LMFDB - Embedded newform 6046.2.a.f.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6046,2,Mod(1,6046)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6046, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6046.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6046 = 2 \cdot 3023 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6046.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:	$48.2775530621$
Analytic rank:	$0$
Dimension:	$67$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	6046.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.34396 q^{3} +1.00000 q^{4} +3.11002 q^{5} -2.34396 q^{6} +1.16030 q^{7} +1.00000 q^{8} +2.49414 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.34396 q^{3} +1.00000 q^{4} +3.11002 q^{5} -2.34396 q^{6} +1.16030 q^{7} +1.00000 q^{8} +2.49414 q^{9} +3.11002 q^{10} +4.64708 q^{11} -2.34396 q^{12} -3.29637 q^{13} +1.16030 q^{14} -7.28976 q^{15} +1.00000 q^{16} +0.266833 q^{17} +2.49414 q^{18} -6.38629 q^{19} +3.11002 q^{20} -2.71970 q^{21} +4.64708 q^{22} +0.998377 q^{23} -2.34396 q^{24} +4.67223 q^{25} -3.29637 q^{26} +1.18571 q^{27} +1.16030 q^{28} +2.35115 q^{29} -7.28976 q^{30} +1.95011 q^{31} +1.00000 q^{32} -10.8926 q^{33} +0.266833 q^{34} +3.60857 q^{35} +2.49414 q^{36} +4.12580 q^{37} -6.38629 q^{38} +7.72655 q^{39} +3.11002 q^{40} +7.34924 q^{41} -2.71970 q^{42} -3.68676 q^{43} +4.64708 q^{44} +7.75684 q^{45} +0.998377 q^{46} +11.0280 q^{47} -2.34396 q^{48} -5.65370 q^{49} +4.67223 q^{50} -0.625445 q^{51} -3.29637 q^{52} -8.39109 q^{53} +1.18571 q^{54} +14.4525 q^{55} +1.16030 q^{56} +14.9692 q^{57} +2.35115 q^{58} -2.88881 q^{59} -7.28976 q^{60} +8.40209 q^{61} +1.95011 q^{62} +2.89396 q^{63} +1.00000 q^{64} -10.2518 q^{65} -10.8926 q^{66} +13.4078 q^{67} +0.266833 q^{68} -2.34015 q^{69} +3.60857 q^{70} +4.94731 q^{71} +2.49414 q^{72} +5.83351 q^{73} +4.12580 q^{74} -10.9515 q^{75} -6.38629 q^{76} +5.39202 q^{77} +7.72655 q^{78} +1.93417 q^{79} +3.11002 q^{80} -10.2617 q^{81} +7.34924 q^{82} +7.29309 q^{83} -2.71970 q^{84} +0.829855 q^{85} -3.68676 q^{86} -5.51101 q^{87} +4.64708 q^{88} -5.02810 q^{89} +7.75684 q^{90} -3.82478 q^{91} +0.998377 q^{92} -4.57099 q^{93} +11.0280 q^{94} -19.8615 q^{95} -2.34396 q^{96} -5.29110 q^{97} -5.65370 q^{98} +11.5905 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 67 q + 67 q^{2} + 21 q^{3} + 67 q^{4} + 21 q^{5} + 21 q^{6} + 38 q^{7} + 67 q^{8} + 90 q^{9}+O(q^{10}) $ 67 * q + 67 * q^2 + 21 * q^3 + 67 * q^4 + 21 * q^5 + 21 * q^6 + 38 * q^7 + 67 * q^8 + 90 * q^9	\( 67 q + 67 q^{2} + 21 q^{3} + 67 q^{4} + 21 q^{5} + 21 q^{6} + 38 q^{7} + 67 q^{8} + 90 q^{9} + 21 q^{10} + 56 q^{11} + 21 q^{12} + 33 q^{13} + 38 q^{14} + 25 q^{15} + 67 q^{16} + 30 q^{17} + 90 q^{18} + 36 q^{19} + 21 q^{20} + 20 q^{21} + 56 q^{22} + 65 q^{23} + 21 q^{24} + 72 q^{25} + 33 q^{26} + 57 q^{27} + 38 q^{28} + 84 q^{29} + 25 q^{30} + 52 q^{31} + 67 q^{32} - 9 q^{33} + 30 q^{34} + 30 q^{35} + 90 q^{36} + 52 q^{37} + 36 q^{38} + 41 q^{39} + 21 q^{40} + 46 q^{41} + 20 q^{42} + 61 q^{43} + 56 q^{44} + 23 q^{45} + 65 q^{46} + 51 q^{47} + 21 q^{48} + 81 q^{49} + 72 q^{50} + 33 q^{51} + 33 q^{52} + 72 q^{53} + 57 q^{54} + 14 q^{55} + 38 q^{56} - 26 q^{57} + 84 q^{58} + 71 q^{59} + 25 q^{60} + 42 q^{61} + 52 q^{62} + 63 q^{63} + 67 q^{64} - 2 q^{65} - 9 q^{66} + 70 q^{67} + 30 q^{68} + 21 q^{69} + 30 q^{70} + 104 q^{71} + 90 q^{72} - 31 q^{73} + 52 q^{74} + 69 q^{75} + 36 q^{76} + 48 q^{77} + 41 q^{78} + 79 q^{79} + 21 q^{80} + 123 q^{81} + 46 q^{82} + 41 q^{83} + 20 q^{84} + 6 q^{85} + 61 q^{86} + 19 q^{87} + 56 q^{88} + 58 q^{89} + 23 q^{90} + 31 q^{91} + 65 q^{92} + 13 q^{93} + 51 q^{94} + 77 q^{95} + 21 q^{96} - 8 q^{97} + 81 q^{98} + 129 q^{99}+O(q^{100}) \) 67 * q + 67 * q^2 + 21 * q^3 + 67 * q^4 + 21 * q^5 + 21 * q^6 + 38 * q^7 + 67 * q^8 + 90 * q^9 + 21 * q^10 + 56 * q^11 + 21 * q^12 + 33 * q^13 + 38 * q^14 + 25 * q^15 + 67 * q^16 + 30 * q^17 + 90 * q^18 + 36 * q^19 + 21 * q^20 + 20 * q^21 + 56 * q^22 + 65 * q^23 + 21 * q^24 + 72 * q^25 + 33 * q^26 + 57 * q^27 + 38 * q^28 + 84 * q^29 + 25 * q^30 + 52 * q^31 + 67 * q^32 - 9 * q^33 + 30 * q^34 + 30 * q^35 + 90 * q^36 + 52 * q^37 + 36 * q^38 + 41 * q^39 + 21 * q^40 + 46 * q^41 + 20 * q^42 + 61 * q^43 + 56 * q^44 + 23 * q^45 + 65 * q^46 + 51 * q^47 + 21 * q^48 + 81 * q^49 + 72 * q^50 + 33 * q^51 + 33 * q^52 + 72 * q^53 + 57 * q^54 + 14 * q^55 + 38 * q^56 - 26 * q^57 + 84 * q^58 + 71 * q^59 + 25 * q^60 + 42 * q^61 + 52 * q^62 + 63 * q^63 + 67 * q^64 - 2 * q^65 - 9 * q^66 + 70 * q^67 + 30 * q^68 + 21 * q^69 + 30 * q^70 + 104 * q^71 + 90 * q^72 - 31 * q^73 + 52 * q^74 + 69 * q^75 + 36 * q^76 + 48 * q^77 + 41 * q^78 + 79 * q^79 + 21 * q^80 + 123 * q^81 + 46 * q^82 + 41 * q^83 + 20 * q^84 + 6 * q^85 + 61 * q^86 + 19 * q^87 + 56 * q^88 + 58 * q^89 + 23 * q^90 + 31 * q^91 + 65 * q^92 + 13 * q^93 + 51 * q^94 + 77 * q^95 + 21 * q^96 - 8 * q^97 + 81 * q^98 + 129 * 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
$3$	−2.34396	−1.35329	−0.676643	−	0.736312i	$-0.736566\pi$
$3$	−2.34396	−1.35329	−0.676643	+	0.736312i	$0.736566\pi$
$4$	1.00000	0.500000
$5$	3.11002	1.39084	0.695422	−	0.718602i	$-0.255218\pi$
$5$	3.11002	1.39084	0.695422	+	0.718602i	$0.255218\pi$
$6$	−2.34396	−0.956917
$7$	1.16030	0.438553	0.219277	−	0.975663i	$-0.429630\pi$
$7$	1.16030	0.438553	0.219277	+	0.975663i	$0.429630\pi$
$8$	1.00000	0.353553
$9$	2.49414	0.831381
$10$	3.11002	0.983475
$11$	4.64708	1.40115	0.700574	−	0.713580i	$-0.252928\pi$
$11$	4.64708	1.40115	0.700574	+	0.713580i	$0.252928\pi$
$12$	−2.34396	−0.676643
$13$	−3.29637	−0.914247	−0.457124	−	0.889403i	$-0.651120\pi$
$13$	−3.29637	−0.914247	−0.457124	+	0.889403i	$0.651120\pi$
$14$	1.16030	0.310104
$15$	−7.28976	−1.88221
$16$	1.00000	0.250000
$17$	0.266833	0.0647164	0.0323582	−	0.999476i	$-0.489698\pi$
$17$	0.266833	0.0647164	0.0323582	+	0.999476i	$0.489698\pi$
$18$	2.49414	0.587875
$19$	−6.38629	−1.46512	−0.732558	−	0.680705i	$-0.761674\pi$
$19$	−6.38629	−1.46512	−0.732558	+	0.680705i	$0.761674\pi$
$20$	3.11002	0.695422
$21$	−2.71970	−0.593488
$22$	4.64708	0.990761
$23$	0.998377	0.208176	0.104088	−	0.994568i	$-0.466808\pi$
$23$	0.998377	0.208176	0.104088	+	0.994568i	$0.466808\pi$
