LMFDB - Embedded newform 6031.2.a.e.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6031,2,Mod(1,6031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6031, 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("6031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6031 = 37 \cdot 163 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6031.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:	$48.1577774590$
Analytic rank:	$0$
Dimension:	$134$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	6031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.39957 q^{2} +0.225532 q^{3} +3.75794 q^{4} -1.91995 q^{5} -0.541181 q^{6} -3.36005 q^{7} -4.21829 q^{8} -2.94914 q^{9} +O(q^{10})$	\(q-2.39957 q^{2} +0.225532 q^{3} +3.75794 q^{4} -1.91995 q^{5} -0.541181 q^{6} -3.36005 q^{7} -4.21829 q^{8} -2.94914 q^{9} +4.60705 q^{10} +2.75219 q^{11} +0.847536 q^{12} +3.46120 q^{13} +8.06267 q^{14} -0.433011 q^{15} +2.60621 q^{16} +7.52354 q^{17} +7.07666 q^{18} +6.06228 q^{19} -7.21505 q^{20} -0.757799 q^{21} -6.60408 q^{22} -1.58372 q^{23} -0.951361 q^{24} -1.31379 q^{25} -8.30539 q^{26} -1.34172 q^{27} -12.6268 q^{28} +0.415077 q^{29} +1.03904 q^{30} +9.61362 q^{31} +2.18279 q^{32} +0.620709 q^{33} -18.0533 q^{34} +6.45112 q^{35} -11.0827 q^{36} +1.00000 q^{37} -14.5469 q^{38} +0.780612 q^{39} +8.09891 q^{40} +0.648582 q^{41} +1.81839 q^{42} +2.96853 q^{43} +10.3426 q^{44} +5.66219 q^{45} +3.80025 q^{46} +4.37572 q^{47} +0.587785 q^{48} +4.28991 q^{49} +3.15254 q^{50} +1.69680 q^{51} +13.0070 q^{52} -8.71292 q^{53} +3.21956 q^{54} -5.28407 q^{55} +14.1737 q^{56} +1.36724 q^{57} -0.996007 q^{58} +12.4609 q^{59} -1.62723 q^{60} +4.46346 q^{61} -23.0686 q^{62} +9.90923 q^{63} -10.4502 q^{64} -6.64533 q^{65} -1.48943 q^{66} -10.4804 q^{67} +28.2730 q^{68} -0.357180 q^{69} -15.4799 q^{70} -2.42366 q^{71} +12.4403 q^{72} -12.0414 q^{73} -2.39957 q^{74} -0.296303 q^{75} +22.7816 q^{76} -9.24750 q^{77} -1.87313 q^{78} -8.24444 q^{79} -5.00380 q^{80} +8.54480 q^{81} -1.55632 q^{82} -3.27015 q^{83} -2.84776 q^{84} -14.4448 q^{85} -7.12321 q^{86} +0.0936133 q^{87} -11.6096 q^{88} -1.81027 q^{89} -13.5868 q^{90} -11.6298 q^{91} -5.95152 q^{92} +2.16818 q^{93} -10.4998 q^{94} -11.6393 q^{95} +0.492290 q^{96} -13.2583 q^{97} -10.2939 q^{98} -8.11659 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 134 q + 9 q^{2} + 7 q^{3} + 149 q^{4} + 22 q^{5} + 20 q^{6} + 11 q^{7} + 27 q^{8} + 181 q^{9}+O(q^{10}) $ 134 * q + 9 * q^2 + 7 * q^3 + 149 * q^4 + 22 * q^5 + 20 * q^6 + 11 * q^7 + 27 * q^8 + 181 * q^9	\( 134 q + 9 q^{2} + 7 q^{3} + 149 q^{4} + 22 q^{5} + 20 q^{6} + 11 q^{7} + 27 q^{8} + 181 q^{9} + 15 q^{10} + 20 q^{11} + 28 q^{12} + 11 q^{13} + 17 q^{14} - 13 q^{15} + 143 q^{16} + 76 q^{17} + 23 q^{18} + 15 q^{19} + 67 q^{20} + 63 q^{21} + 2 q^{22} + 22 q^{23} + 33 q^{24} + 160 q^{25} + 65 q^{26} + 31 q^{27} + 10 q^{28} + 73 q^{29} + 20 q^{30} + 10 q^{31} + 53 q^{32} + 72 q^{33} - 7 q^{34} + 52 q^{35} + 201 q^{36} + 134 q^{37} + 70 q^{38} + 6 q^{39} + 11 q^{40} + 182 q^{41} - 15 q^{42} + 12 q^{43} + 33 q^{44} + 29 q^{45} + 24 q^{46} + 80 q^{47} + 21 q^{48} + 229 q^{49} + 37 q^{50} + 57 q^{51} - 15 q^{52} + 75 q^{53} + 95 q^{54} - 9 q^{55} + 39 q^{56} + 19 q^{57} - 21 q^{58} + 91 q^{59} + 62 q^{60} + 58 q^{61} + 108 q^{62} + 9 q^{63} + 167 q^{64} + 76 q^{65} + 105 q^{66} - 17 q^{67} + 109 q^{68} + 48 q^{69} - 55 q^{70} + 56 q^{71} + 48 q^{72} + 54 q^{73} + 9 q^{74} + 28 q^{75} + 82 q^{76} + 156 q^{77} + 16 q^{78} - 2 q^{79} + 98 q^{80} + 270 q^{81} - 42 q^{82} + 130 q^{83} + 229 q^{84} + 22 q^{85} + 72 q^{86} + 22 q^{87} + 61 q^{88} + 157 q^{89} + 176 q^{90} + 31 q^{91} - 18 q^{92} + 36 q^{93} + 83 q^{94} + 98 q^{95} + 111 q^{96} + 35 q^{97} + 53 q^{98} + 55 q^{99}+O(q^{100}) \) 134 * q + 9 * q^2 + 7 * q^3 + 149 * q^4 + 22 * q^5 + 20 * q^6 + 11 * q^7 + 27 * q^8 + 181 * q^9 + 15 * q^10 + 20 * q^11 + 28 * q^12 + 11 * q^13 + 17 * q^14 - 13 * q^15 + 143 * q^16 + 76 * q^17 + 23 * q^18 + 15 * q^19 + 67 * q^20 + 63 * q^21 + 2 * q^22 + 22 * q^23 + 33 * q^24 + 160 * q^25 + 65 * q^26 + 31 * q^27 + 10 * q^28 + 73 * q^29 + 20 * q^30 + 10 * q^31 + 53 * q^32 + 72 * q^33 - 7 * q^34 + 52 * q^35 + 201 * q^36 + 134 * q^37 + 70 * q^38 + 6 * q^39 + 11 * q^40 + 182 * q^41 - 15 * q^42 + 12 * q^43 + 33 * q^44 + 29 * q^45 + 24 * q^46 + 80 * q^47 + 21 * q^48 + 229 * q^49 + 37 * q^50 + 57 * q^51 - 15 * q^52 + 75 * q^53 + 95 * q^54 - 9 * q^55 + 39 * q^56 + 19 * q^57 - 21 * q^58 + 91 * q^59 + 62 * q^60 + 58 * q^61 + 108 * q^62 + 9 * q^63 + 167 * q^64 + 76 * q^65 + 105 * q^66 - 17 * q^67 + 109 * q^68 + 48 * q^69 - 55 * q^70 + 56 * q^71 + 48 * q^72 + 54 * q^73 + 9 * q^74 + 28 * q^75 + 82 * q^76 + 156 * q^77 + 16 * q^78 - 2 * q^79 + 98 * q^80 + 270 * q^81 - 42 * q^82 + 130 * q^83 + 229 * q^84 + 22 * q^85 + 72 * q^86 + 22 * q^87 + 61 * q^88 + 157 * q^89 + 176 * q^90 + 31 * q^91 - 18 * q^92 + 36 * q^93 + 83 * q^94 + 98 * q^95 + 111 * q^96 + 35 * q^97 + 53 * q^98 + 55 * 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 $

$2$	−2.39957	−1.69675	−0.848376	−	0.529394i	$-0.822419\pi$
$2$	−2.39957	−1.69675	−0.848376	+	0.529394i	$0.822419\pi$
$3$	0.225532	0.130211	0.0651056	−	0.997878i	$-0.479262\pi$
$3$	0.225532	0.130211	0.0651056	+	0.997878i	$0.479262\pi$
$4$	3.75794	1.87897
$5$	−1.91995	−0.858628	−0.429314	−	0.903155i	$-0.641245\pi$
$5$	−1.91995	−0.858628	−0.429314	+	0.903155i	$0.641245\pi$
$6$	−0.541181	−0.220936
$7$	−3.36005	−1.26998	−0.634989	−	0.772521i	$-0.718995\pi$
$7$	−3.36005	−1.26998	−0.634989	+	0.772521i	$0.718995\pi$
$8$	−4.21829	−1.49139
$9$	−2.94914	−0.983045
$10$	4.60705	1.45688
$11$	2.75219	0.829818	0.414909	−	0.909863i	$-0.363813\pi$
$11$	2.75219	0.829818	0.414909	+	0.909863i	$0.363813\pi$
$12$	0.847536	0.244663
$13$	3.46120	0.959964	0.479982	−	0.877278i	$-0.340643\pi$
$13$	3.46120	0.959964	0.479982	+	0.877278i	$0.340643\pi$
$14$	8.06267	2.15484
$15$	−0.433011	−0.111803
$16$	2.60621	0.651553
$17$	7.52354	1.82473	0.912363	−	0.409382i	$-0.134256\pi$
$17$	7.52354	1.82473	0.912363	+	0.409382i	$0.134256\pi$
$18$	7.07666	1.66798
$19$	6.06228	1.39078	0.695391	−	0.718632i	$-0.255231\pi$
$19$	6.06228	1.39078	0.695391	+	0.718632i	$0.255231\pi$
$20$	−7.21505	−1.61333
$21$	−0.757799	−0.165365
