LMFDB - Embedded newform 1805.2.a.p.1.4

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:	$4$
Coefficient field:	4.4.11344.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 4x^{2} + 4x + 3 $ x^4 - 2x^3 - 4x^2 + 4*x + 3
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			1.4
Root			$1.28734$ of defining polynomial
Character	$\chi$	$=$	1805.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.63010 q^{2} -3.04306 q^{3} +4.91744 q^{4} -1.00000 q^{5} -8.00355 q^{6} -0.574672 q^{7} +7.67316 q^{8} +6.26020 q^{9} +O(q^{10})$	\(q+2.63010 q^{2} -3.04306 q^{3} +4.91744 q^{4} -1.00000 q^{5} -8.00355 q^{6} -0.574672 q^{7} +7.67316 q^{8} +6.26020 q^{9} -2.63010 q^{10} +2.57467 q^{11} -14.9641 q^{12} +0.468387 q^{13} -1.51145 q^{14} +3.04306 q^{15} +10.3463 q^{16} -4.08612 q^{17} +16.4650 q^{18} -4.91744 q^{20} +1.74876 q^{21} +6.77165 q^{22} +1.51145 q^{23} -23.3499 q^{24} +1.00000 q^{25} +1.23191 q^{26} -9.92099 q^{27} -2.82591 q^{28} +4.08612 q^{29} +8.00355 q^{30} +9.92099 q^{31} +11.8656 q^{32} -7.83488 q^{33} -10.7469 q^{34} +0.574672 q^{35} +30.7842 q^{36} +8.30326 q^{37} -1.42533 q^{39} -7.67316 q^{40} +1.83488 q^{41} +4.59942 q^{42} -0.574672 q^{43} +12.6608 q^{44} -6.26020 q^{45} +3.97526 q^{46} +7.09508 q^{47} -31.4845 q^{48} -6.66975 q^{49} +2.63010 q^{50} +12.4343 q^{51} +2.30326 q^{52} -4.30326 q^{53} -26.0932 q^{54} -2.57467 q^{55} -4.40955 q^{56} +10.7469 q^{58} +2.68553 q^{59} +14.9641 q^{60} +12.4095 q^{61} +26.0932 q^{62} -3.59756 q^{63} +10.5150 q^{64} -0.468387 q^{65} -20.6065 q^{66} +2.70570 q^{67} -20.0932 q^{68} -4.59942 q^{69} +1.51145 q^{70} +7.40058 q^{71} +48.0356 q^{72} +12.0861 q^{73} +21.8384 q^{74} -3.04306 q^{75} -1.47959 q^{77} -3.74876 q^{78} +6.68553 q^{79} -10.3463 q^{80} +11.4095 q^{81} +4.82591 q^{82} -6.66079 q^{83} +8.59942 q^{84} +4.08612 q^{85} -1.51145 q^{86} -12.4343 q^{87} +19.7559 q^{88} -14.6065 q^{89} -16.4650 q^{90} -0.269169 q^{91} +7.43244 q^{92} -30.1902 q^{93} +18.6608 q^{94} -36.1076 q^{96} -17.4526 q^{97} -17.5421 q^{98} +16.1180 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{3} + 8 q^{4} - 4 q^{5} + 4 q^{7} + 12 q^{8} + 8 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^3 + 8 * q^4 - 4 * q^5 + 4 * q^7 + 12 * q^8 + 8 * q^9	$ 4 q + 2 q^{2} - 2 q^{3} + 8 q^{4} - 4 q^{5} + 4 q^{7} + 12 q^{8} + 8 q^{9} - 2 q^{10} + 4 q^{11} - 6 q^{12} - 2 q^{13} + 8 q^{14} + 2 q^{15} + 4 q^{16} + 4 q^{17} + 34 q^{18} - 8 q^{20} + 4 q^{21} - 4 q^{22} - 8 q^{23} - 24 q^{24} + 4 q^{25} + 4 q^{26} + 4 q^{27} - 8 q^{28} - 4 q^{29} - 4 q^{31} + 6 q^{32} - 8 q^{33} + 4 q^{34} - 4 q^{35} + 40 q^{36} + 6 q^{37} - 12 q^{39} - 12 q^{40} - 16 q^{41} + 28 q^{42} + 4 q^{43} + 24 q^{44} - 8 q^{45} - 12 q^{47} - 38 q^{48} + 20 q^{49} + 2 q^{50} + 36 q^{51} - 18 q^{52} + 10 q^{53} - 20 q^{54} - 4 q^{55} + 12 q^{56} - 4 q^{58} + 6 q^{60} + 20 q^{61} + 20 q^{62} + 20 q^{63} - 4 q^{64} + 2 q^{65} - 28 q^{66} + 18 q^{67} + 4 q^{68} - 28 q^{69} - 8 q^{70} + 20 q^{71} + 52 q^{72} + 28 q^{73} + 32 q^{74} - 2 q^{75} - 40 q^{77} - 12 q^{78} + 16 q^{79} - 4 q^{80} + 16 q^{81} + 16 q^{82} + 44 q^{84} - 4 q^{85} + 8 q^{86} - 36 q^{87} + 12 q^{88} - 4 q^{89} - 34 q^{90} + 36 q^{91} - 28 q^{92} - 40 q^{93} + 48 q^{94} - 52 q^{96} - 30 q^{97} - 38 q^{98} - 4 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^3 + 8 * q^4 - 4 * q^5 + 4 * q^7 + 12 * q^8 + 8 * q^9 - 2 * q^10 + 4 * q^11 - 6 * q^12 - 2 * q^13 + 8 * q^14 + 2 * q^15 + 4 * q^16 + 4 * q^17 + 34 * q^18 - 8 * q^20 + 4 * q^21 - 4 * q^22 - 8 * q^23 - 24 * q^24 + 4 * q^25 + 4 * q^26 + 4 * q^27 - 8 * q^28 - 4 * q^29 - 4 * q^31 + 6 * q^32 - 8 * q^33 + 4 * q^34 - 4 * q^35 + 40 * q^36 + 6 * q^37 - 12 * q^39 - 12 * q^40 - 16 * q^41 + 28 * q^42 + 4 * q^43 + 24 * q^44 - 8 * q^45 - 12 * q^47 - 38 * q^48 + 20 * q^49 + 2 * q^50 + 36 * q^51 - 18 * q^52 + 10 * q^53 - 20 * q^54 - 4 * q^55 + 12 * q^56 - 4 * q^58 + 6 * q^60 + 20 * q^61 + 20 * q^62 + 20 * q^63 - 4 * q^64 + 2 * q^65 - 28 * q^66 + 18 * q^67 + 4 * q^68 - 28 * q^69 - 8 * q^70 + 20 * q^71 + 52 * q^72 + 28 * q^73 + 32 * q^74 - 2 * q^75 - 40 * q^77 - 12 * q^78 + 16 * q^79 - 4 * q^80 + 16 * q^81 + 16 * q^82 + 44 * q^84 - 4 * q^85 + 8 * q^86 - 36 * q^87 + 12 * q^88 - 4 * q^89 - 34 * q^90 + 36 * q^91 - 28 * q^92 - 40 * q^93 + 48 * q^94 - 52 * q^96 - 30 * q^97 - 38 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.63010	1.85976	0.929882	−	0.367859i	$-0.119909\pi$
$2$	2.63010	1.85976	0.929882	+	0.367859i	$0.119909\pi$
$3$	−3.04306	−1.75691	−0.878455	−	0.477825i	$-0.841425\pi$
$3$	−3.04306	−1.75691	−0.878455	+	0.477825i	$0.841425\pi$
$4$	4.91744	2.45872
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−8.00355	−3.26744
$7$	−0.574672	−0.217205	−0.108603	−	0.994085i	$-0.534638\pi$
$7$	−0.574672	−0.217205	−0.108603	+	0.994085i	$0.534638\pi$
$8$	7.67316	2.71287
$9$	6.26020	2.08673
$10$	−2.63010	−0.831711
$11$	2.57467	0.776293	0.388146	−	0.921598i	$-0.373116\pi$
$11$	2.57467	0.776293	0.388146	+	0.921598i	$0.373116\pi$
$12$	−14.9641	−4.31975
$13$	0.468387	0.129907	0.0649536	−	0.997888i	$-0.479310\pi$
$13$	0.468387	0.129907	0.0649536	+	0.997888i	$0.479310\pi$
$14$	−1.51145	−0.403951
$15$	3.04306	0.785714
$16$	10.3463	2.58658
$17$	−4.08612	−0.991029	−0.495514	−	0.868600i	$-0.665020\pi$
$17$	−4.08612	−0.991029	−0.495514	+	0.868600i	$0.665020\pi$
$18$	16.4650	3.88083
$19$	0	0
$19$	0	0
$20$	−4.91744	−1.09957
$21$	1.74876	0.381611
$22$	6.77165	1.44372
$23$	1.51145	0.315158	0.157579	−	0.987506i	$-0.449631\pi$
$23$	1.51145	0.315158	0.157579	+	0.987506i	$0.449631\pi$
$24$	−23.3499	−4.76627
$25$	1.00000	0.200000
$26$	1.23191	0.241596
$27$	−9.92099	−1.90930
$28$	−2.82591	−0.534047
$29$	4.08612	0.758773	0.379386	−	0.925238i	$-0.376135\pi$
$29$	4.08612	0.758773	0.379386	+	0.925238i	$0.376135\pi$
$30$	8.00355	1.46124
$31$	9.92099	1.78186	0.890931	−	0.454138i	$-0.150053\pi$
$31$	9.92099	1.78186	0.890931	+	0.454138i	$0.150053\pi$
$32$	11.8656	2.09755
$33$	−7.83488	−1.36388
$34$	−10.7469	−1.84308
$35$	0.574672	0.0971372
$36$	30.7842	5.13069
$37$	8.30326	1.36505	0.682524	−	0.730863i	$-0.260882\pi$
