LMFDB - Embedded newform 6031.2.a.c.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:	$1$
Dimension:	$110$
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)

$f(q)$	$=$	$q-2.05303 q^{2} -2.17913 q^{3} +2.21492 q^{4} +2.99569 q^{5} +4.47382 q^{6} +4.05870 q^{7} -0.441239 q^{8} +1.74862 q^{9} +O(q^{10})$	\(q-2.05303 q^{2} -2.17913 q^{3} +2.21492 q^{4} +2.99569 q^{5} +4.47382 q^{6} +4.05870 q^{7} -0.441239 q^{8} +1.74862 q^{9} -6.15023 q^{10} -1.65984 q^{11} -4.82661 q^{12} -0.114568 q^{13} -8.33262 q^{14} -6.52800 q^{15} -3.52397 q^{16} -3.99694 q^{17} -3.58997 q^{18} -0.170584 q^{19} +6.63521 q^{20} -8.84445 q^{21} +3.40770 q^{22} +1.35414 q^{23} +0.961520 q^{24} +3.97415 q^{25} +0.235212 q^{26} +2.72692 q^{27} +8.98970 q^{28} +3.92675 q^{29} +13.4022 q^{30} -1.05407 q^{31} +8.11728 q^{32} +3.61702 q^{33} +8.20583 q^{34} +12.1586 q^{35} +3.87306 q^{36} -1.00000 q^{37} +0.350214 q^{38} +0.249659 q^{39} -1.32182 q^{40} -3.75659 q^{41} +18.1579 q^{42} +2.19903 q^{43} -3.67642 q^{44} +5.23833 q^{45} -2.78008 q^{46} -5.33826 q^{47} +7.67919 q^{48} +9.47305 q^{49} -8.15904 q^{50} +8.70987 q^{51} -0.253760 q^{52} -9.08471 q^{53} -5.59844 q^{54} -4.97237 q^{55} -1.79086 q^{56} +0.371725 q^{57} -8.06173 q^{58} +3.60455 q^{59} -14.4590 q^{60} +6.67105 q^{61} +2.16403 q^{62} +7.09713 q^{63} -9.61706 q^{64} -0.343211 q^{65} -7.42583 q^{66} -15.5070 q^{67} -8.85291 q^{68} -2.95085 q^{69} -24.9619 q^{70} -14.7997 q^{71} -0.771561 q^{72} -12.7195 q^{73} +2.05303 q^{74} -8.66020 q^{75} -0.377830 q^{76} -6.73680 q^{77} -0.512557 q^{78} -5.89616 q^{79} -10.5567 q^{80} -11.1882 q^{81} +7.71238 q^{82} -7.78485 q^{83} -19.5898 q^{84} -11.9736 q^{85} -4.51468 q^{86} -8.55691 q^{87} +0.732388 q^{88} +4.20686 q^{89} -10.7544 q^{90} -0.464998 q^{91} +2.99931 q^{92} +2.29695 q^{93} +10.9596 q^{94} -0.511016 q^{95} -17.6886 q^{96} +15.0230 q^{97} -19.4484 q^{98} -2.90244 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 110 q - 9 q^{2} + 97 q^{4} - 26 q^{5} - 26 q^{6} - 4 q^{7} - 27 q^{8} + 62 q^{9}+O(q^{10}) $ 110 * q - 9 * q^2 + 97 * q^4 - 26 * q^5 - 26 * q^6 - 4 * q^7 - 27 * q^8 + 62 * q^9	\( 110 q - 9 q^{2} + 97 q^{4} - 26 q^{5} - 26 q^{6} - 4 q^{7} - 27 q^{8} + 62 q^{9} - 17 q^{10} - 9 q^{11} - 21 q^{13} - 29 q^{14} - 23 q^{15} + 79 q^{16} - 76 q^{17} - 31 q^{18} - 27 q^{19} - 67 q^{20} - 30 q^{21} - 28 q^{22} - 32 q^{23} - 63 q^{24} + 66 q^{25} - 55 q^{26} - 4 q^{28} - 81 q^{29} - 48 q^{30} - 30 q^{31} - 73 q^{32} - 53 q^{33} - 23 q^{34} - 78 q^{35} + 7 q^{36} - 110 q^{37} - 50 q^{38} - 64 q^{39} - 37 q^{40} - 123 q^{41} - 63 q^{42} - 40 q^{43} - 31 q^{44} - 73 q^{45} + 16 q^{46} - 37 q^{47} - 29 q^{48} + 46 q^{49} - 58 q^{50} - 73 q^{51} - 39 q^{52} - 16 q^{53} - 53 q^{54} - 59 q^{55} - 113 q^{56} - 39 q^{57} + 11 q^{58} - 93 q^{59} - 18 q^{60} - 66 q^{61} - 40 q^{62} - 21 q^{63} + 23 q^{64} - 92 q^{65} - 31 q^{66} + q^{67} - 121 q^{68} - 80 q^{69} - 3 q^{70} - 75 q^{71} - 114 q^{72} - 39 q^{73} + 9 q^{74} - 25 q^{75} - 58 q^{76} - 31 q^{77} + 68 q^{78} - 36 q^{79} - 82 q^{80} - 50 q^{81} - 18 q^{82} - 57 q^{83} - 9 q^{84} - 14 q^{85} - 58 q^{86} - 58 q^{87} - 15 q^{88} - 181 q^{89} + 8 q^{90} - 55 q^{91} - 116 q^{92} - 86 q^{93} - 39 q^{94} - 70 q^{95} - 127 q^{96} - 91 q^{97} - 19 q^{98} - 21 q^{99}+O(q^{100}) \) 110 * q - 9 * q^2 + 97 * q^4 - 26 * q^5 - 26 * q^6 - 4 * q^7 - 27 * q^8 + 62 * q^9 - 17 * q^10 - 9 * q^11 - 21 * q^13 - 29 * q^14 - 23 * q^15 + 79 * q^16 - 76 * q^17 - 31 * q^18 - 27 * q^19 - 67 * q^20 - 30 * q^21 - 28 * q^22 - 32 * q^23 - 63 * q^24 + 66 * q^25 - 55 * q^26 - 4 * q^28 - 81 * q^29 - 48 * q^30 - 30 * q^31 - 73 * q^32 - 53 * q^33 - 23 * q^34 - 78 * q^35 + 7 * q^36 - 110 * q^37 - 50 * q^38 - 64 * q^39 - 37 * q^40 - 123 * q^41 - 63 * q^42 - 40 * q^43 - 31 * q^44 - 73 * q^45 + 16 * q^46 - 37 * q^47 - 29 * q^48 + 46 * q^49 - 58 * q^50 - 73 * q^51 - 39 * q^52 - 16 * q^53 - 53 * q^54 - 59 * q^55 - 113 * q^56 - 39 * q^57 + 11 * q^58 - 93 * q^59 - 18 * q^60 - 66 * q^61 - 40 * q^62 - 21 * q^63 + 23 * q^64 - 92 * q^65 - 31 * q^66 + q^67 - 121 * q^68 - 80 * q^69 - 3 * q^70 - 75 * q^71 - 114 * q^72 - 39 * q^73 + 9 * q^74 - 25 * q^75 - 58 * q^76 - 31 * q^77 + 68 * q^78 - 36 * q^79 - 82 * q^80 - 50 * q^81 - 18 * q^82 - 57 * q^83 - 9 * q^84 - 14 * q^85 - 58 * q^86 - 58 * q^87 - 15 * q^88 - 181 * q^89 + 8 * q^90 - 55 * q^91 - 116 * q^92 - 86 * q^93 - 39 * q^94 - 70 * q^95 - 127 * q^96 - 91 * q^97 - 19 * q^98 - 21 * 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 $

$2$	−2.05303	−1.45171	−0.725855	−	0.687848i	$-0.758556\pi$
$2$	−2.05303	−1.45171	−0.725855	+	0.687848i	$0.758556\pi$
$3$	−2.17913	−1.25812	−0.629062	−	0.777355i	$-0.716561\pi$
$3$	−2.17913	−1.25812	−0.629062	+	0.777355i	$0.716561\pi$
$4$	2.21492	1.10746
$5$	2.99569	1.33971	0.669856	−	0.742491i	$-0.266356\pi$
$5$	2.99569	1.33971	0.669856	+	0.742491i	$0.266356\pi$
$6$	4.47382	1.82643
$7$	4.05870	1.53404	0.767022	−	0.641621i	$-0.221738\pi$
$7$	4.05870	1.53404	0.767022	+	0.641621i	$0.221738\pi$
$8$	−0.441239	−0.156002
$9$	1.74862	0.582874
$10$	−6.15023	−1.94487
$11$	−1.65984	−0.500461	−0.250231	−	0.968186i	$-0.580506\pi$
$11$	−1.65984	−0.500461	−0.250231	+	0.968186i	$0.580506\pi$
$12$	−4.82661	−1.39332
$13$	−0.114568	−0.0317755	−0.0158877	−	0.999874i	$-0.505057\pi$
$13$	−0.114568	−0.0317755	−0.0158877	+	0.999874i	$0.505057\pi$
$14$	−8.33262	−2.22699
$15$	−6.52800	−1.68552
$16$	−3.52397	−0.880992
$17$	−3.99694	−0.969401	−0.484700	−	0.874680i	$-0.661071\pi$
$17$	−3.99694	−0.969401	−0.484700	+	0.874680i	$0.661071\pi$
$18$	−3.58997	−0.846164
$19$	−0.170584	−0.0391346	−0.0195673	−	0.999809i	$-0.506229\pi$
$19$	−0.170584	−0.0391346	−0.0195673	+	0.999809i	$0.506229\pi$
$20$	6.63521	1.48368
$21$	−8.84445	−1.93002
$22$	3.40770	0.726524
$23$	1.35414	0.282357	0.141179	−	0.989984i	$-0.454911\pi$
$23$	1.35414	0.282357	0.141179	+	0.989984i	$0.454911\pi$
$24$	0.961520	0.196269
$25$	3.97415	0.794830
$26$	0.235212	0.0461288
$27$	2.72692	0.524796
$28$	8.98970	1.69889
$29$	3.92675	0.729179	0.364590	−	0.931168i	$-0.381209\pi$
$29$	3.92675	0.729179	0.364590	+	0.931168i	$0.381209\pi$
$30$	13.4022	2.44689
