LMFDB - Embedded newform 6001.2.a.c.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6001,2,Mod(1,6001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6001, 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("6001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6001 = 17 \cdot 353 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6001.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:	$47.9182262530$
Analytic rank:	$0$
Dimension:	$121$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	6001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.44940 q^{2} +0.192595 q^{3} +3.99956 q^{4} +1.46027 q^{5} -0.471742 q^{6} -3.96634 q^{7} -4.89773 q^{8} -2.96291 q^{9} +O(q^{10})$	\(q-2.44940 q^{2} +0.192595 q^{3} +3.99956 q^{4} +1.46027 q^{5} -0.471742 q^{6} -3.96634 q^{7} -4.89773 q^{8} -2.96291 q^{9} -3.57679 q^{10} +3.20898 q^{11} +0.770296 q^{12} +5.11663 q^{13} +9.71515 q^{14} +0.281241 q^{15} +3.99737 q^{16} -1.00000 q^{17} +7.25735 q^{18} +3.67372 q^{19} +5.84044 q^{20} -0.763897 q^{21} -7.86007 q^{22} -8.14798 q^{23} -0.943278 q^{24} -2.86761 q^{25} -12.5327 q^{26} -1.14843 q^{27} -15.8636 q^{28} +9.62795 q^{29} -0.688871 q^{30} +8.17471 q^{31} +0.00429093 q^{32} +0.618033 q^{33} +2.44940 q^{34} -5.79192 q^{35} -11.8503 q^{36} -7.45724 q^{37} -8.99840 q^{38} +0.985438 q^{39} -7.15201 q^{40} +8.24516 q^{41} +1.87109 q^{42} +5.68052 q^{43} +12.8345 q^{44} -4.32665 q^{45} +19.9577 q^{46} +9.11914 q^{47} +0.769874 q^{48} +8.73182 q^{49} +7.02392 q^{50} -0.192595 q^{51} +20.4643 q^{52} -12.4719 q^{53} +2.81296 q^{54} +4.68597 q^{55} +19.4260 q^{56} +0.707539 q^{57} -23.5827 q^{58} -6.11265 q^{59} +1.12484 q^{60} +0.888772 q^{61} -20.0231 q^{62} +11.7519 q^{63} -8.00525 q^{64} +7.47167 q^{65} -1.51381 q^{66} -3.67281 q^{67} -3.99956 q^{68} -1.56926 q^{69} +14.1867 q^{70} -9.69117 q^{71} +14.5115 q^{72} -10.2746 q^{73} +18.2658 q^{74} -0.552287 q^{75} +14.6933 q^{76} -12.7279 q^{77} -2.41373 q^{78} +0.518576 q^{79} +5.83724 q^{80} +8.66754 q^{81} -20.1957 q^{82} -7.30712 q^{83} -3.05525 q^{84} -1.46027 q^{85} -13.9139 q^{86} +1.85429 q^{87} -15.7167 q^{88} +15.7459 q^{89} +10.5977 q^{90} -20.2943 q^{91} -32.5884 q^{92} +1.57441 q^{93} -22.3364 q^{94} +5.36462 q^{95} +0.000826413 q^{96} -2.59386 q^{97} -21.3877 q^{98} -9.50790 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 121 q + 9 q^{2} + 13 q^{3} + 127 q^{4} + 21 q^{5} + 19 q^{6} - 13 q^{7} + 24 q^{8} + 134 q^{9}+O(q^{10}) $ 121 * q + 9 * q^2 + 13 * q^3 + 127 * q^4 + 21 * q^5 + 19 * q^6 - 13 * q^7 + 24 * q^8 + 134 * q^9	\( 121 q + 9 q^{2} + 13 q^{3} + 127 q^{4} + 21 q^{5} + 19 q^{6} - 13 q^{7} + 24 q^{8} + 134 q^{9} - q^{10} + 40 q^{11} + 41 q^{12} + 14 q^{13} + 32 q^{14} + 49 q^{15} + 135 q^{16} - 121 q^{17} + 28 q^{18} + 34 q^{19} + 64 q^{20} + 34 q^{21} - 18 q^{22} + 37 q^{23} + 54 q^{24} + 128 q^{25} + 91 q^{26} + 55 q^{27} - 28 q^{28} + 45 q^{29} + 30 q^{30} + 67 q^{31} + 47 q^{32} + 40 q^{33} - 9 q^{34} + 59 q^{35} + 138 q^{36} - 16 q^{37} + 30 q^{38} + 37 q^{39} + 14 q^{40} + 89 q^{41} + 33 q^{42} + 16 q^{43} + 90 q^{44} + 83 q^{45} - 9 q^{46} + 135 q^{47} + 96 q^{48} + 128 q^{49} + 71 q^{50} - 13 q^{51} + 47 q^{52} + 52 q^{53} + 90 q^{54} + 93 q^{55} + 69 q^{56} - 4 q^{57} + 5 q^{58} + 170 q^{59} + 78 q^{60} - 2 q^{61} + 46 q^{62} - 10 q^{63} + 182 q^{64} + 50 q^{65} + 68 q^{66} + 46 q^{67} - 127 q^{68} + 97 q^{69} + 46 q^{70} + 191 q^{71} + 57 q^{72} - 12 q^{73} + 68 q^{74} + 86 q^{75} + 108 q^{76} + 62 q^{77} - 10 q^{78} + 130 q^{80} + 149 q^{81} + 14 q^{82} + 83 q^{83} + 126 q^{84} - 21 q^{85} + 132 q^{86} + 50 q^{87} - 42 q^{88} + 144 q^{89} + 9 q^{90} + 13 q^{91} + 50 q^{92} + 43 q^{93} + 41 q^{94} + 82 q^{95} + 110 q^{96} - 3 q^{97} + 36 q^{98} + 89 q^{99}+O(q^{100}) \) 121 * q + 9 * q^2 + 13 * q^3 + 127 * q^4 + 21 * q^5 + 19 * q^6 - 13 * q^7 + 24 * q^8 + 134 * q^9 - q^10 + 40 * q^11 + 41 * q^12 + 14 * q^13 + 32 * q^14 + 49 * q^15 + 135 * q^16 - 121 * q^17 + 28 * q^18 + 34 * q^19 + 64 * q^20 + 34 * q^21 - 18 * q^22 + 37 * q^23 + 54 * q^24 + 128 * q^25 + 91 * q^26 + 55 * q^27 - 28 * q^28 + 45 * q^29 + 30 * q^30 + 67 * q^31 + 47 * q^32 + 40 * q^33 - 9 * q^34 + 59 * q^35 + 138 * q^36 - 16 * q^37 + 30 * q^38 + 37 * q^39 + 14 * q^40 + 89 * q^41 + 33 * q^42 + 16 * q^43 + 90 * q^44 + 83 * q^45 - 9 * q^46 + 135 * q^47 + 96 * q^48 + 128 * q^49 + 71 * q^50 - 13 * q^51 + 47 * q^52 + 52 * q^53 + 90 * q^54 + 93 * q^55 + 69 * q^56 - 4 * q^57 + 5 * q^58 + 170 * q^59 + 78 * q^60 - 2 * q^61 + 46 * q^62 - 10 * q^63 + 182 * q^64 + 50 * q^65 + 68 * q^66 + 46 * q^67 - 127 * q^68 + 97 * q^69 + 46 * q^70 + 191 * q^71 + 57 * q^72 - 12 * q^73 + 68 * q^74 + 86 * q^75 + 108 * q^76 + 62 * q^77 - 10 * q^78 + 130 * q^80 + 149 * q^81 + 14 * q^82 + 83 * q^83 + 126 * q^84 - 21 * q^85 + 132 * q^86 + 50 * q^87 - 42 * q^88 + 144 * q^89 + 9 * q^90 + 13 * q^91 + 50 * q^92 + 43 * q^93 + 41 * q^94 + 82 * q^95 + 110 * q^96 - 3 * q^97 + 36 * q^98 + 89 * 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 $

$2$	−2.44940	−1.73199	−0.865994	−	0.500055i	$-0.833313\pi$
$2$	−2.44940	−1.73199	−0.865994	+	0.500055i	$0.833313\pi$
$3$	0.192595	0.111195	0.0555974	−	0.998453i	$-0.482294\pi$
$3$	0.192595	0.111195	0.0555974	+	0.998453i	$0.482294\pi$
$4$	3.99956	1.99978
$5$	1.46027	0.653053	0.326526	−	0.945188i	$-0.394122\pi$
$5$	1.46027	0.653053	0.326526	+	0.945188i	$0.394122\pi$
$6$	−0.471742	−0.192588
$7$	−3.96634	−1.49913	−0.749567	−	0.661928i	$-0.769738\pi$
$7$	−3.96634	−1.49913	−0.749567	+	0.661928i	$0.769738\pi$
$8$	−4.89773	−1.73161
$9$	−2.96291	−0.987636
$10$	−3.57679	−1.13108
$11$	3.20898	0.967542	0.483771	−	0.875194i	$-0.339267\pi$
$11$	3.20898	0.967542	0.483771	+	0.875194i	$0.339267\pi$
$12$	0.770296	0.222365
$13$	5.11663	1.41910	0.709550	−	0.704655i	$-0.248898\pi$
$13$	5.11663	1.41910	0.709550	+	0.704655i	$0.248898\pi$
$14$	9.71515	2.59648
$15$	0.281241	0.0726161
$16$	3.99737	0.999343
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	7.25735	1.71057
$19$	3.67372	0.842808	0.421404	−	0.906873i	$-0.361537\pi$
$19$	3.67372	0.842808	0.421404	+	0.906873i	$0.361537\pi$
$20$	5.84044	1.30596
$21$	−0.763897	−0.166696
$22$	−7.86007	−1.67577
$23$	−8.14798	−1.69897	−0.849486	−	0.527611i	$-0.823088\pi$
