LMFDB - Embedded newform 770.2.a.k.1.1

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			1.1
Root			$3.37228$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{11} +2.00000 q^{12} -4.74456 q^{13} +1.00000 q^{14} +2.00000 q^{15} +1.00000 q^{16} +4.74456 q^{17} +1.00000 q^{18} +4.74456 q^{19} +1.00000 q^{20} +2.00000 q^{21} -1.00000 q^{22} +4.74456 q^{23} +2.00000 q^{24} +1.00000 q^{25} -4.74456 q^{26} -4.00000 q^{27} +1.00000 q^{28} -2.74456 q^{29} +2.00000 q^{30} -6.74456 q^{31} +1.00000 q^{32} -2.00000 q^{33} +4.74456 q^{34} +1.00000 q^{35} +1.00000 q^{36} -10.7446 q^{37} +4.74456 q^{38} -9.48913 q^{39} +1.00000 q^{40} -4.00000 q^{41} +2.00000 q^{42} +4.00000 q^{43} -1.00000 q^{44} +1.00000 q^{45} +4.74456 q^{46} -6.74456 q^{47} +2.00000 q^{48} +1.00000 q^{49} +1.00000 q^{50} +9.48913 q^{51} -4.74456 q^{52} -1.25544 q^{53} -4.00000 q^{54} -1.00000 q^{55} +1.00000 q^{56} +9.48913 q^{57} -2.74456 q^{58} +2.74456 q^{59} +2.00000 q^{60} +12.7446 q^{61} -6.74456 q^{62} +1.00000 q^{63} +1.00000 q^{64} -4.74456 q^{65} -2.00000 q^{66} -4.00000 q^{67} +4.74456 q^{68} +9.48913 q^{69} +1.00000 q^{70} -4.00000 q^{71} +1.00000 q^{72} -0.744563 q^{73} -10.7446 q^{74} +2.00000 q^{75} +4.74456 q^{76} -1.00000 q^{77} -9.48913 q^{78} -4.74456 q^{79} +1.00000 q^{80} -11.0000 q^{81} -4.00000 q^{82} +8.00000 q^{83} +2.00000 q^{84} +4.74456 q^{85} +4.00000 q^{86} -5.48913 q^{87} -1.00000 q^{88} -7.48913 q^{89} +1.00000 q^{90} -4.74456 q^{91} +4.74456 q^{92} -13.4891 q^{93} -6.74456 q^{94} +4.74456 q^{95} +2.00000 q^{96} -5.25544 q^{97} +1.00000 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$13$	−4.74456	−1.31590	−0.657952	−	0.753059i	$-0.728577\pi$
$13$	−4.74456	−1.31590	−0.657952	+	0.753059i	$0.728577\pi$
$14$	1.00000	0.267261
$15$	2.00000	0.516398
$16$	1.00000	0.250000
$17$	4.74456	1.15073	0.575363	−	0.817898i	$-0.304861\pi$
$17$	4.74456	1.15073	0.575363	+	0.817898i	$0.304861\pi$
$18$	1.00000	0.235702
$19$	4.74456	1.08848	0.544239	−	0.838930i	$-0.316819\pi$
$19$	4.74456	1.08848	0.544239	+	0.838930i	$0.316819\pi$
$20$	1.00000	0.223607
$21$	2.00000	0.436436
$22$	−1.00000	−0.213201
$23$	4.74456	0.989310	0.494655	−	0.869090i	$-0.335294\pi$
$23$	4.74456	0.989310	0.494655	+	0.869090i	$0.335294\pi$
$24$	2.00000	0.408248
$25$	1.00000	0.200000
$26$	−4.74456	−0.930485
$27$	−4.00000	−0.769800
$28$	1.00000	0.188982
$29$	−2.74456	−0.509652	−0.254826	−	0.966987i	$-0.582018\pi$
$29$	−2.74456	−0.509652	−0.254826	+	0.966987i	$0.582018\pi$
$30$	2.00000	0.365148
$31$	−6.74456	−1.21136	−0.605680	−	0.795709i	$-0.707099\pi$
$31$	−6.74456	−1.21136	−0.605680	+	0.795709i	$0.707099\pi$
$32$	1.00000	0.176777
$33$	−2.00000	−0.348155
$34$	4.74456	0.813686
$35$	1.00000	0.169031
$36$	1.00000	0.166667
$37$	−10.7446	−1.76640	−0.883198	−	0.469001i	$-0.844614\pi$
$37$	−10.7446	−1.76640	−0.883198	+	0.469001i	$0.844614\pi$
$38$	4.74456	0.769670
$39$	−9.48913	−1.51948
$40$	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
$46$	4.74456	0.699548
$47$	−6.74456	−0.983796	−0.491898	−	0.870653i	$-0.663697\pi$
$47$	−6.74456	−0.983796	−0.491898	+	0.870653i	$0.663697\pi$
$48$	2.00000	0.288675
$49$	1.00000	0.142857
$50$	1.00000	0.141421
$51$	9.48913	1.32874
$52$	−4.74456	−0.657952
$53$	−1.25544	−0.172448	−0.0862238	−	0.996276i	$-0.527480\pi$
$53$	−1.25544	−0.172448	−0.0862238	+	0.996276i	$0.527480\pi$
$54$	−4.00000	−0.544331
$55$	−1.00000	−0.134840
$56$	1.00000	0.133631
$57$	9.48913	1.25687
$58$	−2.74456	−0.360379
$59$	2.74456	0.357312	0.178656	−	0.983912i	$-0.442825\pi$
$59$	2.74456	0.357312	0.178656	+	0.983912i	$0.442825\pi$
$60$	2.00000	0.258199
$61$	12.7446	1.63177	0.815887	−	0.578211i	$-0.196249\pi$
$61$	12.7446	1.63177	0.815887	+	0.578211i	$0.196249\pi$
$62$	−6.74456	−0.856560
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	−4.74456	−0.588491
$66$	−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	$0.578571\pi$
$68$	4.74456	0.575363
$69$	9.48913	1.14236
$70$	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
$73$	−0.744563	−0.0871445	−0.0435722	−	0.999050i	$-0.513874\pi$
$73$	−0.744563	−0.0871445	−0.0435722	+	0.999050i	$0.513874\pi$
$74$	−10.7446	−1.24903
$75$	2.00000	0.230940
$76$	4.74456	0.544239
$77$	−1.00000	−0.113961
$78$	−9.48913	−1.07443
$79$	−4.74456	−0.533805	−0.266903	−	0.963724i	$-0.586000\pi$
$79$	−4.74456	−0.533805	−0.266903	+	0.963724i	$0.586000\pi$
$80$	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
$85$	4.74456	0.514620
$86$	4.00000	0.431331
$87$	−5.48913	−0.588496
$88$	−1.00000	−0.106600
$89$	−7.48913	−0.793846	−0.396923	−	0.917852i	$-0.629922\pi$
$89$	−7.48913	−0.793846	−0.396923	+	0.917852i	$0.629922\pi$
$90$	1.00000	0.105409
$91$	−4.74456	−0.497365
$92$	4.74456	0.494655
$93$	−13.4891	−1.39876
$94$	−6.74456	−0.695649
$95$	4.74456	0.486782
$96$	2.00000	0.204124
$97$	−5.25544	−0.533609	−0.266804	−	0.963751i	$-0.585968\pi$
$97$	−5.25544	−0.533609	−0.266804	+	0.963751i	$0.585968\pi$
$98$	1.00000	0.101015
$99$	−1.00000	−0.100504
$100$	1.00000	0.100000
$101$	−8.74456	−0.870117	−0.435058	−	0.900402i	$-0.643272\pi$
