LMFDB - Embedded newform 430.2.a.g.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(1,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, 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("430.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.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:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.41421$ of defining polynomial
Character	$\chi$	$=$	430.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.41421 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.41421 q^{6} +1.00000 q^{7} +1.00000 q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.41421 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.41421 q^{6} +1.00000 q^{7} +1.00000 q^{8} -1.00000 q^{9} +1.00000 q^{10} +3.41421 q^{11} -1.41421 q^{12} +3.82843 q^{13} +1.00000 q^{14} -1.41421 q^{15} +1.00000 q^{16} -1.41421 q^{17} -1.00000 q^{18} -1.00000 q^{19} +1.00000 q^{20} -1.41421 q^{21} +3.41421 q^{22} +9.07107 q^{23} -1.41421 q^{24} +1.00000 q^{25} +3.82843 q^{26} +5.65685 q^{27} +1.00000 q^{28} -7.24264 q^{29} -1.41421 q^{30} +2.41421 q^{31} +1.00000 q^{32} -4.82843 q^{33} -1.41421 q^{34} +1.00000 q^{35} -1.00000 q^{36} -6.24264 q^{37} -1.00000 q^{38} -5.41421 q^{39} +1.00000 q^{40} +3.82843 q^{41} -1.41421 q^{42} +1.00000 q^{43} +3.41421 q^{44} -1.00000 q^{45} +9.07107 q^{46} -7.07107 q^{47} -1.41421 q^{48} -6.00000 q^{49} +1.00000 q^{50} +2.00000 q^{51} +3.82843 q^{52} +5.65685 q^{53} +5.65685 q^{54} +3.41421 q^{55} +1.00000 q^{56} +1.41421 q^{57} -7.24264 q^{58} -6.82843 q^{59} -1.41421 q^{60} -14.0711 q^{61} +2.41421 q^{62} -1.00000 q^{63} +1.00000 q^{64} +3.82843 q^{65} -4.82843 q^{66} +7.24264 q^{67} -1.41421 q^{68} -12.8284 q^{69} +1.00000 q^{70} -7.89949 q^{71} -1.00000 q^{72} -0.757359 q^{73} -6.24264 q^{74} -1.41421 q^{75} -1.00000 q^{76} +3.41421 q^{77} -5.41421 q^{78} -5.58579 q^{79} +1.00000 q^{80} -5.00000 q^{81} +3.82843 q^{82} -7.65685 q^{83} -1.41421 q^{84} -1.41421 q^{85} +1.00000 q^{86} +10.2426 q^{87} +3.41421 q^{88} +5.07107 q^{89} -1.00000 q^{90} +3.82843 q^{91} +9.07107 q^{92} -3.41421 q^{93} -7.07107 q^{94} -1.00000 q^{95} -1.41421 q^{96} -17.5563 q^{97} -6.00000 q^{98} -3.41421 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{4} + 2 q^{5} + 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + 2 * q^4 + 2 * q^5 + 2 * q^7 + 2 * q^8 - 2 * q^9	$ 2 q + 2 q^{2} + 2 q^{4} + 2 q^{5} + 2 q^{7} + 2 q^{8} - 2 q^{9} + 2 q^{10} + 4 q^{11} + 2 q^{13} + 2 q^{14} + 2 q^{16} - 2 q^{18} - 2 q^{19} + 2 q^{20} + 4 q^{22} + 4 q^{23} + 2 q^{25} + 2 q^{26} + 2 q^{28} - 6 q^{29} + 2 q^{31} + 2 q^{32} - 4 q^{33} + 2 q^{35} - 2 q^{36} - 4 q^{37} - 2 q^{38} - 8 q^{39} + 2 q^{40} + 2 q^{41} + 2 q^{43} + 4 q^{44} - 2 q^{45} + 4 q^{46} - 12 q^{49} + 2 q^{50} + 4 q^{51} + 2 q^{52} + 4 q^{55} + 2 q^{56} - 6 q^{58} - 8 q^{59} - 14 q^{61} + 2 q^{62} - 2 q^{63} + 2 q^{64} + 2 q^{65} - 4 q^{66} + 6 q^{67} - 20 q^{69} + 2 q^{70} + 4 q^{71} - 2 q^{72} - 10 q^{73} - 4 q^{74} - 2 q^{76} + 4 q^{77} - 8 q^{78} - 14 q^{79} + 2 q^{80} - 10 q^{81} + 2 q^{82} - 4 q^{83} + 2 q^{86} + 12 q^{87} + 4 q^{88} - 4 q^{89} - 2 q^{90} + 2 q^{91} + 4 q^{92} - 4 q^{93} - 2 q^{95} - 4 q^{97} - 12 q^{98} - 4 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^4 + 2 * q^5 + 2 * q^7 + 2 * q^8 - 2 * q^9 + 2 * q^10 + 4 * q^11 + 2 * q^13 + 2 * q^14 + 2 * q^16 - 2 * q^18 - 2 * q^19 + 2 * q^20 + 4 * q^22 + 4 * q^23 + 2 * q^25 + 2 * q^26 + 2 * q^28 - 6 * q^29 + 2 * q^31 + 2 * q^32 - 4 * q^33 + 2 * q^35 - 2 * q^36 - 4 * q^37 - 2 * q^38 - 8 * q^39 + 2 * q^40 + 2 * q^41 + 2 * q^43 + 4 * q^44 - 2 * q^45 + 4 * q^46 - 12 * q^49 + 2 * q^50 + 4 * q^51 + 2 * q^52 + 4 * q^55 + 2 * q^56 - 6 * q^58 - 8 * q^59 - 14 * q^61 + 2 * q^62 - 2 * q^63 + 2 * q^64 + 2 * q^65 - 4 * q^66 + 6 * q^67 - 20 * q^69 + 2 * q^70 + 4 * q^71 - 2 * q^72 - 10 * q^73 - 4 * q^74 - 2 * q^76 + 4 * q^77 - 8 * q^78 - 14 * q^79 + 2 * q^80 - 10 * q^81 + 2 * q^82 - 4 * q^83 + 2 * q^86 + 12 * q^87 + 4 * q^88 - 4 * q^89 - 2 * q^90 + 2 * q^91 + 4 * q^92 - 4 * q^93 - 2 * q^95 - 4 * q^97 - 12 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.41421	−0.816497	−0.408248	−	0.912871i	$-0.633860\pi$
$3$	−1.41421	−0.816497	−0.408248	+	0.912871i	$0.633860\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.41421	−0.577350
$7$	1.00000	0.377964	0.188982	−	0.981981i	$-0.439481\pi$
$7$	1.00000	0.377964	0.188982	+	0.981981i	$0.439481\pi$
$8$	1.00000	0.353553
$9$	−1.00000	−0.333333
$10$	1.00000	0.316228
$11$	3.41421	1.02942	0.514712	−	0.857363i	$-0.327899\pi$
$11$	3.41421	1.02942	0.514712	+	0.857363i	$0.327899\pi$
$12$	−1.41421	−0.408248
$13$	3.82843	1.06181	0.530907	−	0.847430i	$-0.321851\pi$
$13$	3.82843	1.06181	0.530907	+	0.847430i	$0.321851\pi$
$14$	1.00000	0.267261
$15$	−1.41421	−0.365148
$16$	1.00000	0.250000
$17$	−1.41421	−0.342997	−0.171499	−	0.985184i	$-0.554861\pi$
$17$	−1.41421	−0.342997	−0.171499	+	0.985184i	$0.554861\pi$
$18$	−1.00000	−0.235702
$19$	−1.00000	−0.229416	−0.114708	−	0.993399i	$-0.536593\pi$
$19$	−1.00000	−0.229416	−0.114708	+	0.993399i	$0.536593\pi$
$20$	1.00000	0.223607
$21$	−1.41421	−0.308607
$22$	3.41421	0.727913
$23$	9.07107	1.89145	0.945724	−	0.324970i	$-0.105354\pi$
$23$	9.07107	1.89145	0.945724	+	0.324970i	$0.105354\pi$
$24$	−1.41421	−0.288675
$25$	1.00000	0.200000
$26$	3.82843	0.750816
$27$	5.65685	1.08866
$28$	1.00000	0.188982
$29$	−7.24264	−1.34492	−0.672462	−	0.740131i	$-0.734763\pi$
$29$	−7.24264	−1.34492	−0.672462	+	0.740131i	$0.734763\pi$
$30$	−1.41421	−0.258199
$31$	2.41421	0.433606	0.216803	−	0.976215i	$-0.430437\pi$
$31$	2.41421	0.433606	0.216803	+	0.976215i	$0.430437\pi$
$32$	1.00000	0.176777
$33$	−4.82843	−0.840521
$34$	−1.41421	−0.242536
$35$	1.00000	0.169031
$36$	−1.00000	−0.166667
$37$	−6.24264	−1.02628	−0.513142	−	0.858304i	$-0.671519\pi$
$37$	−6.24264	−1.02628	−0.513142	+	0.858304i	$0.671519\pi$
$38$	−1.00000	−0.162221
$39$	−5.41421	−0.866968
$40$	1.00000	0.158114
$41$	3.82843	0.597900	0.298950	−	0.954269i	$-0.403364\pi$
$41$	3.82843	0.597900	0.298950	+	0.954269i	$0.403364\pi$