$37$	8.30326	1.36505	0.682524	+	0.730863i	$0.260882\pi$
$38$	0	0
$39$	−1.42533	−0.228235
$40$	−7.67316	−1.21323
$41$	1.83488	0.286560	0.143280	−	0.989682i	$-0.454235\pi$
$41$	1.83488	0.286560	0.143280	+	0.989682i	$0.454235\pi$
$42$	4.59942	0.709705
$43$	−0.574672	−0.0876366	−0.0438183	−	0.999040i	$-0.513952\pi$
$43$	−0.574672	−0.0876366	−0.0438183	+	0.999040i	$0.513952\pi$
$44$	12.6608	1.90869
$45$	−6.26020	−0.933216
$46$	3.97526	0.586119
$47$	7.09508	1.03492	0.517462	−	0.855706i	$-0.326877\pi$
$47$	7.09508	1.03492	0.517462	+	0.855706i	$0.326877\pi$
$48$	−31.4845	−4.54439
$49$	−6.66975	−0.952822
$50$	2.63010	0.371953
$51$	12.4343	1.74115
$52$	2.30326	0.319405
$53$	−4.30326	−0.591099	−0.295549	−	0.955327i	$-0.595503\pi$
$53$	−4.30326	−0.591099	−0.295549	+	0.955327i	$0.595503\pi$
$54$	−26.0932	−3.55084
$55$	−2.57467	−0.347169
$56$	−4.40955	−0.589251
$57$	0	0
$58$	10.7469	1.41114
$59$	2.68553	0.349627	0.174813	−	0.984602i	$-0.444068\pi$
$59$	2.68553	0.349627	0.174813	+	0.984602i	$0.444068\pi$
$60$	14.9641	1.93185
$61$	12.4095	1.58888	0.794440	−	0.607343i	$-0.207765\pi$
$61$	12.4095	1.58888	0.794440	+	0.607343i	$0.207765\pi$
$62$	26.0932	3.31384
$63$	−3.59756	−0.453250
$64$	10.5150	1.31438
$65$	−0.468387	−0.0580962
$66$	−20.6065	−2.53649
$67$	2.70570	0.330554	0.165277	−	0.986247i	$-0.447148\pi$
$67$	2.70570	0.330554	0.165277	+	0.986247i	$0.447148\pi$
$68$	−20.0932	−2.43666
$69$	−4.59942	−0.553705
$70$	1.51145	0.180652
$71$	7.40058	0.878288	0.439144	−	0.898417i	$-0.355282\pi$
$71$	7.40058	0.878288	0.439144	+	0.898417i	$0.355282\pi$
$72$	48.0356	5.66104
$73$	12.0861	1.41457	0.707286	−	0.706927i	$-0.249919\pi$
$73$	12.0861	1.41457	0.707286	+	0.706927i	$0.249919\pi$
$74$	21.8384	2.53867
$75$	−3.04306	−0.351382
$76$	0	0
$77$	−1.47959	−0.168615
$78$	−3.74876	−0.424463
$79$	6.68553	0.752181	0.376091	−	0.926583i	$-0.377268\pi$
$79$	6.68553	0.752181	0.376091	+	0.926583i	$0.377268\pi$
$80$	−10.3463	−1.15675
$81$	11.4095	1.26773
$82$	4.82591	0.532933
$83$	−6.66079	−0.731117	−0.365558	−	0.930788i	$-0.619122\pi$
$83$	−6.66079	−0.731117	−0.365558	+	0.930788i	$0.619122\pi$
$84$	8.59942	0.938273
$85$	4.08612	0.443202
$86$	−1.51145	−0.162983
$87$	−12.4343	−1.33310
$88$	19.7559	2.10598
$89$	−14.6065	−1.54829	−0.774144	−	0.633009i	$-0.781820\pi$
$89$	−14.6065	−1.54829	−0.774144	+	0.633009i	$0.781820\pi$
$90$	−16.4650	−1.73556
$91$	−0.269169	−0.0282165
$92$	7.43244	0.774885
$93$	−30.1902	−3.13057
$94$	18.6608	1.92471
$95$	0	0
$96$	−36.1076	−3.68522
$97$	−17.4526	−1.77204	−0.886022	−	0.463643i	$-0.846542\pi$
$97$	−17.4526	−1.77204	−0.886022	+	0.463643i	$0.846542\pi$
$98$	−17.5421	−1.77202
$99$	16.1180	1.61992
$100$	4.91744	0.491744
$101$	14.2831	1.42122	0.710611	−	0.703586i	$-0.248419\pi$
$101$	14.2831	1.42122	0.710611	+	0.703586i	$0.248419\pi$
$102$	32.7035	3.23813
$103$	−4.79182	−0.472152	−0.236076	−	0.971735i	$-0.575861\pi$
$103$	−4.79182	−0.472152	−0.236076	+	0.971735i	$0.575861\pi$
$104$	3.59401	0.352421
$105$	−1.74876	−0.170661
$106$	−11.3180	−1.09930
$107$	−9.22611	−0.891922	−0.445961	−	0.895052i	$-0.647138\pi$
$107$	−9.22611	−0.891922	−0.445961	+	0.895052i	$0.647138\pi$
$108$	−48.7859	−4.69442
$109$	−4.89810	−0.469153	−0.234577	−	0.972098i	$-0.575370\pi$
$109$	−4.89810	−0.469153	−0.234577	+	0.972098i	$0.575370\pi$
$110$	−6.77165	−0.645651
$111$	−25.2673	−2.39827
$112$	−5.94574	−0.561819
$113$	−1.61773	−0.152183	−0.0760916	−	0.997101i	$-0.524244\pi$
$113$	−1.61773	−0.152183	−0.0760916	+	0.997101i	$0.524244\pi$
$114$	0	0
$115$	−1.51145	−0.140943
$116$	20.0932	1.86561
$117$	2.93220	0.271082
$118$	7.06323	0.650223
$119$	2.34818	0.215257
$120$	23.3499	2.13154
$121$	−4.37107	−0.397370
$122$	32.6384	2.95494
$123$	−5.58364	−0.503459
$124$	48.7859	4.38110
$125$	−1.00000	−0.0894427
$126$	−9.46196	−0.842938
$127$	13.1292	1.16503	0.582513	−	0.812821i	$-0.302070\pi$
$127$	13.1292	1.16503	0.582513	+	0.812821i	$0.302070\pi$
$128$	3.92440	0.346871
$129$	1.74876	0.153970
$130$	−1.23191	−0.108045
$131$	−8.17223	−0.714011	−0.357006	−	0.934102i	$-0.616202\pi$
$131$	−8.17223	−0.714011	−0.357006	+	0.934102i	$0.616202\pi$
$132$	−38.5275	−3.35339
$133$	0	0
$134$	7.11627	0.614752
$135$	9.92099	0.853863
$136$	−31.3534	−2.68853
$137$	−14.6065	−1.24792	−0.623960	−	0.781456i	$-0.714477\pi$
$137$	−14.6065	−1.24792	−0.623960	+	0.781456i	$0.714477\pi$
$138$	−12.0969	−1.02976
$139$	−2.07219	−0.175761	−0.0878804	−	0.996131i	$-0.528009\pi$
$139$	−2.07219	−0.175761	−0.0878804	+	0.996131i	$0.528009\pi$
$140$	2.82591	0.238833
$141$	−21.5907	−1.81827
$142$	19.4643	1.63341
$143$	1.20594	0.100846
$144$	64.7701	5.39751
$145$	−4.08612	−0.339334
$146$	31.7877	2.63077
$147$	20.2964	1.67402
$148$	40.8308	3.35627
$149$	8.91203	0.730102	0.365051	−	0.930988i	$-0.381052\pi$
$149$	8.91203	0.730102	0.365051	+	0.930988i	$0.381052\pi$
$150$	−8.00355	−0.653488
$151$	−11.4572	−0.932372	−0.466186	−	0.884687i	$-0.654372\pi$
$151$	−11.4572	−0.932372	−0.466186	+	0.884687i	$0.654372\pi$
$152$	0	0
$153$	−25.5799	−2.06801
$154$	−3.89148	−0.313584
$155$	−9.92099	−0.796873
$156$	−7.00896	−0.561166
$157$	−6.60653	−0.527258	−0.263629	−	0.964624i	$-0.584919\pi$
$157$	−6.60653	−0.527258	−0.263629	+	0.964624i	$0.584919\pi$
$158$	17.5836	1.39888
$159$	13.0951	1.03851
$160$	−11.8656	−0.938055
$161$	−0.868585	−0.0684541
$162$	30.0083	2.35767
$163$	20.2444	1.58567	0.792833	−	0.609439i	$-0.208605\pi$
$163$	20.2444	1.58567	0.792833	+	0.609439i	$0.208605\pi$
$164$	9.02289	0.704569
$165$	7.83488	0.609944
$166$	−17.5186	−1.35970
$167$	5.89372	0.456069	0.228035	−	0.973653i	$-0.426770\pi$
$167$	5.89372	0.456069	0.228035	+	0.973653i	$0.426770\pi$
$168$	13.4185	1.03526
$169$	−12.7806	−0.983124
$170$	10.7469	0.824250
$171$	0	0
$172$	−2.82591	−0.215474
$173$	3.53161	0.268504	0.134252	−	0.990947i	$-0.457137\pi$
$173$	3.53161	0.268504	0.134252	+	0.990947i	$0.457137\pi$
$174$	−32.7035	−2.47924
$175$	−0.574672	−0.0434411
$176$	26.6384	2.00794
$177$	−8.17223	−0.614263
$178$	−38.4167	−2.87945
$179$	−7.18801	−0.537257	−0.268629	−	0.963244i	$-0.586570\pi$
$179$	−7.18801	−0.537257	−0.268629	+	0.963244i	$0.586570\pi$
