LMFDB - Embedded newform 6013.2.a.d.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6013,2,Mod(1,6013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6013, 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("6013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6013 = 7 \cdot 859 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6013.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:	$48.0140467354$
Analytic rank:	$1$
Dimension:	$104$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	6013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.73548 q^{2} -2.83530 q^{3} +5.48288 q^{4} +2.55962 q^{5} +7.75591 q^{6} +1.00000 q^{7} -9.52736 q^{8} +5.03891 q^{9} +O(q^{10})$	\(q-2.73548 q^{2} -2.83530 q^{3} +5.48288 q^{4} +2.55962 q^{5} +7.75591 q^{6} +1.00000 q^{7} -9.52736 q^{8} +5.03891 q^{9} -7.00181 q^{10} +3.33476 q^{11} -15.5456 q^{12} -4.48850 q^{13} -2.73548 q^{14} -7.25729 q^{15} +15.0962 q^{16} -7.45974 q^{17} -13.7838 q^{18} +6.21614 q^{19} +14.0341 q^{20} -2.83530 q^{21} -9.12218 q^{22} +0.696136 q^{23} +27.0129 q^{24} +1.55168 q^{25} +12.2782 q^{26} -5.78090 q^{27} +5.48288 q^{28} -4.39953 q^{29} +19.8522 q^{30} -7.80882 q^{31} -22.2407 q^{32} -9.45503 q^{33} +20.4060 q^{34} +2.55962 q^{35} +27.6277 q^{36} +3.11565 q^{37} -17.0042 q^{38} +12.7262 q^{39} -24.3865 q^{40} -0.324376 q^{41} +7.75591 q^{42} +6.13440 q^{43} +18.2841 q^{44} +12.8977 q^{45} -1.90427 q^{46} +4.93014 q^{47} -42.8022 q^{48} +1.00000 q^{49} -4.24459 q^{50} +21.1506 q^{51} -24.6099 q^{52} +12.2236 q^{53} +15.8136 q^{54} +8.53573 q^{55} -9.52736 q^{56} -17.6246 q^{57} +12.0349 q^{58} -1.60669 q^{59} -39.7909 q^{60} +11.4997 q^{61} +21.3609 q^{62} +5.03891 q^{63} +30.6467 q^{64} -11.4889 q^{65} +25.8641 q^{66} -10.8966 q^{67} -40.9008 q^{68} -1.97375 q^{69} -7.00181 q^{70} -3.23487 q^{71} -48.0075 q^{72} +2.03111 q^{73} -8.52280 q^{74} -4.39947 q^{75} +34.0824 q^{76} +3.33476 q^{77} -34.8124 q^{78} +3.43420 q^{79} +38.6406 q^{80} +1.27385 q^{81} +0.887326 q^{82} -14.4355 q^{83} -15.5456 q^{84} -19.0941 q^{85} -16.7806 q^{86} +12.4740 q^{87} -31.7714 q^{88} -12.6746 q^{89} -35.2815 q^{90} -4.48850 q^{91} +3.81683 q^{92} +22.1403 q^{93} -13.4863 q^{94} +15.9110 q^{95} +63.0590 q^{96} -8.81741 q^{97} -2.73548 q^{98} +16.8035 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 104 q - 17 q^{2} - 34 q^{3} + 99 q^{4} - 46 q^{5} - 18 q^{6} + 104 q^{7} - 48 q^{8} + 98 q^{9}+O(q^{10}) $ 104 * q - 17 * q^2 - 34 * q^3 + 99 * q^4 - 46 * q^5 - 18 * q^6 + 104 * q^7 - 48 * q^8 + 98 * q^9	\( 104 q - 17 q^{2} - 34 q^{3} + 99 q^{4} - 46 q^{5} - 18 q^{6} + 104 q^{7} - 48 q^{8} + 98 q^{9} - 17 q^{10} - 46 q^{11} - 62 q^{12} - 37 q^{13} - 17 q^{14} - 17 q^{15} + 93 q^{16} - 75 q^{17} - 41 q^{18} - 40 q^{19} - 106 q^{20} - 34 q^{21} - 14 q^{22} - 57 q^{23} - 38 q^{24} + 102 q^{25} - 45 q^{26} - 121 q^{27} + 99 q^{28} - 29 q^{29} + 26 q^{30} - 42 q^{31} - 113 q^{32} - 42 q^{33} - 7 q^{34} - 46 q^{35} + 99 q^{36} - 31 q^{37} - 62 q^{38} - 9 q^{39} - 36 q^{40} - 106 q^{41} - 18 q^{42} - 29 q^{43} - 60 q^{44} - 121 q^{45} + 21 q^{46} - 141 q^{47} - 88 q^{48} + 104 q^{49} - 70 q^{50} - 2 q^{51} - 58 q^{52} - 70 q^{53} - 49 q^{54} - 14 q^{55} - 48 q^{56} - 11 q^{57} - 28 q^{58} - 202 q^{59} + 17 q^{60} - 79 q^{61} - 41 q^{62} + 98 q^{63} + 110 q^{64} - 34 q^{65} - 21 q^{66} - 57 q^{67} - 180 q^{68} - 99 q^{69} - 17 q^{70} - 109 q^{71} - 73 q^{72} - 46 q^{73} - 7 q^{74} - 146 q^{75} - 54 q^{76} - 46 q^{77} - 42 q^{78} - 12 q^{79} - 187 q^{80} + 100 q^{81} - 45 q^{82} - 156 q^{83} - 62 q^{84} - 13 q^{85} - 8 q^{86} - 76 q^{87} - 6 q^{88} - 140 q^{89} - 5 q^{90} - 37 q^{91} - 98 q^{92} - q^{93} - 17 q^{94} - 48 q^{95} - 12 q^{96} - 63 q^{97} - 17 q^{98} - 78 q^{99}+O(q^{100}) \) 104 * q - 17 * q^2 - 34 * q^3 + 99 * q^4 - 46 * q^5 - 18 * q^6 + 104 * q^7 - 48 * q^8 + 98 * q^9 - 17 * q^10 - 46 * q^11 - 62 * q^12 - 37 * q^13 - 17 * q^14 - 17 * q^15 + 93 * q^16 - 75 * q^17 - 41 * q^18 - 40 * q^19 - 106 * q^20 - 34 * q^21 - 14 * q^22 - 57 * q^23 - 38 * q^24 + 102 * q^25 - 45 * q^26 - 121 * q^27 + 99 * q^28 - 29 * q^29 + 26 * q^30 - 42 * q^31 - 113 * q^32 - 42 * q^33 - 7 * q^34 - 46 * q^35 + 99 * q^36 - 31 * q^37 - 62 * q^38 - 9 * q^39 - 36 * q^40 - 106 * q^41 - 18 * q^42 - 29 * q^43 - 60 * q^44 - 121 * q^45 + 21 * q^46 - 141 * q^47 - 88 * q^48 + 104 * q^49 - 70 * q^50 - 2 * q^51 - 58 * q^52 - 70 * q^53 - 49 * q^54 - 14 * q^55 - 48 * q^56 - 11 * q^57 - 28 * q^58 - 202 * q^59 + 17 * q^60 - 79 * q^61 - 41 * q^62 + 98 * q^63 + 110 * q^64 - 34 * q^65 - 21 * q^66 - 57 * q^67 - 180 * q^68 - 99 * q^69 - 17 * q^70 - 109 * q^71 - 73 * q^72 - 46 * q^73 - 7 * q^74 - 146 * q^75 - 54 * q^76 - 46 * q^77 - 42 * q^78 - 12 * q^79 - 187 * q^80 + 100 * q^81 - 45 * q^82 - 156 * q^83 - 62 * q^84 - 13 * q^85 - 8 * q^86 - 76 * q^87 - 6 * q^88 - 140 * q^89 - 5 * q^90 - 37 * q^91 - 98 * q^92 - q^93 - 17 * q^94 - 48 * q^95 - 12 * q^96 - 63 * q^97 - 17 * q^98 - 78 * 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 $

$2$	−2.73548	−1.93428	−0.967140	−	0.254244i	$-0.918173\pi$
$2$	−2.73548	−1.93428	−0.967140	+	0.254244i	$0.918173\pi$
$3$	−2.83530	−1.63696	−0.818480	−	0.574536i	$-0.805183\pi$
$3$	−2.83530	−1.63696	−0.818480	+	0.574536i	$0.805183\pi$
$4$	5.48288	2.74144
$5$	2.55962	1.14470	0.572349	−	0.820010i	$-0.306032\pi$
$5$	2.55962	1.14470	0.572349	+	0.820010i	$0.306032\pi$
$6$	7.75591	3.16634
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−9.52736	−3.36843
$9$	5.03891	1.67964
$10$	−7.00181	−2.21417
$11$	3.33476	1.00547	0.502734	−	0.864441i	$-0.332328\pi$
$11$	3.33476	1.00547	0.502734	+	0.864441i	$0.332328\pi$
$12$	−15.5456	−4.48762
$13$	−4.48850	−1.24489	−0.622444	−	0.782665i	$-0.713860\pi$
$13$	−4.48850	−1.24489	−0.622444	+	0.782665i	$0.713860\pi$
$14$	−2.73548	−0.731089
$15$	−7.25729	−1.87383
$16$	15.0962	3.77405
$17$	−7.45974	−1.80925	−0.904626	−	0.426206i	$-0.859850\pi$
$17$	−7.45974	−1.80925	−0.904626	+	0.426206i	$0.859850\pi$
$18$	−13.7838	−3.24888
$19$	6.21614	1.42608	0.713041	−	0.701123i	$-0.247317\pi$
$19$	6.21614	1.42608	0.713041	+	0.701123i	$0.247317\pi$
$20$	14.0341	3.13812
$21$	−2.83530	−0.618712
$22$	−9.12218	−1.94486
$23$	0.696136	0.145154	0.0725772	−	0.997363i	$-0.476878\pi$