$31$	−1.05407	−0.189316	−0.0946580	−	0.995510i	$-0.530176\pi$
$31$	−1.05407	−0.189316	−0.0946580	+	0.995510i	$0.530176\pi$
$32$	8.11728	1.43495
$33$	3.61702	0.629642
$34$	8.20583	1.40729
$35$	12.1586	2.05518
$36$	3.87306	0.645510
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	0.350214	0.0568121
$39$	0.249659	0.0399775
$40$	−1.32182	−0.208997
$41$	−3.75659	−0.586681	−0.293340	−	0.956008i	$-0.594767\pi$
$41$	−3.75659	−0.586681	−0.293340	+	0.956008i	$0.594767\pi$
$42$	18.1579	2.80182
$43$	2.19903	0.335350	0.167675	−	0.985842i	$-0.446374\pi$
$43$	2.19903	0.335350	0.167675	+	0.985842i	$0.446374\pi$
$44$	−3.67642	−0.554241
$45$	5.23833	0.780883
$46$	−2.78008	−0.409901
$47$	−5.33826	−0.778665	−0.389333	−	0.921097i	$-0.627294\pi$
$47$	−5.33826	−0.778665	−0.389333	+	0.921097i	$0.627294\pi$
$48$	7.67919	1.10840
$49$	9.47305	1.35329
$50$	−8.15904	−1.15386
$51$	8.70987	1.21963
$52$	−0.253760	−0.0351901
$53$	−9.08471	−1.24788	−0.623941	−	0.781472i	$-0.714469\pi$
$53$	−9.08471	−1.24788	−0.623941	+	0.781472i	$0.714469\pi$
$54$	−5.59844	−0.761851
$55$	−4.97237	−0.670474
$56$	−1.79086	−0.239314
$57$	0.371725	0.0492362
$58$	−8.06173	−1.05856
$59$	3.60455	0.469273	0.234636	−	0.972083i	$-0.424610\pi$
$59$	3.60455	0.469273	0.234636	+	0.972083i	$0.424610\pi$
$60$	−14.4590	−1.86665
$61$	6.67105	0.854141	0.427070	−	0.904218i	$-0.359546\pi$
$61$	6.67105	0.854141	0.427070	+	0.904218i	$0.359546\pi$
$62$	2.16403	0.274832
$63$	7.09713	0.894154
$64$	−9.61706	−1.20213
$65$	−0.343211	−0.0425700
$66$	−7.42583	−0.914057
$67$	−15.5070	−1.89448	−0.947242	−	0.320520i	$-0.896142\pi$
$67$	−15.5070	−1.89448	−0.947242	+	0.320520i	$0.896142\pi$
$68$	−8.85291	−1.07357
$69$	−2.95085	−0.355240
$70$	−24.9619	−2.98352
$71$	−14.7997	−1.75641	−0.878203	−	0.478288i	$-0.841258\pi$
$71$	−14.7997	−1.75641	−0.878203	+	0.478288i	$0.841258\pi$
$72$	−0.771561	−0.0909293
$73$	−12.7195	−1.48871	−0.744353	−	0.667786i	$-0.767242\pi$
$73$	−12.7195	−1.48871	−0.744353	+	0.667786i	$0.767242\pi$
$74$	2.05303	0.238660
$75$	−8.66020	−0.999994
$76$	−0.377830	−0.0433401
$77$	−6.73680	−0.767730
$78$	−0.512557	−0.0580357
$79$	−5.89616	−0.663370	−0.331685	−	0.943390i	$-0.607617\pi$
$79$	−5.89616	−0.663370	−0.331685	+	0.943390i	$0.607617\pi$
$80$	−10.5567	−1.18028
$81$	−11.1882	−1.24313
$82$	7.71238	0.851690
$83$	−7.78485	−0.854498	−0.427249	−	0.904134i	$-0.640517\pi$
$83$	−7.78485	−0.854498	−0.427249	+	0.904134i	$0.640517\pi$
$84$	−19.5898	−2.13742
$85$	−11.9736	−1.29872
$86$	−4.51468	−0.486830
$87$	−8.55691	−0.917397
$88$	0.732388	0.0780728
$89$	4.20686	0.445927	0.222963	−	0.974827i	$-0.428427\pi$
$89$	4.20686	0.445927	0.222963	+	0.974827i	$0.428427\pi$
$90$	−10.7544	−1.13362
$91$	−0.464998	−0.0487450
$92$	2.99931	0.312700
$93$	2.29695	0.238183
$94$	10.9596	1.13040
$95$	−0.511016	−0.0524292
$96$	−17.6886	−1.80534
$97$	15.0230	1.52535	0.762677	−	0.646780i	$-0.223885\pi$
$97$	15.0230	1.52535	0.762677	+	0.646780i	$0.223885\pi$
$98$	−19.4484	−1.96459
$99$	−2.90244	−0.291706
$100$	8.80243	0.880243
$101$	15.5805	1.55032	0.775161	−	0.631763i	$-0.217669\pi$
$101$	15.5805	1.55032	0.775161	+	0.631763i	$0.217669\pi$
$102$	−17.8816	−1.77054
$103$	19.5899	1.93025	0.965123	−	0.261798i	$-0.0843154\pi$
$103$	19.5899	1.93025	0.965123	+	0.261798i	$0.0843154\pi$
$104$	0.0505520	0.00495703
$105$	−26.4952	−2.58567
$106$	18.6512	1.81156
$107$	−10.2757	−0.993391	−0.496695	−	0.867925i	$-0.665453\pi$
$107$	−10.2757	−0.993391	−0.496695	+	0.867925i	$0.665453\pi$
$108$	6.03991	0.581191
$109$	−11.1798	−1.07083	−0.535416	−	0.844589i	$-0.679845\pi$
$109$	−11.1798	−1.07083	−0.535416	+	0.844589i	$0.679845\pi$
$110$	10.2084	0.973334
$111$	2.17913	0.206834
$112$	−14.3027	−1.35148
$113$	−4.13820	−0.389289	−0.194645	−	0.980874i	$-0.562355\pi$
$113$	−4.13820	−0.389289	−0.194645	+	0.980874i	$0.562355\pi$
$114$	−0.763162	−0.0714767
$115$	4.05658	0.378278
$116$	8.69744	0.807537
$117$	−0.200336	−0.0185211
$118$	−7.40024	−0.681248
$119$	−16.2224	−1.48710
$120$	2.88041	0.262945
$121$	−8.24493	−0.749539
$122$	−13.6959	−1.23996
$123$	8.18611	0.738116
$124$	−2.33467	−0.209660
$125$	−3.07313	−0.274869
$126$	−14.5706	−1.29805
$127$	−12.6712	−1.12439	−0.562194	−	0.827005i	$-0.690043\pi$
$127$	−12.6712	−1.12439	−0.562194	+	0.827005i	$0.690043\pi$
$128$	3.50953	0.310202
$129$	−4.79199	−0.421911
$130$	0.704621	0.0617993
$131$	5.97374	0.521928	0.260964	−	0.965349i	$-0.415960\pi$
$131$	5.97374	0.521928	0.260964	+	0.965349i	$0.415960\pi$
$132$	8.01141	0.697303
$133$	−0.692349	−0.0600343
$134$	31.8363	2.75024
$135$	8.16900	0.703076
$136$	1.76361	0.151228
$137$	−5.93404	−0.506979	−0.253490	−	0.967338i	$-0.581578\pi$
$137$	−5.93404	−0.506979	−0.253490	+	0.967338i	$0.581578\pi$
$138$	6.05817	0.515706
$139$	10.4561	0.886877	0.443439	−	0.896305i	$-0.353758\pi$
$139$	10.4561	0.886877	0.443439	+	0.896305i	$0.353758\pi$
$140$	26.9303	2.27603
$141$	11.6328	0.979657
$142$	30.3843	2.54979
$143$	0.190165	0.0159024
$144$	−6.16208	−0.513507
$145$	11.7633	0.976891
$146$	26.1135	2.16117
$147$	−20.6430	−1.70261
$148$	−2.21492	−0.182065
$149$	−7.04825	−0.577415	−0.288708	−	0.957417i	$-0.593226\pi$
$149$	−7.04825	−0.577415	−0.288708	+	0.957417i	$0.593226\pi$
$150$	17.7796	1.45170
$151$	9.80203	0.797678	0.398839	−	0.917021i	$-0.369413\pi$
$151$	9.80203	0.797678	0.398839	+	0.917021i	$0.369413\pi$
$152$	0.0752684	0.00610507
$153$	−6.98914	−0.565038
$154$	13.8308	1.11452
$155$	−3.15765	−0.253629
$156$	0.552976	0.0442735
$157$	−20.3512	−1.62420	−0.812102	−	0.583515i	$-0.801677\pi$
$157$	−20.3512	−1.62420	−0.812102	+	0.583515i	$0.801677\pi$
$158$	12.1050	0.963020
$159$	19.7968	1.56999
$160$	24.3168	1.92241
$161$	5.49604	0.433149
$162$	22.9697	1.80467
$163$	−1.00000	−0.0783260
$163$	−1.00000	−0.0783260
$164$	−8.32055	−0.649726
$165$	10.8355	0.843539
$166$	15.9825	1.24048
$167$	13.8360	1.07066	0.535331	−	0.844642i	$-0.320187\pi$
$167$	13.8360	1.07066	0.535331	+	0.844642i	$0.320187\pi$
$168$	3.90252	0.301086
$169$	−12.9869	−0.998990
$170$	24.5821	1.88536
$171$	−0.298287	−0.0228106
$172$	4.87069	0.371387
$173$	0.154488	0.0117455	0.00587274	−	0.999983i	$-0.498131\pi$
$173$	0.154488	0.0117455	0.00587274	+	0.999983i	$0.498131\pi$
$174$	17.5676	1.33179
