LMFDB - Embedded newform 6017.2.a.e.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6017,2,Mod(1,6017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6017, 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("6017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6017 = 11 \cdot 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6017.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:	$48.0459868962$
Analytic rank:	$0$
Dimension:	$119$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	6017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.30862 q^{2} +2.25355 q^{3} +3.32972 q^{4} +2.61387 q^{5} -5.20258 q^{6} +1.15866 q^{7} -3.06981 q^{8} +2.07847 q^{9} +O(q^{10})$	\(q-2.30862 q^{2} +2.25355 q^{3} +3.32972 q^{4} +2.61387 q^{5} -5.20258 q^{6} +1.15866 q^{7} -3.06981 q^{8} +2.07847 q^{9} -6.03443 q^{10} +1.00000 q^{11} +7.50367 q^{12} -3.08433 q^{13} -2.67491 q^{14} +5.89048 q^{15} +0.427577 q^{16} +5.18502 q^{17} -4.79840 q^{18} +6.66365 q^{19} +8.70344 q^{20} +2.61110 q^{21} -2.30862 q^{22} +0.358047 q^{23} -6.91795 q^{24} +1.83231 q^{25} +7.12054 q^{26} -2.07670 q^{27} +3.85802 q^{28} +6.63154 q^{29} -13.5989 q^{30} +1.31367 q^{31} +5.15250 q^{32} +2.25355 q^{33} -11.9702 q^{34} +3.02859 q^{35} +6.92073 q^{36} +3.70297 q^{37} -15.3838 q^{38} -6.95068 q^{39} -8.02407 q^{40} +11.4928 q^{41} -6.02803 q^{42} +5.74447 q^{43} +3.32972 q^{44} +5.43286 q^{45} -0.826595 q^{46} -2.05309 q^{47} +0.963565 q^{48} -5.65750 q^{49} -4.23011 q^{50} +11.6847 q^{51} -10.2699 q^{52} +2.78581 q^{53} +4.79431 q^{54} +2.61387 q^{55} -3.55687 q^{56} +15.0168 q^{57} -15.3097 q^{58} -10.4090 q^{59} +19.6136 q^{60} -3.38271 q^{61} -3.03275 q^{62} +2.40825 q^{63} -12.7503 q^{64} -8.06204 q^{65} -5.20258 q^{66} +5.45542 q^{67} +17.2647 q^{68} +0.806877 q^{69} -6.99186 q^{70} -3.35739 q^{71} -6.38051 q^{72} -10.5372 q^{73} -8.54874 q^{74} +4.12920 q^{75} +22.1881 q^{76} +1.15866 q^{77} +16.0465 q^{78} +0.945116 q^{79} +1.11763 q^{80} -10.9154 q^{81} -26.5325 q^{82} -9.20239 q^{83} +8.69422 q^{84} +13.5530 q^{85} -13.2618 q^{86} +14.9445 q^{87} -3.06981 q^{88} +0.250810 q^{89} -12.5424 q^{90} -3.57370 q^{91} +1.19220 q^{92} +2.96041 q^{93} +4.73980 q^{94} +17.4179 q^{95} +11.6114 q^{96} +3.05638 q^{97} +13.0610 q^{98} +2.07847 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 119 q + 15 q^{2} + 15 q^{3} + 133 q^{4} + 6 q^{5} + 16 q^{6} + 72 q^{7} + 39 q^{8} + 128 q^{9}+O(q^{10}) $ 119 * q + 15 * q^2 + 15 * q^3 + 133 * q^4 + 6 * q^5 + 16 * q^6 + 72 * q^7 + 39 * q^8 + 128 * q^9	\( 119 q + 15 q^{2} + 15 q^{3} + 133 q^{4} + 6 q^{5} + 16 q^{6} + 72 q^{7} + 39 q^{8} + 128 q^{9} + 22 q^{10} + 119 q^{11} + 40 q^{12} + 67 q^{13} + 3 q^{14} + 22 q^{15} + 145 q^{16} + 57 q^{17} + 53 q^{18} + 68 q^{19} + 25 q^{20} + 21 q^{21} + 15 q^{22} + 21 q^{23} + 34 q^{24} + 137 q^{25} + 10 q^{26} + 54 q^{27} + 149 q^{28} + 46 q^{29} + 10 q^{30} + 87 q^{31} + 58 q^{32} + 15 q^{33} + 16 q^{34} + 40 q^{35} + 137 q^{36} + 39 q^{37} + 27 q^{38} + 72 q^{39} + 46 q^{40} + 50 q^{41} - 4 q^{42} + 122 q^{43} + 133 q^{44} + 12 q^{45} + 22 q^{46} + 92 q^{47} + 9 q^{48} + 161 q^{49} + 2 q^{50} - 12 q^{51} + 177 q^{52} + 12 q^{53} + 19 q^{54} + 6 q^{55} - 16 q^{56} + 43 q^{57} + 56 q^{58} + 39 q^{59} + 27 q^{60} + 114 q^{61} + 66 q^{62} + 196 q^{63} + 161 q^{64} + 7 q^{65} + 16 q^{66} + 59 q^{67} + 139 q^{68} - 24 q^{69} + 9 q^{70} + 11 q^{71} + 92 q^{72} + 123 q^{73} + q^{74} + 19 q^{75} + 92 q^{76} + 72 q^{77} - 101 q^{78} + 78 q^{79} - 34 q^{80} + 139 q^{81} + 73 q^{82} + 108 q^{83} - 31 q^{84} + 30 q^{85} - 18 q^{86} + 164 q^{87} + 39 q^{88} + 15 q^{89} - 41 q^{90} + 60 q^{91} - 26 q^{92} - 2 q^{93} + 45 q^{94} + 75 q^{95} + 42 q^{96} + 73 q^{97} + 32 q^{98} + 128 q^{99}+O(q^{100}) \) 119 * q + 15 * q^2 + 15 * q^3 + 133 * q^4 + 6 * q^5 + 16 * q^6 + 72 * q^7 + 39 * q^8 + 128 * q^9 + 22 * q^10 + 119 * q^11 + 40 * q^12 + 67 * q^13 + 3 * q^14 + 22 * q^15 + 145 * q^16 + 57 * q^17 + 53 * q^18 + 68 * q^19 + 25 * q^20 + 21 * q^21 + 15 * q^22 + 21 * q^23 + 34 * q^24 + 137 * q^25 + 10 * q^26 + 54 * q^27 + 149 * q^28 + 46 * q^29 + 10 * q^30 + 87 * q^31 + 58 * q^32 + 15 * q^33 + 16 * q^34 + 40 * q^35 + 137 * q^36 + 39 * q^37 + 27 * q^38 + 72 * q^39 + 46 * q^40 + 50 * q^41 - 4 * q^42 + 122 * q^43 + 133 * q^44 + 12 * q^45 + 22 * q^46 + 92 * q^47 + 9 * q^48 + 161 * q^49 + 2 * q^50 - 12 * q^51 + 177 * q^52 + 12 * q^53 + 19 * q^54 + 6 * q^55 - 16 * q^56 + 43 * q^57 + 56 * q^58 + 39 * q^59 + 27 * q^60 + 114 * q^61 + 66 * q^62 + 196 * q^63 + 161 * q^64 + 7 * q^65 + 16 * q^66 + 59 * q^67 + 139 * q^68 - 24 * q^69 + 9 * q^70 + 11 * q^71 + 92 * q^72 + 123 * q^73 + q^74 + 19 * q^75 + 92 * q^76 + 72 * q^77 - 101 * q^78 + 78 * q^79 - 34 * q^80 + 139 * q^81 + 73 * q^82 + 108 * q^83 - 31 * q^84 + 30 * q^85 - 18 * q^86 + 164 * q^87 + 39 * q^88 + 15 * q^89 - 41 * q^90 + 60 * q^91 - 26 * q^92 - 2 * q^93 + 45 * q^94 + 75 * q^95 + 42 * q^96 + 73 * q^97 + 32 * q^98 + 128 * 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 $

$2$	−2.30862	−1.63244	−0.816220	−	0.577742i	$-0.803934\pi$
$2$	−2.30862	−1.63244	−0.816220	+	0.577742i	$0.803934\pi$
$3$	2.25355	1.30109	0.650543	−	0.759469i	$-0.274541\pi$
$3$	2.25355	1.30109	0.650543	+	0.759469i	$0.274541\pi$
$4$	3.32972	1.66486
$5$	2.61387	1.16896	0.584479	−	0.811409i	$-0.301299\pi$
$5$	2.61387	1.16896	0.584479	+	0.811409i	$0.301299\pi$
$6$	−5.20258	−2.12394
$7$	1.15866	0.437933	0.218967	−	0.975732i	$-0.429731\pi$
$7$	1.15866	0.437933	0.218967	+	0.975732i	$0.429731\pi$
$8$	−3.06981	−1.08534
$9$	2.07847	0.692825
$10$	−6.03443	−1.90825
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	7.50367	2.16612
$13$	−3.08433	−0.855439	−0.427720	−	0.903911i	$-0.640683\pi$
$13$	−3.08433	−0.855439	−0.427720	+	0.903911i	$0.640683\pi$
$14$	−2.67491	−0.714900
$15$	5.89048	1.52091
$16$	0.427577	0.106894
$17$	5.18502	1.25755	0.628777	−	0.777586i	$-0.283556\pi$
$17$	5.18502	1.25755	0.628777	+	0.777586i	$0.283556\pi$
$18$	−4.79840	−1.13099
$19$	6.66365	1.52875	0.764373	−	0.644774i	$-0.223049\pi$
$19$	6.66365	1.52875	0.764373	+	0.644774i	$0.223049\pi$
$20$	8.70344	1.94615
$21$	2.61110	0.569789
$22$	−2.30862	−0.492199
$23$	0.358047	0.0746581	0.0373290	−	0.999303i	$-0.488115\pi$
