LMFDB - Embedded newform 770.2.a.k.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(1,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("770.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{33}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 8 $ x^2 - x - 8
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-2.37228$ of defining polynomial
Character	$\chi$	$=$	770.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{11} +2.00000 q^{12} +6.74456 q^{13} +1.00000 q^{14} +2.00000 q^{15} +1.00000 q^{16} -6.74456 q^{17} +1.00000 q^{18} -6.74456 q^{19} +1.00000 q^{20} +2.00000 q^{21} -1.00000 q^{22} -6.74456 q^{23} +2.00000 q^{24} +1.00000 q^{25} +6.74456 q^{26} -4.00000 q^{27} +1.00000 q^{28} +8.74456 q^{29} +2.00000 q^{30} +4.74456 q^{31} +1.00000 q^{32} -2.00000 q^{33} -6.74456 q^{34} +1.00000 q^{35} +1.00000 q^{36} +0.744563 q^{37} -6.74456 q^{38} +13.4891 q^{39} +1.00000 q^{40} -4.00000 q^{41} +2.00000 q^{42} +4.00000 q^{43} -1.00000 q^{44} +1.00000 q^{45} -6.74456 q^{46} +4.74456 q^{47} +2.00000 q^{48} +1.00000 q^{49} +1.00000 q^{50} -13.4891 q^{51} +6.74456 q^{52} -12.7446 q^{53} -4.00000 q^{54} -1.00000 q^{55} +1.00000 q^{56} -13.4891 q^{57} +8.74456 q^{58} -8.74456 q^{59} +2.00000 q^{60} +1.25544 q^{61} +4.74456 q^{62} +1.00000 q^{63} +1.00000 q^{64} +6.74456 q^{65} -2.00000 q^{66} -4.00000 q^{67} -6.74456 q^{68} -13.4891 q^{69} +1.00000 q^{70} -4.00000 q^{71} +1.00000 q^{72} +10.7446 q^{73} +0.744563 q^{74} +2.00000 q^{75} -6.74456 q^{76} -1.00000 q^{77} +13.4891 q^{78} +6.74456 q^{79} +1.00000 q^{80} -11.0000 q^{81} -4.00000 q^{82} +8.00000 q^{83} +2.00000 q^{84} -6.74456 q^{85} +4.00000 q^{86} +17.4891 q^{87} -1.00000 q^{88} +15.4891 q^{89} +1.00000 q^{90} +6.74456 q^{91} -6.74456 q^{92} +9.48913 q^{93} +4.74456 q^{94} -6.74456 q^{95} +2.00000 q^{96} -16.7446 q^{97} +1.00000 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 4 q^{3} + 2 q^{4} + 2 q^{5} + 4 q^{6} + 2 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + 4 * q^3 + 2 * q^4 + 2 * q^5 + 4 * q^6 + 2 * q^7 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} + 4 q^{3} + 2 q^{4} + 2 q^{5} + 4 q^{6} + 2 q^{7} + 2 q^{8} + 2 q^{9} + 2 q^{10} - 2 q^{11} + 4 q^{12} + 2 q^{13} + 2 q^{14} + 4 q^{15} + 2 q^{16} - 2 q^{17} + 2 q^{18} - 2 q^{19} + 2 q^{20} + 4 q^{21} - 2 q^{22} - 2 q^{23} + 4 q^{24} + 2 q^{25} + 2 q^{26} - 8 q^{27} + 2 q^{28} + 6 q^{29} + 4 q^{30} - 2 q^{31} + 2 q^{32} - 4 q^{33} - 2 q^{34} + 2 q^{35} + 2 q^{36} - 10 q^{37} - 2 q^{38} + 4 q^{39} + 2 q^{40} - 8 q^{41} + 4 q^{42} + 8 q^{43} - 2 q^{44} + 2 q^{45} - 2 q^{46} - 2 q^{47} + 4 q^{48} + 2 q^{49} + 2 q^{50} - 4 q^{51} + 2 q^{52} - 14 q^{53} - 8 q^{54} - 2 q^{55} + 2 q^{56} - 4 q^{57} + 6 q^{58} - 6 q^{59} + 4 q^{60} + 14 q^{61} - 2 q^{62} + 2 q^{63} + 2 q^{64} + 2 q^{65} - 4 q^{66} - 8 q^{67} - 2 q^{68} - 4 q^{69} + 2 q^{70} - 8 q^{71} + 2 q^{72} + 10 q^{73} - 10 q^{74} + 4 q^{75} - 2 q^{76} - 2 q^{77} + 4 q^{78} + 2 q^{79} + 2 q^{80} - 22 q^{81} - 8 q^{82} + 16 q^{83} + 4 q^{84} - 2 q^{85} + 8 q^{86} + 12 q^{87} - 2 q^{88} + 8 q^{89} + 2 q^{90} + 2 q^{91} - 2 q^{92} - 4 q^{93} - 2 q^{94} - 2 q^{95} + 4 q^{96} - 22 q^{97} + 2 q^{98} - 2 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 4 * q^3 + 2 * q^4 + 2 * q^5 + 4 * q^6 + 2 * q^7 + 2 * q^8 + 2 * q^9 + 2 * q^10 - 2 * q^11 + 4 * q^12 + 2 * q^13 + 2 * q^14 + 4 * q^15 + 2 * q^16 - 2 * q^17 + 2 * q^18 - 2 * q^19 + 2 * q^20 + 4 * q^21 - 2 * q^22 - 2 * q^23 + 4 * q^24 + 2 * q^25 + 2 * q^26 - 8 * q^27 + 2 * q^28 + 6 * q^29 + 4 * q^30 - 2 * q^31 + 2 * q^32 - 4 * q^33 - 2 * q^34 + 2 * q^35 + 2 * q^36 - 10 * q^37 - 2 * q^38 + 4 * q^39 + 2 * q^40 - 8 * q^41 + 4 * q^42 + 8 * q^43 - 2 * q^44 + 2 * q^45 - 2 * q^46 - 2 * q^47 + 4 * q^48 + 2 * q^49 + 2 * q^50 - 4 * q^51 + 2 * q^52 - 14 * q^53 - 8 * q^54 - 2 * q^55 + 2 * q^56 - 4 * q^57 + 6 * q^58 - 6 * q^59 + 4 * q^60 + 14 * q^61 - 2 * q^62 + 2 * q^63 + 2 * q^64 + 2 * q^65 - 4 * q^66 - 8 * q^67 - 2 * q^68 - 4 * q^69 + 2 * q^70 - 8 * q^71 + 2 * q^72 + 10 * q^73 - 10 * q^74 + 4 * q^75 - 2 * q^76 - 2 * q^77 + 4 * q^78 + 2 * q^79 + 2 * q^80 - 22 * q^81 - 8 * q^82 + 16 * q^83 + 4 * q^84 - 2 * q^85 + 8 * q^86 + 12 * q^87 - 2 * q^88 + 8 * q^89 + 2 * q^90 + 2 * q^91 - 2 * q^92 - 4 * q^93 - 2 * q^94 - 2 * q^95 + 4 * q^96 - 22 * q^97 + 2 * q^98 - 2 * 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
$3$	2.00000	1.15470	0.577350	−	0.816497i	$-0.304087\pi$
$3$	2.00000	1.15470	0.577350	+	0.816497i	$0.304087\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.00000	0.816497
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	2.00000	0.577350
$13$	6.74456	1.87061	0.935303	−	0.353849i	$-0.115127\pi$
$13$	6.74456	1.87061	0.935303	+	0.353849i	$0.115127\pi$
$14$	1.00000	0.267261
$15$	2.00000	0.516398
$16$	1.00000	0.250000
$17$	−6.74456	−1.63580	−0.817898	−	0.575363i	$-0.804861\pi$
$17$	−6.74456	−1.63580	−0.817898	+	0.575363i	$0.804861\pi$
$18$	1.00000	0.235702
$19$	−6.74456	−1.54731	−0.773654	−	0.633608i	$-0.781573\pi$
$19$	−6.74456	−1.54731	−0.773654	+	0.633608i	$0.781573\pi$
$20$	1.00000	0.223607
$21$	2.00000	0.436436
$22$	−1.00000	−0.213201
$23$	−6.74456	−1.40634	−0.703169	−	0.711022i	$-0.748232\pi$
$23$	−6.74456	−1.40634	−0.703169	+	0.711022i	$0.748232\pi$
$24$	2.00000	0.408248
$25$	1.00000	0.200000
$26$	6.74456	1.32272
$27$	−4.00000	−0.769800
$28$	1.00000	0.188982
$29$	8.74456	1.62382	0.811912	−	0.583779i	$-0.198427\pi$
$29$	8.74456	1.62382	0.811912	+	0.583779i	$0.198427\pi$
$30$	2.00000	0.365148
$31$	4.74456	0.852149	0.426074	−	0.904688i	$-0.359896\pi$
$31$	4.74456	0.852149	0.426074	+	0.904688i	$0.359896\pi$
$32$	1.00000	0.176777
$33$	−2.00000	−0.348155
$34$	−6.74456	−1.15668
$35$	1.00000	0.169031
$36$	1.00000	0.166667
$37$	0.744563	0.122405	0.0612027	−	0.998125i	$-0.480506\pi$
$37$	0.744563	0.122405	0.0612027	+	0.998125i	$0.480506\pi$
$38$	−6.74456	−1.09411
$39$	13.4891	2.15999
$40$	1.00000	0.158114
$41$	−4.00000	−0.624695	−0.312348	−	0.949968i	$-0.601115\pi$
$41$	−4.00000	−0.624695	−0.312348	+	0.949968i	$0.601115\pi$
$42$	2.00000	0.308607