$23$	0.696136	0.145154	0.0725772	+	0.997363i	$0.476878\pi$
$24$	27.0129	5.51398
$25$	1.55168	0.310335
$26$	12.2782	2.40796
$27$	−5.78090	−1.11253
$28$	5.48288	1.03617
$29$	−4.39953	−0.816973	−0.408487	−	0.912764i	$-0.633943\pi$
$29$	−4.39953	−0.816973	−0.408487	+	0.912764i	$0.633943\pi$
$30$	19.8522	3.62450
$31$	−7.80882	−1.40251	−0.701253	−	0.712912i	$-0.747376\pi$
$31$	−7.80882	−1.40251	−0.701253	+	0.712912i	$0.747376\pi$
$32$	−22.2407	−3.93164
$33$	−9.45503	−1.64591
$34$	20.4060	3.49960
$35$	2.55962	0.432656
$36$	27.6277	4.60462
$37$	3.11565	0.512209	0.256105	−	0.966649i	$-0.417561\pi$
$37$	3.11565	0.512209	0.256105	+	0.966649i	$0.417561\pi$
$38$	−17.0042	−2.75844
$39$	12.7262	2.03783
$40$	−24.3865	−3.85584
$41$	−0.324376	−0.0506591	−0.0253295	−	0.999679i	$-0.508064\pi$
$41$	−0.324376	−0.0506591	−0.0253295	+	0.999679i	$0.508064\pi$
$42$	7.75591	1.19676
$43$	6.13440	0.935487	0.467743	−	0.883864i	$-0.345067\pi$
$43$	6.13440	0.935487	0.467743	+	0.883864i	$0.345067\pi$
$44$	18.2841	2.75643
$45$	12.8977	1.92268
$46$	−1.90427	−0.280769
$47$	4.93014	0.719135	0.359567	−	0.933119i	$-0.382924\pi$
$47$	4.93014	0.719135	0.359567	+	0.933119i	$0.382924\pi$
$48$	−42.8022	−6.17796
$49$	1.00000	0.142857
$50$	−4.24459	−0.600276
$51$	21.1506	2.96167
$52$	−24.6099	−3.41278
$53$	12.2236	1.67904	0.839521	−	0.543326i	$-0.182835\pi$
$53$	12.2236	1.67904	0.839521	+	0.543326i	$0.182835\pi$
$54$	15.8136	2.15195
$55$	8.53573	1.15096
$56$	−9.52736	−1.27315
$57$	−17.6246	−2.33444
$58$	12.0349	1.58025
$59$	−1.60669	−0.209174	−0.104587	−	0.994516i	$-0.533352\pi$
$59$	−1.60669	−0.209174	−0.104587	+	0.994516i	$0.533352\pi$
$60$	−39.7909	−5.13698
$61$	11.4997	1.47239	0.736195	−	0.676769i	$-0.236621\pi$
$61$	11.4997	1.47239	0.736195	+	0.676769i	$0.236621\pi$
$62$	21.3609	2.71284
$63$	5.03891	0.634842
$64$	30.6467	3.83084
$65$	−11.4889	−1.42502
$66$	25.8641	3.18365
$67$	−10.8966	−1.33123	−0.665614	−	0.746296i	$-0.731830\pi$
$67$	−10.8966	−1.33123	−0.665614	+	0.746296i	$0.731830\pi$
$68$	−40.9008	−4.95996
$69$	−1.97375	−0.237612
$70$	−7.00181	−0.836877
$71$	−3.23487	−0.383908	−0.191954	−	0.981404i	$-0.561482\pi$
$71$	−3.23487	−0.383908	−0.191954	+	0.981404i	$0.561482\pi$
$72$	−48.0075	−5.65773
$73$	2.03111	0.237724	0.118862	−	0.992911i	$-0.462075\pi$
$73$	2.03111	0.237724	0.118862	+	0.992911i	$0.462075\pi$
$74$	−8.52280	−0.990756
$75$	−4.39947	−0.508006
$76$	34.0824	3.90952
$77$	3.33476	0.380031
$78$	−34.8124	−3.94173
$79$	3.43420	0.386377	0.193189	−	0.981162i	$-0.438117\pi$
$79$	3.43420	0.386377	0.193189	+	0.981162i	$0.438117\pi$
$80$	38.6406	4.32015
$81$	1.27385	0.141539
$82$	0.887326	0.0979888
$83$	−14.4355	−1.58450	−0.792248	−	0.610199i	$-0.791090\pi$
$83$	−14.4355	−1.58450	−0.792248	+	0.610199i	$0.791090\pi$
$84$	−15.5456	−1.69616
$85$	−19.0941	−2.07105
$86$	−16.7806	−1.80949
$87$	12.4740	1.33735
$88$	−31.7714	−3.38685
$89$	−12.6746	−1.34351	−0.671754	−	0.740774i	$-0.734459\pi$
$89$	−12.6746	−1.34351	−0.671754	+	0.740774i	$0.734459\pi$
$90$	−35.2815	−3.71899
$91$	−4.48850	−0.470523
$92$	3.81683	0.397932
$93$	22.1403	2.29585
$94$	−13.4863	−1.39101
$95$	15.9110	1.63243
$96$	63.0590	6.43593
$97$	−8.81741	−0.895272	−0.447636	−	0.894216i	$-0.647734\pi$
$97$	−8.81741	−0.895272	−0.447636	+	0.894216i	$0.647734\pi$
$98$	−2.73548	−0.276326
$99$	16.8035	1.68882
$100$	8.50766	0.850766
$101$	−3.64463	−0.362654	−0.181327	−	0.983423i	$-0.558039\pi$
$101$	−3.64463	−0.362654	−0.181327	+	0.983423i	$0.558039\pi$
$102$	−57.8571	−5.72870
$103$	−6.05425	−0.596543	−0.298271	−	0.954481i	$-0.596410\pi$
$103$	−6.05425	−0.596543	−0.298271	+	0.954481i	$0.596410\pi$
$104$	42.7636	4.19332
$105$	−7.25729	−0.708239
$106$	−33.4375	−3.24774
$107$	11.5694	1.11845	0.559227	−	0.829014i	$-0.311098\pi$
$107$	11.5694	1.11845	0.559227	+	0.829014i	$0.311098\pi$
$108$	−31.6960	−3.04995
$109$	−2.54221	−0.243499	−0.121750	−	0.992561i	$-0.538850\pi$
$109$	−2.54221	−0.243499	−0.121750	+	0.992561i	$0.538850\pi$
$110$	−23.3494	−2.22627
$111$	−8.83378	−0.838465
$112$	15.0962	1.42646
$113$	−1.26525	−0.119025	−0.0595125	−	0.998228i	$-0.518955\pi$
$113$	−1.26525	−0.119025	−0.0595125	+	0.998228i	$0.518955\pi$
$114$	48.2119	4.51545
$115$	1.78185	0.166158
$116$	−24.1221	−2.23968
$117$	−22.6171	−2.09096
$118$	4.39509	0.404600
$119$	−7.45974	−0.683833
$120$	69.1429	6.31185
$121$	0.120609	0.0109645
$122$	−31.4573	−2.84801
$123$	0.919703	0.0829268
$124$	−42.8148	−3.84488
$125$	−8.82641	−0.789458
$126$	−13.7838	−1.22796
$127$	14.4215	1.27970	0.639850	−	0.768500i	$-0.278996\pi$
$127$	14.4215	1.27970	0.639850	+	0.768500i	$0.278996\pi$
$128$	−39.3522	−3.47828
$129$	−17.3928	−1.53135
$130$	31.4277	2.75639
$131$	−17.2992	−1.51143	−0.755717	−	0.654898i	$-0.772711\pi$
$131$	−17.2992	−1.51143	−0.755717	+	0.654898i	$0.772711\pi$
$132$	−51.8408	−4.51216
$133$	6.21614	0.539008
$134$	29.8074	2.57497
$135$	−14.7969	−1.27352
$136$	71.0716	6.09434
$137$	−8.21170	−0.701573	−0.350786	−	0.936456i	$-0.614086\pi$
$137$	−8.21170	−0.701573	−0.350786	+	0.936456i	$0.614086\pi$
$138$	5.39917	0.459608
$139$	20.2432	1.71700	0.858502	−	0.512811i	$-0.171396\pi$
$139$	20.2432	1.71700	0.858502	+	0.512811i	$0.171396\pi$
$140$	14.0341	1.18610
$141$	−13.9784	−1.17719
$142$	8.84894	0.742586
$143$	−14.9681	−1.25169
$144$	76.0683	6.33903
$145$	−11.2612	−0.935188
$146$	−5.55608	−0.459825
$147$	−2.83530	−0.233851
$148$	17.0827	1.40419
$149$	16.6089	1.36066	0.680328	−	0.732908i	$-0.261837\pi$
$149$	16.6089	1.36066	0.680328	+	0.732908i	$0.261837\pi$
$150$	12.0347	0.982627
$151$	−21.1871	−1.72418	−0.862089	−	0.506757i	$-0.830844\pi$
$151$	−21.1871	−1.72418	−0.862089	+	0.506757i	$0.830844\pi$
$152$	−59.2235	−4.80366
$153$	−37.5889	−3.03888
$154$	−9.12218	−0.735086
$155$	−19.9877	−1.60545
$156$	69.7764	5.58658
$157$	−5.27268	−0.420806	−0.210403	−	0.977615i	$-0.567478\pi$
$157$	−5.27268	−0.420806	−0.210403	+	0.977615i	$0.567478\pi$
$158$	−9.39419	−0.747362
$159$	−34.6576	−2.74852
$160$	−56.9278	−4.50054
$161$	0.696136	0.0548632
$162$	−3.48460	−0.273776
$163$	−8.48625	−0.664695	−0.332347	−	0.943157i	$-0.607841\pi$
$163$	−8.48625	−0.664695	−0.332347	+	0.943157i	$0.607841\pi$
$164$	−1.77852	−0.138879
$165$	−24.2013	−1.88407
