LMFDB - Embedded newform 6017.2.a.e.1.12

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			1.12
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)

$f(q)$	$=$	$q-2.35458 q^{2} -1.66572 q^{3} +3.54404 q^{4} +1.38814 q^{5} +3.92207 q^{6} -2.86994 q^{7} -3.63557 q^{8} -0.225374 q^{9} +O(q^{10})$	\(q-2.35458 q^{2} -1.66572 q^{3} +3.54404 q^{4} +1.38814 q^{5} +3.92207 q^{6} -2.86994 q^{7} -3.63557 q^{8} -0.225374 q^{9} -3.26849 q^{10} +1.00000 q^{11} -5.90338 q^{12} -3.73311 q^{13} +6.75750 q^{14} -2.31226 q^{15} +1.47215 q^{16} +6.33443 q^{17} +0.530662 q^{18} -5.60830 q^{19} +4.91963 q^{20} +4.78052 q^{21} -2.35458 q^{22} +0.773056 q^{23} +6.05584 q^{24} -3.07306 q^{25} +8.78990 q^{26} +5.37257 q^{27} -10.1712 q^{28} +0.0622701 q^{29} +5.44439 q^{30} -1.69097 q^{31} +3.80484 q^{32} -1.66572 q^{33} -14.9149 q^{34} -3.98389 q^{35} -0.798736 q^{36} -8.66506 q^{37} +13.2052 q^{38} +6.21832 q^{39} -5.04669 q^{40} +5.95083 q^{41} -11.2561 q^{42} +1.28362 q^{43} +3.54404 q^{44} -0.312852 q^{45} -1.82022 q^{46} +5.78341 q^{47} -2.45219 q^{48} +1.23656 q^{49} +7.23577 q^{50} -10.5514 q^{51} -13.2303 q^{52} -8.83698 q^{53} -12.6501 q^{54} +1.38814 q^{55} +10.4339 q^{56} +9.34185 q^{57} -0.146620 q^{58} -12.5103 q^{59} -8.19474 q^{60} -7.40865 q^{61} +3.98152 q^{62} +0.646811 q^{63} -11.9031 q^{64} -5.18209 q^{65} +3.92207 q^{66} -5.16446 q^{67} +22.4495 q^{68} -1.28770 q^{69} +9.38037 q^{70} +14.2340 q^{71} +0.819364 q^{72} +1.29902 q^{73} +20.4026 q^{74} +5.11886 q^{75} -19.8760 q^{76} -2.86994 q^{77} -14.6415 q^{78} -5.68971 q^{79} +2.04356 q^{80} -8.27308 q^{81} -14.0117 q^{82} -1.55956 q^{83} +16.9424 q^{84} +8.79309 q^{85} -3.02239 q^{86} -0.103725 q^{87} -3.63557 q^{88} -7.33954 q^{89} +0.736634 q^{90} +10.7138 q^{91} +2.73974 q^{92} +2.81669 q^{93} -13.6175 q^{94} -7.78511 q^{95} -6.33781 q^{96} +9.68816 q^{97} -2.91158 q^{98} -0.225374 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.35458	−1.66494	−0.832469	−	0.554071i	$-0.813074\pi$
$2$	−2.35458	−1.66494	−0.832469	+	0.554071i	$0.813074\pi$
$3$	−1.66572	−0.961704	−0.480852	−	0.876802i	$-0.659673\pi$
$3$	−1.66572	−0.961704	−0.480852	+	0.876802i	$0.659673\pi$
$4$	3.54404	1.77202
$5$	1.38814	0.620796	0.310398	−	0.950607i	$-0.399538\pi$
$5$	1.38814	0.620796	0.310398	+	0.950607i	$0.399538\pi$
$6$	3.92207	1.60118
$7$	−2.86994	−1.08474	−0.542368	−	0.840141i	$-0.682472\pi$
$7$	−2.86994	−1.08474	−0.542368	+	0.840141i	$0.682472\pi$
$8$	−3.63557	−1.28537
$9$	−0.225374	−0.0751248
$10$	−3.26849	−1.03359
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−5.90338	−1.70416
$13$	−3.73311	−1.03538	−0.517689	−	0.855569i	$-0.673208\pi$
$13$	−3.73311	−1.03538	−0.517689	+	0.855569i	$0.673208\pi$
$14$	6.75750	1.80602
$15$	−2.31226	−0.597022
$16$	1.47215	0.368038
$17$	6.33443	1.53633	0.768163	−	0.640255i	$-0.221171\pi$
$17$	6.33443	1.53633	0.768163	+	0.640255i	$0.221171\pi$
$18$	0.530662	0.125078
$19$	−5.60830	−1.28663	−0.643316	−	0.765601i	$-0.722442\pi$
$19$	−5.60830	−1.28663	−0.643316	+	0.765601i	$0.722442\pi$
$20$	4.91963	1.10006
$21$	4.78052	1.04320
$22$	−2.35458	−0.501998
$23$	0.773056	0.161193	0.0805967	−	0.996747i	$-0.474317\pi$
$23$	0.773056	0.161193	0.0805967	+	0.996747i	$0.474317\pi$
$24$	6.05584	1.23614
$25$	−3.07306	−0.614612
$26$	8.78990	1.72384
$27$	5.37257	1.03395
$28$	−10.1712	−1.92217
$29$	0.0622701	0.0115633	0.00578163	−	0.999983i	$-0.498160\pi$
$29$	0.0622701	0.0115633	0.00578163	+	0.999983i	$0.498160\pi$
$30$	5.44439	0.994005
$31$	−1.69097	−0.303707	−0.151854	−	0.988403i	$-0.548524\pi$
$31$	−1.69097	−0.303707	−0.151854	+	0.988403i	$0.548524\pi$
$32$	3.80484	0.672608
$33$	−1.66572	−0.289965
$34$	−14.9149	−2.55789
$35$	−3.98389	−0.673400
$36$	−0.798736	−0.133123
$37$	−8.66506	−1.42453	−0.712263	−	0.701912i	$-0.752330\pi$
$37$	−8.66506	−1.42453	−0.712263	+	0.701912i	$0.752330\pi$
$38$	13.2052	2.14216
$39$	6.21832	0.995728
$40$	−5.04669	−0.797951
$41$	5.95083	0.929363	0.464682	−	0.885478i	$-0.346169\pi$
$41$	5.95083	0.929363	0.464682	+	0.885478i	$0.346169\pi$
$42$	−11.2561	−1.73686
$43$	1.28362	0.195750	0.0978752	−	0.995199i	$-0.468795\pi$
$43$	1.28362	0.195750	0.0978752	+	0.995199i	$0.468795\pi$
$44$	3.54404	0.534284
$45$	−0.312852	−0.0466372
$46$	−1.82022	−0.268377
$47$	5.78341	0.843597	0.421798	−	0.906690i	$-0.361399\pi$
$47$	5.78341	0.843597	0.421798	+	0.906690i	$0.361399\pi$
$48$	−2.45219	−0.353944
$49$	1.23656	0.176652
$50$	7.23577	1.02329
$51$	−10.5514	−1.47749
$52$	−13.2303	−1.83471
$53$	−8.83698	−1.21385	−0.606926	−	0.794758i	$-0.707598\pi$
$53$	−8.83698	−1.21385	−0.606926	+	0.794758i	$0.707598\pi$
$54$	−12.6501	−1.72147
$55$	1.38814	0.187177
$56$	10.4339	1.39428
$57$	9.34185	1.23736
$58$	−0.146620	−0.0192521
$59$	−12.5103	−1.62870	−0.814348	−	0.580377i	$-0.802905\pi$
$59$	−12.5103	−1.62870	−0.814348	+	0.580377i	$0.802905\pi$
$60$	−8.19474	−1.05794
$61$	−7.40865	−0.948581	−0.474290	−	0.880368i	$-0.657295\pi$
$61$	−7.40865	−0.948581	−0.474290	+	0.880368i	$0.657295\pi$
$62$	3.98152	0.505654
$63$	0.646811	0.0814906
$64$	−11.9031	−1.48789
$65$	−5.18209	−0.642759
$66$	3.92207	0.482774
$67$	−5.16446	−0.630939	−0.315469	−	0.948936i	$-0.602162\pi$
$67$	−5.16446	−0.630939	−0.315469	+	0.948936i	$0.602162\pi$
$68$	22.4495	2.72240
$69$	−1.28770	−0.155020
$70$	9.38037	1.12117
$71$	14.2340	1.68927	0.844635	−	0.535342i	$-0.179817\pi$
$71$	14.2340	1.68927	0.844635	+	0.535342i	$0.179817\pi$
$72$	0.819364	0.0965630
$73$	1.29902	0.152038	0.0760192	−	0.997106i	$-0.475779\pi$
$73$	1.29902	0.152038	0.0760192	+	0.997106i	$0.475779\pi$