$101$	−8.74456	−0.870117	−0.435058	+	0.900402i	$0.643272\pi$
$102$	9.48913	0.939563
$103$	10.7446	1.05869	0.529347	−	0.848406i	$-0.322437\pi$
$103$	10.7446	1.05869	0.529347	+	0.848406i	$0.322437\pi$
$104$	−4.74456	−0.465243
$105$	2.00000	0.195180
$106$	−1.25544	−0.121939
$107$	−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
$109$	16.2337	1.55491	0.777453	−	0.628941i	$-0.216511\pi$
$109$	16.2337	1.55491	0.777453	+	0.628941i	$0.216511\pi$
$110$	−1.00000	−0.0953463
$111$	−21.4891	−2.03966
$112$	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	$0.344124\pi$
$114$	9.48913	0.888738
$115$	4.74456	0.442433
$116$	−2.74456	−0.254826
$117$	−4.74456	−0.438635
$118$	2.74456	0.252657
$119$	4.74456	0.434933
$120$	2.00000	0.182574
$121$	1.00000	0.0909091
$122$	12.7446	1.15384
$123$	−8.00000	−0.721336
$124$	−6.74456	−0.605680
$125$	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
$130$	−4.74456	−0.416126
$131$	8.74456	0.764016	0.382008	−	0.924159i	$-0.375233\pi$
$131$	8.74456	0.764016	0.382008	+	0.924159i	$0.375233\pi$
$132$	−2.00000	−0.174078
$133$	4.74456	0.411406
$134$	−4.00000	−0.345547
$135$	−4.00000	−0.344265
$136$	4.74456	0.406843
$137$	−19.4891	−1.66507	−0.832534	−	0.553974i	$-0.813111\pi$
$137$	−19.4891	−1.66507	−0.832534	+	0.553974i	$0.813111\pi$
$138$	9.48913	0.807768
$139$	3.25544	0.276123	0.138061	−	0.990424i	$-0.455913\pi$
$139$	3.25544	0.276123	0.138061	+	0.990424i	$0.455913\pi$
$140$	1.00000	0.0845154
$141$	−13.4891	−1.13599
$142$	−4.00000	−0.335673
$143$	4.74456	0.396760
$144$	1.00000	0.0833333
$145$	−2.74456	−0.227924
$146$	−0.744563	−0.0616204
$147$	2.00000	0.164957
$148$	−10.7446	−0.883198
$149$	10.7446	0.880229	0.440114	−	0.897942i	$-0.354938\pi$
$149$	10.7446	0.880229	0.440114	+	0.897942i	$0.354938\pi$
$150$	2.00000	0.163299
$151$	−20.7446	−1.68817	−0.844084	−	0.536211i	$-0.819855\pi$
$151$	−20.7446	−1.68817	−0.844084	+	0.536211i	$0.819855\pi$
$152$	4.74456	0.384835
$153$	4.74456	0.383575
$154$	−1.00000	−0.0805823
$155$	−6.74456	−0.541736
$156$	−9.48913	−0.759738
$157$	23.4891	1.87464	0.937318	−	0.348475i	$-0.113300\pi$
$157$	23.4891	1.87464	0.937318	+	0.348475i	$0.113300\pi$
$158$	−4.74456	−0.377457
$159$	−2.51087	−0.199125
$160$	1.00000	0.0790569
$161$	4.74456	0.373924
$162$	−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
$169$	9.51087	0.731606
$170$	4.74456	0.363891
$171$	4.74456	0.362826
$172$	4.00000	0.304997
$173$	−14.2337	−1.08217	−0.541084	−	0.840969i	$-0.681986\pi$
$173$	−14.2337	−1.08217	−0.541084	+	0.840969i	$0.681986\pi$
$174$	−5.48913	−0.416130
$175$	1.00000	0.0755929
$176$	−1.00000	−0.0753778
$177$	5.48913	0.412588
$178$	−7.48913	−0.561334
$179$	−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
$181$	3.48913	0.259345	0.129672	−	0.991557i	$-0.458607\pi$
$181$	3.48913	0.259345	0.129672	+	0.991557i	$0.458607\pi$
$182$	−4.74456	−0.351690
$183$	25.4891	1.88421
$184$	4.74456	0.349774
$185$	−10.7446	−0.789956
$186$	−13.4891	−0.989071
$187$	−4.74456	−0.346957
$188$	−6.74456	−0.491898
$189$	−4.00000	−0.290957
$190$	4.74456	0.344207
$191$	−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	$0.522932\pi$
$194$	−5.25544	−0.377318
$195$	−9.48913	−0.679530
$196$	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
$199$	14.7446	1.04521	0.522607	−	0.852574i	$-0.324959\pi$
$199$	14.7446	1.04521	0.522607	+	0.852574i	$0.324959\pi$
$200$	1.00000	0.0707107
$201$	−8.00000	−0.564276
$202$	−8.74456	−0.615265
$203$	−2.74456	−0.192631
$204$	9.48913	0.664372
$205$	−4.00000	−0.279372
$206$	10.7446	0.748609
$207$	4.74456	0.329770
$208$	−4.74456	−0.328976
$209$	−4.74456	−0.328188
$210$	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	$0.635539\pi$
$212$	−1.25544	−0.0862238
$213$	−8.00000	−0.548151
$214$	−12.0000	−0.820303
$215$	4.00000	0.272798
$216$	−4.00000	−0.272166
$217$	−6.74456	−0.457851
$218$	16.2337	1.09948
$219$	−1.48913	−0.100626
$220$	−1.00000	−0.0674200
$221$	−22.5109	−1.51425
$222$	−21.4891	−1.44226
$223$	26.7446	1.79095	0.895474	−	0.445113i	$-0.146837\pi$
$223$	26.7446	1.79095	0.895474	+	0.445113i	$0.146837\pi$
$224$	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	$0.268975\pi$
$228$	9.48913	0.628433
$229$	−6.00000	−0.396491	−0.198246	−	0.980152i	$-0.563524\pi$
$229$	−6.00000	−0.396491	−0.198246	+	0.980152i	$0.563524\pi$
$230$	4.74456	0.312847
$231$	−2.00000	−0.131590
$232$	−2.74456	−0.180189
$233$	20.9783	1.37433	0.687165	−	0.726501i	$-0.258855\pi$
$233$	20.9783	1.37433	0.687165	+	0.726501i	$0.258855\pi$
$234$	−4.74456	−0.310162
$235$	−6.74456	−0.439967
$236$	2.74456	0.178656
$237$	−9.48913	−0.616385
$238$	4.74456	0.307544
$239$	−3.25544	−0.210577	−0.105288	−	0.994442i	$-0.533577\pi$
$239$	−3.25544	−0.210577	−0.105288	+	0.994442i	$0.533577\pi$
$240$	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
$244$	12.7446	0.815887
$245$	1.00000	0.0638877
$246$	−8.00000	−0.510061
$247$	−22.5109	−1.43233
$248$	−6.74456	−0.428280
$249$	16.0000	1.01396
$250$	1.00000	0.0632456
$251$	8.23369	0.519706	0.259853	−	0.965648i	$-0.416326\pi$
$251$	8.23369	0.519706	0.259853	+	0.965648i	$0.416326\pi$
$252$	1.00000	0.0629941