$23$	0.358047	0.0746581	0.0373290	+	0.999303i	$0.488115\pi$
$24$	−6.91795	−1.41212
$25$	1.83231	0.366463
$26$	7.12054	1.39645
$27$	−2.07670	−0.399661
$28$	3.85802	0.729097
$29$	6.63154	1.23145	0.615723	−	0.787962i	$-0.288864\pi$
$29$	6.63154	1.23145	0.615723	+	0.787962i	$0.288864\pi$
$30$	−13.5989	−2.48280
$31$	1.31367	0.235942	0.117971	−	0.993017i	$-0.462361\pi$
$31$	1.31367	0.235942	0.117971	+	0.993017i	$0.462361\pi$
$32$	5.15250	0.910842
$33$	2.25355	0.392292
$34$	−11.9702	−2.05288
$35$	3.02859	0.511926
$36$	6.92073	1.15345
$37$	3.70297	0.608764	0.304382	−	0.952550i	$-0.401550\pi$
$37$	3.70297	0.608764	0.304382	+	0.952550i	$0.401550\pi$
$38$	−15.3838	−2.49559
$39$	−6.95068	−1.11300
$40$	−8.02407	−1.26872
$41$	11.4928	1.79487	0.897437	−	0.441143i	$-0.145427\pi$
$41$	11.4928	1.79487	0.897437	+	0.441143i	$0.145427\pi$
$42$	−6.02803	−0.930146
$43$	5.74447	0.876024	0.438012	−	0.898969i	$-0.355683\pi$
$43$	5.74447	0.876024	0.438012	+	0.898969i	$0.355683\pi$
$44$	3.32972	0.501974
$45$	5.43286	0.809883
$46$	−0.826595	−0.121875
$47$	−2.05309	−0.299474	−0.149737	−	0.988726i	$-0.547843\pi$
$47$	−2.05309	−0.299474	−0.149737	+	0.988726i	$0.547843\pi$
$48$	0.963565	0.139079
$49$	−5.65750	−0.808214
$50$	−4.23011	−0.598228
$51$	11.6847	1.63618
$52$	−10.2699	−1.42419
$53$	2.78581	0.382661	0.191330	−	0.981526i	$-0.438720\pi$
$53$	2.78581	0.382661	0.191330	+	0.981526i	$0.438720\pi$
$54$	4.79431	0.652423
$55$	2.61387	0.352454
$56$	−3.55687	−0.475307
$57$	15.0168	1.98903
$58$	−15.3097	−2.01026
$59$	−10.4090	−1.35514	−0.677570	−	0.735458i	$-0.736967\pi$
$59$	−10.4090	−1.35514	−0.677570	+	0.735458i	$0.736967\pi$
$60$	19.6136	2.53211
$61$	−3.38271	−0.433111	−0.216556	−	0.976270i	$-0.569482\pi$
$61$	−3.38271	−0.433111	−0.216556	+	0.976270i	$0.569482\pi$
$62$	−3.03275	−0.385160
$63$	2.40825	0.303411
$64$	−12.7503	−1.59379
$65$	−8.06204	−0.999973
$66$	−5.20258	−0.640393
$67$	5.45542	0.666486	0.333243	−	0.942841i	$-0.391857\pi$
$67$	5.45542	0.666486	0.333243	+	0.942841i	$0.391857\pi$
$68$	17.2647	2.09365
$69$	0.806877	0.0971365
$70$	−6.99186	−0.835687
$71$	−3.35739	−0.398449	−0.199225	−	0.979954i	$-0.563842\pi$
$71$	−3.35739	−0.398449	−0.199225	+	0.979954i	$0.563842\pi$
$72$	−6.38051	−0.751951
$73$	−10.5372	−1.23329	−0.616645	−	0.787241i	$-0.711509\pi$
$73$	−10.5372	−1.23329	−0.616645	+	0.787241i	$0.711509\pi$
$74$	−8.54874	−0.993771
$75$	4.12920	0.476799
$76$	22.1881	2.54515
$77$	1.15866	0.132042
$78$	16.0465	1.81691
$79$	0.945116	0.106334	0.0531669	−	0.998586i	$-0.483068\pi$
$79$	0.945116	0.106334	0.0531669	+	0.998586i	$0.483068\pi$
$80$	1.11763	0.124955
$81$	−10.9154	−1.21282
$82$	−26.5325	−2.93002
$83$	−9.20239	−1.01009	−0.505047	−	0.863092i	$-0.668525\pi$
$83$	−9.20239	−1.01009	−0.505047	+	0.863092i	$0.668525\pi$
$84$	8.69422	0.948618
$85$	13.5530	1.47003
$86$	−13.2618	−1.43006
$87$	14.9445	1.60222
$88$	−3.06981	−0.327242
$89$	0.250810	0.0265858	0.0132929	−	0.999912i	$-0.495769\pi$
$89$	0.250810	0.0265858	0.0132929	+	0.999912i	$0.495769\pi$
$90$	−12.5424	−1.32208
$91$	−3.57370	−0.374625
$92$	1.19220	0.124295
$93$	2.96041	0.306980
$94$	4.73980	0.488873
$95$	17.4179	1.78704
$96$	11.6114	1.18508
$97$	3.05638	0.310328	0.155164	−	0.987889i	$-0.450409\pi$
$97$	3.05638	0.310328	0.155164	+	0.987889i	$0.450409\pi$
$98$	13.0610	1.31936
$99$	2.07847	0.208895
$100$	6.10108	0.610108
$101$	1.22352	0.121745	0.0608725	−	0.998146i	$-0.480612\pi$
$101$	1.22352	0.121745	0.0608725	+	0.998146i	$0.480612\pi$
$102$	−26.9755	−2.67097
$103$	−9.81993	−0.967587	−0.483793	−	0.875182i	$-0.660741\pi$
$103$	−9.81993	−0.967587	−0.483793	+	0.875182i	$0.660741\pi$
$104$	9.46830	0.928443
$105$	6.82508	0.666059
$106$	−6.43138	−0.624670
$107$	−7.82789	−0.756750	−0.378375	−	0.925652i	$-0.623517\pi$
$107$	−7.82789	−0.756750	−0.378375	+	0.925652i	$0.623517\pi$
$108$	−6.91483	−0.665379
$109$	−15.1175	−1.44799	−0.723997	−	0.689803i	$-0.757697\pi$
$109$	−15.1175	−1.44799	−0.723997	+	0.689803i	$0.757697\pi$
$110$	−6.03443	−0.575360
$111$	8.34482	0.792055
$112$	0.495418	0.0468126
$113$	0.721370	0.0678608	0.0339304	−	0.999424i	$-0.489198\pi$
$113$	0.721370	0.0678608	0.0339304	+	0.999424i	$0.489198\pi$
$114$	−34.6682	−3.24697
$115$	0.935889	0.0872721
$116$	22.0812	2.05018
$117$	−6.41070	−0.592670
$118$	24.0305	2.21218
$119$	6.00769	0.550724
$120$	−18.0826	−1.65071
$121$	1.00000	0.0909091
$122$	7.80938	0.707028
$123$	25.8996	2.33528
$124$	4.37414	0.392809
$125$	−8.27992	−0.740578
$126$	−5.55973	−0.495300
$127$	21.6420	1.92042	0.960211	−	0.279277i	$-0.0900948\pi$
$127$	21.6420	1.92042	0.960211	+	0.279277i	$0.0900948\pi$
$128$	19.1306	1.69092
$129$	12.9454	1.13978
$130$	18.6122	1.63239
$131$	−11.2957	−0.986910	−0.493455	−	0.869771i	$-0.664266\pi$
$131$	−11.2957	−0.986910	−0.493455	+	0.869771i	$0.664266\pi$
$132$	7.50367	0.653111
$133$	7.72092	0.669489
$134$	−12.5945	−1.08800
$135$	−5.42823	−0.467187
$136$	−15.9170	−1.36487
$137$	6.40082	0.546859	0.273430	−	0.961892i	$-0.411842\pi$
$137$	6.40082	0.546859	0.273430	+	0.961892i	$0.411842\pi$
$138$	−1.86277	−0.158570
$139$	1.06902	0.0906732	0.0453366	−	0.998972i	$-0.485564\pi$
$139$	1.06902	0.0906732	0.0453366	+	0.998972i	$0.485564\pi$
$140$	10.0844	0.852283
$141$	−4.62673	−0.389641
$142$	7.75094	0.650444
$143$	−3.08433	−0.257925
$144$	0.888708	0.0740590
$145$	17.3340	1.43951
$146$	24.3264	2.01327
$147$	−12.7494	−1.05156
$148$	12.3298	1.01351
$149$	−8.29165	−0.679278	−0.339639	−	0.940556i	$-0.610305\pi$
$149$	−8.29165	−0.679278	−0.339639	+	0.940556i	$0.610305\pi$
$150$	−9.53275	−0.778346
$151$	8.69939	0.707946	0.353973	−	0.935256i	$-0.384830\pi$
$151$	8.69939	0.707946	0.353973	+	0.935256i	$0.384830\pi$
$152$	−20.4561	−1.65921
$153$	10.7769	0.871264
$154$	−2.67491	−0.215550
$155$	3.43375	0.275806
$156$	−23.1438	−1.85299
$157$	−23.8926	−1.90684	−0.953420	−	0.301646i	$-0.902464\pi$
$157$	−23.8926	−1.90684	−0.953420	+	0.301646i	$0.902464\pi$
$158$	−2.18191	−0.173584
$159$	6.27796	0.497875
$160$	13.4680	1.06474
$161$	0.414856	0.0326952
$162$	25.1994	1.97985
$163$	13.7198	1.07462	0.537308	−	0.843386i	$-0.319441\pi$
$163$	13.7198	1.07462	0.537308	+	0.843386i	$0.319441\pi$
$164$	38.2678	2.98821
$165$	5.89048	0.458573
$166$	21.2448	1.64892
