LMFDB - Embedded newform 4017.2.a.h.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, 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("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.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:	$32.0759064919$
Analytic rank:	$1$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.70695 q^{2} -1.00000 q^{3} +5.32758 q^{4} +2.36895 q^{5} +2.70695 q^{6} +2.88217 q^{7} -9.00759 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.70695 q^{2} -1.00000 q^{3} +5.32758 q^{4} +2.36895 q^{5} +2.70695 q^{6} +2.88217 q^{7} -9.00759 q^{8} +1.00000 q^{9} -6.41264 q^{10} +1.43966 q^{11} -5.32758 q^{12} +1.00000 q^{13} -7.80188 q^{14} -2.36895 q^{15} +13.7279 q^{16} -6.36313 q^{17} -2.70695 q^{18} +4.50944 q^{19} +12.6208 q^{20} -2.88217 q^{21} -3.89708 q^{22} -8.58325 q^{23} +9.00759 q^{24} +0.611936 q^{25} -2.70695 q^{26} -1.00000 q^{27} +15.3550 q^{28} +7.82756 q^{29} +6.41264 q^{30} -3.17133 q^{31} -19.1457 q^{32} -1.43966 q^{33} +17.2247 q^{34} +6.82771 q^{35} +5.32758 q^{36} -1.65076 q^{37} -12.2068 q^{38} -1.00000 q^{39} -21.3386 q^{40} -3.66176 q^{41} +7.80188 q^{42} -8.42160 q^{43} +7.66988 q^{44} +2.36895 q^{45} +23.2344 q^{46} +3.58105 q^{47} -13.7279 q^{48} +1.30688 q^{49} -1.65648 q^{50} +6.36313 q^{51} +5.32758 q^{52} -8.69432 q^{53} +2.70695 q^{54} +3.41048 q^{55} -25.9614 q^{56} -4.50944 q^{57} -21.1888 q^{58} -11.1910 q^{59} -12.6208 q^{60} -14.9354 q^{61} +8.58463 q^{62} +2.88217 q^{63} +24.3705 q^{64} +2.36895 q^{65} +3.89708 q^{66} +7.12949 q^{67} -33.9001 q^{68} +8.58325 q^{69} -18.4823 q^{70} -6.99727 q^{71} -9.00759 q^{72} -5.65916 q^{73} +4.46854 q^{74} -0.611936 q^{75} +24.0244 q^{76} +4.14933 q^{77} +2.70695 q^{78} -8.18798 q^{79} +32.5208 q^{80} +1.00000 q^{81} +9.91220 q^{82} -17.4489 q^{83} -15.3550 q^{84} -15.0740 q^{85} +22.7968 q^{86} -7.82756 q^{87} -12.9678 q^{88} +8.54413 q^{89} -6.41264 q^{90} +2.88217 q^{91} -45.7279 q^{92} +3.17133 q^{93} -9.69373 q^{94} +10.6827 q^{95} +19.1457 q^{96} -14.5970 q^{97} -3.53766 q^{98} +1.43966 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 4 q^{2} - 25 q^{3} + 28 q^{4} - 5 q^{5} + 4 q^{6} - 7 q^{7} - 9 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q - 4 * q^2 - 25 * q^3 + 28 * q^4 - 5 * q^5 + 4 * q^6 - 7 * q^7 - 9 * q^8 + 25 * q^9	\( 25 q - 4 q^{2} - 25 q^{3} + 28 q^{4} - 5 q^{5} + 4 q^{6} - 7 q^{7} - 9 q^{8} + 25 q^{9} - 12 q^{10} - 23 q^{11} - 28 q^{12} + 25 q^{13} + 5 q^{15} + 26 q^{16} - 14 q^{17} - 4 q^{18} - 4 q^{19} - 12 q^{20} + 7 q^{21} - 7 q^{22} - 47 q^{23} + 9 q^{24} + 26 q^{25} - 4 q^{26} - 25 q^{27} - 38 q^{28} + 6 q^{29} + 12 q^{30} - 8 q^{31} - 62 q^{32} + 23 q^{33} + 25 q^{34} + 28 q^{36} - 20 q^{37} - 2 q^{38} - 25 q^{39} - 8 q^{40} - 33 q^{41} - 13 q^{43} - 13 q^{44} - 5 q^{45} - 21 q^{46} - 48 q^{47} - 26 q^{48} + 40 q^{49} - 9 q^{50} + 14 q^{51} + 28 q^{52} - 24 q^{53} + 4 q^{54} - 2 q^{55} - 14 q^{56} + 4 q^{57} - 31 q^{58} - 36 q^{59} + 12 q^{60} + 25 q^{61} - 7 q^{62} - 7 q^{63} + 45 q^{64} - 5 q^{65} + 7 q^{66} - 2 q^{67} - 32 q^{68} + 47 q^{69} - 13 q^{70} - 60 q^{71} - 9 q^{72} + 28 q^{73} - 16 q^{74} - 26 q^{75} - 12 q^{76} - 17 q^{77} + 4 q^{78} - 29 q^{79} - 88 q^{80} + 25 q^{81} - 22 q^{82} - 71 q^{83} + 38 q^{84} + 3 q^{85} - 3 q^{86} - 6 q^{87} + 23 q^{88} - 46 q^{89} - 12 q^{90} - 7 q^{91} - 69 q^{92} + 8 q^{93} + 4 q^{94} - 47 q^{95} + 62 q^{96} - 14 q^{97} - 71 q^{98} - 23 q^{99}+O(q^{100}) \) 25 * q - 4 * q^2 - 25 * q^3 + 28 * q^4 - 5 * q^5 + 4 * q^6 - 7 * q^7 - 9 * q^8 + 25 * q^9 - 12 * q^10 - 23 * q^11 - 28 * q^12 + 25 * q^13 + 5 * q^15 + 26 * q^16 - 14 * q^17 - 4 * q^18 - 4 * q^19 - 12 * q^20 + 7 * q^21 - 7 * q^22 - 47 * q^23 + 9 * q^24 + 26 * q^25 - 4 * q^26 - 25 * q^27 - 38 * q^28 + 6 * q^29 + 12 * q^30 - 8 * q^31 - 62 * q^32 + 23 * q^33 + 25 * q^34 + 28 * q^36 - 20 * q^37 - 2 * q^38 - 25 * q^39 - 8 * q^40 - 33 * q^41 - 13 * q^43 - 13 * q^44 - 5 * q^45 - 21 * q^46 - 48 * q^47 - 26 * q^48 + 40 * q^49 - 9 * q^50 + 14 * q^51 + 28 * q^52 - 24 * q^53 + 4 * q^54 - 2 * q^55 - 14 * q^56 + 4 * q^57 - 31 * q^58 - 36 * q^59 + 12 * q^60 + 25 * q^61 - 7 * q^62 - 7 * q^63 + 45 * q^64 - 5 * q^65 + 7 * q^66 - 2 * q^67 - 32 * q^68 + 47 * q^69 - 13 * q^70 - 60 * q^71 - 9 * q^72 + 28 * q^73 - 16 * q^74 - 26 * q^75 - 12 * q^76 - 17 * q^77 + 4 * q^78 - 29 * q^79 - 88 * q^80 + 25 * q^81 - 22 * q^82 - 71 * q^83 + 38 * q^84 + 3 * q^85 - 3 * q^86 - 6 * q^87 + 23 * q^88 - 46 * q^89 - 12 * q^90 - 7 * q^91 - 69 * q^92 + 8 * q^93 + 4 * q^94 - 47 * q^95 + 62 * q^96 - 14 * q^97 - 71 * q^98 - 23 * 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 $

$2$	−2.70695	−1.91410	−0.957051	−	0.289918i	$-0.906372\pi$
$2$	−2.70695	−1.91410	−0.957051	+	0.289918i	$0.906372\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.32758	2.66379
$5$	2.36895	1.05943	0.529714	−	0.848176i	$-0.322299\pi$
$5$	2.36895	1.05943	0.529714	+	0.848176i	$0.322299\pi$
$6$	2.70695	1.10511
$7$	2.88217	1.08936	0.544678	−	0.838645i	$-0.316652\pi$
$7$	2.88217	1.08936	0.544678	+	0.838645i	$0.316652\pi$
$8$	−9.00759	−3.18466
$9$	1.00000	0.333333
$10$	−6.41264	−2.02785
$11$	1.43966	0.434072	0.217036	−	0.976164i	$-0.430361\pi$
$11$	1.43966	0.434072	0.217036	+	0.976164i	$0.430361\pi$
$12$	−5.32758	−1.53794
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−7.80188	−2.08514
$15$	−2.36895	−0.611661
$16$	13.7279	3.43199
$17$	−6.36313	−1.54329	−0.771643	−	0.636056i	$-0.780565\pi$
$17$	−6.36313	−1.54329	−0.771643	+	0.636056i	$0.780565\pi$
$18$	−2.70695	−0.638034
$19$	4.50944	1.03454	0.517269	−	0.855823i	$-0.326949\pi$
$19$	4.50944	1.03454	0.517269	+	0.855823i	$0.326949\pi$
$20$	12.6208	2.82209
$21$	−2.88217	−0.628940
$22$	−3.89708	−0.830859
$23$	−8.58325	−1.78973	−0.894865	−	0.446336i	$-0.852728\pi$
$23$	−8.58325	−1.78973	−0.894865	+	0.446336i	$0.852728\pi$
$24$	9.00759	1.83867
$25$	0.611936	0.122387
$26$	−2.70695	−0.530877
$27$	−1.00000	−0.192450
$28$	15.3550	2.90182
$29$	7.82756	1.45354	0.726771	−	0.686880i	$-0.241020\pi$
$29$	7.82756	1.45354	0.726771	+	0.686880i	$0.241020\pi$
$30$	6.41264	1.17078
$31$	−3.17133	−0.569587	−0.284794	−	0.958589i	$-0.591925\pi$
