LMFDB - Embedded newform 6017.2.a.e.1.13

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			1.13
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)

$f(q)$	$=$	$q-2.35115 q^{2} +2.19609 q^{3} +3.52790 q^{4} +0.407257 q^{5} -5.16332 q^{6} -2.35563 q^{7} -3.59233 q^{8} +1.82279 q^{9} +O(q^{10})$	\(q-2.35115 q^{2} +2.19609 q^{3} +3.52790 q^{4} +0.407257 q^{5} -5.16332 q^{6} -2.35563 q^{7} -3.59233 q^{8} +1.82279 q^{9} -0.957522 q^{10} +1.00000 q^{11} +7.74758 q^{12} +0.411830 q^{13} +5.53844 q^{14} +0.894371 q^{15} +1.39030 q^{16} +3.21632 q^{17} -4.28565 q^{18} -0.996022 q^{19} +1.43676 q^{20} -5.17317 q^{21} -2.35115 q^{22} -8.81838 q^{23} -7.88907 q^{24} -4.83414 q^{25} -0.968274 q^{26} -2.58525 q^{27} -8.31045 q^{28} +0.443891 q^{29} -2.10280 q^{30} -6.83110 q^{31} +3.91586 q^{32} +2.19609 q^{33} -7.56206 q^{34} -0.959348 q^{35} +6.43063 q^{36} -3.19037 q^{37} +2.34180 q^{38} +0.904414 q^{39} -1.46300 q^{40} -2.23235 q^{41} +12.1629 q^{42} +6.45493 q^{43} +3.52790 q^{44} +0.742344 q^{45} +20.7333 q^{46} +8.07414 q^{47} +3.05322 q^{48} -1.45100 q^{49} +11.3658 q^{50} +7.06332 q^{51} +1.45290 q^{52} +8.58192 q^{53} +6.07832 q^{54} +0.407257 q^{55} +8.46221 q^{56} -2.18735 q^{57} -1.04365 q^{58} +3.20075 q^{59} +3.15526 q^{60} +11.3857 q^{61} +16.0609 q^{62} -4.29382 q^{63} -11.9874 q^{64} +0.167721 q^{65} -5.16332 q^{66} +5.77170 q^{67} +11.3469 q^{68} -19.3659 q^{69} +2.25557 q^{70} +6.37594 q^{71} -6.54807 q^{72} +13.1644 q^{73} +7.50104 q^{74} -10.6162 q^{75} -3.51387 q^{76} -2.35563 q^{77} -2.12641 q^{78} +13.7445 q^{79} +0.566210 q^{80} -11.1458 q^{81} +5.24858 q^{82} +1.22516 q^{83} -18.2504 q^{84} +1.30987 q^{85} -15.1765 q^{86} +0.974822 q^{87} -3.59233 q^{88} +15.2290 q^{89} -1.74536 q^{90} -0.970120 q^{91} -31.1104 q^{92} -15.0017 q^{93} -18.9835 q^{94} -0.405637 q^{95} +8.59956 q^{96} +0.0538648 q^{97} +3.41151 q^{98} +1.82279 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.35115	−1.66251	−0.831257	−	0.555888i	$-0.812378\pi$
$2$	−2.35115	−1.66251	−0.831257	+	0.555888i	$0.812378\pi$
$3$	2.19609	1.26791	0.633955	−	0.773370i	$-0.281430\pi$
$3$	2.19609	1.26791	0.633955	+	0.773370i	$0.281430\pi$
$4$	3.52790	1.76395
$5$	0.407257	0.182131	0.0910655	−	0.995845i	$-0.470973\pi$
$5$	0.407257	0.182131	0.0910655	+	0.995845i	$0.470973\pi$
$6$	−5.16332	−2.10792
$7$	−2.35563	−0.890345	−0.445173	−	0.895445i	$-0.646858\pi$
$7$	−2.35563	−0.890345	−0.445173	+	0.895445i	$0.646858\pi$
$8$	−3.59233	−1.27008
$9$	1.82279	0.607597
$10$	−0.957522	−0.302795
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	7.74758	2.23653
$13$	0.411830	0.114221	0.0571106	−	0.998368i	$-0.481811\pi$
$13$	0.411830	0.114221	0.0571106	+	0.998368i	$0.481811\pi$
$14$	5.53844	1.48021
$15$	0.894371	0.230926
$16$	1.39030	0.347575
$17$	3.21632	0.780073	0.390037	−	0.920799i	$-0.372462\pi$
$17$	3.21632	0.780073	0.390037	+	0.920799i	$0.372462\pi$
$18$	−4.28565	−1.01014
$19$	−0.996022	−0.228503	−0.114252	−	0.993452i	$-0.536447\pi$
$19$	−0.996022	−0.228503	−0.114252	+	0.993452i	$0.536447\pi$
$20$	1.43676	0.321270
$21$	−5.17317	−1.12888
$22$	−2.35115	−0.501267
$23$	−8.81838	−1.83876	−0.919379	−	0.393372i	$-0.871308\pi$
$23$	−8.81838	−1.83876	−0.919379	+	0.393372i	$0.871308\pi$
$24$	−7.88907	−1.61035
$25$	−4.83414	−0.966828
$26$	−0.968274	−0.189894
$27$	−2.58525	−0.497532
$28$	−8.31045	−1.57053
$29$	0.443891	0.0824284	0.0412142	−	0.999150i	$-0.486877\pi$
$29$	0.443891	0.0824284	0.0412142	+	0.999150i	$0.486877\pi$
$30$	−2.10280	−0.383917
$31$	−6.83110	−1.22690	−0.613451	−	0.789733i	$-0.710219\pi$
$31$	−6.83110	−1.22690	−0.613451	+	0.789733i	$0.710219\pi$
$32$	3.91586	0.692233
$33$	2.19609	0.382289
$34$	−7.56206	−1.29688
$35$	−0.959348	−0.162159
$36$	6.43063	1.07177
$37$	−3.19037	−0.524494	−0.262247	−	0.965001i	$-0.584464\pi$
$37$	−3.19037	−0.524494	−0.262247	+	0.965001i	$0.584464\pi$
$38$	2.34180	0.379889
$39$	0.904414	0.144822
$40$	−1.46300	−0.231321
$41$	−2.23235	−0.348634	−0.174317	−	0.984690i	$-0.555772\pi$
$41$	−2.23235	−0.348634	−0.174317	+	0.984690i	$0.555772\pi$
$42$	12.1629	1.87678
$43$	6.45493	0.984368	0.492184	−	0.870491i	$-0.336199\pi$
$43$	6.45493	0.984368	0.492184	+	0.870491i	$0.336199\pi$
$44$	3.52790	0.531852
$45$	0.742344	0.110662
$46$	20.7333	3.05696
$47$	8.07414	1.17773	0.588867	−	0.808230i	$-0.299574\pi$
$47$	8.07414	1.17773	0.588867	+	0.808230i	$0.299574\pi$
$48$	3.05322	0.440694
$49$	−1.45100	−0.207285
$50$	11.3658	1.60737
$51$	7.06332	0.989063
$52$	1.45290	0.201481
$53$	8.58192	1.17882	0.589409	−	0.807835i	$-0.299361\pi$
$53$	8.58192	1.17882	0.589409	+	0.807835i	$0.299361\pi$
$54$	6.07832	0.827154
$55$	0.407257	0.0549145
$56$	8.46221	1.13081
$57$	−2.18735	−0.289721
$58$	−1.04365	−0.137038
$59$	3.20075	0.416702	0.208351	−	0.978054i	$-0.433190\pi$
$59$	3.20075	0.416702	0.208351	+	0.978054i	$0.433190\pi$
$60$	3.15526	0.407342
$61$	11.3857	1.45779	0.728893	−	0.684628i	$-0.240035\pi$
$61$	11.3857	1.45779	0.728893	+	0.684628i	$0.240035\pi$
$62$	16.0609	2.03974
$63$	−4.29382	−0.540971
$64$	−11.9874	−1.49842
$65$	0.167721	0.0208032
$66$	−5.16332	−0.635561
$67$	5.77170	0.705125	0.352563	−	0.935788i	$-0.385310\pi$
$67$	5.77170	0.705125	0.352563	+	0.935788i	$0.385310\pi$
$68$	11.3469	1.37601
$69$	−19.3659	−2.33138
$70$	2.25557	0.269592
$71$	6.37594	0.756685	0.378342	−	0.925666i	$-0.376494\pi$
$71$	6.37594	0.756685	0.378342	+	0.925666i	$0.376494\pi$
$72$	−6.54807	−0.771697
$73$	13.1644	1.54078	0.770388	−	0.637576i	$-0.220063\pi$
$73$	13.1644	1.54078	0.770388	+	0.637576i	$0.220063\pi$
$74$	7.50104	0.871979