$175$	16.1299	1.21930
$176$	5.84923	0.440902
$177$	−7.85480	−0.590403
$178$	−8.63681	−0.647356
$179$	−22.3448	−1.67013	−0.835064	−	0.550152i	$-0.814570\pi$
$179$	−22.3448	−1.67013	−0.835064	+	0.550152i	$0.814570\pi$
$180$	11.6025	0.864798
$181$	−1.23171	−0.0915522	−0.0457761	−	0.998952i	$-0.514576\pi$
$181$	−1.23171	−0.0915522	−0.0457761	+	0.998952i	$0.514576\pi$
$182$	0.954653	0.0707636
$183$	−14.5371	−1.07461
$184$	−0.597499	−0.0440482
$185$	−2.99569	−0.220247
$186$	−4.71570	−0.345772
$187$	6.63429	0.485147
$188$	−11.8238	−0.862341
$189$	11.0678	0.805060
$190$	1.04913	0.0761119
$191$	−9.72195	−0.703456	−0.351728	−	0.936102i	$-0.614406\pi$
$191$	−9.72195	−0.703456	−0.351728	+	0.936102i	$0.614406\pi$
$192$	20.9569	1.51243
$193$	17.2737	1.24339	0.621694	−	0.783260i	$-0.286445\pi$
$193$	17.2737	1.24339	0.621694	+	0.783260i	$0.286445\pi$
$194$	−30.8426	−2.21437
$195$	0.747902	0.0535583
$196$	20.9821	1.49872
$197$	−23.3207	−1.66153	−0.830766	−	0.556622i	$-0.812097\pi$
$197$	−23.3207	−1.66153	−0.830766	+	0.556622i	$0.812097\pi$
$198$	5.95878	0.423472
$199$	−0.0750513	−0.00532024	−0.00266012	−	0.999996i	$-0.500847\pi$
$199$	−0.0750513	−0.00532024	−0.00266012	+	0.999996i	$0.500847\pi$
$200$	−1.75355	−0.123995
$201$	33.7919	2.38349
$202$	−31.9873	−2.25062
$203$	15.9375	1.11859
$204$	19.2917	1.35069
$205$	−11.2536	−0.785983
$206$	−40.2185	−2.80216
$207$	2.36788	0.164579
$208$	0.403734	0.0279939
$209$	0.283142	0.0195854
$210$	54.3954	3.75364
$211$	21.6070	1.48749	0.743745	−	0.668464i	$-0.233048\pi$
$211$	21.6070	1.48749	0.743745	+	0.668464i	$0.233048\pi$
$212$	−20.1219	−1.38198
$213$	32.2506	2.20978
$214$	21.0963	1.44211
$215$	6.58762	0.449272
$216$	−1.20322	−0.0818691
$217$	−4.27814	−0.290419
$218$	22.9525	1.55454
$219$	27.7175	1.87298
$220$	−11.0134	−0.742524
$221$	0.457922	0.0308032
$222$	−4.47382	−0.300263
$223$	17.2273	1.15362	0.576812	−	0.816877i	$-0.304297\pi$
$223$	17.2273	1.15362	0.576812	+	0.816877i	$0.304297\pi$
$224$	32.9456	2.20127
$225$	6.94928	0.463286
$226$	8.49584	0.565135
$227$	−3.56271	−0.236465	−0.118233	−	0.992986i	$-0.537723\pi$
$227$	−3.56271	−0.236465	−0.118233	+	0.992986i	$0.537723\pi$
$228$	0.823342	0.0545272
$229$	−18.7833	−1.24124	−0.620618	−	0.784113i	$-0.713118\pi$
$229$	−18.7833	−1.24124	−0.620618	+	0.784113i	$0.713118\pi$
$230$	−8.32826	−0.549149
$231$	14.6804	0.965898
$232$	−1.73264	−0.113753
$233$	−13.0586	−0.855499	−0.427750	−	0.903897i	$-0.640693\pi$
$233$	−13.0586	−0.855499	−0.427750	+	0.903897i	$0.640693\pi$
$234$	0.411296	0.0268873
$235$	−15.9918	−1.04319
$236$	7.98380	0.519701
$237$	12.8485	0.834601
$238$	33.3050	2.15884
$239$	−20.3395	−1.31566	−0.657828	−	0.753168i	$-0.728524\pi$
$239$	−20.3395	−1.31566	−0.657828	+	0.753168i	$0.728524\pi$
$240$	23.0045	1.48493
$241$	−7.80883	−0.503011	−0.251506	−	0.967856i	$-0.580926\pi$
$241$	−7.80883	−0.503011	−0.251506	+	0.967856i	$0.580926\pi$
$242$	16.9271	1.08811
$243$	16.1998	1.03922
$244$	14.7759	0.945927
$245$	28.3783	1.81302
$246$	−16.8063	−1.07153
$247$	0.0195435	0.00124352
$248$	0.465096	0.0295336
$249$	16.9642	1.07506
$250$	6.30922	0.399030
$251$	−18.3147	−1.15602	−0.578008	−	0.816031i	$-0.696170\pi$
$251$	−18.3147	−1.15602	−0.578008	+	0.816031i	$0.696170\pi$
$252$	15.7196	0.990241
$253$	−2.24766	−0.141309
$254$	26.0143	1.63228
$255$	26.0920	1.63395
$256$	12.0290	0.751809
$257$	24.7544	1.54414	0.772069	−	0.635539i	$-0.219222\pi$
$257$	24.7544	1.54414	0.772069	+	0.635539i	$0.219222\pi$
$258$	9.83809	0.612492
$259$	−4.05870	−0.252195
$260$	−0.760184	−0.0471446
$261$	6.86640	0.425020
$262$	−12.2642	−0.757688
$263$	13.7612	0.848554	0.424277	−	0.905532i	$-0.360528\pi$
$263$	13.7612	0.848554	0.424277	+	0.905532i	$0.360528\pi$
$264$	−1.59597	−0.0982252
$265$	−27.2150	−1.67180
$266$	1.42141	0.0871523
$267$	−9.16732	−0.561031
$268$	−34.3468	−2.09807
$269$	−11.1336	−0.678829	−0.339414	−	0.940637i	$-0.610229\pi$
$269$	−11.1336	−0.678829	−0.339414	+	0.940637i	$0.610229\pi$
$270$	−16.7712	−1.02066
$271$	−1.75613	−0.106677	−0.0533386	−	0.998576i	$-0.516986\pi$
$271$	−1.75613	−0.106677	−0.0533386	+	0.998576i	$0.516986\pi$
$272$	14.0851	0.854034
$273$	1.01329	0.0613272
$274$	12.1827	0.735986
$275$	−6.59646	−0.397781
$276$	−6.53590	−0.393415
$277$	12.5845	0.756132	0.378066	−	0.925779i	$-0.376589\pi$
$277$	12.5845	0.756132	0.378066	+	0.925779i	$0.376589\pi$
$278$	−21.4667	−1.28749
$279$	−1.84316	−0.110347
$280$	−5.36485	−0.320611
$281$	−13.5810	−0.810173	−0.405087	−	0.914278i	$-0.632759\pi$
$281$	−13.5810	−0.810173	−0.405087	+	0.914278i	$0.632759\pi$
$282$	−23.8824	−1.42218
$283$	−18.1766	−1.08048	−0.540242	−	0.841510i	$-0.681667\pi$
$283$	−18.1766	−1.08048	−0.540242	+	0.841510i	$0.681667\pi$
$284$	−32.7803	−1.94515
$285$	1.11357	0.0659624
$286$	−0.390414	−0.0230857
$287$	−15.2469	−0.899994
$288$	14.1940	0.836392
$289$	−1.02447	−0.0602627
$290$	−24.1504	−1.41816
$291$	−32.7371	−1.91908
$292$	−28.1727	−1.64868
$293$	18.7918	1.09783	0.548913	−	0.835879i	$-0.315042\pi$
$293$	18.7918	1.09783	0.548913	+	0.835879i	$0.315042\pi$
$294$	42.3807	2.47169
$295$	10.7981	0.628691
$296$	0.441239	0.0256465
$297$	−4.52626	−0.262640
$298$	14.4703	0.838239
$299$	−0.155141	−0.00897204
$300$	−19.1817	−1.10745
$301$	8.92522	0.514441
$302$	−20.1238	−1.15800
$303$	−33.9521	−1.95050
$304$	0.601132	0.0344773
$305$	19.9844	1.14430
$306$	14.3489	0.820271
$307$	21.5314	1.22886	0.614432	−	0.788970i	$-0.289385\pi$
$307$	21.5314	1.22886	0.614432	+	0.788970i	$0.289385\pi$
$308$	−14.9215	−0.850230
$309$	−42.6889	−2.42849
$310$	6.48275	0.368196
$311$	19.4272	1.10162	0.550808	−	0.834632i	$-0.314320\pi$
$311$	19.4272	1.10162	0.550808	+	0.834632i	$0.314320\pi$
$312$	−0.110160	−0.00623656
$313$	2.83660	0.160334	0.0801672	−	0.996781i	$-0.474455\pi$
$313$	2.83660	0.160334	0.0801672	+	0.996781i	$0.474455\pi$
$314$	41.7816	2.35787
$315$	21.2608	1.19791
$316$	−13.0595	−0.734656
$317$	−9.14125	−0.513424	−0.256712	−	0.966488i	$-0.582639\pi$
$317$	−9.14125	−0.513424	−0.256712	+	0.966488i	$0.582639\pi$
$318$	−40.6434	−2.27917
$319$	−6.51778	−0.364926
$320$	−28.8097	−1.61051
$321$	22.3922	1.24981
$322$	−11.2835	−0.628806
$323$	0.681814	0.0379371
$324$	−24.7810	−1.37672
