LMFDB - Embedded newform 1805.2.a.v.1.9

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:	$0$
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} - 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			1.9
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	$-0.133549\pi$
$2$	2.58312	1.82654	0.913269	+	0.407356i	$0.133549\pi$
$3$	−0.247720	−0.143021	−0.0715105	−	0.997440i	$-0.522782\pi$
$3$	−0.247720	−0.143021	−0.0715105	+	0.997440i	$0.522782\pi$
$4$	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	$-0.368772\pi$
$13$	2.88939	0.801371	0.400686	+	0.916216i	$0.368772\pi$
$14$	−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	$-0.290648\pi$
$29$	6.58388	1.22260	0.611298	+	0.791400i	$0.290648\pi$
$30$	−0.639888	−0.116827
$31$	−6.26239	−1.12476	−0.562379	−	0.826880i	$-0.690114\pi$
$31$	−6.26239	−1.12476	−0.562379	+	0.826880i	$0.690114\pi$
$32$	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	$-0.470100\pi$
$37$	1.14106	0.187590	0.0937949	+	0.995592i	$0.470100\pi$
$38$	0	0
$39$	−0.715757	−0.114613
$40$	6.90335	1.09151
$41$	2.85947	0.446575	0.223287	−	0.974753i	$-0.428321\pi$
$41$	2.85947	0.446575	0.223287	+	0.974753i	$0.428321\pi$
$42$	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	$-0.179660\pi$
$53$	12.3019	1.68980	0.844899	+	0.534925i	$0.179660\pi$
$54$	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	$-0.531446\pi$
$59$	−1.51517	−0.197259	−0.0986294	+	0.995124i	$0.531446\pi$
$60$	−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	$-0.514726\pi$
$67$	−0.757110	−0.0924957	−0.0462478	+	0.998930i	$0.514726\pi$
$68$	−19.3593	−2.34766
$69$	−0.831973	−0.100158
$70$	−1.03748	−0.124003
$71$	−8.33609	−0.989312	−0.494656	−	0.869089i	$-0.664706\pi$
$71$	−8.33609	−0.989312	−0.494656	+	0.869089i	$0.664706\pi$
$72$	−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	$-0.442597\pi$
$79$	3.18837	0.358720	0.179360	+	0.983783i	$0.442597\pi$
$80$	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	$-0.731047\pi$
$89$	−12.5241	−1.32755	−0.663775	+	0.747932i	$0.731047\pi$
$90$	−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	$-0.649130\pi$
$97$	−8.89456	−0.903106	−0.451553	+	0.892244i	$0.649130\pi$
$98$	−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	$-0.290255\pi$
$103$	12.4278	1.22455	0.612275	+	0.790645i	$0.290255\pi$
$104$	19.9464	1.95591
$105$	0.0994941	0.00970963
$106$	31.7773	3.08648
$107$	−14.5622	−1.40778	−0.703890	−	0.710309i	$-0.748555\pi$
$107$	−14.5622	−1.40778	−0.703890	+	0.710309i	$0.748555\pi$
$108$	6.87377	0.661429
$109$	4.41987	0.423347	0.211673	−	0.977340i	$-0.432109\pi$
$109$	4.41987	0.423347	0.211673	+	0.977340i	$0.432109\pi$
$110$	13.4079	1.27840
$111$	−0.282664	−0.0268293
$112$	−3.40879	−0.322100
$113$	8.08453	0.760528	0.380264	−	0.924878i	$-0.375833\pi$
$113$	8.08453	0.760528	0.380264	+	0.924878i	$0.375833\pi$
$114$	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	$-0.507926\pi$
$127$	−0.561168	−0.0497956	−0.0248978	+	0.999690i	$0.507926\pi$
$128$	−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	$-0.399839\pi$
$151$	7.60636	0.618997	0.309498	+	0.950900i	$0.399839\pi$
$152$	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	$-0.564830\pi$
$167$	−5.22764	−0.404527	−0.202263	+	0.979331i	$0.564830\pi$
$168$	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	$-0.445211\pi$