$253$	−4.74456	−0.298288
$254$	0	0
$255$	9.48913	0.594232
$256$	1.00000	0.0625000
$257$	24.2337	1.51166	0.755828	−	0.654770i	$-0.227235\pi$
$257$	24.2337	1.51166	0.755828	+	0.654770i	$0.227235\pi$
$258$	8.00000	0.498058
$259$	−10.7446	−0.667635
$260$	−4.74456	−0.294245
$261$	−2.74456	−0.169884
$262$	8.74456	0.540241
$263$	−18.9783	−1.17025	−0.585125	−	0.810943i	$-0.698954\pi$
$263$	−18.9783	−1.17025	−0.585125	+	0.810943i	$0.698954\pi$
$264$	−2.00000	−0.123091
$265$	−1.25544	−0.0771209
$266$	4.74456	0.290908
$267$	−14.9783	−0.916654
$268$	−4.00000	−0.244339
$269$	−24.9783	−1.52295	−0.761475	−	0.648194i	$-0.775525\pi$
$269$	−24.9783	−1.52295	−0.761475	+	0.648194i	$0.775525\pi$
$270$	−4.00000	−0.243432
$271$	−30.9783	−1.88179	−0.940897	−	0.338692i	$-0.890016\pi$
$271$	−30.9783	−1.88179	−0.940897	+	0.338692i	$0.890016\pi$
$272$	4.74456	0.287681
$273$	−9.48913	−0.574308
$274$	−19.4891	−1.17738
$275$	−1.00000	−0.0603023
$276$	9.48913	0.571178
$277$	−7.48913	−0.449978	−0.224989	−	0.974361i	$-0.572235\pi$
$277$	−7.48913	−0.449978	−0.224989	+	0.974361i	$0.572235\pi$
$278$	3.25544	0.195248
$279$	−6.74456	−0.403786
$280$	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	$0.362877\pi$
$282$	−13.4891	−0.803266
$283$	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
$285$	9.48913	0.562087
$286$	4.74456	0.280552
$287$	−4.00000	−0.236113
$288$	1.00000	0.0589256
$289$	5.51087	0.324169
$290$	−2.74456	−0.161166
$291$	−10.5109	−0.616158
$292$	−0.744563	−0.0435722
$293$	24.7446	1.44559	0.722796	−	0.691061i	$-0.242856\pi$
$293$	24.7446	1.44559	0.722796	+	0.691061i	$0.242856\pi$
$294$	2.00000	0.116642
$295$	2.74456	0.159795
$296$	−10.7446	−0.624515
$297$	4.00000	0.232104
$298$	10.7446	0.622416
$299$	−22.5109	−1.30184
$300$	2.00000	0.115470
$301$	4.00000	0.230556
$302$	−20.7446	−1.19372
$303$	−17.4891	−1.00472
$304$	4.74456	0.272119
$305$	12.7446	0.729752
$306$	4.74456	0.271229
$307$	21.4891	1.22645	0.613225	−	0.789909i	$-0.289872\pi$
$307$	21.4891	1.22645	0.613225	+	0.789909i	$0.289872\pi$
$308$	−1.00000	−0.0569803
$309$	21.4891	1.22247
$310$	−6.74456	−0.383065
$311$	−9.25544	−0.524828	−0.262414	−	0.964955i	$-0.584519\pi$
$311$	−9.25544	−0.524828	−0.262414	+	0.964955i	$0.584519\pi$
$312$	−9.48913	−0.537216
$313$	32.2337	1.82196	0.910978	−	0.412455i	$-0.135329\pi$
$313$	32.2337	1.82196	0.910978	+	0.412455i	$0.135329\pi$
$314$	23.4891	1.32557
$315$	1.00000	0.0563436
$316$	−4.74456	−0.266903
$317$	−32.2337	−1.81042	−0.905212	−	0.424960i	$-0.860288\pi$
$317$	−32.2337	−1.81042	−0.905212	+	0.424960i	$0.860288\pi$
$318$	−2.51087	−0.140803
$319$	2.74456	0.153666
$320$	1.00000	0.0559017
$321$	−24.0000	−1.33955
$322$	4.74456	0.264404
$323$	22.5109	1.25254
$324$	−11.0000	−0.611111
$325$	−4.74456	−0.263181
$326$	−4.00000	−0.221540
$327$	32.4674	1.79545
$328$	−4.00000	−0.220863
$329$	−6.74456	−0.371840
$330$	−2.00000	−0.110096
$331$	−30.9783	−1.70272	−0.851359	−	0.524583i	$-0.824221\pi$
$331$	−30.9783	−1.70272	−0.851359	+	0.524583i	$0.824221\pi$
$332$	8.00000	0.439057
$333$	−10.7446	−0.588798
$334$	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	$0.249528\pi$
$338$	9.51087	0.517323
$339$	20.0000	1.08625
$340$	4.74456	0.257310
$341$	6.74456	0.365239
$342$	4.74456	0.256557
$343$	1.00000	0.0539949
$344$	4.00000	0.215666
$345$	9.48913	0.510877
$346$	−14.2337	−0.765208
$347$	22.9783	1.23354	0.616769	−	0.787145i	$-0.288441\pi$
$347$	22.9783	1.23354	0.616769	+	0.787145i	$0.288441\pi$
$348$	−5.48913	−0.294248
$349$	19.2554	1.03072	0.515360	−	0.856974i	$-0.327658\pi$
$349$	19.2554	1.03072	0.515360	+	0.856974i	$0.327658\pi$
$350$	1.00000	0.0534522
$351$	18.9783	1.01298
$352$	−1.00000	−0.0533002
$353$	−2.74456	−0.146078	−0.0730392	−	0.997329i	$-0.523270\pi$
$353$	−2.74456	−0.146078	−0.0730392	+	0.997329i	$0.523270\pi$
$354$	5.48913	0.291744
$355$	−4.00000	−0.212298
$356$	−7.48913	−0.396923
$357$	9.48913	0.502218
$358$	−4.00000	−0.211407
$359$	−12.7446	−0.672632	−0.336316	−	0.941749i	$-0.609181\pi$
$359$	−12.7446	−0.672632	−0.336316	+	0.941749i	$0.609181\pi$
$360$	1.00000	0.0527046
$361$	3.51087	0.184783
$362$	3.48913	0.183384
$363$	2.00000	0.104973
$364$	−4.74456	−0.248683
$365$	−0.744563	−0.0389722
$366$	25.4891	1.33234
$367$	2.74456	0.143265	0.0716325	−	0.997431i	$-0.477179\pi$
$367$	2.74456	0.143265	0.0716325	+	0.997431i	$0.477179\pi$
$368$	4.74456	0.247327
$369$	−4.00000	−0.208232
$370$	−10.7446	−0.558583
$371$	−1.25544	−0.0651791
$372$	−13.4891	−0.699379
$373$	28.9783	1.50044	0.750218	−	0.661190i	$-0.229948\pi$
$373$	28.9783	1.50044	0.750218	+	0.661190i	$0.229948\pi$
$374$	−4.74456	−0.245335
$375$	2.00000	0.103280
$376$	−6.74456	−0.347824
$377$	13.0217	0.670654
$378$	−4.00000	−0.205738
$379$	−14.5109	−0.745374	−0.372687	−	0.927957i	$-0.621563\pi$
$379$	−14.5109	−0.745374	−0.372687	+	0.927957i	$0.621563\pi$
$380$	4.74456	0.243391
$381$	0	0
$382$	−16.0000	−0.818631
$383$	−37.7228	−1.92755	−0.963773	−	0.266724i	$-0.914059\pi$
$383$	−37.7228	−1.92755	−0.963773	+	0.266724i	$0.914059\pi$
$384$	2.00000	0.102062
$385$	−1.00000	−0.0509647
$386$	−2.00000	−0.101797
