LMFDB - Embedded newform 6031.2.a.e.1.19

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			1.19
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)

$f(q)$	$=$	$q-2.16741 q^{2} +3.17923 q^{3} +2.69765 q^{4} +1.60787 q^{5} -6.89069 q^{6} +1.52618 q^{7} -1.51209 q^{8} +7.10752 q^{9} +O(q^{10})$	\(q-2.16741 q^{2} +3.17923 q^{3} +2.69765 q^{4} +1.60787 q^{5} -6.89069 q^{6} +1.52618 q^{7} -1.51209 q^{8} +7.10752 q^{9} -3.48491 q^{10} -2.07666 q^{11} +8.57646 q^{12} +1.27944 q^{13} -3.30786 q^{14} +5.11179 q^{15} -2.11798 q^{16} -0.198549 q^{17} -15.4049 q^{18} +4.83743 q^{19} +4.33747 q^{20} +4.85210 q^{21} +4.50096 q^{22} +9.25793 q^{23} -4.80730 q^{24} -2.41476 q^{25} -2.77307 q^{26} +13.0588 q^{27} +4.11711 q^{28} -8.80380 q^{29} -11.0793 q^{30} +6.85433 q^{31} +7.61471 q^{32} -6.60217 q^{33} +0.430336 q^{34} +2.45390 q^{35} +19.1736 q^{36} +1.00000 q^{37} -10.4847 q^{38} +4.06765 q^{39} -2.43125 q^{40} +8.39023 q^{41} -10.5165 q^{42} +2.68742 q^{43} -5.60209 q^{44} +11.4280 q^{45} -20.0657 q^{46} +4.48811 q^{47} -6.73355 q^{48} -4.67076 q^{49} +5.23376 q^{50} -0.631233 q^{51} +3.45149 q^{52} +0.248265 q^{53} -28.3036 q^{54} -3.33899 q^{55} -2.30773 q^{56} +15.3793 q^{57} +19.0814 q^{58} -8.58770 q^{59} +13.7898 q^{60} -10.2738 q^{61} -14.8561 q^{62} +10.8474 q^{63} -12.2682 q^{64} +2.05718 q^{65} +14.3096 q^{66} -16.0343 q^{67} -0.535616 q^{68} +29.4331 q^{69} -5.31861 q^{70} +0.0988069 q^{71} -10.7472 q^{72} +6.86694 q^{73} -2.16741 q^{74} -7.67708 q^{75} +13.0497 q^{76} -3.16936 q^{77} -8.81624 q^{78} -5.29141 q^{79} -3.40544 q^{80} +20.1943 q^{81} -18.1850 q^{82} +16.8717 q^{83} +13.0893 q^{84} -0.319241 q^{85} -5.82474 q^{86} -27.9893 q^{87} +3.14010 q^{88} +12.0550 q^{89} -24.7690 q^{90} +1.95267 q^{91} +24.9747 q^{92} +21.7915 q^{93} -9.72756 q^{94} +7.77796 q^{95} +24.2089 q^{96} -2.41044 q^{97} +10.1234 q^{98} -14.7599 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.16741	−1.53259	−0.766294	−	0.642490i	$-0.777901\pi$
$2$	−2.16741	−1.53259	−0.766294	+	0.642490i	$0.777901\pi$
$3$	3.17923	1.83553	0.917765	−	0.397123i	$-0.129991\pi$
$3$	3.17923	1.83553	0.917765	+	0.397123i	$0.129991\pi$
$4$	2.69765	1.34883
$5$	1.60787	0.719061	0.359530	−	0.933133i	$-0.382937\pi$
$5$	1.60787	0.719061	0.359530	+	0.933133i	$0.382937\pi$
$6$	−6.89069	−2.81311
$7$	1.52618	0.576844	0.288422	−	0.957503i	$-0.406869\pi$
$7$	1.52618	0.576844	0.288422	+	0.957503i	$0.406869\pi$
$8$	−1.51209	−0.534606
$9$	7.10752	2.36917
$10$	−3.48491	−1.10202
$11$	−2.07666	−0.626135	−0.313068	−	0.949731i	$-0.601357\pi$
$11$	−2.07666	−0.626135	−0.313068	+	0.949731i	$0.601357\pi$
$12$	8.57646	2.47581
$13$	1.27944	0.354854	0.177427	−	0.984134i	$-0.443223\pi$
$13$	1.27944	0.354854	0.177427	+	0.984134i	$0.443223\pi$
$14$	−3.30786	−0.884064
$15$	5.11179	1.31986
$16$	−2.11798	−0.529495
$17$	−0.198549	−0.0481552	−0.0240776	−	0.999710i	$-0.507665\pi$
$17$	−0.198549	−0.0481552	−0.0240776	+	0.999710i	$0.507665\pi$
$18$	−15.4049	−3.63097
$19$	4.83743	1.10978	0.554892	−	0.831923i	$-0.312760\pi$
$19$	4.83743	1.10978	0.554892	+	0.831923i	$0.312760\pi$
$20$	4.33747	0.969887
$21$	4.85210	1.05881
$22$	4.50096	0.959607
$23$	9.25793	1.93041	0.965206	−	0.261492i	$-0.0842144\pi$
$23$	9.25793	1.93041	0.965206	+	0.261492i	$0.0842144\pi$
$24$	−4.80730	−0.981285
$25$	−2.41476	−0.482952
$26$	−2.77307	−0.543844
$27$	13.0588	2.51316
$28$	4.11711	0.778061
$29$	−8.80380	−1.63483	−0.817413	−	0.576053i	$-0.804592\pi$
$29$	−8.80380	−1.63483	−0.817413	+	0.576053i	$0.804592\pi$
$30$	−11.0793	−2.02280
$31$	6.85433	1.23107	0.615537	−	0.788108i	$-0.288939\pi$
$31$	6.85433	1.23107	0.615537	+	0.788108i	$0.288939\pi$
$32$	7.61471	1.34610
$33$	−6.60217	−1.14929
$34$	0.430336	0.0738021
$35$	2.45390	0.414786
$36$	19.1736	3.19560
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	−10.4847	−1.70084
$39$	4.06765	0.651345
$40$	−2.43125	−0.384414
$41$	8.39023	1.31033	0.655167	−	0.755484i	$-0.272598\pi$
$41$	8.39023	1.31033	0.655167	+	0.755484i	$0.272598\pi$
$42$	−10.5165	−1.62273
$43$	2.68742	0.409828	0.204914	−	0.978780i	$-0.434309\pi$
$43$	2.68742	0.409828	0.204914	+	0.978780i	$0.434309\pi$
$44$	−5.60209	−0.844547
$45$	11.4280	1.70358
$46$	−20.0657	−2.95853
$47$	4.48811	0.654658	0.327329	−	0.944910i	$-0.393851\pi$
$47$	4.48811	0.654658	0.327329	+	0.944910i	$0.393851\pi$
$48$	−6.73355	−0.971905
$49$	−4.67076	−0.667251
$50$	5.23376	0.740166
$51$	−0.631233	−0.0883904
$52$	3.45149	0.478635
$53$	0.248265	0.0341018	0.0170509	−	0.999855i	$-0.494572\pi$
$53$	0.248265	0.0341018	0.0170509	+	0.999855i	$0.494572\pi$
$54$	−28.3036	−3.85164
$55$	−3.33899	−0.450229
$56$	−2.30773	−0.308384
$57$	15.3793	2.03704
$58$	19.0814	2.50551
$59$	−8.58770	−1.11802	−0.559012	−	0.829160i	$-0.688819\pi$
$59$	−8.58770	−1.11802	−0.559012	+	0.829160i	$0.688819\pi$
$60$	13.7898	1.78026
$61$	−10.2738	−1.31542	−0.657711	−	0.753270i	$-0.728475\pi$
$61$	−10.2738	−1.31542	−0.657711	+	0.753270i	$0.728475\pi$
$62$	−14.8561	−1.88673
$63$	10.8474	1.36664
$64$	−12.2682	−1.53353
$65$	2.05718	0.255161
$66$	14.3096	1.76139
$67$	−16.0343	−1.95890	−0.979448	−	0.201698i	$-0.935354\pi$
$67$	−16.0343	−1.95890	−0.979448	+	0.201698i	$0.935354\pi$
$68$	−0.535616	−0.0649530
$69$	29.4331	3.54333
$70$	−5.31861	−0.635695
$71$	0.0988069	0.0117262	0.00586311	−	0.999983i	$-0.498134\pi$
$71$	0.0988069	0.0117262	0.00586311	+	0.999983i	$0.498134\pi$
$72$	−10.7472	−1.26657
$73$	6.86694	0.803715	0.401857	−	0.915702i	$-0.368365\pi$
$73$	6.86694	0.803715	0.401857	+	0.915702i	$0.368365\pi$
