LMFDB - Embedded newform 5070.2.a.bk.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5070,2,Mod(1,5070)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5070, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("5070.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5070.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:	$40.4841538248$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$0.445042$ of defining polynomial
Character	$\chi$	$=$	5070.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +1.35690 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +1.35690 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +3.19806 q^{11} -1.00000 q^{12} -1.35690 q^{14} +1.00000 q^{15} +1.00000 q^{16} -2.04892 q^{17} -1.00000 q^{18} -5.34481 q^{19} -1.00000 q^{20} -1.35690 q^{21} -3.19806 q^{22} -8.32304 q^{23} +1.00000 q^{24} +1.00000 q^{25} -1.00000 q^{27} +1.35690 q^{28} +8.07069 q^{29} -1.00000 q^{30} -0.185981 q^{31} -1.00000 q^{32} -3.19806 q^{33} +2.04892 q^{34} -1.35690 q^{35} +1.00000 q^{36} -2.46681 q^{37} +5.34481 q^{38} +1.00000 q^{40} +12.2349 q^{41} +1.35690 q^{42} -2.91185 q^{43} +3.19806 q^{44} -1.00000 q^{45} +8.32304 q^{46} +13.0978 q^{47} -1.00000 q^{48} -5.15883 q^{49} -1.00000 q^{50} +2.04892 q^{51} +5.74094 q^{53} +1.00000 q^{54} -3.19806 q^{55} -1.35690 q^{56} +5.34481 q^{57} -8.07069 q^{58} -1.62565 q^{59} +1.00000 q^{60} +5.28382 q^{61} +0.185981 q^{62} +1.35690 q^{63} +1.00000 q^{64} +3.19806 q^{66} +1.55496 q^{67} -2.04892 q^{68} +8.32304 q^{69} +1.35690 q^{70} -2.32304 q^{71} -1.00000 q^{72} -5.11529 q^{73} +2.46681 q^{74} -1.00000 q^{75} -5.34481 q^{76} +4.33944 q^{77} -1.42327 q^{79} -1.00000 q^{80} +1.00000 q^{81} -12.2349 q^{82} +11.1196 q^{83} -1.35690 q^{84} +2.04892 q^{85} +2.91185 q^{86} -8.07069 q^{87} -3.19806 q^{88} +3.37867 q^{89} +1.00000 q^{90} -8.32304 q^{92} +0.185981 q^{93} -13.0978 q^{94} +5.34481 q^{95} +1.00000 q^{96} -4.74094 q^{97} +5.15883 q^{98} +3.19806 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{5} + 3 q^{6} - 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^5 + 3 * q^6 - 3 * q^8 + 3 * q^9	$ 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{5} + 3 q^{6} - 3 q^{8} + 3 q^{9} + 3 q^{10} + 14 q^{11} - 3 q^{12} + 3 q^{15} + 3 q^{16} + 3 q^{17} - 3 q^{18} + 7 q^{19} - 3 q^{20} - 14 q^{22} - 5 q^{23} + 3 q^{24} + 3 q^{25} - 3 q^{27} + 12 q^{29} - 3 q^{30} + 14 q^{31} - 3 q^{32} - 14 q^{33} - 3 q^{34} + 3 q^{36} - 4 q^{37} - 7 q^{38} + 3 q^{40} + 13 q^{41} - 5 q^{43} + 14 q^{44} - 3 q^{45} + 5 q^{46} + 21 q^{47} - 3 q^{48} - 7 q^{49} - 3 q^{50} - 3 q^{51} + 3 q^{53} + 3 q^{54} - 14 q^{55} - 7 q^{57} - 12 q^{58} + 7 q^{59} + 3 q^{60} - 17 q^{61} - 14 q^{62} + 3 q^{64} + 14 q^{66} + 5 q^{67} + 3 q^{68} + 5 q^{69} + 13 q^{71} - 3 q^{72} - 13 q^{73} + 4 q^{74} - 3 q^{75} + 7 q^{76} - 7 q^{77} - 7 q^{79} - 3 q^{80} + 3 q^{81} - 13 q^{82} + 12 q^{83} - 3 q^{85} + 5 q^{86} - 12 q^{87} - 14 q^{88} + 3 q^{89} + 3 q^{90} - 5 q^{92} - 14 q^{93} - 21 q^{94} - 7 q^{95} + 3 q^{96} + 7 q^{98} + 14 q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^5 + 3 * q^6 - 3 * q^8 + 3 * q^9 + 3 * q^10 + 14 * q^11 - 3 * q^12 + 3 * q^15 + 3 * q^16 + 3 * q^17 - 3 * q^18 + 7 * q^19 - 3 * q^20 - 14 * q^22 - 5 * q^23 + 3 * q^24 + 3 * q^25 - 3 * q^27 + 12 * q^29 - 3 * q^30 + 14 * q^31 - 3 * q^32 - 14 * q^33 - 3 * q^34 + 3 * q^36 - 4 * q^37 - 7 * q^38 + 3 * q^40 + 13 * q^41 - 5 * q^43 + 14 * q^44 - 3 * q^45 + 5 * q^46 + 21 * q^47 - 3 * q^48 - 7 * q^49 - 3 * q^50 - 3 * q^51 + 3 * q^53 + 3 * q^54 - 14 * q^55 - 7 * q^57 - 12 * q^58 + 7 * q^59 + 3 * q^60 - 17 * q^61 - 14 * q^62 + 3 * q^64 + 14 * q^66 + 5 * q^67 + 3 * q^68 + 5 * q^69 + 13 * q^71 - 3 * q^72 - 13 * q^73 + 4 * q^74 - 3 * q^75 + 7 * q^76 - 7 * q^77 - 7 * q^79 - 3 * q^80 + 3 * q^81 - 13 * q^82 + 12 * q^83 - 3 * q^85 + 5 * q^86 - 12 * q^87 - 14 * q^88 + 3 * q^89 + 3 * q^90 - 5 * q^92 - 14 * q^93 - 21 * q^94 - 7 * q^95 + 3 * q^96 + 7 * q^98 + 14 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.00000	0.408248
$7$	1.35690	0.512858	0.256429	−	0.966563i	$-0.417454\pi$
$7$	1.35690	0.512858	0.256429	+	0.966563i	$0.417454\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	3.19806	0.964252	0.482126	−	0.876102i	$-0.339865\pi$
$11$	3.19806	0.964252	0.482126	+	0.876102i	$0.339865\pi$
$12$	−1.00000	−0.288675
$13$	0	0
$13$	0	0
$14$	−1.35690	−0.362646
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	−2.04892	−0.496935	−0.248468	−	0.968640i	$-0.579927\pi$
$17$	−2.04892	−0.496935	−0.248468	+	0.968640i	$0.579927\pi$
$18$	−1.00000	−0.235702
$19$	−5.34481	−1.22618	−0.613092	−	0.790011i	$-0.710075\pi$
$19$	−5.34481	−1.22618	−0.613092	+	0.790011i	$0.710075\pi$
$20$	−1.00000	−0.223607
$21$	−1.35690	−0.296099
$22$	−3.19806	−0.681829
$23$	−8.32304	−1.73547	−0.867737	−	0.497023i	$-0.834426\pi$
$23$	−8.32304	−1.73547	−0.867737	+	0.497023i	$0.834426\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	0	0
$27$	−1.00000	−0.192450
$28$	1.35690	0.256429
$29$	8.07069	1.49869	0.749345	−	0.662180i	$-0.230369\pi$
$29$	8.07069	1.49869	0.749345	+	0.662180i	$0.230369\pi$
$30$	−1.00000	−0.182574
$31$	−0.185981	−0.0334031	−0.0167016	−	0.999861i	$-0.505317\pi$
$31$	−0.185981	−0.0334031	−0.0167016	+	0.999861i	$0.505317\pi$
$32$	−1.00000	−0.176777
$33$	−3.19806	−0.556711
$34$	2.04892	0.351386
$35$	−1.35690	−0.229357
$36$	1.00000	0.166667
$37$	−2.46681	−0.405541	−0.202771	−	0.979226i	$-0.564995\pi$
$37$	−2.46681	−0.405541	−0.202771	+	0.979226i	$0.564995\pi$
$38$	5.34481	0.867043
$39$	0	0
$40$	1.00000	0.158114
$41$	12.2349	1.91077	0.955385	−	0.295363i	$-0.0954407\pi$
$41$	12.2349	1.91077	0.955385	+	0.295363i	$0.0954407\pi$
$42$	1.35690	0.209374
$43$	−2.91185	−0.444054	−0.222027	−	0.975041i	$-0.571267\pi$
$43$	−2.91185	−0.444054	−0.222027	+	0.975041i	$0.571267\pi$
$44$	3.19806	0.482126
$45$	−1.00000	−0.149071
$46$	8.32304	1.22717