$387$	4.00000	0.203331
$388$	−5.25544	−0.266804
$389$	15.4891	0.785330	0.392665	−	0.919682i	$-0.371553\pi$
$389$	15.4891	0.785330	0.392665	+	0.919682i	$0.371553\pi$
$390$	−9.48913	−0.480501
$391$	22.5109	1.13842
$392$	1.00000	0.0505076
$393$	17.4891	0.882210
$394$	10.0000	0.503793
$395$	−4.74456	−0.238725
$396$	−1.00000	−0.0502519
$397$	12.5109	0.627903	0.313951	−	0.949439i	$-0.398347\pi$
$397$	12.5109	0.627903	0.313951	+	0.949439i	$0.398347\pi$
$398$	14.7446	0.739078
$399$	9.48913	0.475050
$400$	1.00000	0.0500000
$401$	0.510875	0.0255119	0.0127559	−	0.999919i	$-0.495940\pi$
$401$	0.510875	0.0255119	0.0127559	+	0.999919i	$0.495940\pi$
$402$	−8.00000	−0.399004
$403$	32.0000	1.59403
$404$	−8.74456	−0.435058
$405$	−11.0000	−0.546594
$406$	−2.74456	−0.136210
$407$	10.7446	0.532588
$408$	9.48913	0.469782
$409$	1.48913	0.0736325	0.0368163	−	0.999322i	$-0.488278\pi$
$409$	1.48913	0.0736325	0.0368163	+	0.999322i	$0.488278\pi$
$410$	−4.00000	−0.197546
$411$	−38.9783	−1.92266
$412$	10.7446	0.529347
$413$	2.74456	0.135051
$414$	4.74456	0.233183
$415$	8.00000	0.392705
$416$	−4.74456	−0.232621
$417$	6.51087	0.318839
$418$	−4.74456	−0.232064
$419$	10.7446	0.524906	0.262453	−	0.964945i	$-0.415468\pi$
$419$	10.7446	0.524906	0.262453	+	0.964945i	$0.415468\pi$
$420$	2.00000	0.0975900
$421$	27.4891	1.33974	0.669869	−	0.742479i	$-0.266350\pi$
$421$	27.4891	1.33974	0.669869	+	0.742479i	$0.266350\pi$
$422$	−12.0000	−0.584151
$423$	−6.74456	−0.327932
$424$	−1.25544	−0.0609694
$425$	4.74456	0.230145
$426$	−8.00000	−0.387601
$427$	12.7446	0.616753
$428$	−12.0000	−0.580042
$429$	9.48913	0.458139
$430$	4.00000	0.192897
$431$	−28.7446	−1.38458	−0.692288	−	0.721621i	$-0.743397\pi$
$431$	−28.7446	−1.38458	−0.692288	+	0.721621i	$0.743397\pi$
$432$	−4.00000	−0.192450
$433$	25.2554	1.21370	0.606849	−	0.794817i	$-0.292433\pi$
$433$	25.2554	1.21370	0.606849	+	0.794817i	$0.292433\pi$
$434$	−6.74456	−0.323749
$435$	−5.48913	−0.263183
$436$	16.2337	0.777453
$437$	22.5109	1.07684
$438$	−1.48913	−0.0711532
$439$	−30.9783	−1.47851	−0.739256	−	0.673425i	$-0.764822\pi$
$439$	−30.9783	−1.47851	−0.739256	+	0.673425i	$0.764822\pi$
$440$	−1.00000	−0.0476731
$441$	1.00000	0.0476190
$442$	−22.5109	−1.07073
$443$	−6.51087	−0.309341	−0.154670	−	0.987966i	$-0.549432\pi$
$443$	−6.51087	−0.309341	−0.154670	+	0.987966i	$0.549432\pi$
$444$	−21.4891	−1.01983
$445$	−7.48913	−0.355019
$446$	26.7446	1.26639
$447$	21.4891	1.01640
$448$	1.00000	0.0472456
$449$	40.9783	1.93388	0.966942	−	0.254998i	$-0.0820748\pi$
$449$	40.9783	1.93388	0.966942	+	0.254998i	$0.0820748\pi$
$450$	1.00000	0.0471405
$451$	4.00000	0.188353
$452$	10.0000	0.470360
$453$	−41.4891	−1.94933
$454$	20.0000	0.938647
$455$	−4.74456	−0.222429
$456$	9.48913	0.444369
$457$	−19.4891	−0.911663	−0.455831	−	0.890066i	$-0.650658\pi$
$457$	−19.4891	−0.911663	−0.455831	+	0.890066i	$0.650658\pi$
$458$	−6.00000	−0.280362
$459$	−18.9783	−0.885829
$460$	4.74456	0.221216
$461$	−23.7228	−1.10488	−0.552441	−	0.833552i	$-0.686303\pi$
$461$	−23.7228	−1.10488	−0.552441	+	0.833552i	$0.686303\pi$
$462$	−2.00000	−0.0930484
$463$	12.7446	0.592290	0.296145	−	0.955143i	$-0.404299\pi$
$463$	12.7446	0.592290	0.296145	+	0.955143i	$0.404299\pi$
$464$	−2.74456	−0.127413
$465$	−13.4891	−0.625543
$466$	20.9783	0.971799
$467$	−28.9783	−1.34095	−0.670477	−	0.741931i	$-0.733910\pi$
$467$	−28.9783	−1.34095	−0.670477	+	0.741931i	$0.733910\pi$
$468$	−4.74456	−0.219317
$469$	−4.00000	−0.184703
$470$	−6.74456	−0.311103
$471$	46.9783	2.16464
$472$	2.74456	0.126329
$473$	−4.00000	−0.183920
$474$	−9.48913	−0.435850
$475$	4.74456	0.217695
$476$	4.74456	0.217467
$477$	−1.25544	−0.0574825
$478$	−3.25544	−0.148900
$479$	−18.5109	−0.845783	−0.422892	−	0.906180i	$-0.638985\pi$
$479$	−18.5109	−0.845783	−0.422892	+	0.906180i	$0.638985\pi$
$480$	2.00000	0.0912871
$481$	50.9783	2.32441
$482$	20.0000	0.910975
$483$	9.48913	0.431770
$484$	1.00000	0.0454545
$485$	−5.25544	−0.238637
$486$	−10.0000	−0.453609
$487$	20.7446	0.940026	0.470013	−	0.882660i	$-0.344249\pi$
$487$	20.7446	0.940026	0.470013	+	0.882660i	$0.344249\pi$
$488$	12.7446	0.576919
$489$	−8.00000	−0.361773
$490$	1.00000	0.0451754
$491$	−14.9783	−0.675959	−0.337979	−	0.941153i	$-0.609743\pi$
$491$	−14.9783	−0.675959	−0.337979	+	0.941153i	$0.609743\pi$
$492$	−8.00000	−0.360668
$493$	−13.0217	−0.586470
$494$	−22.5109	−1.01281
$495$	−1.00000	−0.0449467
$496$	−6.74456	−0.302840
$497$	−4.00000	−0.179425
$498$	16.0000	0.716977
$499$	9.48913	0.424792	0.212396	−	0.977184i	$-0.431873\pi$
$499$	9.48913	0.424792	0.212396	+	0.977184i	$0.431873\pi$
$500$	1.00000	0.0447214
$501$	0	0
$502$	8.23369	0.367487
$503$	29.4891	1.31486	0.657428	−	0.753518i	$-0.271645\pi$
$503$	29.4891	1.31486	0.657428	+	0.753518i	$0.271645\pi$
$504$	1.00000	0.0445435
$505$	−8.74456	−0.389128
$506$	−4.74456	−0.210922
$507$	19.0217	0.844786
$508$	0	0
$509$	−12.5109	−0.554535	−0.277267	−	0.960793i	$-0.589429\pi$
$509$	−12.5109	−0.554535	−0.277267	+	0.960793i	$0.589429\pi$
$510$	9.48913	0.420186
$511$	−0.744563	−0.0329375
$512$	1.00000	0.0441942
$513$	−18.9783	−0.837910
