LMFDB - Embedded newform 763.2.a.e.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [763,2,Mod(1,763)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(763, 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("763.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 763 = 7 \cdot 109 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	763.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:	$6.09258567422$
Analytic rank:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 7 x^{16} - 4 x^{15} + 127 x^{14} - 159 x^{13} - 833 x^{12} + 1766 x^{11} + 2316 x^{10} + \cdots + 8 $ x^17 - 7x^16 - 4x^15 + 127x^14 - 159x^13 - 833x^12 + 1766x^11 + 2316x^10 - 7456x^9 - 1858x^8 + 14879x^7 - 2693x^6 - 13874x^5 + 4498x^4 + 5607x^3 - 1594x^2 - 708x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$1.60194$ of defining polynomial
Character	$\chi$	$=$	763.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.60194 q^{2} -2.26320 q^{3} +0.566208 q^{4} -1.99604 q^{5} -3.62551 q^{6} +1.00000 q^{7} -2.29685 q^{8} +2.12208 q^{9} +O(q^{10})$	\(q+1.60194 q^{2} -2.26320 q^{3} +0.566208 q^{4} -1.99604 q^{5} -3.62551 q^{6} +1.00000 q^{7} -2.29685 q^{8} +2.12208 q^{9} -3.19754 q^{10} +6.12170 q^{11} -1.28144 q^{12} +1.39341 q^{13} +1.60194 q^{14} +4.51745 q^{15} -4.81182 q^{16} -1.07390 q^{17} +3.39945 q^{18} +0.472899 q^{19} -1.13018 q^{20} -2.26320 q^{21} +9.80658 q^{22} +9.11283 q^{23} +5.19823 q^{24} -1.01581 q^{25} +2.23216 q^{26} +1.98690 q^{27} +0.566208 q^{28} -1.75159 q^{29} +7.23668 q^{30} +6.15626 q^{31} -3.11455 q^{32} -13.8546 q^{33} -1.72033 q^{34} -1.99604 q^{35} +1.20154 q^{36} +9.41647 q^{37} +0.757555 q^{38} -3.15357 q^{39} +4.58461 q^{40} +9.16143 q^{41} -3.62551 q^{42} +6.65304 q^{43} +3.46615 q^{44} -4.23577 q^{45} +14.5982 q^{46} -12.6169 q^{47} +10.8901 q^{48} +1.00000 q^{49} -1.62727 q^{50} +2.43046 q^{51} +0.788961 q^{52} +5.38247 q^{53} +3.18290 q^{54} -12.2192 q^{55} -2.29685 q^{56} -1.07027 q^{57} -2.80594 q^{58} -12.8654 q^{59} +2.55782 q^{60} -4.35578 q^{61} +9.86195 q^{62} +2.12208 q^{63} +4.63432 q^{64} -2.78131 q^{65} -22.1943 q^{66} -4.31999 q^{67} -0.608054 q^{68} -20.6242 q^{69} -3.19754 q^{70} +4.50243 q^{71} -4.87410 q^{72} -12.0212 q^{73} +15.0846 q^{74} +2.29898 q^{75} +0.267759 q^{76} +6.12170 q^{77} -5.05183 q^{78} -17.3092 q^{79} +9.60461 q^{80} -10.8630 q^{81} +14.6761 q^{82} +10.2123 q^{83} -1.28144 q^{84} +2.14356 q^{85} +10.6578 q^{86} +3.96420 q^{87} -14.0606 q^{88} +3.26884 q^{89} -6.78544 q^{90} +1.39341 q^{91} +5.15976 q^{92} -13.9329 q^{93} -20.2116 q^{94} -0.943927 q^{95} +7.04887 q^{96} +17.3289 q^{97} +1.60194 q^{98} +12.9907 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q + 7 q^{2} + 2 q^{3} + 23 q^{4} + 12 q^{5} - 5 q^{6} + 17 q^{7} + 18 q^{8} + 25 q^{9}+O(q^{10}) $ 17 * q + 7 * q^2 + 2 * q^3 + 23 * q^4 + 12 * q^5 - 5 * q^6 + 17 * q^7 + 18 * q^8 + 25 * q^9	\( 17 q + 7 q^{2} + 2 q^{3} + 23 q^{4} + 12 q^{5} - 5 q^{6} + 17 q^{7} + 18 q^{8} + 25 q^{9} - 6 q^{10} + 20 q^{11} - 9 q^{12} + 11 q^{13} + 7 q^{14} - 3 q^{15} + 23 q^{16} + 19 q^{17} + q^{18} - 4 q^{19} + 10 q^{20} + 2 q^{21} + 3 q^{22} + 22 q^{23} - 21 q^{24} + 21 q^{25} - 12 q^{26} - 7 q^{27} + 23 q^{28} + 37 q^{29} + 2 q^{30} - 10 q^{31} + 18 q^{32} + q^{33} - 7 q^{34} + 12 q^{35} + 42 q^{36} + 13 q^{37} + 18 q^{38} - 17 q^{39} - 17 q^{40} - 6 q^{41} - 5 q^{42} + 9 q^{43} + 35 q^{44} + 28 q^{45} - 17 q^{46} - 4 q^{47} - 43 q^{48} + 17 q^{49} + 37 q^{50} + 5 q^{51} + 36 q^{52} + 45 q^{53} - 22 q^{54} - 13 q^{55} + 18 q^{56} - q^{57} + 4 q^{58} - 12 q^{59} - 51 q^{60} + 6 q^{61} - 24 q^{62} + 25 q^{63} + 20 q^{64} + 15 q^{65} - 15 q^{66} - 3 q^{67} + 60 q^{68} - 50 q^{69} - 6 q^{70} + 36 q^{71} + 72 q^{72} - 4 q^{73} + 13 q^{74} - 22 q^{75} - 74 q^{76} + 20 q^{77} + 12 q^{78} + 5 q^{79} - 25 q^{80} - 7 q^{81} - 24 q^{82} + 7 q^{83} - 9 q^{84} + 8 q^{85} + 2 q^{86} + 13 q^{87} - 55 q^{88} + 13 q^{89} - 92 q^{90} + 11 q^{91} + 36 q^{92} + 7 q^{93} - 37 q^{94} - 34 q^{95} - 33 q^{96} - 23 q^{97} + 7 q^{98} - 5 q^{99}+O(q^{100}) \) 17 * q + 7 * q^2 + 2 * q^3 + 23 * q^4 + 12 * q^5 - 5 * q^6 + 17 * q^7 + 18 * q^8 + 25 * q^9 - 6 * q^10 + 20 * q^11 - 9 * q^12 + 11 * q^13 + 7 * q^14 - 3 * q^15 + 23 * q^16 + 19 * q^17 + q^18 - 4 * q^19 + 10 * q^20 + 2 * q^21 + 3 * q^22 + 22 * q^23 - 21 * q^24 + 21 * q^25 - 12 * q^26 - 7 * q^27 + 23 * q^28 + 37 * q^29 + 2 * q^30 - 10 * q^31 + 18 * q^32 + q^33 - 7 * q^34 + 12 * q^35 + 42 * q^36 + 13 * q^37 + 18 * q^38 - 17 * q^39 - 17 * q^40 - 6 * q^41 - 5 * q^42 + 9 * q^43 + 35 * q^44 + 28 * q^45 - 17 * q^46 - 4 * q^47 - 43 * q^48 + 17 * q^49 + 37 * q^50 + 5 * q^51 + 36 * q^52 + 45 * q^53 - 22 * q^54 - 13 * q^55 + 18 * q^56 - q^57 + 4 * q^58 - 12 * q^59 - 51 * q^60 + 6 * q^61 - 24 * q^62 + 25 * q^63 + 20 * q^64 + 15 * q^65 - 15 * q^66 - 3 * q^67 + 60 * q^68 - 50 * q^69 - 6 * q^70 + 36 * q^71 + 72 * q^72 - 4 * q^73 + 13 * q^74 - 22 * q^75 - 74 * q^76 + 20 * q^77 + 12 * q^78 + 5 * q^79 - 25 * q^80 - 7 * q^81 - 24 * q^82 + 7 * q^83 - 9 * q^84 + 8 * q^85 + 2 * q^86 + 13 * q^87 - 55 * q^88 + 13 * q^89 - 92 * q^90 + 11 * q^91 + 36 * q^92 + 7 * q^93 - 37 * q^94 - 34 * q^95 - 33 * q^96 - 23 * q^97 + 7 * q^98 - 5 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.60194	1.13274	0.566371	−	0.824150i	$-0.308347\pi$
$2$	1.60194	1.13274	0.566371	+	0.824150i	$0.308347\pi$
$3$	−2.26320	−1.30666	−0.653330	−	0.757073i	$-0.726629\pi$
$3$	−2.26320	−1.30666	−0.653330	+	0.757073i	$0.726629\pi$
$4$	0.566208	0.283104
$5$	−1.99604	−0.892658	−0.446329	−	0.894869i	$-0.647269\pi$
$5$	−1.99604	−0.892658	−0.446329	+	0.894869i	$0.647269\pi$
$6$	−3.62551	−1.48011
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−2.29685	−0.812058
$9$	2.12208	0.707361
$10$	−3.19754	−1.01115
$11$	6.12170	1.84576	0.922880	−	0.385087i	$-0.125829\pi$
$11$	6.12170	1.84576	0.922880	+	0.385087i	$0.125829\pi$
$12$	−1.28144	−0.369921
$13$	1.39341	0.386463	0.193232	−	0.981153i	$-0.438103\pi$
$13$	1.39341	0.386463	0.193232	+	0.981153i	$0.438103\pi$
$14$	1.60194	0.428136
$15$	4.51745	1.16640
$16$	−4.81182	−1.20296
$17$	−1.07390	−0.260460	−0.130230	−	0.991484i	$-0.541572\pi$
$17$	−1.07390	−0.260460	−0.130230	+	0.991484i	$0.541572\pi$
$18$	3.39945	0.801257
$19$	0.472899	0.108490	0.0542452	−	0.998528i	$-0.482725\pi$
