LMFDB - Embedded newform 6017.2.a.e.1.4

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			1.4
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)

$f(q)$	$=$	$q-2.67204 q^{2} +2.89488 q^{3} +5.13980 q^{4} +2.14144 q^{5} -7.73524 q^{6} +4.84141 q^{7} -8.38968 q^{8} +5.38033 q^{9} +O(q^{10})$	\(q-2.67204 q^{2} +2.89488 q^{3} +5.13980 q^{4} +2.14144 q^{5} -7.73524 q^{6} +4.84141 q^{7} -8.38968 q^{8} +5.38033 q^{9} -5.72201 q^{10} +1.00000 q^{11} +14.8791 q^{12} +6.56369 q^{13} -12.9364 q^{14} +6.19921 q^{15} +12.1380 q^{16} +1.69003 q^{17} -14.3765 q^{18} +4.02182 q^{19} +11.0066 q^{20} +14.0153 q^{21} -2.67204 q^{22} -7.39752 q^{23} -24.2871 q^{24} -0.414242 q^{25} -17.5385 q^{26} +6.89077 q^{27} +24.8839 q^{28} -6.84218 q^{29} -16.5645 q^{30} -5.77440 q^{31} -15.6538 q^{32} +2.89488 q^{33} -4.51583 q^{34} +10.3676 q^{35} +27.6538 q^{36} -2.51515 q^{37} -10.7465 q^{38} +19.0011 q^{39} -17.9660 q^{40} -6.47002 q^{41} -37.4495 q^{42} +8.93835 q^{43} +5.13980 q^{44} +11.5216 q^{45} +19.7665 q^{46} +6.22930 q^{47} +35.1380 q^{48} +16.4393 q^{49} +1.10687 q^{50} +4.89244 q^{51} +33.7361 q^{52} -9.09691 q^{53} -18.4124 q^{54} +2.14144 q^{55} -40.6179 q^{56} +11.6427 q^{57} +18.2826 q^{58} -5.28248 q^{59} +31.8627 q^{60} +5.84373 q^{61} +15.4294 q^{62} +26.0484 q^{63} +17.5516 q^{64} +14.0557 q^{65} -7.73524 q^{66} -14.0083 q^{67} +8.68643 q^{68} -21.4149 q^{69} -27.7026 q^{70} +8.75598 q^{71} -45.1393 q^{72} -10.0803 q^{73} +6.72059 q^{74} -1.19918 q^{75} +20.6714 q^{76} +4.84141 q^{77} -50.7717 q^{78} -9.70030 q^{79} +25.9927 q^{80} +3.80697 q^{81} +17.2882 q^{82} -7.60100 q^{83} +72.0359 q^{84} +3.61910 q^{85} -23.8836 q^{86} -19.8073 q^{87} -8.38968 q^{88} +2.51487 q^{89} -30.7863 q^{90} +31.7775 q^{91} -38.0218 q^{92} -16.7162 q^{93} -16.6449 q^{94} +8.61249 q^{95} -45.3159 q^{96} +3.02981 q^{97} -43.9264 q^{98} +5.38033 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.67204	−1.88942	−0.944709	−	0.327909i	$-0.893656\pi$
$2$	−2.67204	−1.88942	−0.944709	+	0.327909i	$0.893656\pi$
$3$	2.89488	1.67136	0.835680	−	0.549217i	$-0.185074\pi$
$3$	2.89488	1.67136	0.835680	+	0.549217i	$0.185074\pi$
$4$	5.13980	2.56990
$5$	2.14144	0.957680	0.478840	−	0.877902i	$-0.341057\pi$
$5$	2.14144	0.957680	0.478840	+	0.877902i	$0.341057\pi$
$6$	−7.73524	−3.15790
$7$	4.84141	1.82988	0.914940	−	0.403589i	$-0.132237\pi$
$7$	4.84141	1.82988	0.914940	+	0.403589i	$0.132237\pi$
$8$	−8.38968	−2.96620
$9$	5.38033	1.79344
$10$	−5.72201	−1.80946
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	14.8791	4.29523
$13$	6.56369	1.82044	0.910220	−	0.414125i	$-0.135912\pi$
$13$	6.56369	1.82044	0.910220	+	0.414125i	$0.135912\pi$
$14$	−12.9364	−3.45741
$15$	6.19921	1.60063
$16$	12.1380	3.03449
$17$	1.69003	0.409893	0.204946	−	0.978773i	$-0.434298\pi$
$17$	1.69003	0.409893	0.204946	+	0.978773i	$0.434298\pi$
$18$	−14.3765	−3.38857
$19$	4.02182	0.922670	0.461335	−	0.887226i	$-0.347371\pi$
$19$	4.02182	0.922670	0.461335	+	0.887226i	$0.347371\pi$
$20$	11.0066	2.46114
$21$	14.0153	3.05839
$22$	−2.67204	−0.569681
$23$	−7.39752	−1.54249	−0.771244	−	0.636539i	$-0.780365\pi$
$23$	−7.39752	−1.54249	−0.771244	+	0.636539i	$0.780365\pi$
$24$	−24.2871	−4.95759
$25$	−0.414242	−0.0828483
$26$	−17.5385	−3.43957
$27$	6.89077	1.32613
$28$	24.8839	4.70261
$29$	−6.84218	−1.27056	−0.635281	−	0.772281i	$-0.719116\pi$
$29$	−6.84218	−1.27056	−0.635281	+	0.772281i	$0.719116\pi$
$30$	−16.5645	−3.02426
$31$	−5.77440	−1.03711	−0.518557	−	0.855043i	$-0.673531\pi$
$31$	−5.77440	−1.03711	−0.518557	+	0.855043i	$0.673531\pi$
$32$	−15.6538	−2.76723
$33$	2.89488	0.503934
$34$	−4.51583	−0.774459
$35$	10.3676	1.75244
$36$	27.6538	4.60897
$37$	−2.51515	−0.413488	−0.206744	−	0.978395i	$-0.566287\pi$
$37$	−2.51515	−0.413488	−0.206744	+	0.978395i	$0.566287\pi$
$38$	−10.7465	−1.74331
$39$	19.0011	3.04261
$40$	−17.9660	−2.84067
$41$	−6.47002	−1.01045	−0.505223	−	0.862989i	$-0.668590\pi$
$41$	−6.47002	−1.01045	−0.505223	+	0.862989i	$0.668590\pi$
$42$	−37.4495	−5.77858
$43$	8.93835	1.36309	0.681543	−	0.731778i	$-0.261309\pi$
$43$	8.93835	1.36309	0.681543	+	0.731778i	$0.261309\pi$
$44$	5.13980	0.774855
$45$	11.5216	1.71755
$46$	19.7665	2.91441
$47$	6.22930	0.908637	0.454318	−	0.890839i	$-0.349883\pi$
$47$	6.22930	0.908637	0.454318	+	0.890839i	$0.349883\pi$
$48$	35.1380	5.07173
$49$	16.4393	2.34846
$50$	1.10687	0.156535
$51$	4.89244	0.685078
$52$	33.7361	4.67835
$53$	−9.09691	−1.24956	−0.624778	−	0.780802i	$-0.714811\pi$
$53$	−9.09691	−1.24956	−0.624778	+	0.780802i	$0.714811\pi$
$54$	−18.4124	−2.50561
$55$	2.14144	0.288751
$56$	−40.6179	−5.42780
$57$	11.6427	1.54211
$58$	18.2826	2.40062
$59$	−5.28248	−0.687721	−0.343860	−	0.939021i	$-0.611735\pi$
$59$	−5.28248	−0.687721	−0.343860	+	0.939021i	$0.611735\pi$
$60$	31.8627	4.11346
$61$	5.84373	0.748213	0.374107	−	0.927386i	$-0.377949\pi$
$61$	5.84373	0.748213	0.374107	+	0.927386i	$0.377949\pi$
$62$	15.4294	1.95954
$63$	26.0484	3.28179
$64$	17.5516	2.19396
$65$	14.0557	1.74340
$66$	−7.73524	−0.952142
$67$	−14.0083	−1.71138	−0.855691	−	0.517487i	$-0.826868\pi$
$67$	−14.0083	−1.71138	−0.855691	+	0.517487i	$0.826868\pi$
$68$	8.68643	1.05338
$69$	−21.4149	−2.57805
$70$	−27.7026	−3.31109
$71$	8.75598	1.03914	0.519572	−	0.854427i	$-0.326091\pi$
$71$	8.75598	1.03914	0.519572	+	0.854427i	$0.326091\pi$
$72$	−45.1393	−5.31971
$73$	−10.0803	−1.17981	−0.589903	−	0.807474i	$-0.700834\pi$
$73$	−10.0803	−1.17981	−0.589903	+	0.807474i	$0.700834\pi$
