LMFDB - Embedded newform 1441.2.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1441,2,Mod(1,1441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1441, 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("1441.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1441 = 11 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1441.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:	$11.5064429313$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1441.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.46758 q^{2} -2.74867 q^{3} +4.08895 q^{4} +0.488919 q^{5} +6.78255 q^{6} -1.50214 q^{7} -5.15465 q^{8} +4.55516 q^{9} +O(q^{10})$	\(q-2.46758 q^{2} -2.74867 q^{3} +4.08895 q^{4} +0.488919 q^{5} +6.78255 q^{6} -1.50214 q^{7} -5.15465 q^{8} +4.55516 q^{9} -1.20645 q^{10} +1.00000 q^{11} -11.2392 q^{12} -1.24599 q^{13} +3.70666 q^{14} -1.34388 q^{15} +4.54160 q^{16} +3.29746 q^{17} -11.2402 q^{18} +4.48304 q^{19} +1.99916 q^{20} +4.12889 q^{21} -2.46758 q^{22} +2.86500 q^{23} +14.1684 q^{24} -4.76096 q^{25} +3.07458 q^{26} -4.27463 q^{27} -6.14219 q^{28} -6.33838 q^{29} +3.31612 q^{30} +7.17832 q^{31} -0.897472 q^{32} -2.74867 q^{33} -8.13675 q^{34} -0.734427 q^{35} +18.6258 q^{36} -6.61712 q^{37} -11.0623 q^{38} +3.42481 q^{39} -2.52020 q^{40} +11.6196 q^{41} -10.1884 q^{42} +2.12187 q^{43} +4.08895 q^{44} +2.22711 q^{45} -7.06960 q^{46} -8.05637 q^{47} -12.4833 q^{48} -4.74356 q^{49} +11.7480 q^{50} -9.06362 q^{51} -5.09479 q^{52} -2.36469 q^{53} +10.5480 q^{54} +0.488919 q^{55} +7.74302 q^{56} -12.3224 q^{57} +15.6405 q^{58} -1.23927 q^{59} -5.49504 q^{60} -12.8735 q^{61} -17.7131 q^{62} -6.84252 q^{63} -6.86862 q^{64} -0.609189 q^{65} +6.78255 q^{66} -7.36834 q^{67} +13.4832 q^{68} -7.87491 q^{69} +1.81226 q^{70} -1.51659 q^{71} -23.4803 q^{72} -10.5341 q^{73} +16.3283 q^{74} +13.0863 q^{75} +18.3309 q^{76} -1.50214 q^{77} -8.45100 q^{78} +9.64225 q^{79} +2.22048 q^{80} -1.91597 q^{81} -28.6722 q^{82} +2.52721 q^{83} +16.8828 q^{84} +1.61219 q^{85} -5.23588 q^{86} +17.4221 q^{87} -5.15465 q^{88} +11.2358 q^{89} -5.49556 q^{90} +1.87166 q^{91} +11.7148 q^{92} -19.7308 q^{93} +19.8797 q^{94} +2.19185 q^{95} +2.46685 q^{96} -9.73290 q^{97} +11.7051 q^{98} +4.55516 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 7 q^{2} - 2 q^{3} + 27 q^{4} + 3 q^{5} - q^{6} + 7 q^{7} + 21 q^{8} + 28 q^{9}+O(q^{10}) $ 28 * q + 7 * q^2 - 2 * q^3 + 27 * q^4 + 3 * q^5 - q^6 + 7 * q^7 + 21 * q^8 + 28 * q^9	\( 28 q + 7 q^{2} - 2 q^{3} + 27 q^{4} + 3 q^{5} - q^{6} + 7 q^{7} + 21 q^{8} + 28 q^{9} + 14 q^{10} + 28 q^{11} - 6 q^{12} + 3 q^{13} - q^{14} + 19 q^{15} + 29 q^{16} + 9 q^{17} - 2 q^{18} + 20 q^{19} + 6 q^{20} + 6 q^{21} + 7 q^{22} + 24 q^{23} + 20 q^{24} + 23 q^{25} + 10 q^{26} - 20 q^{27} - 3 q^{28} + 43 q^{29} + 11 q^{30} + 3 q^{31} + 44 q^{32} - 2 q^{33} - 28 q^{34} + 32 q^{35} + 24 q^{36} - 4 q^{37} + 24 q^{38} + 37 q^{39} + 22 q^{40} + 32 q^{41} - 27 q^{42} + 25 q^{43} + 27 q^{44} - 36 q^{45} + 10 q^{46} + 19 q^{47} + 42 q^{48} + 17 q^{49} + q^{50} + 39 q^{51} - 19 q^{52} + 5 q^{53} + 6 q^{54} + 3 q^{55} + 8 q^{56} + 2 q^{57} + 21 q^{58} + 44 q^{59} + 65 q^{60} + 28 q^{61} + 60 q^{62} - 8 q^{63} + 5 q^{64} + 33 q^{65} - q^{66} + 7 q^{67} + 13 q^{68} - 22 q^{69} + 9 q^{70} + 117 q^{71} - 17 q^{72} + 7 q^{73} + 41 q^{74} - 40 q^{75} + 34 q^{76} + 7 q^{77} - 97 q^{78} + 48 q^{79} + 41 q^{80} + 40 q^{81} + 2 q^{82} + 22 q^{83} + 27 q^{84} + 30 q^{85} + 24 q^{86} + 37 q^{87} + 21 q^{88} - 6 q^{89} + 4 q^{90} - 33 q^{91} + 18 q^{92} + 5 q^{93} - 43 q^{94} + 64 q^{95} + 55 q^{96} - 50 q^{97} + 97 q^{98} + 28 q^{99}+O(q^{100}) \) 28 * q + 7 * q^2 - 2 * q^3 + 27 * q^4 + 3 * q^5 - q^6 + 7 * q^7 + 21 * q^8 + 28 * q^9 + 14 * q^10 + 28 * q^11 - 6 * q^12 + 3 * q^13 - q^14 + 19 * q^15 + 29 * q^16 + 9 * q^17 - 2 * q^18 + 20 * q^19 + 6 * q^20 + 6 * q^21 + 7 * q^22 + 24 * q^23 + 20 * q^24 + 23 * q^25 + 10 * q^26 - 20 * q^27 - 3 * q^28 + 43 * q^29 + 11 * q^30 + 3 * q^31 + 44 * q^32 - 2 * q^33 - 28 * q^34 + 32 * q^35 + 24 * q^36 - 4 * q^37 + 24 * q^38 + 37 * q^39 + 22 * q^40 + 32 * q^41 - 27 * q^42 + 25 * q^43 + 27 * q^44 - 36 * q^45 + 10 * q^46 + 19 * q^47 + 42 * q^48 + 17 * q^49 + q^50 + 39 * q^51 - 19 * q^52 + 5 * q^53 + 6 * q^54 + 3 * q^55 + 8 * q^56 + 2 * q^57 + 21 * q^58 + 44 * q^59 + 65 * q^60 + 28 * q^61 + 60 * q^62 - 8 * q^63 + 5 * q^64 + 33 * q^65 - q^66 + 7 * q^67 + 13 * q^68 - 22 * q^69 + 9 * q^70 + 117 * q^71 - 17 * q^72 + 7 * q^73 + 41 * q^74 - 40 * q^75 + 34 * q^76 + 7 * q^77 - 97 * q^78 + 48 * q^79 + 41 * q^80 + 40 * q^81 + 2 * q^82 + 22 * q^83 + 27 * q^84 + 30 * q^85 + 24 * q^86 + 37 * q^87 + 21 * q^88 - 6 * q^89 + 4 * q^90 - 33 * q^91 + 18 * q^92 + 5 * q^93 - 43 * q^94 + 64 * q^95 + 55 * q^96 - 50 * q^97 + 97 * q^98 + 28 * 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 $

$2$	−2.46758	−1.74484	−0.872421	−	0.488755i	$-0.837451\pi$
$2$	−2.46758	−1.74484	−0.872421	+	0.488755i	$0.837451\pi$
$3$	−2.74867	−1.58694	−0.793472	−	0.608607i	$-0.791728\pi$
$3$	−2.74867	−1.58694	−0.793472	+	0.608607i	$0.791728\pi$
$4$	4.08895	2.04447
$5$	0.488919	0.218651	0.109326	−	0.994006i	$-0.465131\pi$
$5$	0.488919	0.218651	0.109326	+	0.994006i	$0.465131\pi$
$6$	6.78255	2.76897
$7$	−1.50214	−0.567757	−0.283879	−	0.958860i	$-0.591621\pi$
$7$	−1.50214	−0.567757	−0.283879	+	0.958860i	$0.591621\pi$
$8$	−5.15465	−1.82244
$9$	4.55516	1.51839
$10$	−1.20645	−0.381512
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−11.2392	−3.24446
$13$	−1.24599	−0.345576	−0.172788	−	0.984959i	$-0.555278\pi$
$13$	−1.24599	−0.345576	−0.172788	+	0.984959i	$0.555278\pi$
$14$	3.70666	0.990647
$15$	−1.34388	−0.346987
$16$	4.54160	1.13540
$17$	3.29746	0.799752	0.399876	−	0.916569i	$-0.369053\pi$
$17$	3.29746	0.799752	0.399876	+	0.916569i	$0.369053\pi$
$18$	−11.2402	−2.64935
$19$	4.48304	1.02848	0.514240	−	0.857646i	$-0.328074\pi$
$19$	4.48304	1.02848	0.514240	+	0.857646i	$0.328074\pi$
$20$	1.99916	0.447027
$21$	4.12889	0.900999
$22$	−2.46758	−0.526090
$23$	2.86500	0.597393	0.298696	−	0.954348i	$-0.403448\pi$
$23$	2.86500	0.597393	0.298696	+	0.954348i	$0.403448\pi$
$24$	14.1684	2.89211
$25$	−4.76096	−0.952192