$514$	24.2337	1.06890
$515$	10.7446	0.473462
$516$	8.00000	0.352180
$517$	6.74456	0.296626
$518$	−10.7446	−0.472089
$519$	−28.4674	−1.24958
$520$	−4.74456	−0.208063
$521$	−2.00000	−0.0876216	−0.0438108	−	0.999040i	$-0.513950\pi$
$521$	−2.00000	−0.0876216	−0.0438108	+	0.999040i	$0.513950\pi$
$522$	−2.74456	−0.120126
$523$	5.48913	0.240023	0.120011	−	0.992773i	$-0.461707\pi$
$523$	5.48913	0.240023	0.120011	+	0.992773i	$0.461707\pi$
$524$	8.74456	0.382008
$525$	2.00000	0.0872872
$526$	−18.9783	−0.827491
$527$	−32.0000	−1.39394
$528$	−2.00000	−0.0870388
$529$	−0.489125	−0.0212663
$530$	−1.25544	−0.0545327
$531$	2.74456	0.119104
$532$	4.74456	0.205703
$533$	18.9783	0.822039
$534$	−14.9783	−0.648172
$535$	−12.0000	−0.518805
$536$	−4.00000	−0.172774
$537$	−8.00000	−0.345225
$538$	−24.9783	−1.07689
$539$	−1.00000	−0.0430730
$540$	−4.00000	−0.172133
$541$	36.2337	1.55781	0.778904	−	0.627143i	$-0.215776\pi$
$541$	36.2337	1.55781	0.778904	+	0.627143i	$0.215776\pi$
$542$	−30.9783	−1.33063
$543$	6.97825	0.299465
$544$	4.74456	0.203421
$545$	16.2337	0.695375
$546$	−9.48913	−0.406097
$547$	−30.9783	−1.32453	−0.662267	−	0.749268i	$-0.730406\pi$
$547$	−30.9783	−1.32453	−0.662267	+	0.749268i	$0.730406\pi$
$548$	−19.4891	−0.832534
$549$	12.7446	0.543925
$550$	−1.00000	−0.0426401
$551$	−13.0217	−0.554745
$552$	9.48913	0.403884
$553$	−4.74456	−0.201759
$554$	−7.48913	−0.318182
$555$	−21.4891	−0.912163
$556$	3.25544	0.138061
$557$	44.9783	1.90579	0.952895	−	0.303301i	$-0.0980887\pi$
$557$	44.9783	1.90579	0.952895	+	0.303301i	$0.0980887\pi$
$558$	−6.74456	−0.285520
$559$	−18.9783	−0.802694
$560$	1.00000	0.0422577
$561$	−9.48913	−0.400631
$562$	14.0000	0.590554
$563$	−17.4891	−0.737079	−0.368539	−	0.929612i	$-0.620142\pi$
$563$	−17.4891	−0.737079	−0.368539	+	0.929612i	$0.620142\pi$
$564$	−13.4891	−0.567995
$565$	10.0000	0.420703
$566$	28.0000	1.17693
$567$	−11.0000	−0.461957
$568$	−4.00000	−0.167836
$569$	39.4891	1.65547	0.827735	−	0.561119i	$-0.189629\pi$
$569$	39.4891	1.65547	0.827735	+	0.561119i	$0.189629\pi$
$570$	9.48913	0.397456
$571$	5.48913	0.229713	0.114856	−	0.993382i	$-0.463359\pi$
$571$	5.48913	0.229713	0.114856	+	0.993382i	$0.463359\pi$
$572$	4.74456	0.198380
$573$	−32.0000	−1.33682
$574$	−4.00000	−0.166957
$575$	4.74456	0.197862
$576$	1.00000	0.0416667
$577$	2.74456	0.114258	0.0571288	−	0.998367i	$-0.481805\pi$
$577$	2.74456	0.114258	0.0571288	+	0.998367i	$0.481805\pi$
$578$	5.51087	0.229222
$579$	−4.00000	−0.166234
$580$	−2.74456	−0.113962
$581$	8.00000	0.331896
$582$	−10.5109	−0.435690
$583$	1.25544	0.0519949
$584$	−0.744563	−0.0308102
$585$	−4.74456	−0.196164
$586$	24.7446	1.02219
$587$	40.9783	1.69135	0.845677	−	0.533696i	$-0.179197\pi$
$587$	40.9783	1.69135	0.845677	+	0.533696i	$0.179197\pi$
$588$	2.00000	0.0824786
$589$	−32.0000	−1.31854
$590$	2.74456	0.112992
$591$	20.0000	0.822690
$592$	−10.7446	−0.441599
$593$	−5.76631	−0.236794	−0.118397	−	0.992966i	$-0.537776\pi$
$593$	−5.76631	−0.236794	−0.118397	+	0.992966i	$0.537776\pi$
$594$	4.00000	0.164122
$595$	4.74456	0.194508
$596$	10.7446	0.440114
$597$	29.4891	1.20691
$598$	−22.5109	−0.920538
$599$	−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
$601$	−10.5109	−0.428748	−0.214374	−	0.976752i	$-0.568771\pi$
$601$	−10.5109	−0.428748	−0.214374	+	0.976752i	$0.568771\pi$
$602$	4.00000	0.163028
$603$	−4.00000	−0.162893
$604$	−20.7446	−0.844084
$605$	1.00000	0.0406558
$606$	−17.4891	−0.710447
$607$	8.00000	0.324710	0.162355	−	0.986732i	$-0.448091\pi$
$607$	8.00000	0.324710	0.162355	+	0.986732i	$0.448091\pi$
$608$	4.74456	0.192417
$609$	−5.48913	−0.222431
$610$	12.7446	0.516012
$611$	32.0000	1.29458
$612$	4.74456	0.191788
$613$	−11.4891	−0.464041	−0.232021	−	0.972711i	$-0.574534\pi$
$613$	−11.4891	−0.464041	−0.232021	+	0.972711i	$0.574534\pi$
$614$	21.4891	0.867231
$615$	−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	$0.564514\pi$
$618$	21.4891	0.864419
$619$	−10.7446	−0.431860	−0.215930	−	0.976409i	$-0.569278\pi$
$619$	−10.7446	−0.431860	−0.215930	+	0.976409i	$0.569278\pi$
$620$	−6.74456	−0.270868
$621$	−18.9783	−0.761571
$622$	−9.25544	−0.371109
$623$	−7.48913	−0.300045
$624$	−9.48913	−0.379869
$625$	1.00000	0.0400000
$626$	32.2337	1.28832
$627$	−9.48913	−0.378959
$628$	23.4891	0.937318
$629$	−50.9783	−2.03264
$630$	1.00000	0.0398410
$631$	42.9783	1.71094	0.855469	−	0.517855i	$-0.173269\pi$
$631$	42.9783	1.71094	0.855469	+	0.517855i	$0.173269\pi$
$632$	−4.74456	−0.188729
$633$	−24.0000	−0.953914
$634$	−32.2337	−1.28016
$635$	0	0
$636$	−2.51087	−0.0995627
$637$	−4.74456	−0.187986
$638$	2.74456	0.108658
$639$	−4.00000	−0.158238
$640$	1.00000	0.0395285
$641$	−11.4891	−0.453793	−0.226897	−	0.973919i	$-0.572858\pi$
$641$	−11.4891	−0.453793	−0.226897	+	0.973919i	$0.572858\pi$
$642$	−24.0000	−0.947204
$643$	−22.4674	−0.886027	−0.443013	−	0.896515i	$-0.646091\pi$
$643$	−22.4674	−0.886027	−0.443013	+	0.896515i	$0.646091\pi$
$644$	4.74456	0.186962
$645$	8.00000	0.315000
$646$	22.5109	0.885679
$647$	−2.74456	−0.107900	−0.0539499	−	0.998544i	$-0.517181\pi$