$47$	13.0978	1.91052	0.955258	−	0.295775i	$-0.0955777\pi$
$47$	13.0978	1.91052	0.955258	+	0.295775i	$0.0955777\pi$
$48$	−1.00000	−0.144338
$49$	−5.15883	−0.736976
$50$	−1.00000	−0.141421
$51$	2.04892	0.286906
$52$	0	0
$53$	5.74094	0.788579	0.394289	−	0.918986i	$-0.370991\pi$
$53$	5.74094	0.788579	0.394289	+	0.918986i	$0.370991\pi$
$54$	1.00000	0.136083
$55$	−3.19806	−0.431227
$56$	−1.35690	−0.181323
$57$	5.34481	0.707938
$58$	−8.07069	−1.05973
$59$	−1.62565	−0.211641	−0.105821	−	0.994385i	$-0.533747\pi$
$59$	−1.62565	−0.211641	−0.105821	+	0.994385i	$0.533747\pi$
$60$	1.00000	0.129099
$61$	5.28382	0.676523	0.338262	−	0.941052i	$-0.390161\pi$
$61$	5.28382	0.676523	0.338262	+	0.941052i	$0.390161\pi$
$62$	0.185981	0.0236196
$63$	1.35690	0.170953
$64$	1.00000	0.125000
$65$	0	0
$66$	3.19806	0.393654
$67$	1.55496	0.189968	0.0949842	−	0.995479i	$-0.469720\pi$
$67$	1.55496	0.189968	0.0949842	+	0.995479i	$0.469720\pi$
$68$	−2.04892	−0.248468
$69$	8.32304	1.00198
$70$	1.35690	0.162180
$71$	−2.32304	−0.275695	−0.137847	−	0.990453i	$-0.544018\pi$
$71$	−2.32304	−0.275695	−0.137847	+	0.990453i	$0.544018\pi$
$72$	−1.00000	−0.117851
$73$	−5.11529	−0.598700	−0.299350	−	0.954143i	$-0.596770\pi$
$73$	−5.11529	−0.598700	−0.299350	+	0.954143i	$0.596770\pi$
$74$	2.46681	0.286761
$75$	−1.00000	−0.115470
$76$	−5.34481	−0.613092
$77$	4.33944	0.494525
$78$	0	0
$79$	−1.42327	−0.160131	−0.0800653	−	0.996790i	$-0.525513\pi$
$79$	−1.42327	−0.160131	−0.0800653	+	0.996790i	$0.525513\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	−12.2349	−1.35112
$83$	11.1196	1.22054	0.610268	−	0.792195i	$-0.291062\pi$
$83$	11.1196	1.22054	0.610268	+	0.792195i	$0.291062\pi$
$84$	−1.35690	−0.148049
$85$	2.04892	0.222236
$86$	2.91185	0.313993
$87$	−8.07069	−0.865269
$88$	−3.19806	−0.340915
$89$	3.37867	0.358138	0.179069	−	0.983837i	$-0.442691\pi$
$89$	3.37867	0.358138	0.179069	+	0.983837i	$0.442691\pi$
$90$	1.00000	0.105409
$91$	0	0
$92$	−8.32304	−0.867737
$93$	0.185981	0.0192853
$94$	−13.0978	−1.35094
$95$	5.34481	0.548366
$96$	1.00000	0.102062
$97$	−4.74094	−0.481369	−0.240685	−	0.970603i	$-0.577372\pi$
$97$	−4.74094	−0.481369	−0.240685	+	0.970603i	$0.577372\pi$
$98$	5.15883	0.521121
$99$	3.19806	0.321417
$100$	1.00000	0.100000
$101$	−12.5918	−1.25293	−0.626465	−	0.779449i	$-0.715499\pi$
$101$	−12.5918	−1.25293	−0.626465	+	0.779449i	$0.715499\pi$
$102$	−2.04892	−0.202873
$103$	−9.00000	−0.886796	−0.443398	−	0.896325i	$-0.646227\pi$
$103$	−9.00000	−0.886796	−0.443398	+	0.896325i	$0.646227\pi$
$104$	0	0
$105$	1.35690	0.132419
$106$	−5.74094	−0.557609
$107$	−5.08815	−0.491890	−0.245945	−	0.969284i	$-0.579098\pi$
$107$	−5.08815	−0.491890	−0.245945	+	0.969284i	$0.579098\pi$
$108$	−1.00000	−0.0962250
$109$	6.43296	0.616166	0.308083	−	0.951360i	$-0.400313\pi$
$109$	6.43296	0.616166	0.308083	+	0.951360i	$0.400313\pi$
$110$	3.19806	0.304923
$111$	2.46681	0.234139
$112$	1.35690	0.128215
$113$	−18.6571	−1.75511	−0.877556	−	0.479473i	$-0.840828\pi$
$113$	−18.6571	−1.75511	−0.877556	+	0.479473i	$0.840828\pi$
$114$	−5.34481	−0.500588
$115$	8.32304	0.776128
$116$	8.07069	0.749345
$117$	0	0
$118$	1.62565	0.149653
$119$	−2.78017	−0.254858
$120$	−1.00000	−0.0912871
$121$	−0.772398	−0.0702180
$122$	−5.28382	−0.478374
$123$	−12.2349	−1.10318
$124$	−0.185981	−0.0167016
$125$	−1.00000	−0.0894427
$126$	−1.35690	−0.120882
$127$	−16.3763	−1.45316	−0.726580	−	0.687082i	$-0.758891\pi$
$127$	−16.3763	−1.45316	−0.726580	+	0.687082i	$0.758891\pi$
$128$	−1.00000	−0.0883883
$129$	2.91185	0.256374
$130$	0	0
$131$	3.00969	0.262958	0.131479	−	0.991319i	$-0.458027\pi$
$131$	3.00969	0.262958	0.131479	+	0.991319i	$0.458027\pi$
$132$	−3.19806	−0.278356
$133$	−7.25236	−0.628859
$134$	−1.55496	−0.134328
$135$	1.00000	0.0860663
$136$	2.04892	0.175693
$137$	20.2892	1.73342	0.866711	−	0.498810i	$-0.166229\pi$
$137$	20.2892	1.73342	0.866711	+	0.498810i	$0.166229\pi$
$138$	−8.32304	−0.708505
$139$	−0.153457	−0.0130160	−0.00650802	−	0.999979i	$-0.502072\pi$
$139$	−0.153457	−0.0130160	−0.00650802	+	0.999979i	$0.502072\pi$
$140$	−1.35690	−0.114679
$141$	−13.0978	−1.10304
$142$	2.32304	0.194946
$143$	0	0
$144$	1.00000	0.0833333
$145$	−8.07069	−0.670234
$146$	5.11529	0.423345
$147$	5.15883	0.425493
$148$	−2.46681	−0.202771
$149$	−10.7724	−0.882509	−0.441255	−	0.897382i	$-0.645466\pi$
$149$	−10.7724	−0.882509	−0.441255	+	0.897382i	$0.645466\pi$
$150$	1.00000	0.0816497
$151$	17.3817	1.41450	0.707249	−	0.706964i	$-0.249936\pi$
$151$	17.3817	1.41450	0.707249	+	0.706964i	$0.249936\pi$
$152$	5.34481	0.433522
$153$	−2.04892	−0.165645
$154$	−4.33944	−0.349682
$155$	0.185981	0.0149383
$156$	0	0
$157$	15.5429	1.24046	0.620228	−	0.784421i	$-0.287040\pi$
$157$	15.5429	1.24046	0.620228	+	0.784421i	$0.287040\pi$
$158$	1.42327	0.113229
$159$	−5.74094	−0.455286
$160$	1.00000	0.0790569
$161$	−11.2935	−0.890053
$162$	−1.00000	−0.0785674
$163$	−2.00239	−0.156840	−0.0784198	−	0.996920i	$-0.524987\pi$
$163$	−2.00239	−0.156840	−0.0784198	+	0.996920i	$0.524987\pi$
$164$	12.2349	0.955385
$165$	3.19806	0.248969
$166$	−11.1196	−0.863049
$167$	−8.24027	−0.637652	−0.318826	−	0.947813i	$-0.603288\pi$
$167$	−8.24027	−0.637652	−0.318826	+	0.947813i	$0.603288\pi$
$168$	1.35690	0.104687
$169$	0	0
$170$	−2.04892	−0.157145
$171$	−5.34481	−0.408728
$172$	−2.91185	−0.222027
$173$	12.7463	0.969084	0.484542	−	0.874768i	$-0.338986\pi$
$173$	12.7463	0.969084	0.484542	+	0.874768i	$0.338986\pi$
$174$	8.07069	0.611837
$175$	1.35690	0.102572
$176$	3.19806	0.241063
$177$	1.62565	0.122191
$178$	−3.37867	−0.253242
$179$	16.0422	1.19905	0.599526	−	0.800356i	$-0.295356\pi$
$179$	16.0422	1.19905	0.599526	+	0.800356i	$0.295356\pi$
$180$	−1.00000	−0.0745356
$181$	3.85086	0.286232	0.143116	−	0.989706i	$-0.454288\pi$
$181$	3.85086	0.286232	0.143116	+	0.989706i	$0.454288\pi$
$182$	0	0
$183$	−5.28382	−0.390591
$184$	8.32304	0.613583
