LMFDB - Embedded newform 845.2.a.o.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(1,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, 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("845.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.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:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 17x^{7} - 9x^{6} + 59x^{5} + 32x^{4} - 44x^{3} - 23x^{2} + x + 1 $ x^9 - 17x^7 - 9x^6 + 59x^5 + 32x^4 - 44x^3 - 23x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.199774$ of defining polynomial
Character	$\chi$	$=$	845.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.04721 q^{2} -2.75868 q^{3} -0.903360 q^{4} +1.00000 q^{5} +2.88890 q^{6} +3.42366 q^{7} +3.04042 q^{8} +4.61031 q^{9} +O(q^{10})$	\(q-1.04721 q^{2} -2.75868 q^{3} -0.903360 q^{4} +1.00000 q^{5} +2.88890 q^{6} +3.42366 q^{7} +3.04042 q^{8} +4.61031 q^{9} -1.04721 q^{10} -2.38793 q^{11} +2.49208 q^{12} -3.58527 q^{14} -2.75868 q^{15} -1.37722 q^{16} -7.43316 q^{17} -4.82794 q^{18} +0.840998 q^{19} -0.903360 q^{20} -9.44477 q^{21} +2.50066 q^{22} +5.46920 q^{23} -8.38753 q^{24} +1.00000 q^{25} -4.44233 q^{27} -3.09279 q^{28} +1.65390 q^{29} +2.88890 q^{30} -8.10151 q^{31} -4.63860 q^{32} +6.58754 q^{33} +7.78405 q^{34} +3.42366 q^{35} -4.16477 q^{36} +6.39379 q^{37} -0.880698 q^{38} +3.04042 q^{40} -6.15846 q^{41} +9.89061 q^{42} +12.0911 q^{43} +2.15716 q^{44} +4.61031 q^{45} -5.72737 q^{46} +2.33083 q^{47} +3.79931 q^{48} +4.72142 q^{49} -1.04721 q^{50} +20.5057 q^{51} +4.35709 q^{53} +4.65203 q^{54} -2.38793 q^{55} +10.4093 q^{56} -2.32004 q^{57} -1.73197 q^{58} +5.11542 q^{59} +2.49208 q^{60} -8.84695 q^{61} +8.48395 q^{62} +15.7841 q^{63} +7.61201 q^{64} -6.89851 q^{66} +7.17992 q^{67} +6.71482 q^{68} -15.0878 q^{69} -3.58527 q^{70} +3.28070 q^{71} +14.0173 q^{72} +9.41601 q^{73} -6.69561 q^{74} -2.75868 q^{75} -0.759724 q^{76} -8.17546 q^{77} +5.89740 q^{79} -1.37722 q^{80} -1.57598 q^{81} +6.44917 q^{82} -5.14271 q^{83} +8.53203 q^{84} -7.43316 q^{85} -12.6619 q^{86} -4.56257 q^{87} -7.26031 q^{88} +6.03426 q^{89} -4.82794 q^{90} -4.94065 q^{92} +22.3495 q^{93} -2.44085 q^{94} +0.840998 q^{95} +12.7964 q^{96} -6.33475 q^{97} -4.94429 q^{98} -11.0091 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 3 q^{2} + 7 q^{3} + 17 q^{4} + 9 q^{5} - 2 q^{6} + 7 q^{7} + 12 q^{8} + 16 q^{9}+O(q^{10}) $ 9 * q + 3 * q^2 + 7 * q^3 + 17 * q^4 + 9 * q^5 - 2 * q^6 + 7 * q^7 + 12 * q^8 + 16 * q^9	\( 9 q + 3 q^{2} + 7 q^{3} + 17 q^{4} + 9 q^{5} - 2 q^{6} + 7 q^{7} + 12 q^{8} + 16 q^{9} + 3 q^{10} - 9 q^{11} + 12 q^{12} - 2 q^{14} + 7 q^{15} + 37 q^{16} - q^{17} - 10 q^{18} - 4 q^{19} + 17 q^{20} - q^{21} + 12 q^{22} + 14 q^{23} - 35 q^{24} + 9 q^{25} + 22 q^{27} + 18 q^{28} + 12 q^{29} - 2 q^{30} - 7 q^{31} + 22 q^{32} - 8 q^{33} - 30 q^{34} + 7 q^{35} + 3 q^{36} - 5 q^{37} - 47 q^{38} + 12 q^{40} - 10 q^{41} - 11 q^{42} + 39 q^{43} - 25 q^{44} + 16 q^{45} + 6 q^{46} + 36 q^{47} - 3 q^{48} + 16 q^{49} + 3 q^{50} + 43 q^{51} - 8 q^{53} - 2 q^{54} - 9 q^{55} - 29 q^{56} - 32 q^{57} + 21 q^{58} - 21 q^{59} + 12 q^{60} - 3 q^{61} - 10 q^{62} + 35 q^{63} + 34 q^{64} - 49 q^{66} + q^{67} - 20 q^{68} - 13 q^{69} - 2 q^{70} - q^{71} - 3 q^{72} - 15 q^{74} + 7 q^{75} - 5 q^{76} - 4 q^{77} + 39 q^{79} + 37 q^{80} + 29 q^{81} - 4 q^{82} + 7 q^{83} + 12 q^{84} - q^{85} - 24 q^{86} + 16 q^{87} + 42 q^{88} - 19 q^{89} - 10 q^{90} - 27 q^{92} + 31 q^{93} + 16 q^{94} - 4 q^{95} - 7 q^{96} - 34 q^{97} + 48 q^{98} - q^{99}+O(q^{100}) \) 9 * q + 3 * q^2 + 7 * q^3 + 17 * q^4 + 9 * q^5 - 2 * q^6 + 7 * q^7 + 12 * q^8 + 16 * q^9 + 3 * q^10 - 9 * q^11 + 12 * q^12 - 2 * q^14 + 7 * q^15 + 37 * q^16 - q^17 - 10 * q^18 - 4 * q^19 + 17 * q^20 - q^21 + 12 * q^22 + 14 * q^23 - 35 * q^24 + 9 * q^25 + 22 * q^27 + 18 * q^28 + 12 * q^29 - 2 * q^30 - 7 * q^31 + 22 * q^32 - 8 * q^33 - 30 * q^34 + 7 * q^35 + 3 * q^36 - 5 * q^37 - 47 * q^38 + 12 * q^40 - 10 * q^41 - 11 * q^42 + 39 * q^43 - 25 * q^44 + 16 * q^45 + 6 * q^46 + 36 * q^47 - 3 * q^48 + 16 * q^49 + 3 * q^50 + 43 * q^51 - 8 * q^53 - 2 * q^54 - 9 * q^55 - 29 * q^56 - 32 * q^57 + 21 * q^58 - 21 * q^59 + 12 * q^60 - 3 * q^61 - 10 * q^62 + 35 * q^63 + 34 * q^64 - 49 * q^66 + q^67 - 20 * q^68 - 13 * q^69 - 2 * q^70 - q^71 - 3 * q^72 - 15 * q^74 + 7 * q^75 - 5 * q^76 - 4 * q^77 + 39 * q^79 + 37 * q^80 + 29 * q^81 - 4 * q^82 + 7 * q^83 + 12 * q^84 - q^85 - 24 * q^86 + 16 * q^87 + 42 * q^88 - 19 * q^89 - 10 * q^90 - 27 * q^92 + 31 * q^93 + 16 * q^94 - 4 * q^95 - 7 * q^96 - 34 * q^97 + 48 * q^98 - 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 $

$2$	−1.04721	−0.740486	−0.370243	−	0.928935i	$-0.620726\pi$
$2$	−1.04721	−0.740486	−0.370243	+	0.928935i	$0.620726\pi$
$3$	−2.75868	−1.59272	−0.796362	−	0.604820i	$-0.793245\pi$
$3$	−2.75868	−1.59272	−0.796362	+	0.604820i	$0.793245\pi$
$4$	−0.903360	−0.451680
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.88890	1.17939
$7$	3.42366	1.29402	0.647010	−	0.762481i	$-0.276019\pi$
$7$	3.42366	1.29402	0.647010	+	0.762481i	$0.276019\pi$
$8$	3.04042	1.07495
$9$	4.61031	1.53677
$10$	−1.04721	−0.331156
$11$	−2.38793	−0.719989	−0.359995	−	0.932954i	$-0.617221\pi$
$11$	−2.38793	−0.719989	−0.359995	+	0.932954i	$0.617221\pi$
$12$	2.49208	0.719402
$13$	0	0
$13$	0	0
$14$	−3.58527	−0.958204
$15$	−2.75868	−0.712288
$16$	−1.37722	−0.344305
$17$	−7.43316	−1.80281	−0.901403	−	0.432981i	$-0.857462\pi$
$17$	−7.43316	−1.80281	−0.901403	+	0.432981i	$0.857462\pi$
$18$	−4.82794	−1.13796
$19$	0.840998	0.192938	0.0964691	−	0.995336i	$-0.469245\pi$
$19$	0.840998	0.192938	0.0964691	+	0.995336i	$0.469245\pi$
$20$	−0.903360	−0.201997
$21$	−9.44477	−2.06102
$22$	2.50066	0.533142
$23$	5.46920	1.14041	0.570203	−	0.821504i	$-0.306865\pi$
$23$	5.46920	1.14041	0.570203	+	0.821504i	$0.306865\pi$
$24$	−8.38753	−1.71210
$25$	1.00000	0.200000
$26$	0	0
$27$	−4.44233	−0.854926
$28$	−3.09279	−0.584483
$29$	1.65390	0.307121	0.153560	−	0.988139i	$-0.450926\pi$
$29$	1.65390	0.307121	0.153560	+	0.988139i	$0.450926\pi$
$30$	2.88890	0.527439
$31$	−8.10151	−1.45507	−0.727537	−	0.686068i	$-0.759335\pi$
