LMFDB - Embedded newform 930.2.a.r.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(1,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, 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("930.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.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:	$7.42608738798$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.37228$ of defining polynomial
Character	$\chi$	$=$	930.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -2.37228 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -2.37228 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +6.37228 q^{11} +1.00000 q^{12} -2.00000 q^{13} -2.37228 q^{14} +1.00000 q^{15} +1.00000 q^{16} +6.74456 q^{17} +1.00000 q^{18} -6.37228 q^{19} +1.00000 q^{20} -2.37228 q^{21} +6.37228 q^{22} -2.37228 q^{23} +1.00000 q^{24} +1.00000 q^{25} -2.00000 q^{26} +1.00000 q^{27} -2.37228 q^{28} +2.74456 q^{29} +1.00000 q^{30} -1.00000 q^{31} +1.00000 q^{32} +6.37228 q^{33} +6.74456 q^{34} -2.37228 q^{35} +1.00000 q^{36} +10.7446 q^{37} -6.37228 q^{38} -2.00000 q^{39} +1.00000 q^{40} -10.7446 q^{41} -2.37228 q^{42} +6.37228 q^{43} +6.37228 q^{44} +1.00000 q^{45} -2.37228 q^{46} +4.74456 q^{47} +1.00000 q^{48} -1.37228 q^{49} +1.00000 q^{50} +6.74456 q^{51} -2.00000 q^{52} -4.37228 q^{53} +1.00000 q^{54} +6.37228 q^{55} -2.37228 q^{56} -6.37228 q^{57} +2.74456 q^{58} -8.74456 q^{59} +1.00000 q^{60} -11.4891 q^{61} -1.00000 q^{62} -2.37228 q^{63} +1.00000 q^{64} -2.00000 q^{65} +6.37228 q^{66} -0.744563 q^{67} +6.74456 q^{68} -2.37228 q^{69} -2.37228 q^{70} -2.37228 q^{71} +1.00000 q^{72} +9.11684 q^{73} +10.7446 q^{74} +1.00000 q^{75} -6.37228 q^{76} -15.1168 q^{77} -2.00000 q^{78} -10.3723 q^{79} +1.00000 q^{80} +1.00000 q^{81} -10.7446 q^{82} -12.0000 q^{83} -2.37228 q^{84} +6.74456 q^{85} +6.37228 q^{86} +2.74456 q^{87} +6.37228 q^{88} +4.37228 q^{89} +1.00000 q^{90} +4.74456 q^{91} -2.37228 q^{92} -1.00000 q^{93} +4.74456 q^{94} -6.37228 q^{95} +1.00000 q^{96} +2.00000 q^{97} -1.37228 q^{98} +6.37228 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} + q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 + q^7 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} + q^{7} + 2 q^{8} + 2 q^{9} + 2 q^{10} + 7 q^{11} + 2 q^{12} - 4 q^{13} + q^{14} + 2 q^{15} + 2 q^{16} + 2 q^{17} + 2 q^{18} - 7 q^{19} + 2 q^{20} + q^{21} + 7 q^{22} + q^{23} + 2 q^{24} + 2 q^{25} - 4 q^{26} + 2 q^{27} + q^{28} - 6 q^{29} + 2 q^{30} - 2 q^{31} + 2 q^{32} + 7 q^{33} + 2 q^{34} + q^{35} + 2 q^{36} + 10 q^{37} - 7 q^{38} - 4 q^{39} + 2 q^{40} - 10 q^{41} + q^{42} + 7 q^{43} + 7 q^{44} + 2 q^{45} + q^{46} - 2 q^{47} + 2 q^{48} + 3 q^{49} + 2 q^{50} + 2 q^{51} - 4 q^{52} - 3 q^{53} + 2 q^{54} + 7 q^{55} + q^{56} - 7 q^{57} - 6 q^{58} - 6 q^{59} + 2 q^{60} - 2 q^{62} + q^{63} + 2 q^{64} - 4 q^{65} + 7 q^{66} + 10 q^{67} + 2 q^{68} + q^{69} + q^{70} + q^{71} + 2 q^{72} + q^{73} + 10 q^{74} + 2 q^{75} - 7 q^{76} - 13 q^{77} - 4 q^{78} - 15 q^{79} + 2 q^{80} + 2 q^{81} - 10 q^{82} - 24 q^{83} + q^{84} + 2 q^{85} + 7 q^{86} - 6 q^{87} + 7 q^{88} + 3 q^{89} + 2 q^{90} - 2 q^{91} + q^{92} - 2 q^{93} - 2 q^{94} - 7 q^{95} + 2 q^{96} + 4 q^{97} + 3 q^{98} + 7 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 + q^7 + 2 * q^8 + 2 * q^9 + 2 * q^10 + 7 * q^11 + 2 * q^12 - 4 * q^13 + q^14 + 2 * q^15 + 2 * q^16 + 2 * q^17 + 2 * q^18 - 7 * q^19 + 2 * q^20 + q^21 + 7 * q^22 + q^23 + 2 * q^24 + 2 * q^25 - 4 * q^26 + 2 * q^27 + q^28 - 6 * q^29 + 2 * q^30 - 2 * q^31 + 2 * q^32 + 7 * q^33 + 2 * q^34 + q^35 + 2 * q^36 + 10 * q^37 - 7 * q^38 - 4 * q^39 + 2 * q^40 - 10 * q^41 + q^42 + 7 * q^43 + 7 * q^44 + 2 * q^45 + q^46 - 2 * q^47 + 2 * q^48 + 3 * q^49 + 2 * q^50 + 2 * q^51 - 4 * q^52 - 3 * q^53 + 2 * q^54 + 7 * q^55 + q^56 - 7 * q^57 - 6 * q^58 - 6 * q^59 + 2 * q^60 - 2 * q^62 + q^63 + 2 * q^64 - 4 * q^65 + 7 * q^66 + 10 * q^67 + 2 * q^68 + q^69 + q^70 + q^71 + 2 * q^72 + q^73 + 10 * q^74 + 2 * q^75 - 7 * q^76 - 13 * q^77 - 4 * q^78 - 15 * q^79 + 2 * q^80 + 2 * q^81 - 10 * q^82 - 24 * q^83 + q^84 + 2 * q^85 + 7 * q^86 - 6 * q^87 + 7 * q^88 + 3 * q^89 + 2 * q^90 - 2 * q^91 + q^92 - 2 * q^93 - 2 * q^94 - 7 * q^95 + 2 * q^96 + 4 * q^97 + 3 * q^98 + 7 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.00000	0.408248
$7$	−2.37228	−0.896638	−0.448319	−	0.893874i	$-0.647977\pi$
$7$	−2.37228	−0.896638	−0.448319	+	0.893874i	$0.647977\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	6.37228	1.92132	0.960658	−	0.277736i	$-0.0895839\pi$
$11$	6.37228	1.92132	0.960658	+	0.277736i	$0.0895839\pi$
$12$	1.00000	0.288675
$13$	−2.00000	−0.554700	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000	−0.554700	−0.277350	+	0.960769i	$0.589456\pi$
$14$	−2.37228	−0.634019
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	6.74456	1.63580	0.817898	−	0.575363i	$-0.195139\pi$
$17$	6.74456	1.63580	0.817898	+	0.575363i	$0.195139\pi$
$18$	1.00000	0.235702
$19$	−6.37228	−1.46190	−0.730951	−	0.682430i	$-0.760923\pi$
$19$	−6.37228	−1.46190	−0.730951	+	0.682430i	$0.760923\pi$
$20$	1.00000	0.223607
$21$	−2.37228	−0.517674
$22$	6.37228	1.35857
$23$	−2.37228	−0.494655	−0.247327	−	0.968932i	$-0.579552\pi$
$23$	−2.37228	−0.494655	−0.247327	+	0.968932i	$0.579552\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	−2.00000	−0.392232
$27$	1.00000	0.192450
$28$	−2.37228	−0.448319
$29$	2.74456	0.509652	0.254826	−	0.966987i	$-0.417982\pi$
$29$	2.74456	0.509652	0.254826	+	0.966987i	$0.417982\pi$
$30$	1.00000	0.182574
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	1.00000	0.176777
$33$	6.37228	1.10927
$34$	6.74456	1.15668
$35$	−2.37228	−0.400989
$36$	1.00000	0.166667
$37$	10.7446	1.76640	0.883198	−	0.469001i	$-0.155386\pi$
$37$	10.7446	1.76640	0.883198	+	0.469001i	$0.155386\pi$
$38$	−6.37228	−1.03372
$39$	−2.00000	−0.320256
$40$	1.00000	0.158114
$41$	−10.7446	−1.67802	−0.839009	−	0.544117i	$-0.816865\pi$
$41$	−10.7446	−1.67802	−0.839009	+	0.544117i	$0.816865\pi$
$42$	−2.37228	−0.366051