$23$	−8.14798	−1.69897	−0.849486	+	0.527611i	$0.823088\pi$
$24$	−0.943278	−0.192546
$25$	−2.86761	−0.573522
$26$	−12.5327	−2.45786
$27$	−1.14843	−0.221015
$28$	−15.8636	−2.99794
$29$	9.62795	1.78787	0.893933	−	0.448201i	$-0.147935\pi$
$29$	9.62795	1.78787	0.893933	+	0.448201i	$0.147935\pi$
$30$	−0.688871	−0.125770
$31$	8.17471	1.46822	0.734111	−	0.679030i	$-0.237599\pi$
$31$	8.17471	1.46822	0.734111	+	0.679030i	$0.237599\pi$
$32$	0.00429093	0.000758537 0
$33$	0.618033	0.107586
$34$	2.44940	0.420069
$35$	−5.79192	−0.979014
$36$	−11.8503	−1.97506
$37$	−7.45724	−1.22596	−0.612981	−	0.790098i	$-0.710030\pi$
$37$	−7.45724	−1.22596	−0.612981	+	0.790098i	$0.710030\pi$
$38$	−8.99840	−1.45973
$39$	0.985438	0.157796
$40$	−7.15201	−1.13083
$41$	8.24516	1.28768	0.643839	−	0.765161i	$-0.277341\pi$
$41$	8.24516	1.28768	0.643839	+	0.765161i	$0.277341\pi$
$42$	1.87109	0.288715
$43$	5.68052	0.866271	0.433136	−	0.901329i	$-0.357407\pi$
$43$	5.68052	0.866271	0.433136	+	0.901329i	$0.357407\pi$
$44$	12.8345	1.93487
$45$	−4.32665	−0.644978
$46$	19.9577	2.94260
$47$	9.11914	1.33016	0.665082	−	0.746771i	$-0.268397\pi$
$47$	9.11914	1.33016	0.665082	+	0.746771i	$0.268397\pi$
$48$	0.769874	0.111122
$49$	8.73182	1.24740
$50$	7.02392	0.993333
$51$	−0.192595	−0.0269687
$52$	20.4643	2.83789
$53$	−12.4719	−1.71315	−0.856575	−	0.516022i	$-0.827412\pi$
$53$	−12.4719	−1.71315	−0.856575	+	0.516022i	$0.827412\pi$
$54$	2.81296	0.382795
$55$	4.68597	0.631856
$56$	19.4260	2.59591
$57$	0.707539	0.0937159
$58$	−23.5827	−3.09656
$59$	−6.11265	−0.795799	−0.397900	−	0.917429i	$-0.630261\pi$
$59$	−6.11265	−0.795799	−0.397900	+	0.917429i	$0.630261\pi$
$60$	1.12484	0.145216
$61$	0.888772	0.113796	0.0568978	−	0.998380i	$-0.481879\pi$
$61$	0.888772	0.113796	0.0568978	+	0.998380i	$0.481879\pi$
$62$	−20.0231	−2.54294
$63$	11.7519	1.48060
$64$	−8.00525	−1.00066
$65$	7.47167	0.926747
$66$	−1.51381	−0.186337
$67$	−3.67281	−0.448705	−0.224353	−	0.974508i	$-0.572027\pi$
$67$	−3.67281	−0.448705	−0.224353	+	0.974508i	$0.572027\pi$
$68$	−3.99956	−0.485018
$69$	−1.56926	−0.188917
$70$	14.1867	1.69564
$71$	−9.69117	−1.15013	−0.575065	−	0.818108i	$-0.695023\pi$
$71$	−9.69117	−1.15013	−0.575065	+	0.818108i	$0.695023\pi$
$72$	14.5115	1.71020
$73$	−10.2746	−1.20255	−0.601274	−	0.799043i	$-0.705340\pi$
$73$	−10.2746	−1.20255	−0.601274	+	0.799043i	$0.705340\pi$
$74$	18.2658	2.12335
$75$	−0.552287	−0.0637727
$76$	14.6933	1.68543
$77$	−12.7279	−1.45048
$78$	−2.41373	−0.273301
$79$	0.518576	0.0583444	0.0291722	−	0.999574i	$-0.490713\pi$
$79$	0.518576	0.0583444	0.0291722	+	0.999574i	$0.490713\pi$
$80$	5.83724	0.652624
$81$	8.66754	0.963060
$82$	−20.1957	−2.23024
$83$	−7.30712	−0.802060	−0.401030	−	0.916065i	$-0.631348\pi$
$83$	−7.30712	−0.802060	−0.401030	+	0.916065i	$0.631348\pi$
$84$	−3.05525	−0.333355
$85$	−1.46027	−0.158389
$86$	−13.9139	−1.50037
$87$	1.85429	0.198801
$88$	−15.7167	−1.67540
$89$	15.7459	1.66906	0.834532	−	0.550960i	$-0.185738\pi$
$89$	15.7459	1.66906	0.834532	+	0.550960i	$0.185738\pi$
$90$	10.5977	1.11709
$91$	−20.2943	−2.12742
$92$	−32.5884	−3.39757
$93$	1.57441	0.163259
$94$	−22.3364	−2.30383
$95$	5.36462	0.550398
$96$	0.000826413 0	8.43454e−5 0
$97$	−2.59386	−0.263367	−0.131683	−	0.991292i	$-0.542038\pi$
$97$	−2.59386	−0.263367	−0.131683	+	0.991292i	$0.542038\pi$
$98$	−21.3877	−2.16049
$99$	−9.50790	−0.955579
$100$	−11.4692	−1.14692
$101$	3.14698	0.313136	0.156568	−	0.987667i	$-0.449957\pi$
$101$	3.14698	0.313136	0.156568	+	0.987667i	$0.449957\pi$
$102$	0.471742	0.0467094
$103$	19.4025	1.91178	0.955892	−	0.293719i	$-0.0948931\pi$
$103$	19.4025	1.91178	0.955892	+	0.293719i	$0.0948931\pi$
$104$	−25.0599	−2.45732
$105$	−1.11550	−0.108861
$106$	30.5487	2.96715
$107$	0.957453	0.0925605	0.0462802	−	0.998928i	$-0.485263\pi$
$107$	0.957453	0.0925605	0.0462802	+	0.998928i	$0.485263\pi$
$108$	−4.59320	−0.441981
$109$	−19.6585	−1.88294	−0.941470	−	0.337098i	$-0.890555\pi$
$109$	−19.6585	−1.88294	−0.941470	+	0.337098i	$0.890555\pi$
$110$	−11.4778	−1.09437
$111$	−1.43623	−0.136321
$112$	−15.8549	−1.49815
$113$	−7.20070	−0.677384	−0.338692	−	0.940897i	$-0.609985\pi$
$113$	−7.20070	−0.677384	−0.338692	+	0.940897i	$0.609985\pi$
$114$	−1.73305	−0.162315
$115$	−11.8983	−1.10952
$116$	38.5076	3.57534
$117$	−15.1601	−1.40155
$118$	14.9723	1.37831
$119$	3.96634	0.363593
$120$	−1.37744	−0.125743
$121$	−0.702477	−0.0638616
$122$	−2.17696	−0.197093
$123$	1.58798	0.143183
$124$	32.6953	2.93612
$125$	−11.4888	−1.02759
$126$	−28.7851	−2.56438
$127$	19.6904	1.74724	0.873622	−	0.486606i	$-0.161765\pi$
$127$	19.6904	1.74724	0.873622	+	0.486606i	$0.161765\pi$
$128$	19.5995	1.73237
$129$	1.09404	0.0963249
$130$	−18.3011	−1.60511
$131$	−8.78926	−0.767921	−0.383961	−	0.923349i	$-0.625440\pi$
$131$	−8.78926	−0.767921	−0.383961	+	0.923349i	$0.625440\pi$
$132$	2.47186	0.215148
$133$	−14.5712	−1.26348
$134$	8.99619	0.777152
$135$	−1.67701	−0.144334
$136$	4.89773	0.419977
$137$	14.7787	1.26263	0.631313	−	0.775528i	$-0.282516\pi$
$137$	14.7787	1.26263	0.631313	+	0.775528i	$0.282516\pi$
$138$	3.84375	0.327202
$139$	15.2365	1.29234	0.646172	−	0.763192i	$-0.276369\pi$
$139$	15.2365	1.29234	0.646172	+	0.763192i	$0.276369\pi$
$140$	−23.1652	−1.95781
$141$	1.75630	0.147907
$142$	23.7376	1.99201
$143$	16.4192	1.37304
$144$	−11.8438	−0.986987
$145$	14.0594	1.16757
$146$	25.1665	2.08280
$147$	1.68171	0.138705
$148$	−29.8257	−2.45166
$149$	4.33872	0.355442	0.177721	−	0.984081i	$-0.443128\pi$
$149$	4.33872	0.355442	0.177721	+	0.984081i	$0.443128\pi$
$150$	1.35277	0.110453
$151$	−12.3066	−1.00149	−0.500747	−	0.865594i	$-0.666941\pi$
$151$	−12.3066	−1.00149	−0.500747	+	0.865594i	$0.666941\pi$
$152$	−17.9929	−1.45941
$153$	2.96291	0.239537
$154$	31.1757	2.51221
$155$	11.9373	0.958826
$156$	3.94132	0.315558
$157$	4.68624	0.374003	0.187002	−	0.982360i	$-0.440123\pi$
$157$	4.68624	0.374003	0.187002	+	0.982360i	$0.440123\pi$
$158$	−1.27020	−0.101052
$159$	−2.40203	−0.190493
$160$	0.00626592	0.000495365 0
$161$	32.3176	2.54699
$162$	−21.2303	−1.66801
$163$	−19.4567	−1.52397	−0.761983	−	0.647597i	$-0.775774\pi$
$163$	−19.4567	−1.52397	−0.761983	+	0.647597i	$0.775774\pi$
$164$	32.9770	2.57507
$165$	0.902495	0.0702591
$166$	17.8981	1.38916
