LMFDB - Embedded newform 1805.2.a.v.1.5

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			1.5
Root			$0.309891$ 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)

$f(q)$	$=$	$q+0.690109 q^{2} -0.694850 q^{3} -1.52375 q^{4} +1.00000 q^{5} -0.479522 q^{6} -2.33464 q^{7} -2.43177 q^{8} -2.51718 q^{9} +O(q^{10})$	\(q+0.690109 q^{2} -0.694850 q^{3} -1.52375 q^{4} +1.00000 q^{5} -0.479522 q^{6} -2.33464 q^{7} -2.43177 q^{8} -2.51718 q^{9} +0.690109 q^{10} +4.57857 q^{11} +1.05878 q^{12} +1.28105 q^{13} -1.61116 q^{14} -0.694850 q^{15} +1.36931 q^{16} -0.654656 q^{17} -1.73713 q^{18} -1.52375 q^{20} +1.62223 q^{21} +3.15971 q^{22} -5.56669 q^{23} +1.68972 q^{24} +1.00000 q^{25} +0.884065 q^{26} +3.83361 q^{27} +3.55741 q^{28} -4.73062 q^{29} -0.479522 q^{30} -4.48089 q^{31} +5.80852 q^{32} -3.18142 q^{33} -0.451784 q^{34} -2.33464 q^{35} +3.83556 q^{36} +7.79252 q^{37} -0.890138 q^{39} -2.43177 q^{40} +8.69901 q^{41} +1.11951 q^{42} +9.58799 q^{43} -6.97660 q^{44} -2.51718 q^{45} -3.84162 q^{46} +6.32695 q^{47} -0.951467 q^{48} -1.54945 q^{49} +0.690109 q^{50} +0.454887 q^{51} -1.95200 q^{52} +6.60153 q^{53} +2.64561 q^{54} +4.57857 q^{55} +5.67731 q^{56} -3.26464 q^{58} +5.89287 q^{59} +1.05878 q^{60} -7.49401 q^{61} -3.09230 q^{62} +5.87672 q^{63} +1.26988 q^{64} +1.28105 q^{65} -2.19553 q^{66} +13.0603 q^{67} +0.997532 q^{68} +3.86801 q^{69} -1.61116 q^{70} +3.75158 q^{71} +6.12121 q^{72} +7.96380 q^{73} +5.37769 q^{74} -0.694850 q^{75} -10.6893 q^{77} -0.614292 q^{78} +6.30946 q^{79} +1.36931 q^{80} +4.88777 q^{81} +6.00326 q^{82} -9.83696 q^{83} -2.47187 q^{84} -0.654656 q^{85} +6.61676 q^{86} +3.28707 q^{87} -11.1340 q^{88} +12.1784 q^{89} -1.73713 q^{90} -2.99080 q^{91} +8.48224 q^{92} +3.11355 q^{93} +4.36629 q^{94} -4.03605 q^{96} +4.20974 q^{97} -1.06929 q^{98} -11.5251 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.690109	0.487981	0.243990	−	0.969778i	$-0.421543\pi$
$2$	0.690109	0.487981	0.243990	+	0.969778i	$0.421543\pi$
$3$	−0.694850	−0.401172	−0.200586	−	0.979676i	$-0.564285\pi$
$3$	−0.694850	−0.401172	−0.200586	+	0.979676i	$0.564285\pi$
$4$	−1.52375	−0.761875
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.479522	−0.195764
$7$	−2.33464	−0.882412	−0.441206	−	0.897406i	$-0.645449\pi$
$7$	−2.33464	−0.882412	−0.441206	+	0.897406i	$0.645449\pi$
$8$	−2.43177	−0.859761
$9$	−2.51718	−0.839061
$10$	0.690109	0.218232
$11$	4.57857	1.38049	0.690246	−	0.723575i	$-0.257502\pi$
$11$	4.57857	1.38049	0.690246	+	0.723575i	$0.257502\pi$
$12$	1.05878	0.305643
$13$	1.28105	0.355300	0.177650	−	0.984094i	$-0.443151\pi$
$13$	1.28105	0.355300	0.177650	+	0.984094i	$0.443151\pi$
$14$	−1.61116	−0.430600
$15$	−0.694850	−0.179409
$16$	1.36931	0.342328
$17$	−0.654656	−0.158777	−0.0793887	−	0.996844i	$-0.525297\pi$
$17$	−0.654656	−0.158777	−0.0793887	+	0.996844i	$0.525297\pi$
$18$	−1.73713	−0.409446
$19$	0	0
$19$	0	0
$20$	−1.52375	−0.340721
$21$	1.62223	0.353999
$22$	3.15971	0.673653
$23$	−5.56669	−1.16073	−0.580367	−	0.814355i	$-0.697091\pi$
$23$	−5.56669	−1.16073	−0.580367	+	0.814355i	$0.697091\pi$
$24$	1.68972	0.344912
$25$	1.00000	0.200000
$26$	0.884065	0.173379
$27$	3.83361	0.737779
$28$	3.55741	0.672287
$29$	−4.73062	−0.878455	−0.439227	−	0.898376i	$-0.644748\pi$
$29$	−4.73062	−0.878455	−0.439227	+	0.898376i	$0.644748\pi$
$30$	−0.479522	−0.0875483
$31$	−4.48089	−0.804792	−0.402396	−	0.915466i	$-0.631823\pi$
$31$	−4.48089	−0.804792	−0.402396	+	0.915466i	$0.631823\pi$
$32$	5.80852	1.02681
$33$	−3.18142	−0.553814
$34$	−0.451784	−0.0774803
$35$	−2.33464	−0.394627
$36$	3.83556	0.639260
$37$	7.79252	1.28108	0.640541	−	0.767924i	$-0.278710\pi$
$37$	7.79252	1.28108	0.640541	+	0.767924i	$0.278710\pi$
$38$	0	0
$39$	−0.890138	−0.142536
$40$	−2.43177	−0.384497
$41$	8.69901	1.35856	0.679279	−	0.733881i	$-0.262293\pi$
$41$	8.69901	1.35856	0.679279	+	0.733881i	$0.262293\pi$
$42$	1.11951	0.172744
$43$	9.58799	1.46215	0.731077	−	0.682295i	$-0.239018\pi$
$43$	9.58799	1.46215	0.731077	+	0.682295i	$0.239018\pi$
$44$	−6.97660	−1.05176
$45$	−2.51718	−0.375240
$46$	−3.84162	−0.566416
$47$	6.32695	0.922881	0.461441	−	0.887171i	$-0.347333\pi$
$47$	6.32695	0.922881	0.461441	+	0.887171i	$0.347333\pi$
$48$	−0.951467	−0.137332
$49$	−1.54945	−0.221349
$50$	0.690109	0.0975961
$51$	0.454887	0.0636970
$52$	−1.95200	−0.270694
$53$	6.60153	0.906790	0.453395	−	0.891310i	$-0.350213\pi$
$53$	6.60153	0.906790	0.453395	+	0.891310i	$0.350213\pi$
$54$	2.64561	0.360022
$55$	4.57857	0.617375
$56$	5.67731	0.758663
$57$	0	0
$58$	−3.26464	−0.428669
$59$	5.89287	0.767186	0.383593	−	0.923502i	$-0.374687\pi$
$59$	5.89287	0.767186	0.383593	+	0.923502i	$0.374687\pi$
$60$	1.05878	0.136688
$61$	−7.49401	−0.959510	−0.479755	−	0.877403i	$-0.659274\pi$
$61$	−7.49401	−0.959510	−0.479755	+	0.877403i	$0.659274\pi$
$62$	−3.09230	−0.392723
$63$	5.87672	0.740398
$64$	1.26988	0.158735
$65$	1.28105	0.158895
$66$	−2.19553	−0.270251
$67$	13.0603	1.59557	0.797785	−	0.602943i	$-0.206005\pi$
$67$	13.0603	1.59557	0.797785	+	0.602943i	$0.206005\pi$
$68$	0.997532	0.120968
$69$	3.86801	0.465654
$70$	−1.61116	−0.192570
$71$	3.75158	0.445230	0.222615	−	0.974906i	$-0.428541\pi$
$71$	3.75158	0.445230	0.222615	+	0.974906i	$0.428541\pi$
$72$	6.12121	0.721392
$73$	7.96380	0.932093	0.466046	−	0.884760i	$-0.345678\pi$
$73$	7.96380	0.932093	0.466046	+	0.884760i	$0.345678\pi$
$74$	5.37769	0.625143
$75$	−0.694850	−0.0802343
$76$	0	0
$77$	−10.6893	−1.21816
$78$	−0.614292	−0.0695549
$79$	6.30946	0.709870	0.354935	−	0.934891i	$-0.384503\pi$
