LMFDB - Embedded newform 430.2.a.f.1.2

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(\sqrt{6}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 6 $ x^2 - 6
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			1.2
Root			$2.44949$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +2.44949 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.44949 q^{6} +1.00000 q^{7} +1.00000 q^{8} +3.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.44949 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.44949 q^{6} +1.00000 q^{7} +1.00000 q^{8} +3.00000 q^{9} -1.00000 q^{10} -0.449490 q^{11} +2.44949 q^{12} -1.00000 q^{13} +1.00000 q^{14} -2.44949 q^{15} +1.00000 q^{16} -2.44949 q^{17} +3.00000 q^{18} -3.89898 q^{19} -1.00000 q^{20} +2.44949 q^{21} -0.449490 q^{22} +4.44949 q^{23} +2.44949 q^{24} +1.00000 q^{25} -1.00000 q^{26} +1.00000 q^{28} +4.55051 q^{29} -2.44949 q^{30} -5.44949 q^{31} +1.00000 q^{32} -1.10102 q^{33} -2.44949 q^{34} -1.00000 q^{35} +3.00000 q^{36} -4.44949 q^{37} -3.89898 q^{38} -2.44949 q^{39} -1.00000 q^{40} -2.10102 q^{41} +2.44949 q^{42} -1.00000 q^{43} -0.449490 q^{44} -3.00000 q^{45} +4.44949 q^{46} -2.44949 q^{47} +2.44949 q^{48} -6.00000 q^{49} +1.00000 q^{50} -6.00000 q^{51} -1.00000 q^{52} +13.7980 q^{53} +0.449490 q^{55} +1.00000 q^{56} -9.55051 q^{57} +4.55051 q^{58} -4.89898 q^{59} -2.44949 q^{60} +1.44949 q^{61} -5.44949 q^{62} +3.00000 q^{63} +1.00000 q^{64} +1.00000 q^{65} -1.10102 q^{66} -0.550510 q^{67} -2.44949 q^{68} +10.8990 q^{69} -1.00000 q^{70} -1.34847 q^{71} +3.00000 q^{72} -2.55051 q^{73} -4.44949 q^{74} +2.44949 q^{75} -3.89898 q^{76} -0.449490 q^{77} -2.44949 q^{78} +6.55051 q^{79} -1.00000 q^{80} -9.00000 q^{81} -2.10102 q^{82} +6.00000 q^{83} +2.44949 q^{84} +2.44949 q^{85} -1.00000 q^{86} +11.1464 q^{87} -0.449490 q^{88} +18.2474 q^{89} -3.00000 q^{90} -1.00000 q^{91} +4.44949 q^{92} -13.3485 q^{93} -2.44949 q^{94} +3.89898 q^{95} +2.44949 q^{96} -11.5505 q^{97} -6.00000 q^{98} -1.34847 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{4} - 2 q^{5} + 2 q^{7} + 2 q^{8} + 6 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + 2 * q^4 - 2 * q^5 + 2 * q^7 + 2 * q^8 + 6 * q^9	$ 2 q + 2 q^{2} + 2 q^{4} - 2 q^{5} + 2 q^{7} + 2 q^{8} + 6 q^{9} - 2 q^{10} + 4 q^{11} - 2 q^{13} + 2 q^{14} + 2 q^{16} + 6 q^{18} + 2 q^{19} - 2 q^{20} + 4 q^{22} + 4 q^{23} + 2 q^{25} - 2 q^{26} + 2 q^{28} + 14 q^{29} - 6 q^{31} + 2 q^{32} - 12 q^{33} - 2 q^{35} + 6 q^{36} - 4 q^{37} + 2 q^{38} - 2 q^{40} - 14 q^{41} - 2 q^{43} + 4 q^{44} - 6 q^{45} + 4 q^{46} - 12 q^{49} + 2 q^{50} - 12 q^{51} - 2 q^{52} + 8 q^{53} - 4 q^{55} + 2 q^{56} - 24 q^{57} + 14 q^{58} - 2 q^{61} - 6 q^{62} + 6 q^{63} + 2 q^{64} + 2 q^{65} - 12 q^{66} - 6 q^{67} + 12 q^{69} - 2 q^{70} + 12 q^{71} + 6 q^{72} - 10 q^{73} - 4 q^{74} + 2 q^{76} + 4 q^{77} + 18 q^{79} - 2 q^{80} - 18 q^{81} - 14 q^{82} + 12 q^{83} - 2 q^{86} - 12 q^{87} + 4 q^{88} + 12 q^{89} - 6 q^{90} - 2 q^{91} + 4 q^{92} - 12 q^{93} - 2 q^{95} - 28 q^{97} - 12 q^{98} + 12 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^4 - 2 * q^5 + 2 * q^7 + 2 * q^8 + 6 * q^9 - 2 * q^10 + 4 * q^11 - 2 * q^13 + 2 * q^14 + 2 * q^16 + 6 * q^18 + 2 * q^19 - 2 * q^20 + 4 * q^22 + 4 * q^23 + 2 * q^25 - 2 * q^26 + 2 * q^28 + 14 * q^29 - 6 * q^31 + 2 * q^32 - 12 * q^33 - 2 * q^35 + 6 * q^36 - 4 * q^37 + 2 * q^38 - 2 * q^40 - 14 * q^41 - 2 * q^43 + 4 * q^44 - 6 * q^45 + 4 * q^46 - 12 * q^49 + 2 * q^50 - 12 * q^51 - 2 * q^52 + 8 * q^53 - 4 * q^55 + 2 * q^56 - 24 * q^57 + 14 * q^58 - 2 * q^61 - 6 * q^62 + 6 * q^63 + 2 * q^64 + 2 * q^65 - 12 * q^66 - 6 * q^67 + 12 * q^69 - 2 * q^70 + 12 * q^71 + 6 * q^72 - 10 * q^73 - 4 * q^74 + 2 * q^76 + 4 * q^77 + 18 * q^79 - 2 * q^80 - 18 * q^81 - 14 * q^82 + 12 * q^83 - 2 * q^86 - 12 * q^87 + 4 * q^88 + 12 * q^89 - 6 * q^90 - 2 * q^91 + 4 * q^92 - 12 * q^93 - 2 * q^95 - 28 * q^97 - 12 * q^98 + 12 * 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
$3$	2.44949	1.41421	0.707107	−	0.707107i	$-0.250000\pi$
$3$	2.44949	1.41421	0.707107	+	0.707107i	$0.250000\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.44949	1.00000
$7$	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
$9$	3.00000	1.00000
$10$	−1.00000	−0.316228
$11$	−0.449490	−0.135526	−0.0677631	−	0.997701i	$-0.521586\pi$
$11$	−0.449490	−0.135526	−0.0677631	+	0.997701i	$0.521586\pi$
$12$	2.44949	0.707107
$13$	−1.00000	−0.277350	−0.138675	−	0.990338i	$-0.544284\pi$
$13$	−1.00000	−0.277350	−0.138675	+	0.990338i	$0.544284\pi$
$14$	1.00000	0.267261
$15$	−2.44949	−0.632456
$16$	1.00000	0.250000
$17$	−2.44949	−0.594089	−0.297044	−	0.954864i	$-0.596001\pi$
$17$	−2.44949	−0.594089	−0.297044	+	0.954864i	$0.596001\pi$
$18$	3.00000	0.707107
$19$	−3.89898	−0.894487	−0.447244	−	0.894412i	$-0.647594\pi$
$19$	−3.89898	−0.894487	−0.447244	+	0.894412i	$0.647594\pi$
$20$	−1.00000	−0.223607
$21$	2.44949	0.534522
$22$	−0.449490	−0.0958315
$23$	4.44949	0.927783	0.463891	−	0.885892i	$-0.346453\pi$
$23$	4.44949	0.927783	0.463891	+	0.885892i	$0.346453\pi$
$24$	2.44949	0.500000
$25$	1.00000	0.200000
$26$	−1.00000	−0.196116
$27$	0	0
$28$	1.00000	0.188982
$29$	4.55051	0.845009	0.422504	−	0.906361i	$-0.361151\pi$
$29$	4.55051	0.845009	0.422504	+	0.906361i	$0.361151\pi$
$30$	−2.44949	−0.447214
$31$	−5.44949	−0.978757	−0.489379	−	0.872071i	$-0.662776\pi$
$31$	−5.44949	−0.978757	−0.489379	+	0.872071i	$0.662776\pi$
$32$	1.00000	0.176777
$33$	−1.10102	−0.191663
$34$	−2.44949	−0.420084
$35$	−1.00000	−0.169031
$36$	3.00000	0.500000
$37$	−4.44949	−0.731492	−0.365746	−	0.930715i	$-0.619186\pi$
$37$	−4.44949	−0.731492	−0.365746	+	0.930715i	$0.619186\pi$
$38$	−3.89898	−0.632498
$39$	−2.44949	−0.392232
$40$	−1.00000	−0.158114
$41$	−2.10102	−0.328124	−0.164062	−	0.986450i	$-0.552460\pi$
$41$	−2.10102	−0.328124	−0.164062	+	0.986450i	$0.552460\pi$
$42$	2.44949	0.377964
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−0.449490	−0.0677631
$45$	−3.00000	−0.447214
$46$	4.44949	0.656041
