LMFDB - Embedded newform 889.2.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [889,2,Mod(1,889)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(889, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("889.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 889 = 7 \cdot 127 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	889.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:	$7.09870073969$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 8 x^{19} + 152 x^{17} - 274 x^{16} - 1061 x^{15} + 3125 x^{14} + 2977 x^{13} - 15474 x^{12} + \cdots + 31 $ x^20 - 8x^19 + 152x^17 - 274x^16 - 1061x^15 + 3125x^14 + 2977x^13 - 15474x^12 - 56x^11 + 39579x^10 - 17664x^9 - 52271x^8 + 35701x^7 + 32493x^6 - 25504x^5 - 8607x^4 + 6812x^3 + 609x^2 - 425x + 31
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.48579$ of defining polynomial
Character	$\chi$	$=$	889.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.48579 q^{2} +1.07586 q^{3} +4.17918 q^{4} +3.35246 q^{5} -2.67437 q^{6} +1.00000 q^{7} -5.41698 q^{8} -1.84252 q^{9} +O(q^{10})$	\(q-2.48579 q^{2} +1.07586 q^{3} +4.17918 q^{4} +3.35246 q^{5} -2.67437 q^{6} +1.00000 q^{7} -5.41698 q^{8} -1.84252 q^{9} -8.33354 q^{10} +1.56393 q^{11} +4.49621 q^{12} +0.560792 q^{13} -2.48579 q^{14} +3.60678 q^{15} +5.10716 q^{16} -1.90633 q^{17} +4.58014 q^{18} +3.15361 q^{19} +14.0105 q^{20} +1.07586 q^{21} -3.88760 q^{22} +7.59584 q^{23} -5.82792 q^{24} +6.23902 q^{25} -1.39401 q^{26} -5.20988 q^{27} +4.17918 q^{28} +7.34983 q^{29} -8.96572 q^{30} -3.72875 q^{31} -1.86138 q^{32} +1.68257 q^{33} +4.73874 q^{34} +3.35246 q^{35} -7.70023 q^{36} -4.98201 q^{37} -7.83922 q^{38} +0.603334 q^{39} -18.1602 q^{40} +6.64574 q^{41} -2.67437 q^{42} -1.33203 q^{43} +6.53592 q^{44} -6.17700 q^{45} -18.8817 q^{46} -2.63698 q^{47} +5.49459 q^{48} +1.00000 q^{49} -15.5089 q^{50} -2.05094 q^{51} +2.34365 q^{52} -2.87115 q^{53} +12.9507 q^{54} +5.24301 q^{55} -5.41698 q^{56} +3.39284 q^{57} -18.2702 q^{58} -11.5527 q^{59} +15.0734 q^{60} +0.252927 q^{61} +9.26890 q^{62} -1.84252 q^{63} -5.58731 q^{64} +1.88004 q^{65} -4.18252 q^{66} -1.89376 q^{67} -7.96688 q^{68} +8.17206 q^{69} -8.33354 q^{70} +7.84857 q^{71} +9.98092 q^{72} +10.3325 q^{73} +12.3843 q^{74} +6.71231 q^{75} +13.1795 q^{76} +1.56393 q^{77} -1.49976 q^{78} -1.28541 q^{79} +17.1216 q^{80} -0.0775297 q^{81} -16.5199 q^{82} +9.61160 q^{83} +4.49621 q^{84} -6.39090 q^{85} +3.31116 q^{86} +7.90739 q^{87} -8.47177 q^{88} -1.02178 q^{89} +15.3547 q^{90} +0.560792 q^{91} +31.7443 q^{92} -4.01161 q^{93} +6.55498 q^{94} +10.5724 q^{95} -2.00258 q^{96} -0.963940 q^{97} -2.48579 q^{98} -2.88157 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 8 q^{2} + 24 q^{4} + 3 q^{5} + 6 q^{6} + 20 q^{7} + 24 q^{8} + 30 q^{9}+O(q^{10}) $ 20 * q + 8 * q^2 + 24 * q^4 + 3 * q^5 + 6 * q^6 + 20 * q^7 + 24 * q^8 + 30 * q^9	\( 20 q + 8 q^{2} + 24 q^{4} + 3 q^{5} + 6 q^{6} + 20 q^{7} + 24 q^{8} + 30 q^{9} - 8 q^{10} + 26 q^{11} - 4 q^{12} - 4 q^{13} + 8 q^{14} + 10 q^{15} + 24 q^{16} + 4 q^{17} + 5 q^{18} + q^{19} - 2 q^{20} + q^{22} + 31 q^{23} - 6 q^{24} + 27 q^{25} + 4 q^{26} - 18 q^{27} + 24 q^{28} + 16 q^{29} - 5 q^{30} + 6 q^{31} + 41 q^{32} - 18 q^{33} - 10 q^{34} + 3 q^{35} + 18 q^{36} + 2 q^{37} + 3 q^{38} + 43 q^{39} - 38 q^{40} + 25 q^{41} + 6 q^{42} + 13 q^{43} + 66 q^{44} - 2 q^{45} + 20 q^{46} + 19 q^{47} - 16 q^{48} + 20 q^{49} - 4 q^{50} + 4 q^{51} + 20 q^{52} + 24 q^{53} + 5 q^{54} - 3 q^{55} + 24 q^{56} - 4 q^{57} + 12 q^{58} + 23 q^{59} + 24 q^{60} - 27 q^{61} + 7 q^{62} + 30 q^{63} + 2 q^{64} + 26 q^{65} + 26 q^{66} + 9 q^{67} - 25 q^{68} - 3 q^{69} - 8 q^{70} + 63 q^{71} + 27 q^{72} - 21 q^{73} + 21 q^{74} - 52 q^{75} - 10 q^{76} + 26 q^{77} - 70 q^{78} + 18 q^{79} - 23 q^{80} + 40 q^{81} - 42 q^{82} - q^{83} - 4 q^{84} - 41 q^{85} - 12 q^{86} - 9 q^{87} + 57 q^{88} - 16 q^{89} + q^{90} - 4 q^{91} + 17 q^{92} - 41 q^{93} + 7 q^{94} + 75 q^{95} - 81 q^{96} - 32 q^{97} + 8 q^{98} + 15 q^{99}+O(q^{100}) \) 20 * q + 8 * q^2 + 24 * q^4 + 3 * q^5 + 6 * q^6 + 20 * q^7 + 24 * q^8 + 30 * q^9 - 8 * q^10 + 26 * q^11 - 4 * q^12 - 4 * q^13 + 8 * q^14 + 10 * q^15 + 24 * q^16 + 4 * q^17 + 5 * q^18 + q^19 - 2 * q^20 + q^22 + 31 * q^23 - 6 * q^24 + 27 * q^25 + 4 * q^26 - 18 * q^27 + 24 * q^28 + 16 * q^29 - 5 * q^30 + 6 * q^31 + 41 * q^32 - 18 * q^33 - 10 * q^34 + 3 * q^35 + 18 * q^36 + 2 * q^37 + 3 * q^38 + 43 * q^39 - 38 * q^40 + 25 * q^41 + 6 * q^42 + 13 * q^43 + 66 * q^44 - 2 * q^45 + 20 * q^46 + 19 * q^47 - 16 * q^48 + 20 * q^49 - 4 * q^50 + 4 * q^51 + 20 * q^52 + 24 * q^53 + 5 * q^54 - 3 * q^55 + 24 * q^56 - 4 * q^57 + 12 * q^58 + 23 * q^59 + 24 * q^60 - 27 * q^61 + 7 * q^62 + 30 * q^63 + 2 * q^64 + 26 * q^65 + 26 * q^66 + 9 * q^67 - 25 * q^68 - 3 * q^69 - 8 * q^70 + 63 * q^71 + 27 * q^72 - 21 * q^73 + 21 * q^74 - 52 * q^75 - 10 * q^76 + 26 * q^77 - 70 * q^78 + 18 * q^79 - 23 * q^80 + 40 * q^81 - 42 * q^82 - q^83 - 4 * q^84 - 41 * q^85 - 12 * q^86 - 9 * q^87 + 57 * q^88 - 16 * q^89 + q^90 - 4 * q^91 + 17 * q^92 - 41 * q^93 + 7 * q^94 + 75 * q^95 - 81 * q^96 - 32 * q^97 + 8 * q^98 + 15 * 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 $

$2$	−2.48579	−1.75772	−0.878861	−	0.477078i	$-0.841696\pi$
$2$	−2.48579	−1.75772	−0.878861	+	0.477078i	$0.841696\pi$
$3$	1.07586	0.621148	0.310574	−	0.950549i	$-0.399479\pi$
$3$	1.07586	0.621148	0.310574	+	0.950549i	$0.399479\pi$
$4$	4.17918	2.08959
$5$	3.35246	1.49927	0.749634	−	0.661853i	$-0.230230\pi$
$5$	3.35246	1.49927	0.749634	+	0.661853i	$0.230230\pi$
$6$	−2.67437	−1.09181
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−5.41698	−1.91519
$9$	−1.84252	−0.614175
$10$	−8.33354	−2.63530
$11$	1.56393	0.471542	0.235771	−	0.971809i	$-0.424239\pi$
$11$	1.56393	0.471542	0.235771	+	0.971809i	$0.424239\pi$
$12$	4.49621	1.29794
$13$	0.560792	0.155536	0.0777679	−	0.996971i	$-0.475221\pi$
$13$	0.560792	0.155536	0.0777679	+	0.996971i	$0.475221\pi$
$14$	−2.48579	−0.664357
$15$	3.60678	0.931268
$16$	5.10716	1.27679
$17$	−1.90633	−0.462352	−0.231176	−	0.972912i	$-0.574257\pi$
$17$	−1.90633	−0.462352	−0.231176	+	0.972912i	$0.574257\pi$
$18$	4.58014	1.07955
$19$	3.15361	0.723487	0.361743	−	0.932278i	$-0.382182\pi$