$79$	6.30946	0.709870	0.354935	+	0.934891i	$0.384503\pi$
$80$	1.36931	0.153094
$81$	4.88777	0.543085
$82$	6.00326	0.662950
$83$	−9.83696	−1.07975	−0.539873	−	0.841746i	$-0.681528\pi$
$83$	−9.83696	−1.07975	−0.539873	+	0.841746i	$0.681528\pi$
$84$	−2.47187	−0.269703
$85$	−0.654656	−0.0710074
$86$	6.61676	0.713503
$87$	3.28707	0.352411
$88$	−11.1340	−1.18689
$89$	12.1784	1.29091	0.645453	−	0.763800i	$-0.276669\pi$
$89$	12.1784	1.29091	0.645453	+	0.763800i	$0.276669\pi$
$90$	−1.73713	−0.183110
$91$	−2.99080	−0.313521
$92$	8.48224	0.884335
$93$	3.11355	0.322860
$94$	4.36629	0.450348
$95$	0	0
$96$	−4.03605	−0.411927
$97$	4.20974	0.427434	0.213717	−	0.976896i	$-0.431443\pi$
$97$	4.20974	0.427434	0.213717	+	0.976896i	$0.431443\pi$
$98$	−1.06929	−0.108014
$99$	−11.5251	−1.15832
$100$	−1.52375	−0.152375
$101$	−0.0570702	−0.00567870	−0.00283935	−	0.999996i	$-0.500904\pi$
$101$	−0.0570702	−0.00567870	−0.00283935	+	0.999996i	$0.500904\pi$
$102$	0.313922	0.0310829
$103$	7.24341	0.713714	0.356857	−	0.934159i	$-0.383848\pi$
$103$	7.24341	0.713714	0.356857	+	0.934159i	$0.383848\pi$
$104$	−3.11522	−0.305473
$105$	1.62223	0.158313
$106$	4.55577	0.442496
$107$	14.8600	1.43657	0.718283	−	0.695751i	$-0.244928\pi$
$107$	14.8600	1.43657	0.718283	+	0.695751i	$0.244928\pi$
$108$	−5.84147	−0.562096
$109$	−13.4191	−1.28532	−0.642659	−	0.766152i	$-0.722169\pi$
$109$	−13.4191	−1.28532	−0.642659	+	0.766152i	$0.722169\pi$
$110$	3.15971	0.301267
$111$	−5.41463	−0.513934
$112$	−3.19686	−0.302075
$113$	−4.23499	−0.398395	−0.199197	−	0.979959i	$-0.563833\pi$
$113$	−4.23499	−0.398395	−0.199197	+	0.979959i	$0.563833\pi$
$114$	0	0
$115$	−5.56669	−0.519096
$116$	7.20829	0.669273
$117$	−3.22464	−0.298118
$118$	4.06672	0.374372
$119$	1.52839	0.140107
$120$	1.68972	0.154249
$121$	9.96333	0.905757
$122$	−5.17168	−0.468222
$123$	−6.04450	−0.545015
$124$	6.82776	0.613151
$125$	1.00000	0.0894427
$126$	4.05558	0.361300
$127$	−18.2675	−1.62098	−0.810491	−	0.585751i	$-0.800800\pi$
$127$	−18.2675	−1.62098	−0.810491	+	0.585751i	$0.800800\pi$
$128$	−10.7407	−0.949351
$129$	−6.66221	−0.586575
$130$	0.884065	0.0775376
$131$	8.40537	0.734380	0.367190	−	0.930146i	$-0.380320\pi$
$131$	8.40537	0.734380	0.367190	+	0.930146i	$0.380320\pi$
$132$	4.84769	0.421937
$133$	0	0
$134$	9.01302	0.778607
$135$	3.83361	0.329945
$136$	1.59197	0.136511
$137$	−11.8592	−1.01320	−0.506598	−	0.862182i	$-0.669097\pi$
$137$	−11.8592	−1.01320	−0.506598	+	0.862182i	$0.669097\pi$
$138$	2.66935	0.227230
$139$	0.0374119	0.00317324	0.00158662	−	0.999999i	$-0.499495\pi$
$139$	0.0374119	0.00317324	0.00158662	+	0.999999i	$0.499495\pi$
$140$	3.55741	0.300656
$141$	−4.39628	−0.370234
$142$	2.58900	0.217264
$143$	5.86539	0.490488
$144$	−3.44681	−0.287235
$145$	−4.73062	−0.392857
$146$	5.49589	0.454843
$147$	1.07663	0.0887991
$148$	−11.8739	−0.976025
$149$	−9.70097	−0.794735	−0.397367	−	0.917660i	$-0.630076\pi$
$149$	−9.70097	−0.794735	−0.397367	+	0.917660i	$0.630076\pi$
$150$	−0.479522	−0.0391528
$151$	4.60766	0.374966	0.187483	−	0.982268i	$-0.439967\pi$
$151$	4.60766	0.374966	0.187483	+	0.982268i	$0.439967\pi$
$152$	0	0
$153$	1.64789	0.133224
$154$	−7.37680	−0.594439
$155$	−4.48089	−0.359914
$156$	1.35635	0.108595
$157$	−20.4033	−1.62836	−0.814181	−	0.580611i	$-0.802814\pi$
$157$	−20.4033	−1.62836	−0.814181	+	0.580611i	$0.802814\pi$
$158$	4.35422	0.346403
$159$	−4.58707	−0.363778
$160$	5.80852	0.459204
$161$	12.9962	1.02425
$162$	3.37309	0.265015
$163$	−3.79362	−0.297139	−0.148569	−	0.988902i	$-0.547467\pi$
$163$	−3.79362	−0.297139	−0.148569	+	0.988902i	$0.547467\pi$
$164$	−13.2551	−1.03505
$165$	−3.18142	−0.247673
$166$	−6.78857	−0.526895
$167$	15.4984	1.19930	0.599650	−	0.800263i	$-0.295307\pi$
$167$	15.4984	1.19930	0.599650	+	0.800263i	$0.295307\pi$
$168$	−3.94488	−0.304354
$169$	−11.3589	−0.873762
$170$	−0.451784	−0.0346502
$171$	0	0
$172$	−14.6097	−1.11398
$173$	16.9161	1.28611	0.643053	−	0.765822i	$-0.277668\pi$
$173$	16.9161	1.28611	0.643053	+	0.765822i	$0.277668\pi$
$174$	2.26844	0.171970
$175$	−2.33464	−0.176482
$176$	6.26950	0.472581
$177$	−4.09466	−0.307773
$178$	8.40441	0.629937
$179$	3.05264	0.228165	0.114082	−	0.993471i	$-0.463607\pi$
$179$	3.05264	0.228165	0.114082	+	0.993471i	$0.463607\pi$
$180$	3.83556	0.285886
$181$	−24.4861	−1.82004	−0.910019	−	0.414568i	$-0.863933\pi$
$181$	−24.4861	−1.82004	−0.910019	+	0.414568i	$0.863933\pi$
$182$	−2.06397	−0.152992
$183$	5.20721	0.384928
$184$	13.5369	0.997954
$185$	7.79252	0.572917
$186$	2.14869	0.157549
$187$	−2.99739	−0.219191
$188$	−9.64070	−0.703120
$189$	−8.95012	−0.651025
$190$	0	0
$191$	−1.69095	−0.122353	−0.0611765	−	0.998127i	$-0.519485\pi$
$191$	−1.69095	−0.122353	−0.0611765	+	0.998127i	$0.519485\pi$
$192$	−0.882376	−0.0636800
$193$	17.7909	1.28062	0.640309	−	0.768117i	$-0.278806\pi$
$193$	17.7909	1.28062	0.640309	+	0.768117i	$0.278806\pi$
$194$	2.90518	0.208580
$195$	−0.890138	−0.0637441
$196$	2.36097	0.168641
$197$	14.5015	1.03319	0.516595	−	0.856230i	$-0.327199\pi$
$197$	14.5015	1.03319	0.516595	+	0.856230i	$0.327199\pi$
$198$	−7.95358	−0.565236
$199$	−12.0337	−0.853043	−0.426522	−	0.904477i	$-0.640261\pi$
$199$	−12.0337	−0.853043	−0.426522	+	0.904477i	$0.640261\pi$
$200$	−2.43177	−0.171952
$201$	−9.07494	−0.640097
$202$	−0.0393847	−0.00277109
$203$	11.0443	0.775159
$204$	−0.693135	−0.0485291
$205$	8.69901	0.607565
$206$	4.99874	0.348279
$207$	14.0124	0.973927
$208$	1.75416	0.121629
$209$	0	0
$210$	1.11951	0.0772537
$211$	8.07544	0.555936	0.277968	−	0.960590i	$-0.410339\pi$
$211$	8.07544	0.555936	0.277968	+	0.960590i	$0.410339\pi$