$19$	0.472899	0.108490	0.0542452	+	0.998528i	$0.482725\pi$
$20$	−1.13018	−0.252715
$21$	−2.26320	−0.493871
$22$	9.80658	2.09077
$23$	9.11283	1.90016	0.950078	−	0.312011i	$-0.101003\pi$
$23$	9.11283	1.90016	0.950078	+	0.312011i	$0.101003\pi$
$24$	5.19823	1.06108
$25$	−1.01581	−0.203162
$26$	2.23216	0.437763
$27$	1.98690	0.382380
$28$	0.566208	0.107003
$29$	−1.75159	−0.325262	−0.162631	−	0.986687i	$-0.551998\pi$
$29$	−1.75159	−0.325262	−0.162631	+	0.986687i	$0.551998\pi$
$30$	7.23668	1.32123
$31$	6.15626	1.10570	0.552849	−	0.833282i	$-0.313541\pi$
$31$	6.15626	1.10570	0.552849	+	0.833282i	$0.313541\pi$
$32$	−3.11455	−0.550581
$33$	−13.8546	−2.41178
$34$	−1.72033	−0.295034
$35$	−1.99604	−0.337393
$36$	1.20154	0.200257
$37$	9.41647	1.54806	0.774029	−	0.633150i	$-0.218238\pi$
$37$	9.41647	1.54806	0.774029	+	0.633150i	$0.218238\pi$
$38$	0.757555	0.122892
$39$	−3.15357	−0.504976
$40$	4.58461	0.724890
$41$	9.16143	1.43078	0.715388	−	0.698728i	$-0.246250\pi$
$41$	9.16143	1.43078	0.715388	+	0.698728i	$0.246250\pi$
$42$	−3.62551	−0.559428
$43$	6.65304	1.01458	0.507290	−	0.861776i	$-0.330647\pi$
$43$	6.65304	1.01458	0.507290	+	0.861776i	$0.330647\pi$
$44$	3.46615	0.522542
$45$	−4.23577	−0.631431
$46$	14.5982	2.15239
$47$	−12.6169	−1.84037	−0.920186	−	0.391482i	$-0.871962\pi$
$47$	−12.6169	−1.84037	−0.920186	+	0.391482i	$0.871962\pi$
$48$	10.8901	1.57185
$49$	1.00000	0.142857
$50$	−1.62727	−0.230130
$51$	2.43046	0.340333
$52$	0.788961	0.109409
$53$	5.38247	0.739339	0.369670	−	0.929163i	$-0.379471\pi$
$53$	5.38247	0.739339	0.369670	+	0.929163i	$0.379471\pi$
$54$	3.18290	0.433138
$55$	−12.2192	−1.64763
$56$	−2.29685	−0.306929
$57$	−1.07027	−0.141760
$58$	−2.80594	−0.368437
$59$	−12.8654	−1.67494	−0.837469	−	0.546485i	$-0.815965\pi$
$59$	−12.8654	−1.67494	−0.837469	+	0.546485i	$0.815965\pi$
$60$	2.55782	0.330213
$61$	−4.35578	−0.557700	−0.278850	−	0.960335i	$-0.589953\pi$
$61$	−4.35578	−0.557700	−0.278850	+	0.960335i	$0.589953\pi$
$62$	9.86195	1.25247
$63$	2.12208	0.267357
$64$	4.63432	0.579290
$65$	−2.78131	−0.344979
$66$	−22.1943	−2.73193
$67$	−4.31999	−0.527771	−0.263885	−	0.964554i	$-0.585004\pi$
$67$	−4.31999	−0.527771	−0.263885	+	0.964554i	$0.585004\pi$
$68$	−0.608054	−0.0737373
$69$	−20.6242	−2.48286
$70$	−3.19754	−0.382179
$71$	4.50243	0.534340	0.267170	−	0.963649i	$-0.413911\pi$
$71$	4.50243	0.534340	0.267170	+	0.963649i	$0.413911\pi$
$72$	−4.87410	−0.574418
$73$	−12.0212	−1.40697	−0.703486	−	0.710709i	$-0.748374\pi$
$73$	−12.0212	−1.40697	−0.703486	+	0.710709i	$0.748374\pi$
$74$	15.0846	1.75355
$75$	2.29898	0.265464
$76$	0.267759	0.0307141
$77$	6.12170	0.697632
$78$	−5.05183	−0.572007
$79$	−17.3092	−1.94744	−0.973719	−	0.227751i	$-0.926863\pi$
$79$	−17.3092	−1.94744	−0.973719	+	0.227751i	$0.926863\pi$
$80$	9.60461	1.07383
$81$	−10.8630	−1.20700
$82$	14.6761	1.62070
$83$	10.2123	1.12094	0.560472	−	0.828173i	$-0.310620\pi$
$83$	10.2123	1.12094	0.560472	+	0.828173i	$0.310620\pi$
$84$	−1.28144	−0.139817
$85$	2.14356	0.232502
$86$	10.6578	1.14926
$87$	3.96420	0.425006
$88$	−14.0606	−1.49886
$89$	3.26884	0.346496	0.173248	−	0.984878i	$-0.444574\pi$
$89$	3.26884	0.346496	0.173248	+	0.984878i	$0.444574\pi$
$90$	−6.78544	−0.715249
$91$	1.39341	0.146069
$92$	5.15976	0.537942
$93$	−13.9329	−1.44477
$94$	−20.2116	−2.08467
$95$	−0.943927	−0.0968449
$96$	7.04887	0.719422
$97$	17.3289	1.75948	0.879739	−	0.475456i	$-0.157717\pi$
$97$	17.3289	1.75948	0.879739	+	0.475456i	$0.157717\pi$
$98$	1.60194	0.161820
$99$	12.9907	1.30562
$100$	−0.575160	−0.0575160
$101$	10.7307	1.06774	0.533872	−	0.845565i	$-0.320736\pi$
$101$	10.7307	1.06774	0.533872	+	0.845565i	$0.320736\pi$
$102$	3.89345	0.385509
$103$	9.19120	0.905636	0.452818	−	0.891603i	$-0.350419\pi$
$103$	9.19120	0.905636	0.452818	+	0.891603i	$0.350419\pi$
$104$	−3.20046	−0.313830
$105$	4.51745	0.440858
$106$	8.62239	0.837480
$107$	−19.6421	−1.89887	−0.949436	−	0.313961i	$-0.898344\pi$
$107$	−19.6421	−1.89887	−0.949436	+	0.313961i	$0.898344\pi$
$108$	1.12500	0.108253
$109$	−1.00000	−0.0957826
$109$	−1.00000	−0.0957826
$110$	−19.5744	−1.86634
$111$	−21.3114	−2.02279
$112$	−4.81182	−0.454675
$113$	11.7018	1.10082	0.550408	−	0.834896i	$-0.314472\pi$
$113$	11.7018	1.10082	0.550408	+	0.834896i	$0.314472\pi$
$114$	−1.71450	−0.160578
$115$	−18.1896	−1.69619
$116$	−0.991763	−0.0920829
$117$	2.95694	0.273369
$118$	−20.6096	−1.89727
$119$	−1.07390	−0.0984447
$120$	−10.3759	−0.947185
$121$	26.4752	2.40683
$122$	−6.97769	−0.631730
$123$	−20.7342	−1.86954
$124$	3.48572	0.313027
$125$	12.0078	1.07401
$126$	3.39945	0.302847
$127$	2.62433	0.232872	0.116436	−	0.993198i	$-0.462853\pi$
$127$	2.62433	0.232872	0.116436	+	0.993198i	$0.462853\pi$
$128$	13.6530	1.20677
$129$	−15.0572	−1.32571
$130$	−4.45549	−0.390773
$131$	13.6672	1.19411	0.597054	−	0.802201i	$-0.296338\pi$
$131$	13.6672	1.19411	0.597054	+	0.802201i	$0.296338\pi$
$132$	−7.84460	−0.682785
$133$	0.472899	0.0410055
$134$	−6.92036	−0.597828
$135$	−3.96595	−0.341334
$136$	2.46660	0.211509
$137$	8.69219	0.742624	0.371312	−	0.928508i	$-0.378908\pi$
$137$	8.69219	0.742624	0.371312	+	0.928508i	$0.378908\pi$
$138$	−33.0387	−2.81244
$139$	3.80216	0.322495	0.161247	−	0.986914i	$-0.448448\pi$
$139$	3.80216	0.322495	0.161247	+	0.986914i	$0.448448\pi$
$140$	−1.13018	−0.0955173
$141$	28.5547	2.40474
$142$	7.21262	0.605269
$143$	8.53005	0.713318
$144$	−10.2111	−0.850924
$145$	3.49625	0.290347
$146$	−19.2572	−1.59374
$147$	−2.26320	−0.186666
$148$	5.33168	0.438261
$149$	3.10677	0.254516	0.127258	−	0.991870i	$-0.459382\pi$
$149$	3.10677	0.254516	0.127258	+	0.991870i	$0.459382\pi$
$150$	3.68283	0.300702
$151$	−18.3238	−1.49117	−0.745585	−	0.666411i	$-0.767830\pi$
$151$	−18.3238	−1.49117	−0.745585	+	0.666411i	$0.767830\pi$
$152$	−1.08618	−0.0881005
$153$	−2.27892	−0.184239
$154$	9.80658	0.790237
$155$	−12.2882	−0.987009
$156$	−1.78558	−0.142961
$157$	−1.36993	−0.109332	−0.0546662	−	0.998505i	$-0.517409\pi$
$157$	−1.36993	−0.109332	−0.0546662	+	0.998505i	$0.517409\pi$
$158$	−27.7283	−2.20595
$159$	−12.1816	−0.966065
$160$	6.21679	0.491480
$161$	9.11283	0.718192
$162$	−17.4019	−1.36722
$163$	19.8865	1.55763	0.778814	−	0.627255i	$-0.215822\pi$
$163$	19.8865	1.55763	0.778814	+	0.627255i	$0.215822\pi$
$164$	5.18728	0.405058