$42$	−1.41421	−0.218218
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	3.41421	0.514712
$45$	−1.00000	−0.149071
$46$	9.07107	1.33746
$47$	−7.07107	−1.03142	−0.515711	−	0.856763i	$-0.672472\pi$
$47$	−7.07107	−1.03142	−0.515711	+	0.856763i	$0.672472\pi$
$48$	−1.41421	−0.204124
$49$	−6.00000	−0.857143
$50$	1.00000	0.141421
$51$	2.00000	0.280056
$52$	3.82843	0.530907
$53$	5.65685	0.777029	0.388514	−	0.921443i	$-0.372988\pi$
$53$	5.65685	0.777029	0.388514	+	0.921443i	$0.372988\pi$
$54$	5.65685	0.769800
$55$	3.41421	0.460372
$56$	1.00000	0.133631
$57$	1.41421	0.187317
$58$	−7.24264	−0.951005
$59$	−6.82843	−0.888985	−0.444493	−	0.895782i	$-0.646616\pi$
$59$	−6.82843	−0.888985	−0.444493	+	0.895782i	$0.646616\pi$
$60$	−1.41421	−0.182574
$61$	−14.0711	−1.80162	−0.900808	−	0.434218i	$-0.857025\pi$
$61$	−14.0711	−1.80162	−0.900808	+	0.434218i	$0.857025\pi$
$62$	2.41421	0.306605
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	3.82843	0.474858
$66$	−4.82843	−0.594338
$67$	7.24264	0.884829	0.442415	−	0.896811i	$-0.354122\pi$
$67$	7.24264	0.884829	0.442415	+	0.896811i	$0.354122\pi$
$68$	−1.41421	−0.171499
$69$	−12.8284	−1.54436
$70$	1.00000	0.119523
$71$	−7.89949	−0.937498	−0.468749	−	0.883332i	$-0.655295\pi$
$71$	−7.89949	−0.937498	−0.468749	+	0.883332i	$0.655295\pi$
$72$	−1.00000	−0.117851
$73$	−0.757359	−0.0886422	−0.0443211	−	0.999017i	$-0.514112\pi$
$73$	−0.757359	−0.0886422	−0.0443211	+	0.999017i	$0.514112\pi$
$74$	−6.24264	−0.725692
$75$	−1.41421	−0.163299
$76$	−1.00000	−0.114708
$77$	3.41421	0.389086
$78$	−5.41421	−0.613039
$79$	−5.58579	−0.628450	−0.314225	−	0.949349i	$-0.601745\pi$
$79$	−5.58579	−0.628450	−0.314225	+	0.949349i	$0.601745\pi$
$80$	1.00000	0.111803
$81$	−5.00000	−0.555556
$82$	3.82843	0.422779
$83$	−7.65685	−0.840449	−0.420224	−	0.907420i	$-0.638049\pi$
$83$	−7.65685	−0.840449	−0.420224	+	0.907420i	$0.638049\pi$
$84$	−1.41421	−0.154303
$85$	−1.41421	−0.153393
$86$	1.00000	0.107833
$87$	10.2426	1.09813
$88$	3.41421	0.363956
$89$	5.07107	0.537532	0.268766	−	0.963205i	$-0.413384\pi$
$89$	5.07107	0.537532	0.268766	+	0.963205i	$0.413384\pi$
$90$	−1.00000	−0.105409
$91$	3.82843	0.401328
$92$	9.07107	0.945724
$93$	−3.41421	−0.354037
$94$	−7.07107	−0.729325
$95$	−1.00000	−0.102598
$96$	−1.41421	−0.144338
$97$	−17.5563	−1.78258	−0.891289	−	0.453436i	$-0.850198\pi$
$97$	−17.5563	−1.78258	−0.891289	+	0.453436i	$0.850198\pi$
$98$	−6.00000	−0.606092
$99$	−3.41421	−0.343141
$100$	1.00000	0.100000
$101$	−1.41421	−0.140720	−0.0703598	−	0.997522i	$-0.522415\pi$
$101$	−1.41421	−0.140720	−0.0703598	+	0.997522i	$0.522415\pi$
$102$	2.00000	0.198030
$103$	−4.82843	−0.475759	−0.237880	−	0.971295i	$-0.576452\pi$
$103$	−4.82843	−0.475759	−0.237880	+	0.971295i	$0.576452\pi$
$104$	3.82843	0.375408
$105$	−1.41421	−0.138013
$106$	5.65685	0.549442
$107$	16.0711	1.55365	0.776824	−	0.629717i	$-0.216829\pi$
$107$	16.0711	1.55365	0.776824	+	0.629717i	$0.216829\pi$
$108$	5.65685	0.544331
$109$	−5.17157	−0.495347	−0.247673	−	0.968844i	$-0.579666\pi$
$109$	−5.17157	−0.495347	−0.247673	+	0.968844i	$0.579666\pi$
$110$	3.41421	0.325532
$111$	8.82843	0.837957
$112$	1.00000	0.0944911
$113$	−14.8995	−1.40163	−0.700813	−	0.713345i	$-0.747179\pi$
$113$	−14.8995	−1.40163	−0.700813	+	0.713345i	$0.747179\pi$
$114$	1.41421	0.132453
$115$	9.07107	0.845881
$116$	−7.24264	−0.672462
$117$	−3.82843	−0.353938
$118$	−6.82843	−0.628608
$119$	−1.41421	−0.129641
$120$	−1.41421	−0.129099
$121$	0.656854	0.0597140
$122$	−14.0711	−1.27393
$123$	−5.41421	−0.488183
$124$	2.41421	0.216803
$125$	1.00000	0.0894427
$126$	−1.00000	−0.0890871
$127$	20.4853	1.81777	0.908887	−	0.417042i	$-0.136933\pi$
$127$	20.4853	1.81777	0.908887	+	0.417042i	$0.136933\pi$
$128$	1.00000	0.0883883
$129$	−1.41421	−0.124515
$130$	3.82843	0.335775
$131$	6.00000	0.524222	0.262111	−	0.965038i	$-0.415581\pi$
$131$	6.00000	0.524222	0.262111	+	0.965038i	$0.415581\pi$
$132$	−4.82843	−0.420261
$133$	−1.00000	−0.0867110
$134$	7.24264	0.625669
$135$	5.65685	0.486864
$136$	−1.41421	−0.121268
$137$	18.0711	1.54392	0.771958	−	0.635674i	$-0.219278\pi$
$137$	18.0711	1.54392	0.771958	+	0.635674i	$0.219278\pi$
$138$	−12.8284	−1.09203
$139$	2.24264	0.190218	0.0951092	−	0.995467i	$-0.469680\pi$
$139$	2.24264	0.190218	0.0951092	+	0.995467i	$0.469680\pi$
$140$	1.00000	0.0845154
$141$	10.0000	0.842152
$142$	−7.89949	−0.662911
$143$	13.0711	1.09306
$144$	−1.00000	−0.0833333
$145$	−7.24264	−0.601469
$146$	−0.757359	−0.0626795
$147$	8.48528	0.699854
$148$	−6.24264	−0.513142
$149$	20.5563	1.68404	0.842021	−	0.539445i	$-0.181366\pi$
$149$	20.5563	1.68404	0.842021	+	0.539445i	$0.181366\pi$
$150$	−1.41421	−0.115470
$151$	−6.48528	−0.527765	−0.263882	−	0.964555i	$-0.585003\pi$
$151$	−6.48528	−0.527765	−0.263882	+	0.964555i	$0.585003\pi$
$152$	−1.00000	−0.0811107
$153$	1.41421	0.114332
$154$	3.41421	0.275125
$155$	2.41421	0.193914
$156$	−5.41421	−0.433484
$157$	1.75736	0.140253	0.0701263	−	0.997538i	$-0.477660\pi$
$157$	1.75736	0.140253	0.0701263	+	0.997538i	$0.477660\pi$
$158$	−5.58579	−0.444381
$159$	−8.00000	−0.634441
$160$	1.00000	0.0790569
$161$	9.07107	0.714900
$162$	−5.00000	−0.392837
$163$	2.34315	0.183529	0.0917647	−	0.995781i	$-0.470749\pi$
$163$	2.34315	0.183529	0.0917647	+	0.995781i	$0.470749\pi$
$164$	3.82843	0.298950
$165$	−4.82843	−0.375893
$166$	−7.65685	−0.594287
$167$	−17.5563	−1.35855	−0.679276	−	0.733883i	$-0.737706\pi$
$167$	−17.5563	−1.35855	−0.679276	+	0.733883i	$0.737706\pi$
$168$	−1.41421	−0.109109
$169$	1.65685	0.127450
$170$	−1.41421	−0.108465
$171$	1.00000	0.0764719
$172$	1.00000	0.0762493
$173$	17.4853	1.32938	0.664691	−	0.747119i	$-0.268563\pi$
$173$	17.4853	1.32938	0.664691	+	0.747119i	$0.268563\pi$
$174$	10.2426	0.776493
$175$	1.00000	0.0755929
$176$	3.41421	0.257356
$177$	9.65685	0.725854
$178$	5.07107	0.380093
$179$	0.514719	0.0384719	0.0192359	−	0.999815i	$-0.493877\pi$
$179$	0.514719	0.0384719	0.0192359	+	0.999815i	$0.493877\pi$
$180$	−1.00000	−0.0745356
$181$	−0.928932	−0.0690470	−0.0345235	−	0.999404i	$-0.510991\pi$
$181$	−0.928932	−0.0690470	−0.0345235	+	0.999404i	$0.510991\pi$
