LMFDB - Embedded newform 1805.2.a.s.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:	$1$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 3x^{8} - 6x^{7} + 16x^{6} + 12x^{5} - 27x^{4} - 8x^{3} + 15x^{2} - 1 $ x^9 - 3x^8 - 6x^7 + 16x^6 + 12x^5 - 27x^4 - 8x^3 + 15*x^2 - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
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	$-0.578457\pi$
$2$	−0.690109	−0.487981	−0.243990	+	0.969778i	$0.578457\pi$
$3$	0.694850	0.401172	0.200586	−	0.979676i	$-0.435715\pi$
$3$	0.694850	0.401172	0.200586	+	0.979676i	$0.435715\pi$
$4$	−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	$-0.556849\pi$
$13$	−1.28105	−0.355300	−0.177650	+	0.984094i	$0.556849\pi$
$14$	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	$-0.355252\pi$
$29$	4.73062	0.878455	0.439227	+	0.898376i	$0.355252\pi$
$30$	−0.479522	−0.0875483
$31$	4.48089	0.804792	0.402396	−	0.915466i	$-0.368177\pi$
$31$	4.48089	0.804792	0.402396	+	0.915466i	$0.368177\pi$
$32$	−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	$-0.721290\pi$
$37$	−7.79252	−1.28108	−0.640541	+	0.767924i	$0.721290\pi$
$38$	0	0
$39$	−0.890138	−0.142536
$40$	2.43177	0.384497
$41$	−8.69901	−1.35856	−0.679279	−	0.733881i	$-0.737707\pi$
$41$	−8.69901	−1.35856	−0.679279	+	0.733881i	$0.737707\pi$
$42$	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	$-0.649787\pi$
$53$	−6.60153	−0.906790	−0.453395	+	0.891310i	$0.649787\pi$
$54$	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	$-0.625313\pi$
$59$	−5.89287	−0.767186	−0.383593	+	0.923502i	$0.625313\pi$
$60$	−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	$-0.793995\pi$
$67$	−13.0603	−1.59557	−0.797785	+	0.602943i	$0.793995\pi$
$68$	0.997532	0.120968
$69$	−3.86801	−0.465654
$70$	1.61116	0.192570
$71$	−3.75158	−0.445230	−0.222615	−	0.974906i	$-0.571459\pi$
$71$	−3.75158	−0.445230	−0.222615	+	0.974906i	$0.571459\pi$
$72$	−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	$-0.615497\pi$
$79$	−6.30946	−0.709870	−0.354935	+	0.934891i	$0.615497\pi$
$80$	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	$-0.723331\pi$
$89$	−12.1784	−1.29091	−0.645453	+	0.763800i	$0.723331\pi$
$90$	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	$-0.568557\pi$
$97$	−4.20974	−0.427434	−0.213717	+	0.976896i	$0.568557\pi$
$98$	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	$-0.616152\pi$
$103$	−7.24341	−0.713714	−0.356857	+	0.934159i	$0.616152\pi$
$104$	−3.11522	−0.305473
$105$	−1.62223	−0.158313
$106$	4.55577	0.442496
$107$	−14.8600	−1.43657	−0.718283	−	0.695751i	$-0.755072\pi$
$107$	−14.8600	−1.43657	−0.718283	+	0.695751i	$0.755072\pi$
$108$	5.84147	0.562096
$109$	13.4191	1.28532	0.642659	−	0.766152i	$-0.277831\pi$
$109$	13.4191	1.28532	0.642659	+	0.766152i	$0.277831\pi$
$110$	−3.15971	−0.301267
$111$	−5.41463	−0.513934
$112$	−3.19686	−0.302075
$113$	4.23499	0.398395	0.199197	−	0.979959i	$-0.436167\pi$
$113$	4.23499	0.398395	0.199197	+	0.979959i	$0.436167\pi$
$114$	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	$-0.199200\pi$
$127$	18.2675	1.62098	0.810491	+	0.585751i	$0.199200\pi$
$128$	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	$-0.560033\pi$
$151$	−4.60766	−0.374966	−0.187483	+	0.982268i	$0.560033\pi$
$152$	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	$-0.704693\pi$