$19$	3.15361	0.723487	0.361743	+	0.932278i	$0.382182\pi$
$20$	14.0105	3.13285
$21$	1.07586	0.234772
$22$	−3.88760	−0.828839
$23$	7.59584	1.58384	0.791921	−	0.610624i	$-0.209081\pi$
$23$	7.59584	1.58384	0.791921	+	0.610624i	$0.209081\pi$
$24$	−5.82792	−1.18962
$25$	6.23902	1.24780
$26$	−1.39401	−0.273389
$27$	−5.20988	−1.00264
$28$	4.17918	0.789790
$29$	7.34983	1.36483	0.682415	−	0.730965i	$-0.260930\pi$
$29$	7.34983	1.36483	0.682415	+	0.730965i	$0.260930\pi$
$30$	−8.96572	−1.63691
$31$	−3.72875	−0.669703	−0.334851	−	0.942271i	$-0.608686\pi$
$31$	−3.72875	−0.669703	−0.334851	+	0.942271i	$0.608686\pi$
$32$	−1.86138	−0.329048
$33$	1.68257	0.292897
$34$	4.73874	0.812687
$35$	3.35246	0.566670
$36$	−7.70023	−1.28337
$37$	−4.98201	−0.819038	−0.409519	−	0.912302i	$-0.634303\pi$
$37$	−4.98201	−0.819038	−0.409519	+	0.912302i	$0.634303\pi$
$38$	−7.83922	−1.27169
$39$	0.603334	0.0966108
$40$	−18.1602	−2.87139
$41$	6.64574	1.03789	0.518945	−	0.854808i	$-0.326325\pi$
$41$	6.64574	1.03789	0.518945	+	0.854808i	$0.326325\pi$
$42$	−2.67437	−0.412664
$43$	−1.33203	−0.203133	−0.101567	−	0.994829i	$-0.532386\pi$
$43$	−1.33203	−0.203133	−0.101567	+	0.994829i	$0.532386\pi$
$44$	6.53592	0.985328
$45$	−6.17700	−0.920813
$46$	−18.8817	−2.78395
$47$	−2.63698	−0.384642	−0.192321	−	0.981332i	$-0.561602\pi$
$47$	−2.63698	−0.384642	−0.192321	+	0.981332i	$0.561602\pi$
$48$	5.49459	0.793075
$49$	1.00000	0.142857
$50$	−15.5089	−2.19329
$51$	−2.05094	−0.287189
$52$	2.34365	0.325006
$53$	−2.87115	−0.394383	−0.197191	−	0.980365i	$-0.563182\pi$
$53$	−2.87115	−0.394383	−0.197191	+	0.980365i	$0.563182\pi$
$54$	12.9507	1.76237
$55$	5.24301	0.706967
$56$	−5.41698	−0.723875
$57$	3.39284	0.449393
$58$	−18.2702	−2.39899
$59$	−11.5527	−1.50403	−0.752017	−	0.659144i	$-0.770919\pi$
$59$	−11.5527	−1.50403	−0.752017	+	0.659144i	$0.770919\pi$
$60$	15.0734	1.94597
$61$	0.252927	0.0323840	0.0161920	−	0.999869i	$-0.494846\pi$
$61$	0.252927	0.0323840	0.0161920	+	0.999869i	$0.494846\pi$
$62$	9.26890	1.17715
$63$	−1.84252	−0.232136
$64$	−5.58731	−0.698414
$65$	1.88004	0.233190
$66$	−4.18252	−0.514832
$67$	−1.89376	−0.231359	−0.115680	−	0.993287i	$-0.536905\pi$
$67$	−1.89376	−0.231359	−0.115680	+	0.993287i	$0.536905\pi$
$68$	−7.96688	−0.966126
$69$	8.17206	0.983800
$70$	−8.33354	−0.996048
$71$	7.84857	0.931454	0.465727	−	0.884929i	$-0.345793\pi$
$71$	7.84857	0.931454	0.465727	+	0.884929i	$0.345793\pi$
$72$	9.98092	1.17626
$73$	10.3325	1.20933	0.604664	−	0.796481i	$-0.293307\pi$
$73$	10.3325	1.20933	0.604664	+	0.796481i	$0.293307\pi$
$74$	12.3843	1.43964
$75$	6.71231	0.775071
$76$	13.1795	1.51179
$77$	1.56393	0.178226
$78$	−1.49976	−0.169815
$79$	−1.28541	−0.144620	−0.0723099	−	0.997382i	$-0.523037\pi$
$79$	−1.28541	−0.144620	−0.0723099	+	0.997382i	$0.523037\pi$
$80$	17.1216	1.91425
$81$	−0.0775297	−0.00861441
$82$	−16.5199	−1.82432
$83$	9.61160	1.05501	0.527505	−	0.849552i	$-0.323128\pi$
$83$	9.61160	1.05501	0.527505	+	0.849552i	$0.323128\pi$
$84$	4.49621	0.490577
$85$	−6.39090	−0.693190
$86$	3.31116	0.357052
$87$	7.90739	0.847761
$88$	−8.47177	−0.903093
$89$	−1.02178	−0.108309	−0.0541543	−	0.998533i	$-0.517246\pi$
$89$	−1.02178	−0.108309	−0.0541543	+	0.998533i	$0.517246\pi$
$90$	15.3547	1.61853
$91$	0.560792	0.0587870
$92$	31.7443	3.30958
$93$	−4.01161	−0.415985
$94$	6.55498	0.676094
$95$	10.5724	1.08470
$96$	−2.00258	−0.204388
$97$	−0.963940	−0.0978733	−0.0489367	−	0.998802i	$-0.515583\pi$
$97$	−0.963940	−0.0978733	−0.0489367	+	0.998802i	$0.515583\pi$
$98$	−2.48579	−0.251103
$99$	−2.88157	−0.289609
$100$	26.0740	2.60740
$101$	11.4022	1.13456	0.567279	−	0.823526i	$-0.307996\pi$
$101$	11.4022	1.13456	0.567279	+	0.823526i	$0.307996\pi$
$102$	5.09822	0.504799
$103$	−17.5045	−1.72477	−0.862384	−	0.506255i	$-0.831029\pi$
$103$	−17.5045	−1.72477	−0.862384	+	0.506255i	$0.831029\pi$
$104$	−3.03780	−0.297881
$105$	3.60678	0.351986
$106$	7.13709	0.693215
$107$	−6.07352	−0.587150	−0.293575	−	0.955936i	$-0.594845\pi$
$107$	−6.07352	−0.587150	−0.293575	+	0.955936i	$0.594845\pi$
$108$	−21.7730	−2.09511
$109$	−5.32495	−0.510038	−0.255019	−	0.966936i	$-0.582082\pi$
$109$	−5.32495	−0.510038	−0.255019	+	0.966936i	$0.582082\pi$
$110$	−13.0330	−1.24265
$111$	−5.35995	−0.508744
$112$	5.10716	0.482581
$113$	16.4435	1.54687	0.773437	−	0.633874i	$-0.218536\pi$
$113$	16.4435	1.54687	0.773437	+	0.633874i	$0.218536\pi$
$114$	−8.43390	−0.789907
$115$	25.4648	2.37460
$116$	30.7162	2.85193
$117$	−1.03327	−0.0955262
$118$	28.7177	2.64367
$119$	−1.90633	−0.174753
$120$	−19.5379	−1.78356
$121$	−8.55413	−0.777648
$122$	−0.628725	−0.0569221
$123$	7.14989	0.644684
$124$	−15.5831	−1.39940
$125$	4.15377	0.371524
$126$	4.58014	0.408031
$127$	−1.00000	−0.0887357
$127$	−1.00000	−0.0887357
$128$	17.6117	1.55667
$129$	−1.43308	−0.126176
$130$	−4.67338	−0.409883
$131$	11.7524	1.02681	0.513404	−	0.858147i	$-0.328384\pi$
$131$	11.7524	1.02681	0.513404	+	0.858147i	$0.328384\pi$
$132$	7.03174	0.612035
$133$	3.15361	0.273452
$134$	4.70749	0.406665
$135$	−17.4659	−1.50323
$136$	10.3265	0.885494
$137$	−13.7085	−1.17119	−0.585597	−	0.810602i	$-0.699140\pi$
$137$	−13.7085	−1.17119	−0.585597	+	0.810602i	$0.699140\pi$
$138$	−20.3141	−1.72925
$139$	18.5651	1.57467	0.787335	−	0.616525i	$-0.211460\pi$
$139$	18.5651	1.57467	0.787335	+	0.616525i	$0.211460\pi$
$140$	14.0105	1.18411
$141$	−2.83702	−0.238920
$142$	−19.5099	−1.63724
$143$	0.877038	0.0733416
$144$	−9.41006	−0.784172
$145$	24.6400	2.04624
$146$	−25.6845	−2.12566
$147$	1.07586	0.0887355
$148$	−20.8207	−1.71145
$149$	−14.7979	−1.21229	−0.606146	−	0.795354i	$-0.707285\pi$
$149$	−14.7979	−1.21229	−0.606146	+	0.795354i	$0.707285\pi$
$150$	−16.6854	−1.36236
$151$	11.4934	0.935317	0.467658	−	0.883909i	$-0.345098\pi$
$151$	11.4934	0.935317	0.467658	+	0.883909i	$0.345098\pi$
$152$	−17.0830	−1.38562
$153$	3.51246	0.283965
$154$	−3.88760	−0.313272
$155$	−12.5005	−1.00406
$156$	2.52144	0.201877
$157$	−17.2200	−1.37431	−0.687153	−	0.726513i	$-0.741140\pi$
$157$	−17.2200	−1.37431	−0.687153	+	0.726513i	$0.741140\pi$
$158$	3.19526	0.254202
$159$	−3.08896	−0.244970
$160$	−6.24020	−0.493331
$161$	7.59584	0.598636
$162$	0.192723	0.0151417
$163$	1.22641	0.0960599	0.0480299	−	0.998846i	$-0.484706\pi$
$163$	1.22641	0.0960599	0.0480299	+	0.998846i	$0.484706\pi$
