LMFDB - Embedded newform 6041.2.a.f.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6041,2,Mod(1,6041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6041, 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("6041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6041 = 7 \cdot 863 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6041.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:	$48.2376278611$
Analytic rank:	$0$
Dimension:	$132$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	6041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.58389 q^{2} +1.40748 q^{3} +4.67649 q^{4} -2.16822 q^{5} -3.63678 q^{6} +1.00000 q^{7} -6.91577 q^{8} -1.01899 q^{9} +O(q^{10})$	\(q-2.58389 q^{2} +1.40748 q^{3} +4.67649 q^{4} -2.16822 q^{5} -3.63678 q^{6} +1.00000 q^{7} -6.91577 q^{8} -1.01899 q^{9} +5.60245 q^{10} -3.16802 q^{11} +6.58209 q^{12} +1.21704 q^{13} -2.58389 q^{14} -3.05174 q^{15} +8.51660 q^{16} +4.73910 q^{17} +2.63296 q^{18} -4.76821 q^{19} -10.1397 q^{20} +1.40748 q^{21} +8.18583 q^{22} -5.72257 q^{23} -9.73383 q^{24} -0.298806 q^{25} -3.14471 q^{26} -5.65666 q^{27} +4.67649 q^{28} -8.90251 q^{29} +7.88536 q^{30} -3.13011 q^{31} -8.17444 q^{32} -4.45894 q^{33} -12.2453 q^{34} -2.16822 q^{35} -4.76530 q^{36} -1.91415 q^{37} +12.3205 q^{38} +1.71297 q^{39} +14.9949 q^{40} +5.76268 q^{41} -3.63678 q^{42} +4.63071 q^{43} -14.8152 q^{44} +2.20940 q^{45} +14.7865 q^{46} +2.89486 q^{47} +11.9870 q^{48} +1.00000 q^{49} +0.772083 q^{50} +6.67021 q^{51} +5.69149 q^{52} -0.623615 q^{53} +14.6162 q^{54} +6.86898 q^{55} -6.91577 q^{56} -6.71117 q^{57} +23.0031 q^{58} -12.4131 q^{59} -14.2714 q^{60} +13.0829 q^{61} +8.08786 q^{62} -1.01899 q^{63} +4.08866 q^{64} -2.63882 q^{65} +11.5214 q^{66} +11.9649 q^{67} +22.1624 q^{68} -8.05442 q^{69} +5.60245 q^{70} -7.16977 q^{71} +7.04710 q^{72} +6.07721 q^{73} +4.94595 q^{74} -0.420565 q^{75} -22.2985 q^{76} -3.16802 q^{77} -4.42612 q^{78} -11.1885 q^{79} -18.4659 q^{80} -4.90469 q^{81} -14.8901 q^{82} +2.54325 q^{83} +6.58209 q^{84} -10.2754 q^{85} -11.9653 q^{86} -12.5301 q^{87} +21.9093 q^{88} -8.94330 q^{89} -5.70885 q^{90} +1.21704 q^{91} -26.7616 q^{92} -4.40558 q^{93} -7.47999 q^{94} +10.3385 q^{95} -11.5054 q^{96} +9.11453 q^{97} -2.58389 q^{98} +3.22819 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 8 q^{2} + 10 q^{3} + 174 q^{4} + 11 q^{5} + 16 q^{6} + 132 q^{7} + 30 q^{8} + 178 q^{9}+O(q^{10}) $ 132 * q + 8 * q^2 + 10 * q^3 + 174 * q^4 + 11 * q^5 + 16 * q^6 + 132 * q^7 + 30 * q^8 + 178 * q^9	\( 132 q + 8 q^{2} + 10 q^{3} + 174 q^{4} + 11 q^{5} + 16 q^{6} + 132 q^{7} + 30 q^{8} + 178 q^{9} + 22 q^{10} + 32 q^{11} + 30 q^{12} + 16 q^{13} + 8 q^{14} + 59 q^{15} + 254 q^{16} + 11 q^{17} + 33 q^{18} + 40 q^{19} + 4 q^{20} + 10 q^{21} + 66 q^{22} + 62 q^{23} + 36 q^{24} + 235 q^{25} + 25 q^{26} + 37 q^{27} + 174 q^{28} + 28 q^{29} + 45 q^{30} + 121 q^{31} + 53 q^{32} - 13 q^{33} + 44 q^{34} + 11 q^{35} + 274 q^{36} + 61 q^{37} - 28 q^{38} + 114 q^{39} + 32 q^{40} - q^{41} + 16 q^{42} + 105 q^{43} + 54 q^{44} + 29 q^{45} + 104 q^{46} + 33 q^{47} + 16 q^{48} + 132 q^{49} - 14 q^{50} + 53 q^{51} - 11 q^{52} + 48 q^{53} + 11 q^{54} + 118 q^{55} + 30 q^{56} + 93 q^{57} + 87 q^{58} + 12 q^{59} + 41 q^{60} + 54 q^{61} - 28 q^{62} + 178 q^{63} + 376 q^{64} + 22 q^{65} + 6 q^{66} + 123 q^{67} - 47 q^{68} + 58 q^{69} + 22 q^{70} + 108 q^{71} + 97 q^{72} + q^{73} - 10 q^{74} + 23 q^{75} + 71 q^{76} + 32 q^{77} + 5 q^{78} + 204 q^{79} - 10 q^{80} + 296 q^{81} + 80 q^{82} - 10 q^{83} + 30 q^{84} + 94 q^{85} + 48 q^{86} + 4 q^{87} + 155 q^{88} + q^{89} - 66 q^{90} + 16 q^{91} + 49 q^{92} + 90 q^{93} + 79 q^{94} + 100 q^{95} + q^{96} + 18 q^{97} + 8 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q + 8 * q^2 + 10 * q^3 + 174 * q^4 + 11 * q^5 + 16 * q^6 + 132 * q^7 + 30 * q^8 + 178 * q^9 + 22 * q^10 + 32 * q^11 + 30 * q^12 + 16 * q^13 + 8 * q^14 + 59 * q^15 + 254 * q^16 + 11 * q^17 + 33 * q^18 + 40 * q^19 + 4 * q^20 + 10 * q^21 + 66 * q^22 + 62 * q^23 + 36 * q^24 + 235 * q^25 + 25 * q^26 + 37 * q^27 + 174 * q^28 + 28 * q^29 + 45 * q^30 + 121 * q^31 + 53 * q^32 - 13 * q^33 + 44 * q^34 + 11 * q^35 + 274 * q^36 + 61 * q^37 - 28 * q^38 + 114 * q^39 + 32 * q^40 - q^41 + 16 * q^42 + 105 * q^43 + 54 * q^44 + 29 * q^45 + 104 * q^46 + 33 * q^47 + 16 * q^48 + 132 * q^49 - 14 * q^50 + 53 * q^51 - 11 * q^52 + 48 * q^53 + 11 * q^54 + 118 * q^55 + 30 * q^56 + 93 * q^57 + 87 * q^58 + 12 * q^59 + 41 * q^60 + 54 * q^61 - 28 * q^62 + 178 * q^63 + 376 * q^64 + 22 * q^65 + 6 * q^66 + 123 * q^67 - 47 * q^68 + 58 * q^69 + 22 * q^70 + 108 * q^71 + 97 * q^72 + q^73 - 10 * q^74 + 23 * q^75 + 71 * q^76 + 32 * q^77 + 5 * q^78 + 204 * q^79 - 10 * q^80 + 296 * q^81 + 80 * q^82 - 10 * q^83 + 30 * q^84 + 94 * q^85 + 48 * q^86 + 4 * q^87 + 155 * q^88 + q^89 - 66 * q^90 + 16 * q^91 + 49 * q^92 + 90 * q^93 + 79 * q^94 + 100 * q^95 + q^96 + 18 * q^97 + 8 * q^98 + 96 * 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 $

$2$	−2.58389	−1.82709	−0.913543	−	0.406741i	$-0.866665\pi$
$2$	−2.58389	−1.82709	−0.913543	+	0.406741i	$0.866665\pi$
$3$	1.40748	0.812611	0.406305	−	0.913737i	$-0.366817\pi$
$3$	1.40748	0.812611	0.406305	+	0.913737i	$0.366817\pi$
$4$	4.67649	2.33825
$5$	−2.16822	−0.969659	−0.484830	−	0.874609i	$-0.661118\pi$
$5$	−2.16822	−0.969659	−0.484830	+	0.874609i	$0.661118\pi$
$6$	−3.63678	−1.48471
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−6.91577	−2.44509
$9$	−1.01899	−0.339663
$10$	5.60245	1.77165
$11$	−3.16802	−0.955195	−0.477597	−	0.878579i	$-0.658492\pi$
$11$	−3.16802	−0.955195	−0.477597	+	0.878579i	$0.658492\pi$
$12$	6.58209	1.90008
$13$	1.21704	0.337547	0.168773	−	0.985655i	$-0.446019\pi$
$13$	1.21704	0.337547	0.168773	+	0.985655i	$0.446019\pi$
$14$	−2.58389	−0.690574
$15$	−3.05174	−0.787956
$16$	8.51660	2.12915
$17$	4.73910	1.14940	0.574701	−	0.818364i	$-0.305118\pi$
$17$	4.73910	1.14940	0.574701	+	0.818364i	$0.305118\pi$
$18$	2.63296	0.620595
$19$	−4.76821	−1.09390	−0.546951	−	0.837165i	$-0.684212\pi$
$19$	−4.76821	−1.09390	−0.546951	+	0.837165i	$0.684212\pi$
$20$	−10.1397	−2.26730
$21$	1.40748	0.307138
$22$	8.18583	1.74522