$167$	−11.6378	−0.900562	−0.450281	−	0.892887i	$-0.648676\pi$
$167$	−11.6378	−0.900562	−0.450281	+	0.892887i	$0.648676\pi$
$168$	3.74136	0.288652
$169$	13.1800	1.01384
$170$	3.57679	0.274327
$171$	−10.8849	−0.832388
$172$	22.7196	1.73235
$173$	−0.290572	−0.0220918	−0.0110459	−	0.999939i	$-0.503516\pi$
$173$	−0.290572	−0.0220918	−0.0110459	+	0.999939i	$0.503516\pi$
$174$	−4.54191	−0.344321
$175$	11.3739	0.859786
$176$	12.8275	0.966907
$177$	−1.17727	−0.0884887
$178$	−38.5680	−2.89080
$179$	14.4316	1.07867	0.539333	−	0.842093i	$-0.318676\pi$
$179$	14.4316	1.07867	0.539333	+	0.842093i	$0.318676\pi$
$180$	−17.3047	−1.28982
$181$	16.3780	1.21737	0.608684	−	0.793412i	$-0.291698\pi$
$181$	16.3780	1.21737	0.608684	+	0.793412i	$0.291698\pi$
$182$	49.7089	3.68467
$183$	0.171173	0.0126535
$184$	39.9066	2.94195
$185$	−10.8896	−0.800618
$186$	−3.85636	−0.282762
$187$	−3.20898	−0.234664
$188$	36.4726	2.66003
$189$	4.55504	0.331331
$190$	−13.1401	−0.953283
$191$	−17.4776	−1.26463	−0.632316	−	0.774711i	$-0.717896\pi$
$191$	−17.4776	−1.26463	−0.632316	+	0.774711i	$0.717896\pi$
$192$	−1.54177	−0.111268
$193$	5.09520	0.366761	0.183380	−	0.983042i	$-0.441296\pi$
$193$	5.09520	0.366761	0.183380	+	0.983042i	$0.441296\pi$
$194$	6.35340	0.456148
$195$	1.43901	0.103049
$196$	34.9235	2.49453
$197$	14.6220	1.04178	0.520888	−	0.853625i	$-0.325601\pi$
$197$	14.6220	1.04178	0.520888	+	0.853625i	$0.325601\pi$
$198$	23.2886	1.65505
$199$	14.5609	1.03220	0.516099	−	0.856529i	$-0.327384\pi$
$199$	14.5609	1.03220	0.516099	+	0.856529i	$0.327384\pi$
$200$	14.0448	0.993115
$201$	−0.707365	−0.0498937
$202$	−7.70821	−0.542348
$203$	−38.1877	−2.68025
$204$	−0.770296	−0.0539315
$205$	12.0402	0.840921
$206$	−47.5244	−3.31119
$207$	24.1417	1.67797
$208$	20.4531	1.41817
$209$	11.7889	0.815453
$210$	2.73230	0.188546
$211$	7.28189	0.501306	0.250653	−	0.968077i	$-0.419355\pi$
$211$	7.28189	0.501306	0.250653	+	0.968077i	$0.419355\pi$
$212$	−49.8822	−3.42592
$213$	−1.86647	−0.127888
$214$	−2.34519	−0.160314
$215$	8.29510	0.565721
$216$	5.62468	0.382711
$217$	−32.4237	−2.20106
$218$	48.1514	3.26123
$219$	−1.97883	−0.133717
$220$	18.7418	1.26357
$221$	−5.11663	−0.344182
$222$	3.51789	0.236106
$223$	13.4328	0.899527	0.449764	−	0.893148i	$-0.351508\pi$
$223$	13.4328	0.899527	0.449764	+	0.893148i	$0.351508\pi$
$224$	−0.0170193	−0.00113715
$225$	8.49646	0.566431
$226$	17.6374	1.17322
$227$	21.2888	1.41299	0.706493	−	0.707720i	$-0.250276\pi$
$227$	21.2888	1.41299	0.706493	+	0.707720i	$0.250276\pi$
$228$	2.82985	0.187411
$229$	−22.0249	−1.45545	−0.727724	−	0.685870i	$-0.759422\pi$
$229$	−22.0249	−1.45545	−0.727724	+	0.685870i	$0.759422\pi$
$230$	29.1436	1.92167
$231$	−2.45133	−0.161285
$232$	−47.1551	−3.09588
$233$	7.16295	0.469260	0.234630	−	0.972085i	$-0.424612\pi$
$233$	7.16295	0.469260	0.234630	+	0.972085i	$0.424612\pi$
$234$	37.1332	2.42747
$235$	13.3164	0.868667
$236$	−24.4479	−1.59142
$237$	0.0998752	0.00648759
$238$	−9.71515	−0.629739
$239$	8.22604	0.532098	0.266049	−	0.963959i	$-0.414282\pi$
$239$	8.22604	0.532098	0.266049	+	0.963959i	$0.414282\pi$
$240$	1.12422	0.0725684
$241$	2.97682	0.191754	0.0958768	−	0.995393i	$-0.469435\pi$
$241$	2.97682	0.191754	0.0958768	+	0.995393i	$0.469435\pi$
$242$	1.72065	0.110607
$243$	5.11460	0.328102
$244$	3.55470	0.227566
$245$	12.7508	0.814620
$246$	−3.88959	−0.247991
$247$	18.7971	1.19603
$248$	−40.0375	−2.54238
$249$	−1.40731	−0.0891849
$250$	28.1408	1.77978
$251$	−10.7948	−0.681364	−0.340682	−	0.940179i	$-0.610658\pi$
$251$	−10.7948	−0.681364	−0.340682	+	0.940179i	$0.610658\pi$
$252$	47.0024	2.96087
$253$	−26.1467	−1.64383
$254$	−48.2297	−3.02620
$255$	−0.281241	−0.0176120
$256$	−31.9965	−1.99978
$257$	9.59353	0.598428	0.299214	−	0.954186i	$-0.403276\pi$
$257$	9.59353	0.598428	0.299214	+	0.954186i	$0.403276\pi$
$258$	−2.67974	−0.166833
$259$	29.5779	1.83788
$260$	29.8834	1.85329
$261$	−28.5267	−1.76576
$262$	21.5284	1.33003
$263$	17.7044	1.09170	0.545850	−	0.837883i	$-0.316207\pi$
$263$	17.7044	1.09170	0.545850	+	0.837883i	$0.316207\pi$
$264$	−3.02696	−0.186296
$265$	−18.2124	−1.11878
$266$	35.6907	2.18834
$267$	3.03258	0.185591
$268$	−14.6896	−0.897313
$269$	0.243516	0.0148474	0.00742372	−	0.999972i	$-0.497637\pi$
$269$	0.243516	0.0148474	0.00742372	+	0.999972i	$0.497637\pi$
$270$	4.10768	0.249985
$271$	10.9093	0.662694	0.331347	−	0.943509i	$-0.392497\pi$
$271$	10.9093	0.662694	0.331347	+	0.943509i	$0.392497\pi$
$272$	−3.99737	−0.242376
$273$	−3.90858	−0.236558
$274$	−36.1988	−2.18685
$275$	−9.20209	−0.554907
$276$	−6.27636	−0.377792
$277$	−5.64987	−0.339468	−0.169734	−	0.985490i	$-0.554291\pi$
$277$	−5.64987	−0.339468	−0.169734	+	0.985490i	$0.554291\pi$
$278$	−37.3203	−2.23832
$279$	−24.2209	−1.45007
$280$	28.3673	1.69527
$281$	−0.214539	−0.0127983	−0.00639916	−	0.999980i	$-0.502037\pi$
$281$	−0.214539	−0.0127983	−0.00639916	+	0.999980i	$0.502037\pi$
$282$	−4.30188	−0.256173
$283$	−21.0437	−1.25092	−0.625458	−	0.780258i	$-0.715088\pi$
$283$	−21.0437	−1.25092	−0.625458	+	0.780258i	$0.715088\pi$
$284$	−38.7604	−2.30001
$285$	1.03320	0.0612014
$286$	−40.2171	−2.37809
$287$	−32.7031	−1.93040
$288$	−0.0127136	−0.000749158 0
$289$	1.00000	0.0588235
$290$	−34.4371	−2.02222
$291$	−0.499564	−0.0292850
$292$	−41.0938	−2.40483
$293$	−8.94936	−0.522827	−0.261414	−	0.965227i	$-0.584189\pi$
$293$	−8.94936	−0.522827	−0.261414	+	0.965227i	$0.584189\pi$
$294$	−4.11917	−0.240235
$295$	−8.92612	−0.519699
$296$	36.5235	2.12289
$297$	−3.68527	−0.213841
$298$	−10.6273	−0.615621
$299$	−41.6903	−2.41101
$300$	−2.20891	−0.127531
$301$	−22.5309	−1.29866
$302$	30.1437	1.73458
$303$	0.606093	0.0348191
$304$	14.6852	0.842255
$305$	1.29785	0.0743145
$306$	−7.25735	−0.414875
$307$	−12.8837	−0.735311	−0.367656	−	0.929962i	$-0.619839\pi$
$307$	−12.8837	−0.735311	−0.367656	+	0.929962i	$0.619839\pi$
$308$	−50.9059	−2.90063
$309$	3.73682	0.212580
$310$	−29.2392	−1.66068
$311$	29.9964	1.70094	0.850469	−	0.526024i	$-0.176318\pi$
$311$	29.9964	1.70094	0.850469	+	0.526024i	$0.176318\pi$
$312$	−4.82641	−0.273242
$313$	−11.8376	−0.669100	−0.334550	−	0.942378i	$-0.608584\pi$
$313$	−11.8376	−0.669100	−0.334550	+	0.942378i	$0.608584\pi$
$314$	−11.4785	−0.647769
$315$	17.1609	0.966909
$316$	2.07408	0.116676