$647$	−2.74456	−0.107900	−0.0539499	+	0.998544i	$0.517181\pi$
$648$	−11.0000	−0.432121
$649$	−2.74456	−0.107734
$650$	−4.74456	−0.186097
$651$	−13.4891	−0.528681
$652$	−4.00000	−0.156652
$653$	−41.7228	−1.63274	−0.816370	−	0.577529i	$-0.804017\pi$
$653$	−41.7228	−1.63274	−0.816370	+	0.577529i	$0.804017\pi$
$654$	32.4674	1.26957
$655$	8.74456	0.341678
$656$	−4.00000	−0.156174
$657$	−0.744563	−0.0290482
$658$	−6.74456	−0.262930
$659$	−18.5109	−0.721081	−0.360541	−	0.932744i	$-0.617408\pi$
$659$	−18.5109	−0.721081	−0.360541	+	0.932744i	$0.617408\pi$
$660$	−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	$0.359271\pi$
$662$	−30.9783	−1.20400
$663$	−45.0217	−1.74850
$664$	8.00000	0.310460
$665$	4.74456	0.183986
$666$	−10.7446	−0.416343
$667$	−13.0217	−0.504204
$668$	0	0
$669$	53.4891	2.06801
$670$	−4.00000	−0.154533
$671$	−12.7446	−0.491998
$672$	2.00000	0.0771517
$673$	−24.9783	−0.962841	−0.481420	−	0.876490i	$-0.659879\pi$
$673$	−24.9783	−0.962841	−0.481420	+	0.876490i	$0.659879\pi$
$674$	26.0000	1.00148
$675$	−4.00000	−0.153960
$676$	9.51087	0.365803
$677$	1.76631	0.0678849	0.0339424	−	0.999424i	$-0.489194\pi$
$677$	1.76631	0.0678849	0.0339424	+	0.999424i	$0.489194\pi$
$678$	20.0000	0.768095
$679$	−5.25544	−0.201685
$680$	4.74456	0.181946
$681$	40.0000	1.53280
$682$	6.74456	0.258263
$683$	0	0		−	1.00000i	$-0.5\pi$
$683$	0	0			1.00000i	$0.5\pi$
$684$	4.74456	0.181413
$685$	−19.4891	−0.744641
$686$	1.00000	0.0381802
$687$	−12.0000	−0.457829
$688$	4.00000	0.152499
$689$	5.95650	0.226925
$690$	9.48913	0.361245
$691$	36.2337	1.37839	0.689197	−	0.724574i	$-0.257963\pi$
$691$	36.2337	1.37839	0.689197	+	0.724574i	$0.257963\pi$
$692$	−14.2337	−0.541084
$693$	−1.00000	−0.0379869
$694$	22.9783	0.872242
$695$	3.25544	0.123486
$696$	−5.48913	−0.208065
$697$	−18.9783	−0.718853
$698$	19.2554	0.728829
$699$	41.9565	1.58694
$700$	1.00000	0.0377964
$701$	−12.2337	−0.462060	−0.231030	−	0.972947i	$-0.574210\pi$
$701$	−12.2337	−0.462060	−0.231030	+	0.972947i	$0.574210\pi$
$702$	18.9783	0.716288
$703$	−50.9783	−1.92268
$704$	−1.00000	−0.0376889
$705$	−13.4891	−0.508030
$706$	−2.74456	−0.103293
$707$	−8.74456	−0.328873
$708$	5.48913	0.206294
$709$	23.4891	0.882153	0.441076	−	0.897470i	$-0.354597\pi$
$709$	23.4891	0.882153	0.441076	+	0.897470i	$0.354597\pi$
$710$	−4.00000	−0.150117
$711$	−4.74456	−0.177935
$712$	−7.48913	−0.280667
$713$	−32.0000	−1.19841
$714$	9.48913	0.355122
$715$	4.74456	0.177437
$716$	−4.00000	−0.149487
$717$	−6.51087	−0.243153
$718$	−12.7446	−0.475623
$719$	−49.7228	−1.85435	−0.927174	−	0.374631i	$-0.877769\pi$
$719$	−49.7228	−1.85435	−0.927174	+	0.374631i	$0.877769\pi$
$720$	1.00000	0.0372678
$721$	10.7446	0.400148
$722$	3.51087	0.130661
$723$	40.0000	1.48762
$724$	3.48913	0.129672
$725$	−2.74456	−0.101930
$726$	2.00000	0.0742270
$727$	−20.2337	−0.750426	−0.375213	−	0.926939i	$-0.622430\pi$
$727$	−20.2337	−0.750426	−0.375213	+	0.926939i	$0.622430\pi$
$728$	−4.74456	−0.175845
$729$	13.0000	0.481481
$730$	−0.744563	−0.0275575
$731$	18.9783	0.701936
$732$	25.4891	0.942105
$733$	18.2337	0.673477	0.336738	−	0.941598i	$-0.390676\pi$
$733$	18.2337	0.673477	0.336738	+	0.941598i	$0.390676\pi$
$734$	2.74456	0.101304
$735$	2.00000	0.0737711
$736$	4.74456	0.174887
$737$	4.00000	0.147342
$738$	−4.00000	−0.147242
$739$	14.9783	0.550984	0.275492	−	0.961303i	$-0.411159\pi$
$739$	14.9783	0.550984	0.275492	+	0.961303i	$0.411159\pi$
$740$	−10.7446	−0.394978
$741$	−45.0217	−1.65392
$742$	−1.25544	−0.0460886
$743$	−18.9783	−0.696244	−0.348122	−	0.937449i	$-0.613181\pi$
$743$	−18.9783	−0.696244	−0.348122	+	0.937449i	$0.613181\pi$
$744$	−13.4891	−0.494535
$745$	10.7446	0.393650
$746$	28.9783	1.06097
$747$	8.00000	0.292705
$748$	−4.74456	−0.173478
$749$	−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	$0.381101\pi$
$752$	−6.74456	−0.245949
$753$	16.4674	0.600105
$754$	13.0217	0.474224
$755$	−20.7446	−0.754972
$756$	−4.00000	−0.145479
$757$	−30.7446	−1.11743	−0.558715	−	0.829360i	$-0.688705\pi$
$757$	−30.7446	−1.11743	−0.558715	+	0.829360i	$0.688705\pi$
$758$	−14.5109	−0.527059
$759$	−9.48913	−0.344433
$760$	4.74456	0.172103
$761$	−6.51087	−0.236019	−0.118010	−	0.993012i	$-0.537651\pi$
$761$	−6.51087	−0.236019	−0.118010	+	0.993012i	$0.537651\pi$
$762$	0	0
$763$	16.2337	0.587699
$764$	−16.0000	−0.578860
$765$	4.74456	0.171540
$766$	−37.7228	−1.36298
$767$	−13.0217	−0.470188
$768$	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
$771$	48.4674	1.74551
$772$	−2.00000	−0.0719816
$773$	−28.5109	−1.02546	−0.512732	−	0.858548i	$-0.671367\pi$
$773$	−28.5109	−1.02546	−0.512732	+	0.858548i	$0.671367\pi$
$774$	4.00000	0.143777
$775$	−6.74456	−0.242272
$776$	−5.25544	−0.188659
$777$	−21.4891	−0.770918
$778$	15.4891	0.555312
$779$	−18.9783	−0.679966
$780$	−9.48913	−0.339765
$781$	4.00000	0.143131
$782$	22.5109	0.804987
$783$	10.9783	0.392331
$784$	1.00000	0.0357143
$785$	23.4891	0.838363
$786$	17.4891	0.623816
$787$	−17.4891	−0.623420	−0.311710	−	0.950177i	$-0.600902\pi$
$787$	−17.4891	−0.623420	−0.311710	+	0.950177i	$0.600902\pi$
$788$	10.0000	0.356235
$789$	−37.9565	−1.35129