$43$	4.00000	0.609994	0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000	0.609994	0.304997	+	0.952353i	$0.401344\pi$
$44$	−1.00000	−0.150756
$45$	1.00000	0.149071
$46$	−6.74456	−0.994432
$47$	4.74456	0.692066	0.346033	−	0.938222i	$-0.387529\pi$
$47$	4.74456	0.692066	0.346033	+	0.938222i	$0.387529\pi$
$48$	2.00000	0.288675
$49$	1.00000	0.142857
$50$	1.00000	0.141421
$51$	−13.4891	−1.88886
$52$	6.74456	0.935303
$53$	−12.7446	−1.75060	−0.875300	−	0.483580i	$-0.839336\pi$
$53$	−12.7446	−1.75060	−0.875300	+	0.483580i	$0.839336\pi$
$54$	−4.00000	−0.544331
$55$	−1.00000	−0.134840
$56$	1.00000	0.133631
$57$	−13.4891	−1.78668
$58$	8.74456	1.14822
$59$	−8.74456	−1.13845	−0.569223	−	0.822183i	$-0.692756\pi$
$59$	−8.74456	−1.13845	−0.569223	+	0.822183i	$0.692756\pi$
$60$	2.00000	0.258199
$61$	1.25544	0.160742	0.0803711	−	0.996765i	$-0.474389\pi$
$61$	1.25544	0.160742	0.0803711	+	0.996765i	$0.474389\pi$
$62$	4.74456	0.602560
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	6.74456	0.836560
$66$	−2.00000	−0.246183
$67$	−4.00000	−0.488678	−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000	−0.488678	−0.244339	+	0.969690i	$0.578571\pi$
$68$	−6.74456	−0.817898
$69$	−13.4891	−1.62390
$70$	1.00000	0.119523
$71$	−4.00000	−0.474713	−0.237356	−	0.971423i	$-0.576281\pi$
$71$	−4.00000	−0.474713	−0.237356	+	0.971423i	$0.576281\pi$
$72$	1.00000	0.117851
$73$	10.7446	1.25756	0.628778	−	0.777585i	$-0.283555\pi$
$73$	10.7446	1.25756	0.628778	+	0.777585i	$0.283555\pi$
$74$	0.744563	0.0865536
$75$	2.00000	0.230940
$76$	−6.74456	−0.773654
$77$	−1.00000	−0.113961
$78$	13.4891	1.52734
$79$	6.74456	0.758823	0.379411	−	0.925228i	$-0.376127\pi$
$79$	6.74456	0.758823	0.379411	+	0.925228i	$0.376127\pi$
$80$	1.00000	0.111803
$81$	−11.0000	−1.22222
$82$	−4.00000	−0.441726
$83$	8.00000	0.878114	0.439057	−	0.898459i	$-0.355313\pi$
$83$	8.00000	0.878114	0.439057	+	0.898459i	$0.355313\pi$
$84$	2.00000	0.218218
$85$	−6.74456	−0.731551
$86$	4.00000	0.431331
$87$	17.4891	1.87503
$88$	−1.00000	−0.106600
$89$	15.4891	1.64184	0.820922	−	0.571040i	$-0.193460\pi$
$89$	15.4891	1.64184	0.820922	+	0.571040i	$0.193460\pi$
$90$	1.00000	0.105409
$91$	6.74456	0.707022
$92$	−6.74456	−0.703169
$93$	9.48913	0.983976
$94$	4.74456	0.489364
$95$	−6.74456	−0.691978
$96$	2.00000	0.204124
$97$	−16.7446	−1.70015	−0.850076	−	0.526659i	$-0.823444\pi$
$97$	−16.7446	−1.70015	−0.850076	+	0.526659i	$0.823444\pi$
$98$	1.00000	0.101015
$99$	−1.00000	−0.100504
$100$	1.00000	0.100000
$101$	2.74456	0.273094	0.136547	−	0.990634i	$-0.456399\pi$
$101$	2.74456	0.273094	0.136547	+	0.990634i	$0.456399\pi$
$102$	−13.4891	−1.33562
$103$	−0.744563	−0.0733639	−0.0366820	−	0.999327i	$-0.511679\pi$
$103$	−0.744563	−0.0733639	−0.0366820	+	0.999327i	$0.511679\pi$
$104$	6.74456	0.661359
$105$	2.00000	0.195180
$106$	−12.7446	−1.23786
$107$	−12.0000	−1.16008	−0.580042	−	0.814587i	$-0.696964\pi$
$107$	−12.0000	−1.16008	−0.580042	+	0.814587i	$0.696964\pi$
$108$	−4.00000	−0.384900
$109$	−18.2337	−1.74647	−0.873235	−	0.487299i	$-0.837982\pi$
$109$	−18.2337	−1.74647	−0.873235	+	0.487299i	$0.837982\pi$
$110$	−1.00000	−0.0953463
$111$	1.48913	0.141342
$112$	1.00000	0.0944911
$113$	10.0000	0.940721	0.470360	−	0.882474i	$-0.344124\pi$
$113$	10.0000	0.940721	0.470360	+	0.882474i	$0.344124\pi$
$114$	−13.4891	−1.26337
$115$	−6.74456	−0.628934
$116$	8.74456	0.811912
$117$	6.74456	0.623535
$118$	−8.74456	−0.805002
$119$	−6.74456	−0.618273
$120$	2.00000	0.182574
$121$	1.00000	0.0909091
$122$	1.25544	0.113662
$123$	−8.00000	−0.721336
$124$	4.74456	0.426074
$125$	1.00000	0.0894427
$126$	1.00000	0.0890871
$127$	0	0		−	1.00000i	$-0.5\pi$
$127$	0	0			1.00000i	$0.5\pi$
$128$	1.00000	0.0883883
$129$	8.00000	0.704361
$130$	6.74456	0.591537
$131$	−2.74456	−0.239794	−0.119897	−	0.992786i	$-0.538256\pi$
$131$	−2.74456	−0.239794	−0.119897	+	0.992786i	$0.538256\pi$
$132$	−2.00000	−0.174078
$133$	−6.74456	−0.584828
$134$	−4.00000	−0.345547
$135$	−4.00000	−0.344265
$136$	−6.74456	−0.578341
$137$	3.48913	0.298096	0.149048	−	0.988830i	$-0.452379\pi$
$137$	3.48913	0.298096	0.149048	+	0.988830i	$0.452379\pi$
$138$	−13.4891	−1.14827
$139$	14.7446	1.25062	0.625309	−	0.780377i	$-0.284973\pi$
$139$	14.7446	1.25062	0.625309	+	0.780377i	$0.284973\pi$
$140$	1.00000	0.0845154
$141$	9.48913	0.799129
$142$	−4.00000	−0.335673
$143$	−6.74456	−0.564009
$144$	1.00000	0.0833333
$145$	8.74456	0.726196
$146$	10.7446	0.889226
$147$	2.00000	0.164957
$148$	0.744563	0.0612027
$149$	−0.744563	−0.0609969	−0.0304985	−	0.999535i	$-0.509709\pi$
$149$	−0.744563	−0.0609969	−0.0304985	+	0.999535i	$0.509709\pi$
$150$	2.00000	0.163299
$151$	−9.25544	−0.753197	−0.376598	−	0.926377i	$-0.622906\pi$
$151$	−9.25544	−0.753197	−0.376598	+	0.926377i	$0.622906\pi$
$152$	−6.74456	−0.547056
$153$	−6.74456	−0.545266
$154$	−1.00000	−0.0805823
$155$	4.74456	0.381092
$156$	13.4891	1.07999
$157$	0.510875	0.0407722	0.0203861	−	0.999792i	$-0.493510\pi$
$157$	0.510875	0.0407722	0.0203861	+	0.999792i	$0.493510\pi$
$158$	6.74456	0.536569
$159$	−25.4891	−2.02142
$160$	1.00000	0.0790569
$161$	−6.74456	−0.531546
$162$	−11.0000	−0.864242
$163$	−4.00000	−0.313304	−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000	−0.313304	−0.156652	+	0.987654i	$0.550070\pi$
$164$	−4.00000	−0.312348
$165$	−2.00000	−0.155700
$166$	8.00000	0.620920
$167$	0	0		−	1.00000i	$-0.5\pi$
$167$	0	0			1.00000i	$0.5\pi$
$168$	2.00000	0.154303
$169$	32.4891	2.49916
$170$	−6.74456	−0.517284
$171$	−6.74456	−0.515770
$172$	4.00000	0.304997
$173$	20.2337	1.53834	0.769169	−	0.639045i	$-0.220670\pi$
$173$	20.2337	1.53834	0.769169	+	0.639045i	$0.220670\pi$
$174$	17.4891	1.32585
$175$	1.00000	0.0755929
$176$	−1.00000	−0.0753778
$177$	−17.4891	−1.31456
$178$	15.4891	1.16096
$179$	−4.00000	−0.298974	−0.149487	−	0.988764i	$-0.547762\pi$
$179$	−4.00000	−0.298974	−0.149487	+	0.988764i	$0.547762\pi$
$180$	1.00000	0.0745356
$181$	−19.4891	−1.44862	−0.724308	−	0.689477i	$-0.757840\pi$
$181$	−19.4891	−1.44862	−0.724308	+	0.689477i	$0.757840\pi$
$182$	6.74456	0.499940
$183$	2.51087	0.185609
$184$	−6.74456	−0.497216