$43$	6.37228	0.971764	0.485882	−	0.874024i	$-0.338499\pi$
$43$	6.37228	0.971764	0.485882	+	0.874024i	$0.338499\pi$
$44$	6.37228	0.960658
$45$	1.00000	0.149071
$46$	−2.37228	−0.349774
$47$	4.74456	0.692066	0.346033	−	0.938222i	$-0.387529\pi$
$47$	4.74456	0.692066	0.346033	+	0.938222i	$0.387529\pi$
$48$	1.00000	0.144338
$49$	−1.37228	−0.196040
$50$	1.00000	0.141421
$51$	6.74456	0.944428
$52$	−2.00000	−0.277350
$53$	−4.37228	−0.600579	−0.300290	−	0.953848i	$-0.597083\pi$
$53$	−4.37228	−0.600579	−0.300290	+	0.953848i	$0.597083\pi$
$54$	1.00000	0.136083
$55$	6.37228	0.859238
$56$	−2.37228	−0.317009
$57$	−6.37228	−0.844029
$58$	2.74456	0.360379
$59$	−8.74456	−1.13845	−0.569223	−	0.822183i	$-0.692756\pi$
$59$	−8.74456	−1.13845	−0.569223	+	0.822183i	$0.692756\pi$
$60$	1.00000	0.129099
$61$	−11.4891	−1.47103	−0.735516	−	0.677507i	$-0.763060\pi$
$61$	−11.4891	−1.47103	−0.735516	+	0.677507i	$0.763060\pi$
$62$	−1.00000	−0.127000
$63$	−2.37228	−0.298879
$64$	1.00000	0.125000
$65$	−2.00000	−0.248069
$66$	6.37228	0.784374
$67$	−0.744563	−0.0909628	−0.0454814	−	0.998965i	$-0.514482\pi$
$67$	−0.744563	−0.0909628	−0.0454814	+	0.998965i	$0.514482\pi$
$68$	6.74456	0.817898
$69$	−2.37228	−0.285589
$70$	−2.37228	−0.283542
$71$	−2.37228	−0.281538	−0.140769	−	0.990042i	$-0.544957\pi$
$71$	−2.37228	−0.281538	−0.140769	+	0.990042i	$0.544957\pi$
$72$	1.00000	0.117851
$73$	9.11684	1.06705	0.533523	−	0.845786i	$-0.320868\pi$
$73$	9.11684	1.06705	0.533523	+	0.845786i	$0.320868\pi$
$74$	10.7446	1.24903
$75$	1.00000	0.115470
$76$	−6.37228	−0.730951
$77$	−15.1168	−1.72272
$78$	−2.00000	−0.226455
$79$	−10.3723	−1.16697	−0.583486	−	0.812123i	$-0.698312\pi$
$79$	−10.3723	−1.16697	−0.583486	+	0.812123i	$0.698312\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	−10.7446	−1.18654
$83$	−12.0000	−1.31717	−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000	−1.31717	−0.658586	+	0.752506i	$0.728845\pi$
$84$	−2.37228	−0.258837
$85$	6.74456	0.731551
$86$	6.37228	0.687141
$87$	2.74456	0.294248
$88$	6.37228	0.679287
$89$	4.37228	0.463461	0.231730	−	0.972780i	$-0.425561\pi$
$89$	4.37228	0.463461	0.231730	+	0.972780i	$0.425561\pi$
$90$	1.00000	0.105409
$91$	4.74456	0.497365
$92$	−2.37228	−0.247327
$93$	−1.00000	−0.103695
$94$	4.74456	0.489364
$95$	−6.37228	−0.653782
$96$	1.00000	0.102062
$97$	2.00000	0.203069	0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000	0.203069	0.101535	+	0.994832i	$0.467625\pi$
$98$	−1.37228	−0.138621
$99$	6.37228	0.640438
$100$	1.00000	0.100000
$101$	−9.11684	−0.907160	−0.453580	−	0.891216i	$-0.649853\pi$
$101$	−9.11684	−0.907160	−0.453580	+	0.891216i	$0.649853\pi$
$102$	6.74456	0.667811
$103$	−8.00000	−0.788263	−0.394132	−	0.919054i	$-0.628955\pi$
$103$	−8.00000	−0.788263	−0.394132	+	0.919054i	$0.628955\pi$
$104$	−2.00000	−0.196116
$105$	−2.37228	−0.231511
$106$	−4.37228	−0.424674
$107$	6.37228	0.616032	0.308016	−	0.951381i	$-0.400335\pi$
$107$	6.37228	0.616032	0.308016	+	0.951381i	$0.400335\pi$
$108$	1.00000	0.0962250
$109$	−6.74456	−0.646012	−0.323006	−	0.946397i	$-0.604693\pi$
$109$	−6.74456	−0.646012	−0.323006	+	0.946397i	$0.604693\pi$
$110$	6.37228	0.607573
$111$	10.7446	1.01983
$112$	−2.37228	−0.224160
$113$	−8.37228	−0.787598	−0.393799	−	0.919197i	$-0.628839\pi$
$113$	−8.37228	−0.787598	−0.393799	+	0.919197i	$0.628839\pi$
$114$	−6.37228	−0.596819
$115$	−2.37228	−0.221216
$116$	2.74456	0.254826
$117$	−2.00000	−0.184900
$118$	−8.74456	−0.805002
$119$	−16.0000	−1.46672
$120$	1.00000	0.0912871
$121$	29.6060	2.69145
$122$	−11.4891	−1.04018
$123$	−10.7446	−0.968805
$124$	−1.00000	−0.0898027
$125$	1.00000	0.0894427
$126$	−2.37228	−0.211340
$127$	−9.48913	−0.842024	−0.421012	−	0.907055i	$-0.638325\pi$
$127$	−9.48913	−0.842024	−0.421012	+	0.907055i	$0.638325\pi$
$128$	1.00000	0.0883883
$129$	6.37228	0.561048
$130$	−2.00000	−0.175412
$131$	18.2337	1.59308	0.796542	−	0.604583i	$-0.206660\pi$
$131$	18.2337	1.59308	0.796542	+	0.604583i	$0.206660\pi$
$132$	6.37228	0.554636
$133$	15.1168	1.31080
$134$	−0.744563	−0.0643204
$135$	1.00000	0.0860663
$136$	6.74456	0.578341
$137$	19.4891	1.66507	0.832534	−	0.553974i	$-0.186889\pi$
$137$	19.4891	1.66507	0.832534	+	0.553974i	$0.186889\pi$
$138$	−2.37228	−0.201942
$139$	0.744563	0.0631530	0.0315765	−	0.999501i	$-0.489947\pi$
$139$	0.744563	0.0631530	0.0315765	+	0.999501i	$0.489947\pi$
$140$	−2.37228	−0.200494
$141$	4.74456	0.399564
$142$	−2.37228	−0.199077
$143$	−12.7446	−1.06575
$144$	1.00000	0.0833333
$145$	2.74456	0.227924
$146$	9.11684	0.754515
$147$	−1.37228	−0.113184
$148$	10.7446	0.883198
$149$	5.11684	0.419188	0.209594	−	0.977788i	$-0.432786\pi$
$149$	5.11684	0.419188	0.209594	+	0.977788i	$0.432786\pi$
$150$	1.00000	0.0816497
$151$	−8.00000	−0.651031	−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000	−0.651031	−0.325515	+	0.945537i	$0.605538\pi$
$152$	−6.37228	−0.516860
$153$	6.74456	0.545266
$154$	−15.1168	−1.21815
$155$	−1.00000	−0.0803219
$156$	−2.00000	−0.160128
$157$	3.62772	0.289523	0.144762	−	0.989467i	$-0.453758\pi$
$157$	3.62772	0.289523	0.144762	+	0.989467i	$0.453758\pi$
$158$	−10.3723	−0.825174
$159$	−4.37228	−0.346744
$160$	1.00000	0.0790569
$161$	5.62772	0.443526
$162$	1.00000	0.0785674
$163$	−10.2337	−0.801564	−0.400782	−	0.916173i	$-0.631262\pi$
$163$	−10.2337	−0.801564	−0.400782	+	0.916173i	$0.631262\pi$
$164$	−10.7446	−0.839009
$165$	6.37228	0.496081
$166$	−12.0000	−0.931381
$167$	−18.3723	−1.42169	−0.710845	−	0.703349i	$-0.751687\pi$
$167$	−18.3723	−1.42169	−0.710845	+	0.703349i	$0.751687\pi$
$168$	−2.37228	−0.183025
$169$	−9.00000	−0.692308
$170$	6.74456	0.517284
$171$	−6.37228	−0.487301
$172$	6.37228	0.485882
$173$	−18.0000	−1.36851	−0.684257	−	0.729241i	$-0.739873\pi$
$173$	−18.0000	−1.36851	−0.684257	+	0.729241i	$0.739873\pi$
$174$	2.74456	0.208065
$175$	−2.37228	−0.179328
$176$	6.37228	0.480329
$177$	−8.74456	−0.657282
$178$	4.37228	0.327716
$179$	−12.0000	−0.896922	−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000	−0.896922	−0.448461	+	0.893802i	$0.648028\pi$