$31$	−8.10151	−1.45507	−0.727537	+	0.686068i	$0.759335\pi$
$32$	−4.63860	−0.819996
$33$	6.58754	1.14674
$34$	7.78405	1.33495
$35$	3.42366	0.578703
$36$	−4.16477	−0.694128
$37$	6.39379	1.05113	0.525566	−	0.850753i	$-0.323854\pi$
$37$	6.39379	1.05113	0.525566	+	0.850753i	$0.323854\pi$
$38$	−0.880698	−0.142868
$39$	0	0
$40$	3.04042	0.480732
$41$	−6.15846	−0.961789	−0.480895	−	0.876778i	$-0.659688\pi$
$41$	−6.15846	−0.961789	−0.480895	+	0.876778i	$0.659688\pi$
$42$	9.89061	1.52615
$43$	12.0911	1.84388	0.921938	−	0.387339i	$-0.126606\pi$
$43$	12.0911	1.84388	0.921938	+	0.387339i	$0.126606\pi$
$44$	2.15716	0.325205
$45$	4.61031	0.687264
$46$	−5.72737	−0.844455
$47$	2.33083	0.339986	0.169993	−	0.985445i	$-0.445625\pi$
$47$	2.33083	0.339986	0.169993	+	0.985445i	$0.445625\pi$
$48$	3.79931	0.548383
$49$	4.72142	0.674488
$50$	−1.04721	−0.148097
$51$	20.5057	2.87137
$52$	0	0
$53$	4.35709	0.598492	0.299246	−	0.954176i	$-0.403265\pi$
$53$	4.35709	0.598492	0.299246	+	0.954176i	$0.403265\pi$
$54$	4.65203	0.633061
$55$	−2.38793	−0.321989
$56$	10.4093	1.39101
$57$	−2.32004	−0.307297
$58$	−1.73197	−0.227419
$59$	5.11542	0.665971	0.332985	−	0.942932i	$-0.391944\pi$
$59$	5.11542	0.665971	0.332985	+	0.942932i	$0.391944\pi$
$60$	2.49208	0.321726
$61$	−8.84695	−1.13274	−0.566368	−	0.824153i	$-0.691652\pi$
$61$	−8.84695	−1.13274	−0.566368	+	0.824153i	$0.691652\pi$
$62$	8.48395	1.07746
$63$	15.7841	1.98861
$64$	7.61201	0.951501
$65$	0	0
$66$	−6.89851	−0.849148
$67$	7.17992	0.877167	0.438584	−	0.898690i	$-0.355480\pi$
$67$	7.17992	0.877167	0.438584	+	0.898690i	$0.355480\pi$
$68$	6.71482	0.814292
$69$	−15.0878	−1.81635
$70$	−3.58527	−0.428522
$71$	3.28070	0.389348	0.194674	−	0.980868i	$-0.437635\pi$
$71$	3.28070	0.389348	0.194674	+	0.980868i	$0.437635\pi$
$72$	14.0173	1.65195
$73$	9.41601	1.10206	0.551030	−	0.834485i	$-0.314235\pi$
$73$	9.41601	1.10206	0.551030	+	0.834485i	$0.314235\pi$
$74$	−6.69561	−0.778349
$75$	−2.75868	−0.318545
$76$	−0.759724	−0.0871464
$77$	−8.17546	−0.931680
$78$	0	0
$79$	5.89740	0.663509	0.331755	−	0.943366i	$-0.392359\pi$
$79$	5.89740	0.663509	0.331755	+	0.943366i	$0.392359\pi$
$80$	−1.37722	−0.153978
$81$	−1.57598	−0.175109
$82$	6.44917	0.712192
$83$	−5.14271	−0.564486	−0.282243	−	0.959343i	$-0.591078\pi$
$83$	−5.14271	−0.564486	−0.282243	+	0.959343i	$0.591078\pi$
$84$	8.53203	0.930920
$85$	−7.43316	−0.806239
$86$	−12.6619	−1.36536
$87$	−4.56257	−0.489158
$88$	−7.26031	−0.773952
$89$	6.03426	0.639630	0.319815	−	0.947480i	$-0.396379\pi$
$89$	6.03426	0.639630	0.319815	+	0.947480i	$0.396379\pi$
$90$	−4.82794	−0.508910
$91$	0	0
$92$	−4.94065	−0.515099
$93$	22.3495	2.31753
$94$	−2.44085	−0.251755
$95$	0.840998	0.0862846
$96$	12.7964	1.30603
$97$	−6.33475	−0.643196	−0.321598	−	0.946876i	$-0.604220\pi$
$97$	−6.33475	−0.643196	−0.321598	+	0.946876i	$0.604220\pi$
$98$	−4.94429	−0.499449
$99$	−11.0091	−1.10646
$100$	−0.903360	−0.0903360
$101$	4.34957	0.432799	0.216399	−	0.976305i	$-0.430569\pi$
$101$	4.34957	0.432799	0.216399	+	0.976305i	$0.430569\pi$
$102$	−21.4737	−2.12621
$103$	2.11946	0.208837	0.104418	−	0.994533i	$-0.466702\pi$
$103$	2.11946	0.208837	0.104418	+	0.994533i	$0.466702\pi$
$104$	0	0
$105$	−9.44477	−0.921715
$106$	−4.56277	−0.443175
$107$	4.79902	0.463939	0.231969	−	0.972723i	$-0.425483\pi$
$107$	4.79902	0.463939	0.231969	+	0.972723i	$0.425483\pi$
$108$	4.01302	0.386153
$109$	7.44950	0.713533	0.356767	−	0.934194i	$-0.383879\pi$
$109$	7.44950	0.713533	0.356767	+	0.934194i	$0.383879\pi$
$110$	2.50066	0.238428
$111$	−17.6384	−1.67416
$112$	−4.71513	−0.445538
$113$	8.60985	0.809947	0.404973	−	0.914328i	$-0.367281\pi$
$113$	8.60985	0.809947	0.404973	+	0.914328i	$0.367281\pi$
$114$	2.42956	0.227549
$115$	5.46920	0.510005
$116$	−1.49406	−0.138720
$117$	0	0
$118$	−5.35690	−0.493142
$119$	−25.4486	−2.33287
$120$	−8.38753	−0.765673
$121$	−5.29777	−0.481616
$122$	9.26457	0.838775
$123$	16.9892	1.53186
$124$	7.31858	0.657228
$125$	1.00000	0.0894427
$126$	−16.5292	−1.47254
$127$	18.7179	1.66095	0.830474	−	0.557057i	$-0.188069\pi$
$127$	18.7179	1.66095	0.830474	+	0.557057i	$0.188069\pi$
$128$	1.30586	0.115423
$129$	−33.3555	−2.93678
$130$	0	0
$131$	9.44189	0.824942	0.412471	−	0.910971i	$-0.364666\pi$
$131$	9.44189	0.824942	0.412471	+	0.910971i	$0.364666\pi$
$132$	−5.95092	−0.517961
$133$	2.87929	0.249666
$134$	−7.51886	−0.649530
$135$	−4.44233	−0.382335
$136$	−22.5999	−1.93792
$137$	−15.6690	−1.33870	−0.669348	−	0.742949i	$-0.733427\pi$
$137$	−15.6690	−1.33870	−0.669348	+	0.742949i	$0.733427\pi$
$138$	15.8000	1.34498
$139$	12.1555	1.03102	0.515509	−	0.856884i	$-0.327603\pi$
$139$	12.1555	1.03102	0.515509	+	0.856884i	$0.327603\pi$
$140$	−3.09279	−0.261389
$141$	−6.43000	−0.541504
$142$	−3.43557	−0.288307
$143$	0	0
$144$	−6.34941	−0.529117
$145$	1.65390	0.137349
$146$	−9.86050	−0.816061
$147$	−13.0249	−1.07427
$148$	−5.77589	−0.474775
$149$	−0.777505	−0.0636957	−0.0318479	−	0.999493i	$-0.510139\pi$
$149$	−0.777505	−0.0636957	−0.0318479	+	0.999493i	$0.510139\pi$
$150$	2.88890	0.235878
$151$	7.75832	0.631363	0.315682	−	0.948865i	$-0.397767\pi$
$151$	7.75832	0.631363	0.315682	+	0.948865i	$0.397767\pi$
$152$	2.55698	0.207399
$153$	−34.2692	−2.77050
$154$	8.56139	0.689897
$155$	−8.10151	−0.650729
$156$	0	0
$157$	12.1350	0.968479	0.484240	−	0.874935i	$-0.339096\pi$
$157$	12.1350	0.968479	0.484240	+	0.874935i	$0.339096\pi$
$158$	−6.17579	−0.491319
$159$	−12.0198	−0.953233
$160$	−4.63860	−0.366713
$161$	18.7246	1.47571
$162$	1.65037	0.129666
$163$	0.186353	0.0145963	0.00729817	−	0.999973i	$-0.497677\pi$
$163$	0.186353	0.0145963	0.00729817	+	0.999973i	$0.497677\pi$
$164$	5.56330	0.434421
$165$	6.58754	0.512839
$166$	5.38548	0.417994
$167$	7.42351	0.574449	0.287224	−	0.957863i	$-0.407268\pi$
$167$	7.42351	0.574449	0.287224	+	0.957863i	$0.407268\pi$
$168$	−28.7160	−2.21549
$169$	0	0
$170$	7.78405	0.597009
$171$	3.87726	0.296502
$172$	−10.9226	−0.832842
$173$	4.62865	0.351910	0.175955	−	0.984398i	$-0.443699\pi$
$173$	4.62865	0.351910	0.175955	+	0.984398i	$0.443699\pi$
$174$	4.77795	0.362215
$175$	3.42366	0.258804
$176$	3.28871	0.247896