$23$	−5.72257	−1.19324	−0.596619	−	0.802525i	$-0.703490\pi$
$23$	−5.72257	−1.19324	−0.596619	+	0.802525i	$0.703490\pi$
$24$	−9.73383	−1.98691
$25$	−0.298806	−0.0597612
$26$	−3.14471	−0.616727
$27$	−5.65666	−1.08863
$28$	4.67649	0.883774
$29$	−8.90251	−1.65315	−0.826577	−	0.562824i	$-0.809715\pi$
$29$	−8.90251	−1.65315	−0.826577	+	0.562824i	$0.809715\pi$
$30$	7.88536	1.43966
$31$	−3.13011	−0.562184	−0.281092	−	0.959681i	$-0.590697\pi$
$31$	−3.13011	−0.562184	−0.281092	+	0.959681i	$0.590697\pi$
$32$	−8.17444	−1.44505
$33$	−4.45894	−0.776202
$34$	−12.2453	−2.10006
$35$	−2.16822	−0.366497
$36$	−4.76530	−0.794217
$37$	−1.91415	−0.314684	−0.157342	−	0.987544i	$-0.550292\pi$
$37$	−1.91415	−0.314684	−0.157342	+	0.987544i	$0.550292\pi$
$38$	12.3205	1.99865
$39$	1.71297	0.274294
$40$	14.9949	2.37091
$41$	5.76268	0.899979	0.449990	−	0.893034i	$-0.351428\pi$
$41$	5.76268	0.899979	0.449990	+	0.893034i	$0.351428\pi$
$42$	−3.63678	−0.561168
$43$	4.63071	0.706177	0.353089	−	0.935590i	$-0.385131\pi$
$43$	4.63071	0.706177	0.353089	+	0.935590i	$0.385131\pi$
$44$	−14.8152	−2.23348
$45$	2.20940	0.329358
$46$	14.7865	2.18015
$47$	2.89486	0.422258	0.211129	−	0.977458i	$-0.432286\pi$
$47$	2.89486	0.422258	0.211129	+	0.977458i	$0.432286\pi$
$48$	11.9870	1.73017
$49$	1.00000	0.142857
$50$	0.772083	0.109189
$51$	6.67021	0.934016
$52$	5.69149	0.789268
$53$	−0.623615	−0.0856601	−0.0428301	−	0.999082i	$-0.513637\pi$
$53$	−0.623615	−0.0856601	−0.0428301	+	0.999082i	$0.513637\pi$
$54$	14.6162	1.98901
$55$	6.86898	0.926213
$56$	−6.91577	−0.924158
$57$	−6.71117	−0.888917
$58$	23.0031	3.02046
$59$	−12.4131	−1.61605	−0.808027	−	0.589145i	$-0.799465\pi$
$59$	−12.4131	−1.61605	−0.808027	+	0.589145i	$0.799465\pi$
$60$	−14.2714	−1.84243
$61$	13.0829	1.67509	0.837544	−	0.546369i	$-0.183991\pi$
$61$	13.0829	1.67509	0.837544	+	0.546369i	$0.183991\pi$
$62$	8.08786	1.02716
$63$	−1.01899	−0.128381
$64$	4.08866	0.511083
$65$	−2.63882	−0.327305
$66$	11.5214	1.41819
$67$	11.9649	1.46174	0.730870	−	0.682517i	$-0.239115\pi$
$67$	11.9649	1.46174	0.730870	+	0.682517i	$0.239115\pi$
$68$	22.1624	2.68758
$69$	−8.05442	−0.969638
$70$	5.60245	0.669621
$71$	−7.16977	−0.850896	−0.425448	−	0.904983i	$-0.639883\pi$
$71$	−7.16977	−0.850896	−0.425448	+	0.904983i	$0.639883\pi$
$72$	7.04710	0.830509
$73$	6.07721	0.711283	0.355642	−	0.934622i	$-0.384262\pi$
$73$	6.07721	0.711283	0.355642	+	0.934622i	$0.384262\pi$
$74$	4.94595	0.574955
$75$	−0.420565	−0.0485626
$76$	−22.2985	−2.55781
$77$	−3.16802	−0.361030
$78$	−4.42612	−0.501159
$79$	−11.1885	−1.25880	−0.629400	−	0.777081i	$-0.716699\pi$
$79$	−11.1885	−1.25880	−0.629400	+	0.777081i	$0.716699\pi$
$80$	−18.4659	−2.06455
$81$	−4.90469	−0.544965
$82$	−14.8901	−1.64434
$83$	2.54325	0.279158	0.139579	−	0.990211i	$-0.455425\pi$
$83$	2.54325	0.279158	0.139579	+	0.990211i	$0.455425\pi$
$84$	6.58209	0.718165
$85$	−10.2754	−1.11453
$86$	−11.9653	−1.29025
$87$	−12.5301	−1.34337
$88$	21.9093	2.33554
$89$	−8.94330	−0.947988	−0.473994	−	0.880528i	$-0.657188\pi$
$89$	−8.94330	−0.947988	−0.473994	+	0.880528i	$0.657188\pi$
$90$	−5.70885	−0.601765
$91$	1.21704	0.127581
$92$	−26.7616	−2.79008
$93$	−4.40558	−0.456837
$94$	−7.47999	−0.771502
$95$	10.3385	1.06071
$96$	−11.5054	−1.17426
$97$	9.11453	0.925441	0.462720	−	0.886504i	$-0.346873\pi$
$97$	9.11453	0.925441	0.462720	+	0.886504i	$0.346873\pi$
$98$	−2.58389	−0.261012
$99$	3.22819	0.324445
$100$	−1.39737	−0.139737
$101$	15.3894	1.53130	0.765650	−	0.643258i	$-0.222418\pi$
$101$	15.3894	1.53130	0.765650	+	0.643258i	$0.222418\pi$
$102$	−17.2351	−1.70653
$103$	9.62828	0.948703	0.474351	−	0.880336i	$-0.342683\pi$
$103$	9.62828	0.948703	0.474351	+	0.880336i	$0.342683\pi$
$104$	−8.41678	−0.825333
$105$	−3.05174	−0.297819
$106$	1.61135	0.156509
$107$	4.81884	0.465855	0.232927	−	0.972494i	$-0.425170\pi$
$107$	4.81884	0.465855	0.232927	+	0.972494i	$0.425170\pi$
$108$	−26.4533	−2.54547
$109$	−4.66377	−0.446708	−0.223354	−	0.974737i	$-0.571701\pi$
$109$	−4.66377	−0.446708	−0.223354	+	0.974737i	$0.571701\pi$
$110$	−17.7487	−1.69227
$111$	−2.69413	−0.255716
$112$	8.51660	0.804743
$113$	−9.47571	−0.891400	−0.445700	−	0.895182i	$-0.647045\pi$
$113$	−9.47571	−0.891400	−0.445700	+	0.895182i	$0.647045\pi$
$114$	17.3409	1.62413
$115$	12.4078	1.15703
$116$	−41.6325	−3.86548
$117$	−1.24015	−0.114652
$118$	32.0742	2.95267
$119$	4.73910	0.434433
$120$	21.1051	1.92662
$121$	−0.963631	−0.0876028
$122$	−33.8047	−3.06053
$123$	8.11088	0.731333
$124$	−14.6379	−1.31453
$125$	11.4890	1.02761
$126$	2.63296	0.234563
$127$	8.40274	0.745622	0.372811	−	0.927907i	$-0.378394\pi$
$127$	8.40274	0.745622	0.372811	+	0.927907i	$0.378394\pi$
$128$	5.78423	0.511258
$129$	6.51765	0.573847
$130$	6.81842	0.598015
$131$	16.9422	1.48025	0.740123	−	0.672472i	$-0.234767\pi$
$131$	16.9422	1.48025	0.740123	+	0.672472i	$0.234767\pi$
$132$	−20.8522	−1.81495
$133$	−4.76821	−0.413456
$134$	−30.9159	−2.67073
$135$	12.2649	1.05560
$136$	−32.7745	−2.81039
$137$	−3.15859	−0.269857	−0.134928	−	0.990855i	$-0.543080\pi$
$137$	−3.15859	−0.269857	−0.134928	+	0.990855i	$0.543080\pi$
$138$	20.8117	1.77161
$139$	−22.6268	−1.91918	−0.959591	−	0.281398i	$-0.909202\pi$
$139$	−22.6268	−1.91918	−0.959591	+	0.281398i	$0.909202\pi$
$140$	−10.1397	−0.856960
$141$	4.07446	0.343132
$142$	18.5259	1.55466
$143$	−3.85562	−0.322423
$144$	−8.67834	−0.723195
$145$	19.3026	1.60300
$146$	−15.7028	−1.29958
$147$	1.40748	0.116087
$148$	−8.95150	−0.735809
$149$	−6.38916	−0.523420	−0.261710	−	0.965147i	$-0.584286\pi$
$149$	−6.38916	−0.523420	−0.261710	+	0.965147i	$0.584286\pi$
$150$	1.08669	0.0887282
$151$	20.3502	1.65607	0.828036	−	0.560675i	$-0.189458\pi$
$151$	20.3502	1.65607	0.828036	+	0.560675i	$0.189458\pi$
$152$	32.9758	2.67469
$153$	−4.82910	−0.390410
$154$	8.18583	0.659633
$155$	6.78678	0.545127
$156$	8.01068	0.641368
$157$	6.88006	0.549089	0.274544	−	0.961574i	$-0.411473\pi$
$157$	6.88006	0.549089	0.274544	+	0.961574i	$0.411473\pi$
$158$	28.9098	2.29994
$159$	−0.877728	−0.0696084
$160$	17.7240	1.40121
$161$	−5.72257	−0.451002
$162$	12.6732	0.995699
$163$	15.5669	1.21929	0.609647	−	0.792673i	$-0.291311\pi$
$163$	15.5669	1.21929	0.609647	+	0.792673i	$0.291311\pi$
$164$	26.9491	2.10437