$75$	−10.6162	−1.22585
$76$	−3.51387	−0.403068
$77$	−2.35563	−0.268449
$78$	−2.12641	−0.240769
$79$	13.7445	1.54638	0.773191	−	0.634174i	$-0.218660\pi$
$79$	13.7445	1.54638	0.773191	+	0.634174i	$0.218660\pi$
$80$	0.566210	0.0633042
$81$	−11.1458	−1.23842
$82$	5.24858	0.579609
$83$	1.22516	0.134479	0.0672395	−	0.997737i	$-0.478581\pi$
$83$	1.22516	0.134479	0.0672395	+	0.997737i	$0.478581\pi$
$84$	−18.2504	−1.99129
$85$	1.30987	0.142075
$86$	−15.1765	−1.63653
$87$	0.974822	0.104512
$88$	−3.59233	−0.382944
$89$	15.2290	1.61427	0.807136	−	0.590365i	$-0.201016\pi$
$89$	15.2290	1.61427	0.807136	+	0.590365i	$0.201016\pi$
$90$	−1.74536	−0.183977
$91$	−0.970120	−0.101696
$92$	−31.1104	−3.24348
$93$	−15.0017	−1.55560
$94$	−18.9835	−1.95800
$95$	−0.405637	−0.0416175
$96$	8.59956	0.877689
$97$	0.0538648	0.00546914	0.00273457	−	0.999996i	$-0.499130\pi$
$97$	0.0538648	0.00546914	0.00273457	+	0.999996i	$0.499130\pi$
$98$	3.41151	0.344615
$99$	1.82279	0.183197
$100$	−17.0544	−1.70544
$101$	8.62445	0.858165	0.429082	−	0.903265i	$-0.358837\pi$
$101$	8.62445	0.858165	0.429082	+	0.903265i	$0.358837\pi$
$102$	−16.6069	−1.64433
$103$	16.2330	1.59949	0.799743	−	0.600342i	$-0.204969\pi$
$103$	16.2330	1.59949	0.799743	+	0.600342i	$0.204969\pi$
$104$	−1.47943	−0.145070
$105$	−2.10681	−0.205604
$106$	−20.1774	−1.95980
$107$	−7.56014	−0.730866	−0.365433	−	0.930838i	$-0.619079\pi$
$107$	−7.56014	−0.730866	−0.365433	+	0.930838i	$0.619079\pi$
$108$	−9.12053	−0.877623
$109$	7.23658	0.693139	0.346569	−	0.938024i	$-0.387347\pi$
$109$	7.23658	0.693139	0.346569	+	0.938024i	$0.387347\pi$
$110$	−0.957522	−0.0912962
$111$	−7.00633	−0.665012
$112$	−3.27504	−0.309462
$113$	−0.825892	−0.0776934	−0.0388467	−	0.999245i	$-0.512368\pi$
$113$	−0.825892	−0.0776934	−0.0388467	+	0.999245i	$0.512368\pi$
$114$	5.14278	0.481666
$115$	−3.59135	−0.334895
$116$	1.56600	0.145400
$117$	0.750680	0.0694004
$118$	−7.52543	−0.692772
$119$	−7.57648	−0.694534
$120$	−3.21288	−0.293294
$121$	1.00000	0.0909091
$122$	−26.7694	−2.42359
$123$	−4.90242	−0.442036
$124$	−24.0995	−2.16420
$125$	−4.00502	−0.358220
$126$	10.0954	0.899372
$127$	−18.5665	−1.64751	−0.823755	−	0.566947i	$-0.808125\pi$
$127$	−18.5665	−1.64751	−0.823755	+	0.566947i	$0.808125\pi$
$128$	20.3524	1.79891
$129$	14.1756	1.24809
$130$	−0.394337	−0.0345856
$131$	7.68416	0.671369	0.335684	−	0.941975i	$-0.391032\pi$
$131$	7.68416	0.671369	0.335684	+	0.941975i	$0.391032\pi$
$132$	7.74758	0.674340
$133$	2.34626	0.203447
$134$	−13.5701	−1.17228
$135$	−1.05286	−0.0906160
$136$	−11.5541	−0.990756
$137$	−11.2894	−0.964518	−0.482259	−	0.876029i	$-0.660184\pi$
$137$	−11.2894	−0.964518	−0.482259	+	0.876029i	$0.660184\pi$
$138$	45.5321	3.87595
$139$	13.9017	1.17913	0.589564	−	0.807722i	$-0.299300\pi$
$139$	13.9017	1.17913	0.589564	+	0.807722i	$0.299300\pi$
$140$	−3.38449	−0.286041
$141$	17.7315	1.49326
$142$	−14.9908	−1.25800
$143$	0.411830	0.0344390
$144$	2.53423	0.211185
$145$	0.180778	0.0150128
$146$	−30.9515	−2.56156
$147$	−3.18651	−0.262819
$148$	−11.2553	−0.925183
$149$	−18.3689	−1.50484	−0.752419	−	0.658685i	$-0.771113\pi$
$149$	−18.3689	−1.50484	−0.752419	+	0.658685i	$0.771113\pi$
$150$	24.9602	2.03800
$151$	22.6900	1.84648	0.923242	−	0.384220i	$-0.125529\pi$
$151$	22.6900	1.84648	0.923242	+	0.384220i	$0.125529\pi$
$152$	3.57804	0.290217
$153$	5.86268	0.473970
$154$	5.53844	0.446301
$155$	−2.78201	−0.223457
$156$	3.19069	0.255459
$157$	17.5255	1.39869	0.699345	−	0.714784i	$-0.253475\pi$
$157$	17.5255	1.39869	0.699345	+	0.714784i	$0.253475\pi$
$158$	−32.3155	−2.57088
$159$	18.8466	1.49463
$160$	1.59476	0.126077
$161$	20.7728	1.63713
$162$	26.2055	2.05890
$163$	−1.78808	−0.140053	−0.0700265	−	0.997545i	$-0.522308\pi$
$163$	−1.78808	−0.140053	−0.0700265	+	0.997545i	$0.522308\pi$
$164$	−7.87550	−0.614973
$165$	0.894371	0.0696267
$166$	−2.88054	−0.223573
$167$	−13.8569	−1.07228	−0.536141	−	0.844128i	$-0.680119\pi$
$167$	−13.8569	−1.07228	−0.536141	+	0.844128i	$0.680119\pi$
$168$	18.5837	1.43377
$169$	−12.8304	−0.986954
$170$	−3.07970	−0.236202
$171$	−1.81554	−0.138838
$172$	22.7724	1.73638
$173$	−8.07944	−0.614269	−0.307134	−	0.951666i	$-0.599370\pi$
$173$	−8.07944	−0.614269	−0.307134	+	0.951666i	$0.599370\pi$
$174$	−2.29195	−0.173752
$175$	11.3875	0.860811
$176$	1.39030	0.104798
$177$	7.02911	0.528340
$178$	−35.8057	−2.68375
$179$	7.26773	0.543215	0.271608	−	0.962408i	$-0.412445\pi$
$179$	7.26773	0.543215	0.271608	+	0.962408i	$0.412445\pi$
$180$	2.61892	0.195203
$181$	8.18095	0.608085	0.304043	−	0.952658i	$-0.401663\pi$
$181$	8.18095	0.608085	0.304043	+	0.952658i	$0.401663\pi$
$182$	2.28090	0.169071
$183$	25.0039	1.84834
$184$	31.6785	2.33537
$185$	−1.29930	−0.0955266
$186$	35.2712	2.58621
$187$	3.21632	0.235201
$188$	28.4848	2.07747
$189$	6.08991	0.442975
$190$	0.953713	0.0691896
$191$	18.9188	1.36892	0.684459	−	0.729052i	$-0.260039\pi$
$191$	18.9188	1.36892	0.684459	+	0.729052i	$0.260039\pi$
$192$	−26.3253	−1.89986
$193$	22.6508	1.63044	0.815219	−	0.579153i	$-0.196616\pi$
$193$	22.6508	1.63044	0.815219	+	0.579153i	$0.196616\pi$
$194$	−0.126644	−0.00909252
$195$	0.368329	0.0263766
$196$	−5.11898	−0.365641
$197$	17.8321	1.27048	0.635242	−	0.772313i	$-0.280901\pi$
$197$	17.8321	1.27048	0.635242	+	0.772313i	$0.280901\pi$
$198$	−4.28565	−0.304568
$199$	−6.79803	−0.481899	−0.240950	−	0.970538i	$-0.577459\pi$
$199$	−6.79803	−0.481899	−0.240950	+	0.970538i	$0.577459\pi$
$200$	17.3658	1.22795
$201$	12.6751	0.894036
$202$	−20.2774	−1.42671
$203$	−1.04564	−0.0733898
$204$	24.9187	1.74466
