LMFDB - Embedded newform 6031.2.a.e.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6031, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6031 = 37 \cdot 163 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6031.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.1577774590$
Analytic rank:	$0$
Dimension:	$134$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
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)

$f(q)$	$=$	$q-2.41121 q^{2} +3.43364 q^{3} +3.81394 q^{4} -3.49586 q^{5} -8.27924 q^{6} +1.03348 q^{7} -4.37378 q^{8} +8.78990 q^{9} +O(q^{10})$	\(q-2.41121 q^{2} +3.43364 q^{3} +3.81394 q^{4} -3.49586 q^{5} -8.27924 q^{6} +1.03348 q^{7} -4.37378 q^{8} +8.78990 q^{9} +8.42926 q^{10} -3.22025 q^{11} +13.0957 q^{12} -6.27534 q^{13} -2.49195 q^{14} -12.0035 q^{15} +2.91823 q^{16} +7.06009 q^{17} -21.1943 q^{18} -7.74575 q^{19} -13.3330 q^{20} +3.54861 q^{21} +7.76469 q^{22} -2.54416 q^{23} -15.0180 q^{24} +7.22105 q^{25} +15.1312 q^{26} +19.8805 q^{27} +3.94164 q^{28} +1.00414 q^{29} +28.9431 q^{30} +1.23625 q^{31} +1.71109 q^{32} -11.0572 q^{33} -17.0234 q^{34} -3.61291 q^{35} +33.5241 q^{36} +1.00000 q^{37} +18.6766 q^{38} -21.5473 q^{39} +15.2901 q^{40} +8.56152 q^{41} -8.55645 q^{42} +4.00022 q^{43} -12.2818 q^{44} -30.7283 q^{45} +6.13451 q^{46} -11.6375 q^{47} +10.0202 q^{48} -5.93191 q^{49} -17.4115 q^{50} +24.2418 q^{51} -23.9337 q^{52} -1.12256 q^{53} -47.9360 q^{54} +11.2575 q^{55} -4.52023 q^{56} -26.5962 q^{57} -2.42120 q^{58} +15.0274 q^{59} -45.7807 q^{60} -3.69775 q^{61} -2.98085 q^{62} +9.08422 q^{63} -9.96225 q^{64} +21.9377 q^{65} +26.6612 q^{66} -2.74794 q^{67} +26.9267 q^{68} -8.73574 q^{69} +8.71150 q^{70} +11.4646 q^{71} -38.4451 q^{72} -5.08480 q^{73} -2.41121 q^{74} +24.7945 q^{75} -29.5418 q^{76} -3.32807 q^{77} +51.9550 q^{78} +8.22847 q^{79} -10.2017 q^{80} +41.8927 q^{81} -20.6436 q^{82} +5.10956 q^{83} +13.5342 q^{84} -24.6811 q^{85} -9.64536 q^{86} +3.44787 q^{87} +14.0846 q^{88} -2.23967 q^{89} +74.0924 q^{90} -6.48546 q^{91} -9.70327 q^{92} +4.24484 q^{93} +28.0603 q^{94} +27.0781 q^{95} +5.87526 q^{96} +11.0477 q^{97} +14.3031 q^{98} -28.3056 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 134 q + 9 q^{2} + 7 q^{3} + 149 q^{4} + 22 q^{5} + 20 q^{6} + 11 q^{7} + 27 q^{8} + 181 q^{9}+O(q^{10}) $ 134 * q + 9 * q^2 + 7 * q^3 + 149 * q^4 + 22 * q^5 + 20 * q^6 + 11 * q^7 + 27 * q^8 + 181 * q^9	\( 134 q + 9 q^{2} + 7 q^{3} + 149 q^{4} + 22 q^{5} + 20 q^{6} + 11 q^{7} + 27 q^{8} + 181 q^{9} + 15 q^{10} + 20 q^{11} + 28 q^{12} + 11 q^{13} + 17 q^{14} - 13 q^{15} + 143 q^{16} + 76 q^{17} + 23 q^{18} + 15 q^{19} + 67 q^{20} + 63 q^{21} + 2 q^{22} + 22 q^{23} + 33 q^{24} + 160 q^{25} + 65 q^{26} + 31 q^{27} + 10 q^{28} + 73 q^{29} + 20 q^{30} + 10 q^{31} + 53 q^{32} + 72 q^{33} - 7 q^{34} + 52 q^{35} + 201 q^{36} + 134 q^{37} + 70 q^{38} + 6 q^{39} + 11 q^{40} + 182 q^{41} - 15 q^{42} + 12 q^{43} + 33 q^{44} + 29 q^{45} + 24 q^{46} + 80 q^{47} + 21 q^{48} + 229 q^{49} + 37 q^{50} + 57 q^{51} - 15 q^{52} + 75 q^{53} + 95 q^{54} - 9 q^{55} + 39 q^{56} + 19 q^{57} - 21 q^{58} + 91 q^{59} + 62 q^{60} + 58 q^{61} + 108 q^{62} + 9 q^{63} + 167 q^{64} + 76 q^{65} + 105 q^{66} - 17 q^{67} + 109 q^{68} + 48 q^{69} - 55 q^{70} + 56 q^{71} + 48 q^{72} + 54 q^{73} + 9 q^{74} + 28 q^{75} + 82 q^{76} + 156 q^{77} + 16 q^{78} - 2 q^{79} + 98 q^{80} + 270 q^{81} - 42 q^{82} + 130 q^{83} + 229 q^{84} + 22 q^{85} + 72 q^{86} + 22 q^{87} + 61 q^{88} + 157 q^{89} + 176 q^{90} + 31 q^{91} - 18 q^{92} + 36 q^{93} + 83 q^{94} + 98 q^{95} + 111 q^{96} + 35 q^{97} + 53 q^{98} + 55 q^{99}+O(q^{100}) \) 134 * q + 9 * q^2 + 7 * q^3 + 149 * q^4 + 22 * q^5 + 20 * q^6 + 11 * q^7 + 27 * q^8 + 181 * q^9 + 15 * q^10 + 20 * q^11 + 28 * q^12 + 11 * q^13 + 17 * q^14 - 13 * q^15 + 143 * q^16 + 76 * q^17 + 23 * q^18 + 15 * q^19 + 67 * q^20 + 63 * q^21 + 2 * q^22 + 22 * q^23 + 33 * q^24 + 160 * q^25 + 65 * q^26 + 31 * q^27 + 10 * q^28 + 73 * q^29 + 20 * q^30 + 10 * q^31 + 53 * q^32 + 72 * q^33 - 7 * q^34 + 52 * q^35 + 201 * q^36 + 134 * q^37 + 70 * q^38 + 6 * q^39 + 11 * q^40 + 182 * q^41 - 15 * q^42 + 12 * q^43 + 33 * q^44 + 29 * q^45 + 24 * q^46 + 80 * q^47 + 21 * q^48 + 229 * q^49 + 37 * q^50 + 57 * q^51 - 15 * q^52 + 75 * q^53 + 95 * q^54 - 9 * q^55 + 39 * q^56 + 19 * q^57 - 21 * q^58 + 91 * q^59 + 62 * q^60 + 58 * q^61 + 108 * q^62 + 9 * q^63 + 167 * q^64 + 76 * q^65 + 105 * q^66 - 17 * q^67 + 109 * q^68 + 48 * q^69 - 55 * q^70 + 56 * q^71 + 48 * q^72 + 54 * q^73 + 9 * q^74 + 28 * q^75 + 82 * q^76 + 156 * q^77 + 16 * q^78 - 2 * q^79 + 98 * q^80 + 270 * q^81 - 42 * q^82 + 130 * q^83 + 229 * q^84 + 22 * q^85 + 72 * q^86 + 22 * q^87 + 61 * q^88 + 157 * q^89 + 176 * q^90 + 31 * q^91 - 18 * q^92 + 36 * q^93 + 83 * q^94 + 98 * q^95 + 111 * q^96 + 35 * q^97 + 53 * q^98 + 55 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.41121	−1.70498	−0.852492	−	0.522741i	$-0.824910\pi$
$2$	−2.41121	−1.70498	−0.852492	+	0.522741i	$0.824910\pi$
$3$	3.43364	1.98241	0.991207	−	0.132318i	$-0.0422419\pi$
$3$	3.43364	1.98241	0.991207	+	0.132318i	$0.0422419\pi$
$4$	3.81394	1.90697
$5$	−3.49586	−1.56340	−0.781699	−	0.623656i	$-0.785646\pi$
$5$	−3.49586	−1.56340	−0.781699	+	0.623656i	$0.785646\pi$
$6$	−8.27924	−3.37998
$7$	1.03348	0.390620	0.195310	−	0.980742i	$-0.437429\pi$
$7$	1.03348	0.390620	0.195310	+	0.980742i	$0.437429\pi$
$8$	−4.37378	−1.54636
$9$	8.78990	2.92997
$10$	8.42926	2.66557
$11$	−3.22025	−0.970940	−0.485470	−	0.874253i	$-0.661352\pi$
$11$	−3.22025	−0.970940	−0.485470	+	0.874253i	$0.661352\pi$
$12$	13.0957	3.78040
$13$	−6.27534	−1.74047	−0.870233	−	0.492640i	$-0.836032\pi$
$13$	−6.27534	−1.74047	−0.870233	+	0.492640i	$0.836032\pi$
$14$	−2.49195	−0.666000
$15$	−12.0035	−3.09930
$16$	2.91823	0.729558
$17$	7.06009	1.71232	0.856162	−	0.516708i	$-0.172843\pi$
$17$	7.06009	1.71232	0.856162	+	0.516708i	$0.172843\pi$
$18$	−21.1943	−4.99555
$19$	−7.74575	−1.77700	−0.888499	−	0.458879i	$-0.848251\pi$
$19$	−7.74575	−1.77700	−0.888499	+	0.458879i	$0.848251\pi$
$20$	−13.3330	−2.98135
$21$	3.54861	0.774371
$22$	7.76469	1.65544
$23$	−2.54416	−0.530494	−0.265247	−	0.964180i	$-0.585454\pi$