$165$	9.66798	0.752651
$166$	−6.57149	−0.510046
$167$	−6.65907	−0.515294	−0.257647	−	0.966239i	$-0.582947\pi$
$167$	−6.65907	−0.515294	−0.257647	+	0.966239i	$0.582947\pi$
$168$	−9.73383	−0.750981
$169$	−11.5188	−0.886062
$170$	26.5506	2.03634
$171$	4.85876	0.371558
$172$	21.6555	1.65122
$173$	10.6468	0.809461	0.404731	−	0.914436i	$-0.367365\pi$
$173$	10.6468	0.809461	0.404731	+	0.914436i	$0.367365\pi$
$174$	32.3765	2.45446
$175$	−0.298806	−0.0225876
$176$	−26.9808	−2.03375
$177$	−17.4713	−1.31322
$178$	23.1085	1.73206
$179$	−14.5977	−1.09108	−0.545542	−	0.838083i	$-0.683676\pi$
$179$	−14.5977	−1.09108	−0.545542	+	0.838083i	$0.683676\pi$
$180$	10.3322	0.770120
$181$	−24.7977	−1.84320	−0.921599	−	0.388142i	$-0.873117\pi$
$181$	−24.7977	−1.84320	−0.921599	+	0.388142i	$0.873117\pi$
$182$	−3.14471	−0.233101
$183$	18.4139	1.36120
$184$	39.5760	2.91758
$185$	4.15030	0.305136
$186$	11.3835	0.834681
$187$	−15.0136	−1.09790
$188$	13.5378	0.987344
$189$	−5.65666	−0.411462
$190$	−26.7137	−1.93801
$191$	16.5849	1.20004	0.600022	−	0.799984i	$-0.295159\pi$
$191$	16.5849	1.20004	0.600022	+	0.799984i	$0.295159\pi$
$192$	5.75472	0.415311
$193$	−9.06703	−0.652659	−0.326329	−	0.945256i	$-0.605812\pi$
$193$	−9.06703	−0.652659	−0.326329	+	0.945256i	$0.605812\pi$
$194$	−23.5510	−1.69086
$195$	−3.71410	−0.265972
$196$	4.67649	0.334035
$197$	−2.64107	−0.188169	−0.0940843	−	0.995564i	$-0.529992\pi$
$197$	−2.64107	−0.188169	−0.0940843	+	0.995564i	$0.529992\pi$
$198$	−8.34128	−0.592789
$199$	18.4052	1.30471	0.652355	−	0.757913i	$-0.273781\pi$
$199$	18.4052	1.30471	0.652355	+	0.757913i	$0.273781\pi$
$200$	2.06647	0.146122
$201$	16.8403	1.18783
$202$	−39.7645	−2.79782
$203$	−8.90251	−0.624834
$204$	31.1932	2.18396
$205$	−12.4948	−0.872673
$206$	−24.8784	−1.73336
$207$	5.83124	0.405299
$208$	10.3651	0.718688
$209$	15.1058	1.04489
$210$	7.88536	0.544142
$211$	18.9919	1.30745	0.653727	−	0.756731i	$-0.273205\pi$
$211$	18.9919	1.30745	0.653727	+	0.756731i	$0.273205\pi$
$212$	−2.91633	−0.200295
$213$	−10.0913	−0.691447
$214$	−12.4514	−0.851157
$215$	−10.0404	−0.684751
$216$	39.1202	2.66179
$217$	−3.13011	−0.212486
$218$	12.0507	0.816175
$219$	8.55357	0.577996
$220$	32.1228	2.16572
$221$	5.76769	0.387977
$222$	6.96134	0.467215
$223$	−22.9562	−1.53726	−0.768629	−	0.639694i	$-0.779061\pi$
$223$	−22.9562	−1.53726	−0.768629	+	0.639694i	$0.779061\pi$
$224$	−8.17444	−0.546178
$225$	0.304481	0.0202987
$226$	24.4842	1.62866
$227$	10.5094	0.697532	0.348766	−	0.937210i	$-0.386601\pi$
$227$	10.5094	0.697532	0.348766	+	0.937210i	$0.386601\pi$
$228$	−31.3848	−2.07851
$229$	21.1762	1.39936	0.699680	−	0.714456i	$-0.253326\pi$
$229$	21.1762	1.39936	0.699680	+	0.714456i	$0.253326\pi$
$230$	−32.0604	−2.11400
$231$	−4.45894	−0.293377
$232$	61.5677	4.04212
$233$	−20.1853	−1.32238	−0.661191	−	0.750217i	$-0.729949\pi$
$233$	−20.1853	−1.32238	−0.661191	+	0.750217i	$0.729949\pi$
$234$	3.20442	0.209480
$235$	−6.27670	−0.409446
$236$	−58.0500	−3.77873
$237$	−15.7476	−1.02291
$238$	−12.2453	−0.793747
$239$	7.99700	0.517283	0.258642	−	0.965973i	$-0.416725\pi$
$239$	7.99700	0.517283	0.258642	+	0.965973i	$0.416725\pi$
$240$	−25.9905	−1.67768
$241$	0.668492	0.0430614	0.0215307	−	0.999768i	$-0.493146\pi$
$241$	0.668492	0.0430614	0.0215307	+	0.999768i	$0.493146\pi$
$242$	2.48992	0.160058
$243$	10.0667	0.645781
$244$	61.1819	3.91677
$245$	−2.16822	−0.138523
$246$	−20.9576	−1.33621
$247$	−5.80311	−0.369243
$248$	21.6471	1.37459
$249$	3.57959	0.226847
$250$	−29.6863	−1.87753
$251$	17.7432	1.11994	0.559969	−	0.828513i	$-0.310813\pi$
$251$	17.7432	1.11994	0.559969	+	0.828513i	$0.310813\pi$
$252$	−4.76530	−0.300186
$253$	18.1292	1.13977
$254$	−21.7118	−1.36232
$255$	−14.4625	−0.905677
$256$	−23.1231	−1.44520
$257$	7.89004	0.492167	0.246083	−	0.969249i	$-0.420856\pi$
$257$	7.89004	0.492167	0.246083	+	0.969249i	$0.420856\pi$
$258$	−16.8409	−1.04847
$259$	−1.91415	−0.118939
$260$	−12.3404	−0.765321
$261$	9.07157	0.561516
$262$	−43.7768	−2.70454
$263$	−11.5866	−0.714461	−0.357230	−	0.934016i	$-0.616279\pi$
$263$	−11.5866	−0.714461	−0.357230	+	0.934016i	$0.616279\pi$
$264$	30.8370	1.89789
$265$	1.35214	0.0830611
$266$	12.3205	0.755420
$267$	−12.5875	−0.770345
$268$	55.9536	3.41791
$269$	11.8549	0.722808	0.361404	−	0.932409i	$-0.382298\pi$
$269$	11.8549	0.722808	0.361404	+	0.932409i	$0.382298\pi$
$270$	−31.6912	−1.92866
$271$	30.5579	1.85626	0.928130	−	0.372256i	$-0.121416\pi$
$271$	30.5579	1.85626	0.928130	+	0.372256i	$0.121416\pi$
$272$	40.3611	2.44725
$273$	1.71297	0.103673
$274$	8.16146	0.493052
$275$	0.946625	0.0570836
$276$	−37.6664	−2.26725
$277$	19.8591	1.19322	0.596609	−	0.802532i	$-0.296514\pi$
$277$	19.8591	1.19322	0.596609	+	0.802532i	$0.296514\pi$
$278$	58.4652	3.50651
$279$	3.18955	0.190953
$280$	14.9949	0.896119
$281$	−11.1487	−0.665075	−0.332538	−	0.943090i	$-0.607905\pi$
$281$	−11.1487	−0.665075	−0.332538	+	0.943090i	$0.607905\pi$
$282$	−10.5280	−0.626931
$283$	2.27771	0.135396	0.0676980	−	0.997706i	$-0.478435\pi$
$283$	2.27771	0.135396	0.0676980	+	0.997706i	$0.478435\pi$
$284$	−33.5294	−1.98960
$285$	14.5513	0.861946
$286$	9.96250	0.589095
$287$	5.76268	0.340160
$288$	8.32968	0.490831
$289$	5.45911	0.321124
$290$	−49.8759	−2.92881
$291$	12.8286	0.752023
$292$	28.4200	1.66316
$293$	−12.3883	−0.723735	−0.361867	−	0.932230i	$-0.617861\pi$
$293$	−12.3883	−0.723735	−0.361867	+	0.932230i	$0.617861\pi$
$294$	−3.63678	−0.212102
$295$	26.9145	1.56702
$296$	13.2378	0.769431
$297$	17.9204	1.03985
$298$	16.5089	0.956334
$299$	−6.96461	−0.402774
$300$	−1.96677	−0.113551
$301$	4.63071	0.266910
$302$	−52.5826	−3.02579
$303$	21.6603	1.24435
$304$	−40.6089	−2.32908
$305$	−28.3666	−1.62426
$306$	12.4779	0.713313
$307$	12.2605	0.699744	0.349872	−	0.936797i	$-0.386225\pi$
$307$	12.2605	0.699744	0.349872	+	0.936797i	$0.386225\pi$
$308$	−14.8152	−0.844177
$309$	13.5516	0.770926
$310$	−17.5363	−0.995995
$311$	10.3731	0.588204	0.294102	−	0.955774i	$-0.404979\pi$
$311$	10.3731	0.588204	0.294102	+	0.955774i	$0.404979\pi$
$312$	−11.8465	−0.670675
$313$	10.3129	0.582918	0.291459	−	0.956583i	$-0.405859\pi$
$313$	10.3129	0.582918	0.291459	+	0.956583i	$0.405859\pi$
$314$	−17.7773	−1.00323
$315$	2.20940	0.124486