$205$	−0.909139	−0.0634970
$206$	−38.1662	−2.65917
$207$	−16.0740	−1.11722
$208$	0.572567	0.0397004
$209$	−0.996022	−0.0688963
$210$	4.95343	0.341819
$211$	6.92856	0.476982	0.238491	−	0.971145i	$-0.423347\pi$
$211$	6.92856	0.476982	0.238491	+	0.971145i	$0.423347\pi$
$212$	30.2762	2.07938
$213$	14.0021	0.959408
$214$	17.7750	1.21507
$215$	2.62882	0.179284
$216$	9.28709	0.631906
$217$	16.0916	1.09237
$218$	−17.0143	−1.15235
$219$	28.9101	1.95357
$220$	1.43676	0.0968666
$221$	1.32458	0.0891008
$222$	16.4729	1.10559
$223$	15.7287	1.05327	0.526636	−	0.850091i	$-0.323453\pi$
$223$	15.7287	1.05327	0.526636	+	0.850091i	$0.323453\pi$
$224$	−9.22432	−0.616326
$225$	−8.81163	−0.587442
$226$	1.94180	0.129166
$227$	−9.80440	−0.650741	−0.325371	−	0.945587i	$-0.605489\pi$
$227$	−9.80440	−0.650741	−0.325371	+	0.945587i	$0.605489\pi$
$228$	−7.71676	−0.511055
$229$	−9.88377	−0.653138	−0.326569	−	0.945173i	$-0.605893\pi$
$229$	−9.88377	−0.653138	−0.326569	+	0.945173i	$0.605893\pi$
$230$	8.44379	0.556767
$231$	−5.17317	−0.340370
$232$	−1.59460	−0.104691
$233$	−17.5736	−1.15128	−0.575641	−	0.817703i	$-0.695247\pi$
$233$	−17.5736	−1.15128	−0.575641	+	0.817703i	$0.695247\pi$
$234$	−1.76496	−0.115379
$235$	3.28825	0.214502
$236$	11.2919	0.735042
$237$	30.1842	1.96067
$238$	17.8134	1.15467
$239$	8.04994	0.520708	0.260354	−	0.965513i	$-0.416161\pi$
$239$	8.04994	0.520708	0.260354	+	0.965513i	$0.416161\pi$
$240$	1.24344	0.0802640
$241$	−16.1740	−1.04186	−0.520929	−	0.853600i	$-0.674414\pi$
$241$	−16.1740	−1.04186	−0.520929	+	0.853600i	$0.674414\pi$
$242$	−2.35115	−0.151138
$243$	−16.7214	−1.07268
$244$	40.1676	2.57147
$245$	−0.590929	−0.0377531
$246$	11.5263	0.734892
$247$	−0.410192	−0.0260999
$248$	24.5396	1.55826
$249$	2.69056	0.170507
$250$	9.41641	0.595546
$251$	−14.1514	−0.893226	−0.446613	−	0.894727i	$-0.647370\pi$
$251$	−14.1514	−0.893226	−0.446613	+	0.894727i	$0.647370\pi$
$252$	−15.1482	−0.954247
$253$	−8.81838	−0.554407
$254$	43.6526	2.73901
$255$	2.87659	0.180139
$256$	−23.8768	−1.49230
$257$	−26.4766	−1.65157	−0.825783	−	0.563989i	$-0.809266\pi$
$257$	−26.4766	−1.65157	−0.825783	+	0.563989i	$0.809266\pi$
$258$	−33.3289	−2.07497
$259$	7.51535	0.466981
$260$	0.591703	0.0366958
$261$	0.809119	0.0500832
$262$	−18.0666	−1.11616
$263$	23.4523	1.44613	0.723066	−	0.690779i	$-0.242732\pi$
$263$	23.4523	1.44613	0.723066	+	0.690779i	$0.242732\pi$
$264$	−7.88907	−0.485538
$265$	3.49505	0.214699
$266$	−5.51641	−0.338233
$267$	33.4442	2.04675
$268$	20.3620	1.24381
$269$	−1.51263	−0.0922264	−0.0461132	−	0.998936i	$-0.514683\pi$
$269$	−1.51263	−0.0922264	−0.0461132	+	0.998936i	$0.514683\pi$
$270$	2.47544	0.150650
$271$	−5.12866	−0.311544	−0.155772	−	0.987793i	$-0.549786\pi$
$271$	−5.12866	−0.311544	−0.155772	+	0.987793i	$0.549786\pi$
$272$	4.47166	0.271134
$273$	−2.13047	−0.128942
$274$	26.5430	1.60352
$275$	−4.83414	−0.291510
$276$	−68.3211	−4.11244
$277$	−0.786739	−0.0472705	−0.0236353	−	0.999721i	$-0.507524\pi$
$277$	−0.786739	−0.0472705	−0.0236353	+	0.999721i	$0.507524\pi$
$278$	−32.6850	−1.96032
$279$	−12.4517	−0.745462
$280$	3.44630	0.205956
$281$	−29.9535	−1.78687	−0.893437	−	0.449188i	$-0.851713\pi$
$281$	−29.9535	−1.78687	−0.893437	+	0.449188i	$0.851713\pi$
$282$	−41.6894	−2.48257
$283$	4.98360	0.296244	0.148122	−	0.988969i	$-0.452677\pi$
$283$	4.98360	0.296244	0.148122	+	0.988969i	$0.452677\pi$
$284$	22.4937	1.33476
$285$	−0.890813	−0.0527672
$286$	−0.968274	−0.0572552
$287$	5.25859	0.310404
$288$	7.13779	0.420598
$289$	−6.65526	−0.391486
$290$	−0.425035	−0.0249589
$291$	0.118292	0.00693438
$292$	46.4427	2.71785
$293$	0.168676	0.00985414	0.00492707	−	0.999988i	$-0.498432\pi$
$293$	0.168676	0.00985414	0.00492707	+	0.999988i	$0.498432\pi$
$294$	7.49197	0.436940
$295$	1.30353	0.0758943
$296$	11.4609	0.666150
$297$	−2.58525	−0.150012
$298$	43.1880	2.50181
$299$	−3.63167	−0.210025
$300$	−37.4529	−2.16234
$301$	−15.2054	−0.876428
$302$	−53.3475	−3.06980
$303$	18.9400	1.08808
$304$	−1.38477	−0.0794220
$305$	4.63690	0.265508
$306$	−13.7840	−0.787982
$307$	6.24646	0.356505	0.178252	−	0.983985i	$-0.442956\pi$
$307$	6.24646	0.356505	0.178252	+	0.983985i	$0.442956\pi$
$308$	−8.31045	−0.473532
$309$	35.6491	2.02801
$310$	6.54093	0.371500
$311$	−8.04076	−0.455950	−0.227975	−	0.973667i	$-0.573210\pi$
$311$	−8.04076	−0.455950	−0.227975	+	0.973667i	$0.573210\pi$
$312$	−3.24895	−0.183936
$313$	−7.15044	−0.404167	−0.202083	−	0.979368i	$-0.564771\pi$
$313$	−7.15044	−0.404167	−0.202083	+	0.979368i	$0.564771\pi$
$314$	−41.2052	−2.32534
$315$	−1.74869	−0.0985275
$316$	48.4894	2.72774
$317$	19.6497	1.10364	0.551818	−	0.833965i	$-0.313934\pi$
$317$	19.6497	1.10364	0.551818	+	0.833965i	$0.313934\pi$
$318$	−44.3112	−2.48485
$319$	0.443891	0.0248531
$320$	−4.88194	−0.272909
$321$	−16.6027	−0.926673
$322$	−48.8401	−2.72175
$323$	−3.20353	−0.178249
$324$	−39.3213	−2.18452
$325$	−1.99084	−0.110432
$326$	4.20404	0.232840
$327$	15.8922	0.878838
$328$	8.01933	0.442793
$329$	−19.0197	−1.04859
$330$	−2.10280	−0.115755
$331$	−30.3457	−1.66795	−0.833974	−	0.551804i	$-0.813940\pi$
$331$	−30.3457	−1.66795	−0.833974	+	0.551804i	$0.813940\pi$
$332$	4.32226	0.237215
$333$	−5.81538	−0.318681
$334$	32.5798	1.78269
$335$	2.35057	0.128425
$336$	−7.19226	−0.392370
$337$	−10.2875	−0.560397	−0.280198	−	0.959942i	$-0.590400\pi$
$337$	−10.2875	−0.560397	−0.280198	+	0.959942i	$0.590400\pi$
$338$	30.1662	1.64082
$339$	−1.81373	−0.0985083
$340$	4.62110	0.250614
$341$	−6.83110	−0.369925
$342$	4.26860	0.230820
$343$	19.9074	1.07490
$344$	−23.1883	−1.25023