$23$	−2.54416	−0.530494	−0.265247	+	0.964180i	$0.585454\pi$
$24$	−15.0180	−3.06554
$25$	7.22105	1.44421
$26$	15.1312	2.96747
$27$	19.8805	3.82600
$28$	3.94164	0.744900
$29$	1.00414	0.186465	0.0932323	−	0.995644i	$-0.470280\pi$
$29$	1.00414	0.186465	0.0932323	+	0.995644i	$0.470280\pi$
$30$	28.9431	5.28426
$31$	1.23625	0.222037	0.111018	−	0.993818i	$-0.464589\pi$
$31$	1.23625	0.222037	0.111018	+	0.993818i	$0.464589\pi$
$32$	1.71109	0.302480
$33$	−11.0572	−1.92481
$34$	−17.0234	−2.91948
$35$	−3.61291	−0.610694
$36$	33.5241	5.58735
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	18.6766	3.02975
$39$	−21.5473	−3.45033
$40$	15.2901	2.41758
$41$	8.56152	1.33709	0.668543	−	0.743674i	$-0.266918\pi$
$41$	8.56152	1.33709	0.668543	+	0.743674i	$0.266918\pi$
$42$	−8.55645	−1.32029
$43$	4.00022	0.610027	0.305014	−	0.952348i	$-0.401339\pi$
$43$	4.00022	0.610027	0.305014	+	0.952348i	$0.401339\pi$
$44$	−12.2818	−1.85155
$45$	−30.7283	−4.58070
$46$	6.13451	0.904484
$47$	−11.6375	−1.69750	−0.848748	−	0.528797i	$-0.822643\pi$
$47$	−11.6375	−1.69750	−0.848748	+	0.528797i	$0.822643\pi$
$48$	10.0202	1.44629
$49$	−5.93191	−0.847416
$50$	−17.4115	−2.46235
$51$	24.2418	3.39454
$52$	−23.9337	−3.31901
$53$	−1.12256	−0.154196	−0.0770981	−	0.997024i	$-0.524565\pi$
$53$	−1.12256	−0.154196	−0.0770981	+	0.997024i	$0.524565\pi$
$54$	−47.9360	−6.52326
$55$	11.2575	1.51797
$56$	−4.52023	−0.604041
$57$	−26.5962	−3.52275
$58$	−2.42120	−0.317919
$59$	15.0274	1.95640	0.978200	−	0.207665i	$-0.0665863\pi$
$59$	15.0274	1.95640	0.978200	+	0.207665i	$0.0665863\pi$
$60$	−45.7807	−5.91027
$61$	−3.69775	−0.473448	−0.236724	−	0.971577i	$-0.576074\pi$
$61$	−3.69775	−0.473448	−0.236724	+	0.971577i	$0.576074\pi$
$62$	−2.98085	−0.378569
$63$	9.08422	1.14450
$64$	−9.96225	−1.24528
$65$	21.9377	2.72104
$66$	26.6612	3.28176
$67$	−2.74794	−0.335714	−0.167857	−	0.985811i	$-0.553685\pi$
$67$	−2.74794	−0.335714	−0.167857	+	0.985811i	$0.553685\pi$
$68$	26.9267	3.26535
$69$	−8.73574	−1.05166
$70$	8.71150	1.04122
$71$	11.4646	1.36060	0.680301	−	0.732933i	$-0.261849\pi$
$71$	11.4646	1.36060	0.680301	+	0.732933i	$0.261849\pi$
$72$	−38.4451	−4.53080
$73$	−5.08480	−0.595131	−0.297566	−	0.954701i	$-0.596175\pi$
$73$	−5.08480	−0.595131	−0.297566	+	0.954701i	$0.596175\pi$
$74$	−2.41121	−0.280298
$75$	24.7945	2.86302
$76$	−29.5418	−3.38868
$77$	−3.32807	−0.379269
$78$	51.9550	5.88275
$79$	8.22847	0.925775	0.462887	−	0.886417i	$-0.346813\pi$
$79$	8.22847	0.925775	0.462887	+	0.886417i	$0.346813\pi$
$80$	−10.2017	−1.14059
$81$	41.8927	4.65474
$82$	−20.6436	−2.27971
$83$	5.10956	0.560847	0.280423	−	0.959876i	$-0.409525\pi$
$83$	5.10956	0.560847	0.280423	+	0.959876i	$0.409525\pi$
$84$	13.5342	1.47670
$85$	−24.6811	−2.67704
$86$	−9.64536	−1.04009
$87$	3.44787	0.369650
$88$	14.0846	1.50143
$89$	−2.23967	−0.237404	−0.118702	−	0.992930i	$-0.537873\pi$
$89$	−2.23967	−0.237404	−0.118702	+	0.992930i	$0.537873\pi$
$90$	74.0924	7.81002
$91$	−6.48546	−0.679861
$92$	−9.70327	−1.01164
$93$	4.24484	0.440169
$94$	28.0603	2.89420
$95$	27.0781	2.77815
$96$	5.87526	0.599641
$97$	11.0477	1.12173	0.560864	−	0.827908i	$-0.310469\pi$
$97$	11.0477	1.12173	0.560864	+	0.827908i	$0.310469\pi$
$98$	14.3031	1.44483
$99$	−28.3056	−2.84482
$100$	27.5406	2.75406
$101$	17.6324	1.75449	0.877244	−	0.480044i	$-0.159379\pi$
$101$	17.6324	1.75449	0.877244	+	0.480044i	$0.159379\pi$
$102$	−58.4522	−5.78763
$103$	−7.87693	−0.776137	−0.388068	−	0.921631i	$-0.626858\pi$
$103$	−7.87693	−0.776137	−0.388068	+	0.921631i	$0.626858\pi$
$104$	27.4470	2.69140
$105$	−12.4055	−1.21065
$106$	2.70674	0.262902
$107$	6.45879	0.624395	0.312198	−	0.950017i	$-0.398935\pi$
$107$	6.45879	0.624395	0.312198	+	0.950017i	$0.398935\pi$
$108$	75.8228	7.29605
$109$	−5.55377	−0.531955	−0.265978	−	0.963979i	$-0.585695\pi$
$109$	−5.55377	−0.531955	−0.265978	+	0.963979i	$0.585695\pi$
$110$	−27.1443	−2.58811
$111$	3.43364	0.325907
$112$	3.01595	0.284980
$113$	1.34970	0.126969	0.0634845	−	0.997983i	$-0.479779\pi$
$113$	1.34970	0.126969	0.0634845	+	0.997983i	$0.479779\pi$
$114$	64.1289	6.00622
$115$	8.89404	0.829373
$116$	3.82973	0.355582
$117$	−55.1596	−5.09951
$118$	−36.2342	−3.33563
$119$	7.29649	0.668868
$120$	52.5009	4.79265
$121$	−0.630021	−0.0572746
$122$	8.91605	0.807221
$123$	29.3972	2.65066
$124$	4.71497	0.423417
$125$	−7.76449	−0.694477
$126$	−21.9040	−1.95136
$127$	13.8442	1.22847	0.614235	−	0.789123i	$-0.289465\pi$
$127$	13.8442	1.22847	0.614235	+	0.789123i	$0.289465\pi$
$128$	20.5989	1.82070
$129$	13.7353	1.20933
$130$	−52.8965	−4.63933
$131$	−0.673230	−0.0588204	−0.0294102	−	0.999567i	$-0.509363\pi$
$131$	−0.673230	−0.0588204	−0.0294102	+	0.999567i	$0.509363\pi$
$132$	−42.1713	−3.67054
$133$	−8.00511	−0.694131
$134$	6.62586	0.572387
$135$	−69.4994	−5.98155
$136$	−30.8793	−2.64788
$137$	−2.34928	−0.200713	−0.100356	−	0.994952i	$-0.531998\pi$
$137$	−2.34928	−0.200713	−0.100356	+	0.994952i	$0.531998\pi$
$138$	21.0637	1.79306
$139$	−6.60550	−0.560271	−0.280135	−	0.959960i	$-0.590379\pi$
$139$	−6.60550	−0.560271	−0.280135	+	0.959960i	$0.590379\pi$
$140$	−13.7794	−1.16457
$141$	−39.9589	−3.36514
$142$	−27.6436	−2.31980
$143$	20.2081	1.68989
$144$	25.6510	2.13758
$145$	−3.51034	−0.291518
$146$	12.2605	1.01469
$147$	−20.3681	−1.67993
$148$	3.81394	0.313504
$149$	−3.30065	−0.270400	−0.135200	−	0.990818i	$-0.543168\pi$
$149$	−3.30065	−0.270400	−0.135200	+	0.990818i	$0.543168\pi$
$150$	−59.7848	−4.88141
$151$	7.99717	0.650800	0.325400	−	0.945576i	$-0.394501\pi$
$151$	7.99717	0.650800	0.325400	+	0.945576i	$0.394501\pi$
$152$	33.8782	2.74789
$153$	62.0575	5.01705
$154$	8.02467	0.646647
$155$	−4.32175	−0.347132
$156$	−82.1799	−6.57966
$157$	11.1920	0.893222	0.446611	−	0.894728i	$-0.352631\pi$
$157$	11.1920	0.893222	0.446611	+	0.894728i	$0.352631\pi$
$158$	−19.8406	−1.57843
$159$	−3.85449	−0.305681
$160$	−5.98172	−0.472896
$161$	−2.62935	−0.207222
$162$	−101.012	−7.93626
$163$	−1.00000	−0.0783260
$163$	−1.00000	−0.0783260
$164$	32.6531	2.54978
$165$	38.6544	3.00924
$166$	−12.3202	−0.956234
$167$	16.2573	1.25803	0.629013	−	0.777395i	$-0.283459\pi$
$167$	16.2573	1.25803	0.629013	+	0.777395i	$0.283459\pi$
$168$	−15.5209	−1.19746