$316$	−52.3228	−2.94339
$317$	−29.3545	−1.64871	−0.824355	−	0.566073i	$-0.808462\pi$
$317$	−29.3545	−1.64871	−0.824355	+	0.566073i	$0.808462\pi$
$318$	2.26795	0.127181
$319$	28.2033	1.57908
$320$	−8.86514	−0.495576
$321$	6.78244	0.378559
$322$	14.7865	0.824019
$323$	−22.5970	−1.25733
$324$	−22.9367	−1.27426
$325$	−0.363660	−0.0201722
$326$	−40.2232	−2.22775
$327$	−6.56418	−0.363000
$328$	−39.8534	−2.20053
$329$	2.89486	0.159599
$330$	−24.9810	−1.37516
$331$	−24.2184	−1.33117	−0.665583	−	0.746324i	$-0.731817\pi$
$331$	−24.2184	−1.33117	−0.665583	+	0.746324i	$0.731817\pi$
$332$	11.8935	0.652741
$333$	1.95050	0.106887
$334$	17.2063	0.941487
$335$	−25.9425	−1.41739
$336$	11.9870	0.653943
$337$	17.6280	0.960256	0.480128	−	0.877198i	$-0.340590\pi$
$337$	17.6280	0.960256	0.480128	+	0.877198i	$0.340590\pi$
$338$	29.7633	1.61891
$339$	−13.3369	−0.724361
$340$	−48.0530	−2.60604
$341$	9.91626	0.536996
$342$	−12.5545	−0.678870
$343$	1.00000	0.0539949
$344$	−32.0249	−1.72667
$345$	17.4638	0.940218
$346$	−27.5102	−1.47896
$347$	−14.4860	−0.777650	−0.388825	−	0.921312i	$-0.627119\pi$
$347$	−14.4860	−0.777650	−0.388825	+	0.921312i	$0.627119\pi$
$348$	−58.5971	−3.14113
$349$	−29.0156	−1.55317	−0.776584	−	0.630013i	$-0.783049\pi$
$349$	−29.0156	−1.55317	−0.776584	+	0.630013i	$0.783049\pi$
$350$	0.772083	0.0412696
$351$	−6.88440	−0.367462
$352$	25.8968	1.38031
$353$	−19.6237	−1.04447	−0.522233	−	0.852803i	$-0.674901\pi$
$353$	−19.6237	−1.04447	−0.522233	+	0.852803i	$0.674901\pi$
$354$	45.1439	2.39937
$355$	15.5457	0.825079
$356$	−41.8233	−2.21663
$357$	6.67021	0.353025
$358$	37.7189	1.99351
$359$	35.2330	1.85953	0.929763	−	0.368160i	$-0.120012\pi$
$359$	35.2330	1.85953	0.929763	+	0.368160i	$0.120012\pi$
$360$	−15.2797	−0.805311
$361$	3.73580	0.196621
$362$	64.0746	3.36768
$363$	−1.35629	−0.0711870
$364$	5.69149	0.298315
$365$	−13.1767	−0.689702
$366$	−47.5795	−2.48702
$367$	32.1168	1.67648	0.838241	−	0.545300i	$-0.183584\pi$
$367$	32.1168	1.67648	0.838241	+	0.545300i	$0.183584\pi$
$368$	−48.7368	−2.54058
$369$	−5.87212	−0.305690
$370$	−10.7239	−0.557510
$371$	−0.623615	−0.0323765
$372$	−20.6027	−1.06820
$373$	14.6269	0.757352	0.378676	−	0.925529i	$-0.376380\pi$
$373$	14.6269	0.757352	0.378676	+	0.925529i	$0.376380\pi$
$374$	38.7935	2.00596
$375$	16.1706	0.835045
$376$	−20.0202	−1.03246
$377$	−10.8347	−0.558017
$378$	14.6162	0.751776
$379$	−30.3842	−1.56073	−0.780366	−	0.625323i	$-0.784967\pi$
$379$	−30.3842	−1.56073	−0.780366	+	0.625323i	$0.784967\pi$
$380$	48.3481	2.48021
$381$	11.8267	0.605901
$382$	−42.8537	−2.19258
$383$	−31.9295	−1.63152	−0.815760	−	0.578390i	$-0.803681\pi$
$383$	−31.9295	−1.63152	−0.815760	+	0.578390i	$0.803681\pi$
$384$	8.14120	0.415454
$385$	6.86898	0.350076
$386$	23.4282	1.19246
$387$	−4.71865	−0.239863
$388$	42.6241	2.16391
$389$	9.15773	0.464315	0.232158	−	0.972678i	$-0.425421\pi$
$389$	9.15773	0.464315	0.232158	+	0.972678i	$0.425421\pi$
$390$	9.59682	0.485954
$391$	−27.1198	−1.37151
$392$	−6.91577	−0.349299
$393$	23.8458	1.20286
$394$	6.82424	0.343800
$395$	24.2591	1.22061
$396$	15.0966	0.758632
$397$	30.1762	1.51450	0.757249	−	0.653126i	$-0.226543\pi$
$397$	30.1762	1.51450	0.757249	+	0.653126i	$0.226543\pi$
$398$	−47.5571	−2.38382
$399$	−6.71117	−0.335979
$400$	−2.54481	−0.127241
$401$	−17.5757	−0.877689	−0.438845	−	0.898563i	$-0.644612\pi$
$401$	−17.5757	−0.877689	−0.438845	+	0.898563i	$0.644612\pi$
$402$	−43.5136	−2.17026
$403$	−3.80948	−0.189764
$404$	71.9683	3.58056
$405$	10.6345	0.528430
$406$	23.0031	1.14163
$407$	6.06406	0.300584
$408$	−46.1296	−2.28376
$409$	9.08657	0.449302	0.224651	−	0.974439i	$-0.427876\pi$
$409$	9.08657	0.449302	0.224651	+	0.974439i	$0.427876\pi$
$410$	32.2851	1.59445
$411$	−4.44567	−0.219289
$412$	45.0266	2.21830
$413$	−12.4131	−0.610811
$414$	−15.0673	−0.740517
$415$	−5.51434	−0.270688
$416$	−9.94864	−0.487772
$417$	−31.8469	−1.55955
$418$	−39.0317	−1.90910
$419$	28.0626	1.37095	0.685474	−	0.728097i	$-0.259595\pi$
$419$	28.0626	1.37095	0.685474	+	0.728097i	$0.259595\pi$
$420$	−14.2714	−0.696375
$421$	−30.2588	−1.47473	−0.737363	−	0.675497i	$-0.763929\pi$
$421$	−30.2588	−1.47473	−0.737363	+	0.675497i	$0.763929\pi$
$422$	−49.0729	−2.38883
$423$	−2.94983	−0.143426
$424$	4.31278	0.209447
$425$	−1.41607	−0.0686897
$426$	26.0749	1.26333
$427$	13.0829	0.633124
$428$	22.5353	1.08928
$429$	−5.42672	−0.262004
$430$	25.9434	1.25110
$431$	−29.1887	−1.40597	−0.702986	−	0.711204i	$-0.748150\pi$
$431$	−29.1887	−1.40597	−0.702986	+	0.711204i	$0.748150\pi$
$432$	−48.1756	−2.31785
$433$	20.7721	0.998244	0.499122	−	0.866532i	$-0.333656\pi$
$433$	20.7721	0.998244	0.499122	+	0.866532i	$0.333656\pi$
$434$	8.08786	0.388230
$435$	27.1681	1.30261
$436$	−21.8101	−1.04451
$437$	27.2864	1.30529
$438$	−22.1015	−1.05605
$439$	0.684286	0.0326592	0.0163296	−	0.999867i	$-0.494802\pi$
$439$	0.684286	0.0326592	0.0163296	+	0.999867i	$0.494802\pi$
$440$	−47.5043	−2.26468
$441$	−1.01899	−0.0485234
$442$	−14.9031	−0.708867
$443$	4.10502	0.195035	0.0975176	−	0.995234i	$-0.468910\pi$
$443$	4.10502	0.195035	0.0975176	+	0.995234i	$0.468910\pi$
$444$	−12.5991	−0.597926
$445$	19.3911	0.919225
$446$	59.3162	2.80871
$447$	−8.99263	−0.425337
$448$	4.08866	0.193171
$449$	−28.5382	−1.34680	−0.673401	−	0.739277i	$-0.735167\pi$
$449$	−28.5382	−1.34680	−0.673401	+	0.739277i	$0.735167\pi$
$450$	−0.786745	−0.0370875
$451$	−18.2563	−0.859656
$452$	−44.3131	−2.08431
$453$	28.6425	1.34574
$454$	−27.1551	−1.27445
$455$	−2.63882	−0.123710
$456$	46.4129	2.17348
$457$	−38.9381	−1.82145	−0.910724	−	0.413016i	$-0.864475\pi$
$457$	−38.9381	−1.82145	−0.910724	+	0.413016i	$0.864475\pi$
$458$	−54.7169	−2.55675
$459$	−26.8075	−1.25127
$460$	58.0250	2.70543
$461$	−26.6744	−1.24235	−0.621175	−	0.783672i	$-0.713345\pi$
$461$	−26.6744	−1.24235	−0.621175	+	0.783672i	$0.713345\pi$
$462$	11.5214	0.536025
$463$	−1.71039	−0.0794884	−0.0397442	−	0.999210i	$-0.512654\pi$
$463$	−1.71039	−0.0794884	−0.0397442	+	0.999210i	$0.512654\pi$
$464$	−75.8191	−3.51982
$465$	9.55228	0.442976
$466$	52.1566	2.41611
$467$	38.5151	1.78227	0.891134	−	0.453740i	$-0.149911\pi$
$467$	38.5151	1.78227	0.891134	+	0.453740i	$0.149911\pi$
$468$	−5.79958	−0.268085