$47$	−2.44949	−0.357295	−0.178647	−	0.983913i	$-0.557172\pi$
$47$	−2.44949	−0.357295	−0.178647	+	0.983913i	$0.557172\pi$
$48$	2.44949	0.353553
$49$	−6.00000	−0.857143
$50$	1.00000	0.141421
$51$	−6.00000	−0.840168
$52$	−1.00000	−0.138675
$53$	13.7980	1.89530	0.947648	−	0.319318i	$-0.103454\pi$
$53$	13.7980	1.89530	0.947648	+	0.319318i	$0.103454\pi$
$54$	0	0
$55$	0.449490	0.0606092
$56$	1.00000	0.133631
$57$	−9.55051	−1.26500
$58$	4.55051	0.597511
$59$	−4.89898	−0.637793	−0.318896	−	0.947790i	$-0.603312\pi$
$59$	−4.89898	−0.637793	−0.318896	+	0.947790i	$0.603312\pi$
$60$	−2.44949	−0.316228
$61$	1.44949	0.185588	0.0927941	−	0.995685i	$-0.470420\pi$
$61$	1.44949	0.185588	0.0927941	+	0.995685i	$0.470420\pi$
$62$	−5.44949	−0.692086
$63$	3.00000	0.377964
$64$	1.00000	0.125000
$65$	1.00000	0.124035
$66$	−1.10102	−0.135526
$67$	−0.550510	−0.0672555	−0.0336278	−	0.999434i	$-0.510706\pi$
$67$	−0.550510	−0.0672555	−0.0336278	+	0.999434i	$0.510706\pi$
$68$	−2.44949	−0.297044
$69$	10.8990	1.31208
$70$	−1.00000	−0.119523
$71$	−1.34847	−0.160034	−0.0800169	−	0.996794i	$-0.525497\pi$
$71$	−1.34847	−0.160034	−0.0800169	+	0.996794i	$0.525497\pi$
$72$	3.00000	0.353553
$73$	−2.55051	−0.298515	−0.149257	−	0.988798i	$-0.547688\pi$
$73$	−2.55051	−0.298515	−0.149257	+	0.988798i	$0.547688\pi$
$74$	−4.44949	−0.517243
$75$	2.44949	0.282843
$76$	−3.89898	−0.447244
$77$	−0.449490	−0.0512241
$78$	−2.44949	−0.277350
$79$	6.55051	0.736990	0.368495	−	0.929630i	$-0.379873\pi$
$79$	6.55051	0.736990	0.368495	+	0.929630i	$0.379873\pi$
$80$	−1.00000	−0.111803
$81$	−9.00000	−1.00000
$82$	−2.10102	−0.232019
$83$	6.00000	0.658586	0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000	0.658586	0.329293	+	0.944228i	$0.393190\pi$
$84$	2.44949	0.267261
$85$	2.44949	0.265684
$86$	−1.00000	−0.107833
$87$	11.1464	1.19502
$88$	−0.449490	−0.0479158
$89$	18.2474	1.93423	0.967113	−	0.254348i	$-0.0818608\pi$
$89$	18.2474	1.93423	0.967113	+	0.254348i	$0.0818608\pi$
$90$	−3.00000	−0.316228
$91$	−1.00000	−0.104828
$92$	4.44949	0.463891
$93$	−13.3485	−1.38417
$94$	−2.44949	−0.252646
$95$	3.89898	0.400027
$96$	2.44949	0.250000
$97$	−11.5505	−1.17278	−0.586388	−	0.810030i	$-0.699451\pi$
$97$	−11.5505	−1.17278	−0.586388	+	0.810030i	$0.699451\pi$
$98$	−6.00000	−0.606092
$99$	−1.34847	−0.135526
$100$	1.00000	0.100000
$101$	−3.34847	−0.333185	−0.166593	−	0.986026i	$-0.553276\pi$
$101$	−3.34847	−0.333185	−0.166593	+	0.986026i	$0.553276\pi$
$102$	−6.00000	−0.594089
$103$	−1.10102	−0.108487	−0.0542434	−	0.998528i	$-0.517275\pi$
$103$	−1.10102	−0.108487	−0.0542434	+	0.998528i	$0.517275\pi$
$104$	−1.00000	−0.0980581
$105$	−2.44949	−0.239046
$106$	13.7980	1.34018
$107$	0.550510	0.0532198	0.0266099	−	0.999646i	$-0.491529\pi$
$107$	0.550510	0.0532198	0.0266099	+	0.999646i	$0.491529\pi$
$108$	0	0
$109$	12.8990	1.23550	0.617749	−	0.786375i	$-0.288045\pi$
$109$	12.8990	1.23550	0.617749	+	0.786375i	$0.288045\pi$
$110$	0.449490	0.0428572
$111$	−10.8990	−1.03449
$112$	1.00000	0.0944911
$113$	−3.44949	−0.324501	−0.162250	−	0.986750i	$-0.551875\pi$
$113$	−3.44949	−0.324501	−0.162250	+	0.986750i	$0.551875\pi$
$114$	−9.55051	−0.894487
$115$	−4.44949	−0.414917
$116$	4.55051	0.422504
$117$	−3.00000	−0.277350
$118$	−4.89898	−0.450988
$119$	−2.44949	−0.224544
$120$	−2.44949	−0.223607
$121$	−10.7980	−0.981633
$122$	1.44949	0.131231
$123$	−5.14643	−0.464038
$124$	−5.44949	−0.489379
$125$	−1.00000	−0.0894427
$126$	3.00000	0.267261
$127$	0.898979	0.0797715	0.0398858	−	0.999204i	$-0.487301\pi$
$127$	0.898979	0.0797715	0.0398858	+	0.999204i	$0.487301\pi$
$128$	1.00000	0.0883883
$129$	−2.44949	−0.215666
$130$	1.00000	0.0877058
$131$	−2.00000	−0.174741	−0.0873704	−	0.996176i	$-0.527846\pi$
$131$	−2.00000	−0.174741	−0.0873704	+	0.996176i	$0.527846\pi$
$132$	−1.10102	−0.0958315
$133$	−3.89898	−0.338084
$134$	−0.550510	−0.0475568
$135$	0	0
$136$	−2.44949	−0.210042
$137$	−5.24745	−0.448320	−0.224160	−	0.974552i	$-0.571964\pi$
$137$	−5.24745	−0.448320	−0.224160	+	0.974552i	$0.571964\pi$
$138$	10.8990	0.927783
$139$	18.2474	1.54773	0.773864	−	0.633352i	$-0.218321\pi$
$139$	18.2474	1.54773	0.773864	+	0.633352i	$0.218321\pi$
$140$	−1.00000	−0.0845154
$141$	−6.00000	−0.505291
$142$	−1.34847	−0.113161
$143$	0.449490	0.0375882
$144$	3.00000	0.250000
$145$	−4.55051	−0.377899
$146$	−2.55051	−0.211082
$147$	−14.6969	−1.21218
$148$	−4.44949	−0.365746
$149$	−2.55051	−0.208946	−0.104473	−	0.994528i	$-0.533316\pi$
$149$	−2.55051	−0.208946	−0.104473	+	0.994528i	$0.533316\pi$
$150$	2.44949	0.200000
$151$	10.8990	0.886946	0.443473	−	0.896288i	$-0.353746\pi$
$151$	10.8990	0.886946	0.443473	+	0.896288i	$0.353746\pi$
$152$	−3.89898	−0.316249
$153$	−7.34847	−0.594089
$154$	−0.449490	−0.0362209
$155$	5.44949	0.437714
$156$	−2.44949	−0.196116
$157$	−20.0454	−1.59980	−0.799899	−	0.600135i	$-0.795114\pi$
$157$	−20.0454	−1.59980	−0.799899	+	0.600135i	$0.795114\pi$
$158$	6.55051	0.521131
$159$	33.7980	2.68035
$160$	−1.00000	−0.0790569
$161$	4.44949	0.350669
$162$	−9.00000	−0.707107
$163$	−5.79796	−0.454131	−0.227066	−	0.973879i	$-0.572913\pi$
$163$	−5.79796	−0.454131	−0.227066	+	0.973879i	$0.572913\pi$
$164$	−2.10102	−0.164062
$165$	1.10102	0.0857143
$166$	6.00000	0.465690
$167$	4.44949	0.344312	0.172156	−	0.985070i	$-0.444927\pi$
$167$	4.44949	0.344312	0.172156	+	0.985070i	$0.444927\pi$
$168$	2.44949	0.188982
$169$	−12.0000	−0.923077
$170$	2.44949	0.187867
$171$	−11.6969	−0.894487
$172$	−1.00000	−0.0762493
$173$	8.79796	0.668896	0.334448	−	0.942414i	$-0.391450\pi$
$173$	8.79796	0.668896	0.334448	+	0.942414i	$0.391450\pi$
$174$	11.1464	0.845009
$175$	1.00000	0.0755929
$176$	−0.449490	−0.0338816
$177$	−12.0000	−0.901975
$178$	18.2474	1.36770
$179$	8.79796	0.657590	0.328795	−	0.944401i	$-0.393357\pi$
$179$	8.79796	0.657590	0.328795	+	0.944401i	$0.393357\pi$
$180$	−3.00000	−0.223607
$181$	23.3485	1.73548	0.867739	−	0.497020i	$-0.165572\pi$
$181$	23.3485	1.73548	0.867739	+	0.497020i	$0.165572\pi$
$182$	−1.00000	−0.0741249
$183$	3.55051	0.262461
$184$	4.44949	0.328021
$185$	4.44949	0.327133