$22$	−6.60408	−1.40800
$23$	−1.58372	−0.330228	−0.165114	−	0.986274i	$-0.552799\pi$
$23$	−1.58372	−0.330228	−0.165114	+	0.986274i	$0.552799\pi$
$24$	−0.951361	−0.194196
$25$	−1.31379	−0.262759
$26$	−8.30539	−1.62882
$27$	−1.34172	−0.258215
$28$	−12.6268	−2.38625
$29$	0.415077	0.0770779	0.0385390	−	0.999257i	$-0.487730\pi$
$29$	0.415077	0.0770779	0.0385390	+	0.999257i	$0.487730\pi$
$30$	1.03904	0.189702
$31$	9.61362	1.72666	0.863329	−	0.504642i	$-0.168375\pi$
$31$	9.61362	1.72666	0.863329	+	0.504642i	$0.168375\pi$
$32$	2.18279	0.385867
$33$	0.620709	0.108052
$34$	−18.0533	−3.09611
$35$	6.45112	1.09044
$36$	−11.0827	−1.84711
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	−14.5469	−2.35981
$39$	0.780612	0.124998
$40$	8.09891	1.28055
$41$	0.648582	0.101291	0.0506457	−	0.998717i	$-0.483872\pi$
$41$	0.648582	0.101291	0.0506457	+	0.998717i	$0.483872\pi$
$42$	1.81839	0.280584
$43$	2.96853	0.452697	0.226349	−	0.974046i	$-0.427321\pi$
$43$	2.96853	0.452697	0.226349	+	0.974046i	$0.427321\pi$
$44$	10.3426	1.55920
$45$	5.66219	0.844070
$46$	3.80025	0.560316
$47$	4.37572	0.638264	0.319132	−	0.947710i	$-0.396609\pi$
$47$	4.37572	0.638264	0.319132	+	0.947710i	$0.396609\pi$
$48$	0.587785	0.0848395
$49$	4.28991	0.612844
$50$	3.15254	0.445836
$51$	1.69680	0.237600
$52$	13.0070	1.80374
$53$	−8.71292	−1.19681	−0.598406	−	0.801193i	$-0.704199\pi$
$53$	−8.71292	−1.19681	−0.598406	+	0.801193i	$0.704199\pi$
$54$	3.21956	0.438126
$55$	−5.28407	−0.712504
$56$	14.1737	1.89403
$57$	1.36724	0.181095
$58$	−0.996007	−0.130782
$59$	12.4609	1.62227	0.811133	−	0.584861i	$-0.198851\pi$
$59$	12.4609	1.62227	0.811133	+	0.584861i	$0.198851\pi$
$60$	−1.62723	−0.210074
$61$	4.46346	0.571488	0.285744	−	0.958306i	$-0.407759\pi$
$61$	4.46346	0.571488	0.285744	+	0.958306i	$0.407759\pi$
$62$	−23.0686	−2.92971
$63$	9.90923	1.24845
$64$	−10.4502	−1.30627
$65$	−6.64533	−0.824252
$66$	−1.48943	−0.183337
$67$	−10.4804	−1.28038	−0.640190	−	0.768217i	$-0.721144\pi$
$67$	−10.4804	−1.28038	−0.640190	+	0.768217i	$0.721144\pi$
$68$	28.2730	3.42860
$69$	−0.357180	−0.0429994
$70$	−15.4799	−1.85020
$71$	−2.42366	−0.287635	−0.143818	−	0.989604i	$-0.545938\pi$
$71$	−2.42366	−0.287635	−0.143818	+	0.989604i	$0.545938\pi$
$72$	12.4403	1.46610
$73$	−12.0414	−1.40934	−0.704671	−	0.709535i	$-0.748905\pi$
$73$	−12.0414	−1.40934	−0.704671	+	0.709535i	$0.748905\pi$
$74$	−2.39957	−0.278944
$75$	−0.296303	−0.0342141
$76$	22.7816	2.61323
$77$	−9.24750	−1.05385
$78$	−1.87313	−0.212091
$79$	−8.24444	−0.927572	−0.463786	−	0.885947i	$-0.653509\pi$
$79$	−8.24444	−0.927572	−0.463786	+	0.885947i	$0.653509\pi$
$80$	−5.00380	−0.559442
$81$	8.54480	0.949423
$82$	−1.55632	−0.171866
$83$	−3.27015	−0.358946	−0.179473	−	0.983763i	$-0.557439\pi$
$83$	−3.27015	−0.358946	−0.179473	+	0.983763i	$0.557439\pi$
$84$	−2.84776	−0.310716
$85$	−14.4448	−1.56676
$86$	−7.12321	−0.768115
$87$	0.0936133	0.0100364
$88$	−11.6096	−1.23758
$89$	−1.81027	−0.191888	−0.0959442	−	0.995387i	$-0.530587\pi$
$89$	−1.81027	−0.191888	−0.0959442	+	0.995387i	$0.530587\pi$
$90$	−13.5868	−1.43218
$91$	−11.6298	−1.21913
$92$	−5.95152	−0.620489
$93$	2.16818	0.224830
$94$	−10.4998	−1.08298
$95$	−11.6393	−1.19416
$96$	0.492290	0.0502441
$97$	−13.2583	−1.34618	−0.673088	−	0.739562i	$-0.735033\pi$
$97$	−13.2583	−1.34618	−0.673088	+	0.739562i	$0.735033\pi$
$98$	−10.2939	−1.03984
$99$	−8.11659	−0.815748
$100$	−4.93715	−0.493715
$101$	−18.6647	−1.85721	−0.928604	−	0.371071i	$-0.878991\pi$
$101$	−18.6647	−1.85721	−0.928604	+	0.371071i	$0.878991\pi$
$102$	−4.07159	−0.403148
$103$	10.9070	1.07470	0.537351	−	0.843359i	$-0.319425\pi$
$103$	10.9070	1.07470	0.537351	+	0.843359i	$0.319425\pi$
$104$	−14.6004	−1.43168
$105$	1.45494	0.141987
$106$	20.9073	2.03069
$107$	14.5317	1.40484	0.702418	−	0.711764i	$-0.252104\pi$
$107$	14.5317	1.40484	0.702418	+	0.711764i	$0.252104\pi$
$108$	−5.04211	−0.485177
$109$	−3.61477	−0.346232	−0.173116	−	0.984901i	$-0.555384\pi$
$109$	−3.61477	−0.346232	−0.173116	+	0.984901i	$0.555384\pi$
$110$	12.6795	1.20894
$111$	0.225532	0.0214066
$112$	−8.75700	−0.827458
$113$	5.89268	0.554337	0.277168	−	0.960821i	$-0.410604\pi$
$113$	5.89268	0.554337	0.277168	+	0.960821i	$0.410604\pi$
$114$	−3.28079	−0.307274
$115$	3.04066	0.283543
$116$	1.55983	0.144827
$117$	−10.2075	−0.943688
$118$	−29.9007	−2.75258
$119$	−25.2794	−2.31736
$120$	1.82657	0.166742
$121$	−3.42543	−0.311403
$122$	−10.7104	−0.969674
$123$	0.146276	0.0131893
$124$	36.1274	3.24433
$125$	12.1222	1.08424
$126$	−23.7779	−2.11830
$127$	−15.6939	−1.39261	−0.696306	−	0.717745i	$-0.745174\pi$
$127$	−15.6939	−1.39261	−0.696306	+	0.717745i	$0.745174\pi$
$128$	20.7104	1.83056
$129$	0.669500	0.0589462
$130$	15.9459	1.39855
$131$	−9.92953	−0.867547	−0.433773	−	0.901022i	$-0.642818\pi$
$131$	−9.92953	−0.867547	−0.433773	+	0.901022i	$0.642818\pi$
$132$	2.33258	0.203025
$133$	−20.3695	−1.76626
$134$	25.1484	2.17249
$135$	2.57604	0.221710
$136$	−31.7365	−2.72138
$137$	15.3675	1.31293	0.656466	−	0.754356i	$-0.272051\pi$
$137$	15.3675	1.31293	0.656466	+	0.754356i	$0.272051\pi$
$138$	0.857079	0.0729594
$139$	17.3616	1.47259	0.736295	−	0.676660i	$-0.236573\pi$
$139$	17.3616	1.47259	0.736295	+	0.676660i	$0.236573\pi$
$140$	24.2429	2.04890
$141$	0.986865	0.0831091
$142$	5.81574	0.488046
$143$	9.52589	0.796595
$144$	−7.68608	−0.640506
$145$	−0.796927	−0.0661812
$146$	28.8942	2.39130
$147$	0.967513	0.0797992
$148$	3.75794	0.308900
$149$	10.4772	0.858326	0.429163	−	0.903227i	$-0.358809\pi$
$149$	10.4772	0.858326	0.429163	+	0.903227i	$0.358809\pi$
$150$	0.711000	0.0580529
$151$	15.1434	1.23235	0.616175	−	0.787609i	$-0.288681\pi$
$151$	15.1434	1.23235	0.616175	+	0.787609i	$0.288681\pi$
$152$	−25.5725	−2.07420
$153$	−22.1879	−1.79379
$154$	22.1900	1.78812
$155$	−18.4577	−1.48256
$156$	2.93349	0.234867
$157$	15.3417	1.22440	0.612199	−	0.790704i	$-0.290285\pi$
$157$	15.3417	1.22440	0.612199	+	0.790704i	$0.290285\pi$
$158$	19.7831	1.57386
$159$	−1.96505	−0.155838
$160$	−4.19085	−0.331316
$161$	5.32137	0.419383
$162$	−20.5039	−1.61094
$163$	−1.00000	−0.0783260
$163$	−1.00000	−0.0783260
$164$	2.43733	0.190323
$165$	−1.19173	−0.0927760
$166$	7.84696	0.609042
$167$	−5.06576	−0.392001	−0.196000	−	0.980604i	$-0.562795\pi$