$180$	−30.7842	−2.29452
$181$	−15.5433	−1.15532	−0.577662	−	0.816276i	$-0.696035\pi$
$181$	−15.5433	−1.15532	−0.577662	+	0.816276i	$0.696035\pi$
$182$	−0.707941	−0.0524761
$183$	−37.7630	−2.79152
$184$	11.5976	0.854984
$185$	−8.30326	−0.610468
$186$	−79.4032	−5.82213
$187$	−10.5204	−0.769329
$188$	34.8896	2.54459
$189$	5.70131	0.414710
$190$	0	0
$191$	13.3216	0.963915	0.481958	−	0.876194i	$-0.339926\pi$
$191$	13.3216	0.963915	0.481958	+	0.876194i	$0.339926\pi$
$192$	−31.9978	−2.30924
$193$	−18.9959	−1.36736	−0.683678	−	0.729784i	$-0.739621\pi$
$193$	−18.9959	−1.36736	−0.683678	+	0.729784i	$0.739621\pi$
$194$	−45.9021	−3.29558
$195$	1.42533	0.102070
$196$	−32.7981	−2.34272
$197$	2.17223	0.154765	0.0773826	−	0.997001i	$-0.475344\pi$
$197$	2.17223	0.154765	0.0773826	+	0.997001i	$0.475344\pi$
$198$	42.3919	3.01266
$199$	−1.87355	−0.132812	−0.0664061	−	0.997793i	$-0.521153\pi$
$199$	−1.87355	−0.132812	−0.0664061	+	0.997793i	$0.521153\pi$
$200$	7.67316	0.542574
$201$	−8.23361	−0.580754
$202$	37.5660	2.64313
$203$	−2.34818	−0.164810
$204$	61.1449	4.28100
$205$	−1.83488	−0.128153
$206$	−12.6030	−0.878091
$207$	9.46196	0.657651
$208$	4.84608	0.336015
$209$	0	0
$210$	−4.59942	−0.317390
$211$	17.1090	1.17783	0.588916	−	0.808194i	$-0.299555\pi$
$211$	17.1090	1.17783	0.588916	+	0.808194i	$0.299555\pi$
$212$	−21.1610	−1.45335
$213$	−22.5204	−1.54307
$214$	−24.2656	−1.65876
$215$	0.574672	0.0391923
$216$	−76.1254	−5.17968
$217$	−5.70131	−0.387030
$218$	−12.8825	−0.872514
$219$	−36.7788	−2.48528
$220$	−12.6608	−0.853590
$221$	−1.91388	−0.128742
$222$	−66.4556	−4.46021
$223$	−5.12918	−0.343475	−0.171737	−	0.985143i	$-0.554938\pi$
$223$	−5.12918	−0.343475	−0.171737	+	0.985143i	$0.554938\pi$
$224$	−6.81880	−0.455600
$225$	6.26020	0.417347
$226$	−4.25480	−0.283025
$227$	7.31223	0.485330	0.242665	−	0.970110i	$-0.421978\pi$
$227$	7.31223	0.485330	0.242665	+	0.970110i	$0.421978\pi$
$228$	0	0
$229$	−8.40955	−0.555719	−0.277859	−	0.960622i	$-0.589625\pi$
$229$	−8.40955	−0.555719	−0.277859	+	0.960622i	$0.589625\pi$
$230$	−3.97526	−0.262121
$231$	4.50248	0.296242
$232$	31.3534	2.05845
$233$	−14.1722	−0.928454	−0.464227	−	0.885716i	$-0.653668\pi$
$233$	−14.1722	−0.928454	−0.464227	+	0.885716i	$0.653668\pi$
$234$	7.71198	0.504148
$235$	−7.09508	−0.462832
$236$	13.2059	0.859634
$237$	−20.3445	−1.32152
$238$	6.17594	0.400327
$239$	−14.1902	−0.917885	−0.458943	−	0.888466i	$-0.651772\pi$
$239$	−14.1902	−0.917885	−0.458943	+	0.888466i	$0.651772\pi$
$240$	31.4845	2.03231
$241$	−27.8807	−1.79595	−0.897976	−	0.440045i	$-0.854962\pi$
$241$	−27.8807	−1.79595	−0.897976	+	0.440045i	$0.854962\pi$
$242$	−11.4964	−0.739013
$243$	−4.95694	−0.317988
$244$	61.0232	3.90661
$245$	6.66975	0.426115
$246$	−14.6855	−0.936315
$247$	0	0
$248$	76.1254	4.83397
$249$	20.2692	1.28451
$250$	−2.63010	−0.166342
$251$	−26.1902	−1.65311	−0.826554	−	0.562857i	$-0.809702\pi$
$251$	−26.1902	−1.65311	−0.826554	+	0.562857i	$0.809702\pi$
$252$	−17.6908	−1.11441
$253$	3.89148	0.244655
$254$	34.5311	2.16667
$255$	−12.4343	−0.778666
$256$	−10.7084	−0.669276
$257$	−9.01831	−0.562547	−0.281273	−	0.959628i	$-0.590757\pi$
$257$	−9.01831	−0.562547	−0.281273	+	0.959628i	$0.590757\pi$
$258$	4.59942	0.286347
$259$	−4.77165	−0.296496
$260$	−2.30326	−0.142842
$261$	25.5799	1.58336
$262$	−21.4938	−1.32789
$263$	−9.00896	−0.555517	−0.277758	−	0.960651i	$-0.589591\pi$
$263$	−9.00896	−0.555517	−0.277758	+	0.960651i	$0.589591\pi$
$264$	−60.1183	−3.70002
$265$	4.30326	0.264347
$266$	0	0
$267$	44.4485	2.72020
$268$	13.3051	0.812739
$269$	30.6136	1.86655	0.933273	−	0.359167i	$-0.116939\pi$
$269$	30.6136	1.86655	0.933273	+	0.359167i	$0.116939\pi$
$270$	26.0932	1.58798
$271$	24.1180	1.46506	0.732531	−	0.680733i	$-0.238339\pi$
$271$	24.1180	1.46506	0.732531	+	0.680733i	$0.238339\pi$
$272$	−42.2763	−2.56338
$273$	0.819096	0.0495739
$274$	−38.4167	−2.32084
$275$	2.57467	0.155259
$276$	−22.6173	−1.36140
$277$	4.56075	0.274029	0.137014	−	0.990569i	$-0.456249\pi$
$277$	4.56075	0.274029	0.137014	+	0.990569i	$0.456249\pi$
$278$	−5.45007	−0.326874
$279$	62.1074	3.71828
$280$	4.40955	0.263521
$281$	6.11563	0.364828	0.182414	−	0.983222i	$-0.441609\pi$
$281$	6.11563	0.364828	0.182414	+	0.983222i	$0.441609\pi$
$282$	−56.7859	−3.38155
$283$	−19.0547	−1.13269	−0.566344	−	0.824169i	$-0.691642\pi$
$283$	−19.0547	−1.13269	−0.566344	+	0.824169i	$0.691642\pi$
$284$	36.3919	2.15946
$285$	0	0
$286$	3.17175	0.187550
$287$	−1.05445	−0.0622423
$288$	74.2808	4.37704
$289$	−0.303649	−0.0178617
$290$	−10.7469	−0.631080
$291$	53.1093	3.11332
$292$	59.4327	3.47804
$293$	6.43887	0.376163	0.188081	−	0.982153i	$-0.439773\pi$
$293$	6.43887	0.376163	0.188081	+	0.982153i	$0.439773\pi$
$294$	53.3817	3.11329
$295$	−2.68553	−0.156358
$296$	63.7123	3.70320
$297$	−25.5433	−1.48217
$298$	23.4395	1.35782
$299$	0.707941	0.0409413
$300$	−14.9641	−0.863950
$301$	0.330247	0.0190351
$302$	−30.1336	−1.73399
$303$	−43.4643	−2.49696
$304$	0	0
$305$	−12.4095	−0.710569
$306$	−67.2778	−3.84602
$307$	6.77389	0.386606	0.193303	−	0.981139i	$-0.438080\pi$
$307$	6.77389	0.386606	0.193303	+	0.981139i	$0.438080\pi$
$308$	−7.27580	−0.414577
$309$	14.5818	0.829529
$310$	−26.0932	−1.48200
$311$	20.6205	1.16928	0.584639	−	0.811293i	$-0.301236\pi$
$311$	20.6205	1.16928	0.584639	+	0.811293i	$0.301236\pi$
$312$	−10.9368	−0.619173
$313$	19.3711	1.09492	0.547459	−	0.836833i	$-0.315595\pi$
$313$	19.3711	1.09492	0.547459	+	0.836833i	$0.315595\pi$
$314$	−17.3758	−0.980575
$315$	3.59756	0.202700
$316$	32.8757	1.84940
$317$	−3.37360	−0.189480	−0.0947401	−	0.995502i	$-0.530202\pi$
$317$	−3.37360	−0.189480	−0.0947401	+	0.995502i	$0.530202\pi$
$318$	34.4414	1.93138
$319$	10.5204	0.589030
$320$	−10.5150	−0.587806
$321$	28.0756	1.56703
$322$	−2.28447	−0.127308
$323$	0	0
$324$	56.1057	3.11699
$325$	0.468387	0.0259814
$326$	53.2449	2.94896
$327$	14.9052	0.824260
$328$	14.0793	0.777399
$329$	−4.07734	−0.224791
$330$	20.6065	1.13435
$331$	32.7788	1.80168	0.900842	−	0.434148i	$-0.142950\pi$
$331$	32.7788	1.80168	0.900842	+	0.434148i	$0.142950\pi$