$164$	27.7737	2.16876
$165$	5.64075	0.439131
$166$	−23.8925	−1.85441
$167$	−8.30479	−0.642644	−0.321322	−	0.946970i	$-0.604127\pi$
$167$	−8.30479	−0.642644	−0.321322	+	0.946970i	$0.604127\pi$
$168$	−5.82792	−0.449634
$169$	−12.6855	−0.975809
$170$	15.8865	1.21844
$171$	−5.81060	−0.444347
$172$	−5.56680	−0.424465
$173$	−6.01867	−0.457591	−0.228796	−	0.973474i	$-0.573479\pi$
$173$	−6.01867	−0.457591	−0.228796	+	0.973474i	$0.573479\pi$
$174$	−19.6561	−1.49013
$175$	6.23902	0.471625
$176$	7.98722	0.602059
$177$	−12.4291	−0.934228
$178$	2.53994	0.190376
$179$	20.2061	1.51028	0.755138	−	0.655566i	$-0.227570\pi$
$179$	20.2061	1.51028	0.755138	+	0.655566i	$0.227570\pi$
$180$	−25.8148	−1.92412
$181$	−12.7951	−0.951053	−0.475527	−	0.879701i	$-0.657742\pi$
$181$	−12.7951	−0.951053	−0.475527	+	0.879701i	$0.657742\pi$
$182$	−1.39401	−0.103331
$183$	0.272114	0.0201153
$184$	−41.1465	−3.03336
$185$	−16.7020	−1.22796
$186$	9.97204	0.731186
$187$	−2.98136	−0.218018
$188$	−11.0204	−0.803744
$189$	−5.20988	−0.378963
$190$	−26.2807	−1.90660
$191$	16.2318	1.17449	0.587247	−	0.809408i	$-0.300212\pi$
$191$	16.2318	1.17449	0.587247	+	0.809408i	$0.300212\pi$
$192$	−6.01117	−0.433819
$193$	−24.2695	−1.74696	−0.873479	−	0.486862i	$-0.838141\pi$
$193$	−24.2695	−1.74696	−0.873479	+	0.486862i	$0.838141\pi$
$194$	2.39616	0.172034
$195$	2.02266	0.144845
$196$	4.17918	0.298513
$197$	6.58820	0.469390	0.234695	−	0.972069i	$-0.424591\pi$
$197$	6.58820	0.469390	0.234695	+	0.972069i	$0.424591\pi$
$198$	7.16300	0.509052
$199$	17.5920	1.24707	0.623533	−	0.781797i	$-0.285697\pi$
$199$	17.5920	1.24707	0.623533	+	0.781797i	$0.285697\pi$
$200$	−33.7967	−2.38978
$201$	−2.03742	−0.143708
$202$	−28.3434	−1.99424
$203$	7.34983	0.515857
$204$	−8.57125	−0.600107
$205$	22.2796	1.55607
$206$	43.5125	3.03166
$207$	−13.9955	−0.972756
$208$	2.86405	0.198586
$209$	4.93201	0.341154
$210$	−8.96572	−0.618694
$211$	−9.19907	−0.633290	−0.316645	−	0.948544i	$-0.602556\pi$
$211$	−9.19907	−0.633290	−0.316645	+	0.948544i	$0.602556\pi$
$212$	−11.9990	−0.824097
$213$	8.44396	0.578571
$214$	15.0975	1.03205
$215$	−4.46560	−0.304551
$216$	28.2218	1.92025
$217$	−3.72875	−0.253124
$218$	13.2367	0.896505
$219$	11.1163	0.751172
$220$	21.9115	1.47727
$221$	−1.06905	−0.0719123
$222$	13.3237	0.894231
$223$	−12.0425	−0.806424	−0.403212	−	0.915107i	$-0.632106\pi$
$223$	−12.0425	−0.806424	−0.403212	+	0.915107i	$0.632106\pi$
$224$	−1.86138	−0.124368
$225$	−11.4955	−0.766370
$226$	−40.8751	−2.71897
$227$	2.27127	0.150749	0.0753747	−	0.997155i	$-0.475985\pi$
$227$	2.27127	0.150749	0.0753747	+	0.997155i	$0.475985\pi$
$228$	14.1793	0.939045
$229$	11.6422	0.769336	0.384668	−	0.923055i	$-0.374316\pi$
$229$	11.6422	0.769336	0.384668	+	0.923055i	$0.374316\pi$
$230$	−63.3002	−4.17389
$231$	1.68257	0.110705
$232$	−39.8139	−2.61391
$233$	−12.1608	−0.796680	−0.398340	−	0.917238i	$-0.630414\pi$
$233$	−12.1608	−0.796680	−0.398340	+	0.917238i	$0.630414\pi$
$234$	2.56851	0.167908
$235$	−8.84037	−0.576682
$236$	−48.2808	−3.14281
$237$	−1.38292	−0.0898304
$238$	4.73874	0.307167
$239$	7.95463	0.514542	0.257271	−	0.966339i	$-0.417177\pi$
$239$	7.95463	0.514542	0.257271	+	0.966339i	$0.417177\pi$
$240$	18.4204	1.18903
$241$	9.79797	0.631143	0.315571	−	0.948902i	$-0.397804\pi$
$241$	9.79797	0.631143	0.315571	+	0.948902i	$0.397804\pi$
$242$	21.2638	1.36689
$243$	15.5462	0.997291
$244$	1.05703	0.0676692
$245$	3.35246	0.214181
$246$	−17.7731	−1.13317
$247$	1.76852	0.112528
$248$	20.1986	1.28261
$249$	10.3407	0.655318
$250$	−10.3254	−0.653036
$251$	15.7157	0.991968	0.495984	−	0.868332i	$-0.334807\pi$
$251$	15.7157	0.991968	0.495984	+	0.868332i	$0.334807\pi$
$252$	−7.70023	−0.485069
$253$	11.8793	0.746847
$254$	2.48579	0.155973
$255$	−6.87571	−0.430574
$256$	−32.6044	−2.03777
$257$	−20.4161	−1.27352	−0.636761	−	0.771061i	$-0.719726\pi$
$257$	−20.4161	−1.27352	−0.636761	+	0.771061i	$0.719726\pi$
$258$	3.56235	0.221782
$259$	−4.98201	−0.309567
$260$	7.85700	0.487270
$261$	−13.5422	−0.838244
$262$	−29.2139	−1.80484
$263$	11.4806	0.707923	0.353961	−	0.935260i	$-0.384834\pi$
$263$	11.4806	0.707923	0.353961	+	0.935260i	$0.384834\pi$
$264$	−9.11444	−0.560955
$265$	−9.62543	−0.591285
$266$	−7.83922	−0.480653
$267$	−1.09929	−0.0672757
$268$	−7.91434	−0.483445
$269$	6.53180	0.398251	0.199125	−	0.979974i	$-0.436190\pi$
$269$	6.53180	0.398251	0.199125	+	0.979974i	$0.436190\pi$
$270$	43.4167	2.64226
$271$	−16.6906	−1.01388	−0.506940	−	0.861982i	$-0.669223\pi$
$271$	−16.6906	−1.01388	−0.506940	+	0.861982i	$0.669223\pi$
$272$	−9.73591	−0.590326
$273$	0.603334	0.0365154
$274$	34.0765	2.05863
$275$	9.75737	0.588391
$276$	34.1525	2.05574
$277$	−15.2783	−0.917985	−0.458992	−	0.888440i	$-0.651790\pi$
$277$	−15.2783	−0.917985	−0.458992	+	0.888440i	$0.651790\pi$
$278$	−46.1490	−2.76783
$279$	6.87031	0.411315
$280$	−18.1602	−1.08528
$281$	−19.1608	−1.14304	−0.571518	−	0.820589i	$-0.693645\pi$
$281$	−19.1608	−1.14304	−0.571518	+	0.820589i	$0.693645\pi$
$282$	7.05224	0.419955
$283$	−26.4492	−1.57224	−0.786120	−	0.618074i	$-0.787913\pi$
$283$	−26.4492	−1.57224	−0.786120	+	0.618074i	$0.787913\pi$
$284$	32.8005	1.94635
$285$	11.3744	0.673760
$286$	−2.18014	−0.128914
$287$	6.64574	0.392286
$288$	3.42963	0.202093
$289$	−13.3659	−0.786230
$290$	−61.2501	−3.59673
$291$	−1.03707	−0.0607938
$292$	43.1814	2.52700
$293$	−21.8930	−1.27900	−0.639502	−	0.768789i	$-0.720859\pi$
$293$	−21.8930	−1.27900	−0.639502	+	0.768789i	$0.720859\pi$
$294$	−2.67437	−0.155972
$295$	−38.7300	−2.25495
$296$	26.9875	1.56862
$297$	−8.14787	−0.472787
$298$	36.7845	2.13087
$299$	4.25969	0.246344
$300$	28.0519	1.61958
$301$	−1.33203	−0.0767772
$302$	−28.5701	−1.64403
$303$	12.2671	0.704728
$304$	16.1060	0.923740
$305$	0.847929	0.0485523
$306$	−8.73124	−0.499132
$307$	25.3593	1.44733	0.723667	−	0.690149i	$-0.242455\pi$
$307$	25.3593	1.44733	0.723667	+	0.690149i	$0.242455\pi$
$308$	6.53592	0.372419
$309$	−18.8324	−1.07134
$310$	31.0737	1.76487
$311$	4.89777	0.277727	0.138864	−	0.990312i	$-0.455655\pi$
$311$	4.89777	0.277727	0.138864	+	0.990312i	$0.455655\pi$
$312$	−3.26825	−0.185028
$313$	−5.31267	−0.300290	−0.150145	−	0.988664i	$-0.547974\pi$
$313$	−5.31267	−0.300290	−0.150145	+	0.988664i	$0.547974\pi$