$31$	−3.17133	−0.569587	−0.284794	+	0.958589i	$0.591925\pi$
$32$	−19.1457	−3.38451
$33$	−1.43966	−0.250612
$34$	17.2247	2.95401
$35$	6.82771	1.15409
$36$	5.32758	0.887930
$37$	−1.65076	−0.271384	−0.135692	−	0.990751i	$-0.543326\pi$
$37$	−1.65076	−0.271384	−0.135692	+	0.990751i	$0.543326\pi$
$38$	−12.2068	−1.98021
$39$	−1.00000	−0.160128
$40$	−21.3386	−3.37392
$41$	−3.66176	−0.571871	−0.285935	−	0.958249i	$-0.592304\pi$
$41$	−3.66176	−0.571871	−0.285935	+	0.958249i	$0.592304\pi$
$42$	7.80188	1.20386
$43$	−8.42160	−1.28428	−0.642141	−	0.766587i	$-0.721954\pi$
$43$	−8.42160	−1.28428	−0.642141	+	0.766587i	$0.721954\pi$
$44$	7.66988	1.15628
$45$	2.36895	0.353143
$46$	23.2344	3.42573
$47$	3.58105	0.522350	0.261175	−	0.965291i	$-0.415890\pi$
$47$	3.58105	0.522350	0.261175	+	0.965291i	$0.415890\pi$
$48$	−13.7279	−1.98146
$49$	1.30688	0.186697
$50$	−1.65648	−0.234262
$51$	6.36313	0.891017
$52$	5.32758	0.738802
$53$	−8.69432	−1.19426	−0.597128	−	0.802146i	$-0.703692\pi$
$53$	−8.69432	−1.19426	−0.597128	+	0.802146i	$0.703692\pi$
$54$	2.70695	0.368369
$55$	3.41048	0.459868
$56$	−25.9614	−3.46923
$57$	−4.50944	−0.597290
$58$	−21.1888	−2.78223
$59$	−11.1910	−1.45694	−0.728472	−	0.685075i	$-0.759769\pi$
$59$	−11.1910	−1.45694	−0.728472	+	0.685075i	$0.759769\pi$
$60$	−12.6208	−1.62934
$61$	−14.9354	−1.91228	−0.956140	−	0.292909i	$-0.905377\pi$
$61$	−14.9354	−1.91228	−0.956140	+	0.292909i	$0.905377\pi$
$62$	8.58463	1.09025
$63$	2.88217	0.363119
$64$	24.3705	3.04631
$65$	2.36895	0.293832
$66$	3.89708	0.479697
$67$	7.12949	0.871006	0.435503	−	0.900187i	$-0.356570\pi$
$67$	7.12949	0.871006	0.435503	+	0.900187i	$0.356570\pi$
$68$	−33.9001	−4.11099
$69$	8.58325	1.03330
$70$	−18.4823	−2.20906
$71$	−6.99727	−0.830424	−0.415212	−	0.909725i	$-0.636293\pi$
$71$	−6.99727	−0.830424	−0.415212	+	0.909725i	$0.636293\pi$
$72$	−9.00759	−1.06155
$73$	−5.65916	−0.662354	−0.331177	−	0.943569i	$-0.607446\pi$
$73$	−5.65916	−0.662354	−0.331177	+	0.943569i	$0.607446\pi$
$74$	4.46854	0.519457
$75$	−0.611936	−0.0706603
$76$	24.0244	2.75579
$77$	4.14933	0.472860
$78$	2.70695	0.306502
$79$	−8.18798	−0.921220	−0.460610	−	0.887603i	$-0.652369\pi$
$79$	−8.18798	−0.921220	−0.460610	+	0.887603i	$0.652369\pi$
$80$	32.5208	3.63594
$81$	1.00000	0.111111
$82$	9.91220	1.09462
$83$	−17.4489	−1.91527	−0.957635	−	0.287985i	$-0.907015\pi$
$83$	−17.4489	−1.91527	−0.957635	+	0.287985i	$0.907015\pi$
$84$	−15.3550	−1.67536
$85$	−15.0740	−1.63500
$86$	22.7968	2.45825
$87$	−7.82756	−0.839203
$88$	−12.9678	−1.38238
$89$	8.54413	0.905676	0.452838	−	0.891593i	$-0.350412\pi$
$89$	8.54413	0.905676	0.452838	+	0.891593i	$0.350412\pi$
$90$	−6.41264	−0.675951
$91$	2.88217	0.302133
$92$	−45.7279	−4.76747
$93$	3.17133	0.328851
$94$	−9.69373	−0.999832
$95$	10.6827	1.09602
$96$	19.1457	1.95405
$97$	−14.5970	−1.48210	−0.741052	−	0.671447i	$-0.765673\pi$
$97$	−14.5970	−1.48210	−0.741052	+	0.671447i	$0.765673\pi$
$98$	−3.53766	−0.357358
$99$	1.43966	0.144691
$100$	3.26014	0.326014
$101$	−1.24144	−0.123527	−0.0617637	−	0.998091i	$-0.519673\pi$
$101$	−1.24144	−0.123527	−0.0617637	+	0.998091i	$0.519673\pi$
$102$	−17.2247	−1.70550
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−9.00759	−0.883267
$105$	−6.82771	−0.666317
$106$	23.5351	2.28593
$107$	−12.1100	−1.17072	−0.585358	−	0.810775i	$-0.699046\pi$
$107$	−12.1100	−1.17072	−0.585358	+	0.810775i	$0.699046\pi$
$108$	−5.32758	−0.512647
$109$	1.05345	0.100902	0.0504509	−	0.998727i	$-0.483934\pi$
$109$	1.05345	0.100902	0.0504509	+	0.998727i	$0.483934\pi$
$110$	−9.23199	−0.880235
$111$	1.65076	0.156684
$112$	39.5662	3.73866
$113$	−1.83942	−0.173038	−0.0865189	−	0.996250i	$-0.527574\pi$
$113$	−1.83942	−0.173038	−0.0865189	+	0.996250i	$0.527574\pi$
$114$	12.2068	1.14328
$115$	−20.3333	−1.89609
$116$	41.7020	3.87193
$117$	1.00000	0.0924500
$118$	30.2935	2.78874
$119$	−18.3396	−1.68119
$120$	21.3386	1.94793
$121$	−8.92739	−0.811581
$122$	40.4294	3.66030
$123$	3.66176	0.330170
$124$	−16.8955	−1.51726
$125$	−10.3951	−0.929767
$126$	−7.80188	−0.695047
$127$	−1.39655	−0.123924	−0.0619618	−	0.998079i	$-0.519736\pi$
$127$	−1.39655	−0.123924	−0.0619618	+	0.998079i	$0.519736\pi$
$128$	−27.6784	−2.44645
$129$	8.42160	0.741480
$130$	−6.41264	−0.562425
$131$	−7.22283	−0.631061	−0.315531	−	0.948915i	$-0.602182\pi$
$131$	−7.22283	−0.631061	−0.315531	+	0.948915i	$0.602182\pi$
$132$	−7.66988	−0.667577
$133$	12.9970	1.12698
$134$	−19.2992	−1.66720
$135$	−2.36895	−0.203887
$136$	57.3165	4.91485
$137$	10.9533	0.935801	0.467900	−	0.883781i	$-0.345011\pi$
$137$	10.9533	0.935801	0.467900	+	0.883781i	$0.345011\pi$
$138$	−23.2344	−1.97785
$139$	10.9263	0.926760	0.463380	−	0.886160i	$-0.346636\pi$
$139$	10.9263	0.926760	0.463380	+	0.886160i	$0.346636\pi$
$140$	36.3752	3.07426
$141$	−3.58105	−0.301579
$142$	18.9413	1.58952
$143$	1.43966	0.120390
$144$	13.7279	1.14400
$145$	18.5431	1.53992
$146$	15.3191	1.26781
$147$	−1.30688	−0.107790
$148$	−8.79458	−0.722910
$149$	−20.5233	−1.68134	−0.840669	−	0.541550i	$-0.817838\pi$
$149$	−20.5233	−1.68134	−0.840669	+	0.541550i	$0.817838\pi$
$150$	1.65648	0.135251
$151$	13.4850	1.09739	0.548695	−	0.836023i	$-0.315125\pi$
$151$	13.4850	1.09739	0.548695	+	0.836023i	$0.315125\pi$
$152$	−40.6192	−3.29465
$153$	−6.36313	−0.514429
$154$	−11.2320	−0.905102
$155$	−7.51273	−0.603437
$156$	−5.32758	−0.426548
$157$	−3.64367	−0.290796	−0.145398	−	0.989373i	$-0.546446\pi$
$157$	−3.64367	−0.290796	−0.145398	+	0.989373i	$0.546446\pi$
$158$	22.1645	1.76331
$159$	8.69432	0.689504
$160$	−45.3552	−3.58564
$161$	−24.7383	−1.94965
$162$	−2.70695	−0.212678
$163$	−12.2935	−0.962903	−0.481451	−	0.876473i	$-0.659890\pi$
$163$	−12.2935	−0.962903	−0.481451	+	0.876473i	$0.659890\pi$
$164$	−19.5083	−1.52334
$165$	−3.41048	−0.265505
$166$	47.2334	3.66602
$167$	14.6416	1.13300	0.566501	−	0.824061i	$-0.308297\pi$
$167$	14.6416	1.13300	0.566501	+	0.824061i	$0.308297\pi$
$168$	25.9614	2.00296
$169$	1.00000	0.0769231
$170$	40.8045	3.12956
$171$	4.50944	0.344846
$172$	−44.8667	−3.42106
$173$	−7.54921	−0.573956	−0.286978	−	0.957937i	$-0.592651\pi$
$173$	−7.54921	−0.573956	−0.286978	+	0.957937i	$0.592651\pi$