$180$	1.00000	0.0745356
$181$	−13.8614	−1.03031	−0.515155	−	0.857097i	$-0.672266\pi$
$181$	−13.8614	−1.03031	−0.515155	+	0.857097i	$0.672266\pi$
$182$	4.74456	0.351690
$183$	−11.4891	−0.849301
$184$	−2.37228	−0.174887
$185$	10.7446	0.789956
$186$	−1.00000	−0.0733236
$187$	42.9783	3.14288
$188$	4.74456	0.346033
$189$	−2.37228	−0.172558
$190$	−6.37228	−0.462294
$191$	16.0000	1.15772	0.578860	−	0.815427i	$-0.303498\pi$
$191$	16.0000	1.15772	0.578860	+	0.815427i	$0.303498\pi$
$192$	1.00000	0.0721688
$193$	−7.48913	−0.539079	−0.269540	−	0.962989i	$-0.586871\pi$
$193$	−7.48913	−0.539079	−0.269540	+	0.962989i	$0.586871\pi$
$194$	2.00000	0.143592
$195$	−2.00000	−0.143223
$196$	−1.37228	−0.0980201
$197$	−3.48913	−0.248590	−0.124295	−	0.992245i	$-0.539667\pi$
$197$	−3.48913	−0.248590	−0.124295	+	0.992245i	$0.539667\pi$
$198$	6.37228	0.452858
$199$	−18.3723	−1.30238	−0.651188	−	0.758916i	$-0.725729\pi$
$199$	−18.3723	−1.30238	−0.651188	+	0.758916i	$0.725729\pi$
$200$	1.00000	0.0707107
$201$	−0.744563	−0.0525174
$202$	−9.11684	−0.641459
$203$	−6.51087	−0.456974
$204$	6.74456	0.472214
$205$	−10.7446	−0.750433
$206$	−8.00000	−0.557386
$207$	−2.37228	−0.164885
$208$	−2.00000	−0.138675
$209$	−40.6060	−2.80877
$210$	−2.37228	−0.163703
$211$	−6.37228	−0.438686	−0.219343	−	0.975648i	$-0.570391\pi$
$211$	−6.37228	−0.438686	−0.219343	+	0.975648i	$0.570391\pi$
$212$	−4.37228	−0.300290
$213$	−2.37228	−0.162546
$214$	6.37228	0.435600
$215$	6.37228	0.434586
$216$	1.00000	0.0680414
$217$	2.37228	0.161041
$218$	−6.74456	−0.456799
$219$	9.11684	0.616059
$220$	6.37228	0.429619
$221$	−13.4891	−0.907377
$222$	10.7446	0.721128
$223$	20.7446	1.38916	0.694579	−	0.719416i	$-0.255591\pi$
$223$	20.7446	1.38916	0.694579	+	0.719416i	$0.255591\pi$
$224$	−2.37228	−0.158505
$225$	1.00000	0.0666667
$226$	−8.37228	−0.556916
$227$	−11.1168	−0.737851	−0.368925	−	0.929459i	$-0.620274\pi$
$227$	−11.1168	−0.737851	−0.368925	+	0.929459i	$0.620274\pi$
$228$	−6.37228	−0.422015
$229$	21.1168	1.39544	0.697720	−	0.716370i	$-0.254198\pi$
$229$	21.1168	1.39544	0.697720	+	0.716370i	$0.254198\pi$
$230$	−2.37228	−0.156424
$231$	−15.1168	−0.994615
$232$	2.74456	0.180189
$233$	13.8614	0.908091	0.454045	−	0.890979i	$-0.349980\pi$
$233$	13.8614	0.908091	0.454045	+	0.890979i	$0.349980\pi$
$234$	−2.00000	−0.130744
$235$	4.74456	0.309501
$236$	−8.74456	−0.569223
$237$	−10.3723	−0.673752
$238$	−16.0000	−1.03713
$239$	−6.51087	−0.421153	−0.210577	−	0.977577i	$-0.567534\pi$
$239$	−6.51087	−0.421153	−0.210577	+	0.977577i	$0.567534\pi$
$240$	1.00000	0.0645497
$241$	27.4891	1.77073	0.885365	−	0.464896i	$-0.153908\pi$
$241$	27.4891	1.77073	0.885365	+	0.464896i	$0.153908\pi$
$242$	29.6060	1.90314
$243$	1.00000	0.0641500
$244$	−11.4891	−0.735516
$245$	−1.37228	−0.0876718
$246$	−10.7446	−0.685048
$247$	12.7446	0.810917
$248$	−1.00000	−0.0635001
$249$	−12.0000	−0.760469
$250$	1.00000	0.0632456
$251$	−4.00000	−0.252478	−0.126239	−	0.992000i	$-0.540291\pi$
$251$	−4.00000	−0.252478	−0.126239	+	0.992000i	$0.540291\pi$
$252$	−2.37228	−0.149440
$253$	−15.1168	−0.950388
$254$	−9.48913	−0.595401
$255$	6.74456	0.422361
$256$	1.00000	0.0625000
$257$	7.62772	0.475804	0.237902	−	0.971289i	$-0.423540\pi$
$257$	7.62772	0.475804	0.237902	+	0.971289i	$0.423540\pi$
$258$	6.37228	0.396721
$259$	−25.4891	−1.58382
$260$	−2.00000	−0.124035
$261$	2.74456	0.169884
$262$	18.2337	1.12648
$263$	26.9783	1.66355	0.831775	−	0.555113i	$-0.187325\pi$
$263$	26.9783	1.66355	0.831775	+	0.555113i	$0.187325\pi$
$264$	6.37228	0.392187
$265$	−4.37228	−0.268587
$266$	15.1168	0.926873
$267$	4.37228	0.267579
$268$	−0.744563	−0.0454814
$269$	−2.00000	−0.121942	−0.0609711	−	0.998140i	$-0.519420\pi$
$269$	−2.00000	−0.121942	−0.0609711	+	0.998140i	$0.519420\pi$
$270$	1.00000	0.0608581
$271$	−31.1168	−1.89021	−0.945107	−	0.326762i	$-0.894043\pi$
$271$	−31.1168	−1.89021	−0.945107	+	0.326762i	$0.894043\pi$
$272$	6.74456	0.408949
$273$	4.74456	0.287154
$274$	19.4891	1.17738
$275$	6.37228	0.384263
$276$	−2.37228	−0.142795
$277$	26.7446	1.60693	0.803463	−	0.595355i	$-0.202989\pi$
$277$	26.7446	1.60693	0.803463	+	0.595355i	$0.202989\pi$
$278$	0.744563	0.0446559
$279$	−1.00000	−0.0598684
$280$	−2.37228	−0.141771
$281$	5.25544	0.313513	0.156757	−	0.987637i	$-0.449896\pi$
$281$	5.25544	0.313513	0.156757	+	0.987637i	$0.449896\pi$
$282$	4.74456	0.282535
$283$	12.0000	0.713326	0.356663	−	0.934233i	$-0.383914\pi$
$283$	12.0000	0.713326	0.356663	+	0.934233i	$0.383914\pi$
$284$	−2.37228	−0.140769
$285$	−6.37228	−0.377461
$286$	−12.7446	−0.753602
$287$	25.4891	1.50458
$288$	1.00000	0.0589256
$289$	28.4891	1.67583
$290$	2.74456	0.161166
$291$	2.00000	0.117242
$292$	9.11684	0.533523
$293$	15.4891	0.904884	0.452442	−	0.891794i	$-0.350553\pi$
$293$	15.4891	0.904884	0.452442	+	0.891794i	$0.350553\pi$
$294$	−1.37228	−0.0800331
$295$	−8.74456	−0.509128
$296$	10.7446	0.624515
$297$	6.37228	0.369757
$298$	5.11684	0.296411
$299$	4.74456	0.274385
$300$	1.00000	0.0577350
$301$	−15.1168	−0.871320
$302$	−8.00000	−0.460348
$303$	−9.11684	−0.523749
$304$	−6.37228	−0.365475
$305$	−11.4891	−0.657865
$306$	6.74456	0.385561
$307$	−14.9783	−0.854854	−0.427427	−	0.904050i	$-0.640580\pi$
$307$	−14.9783	−0.854854	−0.427427	+	0.904050i	$0.640580\pi$
$308$	−15.1168	−0.861362
$309$	−8.00000	−0.455104
$310$	−1.00000	−0.0567962
$311$	8.00000	0.453638	0.226819	−	0.973937i	$-0.427167\pi$
$311$	8.00000	0.453638	0.226819	+	0.973937i	$0.427167\pi$
$312$	−2.00000	−0.113228
$313$	10.0000	0.565233	0.282617	−	0.959233i	$-0.408798\pi$
$313$	10.0000	0.565233	0.282617	+	0.959233i	$0.408798\pi$
$314$	3.62772	0.204724
$315$	−2.37228	−0.133663
$316$	−10.3723	−0.583486
$317$	−13.2554	−0.744500	−0.372250	−	0.928133i	$-0.621414\pi$
$317$	−13.2554	−0.744500	−0.372250	+	0.928133i	$0.621414\pi$
$318$	−4.37228	−0.245185
$319$	17.4891	0.979203
$320$	1.00000	0.0559017
$321$	6.37228	0.355666
$322$	5.62772	0.313621
$323$	−42.9783	−2.39137
$324$	1.00000	0.0555556
