LMFDB - Embedded newform 4015.2.a.c.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4015,2,Mod(1,4015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4015, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4015 = 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4015.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:	$32.0599364115$
Analytic rank:	$1$
Dimension:	$23$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	4015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.83759 q^{2} -0.530531 q^{3} +1.37674 q^{4} +1.00000 q^{5} -0.974898 q^{6} +1.03293 q^{7} -1.14530 q^{8} -2.71854 q^{9} +O(q^{10})$	\(q+1.83759 q^{2} -0.530531 q^{3} +1.37674 q^{4} +1.00000 q^{5} -0.974898 q^{6} +1.03293 q^{7} -1.14530 q^{8} -2.71854 q^{9} +1.83759 q^{10} -1.00000 q^{11} -0.730401 q^{12} +5.54756 q^{13} +1.89811 q^{14} -0.530531 q^{15} -4.85807 q^{16} -7.15200 q^{17} -4.99556 q^{18} -0.476759 q^{19} +1.37674 q^{20} -0.548003 q^{21} -1.83759 q^{22} -4.68524 q^{23} +0.607619 q^{24} +1.00000 q^{25} +10.1941 q^{26} +3.03386 q^{27} +1.42208 q^{28} +0.674083 q^{29} -0.974898 q^{30} -1.92416 q^{31} -6.63653 q^{32} +0.530531 q^{33} -13.1424 q^{34} +1.03293 q^{35} -3.74271 q^{36} -2.63992 q^{37} -0.876087 q^{38} -2.94315 q^{39} -1.14530 q^{40} -5.27325 q^{41} -1.00700 q^{42} -12.5433 q^{43} -1.37674 q^{44} -2.71854 q^{45} -8.60956 q^{46} +7.35999 q^{47} +2.57736 q^{48} -5.93305 q^{49} +1.83759 q^{50} +3.79435 q^{51} +7.63752 q^{52} +3.46525 q^{53} +5.57499 q^{54} -1.00000 q^{55} -1.18302 q^{56} +0.252935 q^{57} +1.23869 q^{58} +8.05647 q^{59} -0.730401 q^{60} +4.27031 q^{61} -3.53581 q^{62} -2.80807 q^{63} -2.47908 q^{64} +5.54756 q^{65} +0.974898 q^{66} -7.45604 q^{67} -9.84641 q^{68} +2.48567 q^{69} +1.89811 q^{70} -10.0132 q^{71} +3.11355 q^{72} +1.00000 q^{73} -4.85108 q^{74} -0.530531 q^{75} -0.656371 q^{76} -1.03293 q^{77} -5.40831 q^{78} -6.03559 q^{79} -4.85807 q^{80} +6.54605 q^{81} -9.69006 q^{82} +15.4481 q^{83} -0.754455 q^{84} -7.15200 q^{85} -23.0495 q^{86} -0.357622 q^{87} +1.14530 q^{88} -2.20736 q^{89} -4.99556 q^{90} +5.73026 q^{91} -6.45034 q^{92} +1.02083 q^{93} +13.5246 q^{94} -0.476759 q^{95} +3.52088 q^{96} -6.83368 q^{97} -10.9025 q^{98} +2.71854 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 23 q - 3 q^{2} - 5 q^{3} + 15 q^{4} + 23 q^{5} - 5 q^{6} - 6 q^{8} + 8 q^{9}+O(q^{10}) $ 23 * q - 3 * q^2 - 5 * q^3 + 15 * q^4 + 23 * q^5 - 5 * q^6 - 6 * q^8 + 8 * q^9	\( 23 q - 3 q^{2} - 5 q^{3} + 15 q^{4} + 23 q^{5} - 5 q^{6} - 6 q^{8} + 8 q^{9} - 3 q^{10} - 23 q^{11} - 18 q^{12} - 5 q^{13} - 17 q^{14} - 5 q^{15} - q^{16} - 36 q^{17} + q^{18} + 6 q^{19} + 15 q^{20} - 18 q^{21} + 3 q^{22} - 14 q^{23} - 7 q^{24} + 23 q^{25} - 21 q^{26} - 29 q^{27} + 28 q^{28} - 36 q^{29} - 5 q^{30} - 16 q^{31} - 5 q^{32} + 5 q^{33} - 28 q^{34} - 14 q^{36} - 24 q^{37} + q^{38} - 10 q^{39} - 6 q^{40} - 36 q^{41} - 5 q^{42} + 17 q^{43} - 15 q^{44} + 8 q^{45} - 25 q^{46} - 21 q^{47} - 17 q^{48} - 27 q^{49} - 3 q^{50} + 19 q^{51} - 21 q^{52} - 28 q^{53} - 15 q^{54} - 23 q^{55} - 46 q^{56} - 23 q^{57} - 16 q^{58} - 61 q^{59} - 18 q^{60} - 17 q^{61} - 22 q^{62} - 9 q^{63} - 18 q^{64} - 5 q^{65} + 5 q^{66} + 2 q^{67} - 39 q^{68} - 36 q^{69} - 17 q^{70} - 50 q^{71} + 15 q^{72} + 23 q^{73} + 17 q^{74} - 5 q^{75} - 21 q^{76} + 49 q^{78} - 18 q^{79} - q^{80} - 57 q^{81} + 14 q^{82} - 20 q^{83} - 38 q^{84} - 36 q^{85} - 45 q^{86} + 37 q^{87} + 6 q^{88} - 93 q^{89} + q^{90} - 42 q^{91} - 39 q^{92} - 18 q^{93} - 6 q^{94} + 6 q^{95} - 9 q^{96} - 31 q^{97} - 31 q^{98} - 8 q^{99}+O(q^{100}) \) 23 * q - 3 * q^2 - 5 * q^3 + 15 * q^4 + 23 * q^5 - 5 * q^6 - 6 * q^8 + 8 * q^9 - 3 * q^10 - 23 * q^11 - 18 * q^12 - 5 * q^13 - 17 * q^14 - 5 * q^15 - q^16 - 36 * q^17 + q^18 + 6 * q^19 + 15 * q^20 - 18 * q^21 + 3 * q^22 - 14 * q^23 - 7 * q^24 + 23 * q^25 - 21 * q^26 - 29 * q^27 + 28 * q^28 - 36 * q^29 - 5 * q^30 - 16 * q^31 - 5 * q^32 + 5 * q^33 - 28 * q^34 - 14 * q^36 - 24 * q^37 + q^38 - 10 * q^39 - 6 * q^40 - 36 * q^41 - 5 * q^42 + 17 * q^43 - 15 * q^44 + 8 * q^45 - 25 * q^46 - 21 * q^47 - 17 * q^48 - 27 * q^49 - 3 * q^50 + 19 * q^51 - 21 * q^52 - 28 * q^53 - 15 * q^54 - 23 * q^55 - 46 * q^56 - 23 * q^57 - 16 * q^58 - 61 * q^59 - 18 * q^60 - 17 * q^61 - 22 * q^62 - 9 * q^63 - 18 * q^64 - 5 * q^65 + 5 * q^66 + 2 * q^67 - 39 * q^68 - 36 * q^69 - 17 * q^70 - 50 * q^71 + 15 * q^72 + 23 * q^73 + 17 * q^74 - 5 * q^75 - 21 * q^76 + 49 * q^78 - 18 * q^79 - q^80 - 57 * q^81 + 14 * q^82 - 20 * q^83 - 38 * q^84 - 36 * q^85 - 45 * q^86 + 37 * q^87 + 6 * q^88 - 93 * q^89 + q^90 - 42 * q^91 - 39 * q^92 - 18 * q^93 - 6 * q^94 + 6 * q^95 - 9 * q^96 - 31 * q^97 - 31 * q^98 - 8 * 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 $

$2$	1.83759	1.29937	0.649686	−	0.760203i	$-0.274900\pi$
$2$	1.83759	1.29937	0.649686	+	0.760203i	$0.274900\pi$
$3$	−0.530531	−0.306302	−0.153151	−	0.988203i	$-0.548942\pi$
$3$	−0.530531	−0.306302	−0.153151	+	0.988203i	$0.548942\pi$
$4$	1.37674	0.688368
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.974898	−0.398000
$7$	1.03293	0.390412	0.195206	−	0.980762i	$-0.437462\pi$
$7$	1.03293	0.390412	0.195206	+	0.980762i	$0.437462\pi$
$8$	−1.14530	−0.404926
$9$	−2.71854	−0.906179
$10$	1.83759	0.581097
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−0.730401	−0.210849
$13$	5.54756	1.53862	0.769308	−	0.638878i	$-0.220601\pi$
$13$	5.54756	1.53862	0.769308	+	0.638878i	$0.220601\pi$
$14$	1.89811	0.507291
$15$	−0.530531	−0.136982
$16$	−4.85807	−1.21452
$17$	−7.15200	−1.73461	−0.867307	−	0.497774i	$-0.834151\pi$
$17$	−7.15200	−1.73461	−0.867307	+	0.497774i	$0.834151\pi$
$18$	−4.99556	−1.17746
$19$	−0.476759	−0.109376	−0.0546880	−	0.998503i	$-0.517416\pi$
$19$	−0.476759	−0.109376	−0.0546880	+	0.998503i	$0.517416\pi$
$20$	1.37674	0.307847
$21$	−0.548003	−0.119584
$22$	−1.83759	−0.391775
$23$	−4.68524	−0.976941	−0.488470	−	0.872580i	$-0.662445\pi$
$23$	−4.68524	−0.976941	−0.488470	+	0.872580i	$0.662445\pi$
$24$	0.607619	0.124030
$25$	1.00000	0.200000
$26$	10.1941	1.99924
$27$	3.03386	0.583867
$28$	1.42208	0.268747
$29$	0.674083	0.125174	0.0625870	−	0.998040i	$-0.480065\pi$
$29$	0.674083	0.125174	0.0625870	+	0.998040i	$0.480065\pi$