$185$	0.744563	0.0547413
$186$	9.48913	0.695776
$187$	6.74456	0.493211
$188$	4.74456	0.346033
$189$	−4.00000	−0.290957
$190$	−6.74456	−0.489302
$191$	−16.0000	−1.15772	−0.578860	−	0.815427i	$-0.696502\pi$
$191$	−16.0000	−1.15772	−0.578860	+	0.815427i	$0.696502\pi$
$192$	2.00000	0.144338
$193$	−2.00000	−0.143963	−0.0719816	−	0.997406i	$-0.522932\pi$
$193$	−2.00000	−0.143963	−0.0719816	+	0.997406i	$0.522932\pi$
$194$	−16.7446	−1.20219
$195$	13.4891	0.965976
$196$	1.00000	0.0714286
$197$	10.0000	0.712470	0.356235	−	0.934396i	$-0.384060\pi$
$197$	10.0000	0.712470	0.356235	+	0.934396i	$0.384060\pi$
$198$	−1.00000	−0.0710669
$199$	3.25544	0.230772	0.115386	−	0.993321i	$-0.463190\pi$
$199$	3.25544	0.230772	0.115386	+	0.993321i	$0.463190\pi$
$200$	1.00000	0.0707107
$201$	−8.00000	−0.564276
$202$	2.74456	0.193107
$203$	8.74456	0.613748
$204$	−13.4891	−0.944428
$205$	−4.00000	−0.279372
$206$	−0.744563	−0.0518761
$207$	−6.74456	−0.468780
$208$	6.74456	0.467651
$209$	6.74456	0.466531
$210$	2.00000	0.138013
$211$	−12.0000	−0.826114	−0.413057	−	0.910705i	$-0.635539\pi$
$211$	−12.0000	−0.826114	−0.413057	+	0.910705i	$0.635539\pi$
$212$	−12.7446	−0.875300
$213$	−8.00000	−0.548151
$214$	−12.0000	−0.820303
$215$	4.00000	0.272798
$216$	−4.00000	−0.272166
$217$	4.74456	0.322082
$218$	−18.2337	−1.23494
$219$	21.4891	1.45210
$220$	−1.00000	−0.0674200
$221$	−45.4891	−3.05993
$222$	1.48913	0.0999435
$223$	15.2554	1.02158	0.510790	−	0.859706i	$-0.329353\pi$
$223$	15.2554	1.02158	0.510790	+	0.859706i	$0.329353\pi$
$224$	1.00000	0.0668153
$225$	1.00000	0.0666667
$226$	10.0000	0.665190
$227$	20.0000	1.32745	0.663723	−	0.747978i	$-0.268975\pi$
$227$	20.0000	1.32745	0.663723	+	0.747978i	$0.268975\pi$
$228$	−13.4891	−0.893339
$229$	−6.00000	−0.396491	−0.198246	−	0.980152i	$-0.563524\pi$
$229$	−6.00000	−0.396491	−0.198246	+	0.980152i	$0.563524\pi$
$230$	−6.74456	−0.444723
$231$	−2.00000	−0.131590
$232$	8.74456	0.574109
$233$	−24.9783	−1.63638	−0.818190	−	0.574948i	$-0.805022\pi$
$233$	−24.9783	−1.63638	−0.818190	+	0.574948i	$0.805022\pi$
$234$	6.74456	0.440906
$235$	4.74456	0.309501
$236$	−8.74456	−0.569223
$237$	13.4891	0.876213
$238$	−6.74456	−0.437185
$239$	−14.7446	−0.953746	−0.476873	−	0.878972i	$-0.658230\pi$
$239$	−14.7446	−0.953746	−0.476873	+	0.878972i	$0.658230\pi$
$240$	2.00000	0.129099
$241$	20.0000	1.28831	0.644157	−	0.764894i	$-0.277208\pi$
$241$	20.0000	1.28831	0.644157	+	0.764894i	$0.277208\pi$
$242$	1.00000	0.0642824
$243$	−10.0000	−0.641500
$244$	1.25544	0.0803711
$245$	1.00000	0.0638877
$246$	−8.00000	−0.510061
$247$	−45.4891	−2.89440
$248$	4.74456	0.301280
$249$	16.0000	1.01396
$250$	1.00000	0.0632456
$251$	−26.2337	−1.65586	−0.827928	−	0.560835i	$-0.810480\pi$
$251$	−26.2337	−1.65586	−0.827928	+	0.560835i	$0.810480\pi$
$252$	1.00000	0.0629941
$253$	6.74456	0.424027
$254$	0	0
$255$	−13.4891	−0.844722
$256$	1.00000	0.0625000
$257$	−10.2337	−0.638360	−0.319180	−	0.947694i	$-0.603407\pi$
$257$	−10.2337	−0.638360	−0.319180	+	0.947694i	$0.603407\pi$
$258$	8.00000	0.498058
$259$	0.744563	0.0462649
$260$	6.74456	0.418280
$261$	8.74456	0.541275
$262$	−2.74456	−0.169560
$263$	26.9783	1.66355	0.831775	−	0.555113i	$-0.187325\pi$
$263$	26.9783	1.66355	0.831775	+	0.555113i	$0.187325\pi$
$264$	−2.00000	−0.123091
$265$	−12.7446	−0.782892
$266$	−6.74456	−0.413536
$267$	30.9783	1.89584
$268$	−4.00000	−0.244339
$269$	20.9783	1.27907	0.639533	−	0.768763i	$-0.279128\pi$
$269$	20.9783	1.27907	0.639533	+	0.768763i	$0.279128\pi$
$270$	−4.00000	−0.243432
$271$	14.9783	0.909864	0.454932	−	0.890526i	$-0.349664\pi$
$271$	14.9783	0.909864	0.454932	+	0.890526i	$0.349664\pi$
$272$	−6.74456	−0.408949
$273$	13.4891	0.816399
$274$	3.48913	0.210786
$275$	−1.00000	−0.0603023
$276$	−13.4891	−0.811950
$277$	15.4891	0.930651	0.465326	−	0.885140i	$-0.345937\pi$
$277$	15.4891	0.930651	0.465326	+	0.885140i	$0.345937\pi$
$278$	14.7446	0.884320
$279$	4.74456	0.284050
$280$	1.00000	0.0597614
$281$	14.0000	0.835170	0.417585	−	0.908638i	$-0.362877\pi$
$281$	14.0000	0.835170	0.417585	+	0.908638i	$0.362877\pi$
$282$	9.48913	0.565069
$283$	28.0000	1.66443	0.832214	−	0.554455i	$-0.187073\pi$
$283$	28.0000	1.66443	0.832214	+	0.554455i	$0.187073\pi$
$284$	−4.00000	−0.237356
$285$	−13.4891	−0.799027
$286$	−6.74456	−0.398814
$287$	−4.00000	−0.236113
$288$	1.00000	0.0589256
$289$	28.4891	1.67583
$290$	8.74456	0.513498
$291$	−33.4891	−1.96317
$292$	10.7446	0.628778
$293$	13.2554	0.774391	0.387195	−	0.921998i	$-0.373444\pi$
$293$	13.2554	0.774391	0.387195	+	0.921998i	$0.373444\pi$
$294$	2.00000	0.116642
$295$	−8.74456	−0.509128
$296$	0.744563	0.0432768
$297$	4.00000	0.232104
$298$	−0.744563	−0.0431314
$299$	−45.4891	−2.63070
$300$	2.00000	0.115470
$301$	4.00000	0.230556
$302$	−9.25544	−0.532591
$303$	5.48913	0.315342
$304$	−6.74456	−0.386827
$305$	1.25544	0.0718861
$306$	−6.74456	−0.385561
$307$	−1.48913	−0.0849889	−0.0424944	−	0.999097i	$-0.513530\pi$
$307$	−1.48913	−0.0849889	−0.0424944	+	0.999097i	$0.513530\pi$
$308$	−1.00000	−0.0569803
$309$	−1.48913	−0.0847134
$310$	4.74456	0.269473
$311$	−20.7446	−1.17632	−0.588158	−	0.808746i	$-0.700147\pi$
$311$	−20.7446	−1.17632	−0.588158	+	0.808746i	$0.700147\pi$
$312$	13.4891	0.763671
$313$	−2.23369	−0.126256	−0.0631278	−	0.998005i	$-0.520108\pi$
$313$	−2.23369	−0.126256	−0.0631278	+	0.998005i	$0.520108\pi$
$314$	0.510875	0.0288303
$315$	1.00000	0.0563436
$316$	6.74456	0.379411
$317$	2.23369	0.125456	0.0627282	−	0.998031i	$-0.480020\pi$
$317$	2.23369	0.125456	0.0627282	+	0.998031i	$0.480020\pi$
$318$	−25.4891	−1.42936
$319$	−8.74456	−0.489602
$320$	1.00000	0.0559017
$321$	−24.0000	−1.33955
$322$	−6.74456	−0.375860
$323$	45.4891	2.53108
$324$	−11.0000	−0.611111
$325$	6.74456	0.374121
$326$	−4.00000	−0.221540
$327$	−36.4674	−2.01665
$328$	−4.00000	−0.220863
$329$	4.74456	0.261576
$330$	−2.00000	−0.110096
$331$	14.9783	0.823279	0.411640	−	0.911347i	$-0.364956\pi$
$331$	14.9783	0.823279	0.411640	+	0.911347i	$0.364956\pi$
$332$	8.00000	0.439057
$333$	0.744563	0.0408018
$334$	0	0
$335$	−4.00000	−0.218543
$336$	2.00000	0.109109