$24$	−2.34396	−0.478459
$25$	4.67223	0.934446
$26$	−3.29637	−0.646471
$27$	1.18571	0.228190
$28$	1.16030	0.219277
$29$	2.35115	0.436598	0.218299	−	0.975882i	$-0.429949\pi$
$29$	2.35115	0.436598	0.218299	+	0.975882i	$0.429949\pi$
$30$	−7.28976	−1.33092
$31$	1.95011	0.350251	0.175125	−	0.984546i	$-0.443967\pi$
$31$	1.95011	0.350251	0.175125	+	0.984546i	$0.443967\pi$
$32$	1.00000	0.176777
$33$	−10.8926	−1.89615
$34$	0.266833	0.0457614
$35$	3.60857	0.609959
$36$	2.49414	0.415690
$37$	4.12580	0.678278	0.339139	−	0.940736i	$-0.389864\pi$
$37$	4.12580	0.678278	0.339139	+	0.940736i	$0.389864\pi$
$38$	−6.38629	−1.03599
$39$	7.72655	1.23724
$40$	3.11002	0.491738
$41$	7.34924	1.14776	0.573879	−	0.818940i	$-0.305438\pi$
$41$	7.34924	1.14776	0.573879	+	0.818940i	$0.305438\pi$
$42$	−2.71970	−0.419659
$43$	−3.68676	−0.562225	−0.281113	−	0.959675i	$-0.590703\pi$
$43$	−3.68676	−0.562225	−0.281113	+	0.959675i	$0.590703\pi$
$44$	4.64708	0.700574
$45$	7.75684	1.15632
$46$	0.998377	0.147203
$47$	11.0280	1.60860	0.804299	−	0.594225i	$-0.202541\pi$
$47$	11.0280	1.60860	0.804299	+	0.594225i	$0.202541\pi$
$48$	−2.34396	−0.338321
$49$	−5.65370	−0.807671
$50$	4.67223	0.660753
$51$	−0.625445	−0.0875798
$52$	−3.29637	−0.457124
$53$	−8.39109	−1.15260	−0.576302	−	0.817237i	$-0.695505\pi$
$53$	−8.39109	−1.15260	−0.576302	+	0.817237i	$0.695505\pi$
$54$	1.18571	0.161354
$55$	14.4525	1.94878
$56$	1.16030	0.155052
$57$	14.9692	1.98272
$58$	2.35115	0.308722
$59$	−2.88881	−0.376091	−0.188045	−	0.982160i	$-0.560215\pi$
$59$	−2.88881	−0.376091	−0.188045	+	0.982160i	$0.560215\pi$
$60$	−7.28976	−0.941104
$61$	8.40209	1.07578	0.537889	−	0.843016i	$-0.319222\pi$
$61$	8.40209	1.07578	0.537889	+	0.843016i	$0.319222\pi$
$62$	1.95011	0.247665
$63$	2.89396	0.364605
$64$	1.00000	0.125000
$65$	−10.2518	−1.27158
$66$	−10.8926	−1.34078
$67$	13.4078	1.63802	0.819009	−	0.573780i	$-0.194524\pi$
$67$	13.4078	1.63802	0.819009	+	0.573780i	$0.194524\pi$
$68$	0.266833	0.0323582
$69$	−2.34015	−0.281721
$70$	3.60857	0.431306
$71$	4.94731	0.587138	0.293569	−	0.955938i	$-0.405157\pi$
$71$	4.94731	0.587138	0.293569	+	0.955938i	$0.405157\pi$
$72$	2.49414	0.293938
$73$	5.83351	0.682761	0.341381	−	0.939925i	$-0.389106\pi$
$73$	5.83351	0.682761	0.341381	+	0.939925i	$0.389106\pi$
$74$	4.12580	0.479615
$75$	−10.9515	−1.26457
$76$	−6.38629	−0.732558
$77$	5.39202	0.614478
$78$	7.72655	0.874859
$79$	1.93417	0.217611	0.108806	−	0.994063i	$-0.465297\pi$
$79$	1.93417	0.217611	0.108806	+	0.994063i	$0.465297\pi$
$80$	3.11002	0.347711
$81$	−10.2617	−1.14019
$82$	7.34924	0.811588
$83$	7.29309	0.800521	0.400260	−	0.916401i	$-0.368920\pi$
$83$	7.29309	0.800521	0.400260	+	0.916401i	$0.368920\pi$
$84$	−2.71970	−0.296744
$85$	0.829855	0.0900104
$86$	−3.68676	−0.397553
$87$	−5.51101	−0.590842
$88$	4.64708	0.495380
$89$	−5.02810	−0.532977	−0.266489	−	0.963838i	$-0.585863\pi$
$89$	−5.02810	−0.532977	−0.266489	+	0.963838i	$0.585863\pi$
$90$	7.75684	0.817642
$91$	−3.82478	−0.400946
$92$	0.998377	0.104088
$93$	−4.57099	−0.473989
$94$	11.0280	1.13745
$95$	−19.8615	−2.03775
$96$	−2.34396	−0.239229
$97$	−5.29110	−0.537230	−0.268615	−	0.963248i	$-0.586566\pi$
$97$	−5.29110	−0.537230	−0.268615	+	0.963248i	$0.586566\pi$
$98$	−5.65370	−0.571110
$99$	11.5905	1.16489
$100$	4.67223	0.467223
$101$	1.75730	0.174858	0.0874290	−	0.996171i	$-0.472135\pi$
$101$	1.75730	0.174858	0.0874290	+	0.996171i	$0.472135\pi$
$102$	−0.625445	−0.0619282
$103$	−1.85944	−0.183216	−0.0916082	−	0.995795i	$-0.529201\pi$
$103$	−1.85944	−0.183216	−0.0916082	+	0.995795i	$0.529201\pi$
$104$	−3.29637	−0.323235
$105$	−8.45833	−0.825449
$106$	−8.39109	−0.815014
$107$	10.2148	0.987507	0.493753	−	0.869602i	$-0.335625\pi$
$107$	10.2148	0.987507	0.493753	+	0.869602i	$0.335625\pi$
$108$	1.18571	0.114095
$109$	5.08434	0.486992	0.243496	−	0.969902i	$-0.421706\pi$
$109$	5.08434	0.486992	0.243496	+	0.969902i	$0.421706\pi$
$110$	14.4525	1.37799
$111$	−9.67071	−0.917903
$112$	1.16030	0.109638
$113$	−3.88702	−0.365660	−0.182830	−	0.983145i	$-0.558526\pi$
$113$	−3.88702	−0.365660	−0.182830	+	0.983145i	$0.558526\pi$
$114$	14.9692	1.40199
$115$	3.10497	0.289540
$116$	2.35115	0.218299
$117$	−8.22161	−0.760088
$118$	−2.88881	−0.265936
$119$	0.309607	0.0283816
$120$	−7.28976	−0.665461
$121$	10.5953	0.963213
$122$	8.40209	0.760689
$123$	−17.2263	−1.55324
$124$	1.95011	0.175125
$125$	−1.01937	−0.0911751
$126$	2.89396	0.257815
$127$	−9.52820	−0.845491	−0.422746	−	0.906248i	$-0.638934\pi$
$127$	−9.52820	−0.845491	−0.422746	+	0.906248i	$0.638934\pi$
$128$	1.00000	0.0883883
$129$	8.64161	0.760851
$130$	−10.2518	−0.899139
$131$	−18.2827	−1.59737	−0.798684	−	0.601751i	$-0.794470\pi$
$131$	−18.2827	−1.59737	−0.798684	+	0.601751i	$0.794470\pi$
$132$	−10.8926	−0.948076
$133$	−7.41004	−0.642532
$134$	13.4078	1.15825
$135$	3.68758	0.317376
$136$	0.266833	0.0228807
$137$	−7.75023	−0.662147	−0.331074	−	0.943605i	$-0.607411\pi$
$137$	−7.75023	−0.662147	−0.331074	+	0.943605i	$0.607411\pi$
$138$	−2.34015	−0.199207
$139$	7.21794	0.612218	0.306109	−	0.951997i	$-0.400973\pi$
$139$	7.21794	0.612218	0.306109	+	0.951997i	$0.400973\pi$
$140$	3.60857	0.304980
$141$	−25.8492	−2.17689
$142$	4.94731	0.415169
$143$	−15.3185	−1.28100
$144$	2.49414	0.207845
$145$	7.31214	0.607240
$146$	5.83351	0.482785
$147$	13.2520	1.09301
$148$	4.12580	0.339139
$149$	8.91558	0.730393	0.365196	−	0.930930i	$-0.381002\pi$
$149$	8.91558	0.730393	0.365196	+	0.930930i	$0.381002\pi$
$150$	−10.9515	−0.894188
$151$	4.41214	0.359055	0.179527	−	0.983753i	$-0.442543\pi$
$151$	4.41214	0.359055	0.179527	+	0.983753i	$0.442543\pi$
$152$	−6.38629	−0.517997
$153$	0.665519	0.0538040
$154$	5.39202	0.434501
$155$	6.06490	0.487144
$156$	7.72655	0.618619
$157$	−1.68585	−0.134546	−0.0672728	−	0.997735i	$-0.521430\pi$
$157$	−1.68585	−0.134546	−0.0672728	+	0.997735i	$0.521430\pi$
$158$	1.93417	0.153875
$159$	19.6684	1.55980
$160$	3.11002	0.245869
$161$	1.15842	0.0912963
$162$	−10.2617	−0.806234
$163$	7.06754	0.553573	0.276786	−	0.960931i	$-0.410731\pi$
$163$	7.06754	0.553573	0.276786	+	0.960931i	$0.410731\pi$
$164$	7.34924	0.573879
$165$	−33.8761	−2.63725
$166$	7.29309	0.566054
$167$	−8.88312	−0.687396	−0.343698	−	0.939080i	$-0.611680\pi$
$167$	−8.88312	−0.687396	−0.343698	+	0.939080i	$0.611680\pi$