$167$	−2.87321	−0.222336	−0.111168	−	0.993802i	$-0.535459\pi$
$167$	−2.87321	−0.222336	−0.111168	+	0.993802i	$0.535459\pi$
$168$	−8.01557	−0.618415
$169$	−3.48691	−0.268224
$170$	−31.2886	−2.39973
$171$	13.8502	1.05915
$172$	19.1275	1.45846
$173$	9.39129	0.714007	0.357003	−	0.934103i	$-0.383798\pi$
$173$	9.39129	0.714007	0.357003	+	0.934103i	$0.383798\pi$
$174$	−34.5011	−2.61552
$175$	2.12303	0.160486
$176$	0.427577	0.0322298
$177$	−23.4572	−1.76315
$178$	−0.579024	−0.0433997
$179$	17.7460	1.32640	0.663200	−	0.748442i	$-0.269198\pi$
$179$	17.7460	1.32640	0.663200	+	0.748442i	$0.269198\pi$
$180$	18.0899	1.34834
$181$	12.3440	0.917526	0.458763	−	0.888559i	$-0.348293\pi$
$181$	12.3440	0.917526	0.458763	+	0.888559i	$0.348293\pi$
$182$	8.25030	0.611553
$183$	−7.62309	−0.563515
$184$	−1.09914	−0.0810294
$185$	9.67908	0.711620
$186$	−6.83446	−0.501127
$187$	5.18502	0.379167
$188$	−6.83621	−0.498582
$189$	−2.40620	−0.175025
$190$	−40.2113	−2.91723
$191$	8.96093	0.648390	0.324195	−	0.945990i	$-0.394907\pi$
$191$	8.96093	0.648390	0.324195	+	0.945990i	$0.394907\pi$
$192$	−28.7334	−2.07366
$193$	−6.43232	−0.463008	−0.231504	−	0.972834i	$-0.574365\pi$
$193$	−6.43232	−0.463008	−0.231504	+	0.972834i	$0.574365\pi$
$194$	−7.05600	−0.506592
$195$	−18.1682	−1.30105
$196$	−18.8379	−1.34556
$197$	5.43028	0.386892	0.193446	−	0.981111i	$-0.438034\pi$
$197$	5.43028	0.386892	0.193446	+	0.981111i	$0.438034\pi$
$198$	−4.79840	−0.341008
$199$	19.9580	1.41479	0.707393	−	0.706821i	$-0.249871\pi$
$199$	19.9580	1.41479	0.707393	+	0.706821i	$0.249871\pi$
$200$	−5.62485	−0.397737
$201$	12.2941	0.867156
$202$	−2.82465	−0.198741
$203$	7.68372	0.539291
$204$	38.9067	2.72402
$205$	30.0407	2.09813
$206$	22.6705	1.57953
$207$	0.744192	0.0517249
$208$	−1.31879	−0.0914416
$209$	6.66365	0.460934
$210$	−15.7565	−1.08730
$211$	6.66955	0.459151	0.229575	−	0.973291i	$-0.426266\pi$
$211$	6.66955	0.459151	0.229575	+	0.973291i	$0.426266\pi$
$212$	9.27596	0.637076
$213$	−7.56604	−0.518417
$214$	18.0716	1.23535
$215$	15.0153	1.02404
$216$	6.37507	0.433769
$217$	1.52210	0.103327
$218$	34.9005	2.36376
$219$	−23.7461	−1.60462
$220$	8.70344	0.586786
$221$	−15.9923	−1.07576
$222$	−19.2650	−1.29298
$223$	−5.05326	−0.338391	−0.169196	−	0.985582i	$-0.554117\pi$
$223$	−5.05326	−0.338391	−0.169196	+	0.985582i	$0.554117\pi$
$224$	5.97001	0.398888
$225$	3.80842	0.253894
$226$	−1.66537	−0.110779
$227$	−3.89214	−0.258330	−0.129165	−	0.991623i	$-0.541230\pi$
$227$	−3.89214	−0.258330	−0.129165	+	0.991623i	$0.541230\pi$
$228$	50.0018	3.31145
$229$	13.1667	0.870083	0.435042	−	0.900410i	$-0.356734\pi$
$229$	13.1667	0.870083	0.435042	+	0.900410i	$0.356734\pi$
$230$	−2.16061	−0.142466
$231$	2.61110	0.171798
$232$	−20.3576	−1.33654
$233$	5.53935	0.362895	0.181448	−	0.983401i	$-0.441922\pi$
$233$	5.53935	0.362895	0.181448	+	0.983401i	$0.441922\pi$
$234$	14.7999	0.967497
$235$	−5.36651	−0.350072
$236$	−34.6591	−2.25612
$237$	2.12986	0.138349
$238$	−13.8695	−0.899024
$239$	−12.7929	−0.827506	−0.413753	−	0.910389i	$-0.635782\pi$
$239$	−12.7929	−0.827506	−0.413753	+	0.910389i	$0.635782\pi$
$240$	2.51863	0.162577
$241$	3.78682	0.243930	0.121965	−	0.992534i	$-0.461080\pi$
$241$	3.78682	0.243930	0.121965	+	0.992534i	$0.461080\pi$
$242$	−2.30862	−0.148404
$243$	−18.3682	−1.17832
$244$	−11.2635	−0.721069
$245$	−14.7880	−0.944769
$246$	−59.7922	−3.81221
$247$	−20.5529	−1.30775
$248$	−4.03270	−0.256077
$249$	−20.7380	−1.31422
$250$	19.1152	1.20895
$251$	−15.8616	−1.00117	−0.500587	−	0.865686i	$-0.666883\pi$
$251$	−15.8616	−1.00117	−0.500587	+	0.865686i	$0.666883\pi$
$252$	8.01879	0.505136
$253$	0.358047	0.0225102
$254$	−49.9632	−3.13497
$255$	30.5423	1.91263
$256$	−18.6646	−1.16654
$257$	−0.410478	−0.0256049	−0.0128025	−	0.999918i	$-0.504075\pi$
$257$	−0.410478	−0.0256049	−0.0128025	+	0.999918i	$0.504075\pi$
$258$	−29.8861	−1.86063
$259$	4.29049	0.266598
$260$	−26.8443	−1.66481
$261$	13.7835	0.853177
$262$	26.0775	1.61107
$263$	29.6722	1.82967	0.914833	−	0.403833i	$-0.132322\pi$
$263$	29.6722	1.82967	0.914833	+	0.403833i	$0.132322\pi$
$264$	−6.91795	−0.425771
$265$	7.28175	0.447314
$266$	−17.8247	−1.09290
$267$	0.565212	0.0345904
$268$	18.1650	1.10960
$269$	−27.5787	−1.68150	−0.840752	−	0.541421i	$-0.817887\pi$
$269$	−27.5787	−1.68150	−0.840752	+	0.541421i	$0.817887\pi$
$270$	12.5317	0.762655
$271$	−2.99941	−0.182201	−0.0911005	−	0.995842i	$-0.529038\pi$
$271$	−2.99941	−0.182201	−0.0911005	+	0.995842i	$0.529038\pi$
$272$	2.21700	0.134425
$273$	−8.05350	−0.487420
$274$	−14.7771	−0.892715
$275$	1.83231	0.110493
$276$	2.68667	0.161719
$277$	13.5967	0.816945	0.408473	−	0.912771i	$-0.366062\pi$
$277$	13.5967	0.816945	0.408473	+	0.912771i	$0.366062\pi$
$278$	−2.46796	−0.148019
$279$	2.73042	0.163466
$280$	−9.29719	−0.555614
$281$	−7.12356	−0.424956	−0.212478	−	0.977166i	$-0.568153\pi$
$281$	−7.12356	−0.424956	−0.212478	+	0.977166i	$0.568153\pi$
$282$	10.6814	0.636066
$283$	9.25652	0.550243	0.275122	−	0.961409i	$-0.411282\pi$
$283$	9.25652	0.550243	0.275122	+	0.961409i	$0.411282\pi$
$284$	−11.1792	−0.663362
$285$	39.2521	2.32509
$286$	7.12054	0.421046
$287$	13.3163	0.786035
$288$	10.7093	0.631054
$289$	9.88448	0.581440
$290$	−40.0176	−2.34991
$291$	6.88769	0.403763
$292$	−35.0860	−2.05325
$293$	−16.0610	−0.938293	−0.469147	−	0.883120i	$-0.655438\pi$
$293$	−16.0610	−0.938293	−0.469147	+	0.883120i	$0.655438\pi$
$294$	29.4336	1.71660
$295$	−27.2078	−1.58410
$296$	−11.3674	−0.660717
$297$	−2.07670	−0.120502
$298$	19.1422	1.10888
$299$	−1.10434	−0.0638654
$300$	13.7491	0.793803
$301$	6.65591	0.383640
$302$	−20.0836	−1.15568
$303$	2.75726	0.158401
$304$	2.84922	0.163414
$305$	−8.84195	−0.506289
$306$	−24.8798	−1.42229
$307$	13.8195	0.788722	0.394361	−	0.918956i	$-0.370966\pi$
$307$	13.8195	0.788722	0.394361	+	0.918956i	$0.370966\pi$
$308$	3.85802	0.219831
$309$	−22.1297	−1.25891
$310$	−7.92723	−0.450236
$311$	−3.77290	−0.213942	−0.106971	−	0.994262i	$-0.534115\pi$
$311$	−3.77290	−0.213942	−0.106971	+	0.994262i	$0.534115\pi$
$312$	21.3373	1.20798
$313$	13.8824	0.784678	0.392339	−	0.919821i	$-0.371666\pi$
$313$	13.8824	0.784678	0.392339	+	0.919821i	$0.371666\pi$
$314$	55.1590	3.11280
$315$	6.29485	0.354675
$316$	3.14697	0.177031
$317$	−6.82092	−0.383101	−0.191551	−	0.981483i	$-0.561352\pi$