$74$	6.72059	0.781253
$75$	−1.19918	−0.138469
$76$	20.6714	2.37117
$77$	4.84141	0.551730
$78$	−50.7717	−5.74876
$79$	−9.70030	−1.09137	−0.545684	−	0.837991i	$-0.683730\pi$
$79$	−9.70030	−1.09137	−0.545684	+	0.837991i	$0.683730\pi$
$80$	25.9927	2.90608
$81$	3.80697	0.422996
$82$	17.2882	1.90916
$83$	−7.60100	−0.834318	−0.417159	−	0.908833i	$-0.636974\pi$
$83$	−7.60100	−0.834318	−0.417159	+	0.908833i	$0.636974\pi$
$84$	72.0359	7.85976
$85$	3.61910	0.392546
$86$	−23.8836	−2.57544
$87$	−19.8073	−2.12356
$88$	−8.38968	−0.894343
$89$	2.51487	0.266576	0.133288	−	0.991077i	$-0.457446\pi$
$89$	2.51487	0.266576	0.133288	+	0.991077i	$0.457446\pi$
$90$	−30.7863	−3.24516
$91$	31.7775	3.33119
$92$	−38.0218	−3.96405
$93$	−16.7162	−1.73339
$94$	−16.6449	−1.71680
$95$	8.61249	0.883623
$96$	−45.3159	−4.62503
$97$	3.02981	0.307630	0.153815	−	0.988100i	$-0.450844\pi$
$97$	3.02981	0.307630	0.153815	+	0.988100i	$0.450844\pi$
$98$	−43.9264	−4.43723
$99$	5.38033	0.540744
$100$	−2.12912	−0.212912
$101$	−0.0961891	−0.00957117	−0.00478559	−	0.999989i	$-0.501523\pi$
$101$	−0.0961891	−0.00957117	−0.00478559	+	0.999989i	$0.501523\pi$
$102$	−13.0728	−1.29440
$103$	−8.15433	−0.803470	−0.401735	−	0.915756i	$-0.631593\pi$
$103$	−8.15433	−0.803470	−0.401735	+	0.915756i	$0.631593\pi$
$104$	−55.0673	−5.39979
$105$	30.0129	2.92896
$106$	24.3073	2.36093
$107$	17.1607	1.65899	0.829495	−	0.558514i	$-0.188628\pi$
$107$	17.1607	1.65899	0.829495	+	0.558514i	$0.188628\pi$
$108$	35.4172	3.40802
$109$	17.8802	1.71261	0.856304	−	0.516472i	$-0.172755\pi$
$109$	17.8802	1.71261	0.856304	+	0.516472i	$0.172755\pi$
$110$	−5.72201	−0.545572
$111$	−7.28106	−0.691088
$112$	58.7649	5.55276
$113$	−0.453027	−0.0426172	−0.0213086	−	0.999773i	$-0.506783\pi$
$113$	−0.453027	−0.0426172	−0.0213086	+	0.999773i	$0.506783\pi$
$114$	−31.1098	−2.91370
$115$	−15.8413	−1.47721
$116$	−35.1675	−3.26522
$117$	35.3148	3.26486
$118$	14.1150	1.29939
$119$	8.18213	0.750055
$120$	−52.0094	−4.74779
$121$	1.00000	0.0909091
$122$	−15.6147	−1.41369
$123$	−18.7299	−1.68882
$124$	−29.6793	−2.66528
$125$	−11.5943	−1.03702
$126$	−69.6024	−6.20067
$127$	9.57289	0.849456	0.424728	−	0.905321i	$-0.360370\pi$
$127$	9.57289	0.849456	0.424728	+	0.905321i	$0.360370\pi$
$128$	−15.5911	−1.37807
$129$	25.8754	2.27821
$130$	−37.5575	−3.29401
$131$	4.74313	0.414409	0.207205	−	0.978298i	$-0.433563\pi$
$131$	4.74313	0.414409	0.207205	+	0.978298i	$0.433563\pi$
$132$	14.8791	1.29506
$133$	19.4713	1.68838
$134$	37.4307	3.23352
$135$	14.7562	1.27001
$136$	−14.1788	−1.21582
$137$	7.90699	0.675540	0.337770	−	0.941229i	$-0.390327\pi$
$137$	7.90699	0.675540	0.337770	+	0.941229i	$0.390327\pi$
$138$	57.2216	4.87102
$139$	−18.8090	−1.59536	−0.797679	−	0.603083i	$-0.793939\pi$
$139$	−18.8090	−1.59536	−0.797679	+	0.603083i	$0.793939\pi$
$140$	53.2873	4.50360
$141$	18.0331	1.51866
$142$	−23.3963	−1.96338
$143$	6.56369	0.548883
$144$	65.3063	5.44219
$145$	−14.6521	−1.21679
$146$	26.9349	2.22915
$147$	47.5897	3.92513
$148$	−12.9274	−1.06262
$149$	−2.21406	−0.181383	−0.0906915	−	0.995879i	$-0.528908\pi$
$149$	−2.21406	−0.181383	−0.0906915	+	0.995879i	$0.528908\pi$
$150$	3.20426	0.261626
$151$	−23.2122	−1.88898	−0.944491	−	0.328537i	$-0.893444\pi$
$151$	−23.2122	−1.88898	−0.944491	+	0.328537i	$0.893444\pi$
$152$	−33.7418	−2.73682
$153$	9.09293	0.735120
$154$	−12.9364	−1.04245
$155$	−12.3655	−0.993223
$156$	97.6619	7.81921
$157$	−6.95924	−0.555408	−0.277704	−	0.960667i	$-0.589573\pi$
$157$	−6.95924	−0.555408	−0.277704	+	0.960667i	$0.589573\pi$
$158$	25.9196	2.06205
$159$	−26.3345	−2.08846
$160$	−33.5216	−2.65012
$161$	−35.8144	−2.82257
$162$	−10.1724	−0.799217
$163$	−17.8432	−1.39758	−0.698792	−	0.715325i	$-0.746279\pi$
$163$	−17.8432	−1.39758	−0.698792	+	0.715325i	$0.746279\pi$
$164$	−33.2546	−2.59675
$165$	6.19921	0.482608
$166$	20.3102	1.57638
$167$	−0.528455	−0.0408931	−0.0204466	−	0.999791i	$-0.506509\pi$
$167$	−0.528455	−0.0408931	−0.0204466	+	0.999791i	$0.506509\pi$
$168$	−117.584	−9.07180
$169$	30.0820	2.31400
$170$	−9.67038	−0.741684
$171$	21.6387	1.65476
$172$	45.9413	3.50300
$173$	16.6158	1.26327	0.631636	−	0.775265i	$-0.282384\pi$
$173$	16.6158	1.26327	0.631636	+	0.775265i	$0.282384\pi$
$174$	52.9259	4.01230
$175$	−2.00551	−0.151603
$176$	12.1380	0.914934
$177$	−15.2922	−1.14943
$178$	−6.71984	−0.503673
$179$	−0.296769	−0.0221815	−0.0110908	−	0.999938i	$-0.503530\pi$
$179$	−0.296769	−0.0221815	−0.0110908	+	0.999938i	$0.503530\pi$
$180$	59.2190	4.41392
$181$	0.934052	0.0694275	0.0347138	−	0.999397i	$-0.488948\pi$
$181$	0.934052	0.0694275	0.0347138	+	0.999397i	$0.488948\pi$
$182$	−84.9108	−6.29401
$183$	16.9169	1.25053
$184$	62.0628	4.57533
$185$	−5.38604	−0.395990
$186$	44.6664	3.27510
$187$	1.69003	0.123587
$188$	32.0174	2.33511
$189$	33.3610	2.42666
$190$	−23.0129	−1.66953
$191$	8.28478	0.599466	0.299733	−	0.954023i	$-0.403102\pi$
$191$	8.28478	0.599466	0.299733	+	0.954023i	$0.403102\pi$
$192$	50.8099	3.66689
$193$	−15.9002	−1.14452	−0.572261	−	0.820071i	$-0.693934\pi$
$193$	−15.9002	−1.14452	−0.572261	+	0.820071i	$0.693934\pi$
$194$	−8.09577	−0.581242
$195$	40.6897	2.91385
$196$	84.4945	6.03532
$197$	16.9753	1.20944	0.604721	−	0.796437i	$-0.293285\pi$
$197$	16.9753	1.20944	0.604721	+	0.796437i	$0.293285\pi$
$198$	−14.3765	−1.02169
$199$	27.0374	1.91663	0.958314	−	0.285718i	$-0.0922321\pi$
$199$	27.0374	1.91663	0.958314	+	0.285718i	$0.0922321\pi$
$200$	3.47536	0.245745
$201$	−40.5522	−2.86034
$202$	0.257021	0.0180840