$167$	−15.4984	−1.19930	−0.599650	+	0.800263i	$0.704693\pi$
$168$	−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	$-0.722332\pi$
$173$	−16.9161	−1.28611	−0.643053	+	0.765822i	$0.722332\pi$
$174$	−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	$-0.536393\pi$
$179$	−3.05264	−0.228165	−0.114082	+	0.993471i	$0.536393\pi$
$180$	3.83556	0.285886
$181$	24.4861	1.82004	0.910019	−	0.414568i	$-0.136067\pi$
$181$	24.4861	1.82004	0.910019	+	0.414568i	$0.136067\pi$
$182$	−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	$-0.721194\pi$
$193$	−17.7909	−1.28062	−0.640309	+	0.768117i	$0.721194\pi$
$194$	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	$-0.589661\pi$
$211$	−8.07544	−0.555936	−0.277968	+	0.960590i	$0.589661\pi$
$212$	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	$-0.669705\pi$
$223$	−15.1794	−1.01649	−0.508244	+	0.861213i	$0.669705\pi$
$224$	13.5608	0.906070
$225$	−2.51718	−0.167812
$226$	−2.92261	−0.194409
$227$	20.9433	1.39005	0.695026	−	0.718984i	$-0.255393\pi$
$227$	20.9433	1.39005	0.695026	+	0.718984i	$0.255393\pi$
$228$	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	$-0.512006\pi$
$241$	−1.17084	−0.0754207	−0.0377104	+	0.999289i	$0.512006\pi$
$242$	−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	$-0.673986\pi$
$257$	−16.6654	−1.03956	−0.519780	+	0.854300i	$0.673986\pi$
$258$	−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	$-0.234481\pi$
$269$	24.2977	1.48146	0.740729	+	0.671804i	$0.234481\pi$
$270$	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	$-0.576156\pi$
$281$	−7.94483	−0.473949	−0.236974	+	0.971516i	$0.576156\pi$
$282$	−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	$-0.454934\pi$
$293$	4.83067	0.282211	0.141105	+	0.989995i	$0.454934\pi$
$294$	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	$-0.443816\pi$
$307$	6.15320	0.351181	0.175591	+	0.984463i	$0.443816\pi$
$308$	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	$-0.163249\pi$
$317$	31.0277	1.74269	0.871344	+	0.490674i	$0.163249\pi$
$318$	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	$-0.660752\pi$
$331$	−17.6048	−0.967645	−0.483823	+	0.875166i	$0.660752\pi$
$332$	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	$-0.771677\pi$
$337$	−27.6679	−1.50717	−0.753584	+	0.657352i	$0.771677\pi$
$338$	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	$-0.459030\pi$
$373$	4.95796	0.256713	0.128357	+	0.991728i	$0.459030\pi$
$374$	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	$-0.466761\pi$
$379$	4.05839	0.208465	0.104233	+	0.994553i	$0.466761\pi$
$380$	0	0
$381$	12.6932	0.650292
$382$	1.16694	0.0597059
$383$	2.40937	0.123113	0.0615566	−	0.998104i	$-0.480394\pi$
$383$	2.40937	0.123113	0.0615566	+	0.998104i	$0.480394\pi$
$384$	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	$-0.213547\pi$
$401$	31.3702	1.56655	0.783277	+	0.621673i	$0.213547\pi$
$402$	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	$-0.236535\pi$
$409$	29.7846	1.47276	0.736378	+	0.676571i	$0.236535\pi$
$410$	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	$-0.122414\pi$
$421$	38.0392	1.85392	0.926958	+	0.375165i	$0.122414\pi$
$422$	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	$-0.435250\pi$
$431$	8.38795	0.404033	0.202017	+	0.979382i	$0.435250\pi$
$432$	−5.24942	−0.252563
$433$	−23.2157	−1.11568	−0.557838	−	0.829950i	$-0.688369\pi$