$74$	−2.16741	−0.251956
$75$	−7.67708	−0.886472
$76$	13.0497	1.49690
$77$	−3.16936	−0.361182
$78$	−8.81624	−0.998243
$79$	−5.29141	−0.595330	−0.297665	−	0.954670i	$-0.596208\pi$
$79$	−5.29141	−0.595330	−0.297665	+	0.954670i	$0.596208\pi$
$80$	−3.40544	−0.380739
$81$	20.1943	2.24381
$82$	−18.1850	−2.00820
$83$	16.8717	1.85191	0.925957	−	0.377629i	$-0.123260\pi$
$83$	16.8717	1.85191	0.925957	+	0.377629i	$0.123260\pi$
$84$	13.0893	1.42816
$85$	−0.319241	−0.0346265
$86$	−5.82474	−0.628097
$87$	−27.9893	−3.00077
$88$	3.14010	0.334735
$89$	12.0550	1.27783	0.638914	−	0.769278i	$-0.279384\pi$
$89$	12.0550	1.27783	0.638914	+	0.769278i	$0.279384\pi$
$90$	−24.7690	−2.61088
$91$	1.95267	0.204695
$92$	24.9747	2.60379
$93$	21.7915	2.25967
$94$	−9.72756	−1.00332
$95$	7.77796	0.798002
$96$	24.2089	2.47081
$97$	−2.41044	−0.244743	−0.122371	−	0.992484i	$-0.539050\pi$
$97$	−2.41044	−0.244743	−0.122371	+	0.992484i	$0.539050\pi$
$98$	10.1234	1.02262
$99$	−14.7599	−1.48342
$100$	−6.51417	−0.651417
$101$	−7.81016	−0.777140	−0.388570	−	0.921419i	$-0.627031\pi$
$101$	−7.81016	−0.777140	−0.388570	+	0.921419i	$0.627031\pi$
$102$	1.36814	0.135466
$103$	−6.64202	−0.654457	−0.327229	−	0.944945i	$-0.606115\pi$
$103$	−6.64202	−0.654457	−0.327229	+	0.944945i	$0.606115\pi$
$104$	−1.93464	−0.189707
$105$	7.80153	0.761352
$106$	−0.538090	−0.0522639
$107$	12.5417	1.21245	0.606225	−	0.795293i	$-0.292683\pi$
$107$	12.5417	1.21245	0.606225	+	0.795293i	$0.292683\pi$
$108$	35.2280	3.38981
$109$	−3.82264	−0.366143	−0.183071	−	0.983100i	$-0.558604\pi$
$109$	−3.82264	−0.366143	−0.183071	+	0.983100i	$0.558604\pi$
$110$	7.23695	0.690016
$111$	3.17923	0.301759
$112$	−3.23243	−0.305436
$113$	−19.2953	−1.81515	−0.907575	−	0.419891i	$-0.862068\pi$
$113$	−19.2953	−1.81515	−0.907575	+	0.419891i	$0.862068\pi$
$114$	−33.3332	−3.12194
$115$	14.8855	1.38808
$116$	−23.7496	−2.20509
$117$	9.09366	0.840709
$118$	18.6130	1.71347
$119$	−0.303022	−0.0277780
$120$	−7.72950	−0.705604
$121$	−6.68750	−0.607955
$122$	22.2675	2.01600
$123$	26.6745	2.40516
$124$	18.4906	1.66050
$125$	−11.9220	−1.06633
$126$	−23.5107	−2.09450
$127$	9.14182	0.811205	0.405603	−	0.914050i	$-0.367062\pi$
$127$	9.14182	0.811205	0.405603	+	0.914050i	$0.367062\pi$
$128$	11.3608	1.00416
$129$	8.54394	0.752252
$130$	−4.45874	−0.391057
$131$	−15.3958	−1.34513	−0.672567	−	0.740036i	$-0.734808\pi$
$131$	−15.3958	−1.34513	−0.672567	+	0.740036i	$0.734808\pi$
$132$	−17.8103	−1.55019
$133$	7.38282	0.640171
$134$	34.7527	3.00218
$135$	20.9968	1.80711
$136$	0.300225	0.0257440
$137$	−15.2443	−1.30241	−0.651204	−	0.758903i	$-0.725736\pi$
$137$	−15.2443	−1.30241	−0.651204	+	0.758903i	$0.725736\pi$
$138$	−63.7935	−5.43046
$139$	15.1655	1.28632	0.643161	−	0.765731i	$-0.277623\pi$
$139$	15.1655	1.28632	0.643161	+	0.765731i	$0.277623\pi$
$140$	6.61978	0.559473
$141$	14.2687	1.20164
$142$	−0.214155	−0.0179715
$143$	−2.65696	−0.222186
$144$	−15.0536	−1.25447
$145$	−14.1554	−1.17554
$146$	−14.8835	−1.23176
$147$	−14.8494	−1.22476
$148$	2.69765	0.221746
$149$	5.22114	0.427733	0.213866	−	0.976863i	$-0.431394\pi$
$149$	5.22114	0.427733	0.213866	+	0.976863i	$0.431394\pi$
$150$	16.6393	1.35860
$151$	−3.20460	−0.260787	−0.130393	−	0.991462i	$-0.541624\pi$
$151$	−3.20460	−0.260787	−0.130393	+	0.991462i	$0.541624\pi$
$152$	−7.31465	−0.593296
$153$	−1.41119	−0.114088
$154$	6.86929	0.553543
$155$	11.0209	0.885217
$156$	10.9731	0.878550
$157$	12.8316	1.02407	0.512037	−	0.858963i	$-0.328891\pi$
$157$	12.8316	1.02407	0.512037	+	0.858963i	$0.328891\pi$
$158$	11.4686	0.912396
$159$	0.789291	0.0625948
$160$	12.2435	0.967930
$161$	14.1293	1.11355
$162$	−43.7692	−3.43883
$163$	−1.00000	−0.0783260
$163$	−1.00000	−0.0783260
$164$	22.6339	1.76741
$165$	−10.6154	−0.826409
$166$	−36.5679	−2.83822
$167$	11.0276	0.853339	0.426669	−	0.904408i	$-0.359687\pi$
$167$	11.0276	0.853339	0.426669	+	0.904408i	$0.359687\pi$
$168$	−7.33682	−0.566048
$169$	−11.3630	−0.874079
$170$	0.691925	0.0530682
$171$	34.3821	2.62927
$172$	7.24973	0.552786
$173$	21.7111	1.65066	0.825332	−	0.564648i	$-0.190988\pi$
$173$	21.7111	1.65066	0.825332	+	0.564648i	$0.190988\pi$
$174$	60.6643	4.59895
$175$	−3.68537	−0.278588
$176$	4.39832	0.331536
$177$	−27.3023	−2.05217
$178$	−26.1281	−1.95838
$179$	3.90752	0.292062	0.146031	−	0.989280i	$-0.453350\pi$
$179$	3.90752	0.292062	0.146031	+	0.989280i	$0.453350\pi$
$180$	30.8286	2.29783
$181$	−15.9917	−1.18865	−0.594325	−	0.804225i	$-0.702581\pi$
$181$	−15.9917	−1.18865	−0.594325	+	0.804225i	$0.702581\pi$
$182$	−4.23222	−0.313713
$183$	−32.6627	−2.41450
$184$	−13.9988	−1.03201
$185$	1.60787	0.118213
$186$	−47.2310	−3.46315
$187$	0.412318	0.0301517
$188$	12.1074	0.883019
$189$	19.9301	1.44970
$190$	−16.8580	−1.22301
$191$	−12.2949	−0.889626	−0.444813	−	0.895623i	$-0.646730\pi$
$191$	−12.2949	−0.889626	−0.444813	+	0.895623i	$0.646730\pi$
$192$	−39.0035	−2.81484
$193$	11.5460	0.831101	0.415551	−	0.909570i	$-0.363589\pi$
$193$	11.5460	0.831101	0.415551	+	0.909570i	$0.363589\pi$
$194$	5.22440	0.375090
$195$	6.54024	0.468356
$196$	−12.6001	−0.900006
$197$	2.15679	0.153665	0.0768324	−	0.997044i	$-0.475519\pi$
$197$	2.15679	0.153665	0.0768324	+	0.997044i	$0.475519\pi$
$198$	31.9906	2.27347
$199$	−7.95841	−0.564157	−0.282078	−	0.959391i	$-0.591024\pi$
$199$	−7.95841	−0.564157	−0.282078	+	0.959391i	$0.591024\pi$
$200$	3.65134	0.258189
$201$	−50.9766	−3.59561
$202$	16.9278	1.19104
$203$	−13.4362	−0.943038
$204$	−1.70285	−0.119223
$205$	13.4904	0.942209
$206$	14.3959	1.00301
