LMFDB - Embedded newform 1805.2.a.s.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1805,2,Mod(1,1805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1805, 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("1805.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1805 = 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1805.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:	$14.4129975648$
Analytic rank:	$1$
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} - 3x^{8} - 6x^{7} + 16x^{6} + 12x^{5} - 27x^{4} - 8x^{3} + 15x^{2} - 1 $ x^9 - 3x^8 - 6x^7 + 16x^6 + 12x^5 - 27x^4 - 8x^3 + 15*x^2 - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.58312$ of defining polynomial
Character	$\chi$	$=$	1805.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.58312 q^{2} +0.247720 q^{3} +4.67249 q^{4} +1.00000 q^{5} -0.639888 q^{6} -0.401640 q^{7} -6.90335 q^{8} -2.93864 q^{9} +O(q^{10})$	\(q-2.58312 q^{2} +0.247720 q^{3} +4.67249 q^{4} +1.00000 q^{5} -0.639888 q^{6} -0.401640 q^{7} -6.90335 q^{8} -2.93864 q^{9} -2.58312 q^{10} +5.19061 q^{11} +1.15747 q^{12} -2.88939 q^{13} +1.03748 q^{14} +0.247720 q^{15} +8.48717 q^{16} -4.14326 q^{17} +7.59083 q^{18} +4.67249 q^{20} -0.0994941 q^{21} -13.4079 q^{22} +3.35853 q^{23} -1.71009 q^{24} +1.00000 q^{25} +7.46362 q^{26} -1.47112 q^{27} -1.87666 q^{28} -6.58388 q^{29} -0.639888 q^{30} +6.26239 q^{31} -8.11665 q^{32} +1.28582 q^{33} +10.7025 q^{34} -0.401640 q^{35} -13.7307 q^{36} -1.14106 q^{37} -0.715757 q^{39} -6.90335 q^{40} -2.85947 q^{41} +0.257005 q^{42} -12.4326 q^{43} +24.2531 q^{44} -2.93864 q^{45} -8.67546 q^{46} +6.76158 q^{47} +2.10244 q^{48} -6.83869 q^{49} -2.58312 q^{50} -1.02637 q^{51} -13.5006 q^{52} -12.3019 q^{53} +3.80006 q^{54} +5.19061 q^{55} +2.77266 q^{56} +17.0069 q^{58} +1.51517 q^{59} +1.15747 q^{60} -6.98744 q^{61} -16.1765 q^{62} +1.18027 q^{63} +3.99190 q^{64} -2.88939 q^{65} -3.32141 q^{66} +0.757110 q^{67} -19.3593 q^{68} +0.831973 q^{69} +1.03748 q^{70} +8.33609 q^{71} +20.2864 q^{72} -9.91844 q^{73} +2.94750 q^{74} +0.247720 q^{75} -2.08476 q^{77} +1.84888 q^{78} -3.18837 q^{79} +8.48717 q^{80} +8.45148 q^{81} +7.38635 q^{82} +5.51941 q^{83} -0.464885 q^{84} -4.14326 q^{85} +32.1149 q^{86} -1.63096 q^{87} -35.8326 q^{88} +12.5241 q^{89} +7.59083 q^{90} +1.16049 q^{91} +15.6927 q^{92} +1.55132 q^{93} -17.4660 q^{94} -2.01065 q^{96} +8.89456 q^{97} +17.6651 q^{98} -15.2533 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 6 q^{2} - 9 q^{3} + 6 q^{4} + 9 q^{5} + 12 q^{6} - 6 q^{8} + 6 q^{9}+O(q^{10}) $ 9 * q - 6 * q^2 - 9 * q^3 + 6 * q^4 + 9 * q^5 + 12 * q^6 - 6 * q^8 + 6 * q^9	$ 9 q - 6 q^{2} - 9 q^{3} + 6 q^{4} + 9 q^{5} + 12 q^{6} - 6 q^{8} + 6 q^{9} - 6 q^{10} - 18 q^{12} - 9 q^{13} - 9 q^{15} + 12 q^{16} - 9 q^{17} - 24 q^{18} + 6 q^{20} - 12 q^{21} - 24 q^{22} - 12 q^{23} + 3 q^{24} + 9 q^{25} - 3 q^{26} - 24 q^{27} - 15 q^{28} - 9 q^{29} + 12 q^{30} - 18 q^{31} - 3 q^{32} + 9 q^{33} + 24 q^{34} + 18 q^{36} - 18 q^{37} + 18 q^{39} - 6 q^{40} - 6 q^{41} - 12 q^{43} + 48 q^{44} + 6 q^{45} + 9 q^{46} + 15 q^{47} + 21 q^{48} - 9 q^{49} - 6 q^{50} + 6 q^{51} - 33 q^{52} - 15 q^{53} + 63 q^{54} + 6 q^{58} - 21 q^{59} - 18 q^{60} - 12 q^{61} - 36 q^{62} + 21 q^{63} - 36 q^{64} - 9 q^{65} + 3 q^{66} - 60 q^{67} - 51 q^{68} + 15 q^{69} + 18 q^{71} + 27 q^{73} + 27 q^{74} - 9 q^{75} - 30 q^{77} + 6 q^{78} - 15 q^{79} + 12 q^{80} + 33 q^{81} + 24 q^{82} + 48 q^{84} - 9 q^{85} + 39 q^{86} + 15 q^{87} - 27 q^{88} + 39 q^{89} - 24 q^{90} - 21 q^{91} - 6 q^{92} + 15 q^{93} - 15 q^{94} - 33 q^{96} - 15 q^{97} + 15 q^{98} - 36 q^{99}+O(q^{100}) $ 9 * q - 6 * q^2 - 9 * q^3 + 6 * q^4 + 9 * q^5 + 12 * q^6 - 6 * q^8 + 6 * q^9 - 6 * q^10 - 18 * q^12 - 9 * q^13 - 9 * q^15 + 12 * q^16 - 9 * q^17 - 24 * q^18 + 6 * q^20 - 12 * q^21 - 24 * q^22 - 12 * q^23 + 3 * q^24 + 9 * q^25 - 3 * q^26 - 24 * q^27 - 15 * q^28 - 9 * q^29 + 12 * q^30 - 18 * q^31 - 3 * q^32 + 9 * q^33 + 24 * q^34 + 18 * q^36 - 18 * q^37 + 18 * q^39 - 6 * q^40 - 6 * q^41 - 12 * q^43 + 48 * q^44 + 6 * q^45 + 9 * q^46 + 15 * q^47 + 21 * q^48 - 9 * q^49 - 6 * q^50 + 6 * q^51 - 33 * q^52 - 15 * q^53 + 63 * q^54 + 6 * q^58 - 21 * q^59 - 18 * q^60 - 12 * q^61 - 36 * q^62 + 21 * q^63 - 36 * q^64 - 9 * q^65 + 3 * q^66 - 60 * q^67 - 51 * q^68 + 15 * q^69 + 18 * q^71 + 27 * q^73 + 27 * q^74 - 9 * q^75 - 30 * q^77 + 6 * q^78 - 15 * q^79 + 12 * q^80 + 33 * q^81 + 24 * q^82 + 48 * q^84 - 9 * q^85 + 39 * q^86 + 15 * q^87 - 27 * q^88 + 39 * q^89 - 24 * q^90 - 21 * q^91 - 6 * q^92 + 15 * q^93 - 15 * q^94 - 33 * q^96 - 15 * q^97 + 15 * q^98 - 36 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.58312	−1.82654	−0.913269	−	0.407356i	$-0.866451\pi$
$2$	−2.58312	−1.82654	−0.913269	+	0.407356i	$0.866451\pi$
$3$	0.247720	0.143021	0.0715105	−	0.997440i	$-0.477218\pi$
$3$	0.247720	0.143021	0.0715105	+	0.997440i	$0.477218\pi$
$4$	4.67249	2.33624
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.639888	−0.261233
$7$	−0.401640	−0.151806	−0.0759028	−	0.997115i	$-0.524184\pi$
$7$	−0.401640	−0.151806	−0.0759028	+	0.997115i	$0.524184\pi$
$8$	−6.90335	−2.44070
$9$	−2.93864	−0.979545
$10$	−2.58312	−0.816853
$11$	5.19061	1.56503	0.782514	−	0.622633i	$-0.213937\pi$
$11$	5.19061	1.56503	0.782514	+	0.622633i	$0.213937\pi$
$12$	1.15747	0.334132
$13$	−2.88939	−0.801371	−0.400686	−	0.916216i	$-0.631228\pi$
$13$	−2.88939	−0.801371	−0.400686	+	0.916216i	$0.631228\pi$
$14$	1.03748	0.277279
$15$	0.247720	0.0639609
$16$	8.48717	2.12179
$17$	−4.14326	−1.00489	−0.502444	−	0.864610i	$-0.667566\pi$
$17$	−4.14326	−1.00489	−0.502444	+	0.864610i	$0.667566\pi$
$18$	7.59083	1.78918
$19$	0	0
$19$	0	0
$20$	4.67249	1.04480
$21$	−0.0994941	−0.0217114
$22$	−13.4079	−2.85858
$23$	3.35853	0.700301	0.350151	−	0.936693i	$-0.386130\pi$
$23$	3.35853	0.700301	0.350151	+	0.936693i	$0.386130\pi$
$24$	−1.71009	−0.349071
$25$	1.00000	0.200000
$26$	7.46362	1.46374
$27$	−1.47112	−0.283116
$28$	−1.87666	−0.354655
$29$	−6.58388	−1.22260	−0.611298	−	0.791400i	$-0.709352\pi$
$29$	−6.58388	−1.22260	−0.611298	+	0.791400i	$0.709352\pi$
$30$	−0.639888	−0.116827
$31$	6.26239	1.12476	0.562379	−	0.826880i	$-0.309886\pi$