$317$	−6.82092	−0.383101	−0.191551	+	0.981483i	$0.561352\pi$
$318$	−14.4934	−0.812750
$319$	6.63154	0.371295
$320$	−33.3276	−1.86307
$321$	−17.6405	−0.984597
$322$	−0.957744	−0.0533730
$323$	34.5512	1.92248
$324$	−36.3451	−2.01917
$325$	−5.65146	−0.313487
$326$	−31.6737	−1.75424
$327$	−34.0680	−1.88397
$328$	−35.2807	−1.94805
$329$	−2.37884	−0.131150
$330$	−13.5989	−0.748593
$331$	−13.9603	−0.767327	−0.383663	−	0.923473i	$-0.625338\pi$
$331$	−13.9603	−0.767327	−0.383663	+	0.923473i	$0.625338\pi$
$332$	−30.6413	−1.68166
$333$	7.69653	0.421767
$334$	6.63314	0.362949
$335$	14.2598	0.779094
$336$	1.11645	0.0609072
$337$	16.5796	0.903146	0.451573	−	0.892234i	$-0.350863\pi$
$337$	16.5796	0.903146	0.451573	+	0.892234i	$0.350863\pi$
$338$	8.04993	0.437859
$339$	1.62564	0.0882928
$340$	45.1276	2.44739
$341$	1.31367	0.0711391
$342$	−31.9749	−1.72900
$343$	−14.6658	−0.791877
$344$	−17.6344	−0.950784
$345$	2.10907	0.113549
$346$	−21.6809	−1.16557
$347$	−1.29114	−0.0693120	−0.0346560	−	0.999399i	$-0.511034\pi$
$347$	−1.29114	−0.0693120	−0.0346560	+	0.999399i	$0.511034\pi$
$348$	49.7609	2.66747
$349$	16.9308	0.906286	0.453143	−	0.891438i	$-0.350303\pi$
$349$	16.9308	0.906286	0.453143	+	0.891438i	$0.350303\pi$
$350$	−4.90127	−0.261984
$351$	6.40523	0.341886
$352$	5.15250	0.274629
$353$	16.3575	0.870619	0.435310	−	0.900281i	$-0.356639\pi$
$353$	16.3575	0.870619	0.435310	+	0.900281i	$0.356639\pi$
$354$	54.1538	2.87824
$355$	−8.77579	−0.465770
$356$	0.835126	0.0442616
$357$	13.5386	0.716540
$358$	−40.9688	−2.16527
$359$	−22.4541	−1.18508	−0.592541	−	0.805540i	$-0.701875\pi$
$359$	−22.4541	−1.18508	−0.592541	+	0.805540i	$0.701875\pi$
$360$	−16.6778	−0.878999
$361$	25.4042	1.33706
$362$	−28.4977	−1.49780
$363$	2.25355	0.118281
$364$	−11.8994	−0.623698
$365$	−27.5430	−1.44166
$366$	17.5988	0.919904
$367$	−2.99769	−0.156478	−0.0782392	−	0.996935i	$-0.524930\pi$
$367$	−2.99769	−0.156478	−0.0782392	+	0.996935i	$0.524930\pi$
$368$	0.153093	0.00798052
$369$	23.8875	1.24353
$370$	−22.3453	−1.16168
$371$	3.22782	0.167580
$372$	9.85733	0.511079
$373$	1.54158	0.0798200	0.0399100	−	0.999203i	$-0.487293\pi$
$373$	1.54158	0.0798200	0.0399100	+	0.999203i	$0.487293\pi$
$374$	−11.9702	−0.618966
$375$	−18.6592	−0.963556
$376$	6.30259	0.325031
$377$	−20.4539	−1.05343
$378$	5.55499	0.285718
$379$	−26.7862	−1.37592	−0.687958	−	0.725750i	$-0.741493\pi$
$379$	−26.7862	−1.37592	−0.687958	+	0.725750i	$0.741493\pi$
$380$	57.9967	2.97517
$381$	48.7714	2.49863
$382$	−20.6874	−1.05846
$383$	−3.19895	−0.163458	−0.0817292	−	0.996655i	$-0.526044\pi$
$383$	−3.19895	−0.163458	−0.0817292	+	0.996655i	$0.526044\pi$
$384$	43.1117	2.20003
$385$	3.02859	0.154351
$386$	14.8498	0.755833
$387$	11.9397	0.606931
$388$	10.1769	0.516652
$389$	21.8602	1.10835	0.554177	−	0.832399i	$-0.313033\pi$
$389$	21.8602	1.10835	0.554177	+	0.832399i	$0.313033\pi$
$390$	41.9434	2.12389
$391$	1.85648	0.0938865
$392$	17.3674	0.877188
$393$	−25.4554	−1.28406
$394$	−12.5365	−0.631577
$395$	2.47041	0.124300
$396$	6.92073	0.347780
$397$	35.1930	1.76629	0.883144	−	0.469102i	$-0.155422\pi$
$397$	35.1930	1.76629	0.883144	+	0.469102i	$0.155422\pi$
$398$	−46.0754	−2.30955
$399$	17.3995	0.871063
$400$	0.783455	0.0391728
$401$	−19.6666	−0.982105	−0.491053	−	0.871130i	$-0.663388\pi$
$401$	−19.6666	−0.982105	−0.491053	+	0.871130i	$0.663388\pi$
$402$	−28.3823	−1.41558
$403$	−4.05178	−0.201834
$404$	4.07398	0.202688
$405$	−28.5313	−1.41773
$406$	−17.7388	−0.880361
$407$	3.70297	0.183549
$408$	−35.8698	−1.77582
$409$	−6.46805	−0.319825	−0.159912	−	0.987131i	$-0.551121\pi$
$409$	−6.46805	−0.319825	−0.159912	+	0.987131i	$0.551121\pi$
$410$	−69.3524	−3.42507
$411$	14.4246	0.711511
$412$	−32.6976	−1.61089
$413$	−12.0606	−0.593461
$414$	−1.71806	−0.0844378
$415$	−24.0538	−1.18076
$416$	−15.8920	−0.779170
$417$	2.40909	0.117974
$418$	−15.3838	−0.752447
$419$	33.7405	1.64833	0.824165	−	0.566350i	$-0.191645\pi$
$419$	33.7405	1.64833	0.824165	+	0.566350i	$0.191645\pi$
$420$	22.7256	1.10889
$421$	−9.35480	−0.455925	−0.227962	−	0.973670i	$-0.573206\pi$
$421$	−9.35480	−0.455925	−0.227962	+	0.973670i	$0.573206\pi$
$422$	−15.3974	−0.749536
$423$	−4.26729	−0.207483
$424$	−8.55190	−0.415317
$425$	9.50059	0.460846
$426$	17.4671	0.846284
$427$	−3.91942	−0.189674
$428$	−26.0646	−1.25988
$429$	−6.95068	−0.335582
$430$	−34.6646	−1.67168
$431$	6.61051	0.318417	0.159209	−	0.987245i	$-0.449106\pi$
$431$	6.61051	0.318417	0.159209	+	0.987245i	$0.449106\pi$
$432$	−0.887950	−0.0427215
$433$	3.56098	0.171130	0.0855649	−	0.996333i	$-0.472730\pi$
$433$	3.56098	0.171130	0.0855649	+	0.996333i	$0.472730\pi$
$434$	−3.51394	−0.168675
$435$	39.0630	1.87293
$436$	−50.3370	−2.41071
$437$	2.38590	0.114133
$438$	54.8208	2.61944
$439$	3.09296	0.147619	0.0738094	−	0.997272i	$-0.476484\pi$
$439$	3.09296	0.147619	0.0738094	+	0.997272i	$0.476484\pi$
$440$	−8.02407	−0.382533
$441$	−11.7590	−0.559951
$442$	36.9202	1.75611
$443$	−24.9215	−1.18405	−0.592027	−	0.805918i	$-0.701672\pi$
$443$	−24.9215	−1.18405	−0.592027	+	0.805918i	$0.701672\pi$
$444$	27.7859	1.31866
$445$	0.655585	0.0310777
$446$	11.6660	0.552403
$447$	−18.6856	−0.883799
$448$	−14.7733	−0.697973
$449$	−8.66428	−0.408893	−0.204446	−	0.978878i	$-0.565539\pi$
$449$	−8.66428	−0.408893	−0.204446	+	0.978878i	$0.565539\pi$
$450$	−8.79218	−0.414467
$451$	11.4928	0.541175
$452$	2.40196	0.112979
$453$	19.6045	0.921099
$454$	8.98546	0.421709
$455$	−9.34118	−0.437921
$456$	−46.0988	−2.15877
$457$	−17.9034	−0.837487	−0.418743	−	0.908105i	$-0.637529\pi$
$457$	−17.9034	−0.837487	−0.418743	+	0.908105i	$0.637529\pi$
$458$	−30.3970	−1.42036
$459$	−10.7677	−0.502595
$460$	3.11625	0.145296
$461$	14.9495	0.696269	0.348134	−	0.937445i	$-0.386815\pi$
$461$	14.9495	0.696269	0.348134	+	0.937445i	$0.386815\pi$
$462$	−6.02803	−0.280450
$463$	12.0078	0.558052	0.279026	−	0.960284i	$-0.409988\pi$
$463$	12.0078	0.558052	0.279026	+	0.960284i	$0.409988\pi$
$464$	2.83550	0.131635
$465$	7.73813	0.358847
$466$	−12.7883	−0.592404
$467$	−2.53603	−0.117353	−0.0586767	−	0.998277i	$-0.518688\pi$
$467$	−2.53603	−0.117353	−0.0586767	+	0.998277i	$0.518688\pi$
$468$	−21.3458	−0.986711
$469$	6.32099	0.291876
$470$	12.3892	0.571472