$207$	65.8009	4.57348
$208$	−2.70984	−0.187893
$209$	−10.0457	−0.694874
$210$	−16.9091	−1.16684
$211$	18.0083	1.23974	0.619872	−	0.784703i	$-0.287185\pi$
$211$	18.0083	1.23974	0.619872	+	0.784703i	$0.287185\pi$
$212$	0.669731	0.0459973
$213$	0.314130	0.0215238
$214$	−27.1829	−1.85819
$215$	4.32102	0.294691
$216$	−19.7461	−1.34355
$217$	10.4610	0.710137
$218$	8.28522	0.561146
$219$	21.8316	1.47524
$220$	−9.00743	−0.607281
$221$	−0.254032	−0.0170880
$222$	−6.89069	−0.462473
$223$	19.7771	1.32437	0.662187	−	0.749339i	$-0.269628\pi$
$223$	19.7771	1.32437	0.662187	+	0.749339i	$0.269628\pi$
$224$	11.6215	0.776491
$225$	−17.1629	−1.14420
$226$	41.8208	2.78188
$227$	−3.37851	−0.224239	−0.112120	−	0.993695i	$-0.535764\pi$
$227$	−3.37851	−0.224239	−0.112120	+	0.993695i	$0.535764\pi$
$228$	41.4880	2.74761
$229$	−13.5858	−0.897773	−0.448886	−	0.893589i	$-0.648179\pi$
$229$	−13.5858	−0.897773	−0.448886	+	0.893589i	$0.648179\pi$
$230$	−32.2630	−2.12736
$231$	−10.0761	−0.662961
$232$	13.3122	0.873987
$233$	−8.64876	−0.566599	−0.283300	−	0.959031i	$-0.591429\pi$
$233$	−8.64876	−0.566599	−0.283300	+	0.959031i	$0.591429\pi$
$234$	−19.7097	−1.28846
$235$	7.21629	0.470739
$236$	−23.1666	−1.50802
$237$	−16.8226	−1.09275
$238$	0.656773	0.0425723
$239$	23.7049	1.53334	0.766671	−	0.642040i	$-0.221912\pi$
$239$	23.7049	1.53334	0.766671	+	0.642040i	$0.221912\pi$
$240$	−10.8267	−0.698859
$241$	−30.6172	−1.97223	−0.986113	−	0.166076i	$-0.946890\pi$
$241$	−30.6172	−1.97223	−0.986113	+	0.166076i	$0.946890\pi$
$242$	14.4945	0.931744
$243$	25.0260	1.60542
$244$	−27.7151	−1.77428
$245$	−7.50997	−0.479794
$246$	−57.8144	−3.68611
$247$	6.18922	0.393810
$248$	−10.3644	−0.658139
$249$	53.6392	3.39925
$250$	25.8397	1.63425
$251$	9.48411	0.598632	0.299316	−	0.954154i	$-0.403242\pi$
$251$	9.48411	0.598632	0.299316	+	0.954154i	$0.403242\pi$
$252$	29.2625	1.84336
$253$	−19.2255	−1.20870
$254$	−19.8140	−1.24324
$255$	−1.01494	−0.0635580
$256$	−0.0870063	−0.00543789
$257$	23.1503	1.44408	0.722039	−	0.691852i	$-0.243205\pi$
$257$	23.1503	1.44408	0.722039	+	0.691852i	$0.243205\pi$
$258$	−18.5182	−1.15289
$259$	1.52618	0.0948325
$260$	5.54954	0.344168
$261$	−62.5732	−3.87318
$262$	33.3689	2.06154
$263$	16.6214	1.02492	0.512460	−	0.858711i	$-0.328734\pi$
$263$	16.6214	1.02492	0.512460	+	0.858711i	$0.328734\pi$
$264$	9.98309	0.614417
$265$	0.399177	0.0245212
$266$	−16.0016	−0.981119
$267$	38.3257	2.34549
$268$	−43.2548	−2.64221
$269$	5.81309	0.354430	0.177215	−	0.984172i	$-0.443291\pi$
$269$	5.81309	0.354430	0.177215	+	0.984172i	$0.443291\pi$
$270$	−45.5085	−2.76956
$271$	5.46580	0.332024	0.166012	−	0.986124i	$-0.446911\pi$
$271$	5.46580	0.332024	0.166012	+	0.986124i	$0.446911\pi$
$272$	0.420523	0.0254980
$273$	6.20798	0.375724
$274$	33.0406	1.99605
$275$	5.01462	0.302393
$276$	79.4002	4.77933
$277$	−10.9413	−0.657398	−0.328699	−	0.944435i	$-0.606610\pi$
$277$	−10.9413	−0.657398	−0.328699	+	0.944435i	$0.606610\pi$
$278$	−32.8698	−1.97140
$279$	48.7173	2.91663
$280$	−3.71053	−0.221747
$281$	11.9400	0.712282	0.356141	−	0.934432i	$-0.384092\pi$
$281$	11.9400	0.712282	0.356141	+	0.934432i	$0.384092\pi$
$282$	−30.9262	−1.84163
$283$	18.5332	1.10169	0.550843	−	0.834609i	$-0.314306\pi$
$283$	18.5332	1.10169	0.550843	+	0.834609i	$0.314306\pi$
$284$	0.266547	0.0158166
$285$	24.7279	1.46476
$286$	5.75871	0.340520
$287$	12.8050	0.755857
$288$	54.1217	3.18915
$289$	−16.9606	−0.997681
$290$	30.6804	1.80162
$291$	−7.66334	−0.449233
$292$	18.5246	1.08407
$293$	−25.9878	−1.51822	−0.759112	−	0.650960i	$-0.774367\pi$
$293$	−25.9878	−1.51822	−0.759112	+	0.650960i	$0.774367\pi$
$294$	32.1848	1.87705
$295$	−13.8079	−0.803927
$296$	−1.51209	−0.0878886
$297$	−27.1185	−1.57358
$298$	−11.3163	−0.655538
$299$	11.8450	0.685013
$300$	−20.7101	−1.19570
$301$	4.10150	0.236407
$302$	6.94567	0.399678
$303$	−24.8303	−1.42646
$304$	−10.2456	−0.587625
$305$	−16.5189	−0.945869
$306$	3.05862	0.174850
$307$	1.07246	0.0612086	0.0306043	−	0.999532i	$-0.490257\pi$
$307$	1.07246	0.0612086	0.0306043	+	0.999532i	$0.490257\pi$
$308$	−8.54983	−0.487172
$309$	−21.1165	−1.20128
$310$	−23.8867	−1.35667
$311$	22.7738	1.29139	0.645693	−	0.763598i	$-0.276569\pi$
$311$	22.7738	1.29139	0.645693	+	0.763598i	$0.276569\pi$
$312$	−6.15066	−0.348212
$313$	−0.692209	−0.0391260	−0.0195630	−	0.999809i	$-0.506227\pi$
$313$	−0.692209	−0.0391260	−0.0195630	+	0.999809i	$0.506227\pi$
$314$	−27.8113	−1.56948
$315$	17.4412	0.982699
$316$	−14.2744	−0.802997
$317$	19.3606	1.08740	0.543699	−	0.839280i	$-0.317023\pi$
$317$	19.3606	1.08740	0.543699	+	0.839280i	$0.317023\pi$
$318$	−1.71071	−0.0959321
$319$	18.2825	1.02362
$320$	−19.7257	−1.10270
$321$	39.8729	2.22549
$322$	−30.6240	−1.70661
$323$	−0.960468	−0.0534418
$324$	54.4771	3.02650
$325$	−3.08954	−0.171377
$326$	2.16741	0.120042
$327$	−12.1531	−0.672067
$328$	−12.6868	−0.700511
$329$	6.84968	0.377635
$330$	23.0079	1.26655
$331$	−28.6716	−1.57593	−0.787966	−	0.615718i	$-0.788866\pi$
$331$	−28.6716	−1.57593	−0.787966	+	0.615718i	$0.788866\pi$
$332$	45.5141	2.49791
$333$	7.10752	0.389490
$334$	−23.9012	−1.30782
$335$	−25.7810	−1.40856
$336$	−10.2766	−0.560637
$337$	19.3626	1.05475	0.527375	−	0.849633i	$-0.323176\pi$
$337$	19.3626	1.05475	0.527375	+	0.849633i	$0.323176\pi$
$338$	24.6283	1.33960
$339$	−61.3443	−3.33176
$340$	−0.861200	−0.0467051
$341$	−14.2341	−0.770818
$342$	−74.5201	−4.02958
$343$	−17.8117	−0.961743
$344$	−4.06363	−0.219096
$345$	47.3246	2.54787
$346$	−47.0568	−2.52979
$347$	6.33174	0.339905	0.169953	−	0.985452i	$-0.445639\pi$