$31$	6.26239	1.12476	0.562379	+	0.826880i	$0.309886\pi$
$32$	−8.11665	−1.43483
$33$	1.28582	0.223832
$34$	10.7025	1.83547
$35$	−0.401640	−0.0678895
$36$	−13.7307	−2.28846
$37$	−1.14106	−0.187590	−0.0937949	−	0.995592i	$-0.529900\pi$
$37$	−1.14106	−0.187590	−0.0937949	+	0.995592i	$0.529900\pi$
$38$	0	0
$39$	−0.715757	−0.114613
$40$	−6.90335	−1.09151
$41$	−2.85947	−0.446575	−0.223287	−	0.974753i	$-0.571679\pi$
$41$	−2.85947	−0.446575	−0.223287	+	0.974753i	$0.571679\pi$
$42$	0.257005	0.0396567
$43$	−12.4326	−1.89596	−0.947978	−	0.318334i	$-0.896877\pi$
$43$	−12.4326	−1.89596	−0.947978	+	0.318334i	$0.896877\pi$
$44$	24.2531	3.65629
$45$	−2.93864	−0.438066
$46$	−8.67546	−1.27913
$47$	6.76158	0.986278	0.493139	−	0.869950i	$-0.335849\pi$
$47$	6.76158	0.986278	0.493139	+	0.869950i	$0.335849\pi$
$48$	2.10244	0.303461
$49$	−6.83869	−0.976955
$50$	−2.58312	−0.365308
$51$	−1.02637	−0.143720
$52$	−13.5006	−1.87220
$53$	−12.3019	−1.68980	−0.844899	−	0.534925i	$-0.820340\pi$
$53$	−12.3019	−1.68980	−0.844899	+	0.534925i	$0.820340\pi$
$54$	3.80006	0.517123
$55$	5.19061	0.699902
$56$	2.77266	0.370512
$57$	0	0
$58$	17.0069	2.23312
$59$	1.51517	0.197259	0.0986294	−	0.995124i	$-0.468554\pi$
$59$	1.51517	0.197259	0.0986294	+	0.995124i	$0.468554\pi$
$60$	1.15747	0.149428
$61$	−6.98744	−0.894650	−0.447325	−	0.894371i	$-0.647623\pi$
$61$	−6.98744	−0.894650	−0.447325	+	0.894371i	$0.647623\pi$
$62$	−16.1765	−2.05441
$63$	1.18027	0.148700
$64$	3.99190	0.498988
$65$	−2.88939	−0.358384
$66$	−3.32141	−0.408837
$67$	0.757110	0.0924957	0.0462478	−	0.998930i	$-0.485274\pi$
$67$	0.757110	0.0924957	0.0462478	+	0.998930i	$0.485274\pi$
$68$	−19.3593	−2.34766
$69$	0.831973	0.100158
$70$	1.03748	0.124003
$71$	8.33609	0.989312	0.494656	−	0.869089i	$-0.335294\pi$
$71$	8.33609	0.989312	0.494656	+	0.869089i	$0.335294\pi$
$72$	20.2864	2.39078
$73$	−9.91844	−1.16087	−0.580433	−	0.814308i	$-0.697117\pi$
$73$	−9.91844	−1.16087	−0.580433	+	0.814308i	$0.697117\pi$
$74$	2.94750	0.342640
$75$	0.247720	0.0286042
$76$	0	0
$77$	−2.08476	−0.237580
$78$	1.84888	0.209345
$79$	−3.18837	−0.358720	−0.179360	−	0.983783i	$-0.557403\pi$
$79$	−3.18837	−0.358720	−0.179360	+	0.983783i	$0.557403\pi$
$80$	8.48717	0.948894
$81$	8.45148	0.939053
$82$	7.38635	0.815686
$83$	5.51941	0.605834	0.302917	−	0.953017i	$-0.402039\pi$
$83$	5.51941	0.605834	0.302917	+	0.953017i	$0.402039\pi$
$84$	−0.464885	−0.0507231
$85$	−4.14326	−0.449400
$86$	32.1149	3.46304
$87$	−1.63096	−0.174857
$88$	−35.8326	−3.81977
$89$	12.5241	1.32755	0.663775	−	0.747932i	$-0.268953\pi$
$89$	12.5241	1.32755	0.663775	+	0.747932i	$0.268953\pi$
$90$	7.59083	0.800144
$91$	1.16049	0.121653
$92$	15.6927	1.63607
$93$	1.55132	0.160864
$94$	−17.4660	−1.80148
$95$	0	0
$96$	−2.01065	−0.205211
$97$	8.89456	0.903106	0.451553	−	0.892244i	$-0.350870\pi$
$97$	8.89456	0.903106	0.451553	+	0.892244i	$0.350870\pi$
$98$	17.6651	1.78445
$99$	−15.2533	−1.53302
$100$	4.67249	0.467249
$101$	1.34598	0.133930	0.0669649	−	0.997755i	$-0.478668\pi$
$101$	1.34598	0.133930	0.0669649	+	0.997755i	$0.478668\pi$
$102$	2.65122	0.262510
$103$	−12.4278	−1.22455	−0.612275	−	0.790645i	$-0.709745\pi$
$103$	−12.4278	−1.22455	−0.612275	+	0.790645i	$0.709745\pi$
$104$	19.9464	1.95591
$105$	−0.0994941	−0.00970963
$106$	31.7773	3.08648
$107$	14.5622	1.40778	0.703890	−	0.710309i	$-0.251445\pi$
$107$	14.5622	1.40778	0.703890	+	0.710309i	$0.251445\pi$
$108$	−6.87377	−0.661429
$109$	−4.41987	−0.423347	−0.211673	−	0.977340i	$-0.567891\pi$
$109$	−4.41987	−0.423347	−0.211673	+	0.977340i	$0.567891\pi$
$110$	−13.4079	−1.27840
$111$	−0.282664	−0.0268293
$112$	−3.40879	−0.322100
$113$	−8.08453	−0.760528	−0.380264	−	0.924878i	$-0.624167\pi$
$113$	−8.08453	−0.760528	−0.380264	+	0.924878i	$0.624167\pi$
$114$	0	0
$115$	3.35853	0.313184
$116$	−30.7631	−2.85628
$117$	8.49085	0.784979
$118$	−3.91387	−0.360301
$119$	1.66410	0.152548
$120$	−1.71009	−0.156110
$121$	15.9424	1.44931
$122$	18.0494	1.63411
$123$	−0.708348	−0.0638696
$124$	29.2609	2.62771
$125$	1.00000	0.0894427
$126$	−3.04878	−0.271607
$127$	0.561168	0.0497956	0.0248978	−	0.999690i	$-0.492074\pi$
$127$	0.561168	0.0497956	0.0248978	+	0.999690i	$0.492074\pi$
$128$	5.92174	0.523413
$129$	−3.07980	−0.271162
$130$	7.46362	0.654603
$131$	−9.87597	−0.862867	−0.431434	−	0.902145i	$-0.641992\pi$
$131$	−9.87597	−0.862867	−0.431434	+	0.902145i	$0.641992\pi$
$132$	6.00796	0.522926
$133$	0	0
$134$	−1.95570	−0.168947
$135$	−1.47112	−0.126614
$136$	28.6024	2.45263
$137$	−8.96292	−0.765754	−0.382877	−	0.923799i	$-0.625067\pi$
$137$	−8.96292	−0.765754	−0.382877	+	0.923799i	$0.625067\pi$
$138$	−2.14908	−0.182942
$139$	−13.1668	−1.11679	−0.558397	−	0.829574i	$-0.688584\pi$
$139$	−13.1668	−1.11679	−0.558397	+	0.829574i	$0.688584\pi$
$140$	−1.87666	−0.158607
$141$	1.67498	0.141058
$142$	−21.5331	−1.80702
$143$	−14.9977	−1.25417
$144$	−24.9407	−2.07839
$145$	−6.58388	−0.546762
$146$	25.6205	2.12037
$147$	−1.69408	−0.139725
$148$	−5.33161	−0.438255
$149$	−8.18362	−0.670429	−0.335214	−	0.942142i	$-0.608809\pi$
$149$	−8.18362	−0.670429	−0.335214	+	0.942142i	$0.608809\pi$
$150$	−0.639888	−0.0522467
$151$	−7.60636	−0.618997	−0.309498	−	0.950900i	$-0.600161\pi$
$151$	−7.60636	−0.618997	−0.309498	+	0.950900i	$0.600161\pi$
$152$	0	0
$153$	12.1755	0.984333
$154$	5.38517	0.433949
$155$	6.26239	0.503007
$156$	−3.34437	−0.267764
$157$	−12.5654	−1.00283	−0.501414	−	0.865207i	$-0.667187\pi$
$157$	−12.5654	−1.00283	−0.501414	+	0.865207i	$0.667187\pi$
$158$	8.23594	0.655216
$159$	−3.04743	−0.241677
$160$	−8.11665	−0.641677
$161$	−1.34892	−0.106310
$162$	−21.8312	−1.71522
$163$	−3.28349	−0.257183	−0.128591	−	0.991698i	$-0.541046\pi$
$163$	−3.28349	−0.257183	−0.128591	+	0.991698i	$0.541046\pi$
$164$	−13.3609	−1.04331
$165$	1.28582	0.100101
$166$	−14.2573	−1.10658
$167$	5.22764	0.404527	0.202263	−	0.979331i	$-0.435170\pi$
$167$	5.22764	0.404527	0.202263	+	0.979331i	$0.435170\pi$
$168$	0.686842	0.0529910
$169$	−4.65145	−0.357804
$170$	10.7025	0.820846
$171$	0	0
$172$	−58.0913	−4.42942
$173$	−4.50557	−0.342552	−0.171276	−	0.985223i	$-0.554789\pi$
$173$	−4.50557	−0.342552	−0.171276	+	0.985223i	$0.554789\pi$