$26$	3.07458	0.602975
$27$	−4.27463	−0.822653
$28$	−6.14219	−1.16077
$29$	−6.33838	−1.17701	−0.588504	−	0.808494i	$-0.700283\pi$
$29$	−6.33838	−1.17701	−0.588504	+	0.808494i	$0.700283\pi$
$30$	3.31612	0.605438
$31$	7.17832	1.28927	0.644633	−	0.764493i	$-0.277010\pi$
$31$	7.17832	1.28927	0.644633	+	0.764493i	$0.277010\pi$
$32$	−0.897472	−0.158652
$33$	−2.74867	−0.478481
$34$	−8.13675	−1.39544
$35$	−0.734427	−0.124141
$36$	18.6258	3.10431
$37$	−6.61712	−1.08785	−0.543924	−	0.839134i	$-0.683062\pi$
$37$	−6.61712	−1.08785	−0.543924	+	0.839134i	$0.683062\pi$
$38$	−11.0623	−1.79454
$39$	3.42481	0.548409
$40$	−2.52020	−0.398479
$41$	11.6196	1.81467	0.907336	−	0.420407i	$-0.138113\pi$
$41$	11.6196	1.81467	0.907336	+	0.420407i	$0.138113\pi$
$42$	−10.1884	−1.57210
$43$	2.12187	0.323582	0.161791	−	0.986825i	$-0.448273\pi$
$43$	2.12187	0.323582	0.161791	+	0.986825i	$0.448273\pi$
$44$	4.08895	0.616432
$45$	2.22711	0.331997
$46$	−7.06960	−1.04236
$47$	−8.05637	−1.17514	−0.587571	−	0.809172i	$-0.699916\pi$
$47$	−8.05637	−1.17514	−0.587571	+	0.809172i	$0.699916\pi$
$48$	−12.4833	−1.80182
$49$	−4.74356	−0.677652
$50$	11.7480	1.66142
$51$	−9.06362	−1.26916
$52$	−5.09479	−0.706521
$53$	−2.36469	−0.324815	−0.162408	−	0.986724i	$-0.551926\pi$
$53$	−2.36469	−0.324815	−0.162408	+	0.986724i	$0.551926\pi$
$54$	10.5480	1.43540
$55$	0.488919	0.0659258
$56$	7.74302	1.03471
$57$	−12.3224	−1.63214
$58$	15.6405	2.05369
$59$	−1.23927	−0.161340	−0.0806698	−	0.996741i	$-0.525706\pi$
$59$	−1.23927	−0.161340	−0.0806698	+	0.996741i	$0.525706\pi$
$60$	−5.49504	−0.709406
$61$	−12.8735	−1.64829	−0.824143	−	0.566381i	$-0.808343\pi$
$61$	−12.8735	−1.64829	−0.824143	+	0.566381i	$0.808343\pi$
$62$	−17.7131	−2.24956
$63$	−6.84252	−0.862076
$64$	−6.86862	−0.858578
$65$	−0.609189	−0.0755606
$66$	6.78255	0.834874
$67$	−7.36834	−0.900187	−0.450093	−	0.892982i	$-0.648609\pi$
$67$	−7.36834	−0.900187	−0.450093	+	0.892982i	$0.648609\pi$
$68$	13.4832	1.63507
$69$	−7.87491	−0.948028
$70$	1.81226	0.216606
$71$	−1.51659	−0.179986	−0.0899930	−	0.995942i	$-0.528684\pi$
$71$	−1.51659	−0.179986	−0.0899930	+	0.995942i	$0.528684\pi$
$72$	−23.4803	−2.76718
$73$	−10.5341	−1.23292	−0.616460	−	0.787386i	$-0.711434\pi$
$73$	−10.5341	−1.23292	−0.616460	+	0.787386i	$0.711434\pi$
$74$	16.3283	1.89812
$75$	13.0863	1.51107
$76$	18.3309	2.10270
$77$	−1.50214	−0.171185
$78$	−8.45100	−0.956887
$79$	9.64225	1.08484	0.542419	−	0.840108i	$-0.317509\pi$
$79$	9.64225	1.08484	0.542419	+	0.840108i	$0.317509\pi$
$80$	2.22048	0.248257
$81$	−1.91597	−0.212885
$82$	−28.6722	−3.16631
$83$	2.52721	0.277398	0.138699	−	0.990335i	$-0.455708\pi$
$83$	2.52721	0.277398	0.138699	+	0.990335i	$0.455708\pi$
$84$	16.8828	1.84207
$85$	1.61219	0.174867
$86$	−5.23588	−0.564600
$87$	17.4221	1.86784
$88$	−5.15465	−0.549487
$89$	11.2358	1.19099	0.595494	−	0.803360i	$-0.296957\pi$
$89$	11.2358	1.19099	0.595494	+	0.803360i	$0.296957\pi$
$90$	−5.49556	−0.579283
$91$	1.87166	0.196203
$92$	11.7148	1.22135
$93$	−19.7308	−2.04599
$94$	19.8797	2.05044
$95$	2.19185	0.224879
$96$	2.46685	0.251772
$97$	−9.73290	−0.988226	−0.494113	−	0.869398i	$-0.664507\pi$
$97$	−9.73290	−0.988226	−0.494113	+	0.869398i	$0.664507\pi$
$98$	11.7051	1.18240
$99$	4.55516	0.457811
$100$	−19.4673	−1.94673
$101$	11.9343	1.18751	0.593755	−	0.804646i	$-0.297645\pi$
$101$	11.9343	1.18751	0.593755	+	0.804646i	$0.297645\pi$
$102$	22.3652	2.21449
$103$	13.8343	1.36314	0.681569	−	0.731754i	$-0.261298\pi$
$103$	13.8343	1.36314	0.681569	+	0.731754i	$0.261298\pi$
$104$	6.42264	0.629792
$105$	2.01869	0.197004
$106$	5.83506	0.566751
$107$	14.2840	1.38089	0.690446	−	0.723384i	$-0.257415\pi$
$107$	14.2840	1.38089	0.690446	+	0.723384i	$0.257415\pi$
$108$	−17.4787	−1.68189
$109$	6.82257	0.653483	0.326742	−	0.945114i	$-0.394049\pi$
$109$	6.82257	0.653483	0.326742	+	0.945114i	$0.394049\pi$
$110$	−1.20645	−0.115030
$111$	18.1883	1.72635
$112$	−6.82214	−0.644632
$113$	5.56512	0.523522	0.261761	−	0.965133i	$-0.415697\pi$
$113$	5.56512	0.523522	0.261761	+	0.965133i	$0.415697\pi$
$114$	30.4065	2.84783
$115$	1.40075	0.130621
$116$	−25.9173	−2.40636
$117$	−5.67570	−0.524718
$118$	3.05801	0.281512
$119$	−4.95327	−0.454065
$120$	6.92720	0.632364
$121$	1.00000	0.0909091
$122$	31.7665	2.87600
$123$	−31.9383	−2.87978
$124$	29.3518	2.63587
$125$	−4.77232	−0.426849
$126$	16.8845	1.50419
$127$	10.1820	0.903505	0.451753	−	0.892143i	$-0.350799\pi$
$127$	10.1820	0.903505	0.451753	+	0.892143i	$0.350799\pi$
$128$	18.7438	1.65673
$129$	−5.83231	−0.513507
$130$	1.50322	0.131841
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	−11.2392	−0.978243
$133$	−6.73418	−0.583927
$134$	18.1820	1.57068
$135$	−2.08995	−0.179874
$136$	−16.9973	−1.45750
$137$	10.7440	0.917918	0.458959	−	0.888457i	$-0.348222\pi$
$137$	10.7440	0.917918	0.458959	+	0.888457i	$0.348222\pi$
$138$	19.4320	1.65416
$139$	−4.59866	−0.390054	−0.195027	−	0.980798i	$-0.562479\pi$
$139$	−4.59866	−0.390054	−0.195027	+	0.980798i	$0.562479\pi$
$140$	−3.00303	−0.253803
$141$	22.1443	1.86488
$142$	3.74230	0.314047
$143$	−1.24599	−0.104195
$144$	20.6877	1.72398
$145$	−3.09896	−0.257354
$146$	25.9937	2.15125
$147$	13.0385	1.07539
$148$	−27.0571	−2.22408
$149$	7.10546	0.582102	0.291051	−	0.956708i	$-0.405995\pi$
$149$	7.10546	0.582102	0.291051	+	0.956708i	$0.405995\pi$
$150$	−32.2914	−2.63659
$151$	−7.59219	−0.617843	−0.308922	−	0.951087i	$-0.599968\pi$
$151$	−7.59219	−0.617843	−0.308922	+	0.951087i	$0.599968\pi$
$152$	−23.1085	−1.87435
$153$	15.0205	1.21433
$154$	3.70666	0.298691
$155$	3.50962	0.281899
$156$	14.0039	1.12121
$157$	3.59426	0.286853	0.143426	−	0.989661i	$-0.454188\pi$
$157$	3.59426	0.286853	0.143426	+	0.989661i	$0.454188\pi$
$158$	−23.7930	−1.89287
$159$	6.49974	0.515463
$160$	−0.438791	−0.0346895
$161$	−4.30364	−0.339174
$162$	4.72781	0.371451
$163$	−3.47971	−0.272552	−0.136276	−	0.990671i	$-0.543513\pi$
$163$	−3.47971	−0.272552	−0.136276	+	0.990671i	$0.543513\pi$
$164$	47.5118	3.71005
$165$	−1.34388	−0.104621
$166$	−6.23610	−0.484016
$167$	5.37093	0.415615	0.207808	−	0.978170i	$-0.433367\pi$
$167$	5.37093	0.415615	0.207808	+	0.978170i	$0.433367\pi$
$168$	−21.2830	−1.64202
$169$	−11.4475	−0.880577