$186$	−13.3485	−0.978757
$187$	1.10102	0.0805146
$188$	−2.44949	−0.178647
$189$	0	0
$190$	3.89898	0.282862
$191$	18.2474	1.32034	0.660170	−	0.751117i	$-0.270484\pi$
$191$	18.2474	1.32034	0.660170	+	0.751117i	$0.270484\pi$
$192$	2.44949	0.176777
$193$	−3.10102	−0.223216	−0.111608	−	0.993752i	$-0.535600\pi$
$193$	−3.10102	−0.223216	−0.111608	+	0.993752i	$0.535600\pi$
$194$	−11.5505	−0.829278
$195$	2.44949	0.175412
$196$	−6.00000	−0.428571
$197$	−7.00000	−0.498729	−0.249365	−	0.968410i	$-0.580222\pi$
$197$	−7.00000	−0.498729	−0.249365	+	0.968410i	$0.580222\pi$
$198$	−1.34847	−0.0958315
$199$	16.4495	1.16607	0.583037	−	0.812446i	$-0.301864\pi$
$199$	16.4495	1.16607	0.583037	+	0.812446i	$0.301864\pi$
$200$	1.00000	0.0707107
$201$	−1.34847	−0.0951137
$202$	−3.34847	−0.235597
$203$	4.55051	0.319383
$204$	−6.00000	−0.420084
$205$	2.10102	0.146742
$206$	−1.10102	−0.0767117
$207$	13.3485	0.927783
$208$	−1.00000	−0.0693375
$209$	1.75255	0.121227
$210$	−2.44949	−0.169031
$211$	23.5959	1.62441	0.812205	−	0.583372i	$-0.198267\pi$
$211$	23.5959	1.62441	0.812205	+	0.583372i	$0.198267\pi$
$212$	13.7980	0.947648
$213$	−3.30306	−0.226322
$214$	0.550510	0.0376321
$215$	1.00000	0.0681994
$216$	0	0
$217$	−5.44949	−0.369935
$218$	12.8990	0.873629
$219$	−6.24745	−0.422163
$220$	0.449490	0.0303046
$221$	2.44949	0.164771
$222$	−10.8990	−0.731492
$223$	4.69694	0.314530	0.157265	−	0.987556i	$-0.449732\pi$
$223$	4.69694	0.314530	0.157265	+	0.987556i	$0.449732\pi$
$224$	1.00000	0.0668153
$225$	3.00000	0.200000
$226$	−3.44949	−0.229457
$227$	6.69694	0.444491	0.222246	−	0.974991i	$-0.428661\pi$
$227$	6.69694	0.444491	0.222246	+	0.974991i	$0.428661\pi$
$228$	−9.55051	−0.632498
$229$	22.4949	1.48650	0.743252	−	0.669011i	$-0.233282\pi$
$229$	22.4949	1.48650	0.743252	+	0.669011i	$0.233282\pi$
$230$	−4.44949	−0.293391
$231$	−1.10102	−0.0724418
$232$	4.55051	0.298756
$233$	−10.6969	−0.700780	−0.350390	−	0.936604i	$-0.613951\pi$
$233$	−10.6969	−0.700780	−0.350390	+	0.936604i	$0.613951\pi$
$234$	−3.00000	−0.196116
$235$	2.44949	0.159787
$236$	−4.89898	−0.318896
$237$	16.0454	1.04226
$238$	−2.44949	−0.158777
$239$	4.34847	0.281279	0.140640	−	0.990061i	$-0.455084\pi$
$239$	4.34847	0.281279	0.140640	+	0.990061i	$0.455084\pi$
$240$	−2.44949	−0.158114
$241$	−3.34847	−0.215694	−0.107847	−	0.994168i	$-0.534396\pi$
$241$	−3.34847	−0.215694	−0.107847	+	0.994168i	$0.534396\pi$
$242$	−10.7980	−0.694119
$243$	−22.0454	−1.41421
$244$	1.44949	0.0927941
$245$	6.00000	0.383326
$246$	−5.14643	−0.328124
$247$	3.89898	0.248086
$248$	−5.44949	−0.346043
$249$	14.6969	0.931381
$250$	−1.00000	−0.0632456
$251$	21.5959	1.36312	0.681561	−	0.731761i	$-0.261301\pi$
$251$	21.5959	1.36312	0.681561	+	0.731761i	$0.261301\pi$
$252$	3.00000	0.188982
$253$	−2.00000	−0.125739
$254$	0.898979	0.0564070
$255$	6.00000	0.375735
$256$	1.00000	0.0625000
$257$	−9.24745	−0.576840	−0.288420	−	0.957504i	$-0.593130\pi$
$257$	−9.24745	−0.576840	−0.288420	+	0.957504i	$0.593130\pi$
$258$	−2.44949	−0.152499
$259$	−4.44949	−0.276478
$260$	1.00000	0.0620174
$261$	13.6515	0.845009
$262$	−2.00000	−0.123560
$263$	25.8990	1.59700	0.798500	−	0.601995i	$-0.205627\pi$
$263$	25.8990	1.59700	0.798500	+	0.601995i	$0.205627\pi$
$264$	−1.10102	−0.0677631
$265$	−13.7980	−0.847602
$266$	−3.89898	−0.239062
$267$	44.6969	2.73541
$268$	−0.550510	−0.0336278
$269$	−20.4949	−1.24960	−0.624798	−	0.780786i	$-0.714819\pi$
$269$	−20.4949	−1.24960	−0.624798	+	0.780786i	$0.714819\pi$
$270$	0	0
$271$	−15.4495	−0.938490	−0.469245	−	0.883068i	$-0.655474\pi$
$271$	−15.4495	−0.938490	−0.469245	+	0.883068i	$0.655474\pi$
$272$	−2.44949	−0.148522
$273$	−2.44949	−0.148250
$274$	−5.24745	−0.317010
$275$	−0.449490	−0.0271053
$276$	10.8990	0.656041
$277$	−20.8990	−1.25570	−0.627849	−	0.778335i	$-0.716064\pi$
$277$	−20.8990	−1.25570	−0.627849	+	0.778335i	$0.716064\pi$
$278$	18.2474	1.09441
$279$	−16.3485	−0.978757
$280$	−1.00000	−0.0597614
$281$	28.5959	1.70589	0.852945	−	0.522001i	$-0.174814\pi$
$281$	28.5959	1.70589	0.852945	+	0.522001i	$0.174814\pi$
$282$	−6.00000	−0.357295
$283$	−26.3485	−1.56625	−0.783127	−	0.621862i	$-0.786377\pi$
$283$	−26.3485	−1.56625	−0.783127	+	0.621862i	$0.786377\pi$
$284$	−1.34847	−0.0800169
$285$	9.55051	0.565723
$286$	0.449490	0.0265789
$287$	−2.10102	−0.124019
$288$	3.00000	0.176777
$289$	−11.0000	−0.647059
$290$	−4.55051	−0.267215
$291$	−28.2929	−1.65856
$292$	−2.55051	−0.149257
$293$	4.20204	0.245486	0.122743	−	0.992438i	$-0.460831\pi$
$293$	4.20204	0.245486	0.122743	+	0.992438i	$0.460831\pi$
$294$	−14.6969	−0.857143
$295$	4.89898	0.285230
$296$	−4.44949	−0.258621
$297$	0	0
$298$	−2.55051	−0.147747
$299$	−4.44949	−0.257321
$300$	2.44949	0.141421
$301$	−1.00000	−0.0576390
$302$	10.8990	0.627166
$303$	−8.20204	−0.471195
$304$	−3.89898	−0.223622
$305$	−1.44949	−0.0829975
$306$	−7.34847	−0.420084
$307$	3.44949	0.196873	0.0984364	−	0.995143i	$-0.468616\pi$
$307$	3.44949	0.196873	0.0984364	+	0.995143i	$0.468616\pi$
$308$	−0.449490	−0.0256121
$309$	−2.69694	−0.153423
$310$	5.44949	0.309510
$311$	10.3485	0.586808	0.293404	−	0.955989i	$-0.405212\pi$
$311$	10.3485	0.586808	0.293404	+	0.955989i	$0.405212\pi$
$312$	−2.44949	−0.138675
$313$	−14.0000	−0.791327	−0.395663	−	0.918396i	$-0.629485\pi$
$313$	−14.0000	−0.791327	−0.395663	+	0.918396i	$0.629485\pi$
$314$	−20.0454	−1.13123
$315$	−3.00000	−0.169031
$316$	6.55051	0.368495
$317$	−24.3939	−1.37010	−0.685048	−	0.728498i	$-0.740219\pi$
$317$	−24.3939	−1.37010	−0.685048	+	0.728498i	$0.740219\pi$
$318$	33.7980	1.89530
$319$	−2.04541	−0.114521
$320$	−1.00000	−0.0559017
$321$	1.34847	0.0752642
$322$	4.44949	0.247960
$323$	9.55051	0.531405
$324$	−9.00000	−0.500000
$325$	−1.00000	−0.0554700
$326$	−5.79796	−0.321119
$327$	31.5959	1.74726
$328$	−2.10102	−0.116009
$329$	−2.44949	−0.135045
$330$	1.10102	0.0606092
$331$	3.79796	0.208755	0.104377	−	0.994538i	$-0.466715\pi$
$331$	3.79796	0.208755	0.104377	+	0.994538i	$0.466715\pi$
$332$	6.00000	0.329293
$333$	−13.3485	−0.731492
$334$	4.44949	0.243465