$337$	26.0000	1.41631	0.708155	−	0.706057i	$-0.249528\pi$
$337$	26.0000	1.41631	0.708155	+	0.706057i	$0.249528\pi$
$338$	32.4891	1.76718
$339$	20.0000	1.08625
$340$	−6.74456	−0.365775
$341$	−4.74456	−0.256932
$342$	−6.74456	−0.364704
$343$	1.00000	0.0539949
$344$	4.00000	0.215666
$345$	−13.4891	−0.726230
$346$	20.2337	1.08777
$347$	−22.9783	−1.23354	−0.616769	−	0.787145i	$-0.711559\pi$
$347$	−22.9783	−1.23354	−0.616769	+	0.787145i	$0.711559\pi$
$348$	17.4891	0.937516
$349$	30.7446	1.64572	0.822859	−	0.568245i	$-0.192377\pi$
$349$	30.7446	1.64572	0.822859	+	0.568245i	$0.192377\pi$
$350$	1.00000	0.0534522
$351$	−26.9783	−1.43999
$352$	−1.00000	−0.0533002
$353$	8.74456	0.465426	0.232713	−	0.972545i	$-0.425240\pi$
$353$	8.74456	0.465426	0.232713	+	0.972545i	$0.425240\pi$
$354$	−17.4891	−0.929537
$355$	−4.00000	−0.212298
$356$	15.4891	0.820922
$357$	−13.4891	−0.713920
$358$	−4.00000	−0.211407
$359$	−1.25544	−0.0662594	−0.0331297	−	0.999451i	$-0.510547\pi$
$359$	−1.25544	−0.0662594	−0.0331297	+	0.999451i	$0.510547\pi$
$360$	1.00000	0.0527046
$361$	26.4891	1.39416
$362$	−19.4891	−1.02433
$363$	2.00000	0.104973
$364$	6.74456	0.353511
$365$	10.7446	0.562396
$366$	2.51087	0.131246
$367$	−8.74456	−0.456462	−0.228231	−	0.973607i	$-0.573294\pi$
$367$	−8.74456	−0.456462	−0.228231	+	0.973607i	$0.573294\pi$
$368$	−6.74456	−0.351585
$369$	−4.00000	−0.208232
$370$	0.744563	0.0387080
$371$	−12.7446	−0.661665
$372$	9.48913	0.491988
$373$	−16.9783	−0.879100	−0.439550	−	0.898218i	$-0.644862\pi$
$373$	−16.9783	−0.879100	−0.439550	+	0.898218i	$0.644862\pi$
$374$	6.74456	0.348753
$375$	2.00000	0.103280
$376$	4.74456	0.244682
$377$	58.9783	3.03753
$378$	−4.00000	−0.205738
$379$	−37.4891	−1.92569	−0.962844	−	0.270060i	$-0.912956\pi$
$379$	−37.4891	−1.92569	−0.962844	+	0.270060i	$0.912956\pi$
$380$	−6.74456	−0.345989
$381$	0	0
$382$	−16.0000	−0.818631
$383$	19.7228	1.00779	0.503894	−	0.863765i	$-0.331900\pi$
$383$	19.7228	1.00779	0.503894	+	0.863765i	$0.331900\pi$
$384$	2.00000	0.102062
$385$	−1.00000	−0.0509647
$386$	−2.00000	−0.101797
$387$	4.00000	0.203331
$388$	−16.7446	−0.850076
$389$	−7.48913	−0.379714	−0.189857	−	0.981812i	$-0.560802\pi$
$389$	−7.48913	−0.379714	−0.189857	+	0.981812i	$0.560802\pi$
$390$	13.4891	0.683048
$391$	45.4891	2.30048
$392$	1.00000	0.0505076
$393$	−5.48913	−0.276890
$394$	10.0000	0.503793
$395$	6.74456	0.339356
$396$	−1.00000	−0.0502519
$397$	35.4891	1.78115	0.890574	−	0.454838i	$-0.150303\pi$
$397$	35.4891	1.78115	0.890574	+	0.454838i	$0.150303\pi$
$398$	3.25544	0.163180
$399$	−13.4891	−0.675301
$400$	1.00000	0.0500000
$401$	23.4891	1.17299	0.586495	−	0.809953i	$-0.300507\pi$
$401$	23.4891	1.17299	0.586495	+	0.809953i	$0.300507\pi$
$402$	−8.00000	−0.399004
$403$	32.0000	1.59403
$404$	2.74456	0.136547
$405$	−11.0000	−0.546594
$406$	8.74456	0.433985
$407$	−0.744563	−0.0369066
$408$	−13.4891	−0.667811
$409$	−21.4891	−1.06257	−0.531284	−	0.847194i	$-0.678290\pi$
$409$	−21.4891	−1.06257	−0.531284	+	0.847194i	$0.678290\pi$
$410$	−4.00000	−0.197546
$411$	6.97825	0.344212
$412$	−0.744563	−0.0366820
$413$	−8.74456	−0.430292
$414$	−6.74456	−0.331477
$415$	8.00000	0.392705
$416$	6.74456	0.330679
$417$	29.4891	1.44409
$418$	6.74456	0.329887
$419$	−0.744563	−0.0363743	−0.0181871	−	0.999835i	$-0.505789\pi$
$419$	−0.744563	−0.0363743	−0.0181871	+	0.999835i	$0.505789\pi$
$420$	2.00000	0.0975900
$421$	4.51087	0.219847	0.109923	−	0.993940i	$-0.464939\pi$
$421$	4.51087	0.219847	0.109923	+	0.993940i	$0.464939\pi$
$422$	−12.0000	−0.584151
$423$	4.74456	0.230689
$424$	−12.7446	−0.618931
$425$	−6.74456	−0.327159
$426$	−8.00000	−0.387601
$427$	1.25544	0.0607549
$428$	−12.0000	−0.580042
$429$	−13.4891	−0.651261
$430$	4.00000	0.192897
$431$	−17.2554	−0.831165	−0.415583	−	0.909555i	$-0.636422\pi$
$431$	−17.2554	−0.831165	−0.415583	+	0.909555i	$0.636422\pi$
$432$	−4.00000	−0.192450
$433$	36.7446	1.76583	0.882915	−	0.469532i	$-0.155577\pi$
$433$	36.7446	1.76583	0.882915	+	0.469532i	$0.155577\pi$
$434$	4.74456	0.227746
$435$	17.4891	0.838539
$436$	−18.2337	−0.873235
$437$	45.4891	2.17604
$438$	21.4891	1.02679
$439$	14.9783	0.714873	0.357436	−	0.933937i	$-0.383651\pi$
$439$	14.9783	0.714873	0.357436	+	0.933937i	$0.383651\pi$
$440$	−1.00000	−0.0476731
$441$	1.00000	0.0476190
$442$	−45.4891	−2.16370
$443$	−29.4891	−1.40107	−0.700535	−	0.713618i	$-0.747055\pi$
$443$	−29.4891	−1.40107	−0.700535	+	0.713618i	$0.747055\pi$
$444$	1.48913	0.0706708
$445$	15.4891	0.734255
$446$	15.2554	0.722366
$447$	−1.48913	−0.0704332
$448$	1.00000	0.0472456
$449$	−4.97825	−0.234938	−0.117469	−	0.993077i	$-0.537478\pi$
$449$	−4.97825	−0.234938	−0.117469	+	0.993077i	$0.537478\pi$
$450$	1.00000	0.0471405
$451$	4.00000	0.188353
$452$	10.0000	0.470360
$453$	−18.5109	−0.869717
$454$	20.0000	0.938647
$455$	6.74456	0.316190
$456$	−13.4891	−0.631686
$457$	3.48913	0.163214	0.0816072	−	0.996665i	$-0.473995\pi$
$457$	3.48913	0.163214	0.0816072	+	0.996665i	$0.473995\pi$
$458$	−6.00000	−0.280362
$459$	26.9783	1.25924
$460$	−6.74456	−0.314467
$461$	33.7228	1.57063	0.785314	−	0.619098i	$-0.212502\pi$
$461$	33.7228	1.57063	0.785314	+	0.619098i	$0.212502\pi$
$462$	−2.00000	−0.0930484
$463$	1.25544	0.0583451	0.0291726	−	0.999574i	$-0.490713\pi$
$463$	1.25544	0.0583451	0.0291726	+	0.999574i	$0.490713\pi$
$464$	8.74456	0.405956
$465$	9.48913	0.440048
$466$	−24.9783	−1.15710
$467$	16.9783	0.785660	0.392830	−	0.919611i	$-0.371496\pi$
$467$	16.9783	0.785660	0.392830	+	0.919611i	$0.371496\pi$
$468$	6.74456	0.311768
$469$	−4.00000	−0.184703
$470$	4.74456	0.218850
$471$	1.02175	0.0470797
$472$	−8.74456	−0.402501
$473$	−4.00000	−0.183920
$474$	13.4891	0.619576
$475$	−6.74456	−0.309462
$476$	−6.74456	−0.309137
$477$	−12.7446	−0.583533
$478$	−14.7446	−0.674401
$479$	−41.4891	−1.89569	−0.947843	−	0.318737i	$-0.896741\pi$
$479$	−41.4891	−1.89569	−0.947843	+	0.318737i	$0.896741\pi$
$480$	2.00000	0.0912871
$481$	5.02175	0.228972
$482$	20.0000	0.910975
$483$	−13.4891	−0.613776
$484$	1.00000	0.0454545
$485$	−16.7446	−0.760331
$486$	−10.0000	−0.453609