$325$	−0.455311	−0.0252561
$326$	2.05303	0.113707
$327$	24.3623	1.34724
$328$	1.65756	0.0915232
$329$	−21.6664	−1.19451
$330$	−22.2455	−1.22457
$331$	−19.5702	−1.07567	−0.537837	−	0.843049i	$-0.680759\pi$
$331$	−19.5702	−1.07567	−0.537837	+	0.843049i	$0.680759\pi$
$332$	−17.2428	−0.946323
$333$	−1.74862	−0.0958239
$334$	−28.4057	−1.55429
$335$	−46.4542	−2.53806
$336$	31.1675	1.70033
$337$	17.4656	0.951414	0.475707	−	0.879604i	$-0.342192\pi$
$337$	17.4656	0.951414	0.475707	+	0.879604i	$0.342192\pi$
$338$	26.6624	1.45024
$339$	9.01769	0.489774
$340$	−26.5206	−1.43828
$341$	1.74958	0.0947453
$342$	0.612391	0.0331143
$343$	10.0374	0.541966
$344$	−0.970301	−0.0523151
$345$	−8.83982	−0.475920
$346$	−0.317167	−0.0170510
$347$	−0.433378	−0.0232649	−0.0116325	−	0.999932i	$-0.503703\pi$
$347$	−0.433378	−0.0232649	−0.0116325	+	0.999932i	$0.503703\pi$
$348$	−18.9529	−1.01598
$349$	−24.8740	−1.33148	−0.665738	−	0.746186i	$-0.731883\pi$
$349$	−24.8740	−1.33148	−0.665738	+	0.746186i	$0.731883\pi$
$350$	−33.1151	−1.77008
$351$	−0.312418	−0.0166757
$352$	−13.4734	−0.718134
$353$	−20.3440	−1.08280	−0.541401	−	0.840765i	$-0.682106\pi$
$353$	−20.3440	−1.08280	−0.541401	+	0.840765i	$0.682106\pi$
$354$	16.1261	0.857093
$355$	−44.3354	−2.35308
$356$	9.31787	0.493846
$357$	35.3507	1.87096
$358$	45.8745	2.42454
$359$	28.1554	1.48599	0.742993	−	0.669299i	$-0.233405\pi$
$359$	28.1554	1.48599	0.742993	+	0.669299i	$0.233405\pi$
$360$	−2.31136	−0.121819
$361$	−18.9709	−0.998468
$362$	2.52873	0.132907
$363$	17.9668	0.943012
$364$	−1.02993	−0.0539832
$365$	−38.1037	−1.99444
$366$	29.8451	1.56003
$367$	8.34607	0.435661	0.217831	−	0.975987i	$-0.430102\pi$
$367$	8.34607	0.435661	0.217831	+	0.975987i	$0.430102\pi$
$368$	−4.77194	−0.248754
$369$	−6.56885	−0.341961
$370$	6.15023	0.319735
$371$	−36.8721	−1.91431
$372$	5.08757	0.263778
$373$	−18.2591	−0.945420	−0.472710	−	0.881218i	$-0.656724\pi$
$373$	−18.2591	−0.945420	−0.472710	+	0.881218i	$0.656724\pi$
$374$	−13.6204	−0.704293
$375$	6.69676	0.345819
$376$	2.35545	0.121473
$377$	−0.449881	−0.0231700
$378$	−22.7224	−1.16871
$379$	1.80656	0.0927967	0.0463984	−	0.998923i	$-0.485226\pi$
$379$	1.80656	0.0927967	0.0463984	+	0.998923i	$0.485226\pi$
$380$	−1.13186	−0.0580633
$381$	27.6122	1.41462
$382$	19.9594	1.02121
$383$	17.0977	0.873652	0.436826	−	0.899546i	$-0.356102\pi$
$383$	17.0977	0.873652	0.436826	+	0.899546i	$0.356102\pi$
$384$	−7.64774	−0.390272
$385$	−20.1814	−1.02854
$386$	−35.4634	−1.80504
$387$	3.84528	0.195467
$388$	33.2748	1.68927
$389$	8.90534	0.451519	0.225759	−	0.974183i	$-0.427514\pi$
$389$	8.90534	0.451519	0.225759	+	0.974183i	$0.427514\pi$
$390$	−1.53546	−0.0777512
$391$	−5.41241	−0.273717
$392$	−4.17988	−0.211116
$393$	−13.0176	−0.656650
$394$	47.8781	2.41206
$395$	−17.6631	−0.888725
$396$	−6.42867	−0.323053
$397$	26.0850	1.30917	0.654585	−	0.755988i	$-0.272843\pi$
$397$	26.0850	1.30917	0.654585	+	0.755988i	$0.272843\pi$
$398$	0.154082	0.00772345
$399$	1.50872	0.0755305
$400$	−14.0048	−0.700238
$401$	12.3759	0.618025	0.309012	−	0.951058i	$-0.400002\pi$
$401$	12.3759	0.618025	0.309012	+	0.951058i	$0.400002\pi$
$402$	−69.3756	−3.46014
$403$	0.120762	0.00601561
$404$	34.5097	1.71692
$405$	−33.5163	−1.66544
$406$	−32.7201	−1.62387
$407$	1.65984	0.0822753
$408$	−3.84314	−0.190264
$409$	21.2822	1.05234	0.526169	−	0.850380i	$-0.323628\pi$
$409$	21.2822	1.05234	0.526169	+	0.850380i	$0.323628\pi$
$410$	23.1039	1.14102
$411$	12.9311	0.637842
$412$	43.3900	2.13767
$413$	14.6298	0.719885
$414$	−4.86131	−0.238920
$415$	−23.3210	−1.14478
$416$	−0.929982	−0.0455961
$417$	−22.7853	−1.11580
$418$	−0.581299	−0.0284323
$419$	−23.4377	−1.14500	−0.572502	−	0.819903i	$-0.694027\pi$
$419$	−23.4377	−1.14500	−0.572502	+	0.819903i	$0.694027\pi$
$420$	−58.6848	−2.86353
$421$	12.5718	0.612711	0.306355	−	0.951917i	$-0.400890\pi$
$421$	12.5718	0.612711	0.306355	+	0.951917i	$0.400890\pi$
$422$	−44.3598	−2.15940
$423$	−9.33460	−0.453864
$424$	4.00853	0.194672
$425$	−15.8844	−0.770508
$426$	−66.2114	−3.20795
$427$	27.0758	1.31029
$428$	−22.7599	−1.10014
$429$	−0.414395	−0.0200072
$430$	−13.5246	−0.652213
$431$	7.06574	0.340345	0.170172	−	0.985414i	$-0.445568\pi$
$431$	7.06574	0.340345	0.170172	+	0.985414i	$0.445568\pi$
$432$	−9.60957	−0.462341
$433$	33.1198	1.59164	0.795818	−	0.605536i	$-0.207041\pi$
$433$	33.1198	1.59164	0.795818	+	0.605536i	$0.207041\pi$
$434$	8.78314	0.421604
$435$	−25.6338	−1.22905
$436$	−24.7624	−1.18590
$437$	−0.230994	−0.0110500
$438$	−56.9048	−2.71902
$439$	17.5649	0.838329	0.419164	−	0.907910i	$-0.362323\pi$
$439$	17.5649	0.838329	0.419164	+	0.907910i	$0.362323\pi$
$440$	2.19401	0.104595
$441$	16.5648	0.788799
$442$	−0.940127	−0.0447173
$443$	4.42096	0.210046	0.105023	−	0.994470i	$-0.466508\pi$
$443$	4.42096	0.210046	0.105023	+	0.994470i	$0.466508\pi$
$444$	4.82661	0.229061
$445$	12.6025	0.597414
$446$	−35.3681	−1.67473
$447$	15.3591	0.726459
$448$	−39.0328	−1.84412
$449$	−35.4341	−1.67224	−0.836120	−	0.548546i	$-0.815181\pi$
$449$	−35.4341	−1.67224	−0.836120	+	0.548546i	$0.815181\pi$
$450$	−14.2671	−0.672556
$451$	6.23534	0.293611
$452$	−9.16579	−0.431123
$453$	−21.3599	−1.00358
$454$	7.31434	0.343279
$455$	−1.39299	−0.0653043
$456$	−0.164020	−0.00768093
$457$	8.59280	0.401954	0.200977	−	0.979596i	$-0.435588\pi$
$457$	8.59280	0.401954	0.200977	+	0.979596i	$0.435588\pi$
$458$	38.5627	1.80192
$459$	−10.8993	−0.508738
$460$	8.98500	0.418928
$461$	15.9900	0.744729	0.372364	−	0.928087i	$-0.378547\pi$
$461$	15.9900	0.744729	0.372364	+	0.928087i	$0.378547\pi$
$462$	−30.1392	−1.40220
$463$	17.6459	0.820074	0.410037	−	0.912069i	$-0.365516\pi$
$463$	17.6459	0.820074	0.410037	+	0.912069i	$0.365516\pi$
$464$	−13.8377	−0.642401
$465$	6.88095	0.319096
$466$	26.8097	1.24194
$467$	3.71548	0.171932	0.0859660	−	0.996298i	$-0.472602\pi$
$467$	3.71548	0.171932	0.0859660	+	0.996298i	$0.472602\pi$
$468$	−0.443729	−0.0205114
$469$	−62.9383	−2.90622
$470$	32.8315	1.51441
$471$	44.3480	2.04345
$472$	−1.59047	−0.0732073
$473$	−3.65005	−0.167829
$474$	−26.3784	−1.21160
$475$	−0.677926	−0.0311054
$476$	−35.9313	−1.64691
$477$	−15.8857	−0.727357
$478$	41.7576	1.90995