$203$	−33.1258	−2.32498
$204$	25.1462	1.76058
$205$	−13.8551	−0.967685
$206$	21.7887	1.51809
$207$	−39.8011	−2.76637
$208$	79.6699	5.52411
$209$	4.02182	0.278195
$210$	−80.1957	−5.53403
$211$	9.57824	0.659393	0.329697	−	0.944087i	$-0.393054\pi$
$211$	9.57824	0.659393	0.329697	+	0.944087i	$0.393054\pi$
$212$	−46.7563	−3.21124
$213$	25.3475	1.73678
$214$	−45.8542	−3.13453
$215$	19.1409	1.30540
$216$	−57.8114	−3.93357
$217$	−27.9563	−1.89779
$218$	−47.7765	−3.23583
$219$	−29.1812	−1.97188
$220$	11.0066	0.742063
$221$	11.0928	0.746185
$222$	19.4553	1.30575
$223$	8.93543	0.598360	0.299180	−	0.954197i	$-0.403287\pi$
$223$	8.93543	0.598360	0.299180	+	0.954197i	$0.403287\pi$
$224$	−75.7865	−5.06370
$225$	−2.22876	−0.148584
$226$	1.21051	0.0805216
$227$	−19.5828	−1.29976	−0.649878	−	0.760039i	$-0.725180\pi$
$227$	−19.5828	−1.29976	−0.649878	+	0.760039i	$0.725180\pi$
$228$	59.8412	3.96308
$229$	−13.3099	−0.879540	−0.439770	−	0.898111i	$-0.644940\pi$
$229$	−13.3099	−0.879540	−0.439770	+	0.898111i	$0.644940\pi$
$230$	42.3287	2.79107
$231$	14.0153	0.922139
$232$	57.4037	3.76874
$233$	3.52154	0.230704	0.115352	−	0.993325i	$-0.463200\pi$
$233$	3.52154	0.230704	0.115352	+	0.993325i	$0.463200\pi$
$234$	−94.3627	−6.16868
$235$	13.3397	0.870184
$236$	−27.1509	−1.76737
$237$	−28.0812	−1.82407
$238$	−21.8630	−1.41717
$239$	−2.26551	−0.146544	−0.0732718	−	0.997312i	$-0.523344\pi$
$239$	−2.26551	−0.146544	−0.0732718	+	0.997312i	$0.523344\pi$
$240$	75.2458	4.85710
$241$	5.24037	0.337562	0.168781	−	0.985654i	$-0.446017\pi$
$241$	5.24037	0.337562	0.168781	+	0.985654i	$0.446017\pi$
$242$	−2.67204	−0.171765
$243$	−9.65161	−0.619151
$244$	30.0356	1.92283
$245$	35.2036	2.24908
$246$	50.0471	3.19089
$247$	26.3980	1.67966
$248$	48.4454	3.07629
$249$	−22.0040	−1.39445
$250$	30.9804	1.95937
$251$	21.7075	1.37017	0.685083	−	0.728465i	$-0.259766\pi$
$251$	21.7075	1.37017	0.685083	+	0.728465i	$0.259766\pi$
$252$	133.884	8.43387
$253$	−7.39752	−0.465078
$254$	−25.5791	−1.60498
$255$	10.4769	0.656086
$256$	6.55683	0.409802
$257$	−12.2553	−0.764465	−0.382232	−	0.924066i	$-0.624845\pi$
$257$	−12.2553	−0.764465	−0.382232	+	0.924066i	$0.624845\pi$
$258$	−69.1402	−4.30448
$259$	−12.1769	−0.756635
$260$	72.2437	4.48037
$261$	−36.8132	−2.27868
$262$	−12.6738	−0.782992
$263$	−7.07311	−0.436147	−0.218073	−	0.975932i	$-0.569977\pi$
$263$	−7.07311	−0.436147	−0.218073	+	0.975932i	$0.569977\pi$
$264$	−24.2871	−1.49477
$265$	−19.4805	−1.19668
$266$	−52.0281	−3.19005
$267$	7.28025	0.445544
$268$	−71.9997	−4.39808
$269$	−16.5784	−1.01080	−0.505401	−	0.862885i	$-0.668655\pi$
$269$	−16.5784	−1.01080	−0.505401	+	0.862885i	$0.668655\pi$
$270$	−39.4291	−2.39958
$271$	−5.08979	−0.309183	−0.154591	−	0.987978i	$-0.549406\pi$
$271$	−5.08979	−0.309183	−0.154591	+	0.987978i	$0.549406\pi$
$272$	20.5136	1.24382
$273$	91.9921	5.56761
$274$	−21.1278	−1.27638
$275$	−0.414242	−0.0249797
$276$	−110.069	−6.62535
$277$	−21.5900	−1.29722	−0.648610	−	0.761121i	$-0.724649\pi$
$277$	−21.5900	−1.29722	−0.648610	+	0.761121i	$0.724649\pi$
$278$	50.2584	3.01430
$279$	−31.0682	−1.86000
$280$	−86.9807	−5.19809
$281$	19.0095	1.13401	0.567005	−	0.823715i	$-0.308102\pi$
$281$	19.0095	1.13401	0.567005	+	0.823715i	$0.308102\pi$
$282$	−48.1851	−2.86938
$283$	10.3765	0.616817	0.308408	−	0.951254i	$-0.400204\pi$
$283$	10.3765	0.616817	0.308408	+	0.951254i	$0.400204\pi$
$284$	45.0040	2.67050
$285$	24.9321	1.47685
$286$	−17.5385	−1.03707
$287$	−31.3240	−1.84900
$288$	−84.2226	−4.96287
$289$	−14.1438	−0.831988
$290$	39.1510	2.29903
$291$	8.77093	0.514161
$292$	−51.8106	−3.03199
$293$	18.3270	1.07068	0.535338	−	0.844638i	$-0.320184\pi$
$293$	18.3270	1.07068	0.535338	+	0.844638i	$0.320184\pi$
$294$	−127.162	−7.41621
$295$	−11.3121	−0.658617
$296$	21.1013	1.22649
$297$	6.89077	0.399843
$298$	5.91607	0.342709
$299$	−48.5550	−2.80801
$300$	−6.16355	−0.355853
$301$	43.2742	2.49428
$302$	62.0240	3.56908
$303$	−0.278456	−0.0159969
$304$	48.8168	2.79984
$305$	12.5140	0.716549
$306$	−24.2967	−1.38895
$307$	−1.19540	−0.0682252	−0.0341126	−	0.999418i	$-0.510860\pi$
$307$	−1.19540	−0.0682252	−0.0341126	+	0.999418i	$0.510860\pi$
$308$	24.8839	1.41789
$309$	−23.6058	−1.34289
$310$	33.0412	1.87661
$311$	11.2879	0.640078	0.320039	−	0.947404i	$-0.396304\pi$
$311$	11.2879	0.640078	0.320039	+	0.947404i	$0.396304\pi$
$312$	−159.413	−9.02500
$313$	0.106085	0.00599629	0.00299814	−	0.999996i	$-0.499046\pi$
$313$	0.106085	0.00599629	0.00299814	+	0.999996i	$0.499046\pi$
$314$	18.5954	1.04940
$315$	55.7810	3.14290
$316$	−49.8576	−2.80471
$317$	−26.2242	−1.47290	−0.736449	−	0.676493i	$-0.763499\pi$
$317$	−26.2242	−1.47290	−0.736449	+	0.676493i	$0.763499\pi$
$318$	70.3667	3.94597
$319$	−6.84218	−0.383089
$320$	37.5858	2.10111
$321$	49.6783	2.77277
$322$	95.6976	5.33302
$323$	6.79701	0.378196
$324$	19.5671	1.08706
$325$	−2.71895	−0.150820
$326$	47.6777	2.64062
$327$	51.7609	2.86238
$328$	54.2814	2.99719
$329$	30.1586	1.66270
$330$	−16.5645	−0.911848
$331$	32.4460	1.78339	0.891696	−	0.452635i	$-0.149516\pi$
$331$	32.4460	1.78339	0.891696	+	0.452635i	$0.149516\pi$
$332$	−39.0677	−2.14412
$333$	−13.5323	−0.741568
$334$	1.41205	0.0772642
$335$	−29.9978	−1.63896
$336$	170.117	9.28066
$337$	−33.3353	−1.81589	−0.907944	−	0.419092i	$-0.862348\pi$
$337$	−33.3353	−1.81589	−0.907944	+	0.419092i	$0.862348\pi$
$338$	−80.3804	−4.37212
$339$	−1.31146	−0.0712286
$340$	18.6015	1.00881
$341$	−5.77440	−0.312701
$342$	−57.8196	−3.12653
$343$	45.6993	2.46753