$212$	−10.0591	−0.690860
$213$	−2.60678	−0.178614
$214$	10.2550	0.701016
$215$	9.58799	0.653895
$216$	−9.32247	−0.634314
$217$	10.4613	0.710158
$218$	−9.26065	−0.627210
$219$	−5.53365	−0.373929
$220$	−6.97660	−0.470362
$221$	−0.838647	−0.0564135
$222$	−3.73668	−0.250790
$223$	15.1794	1.01649	0.508244	−	0.861213i	$-0.330295\pi$
$223$	15.1794	1.01649	0.508244	+	0.861213i	$0.330295\pi$
$224$	−13.5608	−0.906070
$225$	−2.51718	−0.167812
$226$	−2.92261	−0.194409
$227$	−20.9433	−1.39005	−0.695026	−	0.718984i	$-0.744607\pi$
$227$	−20.9433	−1.39005	−0.695026	+	0.718984i	$0.744607\pi$
$228$	0	0
$229$	28.1530	1.86040	0.930200	−	0.367054i	$-0.119633\pi$
$229$	28.1530	1.86040	0.930200	+	0.367054i	$0.119633\pi$
$230$	−3.84162	−0.253309
$231$	7.42748	0.488692
$232$	11.5038	0.755261
$233$	20.8855	1.36826	0.684128	−	0.729362i	$-0.260183\pi$
$233$	20.8855	1.36826	0.684128	+	0.729362i	$0.260183\pi$
$234$	−2.22535	−0.145476
$235$	6.32695	0.412725
$236$	−8.97926	−0.584500
$237$	−4.38413	−0.284780
$238$	1.05475	0.0683695
$239$	−1.23961	−0.0801838	−0.0400919	−	0.999196i	$-0.512765\pi$
$239$	−1.23961	−0.0801838	−0.0400919	+	0.999196i	$0.512765\pi$
$240$	−0.951467	−0.0614169
$241$	1.17084	0.0754207	0.0377104	−	0.999289i	$-0.487994\pi$
$241$	1.17084	0.0754207	0.0377104	+	0.999289i	$0.487994\pi$
$242$	6.87578	0.441992
$243$	−14.8971	−0.955650
$244$	11.4190	0.731026
$245$	−1.54945	−0.0989904
$246$	−4.17137	−0.265957
$247$	0	0
$248$	10.8965	0.691929
$249$	6.83521	0.433164
$250$	0.690109	0.0436463
$251$	21.9943	1.38827	0.694135	−	0.719845i	$-0.255787\pi$
$251$	21.9943	1.38827	0.694135	+	0.719845i	$0.255787\pi$
$252$	−8.95466	−0.564090
$253$	−25.4875	−1.60238
$254$	−12.6066	−0.791008
$255$	0.454887	0.0284862
$256$	−9.95200	−0.622000
$257$	16.6654	1.03956	0.519780	−	0.854300i	$-0.326014\pi$
$257$	16.6654	1.03956	0.519780	+	0.854300i	$0.326014\pi$
$258$	−4.59765	−0.286237
$259$	−18.1927	−1.13044
$260$	−1.95200	−0.121058
$261$	11.9078	0.737077
$262$	5.80062	0.358363
$263$	−4.32310	−0.266574	−0.133287	−	0.991077i	$-0.542553\pi$
$263$	−4.32310	−0.266574	−0.133287	+	0.991077i	$0.542553\pi$
$264$	7.73648	0.476148
$265$	6.60153	0.405529
$266$	0	0
$267$	−8.46214	−0.517875
$268$	−19.9006	−1.21562
$269$	−24.2977	−1.48146	−0.740729	−	0.671804i	$-0.765519\pi$
$269$	−24.2977	−1.48146	−0.740729	+	0.671804i	$0.765519\pi$
$270$	2.64561	0.161007
$271$	−8.21744	−0.499174	−0.249587	−	0.968352i	$-0.580295\pi$
$271$	−8.21744	−0.499174	−0.249587	+	0.968352i	$0.580295\pi$
$272$	−0.896429	−0.0543540
$273$	2.07815	0.125776
$274$	−8.18411	−0.494420
$275$	4.57857	0.276098
$276$	−5.89388	−0.354770
$277$	19.3202	1.16084	0.580419	−	0.814318i	$-0.302889\pi$
$277$	19.3202	1.16084	0.580419	+	0.814318i	$0.302889\pi$
$278$	0.0258183	0.00154848
$279$	11.2792	0.675270
$280$	5.67731	0.339284
$281$	7.94483	0.473949	0.236974	−	0.971516i	$-0.423844\pi$
$281$	7.94483	0.473949	0.236974	+	0.971516i	$0.423844\pi$
$282$	−3.03391	−0.180667
$283$	−16.9129	−1.00537	−0.502683	−	0.864471i	$-0.667654\pi$
$283$	−16.9129	−1.00537	−0.502683	+	0.864471i	$0.667654\pi$
$284$	−5.71646	−0.339210
$285$	0	0
$286$	4.04775	0.239349
$287$	−20.3091	−1.19881
$288$	−14.6211	−0.861557
$289$	−16.5714	−0.974790
$290$	−3.26464	−0.191707
$291$	−2.92514	−0.171475
$292$	−12.1348	−0.710138
$293$	−4.83067	−0.282211	−0.141105	−	0.989995i	$-0.545066\pi$
$293$	−4.83067	−0.282211	−0.141105	+	0.989995i	$0.545066\pi$
$294$	0.742993	0.0433322
$295$	5.89287	0.343096
$296$	−18.9496	−1.10142
$297$	17.5525	1.01850
$298$	−6.69473	−0.387815
$299$	−7.13121	−0.412409
$300$	1.05878	0.0611285
$301$	−22.3845	−1.29022
$302$	3.17979	0.182976
$303$	0.0396552	0.00227813
$304$	0	0
$305$	−7.49401	−0.429106
$306$	1.13722	0.0650107
$307$	−6.15320	−0.351181	−0.175591	−	0.984463i	$-0.556184\pi$
$307$	−6.15320	−0.351181	−0.175591	+	0.984463i	$0.556184\pi$
$308$	16.2879	0.928087
$309$	−5.03308	−0.286322
$310$	−3.09230	−0.175631
$311$	2.86153	0.162262	0.0811311	−	0.996703i	$-0.474147\pi$
$311$	2.86153	0.162262	0.0811311	+	0.996703i	$0.474147\pi$
$312$	2.16461	0.122547
$313$	−6.48116	−0.366337	−0.183168	−	0.983082i	$-0.558635\pi$
$313$	−6.48116	−0.366337	−0.183168	+	0.983082i	$0.558635\pi$
$314$	−14.0805	−0.794609
$315$	5.87672	0.331116
$316$	−9.61405	−0.540832
$317$	−31.0277	−1.74269	−0.871344	−	0.490674i	$-0.836751\pi$
$317$	−31.0277	−1.74269	−0.871344	+	0.490674i	$0.836751\pi$
$318$	−3.16558	−0.177517
$319$	−21.6595	−1.21270
$320$	1.26988	0.0709885
$321$	−10.3254	−0.576310
$322$	8.96881	0.499812
$323$	0	0
$324$	−7.44773	−0.413763
$325$	1.28105	0.0710599
$326$	−2.61801	−0.144998
$327$	9.32427	0.515633
$328$	−21.1540	−1.16803
$329$	−14.7712	−0.814361
$330$	−2.19553	−0.120860
$331$	17.6048	0.967645	0.483823	−	0.875166i	$-0.339248\pi$
$331$	17.6048	0.967645	0.483823	+	0.875166i	$0.339248\pi$
$332$	14.9891	0.822632
$333$	−19.6152	−1.07491
$334$	10.6956	0.585235
$335$	13.0603	0.713560
$336$	2.22134	0.121184
$337$	27.6679	1.50717	0.753584	−	0.657352i	$-0.228323\pi$
$337$	27.6679	1.50717	0.753584	+	0.657352i	$0.228323\pi$
$338$	−7.83888	−0.426379
$339$	2.94268	0.159825
$340$	0.997532	0.0540987
$341$	−20.5161	−1.11101
$342$	0	0
$343$	19.9599	1.07773
$344$	−23.3158	−1.25710
$345$	3.86801	0.208247
$346$	11.6739	0.627594
$347$	−21.2814	−1.14244	−0.571222	−	0.820795i	$-0.693531\pi$
$347$	−21.2814	−1.14244	−0.571222	+	0.820795i	$0.693531\pi$
$348$	−5.00868	−0.268493
$349$	19.6499	1.05183	0.525917	−	0.850536i	$-0.323722\pi$
$349$	19.6499	1.05183	0.525917	+	0.850536i	$0.323722\pi$
$350$	−1.61116	−0.0861200
$351$	4.91105	0.262133
$352$	26.5947	1.41750