$167$	−5.06576	−0.392001	−0.196000	+	0.980604i	$0.562795\pi$
$168$	3.19662	0.246624
$169$	−1.02009	−0.0784688
$170$	34.6613	2.65840
$171$	−17.8785	−1.36720
$172$	11.1556	0.850604
$173$	−5.89575	−0.448245	−0.224123	−	0.974561i	$-0.571952\pi$
$173$	−5.89575	−0.448245	−0.224123	+	0.974561i	$0.571952\pi$
$174$	−0.224632	−0.0170293
$175$	4.41441	0.333698
$176$	7.17280	0.540670
$177$	2.81033	0.211237
$178$	4.34387	0.325587
$179$	19.9031	1.48763	0.743813	−	0.668388i	$-0.233016\pi$
$179$	19.9031	1.48763	0.743813	+	0.668388i	$0.233016\pi$
$180$	21.2782	1.58598
$181$	1.27094	0.0944680	0.0472340	−	0.998884i	$-0.484959\pi$
$181$	1.27094	0.0944680	0.0472340	+	0.998884i	$0.484959\pi$
$182$	27.9065	2.06857
$183$	1.00666	0.0744141
$184$	6.68059	0.492500
$185$	−1.91995	−0.141157
$186$	−5.20271	−0.381481
$187$	20.7062	1.51419
$188$	16.4437	1.19928
$189$	4.50825	0.327927
$190$	27.9292	2.02620
$191$	10.5235	0.761452	0.380726	−	0.924688i	$-0.375674\pi$
$191$	10.5235	0.761452	0.380726	+	0.924688i	$0.375674\pi$
$192$	−2.35686	−0.170091
$193$	−0.00898695	−0.000646895 0	−0.000323448	−	1.00000i	$-0.500103\pi$
$193$	−0.00898695	−0.000646895 0	−0.000323448		1.00000i	$0.500103\pi$
$194$	31.8142	2.28413
$195$	−1.49874	−0.107327
$196$	16.1212	1.15151
$197$	−17.1734	−1.22356	−0.611778	−	0.791030i	$-0.709545\pi$
$197$	−17.1734	−1.22356	−0.611778	+	0.791030i	$0.709545\pi$
$198$	19.4763	1.38412
$199$	−22.1588	−1.57080	−0.785399	−	0.618990i	$-0.787542\pi$
$199$	−22.1588	−1.57080	−0.785399	+	0.618990i	$0.787542\pi$
$200$	5.54196	0.391876
$201$	−2.36366	−0.166720
$202$	44.7873	3.15122
$203$	−1.39468	−0.0978873
$204$	6.37647	0.446442
$205$	−1.24524	−0.0869716
$206$	−26.1722	−1.82350
$207$	4.67061	0.324629
$208$	9.02063	0.625468
$209$	16.6846	1.15410
$210$	−3.49122	−0.240917
$211$	−13.5149	−0.930406	−0.465203	−	0.885204i	$-0.654019\pi$
$211$	−13.5149	−0.930406	−0.465203	+	0.885204i	$0.654019\pi$
$212$	−32.7426	−2.24877
$213$	−0.546614	−0.0374533
$214$	−34.8699	−2.38366
$215$	−5.69944	−0.388698
$216$	5.65978	0.385099
$217$	−32.3022	−2.19282
$218$	8.67390	0.587470
$219$	−2.71573	−0.183512
$220$	−19.8572	−1.33877
$221$	26.0405	1.75167
$222$	−0.541181	−0.0363217
$223$	−3.73200	−0.249913	−0.124957	−	0.992162i	$-0.539879\pi$
$223$	−3.73200	−0.249913	−0.124957	+	0.992162i	$0.539879\pi$
$224$	−7.33428	−0.490042
$225$	3.87456	0.258304
$226$	−14.1399	−0.940572
$227$	−2.87031	−0.190509	−0.0952545	−	0.995453i	$-0.530366\pi$
$227$	−2.87031	−0.190509	−0.0952545	+	0.995453i	$0.530366\pi$
$228$	5.13800	0.340272
$229$	22.0764	1.45885	0.729425	−	0.684060i	$-0.239788\pi$
$229$	22.0764	1.45885	0.729425	+	0.684060i	$0.239788\pi$
$230$	−7.29628	−0.481103
$231$	−2.08561	−0.137223
$232$	−1.75092	−0.114953
$233$	23.5944	1.54572	0.772860	−	0.634576i	$-0.218825\pi$
$233$	23.5944	1.54572	0.772860	+	0.634576i	$0.218825\pi$
$234$	24.4937	1.60120
$235$	−8.40115	−0.548031
$236$	46.8271	3.04819
$237$	−1.85939	−0.120780
$238$	60.6598	3.93199
$239$	23.4009	1.51368	0.756839	−	0.653601i	$-0.226743\pi$
$239$	23.4009	1.51368	0.756839	+	0.653601i	$0.226743\pi$
$240$	−1.12852	−0.0728455
$241$	−2.29015	−0.147522	−0.0737608	−	0.997276i	$-0.523500\pi$
$241$	−2.29015	−0.147522	−0.0737608	+	0.997276i	$0.523500\pi$
$242$	8.21955	0.528373
$243$	5.95230	0.381840
$244$	16.7734	1.07381
$245$	−8.23641	−0.526205
$246$	−0.351000	−0.0223789
$247$	20.9828	1.33510
$248$	−40.5531	−2.57512
$249$	−0.737525	−0.0467388
$250$	−29.0880	−1.83969
$251$	23.5115	1.48403	0.742017	−	0.670381i	$-0.233869\pi$
$251$	23.5115	1.48403	0.742017	+	0.670381i	$0.233869\pi$
$252$	37.2383	2.34579
$253$	−4.35871	−0.274029
$254$	37.6587	2.36292
$255$	−3.25777	−0.204010
$256$	−28.7956	−1.79973
$257$	22.7941	1.42186	0.710929	−	0.703264i	$-0.248275\pi$
$257$	22.7941	1.42186	0.710929	+	0.703264i	$0.248275\pi$
$258$	−1.60651	−0.100017
$259$	−3.36005	−0.208783
$260$	−24.9727	−1.54874
$261$	−1.22412	−0.0757711
$262$	23.8266	1.47201
$263$	−10.6119	−0.654357	−0.327178	−	0.944963i	$-0.606098\pi$
$263$	−10.6119	−0.654357	−0.327178	+	0.944963i	$0.606098\pi$
$264$	−2.61833	−0.161147
$265$	16.7284	1.02762
$266$	48.8781	2.99691
$267$	−0.408275	−0.0249860
$268$	−39.3845	−2.40579
$269$	3.46579	0.211313	0.105656	−	0.994403i	$-0.466306\pi$
$269$	3.46579	0.211313	0.105656	+	0.994403i	$0.466306\pi$
$270$	−6.18139	−0.376187
$271$	−10.6198	−0.645108	−0.322554	−	0.946551i	$-0.604541\pi$
$271$	−10.6198	−0.645108	−0.322554	+	0.946551i	$0.604541\pi$
$272$	19.6079	1.18891
$273$	−2.62289	−0.158745
$274$	−36.8753	−2.22772
$275$	−3.61582	−0.218042
$276$	−1.34226	−0.0807946
$277$	−6.29045	−0.377956	−0.188978	−	0.981981i	$-0.560518\pi$
$277$	−6.29045	−0.377956	−0.188978	+	0.981981i	$0.560518\pi$
$278$	−41.6603	−2.49862
$279$	−28.3519	−1.69738
$280$	−27.2127	−1.62627
$281$	−25.6270	−1.52878	−0.764388	−	0.644756i	$-0.776959\pi$
$281$	−25.6270	−1.52878	−0.764388	+	0.644756i	$0.776959\pi$
$282$	−2.36805	−0.141015
$283$	12.9026	0.766978	0.383489	−	0.923546i	$-0.374722\pi$
$283$	12.9026	0.766978	0.383489	+	0.923546i	$0.374722\pi$
$284$	−9.10796	−0.540458
$285$	−2.62503	−0.155493
$286$	−22.8581	−1.35162
$287$	−2.17926	−0.128638
$288$	−6.43735	−0.379324
$289$	39.6036	2.32963
$290$	1.91228	0.112293
$291$	−2.99018	−0.175287
$292$	−45.2509	−2.64811
$293$	−5.80615	−0.339199	−0.169599	−	0.985513i	$-0.554247\pi$
$293$	−5.80615	−0.339199	−0.169599	+	0.985513i	$0.554247\pi$
$294$	−2.32162	−0.135399
$295$	−23.9242	−1.39292
$296$	−4.21829	−0.245183
$297$	−3.69268	−0.214271
$298$	−25.1408	−1.45637
$299$	−5.48157	−0.317008
$300$	−1.11349	−0.0642872
$301$	−9.97441	−0.574916
$302$	−36.3376	−2.09099
$303$	−4.20950	−0.241829
$304$	15.7996	0.906168
$305$	−8.56963	−0.490695
$306$	53.2415	3.04361
$307$	−6.14541	−0.350737	−0.175369	−	0.984503i	$-0.556112\pi$
$307$	−6.14541	−0.350737	−0.175369	+	0.984503i	$0.556112\pi$
$308$	−34.7515	−1.98015
$309$	2.45989	0.139938
$310$	44.2905	2.51553
$311$	0.657580	0.0372880	0.0186440	−	0.999826i	$-0.494065\pi$
$311$	0.657580	0.0372880	0.0186440	+	0.999826i	$0.494065\pi$
$312$	−3.29285	−0.186421
$313$	2.33254	0.131843	0.0659214	−	0.997825i	$-0.479001\pi$
$313$	2.33254	0.131843	0.0659214	+	0.997825i	$0.479001\pi$
$314$	−36.8134	−2.07750
$315$	−19.0252	−1.07195
$316$	−30.9821	−1.74288
