.14929 q^{14} +2.96664 q^{15} -2.43567 q^{16} +4.65777 q^{17} +6.86047 q^{18} +0.308874 q^{19} +0.601352 q^{20} +10.4084 q^{21} -7.01696 q^{22} -0.491519 q^{23} +9.12680 q^{24} +1.00000 q^{25} -0.216003 q^{26} -8.30944 q^{27} +2.10983 q^{28} +5.76760 q^{29} +3.50848 q^{30} +1.87377 q^{31} +3.27242 q^{32} +17.6019 q^{33} +5.50848 q^{34} +3.50848 q^{35} -3.48842 q^{36} +3.93638 q^{37} +0.365289 q^{38} +0.541840 q^{39} +3.07647 q^{40} +5.02615 q^{41} +12.3094 q^{42} -9.02615 q^{43} +3.56799 q^{44} -5.80096 q^{45} -0.581292 q^{46} +0.0534194 q^{47} +7.22576 q^{48} +5.30944 q^{49} +1.18264 q^{50} -13.8179 q^{51} +0.109834 q^{52} +10.1493 q^{53} -9.82711 q^{54} +5.93328 q^{55} +10.7938 q^{56} -0.916320 q^{57} +6.82102 q^{58} -8.47202 q^{59} -1.78400 q^{60} -12.1268 q^{61} +2.21600 q^{62} -20.3526 q^{63} +8.74145 q^{64} +0.182644 q^{65} +20.8168 q^{66} -1.35920 q^{67} -2.80096 q^{68} +1.45816 q^{69} +4.14929 q^{70} +1.15959 q^{71} -17.8465 q^{72} +13.7877 q^{73} +4.65534 q^{74} -2.96664 q^{75} -0.185742 q^{76} +20.8168 q^{77} +0.640804 q^{78} +5.87377 q^{79} +2.43567 q^{80} +7.24825 q^{81} +5.94415 q^{82} +14.9842 q^{83} -6.25912 q^{84} -4.65777 q^{85} -10.6747 q^{86} -17.1104 q^{87} +18.2536 q^{88} -10.0114 q^{89} -6.86047 q^{90} +0.640804 q^{91} +0.295576 q^{92} -5.55880 q^{93} +0.0631762 q^{94} -0.308874 q^{95} -9.70809 q^{96} +3.36529 q^{97} +6.27918 q^{98} -34.4187 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 4 q^{5} - 7 q^{6} - 7 q^{7} + 9 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 4 * q^5 - 7 * q^6 - 7 * q^7 + 9 * q^8 + 2 * q^9	\( 4 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 4 q^{5} - 7 q^{6} - 7 q^{7} + 9 q^{8} + 2 q^{9} - 2 q^{10} - 4 q^{11} + 2 q^{13} - 4 q^{14} + 2 q^{15} + 6 q^{16} - q^{17} - q^{18} + 11 q^{19} - 2 q^{20} + 5 q^{21} - 14 q^{22} - 9 q^{23} + 11 q^{24} + 4 q^{25} - 8 q^{26} - 5 q^{27} - 3 q^{28} - 8 q^{29} + 7 q^{30} - 5 q^{31} + 5 q^{32} + 28 q^{33} + 15 q^{34} + 7 q^{35} - 13 q^{36} + 4 q^{37} - 4 q^{38} + 5 q^{39} - 9 q^{40} + 3 q^{41} + 21 q^{42} - 19 q^{43} - 2 q^{45} - 4 q^{46} + 4 q^{47} - 5 q^{48} - 7 q^{49} + 2 q^{50} - 20 q^{51} - 11 q^{52} + 28 q^{53} - q^{54} + 4 q^{55} - 5 q^{56} + 2 q^{57} - 9 q^{59} - 23 q^{61} + 16 q^{62} - 22 q^{63} + 21 q^{64} - 2 q^{65} + 10 q^{66} - 11 q^{67} + 10 q^{68} + 3 q^{69} + 4 q^{70} + 27 q^{71} - 38 q^{72} + 18 q^{73} - 20 q^{74} - 2 q^{75} - 6 q^{76} + 10 q^{77} - 3 q^{78} + 11 q^{79} - 6 q^{80} + 8 q^{81} + q^{82} - 2 q^{83} - q^{84} + q^{85} - 9 q^{86} - 19 q^{87} + 22 q^{88} + q^{89} + q^{90} - 3 q^{91} - 5 q^{92} - 11 q^{93} - 37 q^{94} - 11 q^{95} - 15 q^{96} + 8 q^{97} - 5 q^{98} - 22 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 4 * q^5 - 7 * q^6 - 7 * q^7 + 9 * q^8 + 2 * q^9 - 2 * q^10 - 4 * q^11 + 2 * q^13 - 4 * q^14 + 2 * q^15 + 6 * q^16 - q^17 - q^18 + 11 * q^19 - 2 * q^20 + 5 * q^21 - 14 * q^22 - 9 * q^23 + 11 * q^24 + 4 * q^25 - 8 * q^26 - 5 * q^27 - 3 * q^28 - 8 * q^29 + 7 * q^30 - 5 * q^31 + 5 * q^32 + 28 * q^33 + 15 * q^34 + 7 * q^35 - 13 * q^36 + 4 * q^37 - 4 * q^38 + 5 * q^39 - 9 * q^40 + 3 * q^41 + 21 * q^42 - 19 * q^43 - 2 * q^45 - 4 * q^46 + 4 * q^47 - 5 * q^48 - 7 * q^49 + 2 * q^50 - 20 * q^51 - 11 * q^52 + 28 * q^53 - q^54 + 4 * q^55 - 5 * q^56 + 2 * q^57 - 9 * q^59 - 23 * q^61 + 16 * q^62 - 22 * q^63 + 21 * q^64 - 2 * q^65 + 10 * q^66 - 11 * q^67 + 10 * q^68 + 3 * q^69 + 4 * q^70 + 27 * q^71 - 38 * q^72 + 18 * q^73 - 20 * q^74 - 2 * q^75 - 6 * q^76 + 10 * q^77 - 3 * q^78 + 11 * q^79 - 6 * q^80 + 8 * q^81 + q^82 - 2 * q^83 - q^84 + q^85 - 9 * q^86 - 19 * q^87 + 22 * q^88 + q^89 + q^90 - 3 * q^91 - 5 * q^92 - 11 * q^93 - 37 * q^94 - 11 * q^95 - 15 * q^96 + 8 * q^97 - 5 * q^98 - 22 * 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 $

$2$	1.18264	0.836256	0.418128	−	0.908388i	$-0.362686\pi$
$2$	1.18264	0.836256	0.418128	+	0.908388i	$0.362686\pi$
$3$	−2.96664	−1.71279	−0.856396	−	0.516320i	$-0.827301\pi$
$3$	−2.96664	−1.71279	−0.856396	+	0.516320i	$0.827301\pi$
$4$	−0.601352	−0.300676
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−3.50848	−1.43233
$7$	−3.50848	−1.32608	−0.663041	−	0.748583i	$-0.730734\pi$
$7$	−3.50848	−1.32608	−0.663041	+	0.748583i	$0.730734\pi$
$8$	−3.07647	−1.08770
$9$	5.80096	1.93365
$10$	−1.18264	−0.373985
$11$	−5.93328	−1.78895	−0.894476	−	0.447116i	$-0.852451\pi$
$11$	−5.93328	−1.78895	−0.894476	+	0.447116i	$0.852451\pi$
$12$	1.78400	0.514995
$13$	−0.182644	−0.0506564	−0.0253282	−	0.999679i	$-0.508063\pi$
$13$	−0.182644	−0.0506564	−0.0253282	+	0.999679i	$0.508063\pi$
$14$	−4.14929	−1.10894
$15$	2.96664	0.765983
$16$	−2.43567	−0.608918
$17$	4.65777	1.12967	0.564837	−	0.825202i	$-0.308939\pi$
$17$	4.65777	1.12967	0.564837	+	0.825202i	$0.308939\pi$
$18$	6.86047	1.61703
$19$	0.308874	0.0708607	0.0354303	−	0.999372i	$-0.488720\pi$
$19$	0.308874	0.0708607	0.0354303	+	0.999372i	$0.488720\pi$
$20$	0.601352	0.134466
$21$	10.4084	2.27130
$22$	−7.01696	−1.49602
$23$	−0.491519	−0.102489	−0.0512444	−	0.998686i	$-0.516319\pi$
$23$	−0.491519	−0.102489	−0.0512444	+	0.998686i	$0.516319\pi$
$24$	9.12680	1.86300
$25$	1.00000	0.200000
$26$	−0.216003	−0.0423617
$27$	−8.30944	−1.59915
$28$	2.10983	0.398721
$29$	5.76760	1.07102	0.535508	−	0.844530i	$-0.320120\pi$
$29$	5.76760	1.07102	0.535508	+	0.844530i	$0.320120\pi$
$30$	3.50848	0.640558
$31$	1.87377	0.336539	0.168269	−	0.985741i	$-0.446182\pi$
$31$	1.87377	0.336539	0.168269	+	0.985741i	$0.446182\pi$
$32$	3.27242	0.578487
$33$	17.6019	3.06410
$34$	5.50848	0.944697
$35$	3.50848	0.593042
$36$	−3.48842	−0.581403
$37$	3.93638	0.647137	0.323568	−	0.946205i	$-0.395117\pi$
$37$	3.93638	0.647137	0.323568	+	0.946205i	$0.395117\pi$
$38$	0.365289	0.0592576
$39$	0.541840	0.0867639
$40$	3.07647	0.486433
$41$	5.02615	0.784953	0.392477	−	0.919762i	$-0.371618\pi$
$41$	5.02615	0.784953	0.392477	+	0.919762i	$0.371618\pi$
$42$	12.3094	1.89939
$43$	−9.02615	−1.37648	−0.688238	−	0.725485i	$-0.741615\pi$
$43$	−9.02615	−1.37648	−0.688238	+	0.725485i	$0.741615\pi$
$44$	3.56799	0.537895
$45$	−5.80096	−0.864756
$46$	−0.581292	−0.0857068