$469$	11.9649	0.552486
$470$	16.2183	0.748094
$471$	9.68358	0.446196
$472$	85.8465	3.95140
$473$	−14.6702	−0.674537
$474$	40.6900	1.86895
$475$	1.42477	0.0653729
$476$	22.1624	1.01581
$477$	0.635458	0.0290956
$478$	−20.6634	−0.945121
$479$	27.0967	1.23808	0.619039	−	0.785360i	$-0.287522\pi$
$479$	27.0967	1.23808	0.619039	+	0.785360i	$0.287522\pi$
$480$	24.9463	1.13864
$481$	−2.32960	−0.106221
$482$	−1.72731	−0.0786768
$483$	−8.05442	−0.366489
$484$	−4.50641	−0.204837
$485$	−19.7623	−0.897362
$486$	−26.0113	−1.17990
$487$	−18.3006	−0.829278	−0.414639	−	0.909986i	$-0.636092\pi$
$487$	−18.3006	−0.829278	−0.414639	+	0.909986i	$0.636092\pi$
$488$	−90.4780	−4.09575
$489$	21.9101	0.990811
$490$	5.60245	0.253093
$491$	29.4340	1.32834	0.664169	−	0.747583i	$-0.268786\pi$
$491$	29.4340	1.32834	0.664169	+	0.747583i	$0.268786\pi$
$492$	37.9305	1.71004
$493$	−42.1899	−1.90014
$494$	14.9946	0.674639
$495$	−6.99943	−0.314601
$496$	−26.6579	−1.19698
$497$	−7.16977	−0.321608
$498$	−9.24926	−0.414469
$499$	5.64540	0.252723	0.126361	−	0.991984i	$-0.459670\pi$
$499$	5.64540	0.252723	0.126361	+	0.991984i	$0.459670\pi$
$500$	53.7282	2.40280
$501$	−9.37253	−0.418734
$502$	−45.8464	−2.04623
$503$	11.9336	0.532091	0.266046	−	0.963960i	$-0.414283\pi$
$503$	11.9336	0.532091	0.266046	+	0.963960i	$0.414283\pi$
$504$	7.04710	0.313903
$505$	−33.3676	−1.48484
$506$	−46.8439	−2.08247
$507$	−16.2125	−0.720024
$508$	39.2953	1.74345
$509$	9.50300	0.421213	0.210607	−	0.977571i	$-0.432456\pi$
$509$	9.50300	0.421213	0.210607	+	0.977571i	$0.432456\pi$
$510$	37.3695	1.65475
$511$	6.07721	0.268840
$512$	48.1792	2.12924
$513$	26.9721	1.19085
$514$	−20.3870	−0.899232
$515$	−20.8763	−0.919918
$516$	30.4798	1.34180
$517$	−9.17097	−0.403339
$518$	4.94595	0.217312
$519$	14.9852	0.657777
$520$	18.2495	0.800292
$521$	14.5153	0.635929	0.317965	−	0.948103i	$-0.397001\pi$
$521$	14.5153	0.635929	0.317965	+	0.948103i	$0.397001\pi$
$522$	−23.4400	−1.02594
$523$	−27.1413	−1.18680	−0.593402	−	0.804906i	$-0.702216\pi$
$523$	−27.1413	−1.18680	−0.593402	+	0.804906i	$0.702216\pi$
$524$	79.2300	3.46118
$525$	−0.420565	−0.0183550
$526$	29.9385	1.30538
$527$	−14.8339	−0.646175
$528$	−37.9750	−1.65265
$529$	9.74778	0.423817
$530$	−3.49378	−0.151760
$531$	12.6489	0.548915
$532$	−22.2985	−0.966762
$533$	7.01342	0.303785
$534$	32.5249	1.40749
$535$	−10.4483	−0.451720
$536$	−82.7462	−3.57409
$537$	−20.5460	−0.886627
$538$	−30.6318	−1.32063
$539$	−3.16802	−0.136456
$540$	57.3568	2.46824
$541$	−11.9558	−0.514019	−0.257010	−	0.966409i	$-0.582737\pi$
$541$	−11.9558	−0.514019	−0.257010	+	0.966409i	$0.582737\pi$
$542$	−78.9583	−3.39155
$543$	−34.9024	−1.49780
$544$	−38.7395	−1.66094
$545$	10.1121	0.433155
$546$	−4.42612	−0.189420
$547$	21.6130	0.924106	0.462053	−	0.886852i	$-0.347113\pi$
$547$	21.6130	0.924106	0.462053	+	0.886852i	$0.347113\pi$
$548$	−14.7711	−0.630992
$549$	−13.3313	−0.568966
$550$	−2.44598	−0.104297
$551$	42.4490	1.80839
$552$	55.7025	2.37086
$553$	−11.1885	−0.475782
$554$	−51.3138	−2.18011
$555$	5.84148	0.247957
$556$	−105.814	−4.48752
$557$	34.7922	1.47419	0.737096	−	0.675788i	$-0.236197\pi$
$557$	34.7922	1.47419	0.737096	+	0.675788i	$0.236197\pi$
$558$	−8.24145	−0.348889
$559$	5.63578	0.238368
$560$	−18.4659	−0.780327
$561$	−21.1314	−0.892168
$562$	28.8070	1.21515
$563$	30.9153	1.30292	0.651462	−	0.758681i	$-0.274156\pi$
$563$	30.9153	1.30292	0.651462	+	0.758681i	$0.274156\pi$
$564$	19.0542	0.802326
$565$	20.5455	0.864354
$566$	−5.88537	−0.247380
$567$	−4.90469	−0.205977
$568$	49.5845	2.08052
$569$	16.4744	0.690644	0.345322	−	0.938484i	$-0.387770\pi$
$569$	16.4744	0.690644	0.345322	+	0.938484i	$0.387770\pi$
$570$	−37.5990	−1.57485
$571$	−30.5979	−1.28048	−0.640241	−	0.768174i	$-0.721166\pi$
$571$	−30.5979	−1.28048	−0.640241	+	0.768174i	$0.721166\pi$
$572$	−18.0308	−0.753905
$573$	23.3430	0.975168
$574$	−14.8901	−0.621502
$575$	1.70994	0.0713094
$576$	−4.16631	−0.173596
$577$	29.5228	1.22905	0.614526	−	0.788897i	$-0.289347\pi$
$577$	29.5228	1.22905	0.614526	+	0.788897i	$0.289347\pi$
$578$	−14.1057	−0.586721
$579$	−12.7617	−0.530358
$580$	90.2686	3.74820
$581$	2.54325	0.105512
$582$	−33.1476	−1.37401
$583$	1.97563	0.0818221
$584$	−42.0285	−1.73915
$585$	2.68893	0.111174
$586$	32.0101	1.32233
$587$	18.6398	0.769348	0.384674	−	0.923053i	$-0.374314\pi$
$587$	18.6398	0.769348	0.384674	+	0.923053i	$0.374314\pi$
$588$	6.58209	0.271441
$589$	14.9250	0.614974
$590$	−69.5441	−2.86308
$591$	−3.71726	−0.152908
$592$	−16.3020	−0.670010
$593$	4.46977	0.183551	0.0917757	−	0.995780i	$-0.470746\pi$
$593$	4.46977	0.183551	0.0917757	+	0.995780i	$0.470746\pi$
$594$	−46.3045	−1.89989
$595$	−10.2754	−0.421252
$596$	−29.8788	−1.22389
$597$	25.9050	1.06022
$598$	17.9958	0.735903
$599$	23.2416	0.949627	0.474814	−	0.880086i	$-0.342516\pi$
$599$	23.2416	0.949627	0.474814	+	0.880086i	$0.342516\pi$
$600$	2.90853	0.118740
$601$	20.2537	0.826166	0.413083	−	0.910693i	$-0.364452\pi$
$601$	20.2537	0.826166	0.413083	+	0.910693i	$0.364452\pi$
$602$	−11.9653	−0.487668
$603$	−12.1921	−0.496500
$604$	95.1674	3.87230
$605$	2.08937	0.0849448
$606$	−55.9678	−2.27354
$607$	15.8435	0.643067	0.321534	−	0.946898i	$-0.395802\pi$
$607$	15.8435	0.643067	0.321534	+	0.946898i	$0.395802\pi$
$608$	38.9774	1.58074
$609$	−12.5301	−0.507747
$610$	73.2961	2.96767
$611$	3.52316	0.142532
$612$	−22.5833	−0.912874
$613$	−1.88452	−0.0761150	−0.0380575	−	0.999276i	$-0.512117\pi$
$613$	−1.88452	−0.0761150	−0.0380575	+	0.999276i	$0.512117\pi$
$614$	−31.6798	−1.27849
$615$	−17.5862	−0.709144
$616$	21.9093	0.882751
$617$	37.1643	1.49618	0.748089	−	0.663599i	$-0.230972\pi$
$617$	37.1643	1.49618	0.748089	+	0.663599i	$0.230972\pi$
$618$	−35.0160	−1.40855
$619$	8.30855	0.333949	0.166974	−	0.985961i	$-0.446600\pi$
$619$	8.30855	0.333949	0.166974	+	0.985961i	$0.446600\pi$
$620$	31.7383	1.27464
$621$	32.3706	1.29899
$622$	−26.8030	−1.07470
$623$	−8.94330	−0.358306
$624$	14.5887	0.584014
$625$	−23.4167	−0.936667
$626$	−26.6473	−1.06504
$627$	21.2611	0.849088
$628$	32.1746	1.28391
$629$	−9.07134	−0.361698
$630$	−5.70885	−0.227446
$631$	31.2650	1.24464	0.622321	−	0.782762i	$-0.286190\pi$
$631$	31.2650	1.24464	0.622321	+	0.782762i	$0.286190\pi$