$165$	27.6544	2.15290
$166$	16.3595	1.26974
$167$	−7.40554	−0.573058	−0.286529	−	0.958072i	$-0.592501\pi$
$167$	−7.40554	−0.573058	−0.286529	+	0.958072i	$0.592501\pi$
$168$	5.19823	0.401052
$169$	−11.0584	−0.850646
$170$	3.43385	0.263365
$171$	1.00353	0.0767419
$172$	3.76701	0.287232
$173$	22.1960	1.68753	0.843764	−	0.536715i	$-0.180335\pi$
$173$	22.1960	1.68753	0.843764	+	0.536715i	$0.180335\pi$
$174$	6.35040	0.481423
$175$	−1.01581	−0.0767880
$176$	−29.4565	−2.22037
$177$	29.1171	2.18857
$178$	5.23648	0.392491
$179$	3.67198	0.274456	0.137228	−	0.990539i	$-0.456181\pi$
$179$	3.67198	0.274456	0.137228	+	0.990539i	$0.456181\pi$
$180$	−2.39833	−0.178761
$181$	−21.2088	−1.57644	−0.788221	−	0.615393i	$-0.788997\pi$
$181$	−21.2088	−1.57644	−0.788221	+	0.615393i	$0.788997\pi$
$182$	2.23216	0.165459
$183$	9.85801	0.728725
$184$	−20.9308	−1.54304
$185$	−18.7957	−1.38189
$186$	−22.3196	−1.63655
$187$	−6.57412	−0.480747
$188$	−7.14382	−0.521017
$189$	1.98690	0.144526
$190$	−1.51211	−0.109700
$191$	−9.05300	−0.655052	−0.327526	−	0.944842i	$-0.606215\pi$
$191$	−9.05300	−0.655052	−0.327526	+	0.944842i	$0.606215\pi$
$192$	−10.4884	−0.756936
$193$	−17.3437	−1.24842	−0.624212	−	0.781255i	$-0.714580\pi$
$193$	−17.3437	−1.24842	−0.624212	+	0.781255i	$0.714580\pi$
$194$	27.7598	1.99304
$195$	6.29467	0.450771
$196$	0.566208	0.0404434
$197$	8.27588	0.589632	0.294816	−	0.955554i	$-0.404742\pi$
$197$	8.27588	0.589632	0.294816	+	0.955554i	$0.404742\pi$
$198$	20.8104	1.47893
$199$	−5.00511	−0.354803	−0.177401	−	0.984139i	$-0.556769\pi$
$199$	−5.00511	−0.354803	−0.177401	+	0.984139i	$0.556769\pi$
$200$	2.33316	0.164979
$201$	9.77700	0.689617
$202$	17.1899	1.20948
$203$	−1.75159	−0.122937
$204$	1.37615	0.0963496
$205$	−18.2866	−1.27719
$206$	14.7237	1.02585
$207$	19.3382	1.34410
$208$	−6.70486	−0.464898
$209$	2.89494	0.200247
$210$	7.23668	0.499378
$211$	8.91402	0.613666	0.306833	−	0.951763i	$-0.400731\pi$
$211$	8.91402	0.613666	0.306833	+	0.951763i	$0.400731\pi$
$212$	3.04760	0.209310
$213$	−10.1899	−0.698201
$214$	−31.4654	−2.15093
$215$	−13.2798	−0.905672
$216$	−4.56361	−0.310515
$217$	6.15626	0.417914
$218$	−1.60194	−0.108497
$219$	27.2063	1.83843
$220$	−6.91859	−0.466451
$221$	−1.49639	−0.100658
$222$	−34.1395	−2.29129
$223$	6.93475	0.464385	0.232193	−	0.972670i	$-0.425410\pi$
$223$	6.93475	0.464385	0.232193	+	0.972670i	$0.425410\pi$
$224$	−3.11455	−0.208100
$225$	−2.15563	−0.143709
$226$	18.7456	1.24694
$227$	15.8708	1.05338	0.526692	−	0.850056i	$-0.323432\pi$
$227$	15.8708	1.05338	0.526692	+	0.850056i	$0.323432\pi$
$228$	−0.605993	−0.0401329
$229$	−4.59482	−0.303634	−0.151817	−	0.988409i	$-0.548512\pi$
$229$	−4.59482	−0.303634	−0.151817	+	0.988409i	$0.548512\pi$
$230$	−29.1386	−1.92135
$231$	−13.8546	−0.911568
$232$	4.02313	0.264131
$233$	−8.80233	−0.576660	−0.288330	−	0.957531i	$-0.593100\pi$
$233$	−8.80233	−0.576660	−0.288330	+	0.957531i	$0.593100\pi$
$234$	4.73683	0.309656
$235$	25.1840	1.64282
$236$	−7.28452	−0.474182
$237$	39.1742	2.54464
$238$	−1.72033	−0.111512
$239$	−5.70632	−0.369111	−0.184556	−	0.982822i	$-0.559085\pi$
$239$	−5.70632	−0.369111	−0.184556	+	0.982822i	$0.559085\pi$
$240$	−21.7372	−1.40313
$241$	−6.40929	−0.412859	−0.206429	−	0.978461i	$-0.566184\pi$
$241$	−6.40929	−0.412859	−0.206429	+	0.978461i	$0.566184\pi$
$242$	42.4116	2.72632
$243$	18.6245	1.19476
$244$	−2.46628	−0.157887
$245$	−1.99604	−0.127523
$246$	−33.2149	−2.11770
$247$	0.658943	0.0419276
$248$	−14.1400	−0.897890
$249$	−23.1125	−1.46469
$250$	19.2358	1.21658
$251$	4.32925	0.273260	0.136630	−	0.990622i	$-0.456373\pi$
$251$	4.32925	0.273260	0.136630	+	0.990622i	$0.456373\pi$
$252$	1.20154	0.0756899
$253$	55.7860	3.50723
$254$	4.20402	0.263784
$255$	−4.85131	−0.303801
$256$	12.6026	0.787665
$257$	−2.72511	−0.169988	−0.0849940	−	0.996381i	$-0.527087\pi$
$257$	−2.72511	−0.169988	−0.0849940	+	0.996381i	$0.527087\pi$
$258$	−24.1207	−1.50169
$259$	9.41647	0.585111
$260$	−1.57480	−0.0976650
$261$	−3.71701	−0.230077
$262$	21.8940	1.35262
$263$	−1.21325	−0.0748123	−0.0374062	−	0.999300i	$-0.511910\pi$
$263$	−1.21325	−0.0748123	−0.0374062	+	0.999300i	$0.511910\pi$
$264$	31.8220	1.95851
$265$	−10.7436	−0.659977
$266$	0.757555	0.0464487
$267$	−7.39805	−0.452753
$268$	−2.44601	−0.149414
$269$	5.24164	0.319589	0.159794	−	0.987150i	$-0.448917\pi$
$269$	5.24164	0.319589	0.159794	+	0.987150i	$0.448917\pi$
$270$	−6.35320	−0.386644
$271$	−4.50412	−0.273606	−0.136803	−	0.990598i	$-0.543683\pi$
$271$	−4.50412	−0.273606	−0.136803	+	0.990598i	$0.543683\pi$
$272$	5.16744	0.313322
$273$	−3.15357	−0.190863
$274$	13.9244	0.841201
$275$	−6.21848	−0.374988
$276$	−11.6776	−0.702908
$277$	15.5178	0.932375	0.466187	−	0.884686i	$-0.345627\pi$
$277$	15.5178	0.932375	0.466187	+	0.884686i	$0.345627\pi$
$278$	6.09083	0.365303
$279$	13.0641	0.782127
$280$	4.58461	0.273983
$281$	3.12989	0.186713	0.0933567	−	0.995633i	$-0.470240\pi$
$281$	3.12989	0.186713	0.0933567	+	0.995633i	$0.470240\pi$
$282$	45.7429	2.72395
$283$	−9.76593	−0.580524	−0.290262	−	0.956947i	$-0.593742\pi$
$283$	−9.76593	−0.580524	−0.290262	+	0.956947i	$0.593742\pi$
$284$	2.54931	0.151274
$285$	2.13630	0.126543
$286$	13.6646	0.808006
$287$	9.16143	0.540782
$288$	−6.60934	−0.389459
$289$	−15.8467	−0.932160
$290$	5.60077	0.328889
$291$	−39.2187	−2.29904
$292$	−6.80648	−0.398319
$293$	−9.68619	−0.565873	−0.282937	−	0.959139i	$-0.591309\pi$
$293$	−9.68619	−0.565873	−0.282937	+	0.959139i	$0.591309\pi$
$294$	−3.62551	−0.211444
$295$	25.6800	1.49515
$296$	−21.6282	−1.25711
$297$	12.1632	0.705782
$298$	4.97685	0.288301
$299$	12.6979	0.734341
$300$	1.30170	0.0751538
$301$	6.65304	0.383475
$302$	−29.3536	−1.68911
$303$	−24.2857	−1.39518
$304$	−2.27551	−0.130509
$305$	8.69432	0.497836
$306$	−3.65068	−0.208696
$307$	4.43681	0.253222	0.126611	−	0.991952i	$-0.459590\pi$
$307$	4.43681	0.253222	0.126611	+	0.991952i	$0.459590\pi$
$308$	3.46615	0.197502
$309$	−20.8015	−1.18336
$310$	−19.6849	−1.11803
$311$	16.4087	0.930451	0.465225	−	0.885192i	$-0.345973\pi$
$311$	16.4087	0.930451	0.465225	+	0.885192i	$0.345973\pi$
$312$	7.24328	0.410070
$313$	−32.4191	−1.83244	−0.916218	−	0.400679i	$-0.868774\pi$
$313$	−32.4191	−1.83244	−0.916218	+	0.400679i	$0.868774\pi$
$314$	−2.19455	−0.123845
$315$	−4.23577	−0.238659