$347$	6.33174	0.339905	0.169953	+	0.985452i	$0.445639\pi$
$348$	−75.5055	−4.04752
$349$	13.9440	0.746405	0.373203	−	0.927750i	$-0.378260\pi$
$349$	13.9440	0.746405	0.373203	+	0.927750i	$0.378260\pi$
$350$	7.98769	0.426960
$351$	16.7079	0.891803
$352$	−15.8131	−0.842843
$353$	−35.6269	−1.89623	−0.948114	−	0.317930i	$-0.897012\pi$
$353$	−35.6269	−1.89623	−0.948114	+	0.317930i	$0.897012\pi$
$354$	59.1752	3.14513
$355$	0.158869	0.00843187
$356$	32.5202	1.72357
$357$	−0.963379	−0.0509874
$358$	−8.46919	−0.447610
$359$	−21.6553	−1.14292	−0.571461	−	0.820629i	$-0.693623\pi$
$359$	−21.6553	−1.14292	−0.571461	+	0.820629i	$0.693623\pi$
$360$	−17.2801	−0.910743
$361$	4.40075	0.231619
$362$	34.6604	1.82171
$363$	−21.2611	−1.11592
$364$	5.26761	0.276098
$365$	11.0411	0.577920
$366$	70.7934	3.70043
$367$	0.768195	0.0400994	0.0200497	−	0.999799i	$-0.493618\pi$
$367$	0.768195	0.0400994	0.0200497	+	0.999799i	$0.493618\pi$
$368$	−19.6081	−1.02214
$369$	59.6337	3.10441
$370$	−3.48491	−0.181172
$371$	0.378898	0.0196714
$372$	58.7859	3.04791
$373$	−22.6354	−1.17202	−0.586009	−	0.810305i	$-0.699302\pi$
$373$	−22.6354	−1.17202	−0.586009	+	0.810305i	$0.699302\pi$
$374$	−0.893660	−0.0462101
$375$	−37.9027	−1.95729
$376$	−6.78644	−0.349984
$377$	−11.2640	−0.580123
$378$	−43.1966	−2.22179
$379$	−19.7456	−1.01426	−0.507132	−	0.861869i	$-0.669294\pi$
$379$	−19.7456	−1.01426	−0.507132	+	0.861869i	$0.669294\pi$
$380$	20.9822	1.07636
$381$	29.0640	1.48899
$382$	26.6480	1.36343
$383$	−1.00135	−0.0511667	−0.0255834	−	0.999673i	$-0.508144\pi$
$383$	−1.00135	−0.0511667	−0.0255834	+	0.999673i	$0.508144\pi$
$384$	36.1186	1.84317
$385$	−5.09591	−0.259712
$386$	−25.0249	−1.27374
$387$	19.1009	0.970953
$388$	−6.50252	−0.330116
$389$	−37.2469	−1.88849	−0.944246	−	0.329241i	$-0.893207\pi$
$389$	−37.2469	−1.88849	−0.944246	+	0.329241i	$0.893207\pi$
$390$	−14.1754	−0.717797
$391$	−1.83815	−0.0929594
$392$	7.06262	0.356716
$393$	−48.9467	−2.46903
$394$	−4.67464	−0.235505
$395$	−8.50790	−0.428079
$396$	−39.8170	−2.00088
$397$	11.0646	0.555318	0.277659	−	0.960680i	$-0.410441\pi$
$397$	11.0646	0.555318	0.277659	+	0.960680i	$0.410441\pi$
$398$	17.2491	0.864619
$399$	23.4717	1.17505
$400$	5.11441	0.255721
$401$	−18.6789	−0.932780	−0.466390	−	0.884579i	$-0.654446\pi$
$401$	−18.6789	−0.932780	−0.466390	+	0.884579i	$0.654446\pi$
$402$	110.487	5.51059
$403$	8.76972	0.436851
$404$	−21.0691	−1.04823
$405$	32.4697	1.61343
$406$	29.1218	1.44529
$407$	−2.07666	−0.102936
$408$	0.954484	0.0472540
$409$	−5.57968	−0.275897	−0.137949	−	0.990439i	$-0.544051\pi$
$409$	−5.57968	−0.275897	−0.137949	+	0.990439i	$0.544051\pi$
$410$	−29.2391	−1.44402
$411$	−48.4651	−2.39061
$412$	−17.9178	−0.882749
$413$	−13.1064	−0.644925
$414$	−142.617	−7.00926
$415$	27.1275	1.33164
$416$	9.74259	0.477670
$417$	48.2147	2.36108
$418$	21.7731	1.06496
$419$	15.8049	0.772122	0.386061	−	0.922473i	$-0.373835\pi$
$419$	15.8049	0.772122	0.386061	+	0.922473i	$0.373835\pi$
$420$	21.0458	1.02693
$421$	10.9023	0.531346	0.265673	−	0.964063i	$-0.414406\pi$
$421$	10.9023	0.531346	0.265673	+	0.964063i	$0.414406\pi$
$422$	−39.0314	−1.90002
$423$	31.8993	1.55100
$424$	−0.375399	−0.0182310
$425$	0.479448	0.0232566
$426$	−0.680848	−0.0329872
$427$	−15.6797	−0.758793
$428$	33.8331	1.63538
$429$	−8.44710	−0.407830
$430$	−9.36541	−0.451640
$431$	−15.3564	−0.739691	−0.369845	−	0.929093i	$-0.620589\pi$
$431$	−15.3564	−0.739691	−0.369845	+	0.929093i	$0.620589\pi$
$432$	−27.6582	−1.33071
$433$	22.4738	1.08002	0.540011	−	0.841658i	$-0.318420\pi$
$433$	22.4738	1.08002	0.540011	+	0.841658i	$0.318420\pi$
$434$	−22.6732	−1.08835
$435$	−45.0032	−2.15774
$436$	−10.3122	−0.493863
$437$	44.7846	2.14234
$438$	−47.3179	−2.26094
$439$	9.72867	0.464324	0.232162	−	0.972677i	$-0.425420\pi$
$439$	9.72867	0.464324	0.232162	+	0.972677i	$0.425420\pi$
$440$	5.04886	0.240695
$441$	−33.1975	−1.58083
$442$	0.550591	0.0261889
$443$	−23.4478	−1.11404	−0.557020	−	0.830499i	$-0.688055\pi$
$443$	−23.4478	−1.11404	−0.557020	+	0.830499i	$0.688055\pi$
$444$	8.57646	0.407021
$445$	19.3829	0.918836
$446$	−42.8651	−2.02972
$447$	16.5992	0.785116
$448$	−18.7236	−0.884605
$449$	−1.50077	−0.0708256	−0.0354128	−	0.999373i	$-0.511275\pi$
$449$	−1.50077	−0.0708256	−0.0354128	+	0.999373i	$0.511275\pi$
$450$	37.1991	1.75358
$451$	−17.4236	−0.820446
$452$	−52.0520	−2.44832
$453$	−10.1882	−0.478682
$454$	7.32260	0.343667
$455$	3.13963	0.147188
$456$	−23.2550	−1.08901
$457$	−37.8197	−1.76913	−0.884565	−	0.466416i	$-0.845545\pi$
$457$	−37.8197	−1.76913	−0.884565	+	0.466416i	$0.845545\pi$
$458$	29.4459	1.37592
$459$	−2.59280	−0.121022
$460$	40.1560	1.87228
$461$	−5.49985	−0.256154	−0.128077	−	0.991764i	$-0.540880\pi$
$461$	−5.49985	−0.256154	−0.128077	+	0.991764i	$0.540880\pi$
$462$	21.8391	1.01605
$463$	−21.5721	−1.00254	−0.501269	−	0.865291i	$-0.667133\pi$
$463$	−21.5721	−1.00254	−0.501269	+	0.865291i	$0.667133\pi$
$464$	18.6463	0.865632
$465$	35.0379	1.62484
$466$	18.7454	0.868363
$467$	3.16591	0.146501	0.0732504	−	0.997314i	$-0.476663\pi$
$467$	3.16591	0.146501	0.0732504	+	0.997314i	$0.476663\pi$
$468$	24.5315	1.13397
$469$	−24.4712	−1.12998
$470$	−15.6406	−0.721449
$471$	40.7947	1.87972
$472$	12.9854	0.597702
$473$	−5.58085	−0.256608
$474$	36.4615	1.67473
$475$	−11.6812	−0.535972
$476$	−0.817449	−0.0374677
$477$	1.76454	0.0807929
$478$	−51.3782	−2.34998
$479$	−31.6227	−1.44488	−0.722438	−	0.691435i	$-0.756979\pi$
$479$	−31.6227	−1.44488	−0.722438	+	0.691435i	$0.756979\pi$
