LMFDB - Embedded newform 1805.2.a.t.1.6

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} - 12x^{7} - 4x^{6} + 48x^{5} + 27x^{4} - 72x^{3} - 51x^{2} + 27x + 19 $ x^9 - 12x^7 - 4x^6 + 48x^5 + 27x^4 - 72x^3 - 51x^2 + 27*x + 19
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			1.6
Root			$0.719457$ 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)

$f(q)$	$=$	$q+0.719457 q^{2} -1.23428 q^{3} -1.48238 q^{4} -1.00000 q^{5} -0.888013 q^{6} +1.29194 q^{7} -2.50542 q^{8} -1.47655 q^{9} +O(q^{10})$	\(q+0.719457 q^{2} -1.23428 q^{3} -1.48238 q^{4} -1.00000 q^{5} -0.888013 q^{6} +1.29194 q^{7} -2.50542 q^{8} -1.47655 q^{9} -0.719457 q^{10} +5.76762 q^{11} +1.82968 q^{12} +2.35136 q^{13} +0.929495 q^{14} +1.23428 q^{15} +1.16222 q^{16} -6.84996 q^{17} -1.06231 q^{18} +1.48238 q^{20} -1.59462 q^{21} +4.14956 q^{22} +5.66998 q^{23} +3.09240 q^{24} +1.00000 q^{25} +1.69170 q^{26} +5.52532 q^{27} -1.91515 q^{28} -6.02113 q^{29} +0.888013 q^{30} -2.38890 q^{31} +5.84701 q^{32} -7.11888 q^{33} -4.92825 q^{34} -1.29194 q^{35} +2.18881 q^{36} -4.53121 q^{37} -2.90225 q^{39} +2.50542 q^{40} -4.58429 q^{41} -1.14726 q^{42} +0.277025 q^{43} -8.54982 q^{44} +1.47655 q^{45} +4.07930 q^{46} +0.507019 q^{47} -1.43451 q^{48} -5.33089 q^{49} +0.719457 q^{50} +8.45479 q^{51} -3.48562 q^{52} -7.18962 q^{53} +3.97523 q^{54} -5.76762 q^{55} -3.23685 q^{56} -4.33194 q^{58} +5.76420 q^{59} -1.82968 q^{60} -7.20739 q^{61} -1.71871 q^{62} -1.90761 q^{63} +1.88223 q^{64} -2.35136 q^{65} -5.12173 q^{66} -10.2219 q^{67} +10.1543 q^{68} -6.99835 q^{69} -0.929495 q^{70} -1.11959 q^{71} +3.69937 q^{72} +2.39279 q^{73} -3.26001 q^{74} -1.23428 q^{75} +7.45142 q^{77} -2.08804 q^{78} -14.0944 q^{79} -1.16222 q^{80} -2.39017 q^{81} -3.29820 q^{82} +1.21722 q^{83} +2.36383 q^{84} +6.84996 q^{85} +0.199307 q^{86} +7.43178 q^{87} -14.4503 q^{88} -8.94517 q^{89} +1.06231 q^{90} +3.03782 q^{91} -8.40507 q^{92} +2.94858 q^{93} +0.364778 q^{94} -7.21687 q^{96} -10.5948 q^{97} -3.83535 q^{98} -8.51616 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 3 q^{3} + 6 q^{4} - 9 q^{5} - 12 q^{6} + 12 q^{8} + 6 q^{9}+O(q^{10}) $ 9 * q - 3 * q^3 + 6 * q^4 - 9 * q^5 - 12 * q^6 + 12 * q^8 + 6 * q^9	$ 9 q - 3 q^{3} + 6 q^{4} - 9 q^{5} - 12 q^{6} + 12 q^{8} + 6 q^{9} - 6 q^{12} + 3 q^{13} - 12 q^{14} + 3 q^{15} - 12 q^{16} - 9 q^{17} - 6 q^{18} - 6 q^{20} - 12 q^{21} - 12 q^{22} + 15 q^{24} + 9 q^{25} + 21 q^{26} - 6 q^{27} - 15 q^{28} - 15 q^{29} + 12 q^{30} - 30 q^{31} + 9 q^{32} - 9 q^{33} - 6 q^{36} - 30 q^{37} + 6 q^{39} - 12 q^{40} - 18 q^{41} + 36 q^{42} - 6 q^{43} - 24 q^{44} - 6 q^{45} - 21 q^{46} + 21 q^{47} - 15 q^{48} + 3 q^{49} - 18 q^{51} + 3 q^{52} + 9 q^{53} - 9 q^{54} - 36 q^{56} + 18 q^{58} - 27 q^{59} + 6 q^{60} + 12 q^{61} - 6 q^{62} - 15 q^{63} + 24 q^{64} - 3 q^{65} + 3 q^{66} - 36 q^{67} + 3 q^{68} - 27 q^{69} + 12 q^{70} + 6 q^{71} - 12 q^{72} - 9 q^{73} - 9 q^{74} - 3 q^{75} + 12 q^{77} - 54 q^{78} - 45 q^{79} + 12 q^{80} - 15 q^{81} - 48 q^{82} + 12 q^{84} + 9 q^{85} + 9 q^{86} + 45 q^{87} - 39 q^{88} + 9 q^{89} + 6 q^{90} - 51 q^{91} - 54 q^{92} + 9 q^{93} - 33 q^{94} - 9 q^{96} - 45 q^{97} - 33 q^{98} + 12 q^{99}+O(q^{100}) $ 9 * q - 3 * q^3 + 6 * q^4 - 9 * q^5 - 12 * q^6 + 12 * q^8 + 6 * q^9 - 6 * q^12 + 3 * q^13 - 12 * q^14 + 3 * q^15 - 12 * q^16 - 9 * q^17 - 6 * q^18 - 6 * q^20 - 12 * q^21 - 12 * q^22 + 15 * q^24 + 9 * q^25 + 21 * q^26 - 6 * q^27 - 15 * q^28 - 15 * q^29 + 12 * q^30 - 30 * q^31 + 9 * q^32 - 9 * q^33 - 6 * q^36 - 30 * q^37 + 6 * q^39 - 12 * q^40 - 18 * q^41 + 36 * q^42 - 6 * q^43 - 24 * q^44 - 6 * q^45 - 21 * q^46 + 21 * q^47 - 15 * q^48 + 3 * q^49 - 18 * q^51 + 3 * q^52 + 9 * q^53 - 9 * q^54 - 36 * q^56 + 18 * q^58 - 27 * q^59 + 6 * q^60 + 12 * q^61 - 6 * q^62 - 15 * q^63 + 24 * q^64 - 3 * q^65 + 3 * q^66 - 36 * q^67 + 3 * q^68 - 27 * q^69 + 12 * q^70 + 6 * q^71 - 12 * q^72 - 9 * q^73 - 9 * q^74 - 3 * q^75 + 12 * q^77 - 54 * q^78 - 45 * q^79 + 12 * q^80 - 15 * q^81 - 48 * q^82 + 12 * q^84 + 9 * q^85 + 9 * q^86 + 45 * q^87 - 39 * q^88 + 9 * q^89 + 6 * q^90 - 51 * q^91 - 54 * q^92 + 9 * q^93 - 33 * q^94 - 9 * q^96 - 45 * q^97 - 33 * q^98 + 12 * 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 $

$2$	0.719457	0.508733	0.254366	−	0.967108i	$-0.418133\pi$
$2$	0.719457	0.508733	0.254366	+	0.967108i	$0.418133\pi$
$3$	−1.23428	−0.712613	−0.356307	−	0.934369i	$-0.615964\pi$
$3$	−1.23428	−0.712613	−0.356307	+	0.934369i	$0.615964\pi$
$4$	−1.48238	−0.741191
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.888013	−0.362530
$7$	1.29194	0.488307	0.244154	−	0.969737i	$-0.421490\pi$
$7$	1.29194	0.488307	0.244154	+	0.969737i	$0.421490\pi$
$8$	−2.50542	−0.885801
$9$	−1.47655	−0.492182
$10$	−0.719457	−0.227512
$11$	5.76762	1.73900	0.869502	−	0.493929i	$-0.164440\pi$
$11$	5.76762	1.73900	0.869502	+	0.493929i	$0.164440\pi$
$12$	1.82968	0.528183
$13$	2.35136	0.652150	0.326075	−	0.945344i	$-0.394274\pi$
$13$	2.35136	0.652150	0.326075	+	0.945344i	$0.394274\pi$
$14$	0.929495	0.248418
$15$	1.23428	0.318690
$16$	1.16222	0.290555
$17$	−6.84996	−1.66136	−0.830680	−	0.556751i	$-0.812048\pi$
$17$	−6.84996	−1.66136	−0.830680	+	0.556751i	$0.812048\pi$
$18$	−1.06231	−0.250389
$19$	0	0
$19$	0	0
$20$	1.48238	0.331471
$21$	−1.59462	−0.347974
$22$	4.14956	0.884688
$23$	5.66998	1.18227	0.591136	−	0.806572i	$-0.298680\pi$
$23$	5.66998	1.18227	0.591136	+	0.806572i	$0.298680\pi$
$24$	3.09240	0.631234
$25$	1.00000	0.200000
$26$	1.69170	0.331770
$27$	5.52532	1.06335
$28$	−1.91515	−0.361929
$29$	−6.02113	−1.11810	−0.559048	−	0.829135i	$-0.688833\pi$
$29$	−6.02113	−1.11810	−0.559048	+	0.829135i	$0.688833\pi$
$30$	0.888013	0.162128
$31$	−2.38890	−0.429059	−0.214529	−	0.976718i	$-0.568822\pi$
$31$	−2.38890	−0.429059	−0.214529	+	0.976718i	$0.568822\pi$
$32$	5.84701	1.03362
$33$	−7.11888	−1.23924
$34$	−4.92825	−0.845188
$35$	−1.29194	−0.218378
$36$	2.18881	0.364801
$37$	−4.53121	−0.744926	−0.372463	−	0.928047i	$-0.621487\pi$
$37$	−4.53121	−0.744926	−0.372463	+	0.928047i	$0.621487\pi$
$38$	0	0
$39$	−2.90225	−0.464731
$40$	2.50542	0.396142