$174$	21.1888	1.60632
$175$	1.76370	0.133323
$176$	19.7635	1.48973
$177$	11.1910	0.841167
$178$	−23.1285	−1.73356
$179$	−4.76127	−0.355874	−0.177937	−	0.984042i	$-0.556942\pi$
$179$	−4.76127	−0.355874	−0.177937	+	0.984042i	$0.556942\pi$
$180$	12.6208	0.940698
$181$	21.3015	1.58333	0.791664	−	0.610956i	$-0.209215\pi$
$181$	21.3015	1.58333	0.791664	+	0.610956i	$0.209215\pi$
$182$	−7.80188	−0.578314
$183$	14.9354	1.10406
$184$	77.3144	5.69969
$185$	−3.91058	−0.287512
$186$	−8.58463	−0.629455
$187$	−9.16072	−0.669898
$188$	19.0783	1.39143
$189$	−2.88217	−0.209647
$190$	−28.9174	−2.09789
$191$	12.2182	0.884081	0.442040	−	0.896995i	$-0.354255\pi$
$191$	12.2182	0.884081	0.442040	+	0.896995i	$0.354255\pi$
$192$	−24.3705	−1.75879
$193$	17.1808	1.23670	0.618349	−	0.785903i	$-0.287802\pi$
$193$	17.1808	1.23670	0.618349	+	0.785903i	$0.287802\pi$
$194$	39.5134	2.83690
$195$	−2.36895	−0.169644
$196$	6.96252	0.497323
$197$	25.5690	1.82171	0.910857	−	0.412723i	$-0.135422\pi$
$197$	25.5690	1.82171	0.910857	+	0.412723i	$0.135422\pi$
$198$	−3.89708	−0.276953
$199$	23.3291	1.65376	0.826878	−	0.562382i	$-0.190115\pi$
$199$	23.3291	1.65376	0.826878	+	0.562382i	$0.190115\pi$
$200$	−5.51207	−0.389762
$201$	−7.12949	−0.502876
$202$	3.36051	0.236444
$203$	22.5603	1.58343
$204$	33.9001	2.37348
$205$	−8.67453	−0.605856
$206$	−2.70695	−0.188602
$207$	−8.58325	−0.596577
$208$	13.7279	0.951861
$209$	6.49205	0.449064
$210$	18.4823	1.27540
$211$	1.87170	0.128853	0.0644264	−	0.997922i	$-0.479478\pi$
$211$	1.87170	0.128853	0.0644264	+	0.997922i	$0.479478\pi$
$212$	−46.3197	−3.18125
$213$	6.99727	0.479445
$214$	32.7811	2.24087
$215$	−19.9504	−1.36060
$216$	9.00759	0.612889
$217$	−9.14030	−0.620484
$218$	−2.85163	−0.193136
$219$	5.65916	0.382410
$220$	18.1696	1.22499
$221$	−6.36313	−0.428031
$222$	−4.46854	−0.299909
$223$	0.239564	0.0160424	0.00802120	−	0.999968i	$-0.497447\pi$
$223$	0.239564	0.0160424	0.00802120	+	0.999968i	$0.497447\pi$
$224$	−55.1810	−3.68694
$225$	0.611936	0.0407957
$226$	4.97921	0.331212
$227$	16.3059	1.08226	0.541129	−	0.840940i	$-0.317997\pi$
$227$	16.3059	1.08226	0.541129	+	0.840940i	$0.317997\pi$
$228$	−24.0244	−1.59106
$229$	0.849136	0.0561125	0.0280562	−	0.999606i	$-0.491068\pi$
$229$	0.849136	0.0561125	0.0280562	+	0.999606i	$0.491068\pi$
$230$	55.0412	3.62931
$231$	−4.14933	−0.273006
$232$	−70.5075	−4.62904
$233$	21.8722	1.43289	0.716447	−	0.697642i	$-0.245767\pi$
$233$	21.8722	1.43289	0.716447	+	0.697642i	$0.245767\pi$
$234$	−2.70695	−0.176959
$235$	8.48335	0.553392
$236$	−59.6209	−3.88099
$237$	8.18798	0.531867
$238$	49.6444	3.21797
$239$	−23.8835	−1.54489	−0.772447	−	0.635080i	$-0.780967\pi$
$239$	−23.8835	−1.54489	−0.772447	+	0.635080i	$0.780967\pi$
$240$	−32.5208	−2.09921
$241$	−12.3913	−0.798195	−0.399098	−	0.916908i	$-0.630677\pi$
$241$	−12.3913	−0.798195	−0.399098	+	0.916908i	$0.630677\pi$
$242$	24.1660	1.55345
$243$	−1.00000	−0.0641500
$244$	−79.5695	−5.09391
$245$	3.09594	0.197792
$246$	−9.91220	−0.631979
$247$	4.50944	0.286929
$248$	28.5660	1.81394
$249$	17.4489	1.10578
$250$	28.1391	1.77967
$251$	−6.43121	−0.405934	−0.202967	−	0.979186i	$-0.565058\pi$
$251$	−6.43121	−0.405934	−0.202967	+	0.979186i	$0.565058\pi$
$252$	15.3550	0.967272
$253$	−12.3569	−0.776873
$254$	3.78039	0.237203
$255$	15.0740	0.943968
$256$	26.1830	1.63644
$257$	25.7706	1.60752	0.803762	−	0.594951i	$-0.202829\pi$
$257$	25.7706	1.60752	0.803762	+	0.594951i	$0.202829\pi$
$258$	−22.7968	−1.41927
$259$	−4.75778	−0.295634
$260$	12.6208	0.782708
$261$	7.82756	0.484514
$262$	19.5518	1.20792
$263$	−20.1468	−1.24231	−0.621153	−	0.783689i	$-0.713336\pi$
$263$	−20.1468	−1.24231	−0.621153	+	0.783689i	$0.713336\pi$
$264$	12.9678	0.798115
$265$	−20.5964	−1.26523
$266$	−35.1821	−2.15716
$267$	−8.54413	−0.522892
$268$	37.9829	2.32018
$269$	2.39920	0.146282	0.0731410	−	0.997322i	$-0.476698\pi$
$269$	2.39920	0.146282	0.0731410	+	0.997322i	$0.476698\pi$
$270$	6.41264	0.390261
$271$	−22.1622	−1.34626	−0.673128	−	0.739526i	$-0.735050\pi$
$271$	−22.1622	−1.34626	−0.673128	+	0.739526i	$0.735050\pi$
$272$	−87.3527	−5.29654
$273$	−2.88217	−0.174437
$274$	−29.6499	−1.79122
$275$	0.880977	0.0531249
$276$	45.7279	2.75250
$277$	25.9668	1.56019	0.780097	−	0.625659i	$-0.215170\pi$
$277$	25.9668	1.56019	0.780097	+	0.625659i	$0.215170\pi$
$278$	−29.5771	−1.77391
$279$	−3.17133	−0.189862
$280$	−61.5013	−3.67540
$281$	−3.07531	−0.183458	−0.0917288	−	0.995784i	$-0.529239\pi$
$281$	−3.07531	−0.183458	−0.0917288	+	0.995784i	$0.529239\pi$
$282$	9.69373	0.577253
$283$	26.5909	1.58067	0.790333	−	0.612678i	$-0.209908\pi$
$283$	26.5909	1.58067	0.790333	+	0.612678i	$0.209908\pi$
$284$	−37.2785	−2.21207
$285$	−10.6827	−0.632786
$286$	−3.89708	−0.230439
$287$	−10.5538	−0.622971
$288$	−19.1457	−1.12817
$289$	23.4895	1.38173
$290$	−50.1953	−2.94757
$291$	14.5970	0.855693
$292$	−30.1496	−1.76437
$293$	3.55402	0.207628	0.103814	−	0.994597i	$-0.466895\pi$
$293$	3.55402	0.207628	0.103814	+	0.994597i	$0.466895\pi$
$294$	3.53766	0.206321
$295$	−26.5110	−1.54353
$296$	14.8694	0.864267
$297$	−1.43966	−0.0835373
$298$	55.5556	3.21825
$299$	−8.58325	−0.496382
$300$	−3.26014	−0.188224
$301$	−24.2724	−1.39904
$302$	−36.5031	−2.10052
$303$	1.24144	0.0713186
$304$	61.9054	3.55052
$305$	−35.3812	−2.02592
$306$	17.2247	0.984670
$307$	17.9963	1.02710	0.513550	−	0.858059i	$-0.328330\pi$
$307$	17.9963	1.02710	0.513550	+	0.858059i	$0.328330\pi$
$308$	22.1059	1.25960
$309$	−1.00000	−0.0568880
$310$	20.3366	1.15504
$311$	16.0683	0.911149	0.455575	−	0.890198i	$-0.349434\pi$
$311$	16.0683	0.911149	0.455575	+	0.890198i	$0.349434\pi$
$312$	9.00759	0.509954
$313$	6.74804	0.381422	0.190711	−	0.981646i	$-0.438921\pi$
$313$	6.74804	0.381422	0.190711	+	0.981646i	$0.438921\pi$
$314$	9.86322	0.556614
$315$	6.82771	0.384698
$316$	−43.6221	−2.45394
$317$	12.1331	0.681461	0.340730	−	0.940161i	$-0.389326\pi$
$317$	12.1331	0.681461	0.340730	+	0.940161i	$0.389326\pi$
$318$	−23.5351	−1.31978
$319$	11.2690	0.630943
$320$	57.7325	3.22735
$321$	12.1100	0.675913
$322$	66.9655	3.73184
$323$	−28.6942	−1.59659
$324$	5.32758	0.295977