$182$	3.82843	0.283782
$183$	19.8995	1.47101
$184$	9.07107	0.668728
$185$	−6.24264	−0.458968
$186$	−3.41421	−0.250342
$187$	−4.82843	−0.353090
$188$	−7.07107	−0.515711
$189$	5.65685	0.411476
$190$	−1.00000	−0.0725476
$191$	0.100505	0.00727229	0.00363615	−	0.999993i	$-0.498843\pi$
$191$	0.100505	0.00727229	0.00363615	+	0.999993i	$0.498843\pi$
$192$	−1.41421	−0.102062
$193$	1.17157	0.0843317	0.0421658	−	0.999111i	$-0.486574\pi$
$193$	1.17157	0.0843317	0.0421658	+	0.999111i	$0.486574\pi$
$194$	−17.5563	−1.26047
$195$	−5.41421	−0.387720
$196$	−6.00000	−0.428571
$197$	−3.14214	−0.223868	−0.111934	−	0.993716i	$-0.535705\pi$
$197$	−3.14214	−0.223868	−0.111934	+	0.993716i	$0.535705\pi$
$198$	−3.41421	−0.242638
$199$	−19.8995	−1.41064	−0.705319	−	0.708890i	$-0.749196\pi$
$199$	−19.8995	−1.41064	−0.705319	+	0.708890i	$0.749196\pi$
$200$	1.00000	0.0707107
$201$	−10.2426	−0.722460
$202$	−1.41421	−0.0995037
$203$	−7.24264	−0.508334
$204$	2.00000	0.140028
$205$	3.82843	0.267389
$206$	−4.82843	−0.336412
$207$	−9.07107	−0.630483
$208$	3.82843	0.265454
$209$	−3.41421	−0.236166
$210$	−1.41421	−0.0975900
$211$	9.65685	0.664805	0.332403	−	0.943138i	$-0.392141\pi$
$211$	9.65685	0.664805	0.332403	+	0.943138i	$0.392141\pi$
$212$	5.65685	0.388514
$213$	11.1716	0.765464
$214$	16.0711	1.09860
$215$	1.00000	0.0681994
$216$	5.65685	0.384900
$217$	2.41421	0.163887
$218$	−5.17157	−0.350263
$219$	1.07107	0.0723761
$220$	3.41421	0.230186
$221$	−5.41421	−0.364199
$222$	8.82843	0.592525
$223$	−12.1421	−0.813098	−0.406549	−	0.913629i	$-0.633268\pi$
$223$	−12.1421	−0.813098	−0.406549	+	0.913629i	$0.633268\pi$
$224$	1.00000	0.0668153
$225$	−1.00000	−0.0666667
$226$	−14.8995	−0.991100
$227$	14.8284	0.984197	0.492099	−	0.870539i	$-0.336230\pi$
$227$	14.8284	0.984197	0.492099	+	0.870539i	$0.336230\pi$
$228$	1.41421	0.0936586
$229$	−4.82843	−0.319071	−0.159536	−	0.987192i	$-0.551000\pi$
$229$	−4.82843	−0.319071	−0.159536	+	0.987192i	$0.551000\pi$
$230$	9.07107	0.598128
$231$	−4.82843	−0.317687
$232$	−7.24264	−0.475503
$233$	−8.48528	−0.555889	−0.277945	−	0.960597i	$-0.589653\pi$
$233$	−8.48528	−0.555889	−0.277945	+	0.960597i	$0.589653\pi$
$234$	−3.82843	−0.250272
$235$	−7.07107	−0.461266
$236$	−6.82843	−0.444493
$237$	7.89949	0.513127
$238$	−1.41421	−0.0916698
$239$	14.4142	0.932378	0.466189	−	0.884685i	$-0.345627\pi$
$239$	14.4142	0.932378	0.466189	+	0.884685i	$0.345627\pi$
$240$	−1.41421	−0.0912871
$241$	−18.5858	−1.19722	−0.598608	−	0.801042i	$-0.704279\pi$
$241$	−18.5858	−1.19722	−0.598608	+	0.801042i	$0.704279\pi$
$242$	0.656854	0.0422242
$243$	−9.89949	−0.635053
$244$	−14.0711	−0.900808
$245$	−6.00000	−0.383326
$246$	−5.41421	−0.345198
$247$	−3.82843	−0.243597
$248$	2.41421	0.153303
$249$	10.8284	0.686224
$250$	1.00000	0.0632456
$251$	22.9706	1.44989	0.724945	−	0.688807i	$-0.241865\pi$
$251$	22.9706	1.44989	0.724945	+	0.688807i	$0.241865\pi$
$252$	−1.00000	−0.0629941
$253$	30.9706	1.94710
$254$	20.4853	1.28536
$255$	2.00000	0.125245
$256$	1.00000	0.0625000
$257$	−10.8995	−0.679892	−0.339946	−	0.940445i	$-0.610409\pi$
$257$	−10.8995	−0.679892	−0.339946	+	0.940445i	$0.610409\pi$
$258$	−1.41421	−0.0880451
$259$	−6.24264	−0.387899
$260$	3.82843	0.237429
$261$	7.24264	0.448308
$262$	6.00000	0.370681
$263$	0.514719	0.0317389	0.0158695	−	0.999874i	$-0.494948\pi$
$263$	0.514719	0.0317389	0.0158695	+	0.999874i	$0.494948\pi$
$264$	−4.82843	−0.297169
$265$	5.65685	0.347498
$266$	−1.00000	−0.0613139
$267$	−7.17157	−0.438893
$268$	7.24264	0.442415
$269$	14.8284	0.904105	0.452053	−	0.891991i	$-0.350692\pi$
$269$	14.8284	0.904105	0.452053	+	0.891991i	$0.350692\pi$
$270$	5.65685	0.344265
$271$	−10.8995	−0.662097	−0.331049	−	0.943614i	$-0.607402\pi$
$271$	−10.8995	−0.662097	−0.331049	+	0.943614i	$0.607402\pi$
$272$	−1.41421	−0.0857493
$273$	−5.41421	−0.327683
$274$	18.0711	1.09171
$275$	3.41421	0.205885
$276$	−12.8284	−0.772181
$277$	16.4853	0.990505	0.495252	−	0.868749i	$-0.335076\pi$
$277$	16.4853	0.990505	0.495252	+	0.868749i	$0.335076\pi$
$278$	2.24264	0.134505
$279$	−2.41421	−0.144535
$280$	1.00000	0.0597614
$281$	−12.6569	−0.755045	−0.377522	−	0.926000i	$-0.623224\pi$
$281$	−12.6569	−0.755045	−0.377522	+	0.926000i	$0.623224\pi$
$282$	10.0000	0.595491
$283$	27.2426	1.61941	0.809703	−	0.586839i	$-0.199628\pi$
$283$	27.2426	1.61941	0.809703	+	0.586839i	$0.199628\pi$
$284$	−7.89949	−0.468749
$285$	1.41421	0.0837708
$286$	13.0711	0.772908
$287$	3.82843	0.225985
$288$	−1.00000	−0.0589256
$289$	−15.0000	−0.882353
$290$	−7.24264	−0.425303
$291$	24.8284	1.45547
$292$	−0.757359	−0.0443211
$293$	−22.9706	−1.34195	−0.670977	−	0.741478i	$-0.734125\pi$
$293$	−22.9706	−1.34195	−0.670977	+	0.741478i	$0.734125\pi$
$294$	8.48528	0.494872
$295$	−6.82843	−0.397566
$296$	−6.24264	−0.362846
$297$	19.3137	1.12070
$298$	20.5563	1.19080
$299$	34.7279	2.00837
$300$	−1.41421	−0.0816497
$301$	1.00000	0.0576390
$302$	−6.48528	−0.373186
$303$	2.00000	0.114897
$304$	−1.00000	−0.0573539
$305$	−14.0711	−0.805707
$306$	1.41421	0.0808452
$307$	−20.0711	−1.14552	−0.572758	−	0.819724i	$-0.694127\pi$
$307$	−20.0711	−1.14552	−0.572758	+	0.819724i	$0.694127\pi$
$308$	3.41421	0.194543
$309$	6.82843	0.388456
$310$	2.41421	0.137118
$311$	10.0711	0.571078	0.285539	−	0.958367i	$-0.407827\pi$
$311$	10.0711	0.571078	0.285539	+	0.958367i	$0.407827\pi$
$312$	−5.41421	−0.306519
$313$	21.3137	1.20472	0.602361	−	0.798224i	$-0.294227\pi$
$313$	21.3137	1.20472	0.602361	+	0.798224i	$0.294227\pi$
$314$	1.75736	0.0991735
$315$	−1.00000	−0.0563436
$316$	−5.58579	−0.314225
$317$	29.1421	1.63679	0.818393	−	0.574659i	$-0.194865\pi$
$317$	29.1421	1.63679	0.818393	+	0.574659i	$0.194865\pi$
$318$	−8.00000	−0.448618
$319$	−24.7279	−1.38450
$320$	1.00000	0.0559017
$321$	−22.7279	−1.26855
$322$	9.07107	0.505511
$323$	1.41421	0.0786889
$324$	−5.00000	−0.277778
$325$	3.82843	0.212363
$326$	2.34315	0.129775
$327$	7.31371	0.404449
$328$	3.82843	0.211390
$329$	−7.07107	−0.389841
$330$	−4.82843	−0.265796
$331$	−2.68629	−0.147652	−0.0738260	−	0.997271i	$-0.523521\pi$