$177$	−14.1118	−1.06071
$178$	−6.31911	−0.473637
$179$	−11.9605	−0.893972	−0.446986	−	0.894541i	$-0.647503\pi$
$179$	−11.9605	−0.893972	−0.446986	+	0.894541i	$0.647503\pi$
$180$	−4.16477	−0.310424
$181$	12.8070	0.951935	0.475968	−	0.879463i	$-0.342098\pi$
$181$	12.8070	0.951935	0.475968	+	0.879463i	$0.342098\pi$
$182$	0	0
$183$	24.4059	1.80413
$184$	16.6286	1.22588
$185$	6.39379	0.470081
$186$	−23.4045	−1.71610
$187$	17.7499	1.29800
$188$	−2.10558	−0.153565
$189$	−15.2090	−1.10629
$190$	−0.880698	−0.0638926
$191$	17.5284	1.26831	0.634155	−	0.773206i	$-0.281348\pi$
$191$	17.5284	1.26831	0.634155	+	0.773206i	$0.281348\pi$
$192$	−20.9991	−1.51548
$193$	−8.60151	−0.619151	−0.309575	−	0.950875i	$-0.600187\pi$
$193$	−8.60151	−0.619151	−0.309575	+	0.950875i	$0.600187\pi$
$194$	6.63379	0.476278
$195$	0	0
$196$	−4.26514	−0.304653
$197$	8.12364	0.578785	0.289393	−	0.957210i	$-0.406547\pi$
$197$	8.12364	0.578785	0.289393	+	0.957210i	$0.406547\pi$
$198$	11.5288	0.819317
$199$	7.55978	0.535898	0.267949	−	0.963433i	$-0.413654\pi$
$199$	7.55978	0.535898	0.267949	+	0.963433i	$0.413654\pi$
$200$	3.04042	0.214990
$201$	−19.8071	−1.39709
$202$	−4.55490	−0.320481
$203$	5.66237	0.397420
$204$	−18.5240	−1.29694
$205$	−6.15846	−0.430125
$206$	−2.21951	−0.154641
$207$	25.2147	1.75254
$208$	0	0
$209$	−2.00825	−0.138913
$210$	9.89061	0.682517
$211$	20.8167	1.43308	0.716540	−	0.697546i	$-0.245725\pi$
$211$	20.8167	1.43308	0.716540	+	0.697546i	$0.245725\pi$
$212$	−3.93602	−0.270327
$213$	−9.05040	−0.620124
$214$	−5.02556	−0.343540
$215$	12.0911	0.824606
$216$	−13.5065	−0.919002
$217$	−27.7368	−1.88290
$218$	−7.80116	−0.528361
$219$	−25.9757	−1.75528
$220$	2.15716	0.145436
$221$	0	0
$222$	18.4710	1.23969
$223$	17.7214	1.18672	0.593358	−	0.804939i	$-0.297802\pi$
$223$	17.7214	1.18672	0.593358	+	0.804939i	$0.297802\pi$
$224$	−15.8810	−1.06109
$225$	4.61031	0.307354
$226$	−9.01629	−0.599755
$227$	−9.72267	−0.645316	−0.322658	−	0.946516i	$-0.604576\pi$
$227$	−9.72267	−0.645316	−0.322658	+	0.946516i	$0.604576\pi$
$228$	2.09584	0.138800
$229$	−21.5044	−1.42105	−0.710524	−	0.703673i	$-0.751542\pi$
$229$	−21.5044	−1.42105	−0.710524	+	0.703673i	$0.751542\pi$
$230$	−5.72737	−0.377652
$231$	22.5535	1.48391
$232$	5.02853	0.330139
$233$	−17.8626	−1.17022	−0.585111	−	0.810954i	$-0.698949\pi$
$233$	−17.8626	−1.17022	−0.585111	+	0.810954i	$0.698949\pi$
$234$	0	0
$235$	2.33083	0.152046
$236$	−4.62107	−0.300806
$237$	−16.2690	−1.05679
$238$	26.6499	1.72746
$239$	−4.80445	−0.310774	−0.155387	−	0.987854i	$-0.549662\pi$
$239$	−4.80445	−0.310774	−0.155387	+	0.987854i	$0.549662\pi$
$240$	3.79931	0.245244
$241$	21.0062	1.35313	0.676565	−	0.736383i	$-0.263468\pi$
$241$	21.0062	1.35313	0.676565	+	0.736383i	$0.263468\pi$
$242$	5.54786	0.356630
$243$	17.6746	1.13383
$244$	7.99198	0.511634
$245$	4.72142	0.301640
$246$	−17.7912	−1.13432
$247$	0	0
$248$	−24.6320	−1.56413
$249$	14.1871	0.899070
$250$	−1.04721	−0.0662311
$251$	−0.294350	−0.0185792	−0.00928962	−	0.999957i	$-0.502957\pi$
$251$	−0.294350	−0.0185792	−0.00928962	+	0.999957i	$0.502957\pi$
$252$	−14.2587	−0.898216
$253$	−13.0601	−0.821080
$254$	−19.6015	−1.22991
$255$	20.5057	1.28412
$256$	−16.5915	−1.03697
$257$	−21.9428	−1.36875	−0.684376	−	0.729129i	$-0.739925\pi$
$257$	−21.9428	−1.36875	−0.684376	+	0.729129i	$0.739925\pi$
$258$	34.9300	2.17465
$259$	21.8901	1.36019
$260$	0	0
$261$	7.62497	0.471974
$262$	−9.88760	−0.610858
$263$	−26.2189	−1.61673	−0.808363	−	0.588685i	$-0.799646\pi$
$263$	−26.2189	−1.61673	−0.808363	+	0.588685i	$0.799646\pi$
$264$	20.0289	1.23269
$265$	4.35709	0.267654
$266$	−3.01521	−0.184874
$267$	−16.6466	−1.01875
$268$	−6.48606	−0.396199
$269$	15.1362	0.922871	0.461436	−	0.887174i	$-0.347334\pi$
$269$	15.1362	0.922871	0.461436	+	0.887174i	$0.347334\pi$
$270$	4.65203	0.283113
$271$	−11.5436	−0.701221	−0.350611	−	0.936521i	$-0.614026\pi$
$271$	−11.5436	−0.701221	−0.350611	+	0.936521i	$0.614026\pi$
$272$	10.2371	0.620715
$273$	0	0
$274$	16.4087	0.991287
$275$	−2.38793	−0.143998
$276$	13.6297	0.820410
$277$	26.6854	1.60337	0.801686	−	0.597745i	$-0.203937\pi$
$277$	26.6854	1.60337	0.801686	+	0.597745i	$0.203937\pi$
$278$	−12.7293	−0.763455
$279$	−37.3505	−2.23611
$280$	10.4093	0.622077
$281$	−20.4907	−1.22237	−0.611187	−	0.791486i	$-0.709308\pi$
$281$	−20.4907	−1.22237	−0.611187	+	0.791486i	$0.709308\pi$
$282$	6.73353	0.400976
$283$	23.3361	1.38719	0.693593	−	0.720367i	$-0.256027\pi$
$283$	23.3361	1.38719	0.693593	+	0.720367i	$0.256027\pi$
$284$	−2.96366	−0.175861
$285$	−2.32004	−0.137428
$286$	0	0
$287$	−21.0844	−1.24457
$288$	−21.3854	−1.26015
$289$	38.2519	2.25011
$290$	−1.73197	−0.101705
$291$	17.4755	1.02443
$292$	−8.50605	−0.497779
$293$	−12.6983	−0.741842	−0.370921	−	0.928664i	$-0.620958\pi$
$293$	−12.6983	−0.741842	−0.370921	+	0.928664i	$0.620958\pi$
$294$	13.6397	0.795485
$295$	5.11542	0.297831
$296$	19.4398	1.12991
$297$	10.6080	0.615537
$298$	0.814208	0.0471658
$299$	0	0
$300$	2.49208	0.143880
$301$	41.3958	2.38601
$302$	−8.12456	−0.467516
$303$	−11.9991	−0.689329
$304$	−1.15824	−0.0664296
$305$	−8.84695	−0.506575
$306$	35.8869	2.05152
$307$	−9.44324	−0.538954	−0.269477	−	0.963007i	$-0.586851\pi$
$307$	−9.44324	−0.538954	−0.269477	+	0.963007i	$0.586851\pi$
$308$	7.38539	0.420822
$309$	−5.84691	−0.332619
$310$	8.48395	0.481856
$311$	−22.3785	−1.26897	−0.634485	−	0.772935i	$-0.718788\pi$
$311$	−22.3785	−1.26897	−0.634485	+	0.772935i	$0.718788\pi$
$312$	0	0
$313$	−0.953510	−0.0538955	−0.0269478	−	0.999637i	$-0.508579\pi$
$313$	−0.953510	−0.0538955	−0.0269478	+	0.999637i	$0.508579\pi$
$314$	−12.7078	−0.717145
$315$	15.7841	0.889334
$316$	−5.32747	−0.299694
$317$	−2.57505	−0.144629	−0.0723146	−	0.997382i	$-0.523039\pi$
$317$	−2.57505	−0.144629	−0.0723146	+	0.997382i	$0.523039\pi$
$318$	12.5872	0.705856
$319$	−3.94939	−0.221124
$320$	7.61201	0.425524
$321$	−13.2390	−0.738927
$322$	−19.6086	−1.09274
$323$	−6.25127	−0.347830
$324$	1.42368	0.0790931
$325$	0	0
$326$	−0.195150	−0.0108084
$327$	−20.5508	−1.13646
$328$	−18.7243	−1.03387
$329$	7.97995	0.439949
$330$	−6.89851	−0.379751