$173$	4.50557	0.342552	0.171276	+	0.985223i	$0.445211\pi$
$174$	−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	$-0.545017\pi$
$179$	−3.77167	−0.281907	−0.140954	+	0.990016i	$0.545017\pi$
$180$	−13.7307	−1.02343
$181$	19.0953	1.41934	0.709669	−	0.704535i	$-0.248844\pi$
$181$	19.0953	1.41934	0.709669	+	0.704535i	$0.248844\pi$
$182$	−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	$-0.365672\pi$
$193$	11.3804	0.819178	0.409589	+	0.912270i	$0.365672\pi$
$194$	−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	$-0.560692\pi$
$211$	−5.50578	−0.379033	−0.189517	+	0.981877i	$0.560692\pi$
$212$	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	$-0.414117\pi$
$223$	7.96085	0.533098	0.266549	+	0.963821i	$0.414117\pi$
$224$	−3.25997	−0.217816
$225$	−2.93864	−0.195909
$226$	20.8833	1.38913
$227$	8.02439	0.532597	0.266299	−	0.963891i	$-0.414199\pi$
$227$	8.02439	0.532597	0.266299	+	0.963891i	$0.414199\pi$
$228$	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	$-0.635263\pi$
$241$	−12.8002	−0.824534	−0.412267	+	0.911063i	$0.635263\pi$
$242$	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	$-0.319582\pi$
$257$	17.2154	1.07387	0.536934	+	0.843624i	$0.319582\pi$
$258$	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	$-0.739975\pi$
$269$	−22.4529	−1.36898	−0.684490	+	0.729022i	$0.739975\pi$
$270$	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	$-0.296273\pi$
$281$	20.0224	1.19444	0.597218	+	0.802079i	$0.296273\pi$
$282$	−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	$-0.125332\pi$
$293$	31.6149	1.84696	0.923480	+	0.383647i	$0.125332\pi$
$294$	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	$-0.415709\pi$
$307$	9.17155	0.523448	0.261724	+	0.965143i	$0.415709\pi$
$308$	−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	$-0.436814\pi$
$317$	7.02223	0.394408	0.197204	+	0.980363i	$0.436814\pi$
$318$	−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	$-0.341187\pi$
$331$	17.4105	0.956967	0.478483	+	0.878097i	$0.341187\pi$
$332$	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	$-0.849319\pi$
$337$	−32.6777	−1.78007	−0.890033	+	0.455895i	$0.849319\pi$
$338$	−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	$-0.608946\pi$
$373$	−12.9639	−0.671243	−0.335622	+	0.941997i	$0.608946\pi$
$374$	−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	$-0.175954\pi$
$379$	33.1372	1.70214	0.851071	+	0.525051i	$0.175954\pi$
$380$	0	0
$381$	0.139012	0.00712181
$382$	7.48069	0.382745
$383$	20.1934	1.03183	0.515916	−	0.856639i	$-0.327452\pi$
$383$	20.1934	1.03183	0.515916	+	0.856639i	$0.327452\pi$
$384$	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	$-0.616900\pi$
$401$	−14.3800	−0.718103	−0.359051	+	0.933318i	$0.616900\pi$
$402$	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	$-0.498099\pi$
$409$	0.241589	0.0119458	0.00597291	+	0.999982i	$0.498099\pi$
$410$	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	$-0.708269\pi$
$421$	−24.9750	−1.21720	−0.608602	+	0.793475i	$0.708269\pi$
$422$	−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	$-0.358467\pi$
$431$	17.8596	0.860266	0.430133	+	0.902766i	$0.358467\pi$
$432$	12.4856	0.600714
$433$	−39.1117	−1.87959	−0.939794	−	0.341741i	$-0.888983\pi$
$433$	−39.1117	−1.87959	−0.939794	+	0.341741i	$0.888983\pi$