$325$	−2.00000	−0.110940
$326$	−10.2337	−0.566792
$327$	−6.74456	−0.372975
$328$	−10.7446	−0.593269
$329$	−11.2554	−0.620532
$330$	6.37228	0.350783
$331$	21.4891	1.18115	0.590575	−	0.806983i	$-0.298901\pi$
$331$	21.4891	1.18115	0.590575	+	0.806983i	$0.298901\pi$
$332$	−12.0000	−0.658586
$333$	10.7446	0.588798
$334$	−18.3723	−1.00529
$335$	−0.744563	−0.0406798
$336$	−2.37228	−0.129419
$337$	−16.9783	−0.924864	−0.462432	−	0.886655i	$-0.653023\pi$
$337$	−16.9783	−0.924864	−0.462432	+	0.886655i	$0.653023\pi$
$338$	−9.00000	−0.489535
$339$	−8.37228	−0.454720
$340$	6.74456	0.365775
$341$	−6.37228	−0.345078
$342$	−6.37228	−0.344574
$343$	19.8614	1.07242
$344$	6.37228	0.343570
$345$	−2.37228	−0.127719
$346$	−18.0000	−0.967686
$347$	−32.4674	−1.74294	−0.871470	−	0.490449i	$-0.836833\pi$
$347$	−32.4674	−1.74294	−0.871470	+	0.490449i	$0.836833\pi$
$348$	2.74456	0.147124
$349$	18.7446	1.00337	0.501687	−	0.865049i	$-0.332713\pi$
$349$	18.7446	1.00337	0.501687	+	0.865049i	$0.332713\pi$
$350$	−2.37228	−0.126804
$351$	−2.00000	−0.106752
$352$	6.37228	0.339644
$353$	−7.48913	−0.398606	−0.199303	−	0.979938i	$-0.563868\pi$
$353$	−7.48913	−0.398606	−0.199303	+	0.979938i	$0.563868\pi$
$354$	−8.74456	−0.464768
$355$	−2.37228	−0.125908
$356$	4.37228	0.231730
$357$	−16.0000	−0.846810
$358$	−12.0000	−0.634220
$359$	−2.37228	−0.125204	−0.0626021	−	0.998039i	$-0.519940\pi$
$359$	−2.37228	−0.125204	−0.0626021	+	0.998039i	$0.519940\pi$
$360$	1.00000	0.0527046
$361$	21.6060	1.13716
$362$	−13.8614	−0.728539
$363$	29.6060	1.55391
$364$	4.74456	0.248683
$365$	9.11684	0.477197
$366$	−11.4891	−0.600546
$367$	14.2337	0.742992	0.371496	−	0.928434i	$-0.378845\pi$
$367$	14.2337	0.742992	0.371496	+	0.928434i	$0.378845\pi$
$368$	−2.37228	−0.123664
$369$	−10.7446	−0.559340
$370$	10.7446	0.558583
$371$	10.3723	0.538502
$372$	−1.00000	−0.0518476
$373$	−13.8614	−0.717716	−0.358858	−	0.933392i	$-0.616834\pi$
$373$	−13.8614	−0.717716	−0.358858	+	0.933392i	$0.616834\pi$
$374$	42.9783	2.22235
$375$	1.00000	0.0516398
$376$	4.74456	0.244682
$377$	−5.48913	−0.282704
$378$	−2.37228	−0.122017
$379$	−0.138593	−0.00711906	−0.00355953	−	0.999994i	$-0.501133\pi$
$379$	−0.138593	−0.00711906	−0.00355953	+	0.999994i	$0.501133\pi$
$380$	−6.37228	−0.326891
$381$	−9.48913	−0.486143
$382$	16.0000	0.818631
$383$	−9.48913	−0.484872	−0.242436	−	0.970167i	$-0.577946\pi$
$383$	−9.48913	−0.484872	−0.242436	+	0.970167i	$0.577946\pi$
$384$	1.00000	0.0510310
$385$	−15.1168	−0.770426
$386$	−7.48913	−0.381186
$387$	6.37228	0.323921
$388$	2.00000	0.101535
$389$	−28.9783	−1.46926	−0.734628	−	0.678470i	$-0.762643\pi$
$389$	−28.9783	−1.46926	−0.734628	+	0.678470i	$0.762643\pi$
$390$	−2.00000	−0.101274
$391$	−16.0000	−0.809155
$392$	−1.37228	−0.0693107
$393$	18.2337	0.919768
$394$	−3.48913	−0.175780
$395$	−10.3723	−0.521886
$396$	6.37228	0.320219
$397$	38.6060	1.93758	0.968789	−	0.247887i	$-0.0797361\pi$
$397$	38.6060	1.93758	0.968789	+	0.247887i	$0.0797361\pi$
$398$	−18.3723	−0.920919
$399$	15.1168	0.756789
$400$	1.00000	0.0500000
$401$	28.3723	1.41684	0.708422	−	0.705789i	$-0.249407\pi$
$401$	28.3723	1.41684	0.708422	+	0.705789i	$0.249407\pi$
$402$	−0.744563	−0.0371354
$403$	2.00000	0.0996271
$404$	−9.11684	−0.453580
$405$	1.00000	0.0496904
$406$	−6.51087	−0.323129
$407$	68.4674	3.39380
$408$	6.74456	0.333906
$409$	24.2337	1.19828	0.599139	−	0.800645i	$-0.295510\pi$
$409$	24.2337	1.19828	0.599139	+	0.800645i	$0.295510\pi$
$410$	−10.7446	−0.530636
$411$	19.4891	0.961328
$412$	−8.00000	−0.394132
$413$	20.7446	1.02077
$414$	−2.37228	−0.116591
$415$	−12.0000	−0.589057
$416$	−2.00000	−0.0980581
$417$	0.744563	0.0364614
$418$	−40.6060	−1.98610
$419$	−12.0000	−0.586238	−0.293119	−	0.956076i	$-0.594693\pi$
$419$	−12.0000	−0.586238	−0.293119	+	0.956076i	$0.594693\pi$
$420$	−2.37228	−0.115755
$421$	−3.48913	−0.170050	−0.0850248	−	0.996379i	$-0.527097\pi$
$421$	−3.48913	−0.170050	−0.0850248	+	0.996379i	$0.527097\pi$
$422$	−6.37228	−0.310198
$423$	4.74456	0.230689
$424$	−4.37228	−0.212337
$425$	6.74456	0.327159
$426$	−2.37228	−0.114937
$427$	27.2554	1.31898
$428$	6.37228	0.308016
$429$	−12.7446	−0.615313
$430$	6.37228	0.307299
$431$	18.9783	0.914150	0.457075	−	0.889428i	$-0.348897\pi$
$431$	18.9783	0.914150	0.457075	+	0.889428i	$0.348897\pi$
$432$	1.00000	0.0481125
$433$	18.8832	0.907467	0.453733	−	0.891138i	$-0.350092\pi$
$433$	18.8832	0.907467	0.453733	+	0.891138i	$0.350092\pi$
$434$	2.37228	0.113873
$435$	2.74456	0.131592
$436$	−6.74456	−0.323006
$437$	15.1168	0.723137
$438$	9.11684	0.435620
$439$	3.25544	0.155374	0.0776868	−	0.996978i	$-0.475247\pi$
$439$	3.25544	0.155374	0.0776868	+	0.996978i	$0.475247\pi$
$440$	6.37228	0.303787
$441$	−1.37228	−0.0653467
$442$	−13.4891	−0.641612
$443$	−17.3505	−0.824349	−0.412174	−	0.911105i	$-0.635231\pi$
$443$	−17.3505	−0.824349	−0.412174	+	0.911105i	$0.635231\pi$
$444$	10.7446	0.509914
$445$	4.37228	0.207266
$446$	20.7446	0.982284
$447$	5.11684	0.242018
$448$	−2.37228	−0.112080
$449$	36.9783	1.74511	0.872556	−	0.488515i	$-0.162461\pi$
$449$	36.9783	1.74511	0.872556	+	0.488515i	$0.162461\pi$
$450$	1.00000	0.0471405
$451$	−68.4674	−3.22400
$452$	−8.37228	−0.393799
$453$	−8.00000	−0.375873
$454$	−11.1168	−0.521739
$455$	4.74456	0.222429
$456$	−6.37228	−0.298409
$457$	−34.4674	−1.61232	−0.806158	−	0.591700i	$-0.798457\pi$
$457$	−34.4674	−1.61232	−0.806158	+	0.591700i	$0.798457\pi$
$458$	21.1168	0.986725
$459$	6.74456	0.314809
$460$	−2.37228	−0.110608
$461$	37.7228	1.75693	0.878463	−	0.477810i	$-0.158569\pi$
$461$	37.7228	1.75693	0.878463	+	0.477810i	$0.158569\pi$
$462$	−15.1168	−0.703299
$463$	25.4891	1.18458	0.592290	−	0.805725i	$-0.298224\pi$
$463$	25.4891	1.18458	0.592290	+	0.805725i	$0.298224\pi$
$464$	2.74456	0.127413
$465$	−1.00000	−0.0463739
$466$	13.8614	0.642117
$467$	29.4891	1.36459	0.682297	−	0.731075i	$-0.260981\pi$
$467$	29.4891	1.36459	0.682297	+	0.731075i	$0.260981\pi$
$468$	−2.00000	−0.0924500
$469$	1.76631	0.0815607
$470$	4.74456	0.218850