$332$	−32.7540	−1.79761
$333$	51.9801	2.84849
$334$	15.5011	0.848181
$335$	−2.70570	−0.147828
$336$	18.0932	0.987066
$337$	−8.74915	−0.476596	−0.238298	−	0.971192i	$-0.576590\pi$
$337$	−8.74915	−0.476596	−0.238298	+	0.971192i	$0.576590\pi$
$338$	−33.6143	−1.82838
$339$	4.92285	0.267372
$340$	20.0932	1.08971
$341$	25.5433	1.38325
$342$	0	0
$343$	7.85562	0.424164
$344$	−4.40955	−0.237747
$345$	4.59942	0.247624
$346$	9.28850	0.499353
$347$	−18.5028	−0.993281	−0.496640	−	0.867956i	$-0.665433\pi$
$347$	−18.5028	−0.993281	−0.496640	+	0.867956i	$0.665433\pi$
$348$	−61.1449	−3.27771
$349$	3.54330	0.189668	0.0948342	−	0.995493i	$-0.469768\pi$
$349$	3.54330	0.189668	0.0948342	+	0.995493i	$0.469768\pi$
$350$	−1.51145	−0.0807901
$351$	−4.64686	−0.248031
$352$	30.5499	1.62832
$353$	−3.41140	−0.181571	−0.0907853	−	0.995870i	$-0.528938\pi$
$353$	−3.41140	−0.181571	−0.0907853	+	0.995870i	$0.528938\pi$
$354$	−21.4938	−1.14238
$355$	−7.40058	−0.392782
$356$	−71.8267	−3.80681
$357$	−7.14564	−0.378187
$358$	−18.9052	−0.999172
$359$	−1.70609	−0.0900438	−0.0450219	−	0.998986i	$-0.514336\pi$
$359$	−1.70609	−0.0900438	−0.0450219	+	0.998986i	$0.514336\pi$
$360$	−48.0356	−2.53170
$361$	0	0
$362$	−40.8805	−2.14863
$363$	13.3014	0.698143
$364$	−1.32362	−0.0693765
$365$	−12.0861	−0.632616
$366$	−99.3205	−5.19157
$367$	37.6155	1.96351	0.981756	−	0.190144i	$-0.0608953\pi$
$367$	37.6155	1.96351	0.981756	+	0.190144i	$0.0608953\pi$
$368$	15.6379	0.815182
$369$	11.4867	0.597974
$370$	−21.8384	−1.13533
$371$	2.47296	0.128390
$372$	−148.458	−7.69720
$373$	−13.4031	−0.693987	−0.346994	−	0.937868i	$-0.612797\pi$
$373$	−13.4031	−0.693987	−0.346994	+	0.937868i	$0.612797\pi$
$374$	−27.6698	−1.43077
$375$	3.04306	0.157143
$376$	54.4417	2.80762
$377$	1.91388	0.0985700
$378$	14.9950	0.771262
$379$	9.37107	0.481359	0.240680	−	0.970605i	$-0.422630\pi$
$379$	9.37107	0.481359	0.240680	+	0.970605i	$0.422630\pi$
$380$	0	0
$381$	−39.9528	−2.04685
$382$	35.0371	1.79265
$383$	2.09917	0.107263	0.0536314	−	0.998561i	$-0.482920\pi$
$383$	2.09917	0.107263	0.0536314	+	0.998561i	$0.482920\pi$
$384$	−11.9422	−0.609422
$385$	1.47959	0.0754069
$386$	−49.9612	−2.54296
$387$	−3.59756	−0.182874
$388$	−85.8221	−4.35696
$389$	1.07238	0.0543718	0.0271859	−	0.999630i	$-0.491345\pi$
$389$	1.07238	0.0543718	0.0271859	+	0.999630i	$0.491345\pi$
$390$	3.74876	0.189826
$391$	−6.17594	−0.312331
$392$	−51.1781	−2.58488
$393$	24.8686	1.25445
$394$	5.71320	0.287827
$395$	−6.68553	−0.336386
$396$	79.2591	3.98292
$397$	−23.5341	−1.18114	−0.590572	−	0.806985i	$-0.701098\pi$
$397$	−23.5341	−1.18114	−0.590572	+	0.806985i	$0.701098\pi$
$398$	−4.92762	−0.246999
$399$	0	0
$400$	10.3463	0.517316
$401$	−18.6469	−0.931180	−0.465590	−	0.885001i	$-0.654158\pi$
$401$	−18.6469	−0.931180	−0.465590	+	0.885001i	$0.654158\pi$
$402$	−21.6552	−1.08006
$403$	4.64686	0.231477
$404$	70.2362	3.49438
$405$	−11.4095	−0.566945
$406$	−6.17594	−0.306507
$407$	21.3782	1.05968
$408$	95.4103	4.72351
$409$	6.88017	0.340203	0.170101	−	0.985427i	$-0.445590\pi$
$409$	6.88017	0.340203	0.170101	+	0.985427i	$0.445590\pi$
$410$	−4.82591	−0.238335
$411$	44.4485	2.19248
$412$	−23.5635	−1.16089
$413$	−1.54330	−0.0759408
$414$	24.8859	1.22308
$415$	6.66079	0.326965
$416$	5.55767	0.272487
$417$	6.30580	0.308796
$418$	0	0
$419$	13.4796	0.658521	0.329261	−	0.944239i	$-0.393201\pi$
$419$	13.4796	0.658521	0.329261	+	0.944239i	$0.393201\pi$
$420$	−8.59942	−0.419609
$421$	5.83488	0.284374	0.142187	−	0.989840i	$-0.454586\pi$
$421$	5.83488	0.284374	0.142187	+	0.989840i	$0.454586\pi$
$422$	44.9984	2.19049
$423$	44.4167	2.15961
$424$	−33.0196	−1.60357
$425$	−4.08612	−0.198206
$426$	−59.2310	−2.86975
$427$	−7.13142	−0.345113
$428$	−45.3688	−2.19298
$429$	−3.66975	−0.177177
$430$	1.51145	0.0728884
$431$	−29.2039	−1.40670	−0.703351	−	0.710843i	$-0.748314\pi$
$431$	−29.2039	−1.40670	−0.703351	+	0.710843i	$0.748314\pi$
$432$	−102.646	−4.93855
$433$	12.5229	0.601814	0.300907	−	0.953653i	$-0.402711\pi$
$433$	12.5229	0.601814	0.300907	+	0.953653i	$0.402711\pi$
$434$	−14.9950	−0.719785
$435$	12.4343	0.596179
$436$	−24.0861	−1.15352
$437$	0	0
$438$	−96.7319	−4.62203
$439$	−15.6769	−0.748216	−0.374108	−	0.927385i	$-0.622051\pi$
$439$	−15.6769	−0.748216	−0.374108	+	0.927385i	$0.622051\pi$
$440$	−19.7559	−0.941824
$441$	−41.7540	−1.98829
$442$	−5.03371	−0.239429
$443$	−29.8281	−1.41717	−0.708587	−	0.705624i	$-0.750667\pi$
$443$	−29.8281	−1.41717	−0.708587	+	0.705624i	$0.750667\pi$
$444$	−124.250	−5.89667
$445$	14.6065	0.692416
$446$	−13.4903	−0.638782
$447$	−27.1198	−1.28272
$448$	−6.04267	−0.285489
$449$	−29.9668	−1.41422	−0.707110	−	0.707104i	$-0.750001\pi$
$449$	−29.9668	−1.41422	−0.707110	+	0.707104i	$0.750001\pi$
$450$	16.4650	0.776167
$451$	4.72420	0.222454
$452$	−7.95509	−0.374176
$453$	34.8649	1.63809
$454$	19.2319	0.902598
$455$	0.269169	0.0126188
$456$	0	0
$457$	17.6698	0.826556	0.413278	−	0.910605i	$-0.364384\pi$
$457$	17.6698	0.826556	0.413278	+	0.910605i	$0.364384\pi$
$458$	−22.1180	−1.03350
$459$	40.5383	1.89217
$460$	−7.43244	−0.346539
$461$	22.3445	1.04069	0.520343	−	0.853957i	$-0.325804\pi$
$461$	22.3445	1.04069	0.520343	+	0.853957i	$0.325804\pi$
$462$	11.8420	0.550939
$463$	−6.83302	−0.317557	−0.158779	−	0.987314i	$-0.550756\pi$
$463$	−6.83302	−0.317557	−0.158779	+	0.987314i	$0.550756\pi$
$464$	42.2763	1.96263
$465$	30.1902	1.40004
$466$	−37.2744	−1.72670
$467$	9.00896	0.416885	0.208443	−	0.978035i	$-0.433161\pi$
$467$	9.00896	0.416885	0.208443	+	0.978035i	$0.433161\pi$
$468$	14.4189	0.666514
$469$	−1.55489	−0.0717981
$470$	−18.6608	−0.860758
$471$	20.1040	0.926345
$472$	20.6065	0.948492
$473$	−1.47959	−0.0680317
$474$	−53.5080	−2.45771
$475$	0	0
$476$	11.5470	0.529256
$477$	−26.9393	−1.23347
$478$	−37.3216	−1.70705
$479$	9.26731	0.423434	0.211717	−	0.977331i	$-0.432094\pi$
$479$	9.26731	0.423434	0.211717	+	0.977331i	$0.432094\pi$
$480$	36.1076	1.64808
$481$	3.88914	0.177329
$482$	−73.3290	−3.34004
$483$	2.64315	0.120268
$484$	−21.4944	−0.977020
$485$	17.4526	0.792482
$486$	−13.0373	−0.591382