$170$	−3.97821	−0.305115
$171$	20.4210	1.56163
$172$	8.67622	0.661556
$173$	4.48970	0.341345	0.170673	−	0.985328i	$-0.445406\pi$
$173$	4.48970	0.341345	0.170673	+	0.985328i	$0.445406\pi$
$174$	−42.9904	−3.25909
$175$	7.15165	0.540614
$176$	4.54160	0.342336
$177$	3.40635	0.256037
$178$	−27.7251	−2.07808
$179$	7.93997	0.593461	0.296730	−	0.954961i	$-0.404104\pi$
$179$	7.93997	0.593461	0.296730	+	0.954961i	$0.404104\pi$
$180$	9.10653	0.678760
$181$	3.07685	0.228700	0.114350	−	0.993440i	$-0.463521\pi$
$181$	3.07685	0.228700	0.114350	+	0.993440i	$0.463521\pi$
$182$	−4.61847	−0.342344
$183$	35.3850	2.61574
$184$	−14.7680	−1.08871
$185$	−3.23524	−0.237859
$186$	48.6874	3.56993
$187$	3.29746	0.241134
$188$	−32.9421	−2.40255
$189$	6.42111	0.467067
$190$	−5.40855	−0.392378
$191$	−1.47429	−0.106676	−0.0533381	−	0.998577i	$-0.516986\pi$
$191$	−1.47429	−0.106676	−0.0533381	+	0.998577i	$0.516986\pi$
$192$	18.8795	1.36251
$193$	0.405815	0.0292112	0.0146056	−	0.999893i	$-0.495351\pi$
$193$	0.405815	0.0292112	0.0146056	+	0.999893i	$0.495351\pi$
$194$	24.0167	1.72430
$195$	1.67446	0.119910
$196$	−19.3962	−1.38544
$197$	7.61066	0.542237	0.271119	−	0.962546i	$-0.412606\pi$
$197$	7.61066	0.542237	0.271119	+	0.962546i	$0.412606\pi$
$198$	−11.2402	−0.798808
$199$	17.5100	1.24125	0.620626	−	0.784106i	$-0.286878\pi$
$199$	17.5100	1.24125	0.620626	+	0.784106i	$0.286878\pi$
$200$	24.5411	1.73531
$201$	20.2531	1.42854
$202$	−29.4489	−2.07202
$203$	9.52117	0.668255
$204$	−37.0607	−2.59477
$205$	5.68103	0.396780
$206$	−34.1373	−2.37846
$207$	13.0505	0.907074
$208$	−5.65880	−0.392367
$209$	4.48304	0.310099
$210$	−4.98129	−0.343742
$211$	21.8560	1.50463	0.752314	−	0.658805i	$-0.228938\pi$
$211$	21.8560	1.50463	0.752314	+	0.658805i	$0.228938\pi$
$212$	−9.66910	−0.664076
$213$	4.16860	0.285628
$214$	−35.2470	−2.40944
$215$	1.03742	0.0707517
$216$	22.0342	1.49924
$217$	−10.7829	−0.731990
$218$	−16.8352	−1.14023
$219$	28.9547	1.95657
$220$	1.99916	0.134784
$221$	−4.10861	−0.276375
$222$	−44.8810	−3.01221
$223$	0.983547	0.0658632	0.0329316	−	0.999458i	$-0.489516\pi$
$223$	0.983547	0.0658632	0.0329316	+	0.999458i	$0.489516\pi$
$224$	1.34813	0.0900759
$225$	−21.6869	−1.44580
$226$	−13.7324	−0.913464
$227$	−10.6401	−0.706209	−0.353104	−	0.935584i	$-0.614874\pi$
$227$	−10.6401	−0.706209	−0.353104	+	0.935584i	$0.614874\pi$
$228$	−50.3856	−3.33687
$229$	−15.4098	−1.01831	−0.509155	−	0.860675i	$-0.670042\pi$
$229$	−15.4098	−1.01831	−0.509155	+	0.860675i	$0.670042\pi$
$230$	−3.45646	−0.227912
$231$	4.12889	0.271661
$232$	32.6721	2.14503
$233$	−14.1401	−0.926352	−0.463176	−	0.886266i	$-0.653290\pi$
$233$	−14.1401	−0.926352	−0.463176	+	0.886266i	$0.653290\pi$
$234$	14.0052	0.915550
$235$	−3.93891	−0.256946
$236$	−5.06733	−0.329855
$237$	−26.5033	−1.72158
$238$	12.2226	0.792272
$239$	9.86348	0.638015	0.319008	−	0.947752i	$-0.396650\pi$
$239$	9.86348	0.638015	0.319008	+	0.947752i	$0.396650\pi$
$240$	−6.10335	−0.393969
$241$	−16.5477	−1.06593	−0.532964	−	0.846138i	$-0.678922\pi$
$241$	−16.5477	−1.06593	−0.532964	+	0.846138i	$0.678922\pi$
$242$	−2.46758	−0.158622
$243$	18.0902	1.16049
$244$	−52.6392	−3.36988
$245$	−2.31922	−0.148169
$246$	78.8103	5.02476
$247$	−5.58583	−0.355418
$248$	−37.0017	−2.34961
$249$	−6.94647	−0.440215
$250$	11.7761	0.744784
$251$	−1.52551	−0.0962896	−0.0481448	−	0.998840i	$-0.515331\pi$
$251$	−1.52551	−0.0962896	−0.0481448	+	0.998840i	$0.515331\pi$
$252$	−27.9787	−1.76249
$253$	2.86500	0.180121
$254$	−25.1249	−1.57647
$255$	−4.43138	−0.277504
$256$	−32.5146	−2.03216
$257$	11.2930	0.704440	0.352220	−	0.935917i	$-0.385427\pi$
$257$	11.2930	0.704440	0.352220	+	0.935917i	$0.385427\pi$
$258$	14.3917	0.895988
$259$	9.93987	0.617634
$260$	−2.49094	−0.154482
$261$	−28.8724	−1.78716
$262$	2.46758	0.152448
$263$	17.0176	1.04935	0.524676	−	0.851302i	$-0.324186\pi$
$263$	17.0176	1.04935	0.524676	+	0.851302i	$0.324186\pi$
$264$	14.1684	0.872005
$265$	−1.15614	−0.0710213
$266$	16.6171	1.01886
$267$	−30.8833	−1.89003
$268$	−30.1288	−1.84041
$269$	22.2526	1.35676	0.678381	−	0.734710i	$-0.262682\pi$
$269$	22.2526	1.35676	0.678381	+	0.734710i	$0.262682\pi$
$270$	5.15711	0.313852
$271$	17.8037	1.08150	0.540748	−	0.841185i	$-0.318141\pi$
$271$	17.8037	1.08150	0.540748	+	0.841185i	$0.318141\pi$
$272$	14.9758	0.908039
$273$	−5.14457	−0.311363
$274$	−26.5116	−1.60162
$275$	−4.76096	−0.287097
$276$	−32.2001	−1.93822
$277$	17.2383	1.03575	0.517875	−	0.855456i	$-0.326723\pi$
$277$	17.2383	1.03575	0.517875	+	0.855456i	$0.326723\pi$
$278$	11.3476	0.680582
$279$	32.6985	1.95761
$280$	3.78571	0.226240
$281$	10.4427	0.622958	0.311479	−	0.950253i	$-0.399176\pi$
$281$	10.4427	0.622958	0.311479	+	0.950253i	$0.399176\pi$
$282$	−54.6427	−3.25393
$283$	22.5596	1.34103	0.670514	−	0.741897i	$-0.266074\pi$
$283$	22.5596	1.34103	0.670514	+	0.741897i	$0.266074\pi$
$284$	−6.20125	−0.367977
$285$	−6.02465	−0.356869
$286$	3.07458	0.181804
$287$	−17.4543	−1.03029
$288$	−4.08813	−0.240896
$289$	−6.12674	−0.360396
$290$	7.64692	0.449043
$291$	26.7525	1.56826
$292$	−43.0733	−2.52067
$293$	−12.7125	−0.742673	−0.371337	−	0.928498i	$-0.621100\pi$
$293$	−12.7125	−0.742673	−0.371337	+	0.928498i	$0.621100\pi$
$294$	−32.1735	−1.87639
$295$	−0.605905	−0.0352771
$296$	34.1089	1.98254
$297$	−4.27463	−0.248039
$298$	−17.5333	−1.01568
$299$	−3.56976	−0.206444
$300$	53.5091	3.08935
$301$	−3.18736	−0.183716
$302$	18.7343	1.07804
$303$	−32.8035	−1.88451
$304$	20.3602	1.16774
$305$	−6.29411	−0.360400
$306$	−37.0642	−2.11882
$307$	−20.4580	−1.16760	−0.583799	−	0.811898i	$-0.698435\pi$
$307$	−20.4580	−1.16760	−0.583799	+	0.811898i	$0.698435\pi$
$308$	−6.14219	−0.349984
$309$	−38.0260	−2.16322
$310$	−8.66027	−0.491870
$311$	−8.65591	−0.490832	−0.245416	−	0.969418i	$-0.578925\pi$
$311$	−8.65591	−0.490832	−0.245416	+	0.969418i	$0.578925\pi$
$312$	−17.6537	−0.999444
$313$	21.7144	1.22737	0.613685	−	0.789551i	$-0.289687\pi$
$313$	21.7144	1.22737	0.613685	+	0.789551i	$0.289687\pi$
$314$	−8.86911	−0.500513
$315$	−3.34544	−0.188494
$316$	39.4266	2.21792
$317$	12.1289	0.681229	0.340614	−	0.940203i	$-0.389365\pi$
$317$	12.1289	0.681229	0.340614	+	0.940203i	$0.389365\pi$