$174$	4.21295	0.319383
$175$	−0.401640	−0.0303611
$176$	44.0536	3.32066
$177$	0.375338	0.0282121
$178$	−32.3512	−2.42482
$179$	3.77167	0.281907	0.140954	−	0.990016i	$-0.454983\pi$
$179$	3.77167	0.281907	0.140954	+	0.990016i	$0.454983\pi$
$180$	−13.7307	−1.02343
$181$	−19.0953	−1.41934	−0.709669	−	0.704535i	$-0.751156\pi$
$181$	−19.0953	−1.41934	−0.709669	+	0.704535i	$0.751156\pi$
$182$	−2.99769	−0.222203
$183$	−1.73093	−0.127954
$184$	−23.1851	−1.70923
$185$	−1.14106	−0.0838927
$186$	−4.00723	−0.293824
$187$	−21.5060	−1.57268
$188$	31.5934	2.30419
$189$	0.590859	0.0429787
$190$	0	0
$191$	2.89599	0.209547	0.104773	−	0.994496i	$-0.466588\pi$
$191$	2.89599	0.209547	0.104773	+	0.994496i	$0.466588\pi$
$192$	0.988873	0.0713657
$193$	−11.3804	−0.819178	−0.409589	−	0.912270i	$-0.634328\pi$
$193$	−11.3804	−0.819178	−0.409589	+	0.912270i	$0.634328\pi$
$194$	−22.9757	−1.64956
$195$	−0.715757	−0.0512565
$196$	−31.9537	−2.28241
$197$	−10.1509	−0.723221	−0.361610	−	0.932329i	$-0.617773\pi$
$197$	−10.1509	−0.723221	−0.361610	+	0.932329i	$0.617773\pi$
$198$	39.4011	2.80011
$199$	−2.93023	−0.207719	−0.103859	−	0.994592i	$-0.533119\pi$
$199$	−2.93023	−0.207719	−0.103859	+	0.994592i	$0.533119\pi$
$200$	−6.90335	−0.488140
$201$	0.187551	0.0132288
$202$	−3.47682	−0.244628
$203$	2.64435	0.185597
$204$	−4.79569	−0.335765
$205$	−2.85947	−0.199714
$206$	32.1025	2.23669
$207$	−9.86948	−0.685977
$208$	−24.5227	−1.70034
$209$	0	0
$210$	0.257005	0.0177350
$211$	5.50578	0.379033	0.189517	−	0.981877i	$-0.439308\pi$
$211$	5.50578	0.379033	0.189517	+	0.981877i	$0.439308\pi$
$212$	−57.4806	−3.94778
$213$	2.06501	0.141492
$214$	−37.6158	−2.57137
$215$	−12.4326	−0.847898
$216$	10.1556	0.691003
$217$	−2.51523	−0.170745
$218$	11.4170	0.773259
$219$	−2.45699	−0.166028
$220$	24.2531	1.63514
$221$	11.9715	0.805289
$222$	0.730154	0.0490047
$223$	−7.96085	−0.533098	−0.266549	−	0.963821i	$-0.585883\pi$
$223$	−7.96085	−0.533098	−0.266549	+	0.963821i	$0.585883\pi$
$224$	3.25997	0.217816
$225$	−2.93864	−0.195909
$226$	20.8833	1.38913
$227$	−8.02439	−0.532597	−0.266299	−	0.963891i	$-0.585801\pi$
$227$	−8.02439	−0.532597	−0.266299	+	0.963891i	$0.585801\pi$
$228$	0	0
$229$	−28.2466	−1.86659	−0.933295	−	0.359111i	$-0.883080\pi$
$229$	−28.2466	−1.86659	−0.933295	+	0.359111i	$0.883080\pi$
$230$	−8.67546	−0.572043
$231$	−0.516435	−0.0339789
$232$	45.4508	2.98399
$233$	9.44251	0.618599	0.309300	−	0.950965i	$-0.399905\pi$
$233$	9.44251	0.618599	0.309300	+	0.950965i	$0.399905\pi$
$234$	−21.9329	−1.43380
$235$	6.76158	0.441077
$236$	7.07963	0.460845
$237$	−0.789823	−0.0513045
$238$	−4.29856	−0.278634
$239$	11.7928	0.762810	0.381405	−	0.924408i	$-0.375440\pi$
$239$	11.7928	0.762810	0.381405	+	0.924408i	$0.375440\pi$
$240$	2.10244	0.135712
$241$	12.8002	0.824534	0.412267	−	0.911063i	$-0.364737\pi$
$241$	12.8002	0.824534	0.412267	+	0.911063i	$0.364737\pi$
$242$	−41.1811	−2.64722
$243$	6.50695	0.417421
$244$	−32.6487	−2.09012
$245$	−6.83869	−0.436908
$246$	1.82974	0.116660
$247$	0	0
$248$	−43.2314	−2.74520
$249$	1.36727	0.0866470
$250$	−2.58312	−0.163371
$251$	2.39964	0.151464	0.0757318	−	0.997128i	$-0.475871\pi$
$251$	2.39964	0.151464	0.0757318	+	0.997128i	$0.475871\pi$
$252$	5.51481	0.347400
$253$	17.4328	1.09599
$254$	−1.44956	−0.0909536
$255$	−1.02637	−0.0642736
$256$	−23.2804	−1.45502
$257$	−17.2154	−1.07387	−0.536934	−	0.843624i	$-0.680418\pi$
$257$	−17.2154	−1.07387	−0.536934	+	0.843624i	$0.680418\pi$
$258$	7.95549	0.495287
$259$	0.458297	0.0284772
$260$	−13.5006	−0.837273
$261$	19.3476	1.19759
$262$	25.5108	1.57606
$263$	14.6838	0.905441	0.452721	−	0.891652i	$-0.350454\pi$
$263$	14.6838	0.905441	0.452721	+	0.891652i	$0.350454\pi$
$264$	−8.87643	−0.546307
$265$	−12.3019	−0.755701
$266$	0	0
$267$	3.10246	0.189868
$268$	3.53759	0.216092
$269$	22.4529	1.36898	0.684490	−	0.729022i	$-0.260025\pi$
$269$	22.4529	1.36898	0.684490	+	0.729022i	$0.260025\pi$
$270$	3.80006	0.231265
$271$	13.2815	0.806792	0.403396	−	0.915026i	$-0.367830\pi$
$271$	13.2815	0.806792	0.403396	+	0.915026i	$0.367830\pi$
$272$	−35.1645	−2.13216
$273$	0.287477	0.0173989
$274$	23.1523	1.39868
$275$	5.19061	0.313006
$276$	3.88738	0.233993
$277$	3.35927	0.201839	0.100919	−	0.994895i	$-0.467822\pi$
$277$	3.35927	0.201839	0.100919	+	0.994895i	$0.467822\pi$
$278$	34.0114	2.03987
$279$	−18.4029	−1.10175
$280$	2.77266	0.165698
$281$	−20.0224	−1.19444	−0.597218	−	0.802079i	$-0.703727\pi$
$281$	−20.0224	−1.19444	−0.597218	+	0.802079i	$0.703727\pi$
$282$	−4.32666	−0.257649
$283$	0.529983	0.0315042	0.0157521	−	0.999876i	$-0.494986\pi$
$283$	0.529983	0.0315042	0.0157521	+	0.999876i	$0.494986\pi$
$284$	38.9503	2.31127
$285$	0	0
$286$	38.7407	2.29079
$287$	1.14848	0.0677926
$288$	23.8519	1.40548
$289$	0.166604	0.00980023
$290$	17.0069	0.998682
$291$	2.20336	0.129163
$292$	−46.3438	−2.71207
$293$	−31.6149	−1.84696	−0.923480	−	0.383647i	$-0.874668\pi$
$293$	−31.6149	−1.84696	−0.923480	+	0.383647i	$0.874668\pi$
$294$	4.37600	0.255213
$295$	1.51517	0.0882168
$296$	7.87716	0.457851
$297$	−7.63599	−0.443085
$298$	21.1393	1.22456
$299$	−9.70408	−0.561201
$300$	1.15747	0.0668264
$301$	4.99344	0.287817
$302$	19.6481	1.13062
$303$	0.333425	0.0191548
$304$	0	0
$305$	−6.98744	−0.400100
$306$	−31.4508	−1.79792
$307$	−9.17155	−0.523448	−0.261724	−	0.965143i	$-0.584291\pi$
$307$	−9.17155	−0.523448	−0.261724	+	0.965143i	$0.584291\pi$
$308$	−9.74100	−0.555045
$309$	−3.07861	−0.175136
$310$	−16.1765	−0.918762
$311$	−24.0511	−1.36381	−0.681906	−	0.731440i	$-0.738849\pi$
$311$	−24.0511	−1.36381	−0.681906	+	0.731440i	$0.738849\pi$
$312$	4.94112	0.279736
$313$	−2.45957	−0.139023	−0.0695117	−	0.997581i	$-0.522144\pi$
$313$	−2.45957	−0.139023	−0.0695117	+	0.997581i	$0.522144\pi$
$314$	32.4579	1.83171
$315$	1.18027	0.0665009
$316$	−14.8976	−0.838058
$317$	−7.02223	−0.394408	−0.197204	−	0.980363i	$-0.563186\pi$
$317$	−7.02223	−0.394408	−0.197204	+	0.980363i	$0.563186\pi$
$318$	7.87185	0.441432
$319$	−34.1744	−1.91340
$320$	3.99190	0.223154
$321$	3.60734	0.201342
$322$	3.48441	0.194179
$323$	0	0
$324$	39.4894	2.19386
$325$	−2.88939	−0.160274
$326$	8.48164	0.469755
$327$	−1.09489	−0.0605475
$328$	19.7399	1.08996