$487$	38.7694	1.75681	0.878405	−	0.477917i	$-0.158608\pi$
$487$	38.7694	1.75681	0.878405	+	0.477917i	$0.158608\pi$
$488$	95.2205	4.31043
$489$	−61.6050	−2.78587
$490$	17.5421	0.792473
$491$	21.6877	0.978751	0.489376	−	0.872073i	$-0.337225\pi$
$491$	21.6877	0.978751	0.489376	+	0.872073i	$0.337225\pi$
$492$	−27.4572	−1.23787
$493$	−16.6964	−0.751966
$494$	0	0
$495$	−16.1180	−0.724449
$496$	102.646	4.60893
$497$	−4.25291	−0.190769
$498$	53.3100	2.38888
$499$	−27.8372	−1.24616	−0.623082	−	0.782156i	$-0.714120\pi$
$499$	−27.8372	−1.24616	−0.623082	+	0.782156i	$0.714120\pi$
$500$	−4.91744	−0.219915
$501$	−17.9349	−0.801273
$502$	−68.8828	−3.07439
$503$	−41.2449	−1.83902	−0.919510	−	0.393067i	$-0.871414\pi$
$503$	−41.2449	−1.83902	−0.919510	+	0.393067i	$0.871414\pi$
$504$	−27.6047	−1.22961
$505$	−14.2831	−0.635589
$506$	10.2350	0.455000
$507$	38.8922	1.72726
$508$	64.5619	2.86447
$509$	−0.416364	−0.0184550	−0.00922751	−	0.999957i	$-0.502937\pi$
$509$	−0.416364	−0.0184550	−0.00922751	+	0.999957i	$0.502937\pi$
$510$	−32.7035	−1.44813
$511$	−6.94555	−0.307253
$512$	−36.0131	−1.59157
$513$	0	0
$514$	−23.7191	−1.04620
$515$	4.79182	0.211153
$516$	8.59942	0.378568
$517$	18.2675	0.803404
$518$	−12.5499	−0.551412
$519$	−10.7469	−0.471737
$520$	−3.59401	−0.157608
$521$	−24.0458	−1.05346	−0.526732	−	0.850031i	$-0.676583\pi$
$521$	−24.0458	−1.05346	−0.526732	+	0.850031i	$0.676583\pi$
$522$	67.2778	2.94467
$523$	5.19736	0.227265	0.113632	−	0.993523i	$-0.463751\pi$
$523$	5.19736	0.227265	0.113632	+	0.993523i	$0.463751\pi$
$524$	−40.1865	−1.75555
$525$	1.74876	0.0763221
$526$	−23.6945	−1.03313
$527$	−40.5383	−1.76588
$528$	−81.0621	−3.52778
$529$	−20.7155	−0.900675
$530$	11.3180	0.491623
$531$	16.8120	0.729578
$532$	0	0
$533$	0.859432	0.0372261
$534$	116.904	5.05894
$535$	9.22611	0.398880
$536$	20.7613	0.896751
$537$	21.8735	0.943913
$538$	80.5170	3.47133
$539$	−17.1724	−0.739669
$540$	48.7859	2.09941
$541$	−1.93863	−0.0833481	−0.0416741	−	0.999131i	$-0.513269\pi$
$541$	−1.93863	−0.0833481	−0.0416741	+	0.999131i	$0.513269\pi$
$542$	63.4327	2.72467
$543$	47.2992	2.02980
$544$	−48.4841	−2.07874
$545$	4.89810	0.209812
$546$	2.15431	0.0921958
$547$	12.9075	0.551883	0.275941	−	0.961174i	$-0.411010\pi$
$547$	12.9075	0.551883	0.275941	+	0.961174i	$0.411010\pi$
$548$	−71.8267	−3.06828
$549$	77.6863	3.31557
$550$	6.77165	0.288744
$551$	0	0
$552$	−35.2921	−1.50213
$553$	−3.84199	−0.163378
$554$	11.9952	0.509628
$555$	25.2673	1.07254
$556$	−10.1899	−0.432147
$557$	−34.1040	−1.44503	−0.722517	−	0.691353i	$-0.757015\pi$
$557$	−34.1040	−1.44503	−0.722517	+	0.691353i	$0.757015\pi$
$558$	163.349	6.91511
$559$	−0.269169	−0.0113846
$560$	5.94574	0.251253
$561$	32.0142	1.35164
$562$	16.0847	0.678494
$563$	14.4911	0.610727	0.305363	−	0.952236i	$-0.401222\pi$
$563$	14.4911	0.610727	0.305363	+	0.952236i	$0.401222\pi$
$564$	−106.171	−4.47061
$565$	1.61773	0.0680584
$566$	−50.1159	−2.10653
$567$	−6.55674	−0.275357
$568$	56.7859	2.38268
$569$	39.2110	1.64381	0.821906	−	0.569624i	$-0.192911\pi$
$569$	39.2110	1.64381	0.821906	+	0.569624i	$0.192911\pi$
$570$	0	0
$571$	21.9915	0.920316	0.460158	−	0.887837i	$-0.347793\pi$
$571$	21.9915	0.920316	0.460158	+	0.887837i	$0.347793\pi$
$572$	5.93015	0.247952
$573$	−40.5383	−1.69351
$574$	−2.77331	−0.115756
$575$	1.51145	0.0630316
$576$	65.8261	2.74275
$577$	23.8735	0.993869	0.496934	−	0.867788i	$-0.334459\pi$
$577$	23.8735	0.993869	0.496934	+	0.867788i	$0.334459\pi$
$578$	−0.798628	−0.0332185
$579$	57.8057	2.40232
$580$	−20.0932	−0.834326
$581$	3.82777	0.158803
$582$	139.683	5.79004
$583$	−11.0795	−0.458866
$584$	92.7387	3.83756
$585$	−2.93220	−0.121231
$586$	16.9349	0.699574
$587$	17.8281	0.735843	0.367921	−	0.929857i	$-0.380070\pi$
$587$	17.8281	0.735843	0.367921	+	0.929857i	$0.380070\pi$
$588$	99.8065	4.11595
$589$	0	0
$590$	−7.06323	−0.290788
$591$	−6.61023	−0.271909
$592$	85.9082	3.53081
$593$	−21.2446	−0.872412	−0.436206	−	0.899847i	$-0.643678\pi$
$593$	−21.2446	−0.872412	−0.436206	+	0.899847i	$0.643678\pi$
$594$	−67.1815	−2.75649
$595$	−2.34818	−0.0962658
$596$	43.8244	1.79512
$597$	5.70131	0.233339
$598$	1.86196	0.0761411
$599$	−24.3374	−0.994397	−0.497199	−	0.867637i	$-0.665638\pi$
$599$	−24.3374	−0.994397	−0.497199	+	0.867637i	$0.665638\pi$
$600$	−23.3499	−0.953255
$601$	−15.7891	−0.644051	−0.322025	−	0.946731i	$-0.604364\pi$
$601$	−15.7891	−0.644051	−0.322025	+	0.946731i	$0.604364\pi$
$602$	0.868585	0.0354009
$603$	16.9382	0.689779
$604$	−56.3400	−2.29244
$605$	4.37107	0.177709
$606$	−114.316	−4.64375
$607$	−7.81471	−0.317189	−0.158595	−	0.987344i	$-0.550696\pi$
$607$	−7.81471	−0.317189	−0.158595	+	0.987344i	$0.550696\pi$
$608$	0	0
$609$	7.14564	0.289556
$610$	−32.6384	−1.32149
$611$	3.32324	0.134444
$612$	−125.788	−5.08467
$613$	12.9547	0.523235	0.261618	−	0.965172i	$-0.415744\pi$
$613$	12.9547	0.523235	0.261618	+	0.965172i	$0.415744\pi$
$614$	17.8160	0.718996
$615$	5.58364	0.225154
$616$	−11.3531	−0.457431
$617$	18.8873	0.760373	0.380187	−	0.924910i	$-0.375860\pi$
$617$	18.8873	0.760373	0.380187	+	0.924910i	$0.375860\pi$
$618$	38.3516	1.54273
$619$	29.2673	1.17635	0.588176	−	0.808733i	$-0.299846\pi$
$619$	29.2673	1.17635	0.588176	+	0.808733i	$0.299846\pi$
$620$	−48.7859	−1.95929
$621$	−14.9950	−0.601730
$622$	54.2339	2.17458
$623$	8.39396	0.336297
$624$	−14.7469	−0.590349
$625$	1.00000	0.0400000
$626$	50.9479	2.03629
$627$	0	0
$628$	−32.4872	−1.29638
$629$	−33.9281	−1.35280
$630$	9.46196	0.376973
$631$	−5.25309	−0.209122	−0.104561	−	0.994518i	$-0.533344\pi$
$631$	−5.25309	−0.209122	−0.104561	+	0.994518i	$0.533344\pi$
$632$	51.2992	2.04057
$633$	−52.0637	−2.06935
$634$	−8.87291	−0.352388
$635$	−13.1292	−0.521015
$636$	64.3942	2.55340
$637$	−3.12402	−0.123778
$638$	27.6698	1.09546
$639$	46.3292	1.83275
$640$	−3.92440	−0.155126
$641$	13.0021	0.513554	0.256777	−	0.966471i	$-0.417339\pi$
$641$	13.0021	0.513554	0.256777	+	0.966471i	$0.417339\pi$
$642$	73.8417	2.91430
$643$	−17.3534	−0.684353	−0.342176	−	0.939636i	$-0.611164\pi$
$643$	−17.3534	−0.684353	−0.342176	+	0.939636i	$0.611164\pi$
$644$	−4.27121	−0.168309