$790$	−4.74456	−0.168804
$791$	10.0000	0.355559
$792$	−1.00000	−0.0355335
$793$	−60.4674	−2.14726
$794$	12.5109	0.443994
$795$	−2.51087	−0.0890515
$796$	14.7446	0.522607
$797$	26.4674	0.937523	0.468761	−	0.883325i	$-0.344700\pi$
$797$	26.4674	0.937523	0.468761	+	0.883325i	$0.344700\pi$
$798$	9.48913	0.335911
$799$	−32.0000	−1.13208
$800$	1.00000	0.0353553
$801$	−7.48913	−0.264615
$802$	0.510875	0.0180396
$803$	0.744563	0.0262750
$804$	−8.00000	−0.282138
$805$	4.74456	0.167224
$806$	32.0000	1.12715
$807$	−49.9565	−1.75855
$808$	−8.74456	−0.307633
$809$	−34.4674	−1.21181	−0.605904	−	0.795538i	$-0.707189\pi$
$809$	−34.4674	−1.21181	−0.605904	+	0.795538i	$0.707189\pi$
$810$	−11.0000	−0.386501
$811$	−7.25544	−0.254773	−0.127386	−	0.991853i	$-0.540659\pi$
$811$	−7.25544	−0.254773	−0.127386	+	0.991853i	$0.540659\pi$
$812$	−2.74456	−0.0963153
$813$	−61.9565	−2.17291
$814$	10.7446	0.376597
$815$	−4.00000	−0.140114
$816$	9.48913	0.332186
$817$	18.9783	0.663965
$818$	1.48913	0.0520660
$819$	−4.74456	−0.165788
$820$	−4.00000	−0.139686
$821$	−49.7228	−1.73534	−0.867669	−	0.497142i	$-0.834383\pi$
$821$	−49.7228	−1.73534	−0.867669	+	0.497142i	$0.834383\pi$
$822$	−38.9783	−1.35952
$823$	42.2337	1.47217	0.736087	−	0.676887i	$-0.236671\pi$
$823$	42.2337	1.47217	0.736087	+	0.676887i	$0.236671\pi$
$824$	10.7446	0.374305
$825$	−2.00000	−0.0696311
$826$	2.74456	0.0954955
$827$	4.00000	0.139094	0.0695468	−	0.997579i	$-0.477845\pi$
$827$	4.00000	0.139094	0.0695468	+	0.997579i	$0.477845\pi$
$828$	4.74456	0.164885
$829$	−54.4674	−1.89173	−0.945865	−	0.324560i	$-0.894784\pi$
$829$	−54.4674	−1.89173	−0.945865	+	0.324560i	$0.894784\pi$
$830$	8.00000	0.277684
$831$	−14.9783	−0.519590
$832$	−4.74456	−0.164488
$833$	4.74456	0.164389
$834$	6.51087	0.225453
$835$	0	0
$836$	−4.74456	−0.164094
$837$	26.9783	0.932505
$838$	10.7446	0.371165
$839$	−14.7446	−0.509039	−0.254519	−	0.967068i	$-0.581917\pi$
$839$	−14.7446	−0.509039	−0.254519	+	0.967068i	$0.581917\pi$
$840$	2.00000	0.0690066
$841$	−21.4674	−0.740254
$842$	27.4891	0.947338
$843$	28.0000	0.964371
$844$	−12.0000	−0.413057
$845$	9.51087	0.327184
$846$	−6.74456	−0.231883
$847$	1.00000	0.0343604
$848$	−1.25544	−0.0431119
$849$	56.0000	1.92192
$850$	4.74456	0.162737
$851$	−50.9783	−1.74751
$852$	−8.00000	−0.274075
$853$	−11.2554	−0.385379	−0.192689	−	0.981260i	$-0.561721\pi$
$853$	−11.2554	−0.385379	−0.192689	+	0.981260i	$0.561721\pi$
$854$	12.7446	0.436110
$855$	4.74456	0.162261
$856$	−12.0000	−0.410152
$857$	37.2119	1.27114	0.635568	−	0.772045i	$-0.280766\pi$
$857$	37.2119	1.27114	0.635568	+	0.772045i	$0.280766\pi$
$858$	9.48913	0.323953
$859$	51.2119	1.74733	0.873664	−	0.486529i	$-0.161737\pi$
$859$	51.2119	1.74733	0.873664	+	0.486529i	$0.161737\pi$
$860$	4.00000	0.136399
$861$	−8.00000	−0.272639
$862$	−28.7446	−0.979044
$863$	−5.76631	−0.196288	−0.0981438	−	0.995172i	$-0.531291\pi$
$863$	−5.76631	−0.196288	−0.0981438	+	0.995172i	$0.531291\pi$
$864$	−4.00000	−0.136083
$865$	−14.2337	−0.483960
$866$	25.2554	0.858215
$867$	11.0217	0.374318
$868$	−6.74456	−0.228925
$869$	4.74456	0.160948
$870$	−5.48913	−0.186099
$871$	18.9783	0.643053
$872$	16.2337	0.549742
$873$	−5.25544	−0.177870
$874$	22.5109	0.761442
$875$	1.00000	0.0338062
$876$	−1.48913	−0.0503129
$877$	42.4674	1.43402	0.717011	−	0.697062i	$-0.245510\pi$
$877$	42.4674	1.43402	0.717011	+	0.697062i	$0.245510\pi$
$878$	−30.9783	−1.04547
$879$	49.4891	1.66923
$880$	−1.00000	−0.0337100
$881$	−32.5109	−1.09532	−0.547660	−	0.836701i	$-0.684481\pi$
$881$	−32.5109	−1.09532	−0.547660	+	0.836701i	$0.684481\pi$
$882$	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	$0.542978\pi$
$884$	−22.5109	−0.757123
$885$	5.48913	0.184515
$886$	−6.51087	−0.218737
$887$	−18.5109	−0.621534	−0.310767	−	0.950486i	$-0.600586\pi$
$887$	−18.5109	−0.621534	−0.310767	+	0.950486i	$0.600586\pi$
$888$	−21.4891	−0.721128
$889$	0	0
$890$	−7.48913	−0.251036
$891$	11.0000	0.368514
$892$	26.7446	0.895474
$893$	−32.0000	−1.07084
$894$	21.4891	0.718704
$895$	−4.00000	−0.133705
$896$	1.00000	0.0334077
$897$	−45.0217	−1.50323
$898$	40.9783	1.36746
$899$	18.5109	0.617372
$900$	1.00000	0.0333333
$901$	−5.95650	−0.198440
$902$	4.00000	0.133185
$903$	8.00000	0.266223
$904$	10.0000	0.332595
$905$	3.48913	0.115982
$906$	−41.4891	−1.37838
$907$	−37.4891	−1.24481	−0.622403	−	0.782697i	$-0.713843\pi$
$907$	−37.4891	−1.24481	−0.622403	+	0.782697i	$0.713843\pi$
$908$	20.0000	0.663723
$909$	−8.74456	−0.290039
$910$	−4.74456	−0.157281
$911$	20.0000	0.662630	0.331315	−	0.943520i	$-0.392508\pi$
$911$	20.0000	0.662630	0.331315	+	0.943520i	$0.392508\pi$
$912$	9.48913	0.314216
$913$	−8.00000	−0.264761
$914$	−19.4891	−0.644643
$915$	25.4891	0.842644
$916$	−6.00000	−0.198246
$917$	8.74456	0.288771
$918$	−18.9783	−0.626376
$919$	25.2119	0.831665	0.415833	−	0.909441i	$-0.363490\pi$
$919$	25.2119	0.831665	0.415833	+	0.909441i	$0.363490\pi$
$920$	4.74456	0.156424
$921$	42.9783	1.41618
$922$	−23.7228	−0.781269
$923$	18.9783	0.624677
$924$	−2.00000	−0.0657952
$925$	−10.7446	−0.353279
$926$	12.7446	0.418812
$927$	10.7446	0.352898