$30$	−0.974898	−0.177991
$31$	−1.92416	−0.345589	−0.172794	−	0.984958i	$-0.555280\pi$
$31$	−1.92416	−0.345589	−0.172794	+	0.984958i	$0.555280\pi$
$32$	−6.63653	−1.17318
$33$	0.530531	0.0923536
$34$	−13.1424	−2.25391
$35$	1.03293	0.174598
$36$	−3.74271	−0.623784
$37$	−2.63992	−0.434000	−0.217000	−	0.976172i	$-0.569627\pi$
$37$	−2.63992	−0.434000	−0.217000	+	0.976172i	$0.569627\pi$
$38$	−0.876087	−0.142120
$39$	−2.94315	−0.471282
$40$	−1.14530	−0.181089
$41$	−5.27325	−0.823543	−0.411771	−	0.911287i	$-0.635090\pi$
$41$	−5.27325	−0.823543	−0.411771	+	0.911287i	$0.635090\pi$
$42$	−1.00700	−0.155384
$43$	−12.5433	−1.91284	−0.956421	−	0.291992i	$-0.905682\pi$
$43$	−12.5433	−1.91284	−0.956421	+	0.291992i	$0.905682\pi$
$44$	−1.37674	−0.207551
$45$	−2.71854	−0.405256
$46$	−8.60956	−1.26941
$47$	7.35999	1.07356	0.536782	−	0.843721i	$-0.319640\pi$
$47$	7.35999	1.07356	0.536782	+	0.843721i	$0.319640\pi$
$48$	2.57736	0.372009
$49$	−5.93305	−0.847578
$50$	1.83759	0.259874
$51$	3.79435	0.531316
$52$	7.63752	1.05913
$53$	3.46525	0.475988	0.237994	−	0.971267i	$-0.423510\pi$
$53$	3.46525	0.475988	0.237994	+	0.971267i	$0.423510\pi$
$54$	5.57499	0.758660
$55$	−1.00000	−0.134840
$56$	−1.18302	−0.158088
$57$	0.252935	0.0335021
$58$	1.23869	0.162648
$59$	8.05647	1.04886	0.524432	−	0.851453i	$-0.324278\pi$
$59$	8.05647	1.04886	0.524432	+	0.851453i	$0.324278\pi$
$60$	−0.730401	−0.0942943
$61$	4.27031	0.546757	0.273379	−	0.961907i	$-0.411859\pi$
$61$	4.27031	0.546757	0.273379	+	0.961907i	$0.411859\pi$
$62$	−3.53581	−0.449049
$63$	−2.80807	−0.353783
$64$	−2.47908	−0.309885
$65$	5.54756	0.688090
$66$	0.974898	0.120002
$67$	−7.45604	−0.910900	−0.455450	−	0.890261i	$-0.650522\pi$
$67$	−7.45604	−0.910900	−0.455450	+	0.890261i	$0.650522\pi$
$68$	−9.84641	−1.19405
$69$	2.48567	0.299239
$70$	1.89811	0.226867
$71$	−10.0132	−1.18834	−0.594171	−	0.804338i	$-0.702520\pi$
$71$	−10.0132	−1.18834	−0.594171	+	0.804338i	$0.702520\pi$
$72$	3.11355	0.366936
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	−4.85108	−0.563927
$75$	−0.530531	−0.0612604
$76$	−0.656371	−0.0752909
$77$	−1.03293	−0.117714
$78$	−5.40831	−0.612370
$79$	−6.03559	−0.679056	−0.339528	−	0.940596i	$-0.610267\pi$
$79$	−6.03559	−0.679056	−0.339528	+	0.940596i	$0.610267\pi$
$80$	−4.85807	−0.543149
$81$	6.54605	0.727339
$82$	−9.69006	−1.07009
$83$	15.4481	1.69565	0.847825	−	0.530275i	$-0.177911\pi$
$83$	15.4481	1.69565	0.847825	+	0.530275i	$0.177911\pi$
$84$	−0.754455	−0.0823178
$85$	−7.15200	−0.775743
$86$	−23.0495	−2.48549
$87$	−0.357622	−0.0383411
$88$	1.14530	0.122090
$89$	−2.20736	−0.233980	−0.116990	−	0.993133i	$-0.537325\pi$
$89$	−2.20736	−0.233980	−0.116990	+	0.993133i	$0.537325\pi$
$90$	−4.99556	−0.526578
$91$	5.73026	0.600695
$92$	−6.45034	−0.672495
$93$	1.02083	0.105855
$94$	13.5246	1.39496
$95$	−0.476759	−0.0489144
$96$	3.52088	0.359349
$97$	−6.83368	−0.693855	−0.346927	−	0.937892i	$-0.612775\pi$
$97$	−6.83368	−0.693855	−0.346927	+	0.937892i	$0.612775\pi$
$98$	−10.9025	−1.10132
$99$	2.71854	0.273223
$100$	1.37674	0.137674
$101$	−9.28215	−0.923608	−0.461804	−	0.886982i	$-0.652798\pi$
$101$	−9.28215	−0.923608	−0.461804	+	0.886982i	$0.652798\pi$
$102$	6.97247	0.690377
$103$	−13.2696	−1.30750	−0.653748	−	0.756713i	$-0.726804\pi$
$103$	−13.2696	−1.30750	−0.653748	+	0.756713i	$0.726804\pi$
$104$	−6.35365	−0.623026
$105$	−0.548003	−0.0534796
$106$	6.36770	0.618486
$107$	−5.73323	−0.554252	−0.277126	−	0.960834i	$-0.589382\pi$
$107$	−5.73323	−0.554252	−0.277126	+	0.960834i	$0.589382\pi$
$108$	4.17682	0.401915
$109$	−17.2084	−1.64826	−0.824132	−	0.566398i	$-0.808337\pi$
$109$	−17.2084	−1.64826	−0.824132	+	0.566398i	$0.808337\pi$
$110$	−1.83759	−0.175207
$111$	1.40056	0.132935
$112$	−5.01806	−0.474162
$113$	−10.8635	−1.02195	−0.510976	−	0.859595i	$-0.670716\pi$
$113$	−10.8635	−1.02195	−0.510976	+	0.859595i	$0.670716\pi$
$114$	0.464791	0.0435317
$115$	−4.68524	−0.436901
$116$	0.928033	0.0861657
$117$	−15.0813	−1.39426
$118$	14.8045	1.36286
$119$	−7.38754	−0.677214
$120$	0.607619	0.0554678
$121$	1.00000	0.0909091
$122$	7.84708	0.710441
$123$	2.79762	0.252253
$124$	−2.64906	−0.237892
$125$	1.00000	0.0894427
$126$	−5.16008	−0.459696
$127$	20.9188	1.85625	0.928123	−	0.372275i	$-0.121422\pi$
$127$	20.9188	1.85625	0.928123	+	0.372275i	$0.121422\pi$
$128$	8.71753	0.770528
$129$	6.65463	0.585908
$130$	10.1941	0.894085
$131$	12.2643	1.07154	0.535768	−	0.844365i	$-0.320022\pi$
$131$	12.2643	1.07154	0.535768	+	0.844365i	$0.320022\pi$
$132$	0.730401	0.0635732
$133$	−0.492460	−0.0427017
$134$	−13.7011	−1.18360
$135$	3.03386	0.261113
$136$	8.19121	0.702391
$137$	−3.68655	−0.314963	−0.157481	−	0.987522i	$-0.550337\pi$
$137$	−3.68655	−0.314963	−0.157481	+	0.987522i	$0.550337\pi$
$138$	4.56764	0.388823
$139$	−11.2759	−0.956409	−0.478204	−	0.878249i	$-0.658712\pi$
$139$	−11.2759	−0.956409	−0.478204	+	0.878249i	$0.658712\pi$
$140$	1.42208	0.120187
$141$	−3.90470	−0.328835
$142$	−18.4001	−1.54410
$143$	−5.54756	−0.463910
$144$	13.2068	1.10057
$145$	0.674083	0.0559795
$146$	1.83759	0.152080
$147$	3.14767	0.259615
$148$	−3.63447	−0.298751
$149$	0.811603	0.0664891	0.0332445	−	0.999447i	$-0.489416\pi$
$149$	0.811603	0.0664891	0.0332445	+	0.999447i	$0.489416\pi$
$150$	−0.974898	−0.0796001
$151$	19.6254	1.59709	0.798545	−	0.601935i	$-0.205603\pi$
$151$	19.6254	1.59709	0.798545	+	0.601935i	$0.205603\pi$
$152$	0.546034	0.0442892
$153$	19.4430	1.57187
$154$	−1.89811	−0.152954
$155$	−1.92416	−0.154552
$156$	−4.05194	−0.324415
$157$	15.7100	1.25380	0.626898	−	0.779101i	$-0.284324\pi$
$157$	15.7100	1.25380	0.626898	+	0.779101i	$0.284324\pi$
$158$	−11.0909	−0.882347
$159$	−1.83842	−0.145796
$160$	−6.63653	−0.524664
$161$	−4.83955	−0.381410
$162$	12.0290	0.945084
$163$	−20.1718	−1.57997	−0.789987	−	0.613123i	$-0.789913\pi$
$163$	−20.1718	−1.57997	−0.789987	+	0.613123i	$0.789913\pi$
$164$	−7.25986	−0.566900
$165$	0.530531	0.0413018
$166$	28.3873	2.20328
$167$	10.7739	0.833712	0.416856	−	0.908973i	$-0.363132\pi$
$167$	10.7739	0.833712	0.416856	+	0.908973i	$0.363132\pi$
$168$	0.627631	0.0484227
$169$	17.7754	1.36734
$170$	−13.1424	−1.00798
$171$	1.29609	0.0991143
$172$	−17.2689	−1.31674