$331$	5.44348	0.299201	0.149600	−	0.988747i	$-0.452201\pi$
$331$	5.44348	0.299201	0.149600	+	0.988747i	$0.452201\pi$
$332$	4.64572	0.254967
$333$	29.4773	1.61535
$334$	−7.77394	−0.425371
$335$	7.17992	0.392281
$336$	13.0075	0.709618
$337$	7.28071	0.396605	0.198303	−	0.980141i	$-0.436457\pi$
$337$	7.28071	0.396605	0.198303	+	0.980141i	$0.436457\pi$
$338$	0	0
$339$	−23.7518	−1.29002
$340$	6.71482	0.364162
$341$	19.3459	1.04764
$342$	−4.06029	−0.219555
$343$	−7.80108	−0.421219
$344$	36.7620	1.98207
$345$	−15.0878	−0.812297
$346$	−4.84715	−0.260584
$347$	−1.51723	−0.0814494	−0.0407247	−	0.999170i	$-0.512967\pi$
$347$	−1.51723	−0.0814494	−0.0407247	+	0.999170i	$0.512967\pi$
$348$	4.12164	0.220943
$349$	32.7914	1.75529	0.877643	−	0.479315i	$-0.159115\pi$
$349$	32.7914	1.75529	0.877643	+	0.479315i	$0.159115\pi$
$350$	−3.58527	−0.191641
$351$	0	0
$352$	11.0767	0.590388
$353$	−9.97003	−0.530651	−0.265325	−	0.964159i	$-0.585479\pi$
$353$	−9.97003	−0.530651	−0.265325	+	0.964159i	$0.585479\pi$
$354$	14.7780	0.785440
$355$	3.28070	0.174122
$356$	−5.45111	−0.288908
$357$	70.2045	3.71561
$358$	12.5251	0.661974
$359$	−8.06159	−0.425474	−0.212737	−	0.977109i	$-0.568238\pi$
$359$	−8.06159	−0.425474	−0.212737	+	0.977109i	$0.568238\pi$
$360$	14.0173	0.738774
$361$	−18.2927	−0.962775
$362$	−13.4115	−0.704895
$363$	14.6149	0.767081
$364$	0	0
$365$	9.41601	0.492856
$366$	−25.5580	−1.33594
$367$	−1.37366	−0.0717044	−0.0358522	−	0.999357i	$-0.511415\pi$
$367$	−1.37366	−0.0717044	−0.0358522	+	0.999357i	$0.511415\pi$
$368$	−7.53228	−0.392647
$369$	−28.3924	−1.47805
$370$	−6.69561	−0.348088
$371$	14.9172	0.774461
$372$	−20.1896	−1.04678
$373$	−6.14540	−0.318197	−0.159098	−	0.987263i	$-0.550859\pi$
$373$	−6.14540	−0.318197	−0.159098	+	0.987263i	$0.550859\pi$
$374$	−18.5878	−0.961152
$375$	−2.75868	−0.142458
$376$	7.08668	0.365468
$377$	0	0
$378$	15.9269	0.819194
$379$	−30.8770	−1.58604	−0.793021	−	0.609194i	$-0.791493\pi$
$379$	−30.8770	−1.58604	−0.793021	+	0.609194i	$0.791493\pi$
$380$	−0.759724	−0.0389730
$381$	−51.6368	−2.64543
$382$	−18.3558	−0.939166
$383$	33.5485	1.71425	0.857124	−	0.515110i	$-0.172249\pi$
$383$	33.5485	1.71425	0.857124	+	0.515110i	$0.172249\pi$
$384$	−3.60245	−0.183837
$385$	−8.17546	−0.416660
$386$	9.00756	0.458472
$387$	55.7437	2.83361
$388$	5.72256	0.290519
$389$	27.3375	1.38606	0.693032	−	0.720907i	$-0.256274\pi$
$389$	27.3375	1.38606	0.693032	+	0.720907i	$0.256274\pi$
$390$	0	0
$391$	−40.6534	−2.05593
$392$	14.3551	0.725040
$393$	−26.0471	−1.31390
$394$	−8.50712	−0.428583
$395$	5.89740	0.296730
$396$	9.94519	0.499765
$397$	−18.5292	−0.929953	−0.464977	−	0.885323i	$-0.653937\pi$
$397$	−18.5292	−0.929953	−0.464977	+	0.885323i	$0.653937\pi$
$398$	−7.91664	−0.396825
$399$	−7.94303	−0.397649
$400$	−1.37722	−0.0688610
$401$	−35.2525	−1.76043	−0.880214	−	0.474578i	$-0.842601\pi$
$401$	−35.2525	−1.76043	−0.880214	+	0.474578i	$0.842601\pi$
$402$	20.7421	1.03452
$403$	0	0
$404$	−3.92923	−0.195487
$405$	−1.57598	−0.0783110
$406$	−5.92966	−0.294284
$407$	−15.2679	−0.756804
$408$	62.3458	3.08658
$409$	−1.81630	−0.0898103	−0.0449051	−	0.998991i	$-0.514299\pi$
$409$	−1.81630	−0.0898103	−0.0449051	+	0.998991i	$0.514299\pi$
$410$	6.44917	0.318502
$411$	43.2259	2.13217
$412$	−1.91464	−0.0943274
$413$	17.5134	0.861780
$414$	−26.4050	−1.29773
$415$	−5.14271	−0.252446
$416$	0	0
$417$	−33.5332	−1.64213
$418$	2.10305	0.102863
$419$	−5.92370	−0.289392	−0.144696	−	0.989476i	$-0.546220\pi$
$419$	−5.92370	−0.289392	−0.144696	+	0.989476i	$0.546220\pi$
$420$	8.53203	0.416320
$421$	2.22193	0.108290	0.0541451	−	0.998533i	$-0.482757\pi$
$421$	2.22193	0.108290	0.0541451	+	0.998533i	$0.482757\pi$
$422$	−21.7994	−1.06118
$423$	10.7458	0.522480
$424$	13.2474	0.643348
$425$	−7.43316	−0.360561
$426$	9.47764	0.459193
$427$	−30.2889	−1.46578
$428$	−4.33525	−0.209552
$429$	0	0
$430$	−12.6619	−0.610609
$431$	2.91961	0.140633	0.0703163	−	0.997525i	$-0.477599\pi$
$431$	2.91961	0.140633	0.0703163	+	0.997525i	$0.477599\pi$
$432$	6.11806	0.294355
$433$	1.19163	0.0572661	0.0286330	−	0.999590i	$-0.490885\pi$
$433$	1.19163	0.0572661	0.0286330	+	0.999590i	$0.490885\pi$
$434$	29.0461	1.39426
$435$	−4.56257	−0.218758
$436$	−6.72959	−0.322289
$437$	4.59958	0.220028
$438$	27.2019	1.29976
$439$	−0.753548	−0.0359649	−0.0179825	−	0.999838i	$-0.505724\pi$
$439$	−0.753548	−0.0359649	−0.0179825	+	0.999838i	$0.505724\pi$
$440$	−7.26031	−0.346122
$441$	21.7672	1.03653
$442$	0	0
$443$	20.0999	0.954977	0.477488	−	0.878638i	$-0.341547\pi$
$443$	20.0999	0.954977	0.477488	+	0.878638i	$0.341547\pi$
$444$	15.9338	0.756186
$445$	6.03426	0.286051
$446$	−18.5580	−0.878747
$447$	2.14489	0.101450
$448$	26.0609	1.23126
$449$	27.4311	1.29455	0.647276	−	0.762256i	$-0.275908\pi$
$449$	27.4311	1.29455	0.647276	+	0.762256i	$0.275908\pi$
$450$	−4.82794	−0.227591
$451$	14.7060	0.692478
$452$	−7.77780	−0.365837
$453$	−21.4027	−1.00559
$454$	10.1816	0.477848
$455$	0	0
$456$	−7.05390	−0.330329
$457$	−15.2157	−0.711759	−0.355879	−	0.934532i	$-0.615819\pi$
$457$	−15.2157	−0.711759	−0.355879	+	0.934532i	$0.615819\pi$
$458$	22.5195	1.05227
$459$	33.0205	1.54127
$460$	−4.94065	−0.230359
$461$	4.57978	0.213301	0.106651	−	0.994297i	$-0.465987\pi$
$461$	4.57978	0.213301	0.106651	+	0.994297i	$0.465987\pi$
$462$	−23.6181	−1.09881
$463$	14.5795	0.677566	0.338783	−	0.940865i	$-0.389985\pi$
$463$	14.5795	0.677566	0.338783	+	0.940865i	$0.389985\pi$
$464$	−2.27778	−0.105743
$465$	22.3495	1.03643
$466$	18.7059	0.866533
$467$	−38.3834	−1.77617	−0.888087	−	0.459676i	$-0.847965\pi$
$467$	−38.3834	−1.77617	−0.888087	+	0.459676i	$0.847965\pi$
$468$	0	0
$469$	24.5816	1.13507
$470$	−2.44085	−0.112588
$471$	−33.4766	−1.54252
$472$	15.5530	0.715885
$473$	−28.8727	−1.32757
$474$	17.0370	0.782536
$475$	0.840998	0.0385876
$476$	22.9892	1.05371
$477$	20.0875	0.919744
$478$	5.03125	0.230124
$479$	30.9140	1.41250	0.706248	−	0.707964i	$-0.250386\pi$
$479$	30.9140	1.41250	0.706248	+	0.707964i	$0.250386\pi$
$480$	12.7964	0.584073
$481$	0	0
$482$	−21.9978	−1.00197
$483$	−51.6553	−2.35040
$484$	4.78580	0.217536
$485$	−6.33475	−0.287646
$486$	−18.5089	−0.839582