$471$	3.62772	0.167156
$472$	−8.74456	−0.402501
$473$	40.6060	1.86706
$474$	−10.3723	−0.476415
$475$	−6.37228	−0.292380
$476$	−16.0000	−0.733359
$477$	−4.37228	−0.200193
$478$	−6.51087	−0.297800
$479$	−19.8614	−0.907491	−0.453745	−	0.891131i	$-0.649912\pi$
$479$	−19.8614	−0.907491	−0.453745	+	0.891131i	$0.649912\pi$
$480$	1.00000	0.0456435
$481$	−21.4891	−0.979820
$482$	27.4891	1.25210
$483$	5.62772	0.256070
$484$	29.6060	1.34573
$485$	2.00000	0.0908153
$486$	1.00000	0.0453609
$487$	−14.5109	−0.657550	−0.328775	−	0.944408i	$-0.606636\pi$
$487$	−14.5109	−0.657550	−0.328775	+	0.944408i	$0.606636\pi$
$488$	−11.4891	−0.520088
$489$	−10.2337	−0.462783
$490$	−1.37228	−0.0619934
$491$	−12.6060	−0.568899	−0.284450	−	0.958691i	$-0.591811\pi$
$491$	−12.6060	−0.568899	−0.284450	+	0.958691i	$0.591811\pi$
$492$	−10.7446	−0.484402
$493$	18.5109	0.833688
$494$	12.7446	0.573405
$495$	6.37228	0.286413
$496$	−1.00000	−0.0449013
$497$	5.62772	0.252438
$498$	−12.0000	−0.537733
$499$	10.5109	0.470531	0.235266	−	0.971931i	$-0.424404\pi$
$499$	10.5109	0.470531	0.235266	+	0.971931i	$0.424404\pi$
$500$	1.00000	0.0447214
$501$	−18.3723	−0.820813
$502$	−4.00000	−0.178529
$503$	−17.4891	−0.779802	−0.389901	−	0.920857i	$-0.627491\pi$
$503$	−17.4891	−0.779802	−0.389901	+	0.920857i	$0.627491\pi$
$504$	−2.37228	−0.105670
$505$	−9.11684	−0.405694
$506$	−15.1168	−0.672026
$507$	−9.00000	−0.399704
$508$	−9.48913	−0.421012
$509$	−38.7446	−1.71732	−0.858661	−	0.512543i	$-0.828703\pi$
$509$	−38.7446	−1.71732	−0.858661	+	0.512543i	$0.828703\pi$
$510$	6.74456	0.298654
$511$	−21.6277	−0.956754
$512$	1.00000	0.0441942
$513$	−6.37228	−0.281343
$514$	7.62772	0.336444
$515$	−8.00000	−0.352522
$516$	6.37228	0.280524
$517$	30.2337	1.32968
$518$	−25.4891	−1.11993
$519$	−18.0000	−0.790112
$520$	−2.00000	−0.0877058
$521$	−8.97825	−0.393344	−0.196672	−	0.980469i	$-0.563013\pi$
$521$	−8.97825	−0.393344	−0.196672	+	0.980469i	$0.563013\pi$
$522$	2.74456	0.120126
$523$	15.8614	0.693571	0.346785	−	0.937944i	$-0.387273\pi$
$523$	15.8614	0.693571	0.346785	+	0.937944i	$0.387273\pi$
$524$	18.2337	0.796542
$525$	−2.37228	−0.103535
$526$	26.9783	1.17631
$527$	−6.74456	−0.293798
$528$	6.37228	0.277318
$529$	−17.3723	−0.755317
$530$	−4.37228	−0.189920
$531$	−8.74456	−0.379482
$532$	15.1168	0.655398
$533$	21.4891	0.930797
$534$	4.37228	0.189207
$535$	6.37228	0.275498
$536$	−0.744563	−0.0321602
$537$	−12.0000	−0.517838
$538$	−2.00000	−0.0862261
$539$	−8.74456	−0.376655
$540$	1.00000	0.0430331
$541$	7.48913	0.321983	0.160991	−	0.986956i	$-0.448531\pi$
$541$	7.48913	0.321983	0.160991	+	0.986956i	$0.448531\pi$
$542$	−31.1168	−1.33658
$543$	−13.8614	−0.594850
$544$	6.74456	0.289171
$545$	−6.74456	−0.288905
$546$	4.74456	0.203049
$547$	8.74456	0.373890	0.186945	−	0.982370i	$-0.440141\pi$
$547$	8.74456	0.373890	0.186945	+	0.982370i	$0.440141\pi$
$548$	19.4891	0.832534
$549$	−11.4891	−0.490344
$550$	6.37228	0.271715
$551$	−17.4891	−0.745062
$552$	−2.37228	−0.100971
$553$	24.6060	1.04635
$554$	26.7446	1.13627
$555$	10.7446	0.456081
$556$	0.744563	0.0315765
$557$	29.1168	1.23372	0.616860	−	0.787073i	$-0.288404\pi$
$557$	29.1168	1.23372	0.616860	+	0.787073i	$0.288404\pi$
$558$	−1.00000	−0.0423334
$559$	−12.7446	−0.539038
$560$	−2.37228	−0.100247
$561$	42.9783	1.81454
$562$	5.25544	0.221687
$563$	38.9783	1.64274	0.821369	−	0.570398i	$-0.193211\pi$
$563$	38.9783	1.64274	0.821369	+	0.570398i	$0.193211\pi$
$564$	4.74456	0.199782
$565$	−8.37228	−0.352225
$566$	12.0000	0.504398
$567$	−2.37228	−0.0996265
$568$	−2.37228	−0.0995387
$569$	4.37228	0.183296	0.0916478	−	0.995791i	$-0.470787\pi$
$569$	4.37228	0.183296	0.0916478	+	0.995791i	$0.470787\pi$
$570$	−6.37228	−0.266905
$571$	−15.2554	−0.638420	−0.319210	−	0.947684i	$-0.603418\pi$
$571$	−15.2554	−0.638420	−0.319210	+	0.947684i	$0.603418\pi$
$572$	−12.7446	−0.532877
$573$	16.0000	0.668410
$574$	25.4891	1.06390
$575$	−2.37228	−0.0989310
$576$	1.00000	0.0416667
$577$	32.2337	1.34191	0.670953	−	0.741500i	$-0.265885\pi$
$577$	32.2337	1.34191	0.670953	+	0.741500i	$0.265885\pi$
$578$	28.4891	1.18499
$579$	−7.48913	−0.311237
$580$	2.74456	0.113962
$581$	28.4674	1.18103
$582$	2.00000	0.0829027
$583$	−27.8614	−1.15390
$584$	9.11684	0.377258
$585$	−2.00000	−0.0826898
$586$	15.4891	0.639850
$587$	12.0000	0.495293	0.247647	−	0.968850i	$-0.420343\pi$
$587$	12.0000	0.495293	0.247647	+	0.968850i	$0.420343\pi$
$588$	−1.37228	−0.0565919
$589$	6.37228	0.262565
$590$	−8.74456	−0.360008
$591$	−3.48913	−0.143523
$592$	10.7446	0.441599
$593$	−0.978251	−0.0401719	−0.0200860	−	0.999798i	$-0.506394\pi$
$593$	−0.978251	−0.0401719	−0.0200860	+	0.999798i	$0.506394\pi$
$594$	6.37228	0.261458
$595$	−16.0000	−0.655936
$596$	5.11684	0.209594
$597$	−18.3723	−0.751927
$598$	4.74456	0.194020
$599$	−7.11684	−0.290786	−0.145393	−	0.989374i	$-0.546445\pi$
$599$	−7.11684	−0.290786	−0.145393	+	0.989374i	$0.546445\pi$
$600$	1.00000	0.0408248
$601$	35.4891	1.44763	0.723816	−	0.689993i	$-0.242387\pi$
$601$	35.4891	1.44763	0.723816	+	0.689993i	$0.242387\pi$
$602$	−15.1168	−0.616117
$603$	−0.744563	−0.0303209
$604$	−8.00000	−0.325515
$605$	29.6060	1.20365
$606$	−9.11684	−0.370346
$607$	−10.3723	−0.420998	−0.210499	−	0.977594i	$-0.567509\pi$
$607$	−10.3723	−0.420998	−0.210499	+	0.977594i	$0.567509\pi$
$608$	−6.37228	−0.258430
$609$	−6.51087	−0.263834
$610$	−11.4891	−0.465181
$611$	−9.48913	−0.383889
$612$	6.74456	0.272633
$613$	12.5109	0.505309	0.252655	−	0.967557i	$-0.418696\pi$
$613$	12.5109	0.505309	0.252655	+	0.967557i	$0.418696\pi$
$614$	−14.9783	−0.604473
$615$	−10.7446	−0.433263
$616$	−15.1168	−0.609075
$617$	25.1168	1.01117	0.505583	−	0.862778i	$-0.331277\pi$
$617$	25.1168	1.01117	0.505583	+	0.862778i	$0.331277\pi$
$618$	−8.00000	−0.321807
$619$	−18.2337	−0.732874	−0.366437	−	0.930443i	$-0.619422\pi$
$619$	−18.2337	−0.732874	−0.366437	+	0.930443i	$0.619422\pi$
$620$	−1.00000	−0.0401610
$621$	−2.37228	−0.0951964
$622$	8.00000	0.320771
$623$	−10.3723	−0.415557
$624$	−2.00000	−0.0800641