$185$	2.46681	0.181364
$186$	−0.185981	−0.0136368
$187$	−6.55257	−0.479171
$188$	13.0978	0.955258
$189$	−1.35690	−0.0986997
$190$	−5.34481	−0.387754
$191$	11.8280	0.855845	0.427923	−	0.903815i	$-0.359246\pi$
$191$	11.8280	0.855845	0.427923	+	0.903815i	$0.359246\pi$
$192$	−1.00000	−0.0721688
$193$	0.872625	0.0628129	0.0314065	−	0.999507i	$-0.490001\pi$
$193$	0.872625	0.0628129	0.0314065	+	0.999507i	$0.490001\pi$
$194$	4.74094	0.340380
$195$	0	0
$196$	−5.15883	−0.368488
$197$	10.6213	0.756739	0.378369	−	0.925655i	$-0.376485\pi$
$197$	10.6213	0.756739	0.378369	+	0.925655i	$0.376485\pi$
$198$	−3.19806	−0.227276
$199$	12.3424	0.874931	0.437466	−	0.899235i	$-0.355876\pi$
$199$	12.3424	0.874931	0.437466	+	0.899235i	$0.355876\pi$
$200$	−1.00000	−0.0707107
$201$	−1.55496	−0.109678
$202$	12.5918	0.885956
$203$	10.9511	0.768615
$204$	2.04892	0.143453
$205$	−12.2349	−0.854522
$206$	9.00000	0.627060
$207$	−8.32304	−0.578492
$208$	0	0
$209$	−17.0930	−1.18235
$210$	−1.35690	−0.0936347
$211$	6.75733	0.465194	0.232597	−	0.972573i	$-0.425278\pi$
$211$	6.75733	0.465194	0.232597	+	0.972573i	$0.425278\pi$
$212$	5.74094	0.394289
$213$	2.32304	0.159172
$214$	5.08815	0.347819
$215$	2.91185	0.198587
$216$	1.00000	0.0680414
$217$	−0.252356	−0.0171311
$218$	−6.43296	−0.435695
$219$	5.11529	0.345659
$220$	−3.19806	−0.215613
$221$	0	0
$222$	−2.46681	−0.165562
$223$	21.5972	1.44625	0.723127	−	0.690715i	$-0.242704\pi$
$223$	21.5972	1.44625	0.723127	+	0.690715i	$0.242704\pi$
$224$	−1.35690	−0.0906614
$225$	1.00000	0.0666667
$226$	18.6571	1.24105
$227$	10.2862	0.682720	0.341360	−	0.939933i	$-0.389113\pi$
$227$	10.2862	0.682720	0.341360	+	0.939933i	$0.389113\pi$
$228$	5.34481	0.353969
$229$	4.25906	0.281447	0.140723	−	0.990049i	$-0.455057\pi$
$229$	4.25906	0.281447	0.140723	+	0.990049i	$0.455057\pi$
$230$	−8.32304	−0.548805
$231$	−4.33944	−0.285514
$232$	−8.07069	−0.529867
$233$	19.5133	1.27836	0.639181	−	0.769057i	$-0.279274\pi$
$233$	19.5133	1.27836	0.639181	+	0.769057i	$0.279274\pi$
$234$	0	0
$235$	−13.0978	−0.854409
$236$	−1.62565	−0.105821
$237$	1.42327	0.0924514
$238$	2.78017	0.180211
$239$	−7.16315	−0.463345	−0.231673	−	0.972794i	$-0.574420\pi$
$239$	−7.16315	−0.463345	−0.231673	+	0.972794i	$0.574420\pi$
$240$	1.00000	0.0645497
$241$	17.9584	1.15680	0.578400	−	0.815753i	$-0.303677\pi$
$241$	17.9584	1.15680	0.578400	+	0.815753i	$0.303677\pi$
$242$	0.772398	0.0496516
$243$	−1.00000	−0.0641500
$244$	5.28382	0.338262
$245$	5.15883	0.329586
$246$	12.2349	0.780069
$247$	0	0
$248$	0.185981	0.0118098
$249$	−11.1196	−0.704676
$250$	1.00000	0.0632456
$251$	−6.68425	−0.421906	−0.210953	−	0.977496i	$-0.567657\pi$
$251$	−6.68425	−0.421906	−0.210953	+	0.977496i	$0.567657\pi$
$252$	1.35690	0.0854764
$253$	−26.6176	−1.67343
$254$	16.3763	1.02754
$255$	−2.04892	−0.128308
$256$	1.00000	0.0625000
$257$	9.91484	0.618471	0.309235	−	0.950986i	$-0.399927\pi$
$257$	9.91484	0.618471	0.309235	+	0.950986i	$0.399927\pi$
$258$	−2.91185	−0.181284
$259$	−3.34721	−0.207985
$260$	0	0
$261$	8.07069	0.499563
$262$	−3.00969	−0.185939
$263$	13.8509	0.854080	0.427040	−	0.904233i	$-0.359556\pi$
$263$	13.8509	0.854080	0.427040	+	0.904233i	$0.359556\pi$
$264$	3.19806	0.196827
$265$	−5.74094	−0.352663
$266$	7.25236	0.444671
$267$	−3.37867	−0.206771
$268$	1.55496	0.0949842
$269$	−17.8756	−1.08990	−0.544948	−	0.838470i	$-0.683450\pi$
$269$	−17.8756	−1.08990	−0.544948	+	0.838470i	$0.683450\pi$
$270$	−1.00000	−0.0608581
$271$	31.2083	1.89577	0.947886	−	0.318610i	$-0.103216\pi$
$271$	31.2083	1.89577	0.947886	+	0.318610i	$0.103216\pi$
$272$	−2.04892	−0.124234
$273$	0	0
$274$	−20.2892	−1.22571
$275$	3.19806	0.192850
$276$	8.32304	0.500988
$277$	22.9245	1.37740	0.688701	−	0.725046i	$-0.258181\pi$
$277$	22.9245	1.37740	0.688701	+	0.725046i	$0.258181\pi$
$278$	0.153457	0.00920373
$279$	−0.185981	−0.0111344
$280$	1.35690	0.0810900
$281$	28.0683	1.67441	0.837207	−	0.546886i	$-0.184187\pi$
$281$	28.0683	1.67441	0.837207	+	0.546886i	$0.184187\pi$
$282$	13.0978	0.779965
$283$	−24.8364	−1.47637	−0.738185	−	0.674599i	$-0.764317\pi$
$283$	−24.8364	−1.47637	−0.738185	+	0.674599i	$0.764317\pi$
$284$	−2.32304	−0.137847
$285$	−5.34481	−0.316599
$286$	0	0
$287$	16.6015	0.979955
$288$	−1.00000	−0.0589256
$289$	−12.8019	−0.753055
$290$	8.07069	0.473927
$291$	4.74094	0.277919
$292$	−5.11529	−0.299350
$293$	−28.4349	−1.66118	−0.830592	−	0.556882i	$-0.811998\pi$
$293$	−28.4349	−1.66118	−0.830592	+	0.556882i	$0.811998\pi$
$294$	−5.15883	−0.300869
$295$	1.62565	0.0946488
$296$	2.46681	0.143381
$297$	−3.19806	−0.185570
$298$	10.7724	0.624028
$299$	0	0
$300$	−1.00000	−0.0577350
$301$	−3.95108	−0.227737
$302$	−17.3817	−1.00020
$303$	12.5918	0.723380
$304$	−5.34481	−0.306546
$305$	−5.28382	−0.302550
$306$	2.04892	0.117129
$307$	−10.1347	−0.578416	−0.289208	−	0.957266i	$-0.593392\pi$
$307$	−10.1347	−0.578416	−0.289208	+	0.957266i	$0.593392\pi$
$308$	4.33944	0.247262
$309$	9.00000	0.511992
$310$	−0.185981	−0.0105630
$311$	20.0218	1.13533	0.567665	−	0.823259i	$-0.307847\pi$
$311$	20.0218	1.13533	0.567665	+	0.823259i	$0.307847\pi$
$312$	0	0
$313$	8.63640	0.488158	0.244079	−	0.969755i	$-0.421514\pi$
$313$	8.63640	0.488158	0.244079	+	0.969755i	$0.421514\pi$
$314$	−15.5429	−0.877135
$315$	−1.35690	−0.0764524
$316$	−1.42327	−0.0800653
$317$	17.6256	0.989955	0.494977	−	0.868906i	$-0.335176\pi$
$317$	17.6256	0.989955	0.494977	+	0.868906i	$0.335176\pi$
$318$	5.74094	0.321936
$319$	25.8106	1.44511
$320$	−1.00000	−0.0559017
$321$	5.08815	0.283993
$322$	11.2935	0.629362
$323$	10.9511	0.609335
$324$	1.00000	0.0555556
$325$	0	0
$326$	2.00239	0.110902
$327$	−6.43296	−0.355744
$328$	−12.2349	−0.675559
$329$	17.7724	0.979824
$330$	−3.19806	−0.176048
$331$	−31.5163	−1.73229	−0.866147	−	0.499790i	$-0.833411\pi$
$331$	−31.5163	−1.73229	−0.866147	+	0.499790i	$0.833411\pi$
$332$	11.1196	0.610268
$333$	−2.46681	−0.135180