$479$	−2.22645	−0.101729	−0.0508646	−	0.998706i	$-0.516198\pi$
$479$	−2.22645	−0.101729	−0.0508646	+	0.998706i	$0.516198\pi$
$480$	−52.9896	−2.41863
$481$	0.114568	0.00522386
$482$	16.0317	0.730226
$483$	−11.9766	−0.544954
$484$	−18.2619	−0.830085
$485$	45.0042	2.04354
$486$	−33.2586	−1.50864
$487$	25.8091	1.16952	0.584761	−	0.811205i	$-0.301188\pi$
$487$	25.8091	1.16952	0.584761	+	0.811205i	$0.301188\pi$
$488$	−2.94353	−0.133247
$489$	2.17913	0.0985438
$490$	−58.2614	−2.63198
$491$	29.0282	1.31002	0.655011	−	0.755619i	$-0.272664\pi$
$491$	29.0282	1.31002	0.655011	+	0.755619i	$0.272664\pi$
$492$	18.1316	0.817435
$493$	−15.6950	−0.706867
$494$	−0.0401233	−0.00180523
$495$	−8.69479	−0.390802
$496$	3.71449	0.166786
$497$	−60.0677	−2.69441
$498$	−34.8280	−1.56068
$499$	19.8299	0.887707	0.443853	−	0.896099i	$-0.353611\pi$
$499$	19.8299	0.887707	0.443853	+	0.896099i	$0.353611\pi$
$500$	−6.80674	−0.304407
$501$	−30.1505	−1.34703
$502$	37.6007	1.67820
$503$	−32.3430	−1.44210	−0.721051	−	0.692882i	$-0.756341\pi$
$503$	−32.3430	−1.44210	−0.721051	+	0.692882i	$0.756341\pi$
$504$	−3.13153	−0.139490
$505$	46.6745	2.07699
$506$	4.61450	0.205139
$507$	28.3001	1.25685
$508$	−28.0657	−1.24522
$509$	22.9663	1.01796	0.508981	−	0.860778i	$-0.330022\pi$
$509$	22.9663	1.01796	0.508981	+	0.860778i	$0.330022\pi$
$510$	−53.5677	−2.37202
$511$	−51.6247	−2.28374
$512$	−31.7148	−1.40161
$513$	−0.465169	−0.0205377
$514$	−50.8215	−2.24164
$515$	58.6851	2.58597
$516$	−10.6139	−0.467250
$517$	8.86067	0.389692
$518$	8.33262	0.366114
$519$	−0.336649	−0.0147773
$520$	0.151438	0.00664100
$521$	−25.4296	−1.11409	−0.557045	−	0.830482i	$-0.688065\pi$
$521$	−25.4296	−1.11409	−0.557045	+	0.830482i	$0.688065\pi$
$522$	−14.0969	−0.617005
$523$	19.6599	0.859667	0.429833	−	0.902908i	$-0.358572\pi$
$523$	19.6599	0.859667	0.429833	+	0.902908i	$0.358572\pi$
$524$	13.2314	0.578015
$525$	−35.1492	−1.53403
$526$	−28.2522	−1.23185
$527$	4.21304	0.183523
$528$	−12.7462	−0.554709
$529$	−21.1663	−0.920274
$530$	55.8731	2.42697
$531$	6.30300	0.273527
$532$	−1.53350	−0.0664856
$533$	0.430386	0.0186421
$534$	18.8208	0.814454
$535$	−30.7828	−1.33086
$536$	6.84231	0.295543
$537$	48.6923	2.10123
$538$	22.8576	0.985462
$539$	−15.7238	−0.677270
$540$	18.0937	0.778629
$541$	−34.2676	−1.47328	−0.736641	−	0.676284i	$-0.763589\pi$
$541$	−34.2676	−1.47328	−0.736641	+	0.676284i	$0.763589\pi$
$542$	3.60538	0.154864
$543$	2.68406	0.115184
$544$	−32.4443	−1.39104
$545$	−33.4912	−1.43461
$546$	−2.08032	−0.0890294
$547$	−39.7096	−1.69786	−0.848930	−	0.528506i	$-0.822753\pi$
$547$	−39.7096	−1.69786	−0.848930	+	0.528506i	$0.822753\pi$
$548$	−13.1434	−0.561459
$549$	11.6651	0.497856
$550$	13.5427	0.577463
$551$	−0.669841	−0.0285362
$552$	1.30203	0.0554181
$553$	−23.9307	−1.01764
$554$	−25.8364	−1.09768
$555$	6.52800	0.277098
$556$	23.1595	0.982182
$557$	18.2559	0.773528	0.386764	−	0.922179i	$-0.373593\pi$
$557$	18.2559	0.773528	0.386764	+	0.922179i	$0.373593\pi$
$558$	3.78406	0.160192
$559$	−0.251939	−0.0106559
$560$	−42.8465	−1.81059
$561$	−14.4570	−0.610375
$562$	27.8821	1.17614
$563$	17.2113	0.725369	0.362685	−	0.931912i	$-0.381860\pi$
$563$	17.2113	0.725369	0.362685	+	0.931912i	$0.381860\pi$
$564$	25.7657	1.08493
$565$	−12.3968	−0.521536
$566$	37.3170	1.56855
$567$	−45.4095	−1.90702
$568$	6.53023	0.274002
$569$	−16.8944	−0.708251	−0.354126	−	0.935198i	$-0.615221\pi$
$569$	−16.8944	−0.708251	−0.354126	+	0.935198i	$0.615221\pi$
$570$	−2.28620	−0.0957582
$571$	1.27372	0.0533035	0.0266518	−	0.999645i	$-0.491515\pi$
$571$	1.27372	0.0533035	0.0266518	+	0.999645i	$0.491515\pi$
$572$	0.421201	0.0176113
$573$	21.1854	0.885034
$574$	31.3022	1.30653
$575$	5.38155	0.224426
$576$	−16.8166	−0.700692
$577$	−4.82286	−0.200778	−0.100389	−	0.994948i	$-0.532009\pi$
$577$	−4.82286	−0.200778	−0.100389	+	0.994948i	$0.532009\pi$
$578$	2.10326	0.0874839
$579$	−37.6417	−1.56433
$580$	26.0548	1.08187
$581$	−31.5964	−1.31084
$582$	67.2102	2.78595
$583$	15.0792	0.624516
$584$	5.61235	0.232241
$585$	−0.600145	−0.0248130
$586$	−38.5800	−1.59372
$587$	13.1010	0.540737	0.270369	−	0.962757i	$-0.412854\pi$
$587$	13.1010	0.540737	0.270369	+	0.962757i	$0.412854\pi$
$588$	−45.7227	−1.88557
$589$	0.179807	0.00740881
$590$	−22.1688	−0.912676
$591$	50.8189	2.09041
$592$	3.52397	0.144834
$593$	−46.5915	−1.91328	−0.956642	−	0.291265i	$-0.905924\pi$
$593$	−46.5915	−1.91328	−0.956642	+	0.291265i	$0.905924\pi$
$594$	9.29253	0.381277
$595$	−48.5972	−1.99229
$596$	−15.6113	−0.639465
$597$	0.163547	0.00669352
$598$	0.318509	0.0130248
$599$	−16.6789	−0.681483	−0.340742	−	0.940157i	$-0.610678\pi$
$599$	−16.6789	−0.681483	−0.340742	+	0.940157i	$0.610678\pi$
$600$	3.82122	0.156001
$601$	−20.8992	−0.852496	−0.426248	−	0.904606i	$-0.640165\pi$
$601$	−20.8992	−0.852496	−0.426248	+	0.904606i	$0.640165\pi$
$602$	−18.3237	−0.746819
$603$	−27.1159	−1.10424
$604$	21.7107	0.883397
$605$	−24.6992	−1.00417
$606$	69.7046	2.83155
$607$	21.2653	0.863131	0.431566	−	0.902082i	$-0.357961\pi$
$607$	21.2653	0.863131	0.431566	+	0.902082i	$0.357961\pi$
$608$	−1.38468	−0.0561561
$609$	−34.7299	−1.40733
$610$	−41.0285	−1.66120
$611$	0.611595	0.0247425
$612$	−15.4804	−0.625758
$613$	44.4963	1.79719	0.898594	−	0.438781i	$-0.144590\pi$
$613$	44.4963	1.79719	0.898594	+	0.438781i	$0.144590\pi$
$614$	−44.2047	−1.78395
$615$	24.5230	0.988864
$616$	2.97254	0.119767
$617$	35.0053	1.40926	0.704630	−	0.709575i	$-0.251113\pi$
$617$	35.0053	1.40926	0.704630	+	0.709575i	$0.251113\pi$
$618$	87.6415	3.52546
$619$	−12.3936	−0.498142	−0.249071	−	0.968485i	$-0.580125\pi$
$619$	−12.3936	−0.498142	−0.249071	+	0.968485i	$0.580125\pi$
$620$	−6.99396	−0.280884
$621$	3.69263	0.148180
$622$	−39.8846	−1.59923
$623$	17.0744	0.684071
$624$	−0.879791	−0.0352198
$625$	−29.0769	−1.16308
$626$	−5.82362	−0.232759
$627$	−0.617005	−0.0246408
$628$	−45.0764	−1.79874
$629$	3.99694	0.159368
$630$	−43.6490	−1.73902
$631$	−23.8525	−0.949554	−0.474777	−	0.880106i	$-0.657471\pi$
$631$	−23.8525	−0.949554	−0.474777	+	0.880106i	$0.657471\pi$
$632$	2.60162	0.103487
$633$	−47.0846	−1.87144
$634$	18.7672	0.745342
$635$	−37.9590	−1.50636
$636$	43.8484	1.73870
$637$	−1.08531	−0.0430015