$166$	39.4880	3.06486
$167$	0.555678	0.0429997	0.0214998	−	0.999769i	$-0.493156\pi$
$167$	0.555678	0.0429997	0.0214998	+	0.999769i	$0.493156\pi$
$168$	27.0129	2.08409
$169$	7.14667	0.549744
$170$	52.2317	4.00599
$171$	31.3226	2.39530
$172$	33.6342	2.56458
$173$	4.17324	0.317286	0.158643	−	0.987336i	$-0.449288\pi$
$173$	4.17324	0.317286	0.158643	+	0.987336i	$0.449288\pi$
$174$	−34.1224	−2.58681
$175$	1.55168	0.117296
$176$	50.3422	3.79468
$177$	4.55545	0.342409
$178$	34.6713	2.59872
$179$	−5.70916	−0.426723	−0.213361	−	0.976973i	$-0.568441\pi$
$179$	−5.70916	−0.426723	−0.213361	+	0.976973i	$0.568441\pi$
$180$	70.7165	5.27090
$181$	11.6725	0.867612	0.433806	−	0.901006i	$-0.357170\pi$
$181$	11.6725	0.867612	0.433806	+	0.901006i	$0.357170\pi$
$182$	12.2782	0.910123
$183$	−32.6052	−2.41024
$184$	−6.63234	−0.488942
$185$	7.97488	0.586325
$186$	−60.5645	−4.44081
$187$	−24.8764	−1.81914
$188$	27.0313	1.97146
$189$	−5.78090	−0.420499
$190$	−43.5243	−3.15758
$191$	−17.1319	−1.23962	−0.619810	−	0.784752i	$-0.712791\pi$
$191$	−17.1319	−1.23962	−0.619810	+	0.784752i	$0.712791\pi$
$192$	−86.8925	−6.27092
$193$	8.31959	0.598857	0.299429	−	0.954119i	$-0.403204\pi$
$193$	8.31959	0.598857	0.299429	+	0.954119i	$0.403204\pi$
$194$	24.1199	1.73171
$195$	32.5744	2.33270
$196$	5.48288	0.391634
$197$	8.78428	0.625854	0.312927	−	0.949777i	$-0.398691\pi$
$197$	8.78428	0.625854	0.312927	+	0.949777i	$0.398691\pi$
$198$	−45.9658	−3.26665
$199$	−1.00901	−0.0715269	−0.0357634	−	0.999360i	$-0.511386\pi$
$199$	−1.00901	−0.0715269	−0.0357634	+	0.999360i	$0.511386\pi$
$200$	−14.7834	−1.04534
$201$	30.8950	2.17917
$202$	9.96984	0.701475
$203$	−4.39953	−0.308787
$204$	115.966	8.11924
$205$	−0.830282	−0.0579894
$206$	16.5613	1.15388
$207$	3.50776	0.243806
$208$	−67.7593	−4.69827
$209$	20.7293	1.43388
$210$	19.8522	1.36993
$211$	9.21213	0.634189	0.317095	−	0.948394i	$-0.397293\pi$
$211$	9.21213	0.634189	0.317095	+	0.948394i	$0.397293\pi$
$212$	67.0206	4.60299
$213$	9.17181	0.628442
$214$	−31.6479	−2.16340
$215$	15.7018	1.07085
$216$	55.0767	3.74750
$217$	−7.80882	−0.530097
$218$	6.95416	0.470995
$219$	−5.75881	−0.389144
$220$	46.8004	3.15528
$221$	33.4831	2.25232
$222$	24.1647	1.62183
$223$	0.549374	0.0367888	0.0183944	−	0.999831i	$-0.494145\pi$
$223$	0.549374	0.0367888	0.0183944	+	0.999831i	$0.494145\pi$
$224$	−22.2407	−1.48602
$225$	7.81876	0.521250
$226$	3.46108	0.230228
$227$	11.3942	0.756263	0.378131	−	0.925752i	$-0.376567\pi$
$227$	11.3942	0.756263	0.378131	+	0.925752i	$0.376567\pi$
$228$	−96.6336	−6.39972
$229$	5.22151	0.345047	0.172524	−	0.985005i	$-0.444808\pi$
$229$	5.22151	0.345047	0.172524	+	0.985005i	$0.444808\pi$
$230$	−4.87421	−0.321396
$231$	−9.45503	−0.622095
$232$	41.9160	2.75192
$233$	24.8838	1.63019	0.815096	−	0.579326i	$-0.196684\pi$
$233$	24.8838	1.63019	0.815096	+	0.579326i	$0.196684\pi$
$234$	61.8689	4.04449
$235$	12.6193	0.823193
$236$	−8.80930	−0.573437
$237$	−9.73696	−0.632484
$238$	20.4060	1.32272
$239$	−23.2436	−1.50350	−0.751751	−	0.659448i	$-0.770790\pi$
$239$	−23.2436	−1.50350	−0.751751	+	0.659448i	$0.770790\pi$
$240$	−109.558	−7.07191
$241$	29.8865	1.92516	0.962580	−	0.270997i	$-0.0873534\pi$
$241$	29.8865	1.92516	0.962580	+	0.270997i	$0.0873534\pi$
$242$	−0.329925	−0.0212084
$243$	13.7310	0.880841
$244$	63.0516	4.03647
$245$	2.55962	0.163528
$246$	−2.51583	−0.160404
$247$	−27.9012	−1.77531
$248$	74.3975	4.72424
$249$	40.9288	2.59376
$250$	24.1445	1.52703
$251$	−25.8320	−1.63050	−0.815251	−	0.579108i	$-0.803401\pi$
$251$	−25.8320	−1.63050	−0.815251	+	0.579108i	$0.803401\pi$
$252$	27.6277	1.74038
$253$	2.32144	0.145948
$254$	−39.4498	−2.47530
$255$	54.1375	3.39022
$256$	46.3539	2.89712
$257$	−0.918555	−0.0572979	−0.0286489	−	0.999590i	$-0.509120\pi$
$257$	−0.918555	−0.0572979	−0.0286489	+	0.999590i	$0.509120\pi$
$258$	47.5778	2.96207
$259$	3.11565	0.193597
$260$	−62.9922	−3.90661
$261$	−22.1688	−1.37222
$262$	47.3216	2.92354
$263$	−12.1096	−0.746710	−0.373355	−	0.927689i	$-0.621793\pi$
$263$	−12.1096	−0.746710	−0.373355	+	0.927689i	$0.621793\pi$
$264$	90.0814	5.54413
$265$	31.2879	1.92200
$266$	−17.0042	−1.04259
$267$	35.9363	2.19927
$268$	−59.7446	−3.64948
$269$	−4.00826	−0.244388	−0.122194	−	0.992506i	$-0.538993\pi$
$269$	−4.00826	−0.244388	−0.122194	+	0.992506i	$0.538993\pi$
$270$	40.4768	2.46334
$271$	−20.5992	−1.25131	−0.625657	−	0.780099i	$-0.715169\pi$
$271$	−20.5992	−1.25131	−0.625657	+	0.780099i	$0.715169\pi$
$272$	−112.614	−6.82821
$273$	12.7262	0.770227
$274$	22.4630	1.35704
$275$	5.17447	0.312032
$276$	−10.8218	−0.651398
$277$	21.5401	1.29422	0.647108	−	0.762398i	$-0.275978\pi$
$277$	21.5401	1.29422	0.647108	+	0.762398i	$0.275978\pi$
$278$	−55.3749	−3.32117
$279$	−39.3479	−2.35570
$280$	−24.3865	−1.45737
$281$	−26.9486	−1.60762	−0.803808	−	0.594889i	$-0.797196\pi$
$281$	−26.9486	−1.60762	−0.803808	+	0.594889i	$0.797196\pi$
$282$	38.2377	2.27702
$283$	1.76199	0.104739	0.0523697	−	0.998628i	$-0.483323\pi$
$283$	1.76199	0.104739	0.0523697	+	0.998628i	$0.483323\pi$
$284$	−17.7364	−1.05246
$285$	−45.1124	−2.67223
$286$	40.9449	2.42113
$287$	−0.324376	−0.0191473
$288$	−112.069	−6.60372
$289$	38.6477	2.27340
$290$	30.8047	1.80892
$291$	25.0000	1.46552
$292$	11.1364	0.651706
$293$	−31.9393	−1.86591	−0.932956	−	0.359989i	$-0.882780\pi$
$293$	−31.9393	−1.86591	−0.932956	+	0.359989i	$0.882780\pi$
$294$	7.75591	0.452334
$295$	−4.11253	−0.239441
$296$	−29.6839	−1.72534
$297$	−19.2779	−1.11862
$298$	−45.4335	−2.63189
$299$	−3.12461	−0.180701
$300$	−24.1217	−1.39267
$301$	6.13440	0.353581
$302$	57.9569	3.33504
$303$	10.3336	0.593650
$304$	93.8401	5.38210
$305$	29.4350	1.68544
$306$	102.824	5.87805
$307$	−8.50350	−0.485320	−0.242660	−	0.970111i	$-0.578020\pi$
$307$	−8.50350	−0.485320	−0.242660	+	0.970111i	$0.578020\pi$
$308$	18.2841	1.04183
$309$	17.1656	0.976516
$310$	54.6759	3.10538
$311$	−6.23899	−0.353781	−0.176890	−	0.984231i	$-0.556604\pi$
$311$	−6.23899	−0.353781	−0.176890	+	0.984231i	$0.556604\pi$
$312$	−121.247	−6.86429
$313$	17.3326	0.979695	0.489848	−	0.871808i	$-0.337052\pi$
$313$	17.3326	0.979695	0.489848	+	0.871808i	$0.337052\pi$
$314$	14.4233	0.813956
$315$	12.8977	0.726703
$316$	18.8293	1.05923