$334$	8.24027	0.450888
$335$	−1.55496	−0.0849564
$336$	−1.35690	−0.0740247
$337$	−11.8116	−0.643420	−0.321710	−	0.946838i	$-0.604258\pi$
$337$	−11.8116	−0.643420	−0.321710	+	0.946838i	$0.604258\pi$
$338$	0	0
$339$	18.6571	1.01331
$340$	2.04892	0.111118
$341$	−0.594778	−0.0322090
$342$	5.34481	0.289014
$343$	−16.4983	−0.890823
$344$	2.91185	0.156997
$345$	−8.32304	−0.448098
$346$	−12.7463	−0.685246
$347$	−17.4101	−0.934624	−0.467312	−	0.884092i	$-0.654778\pi$
$347$	−17.4101	−0.934624	−0.467312	+	0.884092i	$0.654778\pi$
$348$	−8.07069	−0.432634
$349$	18.6799	0.999914	0.499957	−	0.866050i	$-0.333349\pi$
$349$	18.6799	0.999914	0.499957	+	0.866050i	$0.333349\pi$
$350$	−1.35690	−0.0725291
$351$	0	0
$352$	−3.19806	−0.170457
$353$	25.3991	1.35186	0.675929	−	0.736967i	$-0.263743\pi$
$353$	25.3991	1.35186	0.675929	+	0.736967i	$0.263743\pi$
$354$	−1.62565	−0.0864021
$355$	2.32304	0.123294
$356$	3.37867	0.179069
$357$	2.78017	0.147142
$358$	−16.0422	−0.847857
$359$	34.0103	1.79499	0.897497	−	0.441021i	$-0.145383\pi$
$359$	34.0103	1.79499	0.897497	+	0.441021i	$0.145383\pi$
$360$	1.00000	0.0527046
$361$	9.56704	0.503528
$362$	−3.85086	−0.202396
$363$	0.772398	0.0405404
$364$	0	0
$365$	5.11529	0.267747
$366$	5.28382	0.276189
$367$	−25.6437	−1.33859	−0.669295	−	0.742997i	$-0.733404\pi$
$367$	−25.6437	−1.33859	−0.669295	+	0.742997i	$0.733404\pi$
$368$	−8.32304	−0.433869
$369$	12.2349	0.636923
$370$	−2.46681	−0.128243
$371$	7.78986	0.404429
$372$	0.185981	0.00964265
$373$	−16.3612	−0.847151	−0.423576	−	0.905861i	$-0.639225\pi$
$373$	−16.3612	−0.847151	−0.423576	+	0.905861i	$0.639225\pi$
$374$	6.55257	0.338825
$375$	1.00000	0.0516398
$376$	−13.0978	−0.675469
$377$	0	0
$378$	1.35690	0.0697912
$379$	22.8823	1.17539	0.587693	−	0.809084i	$-0.300036\pi$
$379$	22.8823	1.17539	0.587693	+	0.809084i	$0.300036\pi$
$380$	5.34481	0.274183
$381$	16.3763	0.838982
$382$	−11.8280	−0.605174
$383$	11.9191	0.609040	0.304520	−	0.952506i	$-0.401504\pi$
$383$	11.9191	0.609040	0.304520	+	0.952506i	$0.401504\pi$
$384$	1.00000	0.0510310
$385$	−4.33944	−0.221158
$386$	−0.872625	−0.0444155
$387$	−2.91185	−0.148018
$388$	−4.74094	−0.240685
$389$	8.07606	0.409473	0.204736	−	0.978817i	$-0.434366\pi$
$389$	8.07606	0.409473	0.204736	+	0.978817i	$0.434366\pi$
$390$	0	0
$391$	17.0532	0.862419
$392$	5.15883	0.260560
$393$	−3.00969	−0.151819
$394$	−10.6213	−0.535095
$395$	1.42327	0.0716126
$396$	3.19806	0.160709
$397$	−20.5230	−1.03002	−0.515011	−	0.857184i	$-0.672212\pi$
$397$	−20.5230	−1.03002	−0.515011	+	0.857184i	$0.672212\pi$
$398$	−12.3424	−0.618670
$399$	7.25236	0.363072
$400$	1.00000	0.0500000
$401$	−18.3274	−0.915224	−0.457612	−	0.889152i	$-0.651295\pi$
$401$	−18.3274	−0.915224	−0.457612	+	0.889152i	$0.651295\pi$
$402$	1.55496	0.0775543
$403$	0	0
$404$	−12.5918	−0.626465
$405$	−1.00000	−0.0496904
$406$	−10.9511	−0.543493
$407$	−7.88902	−0.391044
$408$	−2.04892	−0.101437
$409$	9.00000	0.445021	0.222511	−	0.974930i	$-0.428575\pi$
$409$	9.00000	0.445021	0.222511	+	0.974930i	$0.428575\pi$
$410$	12.2349	0.604239
$411$	−20.2892	−1.00079
$412$	−9.00000	−0.443398
$413$	−2.20583	−0.108542
$414$	8.32304	0.409055
$415$	−11.1196	−0.545840
$416$	0	0
$417$	0.153457	0.00751481
$418$	17.0930	0.836048
$419$	−14.4185	−0.704389	−0.352195	−	0.935927i	$-0.614564\pi$
$419$	−14.4185	−0.704389	−0.352195	+	0.935927i	$0.614564\pi$
$420$	1.35690	0.0662097
$421$	−19.9801	−0.973773	−0.486886	−	0.873465i	$-0.661867\pi$
$421$	−19.9801	−0.973773	−0.486886	+	0.873465i	$0.661867\pi$
$422$	−6.75733	−0.328942
$423$	13.0978	0.636839
$424$	−5.74094	−0.278805
$425$	−2.04892	−0.0993871
$426$	−2.32304	−0.112552
$427$	7.16959	0.346961
$428$	−5.08815	−0.245945
$429$	0	0
$430$	−2.91185	−0.140422
$431$	−21.1812	−1.02026	−0.510131	−	0.860097i	$-0.670403\pi$
$431$	−21.1812	−1.02026	−0.510131	+	0.860097i	$0.670403\pi$
$432$	−1.00000	−0.0481125
$433$	31.0291	1.49116	0.745581	−	0.666415i	$-0.232172\pi$
$433$	31.0291	1.49116	0.745581	+	0.666415i	$0.232172\pi$
$434$	0.252356	0.0121135
$435$	8.07069	0.386960
$436$	6.43296	0.308083
$437$	44.4851	2.12801
$438$	−5.11529	−0.244418
$439$	7.33406	0.350036	0.175018	−	0.984565i	$-0.444002\pi$
$439$	7.33406	0.350036	0.175018	+	0.984565i	$0.444002\pi$
$440$	3.19806	0.152462
$441$	−5.15883	−0.245659
$442$	0	0
$443$	−18.1360	−0.861667	−0.430834	−	0.902431i	$-0.641780\pi$
$443$	−18.1360	−0.861667	−0.430834	+	0.902431i	$0.641780\pi$
$444$	2.46681	0.117070
$445$	−3.37867	−0.160164
$446$	−21.5972	−1.02266
$447$	10.7724	0.509517
$448$	1.35690	0.0641073
$449$	4.55496	0.214962	0.107481	−	0.994207i	$-0.465722\pi$
$449$	4.55496	0.214962	0.107481	+	0.994207i	$0.465722\pi$
$450$	−1.00000	−0.0471405
$451$	39.1280	1.84246
$452$	−18.6571	−0.877556
$453$	−17.3817	−0.816661
$454$	−10.2862	−0.482756
$455$	0	0
$456$	−5.34481	−0.250294
$457$	−9.98121	−0.466901	−0.233451	−	0.972369i	$-0.575002\pi$
$457$	−9.98121	−0.466901	−0.233451	+	0.972369i	$0.575002\pi$
$458$	−4.25906	−0.199013
$459$	2.04892	0.0956353
$460$	8.32304	0.388064
$461$	16.1672	0.752981	0.376491	−	0.926420i	$-0.377131\pi$
$461$	16.1672	0.752981	0.376491	+	0.926420i	$0.377131\pi$
$462$	4.33944	0.201889
$463$	−3.88902	−0.180738	−0.0903690	−	0.995908i	$-0.528805\pi$
$463$	−3.88902	−0.180738	−0.0903690	+	0.995908i	$0.528805\pi$
$464$	8.07069	0.374672
$465$	−0.185981	−0.00862465
$466$	−19.5133	−0.903938
$467$	−0.872625	−0.0403803	−0.0201901	−	0.999796i	$-0.506427\pi$
$467$	−0.872625	−0.0403803	−0.0201901	+	0.999796i	$0.506427\pi$
$468$	0	0
$469$	2.10992	0.0974269
$470$	13.0978	0.604158
$471$	−15.5429	−0.716178
$472$	1.62565	0.0748264
$473$	−9.31229	−0.428180
$474$	−1.42327	−0.0653730
$475$	−5.34481	−0.245237
$476$	−2.78017	−0.127429
$477$	5.74094	0.262860
$478$	7.16315	0.327635
$479$	31.6305	1.44524	0.722618	−	0.691247i	$-0.242938\pi$
$479$	31.6305	1.44524	0.722618	+	0.691247i	$0.242938\pi$
$480$	−1.00000	−0.0456435
$481$	0	0