$433$	−23.2157	−1.11568	−0.557838	+	0.829950i	$0.688369\pi$
$434$	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	$-0.638932\pi$
$439$	−17.7148	−0.845482	−0.422741	+	0.906251i	$0.638932\pi$
$440$	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	$-0.567018\pi$
$449$	−8.85687	−0.417982	−0.208991	+	0.977918i	$0.567018\pi$
$450$	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	$-0.724127\pi$
$487$	−28.5720	−1.29472	−0.647360	+	0.762184i	$0.724127\pi$
$488$	−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	$-0.406211\pi$
$509$	13.1036	0.580806	0.290403	+	0.956904i	$0.406211\pi$
$510$	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	$-0.528743\pi$
$521$	−4.11662	−0.180352	−0.0901761	+	0.995926i	$0.528743\pi$
$522$	8.21771	0.359679
$523$	8.31707	0.363680	0.181840	−	0.983328i	$-0.441795\pi$
$523$	8.31707	0.363680	0.181840	+	0.983328i	$0.441795\pi$
$524$	−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	$-0.682263\pi$
$547$	−25.3441	−1.08363	−0.541817	+	0.840497i	$0.682263\pi$
$548$	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	$-0.615193\pi$
$563$	−16.8011	−0.708082	−0.354041	+	0.935230i	$0.615193\pi$
$564$	−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	$-0.223957\pi$
$569$	36.3784	1.52506	0.762530	+	0.646953i	$0.223957\pi$
$570$	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	$-0.579030\pi$
$599$	−12.0286	−0.491473	−0.245737	+	0.969337i	$0.579030\pi$
$600$	1.68972	0.0689823
$601$	12.5963	0.513814	0.256907	−	0.966436i	$-0.417297\pi$
$601$	12.5963	0.513814	0.256907	+	0.966436i	$0.417297\pi$
$602$	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	$-0.533437\pi$
$607$	−5.16663	−0.209707	−0.104854	+	0.994488i	$0.533437\pi$
$608$	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	$-0.321444\pi$
$641$	26.9379	1.06398	0.531992	+	0.846750i	$0.321444\pi$
$642$	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	$-0.711236\pi$
$659$	−31.6251	−1.23194	−0.615970	+	0.787770i	$0.711236\pi$
$660$	−4.84769	−0.188696
$661$	11.3474	0.441362	0.220681	−	0.975346i	$-0.429172\pi$
$661$	11.3474	0.441362	0.220681	+	0.975346i	$0.429172\pi$
$662$	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	$-0.546322\pi$
$673$	−7.52384	−0.290023	−0.145011	+	0.989430i	$0.546322\pi$
$674$	19.0939	0.735468
$675$	−3.83361	−0.147556
$676$	17.3081	0.665698
$677$	18.2370	0.700905	0.350453	−	0.936580i	$-0.386028\pi$
$677$	18.2370	0.700905	0.350453	+	0.936580i	$0.386028\pi$
$678$	−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	$-0.686952\pi$
$683$	−28.9640	−1.10828	−0.554139	+	0.832424i	$0.686952\pi$
$684$	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	$-0.622190\pi$
$743$	−20.4170	−0.749025	−0.374513	+	0.927222i	$0.622190\pi$
$744$	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	$-0.720627\pi$
$751$	−35.0196	−1.27788	−0.638941	+	0.769256i	$0.720627\pi$
$752$	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	$-0.739089\pi$
$773$	−37.9486	−1.36492	−0.682459	+	0.730924i	$0.739089\pi$
$774$	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	$-0.462212\pi$
$787$	6.64512	0.236873	0.118437	+	0.992962i	$0.462212\pi$
$788$	−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	$-0.587837\pi$
$797$	−15.3836	−0.544916	−0.272458	+	0.962168i	$0.587837\pi$
$798$	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	$-0.845709\pi$