$317$	−1.39461	−0.0783292	−0.0391646	−	0.999233i	$-0.512470\pi$
$317$	−1.39461	−0.0783292	−0.0391646	+	0.999233i	$0.512470\pi$
$318$	94.8053	5.31642
$319$	−14.6714	−0.821440
$320$	78.4440	4.38516
$321$	−32.8026	−1.83086
$322$	−1.90427	−0.106121
$323$	−46.3708	−2.58014
$324$	6.98437	0.388020
$325$	−6.96471	−0.386333
$326$	23.2140	1.28571
$327$	7.20790	0.398598
$328$	3.09045	0.170642
$329$	4.93014	0.271807
$330$	66.2023	3.64432
$331$	−23.5901	−1.29663	−0.648313	−	0.761374i	$-0.724525\pi$
$331$	−23.5901	−1.29663	−0.648313	+	0.761374i	$0.724525\pi$
$332$	−79.1478	−4.34380
$333$	15.6994	0.860324
$334$	−1.52005	−0.0831734
$335$	−27.8911	−1.52386
$336$	−42.8022	−2.33505
$337$	−34.6625	−1.88818	−0.944092	−	0.329682i	$-0.893059\pi$
$337$	−34.6625	−1.88818	−0.944092	+	0.329682i	$0.893059\pi$
$338$	−19.5496	−1.06336
$339$	3.58737	0.194839
$340$	−104.691	−5.67766
$341$	−26.0405	−1.41017
$342$	−85.6824	−4.63317
$343$	1.00000	0.0539949
$344$	−58.4446	−3.15112
$345$	−5.05206	−0.271994
$346$	−11.4158	−0.613719
$347$	31.1559	1.67254	0.836268	−	0.548320i	$-0.184733\pi$
$347$	31.1559	1.67254	0.836268	+	0.548320i	$0.184733\pi$
$348$	68.3933	3.66627
$349$	−2.48026	−0.132765	−0.0663826	−	0.997794i	$-0.521146\pi$
$349$	−2.48026	−0.132765	−0.0663826	+	0.997794i	$0.521146\pi$
$350$	−4.24459	−0.226883
$351$	25.9476	1.38498
$352$	−74.1673	−3.95313
$353$	2.20711	0.117472	0.0587362	−	0.998274i	$-0.481293\pi$
$353$	2.20711	0.117472	0.0587362	+	0.998274i	$0.481293\pi$
$354$	−12.4614	−0.662314
$355$	−8.28005	−0.439459
$356$	−69.4935	−3.68315
$357$	21.1506	1.11941
$358$	15.6173	0.825401
$359$	13.4431	0.709498	0.354749	−	0.934962i	$-0.384566\pi$
$359$	13.4431	0.709498	0.354749	+	0.934962i	$0.384566\pi$
$360$	−122.881	−6.47640
$361$	19.6405	1.03371
$362$	−31.9300	−1.67821
$363$	−0.341963	−0.0179484
$364$	−24.6099	−1.28991
$365$	5.19889	0.272122
$366$	89.1909	4.66208
$367$	−16.1949	−0.845369	−0.422684	−	0.906277i	$-0.638912\pi$
$367$	−16.1949	−0.845369	−0.422684	+	0.906277i	$0.638912\pi$
$368$	10.5090	0.547820
$369$	−1.63450	−0.0850887
$370$	−21.8152	−1.13412
$371$	12.2236	0.634619
$372$	121.393	6.29392
$373$	1.90152	0.0984568	0.0492284	−	0.998788i	$-0.484324\pi$
$373$	1.90152	0.0984568	0.0492284	+	0.998788i	$0.484324\pi$
$374$	68.0491	3.51873
$375$	25.0255	1.29231
$376$	−46.9712	−2.42236
$377$	19.7473	1.01704
$378$	15.8136	0.813362
$379$	15.7340	0.808200	0.404100	−	0.914715i	$-0.367585\pi$
$379$	15.7340	0.808200	0.404100	+	0.914715i	$0.367585\pi$
$380$	87.2380	4.47522
$381$	−40.8892	−2.09482
$382$	46.8641	2.39777
$383$	−26.3793	−1.34792	−0.673959	−	0.738768i	$-0.735408\pi$
$383$	−26.3793	−1.34792	−0.673959	+	0.738768i	$0.735408\pi$
$384$	111.575	5.69379
$385$	8.53573	0.435021
$386$	−22.7581	−1.15836
$387$	30.9106	1.57128
$388$	−48.3448	−2.45433
$389$	−6.89319	−0.349499	−0.174749	−	0.984613i	$-0.555911\pi$
$389$	−6.89319	−0.349499	−0.174749	+	0.984613i	$0.555911\pi$
$390$	−89.1068	−4.51210
$391$	−5.19299	−0.262621
$392$	−9.52736	−0.481204
$393$	49.0482	2.47416
$394$	−24.0293	−1.21058
$395$	8.79025	0.442286
$396$	92.1317	4.62979
$397$	−7.65077	−0.383981	−0.191991	−	0.981397i	$-0.561494\pi$
$397$	−7.65077	−0.383981	−0.191991	+	0.981397i	$0.561494\pi$
$398$	2.76013	0.138353
$399$	−17.6246	−0.882334
$400$	23.4244	1.17122
$401$	−26.5401	−1.32535	−0.662676	−	0.748907i	$-0.730579\pi$
$401$	−26.5401	−1.32535	−0.662676	+	0.748907i	$0.730579\pi$
$402$	−84.5128	−4.21512
$403$	35.0499	1.74596
$404$	−19.9831	−0.994195
$405$	3.26058	0.162019
$406$	12.0349	0.597280
$407$	10.3899	0.515009
$408$	−201.509	−9.97619
$409$	−11.6197	−0.574557	−0.287278	−	0.957847i	$-0.592750\pi$
$409$	−11.6197	−0.574557	−0.287278	+	0.957847i	$0.592750\pi$
$410$	2.27122	0.112168
$411$	23.2826	1.14845
$412$	−33.1947	−1.63539
$413$	−1.60669	−0.0790602
$414$	−9.59543	−0.471590
$415$	−36.9493	−1.81377
$416$	99.8275	4.89444
$417$	−57.3954	−2.81066
$418$	−56.7048	−2.77352
$419$	34.8997	1.70496	0.852481	−	0.522758i	$-0.175097\pi$
$419$	34.8997	1.70496	0.852481	+	0.522758i	$0.175097\pi$
$420$	−39.7909	−1.94160
$421$	15.9453	0.777127	0.388564	−	0.921422i	$-0.372971\pi$
$421$	15.9453	0.777127	0.388564	+	0.921422i	$0.372971\pi$
$422$	−25.1997	−1.22670
$423$	24.8425	1.20788
$424$	−116.459	−5.65574
$425$	−11.5751	−0.561475
$426$	−25.0894	−1.21558
$427$	11.4997	0.556511
$428$	63.4335	3.06618
$429$	42.4389	2.04897
$430$	−42.9519	−2.07133
$431$	26.8881	1.29515	0.647576	−	0.762001i	$-0.275783\pi$
$431$	26.8881	1.29515	0.647576	+	0.762001i	$0.275783\pi$
$432$	−87.2696	−4.19876
$433$	1.51615	0.0728616	0.0364308	−	0.999336i	$-0.488401\pi$
$433$	1.51615	0.0728616	0.0364308	+	0.999336i	$0.488401\pi$
$434$	21.3609	1.02536
$435$	31.9287	1.53086
$436$	−13.9386	−0.667538
$437$	4.32728	0.207002
$438$	15.7531	0.752714
$439$	−26.2213	−1.25147	−0.625737	−	0.780034i	$-0.715202\pi$
$439$	−26.2213	−1.25147	−0.625737	+	0.780034i	$0.715202\pi$
$440$	−81.3230	−3.87692
$441$	5.03891	0.239948
$442$	−91.5924	−4.35661
$443$	−31.0743	−1.47639	−0.738193	−	0.674589i	$-0.764321\pi$
$443$	−31.0743	−1.47639	−0.738193	+	0.674589i	$0.764321\pi$
$444$	−48.4345	−2.29860
$445$	−32.4423	−1.53791
$446$	−1.50280	−0.0711599
$447$	−47.0912	−2.22734
$448$	30.6467	1.44792
$449$	−32.8727	−1.55136	−0.775680	−	0.631126i	$-0.782593\pi$
$449$	−32.8727	−1.55136	−0.775680	+	0.631126i	$0.782593\pi$
$450$	−21.3881	−1.00824
$451$	−1.08172	−0.0509360
$452$	−6.93723	−0.326300
$453$	60.0716	2.82241
$454$	−31.1688	−1.46282
$455$	−11.4889	−0.538607
$456$	167.916	7.86339
$457$	12.6035	0.589567	0.294784	−	0.955564i	$-0.404752\pi$
$457$	12.6035	0.589567	0.294784	+	0.955564i	$0.404752\pi$
$458$	−14.2834	−0.667418
$459$	43.1240	2.01286
$460$	9.76964	0.455512
$461$	−8.58856	−0.400009	−0.200004	−	0.979795i	$-0.564096\pi$
$461$	−8.58856	−0.400009	−0.200004	+	0.979795i	$0.564096\pi$
$462$	25.8641	1.20331
$463$	−13.9435	−0.648007	−0.324004	−	0.946056i	$-0.605029\pi$
$463$	−13.9435	−0.648007	−0.324004	+	0.946056i	$0.605029\pi$
$464$	−66.4162	−3.08330
$465$	56.6709	2.62805
$466$	−68.0692	−3.15325
$467$	−39.8577	−1.84439	−0.922197	−	0.386720i	$-0.873608\pi$
$467$	−39.8577	−1.84439	−0.922197	+	0.386720i	$0.873608\pi$
$468$	−124.007	−5.73223
$469$	−10.8966	−0.503157