$47$	0.0534194	0.00779203	0.00389601	−	0.999992i	$-0.498760\pi$
$47$	0.0534194	0.00779203	0.00389601	+	0.999992i	$0.498760\pi$
$48$	7.22576	1.04295
$49$	5.30944	0.758491
$50$	1.18264	0.167251
$51$	−13.8179	−1.93490
$52$	0.109834	0.0152312
$53$	10.1493	1.39411	0.697056	−	0.717017i	$-0.254493\pi$
$53$	10.1493	1.39411	0.697056	+	0.717017i	$0.254493\pi$
$54$	−9.82711	−1.33730
$55$	5.93328	0.800044
$56$	10.7938	1.44238
$57$	−0.916320	−0.121370
$58$	6.82102	0.895644
$59$	−8.47202	−1.10296	−0.551482	−	0.834187i	$-0.685937\pi$
$59$	−8.47202	−1.10296	−0.551482	+	0.834187i	$0.685937\pi$
$60$	−1.78400	−0.230313
$61$	−12.1268	−1.55268	−0.776339	−	0.630316i	$-0.782925\pi$
$61$	−12.1268	−1.55268	−0.776339	+	0.630316i	$0.782925\pi$
$62$	2.21600	0.281433
$63$	−20.3526	−2.56418
$64$	8.74145	1.09268
$65$	0.182644	0.0226542
$66$	20.8168	2.56237
$67$	−1.35920	−0.166052	−0.0830261	−	0.996547i	$-0.526458\pi$
$67$	−1.35920	−0.166052	−0.0830261	+	0.996547i	$0.526458\pi$
$68$	−2.80096	−0.339666
$69$	1.45816	0.175542
$70$	4.14929	0.495934
$71$	1.15959	0.137618	0.0688090	−	0.997630i	$-0.478080\pi$
$71$	1.15959	0.137618	0.0688090	+	0.997630i	$0.478080\pi$
$72$	−17.8465	−2.10323
$73$	13.7877	1.61372	0.806862	−	0.590740i	$-0.201164\pi$
$73$	13.7877	1.61372	0.806862	+	0.590740i	$0.201164\pi$
$74$	4.65534	0.541172
$75$	−2.96664	−0.342558
$76$	−0.185742	−0.0213061
$77$	20.8168	2.37230
$78$	0.640804	0.0725568
$79$	5.87377	0.660851	0.330425	−	0.943832i	$-0.392808\pi$
$79$	5.87377	0.660851	0.330425	+	0.943832i	$0.392808\pi$
$80$	2.43567	0.272316
$81$	7.24825	0.805361
$82$	5.94415	0.656422
$83$	14.9842	1.64473	0.822363	−	0.568963i	$-0.192655\pi$
$83$	14.9842	1.64473	0.822363	+	0.568963i	$0.192655\pi$
$84$	−6.25912	−0.682926
$85$	−4.65777	−0.505206
$86$	−10.6747	−1.15109
$87$	−17.1104	−1.83443
$88$	18.2536	1.94584
$89$	−10.0114	−1.06121	−0.530605	−	0.847619i	$-0.678035\pi$
$89$	−10.0114	−1.06121	−0.530605	+	0.847619i	$0.678035\pi$
$90$	−6.86047	−0.723157
$91$	0.640804	0.0671745
$92$	0.295576	0.0308159
$93$	−5.55880	−0.576421
$94$	0.0631762	0.00651613
$95$	−0.308874	−0.0316899
$96$	−9.70809	−0.990828
$97$	3.36529	0.341693	0.170847	−	0.985298i	$-0.445350\pi$
$97$	3.36529	0.341693	0.170847	+	0.985298i	$0.445350\pi$
$98$	6.27918	0.634293
$99$	−34.4187	−3.45921
$100$	−0.601352	−0.0601352
$101$	−18.9641	−1.88700	−0.943500	−	0.331373i	$-0.892488\pi$
$101$	−18.9641	−1.88700	−0.943500	+	0.331373i	$0.892488\pi$
$102$	−16.3417	−1.61807
$103$	1.63471	0.161073	0.0805364	−	0.996752i	$-0.474337\pi$
$103$	1.63471	0.161073	0.0805364	+	0.996752i	$0.474337\pi$
$104$	0.561901	0.0550989
$105$	−10.4084	−1.01576
$106$	12.0030	1.16583
$107$	−13.0662	−1.26315	−0.631577	−	0.775313i	$-0.717592\pi$
$107$	−13.0662	−1.26315	−0.631577	+	0.775313i	$0.717592\pi$
$108$	4.99690	0.480827
$109$	16.5291	1.58320	0.791601	−	0.611039i	$-0.209248\pi$
$109$	16.5291	1.58320	0.791601	+	0.611039i	$0.209248\pi$
$110$	7.01696	0.669041
$111$	−11.6778	−1.10841
$112$	8.54550	0.807474
$113$	−1.47822	−0.139059	−0.0695296	−	0.997580i	$-0.522150\pi$
$113$	−1.47822	−0.139059	−0.0695296	+	0.997580i	$0.522150\pi$
$114$	−1.08368	−0.101496
$115$	0.491519	0.0458344
$116$	−3.46836	−0.322029
$117$	−1.05951	−0.0979519
$118$	−10.0194	−0.922360
$119$	−16.3417	−1.49804
$120$	−9.12680	−0.833159
$121$	24.2038	2.20035
$122$	−14.3417	−1.29844
$123$	−14.9108	−1.34446
$124$	−1.12680	−0.101189
$125$	−1.00000	−0.0894427
$126$	−24.0698	−2.14431
$127$	3.17102	0.281383	0.140691	−	0.990053i	$-0.455067\pi$
$127$	3.17102	0.281383	0.140691	+	0.990053i	$0.455067\pi$
$128$	3.79319	0.335274
$129$	26.7774	2.35761
$130$	0.216003	0.0189447
$131$	−17.6989	−1.54636	−0.773180	−	0.634187i	$-0.781335\pi$
$131$	−17.6989	−1.54636	−0.773180	+	0.634187i	$0.781335\pi$
$132$	−10.5850	−0.921302
$133$	−1.08368	−0.0939670
$134$	−1.60745	−0.138862
$135$	8.30944	0.715163
$136$	−14.3295	−1.22874
$137$	0.759829	0.0649165	0.0324583	−	0.999473i	$-0.489666\pi$
$137$	0.759829	0.0649165	0.0324583	+	0.999473i	$0.489666\pi$
$138$	1.72448	0.146798
$139$	9.03392	0.766248	0.383124	−	0.923697i	$-0.374848\pi$
$139$	9.03392	0.766248	0.383124	+	0.923697i	$0.374848\pi$
$140$	−2.10983	−0.178313
$141$	−0.158476	−0.0133461
$142$	1.37138	0.115084
$143$	1.08368	0.0906219
$144$	−14.1292	−1.17744
$145$	−5.76760	−0.478973
$146$	16.3059	1.34949
$147$	−15.7512	−1.29914
$148$	−2.36715	−0.194579
$149$	−9.71586	−0.795954	−0.397977	−	0.917395i	$-0.630288\pi$
$149$	−9.71586	−0.795954	−0.397977	+	0.917395i	$0.630288\pi$
$150$	−3.50848	−0.286466
$151$	−2.70341	−0.220001	−0.110000	−	0.993932i	$-0.535085\pi$
$151$	−2.70341	−0.220001	−0.110000	+	0.993932i	$0.535085\pi$
$152$	−0.950245	−0.0770750
$153$	27.0195	2.18440
$154$	24.6189	1.98385
$155$	−1.87377	−0.150505
$156$	−0.325837	−0.0260878
$157$	4.56601	0.364407	0.182204	−	0.983261i	$-0.441677\pi$
$157$	4.56601	0.364407	0.182204	+	0.983261i	$0.441677\pi$
$158$	6.94658	0.552640
$159$	−30.1093	−2.38782
$160$	−3.27242	−0.258707
$161$	1.72448	0.135908
$162$	8.57210	0.673488
$163$	6.80847	0.533281	0.266640	−	0.963796i	$-0.414086\pi$
$163$	6.80847	0.533281	0.266640	+	0.963796i	$0.414086\pi$
$164$	−3.02249	−0.236017
$165$	−17.6019	−1.37031
$166$	17.7209	1.37541
$167$	2.87986	0.222850	0.111425	−	0.993773i	$-0.464458\pi$
$167$	2.87986	0.222850	0.111425	+	0.993773i	$0.464458\pi$
$168$	−32.0212	−2.47049
$169$	−12.9666	−0.997434
$170$	−5.50848	−0.422481
$171$	1.79177	0.137020
$172$	5.42790	0.413873
$173$	−6.29756	−0.478795	−0.239397	−	0.970922i	$-0.576950\pi$
$173$	−6.29756	−0.478795	−0.239397	+	0.970922i	$0.576950\pi$
$174$	−20.2355	−1.53405
$175$	−3.50848	−0.265216
$176$	14.4515	1.08932
$177$	25.1335	1.88915
$178$	−11.8400	−0.887443
$179$	14.0322	1.04882	0.524410	−	0.851466i	$-0.324286\pi$
$179$	14.0322	1.04882	0.524410	+	0.851466i	$0.324286\pi$
$180$	3.48842	0.260012
$181$	−4.57463	−0.340030	−0.170015	−	0.985441i	$-0.554382\pi$
$181$	−4.57463	−0.340030	−0.170015	+	0.985441i	$0.554382\pi$
$182$	0.757843	0.0561751
$183$	35.9759	2.65941
$184$	1.51215	0.111477
$185$	−3.93638	−0.289408
$186$	−6.57409	−0.482035
$187$	−27.6358	−2.02093