$632$	77.3768	3.07788
$633$	26.7307	1.06245
$634$	75.8487	3.01234
$635$	−18.2190	−0.723000
$636$	−4.10469	−0.162762
$637$	1.21704	0.0482210
$638$	−72.8744	−2.88512
$639$	7.30593	0.289018
$640$	−12.5415	−0.495746
$641$	−3.21887	−0.127138	−0.0635688	−	0.997977i	$-0.520248\pi$
$641$	−3.21887	−0.127138	−0.0635688	+	0.997977i	$0.520248\pi$
$642$	−17.5251	−0.691660
$643$	−18.0704	−0.712628	−0.356314	−	0.934366i	$-0.615967\pi$
$643$	−18.0704	−0.712628	−0.356314	+	0.934366i	$0.615967\pi$
$644$	−26.7616	−1.05455
$645$	−14.1317	−0.556436
$646$	58.3883	2.29726
$647$	−27.3717	−1.07609	−0.538047	−	0.842915i	$-0.680838\pi$
$647$	−27.3717	−1.07609	−0.538047	+	0.842915i	$0.680838\pi$
$648$	33.9197	1.33249
$649$	39.3251	1.54365
$650$	0.939657	0.0368564
$651$	−4.40558	−0.172668
$652$	72.7985	2.85101
$653$	23.0635	0.902543	0.451271	−	0.892387i	$-0.350971\pi$
$653$	23.0635	0.902543	0.451271	+	0.892387i	$0.350971\pi$
$654$	16.9611	0.663233
$655$	−36.7344	−1.43533
$656$	49.0785	1.91619
$657$	−6.19262	−0.241597
$658$	−7.47999	−0.291600
$659$	10.5894	0.412503	0.206252	−	0.978499i	$-0.433873\pi$
$659$	10.5894	0.412503	0.206252	+	0.978499i	$0.433873\pi$
$660$	45.2122	1.75988
$661$	−16.6479	−0.647528	−0.323764	−	0.946138i	$-0.604948\pi$
$661$	−16.6479	−0.647528	−0.323764	+	0.946138i	$0.604948\pi$
$662$	62.5778	2.43215
$663$	8.11793	0.315274
$664$	−17.5885	−0.682568
$665$	10.3385	0.400911
$666$	−5.03987	−0.195291
$667$	50.9452	1.97261
$668$	−31.1411	−1.20488
$669$	−32.3104	−1.24919
$670$	67.0326	2.58969
$671$	−41.4468	−1.60004
$672$	−11.5054	−0.443830
$673$	34.7365	1.33899	0.669496	−	0.742815i	$-0.266510\pi$
$673$	34.7365	1.33899	0.669496	+	0.742815i	$0.266510\pi$
$674$	−45.5487	−1.75447
$675$	1.69025	0.0650576
$676$	−53.8676	−2.07183
$677$	−26.8774	−1.03298	−0.516492	−	0.856292i	$-0.672762\pi$
$677$	−26.8774	−1.03298	−0.516492	+	0.856292i	$0.672762\pi$
$678$	34.4611	1.32347
$679$	9.11453	0.349784
$680$	71.0625	2.72512
$681$	14.7918	0.566822
$682$	−25.6225	−0.981138
$683$	23.4514	0.897345	0.448672	−	0.893696i	$-0.351897\pi$
$683$	23.4514	0.897345	0.448672	+	0.893696i	$0.351897\pi$
$684$	22.7219	0.868795
$685$	6.84854	0.261669
$686$	−2.58389	−0.0986534
$687$	29.8051	1.13714
$688$	39.4380	1.50356
$689$	−0.758966	−0.0289143
$690$	−45.1245	−1.71786
$691$	−40.4654	−1.53938	−0.769689	−	0.638419i	$-0.779589\pi$
$691$	−40.4654	−1.53938	−0.769689	+	0.638419i	$0.779589\pi$
$692$	49.7897	1.89272
$693$	3.22819	0.122629
$694$	37.4303	1.42083
$695$	49.0600	1.86095
$696$	86.6555	3.28467
$697$	27.3099	1.03444
$698$	74.9731	2.83777
$699$	−28.4105	−1.07458
$700$	−1.39737	−0.0528154
$701$	16.0954	0.607915	0.303957	−	0.952686i	$-0.401692\pi$
$701$	16.0954	0.607915	0.303957	+	0.952686i	$0.401692\pi$
$702$	17.7885	0.671385
$703$	9.12705	0.344233
$704$	−12.9530	−0.488184
$705$	−8.83434	−0.332721
$706$	50.7056	1.90833
$707$	15.3894	0.578777
$708$	−81.7044	−3.07064
$709$	−25.2079	−0.946703	−0.473352	−	0.880874i	$-0.656956\pi$
$709$	−25.2079	−0.946703	−0.473352	+	0.880874i	$0.656956\pi$
$710$	−40.1683	−1.50749
$711$	11.4009	0.427568
$712$	61.8498	2.31792
$713$	17.9123	0.670820
$714$	−17.2351	−0.645007
$715$	8.35984	0.312640
$716$	−68.2661	−2.55122
$717$	11.2556	0.420350
$718$	−91.0382	−3.39751
$719$	34.6652	1.29279	0.646397	−	0.763001i	$-0.276275\pi$
$719$	34.6652	1.29279	0.646397	+	0.763001i	$0.276275\pi$
$720$	18.8166	0.701253
$721$	9.62828	0.358576
$722$	−9.65290	−0.359244
$723$	0.940891	0.0349921
$724$	−115.966	−4.30985
$725$	2.66012	0.0987945
$726$	3.50452	0.130065
$727$	33.4073	1.23901	0.619505	−	0.784993i	$-0.287333\pi$
$727$	33.4073	1.23901	0.619505	+	0.784993i	$0.287333\pi$
$728$	−8.41678	−0.311947
$729$	28.8828	1.06973
$730$	34.0473	1.26015
$731$	21.9454	0.811681
$732$	86.1125	3.18281
$733$	−35.1577	−1.29858	−0.649289	−	0.760542i	$-0.724933\pi$
$733$	−35.1577	−1.29858	−0.649289	+	0.760542i	$0.724933\pi$
$734$	−82.9863	−3.06308
$735$	−3.05174	−0.112565
$736$	46.7788	1.72429
$737$	−37.9050	−1.39625
$738$	15.1729	0.558522
$739$	−29.9573	−1.10200	−0.550998	−	0.834506i	$-0.685753\pi$
$739$	−29.9573	−1.10200	−0.550998	+	0.834506i	$0.685753\pi$
$740$	19.4088	0.713483
$741$	−8.16778	−0.300051
$742$	1.61135	0.0591547
$743$	38.5524	1.41435	0.707175	−	0.707039i	$-0.249969\pi$
$743$	38.5524	1.41435	0.707175	+	0.707039i	$0.249969\pi$
$744$	30.4679	1.11701
$745$	13.8531	0.507539
$746$	−37.7943	−1.38375
$747$	−2.59155	−0.0948199
$748$	−70.2110	−2.56717
$749$	4.81884	0.176077
$750$	−41.7830	−1.52570
$751$	10.7625	0.392729	0.196364	−	0.980531i	$-0.437086\pi$
$751$	10.7625	0.392729	0.196364	+	0.980531i	$0.437086\pi$
$752$	24.6543	0.899051
$753$	24.9732	0.910074
$754$	27.9958	1.01955
$755$	−44.1237	−1.60583
$756$	−26.4533	−0.962099
$757$	5.24608	0.190672	0.0953360	−	0.995445i	$-0.469607\pi$
$757$	5.24608	0.190672	0.0953360	+	0.995445i	$0.469607\pi$
$758$	78.5095	2.85159
$759$	25.5166	0.926193
$760$	−71.4989	−2.59354
$761$	17.7460	0.643291	0.321646	−	0.946860i	$-0.395764\pi$
$761$	17.7460	0.643291	0.321646	+	0.946860i	$0.395764\pi$
$762$	−30.5589	−1.10703
$763$	−4.66377	−0.168840
$764$	77.5593	2.80600
$765$	10.4706	0.378564
$766$	82.5023	2.98093
$767$	−15.1073	−0.545494
$768$	−32.5454	−1.17438
$769$	12.5287	0.451798	0.225899	−	0.974151i	$-0.427468\pi$
$769$	12.5287	0.451798	0.225899	+	0.974151i	$0.427468\pi$
$770$	−17.7487	−0.639619
$771$	11.1051	0.399940
$772$	−42.4019	−1.52608
$773$	3.54616	0.127547	0.0637733	−	0.997964i	$-0.479687\pi$
$773$	3.54616	0.127547	0.0637733	+	0.997964i	$0.479687\pi$
$774$	12.1925	0.438250
$775$	0.935296	0.0335968
$776$	−63.0340	−2.26279
$777$	−2.69413	−0.0966514
$778$	−23.6626	−0.848344
$779$	−27.4776	−0.984489
$780$	−17.3689	−0.621908
$781$	22.7140	0.812771
$782$	70.0747	2.50587
$783$	50.3585	1.79967
$784$	8.51660	0.304164
$785$	−14.9175	−0.532429
$786$	−61.6151	−2.19774
$787$	−16.3250	−0.581924	−0.290962	−	0.956735i	$-0.593975\pi$
$787$	−16.3250	−0.581924	−0.290962	+	0.956735i	$0.593975\pi$
$788$	−12.3510	−0.439984
$789$	−16.3080	−0.580579
$790$	−62.6828	−2.23016
$791$	−9.47571	−0.336917
$792$	−22.3254	−0.793298
$793$	15.9224	0.565421
$794$	−77.9720	−2.76712
$795$	1.90311	0.0674964
$796$	86.0718	3.05074