$169$	26.3799	2.02922
$170$	59.5113	4.56431
$171$	−68.0844	−5.20655
$172$	15.2566	1.16330
$173$	−7.42417	−0.564449	−0.282225	−	0.959348i	$-0.591072\pi$
$173$	−7.42417	−0.564449	−0.282225	+	0.959348i	$0.591072\pi$
$174$	−8.31353	−0.630247
$175$	7.46284	0.564137
$176$	−9.39743	−0.708358
$177$	51.5987	3.87840
$178$	5.40031	0.404770
$179$	−3.96996	−0.296729	−0.148364	−	0.988933i	$-0.547401\pi$
$179$	−3.96996	−0.296729	−0.148364	+	0.988933i	$0.547401\pi$
$180$	−117.196	−8.73525
$181$	11.2306	0.834763	0.417381	−	0.908731i	$-0.362948\pi$
$181$	11.2306	0.834763	0.417381	+	0.908731i	$0.362948\pi$
$182$	15.6378	1.15915
$183$	−12.6968	−0.938571
$184$	11.1276	0.820338
$185$	−3.49586	−0.257021
$186$	−10.2352	−0.750481
$187$	−22.7352	−1.66256
$188$	−44.3845	−3.23707
$189$	20.5461	1.49451
$190$	−65.2910	−4.73671
$191$	−16.5747	−1.19930	−0.599651	−	0.800262i	$-0.704694\pi$
$191$	−16.5747	−1.19930	−0.599651	+	0.800262i	$0.704694\pi$
$192$	−34.2068	−2.46866
$193$	19.2659	1.38679	0.693397	−	0.720556i	$-0.256113\pi$
$193$	19.2659	1.38679	0.693397	+	0.720556i	$0.256113\pi$
$194$	−26.6384	−1.91253
$195$	75.3263	5.39423
$196$	−22.6239	−1.61600
$197$	11.2688	0.802870	0.401435	−	0.915887i	$-0.368512\pi$
$197$	11.2688	0.802870	0.401435	+	0.915887i	$0.368512\pi$
$198$	68.2509	4.85038
$199$	−7.98808	−0.566260	−0.283130	−	0.959082i	$-0.591373\pi$
$199$	−7.98808	−0.566260	−0.283130	+	0.959082i	$0.591373\pi$
$200$	−31.5833	−2.23328
$201$	−9.43545	−0.665525
$202$	−42.5154	−2.99137
$203$	1.03776	0.0728368
$204$	92.4568	6.47327
$205$	−29.9299	−2.09040
$206$	18.9929	1.32330
$207$	−22.3629	−1.55433
$208$	−18.3129	−1.26977
$209$	24.9432	1.72536
$210$	29.9122	2.06414
$211$	15.3500	1.05673	0.528367	−	0.849016i	$-0.322804\pi$
$211$	15.3500	1.05673	0.528367	+	0.849016i	$0.322804\pi$
$212$	−4.28139	−0.294047
$213$	39.3654	2.69728
$214$	−15.5735	−1.06458
$215$	−13.9842	−0.953715
$216$	−86.9528	−5.91639
$217$	1.27764	0.0867320
$218$	13.3913	0.906974
$219$	−17.4594	−1.17980
$220$	42.9355	2.89471
$221$	−44.3045	−2.98024
$222$	−8.27924	−0.555666
$223$	−3.69237	−0.247260	−0.123630	−	0.992328i	$-0.539454\pi$
$223$	−3.69237	−0.247260	−0.123630	+	0.992328i	$0.539454\pi$
$224$	1.76838	0.118155
$225$	63.4724	4.23149
$226$	−3.25441	−0.216480
$227$	6.47620	0.429841	0.214920	−	0.976632i	$-0.431051\pi$
$227$	6.47620	0.429841	0.214920	+	0.976632i	$0.431051\pi$
$228$	−101.436	−6.71777
$229$	−1.77738	−0.117452	−0.0587262	−	0.998274i	$-0.518704\pi$
$229$	−1.77738	−0.117452	−0.0587262	+	0.998274i	$0.518704\pi$
$230$	−21.4454	−1.41407
$231$	−11.4274	−0.751868
$232$	−4.39190	−0.288342
$233$	8.18017	0.535900	0.267950	−	0.963433i	$-0.413654\pi$
$233$	8.18017	0.535900	0.267950	+	0.963433i	$0.413654\pi$
$234$	133.001	8.69458
$235$	40.6829	2.65386
$236$	57.3135	3.73079
$237$	28.2536	1.83527
$238$	−17.5934	−1.14041
$239$	19.2447	1.24483	0.622417	−	0.782686i	$-0.286151\pi$
$239$	19.2447	1.24483	0.622417	+	0.782686i	$0.286151\pi$
$240$	−35.0291	−2.26112
$241$	23.9117	1.54029	0.770144	−	0.637870i	$-0.220184\pi$
$241$	23.9117	1.54029	0.770144	+	0.637870i	$0.220184\pi$
$242$	1.51911	0.0976522
$243$	84.2032	5.40164
$244$	−14.1030	−0.902851
$245$	20.7371	1.32485
$246$	−70.8829	−4.51933
$247$	48.6072	3.09280
$248$	−5.40708	−0.343350
$249$	17.5444	1.11183
$250$	18.7218	1.18407
$251$	−12.2802	−0.775119	−0.387560	−	0.921845i	$-0.626682\pi$
$251$	−12.2802	−0.775119	−0.387560	+	0.921845i	$0.626682\pi$
$252$	34.6466	2.18253
$253$	8.19282	0.515078
$254$	−33.3812	−2.09452
$255$	−84.7461	−5.30701
$256$	−29.7438	−1.85899
$257$	0.0989184	0.00617036	0.00308518	−	0.999995i	$-0.499018\pi$
$257$	0.0989184	0.00617036	0.00308518	+	0.999995i	$0.499018\pi$
$258$	−33.1187	−2.06188
$259$	1.03348	0.0642175
$260$	83.6691	5.18893
$261$	8.82631	0.546335
$262$	1.62330	0.100288
$263$	21.0037	1.29515	0.647573	−	0.762004i	$-0.275784\pi$
$263$	21.0037	1.29515	0.647573	+	0.762004i	$0.275784\pi$
$264$	48.3616	2.97645
$265$	3.92433	0.241070
$266$	19.3020	1.18348
$267$	−7.69022	−0.470634
$268$	−10.4805	−0.640196
$269$	−26.1518	−1.59450	−0.797252	−	0.603646i	$-0.793714\pi$
$269$	−26.1518	−1.59450	−0.797252	+	0.603646i	$0.793714\pi$
$270$	167.578	10.1984
$271$	−10.9248	−0.663632	−0.331816	−	0.943344i	$-0.607661\pi$
$271$	−10.9248	−0.663632	−0.331816	+	0.943344i	$0.607661\pi$
$272$	20.6030	1.24924
$273$	−22.2687	−1.34777
$274$	5.66461	0.342212
$275$	−23.2536	−1.40224
$276$	−33.3175	−2.00548
$277$	−23.2765	−1.39855	−0.699275	−	0.714853i	$-0.746494\pi$
$277$	−23.2765	−1.39855	−0.699275	+	0.714853i	$0.746494\pi$
$278$	15.9272	0.955253
$279$	10.8665	0.650561
$280$	15.8021	0.944356
$281$	−3.93347	−0.234651	−0.117326	−	0.993093i	$-0.537432\pi$
$281$	−3.93347	−0.234651	−0.117326	+	0.993093i	$0.537432\pi$
$282$	96.3492	5.73751
$283$	7.32757	0.435579	0.217789	−	0.975996i	$-0.430115\pi$
$283$	7.32757	0.435579	0.217789	+	0.975996i	$0.430115\pi$
$284$	43.7254	2.59462
$285$	92.9765	5.50745
$286$	−48.7261	−2.88123
$287$	8.84819	0.522292
$288$	15.0403	0.886257
$289$	32.8449	1.93205
$290$	8.46418	0.497033
$291$	37.9340	2.22373
$292$	−19.3931	−1.13490
$293$	−9.10222	−0.531757	−0.265879	−	0.964007i	$-0.585662\pi$
$293$	−9.10222	−0.531757	−0.265879	+	0.964007i	$0.585662\pi$
$294$	49.1117	2.86425
$295$	−52.5337	−3.05863
$296$	−4.37378	−0.254221
$297$	−64.0200	−3.71482
$298$	7.95856	0.461027
$299$	15.9655	0.923307
$300$	94.5647	5.45970
$301$	4.13416	0.238289
$302$	−19.2829	−1.10960
$303$	60.5433	3.47812
$304$	−22.6039	−1.29642
$305$	12.9268	0.740188
$306$	−149.634	−8.55399
$307$	−7.59943	−0.433723	−0.216861	−	0.976202i	$-0.569582\pi$
$307$	−7.59943	−0.433723	−0.216861	+	0.976202i	$0.569582\pi$
$308$	−12.6930	−0.723253
$309$	−27.0466	−1.53863
$310$	10.4207	0.591854
$311$	−13.9351	−0.790185	−0.395092	−	0.918641i	$-0.629287\pi$
$311$	−13.9351	−0.790185	−0.395092	+	0.918641i	$0.629287\pi$
$312$	94.2430	5.33546
$313$	26.0457	1.47219	0.736095	−	0.676878i	$-0.236668\pi$
$313$	26.0457	1.47219	0.736095	+	0.676878i	$0.236668\pi$
$314$	−26.9864	−1.52293
$315$	−31.7572	−1.78931
$316$	31.3828	1.76542
$317$	13.5318	0.760023	0.380011	−	0.924982i	$-0.375920\pi$
$317$	13.5318	0.760023	0.380011	+	0.924982i	$0.375920\pi$
$318$	9.29398	0.521180