$482$	−17.9584	−0.817982
$483$	11.2935	0.513872
$484$	−0.772398	−0.0351090
$485$	4.74094	0.215275
$486$	1.00000	0.0453609
$487$	−21.7748	−0.986710	−0.493355	−	0.869828i	$-0.664230\pi$
$487$	−21.7748	−0.986710	−0.493355	+	0.869828i	$0.664230\pi$
$488$	−5.28382	−0.239187
$489$	2.00239	0.0905513
$490$	−5.15883	−0.233052
$491$	42.9590	1.93871	0.969356	−	0.245662i	$-0.0790053\pi$
$491$	42.9590	1.93871	0.969356	+	0.245662i	$0.0790053\pi$
$492$	−12.2349	−0.551592
$493$	−16.5362	−0.744752
$494$	0	0
$495$	−3.19806	−0.143742
$496$	−0.185981	−0.00835078
$497$	−3.15213	−0.141392
$498$	11.1196	0.498281
$499$	36.0978	1.61596	0.807981	−	0.589209i	$-0.200561\pi$
$499$	36.0978	1.61596	0.807981	+	0.589209i	$0.200561\pi$
$500$	−1.00000	−0.0447214
$501$	8.24027	0.368148
$502$	6.68425	0.298333
$503$	−21.4534	−0.956560	−0.478280	−	0.878207i	$-0.658740\pi$
$503$	−21.4534	−0.956560	−0.478280	+	0.878207i	$0.658740\pi$
$504$	−1.35690	−0.0604409
$505$	12.5918	0.560327
$506$	26.6176	1.18330
$507$	0	0
$508$	−16.3763	−0.726580
$509$	−0.545860	−0.0241948	−0.0120974	−	0.999927i	$-0.503851\pi$
$509$	−0.545860	−0.0241948	−0.0120974	+	0.999927i	$0.503851\pi$
$510$	2.04892	0.0907276
$511$	−6.94092	−0.307048
$512$	−1.00000	−0.0441942
$513$	5.34481	0.235979
$514$	−9.91484	−0.437325
$515$	9.00000	0.396587
$516$	2.91185	0.128187
$517$	41.8877	1.84222
$518$	3.34721	0.147068
$519$	−12.7463	−0.559501
$520$	0	0
$521$	29.6136	1.29739	0.648697	−	0.761047i	$-0.275314\pi$
$521$	29.6136	1.29739	0.648697	+	0.761047i	$0.275314\pi$
$522$	−8.07069	−0.353244
$523$	44.4543	1.94385	0.971924	−	0.235293i	$-0.0756050\pi$
$523$	44.4543	1.94385	0.971924	+	0.235293i	$0.0756050\pi$
$524$	3.00969	0.131479
$525$	−1.35690	−0.0592198
$526$	−13.8509	−0.603926
$527$	0.381059	0.0165992
$528$	−3.19806	−0.139178
$529$	46.2731	2.01187
$530$	5.74094	0.249370
$531$	−1.62565	−0.0705470
$532$	−7.25236	−0.314430
$533$	0	0
$534$	3.37867	0.146209
$535$	5.08815	0.219980
$536$	−1.55496	−0.0671640
$537$	−16.0422	−0.692273
$538$	17.8756	0.770672
$539$	−16.4983	−0.710631
$540$	1.00000	0.0430331
$541$	−18.7651	−0.806775	−0.403387	−	0.915029i	$-0.632167\pi$
$541$	−18.7651	−0.806775	−0.403387	+	0.915029i	$0.632167\pi$
$542$	−31.2083	−1.34051
$543$	−3.85086	−0.165256
$544$	2.04892	0.0878466
$545$	−6.43296	−0.275558
$546$	0	0
$547$	32.0116	1.36872	0.684359	−	0.729145i	$-0.260082\pi$
$547$	32.0116	1.36872	0.684359	+	0.729145i	$0.260082\pi$
$548$	20.2892	0.866711
$549$	5.28382	0.225508
$550$	−3.19806	−0.136366
$551$	−43.1363	−1.83767
$552$	−8.32304	−0.354252
$553$	−1.93123	−0.0821243
$554$	−22.9245	−0.973970
$555$	−2.46681	−0.104710
$556$	−0.153457	−0.00650802
$557$	8.23490	0.348924	0.174462	−	0.984664i	$-0.444181\pi$
$557$	8.23490	0.348924	0.174462	+	0.984664i	$0.444181\pi$
$558$	0.185981	0.00787319
$559$	0	0
$560$	−1.35690	−0.0573393
$561$	6.55257	0.276650
$562$	−28.0683	−1.18399
$563$	−30.2295	−1.27402	−0.637011	−	0.770855i	$-0.719830\pi$
$563$	−30.2295	−1.27402	−0.637011	+	0.770855i	$0.719830\pi$
$564$	−13.0978	−0.551518
$565$	18.6571	0.784910
$566$	24.8364	1.04395
$567$	1.35690	0.0569843
$568$	2.32304	0.0974728
$569$	44.3110	1.85761	0.928806	−	0.370566i	$-0.120836\pi$
$569$	44.3110	1.85761	0.928806	+	0.370566i	$0.120836\pi$
$570$	5.34481	0.223870
$571$	34.4873	1.44325	0.721623	−	0.692286i	$-0.243396\pi$
$571$	34.4873	1.44325	0.721623	+	0.692286i	$0.243396\pi$
$572$	0	0
$573$	−11.8280	−0.494123
$574$	−16.6015	−0.692932
$575$	−8.32304	−0.347095
$576$	1.00000	0.0416667
$577$	14.1715	0.589968	0.294984	−	0.955502i	$-0.404686\pi$
$577$	14.1715	0.589968	0.294984	+	0.955502i	$0.404686\pi$
$578$	12.8019	0.532490
$579$	−0.872625	−0.0362651
$580$	−8.07069	−0.335117
$581$	15.0881	0.625962
$582$	−4.74094	−0.196518
$583$	18.3599	0.760389
$584$	5.11529	0.211672
$585$	0	0
$586$	28.4349	1.17463
$587$	1.12737	0.0465317	0.0232659	−	0.999729i	$-0.492594\pi$
$587$	1.12737	0.0465317	0.0232659	+	0.999729i	$0.492594\pi$
$588$	5.15883	0.212747
$589$	0.994032	0.0409584
$590$	−1.62565	−0.0669268
$591$	−10.6213	−0.436903
$592$	−2.46681	−0.101385
$593$	−18.3913	−0.755242	−0.377621	−	0.925960i	$-0.623258\pi$
$593$	−18.3913	−0.755242	−0.377621	+	0.925960i	$0.623258\pi$
$594$	3.19806	0.131218
$595$	2.78017	0.113976
$596$	−10.7724	−0.441255
$597$	−12.3424	−0.505142
$598$	0	0
$599$	13.1226	0.536174	0.268087	−	0.963395i	$-0.413608\pi$
$599$	13.1226	0.536174	0.268087	+	0.963395i	$0.413608\pi$
$600$	1.00000	0.0408248
$601$	25.5754	1.04324	0.521621	−	0.853177i	$-0.325327\pi$
$601$	25.5754	1.04324	0.521621	+	0.853177i	$0.325327\pi$
$602$	3.95108	0.161034
$603$	1.55496	0.0633228
$604$	17.3817	0.707249
$605$	0.772398	0.0314024
$606$	−12.5918	−0.511507
$607$	44.4782	1.80531	0.902656	−	0.430362i	$-0.141614\pi$
$607$	44.4782	1.80531	0.902656	+	0.430362i	$0.141614\pi$
$608$	5.34481	0.216761
$609$	−10.9511	−0.443760
$610$	5.28382	0.213935
$611$	0	0
$612$	−2.04892	−0.0828226
$613$	21.7657	0.879108	0.439554	−	0.898216i	$-0.355137\pi$
$613$	21.7657	0.879108	0.439554	+	0.898216i	$0.355137\pi$
$614$	10.1347	0.409002
$615$	12.2349	0.493359
$616$	−4.33944	−0.174841
$617$	17.3569	0.698762	0.349381	−	0.936981i	$-0.386392\pi$
$617$	17.3569	0.698762	0.349381	+	0.936981i	$0.386392\pi$
$618$	−9.00000	−0.362033
$619$	−36.8049	−1.47931	−0.739657	−	0.672984i	$-0.765012\pi$
$619$	−36.8049	−1.47931	−0.739657	+	0.672984i	$0.765012\pi$
$620$	0.185981	0.00746916
$621$	8.32304	0.333992
$622$	−20.0218	−0.802800
$623$	4.58450	0.183674
$624$	0	0
$625$	1.00000	0.0400000
$626$	−8.63640	−0.345180
$627$	17.0930	0.682631
$628$	15.5429	0.620228
$629$	5.05429	0.201528
$630$	1.35690	0.0540600
$631$	−11.7554	−0.467976	−0.233988	−	0.972240i	$-0.575178\pi$
$631$	−11.7554	−0.467976	−0.233988	+	0.972240i	$0.575178\pi$
$632$	1.42327	0.0566147
$633$	−6.75733	−0.268580
$634$	−17.6256	−0.700004
$635$	16.3763	0.649873
$636$	−5.74094	−0.227643
$637$	0	0