$41$	−4.58429	−0.715945	−0.357973	−	0.933732i	$-0.616532\pi$
$41$	−4.58429	−0.715945	−0.357973	+	0.933732i	$0.616532\pi$
$42$	−1.14726	−0.177026
$43$	0.277025	0.0422458	0.0211229	−	0.999777i	$-0.493276\pi$
$43$	0.277025	0.0422458	0.0211229	+	0.999777i	$0.493276\pi$
$44$	−8.54982	−1.28893
$45$	1.47655	0.220111
$46$	4.07930	0.601460
$47$	0.507019	0.0739564	0.0369782	−	0.999316i	$-0.488227\pi$
$47$	0.507019	0.0739564	0.0369782	+	0.999316i	$0.488227\pi$
$48$	−1.43451	−0.207053
$49$	−5.33089	−0.761556
$50$	0.719457	0.101747
$51$	8.45479	1.18391
$52$	−3.48562	−0.483368
$53$	−7.18962	−0.987571	−0.493785	−	0.869584i	$-0.664387\pi$
$53$	−7.18962	−0.987571	−0.493785	+	0.869584i	$0.664387\pi$
$54$	3.97523	0.540961
$55$	−5.76762	−0.777706
$56$	−3.23685	−0.432543
$57$	0	0
$58$	−4.33194	−0.568812
$59$	5.76420	0.750434	0.375217	−	0.926937i	$-0.377568\pi$
$59$	5.76420	0.750434	0.375217	+	0.926937i	$0.377568\pi$
$60$	−1.82968	−0.236210
$61$	−7.20739	−0.922812	−0.461406	−	0.887189i	$-0.652655\pi$
$61$	−7.20739	−0.922812	−0.461406	+	0.887189i	$0.652655\pi$
$62$	−1.71871	−0.218276
$63$	−1.90761	−0.240336
$64$	1.88223	0.235279
$65$	−2.35136	−0.291651
$66$	−5.12173	−0.630441
$67$	−10.2219	−1.24880	−0.624401	−	0.781104i	$-0.714657\pi$
$67$	−10.2219	−1.24880	−0.624401	+	0.781104i	$0.714657\pi$
$68$	10.1543	1.23138
$69$	−6.99835	−0.842503
$70$	−0.929495	−0.111096
$71$	−1.11959	−0.132871	−0.0664356	−	0.997791i	$-0.521163\pi$
$71$	−1.11959	−0.132871	−0.0664356	+	0.997791i	$0.521163\pi$
$72$	3.69937	0.435975
$73$	2.39279	0.280054	0.140027	−	0.990148i	$-0.455281\pi$
$73$	2.39279	0.280054	0.140027	+	0.990148i	$0.455281\pi$
$74$	−3.26001	−0.378968
$75$	−1.23428	−0.142523
$76$	0	0
$77$	7.45142	0.849168
$78$	−2.08804	−0.236424
$79$	−14.0944	−1.58574	−0.792871	−	0.609390i	$-0.791414\pi$
$79$	−14.0944	−1.58574	−0.792871	+	0.609390i	$0.791414\pi$
$80$	−1.16222	−0.129940
$81$	−2.39017	−0.265575
$82$	−3.29820	−0.364225
$83$	1.21722	0.133607	0.0668035	−	0.997766i	$-0.478720\pi$
$83$	1.21722	0.133607	0.0668035	+	0.997766i	$0.478720\pi$
$84$	2.36383	0.257915
$85$	6.84996	0.742982
$86$	0.199307	0.0214918
$87$	7.43178	0.796770
$88$	−14.4503	−1.54041
$89$	−8.94517	−0.948186	−0.474093	−	0.880475i	$-0.657224\pi$
$89$	−8.94517	−0.948186	−0.474093	+	0.880475i	$0.657224\pi$
$90$	1.06231	0.111977
$91$	3.03782	0.318450
$92$	−8.40507	−0.876289
$93$	2.94858	0.305753
$94$	0.364778	0.0376240
$95$	0	0
$96$	−7.21687	−0.736568
$97$	−10.5948	−1.07574	−0.537871	−	0.843027i	$-0.680771\pi$
$97$	−10.5948	−1.07574	−0.537871	+	0.843027i	$0.680771\pi$
$98$	−3.83535	−0.387429
$99$	−8.51616	−0.855907
$100$	−1.48238	−0.148238
$101$	2.16110	0.215037	0.107519	−	0.994203i	$-0.465709\pi$
$101$	2.16110	0.215037	0.107519	+	0.994203i	$0.465709\pi$
$102$	6.08285	0.602292
$103$	9.08309	0.894983	0.447491	−	0.894288i	$-0.352317\pi$
$103$	9.08309	0.894983	0.447491	+	0.894288i	$0.352317\pi$
$104$	−5.89116	−0.577676
$105$	1.59462	0.155619
$106$	−5.17262	−0.502410
$107$	−3.86865	−0.373996	−0.186998	−	0.982360i	$-0.559876\pi$
$107$	−3.86865	−0.373996	−0.186998	+	0.982360i	$0.559876\pi$
$108$	−8.19064	−0.788145
$109$	−16.6918	−1.59879	−0.799394	−	0.600807i	$-0.794846\pi$
$109$	−16.6918	−1.59879	−0.799394	+	0.600807i	$0.794846\pi$
$110$	−4.14956	−0.395645
$111$	5.59279	0.530844
$112$	1.50152	0.141880
$113$	−18.0822	−1.70103	−0.850515	−	0.525951i	$-0.823709\pi$
$113$	−18.0822	−1.70103	−0.850515	+	0.525951i	$0.823709\pi$
$114$	0	0
$115$	−5.66998	−0.528728
$116$	8.92562	0.828723
$117$	−3.47189	−0.320977
$118$	4.14709	0.381771
$119$	−8.84973	−0.811253
$120$	−3.09240	−0.282296
$121$	22.2655	2.02413
$122$	−5.18541	−0.469465
$123$	5.65831	0.510192
$124$	3.54126	0.318014
$125$	−1.00000	−0.0894427
$126$	−1.37244	−0.122267
$127$	10.7927	0.957699	0.478849	−	0.877897i	$-0.341054\pi$
$127$	10.7927	0.957699	0.478849	+	0.877897i	$0.341054\pi$
$128$	−10.3398	−0.913921
$129$	−0.341927	−0.0301050
$130$	−1.69170	−0.148372
$131$	12.6254	1.10309	0.551544	−	0.834146i	$-0.314039\pi$
$131$	12.6254	1.10309	0.551544	+	0.834146i	$0.314039\pi$
$132$	10.5529	0.918512
$133$	0	0
$134$	−7.35421	−0.635307
$135$	−5.52532	−0.475544
$136$	17.1620	1.47163
$137$	−9.20449	−0.786393	−0.393196	−	0.919455i	$-0.628631\pi$
$137$	−9.20449	−0.786393	−0.393196	+	0.919455i	$0.628631\pi$
$138$	−5.03501	−0.428609
$139$	4.74023	0.402061	0.201030	−	0.979585i	$-0.435571\pi$
$139$	4.74023	0.402061	0.201030	+	0.979585i	$0.435571\pi$
$140$	1.91515	0.161859
$141$	−0.625805	−0.0527023
$142$	−0.805498	−0.0675959
$143$	13.5618	1.13409
$144$	−1.71607	−0.143006
$145$	6.02113	0.500028
$146$	1.72151	0.142473
$147$	6.57983	0.542695
$148$	6.71698	0.552132
$149$	9.74862	0.798638	0.399319	−	0.916812i	$-0.369247\pi$
$149$	9.74862	0.798638	0.399319	+	0.916812i	$0.369247\pi$
$150$	−0.888013	−0.0725060
$151$	−13.0214	−1.05967	−0.529834	−	0.848101i	$-0.677746\pi$
$151$	−13.0214	−1.05967	−0.529834	+	0.848101i	$0.677746\pi$
$152$	0	0
$153$	10.1143	0.817691
$154$	5.36097	0.432000
$155$	2.38890	0.191881
$156$	4.30224	0.344455
$157$	18.6172	1.48581	0.742906	−	0.669396i	$-0.233447\pi$
$157$	18.6172	1.48581	0.742906	+	0.669396i	$0.233447\pi$
$158$	−10.1403	−0.806719
$159$	8.87403	0.703756
$160$	−5.84701	−0.462247
$161$	7.32526	0.577312
$162$	−1.71963	−0.135107
$163$	−9.88760	−0.774456	−0.387228	−	0.921984i	$-0.626567\pi$
$163$	−9.88760	−0.774456	−0.387228	+	0.921984i	$0.626567\pi$
$164$	6.79566	0.530652
$165$	7.11888	0.554204
$166$	0.875736	0.0679703
$167$	−12.0044	−0.928926	−0.464463	−	0.885593i	$-0.653753\pi$
$167$	−12.0044	−0.928926	−0.464463	+	0.885593i	$0.653753\pi$
$168$	3.99519	0.308236
$169$	−7.47110	−0.574700
$170$	4.92825	0.377980
$171$	0	0
$172$	−0.410656	−0.0313122
$173$	16.5082	1.25510	0.627548	−	0.778578i	$-0.284059\pi$
$173$	16.5082	1.25510	0.627548	+	0.778578i	$0.284059\pi$
$174$	5.34684	0.405343
$175$	1.29194	0.0976614
$176$	6.70325	0.505276
$177$	−7.11465	−0.534770
$178$	−6.43566	−0.482373
$179$	20.2147	1.51092	0.755458	−	0.655197i	$-0.227414\pi$
$179$	20.2147	1.51092	0.755458	+	0.655197i	$0.227414\pi$
$180$	−2.18881	−0.163144
$181$	0.238655	0.0177391	0.00886956	−	0.999961i	$-0.497177\pi$