$645$	−1.74876	−0.0688573
$646$	0	0
$647$	12.4848	0.490830	0.245415	−	0.969418i	$-0.421076\pi$
$647$	12.4848	0.490830	0.245415	+	0.969418i	$0.421076\pi$
$648$	87.5473	3.43918
$649$	6.91437	0.271413
$650$	1.23191	0.0483193
$651$	17.3494	0.679978
$652$	99.5507	3.89871
$653$	−28.3532	−1.10955	−0.554774	−	0.832001i	$-0.687195\pi$
$653$	−28.3532	−1.10955	−0.554774	+	0.832001i	$0.687195\pi$
$654$	39.2022	1.53293
$655$	8.17223	0.319316
$656$	18.9842	0.741209
$657$	75.6616	2.95184
$658$	−10.7238	−0.418058
$659$	−45.2202	−1.76153	−0.880764	−	0.473556i	$-0.842970\pi$
$659$	−45.2202	−1.76153	−0.880764	+	0.473556i	$0.842970\pi$
$660$	38.5275	1.49968
$661$	14.6086	0.568207	0.284104	−	0.958794i	$-0.408304\pi$
$661$	14.6086	0.568207	0.284104	+	0.958794i	$0.408304\pi$
$662$	86.2115	3.35070
$663$	5.82406	0.226188
$664$	−51.1093	−1.98343
$665$	0	0
$666$	136.713	5.29752
$667$	6.17594	0.239133
$668$	28.9820	1.12135
$669$	15.6084	0.603455
$670$	−7.11627	−0.274926
$671$	31.9505	1.23344
$672$	20.7500	0.800449
$673$	0.440534	0.0169813	0.00849067	−	0.999964i	$-0.497297\pi$
$673$	0.440534	0.0169813	0.00849067	+	0.999964i	$0.497297\pi$
$674$	−23.0111	−0.886356
$675$	−9.92099	−0.381859
$676$	−62.8479	−2.41723
$677$	−32.8057	−1.26083	−0.630414	−	0.776259i	$-0.717115\pi$
$677$	−32.8057	−1.26083	−0.630414	+	0.776259i	$0.717115\pi$
$678$	12.9476	0.497249
$679$	10.0295	0.384898
$680$	31.3534	1.20235
$681$	−22.2515	−0.852681
$682$	67.1815	2.57251
$683$	39.6092	1.51561	0.757803	−	0.652484i	$-0.226273\pi$
$683$	39.6092	1.51561	0.757803	+	0.652484i	$0.226273\pi$
$684$	0	0
$685$	14.6065	0.558087
$686$	20.6611	0.788844
$687$	25.5907	0.976348
$688$	−5.94574	−0.226679
$689$	−2.01559	−0.0767879
$690$	12.0969	0.460522
$691$	−19.8962	−0.756889	−0.378444	−	0.925624i	$-0.623541\pi$
$691$	−19.8962	−0.756889	−0.378444	+	0.925624i	$0.623541\pi$
$692$	17.3665	0.660175
$693$	−9.26254	−0.351855
$694$	−48.6642	−1.84727
$695$	2.07219	0.0786027
$696$	−95.4103	−3.61652
$697$	−7.49752	−0.283989
$698$	9.31924	0.352738
$699$	43.1269	1.63121
$700$	−2.82591	−0.106809
$701$	−14.1251	−0.533497	−0.266748	−	0.963766i	$-0.585949\pi$
$701$	−14.1251	−0.533497	−0.266748	+	0.963766i	$0.585949\pi$
$702$	−12.2217	−0.461279
$703$	0	0
$704$	27.0727	1.02034
$705$	21.5907	0.813155
$706$	−8.97234	−0.337678
$707$	−8.20809	−0.308697
$708$	−40.1865	−1.51030
$709$	−41.1815	−1.54660	−0.773302	−	0.634038i	$-0.781396\pi$
$709$	−41.1815	−1.54660	−0.773302	+	0.634038i	$0.781396\pi$
$710$	−19.4643	−0.730482
$711$	41.8528	1.56960
$712$	−112.078	−4.20031
$713$	14.9950	0.561569
$714$	−18.7938	−0.703338
$715$	−1.20594	−0.0450997
$716$	−35.3466	−1.32097
$717$	43.1815	1.61264
$718$	−4.48718	−0.167460
$719$	−18.0227	−0.672133	−0.336067	−	0.941838i	$-0.609097\pi$
$719$	−18.0227	−0.672133	−0.336067	+	0.941838i	$0.609097\pi$
$720$	−64.7701	−2.41384
$721$	2.75372	0.102554
$722$	0	0
$723$	84.8425	3.15533
$724$	−76.4332	−2.84062
$725$	4.08612	0.151755
$726$	34.9841	1.29838
$727$	−21.1266	−0.783544	−0.391772	−	0.920062i	$-0.628138\pi$
$727$	−21.1266	−0.783544	−0.391772	+	0.920062i	$0.628138\pi$
$728$	−2.06537	−0.0765479
$729$	−19.1444	−0.709051
$730$	−31.7877	−1.17652
$731$	2.34818	0.0868504
$732$	−185.697	−6.86356
$733$	−27.6660	−1.02187	−0.510934	−	0.859620i	$-0.670700\pi$
$733$	−27.6660	−1.02187	−0.510934	+	0.859620i	$0.670700\pi$
$734$	98.9326	3.65167
$735$	−20.2964	−0.748646
$736$	17.9341	0.661061
$737$	6.96629	0.256607
$738$	30.2112	1.11209
$739$	−14.2987	−0.525986	−0.262993	−	0.964798i	$-0.584710\pi$
$739$	−14.2987	−0.525986	−0.262993	+	0.964798i	$0.584710\pi$
$740$	−40.8308	−1.50097
$741$	0	0
$742$	6.50415	0.238775
$743$	−49.9438	−1.83226	−0.916130	−	0.400881i	$-0.868704\pi$
$743$	−49.9438	−1.83226	−0.916130	+	0.400881i	$0.868704\pi$
$744$	−231.654	−8.49285
$745$	−8.91203	−0.326511
$746$	−35.2516	−1.29065
$747$	−41.6979	−1.52565
$748$	−51.7335	−1.89156
$749$	5.30198	0.193730
$750$	8.00355	0.292249
$751$	−9.69216	−0.353672	−0.176836	−	0.984240i	$-0.556586\pi$
$751$	−9.69216	−0.353672	−0.176836	+	0.984240i	$0.556586\pi$
$752$	73.4080	2.67691
$753$	79.6982	2.90436
$754$	5.03371	0.183317
$755$	11.4572	0.416970
$756$	28.0359	1.01965
$757$	46.6889	1.69694	0.848469	−	0.529245i	$-0.177525\pi$
$757$	46.6889	1.69694	0.848469	+	0.529245i	$0.177525\pi$
$758$	24.6469	0.895214
$759$	−11.8420	−0.429837
$760$	0	0
$761$	−38.7361	−1.40418	−0.702091	−	0.712087i	$-0.747750\pi$
$761$	−38.7361	−1.40418	−0.702091	+	0.712087i	$0.747750\pi$
$762$	−105.080	−3.80665
$763$	2.81480	0.101903
$764$	65.5080	2.37000
$765$	25.5799	0.924844
$766$	5.52104	0.199483
$767$	1.25787	0.0454190
$768$	32.5864	1.17586
$769$	−5.38666	−0.194248	−0.0971239	−	0.995272i	$-0.530964\pi$
$769$	−5.38666	−0.194248	−0.0971239	+	0.995272i	$0.530964\pi$
$770$	3.89148	0.140239
$771$	27.4433	0.988345
$772$	−93.4112	−3.36194
$773$	−7.20137	−0.259015	−0.129508	−	0.991578i	$-0.541340\pi$
$773$	−7.20137	−0.259015	−0.129508	+	0.991578i	$0.541340\pi$
$774$	−9.46196	−0.340103
$775$	9.92099	0.356373
$776$	−133.917	−4.80733
$777$	14.5204	0.520917
$778$	2.82047	0.101119
$779$	0	0
$780$	7.00896	0.250961
$781$	19.0541	0.681808
$782$	−16.2434	−0.580861
$783$	−40.5383	−1.44872
$784$	−69.0074	−2.46455
$785$	6.60653	0.235797
$786$	65.4069	2.33299
$787$	33.5231	1.19497	0.597485	−	0.801880i	$-0.296167\pi$
$787$	33.5231	1.19497	0.597485	+	0.801880i	$0.296167\pi$
$788$	10.6818	0.380524
$789$	27.4148	0.975993
$790$	−17.5836	−0.625598
$791$	0.929664	0.0330550
$792$	123.676	4.39463
$793$	5.81247	0.206407
$794$	−61.8972	−2.19665
$795$	−13.0951	−0.464435
$796$	−9.21305	−0.326548
$797$	10.4979	0.371855	0.185927	−	0.982563i	$-0.440471\pi$
$797$	10.4979	0.371855	0.185927	+	0.982563i	$0.440471\pi$
$798$	0	0
$799$	−28.9913	−1.02564
$800$	11.8656	0.419511
$801$	−91.4398	−3.23087
$802$	−49.0432	−1.73177
$803$	31.1178	1.09812
$804$	−40.4882	−1.42791
$805$	0.868585	0.0306136
$806$	12.2217	0.430492
$807$	−93.1591	−3.27936
$808$	109.596	3.85559
$809$	−13.0724	−0.459600	−0.229800	−	0.973238i	$-0.573807\pi$
$809$	−13.0724	−0.459600	−0.229800	+	0.973238i	$0.573807\pi$