$353$	6.46602	0.344151	0.172076	−	0.985084i	$-0.444953\pi$
$353$	6.46602	0.344151	0.172076	+	0.985084i	$0.444953\pi$
$354$	−2.82576	−0.150187
$355$	3.75158	0.199113
$356$	−18.5568	−0.983509
$357$	−1.06200	−0.0562070
$358$	2.10665	0.111340
$359$	−19.3953	−1.02365	−0.511823	−	0.859091i	$-0.671030\pi$
$359$	−19.3953	−1.02365	−0.511823	+	0.859091i	$0.671030\pi$
$360$	6.12121	0.322616
$361$	0	0
$362$	−16.8981	−0.888143
$363$	−6.92302	−0.363364
$364$	4.55723	0.238864
$365$	7.96380	0.416845
$366$	3.59354	0.187837
$367$	30.0325	1.56768	0.783842	−	0.620961i	$-0.213257\pi$
$367$	30.0325	1.56768	0.783842	+	0.620961i	$0.213257\pi$
$368$	−7.62254	−0.397352
$369$	−21.8970	−1.13991
$370$	5.37769	0.279573
$371$	−15.4122	−0.800162
$372$	−4.74427	−0.245979
$373$	−4.95796	−0.256713	−0.128357	−	0.991728i	$-0.540970\pi$
$373$	−4.95796	−0.256713	−0.128357	+	0.991728i	$0.540970\pi$
$374$	−2.06852	−0.106961
$375$	−0.694850	−0.0358819
$376$	−15.3857	−0.793457
$377$	−6.06017	−0.312115
$378$	−6.17655	−0.317688
$379$	−4.05839	−0.208465	−0.104233	−	0.994553i	$-0.533239\pi$
$379$	−4.05839	−0.208465	−0.104233	+	0.994553i	$0.533239\pi$
$380$	0	0
$381$	12.6932	0.650292
$382$	−1.16694	−0.0597059
$383$	−2.40937	−0.123113	−0.0615566	−	0.998104i	$-0.519606\pi$
$383$	−2.40937	−0.123113	−0.0615566	+	0.998104i	$0.519606\pi$
$384$	7.46316	0.380853
$385$	−10.6893	−0.544779
$386$	12.2777	0.624917
$387$	−24.1347	−1.22684
$388$	−6.41459	−0.325652
$389$	−5.97284	−0.302835	−0.151417	−	0.988470i	$-0.548384\pi$
$389$	−5.97284	−0.302835	−0.151417	+	0.988470i	$0.548384\pi$
$390$	−0.614292	−0.0311059
$391$	3.64426	0.184298
$392$	3.76790	0.190307
$393$	−5.84047	−0.294613
$394$	10.0076	0.504177
$395$	6.30946	0.317464
$396$	17.5614	0.882493
$397$	−28.3680	−1.42375	−0.711874	−	0.702307i	$-0.752153\pi$
$397$	−28.3680	−1.42375	−0.711874	+	0.702307i	$0.752153\pi$
$398$	−8.30453	−0.416268
$399$	0	0
$400$	1.36931	0.0684657
$401$	−31.3702	−1.56655	−0.783277	−	0.621673i	$-0.786453\pi$
$401$	−31.3702	−1.56655	−0.783277	+	0.621673i	$0.786453\pi$
$402$	−6.26270	−0.312355
$403$	−5.74025	−0.285942
$404$	0.0869607	0.00432646
$405$	4.88777	0.242875
$406$	7.62178	0.378262
$407$	35.6786	1.76852
$408$	−1.10618	−0.0547642
$409$	−29.7846	−1.47276	−0.736378	−	0.676571i	$-0.763465\pi$
$409$	−29.7846	−1.47276	−0.736378	+	0.676571i	$0.763465\pi$
$410$	6.00326	0.296480
$411$	8.24034	0.406466
$412$	−11.0371	−0.543761
$413$	−13.7577	−0.676974
$414$	9.67006	0.475258
$415$	−9.83696	−0.482877
$416$	7.44101	0.364825
$417$	−0.0259957	−0.00127301
$418$	0	0
$419$	35.7692	1.74744	0.873719	−	0.486431i	$-0.161702\pi$
$419$	35.7692	1.74744	0.873719	+	0.486431i	$0.161702\pi$
$420$	−2.47187	−0.120615
$421$	−38.0392	−1.85392	−0.926958	−	0.375165i	$-0.877586\pi$
$421$	−38.0392	−1.85392	−0.926958	+	0.375165i	$0.877586\pi$
$422$	5.57293	0.271286
$423$	−15.9261	−0.774354
$424$	−16.0534	−0.779622
$425$	−0.654656	−0.0317555
$426$	−1.79896	−0.0871600
$427$	17.4958	0.846683
$428$	−22.6429	−1.09448
$429$	−4.07556	−0.196770
$430$	6.61676	0.319088
$431$	−8.38795	−0.404033	−0.202017	−	0.979382i	$-0.564750\pi$
$431$	−8.38795	−0.404033	−0.202017	+	0.979382i	$0.564750\pi$
$432$	5.24942	0.252563
$433$	23.2157	1.11568	0.557838	−	0.829950i	$-0.311631\pi$
$433$	23.2157	1.11568	0.557838	+	0.829950i	$0.311631\pi$
$434$	7.21942	0.346543
$435$	3.28707	0.157603
$436$	20.4474	0.979252
$437$	0	0
$438$	−3.81882	−0.182470
$439$	17.7148	0.845482	0.422741	−	0.906251i	$-0.361068\pi$
$439$	17.7148	0.845482	0.422741	+	0.906251i	$0.361068\pi$
$440$	−11.1340	−0.530794
$441$	3.90024	0.185726
$442$	−0.578758	−0.0275287
$443$	1.78354	0.0847387	0.0423693	−	0.999102i	$-0.486509\pi$
$443$	1.78354	0.0847387	0.0423693	+	0.999102i	$0.486509\pi$
$444$	8.25054	0.391553
$445$	12.1784	0.577311
$446$	10.4754	0.496026
$447$	6.74072	0.318825
$448$	−2.96472	−0.140070
$449$	8.85687	0.417982	0.208991	−	0.977918i	$-0.432982\pi$
$449$	8.85687	0.417982	0.208991	+	0.977918i	$0.432982\pi$
$450$	−1.73713	−0.0818891
$451$	39.8291	1.87548
$452$	6.45307	0.303527
$453$	−3.20163	−0.150426
$454$	−14.4531	−0.678319
$455$	−2.99080	−0.140211
$456$	0	0
$457$	3.00530	0.140582	0.0702909	−	0.997527i	$-0.477607\pi$
$457$	3.00530	0.140582	0.0702909	+	0.997527i	$0.477607\pi$
$458$	19.4286	0.907839
$459$	−2.50970	−0.117143
$460$	8.48224	0.395486
$461$	20.1165	0.936920	0.468460	−	0.883485i	$-0.344809\pi$
$461$	20.1165	0.936920	0.468460	+	0.883485i	$0.344809\pi$
$462$	5.12577	0.238472
$463$	8.15436	0.378965	0.189483	−	0.981884i	$-0.439319\pi$
$463$	8.15436	0.378965	0.189483	+	0.981884i	$0.439319\pi$
$464$	−6.47771	−0.300720
$465$	3.11355	0.144387
$466$	14.4133	0.667683
$467$	−6.15746	−0.284933	−0.142467	−	0.989800i	$-0.545503\pi$
$467$	−6.15746	−0.284933	−0.142467	+	0.989800i	$0.545503\pi$
$468$	4.91355	0.227129
$469$	−30.4911	−1.40795
$470$	4.36629	0.201402
$471$	14.1772	0.653253
$472$	−14.3301	−0.659596
$473$	43.8993	2.01849
$474$	−3.02553	−0.138967
$475$	0	0
$476$	−2.32888	−0.106744
$477$	−16.6173	−0.760852
$478$	−0.855467	−0.0391281
$479$	34.0906	1.55764	0.778819	−	0.627249i	$-0.215819\pi$
$479$	34.0906	1.55764	0.778819	+	0.627249i	$0.215819\pi$
$480$	−4.03605	−0.184219
$481$	9.98262	0.455168
$482$	0.808010	0.0368039
$483$	−9.03042	−0.410898
$484$	−15.1816	−0.690074
$485$	4.20974	0.191155
$486$	−10.2806	−0.466338
$487$	28.5720	1.29472	0.647360	−	0.762184i	$-0.275873\pi$
$487$	28.5720	1.29472	0.647360	+	0.762184i	$0.275873\pi$
$488$	18.2237	0.824949
$489$	2.63599	0.119204
$490$	−1.06929	−0.0483054
$491$	−5.24108	−0.236527	−0.118263	−	0.992982i	$-0.537733\pi$