$625$	1.00000	0.0400000
$626$	10.0000	0.399680
$627$	−40.6060	−1.62165
$628$	3.62772	0.144762
$629$	72.4674	2.88946
$630$	−2.37228	−0.0945140
$631$	5.35053	0.213001	0.106501	−	0.994313i	$-0.466035\pi$
$631$	5.35053	0.213001	0.106501	+	0.994313i	$0.466035\pi$
$632$	−10.3723	−0.412587
$633$	−6.37228	−0.253275
$634$	−13.2554	−0.526441
$635$	−9.48913	−0.376564
$636$	−4.37228	−0.173372
$637$	2.74456	0.108744
$638$	17.4891	0.692401
$639$	−2.37228	−0.0938460
$640$	1.00000	0.0395285
$641$	18.0000	0.710957	0.355479	−	0.934684i	$-0.384318\pi$
$641$	18.0000	0.710957	0.355479	+	0.934684i	$0.384318\pi$
$642$	6.37228	0.251494
$643$	38.0951	1.50232	0.751162	−	0.660118i	$-0.229494\pi$
$643$	38.0951	1.50232	0.751162	+	0.660118i	$0.229494\pi$
$644$	5.62772	0.221763
$645$	6.37228	0.250908
$646$	−42.9783	−1.69096
$647$	−35.5842	−1.39896	−0.699480	−	0.714652i	$-0.746585\pi$
$647$	−35.5842	−1.39896	−0.699480	+	0.714652i	$0.746585\pi$
$648$	1.00000	0.0392837
$649$	−55.7228	−2.18731
$650$	−2.00000	−0.0784465
$651$	2.37228	0.0929770
$652$	−10.2337	−0.400782
$653$	−4.97825	−0.194814	−0.0974070	−	0.995245i	$-0.531055\pi$
$653$	−4.97825	−0.194814	−0.0974070	+	0.995245i	$0.531055\pi$
$654$	−6.74456	−0.263733
$655$	18.2337	0.712449
$656$	−10.7446	−0.419505
$657$	9.11684	0.355682
$658$	−11.2554	−0.438783
$659$	36.0000	1.40236	0.701180	−	0.712984i	$-0.252657\pi$
$659$	36.0000	1.40236	0.701180	+	0.712984i	$0.252657\pi$
$660$	6.37228	0.248041
$661$	40.9783	1.59387	0.796935	−	0.604066i	$-0.206454\pi$
$661$	40.9783	1.59387	0.796935	+	0.604066i	$0.206454\pi$
$662$	21.4891	0.835199
$663$	−13.4891	−0.523874
$664$	−12.0000	−0.465690
$665$	15.1168	0.586206
$666$	10.7446	0.416343
$667$	−6.51087	−0.252102
$668$	−18.3723	−0.710845
$669$	20.7446	0.802031
$670$	−0.744563	−0.0287650
$671$	−73.2119	−2.82632
$672$	−2.37228	−0.0915127
$673$	−23.4891	−0.905439	−0.452720	−	0.891653i	$-0.649546\pi$
$673$	−23.4891	−0.905439	−0.452720	+	0.891653i	$0.649546\pi$
$674$	−16.9783	−0.653978
$675$	1.00000	0.0384900
$676$	−9.00000	−0.346154
$677$	−1.39403	−0.0535770	−0.0267885	−	0.999641i	$-0.508528\pi$
$677$	−1.39403	−0.0535770	−0.0267885	+	0.999641i	$0.508528\pi$
$678$	−8.37228	−0.321536
$679$	−4.74456	−0.182080
$680$	6.74456	0.258642
$681$	−11.1168	−0.425998
$682$	−6.37228	−0.244007
$683$	15.8614	0.606920	0.303460	−	0.952844i	$-0.401858\pi$
$683$	15.8614	0.606920	0.303460	+	0.952844i	$0.401858\pi$
$684$	−6.37228	−0.243650
$685$	19.4891	0.744641
$686$	19.8614	0.758312
$687$	21.1168	0.805658
$688$	6.37228	0.242941
$689$	8.74456	0.333141
$690$	−2.37228	−0.0903112
$691$	−47.8614	−1.82073	−0.910367	−	0.413802i	$-0.864201\pi$
$691$	−47.8614	−1.82073	−0.910367	+	0.413802i	$0.864201\pi$
$692$	−18.0000	−0.684257
$693$	−15.1168	−0.574241
$694$	−32.4674	−1.23244
$695$	0.744563	0.0282429
$696$	2.74456	0.104032
$697$	−72.4674	−2.74490
$698$	18.7446	0.709492
$699$	13.8614	0.524287
$700$	−2.37228	−0.0896638
$701$	5.39403	0.203730	0.101865	−	0.994798i	$-0.467519\pi$
$701$	5.39403	0.203730	0.101865	+	0.994798i	$0.467519\pi$
$702$	−2.00000	−0.0754851
$703$	−68.4674	−2.58230
$704$	6.37228	0.240164
$705$	4.74456	0.178691
$706$	−7.48913	−0.281857
$707$	21.6277	0.813394
$708$	−8.74456	−0.328641
$709$	22.8832	0.859395	0.429697	−	0.902973i	$-0.358620\pi$
$709$	22.8832	0.859395	0.429697	+	0.902973i	$0.358620\pi$
$710$	−2.37228	−0.0890301
$711$	−10.3723	−0.388991
$712$	4.37228	0.163858
$713$	2.37228	0.0888426
$714$	−16.0000	−0.598785
$715$	−12.7446	−0.476620
$716$	−12.0000	−0.448461
$717$	−6.51087	−0.243153
$718$	−2.37228	−0.0885328
$719$	27.2554	1.01646	0.508228	−	0.861222i	$-0.330301\pi$
$719$	27.2554	1.01646	0.508228	+	0.861222i	$0.330301\pi$
$720$	1.00000	0.0372678
$721$	18.9783	0.706787
$722$	21.6060	0.804091
$723$	27.4891	1.02233
$724$	−13.8614	−0.515155
$725$	2.74456	0.101930
$726$	29.6060	1.09878
$727$	13.6277	0.505424	0.252712	−	0.967542i	$-0.418677\pi$
$727$	13.6277	0.505424	0.252712	+	0.967542i	$0.418677\pi$
$728$	4.74456	0.175845
$729$	1.00000	0.0370370
$730$	9.11684	0.337430
$731$	42.9783	1.58961
$732$	−11.4891	−0.424650
$733$	−34.0000	−1.25582	−0.627909	−	0.778287i	$-0.716089\pi$
$733$	−34.0000	−1.25582	−0.627909	+	0.778287i	$0.716089\pi$
$734$	14.2337	0.525375
$735$	−1.37228	−0.0506174
$736$	−2.37228	−0.0874434
$737$	−4.74456	−0.174768
$738$	−10.7446	−0.395513
$739$	22.9783	0.845269	0.422634	−	0.906300i	$-0.361105\pi$
$739$	22.9783	0.845269	0.422634	+	0.906300i	$0.361105\pi$
$740$	10.7446	0.394978
$741$	12.7446	0.468183
$742$	10.3723	0.380778
$743$	−29.6277	−1.08694	−0.543468	−	0.839430i	$-0.682889\pi$
$743$	−29.6277	−1.08694	−0.543468	+	0.839430i	$0.682889\pi$
$744$	−1.00000	−0.0366618
$745$	5.11684	0.187467
$746$	−13.8614	−0.507502
$747$	−12.0000	−0.439057
$748$	42.9783	1.57144
$749$	−15.1168	−0.552357
$750$	1.00000	0.0365148
$751$	−27.2554	−0.994565	−0.497283	−	0.867589i	$-0.665669\pi$
$751$	−27.2554	−0.994565	−0.497283	+	0.867589i	$0.665669\pi$
$752$	4.74456	0.173016
$753$	−4.00000	−0.145768
$754$	−5.48913	−0.199902
$755$	−8.00000	−0.291150
$756$	−2.37228	−0.0862790
$757$	−26.0000	−0.944986	−0.472493	−	0.881334i	$-0.656646\pi$
$757$	−26.0000	−0.944986	−0.472493	+	0.881334i	$0.656646\pi$
$758$	−0.138593	−0.00503394
$759$	−15.1168	−0.548707
$760$	−6.37228	−0.231147
$761$	−18.1386	−0.657523	−0.328762	−	0.944413i	$-0.606631\pi$
$761$	−18.1386	−0.657523	−0.328762	+	0.944413i	$0.606631\pi$
$762$	−9.48913	−0.343755
$763$	16.0000	0.579239
$764$	16.0000	0.578860
$765$	6.74456	0.243850
$766$	−9.48913	−0.342856
$767$	17.4891	0.631496
$768$	1.00000	0.0360844
$769$	−3.62772	−0.130819	−0.0654094	−	0.997859i	$-0.520835\pi$
$769$	−3.62772	−0.130819	−0.0654094	+	0.997859i	$0.520835\pi$
$770$	−15.1168	−0.544773
$771$	7.62772	0.274706
$772$	−7.48913	−0.269540
$773$	−18.6060	−0.669210	−0.334605	−	0.942358i	$-0.608603\pi$
$773$	−18.6060	−0.669210	−0.334605	+	0.942358i	$0.608603\pi$
$774$	6.37228	0.229047
$775$	−1.00000	−0.0359211
$776$	2.00000	0.0717958
$777$	−25.4891	−0.914417
$778$	−28.9783	−1.03892