$314$	42.8054	2.41565
$315$	−6.17700	−0.348034
$316$	−5.37195	−0.302196
$317$	−15.5568	−0.873755	−0.436877	−	0.899521i	$-0.643916\pi$
$317$	−15.5568	−0.873755	−0.436877	+	0.899521i	$0.643916\pi$
$318$	7.67851	0.430589
$319$	11.4946	0.643574
$320$	−18.7313	−1.04711
$321$	−6.53426	−0.364707
$322$	−18.8817	−1.05224
$323$	−6.01181	−0.334506
$324$	−0.324010	−0.0180006
$325$	3.49879	0.194078
$326$	−3.04860	−0.168847
$327$	−5.72890	−0.316809
$328$	−35.9998	−1.98776
$329$	−2.63698	−0.145381
$330$	−14.0217	−0.771871
$331$	34.1918	1.87935	0.939677	−	0.342064i	$-0.111126\pi$
$331$	34.1918	1.87935	0.939677	+	0.342064i	$0.111126\pi$
$332$	40.1686	2.20454
$333$	9.17948	0.503033
$334$	20.6440	1.12959
$335$	−6.34875	−0.346869
$336$	5.49459	0.299754
$337$	30.3914	1.65552	0.827761	−	0.561080i	$-0.189614\pi$
$337$	30.3914	1.65552	0.827761	+	0.561080i	$0.189614\pi$
$338$	31.5336	1.71520
$339$	17.6909	0.960838
$340$	−26.7087	−1.44848
$341$	−5.83149	−0.315793
$342$	14.4440	0.781039
$343$	1.00000	0.0539949
$344$	7.21560	0.389039
$345$	27.3965	1.47498
$346$	14.9612	0.804319
$347$	−1.66425	−0.0893418	−0.0446709	−	0.999002i	$-0.514224\pi$
$347$	−1.66425	−0.0893418	−0.0446709	+	0.999002i	$0.514224\pi$
$348$	33.0464	1.77147
$349$	12.8777	0.689327	0.344663	−	0.938726i	$-0.387993\pi$
$349$	12.8777	0.689327	0.344663	+	0.938726i	$0.387993\pi$
$350$	−15.5089	−0.828987
$351$	−2.92166	−0.155947
$352$	−2.91106	−0.155160
$353$	−13.5275	−0.719997	−0.359999	−	0.932953i	$-0.617223\pi$
$353$	−13.5275	−0.719997	−0.359999	+	0.932953i	$0.617223\pi$
$354$	30.8962	1.64211
$355$	26.3120	1.39650
$356$	−4.27020	−0.226320
$357$	−2.05094	−0.108547
$358$	−50.2283	−2.65465
$359$	−19.5330	−1.03091	−0.515457	−	0.856915i	$-0.672378\pi$
$359$	−19.5330	−1.03091	−0.515457	+	0.856915i	$0.672378\pi$
$360$	33.4607	1.76353
$361$	−9.05477	−0.476567
$362$	31.8060	1.67169
$363$	−9.20305	−0.483035
$364$	2.34365	0.122841
$365$	34.6394	1.81311
$366$	−0.676420	−0.0353571
$367$	−26.2079	−1.36804	−0.684022	−	0.729462i	$-0.739771\pi$
$367$	−26.2079	−1.36804	−0.684022	+	0.729462i	$0.739771\pi$
$368$	38.7931	2.02223
$369$	−12.2449	−0.637446
$370$	41.5178	2.15841
$371$	−2.87115	−0.149063
$372$	−16.7652	−0.869236
$373$	−32.8179	−1.69925	−0.849624	−	0.527388i	$-0.823171\pi$
$373$	−32.8179	−1.69925	−0.849624	+	0.527388i	$0.823171\pi$
$374$	7.41104	0.383216
$375$	4.46887	0.230772
$376$	14.2844	0.736664
$377$	4.12173	0.212280
$378$	12.9507	0.666112
$379$	15.8173	0.812481	0.406240	−	0.913766i	$-0.366840\pi$
$379$	15.8173	0.812481	0.406240	+	0.913766i	$0.366840\pi$
$380$	44.1837	2.26658
$381$	−1.07586	−0.0551180
$382$	−40.3490	−2.06443
$383$	15.5071	0.792374	0.396187	−	0.918170i	$-0.370333\pi$
$383$	15.5071	0.792374	0.396187	+	0.918170i	$0.370333\pi$
$384$	18.9477	0.966920
$385$	5.24301	0.267209
$386$	60.3290	3.07067
$387$	2.45431	0.124759
$388$	−4.02848	−0.204515
$389$	6.99370	0.354595	0.177297	−	0.984157i	$-0.443265\pi$
$389$	6.99370	0.354595	0.177297	+	0.984157i	$0.443265\pi$
$390$	−5.02791	−0.254598
$391$	−14.4802	−0.732293
$392$	−5.41698	−0.273599
$393$	12.6439	0.637800
$394$	−16.3769	−0.825057
$395$	−4.30929	−0.216824
$396$	−12.0426	−0.605164
$397$	17.8751	0.897128	0.448564	−	0.893751i	$-0.351936\pi$
$397$	17.8751	0.897128	0.448564	+	0.893751i	$0.351936\pi$
$398$	−43.7302	−2.19200
$399$	3.39284	0.169854
$400$	31.8636	1.59318
$401$	−19.0867	−0.953143	−0.476571	−	0.879136i	$-0.658121\pi$
$401$	−19.0867	−0.953143	−0.476571	+	0.879136i	$0.658121\pi$
$402$	5.06460	0.252599
$403$	−2.09105	−0.104163
$404$	47.6516	2.37076
$405$	−0.259915	−0.0129153
$406$	−18.2702	−0.906733
$407$	−7.79151	−0.386211
$408$	11.1099	0.550023
$409$	19.6481	0.971535	0.485768	−	0.874088i	$-0.338540\pi$
$409$	19.6481	0.971535	0.485768	+	0.874088i	$0.338540\pi$
$410$	−55.3825	−2.73515
$411$	−14.7484	−0.727485
$412$	−73.1543	−3.60405
$413$	−11.5527	−0.568472
$414$	34.7900	1.70983
$415$	32.2225	1.58174
$416$	−1.04385	−0.0511787
$417$	19.9734	0.978104
$418$	−12.2600	−0.599654
$419$	−2.20594	−0.107767	−0.0538837	−	0.998547i	$-0.517160\pi$
$419$	−2.20594	−0.107767	−0.0538837	+	0.998547i	$0.517160\pi$
$420$	15.0734	0.735506
$421$	−37.6865	−1.83673	−0.918363	−	0.395738i	$-0.870489\pi$
$421$	−37.6865	−1.83673	−0.918363	+	0.395738i	$0.870489\pi$
$422$	22.8670	1.11315
$423$	4.85869	0.236238
$424$	15.5530	0.755319
$425$	−11.8936	−0.576925
$426$	−20.9900	−1.01697
$427$	0.252927	0.0122400
$428$	−25.3823	−1.22690
$429$	0.943570	0.0455560
$430$	11.1006	0.535316
$431$	−41.2393	−1.98643	−0.993215	−	0.116297i	$-0.962898\pi$
$431$	−41.2393	−1.98643	−0.993215	+	0.116297i	$0.962898\pi$
$432$	−26.6077	−1.28016
$433$	5.90179	0.283622	0.141811	−	0.989894i	$-0.454707\pi$
$433$	5.90179	0.283622	0.141811	+	0.989894i	$0.454707\pi$
$434$	9.26890	0.444921
$435$	26.5092	1.27102
$436$	−22.2539	−1.06577
$437$	23.9543	1.14589
$438$	−27.6329	−1.32035
$439$	18.1597	0.866716	0.433358	−	0.901222i	$-0.357329\pi$
$439$	18.1597	0.866716	0.433358	+	0.901222i	$0.357329\pi$
$440$	−28.4013	−1.35398
$441$	−1.84252	−0.0877393
$442$	2.65745	0.126402
$443$	−24.4277	−1.16060	−0.580298	−	0.814404i	$-0.697064\pi$
$443$	−24.4277	−1.16060	−0.580298	+	0.814404i	$0.697064\pi$
$444$	−22.4002	−1.06307
$445$	−3.42548	−0.162383
$446$	29.9351	1.41747
$447$	−15.9205	−0.753013
$448$	−5.58731	−0.263976
$449$	39.1985	1.84989	0.924946	−	0.380098i	$-0.124110\pi$
$449$	39.1985	1.84989	0.924946	+	0.380098i	$0.124110\pi$
$450$	28.5756	1.34707
$451$	10.3934	0.489408
$452$	68.7202	3.23233
$453$	12.3653	0.580970
$454$	−5.64591	−0.264976
$455$	1.88004	0.0881374
$456$	−18.3790	−0.860673
$457$	−5.85512	−0.273891	−0.136945	−	0.990579i	$-0.543729\pi$
$457$	−5.85512	−0.273891	−0.136945	+	0.990579i	$0.543729\pi$
$458$	−28.9400	−1.35228
$459$	9.93174	0.463574
$460$	106.422	4.96194
$461$	2.53290	0.117969	0.0589845	−	0.998259i	$-0.481214\pi$
$461$	2.53290	0.117969	0.0589845	+	0.998259i	$0.481214\pi$
$462$	−4.18252	−0.194588
$463$	35.6610	1.65731	0.828653	−	0.559763i	$-0.189108\pi$
$463$	35.6610	1.65731	0.828653	+	0.559763i	$0.189108\pi$
$464$	37.5367	1.74260
$465$	−13.4488	−0.623672
$466$	30.2292	1.40034
$467$	−40.7615	−1.88622	−0.943110	−	0.332482i	$-0.892114\pi$
$467$	−40.7615	−1.88622	−0.943110	+	0.332482i	$0.892114\pi$
$468$	−4.31823	−0.199610