$487$	5.37275	0.243463	0.121731	−	0.992563i	$-0.461155\pi$
$487$	5.37275	0.243463	0.121731	+	0.992563i	$0.461155\pi$
$488$	−26.8984	−1.21763
$489$	−0.514089	−0.0232479
$490$	−4.94429	−0.223360
$491$	−0.638413	−0.0288112	−0.0144056	−	0.999896i	$-0.504586\pi$
$491$	−0.638413	−0.0288112	−0.0144056	+	0.999896i	$0.504586\pi$
$492$	−15.3474	−0.691913
$493$	−12.2937	−0.553679
$494$	0	0
$495$	−11.0091	−0.494823
$496$	11.1576	0.500989
$497$	11.2320	0.503824
$498$	−14.8568	−0.665749
$499$	−24.2542	−1.08577	−0.542885	−	0.839807i	$-0.682668\pi$
$499$	−24.2542	−1.08577	−0.542885	+	0.839807i	$0.682668\pi$
$500$	−0.903360	−0.0403995
$501$	−20.4791	−0.914938
$502$	0.308245	0.0137577
$503$	2.66695	0.118914	0.0594568	−	0.998231i	$-0.481063\pi$
$503$	2.66695	0.118914	0.0594568	+	0.998231i	$0.481063\pi$
$504$	47.9902	2.13766
$505$	4.34957	0.193553
$506$	13.6766	0.607998
$507$	0	0
$508$	−16.9090	−0.750218
$509$	28.4006	1.25884	0.629418	−	0.777067i	$-0.283293\pi$
$509$	28.4006	1.25884	0.629418	+	0.777067i	$0.283293\pi$
$510$	−21.4737	−0.950871
$511$	32.2372	1.42609
$512$	14.7630	0.652439
$513$	−3.73599	−0.164948
$514$	22.9786	1.01354
$515$	2.11946	0.0933946
$516$	30.1320	1.32649
$517$	−5.56586	−0.244786
$518$	−22.9235	−1.00720
$519$	−12.7690	−0.560495
$520$	0	0
$521$	−10.4355	−0.457190	−0.228595	−	0.973522i	$-0.573413\pi$
$521$	−10.4355	−0.457190	−0.228595	+	0.973522i	$0.573413\pi$
$522$	−7.98491	−0.349490
$523$	34.3111	1.50032	0.750159	−	0.661257i	$-0.229977\pi$
$523$	34.3111	1.50032	0.750159	+	0.661257i	$0.229977\pi$
$524$	−8.52943	−0.372610
$525$	−9.44477	−0.412203
$526$	27.4566	1.19716
$527$	60.2198	2.62322
$528$	−9.07249	−0.394830
$529$	6.91210	0.300526
$530$	−4.56277	−0.198194
$531$	23.5837	1.02344
$532$	−2.60103	−0.112769
$533$	0	0
$534$	17.4324	0.754373
$535$	4.79902	0.207480
$536$	21.8300	0.942910
$537$	32.9953	1.42385
$538$	−15.8507	−0.683374
$539$	−11.2744	−0.485624
$540$	4.01302	0.172693
$541$	−35.2810	−1.51685	−0.758425	−	0.651761i	$-0.774031\pi$
$541$	−35.2810	−1.51685	−0.758425	+	0.651761i	$0.774031\pi$
$542$	12.0885	0.519245
$543$	−35.3303	−1.51617
$544$	34.4794	1.47829
$545$	7.44950	0.319102
$546$	0	0
$547$	32.8604	1.40501	0.702504	−	0.711679i	$-0.252065\pi$
$547$	32.8604	1.40501	0.702504	+	0.711679i	$0.252065\pi$
$548$	14.1548	0.604663
$549$	−40.7872	−1.74075
$550$	2.50066	0.106628
$551$	1.39092	0.0592553
$552$	−45.8730	−1.95249
$553$	20.1907	0.858594
$554$	−27.9451	−1.18727
$555$	−17.6384	−0.748709
$556$	−10.9808	−0.465691
$557$	18.5254	0.784947	0.392474	−	0.919763i	$-0.371619\pi$
$557$	18.5254	0.784947	0.392474	+	0.919763i	$0.371619\pi$
$558$	39.1136	1.65581
$559$	0	0
$560$	−4.71513	−0.199250
$561$	−48.9663	−2.06736
$562$	21.4580	0.905151
$563$	−20.9662	−0.883622	−0.441811	−	0.897108i	$-0.645664\pi$
$563$	−20.9662	−0.883622	−0.441811	+	0.897108i	$0.645664\pi$
$564$	5.80861	0.244587
$565$	8.60985	0.362219
$566$	−24.4377	−1.02719
$567$	−5.39560	−0.226594
$568$	9.97470	0.418529
$569$	−22.1884	−0.930188	−0.465094	−	0.885261i	$-0.653979\pi$
$569$	−22.1884	−0.930188	−0.465094	+	0.885261i	$0.653979\pi$
$570$	2.42956	0.101763
$571$	−14.8506	−0.621480	−0.310740	−	0.950495i	$-0.600577\pi$
$571$	−14.8506	−0.621480	−0.310740	+	0.950495i	$0.600577\pi$
$572$	0	0
$573$	−48.3552	−2.02007
$574$	22.0797	0.921590
$575$	5.46920	0.228081
$576$	35.0937	1.46224
$577$	−26.9163	−1.12054	−0.560269	−	0.828311i	$-0.689302\pi$
$577$	−26.9163	−1.12054	−0.560269	+	0.828311i	$0.689302\pi$
$578$	−40.0576	−1.66618
$579$	23.7288	0.986136
$580$	−1.49406	−0.0620376
$581$	−17.6069	−0.730456
$582$	−18.3005	−0.758580
$583$	−10.4044	−0.430908
$584$	28.6286	1.18466
$585$	0	0
$586$	13.2977	0.549324
$587$	11.6753	0.481890	0.240945	−	0.970539i	$-0.422543\pi$
$587$	11.6753	0.481890	0.240945	+	0.970539i	$0.422543\pi$
$588$	11.7662	0.485228
$589$	−6.81336	−0.280739
$590$	−5.35690	−0.220540
$591$	−22.4105	−0.921845
$592$	−8.80565	−0.361910
$593$	−16.9271	−0.695111	−0.347556	−	0.937659i	$-0.612988\pi$
$593$	−16.9271	−0.695111	−0.347556	+	0.937659i	$0.612988\pi$
$594$	−11.1087	−0.455797
$595$	−25.4486	−1.04329
$596$	0.702367	0.0287701
$597$	−20.8550	−0.853538
$598$	0	0
$599$	6.57368	0.268593	0.134297	−	0.990941i	$-0.457123\pi$
$599$	6.57368	0.268593	0.134297	+	0.990941i	$0.457123\pi$
$600$	−8.38753	−0.342419
$601$	4.62956	0.188844	0.0944219	−	0.995532i	$-0.469900\pi$
$601$	4.62956	0.188844	0.0944219	+	0.995532i	$0.469900\pi$
$602$	−43.3499	−1.76681
$603$	33.1017	1.34800
$604$	−7.00856	−0.285174
$605$	−5.29777	−0.215385
$606$	12.5655	0.510438
$607$	−10.7891	−0.437915	−0.218958	−	0.975734i	$-0.570266\pi$
$607$	−10.7891	−0.437915	−0.218958	+	0.975734i	$0.570266\pi$
$608$	−3.90105	−0.158209
$609$	−15.6207	−0.632981
$610$	9.26457	0.375112
$611$	0	0
$612$	30.9574	1.25138
$613$	26.4860	1.06976	0.534879	−	0.844928i	$-0.320357\pi$
$613$	26.4860	1.06976	0.534879	+	0.844928i	$0.320357\pi$
$614$	9.88901	0.399088
$615$	16.9892	0.685071
$616$	−24.8568	−1.00151
$617$	28.3651	1.14194	0.570968	−	0.820972i	$-0.306568\pi$
$617$	28.3651	1.14194	0.570968	+	0.820972i	$0.306568\pi$
$618$	6.12292	0.246300
$619$	13.9696	0.561485	0.280742	−	0.959783i	$-0.409419\pi$
$619$	13.9696	0.561485	0.280742	+	0.959783i	$0.409419\pi$
$620$	7.31858	0.293921
$621$	−24.2959	−0.974963
$622$	23.4349	0.939655
$623$	20.6592	0.827694
$624$	0	0
$625$	1.00000	0.0400000
$626$	0.998521	0.0399089
$627$	5.54011	0.221251
$628$	−10.9623	−0.437443
$629$	−47.5260	−1.89499
$630$	−16.5292	−0.658539
$631$	−23.6090	−0.939859	−0.469930	−	0.882704i	$-0.655721\pi$
$631$	−23.6090	−0.939859	−0.469930	+	0.882704i	$0.655721\pi$
$632$	17.9305	0.713239
$633$	−57.4266	−2.28250
$634$	2.69661	0.107096
$635$	18.7179	0.742799
$636$	10.8582	0.430556
$637$	0	0
$638$	4.13583	0.163739
$639$	15.1251	0.598338
$640$	1.30586	0.0516187
$641$	37.9614	1.49939	0.749693	−	0.661785i	$-0.230201\pi$
$641$	37.9614	1.49939	0.749693	+	0.661785i	$0.230201\pi$
$642$	13.8639	0.547165
$643$	−50.6338	−1.99680	−0.998402	−	0.0565186i	$-0.982000\pi$
$643$	−50.6338	−1.99680	−0.998402	+	0.0565186i	$0.982000\pi$
$644$	−16.9151	−0.666548
$645$	−33.3555	−1.31337
$646$	6.54637	0.257563