$345$	−7.88690	−0.424617
$346$	18.9960	1.02123
$347$	13.0581	0.700994	0.350497	−	0.936564i	$-0.386013\pi$
$347$	13.0581	0.700994	0.350497	+	0.936564i	$0.386013\pi$
$348$	3.43908	0.184354
$349$	−16.6850	−0.893125	−0.446563	−	0.894752i	$-0.647352\pi$
$349$	−16.6850	−0.893125	−0.446563	+	0.894752i	$0.647352\pi$
$350$	−26.7736	−1.43111
$351$	−1.06468	−0.0568287
$352$	3.91586	0.208716
$353$	22.5186	1.19854	0.599272	−	0.800545i	$-0.295457\pi$
$353$	22.5186	1.19854	0.599272	+	0.800545i	$0.295457\pi$
$354$	−16.5265	−0.878373
$355$	2.59665	0.137816
$356$	53.7265	2.84750
$357$	−16.6386	−0.880608
$358$	−17.0875	−0.903103
$359$	36.4686	1.92474	0.962371	−	0.271740i	$-0.0875990\pi$
$359$	36.4686	1.92474	0.962371	+	0.271740i	$0.0875990\pi$
$360$	−2.66675	−0.140550
$361$	−18.0079	−0.947786
$362$	−19.2346	−1.01095
$363$	2.19609	0.115265
$364$	−3.42249	−0.179387
$365$	5.36129	0.280623
$366$	−58.7879	−3.07289
$367$	21.4663	1.12053	0.560266	−	0.828313i	$-0.310699\pi$
$367$	21.4663	1.12053	0.560266	+	0.828313i	$0.310699\pi$
$368$	−12.2602	−0.639107
$369$	−4.06910	−0.211829
$370$	3.05485	0.158814
$371$	−20.2158	−1.04955
$372$	−52.9245	−2.74401
$373$	18.5194	0.958899	0.479449	−	0.877569i	$-0.340836\pi$
$373$	18.5194	0.958899	0.479449	+	0.877569i	$0.340836\pi$
$374$	−7.56206	−0.391025
$375$	−8.79537	−0.454191
$376$	−29.0050	−1.49582
$377$	0.182808	0.00941507
$378$	−14.3183	−0.736453
$379$	23.7840	1.22170	0.610851	−	0.791746i	$-0.290828\pi$
$379$	23.7840	1.22170	0.610851	+	0.791746i	$0.290828\pi$
$380$	−1.43105	−0.0734112
$381$	−40.7736	−2.08889
$382$	−44.4810	−2.27584
$383$	32.7181	1.67182	0.835908	−	0.548870i	$-0.184942\pi$
$383$	32.7181	1.67182	0.835908	+	0.548870i	$0.184942\pi$
$384$	44.6956	2.28086
$385$	−0.959348	−0.0488929
$386$	−53.2554	−2.71063
$387$	11.7660	0.598099
$388$	0.190030	0.00964730
$389$	−5.89480	−0.298878	−0.149439	−	0.988771i	$-0.547747\pi$
$389$	−5.89480	−0.298878	−0.149439	+	0.988771i	$0.547747\pi$
$390$	−0.865997	−0.0438514
$391$	−28.3628	−1.43437
$392$	5.21246	0.263269
$393$	16.8751	0.851235
$394$	−41.9259	−2.11220
$395$	5.59756	0.281644
$396$	6.43063	0.323151
$397$	7.57588	0.380223	0.190111	−	0.981763i	$-0.439115\pi$
$397$	7.57588	0.380223	0.190111	+	0.981763i	$0.439115\pi$
$398$	15.9832	0.801164
$399$	5.15259	0.257952
$400$	−6.72091	−0.336045
$401$	−19.7753	−0.987531	−0.493766	−	0.869595i	$-0.664380\pi$
$401$	−19.7753	−0.987531	−0.493766	+	0.869595i	$0.664380\pi$
$402$	−29.8012	−1.48635
$403$	−2.81325	−0.140138
$404$	30.4262	1.51376
$405$	−4.53921	−0.225555
$406$	2.45846	0.122011
$407$	−3.19037	−0.158141
$408$	−25.3738	−1.25619
$409$	24.8896	1.23071	0.615355	−	0.788250i	$-0.289012\pi$
$409$	24.8896	1.23071	0.615355	+	0.788250i	$0.289012\pi$
$410$	2.13752	0.105565
$411$	−24.7925	−1.22292
$412$	57.2685	2.82142
$413$	−7.53978	−0.371008
$414$	37.7925	1.85740
$415$	0.498956	0.0244928
$416$	1.61267	0.0790676
$417$	30.5293	1.49503
$418$	2.34180	0.114541
$419$	−0.277215	−0.0135428	−0.00677142	−	0.999977i	$-0.502155\pi$
$419$	−0.277215	−0.0135428	−0.00677142	+	0.999977i	$0.502155\pi$
$420$	−7.43262	−0.362675
$421$	29.9998	1.46210	0.731051	−	0.682323i	$-0.239030\pi$
$421$	29.9998	1.46210	0.731051	+	0.682323i	$0.239030\pi$
$422$	−16.2901	−0.792989
$423$	14.7175	0.715587
$424$	−30.8291	−1.49719
$425$	−15.5482	−0.754197
$426$	−32.9210	−1.59503
$427$	−26.8205	−1.29793
$428$	−26.6714	−1.28921
$429$	0.904414	0.0436655
$430$	−6.18074	−0.298062
$431$	−1.06617	−0.0513558	−0.0256779	−	0.999670i	$-0.508174\pi$
$431$	−1.06617	−0.0513558	−0.0256779	+	0.999670i	$0.508174\pi$
$432$	−3.59428	−0.172930
$433$	3.36814	0.161863	0.0809313	−	0.996720i	$-0.474211\pi$
$433$	3.36814	0.161863	0.0809313	+	0.996720i	$0.474211\pi$
$434$	−37.8337	−1.81607
$435$	0.397003	0.0190348
$436$	25.5300	1.22266
$437$	8.78329	0.420162
$438$	−67.9720	−3.24783
$439$	3.74280	0.178634	0.0893170	−	0.996003i	$-0.471532\pi$
$439$	3.74280	0.178634	0.0893170	+	0.996003i	$0.471532\pi$
$440$	−1.46300	−0.0697459
$441$	−2.64486	−0.125946
$442$	−3.11428	−0.148131
$443$	11.6404	0.553051	0.276525	−	0.961007i	$-0.410817\pi$
$443$	11.6404	0.553051	0.276525	+	0.961007i	$0.410817\pi$
$444$	−24.7177	−1.17305
$445$	6.20213	0.294009
$446$	−36.9805	−1.75108
$447$	−40.3396	−1.90800
$448$	28.2378	1.33411
$449$	−41.9375	−1.97915	−0.989577	−	0.144003i	$-0.954002\pi$
$449$	−41.9375	−1.97915	−0.989577	+	0.144003i	$0.954002\pi$
$450$	20.7175	0.976630
$451$	−2.23235	−0.105117
$452$	−2.91367	−0.137047
$453$	49.8291	2.34118
$454$	23.0516	1.08187
$455$	−0.395088	−0.0185220
$456$	7.85768	0.367970
$457$	5.52230	0.258322	0.129161	−	0.991624i	$-0.458772\pi$
$457$	5.52230	0.258322	0.129161	+	0.991624i	$0.458772\pi$
$458$	23.2382	1.08585
$459$	−8.31501	−0.388112
$460$	−12.6699	−0.590738
$461$	−2.62783	−0.122390	−0.0611951	−	0.998126i	$-0.519491\pi$
$461$	−2.62783	−0.122390	−0.0611951	+	0.998126i	$0.519491\pi$
$462$	12.1629	0.565869
$463$	16.8401	0.782624	0.391312	−	0.920258i	$-0.372021\pi$
$463$	16.8401	0.782624	0.391312	+	0.920258i	$0.372021\pi$
$464$	0.617141	0.0286501
$465$	−6.10954	−0.283323
$466$	41.3181	1.91402
$467$	−12.9036	−0.597107	−0.298553	−	0.954393i	$-0.596504\pi$
$467$	−12.9036	−0.597107	−0.298553	+	0.954393i	$0.596504\pi$
$468$	2.64833	0.122419
$469$	−13.5960	−0.627805
$470$	−7.73117	−0.356612
$471$	38.4876	1.77341
$472$	−11.4981	−0.529245
$473$	6.45493	0.296798
$474$	−70.9675	−3.25965
$475$	4.81491	0.220923
$476$	−26.7291	−1.22513
$477$	15.6430	0.716246
$478$	−18.9266	−0.865684
$479$	−28.9159	−1.32120	−0.660600	−	0.750738i	$-0.729698\pi$