$74$	20.4026	2.37175
$75$	5.11886	0.591075
$76$	−19.8760	−2.27994
$77$	−2.86994	−0.327060
$78$	−14.6415	−1.65783
$79$	−5.68971	−0.640143	−0.320071	−	0.947393i	$-0.603707\pi$
$79$	−5.68971	−0.640143	−0.320071	+	0.947393i	$0.603707\pi$
$80$	2.04356	0.228476
$81$	−8.27308	−0.919231
$82$	−14.0117	−1.54733
$83$	−1.55956	−0.171183	−0.0855917	−	0.996330i	$-0.527278\pi$
$83$	−1.55956	−0.171183	−0.0855917	+	0.996330i	$0.527278\pi$
$84$	16.9424	1.84856
$85$	8.79309	0.953745
$86$	−3.02239	−0.325912
$87$	−0.103725	−0.0111204
$88$	−3.63557	−0.387553
$89$	−7.33954	−0.777990	−0.388995	−	0.921240i	$-0.627178\pi$
$89$	−7.33954	−0.777990	−0.388995	+	0.921240i	$0.627178\pi$
$90$	0.736634	0.0776480
$91$	10.7138	1.12311
$92$	2.73974	0.285638
$93$	2.81669	0.292077
$94$	−13.6175	−1.40454
$95$	−7.78511	−0.798736
$96$	−6.33781	−0.646850
$97$	9.68816	0.983684	0.491842	−	0.870684i	$-0.336324\pi$
$97$	9.68816	0.983684	0.491842	+	0.870684i	$0.336324\pi$
$98$	−2.91158	−0.294114
$99$	−0.225374	−0.0226510
$100$	−10.8911	−1.08911
$101$	2.30951	0.229804	0.114902	−	0.993377i	$-0.463345\pi$
$101$	2.30951	0.229804	0.114902	+	0.993377i	$0.463345\pi$
$102$	24.8441	2.45993
$103$	6.72494	0.662628	0.331314	−	0.943521i	$-0.392508\pi$
$103$	6.72494	0.662628	0.331314	+	0.943521i	$0.392508\pi$
$104$	13.5720	1.33084
$105$	6.63604	0.647611
$106$	20.8074	2.02099
$107$	8.74749	0.845652	0.422826	−	0.906211i	$-0.361038\pi$
$107$	8.74749	0.845652	0.422826	+	0.906211i	$0.361038\pi$
$108$	19.0406	1.83219
$109$	−19.6045	−1.87777	−0.938887	−	0.344227i	$-0.888141\pi$
$109$	−19.6045	−1.87777	−0.938887	+	0.344227i	$0.888141\pi$
$110$	−3.26849	−0.311638
$111$	14.4336	1.36997
$112$	−4.22499	−0.399224
$113$	−1.99011	−0.187214	−0.0936071	−	0.995609i	$-0.529840\pi$
$113$	−1.99011	−0.187214	−0.0936071	+	0.995609i	$0.529840\pi$
$114$	−21.9961	−2.06013
$115$	1.07311	0.100068
$116$	0.220688	0.0204903
$117$	0.841348	0.0777826
$118$	29.4564	2.71168
$119$	−18.1794	−1.66651
$120$	8.40637	0.767393
$121$	1.00000	0.0909091
$122$	17.4443	1.57933
$123$	−9.91242	−0.893773
$124$	−5.99287	−0.538176
$125$	−11.2066	−1.00234
$126$	−1.52297	−0.135677
$127$	2.66573	0.236546	0.118273	−	0.992981i	$-0.462264\pi$
$127$	2.66573	0.236546	0.118273	+	0.992981i	$0.462264\pi$
$128$	20.4171	1.80464
$129$	−2.13815	−0.188254
$130$	12.2016	1.07015
$131$	−5.65119	−0.493747	−0.246874	−	0.969048i	$-0.579403\pi$
$131$	−5.65119	−0.493747	−0.246874	+	0.969048i	$0.579403\pi$
$132$	−5.90338	−0.513824
$133$	16.0955	1.39566
$134$	12.1601	1.05047
$135$	7.45789	0.641873
$136$	−23.0293	−1.97474
$137$	−3.85281	−0.329168	−0.164584	−	0.986363i	$-0.552628\pi$
$137$	−3.85281	−0.329168	−0.164584	+	0.986363i	$0.552628\pi$
$138$	3.03198	0.258099
$139$	12.6184	1.07028	0.535139	−	0.844764i	$-0.320259\pi$
$139$	12.6184	1.07028	0.535139	+	0.844764i	$0.320259\pi$
$140$	−14.1191	−1.19328
$141$	−9.63354	−0.811291
$142$	−33.5152	−2.81253
$143$	−3.73311	−0.312178
$144$	−0.331785	−0.0276488
$145$	0.0864397	0.00717842
$146$	−3.05864	−0.253135
$147$	−2.05977	−0.169887
$148$	−30.7093	−2.52429
$149$	4.47777	0.366834	0.183417	−	0.983035i	$-0.441284\pi$
$149$	4.47777	0.366834	0.183417	+	0.983035i	$0.441284\pi$
$150$	−12.0528	−0.984104
$151$	15.8869	1.29286	0.646429	−	0.762974i	$-0.276262\pi$
$151$	15.8869	1.29286	0.646429	+	0.762974i	$0.276262\pi$
$152$	20.3893	1.65379
$153$	−1.42762	−0.115416
$154$	6.75750	0.544535
$155$	−2.34731	−0.188540
$156$	22.0380	1.76445
$157$	5.94862	0.474752	0.237376	−	0.971418i	$-0.423713\pi$
$157$	5.94862	0.474752	0.237376	+	0.971418i	$0.423713\pi$
$158$	13.3969	1.06580
$159$	14.7199	1.16737
$160$	5.28166	0.417552
$161$	−2.21863	−0.174852
$162$	19.4796	1.53046
$163$	−5.44790	−0.426712	−0.213356	−	0.976974i	$-0.568439\pi$
$163$	−5.44790	−0.426712	−0.213356	+	0.976974i	$0.568439\pi$
$164$	21.0900	1.64685
$165$	−2.31226	−0.180009
$166$	3.67210	0.285010
$167$	24.7556	1.91565	0.957825	−	0.287353i	$-0.0927754\pi$
$167$	24.7556	1.91565	0.957825	+	0.287353i	$0.0927754\pi$
$168$	−17.3799	−1.34089
$169$	0.936116	0.0720089
$170$	−20.7040	−1.58793
$171$	1.26397	0.0966579
$172$	4.54921	0.346874
$173$	−11.4860	−0.873264	−0.436632	−	0.899640i	$-0.643829\pi$
$173$	−11.4860	−0.873264	−0.436632	+	0.899640i	$0.643829\pi$
$174$	0.244228	0.0185148
$175$	8.81951	0.666692
$176$	1.47215	0.110968
$177$	20.8386	1.56632
$178$	17.2815	1.29531
$179$	−18.9094	−1.41335	−0.706677	−	0.707537i	$-0.749806\pi$
$179$	−18.9094	−1.41335	−0.706677	+	0.707537i	$0.749806\pi$
$180$	−1.10876	−0.0826421
$181$	−5.24551	−0.389896	−0.194948	−	0.980814i	$-0.562454\pi$
$181$	−5.24551	−0.389896	−0.194948	+	0.980814i	$0.562454\pi$
$182$	−25.2265	−1.86991
$183$	12.3407	0.912254
$184$	−2.81050	−0.207193
$185$	−12.0283	−0.884341
$186$	−6.63211	−0.486290
$187$	6.33443	0.463219
$188$	20.4966	1.49487
$189$	−15.4190	−1.12156
$190$	18.3307	1.32985
$191$	−14.1481	−1.02372	−0.511860	−	0.859069i	$-0.671043\pi$
$191$	−14.1481	−1.02372	−0.511860	+	0.859069i	$0.671043\pi$
$192$	19.8272	1.43091
$193$	−4.58932	−0.330346	−0.165173	−	0.986265i	$-0.552818\pi$
$193$	−4.58932	−0.330346	−0.165173	+	0.986265i	$0.552818\pi$
$194$	−22.8115	−1.63777
$195$	8.63191	0.618144
$196$	4.38243	0.313031
$197$	−5.36237	−0.382053	−0.191027	−	0.981585i	$-0.561182\pi$
$197$	−5.36237	−0.382053	−0.191027	+	0.981585i	$0.561182\pi$
$198$	0.530662	0.0377125
$199$	−10.9668	−0.777416	−0.388708	−	0.921361i	$-0.627079\pi$
$199$	−10.9668	−0.777416	−0.388708	+	0.921361i	$0.627079\pi$
$200$	11.1723	0.790003
$201$	8.60254	0.606777
$202$	−5.43792	−0.382610