$331$	−2.68629	−0.147652	−0.0738260	+	0.997271i	$0.523521\pi$
$332$	−7.65685	−0.420224
$333$	6.24264	0.342095
$334$	−17.5563	−0.960641
$335$	7.24264	0.395708
$336$	−1.41421	−0.0771517
$337$	−19.6569	−1.07078	−0.535389	−	0.844606i	$-0.679835\pi$
$337$	−19.6569	−1.07078	−0.535389	+	0.844606i	$0.679835\pi$
$338$	1.65685	0.0901210
$339$	21.0711	1.14442
$340$	−1.41421	−0.0766965
$341$	8.24264	0.446364
$342$	1.00000	0.0540738
$343$	−13.0000	−0.701934
$344$	1.00000	0.0539164
$345$	−12.8284	−0.690659
$346$	17.4853	0.940015
$347$	−13.7574	−0.738534	−0.369267	−	0.929323i	$-0.620391\pi$
$347$	−13.7574	−0.738534	−0.369267	+	0.929323i	$0.620391\pi$
$348$	10.2426	0.549063
$349$	−27.4558	−1.46968	−0.734839	−	0.678242i	$-0.762742\pi$
$349$	−27.4558	−1.46968	−0.734839	+	0.678242i	$0.762742\pi$
$350$	1.00000	0.0534522
$351$	21.6569	1.15596
$352$	3.41421	0.181978
$353$	4.38478	0.233378	0.116689	−	0.993168i	$-0.462772\pi$
$353$	4.38478	0.233378	0.116689	+	0.993168i	$0.462772\pi$
$354$	9.65685	0.513256
$355$	−7.89949	−0.419262
$356$	5.07107	0.268766
$357$	2.00000	0.105851
$358$	0.514719	0.0272037
$359$	−37.5269	−1.98059	−0.990297	−	0.138965i	$-0.955623\pi$
$359$	−37.5269	−1.98059	−0.990297	+	0.138965i	$0.955623\pi$
$360$	−1.00000	−0.0527046
$361$	−18.0000	−0.947368
$362$	−0.928932	−0.0488236
$363$	−0.928932	−0.0487563
$364$	3.82843	0.200664
$365$	−0.757359	−0.0396420
$366$	19.8995	1.04016
$367$	−8.68629	−0.453421	−0.226710	−	0.973962i	$-0.572797\pi$
$367$	−8.68629	−0.453421	−0.226710	+	0.973962i	$0.572797\pi$
$368$	9.07107	0.472862
$369$	−3.82843	−0.199300
$370$	−6.24264	−0.324539
$371$	5.65685	0.293689
$372$	−3.41421	−0.177019
$373$	−10.7279	−0.555471	−0.277735	−	0.960658i	$-0.589584\pi$
$373$	−10.7279	−0.555471	−0.277735	+	0.960658i	$0.589584\pi$
$374$	−4.82843	−0.249672
$375$	−1.41421	−0.0730297
$376$	−7.07107	−0.364662
$377$	−27.7279	−1.42806
$378$	5.65685	0.290957
$379$	−24.1421	−1.24010	−0.620049	−	0.784563i	$-0.712887\pi$
$379$	−24.1421	−1.24010	−0.620049	+	0.784563i	$0.712887\pi$
$380$	−1.00000	−0.0512989
$381$	−28.9706	−1.48421
$382$	0.100505	0.00514229
$383$	14.3137	0.731396	0.365698	−	0.930734i	$-0.380830\pi$
$383$	14.3137	0.731396	0.365698	+	0.930734i	$0.380830\pi$
$384$	−1.41421	−0.0721688
$385$	3.41421	0.174004
$386$	1.17157	0.0596315
$387$	−1.00000	−0.0508329
$388$	−17.5563	−0.891289
$389$	15.1716	0.769229	0.384615	−	0.923077i	$-0.374334\pi$
$389$	15.1716	0.769229	0.384615	+	0.923077i	$0.374334\pi$
$390$	−5.41421	−0.274159
$391$	−12.8284	−0.648761
$392$	−6.00000	−0.303046
$393$	−8.48528	−0.428026
$394$	−3.14214	−0.158299
$395$	−5.58579	−0.281051
$396$	−3.41421	−0.171571
$397$	−3.51472	−0.176399	−0.0881993	−	0.996103i	$-0.528111\pi$
$397$	−3.51472	−0.176399	−0.0881993	+	0.996103i	$0.528111\pi$
$398$	−19.8995	−0.997472
$399$	1.41421	0.0707992
$400$	1.00000	0.0500000
$401$	38.1127	1.90326	0.951629	−	0.307251i	$-0.0994090\pi$
$401$	38.1127	1.90326	0.951629	+	0.307251i	$0.0994090\pi$
$402$	−10.2426	−0.510856
$403$	9.24264	0.460409
$404$	−1.41421	−0.0703598
$405$	−5.00000	−0.248452
$406$	−7.24264	−0.359446
$407$	−21.3137	−1.05648
$408$	2.00000	0.0990148
$409$	15.2132	0.752244	0.376122	−	0.926570i	$-0.377257\pi$
$409$	15.2132	0.752244	0.376122	+	0.926570i	$0.377257\pi$
$410$	3.82843	0.189073
$411$	−25.5563	−1.26060
$412$	−4.82843	−0.237880
$413$	−6.82843	−0.336005
$414$	−9.07107	−0.445819
$415$	−7.65685	−0.375860
$416$	3.82843	0.187704
$417$	−3.17157	−0.155313
$418$	−3.41421	−0.166995
$419$	26.7990	1.30922	0.654608	−	0.755968i	$-0.272834\pi$
$419$	26.7990	1.30922	0.654608	+	0.755968i	$0.272834\pi$
$420$	−1.41421	−0.0690066
$421$	−7.24264	−0.352985	−0.176492	−	0.984302i	$-0.556475\pi$
$421$	−7.24264	−0.352985	−0.176492	+	0.984302i	$0.556475\pi$
$422$	9.65685	0.470088
$423$	7.07107	0.343807
$424$	5.65685	0.274721
$425$	−1.41421	−0.0685994
$426$	11.1716	0.541264
$427$	−14.0711	−0.680947
$428$	16.0711	0.776824
$429$	−18.4853	−0.892478
$430$	1.00000	0.0482243
$431$	34.9706	1.68447	0.842236	−	0.539108i	$-0.181239\pi$
$431$	34.9706	1.68447	0.842236	+	0.539108i	$0.181239\pi$
$432$	5.65685	0.272166
$433$	−21.9289	−1.05384	−0.526919	−	0.849916i	$-0.676653\pi$
$433$	−21.9289	−1.05384	−0.526919	+	0.849916i	$0.676653\pi$
$434$	2.41421	0.115886
$435$	10.2426	0.491097
$436$	−5.17157	−0.247673
$437$	−9.07107	−0.433928
$438$	1.07107	0.0511776
$439$	7.31371	0.349064	0.174532	−	0.984651i	$-0.444159\pi$
$439$	7.31371	0.349064	0.174532	+	0.984651i	$0.444159\pi$
$440$	3.41421	0.162766
$441$	6.00000	0.285714
$442$	−5.41421	−0.257528
$443$	−24.0711	−1.14365	−0.571825	−	0.820375i	$-0.693765\pi$
$443$	−24.0711	−1.14365	−0.571825	+	0.820375i	$0.693765\pi$
$444$	8.82843	0.418979
$445$	5.07107	0.240392
$446$	−12.1421	−0.574947
$447$	−29.0711	−1.37501
$448$	1.00000	0.0472456
$449$	13.7574	0.649250	0.324625	−	0.945843i	$-0.394762\pi$
$449$	13.7574	0.649250	0.324625	+	0.945843i	$0.394762\pi$
$450$	−1.00000	−0.0471405
$451$	13.0711	0.615493
$452$	−14.8995	−0.700813
$453$	9.17157	0.430918
$454$	14.8284	0.695933
$455$	3.82843	0.179479
$456$	1.41421	0.0662266
$457$	−13.5147	−0.632192	−0.316096	−	0.948727i	$-0.602372\pi$
$457$	−13.5147	−0.632192	−0.316096	+	0.948727i	$0.602372\pi$
$458$	−4.82843	−0.225618
$459$	−8.00000	−0.373408
$460$	9.07107	0.422941
$461$	−0.928932	−0.0432647	−0.0216323	−	0.999766i	$-0.506886\pi$
$461$	−0.928932	−0.0432647	−0.0216323	+	0.999766i	$0.506886\pi$
$462$	−4.82843	−0.224639
$463$	7.68629	0.357212	0.178606	−	0.983921i	$-0.442841\pi$
$463$	7.68629	0.357212	0.178606	+	0.983921i	$0.442841\pi$
$464$	−7.24264	−0.336231
$465$	−3.41421	−0.158330
$466$	−8.48528	−0.393073
$467$	−35.0711	−1.62290	−0.811448	−	0.584425i	$-0.801320\pi$
$467$	−35.0711	−1.62290	−0.811448	+	0.584425i	$0.801320\pi$
$468$	−3.82843	−0.176969
$469$	7.24264	0.334434
$470$	−7.07107	−0.326164
$471$	−2.48528	−0.114516
$472$	−6.82843	−0.314304
$473$	3.41421	0.156986
$474$	7.89949	0.362836
$475$	−1.00000	−0.0458831
$476$	−1.41421	−0.0648204
$477$	−5.65685	−0.259010
$478$	14.4142	0.659291
$479$	14.8284	0.677528	0.338764	−	0.940871i	$-0.389991\pi$