$319$	−3.23358	−0.181046
$320$	34.8267	1.94687
$321$	22.1772	1.23781
$322$	6.33991	0.353309
$323$	−54.6857	−3.04280
$324$	159.776	8.87645
$325$	−45.3146	−2.51360
$326$	2.41121	0.133545
$327$	−19.0697	−1.05456
$328$	−37.4462	−2.06762
$329$	−12.0271	−0.663076
$330$	−93.2038	−5.13070
$331$	−28.2957	−1.55527	−0.777636	−	0.628715i	$-0.783581\pi$
$331$	−28.2957	−1.55527	−0.777636	+	0.628715i	$0.783581\pi$
$332$	19.4875	1.06952
$333$	8.78990	0.481684
$334$	−39.1997	−2.14491
$335$	9.60642	0.524855
$336$	10.3557	0.564949
$337$	−2.99840	−0.163333	−0.0816667	−	0.996660i	$-0.526024\pi$
$337$	−2.99840	−0.163333	−0.0816667	+	0.996660i	$0.526024\pi$
$338$	−63.6074	−3.45979
$339$	4.63438	0.251705
$340$	−94.1322	−5.10503
$341$	−3.98102	−0.215584
$342$	164.166	8.87708
$343$	−13.3649	−0.721638
$344$	−17.4961	−0.943325
$345$	30.5389	1.64416
$346$	17.9012	0.962377
$347$	8.58380	0.460803	0.230401	−	0.973096i	$-0.425996\pi$
$347$	8.58380	0.460803	0.230401	+	0.973096i	$0.425996\pi$
$348$	13.1499	0.704911
$349$	−0.647327	−0.0346506	−0.0173253	−	0.999850i	$-0.505515\pi$
$349$	−0.647327	−0.0346506	−0.0173253	+	0.999850i	$0.505515\pi$
$350$	−17.9945	−0.961845
$351$	−124.757	−6.65902
$352$	−5.51011	−0.293690
$353$	18.5347	0.986504	0.493252	−	0.869886i	$-0.335808\pi$
$353$	18.5347	0.986504	0.493252	+	0.869886i	$0.335808\pi$
$354$	−124.415	−6.61260
$355$	−40.0788	−2.12716
$356$	−8.54195	−0.452722
$357$	25.0535	1.32597
$358$	9.57241	0.505917
$359$	−5.10076	−0.269208	−0.134604	−	0.990899i	$-0.542976\pi$
$359$	−5.10076	−0.269208	−0.134604	+	0.990899i	$0.542976\pi$
$360$	134.399	7.08344
$361$	40.9967	2.15772
$362$	−27.0793	−1.42326
$363$	−2.16327	−0.113542
$364$	−24.7351	−1.29647
$365$	17.7758	0.930427
$366$	30.6145	1.60025
$367$	29.5750	1.54381	0.771903	−	0.635741i	$-0.219305\pi$
$367$	29.5750	1.54381	0.771903	+	0.635741i	$0.219305\pi$
$368$	−7.42446	−0.387027
$369$	75.2550	3.91762
$370$	8.42926	0.438216
$371$	−1.16015	−0.0602321
$372$	16.1895	0.839388
$373$	−23.4168	−1.21247	−0.606237	−	0.795284i	$-0.707322\pi$
$373$	−23.4168	−1.21247	−0.606237	+	0.795284i	$0.707322\pi$
$374$	54.8194	2.83464
$375$	−26.6605	−1.37674
$376$	50.8997	2.62495
$377$	−6.30133	−0.324535
$378$	−49.5410	−2.54812
$379$	−35.9278	−1.84549	−0.922745	−	0.385412i	$-0.874059\pi$
$379$	−35.9278	−1.84549	−0.922745	+	0.385412i	$0.874059\pi$
$380$	103.274	5.29785
$381$	47.5359	2.43534
$382$	39.9650	2.04479
$383$	32.3432	1.65266	0.826329	−	0.563188i	$-0.190425\pi$
$383$	32.3432	1.65266	0.826329	+	0.563188i	$0.190425\pi$
$384$	70.7293	3.60939
$385$	11.6345	0.592948
$386$	−46.4543	−2.36446
$387$	35.1615	1.78736
$388$	42.1353	2.13910
$389$	0.813400	0.0412410	0.0206205	−	0.999787i	$-0.493436\pi$
$389$	0.813400	0.0412410	0.0206205	+	0.999787i	$0.493436\pi$
$390$	−181.628	−9.19707
$391$	−17.9620	−0.908378
$392$	25.9449	1.31041
$393$	−2.31163	−0.116606
$394$	−27.1715	−1.36888
$395$	−28.7656	−1.44735
$396$	−107.956	−5.42499
$397$	−11.8526	−0.594865	−0.297432	−	0.954743i	$-0.596130\pi$
$397$	−11.8526	−0.594865	−0.297432	+	0.954743i	$0.596130\pi$
$398$	19.2609	0.965463
$399$	−27.4867	−1.37606
$400$	21.0727	1.05364
$401$	12.0749	0.602992	0.301496	−	0.953467i	$-0.402514\pi$
$401$	12.0749	0.602992	0.301496	+	0.953467i	$0.402514\pi$
$402$	22.7508	1.13471
$403$	−7.75788	−0.386447
$404$	67.2488	3.34575
$405$	−146.451	−7.27721
$406$	−2.50227	−0.124185
$407$	−3.22025	−0.159622
$408$	−106.028	−5.24919
$409$	1.83683	0.0908255	0.0454127	−	0.998968i	$-0.485540\pi$
$409$	1.83683	0.0908255	0.0454127	+	0.998968i	$0.485540\pi$
$410$	72.1673	3.56409
$411$	−8.06659	−0.397895
$412$	−30.0421	−1.48007
$413$	15.5306	0.764209
$414$	53.9217	2.65011
$415$	−17.8623	−0.876826
$416$	−10.7376	−0.526456
$417$	−22.6809	−1.11069
$418$	−60.1434	−2.94171
$419$	−6.15792	−0.300834	−0.150417	−	0.988623i	$-0.548062\pi$
$419$	−6.15792	−0.300834	−0.150417	+	0.988623i	$0.548062\pi$
$420$	−47.3136	−2.30867
$421$	37.8066	1.84258	0.921291	−	0.388875i	$-0.127136\pi$
$421$	37.8066	1.84258	0.921291	+	0.388875i	$0.127136\pi$
$422$	−37.0120	−1.80171
$423$	−102.292	−4.97361
$424$	4.90985	0.238443
$425$	50.9813	2.47296
$426$	−94.9184	−4.59881
$427$	−3.82156	−0.184938
$428$	24.6334	1.19070
$429$	69.3875	3.35006
$430$	33.7189	1.62607
$431$	−6.49139	−0.312679	−0.156340	−	0.987703i	$-0.549969\pi$
$431$	−6.49139	−0.312679	−0.156340	+	0.987703i	$0.549969\pi$
$432$	58.0158	2.79129
$433$	−20.4885	−0.984614	−0.492307	−	0.870422i	$-0.663846\pi$
$433$	−20.4885	−0.984614	−0.492307	+	0.870422i	$0.663846\pi$
$434$	−3.08066	−0.147877
$435$	−12.0533	−0.577910
$436$	−21.1817	−1.01442
$437$	19.7064	0.942687
$438$	42.0983	2.01153
$439$	24.6260	1.17534	0.587668	−	0.809102i	$-0.300046\pi$
$439$	24.6260	1.17534	0.587668	+	0.809102i	$0.300046\pi$
$440$	−49.2380	−2.34733
$441$	−52.1409	−2.48290
$442$	106.827	5.08126
$443$	6.01543	0.285801	0.142901	−	0.989737i	$-0.454357\pi$
$443$	6.01543	0.285801	0.142901	+	0.989737i	$0.454357\pi$
$444$	13.0957	0.621494
$445$	7.82957	0.371157
$446$	8.90309	0.421574
$447$	−11.3332	−0.536044
$448$	−10.2958	−0.486432
$449$	−34.3281	−1.62004	−0.810021	−	0.586401i	$-0.800544\pi$
$449$	−34.3281	−1.62004	−0.810021	+	0.586401i	$0.800544\pi$
$450$	−153.045	−7.21462
$451$	−27.5702	−1.29823
$452$	5.14766	0.242126
$453$	27.4594	1.29016
$454$	−15.6155	−0.732871
$455$	22.6723	1.06289
$456$	116.326	5.44745
$457$	−10.8689	−0.508424	−0.254212	−	0.967149i	$-0.581816\pi$
$457$	−10.8689	−0.508424	−0.254212	+	0.967149i	$0.581816\pi$
$458$	4.28563	0.200254
$459$	140.358	6.55135
$460$	33.9213	1.58159
$461$	30.7185	1.43071	0.715353	−	0.698764i	$-0.246266\pi$
$461$	30.7185	1.43071	0.715353	+	0.698764i	$0.246266\pi$
$462$	27.5539	1.28192
$463$	−5.73537	−0.266545	−0.133273	−	0.991079i	$-0.542549\pi$
$463$	−5.73537	−0.266545	−0.133273	+	0.991079i	$0.542549\pi$
$464$	2.93032	0.136037
$465$	−14.8394	−0.688159
$466$	−19.7241	−0.913701
$467$	−9.45490	−0.437520	−0.218760	−	0.975779i	$-0.570201\pi$
$467$	−9.45490	−0.437520	−0.218760	+	0.975779i	$0.570201\pi$
$468$	−210.375	−9.72460
$469$	−2.83995	−0.131137
$470$	−98.0951	−4.52479
$471$	38.4295	1.77074
$472$	−65.7265	−3.02531
$473$	−12.8817	−0.592300
$474$	−68.1254	−3.12910
$475$	−55.9325	−2.56636