$470$	−34.5199	−1.59228
$471$	14.9496	0.688842
$472$	15.3075	0.704587
$473$	20.4567	0.940601
$474$	26.6353	1.22340
$475$	9.64545	0.442564
$476$	−40.9008	−1.87469
$477$	61.5937	2.82018
$478$	63.5824	2.90819
$479$	−40.4774	−1.84946	−0.924730	−	0.380625i	$-0.875709\pi$
$479$	−40.4774	−1.84946	−0.924730	+	0.380625i	$0.875709\pi$
$480$	161.407	7.36720
$481$	−13.9846	−0.637642
$482$	−81.7541	−3.72380
$483$	−1.97375	−0.0898088
$484$	0.661286	0.0300585
$485$	−22.5693	−1.02482
$486$	−37.5608	−1.70379
$487$	33.2831	1.50820	0.754100	−	0.656760i	$-0.228073\pi$
$487$	33.2831	1.50820	0.754100	+	0.656760i	$0.228073\pi$
$488$	−109.562	−4.95964
$489$	24.0610	1.08808
$490$	−7.00181	−0.316310
$491$	31.8415	1.43699	0.718493	−	0.695535i	$-0.244832\pi$
$491$	31.8415	1.43699	0.718493	+	0.695535i	$0.244832\pi$
$492$	5.04262	0.227339
$493$	32.8194	1.47811
$494$	76.3233	3.43395
$495$	43.0107	1.93319
$496$	−117.884	−5.29313
$497$	−3.23487	−0.145104
$498$	−111.960	−5.01705
$499$	1.27412	0.0570374	0.0285187	−	0.999593i	$-0.490921\pi$
$499$	1.27412	0.0570374	0.0285187	+	0.999593i	$0.490921\pi$
$500$	−48.3941	−2.16425
$501$	−1.57551	−0.0703887
$502$	70.6631	3.15385
$503$	8.24702	0.367717	0.183858	−	0.982953i	$-0.441141\pi$
$503$	8.24702	0.367717	0.183858	+	0.982953i	$0.441141\pi$
$504$	−48.0075	−2.13842
$505$	−9.32889	−0.415130
$506$	−6.35027	−0.282304
$507$	−20.2629	−0.899908
$508$	79.0713	3.50822
$509$	32.8486	1.45599	0.727993	−	0.685584i	$-0.240453\pi$
$509$	32.8486	1.45599	0.727993	+	0.685584i	$0.240453\pi$
$510$	−148.092	−6.55764
$511$	2.03111	0.0898512
$512$	−48.0961	−2.12557
$513$	−35.9349	−1.58657
$514$	2.51269	0.110830
$515$	−15.4966	−0.682862
$516$	−95.3628	−4.19811
$517$	16.4408	0.723066
$518$	−8.52280	−0.374470
$519$	−11.8324	−0.519384
$520$	109.459	4.80008
$521$	−8.71249	−0.381701	−0.190851	−	0.981619i	$-0.561125\pi$
$521$	−8.71249	−0.381701	−0.190851	+	0.981619i	$0.561125\pi$
$522$	60.6425	2.65425
$523$	−6.33495	−0.277008	−0.138504	−	0.990362i	$-0.544229\pi$
$523$	−6.33495	−0.277008	−0.138504	+	0.990362i	$0.544229\pi$
$524$	−94.8491	−4.14350
$525$	−4.39947	−0.192008
$526$	33.1256	1.44435
$527$	58.2518	2.53749
$528$	−142.735	−6.21174
$529$	−22.5154	−0.978930
$530$	−85.5875	−3.71768
$531$	−8.09598	−0.351335
$532$	34.0824	1.47766
$533$	1.45596	0.0630648
$534$	−98.3033	−4.25400
$535$	29.6133	1.28029
$536$	103.816	4.48415
$537$	16.1872	0.698527
$538$	10.9645	0.472715
$539$	3.33476	0.143638
$540$	−81.1298	−3.49127
$541$	−1.05010	−0.0451473	−0.0225736	−	0.999745i	$-0.507186\pi$
$541$	−1.05010	−0.0451473	−0.0225736	+	0.999745i	$0.507186\pi$
$542$	56.3488	2.42039
$543$	−33.0951	−1.42025
$544$	165.910	7.11332
$545$	−6.50709	−0.278733
$546$	−34.8124	−1.48983
$547$	2.28198	0.0975703	0.0487852	−	0.998809i	$-0.484465\pi$
$547$	2.28198	0.0975703	0.0487852	+	0.998809i	$0.484465\pi$
$548$	−45.0237	−1.92332
$549$	57.9461	2.47308
$550$	−14.1547	−0.603558
$551$	−27.3481	−1.16507
$552$	18.8046	0.800379
$553$	3.43420	0.146037
$554$	−58.9225	−2.50338
$555$	−22.6112	−0.959790
$556$	110.991	4.70706
$557$	−31.7542	−1.34547	−0.672734	−	0.739884i	$-0.734880\pi$
$557$	−31.7542	−1.34547	−0.672734	+	0.739884i	$0.734880\pi$
$558$	107.636	4.55658
$559$	−27.5343	−1.16458
$560$	38.6406	1.63286
$561$	70.5320	2.97786
$562$	73.7174	3.10958
$563$	−11.7752	−0.496267	−0.248134	−	0.968726i	$-0.579817\pi$
$563$	−11.7752	−0.496267	−0.248134	+	0.968726i	$0.579817\pi$
$564$	−76.6419	−3.22721
$565$	−3.23857	−0.136248
$566$	−4.81990	−0.202595
$567$	1.27385	0.0534967
$568$	30.8198	1.29317
$569$	40.3844	1.69300	0.846500	−	0.532388i	$-0.178705\pi$
$569$	40.3844	1.69300	0.846500	+	0.532388i	$0.178705\pi$
$570$	123.404	5.16884
$571$	−1.43443	−0.0600292	−0.0300146	−	0.999549i	$-0.509555\pi$
$571$	−1.43443	−0.0600292	−0.0300146	+	0.999549i	$0.509555\pi$
$572$	−82.0681	−3.43144
$573$	48.5740	2.02921
$574$	0.887326	0.0370363
$575$	1.08018	0.0450465
$576$	154.426	6.43441
$577$	−1.43778	−0.0598555	−0.0299277	−	0.999552i	$-0.509528\pi$
$577$	−1.43778	−0.0598555	−0.0299277	+	0.999552i	$0.509528\pi$
$578$	−105.720	−4.39738
$579$	−23.5885	−0.980305
$580$	−61.7435	−2.56376
$581$	−14.4355	−0.598883
$582$	−68.3870	−2.83473
$583$	40.7628	1.68822
$584$	−19.3512	−0.800757
$585$	−57.8914	−2.39352
$586$	87.3694	3.60920
$587$	−4.59323	−0.189583	−0.0947914	−	0.995497i	$-0.530218\pi$
$587$	−4.59323	−0.189583	−0.0947914	+	0.995497i	$0.530218\pi$
$588$	−15.5456	−0.641089
$589$	−48.5408	−2.00009
$590$	11.2498	0.463146
$591$	−24.9060	−1.02450
$592$	47.0344	1.93310
$593$	28.1271	1.15504	0.577521	−	0.816376i	$-0.304020\pi$
$593$	28.1271	1.15504	0.577521	+	0.816376i	$0.304020\pi$
$594$	52.7344	2.16372
$595$	−19.0941	−0.782783
$596$	91.0647	3.73016
$597$	2.86084	0.117087
$598$	8.54732	0.349526
$599$	26.6912	1.09057	0.545287	−	0.838249i	$-0.316421\pi$
$599$	26.6912	1.09057	0.545287	+	0.838249i	$0.316421\pi$
$600$	41.9153	1.71118
$601$	35.9595	1.46682	0.733409	−	0.679787i	$-0.237928\pi$
$601$	35.9595	1.46682	0.733409	+	0.679787i	$0.237928\pi$
$602$	−16.7806	−0.683924
$603$	−54.9068	−2.23598
$604$	−116.166	−4.72673
$605$	0.308715	0.0125510
$606$	−28.2674	−1.14829
$607$	40.7976	1.65592	0.827961	−	0.560785i	$-0.189501\pi$
$607$	40.7976	1.65592	0.827961	+	0.560785i	$0.189501\pi$
$608$	−138.251	−5.60683
$609$	12.4740	0.505471
$610$	−80.5190	−3.26012
$611$	−22.1289	−0.895241
$612$	−206.095	−8.33092
$613$	20.3175	0.820615	0.410308	−	0.911947i	$-0.365421\pi$
$613$	20.3175	0.820615	0.410308	+	0.911947i	$0.365421\pi$
$614$	23.2612	0.938746
$615$	2.35409	0.0949262
$616$	−31.7714	−1.28011
$617$	−22.4324	−0.903093	−0.451546	−	0.892248i	$-0.649127\pi$
$617$	−22.4324	−0.903093	−0.451546	+	0.892248i	$0.649127\pi$
$618$	−46.9562	−1.88886
$619$	2.38046	0.0956786	0.0478393	−	0.998855i	$-0.484766\pi$
$619$	2.38046	0.0956786	0.0478393	+	0.998855i	$0.484766\pi$
$620$	−109.590	−4.40124
$621$	−4.02429	−0.161489
$622$	17.0667	0.684311
$623$	−12.6746	−0.507798
$624$	192.118	7.69087
$625$	−30.3507	−1.21403
$626$	−47.4130	−1.89500
$627$	−58.7738	−2.34720
$628$	−28.9095	−1.15361
$629$	−23.2419	−0.926716
$630$	−35.2815	−1.40565
$631$	−4.80147	−0.191144	−0.0955718	−	0.995423i	$-0.530468\pi$
$631$	−4.80147	−0.191144	−0.0955718	+	0.995423i	$0.530468\pi$