$487$	9.25544	0.419404	0.209702	−	0.977765i	$-0.432751\pi$
$487$	9.25544	0.419404	0.209702	+	0.977765i	$0.432751\pi$
$488$	1.25544	0.0568310
$489$	−8.00000	−0.361773
$490$	1.00000	0.0451754
$491$	30.9783	1.39803	0.699014	−	0.715108i	$-0.253622\pi$
$491$	30.9783	1.39803	0.699014	+	0.715108i	$0.253622\pi$
$492$	−8.00000	−0.360668
$493$	−58.9783	−2.65625
$494$	−45.4891	−2.04665
$495$	−1.00000	−0.0449467
$496$	4.74456	0.213037
$497$	−4.00000	−0.179425
$498$	16.0000	0.716977
$499$	−13.4891	−0.603856	−0.301928	−	0.953331i	$-0.597630\pi$
$499$	−13.4891	−0.603856	−0.301928	+	0.953331i	$0.597630\pi$
$500$	1.00000	0.0447214
$501$	0	0
$502$	−26.2337	−1.17087
$503$	6.51087	0.290306	0.145153	−	0.989409i	$-0.453633\pi$
$503$	6.51087	0.290306	0.145153	+	0.989409i	$0.453633\pi$
$504$	1.00000	0.0445435
$505$	2.74456	0.122131
$506$	6.74456	0.299832
$507$	64.9783	2.88579
$508$	0	0
$509$	−35.4891	−1.57303	−0.786514	−	0.617573i	$-0.788116\pi$
$509$	−35.4891	−1.57303	−0.786514	+	0.617573i	$0.788116\pi$
$510$	−13.4891	−0.597309
$511$	10.7446	0.475311
$512$	1.00000	0.0441942
$513$	26.9783	1.19112
$514$	−10.2337	−0.451389
$515$	−0.744563	−0.0328094
$516$	8.00000	0.352180
$517$	−4.74456	−0.208666
$518$	0.744563	0.0327142
$519$	40.4674	1.77632
$520$	6.74456	0.295769
$521$	−2.00000	−0.0876216	−0.0438108	−	0.999040i	$-0.513950\pi$
$521$	−2.00000	−0.0876216	−0.0438108	+	0.999040i	$0.513950\pi$
$522$	8.74456	0.382739
$523$	−17.4891	−0.764746	−0.382373	−	0.924008i	$-0.624893\pi$
$523$	−17.4891	−0.764746	−0.382373	+	0.924008i	$0.624893\pi$
$524$	−2.74456	−0.119897
$525$	2.00000	0.0872872
$526$	26.9783	1.17631
$527$	−32.0000	−1.39394
$528$	−2.00000	−0.0870388
$529$	22.4891	0.977788
$530$	−12.7446	−0.553588
$531$	−8.74456	−0.379482
$532$	−6.74456	−0.292414
$533$	−26.9783	−1.16856
$534$	30.9783	1.34056
$535$	−12.0000	−0.518805
$536$	−4.00000	−0.172774
$537$	−8.00000	−0.345225
$538$	20.9783	0.904437
$539$	−1.00000	−0.0430730
$540$	−4.00000	−0.172133
$541$	1.76631	0.0759397	0.0379698	−	0.999279i	$-0.487911\pi$
$541$	1.76631	0.0759397	0.0379698	+	0.999279i	$0.487911\pi$
$542$	14.9783	0.643371
$543$	−38.9783	−1.67272
$544$	−6.74456	−0.289171
$545$	−18.2337	−0.781045
$546$	13.4891	0.577281
$547$	14.9783	0.640424	0.320212	−	0.947346i	$-0.396246\pi$
$547$	14.9783	0.640424	0.320212	+	0.947346i	$0.396246\pi$
$548$	3.48913	0.149048
$549$	1.25544	0.0535808
$550$	−1.00000	−0.0426401
$551$	−58.9783	−2.51256
$552$	−13.4891	−0.574135
$553$	6.74456	0.286808
$554$	15.4891	0.658070
$555$	1.48913	0.0632098
$556$	14.7446	0.625309
$557$	−0.978251	−0.0414498	−0.0207249	−	0.999785i	$-0.506597\pi$
$557$	−0.978251	−0.0414498	−0.0207249	+	0.999785i	$0.506597\pi$
$558$	4.74456	0.200853
$559$	26.9783	1.14106
$560$	1.00000	0.0422577
$561$	13.4891	0.569511
$562$	14.0000	0.590554
$563$	5.48913	0.231339	0.115670	−	0.993288i	$-0.463099\pi$
$563$	5.48913	0.231339	0.115670	+	0.993288i	$0.463099\pi$
$564$	9.48913	0.399564
$565$	10.0000	0.420703
$566$	28.0000	1.17693
$567$	−11.0000	−0.461957
$568$	−4.00000	−0.167836
$569$	16.5109	0.692172	0.346086	−	0.938203i	$-0.387511\pi$
$569$	16.5109	0.692172	0.346086	+	0.938203i	$0.387511\pi$
$570$	−13.4891	−0.564997
$571$	−17.4891	−0.731897	−0.365949	−	0.930635i	$-0.619255\pi$
$571$	−17.4891	−0.731897	−0.365949	+	0.930635i	$0.619255\pi$
$572$	−6.74456	−0.282004
$573$	−32.0000	−1.33682
$574$	−4.00000	−0.166957
$575$	−6.74456	−0.281268
$576$	1.00000	0.0416667
$577$	−8.74456	−0.364041	−0.182020	−	0.983295i	$-0.558264\pi$
$577$	−8.74456	−0.364041	−0.182020	+	0.983295i	$0.558264\pi$
$578$	28.4891	1.18499
$579$	−4.00000	−0.166234
$580$	8.74456	0.363098
$581$	8.00000	0.331896
$582$	−33.4891	−1.38817
$583$	12.7446	0.527826
$584$	10.7446	0.444613
$585$	6.74456	0.278853
$586$	13.2554	0.547577
$587$	−4.97825	−0.205474	−0.102737	−	0.994709i	$-0.532760\pi$
$587$	−4.97825	−0.205474	−0.102737	+	0.994709i	$0.532760\pi$
$588$	2.00000	0.0824786
$589$	−32.0000	−1.31854
$590$	−8.74456	−0.360008
$591$	20.0000	0.822690
$592$	0.744563	0.0306013
$593$	−40.2337	−1.65220	−0.826100	−	0.563524i	$-0.809445\pi$
$593$	−40.2337	−1.65220	−0.826100	+	0.563524i	$0.809445\pi$
$594$	4.00000	0.164122
$595$	−6.74456	−0.276500
$596$	−0.744563	−0.0304985
$597$	6.51087	0.266472
$598$	−45.4891	−1.86019
$599$	−12.0000	−0.490307	−0.245153	−	0.969484i	$-0.578838\pi$
$599$	−12.0000	−0.490307	−0.245153	+	0.969484i	$0.578838\pi$
$600$	2.00000	0.0816497
$601$	−33.4891	−1.36605	−0.683025	−	0.730395i	$-0.739336\pi$
$601$	−33.4891	−1.36605	−0.683025	+	0.730395i	$0.739336\pi$
$602$	4.00000	0.163028
$603$	−4.00000	−0.162893
$604$	−9.25544	−0.376598
$605$	1.00000	0.0406558
$606$	5.48913	0.222980
$607$	8.00000	0.324710	0.162355	−	0.986732i	$-0.448091\pi$
$607$	8.00000	0.324710	0.162355	+	0.986732i	$0.448091\pi$
$608$	−6.74456	−0.273528
$609$	17.4891	0.708695
$610$	1.25544	0.0508312
$611$	32.0000	1.29458
$612$	−6.74456	−0.272633
$613$	11.4891	0.464041	0.232021	−	0.972711i	$-0.425466\pi$
$613$	11.4891	0.464041	0.232021	+	0.972711i	$0.425466\pi$
$614$	−1.48913	−0.0600962
$615$	−8.00000	−0.322591
$616$	−1.00000	−0.0402911
$617$	−10.0000	−0.402585	−0.201292	−	0.979531i	$-0.564514\pi$
$617$	−10.0000	−0.402585	−0.201292	+	0.979531i	$0.564514\pi$
$618$	−1.48913	−0.0599014
$619$	0.744563	0.0299265	0.0149632	−	0.999888i	$-0.495237\pi$
$619$	0.744563	0.0299265	0.0149632	+	0.999888i	$0.495237\pi$
$620$	4.74456	0.190546
$621$	26.9783	1.08260
$622$	−20.7446	−0.831781
$623$	15.4891	0.620559
$624$	13.4891	0.539997
$625$	1.00000	0.0400000
$626$	−2.23369	−0.0892761
$627$	13.4891	0.538704
$628$	0.510875	0.0203861
$629$	−5.02175	−0.200230
$630$	1.00000	0.0398410
$631$	−2.97825	−0.118562	−0.0592811	−	0.998241i	$-0.518881\pi$
$631$	−2.97825	−0.118562	−0.0592811	+	0.998241i	$0.518881\pi$
$632$	6.74456	0.268284
$633$	−24.0000	−0.953914
$634$	2.23369	0.0887111
$635$	0	0
$636$	−25.4891	−1.01071
$637$	6.74456	0.267229
$638$	−8.74456	−0.346201
$639$	−4.00000	−0.158238
$640$	1.00000	0.0395285
$641$	11.4891	0.453793	0.226897	−	0.973919i	$-0.427142\pi$
$641$	11.4891	0.453793	0.226897	+	0.973919i	$0.427142\pi$
$642$	−24.0000	−0.947204