$335$	0.550510	0.0300776
$336$	2.44949	0.133631
$337$	35.3939	1.92803	0.964014	−	0.265853i	$-0.0856535\pi$
$337$	35.3939	1.92803	0.964014	+	0.265853i	$0.0856535\pi$
$338$	−12.0000	−0.652714
$339$	−8.44949	−0.458913
$340$	2.44949	0.132842
$341$	2.44949	0.132647
$342$	−11.6969	−0.632498
$343$	−13.0000	−0.701934
$344$	−1.00000	−0.0539164
$345$	−10.8990	−0.586781
$346$	8.79796	0.472981
$347$	26.2474	1.40904	0.704518	−	0.709686i	$-0.251163\pi$
$347$	26.2474	1.40904	0.704518	+	0.709686i	$0.251163\pi$
$348$	11.1464	0.597511
$349$	−9.10102	−0.487166	−0.243583	−	0.969880i	$-0.578323\pi$
$349$	−9.10102	−0.487166	−0.243583	+	0.969880i	$0.578323\pi$
$350$	1.00000	0.0534522
$351$	0	0
$352$	−0.449490	−0.0239579
$353$	26.2474	1.39701	0.698505	−	0.715605i	$-0.253849\pi$
$353$	26.2474	1.39701	0.698505	+	0.715605i	$0.253849\pi$
$354$	−12.0000	−0.637793
$355$	1.34847	0.0715693
$356$	18.2474	0.967113
$357$	−6.00000	−0.317554
$358$	8.79796	0.464987
$359$	−23.4495	−1.23762	−0.618808	−	0.785542i	$-0.712384\pi$
$359$	−23.4495	−1.23762	−0.618808	+	0.785542i	$0.712384\pi$
$360$	−3.00000	−0.158114
$361$	−3.79796	−0.199893
$362$	23.3485	1.22717
$363$	−26.4495	−1.38824
$364$	−1.00000	−0.0524142
$365$	2.55051	0.133500
$366$	3.55051	0.185588
$367$	−3.59592	−0.187705	−0.0938527	−	0.995586i	$-0.529918\pi$
$367$	−3.59592	−0.187705	−0.0938527	+	0.995586i	$0.529918\pi$
$368$	4.44949	0.231946
$369$	−6.30306	−0.328124
$370$	4.44949	0.231318
$371$	13.7980	0.716354
$372$	−13.3485	−0.692086
$373$	6.24745	0.323481	0.161740	−	0.986833i	$-0.448289\pi$
$373$	6.24745	0.323481	0.161740	+	0.986833i	$0.448289\pi$
$374$	1.10102	0.0569324
$375$	−2.44949	−0.126491
$376$	−2.44949	−0.126323
$377$	−4.55051	−0.234363
$378$	0	0
$379$	−26.4949	−1.36095	−0.680476	−	0.732771i	$-0.738227\pi$
$379$	−26.4949	−1.36095	−0.680476	+	0.732771i	$0.738227\pi$
$380$	3.89898	0.200013
$381$	2.20204	0.112814
$382$	18.2474	0.933621
$383$	−7.20204	−0.368007	−0.184004	−	0.982926i	$-0.558906\pi$
$383$	−7.20204	−0.368007	−0.184004	+	0.982926i	$0.558906\pi$
$384$	2.44949	0.125000
$385$	0.449490	0.0229081
$386$	−3.10102	−0.157838
$387$	−3.00000	−0.152499
$388$	−11.5505	−0.586388
$389$	−3.30306	−0.167472	−0.0837359	−	0.996488i	$-0.526685\pi$
$389$	−3.30306	−0.167472	−0.0837359	+	0.996488i	$0.526685\pi$
$390$	2.44949	0.124035
$391$	−10.8990	−0.551185
$392$	−6.00000	−0.303046
$393$	−4.89898	−0.247121
$394$	−7.00000	−0.352655
$395$	−6.55051	−0.329592
$396$	−1.34847	−0.0677631
$397$	−22.6969	−1.13913	−0.569563	−	0.821947i	$-0.692888\pi$
$397$	−22.6969	−1.13913	−0.569563	+	0.821947i	$0.692888\pi$
$398$	16.4495	0.824538
$399$	−9.55051	−0.478124
$400$	1.00000	0.0500000
$401$	5.69694	0.284492	0.142246	−	0.989831i	$-0.454568\pi$
$401$	5.69694	0.284492	0.142246	+	0.989831i	$0.454568\pi$
$402$	−1.34847	−0.0672555
$403$	5.44949	0.271458
$404$	−3.34847	−0.166593
$405$	9.00000	0.447214
$406$	4.55051	0.225838
$407$	2.00000	0.0991363
$408$	−6.00000	−0.297044
$409$	−28.0454	−1.38676	−0.693378	−	0.720574i	$-0.743878\pi$
$409$	−28.0454	−1.38676	−0.693378	+	0.720574i	$0.743878\pi$
$410$	2.10102	0.103762
$411$	−12.8536	−0.634020
$412$	−1.10102	−0.0542434
$413$	−4.89898	−0.241063
$414$	13.3485	0.656041
$415$	−6.00000	−0.294528
$416$	−1.00000	−0.0490290
$417$	44.6969	2.18882
$418$	1.75255	0.0857201
$419$	−23.0000	−1.12362	−0.561812	−	0.827265i	$-0.689895\pi$
$419$	−23.0000	−1.12362	−0.561812	+	0.827265i	$0.689895\pi$
$420$	−2.44949	−0.119523
$421$	8.14643	0.397033	0.198516	−	0.980098i	$-0.436388\pi$
$421$	8.14643	0.397033	0.198516	+	0.980098i	$0.436388\pi$
$422$	23.5959	1.14863
$423$	−7.34847	−0.357295
$424$	13.7980	0.670088
$425$	−2.44949	−0.118818
$426$	−3.30306	−0.160034
$427$	1.44949	0.0701457
$428$	0.550510	0.0266099
$429$	1.10102	0.0531578
$430$	1.00000	0.0482243
$431$	−37.5959	−1.81093	−0.905466	−	0.424419i	$-0.860478\pi$
$431$	−37.5959	−1.81093	−0.905466	+	0.424419i	$0.860478\pi$
$432$	0	0
$433$	−21.6515	−1.04051	−0.520253	−	0.854012i	$-0.674162\pi$
$433$	−21.6515	−1.04051	−0.520253	+	0.854012i	$0.674162\pi$
$434$	−5.44949	−0.261584
$435$	−11.1464	−0.534430
$436$	12.8990	0.617749
$437$	−17.3485	−0.829890
$438$	−6.24745	−0.298515
$439$	−12.0000	−0.572729	−0.286364	−	0.958121i	$-0.592447\pi$
$439$	−12.0000	−0.572729	−0.286364	+	0.958121i	$0.592447\pi$
$440$	0.449490	0.0214286
$441$	−18.0000	−0.857143
$442$	2.44949	0.116510
$443$	−28.1464	−1.33728	−0.668639	−	0.743588i	$-0.733123\pi$
$443$	−28.1464	−1.33728	−0.668639	+	0.743588i	$0.733123\pi$
$444$	−10.8990	−0.517243
$445$	−18.2474	−0.865012
$446$	4.69694	0.222406
$447$	−6.24745	−0.295494
$448$	1.00000	0.0472456
$449$	−15.5505	−0.733874	−0.366937	−	0.930246i	$-0.619594\pi$
$449$	−15.5505	−0.733874	−0.366937	+	0.930246i	$0.619594\pi$
$450$	3.00000	0.141421
$451$	0.944387	0.0444695
$452$	−3.44949	−0.162250
$453$	26.6969	1.25433
$454$	6.69694	0.314303
$455$	1.00000	0.0468807
$456$	−9.55051	−0.447244
$457$	−40.2929	−1.88482	−0.942410	−	0.334459i	$-0.891446\pi$
$457$	−40.2929	−1.88482	−0.942410	+	0.334459i	$0.891446\pi$
$458$	22.4949	1.05112
$459$	0	0
$460$	−4.44949	−0.207459
$461$	33.5505	1.56260	0.781302	−	0.624154i	$-0.214556\pi$
$461$	33.5505	1.56260	0.781302	+	0.624154i	$0.214556\pi$
$462$	−1.10102	−0.0512241
$463$	4.79796	0.222980	0.111490	−	0.993766i	$-0.464438\pi$
$463$	4.79796	0.222980	0.111490	+	0.993766i	$0.464438\pi$
$464$	4.55051	0.211252
$465$	13.3485	0.619020
$466$	−10.6969	−0.495526
$467$	20.2474	0.936940	0.468470	−	0.883479i	$-0.344805\pi$
$467$	20.2474	0.936940	0.468470	+	0.883479i	$0.344805\pi$
$468$	−3.00000	−0.138675
$469$	−0.550510	−0.0254202
$470$	2.44949	0.112987
$471$	−49.1010	−2.26246
$472$	−4.89898	−0.225494
$473$	0.449490	0.0206676
$474$	16.0454	0.736990
$475$	−3.89898	−0.178897
$476$	−2.44949	−0.112272
$477$	41.3939	1.89530
$478$	4.34847	0.198894
$479$	13.3031	0.607832	0.303916	−	0.952699i	$-0.401706\pi$
$479$	13.3031	0.607832	0.303916	+	0.952699i	$0.401706\pi$
$480$	−2.44949	−0.111803
$481$	4.44949	0.202879
$482$	−3.34847	−0.152519
$483$	10.8990	0.495921