$779$	68.4674	2.45310
$780$	−2.00000	−0.0716115
$781$	−15.1168	−0.540923
$782$	−16.0000	−0.572159
$783$	2.74456	0.0980827
$784$	−1.37228	−0.0490100
$785$	3.62772	0.129479
$786$	18.2337	0.650374
$787$	−27.1168	−0.966611	−0.483306	−	0.875452i	$-0.660564\pi$
$787$	−27.1168	−0.966611	−0.483306	+	0.875452i	$0.660564\pi$
$788$	−3.48913	−0.124295
$789$	26.9783	0.960451
$790$	−10.3723	−0.369029
$791$	19.8614	0.706190
$792$	6.37228	0.226429
$793$	22.9783	0.815982
$794$	38.6060	1.37007
$795$	−4.37228	−0.155069
$796$	−18.3723	−0.651188
$797$	−43.4891	−1.54046	−0.770232	−	0.637764i	$-0.779860\pi$
$797$	−43.4891	−1.54046	−0.770232	+	0.637764i	$0.779860\pi$
$798$	15.1168	0.535130
$799$	32.0000	1.13208
$800$	1.00000	0.0353553
$801$	4.37228	0.154487
$802$	28.3723	1.00186
$803$	58.0951	2.05013
$804$	−0.744563	−0.0262587
$805$	5.62772	0.198351
$806$	2.00000	0.0704470
$807$	−2.00000	−0.0704033
$808$	−9.11684	−0.320729
$809$	−30.6060	−1.07605	−0.538024	−	0.842929i	$-0.680829\pi$
$809$	−30.6060	−1.07605	−0.538024	+	0.842929i	$0.680829\pi$
$810$	1.00000	0.0351364
$811$	−46.3723	−1.62835	−0.814176	−	0.580619i	$-0.802811\pi$
$811$	−46.3723	−1.62835	−0.814176	+	0.580619i	$0.802811\pi$
$812$	−6.51087	−0.228487
$813$	−31.1168	−1.09132
$814$	68.4674	2.39978
$815$	−10.2337	−0.358470
$816$	6.74456	0.236107
$817$	−40.6060	−1.42062
$818$	24.2337	0.847311
$819$	4.74456	0.165788
$820$	−10.7446	−0.375216
$821$	26.7446	0.933392	0.466696	−	0.884418i	$-0.345444\pi$
$821$	26.7446	0.933392	0.466696	+	0.884418i	$0.345444\pi$
$822$	19.4891	0.679761
$823$	−28.7446	−1.00197	−0.500986	−	0.865455i	$-0.667029\pi$
$823$	−28.7446	−1.00197	−0.500986	+	0.865455i	$0.667029\pi$
$824$	−8.00000	−0.278693
$825$	6.37228	0.221854
$826$	20.7446	0.721796
$827$	5.48913	0.190876	0.0954378	−	0.995435i	$-0.469575\pi$
$827$	5.48913	0.190876	0.0954378	+	0.995435i	$0.469575\pi$
$828$	−2.37228	−0.0824425
$829$	32.0951	1.11471	0.557354	−	0.830275i	$-0.311816\pi$
$829$	32.0951	1.11471	0.557354	+	0.830275i	$0.311816\pi$
$830$	−12.0000	−0.416526
$831$	26.7446	0.927759
$832$	−2.00000	−0.0693375
$833$	−9.25544	−0.320682
$834$	0.744563	0.0257821
$835$	−18.3723	−0.635799
$836$	−40.6060	−1.40439
$837$	−1.00000	−0.0345651
$838$	−12.0000	−0.414533
$839$	−11.8614	−0.409501	−0.204751	−	0.978814i	$-0.565638\pi$
$839$	−11.8614	−0.409501	−0.204751	+	0.978814i	$0.565638\pi$
$840$	−2.37228	−0.0818515
$841$	−21.4674	−0.740254
$842$	−3.48913	−0.120243
$843$	5.25544	0.181007
$844$	−6.37228	−0.219343
$845$	−9.00000	−0.309609
$846$	4.74456	0.163121
$847$	−70.2337	−2.41326
$848$	−4.37228	−0.150145
$849$	12.0000	0.411839
$850$	6.74456	0.231337
$851$	−25.4891	−0.873756
$852$	−2.37228	−0.0812730
$853$	24.0951	0.825000	0.412500	−	0.910958i	$-0.364656\pi$
$853$	24.0951	0.825000	0.412500	+	0.910958i	$0.364656\pi$
$854$	27.2554	0.932662
$855$	−6.37228	−0.217927
$856$	6.37228	0.217800
$857$	−15.4891	−0.529098	−0.264549	−	0.964372i	$-0.585223\pi$
$857$	−15.4891	−0.529098	−0.264549	+	0.964372i	$0.585223\pi$
$858$	−12.7446	−0.435092
$859$	5.48913	0.187287	0.0936433	−	0.995606i	$-0.470149\pi$
$859$	5.48913	0.187287	0.0936433	+	0.995606i	$0.470149\pi$
$860$	6.37228	0.217293
$861$	25.4891	0.868667
$862$	18.9783	0.646402
$863$	45.3505	1.54375	0.771875	−	0.635774i	$-0.219319\pi$
$863$	45.3505	1.54375	0.771875	+	0.635774i	$0.219319\pi$
$864$	1.00000	0.0340207
$865$	−18.0000	−0.612018
$866$	18.8832	0.641676
$867$	28.4891	0.967541
$868$	2.37228	0.0805205
$869$	−66.0951	−2.24212
$870$	2.74456	0.0930494
$871$	1.48913	0.0504571
$872$	−6.74456	−0.228400
$873$	2.00000	0.0676897
$874$	15.1168	0.511335
$875$	−2.37228	−0.0801977
$876$	9.11684	0.308030
$877$	0.978251	0.0330332	0.0165166	−	0.999864i	$-0.494742\pi$
$877$	0.978251	0.0330332	0.0165166	+	0.999864i	$0.494742\pi$
$878$	3.25544	0.109866
$879$	15.4891	0.522435
$880$	6.37228	0.214810
$881$	−48.9783	−1.65012	−0.825060	−	0.565046i	$-0.808859\pi$
$881$	−48.9783	−1.65012	−0.825060	+	0.565046i	$0.808859\pi$
$882$	−1.37228	−0.0462071
$883$	16.1386	0.543107	0.271553	−	0.962423i	$-0.412463\pi$
$883$	16.1386	0.543107	0.271553	+	0.962423i	$0.412463\pi$
$884$	−13.4891	−0.453688
$885$	−8.74456	−0.293945
$886$	−17.3505	−0.582903
$887$	−19.2554	−0.646534	−0.323267	−	0.946308i	$-0.604781\pi$
$887$	−19.2554	−0.646534	−0.323267	+	0.946308i	$0.604781\pi$
$888$	10.7446	0.360564
$889$	22.5109	0.754991
$890$	4.37228	0.146559
$891$	6.37228	0.213479
$892$	20.7446	0.694579
$893$	−30.2337	−1.01173
$894$	5.11684	0.171133
$895$	−12.0000	−0.401116
$896$	−2.37228	−0.0792524
$897$	4.74456	0.158416
$898$	36.9783	1.23398
$899$	−2.74456	−0.0915363
$900$	1.00000	0.0333333
$901$	−29.4891	−0.982425
$902$	−68.4674	−2.27971
$903$	−15.1168	−0.503057
$904$	−8.37228	−0.278458
$905$	−13.8614	−0.460769
$906$	−8.00000	−0.265782
$907$	5.48913	0.182263	0.0911317	−	0.995839i	$-0.470952\pi$
$907$	5.48913	0.182263	0.0911317	+	0.995839i	$0.470952\pi$
$908$	−11.1168	−0.368925
$909$	−9.11684	−0.302387
$910$	4.74456	0.157281
$911$	−25.4891	−0.844492	−0.422246	−	0.906481i	$-0.638758\pi$
$911$	−25.4891	−0.844492	−0.422246	+	0.906481i	$0.638758\pi$
$912$	−6.37228	−0.211007
$913$	−76.4674	−2.53070
$914$	−34.4674	−1.14008
$915$	−11.4891	−0.379819
$916$	21.1168	0.697720
$917$	−43.2554	−1.42842
$918$	6.74456	0.222604
$919$	22.2337	0.733422	0.366711	−	0.930335i	$-0.380484\pi$
$919$	22.2337	0.733422	0.366711	+	0.930335i	$0.380484\pi$
$920$	−2.37228	−0.0782118
$921$	−14.9783	−0.493550
$922$	37.7228	1.24233
$923$	4.74456	0.156169
$924$	−15.1168	−0.497308
$925$	10.7446	0.353279
$926$	25.4891	0.837625
$927$	−8.00000	−0.262754
$928$	2.74456	0.0900947
$929$	1.11684	0.0366425	0.0183212	−	0.999832i	$-0.494168\pi$
$929$	1.11684	0.0366425	0.0183212	+	0.999832i	$0.494168\pi$
$930$	−1.00000	−0.0327913
$931$	8.74456	0.286591
$932$	13.8614	0.454045
$933$	8.00000	0.261908
$934$	29.4891	0.964914
$935$	42.9783	1.40554
$936$	−2.00000	−0.0653720
$937$	−42.7446	−1.39640	−0.698202	−	0.715901i	$-0.746016\pi$
$937$	−42.7446	−1.39640	−0.698202	+	0.715901i	$0.746016\pi$