$317$	3.25428	0.182779	0.0913893	−	0.995815i	$-0.470869\pi$
$317$	3.25428	0.182779	0.0913893	+	0.995815i	$0.470869\pi$
$318$	5.88353	0.329932
$319$	30.8958	1.72984
$320$	−11.6898	−0.653482
$321$	0.184401	0.0102922
$322$	−79.1588	−4.41135
$323$	−3.67372	−0.204411
$324$	34.6664	1.92591
$325$	−14.6725	−0.813885
$326$	47.6573	2.63949
$327$	−3.78612	−0.209373
$328$	−40.3825	−2.22975
$329$	−36.1696	−1.99409
$330$	−2.21057	−0.121688
$331$	27.3326	1.50234	0.751168	−	0.660111i	$-0.229491\pi$
$331$	27.3326	1.50234	0.751168	+	0.660111i	$0.229491\pi$
$332$	−29.2253	−1.60394
$333$	22.0951	1.21080
$334$	28.5057	1.55976
$335$	−5.36330	−0.293028
$336$	−3.05358	−0.166586
$337$	−6.08818	−0.331644	−0.165822	−	0.986156i	$-0.553028\pi$
$337$	−6.08818	−0.331644	−0.165822	+	0.986156i	$0.553028\pi$
$338$	−32.2830	−1.75596
$339$	−1.38682	−0.0753216
$340$	−5.84044	−0.316742
$341$	26.2324	1.42057
$342$	26.6614	1.44168
$343$	−6.86900	−0.370891
$344$	−27.8216	−1.50004
$345$	−2.29155	−0.123373
$346$	0.711727	0.0382627
$347$	36.4223	1.95525	0.977627	−	0.210347i	$-0.0674594\pi$
$347$	36.4223	1.95525	0.977627	+	0.210347i	$0.0674594\pi$
$348$	7.41637	0.397559
$349$	2.94554	0.157671	0.0788356	−	0.996888i	$-0.474880\pi$
$349$	2.94554	0.157671	0.0788356	+	0.996888i	$0.474880\pi$
$350$	−27.8592	−1.48914
$351$	−5.87608	−0.313642
$352$	0.0137695	0.000733917 0
$353$	1.00000	0.0532246
$353$	1.00000	0.0532246
$354$	2.88360	0.153261
$355$	−14.1517	−0.751096
$356$	62.9768	3.33776
$357$	0.763897	0.0404297
$358$	−35.3487	−1.86824
$359$	4.15379	0.219229	0.109614	−	0.993974i	$-0.465038\pi$
$359$	4.15379	0.219229	0.109614	+	0.993974i	$0.465038\pi$
$360$	21.1907	1.11685
$361$	−5.50381	−0.289674
$362$	−40.1163	−2.10847
$363$	−0.135294	−0.00710108
$364$	−81.1683	−4.25437
$365$	−15.0037	−0.785327
$366$	−0.419271	−0.0219157
$367$	4.33551	0.226312	0.113156	−	0.993577i	$-0.463904\pi$
$367$	4.33551	0.226312	0.113156	+	0.993577i	$0.463904\pi$
$368$	−32.5705	−1.69786
$369$	−24.4296	−1.27176
$370$	26.6729	1.38666
$371$	49.4678	2.56824
$372$	6.29695	0.326481
$373$	−28.5247	−1.47695	−0.738476	−	0.674279i	$-0.764454\pi$
$373$	−28.5247	−1.47695	−0.738476	+	0.674279i	$0.764454\pi$
$374$	7.86007	0.406434
$375$	−2.21269	−0.114263
$376$	−44.6631	−2.30332
$377$	49.2627	2.53716
$378$	−11.1571	−0.573861
$379$	−15.5883	−0.800717	−0.400359	−	0.916359i	$-0.631114\pi$
$379$	−15.5883	−0.800717	−0.400359	+	0.916359i	$0.631114\pi$
$380$	21.4561	1.10068
$381$	3.79228	0.194284
$382$	42.8095	2.19033
$383$	34.2414	1.74966	0.874828	−	0.484434i	$-0.160974\pi$
$383$	34.2414	1.74966	0.874828	+	0.484434i	$0.160974\pi$
$384$	3.77476	0.192630
$385$	−18.5861	−0.947237
$386$	−12.4802	−0.635225
$387$	−16.8309	−0.855561
$388$	−10.3743	−0.526675
$389$	15.6035	0.791130	0.395565	−	0.918438i	$-0.370549\pi$
$389$	15.6035	0.791130	0.395565	+	0.918438i	$0.370549\pi$
$390$	−3.52470	−0.178480
$391$	8.14798	0.412061
$392$	−42.7661	−2.16001
$393$	−1.69277	−0.0853889
$394$	−35.8152	−1.80434
$395$	0.757262	0.0381020
$396$	−38.0274	−1.91095
$397$	32.8191	1.64714	0.823571	−	0.567213i	$-0.191978\pi$
$397$	32.8191	1.64714	0.823571	+	0.567213i	$0.191978\pi$
$398$	−35.6655	−1.78775
$399$	−2.80634	−0.140493
$400$	−11.4629	−0.573145
$401$	37.2479	1.86007	0.930037	−	0.367466i	$-0.119775\pi$
$401$	37.2479	1.86007	0.930037	+	0.367466i	$0.119775\pi$
$402$	1.73262	0.0864153
$403$	41.8270	2.08355
$404$	12.5865	0.626204
$405$	12.6570	0.628929
$406$	93.5369	4.64216
$407$	−23.9301	−1.18617
$408$	0.943278	0.0466992
$409$	−9.29099	−0.459410	−0.229705	−	0.973260i	$-0.573776\pi$
$409$	−9.29099	−0.459410	−0.229705	+	0.973260i	$0.573776\pi$
$410$	−29.4912	−1.45647
$411$	2.84630	0.140397
$412$	77.6014	3.82315
$413$	24.2448	1.19301
$414$	−59.1327	−2.90622
$415$	−10.6704	−0.523788
$416$	0.0219551	0.00107644
$417$	2.93447	0.143702
$418$	−28.8756	−1.41235
$419$	6.23699	0.304697	0.152348	−	0.988327i	$-0.451316\pi$
$419$	6.23699	0.304697	0.152348	+	0.988327i	$0.451316\pi$
$420$	−4.46149	−0.217699
$421$	−4.13653	−0.201602	−0.100801	−	0.994907i	$-0.532141\pi$
$421$	−4.13653	−0.201602	−0.100801	+	0.994907i	$0.532141\pi$
$422$	−17.8363	−0.868256
$423$	−27.0192	−1.31372
$424$	61.0841	2.96650
$425$	2.86761	0.139100
$426$	4.57173	0.221501
$427$	−3.52517	−0.170595
$428$	3.82939	0.185101
$429$	3.16225	0.152675
$430$	−20.3180	−0.979822
$431$	−3.87001	−0.186412	−0.0932059	−	0.995647i	$-0.529711\pi$
$431$	−3.87001	−0.186412	−0.0932059	+	0.995647i	$0.529711\pi$
$432$	−4.59069	−0.220870
$433$	0.720491	0.0346246	0.0173123	−	0.999850i	$-0.494489\pi$
$433$	0.720491	0.0346246	0.0173123	+	0.999850i	$0.494489\pi$
$434$	79.4185	3.81221
$435$	2.70777	0.129828
$436$	−78.6252	−3.76547
$437$	−29.9334	−1.43191
$438$	4.84695	0.231596
$439$	−34.7771	−1.65982	−0.829911	−	0.557896i	$-0.811609\pi$
$439$	−34.7771	−1.65982	−0.829911	+	0.557896i	$0.811609\pi$
$440$	−22.9506	−1.09413
$441$	−25.8716	−1.23198
$442$	12.5327	0.596119
$443$	−15.8554	−0.753315	−0.376657	−	0.926353i	$-0.622927\pi$
$443$	−15.8554	−0.753315	−0.376657	+	0.926353i	$0.622927\pi$
$444$	−5.74428	−0.272611
$445$	22.9933	1.08999
$446$	−32.9023	−1.55797
$447$	0.835617	0.0395233
$448$	31.7515	1.50012
$449$	−6.79290	−0.320577	−0.160288	−	0.987070i	$-0.551242\pi$
$449$	−6.79290	−0.320577	−0.160288	+	0.987070i	$0.551242\pi$
$450$	−20.8112	−0.981051
$451$	26.4585	1.24588
$452$	−28.7996	−1.35462
$453$	−2.37018	−0.111361
$454$	−52.1447	−2.44727
$455$	−29.6352	−1.38932
$456$	−3.46534	−0.162279
$457$	−4.69497	−0.219621	−0.109811	−	0.993953i	$-0.535024\pi$
$457$	−4.69497	−0.219621	−0.109811	+	0.993953i	$0.535024\pi$
$458$	53.9479	2.52082
$459$	1.14843	0.0536039
$460$	−47.5878	−2.21879
$461$	−13.0849	−0.609427	−0.304713	−	0.952444i	$-0.598561\pi$
$461$	−13.0849	−0.609427	−0.304713	+	0.952444i	$0.598561\pi$
$462$	6.00428	0.279344
$463$	6.07716	0.282429	0.141215	−	0.989979i	$-0.454899\pi$
$463$	6.07716	0.282429	0.141215	+	0.989979i	$0.454899\pi$
$464$	38.4865	1.78669
$465$	2.29906	0.106616
$466$	−17.5449	−0.812753
$467$	36.6402	1.69550	0.847752	−	0.530392i	$-0.177955\pi$
$467$	36.6402	1.69550	0.847752	+	0.530392i	$0.177955\pi$
$468$	−60.6338	−2.80280
$469$	14.5676	0.672670
$470$	−32.6172	−1.50452
$471$	0.902547	0.0415872
$472$	29.9381	1.37801
$473$	18.2287	0.838154