$344$	−74.9899	−4.04319
$345$	−45.8587	−2.46895
$346$	−44.3980	−2.38685
$347$	−19.6156	−1.05302	−0.526511	−	0.850168i	$-0.676500\pi$
$347$	−19.6156	−1.05302	−0.526511	+	0.850168i	$0.676500\pi$
$348$	−101.806	−5.45735
$349$	−5.94722	−0.318347	−0.159174	−	0.987251i	$-0.550883\pi$
$349$	−5.94722	−0.318347	−0.159174	+	0.987251i	$0.550883\pi$
$350$	5.35881	0.286441
$351$	45.2289	2.41414
$352$	−15.6538	−0.834350
$353$	14.0809	0.749449	0.374725	−	0.927136i	$-0.377737\pi$
$353$	14.0809	0.749449	0.374725	+	0.927136i	$0.377737\pi$
$354$	40.8613	2.17175
$355$	18.7504	0.995168
$356$	12.9259	0.685074
$357$	23.6863	1.25361
$358$	0.792978	0.0419102
$359$	11.6970	0.617345	0.308673	−	0.951168i	$-0.400115\pi$
$359$	11.6970	0.617345	0.308673	+	0.951168i	$0.400115\pi$
$360$	−96.6630	−5.09459
$361$	−2.82494	−0.148681
$362$	−2.49583	−0.131178
$363$	2.89488	0.151942
$364$	163.330	8.56083
$365$	−21.5863	−1.12988
$366$	−45.2027	−2.36278
$367$	10.4245	0.544154	0.272077	−	0.962275i	$-0.412289\pi$
$367$	10.4245	0.544154	0.272077	+	0.962275i	$0.412289\pi$
$368$	−89.7909	−4.68067
$369$	−34.8108	−1.81218
$370$	14.3917	0.748190
$371$	−44.0419	−2.28654
$372$	−85.9180	−4.45464
$373$	−0.0454630	−0.00235399	−0.00117699	−	0.999999i	$-0.500375\pi$
$373$	−0.0454630	−0.00235399	−0.00117699	+	0.999999i	$0.500375\pi$
$374$	−4.51583	−0.233508
$375$	−33.5640	−1.73324
$376$	−52.2619	−2.69520
$377$	−44.9100	−2.31298
$378$	−89.1421	−4.58497
$379$	−10.9036	−0.560080	−0.280040	−	0.959988i	$-0.590348\pi$
$379$	−10.9036	−0.560080	−0.280040	+	0.959988i	$0.590348\pi$
$380$	44.2665	2.27082
$381$	27.7124	1.41975
$382$	−22.1373	−1.13264
$383$	−1.48727	−0.0759960	−0.0379980	−	0.999278i	$-0.512098\pi$
$383$	−1.48727	−0.0759960	−0.0379980	+	0.999278i	$0.512098\pi$
$384$	−45.1344	−2.30326
$385$	10.3676	0.528381
$386$	42.4860	2.16248
$387$	48.0913	2.44462
$388$	15.5726	0.790579
$389$	−23.2869	−1.18069	−0.590347	−	0.807150i	$-0.701009\pi$
$389$	−23.2869	−1.18069	−0.590347	+	0.807150i	$0.701009\pi$
$390$	−108.724	−5.50548
$391$	−12.5020	−0.632255
$392$	−137.920	−6.96602
$393$	13.7308	0.692627
$394$	−45.3588	−2.28514
$395$	−20.7726	−1.04518
$396$	27.6538	1.38966
$397$	3.86354	0.193906	0.0969528	−	0.995289i	$-0.469090\pi$
$397$	3.86354	0.193906	0.0969528	+	0.995289i	$0.469090\pi$
$398$	−72.2449	−3.62131
$399$	56.3671	2.82188
$400$	−5.02805	−0.251403
$401$	−4.00117	−0.199809	−0.0999044	−	0.994997i	$-0.531854\pi$
$401$	−4.00117	−0.199809	−0.0999044	+	0.994997i	$0.531854\pi$
$402$	108.357	5.40437
$403$	−37.9014	−1.88800
$404$	−0.494393	−0.0245970
$405$	8.15238	0.405095
$406$	88.5135	4.39285
$407$	−2.51515	−0.124671
$408$	−41.0460	−2.03208
$409$	6.56088	0.324415	0.162207	−	0.986757i	$-0.448139\pi$
$409$	6.56088	0.324415	0.162207	+	0.986757i	$0.448139\pi$
$410$	37.0215	1.82836
$411$	22.8898	1.12907
$412$	−41.9117	−2.06484
$413$	−25.5747	−1.25845
$414$	106.350	5.22682
$415$	−16.2771	−0.799010
$416$	−102.747	−5.03757
$417$	−54.4497	−2.66642
$418$	−10.7465	−0.525627
$419$	−18.3199	−0.894988	−0.447494	−	0.894287i	$-0.647683\pi$
$419$	−18.3199	−0.894988	−0.447494	+	0.894287i	$0.647683\pi$
$420$	154.260	7.52714
$421$	−8.62550	−0.420381	−0.210190	−	0.977660i	$-0.567408\pi$
$421$	−8.62550	−0.420381	−0.210190	+	0.977660i	$0.567408\pi$
$422$	−25.5934	−1.24587
$423$	33.5157	1.62959
$424$	76.3202	3.70644
$425$	−0.700081	−0.0339589
$426$	−67.7296	−3.28151
$427$	28.2919	1.36914
$428$	88.2028	4.26344
$429$	19.0011	0.917382
$430$	−51.1453	−2.46645
$431$	−8.86171	−0.426853	−0.213427	−	0.976959i	$-0.568462\pi$
$431$	−8.86171	−0.426853	−0.213427	+	0.976959i	$0.568462\pi$
$432$	83.6400	4.02413
$433$	−20.3654	−0.978697	−0.489348	−	0.872088i	$-0.662765\pi$
$433$	−20.3654	−0.978697	−0.489348	+	0.872088i	$0.662765\pi$
$434$	74.7003	3.58573
$435$	−42.4161	−2.03370
$436$	91.9005	4.40123
$437$	−29.7515	−1.42321
$438$	77.9733	3.72571
$439$	−12.5623	−0.599564	−0.299782	−	0.954008i	$-0.596914\pi$
$439$	−12.5623	−0.599564	−0.299782	+	0.954008i	$0.596914\pi$
$440$	−17.9660	−0.856495
$441$	88.4486	4.21184
$442$	−29.6405	−1.40986
$443$	−6.76735	−0.321527	−0.160763	−	0.986993i	$-0.551396\pi$
$443$	−6.76735	−0.321527	−0.160763	+	0.986993i	$0.551396\pi$
$444$	−37.4232	−1.77603
$445$	5.38544	0.255294
$446$	−23.8758	−1.13055
$447$	−6.40945	−0.303156
$448$	84.9747	4.01468
$449$	15.8833	0.749578	0.374789	−	0.927110i	$-0.377715\pi$
$449$	15.8833	0.749578	0.374789	+	0.927110i	$0.377715\pi$
$450$	5.95533	0.280737
$451$	−6.47002	−0.304661
$452$	−2.32847	−0.109522
$453$	−67.1965	−3.15717
$454$	52.3260	2.45578
$455$	68.0496	3.19021
$456$	−97.6786	−4.57422
$457$	−19.7239	−0.922646	−0.461323	−	0.887232i	$-0.652625\pi$
$457$	−19.7239	−0.922646	−0.461323	+	0.887232i	$0.652625\pi$
$458$	35.5645	1.66182
$459$	11.6456	0.543571
$460$	−81.4213	−3.79629
$461$	−23.1566	−1.07851	−0.539254	−	0.842143i	$-0.681294\pi$
$461$	−23.1566	−1.07851	−0.539254	+	0.842143i	$0.681294\pi$
$462$	−37.4495	−1.74231
$463$	−5.06602	−0.235438	−0.117719	−	0.993047i	$-0.537558\pi$
$463$	−5.06602	−0.235438	−0.117719	+	0.993047i	$0.537558\pi$
$464$	−83.0502	−3.85551
$465$	−35.7967	−1.66003
$466$	−9.40969	−0.435896
$467$	21.9696	1.01663	0.508316	−	0.861170i	$-0.330268\pi$
$467$	21.9696	1.01663	0.508316	+	0.861170i	$0.330268\pi$
$468$	181.511	8.39036
$469$	−67.8198	−3.13163
$470$	−35.6441	−1.64414
$471$	−20.1462	−0.928286
$472$	44.3184	2.03992
$473$	8.93835	0.410986
$474$	75.0341	3.44643
$475$	−1.66601	−0.0764416
$476$	42.0546	1.92757
$477$	−48.9444	−2.24101