$168$	−2.71970	−0.209830
$169$	−2.13397	−0.164152
$170$	0.829855	0.0636470
$171$	−15.9283	−1.21807
$172$	−3.68676	−0.281113
$173$	3.76507	0.286253	0.143127	−	0.989704i	$-0.454284\pi$
$173$	3.76507	0.286253	0.143127	+	0.989704i	$0.454284\pi$
$174$	−5.51101	−0.417789
$175$	5.42120	0.409805
$176$	4.64708	0.350287
$177$	6.77125	0.508958
$178$	−5.02810	−0.376872
$179$	18.5347	1.38535	0.692676	−	0.721249i	$-0.256432\pi$
$179$	18.5347	1.38535	0.692676	+	0.721249i	$0.256432\pi$
$180$	7.75684	0.578160
$181$	−3.19572	−0.237536	−0.118768	−	0.992922i	$-0.537894\pi$
$181$	−3.19572	−0.237536	−0.118768	+	0.992922i	$0.537894\pi$
$182$	−3.82478	−0.283512
$183$	−19.6941	−1.45583
$184$	0.998377	0.0736013
$185$	12.8313	0.943378
$186$	−4.57099	−0.335161
$187$	1.23999	0.0906772
$188$	11.0280	0.804299
$189$	1.37578	0.100073
$190$	−19.8615	−1.44091
$191$	7.41659	0.536646	0.268323	−	0.963329i	$-0.413531\pi$
$191$	7.41659	0.536646	0.268323	+	0.963329i	$0.413531\pi$
$192$	−2.34396	−0.169161
$193$	2.29821	0.165429	0.0827143	−	0.996573i	$-0.473641\pi$
$193$	2.29821	0.165429	0.0827143	+	0.996573i	$0.473641\pi$
$194$	−5.29110	−0.379879
$195$	24.0297	1.72080
$196$	−5.65370	−0.403835
$197$	−15.9774	−1.13834	−0.569171	−	0.822219i	$-0.692736\pi$
$197$	−15.9774	−1.13834	−0.569171	+	0.822219i	$0.692736\pi$
$198$	11.5905	0.823699
$199$	21.7930	1.54487	0.772433	−	0.635096i	$-0.219039\pi$
$199$	21.7930	1.54487	0.772433	+	0.635096i	$0.219039\pi$
$200$	4.67223	0.330377
$201$	−31.4272	−2.21671
$202$	1.75730	0.123643
$203$	2.72805	0.191472
$204$	−0.625445	−0.0437899
$205$	22.8563	1.59635
$206$	−1.85944	−0.129554
$207$	2.49009	0.173074
$208$	−3.29637	−0.228562
$209$	−29.6776	−2.05284
$210$	−8.45833	−0.583680
$211$	25.9924	1.78939	0.894695	−	0.446677i	$-0.147393\pi$
$211$	25.9924	1.78939	0.894695	+	0.446677i	$0.147393\pi$
$212$	−8.39109	−0.576302
$213$	−11.5963	−0.794565
$214$	10.2148	0.698273
$215$	−11.4659	−0.781967
$216$	1.18571	0.0806772
$217$	2.26272	0.153604
$218$	5.08434	0.344355
$219$	−13.6735	−0.923970
$220$	14.4525	0.974388
$221$	−0.879578	−0.0591668
$222$	−9.67071	−0.649056
$223$	15.2207	1.01926	0.509628	−	0.860395i	$-0.329783\pi$
$223$	15.2207	1.01926	0.509628	+	0.860395i	$0.329783\pi$
$224$	1.16030	0.0775260
$225$	11.6532	0.776881
$226$	−3.88702	−0.258561
$227$	1.82157	0.120902	0.0604511	−	0.998171i	$-0.480746\pi$
$227$	1.82157	0.120902	0.0604511	+	0.998171i	$0.480746\pi$
$228$	14.9692	0.991360
$229$	−6.51034	−0.430215	−0.215108	−	0.976590i	$-0.569010\pi$
$229$	−6.51034	−0.430215	−0.215108	+	0.976590i	$0.569010\pi$
$230$	3.10497	0.204736
$231$	−12.6387	−0.831564
$232$	2.35115	0.154361
$233$	−24.7288	−1.62004	−0.810019	−	0.586404i	$-0.800543\pi$
$233$	−24.7288	−1.62004	−0.810019	+	0.586404i	$0.800543\pi$
$234$	−8.22161	−0.537463
$235$	34.2973	2.23731
$236$	−2.88881	−0.188045
$237$	−4.53362	−0.294490
$238$	0.309607	0.0200688
$239$	−21.8821	−1.41544	−0.707718	−	0.706495i	$-0.750275\pi$
$239$	−21.8821	−1.41544	−0.707718	+	0.706495i	$0.750275\pi$
$240$	−7.28976	−0.470552
$241$	13.9303	0.897330	0.448665	−	0.893700i	$-0.351900\pi$
$241$	13.9303	0.897330	0.448665	+	0.893700i	$0.351900\pi$
$242$	10.5953	0.681094
$243$	20.4958	1.31481
$244$	8.40209	0.537889
$245$	−17.5831	−1.12334
$246$	−17.2263	−1.09831
$247$	21.0516	1.33948
$248$	1.95011	0.123832
$249$	−17.0947	−1.08333
$250$	−1.01937	−0.0644705
$251$	−6.41242	−0.404749	−0.202374	−	0.979308i	$-0.564866\pi$
$251$	−6.41242	−0.404749	−0.202374	+	0.979308i	$0.564866\pi$
$252$	2.89396	0.182302
$253$	4.63954	0.291685
$254$	−9.52820	−0.597853
$255$	−1.94515	−0.121810
$256$	1.00000	0.0625000
$257$	20.1300	1.25568	0.627838	−	0.778344i	$-0.283940\pi$
$257$	20.1300	1.25568	0.627838	+	0.778344i	$0.283940\pi$
$258$	8.64161	0.538003
$259$	4.78718	0.297461
$260$	−10.2518	−0.635788
$261$	5.86412	0.362980
$262$	−18.2827	−1.12951
$263$	23.0653	1.42227	0.711133	−	0.703058i	$-0.248182\pi$
$263$	23.0653	1.42227	0.711133	+	0.703058i	$0.248182\pi$
$264$	−10.8926	−0.670391
$265$	−26.0965	−1.60309
$266$	−7.41004	−0.454338
$267$	11.7857	0.721270
$268$	13.4078	0.819009
$269$	23.5435	1.43547	0.717736	−	0.696315i	$-0.245178\pi$
$269$	23.5435	1.43547	0.717736	+	0.696315i	$0.245178\pi$
$270$	3.68758	0.224419
$271$	−19.1767	−1.16490	−0.582451	−	0.812866i	$-0.697906\pi$
$271$	−19.1767	−1.16490	−0.582451	+	0.812866i	$0.697906\pi$
$272$	0.266833	0.0161791
$273$	8.96514	0.542595
$274$	−7.75023	−0.468209
$275$	21.7122	1.30930
$276$	−2.34015	−0.140861
$277$	1.06484	0.0639800	0.0319900	−	0.999488i	$-0.489816\pi$
$277$	1.06484	0.0639800	0.0319900	+	0.999488i	$0.489816\pi$
$278$	7.21794	0.432903
$279$	4.86386	0.291192
$280$	3.60857	0.215653
$281$	4.15354	0.247779	0.123890	−	0.992296i	$-0.460463\pi$
$281$	4.15354	0.247779	0.123890	+	0.992296i	$0.460463\pi$
$282$	−25.8492	−1.53929
$283$	−7.50961	−0.446400	−0.223200	−	0.974773i	$-0.571650\pi$
$283$	−7.50961	−0.446400	−0.223200	+	0.974773i	$0.571650\pi$
$284$	4.94731	0.293569
$285$	46.5545	2.75765
$286$	−15.3185	−0.905800
$287$	8.52734	0.503353
$288$	2.49414	0.146969
$289$	−16.9288	−0.995812
$290$	7.31214	0.429384
$291$	12.4021	0.727025
$292$	5.83351	0.341381
$293$	−30.6688	−1.79169	−0.895846	−	0.444365i	$-0.853429\pi$
$293$	−30.6688	−1.79169	−0.895846	+	0.444365i	$0.853429\pi$
$294$	13.2520	0.772874
$295$	−8.98426	−0.523084
$296$	4.12580	0.239807
$297$	5.51008	0.319727
$298$	8.91558	0.516466
$299$	−3.29102	−0.190324
$300$	−10.9515	−0.632286
$301$	−4.27776	−0.246566
$302$	4.41214	0.253890
$303$	−4.11904	−0.236633
$304$	−6.38629	−0.366279
$305$	26.1307	1.49624
$306$	0.665519	0.0380452
$307$	11.5349	0.658334	0.329167	−	0.944272i	$-0.393232\pi$
$307$	11.5349	0.658334	0.329167	+	0.944272i	$0.393232\pi$
$308$	5.39202	0.307239
$309$	4.35846	0.247944
$310$	6.06490	0.344463
$311$	−29.5703	−1.67678	−0.838389	−	0.545073i	$-0.816502\pi$
$311$	−29.5703	−1.67678	−0.838389	+	0.545073i	$0.816502\pi$
$312$	7.72655	0.437430
$313$	10.6697	0.603089	0.301544	−	0.953452i	$-0.402498\pi$
$313$	10.6697	0.603089	0.301544	+	0.953452i	$0.402498\pi$
$314$	−1.68585	−0.0951382
$315$	9.00028	0.507108
$316$	1.93417	0.108806
$317$	6.98131	0.392110	0.196055	−	0.980593i	$-0.437187\pi$
$317$	6.98131	0.392110	0.196055	+	0.980593i	$0.437187\pi$