$317$	9.80154	0.550509	0.275255	−	0.961371i	$-0.411238\pi$
$317$	9.80154	0.550509	0.275255	+	0.961371i	$0.411238\pi$
$318$	4.71526	0.264419
$319$	1.14237	0.0639606
$320$	20.0638	1.12160
$321$	3.27738	0.182925
$322$	−12.7690	−0.711589
$323$	45.6098	2.53780
$324$	32.1108	1.78393
$325$	−4.54730	−0.252239
$326$	2.39957	0.132900
$327$	−0.815248	−0.0450833
$328$	−2.73591	−0.151065
$329$	−14.7026	−0.810581
$330$	2.85964	0.157418
$331$	−20.0262	−1.10074	−0.550370	−	0.834921i	$-0.685513\pi$
$331$	−20.0262	−1.10074	−0.550370	+	0.834921i	$0.685513\pi$
$332$	−12.2890	−0.674448
$333$	−2.94914	−0.161612
$334$	12.1557	0.665128
$335$	20.1218	1.09937
$336$	−1.97499	−0.107744
$337$	32.7645	1.78479	0.892397	−	0.451251i	$-0.149022\pi$
$337$	32.7645	1.78479	0.892397	+	0.451251i	$0.149022\pi$
$338$	2.44779	0.133142
$339$	1.32899	0.0721808
$340$	−54.2827	−2.94389
$341$	26.4586	1.43281
$342$	42.9006	2.31980
$343$	9.10603	0.491679
$344$	−12.5221	−0.675149
$345$	0.685768	0.0369205
$346$	14.1473	0.760561
$347$	−4.23169	−0.227169	−0.113584	−	0.993528i	$-0.536233\pi$
$347$	−4.23169	−0.227169	−0.113584	+	0.993528i	$0.536233\pi$
$348$	0.351793	0.0188581
$349$	12.4007	0.663793	0.331897	−	0.943316i	$-0.392311\pi$
$349$	12.4007	0.663793	0.331897	+	0.943316i	$0.392311\pi$
$350$	−10.5927	−0.566203
$351$	−4.64397	−0.247877
$352$	6.00747	0.320199
$353$	−28.4674	−1.51517	−0.757585	−	0.652737i	$-0.773621\pi$
$353$	−28.4674	−1.51517	−0.757585	+	0.652737i	$0.773621\pi$
$354$	−6.74358	−0.358417
$355$	4.65330	0.246972
$356$	−6.80289	−0.360552
$357$	−5.70133	−0.301746
$358$	−47.7588	−2.52413
$359$	−15.8526	−0.836668	−0.418334	−	0.908293i	$-0.637386\pi$
$359$	−15.8526	−0.836668	−0.418334	+	0.908293i	$0.637386\pi$
$360$	−23.8848	−1.25884
$361$	17.7512	0.934274
$362$	−3.04970	−0.160289
$363$	−0.772545	−0.0405481
$364$	−43.7040	−2.29071
$365$	23.1189	1.21010
$366$	−2.41554	−0.126262
$367$	13.2398	0.691111	0.345556	−	0.938398i	$-0.387690\pi$
$367$	13.2398	0.691111	0.345556	+	0.938398i	$0.387690\pi$
$368$	−4.12751	−0.215161
$369$	−1.91275	−0.0995740
$370$	4.60705	0.239509
$371$	29.2758	1.51992
$372$	8.14789	0.422449
$373$	−36.1042	−1.86940	−0.934702	−	0.355432i	$-0.884334\pi$
$373$	−36.1042	−1.86940	−0.934702	+	0.355432i	$0.884334\pi$
$374$	−49.6861	−2.56921
$375$	2.73394	0.141180
$376$	−18.4580	−0.951901
$377$	1.43667	0.0739920
$378$	−10.8179	−0.556411
$379$	5.83175	0.299557	0.149779	−	0.988720i	$-0.452144\pi$
$379$	5.83175	0.299557	0.149779	+	0.988720i	$0.452144\pi$
$380$	−43.7396	−2.24380
$381$	−3.53949	−0.181334
$382$	−25.2518	−1.29200
$383$	18.0071	0.920119	0.460060	−	0.887888i	$-0.347828\pi$
$383$	18.0071	0.920119	0.460060	+	0.887888i	$0.347828\pi$
$384$	4.67086	0.238359
$385$	17.7547	0.904865
$386$	0.0215648	0.00109762
$387$	−8.75461	−0.445022
$388$	−49.8239	−2.52942
$389$	24.5791	1.24621	0.623105	−	0.782138i	$-0.285871\pi$
$389$	24.5791	1.24621	0.623105	+	0.782138i	$0.285871\pi$
$390$	3.59632	0.182107
$391$	−11.9152	−0.602577
$392$	−18.0961	−0.913991
$393$	−2.23943	−0.112964
$394$	41.2088	2.07607
$395$	15.8289	0.796439
$396$	−30.5016	−1.53276
$397$	−32.0065	−1.60636	−0.803179	−	0.595737i	$-0.796860\pi$
$397$	−32.0065	−1.60636	−0.803179	+	0.595737i	$0.796860\pi$
$398$	53.1717	2.66526
$399$	−4.59399	−0.229987
$400$	−3.42403	−0.171201
$401$	10.1193	0.505335	0.252667	−	0.967553i	$-0.418692\pi$
$401$	10.1193	0.505335	0.252667	+	0.967553i	$0.418692\pi$
$402$	5.67177	0.282882
$403$	33.2747	1.65753
$404$	−70.1408	−3.48964
$405$	−16.4056	−0.815200
$406$	3.34663	0.166090
$407$	2.75219	0.136421
$408$	−7.15760	−0.354354
$409$	−14.4181	−0.712929	−0.356464	−	0.934309i	$-0.616018\pi$
$409$	−14.4181	−0.712929	−0.356464	+	0.934309i	$0.616018\pi$
$410$	2.98805	0.147569
$411$	3.46586	0.170958
$412$	40.9879	2.01933
$413$	−41.8691	−2.06024
$414$	−11.2074	−0.550816
$415$	6.27853	0.308201
$416$	7.55508	0.370418
$417$	3.91560	0.191748
$418$	−40.0358	−1.95821
$419$	−33.2187	−1.62284	−0.811419	−	0.584465i	$-0.801304\pi$
$419$	−33.2187	−1.62284	−0.811419	+	0.584465i	$0.801304\pi$
$420$	5.46756	0.266789
$421$	35.5987	1.73497	0.867487	−	0.497460i	$-0.165734\pi$
$421$	35.5987	1.73497	0.867487	+	0.497460i	$0.165734\pi$
$422$	32.4300	1.57867
$423$	−12.9046	−0.627442
$424$	36.7536	1.78491
$425$	−9.88438	−0.479463
$426$	1.31164	0.0635490
$427$	−14.9974	−0.725777
$428$	54.6094	2.63964
$429$	2.14840	0.103726
$430$	13.6762	0.659525
$431$	38.8556	1.87161	0.935805	−	0.352518i	$-0.114674\pi$
$431$	38.8556	1.87161	0.935805	+	0.352518i	$0.114674\pi$
$432$	−3.49681	−0.168241
$433$	−28.4101	−1.36530	−0.682651	−	0.730745i	$-0.739173\pi$
$433$	−28.4101	−1.36530	−0.682651	+	0.730745i	$0.739173\pi$
$434$	77.5114	3.72067
$435$	−0.179733	−0.00861753
$436$	−13.5841	−0.650559
$437$	−9.60095	−0.459276
$438$	6.51658	0.311374
$439$	−33.2039	−1.58473	−0.792367	−	0.610044i	$-0.791152\pi$
$439$	−33.2039	−1.58473	−0.792367	+	0.610044i	$0.791152\pi$
$440$	22.2898	1.06262
$441$	−12.6515	−0.602454
$442$	−62.4859	−2.97215
$443$	15.3912	0.731259	0.365630	−	0.930760i	$-0.380854\pi$
$443$	15.3912	0.731259	0.365630	+	0.930760i	$0.380854\pi$
$444$	0.847536	0.0402223
$445$	3.47563	0.164761
$446$	8.95520	0.424041
$447$	2.36295	0.111764
$448$	35.1131	1.65894
$449$	12.5538	0.592450	0.296225	−	0.955118i	$-0.404272\pi$
$449$	12.5538	0.592450	0.296225	+	0.955118i	$0.404272\pi$
$450$	−9.29727	−0.438277
$451$	1.78502	0.0840534
$452$	22.1443	1.04158
$453$	3.41532	0.160466
$454$	6.88751	0.323247
$455$	22.3286	1.04678
$456$	−5.76741	−0.270084
$457$	25.6499	1.19985	0.599926	−	0.800055i	$-0.295197\pi$
$457$	25.6499	1.19985	0.599926	+	0.800055i	$0.295197\pi$
$458$	−52.9739	−2.47531
$459$	−10.0945	−0.471171
$460$	11.4266	0.532769
$461$	25.6916	1.19658	0.598288	−	0.801281i	$-0.295848\pi$
$461$	25.6916	1.19658	0.598288	+	0.801281i	$0.295848\pi$
$462$	5.00457	0.232834
$463$	2.19538	0.102028	0.0510140	−	0.998698i	$-0.483755\pi$
$463$	2.19538	0.102028	0.0510140	+	0.998698i	$0.483755\pi$
$464$	1.08178	0.0502204
$465$	−4.16280	−0.193045
$466$	−56.6164	−2.62270
$467$	11.7390	0.543217	0.271609	−	0.962408i	$-0.412444\pi$
$467$	11.7390	0.543217	0.271609	+	0.962408i	$0.412444\pi$
$468$	−38.3593	−1.77316
$469$	35.2145	1.62605
$470$	20.1592	0.929873
$471$	3.46004	0.159430
$472$	−52.5636	−2.41943