$491$	−5.24108	−0.236527	−0.118263	+	0.992982i	$0.537733\pi$
$492$	9.21031	0.415233
$493$	3.09693	0.139479
$494$	0	0
$495$	−11.5251	−0.518015
$496$	−6.13575	−0.275503
$497$	−8.75859	−0.392876
$498$	4.71704	0.211375
$499$	37.8830	1.69588	0.847939	−	0.530094i	$-0.177843\pi$
$499$	37.8830	1.69588	0.847939	+	0.530094i	$0.177843\pi$
$500$	−1.52375	−0.0681442
$501$	−10.7690	−0.481125
$502$	15.1785	0.677449
$503$	14.9240	0.665429	0.332714	−	0.943028i	$-0.392035\pi$
$503$	14.9240	0.665429	0.332714	+	0.943028i	$0.392035\pi$
$504$	−14.2908	−0.636565
$505$	−0.0570702	−0.00253959
$506$	−17.5891	−0.781932
$507$	7.89273	0.350529
$508$	27.8352	1.23499
$509$	−13.1036	−0.580806	−0.290403	−	0.956904i	$-0.593789\pi$
$509$	−13.1036	−0.580806	−0.290403	+	0.956904i	$0.593789\pi$
$510$	0.313922	0.0139007
$511$	−18.5926	−0.822490
$512$	14.6134	0.645827
$513$	0	0
$514$	11.5010	0.507285
$515$	7.24341	0.319183
$516$	10.1515	0.446897
$517$	28.9684	1.27403
$518$	−12.5550	−0.551634
$519$	−11.7541	−0.515949
$520$	−3.11522	−0.136612
$521$	4.11662	0.180352	0.0901761	−	0.995926i	$-0.471257\pi$
$521$	4.11662	0.180352	0.0901761	+	0.995926i	$0.471257\pi$
$522$	8.21771	0.359679
$523$	−8.31707	−0.363680	−0.181840	−	0.983328i	$-0.558205\pi$
$523$	−8.31707	−0.363680	−0.181840	+	0.983328i	$0.558205\pi$
$524$	−12.8077	−0.559506
$525$	1.62223	0.0707997
$526$	−2.98341	−0.130083
$527$	2.93344	0.127783
$528$	−4.35636	−0.189586
$529$	7.98801	0.347305
$530$	4.55577	0.197890
$531$	−14.8334	−0.643716
$532$	0	0
$533$	11.1439	0.482695
$534$	−5.83980	−0.252713
$535$	14.8600	0.642452
$536$	−31.7596	−1.37181
$537$	−2.12112	−0.0915332
$538$	−16.7681	−0.722922
$539$	−7.09425	−0.305571
$540$	−5.84147	−0.251377
$541$	−40.1330	−1.72545	−0.862727	−	0.505671i	$-0.831245\pi$
$541$	−40.1330	−1.72545	−0.862727	+	0.505671i	$0.831245\pi$
$542$	−5.67093	−0.243587
$543$	17.0142	0.730147
$544$	−3.80258	−0.163034
$545$	−13.4191	−0.574812
$546$	1.43415	0.0613760
$547$	25.3441	1.08363	0.541817	−	0.840497i	$-0.317737\pi$
$547$	25.3441	1.08363	0.541817	+	0.840497i	$0.317737\pi$
$548$	18.0704	0.771929
$549$	18.8638	0.805087
$550$	3.15971	0.134731
$551$	0	0
$552$	−9.40612	−0.400351
$553$	−14.7303	−0.626398
$554$	13.3330	0.566466
$555$	−5.41463	−0.229838
$556$	−0.0570064	−0.00241761
$557$	11.6827	0.495013	0.247506	−	0.968886i	$-0.420389\pi$
$557$	11.6827	0.495013	0.247506	+	0.968886i	$0.420389\pi$
$558$	7.78390	0.329519
$559$	12.2827	0.519503
$560$	−3.19686	−0.135092
$561$	2.08273	0.0879331
$562$	5.48279	0.231278
$563$	16.8011	0.708082	0.354041	−	0.935230i	$-0.384807\pi$
$563$	16.8011	0.708082	0.354041	+	0.935230i	$0.384807\pi$
$564$	6.69883	0.282072
$565$	−4.23499	−0.178168
$566$	−11.6717	−0.490599
$567$	−11.4112	−0.479225
$568$	−9.12297	−0.382792
$569$	−36.3784	−1.52506	−0.762530	−	0.646953i	$-0.776043\pi$
$569$	−36.3784	−1.52506	−0.762530	+	0.646953i	$0.776043\pi$
$570$	0	0
$571$	33.6369	1.40766	0.703831	−	0.710368i	$-0.251471\pi$
$571$	33.6369	1.40766	0.703831	+	0.710368i	$0.251471\pi$
$572$	−8.93738	−0.373691
$573$	1.17496	0.0490845
$574$	−14.0155	−0.584995
$575$	−5.56669	−0.232147
$576$	−3.19652	−0.133189
$577$	26.8493	1.11775	0.558876	−	0.829251i	$-0.311233\pi$
$577$	26.8493	1.11775	0.558876	+	0.829251i	$0.311233\pi$
$578$	−11.4361	−0.475678
$579$	−12.3620	−0.513748
$580$	7.20829	0.299308
$581$	22.9658	0.952781
$582$	−2.01866	−0.0836763
$583$	30.2256	1.25182
$584$	−19.3661	−0.801377
$585$	−3.22464	−0.133323
$586$	−3.33369	−0.137713
$587$	17.1108	0.706239	0.353119	−	0.935578i	$-0.385121\pi$
$587$	17.1108	0.706239	0.353119	+	0.935578i	$0.385121\pi$
$588$	−1.64052	−0.0676538
$589$	0	0
$590$	4.06672	0.167424
$591$	−10.0764	−0.414487
$592$	10.6704	0.438551
$593$	−40.7457	−1.67323	−0.836613	−	0.547795i	$-0.815468\pi$
$593$	−40.7457	−1.67323	−0.836613	+	0.547795i	$0.815468\pi$
$594$	12.1131	0.497007
$595$	1.52839	0.0626578
$596$	14.7819	0.605488
$597$	8.36158	0.342217
$598$	−4.92131	−0.201247
$599$	12.0286	0.491473	0.245737	−	0.969337i	$-0.420970\pi$
$599$	12.0286	0.491473	0.245737	+	0.969337i	$0.420970\pi$
$600$	1.68972	0.0689823
$601$	−12.5963	−0.513814	−0.256907	−	0.966436i	$-0.582703\pi$
$601$	−12.5963	−0.513814	−0.256907	+	0.966436i	$0.582703\pi$
$602$	−15.4478	−0.629604
$603$	−32.8752	−1.33878
$604$	−7.02092	−0.285677
$605$	9.96333	0.405067
$606$	0.0273664	0.00111168
$607$	5.16663	0.209707	0.104854	−	0.994488i	$-0.466563\pi$
$607$	5.16663	0.209707	0.104854	+	0.994488i	$0.466563\pi$
$608$	0	0
$609$	−7.67414	−0.310972
$610$	−5.17168	−0.209395
$611$	8.10515	0.327899
$612$	−2.51097	−0.101500
$613$	−0.405786	−0.0163895	−0.00819477	−	0.999966i	$-0.502609\pi$
$613$	−0.405786	−0.0163895	−0.00819477	+	0.999966i	$0.502609\pi$
$614$	−4.24637	−0.171370
$615$	−6.04450	−0.243738
$616$	25.9940	1.04733
$617$	10.0431	0.404320	0.202160	−	0.979353i	$-0.435204\pi$
$617$	10.0431	0.404320	0.202160	+	0.979353i	$0.435204\pi$
$618$	−3.47337	−0.139720
$619$	−16.3316	−0.656424	−0.328212	−	0.944604i	$-0.606446\pi$
$619$	−16.3316	−0.656424	−0.328212	+	0.944604i	$0.606446\pi$
$620$	6.82776	0.274210
$621$	−21.3405	−0.856366
$622$	1.97476	0.0791808
$623$	−28.4322	−1.13911
$624$	−1.21888	−0.0487942
$625$	1.00000	0.0400000
$626$	−4.47271	−0.178765
$627$	0	0
$628$	31.0896	1.24061
$629$	−5.10142	−0.203407
$630$	4.05558	0.161578
$631$	4.62540	0.184134	0.0920671	−	0.995753i	$-0.470653\pi$
$631$	4.62540	0.184134	0.0920671	+	0.995753i	$0.470653\pi$
$632$	−15.3432	−0.610319
$633$	−5.61122	−0.223026
$634$	−21.4125	−0.850397
$635$	−18.2675	−0.724925
$636$	6.98955	0.277154
$637$	−1.98492	−0.0786453