$181$	0.238655	0.0177391	0.00886956	+	0.999961i	$0.497177\pi$
$182$	2.18558	0.162006
$183$	8.89596	0.657608
$184$	−14.2057	−1.04726
$185$	4.53121	0.333141
$186$	2.12137	0.155547
$187$	−39.5080	−2.88911
$188$	−0.751596	−0.0548158
$189$	7.13838	0.519241
$190$	0	0
$191$	−0.323227	−0.0233879	−0.0116939	−	0.999932i	$-0.503722\pi$
$191$	−0.323227	−0.0233879	−0.0116939	+	0.999932i	$0.503722\pi$
$192$	−2.32321	−0.167663
$193$	1.46354	0.105348	0.0526740	−	0.998612i	$-0.483226\pi$
$193$	1.46354	0.105348	0.0526740	+	0.998612i	$0.483226\pi$
$194$	−7.62252	−0.547265
$195$	2.90225	0.207834
$196$	7.90242	0.564459
$197$	−9.55005	−0.680413	−0.340206	−	0.940351i	$-0.610497\pi$
$197$	−9.55005	−0.680413	−0.340206	+	0.940351i	$0.610497\pi$
$198$	−6.12701	−0.435428
$199$	1.39820	0.0991159	0.0495580	−	0.998771i	$-0.484219\pi$
$199$	1.39820	0.0991159	0.0495580	+	0.998771i	$0.484219\pi$
$200$	−2.50542	−0.177160
$201$	12.6167	0.889913
$202$	1.55482	0.109397
$203$	−7.77894	−0.545974
$204$	−12.5332	−0.877501
$205$	4.58429	0.320180
$206$	6.53489	0.455307
$207$	−8.37198	−0.581893
$208$	2.73280	0.189486
$209$	0	0
$210$	1.14726	0.0791684
$211$	−16.9888	−1.16955	−0.584777	−	0.811194i	$-0.698818\pi$
$211$	−16.9888	−1.16955	−0.584777	+	0.811194i	$0.698818\pi$
$212$	10.6578	0.731978
$213$	1.38189	0.0946857
$214$	−2.78333	−0.190264
$215$	−0.277025	−0.0188929
$216$	−13.8433	−0.941916
$217$	−3.08631	−0.209512
$218$	−12.0091	−0.813356
$219$	−2.95337	−0.199571
$220$	8.54982	0.576429
$221$	−16.1067	−1.08346
$222$	4.02377	0.270058
$223$	11.7678	0.788032	0.394016	−	0.919104i	$-0.371086\pi$
$223$	11.7678	0.788032	0.394016	+	0.919104i	$0.371086\pi$
$224$	7.55399	0.504722
$225$	−1.47655	−0.0984364
$226$	−13.0094	−0.865370
$227$	27.5106	1.82594	0.912971	−	0.408025i	$-0.133782\pi$
$227$	27.5106	1.82594	0.912971	+	0.408025i	$0.133782\pi$
$228$	0	0
$229$	−9.40958	−0.621802	−0.310901	−	0.950442i	$-0.600631\pi$
$229$	−9.40958	−0.621802	−0.310901	+	0.950442i	$0.600631\pi$
$230$	−4.07930	−0.268981
$231$	−9.19716	−0.605129
$232$	15.0855	0.990411
$233$	1.11733	0.0731985	0.0365993	−	0.999330i	$-0.488347\pi$
$233$	1.11733	0.0731985	0.0365993	+	0.999330i	$0.488347\pi$
$234$	−2.49788	−0.163291
$235$	−0.507019	−0.0330743
$236$	−8.54474	−0.556215
$237$	17.3964	1.13002
$238$	−6.36700	−0.412711
$239$	−12.9655	−0.838670	−0.419335	−	0.907831i	$-0.637737\pi$
$239$	−12.9655	−0.838670	−0.419335	+	0.907831i	$0.637737\pi$
$240$	1.43451	0.0925971
$241$	−20.4349	−1.31633	−0.658163	−	0.752875i	$-0.728666\pi$
$241$	−20.4349	−1.31633	−0.658163	+	0.752875i	$0.728666\pi$
$242$	16.0191	1.02974
$243$	−13.6258	−0.874097
$244$	10.6841	0.683980
$245$	5.33089	0.340578
$246$	4.07091	0.259552
$247$	0	0
$248$	5.98520	0.380061
$249$	−1.50239	−0.0952102
$250$	−0.719457	−0.0455024
$251$	−16.5297	−1.04334	−0.521672	−	0.853146i	$-0.674691\pi$
$251$	−16.5297	−1.04334	−0.521672	+	0.853146i	$0.674691\pi$
$252$	2.82780	0.178135
$253$	32.7023	2.05597
$254$	7.76490	0.487213
$255$	−8.45479	−0.529459
$256$	−11.2035	−0.700221
$257$	−11.6731	−0.728149	−0.364074	−	0.931370i	$-0.618615\pi$
$257$	−11.6731	−0.728149	−0.364074	+	0.931370i	$0.618615\pi$
$258$	−0.246001	−0.0153154
$259$	−5.85404	−0.363753
$260$	3.48562	0.216169
$261$	8.89048	0.550307
$262$	9.08344	0.561177
$263$	−6.98033	−0.430425	−0.215213	−	0.976567i	$-0.569044\pi$
$263$	−6.98033	−0.430425	−0.215213	+	0.976567i	$0.569044\pi$
$264$	17.8358	1.09772
$265$	7.18962	0.441655
$266$	0	0
$267$	11.0409	0.675690
$268$	15.1527	0.925601
$269$	−5.14736	−0.313840	−0.156920	−	0.987611i	$-0.550157\pi$
$269$	−5.14736	−0.313840	−0.156920	+	0.987611i	$0.550157\pi$
$270$	−3.97523	−0.241925
$271$	−3.45491	−0.209871	−0.104935	−	0.994479i	$-0.533464\pi$
$271$	−3.45491	−0.209871	−0.104935	+	0.994479i	$0.533464\pi$
$272$	−7.96116	−0.482716
$273$	−3.74952	−0.226932
$274$	−6.62223	−0.400064
$275$	5.76762	0.347801
$276$	10.3742	0.624455
$277$	8.18014	0.491497	0.245749	−	0.969334i	$-0.420966\pi$
$277$	8.18014	0.491497	0.245749	+	0.969334i	$0.420966\pi$
$278$	3.41039	0.204542
$279$	3.52732	0.211175
$280$	3.23685	0.193439
$281$	11.1826	0.667096	0.333548	−	0.942733i	$-0.391754\pi$
$281$	11.1826	0.667096	0.333548	+	0.942733i	$0.391754\pi$
$282$	−0.450240	−0.0268114
$283$	17.3758	1.03289	0.516443	−	0.856322i	$-0.327256\pi$
$283$	17.3758	1.03289	0.516443	+	0.856322i	$0.327256\pi$
$284$	1.65966	0.0984829
$285$	0	0
$286$	9.75711	0.576950
$287$	−5.92262	−0.349601
$288$	−8.63339	−0.508727
$289$	29.9219	1.76011
$290$	4.33194	0.254381
$291$	13.0770	0.766588
$292$	−3.54702	−0.207574
$293$	2.86097	0.167140	0.0835699	−	0.996502i	$-0.473368\pi$
$293$	2.86097	0.167140	0.0835699	+	0.996502i	$0.473368\pi$
$294$	4.73390	0.276087
$295$	−5.76420	−0.335604
$296$	11.3526	0.659856
$297$	31.8680	1.84917
$298$	7.01371	0.406293
$299$	13.3322	0.771019
$300$	1.82968	0.105637
$301$	0.357899	0.0206289
$302$	−9.36835	−0.539088
$303$	−2.66741	−0.153239
$304$	0	0
$305$	7.20739	0.412694
$306$	7.27679	0.415986
$307$	28.0045	1.59830	0.799150	−	0.601132i	$-0.205283\pi$
$307$	28.0045	1.59830	0.799150	+	0.601132i	$0.205283\pi$
$308$	−11.0458	−0.629396
$309$	−11.2111	−0.637777
$310$	1.71871	0.0976161
$311$	−21.9292	−1.24349	−0.621744	−	0.783220i	$-0.713576\pi$
$311$	−21.9292	−1.24349	−0.621744	+	0.783220i	$0.713576\pi$
$312$	7.27135	0.411659
$313$	1.18000	0.0666974	0.0333487	−	0.999444i	$-0.489383\pi$
$313$	1.18000	0.0666974	0.0333487	+	0.999444i	$0.489383\pi$
$314$	13.3942	0.755881
$315$	1.90761	0.107482
$316$	20.8932	1.17534
$317$	29.7423	1.67050	0.835248	−	0.549873i	$-0.185324\pi$
$317$	29.7423	1.67050	0.835248	+	0.549873i	$0.185324\pi$
$318$	6.38448	0.358024
$319$	−34.7276	−1.94437
$320$	−1.88223	−0.105220
$321$	4.77501	0.266515
$322$	5.27021	0.293697
$323$	0	0
$324$	3.54315	0.196842
$325$	2.35136	0.130430
$326$	−7.11370	−0.393991
$327$	20.6024	1.13932
$328$	11.4856	0.634185
$329$	0.655038	0.0361134
$330$	5.12173	0.281942
$331$	−25.4385	−1.39823	−0.699113	−	0.715011i	$-0.746422\pi$
$331$	−25.4385	−1.39823	−0.699113	+	0.715011i	$0.746422\pi$
$332$	−1.80438	−0.0990283
$333$	6.69054	0.366639