$325$	0.611936	0.0339441
$326$	33.2779	1.84309
$327$	−1.05345	−0.0582557
$328$	32.9836	1.82122
$329$	10.3212	0.569026
$330$	9.23199	0.508204
$331$	−26.5692	−1.46038	−0.730188	−	0.683246i	$-0.760568\pi$
$331$	−26.5692	−1.46038	−0.730188	+	0.683246i	$0.760568\pi$
$332$	−92.9606	−5.10188
$333$	−1.65076	−0.0904613
$334$	−39.6341	−2.16868
$335$	16.8894	0.922768
$336$	−39.5662	−2.15851
$337$	−17.2187	−0.937964	−0.468982	−	0.883208i	$-0.655379\pi$
$337$	−17.2187	−0.937964	−0.468982	+	0.883208i	$0.655379\pi$
$338$	−2.70695	−0.147239
$339$	1.83942	0.0999034
$340$	−80.3077	−4.35530
$341$	−4.56562	−0.247242
$342$	−12.2068	−0.660070
$343$	−16.4085	−0.885976
$344$	75.8583	4.09001
$345$	20.3333	1.09471
$346$	20.4353	1.09861
$347$	4.12475	0.221428	0.110714	−	0.993852i	$-0.464686\pi$
$347$	4.12475	0.221428	0.110714	+	0.993852i	$0.464686\pi$
$348$	−41.7020	−2.23546
$349$	19.8512	1.06261	0.531305	−	0.847181i	$-0.321702\pi$
$349$	19.8512	1.06261	0.531305	+	0.847181i	$0.321702\pi$
$350$	−4.77425	−0.255194
$351$	−1.00000	−0.0533761
$352$	−27.5632	−1.46912
$353$	−16.8010	−0.894228	−0.447114	−	0.894477i	$-0.647548\pi$
$353$	−16.8010	−0.894228	−0.447114	+	0.894477i	$0.647548\pi$
$354$	−30.2935	−1.61008
$355$	−16.5762	−0.879774
$356$	45.5195	2.41253
$357$	18.3396	0.970635
$358$	12.8885	0.681180
$359$	0.192331	0.0101508	0.00507541	−	0.999987i	$-0.498384\pi$
$359$	0.192331	0.0101508	0.00507541	+	0.999987i	$0.498384\pi$
$360$	−21.3386	−1.12464
$361$	1.33509	0.0702678
$362$	−57.6621	−3.03065
$363$	8.92739	0.468567
$364$	15.3550	0.804819
$365$	−13.4063	−0.701716
$366$	−40.4294	−2.11328
$367$	−10.1489	−0.529767	−0.264884	−	0.964280i	$-0.585334\pi$
$367$	−10.1489	−0.529767	−0.264884	+	0.964280i	$0.585334\pi$
$368$	−117.830	−6.14233
$369$	−3.66176	−0.190624
$370$	10.5858	0.550327
$371$	−25.0585	−1.30097
$372$	16.8955	0.875991
$373$	−22.1810	−1.14849	−0.574245	−	0.818684i	$-0.694704\pi$
$373$	−22.1810	−1.14849	−0.574245	+	0.818684i	$0.694704\pi$
$374$	24.7976	1.28225
$375$	10.3951	0.536801
$376$	−32.2567	−1.66351
$377$	7.82756	0.403140
$378$	7.80188	0.401285
$379$	−0.781825	−0.0401597	−0.0200798	−	0.999798i	$-0.506392\pi$
$379$	−0.781825	−0.0401597	−0.0200798	+	0.999798i	$0.506392\pi$
$380$	56.9127	2.91956
$381$	1.39655	0.0715473
$382$	−33.0742	−1.69222
$383$	−19.9519	−1.01949	−0.509747	−	0.860324i	$-0.670261\pi$
$383$	−19.9519	−1.01949	−0.509747	+	0.860324i	$0.670261\pi$
$384$	27.6784	1.41246
$385$	9.82956	0.500961
$386$	−46.5075	−2.36717
$387$	−8.42160	−0.428094
$388$	−77.7669	−3.94801
$389$	−0.353209	−0.0179084	−0.00895420	−	0.999960i	$-0.502850\pi$
$389$	−0.353209	−0.0179084	−0.00895420	+	0.999960i	$0.502850\pi$
$390$	6.41264	0.324716
$391$	54.6163	2.76207
$392$	−11.7719	−0.594569
$393$	7.22283	0.364343
$394$	−69.2139	−3.48695
$395$	−19.3969	−0.975966
$396$	7.66988	0.385426
$397$	−11.2678	−0.565514	−0.282757	−	0.959192i	$-0.591249\pi$
$397$	−11.2678	−0.565514	−0.282757	+	0.959192i	$0.591249\pi$
$398$	−63.1507	−3.16546
$399$	−12.9970	−0.650662
$400$	8.40062	0.420031
$401$	35.7870	1.78712	0.893559	−	0.448946i	$-0.148201\pi$
$401$	35.7870	1.78712	0.893559	+	0.448946i	$0.148201\pi$
$402$	19.2992	0.962556
$403$	−3.17133	−0.157975
$404$	−6.61385	−0.329051
$405$	2.36895	0.117714
$406$	−61.0697	−3.03084
$407$	−2.37653	−0.117800
$408$	−57.3165	−2.83759
$409$	−5.22982	−0.258598	−0.129299	−	0.991606i	$-0.541273\pi$
$409$	−5.22982	−0.258598	−0.129299	+	0.991606i	$0.541273\pi$
$410$	23.4815	1.15967
$411$	−10.9533	−0.540285
$412$	5.32758	0.262471
$413$	−32.2543	−1.58713
$414$	23.2344	1.14191
$415$	−41.3357	−2.02909
$416$	−19.1457	−0.938694
$417$	−10.9263	−0.535065
$418$	−17.5736	−0.859555
$419$	−0.314161	−0.0153477	−0.00767387	−	0.999971i	$-0.502443\pi$
$419$	−0.314161	−0.0153477	−0.00767387	+	0.999971i	$0.502443\pi$
$420$	−36.3752	−1.77493
$421$	−18.3659	−0.895098	−0.447549	−	0.894259i	$-0.647703\pi$
$421$	−18.3659	−0.895098	−0.447549	+	0.894259i	$0.647703\pi$
$422$	−5.06659	−0.246638
$423$	3.58105	0.174117
$424$	78.3148	3.80330
$425$	−3.89383	−0.188879
$426$	−18.9413	−0.917708
$427$	−43.0463	−2.08316
$428$	−64.5169	−3.11854
$429$	−1.43966	−0.0695072
$430$	54.0047	2.60434
$431$	13.6757	0.658734	0.329367	−	0.944202i	$-0.393165\pi$
$431$	13.6757	0.658734	0.329367	+	0.944202i	$0.393165\pi$
$432$	−13.7279	−0.660486
$433$	−8.69751	−0.417976	−0.208988	−	0.977918i	$-0.567017\pi$
$433$	−8.69751	−0.417976	−0.208988	+	0.977918i	$0.567017\pi$
$434$	24.7423	1.18767
$435$	−18.5431	−0.889075
$436$	5.61232	0.268781
$437$	−38.7057	−1.85154
$438$	−15.3191	−0.731973
$439$	22.2828	1.06350	0.531749	−	0.846902i	$-0.321535\pi$
$439$	22.2828	1.06350	0.531749	+	0.846902i	$0.321535\pi$
$440$	−30.7202	−1.46453
$441$	1.30688	0.0622325
$442$	17.2247	0.819295
$443$	11.4443	0.543734	0.271867	−	0.962335i	$-0.412359\pi$
$443$	11.4443	0.543734	0.271867	+	0.962335i	$0.412359\pi$
$444$	8.79458	0.417372
$445$	20.2406	0.959498
$446$	−0.648488	−0.0307068
$447$	20.5233	0.970720
$448$	70.2398	3.31852
$449$	34.6111	1.63340	0.816699	−	0.577064i	$-0.195802\pi$
$449$	34.6111	1.63340	0.816699	+	0.577064i	$0.195802\pi$
$450$	−1.65648	−0.0780872
$451$	−5.27167	−0.248233
$452$	−9.79964	−0.460936
$453$	−13.4850	−0.633578
$454$	−44.1391	−2.07155
$455$	6.82771	0.320088
$456$	40.6192	1.90217
$457$	20.1424	0.942223	0.471111	−	0.882074i	$-0.343853\pi$
$457$	20.1424	0.942223	0.471111	+	0.882074i	$0.343853\pi$
$458$	−2.29857	−0.107405
$459$	6.36313	0.297006
$460$	−108.327	−5.05079
$461$	9.41990	0.438729	0.219364	−	0.975643i	$-0.429602\pi$
$461$	9.41990	0.438729	0.219364	+	0.975643i	$0.429602\pi$
$462$	11.2320	0.522561
$463$	−16.0433	−0.745596	−0.372798	−	0.927913i	$-0.621602\pi$
$463$	−16.0433	−0.745596	−0.372798	+	0.927913i	$0.621602\pi$
$464$	107.456	4.98853
$465$	7.51273	0.348394
$466$	−59.2069	−2.74271
$467$	−24.4262	−1.13031	−0.565155	−	0.824985i	$-0.691184\pi$
$467$	−24.4262	−1.13031	−0.565155	+	0.824985i	$0.691184\pi$
$468$	5.32758	0.246267
$469$	20.5484	0.948836
$470$	−22.9640	−1.05925
$471$	3.64367	0.167891
$472$	100.804	4.63988
$473$	−12.1242	−0.557471
$474$	−22.1645	−1.01805
$475$	2.75949	0.126614
$476$	−97.7057	−4.47833
$477$	−8.69432	−0.398085