$173$	−21.0109	−1.59743	−0.798716	−	0.601708i	$-0.794487\pi$
$173$	−21.0109	−1.59743	−0.798716	+	0.601708i	$0.794487\pi$
$174$	−0.657162	−0.0498193
$175$	1.03293	0.0780824
$176$	4.85807	0.366191
$177$	−4.27421	−0.321269
$178$	−4.05622	−0.304027
$179$	−25.5400	−1.90895	−0.954474	−	0.298295i	$-0.903582\pi$
$179$	−25.5400	−1.90895	−0.954474	+	0.298295i	$0.903582\pi$
$180$	−3.74271	−0.278965
$181$	13.9487	1.03680	0.518398	−	0.855139i	$-0.326528\pi$
$181$	13.9487	1.03680	0.518398	+	0.855139i	$0.326528\pi$
$182$	10.5299	0.780526
$183$	−2.26553	−0.167473
$184$	5.36603	0.395589
$185$	−2.63992	−0.194091
$186$	1.87586	0.137545
$187$	7.15200	0.523006
$188$	10.1328	0.739007
$189$	3.13378	0.227949
$190$	−0.876087	−0.0635581
$191$	6.56004	0.474668	0.237334	−	0.971428i	$-0.423727\pi$
$191$	6.56004	0.474668	0.237334	+	0.971428i	$0.423727\pi$
$192$	1.31523	0.0949184
$193$	−15.1154	−1.08803	−0.544015	−	0.839075i	$-0.683097\pi$
$193$	−15.1154	−1.08803	−0.544015	+	0.839075i	$0.683097\pi$
$194$	−12.5575	−0.901576
$195$	−2.94315	−0.210764
$196$	−8.16824	−0.583446
$197$	2.40866	0.171610	0.0858050	−	0.996312i	$-0.472654\pi$
$197$	2.40866	0.171610	0.0858050	+	0.996312i	$0.472654\pi$
$198$	4.99556	0.355019
$199$	19.6037	1.38967	0.694836	−	0.719169i	$-0.255477\pi$
$199$	19.6037	1.38967	0.694836	+	0.719169i	$0.255477\pi$
$200$	−1.14530	−0.0809853
$201$	3.95566	0.279011
$202$	−17.0568	−1.20011
$203$	0.696283	0.0488695
$204$	5.22382	0.365741
$205$	−5.27325	−0.368299
$206$	−24.3841	−1.69892
$207$	12.7370	0.885283
$208$	−26.9504	−1.86868
$209$	0.476759	0.0329781
$210$	−1.00700	−0.0694899
$211$	−19.3694	−1.33345	−0.666723	−	0.745305i	$-0.732304\pi$
$211$	−19.3694	−1.33345	−0.666723	+	0.745305i	$0.732304\pi$
$212$	4.77073	0.327655
$213$	5.31229	0.363992
$214$	−10.5353	−0.720180
$215$	−12.5433	−0.855449
$216$	−3.47469	−0.236423
$217$	−1.98753	−0.134922
$218$	−31.6219	−2.14171
$219$	−0.530531	−0.0358500
$220$	−1.37674	−0.0928195
$221$	−39.6761	−2.66891
$222$	2.57365	0.172732
$223$	−3.37268	−0.225851	−0.112926	−	0.993603i	$-0.536022\pi$
$223$	−3.37268	−0.225851	−0.112926	+	0.993603i	$0.536022\pi$
$224$	−6.85509	−0.458025
$225$	−2.71854	−0.181236
$226$	−19.9626	−1.32790
$227$	−13.0123	−0.863658	−0.431829	−	0.901956i	$-0.642132\pi$
$227$	−13.0123	−0.863658	−0.431829	+	0.901956i	$0.642132\pi$
$228$	0.348225	0.0230618
$229$	20.1077	1.32875	0.664377	−	0.747398i	$-0.268697\pi$
$229$	20.1077	1.32875	0.664377	+	0.747398i	$0.268697\pi$
$230$	−8.60956	−0.567697
$231$	0.548003	0.0360560
$232$	−0.772030	−0.0506862
$233$	−14.3271	−0.938602	−0.469301	−	0.883038i	$-0.655494\pi$
$233$	−14.3271	−0.938602	−0.469301	+	0.883038i	$0.655494\pi$
$234$	−27.7132	−1.81167
$235$	7.35999	0.480113
$236$	11.0916	0.722003
$237$	3.20206	0.207996
$238$	−13.5753	−0.879953
$239$	7.80160	0.504644	0.252322	−	0.967643i	$-0.418806\pi$
$239$	7.80160	0.504644	0.252322	+	0.967643i	$0.418806\pi$
$240$	2.57736	0.166368
$241$	28.2981	1.82284	0.911419	−	0.411479i	$-0.134987\pi$
$241$	28.2981	1.82284	0.911419	+	0.411479i	$0.134987\pi$
$242$	1.83759	0.118125
$243$	−12.5745	−0.806652
$244$	5.87909	0.376370
$245$	−5.93305	−0.379049
$246$	5.14088	0.327770
$247$	−2.64485	−0.168288
$248$	2.20375	0.139938
$249$	−8.19570	−0.519382
$250$	1.83759	0.116219
$251$	8.39716	0.530024	0.265012	−	0.964245i	$-0.414624\pi$
$251$	8.39716	0.530024	0.265012	+	0.964245i	$0.414624\pi$
$252$	−3.86597	−0.243533
$253$	4.68524	0.294559
$254$	38.4402	2.41195
$255$	3.79435	0.237612
$256$	20.9774	1.31109
$257$	−8.37860	−0.522643	−0.261321	−	0.965252i	$-0.584158\pi$
$257$	−8.37860	−0.522643	−0.261321	+	0.965252i	$0.584158\pi$
$258$	12.2285	0.761312
$259$	−2.72686	−0.169439
$260$	7.63752	0.473659
$261$	−1.83252	−0.113430
$262$	22.5367	1.39232
$263$	−3.88264	−0.239414	−0.119707	−	0.992809i	$-0.538195\pi$
$263$	−3.88264	−0.239414	−0.119707	+	0.992809i	$0.538195\pi$
$264$	−0.607619	−0.0373964
$265$	3.46525	0.212868
$266$	−0.904940	−0.0554854
$267$	1.17107	0.0716685
$268$	−10.2650	−0.627034
$269$	−16.7514	−1.02135	−0.510676	−	0.859773i	$-0.670605\pi$
$269$	−16.7514	−1.02135	−0.510676	+	0.859773i	$0.670605\pi$
$270$	5.57499	0.339283
$271$	11.7977	0.716658	0.358329	−	0.933595i	$-0.383347\pi$
$271$	11.7977	0.716658	0.358329	+	0.933595i	$0.383347\pi$
$272$	34.7449	2.10672
$273$	−3.04008	−0.183994
$274$	−6.77436	−0.409254
$275$	−1.00000	−0.0603023
$276$	3.42211	0.205987
$277$	5.16555	0.310368	0.155184	−	0.987886i	$-0.450403\pi$
$277$	5.16555	0.310368	0.155184	+	0.987886i	$0.450403\pi$
$278$	−20.7205	−1.24273
$279$	5.23089	0.313165
$280$	−1.18302	−0.0706992
$281$	22.0671	1.31641	0.658207	−	0.752837i	$-0.271315\pi$
$281$	22.0671	1.31641	0.658207	+	0.752837i	$0.271315\pi$
$282$	−7.17524	−0.427279
$283$	−1.19561	−0.0710713	−0.0355357	−	0.999368i	$-0.511314\pi$
$283$	−1.19561	−0.0710713	−0.0355357	+	0.999368i	$0.511314\pi$
$284$	−13.7855	−0.818017
$285$	0.252935	0.0149826
$286$	−10.1941	−0.602792
$287$	−5.44691	−0.321521
$288$	18.0417	1.06311
$289$	34.1510	2.00889
$290$	1.23869	0.0727382
$291$	3.62548	0.212529
$292$	1.37674	0.0805673
$293$	−2.26978	−0.132602	−0.0663011	−	0.997800i	$-0.521120\pi$
$293$	−2.26978	−0.132602	−0.0663011	+	0.997800i	$0.521120\pi$
$294$	5.78412	0.337337
$295$	8.05647	0.469066
$296$	3.02351	0.175738
$297$	−3.03386	−0.176042
$298$	1.49139	0.0863940
$299$	−25.9917	−1.50314
$300$	−0.730401	−0.0421697
$301$	−12.9564	−0.746797
$302$	36.0634	2.07521
$303$	4.92447	0.282903
$304$	2.31613	0.132839
$305$	4.27031	0.244517
$306$	35.7282	2.04244
$307$	13.8235	0.788951	0.394475	−	0.918906i	$-0.370926\pi$
$307$	13.8235	0.788951	0.394475	+	0.918906i	$0.370926\pi$
$308$	−1.42208	−0.0810303
$309$	7.03995	0.400489
$310$	−3.53581	−0.200821
$311$	22.9199	1.29967	0.649835	−	0.760075i	$-0.274838\pi$
$311$	22.9199	1.29967	0.649835	+	0.760075i	$0.274838\pi$
$312$	3.37081	0.190834
$313$	14.4117	0.814599	0.407299	−	0.913295i	$-0.366471\pi$
$313$	14.4117	0.814599	0.407299	+	0.913295i	$0.366471\pi$
$314$	28.8686	1.62915
$315$	−2.80807	−0.158217
$316$	−8.30940	−0.467441
$317$	−7.71862	−0.433521	−0.216760	−	0.976225i	$-0.569549\pi$
$317$	−7.71862	−0.433521	−0.216760	+	0.976225i	$0.569549\pi$
$318$	−3.37826	−0.189444
$319$	−0.674083	−0.0377414