$474$	−0.244634	−0.0112364
$475$	−10.5348	−0.483369
$476$	15.8636	0.727107
$477$	36.9531	1.69197
$478$	−20.1489	−0.921588
$479$	39.3934	1.79993	0.899966	−	0.435960i	$-0.143591\pi$
$479$	39.3934	1.79993	0.899966	+	0.435960i	$0.143591\pi$
$480$	0.00120679	5.50820e−5 0
$481$	−38.1560	−1.73976
$482$	−7.29142	−0.332115
$483$	6.22422	0.283212
$484$	−2.80960	−0.127709
$485$	−3.78774	−0.171992
$486$	−12.5277	−0.568269
$487$	−21.9048	−0.992603	−0.496301	−	0.868150i	$-0.665309\pi$
$487$	−21.9048	−0.992603	−0.496301	+	0.868150i	$0.665309\pi$
$488$	−4.35296	−0.197049
$489$	−3.74726	−0.169457
$490$	−31.2319	−1.41091
$491$	14.7880	0.667371	0.333686	−	0.942684i	$-0.391708\pi$
$491$	14.7880	0.667371	0.333686	+	0.942684i	$0.391708\pi$
$492$	6.35121	0.286335
$493$	−9.62795	−0.433621
$494$	−46.0415	−2.07151
$495$	−13.8841	−0.624044
$496$	32.6774	1.46726
$497$	38.4384	1.72420
$498$	3.44708	0.154467
$499$	−13.5733	−0.607626	−0.303813	−	0.952732i	$-0.598260\pi$
$499$	−13.5733	−0.607626	−0.303813	+	0.952732i	$0.598260\pi$
$500$	−45.9503	−2.05496
$501$	−2.24139	−0.100138
$502$	26.4409	1.18011
$503$	−0.962694	−0.0429244	−0.0214622	−	0.999770i	$-0.506832\pi$
$503$	−0.962694	−0.0429244	−0.0214622	+	0.999770i	$0.506832\pi$
$504$	−57.5575	−2.56382
$505$	4.59544	0.204494
$506$	64.0437	2.84709
$507$	2.53839	0.112734
$508$	78.7531	3.49410
$509$	−33.6953	−1.49352	−0.746759	−	0.665095i	$-0.768391\pi$
$509$	−33.6953	−1.49352	−0.746759	+	0.665095i	$0.768391\pi$
$510$	0.688871	0.0305037
$511$	40.7524	1.80278
$512$	39.1732	1.73123
$513$	−4.21899	−0.186273
$514$	−23.4984	−1.03647
$515$	28.3329	1.24850
$516$	4.37568	0.192629
$517$	29.2631	1.28699
$518$	−72.4481	−3.18319
$519$	−0.0559627	−0.00245649
$520$	−36.5942	−1.60476
$521$	1.48409	0.0650192	0.0325096	−	0.999471i	$-0.489650\pi$
$521$	1.48409	0.0650192	0.0325096	+	0.999471i	$0.489650\pi$
$522$	69.8734	3.05827
$523$	−10.9555	−0.479053	−0.239526	−	0.970890i	$-0.576992\pi$
$523$	−10.9555	−0.479053	−0.239526	+	0.970890i	$0.576992\pi$
$524$	−35.1532	−1.53567
$525$	2.19056	0.0956038
$526$	−43.3651	−1.89081
$527$	−8.17471	−0.356096
$528$	2.47051	0.107515
$529$	43.3896	1.88651
$530$	44.6094	1.93771
$531$	18.1112	0.785960
$532$	−58.2784	−2.52669
$533$	42.1875	1.82734
$534$	−7.42801	−0.321442
$535$	1.39814	0.0604469
$536$	17.9884	0.776982
$537$	2.77945	0.119942
$538$	−0.596469	−0.0257156
$539$	28.0202	1.20692
$540$	−6.70732	−0.288637
$541$	−3.19187	−0.137229	−0.0686147	−	0.997643i	$-0.521858\pi$
$541$	−3.19187	−0.137229	−0.0686147	+	0.997643i	$0.521858\pi$
$542$	−26.7213	−1.14778
$543$	3.15433	0.135365
$544$	−0.00429093	−0.000183972 0
$545$	−28.7067	−1.22966
$546$	9.57368	0.409716
$547$	26.5735	1.13620	0.568101	−	0.822959i	$-0.307678\pi$
$547$	26.5735	1.13620	0.568101	+	0.822959i	$0.307678\pi$
$548$	59.1081	2.52497
$549$	−2.63335	−0.112389
$550$	22.5396	0.961092
$551$	35.3703	1.50683
$552$	7.68581	0.327130
$553$	−2.05685	−0.0874661
$554$	13.8388	0.587954
$555$	−2.09728	−0.0890245
$556$	60.9393	2.58440
$557$	20.6929	0.876785	0.438392	−	0.898784i	$-0.355548\pi$
$557$	20.6929	0.876785	0.438392	+	0.898784i	$0.355548\pi$
$558$	59.3267	2.51150
$559$	29.0652	1.22933
$560$	−23.1525	−0.978371
$561$	−0.618033	−0.0260934
$562$	0.525492	0.0221665
$563$	−29.5380	−1.24488	−0.622439	−	0.782669i	$-0.713858\pi$
$563$	−29.5380	−1.24488	−0.622439	+	0.782669i	$0.713858\pi$
$564$	7.02443	0.295782
$565$	−10.5150	−0.442368
$566$	51.5444	2.16657
$567$	−34.3784	−1.44376
$568$	47.4647	1.99157
$569$	−3.92157	−0.164401	−0.0822004	−	0.996616i	$-0.526195\pi$
$569$	−3.92157	−0.164401	−0.0822004	+	0.996616i	$0.526195\pi$
$570$	−2.53072	−0.106000
$571$	−30.4936	−1.27612	−0.638058	−	0.769988i	$-0.720262\pi$
$571$	−30.4936	−1.27612	−0.638058	+	0.769988i	$0.720262\pi$
$572$	65.6694	2.74578
$573$	−3.36609	−0.140620
$574$	80.1029	3.34343
$575$	23.3652	0.974398
$576$	23.7188	0.988284
$577$	−21.7812	−0.906762	−0.453381	−	0.891317i	$-0.649782\pi$
$577$	−21.7812	−0.906762	−0.453381	+	0.891317i	$0.649782\pi$
$578$	−2.44940	−0.101882
$579$	0.981310	0.0407819
$580$	56.2315	2.33489
$581$	28.9825	1.20240
$582$	1.22363	0.0507212
$583$	−40.0221	−1.65755
$584$	50.3221	2.08234
$585$	−22.1379	−0.915288
$586$	21.9206	0.905530
$587$	−42.7786	−1.76566	−0.882831	−	0.469690i	$-0.844366\pi$
$587$	−42.7786	−1.76566	−0.882831	+	0.469690i	$0.844366\pi$
$588$	6.72609	0.277379
$589$	30.0316	1.23743
$590$	21.8636	0.900112
$591$	2.81613	0.115840
$592$	−29.8093	−1.22516
$593$	47.0717	1.93300	0.966501	−	0.256663i	$-0.0826230\pi$
$593$	47.0717	1.93300	0.966501	+	0.256663i	$0.0826230\pi$
$594$	9.02670	0.370370
$595$	5.79192	0.237446
$596$	17.3530	0.710806
$597$	2.80436	0.114775
$598$	102.116	4.17584
$599$	28.6998	1.17264	0.586320	−	0.810079i	$-0.300576\pi$
$599$	28.6998	1.17264	0.586320	+	0.810079i	$0.300576\pi$
$600$	2.70495	0.110429
$601$	−3.70833	−0.151266	−0.0756330	−	0.997136i	$-0.524098\pi$
$601$	−3.70833	−0.151266	−0.0756330	+	0.997136i	$0.524098\pi$
$602$	55.1871	2.24926
$603$	10.8822	0.443158
$604$	−49.2209	−2.00277
$605$	−1.02581	−0.0417050
$606$	−1.48456	−0.0603063
$607$	−5.41113	−0.219631	−0.109816	−	0.993952i	$-0.535026\pi$
$607$	−5.41113	−0.219631	−0.109816	+	0.993952i	$0.535026\pi$
$608$	0.0157637	0.000639301 0
$609$	−7.35476	−0.298030
$610$	−3.17895	−0.128712
$611$	46.6593	1.88763
$612$	11.8503	0.479021
$613$	28.8506	1.16526	0.582631	−	0.812736i	$-0.302023\pi$
$613$	28.8506	1.16526	0.582631	+	0.812736i	$0.302023\pi$
$614$	31.5573	1.27355
$615$	2.31887	0.0935061
$616$	62.3377	2.51166
$617$	10.5288	0.423874	0.211937	−	0.977283i	$-0.432023\pi$
$617$	10.5288	0.423874	0.211937	+	0.977283i	$0.432023\pi$
$618$	−9.15297	−0.368187
$619$	−1.60767	−0.0646177	−0.0323089	−	0.999478i	$-0.510286\pi$
$619$	−1.60767	−0.0646177	−0.0323089	+	0.999478i	$0.510286\pi$
$620$	47.7439	1.91744
$621$	9.35736	0.375498
$622$	−73.4732	−2.94601
$623$	−62.4536	−2.50215
$624$	3.93916	0.157693
$625$	−2.43876	−0.0975505
$626$	28.9950	1.15887
$627$	2.27048	0.0906741
$628$	18.7429	0.747924
$629$	7.45724	0.297339
$630$	−42.0340	−1.67467
$631$	37.8451	1.50659	0.753294	−	0.657683i	$-0.228464\pi$
$631$	37.8451	1.50659	0.753294	+	0.657683i	$0.228464\pi$
$632$	−2.53985	−0.101030
$633$	1.40246	0.0557426
$634$	−7.97104	−0.316570
$635$	28.7534	1.14104