$476$	27.8283	1.27551
$477$	−9.86724	−0.451790
$478$	−46.4030	−2.12242
$479$	4.79899	0.219271	0.109636	−	0.993972i	$-0.465032\pi$
$479$	4.79899	0.219271	0.109636	+	0.993972i	$0.465032\pi$
$480$	−20.5391	−0.937477
$481$	−6.27534	−0.286131
$482$	−57.6561	−2.62616
$483$	−9.02824	−0.410799
$484$	−2.40286	−0.109221
$485$	−38.6213	−1.75370
$486$	−203.032	−9.20970
$487$	−8.05120	−0.364835	−0.182417	−	0.983221i	$-0.558392\pi$
$487$	−8.05120	−0.364835	−0.182417	+	0.983221i	$0.558392\pi$
$488$	16.1731	0.732124
$489$	−3.43364	−0.155275
$490$	−50.0016	−2.25884
$491$	3.98610	0.179890	0.0899451	−	0.995947i	$-0.471331\pi$
$491$	3.98610	0.179890	0.0899451	+	0.995947i	$0.471331\pi$
$492$	112.119	5.05472
$493$	7.08934	0.319288
$494$	−117.202	−5.27318
$495$	98.9526	4.44759
$496$	3.60766	0.161989
$497$	11.8485	0.531478
$498$	−42.3032	−1.89565
$499$	−8.71103	−0.389959	−0.194980	−	0.980807i	$-0.562464\pi$
$499$	−8.71103	−0.389959	−0.194980	+	0.980807i	$0.562464\pi$
$500$	−29.6133	−1.32435
$501$	55.8217	2.49393
$502$	29.6101	1.32157
$503$	−23.1236	−1.03103	−0.515516	−	0.856880i	$-0.672400\pi$
$503$	−23.1236	−1.03103	−0.515516	+	0.856880i	$0.672400\pi$
$504$	−39.7324	−1.76982
$505$	−61.6404	−2.74296
$506$	−19.7546	−0.878200
$507$	90.5791	4.02276
$508$	52.8007	2.34265
$509$	−7.28950	−0.323101	−0.161551	−	0.986864i	$-0.551650\pi$
$509$	−7.28950	−0.323101	−0.161551	+	0.986864i	$0.551650\pi$
$510$	204.341	9.04836
$511$	−5.25506	−0.232470
$512$	30.5208	1.34884
$513$	−153.989	−6.79879
$514$	−0.238513	−0.0105204
$515$	27.5367	1.21341
$516$	52.3856	2.30615
$517$	37.4754	1.64817
$518$	−2.49195	−0.109490
$519$	−25.4920	−1.11897
$520$	−95.9508	−4.20772
$521$	28.7125	1.25792	0.628958	−	0.777439i	$-0.283482\pi$
$521$	28.7125	1.25792	0.628958	+	0.777439i	$0.283482\pi$
$522$	−21.2821	−0.931492
$523$	−22.6579	−0.990763	−0.495381	−	0.868676i	$-0.664972\pi$
$523$	−22.6579	−0.990763	−0.495381	+	0.868676i	$0.664972\pi$
$524$	−2.56766	−0.112169
$525$	25.6247	1.11835
$526$	−50.6444	−2.20820
$527$	8.72803	0.380199
$528$	−32.2674	−1.40426
$529$	−16.5272	−0.718576
$530$	−9.46239	−0.411020
$531$	132.089	5.73219
$532$	−30.5310	−1.32369
$533$	−53.7265	−2.32715
$534$	18.5427	0.802423
$535$	−22.5790	−0.976177
$536$	12.0189	0.519137
$537$	−13.6314	−0.588239
$538$	63.0575	2.71860
$539$	19.1022	0.822791
$540$	−265.066	−11.4066
$541$	26.8593	1.15477	0.577387	−	0.816471i	$-0.304073\pi$
$541$	26.8593	1.15477	0.577387	+	0.816471i	$0.304073\pi$
$542$	26.3419	1.13148
$543$	38.5618	1.65485
$544$	12.0804	0.517944
$545$	19.4152	0.831657
$546$	53.6946	2.29792
$547$	43.2798	1.85051	0.925256	−	0.379344i	$-0.123850\pi$
$547$	43.2798	1.85051	0.925256	+	0.379344i	$0.123850\pi$
$548$	−8.96000	−0.382752
$549$	−32.5029	−1.38719
$550$	56.0692	2.39080
$551$	−7.77784	−0.331347
$552$	38.2082	1.62625
$553$	8.50398	0.361626
$554$	56.1246	2.38450
$555$	−12.0035	−0.509522
$556$	−25.1929	−1.06842
$557$	−26.1322	−1.10726	−0.553629	−	0.832764i	$-0.686757\pi$
$557$	−26.1322	−1.10726	−0.553629	+	0.832764i	$0.686757\pi$
$558$	−26.2014	−1.10919
$559$	−25.1027	−1.06173
$560$	−10.5433	−0.445537
$561$	−78.0646	−3.29589
$562$	9.48443	0.400076
$563$	25.9177	1.09230	0.546149	−	0.837688i	$-0.316093\pi$
$563$	25.9177	1.09230	0.546149	+	0.837688i	$0.316093\pi$
$564$	−152.400	−6.41722
$565$	−4.71836	−0.198503
$566$	−17.6683	−0.742655
$567$	43.2954	1.81824
$568$	−50.1438	−2.10399
$569$	−3.97854	−0.166789	−0.0833946	−	0.996517i	$-0.526576\pi$
$569$	−3.97854	−0.166789	−0.0833946	+	0.996517i	$0.526576\pi$
$570$	−224.186	−9.39011
$571$	−6.88338	−0.288060	−0.144030	−	0.989573i	$-0.546006\pi$
$571$	−6.88338	−0.288060	−0.144030	+	0.989573i	$0.546006\pi$
$572$	77.0725	3.22256
$573$	−56.9115	−2.37751
$574$	−21.3348	−0.890499
$575$	−18.3715	−0.766145
$576$	−87.5673	−3.64864
$577$	−11.4806	−0.477945	−0.238972	−	0.971026i	$-0.576811\pi$
$577$	−11.4806	−0.477945	−0.238972	+	0.971026i	$0.576811\pi$
$578$	−79.1959	−3.29412
$579$	66.1524	2.74920
$580$	−13.3882	−0.555916
$581$	5.28064	0.219078
$582$	−91.4668	−3.79142
$583$	3.61493	0.149715
$584$	22.2398	0.920290
$585$	192.830	7.97256
$586$	21.9474	0.906637
$587$	−4.80054	−0.198139	−0.0990697	−	0.995080i	$-0.531587\pi$
$587$	−4.80054	−0.198139	−0.0990697	+	0.995080i	$0.531587\pi$
$588$	−77.6825	−3.20357
$589$	−9.57568	−0.394559
$590$	126.670	5.21491
$591$	38.6931	1.59162
$592$	2.91823	0.119939
$593$	25.4664	1.04578	0.522890	−	0.852400i	$-0.324854\pi$
$593$	25.4664	1.04578	0.522890	+	0.852400i	$0.324854\pi$
$594$	154.366	6.33370
$595$	−25.5075	−1.04571
$596$	−12.5885	−0.515643
$597$	−27.4282	−1.12256
$598$	−38.4961	−1.57422
$599$	2.80685	0.114685	0.0573424	−	0.998355i	$-0.481737\pi$
$599$	2.80685	0.114685	0.0573424	+	0.998355i	$0.481737\pi$
$600$	−108.446	−4.42728
$601$	−11.0412	−0.450378	−0.225189	−	0.974315i	$-0.572300\pi$
$601$	−11.0412	−0.450378	−0.225189	+	0.974315i	$0.572300\pi$
$602$	−9.96832	−0.406278
$603$	−24.1541	−0.983632
$604$	30.5007	1.24106
$605$	2.20247	0.0895429
$606$	−145.983	−5.93014
$607$	33.6774	1.36692	0.683461	−	0.729987i	$-0.260474\pi$
$607$	33.6774	1.36692	0.683461	+	0.729987i	$0.260474\pi$
$608$	−13.2536	−0.537506
$609$	3.56331	0.144393
$610$	−31.1693	−1.26201
$611$	73.0289	2.95444
$612$	236.683	9.56736
$613$	29.3683	1.18617	0.593086	−	0.805139i	$-0.297909\pi$
$613$	29.3683	1.18617	0.593086	+	0.805139i	$0.297909\pi$
$614$	18.3238	0.739490
$615$	−102.769	−4.14403
$616$	14.5562	0.586488
$617$	−41.5413	−1.67239	−0.836195	−	0.548432i	$-0.815225\pi$
$617$	−41.5413	−1.67239	−0.836195	+	0.548432i	$0.815225\pi$
$618$	65.2150	2.62333
$619$	−11.3338	−0.455542	−0.227771	−	0.973715i	$-0.573144\pi$
$619$	−11.3338	−0.455542	−0.227771	+	0.973715i	$0.573144\pi$
$620$	−16.4829	−0.661969
$621$	−50.5791	−2.02967
$622$	33.6004	1.34725
$623$	−2.31466	−0.0927348
$624$	−62.8800	−2.51721
$625$	−8.96166	−0.358466
$626$	−62.8017	−2.51006
$627$	85.6461	3.42038
$628$	42.6857	1.70335
$629$	7.06009	0.281504
$630$	76.5732	3.05075
$631$	−5.43762	−0.216468	−0.108234	−	0.994125i	$-0.534520\pi$
$631$	−5.43762	−0.216468	−0.108234	+	0.994125i	$0.534520\pi$
$632$	−35.9895	−1.43159
$633$	52.7063	2.09489
$634$	−32.6281	−1.29583
$635$	−48.3973	−1.92059