$203$	−0.178711	−0.0125431
$204$	−37.3946	−2.61814
$205$	8.26059	0.576945
$206$	−15.8344	−1.10324
$207$	−0.174227	−0.0121096
$208$	−5.49570	−0.381059
$209$	−5.60830	−0.387934
$210$	−15.6251	−1.07823
$211$	9.17364	0.631539	0.315770	−	0.948836i	$-0.397737\pi$
$211$	9.17364	0.631539	0.315770	+	0.948836i	$0.397737\pi$
$212$	−31.3186	−2.15097
$213$	−23.7099	−1.62458
$214$	−20.5967	−1.40796
$215$	1.78185	0.121521
$216$	−19.5324	−1.32901
$217$	4.85299	0.329442
$218$	46.1604	3.12638
$219$	−2.16380	−0.146216
$220$	4.91963	0.331682
$221$	−23.6471	−1.59068
$222$	−33.9850	−2.28092
$223$	−10.4589	−0.700381	−0.350191	−	0.936678i	$-0.613883\pi$
$223$	−10.4589	−0.700381	−0.350191	+	0.936678i	$0.613883\pi$
$224$	−10.9197	−0.729601
$225$	0.692589	0.0461726
$226$	4.68588	0.311700
$227$	2.91943	0.193769	0.0968847	−	0.995296i	$-0.469112\pi$
$227$	2.91943	0.193769	0.0968847	+	0.995296i	$0.469112\pi$
$228$	33.1079	2.19263
$229$	−5.68486	−0.375666	−0.187833	−	0.982201i	$-0.560146\pi$
$229$	−5.68486	−0.375666	−0.187833	+	0.982201i	$0.560146\pi$
$230$	−2.52673	−0.166607
$231$	4.78052	0.314535
$232$	−0.226387	−0.0148630
$233$	22.9520	1.50364	0.751819	−	0.659370i	$-0.229177\pi$
$233$	22.9520	1.50364	0.751819	+	0.659370i	$0.229177\pi$
$234$	−1.98102	−0.129503
$235$	8.02819	0.523702
$236$	−44.3369	−2.88608
$237$	9.47748	0.615628
$238$	42.8049	2.77463
$239$	−5.90621	−0.382041	−0.191020	−	0.981586i	$-0.561180\pi$
$239$	−5.90621	−0.382041	−0.191020	+	0.981586i	$0.561180\pi$
$240$	−3.40399	−0.219727
$241$	−25.8300	−1.66386	−0.831929	−	0.554882i	$-0.812763\pi$
$241$	−25.8300	−1.66386	−0.831929	+	0.554882i	$0.812763\pi$
$242$	−2.35458	−0.151358
$243$	−2.33707	−0.149923
$244$	−26.2566	−1.68091
$245$	1.71652	0.109665
$246$	23.3396	1.48808
$247$	20.9364	1.33215
$248$	6.14764	0.390376
$249$	2.59778	0.164628
$250$	26.3867	1.66884
$251$	−11.3925	−0.719089	−0.359544	−	0.933128i	$-0.617068\pi$
$251$	−11.3925	−0.719089	−0.359544	+	0.933128i	$0.617068\pi$
$252$	2.29233	0.144403
$253$	0.773056	0.0486016
$254$	−6.27668	−0.393834
$255$	−14.6468	−0.917220
$256$	−24.2675	−1.51672
$257$	2.23635	0.139500	0.0697499	−	0.997565i	$-0.477780\pi$
$257$	2.23635	0.139500	0.0697499	+	0.997565i	$0.477780\pi$
$258$	5.03445	0.313431
$259$	24.8682	1.54524
$260$	−18.3655	−1.13898
$261$	−0.0140341	−0.000868687 0
$262$	13.3062	0.822059
$263$	31.2326	1.92589	0.962943	−	0.269707i	$-0.0869267\pi$
$263$	31.2326	1.92589	0.962943	+	0.269707i	$0.0869267\pi$
$264$	6.05584	0.372711
$265$	−12.2670	−0.753555
$266$	−37.8981	−2.32368
$267$	12.2256	0.748196
$268$	−18.3031	−1.11804
$269$	−20.6887	−1.26141	−0.630707	−	0.776021i	$-0.717235\pi$
$269$	−20.6887	−1.26141	−0.630707	+	0.776021i	$0.717235\pi$
$270$	−17.5602	−1.06868
$271$	−9.65615	−0.586570	−0.293285	−	0.956025i	$-0.594748\pi$
$271$	−9.65615	−0.586570	−0.293285	+	0.956025i	$0.594748\pi$
$272$	9.32524	0.565426
$273$	−17.8462	−1.08010
$274$	9.07174	0.548044
$275$	−3.07306	−0.185313
$276$	−4.56365	−0.274699
$277$	−1.75719	−0.105579	−0.0527895	−	0.998606i	$-0.516811\pi$
$277$	−1.75719	−0.105579	−0.0527895	+	0.998606i	$0.516811\pi$
$278$	−29.7110	−1.78195
$279$	0.381102	0.0228160
$280$	14.4837	0.865566
$281$	19.4190	1.15844	0.579220	−	0.815172i	$-0.303357\pi$
$281$	19.4190	1.15844	0.579220	+	0.815172i	$0.303357\pi$
$282$	22.6829	1.35075
$283$	−27.3716	−1.62707	−0.813535	−	0.581516i	$-0.802460\pi$
$283$	−27.3716	−1.62707	−0.813535	+	0.581516i	$0.802460\pi$
$284$	50.4461	2.99342
$285$	12.9678	0.768147
$286$	8.78990	0.519758
$287$	−17.0785	−1.00811
$288$	−0.857514	−0.0505295
$289$	23.1250	1.36030
$290$	−0.203529	−0.0119516
$291$	−16.1378	−0.946013
$292$	4.60377	0.269415
$293$	−22.7840	−1.33105	−0.665527	−	0.746374i	$-0.731793\pi$
$293$	−22.7840	−1.33105	−0.665527	+	0.746374i	$0.731793\pi$
$294$	4.84989	0.282851
$295$	−17.3660	−1.01109
$296$	31.5024	1.83104
$297$	5.37257	0.311748
$298$	−10.5433	−0.610755
$299$	−2.88590	−0.166896
$300$	18.1415	1.04740
$301$	−3.68392	−0.212337
$302$	−37.4070	−2.15253
$303$	−3.84699	−0.221004
$304$	−8.25626	−0.473529
$305$	−10.2843	−0.588875
$306$	3.36144	0.192161
$307$	−21.8132	−1.24495	−0.622473	−	0.782641i	$-0.713872\pi$
$307$	−21.8132	−1.24495	−0.622473	+	0.782641i	$0.713872\pi$
$308$	−10.1712	−0.579558
$309$	−11.2019	−0.637252
$310$	5.52692	0.313908
$311$	10.9202	0.619228	0.309614	−	0.950862i	$-0.399800\pi$
$311$	10.9202	0.619228	0.309614	+	0.950862i	$0.399800\pi$
$312$	−22.6071	−1.27988
$313$	11.6484	0.658406	0.329203	−	0.944259i	$-0.393220\pi$
$313$	11.6484	0.658406	0.329203	+	0.944259i	$0.393220\pi$
$314$	−14.0065	−0.790433
$315$	0.897866	0.0505890
$316$	−20.1646	−1.13435
$317$	−1.82210	−0.102339	−0.0511696	−	0.998690i	$-0.516295\pi$
$317$	−1.82210	−0.102339	−0.0511696	+	0.998690i	$0.516295\pi$
$318$	−34.6593	−1.94360
$319$	0.0622701	0.00348645
$320$	−16.5232	−0.923675
$321$	−14.5709	−0.813267
$322$	5.22393	0.291118
$323$	−35.5254	−1.97668
$324$	−29.3202	−1.62890
$325$	11.4721	0.636356
$326$	12.8275	0.710450
$327$	32.6557	1.80586
$328$	−21.6346	−1.19457
$329$	−16.5980	−0.915080
$330$	5.44439	0.299704
$331$	−10.3301	−0.567793	−0.283896	−	0.958855i	$-0.591627\pi$
$331$	−10.3301	−0.567793	−0.283896	+	0.958855i	$0.591627\pi$
$332$	−5.52713	−0.303341
$333$	1.95288	0.107017
$334$	−58.2891	−3.18944
$335$	−7.16900	−0.391684
$336$	7.03765	0.383935
$337$	−10.6119	−0.578067	−0.289033	−	0.957319i	$-0.593334\pi$
$337$	−10.6119	−0.578067	−0.289033	+	0.957319i	$0.593334\pi$
$338$	−2.20416	−0.119890
$339$	3.31497	0.180045
$340$	31.1631	1.69006
$341$	−1.69097	−0.0915712
$342$	−2.97611	−0.160930