$636$	−9.60707	−0.380945
$637$	44.6776	1.77019
$638$	−75.6763	−2.99605
$639$	28.7140	1.13591
$640$	28.6206	1.13133
$641$	30.5735	1.20758	0.603791	−	0.797143i	$-0.293656\pi$
$641$	30.5735	1.20758	0.603791	+	0.797143i	$0.293656\pi$
$642$	−0.451671	−0.0178260
$643$	24.9713	0.984771	0.492385	−	0.870377i	$-0.336125\pi$
$643$	24.9713	0.984771	0.492385	+	0.870377i	$0.336125\pi$
$644$	129.256	5.09342
$645$	1.59759	0.0629052
$646$	8.99840	0.354037
$647$	49.1413	1.93194	0.965971	−	0.258649i	$-0.0832773\pi$
$647$	49.1413	1.93194	0.965971	+	0.258649i	$0.0832773\pi$
$648$	−42.4513	−1.66764
$649$	−19.6153	−0.769969
$650$	35.9389	1.40964
$651$	−6.24464	−0.244747
$652$	−77.8183	−3.04760
$653$	−10.1484	−0.397138	−0.198569	−	0.980087i	$-0.563629\pi$
$653$	−10.1484	−0.397138	−0.198569	+	0.980087i	$0.563629\pi$
$654$	9.27373	0.362631
$655$	−12.8347	−0.501493
$656$	32.9590	1.28683
$657$	30.4426	1.18768
$658$	88.5938	3.45374
$659$	47.3753	1.84548	0.922740	−	0.385423i	$-0.125944\pi$
$659$	47.3753	1.84548	0.922740	+	0.385423i	$0.125944\pi$
$660$	3.60958	0.140503
$661$	−30.9698	−1.20458	−0.602292	−	0.798276i	$-0.705746\pi$
$661$	−30.9698	−1.20458	−0.602292	+	0.798276i	$0.705746\pi$
$662$	−66.9485	−2.60203
$663$	−0.985438	−0.0382713
$664$	35.7883	1.38885
$665$	−21.2779	−0.825121
$666$	−54.1197	−2.09710
$667$	−78.4484	−3.03753
$668$	−46.5462	−1.80093
$669$	2.58709	0.100023
$670$	13.1369	0.507522
$671$	2.85205	0.110102
$672$	−0.00327783	−0.000126445 0
$673$	−4.09240	−0.157750	−0.0788752	−	0.996884i	$-0.525133\pi$
$673$	−4.09240	−0.157750	−0.0788752	+	0.996884i	$0.525133\pi$
$674$	14.9124	0.574404
$675$	3.29324	0.126757
$676$	52.7140	2.02746
$677$	14.2216	0.546582	0.273291	−	0.961931i	$-0.411888\pi$
$677$	14.2216	0.546582	0.273291	+	0.961931i	$0.411888\pi$
$678$	3.39687	0.130456
$679$	10.2881	0.394822
$680$	7.15201	0.274267
$681$	4.10011	0.157117
$682$	−64.2538	−2.46040
$683$	48.4610	1.85431	0.927153	−	0.374682i	$-0.122248\pi$
$683$	48.4610	1.85431	0.927153	+	0.374682i	$0.122248\pi$
$684$	−43.5347	−1.66459
$685$	21.5808	0.824561
$686$	16.8249	0.642379
$687$	−4.24189	−0.161838
$688$	22.7072	0.865702
$689$	−63.8143	−2.43113
$690$	5.61291	0.213680
$691$	7.95233	0.302521	0.151260	−	0.988494i	$-0.451667\pi$
$691$	7.95233	0.302521	0.151260	+	0.988494i	$0.451667\pi$
$692$	−1.16216	−0.0441787
$693$	37.7115	1.43254
$694$	−89.2129	−3.38647
$695$	22.2494	0.843969
$696$	−9.08183	−0.344246
$697$	−8.24516	−0.312308
$698$	−7.21481	−0.273084
$699$	1.37955	0.0521793
$700$	45.4906	1.71938
$701$	21.3897	0.807879	0.403939	−	0.914786i	$-0.367641\pi$
$701$	21.3897	0.807879	0.403939	+	0.914786i	$0.367641\pi$
$702$	14.3929	0.543224
$703$	−27.3958	−1.03325
$704$	−25.6887	−0.968178
$705$	2.56467	0.0965912
$706$	−2.44940	−0.0921844
$707$	−12.4820	−0.469433
$708$	−4.70855	−0.176958
$709$	10.9413	0.410909	0.205454	−	0.978667i	$-0.434133\pi$
$709$	10.9413	0.410909	0.205454	+	0.978667i	$0.434133\pi$
$710$	34.6632	1.30089
$711$	−1.53649	−0.0576230
$712$	−77.1192	−2.89016
$713$	−66.6074	−2.49447
$714$	−1.87109	−0.0700237
$715$	23.9764	0.896667
$716$	57.7200	2.15710
$717$	1.58429	0.0591666
$718$	−10.1743	−0.379702
$719$	8.79119	0.327856	0.163928	−	0.986472i	$-0.447584\pi$
$719$	8.79119	0.327856	0.163928	+	0.986472i	$0.447584\pi$
$720$	−17.2952	−0.644555
$721$	−76.9568	−2.86602
$722$	13.4810	0.501712
$723$	0.573320	0.0213220
$724$	65.5049	2.43447
$725$	−27.6092	−1.02538
$726$	0.331388	0.0122990
$727$	30.0643	1.11502	0.557512	−	0.830169i	$-0.311756\pi$
$727$	30.0643	1.11502	0.557512	+	0.830169i	$0.311756\pi$
$728$	99.3959	3.68386
$729$	−25.0176	−0.926577
$730$	36.7500	1.36018
$731$	−5.68052	−0.210102
$732$	0.684617	0.0253042
$733$	12.2030	0.450728	0.225364	−	0.974275i	$-0.427643\pi$
$733$	12.2030	0.450728	0.225364	+	0.974275i	$0.427643\pi$
$734$	−10.6194	−0.391969
$735$	2.45575	0.0905815
$736$	−0.0349625	−0.00128873
$737$	−11.7860	−0.434142
$738$	59.8380	2.20267
$739$	−21.7569	−0.800342	−0.400171	−	0.916441i	$-0.631049\pi$
$739$	−21.7569	−0.800342	−0.400171	+	0.916441i	$0.631049\pi$
$740$	−43.5536	−1.60106
$741$	3.62022	0.132992
$742$	−121.167	−4.44816
$743$	−23.2599	−0.853322	−0.426661	−	0.904412i	$-0.640310\pi$
$743$	−23.2599	−0.853322	−0.426661	+	0.904412i	$0.640310\pi$
$744$	−7.71103	−0.282700
$745$	6.33571	0.232122
$746$	69.8684	2.55806
$747$	21.6503	0.792143
$748$	−12.8345	−0.469276
$749$	−3.79758	−0.138761
$750$	5.41977	0.197902
$751$	−29.2394	−1.06696	−0.533481	−	0.845812i	$-0.679116\pi$
$751$	−29.2394	−1.06696	−0.533481	+	0.845812i	$0.679116\pi$
$752$	36.4526	1.32929
$753$	−2.07903	−0.0757641
$754$	−120.664	−4.39433
$755$	−17.9709	−0.654029
$756$	18.2182	0.662589
$757$	−14.1482	−0.514226	−0.257113	−	0.966381i	$-0.582771\pi$
$757$	−14.1482	−0.514226	−0.257113	+	0.966381i	$0.582771\pi$
$758$	38.1820	1.38683
$759$	−5.03572	−0.182785
$760$	−26.2744	−0.953074
$761$	−4.14378	−0.150212	−0.0751059	−	0.997176i	$-0.523929\pi$
$761$	−4.14378	−0.150212	−0.0751059	+	0.997176i	$0.523929\pi$
$762$	−9.28881	−0.336498
$763$	77.9721	2.82278
$764$	−69.9026	−2.52899
$765$	4.32665	0.156430
$766$	−83.8710	−3.03038
$767$	−31.2762	−1.12932
$768$	−6.16236	−0.222365
$769$	40.2774	1.45244	0.726220	−	0.687463i	$-0.241275\pi$
$769$	40.2774	1.45244	0.726220	+	0.687463i	$0.241275\pi$
$770$	45.5249	1.64060
$771$	1.84767	0.0665421
$772$	20.3786	0.733441
$773$	−28.6055	−1.02887	−0.514433	−	0.857530i	$-0.671998\pi$
$773$	−28.6055	−1.02887	−0.514433	+	0.857530i	$0.671998\pi$
$774$	41.2255	1.48182
$775$	−23.4419	−0.842057
$776$	12.7040	0.456048
$777$	5.69656	0.204363
$778$	−38.2193	−1.37023
$779$	30.2904	1.08526
$780$	5.75540	0.206076
$781$	−31.0987	−1.11280
$782$	−19.9577	−0.713685
$783$	−11.0570	−0.395145
$784$	34.9044	1.24658
$785$	6.84318	0.244244
$786$	4.14627	0.147892
$787$	44.8561	1.59895	0.799473	−	0.600702i	$-0.205112\pi$
$787$	44.8561	1.59895	0.799473	+	0.600702i	$0.205112\pi$
$788$	58.4817	2.08332
$789$	3.40978	0.121391
$790$	−1.85484	−0.0659921
$791$	28.5604	1.01549
$792$	46.5671	1.65469
$793$	4.54752	0.161487
$794$	−80.3871	−2.85283
$795$	−3.50761	−0.124402
$796$	58.2373	2.06417
$797$	23.4702	0.831358	0.415679	−	0.909511i	$-0.363544\pi$
$797$	23.4702	0.831358	0.415679	+	0.909511i	$0.363544\pi$
$798$	6.87385	0.243332