$928$	−2.74456	−0.0900947
$929$	16.9783	0.557038	0.278519	−	0.960431i	$-0.410156\pi$
$929$	16.9783	0.557038	0.278519	+	0.960431i	$0.410156\pi$
$930$	−13.4891	−0.442326
$931$	4.74456	0.155497
$932$	20.9783	0.687165
$933$	−18.5109	−0.606019
$934$	−28.9783	−0.948197
$935$	−4.74456	−0.155164
$936$	−4.74456	−0.155081
$937$	−7.25544	−0.237025	−0.118512	−	0.992953i	$-0.537813\pi$
$937$	−7.25544	−0.237025	−0.118512	+	0.992953i	$0.537813\pi$
$938$	−4.00000	−0.130605
$939$	64.4674	2.10381
$940$	−6.74456	−0.219983
$941$	−22.2337	−0.724798	−0.362399	−	0.932023i	$-0.618042\pi$
$941$	−22.2337	−0.724798	−0.362399	+	0.932023i	$0.618042\pi$
$942$	46.9783	1.53063
$943$	−18.9783	−0.618017
$944$	2.74456	0.0893279
$945$	−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	$0.541492\pi$
$948$	−9.48913	−0.308192
$949$	3.53262	0.114674
$950$	4.74456	0.153934
$951$	−64.4674	−2.09050
$952$	4.74456	0.153772
$953$	6.00000	0.194359	0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000	0.194359	0.0971795	+	0.995267i	$0.469018\pi$
$954$	−1.25544	−0.0406463
$955$	−16.0000	−0.517748
$956$	−3.25544	−0.105288
$957$	5.48913	0.177438
$958$	−18.5109	−0.598059
$959$	−19.4891	−0.629337
$960$	2.00000	0.0645497
$961$	14.4891	0.467391
$962$	50.9783	1.64360
$963$	−12.0000	−0.386695
$964$	20.0000	0.644157
$965$	−2.00000	−0.0643823
$966$	9.48913	0.305308
$967$	−5.02175	−0.161489	−0.0807443	−	0.996735i	$-0.525730\pi$
$967$	−5.02175	−0.161489	−0.0807443	+	0.996735i	$0.525730\pi$
$968$	1.00000	0.0321412
$969$	45.0217	1.44631
$970$	−5.25544	−0.168742
$971$	−37.7228	−1.21058	−0.605291	−	0.796004i	$-0.706943\pi$
$971$	−37.7228	−1.21058	−0.605291	+	0.796004i	$0.706943\pi$
$972$	−10.0000	−0.320750
$973$	3.25544	0.104365
$974$	20.7446	0.664699
$975$	−9.48913	−0.303895
$976$	12.7446	0.407944
$977$	−32.9783	−1.05507	−0.527534	−	0.849534i	$-0.676883\pi$
$977$	−32.9783	−1.05507	−0.527534	+	0.849534i	$0.676883\pi$
$978$	−8.00000	−0.255812
$979$	7.48913	0.239353
$980$	1.00000	0.0319438
$981$	16.2337	0.518302
$982$	−14.9783	−0.477975
$983$	−32.2337	−1.02809	−0.514047	−	0.857762i	$-0.671854\pi$
$983$	−32.2337	−1.02809	−0.514047	+	0.857762i	$0.671854\pi$
$984$	−8.00000	−0.255031
$985$	10.0000	0.318626
$986$	−13.0217	−0.414697
$987$	−13.4891	−0.429364
$988$	−22.5109	−0.716166
$989$	18.9783	0.603473
$990$	−1.00000	−0.0317821
$991$	−21.4891	−0.682625	−0.341312	−	0.939950i	$-0.610871\pi$
$991$	−21.4891	−0.682625	−0.341312	+	0.939950i	$0.610871\pi$
$992$	−6.74456	−0.214140
$993$	−61.9565	−1.96613
$994$	−4.00000	−0.126872
$995$	14.7446	0.467434
$996$	16.0000	0.506979
$997$	−41.2119	−1.30520	−0.652598	−	0.757705i	$-0.726321\pi$
$997$	−41.2119	−1.30520	−0.652598	+	0.757705i	$0.726321\pi$
$998$	9.48913	0.300373
$999$	42.9783	1.35977

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.a.k.1.1	✓	2
3.2	odd	2		6930.2.a.bo.1.1		2
4.3	odd	2		6160.2.a.r.1.1		2
5.2	odd	4		3850.2.c.y.1849.4		4
5.3	odd	4		3850.2.c.y.1849.1		4
5.4	even	2		3850.2.a.bc.1.2		2
7.6	odd	2		5390.2.a.bq.1.2		2
11.10	odd	2		8470.2.a.bu.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.a.k.1.1	✓	2	1.1	even	1	trivial
3850.2.a.bc.1.2		2	5.4	even	2
3850.2.c.y.1849.1		4	5.3	odd	4
3850.2.c.y.1849.4		4	5.2	odd	4
5390.2.a.bq.1.2		2	7.6	odd	2
6160.2.a.r.1.1		2	4.3	odd	2
6930.2.a.bo.1.1		2	3.2	odd	2
8470.2.a.bu.1.2		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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{11} +2.00000 q^{12} -4.74456 q^{13} +1.00000 q^{14} +2.00000 q^{15} +1.00000 q^{16} +4.74456 q^{17} +1.00000 q^{18} +4.74456 q^{19} +1.00000 q^{20} +2.00000 q^{21} -1.00000 q^{22} +4.74456 q^{23} +2.00000 q^{24} +1.00000 q^{25} -4.74456 q^{26} -4.00000 q^{27} +1.00000 q^{28} -2.74456 q^{29} +2.00000 q^{30} -6.74456 q^{31} +1.00000 q^{32} -2.00000 q^{33} +4.74456 q^{34} +1.00000 q^{35} +1.00000 q^{36} -10.7446 q^{37} +4.74456 q^{38} -9.48913 q^{39} +1.00000 q^{40} -4.00000 q^{41} +2.00000 q^{42} +4.00000 q^{43} -1.00000 q^{44} +1.00000 q^{45} +4.74456 q^{46} -6.74456 q^{47} +2.00000 q^{48} +1.00000 q^{49} +1.00000 q^{50} +9.48913 q^{51} -4.74456 q^{52} -1.25544 q^{53} -4.00000 q^{54} -1.00000 q^{55} +1.00000 q^{56} +9.48913 q^{57} -2.74456 q^{58} +2.74456 q^{59} +2.00000 q^{60} +12.7446 q^{61} -6.74456 q^{62} +1.00000 q^{63} +1.00000 q^{64} -4.74456 q^{65} -2.00000 q^{66} -4.00000 q^{67} +4.74456 q^{68} +9.48913 q^{69} +1.00000 q^{70} -4.00000 q^{71} +1.00000 q^{72} -0.744563 q^{73} -10.7446 q^{74} +2.00000 q^{75} +4.74456 q^{76} -1.00000 q^{77} -9.48913 q^{78} -4.74456 q^{79} +1.00000 q^{80} -11.0000 q^{81} -4.00000 q^{82} +8.00000 q^{83} +2.00000 q^{84} +4.74456 q^{85} +4.00000 q^{86} -5.48913 q^{87} -1.00000 q^{88} -7.48913 q^{89} +1.00000 q^{90} -4.74456 q^{91} +4.74456 q^{92} -13.4891 q^{93} -6.74456 q^{94} +4.74456 q^{95} +2.00000 q^{96} -5.25544 q^{97} +1.00000 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 4 q^{3} + 2 q^{4} + 2 q^{5} + 4 q^{6} + 2 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 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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