$638$	13.3812	0.529766
$639$	−25.8792	−1.02376
$640$	10.5135	0.415581
$641$	−37.7287	−1.49019	−0.745096	−	0.666957i	$-0.767596\pi$
$641$	−37.7287	−1.49019	−0.745096	+	0.666957i	$0.767596\pi$
$642$	−45.9717	−1.81436
$643$	−22.9160	−0.903718	−0.451859	−	0.892089i	$-0.649239\pi$
$643$	−22.9160	−0.903718	−0.451859	+	0.892089i	$0.649239\pi$
$644$	12.1733	0.479695
$645$	−14.3553	−0.565240
$646$	−1.39978	−0.0550737
$647$	−0.822594	−0.0323395	−0.0161698	−	0.999869i	$-0.505147\pi$
$647$	−0.822594	−0.0323395	−0.0161698	+	0.999869i	$0.505147\pi$
$648$	4.93667	0.193931
$649$	−5.98299	−0.234853
$650$	0.934766	0.0366645
$651$	9.32264	0.365383
$652$	−2.21492	−0.0867430
$653$	31.1607	1.21941	0.609706	−	0.792627i	$-0.291287\pi$
$653$	31.1607	1.21941	0.609706	+	0.792627i	$0.291287\pi$
$654$	−50.0165	−1.95580
$655$	17.8955	0.699233
$656$	13.2381	0.516861
$657$	−22.2416	−0.867728
$658$	44.4817	1.73408
$659$	−9.60327	−0.374090	−0.187045	−	0.982351i	$-0.559891\pi$
$659$	−9.60327	−0.374090	−0.187045	+	0.982351i	$0.559891\pi$
$660$	23.9997	0.934186
$661$	−17.1681	−0.667763	−0.333882	−	0.942615i	$-0.608359\pi$
$661$	−17.1681	−0.667763	−0.333882	+	0.942615i	$0.608359\pi$
$662$	40.1781	1.56157
$663$	−0.997874	−0.0387542
$664$	3.43498	0.133303
$665$	−2.07406	−0.0804287
$666$	3.58997	0.139108
$667$	5.31736	0.205889
$668$	30.6457	1.18572
$669$	−37.5405	−1.45140
$670$	95.3717	3.68453
$671$	−11.0729	−0.427464
$672$	−71.7928	−2.76947
$673$	8.02524	0.309350	0.154675	−	0.987965i	$-0.450567\pi$
$673$	8.02524	0.309350	0.154675	+	0.987965i	$0.450567\pi$
$674$	−35.8574	−1.38118
$675$	10.8372	0.417124
$676$	−28.7649	−1.10634
$677$	−21.0133	−0.807608	−0.403804	−	0.914845i	$-0.632312\pi$
$677$	−21.0133	−0.807608	−0.403804	+	0.914845i	$0.632312\pi$
$678$	−18.5136	−0.711010
$679$	60.9738	2.33996
$680$	5.28322	0.202602
$681$	7.76362	0.297502
$682$	−3.59194	−0.137543
$683$	−49.9295	−1.91050	−0.955250	−	0.295799i	$-0.904414\pi$
$683$	−49.9295	−1.91050	−0.955250	+	0.295799i	$0.904414\pi$
$684$	−0.660682	−0.0252618
$685$	−17.7765	−0.679206
$686$	−20.6070	−0.786777
$687$	40.9314	1.56163
$688$	−7.74932	−0.295440
$689$	1.04082	0.0396520
$690$	18.1484	0.690897
$691$	21.8487	0.831165	0.415582	−	0.909556i	$-0.363578\pi$
$691$	21.8487	0.831165	0.415582	+	0.909556i	$0.363578\pi$
$692$	0.342178	0.0130077
$693$	−11.7801	−0.447490
$694$	0.889736	0.0337739
$695$	31.3233	1.18816
$696$	3.77565	0.143116
$697$	15.0149	0.568728
$698$	51.0670	1.93292
$699$	28.4565	1.07632
$700$	35.7264	1.35033
$701$	−42.8362	−1.61790	−0.808950	−	0.587878i	$-0.799964\pi$
$701$	−42.8362	−1.61790	−0.808950	+	0.587878i	$0.799964\pi$
$702$	0.641403	0.0242082
$703$	0.170584	0.00643370
$704$	15.9628	0.601621
$705$	34.8482	1.31246
$706$	41.7668	1.57191
$707$	63.2368	2.37826
$708$	−17.3978	−0.653848
$709$	48.6424	1.82680	0.913401	−	0.407060i	$-0.133446\pi$
$709$	48.6424	1.82680	0.913401	+	0.407060i	$0.133446\pi$
$710$	91.0218	3.41599
$711$	−10.3102	−0.386661
$712$	−1.85623	−0.0695653
$713$	−1.42735	−0.0534547
$714$	−72.5760	−2.71609
$715$	0.569675	0.0213046
$716$	−49.4920	−1.84960
$717$	44.3226	1.65526
$718$	−57.8039	−2.15722
$719$	−31.5501	−1.17662	−0.588311	−	0.808635i	$-0.700207\pi$
$719$	−31.5501	−1.17662	−0.588311	+	0.808635i	$0.700207\pi$
$720$	−18.4597	−0.687952
$721$	79.5093	2.96108
$722$	38.9478	1.44949
$723$	17.0165	0.632850
$724$	−2.72814	−0.101390
$725$	15.6055	0.579573
$726$	−36.8863	−1.36898
$727$	20.1192	0.746180	0.373090	−	0.927795i	$-0.378298\pi$
$727$	20.1192	0.746180	0.373090	+	0.927795i	$0.378298\pi$
$728$	0.205175	0.00760431
$729$	−1.73694	−0.0643310
$730$	78.2279	2.89535
$731$	−8.78941	−0.325088
$732$	−32.1986	−1.19009
$733$	−49.3118	−1.82137	−0.910686	−	0.413100i	$-0.864446\pi$
$733$	−49.3118	−1.82137	−0.910686	+	0.413100i	$0.864446\pi$
$734$	−17.1347	−0.632454
$735$	−61.8401	−2.28101
$736$	10.9919	0.405167
$737$	25.7392	0.948115
$738$	13.4860	0.496428
$739$	21.1028	0.776281	0.388140	−	0.921600i	$-0.373118\pi$
$739$	21.1028	0.776281	0.388140	+	0.921600i	$0.373118\pi$
$740$	−6.63521	−0.243915
$741$	−0.0425879	−0.00156450
$742$	75.6995	2.77902
$743$	15.1153	0.554525	0.277262	−	0.960794i	$-0.410573\pi$
$743$	15.1153	0.554525	0.277262	+	0.960794i	$0.410573\pi$
$744$	−1.01351	−0.0371569
$745$	−21.1144	−0.773570
$746$	37.4864	1.37247
$747$	−13.6127	−0.498064
$748$	14.6944	0.537282
$749$	−41.7060	−1.52391
$750$	−13.7486	−0.502029
$751$	−3.27741	−0.119594	−0.0597972	−	0.998211i	$-0.519045\pi$
$751$	−3.27741	−0.119594	−0.0597972	+	0.998211i	$0.519045\pi$
$752$	18.8118	0.685997
$753$	39.9103	1.45441
$754$	0.923617	0.0336362
$755$	29.3638	1.06866
$756$	24.5142	0.891573
$757$	−24.5869	−0.893626	−0.446813	−	0.894627i	$-0.647441\pi$
$757$	−24.5869	−0.893626	−0.446813	+	0.894627i	$0.647441\pi$
$758$	−3.70892	−0.134714
$759$	4.89794	0.177784
$760$	0.225481	0.00817904
$761$	−32.8414	−1.19050	−0.595251	−	0.803540i	$-0.702947\pi$
$761$	−32.8414	−1.19050	−0.595251	+	0.803540i	$0.702947\pi$
$762$	−56.6887	−2.05361
$763$	−45.3755	−1.64270
$764$	−21.5334	−0.779049
$765$	−20.9373	−0.756989
$766$	−35.1021	−1.26829
$767$	−0.412967	−0.0149114
$768$	−26.2127	−0.945869
$769$	−20.2384	−0.729816	−0.364908	−	0.931044i	$-0.618900\pi$
$769$	−20.2384	−0.729816	−0.364908	+	0.931044i	$0.618900\pi$
$770$	41.4329	1.49314
$771$	−53.9431	−1.94271
$772$	38.2599	1.37700
$773$	−38.1627	−1.37262	−0.686308	−	0.727311i	$-0.740770\pi$
$773$	−38.1627	−1.37262	−0.686308	+	0.727311i	$0.740770\pi$
$774$	−7.89446	−0.283761
$775$	−4.18902	−0.150474
$776$	−6.62874	−0.237958
$777$	8.84445	0.317293
$778$	−18.2829	−0.655474
$779$	0.640814	0.0229595
$780$	1.65654	0.0593138
$781$	24.5652	0.879013
$782$	11.1118	0.397358
$783$	10.7079	0.382670
$784$	−33.3827	−1.19224
$785$	−60.9659	−2.17597
$786$	26.7254	0.953264
$787$	−3.03436	−0.108163	−0.0540815	−	0.998537i	$-0.517223\pi$
$787$	−3.03436	−0.108163	−0.0540815	+	0.998537i	$0.517223\pi$
$788$	−51.6535	−1.84008
$789$	−29.9876	−1.06759
$790$	36.2627	1.29017
$791$	−16.7957	−0.597187
$792$	1.28067	0.0455066
$793$	−0.764290	−0.0271407
$794$	−53.5533	−1.90053
$795$	59.3050	2.10333
$796$	−0.166233	−0.00589196
$797$	−11.6355	−0.412149	−0.206074	−	0.978536i	$-0.566069\pi$