$320$	−2.47908	−0.138585
$321$	3.04166	0.169769
$322$	−8.89310	−0.495593
$323$	3.40978	0.189725
$324$	9.01218	0.500677
$325$	5.54756	0.307723
$326$	−37.0674	−2.05297
$327$	9.12958	0.504867
$328$	6.03947	0.333474
$329$	7.60238	0.419133
$330$	0.974898	0.0536664
$331$	−7.68414	−0.422358	−0.211179	−	0.977447i	$-0.567730\pi$
$331$	−7.68414	−0.422358	−0.211179	+	0.977447i	$0.567730\pi$
$332$	21.2680	1.16723
$333$	7.17671	0.393281
$334$	19.7981	1.08330
$335$	−7.45604	−0.407367
$336$	2.66224	0.145237
$337$	−5.35418	−0.291661	−0.145830	−	0.989310i	$-0.546585\pi$
$337$	−5.35418	−0.291661	−0.145830	+	0.989310i	$0.546585\pi$
$338$	32.6640	1.77669
$339$	5.76342	0.313026
$340$	−9.84641	−0.533996
$341$	1.92416	0.104199
$342$	2.38168	0.128786
$343$	−13.3590	−0.721317
$344$	14.3659	0.774560
$345$	2.48567	0.133824
$346$	−38.6095	−2.07566
$347$	−1.43947	−0.0772746	−0.0386373	−	0.999253i	$-0.512302\pi$
$347$	−1.43947	−0.0772746	−0.0386373	+	0.999253i	$0.512302\pi$
$348$	−0.492350	−0.0263928
$349$	−23.6737	−1.26722	−0.633612	−	0.773651i	$-0.718429\pi$
$349$	−23.6737	−1.26722	−0.633612	+	0.773651i	$0.718429\pi$
$350$	1.89811	0.101458
$351$	16.8305	0.898347
$352$	6.63653	0.353728
$353$	27.7421	1.47656	0.738281	−	0.674493i	$-0.235638\pi$
$353$	27.7421	1.47656	0.738281	+	0.674493i	$0.235638\pi$
$354$	−7.85424	−0.417448
$355$	−10.0132	−0.531443
$356$	−3.03895	−0.161064
$357$	3.91932	0.207432
$358$	−46.9320	−2.48043
$359$	−33.1582	−1.75002	−0.875010	−	0.484104i	$-0.839146\pi$
$359$	−33.1582	−1.75002	−0.875010	+	0.484104i	$0.839146\pi$
$360$	3.11355	0.164099
$361$	−18.7727	−0.988037
$362$	25.6319	1.34718
$363$	−0.530531	−0.0278457
$364$	7.88906	0.413499
$365$	1.00000	0.0523424
$366$	−4.16312	−0.217610
$367$	26.1965	1.36745	0.683724	−	0.729740i	$-0.260359\pi$
$367$	26.1965	1.36745	0.683724	+	0.729740i	$0.260359\pi$
$368$	22.7612	1.18651
$369$	14.3355	0.746277
$370$	−4.85108	−0.252196
$371$	3.57937	0.185832
$372$	1.40541	0.0728669
$373$	−15.4496	−0.799950	−0.399975	−	0.916526i	$-0.630981\pi$
$373$	−15.4496	−0.799950	−0.399975	+	0.916526i	$0.630981\pi$
$374$	13.1424	0.679579
$375$	−0.530531	−0.0273965
$376$	−8.42943	−0.434715
$377$	3.73952	0.192595
$378$	5.75859	0.296190
$379$	3.84194	0.197347	0.0986735	−	0.995120i	$-0.468540\pi$
$379$	3.84194	0.197347	0.0986735	+	0.995120i	$0.468540\pi$
$380$	−0.656371	−0.0336711
$381$	−11.0981	−0.568572
$382$	12.0547	0.616770
$383$	−19.1768	−0.979887	−0.489943	−	0.871754i	$-0.662983\pi$
$383$	−19.1768	−0.979887	−0.489943	+	0.871754i	$0.662983\pi$
$384$	−4.62492	−0.236014
$385$	−1.03293	−0.0526432
$386$	−27.7759	−1.41376
$387$	34.0995	1.73338
$388$	−9.40817	−0.477627
$389$	−39.2117	−1.98811	−0.994055	−	0.108880i	$-0.965274\pi$
$389$	−39.2117	−1.98811	−0.994055	+	0.108880i	$0.965274\pi$
$390$	−5.40831	−0.273860
$391$	33.5088	1.69462
$392$	6.79515	0.343207
$393$	−6.50658	−0.328214
$394$	4.42613	0.222985
$395$	−6.03559	−0.303683
$396$	3.74271	0.188078
$397$	35.2240	1.76784	0.883921	−	0.467635i	$-0.154894\pi$
$397$	35.2240	1.76784	0.883921	+	0.467635i	$0.154894\pi$
$398$	36.0236	1.80570
$399$	0.261265	0.0130796
$400$	−4.85807	−0.242904
$401$	−19.8649	−0.992005	−0.496003	−	0.868321i	$-0.665199\pi$
$401$	−19.8649	−0.992005	−0.496003	+	0.868321i	$0.665199\pi$
$402$	7.26887	0.362538
$403$	−10.6744	−0.531729
$404$	−12.7791	−0.635782
$405$	6.54605	0.325276
$406$	1.27948	0.0634996
$407$	2.63992	0.130856
$408$	−4.34569	−0.215144
$409$	18.7747	0.928351	0.464176	−	0.885743i	$-0.346351\pi$
$409$	18.7747	0.928351	0.464176	+	0.885743i	$0.346351\pi$
$410$	−9.69006	−0.478558
$411$	1.95583	0.0964738
$412$	−18.2688	−0.900038
$413$	8.32180	0.409489
$414$	23.4054	1.15031
$415$	15.4481	0.758318
$416$	−36.8166	−1.80508
$417$	5.98221	0.292950
$418$	0.876087	0.0428508
$419$	1.81275	0.0885584	0.0442792	−	0.999019i	$-0.485901\pi$
$419$	1.81275	0.0885584	0.0442792	+	0.999019i	$0.485901\pi$
$420$	−0.754455	−0.0368137
$421$	25.6345	1.24935	0.624676	−	0.780884i	$-0.285231\pi$
$421$	25.6345	1.24935	0.624676	+	0.780884i	$0.285231\pi$
$422$	−35.5931	−1.73264
$423$	−20.0084	−0.972842
$424$	−3.96876	−0.192740
$425$	−7.15200	−0.346923
$426$	9.76180	0.472961
$427$	4.41095	0.213461
$428$	−7.89314	−0.381529
$429$	2.94315	0.142097
$430$	−23.0495	−1.11155
$431$	2.76589	0.133228	0.0666140	−	0.997779i	$-0.478780\pi$
$431$	2.76589	0.133228	0.0666140	+	0.997779i	$0.478780\pi$
$432$	−14.7387	−0.709116
$433$	−12.8186	−0.616023	−0.308012	−	0.951383i	$-0.599664\pi$
$433$	−12.8186	−0.616023	−0.308012	+	0.951383i	$0.599664\pi$
$434$	−3.65226	−0.175314
$435$	−0.357622	−0.0171466
$436$	−23.6914	−1.13461
$437$	2.23373	0.106854
$438$	−0.974898	−0.0465824
$439$	−23.0414	−1.09971	−0.549853	−	0.835261i	$-0.685316\pi$
$439$	−23.0414	−1.09971	−0.549853	+	0.835261i	$0.685316\pi$
$440$	1.14530	0.0546003
$441$	16.1292	0.768058
$442$	−72.9085	−3.46790
$443$	19.7994	0.940700	0.470350	−	0.882480i	$-0.344128\pi$
$443$	19.7994	0.940700	0.470350	+	0.882480i	$0.344128\pi$
$444$	1.92820	0.0915082
$445$	−2.20736	−0.104639
$446$	−6.19760	−0.293465
$447$	−0.430580	−0.0203657
$448$	−2.56072	−0.120983
$449$	5.26584	0.248510	0.124255	−	0.992250i	$-0.460346\pi$
$449$	5.26584	0.248510	0.124255	+	0.992250i	$0.460346\pi$
$450$	−4.99556	−0.235493
$451$	5.27325	0.248307
$452$	−14.9562	−0.703479
$453$	−10.4119	−0.489192
$454$	−23.9113	−1.12221
$455$	5.73026	0.268639
$456$	−0.289688	−0.0135659
$457$	2.91781	0.136490	0.0682448	−	0.997669i	$-0.478260\pi$
$457$	2.91781	0.136490	0.0682448	+	0.997669i	$0.478260\pi$
$458$	36.9497	1.72655
$459$	−21.6982	−1.01278
$460$	−6.45034	−0.300749
$461$	−11.7944	−0.549321	−0.274660	−	0.961541i	$-0.588565\pi$
$461$	−11.7944	−0.549321	−0.274660	+	0.961541i	$0.588565\pi$
$462$	1.00700	0.0468501
$463$	13.1805	0.612548	0.306274	−	0.951943i	$-0.400918\pi$
$463$	13.1805	0.612548	0.306274	+	0.951943i	$0.400918\pi$
$464$	−3.27474	−0.152026
$465$	1.02083	0.0473396
$466$	−26.3274	−1.21959
$467$	35.5870	1.64677	0.823385	−	0.567484i	$-0.192083\pi$
$467$	35.5870	1.64677	0.823385	+	0.567484i	$0.192083\pi$
$468$	−20.7629	−0.959765
$469$	−7.70159	−0.355626
$470$	13.5246	0.623845
$471$	−8.33465	−0.384040
$472$	−9.22711	−0.424712
$473$	12.5433	0.576743
$474$	5.88408	0.270265