$638$	−25.8106	−1.02185
$639$	−2.32304	−0.0918982
$640$	1.00000	0.0395285
$641$	33.0858	1.30681	0.653404	−	0.757009i	$-0.273340\pi$
$641$	33.0858	1.30681	0.653404	+	0.757009i	$0.273340\pi$
$642$	−5.08815	−0.200813
$643$	10.3461	0.408012	0.204006	−	0.978970i	$-0.434604\pi$
$643$	10.3461	0.408012	0.204006	+	0.978970i	$0.434604\pi$
$644$	−11.2935	−0.445026
$645$	−2.91185	−0.114654
$646$	−10.9511	−0.430865
$647$	−11.0030	−0.432572	−0.216286	−	0.976330i	$-0.569394\pi$
$647$	−11.0030	−0.432572	−0.216286	+	0.976330i	$0.569394\pi$
$648$	−1.00000	−0.0392837
$649$	−5.19892	−0.204075
$650$	0	0
$651$	0.252356	0.00989063
$652$	−2.00239	−0.0784198
$653$	−30.8224	−1.20617	−0.603086	−	0.797676i	$-0.706063\pi$
$653$	−30.8224	−1.20617	−0.603086	+	0.797676i	$0.706063\pi$
$654$	6.43296	0.251549
$655$	−3.00969	−0.117598
$656$	12.2349	0.477693
$657$	−5.11529	−0.199567
$658$	−17.7724	−0.692840
$659$	−33.2010	−1.29333	−0.646665	−	0.762774i	$-0.723837\pi$
$659$	−33.2010	−1.29333	−0.646665	+	0.762774i	$0.723837\pi$
$660$	3.19806	0.124484
$661$	−37.4252	−1.45567	−0.727836	−	0.685752i	$-0.759474\pi$
$661$	−37.4252	−1.45567	−0.727836	+	0.685752i	$0.759474\pi$
$662$	31.5163	1.22492
$663$	0	0
$664$	−11.1196	−0.431524
$665$	7.25236	0.281234
$666$	2.46681	0.0955870
$667$	−67.1727	−2.60094
$668$	−8.24027	−0.318826
$669$	−21.5972	−0.834995
$670$	1.55496	0.0600733
$671$	16.8980	0.652339
$672$	1.35690	0.0523434
$673$	−34.9409	−1.34687	−0.673437	−	0.739245i	$-0.735183\pi$
$673$	−34.9409	−1.34687	−0.673437	+	0.739245i	$0.735183\pi$
$674$	11.8116	0.454967
$675$	−1.00000	−0.0384900
$676$	0	0
$677$	29.3913	1.12960	0.564800	−	0.825228i	$-0.308953\pi$
$677$	29.3913	1.12960	0.564800	+	0.825228i	$0.308953\pi$
$678$	−18.6571	−0.716522
$679$	−6.43296	−0.246874
$680$	−2.04892	−0.0785724
$681$	−10.2862	−0.394168
$682$	0.594778	0.0227752
$683$	−28.9855	−1.10910	−0.554550	−	0.832150i	$-0.687110\pi$
$683$	−28.9855	−1.10910	−0.554550	+	0.832150i	$0.687110\pi$
$684$	−5.34481	−0.204364
$685$	−20.2892	−0.775210
$686$	16.4983	0.629907
$687$	−4.25906	−0.162493
$688$	−2.91185	−0.111013
$689$	0	0
$690$	8.32304	0.316853
$691$	1.37627	0.0523559	0.0261780	−	0.999657i	$-0.491666\pi$
$691$	1.37627	0.0523559	0.0261780	+	0.999657i	$0.491666\pi$
$692$	12.7463	0.484542
$693$	4.33944	0.164842
$694$	17.4101	0.660879
$695$	0.153457	0.00582095
$696$	8.07069	0.305919
$697$	−25.0683	−0.949529
$698$	−18.6799	−0.707046
$699$	−19.5133	−0.738062
$700$	1.35690	0.0512858
$701$	9.21014	0.347862	0.173931	−	0.984758i	$-0.444353\pi$
$701$	9.21014	0.347862	0.173931	+	0.984758i	$0.444353\pi$
$702$	0	0
$703$	13.1847	0.497269
$704$	3.19806	0.120532
$705$	13.0978	0.493293
$706$	−25.3991	−0.955908
$707$	−17.0858	−0.642576
$708$	1.62565	0.0610955
$709$	46.1613	1.73363	0.866813	−	0.498634i	$-0.166165\pi$
$709$	46.1613	1.73363	0.866813	+	0.498634i	$0.166165\pi$
$710$	−2.32304	−0.0871823
$711$	−1.42327	−0.0533769
$712$	−3.37867	−0.126621
$713$	1.54793	0.0579703
$714$	−2.78017	−0.104045
$715$	0	0
$716$	16.0422	0.599526
$717$	7.16315	0.267513
$718$	−34.0103	−1.26925
$719$	−46.3588	−1.72889	−0.864446	−	0.502726i	$-0.832331\pi$
$719$	−46.3588	−1.72889	−0.864446	+	0.502726i	$0.832331\pi$
$720$	−1.00000	−0.0372678
$721$	−12.2121	−0.454801
$722$	−9.56704	−0.356048
$723$	−17.9584	−0.667879
$724$	3.85086	0.143116
$725$	8.07069	0.299738
$726$	−0.772398	−0.0286664
$727$	−1.67217	−0.0620174	−0.0310087	−	0.999519i	$-0.509872\pi$
$727$	−1.67217	−0.0620174	−0.0310087	+	0.999519i	$0.509872\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−5.11529	−0.189325
$731$	5.96615	0.220666
$732$	−5.28382	−0.195295
$733$	−33.6189	−1.24174	−0.620872	−	0.783912i	$-0.713221\pi$
$733$	−33.6189	−1.24174	−0.620872	+	0.783912i	$0.713221\pi$
$734$	25.6437	0.946526
$735$	−5.15883	−0.190286
$736$	8.32304	0.306791
$737$	4.97285	0.183177
$738$	−12.2349	−0.450373
$739$	−31.8437	−1.17139	−0.585694	−	0.810532i	$-0.699178\pi$
$739$	−31.8437	−1.17139	−0.585694	+	0.810532i	$0.699178\pi$
$740$	2.46681	0.0906818
$741$	0	0
$742$	−7.78986	−0.285975
$743$	23.4010	0.858500	0.429250	−	0.903186i	$-0.358778\pi$
$743$	23.4010	0.858500	0.429250	+	0.903186i	$0.358778\pi$
$744$	−0.185981	−0.00681838
$745$	10.7724	0.394670
$746$	16.3612	0.599026
$747$	11.1196	0.406845
$748$	−6.55257	−0.239586
$749$	−6.90408	−0.252270
$750$	−1.00000	−0.0365148
$751$	−39.0146	−1.42366	−0.711831	−	0.702350i	$-0.752134\pi$
$751$	−39.0146	−1.42366	−0.711831	+	0.702350i	$0.752134\pi$
$752$	13.0978	0.477629
$753$	6.68425	0.243588
$754$	0	0
$755$	−17.3817	−0.632583
$756$	−1.35690	−0.0493498
$757$	43.0224	1.56367	0.781837	−	0.623483i	$-0.214283\pi$
$757$	43.0224	1.56367	0.781837	+	0.623483i	$0.214283\pi$
$758$	−22.8823	−0.831123
$759$	26.6176	0.966158
$760$	−5.34481	−0.193877
$761$	14.9903	0.543398	0.271699	−	0.962382i	$-0.412414\pi$
$761$	14.9903	0.543398	0.271699	+	0.962382i	$0.412414\pi$
$762$	−16.3763	−0.593250
$763$	8.72886	0.316006
$764$	11.8280	0.427923
$765$	2.04892	0.0740788
$766$	−11.9191	−0.430656
$767$	0	0
$768$	−1.00000	−0.0360844
$769$	−19.9138	−0.718109	−0.359055	−	0.933317i	$-0.616901\pi$
$769$	−19.9138	−0.718109	−0.359055	+	0.933317i	$0.616901\pi$
$770$	4.33944	0.156382
$771$	−9.91484	−0.357074
$772$	0.872625	0.0314065
$773$	25.5566	0.919208	0.459604	−	0.888124i	$-0.347991\pi$
$773$	25.5566	0.919208	0.459604	+	0.888124i	$0.347991\pi$
$774$	2.91185	0.104664
$775$	−0.185981	−0.00668062
$776$	4.74094	0.170190
$777$	3.34721	0.120080
$778$	−8.07606	−0.289541
$779$	−65.3933	−2.34296
$780$	0	0
$781$	−7.42924	−0.265839
$782$	−17.0532	−0.609822
$783$	−8.07069	−0.288423
$784$	−5.15883	−0.184244
$785$	−15.5429	−0.554749
$786$	3.00969	0.107352
$787$	28.6297	1.02054	0.510269	−	0.860015i	$-0.329546\pi$
$787$	28.6297	1.02054	0.510269	+	0.860015i	$0.329546\pi$
$788$	10.6213	0.378369
$789$	−13.8509	−0.493103
$790$	−1.42327	−0.0506377
$791$	−25.3157	−0.900124
$792$	−3.19806	−0.113638