$480$	38.9248	1.77667
$481$	1.27944	0.0583376
$482$	66.3599	3.02261
$483$	44.9204	2.04395
$484$	−18.0405	−0.820025
$485$	−3.87567	−0.175985
$486$	−54.2415	−2.46044
$487$	36.0644	1.63423	0.817116	−	0.576473i	$-0.195571\pi$
$487$	36.0644	1.63423	0.817116	+	0.576473i	$0.195571\pi$
$488$	15.5349	0.703232
$489$	−3.17923	−0.143770
$490$	16.2772	0.735327
$491$	1.11132	0.0501532	0.0250766	−	0.999686i	$-0.492017\pi$
$491$	1.11132	0.0501532	0.0250766	+	0.999686i	$0.492017\pi$
$492$	71.9584	3.24414
$493$	1.74799	0.0787254
$494$	−13.4145	−0.603549
$495$	−23.7319	−1.06667
$496$	−14.5173	−0.651848
$497$	0.150798	0.00676420
$498$	−116.258	−5.20964
$499$	−5.13554	−0.229898	−0.114949	−	0.993371i	$-0.536671\pi$
$499$	−5.13554	−0.229898	−0.114949	+	0.993371i	$0.536671\pi$
$500$	−32.1613	−1.43830
$501$	35.0592	1.56633
$502$	−20.5559	−0.917456
$503$	28.5977	1.27511	0.637554	−	0.770406i	$-0.279946\pi$
$503$	28.5977	1.27511	0.637554	+	0.770406i	$0.279946\pi$
$504$	−16.4023	−0.730615
$505$	−12.5577	−0.558811
$506$	41.6695	1.85244
$507$	−36.1257	−1.60440
$508$	24.6614	1.09417
$509$	−29.7333	−1.31791	−0.658953	−	0.752185i	$-0.729000\pi$
$509$	−29.7333	−1.31791	−0.658953	+	0.752185i	$0.729000\pi$
$510$	2.19979	0.0974083
$511$	10.4802	0.463618
$512$	−22.5330	−0.995827
$513$	63.1708	2.78906
$514$	−50.1762	−2.21318
$515$	−10.6795	−0.470595
$516$	23.0486	1.01466
$517$	−9.32025	−0.409904
$518$	−3.30786	−0.145339
$519$	69.0246	3.02984
$520$	−3.11064	−0.136411
$521$	27.0836	1.18655	0.593277	−	0.804999i	$-0.297834\pi$
$521$	27.0836	1.18655	0.593277	+	0.804999i	$0.297834\pi$
$522$	135.622	5.93599
$523$	4.79362	0.209610	0.104805	−	0.994493i	$-0.466578\pi$
$523$	4.79362	0.209610	0.104805	+	0.994493i	$0.466578\pi$
$524$	−41.5324	−1.81435
$525$	−11.7166	−0.511356
$526$	−36.0254	−1.57078
$527$	−1.36092	−0.0592826
$528$	13.9833	0.608544
$529$	62.7092	2.72649
$530$	−0.865178	−0.0375809
$531$	−61.0372	−2.64879
$532$	19.9163	0.863479
$533$	10.7348	0.464976
$534$	−83.0673	−3.59467
$535$	20.1654	0.871825
$536$	24.2453	1.04724
$537$	12.4229	0.536088
$538$	−12.5993	−0.543196
$539$	9.69956	0.417790
$540$	56.6419	2.43748
$541$	−16.8932	−0.726293	−0.363147	−	0.931732i	$-0.618298\pi$
$541$	−16.8932	−0.726293	−0.363147	+	0.931732i	$0.618298\pi$
$542$	−11.8466	−0.508855
$543$	−50.8412	−2.18180
$544$	−1.51189	−0.0648219
$545$	−6.14631	−0.263279
$546$	−13.4552	−0.575830
$547$	−38.8468	−1.66097	−0.830484	−	0.557042i	$-0.811936\pi$
$547$	−38.8468	−1.66097	−0.830484	+	0.557042i	$0.811936\pi$
$548$	−41.1238	−1.75672
$549$	−73.0211	−3.11646
$550$	−10.8687	−0.463444
$551$	−42.5878	−1.81430
$552$	−44.5056	−1.89428
$553$	−8.07567	−0.343413
$554$	23.7142	1.00752
$555$	5.11179	0.216983
$556$	40.9112	1.73502
$557$	41.4697	1.75713	0.878563	−	0.477627i	$-0.158503\pi$
$557$	41.4697	1.75713	0.878563	+	0.477627i	$0.158503\pi$
$558$	−105.590	−4.46999
$559$	3.43840	0.145429
$560$	−5.19732	−0.219627
$561$	1.31085	0.0553443
$562$	−25.8789	−1.09164
$563$	−26.3518	−1.11060	−0.555299	−	0.831651i	$-0.687396\pi$
$563$	−26.3518	−1.11060	−0.555299	+	0.831651i	$0.687396\pi$
$564$	38.4921	1.62081
$565$	−31.0243	−1.30520
$566$	−40.1691	−1.68843
$567$	30.8202	1.29433
$568$	−0.149405	−0.00626891
$569$	45.7609	1.91840	0.959199	−	0.282732i	$-0.0912408\pi$
$569$	45.7609	1.91840	0.959199	+	0.282732i	$0.0912408\pi$
$570$	−53.5955	−2.24487
$571$	12.0557	0.504517	0.252259	−	0.967660i	$-0.418827\pi$
$571$	12.0557	0.504517	0.252259	+	0.967660i	$0.418827\pi$
$572$	−7.16755	−0.299690
$573$	−39.0883	−1.63294
$574$	−27.7537	−1.15842
$575$	−22.3557	−0.932295
$576$	−87.1966	−3.63319
$577$	−3.20205	−0.133303	−0.0666514	−	0.997776i	$-0.521232\pi$
$577$	−3.20205	−0.133303	−0.0666514	+	0.997776i	$0.521232\pi$
$578$	36.7605	1.52903
$579$	36.7075	1.52551
$580$	−38.1862	−1.58560
$581$	25.7494	1.06826
$582$	16.6096	0.688489
$583$	−0.515560	−0.0213523
$584$	−10.3835	−0.429670
$585$	14.6214	0.604521
$586$	56.3261	2.32681
$587$	45.5612	1.88051	0.940257	−	0.340466i	$-0.110585\pi$
$587$	45.5612	1.88051	0.940257	+	0.340466i	$0.110585\pi$
$588$	−40.0586	−1.65199
$589$	33.1573	1.36622
$590$	29.9273	1.23209
$591$	6.85693	0.282056
$592$	−2.11798	−0.0870485
$593$	−40.9035	−1.67970	−0.839852	−	0.542816i	$-0.817358\pi$
$593$	−40.9035	−1.67970	−0.839852	+	0.542816i	$0.817358\pi$
$594$	58.7769	2.41164
$595$	−0.487220	−0.0199741
$596$	14.0848	0.576937
$597$	−25.3016	−1.03553
$598$	−25.6729	−1.04984
$599$	−0.434960	−0.0177720	−0.00888599	−	0.999961i	$-0.502829\pi$
$599$	−0.434960	−0.0177720	−0.00888599	+	0.999961i	$0.502829\pi$
$600$	11.6085	0.473913
$601$	−20.2452	−0.825818	−0.412909	−	0.910772i	$-0.635487\pi$
$601$	−20.2452	−0.825818	−0.412909	+	0.910772i	$0.635487\pi$
$602$	−8.88962	−0.362314
$603$	−113.964	−4.64096
$604$	−8.64489	−0.351756
$605$	−10.7526	−0.437156
$606$	53.8174	2.18618
$607$	−37.1206	−1.50668	−0.753339	−	0.657632i	$-0.771558\pi$
$607$	−37.1206	−1.50668	−0.753339	+	0.657632i	$0.771558\pi$
$608$	36.8357	1.49388
$609$	−42.7169	−1.73098
$610$	35.8031	1.44963
$611$	5.74228	0.232308
$612$	−3.80690	−0.153885
$613$	−35.8068	−1.44622	−0.723111	−	0.690732i	$-0.757288\pi$
$613$	−35.8068	−1.44622	−0.723111	+	0.690732i	$0.757288\pi$
$614$	−2.32446	−0.0938076
$615$	42.8891	1.72945
$616$	4.79237	0.193090
$617$	8.80378	0.354427	0.177213	−	0.984172i	$-0.443292\pi$
$617$	8.80378	0.354427	0.177213	+	0.984172i	$0.443292\pi$
$618$	45.7681	1.84106
$619$	16.0191	0.643862	0.321931	−	0.946763i	$-0.395668\pi$
$619$	16.0191	0.643862	0.321931	+	0.946763i	$0.395668\pi$
$620$	29.7304	1.19400