$475$	−0.476759	−0.0218752
$476$	−10.1707	−0.466172
$477$	−9.42040	−0.431331
$478$	14.3361	0.655720
$479$	−34.6024	−1.58102	−0.790512	−	0.612446i	$-0.790186\pi$
$479$	−34.6024	−1.58102	−0.790512	+	0.612446i	$0.790186\pi$
$480$	3.52088	0.160706
$481$	−14.6451	−0.667759
$482$	52.0002	2.36855
$483$	2.56753	0.116827
$484$	1.37674	0.0625789
$485$	−6.83368	−0.310301
$486$	−23.1067	−1.04814
$487$	15.0897	0.683779	0.341890	−	0.939740i	$-0.388933\pi$
$487$	15.0897	0.683779	0.341890	+	0.939740i	$0.388933\pi$
$488$	−4.89080	−0.221396
$489$	10.7017	0.483950
$490$	−10.9025	−0.492525
$491$	39.8850	1.79999	0.899993	−	0.435903i	$-0.143571\pi$
$491$	39.8850	1.79999	0.899993	+	0.435903i	$0.143571\pi$
$492$	3.85158	0.173643
$493$	−4.82104	−0.217129
$494$	−4.86015	−0.218668
$495$	2.71854	0.122189
$496$	9.34769	0.419724
$497$	−10.3429	−0.463943
$498$	−15.0603	−0.674870
$499$	25.6263	1.14719	0.573596	−	0.819138i	$-0.305548\pi$
$499$	25.6263	1.14719	0.573596	+	0.819138i	$0.305548\pi$
$500$	1.37674	0.0615695
$501$	−5.71590	−0.255368
$502$	15.4305	0.688698
$503$	5.20249	0.231967	0.115984	−	0.993251i	$-0.462998\pi$
$503$	5.20249	0.231967	0.115984	+	0.993251i	$0.462998\pi$
$504$	3.21609	0.143256
$505$	−9.28215	−0.413050
$506$	8.60956	0.382741
$507$	−9.43042	−0.418820
$508$	28.7997	1.27778
$509$	−30.1119	−1.33469	−0.667343	−	0.744750i	$-0.732569\pi$
$509$	−30.1119	−1.33469	−0.667343	+	0.744750i	$0.732569\pi$
$510$	6.97247	0.308746
$511$	1.03293	0.0456943
$512$	21.1128	0.933062
$513$	−1.44642	−0.0638610
$514$	−15.3964	−0.679107
$515$	−13.2696	−0.584730
$516$	9.16167	0.403320
$517$	−7.35999	−0.323692
$518$	−5.01085	−0.220164
$519$	11.1469	0.489297
$520$	−6.35365	−0.278626
$521$	12.5121	0.548165	0.274082	−	0.961706i	$-0.411626\pi$
$521$	12.5121	0.548165	0.274082	+	0.961706i	$0.411626\pi$
$522$	−3.36742	−0.147388
$523$	−8.45383	−0.369660	−0.184830	−	0.982771i	$-0.559173\pi$
$523$	−8.45383	−0.369660	−0.184830	+	0.982771i	$0.559173\pi$
$524$	16.8847	0.737610
$525$	−0.548003	−0.0239168
$526$	−7.13469	−0.311087
$527$	13.7616	0.599463
$528$	−2.57736	−0.112165
$529$	−1.04849	−0.0455864
$530$	6.36770	0.276595
$531$	−21.9018	−0.950458
$532$	−0.677988	−0.0293945
$533$	−29.2537	−1.26712
$534$	2.15195	0.0931241
$535$	−5.73323	−0.247869
$536$	8.53943	0.368847
$537$	13.5497	0.584715
$538$	−30.7822	−1.32712
$539$	5.93305	0.255554
$540$	4.17682	0.179742
$541$	16.5756	0.712643	0.356321	−	0.934363i	$-0.384031\pi$
$541$	16.5756	0.712643	0.356321	+	0.934363i	$0.384031\pi$
$542$	21.6793	0.931205
$543$	−7.40020	−0.317573
$544$	47.4644	2.03502
$545$	−17.2084	−0.737126
$546$	−5.58642	−0.239077
$547$	23.3738	0.999392	0.499696	−	0.866201i	$-0.333445\pi$
$547$	23.3738	0.999392	0.499696	+	0.866201i	$0.333445\pi$
$548$	−5.07540	−0.216810
$549$	−11.6090	−0.495460
$550$	−1.83759	−0.0783551
$551$	−0.321375	−0.0136910
$552$	−2.84685	−0.121170
$553$	−6.23436	−0.265112
$554$	9.49216	0.403283
$555$	1.40056	0.0594504
$556$	−15.5239	−0.658361
$557$	−40.0974	−1.69898	−0.849491	−	0.527603i	$-0.823091\pi$
$557$	−40.0974	−1.69898	−0.849491	+	0.527603i	$0.823091\pi$
$558$	9.61224	0.406918
$559$	−69.5850	−2.94313
$560$	−5.01806	−0.212052
$561$	−3.79435	−0.160198
$562$	40.5503	1.71051
$563$	15.5565	0.655629	0.327814	−	0.944742i	$-0.393688\pi$
$563$	15.5565	0.655629	0.327814	+	0.944742i	$0.393688\pi$
$564$	−5.37574	−0.226360
$565$	−10.8635	−0.457031
$566$	−2.19703	−0.0923481
$567$	6.76164	0.283962
$568$	11.4681	0.481191
$569$	5.14175	0.215553	0.107777	−	0.994175i	$-0.465627\pi$
$569$	5.14175	0.215553	0.107777	+	0.994175i	$0.465627\pi$
$570$	0.464791	0.0194680
$571$	−46.9669	−1.96550	−0.982752	−	0.184931i	$-0.940794\pi$
$571$	−46.9669	−1.96550	−0.982752	+	0.184931i	$0.940794\pi$
$572$	−7.63752	−0.319341
$573$	−3.48030	−0.145392
$574$	−10.0092	−0.417775
$575$	−4.68524	−0.195388
$576$	6.73947	0.280811
$577$	35.2882	1.46907	0.734534	−	0.678572i	$-0.237401\pi$
$577$	35.2882	1.46907	0.734534	+	0.678572i	$0.237401\pi$
$578$	62.7556	2.61029
$579$	8.01919	0.333266
$580$	0.928033	0.0385345
$581$	15.9569	0.662003
$582$	6.66214	0.276155
$583$	−3.46525	−0.143516
$584$	−1.14530	−0.0473930
$585$	−15.0813	−0.623533
$586$	−4.17093	−0.172300
$587$	27.8836	1.15088	0.575439	−	0.817844i	$-0.304831\pi$
$587$	27.8836	1.15088	0.575439	+	0.817844i	$0.304831\pi$
$588$	4.33350	0.178711
$589$	0.917360	0.0377991
$590$	14.8045	0.609491
$591$	−1.27787	−0.0525645
$592$	12.8249	0.527100
$593$	−18.8619	−0.774565	−0.387282	−	0.921961i	$-0.626586\pi$
$593$	−18.8619	−0.774565	−0.387282	+	0.921961i	$0.626586\pi$
$594$	−5.57499	−0.228745
$595$	−7.38754	−0.302859
$596$	1.11736	0.0457689
$597$	−10.4004	−0.425659
$598$	−47.7620	−1.95314
$599$	−29.9037	−1.22183	−0.610917	−	0.791695i	$-0.709199\pi$
$599$	−29.9037	−1.22183	−0.610917	+	0.791695i	$0.709199\pi$
$600$	0.607619	0.0248060
$601$	16.5669	0.675777	0.337888	−	0.941186i	$-0.390287\pi$
$601$	16.5669	0.675777	0.337888	+	0.941186i	$0.390287\pi$
$602$	−23.8086	−0.970367
$603$	20.2695	0.825438
$604$	27.0189	1.09939
$605$	1.00000	0.0406558
$606$	9.04915	0.367597
$607$	20.2685	0.822671	0.411336	−	0.911484i	$-0.365062\pi$
$607$	20.2685	0.822671	0.411336	+	0.911484i	$0.365062\pi$
$608$	3.16403	0.128318
$609$	−0.369399	−0.0149688
$610$	7.84708	0.317719
$611$	40.8300	1.65181
$612$	26.7678	1.08202
$613$	11.1367	0.449809	0.224904	−	0.974381i	$-0.427793\pi$
$613$	11.1367	0.449809	0.224904	+	0.974381i	$0.427793\pi$
$614$	25.4020	1.02514
$615$	2.79762	0.112811
$616$	1.18302	0.0476654
$617$	−13.7199	−0.552343	−0.276172	−	0.961108i	$-0.589066\pi$
$617$	−13.7199	−0.552343	−0.276172	+	0.961108i	$0.589066\pi$
$618$	12.9365	0.520384
$619$	16.2132	0.651663	0.325831	−	0.945428i	$-0.394356\pi$
$619$	16.2132	0.651663	0.325831	+	0.945428i	$0.394356\pi$
$620$	−2.64906	−0.106389
$621$	−14.2144	−0.570403
$622$	42.1174	1.68875
$623$	−2.28006	−0.0913486
$624$	14.2980	0.572380
$625$	1.00000	0.0400000
$626$	26.4828	1.05847
$627$	−0.252935	−0.0101013
$628$	21.6285	0.863073
$629$	18.8807	0.752822
$630$	−5.16008	−0.205582
$631$	44.6222	1.77638	0.888190	−	0.459476i	$-0.151963\pi$
$631$	44.6222	1.77638	0.888190	+	0.459476i	$0.151963\pi$
$632$	6.91258	0.274968
$633$	10.2761	0.408437