$434$	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	$-0.352463\pi$
$439$	18.7348	0.894163	0.447082	+	0.894493i	$0.352463\pi$
$440$	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	$-0.407025\pi$
$449$	12.2032	0.575906	0.287953	+	0.957645i	$0.407025\pi$
$450$	−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	$-0.449376\pi$
$487$	6.98986	0.316741	0.158370	+	0.987380i	$0.449376\pi$
$488$	−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	$-0.789747\pi$
$509$	−35.6314	−1.57934	−0.789668	+	0.613535i	$0.789747\pi$
$510$	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	$-0.222643\pi$
$521$	34.9318	1.53039	0.765194	+	0.643800i	$0.222643\pi$
$522$	−49.9772	−2.18744
$523$	−13.5927	−0.594369	−0.297184	−	0.954820i	$-0.596048\pi$
$523$	−13.5927	−0.594369	−0.297184	+	0.954820i	$0.596048\pi$
$524$	−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	$-0.307890\pi$
$547$	26.5480	1.13511	0.567555	+	0.823336i	$0.307890\pi$
$548$	−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	$-0.582617\pi$
$563$	−12.1792	−0.513292	−0.256646	+	0.966506i	$0.582617\pi$
$564$	−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	$-0.340918\pi$
$569$	22.8626	0.958451	0.479226	+	0.877692i	$0.340918\pi$
$570$	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	$-0.380951\pi$
$599$	17.8832	0.730689	0.365345	+	0.930872i	$0.380951\pi$
$600$	−1.71009	−0.0698143
$601$	0.711931	0.0290403	0.0145201	−	0.999895i	$-0.495378\pi$
$601$	0.711931	0.0290403	0.0145201	+	0.999895i	$0.495378\pi$
$602$	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	$-0.745456\pi$
$607$	−34.3415	−1.39388	−0.696940	+	0.717129i	$0.745456\pi$
$608$	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	$-0.330820\pi$
$641$	25.6634	1.01364	0.506822	+	0.862051i	$0.330820\pi$
$642$	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	$-0.706442\pi$
$659$	−31.0125	−1.20807	−0.604037	+	0.796956i	$0.706442\pi$
$660$	−6.00796	−0.233859
$661$	−18.2642	−0.710396	−0.355198	−	0.934791i	$-0.615587\pi$
$661$	−18.2642	−0.710396	−0.355198	+	0.934791i	$0.615587\pi$
$662$	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	$-0.332697\pi$
$673$	26.0320	1.00346	0.501731	+	0.865024i	$0.332697\pi$
$674$	−84.4102	−3.25136
$675$	1.47112	0.0566233
$676$	−21.7338	−0.835917
$677$	−0.0601276	−0.00231089	−0.00115545	−	0.999999i	$-0.500368\pi$
$677$	−0.0601276	−0.00231089	−0.00115545	+	0.999999i	$0.500368\pi$
$678$	−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	$-0.706002\pi$
$683$	−31.5145	−1.20587	−0.602935	+	0.797790i	$0.706002\pi$
$684$	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	$-0.249350\pi$
$743$	38.6273	1.41710	0.708550	+	0.705661i	$0.249350\pi$
$744$	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	$-0.405828\pi$
$751$	15.9797	0.583109	0.291554	+	0.956554i	$0.405828\pi$
$752$	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	$-0.722184\pi$
$773$	−35.7375	−1.28539	−0.642695	+	0.766122i	$0.722184\pi$
$774$	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	$-0.488990\pi$
$787$	1.94031	0.0691644	0.0345822	+	0.999402i	$0.488990\pi$
$788$	−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	$-0.212475\pi$
$797$	44.3436	1.57073	0.785365	+	0.619033i	$0.212475\pi$
$798$	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	$-0.320191\pi$
$811$	30.4897	1.07064	0.535320	+	0.844649i	$0.320191\pi$