$318$	−16.0386	−0.899402
$319$	−6.33838	−0.354881
$320$	−3.35820	−0.187729
$321$	−39.2621	−2.19140
$322$	10.6196	0.591805
$323$	14.7827	0.822530
$324$	−7.83430	−0.435239
$325$	5.93211	0.329054
$326$	8.58646	0.475560
$327$	−18.7530	−1.03704
$328$	−59.8947	−3.30713
$329$	12.1018	0.667196
$330$	3.31612	0.182546
$331$	−15.9834	−0.878526	−0.439263	−	0.898359i	$-0.644760\pi$
$331$	−15.9834	−0.878526	−0.439263	+	0.898359i	$0.644760\pi$
$332$	10.3337	0.567133
$333$	−30.1421	−1.65178
$334$	−13.2532	−0.725183
$335$	−3.60252	−0.196827
$336$	18.7518	1.02299
$337$	9.71470	0.529193	0.264597	−	0.964359i	$-0.414761\pi$
$337$	9.71470	0.529193	0.264597	+	0.964359i	$0.414761\pi$
$338$	28.2476	1.53647
$339$	−15.2966	−0.830800
$340$	6.59217	0.357511
$341$	7.17832	0.388728
$342$	−50.3904	−2.72480
$343$	17.6405	0.952499
$344$	−10.9375	−0.589710
$345$	−3.85020	−0.207288
$346$	−11.0787	−0.595594
$347$	−24.8436	−1.33367	−0.666837	−	0.745203i	$-0.732352\pi$
$347$	−24.8436	−1.33367	−0.666837	+	0.745203i	$0.732352\pi$
$348$	71.2381	3.81876
$349$	14.8579	0.795325	0.397662	−	0.917532i	$-0.369821\pi$
$349$	14.8579	0.795325	0.397662	+	0.917532i	$0.369821\pi$
$350$	−17.6473	−0.943286
$351$	5.32615	0.284289
$352$	−0.897472	−0.0478354
$353$	−29.3823	−1.56386	−0.781930	−	0.623366i	$-0.785765\pi$
$353$	−29.3823	−1.56386	−0.781930	+	0.623366i	$0.785765\pi$
$354$	−8.40544	−0.446744
$355$	−0.741489	−0.0393542
$356$	45.9424	2.43494
$357$	13.6149	0.720576
$358$	−19.5925	−1.03550
$359$	5.22490	0.275760	0.137880	−	0.990449i	$-0.455971\pi$
$359$	5.22490	0.275760	0.137880	+	0.990449i	$0.455971\pi$
$360$	−11.4799	−0.605046
$361$	1.09767	0.0577723
$362$	−7.59237	−0.399046
$363$	−2.74867	−0.144268
$364$	7.65312	0.401132
$365$	−5.15031	−0.269580
$366$	−87.3154	−4.56405
$367$	−10.7080	−0.558952	−0.279476	−	0.960153i	$-0.590161\pi$
$367$	−10.7080	−0.558952	−0.279476	+	0.960153i	$0.590161\pi$
$368$	13.0117	0.678280
$369$	52.9290	2.75538
$370$	7.98320	0.415027
$371$	3.55211	0.184416
$372$	−80.6783	−4.18297
$373$	27.5282	1.42535	0.712677	−	0.701492i	$-0.247483\pi$
$373$	27.5282	1.42535	0.712677	+	0.701492i	$0.247483\pi$
$374$	−8.13675	−0.420741
$375$	13.1175	0.677385
$376$	41.5277	2.14163
$377$	7.89757	0.406745
$378$	−15.8446	−0.814958
$379$	4.07171	0.209150	0.104575	−	0.994517i	$-0.466652\pi$
$379$	4.07171	0.209150	0.104575	+	0.994517i	$0.466652\pi$
$380$	8.96234	0.459758
$381$	−27.9869	−1.43381
$382$	3.63794	0.186133
$383$	17.8852	0.913890	0.456945	−	0.889495i	$-0.348944\pi$
$383$	17.8852	0.913890	0.456945	+	0.889495i	$0.348944\pi$
$384$	−51.5205	−2.62914
$385$	−0.734427	−0.0374299
$386$	−1.00138	−0.0509690
$387$	9.66547	0.491323
$388$	−39.7973	−2.02040
$389$	−21.8075	−1.10569	−0.552843	−	0.833286i	$-0.686457\pi$
$389$	−21.8075	−1.10569	−0.552843	+	0.833286i	$0.686457\pi$
$390$	−4.13185	−0.209225
$391$	9.44722	0.477766
$392$	24.4514	1.23498
$393$	2.74867	0.138652
$394$	−18.7799	−0.946118
$395$	4.71428	0.237201
$396$	18.6258	0.935983
$397$	37.0338	1.85867	0.929337	−	0.369234i	$-0.120380\pi$
$397$	37.0338	1.85867	0.929337	+	0.369234i	$0.120380\pi$
$398$	−43.2074	−2.16579
$399$	18.5100	0.926659
$400$	−21.6224	−1.08112
$401$	35.1310	1.75436	0.877180	−	0.480162i	$-0.159422\pi$
$401$	35.1310	1.75436	0.877180	+	0.480162i	$0.159422\pi$
$402$	−49.9762	−2.49259
$403$	−8.94413	−0.445539
$404$	48.7989	2.42784
$405$	−0.936754	−0.0465477
$406$	−23.4942	−1.16600
$407$	−6.61712	−0.327999
$408$	46.7198	2.31297
$409$	−9.19325	−0.454577	−0.227289	−	0.973827i	$-0.572986\pi$
$409$	−9.19325	−0.454577	−0.227289	+	0.973827i	$0.572986\pi$
$410$	−14.0184	−0.692319
$411$	−29.5315	−1.45668
$412$	56.5679	2.78690
$413$	1.86157	0.0916018
$414$	−32.2032	−1.58270
$415$	1.23560	0.0606534
$416$	1.11824	0.0548263
$417$	12.6402	0.618993
$418$	−11.0623	−0.541073
$419$	−10.6551	−0.520534	−0.260267	−	0.965537i	$-0.583811\pi$
$419$	−10.6551	−0.520534	−0.260267	+	0.965537i	$0.583811\pi$
$420$	8.25434	0.402771
$421$	−27.2476	−1.32797	−0.663983	−	0.747748i	$-0.731135\pi$
$421$	−27.2476	−1.32797	−0.663983	+	0.747748i	$0.731135\pi$
$422$	−53.9313	−2.62534
$423$	−36.6981	−1.78432
$424$	12.1891	0.591957
$425$	−15.6991	−0.761517
$426$	−10.2863	−0.498375
$427$	19.3379	0.935827
$428$	58.4067	2.82320
$429$	3.42481	0.165352
$430$	−2.55992	−0.123450
$431$	19.4736	0.938009	0.469005	−	0.883196i	$-0.344613\pi$
$431$	19.4736	0.938009	0.469005	+	0.883196i	$0.344613\pi$
$432$	−19.4137	−0.934040
$433$	29.3489	1.41042	0.705209	−	0.709000i	$-0.250853\pi$
$433$	29.3489	1.41042	0.705209	+	0.709000i	$0.250853\pi$
$434$	26.6076	1.27721
$435$	8.51800	0.408407
$436$	27.8971	1.33603
$437$	12.8439	0.614407
$438$	−71.4479	−3.41391
$439$	27.6276	1.31860	0.659298	−	0.751882i	$-0.270854\pi$
$439$	27.6276	1.31860	0.659298	+	0.751882i	$0.270854\pi$
$440$	−2.52020	−0.120146
$441$	−21.6077	−1.02894
$442$	10.1383	0.482231
$443$	18.7540	0.891029	0.445514	−	0.895275i	$-0.353021\pi$
$443$	18.7540	0.891029	0.445514	+	0.895275i	$0.353021\pi$
$444$	74.3708	3.52948
$445$	5.49337	0.260411
$446$	−2.42698	−0.114921
$447$	−19.5305	−0.923763
$448$	10.3177	0.487464
$449$	−15.4527	−0.729259	−0.364630	−	0.931153i	$-0.618804\pi$
$449$	−15.4527	−0.729259	−0.364630	+	0.931153i	$0.618804\pi$
$450$	53.5143	2.52269
$451$	11.6196	0.547144
$452$	22.7555	1.07033
$453$	20.8684	0.980482
$454$	26.2553	1.23222
$455$	0.915090	0.0429001
$456$	63.5175	2.97448
$457$	21.7056	1.01535	0.507674	−	0.861549i	$-0.330506\pi$
$457$	21.7056	1.01535	0.507674	+	0.861549i	$0.330506\pi$
$458$	38.0250	1.77679
$459$	−14.0954	−0.657918
$460$	5.72760	0.267051
$461$	37.8300	1.76192	0.880960	−	0.473191i	$-0.156898\pi$
$461$	37.8300	1.76192	0.880960	+	0.473191i	$0.156898\pi$
$462$	−10.1884	−0.474006
$463$	26.0566	1.21095	0.605476	−	0.795864i	$-0.292983\pi$
$463$	26.0566	1.21095	0.605476	+	0.795864i	$0.292983\pi$
$464$	−28.7864	−1.33638
$465$	−9.64677	−0.447358
$466$	34.8919	1.61634
$467$	7.42007	0.343360	0.171680	−	0.985153i	$-0.445081\pi$
$467$	7.42007	0.343360	0.171680	+	0.985153i	$0.445081\pi$
$468$	−23.2076	−1.07277
$469$	11.0683	0.511088
$470$	9.71958	0.448331
$471$	−9.87941	−0.455219
$472$	6.38802	0.294032
$473$	2.12187	0.0975637
$474$	65.3990	3.00388
$475$	−21.3436	−0.979311