$478$	64.6514	2.95708
$479$	29.5272	1.34913	0.674566	−	0.738215i	$-0.264331\pi$
$479$	29.5272	1.34913	0.674566	+	0.738215i	$0.264331\pi$
$480$	45.3552	2.07017
$481$	−1.65076	−0.0752684
$482$	33.5427	1.52783
$483$	24.7383	1.12563
$484$	−47.5614	−2.16188
$485$	−34.5797	−1.57018
$486$	2.70695	0.122790
$487$	−10.6990	−0.484817	−0.242408	−	0.970174i	$-0.577937\pi$
$487$	−10.6990	−0.484817	−0.242408	+	0.970174i	$0.577937\pi$
$488$	134.532	6.08997
$489$	12.2935	0.555932
$490$	−8.38056	−0.378595
$491$	−19.2654	−0.869435	−0.434717	−	0.900567i	$-0.643152\pi$
$491$	−19.2654	−0.869435	−0.434717	+	0.900567i	$0.643152\pi$
$492$	19.5083	0.879502
$493$	−49.8078	−2.24323
$494$	−12.2068	−0.549212
$495$	3.41048	0.153289
$496$	−43.5358	−1.95482
$497$	−20.1673	−0.904627
$498$	−47.2334	−2.11658
$499$	−27.9588	−1.25161	−0.625804	−	0.779980i	$-0.715229\pi$
$499$	−27.9588	−1.25161	−0.625804	+	0.779980i	$0.715229\pi$
$500$	−55.3808	−2.47670
$501$	−14.6416	−0.654139
$502$	17.4090	0.777000
$503$	−1.31404	−0.0585902	−0.0292951	−	0.999571i	$-0.509326\pi$
$503$	−1.31404	−0.0585902	−0.0292951	+	0.999571i	$0.509326\pi$
$504$	−25.9614	−1.15641
$505$	−2.94090	−0.130868
$506$	33.4496	1.48701
$507$	−1.00000	−0.0444116
$508$	−7.44022	−0.330106
$509$	25.0694	1.11118	0.555592	−	0.831455i	$-0.312492\pi$
$509$	25.0694	1.11118	0.555592	+	0.831455i	$0.312492\pi$
$510$	−40.8045	−1.80685
$511$	−16.3106	−0.721540
$512$	−15.5193	−0.685862
$513$	−4.50944	−0.199097
$514$	−69.7597	−3.07697
$515$	2.36895	0.104389
$516$	44.8667	1.97515
$517$	5.15548	0.226738
$518$	12.8791	0.565874
$519$	7.54921	0.331374
$520$	−21.3386	−0.935758
$521$	1.69693	0.0743439	0.0371720	−	0.999309i	$-0.488165\pi$
$521$	1.69693	0.0743439	0.0371720	+	0.999309i	$0.488165\pi$
$522$	−21.1888	−0.927410
$523$	28.7531	1.25728	0.628642	−	0.777695i	$-0.283611\pi$
$523$	28.7531	1.25728	0.628642	+	0.777695i	$0.283611\pi$
$524$	−38.4802	−1.68101
$525$	−1.76370	−0.0769742
$526$	54.5364	2.37790
$527$	20.1796	0.879036
$528$	−19.7635	−0.860096
$529$	50.6721	2.20314
$530$	55.7535	2.42178
$531$	−11.1910	−0.485648
$532$	69.2424	3.00204
$533$	−3.66176	−0.158608
$534$	23.1285	1.00087
$535$	−28.6880	−1.24029
$536$	−64.2196	−2.77386
$537$	4.76127	0.205464
$538$	−6.49452	−0.279999
$539$	1.88146	0.0810402
$540$	−12.6208	−0.543112
$541$	−13.1455	−0.565170	−0.282585	−	0.959242i	$-0.591192\pi$
$541$	−13.1455	−0.565170	−0.282585	+	0.959242i	$0.591192\pi$
$542$	59.9919	2.57687
$543$	−21.3015	−0.914135
$544$	121.826	5.22327
$545$	2.49556	0.106898
$546$	7.80188	0.333890
$547$	40.1230	1.71554	0.857768	−	0.514036i	$-0.171850\pi$
$547$	40.1230	1.71554	0.857768	+	0.514036i	$0.171850\pi$
$548$	58.3544	2.49278
$549$	−14.9354	−0.637427
$550$	−2.38476	−0.101687
$551$	35.2980	1.50374
$552$	−77.3144	−3.29072
$553$	−23.5991	−1.00354
$554$	−70.2908	−2.98637
$555$	3.91058	0.165995
$556$	58.2109	2.46869
$557$	19.3480	0.819800	0.409900	−	0.912130i	$-0.365564\pi$
$557$	19.3480	0.819800	0.409900	+	0.912130i	$0.365564\pi$
$558$	8.58463	0.363416
$559$	−8.42160	−0.356196
$560$	93.7305	3.96084
$561$	9.16072	0.386766
$562$	8.32471	0.351157
$563$	18.0120	0.759116	0.379558	−	0.925168i	$-0.376076\pi$
$563$	18.0120	0.759116	0.379558	+	0.925168i	$0.376076\pi$
$564$	−19.0783	−0.803343
$565$	−4.35749	−0.183321
$566$	−71.9803	−3.02556
$567$	2.88217	0.121040
$568$	63.0286	2.64462
$569$	24.0442	1.00799	0.503993	−	0.863708i	$-0.331864\pi$
$569$	24.0442	1.00799	0.503993	+	0.863708i	$0.331864\pi$
$570$	28.9174	1.21122
$571$	−20.4649	−0.856428	−0.428214	−	0.903677i	$-0.640857\pi$
$571$	−20.4649	−0.856428	−0.428214	+	0.903677i	$0.640857\pi$
$572$	7.66988	0.320694
$573$	−12.2182	−0.510424
$574$	28.5686	1.19243
$575$	−5.25240	−0.219040
$576$	24.3705	1.01544
$577$	18.4994	0.770140	0.385070	−	0.922887i	$-0.374177\pi$
$577$	18.4994	0.770140	0.385070	+	0.922887i	$0.374177\pi$
$578$	−63.5848	−2.64478
$579$	−17.1808	−0.714008
$580$	98.7900	4.10203
$581$	−50.2907	−2.08641
$582$	−39.5134	−1.63788
$583$	−12.5168	−0.518394
$584$	50.9754	2.10938
$585$	2.36895	0.0979441
$586$	−9.62055	−0.397421
$587$	−14.6655	−0.605311	−0.302655	−	0.953100i	$-0.597873\pi$
$587$	−14.6655	−0.605311	−0.302655	+	0.953100i	$0.597873\pi$
$588$	−6.96252	−0.287129
$589$	−14.3009	−0.589260
$590$	71.7638	2.95447
$591$	−25.5690	−1.05177
$592$	−22.6616	−0.931386
$593$	10.0581	0.413037	0.206518	−	0.978443i	$-0.433787\pi$
$593$	10.0581	0.413037	0.206518	+	0.978443i	$0.433787\pi$
$594$	3.89708	0.159899
$595$	−43.4457	−1.78110
$596$	−109.340	−4.47873
$597$	−23.3291	−0.954796
$598$	23.2344	0.950126
$599$	19.8599	0.811454	0.405727	−	0.913994i	$-0.367018\pi$
$599$	19.8599	0.811454	0.405727	+	0.913994i	$0.367018\pi$
$600$	5.51207	0.225029
$601$	−1.19792	−0.0488642	−0.0244321	−	0.999701i	$-0.507778\pi$
$601$	−1.19792	−0.0488642	−0.0244321	+	0.999701i	$0.507778\pi$
$602$	65.7043	2.67791
$603$	7.12949	0.290335
$604$	71.8422	2.92322
$605$	−21.1486	−0.859812
$606$	−3.36051	−0.136511
$607$	37.7620	1.53271	0.766356	−	0.642416i	$-0.222068\pi$
$607$	37.7620	1.53271	0.766356	+	0.642416i	$0.222068\pi$
$608$	−86.3363	−3.50140
$609$	−22.5603	−0.914191
$610$	95.7752	3.87783
$611$	3.58105	0.144874
$612$	−33.9001	−1.37033
$613$	−36.7133	−1.48284	−0.741418	−	0.671043i	$-0.765846\pi$
$613$	−36.7133	−1.48284	−0.741418	+	0.671043i	$0.765846\pi$
$614$	−48.7150	−1.96598
$615$	8.67453	0.349791
$616$	−37.3754	−1.50590
$617$	−33.7505	−1.35874	−0.679372	−	0.733794i	$-0.737748\pi$
$617$	−33.7505	−1.35874	−0.679372	+	0.733794i	$0.737748\pi$
$618$	2.70695	0.108890
$619$	−43.7022	−1.75654	−0.878271	−	0.478164i	$-0.841303\pi$
$619$	−43.7022	−1.75654	−0.878271	+	0.478164i	$0.841303\pi$
$620$	−40.0246	−1.60743
$621$	8.58325	0.344434
$622$	−43.4961	−1.74403
$623$	24.6256	0.986604
$624$	−13.7279	−0.549557
$625$	−27.6852	−1.10741
$626$	−18.2666	−0.730081
$627$	−6.49205	−0.259267
$628$	−19.4119	−0.774620
$629$	10.5040	0.418823
$630$	−18.4823	−0.736352
$631$	38.8267	1.54567	0.772834	−	0.634609i	$-0.218839\pi$
$631$	38.8267	1.54567	0.772834	+	0.634609i	$0.218839\pi$
$632$	73.7540	2.93378
$633$	−1.87170	−0.0743932
$634$	−32.8436	−1.30439
$635$	−3.30836	−0.131288