$479$	14.8284	0.677528	0.338764	+	0.940871i	$0.389991\pi$
$480$	−1.41421	−0.0645497
$481$	−23.8995	−1.08972
$482$	−18.5858	−0.846559
$483$	−12.8284	−0.583714
$484$	0.656854	0.0298570
$485$	−17.5563	−0.797193
$486$	−9.89949	−0.449050
$487$	9.21320	0.417490	0.208745	−	0.977970i	$-0.433062\pi$
$487$	9.21320	0.417490	0.208745	+	0.977970i	$0.433062\pi$
$488$	−14.0711	−0.636967
$489$	−3.31371	−0.149851
$490$	−6.00000	−0.271052
$491$	−28.6274	−1.29194	−0.645969	−	0.763364i	$-0.723546\pi$
$491$	−28.6274	−1.29194	−0.645969	+	0.763364i	$0.723546\pi$
$492$	−5.41421	−0.244092
$493$	10.2426	0.461305
$494$	−3.82843	−0.172249
$495$	−3.41421	−0.153457
$496$	2.41421	0.108401
$497$	−7.89949	−0.354341
$498$	10.8284	0.485233
$499$	16.4558	0.736665	0.368332	−	0.929694i	$-0.379929\pi$
$499$	16.4558	0.736665	0.368332	+	0.929694i	$0.379929\pi$
$500$	1.00000	0.0447214
$501$	24.8284	1.10925
$502$	22.9706	1.02523
$503$	−20.3431	−0.907056	−0.453528	−	0.891242i	$-0.649835\pi$
$503$	−20.3431	−0.907056	−0.453528	+	0.891242i	$0.649835\pi$
$504$	−1.00000	−0.0445435
$505$	−1.41421	−0.0629317
$506$	30.9706	1.37681
$507$	−2.34315	−0.104063
$508$	20.4853	0.908887
$509$	−3.51472	−0.155787	−0.0778936	−	0.996962i	$-0.524819\pi$
$509$	−3.51472	−0.155787	−0.0778936	+	0.996962i	$0.524819\pi$
$510$	2.00000	0.0885615
$511$	−0.757359	−0.0335036
$512$	1.00000	0.0441942
$513$	−5.65685	−0.249756
$514$	−10.8995	−0.480756
$515$	−4.82843	−0.212766
$516$	−1.41421	−0.0622573
$517$	−24.1421	−1.06177
$518$	−6.24264	−0.274286
$519$	−24.7279	−1.08544
$520$	3.82843	0.167888
$521$	3.07107	0.134546	0.0672730	−	0.997735i	$-0.478570\pi$
$521$	3.07107	0.134546	0.0672730	+	0.997735i	$0.478570\pi$
$522$	7.24264	0.317002
$523$	−14.7279	−0.644007	−0.322004	−	0.946738i	$-0.604356\pi$
$523$	−14.7279	−0.644007	−0.322004	+	0.946738i	$0.604356\pi$
$524$	6.00000	0.262111
$525$	−1.41421	−0.0617213
$526$	0.514719	0.0224428
$527$	−3.41421	−0.148725
$528$	−4.82843	−0.210130
$529$	59.2843	2.57758
$530$	5.65685	0.245718
$531$	6.82843	0.296328
$532$	−1.00000	−0.0433555
$533$	14.6569	0.634859
$534$	−7.17157	−0.310344
$535$	16.0711	0.694813
$536$	7.24264	0.312834
$537$	−0.727922	−0.0314122
$538$	14.8284	0.639299
$539$	−20.4853	−0.882364
$540$	5.65685	0.243432
$541$	36.1421	1.55387	0.776936	−	0.629580i	$-0.216773\pi$
$541$	36.1421	1.55387	0.776936	+	0.629580i	$0.216773\pi$
$542$	−10.8995	−0.468173
$543$	1.31371	0.0563766
$544$	−1.41421	−0.0606339
$545$	−5.17157	−0.221526
$546$	−5.41421	−0.231707
$547$	−12.0000	−0.513083	−0.256541	−	0.966533i	$-0.582583\pi$
$547$	−12.0000	−0.513083	−0.256541	+	0.966533i	$0.582583\pi$
$548$	18.0711	0.771958
$549$	14.0711	0.600539
$550$	3.41421	0.145583
$551$	7.24264	0.308547
$552$	−12.8284	−0.546014
$553$	−5.58579	−0.237532
$554$	16.4853	0.700392
$555$	8.82843	0.374746
$556$	2.24264	0.0951092
$557$	36.1716	1.53264	0.766319	−	0.642460i	$-0.222086\pi$
$557$	36.1716	1.53264	0.766319	+	0.642460i	$0.222086\pi$
$558$	−2.41421	−0.102202
$559$	3.82843	0.161925
$560$	1.00000	0.0422577
$561$	6.82843	0.288296
$562$	−12.6569	−0.533897
$563$	−16.0711	−0.677315	−0.338657	−	0.940910i	$-0.609973\pi$
$563$	−16.0711	−0.677315	−0.338657	+	0.940910i	$0.609973\pi$
$564$	10.0000	0.421076
$565$	−14.8995	−0.626826
$566$	27.2426	1.14509
$567$	−5.00000	−0.209980
$568$	−7.89949	−0.331455
$569$	−16.7990	−0.704250	−0.352125	−	0.935953i	$-0.614541\pi$
$569$	−16.7990	−0.704250	−0.352125	+	0.935953i	$0.614541\pi$
$570$	1.41421	0.0592349
$571$	33.0000	1.38101	0.690504	−	0.723329i	$-0.257389\pi$
$571$	33.0000	1.38101	0.690504	+	0.723329i	$0.257389\pi$
$572$	13.0711	0.546529
$573$	−0.142136	−0.00593780
$574$	3.82843	0.159795
$575$	9.07107	0.378290
$576$	−1.00000	−0.0416667
$577$	−8.41421	−0.350288	−0.175144	−	0.984543i	$-0.556039\pi$
$577$	−8.41421	−0.350288	−0.175144	+	0.984543i	$0.556039\pi$
$578$	−15.0000	−0.623918
$579$	−1.65685	−0.0688565
$580$	−7.24264	−0.300734
$581$	−7.65685	−0.317660
$582$	24.8284	1.02917
$583$	19.3137	0.799892
$584$	−0.757359	−0.0313398
$585$	−3.82843	−0.158286
$586$	−22.9706	−0.948905
$587$	3.55635	0.146786	0.0733931	−	0.997303i	$-0.476617\pi$
$587$	3.55635	0.146786	0.0733931	+	0.997303i	$0.476617\pi$
$588$	8.48528	0.349927
$589$	−2.41421	−0.0994759
$590$	−6.82843	−0.281122
$591$	4.44365	0.182787
$592$	−6.24264	−0.256571
$593$	1.24264	0.0510291	0.0255146	−	0.999674i	$-0.491878\pi$
$593$	1.24264	0.0510291	0.0255146	+	0.999674i	$0.491878\pi$
$594$	19.3137	0.792451
$595$	−1.41421	−0.0579771
$596$	20.5563	0.842021
$597$	28.1421	1.15178
$598$	34.7279	1.42013
$599$	38.1421	1.55845	0.779223	−	0.626747i	$-0.215614\pi$
$599$	38.1421	1.55845	0.779223	+	0.626747i	$0.215614\pi$
$600$	−1.41421	−0.0577350
$601$	−28.0000	−1.14214	−0.571072	−	0.820900i	$-0.693472\pi$
$601$	−28.0000	−1.14214	−0.571072	+	0.820900i	$0.693472\pi$
$602$	1.00000	0.0407570
$603$	−7.24264	−0.294943
$604$	−6.48528	−0.263882
$605$	0.656854	0.0267049
$606$	2.00000	0.0812444
$607$	6.00000	0.243532	0.121766	−	0.992559i	$-0.461144\pi$
$607$	6.00000	0.243532	0.121766	+	0.992559i	$0.461144\pi$
$608$	−1.00000	−0.0405554
$609$	10.2426	0.415053
$610$	−14.0711	−0.569721
$611$	−27.0711	−1.09518
$612$	1.41421	0.0571662
$613$	43.8284	1.77021	0.885107	−	0.465388i	$-0.154085\pi$
$613$	43.8284	1.77021	0.885107	+	0.465388i	$0.154085\pi$
$614$	−20.0711	−0.810002
$615$	−5.41421	−0.218322
$616$	3.41421	0.137563
$617$	40.2843	1.62178	0.810892	−	0.585196i	$-0.198982\pi$
$617$	40.2843	1.62178	0.810892	+	0.585196i	$0.198982\pi$
$618$	6.82843	0.274680
$619$	−19.8995	−0.799828	−0.399914	−	0.916553i	$-0.630960\pi$
$619$	−19.8995	−0.799828	−0.399914	+	0.916553i	$0.630960\pi$
$620$	2.41421	0.0969571
$621$	51.3137	2.05915
$622$	10.0711	0.403813
$623$	5.07107	0.203168
$624$	−5.41421	−0.216742
$625$	1.00000	0.0400000
$626$	21.3137	0.851867
$627$	4.82843	0.192829
$628$	1.75736	0.0701263
$629$	8.82843	0.352012
$630$	−1.00000	−0.0398410
$631$	45.6985	1.81923	0.909614	−	0.415454i	$-0.136377\pi$
$631$	45.6985	1.81923	0.909614	+	0.415454i	$0.136377\pi$
$632$	−5.58579	−0.222191
$633$	−13.6569	−0.542811
$634$	29.1421	1.15738