$343$	16.5407	0.893115
$344$	−4.66669	−0.251611
$345$	−1.78750	−0.0962360
$346$	27.0447	1.45393
$347$	−4.90550	−0.263341	−0.131670	−	0.991294i	$-0.542034\pi$
$347$	−4.90550	−0.263341	−0.131670	+	0.991294i	$0.542034\pi$
$348$	−0.367604	−0.0197056
$349$	12.1290	0.649253	0.324626	−	0.945842i	$-0.394761\pi$
$349$	12.1290	0.649253	0.324626	+	0.945842i	$0.394761\pi$
$350$	−20.7662	−1.11000
$351$	−20.0564	−1.07053
$352$	3.80484	0.202799
$353$	−8.88979	−0.473156	−0.236578	−	0.971613i	$-0.576026\pi$
$353$	−8.88979	−0.473156	−0.236578	+	0.971613i	$0.576026\pi$
$354$	−49.0661	−2.60783
$355$	19.7589	1.04869
$356$	−26.0117	−1.37861
$357$	30.2819	1.60269
$358$	44.5236	2.35315
$359$	28.7165	1.51560	0.757800	−	0.652487i	$-0.226274\pi$
$359$	28.7165	1.51560	0.757800	+	0.652487i	$0.226274\pi$
$360$	1.13739	0.0599459
$361$	12.4530	0.655420
$362$	12.3510	0.649153
$363$	−1.66572	−0.0874277
$364$	37.9702	1.99018
$365$	1.80322	0.0943849
$366$	−29.0573	−1.51885
$367$	−10.5484	−0.550622	−0.275311	−	0.961355i	$-0.588781\pi$
$367$	−10.5484	−0.550622	−0.275311	+	0.961355i	$0.588781\pi$
$368$	1.13806	0.0593252
$369$	−1.34116	−0.0698182
$370$	28.3217	1.47237
$371$	25.3616	1.31671
$372$	9.98245	0.517566
$373$	8.25646	0.427503	0.213752	−	0.976888i	$-0.431432\pi$
$373$	8.25646	0.427503	0.213752	+	0.976888i	$0.431432\pi$
$374$	−14.9149	−0.771232
$375$	18.6670	0.963959
$376$	−21.0260	−1.08433
$377$	−0.232461	−0.0119724
$378$	36.3052	1.86734
$379$	15.9374	0.818648	0.409324	−	0.912389i	$-0.365764\pi$
$379$	15.9374	0.818648	0.409324	+	0.912389i	$0.365764\pi$
$380$	−27.5908	−1.41538
$381$	−4.44037	−0.227487
$382$	33.3128	1.70443
$383$	30.8132	1.57448	0.787242	−	0.616645i	$-0.211508\pi$
$383$	30.8132	1.57448	0.787242	+	0.616645i	$0.211508\pi$
$384$	−34.0092	−1.73553
$385$	−3.98389	−0.203038
$386$	10.8059	0.550006
$387$	−0.289295	−0.0147057
$388$	34.3353	1.74311
$389$	−34.7201	−1.76038	−0.880190	−	0.474622i	$-0.842585\pi$
$389$	−34.7201	−1.76038	−0.880190	+	0.474622i	$0.842585\pi$
$390$	−20.3245	−1.02917
$391$	4.89687	0.247645
$392$	−4.49561	−0.227063
$393$	9.41331	0.474839
$394$	12.6261	0.636095
$395$	−7.89813	−0.397398
$396$	−0.798736	−0.0401380
$397$	23.6289	1.18590	0.592951	−	0.805239i	$-0.297963\pi$
$397$	23.6289	1.18590	0.592951	+	0.805239i	$0.297963\pi$
$398$	25.8222	1.29435
$399$	−26.8106	−1.34221
$400$	−4.52401	−0.226201
$401$	36.9377	1.84458	0.922292	−	0.386495i	$-0.126314\pi$
$401$	36.9377	1.84458	0.922292	+	0.386495i	$0.126314\pi$
$402$	−20.2554	−1.01025
$403$	6.31258	0.314452
$404$	8.18499	0.407218
$405$	−11.4842	−0.570655
$406$	0.420790	0.0208835
$407$	−8.66506	−0.429511
$408$	38.3603	1.89912
$409$	−29.1194	−1.43986	−0.719930	−	0.694047i	$-0.755826\pi$
$409$	−29.1194	−1.43986	−0.719930	+	0.694047i	$0.755826\pi$
$410$	−19.4502	−0.960578
$411$	6.41770	0.316562
$412$	23.8335	1.17419
$413$	35.9037	1.76671
$414$	0.410231	0.0201618
$415$	−2.16488	−0.106270
$416$	−14.2039	−0.696403
$417$	−21.0187	−1.02929
$418$	13.2052	0.645886
$419$	−1.27071	−0.0620783	−0.0310391	−	0.999518i	$-0.509882\pi$
$419$	−1.27071	−0.0620783	−0.0310391	+	0.999518i	$0.509882\pi$
$420$	23.5184	1.14758
$421$	−5.43002	−0.264643	−0.132321	−	0.991207i	$-0.542243\pi$
$421$	−5.43002	−0.264643	−0.132321	+	0.991207i	$0.542243\pi$
$422$	−21.6001	−1.05147
$423$	−1.30343	−0.0633750
$424$	32.1275	1.56025
$425$	−19.4661	−0.944244
$426$	55.8269	2.70482
$427$	21.2624	1.02896
$428$	31.0015	1.49851
$429$	6.21832	0.300223
$430$	−4.19550	−0.202325
$431$	19.0486	0.917540	0.458770	−	0.888555i	$-0.348290\pi$
$431$	19.0486	0.917540	0.458770	+	0.888555i	$0.348290\pi$
$432$	7.90924	0.380534
$433$	−28.5323	−1.37118	−0.685588	−	0.727990i	$-0.740455\pi$
$433$	−28.5323	−1.37118	−0.685588	+	0.727990i	$0.740455\pi$
$434$	−11.4267	−0.548501
$435$	−0.143984	−0.00690352
$436$	−69.4793	−3.32745
$437$	−4.33553	−0.207396
$438$	5.09484	0.243441
$439$	34.2022	1.63238	0.816191	−	0.577783i	$-0.196082\pi$
$439$	34.2022	1.63238	0.816191	+	0.577783i	$0.196082\pi$
$440$	−5.04669	−0.240591
$441$	−0.278690	−0.0132709
$442$	55.6790	2.64838
$443$	22.5214	1.07002	0.535011	−	0.844845i	$-0.320307\pi$
$443$	22.5214	1.07002	0.535011	+	0.844845i	$0.320307\pi$
$444$	51.1532	2.42762
$445$	−10.1883	−0.482973
$446$	24.6264	1.16609
$447$	−7.45872	−0.352785
$448$	34.1612	1.61397
$449$	11.5721	0.546121	0.273061	−	0.961997i	$-0.411964\pi$
$449$	11.5721	0.546121	0.273061	+	0.961997i	$0.411964\pi$
$450$	−1.63076	−0.0768746
$451$	5.95083	0.280214
$452$	−7.05305	−0.331747
$453$	−26.4631	−1.24335
$454$	−6.87403	−0.322614
$455$	14.8723	0.697224
$456$	−33.9630	−1.59046
$457$	16.9333	0.792107	0.396053	−	0.918227i	$-0.370380\pi$
$457$	16.9333	0.792107	0.396053	+	0.918227i	$0.370380\pi$
$458$	13.3855	0.625461
$459$	34.0322	1.58849
$460$	3.80315	0.177323
$461$	12.3453	0.574979	0.287489	−	0.957784i	$-0.407179\pi$
$461$	12.3453	0.574979	0.287489	+	0.957784i	$0.407179\pi$
$462$	−11.2561	−0.523682
$463$	11.3995	0.529779	0.264890	−	0.964279i	$-0.414664\pi$
$463$	11.3995	0.529779	0.264890	+	0.964279i	$0.414664\pi$
$464$	0.0916709	0.00425572
$465$	3.90996	0.181320
$466$	−54.0424	−2.50346
$467$	5.64044	0.261008	0.130504	−	0.991448i	$-0.458340\pi$
$467$	5.64044	0.261008	0.130504	+	0.991448i	$0.458340\pi$
$468$	2.98177	0.137832
$469$	14.8217	0.684402
$470$	−18.9030	−0.871931
$471$	−9.90874	−0.456571
$472$	45.4819	2.09347
$473$	1.28362	0.0590209
$474$	−22.3155	−1.02498
$475$	17.2346	0.790779
$476$	−64.4287	−2.95309
$477$	1.99163	0.0911904
$478$	13.9066	0.636075
$479$	8.71925	0.398393	0.199196	−	0.979960i	$-0.436167\pi$