$329$	−2.71572	−0.149723
$330$	−3.32141	−0.182838
$331$	−17.4105	−0.956967	−0.478483	−	0.878097i	$-0.658813\pi$
$331$	−17.4105	−0.956967	−0.478483	+	0.878097i	$0.658813\pi$
$332$	25.7894	1.41538
$333$	3.35317	0.183753
$334$	−13.5036	−0.738884
$335$	0.757110	0.0413653
$336$	−0.844423	−0.0460670
$337$	32.6777	1.78007	0.890033	−	0.455895i	$-0.150681\pi$
$337$	32.6777	1.78007	0.890033	+	0.455895i	$0.150681\pi$
$338$	12.0152	0.653543
$339$	−2.00270	−0.108771
$340$	−19.3593	−1.04991
$341$	32.5056	1.76028
$342$	0	0
$343$	5.55817	0.300113
$344$	85.8267	4.62747
$345$	0.831973	0.0447919
$346$	11.6384	0.625685
$347$	7.12953	0.382733	0.191367	−	0.981519i	$-0.438708\pi$
$347$	7.12953	0.382733	0.191367	+	0.981519i	$0.438708\pi$
$348$	−7.62063	−0.408508
$349$	22.7009	1.21515	0.607575	−	0.794262i	$-0.292142\pi$
$349$	22.7009	1.21515	0.607575	+	0.794262i	$0.292142\pi$
$350$	1.03748	0.0554558
$351$	4.25062	0.226881
$352$	−42.1303	−2.24556
$353$	−4.49389	−0.239186	−0.119593	−	0.992823i	$-0.538159\pi$
$353$	−4.49389	−0.239186	−0.119593	+	0.992823i	$0.538159\pi$
$354$	−0.969542	−0.0515306
$355$	8.33609	0.442434
$356$	58.5186	3.10148
$357$	0.412230	0.0218175
$358$	−9.74265	−0.514915
$359$	10.5846	0.558633	0.279317	−	0.960199i	$-0.409892\pi$
$359$	10.5846	0.558633	0.279317	+	0.960199i	$0.409892\pi$
$360$	20.2864	1.06919
$361$	0	0
$362$	49.3252	2.59248
$363$	3.94925	0.207282
$364$	5.42239	0.284210
$365$	−9.91844	−0.519155
$366$	4.47118	0.233712
$367$	−1.80475	−0.0942071	−0.0471036	−	0.998890i	$-0.514999\pi$
$367$	−1.80475	−0.0942071	−0.0471036	+	0.998890i	$0.514999\pi$
$368$	28.5044	1.48589
$369$	8.40295	0.437440
$370$	2.94750	0.153233
$371$	4.94094	0.256521
$372$	7.24851	0.375818
$373$	12.9639	0.671243	0.335622	−	0.941997i	$-0.391054\pi$
$373$	12.9639	0.671243	0.335622	+	0.941997i	$0.391054\pi$
$374$	55.5526	2.87256
$375$	0.247720	0.0127922
$376$	−46.6776	−2.40721
$377$	19.0234	0.979754
$378$	−1.52626	−0.0785022
$379$	−33.1372	−1.70214	−0.851071	−	0.525051i	$-0.824046\pi$
$379$	−33.1372	−1.70214	−0.851071	+	0.525051i	$0.824046\pi$
$380$	0	0
$381$	0.139012	0.00712181
$382$	−7.48069	−0.382745
$383$	−20.1934	−1.03183	−0.515916	−	0.856639i	$-0.672548\pi$
$383$	−20.1934	−1.03183	−0.515916	+	0.856639i	$0.672548\pi$
$384$	1.46693	0.0748591
$385$	−2.08476	−0.106249
$386$	29.3969	1.49626
$387$	36.5349	1.85718
$388$	41.5597	2.10988
$389$	−2.02884	−0.102866	−0.0514330	−	0.998676i	$-0.516379\pi$
$389$	−2.02884	−0.102866	−0.0514330	+	0.998676i	$0.516379\pi$
$390$	1.84888	0.0936219
$391$	−13.9152	−0.703724
$392$	47.2098	2.38446
$393$	−2.44647	−0.123408
$394$	26.2209	1.32099
$395$	−3.18837	−0.160425
$396$	−71.2709	−3.58150
$397$	8.03282	0.403155	0.201578	−	0.979473i	$-0.435393\pi$
$397$	8.03282	0.403155	0.201578	+	0.979473i	$0.435393\pi$
$398$	7.56914	0.379406
$399$	0	0
$400$	8.48717	0.424358
$401$	14.3800	0.718103	0.359051	−	0.933318i	$-0.383100\pi$
$401$	14.3800	0.718103	0.359051	+	0.933318i	$0.383100\pi$
$402$	−0.484466	−0.0241630
$403$	−18.0945	−0.901349
$404$	6.28907	0.312893
$405$	8.45148	0.419957
$406$	−6.83066	−0.339000
$407$	−5.92282	−0.293583
$408$	7.08536	0.350778
$409$	−0.241589	−0.0119458	−0.00597291	−	0.999982i	$-0.501901\pi$
$409$	−0.241589	−0.0119458	−0.00597291	+	0.999982i	$0.501901\pi$
$410$	7.38635	0.364786
$411$	−2.22029	−0.109519
$412$	−58.0688	−2.86085
$413$	−0.608554	−0.0299450
$414$	25.4940	1.25296
$415$	5.51941	0.270937
$416$	23.4521	1.14984
$417$	−3.26168	−0.159725
$418$	0	0
$419$	−22.7086	−1.10939	−0.554693	−	0.832055i	$-0.687164\pi$
$419$	−22.7086	−1.10939	−0.554693	+	0.832055i	$0.687164\pi$
$420$	−0.464885	−0.0226841
$421$	24.9750	1.21720	0.608602	−	0.793475i	$-0.291731\pi$
$421$	24.9750	1.21720	0.608602	+	0.793475i	$0.291731\pi$
$422$	−14.2221	−0.692319
$423$	−19.8698	−0.966104
$424$	84.9244	4.12429
$425$	−4.14326	−0.200978
$426$	−5.33417	−0.258441
$427$	2.80643	0.135813
$428$	68.0417	3.28892
$429$	−3.71522	−0.179372
$430$	32.1149	1.54872
$431$	−17.8596	−0.860266	−0.430133	−	0.902766i	$-0.641533\pi$
$431$	−17.8596	−0.860266	−0.430133	+	0.902766i	$0.641533\pi$
$432$	−12.4856	−0.600714
$433$	39.1117	1.87959	0.939794	−	0.341741i	$-0.111017\pi$
$433$	39.1117	1.87959	0.939794	+	0.341741i	$0.111017\pi$
$434$	6.49712	0.311872
$435$	−1.63096	−0.0781984
$436$	−20.6518	−0.989042
$437$	0	0
$438$	6.34670	0.303257
$439$	−18.7348	−0.894163	−0.447082	−	0.894493i	$-0.647537\pi$
$439$	−18.7348	−0.894163	−0.447082	+	0.894493i	$0.647537\pi$
$440$	−35.8326	−1.70825
$441$	20.0964	0.956971
$442$	−30.9237	−1.47089
$443$	17.0513	0.810134	0.405067	−	0.914287i	$-0.367248\pi$
$443$	17.0513	0.810134	0.405067	+	0.914287i	$0.367248\pi$
$444$	−1.32074	−0.0626797
$445$	12.5241	0.593699
$446$	20.5638	0.973724
$447$	−2.02724	−0.0958854
$448$	−1.60331	−0.0757492
$449$	−12.2032	−0.575906	−0.287953	−	0.957645i	$-0.592975\pi$
$449$	−12.2032	−0.575906	−0.287953	+	0.957645i	$0.592975\pi$
$450$	7.59083	0.357835
$451$	−14.8424	−0.698902
$452$	−37.7749	−1.77678
$453$	−1.88424	−0.0885295
$454$	20.7279	0.972810
$455$	1.16049	0.0544047
$456$	0	0
$457$	−13.4079	−0.627193	−0.313596	−	0.949556i	$-0.601534\pi$
$457$	−13.4079	−0.627193	−0.313596	+	0.949556i	$0.601534\pi$
$458$	72.9643	3.40940
$459$	6.09522	0.284500
$460$	15.6927	0.731675
$461$	−14.0162	−0.652801	−0.326401	−	0.945232i	$-0.605836\pi$
$461$	−14.0162	−0.652801	−0.326401	+	0.945232i	$0.605836\pi$
$462$	1.33401	0.0620638
$463$	26.1778	1.21658	0.608292	−	0.793713i	$-0.291855\pi$
$463$	26.1778	1.21658	0.608292	+	0.793713i	$0.291855\pi$
$464$	−55.8785	−2.59410
$465$	1.55132	0.0719406
$466$	−24.3911	−1.12990
$467$	−39.5881	−1.83192	−0.915960	−	0.401270i	$-0.868569\pi$
$467$	−39.5881	−1.83192	−0.915960	+	0.401270i	$0.868569\pi$
$468$	39.6734	1.83390
$469$	−0.304085	−0.0140414
$470$	−17.4660	−0.805644
$471$	−3.11270	−0.143426
$472$	−10.4598	−0.481450
$473$	−64.5329	−2.96723
$474$	2.04020	0.0937097
$475$	0	0
$476$	7.77548	0.356389
$477$	36.1508	1.65523
$478$	−30.4621	−1.39330
$479$	3.77884	0.172660	0.0863298	−	0.996267i	$-0.472486\pi$
$479$	3.77884	0.172660	0.0863298	+	0.996267i	$0.472486\pi$
$480$	−2.01065	−0.0917733
$481$	3.29697	0.150329
$482$	−33.0644	−1.50604