$636$	46.3197	1.83669
$637$	1.30688	0.0517806
$638$	−30.5046	−1.20769
$639$	−6.99727	−0.276808
$640$	−65.5687	−2.59183
$641$	21.7747	0.860048	0.430024	−	0.902818i	$-0.358505\pi$
$641$	21.7747	0.860048	0.430024	+	0.902818i	$0.358505\pi$
$642$	−32.7811	−1.29377
$643$	20.3863	0.803957	0.401979	−	0.915649i	$-0.368323\pi$
$643$	20.3863	0.803957	0.401979	+	0.915649i	$0.368323\pi$
$644$	−131.795	−5.19347
$645$	19.9504	0.785545
$646$	77.6737	3.05603
$647$	−14.0218	−0.551253	−0.275627	−	0.961265i	$-0.588885\pi$
$647$	−14.0218	−0.551253	−0.275627	+	0.961265i	$0.588885\pi$
$648$	−9.00759	−0.353852
$649$	−16.1112	−0.632419
$650$	−1.65648	−0.0649725
$651$	9.14030	0.358236
$652$	−65.4947	−2.56497
$653$	4.78811	0.187373	0.0936867	−	0.995602i	$-0.470135\pi$
$653$	4.78811	0.187373	0.0936867	+	0.995602i	$0.470135\pi$
$654$	2.85163	0.111507
$655$	−17.1105	−0.668564
$656$	−50.2684	−1.96265
$657$	−5.65916	−0.220785
$658$	−27.9389	−1.08917
$659$	19.9124	0.775676	0.387838	−	0.921728i	$-0.373222\pi$
$659$	19.9124	0.775676	0.387838	+	0.921728i	$0.373222\pi$
$660$	−18.1696	−0.707250
$661$	−3.06361	−0.119161	−0.0595804	−	0.998224i	$-0.518976\pi$
$661$	−3.06361	−0.119161	−0.0595804	+	0.998224i	$0.518976\pi$
$662$	71.9216	2.79531
$663$	6.36313	0.247124
$664$	157.173	6.09949
$665$	30.7892	1.19395
$666$	4.46854	0.173152
$667$	−67.1859	−2.60145
$668$	78.0043	3.01808
$669$	−0.239564	−0.00926209
$670$	−45.7188	−1.76627
$671$	−21.5018	−0.830068
$672$	55.1810	2.12865
$673$	−23.6961	−0.913418	−0.456709	−	0.889616i	$-0.650972\pi$
$673$	−23.6961	−0.913418	−0.456709	+	0.889616i	$0.650972\pi$
$674$	46.6103	1.79536
$675$	−0.611936	−0.0235534
$676$	5.32758	0.204907
$677$	1.74431	0.0670393	0.0335196	−	0.999438i	$-0.489328\pi$
$677$	1.74431	0.0670393	0.0335196	+	0.999438i	$0.489328\pi$
$678$	−4.97921	−0.191225
$679$	−42.0711	−1.61454
$680$	135.780	5.20693
$681$	−16.3059	−0.624842
$682$	12.3589	0.473247
$683$	36.5552	1.39875	0.699373	−	0.714757i	$-0.253463\pi$
$683$	36.5552	1.39875	0.699373	+	0.714757i	$0.253463\pi$
$684$	24.0244	0.918597
$685$	25.9478	0.991413
$686$	44.4170	1.69585
$687$	−0.849136	−0.0323966
$688$	−115.611	−4.40764
$689$	−8.69432	−0.331227
$690$	−55.0412	−2.09538
$691$	−21.7402	−0.827035	−0.413518	−	0.910496i	$-0.635700\pi$
$691$	−21.7402	−0.827035	−0.413518	+	0.910496i	$0.635700\pi$
$692$	−40.2190	−1.52890
$693$	4.14933	0.157620
$694$	−11.1655	−0.423836
$695$	25.8840	0.981835
$696$	70.5075	2.67258
$697$	23.3003	0.882560
$698$	−53.7362	−2.03394
$699$	−21.8722	−0.827282
$700$	9.39626	0.355145
$701$	51.5339	1.94641	0.973204	−	0.229942i	$-0.0738537\pi$
$701$	51.5339	1.94641	0.973204	+	0.229942i	$0.0738537\pi$
$702$	2.70695	0.102167
$703$	−7.44403	−0.280757
$704$	35.0851	1.32232
$705$	−8.48335	−0.319501
$706$	45.4795	1.71165
$707$	−3.57802	−0.134565
$708$	59.6209	2.24069
$709$	12.9890	0.487811	0.243905	−	0.969799i	$-0.421571\pi$
$709$	12.9890	0.487811	0.243905	+	0.969799i	$0.421571\pi$
$710$	44.8710	1.68398
$711$	−8.18798	−0.307073
$712$	−76.9620	−2.88427
$713$	27.2203	1.01941
$714$	−49.6444	−1.85789
$715$	3.41048	0.127545
$716$	−25.3661	−0.947974
$717$	23.8835	0.891945
$718$	−0.520630	−0.0194297
$719$	9.28966	0.346446	0.173223	−	0.984883i	$-0.444582\pi$
$719$	9.28966	0.346446	0.173223	+	0.984883i	$0.444582\pi$
$720$	32.5208	1.21198
$721$	2.88217	0.107337
$722$	−3.61402	−0.134500
$723$	12.3913	0.460838
$724$	113.485	4.21765
$725$	4.78997	0.177895
$726$	−24.1660	−0.896885
$727$	−7.44953	−0.276288	−0.138144	−	0.990412i	$-0.544114\pi$
$727$	−7.44953	−0.276288	−0.138144	+	0.990412i	$0.544114\pi$
$728$	−25.9614	−0.962193
$729$	1.00000	0.0370370
$730$	36.2901	1.34316
$731$	53.5877	1.98201
$732$	79.5695	2.94097
$733$	44.7543	1.65304	0.826520	−	0.562908i	$-0.190317\pi$
$733$	44.7543	1.65304	0.826520	+	0.562908i	$0.190317\pi$
$734$	27.4725	1.01403
$735$	−3.09594	−0.114196
$736$	164.332	6.05736
$737$	10.2640	0.378080
$738$	9.91220	0.364873
$739$	−38.5556	−1.41829	−0.709146	−	0.705061i	$-0.750919\pi$
$739$	−38.5556	−1.41829	−0.709146	+	0.705061i	$0.750919\pi$
$740$	−20.8339	−0.765871
$741$	−4.50944	−0.165659
$742$	67.8320	2.49019
$743$	−16.8829	−0.619373	−0.309686	−	0.950839i	$-0.600224\pi$
$743$	−16.8829	−0.619373	−0.309686	+	0.950839i	$0.600224\pi$
$744$	−28.5660	−1.04728
$745$	−48.6188	−1.78126
$746$	60.0429	2.19833
$747$	−17.4489	−0.638423
$748$	−48.8045	−1.78447
$749$	−34.9030	−1.27533
$750$	−28.1391	−1.02749
$751$	−46.6598	−1.70264	−0.851320	−	0.524647i	$-0.824197\pi$
$751$	−46.6598	−1.70264	−0.851320	+	0.524647i	$0.824197\pi$
$752$	49.1605	1.79270
$753$	6.43121	0.234366
$754$	−21.1888	−0.771651
$755$	31.9452	1.16261
$756$	−15.3550	−0.558455
$757$	−16.6434	−0.604916	−0.302458	−	0.953163i	$-0.597807\pi$
$757$	−16.6434	−0.604916	−0.302458	+	0.953163i	$0.597807\pi$
$758$	2.11636	0.0768697
$759$	12.3569	0.448528
$760$	−96.2250	−3.49045
$761$	19.8469	0.719448	0.359724	−	0.933059i	$-0.382871\pi$
$761$	19.8469	0.719448	0.359724	+	0.933059i	$0.382871\pi$
$762$	−3.78039	−0.136949
$763$	3.03621	0.109918
$764$	65.0936	2.35501
$765$	−15.0740	−0.545000
$766$	54.0087	1.95142
$767$	−11.1910	−0.404084
$768$	−26.1830	−0.944797
$769$	−27.9673	−1.00853	−0.504263	−	0.863550i	$-0.668236\pi$
$769$	−27.9673	−1.00853	−0.504263	+	0.863550i	$0.668236\pi$
$770$	−26.6081	−0.958890
$771$	−25.7706	−0.928104
$772$	91.5319	3.29431
$773$	−52.8731	−1.90171	−0.950856	−	0.309632i	$-0.899794\pi$
$773$	−52.8731	−1.90171	−0.950856	+	0.309632i	$0.899794\pi$
$774$	22.7968	0.819416
$775$	−1.94065	−0.0697102
$776$	131.484	4.72000
$777$	4.75778	0.170684
$778$	0.956118	0.0342785
$779$	−16.5125	−0.591622
$780$	−12.6208	−0.451896
$781$	−10.0737	−0.360464
$782$	−147.844	−5.28688
$783$	−7.82756	−0.279734
$784$	17.9408	0.640743
$785$	−8.63167	−0.308078
$786$	−19.5518	−0.697391
$787$	7.76223	0.276694	0.138347	−	0.990384i	$-0.455821\pi$
$787$	7.76223	0.276694	0.138347	+	0.990384i	$0.455821\pi$
$788$	136.221	4.85266
$789$	20.1468	0.717246
$790$	52.5066	1.86810
$791$	−5.30151	−0.188500
$792$	−12.9678	−0.460792
$793$	−14.9354	−0.530371
$794$	30.5013	1.08245
$795$	20.5964	0.730480
$796$	124.288	4.40526
$797$	18.3084	0.648515	0.324258	−	0.945969i	$-0.394886\pi$