$635$	20.4853	0.812934
$636$	−8.00000	−0.317221
$637$	−22.9706	−0.910127
$638$	−24.7279	−0.978988
$639$	7.89949	0.312499
$640$	1.00000	0.0395285
$641$	−30.7696	−1.21532	−0.607662	−	0.794196i	$-0.707893\pi$
$641$	−30.7696	−1.21532	−0.607662	+	0.794196i	$0.707893\pi$
$642$	−22.7279	−0.897000
$643$	14.2721	0.562836	0.281418	−	0.959585i	$-0.409195\pi$
$643$	14.2721	0.562836	0.281418	+	0.959585i	$0.409195\pi$
$644$	9.07107	0.357450
$645$	−1.41421	−0.0556846
$646$	1.41421	0.0556415
$647$	44.7990	1.76123	0.880615	−	0.473832i	$-0.157130\pi$
$647$	44.7990	1.76123	0.880615	+	0.473832i	$0.157130\pi$
$648$	−5.00000	−0.196419
$649$	−23.3137	−0.915143
$650$	3.82843	0.150163
$651$	−3.41421	−0.133814
$652$	2.34315	0.0917647
$653$	−9.41421	−0.368407	−0.184203	−	0.982888i	$-0.558970\pi$
$653$	−9.41421	−0.368407	−0.184203	+	0.982888i	$0.558970\pi$
$654$	7.31371	0.285989
$655$	6.00000	0.234439
$656$	3.82843	0.149475
$657$	0.757359	0.0295474
$658$	−7.07107	−0.275659
$659$	−12.3848	−0.482442	−0.241221	−	0.970470i	$-0.577548\pi$
$659$	−12.3848	−0.482442	−0.241221	+	0.970470i	$0.577548\pi$
$660$	−4.82843	−0.187946
$661$	−28.8701	−1.12292	−0.561458	−	0.827506i	$-0.689759\pi$
$661$	−28.8701	−1.12292	−0.561458	+	0.827506i	$0.689759\pi$
$662$	−2.68629	−0.104406
$663$	7.65685	0.297368
$664$	−7.65685	−0.297144
$665$	−1.00000	−0.0387783
$666$	6.24264	0.241897
$667$	−65.6985	−2.54386
$668$	−17.5563	−0.679276
$669$	17.1716	0.663891
$670$	7.24264	0.279808
$671$	−48.0416	−1.85463
$672$	−1.41421	−0.0545545
$673$	17.5858	0.677882	0.338941	−	0.940808i	$-0.389931\pi$
$673$	17.5858	0.677882	0.338941	+	0.940808i	$0.389931\pi$
$674$	−19.6569	−0.757154
$675$	5.65685	0.217732
$676$	1.65685	0.0637252
$677$	−7.45584	−0.286551	−0.143276	−	0.989683i	$-0.545764\pi$
$677$	−7.45584	−0.286551	−0.143276	+	0.989683i	$0.545764\pi$
$678$	21.0711	0.809229
$679$	−17.5563	−0.673751
$680$	−1.41421	−0.0542326
$681$	−20.9706	−0.803594
$682$	8.24264	0.315627
$683$	−20.4853	−0.783848	−0.391924	−	0.919998i	$-0.628190\pi$
$683$	−20.4853	−0.783848	−0.391924	+	0.919998i	$0.628190\pi$
$684$	1.00000	0.0382360
$685$	18.0711	0.690460
$686$	−13.0000	−0.496342
$687$	6.82843	0.260521
$688$	1.00000	0.0381246
$689$	21.6569	0.825060
$690$	−12.8284	−0.488370
$691$	1.51472	0.0576226	0.0288113	−	0.999585i	$-0.490828\pi$
$691$	1.51472	0.0576226	0.0288113	+	0.999585i	$0.490828\pi$
$692$	17.4853	0.664691
$693$	−3.41421	−0.129695
$694$	−13.7574	−0.522222
$695$	2.24264	0.0850682
$696$	10.2426	0.388246
$697$	−5.41421	−0.205078
$698$	−27.4558	−1.03922
$699$	12.0000	0.453882
$700$	1.00000	0.0377964
$701$	36.7279	1.38719	0.693597	−	0.720363i	$-0.256025\pi$
$701$	36.7279	1.38719	0.693597	+	0.720363i	$0.256025\pi$
$702$	21.6569	0.817385
$703$	6.24264	0.235446
$704$	3.41421	0.128678
$705$	10.0000	0.376622
$706$	4.38478	0.165023
$707$	−1.41421	−0.0531870
$708$	9.65685	0.362927
$709$	35.2132	1.32246	0.661230	−	0.750183i	$-0.270035\pi$
$709$	35.2132	1.32246	0.661230	+	0.750183i	$0.270035\pi$
$710$	−7.89949	−0.296463
$711$	5.58579	0.209483
$712$	5.07107	0.190046
$713$	21.8995	0.820143
$714$	2.00000	0.0748481
$715$	13.0711	0.488830
$716$	0.514719	0.0192359
$717$	−20.3848	−0.761283
$718$	−37.5269	−1.40049
$719$	8.62742	0.321748	0.160874	−	0.986975i	$-0.448569\pi$
$719$	8.62742	0.321748	0.160874	+	0.986975i	$0.448569\pi$
$720$	−1.00000	−0.0372678
$721$	−4.82843	−0.179820
$722$	−18.0000	−0.669891
$723$	26.2843	0.977523
$724$	−0.928932	−0.0345235
$725$	−7.24264	−0.268985
$726$	−0.928932	−0.0344759
$727$	−14.0000	−0.519231	−0.259616	−	0.965712i	$-0.583596\pi$
$727$	−14.0000	−0.519231	−0.259616	+	0.965712i	$0.583596\pi$
$728$	3.82843	0.141891
$729$	29.0000	1.07407
$730$	−0.757359	−0.0280311
$731$	−1.41421	−0.0523066
$732$	19.8995	0.735506
$733$	36.2426	1.33865	0.669326	−	0.742969i	$-0.266583\pi$
$733$	36.2426	1.33865	0.669326	+	0.742969i	$0.266583\pi$
$734$	−8.68629	−0.320617
$735$	8.48528	0.312984
$736$	9.07107	0.334364
$737$	24.7279	0.910865
$738$	−3.82843	−0.140926
$739$	41.9706	1.54391	0.771956	−	0.635676i	$-0.219279\pi$
$739$	41.9706	1.54391	0.771956	+	0.635676i	$0.219279\pi$
$740$	−6.24264	−0.229484
$741$	5.41421	0.198896
$742$	5.65685	0.207670
$743$	−20.3137	−0.745238	−0.372619	−	0.927984i	$-0.621540\pi$
$743$	−20.3137	−0.745238	−0.372619	+	0.927984i	$0.621540\pi$
$744$	−3.41421	−0.125171
$745$	20.5563	0.753126
$746$	−10.7279	−0.392777
$747$	7.65685	0.280150
$748$	−4.82843	−0.176545
$749$	16.0711	0.587224
$750$	−1.41421	−0.0516398
$751$	16.7279	0.610411	0.305205	−	0.952287i	$-0.401275\pi$
$751$	16.7279	0.610411	0.305205	+	0.952287i	$0.401275\pi$
$752$	−7.07107	−0.257855
$753$	−32.4853	−1.18383
$754$	−27.7279	−1.00979
$755$	−6.48528	−0.236024
$756$	5.65685	0.205738
$757$	−48.4264	−1.76009	−0.880044	−	0.474892i	$-0.842487\pi$
$757$	−48.4264	−1.76009	−0.880044	+	0.474892i	$0.842487\pi$
$758$	−24.1421	−0.876882
$759$	−43.7990	−1.58980
$760$	−1.00000	−0.0362738
$761$	−39.1716	−1.41997	−0.709984	−	0.704218i	$-0.751298\pi$
$761$	−39.1716	−1.41997	−0.709984	+	0.704218i	$0.751298\pi$
$762$	−28.9706	−1.04949
$763$	−5.17157	−0.187224
$764$	0.100505	0.00363615
$765$	1.41421	0.0511310
$766$	14.3137	0.517175
$767$	−26.1421	−0.943938
$768$	−1.41421	−0.0510310
$769$	21.0000	0.757279	0.378640	−	0.925544i	$-0.376392\pi$
$769$	21.0000	0.757279	0.378640	+	0.925544i	$0.376392\pi$
$770$	3.41421	0.123040
$771$	15.4142	0.555129
$772$	1.17157	0.0421658
$773$	−10.9289	−0.393086	−0.196543	−	0.980495i	$-0.562972\pi$
$773$	−10.9289	−0.393086	−0.196543	+	0.980495i	$0.562972\pi$
$774$	−1.00000	−0.0359443
$775$	2.41421	0.0867211
$776$	−17.5563	−0.630236
$777$	8.82843	0.316718
$778$	15.1716	0.543927
$779$	−3.82843	−0.137168
$780$	−5.41421	−0.193860
$781$	−26.9706	−0.965083
$782$	−12.8284	−0.458744
$783$	−40.9706	−1.46417
$784$	−6.00000	−0.214286
$785$	1.75736	0.0627228
$786$	−8.48528	−0.302660
$787$	22.7574	0.811212	0.405606	−	0.914048i	$-0.367060\pi$
$787$	22.7574	0.811212	0.405606	+	0.914048i	$0.367060\pi$
$788$	−3.14214	−0.111934
$789$	−0.727922	−0.0259147
$790$	−5.58579	−0.198733
$791$	−14.8995	−0.529765