$476$	−20.2537	−0.928325
$477$	−10.7716	−0.493196
$478$	−24.3389	−1.11324
$479$	−3.34374	−0.152779	−0.0763897	−	0.997078i	$-0.524339\pi$
$479$	−3.34374	−0.152779	−0.0763897	+	0.997078i	$0.524339\pi$
$480$	1.20609	0.0550502
$481$	8.24487	0.375934
$482$	40.8327	1.85988
$483$	11.8293	0.538250
$484$	4.08895	0.185861
$485$	−4.75860	−0.216077
$486$	−44.6391	−2.02487
$487$	15.6735	0.710236	0.355118	−	0.934821i	$-0.384441\pi$
$487$	15.6735	0.710236	0.355118	+	0.934821i	$0.384441\pi$
$488$	66.3585	3.00391
$489$	9.56456	0.432524
$490$	5.72285	0.258532
$491$	−34.2184	−1.54426	−0.772128	−	0.635468i	$-0.780807\pi$
$491$	−34.2184	−1.54426	−0.772128	+	0.635468i	$0.780807\pi$
$492$	−130.594	−5.88764
$493$	−20.9006	−0.941315
$494$	13.7835	0.620148
$495$	2.22711	0.100101
$496$	32.6011	1.46383
$497$	2.27814	0.102188
$498$	17.1410	0.768105
$499$	−37.1402	−1.66262	−0.831312	−	0.555806i	$-0.812410\pi$
$499$	−37.1402	−1.66262	−0.831312	+	0.555806i	$0.812410\pi$
$500$	−19.5138	−0.872682
$501$	−14.7629	−0.659558
$502$	3.76433	0.168010
$503$	−16.7740	−0.747918	−0.373959	−	0.927445i	$-0.622000\pi$
$503$	−16.7740	−0.747918	−0.373959	+	0.927445i	$0.622000\pi$
$504$	35.2707	1.57108
$505$	5.83493	0.259651
$506$	−7.06960	−0.314282
$507$	31.4654	1.39743
$508$	41.6336	1.84719
$509$	6.46008	0.286338	0.143169	−	0.989698i	$-0.454271\pi$
$509$	6.46008	0.286338	0.143169	+	0.989698i	$0.454271\pi$
$510$	10.9348	0.484200
$511$	15.8237	0.699999
$512$	42.7447	1.88907
$513$	−19.1633	−0.846082
$514$	−27.8665	−1.22914
$515$	6.76387	0.298052
$516$	−23.8480	−1.04985
$517$	−8.05637	−0.354319
$518$	−24.5274	−1.07767
$519$	−12.3407	−0.541696
$520$	3.14015	0.137705
$521$	−28.0717	−1.22985	−0.614923	−	0.788587i	$-0.710813\pi$
$521$	−28.0717	−1.22985	−0.614923	+	0.788587i	$0.710813\pi$
$522$	71.2449	3.11830
$523$	22.3123	0.975648	0.487824	−	0.872942i	$-0.337791\pi$
$523$	22.3123	0.975648	0.487824	+	0.872942i	$0.337791\pi$
$524$	−4.08895	−0.178627
$525$	−19.6575	−0.857923
$526$	−41.9924	−1.83095
$527$	23.6703	1.03109
$528$	−12.4833	−0.543268
$529$	−14.7918	−0.643122
$530$	2.85287	0.123921
$531$	−5.64510	−0.244976
$532$	−27.5357	−1.19382
$533$	−14.4779	−0.627106
$534$	76.2071	3.29780
$535$	6.98374	0.301934
$536$	37.9812	1.64054
$537$	−21.8243	−0.941789
$538$	−54.9099	−2.36734
$539$	−4.74356	−0.204320
$540$	−8.54569	−0.367748
$541$	1.45640	0.0626155	0.0313078	−	0.999510i	$-0.490033\pi$
$541$	1.45640	0.0626155	0.0313078	+	0.999510i	$0.490033\pi$
$542$	−43.9320	−1.88704
$543$	−8.45723	−0.362935
$544$	−2.95938	−0.126882
$545$	3.33568	0.142885
$546$	12.6946	0.543280
$547$	−32.5044	−1.38979	−0.694893	−	0.719113i	$-0.744548\pi$
$547$	−32.5044	−1.38979	−0.694893	+	0.719113i	$0.744548\pi$
$548$	43.9315	1.87666
$549$	−58.6411	−2.50274
$550$	11.7480	0.500938
$551$	−28.4152	−1.21053
$552$	40.5924	1.72773
$553$	−14.4840	−0.615924
$554$	−42.5369	−1.80722
$555$	8.89259	0.377469
$556$	−18.8037	−0.797454
$557$	−4.35436	−0.184500	−0.0922500	−	0.995736i	$-0.529406\pi$
$557$	−4.35436	−0.184500	−0.0922500	+	0.995736i	$0.529406\pi$
$558$	−80.6860	−3.41571
$559$	−2.64383	−0.111822
$560$	−3.33548	−0.140950
$561$	−9.06362	−0.382667
$562$	−25.7682	−1.08696
$563$	−21.5823	−0.909584	−0.454792	−	0.890598i	$-0.650286\pi$
$563$	−21.5823	−0.909584	−0.454792	+	0.890598i	$0.650286\pi$
$564$	90.5468	3.81271
$565$	2.72089	0.114469
$566$	−55.6676	−2.33988
$567$	2.87806	0.120867
$568$	7.81748	0.328014
$569$	39.7229	1.66527	0.832635	−	0.553822i	$-0.186831\pi$
$569$	39.7229	1.66527	0.832635	+	0.553822i	$0.186831\pi$
$570$	14.8663	0.622681
$571$	9.39277	0.393075	0.196538	−	0.980496i	$-0.437030\pi$
$571$	9.39277	0.393075	0.196538	+	0.980496i	$0.437030\pi$
$572$	−5.09479	−0.213024
$573$	4.05234	0.169289
$574$	43.0698	1.79770
$575$	−13.6401	−0.568832
$576$	−31.2877	−1.30365
$577$	−47.5028	−1.97757	−0.988783	−	0.149358i	$-0.952279\pi$
$577$	−47.5028	−1.97757	−0.988783	+	0.149358i	$0.952279\pi$
$578$	15.1182	0.628835
$579$	−1.11545	−0.0463566
$580$	−12.6715	−0.526154
$581$	−3.79624	−0.157495
$582$	−66.0139	−2.73636
$583$	−2.36469	−0.0979355
$584$	54.2994	2.24693
$585$	−2.77496	−0.114730
$586$	31.3692	1.29585
$587$	3.45995	0.142807	0.0714036	−	0.997448i	$-0.477252\pi$
$587$	3.45995	0.142807	0.0714036	+	0.997448i	$0.477252\pi$
$588$	53.3136	2.19862
$589$	32.1807	1.32598
$590$	1.49512	0.0615530
$591$	−20.9192	−0.860500
$592$	−30.0523	−1.23514
$593$	30.2561	1.24247	0.621234	−	0.783625i	$-0.286632\pi$
$593$	30.2561	1.24247	0.621234	+	0.783625i	$0.286632\pi$
$594$	10.5480	0.432789
$595$	−2.42175	−0.0992819
$596$	29.0539	1.19009
$597$	−48.1292	−1.96980
$598$	8.80866	0.360213
$599$	25.3314	1.03501	0.517507	−	0.855679i	$-0.326860\pi$
$599$	25.3314	1.03501	0.517507	+	0.855679i	$0.326860\pi$
$600$	−67.4552	−2.75385
$601$	−15.8565	−0.646799	−0.323399	−	0.946263i	$-0.604826\pi$
$601$	−15.8565	−0.646799	−0.323399	+	0.946263i	$0.604826\pi$
$602$	7.86506	0.320556
$603$	−33.5640	−1.36683
$604$	−31.0441	−1.26317
$605$	0.488919	0.0198774
$606$	80.9453	3.28818
$607$	3.40545	0.138223	0.0691115	−	0.997609i	$-0.477984\pi$
$607$	3.40545	0.138223	0.0691115	+	0.997609i	$0.477984\pi$
$608$	−4.02341	−0.163171
$609$	−26.1705	−1.06048
$610$	15.5312	0.628841
$611$	10.0382	0.406101
$612$	61.4180	2.48268
$613$	28.1291	1.13613	0.568063	−	0.822985i	$-0.307693\pi$
$613$	28.1291	1.13613	0.568063	+	0.822985i	$0.307693\pi$
$614$	50.4817	2.03728
$615$	−15.6152	−0.629667
$616$	7.74302	0.311975
$617$	14.2650	0.574285	0.287143	−	0.957888i	$-0.407295\pi$
$617$	14.2650	0.574285	0.287143	+	0.957888i	$0.407295\pi$
$618$	93.8321	3.77448
$619$	−25.7288	−1.03413	−0.517064	−	0.855947i	$-0.672975\pi$
$619$	−25.7288	−1.03413	−0.517064	+	0.855947i	$0.672975\pi$
$620$	14.3507	0.576336
$621$	−12.2468	−0.491447
$622$	21.3592	0.856424
$623$	−16.8777	−0.676192
$624$	15.5541	0.622664
$625$	21.4715	0.858861
$626$	−53.5820	−2.14157
$627$	−12.3224	−0.492109
$628$	14.6967	0.586463
$629$	−21.8197	−0.870009
$630$	8.25513	0.328892
$631$	37.8068	1.50506	0.752532	−	0.658556i	$-0.228832\pi$
$631$	37.8068	1.50506	0.752532	+	0.658556i	$0.228832\pi$
$632$	−49.7024	−1.97705
$633$	−60.0748	−2.38776
$634$	−29.9291	−1.18864
$635$	4.97817	0.197553