$188$	−0.0321239	−0.00234288
$189$	29.1535	2.12061
$190$	−0.365289	−0.0265008
$191$	25.9114	1.87488	0.937440	−	0.348147i	$-0.113189\pi$
$191$	25.9114	1.87488	0.937440	+	0.348147i	$0.113189\pi$
$192$	−25.9327	−1.87153
$193$	−12.2453	−0.881433	−0.440716	−	0.897646i	$-0.645276\pi$
$193$	−12.2453	−0.881433	−0.440716	+	0.897646i	$0.645276\pi$
$194$	3.97994	0.285743
$195$	−0.541840	−0.0388020
$196$	−3.19284	−0.228060
$197$	9.53053	0.679022	0.339511	−	0.940602i	$-0.389738\pi$
$197$	9.53053	0.679022	0.339511	+	0.940602i	$0.389738\pi$
$198$	−40.7051	−2.89279
$199$	5.82756	0.413104	0.206552	−	0.978436i	$-0.433776\pi$
$199$	5.82756	0.413104	0.206552	+	0.978436i	$0.433776\pi$
$200$	−3.07647	−0.217540
$201$	4.03225	0.284413
$202$	−22.4278	−1.57801
$203$	−20.2355	−1.42025
$204$	8.30944	0.581777
$205$	−5.02615	−0.351042
$206$	1.93328	0.134698
$207$	−2.85128	−0.198178
$208$	0.444861	0.0308456
$209$	−1.83264	−0.126766
$210$	−12.3094	−0.849432
$211$	−3.44543	−0.237193	−0.118596	−	0.992943i	$-0.537839\pi$
$211$	−3.44543	−0.237193	−0.118596	+	0.992943i	$0.537839\pi$
$212$	−6.10330	−0.419176
$213$	−3.44008	−0.235711
$214$	−15.4526	−1.05632
$215$	9.02615	0.615579
$216$	25.5638	1.73940
$217$	−6.57409	−0.446278
$218$	19.5481	1.32396
$219$	−40.9030	−2.76397
$220$	−3.56799	−0.240554
$221$	−0.850715	−0.0572253
$222$	−13.8107	−0.926915
$223$	9.30634	0.623199	0.311599	−	0.950214i	$-0.399135\pi$
$223$	9.30634	0.623199	0.311599	+	0.950214i	$0.399135\pi$
$224$	−11.4812	−0.767121
$225$	5.80096	0.386731
$226$	−1.74821	−0.116289
$227$	16.4662	1.09290	0.546451	−	0.837491i	$-0.315978\pi$
$227$	16.4662	1.09290	0.546451	+	0.837491i	$0.315978\pi$
$228$	0.551031	0.0364929
$229$	−17.7847	−1.17524	−0.587622	−	0.809136i	$-0.699936\pi$
$229$	−17.7847	−1.17524	−0.587622	+	0.809136i	$0.699936\pi$
$230$	0.581292	0.0383293
$231$	−61.7560	−4.06325
$232$	−17.7439	−1.16494
$233$	29.7773	1.95077	0.975386	−	0.220503i	$-0.0707698\pi$
$233$	29.7773	1.95077	0.975386	+	0.220503i	$0.0707698\pi$
$234$	−1.25303	−0.0819129
$235$	−0.0534194	−0.00348470
$236$	5.09467	0.331635
$237$	−17.4254	−1.13190
$238$	−19.3264	−1.25274
$239$	−11.3542	−0.734444	−0.367222	−	0.930133i	$-0.619691\pi$
$239$	−11.3542	−0.734444	−0.367222	+	0.930133i	$0.619691\pi$
$240$	−7.22576	−0.466421
$241$	−12.1626	−0.783461	−0.391730	−	0.920080i	$-0.628123\pi$
$241$	−12.1626	−0.783461	−0.391730	+	0.920080i	$0.628123\pi$
$242$	28.6245	1.84005
$243$	3.42537	0.219737
$244$	7.29248	0.466853
$245$	−5.30944	−0.339208
$246$	−17.6342	−1.12431
$247$	−0.0564142	−0.00358955
$248$	−5.76461	−0.366053
$249$	−44.4527	−2.81707
$250$	−1.18264	−0.0747970
$251$	17.1857	1.08475	0.542377	−	0.840135i	$-0.317524\pi$
$251$	17.1857	1.08475	0.542377	+	0.840135i	$0.317524\pi$
$252$	12.2391	0.770988
$253$	2.91632	0.183347
$254$	3.75019	0.235308
$255$	13.8179	0.865312
$256$	−12.9969	−0.812306
$257$	5.07028	0.316275	0.158138	−	0.987417i	$-0.449451\pi$
$257$	5.07028	0.316275	0.158138	+	0.987417i	$0.449451\pi$
$258$	31.6681	1.97157
$259$	−13.8107	−0.858156
$260$	−0.109834	−0.00681159
$261$	33.4576	2.07097
$262$	−20.9315	−1.29315
$263$	−19.3629	−1.19397	−0.596983	−	0.802254i	$-0.703634\pi$
$263$	−19.3629	−1.19397	−0.596983	+	0.802254i	$0.703634\pi$
$264$	−54.1519	−3.33282
$265$	−10.1493	−0.623466
$266$	−1.28161	−0.0785804
$267$	29.7003	1.81763
$268$	0.817356	0.0499279
$269$	−1.61943	−0.0987382	−0.0493691	−	0.998781i	$-0.515721\pi$
$269$	−1.61943	−0.0987382	−0.0493691	+	0.998781i	$0.515721\pi$
$270$	9.82711	0.598059
$271$	6.37814	0.387445	0.193722	−	0.981056i	$-0.437944\pi$
$271$	6.37814	0.387445	0.193722	+	0.981056i	$0.437944\pi$
$272$	−11.3448	−0.687879
$273$	−1.90104	−0.115056
$274$	0.898607	0.0542868
$275$	−5.93328	−0.357790
$276$	−0.876868	−0.0527812
$277$	−29.9950	−1.80223	−0.901114	−	0.433583i	$-0.857249\pi$
$277$	−29.9950	−1.80223	−0.901114	+	0.433583i	$0.857249\pi$
$278$	10.6839	0.640779
$279$	10.8697	0.650750
$280$	−10.7938	−0.645050
$281$	−4.43268	−0.264431	−0.132216	−	0.991221i	$-0.542209\pi$
$281$	−4.43268	−0.264431	−0.132216	+	0.991221i	$0.542209\pi$
$282$	−0.187421	−0.0111608
$283$	1.52310	0.0905386	0.0452693	−	0.998975i	$-0.485585\pi$
$283$	1.52310	0.0905386	0.0452693	+	0.998975i	$0.485585\pi$
$284$	−0.697322	−0.0413784
$285$	0.916320	0.0542781
$286$	1.28161	0.0757831
$287$	−17.6342	−1.04091
$288$	18.9832	1.11859
$289$	4.69479	0.276164
$290$	−6.82102	−0.400544
$291$	−9.98360	−0.585249
$292$	−8.29124	−0.485208
$293$	−0.685033	−0.0400200	−0.0200100	−	0.999800i	$-0.506370\pi$
$293$	−0.685033	−0.0400200	−0.0200100	+	0.999800i	$0.506370\pi$
$294$	−18.6281	−1.08641
$295$	8.47202	0.493260
$296$	−12.1102	−0.703890
$297$	49.3023	2.86081
$298$	−11.4904	−0.665621
$299$	0.0897731	0.00519171
$300$	1.78400	0.102999
$301$	31.6681	1.82532
$302$	−3.19718	−0.183977
$303$	56.2597	3.23204
$304$	−0.752316	−0.0431483
$305$	12.1268	0.694378
$306$	31.9545	1.82672
$307$	−16.6967	−0.952928	−0.476464	−	0.879194i	$-0.658082\pi$
$307$	−16.6967	−0.952928	−0.476464	+	0.879194i	$0.658082\pi$
$308$	−12.5182	−0.713293
$309$	−4.84960	−0.275884
$310$	−2.21600	−0.125861
$311$	27.3408	1.55036	0.775178	−	0.631743i	$-0.217660\pi$
$311$	27.3408	1.55036	0.775178	+	0.631743i	$0.217660\pi$
$312$	−1.66696	−0.0943729
$313$	13.4126	0.758126	0.379063	−	0.925371i	$-0.376246\pi$
$313$	13.4126	0.758126	0.379063	+	0.925371i	$0.376246\pi$
$314$	5.39996	0.304738
$315$	20.3526	1.14674
$316$	−3.53221	−0.198702
$317$	−2.12202	−0.119184	−0.0595922	−	0.998223i	$-0.518980\pi$
$317$	−2.12202	−0.119184	−0.0595922	+	0.998223i	$0.518980\pi$
$318$	−35.6086	−1.99683
$319$	−34.2208	−1.91600
$320$	−8.74145	−0.488662
$321$	38.7626	2.16352
$322$	2.03945	0.113654
$323$	1.43867	0.0800495
$324$	−4.35875	−0.242153
$325$	−0.182644	−0.0101313
$326$	8.05200	0.445959
$327$	−49.0359	−2.71169
$328$	−15.4628	−0.853792
$329$	−0.187421	−0.0103329
$330$	−20.8168	−1.14593
$331$	21.7634	1.19622	0.598112	−	0.801413i	$-0.295918\pi$
$331$	21.7634	1.19622	0.598112	+	0.801413i	$0.295918\pi$
$332$	−9.01077	−0.494530
$333$	22.8348	1.25134
$334$	3.40585	0.186360
$335$	1.35920	0.0742608
$336$	−25.3514	−1.38303