$318$	19.6684	1.10295
$319$	10.9260	0.611739
$320$	3.11002	0.173855
$321$	−23.9432	−1.33638
$322$	1.15842	0.0645562
$323$	−1.70407	−0.0948171
$324$	−10.2617	−0.570093
$325$	−15.4014	−0.854315
$326$	7.06754	0.391435
$327$	−11.9175	−0.659039
$328$	7.34924	0.405794
$329$	12.7958	0.705456
$330$	−33.8761	−1.86482
$331$	−4.18750	−0.230166	−0.115083	−	0.993356i	$-0.536713\pi$
$331$	−4.18750	−0.230166	−0.115083	+	0.993356i	$0.536713\pi$
$332$	7.29309	0.400260
$333$	10.2903	0.563907
$334$	−8.88312	−0.486063
$335$	41.6984	2.27823
$336$	−2.71970	−0.148372
$337$	6.87010	0.374238	0.187119	−	0.982337i	$-0.440085\pi$
$337$	6.87010	0.374238	0.187119	+	0.982337i	$0.440085\pi$
$338$	−2.13397	−0.116073
$339$	9.11101	0.494842
$340$	0.829855	0.0450052
$341$	9.06234	0.490753
$342$	−15.9283	−0.861305
$343$	−14.6821	−0.792760
$344$	−3.68676	−0.198777
$345$	−7.27793	−0.391831
$346$	3.76507	0.202412
$347$	−8.64845	−0.464273	−0.232136	−	0.972683i	$-0.574572\pi$
$347$	−8.64845	−0.464273	−0.232136	+	0.972683i	$0.574572\pi$
$348$	−5.51101	−0.295421
$349$	−1.30551	−0.0698824	−0.0349412	−	0.999389i	$-0.511124\pi$
$349$	−1.30551	−0.0698824	−0.0349412	+	0.999389i	$0.511124\pi$
$350$	5.42120	0.289776
$351$	−3.90853	−0.208622
$352$	4.64708	0.247690
$353$	5.70102	0.303435	0.151717	−	0.988424i	$-0.451520\pi$
$353$	5.70102	0.303435	0.151717	+	0.988424i	$0.451520\pi$
$354$	6.77125	0.359888
$355$	15.3863	0.816617
$356$	−5.02810	−0.266489
$357$	−0.725705	−0.0384084
$358$	18.5347	0.979591
$359$	33.2614	1.75547	0.877734	−	0.479148i	$-0.159054\pi$
$359$	33.2614	1.75547	0.877734	+	0.479148i	$0.159054\pi$
$360$	7.75684	0.408821
$361$	21.7847	1.14657
$362$	−3.19572	−0.167963
$363$	−24.8350	−1.30350
$364$	−3.82478	−0.200473
$365$	18.1423	0.949614
$366$	−19.6941	−1.02943
$367$	−5.82537	−0.304082	−0.152041	−	0.988374i	$-0.548585\pi$
$367$	−5.82537	−0.304082	−0.152041	+	0.988374i	$0.548585\pi$
$368$	0.998377	0.0520440
$369$	18.3300	0.954224
$370$	12.8313	0.667069
$371$	−9.73621	−0.505479
$372$	−4.57099	−0.236995
$373$	4.34508	0.224980	0.112490	−	0.993653i	$-0.464117\pi$
$373$	4.34508	0.224980	0.112490	+	0.993653i	$0.464117\pi$
$374$	1.23999	0.0641185
$375$	2.38936	0.123386
$376$	11.0280	0.568725
$377$	−7.75027	−0.399159
$378$	1.37578	0.0707626
$379$	35.9772	1.84802	0.924011	−	0.382365i	$-0.124890\pi$
$379$	35.9772	1.84802	0.924011	+	0.382365i	$0.124890\pi$
$380$	−19.8615	−1.01887
$381$	22.3337	1.14419
$382$	7.41659	0.379466
$383$	7.37619	0.376905	0.188453	−	0.982082i	$-0.439653\pi$
$383$	7.37619	0.376905	0.188453	+	0.982082i	$0.439653\pi$
$384$	−2.34396	−0.119615
$385$	16.7693	0.854643
$386$	2.29821	0.116976
$387$	−9.19530	−0.467423
$388$	−5.29110	−0.268615
$389$	15.5213	0.786959	0.393480	−	0.919333i	$-0.371271\pi$
$389$	15.5213	0.786959	0.393480	+	0.919333i	$0.371271\pi$
$390$	24.0297	1.21679
$391$	0.266400	0.0134724
$392$	−5.65370	−0.285555
$393$	42.8539	2.16169
$394$	−15.9774	−0.804929
$395$	6.01532	0.302664
$396$	11.5905	0.582443
$397$	−37.0377	−1.85887	−0.929434	−	0.368990i	$-0.879704\pi$
$397$	−37.0377	−1.85887	−0.929434	+	0.368990i	$0.879704\pi$
$398$	21.7930	1.09239
$399$	17.3688	0.869529
$400$	4.67223	0.233612
$401$	3.61376	0.180462	0.0902312	−	0.995921i	$-0.471239\pi$
$401$	3.61376	0.180462	0.0902312	+	0.995921i	$0.471239\pi$
$402$	−31.4272	−1.56745
$403$	−6.42829	−0.320216
$404$	1.75730	0.0874290
$405$	−31.9140	−1.58582
$406$	2.72805	0.135391
$407$	19.1729	0.950367
$408$	−0.625445	−0.0309641
$409$	14.0509	0.694771	0.347386	−	0.937722i	$-0.387069\pi$
$409$	14.0509	0.694771	0.347386	+	0.937722i	$0.387069\pi$
$410$	22.8563	1.12879
$411$	18.1662	0.896074
$412$	−1.85944	−0.0916082
$413$	−3.35189	−0.164936
$414$	2.49009	0.122381
$415$	22.6817	1.11340
$416$	−3.29637	−0.161618
$417$	−16.9186	−0.828505
$418$	−29.6776	−1.45158
$419$	6.31658	0.308585	0.154293	−	0.988025i	$-0.450690\pi$
$419$	6.31658	0.308585	0.154293	+	0.988025i	$0.450690\pi$
$420$	−8.45833	−0.412724
$421$	40.6194	1.97967	0.989835	−	0.142222i	$-0.0454246\pi$
$421$	40.6194	1.97967	0.989835	+	0.142222i	$0.0454246\pi$
$422$	25.9924	1.26529
$423$	27.5054	1.33736
$424$	−8.39109	−0.407507
$425$	1.24670	0.0604740
$426$	−11.5963	−0.561843
$427$	9.74897	0.471786
$428$	10.2148	0.493753
$429$	35.9059	1.73355
$430$	−11.4659	−0.552934
$431$	36.9823	1.78138	0.890688	−	0.454614i	$-0.150223\pi$
$431$	36.9823	1.78138	0.890688	+	0.454614i	$0.150223\pi$
$432$	1.18571	0.0570474
$433$	−16.0170	−0.769728	−0.384864	−	0.922973i	$-0.625752\pi$
$433$	−16.0170	−0.769728	−0.384864	+	0.922973i	$0.625752\pi$
$434$	2.26272	0.108614
$435$	−17.1394	−0.821769
$436$	5.08434	0.243496
$437$	−6.37593	−0.305002
$438$	−13.6735	−0.653346
$439$	3.10350	0.148122	0.0740610	−	0.997254i	$-0.476404\pi$
$439$	3.10350	0.148122	0.0740610	+	0.997254i	$0.476404\pi$
$440$	14.4525	0.688997
$441$	−14.1011	−0.671482
$442$	−0.879578	−0.0418373
$443$	−25.4901	−1.21107	−0.605535	−	0.795819i	$-0.707041\pi$
$443$	−25.4901	−1.21107	−0.605535	+	0.795819i	$0.707041\pi$
$444$	−9.67071	−0.458952
$445$	−15.6375	−0.741288
$446$	15.2207	0.720723
$447$	−20.8978	−0.988430
$448$	1.16030	0.0548192
$449$	17.4052	0.821404	0.410702	−	0.911770i	$-0.365284\pi$
$449$	17.4052	0.821404	0.410702	+	0.911770i	$0.365284\pi$
$450$	11.6532	0.549338
$451$	34.1525	1.60818
$452$	−3.88702	−0.182830
$453$	−10.3419	−0.485903
$454$	1.82157	0.0854907
$455$	−11.8952	−0.557654
$456$	14.9692	0.700997
$457$	15.0978	0.706245	0.353123	−	0.935577i	$-0.385120\pi$
$457$	15.0978	0.706245	0.353123	+	0.935577i	$0.385120\pi$
$458$	−6.51034	−0.304208
$459$	0.316386	0.0147676
$460$	3.10497	0.144770
$461$	−30.6832	−1.42906	−0.714530	−	0.699604i	$-0.753360\pi$
$461$	−30.6832	−1.42906	−0.714530	+	0.699604i	$0.753360\pi$
$462$	−12.6387	−0.588004
$463$	15.1792	0.705437	0.352719	−	0.935729i	$-0.385257\pi$
$463$	15.1792	0.705437	0.352719	+	0.935729i	$0.385257\pi$
$464$	2.35115	0.109150
$465$	−14.2159	−0.659245
$466$	−24.7288	−1.14554
$467$	21.6933	1.00385	0.501923	−	0.864912i	$-0.332626\pi$
$467$	21.6933	1.00385	0.501923	+	0.864912i	$0.332626\pi$
$468$	−8.22161	−0.380044
$469$	15.5571	0.718359
$470$	34.2973	1.58202
$471$	3.95157	0.182079
$472$	−2.88881	−0.132968
$473$	−17.1327	−0.787760
$474$	−4.53362	−0.208236
$475$	−29.8382	−1.36907