$483$	−0.334153	−0.0152045
$484$	74.4908	3.38595
$485$	8.89456	0.403881
$486$	−16.8082	−0.762435
$487$	−6.98986	−0.316741	−0.158370	−	0.987380i	$-0.550624\pi$
$487$	−6.98986	−0.316741	−0.158370	+	0.987380i	$0.550624\pi$
$488$	48.2367	2.18357
$489$	−0.813385	−0.0367825
$490$	17.6651	0.798029
$491$	−32.6387	−1.47296	−0.736482	−	0.676458i	$-0.763514\pi$
$491$	−32.6387	−1.47296	−0.736482	+	0.676458i	$0.763514\pi$
$492$	−3.30975	−0.149215
$493$	27.2787	1.22857
$494$	0	0
$495$	−15.2533	−0.685585
$496$	53.1499	2.38650
$497$	−3.34811	−0.150183
$498$	−3.53181	−0.158264
$499$	27.7930	1.24418	0.622092	−	0.782944i	$-0.286283\pi$
$499$	27.7930	1.24418	0.622092	+	0.782944i	$0.286283\pi$
$500$	4.67249	0.208960
$501$	1.29499	0.0578558
$502$	−6.19854	−0.276654
$503$	16.3700	0.729901	0.364951	−	0.931027i	$-0.381086\pi$
$503$	16.3700	0.729901	0.364951	+	0.931027i	$0.381086\pi$
$504$	−8.14783	−0.362933
$505$	1.34598	0.0598952
$506$	−45.0309	−2.00187
$507$	−1.15226	−0.0511734
$508$	2.62205	0.116335
$509$	35.6314	1.57934	0.789668	−	0.613535i	$-0.210253\pi$
$509$	35.6314	1.57934	0.789668	+	0.613535i	$0.210253\pi$
$510$	2.65122	0.117398
$511$	3.98364	0.176226
$512$	48.2924	2.13424
$513$	0	0
$514$	44.4694	1.96146
$515$	−12.4278	−0.547635
$516$	−14.3903	−0.633500
$517$	35.0967	1.54355
$518$	−1.18383	−0.0520147
$519$	−1.11612	−0.0489921
$520$	19.9464	0.874709
$521$	−34.9318	−1.53039	−0.765194	−	0.643800i	$-0.777357\pi$
$521$	−34.9318	−1.53039	−0.765194	+	0.643800i	$0.777357\pi$
$522$	−49.9772	−2.18744
$523$	13.5927	0.594369	0.297184	−	0.954820i	$-0.403952\pi$
$523$	13.5927	0.594369	0.297184	+	0.954820i	$0.403952\pi$
$524$	−46.1453	−2.01587
$525$	−0.0994941	−0.00434228
$526$	−37.9299	−1.65382
$527$	−25.9467	−1.13026
$528$	10.9129	0.474924
$529$	−11.7203	−0.509578
$530$	31.7773	1.38032
$531$	−4.45254	−0.193224
$532$	0	0
$533$	8.26213	0.357872
$534$	−8.01402	−0.346800
$535$	14.5622	0.629579
$536$	−5.22659	−0.225754
$537$	0.934315	0.0403187
$538$	−57.9986	−2.50050
$539$	−35.4969	−1.52896
$540$	−6.87377	−0.295800
$541$	−7.86277	−0.338047	−0.169023	−	0.985612i	$-0.554061\pi$
$541$	−7.86277	−0.338047	−0.169023	+	0.985612i	$0.554061\pi$
$542$	−34.3076	−1.47364
$543$	−4.73027	−0.202995
$544$	33.6294	1.44185
$545$	−4.41987	−0.189326
$546$	−0.742586	−0.0317797
$547$	−26.5480	−1.13511	−0.567555	−	0.823336i	$-0.692110\pi$
$547$	−26.5480	−1.13511	−0.567555	+	0.823336i	$0.692110\pi$
$548$	−41.8792	−1.78899
$549$	20.5335	0.876350
$550$	−13.4079	−0.571717
$551$	0	0
$552$	−5.74340	−0.244455
$553$	1.28058	0.0544557
$554$	−8.67737	−0.368666
$555$	−0.282664	−0.0119984
$556$	−61.5218	−2.60911
$557$	3.81018	0.161442	0.0807212	−	0.996737i	$-0.474278\pi$
$557$	3.81018	0.161442	0.0807212	+	0.996737i	$0.474278\pi$
$558$	47.5368	2.01239
$559$	35.9226	1.51937
$560$	−3.40879	−0.144047
$561$	−5.32747	−0.224926
$562$	51.7202	2.18168
$563$	12.1792	0.513292	0.256646	−	0.966506i	$-0.417383\pi$
$563$	12.1792	0.513292	0.256646	+	0.966506i	$0.417383\pi$
$564$	7.82631	0.329547
$565$	−8.08453	−0.340119
$566$	−1.36901	−0.0575437
$567$	−3.39445	−0.142554
$568$	−57.5469	−2.41462
$569$	−22.8626	−0.958451	−0.479226	−	0.877692i	$-0.659082\pi$
$569$	−22.8626	−0.958451	−0.479226	+	0.877692i	$0.659082\pi$
$570$	0	0
$571$	40.3908	1.69030	0.845152	−	0.534527i	$-0.179510\pi$
$571$	40.3908	1.69030	0.845152	+	0.534527i	$0.179510\pi$
$572$	−70.0765	−2.93004
$573$	0.717394	0.0299696
$574$	−2.96665	−0.123826
$575$	3.35853	0.140060
$576$	−11.7307	−0.488781
$577$	−7.86381	−0.327375	−0.163687	−	0.986512i	$-0.552339\pi$
$577$	−7.86381	−0.327375	−0.163687	+	0.986512i	$0.552339\pi$
$578$	−0.430357	−0.0179005
$579$	−2.81914	−0.117160
$580$	−30.7631	−1.27737
$581$	−2.21682	−0.0919691
$582$	−5.69153	−0.235921
$583$	−63.8545	−2.64458
$584$	68.4705	2.83333
$585$	8.49085	0.351053
$586$	81.6649	3.37354
$587$	40.2217	1.66013	0.830064	−	0.557668i	$-0.188304\pi$
$587$	40.2217	1.66013	0.830064	+	0.557668i	$0.188304\pi$
$588$	−7.91555	−0.326432
$589$	0	0
$590$	−3.91387	−0.161131
$591$	−2.51457	−0.103436
$592$	−9.68440	−0.398026
$593$	34.0757	1.39932	0.699660	−	0.714476i	$-0.253335\pi$
$593$	34.0757	1.39932	0.699660	+	0.714476i	$0.253335\pi$
$594$	19.7246	0.809312
$595$	1.66410	0.0682214
$596$	−38.2379	−1.56628
$597$	−0.725876	−0.0297081
$598$	25.0668	1.02506
$599$	−17.8832	−0.730689	−0.365345	−	0.930872i	$-0.619049\pi$
$599$	−17.8832	−0.730689	−0.365345	+	0.930872i	$0.619049\pi$
$600$	−1.71009	−0.0698143
$601$	−0.711931	−0.0290403	−0.0145201	−	0.999895i	$-0.504622\pi$
$601$	−0.711931	−0.0290403	−0.0145201	+	0.999895i	$0.504622\pi$
$602$	−12.8986	−0.525709
$603$	−2.22487	−0.0906037
$604$	−35.5406	−1.44613
$605$	15.9424	0.648152
$606$	−0.861276	−0.0349869
$607$	34.3415	1.39388	0.696940	−	0.717129i	$-0.254544\pi$
$607$	34.3415	1.39388	0.696940	+	0.717129i	$0.254544\pi$
$608$	0	0
$609$	0.655057	0.0265443
$610$	18.0494	0.730798
$611$	−19.5368	−0.790375
$612$	56.8900	2.29964
$613$	29.9782	1.21081	0.605405	−	0.795918i	$-0.293011\pi$
$613$	29.9782	1.21081	0.605405	+	0.795918i	$0.293011\pi$
$614$	23.6912	0.956099
$615$	−0.708348	−0.0285633
$616$	14.3918	0.579862
$617$	22.1005	0.889734	0.444867	−	0.895597i	$-0.353251\pi$
$617$	22.1005	0.889734	0.444867	+	0.895597i	$0.353251\pi$
$618$	7.95242	0.319893
$619$	19.4472	0.781648	0.390824	−	0.920465i	$-0.372190\pi$
$619$	19.4472	0.781648	0.390824	+	0.920465i	$0.372190\pi$
$620$	29.2609	1.17515
$621$	−4.94078	−0.198267
$622$	62.1267	2.49105
$623$	−5.03017	−0.201530
$624$	−6.07475	−0.243185
$625$	1.00000	0.0400000
$626$	6.35337	0.253932
$627$	0	0
$628$	−58.7117	−2.34285
$629$	4.72772	0.188507
$630$	−3.04878	−0.121466
$631$	4.43028	0.176367	0.0881833	−	0.996104i	$-0.471894\pi$
$631$	4.43028	0.176367	0.0881833	+	0.996104i	$0.471894\pi$
$632$	22.0105	0.875529
$633$	1.36389	0.0542097
$634$	18.1392	0.720401
$635$	0.561168	0.0222693
$636$	−14.2391	−0.564616
$637$	19.7596	0.782904
$638$	88.2764	3.49489
$639$	−24.4967	−0.969076
$640$	5.92174	0.234077
$641$	−25.6634	−1.01364	−0.506822	−	0.862051i	$-0.669180\pi$
$641$	−25.6634	−1.01364	−0.506822	+	0.862051i	$0.669180\pi$
$642$	−9.31818	−0.367759
$643$	37.1678	1.46576	0.732878	−	0.680360i	$-0.238177\pi$