$469$	−1.89376	−0.0874456
$470$	21.9753	1.01365
$471$	−18.5263	−0.853647
$472$	62.5808	2.88052
$473$	−2.08320	−0.0957858
$474$	3.43766	0.157897
$475$	19.6754	0.902770
$476$	−7.96688	−0.365161
$477$	5.29016	0.242220
$478$	−19.7736	−0.904423
$479$	−30.8787	−1.41088	−0.705441	−	0.708769i	$-0.749251\pi$
$479$	−30.8787	−1.41088	−0.705441	+	0.708769i	$0.749251\pi$
$480$	−6.71358	−0.306432
$481$	−2.79387	−0.127390
$482$	−24.3557	−1.10937
$483$	8.17206	0.371842
$484$	−35.7492	−1.62496
$485$	−3.23158	−0.146738
$486$	−38.6447	−1.75296
$487$	−14.0096	−0.634836	−0.317418	−	0.948286i	$-0.602816\pi$
$487$	−14.0096	−0.634836	−0.317418	+	0.948286i	$0.602816\pi$
$488$	−1.37010	−0.0620216
$489$	1.31945	0.0596674
$490$	−8.33354	−0.376471
$491$	−21.2640	−0.959630	−0.479815	−	0.877370i	$-0.659296\pi$
$491$	−21.2640	−0.959630	−0.479815	+	0.877370i	$0.659296\pi$
$492$	29.8806	1.34712
$493$	−14.0112	−0.631032
$494$	−4.39617	−0.197793
$495$	−9.66037	−0.434202
$496$	−19.0433	−0.855069
$497$	7.84857	0.352056
$498$	−25.7050	−1.15187
$499$	11.4598	0.513013	0.256506	−	0.966543i	$-0.417429\pi$
$499$	11.4598	0.513013	0.256506	+	0.966543i	$0.417429\pi$
$500$	17.3593	0.776332
$501$	−8.93479	−0.399177
$502$	−39.0661	−1.74360
$503$	−16.6579	−0.742741	−0.371371	−	0.928485i	$-0.621112\pi$
$503$	−16.6579	−0.742741	−0.371371	+	0.928485i	$0.621112\pi$
$504$	9.98092	0.444586
$505$	38.2253	1.70101
$506$	−29.5296	−1.31275
$507$	−13.6478	−0.606122
$508$	−4.17918	−0.185421
$509$	−29.7651	−1.31932	−0.659658	−	0.751566i	$-0.729299\pi$
$509$	−29.7651	−1.31932	−0.659658	+	0.751566i	$0.729299\pi$
$510$	17.0916	0.756829
$511$	10.3325	0.457083
$512$	45.8244	2.02517
$513$	−16.4299	−0.725398
$514$	50.7503	2.23850
$515$	−58.6831	−2.58589
$516$	−5.98910	−0.263656
$517$	−4.12404	−0.181375
$518$	12.3843	0.544133
$519$	−6.47525	−0.284232
$520$	−10.1841	−0.446603
$521$	−42.7616	−1.87342	−0.936709	−	0.350108i	$-0.886145\pi$
$521$	−42.7616	−1.87342	−0.936709	+	0.350108i	$0.886145\pi$
$522$	33.6632	1.47340
$523$	−21.4721	−0.938911	−0.469456	−	0.882956i	$-0.655550\pi$
$523$	−21.4721	−0.938911	−0.469456	+	0.882956i	$0.655550\pi$
$524$	49.1151	2.14560
$525$	6.71231	0.292949
$526$	−28.5384	−1.24433
$527$	7.10821	0.309639
$528$	8.59313	0.373968
$529$	34.6967	1.50855
$530$	23.9268	1.03932
$531$	21.2861	0.923740
$532$	13.1795	0.571403
$533$	3.72688	0.161429
$534$	2.73262	0.118252
$535$	−20.3613	−0.880295
$536$	10.2584	0.443098
$537$	21.7390	0.938105
$538$	−16.2367	−0.700014
$539$	1.56393	0.0673631
$540$	−72.9932	−3.14113
$541$	29.7590	1.27944	0.639720	−	0.768608i	$-0.279050\pi$
$541$	29.7590	1.27944	0.639720	+	0.768608i	$0.279050\pi$
$542$	41.4893	1.78212
$543$	−13.7658	−0.590745
$544$	3.54839	0.152136
$545$	−17.8517	−0.764683
$546$	−1.49976	−0.0641840
$547$	37.4972	1.60326	0.801631	−	0.597819i	$-0.203966\pi$
$547$	37.4972	1.60326	0.801631	+	0.597819i	$0.203966\pi$
$548$	−57.2901	−2.44731
$549$	−0.466024	−0.0198894
$550$	−24.2548	−1.03423
$551$	23.1785	0.987436
$552$	−44.2679	−1.88417
$553$	−1.28541	−0.0546612
$554$	37.9788	1.61356
$555$	−17.9690	−0.762744
$556$	77.5868	3.29041
$557$	−15.0550	−0.637902	−0.318951	−	0.947771i	$-0.603331\pi$
$557$	−15.0550	−0.637902	−0.318951	+	0.947771i	$0.603331\pi$
$558$	−17.0782	−0.722977
$559$	−0.746994	−0.0315945
$560$	17.1216	0.723518
$561$	−3.20752	−0.135422
$562$	47.6298	2.00914
$563$	−39.8707	−1.68035	−0.840176	−	0.542315i	$-0.817548\pi$
$563$	−39.8707	−1.68035	−0.840176	+	0.542315i	$0.817548\pi$
$564$	−11.8564	−0.499244
$565$	55.1262	2.31918
$566$	65.7472	2.76356
$567$	−0.0775297	−0.00325594
$568$	−42.5156	−1.78391
$569$	−15.6121	−0.654494	−0.327247	−	0.944939i	$-0.606121\pi$
$569$	−15.6121	−0.654494	−0.327247	+	0.944939i	$0.606121\pi$
$570$	−28.2744	−1.18428
$571$	−20.1708	−0.844122	−0.422061	−	0.906567i	$-0.638693\pi$
$571$	−20.1708	−0.844122	−0.422061	+	0.906567i	$0.638693\pi$
$572$	3.66530	0.153254
$573$	17.4632	0.729535
$574$	−16.5199	−0.689529
$575$	47.3906	1.97632
$576$	10.2948	0.428948
$577$	−2.60463	−0.108432	−0.0542160	−	0.998529i	$-0.517266\pi$
$577$	−2.60463	−0.108432	−0.0542160	+	0.998529i	$0.517266\pi$
$578$	33.2249	1.38197
$579$	−26.1106	−1.08512
$580$	102.975	4.27581
$581$	9.61160	0.398756
$582$	2.57793	0.106859
$583$	−4.49027	−0.185968
$584$	−55.9710	−2.31610
$585$	−3.46401	−0.143219
$586$	54.4216	2.24813
$587$	3.91484	0.161583	0.0807915	−	0.996731i	$-0.474255\pi$
$587$	3.91484	0.161583	0.0807915	+	0.996731i	$0.474255\pi$
$588$	4.49621	0.185421
$589$	−11.7590	−0.484521
$590$	96.2749	3.96358
$591$	7.08798	0.291561
$592$	−25.4439	−1.04574
$593$	−12.3640	−0.507729	−0.253865	−	0.967240i	$-0.581702\pi$
$593$	−12.3640	−0.507729	−0.253865	+	0.967240i	$0.581702\pi$
$594$	20.2539	0.831029
$595$	−6.39090	−0.262001
$596$	−61.8430	−2.53319
$597$	18.9266	0.774613
$598$	−10.5887	−0.433004
$599$	5.47290	0.223616	0.111808	−	0.993730i	$-0.464336\pi$
$599$	5.47290	0.223616	0.111808	+	0.993730i	$0.464336\pi$
$600$	−36.3605	−1.48441
$601$	−48.3519	−1.97232	−0.986158	−	0.165810i	$-0.946976\pi$
$601$	−48.3519	−1.97232	−0.986158	+	0.165810i	$0.946976\pi$
$602$	3.31116	0.134953
$603$	3.48929	0.142095
$604$	48.0328	1.95443
$605$	−28.6774	−1.16590
$606$	−30.4936	−1.23872
$607$	−3.89921	−0.158264	−0.0791319	−	0.996864i	$-0.525215\pi$
$607$	−3.89921	−0.158264	−0.0791319	+	0.996864i	$0.525215\pi$
$608$	−5.87005	−0.238062
$609$	7.90739	0.320424
$610$	−2.10778	−0.0853414
$611$	−1.47880	−0.0598256
$612$	14.6792	0.593370
$613$	12.4010	0.500872	0.250436	−	0.968133i	$-0.419426\pi$
$613$	12.4010	0.500872	0.250436	+	0.968133i	$0.419426\pi$
$614$	−63.0381	−2.54401
$615$	23.9697	0.966553
$616$	−8.47177	−0.341337
$617$	9.77656	0.393589	0.196795	−	0.980445i	$-0.436947\pi$
$617$	9.77656	0.393589	0.196795	+	0.980445i	$0.436947\pi$
$618$	46.8134	1.88311
$619$	−28.9771	−1.16469	−0.582344	−	0.812942i	$-0.697864\pi$
$619$	−28.9771	−1.16469	−0.582344	+	0.812942i	$0.697864\pi$
$620$	−52.2417	−2.09808
$621$	−39.5734	−1.58803
$622$	−12.1749	−0.488167
$623$	−1.02178	−0.0409368
$624$	3.08132	0.123352
$625$	−17.2697	−0.690790
$626$	13.2062	0.527826
$627$	5.30615	0.211907
$628$	−71.9654	−2.87173
$629$	9.49735	0.378684
$630$	15.3547	0.611748
$631$	9.75643	0.388397	0.194199	−	0.980962i	$-0.437789\pi$