$476$	0.309607	0.0141908
$477$	−20.9286	−0.958253
$478$	−21.8821	−1.00086
$479$	−18.2804	−0.835254	−0.417627	−	0.908619i	$-0.637138\pi$
$479$	−18.2804	−0.835254	−0.417627	+	0.908619i	$0.637138\pi$
$480$	−7.28976	−0.332731
$481$	−13.6002	−0.620114
$482$	13.9303	0.634508
$483$	−2.71529	−0.123550
$484$	10.5953	0.481606
$485$	−16.4554	−0.747203
$486$	20.4958	0.929710
$487$	2.59876	0.117761	0.0588804	−	0.998265i	$-0.481247\pi$
$487$	2.59876	0.117761	0.0588804	+	0.998265i	$0.481247\pi$
$488$	8.40209	0.380345
$489$	−16.5660	−0.749142
$490$	−17.5831	−0.794324
$491$	−6.63906	−0.299617	−0.149808	−	0.988715i	$-0.547866\pi$
$491$	−6.63906	−0.299617	−0.149808	+	0.988715i	$0.547866\pi$
$492$	−17.2263	−0.776622
$493$	0.627365	0.0282551
$494$	21.0516	0.947154
$495$	36.0466	1.62018
$496$	1.95011	0.0875627
$497$	5.74039	0.257491
$498$	−17.0947	−0.766032
$499$	−6.61176	−0.295983	−0.147991	−	0.988989i	$-0.547281\pi$
$499$	−6.61176	−0.295983	−0.147991	+	0.988989i	$0.547281\pi$
$500$	−1.01937	−0.0455876
$501$	20.8217	0.930244
$502$	−6.41242	−0.286200
$503$	−36.5264	−1.62863	−0.814317	−	0.580421i	$-0.802888\pi$
$503$	−36.5264	−1.62863	−0.814317	+	0.580421i	$0.802888\pi$
$504$	2.89396	0.128907
$505$	5.46524	0.243200
$506$	4.63954	0.206253
$507$	5.00194	0.222144
$508$	−9.52820	−0.422746
$509$	−42.1383	−1.86775	−0.933873	−	0.357606i	$-0.883593\pi$
$509$	−42.1383	−1.86775	−0.933873	+	0.357606i	$0.883593\pi$
$510$	−1.94515	−0.0861325
$511$	6.76864	0.299427
$512$	1.00000	0.0441942
$513$	−7.57228	−0.334324
$514$	20.1300	0.887897
$515$	−5.78291	−0.254825
$516$	8.64161	0.380425
$517$	51.2479	2.25388
$518$	4.78718	0.210337
$519$	−8.82517	−0.387382
$520$	−10.2518	−0.449570
$521$	2.01251	0.0881696	0.0440848	−	0.999028i	$-0.485963\pi$
$521$	2.01251	0.0881696	0.0440848	+	0.999028i	$0.485963\pi$
$522$	5.86412	0.256665
$523$	−28.9307	−1.26505	−0.632527	−	0.774539i	$-0.717982\pi$
$523$	−28.9307	−1.26505	−0.632527	+	0.774539i	$0.717982\pi$
$524$	−18.2827	−0.798684
$525$	−12.7071	−0.554582
$526$	23.0653	1.00569
$527$	0.520354	0.0226670
$528$	−10.8926	−0.474038
$529$	−22.0032	−0.956663
$530$	−26.0965	−1.13356
$531$	−7.20510	−0.312675
$532$	−7.41004	−0.321266
$533$	−24.2258	−1.04933
$534$	11.7857	0.510015
$535$	31.7684	1.37347
$536$	13.4078	0.579127
$537$	−43.4447	−1.87478
$538$	23.5435	1.01503
$539$	−26.2732	−1.13167
$540$	3.68758	0.158688
$541$	7.59276	0.326438	0.163219	−	0.986590i	$-0.447812\pi$
$541$	7.59276	0.326438	0.163219	+	0.986590i	$0.447812\pi$
$542$	−19.1767	−0.823710
$543$	7.49063	0.321454
$544$	0.266833	0.0114404
$545$	15.8124	0.677329
$546$	8.96514	0.383672
$547$	20.2211	0.864593	0.432297	−	0.901732i	$-0.357703\pi$
$547$	20.2211	0.864593	0.432297	+	0.901732i	$0.357703\pi$
$548$	−7.75023	−0.331074
$549$	20.9560	0.894381
$550$	21.7122	0.925812
$551$	−15.0152	−0.639667
$552$	−2.34015	−0.0996036
$553$	2.24423	0.0954342
$554$	1.06484	0.0452407
$555$	−30.0761	−1.27666
$556$	7.21794	0.306109
$557$	26.6710	1.13009	0.565043	−	0.825062i	$-0.308860\pi$
$557$	26.6710	1.13009	0.565043	+	0.825062i	$0.308860\pi$
$558$	4.86386	0.205904
$559$	12.1529	0.514013
$560$	3.60857	0.152490
$561$	−2.90649	−0.122712
$562$	4.15354	0.175206
$563$	10.7781	0.454241	0.227120	−	0.973867i	$-0.427069\pi$
$563$	10.7781	0.454241	0.227120	+	0.973867i	$0.427069\pi$
$564$	−25.8492	−1.08845
$565$	−12.0887	−0.508576
$566$	−7.50961	−0.315652
$567$	−11.9067	−0.500033
$568$	4.94731	0.207585
$569$	17.7195	0.742842	0.371421	−	0.928465i	$-0.378871\pi$
$569$	17.7195	0.742842	0.371421	+	0.928465i	$0.378871\pi$
$570$	46.5545	1.94996
$571$	22.7092	0.950352	0.475176	−	0.879891i	$-0.342384\pi$
$571$	22.7092	0.950352	0.475176	+	0.879891i	$0.342384\pi$
$572$	−15.3185	−0.640498
$573$	−17.3842	−0.726235
$574$	8.52734	0.355924
$575$	4.66465	0.194529
$576$	2.49414	0.103923
$577$	−12.3609	−0.514589	−0.257294	−	0.966333i	$-0.582831\pi$
$577$	−12.3609	−0.514589	−0.257294	+	0.966333i	$0.582831\pi$
$578$	−16.9288	−0.704145
$579$	−5.38691	−0.223872
$580$	7.31214	0.303620
$581$	8.46220	0.351071
$582$	12.4021	0.514085
$583$	−38.9940	−1.61497
$584$	5.83351	0.241392
$585$	−25.5694	−1.05716
$586$	−30.6688	−1.26692
$587$	−14.4829	−0.597775	−0.298887	−	0.954288i	$-0.596616\pi$
$587$	−14.4829	−0.597775	−0.298887	+	0.954288i	$0.596616\pi$
$588$	13.2520	0.546505
$589$	−12.4540	−0.513158
$590$	−8.98426	−0.369876
$591$	37.4503	1.54050
$592$	4.12580	0.169569
$593$	−18.9189	−0.776908	−0.388454	−	0.921468i	$-0.626991\pi$
$593$	−18.9189	−0.776908	−0.388454	+	0.921468i	$0.626991\pi$
$594$	5.51008	0.226081
$595$	0.962884	0.0394744
$596$	8.91558	0.365196
$597$	−51.0820	−2.09065
$598$	−3.29102	−0.134580
$599$	−28.3675	−1.15906	−0.579531	−	0.814950i	$-0.696764\pi$
$599$	−28.3675	−1.15906	−0.579531	+	0.814950i	$0.696764\pi$
$600$	−10.9515	−0.447094
$601$	−37.5989	−1.53369	−0.766845	−	0.641832i	$-0.778175\pi$
$601$	−37.5989	−1.53369	−0.766845	+	0.641832i	$0.778175\pi$
$602$	−4.27776	−0.174348
$603$	33.4409	1.36182
$604$	4.41214	0.179527
$605$	32.9517	1.33968
$606$	−4.11904	−0.167325
$607$	−24.1999	−0.982245	−0.491122	−	0.871091i	$-0.663413\pi$
$607$	−24.1999	−0.982245	−0.491122	+	0.871091i	$0.663413\pi$
$608$	−6.38629	−0.258998
$609$	−6.39444	−0.259116
$610$	26.1307	1.05800
$611$	−36.3523	−1.47066
$612$	0.665519	0.0269020
$613$	−22.6825	−0.916139	−0.458069	−	0.888916i	$-0.651459\pi$
$613$	−22.6825	−0.916139	−0.458069	+	0.888916i	$0.651459\pi$
$614$	11.5349	0.465512
$615$	−53.5742	−2.16032
$616$	5.39202	0.217251
$617$	−18.1593	−0.731064	−0.365532	−	0.930799i	$-0.619113\pi$
$617$	−18.1593	−0.731064	−0.365532	+	0.930799i	$0.619113\pi$
$618$	4.35846	0.175323
$619$	−4.68300	−0.188226	−0.0941128	−	0.995562i	$-0.530001\pi$
$619$	−4.68300	−0.188226	−0.0941128	+	0.995562i	$0.530001\pi$
$620$	6.06490	0.243572
$621$	1.18378	0.0475036
$622$	−29.5703	−1.18566
$623$	−5.83412	−0.233739
$624$	7.72655	0.309309
$625$	−26.5314	−1.06126
$626$	10.6697	0.426448
$627$	69.5631	2.77808
$628$	−1.68585	−0.0672728
$629$	1.10090	0.0438957
$630$	9.00028	0.358580
$631$	28.8700	1.14930	0.574649	−	0.818400i	$-0.305139\pi$
$631$	28.8700	1.14930	0.574649	+	0.818400i	$0.305139\pi$
$632$	1.93417	0.0769373
$633$	−60.9251	−2.42156
$634$	6.98131	0.277263
$635$	−29.6329	−1.17595
$636$	19.6684	0.779901