$643$	46.4674	1.83249	0.916247	−	0.400613i	$-0.131203\pi$
$643$	46.4674	1.83249	0.916247	+	0.400613i	$0.131203\pi$
$644$	−6.74456	−0.265773
$645$	8.00000	0.315000
$646$	45.4891	1.78975
$647$	8.74456	0.343784	0.171892	−	0.985116i	$-0.445012\pi$
$647$	8.74456	0.343784	0.171892	+	0.985116i	$0.445012\pi$
$648$	−11.0000	−0.432121
$649$	8.74456	0.343254
$650$	6.74456	0.264544
$651$	9.48913	0.371908
$652$	−4.00000	−0.156652
$653$	15.7228	0.615281	0.307641	−	0.951503i	$-0.400461\pi$
$653$	15.7228	0.615281	0.307641	+	0.951503i	$0.400461\pi$
$654$	−36.4674	−1.42599
$655$	−2.74456	−0.107239
$656$	−4.00000	−0.156174
$657$	10.7446	0.419185
$658$	4.74456	0.184962
$659$	−41.4891	−1.61619	−0.808093	−	0.589054i	$-0.799500\pi$
$659$	−41.4891	−1.61619	−0.808093	+	0.589054i	$0.799500\pi$
$660$	−2.00000	−0.0778499
$661$	22.0000	0.855701	0.427850	−	0.903850i	$-0.359271\pi$
$661$	22.0000	0.855701	0.427850	+	0.903850i	$0.359271\pi$
$662$	14.9783	0.582146
$663$	−90.9783	−3.53330
$664$	8.00000	0.310460
$665$	−6.74456	−0.261543
$666$	0.744563	0.0288512
$667$	−58.9783	−2.28365
$668$	0	0
$669$	30.5109	1.17962
$670$	−4.00000	−0.154533
$671$	−1.25544	−0.0484656
$672$	2.00000	0.0771517
$673$	20.9783	0.808652	0.404326	−	0.914615i	$-0.367506\pi$
$673$	20.9783	0.808652	0.404326	+	0.914615i	$0.367506\pi$
$674$	26.0000	1.00148
$675$	−4.00000	−0.153960
$676$	32.4891	1.24958
$677$	36.2337	1.39257	0.696287	−	0.717764i	$-0.254834\pi$
$677$	36.2337	1.39257	0.696287	+	0.717764i	$0.254834\pi$
$678$	20.0000	0.768095
$679$	−16.7446	−0.642597
$680$	−6.74456	−0.258642
$681$	40.0000	1.53280
$682$	−4.74456	−0.181679
$683$	0	0		−	1.00000i	$-0.5\pi$
$683$	0	0			1.00000i	$0.5\pi$
$684$	−6.74456	−0.257885
$685$	3.48913	0.133313
$686$	1.00000	0.0381802
$687$	−12.0000	−0.457829
$688$	4.00000	0.152499
$689$	−85.9565	−3.27468
$690$	−13.4891	−0.513522
$691$	1.76631	0.0671937	0.0335968	−	0.999435i	$-0.489304\pi$
$691$	1.76631	0.0671937	0.0335968	+	0.999435i	$0.489304\pi$
$692$	20.2337	0.769169
$693$	−1.00000	−0.0379869
$694$	−22.9783	−0.872242
$695$	14.7446	0.559293
$696$	17.4891	0.662924
$697$	26.9783	1.02187
$698$	30.7446	1.16370
$699$	−49.9565	−1.88953
$700$	1.00000	0.0377964
$701$	22.2337	0.839755	0.419877	−	0.907581i	$-0.362073\pi$
$701$	22.2337	0.839755	0.419877	+	0.907581i	$0.362073\pi$
$702$	−26.9783	−1.01823
$703$	−5.02175	−0.189399
$704$	−1.00000	−0.0376889
$705$	9.48913	0.357381
$706$	8.74456	0.329106
$707$	2.74456	0.103220
$708$	−17.4891	−0.657282
$709$	0.510875	0.0191863	0.00959315	−	0.999954i	$-0.496946\pi$
$709$	0.510875	0.0191863	0.00959315	+	0.999954i	$0.496946\pi$
$710$	−4.00000	−0.150117
$711$	6.74456	0.252941
$712$	15.4891	0.580480
$713$	−32.0000	−1.19841
$714$	−13.4891	−0.504818
$715$	−6.74456	−0.252232
$716$	−4.00000	−0.149487
$717$	−29.4891	−1.10129
$718$	−1.25544	−0.0468525
$719$	7.72281	0.288012	0.144006	−	0.989577i	$-0.454001\pi$
$719$	7.72281	0.288012	0.144006	+	0.989577i	$0.454001\pi$
$720$	1.00000	0.0372678
$721$	−0.744563	−0.0277290
$722$	26.4891	0.985823
$723$	40.0000	1.48762
$724$	−19.4891	−0.724308
$725$	8.74456	0.324765
$726$	2.00000	0.0742270
$727$	14.2337	0.527898	0.263949	−	0.964537i	$-0.414975\pi$
$727$	14.2337	0.527898	0.263949	+	0.964537i	$0.414975\pi$
$728$	6.74456	0.249970
$729$	13.0000	0.481481
$730$	10.7446	0.397674
$731$	−26.9783	−0.997827
$732$	2.51087	0.0928046
$733$	−16.2337	−0.599605	−0.299802	−	0.954001i	$-0.596921\pi$
$733$	−16.2337	−0.599605	−0.299802	+	0.954001i	$0.596921\pi$
$734$	−8.74456	−0.322768
$735$	2.00000	0.0737711
$736$	−6.74456	−0.248608
$737$	4.00000	0.147342
$738$	−4.00000	−0.147242
$739$	−30.9783	−1.13955	−0.569777	−	0.821800i	$-0.692970\pi$
$739$	−30.9783	−1.13955	−0.569777	+	0.821800i	$0.692970\pi$
$740$	0.744563	0.0273707
$741$	−90.9783	−3.34217
$742$	−12.7446	−0.467868
$743$	26.9783	0.989736	0.494868	−	0.868968i	$-0.335216\pi$
$743$	26.9783	0.989736	0.494868	+	0.868968i	$0.335216\pi$
$744$	9.48913	0.347888
$745$	−0.744563	−0.0272787
$746$	−16.9783	−0.621618
$747$	8.00000	0.292705
$748$	6.74456	0.246606
$749$	−12.0000	−0.438470
$750$	2.00000	0.0730297
$751$	20.0000	0.729810	0.364905	−	0.931045i	$-0.381101\pi$
$751$	20.0000	0.729810	0.364905	+	0.931045i	$0.381101\pi$
$752$	4.74456	0.173016
$753$	−52.4674	−1.91202
$754$	58.9783	2.14786
$755$	−9.25544	−0.336840
$756$	−4.00000	−0.145479
$757$	−19.2554	−0.699851	−0.349925	−	0.936778i	$-0.613793\pi$
$757$	−19.2554	−0.699851	−0.349925	+	0.936778i	$0.613793\pi$
$758$	−37.4891	−1.36167
$759$	13.4891	0.489624
$760$	−6.74456	−0.244651
$761$	−29.4891	−1.06898	−0.534490	−	0.845175i	$-0.679496\pi$
$761$	−29.4891	−1.06898	−0.534490	+	0.845175i	$0.679496\pi$
$762$	0	0
$763$	−18.2337	−0.660104
$764$	−16.0000	−0.578860
$765$	−6.74456	−0.243850
$766$	19.7228	0.712614
$767$	−58.9783	−2.12958
$768$	2.00000	0.0721688
$769$	−8.00000	−0.288487	−0.144244	−	0.989542i	$-0.546075\pi$
$769$	−8.00000	−0.288487	−0.144244	+	0.989542i	$0.546075\pi$
$770$	−1.00000	−0.0360375
$771$	−20.4674	−0.737115
$772$	−2.00000	−0.0719816
$773$	−51.4891	−1.85194	−0.925968	−	0.377603i	$-0.876748\pi$
$773$	−51.4891	−1.85194	−0.925968	+	0.377603i	$0.876748\pi$
$774$	4.00000	0.143777
$775$	4.74456	0.170430
$776$	−16.7446	−0.601095
$777$	1.48913	0.0534221
$778$	−7.48913	−0.268498
$779$	26.9783	0.966596
$780$	13.4891	0.482988
$781$	4.00000	0.143131
$782$	45.4891	1.62669
$783$	−34.9783	−1.25002
$784$	1.00000	0.0357143
$785$	0.510875	0.0182339
$786$	−5.48913	−0.195791
$787$	5.48913	0.195666	0.0978331	−	0.995203i	$-0.468809\pi$
$787$	5.48913	0.195666	0.0978331	+	0.995203i	$0.468809\pi$
$788$	10.0000	0.356235
$789$	53.9565	1.92090
$790$	6.74456	0.239961
$791$	10.0000	0.355559
$792$	−1.00000	−0.0355335
$793$	8.46738	0.300685
$794$	35.4891	1.25946
$795$	−25.4891	−0.904006
$796$	3.25544	0.115386
$797$	−42.4674	−1.50427	−0.752136	−	0.659008i	$-0.770976\pi$
$797$	−42.4674	−1.50427	−0.752136	+	0.659008i	$0.770976\pi$
$798$	−13.4891	−0.477510
$799$	−32.0000	−1.13208
$800$	1.00000	0.0353553
$801$	15.4891	0.547281
$802$	23.4891	0.829430
$803$	−10.7446	−0.379167
$804$	−8.00000	−0.282138