$631$	9.75643	0.388397	0.194199	+	0.980962i	$0.437789\pi$
$632$	6.96304	0.276975
$633$	−9.89692	−0.393367
$634$	38.6709	1.53582
$635$	−3.35246	−0.133038
$636$	−12.9093	−0.511887
$637$	0.560792	0.0222194
$638$	−28.5732	−1.13122
$639$	−14.4612	−0.572075
$640$	59.0425	2.33386
$641$	−43.0884	−1.70189	−0.850944	−	0.525256i	$-0.823969\pi$
$641$	−43.0884	−1.70189	−0.850944	+	0.525256i	$0.823969\pi$
$642$	16.2428	0.641054
$643$	−27.8194	−1.09709	−0.548545	−	0.836121i	$-0.684818\pi$
$643$	−27.8194	−1.09709	−0.548545	+	0.836121i	$0.684818\pi$
$644$	31.7443	1.25090
$645$	−4.80436	−0.189171
$646$	14.9441	0.587968
$647$	−4.76600	−0.187371	−0.0936854	−	0.995602i	$-0.529865\pi$
$647$	−4.76600	−0.187371	−0.0936854	+	0.995602i	$0.529865\pi$
$648$	0.419977	0.0164982
$649$	−18.0676	−0.709215
$650$	−8.69728	−0.341135
$651$	−4.01161	−0.157227
$652$	5.12538	0.200726
$653$	39.6544	1.55180	0.775898	−	0.630859i	$-0.217297\pi$
$653$	39.6544	1.55180	0.775898	+	0.630859i	$0.217297\pi$
$654$	14.2409	0.556862
$655$	39.3993	1.53946
$656$	33.9408	1.32517
$657$	−19.0379	−0.742739
$658$	6.55498	0.255540
$659$	33.0049	1.28569	0.642844	−	0.765997i	$-0.277754\pi$
$659$	33.0049	1.28569	0.642844	+	0.765997i	$0.277754\pi$
$660$	23.5737	0.917604
$661$	−15.9798	−0.621542	−0.310771	−	0.950485i	$-0.600587\pi$
$661$	−15.9798	−0.621542	−0.310771	+	0.950485i	$0.600587\pi$
$662$	−84.9939	−3.30338
$663$	−1.15015	−0.0446682
$664$	−52.0659	−2.02055
$665$	10.5724	0.409978
$666$	−22.8183	−0.884192
$667$	55.8281	2.16167
$668$	−34.7072	−1.34286
$669$	−12.9560	−0.500909
$670$	15.7817	0.609700
$671$	0.395560	0.0152704
$672$	−2.00258	−0.0772512
$673$	10.3527	0.399066	0.199533	−	0.979891i	$-0.436057\pi$
$673$	10.3527	0.399066	0.199533	+	0.979891i	$0.436057\pi$
$674$	−75.5467	−2.90995
$675$	−32.5045	−1.25110
$676$	−53.0150	−2.03904
$677$	−35.7986	−1.37585	−0.687926	−	0.725781i	$-0.741479\pi$
$677$	−35.7986	−1.37585	−0.687926	+	0.725781i	$0.741479\pi$
$678$	−43.9759	−1.68889
$679$	−0.963940	−0.0369926
$680$	34.6194	1.32759
$681$	2.44357	0.0936377
$682$	14.4959	0.555076
$683$	28.0300	1.07254	0.536268	−	0.844047i	$-0.319833\pi$
$683$	28.0300	1.07254	0.536268	+	0.844047i	$0.319833\pi$
$684$	−24.2835	−0.928503
$685$	−45.9572	−1.75593
$686$	−2.48579	−0.0949081
$687$	12.5253	0.477872
$688$	−6.80291	−0.259358
$689$	−1.61012	−0.0613406
$690$	−68.1022	−2.59261
$691$	17.1163	0.651136	0.325568	−	0.945519i	$-0.394444\pi$
$691$	17.1163	0.651136	0.325568	+	0.945519i	$0.394444\pi$
$692$	−25.1531	−0.956177
$693$	−2.88157	−0.109462
$694$	4.13699	0.157038
$695$	62.2388	2.36085
$696$	−42.8342	−1.62363
$697$	−12.6690	−0.479871
$698$	−32.0113	−1.21165
$699$	−13.0833	−0.494857
$700$	26.0740	0.985503
$701$	−26.1867	−0.989057	−0.494529	−	0.869161i	$-0.664659\pi$
$701$	−26.1867	−0.989057	−0.494529	+	0.869161i	$0.664659\pi$
$702$	7.26265	0.274111
$703$	−15.7113	−0.592563
$704$	−8.73815	−0.329331
$705$	−9.51100	−0.358205
$706$	33.6266	1.26556
$707$	11.4022	0.428822
$708$	−51.9434	−1.95215
$709$	−11.5413	−0.433442	−0.216721	−	0.976234i	$-0.569536\pi$
$709$	−11.5413	−0.433442	−0.216721	+	0.976234i	$0.569536\pi$
$710$	−65.4063	−2.45466
$711$	2.36840	0.0888219
$712$	5.53497	0.207432
$713$	−28.3230	−1.06070
$714$	5.09822	0.190796
$715$	2.94024	0.109959
$716$	84.4449	3.15585
$717$	8.55807	0.319607
$718$	48.5551	1.81206
$719$	1.67651	0.0625231	0.0312615	−	0.999511i	$-0.490048\pi$
$719$	1.67651	0.0625231	0.0312615	+	0.999511i	$0.490048\pi$
$720$	−31.5469	−1.17568
$721$	−17.5045	−0.651901
$722$	22.5083	0.837672
$723$	10.5413	0.392033
$724$	−53.4730	−1.98731
$725$	45.8557	1.70304
$726$	22.8769	0.849041
$727$	−37.3667	−1.38585	−0.692927	−	0.721007i	$-0.743679\pi$
$727$	−37.3667	−1.38585	−0.692927	+	0.721007i	$0.743679\pi$
$728$	−3.03780	−0.112588
$729$	16.9582	0.628080
$730$	−86.1063	−3.18694
$731$	2.53929	0.0939192
$732$	1.13721	0.0420326
$733$	18.2078	0.672519	0.336259	−	0.941769i	$-0.390838\pi$
$733$	18.2078	0.672519	0.336259	+	0.941769i	$0.390838\pi$
$734$	65.1476	2.40464
$735$	3.60678	0.133038
$736$	−14.1387	−0.521160
$737$	−2.96170	−0.109096
$738$	30.4384	1.12045
$739$	34.4240	1.26631	0.633153	−	0.774027i	$-0.281760\pi$
$739$	34.4240	1.26631	0.633153	+	0.774027i	$0.281760\pi$
$740$	−69.8007	−2.56592
$741$	1.90268	0.0698966
$742$	7.13709	0.262011
$743$	38.3673	1.40756	0.703779	−	0.710419i	$-0.251494\pi$
$743$	38.3673	1.40756	0.703779	+	0.710419i	$0.251494\pi$
$744$	21.7308	0.796691
$745$	−49.6094	−1.81755
$746$	81.5787	2.98681
$747$	−17.7096	−0.647961
$748$	−12.4596	−0.455569
$749$	−6.07352	−0.221922
$750$	−11.1087	−0.405632
$751$	−36.1410	−1.31880	−0.659401	−	0.751791i	$-0.729190\pi$
$751$	−36.1410	−1.31880	−0.659401	+	0.751791i	$0.729190\pi$
$752$	−13.4674	−0.491107
$753$	16.9079	0.616159
$754$	−10.2458	−0.373129
$755$	38.5311	1.40229
$756$	−21.7730	−0.791876
$757$	14.6536	0.532594	0.266297	−	0.963891i	$-0.414200\pi$
$757$	14.6536	0.532594	0.266297	+	0.963891i	$0.414200\pi$
$758$	−39.3186	−1.42812
$759$	12.7805	0.463903
$760$	−57.2703	−2.07741
$761$	0.148905	0.00539779	0.00269890	−	0.999996i	$-0.499141\pi$
$761$	0.148905	0.00539779	0.00269890	+	0.999996i	$0.499141\pi$
$762$	2.67437	0.0968821
$763$	−5.32495	−0.192776
$764$	67.8357	2.45421
$765$	11.7754	0.425740
$766$	−38.5474	−1.39277
$767$	−6.47867	−0.233931
$768$	−35.0777	−1.26576
$769$	12.0858	0.435824	0.217912	−	0.975968i	$-0.430075\pi$
$769$	12.0858	0.435824	0.217912	+	0.975968i	$0.430075\pi$
$770$	−13.0330	−0.469678
$771$	−21.9649	−0.791046
$772$	−101.427	−3.65042
$773$	24.1533	0.868734	0.434367	−	0.900736i	$-0.356972\pi$
$773$	24.1533	0.868734	0.434367	+	0.900736i	$0.356972\pi$
$774$	−6.10090	−0.219292
$775$	−23.2637	−0.835658
$776$	5.22165	0.187446
$777$	−5.35995	−0.192287
$778$	−17.3849	−0.623279
$779$	20.9580	0.750900
$780$	8.45303	0.302667
$781$	12.2746	0.439219
$782$	35.9947	1.28717
$783$	−38.2917	−1.36843
$784$	5.10716	0.182398
$785$	−57.7294	−2.06045
$786$	−31.4301	−1.12108
$787$	−27.6573	−0.985875	−0.492938	−	0.870065i	$-0.664077\pi$
$787$	−27.6573	−0.985875	−0.492938	+	0.870065i	$0.664077\pi$
$788$	27.5332	0.980831
$789$	12.3515	0.439725
$790$	10.7120	0.381116
$791$	16.4435	0.584663
$792$	15.6094	0.554657
$793$	0.141840	0.00503687
$794$	−44.4339	−1.57690
$795$	−10.3556	−0.367276
$796$	73.5202	2.60585