$799$	−9.11914	−0.322612
$800$	−0.0123047	−0.000435038 0
$801$	−46.6537	−1.64843
$802$	−91.2351	−3.22162
$803$	−32.9709	−1.16352
$804$	−2.82915	−0.0997765
$805$	47.1925	1.66332
$806$	−102.451	−3.60869
$807$	0.0469000	0.00165096
$808$	−15.4130	−0.542229
$809$	−19.3807	−0.681387	−0.340694	−	0.940174i	$-0.610662\pi$
$809$	−19.3807	−0.681387	−0.340694	+	0.940174i	$0.610662\pi$
$810$	−31.0019	−1.08930
$811$	5.17798	0.181823	0.0909117	−	0.995859i	$-0.471022\pi$
$811$	5.17798	0.181823	0.0909117	+	0.995859i	$0.471022\pi$
$812$	−152.734	−5.35991
$813$	2.10108	0.0736881
$814$	58.6144	2.05443
$815$	−28.4120	−0.995231
$816$	−0.769874	−0.0269510
$817$	20.8686	0.730101
$818$	22.7574	0.795693
$819$	60.1301	2.10112
$820$	48.1554	1.68166
$821$	−23.4297	−0.817701	−0.408851	−	0.912601i	$-0.634070\pi$
$821$	−23.4297	−0.817701	−0.408851	+	0.912601i	$0.634070\pi$
$822$	−6.97172	−0.243167
$823$	34.4428	1.20060	0.600300	−	0.799775i	$-0.295048\pi$
$823$	34.4428	1.20060	0.600300	+	0.799775i	$0.295048\pi$
$824$	−95.0281	−3.31046
$825$	−1.77228	−0.0617028
$826$	−59.3853	−2.06628
$827$	27.0627	0.941063	0.470531	−	0.882383i	$-0.344062\pi$
$827$	27.0627	0.941063	0.470531	+	0.882383i	$0.344062\pi$
$828$	96.5563	3.35556
$829$	−32.3660	−1.12412	−0.562060	−	0.827097i	$-0.689991\pi$
$829$	−32.3660	−1.12412	−0.562060	+	0.827097i	$0.689991\pi$
$830$	26.1360	0.907194
$831$	−1.08814	−0.0377471
$832$	−40.9600	−1.42003
$833$	−8.73182	−0.302540
$834$	−7.18770	−0.248890
$835$	−16.9944	−0.588114
$836$	47.1503	1.63073
$837$	−9.38805	−0.324499
$838$	−15.2769	−0.527731
$839$	38.2524	1.32062	0.660310	−	0.750993i	$-0.270425\pi$
$839$	38.2524	1.32062	0.660310	+	0.750993i	$0.270425\pi$
$840$	5.46339	0.188505
$841$	63.6974	2.19646
$842$	10.1320	0.349172
$843$	−0.0413192	−0.00142311
$844$	29.1244	1.00250
$845$	19.2463	0.662093
$846$	66.1807	2.27534
$847$	2.78626	0.0957371
$848$	−49.8549	−1.71202
$849$	−4.05290	−0.139095
$850$	−7.02392	−0.240919
$851$	60.7614	2.08287
$852$	−7.46507	−0.255749
$853$	−15.2598	−0.522486	−0.261243	−	0.965273i	$-0.584132\pi$
$853$	−15.2598	−0.522486	−0.261243	+	0.965273i	$0.584132\pi$
$854$	8.63455	0.295468
$855$	−15.8949	−0.543593
$856$	−4.68934	−0.160278
$857$	54.0751	1.84717	0.923584	−	0.383395i	$-0.125245\pi$
$857$	54.0751	1.84717	0.923584	+	0.383395i	$0.125245\pi$
$858$	−7.74561	−0.264431
$859$	7.34739	0.250690	0.125345	−	0.992113i	$-0.459996\pi$
$859$	7.34739	0.250690	0.125345	+	0.992113i	$0.459996\pi$
$860$	33.1768	1.13132
$861$	−6.29845	−0.214651
$862$	9.47920	0.322863
$863$	9.13833	0.311073	0.155536	−	0.987830i	$-0.450289\pi$
$863$	9.13833	0.311073	0.155536	+	0.987830i	$0.450289\pi$
$864$	−0.00492782	−0.000167648 0
$865$	−0.424313	−0.0144271
$866$	−1.76477	−0.0599694
$867$	0.192595	0.00654087
$868$	−129.680	−4.40164
$869$	1.66410	0.0564507
$870$	−6.63242	−0.224860
$871$	−18.7924	−0.636758
$872$	96.2818	3.26051
$873$	7.68536	0.260110
$874$	73.3188	2.48005
$875$	45.5686	1.54050
$876$	−7.91446	−0.267405
$877$	−22.2798	−0.752335	−0.376168	−	0.926552i	$-0.622758\pi$
$877$	−22.2798	−0.752335	−0.376168	+	0.926552i	$0.622758\pi$
$878$	85.1831	2.87479
$879$	−1.72360	−0.0581356
$880$	18.7316	0.631441
$881$	−25.5340	−0.860263	−0.430131	−	0.902766i	$-0.641533\pi$
$881$	−25.5340	−0.860263	−0.430131	+	0.902766i	$0.641533\pi$
$882$	63.3699	2.13377
$883$	−5.19272	−0.174749	−0.0873745	−	0.996176i	$-0.527848\pi$
$883$	−5.19272	−0.174749	−0.0873745	+	0.996176i	$0.527848\pi$
$884$	−20.4643	−0.688289
$885$	−1.71913	−0.0577878
$886$	38.8363	1.30473
$887$	−34.6634	−1.16388	−0.581942	−	0.813231i	$-0.697707\pi$
$887$	−34.6634	−1.16388	−0.581942	+	0.813231i	$0.697707\pi$
$888$	7.03425	0.236054
$889$	−78.0989	−2.61935
$890$	−56.3198	−1.88784
$891$	27.8139	0.931801
$892$	53.7253	1.79886
$893$	33.5011	1.12107
$894$	−2.04676	−0.0684539
$895$	21.0740	0.704426
$896$	−77.7382	−2.59705
$897$	−8.02933	−0.268092
$898$	16.6385	0.555235
$899$	78.7057	2.62498
$900$	33.9821	1.13274
$901$	12.4719	0.415500
$902$	−64.8075	−2.15785
$903$	−4.33933	−0.144404
$904$	35.2670	1.17296
$905$	23.9163	0.795006
$906$	5.80553	0.192876
$907$	−27.3658	−0.908668	−0.454334	−	0.890832i	$-0.650123\pi$
$907$	−27.3658	−0.908668	−0.454334	+	0.890832i	$0.650123\pi$
$908$	85.1458	2.82566
$909$	−9.32421	−0.309264
$910$	72.5884	2.40628
$911$	−15.9220	−0.527520	−0.263760	−	0.964588i	$-0.584963\pi$
$911$	−15.9220	−0.527520	−0.263760	+	0.964588i	$0.584963\pi$
$912$	2.82830	0.0936543
$913$	−23.4484	−0.776027
$914$	11.4999	0.380382
$915$	0.249959	0.00826339
$916$	−88.0901	−2.91058
$917$	34.8612	1.15122
$918$	−2.81296	−0.0928414
$919$	−15.6312	−0.515627	−0.257814	−	0.966195i	$-0.583002\pi$
$919$	−15.6312	−0.515627	−0.257814	+	0.966195i	$0.583002\pi$
$920$	58.2744	1.92125
$921$	−2.48134	−0.0817628
$922$	32.0503	1.05552
$923$	−49.5862	−1.63215
$924$	−9.80423	−0.322535
$925$	21.3844	0.703116
$926$	−14.8854	−0.489164
$927$	−57.4878	−1.88815
$928$	0.0413129	0.00135616
$929$	−9.40043	−0.308418	−0.154209	−	0.988038i	$-0.549283\pi$
$929$	−9.40043	−0.308418	−0.154209	+	0.988038i	$0.549283\pi$
$930$	−5.63133	−0.184658
$931$	32.0782	1.05132
$932$	28.6487	0.938418
$933$	5.77715	0.189136
$934$	−89.7464	−2.93659
$935$	−4.68597	−0.153248
$936$	74.2501	2.42694
$937$	2.48267	0.0811054	0.0405527	−	0.999177i	$-0.487088\pi$
$937$	2.48267	0.0811054	0.0405527	+	0.999177i	$0.487088\pi$
$938$	−35.6819	−1.16506
$939$	−2.27986	−0.0744005
$940$	53.2598	1.73714
$941$	−16.9931	−0.553960	−0.276980	−	0.960876i	$-0.589334\pi$
$941$	−16.9931	−0.553960	−0.276980	+	0.960876i	$0.589334\pi$
$942$	−2.21070	−0.0720285
$943$	−67.1814	−2.18773
$944$	−24.4345	−0.795276
$945$	6.65160	0.216376
$946$	−44.6493	−1.45167
$947$	−22.2843	−0.724143	−0.362072	−	0.932150i	$-0.617930\pi$
$947$	−22.2843	−0.724143	−0.362072	+	0.932150i	$0.617930\pi$
$948$	0.399457	0.0129738
$949$	−52.5712	−1.70653
$950$	25.8039	0.837189
$951$	0.626758	0.0203240
$952$	−19.4260	−0.629601
$953$	27.5107	0.891159	0.445579	−	0.895242i	$-0.352998\pi$
$953$	27.5107	0.891159	0.445579	+	0.895242i	$0.352998\pi$
$954$	−90.5130	−2.93047
$955$	−25.5220	−0.825871
$956$	32.9006	1.06408
$957$	5.95039	0.192349
$958$	−96.4903	−3.11746
$959$	−58.6171	−1.89285
$960$	−2.25140	−0.0726638
$961$	35.8259	1.15567
$962$	93.4592	3.01325