$334$	−8.63662	−0.472575
$335$	10.2219	0.558481
$336$	−1.85330	−0.101106
$337$	11.8050	0.643061	0.321530	−	0.946899i	$-0.395803\pi$
$337$	11.8050	0.643061	0.321530	+	0.946899i	$0.395803\pi$
$338$	−5.37513	−0.292369
$339$	22.3185	1.21218
$340$	−10.1543	−0.550692
$341$	−13.7783	−0.746135
$342$	0	0
$343$	−15.9308	−0.860180
$344$	−0.694064	−0.0374214
$345$	6.99835	0.376779
$346$	11.8769	0.638508
$347$	−4.91947	−0.264091	−0.132045	−	0.991244i	$-0.542154\pi$
$347$	−4.91947	−0.264091	−0.132045	+	0.991244i	$0.542154\pi$
$348$	−11.0167	−0.590559
$349$	−36.2316	−1.93943	−0.969717	−	0.244230i	$-0.921465\pi$
$349$	−36.2316	−1.93943	−0.969717	+	0.244230i	$0.921465\pi$
$350$	0.929495	0.0496836
$351$	12.9920	0.693464
$352$	33.7234	1.79746
$353$	−25.5905	−1.36204	−0.681022	−	0.732263i	$-0.738464\pi$
$353$	−25.5905	−1.36204	−0.681022	+	0.732263i	$0.738464\pi$
$354$	−5.11868	−0.272055
$355$	1.11959	0.0594218
$356$	13.2602	0.702787
$357$	10.9231	0.578110
$358$	14.5436	0.768653
$359$	30.7999	1.62556	0.812779	−	0.582572i	$-0.197953\pi$
$359$	30.7999	1.62556	0.812779	+	0.582572i	$0.197953\pi$
$360$	−3.69937	−0.194974
$361$	0	0
$362$	0.171702	0.00902447
$363$	−27.4819	−1.44243
$364$	−4.50320	−0.236032
$365$	−2.39279	−0.125244
$366$	6.40026	0.334547
$367$	30.1343	1.57300	0.786498	−	0.617592i	$-0.211892\pi$
$367$	30.1343	1.57300	0.786498	+	0.617592i	$0.211892\pi$
$368$	6.58976	0.343515
$369$	6.76891	0.352375
$370$	3.26001	0.169480
$371$	−9.28856	−0.482238
$372$	−4.37091	−0.226621
$373$	−28.0245	−1.45105	−0.725526	−	0.688195i	$-0.758404\pi$
$373$	−28.0245	−1.45105	−0.725526	+	0.688195i	$0.758404\pi$
$374$	−28.4243	−1.46979
$375$	1.23428	0.0637381
$376$	−1.27030	−0.0655106
$377$	−14.1579	−0.729167
$378$	5.13576	0.264155
$379$	−22.6159	−1.16170	−0.580851	−	0.814010i	$-0.697280\pi$
$379$	−22.6159	−1.16170	−0.580851	+	0.814010i	$0.697280\pi$
$380$	0	0
$381$	−13.3213	−0.682469
$382$	−0.232548	−0.0118982
$383$	10.0232	0.512162	0.256081	−	0.966655i	$-0.417569\pi$
$383$	10.0232	0.512162	0.256081	+	0.966655i	$0.417569\pi$
$384$	12.7623	0.651273
$385$	−7.45142	−0.379759
$386$	1.05296	0.0535940
$387$	−0.409040	−0.0207926
$388$	15.7056	0.797330
$389$	−7.30170	−0.370211	−0.185106	−	0.982719i	$-0.559263\pi$
$389$	−7.30170	−0.370211	−0.185106	+	0.982719i	$0.559263\pi$
$390$	2.08804	0.105732
$391$	−38.8391	−1.96418
$392$	13.3561	0.674587
$393$	−15.5833	−0.786075
$394$	−6.87085	−0.346148
$395$	14.0944	0.709165
$396$	12.6242	0.634390
$397$	−36.3662	−1.82517	−0.912584	−	0.408889i	$-0.865916\pi$
$397$	−36.3662	−1.82517	−0.912584	+	0.408889i	$0.865916\pi$
$398$	1.00595	0.0504235
$399$	0	0
$400$	1.16222	0.0581110
$401$	9.14621	0.456740	0.228370	−	0.973574i	$-0.426660\pi$
$401$	9.14621	0.456740	0.228370	+	0.973574i	$0.426660\pi$
$402$	9.07717	0.452728
$403$	−5.61716	−0.279811
$404$	−3.20357	−0.159384
$405$	2.39017	0.118769
$406$	−5.59661	−0.277755
$407$	−26.1343	−1.29543
$408$	−21.1828	−1.04871
$409$	−4.69281	−0.232045	−0.116022	−	0.993247i	$-0.537014\pi$
$409$	−4.69281	−0.232045	−0.116022	+	0.993247i	$0.537014\pi$
$410$	3.29820	0.162886
$411$	11.3609	0.560394
$412$	−13.4646	−0.663353
$413$	7.44699	0.366442
$414$	−6.02328	−0.296028
$415$	−1.21722	−0.0597509
$416$	13.7484	0.674073
$417$	−5.85078	−0.286514
$418$	0	0
$419$	−0.588477	−0.0287490	−0.0143745	−	0.999897i	$-0.504576\pi$
$419$	−0.588477	−0.0287490	−0.0143745	+	0.999897i	$0.504576\pi$
$420$	−2.36383	−0.115343
$421$	−6.15246	−0.299853	−0.149926	−	0.988697i	$-0.547904\pi$
$421$	−6.15246	−0.299853	−0.149926	+	0.988697i	$0.547904\pi$
$422$	−12.2227	−0.594991
$423$	−0.748637	−0.0364000
$424$	18.0130	0.874791
$425$	−6.84996	−0.332272
$426$	0.994212	0.0481697
$427$	−9.31151	−0.450616
$428$	5.73482	0.277203
$429$	−16.7391	−0.808169
$430$	−0.199307	−0.00961145
$431$	−0.315615	−0.0152026	−0.00760132	−	0.999971i	$-0.502420\pi$
$431$	−0.315615	−0.0152026	−0.00760132	+	0.999971i	$0.502420\pi$
$432$	6.42164	0.308961
$433$	34.2499	1.64595	0.822973	−	0.568081i	$-0.192314\pi$
$433$	34.2499	1.64595	0.822973	+	0.568081i	$0.192314\pi$
$434$	−2.22047	−0.106586
$435$	−7.43178	−0.356326
$436$	24.7437	1.18501
$437$	0	0
$438$	−2.12483	−0.101528
$439$	−2.09175	−0.0998339	−0.0499170	−	0.998753i	$-0.515896\pi$
$439$	−2.09175	−0.0998339	−0.0499170	+	0.998753i	$0.515896\pi$
$440$	14.4503	0.688893
$441$	7.87131	0.374824
$442$	−11.5881	−0.551190
$443$	−8.50259	−0.403970	−0.201985	−	0.979389i	$-0.564739\pi$
$443$	−8.50259	−0.403970	−0.201985	+	0.979389i	$0.564739\pi$
$444$	−8.29065	−0.393457
$445$	8.94517	0.424042
$446$	8.46644	0.400898
$447$	−12.0326	−0.569120
$448$	2.43173	0.114889
$449$	−15.5170	−0.732292	−0.366146	−	0.930557i	$-0.619323\pi$
$449$	−15.5170	−0.732292	−0.366146	+	0.930557i	$0.619323\pi$
$450$	−1.06231	−0.0500778
$451$	−26.4404	−1.24503
$452$	26.8047	1.26079
$453$	16.0721	0.755134
$454$	19.7927	0.928916
$455$	−3.03782	−0.142415
$456$	0	0
$457$	37.2930	1.74449	0.872247	−	0.489065i	$-0.162662\pi$
$457$	37.2930	1.74449	0.872247	+	0.489065i	$0.162662\pi$
$458$	−6.76978	−0.316331
$459$	−37.8482	−1.76660
$460$	8.40507	0.391888
$461$	−17.5231	−0.816131	−0.408065	−	0.912953i	$-0.633796\pi$
$461$	−17.5231	−0.816131	−0.408065	+	0.912953i	$0.633796\pi$
$462$	−6.61696	−0.307849
$463$	−33.4375	−1.55397	−0.776987	−	0.629516i	$-0.783253\pi$
$463$	−33.4375	−1.55397	−0.776987	+	0.629516i	$0.783253\pi$
$464$	−6.99788	−0.324868
$465$	−2.94858	−0.136737
$466$	0.803869	0.0372385
$467$	14.9618	0.692351	0.346175	−	0.938170i	$-0.387480\pi$
$467$	14.9618	0.692351	0.346175	+	0.938170i	$0.387480\pi$
$468$	5.14667	0.237905
$469$	−13.2061	−0.609799
$470$	−0.364778	−0.0168260
$471$	−22.9788	−1.05881
$472$	−14.4418	−0.664735
$473$	1.59777	0.0734657
$474$	12.5160	0.574878
$475$	0	0
$476$	13.1187	0.601294
$477$	10.6158	0.486065
$478$	−9.32814	−0.426659
$479$	−15.8357	−0.723550	−0.361775	−	0.932265i	$-0.617829\pi$
$479$	−15.8357	−0.723550	−0.361775	+	0.932265i	$0.617829\pi$
$480$	7.21687	0.329403
$481$	−10.6545	−0.485804
$482$	−14.7020	−0.669659
$483$	−9.04145	−0.411400
$484$	−33.0059	−1.50027
$485$	10.5948	0.481086
$486$	−9.80319	−0.444682