$797$	−11.6355	−0.412149	−0.206074	+	0.978536i	$0.566069\pi$
$798$	−3.09745	−0.109648
$799$	21.3367	0.754838
$800$	32.2593	1.14054
$801$	7.35621	0.259919
$802$	−25.4081	−0.897193
$803$	21.1124	0.745040
$804$	74.8463	2.63963
$805$	16.4644	0.580295
$806$	−0.247929	−0.00873291
$807$	24.2616	0.854050
$808$	−6.87475	−0.241853
$809$	−37.8579	−1.33101	−0.665507	−	0.746392i	$-0.731785\pi$
$809$	−37.8579	−1.33101	−0.665507	+	0.746392i	$0.731785\pi$
$810$	68.8099	2.41773
$811$	−16.6344	−0.584113	−0.292056	−	0.956401i	$-0.594339\pi$
$811$	−16.6344	−0.584113	−0.292056	+	0.956401i	$0.594339\pi$
$812$	35.3003	1.23880
$813$	3.82684	0.134213
$814$	−3.40770	−0.119440
$815$	−2.99569	−0.104934
$816$	−30.6933	−1.07448
$817$	−0.375120	−0.0131238
$818$	−43.6929	−1.52769
$819$	−0.813105	−0.0284122
$820$	−24.9258	−0.870446
$821$	26.2929	0.917627	0.458814	−	0.888533i	$-0.348275\pi$
$821$	26.2929	0.917627	0.458814	+	0.888533i	$0.348275\pi$
$822$	−26.5478	−0.925962
$823$	−3.17223	−0.110577	−0.0552886	−	0.998470i	$-0.517608\pi$
$823$	−3.17223	−0.110577	−0.0552886	+	0.998470i	$0.517608\pi$
$824$	−8.64382	−0.301122
$825$	14.3746	0.500458
$826$	−30.0354	−1.04506
$827$	23.8232	0.828413	0.414206	−	0.910183i	$-0.364059\pi$
$827$	23.8232	0.828413	0.414206	+	0.910183i	$0.364059\pi$
$828$	5.24466	0.182264
$829$	27.8691	0.967935	0.483967	−	0.875086i	$-0.339195\pi$
$829$	27.8691	0.967935	0.483967	+	0.875086i	$0.339195\pi$
$830$	47.8786	1.66189
$831$	−27.4234	−0.951307
$832$	1.10181	0.0381984
$833$	−37.8632	−1.31188
$834$	46.7788	1.61982
$835$	41.4484	1.43438
$836$	0.627138	0.0216900
$837$	−2.87435	−0.0993522
$838$	48.1182	1.66221
$839$	45.5461	1.57243	0.786213	−	0.617955i	$-0.212039\pi$
$839$	45.5461	1.57243	0.786213	+	0.617955i	$0.212039\pi$
$840$	11.6907	0.403369
$841$	−13.5806	−0.468298
$842$	−25.8102	−0.889478
$843$	29.5948	1.01930
$844$	47.8579	1.64734
$845$	−38.9046	−1.33836
$846$	19.1642	0.658878
$847$	−33.4637	−1.14983
$848$	32.0142	1.09937
$849$	39.6091	1.35938
$850$	32.6112	1.11855
$851$	−1.35414	−0.0464193
$852$	71.4326	2.44724
$853$	38.8108	1.32886	0.664428	−	0.747352i	$-0.268675\pi$
$853$	38.8108	1.32886	0.664428	+	0.747352i	$0.268675\pi$
$854$	−55.5874	−1.90216
$855$	−0.893574	−0.0305596
$856$	4.53405	0.154971
$857$	−15.8142	−0.540204	−0.270102	−	0.962832i	$-0.587057\pi$
$857$	−15.8142	−0.540204	−0.270102	+	0.962832i	$0.587057\pi$
$858$	0.850764	0.0290446
$859$	48.1716	1.64359	0.821797	−	0.569780i	$-0.192972\pi$
$859$	48.1716	1.64359	0.821797	+	0.569780i	$0.192972\pi$
$860$	14.5911	0.497551
$861$	33.2250	1.13230
$862$	−14.5062	−0.494082
$863$	−1.92624	−0.0655701	−0.0327851	−	0.999462i	$-0.510438\pi$
$863$	−1.92624	−0.0655701	−0.0327851	+	0.999462i	$0.510438\pi$
$864$	22.1352	0.753054
$865$	0.462797	0.0157356
$866$	−67.9958	−2.31059
$867$	2.23245	0.0758179
$868$	−9.47574	−0.321628
$869$	9.78669	0.331991
$870$	52.6270	1.78422
$871$	1.77661	0.0601982
$872$	4.93298	0.167052
$873$	26.2695	0.889089
$874$	0.474238	0.0160413
$875$	−12.4729	−0.421661
$876$	61.3921	2.07425
$877$	2.41088	0.0814096	0.0407048	−	0.999171i	$-0.487040\pi$
$877$	2.41088	0.0814096	0.0407048	+	0.999171i	$0.487040\pi$
$878$	−36.0613	−1.21701
$879$	−40.9497	−1.38120
$880$	17.5225	0.590682
$881$	−14.6714	−0.494291	−0.247146	−	0.968978i	$-0.579493\pi$
$881$	−14.6714	−0.494291	−0.247146	+	0.968978i	$0.579493\pi$
$882$	−34.0079	−1.14511
$883$	41.2277	1.38742	0.693711	−	0.720254i	$-0.255975\pi$
$883$	41.2277	1.38742	0.693711	+	0.720254i	$0.255975\pi$
$884$	1.01426	0.0341133
$885$	−23.5305	−0.790970
$886$	−9.07636	−0.304926
$887$	1.01299	0.0340129	0.0170064	−	0.999855i	$-0.494586\pi$
$887$	1.01299	0.0340129	0.0170064	+	0.999855i	$0.494586\pi$
$888$	−0.961520	−0.0322665
$889$	−51.4286	−1.72486
$890$	−25.8732	−0.867271
$891$	18.5706	0.622139
$892$	38.1571	1.27759
$893$	0.910622	0.0304728
$894$	−31.5326	−1.05461
$895$	−66.9381	−2.23749
$896$	14.2441	0.475864
$897$	0.338073	0.0112879
$898$	72.7473	2.42761
$899$	−4.13906	−0.138045
$900$	15.3921	0.513071
$901$	36.3111	1.20970
$902$	−12.8013	−0.426238
$903$	−19.4492	−0.647230
$904$	1.82594	0.0607298
$905$	−3.68982	−0.122654
$906$	43.8525	1.45690
$907$	9.67128	0.321129	0.160565	−	0.987025i	$-0.448668\pi$
$907$	9.67128	0.321129	0.160565	+	0.987025i	$0.448668\pi$
$908$	−7.89112	−0.261876
$909$	27.2445	0.903642
$910$	2.85984	0.0948029
$911$	10.4327	0.345651	0.172825	−	0.984952i	$-0.444710\pi$
$911$	10.4327	0.345651	0.172825	+	0.984952i	$0.444710\pi$
$912$	−1.30995	−0.0433767
$913$	12.9216	0.427643
$914$	−17.6412	−0.583521
$915$	−43.5487	−1.43967
$916$	−41.6036	−1.37462
$917$	24.2456	0.800661
$918$	22.3766	0.738539
$919$	46.3512	1.52899	0.764493	−	0.644632i	$-0.222989\pi$
$919$	46.3512	1.52899	0.764493	+	0.644632i	$0.222989\pi$
$920$	−1.78992	−0.0590120
$921$	−46.9199	−1.54606
$922$	−32.8279	−1.08113
$923$	1.69558	0.0558107
$924$	32.5159	1.06969
$925$	−3.97415	−0.130669
$926$	−36.2275	−1.19051
$927$	34.2552	1.12509
$928$	31.8745	1.04633
$929$	−39.0619	−1.28158	−0.640790	−	0.767716i	$-0.721393\pi$
$929$	−39.0619	−1.28158	−0.640790	+	0.767716i	$0.721393\pi$
$930$	−14.1268	−0.463235
$931$	−1.61595	−0.0529606
$932$	−28.9238	−0.947432
$933$	−42.3345	−1.38597
$934$	−7.62798	−0.249595
$935$	19.8743	0.649958
$936$	0.0883963	0.00288932
$937$	20.5751	0.672159	0.336079	−	0.941834i	$-0.390899\pi$
$937$	20.5751	0.672159	0.336079	+	0.941834i	$0.390899\pi$
$938$	129.214	4.21899
$939$	−6.18134	−0.201720
$940$	−35.4205	−1.15529
$941$	9.43315	0.307512	0.153756	−	0.988109i	$-0.450863\pi$
$941$	9.43315	0.307512	0.153756	+	0.988109i	$0.450863\pi$
$942$	−91.0477	−2.96650
$943$	−5.08694	−0.165654
$944$	−12.7023	−0.413425
$945$	33.1555	1.07855
$946$	7.49365	0.243640
$947$	−9.85164	−0.320135	−0.160068	−	0.987106i	$-0.551171\pi$
$947$	−9.85164	−0.320135	−0.160068	+	0.987106i	$0.551171\pi$
$948$	28.4585	0.924288
$949$	1.45725	0.0473044
$950$	1.39180	0.0451560
$951$	19.9200	0.645950
$952$	7.15796	0.231991
$953$	23.7787	0.770267	0.385133	−	0.922861i	$-0.374155\pi$
$953$	23.7787	0.770267	0.385133	+	0.922861i	$0.374155\pi$
$954$	32.6138	1.05591
$955$	−29.1239	−0.942428
$956$	−45.0505	−1.45704
$957$	14.2031	0.459122