$797$	−23.2658	−0.824115	−0.412058	−	0.911158i	$-0.635190\pi$
$797$	−23.2658	−0.824115	−0.412058	+	0.911158i	$0.635190\pi$
$798$	17.3409	0.613863
$799$	13.7190	0.485344
$800$	2.44257	0.0863580
$801$	9.11314	0.321997
$802$	45.4137	1.60361
$803$	−19.2527	−0.679414
$804$	78.7537	2.77743
$805$	12.4078	0.437318
$806$	9.84327	0.346714
$807$	16.6856	0.587361
$808$	−106.429	−3.74417
$809$	52.5787	1.84857	0.924285	−	0.381704i	$-0.124662\pi$
$809$	52.5787	1.84857	0.924285	+	0.381704i	$0.124662\pi$
$810$	−27.4783	−0.965488
$811$	13.1212	0.460749	0.230374	−	0.973102i	$-0.426005\pi$
$811$	13.1212	0.460749	0.230374	+	0.973102i	$0.426005\pi$
$812$	−41.6325	−1.46101
$813$	43.0097	1.50842
$814$	−15.6689	−0.549194
$815$	−33.7525	−1.18230
$816$	56.8075	1.98866
$817$	−22.0802	−0.772489
$818$	−23.4787	−0.820914
$819$	−1.24015	−0.0433345
$820$	−58.4317	−2.04053
$821$	−19.1866	−0.669617	−0.334809	−	0.942286i	$-0.608672\pi$
$821$	−19.1866	−0.669617	−0.334809	+	0.942286i	$0.608672\pi$
$822$	11.4871	0.400659
$823$	−52.2064	−1.81980	−0.909900	−	0.414827i	$-0.863842\pi$
$823$	−52.2064	−1.81980	−0.909900	+	0.414827i	$0.863842\pi$
$824$	−66.5869	−2.31967
$825$	1.33236	0.0463868
$826$	32.0742	1.11601
$827$	−17.8820	−0.621819	−0.310909	−	0.950440i	$-0.600634\pi$
$827$	−17.8820	−0.621819	−0.310909	+	0.950440i	$0.600634\pi$
$828$	27.2698	0.947690
$829$	−56.3134	−1.95584	−0.977922	−	0.208968i	$-0.932989\pi$
$829$	−56.3134	−1.95584	−0.977922	+	0.208968i	$0.932989\pi$
$830$	14.2485	0.494571
$831$	27.9514	0.969622
$832$	4.97608	0.172514
$833$	4.73910	0.164200
$834$	82.2889	2.84943
$835$	14.4383	0.499660
$836$	70.6421	2.44321
$837$	17.7060	0.612008
$838$	−72.5107	−2.50484
$839$	20.2365	0.698642	0.349321	−	0.937003i	$-0.386412\pi$
$839$	20.2365	0.698642	0.349321	+	0.937003i	$0.386412\pi$
$840$	21.1051	0.728196
$841$	50.2546	1.73292
$842$	78.1855	2.69445
$843$	−15.6916	−0.540447
$844$	88.8153	3.05715
$845$	24.9754	0.859178
$846$	7.62204	0.262051
$847$	−0.963631	−0.0331107
$848$	−5.31108	−0.182383
$849$	3.20584	0.110024
$850$	3.65898	0.125502
$851$	10.9538	0.375493
$852$	−47.1921	−1.61677
$853$	0.939780	0.0321775	0.0160887	−	0.999871i	$-0.494879\pi$
$853$	0.939780	0.0321775	0.0160887	+	0.999871i	$0.494879\pi$
$854$	−33.8047	−1.15677
$855$	−10.5349	−0.360285
$856$	−33.3260	−1.13906
$857$	4.78546	0.163468	0.0817342	−	0.996654i	$-0.473954\pi$
$857$	4.78546	0.163468	0.0817342	+	0.996654i	$0.473954\pi$
$858$	14.0221	0.478705
$859$	12.6053	0.430086	0.215043	−	0.976605i	$-0.431011\pi$
$859$	12.6053	0.430086	0.215043	+	0.976605i	$0.431011\pi$
$860$	−46.9540	−1.60112
$861$	8.11088	0.276418
$862$	75.4205	2.56883
$863$	−1.00000	−0.0340404
$863$	−1.00000	−0.0340404
$864$	46.2401	1.57312
$865$	−23.0846	−0.784901
$866$	−53.6729	−1.82388
$867$	7.68360	0.260949
$868$	−14.6379	−0.496844
$869$	35.4453	1.20240
$870$	−70.1995	−2.37999
$871$	14.5617	0.493406
$872$	32.2536	1.09224
$873$	−9.28762	−0.314338
$874$	−70.5051	−2.38487
$875$	11.4890	0.388399
$876$	40.0007	1.35150
$877$	17.9131	0.604881	0.302441	−	0.953168i	$-0.402199\pi$
$877$	17.9131	0.604881	0.302441	+	0.953168i	$0.402199\pi$
$878$	−1.76812	−0.0596712
$879$	−17.4364	−0.588115
$880$	58.5004	1.97205
$881$	33.5258	1.12951	0.564757	−	0.825258i	$-0.308970\pi$
$881$	33.5258	1.12951	0.564757	+	0.825258i	$0.308970\pi$
$882$	2.63296	0.0886564
$883$	12.0913	0.406904	0.203452	−	0.979085i	$-0.434784\pi$
$883$	12.0913	0.406904	0.203452	+	0.979085i	$0.434784\pi$
$884$	26.9726	0.907186
$885$	37.8817	1.27338
$886$	−10.6069	−0.356346
$887$	24.5908	0.825680	0.412840	−	0.910804i	$-0.364537\pi$
$887$	24.5908	0.825680	0.412840	+	0.910804i	$0.364537\pi$
$888$	18.6320	0.625248
$889$	8.40274	0.281819
$890$	−50.1044	−1.67950
$891$	15.5382	0.520548
$892$	−107.354	−3.59449
$893$	−13.8033	−0.461909
$894$	23.2360	0.777127
$895$	31.6511	1.05798
$896$	5.78423	0.193237
$897$	−9.80257	−0.327298
$898$	73.7397	2.46072
$899$	27.8658	0.929377
$900$	1.42390	0.0474634
$901$	−2.95538	−0.0984579
$902$	47.1723	1.57067
$903$	6.51765	0.216894
$904$	65.5318	2.17956
$905$	53.7670	1.78727
$906$	−74.0091	−2.45879
$907$	46.2903	1.53705	0.768523	−	0.639822i	$-0.220992\pi$
$907$	46.2903	1.53705	0.768523	+	0.639822i	$0.220992\pi$
$908$	49.1470	1.63100
$909$	−15.6816	−0.520127
$910$	6.81842	0.226029
$911$	−41.3060	−1.36853	−0.684265	−	0.729233i	$-0.739877\pi$
$911$	−41.3060	−1.36853	−0.684265	+	0.729233i	$0.739877\pi$
$912$	−57.1564	−1.89264
$913$	−8.05708	−0.266651
$914$	100.612	3.32794
$915$	−39.9255	−1.31990
$916$	99.0302	3.27205
$917$	16.9422	0.559480
$918$	69.2677	2.28617
$919$	1.96299	0.0647530	0.0323765	−	0.999476i	$-0.489692\pi$
$919$	1.96299	0.0647530	0.0323765	+	0.999476i	$0.489692\pi$
$920$	−85.8095	−2.82906
$921$	17.2565	0.568620
$922$	68.9237	2.26988
$923$	−8.72592	−0.287217
$924$	−20.8522	−0.685987
$925$	0.571959	0.0188059
$926$	4.41945	0.145232
$927$	−9.81113	−0.322240
$928$	72.7730	2.38889
$929$	34.1404	1.12011	0.560054	−	0.828456i	$-0.310780\pi$
$929$	34.1404	1.12011	0.560054	+	0.828456i	$0.310780\pi$
$930$	−24.6820	−0.809356
$931$	−4.76821	−0.156272
$932$	−94.3964	−3.09206
$933$	14.6000	0.477981
$934$	−99.5189	−3.25636
$935$	32.5528	1.06459
$936$	8.57662	0.280336
$937$	−38.4027	−1.25456	−0.627280	−	0.778794i	$-0.715832\pi$
$937$	−38.4027	−1.25456	−0.627280	+	0.778794i	$0.715832\pi$
$938$	−30.9159	−1.00944
$939$	14.5152	0.473685
$940$	−29.3529	−0.957387
$941$	26.2195	0.854730	0.427365	−	0.904079i	$-0.359442\pi$
$941$	26.2195	0.854730	0.427365	+	0.904079i	$0.359442\pi$
$942$	−25.0213	−0.815238
$943$	−32.9773	−1.07389
$944$	−105.718	−3.44082
$945$	12.2649	0.398978
$946$	37.9062	1.23244
$947$	−40.1010	−1.30311	−0.651554	−	0.758603i	$-0.725882\pi$
$947$	−40.1010	−1.30311	−0.651554	+	0.758603i	$0.725882\pi$
$948$	−73.6434	−2.39183
$949$	7.39622	0.240091
$950$	−3.68145	−0.119442
$951$	−41.3159	−1.33976
$952$	−32.7745	−1.06223
$953$	21.1875	0.686332	0.343166	−	0.939275i	$-0.388501\pi$
$953$	21.1875	0.686332	0.343166	+	0.939275i	$0.388501\pi$
$954$	−1.64195	−0.0531602
$955$	−35.9598	−1.16363
$956$	37.3979	1.20954
$957$	39.6957	1.28318
$958$	−70.0148	−2.26208
$959$	−3.15859	−0.101996
$960$	−12.4775	−0.402711
$961$	−21.2024	−0.683949
$962$	6.01943	0.194074