$805$	−6.74456	−0.237715
$806$	32.0000	1.12715
$807$	41.9565	1.47694
$808$	2.74456	0.0965534
$809$	34.4674	1.21181	0.605904	−	0.795538i	$-0.292811\pi$
$809$	34.4674	1.21181	0.605904	+	0.795538i	$0.292811\pi$
$810$	−11.0000	−0.386501
$811$	−18.7446	−0.658211	−0.329105	−	0.944293i	$-0.606747\pi$
$811$	−18.7446	−0.658211	−0.329105	+	0.944293i	$0.606747\pi$
$812$	8.74456	0.306874
$813$	29.9565	1.05062
$814$	−0.744563	−0.0260969
$815$	−4.00000	−0.140114
$816$	−13.4891	−0.472214
$817$	−26.9783	−0.943850
$818$	−21.4891	−0.751350
$819$	6.74456	0.235674
$820$	−4.00000	−0.139686
$821$	7.72281	0.269528	0.134764	−	0.990878i	$-0.456972\pi$
$821$	7.72281	0.269528	0.134764	+	0.990878i	$0.456972\pi$
$822$	6.97825	0.243394
$823$	7.76631	0.270717	0.135358	−	0.990797i	$-0.456781\pi$
$823$	7.76631	0.270717	0.135358	+	0.990797i	$0.456781\pi$
$824$	−0.744563	−0.0259381
$825$	−2.00000	−0.0696311
$826$	−8.74456	−0.304262
$827$	4.00000	0.139094	0.0695468	−	0.997579i	$-0.477845\pi$
$827$	4.00000	0.139094	0.0695468	+	0.997579i	$0.477845\pi$
$828$	−6.74456	−0.234390
$829$	14.4674	0.502473	0.251236	−	0.967926i	$-0.419163\pi$
$829$	14.4674	0.502473	0.251236	+	0.967926i	$0.419163\pi$
$830$	8.00000	0.277684
$831$	30.9783	1.07462
$832$	6.74456	0.233826
$833$	−6.74456	−0.233685
$834$	29.4891	1.02112
$835$	0	0
$836$	6.74456	0.233266
$837$	−18.9783	−0.655984
$838$	−0.744563	−0.0257205
$839$	−3.25544	−0.112390	−0.0561951	−	0.998420i	$-0.517897\pi$
$839$	−3.25544	−0.112390	−0.0561951	+	0.998420i	$0.517897\pi$
$840$	2.00000	0.0690066
$841$	47.4674	1.63681
$842$	4.51087	0.155455
$843$	28.0000	0.964371
$844$	−12.0000	−0.413057
$845$	32.4891	1.11766
$846$	4.74456	0.163121
$847$	1.00000	0.0343604
$848$	−12.7446	−0.437650
$849$	56.0000	1.92192
$850$	−6.74456	−0.231337
$851$	−5.02175	−0.172143
$852$	−8.00000	−0.274075
$853$	−22.7446	−0.778759	−0.389379	−	0.921077i	$-0.627311\pi$
$853$	−22.7446	−0.778759	−0.389379	+	0.921077i	$0.627311\pi$
$854$	1.25544	0.0429602
$855$	−6.74456	−0.230659
$856$	−12.0000	−0.410152
$857$	−43.2119	−1.47609	−0.738046	−	0.674751i	$-0.764251\pi$
$857$	−43.2119	−1.47609	−0.738046	+	0.674751i	$0.764251\pi$
$858$	−13.4891	−0.460511
$859$	−29.2119	−0.996698	−0.498349	−	0.866976i	$-0.666060\pi$
$859$	−29.2119	−0.996698	−0.498349	+	0.866976i	$0.666060\pi$
$860$	4.00000	0.136399
$861$	−8.00000	−0.272639
$862$	−17.2554	−0.587723
$863$	−40.2337	−1.36957	−0.684785	−	0.728745i	$-0.740104\pi$
$863$	−40.2337	−1.36957	−0.684785	+	0.728745i	$0.740104\pi$
$864$	−4.00000	−0.136083
$865$	20.2337	0.687966
$866$	36.7446	1.24863
$867$	56.9783	1.93508
$868$	4.74456	0.161041
$869$	−6.74456	−0.228794
$870$	17.4891	0.592937
$871$	−26.9783	−0.914123
$872$	−18.2337	−0.617471
$873$	−16.7446	−0.566718
$874$	45.4891	1.53869
$875$	1.00000	0.0338062
$876$	21.4891	0.726050
$877$	−26.4674	−0.893740	−0.446870	−	0.894599i	$-0.647461\pi$
$877$	−26.4674	−0.893740	−0.446870	+	0.894599i	$0.647461\pi$
$878$	14.9783	0.505491
$879$	26.5109	0.894190
$880$	−1.00000	−0.0337100
$881$	−55.4891	−1.86948	−0.934738	−	0.355338i	$-0.884366\pi$
$881$	−55.4891	−1.86948	−0.934738	+	0.355338i	$0.884366\pi$
$882$	1.00000	0.0336718
$883$	−8.00000	−0.269221	−0.134611	−	0.990899i	$-0.542978\pi$
$883$	−8.00000	−0.269221	−0.134611	+	0.990899i	$0.542978\pi$
$884$	−45.4891	−1.52996
$885$	−17.4891	−0.587891
$886$	−29.4891	−0.990707
$887$	−41.4891	−1.39307	−0.696534	−	0.717524i	$-0.745276\pi$
$887$	−41.4891	−1.39307	−0.696534	+	0.717524i	$0.745276\pi$
$888$	1.48913	0.0499718
$889$	0	0
$890$	15.4891	0.519197
$891$	11.0000	0.368514
$892$	15.2554	0.510790
$893$	−32.0000	−1.07084
$894$	−1.48913	−0.0498038
$895$	−4.00000	−0.133705
$896$	1.00000	0.0334077
$897$	−90.9783	−3.03768
$898$	−4.97825	−0.166126
$899$	41.4891	1.38374
$900$	1.00000	0.0333333
$901$	85.9565	2.86363
$902$	4.00000	0.133185
$903$	8.00000	0.266223
$904$	10.0000	0.332595
$905$	−19.4891	−0.647840
$906$	−18.5109	−0.614983
$907$	−14.5109	−0.481826	−0.240913	−	0.970547i	$-0.577447\pi$
$907$	−14.5109	−0.481826	−0.240913	+	0.970547i	$0.577447\pi$
$908$	20.0000	0.663723
$909$	2.74456	0.0910314
$910$	6.74456	0.223580
$911$	20.0000	0.662630	0.331315	−	0.943520i	$-0.392508\pi$
$911$	20.0000	0.662630	0.331315	+	0.943520i	$0.392508\pi$
$912$	−13.4891	−0.446670
$913$	−8.00000	−0.264761
$914$	3.48913	0.115410
$915$	2.51087	0.0830070
$916$	−6.00000	−0.198246
$917$	−2.74456	−0.0906334
$918$	26.9783	0.890415
$919$	−55.2119	−1.82127	−0.910637	−	0.413207i	$-0.864408\pi$
$919$	−55.2119	−1.82127	−0.910637	+	0.413207i	$0.864408\pi$
$920$	−6.74456	−0.222362
$921$	−2.97825	−0.0981367
$922$	33.7228	1.11060
$923$	−26.9783	−0.888000
$924$	−2.00000	−0.0657952
$925$	0.744563	0.0244811
$926$	1.25544	0.0412562
$927$	−0.744563	−0.0244546
$928$	8.74456	0.287054
$929$	−28.9783	−0.950746	−0.475373	−	0.879784i	$-0.657687\pi$
$929$	−28.9783	−0.950746	−0.475373	+	0.879784i	$0.657687\pi$
$930$	9.48913	0.311161
$931$	−6.74456	−0.221044
$932$	−24.9783	−0.818190
$933$	−41.4891	−1.35829
$934$	16.9783	0.555545
$935$	6.74456	0.220571
$936$	6.74456	0.220453
$937$	−18.7446	−0.612358	−0.306179	−	0.951974i	$-0.599051\pi$
$937$	−18.7446	−0.612358	−0.306179	+	0.951974i	$0.599051\pi$
$938$	−4.00000	−0.130605
$939$	−4.46738	−0.145787
$940$	4.74456	0.154751
$941$	12.2337	0.398807	0.199403	−	0.979917i	$-0.436100\pi$
$941$	12.2337	0.398807	0.199403	+	0.979917i	$0.436100\pi$
$942$	1.02175	0.0332904
$943$	26.9783	0.878533
$944$	−8.74456	−0.284611
$945$	−4.00000	−0.130120
$946$	−4.00000	−0.130051
$947$	−8.00000	−0.259965	−0.129983	−	0.991516i	$-0.541492\pi$
$947$	−8.00000	−0.259965	−0.129983	+	0.991516i	$0.541492\pi$
$948$	13.4891	0.438106
$949$	72.4674	2.35239
$950$	−6.74456	−0.218823
$951$	4.46738	0.144865
$952$	−6.74456	−0.218593
$953$	6.00000	0.194359	0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000	0.194359	0.0971795	+	0.995267i	$0.469018\pi$
$954$	−12.7446	−0.412620
$955$	−16.0000	−0.517748
$956$	−14.7446	−0.476873
$957$	−17.4891	−0.565343
$958$	−41.4891	−1.34045
$959$	3.48913	0.112670
$960$	2.00000	0.0645497
$961$	−8.48913	−0.273843
$962$	5.02175	0.161908