$473$	8.16998	0.375656
$474$	4.46173	0.204934
$475$	−7.96458	−0.365440
$476$	−94.9985	−4.35425
$477$	25.6956	1.17652
$478$	−56.1521	−2.56834
$479$	−23.5639	−1.07666	−0.538331	−	0.842733i	$-0.680945\pi$
$479$	−23.5639	−1.07666	−0.538331	+	0.842733i	$0.680945\pi$
$480$	−0.945172	−0.0431410
$481$	3.46120	0.157817
$482$	5.49538	0.250308
$483$	1.20014	0.0546083
$484$	−12.8725	−0.585116
$485$	25.4553	1.15586
$486$	−14.2830	−0.647888
$487$	−31.7603	−1.43920	−0.719599	−	0.694390i	$-0.755674\pi$
$487$	−31.7603	−1.43920	−0.719599	+	0.694390i	$0.755674\pi$
$488$	−18.8282	−0.852312
$489$	−0.225532	−0.0101989
$490$	19.7638	0.892840
$491$	2.72800	0.123113	0.0615564	−	0.998104i	$-0.480394\pi$
$491$	2.72800	0.123113	0.0615564	+	0.998104i	$0.480394\pi$
$492$	0.549696	0.0247822
$493$	3.12285	0.140646
$494$	−50.3496	−2.26533
$495$	15.5834	0.700424
$496$	25.0552	1.12501
$497$	8.14361	0.365291
$498$	1.76974	0.0793041
$499$	−19.0392	−0.852311	−0.426156	−	0.904650i	$-0.640132\pi$
$499$	−19.0392	−0.852311	−0.426156	+	0.904650i	$0.640132\pi$
$500$	45.5543	2.03725
$501$	−1.14249	−0.0510428
$502$	−56.4176	−2.51804
$503$	−38.3497	−1.70993	−0.854965	−	0.518686i	$-0.826421\pi$
$503$	−38.3497	−1.70993	−0.854965	+	0.518686i	$0.826421\pi$
$504$	−41.8000	−1.86192
$505$	35.8353	1.59465
$506$	10.4590	0.464960
$507$	−0.230064	−0.0102175
$508$	−58.9768	−2.61667
$509$	−6.56380	−0.290935	−0.145468	−	0.989363i	$-0.546469\pi$
$509$	−6.56380	−0.290935	−0.145468	+	0.989363i	$0.546469\pi$
$510$	7.81725	0.346154
$511$	40.4597	1.78983
$512$	27.6764	1.22313
$513$	−8.13389	−0.359120
$514$	−54.6961	−2.41254
$515$	−20.9409	−0.922768
$516$	2.51594	0.110758
$517$	12.0428	0.529643
$518$	8.06267	0.354253
$519$	−1.32968	−0.0583665
$520$	28.0319	1.22928
$521$	19.7963	0.867291	0.433646	−	0.901084i	$-0.357227\pi$
$521$	19.7963	0.867291	0.433646	+	0.901084i	$0.357227\pi$
$522$	2.93736	0.128565
$523$	44.6656	1.95309	0.976546	−	0.215311i	$-0.0690764\pi$
$523$	44.6656	1.95309	0.976546	+	0.215311i	$0.0690764\pi$
$524$	−37.3145	−1.63009
$525$	0.995592	0.0434512
$526$	25.4640	1.11028
$527$	72.3285	3.15068
$528$	1.61770	0.0704013
$529$	−20.4918	−0.890949
$530$	−40.1409	−1.74361
$531$	−36.7488	−1.59476
$532$	−76.5474	−3.31875
$533$	2.24487	0.0972361
$534$	0.979684	0.0423951
$535$	−27.9002	−1.20623
$536$	44.2092	1.90955
$537$	4.48878	0.193705
$538$	−8.31640	−0.358546
$539$	11.8067	0.508549
$540$	9.68059	0.416586
$541$	9.66399	0.415487	0.207744	−	0.978183i	$-0.433388\pi$
$541$	9.66399	0.415487	0.207744	+	0.978183i	$0.433388\pi$
$542$	25.4830	1.09459
$543$	0.286637	0.0123008
$544$	16.4223	0.704101
$545$	6.94018	0.297285
$546$	6.29382	0.269351
$547$	31.0022	1.32556	0.662779	−	0.748815i	$-0.269377\pi$
$547$	31.0022	1.32556	0.662779	+	0.748815i	$0.269377\pi$
$548$	57.7500	2.46696
$549$	−13.1634	−0.561798
$550$	8.67640	0.369963
$551$	2.51631	0.107199
$552$	1.50669	0.0641290
$553$	27.7017	1.17800
$554$	15.0944	0.641298
$555$	−0.433011	−0.0183803
$556$	65.2437	2.76695
$557$	−11.6009	−0.491547	−0.245774	−	0.969327i	$-0.579042\pi$
$557$	−11.6009	−0.491547	−0.245774	+	0.969327i	$0.579042\pi$
$558$	68.0323	2.88004
$559$	10.2747	0.434573
$560$	16.8130	0.710479
$561$	4.66993	0.197164
$562$	61.4937	2.59395
$563$	−10.5181	−0.443286	−0.221643	−	0.975128i	$-0.571142\pi$
$563$	−10.5181	−0.443286	−0.221643	+	0.975128i	$0.571142\pi$
$564$	3.70858	0.156159
$565$	−11.3136	−0.475969
$566$	−30.9606	−1.30137
$567$	−28.7109	−1.20575
$568$	10.2237	0.428977
$569$	38.7980	1.62650	0.813248	−	0.581918i	$-0.197697\pi$
$569$	38.7980	1.62650	0.813248	+	0.581918i	$0.197697\pi$
$570$	6.29894	0.263834
$571$	20.1128	0.841693	0.420846	−	0.907132i	$-0.361733\pi$
$571$	20.1128	0.841693	0.420846	+	0.907132i	$0.361733\pi$
$572$	35.7977	1.49678
$573$	2.37339	0.0991496
$574$	5.22930	0.218267
$575$	2.08068	0.0867704
$576$	30.8190	1.28413
$577$	−1.89431	−0.0788613	−0.0394307	−	0.999222i	$-0.512554\pi$
$577$	−1.89431	−0.0788613	−0.0394307	+	0.999222i	$0.512554\pi$
$578$	−95.0317	−3.95280
$579$	−0.00202685	−8.42329e−5 0
$580$	−2.99480	−0.124352
$581$	10.9879	0.455854
$582$	7.17514	0.297419
$583$	−23.9796	−0.993136
$584$	50.7942	2.10188
$585$	19.5980	0.810277
$586$	13.9323	0.575536
$587$	−13.8276	−0.570724	−0.285362	−	0.958420i	$-0.592114\pi$
$587$	−13.8276	−0.570724	−0.285362	+	0.958420i	$0.592114\pi$
$588$	3.63585	0.149940
$589$	58.2804	2.40140
$590$	57.4079	2.36345
$591$	−3.87316	−0.159321
$592$	2.60621	0.107115
$593$	18.9688	0.778957	0.389479	−	0.921036i	$-0.372655\pi$
$593$	18.9688	0.778957	0.389479	+	0.921036i	$0.372655\pi$
$594$	8.86084	0.363565
$595$	48.5352	1.98975
$596$	39.3727	1.61277
$597$	−4.99753	−0.204535
$598$	13.1534	0.537883
$599$	3.18505	0.130138	0.0650688	−	0.997881i	$-0.479273\pi$
$599$	3.18505	0.130138	0.0650688	+	0.997881i	$0.479273\pi$
$600$	1.24989	0.0510266
$601$	−15.9573	−0.650910	−0.325455	−	0.945557i	$-0.605518\pi$
$601$	−15.9573	−0.650910	−0.325455	+	0.945557i	$0.605518\pi$
$602$	23.9343	0.975489
$603$	30.9080	1.25867
$604$	56.9079	2.31555
$605$	6.57665	0.267379
$606$	10.1010	0.410324
$607$	−3.81626	−0.154897	−0.0774486	−	0.996996i	$-0.524677\pi$
$607$	−3.81626	−0.154897	−0.0774486	+	0.996996i	$0.524677\pi$
$608$	13.2327	0.536656
$609$	−0.314545	−0.0127460
$610$	20.5634	0.832588
$611$	15.1452	0.612710
$612$	−83.3808	−3.37047
$613$	−32.9134	−1.32936	−0.664680	−	0.747128i	$-0.731432\pi$
$613$	−32.9134	−1.32936	−0.664680	+	0.747128i	$0.731432\pi$
$614$	14.7464	0.595114
$615$	−0.280843	−0.0113247
$616$	39.0086	1.57170
$617$	−0.656439	−0.0264272	−0.0132136	−	0.999913i	$-0.504206\pi$
$617$	−0.656439	−0.0264272	−0.0132136	+	0.999913i	$0.504206\pi$
$618$	−5.90267	−0.237440
$619$	−11.0158	−0.442763	−0.221381	−	0.975187i	$-0.571057\pi$
$619$	−11.0158	−0.442763	−0.221381	+	0.975187i	$0.571057\pi$
$620$	−69.3628	−2.78568
$621$	2.12491	0.0852698
$622$	−1.57791	−0.0632684
$623$	6.08260	0.243694
$624$	2.03444	0.0814429
$625$	−16.7050	−0.668199
$626$	−5.59708	−0.223704
$627$	3.76291	0.150276
$628$	57.6530	2.30061
$629$	7.52354	0.299983
$630$	45.6524	1.81883
$631$	−6.30620	−0.251046	−0.125523	−	0.992091i	$-0.540061\pi$
$631$	−6.30620	−0.251046	−0.125523	+	0.992091i	$0.540061\pi$
$632$	34.7774	1.38337
$633$	−3.04805	−0.121149
$634$	−23.5195	−0.934078