$792$	−3.41421	−0.121319
$793$	−53.8701	−1.91298
$794$	−3.51472	−0.124733
$795$	−8.00000	−0.283731
$796$	−19.8995	−0.705319
$797$	24.9411	0.883460	0.441730	−	0.897148i	$-0.354365\pi$
$797$	24.9411	0.883460	0.441730	+	0.897148i	$0.354365\pi$
$798$	1.41421	0.0500626
$799$	10.0000	0.353775
$800$	1.00000	0.0353553
$801$	−5.07107	−0.179177
$802$	38.1127	1.34581
$803$	−2.58579	−0.0912504
$804$	−10.2426	−0.361230
$805$	9.07107	0.319713
$806$	9.24264	0.325558
$807$	−20.9706	−0.738199
$808$	−1.41421	−0.0497519
$809$	10.7990	0.379672	0.189836	−	0.981816i	$-0.439204\pi$
$809$	10.7990	0.379672	0.189836	+	0.981816i	$0.439204\pi$
$810$	−5.00000	−0.175682
$811$	14.1127	0.495564	0.247782	−	0.968816i	$-0.420298\pi$
$811$	14.1127	0.495564	0.247782	+	0.968816i	$0.420298\pi$
$812$	−7.24264	−0.254167
$813$	15.4142	0.540600
$814$	−21.3137	−0.747045
$815$	2.34315	0.0820768
$816$	2.00000	0.0700140
$817$	−1.00000	−0.0349856
$818$	15.2132	0.531917
$819$	−3.82843	−0.133776
$820$	3.82843	0.133694
$821$	8.14214	0.284162	0.142081	−	0.989855i	$-0.454621\pi$
$821$	8.14214	0.284162	0.142081	+	0.989855i	$0.454621\pi$
$822$	−25.5563	−0.891380
$823$	30.4853	1.06265	0.531325	−	0.847168i	$-0.321694\pi$
$823$	30.4853	1.06265	0.531325	+	0.847168i	$0.321694\pi$
$824$	−4.82843	−0.168206
$825$	−4.82843	−0.168104
$826$	−6.82843	−0.237591
$827$	21.5269	0.748564	0.374282	−	0.927315i	$-0.377889\pi$
$827$	21.5269	0.748564	0.374282	+	0.927315i	$0.377889\pi$
$828$	−9.07107	−0.315241
$829$	−5.24264	−0.182084	−0.0910422	−	0.995847i	$-0.529020\pi$
$829$	−5.24264	−0.182084	−0.0910422	+	0.995847i	$0.529020\pi$
$830$	−7.65685	−0.265773
$831$	−23.3137	−0.808744
$832$	3.82843	0.132727
$833$	8.48528	0.293998
$834$	−3.17157	−0.109823
$835$	−17.5563	−0.607563
$836$	−3.41421	−0.118083
$837$	13.6569	0.472050
$838$	26.7990	0.925756
$839$	31.0122	1.07066	0.535330	−	0.844643i	$-0.320187\pi$
$839$	31.0122	1.07066	0.535330	+	0.844643i	$0.320187\pi$
$840$	−1.41421	−0.0487950
$841$	23.4558	0.808822
$842$	−7.24264	−0.249598
$843$	17.8995	0.616491
$844$	9.65685	0.332403
$845$	1.65685	0.0569975
$846$	7.07107	0.243108
$847$	0.656854	0.0225698
$848$	5.65685	0.194257
$849$	−38.5269	−1.32224
$850$	−1.41421	−0.0485071
$851$	−56.6274	−1.94116
$852$	11.1716	0.382732
$853$	31.9411	1.09364	0.546822	−	0.837249i	$-0.315838\pi$
$853$	31.9411	1.09364	0.546822	+	0.837249i	$0.315838\pi$
$854$	−14.0711	−0.481502
$855$	1.00000	0.0341993
$856$	16.0711	0.549298
$857$	32.9289	1.12483	0.562415	−	0.826855i	$-0.309872\pi$
$857$	32.9289	1.12483	0.562415	+	0.826855i	$0.309872\pi$
$858$	−18.4853	−0.631077
$859$	−33.4853	−1.14250	−0.571252	−	0.820775i	$-0.693542\pi$
$859$	−33.4853	−1.14250	−0.571252	+	0.820775i	$0.693542\pi$
$860$	1.00000	0.0340997
$861$	−5.41421	−0.184516
$862$	34.9706	1.19110
$863$	−35.1716	−1.19725	−0.598627	−	0.801028i	$-0.704287\pi$
$863$	−35.1716	−1.19725	−0.598627	+	0.801028i	$0.704287\pi$
$864$	5.65685	0.192450
$865$	17.4853	0.594517
$866$	−21.9289	−0.745175
$867$	21.2132	0.720438
$868$	2.41421	0.0819437
$869$	−19.0711	−0.646942
$870$	10.2426	0.347258
$871$	27.7279	0.939525
$872$	−5.17157	−0.175132
$873$	17.5563	0.594192
$874$	−9.07107	−0.306833
$875$	1.00000	0.0338062
$876$	1.07107	0.0361880
$877$	26.6274	0.899144	0.449572	−	0.893244i	$-0.351577\pi$
$877$	26.6274	0.899144	0.449572	+	0.893244i	$0.351577\pi$
$878$	7.31371	0.246826
$879$	32.4853	1.09570
$880$	3.41421	0.115093
$881$	−40.7990	−1.37455	−0.687276	−	0.726396i	$-0.741194\pi$
$881$	−40.7990	−1.37455	−0.687276	+	0.726396i	$0.741194\pi$
$882$	6.00000	0.202031
$883$	−16.2132	−0.545618	−0.272809	−	0.962068i	$-0.587953\pi$
$883$	−16.2132	−0.545618	−0.272809	+	0.962068i	$0.587953\pi$
$884$	−5.41421	−0.182100
$885$	9.65685	0.324612
$886$	−24.0711	−0.808683
$887$	6.11270	0.205244	0.102622	−	0.994720i	$-0.467277\pi$
$887$	6.11270	0.205244	0.102622	+	0.994720i	$0.467277\pi$
$888$	8.82843	0.296263
$889$	20.4853	0.687054
$890$	5.07107	0.169983
$891$	−17.0711	−0.571902
$892$	−12.1421	−0.406549
$893$	7.07107	0.236624
$894$	−29.0711	−0.972282
$895$	0.514719	0.0172051
$896$	1.00000	0.0334077
$897$	−49.1127	−1.63983
$898$	13.7574	0.459089
$899$	−17.4853	−0.583167
$900$	−1.00000	−0.0333333
$901$	−8.00000	−0.266519
$902$	13.0711	0.435219
$903$	−1.41421	−0.0470621
$904$	−14.8995	−0.495550
$905$	−0.928932	−0.0308788
$906$	9.17157	0.304705
$907$	−4.89949	−0.162685	−0.0813425	−	0.996686i	$-0.525921\pi$
$907$	−4.89949	−0.162685	−0.0813425	+	0.996686i	$0.525921\pi$
$908$	14.8284	0.492099
$909$	1.41421	0.0469065
$910$	3.82843	0.126911
$911$	16.3848	0.542852	0.271426	−	0.962459i	$-0.412505\pi$
$911$	16.3848	0.542852	0.271426	+	0.962459i	$0.412505\pi$
$912$	1.41421	0.0468293
$913$	−26.1421	−0.865178
$914$	−13.5147	−0.447027
$915$	19.8995	0.657857
$916$	−4.82843	−0.159536
$917$	6.00000	0.198137
$918$	−8.00000	−0.264039
$919$	−15.1005	−0.498120	−0.249060	−	0.968488i	$-0.580122\pi$
$919$	−15.1005	−0.498120	−0.249060	+	0.968488i	$0.580122\pi$
$920$	9.07107	0.299064
$921$	28.3848	0.935310
$922$	−0.928932	−0.0305928
$923$	−30.2426	−0.995449
$924$	−4.82843	−0.158844
$925$	−6.24264	−0.205257
$926$	7.68629	0.252587
$927$	4.82843	0.158586
$928$	−7.24264	−0.237751
$929$	25.7990	0.846437	0.423219	−	0.906028i	$-0.360900\pi$
$929$	25.7990	0.846437	0.423219	+	0.906028i	$0.360900\pi$
$930$	−3.41421	−0.111956
$931$	6.00000	0.196642
$932$	−8.48528	−0.277945
$933$	−14.2426	−0.466283
$934$	−35.0711	−1.14756
$935$	−4.82843	−0.157906
$936$	−3.82843	−0.125136
$937$	50.4264	1.64736	0.823679	−	0.567056i	$-0.191918\pi$
$937$	50.4264	1.64736	0.823679	+	0.567056i	$0.191918\pi$
$938$	7.24264	0.236481
$939$	−30.1421	−0.983651
$940$	−7.07107	−0.230633
$941$	−38.9289	−1.26905	−0.634523	−	0.772904i	$-0.718804\pi$
$941$	−38.9289	−1.26905	−0.634523	+	0.772904i	$0.718804\pi$
$942$	−2.48528	−0.0809748
$943$	34.7279	1.13090
$944$	−6.82843	−0.222246
$945$	5.65685	0.184017
$946$	3.41421	0.111006
$947$	−17.1838	−0.558397	−0.279199	−	0.960233i	$-0.590069\pi$
$947$	−17.1838	−0.558397	−0.279199	+	0.960233i	$0.590069\pi$
$948$	7.89949	0.256564
$949$	−2.89949	−0.0941216