$478$	6.05353	0.276882
$479$	39.3859	1.79959	0.899793	−	0.436317i	$-0.143717\pi$
$479$	39.3859	1.79959	0.899793	+	0.436317i	$0.143717\pi$
$480$	−97.0412	−4.42930
$481$	−16.5087	−0.752731
$482$	−14.0025	−0.637795
$483$	−103.678	−4.71753
$484$	5.13980	0.233627
$485$	6.48814	0.294611
$486$	25.7895	1.16984
$487$	4.10084	0.185827	0.0929135	−	0.995674i	$-0.470382\pi$
$487$	4.10084	0.185827	0.0929135	+	0.995674i	$0.470382\pi$
$488$	−49.0271	−2.21935
$489$	−51.6538	−2.33587
$490$	−94.0656	−4.24945
$491$	−31.0069	−1.39932	−0.699661	−	0.714475i	$-0.746666\pi$
$491$	−31.0069	−1.39932	−0.699661	+	0.714475i	$0.746666\pi$
$492$	−96.2681	−4.34010
$493$	−11.5635	−0.520794
$494$	−70.5366	−3.17359
$495$	11.5216	0.517860
$496$	−70.0896	−3.14711
$497$	42.3913	1.90151
$498$	58.7956	2.63469
$499$	−8.09339	−0.362310	−0.181155	−	0.983455i	$-0.557984\pi$
$499$	−8.09339	−0.362310	−0.181155	+	0.983455i	$0.557984\pi$
$500$	−59.5922	−2.66505
$501$	−1.52982	−0.0683471
$502$	−58.0033	−2.58882
$503$	−5.36045	−0.239011	−0.119505	−	0.992834i	$-0.538131\pi$
$503$	−5.36045	−0.239011	−0.119505	+	0.992834i	$0.538131\pi$
$504$	−218.538	−9.73445
$505$	−0.205983	−0.00916612
$506$	19.7665	0.878727
$507$	87.0839	3.86753
$508$	49.2028	2.18302
$509$	24.4912	1.08555	0.542776	−	0.839877i	$-0.317373\pi$
$509$	24.4912	1.08555	0.542776	+	0.839877i	$0.317373\pi$
$510$	−27.9946	−1.23962
$511$	−48.8027	−2.15890
$512$	13.6621	0.603787
$513$	27.7135	1.22358
$514$	32.7467	1.44439
$515$	−17.4620	−0.769467
$516$	132.995	5.85477
$517$	6.22930	0.273964
$518$	32.5371	1.42960
$519$	48.1006	2.11138
$520$	−117.923	−5.17128
$521$	6.70943	0.293946	0.146973	−	0.989141i	$-0.453047\pi$
$521$	6.70943	0.293946	0.146973	+	0.989141i	$0.453047\pi$
$522$	98.3664	4.30538
$523$	1.28831	0.0563338	0.0281669	−	0.999603i	$-0.491033\pi$
$523$	1.28831	0.0563338	0.0281669	+	0.999603i	$0.491033\pi$
$524$	24.3788	1.06499
$525$	−5.80572	−0.253382
$526$	18.8996	0.824064
$527$	−9.75892	−0.425105
$528$	35.1380	1.52918
$529$	31.7233	1.37927
$530$	52.0526	2.26102
$531$	−28.4215	−1.23339
$532$	100.079	4.33896
$533$	−42.4672	−1.83946
$534$	−19.4531	−0.841819
$535$	36.7487	1.58878
$536$	117.525	5.07630
$537$	−0.859110	−0.0370733
$538$	44.2981	1.90983
$539$	16.4393	0.708089
$540$	75.8438	3.26380
$541$	−11.6972	−0.502903	−0.251452	−	0.967870i	$-0.580908\pi$
$541$	−11.6972	−0.502903	−0.251452	+	0.967870i	$0.580908\pi$
$542$	13.6001	0.584176
$543$	2.70397	0.116038
$544$	−26.4554	−1.13427
$545$	38.2892	1.64013
$546$	−245.807	−10.5196
$547$	−1.00000	−0.0427569
$547$	−1.00000	−0.0427569
$548$	40.6404	1.73607
$549$	31.4412	1.34188
$550$	1.10687	0.0471971
$551$	−27.5180	−1.17231
$552$	179.664	7.64703
$553$	−46.9631	−1.99707
$554$	57.6895	2.45099
$555$	−15.5919	−0.661841
$556$	−96.6745	−4.09991
$557$	−8.05244	−0.341193	−0.170596	−	0.985341i	$-0.554569\pi$
$557$	−8.05244	−0.341193	−0.170596	+	0.985341i	$0.554569\pi$
$558$	83.0155	3.51433
$559$	58.6685	2.48141
$560$	125.841	5.31777
$561$	4.89244	0.206559
$562$	−50.7941	−2.14262
$563$	27.3273	1.15171	0.575854	−	0.817552i	$-0.304670\pi$
$563$	27.3273	1.15171	0.575854	+	0.817552i	$0.304670\pi$
$564$	92.6865	3.90280
$565$	−0.970129	−0.0408136
$566$	−27.7263	−1.16543
$567$	18.4311	0.774033
$568$	−73.4599	−3.08231
$569$	−26.7162	−1.12000	−0.560000	−	0.828493i	$-0.689199\pi$
$569$	−26.7162	−1.12000	−0.560000	+	0.828493i	$0.689199\pi$
$570$	−66.6196	−2.79039
$571$	32.6084	1.36462	0.682309	−	0.731064i	$-0.260976\pi$
$571$	32.6084	1.36462	0.682309	+	0.731064i	$0.260976\pi$
$572$	33.7361	1.41058
$573$	23.9835	1.00192
$574$	83.6990	3.49353
$575$	3.06436	0.127793
$576$	94.4337	3.93474
$577$	30.1520	1.25524	0.627622	−	0.778518i	$-0.284028\pi$
$577$	30.1520	1.25524	0.627622	+	0.778518i	$0.284028\pi$
$578$	37.7928	1.57197
$579$	−46.0292	−1.91291
$580$	−75.3090	−3.12703
$581$	−36.7996	−1.52670
$582$	−23.4363	−0.971465
$583$	−9.09691	−0.376755
$584$	84.5703	3.49954
$585$	75.6245	3.12669
$586$	−48.9705	−2.02295
$587$	−31.6082	−1.30461	−0.652306	−	0.757956i	$-0.726198\pi$
$587$	−31.6082	−1.30461	−0.652306	+	0.757956i	$0.726198\pi$
$588$	244.602	10.0872
$589$	−23.2236	−0.956913
$590$	30.2264	1.24440
$591$	49.1415	2.02141
$592$	−30.5289	−1.25473
$593$	42.0643	1.72737	0.863686	−	0.504030i	$-0.168150\pi$
$593$	42.0643	1.72737	0.863686	+	0.504030i	$0.168150\pi$
$594$	−18.4124	−0.755471
$595$	17.5215	0.718313
$596$	−11.3798	−0.466137
$597$	78.2699	3.20337
$598$	129.741	5.30550
$599$	−26.5555	−1.08503	−0.542515	−	0.840046i	$-0.682528\pi$
$599$	−26.5555	−1.08503	−0.542515	+	0.840046i	$0.682528\pi$
$600$	10.0607	0.410728
$601$	−6.75341	−0.275477	−0.137739	−	0.990469i	$-0.543983\pi$
$601$	−6.75341	−0.275477	−0.137739	+	0.990469i	$0.543983\pi$
$602$	−115.630	−4.71275
$603$	−75.3691	−3.06927
$604$	−119.306	−4.85450
$605$	2.14144	0.0870619
$606$	0.744046	0.0302248
$607$	26.8518	1.08988	0.544940	−	0.838475i	$-0.316552\pi$
$607$	26.8518	1.08988	0.544940	+	0.838475i	$0.316552\pi$
$608$	−62.9568	−2.55324
$609$	−95.8952	−3.88587
$610$	−33.4379	−1.35386
$611$	40.8872	1.65412
$612$	46.7359	1.88919
$613$	19.8964	0.803608	0.401804	−	0.915726i	$-0.368383\pi$
$613$	19.8964	0.803608	0.401804	+	0.915726i	$0.368383\pi$
$614$	3.19416	0.128906
$615$	−40.1090	−1.61735
$616$	−40.6179	−1.63654
$617$	−1.62190	−0.0652953	−0.0326476	−	0.999467i	$-0.510394\pi$
$617$	−1.62190	−0.0652953	−0.0326476	+	0.999467i	$0.510394\pi$
$618$	63.0757	2.53728
$619$	9.42660	0.378887	0.189444	−	0.981892i	$-0.439332\pi$