$643$	37.1678	1.46576	0.732878	+	0.680360i	$0.238177\pi$
$644$	−6.30280	−0.248365
$645$	−3.07980	−0.121267
$646$	0	0
$647$	20.6750	0.812819	0.406409	−	0.913691i	$-0.366781\pi$
$647$	20.6750	0.812819	0.406409	+	0.913691i	$0.366781\pi$
$648$	−58.3435	−2.29195
$649$	7.86467	0.308715
$650$	7.46362	0.292747
$651$	−0.623070	−0.0244201
$652$	−15.3421	−0.600842
$653$	34.0336	1.33184	0.665919	−	0.746024i	$-0.268039\pi$
$653$	34.0336	1.33184	0.665919	+	0.746024i	$0.268039\pi$
$654$	2.82822	0.110592
$655$	−9.87597	−0.385886
$656$	−24.2688	−0.947539
$657$	29.1467	1.13712
$658$	7.01502	0.273474
$659$	31.0125	1.20807	0.604037	−	0.796956i	$-0.293558\pi$
$659$	31.0125	1.20807	0.604037	+	0.796956i	$0.293558\pi$
$660$	6.00796	0.233859
$661$	18.2642	0.710396	0.355198	−	0.934791i	$-0.384413\pi$
$661$	18.2642	0.710396	0.355198	+	0.934791i	$0.384413\pi$
$662$	44.9733	1.74794
$663$	2.96557	0.115173
$664$	−38.1024	−1.47866
$665$	0	0
$666$	−8.66163	−0.335631
$667$	−22.1121	−0.856186
$668$	24.4261	0.945073
$669$	−1.97206	−0.0762441
$670$	−1.95570	−0.0755554
$671$	−36.2691	−1.40015
$672$	0.807558	0.0311522
$673$	−26.0320	−1.00346	−0.501731	−	0.865024i	$-0.667303\pi$
$673$	−26.0320	−1.00346	−0.501731	+	0.865024i	$0.667303\pi$
$674$	−84.4102	−3.25136
$675$	−1.47112	−0.0566233
$676$	−21.7338	−0.835917
$677$	0.0601276	0.00231089	0.00115545	−	0.999999i	$-0.499632\pi$
$677$	0.0601276	0.00231089	0.00115545	+	0.999999i	$0.499632\pi$
$678$	5.17319	0.198675
$679$	−3.57241	−0.137097
$680$	28.6024	1.09685
$681$	−1.98780	−0.0761726
$682$	−83.9658	−3.21522
$683$	31.5145	1.20587	0.602935	−	0.797790i	$-0.293998\pi$
$683$	31.5145	1.20587	0.602935	+	0.797790i	$0.293998\pi$
$684$	0	0
$685$	−8.96292	−0.342456
$686$	−14.3574	−0.548168
$687$	−6.99724	−0.266961
$688$	−105.518	−4.02283
$689$	35.5450	1.35416
$690$	−2.14908	−0.0818142
$691$	9.39530	0.357414	0.178707	−	0.983902i	$-0.442809\pi$
$691$	9.39530	0.357414	0.178707	+	0.983902i	$0.442809\pi$
$692$	−21.0522	−0.800285
$693$	6.12634	0.232720
$694$	−18.4164	−0.699077
$695$	−13.1668	−0.499446
$696$	11.2591	0.426774
$697$	11.8475	0.448758
$698$	−58.6390	−2.21952
$699$	2.33909	0.0884727
$700$	−1.87666	−0.0709310
$701$	−7.39883	−0.279450	−0.139725	−	0.990190i	$-0.544622\pi$
$701$	−7.39883	−0.279450	−0.139725	+	0.990190i	$0.544622\pi$
$702$	−10.9798	−0.414408
$703$	0	0
$704$	20.7204	0.780930
$705$	1.67498	0.0630833
$706$	11.6082	0.436882
$707$	−0.540599	−0.0203313
$708$	1.75376	0.0659104
$709$	−43.2773	−1.62531	−0.812656	−	0.582743i	$-0.801979\pi$
$709$	−43.2773	−1.62531	−0.812656	+	0.582743i	$0.801979\pi$
$710$	−21.5331	−0.808123
$711$	9.36947	0.351383
$712$	−86.4581	−3.24015
$713$	21.0324	0.787669
$714$	−1.06484	−0.0398505
$715$	−14.9977	−0.560881
$716$	17.6231	0.658605
$717$	2.92130	0.109098
$718$	−27.3412	−1.02037
$719$	32.3509	1.20648	0.603242	−	0.797558i	$-0.293875\pi$
$719$	32.3509	1.20648	0.603242	+	0.797558i	$0.293875\pi$
$720$	−24.9407	−0.929485
$721$	4.99151	0.185894
$722$	0	0
$723$	3.17086	0.117926
$724$	−89.2223	−3.31592
$725$	−6.58388	−0.244519
$726$	−10.2014	−0.378609
$727$	49.6728	1.84226	0.921131	−	0.389252i	$-0.127267\pi$
$727$	49.6728	1.84226	0.921131	+	0.389252i	$0.127267\pi$
$728$	−8.01128	−0.296918
$729$	−23.7425	−0.879354
$730$	25.6205	0.948257
$731$	51.5116	1.90522
$732$	−8.08773	−0.298931
$733$	1.36840	0.0505431	0.0252715	−	0.999681i	$-0.491955\pi$
$733$	1.36840	0.0505431	0.0252715	+	0.999681i	$0.491955\pi$
$734$	4.66188	0.172073
$735$	−1.69408	−0.0624869
$736$	−27.2600	−1.00482
$737$	3.92986	0.144758
$738$	−21.7058	−0.799001
$739$	17.7716	0.653737	0.326869	−	0.945070i	$-0.394007\pi$
$739$	17.7716	0.653737	0.326869	+	0.945070i	$0.394007\pi$
$740$	−5.33161	−0.195994
$741$	0	0
$742$	−12.7630	−0.468545
$743$	−38.6273	−1.41710	−0.708550	−	0.705661i	$-0.750650\pi$
$743$	−38.6273	−1.41710	−0.708550	+	0.705661i	$0.750650\pi$
$744$	−10.7093	−0.392621
$745$	−8.18362	−0.299825
$746$	−33.4871	−1.22605
$747$	−16.2195	−0.593442
$748$	−100.487	−3.67416
$749$	−5.84876	−0.213709
$750$	−0.639888	−0.0233654
$751$	−15.9797	−0.583109	−0.291554	−	0.956554i	$-0.594172\pi$
$751$	−15.9797	−0.583109	−0.291554	+	0.956554i	$0.594172\pi$
$752$	57.3867	2.09268
$753$	0.594437	0.0216625
$754$	−49.1396	−1.78956
$755$	−7.60636	−0.276824
$756$	2.76078	0.100409
$757$	1.94915	0.0708431	0.0354215	−	0.999372i	$-0.488723\pi$
$757$	1.94915	0.0708431	0.0354215	+	0.999372i	$0.488723\pi$
$758$	85.5971	3.10903
$759$	4.31845	0.156750
$760$	0	0
$761$	−48.1168	−1.74423	−0.872115	−	0.489300i	$-0.837252\pi$
$761$	−48.1168	−1.74423	−0.872115	+	0.489300i	$0.837252\pi$
$762$	−0.359085	−0.0130083
$763$	1.77520	0.0642664
$764$	13.5315	0.489552
$765$	12.1755	0.440207
$766$	52.1618	1.88468
$767$	−4.37792	−0.158078
$768$	−5.76700	−0.208099
$769$	−6.39137	−0.230479	−0.115239	−	0.993338i	$-0.536764\pi$
$769$	−6.39137	−0.230479	−0.115239	+	0.993338i	$0.536764\pi$
$770$	5.38517	0.194068
$771$	−4.26460	−0.153586
$772$	−53.1747	−1.91380
$773$	35.7375	1.28539	0.642695	−	0.766122i	$-0.277816\pi$
$773$	35.7375	1.28539	0.642695	+	0.766122i	$0.277816\pi$
$774$	−94.3740	−3.39220
$775$	6.26239	0.224952
$776$	−61.4022	−2.20421
$777$	0.113529	0.00407283
$778$	5.24072	0.187889
$779$	0	0
$780$	−3.34437	−0.119748
$781$	43.2694	1.54830
$782$	35.9447	1.28538
$783$	9.68566	0.346137
$784$	−58.0411	−2.07290
$785$	−12.5654	−0.448479
$786$	6.31952	0.225410
$787$	−1.94031	−0.0691644	−0.0345822	−	0.999402i	$-0.511010\pi$
$787$	−1.94031	−0.0691644	−0.0345822	+	0.999402i	$0.511010\pi$
$788$	−47.4299	−1.68962
$789$	3.63746	0.129497
$790$	8.23594	0.293022
$791$	3.24707	0.115452
$792$	105.299	3.74163
$793$	20.1894	0.716947
$794$	−20.7497	−0.736379
$795$	−3.04743	−0.108081
$796$	−13.6915	−0.485282
$797$	−44.3436	−1.57073	−0.785365	−	0.619033i	$-0.787525\pi$
$797$	−44.3436	−1.57073	−0.785365	+	0.619033i	$0.787525\pi$
$798$	0	0
$799$	−28.0150	−0.991099
$800$	−8.11665	−0.286967
$801$	−36.8037	−1.30040
$802$	−37.1452	−1.31164
$803$	−51.4828	−1.81679
$804$	0.876329	0.0309058
$805$	−1.34892	−0.0475431
$806$	46.7401	1.64635
$807$	5.56203	0.195793
$808$	−9.29175	−0.326883
$809$	−27.8638	−0.979639	−0.489819	−	0.871824i	$-0.662937\pi$