$316$	−9.80062	−0.551328
$317$	−7.58257	−0.425879	−0.212940	−	0.977065i	$-0.568304\pi$
$317$	−7.58257	−0.425879	−0.212940	+	0.977065i	$0.568304\pi$
$318$	−19.5142	−1.09430
$319$	−10.7227	−0.600355
$320$	−9.25031	−0.517108
$321$	44.4540	2.48118
$322$	14.5982	0.813526
$323$	−0.507848	−0.0282574
$324$	−6.15073	−0.341707
$325$	−1.41544	−0.0785146
$326$	31.8569	1.76439
$327$	2.26320	0.125155
$328$	−21.0424	−1.16187
$329$	−12.6169	−0.695595
$330$	44.3007	2.43868
$331$	−22.3483	−1.22837	−0.614186	−	0.789161i	$-0.710516\pi$
$331$	−22.3483	−1.22837	−0.614186	+	0.789161i	$0.710516\pi$
$332$	5.78228	0.317344
$333$	19.9825	1.09504
$334$	−11.8632	−0.649126
$335$	8.62288	0.471118
$336$	10.8901	0.594105
$337$	14.9903	0.816576	0.408288	−	0.912853i	$-0.366126\pi$
$337$	14.9903	0.816576	0.408288	+	0.912853i	$0.366126\pi$
$338$	−17.7149	−0.963563
$339$	−26.4836	−1.43839
$340$	1.21370	0.0658222
$341$	37.6868	2.04085
$342$	1.60759	0.0869288
$343$	1.00000	0.0539949
$344$	−15.2810	−0.823897
$345$	41.1668	2.21634
$346$	35.5566	1.91153
$347$	−22.0354	−1.18292	−0.591462	−	0.806333i	$-0.701449\pi$
$347$	−22.0354	−1.18292	−0.591462	+	0.806333i	$0.701449\pi$
$348$	2.24456	0.120321
$349$	0.610848	0.0326979	0.0163490	−	0.999866i	$-0.494796\pi$
$349$	0.610848	0.0326979	0.0163490	+	0.999866i	$0.494796\pi$
$350$	−1.62727	−0.0869810
$351$	2.76858	0.147776
$352$	−19.0664	−1.01624
$353$	7.61170	0.405130	0.202565	−	0.979269i	$-0.435072\pi$
$353$	7.61170	0.405130	0.202565	+	0.979269i	$0.435072\pi$
$354$	46.6438	2.47909
$355$	−8.98705	−0.476983
$356$	1.85084	0.0980945
$357$	2.43046	0.128634
$358$	5.88228	0.310888
$359$	−13.3788	−0.706105	−0.353052	−	0.935604i	$-0.614856\pi$
$359$	−13.3788	−0.706105	−0.353052	+	0.935604i	$0.614856\pi$
$360$	9.72892	0.512759
$361$	−18.7764	−0.988230
$362$	−33.9753	−1.78570
$363$	−59.9186	−3.14491
$364$	0.788961	0.0413528
$365$	23.9948	1.25594
$366$	15.7919	0.825457
$367$	4.50858	0.235346	0.117673	−	0.993052i	$-0.462457\pi$
$367$	4.50858	0.235346	0.117673	+	0.993052i	$0.462457\pi$
$368$	−43.8494	−2.28581
$369$	19.4413	1.01207
$370$	−30.1095	−1.56532
$371$	5.38247	0.279444
$372$	−7.88890	−0.409020
$373$	15.0141	0.777403	0.388702	−	0.921364i	$-0.372924\pi$
$373$	15.0141	0.777403	0.388702	+	0.921364i	$0.372924\pi$
$374$	−10.5313	−0.544562
$375$	−27.1761	−1.40337
$376$	28.9792	1.49449
$377$	−2.44068	−0.125702
$378$	3.18290	0.163711
$379$	2.28578	0.117413	0.0587063	−	0.998275i	$-0.481302\pi$
$379$	2.28578	0.117413	0.0587063	+	0.998275i	$0.481302\pi$
$380$	−0.534459	−0.0274172
$381$	−5.93939	−0.304284
$382$	−14.5024	−0.742005
$383$	−27.3077	−1.39536	−0.697679	−	0.716411i	$-0.745784\pi$
$383$	−27.3077	−1.39536	−0.697679	+	0.716411i	$0.745784\pi$
$384$	−30.8995	−1.57683
$385$	−12.2192	−0.622747
$386$	−27.7835	−1.41414
$387$	14.1183	0.717674
$388$	9.81174	0.498116
$389$	4.87520	0.247182	0.123591	−	0.992333i	$-0.460559\pi$
$389$	4.87520	0.247182	0.123591	+	0.992333i	$0.460559\pi$
$390$	10.0837	0.510607
$391$	−9.78632	−0.494915
$392$	−2.29685	−0.116008
$393$	−30.9316	−1.56029
$394$	13.2575	0.667901
$395$	34.5499	1.73840
$396$	7.35546	0.369626
$397$	1.79380	0.0900284	0.0450142	−	0.998986i	$-0.485667\pi$
$397$	1.79380	0.0900284	0.0450142	+	0.998986i	$0.485667\pi$
$398$	−8.01788	−0.401900
$399$	−1.07027	−0.0535803
$400$	4.88790	0.244395
$401$	−13.7982	−0.689050	−0.344525	−	0.938777i	$-0.611960\pi$
$401$	−13.7982	−0.689050	−0.344525	+	0.938777i	$0.611960\pi$
$402$	15.6622	0.781158
$403$	8.57821	0.427311
$404$	6.07581	0.302283
$405$	21.6830	1.07744
$406$	−2.80594	−0.139256
$407$	57.6447	2.85734
$408$	−5.58240	−0.276370
$409$	−30.6819	−1.51712	−0.758562	−	0.651601i	$-0.774098\pi$
$409$	−30.6819	−1.51712	−0.758562	+	0.651601i	$0.774098\pi$
$410$	−29.2941	−1.44673
$411$	−19.6722	−0.970357
$412$	5.20413	0.256389
$413$	−12.8654	−0.633067
$414$	30.9786	1.52251
$415$	−20.3842	−1.00062
$416$	−4.33986	−0.212779
$417$	−8.60505	−0.421391
$418$	4.63752	0.226829
$419$	−22.6245	−1.10528	−0.552640	−	0.833420i	$-0.686380\pi$
$419$	−22.6245	−1.10528	−0.552640	+	0.833420i	$0.686380\pi$
$420$	2.55782	0.124809
$421$	−20.8482	−1.01608	−0.508040	−	0.861333i	$-0.669630\pi$
$421$	−20.8482	−1.01608	−0.508040	+	0.861333i	$0.669630\pi$
$422$	14.2797	0.695125
$423$	−26.7742	−1.30181
$424$	−12.3627	−0.600386
$425$	1.09088	0.0529156
$426$	−16.3236	−0.790881
$427$	−4.35578	−0.210791
$428$	−11.1215	−0.537578
$429$	−19.3052	−0.932065
$430$	−21.2734	−1.02589
$431$	−13.9803	−0.673408	−0.336704	−	0.941610i	$-0.609312\pi$
$431$	−13.9803	−0.673408	−0.336704	+	0.941610i	$0.609312\pi$
$432$	−9.56063	−0.459986
$433$	−20.4512	−0.982821	−0.491411	−	0.870928i	$-0.663519\pi$
$433$	−20.4512	−0.982821	−0.491411	+	0.870928i	$0.663519\pi$
$434$	9.86195	0.473389
$435$	−7.91271	−0.379385
$436$	−0.566208	−0.0271164
$437$	4.30945	0.206149
$438$	43.5829	2.08247
$439$	23.0301	1.09917	0.549583	−	0.835439i	$-0.314787\pi$
$439$	23.0301	1.09917	0.549583	+	0.835439i	$0.314787\pi$
$440$	28.0656	1.33797
$441$	2.12208	0.101052
$442$	−2.39713	−0.114020
$443$	1.97532	0.0938504	0.0469252	−	0.998898i	$-0.485058\pi$
$443$	1.97532	0.0938504	0.0469252	+	0.998898i	$0.485058\pi$
$444$	−12.0667	−0.572659
$445$	−6.52475	−0.309303
$446$	11.1090	0.526028
$447$	−7.03124	−0.332566
$448$	4.63432	0.218951
$449$	10.5385	0.497343	0.248672	−	0.968588i	$-0.420006\pi$
$449$	10.5385	0.497343	0.248672	+	0.968588i	$0.420006\pi$
$450$	−3.45319	−0.162785
$451$	56.0835	2.64087
$452$	6.62567	0.311645
$453$	41.4705	1.94845
$454$	25.4241	1.19321
$455$	−2.78131	−0.130390
$456$	2.45824	0.115117
$457$	−34.6026	−1.61864	−0.809320	−	0.587368i	$-0.800164\pi$
$457$	−34.6026	−1.61864	−0.809320	+	0.587368i	$0.800164\pi$
$458$	−7.36061	−0.343939
$459$	−2.13375	−0.0995947
$460$	−10.2991	−0.480198
$461$	38.3892	1.78796	0.893982	−	0.448102i	$-0.147900\pi$
$461$	38.3892	1.78796	0.893982	+	0.448102i	$0.147900\pi$
$462$	−22.1943	−1.03257
$463$	−3.68302	−0.171164	−0.0855822	−	0.996331i	$-0.527275\pi$
$463$	−3.68302	−0.171164	−0.0855822	+	0.996331i	$0.527275\pi$
$464$	8.42833	0.391275
$465$	27.8106	1.28969
$466$	−14.1008	−0.653207
$467$	−23.0281	−1.06561	−0.532807	−	0.846237i	$-0.678863\pi$
$467$	−23.0281	−1.06561	−0.532807	+	0.846237i	$0.678863\pi$
$468$	1.67424	0.0773918
$469$	−4.31999	−0.199479
$470$	40.3432	1.86089