$636$	26.5771	1.05385
$637$	5.91044	0.234180
$638$	15.6405	0.619212
$639$	−6.90831	−0.273289
$640$	9.16421	0.362247
$641$	−35.1952	−1.39013	−0.695064	−	0.718948i	$-0.744624\pi$
$641$	−35.1952	−1.39013	−0.695064	+	0.718948i	$0.744624\pi$
$642$	96.8823	3.82364
$643$	−43.9319	−1.73250	−0.866252	−	0.499608i	$-0.833478\pi$
$643$	−43.9319	−1.73250	−0.866252	+	0.499608i	$0.833478\pi$
$644$	−17.5973	−0.693433
$645$	−2.85153	−0.112279
$646$	−36.4774	−1.43518
$647$	−18.5630	−0.729787	−0.364893	−	0.931049i	$-0.618895\pi$
$647$	−18.5630	−0.729787	−0.364893	+	0.931049i	$0.618895\pi$
$648$	9.87614	0.387971
$649$	−1.23927	−0.0486457
$650$	−14.6380	−0.574148
$651$	29.6385	1.16163
$652$	−14.2283	−0.557225
$653$	−39.6487	−1.55157	−0.775787	−	0.630995i	$-0.782647\pi$
$653$	−39.6487	−1.55157	−0.775787	+	0.630995i	$0.782647\pi$
$654$	46.2744	1.80947
$655$	−0.488919	−0.0191036
$656$	52.7714	2.06038
$657$	−47.9844	−1.87205
$658$	−29.8622	−1.16415
$659$	−16.8390	−0.655952	−0.327976	−	0.944686i	$-0.606367\pi$
$659$	−16.8390	−0.655952	−0.327976	+	0.944686i	$0.606367\pi$
$660$	−5.49504	−0.213894
$661$	23.8713	0.928487	0.464244	−	0.885708i	$-0.346326\pi$
$661$	23.8713	0.928487	0.464244	+	0.885708i	$0.346326\pi$
$662$	39.4402	1.53289
$663$	11.2932	0.438591
$664$	−13.0269	−0.505542
$665$	−3.29247	−0.127676
$666$	74.3780	2.88209
$667$	−18.1594	−0.703136
$668$	21.9615	0.849715
$669$	−2.70344	−0.104521
$670$	8.88952	0.343432
$671$	−12.8735	−0.496977
$672$	−3.70557	−0.142945
$673$	22.8435	0.880553	0.440277	−	0.897862i	$-0.354880\pi$
$673$	22.8435	0.880553	0.440277	+	0.897862i	$0.354880\pi$
$674$	−23.9718	−0.923359
$675$	20.3513	0.783323
$676$	−46.8083	−1.80032
$677$	−6.23250	−0.239534	−0.119767	−	0.992802i	$-0.538215\pi$
$677$	−6.23250	−0.239534	−0.119767	+	0.992802i	$0.538215\pi$
$678$	37.7457	1.44961
$679$	14.6202	0.561073
$680$	−8.31028	−0.318685
$681$	29.2461	1.12071
$682$	−17.7131	−0.678269
$683$	18.5112	0.708310	0.354155	−	0.935187i	$-0.384769\pi$
$683$	18.5112	0.708310	0.354155	+	0.935187i	$0.384769\pi$
$684$	83.5004	3.19272
$685$	5.25293	0.200704
$686$	−43.5294	−1.66196
$687$	42.3565	1.61600
$688$	9.63669	0.367395
$689$	2.94638	0.112248
$690$	9.50066	0.361684
$691$	38.8775	1.47897	0.739484	−	0.673174i	$-0.235069\pi$
$691$	38.8775	1.47897	0.739484	+	0.673174i	$0.235069\pi$
$692$	18.3581	0.697872
$693$	−6.84252	−0.259926
$694$	61.3036	2.32705
$695$	−2.24837	−0.0852857
$696$	−89.8047	−3.40404
$697$	38.3151	1.45129
$698$	−36.6630	−1.38772
$699$	38.8665	1.47007
$700$	29.2427	1.10527
$701$	32.9453	1.24433	0.622163	−	0.782888i	$-0.286254\pi$
$701$	32.9453	1.24433	0.622163	+	0.782888i	$0.286254\pi$
$702$	−13.1427	−0.496039
$703$	−29.6648	−1.11883
$704$	−6.86862	−0.258871
$705$	10.8268	0.407759
$706$	72.5031	2.72869
$707$	−17.9271	−0.674218
$708$	13.9284	0.523461
$709$	25.7750	0.968002	0.484001	−	0.875068i	$-0.339183\pi$
$709$	25.7750	0.968002	0.484001	+	0.875068i	$0.339183\pi$
$710$	1.82968	0.0686668
$711$	43.9220	1.64720
$712$	−57.9163	−2.17051
$713$	20.5659	0.770198
$714$	−33.5958	−1.25729
$715$	−0.609189	−0.0227824
$716$	32.4661	1.21332
$717$	−27.1114	−1.01249
$718$	−12.8928	−0.481157
$719$	−26.0581	−0.971803	−0.485901	−	0.874014i	$-0.661509\pi$
$719$	−26.0581	−0.971803	−0.485901	+	0.874014i	$0.661509\pi$
$720$	10.1146	0.376950
$721$	−20.7812	−0.773931
$722$	−2.70860	−0.100804
$723$	45.4840	1.69157
$724$	12.5811	0.467572
$725$	30.1768	1.12074
$726$	6.78255	0.251724
$727$	6.44564	0.239056	0.119528	−	0.992831i	$-0.461862\pi$
$727$	6.44564	0.239056	0.119528	+	0.992831i	$0.461862\pi$
$728$	−9.64774	−0.357569
$729$	−43.9761	−1.62875
$730$	12.7088	0.470374
$731$	6.99679	0.258786
$732$	144.688	5.34781
$733$	36.5095	1.34851	0.674254	−	0.738499i	$-0.264465\pi$
$733$	36.5095	1.34851	0.674254	+	0.738499i	$0.264465\pi$
$734$	26.4228	0.975282
$735$	6.37475	0.235136
$736$	−2.57125	−0.0947777
$737$	−7.36834	−0.271416
$738$	−130.607	−4.80769
$739$	−15.7080	−0.577827	−0.288914	−	0.957355i	$-0.593294\pi$
$739$	−15.7080	−0.577827	−0.288914	+	0.957355i	$0.593294\pi$
$740$	−13.2287	−0.486297
$741$	15.3536	0.564028
$742$	−8.76511	−0.321777
$743$	51.1774	1.87752	0.938759	−	0.344574i	$-0.111977\pi$
$743$	51.1774	1.87752	0.938759	+	0.344574i	$0.111977\pi$
$744$	101.705	3.72870
$745$	3.47400	0.127277
$746$	−67.9279	−2.48702
$747$	11.5119	0.421198
$748$	13.4832	0.492993
$749$	−21.4567	−0.784011
$750$	−32.3685	−1.18193
$751$	30.6238	1.11748	0.558739	−	0.829344i	$-0.311285\pi$
$751$	30.6238	1.11748	0.558739	+	0.829344i	$0.311285\pi$
$752$	−36.5888	−1.33426
$753$	4.19313	0.152806
$754$	−19.4879	−0.709707
$755$	−3.71197	−0.135092
$756$	26.2556	0.954906
$757$	13.6414	0.495806	0.247903	−	0.968785i	$-0.420259\pi$
$757$	13.6414	0.495806	0.247903	+	0.968785i	$0.420259\pi$
$758$	−10.0473	−0.364934
$759$	−7.87491	−0.285841
$760$	−11.2982	−0.409828
$761$	46.6971	1.69277	0.846383	−	0.532574i	$-0.178775\pi$
$761$	46.6971	1.69277	0.846383	+	0.532574i	$0.178775\pi$
$762$	69.0599	2.50177
$763$	−10.2485	−0.371020
$764$	−6.02831	−0.218097
$765$	7.34380	0.265516
$766$	−44.1331	−1.59459
$767$	1.54412	0.0557551
$768$	89.3718	3.22493
$769$	−29.0746	−1.04846	−0.524228	−	0.851578i	$-0.675646\pi$
$769$	−29.0746	−1.04846	−0.524228	+	0.851578i	$0.675646\pi$
$770$	1.81226	0.0653092
$771$	−31.0408	−1.11791
$772$	1.65936	0.0597216
$773$	0.809926	0.0291310	0.0145655	−	0.999894i	$-0.495363\pi$
$773$	0.809926	0.0291310	0.0145655	+	0.999894i	$0.495363\pi$
$774$	−23.8503	−0.857282
$775$	−34.1757	−1.22763
$776$	50.1697	1.80099
$777$	−27.3214	−0.980149
$778$	53.8118	1.92925
$779$	52.0910	1.86635
$780$	6.84677	0.245154
$781$	−1.51659	−0.0542678
$782$	−23.3118	−0.833627
$783$	27.0942	0.968269
$784$	−21.5434	−0.769406
$785$	1.75730	0.0627207
$786$	−6.78255	−0.241926
$787$	−19.7607	−0.704394	−0.352197	−	0.935926i	$-0.614565\pi$
$787$	−19.7607	−0.704394	−0.352197	+	0.935926i	$0.614565\pi$
$788$	31.1196	1.10859
$789$	−46.7758	−1.66526
$790$	−11.6329	−0.413878
$791$	−8.35961	−0.297234
$792$	−23.4803	−0.834335
$793$	16.0403	0.569608
$794$	−91.3839	−3.24309
$795$	3.17785	0.112707
$796$	71.5976	2.53771
$797$	−48.4763	−1.71712	−0.858559	−	0.512714i	$-0.828640\pi$