$811$	−50.3951	−1.76961	−0.884806	+	0.465960i	$0.845709\pi$
$812$	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	$-0.383885\pi$
$827$	20.5185	0.713499	0.356750	+	0.934200i	$0.383885\pi$
$828$	−21.3514	−0.742011
$829$	8.58215	0.298070	0.149035	−	0.988832i	$-0.452383\pi$
$829$	8.58215	0.298070	0.149035	+	0.988832i	$0.452383\pi$
$830$	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	$-0.758069\pi$
$839$	−41.9885	−1.44961	−0.724803	+	0.688957i	$0.758069\pi$
$840$	−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	$-0.649905\pi$
$857$	−26.5651	−0.907447	−0.453723	+	0.891143i	$0.649905\pi$
$858$	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	$-0.499378\pi$
$863$	0.114750	0.00390613	0.00195307	+	0.999998i	$0.499378\pi$
$864$	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	$-0.628077\pi$
$877$	−23.1936	−0.783193	−0.391596	+	0.920137i	$0.628077\pi$
$878$	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	$-0.438197\pi$
$887$	11.4927	0.385886	0.192943	+	0.981210i	$0.438197\pi$
$888$	−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	$-0.629292\pi$
$907$	−23.7983	−0.790209	−0.395104	+	0.918636i	$0.629292\pi$
$908$	−31.9123	−1.05905
$909$	0.143656	0.00476478
$910$	−2.06397	−0.0684201
$911$	−23.2831	−0.771405	−0.385702	−	0.922623i	$-0.626041\pi$
$911$	−23.2831	−0.771405	−0.385702	+	0.922623i	$0.626041\pi$
$912$	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	$-0.522107\pi$
$941$	−4.25742	−0.138788	−0.0693939	+	0.997589i	$0.522107\pi$
$942$	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	$-0.662507\pi$
$953$	−30.1693	−0.977281	−0.488640	+	0.872485i	$0.662507\pi$
$954$	−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	$-0.342603\pi$
$971$	29.5761	0.949141	0.474571	+	0.880217i	$0.342603\pi$
$972$	−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	$-0.283090\pi$
$977$	39.3785	1.25983	0.629915	+	0.776664i	$0.283090\pi$
$978$	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	$-0.290077\pi$
$983$	38.4207	1.22543	0.612716	+	0.790303i	$0.290077\pi$
$984$	−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	$-0.553180\pi$
$991$	−10.4699	−0.332589	−0.166294	+	0.986076i	$0.553180\pi$
$992$	−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.s.1.5		9
5.4	even	2		9025.2.a.cf.1.5		9
19.14	odd	18		95.2.k.a.6.2	✓	18
19.15	odd	18		95.2.k.a.16.2	yes	18
19.18	odd	2		1805.2.a.v.1.5		9
57.14	even	18		855.2.bs.c.766.2		18
57.53	even	18		855.2.bs.c.586.2		18
95.14	odd	18		475.2.l.c.101.2		18
95.33	even	36		475.2.u.b.424.2		36
95.34	odd	18		475.2.l.c.301.2		18
95.52	even	36		475.2.u.b.424.5		36
95.53	even	36		475.2.u.b.149.5		36
95.72	even	36		475.2.u.b.149.2		36
95.94	odd	2		9025.2.a.cc.1.5		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.a.6.2	✓	18	19.14	odd	18
95.2.k.a.16.2	yes	18	19.15	odd	18
475.2.l.c.101.2		18	95.14	odd	18
475.2.l.c.301.2		18	95.34	odd	18
475.2.u.b.149.2		36	95.72	even	36
475.2.u.b.149.5		36	95.53	even	36
475.2.u.b.424.2		36	95.33	even	36
475.2.u.b.424.5		36	95.52	even	36
855.2.bs.c.586.2		18	57.53	even	18
855.2.bs.c.766.2		18	57.14	even	18
1805.2.a.s.1.5		9	1.1	even	1	trivial
1805.2.a.v.1.5		9	19.18	odd	2
9025.2.a.cc.1.5		9	95.94	odd	2
9025.2.a.cf.1.5		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)

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