$637$	18.6367	0.738411
$638$	10.9260	0.432565
$639$	12.3393	0.488136
$640$	3.11002	0.122934
$641$	8.44533	0.333570	0.166785	−	0.985993i	$-0.446661\pi$
$641$	8.44533	0.333570	0.166785	+	0.985993i	$0.446661\pi$
$642$	−23.9432	−0.944962
$643$	−7.47870	−0.294931	−0.147466	−	0.989067i	$-0.547112\pi$
$643$	−7.47870	−0.294931	−0.147466	+	0.989067i	$0.547112\pi$
$644$	1.15842	0.0456481
$645$	26.8756	1.05822
$646$	−1.70407	−0.0670458
$647$	−44.1539	−1.73587	−0.867935	−	0.496679i	$-0.834553\pi$
$647$	−44.1539	−1.73587	−0.867935	+	0.496679i	$0.834553\pi$
$648$	−10.2617	−0.403117
$649$	−13.4245	−0.526959
$650$	−15.4014	−0.604092
$651$	−5.30373	−0.207870
$652$	7.06754	0.276786
$653$	4.96116	0.194145	0.0970726	−	0.995277i	$-0.469052\pi$
$653$	4.96116	0.194145	0.0970726	+	0.995277i	$0.469052\pi$
$654$	−11.9175	−0.466011
$655$	−56.8596	−2.22169
$656$	7.34924	0.286940
$657$	14.5496	0.567635
$658$	12.7958	0.498833
$659$	−2.17217	−0.0846156	−0.0423078	−	0.999105i	$-0.513471\pi$
$659$	−2.17217	−0.0846156	−0.0423078	+	0.999105i	$0.513471\pi$
$660$	−33.8761	−1.31863
$661$	13.8132	0.537270	0.268635	−	0.963242i	$-0.413427\pi$
$661$	13.8132	0.537270	0.268635	+	0.963242i	$0.413427\pi$
$662$	−4.18750	−0.162752
$663$	2.06169	0.0800696
$664$	7.29309	0.283027
$665$	−23.0454	−0.893661
$666$	10.2903	0.398743
$667$	2.34734	0.0908893
$668$	−8.88312	−0.343698
$669$	−35.6768	−1.37934
$670$	41.6984	1.61095
$671$	39.0452	1.50732
$672$	−2.71970	−0.104915
$673$	−37.7729	−1.45604	−0.728020	−	0.685556i	$-0.759559\pi$
$673$	−37.7729	−1.45604	−0.728020	+	0.685556i	$0.759559\pi$
$674$	6.87010	0.264626
$675$	5.53990	0.213231
$676$	−2.13397	−0.0820758
$677$	−12.1194	−0.465786	−0.232893	−	0.972502i	$-0.574819\pi$
$677$	−12.1194	−0.465786	−0.232893	+	0.972502i	$0.574819\pi$
$678$	9.11101	0.349906
$679$	−6.13928	−0.235604
$680$	0.829855	0.0318235
$681$	−4.26970	−0.163615
$682$	9.06234	0.347015
$683$	−49.6544	−1.89997	−0.949986	−	0.312292i	$-0.898903\pi$
$683$	−49.6544	−1.89997	−0.949986	+	0.312292i	$0.898903\pi$
$684$	−15.9283	−0.609035
$685$	−24.1034	−0.920943
$686$	−14.6821	−0.560566
$687$	15.2600	0.582204
$688$	−3.68676	−0.140556
$689$	27.6601	1.05377
$690$	−7.27793	−0.277066
$691$	22.4622	0.854500	0.427250	−	0.904133i	$-0.359482\pi$
$691$	22.4622	0.854500	0.427250	+	0.904133i	$0.359482\pi$
$692$	3.76507	0.143127
$693$	13.4485	0.510865
$694$	−8.64845	−0.328291
$695$	22.4479	0.851499
$696$	−5.51101	−0.208894
$697$	1.96102	0.0742788
$698$	−1.30551	−0.0494143
$699$	57.9633	2.19237
$700$	5.42120	0.204902
$701$	30.7859	1.16277	0.581383	−	0.813630i	$-0.302512\pi$
$701$	30.7859	1.16277	0.581383	+	0.813630i	$0.302512\pi$
$702$	−3.90853	−0.147518
$703$	−26.3486	−0.993755
$704$	4.64708	0.175143
$705$	−80.3914	−3.02772
$706$	5.70102	0.214561
$707$	2.03900	0.0766846
$708$	6.77125	0.254479
$709$	30.2830	1.13730	0.568650	−	0.822579i	$-0.307466\pi$
$709$	30.2830	1.13730	0.568650	+	0.822579i	$0.307466\pi$
$710$	15.3863	0.577436
$711$	4.82410	0.180918
$712$	−5.02810	−0.188436
$713$	1.94695	0.0729138
$714$	−0.725705	−0.0271588
$715$	−47.6408	−1.78166
$716$	18.5347	0.692676
$717$	51.2907	1.91549
$718$	33.2614	1.24130
$719$	38.6239	1.44043	0.720214	−	0.693752i	$-0.244044\pi$
$719$	38.6239	1.44043	0.720214	+	0.693752i	$0.244044\pi$
$720$	7.75684	0.289080
$721$	−2.15752	−0.0803502
$722$	21.7847	0.810744
$723$	−32.6521	−1.21434
$724$	−3.19572	−0.118768
$725$	10.9851	0.407978
$726$	−24.8350	−0.921715
$727$	31.3640	1.16323	0.581614	−	0.813465i	$-0.302422\pi$
$727$	31.3640	1.16323	0.581614	+	0.813465i	$0.302422\pi$
$728$	−3.82478	−0.141756
$729$	−17.2563	−0.639124
$730$	18.1423	0.671478
$731$	−0.983747	−0.0363852
$732$	−19.6941	−0.727917
$733$	3.24123	0.119718	0.0598588	−	0.998207i	$-0.480935\pi$
$733$	3.24123	0.119718	0.0598588	+	0.998207i	$0.480935\pi$
$734$	−5.82537	−0.215018
$735$	41.2141	1.52020
$736$	0.998377	0.0368007
$737$	62.3069	2.29510
$738$	18.3300	0.674738
$739$	−17.5661	−0.646180	−0.323090	−	0.946368i	$-0.604722\pi$
$739$	−17.5661	−0.646180	−0.323090	+	0.946368i	$0.604722\pi$
$740$	12.8313	0.471689
$741$	−49.3440	−1.81270
$742$	−9.73621	−0.357427
$743$	30.6958	1.12612	0.563060	−	0.826416i	$-0.309624\pi$
$743$	30.6958	1.12612	0.563060	+	0.826416i	$0.309624\pi$
$744$	−4.57099	−0.167581
$745$	27.7276	1.01586
$746$	4.34508	0.159085
$747$	18.1900	0.665538
$748$	1.23999	0.0453386
$749$	11.8523	0.433074
$750$	2.38936	0.0872470
$751$	−15.4091	−0.562287	−0.281144	−	0.959666i	$-0.590714\pi$
$751$	−15.4091	−0.562287	−0.281144	+	0.959666i	$0.590714\pi$
$752$	11.0280	0.402149
$753$	15.0305	0.547740
$754$	−7.75027	−0.282248
$755$	13.7218	0.499389
$756$	1.37578	0.0500367
$757$	−47.3866	−1.72230	−0.861148	−	0.508354i	$-0.830254\pi$
$757$	−47.3866	−1.72230	−0.861148	+	0.508354i	$0.830254\pi$
$758$	35.9772	1.30675
$759$	−10.8749	−0.394733
$760$	−19.8615	−0.720453
$761$	−13.8086	−0.500563	−0.250281	−	0.968173i	$-0.580523\pi$
$761$	−13.8086	−0.500563	−0.250281	+	0.968173i	$0.580523\pi$
$762$	22.3337	0.809065
$763$	5.89938	0.213572
$764$	7.41659	0.268323
$765$	2.06978	0.0748329
$766$	7.37619	0.266512
$767$	9.52257	0.343840
$768$	−2.34396	−0.0845803
$769$	−28.2895	−1.02014	−0.510072	−	0.860132i	$-0.670381\pi$
$769$	−28.2895	−1.02014	−0.510072	+	0.860132i	$0.670381\pi$
$770$	16.7693	0.604324
$771$	−47.1839	−1.69929
$772$	2.29821	0.0827143
$773$	−43.0099	−1.54696	−0.773479	−	0.633821i	$-0.781485\pi$
$773$	−43.0099	−1.54696	−0.773479	+	0.633821i	$0.781485\pi$
$774$	−9.19530	−0.330518
$775$	9.11139	0.327291
$776$	−5.29110	−0.189939
$777$	−11.2210	−0.402550
$778$	15.5213	0.556464
$779$	−46.9344	−1.68160
$780$	24.0297	0.860402
$781$	22.9906	0.822667
$782$	0.266400	0.00952643
$783$	2.78778	0.0996273
$784$	−5.65370	−0.201918
$785$	−5.24304	−0.187132
$786$	42.8539	1.52855
$787$	18.5997	0.663009	0.331505	−	0.943454i	$-0.392444\pi$
$787$	18.5997	0.663009	0.331505	+	0.943454i	$0.392444\pi$
$788$	−15.9774	−0.569171
$789$	−54.0640	−1.92473
$790$	6.01532	0.214015
$791$	−4.51012	−0.160361
$792$	11.5905	0.411850
$793$	−27.6964	−0.983527
$794$	−37.0377	−1.31442
$795$	61.1690	2.16944
$796$	21.7930	0.772433
$797$	10.3733	0.367440	0.183720	−	0.982979i	$-0.441186\pi$
$797$	10.3733	0.367440	0.183720	+	0.982979i	$0.441186\pi$
$798$	17.3688	0.614850