$793$	0	0
$794$	20.5230	0.728335
$795$	5.74094	0.203610
$796$	12.3424	0.437466
$797$	1.00431	0.0355746	0.0177873	−	0.999842i	$-0.494338\pi$
$797$	1.00431	0.0355746	0.0177873	+	0.999842i	$0.494338\pi$
$798$	−7.25236	−0.256731
$799$	−26.8364	−0.949403
$800$	−1.00000	−0.0353553
$801$	3.37867	0.119379
$802$	18.3274	0.647161
$803$	−16.3590	−0.577297
$804$	−1.55496	−0.0548391
$805$	11.2935	0.398044
$806$	0	0
$807$	17.8756	0.629251
$808$	12.5918	0.442978
$809$	49.8743	1.75349	0.876743	−	0.480959i	$-0.159711\pi$
$809$	49.8743	1.75349	0.876743	+	0.480959i	$0.159711\pi$
$810$	1.00000	0.0351364
$811$	−7.95646	−0.279389	−0.139695	−	0.990195i	$-0.544612\pi$
$811$	−7.95646	−0.279389	−0.139695	+	0.990195i	$0.544612\pi$
$812$	10.9511	0.384308
$813$	−31.2083	−1.09452
$814$	7.88902	0.276510
$815$	2.00239	0.0701408
$816$	2.04892	0.0717265
$817$	15.5633	0.544492
$818$	−9.00000	−0.314678
$819$	0	0
$820$	−12.2349	−0.427261
$821$	−52.9071	−1.84647	−0.923235	−	0.384236i	$-0.874465\pi$
$821$	−52.9071	−1.84647	−0.923235	+	0.384236i	$0.874465\pi$
$822$	20.2892	0.707667
$823$	21.8006	0.759921	0.379961	−	0.925003i	$-0.375937\pi$
$823$	21.8006	0.759921	0.379961	+	0.925003i	$0.375937\pi$
$824$	9.00000	0.313530
$825$	−3.19806	−0.111342
$826$	2.20583	0.0767507
$827$	27.3139	0.949799	0.474899	−	0.880040i	$-0.342484\pi$
$827$	27.3139	0.949799	0.474899	+	0.880040i	$0.342484\pi$
$828$	−8.32304	−0.289246
$829$	40.8471	1.41868	0.709340	−	0.704867i	$-0.248993\pi$
$829$	40.8471	1.41868	0.709340	+	0.704867i	$0.248993\pi$
$830$	11.1196	0.385967
$831$	−22.9245	−0.795243
$832$	0	0
$833$	10.5700	0.366230
$834$	−0.153457	−0.00531377
$835$	8.24027	0.285166
$836$	−17.0930	−0.591175
$837$	0.185981	0.00642843
$838$	14.4185	0.498078
$839$	−43.0823	−1.48737	−0.743683	−	0.668532i	$-0.766923\pi$
$839$	−43.0823	−1.48737	−0.743683	+	0.668532i	$0.766923\pi$
$840$	−1.35690	−0.0468174
$841$	36.1360	1.24607
$842$	19.9801	0.688561
$843$	−28.0683	−0.966723
$844$	6.75733	0.232597
$845$	0	0
$846$	−13.0978	−0.450313
$847$	−1.04806	−0.0360119
$848$	5.74094	0.197145
$849$	24.8364	0.852382
$850$	2.04892	0.0702773
$851$	20.5314	0.703807
$852$	2.32304	0.0795862
$853$	24.6813	0.845071	0.422535	−	0.906346i	$-0.361140\pi$
$853$	24.6813	0.845071	0.422535	+	0.906346i	$0.361140\pi$
$854$	−7.16959	−0.245338
$855$	5.34481	0.182789
$856$	5.08815	0.173909
$857$	43.1075	1.47252	0.736262	−	0.676696i	$-0.236589\pi$
$857$	43.1075	1.47252	0.736262	+	0.676696i	$0.236589\pi$
$858$	0	0
$859$	−42.1323	−1.43753	−0.718767	−	0.695251i	$-0.755293\pi$
$859$	−42.1323	−1.43753	−0.718767	+	0.695251i	$0.755293\pi$
$860$	2.91185	0.0992934
$861$	−16.6015	−0.565777
$862$	21.1812	0.721434
$863$	−47.9342	−1.63170	−0.815850	−	0.578264i	$-0.803730\pi$
$863$	−47.9342	−1.63170	−0.815850	+	0.578264i	$0.803730\pi$
$864$	1.00000	0.0340207
$865$	−12.7463	−0.433388
$866$	−31.0291	−1.05441
$867$	12.8019	0.434777
$868$	−0.252356	−0.00856553
$869$	−4.55171	−0.154406
$870$	−8.07069	−0.273622
$871$	0	0
$872$	−6.43296	−0.217848
$873$	−4.74094	−0.160456
$874$	−44.4851	−1.50473
$875$	−1.35690	−0.0458715
$876$	5.11529	0.172830
$877$	38.6674	1.30570	0.652852	−	0.757485i	$-0.273572\pi$
$877$	38.6674	1.30570	0.652852	+	0.757485i	$0.273572\pi$
$878$	−7.33406	−0.247513
$879$	28.4349	0.959085
$880$	−3.19806	−0.107807
$881$	25.4980	0.859050	0.429525	−	0.903055i	$-0.358681\pi$
$881$	25.4980	0.859050	0.429525	+	0.903055i	$0.358681\pi$
$882$	5.15883	0.173707
$883$	−31.8377	−1.07142	−0.535712	−	0.844401i	$-0.679957\pi$
$883$	−31.8377	−1.07142	−0.535712	+	0.844401i	$0.679957\pi$
$884$	0	0
$885$	−1.62565	−0.0546455
$886$	18.1360	0.609291
$887$	−7.83446	−0.263055	−0.131528	−	0.991312i	$-0.541988\pi$
$887$	−7.83446	−0.263055	−0.131528	+	0.991312i	$0.541988\pi$
$888$	−2.46681	−0.0827808
$889$	−22.2209	−0.745265
$890$	3.37867	0.113253
$891$	3.19806	0.107139
$892$	21.5972	0.723127
$893$	−70.0055	−2.34264
$894$	−10.7724	−0.360283
$895$	−16.0422	−0.536232
$896$	−1.35690	−0.0453307
$897$	0	0
$898$	−4.55496	−0.152001
$899$	−1.50099	−0.0500609
$900$	1.00000	0.0333333
$901$	−11.7627	−0.391873
$902$	−39.1280	−1.30282
$903$	3.95108	0.131484
$904$	18.6571	0.620526
$905$	−3.85086	−0.128007
$906$	17.3817	0.577467
$907$	33.1089	1.09936	0.549681	−	0.835375i	$-0.314749\pi$
$907$	33.1089	1.09936	0.549681	+	0.835375i	$0.314749\pi$
$908$	10.2862	0.341360
$909$	−12.5918	−0.417643
$910$	0	0
$911$	−14.0556	−0.465684	−0.232842	−	0.972515i	$-0.574802\pi$
$911$	−14.0556	−0.465684	−0.232842	+	0.972515i	$0.574802\pi$
$912$	5.34481	0.176984
$913$	35.5612	1.17690
$914$	9.98121	0.330149
$915$	5.28382	0.174678
$916$	4.25906	0.140723
$917$	4.08383	0.134860
$918$	−2.04892	−0.0676243
$919$	−27.1830	−0.896684	−0.448342	−	0.893862i	$-0.647985\pi$
$919$	−27.1830	−0.896684	−0.448342	+	0.893862i	$0.647985\pi$
$920$	−8.32304	−0.274403
$921$	10.1347	0.333949
$922$	−16.1672	−0.532438
$923$	0	0
$924$	−4.33944	−0.142757
$925$	−2.46681	−0.0811083
$926$	3.88902	0.127801
$927$	−9.00000	−0.295599
$928$	−8.07069	−0.264933
$929$	50.3521	1.65200	0.826000	−	0.563671i	$-0.190611\pi$
$929$	50.3521	1.65200	0.826000	+	0.563671i	$0.190611\pi$
$930$	0.185981	0.00609855
$931$	27.5730	0.903669
$932$	19.5133	0.639181
$933$	−20.0218	−0.655483
$934$	0.872625	0.0285532
$935$	6.55257	0.214292
$936$	0	0
$937$	26.6394	0.870271	0.435135	−	0.900365i	$-0.356701\pi$
$937$	26.6394	0.870271	0.435135	+	0.900365i	$0.356701\pi$
$938$	−2.10992	−0.0688912
$939$	−8.63640	−0.281838
$940$	−13.0978	−0.427204
$941$	25.7198	0.838440	0.419220	−	0.907885i	$-0.362304\pi$
$941$	25.7198	0.838440	0.419220	+	0.907885i	$0.362304\pi$
$942$	15.5429	0.506414
$943$	−101.832	−3.31609
$944$	−1.62565	−0.0529103
$945$	1.35690	0.0441398
$946$	9.31229	0.302769
$947$	−14.4862	−0.470738	−0.235369	−	0.971906i	$-0.575630\pi$
$947$	−14.4862	−0.470738	−0.235369	+	0.971906i	$0.575630\pi$
$948$	1.42327	0.0462257
$949$	0	0
$950$	5.34481	0.173409