$479$	8.71925	0.398393	0.199196	+	0.979960i	$0.436167\pi$
$480$	−8.79777	−0.401562
$481$	32.3476	1.47492
$482$	60.8188	2.77022
$483$	3.69561	0.168156
$484$	3.54404	0.161093
$485$	13.4485	0.610667
$486$	5.50282	0.249613
$487$	−14.2038	−0.643636	−0.321818	−	0.946802i	$-0.604294\pi$
$487$	−14.2038	−0.643636	−0.321818	+	0.946802i	$0.604294\pi$
$488$	26.9347	1.21928
$489$	9.07468	0.410371
$490$	−4.04169	−0.182585
$491$	15.3655	0.693436	0.346718	−	0.937969i	$-0.387296\pi$
$491$	15.3655	0.693436	0.346718	+	0.937969i	$0.387296\pi$
$492$	−35.1300	−1.58378
$493$	0.394445	0.0177649
$494$	−49.2964	−2.21795
$495$	−0.312852	−0.0140616
$496$	−2.48936	−0.111776
$497$	−40.8509	−1.83241
$498$	−6.11669	−0.274095
$499$	42.3665	1.89659	0.948293	−	0.317395i	$-0.102808\pi$
$499$	42.3665	1.89659	0.948293	+	0.317395i	$0.102808\pi$
$500$	−39.7165	−1.77618
$501$	−41.2360	−1.84229
$502$	26.8246	1.19724
$503$	27.4878	1.22562	0.612810	−	0.790230i	$-0.290039\pi$
$503$	27.4878	1.22562	0.612810	+	0.790230i	$0.290039\pi$
$504$	−2.35153	−0.104745
$505$	3.20592	0.142662
$506$	−1.82022	−0.0809187
$507$	−1.55931	−0.0692513
$508$	9.44747	0.419164
$509$	−5.02388	−0.222680	−0.111340	−	0.993782i	$-0.535514\pi$
$509$	−5.02388	−0.222680	−0.111340	+	0.993782i	$0.535514\pi$
$510$	34.4871	1.52712
$511$	−3.72810	−0.164922
$512$	16.3055	0.720609
$513$	−30.1310	−1.33032
$514$	−5.26566	−0.232258
$515$	9.33517	0.411357
$516$	−7.57771	−0.333590
$517$	5.78341	0.254354
$518$	−58.5542	−2.57272
$519$	19.1325	0.839821
$520$	18.8398	0.826182
$521$	11.9750	0.524633	0.262317	−	0.964982i	$-0.415513\pi$
$521$	11.9750	0.524633	0.262317	+	0.964982i	$0.415513\pi$
$522$	0.0330443	0.00144631
$523$	−21.5536	−0.942472	−0.471236	−	0.882007i	$-0.656192\pi$
$523$	−21.5536	−0.942472	−0.471236	+	0.882007i	$0.656192\pi$
$524$	−20.0281	−0.874930
$525$	−14.6908	−0.641161
$526$	−73.5396	−3.20648
$527$	−10.7113	−0.466593
$528$	−2.45219	−0.106718
$529$	−22.4024	−0.974017
$530$	28.8836	1.25462
$531$	2.81949	0.122355
$532$	57.0431	2.47313
$533$	−22.2151	−0.962243
$534$	−28.7862	−1.24570
$535$	12.1428	0.524977
$536$	18.7757	0.810989
$537$	31.4977	1.35923
$538$	48.7133	2.10018
$539$	1.23656	0.0532625
$540$	26.4311	1.13741
$541$	−20.6142	−0.886272	−0.443136	−	0.896454i	$-0.646134\pi$
$541$	−20.6142	−0.886272	−0.443136	+	0.896454i	$0.646134\pi$
$542$	22.7362	0.976602
$543$	8.73756	0.374965
$544$	24.1015	1.03334
$545$	−27.2139	−1.16571
$546$	42.0203	1.79830
$547$	−1.00000	−0.0427569
$547$	−1.00000	−0.0427569
$548$	−13.6545	−0.583292
$549$	1.66972	0.0712619
$550$	7.23577	0.308534
$551$	−0.349229	−0.0148776
$552$	4.68151	0.199258
$553$	16.3291	0.694386
$554$	4.13743	0.175783
$555$	20.0358	0.850474
$556$	44.7201	1.89656
$557$	−2.73562	−0.115912	−0.0579559	−	0.998319i	$-0.518458\pi$
$557$	−2.73562	−0.115912	−0.0579559	+	0.998319i	$0.518458\pi$
$558$	−0.897334	−0.0379872
$559$	−4.79190	−0.202676
$560$	−5.86488	−0.247837
$561$	−10.5514	−0.445480
$562$	−45.7235	−1.92873
$563$	35.2613	1.48609	0.743044	−	0.669242i	$-0.233381\pi$
$563$	35.2613	1.48609	0.743044	+	0.669242i	$0.233381\pi$
$564$	−34.1417	−1.43762
$565$	−2.76256	−0.116222
$566$	64.4485	2.70897
$567$	23.7433	0.997123
$568$	−51.7489	−2.17133
$569$	34.3979	1.44204	0.721019	−	0.692916i	$-0.243674\pi$
$569$	34.3979	1.44204	0.721019	+	0.692916i	$0.243674\pi$
$570$	−30.5338	−1.27892
$571$	−22.8884	−0.957851	−0.478925	−	0.877856i	$-0.658974\pi$
$571$	−22.8884	−0.957851	−0.478925	+	0.877856i	$0.658974\pi$
$572$	−13.2303	−0.553187
$573$	23.5668	0.984517
$574$	40.2127	1.67845
$575$	−2.37565	−0.0990714
$576$	2.68266	0.111777
$577$	27.5597	1.14732	0.573662	−	0.819092i	$-0.305522\pi$
$577$	27.5597	1.14732	0.573662	+	0.819092i	$0.305522\pi$
$578$	−54.4497	−2.26481
$579$	7.64452	0.317695
$580$	0.306346	0.0127203
$581$	4.47583	0.185689
$582$	37.9977	1.57505
$583$	−8.83698	−0.365990
$584$	−4.72267	−0.195425
$585$	1.16791	0.0482871
$586$	53.6467	2.21612
$587$	−41.1116	−1.69686	−0.848429	−	0.529309i	$-0.822451\pi$
$587$	−41.1116	−1.69686	−0.848429	+	0.529309i	$0.822451\pi$
$588$	−7.29991	−0.301043
$589$	9.48346	0.390759
$590$	40.8896	1.68340
$591$	8.93221	0.367422
$592$	−12.7563	−0.524280
$593$	19.6386	0.806463	0.403231	−	0.915098i	$-0.367887\pi$
$593$	19.6386	0.806463	0.403231	+	0.915098i	$0.367887\pi$
$594$	−12.6501	−0.519042
$595$	−25.2357	−1.03456
$596$	15.8694	0.650037
$597$	18.2676	0.747645
$598$	6.79509	0.277872
$599$	−28.0597	−1.14649	−0.573244	−	0.819385i	$-0.694315\pi$
$599$	−28.0597	−1.14649	−0.573244	+	0.819385i	$0.694315\pi$
$600$	−18.6100	−0.759749
$601$	−27.1364	−1.10692	−0.553459	−	0.832876i	$-0.686692\pi$
$601$	−27.1364	−1.10692	−0.553459	+	0.832876i	$0.686692\pi$
$602$	8.67407	0.353529
$603$	1.16394	0.0473992
$604$	56.3038	2.29097
$605$	1.38814	0.0564360
$606$	9.05805	0.367958
$607$	−31.5353	−1.27998	−0.639989	−	0.768384i	$-0.721061\pi$
$607$	−31.5353	−1.27998	−0.639989	+	0.768384i	$0.721061\pi$
$608$	−21.3387	−0.865398
$609$	0.297683	0.0120627
$610$	24.2151	0.980441
$611$	−21.5901	−0.873442
$612$	−5.05954	−0.204520
$613$	35.4358	1.43124	0.715620	−	0.698490i	$-0.246144\pi$
$613$	35.4358	1.43124	0.715620	+	0.698490i	$0.246144\pi$
$614$	51.3610	2.07276
$615$	−13.7598	−0.554850
$616$	10.4339	0.420393
$617$	32.5257	1.30944	0.654718	−	0.755873i	$-0.272787\pi$
$617$	32.5257	1.30944	0.654718	+	0.755873i	$0.272787\pi$
$618$	26.3757	1.06099
$619$	−17.4606	−0.701801	−0.350901	−	0.936413i	$-0.614125\pi$
$619$	−17.4606	−0.701801	−0.350901	+	0.936413i	$0.614125\pi$
$620$	−8.31896	−0.334097
$621$	4.15330	0.166666