$950$	−1.00000	−0.0324443
$951$	−41.2132	−1.33643
$952$	−1.41421	−0.0458349
$953$	−28.8995	−0.936146	−0.468073	−	0.883690i	$-0.655052\pi$
$953$	−28.8995	−0.936146	−0.468073	+	0.883690i	$0.655052\pi$
$954$	−5.65685	−0.183147
$955$	0.100505	0.00325227
$956$	14.4142	0.466189
$957$	34.9706	1.13044
$958$	14.8284	0.479085
$959$	18.0711	0.583545
$960$	−1.41421	−0.0456435
$961$	−25.1716	−0.811986
$962$	−23.8995	−0.770551
$963$	−16.0711	−0.517883
$964$	−18.5858	−0.598608
$965$	1.17157	0.0377143
$966$	−12.8284	−0.412748
$967$	27.7574	0.892616	0.446308	−	0.894879i	$-0.352738\pi$
$967$	27.7574	0.892616	0.446308	+	0.894879i	$0.352738\pi$
$968$	0.656854	0.0211121
$969$	−2.00000	−0.0642493
$970$	−17.5563	−0.563700
$971$	6.92893	0.222360	0.111180	−	0.993800i	$-0.464537\pi$
$971$	6.92893	0.222360	0.111180	+	0.993800i	$0.464537\pi$
$972$	−9.89949	−0.317526
$973$	2.24264	0.0718958
$974$	9.21320	0.295210
$975$	−5.41421	−0.173394
$976$	−14.0711	−0.450404
$977$	−2.92893	−0.0937048	−0.0468524	−	0.998902i	$-0.514919\pi$
$977$	−2.92893	−0.0937048	−0.0468524	+	0.998902i	$0.514919\pi$
$978$	−3.31371	−0.105961
$979$	17.3137	0.553349
$980$	−6.00000	−0.191663
$981$	5.17157	0.165116
$982$	−28.6274	−0.913538
$983$	−38.6569	−1.23296	−0.616481	−	0.787370i	$-0.711442\pi$
$983$	−38.6569	−1.23296	−0.616481	+	0.787370i	$0.711442\pi$
$984$	−5.41421	−0.172599
$985$	−3.14214	−0.100117
$986$	10.2426	0.326192
$987$	10.0000	0.318304
$988$	−3.82843	−0.121798
$989$	9.07107	0.288443
$990$	−3.41421	−0.108511
$991$	−49.2548	−1.56463	−0.782316	−	0.622882i	$-0.785962\pi$
$991$	−49.2548	−1.56463	−0.782316	+	0.622882i	$0.785962\pi$
$992$	2.41421	0.0766514
$993$	3.79899	0.120557
$994$	−7.89949	−0.250557
$995$	−19.8995	−0.630856
$996$	10.8284	0.343112
$997$	42.8284	1.35639	0.678195	−	0.734882i	$-0.262762\pi$
$997$	42.8284	1.35639	0.678195	+	0.734882i	$0.262762\pi$
$998$	16.4558	0.520901
$999$	−35.3137	−1.11728

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.a.g.1.1	✓	2
3.2	odd	2		3870.2.a.bc.1.1		2
4.3	odd	2		3440.2.a.j.1.2		2
5.2	odd	4		2150.2.b.o.1549.4		4
5.3	odd	4		2150.2.b.o.1549.1		4
5.4	even	2		2150.2.a.v.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.a.g.1.1	✓	2	1.1	even	1	trivial
2150.2.a.v.1.2		2	5.4	even	2
2150.2.b.o.1549.1		4	5.3	odd	4
2150.2.b.o.1549.4		4	5.2	odd	4
3440.2.a.j.1.2		2	4.3	odd	2
3870.2.a.bc.1.1		2	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.41421 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.41421 q^{6} +1.00000 q^{7} +1.00000 q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.41421 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.41421 q^{6} +1.00000 q^{7} +1.00000 q^{8} -1.00000 q^{9} +1.00000 q^{10} +3.41421 q^{11} -1.41421 q^{12} +3.82843 q^{13} +1.00000 q^{14} -1.41421 q^{15} +1.00000 q^{16} -1.41421 q^{17} -1.00000 q^{18} -1.00000 q^{19} +1.00000 q^{20} -1.41421 q^{21} +3.41421 q^{22} +9.07107 q^{23} -1.41421 q^{24} +1.00000 q^{25} +3.82843 q^{26} +5.65685 q^{27} +1.00000 q^{28} -7.24264 q^{29} -1.41421 q^{30} +2.41421 q^{31} +1.00000 q^{32} -4.82843 q^{33} -1.41421 q^{34} +1.00000 q^{35} -1.00000 q^{36} -6.24264 q^{37} -1.00000 q^{38} -5.41421 q^{39} +1.00000 q^{40} +3.82843 q^{41} -1.41421 q^{42} +1.00000 q^{43} +3.41421 q^{44} -1.00000 q^{45} +9.07107 q^{46} -7.07107 q^{47} -1.41421 q^{48} -6.00000 q^{49} +1.00000 q^{50} +2.00000 q^{51} +3.82843 q^{52} +5.65685 q^{53} +5.65685 q^{54} +3.41421 q^{55} +1.00000 q^{56} +1.41421 q^{57} -7.24264 q^{58} -6.82843 q^{59} -1.41421 q^{60} -14.0711 q^{61} +2.41421 q^{62} -1.00000 q^{63} +1.00000 q^{64} +3.82843 q^{65} -4.82843 q^{66} +7.24264 q^{67} -1.41421 q^{68} -12.8284 q^{69} +1.00000 q^{70} -7.89949 q^{71} -1.00000 q^{72} -0.757359 q^{73} -6.24264 q^{74} -1.41421 q^{75} -1.00000 q^{76} +3.41421 q^{77} -5.41421 q^{78} -5.58579 q^{79} +1.00000 q^{80} -5.00000 q^{81} +3.82843 q^{82} -7.65685 q^{83} -1.41421 q^{84} -1.41421 q^{85} +1.00000 q^{86} +10.2426 q^{87} +3.41421 q^{88} +5.07107 q^{89} -1.00000 q^{90} +3.82843 q^{91} +9.07107 q^{92} -3.41421 q^{93} -7.07107 q^{94} -1.00000 q^{95} -1.41421 q^{96} -17.5563 q^{97} -6.00000 q^{98} -3.41421 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{4} + 2 q^{5} + 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 2 * q^4 + 2 * q^5 + 2 * q^7 + 2 * q^8 - 2 * q^9	\( 2 q + 2 q^{2} + 2 q^{4} + 2 q^{5} + 2 q^{7} + 2 q^{8} - 2 q^{9} + 2 q^{10} + 4 q^{11} + 2 q^{13} + 2 q^{14} + 2 q^{16} - 2 q^{18} - 2 q^{19} + 2 q^{20} + 4 q^{22} + 4 q^{23} + 2 q^{25} + 2 q^{26} + 2 q^{28} - 6 q^{29} + 2 q^{31} + 2 q^{32} - 4 q^{33} + 2 q^{35} - 2 q^{36} - 4 q^{37} - 2 q^{38} - 8 q^{39} + 2 q^{40} + 2 q^{41} + 2 q^{43} + 4 q^{44} - 2 q^{45} + 4 q^{46} - 12 q^{49} + 2 q^{50} + 4 q^{51} + 2 q^{52} + 4 q^{55} + 2 q^{56} - 6 q^{58} - 8 q^{59} - 14 q^{61} + 2 q^{62} - 2 q^{63} + 2 q^{64} + 2 q^{65} - 4 q^{66} + 6 q^{67} - 20 q^{69} + 2 q^{70} + 4 q^{71} - 2 q^{72} - 10 q^{73} - 4 q^{74} - 2 q^{76} + 4 q^{77} - 8 q^{78} - 14 q^{79} + 2 q^{80} - 10 q^{81} + 2 q^{82} - 4 q^{83} + 2 q^{86} + 12 q^{87} + 4 q^{88} - 4 q^{89} - 2 q^{90} + 2 q^{91} + 4 q^{92} - 4 q^{93} - 2 q^{95} - 4 q^{97} - 12 q^{98} - 4 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^4 + 2 * q^5 + 2 * q^7 + 2 * q^8 - 2 * q^9 + 2 * q^10 + 4 * q^11 + 2 * q^13 + 2 * q^14 + 2 * q^16 - 2 * q^18 - 2 * q^19 + 2 * q^20 + 4 * q^22 + 4 * q^23 + 2 * q^25 + 2 * q^26 + 2 * q^28 - 6 * q^29 + 2 * q^31 + 2 * q^32 - 4 * q^33 + 2 * q^35 - 2 * q^36 - 4 * q^37 - 2 * q^38 - 8 * q^39 + 2 * q^40 + 2 * q^41 + 2 * q^43 + 4 * q^44 - 2 * q^45 + 4 * q^46 - 12 * q^49 + 2 * q^50 + 4 * q^51 + 2 * q^52 + 4 * q^55 + 2 * q^56 - 6 * q^58 - 8 * q^59 - 14 * q^61 + 2 * q^62 - 2 * q^63 + 2 * q^64 + 2 * q^65 - 4 * q^66 + 6 * q^67 - 20 * q^69 + 2 * q^70 + 4 * q^71 - 2 * q^72 - 10 * q^73 - 4 * q^74 - 2 * q^76 + 4 * q^77 - 8 * q^78 - 14 * q^79 + 2 * q^80 - 10 * q^81 + 2 * q^82 - 4 * q^83 + 2 * q^86 + 12 * q^87 + 4 * q^88 - 4 * q^89 - 2 * q^90 + 2 * q^91 + 4 * q^92 - 4 * q^93 - 2 * q^95 - 4 * q^97 - 12 * q^98 - 4 * q^99

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