$812$	−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	$-0.503297\pi$
$827$	−0.595730	−0.0207156	−0.0103578	+	0.999946i	$0.503297\pi$
$828$	−46.1150	−1.60261
$829$	19.2479	0.668509	0.334254	−	0.942483i	$-0.391516\pi$
$829$	19.2479	0.668509	0.334254	+	0.942483i	$0.391516\pi$
$830$	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	$-0.841883\pi$
$839$	−50.9295	−1.75828	−0.879140	+	0.476563i	$0.841883\pi$
$840$	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	$-0.258930\pi$
$857$	40.2229	1.37399	0.686994	+	0.726663i	$0.258930\pi$
$858$	−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	$-0.670198\pi$
$863$	−29.9395	−1.01915	−0.509577	+	0.860425i	$0.670198\pi$
$864$	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	$-0.543697\pi$
$877$	−8.10527	−0.273696	−0.136848	+	0.990592i	$0.543697\pi$
$878$	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	$-0.345210\pi$
$887$	27.8375	0.934692	0.467346	+	0.884075i	$0.345210\pi$
$888$	−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	$-0.323786\pi$
$907$	31.6673	1.05149	0.525747	+	0.850641i	$0.323786\pi$
$908$	37.4939	1.24428
$909$	−3.95534	−0.131190
$910$	−2.99769	−0.0993724
$911$	10.4766	0.347104	0.173552	−	0.984825i	$-0.444476\pi$
$911$	10.4766	0.347104	0.173552	+	0.984825i	$0.444476\pi$
$912$	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	$-0.664970\pi$
$941$	−30.3922	−0.990756	−0.495378	+	0.868677i	$0.664970\pi$
$942$	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	$-0.617425\pi$
$953$	−22.2633	−0.721180	−0.360590	+	0.932724i	$0.617425\pi$
$954$	−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	$-0.586729\pi$
$971$	−16.7713	−0.538218	−0.269109	+	0.963110i	$0.586729\pi$
$972$	−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	$-0.652308\pi$
$977$	−28.7840	−0.920880	−0.460440	+	0.887691i	$0.652308\pi$
$978$	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	$-0.658312\pi$
$983$	−29.9169	−0.954200	−0.477100	+	0.878849i	$0.658312\pi$
$984$	−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	$-0.239874\pi$
$991$	45.9131	1.45848	0.729239	+	0.684259i	$0.239874\pi$
$992$	−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.v.1.9		9
5.4	even	2		9025.2.a.cc.1.1		9
19.9	even	9		95.2.k.a.81.1	yes	18
19.17	even	9		95.2.k.a.61.1	✓	18
19.18	odd	2		1805.2.a.s.1.1		9
57.17	odd	18		855.2.bs.c.631.3		18
57.47	odd	18		855.2.bs.c.271.3		18
95.9	even	18		475.2.l.c.176.3		18
95.17	odd	36		475.2.u.b.99.6		36
95.28	odd	36		475.2.u.b.24.6		36
95.47	odd	36		475.2.u.b.24.1		36
95.74	even	18		475.2.l.c.251.3		18
95.93	odd	36		475.2.u.b.99.1		36
95.94	odd	2		9025.2.a.cf.1.9		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.a.61.1	✓	18	19.17	even	9
95.2.k.a.81.1	yes	18	19.9	even	9
475.2.l.c.176.3		18	95.9	even	18
475.2.l.c.251.3		18	95.74	even	18
475.2.u.b.24.1		36	95.47	odd	36
475.2.u.b.24.6		36	95.28	odd	36
475.2.u.b.99.1		36	95.93	odd	36
475.2.u.b.99.6		36	95.17	odd	36
855.2.bs.c.271.3		18	57.47	odd	18
855.2.bs.c.631.3		18	57.17	odd	18
1805.2.a.s.1.1		9	19.18	odd	2
1805.2.a.v.1.9		9	1.1	even	1	trivial
9025.2.a.cc.1.1		9	5.4	even	2
9025.2.a.cf.1.9		9	95.94	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:	\( N \)	\(=\)	\( 1805 = 5 \cdot 19^{2} \)
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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