$963$	−2.83684	−0.0914160
$964$	11.9060	0.383465
$965$	7.44037	0.239514
$966$	−15.2456	−0.490519
$967$	60.6327	1.94982	0.974908	−	0.222608i	$-0.0714569\pi$
$967$	60.6327	1.94982	0.974908	+	0.222608i	$0.0714569\pi$
$968$	3.44054	0.110583
$969$	−0.707539	−0.0227294
$970$	9.27768	0.297888
$971$	−22.4098	−0.719164	−0.359582	−	0.933113i	$-0.617081\pi$
$971$	−22.4098	−0.719164	−0.359582	+	0.933113i	$0.617081\pi$
$972$	20.4562	0.656132
$973$	−60.4331	−1.93740
$974$	53.6537	1.71918
$975$	−2.82585	−0.0904997
$976$	3.55275	0.113721
$977$	10.9135	0.349154	0.174577	−	0.984644i	$-0.444144\pi$
$977$	10.9135	0.349154	0.174577	+	0.984644i	$0.444144\pi$
$978$	9.17855	0.293498
$979$	50.5282	1.61489
$980$	50.9977	1.62906
$981$	58.2462	1.85966
$982$	−36.2216	−1.15588
$983$	−23.2106	−0.740304	−0.370152	−	0.928971i	$-0.620694\pi$
$983$	−23.2106	−0.740304	−0.370152	+	0.928971i	$0.620694\pi$
$984$	−7.77748	−0.247937
$985$	21.3521	0.680335
$986$	23.5827	0.751026
$987$	−6.96608	−0.221733
$988$	75.1800	2.39180
$989$	−46.2848	−1.47177
$990$	34.0077	1.08084
$991$	32.5276	1.03327	0.516636	−	0.856205i	$-0.327184\pi$
$991$	32.5276	1.03327	0.516636	+	0.856205i	$0.327184\pi$
$992$	0.0350772	0.00111370
$993$	5.26412	0.167052
$994$	−94.1511	−2.98629
$995$	21.2629	0.674079
$996$	−5.62864	−0.178350
$997$	13.0285	0.412617	0.206308	−	0.978487i	$-0.433855\pi$
$997$	13.0285	0.412617	0.206308	+	0.978487i	$0.433855\pi$
$998$	33.2466	1.05240
$999$	8.56408	0.270956

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6001.2.a.c.1.11	✓	121

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6001.2.a.c.1.11	✓	121	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:	\( N \)	\(=\)	\( 6001 = 17 \cdot 353 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6001.a (trivial)

\(f(q)\)	\(=\)	\(q-2.44940 q^{2} +0.192595 q^{3} +3.99956 q^{4} +1.46027 q^{5} -0.471742 q^{6} -3.96634 q^{7} -4.89773 q^{8} -2.96291 q^{9} +O(q^{10})\)	\(q-2.44940 q^{2} +0.192595 q^{3} +3.99956 q^{4} +1.46027 q^{5} -0.471742 q^{6} -3.96634 q^{7} -4.89773 q^{8} -2.96291 q^{9} -3.57679 q^{10} +3.20898 q^{11} +0.770296 q^{12} +5.11663 q^{13} +9.71515 q^{14} +0.281241 q^{15} +3.99737 q^{16} -1.00000 q^{17} +7.25735 q^{18} +3.67372 q^{19} +5.84044 q^{20} -0.763897 q^{21} -7.86007 q^{22} -8.14798 q^{23} -0.943278 q^{24} -2.86761 q^{25} -12.5327 q^{26} -1.14843 q^{27} -15.8636 q^{28} +9.62795 q^{29} -0.688871 q^{30} +8.17471 q^{31} +0.00429093 q^{32} +0.618033 q^{33} +2.44940 q^{34} -5.79192 q^{35} -11.8503 q^{36} -7.45724 q^{37} -8.99840 q^{38} +0.985438 q^{39} -7.15201 q^{40} +8.24516 q^{41} +1.87109 q^{42} +5.68052 q^{43} +12.8345 q^{44} -4.32665 q^{45} +19.9577 q^{46} +9.11914 q^{47} +0.769874 q^{48} +8.73182 q^{49} +7.02392 q^{50} -0.192595 q^{51} +20.4643 q^{52} -12.4719 q^{53} +2.81296 q^{54} +4.68597 q^{55} +19.4260 q^{56} +0.707539 q^{57} -23.5827 q^{58} -6.11265 q^{59} +1.12484 q^{60} +0.888772 q^{61} -20.0231 q^{62} +11.7519 q^{63} -8.00525 q^{64} +7.47167 q^{65} -1.51381 q^{66} -3.67281 q^{67} -3.99956 q^{68} -1.56926 q^{69} +14.1867 q^{70} -9.69117 q^{71} +14.5115 q^{72} -10.2746 q^{73} +18.2658 q^{74} -0.552287 q^{75} +14.6933 q^{76} -12.7279 q^{77} -2.41373 q^{78} +0.518576 q^{79} +5.83724 q^{80} +8.66754 q^{81} -20.1957 q^{82} -7.30712 q^{83} -3.05525 q^{84} -1.46027 q^{85} -13.9139 q^{86} +1.85429 q^{87} -15.7167 q^{88} +15.7459 q^{89} +10.5977 q^{90} -20.2943 q^{91} -32.5884 q^{92} +1.57441 q^{93} -22.3364 q^{94} +5.36462 q^{95} +0.000826413 q^{96} -2.59386 q^{97} -21.3877 q^{98} -9.50790 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 121 q + 9 q^{2} + 13 q^{3} + 127 q^{4} + 21 q^{5} + 19 q^{6} - 13 q^{7} + 24 q^{8} + 134 q^{9}+O(q^{10}) \) 121 * q + 9 * q^2 + 13 * q^3 + 127 * q^4 + 21 * q^5 + 19 * q^6 - 13 * q^7 + 24 * q^8 + 134 * q^9	\( 121 q + 9 q^{2} + 13 q^{3} + 127 q^{4} + 21 q^{5} + 19 q^{6} - 13 q^{7} + 24 q^{8} + 134 q^{9} - q^{10} + 40 q^{11} + 41 q^{12} + 14 q^{13} + 32 q^{14} + 49 q^{15} + 135 q^{16} - 121 q^{17} + 28 q^{18} + 34 q^{19} + 64 q^{20} + 34 q^{21} - 18 q^{22} + 37 q^{23} + 54 q^{24} + 128 q^{25} + 91 q^{26} + 55 q^{27} - 28 q^{28} + 45 q^{29} + 30 q^{30} + 67 q^{31} + 47 q^{32} + 40 q^{33} - 9 q^{34} + 59 q^{35} + 138 q^{36} - 16 q^{37} + 30 q^{38} + 37 q^{39} + 14 q^{40} + 89 q^{41} + 33 q^{42} + 16 q^{43} + 90 q^{44} + 83 q^{45} - 9 q^{46} + 135 q^{47} + 96 q^{48} + 128 q^{49} + 71 q^{50} - 13 q^{51} + 47 q^{52} + 52 q^{53} + 90 q^{54} + 93 q^{55} + 69 q^{56} - 4 q^{57} + 5 q^{58} + 170 q^{59} + 78 q^{60} - 2 q^{61} + 46 q^{62} - 10 q^{63} + 182 q^{64} + 50 q^{65} + 68 q^{66} + 46 q^{67} - 127 q^{68} + 97 q^{69} + 46 q^{70} + 191 q^{71} + 57 q^{72} - 12 q^{73} + 68 q^{74} + 86 q^{75} + 108 q^{76} + 62 q^{77} - 10 q^{78} + 130 q^{80} + 149 q^{81} + 14 q^{82} + 83 q^{83} + 126 q^{84} - 21 q^{85} + 132 q^{86} + 50 q^{87} - 42 q^{88} + 144 q^{89} + 9 q^{90} + 13 q^{91} + 50 q^{92} + 43 q^{93} + 41 q^{94} + 82 q^{95} + 110 q^{96} - 3 q^{97} + 36 q^{98} + 89 q^{99}+O(q^{100}) \) 121 * q + 9 * q^2 + 13 * q^3 + 127 * q^4 + 21 * q^5 + 19 * q^6 - 13 * q^7 + 24 * q^8 + 134 * q^9 - q^10 + 40 * q^11 + 41 * q^12 + 14 * q^13 + 32 * q^14 + 49 * q^15 + 135 * q^16 - 121 * q^17 + 28 * q^18 + 34 * q^19 + 64 * q^20 + 34 * q^21 - 18 * q^22 + 37 * q^23 + 54 * q^24 + 128 * q^25 + 91 * q^26 + 55 * q^27 - 28 * q^28 + 45 * q^29 + 30 * q^30 + 67 * q^31 + 47 * q^32 + 40 * q^33 - 9 * q^34 + 59 * q^35 + 138 * q^36 - 16 * q^37 + 30 * q^38 + 37 * q^39 + 14 * q^40 + 89 * q^41 + 33 * q^42 + 16 * q^43 + 90 * q^44 + 83 * q^45 - 9 * q^46 + 135 * q^47 + 96 * q^48 + 128 * q^49 + 71 * q^50 - 13 * q^51 + 47 * q^52 + 52 * q^53 + 90 * q^54 + 93 * q^55 + 69 * q^56 - 4 * q^57 + 5 * q^58 + 170 * q^59 + 78 * q^60 - 2 * q^61 + 46 * q^62 - 10 * q^63 + 182 * q^64 + 50 * q^65 + 68 * q^66 + 46 * q^67 - 127 * q^68 + 97 * q^69 + 46 * q^70 + 191 * q^71 + 57 * q^72 - 12 * q^73 + 68 * q^74 + 86 * q^75 + 108 * q^76 + 62 * q^77 - 10 * q^78 + 130 * q^80 + 149 * q^81 + 14 * q^82 + 83 * q^83 + 126 * q^84 - 21 * q^85 + 132 * q^86 + 50 * q^87 - 42 * q^88 + 144 * q^89 + 9 * q^90 + 13 * q^91 + 50 * q^92 + 43 * q^93 + 41 * q^94 + 82 * q^95 + 110 * q^96 - 3 * q^97 + 36 * q^98 + 89 * q^99

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