$809$	−27.8638	−0.979639	−0.489819	+	0.871824i	$0.662937\pi$
$810$	−21.8312	−0.767069
$811$	−30.4897	−1.07064	−0.535320	−	0.844649i	$-0.679809\pi$
$811$	−30.4897	−1.07064	−0.535320	+	0.844649i	$0.679809\pi$
$812$	12.3557	0.433600
$813$	3.29008	0.115388
$814$	15.2993	0.536241
$815$	−3.28349	−0.115016
$816$	−8.71095	−0.304944
$817$	0	0
$818$	0.624053	0.0218195
$819$	−3.41026	−0.119164
$820$	−13.3609	−0.466581
$821$	50.2212	1.75273	0.876365	−	0.481647i	$-0.159961\pi$
$821$	50.2212	1.75273	0.876365	+	0.481647i	$0.159961\pi$
$822$	5.73527	0.200041
$823$	43.4872	1.51587	0.757934	−	0.652331i	$-0.226209\pi$
$823$	43.4872	1.51587	0.757934	+	0.652331i	$0.226209\pi$
$824$	85.7936	2.98876
$825$	1.28582	0.0447664
$826$	1.57197	0.0546957
$827$	0.595730	0.0207156	0.0103578	−	0.999946i	$-0.496703\pi$
$827$	0.595730	0.0207156	0.0103578	+	0.999946i	$0.496703\pi$
$828$	−46.1150	−1.60261
$829$	−19.2479	−0.668509	−0.334254	−	0.942483i	$-0.608484\pi$
$829$	−19.2479	−0.668509	−0.334254	+	0.942483i	$0.608484\pi$
$830$	−14.2573	−0.494878
$831$	0.832156	0.0288672
$832$	−11.5341	−0.399875
$833$	28.3345	0.981731
$834$	8.42529	0.291744
$835$	5.22764	0.180910
$836$	0	0
$837$	−9.21270	−0.318438
$838$	58.6589	2.02634
$839$	50.9295	1.75828	0.879140	−	0.476563i	$-0.158117\pi$
$839$	50.9295	1.75828	0.879140	+	0.476563i	$0.158117\pi$
$840$	0.686842	0.0236983
$841$	14.3475	0.494742
$842$	−64.5132	−2.22327
$843$	−4.95994	−0.170829
$844$	25.7257	0.885514
$845$	−4.65145	−0.160015
$846$	51.3261	1.76463
$847$	−6.40312	−0.220014
$848$	−104.408	−3.58540
$849$	0.131287	0.00450576
$850$	10.7025	0.367093
$851$	−3.83229	−0.131369
$852$	9.64875	0.330561
$853$	−2.59950	−0.0890052	−0.0445026	−	0.999009i	$-0.514170\pi$
$853$	−2.59950	−0.0890052	−0.0445026	+	0.999009i	$0.514170\pi$
$854$	−7.24935	−0.248067
$855$	0	0
$856$	−100.528	−3.43597
$857$	−40.2229	−1.37399	−0.686994	−	0.726663i	$-0.741070\pi$
$857$	−40.2229	−1.37399	−0.686994	+	0.726663i	$0.741070\pi$
$858$	9.59684	0.327631
$859$	−28.0859	−0.958277	−0.479138	−	0.877739i	$-0.659051\pi$
$859$	−28.0859	−0.958277	−0.479138	+	0.877739i	$0.659051\pi$
$860$	−58.0913	−1.98090
$861$	0.284501	0.00969576
$862$	46.1334	1.57131
$863$	29.9395	1.01915	0.509577	−	0.860425i	$-0.329802\pi$
$863$	29.9395	1.01915	0.509577	+	0.860425i	$0.329802\pi$
$864$	11.9405	0.406225
$865$	−4.50557	−0.153194
$866$	−101.030	−3.43314
$867$	0.0412710	0.00140164
$868$	−11.7524	−0.398901
$869$	−16.5496	−0.561407
$870$	4.21295	0.142832
$871$	−2.18758	−0.0741234
$872$	30.5119	1.03326
$873$	−26.1379	−0.884633
$874$	0	0
$875$	−0.401640	−0.0135779
$876$	−11.4803	−0.387882
$877$	8.10527	0.273696	0.136848	−	0.990592i	$-0.456303\pi$
$877$	8.10527	0.273696	0.136848	+	0.990592i	$0.456303\pi$
$878$	48.3942	1.63322
$879$	−7.83162	−0.264154
$880$	44.0536	1.48505
$881$	8.93196	0.300925	0.150463	−	0.988616i	$-0.451924\pi$
$881$	8.93196	0.300925	0.150463	+	0.988616i	$0.451924\pi$
$882$	−51.9113	−1.74795
$883$	−1.51178	−0.0508756	−0.0254378	−	0.999676i	$-0.508098\pi$
$883$	−1.51178	−0.0508756	−0.0254378	+	0.999676i	$0.508098\pi$
$884$	55.9366	1.88135
$885$	0.375338	0.0126168
$886$	−44.0456	−1.47974
$887$	−27.8375	−0.934692	−0.467346	−	0.884075i	$-0.654790\pi$
$887$	−27.8375	−0.934692	−0.467346	+	0.884075i	$0.654790\pi$
$888$	1.95133	0.0654822
$889$	−0.225387	−0.00755925
$890$	−32.3512	−1.08441
$891$	43.8683	1.46964
$892$	−37.1970	−1.24545
$893$	0	0
$894$	5.23661	0.175138
$895$	3.77167	0.126073
$896$	−2.37841	−0.0794571
$897$	−2.40389	−0.0802636
$898$	31.5223	1.05191
$899$	−41.2308	−1.37513
$900$	−13.7307	−0.457691
$901$	50.9700	1.69806
$902$	38.3397	1.27657
$903$	1.23697	0.0411638
$904$	55.8103	1.85622
$905$	−19.0953	−0.634748
$906$	4.86722	0.161703
$907$	−31.6673	−1.05149	−0.525747	−	0.850641i	$-0.676214\pi$
$907$	−31.6673	−1.05149	−0.525747	+	0.850641i	$0.676214\pi$
$908$	−37.4939	−1.24428
$909$	−3.95534	−0.131190
$910$	−2.99769	−0.0993724
$911$	−10.4766	−0.347104	−0.173552	−	0.984825i	$-0.555524\pi$
$911$	−10.4766	−0.347104	−0.173552	+	0.984825i	$0.555524\pi$
$912$	0	0
$913$	28.6491	0.948148
$914$	34.6340	1.14559
$915$	−1.73093	−0.0572226
$916$	−131.982	−4.36081
$917$	3.96658	0.130988
$918$	−15.7447	−0.519651
$919$	−10.6093	−0.349968	−0.174984	−	0.984571i	$-0.555987\pi$
$919$	−10.6093	−0.349968	−0.174984	+	0.984571i	$0.555987\pi$
$920$	−23.1851	−0.764389
$921$	−2.27197	−0.0748641
$922$	36.2056	1.19237
$923$	−24.0862	−0.792807
$924$	−2.41304	−0.0793830
$925$	−1.14106	−0.0375180
$926$	−67.6202	−2.22214
$927$	36.5208	1.19950
$928$	53.4391	1.75422
$929$	−14.1839	−0.465357	−0.232679	−	0.972554i	$-0.574749\pi$
$929$	−14.1839	−0.465357	−0.232679	+	0.972554i	$0.574749\pi$
$930$	−4.00723	−0.131402
$931$	0	0
$932$	44.1200	1.44520
$933$	−5.95792	−0.195054
$934$	102.261	3.34607
$935$	−21.5060	−0.703323
$936$	−58.6153	−1.91590
$937$	44.5421	1.45513	0.727563	−	0.686040i	$-0.240653\pi$
$937$	44.5421	1.45513	0.727563	+	0.686040i	$0.240653\pi$
$938$	0.785488	0.0256471
$939$	−0.609285	−0.0198833
$940$	31.5934	1.03046
$941$	30.3922	0.990756	0.495378	−	0.868677i	$-0.335030\pi$
$941$	30.3922	0.990756	0.495378	+	0.868677i	$0.335030\pi$
$942$	8.04046	0.261972
$943$	−9.60362	−0.312737
$944$	12.8595	0.418542
$945$	0.590859	0.0192206
$946$	166.696	5.41975
$947$	−30.9751	−1.00656	−0.503278	−	0.864125i	$-0.667873\pi$
$947$	−30.9751	−1.00656	−0.503278	+	0.864125i	$0.667873\pi$
$948$	−3.69044	−0.119860
$949$	28.6582	0.930285
$950$	0	0
$951$	−1.73954	−0.0564086
$952$	−11.4878	−0.372323
$953$	22.2633	0.721180	0.360590	−	0.932724i	$-0.382575\pi$
$953$	22.2633	0.721180	0.360590	+	0.932724i	$0.382575\pi$
$954$	−93.3818	−3.02335
$955$	2.89599	0.0937122
$956$	55.1015	1.78211
$957$	−8.46566	−0.273656
$958$	−9.76118	−0.315370
$959$	3.59987	0.116246
$960$	0.988873	0.0319157
$961$	8.21751	0.265081
$962$	−8.51647	−0.274582
$963$	−42.7930	−1.37898
$964$	59.8088	1.92631
$965$	−11.3804	−0.366348
$966$	0.863157	0.0277716
$967$	−17.5394	−0.564029	−0.282014	−	0.959410i	$-0.591003\pi$
$967$	−17.5394	−0.564029	−0.282014	+	0.959410i	$0.591003\pi$
$968$	−110.056	−3.53734
$969$	0	0
$970$	−22.9757	−0.737705
$971$	16.7713	0.538218	0.269109	−	0.963110i	$-0.413271\pi$