$479$	−28.9159	−1.32120	−0.660600	+	0.750738i	$0.729698\pi$
$480$	3.50223	0.159854
$481$	−1.31389	−0.0599083
$482$	38.0275	1.73210
$483$	45.6189	2.07573
$484$	3.52790	0.160359
$485$	0.0219368	0.000996100 0
$486$	39.3145	1.78334
$487$	−18.0811	−0.819334	−0.409667	−	0.912235i	$-0.634355\pi$
$487$	−18.0811	−0.819334	−0.409667	+	0.912235i	$0.634355\pi$
$488$	−40.9011	−1.85151
$489$	−3.92677	−0.177575
$490$	1.38936	0.0627650
$491$	−5.11059	−0.230638	−0.115319	−	0.993329i	$-0.536789\pi$
$491$	−5.11059	−0.230638	−0.115319	+	0.993329i	$0.536789\pi$
$492$	−17.2953	−0.779731
$493$	1.42770	0.0643002
$494$	0.964422	0.0433914
$495$	0.742344	0.0333659
$496$	−9.49728	−0.426441
$497$	−15.0194	−0.673711
$498$	−6.32591	−0.283471
$499$	−32.2649	−1.44438	−0.722188	−	0.691697i	$-0.756863\pi$
$499$	−32.2649	−1.44438	−0.722188	+	0.691697i	$0.756863\pi$
$500$	−14.1293	−0.631883
$501$	−30.4310	−1.35956
$502$	33.2720	1.48500
$503$	−30.1468	−1.34418	−0.672089	−	0.740470i	$-0.734603\pi$
$503$	−30.1468	−1.34418	−0.672089	+	0.740470i	$0.734603\pi$
$504$	15.4248	0.687077
$505$	3.51237	0.156298
$506$	20.7333	0.921708
$507$	−28.1766	−1.25137
$508$	−65.5008	−2.90613
$509$	−7.38840	−0.327485	−0.163743	−	0.986503i	$-0.552357\pi$
$509$	−7.38840	−0.327485	−0.163743	+	0.986503i	$0.552357\pi$
$510$	−6.76329	−0.299483
$511$	−31.0105	−1.37182
$512$	15.4331	0.682051
$513$	2.57497	0.113688
$514$	62.2505	2.74575
$515$	6.61101	0.291316
$516$	50.0101	2.20157
$517$	8.07414	0.355100
$518$	−17.6697	−0.776362
$519$	−17.7431	−0.778838
$520$	−0.602508	−0.0264217
$521$	−6.46609	−0.283285	−0.141642	−	0.989918i	$-0.545238\pi$
$521$	−6.46609	−0.283285	−0.141642	+	0.989918i	$0.545238\pi$
$522$	−1.90236	−0.0832641
$523$	−15.6345	−0.683648	−0.341824	−	0.939764i	$-0.611045\pi$
$523$	−15.6345	−0.683648	−0.341824	+	0.939764i	$0.611045\pi$
$524$	27.1090	1.18426
$525$	25.0078	1.09143
$526$	−55.1399	−2.40421
$527$	−21.9710	−0.957073
$528$	3.05322	0.132874
$529$	54.7637	2.38103
$530$	−8.21738	−0.356940
$531$	5.83429	0.253187
$532$	8.27738	0.358870
$533$	−0.919347	−0.0398213
$534$	−78.6324	−3.40276
$535$	−3.07892	−0.133113
$536$	−20.7339	−0.895566
$537$	15.9605	0.688748
$538$	3.55641	0.153328
$539$	−1.45100	−0.0624989
$540$	−3.71440	−0.159842
$541$	−35.3101	−1.51810	−0.759049	−	0.651033i	$-0.774336\pi$
$541$	−35.3101	−1.51810	−0.759049	+	0.651033i	$0.774336\pi$
$542$	12.0582	0.517946
$543$	17.9661	0.770998
$544$	12.5947	0.539992
$545$	2.94715	0.126242
$546$	5.00905	0.214367
$547$	−1.00000	−0.0427569
$547$	−1.00000	−0.0427569
$548$	−39.8279	−1.70136
$549$	20.7537	0.885746
$550$	11.3658	0.484639
$551$	−0.442125	−0.0188351
$552$	69.5687	2.96104
$553$	−32.3771	−1.37681
$554$	1.84974	0.0785879
$555$	−2.85338	−0.121119
$556$	49.0439	2.07993
$557$	−15.6289	−0.662219	−0.331109	−	0.943592i	$-0.607423\pi$
$557$	−15.6289	−0.662219	−0.331109	+	0.943592i	$0.607423\pi$
$558$	29.2757	1.23934
$559$	2.65834	0.112436
$560$	−1.33378	−0.0563626
$561$	7.06332	0.298214
$562$	70.4251	2.97070
$563$	16.2363	0.684278	0.342139	−	0.939649i	$-0.388849\pi$
$563$	16.2363	0.684278	0.342139	+	0.939649i	$0.388849\pi$
$564$	62.5550	2.63404
$565$	−0.336351	−0.0141504
$566$	−11.7172	−0.492510
$567$	26.2554	1.10262
$568$	−22.9045	−0.961051
$569$	−3.20940	−0.134545	−0.0672725	−	0.997735i	$-0.521430\pi$
$569$	−3.20940	−0.134545	−0.0672725	+	0.997735i	$0.521430\pi$
$570$	2.09444	0.0877262
$571$	38.8620	1.62632	0.813162	−	0.582037i	$-0.197744\pi$
$571$	38.8620	1.62632	0.813162	+	0.582037i	$0.197744\pi$
$572$	1.45290	0.0607487
$573$	41.5473	1.73566
$574$	−12.3637	−0.516052
$575$	42.6293	1.77776
$576$	−21.8505	−0.910436
$577$	4.25354	0.177077	0.0885385	−	0.996073i	$-0.471780\pi$
$577$	4.25354	0.177077	0.0885385	+	0.996073i	$0.471780\pi$
$578$	15.6475	0.650851
$579$	49.7430	2.06725
$580$	0.637766	0.0264818
$581$	−2.88603	−0.119733
$582$	−0.278121	−0.0115285
$583$	8.58192	0.355427
$584$	−47.2909	−1.95691
$585$	0.305720	0.0126400
$586$	−0.396582	−0.0163826
$587$	30.6685	1.26583	0.632913	−	0.774223i	$-0.281859\pi$
$587$	30.6685	1.26583	0.632913	+	0.774223i	$0.281859\pi$
$588$	−11.2417	−0.463600
$589$	6.80392	0.280351
$590$	−3.06479	−0.126175
$591$	39.1608	1.61086
$592$	−4.43558	−0.182301
$593$	14.6253	0.600590	0.300295	−	0.953846i	$-0.402915\pi$
$593$	14.6253	0.600590	0.300295	+	0.953846i	$0.402915\pi$
$594$	6.07832	0.249396
$595$	−3.08557	−0.126496
$596$	−64.8037	−2.65446
$597$	−14.9290	−0.611005
$598$	8.53860	0.349170
$599$	1.76260	0.0720179	0.0360089	−	0.999351i	$-0.488536\pi$
$599$	1.76260	0.0720179	0.0360089	+	0.999351i	$0.488536\pi$
$600$	38.1369	1.55693
$601$	−39.1408	−1.59658	−0.798292	−	0.602270i	$-0.794263\pi$
$601$	−39.1408	−1.59658	−0.798292	+	0.602270i	$0.794263\pi$
$602$	35.7503	1.45707
$603$	10.5206	0.428432
$604$	80.0480	3.25711
$605$	0.407257	0.0165574
$606$	−44.5308	−1.80894
$607$	14.5954	0.592409	0.296204	−	0.955125i	$-0.404279\pi$
$607$	14.5954	0.592409	0.296204	+	0.955125i	$0.404279\pi$
$608$	−3.90028	−0.158177
$609$	−2.29632	−0.0930516
$610$	−10.9020	−0.441411
$611$	3.32517	0.134522
$612$	20.6830	0.836060
$613$	−2.86715	−0.115803	−0.0579016	−	0.998322i	$-0.518441\pi$
$613$	−2.86715	−0.115803	−0.0579016	+	0.998322i	$0.518441\pi$
$614$	−14.6864	−0.592694
$615$	−1.99655	−0.0805085
$616$	8.46221	0.340952
$617$	−15.1153	−0.608518	−0.304259	−	0.952589i	$-0.598409\pi$
$617$	−15.1153	−0.608518	−0.304259	+	0.952589i	$0.598409\pi$
$618$	−83.8163	−3.37159
$619$	11.6101	0.466650	0.233325	−	0.972399i	$-0.425039\pi$
$619$	11.6101	0.466650	0.233325	+	0.972399i	$0.425039\pi$