$951$	−17.6256	−0.571551
$952$	2.78017	0.0901057
$953$	−29.3690	−0.951354	−0.475677	−	0.879620i	$-0.657797\pi$
$953$	−29.3690	−0.951354	−0.475677	+	0.879620i	$0.657797\pi$
$954$	−5.74094	−0.185870
$955$	−11.8280	−0.382746
$956$	−7.16315	−0.231673
$957$	−25.8106	−0.834337
$958$	−31.6305	−1.02194
$959$	27.5303	0.889000
$960$	1.00000	0.0322749
$961$	−30.9654	−0.998884
$962$	0	0
$963$	−5.08815	−0.163963
$964$	17.9584	0.578400
$965$	−0.872625	−0.0280908
$966$	−11.2935	−0.363363
$967$	21.9360	0.705415	0.352707	−	0.935734i	$-0.385261\pi$
$967$	21.9360	0.705415	0.352707	+	0.935734i	$0.385261\pi$
$968$	0.772398	0.0248258
$969$	−10.9511	−0.351799
$970$	−4.74094	−0.152222
$971$	34.9754	1.12241	0.561206	−	0.827676i	$-0.310337\pi$
$971$	34.9754	1.12241	0.561206	+	0.827676i	$0.310337\pi$
$972$	−1.00000	−0.0320750
$973$	−0.208225	−0.00667538
$974$	21.7748	0.697709
$975$	0	0
$976$	5.28382	0.169131
$977$	7.72289	0.247077	0.123539	−	0.992340i	$-0.460576\pi$
$977$	7.72289	0.247077	0.123539	+	0.992340i	$0.460576\pi$
$978$	−2.00239	−0.0640295
$979$	10.8052	0.345335
$980$	5.15883	0.164793
$981$	6.43296	0.205389
$982$	−42.9590	−1.37088
$983$	−29.0489	−0.926517	−0.463258	−	0.886223i	$-0.653320\pi$
$983$	−29.0489	−0.926517	−0.463258	+	0.886223i	$0.653320\pi$
$984$	12.2349	0.390034
$985$	−10.6213	−0.338424
$986$	16.5362	0.526619
$987$	−17.7724	−0.565702
$988$	0	0
$989$	24.2355	0.770644
$990$	3.19806	0.101641
$991$	37.7192	1.19819	0.599094	−	0.800678i	$-0.295527\pi$
$991$	37.7192	1.19819	0.599094	+	0.800678i	$0.295527\pi$
$992$	0.185981	0.00590489
$993$	31.5163	1.00014
$994$	3.15213	0.0999795
$995$	−12.3424	−0.391281
$996$	−11.1196	−0.352338
$997$	−7.18060	−0.227412	−0.113706	−	0.993514i	$-0.536272\pi$
$997$	−7.18060	−0.227412	−0.113706	+	0.993514i	$0.536272\pi$
$998$	−36.0978	−1.14266
$999$	2.46681	0.0780465

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5070.2.a.bk.1.2	✓	3
13.5	odd	4		5070.2.b.s.1351.5		6
13.8	odd	4		5070.2.b.s.1351.2		6
13.12	even	2		5070.2.a.bt.1.2	yes	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5070.2.a.bk.1.2	✓	3	1.1	even	1	trivial
5070.2.a.bt.1.2	yes	3	13.12	even	2
5070.2.b.s.1351.2		6	13.8	odd	4
5070.2.b.s.1351.5		6	13.5	odd	4

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:	\( N \)	\(=\)	\( 5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5070.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +1.35690 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +1.35690 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +3.19806 q^{11} -1.00000 q^{12} -1.35690 q^{14} +1.00000 q^{15} +1.00000 q^{16} -2.04892 q^{17} -1.00000 q^{18} -5.34481 q^{19} -1.00000 q^{20} -1.35690 q^{21} -3.19806 q^{22} -8.32304 q^{23} +1.00000 q^{24} +1.00000 q^{25} -1.00000 q^{27} +1.35690 q^{28} +8.07069 q^{29} -1.00000 q^{30} -0.185981 q^{31} -1.00000 q^{32} -3.19806 q^{33} +2.04892 q^{34} -1.35690 q^{35} +1.00000 q^{36} -2.46681 q^{37} +5.34481 q^{38} +1.00000 q^{40} +12.2349 q^{41} +1.35690 q^{42} -2.91185 q^{43} +3.19806 q^{44} -1.00000 q^{45} +8.32304 q^{46} +13.0978 q^{47} -1.00000 q^{48} -5.15883 q^{49} -1.00000 q^{50} +2.04892 q^{51} +5.74094 q^{53} +1.00000 q^{54} -3.19806 q^{55} -1.35690 q^{56} +5.34481 q^{57} -8.07069 q^{58} -1.62565 q^{59} +1.00000 q^{60} +5.28382 q^{61} +0.185981 q^{62} +1.35690 q^{63} +1.00000 q^{64} +3.19806 q^{66} +1.55496 q^{67} -2.04892 q^{68} +8.32304 q^{69} +1.35690 q^{70} -2.32304 q^{71} -1.00000 q^{72} -5.11529 q^{73} +2.46681 q^{74} -1.00000 q^{75} -5.34481 q^{76} +4.33944 q^{77} -1.42327 q^{79} -1.00000 q^{80} +1.00000 q^{81} -12.2349 q^{82} +11.1196 q^{83} -1.35690 q^{84} +2.04892 q^{85} +2.91185 q^{86} -8.07069 q^{87} -3.19806 q^{88} +3.37867 q^{89} +1.00000 q^{90} -8.32304 q^{92} +0.185981 q^{93} -13.0978 q^{94} +5.34481 q^{95} +1.00000 q^{96} -4.74094 q^{97} +5.15883 q^{98} +3.19806 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{5} + 3 q^{6} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^5 + 3 * q^6 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{5} + 3 q^{6} - 3 q^{8} + 3 q^{9} + 3 q^{10} + 14 q^{11} - 3 q^{12} + 3 q^{15} + 3 q^{16} + 3 q^{17} - 3 q^{18} + 7 q^{19} - 3 q^{20} - 14 q^{22} - 5 q^{23} + 3 q^{24} + 3 q^{25} - 3 q^{27} + 12 q^{29} - 3 q^{30} + 14 q^{31} - 3 q^{32} - 14 q^{33} - 3 q^{34} + 3 q^{36} - 4 q^{37} - 7 q^{38} + 3 q^{40} + 13 q^{41} - 5 q^{43} + 14 q^{44} - 3 q^{45} + 5 q^{46} + 21 q^{47} - 3 q^{48} - 7 q^{49} - 3 q^{50} - 3 q^{51} + 3 q^{53} + 3 q^{54} - 14 q^{55} - 7 q^{57} - 12 q^{58} + 7 q^{59} + 3 q^{60} - 17 q^{61} - 14 q^{62} + 3 q^{64} + 14 q^{66} + 5 q^{67} + 3 q^{68} + 5 q^{69} + 13 q^{71} - 3 q^{72} - 13 q^{73} + 4 q^{74} - 3 q^{75} + 7 q^{76} - 7 q^{77} - 7 q^{79} - 3 q^{80} + 3 q^{81} - 13 q^{82} + 12 q^{83} - 3 q^{85} + 5 q^{86} - 12 q^{87} - 14 q^{88} + 3 q^{89} + 3 q^{90} - 5 q^{92} - 14 q^{93} - 21 q^{94} - 7 q^{95} + 3 q^{96} + 7 q^{98} + 14 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^5 + 3 * q^6 - 3 * q^8 + 3 * q^9 + 3 * q^10 + 14 * q^11 - 3 * q^12 + 3 * q^15 + 3 * q^16 + 3 * q^17 - 3 * q^18 + 7 * q^19 - 3 * q^20 - 14 * q^22 - 5 * q^23 + 3 * q^24 + 3 * q^25 - 3 * q^27 + 12 * q^29 - 3 * q^30 + 14 * q^31 - 3 * q^32 - 14 * q^33 - 3 * q^34 + 3 * q^36 - 4 * q^37 - 7 * q^38 + 3 * q^40 + 13 * q^41 - 5 * q^43 + 14 * q^44 - 3 * q^45 + 5 * q^46 + 21 * q^47 - 3 * q^48 - 7 * q^49 - 3 * q^50 - 3 * q^51 + 3 * q^53 + 3 * q^54 - 14 * q^55 - 7 * q^57 - 12 * q^58 + 7 * q^59 + 3 * q^60 - 17 * q^61 - 14 * q^62 + 3 * q^64 + 14 * q^66 + 5 * q^67 + 3 * q^68 + 5 * q^69 + 13 * q^71 - 3 * q^72 - 13 * q^73 + 4 * q^74 - 3 * q^75 + 7 * q^76 - 7 * q^77 - 7 * q^79 - 3 * q^80 + 3 * q^81 - 13 * q^82 + 12 * q^83 - 3 * q^85 + 5 * q^86 - 12 * q^87 - 14 * q^88 + 3 * q^89 + 3 * q^90 - 5 * q^92 - 14 * q^93 - 21 * q^94 - 7 * q^95 + 3 * q^96 + 7 * q^98 + 14 * q^99

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