$619$	9.42660	0.378887	0.189444	+	0.981892i	$0.439332\pi$
$620$	−63.5564	−2.55249
$621$	−50.9746	−2.04554
$622$	−30.1617	−1.20938
$623$	12.1755	0.487802
$624$	230.635	9.23278
$625$	−22.7572	−0.910288
$626$	−0.283464	−0.0113295
$627$	11.6427	0.464965
$628$	−35.7691	−1.42734
$629$	−4.25069	−0.169486
$630$	−149.049	−5.93826
$631$	−47.7071	−1.89919	−0.949595	−	0.313478i	$-0.898506\pi$
$631$	−47.7071	−1.89919	−0.949595	+	0.313478i	$0.898506\pi$
$632$	81.3824	3.23722
$633$	27.7278	1.10208
$634$	70.0721	2.78292
$635$	20.4997	0.813508
$636$	−135.354	−5.36713
$637$	107.902	4.27524
$638$	18.2826	0.723815
$639$	47.1101	1.86365
$640$	−33.3874	−1.31975
$641$	20.5222	0.810579	0.405289	−	0.914189i	$-0.367171\pi$
$641$	20.5222	0.810579	0.405289	+	0.914189i	$0.367171\pi$
$642$	−132.742	−5.23892
$643$	−0.560006	−0.0220845	−0.0110422	−	0.999939i	$-0.503515\pi$
$643$	−0.560006	−0.0220845	−0.0110422	+	0.999939i	$0.503515\pi$
$644$	−184.079	−7.25373
$645$	55.4107	2.18179
$646$	−18.1619	−0.714570
$647$	20.2179	0.794848	0.397424	−	0.917635i	$-0.369904\pi$
$647$	20.2179	0.794848	0.397424	+	0.917635i	$0.369904\pi$
$648$	−31.9392	−1.25469
$649$	−5.28248	−0.207356
$650$	7.26515	0.284963
$651$	−80.9300	−3.17190
$652$	−91.7104	−3.59166
$653$	14.3043	0.559770	0.279885	−	0.960034i	$-0.409704\pi$
$653$	14.3043	0.559770	0.279885	+	0.960034i	$0.409704\pi$
$654$	−138.307	−5.40824
$655$	10.1571	0.396872
$656$	−78.5329	−3.06620
$657$	−54.2352	−2.11592
$658$	−80.5850	−3.14153
$659$	20.6854	0.805790	0.402895	−	0.915246i	$-0.368004\pi$
$659$	20.6854	0.805790	0.402895	+	0.915246i	$0.368004\pi$
$660$	31.8627	1.24025
$661$	−15.9403	−0.620005	−0.310003	−	0.950736i	$-0.600330\pi$
$661$	−15.9403	−0.620005	−0.310003	+	0.950736i	$0.600330\pi$
$662$	−86.6969	−3.36957
$663$	32.1124	1.24714
$664$	63.7700	2.47476
$665$	41.6966	1.61692
$666$	36.1590	1.40113
$667$	50.6152	1.95983
$668$	−2.71616	−0.105091
$669$	25.8670	1.00008
$670$	80.1555	3.09668
$671$	5.84373	0.225595
$672$	−219.393	−8.46326
$673$	−38.7298	−1.49293	−0.746463	−	0.665427i	$-0.768249\pi$
$673$	−38.7298	−1.49293	−0.746463	+	0.665427i	$0.768249\pi$
$674$	89.0732	3.43097
$675$	−2.85444	−0.109868
$676$	154.616	5.94676
$677$	38.7726	1.49015	0.745076	−	0.666979i	$-0.232413\pi$
$677$	38.7726	1.49015	0.745076	+	0.666979i	$0.232413\pi$
$678$	3.50427	0.134581
$679$	14.6685	0.562927
$680$	−30.3631	−1.16437
$681$	−56.6898	−2.17236
$682$	15.4294	0.590824
$683$	7.07586	0.270750	0.135375	−	0.990794i	$-0.456776\pi$
$683$	7.07586	0.270750	0.135375	+	0.990794i	$0.456776\pi$
$684$	111.219	4.25256
$685$	16.9323	0.646951
$686$	−122.110	−4.66220
$687$	−38.5304	−1.47003
$688$	108.493	4.13627
$689$	−59.7093	−2.27474
$690$	122.536	4.66488
$691$	23.5042	0.894144	0.447072	−	0.894498i	$-0.352467\pi$
$691$	23.5042	0.894144	0.447072	+	0.894498i	$0.352467\pi$
$692$	85.4017	3.24649
$693$	26.0484	0.989496
$694$	52.4138	1.98960
$695$	−40.2783	−1.52784
$696$	166.177	6.29892
$697$	−10.9345	−0.414175
$698$	15.8912	0.601491
$699$	10.1944	0.385589
$700$	−10.3079	−0.389604
$701$	4.03468	0.152388	0.0761938	−	0.997093i	$-0.475723\pi$
$701$	4.03468	0.152388	0.0761938	+	0.997093i	$0.475723\pi$
$702$	−120.853	−4.56132
$703$	−10.1155	−0.381513
$704$	17.5516	0.661503
$705$	38.6167	1.45439
$706$	−37.6247	−1.41602
$707$	−0.465691	−0.0175141
$708$	−78.5987	−2.95392
$709$	2.99919	0.112637	0.0563185	−	0.998413i	$-0.482064\pi$
$709$	2.99919	0.112637	0.0563185	+	0.998413i	$0.482064\pi$
$710$	−50.1018	−1.88029
$711$	−52.1908	−1.95731
$712$	−21.0990	−0.790718
$713$	42.7163	1.59974
$714$	−63.2908	−2.36860
$715$	14.0557	0.525655
$716$	−1.52533	−0.0570044
$717$	−6.55838	−0.244927
$718$	−31.2549	−1.16642
$719$	−48.9007	−1.82369	−0.911844	−	0.410537i	$-0.865341\pi$
$719$	−48.9007	−1.82369	−0.911844	+	0.410537i	$0.865341\pi$
$720$	139.849	5.21188
$721$	−39.4785	−1.47025
$722$	7.54834	0.280920
$723$	15.1702	0.564187
$724$	4.80084	0.178422
$725$	2.83432	0.105264
$726$	−7.73524	−0.287082
$727$	6.36181	0.235946	0.117973	−	0.993017i	$-0.462360\pi$
$727$	6.36181	0.235946	0.117973	+	0.993017i	$0.462360\pi$
$728$	−266.603	−9.88098
$729$	−39.3611	−1.45782
$730$	57.6794	2.13481
$731$	15.1061	0.558719
$732$	86.9496	3.21375
$733$	30.6006	1.13026	0.565130	−	0.825002i	$-0.308826\pi$
$733$	30.6006	1.13026	0.565130	+	0.825002i	$0.308826\pi$
$734$	−27.8547	−1.02814
$735$	101.910	3.75902
$736$	115.799	4.26842
$737$	−14.0083	−0.516001
$738$	93.0160	3.42397
$739$	41.5106	1.52699	0.763496	−	0.645812i	$-0.223481\pi$
$739$	41.5106	1.52699	0.763496	+	0.645812i	$0.223481\pi$
$740$	−27.6832	−1.01765
$741$	76.4191	2.80732
$742$	117.682	4.32023
$743$	−21.4167	−0.785701	−0.392850	−	0.919602i	$-0.628511\pi$
$743$	−21.4167	−0.785701	−0.392850	+	0.919602i	$0.628511\pi$
$744$	140.244	5.14158
$745$	−4.74128	−0.173707
$746$	0.121479	0.00444767
$747$	−40.8959	−1.49630
$748$	8.68643	0.317607
$749$	83.0822	3.03576
$750$	89.6844	3.27481
$751$	−40.7175	−1.48580	−0.742902	−	0.669400i	$-0.766551\pi$
$751$	−40.7175	−1.48580	−0.742902	+	0.669400i	$0.766551\pi$
$752$	75.6111	2.75725
$753$	62.8406	2.29004
$754$	120.001	4.37019
$755$	−49.7075	−1.80904
$756$	171.469	6.23628
$757$	41.2484	1.49920	0.749599	−	0.661892i	$-0.230246\pi$
$757$	41.2484	1.49920	0.749599	+	0.661892i	$0.230246\pi$
$758$	29.1349	1.05823
$759$	−21.4149	−0.777313
$760$	−72.2561	−2.62100
$761$	7.57664	0.274653	0.137326	−	0.990526i	$-0.456149\pi$
$761$	7.57664	0.274653	0.137326	+	0.990526i	$0.456149\pi$
$762$	−74.0486	−2.68250
$763$	86.5651	3.13387
$764$	42.5822	1.54057