$636$	−14.7008	−0.582923
$637$	37.2248	1.47490
$638$	7.79685	0.308680
$639$	100.773	3.98652
$640$	−72.0110	−2.84648
$641$	38.9746	1.53941	0.769703	−	0.638402i	$-0.220404\pi$
$641$	38.9746	1.53941	0.769703	+	0.638402i	$0.220404\pi$
$642$	−53.4739	−2.11045
$643$	−0.100526	−0.00396437	−0.00198219	−	0.999998i	$-0.500631\pi$
$643$	−0.100526	−0.00396437	−0.00198219	+	0.999998i	$0.500631\pi$
$644$	−10.0282	−0.395165
$645$	−48.0168	−1.89066
$646$	131.859	5.18792
$647$	−1.80238	−0.0708588	−0.0354294	−	0.999372i	$-0.511280\pi$
$647$	−1.80238	−0.0708588	−0.0354294	+	0.999372i	$0.511280\pi$
$648$	−183.229	−7.19793
$649$	−48.3919	−1.89955
$650$	109.263	4.28564
$651$	4.38697	0.171939
$652$	−3.81394	−0.149365
$653$	29.7896	1.16576	0.582879	−	0.812559i	$-0.301926\pi$
$653$	29.7896	1.16576	0.582879	+	0.812559i	$0.301926\pi$
$654$	45.9810	1.79800
$655$	2.35352	0.0919596
$656$	24.9845	0.975482
$657$	−44.6949	−1.74372
$658$	28.9999	1.13053
$659$	−23.6020	−0.919404	−0.459702	−	0.888073i	$-0.652044\pi$
$659$	−23.6020	−0.919404	−0.459702	+	0.888073i	$0.652044\pi$
$660$	147.425	5.73852
$661$	43.5919	1.69553	0.847764	−	0.530374i	$-0.177948\pi$
$661$	43.5919	1.69553	0.847764	+	0.530374i	$0.177948\pi$
$662$	68.2269	2.65171
$663$	−152.126	−5.90807
$664$	−22.3481	−0.867274
$665$	27.9848	1.08520
$666$	−21.1943	−0.821263
$667$	−2.55470	−0.0989184
$668$	62.0042	2.39901
$669$	−12.6783	−0.490171
$670$	−23.1631	−0.894869
$671$	11.9077	0.459690
$672$	6.07198	0.234232
$673$	−5.35743	−0.206514	−0.103257	−	0.994655i	$-0.532926\pi$
$673$	−5.35743	−0.206514	−0.103257	+	0.994655i	$0.532926\pi$
$674$	7.22978	0.278481
$675$	143.558	5.52555
$676$	100.611	3.86966
$677$	7.46810	0.287022	0.143511	−	0.989649i	$-0.454161\pi$
$677$	7.46810	0.287022	0.143511	+	0.989649i	$0.454161\pi$
$678$	−11.1745	−0.429153
$679$	11.4176	0.438169
$680$	107.950	4.13968
$681$	22.2370	0.852123
$682$	9.59908	0.367568
$683$	−20.2554	−0.775050	−0.387525	−	0.921859i	$-0.626670\pi$
$683$	−20.2554	−0.775050	−0.387525	+	0.921859i	$0.626670\pi$
$684$	−259.670	−9.92872
$685$	8.21276	0.313793
$686$	32.2256	1.23038
$687$	−6.10288	−0.232839
$688$	11.6736	0.445051
$689$	7.04447	0.268373
$690$	−73.6358	−2.80327
$691$	32.5851	1.23960	0.619798	−	0.784762i	$-0.287215\pi$
$691$	32.5851	1.23960	0.619798	+	0.784762i	$0.287215\pi$
$692$	−28.3153	−1.07639
$693$	−29.2534	−1.11125
$694$	−20.6974	−0.785661
$695$	23.0919	0.875926
$696$	−15.0802	−0.571614
$697$	60.4451	2.28952
$698$	1.56084	0.0590788
$699$	28.0878	1.06238
$700$	28.4628	1.07579
$701$	−38.7361	−1.46304	−0.731522	−	0.681818i	$-0.761189\pi$
$701$	−38.7361	−1.46304	−0.731522	+	0.681818i	$0.761189\pi$
$702$	300.815	11.3535
$703$	−7.74575	−0.292137
$704$	32.0809	1.20909
$705$	139.691	5.26105
$706$	−44.6911	−1.68197
$707$	18.2228	0.685338
$708$	196.794	7.39598
$709$	21.2748	0.798993	0.399496	−	0.916735i	$-0.369185\pi$
$709$	21.2748	0.798993	0.399496	+	0.916735i	$0.369185\pi$
$710$	96.6383	3.62677
$711$	72.3274	2.71249
$712$	9.79581	0.367114
$713$	−3.14521	−0.117789
$714$	−60.4093	−2.26076
$715$	−70.6448	−2.64197
$716$	−15.1412	−0.565852
$717$	66.0793	2.46778
$718$	12.2990	0.458995
$719$	−8.11780	−0.302743	−0.151371	−	0.988477i	$-0.548369\pi$
$719$	−8.11780	−0.302743	−0.151371	+	0.988477i	$0.548369\pi$
$720$	−89.6723	−3.34189
$721$	−8.14067	−0.303175
$722$	−98.8517	−3.67888
$723$	82.1042	3.05349
$724$	42.8327	1.59187
$725$	7.25096	0.269294
$726$	5.21609	0.193587
$727$	−15.8640	−0.588362	−0.294181	−	0.955750i	$-0.595047\pi$
$727$	−15.8640	−0.588362	−0.294181	+	0.955750i	$0.595047\pi$
$728$	28.3660	1.05131
$729$	163.446	6.05354
$730$	−42.8611	−1.58636
$731$	28.2419	1.04456
$732$	−48.4246	−1.78982
$733$	8.01128	0.295904	0.147952	−	0.988995i	$-0.452732\pi$
$733$	8.01128	0.295904	0.147952	+	0.988995i	$0.452732\pi$
$734$	−71.3117	−2.63216
$735$	71.2040	2.62640
$736$	−4.35328	−0.160464
$737$	8.84904	0.325959
$738$	−181.456	−6.67947
$739$	−14.6551	−0.539096	−0.269548	−	0.962987i	$-0.586874\pi$
$739$	−14.6551	−0.539096	−0.269548	+	0.962987i	$0.586874\pi$
$740$	−13.3330	−0.490131
$741$	166.900	6.13122
$742$	2.79737	0.102695
$743$	41.8083	1.53380	0.766898	−	0.641769i	$-0.221799\pi$
$743$	41.8083	1.53380	0.766898	+	0.641769i	$0.221799\pi$
$744$	−18.5660	−0.680662
$745$	11.5386	0.422742
$746$	56.4627	2.06725
$747$	44.9125	1.64326
$748$	−86.7107	−3.17046
$749$	6.67505	0.243901
$750$	64.2841	2.34732
$751$	21.8531	0.797430	0.398715	−	0.917075i	$-0.369456\pi$
$751$	21.8531	0.797430	0.398715	+	0.917075i	$0.369456\pi$
$752$	−33.9608	−1.23842
$753$	−42.1658	−1.53661
$754$	15.1938	0.553327
$755$	−27.9570	−1.01746
$756$	78.3616	2.84998
$757$	−35.3616	−1.28524	−0.642619	−	0.766186i	$-0.722152\pi$
$757$	−35.3616	−1.28524	−0.642619	+	0.766186i	$0.722152\pi$
$758$	86.6296	3.14653
$759$	28.1312	1.02110
$760$	−118.434	−4.29604
$761$	25.2554	0.915508	0.457754	−	0.889079i	$-0.348654\pi$
$761$	25.2554	0.915508	0.457754	+	0.889079i	$0.348654\pi$
$762$	−114.619	−4.15221
$763$	−5.73973	−0.207792
$764$	−63.2147	−2.28703
$765$	−216.945	−7.84365
$766$	−77.9861	−2.81775
$767$	−94.3020	−3.40505
$768$	−102.130	−3.68529
$769$	1.20577	0.0434812	0.0217406	−	0.999764i	$-0.493079\pi$
$769$	1.20577	0.0434812	0.0217406	+	0.999764i	$0.493079\pi$
$770$	−28.0532	−1.01097
$771$	0.339651	0.0122322
$772$	73.4791	2.64457
$773$	5.74693	0.206703	0.103351	−	0.994645i	$-0.467043\pi$
$773$	5.74693	0.206703	0.103351	+	0.994645i	$0.467043\pi$
$774$	−84.7818	−3.04742
$775$	8.92701	0.320668
$776$	−48.3203	−1.73460
$777$	3.54861	0.127306
$778$	−1.96128	−0.0703152
$779$	−66.3154	−2.37600
$780$	287.290	10.2866
$781$	−36.9189	−1.32106
$782$	43.3102	1.54877
$783$	19.9628	0.713413
$784$	−17.3107	−0.618240
$785$	−39.1258	−1.39646
$786$	5.57383	0.198812
$787$	−6.77155	−0.241380	−0.120690	−	0.992690i	$-0.538511\pi$
$787$	−6.77155	−0.241380	−0.120690	+	0.992690i	$0.538511\pi$
$788$	42.9786	1.53105
$789$	72.1193	2.56752
$790$	69.3599	2.46771
$791$	1.39489	0.0495966
$792$	123.803	4.39914
$793$	23.2046	0.824021
$794$	28.5791	1.01423
$795$	13.4748	0.477900
$796$	−30.4660	−1.07984
$797$	5.21635	0.184773	0.0923863	−	0.995723i	$-0.470551\pi$
$797$	5.21635	0.184773	0.0923863	+	0.995723i	$0.470551\pi$