$634$	−14.1837	−0.563305
$635$	20.9188	0.830138
$636$	−2.53102	−0.100361
$637$	−32.9140	−1.30410
$638$	−1.23869	−0.0490401
$639$	27.2211	1.07685
$640$	8.71753	0.344591
$641$	1.88052	0.0742760	0.0371380	−	0.999310i	$-0.488176\pi$
$641$	1.88052	0.0742760	0.0371380	+	0.999310i	$0.488176\pi$
$642$	5.58932	0.220593
$643$	28.8236	1.13669	0.568346	−	0.822790i	$-0.307583\pi$
$643$	28.8236	1.13669	0.568346	+	0.822790i	$0.307583\pi$
$644$	−6.66277	−0.262550
$645$	6.65463	0.262026
$646$	6.26577	0.246524
$647$	9.41592	0.370178	0.185089	−	0.982722i	$-0.440743\pi$
$647$	9.41592	0.370178	0.185089	+	0.982722i	$0.440743\pi$
$648$	−7.49723	−0.294519
$649$	−8.05647	−0.316244
$650$	10.1941	0.399847
$651$	1.05444	0.0413269
$652$	−27.7712	−1.08760
$653$	45.7782	1.79144	0.895720	−	0.444619i	$-0.146661\pi$
$653$	45.7782	1.79144	0.895720	+	0.444619i	$0.146661\pi$
$654$	16.7764	0.656010
$655$	12.2643	0.479205
$656$	25.6178	1.00021
$657$	−2.71854	−0.106060
$658$	13.9701	0.544609
$659$	3.63516	0.141606	0.0708029	−	0.997490i	$-0.477444\pi$
$659$	3.63516	0.141606	0.0708029	+	0.997490i	$0.477444\pi$
$660$	0.730401	0.0284308
$661$	−10.1973	−0.396628	−0.198314	−	0.980139i	$-0.563547\pi$
$661$	−10.1973	−0.396628	−0.198314	+	0.980139i	$0.563547\pi$
$662$	−14.1203	−0.548801
$663$	21.0494	0.817492
$664$	−17.6928	−0.686614
$665$	−0.492460	−0.0190968
$666$	13.1879	0.511019
$667$	−3.15824	−0.122288
$668$	14.8329	0.573900
$669$	1.78931	0.0691787
$670$	−13.7011	−0.529321
$671$	−4.27031	−0.164853
$672$	3.63684	0.140294
$673$	20.7069	0.798193	0.399096	−	0.916909i	$-0.369324\pi$
$673$	20.7069	0.798193	0.399096	+	0.916909i	$0.369324\pi$
$674$	−9.83879	−0.378976
$675$	3.03386	0.116773
$676$	24.4721	0.941234
$677$	−8.06987	−0.310150	−0.155075	−	0.987903i	$-0.549562\pi$
$677$	−8.06987	−0.310150	−0.155075	+	0.987903i	$0.549562\pi$
$678$	10.5908	0.406737
$679$	−7.05873	−0.270889
$680$	8.19121	0.314119
$681$	6.90344	0.264540
$682$	3.53581	0.135393
$683$	−44.5421	−1.70436	−0.852178	−	0.523252i	$-0.824719\pi$
$683$	−44.5421	−1.70436	−0.852178	+	0.523252i	$0.824719\pi$
$684$	1.78437	0.0682270
$685$	−3.68655	−0.140856
$686$	−24.5483	−0.937259
$687$	−10.6678	−0.407000
$688$	60.9364	2.32318
$689$	19.2237	0.732364
$690$	4.56764	0.173887
$691$	3.58276	0.136295	0.0681473	−	0.997675i	$-0.478291\pi$
$691$	3.58276	0.136295	0.0681473	+	0.997675i	$0.478291\pi$
$692$	−28.9265	−1.09962
$693$	2.80807	0.106670
$694$	−2.64515	−0.100408
$695$	−11.2759	−0.427719
$696$	0.409586	0.0155253
$697$	37.7142	1.42853
$698$	−43.5026	−1.64660
$699$	7.60099	0.287496
$700$	1.42208	0.0537494
$701$	−7.62880	−0.288136	−0.144068	−	0.989568i	$-0.546018\pi$
$701$	−7.62880	−0.288136	−0.144068	+	0.989568i	$0.546018\pi$
$702$	30.9276	1.16729
$703$	1.25860	0.0474692
$704$	2.47908	0.0934338
$705$	−3.90470	−0.147060
$706$	50.9786	1.91860
$707$	−9.58784	−0.360588
$708$	−5.88445	−0.221151
$709$	−12.2359	−0.459529	−0.229764	−	0.973246i	$-0.573796\pi$
$709$	−12.2359	−0.459529	−0.229764	+	0.973246i	$0.573796\pi$
$710$	−18.4001	−0.690542
$711$	16.4080	0.615347
$712$	2.52810	0.0947446
$713$	9.01515	0.337620
$714$	7.20209	0.269532
$715$	−5.54756	−0.207467
$716$	−35.1618	−1.31406
$717$	−4.13899	−0.154573
$718$	−60.9311	−2.27393
$719$	−44.1826	−1.64773	−0.823866	−	0.566785i	$-0.808187\pi$
$719$	−44.1826	−1.64773	−0.823866	+	0.566785i	$0.808187\pi$
$720$	13.2068	0.492190
$721$	−13.7066	−0.510462
$722$	−34.4965	−1.28383
$723$	−15.0130	−0.558339
$724$	19.2036	0.713697
$725$	0.674083	0.0250348
$726$	−0.974898	−0.0361819
$727$	−19.3862	−0.718995	−0.359498	−	0.933146i	$-0.617052\pi$
$727$	−19.3862	−0.718995	−0.359498	+	0.933146i	$0.617052\pi$
$728$	−6.56290	−0.243237
$729$	−12.9670	−0.480260
$730$	1.83759	0.0680122
$731$	89.7099	3.31804
$732$	−3.11904	−0.115283
$733$	−11.0198	−0.407027	−0.203513	−	0.979072i	$-0.565236\pi$
$733$	−11.0198	−0.407027	−0.203513	+	0.979072i	$0.565236\pi$
$734$	48.1385	1.77682
$735$	3.14767	0.116103
$736$	31.0938	1.14613
$737$	7.45604	0.274647
$738$	26.3428	0.969691
$739$	45.7585	1.68325	0.841626	−	0.540061i	$-0.181599\pi$
$739$	45.7585	1.68325	0.841626	+	0.540061i	$0.181599\pi$
$740$	−3.63447	−0.133606
$741$	1.40317	0.0515469
$742$	6.57741	0.241464
$743$	−31.0922	−1.14066	−0.570331	−	0.821415i	$-0.693185\pi$
$743$	−31.0922	−1.14066	−0.570331	+	0.821415i	$0.693185\pi$
$744$	−1.16916	−0.0428633
$745$	0.811603	0.0297348
$746$	−28.3900	−1.03943
$747$	−41.9963	−1.53656
$748$	9.84641	0.360020
$749$	−5.92205	−0.216387
$750$	−0.974898	−0.0355982
$751$	−31.5943	−1.15289	−0.576446	−	0.817135i	$-0.695561\pi$
$751$	−31.5943	−1.15289	−0.576446	+	0.817135i	$0.695561\pi$
$752$	−35.7554	−1.30386
$753$	−4.45495	−0.162347
$754$	6.87169	0.250252
$755$	19.6254	0.714240
$756$	4.31438	0.156913
$757$	−27.4564	−0.997920	−0.498960	−	0.866625i	$-0.666285\pi$
$757$	−27.4564	−0.997920	−0.498960	+	0.866625i	$0.666285\pi$
$758$	7.05990	0.256427
$759$	−2.48567	−0.0902240
$760$	0.546034	0.0198067
$761$	5.99193	0.217207	0.108604	−	0.994085i	$-0.465362\pi$
$761$	5.99193	0.217207	0.108604	+	0.994085i	$0.465362\pi$
$762$	−20.3937	−0.738786
$763$	−17.7751	−0.643502
$764$	9.03143	0.326746
$765$	19.4430	0.702962
$766$	−35.2390	−1.27324
$767$	44.6938	1.61380
$768$	−11.1292	−0.401589
$769$	14.6156	0.527053	0.263527	−	0.964652i	$-0.415114\pi$
$769$	14.6156	0.527053	0.263527	+	0.964652i	$0.415114\pi$
$770$	−1.89811	−0.0684031
$771$	4.44511	0.160087
$772$	−20.8099	−0.748965
$773$	22.6970	0.816356	0.408178	−	0.912902i	$-0.366164\pi$
$773$	22.6970	0.816356	0.408178	+	0.912902i	$0.366164\pi$
$774$	62.6610	2.25230
$775$	−1.92416	−0.0691178
$776$	7.82664	0.280960
$777$	1.44668	0.0518995
$778$	−72.0549	−2.58329
$779$	2.51407	0.0900758
$780$	−4.05194	−0.145083
$781$	10.0132	0.358299
$782$	61.5755	2.20194
$783$	2.04507	0.0730849
$784$	28.8232	1.02940
$785$	15.7100	0.560715
$786$	−11.9564	−0.426472
$787$	−20.3304	−0.724701	−0.362350	−	0.932042i	$-0.618026\pi$
$787$	−20.3304	−0.724701	−0.362350	+	0.932042i	$0.618026\pi$
$788$	3.31609	0.118131
$789$	2.05986	0.0733329
$790$	−11.0909	−0.394598
$791$	−11.2213	−0.398982
$792$	−3.11355	−0.110635
$793$	23.6898	0.841250
$794$	64.7273	2.29709
$795$	−1.83842	−0.0652021
$796$	26.9891	0.956605