$765$	19.4719	0.704010
$766$	3.97405	0.143588
$767$	−34.6726	−1.25195
$768$	18.9812	0.684926
$769$	21.1279	0.761890	0.380945	−	0.924598i	$-0.375599\pi$
$769$	21.1279	0.761890	0.380945	+	0.924598i	$0.375599\pi$
$770$	−27.7026	−0.998333
$771$	−35.4776	−1.27770
$772$	−81.7240	−2.94131
$773$	−38.2586	−1.37607	−0.688033	−	0.725680i	$-0.741525\pi$
$773$	−38.2586	−1.37607	−0.688033	+	0.725680i	$0.741525\pi$
$774$	−128.502	−4.61890
$775$	2.39200	0.0859231
$776$	−25.4191	−0.912493
$777$	−35.2506	−1.26461
$778$	62.2236	2.23082
$779$	−26.0213	−0.932309
$780$	209.137	7.48830
$781$	8.75598	0.313314
$782$	33.4060	1.19459
$783$	−47.1479	−1.68493
$784$	199.539	7.12640
$785$	−14.9028	−0.531903
$786$	−36.6892	−1.30866
$787$	−5.85274	−0.208627	−0.104314	−	0.994544i	$-0.533265\pi$
$787$	−5.85274	−0.208627	−0.104314	+	0.994544i	$0.533265\pi$
$788$	87.2499	3.10815
$789$	−20.4758	−0.728958
$790$	55.5052	1.97479
$791$	−2.19329	−0.0779843
$792$	−45.1393	−1.60395
$793$	38.3565	1.36208
$794$	−10.3235	−0.366369
$795$	−56.3936	−2.00008
$796$	138.967	4.92554
$797$	9.32280	0.330231	0.165115	−	0.986274i	$-0.447200\pi$
$797$	9.32280	0.330231	0.165115	+	0.986274i	$0.447200\pi$
$798$	−150.615	−5.33172
$799$	10.5277	0.372444
$800$	6.48445	0.229260
$801$	13.5308	0.478089
$802$	10.6913	0.377523
$803$	−10.0803	−0.355725
$804$	−208.431	−7.35078
$805$	−76.6944	−2.70312
$806$	101.274	3.56723
$807$	−47.9924	−1.68941
$808$	0.806996	0.0283900
$809$	−4.42866	−0.155703	−0.0778516	−	0.996965i	$-0.524806\pi$
$809$	−4.42866	−0.155703	−0.0778516	+	0.996965i	$0.524806\pi$
$810$	−21.7835	−0.765394
$811$	6.14997	0.215954	0.107977	−	0.994153i	$-0.465563\pi$
$811$	6.14997	0.215954	0.107977	+	0.994153i	$0.465563\pi$
$812$	−170.260	−5.97496
$813$	−14.7343	−0.516756
$814$	6.72059	0.235557
$815$	−38.2100	−1.33844
$816$	59.3843	2.07887
$817$	35.9485	1.25768
$818$	−17.5310	−0.612955
$819$	170.974	5.97430
$820$	−71.2127	−2.48686
$821$	33.3364	1.16345	0.581724	−	0.813386i	$-0.302378\pi$
$821$	33.3364	1.16345	0.581724	+	0.813386i	$0.302378\pi$
$822$	−61.1625	−2.13329
$823$	−50.0725	−1.74542	−0.872708	−	0.488242i	$-0.837638\pi$
$823$	−50.0725	−1.74542	−0.872708	+	0.488242i	$0.837638\pi$
$824$	68.4123	2.38325
$825$	−1.19918	−0.0417501
$826$	68.3366	2.37773
$827$	−40.5903	−1.41146	−0.705732	−	0.708479i	$-0.749382\pi$
$827$	−40.5903	−1.41146	−0.705732	+	0.708479i	$0.749382\pi$
$828$	−204.570	−7.10929
$829$	52.7845	1.83328	0.916640	−	0.399713i	$-0.130890\pi$
$829$	52.7845	1.83328	0.916640	+	0.399713i	$0.130890\pi$
$830$	43.4930	1.50966
$831$	−62.5006	−2.16812
$832$	115.204	3.99397
$833$	27.7829	0.962619
$834$	145.492	5.03797
$835$	−1.13165	−0.0391625
$836$	20.6714	0.714935
$837$	−39.7901	−1.37535
$838$	48.9516	1.69101
$839$	10.3029	0.355697	0.177848	−	0.984058i	$-0.443086\pi$
$839$	10.3029	0.355697	0.177848	+	0.984058i	$0.443086\pi$
$840$	−251.799	−8.68788
$841$	17.8154	0.614326
$842$	23.0477	0.794276
$843$	55.0301	1.89534
$844$	49.2303	1.69458
$845$	64.4188	2.21607
$846$	−89.5553	−3.07898
$847$	4.84141	0.166353
$848$	−110.418	−3.79177
$849$	30.0386	1.03092
$850$	1.87065	0.0641626
$851$	18.6059	0.637801
$852$	130.281	4.46336
$853$	38.6350	1.32284	0.661419	−	0.750016i	$-0.269954\pi$
$853$	38.6350	1.32284	0.661419	+	0.750016i	$0.269954\pi$
$854$	−75.5971	−2.58688
$855$	46.3380	1.58473
$856$	−143.973	−4.92090
$857$	−27.1100	−0.926061	−0.463031	−	0.886342i	$-0.653238\pi$
$857$	−27.1100	−0.926061	−0.463031	+	0.886342i	$0.653238\pi$
$858$	−50.7717	−1.73332
$859$	43.6041	1.48775	0.743876	−	0.668317i	$-0.232985\pi$
$859$	43.6041	1.48775	0.743876	+	0.668317i	$0.232985\pi$
$860$	98.3806	3.35475
$861$	−90.6792	−3.09034
$862$	23.6788	0.806505
$863$	−47.2978	−1.61004	−0.805018	−	0.593250i	$-0.797845\pi$
$863$	−47.2978	−1.61004	−0.805018	+	0.593250i	$0.797845\pi$
$864$	−107.867	−3.66970
$865$	35.5816	1.20981
$866$	54.4171	1.84917
$867$	−40.9446	−1.39055
$868$	−143.690	−4.87715
$869$	−9.70030	−0.329060
$870$	113.338	3.84250
$871$	−91.9459	−3.11547
$872$	−150.009	−5.07994
$873$	16.3014	0.551717
$874$	79.4973	2.68903
$875$	−56.1326	−1.89763
$876$	−149.985	−5.06754
$877$	−14.8300	−0.500774	−0.250387	−	0.968146i	$-0.580558\pi$
$877$	−14.8300	−0.500774	−0.250387	+	0.968146i	$0.580558\pi$
$878$	33.5669	1.13283
$879$	53.0545	1.78948
$880$	25.9927	0.876215
$881$	26.8650	0.905103	0.452552	−	0.891738i	$-0.350514\pi$
$881$	26.8650	0.905103	0.452552	+	0.891738i	$0.350514\pi$
$882$	−236.338	−7.95792
$883$	25.8894	0.871248	0.435624	−	0.900129i	$-0.356528\pi$
$883$	25.8894	0.871248	0.435624	+	0.900129i	$0.356528\pi$
$884$	57.0150	1.91762
$885$	−32.7472	−1.10079
$886$	18.0826	0.607498
$887$	0.423662	0.0142252	0.00711259	−	0.999975i	$-0.497736\pi$
$887$	0.423662	0.0142252	0.00711259	+	0.999975i	$0.497736\pi$
$888$	61.0858	2.04991
$889$	46.3463	1.55440
$890$	−14.3901	−0.482358
$891$	3.80697	0.127538
$892$	45.9263	1.53773
$893$	25.0531	0.838372
$894$	17.1263	0.572789
$895$	−0.635512	−0.0212428
$896$	−75.4830	−2.52171
$897$	−140.561	−4.69319
$898$	−42.4407	−1.41627
$899$	39.5095	1.31772
$900$	−11.4554	−0.381846
$901$	−15.3741	−0.512184
$902$	17.2882	0.575632
$903$	125.274	4.16885
$904$	3.80075	0.126411
$905$	2.00021	0.0664894
$906$	179.552	5.96521
$907$	11.6456	0.386687	0.193343	−	0.981131i	$-0.438067\pi$
$907$	11.6456	0.386687	0.193343	+	0.981131i	$0.438067\pi$
$908$	−100.652	−3.34025
$909$	−0.517529	−0.0171654
$910$	−181.831	−6.02765
$911$	27.6124	0.914840	0.457420	−	0.889251i	$-0.348774\pi$