$632$	−32.7188	−1.30148
$633$	−26.1191	−1.03814
$634$	3.81494	0.151511
$635$	36.9136	1.46487
$636$	−190.023	−7.53491
$637$	−4.48850	−0.177841
$638$	40.1333	1.58889
$639$	−16.3002	−0.644826
$640$	−100.727	−3.98158
$641$	20.3704	0.804581	0.402291	−	0.915512i	$-0.368214\pi$
$641$	20.3704	0.804581	0.402291	+	0.915512i	$0.368214\pi$
$642$	89.7311	3.54140
$643$	0.736385	0.0290402	0.0145201	−	0.999895i	$-0.495378\pi$
$643$	0.736385	0.0290402	0.0145201	+	0.999895i	$0.495378\pi$
$644$	3.81683	0.150404
$645$	−44.5191	−1.75294
$646$	126.847	4.99072
$647$	−45.6640	−1.79524	−0.897619	−	0.440772i	$-0.854705\pi$
$647$	−45.6640	−1.79524	−0.897619	+	0.440772i	$0.854705\pi$
$648$	−12.1364	−0.476764
$649$	−5.35793	−0.210317
$650$	19.0519	0.747275
$651$	22.1403	0.867748
$652$	−46.5291	−1.82222
$653$	−23.5237	−0.920555	−0.460278	−	0.887775i	$-0.652250\pi$
$653$	−23.5237	−0.920555	−0.460278	+	0.887775i	$0.652250\pi$
$654$	−19.7171	−0.771000
$655$	−44.2793	−1.73014
$656$	−4.89685	−0.191190
$657$	10.2346	0.399289
$658$	−13.4863	−0.525751
$659$	−8.57458	−0.334018	−0.167009	−	0.985955i	$-0.553411\pi$
$659$	−8.57458	−0.334018	−0.167009	+	0.985955i	$0.553411\pi$
$660$	−132.693	−5.16506
$661$	−15.6364	−0.608184	−0.304092	−	0.952643i	$-0.598353\pi$
$661$	−15.6364	−0.608184	−0.304092	+	0.952643i	$0.598353\pi$
$662$	64.5302	2.50804
$663$	−94.9344	−3.68695
$664$	137.532	5.33727
$665$	15.9110	0.617002
$666$	−42.9456	−1.66411
$667$	−3.06267	−0.118587
$668$	3.04672	0.117881
$669$	−1.55764	−0.0602218
$670$	76.2958	2.94756
$671$	38.3488	1.48044
$672$	63.0590	2.43255
$673$	49.5087	1.90842	0.954209	−	0.299140i	$-0.0966998\pi$
$673$	49.5087	1.90842	0.954209	+	0.299140i	$0.0966998\pi$
$674$	94.8186	3.65228
$675$	−8.97009	−0.345259
$676$	39.1843	1.50709
$677$	21.0248	0.808047	0.404023	−	0.914749i	$-0.367611\pi$
$677$	21.0248	0.808047	0.404023	+	0.914749i	$0.367611\pi$
$678$	−9.81319	−0.376873
$679$	−8.81741	−0.338381
$680$	181.917	6.97619
$681$	−32.3061	−1.23797
$682$	71.2335	2.72767
$683$	7.46049	0.285468	0.142734	−	0.989761i	$-0.454411\pi$
$683$	7.46049	0.285468	0.142734	+	0.989761i	$0.454411\pi$
$684$	171.738	6.56656
$685$	−21.0189	−0.803089
$686$	−2.73548	−0.104441
$687$	−14.8045	−0.564828
$688$	92.6061	3.53057
$689$	−54.8658	−2.09022
$690$	13.8198	0.526112
$691$	−18.9312	−0.720177	−0.360089	−	0.932918i	$-0.617254\pi$
$691$	−18.9312	−0.720177	−0.360089	+	0.932918i	$0.617254\pi$
$692$	22.8814	0.869819
$693$	16.8035	0.638313
$694$	−85.2265	−3.23515
$695$	51.8149	1.96545
$696$	−118.844	−4.50478
$697$	2.41976	0.0916550
$698$	6.78471	0.256805
$699$	−70.5529	−2.66856
$700$	8.50766	0.321559
$701$	6.50307	0.245618	0.122809	−	0.992430i	$-0.460810\pi$
$701$	6.50307	0.245618	0.122809	+	0.992430i	$0.460810\pi$
$702$	−70.9793	−2.67894
$703$	19.3673	0.730452
$704$	102.199	3.85178
$705$	−35.7795	−1.34753
$706$	−6.03751	−0.227225
$707$	−3.64463	−0.137070
$708$	24.9770	0.938693
$709$	−37.2813	−1.40013	−0.700065	−	0.714080i	$-0.746845\pi$
$709$	−37.2813	−1.40013	−0.700065	+	0.714080i	$0.746845\pi$
$710$	22.6500	0.850038
$711$	17.3046	0.648973
$712$	120.756	4.52551
$713$	−5.43600	−0.203580
$714$	−57.8571	−2.16525
$715$	−38.3127	−1.43281
$716$	−31.3026	−1.16983
$717$	65.9024	2.46117
$718$	−36.7733	−1.37237
$719$	−18.7901	−0.700751	−0.350376	−	0.936609i	$-0.613946\pi$
$719$	−18.7901	−0.700751	−0.350376	+	0.936609i	$0.613946\pi$
$720$	194.706	7.25628
$721$	−6.05425	−0.225472
$722$	−53.7262	−1.99948
$723$	−84.7372	−3.15141
$724$	63.9991	2.37851
$725$	−6.82666	−0.253536
$726$	0.935435	0.0347172
$727$	−29.0225	−1.07639	−0.538193	−	0.842822i	$-0.680893\pi$
$727$	−29.0225	−1.07639	−0.538193	+	0.842822i	$0.680893\pi$
$728$	42.7636	1.58492
$729$	−42.7529	−1.58344
$730$	−14.2215	−0.526361
$731$	−45.7610	−1.69253
$732$	−178.770	−6.60753
$733$	13.3222	0.492065	0.246033	−	0.969262i	$-0.420873\pi$
$733$	13.3222	0.492065	0.246033	+	0.969262i	$0.420873\pi$
$734$	44.3010	1.63518
$735$	−7.25729	−0.267689
$736$	−15.4825	−0.570694
$737$	−36.3374	−1.33851
$738$	4.47115	0.164585
$739$	−26.9563	−0.991602	−0.495801	−	0.868436i	$-0.665125\pi$
$739$	−26.9563	−0.991602	−0.495801	+	0.868436i	$0.665125\pi$
$740$	43.7253	1.60737
$741$	79.1081	2.90611
$742$	−33.4375	−1.22753
$743$	−48.5971	−1.78285	−0.891427	−	0.453163i	$-0.850295\pi$
$743$	−48.5971	−1.78285	−0.891427	+	0.453163i	$0.850295\pi$
$744$	−210.939	−7.73339
$745$	42.5126	1.55754
$746$	−5.20157	−0.190443
$747$	−72.7389	−2.66138
$748$	−136.394	−4.98707
$749$	11.5694	0.422736
$750$	−68.4569	−2.49969
$751$	34.6907	1.26588	0.632940	−	0.774201i	$-0.281848\pi$
$751$	34.6907	1.26588	0.632940	+	0.774201i	$0.281848\pi$
$752$	74.4263	2.71405
$753$	73.2414	2.66907
$754$	−54.0185	−1.96724
$755$	−54.2309	−1.97366
$756$	−31.6960	−1.15277
$757$	19.0638	0.692884	0.346442	−	0.938071i	$-0.387390\pi$
$757$	19.0638	0.692884	0.346442	+	0.938071i	$0.387390\pi$
$758$	−43.0401	−1.56329
$759$	−6.58198	−0.238911
$760$	−151.590	−5.49874
$761$	−28.9635	−1.04993	−0.524963	−	0.851125i	$-0.675921\pi$
$761$	−28.9635	−1.04993	−0.524963	+	0.851125i	$0.675921\pi$
$762$	111.852	4.05196
$763$	−2.54221	−0.0920340
$764$	−93.9321	−3.39835
$765$	−96.2135	−3.47861
$766$	72.1601	2.60725
$767$	7.21165	0.260398
$768$	−131.427	−4.74247
$769$	−27.5188	−0.992352	−0.496176	−	0.868222i	$-0.665263\pi$
$769$	−27.5188	−0.992352	−0.496176	+	0.868222i	$0.665263\pi$
$770$	−23.3494	−0.841452
$771$	2.60438	0.0937943
$772$	45.6153	1.64173
$773$	14.0914	0.506834	0.253417	−	0.967357i	$-0.418446\pi$
$773$	14.0914	0.506834	0.253417	+	0.967357i	$0.418446\pi$
$774$	−84.5556	−3.03929
$775$	−12.1168	−0.435247
$776$	84.0067	3.01566
$777$	−8.83378	−0.316910
$778$	18.8562	0.676028
$779$	−2.01637	−0.0722439
$780$	178.601	6.39496
$781$	−10.7875	−0.386007
$782$	14.2053	0.507982
$783$	25.4333	0.908911
$784$	15.0962	0.539150
$785$	−13.4961	−0.481696
$786$	−134.171	−4.78571
$787$	35.1528	1.25306	0.626531	−	0.779396i	$-0.284474\pi$
$787$	35.1528	1.25306	0.626531	+	0.779396i	$0.284474\pi$
$788$	48.1631	1.71574
$789$	34.3343	1.22233
$790$	−24.0456	−0.855504
$791$	−1.26525	−0.0449872
$792$	−160.093	−5.68867
$793$	−51.6166	−1.83296
$794$	20.9286	0.742727
$795$	−88.7104	−3.14623
$796$	−5.53228	−0.196087