$471$	3.10043	0.142860
$472$	29.5499	1.36015
$473$	40.7279	1.87267
$474$	62.7548	2.88242
$475$	−0.480375	−0.0220411
$476$	−0.608054	−0.0278701
$477$	11.4220	0.522980
$478$	−9.14117	−0.418108
$479$	29.8640	1.36452	0.682261	−	0.731108i	$-0.260997\pi$
$479$	29.8640	1.36452	0.682261	+	0.731108i	$0.260997\pi$
$480$	−14.0698	−0.642198
$481$	13.1210	0.598267
$482$	−10.2673	−0.467663
$483$	−20.6242	−0.938433
$484$	14.9904	0.681384
$485$	−34.5892	−1.57061
$486$	29.8353	1.35336
$487$	−2.67472	−0.121203	−0.0606015	−	0.998162i	$-0.519302\pi$
$487$	−2.67472	−0.121203	−0.0606015	+	0.998162i	$0.519302\pi$
$488$	10.0046	0.452885
$489$	−45.0071	−2.03529
$490$	−3.19754	−0.144450
$491$	1.85728	0.0838177	0.0419088	−	0.999121i	$-0.486656\pi$
$491$	1.85728	0.0838177	0.0419088	+	0.999121i	$0.486656\pi$
$492$	−11.7399	−0.529274
$493$	1.88104	0.0847177
$494$	1.05559	0.0474931
$495$	−25.9301	−1.16547
$496$	−29.6229	−1.33011
$497$	4.50243	0.201962
$498$	−37.0248	−1.65912
$499$	−27.1990	−1.21759	−0.608797	−	0.793326i	$-0.708347\pi$
$499$	−27.1990	−1.21759	−0.608797	+	0.793326i	$0.708347\pi$
$500$	6.79892	0.304057
$501$	16.7602	0.748792
$502$	6.93519	0.309533
$503$	−5.67751	−0.253148	−0.126574	−	0.991957i	$-0.540398\pi$
$503$	−5.67751	−0.253148	−0.126574	+	0.991957i	$0.540398\pi$
$504$	−4.87410	−0.217110
$505$	−21.4189	−0.953130
$506$	89.3657	3.97279
$507$	25.0274	1.11151
$508$	1.48592	0.0659269
$509$	33.6191	1.49014	0.745071	−	0.666985i	$-0.232416\pi$
$509$	33.6191	1.49014	0.745071	+	0.666985i	$0.232416\pi$
$510$	−7.77150	−0.344128
$511$	−12.0212	−0.531785
$512$	−7.11736	−0.314546
$513$	0.939605	0.0414846
$514$	−4.36547	−0.192552
$515$	−18.3460	−0.808423
$516$	−8.52550	−0.375314
$517$	−77.2371	−3.39688
$518$	15.0846	0.662780
$519$	−50.2339	−2.20503
$520$	6.38825	0.280143
$521$	0.398531	0.0174599	0.00872997	−	0.999962i	$-0.497221\pi$
$521$	0.398531	0.0174599	0.00872997	+	0.999962i	$0.497221\pi$
$522$	−5.95443	−0.260618
$523$	29.0930	1.27215	0.636073	−	0.771629i	$-0.280558\pi$
$523$	29.0930	1.27215	0.636073	+	0.771629i	$0.280558\pi$
$524$	7.73847	0.338057
$525$	2.29898	0.100336
$526$	−1.94356	−0.0847431
$527$	−6.61124	−0.287990
$528$	66.6661	2.90127
$529$	60.0437	2.61060
$530$	−17.2107	−0.747583
$531$	−27.3015	−1.18479
$532$	0.267759	0.0116088
$533$	12.7657	0.552942
$534$	−11.8512	−0.512852
$535$	39.2065	1.69504
$536$	9.92235	0.428580
$537$	−8.31042	−0.358621
$538$	8.39679	0.362011
$539$	6.12170	0.263680
$540$	−2.24555	−0.0966331
$541$	−2.01105	−0.0864617	−0.0432309	−	0.999065i	$-0.513765\pi$
$541$	−2.01105	−0.0864617	−0.0432309	+	0.999065i	$0.513765\pi$
$542$	−7.21532	−0.309925
$543$	47.9999	2.05987
$544$	3.34474	0.143404
$545$	1.99604	0.0855011
$546$	−5.05183	−0.216198
$547$	−2.65049	−0.113327	−0.0566633	−	0.998393i	$-0.518046\pi$
$547$	−2.65049	−0.113327	−0.0566633	+	0.998393i	$0.518046\pi$
$548$	4.92159	0.210240
$549$	−9.24332	−0.394495
$550$	−9.96162	−0.424765
$551$	−0.828324	−0.0352878
$552$	47.3706	2.01623
$553$	−17.3092	−0.736063
$554$	24.8586	1.05614
$555$	42.5384	1.80566
$556$	2.15281	0.0912996
$557$	29.0053	1.22900	0.614498	−	0.788919i	$-0.289359\pi$
$557$	29.0053	1.22900	0.614498	+	0.788919i	$0.289359\pi$
$558$	20.9279	0.885948
$559$	9.27043	0.392098
$560$	9.60461	0.405869
$561$	14.8786	0.628173
$562$	5.01389	0.211498
$563$	−1.80605	−0.0761158	−0.0380579	−	0.999276i	$-0.512117\pi$
$563$	−1.80605	−0.0761158	−0.0380579	+	0.999276i	$0.512117\pi$
$564$	16.1679	0.680792
$565$	−23.3574	−0.982652
$566$	−15.6444	−0.657584
$567$	−10.8630	−0.456204
$568$	−10.3414	−0.433915
$569$	28.7429	1.20496	0.602481	−	0.798133i	$-0.294179\pi$
$569$	28.7429	1.20496	0.602481	+	0.798133i	$0.294179\pi$
$570$	3.42222	0.143341
$571$	−8.32124	−0.348233	−0.174117	−	0.984725i	$-0.555707\pi$
$571$	−8.32124	−0.348233	−0.174117	+	0.984725i	$0.555707\pi$
$572$	4.82978	0.201943
$573$	20.4888	0.855930
$574$	14.6761	0.612567
$575$	−9.25690	−0.386040
$576$	9.83442	0.409767
$577$	16.2484	0.676432	0.338216	−	0.941069i	$-0.390177\pi$
$577$	16.2484	0.676432	0.338216	+	0.941069i	$0.390177\pi$
$578$	−25.3855	−1.05590
$579$	39.2522	1.63127
$580$	1.97960	0.0821985
$581$	10.2123	0.423677
$582$	−62.8260	−2.60422
$583$	32.9498	1.36464
$584$	27.6108	1.14254
$585$	−5.90217	−0.244025
$586$	−15.5167	−0.640989
$587$	2.71317	0.111985	0.0559923	−	0.998431i	$-0.482168\pi$
$587$	2.71317	0.111985	0.0559923	+	0.998431i	$0.482168\pi$
$588$	−1.28144	−0.0528458
$589$	2.91129	0.119958
$590$	41.1378	1.69361
$591$	−18.7300	−0.770449
$592$	−45.3104	−1.86225
$593$	16.1388	0.662740	0.331370	−	0.943501i	$-0.392489\pi$
$593$	16.1388	0.662740	0.331370	+	0.943501i	$0.392489\pi$
$594$	19.4847	0.799468
$595$	2.14356	0.0878774
$596$	1.75908	0.0720546
$597$	11.3276	0.463607
$598$	20.3413	0.831818
$599$	−3.28946	−0.134404	−0.0672019	−	0.997739i	$-0.521407\pi$
$599$	−3.28946	−0.134404	−0.0672019	+	0.997739i	$0.521407\pi$
$600$	−5.28041	−0.215572
$601$	−6.05430	−0.246960	−0.123480	−	0.992347i	$-0.539405\pi$
$601$	−6.05430	−0.246960	−0.123480	+	0.992347i	$0.539405\pi$
$602$	10.6578	0.434378
$603$	−9.16737	−0.373324
$604$	−10.3751	−0.422156
$605$	−52.8456	−2.14848
$606$	−38.9043	−1.58038
$607$	−31.3177	−1.27115	−0.635573	−	0.772041i	$-0.719236\pi$
$607$	−31.3177	−1.27115	−0.635573	+	0.772041i	$0.719236\pi$
$608$	−1.47287	−0.0597327
$609$	3.96420	0.160637
$610$	13.9278	0.563919
$611$	−17.5806	−0.711236
$612$	−1.29034	−0.0521589
$613$	5.87627	0.237340	0.118670	−	0.992934i	$-0.462137\pi$
$613$	5.87627	0.237340	0.118670	+	0.992934i	$0.462137\pi$
$614$	7.10749	0.286835
$615$	41.3863	1.66886
$616$	−14.0606	−0.566518
$617$	10.9834	0.442173	0.221087	−	0.975254i	$-0.429040\pi$
$617$	10.9834	0.442173	0.221087	+	0.975254i	$0.429040\pi$
$618$	−33.3228	−1.34044
$619$	−7.17635	−0.288442	−0.144221	−	0.989546i	$-0.546068\pi$
$619$	−7.17635	−0.288442	−0.144221	+	0.989546i	$0.546068\pi$
$620$	−6.95766	−0.279426
$621$	18.1063	0.726582
$622$	26.2857	1.05396
$623$	3.26884	0.130963
$624$	15.1744	0.607464
$625$	−18.8891	−0.755563
$626$	−51.9334	−2.07568
$627$	−6.55184	−0.261655
$628$	−0.775666	−0.0309525
$629$	−10.1124	−0.403207
$630$	−6.78544	−0.270339
$631$	−27.1529	−1.08094	−0.540469	−	0.841364i	$-0.681753\pi$
$631$	−27.1529	−1.08094	−0.540469	+	0.841364i	$0.681753\pi$
$632$	39.7566	1.58143