$484$	−10.7980	−0.490816
$485$	11.5505	0.524482
$486$	−22.0454	−1.00000
$487$	7.34847	0.332991	0.166495	−	0.986042i	$-0.446755\pi$
$487$	7.34847	0.332991	0.166495	+	0.986042i	$0.446755\pi$
$488$	1.44949	0.0656153
$489$	−14.2020	−0.642238
$490$	6.00000	0.271052
$491$	−20.2020	−0.911705	−0.455853	−	0.890055i	$-0.650666\pi$
$491$	−20.2020	−0.911705	−0.455853	+	0.890055i	$0.650666\pi$
$492$	−5.14643	−0.232019
$493$	−11.1464	−0.502010
$494$	3.89898	0.175423
$495$	1.34847	0.0606092
$496$	−5.44949	−0.244689
$497$	−1.34847	−0.0604871
$498$	14.6969	0.658586
$499$	15.2020	0.680537	0.340268	−	0.940328i	$-0.389482\pi$
$499$	15.2020	0.680537	0.340268	+	0.940328i	$0.389482\pi$
$500$	−1.00000	−0.0447214
$501$	10.8990	0.486930
$502$	21.5959	0.963873
$503$	26.0000	1.15928	0.579641	−	0.814872i	$-0.303193\pi$
$503$	26.0000	1.15928	0.579641	+	0.814872i	$0.303193\pi$
$504$	3.00000	0.133631
$505$	3.34847	0.149005
$506$	−2.00000	−0.0889108
$507$	−29.3939	−1.30543
$508$	0.898979	0.0398858
$509$	10.6969	0.474133	0.237067	−	0.971493i	$-0.423814\pi$
$509$	10.6969	0.474133	0.237067	+	0.971493i	$0.423814\pi$
$510$	6.00000	0.265684
$511$	−2.55051	−0.112828
$512$	1.00000	0.0441942
$513$	0	0
$514$	−9.24745	−0.407887
$515$	1.10102	0.0485168
$516$	−2.44949	−0.107833
$517$	1.10102	0.0484228
$518$	−4.44949	−0.195499
$519$	21.5505	0.945962
$520$	1.00000	0.0438529
$521$	−36.7423	−1.60971	−0.804856	−	0.593471i	$-0.797757\pi$
$521$	−36.7423	−1.60971	−0.804856	+	0.593471i	$0.797757\pi$
$522$	13.6515	0.597511
$523$	−33.3485	−1.45823	−0.729113	−	0.684393i	$-0.760067\pi$
$523$	−33.3485	−1.45823	−0.729113	+	0.684393i	$0.760067\pi$
$524$	−2.00000	−0.0873704
$525$	2.44949	0.106904
$526$	25.8990	1.12925
$527$	13.3485	0.581468
$528$	−1.10102	−0.0479158
$529$	−3.20204	−0.139219
$530$	−13.7980	−0.599345
$531$	−14.6969	−0.637793
$532$	−3.89898	−0.169042
$533$	2.10102	0.0910053
$534$	44.6969	1.93423
$535$	−0.550510	−0.0238006
$536$	−0.550510	−0.0237784
$537$	21.5505	0.929973
$538$	−20.4949	−0.883598
$539$	2.69694	0.116165
$540$	0	0
$541$	−28.6969	−1.23378	−0.616889	−	0.787050i	$-0.711607\pi$
$541$	−28.6969	−1.23378	−0.616889	+	0.787050i	$0.711607\pi$
$542$	−15.4495	−0.663612
$543$	57.1918	2.45434
$544$	−2.44949	−0.105021
$545$	−12.8990	−0.552532
$546$	−2.44949	−0.104828
$547$	45.7980	1.95818	0.979090	−	0.203429i	$-0.0652087\pi$
$547$	45.7980	1.95818	0.979090	+	0.203429i	$0.0652087\pi$
$548$	−5.24745	−0.224160
$549$	4.34847	0.185588
$550$	−0.449490	−0.0191663
$551$	−17.7423	−0.755849
$552$	10.8990	0.463891
$553$	6.55051	0.278556
$554$	−20.8990	−0.887913
$555$	10.8990	0.462636
$556$	18.2474	0.773864
$557$	−15.0000	−0.635570	−0.317785	−	0.948163i	$-0.602939\pi$
$557$	−15.0000	−0.635570	−0.317785	+	0.948163i	$0.602939\pi$
$558$	−16.3485	−0.692086
$559$	1.00000	0.0422955
$560$	−1.00000	−0.0422577
$561$	2.69694	0.113865
$562$	28.5959	1.20625
$563$	−35.7423	−1.50636	−0.753180	−	0.657814i	$-0.771481\pi$
$563$	−35.7423	−1.50636	−0.753180	+	0.657814i	$0.771481\pi$
$564$	−6.00000	−0.252646
$565$	3.44949	0.145121
$566$	−26.3485	−1.10751
$567$	−9.00000	−0.377964
$568$	−1.34847	−0.0565805
$569$	−2.30306	−0.0965494	−0.0482747	−	0.998834i	$-0.515372\pi$
$569$	−2.30306	−0.0965494	−0.0482747	+	0.998834i	$0.515372\pi$
$570$	9.55051	0.400027
$571$	4.30306	0.180078	0.0900388	−	0.995938i	$-0.471301\pi$
$571$	4.30306	0.180078	0.0900388	+	0.995938i	$0.471301\pi$
$572$	0.449490	0.0187941
$573$	44.6969	1.86724
$574$	−2.10102	−0.0876949
$575$	4.44949	0.185557
$576$	3.00000	0.125000
$577$	−8.14643	−0.339140	−0.169570	−	0.985518i	$-0.554238\pi$
$577$	−8.14643	−0.339140	−0.169570	+	0.985518i	$0.554238\pi$
$578$	−11.0000	−0.457540
$579$	−7.59592	−0.315676
$580$	−4.55051	−0.188950
$581$	6.00000	0.248922
$582$	−28.2929	−1.17278
$583$	−6.20204	−0.256862
$584$	−2.55051	−0.105541
$585$	3.00000	0.124035
$586$	4.20204	0.173585
$587$	−21.1464	−0.872806	−0.436403	−	0.899751i	$-0.643748\pi$
$587$	−21.1464	−0.872806	−0.436403	+	0.899751i	$0.643748\pi$
$588$	−14.6969	−0.606092
$589$	21.2474	0.875486
$590$	4.89898	0.201688
$591$	−17.1464	−0.705310
$592$	−4.44949	−0.182873
$593$	33.2474	1.36531	0.682655	−	0.730741i	$-0.260825\pi$
$593$	33.2474	1.36531	0.682655	+	0.730741i	$0.260825\pi$
$594$	0	0
$595$	2.44949	0.100419
$596$	−2.55051	−0.104473
$597$	40.2929	1.64908
$598$	−4.44949	−0.181953
$599$	−20.8990	−0.853909	−0.426955	−	0.904273i	$-0.640414\pi$
$599$	−20.8990	−0.853909	−0.426955	+	0.904273i	$0.640414\pi$
$600$	2.44949	0.100000
$601$	9.79796	0.399667	0.199834	−	0.979830i	$-0.435960\pi$
$601$	9.79796	0.399667	0.199834	+	0.979830i	$0.435960\pi$
$602$	−1.00000	−0.0407570
$603$	−1.65153	−0.0672555
$604$	10.8990	0.443473
$605$	10.7980	0.438999
$606$	−8.20204	−0.333185
$607$	−1.59592	−0.0647763	−0.0323882	−	0.999475i	$-0.510311\pi$
$607$	−1.59592	−0.0647763	−0.0323882	+	0.999475i	$0.510311\pi$
$608$	−3.89898	−0.158124
$609$	11.1464	0.451676
$610$	−1.44949	−0.0586881
$611$	2.44949	0.0990957
$612$	−7.34847	−0.297044
$613$	−46.3939	−1.87383	−0.936916	−	0.349556i	$-0.886332\pi$
$613$	−46.3939	−1.87383	−0.936916	+	0.349556i	$0.886332\pi$
$614$	3.44949	0.139210
$615$	5.14643	0.207524
$616$	−0.449490	−0.0181105
$617$	−19.5959	−0.788902	−0.394451	−	0.918917i	$-0.629065\pi$
$617$	−19.5959	−0.788902	−0.394451	+	0.918917i	$0.629065\pi$
$618$	−2.69694	−0.108487
$619$	40.9444	1.64569	0.822847	−	0.568263i	$-0.192384\pi$
$619$	40.9444	1.64569	0.822847	+	0.568263i	$0.192384\pi$
$620$	5.44949	0.218857
$621$	0	0
$622$	10.3485	0.414936
$623$	18.2474	0.731069
$624$	−2.44949	−0.0980581
$625$	1.00000	0.0400000
$626$	−14.0000	−0.559553
$627$	4.29286	0.171440
$628$	−20.0454	−0.799899
$629$	10.8990	0.434571
$630$	−3.00000	−0.119523
$631$	14.4495	0.575225	0.287613	−	0.957747i	$-0.407138\pi$
$631$	14.4495	0.575225	0.287613	+	0.957747i	$0.407138\pi$
$632$	6.55051	0.260565
$633$	57.7980	2.29726
$634$	−24.3939	−0.968805
$635$	−0.898979	−0.0356749
$636$	33.7980	1.34018
$637$	6.00000	0.237729
$638$	−2.04541	−0.0809785
$639$	−4.04541	−0.160034