$471$	−53.8432	−2.48096
$472$	31.9537	1.47079
$473$	5.74447	0.264131
$474$	−4.91704	−0.225847
$475$	12.2099	0.560228
$476$	20.0039	0.916878
$477$	5.79024	0.265117
$478$	29.5340	1.35085
$479$	−21.2389	−0.970430	−0.485215	−	0.874395i	$-0.661259\pi$
$479$	−21.2389	−0.970430	−0.485215	+	0.874395i	$0.661259\pi$
$480$	30.3507	1.38531
$481$	−11.4212	−0.520761
$482$	−8.74232	−0.398202
$483$	0.934898	0.0425393
$484$	3.32972	0.151351
$485$	7.98897	0.362760
$486$	42.4051	1.92354
$487$	−15.1208	−0.685188	−0.342594	−	0.939484i	$-0.611305\pi$
$487$	−15.1208	−0.685188	−0.342594	+	0.939484i	$0.611305\pi$
$488$	10.3843	0.470073
$489$	30.9181	1.39817
$490$	34.1398	1.54228
$491$	−25.5118	−1.15133	−0.575667	−	0.817685i	$-0.695257\pi$
$491$	−25.5118	−1.15133	−0.575667	+	0.817685i	$0.695257\pi$
$492$	86.2382	3.88792
$493$	34.3847	1.54861
$494$	47.4488	2.13482
$495$	5.43286	0.244189
$496$	0.561694	0.0252208
$497$	−3.89009	−0.174494
$498$	47.8762	2.14538
$499$	−19.8548	−0.888821	−0.444410	−	0.895823i	$-0.646587\pi$
$499$	−19.8548	−0.888821	−0.444410	+	0.895823i	$0.646587\pi$
$500$	−27.5698	−1.23296
$501$	−6.47491	−0.289278
$502$	36.6183	1.63436
$503$	−7.30920	−0.325901	−0.162951	−	0.986634i	$-0.552101\pi$
$503$	−7.30920	−0.325901	−0.162951	+	0.986634i	$0.552101\pi$
$504$	−7.39286	−0.329304
$505$	3.19813	0.142315
$506$	−0.826595	−0.0367466
$507$	−7.85791	−0.348982
$508$	72.0619	3.19723
$509$	29.4930	1.30725	0.653627	−	0.756817i	$-0.273247\pi$
$509$	29.4930	1.30725	0.653627	+	0.756817i	$0.273247\pi$
$510$	−70.5104	−3.12225
$511$	−12.2091	−0.540099
$512$	4.82825	0.213381
$513$	−13.8384	−0.610981
$514$	0.947637	0.0417985
$515$	−25.6680	−1.13107
$516$	43.1046	1.89758
$517$	−2.05309	−0.0902948
$518$	−9.90511	−0.435205
$519$	21.1637	0.928984
$520$	24.7489	1.08531
$521$	−32.0954	−1.40613	−0.703063	−	0.711128i	$-0.748185\pi$
$521$	−32.0954	−1.40613	−0.703063	+	0.711128i	$0.748185\pi$
$522$	−31.8208	−1.39276
$523$	20.8574	0.912028	0.456014	−	0.889973i	$-0.349277\pi$
$523$	20.8574	0.912028	0.456014	+	0.889973i	$0.349277\pi$
$524$	−37.6115	−1.64307
$525$	4.78435	0.208806
$526$	−68.5017	−2.98682
$527$	6.81140	0.296709
$528$	0.963565	0.0419338
$529$	−22.8718	−0.994426
$530$	−16.8108	−0.730214
$531$	−21.6349	−0.938875
$532$	25.7085	1.11460
$533$	−35.4476	−1.53541
$534$	−1.30486	−0.0564668
$535$	−20.4611	−0.884609
$536$	−16.7471	−0.723364
$537$	39.9915	1.72576
$538$	63.6687	2.74495
$539$	−5.65750	−0.243686
$540$	−18.0745	−0.777801
$541$	34.3011	1.47472	0.737359	−	0.675501i	$-0.236073\pi$
$541$	34.3011	1.47472	0.737359	+	0.675501i	$0.236073\pi$
$542$	6.92448	0.297432
$543$	27.8179	1.19378
$544$	26.7158	1.14543
$545$	−39.5152	−1.69264
$546$	18.5924	0.795683
$547$	−1.00000	−0.0427569
$547$	−1.00000	−0.0427569
$548$	21.3129	0.910443
$549$	−7.03087	−0.300070
$550$	−4.23011	−0.180373
$551$	44.1903	1.88257
$552$	−2.47696	−0.105426
$553$	1.09507	0.0465671
$554$	−31.3895	−1.33361
$555$	21.8123	0.925879
$556$	3.55954	0.150958
$557$	−25.2685	−1.07066	−0.535329	−	0.844643i	$-0.679813\pi$
$557$	−25.2685	−1.07066	−0.535329	+	0.844643i	$0.679813\pi$
$558$	−6.30350	−0.266849
$559$	−17.7179	−0.749385
$560$	1.29496	0.0547219
$561$	11.6847	0.493328
$562$	16.4456	0.693715
$563$	−33.3231	−1.40440	−0.702200	−	0.711980i	$-0.747799\pi$
$563$	−33.3231	−1.40440	−0.702200	+	0.711980i	$0.747799\pi$
$564$	−15.4057	−0.648698
$565$	1.88557	0.0793264
$566$	−21.3698	−0.898239
$567$	−12.6472	−0.531134
$568$	10.3065	0.432453
$569$	−3.17204	−0.132979	−0.0664894	−	0.997787i	$-0.521180\pi$
$569$	−3.17204	−0.132979	−0.0664894	+	0.997787i	$0.521180\pi$
$570$	−90.6180	−3.79557
$571$	−9.68802	−0.405431	−0.202715	−	0.979238i	$-0.564977\pi$
$571$	−9.68802	−0.405431	−0.202715	+	0.979238i	$0.564977\pi$
$572$	−10.2699	−0.429408
$573$	20.1939	0.843611
$574$	−30.7422	−1.28315
$575$	0.656055	0.0273594
$576$	−26.5012	−1.10422
$577$	−19.8688	−0.827149	−0.413574	−	0.910470i	$-0.635720\pi$
$577$	−19.8688	−0.827149	−0.413574	+	0.910470i	$0.635720\pi$
$578$	−22.8195	−0.949166
$579$	−14.4955	−0.602414
$580$	57.7173	2.39658
$581$	−10.6625	−0.442354
$582$	−15.9010	−0.659119
$583$	2.78581	0.115377
$584$	32.3473	1.33854
$585$	−16.7567	−0.692806
$586$	37.0787	1.53171
$587$	−13.2409	−0.546512	−0.273256	−	0.961941i	$-0.588101\pi$
$587$	−13.2409	−0.546512	−0.273256	+	0.961941i	$0.588101\pi$
$588$	−42.4520	−1.75069
$589$	8.75382	0.360695
$590$	62.8125	2.58595
$591$	12.2374	0.503379
$592$	1.58331	0.0650734
$593$	12.8725	0.528611	0.264305	−	0.964439i	$-0.414857\pi$
$593$	12.8725	0.528611	0.264305	+	0.964439i	$0.414857\pi$
$594$	4.79431	0.196713
$595$	15.7033	0.643774
$596$	−27.6088	−1.13090
$597$	44.9763	1.84076
$598$	2.54949	0.104256
$599$	27.7586	1.13419	0.567093	−	0.823654i	$-0.308068\pi$
$599$	27.7586	1.13419	0.567093	+	0.823654i	$0.308068\pi$
$600$	−12.6759	−0.517490
$601$	6.33049	0.258226	0.129113	−	0.991630i	$-0.458787\pi$
$601$	6.33049	0.258226	0.129113	+	0.991630i	$0.458787\pi$
$602$	−15.3659	−0.626269
$603$	11.3390	0.461758
$604$	28.9665	1.17863
$605$	2.61387	0.106269
$606$	−6.36547	−0.258580
$607$	−15.2421	−0.618658	−0.309329	−	0.950955i	$-0.600105\pi$
$607$	−15.2421	−0.618658	−0.309329	+	0.950955i	$0.600105\pi$
$608$	34.3345	1.39245
$609$	17.3156	0.701665
$610$	20.4127	0.826486
$611$	6.33241	0.256182
$612$	35.8842	1.45053
$613$	−1.57893	−0.0637725	−0.0318863	−	0.999492i	$-0.510151\pi$
$613$	−1.57893	−0.0637725	−0.0318863	+	0.999492i	$0.510151\pi$
$614$	−31.9040	−1.28754
$615$	67.6981	2.72985
$616$	−3.55687	−0.143310
$617$	18.3719	0.739625	0.369813	−	0.929106i	$-0.379422\pi$
$617$	18.3719	0.739625	0.369813	+	0.929106i	$0.379422\pi$
$618$	51.0890	2.05510
$619$	21.1119	0.848558	0.424279	−	0.905532i	$-0.360528\pi$
$619$	21.1119	0.848558	0.424279	+	0.905532i	$0.360528\pi$
$620$	11.4334	0.459177
$621$	−0.743558	−0.0298379
$622$	8.71019	0.349247
$623$	0.290604	0.0116428
$624$	−2.97195	−0.118973
$625$	−30.8042	−1.23217
$626$	−32.0491	−1.28094
$627$	15.0168	0.599715
$628$	−79.5557	−3.17462
$629$	19.2000	0.765554
$630$	−14.5324	−0.578985
$631$	40.2048	1.60053	0.800264	−	0.599648i	$-0.204693\pi$
$631$	40.2048	1.60053	0.800264	+	0.599648i	$0.204693\pi$
$632$	−2.90132	−0.115408
$633$	15.0302	0.597395
$634$	15.7469	0.625389
$635$	56.5695	2.24489