$797$	24.9036	0.882132	0.441066	−	0.897475i	$-0.354600\pi$
$797$	24.9036	0.882132	0.441066	+	0.897475i	$0.354600\pi$
$798$	−8.43390	−0.298557
$799$	5.02694	0.177840
$800$	−11.6132	−0.410587
$801$	1.88266	0.0665204
$802$	47.4455	1.67536
$803$	16.1593	0.570249
$804$	−8.51473	−0.300291
$805$	25.4648	0.897515
$806$	5.19793	0.183089
$807$	7.02730	0.247373
$808$	−61.7653	−2.17290
$809$	41.8035	1.46973	0.734867	−	0.678211i	$-0.237244\pi$
$809$	41.8035	1.46973	0.734867	+	0.678211i	$0.237244\pi$
$810$	0.646097	0.0227015
$811$	15.7021	0.551375	0.275688	−	0.961247i	$-0.411094\pi$
$811$	15.7021	0.551375	0.275688	+	0.961247i	$0.411094\pi$
$812$	30.7162	1.07793
$813$	−17.9567	−0.629769
$814$	19.3681	0.678851
$815$	4.11150	0.144019
$816$	−10.4745	−0.366680
$817$	−4.20071	−0.146964
$818$	−48.8411	−1.70769
$819$	−1.03327	−0.0361055
$820$	93.1104	3.25155
$821$	44.3132	1.54654	0.773271	−	0.634075i	$-0.218619\pi$
$821$	44.3132	1.54654	0.773271	+	0.634075i	$0.218619\pi$
$822$	36.6615	1.27872
$823$	24.2151	0.844085	0.422042	−	0.906576i	$-0.361313\pi$
$823$	24.2151	0.844085	0.422042	+	0.906576i	$0.361313\pi$
$824$	94.8215	3.30326
$825$	10.4976	0.365478
$826$	28.7177	0.999215
$827$	−19.1531	−0.666018	−0.333009	−	0.942924i	$-0.608064\pi$
$827$	−19.1531	−0.666018	−0.333009	+	0.942924i	$0.608064\pi$
$828$	−58.4897	−2.03266
$829$	4.55255	0.158117	0.0790583	−	0.996870i	$-0.474809\pi$
$829$	4.55255	0.158117	0.0790583	+	0.996870i	$0.474809\pi$
$830$	−80.0986	−2.78026
$831$	−16.4373	−0.570205
$832$	−3.13332	−0.108628
$833$	−1.90633	−0.0660503
$834$	−49.6499	−1.71923
$835$	−27.8415	−0.963495
$836$	20.6117	0.712872
$837$	19.4263	0.671472
$838$	5.48352	0.189425
$839$	−3.76876	−0.130112	−0.0650561	−	0.997882i	$-0.520723\pi$
$839$	−3.76876	−0.130112	−0.0650561	+	0.997882i	$0.520723\pi$
$840$	−19.5379	−0.674121
$841$	25.0200	0.862759
$842$	93.6808	3.22846
$843$	−20.6143	−0.709995
$844$	−38.4445	−1.32332
$845$	−42.5277	−1.46300
$846$	−12.0777	−0.415240
$847$	−8.55413	−0.293923
$848$	−14.6634	−0.503543
$849$	−28.4556	−0.976594
$850$	29.5651	1.01407
$851$	−37.8426	−1.29723
$852$	35.2888	1.20897
$853$	35.2843	1.20811	0.604056	−	0.796942i	$-0.293550\pi$
$853$	35.2843	1.20811	0.604056	+	0.796942i	$0.293550\pi$
$854$	−0.628725	−0.0215145
$855$	−19.4798	−0.666196
$856$	32.9002	1.12450
$857$	4.31950	0.147551	0.0737756	−	0.997275i	$-0.476495\pi$
$857$	4.31950	0.147551	0.0737756	+	0.997275i	$0.476495\pi$
$858$	−2.34552	−0.0800748
$859$	55.1455	1.88154	0.940771	−	0.339044i	$-0.110103\pi$
$859$	55.1455	1.88154	0.940771	+	0.339044i	$0.110103\pi$
$860$	−18.6625	−0.636386
$861$	7.14989	0.243667
$862$	102.513	3.49159
$863$	9.45516	0.321857	0.160929	−	0.986966i	$-0.448551\pi$
$863$	9.45516	0.321857	0.160929	+	0.986966i	$0.448551\pi$
$864$	9.69755	0.329917
$865$	−20.1774	−0.686052
$866$	−14.6706	−0.498529
$867$	−14.3799	−0.488366
$868$	−15.5831	−0.528924
$869$	−2.01029	−0.0681943
$870$	−65.8965	−2.23410
$871$	−1.06200	−0.0359846
$872$	28.8452	0.976820
$873$	1.77608	0.0601113
$874$	−59.5454	−2.01415
$875$	4.15377	0.140423
$876$	46.4571	1.56964
$877$	−46.5998	−1.57356	−0.786782	−	0.617231i	$-0.788254\pi$
$877$	−46.5998	−1.57356	−0.786782	+	0.617231i	$0.788254\pi$
$878$	−45.1413	−1.52345
$879$	−23.5538	−0.794451
$880$	26.7769	0.902648
$881$	−22.5999	−0.761409	−0.380705	−	0.924697i	$-0.624319\pi$
$881$	−22.5999	−0.761409	−0.380705	+	0.924697i	$0.624319\pi$
$882$	4.58014	0.154221
$883$	−8.21563	−0.276478	−0.138239	−	0.990399i	$-0.544144\pi$
$883$	−8.21563	−0.276478	−0.138239	+	0.990399i	$0.544144\pi$
$884$	−4.46776	−0.150267
$885$	−41.6681	−1.40066
$886$	60.7223	2.04001
$887$	39.4261	1.32380	0.661899	−	0.749593i	$-0.269751\pi$
$887$	39.4261	1.32380	0.661899	+	0.749593i	$0.269751\pi$
$888$	29.0348	0.974343
$889$	−1.00000	−0.0335389
$890$	8.51505	0.285425
$891$	−0.121251	−0.00406205
$892$	−50.3276	−1.68509
$893$	−8.31598	−0.278284
$894$	39.5750	1.32359
$895$	67.7403	2.26431
$896$	17.6117	0.588364
$897$	4.58283	0.153016
$898$	−97.4395	−3.25160
$899$	−27.4057	−0.914030
$900$	−48.0419	−1.60140
$901$	5.47335	0.182344
$902$	−25.8360	−0.860244
$903$	−1.43308	−0.0476900
$904$	−89.0741	−2.96256
$905$	−42.8952	−1.42588
$906$	−30.7375	−1.02118
$907$	7.21394	0.239535	0.119767	−	0.992802i	$-0.461785\pi$
$907$	7.21394	0.239535	0.119767	+	0.992802i	$0.461785\pi$
$908$	9.49203	0.315004
$909$	−21.0088	−0.696817
$910$	−4.67338	−0.154921
$911$	−3.62410	−0.120072	−0.0600360	−	0.998196i	$-0.519122\pi$
$911$	−3.62410	−0.120072	−0.0600360	+	0.998196i	$0.519122\pi$
$912$	17.3278	0.573780
$913$	15.0318	0.497481
$914$	14.5546	0.481424
$915$	0.912254	0.0301582
$916$	48.6547	1.60760
$917$	11.7524	0.388097
$918$	−24.6883	−0.814834
$919$	12.3836	0.408498	0.204249	−	0.978919i	$-0.434525\pi$
$919$	12.3836	0.408498	0.204249	+	0.978919i	$0.434525\pi$
$920$	−137.942	−4.54782
$921$	27.2831	0.899009
$922$	−6.29627	−0.207357
$923$	4.40142	0.144874
$924$	7.03174	0.231327
$925$	−31.0829	−1.02200
$926$	−88.6458	−2.91308
$927$	32.2524	1.05931
$928$	−13.6808	−0.449094
$929$	56.3033	1.84725	0.923625	−	0.383296i	$-0.125211\pi$
$929$	56.3033	1.84725	0.923625	+	0.383296i	$0.125211\pi$
$930$	33.4309	1.09624
$931$	3.15361	0.103355
$932$	−50.8221	−1.66473
$933$	5.26932	0.172510
$934$	101.325	3.31545
$935$	−9.99489	−0.326868
$936$	5.59722	0.182951
$937$	−14.5952	−0.476805	−0.238403	−	0.971166i	$-0.576624\pi$
$937$	−14.5952	−0.476805	−0.238403	+	0.971166i	$0.576624\pi$
$938$	4.70749	0.153705
$939$	−5.71569	−0.186525
$940$	−36.9454	−1.20503
$941$	59.0179	1.92393	0.961965	−	0.273173i	$-0.0880730\pi$
$941$	59.0179	1.92393	0.961965	+	0.273173i	$0.0880730\pi$
$942$	46.0526	1.50048
$943$	50.4799	1.64385
$944$	−59.0015	−1.92033
$945$	−17.4659	−0.568167
$946$	5.17842	0.168365
$947$	7.29868	0.237175	0.118588	−	0.992944i	$-0.462163\pi$
$947$	7.29868	0.237175	0.118588	+	0.992944i	$0.462163\pi$
$948$	−5.77947	−0.187708
$949$	5.79439	0.188094
$950$	−48.9090	−1.58682
$951$	−16.7369	−0.542731
$952$	10.3265	0.334685
$953$	20.8825	0.676449	0.338225	−	0.941065i	$-0.390174\pi$
$953$	20.8825	0.676449	0.338225	+	0.941065i	$0.390174\pi$
$954$	−13.1503	−0.425755
$955$	54.4166	1.76088
$956$	33.2438	1.07518
$957$	12.3666	0.399755
$958$	76.7580	2.47994
$959$	−13.7085	−0.442670