$797$	−52.4189	−1.85677	−0.928386	−	0.371618i	$-0.878803\pi$
$797$	−52.4189	−1.85677	−0.928386	+	0.371618i	$0.878803\pi$
$798$	0.480099	0.0169953
$799$	−52.6386	−1.86222
$800$	−6.63653	−0.234637
$801$	6.00079	0.212028
$802$	−36.5035	−1.28898
$803$	−1.00000	−0.0352892
$804$	5.44589	0.192062
$805$	−4.83955	−0.170572
$806$	−19.6151	−0.690914
$807$	8.88714	0.312842
$808$	10.6309	0.373993
$809$	20.0049	0.703335	0.351668	−	0.936125i	$-0.385615\pi$
$809$	20.0049	0.703335	0.351668	+	0.936125i	$0.385615\pi$
$810$	12.0290	0.422655
$811$	−35.7702	−1.25606	−0.628032	−	0.778188i	$-0.716139\pi$
$811$	−35.7702	−1.25606	−0.628032	+	0.778188i	$0.716139\pi$
$812$	0.958597	0.0336402
$813$	−6.25903	−0.219514
$814$	4.85108	0.170030
$815$	−20.1718	−0.706586
$816$	−18.4332	−0.645293
$817$	5.98015	0.209219
$818$	34.5003	1.20627
$819$	−15.5779	−0.544337
$820$	−7.25986	−0.253525
$821$	−50.7391	−1.77081	−0.885403	−	0.464824i	$-0.846118\pi$
$821$	−50.7391	−1.77081	−0.885403	+	0.464824i	$0.846118\pi$
$822$	3.59401	0.125355
$823$	−13.8781	−0.483760	−0.241880	−	0.970306i	$-0.577764\pi$
$823$	−13.8781	−0.483760	−0.241880	+	0.970306i	$0.577764\pi$
$824$	15.1978	0.529439
$825$	0.530531	0.0184707
$826$	15.2920	0.532078
$827$	−32.2624	−1.12187	−0.560937	−	0.827858i	$-0.689559\pi$
$827$	−32.2624	−1.12187	−0.560937	+	0.827858i	$0.689559\pi$
$828$	17.5355	0.609400
$829$	−6.84027	−0.237572	−0.118786	−	0.992920i	$-0.537900\pi$
$829$	−6.84027	−0.237572	−0.118786	+	0.992920i	$0.537900\pi$
$830$	28.3873	0.985337
$831$	−2.74048	−0.0950664
$832$	−13.7528	−0.476794
$833$	42.4331	1.47022
$834$	10.9928	0.380651
$835$	10.7739	0.372847
$836$	0.656371	0.0227011
$837$	−5.83763	−0.201778
$838$	3.33108	0.115070
$839$	5.83130	0.201319	0.100659	−	0.994921i	$-0.467905\pi$
$839$	5.83130	0.201319	0.100659	+	0.994921i	$0.467905\pi$
$840$	0.627631	0.0216553
$841$	−28.5456	−0.984331
$842$	47.1058	1.62337
$843$	−11.7073	−0.403220
$844$	−26.6666	−0.917901
$845$	17.7754	0.611494
$846$	−36.7672	−1.26408
$847$	1.03293	0.0354920
$848$	−16.8344	−0.578096
$849$	0.634305	0.0217693
$850$	−13.1424	−0.450782
$851$	12.3687	0.423992
$852$	7.31361	0.250560
$853$	−19.1674	−0.656281	−0.328140	−	0.944629i	$-0.606422\pi$
$853$	−19.1674	−0.656281	−0.328140	+	0.944629i	$0.606422\pi$
$854$	8.10551	0.277365
$855$	1.29609	0.0443252
$856$	6.56630	0.224431
$857$	−4.38158	−0.149672	−0.0748360	−	0.997196i	$-0.523843\pi$
$857$	−4.38158	−0.149672	−0.0748360	+	0.997196i	$0.523843\pi$
$858$	5.40831	0.184637
$859$	44.8983	1.53191	0.765956	−	0.642893i	$-0.222266\pi$
$859$	44.8983	1.53191	0.765956	+	0.642893i	$0.222266\pi$
$860$	−17.2689	−0.588863
$861$	2.88976	0.0984826
$862$	5.08256	0.173113
$863$	30.7334	1.04618	0.523089	−	0.852278i	$-0.324779\pi$
$863$	30.7334	1.04618	0.523089	+	0.852278i	$0.324779\pi$
$864$	−20.1343	−0.684983
$865$	−21.0109	−0.714393
$866$	−23.5554	−0.800443
$867$	−18.1182	−0.615326
$868$	−2.73630	−0.0928760
$869$	6.03559	0.204743
$870$	−0.657162	−0.0222799
$871$	−41.3628	−1.40153
$872$	19.7088	0.667425
$873$	18.5776	0.628757
$874$	4.10468	0.138843
$875$	1.03293	0.0349195
$876$	−0.730401	−0.0246780
$877$	23.9504	0.808747	0.404374	−	0.914594i	$-0.367490\pi$
$877$	23.9504	0.808747	0.404374	+	0.914594i	$0.367490\pi$
$878$	−42.3407	−1.42893
$879$	1.20419	0.0406163
$880$	4.85807	0.163766
$881$	−27.5693	−0.928832	−0.464416	−	0.885617i	$-0.653736\pi$
$881$	−27.5693	−0.928832	−0.464416	+	0.885617i	$0.653736\pi$
$882$	29.6389	0.997993
$883$	48.8576	1.64419	0.822094	−	0.569352i	$-0.192806\pi$
$883$	48.8576	1.64419	0.822094	+	0.569352i	$0.192806\pi$
$884$	−54.6235	−1.83719
$885$	−4.27421	−0.143676
$886$	36.3832	1.22232
$887$	0.708724	0.0237966	0.0118983	−	0.999929i	$-0.496213\pi$
$887$	0.708724	0.0237966	0.0118983	+	0.999929i	$0.496213\pi$
$888$	−1.60407	−0.0538289
$889$	21.6078	0.724701
$890$	−4.05622	−0.135965
$891$	−6.54605	−0.219301
$892$	−4.64329	−0.155469
$893$	−3.50894	−0.117422
$894$	−0.791230	−0.0264627
$895$	−25.5400	−0.853707
$896$	9.00463	0.300824
$897$	13.7894	0.460414
$898$	9.67646	0.322908
$899$	−1.29704	−0.0432588
$900$	−3.74271	−0.124757
$901$	−24.7834	−0.825656
$902$	9.69006	0.322644
$903$	6.87379	0.228745
$904$	12.4420	0.413815
$905$	13.9487	0.463670
$906$	−19.1327	−0.635643
$907$	13.9979	0.464791	0.232396	−	0.972621i	$-0.425344\pi$
$907$	13.9979	0.464791	0.232396	+	0.972621i	$0.425344\pi$
$908$	−17.9145	−0.594514
$909$	25.2339	0.836954
$910$	10.5299	0.349062
$911$	−41.9642	−1.39034	−0.695168	−	0.718847i	$-0.744670\pi$
$911$	−41.9642	−1.39034	−0.695168	+	0.718847i	$0.744670\pi$
$912$	−1.22878	−0.0406889
$913$	−15.4481	−0.511258
$914$	5.36175	0.177351
$915$	−2.26553	−0.0748961
$916$	27.6830	0.914671
$917$	12.6682	0.418341
$918$	−39.8723	−1.31598
$919$	32.9158	1.08579	0.542895	−	0.839800i	$-0.317328\pi$
$919$	32.9158	1.08579	0.542895	+	0.839800i	$0.317328\pi$
$920$	5.36603	0.176913
$921$	−7.33381	−0.241657
$922$	−21.6733	−0.713772
$923$	−55.5486	−1.82840
$924$	0.754455	0.0248198
$925$	−2.63992	−0.0867999
$926$	24.2203	0.795928
$927$	36.0740	1.18482
$928$	−4.47357	−0.146852
$929$	−32.5525	−1.06801	−0.534006	−	0.845481i	$-0.679314\pi$
$929$	−32.5525	−1.06801	−0.534006	+	0.845481i	$0.679314\pi$
$930$	1.87586	0.0615118
$931$	2.82863	0.0927047
$932$	−19.7247	−0.646103
$933$	−12.1597	−0.398092
$934$	65.3943	2.13977
$935$	7.15200	0.233895
$936$	17.2726	0.564573
$937$	41.2281	1.34686	0.673431	−	0.739250i	$-0.264820\pi$
$937$	41.2281	1.34686	0.673431	+	0.739250i	$0.264820\pi$
$938$	−14.1524	−0.462091
$939$	−7.64587	−0.249513
$940$	10.1328	0.330494
$941$	3.67333	0.119747	0.0598736	−	0.998206i	$-0.480930\pi$
$941$	3.67333	0.119747	0.0598736	+	0.998206i	$0.480930\pi$
$942$	−15.3157	−0.499011
$943$	24.7064	0.804552
$944$	−39.1389	−1.27386
$945$	3.13378	0.101942
$946$	23.0495	0.749404
$947$	−9.43993	−0.306757	−0.153378	−	0.988168i	$-0.549015\pi$
$947$	−9.43993	−0.306757	−0.153378	+	0.988168i	$0.549015\pi$
$948$	4.40840	0.143178
$949$	5.54756	0.180081
$950$	−0.876087	−0.0284240
$951$	4.09497	0.132788
$952$	8.46098	0.274222
$953$	37.3259	1.20910	0.604551	−	0.796566i	$-0.293352\pi$
$953$	37.3259	1.20910	0.604551	+	0.796566i	$0.293352\pi$
$954$	−17.3108	−0.560459
$955$	6.56004	0.212278
$956$	10.7407	0.347380