$487$	6.49535	0.294332	0.147166	−	0.989112i	$-0.452985\pi$
$487$	6.49535	0.294332	0.147166	+	0.989112i	$0.452985\pi$
$488$	18.0576	0.817428
$489$	12.2041	0.551888
$490$	3.83535	0.173263
$491$	−1.68321	−0.0759624	−0.0379812	−	0.999278i	$-0.512093\pi$
$491$	−1.68321	−0.0759624	−0.0379812	+	0.999278i	$0.512093\pi$
$492$	−8.38777	−0.378150
$493$	41.2445	1.85756
$494$	0	0
$495$	8.51616	0.382773
$496$	−2.77642	−0.124665
$497$	−1.44644	−0.0648819
$498$	−1.08091	−0.0484365
$499$	13.3363	0.597016	0.298508	−	0.954407i	$-0.403511\pi$
$499$	13.3363	0.597016	0.298508	+	0.954407i	$0.403511\pi$
$500$	1.48238	0.0662941
$501$	14.8168	0.661965
$502$	−11.8924	−0.530783
$503$	7.61904	0.339716	0.169858	−	0.985469i	$-0.445669\pi$
$503$	7.61904	0.339716	0.169858	+	0.985469i	$0.445669\pi$
$504$	4.77937	0.212890
$505$	−2.16110	−0.0961677
$506$	23.5279	1.04594
$507$	9.22145	0.409539
$508$	−15.9989	−0.709838
$509$	18.9939	0.841888	0.420944	−	0.907087i	$-0.361699\pi$
$509$	18.9939	0.841888	0.420944	+	0.907087i	$0.361699\pi$
$510$	−6.08285	−0.269353
$511$	3.09133	0.136753
$512$	12.6192	0.557696
$513$	0	0
$514$	−8.39830	−0.370433
$515$	−9.08309	−0.400249
$516$	0.506866	0.0223135
$517$	2.92430	0.128610
$518$	−4.21173	−0.185053
$519$	−20.3758	−0.894398
$520$	5.89116	0.258344
$521$	20.3021	0.889449	0.444724	−	0.895667i	$-0.353302\pi$
$521$	20.3021	0.889449	0.444724	+	0.895667i	$0.353302\pi$
$522$	6.39632	0.279959
$523$	−15.3717	−0.672159	−0.336080	−	0.941834i	$-0.609101\pi$
$523$	−15.3717	−0.672159	−0.336080	+	0.941834i	$0.609101\pi$
$524$	−18.7157	−0.817599
$525$	−1.59462	−0.0695948
$526$	−5.02204	−0.218972
$527$	16.3639	0.712821
$528$	−8.27370	−0.360067
$529$	9.14862	0.397766
$530$	5.17262	0.224684
$531$	−8.51110	−0.369350
$532$	0	0
$533$	−10.7793	−0.466904
$534$	7.94342	0.343746
$535$	3.86865	0.167256
$536$	25.6102	1.10619
$537$	−24.9506	−1.07670
$538$	−3.70331	−0.159661
$539$	−30.7466	−1.32435
$540$	8.19064	0.352469
$541$	13.0387	0.560577	0.280288	−	0.959916i	$-0.409570\pi$
$541$	13.0387	0.560577	0.280288	+	0.959916i	$0.409570\pi$
$542$	−2.48566	−0.106768
$543$	−0.294568	−0.0126411
$544$	−40.0518	−1.71721
$545$	16.6918	0.715000
$546$	−2.69762	−0.115448
$547$	14.6566	0.626671	0.313335	−	0.949643i	$-0.398554\pi$
$547$	14.6566	0.626671	0.313335	+	0.949643i	$0.398554\pi$
$548$	13.6446	0.582867
$549$	10.6420	0.454192
$550$	4.14956	0.176938
$551$	0	0
$552$	17.5338	0.746290
$553$	−18.2091	−0.774329
$554$	5.88526	0.250041
$555$	−5.59279	−0.237401
$556$	−7.02683	−0.298004
$557$	−30.2255	−1.28070	−0.640349	−	0.768084i	$-0.721210\pi$
$557$	−30.2255	−1.28070	−0.640349	+	0.768084i	$0.721210\pi$
$558$	2.53775	0.107432
$559$	0.651385	0.0275506
$560$	−1.50152	−0.0634507
$561$	48.7640	2.05882
$562$	8.04538	0.339374
$563$	18.0260	0.759706	0.379853	−	0.925047i	$-0.375975\pi$
$563$	18.0260	0.759706	0.379853	+	0.925047i	$0.375975\pi$
$564$	0.927682	0.0390625
$565$	18.0822	0.760724
$566$	12.5012	0.525463
$567$	−3.08796	−0.129682
$568$	2.80505	0.117697
$569$	−39.6582	−1.66256	−0.831280	−	0.555854i	$-0.812391\pi$
$569$	−39.6582	−1.66256	−0.831280	+	0.555854i	$0.812391\pi$
$570$	0	0
$571$	−31.2303	−1.30695	−0.653473	−	0.756950i	$-0.726689\pi$
$571$	−31.2303	−1.30695	−0.653473	+	0.756950i	$0.726689\pi$
$572$	−20.1037	−0.840579
$573$	0.398954	0.0166665
$574$	−4.26107	−0.177854
$575$	5.66998	0.236454
$576$	−2.77921	−0.115800
$577$	17.6542	0.734953	0.367476	−	0.930033i	$-0.380222\pi$
$577$	17.6542	0.734953	0.367476	+	0.930033i	$0.380222\pi$
$578$	21.5275	0.895428
$579$	−1.80643	−0.0750725
$580$	−8.92562	−0.370616
$581$	1.57257	0.0652413
$582$	9.40835	0.389989
$583$	−41.4670	−1.71739
$584$	−5.99494	−0.248072
$585$	3.47189	0.143545
$586$	2.05835	0.0850295
$587$	4.74917	0.196019	0.0980095	−	0.995185i	$-0.468752\pi$
$587$	4.74917	0.196019	0.0980095	+	0.995185i	$0.468752\pi$
$588$	−9.75382	−0.402241
$589$	0	0
$590$	−4.14709	−0.170733
$591$	11.7875	0.484871
$592$	−5.26626	−0.216442
$593$	4.66896	0.191731	0.0958656	−	0.995394i	$-0.469438\pi$
$593$	4.66896	0.191731	0.0958656	+	0.995394i	$0.469438\pi$
$594$	22.9276	0.940732
$595$	8.84973	0.362804
$596$	−14.4512	−0.591943
$597$	−1.72578	−0.0706314
$598$	9.59192	0.392243
$599$	33.1849	1.35590	0.677949	−	0.735109i	$-0.262869\pi$
$599$	33.1849	1.35590	0.677949	+	0.735109i	$0.262869\pi$
$600$	3.09240	0.126247
$601$	−18.7005	−0.762810	−0.381405	−	0.924408i	$-0.624560\pi$
$601$	−18.7005	−0.762810	−0.381405	+	0.924408i	$0.624560\pi$
$602$	0.257493	0.0104946
$603$	15.0931	0.614638
$604$	19.3027	0.785416
$605$	−22.2655	−0.905221
$606$	−1.91908	−0.0779575
$607$	8.41685	0.341629	0.170815	−	0.985303i	$-0.445360\pi$
$607$	8.41685	0.341629	0.170815	+	0.985303i	$0.445360\pi$
$608$	0	0
$609$	9.60141	0.389069
$610$	5.18541	0.209951
$611$	1.19219	0.0482307
$612$	−14.9932	−0.606065
$613$	−34.8853	−1.40900	−0.704502	−	0.709702i	$-0.748830\pi$
$613$	−34.8853	−1.40900	−0.704502	+	0.709702i	$0.748830\pi$
$614$	20.1480	0.813107
$615$	−5.65831	−0.228165
$616$	−18.6690	−0.752194
$617$	41.1752	1.65765	0.828825	−	0.559508i	$-0.189010\pi$
$617$	41.1752	1.65765	0.828825	+	0.559508i	$0.189010\pi$
$618$	−8.06590	−0.324458
$619$	17.1830	0.690642	0.345321	−	0.938485i	$-0.387770\pi$
$619$	17.1830	0.690642	0.345321	+	0.938485i	$0.387770\pi$
$620$	−3.54126	−0.142220
$621$	31.3284	1.25717
$622$	−15.7771	−0.632603
$623$	−11.5566	−0.463006
$624$	−3.37305	−0.135030
$625$	1.00000	0.0400000
$626$	0.848957	0.0339311
$627$	0	0
$628$	−27.5978	−1.10127
$629$	31.0386	1.23759
$630$	1.37244	0.0546794
$631$	10.4934	0.417737	0.208869	−	0.977944i	$-0.433022\pi$
$631$	10.4934	0.417737	0.208869	+	0.977944i	$0.433022\pi$
$632$	35.3124	1.40465
$633$	20.9689	0.833440
$634$	21.3983	0.849836
$635$	−10.7927	−0.428296
$636$	−13.1547	−0.521618
$637$	−12.5349	−0.496649
$638$	−24.9850	−0.989167
$639$	1.65313	0.0653968
$640$	10.3398	0.408718
$641$	−3.73946	−0.147700	−0.0738499	−	0.997269i	$-0.523529\pi$
$641$	−3.73946	−0.147700	−0.0738499	+	0.997269i	$0.523529\pi$
$642$	3.43541	0.135585
$643$	−14.1144	−0.556616	−0.278308	−	0.960492i	$-0.589774\pi$
$643$	−14.1144	−0.556616	−0.278308	+	0.960492i	$0.589774\pi$