$958$	4.57096	0.147681
$959$	−24.0845	−0.777729
$960$	62.7802	2.02622
$961$	−29.8889	−0.964159
$962$	−0.235212	−0.00758353
$963$	−17.9683	−0.579022
$964$	−17.2959	−0.557065
$965$	51.7466	1.66578
$966$	24.5883	0.791115
$967$	9.97776	0.320863	0.160432	−	0.987047i	$-0.448711\pi$
$967$	9.97776	0.320863	0.160432	+	0.987047i	$0.448711\pi$
$968$	3.63799	0.116929
$969$	−1.48576	−0.0477296
$970$	−92.3949	−2.96662
$971$	−20.6458	−0.662555	−0.331278	−	0.943533i	$-0.607480\pi$
$971$	−20.6458	−0.662555	−0.331278	+	0.943533i	$0.607480\pi$
$972$	35.8813	1.15089
$973$	42.4383	1.36051
$974$	−52.9868	−1.69781
$975$	0.992183	0.0317753
$976$	−23.5086	−0.752491
$977$	−45.6641	−1.46092	−0.730462	−	0.682953i	$-0.760695\pi$
$977$	−45.6641	−1.46092	−0.730462	+	0.682953i	$0.760695\pi$
$978$	−4.47382	−0.143057
$979$	−6.98273	−0.223169
$980$	62.8557	2.00785
$981$	−19.5493	−0.624160
$982$	−59.5956	−1.90177
$983$	−43.6038	−1.39074	−0.695372	−	0.718650i	$-0.744760\pi$
$983$	−43.6038	−1.39074	−0.695372	+	0.718650i	$0.744760\pi$
$984$	−3.61203	−0.115147
$985$	−69.8616	−2.22597
$986$	32.2222	1.02617
$987$	47.2140	1.50284
$988$	0.0432873	0.00137715
$989$	2.97780	0.0946884
$990$	17.8506	0.567331
$991$	16.3098	0.518099	0.259050	−	0.965864i	$-0.416591\pi$
$991$	16.3098	0.518099	0.259050	+	0.965864i	$0.416591\pi$
$992$	−8.55615	−0.271658
$993$	42.6460	1.35333
$994$	123.321	3.91149
$995$	−0.224830	−0.00712760
$996$	37.5744	1.19059
$997$	−16.7436	−0.530275	−0.265137	−	0.964211i	$-0.585417\pi$
$997$	−16.7436	−0.530275	−0.265137	+	0.964211i	$0.585417\pi$
$998$	−40.7113	−1.28869
$999$	−2.72692	−0.0862759

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6031.2.a.c.1.19	✓	110

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6031.2.a.c.1.19	✓	110	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)

\(f(q)\)	\(=\)	\(q-2.05303 q^{2} -2.17913 q^{3} +2.21492 q^{4} +2.99569 q^{5} +4.47382 q^{6} +4.05870 q^{7} -0.441239 q^{8} +1.74862 q^{9} +O(q^{10})\)	\(q-2.05303 q^{2} -2.17913 q^{3} +2.21492 q^{4} +2.99569 q^{5} +4.47382 q^{6} +4.05870 q^{7} -0.441239 q^{8} +1.74862 q^{9} -6.15023 q^{10} -1.65984 q^{11} -4.82661 q^{12} -0.114568 q^{13} -8.33262 q^{14} -6.52800 q^{15} -3.52397 q^{16} -3.99694 q^{17} -3.58997 q^{18} -0.170584 q^{19} +6.63521 q^{20} -8.84445 q^{21} +3.40770 q^{22} +1.35414 q^{23} +0.961520 q^{24} +3.97415 q^{25} +0.235212 q^{26} +2.72692 q^{27} +8.98970 q^{28} +3.92675 q^{29} +13.4022 q^{30} -1.05407 q^{31} +8.11728 q^{32} +3.61702 q^{33} +8.20583 q^{34} +12.1586 q^{35} +3.87306 q^{36} -1.00000 q^{37} +0.350214 q^{38} +0.249659 q^{39} -1.32182 q^{40} -3.75659 q^{41} +18.1579 q^{42} +2.19903 q^{43} -3.67642 q^{44} +5.23833 q^{45} -2.78008 q^{46} -5.33826 q^{47} +7.67919 q^{48} +9.47305 q^{49} -8.15904 q^{50} +8.70987 q^{51} -0.253760 q^{52} -9.08471 q^{53} -5.59844 q^{54} -4.97237 q^{55} -1.79086 q^{56} +0.371725 q^{57} -8.06173 q^{58} +3.60455 q^{59} -14.4590 q^{60} +6.67105 q^{61} +2.16403 q^{62} +7.09713 q^{63} -9.61706 q^{64} -0.343211 q^{65} -7.42583 q^{66} -15.5070 q^{67} -8.85291 q^{68} -2.95085 q^{69} -24.9619 q^{70} -14.7997 q^{71} -0.771561 q^{72} -12.7195 q^{73} +2.05303 q^{74} -8.66020 q^{75} -0.377830 q^{76} -6.73680 q^{77} -0.512557 q^{78} -5.89616 q^{79} -10.5567 q^{80} -11.1882 q^{81} +7.71238 q^{82} -7.78485 q^{83} -19.5898 q^{84} -11.9736 q^{85} -4.51468 q^{86} -8.55691 q^{87} +0.732388 q^{88} +4.20686 q^{89} -10.7544 q^{90} -0.464998 q^{91} +2.99931 q^{92} +2.29695 q^{93} +10.9596 q^{94} -0.511016 q^{95} -17.6886 q^{96} +15.0230 q^{97} -19.4484 q^{98} -2.90244 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 110 q - 9 q^{2} + 97 q^{4} - 26 q^{5} - 26 q^{6} - 4 q^{7} - 27 q^{8} + 62 q^{9}+O(q^{10}) \) 110 * q - 9 * q^2 + 97 * q^4 - 26 * q^5 - 26 * q^6 - 4 * q^7 - 27 * q^8 + 62 * q^9	\( 110 q - 9 q^{2} + 97 q^{4} - 26 q^{5} - 26 q^{6} - 4 q^{7} - 27 q^{8} + 62 q^{9} - 17 q^{10} - 9 q^{11} - 21 q^{13} - 29 q^{14} - 23 q^{15} + 79 q^{16} - 76 q^{17} - 31 q^{18} - 27 q^{19} - 67 q^{20} - 30 q^{21} - 28 q^{22} - 32 q^{23} - 63 q^{24} + 66 q^{25} - 55 q^{26} - 4 q^{28} - 81 q^{29} - 48 q^{30} - 30 q^{31} - 73 q^{32} - 53 q^{33} - 23 q^{34} - 78 q^{35} + 7 q^{36} - 110 q^{37} - 50 q^{38} - 64 q^{39} - 37 q^{40} - 123 q^{41} - 63 q^{42} - 40 q^{43} - 31 q^{44} - 73 q^{45} + 16 q^{46} - 37 q^{47} - 29 q^{48} + 46 q^{49} - 58 q^{50} - 73 q^{51} - 39 q^{52} - 16 q^{53} - 53 q^{54} - 59 q^{55} - 113 q^{56} - 39 q^{57} + 11 q^{58} - 93 q^{59} - 18 q^{60} - 66 q^{61} - 40 q^{62} - 21 q^{63} + 23 q^{64} - 92 q^{65} - 31 q^{66} + q^{67} - 121 q^{68} - 80 q^{69} - 3 q^{70} - 75 q^{71} - 114 q^{72} - 39 q^{73} + 9 q^{74} - 25 q^{75} - 58 q^{76} - 31 q^{77} + 68 q^{78} - 36 q^{79} - 82 q^{80} - 50 q^{81} - 18 q^{82} - 57 q^{83} - 9 q^{84} - 14 q^{85} - 58 q^{86} - 58 q^{87} - 15 q^{88} - 181 q^{89} + 8 q^{90} - 55 q^{91} - 116 q^{92} - 86 q^{93} - 39 q^{94} - 70 q^{95} - 127 q^{96} - 91 q^{97} - 19 q^{98} - 21 q^{99}+O(q^{100}) \) 110 * q - 9 * q^2 + 97 * q^4 - 26 * q^5 - 26 * q^6 - 4 * q^7 - 27 * q^8 + 62 * q^9 - 17 * q^10 - 9 * q^11 - 21 * q^13 - 29 * q^14 - 23 * q^15 + 79 * q^16 - 76 * q^17 - 31 * q^18 - 27 * q^19 - 67 * q^20 - 30 * q^21 - 28 * q^22 - 32 * q^23 - 63 * q^24 + 66 * q^25 - 55 * q^26 - 4 * q^28 - 81 * q^29 - 48 * q^30 - 30 * q^31 - 73 * q^32 - 53 * q^33 - 23 * q^34 - 78 * q^35 + 7 * q^36 - 110 * q^37 - 50 * q^38 - 64 * q^39 - 37 * q^40 - 123 * q^41 - 63 * q^42 - 40 * q^43 - 31 * q^44 - 73 * q^45 + 16 * q^46 - 37 * q^47 - 29 * q^48 + 46 * q^49 - 58 * q^50 - 73 * q^51 - 39 * q^52 - 16 * q^53 - 53 * q^54 - 59 * q^55 - 113 * q^56 - 39 * q^57 + 11 * q^58 - 93 * q^59 - 18 * q^60 - 66 * q^61 - 40 * q^62 - 21 * q^63 + 23 * q^64 - 92 * q^65 - 31 * q^66 + q^67 - 121 * q^68 - 80 * q^69 - 3 * q^70 - 75 * q^71 - 114 * q^72 - 39 * q^73 + 9 * q^74 - 25 * q^75 - 58 * q^76 - 31 * q^77 + 68 * q^78 - 36 * q^79 - 82 * q^80 - 50 * q^81 - 18 * q^82 - 57 * q^83 - 9 * q^84 - 14 * q^85 - 58 * q^86 - 58 * q^87 - 15 * q^88 - 181 * q^89 + 8 * q^90 - 55 * q^91 - 116 * q^92 - 86 * q^93 - 39 * q^94 - 70 * q^95 - 127 * q^96 - 91 * q^97 - 19 * q^98 - 21 * q^99

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