$635$	30.1316	1.19574
$636$	−7.38451	−0.292815
$637$	14.8482	0.588309
$638$	−2.74120	−0.108525
$639$	7.14770	0.282759
$640$	−39.7629	−1.57177
$641$	17.0863	0.674868	0.337434	−	0.941349i	$-0.390441\pi$
$641$	17.0863	0.674868	0.337434	+	0.941349i	$0.390441\pi$
$642$	−7.86430	−0.310379
$643$	−26.3041	−1.03733	−0.518666	−	0.854977i	$-0.673571\pi$
$643$	−26.3041	−1.03733	−0.518666	+	0.854977i	$0.673571\pi$
$644$	19.9974	0.788007
$645$	−1.28541	−0.0506129
$646$	−109.444	−4.30601
$647$	−36.1382	−1.42074	−0.710370	−	0.703828i	$-0.751472\pi$
$647$	−36.1382	−1.42074	−0.710370	+	0.703828i	$0.751472\pi$
$648$	−36.0445	−1.41596
$649$	34.2947	1.34619
$650$	10.9116	0.427987
$651$	−7.28519	−0.285529
$652$	−3.75794	−0.147172
$653$	−37.4068	−1.46384	−0.731921	−	0.681390i	$-0.761376\pi$
$653$	−37.4068	−1.46384	−0.731921	+	0.681390i	$0.761376\pi$
$654$	1.95624	0.0764952
$655$	19.0642	0.744899
$656$	1.69034	0.0659968
$657$	35.5118	1.38545
$658$	35.2799	1.37536
$659$	32.8863	1.28107	0.640533	−	0.767930i	$-0.278713\pi$
$659$	32.8863	1.28107	0.640533	+	0.767930i	$0.278713\pi$
$660$	−4.47844	−0.174323
$661$	19.7806	0.769374	0.384687	−	0.923047i	$-0.374309\pi$
$661$	19.7806	0.769374	0.384687	+	0.923047i	$0.374309\pi$
$662$	48.0543	1.86768
$663$	5.87297	0.228087
$664$	13.7945	0.535329
$665$	39.1085	1.51656
$666$	7.07666	0.274215
$667$	−0.657366	−0.0254533
$668$	−19.0368	−0.736557
$669$	−0.841687	−0.0325415
$670$	−48.2836	−1.86536
$671$	12.2843	0.474231
$672$	−1.65412	−0.0638090
$673$	−27.0765	−1.04372	−0.521862	−	0.853030i	$-0.674762\pi$
$673$	−27.0765	−1.04372	−0.521862	+	0.853030i	$0.674762\pi$
$674$	−78.6206	−3.02835
$675$	1.76275	0.0678481
$676$	−3.83345	−0.147440
$677$	27.1967	1.04525	0.522627	−	0.852561i	$-0.324952\pi$
$677$	27.1967	1.04525	0.522627	+	0.852561i	$0.324952\pi$
$678$	−3.18900	−0.122473
$679$	44.5485	1.70961
$680$	60.9324	2.33665
$681$	−0.647347	−0.0248064
$682$	−63.4892	−2.43113
$683$	18.2678	0.698996	0.349498	−	0.936937i	$-0.386352\pi$
$683$	18.2678	0.698996	0.349498	+	0.936937i	$0.386352\pi$
$684$	−67.1862	−2.56893
$685$	−29.5048	−1.12732
$686$	−21.8505	−0.834258
$687$	4.97894	0.189959
$688$	7.73663	0.294956
$689$	−30.1572	−1.14890
$690$	−1.64555	−0.0626449
$691$	15.1451	0.576148	0.288074	−	0.957608i	$-0.406985\pi$
$691$	15.1451	0.576148	0.288074	+	0.957608i	$0.406985\pi$
$692$	−22.1558	−0.842239
$693$	27.2721	1.03598
$694$	10.1542	0.385449
$695$	−33.3334	−1.26441
$696$	−0.394888	−0.0149682
$697$	4.87963	0.184829
$698$	−29.7563	−1.12629
$699$	5.32130	0.201270
$700$	16.5891	0.627008
$701$	43.8440	1.65597	0.827983	−	0.560753i	$-0.189488\pi$
$701$	43.8440	1.65597	0.827983	+	0.560753i	$0.189488\pi$
$702$	11.1435	0.420585
$703$	6.06228	0.228643
$704$	−28.7609	−1.08397
$705$	−1.89473	−0.0713597
$706$	68.3096	2.57087
$707$	62.7143	2.35861
$708$	10.5610	0.396908
$709$	18.3209	0.688057	0.344029	−	0.938959i	$-0.388208\pi$
$709$	18.3209	0.688057	0.344029	+	0.938959i	$0.388208\pi$
$710$	−11.1659	−0.419050
$711$	24.3140	0.911845
$712$	7.63625	0.286181
$713$	−15.2253	−0.570192
$714$	13.6807	0.511989
$715$	−18.2892	−0.683979
$716$	74.7945	2.79520
$717$	5.27766	0.197098
$718$	38.0394	1.41962
$719$	38.2617	1.42692	0.713461	−	0.700695i	$-0.247126\pi$
$719$	38.2617	1.42692	0.713461	+	0.700695i	$0.247126\pi$
$720$	14.7569	0.549956
$721$	−36.6481	−1.36485
$722$	−42.5952	−1.58523
$723$	−0.516503	−0.0192090
$724$	4.77610	0.177502
$725$	−0.545326	−0.0202529
$726$	1.85378	0.0688001
$727$	−11.3160	−0.419688	−0.209844	−	0.977735i	$-0.567296\pi$
$727$	−11.3160	−0.419688	−0.209844	+	0.977735i	$0.567296\pi$
$728$	49.0579	1.81821
$729$	−24.2920	−0.899703
$730$	−55.4755	−2.05324
$731$	22.3339	0.826049
$732$	3.78295	0.139822
$733$	−34.7659	−1.28411	−0.642055	−	0.766659i	$-0.721918\pi$
$733$	−34.7659	−1.28411	−0.642055	+	0.766659i	$0.721918\pi$
$734$	−31.7698	−1.17264
$735$	−1.85758	−0.0685178
$736$	−3.45693	−0.127424
$737$	−28.8440	−1.06248
$738$	4.58979	0.168952
$739$	−51.2770	−1.88626	−0.943128	−	0.332431i	$-0.892131\pi$
$739$	−51.2770	−1.88626	−0.943128	+	0.332431i	$0.892131\pi$
$740$	−7.21505	−0.265230
$741$	4.73229	0.173845
$742$	−70.2494	−2.57894
$743$	14.0239	0.514485	0.257243	−	0.966347i	$-0.417186\pi$
$743$	14.0239	0.514485	0.257243	+	0.966347i	$0.417186\pi$
$744$	−9.14603	−0.335310
$745$	−20.1157	−0.736983
$746$	86.6346	3.17192
$747$	9.64413	0.352860
$748$	77.8127	2.84512
$749$	−48.8273	−1.78411
$750$	−6.56028	−0.239548
$751$	−40.3500	−1.47239	−0.736197	−	0.676767i	$-0.763380\pi$
$751$	−40.3500	−1.47239	−0.736197	+	0.676767i	$0.763380\pi$
$752$	11.4040	0.415863
$753$	5.30261	0.193238
$754$	−3.44738	−0.125546
$755$	−29.0745	−1.05813
$756$	16.9417	0.616164
$757$	−38.2361	−1.38971	−0.694857	−	0.719148i	$-0.744532\pi$
$757$	−38.2361	−1.38971	−0.694857	+	0.719148i	$0.744532\pi$
$758$	−13.9937	−0.508274
$759$	−0.983029	−0.0356817
$760$	49.0978	1.78096
$761$	36.2684	1.31473	0.657365	−	0.753573i	$-0.271671\pi$
$761$	36.2684	1.31473	0.657365	+	0.753573i	$0.271671\pi$
$762$	8.49326	0.307678
$763$	12.1458	0.439707
$764$	39.5466	1.43074
$765$	42.5997	1.54020
$766$	−43.2093	−1.56121
$767$	43.1296	1.55732
$768$	−6.49434	−0.234344
$769$	2.79623	0.100835	0.0504174	−	0.998728i	$-0.483945\pi$
$769$	2.79623	0.100835	0.0504174	+	0.998728i	$0.483945\pi$
$770$	−42.6037	−1.53533
$771$	5.14081	0.185142
$772$	−0.0337724	−0.00121550
$773$	32.6945	1.17594	0.587969	−	0.808883i	$-0.299928\pi$
$773$	32.6945	1.17594	0.587969	+	0.808883i	$0.299928\pi$
$774$	21.0073	0.755092
$775$	−12.6303	−0.453694
$776$	55.9274	2.00768
$777$	−0.757799	−0.0271859
$778$	−58.9793	−2.11451
$779$	3.93188	0.140874
$780$	−5.63216	−0.201664
$781$	−6.67038	−0.238685
$782$	28.5913	1.02242
$783$	−0.556918	−0.0199026
$784$	11.1804	0.399301
$785$	−29.4552	−1.05130
$786$	5.37367	0.191672
$787$	−1.74859	−0.0623304	−0.0311652	−	0.999514i	$-0.509922\pi$
$787$	−1.74859	−0.0623304	−0.0311652	+	0.999514i	$0.509922\pi$
$788$	−64.5366	−2.29902
$789$	−2.39332	−0.0852045
$790$	−37.9826	−1.35136
$791$	−19.7997	−0.703995
$792$	34.2382	1.21660
$793$	15.4489	0.548608
$794$	76.8018	2.72559
$795$	3.77279	0.133807
$796$	−83.2715	−2.95148
$797$	23.2077	0.822060	0.411030	−	0.911622i	$-0.365169\pi$
$797$	23.2077	0.822060	0.411030	+	0.911622i	$0.365169\pi$