$620$	−9.81468	−0.394167
$621$	22.7977	0.914841
$622$	18.9050	0.758023
$623$	−35.8740	−1.43726
$624$	1.25741	0.0503366
$625$	22.5396	0.901585
$626$	16.8117	0.671933
$627$	−2.18735	−0.0873543
$628$	61.8284	2.46722
$629$	−10.2613	−0.409144
$630$	4.11143	0.163803
$631$	25.2126	1.00370	0.501849	−	0.864956i	$-0.332653\pi$
$631$	25.2126	1.00370	0.501849	+	0.864956i	$0.332653\pi$
$632$	−49.3749	−1.96403
$633$	15.2157	0.604770
$634$	−46.1993	−1.83481
$635$	−7.56133	−0.300062
$636$	66.4891	2.63646
$637$	−0.597564	−0.0236764
$638$	−1.04365	−0.0413186
$639$	11.6220	0.459759
$640$	8.28865	0.327638
$641$	−22.5320	−0.889960	−0.444980	−	0.895540i	$-0.646789\pi$
$641$	−22.5320	−0.889960	−0.444980	+	0.895540i	$0.646789\pi$
$642$	39.0354	1.54061
$643$	−33.7395	−1.33055	−0.665277	−	0.746596i	$-0.731687\pi$
$643$	−33.7395	−1.33055	−0.665277	+	0.746596i	$0.731687\pi$
$644$	73.2846	2.88782
$645$	5.77311	0.227316
$646$	7.53197	0.296342
$647$	−24.6703	−0.969890	−0.484945	−	0.874545i	$-0.661160\pi$
$647$	−24.6703	−0.969890	−0.484945	+	0.874545i	$0.661160\pi$
$648$	40.0394	1.57290
$649$	3.20075	0.125640
$650$	4.68077	0.183595
$651$	35.3384	1.38502
$652$	−6.30816	−0.247047
$653$	−46.4149	−1.81636	−0.908179	−	0.418583i	$-0.862527\pi$
$653$	−46.4149	−1.81636	−0.908179	+	0.418583i	$0.862527\pi$
$654$	−37.3648	−1.46108
$655$	3.12943	0.122277
$656$	−3.10363	−0.121176
$657$	23.9959	0.936170
$658$	44.7182	1.74330
$659$	16.4856	0.642188	0.321094	−	0.947047i	$-0.395949\pi$
$659$	16.4856	0.642188	0.321094	+	0.947047i	$0.395949\pi$
$660$	3.15526	0.122818
$661$	29.9883	1.16641	0.583204	−	0.812326i	$-0.301799\pi$
$661$	29.9883	1.16641	0.583204	+	0.812326i	$0.301799\pi$
$662$	71.3472	2.77299
$663$	2.90889	0.112972
$664$	−4.40119	−0.170799
$665$	0.955531	0.0370539
$666$	13.6728	0.529811
$667$	−3.91439	−0.151566
$668$	−48.8860	−1.89146
$669$	34.5416	1.33545
$670$	−5.52653	−0.213508
$671$	11.3857	0.439539
$672$	−20.2574	−0.781446
$673$	−1.03973	−0.0400785	−0.0200392	−	0.999799i	$-0.506379\pi$
$673$	−1.03973	−0.0400785	−0.0200392	+	0.999799i	$0.506379\pi$
$674$	24.1875	0.931668
$675$	12.4975	0.481028
$676$	−45.2644	−1.74094
$677$	21.2418	0.816390	0.408195	−	0.912895i	$-0.366158\pi$
$677$	21.2418	0.816390	0.408195	+	0.912895i	$0.366158\pi$
$678$	4.26435	0.163771
$679$	−0.126886	−0.00486942
$680$	−4.70549	−0.180447
$681$	−21.5313	−0.825081
$682$	16.0609	0.615005
$683$	50.6137	1.93668	0.968340	−	0.249634i	$-0.0803104\pi$
$683$	50.6137	1.93668	0.968340	+	0.249634i	$0.0803104\pi$
$684$	−6.40505	−0.244903
$685$	−4.59768	−0.175669
$686$	−46.8054	−1.78704
$687$	−21.7056	−0.828120
$688$	8.97430	0.342142
$689$	3.53429	0.134646
$690$	18.5433	0.705931
$691$	40.3814	1.53618	0.768090	−	0.640342i	$-0.221207\pi$
$691$	40.3814	1.53618	0.768090	+	0.640342i	$0.221207\pi$
$692$	−28.5035	−1.08354
$693$	−4.29382	−0.163109
$694$	−30.7015	−1.16541
$695$	5.66157	0.214756
$696$	−3.50188	−0.132739
$697$	−7.17995	−0.271960
$698$	39.2288	1.48483
$699$	−38.5930	−1.45972
$700$	40.1739	1.51843
$701$	28.2141	1.06563	0.532816	−	0.846231i	$-0.321134\pi$
$701$	28.2141	1.06563	0.532816	+	0.846231i	$0.321134\pi$
$702$	2.50323	0.0944785
$703$	3.17768	0.119849
$704$	−11.9874	−0.451791
$705$	7.22128	0.271969
$706$	−52.9446	−1.99260
$707$	−20.3160	−0.764063
$708$	24.7980	0.931967
$709$	45.4417	1.70660	0.853299	−	0.521422i	$-0.174598\pi$
$709$	45.4417	1.70660	0.853299	+	0.521422i	$0.174598\pi$
$710$	−6.10510	−0.229120
$711$	25.0534	0.939576
$712$	−54.7077	−2.05026
$713$	60.2392	2.25598
$714$	39.1198	1.46402
$715$	0.167721	0.00627240
$716$	25.6398	0.958206
$717$	17.6784	0.660211
$718$	−85.7432	−3.19991
$719$	−45.8660	−1.71051	−0.855256	−	0.518206i	$-0.826600\pi$
$719$	−45.8660	−1.71051	−0.855256	+	0.518206i	$0.826600\pi$
$720$	1.03208	0.0384634
$721$	−38.2390	−1.42409
$722$	42.3394	1.57571
$723$	−35.5195	−1.32098
$724$	28.8616	1.07263
$725$	−2.14583	−0.0796941
$726$	−5.16332	−0.191629
$727$	−14.1619	−0.525237	−0.262619	−	0.964900i	$-0.584586\pi$
$727$	−14.1619	−0.525237	−0.262619	+	0.964900i	$0.584586\pi$
$728$	3.48499	0.129162
$729$	−3.28416	−0.121636
$730$	−12.6052	−0.466539
$731$	20.7612	0.767879
$732$	88.2114	3.26039
$733$	−10.8800	−0.401861	−0.200930	−	0.979606i	$-0.564396\pi$
$733$	−10.8800	−0.401861	−0.200930	+	0.979606i	$0.564396\pi$
$734$	−50.4705	−1.86290
$735$	−1.29773	−0.0478675
$736$	−34.5315	−1.27285
$737$	5.77170	0.212603
$738$	9.56706	0.352168
$739$	−21.0151	−0.773052	−0.386526	−	0.922279i	$-0.626325\pi$
$739$	−21.0151	−0.773052	−0.386526	+	0.922279i	$0.626325\pi$
$740$	−4.58381	−0.168504
$741$	−0.900816	−0.0330923
$742$	47.5305	1.74490
$743$	−18.6216	−0.683161	−0.341580	−	0.939853i	$-0.610962\pi$
$743$	−18.6216	−0.683161	−0.341580	+	0.939853i	$0.610962\pi$
$744$	53.8910	1.97574
$745$	−7.48086	−0.274078
$746$	−43.5419	−1.59418
$747$	2.23321	0.0817090
$748$	11.3469	0.414883
$749$	17.8089	0.650723
$750$	20.6792	0.755099
$751$	29.2544	1.06751	0.533755	−	0.845639i	$-0.320781\pi$
$751$	29.2544	1.06751	0.533755	+	0.845639i	$0.320781\pi$
$752$	11.2255	0.409351
$753$	−31.0776	−1.13253
$754$	−0.429808	−0.0156527
$755$	9.24065	0.336302
$756$	21.4846	0.781387
$757$	−12.8252	−0.466140	−0.233070	−	0.972460i	$-0.574877\pi$
$757$	−12.8252	−0.466140	−0.233070	+	0.972460i	$0.574877\pi$
$758$	−55.9197	−2.03110
$759$	−19.3659	−0.702938
$760$	1.45718	0.0528576
$761$	8.74112	0.316865	0.158433	−	0.987370i	$-0.449356\pi$
$761$	8.74112	0.316865	0.158433	+	0.987370i	$0.449356\pi$
$762$	95.8648	3.47281
$763$	−17.0467	−0.617133
$764$	66.7438	2.41470
$765$	2.38762	0.0863246