$963$	−4.91035	−0.158234
$964$	3.12620	0.100688
$965$	19.6593	0.632857
$966$	20.8117	0.669607
$967$	7.11479	0.228796	0.114398	−	0.993435i	$-0.463506\pi$
$967$	7.11479	0.228796	0.114398	+	0.993435i	$0.463506\pi$
$968$	6.66425	0.214197
$969$	−31.8049	−1.02172
$970$	51.0638	1.63956
$971$	−1.50885	−0.0484213	−0.0242107	−	0.999707i	$-0.507707\pi$
$971$	−1.50885	−0.0484213	−0.0242107	+	0.999707i	$0.507707\pi$
$972$	47.0770	1.50999
$973$	−22.6268	−0.725383
$974$	47.2867	1.51516
$975$	−0.511845	−0.0163922
$976$	111.422	3.56652
$977$	24.3726	0.779749	0.389874	−	0.920868i	$-0.372518\pi$
$977$	24.3726	0.779749	0.389874	+	0.920868i	$0.372518\pi$
$978$	−56.6134	−1.81030
$979$	28.3326	0.905513
$980$	−10.1397	−0.323900
$981$	4.75234	0.151730
$982$	−76.0542	−2.42699
$983$	−22.4254	−0.715261	−0.357630	−	0.933863i	$-0.616415\pi$
$983$	−22.4254	−0.715261	−0.357630	+	0.933863i	$0.616415\pi$
$984$	−56.0929	−1.78818
$985$	5.72643	0.182459
$986$	109.014	3.47172
$987$	4.07446	0.129692
$988$	−27.1382	−0.863381
$989$	−26.4996	−0.842637
$990$	18.0858	0.574803
$991$	29.8617	0.948588	0.474294	−	0.880367i	$-0.342703\pi$
$991$	29.8617	0.948588	0.474294	+	0.880367i	$0.342703\pi$
$992$	25.5869	0.812385
$993$	−34.0870	−1.08172
$994$	18.5259	0.587606
$995$	−39.9066	−1.26512
$996$	16.7399	0.530424
$997$	−29.8203	−0.944418	−0.472209	−	0.881487i	$-0.656543\pi$
$997$	−29.8203	−0.944418	−0.472209	+	0.881487i	$0.656543\pi$
$998$	−14.5871	−0.461746
$999$	10.8277	0.342573

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6041.2.a.f.1.10	✓	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6041.2.a.f.1.10	✓	132	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:	\( N \)	\(=\)	\( 6041 = 7 \cdot 863 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.58389 q^{2} +1.40748 q^{3} +4.67649 q^{4} -2.16822 q^{5} -3.63678 q^{6} +1.00000 q^{7} -6.91577 q^{8} -1.01899 q^{9} +O(q^{10})\)	\(q-2.58389 q^{2} +1.40748 q^{3} +4.67649 q^{4} -2.16822 q^{5} -3.63678 q^{6} +1.00000 q^{7} -6.91577 q^{8} -1.01899 q^{9} +5.60245 q^{10} -3.16802 q^{11} +6.58209 q^{12} +1.21704 q^{13} -2.58389 q^{14} -3.05174 q^{15} +8.51660 q^{16} +4.73910 q^{17} +2.63296 q^{18} -4.76821 q^{19} -10.1397 q^{20} +1.40748 q^{21} +8.18583 q^{22} -5.72257 q^{23} -9.73383 q^{24} -0.298806 q^{25} -3.14471 q^{26} -5.65666 q^{27} +4.67649 q^{28} -8.90251 q^{29} +7.88536 q^{30} -3.13011 q^{31} -8.17444 q^{32} -4.45894 q^{33} -12.2453 q^{34} -2.16822 q^{35} -4.76530 q^{36} -1.91415 q^{37} +12.3205 q^{38} +1.71297 q^{39} +14.9949 q^{40} +5.76268 q^{41} -3.63678 q^{42} +4.63071 q^{43} -14.8152 q^{44} +2.20940 q^{45} +14.7865 q^{46} +2.89486 q^{47} +11.9870 q^{48} +1.00000 q^{49} +0.772083 q^{50} +6.67021 q^{51} +5.69149 q^{52} -0.623615 q^{53} +14.6162 q^{54} +6.86898 q^{55} -6.91577 q^{56} -6.71117 q^{57} +23.0031 q^{58} -12.4131 q^{59} -14.2714 q^{60} +13.0829 q^{61} +8.08786 q^{62} -1.01899 q^{63} +4.08866 q^{64} -2.63882 q^{65} +11.5214 q^{66} +11.9649 q^{67} +22.1624 q^{68} -8.05442 q^{69} +5.60245 q^{70} -7.16977 q^{71} +7.04710 q^{72} +6.07721 q^{73} +4.94595 q^{74} -0.420565 q^{75} -22.2985 q^{76} -3.16802 q^{77} -4.42612 q^{78} -11.1885 q^{79} -18.4659 q^{80} -4.90469 q^{81} -14.8901 q^{82} +2.54325 q^{83} +6.58209 q^{84} -10.2754 q^{85} -11.9653 q^{86} -12.5301 q^{87} +21.9093 q^{88} -8.94330 q^{89} -5.70885 q^{90} +1.21704 q^{91} -26.7616 q^{92} -4.40558 q^{93} -7.47999 q^{94} +10.3385 q^{95} -11.5054 q^{96} +9.11453 q^{97} -2.58389 q^{98} +3.22819 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 8 q^{2} + 10 q^{3} + 174 q^{4} + 11 q^{5} + 16 q^{6} + 132 q^{7} + 30 q^{8} + 178 q^{9}+O(q^{10}) \) 132 * q + 8 * q^2 + 10 * q^3 + 174 * q^4 + 11 * q^5 + 16 * q^6 + 132 * q^7 + 30 * q^8 + 178 * q^9	\( 132 q + 8 q^{2} + 10 q^{3} + 174 q^{4} + 11 q^{5} + 16 q^{6} + 132 q^{7} + 30 q^{8} + 178 q^{9} + 22 q^{10} + 32 q^{11} + 30 q^{12} + 16 q^{13} + 8 q^{14} + 59 q^{15} + 254 q^{16} + 11 q^{17} + 33 q^{18} + 40 q^{19} + 4 q^{20} + 10 q^{21} + 66 q^{22} + 62 q^{23} + 36 q^{24} + 235 q^{25} + 25 q^{26} + 37 q^{27} + 174 q^{28} + 28 q^{29} + 45 q^{30} + 121 q^{31} + 53 q^{32} - 13 q^{33} + 44 q^{34} + 11 q^{35} + 274 q^{36} + 61 q^{37} - 28 q^{38} + 114 q^{39} + 32 q^{40} - q^{41} + 16 q^{42} + 105 q^{43} + 54 q^{44} + 29 q^{45} + 104 q^{46} + 33 q^{47} + 16 q^{48} + 132 q^{49} - 14 q^{50} + 53 q^{51} - 11 q^{52} + 48 q^{53} + 11 q^{54} + 118 q^{55} + 30 q^{56} + 93 q^{57} + 87 q^{58} + 12 q^{59} + 41 q^{60} + 54 q^{61} - 28 q^{62} + 178 q^{63} + 376 q^{64} + 22 q^{65} + 6 q^{66} + 123 q^{67} - 47 q^{68} + 58 q^{69} + 22 q^{70} + 108 q^{71} + 97 q^{72} + q^{73} - 10 q^{74} + 23 q^{75} + 71 q^{76} + 32 q^{77} + 5 q^{78} + 204 q^{79} - 10 q^{80} + 296 q^{81} + 80 q^{82} - 10 q^{83} + 30 q^{84} + 94 q^{85} + 48 q^{86} + 4 q^{87} + 155 q^{88} + q^{89} - 66 q^{90} + 16 q^{91} + 49 q^{92} + 90 q^{93} + 79 q^{94} + 100 q^{95} + q^{96} + 18 q^{97} + 8 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q + 8 * q^2 + 10 * q^3 + 174 * q^4 + 11 * q^5 + 16 * q^6 + 132 * q^7 + 30 * q^8 + 178 * q^9 + 22 * q^10 + 32 * q^11 + 30 * q^12 + 16 * q^13 + 8 * q^14 + 59 * q^15 + 254 * q^16 + 11 * q^17 + 33 * q^18 + 40 * q^19 + 4 * q^20 + 10 * q^21 + 66 * q^22 + 62 * q^23 + 36 * q^24 + 235 * q^25 + 25 * q^26 + 37 * q^27 + 174 * q^28 + 28 * q^29 + 45 * q^30 + 121 * q^31 + 53 * q^32 - 13 * q^33 + 44 * q^34 + 11 * q^35 + 274 * q^36 + 61 * q^37 - 28 * q^38 + 114 * q^39 + 32 * q^40 - q^41 + 16 * q^42 + 105 * q^43 + 54 * q^44 + 29 * q^45 + 104 * q^46 + 33 * q^47 + 16 * q^48 + 132 * q^49 - 14 * q^50 + 53 * q^51 - 11 * q^52 + 48 * q^53 + 11 * q^54 + 118 * q^55 + 30 * q^56 + 93 * q^57 + 87 * q^58 + 12 * q^59 + 41 * q^60 + 54 * q^61 - 28 * q^62 + 178 * q^63 + 376 * q^64 + 22 * q^65 + 6 * q^66 + 123 * q^67 - 47 * q^68 + 58 * q^69 + 22 * q^70 + 108 * q^71 + 97 * q^72 + q^73 - 10 * q^74 + 23 * q^75 + 71 * q^76 + 32 * q^77 + 5 * q^78 + 204 * q^79 - 10 * q^80 + 296 * q^81 + 80 * q^82 - 10 * q^83 + 30 * q^84 + 94 * q^85 + 48 * q^86 + 4 * q^87 + 155 * q^88 + q^89 - 66 * q^90 + 16 * q^91 + 49 * q^92 + 90 * q^93 + 79 * q^94 + 100 * q^95 + q^96 + 18 * q^97 + 8 * q^98 + 96 * q^99

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