$797$	−48.4763	−1.71712	−0.858559	+	0.512714i	$0.828640\pi$
$798$	−45.6749	−1.61687
$799$	−26.5656	−0.939823
$800$	4.27283	0.151067
$801$	51.1807	1.80838
$802$	−86.6886	−3.06108
$803$	−10.5341	−0.371739
$804$	82.8140	2.92062
$805$	−2.10413	−0.0741608
$806$	22.0703	0.777395
$807$	−61.1648	−2.15310
$808$	−61.5173	−2.16417
$809$	−44.4489	−1.56274	−0.781371	−	0.624067i	$-0.785479\pi$
$809$	−44.4489	−1.56274	−0.781371	+	0.624067i	$0.785479\pi$
$810$	2.31151	0.0812183
$811$	−39.0194	−1.37016	−0.685078	−	0.728470i	$-0.740232\pi$
$811$	−39.0194	−1.37016	−0.685078	+	0.728470i	$0.740232\pi$
$812$	38.9316	1.36623
$813$	−48.9363	−1.71627
$814$	16.3283	0.572306
$815$	−1.70130	−0.0595938
$816$	−41.1634	−1.44101
$817$	9.51244	0.332798
$818$	22.6851	0.793165
$819$	8.52571	0.297913
$820$	23.2294	0.811207
$821$	−17.3054	−0.603964	−0.301982	−	0.953314i	$-0.597648\pi$
$821$	−17.3054	−0.603964	−0.301982	+	0.953314i	$0.597648\pi$
$822$	72.8714	2.54168
$823$	37.3009	1.30023	0.650113	−	0.759837i	$-0.274721\pi$
$823$	37.3009	1.30023	0.650113	+	0.759837i	$0.274721\pi$
$824$	−71.3111	−2.48424
$825$	13.0863	0.455606
$826$	−4.59357	−0.159831
$827$	39.8320	1.38509	0.692547	−	0.721372i	$-0.256488\pi$
$827$	39.8320	1.38509	0.692547	+	0.721372i	$0.256488\pi$
$828$	53.3629	1.85449
$829$	−34.1408	−1.18576	−0.592879	−	0.805292i	$-0.702009\pi$
$829$	−34.1408	−1.18576	−0.592879	+	0.805292i	$0.702009\pi$
$830$	−3.04895	−0.105831
$831$	−47.3824	−1.64368
$832$	8.55824	0.296704
$833$	−15.6417	−0.541953
$834$	−31.1907	−1.08004
$835$	2.62595	0.0908748
$836$	18.3309	0.633989
$837$	−30.6847	−1.06062
$838$	26.2922	0.908250
$839$	43.6686	1.50761	0.753803	−	0.657100i	$-0.228217\pi$
$839$	43.6686	1.50761	0.753803	+	0.657100i	$0.228217\pi$
$840$	−10.4057	−0.359029
$841$	11.1751	0.385348
$842$	67.2356	2.31709
$843$	−28.7035	−0.988599
$844$	89.3679	3.07617
$845$	−5.59690	−0.192539
$846$	90.5555	3.11336
$847$	−1.50214	−0.0516143
$848$	−10.7395	−0.368795
$849$	−62.0088	−2.12814
$850$	38.7387	1.32873
$851$	−18.9580	−0.649873
$852$	17.0452	0.583958
$853$	36.9031	1.26354	0.631768	−	0.775157i	$-0.282329\pi$
$853$	36.9031	1.26354	0.631768	+	0.775157i	$0.282329\pi$
$854$	−47.7178	−1.63287
$855$	9.98422	0.341453
$856$	−73.6292	−2.51659
$857$	3.71838	0.127018	0.0635088	−	0.997981i	$-0.479771\pi$
$857$	3.71838	0.127018	0.0635088	+	0.997981i	$0.479771\pi$
$858$	−8.45100	−0.288512
$859$	−12.1079	−0.413116	−0.206558	−	0.978434i	$-0.566226\pi$
$859$	−12.1079	−0.413116	−0.206558	+	0.978434i	$0.566226\pi$
$860$	4.24197	0.144650
$861$	47.9759	1.63502
$862$	−48.0526	−1.63668
$863$	3.96462	0.134957	0.0674786	−	0.997721i	$-0.478505\pi$
$863$	3.96462	0.134957	0.0674786	+	0.997721i	$0.478505\pi$
$864$	3.83636	0.130516
$865$	2.19510	0.0746356
$866$	−72.4207	−2.46096
$867$	16.8404	0.571929
$868$	−44.0906	−1.49653
$869$	9.64225	0.327091
$870$	−21.0188	−0.712605
$871$	9.18089	0.311083
$872$	−35.1679	−1.19094
$873$	−44.3350	−1.50051
$874$	−31.6933	−1.07204
$875$	7.16871	0.242347
$876$	118.394	4.00016
$877$	−21.5297	−0.727005	−0.363503	−	0.931593i	$-0.618419\pi$
$877$	−21.5297	−0.727005	−0.363503	+	0.931593i	$0.618419\pi$
$878$	−68.1734	−2.30074
$879$	34.9425	1.17858
$880$	2.22048	0.0748522
$881$	−15.6698	−0.527929	−0.263964	−	0.964532i	$-0.585030\pi$
$881$	−15.6698	−0.527929	−0.263964	+	0.964532i	$0.585030\pi$
$882$	53.3187	1.79533
$883$	22.7698	0.766264	0.383132	−	0.923694i	$-0.374845\pi$
$883$	22.7698	0.766264	0.383132	+	0.923694i	$0.374845\pi$
$884$	−16.7999	−0.565042
$885$	1.66543	0.0559828
$886$	−46.2770	−1.55470
$887$	33.1878	1.11434	0.557169	−	0.830399i	$-0.311887\pi$
$887$	33.1878	1.11434	0.557169	+	0.830399i	$0.311887\pi$
$888$	−93.7540	−3.14618
$889$	−15.2948	−0.512972
$890$	−13.5553	−0.454376
$891$	−1.91597	−0.0641874
$892$	4.02167	0.134656
$893$	−36.1171	−1.20861
$894$	48.1932	1.61182
$895$	3.88200	0.129761
$896$	−28.1559	−0.940623
$897$	9.81207	0.327616
$898$	38.1308	1.27244
$899$	−45.4990	−1.51748
$900$	−88.6768	−2.95589
$901$	−7.79748	−0.259772
$902$	−28.6722	−0.954680
$903$	8.76098	0.291547
$904$	−28.6862	−0.954089
$905$	1.50433	0.0500056
$906$	−51.4944	−1.71079
$907$	−0.864791	−0.0287149	−0.0143575	−	0.999897i	$-0.504570\pi$
$907$	−0.864791	−0.0287149	−0.0143575	+	0.999897i	$0.504570\pi$
$908$	−43.5068	−1.44383
$909$	54.3629	1.80310
$910$	−2.25806	−0.0748539
$911$	2.74554	0.0909638	0.0454819	−	0.998965i	$-0.485518\pi$
$911$	2.74554	0.0909638	0.0454819	+	0.998965i	$0.485518\pi$
$912$	−55.9634	−1.85313
$913$	2.52721	0.0836386
$914$	−53.5604	−1.77162
$915$	17.3004	0.571934
$916$	−63.0100	−2.08191
$917$	1.50214	0.0496052
$918$	34.7816	1.14796
$919$	−25.2495	−0.832904	−0.416452	−	0.909158i	$-0.636727\pi$
$919$	−25.2495	−0.832904	−0.416452	+	0.909158i	$0.636727\pi$
$920$	−7.22037	−0.238049
$921$	56.2322	1.85291
$922$	−93.3486	−3.07427
$923$	1.88966	0.0621988
$924$	16.8828	0.555404
$925$	31.5038	1.03584
$926$	−64.2966	−2.11292
$927$	63.0177	2.06977
$928$	5.68852	0.186735
$929$	−47.4664	−1.55732	−0.778662	−	0.627444i	$-0.784101\pi$
$929$	−47.4664	−1.55732	−0.778662	+	0.627444i	$0.784101\pi$
$930$	23.8042	0.780570
$931$	−21.2656	−0.696952
$932$	−57.8183	−1.89390
$933$	23.7922	0.778922
$934$	−18.3096	−0.599108
$935$	1.61219	0.0527243
$936$	29.2562	0.956269
$937$	−21.7755	−0.711376	−0.355688	−	0.934605i	$-0.615753\pi$
$937$	−21.7755	−0.711376	−0.355688	+	0.934605i	$0.615753\pi$
$938$	−27.3120	−0.891767
$939$	−59.6856	−1.94777
$940$	−16.1060	−0.525320
$941$	−1.21472	−0.0395989	−0.0197994	−	0.999804i	$-0.506303\pi$
$941$	−1.21472	−0.0395989	−0.0197994	+	0.999804i	$0.506303\pi$
$942$	24.3782	0.794286
$943$	33.2900	1.08407
$944$	−5.62829	−0.183185
$945$	3.13940	0.102125
$946$	−5.23588	−0.170233
$947$	43.9518	1.42824	0.714120	−	0.700023i	$-0.246827\pi$
$947$	43.9518	1.42824	0.714120	+	0.700023i	$0.246827\pi$
$948$	−108.371	−3.51972
$949$	13.1254	0.426067
$950$	52.6670	1.70874
$951$	−33.3384	−1.08107
$952$	25.5323	0.827508
$953$	10.6166	0.343905	0.171952	−	0.985105i	$-0.444993\pi$
$953$	10.6166	0.343905	0.171952	+	0.985105i	$0.444993\pi$
$954$	26.5797	0.860548
$955$	−0.720811	−0.0233249
$956$	40.3312	1.30441
$957$	17.4221	0.563176
$958$	8.25095	0.266576
$959$	−16.1390	−0.521155