$810$	−30.0083	−1.05438
$811$	10.0790	0.353922	0.176961	−	0.984218i	$-0.443373\pi$
$811$	10.0790	0.353922	0.176961	+	0.984218i	$0.443373\pi$
$812$	−11.5470	−0.405221
$813$	−73.3924	−2.57398
$814$	56.2268	1.97075
$815$	−20.2444	−0.709131
$816$	128.649	4.50362
$817$	0	0
$818$	18.0956	0.632697
$819$	−1.68505	−0.0588804
$820$	−9.02289	−0.315093
$821$	40.2987	1.40643	0.703217	−	0.710975i	$-0.251746\pi$
$821$	40.2987	1.40643	0.703217	+	0.710975i	$0.251746\pi$
$822$	116.904	4.07750
$823$	−5.07715	−0.176978	−0.0884892	−	0.996077i	$-0.528204\pi$
$823$	−5.07715	−0.176978	−0.0884892	+	0.996077i	$0.528204\pi$
$824$	−36.7684	−1.28089
$825$	−7.83488	−0.272775
$826$	−4.05904	−0.141232
$827$	42.8077	1.48857	0.744285	−	0.667862i	$-0.232791\pi$
$827$	42.8077	1.48857	0.744285	+	0.667862i	$0.232791\pi$
$828$	46.5286	1.61698
$829$	−24.2018	−0.840562	−0.420281	−	0.907394i	$-0.638068\pi$
$829$	−24.2018	−0.840562	−0.420281	+	0.907394i	$0.638068\pi$
$830$	17.5186	0.608078
$831$	−13.8786	−0.481444
$832$	4.92509	0.170747
$833$	27.2534	0.944274
$834$	16.5849	0.574288
$835$	−5.89372	−0.203960
$836$	0	0
$837$	−98.4261	−3.40210
$838$	35.4527	1.22469
$839$	8.63975	0.298277	0.149139	−	0.988816i	$-0.452350\pi$
$839$	8.63975	0.298277	0.149139	+	0.988816i	$0.452350\pi$
$840$	−13.4185	−0.462983
$841$	−12.3036	−0.424264
$842$	15.3463	0.528869
$843$	−18.6102	−0.640971
$844$	84.1325	2.89596
$845$	12.7806	0.439666
$846$	116.820	4.01637
$847$	2.51193	0.0863109
$848$	−44.5229	−1.52892
$849$	57.9847	1.99003
$850$	−10.7469	−0.368616
$851$	12.5499	0.430206
$852$	−110.743	−3.79398
$853$	−13.0229	−0.445895	−0.222948	−	0.974830i	$-0.571568\pi$
$853$	−13.0229	−0.445895	−0.222948	+	0.974830i	$0.571568\pi$
$854$	−18.7564	−0.641829
$855$	0	0
$856$	−70.7934	−2.41967
$857$	2.82367	0.0964548	0.0482274	−	0.998836i	$-0.484643\pi$
$857$	2.82367	0.0964548	0.0482274	+	0.998836i	$0.484643\pi$
$858$	−9.65182	−0.329508
$859$	24.1227	0.823057	0.411529	−	0.911397i	$-0.364995\pi$
$859$	24.1227	0.823057	0.411529	+	0.911397i	$0.364995\pi$
$860$	2.82591	0.0963628
$861$	3.20876	0.109354
$862$	−76.8092	−2.61613
$863$	−32.7307	−1.11417	−0.557084	−	0.830456i	$-0.688080\pi$
$863$	−32.7307	−1.11417	−0.557084	+	0.830456i	$0.688080\pi$
$864$	−117.718	−4.00485
$865$	−3.53161	−0.120078
$866$	32.9366	1.11923
$867$	0.924022	0.0313814
$868$	−28.0359	−0.951599
$869$	17.2131	0.583913
$870$	32.7035	1.10875
$871$	1.26731	0.0429413
$872$	−37.5839	−1.27275
$873$	−109.257	−3.69779
$874$	0	0
$875$	0.574672	0.0194274
$876$	−180.857	−6.11060
$877$	49.5072	1.67174	0.835869	−	0.548929i	$-0.184964\pi$
$877$	49.5072	1.67174	0.835869	+	0.548929i	$0.184964\pi$
$878$	−41.2318	−1.39150
$879$	−19.5939	−0.660884
$880$	−26.6384	−0.897980
$881$	40.3152	1.35826	0.679128	−	0.734020i	$-0.262358\pi$
$881$	40.3152	1.35826	0.679128	+	0.734020i	$0.262358\pi$
$882$	−109.817	−3.69774
$883$	−29.3347	−0.987192	−0.493596	−	0.869691i	$-0.664318\pi$
$883$	−29.3347	−0.987192	−0.493596	+	0.869691i	$0.664318\pi$
$884$	−9.41140	−0.316540
$885$	8.17223	0.274707
$886$	−78.4508	−2.63561
$887$	−43.3214	−1.45459	−0.727295	−	0.686325i	$-0.759223\pi$
$887$	−43.3214	−1.45459	−0.727295	+	0.686325i	$0.759223\pi$
$888$	−193.880	−6.50619
$889$	−7.54496	−0.253050
$890$	38.4167	1.28773
$891$	29.3758	0.984128
$892$	−25.2224	−0.844508
$893$	0	0
$894$	−71.3279	−2.38556
$895$	7.18801	0.240269
$896$	−2.25524	−0.0753424
$897$	−2.15431	−0.0719302
$898$	−78.8157	−2.63011
$899$	40.5383	1.35203
$900$	30.7842	1.02614
$901$	17.5836	0.585796
$902$	12.4251	0.413712
$903$	−1.00496	−0.0334431
$904$	−12.4131	−0.412854
$905$	15.5433	0.516677
$906$	91.6982	3.04647
$907$	−14.0731	−0.467288	−0.233644	−	0.972322i	$-0.575065\pi$
$907$	−14.0731	−0.467288	−0.233644	+	0.972322i	$0.575065\pi$
$908$	35.9574	1.19329
$909$	89.4151	2.96571
$910$	0.707941	0.0234680
$911$	−30.0725	−0.996346	−0.498173	−	0.867078i	$-0.665996\pi$
$911$	−30.0725	−0.996346	−0.498173	+	0.867078i	$0.665996\pi$
$912$	0	0
$913$	−17.1493	−0.567560
$914$	46.4733	1.53720
$915$	37.7630	1.24841
$916$	−41.3534	−1.36636
$917$	4.69635	0.155087
$918$	106.620	3.51898
$919$	29.6518	0.978123	0.489062	−	0.872249i	$-0.337339\pi$
$919$	29.6518	0.978123	0.489062	+	0.872249i	$0.337339\pi$
$920$	−11.5976	−0.382360
$921$	−20.6133	−0.679233
$922$	58.7682	1.93543
$923$	3.46634	0.114096
$924$	22.1407	0.728375
$925$	8.30326	0.273010
$926$	−17.9715	−0.590582
$927$	−29.9978	−0.985256
$928$	48.4841	1.59157
$929$	58.3803	1.91540	0.957698	−	0.287775i	$-0.0929154\pi$
$929$	58.3803	1.91540	0.957698	+	0.287775i	$0.0929154\pi$
$930$	79.4032	2.60373
$931$	0	0
$932$	−69.6911	−2.28281
$933$	−62.7492	−2.05432
$934$	23.6945	0.775308
$935$	10.5204	0.344054
$936$	22.4992	0.735410
$937$	−3.15850	−0.103184	−0.0515918	−	0.998668i	$-0.516429\pi$
$937$	−3.15850	−0.103184	−0.0515918	+	0.998668i	$0.516429\pi$
$938$	−4.08952	−0.133528
$939$	−58.9473	−1.92367
$940$	−34.8896	−1.13797
$941$	9.66975	0.315225	0.157612	−	0.987501i	$-0.449620\pi$
$941$	9.66975	0.315225	0.157612	+	0.987501i	$0.449620\pi$
$942$	52.8757	1.72278
$943$	2.77331	0.0903116
$944$	27.7854	0.904337
$945$	−5.70131	−0.185464
$946$	−3.89148	−0.126523
$947$	31.3714	1.01943	0.509716	−	0.860343i	$-0.329750\pi$
$947$	31.3714	1.01943	0.509716	+	0.860343i	$0.329750\pi$
$948$	−100.043	−3.24923
$949$	5.66098	0.183763
$950$	0	0
$951$	10.2661	0.332900
$952$	18.0179	0.583964
$953$	13.1224	0.425075	0.212537	−	0.977153i	$-0.431827\pi$
$953$	13.1224	0.425075	0.212537	+	0.977153i	$0.431827\pi$
$954$	−70.8531	−2.29395
$955$	−13.3216	−0.431076
$956$	−69.7792	−2.25682
$957$	−32.0142	−1.03487
$958$	24.3740	0.787488
$959$	8.39396	0.271055
$960$	31.9978	1.03272
$961$	67.4261	2.17504
$962$	10.2288	0.329791
$963$	−57.7573	−1.86120
$964$	−137.101	−4.41574
$965$	18.9959	0.611500
$966$	6.95177	0.223669
$967$	−44.4400	−1.42910	−0.714548	−	0.699587i	$-0.753367\pi$
$967$	−44.4400	−1.42910	−0.714548	+	0.699587i	$0.753367\pi$
$968$	−33.5399	−1.07801
$969$	0	0
$970$	45.9021	1.47383
$971$	5.69927	0.182898	0.0914491	−	0.995810i	$-0.470850\pi$
$971$	5.69927	0.182898	0.0914491	+	0.995810i	$0.470850\pi$