$636$	20.9038	0.828890
$637$	17.4496	0.691378
$638$	−15.3097	−0.606117
$639$	−6.97826	−0.276056
$640$	50.0049	1.97662
$641$	15.5255	0.613220	0.306610	−	0.951835i	$-0.400805\pi$
$641$	15.5255	0.613220	0.306610	+	0.951835i	$0.400805\pi$
$642$	40.7252	1.60730
$643$	−8.00834	−0.315818	−0.157909	−	0.987454i	$-0.550475\pi$
$643$	−8.00834	−0.315818	−0.157909	+	0.987454i	$0.550475\pi$
$644$	1.38135	0.0544329
$645$	33.8377	1.33236
$646$	−79.7655	−3.13833
$647$	−6.09661	−0.239683	−0.119841	−	0.992793i	$-0.538239\pi$
$647$	−6.09661	−0.239683	−0.119841	+	0.992793i	$0.538239\pi$
$648$	33.5081	1.31632
$649$	−10.4090	−0.408590
$650$	13.0471	0.511748
$651$	3.43012	0.134437
$652$	45.6829	1.78908
$653$	−14.6981	−0.575182	−0.287591	−	0.957753i	$-0.592854\pi$
$653$	−14.6981	−0.575182	−0.287591	+	0.957753i	$0.592854\pi$
$654$	78.6500	3.07546
$655$	−29.5255	−1.15366
$656$	4.91406	0.191862
$657$	−21.9014	−0.854454
$658$	5.49183	0.214094
$659$	−18.4322	−0.718018	−0.359009	−	0.933334i	$-0.616885\pi$
$659$	−18.4322	−0.718018	−0.359009	+	0.933334i	$0.616885\pi$
$660$	19.6136	0.763459
$661$	50.2867	1.95592	0.977962	−	0.208782i	$-0.0669498\pi$
$661$	50.2867	1.95592	0.977962	+	0.208782i	$0.0669498\pi$
$662$	32.2290	1.25261
$663$	−36.0395	−1.39966
$664$	28.2496	1.09630
$665$	20.1815	0.782604
$666$	−17.7683	−0.688509
$667$	2.37441	0.0919374
$668$	−9.56697	−0.370157
$669$	−11.3878	−0.440276
$670$	−32.9203	−1.27182
$671$	−3.38271	−0.130588
$672$	13.4537	0.518988
$673$	12.5808	0.484953	0.242476	−	0.970157i	$-0.422040\pi$
$673$	12.5808	0.484953	0.242476	+	0.970157i	$0.422040\pi$
$674$	−38.2759	−1.47433
$675$	−3.80517	−0.146461
$676$	−11.6104	−0.446554
$677$	14.8725	0.571598	0.285799	−	0.958290i	$-0.407741\pi$
$677$	14.8725	0.571598	0.285799	+	0.958290i	$0.407741\pi$
$678$	−3.75299	−0.144133
$679$	3.54131	0.135903
$680$	−41.6050	−1.59548
$681$	−8.77112	−0.336110
$682$	−3.03275	−0.116130
$683$	−41.1437	−1.57432	−0.787160	−	0.616748i	$-0.788450\pi$
$683$	−41.1437	−1.57432	−0.787160	+	0.616748i	$0.788450\pi$
$684$	46.1173	1.76334
$685$	16.7309	0.639256
$686$	33.8577	1.29269
$687$	29.6719	1.13205
$688$	2.45621	0.0936420
$689$	−8.59237	−0.327343
$690$	−4.86904	−0.185361
$691$	−37.4898	−1.42618	−0.713089	−	0.701074i	$-0.752704\pi$
$691$	−37.4898	−1.42618	−0.713089	+	0.701074i	$0.752704\pi$
$692$	31.2703	1.18872
$693$	2.40825	0.0914819
$694$	2.98075	0.113148
$695$	2.79428	0.105993
$696$	−45.8767	−1.73895
$697$	59.5904	2.25715
$698$	−39.0868	−1.47946
$699$	12.4832	0.472158
$700$	7.06910	0.267187
$701$	−17.9201	−0.676831	−0.338416	−	0.940997i	$-0.609891\pi$
$701$	−17.9201	−0.676831	−0.338416	+	0.940997i	$0.609891\pi$
$702$	−14.7872	−0.558108
$703$	24.6753	0.930646
$704$	−12.7503	−0.480545
$705$	−12.0937	−0.455474
$706$	−37.7631	−1.42123
$707$	1.41765	0.0533162
$708$	−78.1060	−2.93540
$709$	51.8402	1.94690	0.973450	−	0.228901i	$-0.0735134\pi$
$709$	51.8402	1.94690	0.973450	+	0.228901i	$0.0735134\pi$
$710$	20.2599	0.760342
$711$	1.96440	0.0736707
$712$	−0.769938	−0.0288546
$713$	0.470355	0.0176149
$714$	−31.2555	−1.16971
$715$	−8.06204	−0.301503
$716$	59.0892	2.20827
$717$	−28.8295	−1.07666
$718$	51.8380	1.93458
$719$	28.7163	1.07094	0.535469	−	0.844555i	$-0.320135\pi$
$719$	28.7163	1.07094	0.535469	+	0.844555i	$0.320135\pi$
$720$	2.32297	0.0865719
$721$	−11.3780	−0.423738
$722$	−58.6486	−2.18268
$723$	8.53378	0.317375
$724$	41.1022	1.52755
$725$	12.1511	0.451279
$726$	−5.20258	−0.193086
$727$	−4.40221	−0.163269	−0.0816345	−	0.996662i	$-0.526014\pi$
$727$	−4.40221	−0.163269	−0.0816345	+	0.996662i	$0.526014\pi$
$728$	10.9706	0.406596
$729$	−8.64748	−0.320277
$730$	63.5861	2.35343
$731$	29.7852	1.10165
$732$	−25.3827	−0.938172
$733$	−13.2263	−0.488526	−0.244263	−	0.969709i	$-0.578546\pi$
$733$	−13.2263	−0.488526	−0.244263	+	0.969709i	$0.578546\pi$
$734$	6.92053	0.255441
$735$	−33.3254	−1.22923
$736$	1.84484	0.0680017
$737$	5.45542	0.200953
$738$	−55.1471	−2.02999
$739$	27.9165	1.02693	0.513463	−	0.858112i	$-0.328362\pi$
$739$	27.9165	1.02693	0.513463	+	0.858112i	$0.328362\pi$
$740$	32.2286	1.18475
$741$	−46.3169	−1.70149
$742$	−7.45180	−0.273564
$743$	25.2819	0.927503	0.463752	−	0.885965i	$-0.346503\pi$
$743$	25.2819	0.927503	0.463752	+	0.885965i	$0.346503\pi$
$744$	−9.08789	−0.333178
$745$	−21.6733	−0.794048
$746$	−3.55892	−0.130301
$747$	−19.1269	−0.699818
$748$	17.2647	0.631259
$749$	−9.06988	−0.331406
$750$	43.0769	1.57295
$751$	−20.1471	−0.735178	−0.367589	−	0.929988i	$-0.619817\pi$
$751$	−20.1471	−0.735178	−0.367589	+	0.929988i	$0.619817\pi$
$752$	−0.877854	−0.0320121
$753$	−35.7448	−1.30261
$754$	47.2202	1.71966
$755$	22.7391	0.827559
$756$	−8.01195	−0.291392
$757$	−10.8109	−0.392928	−0.196464	−	0.980511i	$-0.562946\pi$
$757$	−10.8109	−0.392928	−0.196464	+	0.980511i	$0.562946\pi$
$758$	61.8392	2.24610
$759$	0.806877	0.0292878
$760$	−53.4696	−1.93955
$761$	37.2648	1.35085	0.675423	−	0.737430i	$-0.263961\pi$
$761$	37.2648	1.35085	0.675423	+	0.737430i	$0.263961\pi$
$762$	−112.594	−4.07887
$763$	−17.5161	−0.634125
$764$	29.8374	1.07948
$765$	28.1695	1.01847
$766$	7.38514	0.266836
$767$	32.1049	1.15924
$768$	−42.0616	−1.51777
$769$	32.6535	1.17752	0.588759	−	0.808309i	$-0.299617\pi$
$769$	32.6535	1.17752	0.588759	+	0.808309i	$0.299617\pi$
$770$	−6.99186	−0.251969
$771$	−0.925032	−0.0333142
$772$	−21.4178	−0.770843
$773$	−3.21496	−0.115634	−0.0578170	−	0.998327i	$-0.518414\pi$
$773$	−3.21496	−0.115634	−0.0578170	+	0.998327i	$0.518414\pi$
$774$	−27.5643	−0.990778
$775$	2.40705	0.0864638
$776$	−9.38248	−0.336811
$777$	9.66883	0.346867
$778$	−50.4668	−1.80932
$779$	76.5840	2.74391
$780$	−60.4949	−2.16606
$781$	−3.35739	−0.120137
$782$	−4.28591	−0.153264
$783$	−13.7717	−0.492162
$784$	−2.41902	−0.0863935
$785$	−62.4522	−2.22902
$786$	58.7668	2.09614
$787$	38.8381	1.38443	0.692214	−	0.721692i	$-0.256635\pi$
$787$	38.8381	1.38443	0.692214	+	0.721692i	$0.256635\pi$
$788$	18.0813	0.644120
$789$	66.8677	2.38055
$790$	−5.70323	−0.202912
$791$	0.835825	0.0297185
$792$	−6.38051	−0.226722
$793$	10.4334	0.370500
$794$	−81.2473	−2.88336
$795$	16.4098	0.581994
$796$	66.4545	2.35542
$797$	−49.7010	−1.76050	−0.880249	−	0.474512i	$-0.842625\pi$
$797$	−49.7010	−1.76050	−0.880249	+	0.474512i	$0.842625\pi$