$647$	34.3014	1.34853	0.674264	−	0.738490i	$-0.264461\pi$
$647$	34.3014	1.34853	0.674264	+	0.738490i	$0.264461\pi$
$648$	−4.79163	−0.188233
$649$	−12.2153	−0.479492
$650$	0	0
$651$	76.5169	2.99893
$652$	−0.168344	−0.00659287
$653$	−19.2672	−0.753985	−0.376993	−	0.926216i	$-0.623042\pi$
$653$	−19.2672	−0.753985	−0.376993	+	0.926216i	$0.623042\pi$
$654$	21.5209	0.841534
$655$	9.44189	0.368925
$656$	8.48155	0.331149
$657$	43.4107	1.69361
$658$	−8.35665	−0.325776
$659$	−36.4980	−1.42176	−0.710880	−	0.703314i	$-0.751703\pi$
$659$	−36.4980	−1.42176	−0.710880	+	0.703314i	$0.751703\pi$
$660$	−5.95092	−0.231639
$661$	−13.5048	−0.525276	−0.262638	−	0.964895i	$-0.584592\pi$
$661$	−13.5048	−0.525276	−0.262638	+	0.964895i	$0.584592\pi$
$662$	−5.70044	−0.221554
$663$	0	0
$664$	−15.6360	−0.606794
$665$	2.87929	0.111654
$666$	−30.8688	−1.19614
$667$	9.04548	0.350242
$668$	−6.70610	−0.259467
$669$	−48.8878	−1.89011
$670$	−7.51886	−0.290479
$671$	21.1259	0.815557
$672$	43.8105	1.69003
$673$	3.45492	0.133177	0.0665887	−	0.997781i	$-0.478788\pi$
$673$	3.45492	0.133177	0.0665887	+	0.997781i	$0.478788\pi$
$674$	−7.62440	−0.293681
$675$	−4.44233	−0.170985
$676$	0	0
$677$	9.65561	0.371095	0.185548	−	0.982635i	$-0.440594\pi$
$677$	9.65561	0.371095	0.185548	+	0.982635i	$0.440594\pi$
$678$	24.8730	0.955243
$679$	−21.6880	−0.832309
$680$	−22.5999	−0.866666
$681$	26.8217	1.02781
$682$	−20.2591	−0.775761
$683$	−20.1271	−0.770144	−0.385072	−	0.922887i	$-0.625823\pi$
$683$	−20.1271	−0.770144	−0.385072	+	0.922887i	$0.625823\pi$
$684$	−3.50256	−0.133924
$685$	−15.6690	−0.598683
$686$	8.16934	0.311907
$687$	59.3236	2.26334
$688$	−16.6521	−0.634855
$689$	0	0
$690$	15.8000	0.601495
$691$	9.23887	0.351463	0.175732	−	0.984438i	$-0.443771\pi$
$691$	9.23887	0.351463	0.175732	+	0.984438i	$0.443771\pi$
$692$	−4.18134	−0.158951
$693$	−37.6914	−1.43178
$694$	1.58886	0.0603121
$695$	12.1555	0.461085
$696$	−13.8721	−0.525820
$697$	45.7768	1.73392
$698$	−34.3394	−1.29977
$699$	49.2773	1.86384
$700$	−3.09279	−0.116897
$701$	8.20434	0.309874	0.154937	−	0.987924i	$-0.450483\pi$
$701$	8.20434	0.309874	0.154937	+	0.987924i	$0.450483\pi$
$702$	0	0
$703$	5.37716	0.202804
$704$	−18.1770	−0.685070
$705$	−6.43000	−0.242168
$706$	10.4407	0.392940
$707$	14.8914	0.560050
$708$	12.7480	0.479101
$709$	32.8408	1.23336	0.616682	−	0.787213i	$-0.288477\pi$
$709$	32.8408	1.23336	0.616682	+	0.787213i	$0.288477\pi$
$710$	−3.43557	−0.128935
$711$	27.1888	1.01966
$712$	18.3466	0.687569
$713$	−44.3087	−1.65938
$714$	−73.5185	−2.75136
$715$	0	0
$716$	10.8047	0.403790
$717$	13.2539	0.494977
$718$	8.44214	0.315058
$719$	−9.98530	−0.372389	−0.186194	−	0.982513i	$-0.559615\pi$
$719$	−9.98530	−0.372389	−0.186194	+	0.982513i	$0.559615\pi$
$720$	−6.34941	−0.236628
$721$	7.25631	0.270239
$722$	19.1562	0.712922
$723$	−57.9494	−2.15516
$724$	−11.5693	−0.429970
$725$	1.65390	0.0614241
$726$	−15.3048	−0.568013
$727$	19.8629	0.736673	0.368336	−	0.929693i	$-0.379927\pi$
$727$	19.8629	0.736673	0.368336	+	0.929693i	$0.379927\pi$
$728$	0	0
$729$	−44.0306	−1.63076
$730$	−9.86050	−0.364953
$731$	−89.8751	−3.32415
$732$	−22.0473	−0.814892
$733$	13.4222	0.495761	0.247881	−	0.968791i	$-0.420266\pi$
$733$	13.4222	0.495761	0.247881	+	0.968791i	$0.420266\pi$
$734$	1.43850	0.0530961
$735$	−13.0249	−0.480430
$736$	−25.3694	−0.935129
$737$	−17.1452	−0.631551
$738$	29.7327	1.09447
$739$	−42.4122	−1.56016	−0.780079	−	0.625681i	$-0.784821\pi$
$739$	−42.4122	−1.56016	−0.780079	+	0.625681i	$0.784821\pi$
$740$	−5.77589	−0.212326
$741$	0	0
$742$	−15.6213	−0.573477
$743$	15.1678	0.556451	0.278225	−	0.960516i	$-0.410254\pi$
$743$	15.1678	0.556451	0.278225	+	0.960516i	$0.410254\pi$
$744$	67.9517	2.49123
$745$	−0.777505	−0.0284856
$746$	6.43549	0.235620
$747$	−23.7095	−0.867485
$748$	−16.0345	−0.586281
$749$	16.4302	0.600346
$750$	2.88890	0.105488
$751$	−51.0088	−1.86134	−0.930669	−	0.365862i	$-0.880774\pi$
$751$	−51.0088	−1.86134	−0.930669	+	0.365862i	$0.880774\pi$
$752$	−3.21006	−0.117059
$753$	0.812018	0.0295916
$754$	0	0
$755$	7.75832	0.282354
$756$	13.7392	0.499690
$757$	18.4750	0.671486	0.335743	−	0.941954i	$-0.391013\pi$
$757$	18.4750	0.671486	0.335743	+	0.941954i	$0.391013\pi$
$758$	32.3345	1.17444
$759$	36.0286	1.30775
$760$	2.55698	0.0927516
$761$	−17.8713	−0.647835	−0.323918	−	0.946085i	$-0.605000\pi$
$761$	−17.8713	−0.647835	−0.323918	+	0.946085i	$0.605000\pi$
$762$	54.0743	1.95891
$763$	25.5045	0.923326
$764$	−15.8344	−0.572870
$765$	−34.2692	−1.23900
$766$	−35.1322	−1.26938
$767$	0	0
$768$	45.7707	1.65161
$769$	−19.7597	−0.712552	−0.356276	−	0.934381i	$-0.615954\pi$
$769$	−19.7597	−0.712552	−0.356276	+	0.934381i	$0.615954\pi$
$770$	8.56139	0.308531
$771$	60.5330	2.18004
$772$	7.77027	0.279658
$773$	49.5340	1.78161	0.890806	−	0.454383i	$-0.150140\pi$
$773$	49.5340	1.78161	0.890806	+	0.454383i	$0.150140\pi$
$774$	−58.3751	−2.09825
$775$	−8.10151	−0.291015
$776$	−19.2603	−0.691404
$777$	−60.3878	−2.16640
$778$	−28.6279	−1.02636
$779$	−5.17925	−0.185566
$780$	0	0
$781$	−7.83410	−0.280326
$782$	42.5725	1.52239
$783$	−7.34714	−0.262565
$784$	−6.50243	−0.232230
$785$	12.1350	0.433117
$786$	27.2767	0.972928
$787$	−37.7290	−1.34490	−0.672448	−	0.740145i	$-0.734757\pi$
$787$	−37.7290	−1.34490	−0.672448	+	0.740145i	$0.734757\pi$
$788$	−7.33857	−0.261426
$789$	72.3295	2.57500
$790$	−6.17579	−0.219725
$791$	29.4772	1.04809
$792$	−33.4723	−1.18939
$793$	0	0
$794$	19.4039	0.688617
$795$	−12.0198	−0.426299
$796$	−6.82920	−0.242055
$797$	−42.6042	−1.50912	−0.754559	−	0.656232i	$-0.772149\pi$
$797$	−42.6042	−1.50912	−0.754559	+	0.656232i	$0.772149\pi$
$798$	8.31799	0.294454
$799$	−17.3254	−0.612929
$800$	−4.63860	−0.163999
$801$	27.8198	0.982964
$802$	36.9166	1.30357
$803$	−22.4848	−0.793472
$804$	17.8930	0.631036
$805$	18.7246	0.659957
$806$	0	0
$807$	−41.7560	−1.46988
$808$	13.2245	0.465237
$809$	−13.1167	−0.461157	−0.230579	−	0.973054i	$-0.574062\pi$
$809$	−13.1167	−0.461157	−0.230579	+	0.973054i	$0.574062\pi$
$810$	1.65037	0.0579882
$811$	−38.4234	−1.34923	−0.674614	−	0.738171i	$-0.735690\pi$
$811$	−38.4234	−1.34923	−0.674614	+	0.738171i	$0.735690\pi$