$957$	0.357622	0.0115603
$958$	−63.5850	−2.05434
$959$	−3.80796	−0.122965
$960$	1.31523	0.0424488
$961$	−27.2976	−0.880568
$962$	−26.9117	−0.867668
$963$	15.5860	0.502252
$964$	38.9590	1.25478
$965$	−15.1154	−0.486582
$966$	4.71806	0.151801
$967$	6.76173	0.217443	0.108721	−	0.994072i	$-0.465324\pi$
$967$	6.76173	0.217443	0.108721	+	0.994072i	$0.465324\pi$
$968$	−1.14530	−0.0368115
$969$	−1.80899	−0.0581132
$970$	−12.5575	−0.403197
$971$	10.1547	0.325880	0.162940	−	0.986636i	$-0.447902\pi$
$971$	10.1547	0.325880	0.162940	+	0.986636i	$0.447902\pi$
$972$	−17.3117	−0.555273
$973$	−11.6472	−0.373394
$974$	27.7287	0.888484
$975$	−2.94315	−0.0942563
$976$	−20.7455	−0.664046
$977$	−47.4461	−1.51793	−0.758967	−	0.651129i	$-0.774296\pi$
$977$	−47.4461	−1.51793	−0.758967	+	0.651129i	$0.774296\pi$
$978$	19.6654	0.628831
$979$	2.20736	0.0705476
$980$	−8.16824	−0.260925
$981$	46.7816	1.49362
$982$	73.2923	2.33885
$983$	−2.29673	−0.0732544	−0.0366272	−	0.999329i	$-0.511661\pi$
$983$	−2.29673	−0.0732544	−0.0366272	+	0.999329i	$0.511661\pi$
$984$	−3.20413	−0.102144
$985$	2.40866	0.0767463
$986$	−8.85909	−0.282131
$987$	−4.03330	−0.128381
$988$	−3.64126	−0.115844
$989$	58.7686	1.86873
$990$	4.99556	0.158769
$991$	−55.0447	−1.74855	−0.874277	−	0.485428i	$-0.838664\pi$
$991$	−55.0447	−1.74855	−0.874277	+	0.485428i	$0.838664\pi$
$992$	12.7697	0.405439
$993$	4.07667	0.129369
$994$	−19.0060	−0.602835
$995$	19.6037	0.621480
$996$	−11.2833	−0.357525
$997$	−56.2367	−1.78103	−0.890517	−	0.454950i	$-0.849657\pi$
$997$	−56.2367	−1.78103	−0.890517	+	0.454950i	$0.849657\pi$
$998$	47.0907	1.49063
$999$	−8.00914	−0.253398

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.c.1.19	✓	23

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.c.1.19	✓	23	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:	\( N \)	\(=\)	\( 4015 = 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4015.a (trivial)

\(f(q)\)	\(=\)	\(q+1.83759 q^{2} -0.530531 q^{3} +1.37674 q^{4} +1.00000 q^{5} -0.974898 q^{6} +1.03293 q^{7} -1.14530 q^{8} -2.71854 q^{9} +O(q^{10})\)	\(q+1.83759 q^{2} -0.530531 q^{3} +1.37674 q^{4} +1.00000 q^{5} -0.974898 q^{6} +1.03293 q^{7} -1.14530 q^{8} -2.71854 q^{9} +1.83759 q^{10} -1.00000 q^{11} -0.730401 q^{12} +5.54756 q^{13} +1.89811 q^{14} -0.530531 q^{15} -4.85807 q^{16} -7.15200 q^{17} -4.99556 q^{18} -0.476759 q^{19} +1.37674 q^{20} -0.548003 q^{21} -1.83759 q^{22} -4.68524 q^{23} +0.607619 q^{24} +1.00000 q^{25} +10.1941 q^{26} +3.03386 q^{27} +1.42208 q^{28} +0.674083 q^{29} -0.974898 q^{30} -1.92416 q^{31} -6.63653 q^{32} +0.530531 q^{33} -13.1424 q^{34} +1.03293 q^{35} -3.74271 q^{36} -2.63992 q^{37} -0.876087 q^{38} -2.94315 q^{39} -1.14530 q^{40} -5.27325 q^{41} -1.00700 q^{42} -12.5433 q^{43} -1.37674 q^{44} -2.71854 q^{45} -8.60956 q^{46} +7.35999 q^{47} +2.57736 q^{48} -5.93305 q^{49} +1.83759 q^{50} +3.79435 q^{51} +7.63752 q^{52} +3.46525 q^{53} +5.57499 q^{54} -1.00000 q^{55} -1.18302 q^{56} +0.252935 q^{57} +1.23869 q^{58} +8.05647 q^{59} -0.730401 q^{60} +4.27031 q^{61} -3.53581 q^{62} -2.80807 q^{63} -2.47908 q^{64} +5.54756 q^{65} +0.974898 q^{66} -7.45604 q^{67} -9.84641 q^{68} +2.48567 q^{69} +1.89811 q^{70} -10.0132 q^{71} +3.11355 q^{72} +1.00000 q^{73} -4.85108 q^{74} -0.530531 q^{75} -0.656371 q^{76} -1.03293 q^{77} -5.40831 q^{78} -6.03559 q^{79} -4.85807 q^{80} +6.54605 q^{81} -9.69006 q^{82} +15.4481 q^{83} -0.754455 q^{84} -7.15200 q^{85} -23.0495 q^{86} -0.357622 q^{87} +1.14530 q^{88} -2.20736 q^{89} -4.99556 q^{90} +5.73026 q^{91} -6.45034 q^{92} +1.02083 q^{93} +13.5246 q^{94} -0.476759 q^{95} +3.52088 q^{96} -6.83368 q^{97} -10.9025 q^{98} +2.71854 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 23 q - 3 q^{2} - 5 q^{3} + 15 q^{4} + 23 q^{5} - 5 q^{6} - 6 q^{8} + 8 q^{9}+O(q^{10}) \) 23 * q - 3 * q^2 - 5 * q^3 + 15 * q^4 + 23 * q^5 - 5 * q^6 - 6 * q^8 + 8 * q^9	\( 23 q - 3 q^{2} - 5 q^{3} + 15 q^{4} + 23 q^{5} - 5 q^{6} - 6 q^{8} + 8 q^{9} - 3 q^{10} - 23 q^{11} - 18 q^{12} - 5 q^{13} - 17 q^{14} - 5 q^{15} - q^{16} - 36 q^{17} + q^{18} + 6 q^{19} + 15 q^{20} - 18 q^{21} + 3 q^{22} - 14 q^{23} - 7 q^{24} + 23 q^{25} - 21 q^{26} - 29 q^{27} + 28 q^{28} - 36 q^{29} - 5 q^{30} - 16 q^{31} - 5 q^{32} + 5 q^{33} - 28 q^{34} - 14 q^{36} - 24 q^{37} + q^{38} - 10 q^{39} - 6 q^{40} - 36 q^{41} - 5 q^{42} + 17 q^{43} - 15 q^{44} + 8 q^{45} - 25 q^{46} - 21 q^{47} - 17 q^{48} - 27 q^{49} - 3 q^{50} + 19 q^{51} - 21 q^{52} - 28 q^{53} - 15 q^{54} - 23 q^{55} - 46 q^{56} - 23 q^{57} - 16 q^{58} - 61 q^{59} - 18 q^{60} - 17 q^{61} - 22 q^{62} - 9 q^{63} - 18 q^{64} - 5 q^{65} + 5 q^{66} + 2 q^{67} - 39 q^{68} - 36 q^{69} - 17 q^{70} - 50 q^{71} + 15 q^{72} + 23 q^{73} + 17 q^{74} - 5 q^{75} - 21 q^{76} + 49 q^{78} - 18 q^{79} - q^{80} - 57 q^{81} + 14 q^{82} - 20 q^{83} - 38 q^{84} - 36 q^{85} - 45 q^{86} + 37 q^{87} + 6 q^{88} - 93 q^{89} + q^{90} - 42 q^{91} - 39 q^{92} - 18 q^{93} - 6 q^{94} + 6 q^{95} - 9 q^{96} - 31 q^{97} - 31 q^{98} - 8 q^{99}+O(q^{100}) \) 23 * q - 3 * q^2 - 5 * q^3 + 15 * q^4 + 23 * q^5 - 5 * q^6 - 6 * q^8 + 8 * q^9 - 3 * q^10 - 23 * q^11 - 18 * q^12 - 5 * q^13 - 17 * q^14 - 5 * q^15 - q^16 - 36 * q^17 + q^18 + 6 * q^19 + 15 * q^20 - 18 * q^21 + 3 * q^22 - 14 * q^23 - 7 * q^24 + 23 * q^25 - 21 * q^26 - 29 * q^27 + 28 * q^28 - 36 * q^29 - 5 * q^30 - 16 * q^31 - 5 * q^32 + 5 * q^33 - 28 * q^34 - 14 * q^36 - 24 * q^37 + q^38 - 10 * q^39 - 6 * q^40 - 36 * q^41 - 5 * q^42 + 17 * q^43 - 15 * q^44 + 8 * q^45 - 25 * q^46 - 21 * q^47 - 17 * q^48 - 27 * q^49 - 3 * q^50 + 19 * q^51 - 21 * q^52 - 28 * q^53 - 15 * q^54 - 23 * q^55 - 46 * q^56 - 23 * q^57 - 16 * q^58 - 61 * q^59 - 18 * q^60 - 17 * q^61 - 22 * q^62 - 9 * q^63 - 18 * q^64 - 5 * q^65 + 5 * q^66 + 2 * q^67 - 39 * q^68 - 36 * q^69 - 17 * q^70 - 50 * q^71 + 15 * q^72 + 23 * q^73 + 17 * q^74 - 5 * q^75 - 21 * q^76 + 49 * q^78 - 18 * q^79 - q^80 - 57 * q^81 + 14 * q^82 - 20 * q^83 - 38 * q^84 - 36 * q^85 - 45 * q^86 + 37 * q^87 + 6 * q^88 - 93 * q^89 + q^90 - 42 * q^91 - 39 * q^92 - 18 * q^93 - 6 * q^94 + 6 * q^95 - 9 * q^96 - 31 * q^97 - 31 * q^98 - 8 * q^99

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