$644$	−10.8588	−0.427898
$645$	0.341927	0.0134633
$646$	0	0
$647$	−41.4758	−1.63058	−0.815291	−	0.579052i	$-0.803423\pi$
$647$	−41.4758	−1.63058	−0.815291	+	0.579052i	$0.803423\pi$
$648$	5.98839	0.235246
$649$	33.2457	1.30501
$650$	1.69170	0.0663541
$651$	3.80938	0.149301
$652$	14.6572	0.574020
$653$	36.5080	1.42867	0.714334	−	0.699805i	$-0.246730\pi$
$653$	36.5080	1.42867	0.714334	+	0.699805i	$0.246730\pi$
$654$	14.8226	0.579608
$655$	−12.6254	−0.493316
$656$	−5.32795	−0.208021
$657$	−3.53306	−0.137838
$658$	0.471272	0.0183721
$659$	16.7047	0.650722	0.325361	−	0.945590i	$-0.394514\pi$
$659$	16.7047	0.650722	0.325361	+	0.945590i	$0.394514\pi$
$660$	−10.5529	−0.410771
$661$	−4.28682	−0.166738	−0.0833691	−	0.996519i	$-0.526568\pi$
$661$	−4.28682	−0.166738	−0.0833691	+	0.996519i	$0.526568\pi$
$662$	−18.3019	−0.711323
$663$	19.8803	0.772085
$664$	−3.04965	−0.118349
$665$	0	0
$666$	4.81355	0.186521
$667$	−34.1397	−1.32189
$668$	17.7951	0.688511
$669$	−14.5248	−0.561562
$670$	7.35421	0.284118
$671$	−41.5695	−1.60477
$672$	−9.32375	−0.359672
$673$	−23.7977	−0.917333	−0.458666	−	0.888609i	$-0.651673\pi$
$673$	−23.7977	−0.917333	−0.458666	+	0.888609i	$0.651673\pi$
$674$	8.49321	0.327146
$675$	5.52532	0.212670
$676$	11.0750	0.425962
$677$	17.9049	0.688143	0.344072	−	0.938943i	$-0.388194\pi$
$677$	17.9049	0.688143	0.344072	+	0.938943i	$0.388194\pi$
$678$	16.0572	0.616674
$679$	−13.6879	−0.525292
$680$	−17.1620	−0.658134
$681$	−33.9558	−1.30119
$682$	−9.91287	−0.379583
$683$	8.10967	0.310308	0.155154	−	0.987890i	$-0.450413\pi$
$683$	8.10967	0.310308	0.155154	+	0.987890i	$0.450413\pi$
$684$	0	0
$685$	9.20449	0.351686
$686$	−11.4615	−0.437602
$687$	11.6141	0.443105
$688$	0.321963	0.0122747
$689$	−16.9054	−0.644045
$690$	5.03501	0.191680
$691$	9.23634	0.351367	0.175683	−	0.984447i	$-0.443786\pi$
$691$	9.23634	0.351367	0.175683	+	0.984447i	$0.443786\pi$
$692$	−24.4715	−0.930265
$693$	−11.0024	−0.417945
$694$	−3.53935	−0.134352
$695$	−4.74023	−0.179807
$696$	−18.6198	−0.705780
$697$	31.4022	1.18944
$698$	−26.0671	−0.986654
$699$	−1.37910	−0.0521623
$700$	−1.91515	−0.0723858
$701$	−42.7500	−1.61464	−0.807322	−	0.590111i	$-0.799084\pi$
$701$	−42.7500	−1.61464	−0.807322	+	0.590111i	$0.799084\pi$
$702$	9.34721	0.352788
$703$	0	0
$704$	10.8560	0.409152
$705$	0.625805	0.0235692
$706$	−18.4113	−0.692917
$707$	2.79201	0.105004
$708$	10.5466	0.396366
$709$	22.7937	0.856036	0.428018	−	0.903770i	$-0.359212\pi$
$709$	22.7937	0.856036	0.428018	+	0.903770i	$0.359212\pi$
$710$	0.805498	0.0302298
$711$	20.8110	0.780473
$712$	22.4114	0.839904
$713$	−13.5450	−0.507264
$714$	7.85868	0.294104
$715$	−13.5618	−0.507181
$716$	−29.9659	−1.11988
$717$	16.0031	0.597648
$718$	22.1592	0.826975
$719$	28.3256	1.05637	0.528183	−	0.849130i	$-0.322873\pi$
$719$	28.3256	1.05637	0.528183	+	0.849130i	$0.322873\pi$
$720$	1.71607	0.0639542
$721$	11.7348	0.437027
$722$	0	0
$723$	25.2224	0.938032
$724$	−0.353779	−0.0131481
$725$	−6.02113	−0.223619
$726$	−19.7720	−0.733809
$727$	29.0001	1.07555	0.537777	−	0.843087i	$-0.319264\pi$
$727$	29.0001	1.07555	0.537777	+	0.843087i	$0.319264\pi$
$728$	−7.61102	−0.282083
$729$	23.9886	0.888468
$730$	−1.72151	−0.0637158
$731$	−1.89761	−0.0701855
$732$	−13.1872	−0.487413
$733$	16.7543	0.618833	0.309417	−	0.950927i	$-0.399866\pi$
$733$	16.7543	0.618833	0.309417	+	0.950927i	$0.399866\pi$
$734$	21.6803	0.800235
$735$	−6.57983	−0.242701
$736$	33.1524	1.22201
$737$	−58.9560	−2.17167
$738$	4.86994	0.179265
$739$	1.46816	0.0540071	0.0270036	−	0.999635i	$-0.491403\pi$
$739$	1.46816	0.0540071	0.0270036	+	0.999635i	$0.491403\pi$
$740$	−6.71698	−0.246921
$741$	0	0
$742$	−6.68271	−0.245330
$743$	28.7278	1.05392	0.526961	−	0.849889i	$-0.323331\pi$
$743$	28.7278	1.05392	0.526961	+	0.849889i	$0.323331\pi$
$744$	−7.38743	−0.270836
$745$	−9.74862	−0.357162
$746$	−20.1624	−0.738198
$747$	−1.79728	−0.0657590
$748$	58.5659	2.14138
$749$	−4.99806	−0.182625
$750$	0.888013	0.0324257
$751$	−50.5651	−1.84515	−0.922574	−	0.385821i	$-0.873918\pi$
$751$	−50.5651	−1.84515	−0.922574	+	0.385821i	$0.873918\pi$
$752$	0.589268	0.0214884
$753$	20.4023	0.743500
$754$	−10.1860	−0.370951
$755$	13.0214	0.473898
$756$	−10.5818	−0.384857
$757$	7.68370	0.279269	0.139634	−	0.990203i	$-0.455407\pi$
$757$	7.68370	0.279269	0.139634	+	0.990203i	$0.455407\pi$
$758$	−16.2712	−0.590996
$759$	−40.3639	−1.46512
$760$	0	0
$761$	39.1347	1.41863	0.709315	−	0.704891i	$-0.249004\pi$
$761$	39.1347	1.41863	0.709315	+	0.704891i	$0.249004\pi$
$762$	−9.58408	−0.347194
$763$	−21.5648	−0.780700
$764$	0.479146	0.0173349
$765$	−10.1143	−0.365683
$766$	7.21126	0.260553
$767$	13.5537	0.489396
$768$	13.8283	0.498987
$769$	−33.4897	−1.20767	−0.603835	−	0.797110i	$-0.706361\pi$
$769$	−33.4897	−1.20767	−0.603835	+	0.797110i	$0.706361\pi$
$770$	−5.36097	−0.193196
$771$	14.4079	0.518889
$772$	−2.16953	−0.0780831
$773$	0.471464	0.0169574	0.00847869	−	0.999964i	$-0.497301\pi$
$773$	0.471464	0.0169574	0.00847869	+	0.999964i	$0.497301\pi$
$774$	−0.294286	−0.0105779
$775$	−2.38890	−0.0858117
$776$	26.5445	0.952893
$777$	7.22554	0.259215
$778$	−5.25326	−0.188338
$779$	0	0
$780$	−4.30224	−0.154045
$781$	−6.45738	−0.231063
$782$	−27.9431	−0.999242
$783$	−33.2687	−1.18893
$784$	−6.19567	−0.221274
$785$	−18.6172	−0.664475
$786$	−11.2115	−0.399902
$787$	−1.87171	−0.0667193	−0.0333596	−	0.999443i	$-0.510621\pi$
$787$	−1.87171	−0.0667193	−0.0333596	+	0.999443i	$0.510621\pi$
$788$	14.1568	0.504316
$789$	8.61570	0.306727
$790$	10.1403	0.360775
$791$	−23.3611	−0.830625
$792$	21.3366	0.758163
$793$	−16.9472	−0.601812
$794$	−26.1639	−0.928523
$795$	−8.87403	−0.314729
$796$	−2.07267	−0.0734638
$797$	−38.5450	−1.36533	−0.682666	−	0.730730i	$-0.739180\pi$
$797$	−38.5450	−1.36533	−0.682666	+	0.730730i	$0.739180\pi$
$798$	0	0
$799$	−3.47306	−0.122868
$800$	5.84701	0.206723
$801$	13.2080	0.466680
$802$	6.58030	0.232359
$803$	13.8007	0.487016
$804$	−18.7028	−0.659596
$805$	−7.32526	−0.258182
$806$	−4.04131	−0.142349
$807$	6.35330	0.223647
$808$	−5.41447	−0.190480
$809$	17.5674	0.617638	0.308819	−	0.951121i	$-0.400066\pi$