$798$	11.0236	0.390231
$799$	32.9209	1.16466
$800$	−2.86774	−0.101390
$801$	5.33874	0.188635
$802$	−24.2820	−0.857428
$803$	−33.1403	−1.16950
$804$	−8.88248	−0.313261
$805$	−10.2168	−0.360094
$806$	−79.8449	−2.81242
$807$	0.781648	0.0275153
$808$	78.7332	2.76983
$809$	−10.0986	−0.355049	−0.177525	−	0.984116i	$-0.556809\pi$
$809$	−10.0986	−0.355049	−0.177525	+	0.984116i	$0.556809\pi$
$810$	39.3664	1.38319
$811$	20.7682	0.729271	0.364636	−	0.931150i	$-0.381194\pi$
$811$	20.7682	0.729271	0.364636	+	0.931150i	$0.381194\pi$
$812$	−5.24111	−0.183927
$813$	−2.39511	−0.0840003
$814$	−6.60408	−0.231473
$815$	1.91995	0.0672529
$816$	4.42223	0.154809
$817$	17.9961	0.629603
$818$	34.5972	1.20966
$819$	34.2978	1.19846
$820$	−4.67955	−0.163417
$821$	26.5279	0.925831	0.462915	−	0.886402i	$-0.346803\pi$
$821$	26.5279	0.925831	0.462915	+	0.886402i	$0.346803\pi$
$822$	−8.31658	−0.290074
$823$	−28.3972	−0.989865	−0.494933	−	0.868931i	$-0.664807\pi$
$823$	−28.3972	−0.989865	−0.494933	+	0.868931i	$0.664807\pi$
$824$	−46.0090	−1.60280
$825$	−0.815483	−0.0283915
$826$	100.468	3.49572
$827$	5.01300	0.174319	0.0871596	−	0.996194i	$-0.472221\pi$
$827$	5.01300	0.174319	0.0871596	+	0.996194i	$0.472221\pi$
$828$	17.5518	0.609968
$829$	20.1681	0.700466	0.350233	−	0.936663i	$-0.386102\pi$
$829$	20.1681	0.700466	0.350233	+	0.936663i	$0.386102\pi$
$830$	−15.0658	−0.522941
$831$	−1.41870	−0.0492141
$832$	−36.1702	−1.25398
$833$	32.2753	1.11827
$834$	−9.39575	−0.325348
$835$	9.72601	0.336583
$836$	62.6995	2.16851
$837$	−12.8988	−0.445848
$838$	79.7105	2.75355
$839$	28.0950	0.969948	0.484974	−	0.874529i	$-0.338829\pi$
$839$	28.0950	0.969948	0.484974	+	0.874529i	$0.338829\pi$
$840$	−6.13734	−0.211758
$841$	−28.8277	−0.994059
$842$	−85.4215	−2.94382
$843$	−5.77971	−0.199064
$844$	−50.7883	−1.74820
$845$	1.95853	0.0673754
$846$	30.9654	1.06461
$847$	11.5096	0.395474
$848$	−22.7077	−0.779787
$849$	2.90994	0.0998690
$850$	23.7183	0.813530
$851$	−1.58372	−0.0542892
$852$	−2.05414	−0.0703736
$853$	8.13709	0.278609	0.139304	−	0.990250i	$-0.455513\pi$
$853$	8.13709	0.278609	0.139304	+	0.990250i	$0.455513\pi$
$854$	35.9874	1.23146
$855$	34.3258	1.17392
$856$	−61.2991	−2.09516
$857$	−13.7297	−0.468996	−0.234498	−	0.972117i	$-0.575345\pi$
$857$	−13.7297	−0.468996	−0.234498	+	0.972117i	$0.575345\pi$
$858$	−5.15523	−0.175997
$859$	17.8486	0.608986	0.304493	−	0.952515i	$-0.401513\pi$
$859$	17.8486	0.608986	0.304493	+	0.952515i	$0.401513\pi$
$860$	−21.4181	−0.730352
$861$	−0.491494	−0.0167501
$862$	−93.2368	−3.17566
$863$	−52.0332	−1.77123	−0.885615	−	0.464421i	$-0.846263\pi$
$863$	−52.0332	−1.77123	−0.885615	+	0.464421i	$0.846263\pi$
$864$	−2.92870	−0.0996364
$865$	11.3195	0.384876
$866$	68.1720	2.31658
$867$	8.93190	0.303343
$868$	−121.390	−4.12023
$869$	−22.6903	−0.769715
$870$	0.431282	0.0146218
$871$	−36.2746	−1.22912
$872$	15.2482	0.516368
$873$	39.1005	1.32335
$874$	23.0382	0.779277
$875$	−40.7310	−1.37696
$876$	−10.2055	−0.344813
$877$	−22.0353	−0.744079	−0.372039	−	0.928217i	$-0.621341\pi$
$877$	−22.0353	−0.744079	−0.372039	+	0.928217i	$0.621341\pi$
$878$	79.6750	2.68890
$879$	−1.30947	−0.0441675
$880$	−13.7714	−0.464235
$881$	−0.497739	−0.0167692	−0.00838462	−	0.999965i	$-0.502669\pi$
$881$	−0.497739	−0.0167692	−0.00838462	+	0.999965i	$0.502669\pi$
$882$	30.3582	1.02221
$883$	4.93012	0.165912	0.0829559	−	0.996553i	$-0.473564\pi$
$883$	4.93012	0.165912	0.0829559	+	0.996553i	$0.473564\pi$
$884$	97.8585	3.29134
$885$	−5.39569	−0.181374
$886$	−36.9323	−1.24077
$887$	12.5021	0.419780	0.209890	−	0.977725i	$-0.432689\pi$
$887$	12.5021	0.419780	0.209890	+	0.977725i	$0.432689\pi$
$888$	−0.951361	−0.0319256
$889$	52.7324	1.76859
$890$	−8.34002	−0.279558
$891$	23.5170	0.787848
$892$	−14.0246	−0.469579
$893$	26.5268	0.887686
$894$	−5.67006	−0.189635
$895$	−38.2129	−1.27732
$896$	−69.5878	−2.32477
$897$	−1.23627	−0.0412779
$898$	−30.1237	−1.00524
$899$	3.99040	0.133087
$900$	14.5603	0.485344
$901$	−65.5520	−2.18385
$902$	−4.28329	−0.142618
$903$	−2.24955	−0.0748604
$904$	−24.8570	−0.826733
$905$	−2.44013	−0.0811128
$906$	−8.19530	−0.272271
$907$	49.2457	1.63518	0.817588	−	0.575804i	$-0.195311\pi$
$907$	49.2457	1.63518	0.817588	+	0.575804i	$0.195311\pi$
$908$	−10.7864	−0.357960
$909$	55.0448	1.82572
$910$	−53.5791	−1.77613
$911$	36.5597	1.21128	0.605639	−	0.795740i	$-0.292918\pi$
$911$	36.5597	1.21128	0.605639	+	0.795740i	$0.292918\pi$
$912$	3.56332	0.117993
$913$	−9.00010	−0.297860
$914$	−61.5488	−2.03585
$915$	−1.93273	−0.0638940
$916$	82.9618	2.74113
$917$	33.3637	1.10177
$918$	24.2225	0.799460
$919$	14.6305	0.482616	0.241308	−	0.970449i	$-0.422424\pi$
$919$	14.6305	0.482616	0.241308	+	0.970449i	$0.422424\pi$
$920$	−12.8264	−0.422874
$921$	−1.38599	−0.0456699
$922$	−61.6487	−2.03029
$923$	−8.38877	−0.276120
$924$	−7.83759	−0.257838
$925$	−1.31379	−0.0431973
$926$	−5.26797	−0.173116
$927$	−32.1663	−1.05648
$928$	0.906027	0.0297418
$929$	29.4653	0.966724	0.483362	−	0.875421i	$-0.339416\pi$
$929$	29.4653	0.966724	0.483362	+	0.875421i	$0.339416\pi$
$930$	9.98893	0.327550
$931$	26.0066	0.852333
$932$	88.6662	2.90436
$933$	0.148306	0.00485531
$934$	−28.1686	−0.921705
$935$	−39.7549	−1.30013
$936$	43.0584	1.40741
$937$	31.3184	1.02313	0.511564	−	0.859245i	$-0.329066\pi$
$937$	31.3184	1.02313	0.511564	+	0.859245i	$0.329066\pi$
$938$	−84.4996	−2.75901
$939$	0.526062	0.0171674
$940$	−31.5710	−1.02973
$941$	4.40662	0.143652	0.0718259	−	0.997417i	$-0.477117\pi$
$941$	4.40662	0.143652	0.0718259	+	0.997417i	$0.477117\pi$
$942$	−8.30261	−0.270514
$943$	−1.02717	−0.0334493
$944$	32.4757	1.05699
$945$	−8.65561	−0.281567
$946$	−19.6044	−0.637396
$947$	−11.2527	−0.365665	−0.182832	−	0.983144i	$-0.558527\pi$
$947$	−11.2527	−0.365665	−0.182832	+	0.983144i	$0.558527\pi$
$948$	−6.98746	−0.226942
$949$	−41.6778	−1.35292
$950$	19.1116	0.620061
$951$	2.21056	0.0716824
$952$	106.636	3.45609
$953$	21.5507	0.698097	0.349049	−	0.937105i	$-0.386505\pi$
$953$	21.5507	0.698097	0.349049	+	0.937105i	$0.386505\pi$
$954$	−61.6583	−1.99626
$955$	−20.2046	−0.653804
$956$	87.9391	2.84415
$957$	0.257642	0.00832839
$958$	56.5433	1.82683
$959$	−51.6354	−1.66739
$960$	4.52504	0.146045
$961$	61.4217	1.98135
$962$	−8.30539	−0.267777