$337$	20.4396	1.11342	0.556709	−	0.830708i	$-0.312064\pi$
$337$	20.4396	1.11342	0.556709	+	0.830708i	$0.312064\pi$
$338$	−15.3349	−0.834110
$339$	4.38535	0.238179
$340$	2.80096	0.151903
$341$	−11.1176	−0.602052
$342$	2.11902	0.114584
$343$	5.93130	0.320260
$344$	27.7687	1.49719
$345$	−1.45816	−0.0785047
$346$	−7.44778	−0.400395
$347$	−20.6886	−1.11062	−0.555311	−	0.831643i	$-0.687401\pi$
$347$	−20.6886	−1.11062	−0.555311	+	0.831643i	$0.687401\pi$
$348$	10.2894	0.551569
$349$	−0.515243	−0.0275803	−0.0137902	−	0.999905i	$-0.504390\pi$
$349$	−0.515243	−0.0275803	−0.0137902	+	0.999905i	$0.504390\pi$
$350$	−4.14929	−0.221789
$351$	1.51767	0.0810073
$352$	−19.4162	−1.03489
$353$	−31.8817	−1.69689	−0.848445	−	0.529284i	$-0.822461\pi$
$353$	−31.8817	−1.69689	−0.848445	+	0.529284i	$0.822461\pi$
$354$	29.7239	1.57981
$355$	−1.15959	−0.0615446
$356$	6.02040	0.319081
$357$	48.4799	2.56583
$358$	16.5952	0.877081
$359$	−2.70752	−0.142898	−0.0714488	−	0.997444i	$-0.522762\pi$
$359$	−2.70752	−0.142898	−0.0714488	+	0.997444i	$0.522762\pi$
$360$	17.8465	0.940593
$361$	−18.9046	−0.994979
$362$	−5.41016	−0.284352
$363$	−71.8041	−3.76874
$364$	−0.385349	−0.0201978
$365$	−13.7877	−0.721679
$366$	42.5466	2.22395
$367$	−9.55328	−0.498677	−0.249338	−	0.968416i	$-0.580213\pi$
$367$	−9.55328	−0.498677	−0.249338	+	0.968416i	$0.580213\pi$
$368$	1.19718	0.0624072
$369$	29.1565	1.51783
$370$	−4.65534	−0.242019
$371$	−35.6086	−1.84871
$372$	3.34280	0.173316
$373$	8.64757	0.447754	0.223877	−	0.974617i	$-0.428129\pi$
$373$	8.64757	0.447754	0.223877	+	0.974617i	$0.428129\pi$
$374$	−32.6834	−1.69002
$375$	2.96664	0.153197
$376$	−0.164344	−0.00847537
$377$	−1.05342	−0.0542539
$378$	34.4782	1.77337
$379$	13.9621	0.717186	0.358593	−	0.933494i	$-0.383257\pi$
$379$	13.9621	0.717186	0.358593	+	0.933494i	$0.383257\pi$
$380$	0.185742	0.00952838
$381$	−9.40729	−0.481950
$382$	30.6439	1.56788
$383$	−0.594147	−0.0303595	−0.0151797	−	0.999885i	$-0.504832\pi$
$383$	−0.594147	−0.0303595	−0.0151797	+	0.999885i	$0.504832\pi$
$384$	−11.2530	−0.574254
$385$	−20.8168	−1.06092
$386$	−14.4818	−0.737103
$387$	−52.3603	−2.66163
$388$	−2.02372	−0.102739
$389$	−34.4532	−1.74685	−0.873423	−	0.486962i	$-0.838105\pi$
$389$	−34.4532	−1.74685	−0.873423	+	0.486962i	$0.838105\pi$
$390$	−0.640804	−0.0324484
$391$	−2.28938	−0.115779
$392$	−16.3344	−0.825010
$393$	52.5063	2.64859
$394$	11.2712	0.567836
$395$	−5.87377	−0.295541
$396$	20.6978	1.04010
$397$	−4.60755	−0.231246	−0.115623	−	0.993293i	$-0.536886\pi$
$397$	−4.60755	−0.231246	−0.115623	+	0.993293i	$0.536886\pi$
$398$	6.89193	0.345461
$399$	3.21489	0.160946
$400$	−2.43567	−0.121784
$401$	2.81426	0.140537	0.0702687	−	0.997528i	$-0.477614\pi$
$401$	2.81426	0.140537	0.0702687	+	0.997528i	$0.477614\pi$
$402$	4.76871	0.237842
$403$	−0.342233	−0.0170479
$404$	11.4041	0.567376
$405$	−7.24825	−0.360168
$406$	−23.9314	−1.18770
$407$	−23.3557	−1.15770
$408$	42.5105	2.10458
$409$	−21.5325	−1.06471	−0.532357	−	0.846520i	$-0.678694\pi$
$409$	−21.5325	−1.06471	−0.532357	+	0.846520i	$0.678694\pi$
$410$	−5.94415	−0.293561
$411$	−2.25414	−0.111188
$412$	−0.983038	−0.0484308
$413$	29.7239	1.46262
$414$	−3.37205	−0.165727
$415$	−14.9842	−0.735544
$416$	−0.597688	−0.0293041
$417$	−26.8004	−1.31242
$418$	−2.16736	−0.106009
$419$	−0.864013	−0.0422098	−0.0211049	−	0.999777i	$-0.506718\pi$
$419$	−0.864013	−0.0422098	−0.0211049	+	0.999777i	$0.506718\pi$
$420$	6.25912	0.305414
$421$	−21.4987	−1.04778	−0.523892	−	0.851785i	$-0.675521\pi$
$421$	−21.4987	−1.04778	−0.523892	+	0.851785i	$0.675521\pi$
$422$	−4.07471	−0.198354
$423$	0.309884	0.0150671
$424$	−31.2240	−1.51637
$425$	4.65777	0.225935
$426$	−4.06840	−0.197114
$427$	42.5466	2.05898
$428$	7.85737	0.379800
$429$	−3.21489	−0.155216
$430$	10.6747	0.514781
$431$	−3.41618	−0.164551	−0.0822757	−	0.996610i	$-0.526219\pi$
$431$	−3.41618	−0.164551	−0.0822757	+	0.996610i	$0.526219\pi$
$432$	20.2391	0.973752
$433$	−4.12202	−0.198092	−0.0990458	−	0.995083i	$-0.531579\pi$
$433$	−4.12202	−0.198092	−0.0990458	+	0.995083i	$0.531579\pi$
$434$	−7.77481	−0.373203
$435$	17.1104	0.820381
$436$	−9.93982	−0.476031
$437$	−0.151818	−0.00726242
$438$	−48.3737	−2.31139
$439$	38.1897	1.82269	0.911347	−	0.411639i	$-0.135043\pi$
$439$	38.1897	1.82269	0.911347	+	0.411639i	$0.135043\pi$
$440$	−18.2536	−0.870206
$441$	30.7998	1.46666
$442$	−1.00609	−0.0478550
$443$	6.17048	0.293168	0.146584	−	0.989198i	$-0.453172\pi$
$443$	6.17048	0.293168	0.146584	+	0.989198i	$0.453172\pi$
$444$	7.02249	0.333273
$445$	10.0114	0.474588
$446$	11.0061	0.521154
$447$	28.8235	1.36330
$448$	−30.6692	−1.44898
$449$	−20.8910	−0.985909	−0.492955	−	0.870055i	$-0.664083\pi$
$449$	−20.8910	−0.985909	−0.492955	+	0.870055i	$0.664083\pi$
$450$	6.86047	0.323406
$451$	−29.8216	−1.40424
$452$	0.888931	0.0418118
$453$	8.02006	0.376815
$454$	19.4737	0.913946
$455$	−0.640804	−0.0300414
$456$	2.81903	0.132013
$457$	−9.10196	−0.425772	−0.212886	−	0.977077i	$-0.568286\pi$
$457$	−9.10196	−0.425772	−0.212886	+	0.977077i	$0.568286\pi$
$458$	−21.0329	−0.982804
$459$	−38.7034	−1.80652
$460$	−0.295576	−0.0137813
$461$	25.9453	1.20839	0.604196	−	0.796836i	$-0.293494\pi$
$461$	25.9453	1.20839	0.604196	+	0.796836i	$0.293494\pi$
$462$	−73.0354	−3.39791
$463$	−31.7490	−1.47550	−0.737750	−	0.675074i	$-0.764111\pi$
$463$	−31.7490	−1.47550	−0.737750	+	0.675074i	$0.764111\pi$
$464$	−14.0480	−0.652161
$465$	5.55880	0.257783
$466$	35.2159	1.63135
$467$	31.7766	1.47045	0.735223	−	0.677825i	$-0.237077\pi$
$467$	31.7766	1.47045	0.735223	+	0.677825i	$0.237077\pi$
$468$	0.637140	0.0294518
$469$	4.76871	0.220199
$470$	−0.0631762	−0.00291410
$471$	−13.5457	−0.624153
$472$	26.0640	1.19969
$473$	53.5547	2.46245
$474$	−20.6080	−0.946557
$475$	0.308874	0.0141721
$476$	9.82711	0.450425
$477$	58.8756	2.69573
$478$	−13.4280	−0.614183
$479$	−29.4085	−1.34371	−0.671855	−	0.740683i	$-0.734502\pi$
$479$	−29.4085	−1.34371	−0.671855	+	0.740683i	$0.734502\pi$
$480$	9.70809	0.443112
$481$	−0.718957	−0.0327816
$482$	−14.3840	−0.655174
$483$	−5.11593	−0.232783
$484$	−14.5550	−0.661593
$485$	−3.36529	−0.152810