$622$	−25.7125	−1.03098
$623$	21.0641	0.843914
$624$	9.15431	0.366466
$625$	−0.190985	−0.00763938
$626$	−27.4270	−1.09620
$627$	9.34185	0.373078
$628$	21.0822	0.841270
$629$	−54.8882	−2.18854
$630$	−2.11410	−0.0842276
$631$	17.7446	0.706403	0.353201	−	0.935547i	$-0.385093\pi$
$631$	17.7446	0.706403	0.353201	+	0.935547i	$0.385093\pi$
$632$	20.6854	0.822819
$633$	−15.2807	−0.607354
$634$	4.29027	0.170388
$635$	3.70042	0.146847
$636$	52.1681	2.06860
$637$	−4.61623	−0.182902
$638$	−0.146620	−0.00580473
$639$	−3.20799	−0.126906
$640$	28.3419	1.12031
$641$	11.9437	0.471747	0.235873	−	0.971784i	$-0.424205\pi$
$641$	11.9437	0.471747	0.235873	+	0.971784i	$0.424205\pi$
$642$	34.3083	1.35404
$643$	43.0248	1.69673	0.848366	−	0.529410i	$-0.177587\pi$
$643$	43.0248	1.69673	0.848366	+	0.529410i	$0.177587\pi$
$644$	−7.86290	−0.309842
$645$	−2.96806	−0.116867
$646$	83.6473	3.29106
$647$	18.4397	0.724938	0.362469	−	0.931996i	$-0.381934\pi$
$647$	18.4397	0.724938	0.362469	+	0.931996i	$0.381934\pi$
$648$	30.0774	1.18155
$649$	−12.5103	−0.491070
$650$	−27.0119	−1.05949
$651$	−8.08372	−0.316826
$652$	−19.3076	−0.756143
$653$	7.64932	0.299341	0.149671	−	0.988736i	$-0.452179\pi$
$653$	7.64932	0.299341	0.149671	+	0.988736i	$0.452179\pi$
$654$	−76.8903	−3.00665
$655$	−7.84466	−0.306516
$656$	8.76052	0.342041
$657$	−0.292765	−0.0114219
$658$	39.0814	1.52355
$659$	31.3137	1.21981	0.609904	−	0.792476i	$-0.291208\pi$
$659$	31.3137	1.21981	0.609904	+	0.792476i	$0.291208\pi$
$660$	−8.19474	−0.318980
$661$	32.4139	1.26076	0.630378	−	0.776288i	$-0.282900\pi$
$661$	32.4139	1.26076	0.630378	+	0.776288i	$0.282900\pi$
$662$	24.3230	0.945341
$663$	39.3895	1.52976
$664$	5.66987	0.220034
$665$	22.3428	0.866417
$666$	−4.59822	−0.178177
$667$	0.0481382	0.00186392
$668$	87.7351	3.39457
$669$	17.4216	0.673560
$670$	16.8800	0.652130
$671$	−7.40865	−0.286008
$672$	18.1891	0.701661
$673$	30.0003	1.15643	0.578213	−	0.815886i	$-0.303750\pi$
$673$	30.0003	1.15643	0.578213	+	0.815886i	$0.303750\pi$
$674$	24.9865	0.962445
$675$	−16.5102	−0.635480
$676$	3.31764	0.127601
$677$	40.4132	1.55320	0.776602	−	0.629991i	$-0.216942\pi$
$677$	40.4132	1.55320	0.776602	+	0.629991i	$0.216942\pi$
$678$	−7.80537	−0.299763
$679$	−27.8045	−1.06704
$680$	−31.9679	−1.22591
$681$	−4.86295	−0.186349
$682$	3.98152	0.152460
$683$	9.65565	0.369463	0.184732	−	0.982789i	$-0.440858\pi$
$683$	9.65565	0.369463	0.184732	+	0.982789i	$0.440858\pi$
$684$	4.47955	0.171280
$685$	−5.34825	−0.204346
$686$	−38.9464	−1.48698
$687$	9.46939	0.361280
$688$	1.88968	0.0720435
$689$	32.9894	1.25680
$690$	4.20882	0.160227
$691$	4.44301	0.169020	0.0845100	−	0.996423i	$-0.473067\pi$
$691$	4.44301	0.169020	0.0845100	+	0.996423i	$0.473067\pi$
$692$	−40.7068	−1.54744
$693$	0.646811	0.0245703
$694$	11.5504	0.438447
$695$	17.5161	0.664425
$696$	0.377098	0.0142939
$697$	37.6951	1.42780
$698$	−28.5588	−1.08097
$699$	−38.2317	−1.44605
$700$	31.2567	1.18139
$701$	13.8530	0.523221	0.261611	−	0.965173i	$-0.415746\pi$
$701$	13.8530	0.523221	0.261611	+	0.965173i	$0.415746\pi$
$702$	47.2244	1.78237
$703$	48.5962	1.83284
$704$	−11.9031	−0.448615
$705$	−13.3727	−0.503646
$706$	20.9317	0.787776
$707$	−6.62815	−0.249277
$708$	73.8528	2.77556
$709$	−18.5351	−0.696102	−0.348051	−	0.937476i	$-0.613156\pi$
$709$	−18.5351	−0.696102	−0.348051	+	0.937476i	$0.613156\pi$
$710$	−46.5238	−1.74601
$711$	1.28232	0.0480906
$712$	26.6834	1.00000
$713$	−1.30722	−0.0489556
$714$	−71.3011	−2.66838
$715$	−5.18209	−0.193799
$716$	−67.0156	−2.50449
$717$	9.83809	0.367410
$718$	−67.6153	−2.52338
$719$	23.9248	0.892246	0.446123	−	0.894972i	$-0.352804\pi$
$719$	23.9248	0.892246	0.446123	+	0.894972i	$0.352804\pi$
$720$	−0.460565	−0.0171642
$721$	−19.3002	−0.718776
$722$	−29.3215	−1.09123
$723$	43.0256	1.60014
$724$	−18.5903	−0.690904
$725$	−0.191360	−0.00710692
$726$	3.92207	0.145562
$727$	53.7291	1.99270	0.996350	−	0.0853597i	$-0.0272039\pi$
$727$	53.7291	1.99270	0.996350	+	0.0853597i	$0.0272039\pi$
$728$	−38.9508	−1.44361
$729$	28.7122	1.06341
$730$	−4.24583	−0.157145
$731$	8.13101	0.300736
$732$	43.7361	1.61653
$733$	35.0052	1.29295	0.646474	−	0.762936i	$-0.276243\pi$
$733$	35.0052	1.29295	0.646474	+	0.762936i	$0.276243\pi$
$734$	24.8370	0.916751
$735$	−2.85925	−0.105465
$736$	2.94136	0.108420
$737$	−5.16446	−0.190235
$738$	3.15788	0.116243
$739$	−7.08496	−0.260624	−0.130312	−	0.991473i	$-0.541598\pi$
$739$	−7.08496	−0.260624	−0.130312	+	0.991473i	$0.541598\pi$
$740$	−42.6289	−1.56707
$741$	−34.8742	−1.28113
$742$	−59.7159	−2.19224
$743$	−48.1097	−1.76498	−0.882488	−	0.470336i	$-0.844133\pi$
$743$	−48.1097	−1.76498	−0.882488	+	0.470336i	$0.844133\pi$
$744$	−10.2403	−0.375426
$745$	6.21579	0.227729
$746$	−19.4405	−0.711767
$747$	0.351484	0.0128601
$748$	22.4495	0.820835
$749$	−25.1048	−0.917309
$750$	−43.9529	−1.60493
$751$	26.5030	0.967108	0.483554	−	0.875315i	$-0.339346\pi$
$751$	26.5030	0.967108	0.483554	+	0.875315i	$0.339346\pi$
$752$	8.51405	0.310476
$753$	18.9767	0.691551
$754$	0.547348	0.0199332
$755$	22.0533	0.802601
$756$	−54.6455	−1.98744
$757$	−2.00797	−0.0729809	−0.0364905	−	0.999334i	$-0.511618\pi$
$757$	−2.00797	−0.0729809	−0.0364905	+	0.999334i	$0.511618\pi$
$758$	−37.5258	−1.36300
$759$	−1.28770	−0.0467404
$760$	28.3033	1.02667
$761$	−53.7137	−1.94712	−0.973561	−	0.228429i	$-0.926641\pi$
$761$	−53.7137	−1.94712	−0.973561	+	0.228429i	$0.926641\pi$
$762$	10.4552	0.378752
$763$	56.2638	2.03689
$764$	−50.1415	−1.81405
$765$	−1.98174	−0.0716499
$766$	−72.5522	−2.62142
$767$	46.7022	1.68632