$633$	−20.1742	−0.801853
$634$	−12.1468	−0.482411
$635$	−5.23828	−0.207875
$636$	−6.89733	−0.273497
$637$	1.39341	0.0552090
$638$	−17.1771	−0.680047
$639$	9.55453	0.377971
$640$	−27.2520	−1.07723
$641$	2.45267	0.0968748	0.0484374	−	0.998826i	$-0.484576\pi$
$641$	2.45267	0.0968748	0.0484374	+	0.998826i	$0.484576\pi$
$642$	71.2126	2.81054
$643$	−32.7507	−1.29156	−0.645780	−	0.763523i	$-0.723468\pi$
$643$	−32.7507	−1.29156	−0.645780	+	0.763523i	$0.723468\pi$
$644$	5.15976	0.203323
$645$	30.0548	1.18341
$646$	−0.813542	−0.0320084
$647$	4.95628	0.194852	0.0974258	−	0.995243i	$-0.468939\pi$
$647$	4.95628	0.194852	0.0974258	+	0.995243i	$0.468939\pi$
$648$	24.9507	0.980155
$649$	−78.7583	−3.09153
$650$	−2.26745	−0.0889368
$651$	−13.9329	−0.546072
$652$	11.2599	0.440971
$653$	−31.5005	−1.23271	−0.616354	−	0.787469i	$-0.711391\pi$
$653$	−31.5005	−1.23271	−0.616354	+	0.787469i	$0.711391\pi$
$654$	3.62551	0.141769
$655$	−27.2803	−1.06593
$656$	−44.0832	−1.72116
$657$	−25.5099	−0.995237
$658$	−20.2116	−0.787930
$659$	−4.91001	−0.191267	−0.0956334	−	0.995417i	$-0.530488\pi$
$659$	−4.91001	−0.191267	−0.0956334	+	0.995417i	$0.530488\pi$
$660$	15.6582	0.609494
$661$	−14.9711	−0.582309	−0.291155	−	0.956676i	$-0.594039\pi$
$661$	−14.9711	−0.582309	−0.291155	+	0.956676i	$0.594039\pi$
$662$	−35.8006	−1.39143
$663$	3.38664	0.131526
$664$	−23.4561	−0.910272
$665$	−0.943927	−0.0366039
$666$	32.0108	1.24039
$667$	−15.9619	−0.618048
$668$	−4.19308	−0.162235
$669$	−15.6947	−0.606793
$670$	13.8133	0.533656
$671$	−26.6647	−1.02938
$672$	7.04887	0.271916
$673$	−37.5332	−1.44680	−0.723400	−	0.690429i	$-0.757422\pi$
$673$	−37.5332	−1.44680	−0.723400	+	0.690429i	$0.757422\pi$
$674$	24.0136	0.924970
$675$	−2.01832	−0.0776850
$676$	−6.26136	−0.240821
$677$	34.1871	1.31392	0.656958	−	0.753927i	$-0.271843\pi$
$677$	34.1871	1.31392	0.656958	+	0.753927i	$0.271843\pi$
$678$	−42.4251	−1.62933
$679$	17.3289	0.665020
$680$	−4.92343	−0.188805
$681$	−35.9189	−1.37642
$682$	60.3719	2.31176
$683$	−3.65035	−0.139677	−0.0698384	−	0.997558i	$-0.522248\pi$
$683$	−3.65035	−0.139677	−0.0698384	+	0.997558i	$0.522248\pi$
$684$	0.568207	0.0217259
$685$	−17.3500	−0.662909
$686$	1.60194	0.0611623
$687$	10.3990	0.396746
$688$	−32.0133	−1.22049
$689$	7.50000	0.285727
$690$	65.9466	2.51055
$691$	24.4230	0.929095	0.464548	−	0.885548i	$-0.346217\pi$
$691$	24.4230	0.929095	0.464548	+	0.885548i	$0.346217\pi$
$692$	12.5675	0.477746
$693$	12.9907	0.493478
$694$	−35.2994	−1.33995
$695$	−7.58927	−0.287878
$696$	−9.10515	−0.345130
$697$	−9.83851	−0.372660
$698$	0.978541	0.0370383
$699$	19.9215	0.753498
$700$	−0.575160	−0.0217390
$701$	−41.2310	−1.55727	−0.778636	−	0.627476i	$-0.784088\pi$
$701$	−41.2310	−1.55727	−0.778636	+	0.627476i	$0.784088\pi$
$702$	4.43509	0.167392
$703$	4.45304	0.167949
$704$	28.3699	1.06923
$705$	−56.9964	−2.14661
$706$	12.1935	0.458908
$707$	10.7307	0.403569
$708$	16.4863	0.619594
$709$	14.3586	0.539249	0.269625	−	0.962966i	$-0.413100\pi$
$709$	14.3586	0.539249	0.269625	+	0.962966i	$0.413100\pi$
$710$	−14.3967	−0.540298
$711$	−36.7316	−1.37754
$712$	−7.50803	−0.281375
$713$	56.1010	2.10100
$714$	3.89345	0.145709
$715$	−17.0263	−0.636749
$716$	2.07910	0.0776997
$717$	12.9146	0.482303
$718$	−21.4320	−0.799834
$719$	−37.0201	−1.38062	−0.690308	−	0.723515i	$-0.742525\pi$
$719$	−37.0201	−1.38062	−0.690308	+	0.723515i	$0.742525\pi$
$720$	20.3818	0.759584
$721$	9.19120	0.342298
$722$	−30.0786	−1.11941
$723$	14.5055	0.539466
$724$	−12.0086	−0.446297
$725$	1.77928	0.0660808
$726$	−95.9860	−3.56237
$727$	−5.83724	−0.216491	−0.108246	−	0.994124i	$-0.534523\pi$
$727$	−5.83724	−0.216491	−0.108246	+	0.994124i	$0.534523\pi$
$728$	−3.20046	−0.118617
$729$	−9.56192	−0.354145
$730$	38.4382	1.42266
$731$	−7.14474	−0.264258
$732$	5.58168	0.206305
$733$	17.6337	0.651316	0.325658	−	0.945488i	$-0.394414\pi$
$733$	17.6337	0.651316	0.325658	+	0.945488i	$0.394414\pi$
$734$	7.22247	0.266586
$735$	4.51745	0.166629
$736$	−28.3824	−1.04619
$737$	−26.4456	−0.974138
$738$	31.1438	1.14642
$739$	−14.3976	−0.529625	−0.264813	−	0.964300i	$-0.585310\pi$
$739$	−14.3976	−0.529625	−0.264813	+	0.964300i	$0.585310\pi$
$740$	−10.6423	−0.391218
$741$	−1.49132	−0.0547851
$742$	8.62239	0.316538
$743$	22.6064	0.829350	0.414675	−	0.909970i	$-0.363895\pi$
$743$	22.6064	0.829350	0.414675	+	0.909970i	$0.363895\pi$
$744$	32.0017	1.17324
$745$	−6.20124	−0.227196
$746$	24.0517	0.880597
$747$	21.6713	0.792912
$748$	−3.72232	−0.136101
$749$	−19.6421	−0.717706
$750$	−43.5345	−1.58965
$751$	−5.29574	−0.193244	−0.0966222	−	0.995321i	$-0.530804\pi$
$751$	−5.29574	−0.193244	−0.0966222	+	0.995321i	$0.530804\pi$
$752$	60.7105	2.21389
$753$	−9.79796	−0.357057
$754$	−3.90983	−0.142387
$755$	36.5751	1.33110
$756$	1.12500	0.0409159
$757$	50.5713	1.83805	0.919023	−	0.394203i	$-0.128979\pi$
$757$	50.5713	1.83805	0.919023	+	0.394203i	$0.128979\pi$
$758$	3.66168	0.132998
$759$	−126.255	−4.58276
$760$	2.16806	0.0786436
$761$	16.0567	0.582056	0.291028	−	0.956715i	$-0.406003\pi$
$761$	16.0567	0.582056	0.291028	+	0.956715i	$0.406003\pi$
$762$	−9.51454	−0.344676
$763$	−1.00000	−0.0362024
$764$	−5.12588	−0.185448
$765$	4.54881	0.164463
$766$	−43.7452	−1.58058
$767$	−17.9269	−0.647302
$768$	−28.5223	−1.02921
$769$	−27.1569	−0.979303	−0.489651	−	0.871918i	$-0.662876\pi$
$769$	−27.1569	−0.979303	−0.489651	+	0.871918i	$0.662876\pi$
$770$	−19.5744	−0.705411
$771$	6.16748	0.222116
$772$	−9.82013	−0.353434
$773$	−8.22488	−0.295828	−0.147914	−	0.989000i	$-0.547256\pi$
$773$	−8.22488	−0.295828	−0.147914	+	0.989000i	$0.547256\pi$
$774$	22.6167	0.812939
$775$	−6.25359	−0.224636
$776$	−39.8017	−1.42880
$777$	−21.3114	−0.764541
$778$	7.80977	0.279994
$779$	4.33243	0.155225
$780$	3.56409	0.127615
$781$	27.5625	0.986264
$782$	−15.6771	−0.560611
$783$	−3.48024	−0.124373
$784$	−4.81182	−0.171851
$785$	2.73444	0.0975965
$786$	−49.5505	−1.76741
$787$	−10.7476	−0.383110	−0.191555	−	0.981482i	$-0.561353\pi$
$787$	−10.7476	−0.383110	−0.191555	+	0.981482i	$0.561353\pi$
$788$	4.68587	0.166927
$789$	2.74583	0.0977543
$790$	55.3469	1.96915
$791$	11.7018	0.416069
$792$	−29.8378	−1.06024
$793$	−6.06940	−0.215531
$794$	2.87356	0.101979
$795$	24.3150	0.862366
$796$	−2.83393	−0.100446
$797$	15.3250	0.542841	0.271420	−	0.962461i	$-0.412507\pi$