$809$	17.5674	0.617638	0.308819	+	0.951121i	$0.400066\pi$
$810$	1.71963	0.0604215
$811$	−35.6187	−1.25074	−0.625372	−	0.780327i	$-0.715053\pi$
$811$	−35.6187	−1.25074	−0.625372	+	0.780327i	$0.715053\pi$
$812$	11.5314	0.404671
$813$	4.26434	0.149557
$814$	−18.8025	−0.659027
$815$	9.88760	0.346347
$816$	9.82632	0.343990
$817$	0	0
$818$	−3.37628	−0.118049
$819$	−4.48548	−0.156735
$820$	−6.79566	−0.237315
$821$	−25.7289	−0.897944	−0.448972	−	0.893546i	$-0.648210\pi$
$821$	−25.7289	−0.897944	−0.448972	+	0.893546i	$0.648210\pi$
$822$	8.17371	0.285091
$823$	−13.4385	−0.468438	−0.234219	−	0.972184i	$-0.575253\pi$
$823$	−13.4385	−0.468438	−0.234219	+	0.972184i	$0.575253\pi$
$824$	−22.7570	−0.792777
$825$	−7.11888	−0.247848
$826$	5.35779	0.186421
$827$	−8.54379	−0.297097	−0.148548	−	0.988905i	$-0.547460\pi$
$827$	−8.54379	−0.297097	−0.148548	+	0.988905i	$0.547460\pi$
$828$	12.4105	0.431294
$829$	−13.4912	−0.468568	−0.234284	−	0.972168i	$-0.575275\pi$
$829$	−13.4912	−0.468568	−0.234284	+	0.972168i	$0.575275\pi$
$830$	−0.875736	−0.0303972
$831$	−10.0966	−0.350247
$832$	4.42581	0.153438
$833$	36.5164	1.26522
$834$	−4.20938	−0.145759
$835$	12.0044	0.415428
$836$	0	0
$837$	−13.1994	−0.456239
$838$	−0.423384	−0.0146255
$839$	−2.49129	−0.0860087	−0.0430044	−	0.999075i	$-0.513693\pi$
$839$	−2.49129	−0.0860087	−0.0430044	+	0.999075i	$0.513693\pi$
$840$	−3.99519	−0.137847
$841$	7.25403	0.250139
$842$	−4.42643	−0.152545
$843$	−13.8025	−0.475382
$844$	25.1838	0.866863
$845$	7.47110	0.257014
$846$	−0.538612	−0.0185179
$847$	28.7657	0.988399
$848$	−8.35592	−0.286944
$849$	−21.4467	−0.736048
$850$	−4.92825	−0.169038
$851$	−25.6918	−0.880705
$852$	−2.04849	−0.0701802
$853$	−33.5365	−1.14827	−0.574134	−	0.818761i	$-0.694661\pi$
$853$	−33.5365	−1.14827	−0.574134	+	0.818761i	$0.694661\pi$
$854$	−6.69923	−0.229243
$855$	0	0
$856$	9.69260	0.331286
$857$	10.1729	0.347498	0.173749	−	0.984790i	$-0.444412\pi$
$857$	10.1729	0.347498	0.173749	+	0.984790i	$0.444412\pi$
$858$	−12.0430	−0.411142
$859$	27.2696	0.930428	0.465214	−	0.885198i	$-0.345977\pi$
$859$	27.2696	0.930428	0.465214	+	0.885198i	$0.345977\pi$
$860$	0.410656	0.0140033
$861$	7.31019	0.249131
$862$	−0.227071	−0.00773408
$863$	18.7587	0.638555	0.319278	−	0.947661i	$-0.396560\pi$
$863$	18.7587	0.638555	0.319278	+	0.947661i	$0.396560\pi$
$864$	32.3066	1.09909
$865$	−16.5082	−0.561296
$866$	24.6413	0.837346
$867$	−36.9321	−1.25428
$868$	4.57509	0.155289
$869$	−81.2911	−2.75761
$870$	−5.34684	−0.181275
$871$	−24.0354	−0.814407
$872$	41.8201	1.41621
$873$	15.6438	0.529461
$874$	0	0
$875$	−1.29194	−0.0436755
$876$	4.37803	0.147920
$877$	23.0881	0.779628	0.389814	−	0.920894i	$-0.372539\pi$
$877$	23.0881	0.779628	0.389814	+	0.920894i	$0.372539\pi$
$878$	−1.50493	−0.0507888
$879$	−3.53125	−0.119106
$880$	−6.70325	−0.225966
$881$	54.6206	1.84022	0.920108	−	0.391664i	$-0.128101\pi$
$881$	54.6206	1.84022	0.920108	+	0.391664i	$0.128101\pi$
$882$	5.66307	0.190685
$883$	−18.6008	−0.625966	−0.312983	−	0.949759i	$-0.601328\pi$
$883$	−18.6008	−0.625966	−0.312983	+	0.949759i	$0.601328\pi$
$884$	23.8763	0.803048
$885$	7.11465	0.239156
$886$	−6.11724	−0.205513
$887$	−3.75954	−0.126233	−0.0631165	−	0.998006i	$-0.520104\pi$
$887$	−3.75954	−0.126233	−0.0631165	+	0.998006i	$0.520104\pi$
$888$	−14.0123	−0.470222
$889$	13.9435	0.467651
$890$	6.43566	0.215724
$891$	−13.7856	−0.461835
$892$	−17.4444	−0.584082
$893$	0	0
$894$	−8.65690	−0.289530
$895$	−20.2147	−0.675702
$896$	−13.3584	−0.446274
$897$	−16.4557	−0.549438
$898$	−11.1638	−0.372541
$899$	14.3839	0.479729
$900$	2.18881	0.0729602
$901$	49.2486	1.64071
$902$	−19.0228	−0.633388
$903$	−0.441748	−0.0147005
$904$	45.3036	1.50677
$905$	−0.238655	−0.00793318
$906$	11.5632	0.384161
$907$	−24.2061	−0.803749	−0.401875	−	0.915695i	$-0.631641\pi$
$907$	−24.2061	−0.803749	−0.401875	+	0.915695i	$0.631641\pi$
$908$	−40.7812	−1.35337
$909$	−3.19096	−0.105838
$910$	−2.18558	−0.0724512
$911$	29.7647	0.986148	0.493074	−	0.869987i	$-0.335873\pi$
$911$	29.7647	0.986148	0.493074	+	0.869987i	$0.335873\pi$
$912$	0	0
$913$	7.02046	0.232343
$914$	26.8307	0.887481
$915$	−8.89596	−0.294091
$916$	13.9486	0.460874
$917$	16.3113	0.538646
$918$	−27.2302	−0.898730
$919$	45.6349	1.50536	0.752678	−	0.658389i	$-0.228762\pi$
$919$	45.6349	1.50536	0.752678	+	0.658389i	$0.228762\pi$
$920$	14.2057	0.468348
$921$	−34.5654	−1.13897
$922$	−12.6071	−0.415193
$923$	−2.63257	−0.0866520
$924$	13.6337	0.448516
$925$	−4.53121	−0.148985
$926$	−24.0569	−0.790558
$927$	−13.4116	−0.440495
$928$	−35.2056	−1.15568
$929$	−27.2784	−0.894977	−0.447488	−	0.894290i	$-0.647681\pi$
$929$	−27.2784	−0.894977	−0.447488	+	0.894290i	$0.647681\pi$
$930$	−2.12137	−0.0695625
$931$	0	0
$932$	−1.65631	−0.0542541
$933$	27.0668	0.886127
$934$	10.7644	0.352222
$935$	39.5080	1.29205
$936$	8.69857	0.284322
$937$	43.8434	1.43230	0.716151	−	0.697946i	$-0.245902\pi$
$937$	43.8434	1.43230	0.716151	+	0.697946i	$0.245902\pi$
$938$	−9.50119	−0.310225
$939$	−1.45645	−0.0475295
$940$	0.751596	0.0245144
$941$	−43.8325	−1.42890	−0.714450	−	0.699687i	$-0.753323\pi$
$941$	−43.8325	−1.42890	−0.714450	+	0.699687i	$0.753323\pi$
$942$	−16.5323	−0.538651
$943$	−25.9928	−0.846442
$944$	6.69926	0.218042
$945$	−7.13838	−0.232212
$946$	1.14953	0.0373744
$947$	13.6366	0.443129	0.221564	−	0.975146i	$-0.428884\pi$
$947$	13.6366	0.443129	0.221564	+	0.975146i	$0.428884\pi$
$948$	−25.7882	−0.837561
$949$	5.62631	0.182638
$950$	0	0
$951$	−36.7104	−1.19042
$952$	22.1723	0.718609
$953$	12.3615	0.400428	0.200214	−	0.979752i	$-0.435836\pi$
$953$	12.3615	0.400428	0.200214	+	0.979752i	$0.435836\pi$
$954$	7.63762	0.247277
$955$	0.323227	0.0104594
$956$	19.2199	0.621615
$957$	42.8637	1.38559
$958$	−11.3931	−0.368094
$959$	−11.8916	−0.384001
$960$	2.32321	0.0749813
$961$	−25.2932	−0.815909
$962$	−7.66546	−0.247144
$963$	5.71224	0.184074
$964$	30.2923	0.975649
$965$	−1.46354	−0.0471131
$966$	−6.50493	−0.209293
$967$	−16.2469	−0.522467	−0.261233	−	0.965276i	$-0.584129\pi$
$967$	−16.2469	−0.522467	−0.261233	+	0.965276i	$0.584129\pi$
$968$	−55.7845	−1.79298
$969$	0	0
$970$	7.62252	0.244744