$797$	18.3084	0.648515	0.324258	+	0.945969i	$0.394886\pi$
$798$	35.1821	1.24543
$799$	−22.7867	−0.806136
$800$	−11.7159	−0.414221
$801$	8.54413	0.301892
$802$	−96.8736	−3.42073
$803$	−8.14723	−0.287510
$804$	−37.9829	−1.33955
$805$	−58.6040	−2.06552
$806$	8.58463	0.302381
$807$	−2.39920	−0.0844559
$808$	11.1823	0.393394
$809$	32.6455	1.14776	0.573878	−	0.818941i	$-0.305438\pi$
$809$	32.6455	1.14776	0.573878	+	0.818941i	$0.305438\pi$
$810$	−6.41264	−0.225317
$811$	−20.3517	−0.714646	−0.357323	−	0.933981i	$-0.616310\pi$
$811$	−20.3517	−0.714646	−0.357323	+	0.933981i	$0.616310\pi$
$812$	120.192	4.21791
$813$	22.1622	0.777262
$814$	6.43315	0.225482
$815$	−29.1228	−1.02013
$816$	87.3527	3.05796
$817$	−37.9767	−1.32864
$818$	14.1569	0.494983
$819$	2.88217	0.100711
$820$	−46.2143	−1.61387
$821$	29.2879	1.02216	0.511078	−	0.859535i	$-0.329247\pi$
$821$	29.2879	1.02216	0.511078	+	0.859535i	$0.329247\pi$
$822$	29.6499	1.03416
$823$	−12.1835	−0.424690	−0.212345	−	0.977195i	$-0.568110\pi$
$823$	−12.1835	−0.424690	−0.212345	+	0.977195i	$0.568110\pi$
$824$	−9.00759	−0.313794
$825$	−0.880977	−0.0306717
$826$	87.3109	3.03793
$827$	−28.6393	−0.995885	−0.497942	−	0.867210i	$-0.665911\pi$
$827$	−28.6393	−0.995885	−0.497942	+	0.867210i	$0.665911\pi$
$828$	−45.7279	−1.58916
$829$	−12.8446	−0.446112	−0.223056	−	0.974806i	$-0.571603\pi$
$829$	−12.8446	−0.446112	−0.223056	+	0.974806i	$0.571603\pi$
$830$	111.894	3.88389
$831$	−25.9668	−0.900778
$832$	24.3705	0.844895
$833$	−8.31586	−0.288128
$834$	29.5771	1.02417
$835$	34.6853	1.20033
$836$	34.5869	1.19621
$837$	3.17133	0.109617
$838$	0.850417	0.0293772
$839$	−28.2167	−0.974147	−0.487074	−	0.873361i	$-0.661936\pi$
$839$	−28.2167	−0.974147	−0.487074	+	0.873361i	$0.661936\pi$
$840$	61.5013	2.12200
$841$	32.2708	1.11278
$842$	49.7155	1.71331
$843$	3.07531	0.105919
$844$	9.97161	0.343237
$845$	2.36895	0.0814944
$846$	−9.69373	−0.333277
$847$	−25.7302	−0.884101
$848$	−119.355	−4.09867
$849$	−26.5909	−0.912598
$850$	10.5404	0.361533
$851$	14.1689	0.485704
$852$	37.2785	1.27714
$853$	38.9198	1.33259	0.666294	−	0.745689i	$-0.267880\pi$
$853$	38.9198	1.33259	0.666294	+	0.745689i	$0.267880\pi$
$854$	116.524	3.98737
$855$	10.6827	0.365339
$856$	109.082	3.72834
$857$	18.7773	0.641419	0.320709	−	0.947178i	$-0.396079\pi$
$857$	18.7773	0.641419	0.320709	+	0.947178i	$0.396079\pi$
$858$	3.89708	0.133044
$859$	−57.5886	−1.96490	−0.982449	−	0.186531i	$-0.940276\pi$
$859$	−57.5886	−1.96490	−0.982449	+	0.186531i	$0.940276\pi$
$860$	−106.287	−3.62436
$861$	10.5538	0.359672
$862$	−37.0194	−1.26088
$863$	1.32793	0.0452032	0.0226016	−	0.999745i	$-0.492805\pi$
$863$	1.32793	0.0452032	0.0226016	+	0.999745i	$0.492805\pi$
$864$	19.1457	0.651349
$865$	−17.8837	−0.608065
$866$	23.5437	0.800049
$867$	−23.4895	−0.797744
$868$	−48.6956	−1.65284
$869$	−11.7879	−0.399876
$870$	50.1953	1.70178
$871$	7.12949	0.241574
$872$	−9.48901	−0.321338
$873$	−14.5970	−0.494035
$874$	104.774	3.54404
$875$	−29.9604	−1.01285
$876$	30.1496	1.01866
$877$	9.61164	0.324562	0.162281	−	0.986745i	$-0.448115\pi$
$877$	9.61164	0.324562	0.162281	+	0.986745i	$0.448115\pi$
$878$	−60.3183	−2.03565
$879$	−3.55402	−0.119874
$880$	46.8188	1.57826
$881$	12.3172	0.414976	0.207488	−	0.978238i	$-0.433471\pi$
$881$	12.3172	0.414976	0.207488	+	0.978238i	$0.433471\pi$
$882$	−3.53766	−0.119119
$883$	−32.8328	−1.10491	−0.552456	−	0.833542i	$-0.686309\pi$
$883$	−32.8328	−1.10491	−0.552456	+	0.833542i	$0.686309\pi$
$884$	−33.9001	−1.14018
$885$	26.5110	0.891156
$886$	−30.9791	−1.04076
$887$	−19.8148	−0.665317	−0.332658	−	0.943047i	$-0.607946\pi$
$887$	−19.8148	−0.665317	−0.332658	+	0.943047i	$0.607946\pi$
$888$	−14.8694	−0.498985
$889$	−4.02508	−0.134997
$890$	−54.7904	−1.83658
$891$	1.43966	0.0482303
$892$	1.27630	0.0427336
$893$	16.1486	0.540391
$894$	−55.5556	−1.85806
$895$	−11.2792	−0.377023
$896$	−79.7737	−2.66505
$897$	8.58325	0.286586
$898$	−93.6904	−3.12649
$899$	−24.8238	−0.827919
$900$	3.26014	0.108671
$901$	55.3231	1.84308
$902$	14.2702	0.475144
$903$	24.2724	0.807736
$904$	16.5687	0.551067
$905$	50.4623	1.67742
$906$	36.5031	1.21273
$907$	−25.0782	−0.832709	−0.416355	−	0.909202i	$-0.636692\pi$
$907$	−25.0782	−0.832709	−0.416355	+	0.909202i	$0.636692\pi$
$908$	86.8707	2.88291
$909$	−1.24144	−0.0411758
$910$	−18.4823	−0.612682
$911$	2.51233	0.0832372	0.0416186	−	0.999134i	$-0.486749\pi$
$911$	2.51233	0.0832372	0.0416186	+	0.999134i	$0.486749\pi$
$912$	−61.9054	−2.04989
$913$	−25.1205	−0.831366
$914$	−54.5245	−1.80351
$915$	35.3812	1.16967
$916$	4.52384	0.149472
$917$	−20.8174	−0.687451
$918$	−17.2247	−0.568499
$919$	26.0344	0.858795	0.429397	−	0.903116i	$-0.358726\pi$
$919$	26.0344	0.858795	0.429397	+	0.903116i	$0.358726\pi$
$920$	183.154	6.03841
$921$	−17.9963	−0.592997
$922$	−25.4992	−0.839772
$923$	−6.99727	−0.230318
$924$	−22.1059	−0.727230
$925$	−1.01016	−0.0332139
$926$	43.4284	1.42715
$927$	1.00000	0.0328443
$928$	−149.864	−4.91953
$929$	−51.6600	−1.69491	−0.847455	−	0.530867i	$-0.821866\pi$
$929$	−51.6600	−1.69491	−0.847455	+	0.530867i	$0.821866\pi$
$930$	−20.3366	−0.666863
$931$	5.89331	0.193145
$932$	116.526	3.81693
$933$	−16.0683	−0.526052
$934$	66.1205	2.16353
$935$	−21.7013	−0.709709
$936$	−9.00759	−0.294422
$937$	−45.2002	−1.47663	−0.738313	−	0.674458i	$-0.764377\pi$
$937$	−45.2002	−1.47663	−0.738313	+	0.674458i	$0.764377\pi$
$938$	−55.6235	−1.81617
$939$	−6.74804	−0.220214
$940$	45.1957	1.47412
$941$	−13.7137	−0.447052	−0.223526	−	0.974698i	$-0.571757\pi$
$941$	−13.7137	−0.447052	−0.223526	+	0.974698i	$0.571757\pi$
$942$	−9.86322	−0.321361
$943$	31.4298	1.02349
$944$	−153.629	−5.00021
$945$	−6.82771	−0.222106
$946$	32.8196	1.06706
$947$	−17.7283	−0.576093	−0.288047	−	0.957616i	$-0.593006\pi$
$947$	−17.7283	−0.576093	−0.288047	+	0.957616i	$0.593006\pi$
$948$	43.6221	1.41678
$949$	−5.65916	−0.183704
$950$	−7.46981	−0.242353
$951$	−12.1331	−0.393442
$952$	165.196	5.35402
$953$	25.3677	0.821742	0.410871	−	0.911694i	$-0.365225\pi$
$953$	25.3677	0.821742	0.410871	+	0.911694i	$0.365225\pi$
$954$	23.5351	0.761976
$955$	28.9444	0.936620
$956$	−127.241	−4.11527