$797$	15.3250	0.542841	0.271420	+	0.962461i	$0.412507\pi$
$798$	−1.71450	−0.0606926
$799$	13.5494	0.479343
$800$	3.16380	0.111857
$801$	6.93675	0.245098
$802$	−22.1039	−0.780516
$803$	−73.5899	−2.59693
$804$	5.53582	0.195233
$805$	−18.1896	−0.641100
$806$	13.7418	0.484033
$807$	−11.8629	−0.417594
$808$	−24.6468	−0.867070
$809$	44.5786	1.56730	0.783651	−	0.621202i	$-0.213355\pi$
$809$	44.5786	1.56730	0.783651	+	0.621202i	$0.213355\pi$
$810$	34.7349	1.22046
$811$	−2.71546	−0.0953528	−0.0476764	−	0.998863i	$-0.515182\pi$
$811$	−2.71546	−0.0953528	−0.0476764	+	0.998863i	$0.515182\pi$
$812$	−0.991763	−0.0348041
$813$	10.1937	0.357510
$814$	92.3434	3.23663
$815$	−39.6942	−1.39043
$816$	−11.6950	−0.409406
$817$	3.14622	0.110072
$818$	−49.1506	−1.71851
$819$	2.95694	0.103324
$820$	−10.3540	−0.361579
$821$	−33.2946	−1.16199	−0.580994	−	0.813908i	$-0.697336\pi$
$821$	−33.2946	−1.16199	−0.580994	+	0.813908i	$0.697336\pi$
$822$	−31.5136	−1.09916
$823$	−19.2141	−0.669762	−0.334881	−	0.942260i	$-0.608696\pi$
$823$	−19.2141	−0.669762	−0.334881	+	0.942260i	$0.608696\pi$
$824$	−21.1108	−0.735429
$825$	14.0737	0.489982
$826$	−20.6096	−0.717101
$827$	26.6969	0.928342	0.464171	−	0.885746i	$-0.346352\pi$
$827$	26.6969	0.928342	0.464171	+	0.885746i	$0.346352\pi$
$828$	10.9494	0.380519
$829$	12.4422	0.432134	0.216067	−	0.976378i	$-0.430677\pi$
$829$	12.4422	0.432134	0.216067	+	0.976378i	$0.430677\pi$
$830$	−32.6542	−1.13344
$831$	−35.1199	−1.21830
$832$	6.45752	0.223874
$833$	−1.07390	−0.0372086
$834$	−13.7848	−0.477327
$835$	14.7818	0.511544
$836$	1.63914	0.0566908
$837$	12.2319	0.422796
$838$	−36.2431	−1.25200
$839$	35.6063	1.22927	0.614633	−	0.788813i	$-0.289304\pi$
$839$	35.6063	1.22927	0.614633	+	0.788813i	$0.289304\pi$
$840$	−10.3759	−0.358002
$841$	−25.9319	−0.894205
$842$	−33.3976	−1.15096
$843$	−7.08356	−0.243971
$844$	5.04719	0.173731
$845$	22.0731	0.759336
$846$	−42.8907	−1.47461
$847$	26.4752	0.909697
$848$	−25.8995	−0.889393
$849$	22.1023	0.758548
$850$	1.74753	0.0599397
$851$	85.8107	2.94155
$852$	−5.76961	−0.197664
$853$	−0.984186	−0.0336979	−0.0168489	−	0.999858i	$-0.505363\pi$
$853$	−0.984186	−0.0336979	−0.0168489	+	0.999858i	$0.505363\pi$
$854$	−6.97769	−0.238772
$855$	−2.00309	−0.0685043
$856$	45.1149	1.54199
$857$	−15.2667	−0.521500	−0.260750	−	0.965406i	$-0.583970\pi$
$857$	−15.2667	−0.521500	−0.260750	+	0.965406i	$0.583970\pi$
$858$	−30.9258	−1.05579
$859$	−42.8825	−1.46313	−0.731566	−	0.681771i	$-0.761210\pi$
$859$	−42.8825	−1.46313	−0.731566	+	0.681771i	$0.761210\pi$
$860$	−7.51911	−0.256400
$861$	−20.7342	−0.706619
$862$	−22.3956	−0.762798
$863$	31.4420	1.07030	0.535149	−	0.844758i	$-0.320255\pi$
$863$	31.4420	1.07030	0.535149	+	0.844758i	$0.320255\pi$
$864$	−6.18832	−0.210531
$865$	−44.3041	−1.50638
$866$	−32.7616	−1.11328
$867$	35.8643	1.21802
$868$	3.48572	0.118313
$869$	−105.962	−3.59451
$870$	−12.6757	−0.429746
$871$	−6.01953	−0.203964
$872$	2.29685	0.0777811
$873$	36.7733	1.24459
$874$	6.90347	0.233513
$875$	12.0078	0.405938
$876$	15.4044	0.520468
$877$	24.2732	0.819647	0.409823	−	0.912165i	$-0.365590\pi$
$877$	24.2732	0.819647	0.409823	+	0.912165i	$0.365590\pi$
$878$	36.8928	1.24507
$879$	21.9218	0.739404
$880$	58.7965	1.98203
$881$	0.807379	0.0272013	0.0136006	−	0.999908i	$-0.495671\pi$
$881$	0.807379	0.0272013	0.0136006	+	0.999908i	$0.495671\pi$
$882$	3.39945	0.114465
$883$	2.76822	0.0931581	0.0465790	−	0.998915i	$-0.485168\pi$
$883$	2.76822	0.0931581	0.0465790	+	0.998915i	$0.485168\pi$
$884$	−0.847270	−0.0284968
$885$	−58.1190	−1.95365
$886$	3.16435	0.106308
$887$	−28.5910	−0.959991	−0.479996	−	0.877271i	$-0.659362\pi$
$887$	−28.5910	−0.959991	−0.479996	+	0.877271i	$0.659362\pi$
$888$	48.9490	1.64262
$889$	2.62433	0.0880173
$890$	−10.4522	−0.350360
$891$	−66.5001	−2.22784
$892$	3.92651	0.131469
$893$	−5.96654	−0.199663
$894$	−11.2636	−0.376712
$895$	−7.32942	−0.244996
$896$	13.6530	0.456115
$897$	−28.7380	−0.959534
$898$	16.8821	0.563362
$899$	−10.7832	−0.359641
$900$	−1.22054	−0.0406845
$901$	−5.78026	−0.192568
$902$	89.8423	2.99142
$903$	−15.0572	−0.501072
$904$	−26.8773	−0.893926
$905$	42.3338	1.40722
$906$	66.4331	2.20709
$907$	11.5318	0.382909	0.191454	−	0.981502i	$-0.438680\pi$
$907$	11.5318	0.382909	0.191454	+	0.981502i	$0.438680\pi$
$908$	8.98620	0.298218
$909$	22.7714	0.755281
$910$	−4.45549	−0.147698
$911$	−50.8597	−1.68506	−0.842528	−	0.538652i	$-0.818934\pi$
$911$	−50.8597	−1.68506	−0.842528	+	0.538652i	$0.818934\pi$
$912$	5.14993	0.170531
$913$	62.5165	2.06900
$914$	−55.4312	−1.83350
$915$	−19.6770	−0.650502
$916$	−2.60162	−0.0859600
$917$	13.6672	0.451330
$918$	−3.41813	−0.112815
$919$	−12.9498	−0.427174	−0.213587	−	0.976924i	$-0.568515\pi$
$919$	−12.9498	−0.427174	−0.213587	+	0.976924i	$0.568515\pi$
$920$	41.7788	1.37740
$921$	−10.0414	−0.330875
$922$	61.4972	2.02530
$923$	6.27374	0.206503
$924$	−7.84460	−0.258069
$925$	−9.56534	−0.314506
$926$	−5.89997	−0.193885
$927$	19.5045	0.640612
$928$	5.45542	0.179083
$929$	2.37168	0.0778122	0.0389061	−	0.999243i	$-0.487613\pi$
$929$	2.37168	0.0778122	0.0389061	+	0.999243i	$0.487613\pi$
$930$	44.5509	1.46088
$931$	0.472899	0.0154986
$932$	−4.98395	−0.163255
$933$	−37.1362	−1.21578
$934$	−36.8896	−1.20706
$935$	13.1222	0.429143
$936$	−6.79163	−0.221991
$937$	27.1556	0.887135	0.443567	−	0.896241i	$-0.353713\pi$
$937$	27.1556	0.887135	0.443567	+	0.896241i	$0.353713\pi$
$938$	−6.92036	−0.225958
$939$	73.3710	2.39437
$940$	14.2594	0.465090
$941$	−44.0537	−1.43611	−0.718055	−	0.695987i	$-0.754967\pi$
$941$	−44.0537	−1.43611	−0.718055	+	0.695987i	$0.754967\pi$
$942$	4.96670	0.161824
$943$	83.4866	2.71870
$944$	61.9062	2.01488
$945$	−3.96595	−0.129012
$946$	65.2436	2.12125
$947$	24.3557	0.791455	0.395728	−	0.918368i	$-0.370492\pi$
$947$	24.3557	0.791455	0.395728	+	0.918368i	$0.370492\pi$
$948$	22.1808	0.720398
$949$	−16.7504	−0.543743
$950$	−0.769532	−0.0249669
$951$	17.1609	0.556480
$952$	2.46660	0.0799428
$953$	11.3397	0.367330	0.183665	−	0.982989i	$-0.441204\pi$
$953$	11.3397	0.367330	0.183665	+	0.982989i	$0.441204\pi$
$954$	18.2974	0.592401
$955$	18.0702	0.584737
$956$	−3.23096	−0.104497
$957$	24.2676	0.784460
$958$	47.8404	1.54565
$959$	8.69219	0.280685
$960$	20.9353	0.675685
$961$	6.89956	0.222566