$798$	−40.1687	−1.42196
$799$	−10.6453	−0.376604
$800$	9.44100	0.333790
$801$	0.521302	0.0184193
$802$	45.4028	1.60323
$803$	−10.5372	−0.371851
$804$	40.9357	1.44369
$805$	1.08438	0.0382194
$806$	9.35402	0.329481
$807$	−62.1499	−2.18778
$808$	−3.75598	−0.132135
$809$	−10.7545	−0.378107	−0.189054	−	0.981967i	$-0.560542\pi$
$809$	−10.7545	−0.378107	−0.189054	+	0.981967i	$0.560542\pi$
$810$	65.8680	2.31436
$811$	−31.0650	−1.09084	−0.545419	−	0.838164i	$-0.683629\pi$
$811$	−31.0650	−1.09084	−0.545419	+	0.838164i	$0.683629\pi$
$812$	25.5846	0.897844
$813$	−6.75930	−0.237059
$814$	−8.54874	−0.299633
$815$	35.8617	1.25618
$816$	4.99611	0.174899
$817$	38.2792	1.33922
$818$	14.9323	0.522094
$819$	−7.42784	−0.259550
$820$	100.027	3.49309
$821$	0.549372	0.0191732	0.00958661	−	0.999954i	$-0.496948\pi$
$821$	0.549372	0.0191732	0.00958661	+	0.999954i	$0.496948\pi$
$822$	−33.3008	−1.16150
$823$	−0.373248	−0.0130106	−0.00650530	−	0.999979i	$-0.502071\pi$
$823$	−0.373248	−0.0130106	−0.00650530	+	0.999979i	$0.502071\pi$
$824$	30.1453	1.05016
$825$	4.12920	0.143760
$826$	27.8432	0.968789
$827$	−29.2463	−1.01699	−0.508496	−	0.861064i	$-0.669798\pi$
$827$	−29.2463	−1.01699	−0.508496	+	0.861064i	$0.669798\pi$
$828$	2.47795	0.0861147
$829$	−18.8374	−0.654251	−0.327125	−	0.944981i	$-0.606080\pi$
$829$	−18.8374	−0.654251	−0.327125	+	0.944981i	$0.606080\pi$
$830$	55.5311	1.92751
$831$	30.6408	1.06292
$832$	39.3262	1.36339
$833$	−29.3343	−1.01637
$834$	−5.56167	−0.192585
$835$	−7.51019	−0.259901
$836$	22.1881	0.767390
$837$	−2.72809	−0.0942967
$838$	−77.8938	−2.69080
$839$	29.9609	1.03436	0.517182	−	0.855875i	$-0.326981\pi$
$839$	29.9609	1.03436	0.517182	+	0.855875i	$0.326981\pi$
$840$	−20.9517	−0.722901
$841$	14.9774	0.516461
$842$	21.5966	0.744270
$843$	−16.0533	−0.552904
$844$	22.2077	0.764421
$845$	−9.11432	−0.313542
$846$	9.85155	0.338703
$847$	1.15866	0.0398121
$848$	1.19115	0.0409043
$849$	20.8600	0.715914
$850$	−21.9332	−0.752304
$851$	1.32584	0.0454492
$852$	−25.1928	−0.863090
$853$	22.7535	0.779066	0.389533	−	0.921012i	$-0.372636\pi$
$853$	22.7535	0.779066	0.389533	+	0.921012i	$0.372636\pi$
$854$	9.04843	0.309631
$855$	36.2027	1.23811
$856$	24.0301	0.821332
$857$	39.0232	1.33301	0.666503	−	0.745502i	$-0.267790\pi$
$857$	39.0232	1.33301	0.666503	+	0.745502i	$0.267790\pi$
$858$	16.0465	0.547818
$859$	−4.72833	−0.161328	−0.0806642	−	0.996741i	$-0.525704\pi$
$859$	−4.72833	−0.161328	−0.0806642	+	0.996741i	$0.525704\pi$
$860$	49.9967	1.70487
$861$	30.0089	1.02270
$862$	−15.2611	−0.519797
$863$	−2.91803	−0.0993310	−0.0496655	−	0.998766i	$-0.515816\pi$
$863$	−2.91803	−0.0993310	−0.0496655	+	0.998766i	$0.515816\pi$
$864$	−10.7002	−0.364028
$865$	24.5476	0.834644
$866$	−8.22095	−0.279359
$867$	22.2751	0.756504
$868$	5.06815	0.172024
$869$	0.945116	0.0320609
$870$	−90.1814	−3.05744
$871$	−16.8263	−0.570138
$872$	46.4078	1.57157
$873$	6.35260	0.215003
$874$	−5.50814	−0.186316
$875$	−9.59363	−0.324324
$876$	−79.0679	−2.67146
$877$	17.0581	0.576011	0.288005	−	0.957629i	$-0.407008\pi$
$877$	17.0581	0.576011	0.288005	+	0.957629i	$0.407008\pi$
$878$	−7.14046	−0.240979
$879$	−36.1942	−1.22080
$880$	1.11763	0.0376753
$881$	−45.4903	−1.53261	−0.766303	−	0.642480i	$-0.777906\pi$
$881$	−45.4903	−1.53261	−0.766303	+	0.642480i	$0.777906\pi$
$882$	27.1470	0.914086
$883$	3.70333	0.124627	0.0623135	−	0.998057i	$-0.480152\pi$
$883$	3.70333	0.124627	0.0623135	+	0.998057i	$0.480152\pi$
$884$	−53.2499	−1.79099
$885$	−61.3142	−2.06105
$886$	57.5341	1.93290
$887$	15.1422	0.508424	0.254212	−	0.967148i	$-0.418184\pi$
$887$	15.1422	0.508424	0.254212	+	0.967148i	$0.418184\pi$
$888$	−25.6170	−0.859649
$889$	25.0758	0.841016
$890$	−1.51349	−0.0507324
$891$	−10.9154	−0.365679
$892$	−16.8259	−0.563374
$893$	−13.6811	−0.457820
$894$	43.1379	1.44275
$895$	46.3858	1.55051
$896$	22.1659	0.740511
$897$	−2.48867	−0.0830944
$898$	20.0025	0.667492
$899$	8.71164	0.290549
$900$	12.6809	0.422698
$901$	14.4445	0.481216
$902$	−26.5325	−0.883435
$903$	14.9994	0.499149
$904$	−2.21447	−0.0736521
$905$	32.2657	1.07255
$906$	−45.2592	−1.50364
$907$	25.3868	0.842956	0.421478	−	0.906839i	$-0.361512\pi$
$907$	25.3868	0.842956	0.421478	+	0.906839i	$0.361512\pi$
$908$	−12.9597	−0.430083
$909$	2.54306	0.0843480
$910$	21.5652	0.714880
$911$	32.0554	1.06204	0.531021	−	0.847359i	$-0.321809\pi$
$911$	32.0554	1.06204	0.531021	+	0.847359i	$0.321809\pi$
$912$	6.42086	0.212616
$913$	−9.20239	−0.304555
$914$	41.3322	1.36715
$915$	−19.9258	−0.658725
$916$	43.8415	1.44856
$917$	−13.0879	−0.432201
$918$	24.8586	0.820457
$919$	−0.555571	−0.0183266	−0.00916330	−	0.999958i	$-0.502917\pi$
$919$	−0.555571	−0.0183266	−0.00916330	+	0.999958i	$0.502917\pi$
$920$	−2.87300	−0.0947200
$921$	31.1430	1.02620
$922$	−34.5127	−1.13662
$923$	10.3553	0.340849
$924$	8.69422	0.286019
$925$	6.78500	0.223089
$926$	−27.7215	−0.910986
$927$	−20.4105	−0.670368
$928$	34.1690	1.12165
$929$	33.4631	1.09789	0.548945	−	0.835858i	$-0.315030\pi$
$929$	33.4631	1.09789	0.548945	+	0.835858i	$0.315030\pi$
$930$	−17.8644	−0.585796
$931$	−37.6996	−1.23555
$932$	18.4445	0.604169
$933$	−8.50241	−0.278357
$934$	5.85472	0.191572
$935$	13.5530	0.443230
$936$	19.6796	0.643248
$937$	−30.8212	−1.00689	−0.503443	−	0.864029i	$-0.667933\pi$
$937$	−30.8212	−1.00689	−0.503443	+	0.864029i	$0.667933\pi$
$938$	−14.5928	−0.476471
$939$	31.2846	1.02093
$940$	−17.8690	−0.582821
$941$	27.0814	0.882827	0.441413	−	0.897304i	$-0.354477\pi$
$941$	27.0814	0.882827	0.441413	+	0.897304i	$0.354477\pi$
$942$	124.303	4.05002
$943$	4.11497	0.134002
$944$	−4.45066	−0.144857
$945$	−6.28948	−0.204597
$946$	−13.2618	−0.431178
$947$	17.5003	0.568682	0.284341	−	0.958723i	$-0.408225\pi$
$947$	17.5003	0.568682	0.284341	+	0.958723i	$0.408225\pi$
$948$	7.09184	0.230332
$949$	32.5003	1.05500
$950$	−28.1880	−0.914539
$951$	−15.3713	−0.498448
$952$	−18.4425	−0.597723
$953$	−22.6349	−0.733218	−0.366609	−	0.930375i	$-0.619481\pi$
$953$	−22.6349	−0.733218	−0.366609	+	0.930375i	$0.619481\pi$
$954$	−13.3674	−0.432787
$955$	23.4227	0.757941
$956$	−42.5968	−1.37768
$957$	14.9445	0.483087
$958$	49.0325	1.58417
$959$	7.41640	0.239488
$960$	−75.1054	−2.42402
$961$	−29.2743	−0.944332
$962$	26.3671	0.850111