$766$	−76.9251	−2.77942
$767$	1.31816	0.0475961
$768$	−52.4354	−1.89210
$769$	46.6000	1.68044	0.840219	−	0.542247i	$-0.182426\pi$
$769$	46.6000	1.68044	0.840219	+	0.542247i	$0.182426\pi$
$770$	2.25557	0.0812851
$771$	−58.1449	−2.09404
$772$	79.9098	2.87602
$773$	26.7337	0.961544	0.480772	−	0.876846i	$-0.340356\pi$
$773$	26.7337	0.961544	0.480772	+	0.876846i	$0.340356\pi$
$774$	−27.6636	−0.994348
$775$	33.0225	1.18620
$776$	−0.193500	−0.00694625
$777$	16.5043	0.592090
$778$	13.8596	0.496889
$779$	2.22346	0.0796639
$780$	1.29943	0.0465270
$781$	6.37594	0.228149
$782$	66.6851	2.38465
$783$	−1.14757	−0.0410108
$784$	−2.01732	−0.0720472
$785$	7.13740	0.254745
$786$	−39.6758	−1.41519
$787$	51.5791	1.83860	0.919299	−	0.393561i	$-0.128757\pi$
$787$	51.5791	1.83860	0.919299	+	0.393561i	$0.128757\pi$
$788$	62.9099	2.24107
$789$	51.5033	1.83357
$790$	−13.1607	−0.468237
$791$	1.94550	0.0691740
$792$	−6.54807	−0.232675
$793$	4.68896	0.166510
$794$	−17.8120	−0.632125
$795$	7.67542	0.272219
$796$	−23.9828	−0.850048
$797$	24.0230	0.850937	0.425468	−	0.904973i	$-0.360109\pi$
$797$	24.0230	0.850937	0.425468	+	0.904973i	$0.360109\pi$
$798$	−12.1145	−0.428849
$799$	25.9690	0.918719
$800$	−18.9298	−0.669270
$801$	27.7593	0.980827
$802$	46.4947	1.64178
$803$	13.1644	0.464561
$804$	44.7167	1.57704
$805$	8.45989	0.298172
$806$	6.61438	0.232982
$807$	−3.32185	−0.116935
$808$	−30.9819	−1.08994
$809$	1.64128	0.0577043	0.0288522	−	0.999584i	$-0.490815\pi$
$809$	1.64128	0.0577043	0.0288522	+	0.999584i	$0.490815\pi$
$810$	10.6724	0.374988
$811$	53.6904	1.88533	0.942663	−	0.333747i	$-0.108313\pi$
$811$	53.6904	1.88533	0.942663	+	0.333747i	$0.108313\pi$
$812$	−3.68893	−0.129456
$813$	−11.2630	−0.395009
$814$	7.50104	0.262911
$815$	−0.728207	−0.0255080
$816$	9.82014	0.343774
$817$	−6.42925	−0.224931
$818$	−58.5191	−2.04607
$819$	−1.76833	−0.0617903
$820$	−3.20735	−0.112006
$821$	−18.8504	−0.657883	−0.328942	−	0.944350i	$-0.606692\pi$
$821$	−18.8504	−0.657883	−0.328942	+	0.944350i	$0.606692\pi$
$822$	58.2908	2.03312
$823$	−54.3151	−1.89330	−0.946652	−	0.322257i	$-0.895559\pi$
$823$	−54.3151	−1.89330	−0.946652	+	0.322257i	$0.895559\pi$
$824$	−58.3144	−2.03148
$825$	−10.6162	−0.369608
$826$	17.7272	0.616807
$827$	16.0290	0.557381	0.278691	−	0.960381i	$-0.410100\pi$
$827$	16.0290	0.557381	0.278691	+	0.960381i	$0.410100\pi$
$828$	−56.7077	−1.97073
$829$	17.5479	0.609462	0.304731	−	0.952438i	$-0.401433\pi$
$829$	17.5479	0.609462	0.304731	+	0.952438i	$0.401433\pi$
$830$	−1.17312	−0.0407196
$831$	−1.72775	−0.0599348
$832$	−4.93676	−0.171151
$833$	−4.66688	−0.161698
$834$	−71.7791	−2.48551
$835$	−5.64334	−0.195296
$836$	−3.51387	−0.121530
$837$	17.6601	0.610423
$838$	0.651774	0.0225152
$839$	−19.6974	−0.680031	−0.340016	−	0.940420i	$-0.610432\pi$
$839$	−19.6974	−0.680031	−0.340016	+	0.940420i	$0.610432\pi$
$840$	7.56836	0.261133
$841$	−28.8030	−0.993206
$842$	−70.5340	−2.43076
$843$	−65.7804	−2.26560
$844$	24.4433	0.841373
$845$	−5.22527	−0.179755
$846$	−34.6029	−1.18967
$847$	−2.35563	−0.0809405
$848$	11.9314	0.409728
$849$	10.9444	0.375611
$850$	36.5561	1.25386
$851$	28.1339	0.964418
$852$	49.3981	1.69235
$853$	12.1438	0.415795	0.207897	−	0.978151i	$-0.433338\pi$
$853$	12.1438	0.415795	0.207897	+	0.978151i	$0.433338\pi$
$854$	63.0589	2.15783
$855$	−0.739391	−0.0252866
$856$	27.1585	0.928259
$857$	−33.2251	−1.13495	−0.567474	−	0.823391i	$-0.692079\pi$
$857$	−33.2251	−1.13495	−0.567474	+	0.823391i	$0.692079\pi$
$858$	−2.12641	−0.0725945
$859$	−31.5136	−1.07523	−0.537615	−	0.843191i	$-0.680675\pi$
$859$	−31.5136	−1.07523	−0.537615	+	0.843191i	$0.680675\pi$
$860$	9.27422	0.316248
$861$	11.5483	0.393565
$862$	2.50673	0.0853797
$863$	54.4417	1.85322	0.926608	−	0.376028i	$-0.122710\pi$
$863$	54.4417	1.85322	0.926608	+	0.376028i	$0.122710\pi$
$864$	−10.1235	−0.344408
$865$	−3.29041	−0.111877
$866$	−7.91901	−0.269099
$867$	−14.6155	−0.496369
$868$	56.7695	1.92688
$869$	13.7445	0.466252
$870$	−0.933414	−0.0316457
$871$	2.37696	0.0805402
$872$	−25.9962	−0.880342
$873$	0.0981842	0.00332303
$874$	−20.6508	−0.698525
$875$	9.43436	0.318940
$876$	101.992	3.44600
$877$	18.9543	0.640041	0.320020	−	0.947411i	$-0.396310\pi$
$877$	18.9543	0.640041	0.320020	+	0.947411i	$0.396310\pi$
$878$	−8.79988	−0.296982
$879$	0.370426	0.0124942
$880$	0.566210	0.0190869
$881$	56.1985	1.89338	0.946688	−	0.322152i	$-0.104406\pi$
$881$	56.1985	1.89338	0.946688	+	0.322152i	$0.104406\pi$
$882$	6.21847	0.209387
$883$	−9.16247	−0.308342	−0.154171	−	0.988044i	$-0.549271\pi$
$883$	−9.16247	−0.308342	−0.154171	+	0.988044i	$0.549271\pi$
$884$	4.67299	0.157170
$885$	2.86266	0.0962271
$886$	−27.3683	−0.919455
$887$	−23.7730	−0.798219	−0.399109	−	0.916903i	$-0.630681\pi$
$887$	−23.7730	−0.798219	−0.399109	+	0.916903i	$0.630681\pi$
$888$	25.1691	0.844619
$889$	43.7358	1.46685
$890$	−14.5821	−0.488794
$891$	−11.1458	−0.373399
$892$	55.4894	1.85792
$893$	−8.04202	−0.269116
$894$	94.8445	3.17208
$895$	2.95983	0.0989363
$896$	−47.9427	−1.60165
$897$	−7.97546	−0.266293
$898$	98.6014	3.29037
$899$	−3.03226	−0.101132
$900$	−31.0866	−1.03622
$901$	27.6022	0.919564
$902$	5.24858	0.174759
$903$	−33.3925	−1.11123
$904$	2.96688	0.0986769
$905$	3.33175	0.110751
$906$	−117.156	−3.89224
$907$	28.5107	0.946682	0.473341	−	0.880879i	$-0.343048\pi$
$907$	28.5107	0.946682	0.473341	+	0.880879i	$0.343048\pi$
$908$	−34.5890	−1.14788
$909$	15.7206	0.521418
$910$	0.928912	0.0307931
$911$	−31.3780	−1.03960	−0.519800	−	0.854288i	$-0.673994\pi$
$911$	−31.3780	−1.03960	−0.519800	+	0.854288i	$0.673994\pi$