$768$	40.4229	1.45864
$769$	−24.1188	−0.869748	−0.434874	−	0.900491i	$-0.643207\pi$
$769$	−24.1188	−0.869748	−0.434874	+	0.900491i	$0.643207\pi$
$770$	9.38037	0.338045
$771$	−3.72514	−0.134157
$772$	−16.2647	−0.585380
$773$	−14.3450	−0.515952	−0.257976	−	0.966151i	$-0.583056\pi$
$773$	−14.3450	−0.515952	−0.257976	+	0.966151i	$0.583056\pi$
$774$	0.681169	0.0244841
$775$	5.19646	0.186662
$776$	−35.2220	−1.26440
$777$	−41.4235	−1.48606
$778$	81.7512	2.93092
$779$	−33.3740	−1.19575
$780$	30.5919	1.09536
$781$	14.2340	0.509334
$782$	−11.5301	−0.412314
$783$	0.334550	0.0119559
$784$	1.82041	0.0650145
$785$	8.25753	0.294724
$786$	−22.1644	−0.790577
$787$	35.8759	1.27884	0.639419	−	0.768858i	$-0.279175\pi$
$787$	35.8759	1.27884	0.639419	+	0.768858i	$0.279175\pi$
$788$	−19.0045	−0.677006
$789$	−52.0248	−1.85213
$790$	18.5968	0.661644
$791$	5.71151	0.203078
$792$	0.819364	0.0291148
$793$	27.6573	0.982140
$794$	−55.6362	−1.97445
$795$	20.4334	0.724697
$796$	−38.8668	−1.37760
$797$	−26.3706	−0.934095	−0.467048	−	0.884232i	$-0.654682\pi$
$797$	−26.3706	−0.934095	−0.467048	+	0.884232i	$0.654682\pi$
$798$	63.1276	2.23469
$799$	36.6346	1.29604
$800$	−11.6925	−0.413393
$801$	1.65415	0.0584463
$802$	−86.9728	−3.07112
$803$	1.29902	0.0458413
$804$	30.4878	1.07522
$805$	−3.07977	−0.108548
$806$	−14.8635	−0.523543
$807$	34.4617	1.21311
$808$	−8.39637	−0.295383
$809$	−8.02139	−0.282017	−0.141009	−	0.990008i	$-0.545035\pi$
$809$	−8.02139	−0.282017	−0.141009	+	0.990008i	$0.545035\pi$
$810$	27.0405	0.950106
$811$	3.21076	0.112745	0.0563726	−	0.998410i	$-0.482047\pi$
$811$	3.21076	0.112745	0.0563726	+	0.998410i	$0.482047\pi$
$812$	−0.633361	−0.0222266
$813$	16.0845	0.564107
$814$	20.4026	0.715109
$815$	−7.56246	−0.264901
$816$	−15.5332	−0.543772
$817$	−7.19893	−0.251859
$818$	68.5638	2.39728
$819$	−2.41462	−0.0843736
$820$	29.2759	1.02236
$821$	26.2048	0.914552	0.457276	−	0.889325i	$-0.348825\pi$
$821$	26.2048	0.914552	0.457276	+	0.889325i	$0.348825\pi$
$822$	−15.1110	−0.527056
$823$	−8.31562	−0.289864	−0.144932	−	0.989442i	$-0.546296\pi$
$823$	−8.31562	−0.289864	−0.144932	+	0.989442i	$0.546296\pi$
$824$	−24.4490	−0.851721
$825$	5.11886	0.178216
$826$	−84.5381	−2.94146
$827$	20.3186	0.706548	0.353274	−	0.935520i	$-0.385068\pi$
$827$	20.3186	0.706548	0.353274	+	0.935520i	$0.385068\pi$
$828$	−0.617468	−0.0214585
$829$	42.5387	1.47743	0.738715	−	0.674018i	$-0.235433\pi$
$829$	42.5387	1.47743	0.738715	+	0.674018i	$0.235433\pi$
$830$	5.09739	0.176933
$831$	2.92698	0.101536
$832$	44.4356	1.54053
$833$	7.83292	0.271395
$834$	49.4903	1.71371
$835$	34.3644	1.18923
$836$	−19.8760	−0.687427
$837$	−9.08486	−0.314019
$838$	2.99199	0.103357
$839$	37.0266	1.27830	0.639150	−	0.769082i	$-0.279286\pi$
$839$	37.0266	1.27830	0.639150	+	0.769082i	$0.279286\pi$
$840$	−24.1258	−0.832419
$841$	−28.9961	−0.999866
$842$	12.7854	0.440614
$843$	−32.3466	−1.11408
$844$	32.5118	1.11910
$845$	1.29946	0.0447029
$846$	3.06903	0.105516
$847$	−2.86994	−0.0986123
$848$	−13.0094	−0.446744
$849$	45.5934	1.56476
$850$	45.8345	1.57211
$851$	−6.69858	−0.229624
$852$	−84.0290	−2.87879
$853$	0.0823782	0.00282058	0.00141029	−	0.999999i	$-0.499551\pi$
$853$	0.0823782	0.00282058	0.00141029	+	0.999999i	$0.499551\pi$
$854$	−50.0640	−1.71315
$855$	1.75456	0.0600048
$856$	−31.8021	−1.08697
$857$	18.2328	0.622820	0.311410	−	0.950276i	$-0.399199\pi$
$857$	18.2328	0.622820	0.311410	+	0.950276i	$0.399199\pi$
$858$	−14.6415	−0.499853
$859$	−13.5547	−0.462481	−0.231240	−	0.972897i	$-0.574278\pi$
$859$	−13.5547	−0.462481	−0.231240	+	0.972897i	$0.574278\pi$
$860$	6.31495	0.215338
$861$	28.4481	0.969507
$862$	−44.8515	−1.52765
$863$	−51.1967	−1.74275	−0.871377	−	0.490613i	$-0.836773\pi$
$863$	−51.1967	−1.74275	−0.871377	+	0.490613i	$0.836773\pi$
$864$	20.4418	0.695444
$865$	−15.9442	−0.542119
$866$	67.1816	2.28292
$867$	−38.5198	−1.30820
$868$	17.1992	0.583779
$869$	−5.68971	−0.193010
$870$	0.339023	0.0114939
$871$	19.2795	0.653261
$872$	71.2736	2.41363
$873$	−2.18346	−0.0738991
$874$	10.2083	0.345302
$875$	32.1622	1.08728
$876$	−7.66860	−0.259098
$877$	47.0077	1.58734	0.793669	−	0.608350i	$-0.208168\pi$
$877$	47.0077	1.58734	0.793669	+	0.608350i	$0.208168\pi$
$878$	−80.5317	−2.71781
$879$	37.9517	1.28008
$880$	2.04356	0.0688882
$881$	−2.95153	−0.0994397	−0.0497199	−	0.998763i	$-0.515833\pi$
$881$	−2.95153	−0.0994397	−0.0497199	+	0.998763i	$0.515833\pi$
$882$	0.656197	0.0220953
$883$	−1.62548	−0.0547016	−0.0273508	−	0.999626i	$-0.508707\pi$
$883$	−1.62548	−0.0547016	−0.0273508	+	0.999626i	$0.508707\pi$
$884$	−83.8064	−2.81872
$885$	28.9269	0.972368
$886$	−53.0283	−1.78152
$887$	19.6122	0.658515	0.329257	−	0.944240i	$-0.393202\pi$
$887$	19.6122	0.658515	0.329257	+	0.944240i	$0.393202\pi$
$888$	−52.4742	−1.76092
$889$	−7.65050	−0.256589
$890$	23.9892	0.804121
$891$	−8.27308	−0.277159
$892$	−37.0669	−1.24109
$893$	−32.4351	−1.08540
$894$	17.5621	0.587366
$895$	−26.2489	−0.877404
$896$	−58.5959	−1.95755
$897$	4.80711	0.160505
$898$	−27.2474	−0.909258
$899$	−0.105297	−0.00351185
$900$	2.45457	0.0818189
$901$	−55.9772	−1.86487
$902$	−14.0117	−0.466538
$903$	6.13638	0.204206
$904$	7.23520	0.240639
$905$	−7.28152	−0.242046
$906$	62.3095	2.07010
$907$	−38.7576	−1.28693	−0.643463	−	0.765477i	$-0.722503\pi$
$907$	−38.7576	−1.28693	−0.643463	+	0.765477i	$0.722503\pi$
$908$	10.3466	0.343363
$909$	−0.520504	−0.0172640
$910$	−35.0180	−1.16083
$911$	9.87679	0.327233	0.163616	−	0.986524i	$-0.447684\pi$
$911$	9.87679	0.327233	0.163616	+	0.986524i	$0.447684\pi$