$799$	2.94263	0.104103
$800$	4.67223	0.165188
$801$	−12.5408	−0.443107
$802$	3.61376	0.127606
$803$	27.1088	0.956649
$804$	−31.4272	−1.10835
$805$	3.60271	0.126979
$806$	−6.42829	−0.226427
$807$	−55.1850	−1.94260
$808$	1.75730	0.0618216
$809$	−4.04781	−0.142313	−0.0711567	−	0.997465i	$-0.522669\pi$
$809$	−4.04781	−0.142313	−0.0711567	+	0.997465i	$0.522669\pi$
$810$	−31.9140	−1.12135
$811$	−17.6489	−0.619735	−0.309868	−	0.950780i	$-0.600285\pi$
$811$	−17.6489	−0.619735	−0.309868	+	0.950780i	$0.600285\pi$
$812$	2.72805	0.0957359
$813$	44.9494	1.57645
$814$	19.1729	0.672011
$815$	21.9802	0.769933
$816$	−0.625445	−0.0218949
$817$	23.5447	0.823725
$818$	14.0509	0.491277
$819$	−9.53956	−0.333339
$820$	22.8563	0.798176
$821$	51.8726	1.81036	0.905182	−	0.425024i	$-0.139734\pi$
$821$	51.8726	1.81036	0.905182	+	0.425024i	$0.139734\pi$
$822$	18.1662	0.633620
$823$	−42.7198	−1.48912	−0.744559	−	0.667557i	$-0.767340\pi$
$823$	−42.7198	−1.48912	−0.744559	+	0.667557i	$0.767340\pi$
$824$	−1.85944	−0.0647768
$825$	−50.8926	−1.77185
$826$	−3.35189	−0.116627
$827$	4.58896	0.159574	0.0797869	−	0.996812i	$-0.474576\pi$
$827$	4.58896	0.159574	0.0797869	+	0.996812i	$0.474576\pi$
$828$	2.49009	0.0865368
$829$	−12.2403	−0.425124	−0.212562	−	0.977148i	$-0.568181\pi$
$829$	−12.2403	−0.425124	−0.212562	+	0.977148i	$0.568181\pi$
$830$	22.6817	0.787292
$831$	−2.49594	−0.0865831
$832$	−3.29637	−0.114281
$833$	−1.50859	−0.0522696
$834$	−16.9186	−0.585842
$835$	−27.6267	−0.956061
$836$	−29.6776	−1.02642
$837$	2.31227	0.0799237
$838$	6.31658	0.218203
$839$	−29.0158	−1.00174	−0.500868	−	0.865524i	$-0.666986\pi$
$839$	−29.0158	−1.00174	−0.500868	+	0.865524i	$0.666986\pi$
$840$	−8.45833	−0.291840
$841$	−23.4721	−0.809382
$842$	40.6194	1.39984
$843$	−9.73572	−0.335316
$844$	25.9924	0.894695
$845$	−6.63670	−0.228309
$846$	27.5054	0.945654
$847$	12.2938	0.422420
$848$	−8.39109	−0.288151
$849$	17.6022	0.604106
$850$	1.24670	0.0427616
$851$	4.11911	0.141201
$852$	−11.5963	−0.397283
$853$	13.0151	0.445627	0.222814	−	0.974861i	$-0.428476\pi$
$853$	13.0151	0.445627	0.222814	+	0.974861i	$0.428476\pi$
$854$	9.74897	0.333603
$855$	−49.5374	−1.69414
$856$	10.2148	0.349136
$857$	−46.2493	−1.57984	−0.789922	−	0.613207i	$-0.789879\pi$
$857$	−46.2493	−1.57984	−0.789922	+	0.613207i	$0.789879\pi$
$858$	35.9059	1.22581
$859$	−23.4266	−0.799305	−0.399652	−	0.916667i	$-0.630869\pi$
$859$	−23.4266	−0.799305	−0.399652	+	0.916667i	$0.630869\pi$
$860$	−11.4659	−0.390984
$861$	−19.9877	−0.681180
$862$	36.9823	1.25962
$863$	51.6889	1.75951	0.879755	−	0.475427i	$-0.157707\pi$
$863$	51.6889	1.75951	0.879755	+	0.475427i	$0.157707\pi$
$864$	1.18571	0.0403386
$865$	11.7095	0.398133
$866$	−16.0170	−0.544280
$867$	39.6804	1.34762
$868$	2.26272	0.0768019
$869$	8.98825	0.304906
$870$	−17.1394	−0.581079
$871$	−44.1969	−1.49755
$872$	5.08434	0.172178
$873$	−13.1968	−0.446643
$874$	−6.37593	−0.215669
$875$	−1.18278	−0.0399852
$876$	−13.6735	−0.461985
$877$	−46.4747	−1.56934	−0.784670	−	0.619914i	$-0.787167\pi$
$877$	−46.4747	−1.56934	−0.784670	+	0.619914i	$0.787167\pi$
$878$	3.10350	0.104738
$879$	71.8865	2.42467
$880$	14.4525	0.487194
$881$	21.0971	0.710780	0.355390	−	0.934718i	$-0.384348\pi$
$881$	21.0971	0.710780	0.355390	+	0.934718i	$0.384348\pi$
$882$	−14.1011	−0.474810
$883$	28.5995	0.962451	0.481226	−	0.876597i	$-0.340192\pi$
$883$	28.5995	0.962451	0.481226	+	0.876597i	$0.340192\pi$
$884$	−0.879578	−0.0295834
$885$	21.0587	0.707881
$886$	−25.4901	−0.856355
$887$	11.7317	0.393912	0.196956	−	0.980412i	$-0.436894\pi$
$887$	11.7317	0.393912	0.196956	+	0.980412i	$0.436894\pi$
$888$	−9.67071	−0.324528
$889$	−11.0556	−0.370793
$890$	−15.6375	−0.524170
$891$	−47.6868	−1.59757
$892$	15.2207	0.509628
$893$	−70.4280	−2.35678
$894$	−20.8978	−0.698925
$895$	57.6434	1.92681
$896$	1.16030	0.0387630
$897$	7.71401	0.257563
$898$	17.4052	0.580820
$899$	4.58502	0.152919
$900$	11.6532	0.388440
$901$	−2.23902	−0.0745924
$902$	34.1525	1.13715
$903$	10.0269	0.333674
$904$	−3.88702	−0.129280
$905$	−9.93875	−0.330375
$906$	−10.3419	−0.343586
$907$	−17.7966	−0.590927	−0.295464	−	0.955354i	$-0.595474\pi$
$907$	−17.7966	−0.590927	−0.295464	+	0.955354i	$0.595474\pi$
$908$	1.82157	0.0604511
$909$	4.38296	0.145374
$910$	−11.8952	−0.394321
$911$	−10.4426	−0.345979	−0.172989	−	0.984924i	$-0.555343\pi$
$911$	−10.4426	−0.345979	−0.172989	+	0.984924i	$0.555343\pi$
$912$	14.9692	0.495680
$913$	33.8916	1.12165
$914$	15.0978	0.499391
$915$	−61.2492	−2.02484
$916$	−6.51034	−0.215108
$917$	−21.2135	−0.700531
$918$	0.316386	0.0104423
$919$	25.3154	0.835079	0.417540	−	0.908659i	$-0.362892\pi$
$919$	25.3154	0.835079	0.417540	+	0.908659i	$0.362892\pi$
$920$	3.10497	0.102368
$921$	−27.0374	−0.890913
$922$	−30.6832	−1.01050
$923$	−16.3082	−0.536790
$924$	−12.6387	−0.415782
$925$	19.2767	0.633814
$926$	15.1792	0.498820
$927$	−4.63772	−0.152323
$928$	2.35115	0.0771804
$929$	−44.9852	−1.47592	−0.737959	−	0.674846i	$-0.764210\pi$
$929$	−44.9852	−1.47592	−0.737959	+	0.674846i	$0.764210\pi$
$930$	−14.2159	−0.466157
$931$	36.1062	1.18333
$932$	−24.7288	−0.810019
$933$	69.3115	2.26916
$934$	21.6933	0.709827
$935$	3.85640	0.126118
$936$	−8.22161	−0.268732
$937$	39.1468	1.27887	0.639435	−	0.768845i	$-0.279168\pi$
$937$	39.1468	1.27887	0.639435	+	0.768845i	$0.279168\pi$
$938$	15.5571	0.507956
$939$	−25.0094	−0.816151
$940$	34.2973	1.11865
$941$	−51.3013	−1.67237	−0.836187	−	0.548445i	$-0.815220\pi$
$941$	−51.3013	−1.67237	−0.836187	+	0.548445i	$0.815220\pi$
$942$	3.95157	0.128749
$943$	7.33731	0.238936
$944$	−2.88881	−0.0940227
$945$	4.27871	0.139186
$946$	−17.1327	−0.557031
$947$	−26.1964	−0.851269	−0.425635	−	0.904895i	$-0.639949\pi$
$947$	−26.1964	−0.851269	−0.425635	+	0.904895i	$0.639949\pi$
$948$	−4.53362	−0.147245
$949$	−19.2294	−0.624213
$950$	−29.8382	−0.968080
$951$	−16.3639	−0.530636
$952$	0.309607	0.0100344
$953$	23.3911	0.757713	0.378856	−	0.925456i	$-0.376317\pi$
$953$	23.3911	0.757713	0.378856	+	0.925456i	$0.376317\pi$
$954$	−20.9286	−0.677587
$955$	23.0658	0.746390
$956$	−21.8821	−0.707718
$957$	−25.6101	−0.827857
$958$	−18.2804	−0.590614
$959$	−8.99262	−0.290387
$960$	−7.28976	−0.235276
$961$	−27.1971	−0.877324
$962$	−13.6002	−0.438487
$963$	25.4773	0.820994