$621$	120.897	4.85143
$622$	−49.3601	−1.97916
$623$	18.3982	0.737107
$624$	−8.61520	−0.344884
$625$	−7.09515	−0.283806
$626$	1.50030	0.0599640
$627$	−31.9375	−1.27546
$628$	34.6152	1.38130
$629$	−0.198549	−0.00791667
$630$	−37.8021	−1.50607
$631$	−48.6680	−1.93744	−0.968720	−	0.248155i	$-0.920176\pi$
$631$	−48.6680	−1.93744	−0.968720	+	0.248155i	$0.920176\pi$
$632$	8.00111	0.318267
$633$	57.2526	2.27559
$634$	−41.9622	−1.66653
$635$	14.6988	0.583306
$636$	2.12923	0.0844295
$637$	−5.97597	−0.236777
$638$	−39.6255	−1.56879
$639$	0.702272	0.0277814
$640$	18.2666	0.722053
$641$	10.3747	0.409778	0.204889	−	0.978785i	$-0.434317\pi$
$641$	10.3747	0.409778	0.204889	+	0.978785i	$0.434317\pi$
$642$	−86.4208	−3.41076
$643$	27.5208	1.08531	0.542657	−	0.839954i	$-0.317418\pi$
$643$	27.5208	1.08531	0.542657	+	0.839954i	$0.317418\pi$
$644$	38.1159	1.50198
$645$	13.7375	0.540915
$646$	2.08172	0.0819043
$647$	6.34518	0.249455	0.124727	−	0.992191i	$-0.460194\pi$
$647$	6.34518	0.249455	0.124727	+	0.992191i	$0.460194\pi$
$648$	−30.5356	−1.19955
$649$	17.8337	0.700034
$650$	6.69630	0.262650
$651$	33.2579	1.30348
$652$	−2.69765	−0.105648
$653$	−24.9990	−0.978287	−0.489144	−	0.872203i	$-0.662691\pi$
$653$	−24.9990	−0.978287	−0.489144	+	0.872203i	$0.662691\pi$
$654$	26.3407	1.03000
$655$	−24.7544	−0.967233
$656$	−17.7703	−0.693815
$657$	48.8069	1.90414
$658$	−14.8460	−0.578759
$659$	20.0566	0.781294	0.390647	−	0.920541i	$-0.372251\pi$
$659$	20.0566	0.781294	0.390647	+	0.920541i	$0.372251\pi$
$660$	−28.6367	−1.11468
$661$	−37.0241	−1.44007	−0.720035	−	0.693937i	$-0.755874\pi$
$661$	−37.0241	−1.44007	−0.720035	+	0.693937i	$0.755874\pi$
$662$	62.1430	2.41525
$663$	−0.807627	−0.0313656
$664$	−25.5116	−0.990044
$665$	11.8706	0.460322
$666$	−15.4049	−0.596927
$667$	−81.5050	−3.15589
$668$	29.7485	1.15101
$669$	62.8761	2.43093
$670$	55.8778	2.15875
$671$	21.3351	0.823632
$672$	36.9473	1.42527
$673$	7.43806	0.286716	0.143358	−	0.989671i	$-0.454210\pi$
$673$	7.43806	0.286716	0.143358	+	0.989671i	$0.454210\pi$
$674$	−41.9667	−1.61650
$675$	−31.5337	−1.21373
$676$	−30.6535	−1.17898
$677$	30.5314	1.17342	0.586708	−	0.809799i	$-0.300424\pi$
$677$	30.5314	1.17342	0.586708	+	0.809799i	$0.300424\pi$
$678$	132.958	5.10622
$679$	−3.67877	−0.141178
$680$	0.482722	0.0185115
$681$	−10.7411	−0.411598
$682$	30.8510	1.18135
$683$	46.2082	1.76811	0.884053	−	0.467387i	$-0.154804\pi$
$683$	46.2082	1.76811	0.884053	+	0.467387i	$0.154804\pi$
$684$	92.7510	3.54642
$685$	−24.5108	−0.936510
$686$	38.6053	1.47396
$687$	−43.1923	−1.64789
$688$	−5.69191	−0.217002
$689$	0.317640	0.0121011
$690$	−102.572	−3.90483
$691$	−10.2804	−0.391087	−0.195543	−	0.980695i	$-0.562647\pi$
$691$	−10.2804	−0.391087	−0.195543	+	0.980695i	$0.562647\pi$
$692$	58.5689	2.22646
$693$	−22.5263	−0.855703
$694$	−13.7234	−0.520935
$695$	24.3841	0.924943
$696$	42.3225	1.60423
$697$	−1.66587	−0.0630994
$698$	−30.2223	−1.14393
$699$	−27.4964	−1.04001
$700$	−9.94183	−0.375766
$701$	−13.0774	−0.493925	−0.246963	−	0.969025i	$-0.579433\pi$
$701$	−13.0774	−0.493925	−0.246963	+	0.969025i	$0.579433\pi$
$702$	−36.2129	−1.36677
$703$	4.83743	0.182447
$704$	25.4769	0.960195
$705$	22.9423	0.864056
$706$	77.2180	2.90614
$707$	−11.9197	−0.448288
$708$	−73.6521	−2.76801
$709$	4.25051	0.159631	0.0798156	−	0.996810i	$-0.474567\pi$
$709$	4.25051	0.159631	0.0798156	+	0.996810i	$0.474567\pi$
$710$	−0.344333	−0.0129226
$711$	−37.6088	−1.41044
$712$	−18.2283	−0.683134
$713$	63.4569	2.37648
$714$	2.08803	0.0781427
$715$	−4.27204	−0.159765
$716$	10.5411	0.393940
$717$	75.3634	2.81450
$718$	46.9358	1.75163
$719$	−2.86684	−0.106915	−0.0534575	−	0.998570i	$-0.517024\pi$
$719$	−2.86684	−0.106915	−0.0534575	+	0.998570i	$0.517024\pi$
$720$	−24.2042	−0.902037
$721$	−10.1369	−0.377519
$722$	−9.53822	−0.354976
$723$	−97.3391	−3.62008
$724$	−43.1399	−1.60328
$725$	21.2591	0.789541
$726$	46.0815	1.71025
$727$	0.444166	0.0164732	0.00823661	−	0.999966i	$-0.497378\pi$
$727$	0.444166	0.0164732	0.00823661	+	0.999966i	$0.497378\pi$
$728$	−2.95261	−0.109431
$729$	18.9806	0.702986
$730$	−23.9306	−0.885713
$731$	−0.533585	−0.0197354
$732$	−88.1126	−3.25674
$733$	20.7573	0.766687	0.383343	−	0.923606i	$-0.374773\pi$
$733$	20.7573	0.766687	0.383343	+	0.923606i	$0.374773\pi$
$734$	−1.66499	−0.0614559
$735$	−23.8759	−0.880677
$736$	70.4965	2.59853
$737$	33.2976	1.22653
$738$	−129.250	−4.75777
$739$	34.9605	1.28604	0.643022	−	0.765848i	$-0.277680\pi$
$739$	34.9605	1.28604	0.643022	+	0.765848i	$0.277680\pi$
$740$	4.33747	0.159449
$741$	19.6770	0.722851
$742$	−0.821225	−0.0301481
$743$	41.7105	1.53021	0.765105	−	0.643906i	$-0.222687\pi$
$743$	41.7105	1.53021	0.765105	+	0.643906i	$0.222687\pi$
$744$	−32.9508	−1.20803
$745$	8.39491	0.307566
$746$	49.0601	1.79622
$747$	119.916	4.38750
$748$	1.11229	0.0406693
$749$	19.1409	0.699394
$750$	82.1505	2.99971
$751$	−14.7936	−0.539827	−0.269914	−	0.962885i	$-0.586995\pi$
$751$	−14.7936	−0.539827	−0.269914	+	0.962885i	$0.586995\pi$
$752$	−9.50573	−0.346638
$753$	30.1522	1.09881
$754$	24.4136	0.889090
$755$	−5.15258	−0.187521
$756$	53.7644	1.95539
$757$	38.7174	1.40721	0.703604	−	0.710592i	$-0.251573\pi$
$757$	38.7174	1.40721	0.703604	+	0.710592i	$0.251573\pi$
$758$	42.7967	1.55445
$759$	−61.1224	−2.21860
$760$	−11.7610	−0.426616
$761$	37.5184	1.36004	0.680020	−	0.733194i	$-0.261971\pi$
$761$	37.5184	1.36004	0.680020	+	0.733194i	$0.261971\pi$
$762$	−62.9934	−2.28201
$763$	−5.83406	−0.211207
$764$	−33.1673	−1.19995
$765$	−2.26901	−0.0820362