$640$	−1.00000	−0.0395285
$641$	8.69694	0.343508	0.171754	−	0.985140i	$-0.445057\pi$
$641$	8.69694	0.343508	0.171754	+	0.985140i	$0.445057\pi$
$642$	1.34847	0.0532198
$643$	−32.1464	−1.26773	−0.633866	−	0.773443i	$-0.718533\pi$
$643$	−32.1464	−1.26773	−0.633866	+	0.773443i	$0.718533\pi$
$644$	4.44949	0.175334
$645$	2.44949	0.0964486
$646$	9.55051	0.375760
$647$	−39.0908	−1.53682	−0.768409	−	0.639959i	$-0.778951\pi$
$647$	−39.0908	−1.53682	−0.768409	+	0.639959i	$0.778951\pi$
$648$	−9.00000	−0.353553
$649$	2.20204	0.0864377
$650$	−1.00000	−0.0392232
$651$	−13.3485	−0.523168
$652$	−5.79796	−0.227066
$653$	2.44949	0.0958559	0.0479280	−	0.998851i	$-0.484738\pi$
$653$	2.44949	0.0958559	0.0479280	+	0.998851i	$0.484738\pi$
$654$	31.5959	1.23550
$655$	2.00000	0.0781465
$656$	−2.10102	−0.0820311
$657$	−7.65153	−0.298515
$658$	−2.44949	−0.0954911
$659$	33.8434	1.31835	0.659175	−	0.751989i	$-0.270906\pi$
$659$	33.8434	1.31835	0.659175	+	0.751989i	$0.270906\pi$
$660$	1.10102	0.0428572
$661$	31.1464	1.21146	0.605728	−	0.795672i	$-0.292882\pi$
$661$	31.1464	1.21146	0.605728	+	0.795672i	$0.292882\pi$
$662$	3.79796	0.147612
$663$	6.00000	0.233021
$664$	6.00000	0.232845
$665$	3.89898	0.151196
$666$	−13.3485	−0.517243
$667$	20.2474	0.783984
$668$	4.44949	0.172156
$669$	11.5051	0.444813
$670$	0.550510	0.0212681
$671$	−0.651531	−0.0251521
$672$	2.44949	0.0944911
$673$	−16.7526	−0.645763	−0.322882	−	0.946439i	$-0.604652\pi$
$673$	−16.7526	−0.645763	−0.322882	+	0.946439i	$0.604652\pi$
$674$	35.3939	1.36332
$675$	0	0
$676$	−12.0000	−0.461538
$677$	42.0908	1.61768	0.808841	−	0.588028i	$-0.200095\pi$
$677$	42.0908	1.61768	0.808841	+	0.588028i	$0.200095\pi$
$678$	−8.44949	−0.324501
$679$	−11.5505	−0.443268
$680$	2.44949	0.0939336
$681$	16.4041	0.628606
$682$	2.44949	0.0937958
$683$	13.3031	0.509028	0.254514	−	0.967069i	$-0.418085\pi$
$683$	13.3031	0.509028	0.254514	+	0.967069i	$0.418085\pi$
$684$	−11.6969	−0.447244
$685$	5.24745	0.200495
$686$	−13.0000	−0.496342
$687$	55.1010	2.10224
$688$	−1.00000	−0.0381246
$689$	−13.7980	−0.525660
$690$	−10.8990	−0.414917
$691$	19.3031	0.734323	0.367162	−	0.930157i	$-0.380330\pi$
$691$	19.3031	0.734323	0.367162	+	0.930157i	$0.380330\pi$
$692$	8.79796	0.334448
$693$	−1.34847	−0.0512241
$694$	26.2474	0.996340
$695$	−18.2474	−0.692165
$696$	11.1464	0.422504
$697$	5.14643	0.194935
$698$	−9.10102	−0.344479
$699$	−26.2020	−0.991052
$700$	1.00000	0.0377964
$701$	48.7423	1.84097	0.920487	−	0.390774i	$-0.127793\pi$
$701$	48.7423	1.84097	0.920487	+	0.390774i	$0.127793\pi$
$702$	0	0
$703$	17.3485	0.654310
$704$	−0.449490	−0.0169408
$705$	6.00000	0.225973
$706$	26.2474	0.987836
$707$	−3.34847	−0.125932
$708$	−12.0000	−0.450988
$709$	26.2474	0.985744	0.492872	−	0.870102i	$-0.335947\pi$
$709$	26.2474	0.985744	0.492872	+	0.870102i	$0.335947\pi$
$710$	1.34847	0.0506071
$711$	19.6515	0.736990
$712$	18.2474	0.683852
$713$	−24.2474	−0.908074
$714$	−6.00000	−0.224544
$715$	−0.449490	−0.0168100
$716$	8.79796	0.328795
$717$	10.6515	0.397789
$718$	−23.4495	−0.875127
$719$	−24.2020	−0.902584	−0.451292	−	0.892376i	$-0.649037\pi$
$719$	−24.2020	−0.902584	−0.451292	+	0.892376i	$0.649037\pi$
$720$	−3.00000	−0.111803
$721$	−1.10102	−0.0410041
$722$	−3.79796	−0.141345
$723$	−8.20204	−0.305037
$724$	23.3485	0.867739
$725$	4.55051	0.169002
$726$	−26.4495	−0.981633
$727$	−37.5959	−1.39436	−0.697178	−	0.716898i	$-0.745561\pi$
$727$	−37.5959	−1.39436	−0.697178	+	0.716898i	$0.745561\pi$
$728$	−1.00000	−0.0370625
$729$	−27.0000	−1.00000
$730$	2.55051	0.0943986
$731$	2.44949	0.0905977
$732$	3.55051	0.131231
$733$	−7.75255	−0.286347	−0.143174	−	0.989698i	$-0.545731\pi$
$733$	−7.75255	−0.286347	−0.143174	+	0.989698i	$0.545731\pi$
$734$	−3.59592	−0.132728
$735$	14.6969	0.542105
$736$	4.44949	0.164010
$737$	0.247449	0.00911489
$738$	−6.30306	−0.232019
$739$	19.4949	0.717131	0.358566	−	0.933504i	$-0.383266\pi$
$739$	19.4949	0.717131	0.358566	+	0.933504i	$0.383266\pi$
$740$	4.44949	0.163566
$741$	9.55051	0.350847
$742$	13.7980	0.506539
$743$	−52.5959	−1.92956	−0.964779	−	0.263063i	$-0.915267\pi$
$743$	−52.5959	−1.92956	−0.964779	+	0.263063i	$0.915267\pi$
$744$	−13.3485	−0.489379
$745$	2.55051	0.0934435
$746$	6.24745	0.228735
$747$	18.0000	0.658586
$748$	1.10102	0.0402573
$749$	0.550510	0.0201152
$750$	−2.44949	−0.0894427
$751$	−22.9444	−0.837253	−0.418626	−	0.908159i	$-0.637488\pi$
$751$	−22.9444	−0.837253	−0.418626	+	0.908159i	$0.637488\pi$
$752$	−2.44949	−0.0893237
$753$	52.8990	1.92775
$754$	−4.55051	−0.165720
$755$	−10.8990	−0.396654
$756$	0	0
$757$	23.3031	0.846964	0.423482	−	0.905904i	$-0.360808\pi$
$757$	23.3031	0.846964	0.423482	+	0.905904i	$0.360808\pi$
$758$	−26.4949	−0.962338
$759$	−4.89898	−0.177822
$760$	3.89898	0.141431
$761$	−14.4949	−0.525440	−0.262720	−	0.964872i	$-0.584619\pi$
$761$	−14.4949	−0.525440	−0.262720	+	0.964872i	$0.584619\pi$
$762$	2.20204	0.0797715
$763$	12.8990	0.466974
$764$	18.2474	0.660170
$765$	7.34847	0.265684
$766$	−7.20204	−0.260220
$767$	4.89898	0.176892
$768$	2.44949	0.0883883
$769$	25.0000	0.901523	0.450762	−	0.892644i	$-0.351152\pi$
$769$	25.0000	0.901523	0.450762	+	0.892644i	$0.351152\pi$
$770$	0.449490	0.0161985
$771$	−22.6515	−0.815775
$772$	−3.10102	−0.111608
$773$	13.3485	0.480111	0.240056	−	0.970759i	$-0.422834\pi$
$773$	13.3485	0.480111	0.240056	+	0.970759i	$0.422834\pi$
$774$	−3.00000	−0.107833
$775$	−5.44949	−0.195751
$776$	−11.5505	−0.414639
$777$	−10.8990	−0.390999
$778$	−3.30306	−0.118420
$779$	8.19184	0.293503
$780$	2.44949	0.0877058
$781$	0.606123	0.0216888
$782$	−10.8990	−0.389747
$783$	0	0
$784$	−6.00000	−0.214286
$785$	20.0454	0.715451
$786$	−4.89898	−0.174741
$787$	31.9444	1.13869	0.569347	−	0.822097i	$-0.307196\pi$
$787$	31.9444	1.13869	0.569347	+	0.822097i	$0.307196\pi$
$788$	−7.00000	−0.249365
$789$	63.4393	2.25850
$790$	−6.55051	−0.233057
$791$	−3.44949	−0.122650
$792$	−1.34847	−0.0479158
$793$	−1.44949	−0.0514729
$794$	−22.6969	−0.805484
$795$	−33.7980	−1.19869
$796$	16.4495	0.583037