$638$	−14.9474	−0.591774
$639$	−9.44341	−0.373575
$640$	−10.7407	−0.424563
$641$	−26.9379	−1.06398	−0.531992	−	0.846750i	$-0.678556\pi$
$641$	−26.9379	−1.06398	−0.531992	+	0.846750i	$0.678556\pi$
$642$	−7.12567	−0.281228
$643$	−6.07573	−0.239604	−0.119802	−	0.992798i	$-0.538226\pi$
$643$	−6.07573	−0.239604	−0.119802	+	0.992798i	$0.538226\pi$
$644$	−19.8030	−0.780347
$645$	−6.66221	−0.262324
$646$	0	0
$647$	−14.8936	−0.585529	−0.292765	−	0.956185i	$-0.594575\pi$
$647$	−14.8936	−0.585529	−0.292765	+	0.956185i	$0.594575\pi$
$648$	−11.8859	−0.466923
$649$	26.9809	1.05909
$650$	0.884065	0.0346759
$651$	−7.26902	−0.284895
$652$	5.78052	0.226383
$653$	5.04594	0.197463	0.0987315	−	0.995114i	$-0.468522\pi$
$653$	5.04594	0.197463	0.0987315	+	0.995114i	$0.468522\pi$
$654$	6.43476	0.251619
$655$	8.40537	0.328425
$656$	11.9117	0.465073
$657$	−20.0464	−0.782083
$658$	−10.1937	−0.397392
$659$	31.6251	1.23194	0.615970	−	0.787770i	$-0.288764\pi$
$659$	31.6251	1.23194	0.615970	+	0.787770i	$0.288764\pi$
$660$	4.84769	0.188696
$661$	−11.3474	−0.441362	−0.220681	−	0.975346i	$-0.570828\pi$
$661$	−11.3474	−0.441362	−0.220681	+	0.975346i	$0.570828\pi$
$662$	12.1492	0.472192
$663$	0.582734	0.0226315
$664$	23.9212	0.928323
$665$	0	0
$666$	−13.5366	−0.524534
$667$	26.3339	1.01965
$668$	−23.6156	−0.913716
$669$	−10.5474	−0.407786
$670$	9.01302	0.348204
$671$	−34.3119	−1.32459
$672$	9.42272	0.363489
$673$	7.52384	0.290023	0.145011	−	0.989430i	$-0.453678\pi$
$673$	7.52384	0.290023	0.145011	+	0.989430i	$0.453678\pi$
$674$	19.0939	0.735468
$675$	3.83361	0.147556
$676$	17.3081	0.665698
$677$	−18.2370	−0.700905	−0.350453	−	0.936580i	$-0.613972\pi$
$677$	−18.2370	−0.700905	−0.350453	+	0.936580i	$0.613972\pi$
$678$	2.03077	0.0779913
$679$	−9.82824	−0.377173
$680$	1.59197	0.0610494
$681$	14.5524	0.557650
$682$	−14.1583	−0.542151
$683$	28.9640	1.10828	0.554139	−	0.832424i	$-0.313048\pi$
$683$	28.9640	1.10828	0.554139	+	0.832424i	$0.313048\pi$
$684$	0	0
$685$	−11.8592	−0.453115
$686$	13.7745	0.525913
$687$	−19.5621	−0.746340
$688$	13.1290	0.500537
$689$	8.45689	0.322182
$690$	2.66935	0.101620
$691$	−32.6010	−1.24020	−0.620100	−	0.784523i	$-0.712908\pi$
$691$	−32.6010	−1.24020	−0.620100	+	0.784523i	$0.712908\pi$
$692$	−25.7759	−0.979851
$693$	26.9070	1.02211
$694$	−14.6865	−0.557491
$695$	0.0374119	0.00141911
$696$	−7.99341	−0.302989
$697$	−5.69486	−0.215708
$698$	13.5606	0.513275
$699$	−14.5123	−0.548906
$700$	3.55741	0.134457
$701$	−0.915294	−0.0345702	−0.0172851	−	0.999851i	$-0.505502\pi$
$701$	−0.915294	−0.0345702	−0.0172851	+	0.999851i	$0.505502\pi$
$702$	3.38916	0.127916
$703$	0	0
$704$	5.81424	0.219133
$705$	−4.39628	−0.165574
$706$	4.46226	0.167939
$707$	0.133239	0.00501095
$708$	6.23923	0.234485
$709$	16.0499	0.602766	0.301383	−	0.953503i	$-0.402552\pi$
$709$	16.0499	0.602766	0.301383	+	0.953503i	$0.402552\pi$
$710$	2.58900	0.0971633
$711$	−15.8821	−0.595625
$712$	−29.6150	−1.10987
$713$	24.9437	0.934150
$714$	−0.732895	−0.0274279
$715$	5.86539	0.219353
$716$	−4.65146	−0.173833
$717$	0.861344	0.0321675
$718$	−13.3849	−0.499520
$719$	−32.9750	−1.22976	−0.614881	−	0.788620i	$-0.710796\pi$
$719$	−32.9750	−1.22976	−0.614881	+	0.788620i	$0.710796\pi$
$720$	−3.44681	−0.128455
$721$	−16.9108	−0.629790
$722$	0	0
$723$	−0.813561	−0.0302567
$724$	37.3107	1.38664
$725$	−4.73062	−0.175691
$726$	−4.77763	−0.177315
$727$	9.45972	0.350842	0.175421	−	0.984494i	$-0.443871\pi$
$727$	9.45972	0.350842	0.175421	+	0.984494i	$0.443871\pi$
$728$	7.27293	0.269553
$729$	−4.31205	−0.159706
$730$	5.49589	0.203412
$731$	−6.27683	−0.232157
$732$	−7.93449	−0.293267
$733$	10.4590	0.386313	0.193156	−	0.981168i	$-0.438127\pi$
$733$	10.4590	0.386313	0.193156	+	0.981168i	$0.438127\pi$
$734$	20.7257	0.764999
$735$	1.07663	0.0397122
$736$	−32.3342	−1.19185
$737$	59.7975	2.20267
$738$	−15.1113	−0.556255
$739$	−7.79695	−0.286816	−0.143408	−	0.989664i	$-0.545806\pi$
$739$	−7.79695	−0.286816	−0.143408	+	0.989664i	$0.545806\pi$
$740$	−11.8739	−0.436491
$741$	0	0
$742$	−10.6361	−0.390463
$743$	20.4170	0.749025	0.374513	−	0.927222i	$-0.377810\pi$
$743$	20.4170	0.749025	0.374513	+	0.927222i	$0.377810\pi$
$744$	−7.57143	−0.277582
$745$	−9.70097	−0.355416
$746$	−3.42153	−0.125271
$747$	24.7614	0.905973
$748$	4.56727	0.166996
$749$	−34.6927	−1.26764
$750$	−0.479522	−0.0175097
$751$	35.0196	1.27788	0.638941	−	0.769256i	$-0.279373\pi$
$751$	35.0196	1.27788	0.638941	+	0.769256i	$0.279373\pi$
$752$	8.66358	0.315928
$753$	−15.2828	−0.556935
$754$	−4.18218	−0.152306
$755$	4.60766	0.167690
$756$	13.6377	0.496000
$757$	35.4906	1.28993	0.644965	−	0.764212i	$-0.276872\pi$
$757$	35.4906	1.28993	0.644965	+	0.764212i	$0.276872\pi$
$758$	−2.80073	−0.101727
$759$	17.7100	0.642831
$760$	0	0
$761$	−24.2563	−0.879290	−0.439645	−	0.898172i	$-0.644896\pi$
$761$	−24.2563	−0.879290	−0.439645	+	0.898172i	$0.644896\pi$
$762$	8.75969	0.317330
$763$	31.3288	1.13418
$764$	2.57659	0.0932177
$765$	1.64789	0.0595796
$766$	−1.66273	−0.0600768
$767$	7.54907	0.272581
$768$	6.91514	0.249529
$769$	−25.7679	−0.929214	−0.464607	−	0.885517i	$-0.653804\pi$
$769$	−25.7679	−0.929214	−0.464607	+	0.885517i	$0.653804\pi$
$770$	−7.37680	−0.265841
$771$	−11.5800	−0.417042
$772$	−27.1089	−0.975671
$773$	37.9486	1.36492	0.682459	−	0.730924i	$-0.260911\pi$
$773$	37.9486	1.36492	0.682459	+	0.730924i	$0.260911\pi$
$774$	−16.6556	−0.598673
$775$	−4.48089	−0.160958
$776$	−10.2371	−0.367491
$777$	12.6412	0.453501
$778$	−4.12191	−0.147778
$779$	0	0
$780$	1.35635	0.0485650
$781$	17.1769	0.614637
$782$	2.51494	0.0899340