$766$	2.17034	0.0784175
$767$	−10.9875	−0.396735
$768$	−0.276613	−0.00998142
$769$	−31.1493	−1.12327	−0.561637	−	0.827384i	$-0.689828\pi$
$769$	−31.1493	−1.12327	−0.561637	+	0.827384i	$0.689828\pi$
$770$	11.0449	0.398031
$771$	73.6003	2.65065
$772$	31.1471	1.12101
$773$	−46.7294	−1.68074	−0.840369	−	0.542014i	$-0.817662\pi$
$773$	−46.7294	−1.68074	−0.840369	+	0.542014i	$0.817662\pi$
$774$	−41.3994	−1.48807
$775$	−16.5515	−0.594549
$776$	3.64481	0.130841
$777$	4.85210	0.174068
$778$	80.7291	2.89428
$779$	40.5872	1.45419
$780$	17.6433	0.631731
$781$	−0.205188	−0.00734220
$782$	3.98402	0.142468
$783$	−114.967	−4.10857
$784$	9.89258	0.353307
$785$	20.6315	0.736372
$786$	106.087	3.78401
$787$	45.6743	1.62811	0.814056	−	0.580787i	$-0.197255\pi$
$787$	45.6743	1.62811	0.814056	+	0.580787i	$0.197255\pi$
$788$	5.81826	0.207267
$789$	52.8433	1.88127
$790$	18.4401	0.656068
$791$	−29.4482	−1.04706
$792$	22.3183	0.793046
$793$	−13.1447	−0.466782
$794$	−23.9815	−0.851073
$795$	1.26908	0.0450095
$796$	−21.4690	−0.760949
$797$	40.9062	1.44897	0.724486	−	0.689290i	$-0.242077\pi$
$797$	40.9062	1.44897	0.724486	+	0.689290i	$0.242077\pi$
$798$	−50.8727	−1.80087
$799$	−0.891110	−0.0315252
$800$	−18.3877	−0.650103
$801$	85.6812	3.02739
$802$	40.4848	1.42957
$803$	−14.2603	−0.503234
$804$	−137.517	−4.84985
$805$	22.7181	0.800707
$806$	−19.0075	−0.669512
$807$	18.4812	0.650568
$808$	11.8097	0.415463
$809$	23.7841	0.836206	0.418103	−	0.908400i	$-0.362695\pi$
$809$	23.7841	0.836206	0.418103	+	0.908400i	$0.362695\pi$
$810$	−70.3751	−2.47273
$811$	−15.3494	−0.538990	−0.269495	−	0.963002i	$-0.586857\pi$
$811$	−15.3494	−0.538990	−0.269495	+	0.963002i	$0.586857\pi$
$812$	−36.2463	−1.27199
$813$	17.3770	0.609440
$814$	4.50096	0.157758
$815$	−1.60787	−0.0563212
$816$	1.33694	0.0468023
$817$	13.0002	0.454820
$818$	12.0934	0.422837
$819$	13.8786	0.484958
$820$	36.3923	1.27088
$821$	35.6067	1.24268	0.621342	−	0.783540i	$-0.286588\pi$
$821$	35.6067	1.24268	0.621342	+	0.783540i	$0.286588\pi$
$822$	105.044	3.66382
$823$	43.3255	1.51023	0.755115	−	0.655592i	$-0.227581\pi$
$823$	43.3255	1.51023	0.755115	+	0.655592i	$0.227581\pi$
$824$	10.0433	0.349877
$825$	15.9426	0.555052
$826$	28.4069	0.988404
$827$	−18.6839	−0.649704	−0.324852	−	0.945765i	$-0.605315\pi$
$827$	−18.6839	−0.649704	−0.324852	+	0.945765i	$0.605315\pi$
$828$	177.508	6.16882
$829$	−7.59699	−0.263854	−0.131927	−	0.991259i	$-0.542116\pi$
$829$	−7.59699	−0.263854	−0.131927	+	0.991259i	$0.542116\pi$
$830$	−58.7964	−2.04085
$831$	−34.7849	−1.20667
$832$	−15.6965	−0.544177
$833$	0.927375	0.0321316
$834$	−104.501	−3.61857
$835$	17.7309	0.613603
$836$	−27.0997	−0.937264
$837$	89.5090	3.09388
$838$	−34.2557	−1.18334
$839$	25.8967	0.894054	0.447027	−	0.894521i	$-0.352483\pi$
$839$	25.8967	0.894054	0.447027	+	0.894521i	$0.352483\pi$
$840$	−11.7966	−0.407023
$841$	48.5069	1.67265
$842$	−23.6297	−0.814334
$843$	37.9601	1.30742
$844$	48.5802	1.67220
$845$	−18.2703	−0.628516
$846$	−69.1388	−2.37704
$847$	−10.2064	−0.350695
$848$	−0.525820	−0.0180567
$849$	58.9215	2.02218
$850$	−1.03916	−0.0356428
$851$	9.25793	0.317358
$852$	0.847413	0.0290319
$853$	−41.6087	−1.42466	−0.712328	−	0.701847i	$-0.752359\pi$
$853$	−41.6087	−1.42466	−0.712328	+	0.701847i	$0.752359\pi$
$854$	33.9842	1.16292
$855$	55.2820	1.89060
$856$	−18.9642	−0.648183
$857$	0.212726	0.00726659	0.00363329	−	0.999993i	$-0.498843\pi$
$857$	0.212726	0.00726659	0.00363329	+	0.999993i	$0.498843\pi$
$858$	18.3083	0.625035
$859$	22.8073	0.778175	0.389088	−	0.921201i	$-0.372790\pi$
$859$	22.8073	0.778175	0.389088	+	0.921201i	$0.372790\pi$
$860$	11.6566	0.397487
$861$	40.7102	1.38740
$862$	33.2835	1.13364
$863$	31.4739	1.07138	0.535692	−	0.844414i	$-0.320051\pi$
$863$	31.4739	1.07138	0.535692	+	0.844414i	$0.320051\pi$
$864$	99.4387	3.38297
$865$	34.9086	1.18693
$866$	−48.7099	−1.65523
$867$	−53.9216	−1.83127
$868$	28.2200	0.957851
$869$	10.9884	0.372757
$870$	97.5402	3.30692
$871$	−20.5149	−0.695121
$872$	5.78019	0.195742
$873$	−17.1322	−0.579838
$874$	−97.0664	−3.28332
$875$	−18.1951	−0.615107
$876$	58.8940	1.98984
$877$	13.7794	0.465299	0.232649	−	0.972561i	$-0.425261\pi$
$877$	13.7794	0.465299	0.232649	+	0.972561i	$0.425261\pi$
$878$	−21.0860	−0.711618
$879$	−82.6213	−2.78675
$880$	7.07192	0.238394
$881$	−27.3657	−0.921972	−0.460986	−	0.887407i	$-0.652504\pi$
$881$	−27.3657	−0.921972	−0.460986	+	0.887407i	$0.652504\pi$
$882$	71.9525	2.42277
$883$	−10.1002	−0.339898	−0.169949	−	0.985453i	$-0.554360\pi$
$883$	−10.1002	−0.339898	−0.169949	+	0.985453i	$0.554360\pi$
$884$	−0.685290	−0.0230488
$885$	−43.8985	−1.47563
$886$	50.8210	1.70736
$887$	21.4551	0.720391	0.360196	−	0.932877i	$-0.382710\pi$
$887$	21.4551	0.720391	0.360196	+	0.932877i	$0.382710\pi$
$888$	−4.80730	−0.161322
$889$	13.9521	0.467938
$890$	−42.0105	−1.40820
$891$	−41.9365	−1.40493
$892$	53.3518	1.78635
$893$	21.7109	0.726528
$894$	−35.9773	−1.20326
$895$	6.28278	0.210010
$896$	17.3387	0.579244
$897$	37.6580	1.25736
$898$	3.25277	0.108546
$899$	−60.3442	−2.01259
$900$	−46.2996	−1.54332
$901$	−0.0492927	−0.00164218
$902$	37.7640	1.25740
$903$	13.0396	0.433932
$904$	29.1763	0.970389
$905$	−25.7125	−0.854712
$906$	22.0819	0.733622
$907$	−28.9384	−0.960884	−0.480442	−	0.877027i	$-0.659524\pi$
$907$	−28.9384	−0.960884	−0.480442	+	0.877027i	$0.659524\pi$
$908$	−9.11404	−0.302460
$909$	−55.5109	−1.84118
$910$	−6.80486	−0.225579
$911$	−12.5245	−0.414954	−0.207477	−	0.978240i	$-0.566525\pi$
$911$	−12.5245	−0.414954	−0.207477	+	0.978240i	$0.566525\pi$