$962$	21.0191	0.677682
$963$	−41.6821	−1.34319
$964$	−3.62899	−0.116882
$965$	34.6187	1.11442
$966$	−33.0387	−1.06300
$967$	1.98292	0.0637663	0.0318832	−	0.999492i	$-0.489850\pi$
$967$	1.98292	0.0637663	0.0318832	+	0.999492i	$0.489850\pi$
$968$	−60.8094	−1.95449
$969$	1.14936	0.0369229
$970$	−55.4097	−1.77910
$971$	8.88322	0.285076	0.142538	−	0.989789i	$-0.454474\pi$
$971$	8.88322	0.285076	0.142538	+	0.989789i	$0.454474\pi$
$972$	10.5453	0.338242
$973$	3.80216	0.121892
$974$	−4.28474	−0.137292
$975$	3.20343	0.102592
$976$	20.9592	0.670889
$977$	−37.4644	−1.19859	−0.599297	−	0.800527i	$-0.704553\pi$
$977$	−37.4644	−1.19859	−0.599297	+	0.800527i	$0.704553\pi$
$978$	−72.0986	−2.30546
$979$	20.0108	0.639549
$980$	−1.13018	−0.0361021
$981$	−2.12208	−0.0677529
$982$	2.97524	0.0949438
$983$	40.6491	1.29650	0.648252	−	0.761426i	$-0.275500\pi$
$983$	40.6491	1.29650	0.648252	+	0.761426i	$0.275500\pi$
$984$	47.6232	1.51817
$985$	−16.5190	−0.526340
$986$	3.01331	0.0959633
$987$	28.5547	0.908906
$988$	0.373099	0.0118699
$989$	60.6281	1.92786
$990$	−41.5384	−1.32018
$991$	−42.4526	−1.34855	−0.674276	−	0.738480i	$-0.735544\pi$
$991$	−42.4526	−1.34855	−0.674276	+	0.738480i	$0.735544\pi$
$992$	−19.1740	−0.608776
$993$	50.5787	1.60507
$994$	7.21262	0.228770
$995$	9.99042	0.316718
$996$	−13.0865	−0.414661
$997$	−36.4256	−1.15361	−0.576805	−	0.816882i	$-0.695701\pi$
$997$	−36.4256	−1.15361	−0.576805	+	0.816882i	$0.695701\pi$
$998$	−43.5711	−1.37922
$999$	18.7096	0.591946

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	763.2.a.e.1.11	✓	17
3.2	odd	2		6867.2.a.r.1.7		17
7.6	odd	2		5341.2.a.j.1.11		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
763.2.a.e.1.11	✓	17	1.1	even	1	trivial
5341.2.a.j.1.11		17	7.6	odd	2
6867.2.a.r.1.7		17	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:	\( N \)	\(=\)	\( 763 = 7 \cdot 109 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	763.a (trivial)

\(f(q)\)	\(=\)	\(q+1.60194 q^{2} -2.26320 q^{3} +0.566208 q^{4} -1.99604 q^{5} -3.62551 q^{6} +1.00000 q^{7} -2.29685 q^{8} +2.12208 q^{9} +O(q^{10})\)	\(q+1.60194 q^{2} -2.26320 q^{3} +0.566208 q^{4} -1.99604 q^{5} -3.62551 q^{6} +1.00000 q^{7} -2.29685 q^{8} +2.12208 q^{9} -3.19754 q^{10} +6.12170 q^{11} -1.28144 q^{12} +1.39341 q^{13} +1.60194 q^{14} +4.51745 q^{15} -4.81182 q^{16} -1.07390 q^{17} +3.39945 q^{18} +0.472899 q^{19} -1.13018 q^{20} -2.26320 q^{21} +9.80658 q^{22} +9.11283 q^{23} +5.19823 q^{24} -1.01581 q^{25} +2.23216 q^{26} +1.98690 q^{27} +0.566208 q^{28} -1.75159 q^{29} +7.23668 q^{30} +6.15626 q^{31} -3.11455 q^{32} -13.8546 q^{33} -1.72033 q^{34} -1.99604 q^{35} +1.20154 q^{36} +9.41647 q^{37} +0.757555 q^{38} -3.15357 q^{39} +4.58461 q^{40} +9.16143 q^{41} -3.62551 q^{42} +6.65304 q^{43} +3.46615 q^{44} -4.23577 q^{45} +14.5982 q^{46} -12.6169 q^{47} +10.8901 q^{48} +1.00000 q^{49} -1.62727 q^{50} +2.43046 q^{51} +0.788961 q^{52} +5.38247 q^{53} +3.18290 q^{54} -12.2192 q^{55} -2.29685 q^{56} -1.07027 q^{57} -2.80594 q^{58} -12.8654 q^{59} +2.55782 q^{60} -4.35578 q^{61} +9.86195 q^{62} +2.12208 q^{63} +4.63432 q^{64} -2.78131 q^{65} -22.1943 q^{66} -4.31999 q^{67} -0.608054 q^{68} -20.6242 q^{69} -3.19754 q^{70} +4.50243 q^{71} -4.87410 q^{72} -12.0212 q^{73} +15.0846 q^{74} +2.29898 q^{75} +0.267759 q^{76} +6.12170 q^{77} -5.05183 q^{78} -17.3092 q^{79} +9.60461 q^{80} -10.8630 q^{81} +14.6761 q^{82} +10.2123 q^{83} -1.28144 q^{84} +2.14356 q^{85} +10.6578 q^{86} +3.96420 q^{87} -14.0606 q^{88} +3.26884 q^{89} -6.78544 q^{90} +1.39341 q^{91} +5.15976 q^{92} -13.9329 q^{93} -20.2116 q^{94} -0.943927 q^{95} +7.04887 q^{96} +17.3289 q^{97} +1.60194 q^{98} +12.9907 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 7 q^{2} + 2 q^{3} + 23 q^{4} + 12 q^{5} - 5 q^{6} + 17 q^{7} + 18 q^{8} + 25 q^{9}+O(q^{10}) \) 17 * q + 7 * q^2 + 2 * q^3 + 23 * q^4 + 12 * q^5 - 5 * q^6 + 17 * q^7 + 18 * q^8 + 25 * q^9	\( 17 q + 7 q^{2} + 2 q^{3} + 23 q^{4} + 12 q^{5} - 5 q^{6} + 17 q^{7} + 18 q^{8} + 25 q^{9} - 6 q^{10} + 20 q^{11} - 9 q^{12} + 11 q^{13} + 7 q^{14} - 3 q^{15} + 23 q^{16} + 19 q^{17} + q^{18} - 4 q^{19} + 10 q^{20} + 2 q^{21} + 3 q^{22} + 22 q^{23} - 21 q^{24} + 21 q^{25} - 12 q^{26} - 7 q^{27} + 23 q^{28} + 37 q^{29} + 2 q^{30} - 10 q^{31} + 18 q^{32} + q^{33} - 7 q^{34} + 12 q^{35} + 42 q^{36} + 13 q^{37} + 18 q^{38} - 17 q^{39} - 17 q^{40} - 6 q^{41} - 5 q^{42} + 9 q^{43} + 35 q^{44} + 28 q^{45} - 17 q^{46} - 4 q^{47} - 43 q^{48} + 17 q^{49} + 37 q^{50} + 5 q^{51} + 36 q^{52} + 45 q^{53} - 22 q^{54} - 13 q^{55} + 18 q^{56} - q^{57} + 4 q^{58} - 12 q^{59} - 51 q^{60} + 6 q^{61} - 24 q^{62} + 25 q^{63} + 20 q^{64} + 15 q^{65} - 15 q^{66} - 3 q^{67} + 60 q^{68} - 50 q^{69} - 6 q^{70} + 36 q^{71} + 72 q^{72} - 4 q^{73} + 13 q^{74} - 22 q^{75} - 74 q^{76} + 20 q^{77} + 12 q^{78} + 5 q^{79} - 25 q^{80} - 7 q^{81} - 24 q^{82} + 7 q^{83} - 9 q^{84} + 8 q^{85} + 2 q^{86} + 13 q^{87} - 55 q^{88} + 13 q^{89} - 92 q^{90} + 11 q^{91} + 36 q^{92} + 7 q^{93} - 37 q^{94} - 34 q^{95} - 33 q^{96} - 23 q^{97} + 7 q^{98} - 5 q^{99}+O(q^{100}) \) 17 * q + 7 * q^2 + 2 * q^3 + 23 * q^4 + 12 * q^5 - 5 * q^6 + 17 * q^7 + 18 * q^8 + 25 * q^9 - 6 * q^10 + 20 * q^11 - 9 * q^12 + 11 * q^13 + 7 * q^14 - 3 * q^15 + 23 * q^16 + 19 * q^17 + q^18 - 4 * q^19 + 10 * q^20 + 2 * q^21 + 3 * q^22 + 22 * q^23 - 21 * q^24 + 21 * q^25 - 12 * q^26 - 7 * q^27 + 23 * q^28 + 37 * q^29 + 2 * q^30 - 10 * q^31 + 18 * q^32 + q^33 - 7 * q^34 + 12 * q^35 + 42 * q^36 + 13 * q^37 + 18 * q^38 - 17 * q^39 - 17 * q^40 - 6 * q^41 - 5 * q^42 + 9 * q^43 + 35 * q^44 + 28 * q^45 - 17 * q^46 - 4 * q^47 - 43 * q^48 + 17 * q^49 + 37 * q^50 + 5 * q^51 + 36 * q^52 + 45 * q^53 - 22 * q^54 - 13 * q^55 + 18 * q^56 - q^57 + 4 * q^58 - 12 * q^59 - 51 * q^60 + 6 * q^61 - 24 * q^62 + 25 * q^63 + 20 * q^64 + 15 * q^65 - 15 * q^66 - 3 * q^67 + 60 * q^68 - 50 * q^69 - 6 * q^70 + 36 * q^71 + 72 * q^72 - 4 * q^73 + 13 * q^74 - 22 * q^75 - 74 * q^76 + 20 * q^77 + 12 * q^78 + 5 * q^79 - 25 * q^80 - 7 * q^81 - 24 * q^82 + 7 * q^83 - 9 * q^84 + 8 * q^85 + 2 * q^86 + 13 * q^87 - 55 * q^88 + 13 * q^89 - 92 * q^90 + 11 * q^91 + 36 * q^92 + 7 * q^93 - 37 * q^94 - 34 * q^95 - 33 * q^96 - 23 * q^97 + 7 * q^98 - 5 * q^99

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