$912$	−3.04107	−0.100700
$913$	1.22516	0.0405470
$914$	−12.9838	−0.429464
$915$	10.1830	0.336640
$916$	−34.8690	−1.15210
$917$	−18.1011	−0.597750
$918$	19.5498	0.645241
$919$	54.1705	1.78692	0.893459	−	0.449144i	$-0.148271\pi$
$919$	54.1705	1.78692	0.893459	+	0.449144i	$0.148271\pi$
$920$	12.9013	0.425343
$921$	13.7178	0.452016
$922$	6.17842	0.203475
$923$	2.62580	0.0864294
$924$	−18.2504	−0.600396
$925$	15.4227	0.507096
$926$	−39.5935	−1.30112
$927$	29.5894	0.971843
$928$	1.73821	0.0570596
$929$	−53.6908	−1.76154	−0.880768	−	0.473547i	$-0.842973\pi$
$929$	−53.6908	−1.76154	−0.880768	+	0.473547i	$0.842973\pi$
$930$	14.3644	0.471029
$931$	1.44522	0.0473653
$932$	−61.9978	−2.03081
$933$	−17.6582	−0.578103
$934$	30.3383	0.992698
$935$	1.30987	0.0428374
$936$	−2.69669	−0.0881441
$937$	−43.2634	−1.41335	−0.706677	−	0.707536i	$-0.749807\pi$
$937$	−43.2634	−1.41335	−0.706677	+	0.707536i	$0.749807\pi$
$938$	31.9662	1.04373
$939$	−15.7030	−0.512447
$940$	11.6006	0.378371
$941$	−50.0315	−1.63098	−0.815490	−	0.578772i	$-0.803532\pi$
$941$	−50.0315	−1.63098	−0.815490	+	0.578772i	$0.803532\pi$
$942$	−90.4900	−2.94832
$943$	19.6857	0.641053
$944$	4.45000	0.144835
$945$	2.48016	0.0806795
$946$	−15.1765	−0.493431
$947$	2.64747	0.0860312	0.0430156	−	0.999074i	$-0.486303\pi$
$947$	2.64747	0.0860312	0.0430156	+	0.999074i	$0.486303\pi$
$948$	106.487	3.45853
$949$	5.42149	0.175989
$950$	−11.3206	−0.367288
$951$	43.1523	1.39931
$952$	27.2172	0.882115
$953$	22.6548	0.733862	0.366931	−	0.930248i	$-0.380409\pi$
$953$	22.6548	0.733862	0.366931	+	0.930248i	$0.380409\pi$
$954$	−36.7791	−1.19077
$955$	7.70482	0.249322
$956$	28.3994	0.918503
$957$	0.974822	0.0315115
$958$	67.9856	2.19651
$959$	26.5937	0.858754
$960$	−10.7212	−0.346024
$961$	15.6639	0.505288
$962$	3.08916	0.0995984
$963$	−13.7805	−0.444072
$964$	−57.0603	−1.83779
$965$	9.22469	0.296953
$966$	−107.257	−3.45094
$967$	−0.248311	−0.00798513	−0.00399256	−	0.999992i	$-0.501271\pi$
$967$	−0.248311	−0.00798513	−0.00399256	+	0.999992i	$0.501271\pi$
$968$	−3.59233	−0.115462
$969$	−7.03522	−0.226004
$970$	−0.0515767	−0.00165603
$971$	−42.8861	−1.37628	−0.688140	−	0.725578i	$-0.741573\pi$
$971$	−42.8861	−1.37628	−0.688140	+	0.725578i	$0.741573\pi$
$972$	−58.9914	−1.89215
$973$	−32.7473	−1.04983
$974$	42.5114	1.36215
$975$	−4.37206	−0.140018
$976$	15.8295	0.506690
$977$	10.0815	0.322537	0.161269	−	0.986911i	$-0.448441\pi$
$977$	10.0815	0.322537	0.161269	+	0.986911i	$0.448441\pi$
$978$	9.23242	0.295220
$979$	15.2290	0.486722
$980$	−2.08474	−0.0665946
$981$	13.1908	0.421149
$982$	12.0158	0.383438
$983$	−0.536252	−0.0171038	−0.00855189	−	0.999963i	$-0.502722\pi$
$983$	−0.536252	−0.0171038	−0.00855189	+	0.999963i	$0.502722\pi$
$984$	17.6111	0.561422
$985$	7.26224	0.231394
$986$	−3.35673	−0.106900
$987$	−41.7689	−1.32952
$988$	−1.44712	−0.0460389
$989$	−56.9220	−1.81002
$990$	−1.74536	−0.0554713
$991$	−21.6442	−0.687551	−0.343775	−	0.939052i	$-0.611706\pi$
$991$	−21.6442	−0.687551	−0.343775	+	0.939052i	$0.611706\pi$
$992$	−26.7496	−0.849301
$993$	−66.6416	−2.11481
$994$	35.3128	1.12005
$995$	−2.76855	−0.0877688
$996$	9.49204	0.300767
$997$	40.6135	1.28624	0.643121	−	0.765765i	$-0.277639\pi$
$997$	40.6135	1.28624	0.643121	+	0.765765i	$0.277639\pi$
$998$	75.8596	2.40130
$999$	8.24792	0.260953

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6017.2.a.e.1.13	✓	119

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6017.2.a.e.1.13	✓	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)

\(f(q)\)	\(=\)	\(q-2.35115 q^{2} +2.19609 q^{3} +3.52790 q^{4} +0.407257 q^{5} -5.16332 q^{6} -2.35563 q^{7} -3.59233 q^{8} +1.82279 q^{9} +O(q^{10})\)	\(q-2.35115 q^{2} +2.19609 q^{3} +3.52790 q^{4} +0.407257 q^{5} -5.16332 q^{6} -2.35563 q^{7} -3.59233 q^{8} +1.82279 q^{9} -0.957522 q^{10} +1.00000 q^{11} +7.74758 q^{12} +0.411830 q^{13} +5.53844 q^{14} +0.894371 q^{15} +1.39030 q^{16} +3.21632 q^{17} -4.28565 q^{18} -0.996022 q^{19} +1.43676 q^{20} -5.17317 q^{21} -2.35115 q^{22} -8.81838 q^{23} -7.88907 q^{24} -4.83414 q^{25} -0.968274 q^{26} -2.58525 q^{27} -8.31045 q^{28} +0.443891 q^{29} -2.10280 q^{30} -6.83110 q^{31} +3.91586 q^{32} +2.19609 q^{33} -7.56206 q^{34} -0.959348 q^{35} +6.43063 q^{36} -3.19037 q^{37} +2.34180 q^{38} +0.904414 q^{39} -1.46300 q^{40} -2.23235 q^{41} +12.1629 q^{42} +6.45493 q^{43} +3.52790 q^{44} +0.742344 q^{45} +20.7333 q^{46} +8.07414 q^{47} +3.05322 q^{48} -1.45100 q^{49} +11.3658 q^{50} +7.06332 q^{51} +1.45290 q^{52} +8.58192 q^{53} +6.07832 q^{54} +0.407257 q^{55} +8.46221 q^{56} -2.18735 q^{57} -1.04365 q^{58} +3.20075 q^{59} +3.15526 q^{60} +11.3857 q^{61} +16.0609 q^{62} -4.29382 q^{63} -11.9874 q^{64} +0.167721 q^{65} -5.16332 q^{66} +5.77170 q^{67} +11.3469 q^{68} -19.3659 q^{69} +2.25557 q^{70} +6.37594 q^{71} -6.54807 q^{72} +13.1644 q^{73} +7.50104 q^{74} -10.6162 q^{75} -3.51387 q^{76} -2.35563 q^{77} -2.12641 q^{78} +13.7445 q^{79} +0.566210 q^{80} -11.1458 q^{81} +5.24858 q^{82} +1.22516 q^{83} -18.2504 q^{84} +1.30987 q^{85} -15.1765 q^{86} +0.974822 q^{87} -3.59233 q^{88} +15.2290 q^{89} -1.74536 q^{90} -0.970120 q^{91} -31.1104 q^{92} -15.0017 q^{93} -18.9835 q^{94} -0.405637 q^{95} +8.59956 q^{96} +0.0538648 q^{97} +3.41151 q^{98} +1.82279 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 119 q + 15 q^{2} + 15 q^{3} + 133 q^{4} + 6 q^{5} + 16 q^{6} + 72 q^{7} + 39 q^{8} + 128 q^{9}+O(q^{10}) \) 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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