$783$	−18.1354	−0.648106
$784$	−2.12168	−0.0757742
$785$	−20.4033	−0.728226
$786$	−4.03056	−0.143765
$787$	−6.64512	−0.236873	−0.118437	−	0.992962i	$-0.537788\pi$
$787$	−6.64512	−0.236873	−0.118437	+	0.992962i	$0.537788\pi$
$788$	−22.0967	−0.787162
$789$	3.00391	0.106942
$790$	4.35422	0.154916
$791$	9.88720	0.351548
$792$	28.0264	0.995876
$793$	−9.60021	−0.340913
$794$	−19.5770	−0.694761
$795$	−4.58707	−0.162687
$796$	18.3363	0.649912
$797$	15.3836	0.544916	0.272458	−	0.962168i	$-0.412163\pi$
$797$	15.3836	0.544916	0.272458	+	0.962168i	$0.412163\pi$
$798$	0	0
$799$	−4.14198	−0.146533
$800$	5.80852	0.205362
$801$	−30.6552	−1.08315
$802$	−21.6489	−0.764448
$803$	36.4629	1.28675
$804$	13.8279	0.487674
$805$	12.9962	0.458057
$806$	−3.96140	−0.139534
$807$	16.8833	0.594319
$808$	0.138782	0.00488232
$809$	12.2547	0.430853	0.215426	−	0.976520i	$-0.430886\pi$
$809$	12.2547	0.430853	0.215426	+	0.976520i	$0.430886\pi$
$810$	3.37309	0.118518
$811$	50.3951	1.76961	0.884806	−	0.465960i	$-0.154291\pi$
$811$	50.3951	1.76961	0.884806	+	0.465960i	$0.154291\pi$
$812$	−16.8288	−0.590574
$813$	5.70989	0.200255
$814$	24.6221	0.863005
$815$	−3.79362	−0.132885
$816$	0.622883	0.0218053
$817$	0	0
$818$	−20.5546	−0.718676
$819$	7.52838	0.263063
$820$	−13.2551	−0.462889
$821$	−6.18354	−0.215807	−0.107903	−	0.994161i	$-0.534414\pi$
$821$	−6.18354	−0.215807	−0.107903	+	0.994161i	$0.534414\pi$
$822$	5.68673	0.198347
$823$	28.8312	1.00499	0.502496	−	0.864579i	$-0.332415\pi$
$823$	28.8312	1.00499	0.502496	+	0.864579i	$0.332415\pi$
$824$	−17.6143	−0.613624
$825$	−3.18142	−0.110763
$826$	−9.49434	−0.330350
$827$	−20.5185	−0.713499	−0.356750	−	0.934200i	$-0.616115\pi$
$827$	−20.5185	−0.713499	−0.356750	+	0.934200i	$0.616115\pi$
$828$	−21.3514	−0.742011
$829$	−8.58215	−0.298070	−0.149035	−	0.988832i	$-0.547617\pi$
$829$	−8.58215	−0.298070	−0.149035	+	0.988832i	$0.547617\pi$
$830$	−6.78857	−0.235635
$831$	−13.4246	−0.465695
$832$	1.62678	0.0563985
$833$	1.01435	0.0351453
$834$	−0.0179398	−0.000621206 0
$835$	15.4984	0.536343
$836$	0	0
$837$	−17.1780	−0.593759
$838$	24.6846	0.852716
$839$	41.9885	1.44961	0.724803	−	0.688957i	$-0.241931\pi$
$839$	41.9885	1.44961	0.724803	+	0.688957i	$0.241931\pi$
$840$	−3.94488	−0.136111
$841$	−6.62120	−0.228317
$842$	−26.2512	−0.904675
$843$	−5.52046	−0.190135
$844$	−12.3050	−0.423554
$845$	−11.3589	−0.390758
$846$	−10.9907	−0.377870
$847$	−23.2608	−0.799251
$848$	9.03956	0.310420
$849$	11.7519	0.403324
$850$	−0.451784	−0.0154961
$851$	−43.3785	−1.48700
$852$	3.97208	0.136081
$853$	−15.4622	−0.529415	−0.264708	−	0.964329i	$-0.585275\pi$
$853$	−15.4622	−0.529415	−0.264708	+	0.964329i	$0.585275\pi$
$854$	12.0740	0.413165
$855$	0	0
$856$	−36.1360	−1.23510
$857$	26.5651	0.907447	0.453723	−	0.891143i	$-0.350095\pi$
$857$	26.5651	0.907447	0.453723	+	0.891143i	$0.350095\pi$
$858$	−2.81258	−0.0960199
$859$	23.2572	0.793527	0.396763	−	0.917921i	$-0.370133\pi$
$859$	23.2572	0.793527	0.396763	+	0.917921i	$0.370133\pi$
$860$	−14.6097	−0.498187
$861$	14.1118	0.480927
$862$	−5.78860	−0.197160
$863$	−0.114750	−0.00390613	−0.00195307	−	0.999998i	$-0.500622\pi$
$863$	−0.114750	−0.00390613	−0.00195307	+	0.999998i	$0.500622\pi$
$864$	22.2676	0.757559
$865$	16.9161	0.575164
$866$	16.0214	0.544428
$867$	11.5146	0.391058
$868$	−15.9404	−0.541052
$869$	28.8883	0.979970
$870$	2.26844	0.0769072
$871$	16.7309	0.566905
$872$	32.6322	1.10507
$873$	−10.5967	−0.358644
$874$	0	0
$875$	−2.33464	−0.0789253
$876$	8.43189	0.284887
$877$	23.1936	0.783193	0.391596	−	0.920137i	$-0.371923\pi$
$877$	23.1936	0.783193	0.391596	+	0.920137i	$0.371923\pi$
$878$	12.2252	0.412579
$879$	3.35659	0.113215
$880$	6.26950	0.211345
$881$	8.30638	0.279849	0.139924	−	0.990162i	$-0.455314\pi$
$881$	8.30638	0.279849	0.139924	+	0.990162i	$0.455314\pi$
$882$	2.69159	0.0906305
$883$	−29.7372	−1.00074	−0.500368	−	0.865813i	$-0.666802\pi$
$883$	−29.7372	−1.00074	−0.500368	+	0.865813i	$0.666802\pi$
$884$	1.27789	0.0429801
$885$	−4.09466	−0.137640
$886$	1.23084	0.0413508
$887$	−11.4927	−0.385886	−0.192943	−	0.981210i	$-0.561803\pi$
$887$	−11.4927	−0.385886	−0.192943	+	0.981210i	$0.561803\pi$
$888$	13.1671	0.441860
$889$	42.6482	1.43037
$890$	8.40441	0.281716
$891$	22.3790	0.749725
$892$	−23.1296	−0.774436
$893$	0	0
$894$	4.65183	0.155580
$895$	3.05264	0.102038
$896$	25.0756	0.837718
$897$	4.95512	0.165447
$898$	6.11221	0.203967
$899$	21.1974	0.706974
$900$	3.83556	0.127852
$901$	−4.32173	−0.143978
$902$	27.4864	0.915196
$903$	15.5539	0.517601
$904$	10.2985	0.342524
$905$	−24.4861	−0.813945
$906$	−2.20947	−0.0734048
$907$	23.7983	0.790209	0.395104	−	0.918636i	$-0.370708\pi$
$907$	23.7983	0.790209	0.395104	+	0.918636i	$0.370708\pi$
$908$	31.9123	1.05905
$909$	0.143656	0.00476478
$910$	−2.06397	−0.0684201
$911$	23.2831	0.771405	0.385702	−	0.922623i	$-0.373959\pi$
$911$	23.2831	0.771405	0.385702	+	0.922623i	$0.373959\pi$
$912$	0	0
$913$	−45.0392	−1.49058
$914$	2.07398	0.0686012
$915$	5.20721	0.172145
$916$	−42.8981	−1.41739
$917$	−19.6235	−0.648026
$918$	−1.73196	−0.0571633
$919$	37.0813	1.22320	0.611599	−	0.791168i	$-0.290526\pi$
$919$	37.0813	1.22320	0.611599	+	0.791168i	$0.290526\pi$
$920$	13.5369	0.446299
$921$	4.27555	0.140884
$922$	13.8826	0.457199
$923$	4.80596	0.158190
$924$	−11.3176	−0.372322
$925$	7.79252	0.256216
$926$	5.62740	0.184928
$927$	−18.2330	−0.598850
$928$	−27.4779	−0.902006
$929$	20.0904	0.659144	0.329572	−	0.944130i	$-0.393096\pi$
$929$	20.0904	0.659144	0.329572	+	0.944130i	$0.393096\pi$
$930$	2.14869	0.0704582
$931$	0	0