$964$	13.9303	0.448665
$965$	7.14748	0.230085
$966$	−2.71529	−0.0873630
$967$	−13.2864	−0.427262	−0.213631	−	0.976914i	$-0.568529\pi$
$967$	−13.2864	−0.427262	−0.213631	+	0.976914i	$0.568529\pi$
$968$	10.5953	0.340547
$969$	3.99427	0.128315
$970$	−16.4554	−0.528352
$971$	−38.9810	−1.25096	−0.625480	−	0.780241i	$-0.715097\pi$
$971$	−38.9810	−1.25096	−0.625480	+	0.780241i	$0.715097\pi$
$972$	20.4958	0.657404
$973$	8.37500	0.268490
$974$	2.59876	0.0832695
$975$	36.1002	1.15613
$976$	8.40209	0.268944
$977$	−26.5839	−0.850493	−0.425247	−	0.905077i	$-0.639813\pi$
$977$	−26.5839	−0.850493	−0.425247	+	0.905077i	$0.639813\pi$
$978$	−16.5660	−0.529723
$979$	−23.3660	−0.746779
$980$	−17.5831	−0.561672
$981$	12.6811	0.404876
$982$	−6.63906	−0.211861
$983$	11.5941	0.369794	0.184897	−	0.982758i	$-0.440805\pi$
$983$	11.5941	0.369794	0.184897	+	0.982758i	$0.440805\pi$
$984$	−17.2263	−0.549155
$985$	−49.6900	−1.58326
$986$	0.627365	0.0199794
$987$	−29.9929	−0.954683
$988$	21.0516	0.669739
$989$	−3.68077	−0.117042
$990$	36.0466	1.14564
$991$	39.7107	1.26145	0.630727	−	0.776005i	$-0.282757\pi$
$991$	39.7107	1.26145	0.630727	+	0.776005i	$0.282757\pi$
$992$	1.95011	0.0619162
$993$	9.81532	0.311480
$994$	5.74039	0.182074
$995$	67.7768	2.14867
$996$	−17.0947	−0.541667
$997$	−15.9012	−0.503595	−0.251798	−	0.967780i	$-0.581022\pi$
$997$	−15.9012	−0.503595	−0.251798	+	0.967780i	$0.581022\pi$
$998$	−6.61176	−0.209291
$999$	4.89200	0.154776

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6046.2.a.f.1.11	✓	67

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6046.2.a.f.1.11	✓	67	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:	\( N \)	\(=\)	\( 6046 = 2 \cdot 3023 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6046.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.34396 q^{3} +1.00000 q^{4} +3.11002 q^{5} -2.34396 q^{6} +1.16030 q^{7} +1.00000 q^{8} +2.49414 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.34396 q^{3} +1.00000 q^{4} +3.11002 q^{5} -2.34396 q^{6} +1.16030 q^{7} +1.00000 q^{8} +2.49414 q^{9} +3.11002 q^{10} +4.64708 q^{11} -2.34396 q^{12} -3.29637 q^{13} +1.16030 q^{14} -7.28976 q^{15} +1.00000 q^{16} +0.266833 q^{17} +2.49414 q^{18} -6.38629 q^{19} +3.11002 q^{20} -2.71970 q^{21} +4.64708 q^{22} +0.998377 q^{23} -2.34396 q^{24} +4.67223 q^{25} -3.29637 q^{26} +1.18571 q^{27} +1.16030 q^{28} +2.35115 q^{29} -7.28976 q^{30} +1.95011 q^{31} +1.00000 q^{32} -10.8926 q^{33} +0.266833 q^{34} +3.60857 q^{35} +2.49414 q^{36} +4.12580 q^{37} -6.38629 q^{38} +7.72655 q^{39} +3.11002 q^{40} +7.34924 q^{41} -2.71970 q^{42} -3.68676 q^{43} +4.64708 q^{44} +7.75684 q^{45} +0.998377 q^{46} +11.0280 q^{47} -2.34396 q^{48} -5.65370 q^{49} +4.67223 q^{50} -0.625445 q^{51} -3.29637 q^{52} -8.39109 q^{53} +1.18571 q^{54} +14.4525 q^{55} +1.16030 q^{56} +14.9692 q^{57} +2.35115 q^{58} -2.88881 q^{59} -7.28976 q^{60} +8.40209 q^{61} +1.95011 q^{62} +2.89396 q^{63} +1.00000 q^{64} -10.2518 q^{65} -10.8926 q^{66} +13.4078 q^{67} +0.266833 q^{68} -2.34015 q^{69} +3.60857 q^{70} +4.94731 q^{71} +2.49414 q^{72} +5.83351 q^{73} +4.12580 q^{74} -10.9515 q^{75} -6.38629 q^{76} +5.39202 q^{77} +7.72655 q^{78} +1.93417 q^{79} +3.11002 q^{80} -10.2617 q^{81} +7.34924 q^{82} +7.29309 q^{83} -2.71970 q^{84} +0.829855 q^{85} -3.68676 q^{86} -5.51101 q^{87} +4.64708 q^{88} -5.02810 q^{89} +7.75684 q^{90} -3.82478 q^{91} +0.998377 q^{92} -4.57099 q^{93} +11.0280 q^{94} -19.8615 q^{95} -2.34396 q^{96} -5.29110 q^{97} -5.65370 q^{98} +11.5905 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 67 q + 67 q^{2} + 21 q^{3} + 67 q^{4} + 21 q^{5} + 21 q^{6} + 38 q^{7} + 67 q^{8} + 90 q^{9}+O(q^{10}) \) 67 * q + 67 * q^2 + 21 * q^3 + 67 * q^4 + 21 * q^5 + 21 * q^6 + 38 * q^7 + 67 * q^8 + 90 * q^9	\( 67 q + 67 q^{2} + 21 q^{3} + 67 q^{4} + 21 q^{5} + 21 q^{6} + 38 q^{7} + 67 q^{8} + 90 q^{9} + 21 q^{10} + 56 q^{11} + 21 q^{12} + 33 q^{13} + 38 q^{14} + 25 q^{15} + 67 q^{16} + 30 q^{17} + 90 q^{18} + 36 q^{19} + 21 q^{20} + 20 q^{21} + 56 q^{22} + 65 q^{23} + 21 q^{24} + 72 q^{25} + 33 q^{26} + 57 q^{27} + 38 q^{28} + 84 q^{29} + 25 q^{30} + 52 q^{31} + 67 q^{32} - 9 q^{33} + 30 q^{34} + 30 q^{35} + 90 q^{36} + 52 q^{37} + 36 q^{38} + 41 q^{39} + 21 q^{40} + 46 q^{41} + 20 q^{42} + 61 q^{43} + 56 q^{44} + 23 q^{45} + 65 q^{46} + 51 q^{47} + 21 q^{48} + 81 q^{49} + 72 q^{50} + 33 q^{51} + 33 q^{52} + 72 q^{53} + 57 q^{54} + 14 q^{55} + 38 q^{56} - 26 q^{57} + 84 q^{58} + 71 q^{59} + 25 q^{60} + 42 q^{61} + 52 q^{62} + 63 q^{63} + 67 q^{64} - 2 q^{65} - 9 q^{66} + 70 q^{67} + 30 q^{68} + 21 q^{69} + 30 q^{70} + 104 q^{71} + 90 q^{72} - 31 q^{73} + 52 q^{74} + 69 q^{75} + 36 q^{76} + 48 q^{77} + 41 q^{78} + 79 q^{79} + 21 q^{80} + 123 q^{81} + 46 q^{82} + 41 q^{83} + 20 q^{84} + 6 q^{85} + 61 q^{86} + 19 q^{87} + 56 q^{88} + 58 q^{89} + 23 q^{90} + 31 q^{91} + 65 q^{92} + 13 q^{93} + 51 q^{94} + 77 q^{95} + 21 q^{96} - 8 q^{97} + 81 q^{98} + 129 q^{99}+O(q^{100}) \) 67 * q + 67 * q^2 + 21 * q^3 + 67 * q^4 + 21 * q^5 + 21 * q^6 + 38 * q^7 + 67 * q^8 + 90 * q^9 + 21 * q^10 + 56 * q^11 + 21 * q^12 + 33 * q^13 + 38 * q^14 + 25 * q^15 + 67 * q^16 + 30 * q^17 + 90 * q^18 + 36 * q^19 + 21 * q^20 + 20 * q^21 + 56 * q^22 + 65 * q^23 + 21 * q^24 + 72 * q^25 + 33 * q^26 + 57 * q^27 + 38 * q^28 + 84 * q^29 + 25 * q^30 + 52 * q^31 + 67 * q^32 - 9 * q^33 + 30 * q^34 + 30 * q^35 + 90 * q^36 + 52 * q^37 + 36 * q^38 + 41 * q^39 + 21 * q^40 + 46 * q^41 + 20 * q^42 + 61 * q^43 + 56 * q^44 + 23 * q^45 + 65 * q^46 + 51 * q^47 + 21 * q^48 + 81 * q^49 + 72 * q^50 + 33 * q^51 + 33 * q^52 + 72 * q^53 + 57 * q^54 + 14 * q^55 + 38 * q^56 - 26 * q^57 + 84 * q^58 + 71 * q^59 + 25 * q^60 + 42 * q^61 + 52 * q^62 + 63 * q^63 + 67 * q^64 - 2 * q^65 - 9 * q^66 + 70 * q^67 + 30 * q^68 + 21 * q^69 + 30 * q^70 + 104 * q^71 + 90 * q^72 - 31 * q^73 + 52 * q^74 + 69 * q^75 + 36 * q^76 + 48 * q^77 + 41 * q^78 + 79 * q^79 + 21 * q^80 + 123 * q^81 + 46 * q^82 + 41 * q^83 + 20 * q^84 + 6 * q^85 + 61 * q^86 + 19 * q^87 + 56 * q^88 + 58 * q^89 + 23 * q^90 + 31 * q^91 + 65 * q^92 + 13 * q^93 + 51 * q^94 + 77 * q^95 + 21 * q^96 - 8 * q^97 + 81 * q^98 + 129 * q^99

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