$797$	−21.6983	−0.768593	−0.384296	−	0.923210i	$-0.625556\pi$
$797$	−21.6983	−0.768593	−0.384296	+	0.923210i	$0.625556\pi$
$798$	48.2119	1.70668
$799$	−36.7775	−1.30110
$800$	−34.5104	−1.22013
$801$	−63.8663	−2.25660
$802$	72.6002	2.56360
$803$	6.77327	0.239024
$804$	169.394	5.97405
$805$	1.78185	0.0628018
$806$	−95.8786	−3.37718
$807$	11.3646	0.400054
$808$	34.7237	1.22158
$809$	−14.3461	−0.504381	−0.252190	−	0.967678i	$-0.581151\pi$
$809$	−14.3461	−0.504381	−0.252190	+	0.967678i	$0.581151\pi$
$810$	−8.91927	−0.313391
$811$	42.3009	1.48539	0.742693	−	0.669632i	$-0.233548\pi$
$811$	42.3009	1.48539	0.742693	+	0.669632i	$0.233548\pi$
$812$	−24.1221	−0.846520
$813$	58.4049	2.04835
$814$	−28.4215	−0.996172
$815$	−21.7216	−0.760875
$816$	319.293	11.1775
$817$	38.1323	1.33408
$818$	31.7855	1.11135
$819$	−22.6171	−0.790307
$820$	−4.55233	−0.158974
$821$	−6.86231	−0.239496	−0.119748	−	0.992804i	$-0.538209\pi$
$821$	−6.86231	−0.239496	−0.119748	+	0.992804i	$0.538209\pi$
$822$	−63.6892	−2.22142
$823$	22.0196	0.767555	0.383778	−	0.923426i	$-0.374623\pi$
$823$	22.0196	0.767555	0.383778	+	0.923426i	$0.374623\pi$
$824$	57.6810	2.00941
$825$	−14.6712	−0.510784
$826$	4.39509	0.152925
$827$	−5.07915	−0.176619	−0.0883096	−	0.996093i	$-0.528146\pi$
$827$	−5.07915	−0.176619	−0.0883096	+	0.996093i	$0.528146\pi$
$828$	19.2326	0.668380
$829$	−49.6848	−1.72562	−0.862812	−	0.505525i	$-0.831299\pi$
$829$	−49.6848	−1.72562	−0.862812	+	0.505525i	$0.831299\pi$
$830$	101.074	3.50834
$831$	−61.0724	−2.11858
$832$	−137.558	−4.76896
$833$	−7.45974	−0.258465
$834$	157.004	5.43661
$835$	1.42233	0.0492217
$836$	113.656	3.93089
$837$	45.1420	1.56034
$838$	−95.4677	−3.29788
$839$	−6.70806	−0.231588	−0.115794	−	0.993273i	$-0.536941\pi$
$839$	−6.70806	−0.231588	−0.115794	+	0.993273i	$0.536941\pi$
$840$	69.1429	2.38566
$841$	−9.64409	−0.332555
$842$	−43.6182	−1.50318
$843$	76.4072	2.63160
$844$	50.5090	1.73859
$845$	18.2928	0.629291
$846$	−67.9563	−2.33639
$847$	0.120609	0.00414418
$848$	184.530	6.33679
$849$	−4.99577	−0.171454
$850$	31.6635	1.08605
$851$	2.16891	0.0743494
$852$	50.2879	1.72284
$853$	33.3801	1.14291	0.571456	−	0.820633i	$-0.306379\pi$
$853$	33.3801	1.14291	0.571456	+	0.820633i	$0.306379\pi$
$854$	−31.4573	−1.07645
$855$	80.1740	2.74189
$856$	−110.226	−3.76744
$857$	−10.5778	−0.361329	−0.180665	−	0.983545i	$-0.557825\pi$
$857$	−10.5778	−0.361329	−0.180665	+	0.983545i	$0.557825\pi$
$858$	−116.091	−3.96328
$859$	1.00000	0.0341196
$859$	1.00000	0.0341196
$860$	86.0908	2.93567
$861$	0.919703	0.0313434
$862$	−73.5519	−2.50519
$863$	20.8306	0.709082	0.354541	−	0.935041i	$-0.384637\pi$
$863$	20.8306	0.709082	0.354541	+	0.935041i	$0.384637\pi$
$864$	128.571	4.37408
$865$	10.6819	0.363197
$866$	−4.14741	−0.140935
$867$	−109.578	−3.72145
$868$	−42.8148	−1.45323
$869$	11.4522	0.388490
$870$	−87.3405	−2.96112
$871$	48.9093	1.65723
$872$	24.2205	0.820210
$873$	−44.4301	−1.50373
$874$	−11.8372	−0.400400
$875$	−8.82641	−0.298387
$876$	−31.5749	−1.06682
$877$	−45.3576	−1.53162	−0.765808	−	0.643069i	$-0.777661\pi$
$877$	−45.3576	−1.53162	−0.765808	+	0.643069i	$0.777661\pi$
$878$	71.7280	2.42070
$879$	90.5573	3.05442
$880$	128.857	4.34377
$881$	20.6638	0.696182	0.348091	−	0.937461i	$-0.386830\pi$
$881$	20.6638	0.696182	0.348091	+	0.937461i	$0.386830\pi$
$882$	−13.7838	−0.464126
$883$	−17.7919	−0.598746	−0.299373	−	0.954136i	$-0.596778\pi$
$883$	−17.7919	−0.598746	−0.299373	+	0.954136i	$0.596778\pi$
$884$	183.584	6.17459
$885$	11.6602	0.391955
$886$	85.0034	2.85575
$887$	−44.3296	−1.48844	−0.744221	−	0.667933i	$-0.767179\pi$
$887$	−44.3296	−1.48844	−0.744221	+	0.667933i	$0.767179\pi$
$888$	84.1626	2.82431
$889$	14.4215	0.483681
$890$	88.7454	2.97475
$891$	4.24798	0.142313
$892$	3.01215	0.100854
$893$	30.6465	1.02554
$894$	128.817	4.30830
$895$	−14.6133	−0.488469
$896$	−39.3522	−1.31466
$897$	8.85919	0.295800
$898$	89.9229	3.00077
$899$	34.3552	1.14581
$900$	42.8693	1.42898
$901$	−91.1850	−3.03781
$902$	2.95902	0.0985246
$903$	−17.3928	−0.578797
$904$	12.0545	0.400928
$905$	29.8773	0.993155
$906$	−164.325	−5.45933
$907$	47.4453	1.57540	0.787698	−	0.616062i	$-0.211273\pi$
$907$	47.4453	1.57540	0.787698	+	0.616062i	$0.211273\pi$
$908$	62.4733	2.07325
$909$	−18.3650	−0.609127
$910$	31.4277	1.04182
$911$	−58.7037	−1.94494	−0.972470	−	0.233030i	$-0.925136\pi$
$911$	−58.7037	−1.94494	−0.972470	+	0.233030i	$0.925136\pi$
$912$	−266.065	−8.81028
$913$	−48.1387	−1.59316
$914$	−34.4767	−1.14039
$915$	−83.4569	−2.75900
$916$	28.6289	0.945926
$917$	−17.2992	−0.571268
$918$	−117.965	−3.89343
$919$	−39.3190	−1.29701	−0.648507	−	0.761208i	$-0.724606\pi$
$919$	−39.3190	−1.29701	−0.648507	+	0.761208i	$0.724606\pi$
$920$	−16.9763	−0.559692
$921$	24.1099	0.794450
$922$	23.4939	0.773729
$923$	14.5197	0.477923
$924$	−51.8408	−1.70544
$925$	4.83448	0.158957
$926$	38.1421	1.25343
$927$	−30.5068	−1.00197
$928$	97.8487	3.21204
$929$	−19.8843	−0.652383	−0.326191	−	0.945304i	$-0.605765\pi$
$929$	−19.8843	−0.652383	−0.326191	+	0.945304i	$0.605765\pi$
$930$	−155.022	−5.08339
$931$	6.21614	0.203726
$932$	136.435	4.46907
$933$	17.6894	0.579125
$934$	109.030	3.56758
$935$	−63.6743	−2.08237
$936$	215.482	7.04324
$937$	−31.9669	−1.04431	−0.522156	−	0.852850i	$-0.674872\pi$
$937$	−31.9669	−1.04431	−0.522156	+	0.852850i	$0.674872\pi$
$938$	29.8074	0.973246
$939$	−49.1430	−1.60372
$940$	69.1901	2.25673
$941$	−11.1066	−0.362066	−0.181033	−	0.983477i	$-0.557944\pi$
$941$	−11.1066	−0.362066	−0.181033	+	0.983477i	$0.557944\pi$
$942$	−40.8944	−1.33241
$943$	−0.225810	−0.00735338
$944$	−24.2550	−0.789432
$945$	−14.7969	−0.481344
$946$	−55.9591	−1.81939
$947$	−57.7119	−1.87539	−0.937693	−	0.347466i	$-0.887042\pi$
$947$	−57.7119	−1.87539	−0.937693	+	0.347466i	$0.887042\pi$
$948$	−53.3866	−1.73392
$949$	−9.11666	−0.295939
$950$	−26.3850	−0.856042
$951$	3.95414	0.128222
$952$	71.0716	2.30344
$953$	5.37787	0.174206	0.0871032	−	0.996199i	$-0.472239\pi$
$953$	5.37787	0.174206	0.0871032	+	0.996199i	$0.472239\pi$
$954$	−168.489	−5.45502
$955$	−43.8512	−1.41899
$956$	−127.442	−4.12176
$957$	41.5977	1.34466
$958$	110.725	3.57737
$959$	−8.21170	−0.265170
$960$	−222.412	−7.17832
$961$	29.9777	0.967023
$962$	38.2546	1.23338