$798$	66.2762	2.34615
$799$	−82.1615	−2.90666
$800$	12.3558	0.436845
$801$	−19.6865	−0.695587
$802$	−29.1152	−1.02809
$803$	16.3743	0.577837
$804$	−35.9862	−1.26913
$805$	9.19184	0.323970
$806$	18.7059	0.658886
$807$	−89.7960	−3.16097
$808$	−77.1202	−2.71308
$809$	36.9611	1.29948	0.649742	−	0.760155i	$-0.274877\pi$
$809$	36.9611	1.29948	0.649742	+	0.760155i	$0.274877\pi$
$810$	353.124	12.4075
$811$	2.52590	0.0886963	0.0443482	−	0.999016i	$-0.485879\pi$
$811$	2.52590	0.0886963	0.0443482	+	0.999016i	$0.485879\pi$
$812$	3.95797	0.138897
$813$	−37.5117	−1.31559
$814$	7.76469	0.272152
$815$	3.49586	0.122455
$816$	70.7433	2.47651
$817$	−30.9847	−1.08402
$818$	−4.42899	−0.154856
$819$	−57.0065	−1.99197
$820$	−114.151	−3.98632
$821$	−20.6041	−0.719086	−0.359543	−	0.933128i	$-0.617067\pi$
$821$	−20.6041	−0.719086	−0.359543	+	0.933128i	$0.617067\pi$
$822$	19.4502	0.678405
$823$	−52.5906	−1.83319	−0.916596	−	0.399815i	$-0.869074\pi$
$823$	−52.5906	−1.83319	−0.916596	+	0.399815i	$0.869074\pi$
$824$	34.4520	1.20019
$825$	−79.8444	−2.77983
$826$	−37.4474	−1.30296
$827$	48.0025	1.66921	0.834605	−	0.550848i	$-0.185696\pi$
$827$	48.0025	1.66921	0.834605	+	0.550848i	$0.185696\pi$
$828$	−85.2908	−2.96406
$829$	12.4682	0.433039	0.216520	−	0.976278i	$-0.430529\pi$
$829$	12.4682	0.433039	0.216520	+	0.976278i	$0.430529\pi$
$830$	43.0698	1.49497
$831$	−79.9232	−2.77251
$832$	62.5165	2.16737
$833$	−41.8798	−1.45105
$834$	54.6885	1.89371
$835$	−56.8332	−1.96679
$836$	95.1319	3.29020
$837$	24.5772	0.849512
$838$	14.8480	0.512917
$839$	−1.93498	−0.0668030	−0.0334015	−	0.999442i	$-0.510634\pi$
$839$	−1.93498	−0.0668030	−0.0334015	+	0.999442i	$0.510634\pi$
$840$	54.2588	1.87210
$841$	−27.9917	−0.965231
$842$	−91.1597	−3.14157
$843$	−13.5061	−0.465176
$844$	58.5437	2.01516
$845$	−92.2204	−3.17248
$846$	246.648	8.47992
$847$	−0.651116	−0.0223726
$848$	−3.27591	−0.112495
$849$	25.1603	0.863498
$850$	−122.927	−4.21635
$851$	−2.54416	−0.0872127
$852$	150.137	5.14362
$853$	−57.7397	−1.97697	−0.988485	−	0.151320i	$-0.951648\pi$
$853$	−57.7397	−1.97697	−0.988485	+	0.151320i	$0.951648\pi$
$854$	9.21459	0.315317
$855$	238.014	8.13990
$856$	−28.2493	−0.965543
$857$	5.05520	0.172682	0.0863411	−	0.996266i	$-0.472483\pi$
$857$	5.05520	0.172682	0.0863411	+	0.996266i	$0.472483\pi$
$858$	−167.308	−5.71180
$859$	−2.55129	−0.0870488	−0.0435244	−	0.999052i	$-0.513859\pi$
$859$	−2.55129	−0.0870488	−0.0435244	+	0.999052i	$0.513859\pi$
$860$	−53.3349	−1.81870
$861$	30.3815	1.03540
$862$	15.6521	0.533113
$863$	−27.1726	−0.924966	−0.462483	−	0.886628i	$-0.653041\pi$
$863$	−27.1726	−0.924966	−0.462483	+	0.886628i	$0.653041\pi$
$864$	34.0172	1.15729
$865$	25.9539	0.882459
$866$	49.4021	1.67875
$867$	112.778	3.83013
$868$	4.87284	0.165395
$869$	−26.4977	−0.898872
$870$	29.0630	0.985326
$871$	17.2443	0.584299
$872$	24.2910	0.822597
$873$	97.1085	3.28662
$874$	−47.5164	−1.60727
$875$	−8.02447	−0.271277
$876$	−66.5890	−2.24984
$877$	−30.0202	−1.01371	−0.506856	−	0.862031i	$-0.669192\pi$
$877$	−30.0202	−1.01371	−0.506856	+	0.862031i	$0.669192\pi$
$878$	−59.3785	−2.00393
$879$	−31.2538	−1.05416
$880$	32.8521	1.10744
$881$	−20.6706	−0.696409	−0.348204	−	0.937419i	$-0.613208\pi$
$881$	−20.6706	−0.696409	−0.348204	+	0.937419i	$0.613208\pi$
$882$	125.723	4.23331
$883$	−5.56303	−0.187211	−0.0936054	−	0.995609i	$-0.529839\pi$
$883$	−5.56303	−0.187211	−0.0936054	+	0.995609i	$0.529839\pi$
$884$	−168.974	−5.68322
$885$	−180.382	−6.06347
$886$	−14.5045	−0.487287
$887$	−33.1211	−1.11210	−0.556049	−	0.831149i	$-0.687683\pi$
$887$	−33.1211	−1.11210	−0.556049	+	0.831149i	$0.687683\pi$
$888$	−15.0180	−0.503971
$889$	14.3077	0.479865
$890$	−18.8787	−0.632817
$891$	−134.905	−4.51948
$892$	−14.0825	−0.471516
$893$	90.1408	3.01645
$894$	27.3268	0.913946
$895$	13.8784	0.463905
$896$	21.2886	0.711203
$897$	54.8197	1.83038
$898$	82.7722	2.76214
$899$	1.24137	0.0414020
$900$	242.080	8.06932
$901$	−7.92541	−0.264034
$902$	66.4776	2.21346
$903$	14.1952	0.472387
$904$	−5.90328	−0.196340
$905$	−39.2606	−1.30507
$906$	−66.2104	−2.19969
$907$	0.295193	0.00980171	0.00490086	−	0.999988i	$-0.498440\pi$
$907$	0.295193	0.00980171	0.00490086	+	0.999988i	$0.498440\pi$
$908$	24.6998	0.819693
$909$	154.987	5.14060
$910$	−54.6676	−1.81221
$911$	48.6159	1.61072	0.805359	−	0.592787i	$-0.201972\pi$
$911$	48.6159	1.61072	0.805359	+	0.592787i	$0.201972\pi$
$912$	−77.6138	−2.57005
$913$	−16.4540	−0.544549
$914$	26.2071	0.866854
$915$	44.3861	1.46736
$916$	−6.77880	−0.223978
$917$	−0.695772	−0.0229764
$918$	−338.432	−11.1699
$919$	−2.40127	−0.0792107	−0.0396054	−	0.999215i	$-0.512610\pi$
$919$	−2.40127	−0.0792107	−0.0396054	+	0.999215i	$0.512610\pi$
$920$	−38.9006	−1.28251
$921$	−26.0937	−0.859818
$922$	−74.0689	−2.43933
$923$	−71.9444	−2.36808
$924$	−43.5834	−1.43379
$925$	7.22105	0.237427
$926$	13.8292	0.454455
$927$	−69.2375	−2.27406
$928$	1.71817	0.0564018
$929$	47.1753	1.54777	0.773886	−	0.633325i	$-0.218310\pi$
$929$	47.1753	1.54777	0.773886	+	0.633325i	$0.218310\pi$
$930$	35.7808	1.17330
$931$	45.9471	1.50586
$932$	31.1986	1.02194
$933$	−47.8480	−1.56647
$934$	22.7977	0.745965
$935$	79.4792	2.59925
$936$	241.256	7.88570
$937$	25.2807	0.825886	0.412943	−	0.910757i	$-0.364501\pi$
$937$	25.2807	0.825886	0.412943	+	0.910757i	$0.364501\pi$
$938$	6.84772	0.223586
$939$	89.4316	2.91849
$940$	155.162	5.06083
$941$	−52.7804	−1.72059	−0.860297	−	0.509794i	$-0.829722\pi$
$941$	−52.7804	−1.72059	−0.860297	+	0.509794i	$0.829722\pi$
$942$	−92.6616	−3.01908
$943$	−21.7819	−0.709316
$944$	43.8534	1.42731
$945$	−71.8264	−2.33651
$946$	31.0604	1.00986
$947$	−4.18849	−0.136108	−0.0680538	−	0.997682i	$-0.521679\pi$
$947$	−4.18849	−0.136108	−0.0680538	+	0.997682i	$0.521679\pi$
$948$	107.757	3.49980
$949$	31.9089	1.03581
$950$	134.865	4.37560
$951$	46.4634	1.50668
$952$	−31.9132	−1.03431
$953$	−27.7883	−0.900153	−0.450076	−	0.892990i	$-0.648603\pi$
$953$	−27.7883	−0.900153	−0.450076	+	0.892990i	$0.648603\pi$
$954$	23.7920	0.770294
$955$	57.9428	1.87498
$956$	73.3980	2.37386
$957$	−11.1030	−0.358908
$958$	−11.5714	−0.373854
$959$	−2.42794	−0.0784023
$960$	119.582	3.85950
$961$	−29.4717	−0.950700
$962$	15.1312	0.487848