$486$	4.05099	0.183757
$487$	38.8956	1.76253	0.881265	−	0.472623i	$-0.156693\pi$
$487$	38.8956	1.76253	0.881265	+	0.472623i	$0.156693\pi$
$488$	37.3078	1.68884
$489$	−20.1983	−0.913398
$490$	−6.27918	−0.283664
$491$	−16.2126	−0.731666	−0.365833	−	0.930680i	$-0.619216\pi$
$491$	−16.2126	−0.731666	−0.365833	+	0.930680i	$0.619216\pi$
$492$	8.96664	0.404247
$493$	26.8641	1.20990
$494$	−0.0667179	−0.00300178
$495$	34.4187	1.54701
$496$	−4.56389	−0.204925
$497$	−4.06840	−0.182493
$498$	−52.5717	−2.35579
$499$	−11.5371	−0.516470	−0.258235	−	0.966082i	$-0.583141\pi$
$499$	−11.5371	−0.516470	−0.258235	+	0.966082i	$0.583141\pi$
$500$	0.601352	0.0268933
$501$	−8.54352	−0.381696
$502$	20.3246	0.907132
$503$	5.34859	0.238482	0.119241	−	0.992865i	$-0.461954\pi$
$503$	5.34859	0.238482	0.119241	+	0.992865i	$0.461954\pi$
$504$	62.6141	2.78905
$505$	18.9641	0.843892
$506$	3.44897	0.153325
$507$	38.4674	1.70840
$508$	−1.90690	−0.0846051
$509$	−28.3812	−1.25798	−0.628988	−	0.777415i	$-0.716531\pi$
$509$	−28.3812	−1.25798	−0.628988	+	0.777415i	$0.716531\pi$
$510$	16.3417	0.723622
$511$	−48.3737	−2.13993
$512$	−22.9571	−1.01457
$513$	−2.56657	−0.113317
$514$	5.99634	0.264487
$515$	−1.63471	−0.0720340
$516$	−16.1026	−0.708879
$517$	−0.316953	−0.0139396
$518$	−16.3332	−0.717638
$519$	18.6826	0.820075
$520$	−0.561901	−0.0246410
$521$	15.8704	0.695295	0.347648	−	0.937625i	$-0.386981\pi$
$521$	15.8704	0.695295	0.347648	+	0.937625i	$0.386981\pi$
$522$	39.5685	1.73186
$523$	−37.5403	−1.64152	−0.820761	−	0.571272i	$-0.806450\pi$
$523$	−37.5403	−1.64152	−0.820761	+	0.571272i	$0.806450\pi$
$524$	10.6433	0.464954
$525$	10.4084	0.454260
$526$	−22.8994	−0.998460
$527$	8.72758	0.380179
$528$	−42.8725	−1.86578
$529$	−22.7584	−0.989496
$530$	−12.0030	−0.521377
$531$	−49.1459	−2.13275
$532$	0.651674	0.0282536
$533$	−0.917998	−0.0397629
$534$	35.1249	1.52000
$535$	13.0662	0.564900
$536$	4.18153	0.180615
$537$	−41.6286	−1.79641
$538$	−1.91521	−0.0825704
$539$	−31.5024	−1.35690
$540$	−4.99690	−0.215032
$541$	−17.4266	−0.749227	−0.374614	−	0.927181i	$-0.622225\pi$
$541$	−17.4266	−0.749227	−0.374614	+	0.927181i	$0.622225\pi$
$542$	7.54308	0.324003
$543$	13.5713	0.582400
$544$	15.2422	0.653502
$545$	−16.5291	−0.708029
$546$	−2.24825	−0.0962162
$547$	7.87153	0.336562	0.168281	−	0.985739i	$-0.446178\pi$
$547$	7.87153	0.336562	0.168281	+	0.985739i	$0.446178\pi$
$548$	−0.456925	−0.0195189
$549$	−70.3470	−3.00234
$550$	−7.01696	−0.299204
$551$	1.78146	0.0758929
$552$	−4.48599	−0.190936
$553$	−20.6080	−0.876342
$554$	−35.4735	−1.50712
$555$	11.6778	0.495696
$556$	−5.43257	−0.230392
$557$	−3.10394	−0.131518	−0.0657592	−	0.997836i	$-0.520947\pi$
$557$	−3.10394	−0.131518	−0.0657592	+	0.997836i	$0.520947\pi$
$558$	12.8549	0.544193
$559$	1.64858	0.0697273
$560$	−8.54550	−0.361113
$561$	81.9856	3.46144
$562$	−5.24228	−0.221132
$563$	28.6791	1.20868	0.604339	−	0.796727i	$-0.293437\pi$
$563$	28.6791	1.20868	0.604339	+	0.796727i	$0.293437\pi$
$564$	0.0953001	0.00401286
$565$	1.47822	0.0621892
$566$	1.80128	0.0757135
$567$	−25.4303	−1.06797
$568$	−3.56745	−0.149687
$569$	23.9089	1.00231	0.501157	−	0.865356i	$-0.332908\pi$
$569$	23.9089	1.00231	0.501157	+	0.865356i	$0.332908\pi$
$570$	1.08368	0.0453904
$571$	24.6363	1.03100	0.515499	−	0.856890i	$-0.327606\pi$
$571$	24.6363	1.03100	0.515499	+	0.856890i	$0.327606\pi$
$572$	−0.651674	−0.0272478
$573$	−76.8697	−3.21128
$574$	−20.8549	−0.870469
$575$	−0.491519	−0.0204978
$576$	50.7088	2.11287
$577$	18.7478	0.780483	0.390242	−	0.920713i	$-0.372392\pi$
$577$	18.7478	0.780483	0.390242	+	0.920713i	$0.372392\pi$
$578$	5.55227	0.230944
$579$	36.3273	1.50971
$580$	3.46836	0.144016
$581$	−52.5717	−2.18104
$582$	−11.8071	−0.489418
$583$	−60.2186	−2.49400
$584$	−42.4174	−1.75524
$585$	1.05951	0.0438054
$586$	−0.810150	−0.0334670
$587$	32.3428	1.33493	0.667465	−	0.744641i	$-0.267379\pi$
$587$	32.3428	1.33493	0.667465	+	0.744641i	$0.267379\pi$
$588$	9.47202	0.390620
$589$	0.578760	0.0238474
$590$	10.0194	0.412492
$591$	−28.2737	−1.16302
$592$	−9.58773	−0.394053
$593$	6.50923	0.267302	0.133651	−	0.991028i	$-0.457330\pi$
$593$	6.50923	0.267302	0.133651	+	0.991028i	$0.457330\pi$
$594$	58.3070	2.39237
$595$	16.3417	0.669944
$596$	5.84266	0.239324
$597$	−17.2883	−0.707562
$598$	0.106170	0.00434160
$599$	−31.9374	−1.30493	−0.652464	−	0.757820i	$-0.726264\pi$
$599$	−31.9374	−1.30493	−0.652464	+	0.757820i	$0.726264\pi$
$600$	9.12680	0.372600
$601$	−24.3350	−0.992647	−0.496324	−	0.868138i	$-0.665317\pi$
$601$	−24.3350	−0.992647	−0.496324	+	0.868138i	$0.665317\pi$
$602$	37.4521	1.52643
$603$	−7.88464	−0.321087
$604$	1.62570	0.0661490
$605$	−24.2038	−0.984026
$606$	66.5352	2.70281
$607$	18.4854	0.750300	0.375150	−	0.926964i	$-0.377591\pi$
$607$	18.4854	0.750300	0.375150	+	0.926964i	$0.377591\pi$
$608$	1.01077	0.0409920
$609$	60.0315	2.43260
$610$	14.3417	0.580678
$611$	−0.00975676	−0.000394716 0
$612$	−16.2482	−0.656797
$613$	38.7310	1.56433	0.782165	−	0.623071i	$-0.214115\pi$
$613$	38.7310	1.56433	0.782165	+	0.623071i	$0.214115\pi$
$614$	−19.7462	−0.796892
$615$	14.9108	0.601261
$616$	−64.0424	−2.58034
$617$	−4.14619	−0.166919	−0.0834596	−	0.996511i	$-0.526597\pi$
$617$	−4.14619	−0.166919	−0.0834596	+	0.996511i	$0.526597\pi$
$618$	−5.73535	−0.230710
$619$	32.1606	1.29264	0.646322	−	0.763065i	$-0.276307\pi$
$619$	32.1606	1.29264	0.646322	+	0.763065i	$0.276307\pi$
$620$	1.12680	0.0452532
$621$	4.08425	0.163895
$622$	32.3345	1.29649
$623$	35.1249	1.40725
$624$	−1.31974	−0.0528320
$625$	1.00000	0.0400000
$626$	15.8624	0.633987
$627$	5.43678	0.217124
$628$	−2.74578	−0.109569
$629$	18.3347	0.731054
$630$	24.0698	0.958965
$631$	−8.76495	−0.348927	−0.174463	−	0.984664i	$-0.555819\pi$
$631$	−8.76495	−0.348927	−0.174463	+	0.984664i	$0.555819\pi$
$632$	−18.0705	−0.718806
$633$	10.2213	0.406262
$634$	−2.50959	−0.0996687
$635$	−3.17102	−0.125838
$636$	18.1063	0.717961
$637$	−0.969739	−0.0384225
$638$	−40.4710	−1.60226
$639$	6.72673	0.266105
$640$	−3.79319	−0.149939
$641$	−10.0706	−0.397763	−0.198882	−	0.980023i	$-0.563731\pi$