$971$	32.5053	1.04315	0.521573	−	0.853207i	$-0.325345\pi$
$971$	32.5053	1.04315	0.521573	+	0.853207i	$0.325345\pi$
$972$	20.1987	0.647873
$973$	6.12408	0.196329
$974$	4.67312	0.149737
$975$	−2.90225	−0.0929462
$976$	−8.37657	−0.268128
$977$	12.5889	0.402756	0.201378	−	0.979514i	$-0.435458\pi$
$977$	12.5889	0.402756	0.201378	+	0.979514i	$0.435458\pi$
$978$	8.78032	0.280764
$979$	−51.5923	−1.64890
$980$	−7.90242	−0.252434
$981$	24.6463	0.786895
$982$	−1.21100	−0.0386445
$983$	31.8919	1.01719	0.508597	−	0.861005i	$-0.330164\pi$
$983$	31.8919	1.01719	0.508597	+	0.861005i	$0.330164\pi$
$984$	−14.1765	−0.451929
$985$	9.55005	0.304290
$986$	29.6736	0.945001
$987$	−0.808502	−0.0257349
$988$	0	0
$989$	1.57072	0.0499461
$990$	6.12701	0.194729
$991$	8.19376	0.260283	0.130142	−	0.991495i	$-0.458457\pi$
$991$	8.19376	0.260283	0.130142	+	0.991495i	$0.458457\pi$
$992$	−13.9679	−0.443482
$993$	31.3983	0.996394
$994$	−1.04065	−0.0330076
$995$	−1.39820	−0.0443260
$996$	2.22712	0.0705689
$997$	−16.4479	−0.520911	−0.260455	−	0.965486i	$-0.583873\pi$
$997$	−16.4479	−0.520911	−0.260455	+	0.965486i	$0.583873\pi$
$998$	9.59491	0.303722
$999$	−25.0364	−0.792116

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.a.t.1.6		9
5.4	even	2		9025.2.a.ce.1.4		9
19.6	even	9		95.2.k.b.36.2	✓	18
19.16	even	9		95.2.k.b.66.2	yes	18
19.18	odd	2		1805.2.a.u.1.4		9
57.35	odd	18		855.2.bs.b.541.2		18
57.44	odd	18		855.2.bs.b.226.2		18
95.44	even	18		475.2.l.b.226.2		18
95.54	even	18		475.2.l.b.351.2		18
95.63	odd	36		475.2.u.c.74.3		36
95.73	odd	36		475.2.u.c.199.4		36
95.82	odd	36		475.2.u.c.74.4		36
95.92	odd	36		475.2.u.c.199.3		36
95.94	odd	2		9025.2.a.cd.1.6		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.b.36.2	✓	18	19.6	even	9
95.2.k.b.66.2	yes	18	19.16	even	9
475.2.l.b.226.2		18	95.44	even	18
475.2.l.b.351.2		18	95.54	even	18
475.2.u.c.74.3		36	95.63	odd	36
475.2.u.c.74.4		36	95.82	odd	36
475.2.u.c.199.3		36	95.92	odd	36
475.2.u.c.199.4		36	95.73	odd	36
855.2.bs.b.226.2		18	57.44	odd	18
855.2.bs.b.541.2		18	57.35	odd	18
1805.2.a.t.1.6		9	1.1	even	1	trivial
1805.2.a.u.1.4		9	19.18	odd	2
9025.2.a.cd.1.6		9	95.94	odd	2
9025.2.a.ce.1.4		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)

\(f(q)\)	\(=\)	\(q+0.719457 q^{2} -1.23428 q^{3} -1.48238 q^{4} -1.00000 q^{5} -0.888013 q^{6} +1.29194 q^{7} -2.50542 q^{8} -1.47655 q^{9} +O(q^{10})\)	\(q+0.719457 q^{2} -1.23428 q^{3} -1.48238 q^{4} -1.00000 q^{5} -0.888013 q^{6} +1.29194 q^{7} -2.50542 q^{8} -1.47655 q^{9} -0.719457 q^{10} +5.76762 q^{11} +1.82968 q^{12} +2.35136 q^{13} +0.929495 q^{14} +1.23428 q^{15} +1.16222 q^{16} -6.84996 q^{17} -1.06231 q^{18} +1.48238 q^{20} -1.59462 q^{21} +4.14956 q^{22} +5.66998 q^{23} +3.09240 q^{24} +1.00000 q^{25} +1.69170 q^{26} +5.52532 q^{27} -1.91515 q^{28} -6.02113 q^{29} +0.888013 q^{30} -2.38890 q^{31} +5.84701 q^{32} -7.11888 q^{33} -4.92825 q^{34} -1.29194 q^{35} +2.18881 q^{36} -4.53121 q^{37} -2.90225 q^{39} +2.50542 q^{40} -4.58429 q^{41} -1.14726 q^{42} +0.277025 q^{43} -8.54982 q^{44} +1.47655 q^{45} +4.07930 q^{46} +0.507019 q^{47} -1.43451 q^{48} -5.33089 q^{49} +0.719457 q^{50} +8.45479 q^{51} -3.48562 q^{52} -7.18962 q^{53} +3.97523 q^{54} -5.76762 q^{55} -3.23685 q^{56} -4.33194 q^{58} +5.76420 q^{59} -1.82968 q^{60} -7.20739 q^{61} -1.71871 q^{62} -1.90761 q^{63} +1.88223 q^{64} -2.35136 q^{65} -5.12173 q^{66} -10.2219 q^{67} +10.1543 q^{68} -6.99835 q^{69} -0.929495 q^{70} -1.11959 q^{71} +3.69937 q^{72} +2.39279 q^{73} -3.26001 q^{74} -1.23428 q^{75} +7.45142 q^{77} -2.08804 q^{78} -14.0944 q^{79} -1.16222 q^{80} -2.39017 q^{81} -3.29820 q^{82} +1.21722 q^{83} +2.36383 q^{84} +6.84996 q^{85} +0.199307 q^{86} +7.43178 q^{87} -14.4503 q^{88} -8.94517 q^{89} +1.06231 q^{90} +3.03782 q^{91} -8.40507 q^{92} +2.94858 q^{93} +0.364778 q^{94} -7.21687 q^{96} -10.5948 q^{97} -3.83535 q^{98} -8.51616 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 3 q^{3} + 6 q^{4} - 9 q^{5} - 12 q^{6} + 12 q^{8} + 6 q^{9}+O(q^{10}) \) 9 * q - 3 * q^3 + 6 * q^4 - 9 * q^5 - 12 * q^6 + 12 * q^8 + 6 * q^9	\( 9 q - 3 q^{3} + 6 q^{4} - 9 q^{5} - 12 q^{6} + 12 q^{8} + 6 q^{9} - 6 q^{12} + 3 q^{13} - 12 q^{14} + 3 q^{15} - 12 q^{16} - 9 q^{17} - 6 q^{18} - 6 q^{20} - 12 q^{21} - 12 q^{22} + 15 q^{24} + 9 q^{25} + 21 q^{26} - 6 q^{27} - 15 q^{28} - 15 q^{29} + 12 q^{30} - 30 q^{31} + 9 q^{32} - 9 q^{33} - 6 q^{36} - 30 q^{37} + 6 q^{39} - 12 q^{40} - 18 q^{41} + 36 q^{42} - 6 q^{43} - 24 q^{44} - 6 q^{45} - 21 q^{46} + 21 q^{47} - 15 q^{48} + 3 q^{49} - 18 q^{51} + 3 q^{52} + 9 q^{53} - 9 q^{54} - 36 q^{56} + 18 q^{58} - 27 q^{59} + 6 q^{60} + 12 q^{61} - 6 q^{62} - 15 q^{63} + 24 q^{64} - 3 q^{65} + 3 q^{66} - 36 q^{67} + 3 q^{68} - 27 q^{69} + 12 q^{70} + 6 q^{71} - 12 q^{72} - 9 q^{73} - 9 q^{74} - 3 q^{75} + 12 q^{77} - 54 q^{78} - 45 q^{79} + 12 q^{80} - 15 q^{81} - 48 q^{82} + 12 q^{84} + 9 q^{85} + 9 q^{86} + 45 q^{87} - 39 q^{88} + 9 q^{89} + 6 q^{90} - 51 q^{91} - 54 q^{92} + 9 q^{93} - 33 q^{94} - 9 q^{96} - 45 q^{97} - 33 q^{98} + 12 q^{99}+O(q^{100}) \) 9 * q - 3 * q^3 + 6 * q^4 - 9 * q^5 - 12 * q^6 + 12 * q^8 + 6 * q^9 - 6 * q^12 + 3 * q^13 - 12 * q^14 + 3 * q^15 - 12 * q^16 - 9 * q^17 - 6 * q^18 - 6 * q^20 - 12 * q^21 - 12 * q^22 + 15 * q^24 + 9 * q^25 + 21 * q^26 - 6 * q^27 - 15 * q^28 - 15 * q^29 + 12 * q^30 - 30 * q^31 + 9 * q^32 - 9 * q^33 - 6 * q^36 - 30 * q^37 + 6 * q^39 - 12 * q^40 - 18 * q^41 + 36 * q^42 - 6 * q^43 - 24 * q^44 - 6 * q^45 - 21 * q^46 + 21 * q^47 - 15 * q^48 + 3 * q^49 - 18 * q^51 + 3 * q^52 + 9 * q^53 - 9 * q^54 - 36 * q^56 + 18 * q^58 - 27 * q^59 + 6 * q^60 + 12 * q^61 - 6 * q^62 - 15 * q^63 + 24 * q^64 - 3 * q^65 + 3 * q^66 - 36 * q^67 + 3 * q^68 - 27 * q^69 + 12 * q^70 + 6 * q^71 - 12 * q^72 - 9 * q^73 - 9 * q^74 - 3 * q^75 + 12 * q^77 - 54 * q^78 - 45 * q^79 + 12 * q^80 - 15 * q^81 - 48 * q^82 + 12 * q^84 + 9 * q^85 + 9 * q^86 + 45 * q^87 - 39 * q^88 + 9 * q^89 + 6 * q^90 - 51 * q^91 - 54 * q^92 + 9 * q^93 - 33 * q^94 - 9 * q^96 - 45 * q^97 - 33 * q^98 + 12 * q^99

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