$963$	56.7722	1.82946
$964$	91.1977	2.93728
$965$	−67.3511	−2.16811
$966$	21.7690	0.700406
$967$	8.23036	0.264670	0.132335	−	0.991205i	$-0.457752\pi$
$967$	8.23036	0.264670	0.132335	+	0.991205i	$0.457752\pi$
$968$	2.75557	0.0885674
$969$	−187.771	−6.03208
$970$	93.1242	2.99004
$971$	56.9236	1.82677	0.913383	−	0.407102i	$-0.133461\pi$
$971$	56.9236	1.82677	0.913383	+	0.407102i	$0.133461\pi$
$972$	321.146	10.3007
$973$	−6.82667	−0.218853
$974$	19.4131	0.622037
$975$	−155.594	−4.98300
$976$	−10.7909	−0.345408
$977$	−38.5822	−1.23435	−0.617177	−	0.786824i	$-0.711724\pi$
$977$	−38.5822	−1.23435	−0.617177	+	0.786824i	$0.711724\pi$
$978$	8.27924	0.264741
$979$	7.21228	0.230505
$980$	79.0902	2.52644
$981$	−48.8171	−1.55861
$982$	−9.61132	−0.306710
$983$	11.3733	0.362751	0.181376	−	0.983414i	$-0.441945\pi$
$983$	11.3733	0.362751	0.181376	+	0.983414i	$0.441945\pi$
$984$	−128.577	−4.09888
$985$	−39.3942	−1.25520
$986$	−17.0939	−0.544380
$987$	−41.2968	−1.31449
$988$	185.385	5.89788
$989$	−10.1772	−0.323616
$990$	−238.596	−7.58307
$991$	−12.4193	−0.394512	−0.197256	−	0.980352i	$-0.563203\pi$
$991$	−12.4193	−0.394512	−0.197256	+	0.980352i	$0.563203\pi$
$992$	2.11533	0.0671617
$993$	−97.1573	−3.08319
$994$	−28.5692	−0.906161
$995$	27.9252	0.885289
$996$	66.9132	2.12023
$997$	37.5596	1.18952	0.594762	−	0.803902i	$-0.297246\pi$
$997$	37.5596	1.18952	0.594762	+	0.803902i	$0.297246\pi$
$998$	21.0041	0.664874
$999$	19.8805	0.628990

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6031.2.a.e.1.13	✓	134

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6031.2.a.e.1.13	✓	134	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6031 = 37 \cdot 163 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.41121 q^{2} +3.43364 q^{3} +3.81394 q^{4} -3.49586 q^{5} -8.27924 q^{6} +1.03348 q^{7} -4.37378 q^{8} +8.78990 q^{9} +O(q^{10})\)	\(q-2.41121 q^{2} +3.43364 q^{3} +3.81394 q^{4} -3.49586 q^{5} -8.27924 q^{6} +1.03348 q^{7} -4.37378 q^{8} +8.78990 q^{9} +8.42926 q^{10} -3.22025 q^{11} +13.0957 q^{12} -6.27534 q^{13} -2.49195 q^{14} -12.0035 q^{15} +2.91823 q^{16} +7.06009 q^{17} -21.1943 q^{18} -7.74575 q^{19} -13.3330 q^{20} +3.54861 q^{21} +7.76469 q^{22} -2.54416 q^{23} -15.0180 q^{24} +7.22105 q^{25} +15.1312 q^{26} +19.8805 q^{27} +3.94164 q^{28} +1.00414 q^{29} +28.9431 q^{30} +1.23625 q^{31} +1.71109 q^{32} -11.0572 q^{33} -17.0234 q^{34} -3.61291 q^{35} +33.5241 q^{36} +1.00000 q^{37} +18.6766 q^{38} -21.5473 q^{39} +15.2901 q^{40} +8.56152 q^{41} -8.55645 q^{42} +4.00022 q^{43} -12.2818 q^{44} -30.7283 q^{45} +6.13451 q^{46} -11.6375 q^{47} +10.0202 q^{48} -5.93191 q^{49} -17.4115 q^{50} +24.2418 q^{51} -23.9337 q^{52} -1.12256 q^{53} -47.9360 q^{54} +11.2575 q^{55} -4.52023 q^{56} -26.5962 q^{57} -2.42120 q^{58} +15.0274 q^{59} -45.7807 q^{60} -3.69775 q^{61} -2.98085 q^{62} +9.08422 q^{63} -9.96225 q^{64} +21.9377 q^{65} +26.6612 q^{66} -2.74794 q^{67} +26.9267 q^{68} -8.73574 q^{69} +8.71150 q^{70} +11.4646 q^{71} -38.4451 q^{72} -5.08480 q^{73} -2.41121 q^{74} +24.7945 q^{75} -29.5418 q^{76} -3.32807 q^{77} +51.9550 q^{78} +8.22847 q^{79} -10.2017 q^{80} +41.8927 q^{81} -20.6436 q^{82} +5.10956 q^{83} +13.5342 q^{84} -24.6811 q^{85} -9.64536 q^{86} +3.44787 q^{87} +14.0846 q^{88} -2.23967 q^{89} +74.0924 q^{90} -6.48546 q^{91} -9.70327 q^{92} +4.24484 q^{93} +28.0603 q^{94} +27.0781 q^{95} +5.87526 q^{96} +11.0477 q^{97} +14.3031 q^{98} -28.3056 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 134 q + 9 q^{2} + 7 q^{3} + 149 q^{4} + 22 q^{5} + 20 q^{6} + 11 q^{7} + 27 q^{8} + 181 q^{9}+O(q^{10}) \) 134 * q + 9 * q^2 + 7 * q^3 + 149 * q^4 + 22 * q^5 + 20 * q^6 + 11 * q^7 + 27 * q^8 + 181 * q^9	\( 134 q + 9 q^{2} + 7 q^{3} + 149 q^{4} + 22 q^{5} + 20 q^{6} + 11 q^{7} + 27 q^{8} + 181 q^{9} + 15 q^{10} + 20 q^{11} + 28 q^{12} + 11 q^{13} + 17 q^{14} - 13 q^{15} + 143 q^{16} + 76 q^{17} + 23 q^{18} + 15 q^{19} + 67 q^{20} + 63 q^{21} + 2 q^{22} + 22 q^{23} + 33 q^{24} + 160 q^{25} + 65 q^{26} + 31 q^{27} + 10 q^{28} + 73 q^{29} + 20 q^{30} + 10 q^{31} + 53 q^{32} + 72 q^{33} - 7 q^{34} + 52 q^{35} + 201 q^{36} + 134 q^{37} + 70 q^{38} + 6 q^{39} + 11 q^{40} + 182 q^{41} - 15 q^{42} + 12 q^{43} + 33 q^{44} + 29 q^{45} + 24 q^{46} + 80 q^{47} + 21 q^{48} + 229 q^{49} + 37 q^{50} + 57 q^{51} - 15 q^{52} + 75 q^{53} + 95 q^{54} - 9 q^{55} + 39 q^{56} + 19 q^{57} - 21 q^{58} + 91 q^{59} + 62 q^{60} + 58 q^{61} + 108 q^{62} + 9 q^{63} + 167 q^{64} + 76 q^{65} + 105 q^{66} - 17 q^{67} + 109 q^{68} + 48 q^{69} - 55 q^{70} + 56 q^{71} + 48 q^{72} + 54 q^{73} + 9 q^{74} + 28 q^{75} + 82 q^{76} + 156 q^{77} + 16 q^{78} - 2 q^{79} + 98 q^{80} + 270 q^{81} - 42 q^{82} + 130 q^{83} + 229 q^{84} + 22 q^{85} + 72 q^{86} + 22 q^{87} + 61 q^{88} + 157 q^{89} + 176 q^{90} + 31 q^{91} - 18 q^{92} + 36 q^{93} + 83 q^{94} + 98 q^{95} + 111 q^{96} + 35 q^{97} + 53 q^{98} + 55 q^{99}+O(q^{100}) \) 134 * q + 9 * q^2 + 7 * q^3 + 149 * q^4 + 22 * q^5 + 20 * q^6 + 11 * q^7 + 27 * q^8 + 181 * q^9 + 15 * q^10 + 20 * q^11 + 28 * q^12 + 11 * q^13 + 17 * q^14 - 13 * q^15 + 143 * q^16 + 76 * q^17 + 23 * q^18 + 15 * q^19 + 67 * q^20 + 63 * q^21 + 2 * q^22 + 22 * q^23 + 33 * q^24 + 160 * q^25 + 65 * q^26 + 31 * q^27 + 10 * q^28 + 73 * q^29 + 20 * q^30 + 10 * q^31 + 53 * q^32 + 72 * q^33 - 7 * q^34 + 52 * q^35 + 201 * q^36 + 134 * q^37 + 70 * q^38 + 6 * q^39 + 11 * q^40 + 182 * q^41 - 15 * q^42 + 12 * q^43 + 33 * q^44 + 29 * q^45 + 24 * q^46 + 80 * q^47 + 21 * q^48 + 229 * q^49 + 37 * q^50 + 57 * q^51 - 15 * q^52 + 75 * q^53 + 95 * q^54 - 9 * q^55 + 39 * q^56 + 19 * q^57 - 21 * q^58 + 91 * q^59 + 62 * q^60 + 58 * q^61 + 108 * q^62 + 9 * q^63 + 167 * q^64 + 76 * q^65 + 105 * q^66 - 17 * q^67 + 109 * q^68 + 48 * q^69 - 55 * q^70 + 56 * q^71 + 48 * q^72 + 54 * q^73 + 9 * q^74 + 28 * q^75 + 82 * q^76 + 156 * q^77 + 16 * q^78 - 2 * q^79 + 98 * q^80 + 270 * q^81 - 42 * q^82 + 130 * q^83 + 229 * q^84 + 22 * q^85 + 72 * q^86 + 22 * q^87 + 61 * q^88 + 157 * q^89 + 176 * q^90 + 31 * q^91 - 18 * q^92 + 36 * q^93 + 83 * q^94 + 98 * q^95 + 111 * q^96 + 35 * q^97 + 53 * q^98 + 55 * q^99

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