$912$	13.7526	0.455395
$913$	−1.55956	−0.0516138
$914$	−39.8708	−1.31881
$915$	17.1307	0.566324
$916$	−20.1474	−0.665689
$917$	16.2186	0.535585
$918$	−80.1315	−2.64473
$919$	−19.8421	−0.654532	−0.327266	−	0.944932i	$-0.606127\pi$
$919$	−19.8421	−0.654532	−0.327266	+	0.944932i	$0.606127\pi$
$920$	−3.90137	−0.128624
$921$	36.3347	1.19727
$922$	−29.0680	−0.957304
$923$	−53.1373	−1.74903
$924$	16.9424	0.557363
$925$	26.6283	0.875532
$926$	−26.8410	−0.882050
$927$	−1.51563	−0.0497798
$928$	0.236928	0.00777753
$929$	19.3105	0.633557	0.316778	−	0.948500i	$-0.397399\pi$
$929$	19.3105	0.633557	0.316778	+	0.948500i	$0.397399\pi$
$930$	−9.20631	−0.301887
$931$	−6.93501	−0.227286
$932$	81.3430	2.66448
$933$	−18.1900	−0.595514
$934$	−13.2809	−0.434563
$935$	8.79309	0.287565
$936$	−3.05878	−0.0999793
$937$	−15.3547	−0.501616	−0.250808	−	0.968037i	$-0.580696\pi$
$937$	−15.3547	−0.501616	−0.250808	+	0.968037i	$0.580696\pi$
$938$	−34.8988	−1.13949
$939$	−19.4030	−0.633191
$940$	28.4523	0.928010
$941$	−4.19573	−0.136777	−0.0683884	−	0.997659i	$-0.521786\pi$
$941$	−4.19573	−0.136777	−0.0683884	+	0.997659i	$0.521786\pi$
$942$	23.3309	0.760163
$943$	4.60032	0.149807
$944$	−18.4170	−0.599422
$945$	−21.4037	−0.696263
$946$	−3.02239	−0.0982663
$947$	31.2834	1.01658	0.508288	−	0.861187i	$-0.330279\pi$
$947$	31.2834	1.01658	0.508288	+	0.861187i	$0.330279\pi$
$948$	33.5886	1.09091
$949$	−4.84938	−0.157417
$950$	−40.5803	−1.31660
$951$	3.03510	0.0984200
$952$	66.0926	2.14207
$953$	3.91582	0.126846	0.0634230	−	0.997987i	$-0.479798\pi$
$953$	3.91582	0.126846	0.0634230	+	0.997987i	$0.479798\pi$
$954$	−4.68945	−0.151827
$955$	−19.6396	−0.635522
$956$	−20.9319	−0.676985
$957$	−0.103725	−0.00335294
$958$	−20.5302	−0.663300
$959$	11.0573	0.357060
$960$	27.5230	0.888302
$961$	−28.1406	−0.907762
$962$	−76.1650	−2.45566
$963$	−1.97146	−0.0635294
$964$	−91.5427	−2.94839
$965$	−6.37062	−0.205078
$966$	−8.70161	−0.279970
$967$	41.5113	1.33491	0.667457	−	0.744648i	$-0.267383\pi$
$967$	41.5113	1.33491	0.667457	+	0.744648i	$0.267383\pi$
$968$	−3.63557	−0.116852
$969$	59.1753	1.90099
$970$	−31.6657	−1.01672
$971$	3.61523	0.116018	0.0580091	−	0.998316i	$-0.481525\pi$
$971$	3.61523	0.116018	0.0580091	+	0.998316i	$0.481525\pi$
$972$	−8.28268	−0.265667
$973$	−36.2141	−1.16097
$974$	33.4440	1.07161
$975$	−19.1093	−0.611987
$976$	−10.9067	−0.349114
$977$	−28.1576	−0.900843	−0.450421	−	0.892816i	$-0.648726\pi$
$977$	−28.1576	−0.900843	−0.450421	+	0.892816i	$0.648726\pi$
$978$	−21.3670	−0.683243
$979$	−7.33954	−0.234573
$980$	6.08344	0.194328
$981$	4.41836	0.141067
$982$	−36.1793	−1.15453
$983$	−32.2946	−1.03004	−0.515019	−	0.857179i	$-0.672215\pi$
$983$	−32.2946	−1.03004	−0.515019	+	0.857179i	$0.672215\pi$
$984$	36.0373	1.14883
$985$	−7.44373	−0.237177
$986$	−0.928753	−0.0295775
$987$	27.6477	0.880036
$988$	74.1994	2.36060
$989$	0.992311	0.0315536
$990$	0.736634	0.0234118
$991$	−19.1991	−0.609880	−0.304940	−	0.952372i	$-0.598636\pi$
$991$	−19.1991	−0.609880	−0.304940	+	0.952372i	$0.598636\pi$
$992$	−6.43388	−0.204276
$993$	17.2070	0.546049
$994$	96.1866	3.05085
$995$	−15.2235	−0.482617
$996$	9.20666	0.291724
$997$	−10.0703	−0.318928	−0.159464	−	0.987204i	$-0.550977\pi$
$997$	−10.0703	−0.318928	−0.159464	+	0.987204i	$0.550977\pi$
$998$	−99.7554	−3.15770
$999$	−46.5537	−1.47289

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6017.2.a.e.1.12	✓	119

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6017.2.a.e.1.12	✓	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)

\(f(q)\)	\(=\)	\(q-2.35458 q^{2} -1.66572 q^{3} +3.54404 q^{4} +1.38814 q^{5} +3.92207 q^{6} -2.86994 q^{7} -3.63557 q^{8} -0.225374 q^{9} +O(q^{10})\)	\(q-2.35458 q^{2} -1.66572 q^{3} +3.54404 q^{4} +1.38814 q^{5} +3.92207 q^{6} -2.86994 q^{7} -3.63557 q^{8} -0.225374 q^{9} -3.26849 q^{10} +1.00000 q^{11} -5.90338 q^{12} -3.73311 q^{13} +6.75750 q^{14} -2.31226 q^{15} +1.47215 q^{16} +6.33443 q^{17} +0.530662 q^{18} -5.60830 q^{19} +4.91963 q^{20} +4.78052 q^{21} -2.35458 q^{22} +0.773056 q^{23} +6.05584 q^{24} -3.07306 q^{25} +8.78990 q^{26} +5.37257 q^{27} -10.1712 q^{28} +0.0622701 q^{29} +5.44439 q^{30} -1.69097 q^{31} +3.80484 q^{32} -1.66572 q^{33} -14.9149 q^{34} -3.98389 q^{35} -0.798736 q^{36} -8.66506 q^{37} +13.2052 q^{38} +6.21832 q^{39} -5.04669 q^{40} +5.95083 q^{41} -11.2561 q^{42} +1.28362 q^{43} +3.54404 q^{44} -0.312852 q^{45} -1.82022 q^{46} +5.78341 q^{47} -2.45219 q^{48} +1.23656 q^{49} +7.23577 q^{50} -10.5514 q^{51} -13.2303 q^{52} -8.83698 q^{53} -12.6501 q^{54} +1.38814 q^{55} +10.4339 q^{56} +9.34185 q^{57} -0.146620 q^{58} -12.5103 q^{59} -8.19474 q^{60} -7.40865 q^{61} +3.98152 q^{62} +0.646811 q^{63} -11.9031 q^{64} -5.18209 q^{65} +3.92207 q^{66} -5.16446 q^{67} +22.4495 q^{68} -1.28770 q^{69} +9.38037 q^{70} +14.2340 q^{71} +0.819364 q^{72} +1.29902 q^{73} +20.4026 q^{74} +5.11886 q^{75} -19.8760 q^{76} -2.86994 q^{77} -14.6415 q^{78} -5.68971 q^{79} +2.04356 q^{80} -8.27308 q^{81} -14.0117 q^{82} -1.55956 q^{83} +16.9424 q^{84} +8.79309 q^{85} -3.02239 q^{86} -0.103725 q^{87} -3.63557 q^{88} -7.33954 q^{89} +0.736634 q^{90} +10.7138 q^{91} +2.73974 q^{92} +2.81669 q^{93} -13.6175 q^{94} -7.78511 q^{95} -6.33781 q^{96} +9.68816 q^{97} -2.91158 q^{98} -0.225374 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 119 q + 15 q^{2} + 15 q^{3} + 133 q^{4} + 6 q^{5} + 16 q^{6} + 72 q^{7} + 39 q^{8} + 128 q^{9}+O(q^{10}) \) 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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