$963$	−12.0000	−0.386695
$964$	20.0000	0.644157
$965$	−2.00000	−0.0643823
$966$	−13.4891	−0.434005
$967$	−50.9783	−1.63935	−0.819675	−	0.572829i	$-0.805846\pi$
$967$	−50.9783	−1.63935	−0.819675	+	0.572829i	$0.805846\pi$
$968$	1.00000	0.0321412
$969$	90.9783	2.92264
$970$	−16.7446	−0.537636
$971$	19.7228	0.632935	0.316468	−	0.948603i	$-0.397503\pi$
$971$	19.7228	0.632935	0.316468	+	0.948603i	$0.397503\pi$
$972$	−10.0000	−0.320750
$973$	14.7446	0.472689
$974$	9.25544	0.296563
$975$	13.4891	0.431998
$976$	1.25544	0.0401856
$977$	12.9783	0.415211	0.207606	−	0.978213i	$-0.433433\pi$
$977$	12.9783	0.415211	0.207606	+	0.978213i	$0.433433\pi$
$978$	−8.00000	−0.255812
$979$	−15.4891	−0.495035
$980$	1.00000	0.0319438
$981$	−18.2337	−0.582157
$982$	30.9783	0.988556
$983$	2.23369	0.0712436	0.0356218	−	0.999365i	$-0.488659\pi$
$983$	2.23369	0.0712436	0.0356218	+	0.999365i	$0.488659\pi$
$984$	−8.00000	−0.255031
$985$	10.0000	0.318626
$986$	−58.9783	−1.87825
$987$	9.48913	0.302042
$988$	−45.4891	−1.44720
$989$	−26.9783	−0.857858
$990$	−1.00000	−0.0317821
$991$	1.48913	0.0473036	0.0236518	−	0.999720i	$-0.492471\pi$
$991$	1.48913	0.0473036	0.0236518	+	0.999720i	$0.492471\pi$
$992$	4.74456	0.150640
$993$	29.9565	0.950641
$994$	−4.00000	−0.126872
$995$	3.25544	0.103204
$996$	16.0000	0.506979
$997$	39.2119	1.24185	0.620927	−	0.783868i	$-0.286756\pi$
$997$	39.2119	1.24185	0.620927	+	0.783868i	$0.286756\pi$
$998$	−13.4891	−0.426991
$999$	−2.97825	−0.0942277

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.a.k.1.2	✓	2
3.2	odd	2		6930.2.a.bo.1.2		2
4.3	odd	2		6160.2.a.r.1.2		2
5.2	odd	4		3850.2.c.y.1849.3		4
5.3	odd	4		3850.2.c.y.1849.2		4
5.4	even	2		3850.2.a.bc.1.1		2
7.6	odd	2		5390.2.a.bq.1.1		2
11.10	odd	2		8470.2.a.bu.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.a.k.1.2	✓	2	1.1	even	1	trivial
3850.2.a.bc.1.1		2	5.4	even	2
3850.2.c.y.1849.2		4	5.3	odd	4
3850.2.c.y.1849.3		4	5.2	odd	4
5390.2.a.bq.1.1		2	7.6	odd	2
6160.2.a.r.1.2		2	4.3	odd	2
6930.2.a.bo.1.2		2	3.2	odd	2
8470.2.a.bu.1.1		2	11.10	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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{11} +2.00000 q^{12} +6.74456 q^{13} +1.00000 q^{14} +2.00000 q^{15} +1.00000 q^{16} -6.74456 q^{17} +1.00000 q^{18} -6.74456 q^{19} +1.00000 q^{20} +2.00000 q^{21} -1.00000 q^{22} -6.74456 q^{23} +2.00000 q^{24} +1.00000 q^{25} +6.74456 q^{26} -4.00000 q^{27} +1.00000 q^{28} +8.74456 q^{29} +2.00000 q^{30} +4.74456 q^{31} +1.00000 q^{32} -2.00000 q^{33} -6.74456 q^{34} +1.00000 q^{35} +1.00000 q^{36} +0.744563 q^{37} -6.74456 q^{38} +13.4891 q^{39} +1.00000 q^{40} -4.00000 q^{41} +2.00000 q^{42} +4.00000 q^{43} -1.00000 q^{44} +1.00000 q^{45} -6.74456 q^{46} +4.74456 q^{47} +2.00000 q^{48} +1.00000 q^{49} +1.00000 q^{50} -13.4891 q^{51} +6.74456 q^{52} -12.7446 q^{53} -4.00000 q^{54} -1.00000 q^{55} +1.00000 q^{56} -13.4891 q^{57} +8.74456 q^{58} -8.74456 q^{59} +2.00000 q^{60} +1.25544 q^{61} +4.74456 q^{62} +1.00000 q^{63} +1.00000 q^{64} +6.74456 q^{65} -2.00000 q^{66} -4.00000 q^{67} -6.74456 q^{68} -13.4891 q^{69} +1.00000 q^{70} -4.00000 q^{71} +1.00000 q^{72} +10.7446 q^{73} +0.744563 q^{74} +2.00000 q^{75} -6.74456 q^{76} -1.00000 q^{77} +13.4891 q^{78} +6.74456 q^{79} +1.00000 q^{80} -11.0000 q^{81} -4.00000 q^{82} +8.00000 q^{83} +2.00000 q^{84} -6.74456 q^{85} +4.00000 q^{86} +17.4891 q^{87} -1.00000 q^{88} +15.4891 q^{89} +1.00000 q^{90} +6.74456 q^{91} -6.74456 q^{92} +9.48913 q^{93} +4.74456 q^{94} -6.74456 q^{95} +2.00000 q^{96} -16.7446 q^{97} +1.00000 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 4 q^{3} + 2 q^{4} + 2 q^{5} + 4 q^{6} + 2 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 4 * q^3 + 2 * q^4 + 2 * q^5 + 4 * q^6 + 2 * q^7 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} + 4 q^{3} + 2 q^{4} + 2 q^{5} + 4 q^{6} + 2 q^{7} + 2 q^{8} + 2 q^{9} + 2 q^{10} - 2 q^{11} + 4 q^{12} + 2 q^{13} + 2 q^{14} + 4 q^{15} + 2 q^{16} - 2 q^{17} + 2 q^{18} - 2 q^{19} + 2 q^{20} + 4 q^{21} - 2 q^{22} - 2 q^{23} + 4 q^{24} + 2 q^{25} + 2 q^{26} - 8 q^{27} + 2 q^{28} + 6 q^{29} + 4 q^{30} - 2 q^{31} + 2 q^{32} - 4 q^{33} - 2 q^{34} + 2 q^{35} + 2 q^{36} - 10 q^{37} - 2 q^{38} + 4 q^{39} + 2 q^{40} - 8 q^{41} + 4 q^{42} + 8 q^{43} - 2 q^{44} + 2 q^{45} - 2 q^{46} - 2 q^{47} + 4 q^{48} + 2 q^{49} + 2 q^{50} - 4 q^{51} + 2 q^{52} - 14 q^{53} - 8 q^{54} - 2 q^{55} + 2 q^{56} - 4 q^{57} + 6 q^{58} - 6 q^{59} + 4 q^{60} + 14 q^{61} - 2 q^{62} + 2 q^{63} + 2 q^{64} + 2 q^{65} - 4 q^{66} - 8 q^{67} - 2 q^{68} - 4 q^{69} + 2 q^{70} - 8 q^{71} + 2 q^{72} + 10 q^{73} - 10 q^{74} + 4 q^{75} - 2 q^{76} - 2 q^{77} + 4 q^{78} + 2 q^{79} + 2 q^{80} - 22 q^{81} - 8 q^{82} + 16 q^{83} + 4 q^{84} - 2 q^{85} + 8 q^{86} + 12 q^{87} - 2 q^{88} + 8 q^{89} + 2 q^{90} + 2 q^{91} - 2 q^{92} - 4 q^{93} - 2 q^{94} - 2 q^{95} + 4 q^{96} - 22 q^{97} + 2 q^{98} - 2 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 4 * q^3 + 2 * q^4 + 2 * q^5 + 4 * q^6 + 2 * q^7 + 2 * q^8 + 2 * q^9 + 2 * q^10 - 2 * q^11 + 4 * q^12 + 2 * q^13 + 2 * q^14 + 4 * q^15 + 2 * q^16 - 2 * q^17 + 2 * q^18 - 2 * q^19 + 2 * q^20 + 4 * q^21 - 2 * q^22 - 2 * q^23 + 4 * q^24 + 2 * q^25 + 2 * q^26 - 8 * q^27 + 2 * q^28 + 6 * q^29 + 4 * q^30 - 2 * q^31 + 2 * q^32 - 4 * q^33 - 2 * q^34 + 2 * q^35 + 2 * q^36 - 10 * q^37 - 2 * q^38 + 4 * q^39 + 2 * q^40 - 8 * q^41 + 4 * q^42 + 8 * q^43 - 2 * q^44 + 2 * q^45 - 2 * q^46 - 2 * q^47 + 4 * q^48 + 2 * q^49 + 2 * q^50 - 4 * q^51 + 2 * q^52 - 14 * q^53 - 8 * q^54 - 2 * q^55 + 2 * q^56 - 4 * q^57 + 6 * q^58 - 6 * q^59 + 4 * q^60 + 14 * q^61 - 2 * q^62 + 2 * q^63 + 2 * q^64 + 2 * q^65 - 4 * q^66 - 8 * q^67 - 2 * q^68 - 4 * q^69 + 2 * q^70 - 8 * q^71 + 2 * q^72 + 10 * q^73 - 10 * q^74 + 4 * q^75 - 2 * q^76 - 2 * q^77 + 4 * q^78 + 2 * q^79 + 2 * q^80 - 22 * q^81 - 8 * q^82 + 16 * q^83 + 4 * q^84 - 2 * q^85 + 8 * q^86 + 12 * q^87 - 2 * q^88 + 8 * q^89 + 2 * q^90 + 2 * q^91 - 2 * q^92 - 4 * q^93 - 2 * q^94 - 2 * q^95 + 4 * q^96 - 22 * q^97 + 2 * q^98 - 2 * q^99

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