$797$	−43.4949	−1.54067	−0.770334	−	0.637640i	$-0.779911\pi$
$797$	−43.4949	−1.54067	−0.770334	+	0.637640i	$0.779911\pi$
$798$	−9.55051	−0.338084
$799$	6.00000	0.212265
$800$	1.00000	0.0353553
$801$	54.7423	1.93423
$802$	5.69694	0.201166
$803$	1.14643	0.0404566
$804$	−1.34847	−0.0475568
$805$	−4.44949	−0.156824
$806$	5.44949	0.191950
$807$	−50.2020	−1.76720
$808$	−3.34847	−0.117799
$809$	−3.69694	−0.129977	−0.0649887	−	0.997886i	$-0.520701\pi$
$809$	−3.69694	−0.129977	−0.0649887	+	0.997886i	$0.520701\pi$
$810$	9.00000	0.316228
$811$	16.5959	0.582761	0.291381	−	0.956607i	$-0.405885\pi$
$811$	16.5959	0.582761	0.291381	+	0.956607i	$0.405885\pi$
$812$	4.55051	0.159692
$813$	−37.8434	−1.32722
$814$	2.00000	0.0701000
$815$	5.79796	0.203094
$816$	−6.00000	−0.210042
$817$	3.89898	0.136408
$818$	−28.0454	−0.980585
$819$	−3.00000	−0.104828
$820$	2.10102	0.0733708
$821$	−6.49490	−0.226673	−0.113337	−	0.993557i	$-0.536154\pi$
$821$	−6.49490	−0.226673	−0.113337	+	0.993557i	$0.536154\pi$
$822$	−12.8536	−0.448320
$823$	19.3031	0.672862	0.336431	−	0.941708i	$-0.390780\pi$
$823$	19.3031	0.672862	0.336431	+	0.941708i	$0.390780\pi$
$824$	−1.10102	−0.0383559
$825$	−1.10102	−0.0383326
$826$	−4.89898	−0.170457
$827$	−28.3485	−0.985773	−0.492886	−	0.870094i	$-0.664058\pi$
$827$	−28.3485	−0.985773	−0.492886	+	0.870094i	$0.664058\pi$
$828$	13.3485	0.463891
$829$	−52.6413	−1.82831	−0.914154	−	0.405366i	$-0.867144\pi$
$829$	−52.6413	−1.82831	−0.914154	+	0.405366i	$0.867144\pi$
$830$	−6.00000	−0.208263
$831$	−51.1918	−1.77583
$832$	−1.00000	−0.0346688
$833$	14.6969	0.509219
$834$	44.6969	1.54773
$835$	−4.44949	−0.153981
$836$	1.75255	0.0606133
$837$	0	0
$838$	−23.0000	−0.794522
$839$	−44.9444	−1.55165	−0.775826	−	0.630947i	$-0.782667\pi$
$839$	−44.9444	−1.55165	−0.775826	+	0.630947i	$0.782667\pi$
$840$	−2.44949	−0.0845154
$841$	−8.29286	−0.285961
$842$	8.14643	0.280744
$843$	70.0454	2.41249
$844$	23.5959	0.812205
$845$	12.0000	0.412813
$846$	−7.34847	−0.252646
$847$	−10.7980	−0.371022
$848$	13.7980	0.473824
$849$	−64.5403	−2.21502
$850$	−2.44949	−0.0840168
$851$	−19.7980	−0.678665
$852$	−3.30306	−0.113161
$853$	−14.0000	−0.479351	−0.239675	−	0.970853i	$-0.577041\pi$
$853$	−14.0000	−0.479351	−0.239675	+	0.970853i	$0.577041\pi$
$854$	1.44949	0.0496005
$855$	11.6969	0.400027
$856$	0.550510	0.0188161
$857$	−38.4495	−1.31341	−0.656705	−	0.754148i	$-0.728050\pi$
$857$	−38.4495	−1.31341	−0.656705	+	0.754148i	$0.728050\pi$
$858$	1.10102	0.0375882
$859$	19.2020	0.655165	0.327583	−	0.944823i	$-0.393766\pi$
$859$	19.2020	0.655165	0.327583	+	0.944823i	$0.393766\pi$
$860$	1.00000	0.0340997
$861$	−5.14643	−0.175390
$862$	−37.5959	−1.28052
$863$	−10.4949	−0.357250	−0.178625	−	0.983917i	$-0.557165\pi$
$863$	−10.4949	−0.357250	−0.178625	+	0.983917i	$0.557165\pi$
$864$	0	0
$865$	−8.79796	−0.299140
$866$	−21.6515	−0.735749
$867$	−26.9444	−0.915079
$868$	−5.44949	−0.184968
$869$	−2.94439	−0.0998815
$870$	−11.1464	−0.377899
$871$	0.550510	0.0186533
$872$	12.8990	0.436815
$873$	−34.6515	−1.17278
$874$	−17.3485	−0.586821
$875$	−1.00000	−0.0338062
$876$	−6.24745	−0.211082
$877$	6.20204	0.209428	0.104714	−	0.994502i	$-0.466607\pi$
$877$	6.20204	0.209428	0.104714	+	0.994502i	$0.466607\pi$
$878$	−12.0000	−0.404980
$879$	10.2929	0.347169
$880$	0.449490	0.0151523
$881$	−9.89898	−0.333505	−0.166753	−	0.985999i	$-0.553328\pi$
$881$	−9.89898	−0.333505	−0.166753	+	0.985999i	$0.553328\pi$
$882$	−18.0000	−0.606092
$883$	12.5505	0.422358	0.211179	−	0.977447i	$-0.432270\pi$
$883$	12.5505	0.422358	0.211179	+	0.977447i	$0.432270\pi$
$884$	2.44949	0.0823853
$885$	12.0000	0.403376
$886$	−28.1464	−0.945598
$887$	−23.2929	−0.782098	−0.391049	−	0.920370i	$-0.627888\pi$
$887$	−23.2929	−0.782098	−0.391049	+	0.920370i	$0.627888\pi$
$888$	−10.8990	−0.365746
$889$	0.898979	0.0301508
$890$	−18.2474	−0.611656
$891$	4.04541	0.135526
$892$	4.69694	0.157265
$893$	9.55051	0.319596
$894$	−6.24745	−0.208946
$895$	−8.79796	−0.294083
$896$	1.00000	0.0334077
$897$	−10.8990	−0.363906
$898$	−15.5505	−0.518927
$899$	−24.7980	−0.827058
$900$	3.00000	0.100000
$901$	−33.7980	−1.12597
$902$	0.944387	0.0314447
$903$	−2.44949	−0.0815139
$904$	−3.44949	−0.114728
$905$	−23.3485	−0.776129
$906$	26.6969	0.886946
$907$	50.3485	1.67179	0.835897	−	0.548887i	$-0.184948\pi$
$907$	50.3485	1.67179	0.835897	+	0.548887i	$0.184948\pi$
$908$	6.69694	0.222246
$909$	−10.0454	−0.333185
$910$	1.00000	0.0331497
$911$	0.449490	0.0148923	0.00744613	−	0.999972i	$-0.497630\pi$
$911$	0.449490	0.0148923	0.00744613	+	0.999972i	$0.497630\pi$
$912$	−9.55051	−0.316249
$913$	−2.69694	−0.0892556
$914$	−40.2929	−1.33277
$915$	−3.55051	−0.117376
$916$	22.4949	0.743252
$917$	−2.00000	−0.0660458
$918$	0	0
$919$	−6.95459	−0.229411	−0.114705	−	0.993400i	$-0.536592\pi$
$919$	−6.95459	−0.229411	−0.114705	+	0.993400i	$0.536592\pi$
$920$	−4.44949	−0.146695
$921$	8.44949	0.278420
$922$	33.5505	1.10493
$923$	1.34847	0.0443854
$924$	−1.10102	−0.0362209
$925$	−4.44949	−0.146298
$926$	4.79796	0.157671
$927$	−3.30306	−0.108487
$928$	4.55051	0.149378
$929$	−59.8888	−1.96489	−0.982443	−	0.186560i	$-0.940266\pi$
$929$	−59.8888	−1.96489	−0.982443	+	0.186560i	$0.940266\pi$
$930$	13.3485	0.437714
$931$	23.3939	0.766703
$932$	−10.6969	−0.350390
$933$	25.3485	0.829872
$934$	20.2474	0.662517
$935$	−1.10102	−0.0360072
$936$	−3.00000	−0.0980581
$937$	−24.8990	−0.813414	−0.406707	−	0.913559i	$-0.633323\pi$
$937$	−24.8990	−0.813414	−0.406707	+	0.913559i	$0.633323\pi$
$938$	−0.550510	−0.0179748
$939$	−34.2929	−1.11911
$940$	2.44949	0.0798935
$941$	−22.2474	−0.725246	−0.362623	−	0.931936i	$-0.618119\pi$
$941$	−22.2474	−0.725246	−0.362623	+	0.931936i	$0.618119\pi$
$942$	−49.1010	−1.59980
$943$	−9.34847	−0.304428
$944$	−4.89898	−0.159448
$945$	0	0
$946$	0.449490	0.0146142
$947$	13.9444	0.453132	0.226566	−	0.973996i	$-0.427250\pi$
$947$	13.9444	0.453132	0.226566	+	0.973996i	$0.427250\pi$
$948$	16.0454	0.521131
$949$	2.55051	0.0827931
$950$	−3.89898	−0.126500
$951$	−59.7526	−1.93761
$952$	−2.44949	−0.0793884