$963$	58.2970	1.87860
$964$	163.864	5.27771
$965$	21.2950	0.685511
$966$	5.39917	0.173715
$967$	−9.18337	−0.295317	−0.147659	−	0.989038i	$-0.547174\pi$
$967$	−9.18337	−0.295317	−0.147659	+	0.989038i	$0.547174\pi$
$968$	−1.14909	−0.0369331
$969$	131.475	4.22359
$970$	61.7379	1.98228
$971$	3.90312	0.125257	0.0626286	−	0.998037i	$-0.480052\pi$
$971$	3.90312	0.125257	0.0626286	+	0.998037i	$0.480052\pi$
$972$	75.2852	2.41477
$973$	20.2432	0.648966
$974$	−91.0454	−2.91728
$975$	19.7470	0.632411
$976$	173.602	5.55687
$977$	25.0480	0.801358	0.400679	−	0.916219i	$-0.368774\pi$
$977$	25.0480	0.801358	0.400679	+	0.916219i	$0.368774\pi$
$978$	−65.8186	−2.10465
$979$	−42.2668	−1.35085
$980$	14.0341	0.448303
$981$	−12.8099	−0.408990
$982$	−87.1019	−2.77953
$983$	−18.2931	−0.583458	−0.291729	−	0.956501i	$-0.594231\pi$
$983$	−18.2931	−0.583458	−0.291729	+	0.956501i	$0.594231\pi$
$984$	−8.76234	−0.279333
$985$	22.4844	0.716414
$986$	−89.7769	−2.85908
$987$	−13.9784	−0.444937
$988$	−152.979	−4.86690
$989$	4.27037	0.135790
$990$	−117.655	−3.73933
$991$	2.47879	0.0787415	0.0393707	−	0.999225i	$-0.487465\pi$
$991$	2.47879	0.0787415	0.0393707	+	0.999225i	$0.487465\pi$
$992$	173.674	5.51414
$993$	66.8848	2.12252
$994$	8.84894	0.280671
$995$	−2.58269	−0.0818767
$996$	224.408	7.11062
$997$	−23.5818	−0.746842	−0.373421	−	0.927662i	$-0.621815\pi$
$997$	−23.5818	−0.746842	−0.373421	+	0.927662i	$0.621815\pi$
$998$	−3.48534	−0.110326
$999$	−18.0112	−0.569850

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6013.2.a.d.1.4	✓	104

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6013.2.a.d.1.4	✓	104	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:	\( N \)	\(=\)	\( 6013 = 7 \cdot 859 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.73548 q^{2} -2.83530 q^{3} +5.48288 q^{4} +2.55962 q^{5} +7.75591 q^{6} +1.00000 q^{7} -9.52736 q^{8} +5.03891 q^{9} +O(q^{10})\)	\(q-2.73548 q^{2} -2.83530 q^{3} +5.48288 q^{4} +2.55962 q^{5} +7.75591 q^{6} +1.00000 q^{7} -9.52736 q^{8} +5.03891 q^{9} -7.00181 q^{10} +3.33476 q^{11} -15.5456 q^{12} -4.48850 q^{13} -2.73548 q^{14} -7.25729 q^{15} +15.0962 q^{16} -7.45974 q^{17} -13.7838 q^{18} +6.21614 q^{19} +14.0341 q^{20} -2.83530 q^{21} -9.12218 q^{22} +0.696136 q^{23} +27.0129 q^{24} +1.55168 q^{25} +12.2782 q^{26} -5.78090 q^{27} +5.48288 q^{28} -4.39953 q^{29} +19.8522 q^{30} -7.80882 q^{31} -22.2407 q^{32} -9.45503 q^{33} +20.4060 q^{34} +2.55962 q^{35} +27.6277 q^{36} +3.11565 q^{37} -17.0042 q^{38} +12.7262 q^{39} -24.3865 q^{40} -0.324376 q^{41} +7.75591 q^{42} +6.13440 q^{43} +18.2841 q^{44} +12.8977 q^{45} -1.90427 q^{46} +4.93014 q^{47} -42.8022 q^{48} +1.00000 q^{49} -4.24459 q^{50} +21.1506 q^{51} -24.6099 q^{52} +12.2236 q^{53} +15.8136 q^{54} +8.53573 q^{55} -9.52736 q^{56} -17.6246 q^{57} +12.0349 q^{58} -1.60669 q^{59} -39.7909 q^{60} +11.4997 q^{61} +21.3609 q^{62} +5.03891 q^{63} +30.6467 q^{64} -11.4889 q^{65} +25.8641 q^{66} -10.8966 q^{67} -40.9008 q^{68} -1.97375 q^{69} -7.00181 q^{70} -3.23487 q^{71} -48.0075 q^{72} +2.03111 q^{73} -8.52280 q^{74} -4.39947 q^{75} +34.0824 q^{76} +3.33476 q^{77} -34.8124 q^{78} +3.43420 q^{79} +38.6406 q^{80} +1.27385 q^{81} +0.887326 q^{82} -14.4355 q^{83} -15.5456 q^{84} -19.0941 q^{85} -16.7806 q^{86} +12.4740 q^{87} -31.7714 q^{88} -12.6746 q^{89} -35.2815 q^{90} -4.48850 q^{91} +3.81683 q^{92} +22.1403 q^{93} -13.4863 q^{94} +15.9110 q^{95} +63.0590 q^{96} -8.81741 q^{97} -2.73548 q^{98} +16.8035 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 104 q - 17 q^{2} - 34 q^{3} + 99 q^{4} - 46 q^{5} - 18 q^{6} + 104 q^{7} - 48 q^{8} + 98 q^{9}+O(q^{10}) \) 104 * q - 17 * q^2 - 34 * q^3 + 99 * q^4 - 46 * q^5 - 18 * q^6 + 104 * q^7 - 48 * q^8 + 98 * q^9	\( 104 q - 17 q^{2} - 34 q^{3} + 99 q^{4} - 46 q^{5} - 18 q^{6} + 104 q^{7} - 48 q^{8} + 98 q^{9} - 17 q^{10} - 46 q^{11} - 62 q^{12} - 37 q^{13} - 17 q^{14} - 17 q^{15} + 93 q^{16} - 75 q^{17} - 41 q^{18} - 40 q^{19} - 106 q^{20} - 34 q^{21} - 14 q^{22} - 57 q^{23} - 38 q^{24} + 102 q^{25} - 45 q^{26} - 121 q^{27} + 99 q^{28} - 29 q^{29} + 26 q^{30} - 42 q^{31} - 113 q^{32} - 42 q^{33} - 7 q^{34} - 46 q^{35} + 99 q^{36} - 31 q^{37} - 62 q^{38} - 9 q^{39} - 36 q^{40} - 106 q^{41} - 18 q^{42} - 29 q^{43} - 60 q^{44} - 121 q^{45} + 21 q^{46} - 141 q^{47} - 88 q^{48} + 104 q^{49} - 70 q^{50} - 2 q^{51} - 58 q^{52} - 70 q^{53} - 49 q^{54} - 14 q^{55} - 48 q^{56} - 11 q^{57} - 28 q^{58} - 202 q^{59} + 17 q^{60} - 79 q^{61} - 41 q^{62} + 98 q^{63} + 110 q^{64} - 34 q^{65} - 21 q^{66} - 57 q^{67} - 180 q^{68} - 99 q^{69} - 17 q^{70} - 109 q^{71} - 73 q^{72} - 46 q^{73} - 7 q^{74} - 146 q^{75} - 54 q^{76} - 46 q^{77} - 42 q^{78} - 12 q^{79} - 187 q^{80} + 100 q^{81} - 45 q^{82} - 156 q^{83} - 62 q^{84} - 13 q^{85} - 8 q^{86} - 76 q^{87} - 6 q^{88} - 140 q^{89} - 5 q^{90} - 37 q^{91} - 98 q^{92} - q^{93} - 17 q^{94} - 48 q^{95} - 12 q^{96} - 63 q^{97} - 17 q^{98} - 78 q^{99}+O(q^{100}) \) 104 * q - 17 * q^2 - 34 * q^3 + 99 * q^4 - 46 * q^5 - 18 * q^6 + 104 * q^7 - 48 * q^8 + 98 * q^9 - 17 * q^10 - 46 * q^11 - 62 * q^12 - 37 * q^13 - 17 * q^14 - 17 * q^15 + 93 * q^16 - 75 * q^17 - 41 * q^18 - 40 * q^19 - 106 * q^20 - 34 * q^21 - 14 * q^22 - 57 * q^23 - 38 * q^24 + 102 * q^25 - 45 * q^26 - 121 * q^27 + 99 * q^28 - 29 * q^29 + 26 * q^30 - 42 * q^31 - 113 * q^32 - 42 * q^33 - 7 * q^34 - 46 * q^35 + 99 * q^36 - 31 * q^37 - 62 * q^38 - 9 * q^39 - 36 * q^40 - 106 * q^41 - 18 * q^42 - 29 * q^43 - 60 * q^44 - 121 * q^45 + 21 * q^46 - 141 * q^47 - 88 * q^48 + 104 * q^49 - 70 * q^50 - 2 * q^51 - 58 * q^52 - 70 * q^53 - 49 * q^54 - 14 * q^55 - 48 * q^56 - 11 * q^57 - 28 * q^58 - 202 * q^59 + 17 * q^60 - 79 * q^61 - 41 * q^62 + 98 * q^63 + 110 * q^64 - 34 * q^65 - 21 * q^66 - 57 * q^67 - 180 * q^68 - 99 * q^69 - 17 * q^70 - 109 * q^71 - 73 * q^72 - 46 * q^73 - 7 * q^74 - 146 * q^75 - 54 * q^76 - 46 * q^77 - 42 * q^78 - 12 * q^79 - 187 * q^80 + 100 * q^81 - 45 * q^82 - 156 * q^83 - 62 * q^84 - 13 * q^85 - 8 * q^86 - 76 * q^87 - 6 * q^88 - 140 * q^89 - 5 * q^90 - 37 * q^91 - 98 * q^92 - q^93 - 17 * q^94 - 48 * q^95 - 12 * q^96 - 63 * q^97 - 17 * q^98 - 78 * q^99

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