$960$	9.23057	0.297915
$961$	20.5283	0.662205
$962$	−20.3449	−0.655945
$963$	65.0662	2.09673
$964$	−67.6625	−2.17926
$965$	0.198411	0.00638707
$966$	−29.1896	−0.939161
$967$	5.16864	0.166212	0.0831062	−	0.996541i	$-0.473516\pi$
$967$	5.16864	0.166212	0.0831062	+	0.996541i	$0.473516\pi$
$968$	−5.15465	−0.165677
$969$	−40.6326	−1.30531
$970$	11.7422	0.377020
$971$	−25.1205	−0.806154	−0.403077	−	0.915166i	$-0.632059\pi$
$971$	−25.1205	−0.806154	−0.403077	+	0.915166i	$0.632059\pi$
$972$	73.9701	2.37259
$973$	6.90786	0.221456
$974$	−38.6757	−1.23925
$975$	−16.3054	−0.522191
$976$	−58.4665	−1.87147
$977$	50.1391	1.60409	0.802047	−	0.597261i	$-0.203744\pi$
$977$	50.1391	1.60409	0.802047	+	0.597261i	$0.203744\pi$
$978$	−23.6013	−0.754687
$979$	11.2358	0.359096
$980$	−9.48316	−0.302928
$981$	31.0779	0.992241
$982$	84.4366	2.69448
$983$	−14.4041	−0.459420	−0.229710	−	0.973259i	$-0.573778\pi$
$983$	−14.4041	−0.459420	−0.229710	+	0.973259i	$0.573778\pi$
$984$	164.631	5.24823
$985$	3.72100	0.118561
$986$	51.5738	1.64245
$987$	−33.2639	−1.05880
$988$	−22.8402	−0.726643
$989$	6.07915	0.193306
$990$	−5.49556	−0.174660
$991$	−45.2017	−1.43588	−0.717940	−	0.696105i	$-0.754915\pi$
$991$	−45.2017	−1.43588	−0.717940	+	0.696105i	$0.754915\pi$
$992$	−6.44235	−0.204545
$993$	43.9329	1.39417
$994$	−5.62148	−0.178303
$995$	8.56098	0.271401
$996$	−28.4038	−0.900007
$997$	−15.4851	−0.490417	−0.245208	−	0.969470i	$-0.578856\pi$
$997$	−15.4851	−0.490417	−0.245208	+	0.969470i	$0.578856\pi$
$998$	91.6464	2.90102
$999$	28.2857	0.894921

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.2.a.e.1.1	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.2.a.e.1.1	✓	28	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:	\( N \)	\(=\)	\( 1441 = 11 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1441.a (trivial)

\(f(q)\)	\(=\)	\(q-2.46758 q^{2} -2.74867 q^{3} +4.08895 q^{4} +0.488919 q^{5} +6.78255 q^{6} -1.50214 q^{7} -5.15465 q^{8} +4.55516 q^{9} +O(q^{10})\)	\(q-2.46758 q^{2} -2.74867 q^{3} +4.08895 q^{4} +0.488919 q^{5} +6.78255 q^{6} -1.50214 q^{7} -5.15465 q^{8} +4.55516 q^{9} -1.20645 q^{10} +1.00000 q^{11} -11.2392 q^{12} -1.24599 q^{13} +3.70666 q^{14} -1.34388 q^{15} +4.54160 q^{16} +3.29746 q^{17} -11.2402 q^{18} +4.48304 q^{19} +1.99916 q^{20} +4.12889 q^{21} -2.46758 q^{22} +2.86500 q^{23} +14.1684 q^{24} -4.76096 q^{25} +3.07458 q^{26} -4.27463 q^{27} -6.14219 q^{28} -6.33838 q^{29} +3.31612 q^{30} +7.17832 q^{31} -0.897472 q^{32} -2.74867 q^{33} -8.13675 q^{34} -0.734427 q^{35} +18.6258 q^{36} -6.61712 q^{37} -11.0623 q^{38} +3.42481 q^{39} -2.52020 q^{40} +11.6196 q^{41} -10.1884 q^{42} +2.12187 q^{43} +4.08895 q^{44} +2.22711 q^{45} -7.06960 q^{46} -8.05637 q^{47} -12.4833 q^{48} -4.74356 q^{49} +11.7480 q^{50} -9.06362 q^{51} -5.09479 q^{52} -2.36469 q^{53} +10.5480 q^{54} +0.488919 q^{55} +7.74302 q^{56} -12.3224 q^{57} +15.6405 q^{58} -1.23927 q^{59} -5.49504 q^{60} -12.8735 q^{61} -17.7131 q^{62} -6.84252 q^{63} -6.86862 q^{64} -0.609189 q^{65} +6.78255 q^{66} -7.36834 q^{67} +13.4832 q^{68} -7.87491 q^{69} +1.81226 q^{70} -1.51659 q^{71} -23.4803 q^{72} -10.5341 q^{73} +16.3283 q^{74} +13.0863 q^{75} +18.3309 q^{76} -1.50214 q^{77} -8.45100 q^{78} +9.64225 q^{79} +2.22048 q^{80} -1.91597 q^{81} -28.6722 q^{82} +2.52721 q^{83} +16.8828 q^{84} +1.61219 q^{85} -5.23588 q^{86} +17.4221 q^{87} -5.15465 q^{88} +11.2358 q^{89} -5.49556 q^{90} +1.87166 q^{91} +11.7148 q^{92} -19.7308 q^{93} +19.8797 q^{94} +2.19185 q^{95} +2.46685 q^{96} -9.73290 q^{97} +11.7051 q^{98} +4.55516 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 7 q^{2} - 2 q^{3} + 27 q^{4} + 3 q^{5} - q^{6} + 7 q^{7} + 21 q^{8} + 28 q^{9}+O(q^{10}) \) 28 * q + 7 * q^2 - 2 * q^3 + 27 * q^4 + 3 * q^5 - q^6 + 7 * q^7 + 21 * q^8 + 28 * q^9	\( 28 q + 7 q^{2} - 2 q^{3} + 27 q^{4} + 3 q^{5} - q^{6} + 7 q^{7} + 21 q^{8} + 28 q^{9} + 14 q^{10} + 28 q^{11} - 6 q^{12} + 3 q^{13} - q^{14} + 19 q^{15} + 29 q^{16} + 9 q^{17} - 2 q^{18} + 20 q^{19} + 6 q^{20} + 6 q^{21} + 7 q^{22} + 24 q^{23} + 20 q^{24} + 23 q^{25} + 10 q^{26} - 20 q^{27} - 3 q^{28} + 43 q^{29} + 11 q^{30} + 3 q^{31} + 44 q^{32} - 2 q^{33} - 28 q^{34} + 32 q^{35} + 24 q^{36} - 4 q^{37} + 24 q^{38} + 37 q^{39} + 22 q^{40} + 32 q^{41} - 27 q^{42} + 25 q^{43} + 27 q^{44} - 36 q^{45} + 10 q^{46} + 19 q^{47} + 42 q^{48} + 17 q^{49} + q^{50} + 39 q^{51} - 19 q^{52} + 5 q^{53} + 6 q^{54} + 3 q^{55} + 8 q^{56} + 2 q^{57} + 21 q^{58} + 44 q^{59} + 65 q^{60} + 28 q^{61} + 60 q^{62} - 8 q^{63} + 5 q^{64} + 33 q^{65} - q^{66} + 7 q^{67} + 13 q^{68} - 22 q^{69} + 9 q^{70} + 117 q^{71} - 17 q^{72} + 7 q^{73} + 41 q^{74} - 40 q^{75} + 34 q^{76} + 7 q^{77} - 97 q^{78} + 48 q^{79} + 41 q^{80} + 40 q^{81} + 2 q^{82} + 22 q^{83} + 27 q^{84} + 30 q^{85} + 24 q^{86} + 37 q^{87} + 21 q^{88} - 6 q^{89} + 4 q^{90} - 33 q^{91} + 18 q^{92} + 5 q^{93} - 43 q^{94} + 64 q^{95} + 55 q^{96} - 50 q^{97} + 97 q^{98} + 28 q^{99}+O(q^{100}) \) 28 * q + 7 * q^2 - 2 * q^3 + 27 * q^4 + 3 * q^5 - q^6 + 7 * q^7 + 21 * q^8 + 28 * q^9 + 14 * q^10 + 28 * q^11 - 6 * q^12 + 3 * q^13 - q^14 + 19 * q^15 + 29 * q^16 + 9 * q^17 - 2 * q^18 + 20 * q^19 + 6 * q^20 + 6 * q^21 + 7 * q^22 + 24 * q^23 + 20 * q^24 + 23 * q^25 + 10 * q^26 - 20 * q^27 - 3 * q^28 + 43 * q^29 + 11 * q^30 + 3 * q^31 + 44 * q^32 - 2 * q^33 - 28 * q^34 + 32 * q^35 + 24 * q^36 - 4 * q^37 + 24 * q^38 + 37 * q^39 + 22 * q^40 + 32 * q^41 - 27 * q^42 + 25 * q^43 + 27 * q^44 - 36 * q^45 + 10 * q^46 + 19 * q^47 + 42 * q^48 + 17 * q^49 + q^50 + 39 * q^51 - 19 * q^52 + 5 * q^53 + 6 * q^54 + 3 * q^55 + 8 * q^56 + 2 * q^57 + 21 * q^58 + 44 * q^59 + 65 * q^60 + 28 * q^61 + 60 * q^62 - 8 * q^63 + 5 * q^64 + 33 * q^65 - q^66 + 7 * q^67 + 13 * q^68 - 22 * q^69 + 9 * q^70 + 117 * q^71 - 17 * q^72 + 7 * q^73 + 41 * q^74 - 40 * q^75 + 34 * q^76 + 7 * q^77 - 97 * q^78 + 48 * q^79 + 41 * q^80 + 40 * q^81 + 2 * q^82 + 22 * q^83 + 27 * q^84 + 30 * q^85 + 24 * q^86 + 37 * q^87 + 21 * q^88 - 6 * q^89 + 4 * q^90 - 33 * q^91 + 18 * q^92 + 5 * q^93 - 43 * q^94 + 64 * q^95 + 55 * q^96 - 50 * q^97 + 97 * q^98 + 28 * q^99

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