$812$	−5.11516	−0.179507
$813$	31.8450	1.11685
$814$	15.9887	0.560403
$815$	0.186353	0.00652768
$816$	−28.2409	−0.988628
$817$	10.1686	0.355754
$818$	1.90204	0.0665033
$819$	0	0
$820$	5.56330	0.194279
$821$	−29.0515	−1.01390	−0.506951	−	0.861975i	$-0.669228\pi$
$821$	−29.0515	−1.01390	−0.506951	+	0.861975i	$0.669228\pi$
$822$	−45.2664	−1.57885
$823$	−25.2103	−0.878777	−0.439388	−	0.898297i	$-0.644805\pi$
$823$	−25.2103	−0.878777	−0.439388	+	0.898297i	$0.644805\pi$
$824$	6.44404	0.224489
$825$	6.58754	0.229349
$826$	−18.3402	−0.638136
$827$	−2.27577	−0.0791361	−0.0395681	−	0.999217i	$-0.512598\pi$
$827$	−2.27577	−0.0791361	−0.0395681	+	0.999217i	$0.512598\pi$
$828$	−22.7779	−0.791588
$829$	−34.8474	−1.21030	−0.605149	−	0.796112i	$-0.706887\pi$
$829$	−34.8474	−1.21030	−0.605149	+	0.796112i	$0.706887\pi$
$830$	5.38548	0.186933
$831$	−73.6165	−2.55373
$832$	0	0
$833$	−35.0950	−1.21597
$834$	35.1162	1.21597
$835$	7.42351	0.256901
$836$	1.81417	0.0627444
$837$	35.9896	1.24398
$838$	6.20333	0.214290
$839$	−50.7285	−1.75134	−0.875672	−	0.482907i	$-0.839581\pi$
$839$	−50.7285	−1.75134	−0.875672	+	0.482907i	$0.839581\pi$
$840$	−28.7160	−0.990797
$841$	−26.2646	−0.905677
$842$	−2.32682	−0.0801874
$843$	56.5273	1.94690
$844$	−18.8050	−0.647294
$845$	0	0
$846$	−11.2531	−0.386889
$847$	−18.1377	−0.623220
$848$	−6.00067	−0.206064
$849$	−64.3767	−2.20940
$850$	7.78405	0.266991
$851$	34.9689	1.19872
$852$	8.17578	0.280097
$853$	−50.2475	−1.72044	−0.860221	−	0.509921i	$-0.829674\pi$
$853$	−50.2475	−1.72044	−0.860221	+	0.509921i	$0.829674\pi$
$854$	31.7187	1.08539
$855$	3.87726	0.132600
$856$	14.5910	0.498711
$857$	−44.5420	−1.52153	−0.760763	−	0.649030i	$-0.775175\pi$
$857$	−44.5420	−1.52153	−0.760763	+	0.649030i	$0.775175\pi$
$858$	0	0
$859$	16.8945	0.576432	0.288216	−	0.957565i	$-0.406938\pi$
$859$	16.8945	0.576432	0.288216	+	0.957565i	$0.406938\pi$
$860$	−10.9226	−0.372458
$861$	58.1652	1.98226
$862$	−3.05743	−0.104137
$863$	48.4137	1.64802	0.824011	−	0.566574i	$-0.191732\pi$
$863$	48.4137	1.64802	0.824011	+	0.566574i	$0.191732\pi$
$864$	20.6062	0.701036
$865$	4.62865	0.157379
$866$	−1.24788	−0.0424048
$867$	−105.525	−3.58380
$868$	25.0563	0.850467
$869$	−14.0826	−0.477719
$870$	4.77795	0.161988
$871$	0	0
$872$	22.6496	0.767012
$873$	−29.2052	−0.988445
$874$	−4.81671	−0.162928
$875$	3.42366	0.115741
$876$	23.4655	0.792824
$877$	−8.18430	−0.276364	−0.138182	−	0.990407i	$-0.544126\pi$
$877$	−8.18430	−0.276364	−0.138182	+	0.990407i	$0.544126\pi$
$878$	0.789120	0.0266315
$879$	35.0305	1.18155
$880$	3.28871	0.110862
$881$	−15.6088	−0.525874	−0.262937	−	0.964813i	$-0.584691\pi$
$881$	−15.6088	−0.525874	−0.262937	+	0.964813i	$0.584691\pi$
$882$	−22.7947	−0.767538
$883$	−0.0864274	−0.00290851	−0.00145426	−	0.999999i	$-0.500463\pi$
$883$	−0.0864274	−0.00290851	−0.00145426	+	0.999999i	$0.500463\pi$
$884$	0	0
$885$	−14.1118	−0.474363
$886$	−21.0488	−0.707147
$887$	52.4753	1.76195	0.880975	−	0.473163i	$-0.156888\pi$
$887$	52.4753	1.76195	0.880975	+	0.473163i	$0.156888\pi$
$888$	−53.6281	−1.79964
$889$	64.0838	2.14930
$890$	−6.31911	−0.211817
$891$	3.76333	0.126076
$892$	−16.0089	−0.536016
$893$	1.96022	0.0655963
$894$	−2.24614	−0.0751221
$895$	−11.9605	−0.399797
$896$	4.47082	0.149360
$897$	0	0
$898$	−28.7260	−0.958598
$899$	−13.3991	−0.446883
$900$	−4.16477	−0.138826
$901$	−32.3869	−1.07897
$902$	−15.4002	−0.512770
$903$	−114.198	−3.80026
$904$	26.1775	0.870652
$905$	12.8070	0.425718
$906$	22.4130	0.744624
$907$	22.9724	0.762787	0.381393	−	0.924413i	$-0.375444\pi$
$907$	22.9724	0.762787	0.381393	+	0.924413i	$0.375444\pi$
$908$	8.78307	0.291477
$909$	20.0529	0.665112
$910$	0	0
$911$	−7.20421	−0.238686	−0.119343	−	0.992853i	$-0.538079\pi$
$911$	−7.20421	−0.238686	−0.119343	+	0.992853i	$0.538079\pi$
$912$	3.19521	0.105804
$913$	12.2805	0.406424
$914$	15.9339	0.527048
$915$	24.4059	0.806834
$916$	19.4262	0.641859
$917$	32.3258	1.06749
$918$	−34.5793	−1.14129
$919$	−47.1095	−1.55400	−0.776999	−	0.629502i	$-0.783259\pi$
$919$	−47.1095	−1.55400	−0.776999	+	0.629502i	$0.783259\pi$
$920$	16.6286	0.548230
$921$	26.0509	0.858405
$922$	−4.79597	−0.157947
$923$	0	0
$924$	−20.3739	−0.670253
$925$	6.39379	0.210226
$926$	−15.2677	−0.501728
$927$	9.77137	0.320934
$928$	−7.67176	−0.251838
$929$	56.8858	1.86636	0.933181	−	0.359406i	$-0.117021\pi$
$929$	56.8858	1.86636	0.933181	+	0.359406i	$0.117021\pi$
$930$	−23.4045	−0.767463
$931$	3.97070	0.130135
$932$	16.1364	0.528566
$933$	61.7352	2.02112
$934$	40.1953	1.31523
$935$	17.7499	0.580484
$936$	0	0
$937$	−12.1029	−0.395385	−0.197693	−	0.980264i	$-0.563345\pi$
$937$	−12.1029	−0.395385	−0.197693	+	0.980264i	$0.563345\pi$
$938$	−25.7420	−0.840505
$939$	2.63043	0.0858407
$940$	−2.10558	−0.0686763
$941$	−14.2400	−0.464210	−0.232105	−	0.972691i	$-0.574561\pi$
$941$	−14.2400	−0.464210	−0.232105	+	0.972691i	$0.574561\pi$
$942$	35.0569	1.14221
$943$	−33.6818	−1.09683
$944$	−7.04506	−0.229297
$945$	−15.2090	−0.494749
$946$	30.2357	0.983047
$947$	−53.7892	−1.74791	−0.873957	−	0.486004i	$-0.838454\pi$
$947$	−53.7892	−1.74791	−0.873957	+	0.486004i	$0.838454\pi$
$948$	14.6968	0.477330
$949$	0	0
$950$	−0.880698	−0.0285736
$951$	7.10374	0.230355
$952$	−77.3742	−2.50771
$953$	45.8325	1.48466	0.742330	−	0.670034i	$-0.233720\pi$
$953$	45.8325	1.48466	0.742330	+	0.670034i	$0.233720\pi$
$954$	−21.0358	−0.681058
$955$	17.5284	0.567205
$956$	4.34015	0.140371
$957$	10.8951	0.352189
$958$	−32.3733	−1.04593
$959$	−53.6454	−1.73230
$960$	−20.9991	−0.677742
$961$	34.6345	1.11724
$962$	0	0
$963$	22.1250	0.712967
$964$	−18.9762	−0.611182
$965$	−8.60151	−0.276893
$966$	54.0937	1.74044
$967$	34.6342	1.11376	0.556881	−	0.830592i	$-0.311998\pi$
$967$	34.6342	1.11376	0.556881	+	0.830592i	$0.311998\pi$
$968$	−16.1074	−0.517712
$969$	17.2453	0.553998
$970$	6.63379	0.212998
$971$	21.0966	0.677021	0.338511	−	0.940963i	$-0.390077\pi$
$971$	21.0966	0.677021	0.338511	+	0.940963i	$0.390077\pi$
$972$	−15.9665	−0.512127
$973$	41.6163	1.33416
$974$	−5.62638	−0.180281
$975$	0	0
$976$	12.1842	0.390006
$977$	37.8931	1.21231	0.606154	−	0.795347i	$-0.292712\pi$