$641$	−10.0706	−0.397763	−0.198882	+	0.980023i	$0.563731\pi$
$642$	45.8424	1.80926
$643$	−3.28029	−0.129362	−0.0646810	−	0.997906i	$-0.520603\pi$
$643$	−3.28029	−0.129362	−0.0646810	+	0.997906i	$0.520603\pi$
$644$	−1.03702	−0.0408644
$645$	−26.7774	−1.05436
$646$	1.70143	0.0669418
$647$	−27.6846	−1.08839	−0.544197	−	0.838958i	$-0.683165\pi$
$647$	−27.6846	−1.08839	−0.544197	+	0.838958i	$0.683165\pi$
$648$	−22.2991	−0.875990
$649$	50.2669	1.97315
$650$	−0.216003	−0.00847235
$651$	19.5030	0.764381
$652$	−4.09429	−0.160345
$653$	44.0561	1.72405	0.862024	−	0.506867i	$-0.169197\pi$
$653$	44.0561	1.72405	0.862024	+	0.506867i	$0.169197\pi$
$654$	−57.9921	−2.26767
$655$	17.6989	0.691553
$656$	−12.2421	−0.477972
$657$	79.9817	3.12038
$658$	−0.221652	−0.00864091
$659$	1.93948	0.0755513	0.0377757	−	0.999286i	$-0.487973\pi$
$659$	1.93948	0.0755513	0.0377757	+	0.999286i	$0.487973\pi$
$660$	10.5850	0.412019
$661$	−12.7009	−0.494007	−0.247004	−	0.969015i	$-0.579446\pi$
$661$	−12.7009	−0.494007	−0.247004	+	0.969015i	$0.579446\pi$
$662$	25.7383	1.00035
$663$	2.52376	0.0980149
$664$	−46.0984	−1.78897
$665$	1.08368	0.0420233
$666$	27.0054	1.04644
$667$	−2.83488	−0.109767
$668$	−1.73181	−0.0670058
$669$	−27.6086	−1.06741
$670$	1.60745	0.0621010
$671$	71.9517	2.77766
$672$	34.0606	1.31392
$673$	44.2207	1.70458	0.852291	−	0.523067i	$-0.175212\pi$
$673$	44.2207	1.70458	0.852291	+	0.523067i	$0.175212\pi$
$674$	24.1728	0.931102
$675$	−8.30944	−0.319831
$676$	7.79752	0.299905
$677$	36.3240	1.39604	0.698022	−	0.716076i	$-0.254064\pi$
$677$	36.3240	1.39604	0.698022	+	0.716076i	$0.254064\pi$
$678$	5.18631	0.199179
$679$	−11.8071	−0.453113
$680$	14.3295	0.549511
$681$	−48.8494	−1.87191
$682$	−13.1482	−0.503470
$683$	15.4292	0.590381	0.295190	−	0.955438i	$-0.404617\pi$
$683$	15.4292	0.590381	0.295190	+	0.955438i	$0.404617\pi$
$684$	−1.07748	−0.0411986
$685$	−0.759829	−0.0290316
$686$	7.01461	0.267819
$687$	52.7607	2.01295
$688$	21.9847	0.838160
$689$	−1.85371	−0.0706207
$690$	−1.72448	−0.0656500
$691$	37.3322	1.42018	0.710092	−	0.704109i	$-0.248653\pi$
$691$	37.3322	1.42018	0.710092	+	0.704109i	$0.248653\pi$
$692$	3.78705	0.143962
$693$	120.757	4.58720
$694$	−24.4672	−0.928764
$695$	−9.03392	−0.342676
$696$	52.6397	1.99530
$697$	23.4106	0.886742
$698$	−0.609349	−0.0230642
$699$	−88.3384	−3.34127
$700$	2.10983	0.0797442
$701$	−4.82554	−0.182258	−0.0911290	−	0.995839i	$-0.529048\pi$
$701$	−4.82554	−0.182258	−0.0911290	+	0.995839i	$0.529048\pi$
$702$	1.79487	0.0677429
$703$	1.21585	0.0458566
$704$	−51.8655	−1.95475
$705$	0.158476	0.00596856
$706$	−37.7047	−1.41903
$707$	66.5352	2.50231
$708$	−15.1141	−0.568021
$709$	2.45308	0.0921272	0.0460636	−	0.998939i	$-0.485332\pi$
$709$	2.45308	0.0921272	0.0460636	+	0.998939i	$0.485332\pi$
$710$	−1.37138	−0.0514670
$711$	34.0735	1.27786
$712$	30.7999	1.15428
$713$	−0.920993	−0.0344915
$714$	57.3345	2.14569
$715$	−1.08368	−0.0405273
$716$	−8.43832	−0.315355
$717$	33.6839	1.25795
$718$	−3.20204	−0.119499
$719$	−11.5318	−0.430065	−0.215033	−	0.976607i	$-0.568986\pi$
$719$	−11.5318	−0.430065	−0.215033	+	0.976607i	$0.568986\pi$
$720$	14.1292	0.526565
$721$	−5.73535	−0.213596
$722$	−22.3574	−0.832057
$723$	36.0820	1.34190
$724$	2.75097	0.102239
$725$	5.76760	0.214203
$726$	−84.9187	−3.15163
$727$	−25.8009	−0.956901	−0.478450	−	0.878115i	$-0.658801\pi$
$727$	−25.8009	−0.956901	−0.478450	+	0.878115i	$0.658801\pi$
$728$	−1.97142	−0.0730656
$729$	−31.9066	−1.18173
$730$	−16.3059	−0.603508
$731$	−42.0417	−1.55497
$732$	−21.6342	−0.799622
$733$	−20.5564	−0.759268	−0.379634	−	0.925137i	$-0.623950\pi$
$733$	−20.5564	−0.759268	−0.379634	+	0.925137i	$0.623950\pi$
$734$	−11.2981	−0.417021
$735$	15.7512	0.580992
$736$	−1.60845	−0.0592884
$737$	8.06449	0.297059
$738$	34.4818	1.26929
$739$	17.2107	0.633105	0.316553	−	0.948575i	$-0.397475\pi$
$739$	17.2107	0.633105	0.316553	+	0.948575i	$0.397475\pi$
$740$	2.36715	0.0870182
$741$	0.167361	0.00614814
$742$	−42.1123	−1.54599
$743$	−12.3656	−0.453650	−0.226825	−	0.973936i	$-0.572834\pi$
$743$	−12.3656	−0.453650	−0.226825	+	0.973936i	$0.572834\pi$
$744$	17.1015	0.626972
$745$	9.71586	0.355962
$746$	10.2270	0.374437
$747$	86.9226	3.18033
$748$	16.6189	0.607646
$749$	45.8424	1.67505
$750$	3.50848	0.128112
$751$	14.3525	0.523728	0.261864	−	0.965105i	$-0.415663\pi$
$751$	14.3525	0.523728	0.261864	+	0.965105i	$0.415663\pi$
$752$	−0.130112	−0.00474470
$753$	−50.9839	−1.85796
$754$	−1.24582	−0.0453701
$755$	2.70341	0.0983873
$756$	−17.5315	−0.637616
$757$	−53.7879	−1.95496	−0.977478	−	0.211038i	$-0.932316\pi$
$757$	−53.7879	−1.95496	−0.977478	+	0.211038i	$0.932316\pi$
$758$	16.5122	0.599751
$759$	−8.65167	−0.314036
$760$	0.950245	0.0344690
$761$	2.12501	0.0770317	0.0385158	−	0.999258i	$-0.487737\pi$
$761$	2.12501	0.0770317	0.0385158	+	0.999258i	$0.487737\pi$
$762$	−11.1255	−0.403034
$763$	−57.9921	−2.09945
$764$	−15.5819	−0.563732
$765$	−27.0195	−0.976893
$766$	−0.702664	−0.0253883
$767$	1.54737	0.0558722
$768$	38.5571	1.39131
$769$	20.8110	0.750465	0.375232	−	0.926931i	$-0.377563\pi$
$769$	20.8110	0.750465	0.375232	+	0.926931i	$0.377563\pi$
$770$	−24.6189	−0.887203
$771$	−15.0417	−0.541713
$772$	7.36371	0.265026
$773$	−7.14011	−0.256812	−0.128406	−	0.991722i	$-0.540986\pi$
$773$	−7.14011	−0.256812	−0.128406	+	0.991722i	$0.540986\pi$
$774$	−61.9237	−2.22580
$775$	1.87377	0.0673078
$776$	−10.3532	−0.371659
$777$	40.9714	1.46984
$778$	−40.7459	−1.46081
$779$	1.55245	0.0556223
$780$	0.325837	0.0116668
$781$	−6.88017	−0.246192
$782$	−2.70752	−0.0968208
$783$	−47.9255	−1.71272
$784$	−12.9320	−0.461859
$785$	−4.56601	−0.162968
$786$	62.0962	2.21490
$787$	46.1635	1.64555	0.822775	−	0.568367i	$-0.192425\pi$
$787$	46.1635	1.64555	0.822775	+	0.568367i	$0.192425\pi$
$788$	−5.73121	−0.204166
$789$	57.4427	2.04501
$790$	−6.94658	−0.247148
$791$	5.18631	0.184404
$792$	105.888	3.76258
$793$	2.21489	0.0786531
$794$	−5.44909	−0.193381
$795$	30.1093	1.06787
$796$	−3.50441	−0.124211
$797$	−2.18135	−0.0772673	−0.0386336	−	0.999253i	$-0.512301\pi$
$797$	−2.18135	−0.0772673	−0.0386336	+	0.999253i	$0.512301\pi$