$957$	−11.2690	−0.364275
$958$	−79.9286	−2.58238
$959$	31.5691	1.01942
$960$	−57.7325	−1.86331
$961$	−20.9427	−0.675570
$962$	4.46854	0.144071
$963$	−12.1100	−0.390239
$964$	−66.0157	−2.12622
$965$	40.7004	1.31019
$966$	−66.9655	−2.15458
$967$	40.8239	1.31281	0.656403	−	0.754410i	$-0.272077\pi$
$967$	40.8239	1.31281	0.656403	+	0.754410i	$0.272077\pi$
$968$	80.4143	2.58461
$969$	28.6942	0.921790
$970$	93.6055	3.00549
$971$	−47.5563	−1.52615	−0.763077	−	0.646308i	$-0.776312\pi$
$971$	−47.5563	−1.52615	−0.763077	+	0.646308i	$0.776312\pi$
$972$	−5.32758	−0.170882
$973$	31.4915	1.00957
$974$	28.9616	0.927989
$975$	−0.611936	−0.0195976
$976$	−205.032	−6.56292
$977$	−2.10535	−0.0673561	−0.0336780	−	0.999433i	$-0.510722\pi$
$977$	−2.10535	−0.0673561	−0.0336780	+	0.999433i	$0.510722\pi$
$978$	−33.2779	−1.06411
$979$	12.3006	0.393129
$980$	16.4939	0.526877
$981$	1.05345	0.0336339
$982$	52.1504	1.66419
$983$	9.75992	0.311293	0.155646	−	0.987813i	$-0.450254\pi$
$983$	9.75992	0.311293	0.155646	+	0.987813i	$0.450254\pi$
$984$	−32.9836	−1.05148
$985$	60.5717	1.92997
$986$	134.827	4.29378
$987$	−10.3212	−0.328527
$988$	24.0244	0.764319
$989$	72.2847	2.29852
$990$	−9.23199	−0.293412
$991$	−8.42091	−0.267499	−0.133750	−	0.991015i	$-0.542702\pi$
$991$	−8.42091	−0.267499	−0.133750	+	0.991015i	$0.542702\pi$
$992$	60.7172	1.92777
$993$	26.5692	0.843149
$994$	54.5919	1.73155
$995$	55.2655	1.75203
$996$	92.9606	2.94557
$997$	57.6328	1.82525	0.912624	−	0.408799i	$-0.134052\pi$
$997$	57.6328	1.82525	0.912624	+	0.408799i	$0.134052\pi$
$998$	75.6831	2.39571
$999$	1.65076	0.0522279

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.h.1.2	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.h.1.2	✓	25	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:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.70695 q^{2} -1.00000 q^{3} +5.32758 q^{4} +2.36895 q^{5} +2.70695 q^{6} +2.88217 q^{7} -9.00759 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.70695 q^{2} -1.00000 q^{3} +5.32758 q^{4} +2.36895 q^{5} +2.70695 q^{6} +2.88217 q^{7} -9.00759 q^{8} +1.00000 q^{9} -6.41264 q^{10} +1.43966 q^{11} -5.32758 q^{12} +1.00000 q^{13} -7.80188 q^{14} -2.36895 q^{15} +13.7279 q^{16} -6.36313 q^{17} -2.70695 q^{18} +4.50944 q^{19} +12.6208 q^{20} -2.88217 q^{21} -3.89708 q^{22} -8.58325 q^{23} +9.00759 q^{24} +0.611936 q^{25} -2.70695 q^{26} -1.00000 q^{27} +15.3550 q^{28} +7.82756 q^{29} +6.41264 q^{30} -3.17133 q^{31} -19.1457 q^{32} -1.43966 q^{33} +17.2247 q^{34} +6.82771 q^{35} +5.32758 q^{36} -1.65076 q^{37} -12.2068 q^{38} -1.00000 q^{39} -21.3386 q^{40} -3.66176 q^{41} +7.80188 q^{42} -8.42160 q^{43} +7.66988 q^{44} +2.36895 q^{45} +23.2344 q^{46} +3.58105 q^{47} -13.7279 q^{48} +1.30688 q^{49} -1.65648 q^{50} +6.36313 q^{51} +5.32758 q^{52} -8.69432 q^{53} +2.70695 q^{54} +3.41048 q^{55} -25.9614 q^{56} -4.50944 q^{57} -21.1888 q^{58} -11.1910 q^{59} -12.6208 q^{60} -14.9354 q^{61} +8.58463 q^{62} +2.88217 q^{63} +24.3705 q^{64} +2.36895 q^{65} +3.89708 q^{66} +7.12949 q^{67} -33.9001 q^{68} +8.58325 q^{69} -18.4823 q^{70} -6.99727 q^{71} -9.00759 q^{72} -5.65916 q^{73} +4.46854 q^{74} -0.611936 q^{75} +24.0244 q^{76} +4.14933 q^{77} +2.70695 q^{78} -8.18798 q^{79} +32.5208 q^{80} +1.00000 q^{81} +9.91220 q^{82} -17.4489 q^{83} -15.3550 q^{84} -15.0740 q^{85} +22.7968 q^{86} -7.82756 q^{87} -12.9678 q^{88} +8.54413 q^{89} -6.41264 q^{90} +2.88217 q^{91} -45.7279 q^{92} +3.17133 q^{93} -9.69373 q^{94} +10.6827 q^{95} +19.1457 q^{96} -14.5970 q^{97} -3.53766 q^{98} +1.43966 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 4 q^{2} - 25 q^{3} + 28 q^{4} - 5 q^{5} + 4 q^{6} - 7 q^{7} - 9 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q - 4 * q^2 - 25 * q^3 + 28 * q^4 - 5 * q^5 + 4 * q^6 - 7 * q^7 - 9 * q^8 + 25 * q^9	\( 25 q - 4 q^{2} - 25 q^{3} + 28 q^{4} - 5 q^{5} + 4 q^{6} - 7 q^{7} - 9 q^{8} + 25 q^{9} - 12 q^{10} - 23 q^{11} - 28 q^{12} + 25 q^{13} + 5 q^{15} + 26 q^{16} - 14 q^{17} - 4 q^{18} - 4 q^{19} - 12 q^{20} + 7 q^{21} - 7 q^{22} - 47 q^{23} + 9 q^{24} + 26 q^{25} - 4 q^{26} - 25 q^{27} - 38 q^{28} + 6 q^{29} + 12 q^{30} - 8 q^{31} - 62 q^{32} + 23 q^{33} + 25 q^{34} + 28 q^{36} - 20 q^{37} - 2 q^{38} - 25 q^{39} - 8 q^{40} - 33 q^{41} - 13 q^{43} - 13 q^{44} - 5 q^{45} - 21 q^{46} - 48 q^{47} - 26 q^{48} + 40 q^{49} - 9 q^{50} + 14 q^{51} + 28 q^{52} - 24 q^{53} + 4 q^{54} - 2 q^{55} - 14 q^{56} + 4 q^{57} - 31 q^{58} - 36 q^{59} + 12 q^{60} + 25 q^{61} - 7 q^{62} - 7 q^{63} + 45 q^{64} - 5 q^{65} + 7 q^{66} - 2 q^{67} - 32 q^{68} + 47 q^{69} - 13 q^{70} - 60 q^{71} - 9 q^{72} + 28 q^{73} - 16 q^{74} - 26 q^{75} - 12 q^{76} - 17 q^{77} + 4 q^{78} - 29 q^{79} - 88 q^{80} + 25 q^{81} - 22 q^{82} - 71 q^{83} + 38 q^{84} + 3 q^{85} - 3 q^{86} - 6 q^{87} + 23 q^{88} - 46 q^{89} - 12 q^{90} - 7 q^{91} - 69 q^{92} + 8 q^{93} + 4 q^{94} - 47 q^{95} + 62 q^{96} - 14 q^{97} - 71 q^{98} - 23 q^{99}+O(q^{100}) \) 25 * q - 4 * q^2 - 25 * q^3 + 28 * q^4 - 5 * q^5 + 4 * q^6 - 7 * q^7 - 9 * q^8 + 25 * q^9 - 12 * q^10 - 23 * q^11 - 28 * q^12 + 25 * q^13 + 5 * q^15 + 26 * q^16 - 14 * q^17 - 4 * q^18 - 4 * q^19 - 12 * q^20 + 7 * q^21 - 7 * q^22 - 47 * q^23 + 9 * q^24 + 26 * q^25 - 4 * q^26 - 25 * q^27 - 38 * q^28 + 6 * q^29 + 12 * q^30 - 8 * q^31 - 62 * q^32 + 23 * q^33 + 25 * q^34 + 28 * q^36 - 20 * q^37 - 2 * q^38 - 25 * q^39 - 8 * q^40 - 33 * q^41 - 13 * q^43 - 13 * q^44 - 5 * q^45 - 21 * q^46 - 48 * q^47 - 26 * q^48 + 40 * q^49 - 9 * q^50 + 14 * q^51 + 28 * q^52 - 24 * q^53 + 4 * q^54 - 2 * q^55 - 14 * q^56 + 4 * q^57 - 31 * q^58 - 36 * q^59 + 12 * q^60 + 25 * q^61 - 7 * q^62 - 7 * q^63 + 45 * q^64 - 5 * q^65 + 7 * q^66 - 2 * q^67 - 32 * q^68 + 47 * q^69 - 13 * q^70 - 60 * q^71 - 9 * q^72 + 28 * q^73 - 16 * q^74 - 26 * q^75 - 12 * q^76 - 17 * q^77 + 4 * q^78 - 29 * q^79 - 88 * q^80 + 25 * q^81 - 22 * q^82 - 71 * q^83 + 38 * q^84 + 3 * q^85 - 3 * q^86 - 6 * q^87 + 23 * q^88 - 46 * q^89 - 12 * q^90 - 7 * q^91 - 69 * q^92 + 8 * q^93 + 4 * q^94 - 47 * q^95 + 62 * q^96 - 14 * q^97 - 71 * q^98 - 23 * q^99

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