$963$	−42.8561	−1.38102
$964$	−8.60624	−0.277188
$965$	0.0172545	0.000555442 0
$966$	−2.87982	−0.0926568
$967$	49.4611	1.59056	0.795281	−	0.606241i	$-0.207323\pi$
$967$	49.4611	1.59056	0.795281	+	0.606241i	$0.207323\pi$
$968$	14.4495	0.464423
$969$	10.2865	0.330449
$970$	−61.0817	−1.96122
$971$	−4.29143	−0.137719	−0.0688593	−	0.997626i	$-0.521936\pi$
$971$	−4.29143	−0.137719	−0.0688593	+	0.997626i	$0.521936\pi$
$972$	22.3684	0.717465
$973$	−58.3357	−1.87016
$974$	76.2112	2.44196
$975$	−1.02556	−0.0328443
$976$	11.6327	0.372355
$977$	−51.4277	−1.64532	−0.822658	−	0.568536i	$-0.807510\pi$
$977$	−51.4277	−1.64532	−0.822658	+	0.568536i	$0.807510\pi$
$978$	0.541181	0.0173050
$979$	−4.98222	−0.159232
$980$	−30.9519	−0.988722
$981$	10.6604	0.340362
$982$	−6.54602	−0.208892
$983$	−25.9963	−0.829152	−0.414576	−	0.910015i	$-0.636070\pi$
$983$	−25.9963	−0.829152	−0.414576	+	0.910015i	$0.636070\pi$
$984$	−0.617035	−0.0196704
$985$	32.9721	1.05058
$986$	−7.49350	−0.238642
$987$	−3.31591	−0.105547
$988$	78.8518	2.50861
$989$	−4.70133	−0.149494
$990$	−37.3936	−1.18845
$991$	26.8599	0.853232	0.426616	−	0.904433i	$-0.359706\pi$
$991$	26.8599	0.853232	0.426616	+	0.904433i	$0.359706\pi$
$992$	20.9845	0.666260
$993$	−4.51656	−0.143329
$994$	−19.5412	−0.619808
$995$	42.5438	1.34873
$996$	−2.77157	−0.0878207
$997$	44.0175	1.39405	0.697024	−	0.717048i	$-0.254507\pi$
$997$	44.0175	1.39405	0.697024	+	0.717048i	$0.254507\pi$
$998$	45.6859	1.44616
$999$	−1.34172	−0.0424502

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6031.2.a.e.1.14	✓	134

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6031.2.a.e.1.14	✓	134	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:	\( N \)	\(=\)	\( 6031 = 37 \cdot 163 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.39957 q^{2} +0.225532 q^{3} +3.75794 q^{4} -1.91995 q^{5} -0.541181 q^{6} -3.36005 q^{7} -4.21829 q^{8} -2.94914 q^{9} +O(q^{10})\)	\(q-2.39957 q^{2} +0.225532 q^{3} +3.75794 q^{4} -1.91995 q^{5} -0.541181 q^{6} -3.36005 q^{7} -4.21829 q^{8} -2.94914 q^{9} +4.60705 q^{10} +2.75219 q^{11} +0.847536 q^{12} +3.46120 q^{13} +8.06267 q^{14} -0.433011 q^{15} +2.60621 q^{16} +7.52354 q^{17} +7.07666 q^{18} +6.06228 q^{19} -7.21505 q^{20} -0.757799 q^{21} -6.60408 q^{22} -1.58372 q^{23} -0.951361 q^{24} -1.31379 q^{25} -8.30539 q^{26} -1.34172 q^{27} -12.6268 q^{28} +0.415077 q^{29} +1.03904 q^{30} +9.61362 q^{31} +2.18279 q^{32} +0.620709 q^{33} -18.0533 q^{34} +6.45112 q^{35} -11.0827 q^{36} +1.00000 q^{37} -14.5469 q^{38} +0.780612 q^{39} +8.09891 q^{40} +0.648582 q^{41} +1.81839 q^{42} +2.96853 q^{43} +10.3426 q^{44} +5.66219 q^{45} +3.80025 q^{46} +4.37572 q^{47} +0.587785 q^{48} +4.28991 q^{49} +3.15254 q^{50} +1.69680 q^{51} +13.0070 q^{52} -8.71292 q^{53} +3.21956 q^{54} -5.28407 q^{55} +14.1737 q^{56} +1.36724 q^{57} -0.996007 q^{58} +12.4609 q^{59} -1.62723 q^{60} +4.46346 q^{61} -23.0686 q^{62} +9.90923 q^{63} -10.4502 q^{64} -6.64533 q^{65} -1.48943 q^{66} -10.4804 q^{67} +28.2730 q^{68} -0.357180 q^{69} -15.4799 q^{70} -2.42366 q^{71} +12.4403 q^{72} -12.0414 q^{73} -2.39957 q^{74} -0.296303 q^{75} +22.7816 q^{76} -9.24750 q^{77} -1.87313 q^{78} -8.24444 q^{79} -5.00380 q^{80} +8.54480 q^{81} -1.55632 q^{82} -3.27015 q^{83} -2.84776 q^{84} -14.4448 q^{85} -7.12321 q^{86} +0.0936133 q^{87} -11.6096 q^{88} -1.81027 q^{89} -13.5868 q^{90} -11.6298 q^{91} -5.95152 q^{92} +2.16818 q^{93} -10.4998 q^{94} -11.6393 q^{95} +0.492290 q^{96} -13.2583 q^{97} -10.2939 q^{98} -8.11659 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 134 q + 9 q^{2} + 7 q^{3} + 149 q^{4} + 22 q^{5} + 20 q^{6} + 11 q^{7} + 27 q^{8} + 181 q^{9}+O(q^{10}) \) 134 * q + 9 * q^2 + 7 * q^3 + 149 * q^4 + 22 * q^5 + 20 * q^6 + 11 * q^7 + 27 * q^8 + 181 * q^9	\( 134 q + 9 q^{2} + 7 q^{3} + 149 q^{4} + 22 q^{5} + 20 q^{6} + 11 q^{7} + 27 q^{8} + 181 q^{9} + 15 q^{10} + 20 q^{11} + 28 q^{12} + 11 q^{13} + 17 q^{14} - 13 q^{15} + 143 q^{16} + 76 q^{17} + 23 q^{18} + 15 q^{19} + 67 q^{20} + 63 q^{21} + 2 q^{22} + 22 q^{23} + 33 q^{24} + 160 q^{25} + 65 q^{26} + 31 q^{27} + 10 q^{28} + 73 q^{29} + 20 q^{30} + 10 q^{31} + 53 q^{32} + 72 q^{33} - 7 q^{34} + 52 q^{35} + 201 q^{36} + 134 q^{37} + 70 q^{38} + 6 q^{39} + 11 q^{40} + 182 q^{41} - 15 q^{42} + 12 q^{43} + 33 q^{44} + 29 q^{45} + 24 q^{46} + 80 q^{47} + 21 q^{48} + 229 q^{49} + 37 q^{50} + 57 q^{51} - 15 q^{52} + 75 q^{53} + 95 q^{54} - 9 q^{55} + 39 q^{56} + 19 q^{57} - 21 q^{58} + 91 q^{59} + 62 q^{60} + 58 q^{61} + 108 q^{62} + 9 q^{63} + 167 q^{64} + 76 q^{65} + 105 q^{66} - 17 q^{67} + 109 q^{68} + 48 q^{69} - 55 q^{70} + 56 q^{71} + 48 q^{72} + 54 q^{73} + 9 q^{74} + 28 q^{75} + 82 q^{76} + 156 q^{77} + 16 q^{78} - 2 q^{79} + 98 q^{80} + 270 q^{81} - 42 q^{82} + 130 q^{83} + 229 q^{84} + 22 q^{85} + 72 q^{86} + 22 q^{87} + 61 q^{88} + 157 q^{89} + 176 q^{90} + 31 q^{91} - 18 q^{92} + 36 q^{93} + 83 q^{94} + 98 q^{95} + 111 q^{96} + 35 q^{97} + 53 q^{98} + 55 q^{99}+O(q^{100}) \) 134 * q + 9 * q^2 + 7 * q^3 + 149 * q^4 + 22 * q^5 + 20 * q^6 + 11 * q^7 + 27 * q^8 + 181 * q^9 + 15 * q^10 + 20 * q^11 + 28 * q^12 + 11 * q^13 + 17 * q^14 - 13 * q^15 + 143 * q^16 + 76 * q^17 + 23 * q^18 + 15 * q^19 + 67 * q^20 + 63 * q^21 + 2 * q^22 + 22 * q^23 + 33 * q^24 + 160 * q^25 + 65 * q^26 + 31 * q^27 + 10 * q^28 + 73 * q^29 + 20 * q^30 + 10 * q^31 + 53 * q^32 + 72 * q^33 - 7 * q^34 + 52 * q^35 + 201 * q^36 + 134 * q^37 + 70 * q^38 + 6 * q^39 + 11 * q^40 + 182 * q^41 - 15 * q^42 + 12 * q^43 + 33 * q^44 + 29 * q^45 + 24 * q^46 + 80 * q^47 + 21 * q^48 + 229 * q^49 + 37 * q^50 + 57 * q^51 - 15 * q^52 + 75 * q^53 + 95 * q^54 - 9 * q^55 + 39 * q^56 + 19 * q^57 - 21 * q^58 + 91 * q^59 + 62 * q^60 + 58 * q^61 + 108 * q^62 + 9 * q^63 + 167 * q^64 + 76 * q^65 + 105 * q^66 - 17 * q^67 + 109 * q^68 + 48 * q^69 - 55 * q^70 + 56 * q^71 + 48 * q^72 + 54 * q^73 + 9 * q^74 + 28 * q^75 + 82 * q^76 + 156 * q^77 + 16 * q^78 - 2 * q^79 + 98 * q^80 + 270 * q^81 - 42 * q^82 + 130 * q^83 + 229 * q^84 + 22 * q^85 + 72 * q^86 + 22 * q^87 + 61 * q^88 + 157 * q^89 + 176 * q^90 + 31 * q^91 - 18 * q^92 + 36 * q^93 + 83 * q^94 + 98 * q^95 + 111 * q^96 + 35 * q^97 + 53 * q^98 + 55 * q^99

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