$798$	3.80207	0.134592
$799$	0.248815	0.00880245
$800$	3.27242	0.115697
$801$	−58.0759	−2.05201
$802$	3.32827	0.117525
$803$	−81.8061	−2.88687
$804$	−2.42480	−0.0855161
$805$	−1.72448	−0.0607801
$806$	−0.404740	−0.0142564
$807$	4.80426	0.169118
$808$	58.3426	2.05249
$809$	−23.8434	−0.838290	−0.419145	−	0.907919i	$-0.637670\pi$
$809$	−23.8434	−0.838290	−0.419145	+	0.907919i	$0.637670\pi$
$810$	−8.57210	−0.301193
$811$	39.1911	1.37619	0.688093	−	0.725623i	$-0.258448\pi$
$811$	39.1911	1.37619	0.688093	+	0.725623i	$0.258448\pi$
$812$	12.1687	0.427037
$813$	−18.9217	−0.663612
$814$	−27.6214	−0.968131
$815$	−6.80847	−0.238490
$816$	33.6559	1.17819
$817$	−2.78795	−0.0975380
$818$	−25.4653	−0.890373
$819$	3.71728	0.129892
$820$	3.02249	0.105550
$821$	3.21758	0.112294	0.0561471	−	0.998423i	$-0.482118\pi$
$821$	3.21758	0.112294	0.0561471	+	0.998423i	$0.482118\pi$
$822$	−2.66584	−0.0929820
$823$	−28.5341	−0.994636	−0.497318	−	0.867568i	$-0.665682\pi$
$823$	−28.5341	−0.994636	−0.497318	+	0.867568i	$0.665682\pi$
$824$	−5.02915	−0.175199
$825$	17.6019	0.612820
$826$	35.1528	1.22312
$827$	−5.38271	−0.187175	−0.0935876	−	0.995611i	$-0.529834\pi$
$827$	−5.38271	−0.187175	−0.0935876	+	0.995611i	$0.529834\pi$
$828$	1.71462	0.0595873
$829$	−4.59469	−0.159580	−0.0797902	−	0.996812i	$-0.525425\pi$
$829$	−4.59469	−0.159580	−0.0797902	+	0.996812i	$0.525425\pi$
$830$	−17.7209	−0.615103
$831$	88.9845	3.08684
$832$	−1.59658	−0.0553513
$833$	24.7301	0.856848
$834$	−31.6954	−1.09752
$835$	−2.87986	−0.0996618
$836$	1.10206	0.0381156
$837$	−15.5700	−0.538177
$838$	−1.02182	−0.0352982
$839$	−7.65309	−0.264214	−0.132107	−	0.991235i	$-0.542174\pi$
$839$	−7.65309	−0.264214	−0.132107	+	0.991235i	$0.542174\pi$
$840$	32.0212	1.10484
$841$	4.26521	0.147076
$842$	−25.4254	−0.876216
$843$	13.1502	0.452915
$844$	2.07192	0.0713183
$845$	12.9666	0.446066
$846$	0.366482	0.0125999
$847$	−84.9187	−2.91784
$848$	−24.7203	−0.848899
$849$	−4.51848	−0.155074
$850$	5.50848	0.188939
$851$	−1.93480	−0.0663243
$852$	2.06870	0.0708726
$853$	21.6046	0.739728	0.369864	−	0.929086i	$-0.379404\pi$
$853$	21.6046	0.739728	0.369864	+	0.929086i	$0.379404\pi$
$854$	50.3175	1.72183
$855$	−1.79177	−0.0612772
$856$	40.1977	1.37393
$857$	1.45581	0.0497296	0.0248648	−	0.999691i	$-0.492084\pi$
$857$	1.45581	0.0497296	0.0248648	+	0.999691i	$0.492084\pi$
$858$	−3.80207	−0.129801
$859$	−52.2525	−1.78283	−0.891416	−	0.453186i	$-0.850287\pi$
$859$	−52.2525	−1.78283	−0.891416	+	0.453186i	$0.850287\pi$
$860$	−5.42790	−0.185090
$861$	52.3142	1.78286
$862$	−4.04012	−0.137607
$863$	4.26730	0.145261	0.0726303	−	0.997359i	$-0.476861\pi$
$863$	4.26730	0.145261	0.0726303	+	0.997359i	$0.476861\pi$
$864$	−27.1920	−0.925089
$865$	6.29756	0.214124
$866$	−4.87488	−0.165655
$867$	−13.9278	−0.473011
$868$	3.95334	0.134185
$869$	−34.8507	−1.18223
$870$	20.2355	0.686048
$871$	0.248249	0.00841161
$872$	−50.8514	−1.72205
$873$	19.5219	0.660716
$874$	−0.179546	−0.00607324
$875$	3.50848	0.118608
$876$	24.5971	0.831060
$877$	−39.3500	−1.32876	−0.664378	−	0.747396i	$-0.731304\pi$
$877$	−39.3500	−1.32876	−0.664378	+	0.747396i	$0.731304\pi$
$878$	45.1648	1.52424
$879$	2.03225	0.0685460
$880$	−14.4515	−0.487161
$881$	−12.0162	−0.404836	−0.202418	−	0.979299i	$-0.564880\pi$
$881$	−12.0162	−0.404836	−0.202418	+	0.979299i	$0.564880\pi$
$882$	36.4253	1.22650
$883$	−27.3798	−0.921404	−0.460702	−	0.887555i	$-0.652402\pi$
$883$	−27.3798	−0.921404	−0.460702	+	0.887555i	$0.652402\pi$
$884$	0.511579	0.0172063
$885$	−25.1335	−0.844852
$886$	7.29748	0.245164
$887$	−9.56812	−0.321266	−0.160633	−	0.987014i	$-0.551354\pi$
$887$	−9.56812	−0.321266	−0.160633	+	0.987014i	$0.551354\pi$
$888$	35.9265	1.20562
$889$	−11.1255	−0.373137
$890$	11.8400	0.396877
$891$	−43.0059	−1.44075
$892$	−5.59639	−0.187381
$893$	0.0164999	0.000552148 0
$894$	34.0879	1.14007
$895$	−14.0322	−0.469046
$896$	−13.3083	−0.444600
$897$	−0.266325	−0.00889232
$898$	−24.7067	−0.824472
$899$	10.8072	0.360439
$900$	−3.48842	−0.116281
$901$	47.2730	1.57489
$902$	−35.2683	−1.17431
$903$	−93.9479	−3.12639
$904$	4.54771	0.151254
$905$	4.57463	0.152066
$906$	9.48488	0.315114
$907$	−52.8616	−1.75524	−0.877620	−	0.479356i	$-0.840870\pi$
$907$	−52.8616	−1.75524	−0.877620	+	0.479356i	$0.840870\pi$
$908$	−9.90201	−0.328610
$909$	−110.010	−3.64880
$910$	−0.757843	−0.0251223
$911$	26.9039	0.891368	0.445684	−	0.895190i	$-0.352961\pi$
$911$	26.9039	0.891368	0.445684	+	0.895190i	$0.352961\pi$
$912$	2.23185	0.0739040
$913$	−88.9053	−2.94234
$914$	−10.7644	−0.356054
$915$	−35.9759	−1.18932
$916$	10.6949	0.353368
$917$	62.0962	2.05060
$918$	−45.7724	−1.51071
$919$	43.6220	1.43896	0.719479	−	0.694514i	$-0.244381\pi$
$919$	43.6220	1.43896	0.719479	+	0.694514i	$0.244381\pi$
$920$	−1.51215	−0.0498539
$921$	49.5330	1.63217
$922$	30.6840	1.01053
$923$	−0.211792	−0.00697123
$924$	37.1371	1.22172
$925$	3.93638	0.129427
$926$	−37.5477	−1.23389
$927$	9.48289	0.311459
$928$	18.8740	0.619569
$929$	−44.9073	−1.47336	−0.736680	−	0.676242i	$-0.763607\pi$
$929$	−44.9073	−1.47336	−0.736680	+	0.676242i	$0.763607\pi$
$930$	6.57409	0.215573
$931$	1.63995	0.0537472
$932$	−17.9066	−0.586551
$933$	−81.1104	−2.65544
$934$	37.5804	1.22967
$935$	27.6358	0.903789
$936$	3.25956	0.106542
$937$	31.3628	1.02458	0.512289	−	0.858813i	$-0.328798\pi$
$937$	31.3628	1.02458	0.512289	+	0.858813i	$0.328798\pi$
$938$	5.63969	0.184142
$939$	−39.7904	−1.29851
$940$	0.0321239	0.00104777
$941$	−14.5283	−0.473608	−0.236804	−	0.971557i	$-0.576100\pi$
$941$	−14.5283	−0.473608	−0.236804	+	0.971557i	$0.576100\pi$
$942$	−16.0198	−0.521952
$943$	−2.47045	−0.0804489
$944$	20.6351	0.671614
$945$	−29.1535	−0.948364
$946$	63.3362	2.05924
$947$	−53.6481	−1.74333	−0.871665	−	0.490102i	$-0.836959\pi$
$947$	−53.6481	−1.74333	−0.871665	+	0.490102i	$0.836959\pi$
$948$	10.4788	0.340335
$949$	−2.51824	−0.0817455
$950$	0.365289	0.0118515
$951$	6.29527	0.204138
$952$	50.2748	1.62942
$953$	7.45336	0.241438	0.120719	−	0.992687i	$-0.461480\pi$
$953$	7.45336	0.241438	0.120719	+	0.992687i	$0.461480\pi$
$954$	69.6289	2.25432
$955$	−25.9114	−0.838472