$972$	−24.3755	−0.781843
$973$	1.19083	0.0381762
$974$	101.968	3.26725
$975$	−1.42533	−0.0456470
$976$	128.393	4.10977
$977$	23.9164	0.765154	0.382577	−	0.923924i	$-0.375037\pi$
$977$	23.9164	0.765154	0.382577	+	0.923924i	$0.375037\pi$
$978$	−162.027	−5.18106
$979$	−37.6070	−1.20193
$980$	32.7981	1.04770
$981$	−30.6631	−0.978998
$982$	57.0408	1.82025
$983$	45.5302	1.45219	0.726095	−	0.687595i	$-0.241333\pi$
$983$	45.5302	1.45219	0.726095	+	0.687595i	$0.241333\pi$
$984$	−42.8441	−1.36582
$985$	−2.17223	−0.0692131
$986$	−43.9131	−1.39848
$987$	12.4076	0.394938
$988$	0	0
$989$	−0.868585	−0.0276194
$990$	−42.3919	−1.34730
$991$	−27.5521	−0.875220	−0.437610	−	0.899165i	$-0.644175\pi$
$991$	−27.5521	−0.875220	−0.437610	+	0.899165i	$0.644175\pi$
$992$	117.718	3.73756
$993$	−99.7477	−3.16540
$994$	−11.1856	−0.354785
$995$	1.87355	0.0593954
$996$	99.6724	3.15824
$997$	16.8557	0.533826	0.266913	−	0.963721i	$-0.413996\pi$
$997$	16.8557	0.533826	0.266913	+	0.963721i	$0.413996\pi$
$998$	−73.2147	−2.31757
$999$	−82.3766	−2.60628

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.a.p.1.4		4
5.4	even	2		9025.2.a.bf.1.1		4
19.18	odd	2		95.2.a.b.1.1	✓	4
57.56	even	2		855.2.a.m.1.4		4
76.75	even	2		1520.2.a.t.1.1		4
95.18	even	4		475.2.b.e.324.8		8
95.37	even	4		475.2.b.e.324.1		8
95.94	odd	2		475.2.a.i.1.4		4
133.132	even	2		4655.2.a.y.1.1		4
152.37	odd	2		6080.2.a.cc.1.1		4
152.75	even	2		6080.2.a.ch.1.4		4
285.284	even	2		4275.2.a.bo.1.1		4
380.379	even	2		7600.2.a.cf.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.a.b.1.1	✓	4	19.18	odd	2
475.2.a.i.1.4		4	95.94	odd	2
475.2.b.e.324.1		8	95.37	even	4
475.2.b.e.324.8		8	95.18	even	4
855.2.a.m.1.4		4	57.56	even	2
1520.2.a.t.1.1		4	76.75	even	2
1805.2.a.p.1.4		4	1.1	even	1	trivial
4275.2.a.bo.1.1		4	285.284	even	2
4655.2.a.y.1.1		4	133.132	even	2
6080.2.a.cc.1.1		4	152.37	odd	2
6080.2.a.ch.1.4		4	152.75	even	2
7600.2.a.cf.1.4		4	380.379	even	2
9025.2.a.bf.1.1		4	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1805 = 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1805.a (trivial)

\(f(q)\)	\(=\)	\(q+2.63010 q^{2} -3.04306 q^{3} +4.91744 q^{4} -1.00000 q^{5} -8.00355 q^{6} -0.574672 q^{7} +7.67316 q^{8} +6.26020 q^{9} +O(q^{10})\)	\(q+2.63010 q^{2} -3.04306 q^{3} +4.91744 q^{4} -1.00000 q^{5} -8.00355 q^{6} -0.574672 q^{7} +7.67316 q^{8} +6.26020 q^{9} -2.63010 q^{10} +2.57467 q^{11} -14.9641 q^{12} +0.468387 q^{13} -1.51145 q^{14} +3.04306 q^{15} +10.3463 q^{16} -4.08612 q^{17} +16.4650 q^{18} -4.91744 q^{20} +1.74876 q^{21} +6.77165 q^{22} +1.51145 q^{23} -23.3499 q^{24} +1.00000 q^{25} +1.23191 q^{26} -9.92099 q^{27} -2.82591 q^{28} +4.08612 q^{29} +8.00355 q^{30} +9.92099 q^{31} +11.8656 q^{32} -7.83488 q^{33} -10.7469 q^{34} +0.574672 q^{35} +30.7842 q^{36} +8.30326 q^{37} -1.42533 q^{39} -7.67316 q^{40} +1.83488 q^{41} +4.59942 q^{42} -0.574672 q^{43} +12.6608 q^{44} -6.26020 q^{45} +3.97526 q^{46} +7.09508 q^{47} -31.4845 q^{48} -6.66975 q^{49} +2.63010 q^{50} +12.4343 q^{51} +2.30326 q^{52} -4.30326 q^{53} -26.0932 q^{54} -2.57467 q^{55} -4.40955 q^{56} +10.7469 q^{58} +2.68553 q^{59} +14.9641 q^{60} +12.4095 q^{61} +26.0932 q^{62} -3.59756 q^{63} +10.5150 q^{64} -0.468387 q^{65} -20.6065 q^{66} +2.70570 q^{67} -20.0932 q^{68} -4.59942 q^{69} +1.51145 q^{70} +7.40058 q^{71} +48.0356 q^{72} +12.0861 q^{73} +21.8384 q^{74} -3.04306 q^{75} -1.47959 q^{77} -3.74876 q^{78} +6.68553 q^{79} -10.3463 q^{80} +11.4095 q^{81} +4.82591 q^{82} -6.66079 q^{83} +8.59942 q^{84} +4.08612 q^{85} -1.51145 q^{86} -12.4343 q^{87} +19.7559 q^{88} -14.6065 q^{89} -16.4650 q^{90} -0.269169 q^{91} +7.43244 q^{92} -30.1902 q^{93} +18.6608 q^{94} -36.1076 q^{96} -17.4526 q^{97} -17.5421 q^{98} +16.1180 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{3} + 8 q^{4} - 4 q^{5} + 4 q^{7} + 12 q^{8} + 8 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^3 + 8 * q^4 - 4 * q^5 + 4 * q^7 + 12 * q^8 + 8 * q^9	\( 4 q + 2 q^{2} - 2 q^{3} + 8 q^{4} - 4 q^{5} + 4 q^{7} + 12 q^{8} + 8 q^{9} - 2 q^{10} + 4 q^{11} - 6 q^{12} - 2 q^{13} + 8 q^{14} + 2 q^{15} + 4 q^{16} + 4 q^{17} + 34 q^{18} - 8 q^{20} + 4 q^{21} - 4 q^{22} - 8 q^{23} - 24 q^{24} + 4 q^{25} + 4 q^{26} + 4 q^{27} - 8 q^{28} - 4 q^{29} - 4 q^{31} + 6 q^{32} - 8 q^{33} + 4 q^{34} - 4 q^{35} + 40 q^{36} + 6 q^{37} - 12 q^{39} - 12 q^{40} - 16 q^{41} + 28 q^{42} + 4 q^{43} + 24 q^{44} - 8 q^{45} - 12 q^{47} - 38 q^{48} + 20 q^{49} + 2 q^{50} + 36 q^{51} - 18 q^{52} + 10 q^{53} - 20 q^{54} - 4 q^{55} + 12 q^{56} - 4 q^{58} + 6 q^{60} + 20 q^{61} + 20 q^{62} + 20 q^{63} - 4 q^{64} + 2 q^{65} - 28 q^{66} + 18 q^{67} + 4 q^{68} - 28 q^{69} - 8 q^{70} + 20 q^{71} + 52 q^{72} + 28 q^{73} + 32 q^{74} - 2 q^{75} - 40 q^{77} - 12 q^{78} + 16 q^{79} - 4 q^{80} + 16 q^{81} + 16 q^{82} + 44 q^{84} - 4 q^{85} + 8 q^{86} - 36 q^{87} + 12 q^{88} - 4 q^{89} - 34 q^{90} + 36 q^{91} - 28 q^{92} - 40 q^{93} + 48 q^{94} - 52 q^{96} - 30 q^{97} - 38 q^{98} - 4 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^3 + 8 * q^4 - 4 * q^5 + 4 * q^7 + 12 * q^8 + 8 * q^9 - 2 * q^10 + 4 * q^11 - 6 * q^12 - 2 * q^13 + 8 * q^14 + 2 * q^15 + 4 * q^16 + 4 * q^17 + 34 * q^18 - 8 * q^20 + 4 * q^21 - 4 * q^22 - 8 * q^23 - 24 * q^24 + 4 * q^25 + 4 * q^26 + 4 * q^27 - 8 * q^28 - 4 * q^29 - 4 * q^31 + 6 * q^32 - 8 * q^33 + 4 * q^34 - 4 * q^35 + 40 * q^36 + 6 * q^37 - 12 * q^39 - 12 * q^40 - 16 * q^41 + 28 * q^42 + 4 * q^43 + 24 * q^44 - 8 * q^45 - 12 * q^47 - 38 * q^48 + 20 * q^49 + 2 * q^50 + 36 * q^51 - 18 * q^52 + 10 * q^53 - 20 * q^54 - 4 * q^55 + 12 * q^56 - 4 * q^58 + 6 * q^60 + 20 * q^61 + 20 * q^62 + 20 * q^63 - 4 * q^64 + 2 * q^65 - 28 * q^66 + 18 * q^67 + 4 * q^68 - 28 * q^69 - 8 * q^70 + 20 * q^71 + 52 * q^72 + 28 * q^73 + 32 * q^74 - 2 * q^75 - 40 * q^77 - 12 * q^78 + 16 * q^79 - 4 * q^80 + 16 * q^81 + 16 * q^82 + 44 * q^84 - 4 * q^85 + 8 * q^86 - 36 * q^87 + 12 * q^88 - 4 * q^89 - 34 * q^90 + 36 * q^91 - 28 * q^92 - 40 * q^93 + 48 * q^94 - 52 * q^96 - 30 * q^97 - 38 * q^98 - 4 * q^99

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