$953$	19.9444	0.646062	0.323031	−	0.946388i	$-0.395298\pi$
$953$	19.9444	0.646062	0.323031	+	0.946388i	$0.395298\pi$
$954$	41.3939	1.34018
$955$	−18.2474	−0.590474
$956$	4.34847	0.140640
$957$	−5.01021	−0.161957
$958$	13.3031	0.429802
$959$	−5.24745	−0.169449
$960$	−2.44949	−0.0790569
$961$	−1.30306	−0.0420342
$962$	4.44949	0.143457
$963$	1.65153	0.0532198
$964$	−3.34847	−0.107847
$965$	3.10102	0.0998254
$966$	10.8990	0.350669
$967$	−26.9444	−0.866473	−0.433237	−	0.901280i	$-0.642629\pi$
$967$	−26.9444	−0.866473	−0.433237	+	0.901280i	$0.642629\pi$
$968$	−10.7980	−0.347060
$969$	23.3939	0.751520
$970$	11.5505	0.370865
$971$	−37.3485	−1.19857	−0.599285	−	0.800536i	$-0.704548\pi$
$971$	−37.3485	−1.19857	−0.599285	+	0.800536i	$0.704548\pi$
$972$	−22.0454	−0.707107
$973$	18.2474	0.584986
$974$	7.34847	0.235460
$975$	−2.44949	−0.0784465
$976$	1.44949	0.0463970
$977$	−3.95459	−0.126519	−0.0632593	−	0.997997i	$-0.520150\pi$
$977$	−3.95459	−0.126519	−0.0632593	+	0.997997i	$0.520150\pi$
$978$	−14.2020	−0.454131
$979$	−8.20204	−0.262138
$980$	6.00000	0.191663
$981$	38.6969	1.23550
$982$	−20.2020	−0.644673
$983$	47.9898	1.53064	0.765318	−	0.643652i	$-0.222582\pi$
$983$	47.9898	1.53064	0.765318	+	0.643652i	$0.222582\pi$
$984$	−5.14643	−0.164062
$985$	7.00000	0.223039
$986$	−11.1464	−0.354975
$987$	−6.00000	−0.190982
$988$	3.89898	0.124043
$989$	−4.44949	−0.141486
$990$	1.34847	0.0428572
$991$	−8.00000	−0.254128	−0.127064	−	0.991894i	$-0.540555\pi$
$991$	−8.00000	−0.254128	−0.127064	+	0.991894i	$0.540555\pi$
$992$	−5.44949	−0.173021
$993$	9.30306	0.295224
$994$	−1.34847	−0.0427708
$995$	−16.4495	−0.521484
$996$	14.6969	0.465690
$997$	24.8990	0.788559	0.394279	−	0.918991i	$-0.370994\pi$
$997$	24.8990	0.788559	0.394279	+	0.918991i	$0.370994\pi$
$998$	15.2020	0.481212
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.a.f.1.2	✓	2
3.2	odd	2		3870.2.a.bg.1.2		2
4.3	odd	2		3440.2.a.h.1.1		2
5.2	odd	4		2150.2.b.m.1549.3		4
5.3	odd	4		2150.2.b.m.1549.2		4
5.4	even	2		2150.2.a.w.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.a.f.1.2	✓	2	1.1	even	1	trivial
2150.2.a.w.1.1		2	5.4	even	2
2150.2.b.m.1549.2		4	5.3	odd	4
2150.2.b.m.1549.3		4	5.2	odd	4
3440.2.a.h.1.1		2	4.3	odd	2
3870.2.a.bg.1.2		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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.44949 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.44949 q^{6} +1.00000 q^{7} +1.00000 q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.44949 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.44949 q^{6} +1.00000 q^{7} +1.00000 q^{8} +3.00000 q^{9} -1.00000 q^{10} -0.449490 q^{11} +2.44949 q^{12} -1.00000 q^{13} +1.00000 q^{14} -2.44949 q^{15} +1.00000 q^{16} -2.44949 q^{17} +3.00000 q^{18} -3.89898 q^{19} -1.00000 q^{20} +2.44949 q^{21} -0.449490 q^{22} +4.44949 q^{23} +2.44949 q^{24} +1.00000 q^{25} -1.00000 q^{26} +1.00000 q^{28} +4.55051 q^{29} -2.44949 q^{30} -5.44949 q^{31} +1.00000 q^{32} -1.10102 q^{33} -2.44949 q^{34} -1.00000 q^{35} +3.00000 q^{36} -4.44949 q^{37} -3.89898 q^{38} -2.44949 q^{39} -1.00000 q^{40} -2.10102 q^{41} +2.44949 q^{42} -1.00000 q^{43} -0.449490 q^{44} -3.00000 q^{45} +4.44949 q^{46} -2.44949 q^{47} +2.44949 q^{48} -6.00000 q^{49} +1.00000 q^{50} -6.00000 q^{51} -1.00000 q^{52} +13.7980 q^{53} +0.449490 q^{55} +1.00000 q^{56} -9.55051 q^{57} +4.55051 q^{58} -4.89898 q^{59} -2.44949 q^{60} +1.44949 q^{61} -5.44949 q^{62} +3.00000 q^{63} +1.00000 q^{64} +1.00000 q^{65} -1.10102 q^{66} -0.550510 q^{67} -2.44949 q^{68} +10.8990 q^{69} -1.00000 q^{70} -1.34847 q^{71} +3.00000 q^{72} -2.55051 q^{73} -4.44949 q^{74} +2.44949 q^{75} -3.89898 q^{76} -0.449490 q^{77} -2.44949 q^{78} +6.55051 q^{79} -1.00000 q^{80} -9.00000 q^{81} -2.10102 q^{82} +6.00000 q^{83} +2.44949 q^{84} +2.44949 q^{85} -1.00000 q^{86} +11.1464 q^{87} -0.449490 q^{88} +18.2474 q^{89} -3.00000 q^{90} -1.00000 q^{91} +4.44949 q^{92} -13.3485 q^{93} -2.44949 q^{94} +3.89898 q^{95} +2.44949 q^{96} -11.5505 q^{97} -6.00000 q^{98} -1.34847 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{4} - 2 q^{5} + 2 q^{7} + 2 q^{8} + 6 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 2 * q^4 - 2 * q^5 + 2 * q^7 + 2 * q^8 + 6 * q^9	\( 2 q + 2 q^{2} + 2 q^{4} - 2 q^{5} + 2 q^{7} + 2 q^{8} + 6 q^{9} - 2 q^{10} + 4 q^{11} - 2 q^{13} + 2 q^{14} + 2 q^{16} + 6 q^{18} + 2 q^{19} - 2 q^{20} + 4 q^{22} + 4 q^{23} + 2 q^{25} - 2 q^{26} + 2 q^{28} + 14 q^{29} - 6 q^{31} + 2 q^{32} - 12 q^{33} - 2 q^{35} + 6 q^{36} - 4 q^{37} + 2 q^{38} - 2 q^{40} - 14 q^{41} - 2 q^{43} + 4 q^{44} - 6 q^{45} + 4 q^{46} - 12 q^{49} + 2 q^{50} - 12 q^{51} - 2 q^{52} + 8 q^{53} - 4 q^{55} + 2 q^{56} - 24 q^{57} + 14 q^{58} - 2 q^{61} - 6 q^{62} + 6 q^{63} + 2 q^{64} + 2 q^{65} - 12 q^{66} - 6 q^{67} + 12 q^{69} - 2 q^{70} + 12 q^{71} + 6 q^{72} - 10 q^{73} - 4 q^{74} + 2 q^{76} + 4 q^{77} + 18 q^{79} - 2 q^{80} - 18 q^{81} - 14 q^{82} + 12 q^{83} - 2 q^{86} - 12 q^{87} + 4 q^{88} + 12 q^{89} - 6 q^{90} - 2 q^{91} + 4 q^{92} - 12 q^{93} - 2 q^{95} - 28 q^{97} - 12 q^{98} + 12 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^4 - 2 * q^5 + 2 * q^7 + 2 * q^8 + 6 * q^9 - 2 * q^10 + 4 * q^11 - 2 * q^13 + 2 * q^14 + 2 * q^16 + 6 * q^18 + 2 * q^19 - 2 * q^20 + 4 * q^22 + 4 * q^23 + 2 * q^25 - 2 * q^26 + 2 * q^28 + 14 * q^29 - 6 * q^31 + 2 * q^32 - 12 * q^33 - 2 * q^35 + 6 * q^36 - 4 * q^37 + 2 * q^38 - 2 * q^40 - 14 * q^41 - 2 * q^43 + 4 * q^44 - 6 * q^45 + 4 * q^46 - 12 * q^49 + 2 * q^50 - 12 * q^51 - 2 * q^52 + 8 * q^53 - 4 * q^55 + 2 * q^56 - 24 * q^57 + 14 * q^58 - 2 * q^61 - 6 * q^62 + 6 * q^63 + 2 * q^64 + 2 * q^65 - 12 * q^66 - 6 * q^67 + 12 * q^69 - 2 * q^70 + 12 * q^71 + 6 * q^72 - 10 * q^73 - 4 * q^74 + 2 * q^76 + 4 * q^77 + 18 * q^79 - 2 * q^80 - 18 * q^81 - 14 * q^82 + 12 * q^83 - 2 * q^86 - 12 * q^87 + 4 * q^88 + 12 * q^89 - 6 * q^90 - 2 * q^91 + 4 * q^92 - 12 * q^93 - 2 * q^95 - 28 * q^97 - 12 * q^98 + 12 * q^99

Introduction

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