$956$	6.82790	0.220830
$957$	101.521	3.28170
$958$	−34.7798	−1.12369
$959$	−2.66584	−0.0860846
$960$	25.9327	0.836975
$961$	−27.4890	−0.886742
$962$	−0.850271	−0.0274138
$963$	−75.7963	−2.44250
$964$	7.31400	0.235568
$965$	12.2453	0.394189
$966$	−6.05032	−0.194666
$967$	7.76673	0.249761	0.124881	−	0.992172i	$-0.460145\pi$
$967$	7.76673	0.249761	0.124881	+	0.992172i	$0.460145\pi$
$968$	−74.4625	−2.39332
$969$	−4.26800	−0.137108
$970$	−3.97994	−0.127788
$971$	41.1029	1.31905	0.659527	−	0.751681i	$-0.270757\pi$
$971$	41.1029	1.31905	0.659527	+	0.751681i	$0.270757\pi$
$972$	−2.05985	−0.0660698
$973$	−31.6954	−1.01611
$974$	45.9997	1.47393
$975$	0.541840	0.0173528
$976$	29.5369	0.945452
$977$	−10.4374	−0.333924	−0.166962	−	0.985963i	$-0.553396\pi$
$977$	−10.4374	−0.333924	−0.166962	+	0.985963i	$0.553396\pi$
$978$	−23.8874	−0.763835
$979$	59.4007	1.89845
$980$	3.19284	0.101992
$981$	95.8847	3.06136
$982$	−19.1738	−0.611860
$983$	36.5070	1.16439	0.582197	−	0.813048i	$-0.302193\pi$
$983$	36.5070	1.16439	0.582197	+	0.813048i	$0.302193\pi$
$984$	45.8727	1.46237
$985$	−9.53053	−0.303668
$986$	31.7707	1.01179
$987$	0.556011	0.0176980
$988$	0.0339248	0.00107929
$989$	4.43652	0.141073
$990$	40.7051	1.29369
$991$	24.5031	0.778368	0.389184	−	0.921160i	$-0.372757\pi$
$991$	24.5031	0.778368	0.389184	+	0.921160i	$0.372757\pi$
$992$	6.13176	0.194683
$993$	−64.5642	−2.04888
$994$	−4.81147	−0.152610
$995$	−5.82756	−0.184746
$996$	26.7317	0.847027
$997$	−0.752657	−0.0238369	−0.0119184	−	0.999929i	$-0.503794\pi$
$997$	−0.752657	−0.0238369	−0.0119184	+	0.999929i	$0.503794\pi$
$998$	−13.6442	−0.431901
$999$	−32.7091	−1.03487

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6005.2.a.c.1.3	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6005.2.a.c.1.3	✓	4	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:	\( N \)	\(=\)	\( 6005 = 5 \cdot 1201 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6005.a (trivial)

\(f(q)\)	\(=\)	\(q+1.18264 q^{2} -2.96664 q^{3} -0.601352 q^{4} -1.00000 q^{5} -3.50848 q^{6} -3.50848 q^{7} -3.07647 q^{8} +5.80096 q^{9} +O(q^{10})\)	\(q+1.18264 q^{2} -2.96664 q^{3} -0.601352 q^{4} -1.00000 q^{5} -3.50848 q^{6} -3.50848 q^{7} -3.07647 q^{8} +5.80096 q^{9} -1.18264 q^{10} -5.93328 q^{11} +1.78400 q^{12} -0.182644 q^{13} -4.14929 q^{14} +2.96664 q^{15} -2.43567 q^{16} +4.65777 q^{17} +6.86047 q^{18} +0.308874 q^{19} +0.601352 q^{20} +10.4084 q^{21} -7.01696 q^{22} -0.491519 q^{23} +9.12680 q^{24} +1.00000 q^{25} -0.216003 q^{26} -8.30944 q^{27} +2.10983 q^{28} +5.76760 q^{29} +3.50848 q^{30} +1.87377 q^{31} +3.27242 q^{32} +17.6019 q^{33} +5.50848 q^{34} +3.50848 q^{35} -3.48842 q^{36} +3.93638 q^{37} +0.365289 q^{38} +0.541840 q^{39} +3.07647 q^{40} +5.02615 q^{41} +12.3094 q^{42} -9.02615 q^{43} +3.56799 q^{44} -5.80096 q^{45} -0.581292 q^{46} +0.0534194 q^{47} +7.22576 q^{48} +5.30944 q^{49} +1.18264 q^{50} -13.8179 q^{51} +0.109834 q^{52} +10.1493 q^{53} -9.82711 q^{54} +5.93328 q^{55} +10.7938 q^{56} -0.916320 q^{57} +6.82102 q^{58} -8.47202 q^{59} -1.78400 q^{60} -12.1268 q^{61} +2.21600 q^{62} -20.3526 q^{63} +8.74145 q^{64} +0.182644 q^{65} +20.8168 q^{66} -1.35920 q^{67} -2.80096 q^{68} +1.45816 q^{69} +4.14929 q^{70} +1.15959 q^{71} -17.8465 q^{72} +13.7877 q^{73} +4.65534 q^{74} -2.96664 q^{75} -0.185742 q^{76} +20.8168 q^{77} +0.640804 q^{78} +5.87377 q^{79} +2.43567 q^{80} +7.24825 q^{81} +5.94415 q^{82} +14.9842 q^{83} -6.25912 q^{84} -4.65777 q^{85} -10.6747 q^{86} -17.1104 q^{87} +18.2536 q^{88} -10.0114 q^{89} -6.86047 q^{90} +0.640804 q^{91} +0.295576 q^{92} -5.55880 q^{93} +0.0631762 q^{94} -0.308874 q^{95} -9.70809 q^{96} +3.36529 q^{97} +6.27918 q^{98} -34.4187 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 4 q^{5} - 7 q^{6} - 7 q^{7} + 9 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 4 * q^5 - 7 * q^6 - 7 * q^7 + 9 * q^8 + 2 * q^9	\( 4 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 4 q^{5} - 7 q^{6} - 7 q^{7} + 9 q^{8} + 2 q^{9} - 2 q^{10} - 4 q^{11} + 2 q^{13} - 4 q^{14} + 2 q^{15} + 6 q^{16} - q^{17} - q^{18} + 11 q^{19} - 2 q^{20} + 5 q^{21} - 14 q^{22} - 9 q^{23} + 11 q^{24} + 4 q^{25} - 8 q^{26} - 5 q^{27} - 3 q^{28} - 8 q^{29} + 7 q^{30} - 5 q^{31} + 5 q^{32} + 28 q^{33} + 15 q^{34} + 7 q^{35} - 13 q^{36} + 4 q^{37} - 4 q^{38} + 5 q^{39} - 9 q^{40} + 3 q^{41} + 21 q^{42} - 19 q^{43} - 2 q^{45} - 4 q^{46} + 4 q^{47} - 5 q^{48} - 7 q^{49} + 2 q^{50} - 20 q^{51} - 11 q^{52} + 28 q^{53} - q^{54} + 4 q^{55} - 5 q^{56} + 2 q^{57} - 9 q^{59} - 23 q^{61} + 16 q^{62} - 22 q^{63} + 21 q^{64} - 2 q^{65} + 10 q^{66} - 11 q^{67} + 10 q^{68} + 3 q^{69} + 4 q^{70} + 27 q^{71} - 38 q^{72} + 18 q^{73} - 20 q^{74} - 2 q^{75} - 6 q^{76} + 10 q^{77} - 3 q^{78} + 11 q^{79} - 6 q^{80} + 8 q^{81} + q^{82} - 2 q^{83} - q^{84} + q^{85} - 9 q^{86} - 19 q^{87} + 22 q^{88} + q^{89} + q^{90} - 3 q^{91} - 5 q^{92} - 11 q^{93} - 37 q^{94} - 11 q^{95} - 15 q^{96} + 8 q^{97} - 5 q^{98} - 22 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 4 * q^5 - 7 * q^6 - 7 * q^7 + 9 * q^8 + 2 * q^9 - 2 * q^10 - 4 * q^11 + 2 * q^13 - 4 * q^14 + 2 * q^15 + 6 * q^16 - q^17 - q^18 + 11 * q^19 - 2 * q^20 + 5 * q^21 - 14 * q^22 - 9 * q^23 + 11 * q^24 + 4 * q^25 - 8 * q^26 - 5 * q^27 - 3 * q^28 - 8 * q^29 + 7 * q^30 - 5 * q^31 + 5 * q^32 + 28 * q^33 + 15 * q^34 + 7 * q^35 - 13 * q^36 + 4 * q^37 - 4 * q^38 + 5 * q^39 - 9 * q^40 + 3 * q^41 + 21 * q^42 - 19 * q^43 - 2 * q^45 - 4 * q^46 + 4 * q^47 - 5 * q^48 - 7 * q^49 + 2 * q^50 - 20 * q^51 - 11 * q^52 + 28 * q^53 - q^54 + 4 * q^55 - 5 * q^56 + 2 * q^57 - 9 * q^59 - 23 * q^61 + 16 * q^62 - 22 * q^63 + 21 * q^64 - 2 * q^65 + 10 * q^66 - 11 * q^67 + 10 * q^68 + 3 * q^69 + 4 * q^70 + 27 * q^71 - 38 * q^72 + 18 * q^73 - 20 * q^74 - 2 * q^75 - 6 * q^76 + 10 * q^77 - 3 * q^78 + 11 * q^79 - 6 * q^80 + 8 * q^81 + q^82 - 2 * q^83 - q^84 + q^85 - 9 * q^86 - 19 * q^87 + 22 * q^88 + q^89 + q^90 - 3 * q^91 - 5 * q^92 - 11 * q^93 - 37 * q^94 - 11 * q^95 - 15 * q^96 + 8 * q^97 - 5 * q^98 - 22 * q^99

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