$912$	−32.5731	−1.07860
$913$	−35.0368	−1.15955
$914$	81.9707	2.71135
$915$	−52.5174	−1.73617
$916$	−36.6497	−1.21094
$917$	−23.4968	−0.775932
$918$	5.61966	0.185476
$919$	−0.670485	−0.0221173	−0.0110586	−	0.999939i	$-0.503520\pi$
$919$	−0.670485	−0.0221173	−0.0110586	+	0.999939i	$0.503520\pi$
$920$	−22.5083	−0.742077
$921$	3.40960	0.112350
$922$	11.9204	0.392578
$923$	0.126418	0.00416109
$924$	−27.1819	−0.894218
$925$	−2.41476	−0.0793968
$926$	46.7554	1.53648
$927$	−47.2082	−1.55052
$928$	−67.0384	−2.20064
$929$	−24.4283	−0.801467	−0.400734	−	0.916195i	$-0.631245\pi$
$929$	−24.4283	−0.801467	−0.400734	+	0.916195i	$0.631245\pi$
$930$	−75.9413	−2.49021
$931$	−22.5945	−0.740504
$932$	−23.3313	−0.764243
$933$	72.4033	2.37038
$934$	−6.86181	−0.224525
$935$	0.662953	0.0216809
$936$	−13.7505	−0.449448
$937$	8.95072	0.292407	0.146204	−	0.989255i	$-0.453295\pi$
$937$	8.95072	0.292407	0.146204	+	0.989255i	$0.453295\pi$
$938$	53.0391	1.73179
$939$	−2.20069	−0.0718169
$940$	19.4670	0.634945
$941$	−22.7652	−0.742126	−0.371063	−	0.928608i	$-0.621007\pi$
$941$	−22.7652	−0.742126	−0.371063	+	0.928608i	$0.621007\pi$
$942$	−88.4186	−2.88084
$943$	77.6761	2.52948
$944$	18.1886	0.591988
$945$	32.0449	1.04242
$946$	12.0960	0.393274
$947$	30.7954	1.00072	0.500359	−	0.865818i	$-0.333202\pi$
$947$	30.7954	1.00072	0.500359	+	0.865818i	$0.333202\pi$
$948$	−45.3816	−1.47393
$949$	8.78586	0.285201
$950$	25.3180	0.821423
$951$	61.5518	1.99595
$952$	0.458198	0.0148503
$953$	40.5180	1.31251	0.656253	−	0.754541i	$-0.272140\pi$
$953$	40.5180	1.31251	0.656253	+	0.754541i	$0.272140\pi$
$954$	−3.82449	−0.123822
$955$	−19.7685	−0.639695
$956$	63.9476	2.06821
$957$	58.1242	1.87889
$958$	68.5392	2.21440
$959$	−23.2656	−0.751285
$960$	−62.7125	−2.02404
$961$	15.9818	0.515542
$962$	−2.77307	−0.0894074
$963$	89.1402	2.87250
$964$	−82.5945	−2.66019
$965$	18.5645	0.597612
$966$	−97.3607	−3.13253
$967$	−2.46735	−0.0793448	−0.0396724	−	0.999213i	$-0.512631\pi$
$967$	−2.46735	−0.0793448	−0.0396724	+	0.999213i	$0.512631\pi$
$968$	10.1121	0.325016
$969$	−3.05355	−0.0980941
$970$	8.40015	0.269713
$971$	−18.3502	−0.588885	−0.294443	−	0.955669i	$-0.595134\pi$
$971$	−18.3502	−0.588885	−0.294443	+	0.955669i	$0.595134\pi$
$972$	67.5114	2.16543
$973$	23.1454	0.742006
$974$	−78.1661	−2.50460
$975$	−9.82238	−0.314568
$976$	21.7597	0.696510
$977$	−41.2988	−1.32126	−0.660632	−	0.750710i	$-0.729712\pi$
$977$	−41.2988	−1.32126	−0.660632	+	0.750710i	$0.729712\pi$
$978$	6.89069	0.220340
$979$	−25.0341	−0.800093
$980$	−20.2593	−0.647159
$981$	−27.1695	−0.867456
$982$	−2.40868	−0.0768642
$983$	16.4952	0.526116	0.263058	−	0.964780i	$-0.415269\pi$
$983$	16.4952	0.526116	0.263058	+	0.964780i	$0.415269\pi$
$984$	−40.3343	−1.28581
$985$	3.46783	0.110494
$986$	−3.78860	−0.120654
$987$	21.7767	0.693161
$988$	16.6963	0.531182
$989$	24.8800	0.791137
$990$	51.4367	1.63477
$991$	16.1501	0.513024	0.256512	−	0.966541i	$-0.417427\pi$
$991$	16.1501	0.513024	0.256512	+	0.966541i	$0.417427\pi$
$992$	52.1937	1.65715
$993$	−91.1536	−2.89267
$994$	−0.326840	−0.0103667
$995$	−12.7961	−0.405663
$996$	144.700	4.58499
$997$	18.0719	0.572342	0.286171	−	0.958179i	$-0.407617\pi$
$997$	18.0719	0.572342	0.286171	+	0.958179i	$0.407617\pi$
$998$	11.1308	0.352339
$999$	13.0588	0.413161

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6031.2.a.e.1.19	✓	134

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6031.2.a.e.1.19	✓	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)

\(f(q)\)	\(=\)	\(q-2.16741 q^{2} +3.17923 q^{3} +2.69765 q^{4} +1.60787 q^{5} -6.89069 q^{6} +1.52618 q^{7} -1.51209 q^{8} +7.10752 q^{9} +O(q^{10})\)	\(q-2.16741 q^{2} +3.17923 q^{3} +2.69765 q^{4} +1.60787 q^{5} -6.89069 q^{6} +1.52618 q^{7} -1.51209 q^{8} +7.10752 q^{9} -3.48491 q^{10} -2.07666 q^{11} +8.57646 q^{12} +1.27944 q^{13} -3.30786 q^{14} +5.11179 q^{15} -2.11798 q^{16} -0.198549 q^{17} -15.4049 q^{18} +4.83743 q^{19} +4.33747 q^{20} +4.85210 q^{21} +4.50096 q^{22} +9.25793 q^{23} -4.80730 q^{24} -2.41476 q^{25} -2.77307 q^{26} +13.0588 q^{27} +4.11711 q^{28} -8.80380 q^{29} -11.0793 q^{30} +6.85433 q^{31} +7.61471 q^{32} -6.60217 q^{33} +0.430336 q^{34} +2.45390 q^{35} +19.1736 q^{36} +1.00000 q^{37} -10.4847 q^{38} +4.06765 q^{39} -2.43125 q^{40} +8.39023 q^{41} -10.5165 q^{42} +2.68742 q^{43} -5.60209 q^{44} +11.4280 q^{45} -20.0657 q^{46} +4.48811 q^{47} -6.73355 q^{48} -4.67076 q^{49} +5.23376 q^{50} -0.631233 q^{51} +3.45149 q^{52} +0.248265 q^{53} -28.3036 q^{54} -3.33899 q^{55} -2.30773 q^{56} +15.3793 q^{57} +19.0814 q^{58} -8.58770 q^{59} +13.7898 q^{60} -10.2738 q^{61} -14.8561 q^{62} +10.8474 q^{63} -12.2682 q^{64} +2.05718 q^{65} +14.3096 q^{66} -16.0343 q^{67} -0.535616 q^{68} +29.4331 q^{69} -5.31861 q^{70} +0.0988069 q^{71} -10.7472 q^{72} +6.86694 q^{73} -2.16741 q^{74} -7.67708 q^{75} +13.0497 q^{76} -3.16936 q^{77} -8.81624 q^{78} -5.29141 q^{79} -3.40544 q^{80} +20.1943 q^{81} -18.1850 q^{82} +16.8717 q^{83} +13.0893 q^{84} -0.319241 q^{85} -5.82474 q^{86} -27.9893 q^{87} +3.14010 q^{88} +12.0550 q^{89} -24.7690 q^{90} +1.95267 q^{91} +24.9747 q^{92} +21.7915 q^{93} -9.72756 q^{94} +7.77796 q^{95} +24.2089 q^{96} -2.41044 q^{97} +10.1234 q^{98} -14.7599 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 134 q + 9 q^{2} + 7 q^{3} + 149 q^{4} + 22 q^{5} + 20 q^{6} + 11 q^{7} + 27 q^{8} + 181 q^{9}+O(q^{10}) \) 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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