$971$	16.7713	0.538218	0.269109	+	0.963110i	$0.413271\pi$
$972$	30.4036	0.975197
$973$	5.28832	0.169536
$974$	18.0556	0.578539
$975$	−0.715757	−0.0229226
$976$	−59.3036	−1.89826
$977$	28.7840	0.920880	0.460440	−	0.887691i	$-0.347692\pi$
$977$	28.7840	0.920880	0.460440	+	0.887691i	$0.347692\pi$
$978$	2.10107	0.0671847
$979$	65.0076	2.07765
$980$	−31.9537	−1.02072
$981$	12.9884	0.414687
$982$	84.3095	2.69042
$983$	29.9169	0.954200	0.477100	−	0.878849i	$-0.341688\pi$
$983$	29.9169	0.954200	0.477100	+	0.878849i	$0.341688\pi$
$984$	4.88997	0.155887
$985$	−10.1509	−0.323434
$986$	−70.4642	−2.24404
$987$	−0.672737	−0.0214135
$988$	0	0
$989$	−41.7553	−1.32774
$990$	39.4011	1.25225
$991$	−45.9131	−1.45848	−0.729239	−	0.684259i	$-0.760126\pi$
$991$	−45.9131	−1.45848	−0.729239	+	0.684259i	$0.760126\pi$
$992$	−50.8296	−1.61384
$993$	−4.31292	−0.136866
$994$	8.64855	0.274315
$995$	−2.93023	−0.0928947
$996$	6.38854	0.202429
$997$	−53.9500	−1.70861	−0.854306	−	0.519770i	$-0.826018\pi$
$997$	−53.9500	−1.70861	−0.854306	+	0.519770i	$0.826018\pi$
$998$	−71.7924	−2.27255
$999$	1.67864	0.0531097

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.a.s.1.1		9
5.4	even	2		9025.2.a.cf.1.9		9
19.2	odd	18		95.2.k.a.61.1	✓	18
19.10	odd	18		95.2.k.a.81.1	yes	18
19.18	odd	2		1805.2.a.v.1.9		9
57.2	even	18		855.2.bs.c.631.3		18
57.29	even	18		855.2.bs.c.271.3		18
95.2	even	36		475.2.u.b.99.6		36
95.29	odd	18		475.2.l.c.176.3		18
95.48	even	36		475.2.u.b.24.6		36
95.59	odd	18		475.2.l.c.251.3		18
95.67	even	36		475.2.u.b.24.1		36
95.78	even	36		475.2.u.b.99.1		36
95.94	odd	2		9025.2.a.cc.1.1		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.a.61.1	✓	18	19.2	odd	18
95.2.k.a.81.1	yes	18	19.10	odd	18
475.2.l.c.176.3		18	95.29	odd	18
475.2.l.c.251.3		18	95.59	odd	18
475.2.u.b.24.1		36	95.67	even	36
475.2.u.b.24.6		36	95.48	even	36
475.2.u.b.99.1		36	95.78	even	36
475.2.u.b.99.6		36	95.2	even	36
855.2.bs.c.271.3		18	57.29	even	18
855.2.bs.c.631.3		18	57.2	even	18
1805.2.a.s.1.1		9	1.1	even	1	trivial
1805.2.a.v.1.9		9	19.18	odd	2
9025.2.a.cc.1.1		9	95.94	odd	2
9025.2.a.cf.1.9		9	5.4	even	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:	\( N \)	\(=\)	\( 1805 = 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1805.a (trivial)

\(f(q)\)	\(=\)	\(q-2.58312 q^{2} +0.247720 q^{3} +4.67249 q^{4} +1.00000 q^{5} -0.639888 q^{6} -0.401640 q^{7} -6.90335 q^{8} -2.93864 q^{9} +O(q^{10})\)	\(q-2.58312 q^{2} +0.247720 q^{3} +4.67249 q^{4} +1.00000 q^{5} -0.639888 q^{6} -0.401640 q^{7} -6.90335 q^{8} -2.93864 q^{9} -2.58312 q^{10} +5.19061 q^{11} +1.15747 q^{12} -2.88939 q^{13} +1.03748 q^{14} +0.247720 q^{15} +8.48717 q^{16} -4.14326 q^{17} +7.59083 q^{18} +4.67249 q^{20} -0.0994941 q^{21} -13.4079 q^{22} +3.35853 q^{23} -1.71009 q^{24} +1.00000 q^{25} +7.46362 q^{26} -1.47112 q^{27} -1.87666 q^{28} -6.58388 q^{29} -0.639888 q^{30} +6.26239 q^{31} -8.11665 q^{32} +1.28582 q^{33} +10.7025 q^{34} -0.401640 q^{35} -13.7307 q^{36} -1.14106 q^{37} -0.715757 q^{39} -6.90335 q^{40} -2.85947 q^{41} +0.257005 q^{42} -12.4326 q^{43} +24.2531 q^{44} -2.93864 q^{45} -8.67546 q^{46} +6.76158 q^{47} +2.10244 q^{48} -6.83869 q^{49} -2.58312 q^{50} -1.02637 q^{51} -13.5006 q^{52} -12.3019 q^{53} +3.80006 q^{54} +5.19061 q^{55} +2.77266 q^{56} +17.0069 q^{58} +1.51517 q^{59} +1.15747 q^{60} -6.98744 q^{61} -16.1765 q^{62} +1.18027 q^{63} +3.99190 q^{64} -2.88939 q^{65} -3.32141 q^{66} +0.757110 q^{67} -19.3593 q^{68} +0.831973 q^{69} +1.03748 q^{70} +8.33609 q^{71} +20.2864 q^{72} -9.91844 q^{73} +2.94750 q^{74} +0.247720 q^{75} -2.08476 q^{77} +1.84888 q^{78} -3.18837 q^{79} +8.48717 q^{80} +8.45148 q^{81} +7.38635 q^{82} +5.51941 q^{83} -0.464885 q^{84} -4.14326 q^{85} +32.1149 q^{86} -1.63096 q^{87} -35.8326 q^{88} +12.5241 q^{89} +7.59083 q^{90} +1.16049 q^{91} +15.6927 q^{92} +1.55132 q^{93} -17.4660 q^{94} -2.01065 q^{96} +8.89456 q^{97} +17.6651 q^{98} -15.2533 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 6 q^{2} - 9 q^{3} + 6 q^{4} + 9 q^{5} + 12 q^{6} - 6 q^{8} + 6 q^{9}+O(q^{10}) \) 9 * q - 6 * q^2 - 9 * q^3 + 6 * q^4 + 9 * q^5 + 12 * q^6 - 6 * q^8 + 6 * q^9	\( 9 q - 6 q^{2} - 9 q^{3} + 6 q^{4} + 9 q^{5} + 12 q^{6} - 6 q^{8} + 6 q^{9} - 6 q^{10} - 18 q^{12} - 9 q^{13} - 9 q^{15} + 12 q^{16} - 9 q^{17} - 24 q^{18} + 6 q^{20} - 12 q^{21} - 24 q^{22} - 12 q^{23} + 3 q^{24} + 9 q^{25} - 3 q^{26} - 24 q^{27} - 15 q^{28} - 9 q^{29} + 12 q^{30} - 18 q^{31} - 3 q^{32} + 9 q^{33} + 24 q^{34} + 18 q^{36} - 18 q^{37} + 18 q^{39} - 6 q^{40} - 6 q^{41} - 12 q^{43} + 48 q^{44} + 6 q^{45} + 9 q^{46} + 15 q^{47} + 21 q^{48} - 9 q^{49} - 6 q^{50} + 6 q^{51} - 33 q^{52} - 15 q^{53} + 63 q^{54} + 6 q^{58} - 21 q^{59} - 18 q^{60} - 12 q^{61} - 36 q^{62} + 21 q^{63} - 36 q^{64} - 9 q^{65} + 3 q^{66} - 60 q^{67} - 51 q^{68} + 15 q^{69} + 18 q^{71} + 27 q^{73} + 27 q^{74} - 9 q^{75} - 30 q^{77} + 6 q^{78} - 15 q^{79} + 12 q^{80} + 33 q^{81} + 24 q^{82} + 48 q^{84} - 9 q^{85} + 39 q^{86} + 15 q^{87} - 27 q^{88} + 39 q^{89} - 24 q^{90} - 21 q^{91} - 6 q^{92} + 15 q^{93} - 15 q^{94} - 33 q^{96} - 15 q^{97} + 15 q^{98} - 36 q^{99}+O(q^{100}) \) 9 * q - 6 * q^2 - 9 * q^3 + 6 * q^4 + 9 * q^5 + 12 * q^6 - 6 * q^8 + 6 * q^9 - 6 * q^10 - 18 * q^12 - 9 * q^13 - 9 * q^15 + 12 * q^16 - 9 * q^17 - 24 * q^18 + 6 * q^20 - 12 * q^21 - 24 * q^22 - 12 * q^23 + 3 * q^24 + 9 * q^25 - 3 * q^26 - 24 * q^27 - 15 * q^28 - 9 * q^29 + 12 * q^30 - 18 * q^31 - 3 * q^32 + 9 * q^33 + 24 * q^34 + 18 * q^36 - 18 * q^37 + 18 * q^39 - 6 * q^40 - 6 * q^41 - 12 * q^43 + 48 * q^44 + 6 * q^45 + 9 * q^46 + 15 * q^47 + 21 * q^48 - 9 * q^49 - 6 * q^50 + 6 * q^51 - 33 * q^52 - 15 * q^53 + 63 * q^54 + 6 * q^58 - 21 * q^59 - 18 * q^60 - 12 * q^61 - 36 * q^62 + 21 * q^63 - 36 * q^64 - 9 * q^65 + 3 * q^66 - 60 * q^67 - 51 * q^68 + 15 * q^69 + 18 * q^71 + 27 * q^73 + 27 * q^74 - 9 * q^75 - 30 * q^77 + 6 * q^78 - 15 * q^79 + 12 * q^80 + 33 * q^81 + 24 * q^82 + 48 * q^84 - 9 * q^85 + 39 * q^86 + 15 * q^87 - 27 * q^88 + 39 * q^89 - 24 * q^90 - 21 * q^91 - 6 * q^92 + 15 * q^93 - 15 * q^94 - 33 * q^96 - 15 * q^97 + 15 * q^98 - 36 * q^99

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