$977$	37.8931	1.21231	0.606154	+	0.795347i	$0.292712\pi$
$978$	0.538357	0.0172148
$979$	−14.4094	−0.460526
$980$	−4.26514	−0.136245
$981$	34.3445	1.09654
$982$	0.668549	0.0213343
$983$	18.8772	0.602089	0.301045	−	0.953610i	$-0.402665\pi$
$983$	18.8772	0.602089	0.301045	+	0.953610i	$0.402665\pi$
$984$	51.6542	1.64668
$985$	8.12364	0.258841
$986$	12.8740	0.409992
$987$	−22.0141	−0.700717
$988$	0	0
$989$	66.1286	2.10277
$990$	11.5288	0.366409
$991$	52.6982	1.67401	0.837007	−	0.547193i	$-0.184303\pi$
$991$	52.6982	1.67401	0.837007	+	0.547193i	$0.184303\pi$
$992$	37.5797	1.19316
$993$	−15.0168	−0.476544
$994$	−11.7622	−0.373075
$995$	7.55978	0.239661
$996$	−12.8161	−0.406092
$997$	53.7219	1.70139	0.850695	−	0.525659i	$-0.176181\pi$
$997$	53.7219	1.70139	0.850695	+	0.525659i	$0.176181\pi$
$998$	25.3992	0.803997
$999$	−28.4033	−0.898640

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.a.o.1.3	yes	9
3.2	odd	2		7605.2.a.cp.1.7		9
5.4	even	2		4225.2.a.bs.1.7		9
13.2	odd	12		845.2.m.j.316.7		36
13.3	even	3		845.2.e.o.191.7		18
13.4	even	6		845.2.e.p.146.3		18
13.5	odd	4		845.2.c.h.506.12		18
13.6	odd	12		845.2.m.j.361.12		36
13.7	odd	12		845.2.m.j.361.7		36
13.8	odd	4		845.2.c.h.506.7		18
13.9	even	3		845.2.e.o.146.7		18
13.10	even	6		845.2.e.p.191.3		18
13.11	odd	12		845.2.m.j.316.12		36
13.12	even	2		845.2.a.n.1.7	✓	9
39.38	odd	2		7605.2.a.cs.1.3		9
65.64	even	2		4225.2.a.bt.1.3		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
845.2.a.n.1.7	✓	9	13.12	even	2
845.2.a.o.1.3	yes	9	1.1	even	1	trivial
845.2.c.h.506.7		18	13.8	odd	4
845.2.c.h.506.12		18	13.5	odd	4
845.2.e.o.146.7		18	13.9	even	3
845.2.e.o.191.7		18	13.3	even	3
845.2.e.p.146.3		18	13.4	even	6
845.2.e.p.191.3		18	13.10	even	6
845.2.m.j.316.7		36	13.2	odd	12
845.2.m.j.316.12		36	13.11	odd	12
845.2.m.j.361.7		36	13.7	odd	12
845.2.m.j.361.12		36	13.6	odd	12
4225.2.a.bs.1.7		9	5.4	even	2
4225.2.a.bt.1.3		9	65.64	even	2
7605.2.a.cp.1.7		9	3.2	odd	2
7605.2.a.cs.1.3		9	39.38	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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.a (trivial)

\(f(q)\)	\(=\)	\(q-1.04721 q^{2} -2.75868 q^{3} -0.903360 q^{4} +1.00000 q^{5} +2.88890 q^{6} +3.42366 q^{7} +3.04042 q^{8} +4.61031 q^{9} +O(q^{10})\)	\(q-1.04721 q^{2} -2.75868 q^{3} -0.903360 q^{4} +1.00000 q^{5} +2.88890 q^{6} +3.42366 q^{7} +3.04042 q^{8} +4.61031 q^{9} -1.04721 q^{10} -2.38793 q^{11} +2.49208 q^{12} -3.58527 q^{14} -2.75868 q^{15} -1.37722 q^{16} -7.43316 q^{17} -4.82794 q^{18} +0.840998 q^{19} -0.903360 q^{20} -9.44477 q^{21} +2.50066 q^{22} +5.46920 q^{23} -8.38753 q^{24} +1.00000 q^{25} -4.44233 q^{27} -3.09279 q^{28} +1.65390 q^{29} +2.88890 q^{30} -8.10151 q^{31} -4.63860 q^{32} +6.58754 q^{33} +7.78405 q^{34} +3.42366 q^{35} -4.16477 q^{36} +6.39379 q^{37} -0.880698 q^{38} +3.04042 q^{40} -6.15846 q^{41} +9.89061 q^{42} +12.0911 q^{43} +2.15716 q^{44} +4.61031 q^{45} -5.72737 q^{46} +2.33083 q^{47} +3.79931 q^{48} +4.72142 q^{49} -1.04721 q^{50} +20.5057 q^{51} +4.35709 q^{53} +4.65203 q^{54} -2.38793 q^{55} +10.4093 q^{56} -2.32004 q^{57} -1.73197 q^{58} +5.11542 q^{59} +2.49208 q^{60} -8.84695 q^{61} +8.48395 q^{62} +15.7841 q^{63} +7.61201 q^{64} -6.89851 q^{66} +7.17992 q^{67} +6.71482 q^{68} -15.0878 q^{69} -3.58527 q^{70} +3.28070 q^{71} +14.0173 q^{72} +9.41601 q^{73} -6.69561 q^{74} -2.75868 q^{75} -0.759724 q^{76} -8.17546 q^{77} +5.89740 q^{79} -1.37722 q^{80} -1.57598 q^{81} +6.44917 q^{82} -5.14271 q^{83} +8.53203 q^{84} -7.43316 q^{85} -12.6619 q^{86} -4.56257 q^{87} -7.26031 q^{88} +6.03426 q^{89} -4.82794 q^{90} -4.94065 q^{92} +22.3495 q^{93} -2.44085 q^{94} +0.840998 q^{95} +12.7964 q^{96} -6.33475 q^{97} -4.94429 q^{98} -11.0091 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 3 q^{2} + 7 q^{3} + 17 q^{4} + 9 q^{5} - 2 q^{6} + 7 q^{7} + 12 q^{8} + 16 q^{9}+O(q^{10}) \) 9 * q + 3 * q^2 + 7 * q^3 + 17 * q^4 + 9 * q^5 - 2 * q^6 + 7 * q^7 + 12 * q^8 + 16 * q^9	\( 9 q + 3 q^{2} + 7 q^{3} + 17 q^{4} + 9 q^{5} - 2 q^{6} + 7 q^{7} + 12 q^{8} + 16 q^{9} + 3 q^{10} - 9 q^{11} + 12 q^{12} - 2 q^{14} + 7 q^{15} + 37 q^{16} - q^{17} - 10 q^{18} - 4 q^{19} + 17 q^{20} - q^{21} + 12 q^{22} + 14 q^{23} - 35 q^{24} + 9 q^{25} + 22 q^{27} + 18 q^{28} + 12 q^{29} - 2 q^{30} - 7 q^{31} + 22 q^{32} - 8 q^{33} - 30 q^{34} + 7 q^{35} + 3 q^{36} - 5 q^{37} - 47 q^{38} + 12 q^{40} - 10 q^{41} - 11 q^{42} + 39 q^{43} - 25 q^{44} + 16 q^{45} + 6 q^{46} + 36 q^{47} - 3 q^{48} + 16 q^{49} + 3 q^{50} + 43 q^{51} - 8 q^{53} - 2 q^{54} - 9 q^{55} - 29 q^{56} - 32 q^{57} + 21 q^{58} - 21 q^{59} + 12 q^{60} - 3 q^{61} - 10 q^{62} + 35 q^{63} + 34 q^{64} - 49 q^{66} + q^{67} - 20 q^{68} - 13 q^{69} - 2 q^{70} - q^{71} - 3 q^{72} - 15 q^{74} + 7 q^{75} - 5 q^{76} - 4 q^{77} + 39 q^{79} + 37 q^{80} + 29 q^{81} - 4 q^{82} + 7 q^{83} + 12 q^{84} - q^{85} - 24 q^{86} + 16 q^{87} + 42 q^{88} - 19 q^{89} - 10 q^{90} - 27 q^{92} + 31 q^{93} + 16 q^{94} - 4 q^{95} - 7 q^{96} - 34 q^{97} + 48 q^{98} - q^{99}+O(q^{100}) \) 9 * q + 3 * q^2 + 7 * q^3 + 17 * q^4 + 9 * q^5 - 2 * q^6 + 7 * q^7 + 12 * q^8 + 16 * q^9 + 3 * q^10 - 9 * q^11 + 12 * q^12 - 2 * q^14 + 7 * q^15 + 37 * q^16 - q^17 - 10 * q^18 - 4 * q^19 + 17 * q^20 - q^21 + 12 * q^22 + 14 * q^23 - 35 * q^24 + 9 * q^25 + 22 * q^27 + 18 * q^28 + 12 * q^29 - 2 * q^30 - 7 * q^31 + 22 * q^32 - 8 * q^33 - 30 * q^34 + 7 * q^35 + 3 * q^36 - 5 * q^37 - 47 * q^38 + 12 * q^40 - 10 * q^41 - 11 * q^42 + 39 * q^43 - 25 * q^44 + 16 * q^45 + 6 * q^46 + 36 * q^47 - 3 * q^48 + 16 * q^49 + 3 * q^50 + 43 * q^51 - 8 * q^53 - 2 * q^54 - 9 * q^55 - 29 * q^56 - 32 * q^57 + 21 * q^58 - 21 * q^59 + 12 * q^60 - 3 * q^61 - 10 * q^62 + 35 * q^63 + 34 * q^64 - 49 * q^66 + q^67 - 20 * q^68 - 13 * q^69 - 2 * q^70 - q^71 - 3 * q^72 - 15 * q^74 + 7 * q^75 - 5 * q^76 - 4 * q^77 + 39 * q^79 + 37 * q^80 + 29 * q^81 - 4 * q^82 + 7 * q^83 + 12 * q^84 - q^85 - 24 * q^86 + 16 * q^87 + 42 * q^88 - 19 * q^89 - 10 * q^90 - 27 * q^92 + 31 * q^93 + 16 * q^94 - 4 * q^95 - 7 * q^96 - 34 * q^97 + 48 * q^98 - q^99

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