$963$	−16.2701	−0.524295
$964$	12.6090	0.406110
$965$	−16.8132	−0.541237
$966$	−2.15832	−0.0694429
$967$	−28.6954	−0.922783	−0.461392	−	0.887197i	$-0.652650\pi$
$967$	−28.6954	−0.922783	−0.461392	+	0.887197i	$0.652650\pi$
$968$	−3.06981	−0.0986673
$969$	77.8627	2.50131
$970$	−18.4435	−0.592184
$971$	1.89569	0.0608355	0.0304177	−	0.999537i	$-0.490316\pi$
$971$	1.89569	0.0608355	0.0304177	+	0.999537i	$0.490316\pi$
$972$	−61.1609	−1.96174
$973$	1.23864	0.0397088
$974$	34.9081	1.11853
$975$	−12.7358	−0.407873
$976$	−1.44637	−0.0462971
$977$	−6.23158	−0.199366	−0.0996829	−	0.995019i	$-0.531783\pi$
$977$	−6.23158	−0.199366	−0.0996829	+	0.995019i	$0.531783\pi$
$978$	−71.3782	−2.28242
$979$	0.250810	0.00801592
$980$	−49.2397	−1.57291
$981$	−31.4214	−1.00321
$982$	58.8971	1.87948
$983$	−61.6372	−1.96592	−0.982961	−	0.183816i	$-0.941155\pi$
$983$	−61.6372	−1.96592	−0.982961	+	0.183816i	$0.941155\pi$
$984$	−79.5066	−2.53458
$985$	14.1941	0.452260
$986$	−79.3812	−2.52801
$987$	−5.36082	−0.170637
$988$	−68.4353	−2.17722
$989$	2.05679	0.0654022
$990$	−12.5424	−0.398624
$991$	19.8717	0.631246	0.315623	−	0.948885i	$-0.397787\pi$
$991$	19.8717	0.631246	0.315623	+	0.948885i	$0.397787\pi$
$992$	6.76867	0.214905
$993$	−31.4602	−0.998358
$994$	8.98072	0.284851
$995$	52.1676	1.65383
$996$	−69.0517	−2.18799
$997$	18.0561	0.571842	0.285921	−	0.958253i	$-0.407701\pi$
$997$	18.0561	0.571842	0.285921	+	0.958253i	$0.407701\pi$
$998$	45.8370	1.45095
$999$	−7.68996	−0.243300

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6017.2.a.e.1.15	✓	119

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6017.2.a.e.1.15	✓	119	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:	\( N \)	\(=\)	\( 6017 = 11 \cdot 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.30862 q^{2} +2.25355 q^{3} +3.32972 q^{4} +2.61387 q^{5} -5.20258 q^{6} +1.15866 q^{7} -3.06981 q^{8} +2.07847 q^{9} +O(q^{10})\)	\(q-2.30862 q^{2} +2.25355 q^{3} +3.32972 q^{4} +2.61387 q^{5} -5.20258 q^{6} +1.15866 q^{7} -3.06981 q^{8} +2.07847 q^{9} -6.03443 q^{10} +1.00000 q^{11} +7.50367 q^{12} -3.08433 q^{13} -2.67491 q^{14} +5.89048 q^{15} +0.427577 q^{16} +5.18502 q^{17} -4.79840 q^{18} +6.66365 q^{19} +8.70344 q^{20} +2.61110 q^{21} -2.30862 q^{22} +0.358047 q^{23} -6.91795 q^{24} +1.83231 q^{25} +7.12054 q^{26} -2.07670 q^{27} +3.85802 q^{28} +6.63154 q^{29} -13.5989 q^{30} +1.31367 q^{31} +5.15250 q^{32} +2.25355 q^{33} -11.9702 q^{34} +3.02859 q^{35} +6.92073 q^{36} +3.70297 q^{37} -15.3838 q^{38} -6.95068 q^{39} -8.02407 q^{40} +11.4928 q^{41} -6.02803 q^{42} +5.74447 q^{43} +3.32972 q^{44} +5.43286 q^{45} -0.826595 q^{46} -2.05309 q^{47} +0.963565 q^{48} -5.65750 q^{49} -4.23011 q^{50} +11.6847 q^{51} -10.2699 q^{52} +2.78581 q^{53} +4.79431 q^{54} +2.61387 q^{55} -3.55687 q^{56} +15.0168 q^{57} -15.3097 q^{58} -10.4090 q^{59} +19.6136 q^{60} -3.38271 q^{61} -3.03275 q^{62} +2.40825 q^{63} -12.7503 q^{64} -8.06204 q^{65} -5.20258 q^{66} +5.45542 q^{67} +17.2647 q^{68} +0.806877 q^{69} -6.99186 q^{70} -3.35739 q^{71} -6.38051 q^{72} -10.5372 q^{73} -8.54874 q^{74} +4.12920 q^{75} +22.1881 q^{76} +1.15866 q^{77} +16.0465 q^{78} +0.945116 q^{79} +1.11763 q^{80} -10.9154 q^{81} -26.5325 q^{82} -9.20239 q^{83} +8.69422 q^{84} +13.5530 q^{85} -13.2618 q^{86} +14.9445 q^{87} -3.06981 q^{88} +0.250810 q^{89} -12.5424 q^{90} -3.57370 q^{91} +1.19220 q^{92} +2.96041 q^{93} +4.73980 q^{94} +17.4179 q^{95} +11.6114 q^{96} +3.05638 q^{97} +13.0610 q^{98} +2.07847 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 119 q + 15 q^{2} + 15 q^{3} + 133 q^{4} + 6 q^{5} + 16 q^{6} + 72 q^{7} + 39 q^{8} + 128 q^{9}+O(q^{10}) \) 119 * q + 15 * q^2 + 15 * q^3 + 133 * q^4 + 6 * q^5 + 16 * q^6 + 72 * q^7 + 39 * q^8 + 128 * q^9	\( 119 q + 15 q^{2} + 15 q^{3} + 133 q^{4} + 6 q^{5} + 16 q^{6} + 72 q^{7} + 39 q^{8} + 128 q^{9} + 22 q^{10} + 119 q^{11} + 40 q^{12} + 67 q^{13} + 3 q^{14} + 22 q^{15} + 145 q^{16} + 57 q^{17} + 53 q^{18} + 68 q^{19} + 25 q^{20} + 21 q^{21} + 15 q^{22} + 21 q^{23} + 34 q^{24} + 137 q^{25} + 10 q^{26} + 54 q^{27} + 149 q^{28} + 46 q^{29} + 10 q^{30} + 87 q^{31} + 58 q^{32} + 15 q^{33} + 16 q^{34} + 40 q^{35} + 137 q^{36} + 39 q^{37} + 27 q^{38} + 72 q^{39} + 46 q^{40} + 50 q^{41} - 4 q^{42} + 122 q^{43} + 133 q^{44} + 12 q^{45} + 22 q^{46} + 92 q^{47} + 9 q^{48} + 161 q^{49} + 2 q^{50} - 12 q^{51} + 177 q^{52} + 12 q^{53} + 19 q^{54} + 6 q^{55} - 16 q^{56} + 43 q^{57} + 56 q^{58} + 39 q^{59} + 27 q^{60} + 114 q^{61} + 66 q^{62} + 196 q^{63} + 161 q^{64} + 7 q^{65} + 16 q^{66} + 59 q^{67} + 139 q^{68} - 24 q^{69} + 9 q^{70} + 11 q^{71} + 92 q^{72} + 123 q^{73} + q^{74} + 19 q^{75} + 92 q^{76} + 72 q^{77} - 101 q^{78} + 78 q^{79} - 34 q^{80} + 139 q^{81} + 73 q^{82} + 108 q^{83} - 31 q^{84} + 30 q^{85} - 18 q^{86} + 164 q^{87} + 39 q^{88} + 15 q^{89} - 41 q^{90} + 60 q^{91} - 26 q^{92} - 2 q^{93} + 45 q^{94} + 75 q^{95} + 42 q^{96} + 73 q^{97} + 32 q^{98} + 128 q^{99}+O(q^{100}) \) 119 * q + 15 * q^2 + 15 * q^3 + 133 * q^4 + 6 * q^5 + 16 * q^6 + 72 * q^7 + 39 * q^8 + 128 * q^9 + 22 * q^10 + 119 * q^11 + 40 * q^12 + 67 * q^13 + 3 * q^14 + 22 * q^15 + 145 * q^16 + 57 * q^17 + 53 * q^18 + 68 * q^19 + 25 * q^20 + 21 * q^21 + 15 * q^22 + 21 * q^23 + 34 * q^24 + 137 * q^25 + 10 * q^26 + 54 * q^27 + 149 * q^28 + 46 * q^29 + 10 * q^30 + 87 * q^31 + 58 * q^32 + 15 * q^33 + 16 * q^34 + 40 * q^35 + 137 * q^36 + 39 * q^37 + 27 * q^38 + 72 * q^39 + 46 * q^40 + 50 * q^41 - 4 * q^42 + 122 * q^43 + 133 * q^44 + 12 * q^45 + 22 * q^46 + 92 * q^47 + 9 * q^48 + 161 * q^49 + 2 * q^50 - 12 * q^51 + 177 * q^52 + 12 * q^53 + 19 * q^54 + 6 * q^55 - 16 * q^56 + 43 * q^57 + 56 * q^58 + 39 * q^59 + 27 * q^60 + 114 * q^61 + 66 * q^62 + 196 * q^63 + 161 * q^64 + 7 * q^65 + 16 * q^66 + 59 * q^67 + 139 * q^68 - 24 * q^69 + 9 * q^70 + 11 * q^71 + 92 * q^72 + 123 * q^73 + q^74 + 19 * q^75 + 92 * q^76 + 72 * q^77 - 101 * q^78 + 78 * q^79 - 34 * q^80 + 139 * q^81 + 73 * q^82 + 108 * q^83 - 31 * q^84 + 30 * q^85 - 18 * q^86 + 164 * q^87 + 39 * q^88 + 15 * q^89 - 41 * q^90 + 60 * q^91 - 26 * q^92 - 2 * q^93 + 45 * q^94 + 75 * q^95 + 42 * q^96 + 73 * q^97 + 32 * q^98 + 128 * q^99

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