$932$	−31.8243	−1.04244
$933$	−1.98833	−0.0650950
$934$	−4.24932	−0.139042
$935$	−2.99739	−0.0980251
$936$	7.84159	0.256310
$937$	−20.0938	−0.656435	−0.328217	−	0.944602i	$-0.606448\pi$
$937$	−20.0938	−0.656435	−0.328217	+	0.944602i	$0.606448\pi$
$938$	−21.0422	−0.687052
$939$	4.50343	0.146964
$940$	−9.64070	−0.314445
$941$	4.25742	0.138788	0.0693939	−	0.997589i	$-0.477893\pi$
$941$	4.25742	0.138788	0.0693939	+	0.997589i	$0.477893\pi$
$942$	9.78384	0.318775
$943$	−48.4247	−1.57692
$944$	8.06918	0.262630
$945$	−8.95012	−0.291147
$946$	30.2953	0.984985
$947$	−43.8324	−1.42436	−0.712181	−	0.701996i	$-0.752292\pi$
$947$	−43.8324	−1.42436	−0.712181	+	0.701996i	$0.752292\pi$
$948$	6.68032	0.216967
$949$	10.2020	0.331172
$950$	0	0
$951$	21.5596	0.699117
$952$	−3.71669	−0.120459
$953$	30.1693	0.977281	0.488640	−	0.872485i	$-0.337493\pi$
$953$	30.1693	0.977281	0.488640	+	0.872485i	$0.337493\pi$
$954$	−11.4677	−0.371281
$955$	−1.69095	−0.0547179
$956$	1.88886	0.0610900
$957$	15.0501	0.486501
$958$	23.5262	0.760097
$959$	27.6869	0.894057
$960$	−0.882376	−0.0284786
$961$	−10.9216	−0.352309
$962$	6.88909	0.222113
$963$	−37.4052	−1.20537
$964$	−1.78407	−0.0574612
$965$	17.7909	0.572710
$966$	−6.23197	−0.200510
$967$	12.4401	0.400047	0.200023	−	0.979791i	$-0.435898\pi$
$967$	12.4401	0.400047	0.200023	+	0.979791i	$0.435898\pi$
$968$	−24.2285	−0.778735
$969$	0	0
$970$	2.90518	0.0932797
$971$	−29.5761	−0.949141	−0.474571	−	0.880217i	$-0.657397\pi$
$971$	−29.5761	−0.949141	−0.474571	+	0.880217i	$0.657397\pi$
$972$	22.6995	0.728086
$973$	−0.0873434	−0.00280010
$974$	19.7178	0.631799
$975$	−0.890138	−0.0285072
$976$	−10.2616	−0.328467
$977$	−39.3785	−1.25983	−0.629915	−	0.776664i	$-0.716910\pi$
$977$	−39.3785	−1.25983	−0.629915	+	0.776664i	$0.716910\pi$
$978$	1.81912	0.0581691
$979$	55.7596	1.78208
$980$	2.36097	0.0754183
$981$	33.7784	1.07846
$982$	−3.61691	−0.115420
$983$	−38.4207	−1.22543	−0.612716	−	0.790303i	$-0.709923\pi$
$983$	−38.4207	−1.22543	−0.612716	+	0.790303i	$0.709923\pi$
$984$	14.6988	0.468582
$985$	14.5015	0.462057
$986$	2.13722	0.0680629
$987$	10.2637	0.326699
$988$	0	0
$989$	−53.3733	−1.69717
$990$	−7.95358	−0.252781
$991$	10.4699	0.332589	0.166294	−	0.986076i	$-0.446820\pi$
$991$	10.4699	0.332589	0.166294	+	0.986076i	$0.446820\pi$
$992$	−26.0273	−0.826369
$993$	−12.2327	−0.388192
$994$	−6.04438	−0.191716
$995$	−12.0337	−0.381492
$996$	−10.4151	−0.330016
$997$	−3.60915	−0.114303	−0.0571515	−	0.998366i	$-0.518202\pi$
$997$	−3.60915	−0.114303	−0.0571515	+	0.998366i	$0.518202\pi$
$998$	26.1434	0.827555
$999$	29.8735	0.945156

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.a.v.1.5		9
5.4	even	2		9025.2.a.cc.1.5		9
19.4	even	9		95.2.k.a.16.2	yes	18
19.5	even	9		95.2.k.a.6.2	✓	18
19.18	odd	2		1805.2.a.s.1.5		9
57.5	odd	18		855.2.bs.c.766.2		18
57.23	odd	18		855.2.bs.c.586.2		18
95.4	even	18		475.2.l.c.301.2		18
95.23	odd	36		475.2.u.b.149.5		36
95.24	even	18		475.2.l.c.101.2		18
95.42	odd	36		475.2.u.b.149.2		36
95.43	odd	36		475.2.u.b.424.2		36
95.62	odd	36		475.2.u.b.424.5		36
95.94	odd	2		9025.2.a.cf.1.5		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.a.6.2	✓	18	19.5	even	9
95.2.k.a.16.2	yes	18	19.4	even	9
475.2.l.c.101.2		18	95.24	even	18
475.2.l.c.301.2		18	95.4	even	18
475.2.u.b.149.2		36	95.42	odd	36
475.2.u.b.149.5		36	95.23	odd	36
475.2.u.b.424.2		36	95.43	odd	36
475.2.u.b.424.5		36	95.62	odd	36
855.2.bs.c.586.2		18	57.23	odd	18
855.2.bs.c.766.2		18	57.5	odd	18
1805.2.a.s.1.5		9	19.18	odd	2
1805.2.a.v.1.5		9	1.1	even	1	trivial
9025.2.a.cc.1.5		9	5.4	even	2
9025.2.a.cf.1.5		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)

\(f(q)\)	\(=\)	\(q+0.690109 q^{2} -0.694850 q^{3} -1.52375 q^{4} +1.00000 q^{5} -0.479522 q^{6} -2.33464 q^{7} -2.43177 q^{8} -2.51718 q^{9} +O(q^{10})\)	\(q+0.690109 q^{2} -0.694850 q^{3} -1.52375 q^{4} +1.00000 q^{5} -0.479522 q^{6} -2.33464 q^{7} -2.43177 q^{8} -2.51718 q^{9} +0.690109 q^{10} +4.57857 q^{11} +1.05878 q^{12} +1.28105 q^{13} -1.61116 q^{14} -0.694850 q^{15} +1.36931 q^{16} -0.654656 q^{17} -1.73713 q^{18} -1.52375 q^{20} +1.62223 q^{21} +3.15971 q^{22} -5.56669 q^{23} +1.68972 q^{24} +1.00000 q^{25} +0.884065 q^{26} +3.83361 q^{27} +3.55741 q^{28} -4.73062 q^{29} -0.479522 q^{30} -4.48089 q^{31} +5.80852 q^{32} -3.18142 q^{33} -0.451784 q^{34} -2.33464 q^{35} +3.83556 q^{36} +7.79252 q^{37} -0.890138 q^{39} -2.43177 q^{40} +8.69901 q^{41} +1.11951 q^{42} +9.58799 q^{43} -6.97660 q^{44} -2.51718 q^{45} -3.84162 q^{46} +6.32695 q^{47} -0.951467 q^{48} -1.54945 q^{49} +0.690109 q^{50} +0.454887 q^{51} -1.95200 q^{52} +6.60153 q^{53} +2.64561 q^{54} +4.57857 q^{55} +5.67731 q^{56} -3.26464 q^{58} +5.89287 q^{59} +1.05878 q^{60} -7.49401 q^{61} -3.09230 q^{62} +5.87672 q^{63} +1.26988 q^{64} +1.28105 q^{65} -2.19553 q^{66} +13.0603 q^{67} +0.997532 q^{68} +3.86801 q^{69} -1.61116 q^{70} +3.75158 q^{71} +6.12121 q^{72} +7.96380 q^{73} +5.37769 q^{74} -0.694850 q^{75} -10.6893 q^{77} -0.614292 q^{78} +6.30946 q^{79} +1.36931 q^{80} +4.88777 q^{81} +6.00326 q^{82} -9.83696 q^{83} -2.47187 q^{84} -0.654656 q^{85} +6.61676 q^{86} +3.28707 q^{87} -11.1340 q^{88} +12.1784 q^{89} -1.73713 q^{90} -2.99080 q^{91} +8.48224 q^{92} +3.11355 q^{93} +4.36629 q^{94} -4.03605 q^{96} +4.20974 q^{97} -1.06929 q^{98} -11.5251 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 6 q^{2} + 9 q^{3} + 6 q^{4} + 9 q^{5} + 12 q^{6} + 6 q^{8} + 6 q^{9}+O(q^{10}) \) 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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