$911$	27.6124	0.914840	0.457420	+	0.889251i	$0.348774\pi$
$912$	141.319	4.67953
$913$	−7.60100	−0.251556
$914$	52.7031	1.74326
$915$	36.2265	1.19761
$916$	−68.4100	−2.26033
$917$	22.9634	0.758320
$918$	−31.1176	−1.02703
$919$	−47.7355	−1.57465	−0.787324	−	0.616540i	$-0.788534\pi$
$919$	−47.7355	−1.57465	−0.787324	+	0.616540i	$0.788534\pi$
$920$	132.904	4.38171
$921$	−3.46055	−0.114029
$922$	61.8753	2.03775
$923$	57.4716	1.89170
$924$	72.0359	2.36981
$925$	1.04188	0.0342568
$926$	13.5366	0.444841
$927$	−43.8730	−1.44098
$928$	107.106	3.51593
$929$	6.92757	0.227286	0.113643	−	0.993522i	$-0.463748\pi$
$929$	6.92757	0.227286	0.113643	+	0.993522i	$0.463748\pi$
$930$	95.6503	3.13650
$931$	66.1158	2.16686
$932$	18.1000	0.592886
$933$	32.6771	1.06980
$934$	−58.7037	−1.92084
$935$	3.61910	0.118357
$936$	−296.280	−9.68422
$937$	32.9791	1.07738	0.538690	−	0.842504i	$-0.318919\pi$
$937$	32.9791	1.07738	0.538690	+	0.842504i	$0.318919\pi$
$938$	181.217	5.91695
$939$	0.307104	0.0100220
$940$	68.5633	2.23629
$941$	39.7600	1.29614	0.648069	−	0.761582i	$-0.275577\pi$
$941$	39.7600	1.29614	0.648069	+	0.761582i	$0.275577\pi$
$942$	53.8314	1.75392
$943$	47.8621	1.55860
$944$	−64.1186	−2.08688
$945$	71.4406	2.32396
$946$	−23.8836	−0.776524
$947$	41.7048	1.35522	0.677612	−	0.735419i	$-0.263015\pi$
$947$	41.7048	1.35522	0.677612	+	0.735419i	$0.263015\pi$
$948$	−144.332	−4.68768
$949$	−66.1638	−2.14777
$950$	4.45164	0.144430
$951$	−75.9159	−2.46174
$952$	−68.6455	−2.22481
$953$	34.2835	1.11055	0.555276	−	0.831666i	$-0.312613\pi$
$953$	34.2835	1.11055	0.555276	+	0.831666i	$0.312613\pi$
$954$	130.781	4.23420
$955$	17.7414	0.574097
$956$	−11.6443	−0.376603
$957$	−19.8073	−0.640279
$958$	−105.241	−3.40017
$959$	38.2810	1.23616
$960$	108.806	3.51171
$961$	2.34374	0.0756044
$962$	44.1119	1.42222
$963$	92.3304	2.97531
$964$	26.9345	0.867501
$965$	−34.0493	−1.09609
$966$	277.033	8.91339
$967$	26.9141	0.865498	0.432749	−	0.901514i	$-0.357544\pi$
$967$	26.9141	0.865498	0.432749	+	0.901514i	$0.357544\pi$
$968$	−8.38968	−0.269655
$969$	19.6765	0.632101
$970$	−17.3366	−0.556644
$971$	45.4297	1.45791	0.728954	−	0.684562i	$-0.240007\pi$
$971$	45.4297	1.45791	0.728954	+	0.684562i	$0.240007\pi$
$972$	−49.6074	−1.59116
$973$	−91.0620	−2.91931
$974$	−10.9576	−0.351105
$975$	−7.87104	−0.252075
$976$	70.9311	2.27045
$977$	−51.2518	−1.63969	−0.819845	−	0.572585i	$-0.805941\pi$
$977$	−51.2518	−1.63969	−0.819845	+	0.572585i	$0.805941\pi$
$978$	138.021	4.41343
$979$	2.51487	0.0803756
$980$	180.940	5.77991
$981$	96.2011	3.07147
$982$	82.8517	2.64390
$983$	−2.04463	−0.0652134	−0.0326067	−	0.999468i	$-0.510381\pi$
$983$	−2.04463	−0.0652134	−0.0326067	+	0.999468i	$0.510381\pi$
$984$	157.138	5.00938
$985$	36.3516	1.15826
$986$	30.8982	0.983998
$987$	87.3055	2.77897
$988$	135.681	4.31657
$989$	−66.1216	−2.10254
$990$	−30.7863	−0.978453
$991$	−10.1879	−0.323629	−0.161814	−	0.986821i	$-0.551735\pi$
$991$	−10.1879	−0.323629	−0.161814	+	0.986821i	$0.551735\pi$
$992$	90.3914	2.86993
$993$	93.9272	2.98069
$994$	−113.271	−3.59275
$995$	57.8988	1.83552
$996$	−113.096	−3.58359
$997$	0.675470	0.0213924	0.0106962	−	0.999943i	$-0.496595\pi$
$997$	0.675470	0.0213924	0.0106962	+	0.999943i	$0.496595\pi$
$998$	21.6259	0.684555
$999$	−17.3313	−0.548339

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6017.2.a.e.1.4	✓	119

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6017.2.a.e.1.4	✓	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)

\(f(q)\)	\(=\)	\(q-2.67204 q^{2} +2.89488 q^{3} +5.13980 q^{4} +2.14144 q^{5} -7.73524 q^{6} +4.84141 q^{7} -8.38968 q^{8} +5.38033 q^{9} +O(q^{10})\)	\(q-2.67204 q^{2} +2.89488 q^{3} +5.13980 q^{4} +2.14144 q^{5} -7.73524 q^{6} +4.84141 q^{7} -8.38968 q^{8} +5.38033 q^{9} -5.72201 q^{10} +1.00000 q^{11} +14.8791 q^{12} +6.56369 q^{13} -12.9364 q^{14} +6.19921 q^{15} +12.1380 q^{16} +1.69003 q^{17} -14.3765 q^{18} +4.02182 q^{19} +11.0066 q^{20} +14.0153 q^{21} -2.67204 q^{22} -7.39752 q^{23} -24.2871 q^{24} -0.414242 q^{25} -17.5385 q^{26} +6.89077 q^{27} +24.8839 q^{28} -6.84218 q^{29} -16.5645 q^{30} -5.77440 q^{31} -15.6538 q^{32} +2.89488 q^{33} -4.51583 q^{34} +10.3676 q^{35} +27.6538 q^{36} -2.51515 q^{37} -10.7465 q^{38} +19.0011 q^{39} -17.9660 q^{40} -6.47002 q^{41} -37.4495 q^{42} +8.93835 q^{43} +5.13980 q^{44} +11.5216 q^{45} +19.7665 q^{46} +6.22930 q^{47} +35.1380 q^{48} +16.4393 q^{49} +1.10687 q^{50} +4.89244 q^{51} +33.7361 q^{52} -9.09691 q^{53} -18.4124 q^{54} +2.14144 q^{55} -40.6179 q^{56} +11.6427 q^{57} +18.2826 q^{58} -5.28248 q^{59} +31.8627 q^{60} +5.84373 q^{61} +15.4294 q^{62} +26.0484 q^{63} +17.5516 q^{64} +14.0557 q^{65} -7.73524 q^{66} -14.0083 q^{67} +8.68643 q^{68} -21.4149 q^{69} -27.7026 q^{70} +8.75598 q^{71} -45.1393 q^{72} -10.0803 q^{73} +6.72059 q^{74} -1.19918 q^{75} +20.6714 q^{76} +4.84141 q^{77} -50.7717 q^{78} -9.70030 q^{79} +25.9927 q^{80} +3.80697 q^{81} +17.2882 q^{82} -7.60100 q^{83} +72.0359 q^{84} +3.61910 q^{85} -23.8836 q^{86} -19.8073 q^{87} -8.38968 q^{88} +2.51487 q^{89} -30.7863 q^{90} +31.7775 q^{91} -38.0218 q^{92} -16.7162 q^{93} -16.6449 q^{94} +8.61249 q^{95} -45.3159 q^{96} +3.02981 q^{97} -43.9264 q^{98} +5.38033 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 119 q + 15 q^{2} + 15 q^{3} + 133 q^{4} + 6 q^{5} + 16 q^{6} + 72 q^{7} + 39 q^{8} + 128 q^{9}+O(q^{10}) \) 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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