$960$	−20.1522	−0.650410
$961$	−17.0964	−0.551498
$962$	6.94500	0.223916
$963$	11.1906	0.360613
$964$	40.9474	1.31883
$965$	−81.3627	−2.61916
$966$	−20.3141	−0.653594
$967$	−8.16712	−0.262637	−0.131318	−	0.991340i	$-0.541921\pi$
$967$	−8.16712	−0.262637	−0.131318	+	0.991340i	$0.541921\pi$
$968$	46.3376	1.48935
$969$	−6.46786	−0.207778
$970$	8.03303	0.257925
$971$	−21.7639	−0.698438	−0.349219	−	0.937041i	$-0.613553\pi$
$971$	−21.7639	−0.698438	−0.349219	+	0.937041i	$0.613553\pi$
$972$	64.9704	2.08393
$973$	18.5651	0.595170
$974$	34.8250	1.11586
$975$	3.76421	0.120551
$976$	1.29174	0.0413475
$977$	26.9152	0.861093	0.430547	−	0.902568i	$-0.358321\pi$
$977$	26.9152	0.861093	0.430547	+	0.902568i	$0.358321\pi$
$978$	−3.27987	−0.104879
$979$	−1.59799	−0.0510720
$980$	14.0105	0.447550
$981$	9.81135	0.313252
$982$	52.8579	1.68676
$983$	25.9287	0.826997	0.413499	−	0.910505i	$-0.364307\pi$
$983$	25.9287	0.826997	0.413499	+	0.910505i	$0.364307\pi$
$984$	−38.7308	−1.23469
$985$	22.0867	0.703741
$986$	34.8289	1.10918
$987$	−2.83702	−0.0903032
$988$	7.39095	0.235137
$989$	−10.1179	−0.321731
$990$	24.0137	0.763206
$991$	−16.9040	−0.536972	−0.268486	−	0.963284i	$-0.586523\pi$
$991$	−16.9040	−0.536972	−0.268486	+	0.963284i	$0.586523\pi$
$992$	6.94060	0.220364
$993$	36.7856	1.16736
$994$	−19.5099	−0.618817
$995$	58.9767	1.86969
$996$	43.2158	1.36934
$997$	−19.5107	−0.617909	−0.308955	−	0.951077i	$-0.599979\pi$
$997$	−19.5107	−0.617909	−0.308955	+	0.951077i	$0.599979\pi$
$998$	−28.4868	−0.901734
$999$	25.9557	0.821202

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	889.2.a.d.1.1	✓	20
3.2	odd	2		8001.2.a.w.1.20		20
7.6	odd	2		6223.2.a.l.1.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
889.2.a.d.1.1	✓	20	1.1	even	1	trivial
6223.2.a.l.1.1		20	7.6	odd	2
8001.2.a.w.1.20		20	3.2	odd	2

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:	\( N \)	\(=\)	\( 889 = 7 \cdot 127 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	889.a (trivial)

\(f(q)\)	\(=\)	\(q-2.48579 q^{2} +1.07586 q^{3} +4.17918 q^{4} +3.35246 q^{5} -2.67437 q^{6} +1.00000 q^{7} -5.41698 q^{8} -1.84252 q^{9} +O(q^{10})\)	\(q-2.48579 q^{2} +1.07586 q^{3} +4.17918 q^{4} +3.35246 q^{5} -2.67437 q^{6} +1.00000 q^{7} -5.41698 q^{8} -1.84252 q^{9} -8.33354 q^{10} +1.56393 q^{11} +4.49621 q^{12} +0.560792 q^{13} -2.48579 q^{14} +3.60678 q^{15} +5.10716 q^{16} -1.90633 q^{17} +4.58014 q^{18} +3.15361 q^{19} +14.0105 q^{20} +1.07586 q^{21} -3.88760 q^{22} +7.59584 q^{23} -5.82792 q^{24} +6.23902 q^{25} -1.39401 q^{26} -5.20988 q^{27} +4.17918 q^{28} +7.34983 q^{29} -8.96572 q^{30} -3.72875 q^{31} -1.86138 q^{32} +1.68257 q^{33} +4.73874 q^{34} +3.35246 q^{35} -7.70023 q^{36} -4.98201 q^{37} -7.83922 q^{38} +0.603334 q^{39} -18.1602 q^{40} +6.64574 q^{41} -2.67437 q^{42} -1.33203 q^{43} +6.53592 q^{44} -6.17700 q^{45} -18.8817 q^{46} -2.63698 q^{47} +5.49459 q^{48} +1.00000 q^{49} -15.5089 q^{50} -2.05094 q^{51} +2.34365 q^{52} -2.87115 q^{53} +12.9507 q^{54} +5.24301 q^{55} -5.41698 q^{56} +3.39284 q^{57} -18.2702 q^{58} -11.5527 q^{59} +15.0734 q^{60} +0.252927 q^{61} +9.26890 q^{62} -1.84252 q^{63} -5.58731 q^{64} +1.88004 q^{65} -4.18252 q^{66} -1.89376 q^{67} -7.96688 q^{68} +8.17206 q^{69} -8.33354 q^{70} +7.84857 q^{71} +9.98092 q^{72} +10.3325 q^{73} +12.3843 q^{74} +6.71231 q^{75} +13.1795 q^{76} +1.56393 q^{77} -1.49976 q^{78} -1.28541 q^{79} +17.1216 q^{80} -0.0775297 q^{81} -16.5199 q^{82} +9.61160 q^{83} +4.49621 q^{84} -6.39090 q^{85} +3.31116 q^{86} +7.90739 q^{87} -8.47177 q^{88} -1.02178 q^{89} +15.3547 q^{90} +0.560792 q^{91} +31.7443 q^{92} -4.01161 q^{93} +6.55498 q^{94} +10.5724 q^{95} -2.00258 q^{96} -0.963940 q^{97} -2.48579 q^{98} -2.88157 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 8 q^{2} + 24 q^{4} + 3 q^{5} + 6 q^{6} + 20 q^{7} + 24 q^{8} + 30 q^{9}+O(q^{10}) \) 20 * q + 8 * q^2 + 24 * q^4 + 3 * q^5 + 6 * q^6 + 20 * q^7 + 24 * q^8 + 30 * q^9	\( 20 q + 8 q^{2} + 24 q^{4} + 3 q^{5} + 6 q^{6} + 20 q^{7} + 24 q^{8} + 30 q^{9} - 8 q^{10} + 26 q^{11} - 4 q^{12} - 4 q^{13} + 8 q^{14} + 10 q^{15} + 24 q^{16} + 4 q^{17} + 5 q^{18} + q^{19} - 2 q^{20} + q^{22} + 31 q^{23} - 6 q^{24} + 27 q^{25} + 4 q^{26} - 18 q^{27} + 24 q^{28} + 16 q^{29} - 5 q^{30} + 6 q^{31} + 41 q^{32} - 18 q^{33} - 10 q^{34} + 3 q^{35} + 18 q^{36} + 2 q^{37} + 3 q^{38} + 43 q^{39} - 38 q^{40} + 25 q^{41} + 6 q^{42} + 13 q^{43} + 66 q^{44} - 2 q^{45} + 20 q^{46} + 19 q^{47} - 16 q^{48} + 20 q^{49} - 4 q^{50} + 4 q^{51} + 20 q^{52} + 24 q^{53} + 5 q^{54} - 3 q^{55} + 24 q^{56} - 4 q^{57} + 12 q^{58} + 23 q^{59} + 24 q^{60} - 27 q^{61} + 7 q^{62} + 30 q^{63} + 2 q^{64} + 26 q^{65} + 26 q^{66} + 9 q^{67} - 25 q^{68} - 3 q^{69} - 8 q^{70} + 63 q^{71} + 27 q^{72} - 21 q^{73} + 21 q^{74} - 52 q^{75} - 10 q^{76} + 26 q^{77} - 70 q^{78} + 18 q^{79} - 23 q^{80} + 40 q^{81} - 42 q^{82} - q^{83} - 4 q^{84} - 41 q^{85} - 12 q^{86} - 9 q^{87} + 57 q^{88} - 16 q^{89} + q^{90} - 4 q^{91} + 17 q^{92} - 41 q^{93} + 7 q^{94} + 75 q^{95} - 81 q^{96} - 32 q^{97} + 8 q^{98} + 15 q^{99}+O(q^{100}) \) 20 * q + 8 * q^2 + 24 * q^4 + 3 * q^5 + 6 * q^6 + 20 * q^7 + 24 * q^8 + 30 * q^9 - 8 * q^10 + 26 * q^11 - 4 * q^12 - 4 * q^13 + 8 * q^14 + 10 * q^15 + 24 * q^16 + 4 * q^17 + 5 * q^18 + q^19 - 2 * q^20 + q^22 + 31 * q^23 - 6 * q^24 + 27 * q^25 + 4 * q^26 - 18 * q^27 + 24 * q^28 + 16 * q^29 - 5 * q^30 + 6 * q^31 + 41 * q^32 - 18 * q^33 - 10 * q^34 + 3 * q^35 + 18 * q^36 + 2 * q^37 + 3 * q^38 + 43 * q^39 - 38 * q^40 + 25 * q^41 + 6 * q^42 + 13 * q^43 + 66 * q^44 - 2 * q^45 + 20 * q^46 + 19 * q^47 - 16 * q^48 + 20 * q^49 - 4 * q^50 + 4 * q^51 + 20 * q^52 + 24 * q^53 + 5 * q^54 - 3 * q^55 + 24 * q^56 - 4 * q^57 + 12 * q^58 + 23 * q^59 + 24 * q^60 - 27 * q^61 + 7 * q^62 + 30 * q^63 + 2 * q^64 + 26 * q^65 + 26 * q^66 + 9 * q^67 - 25 * q^68 - 3 * q^69 - 8 * q^70 + 63 * q^71 + 27 * q^72 - 21 * q^73 + 21 * q^74 - 52 * q^75 - 10 * q^76 + 26 * q^77 - 70 * q^78 + 18 * q^79 - 23 * q^80 + 40 * q^81 - 42 * q^82 - q^83 - 4 * q^84 - 41 * q^85 - 12 * q^86 - 9 * q^87 + 57 * q^88 - 16 * q^89 + q^90 - 4 * q^91 + 17 * q^92 - 41 * q^93 + 7 * q^94 + 75 * q^95 - 81 * q^96 - 32 * q^97 + 8 * q^98 + 15 * q^99

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