$938$	1.76631	0.0576721
$939$	10.0000	0.326338
$940$	4.74456	0.154751
$941$	37.7228	1.22973	0.614864	−	0.788633i	$-0.289211\pi$
$941$	37.7228	1.22973	0.614864	+	0.788633i	$0.289211\pi$
$942$	3.62772	0.118197
$943$	25.4891	0.830040
$944$	−8.74456	−0.284611
$945$	−2.37228	−0.0771703
$946$	40.6060	1.32021
$947$	8.74456	0.284160	0.142080	−	0.989855i	$-0.454621\pi$
$947$	8.74456	0.284160	0.142080	+	0.989855i	$0.454621\pi$
$948$	−10.3723	−0.336876
$949$	−18.2337	−0.591891
$950$	−6.37228	−0.206744
$951$	−13.2554	−0.429837
$952$	−16.0000	−0.518563
$953$	−45.7228	−1.48111	−0.740554	−	0.671997i	$-0.765437\pi$
$953$	−45.7228	−1.48111	−0.740554	+	0.671997i	$0.765437\pi$
$954$	−4.37228	−0.141558
$955$	16.0000	0.517748
$956$	−6.51087	−0.210577
$957$	17.4891	0.565343
$958$	−19.8614	−0.641693
$959$	−46.2337	−1.49296
$960$	1.00000	0.0322749
$961$	1.00000	0.0322581
$962$	−21.4891	−0.692837
$963$	6.37228	0.205344
$964$	27.4891	0.885365
$965$	−7.48913	−0.241083
$966$	5.62772	0.181069
$967$	8.00000	0.257263	0.128631	−	0.991692i	$-0.458942\pi$
$967$	8.00000	0.257263	0.128631	+	0.991692i	$0.458942\pi$
$968$	29.6060	0.951572
$969$	−42.9783	−1.38066
$970$	2.00000	0.0642161
$971$	54.7011	1.75544	0.877720	−	0.479173i	$-0.159063\pi$
$971$	54.7011	1.75544	0.877720	+	0.479173i	$0.159063\pi$
$972$	1.00000	0.0320750
$973$	−1.76631	−0.0566254
$974$	−14.5109	−0.464958
$975$	−2.00000	−0.0640513
$976$	−11.4891	−0.367758
$977$	−46.0000	−1.47167	−0.735835	−	0.677161i	$-0.763210\pi$
$977$	−46.0000	−1.47167	−0.735835	+	0.677161i	$0.763210\pi$
$978$	−10.2337	−0.327237
$979$	27.8614	0.890454
$980$	−1.37228	−0.0438359
$981$	−6.74456	−0.215337
$982$	−12.6060	−0.402273
$983$	42.9783	1.37079	0.685397	−	0.728170i	$-0.259629\pi$
$983$	42.9783	1.37079	0.685397	+	0.728170i	$0.259629\pi$
$984$	−10.7446	−0.342524
$985$	−3.48913	−0.111173
$986$	18.5109	0.589506
$987$	−11.2554	−0.358265
$988$	12.7446	0.405459
$989$	−15.1168	−0.480688
$990$	6.37228	0.202524
$991$	−7.39403	−0.234879	−0.117440	−	0.993080i	$-0.537469\pi$
$991$	−7.39403	−0.234879	−0.117440	+	0.993080i	$0.537469\pi$
$992$	−1.00000	−0.0317500
$993$	21.4891	0.681937
$994$	5.62772	0.178500
$995$	−18.3723	−0.582440
$996$	−12.0000	−0.380235
$997$	6.00000	0.190022	0.0950110	−	0.995476i	$-0.469711\pi$
$997$	6.00000	0.190022	0.0950110	+	0.995476i	$0.469711\pi$
$998$	10.5109	0.332716
$999$	10.7446	0.339943

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.a.r.1.1	✓	2
3.2	odd	2		2790.2.a.bd.1.1		2
4.3	odd	2		7440.2.a.bg.1.2		2
5.2	odd	4		4650.2.d.bh.3349.3		4
5.3	odd	4		4650.2.d.bh.3349.2		4
5.4	even	2		4650.2.a.by.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.a.r.1.1	✓	2	1.1	even	1	trivial
2790.2.a.bd.1.1		2	3.2	odd	2
4650.2.a.by.1.2		2	5.4	even	2
4650.2.d.bh.3349.2		4	5.3	odd	4
4650.2.d.bh.3349.3		4	5.2	odd	4
7440.2.a.bg.1.2		2	4.3	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -2.37228 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -2.37228 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +6.37228 q^{11} +1.00000 q^{12} -2.00000 q^{13} -2.37228 q^{14} +1.00000 q^{15} +1.00000 q^{16} +6.74456 q^{17} +1.00000 q^{18} -6.37228 q^{19} +1.00000 q^{20} -2.37228 q^{21} +6.37228 q^{22} -2.37228 q^{23} +1.00000 q^{24} +1.00000 q^{25} -2.00000 q^{26} +1.00000 q^{27} -2.37228 q^{28} +2.74456 q^{29} +1.00000 q^{30} -1.00000 q^{31} +1.00000 q^{32} +6.37228 q^{33} +6.74456 q^{34} -2.37228 q^{35} +1.00000 q^{36} +10.7446 q^{37} -6.37228 q^{38} -2.00000 q^{39} +1.00000 q^{40} -10.7446 q^{41} -2.37228 q^{42} +6.37228 q^{43} +6.37228 q^{44} +1.00000 q^{45} -2.37228 q^{46} +4.74456 q^{47} +1.00000 q^{48} -1.37228 q^{49} +1.00000 q^{50} +6.74456 q^{51} -2.00000 q^{52} -4.37228 q^{53} +1.00000 q^{54} +6.37228 q^{55} -2.37228 q^{56} -6.37228 q^{57} +2.74456 q^{58} -8.74456 q^{59} +1.00000 q^{60} -11.4891 q^{61} -1.00000 q^{62} -2.37228 q^{63} +1.00000 q^{64} -2.00000 q^{65} +6.37228 q^{66} -0.744563 q^{67} +6.74456 q^{68} -2.37228 q^{69} -2.37228 q^{70} -2.37228 q^{71} +1.00000 q^{72} +9.11684 q^{73} +10.7446 q^{74} +1.00000 q^{75} -6.37228 q^{76} -15.1168 q^{77} -2.00000 q^{78} -10.3723 q^{79} +1.00000 q^{80} +1.00000 q^{81} -10.7446 q^{82} -12.0000 q^{83} -2.37228 q^{84} +6.74456 q^{85} +6.37228 q^{86} +2.74456 q^{87} +6.37228 q^{88} +4.37228 q^{89} +1.00000 q^{90} +4.74456 q^{91} -2.37228 q^{92} -1.00000 q^{93} +4.74456 q^{94} -6.37228 q^{95} +1.00000 q^{96} +2.00000 q^{97} -1.37228 q^{98} +6.37228 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} + q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 + q^7 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} + q^{7} + 2 q^{8} + 2 q^{9} + 2 q^{10} + 7 q^{11} + 2 q^{12} - 4 q^{13} + q^{14} + 2 q^{15} + 2 q^{16} + 2 q^{17} + 2 q^{18} - 7 q^{19} + 2 q^{20} + q^{21} + 7 q^{22} + q^{23} + 2 q^{24} + 2 q^{25} - 4 q^{26} + 2 q^{27} + q^{28} - 6 q^{29} + 2 q^{30} - 2 q^{31} + 2 q^{32} + 7 q^{33} + 2 q^{34} + q^{35} + 2 q^{36} + 10 q^{37} - 7 q^{38} - 4 q^{39} + 2 q^{40} - 10 q^{41} + q^{42} + 7 q^{43} + 7 q^{44} + 2 q^{45} + q^{46} - 2 q^{47} + 2 q^{48} + 3 q^{49} + 2 q^{50} + 2 q^{51} - 4 q^{52} - 3 q^{53} + 2 q^{54} + 7 q^{55} + q^{56} - 7 q^{57} - 6 q^{58} - 6 q^{59} + 2 q^{60} - 2 q^{62} + q^{63} + 2 q^{64} - 4 q^{65} + 7 q^{66} + 10 q^{67} + 2 q^{68} + q^{69} + q^{70} + q^{71} + 2 q^{72} + q^{73} + 10 q^{74} + 2 q^{75} - 7 q^{76} - 13 q^{77} - 4 q^{78} - 15 q^{79} + 2 q^{80} + 2 q^{81} - 10 q^{82} - 24 q^{83} + q^{84} + 2 q^{85} + 7 q^{86} - 6 q^{87} + 7 q^{88} + 3 q^{89} + 2 q^{90} - 2 q^{91} + q^{92} - 2 q^{93} - 2 q^{94} - 7 q^{95} + 2 q^{96} + 4 q^{97} + 3 q^{98} + 7 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 + q^7 + 2 * q^8 + 2 * q^9 + 2 * q^10 + 7 * q^11 + 2 * q^12 - 4 * q^13 + q^14 + 2 * q^15 + 2 * q^16 + 2 * q^17 + 2 * q^18 - 7 * q^19 + 2 * q^20 + q^21 + 7 * q^22 + q^23 + 2 * q^24 + 2 * q^25 - 4 * q^26 + 2 * q^27 + q^28 - 6 * q^29 + 2 * q^30 - 2 * q^31 + 2 * q^32 + 7 * q^33 + 2 * q^34 + q^35 + 2 * q^36 + 10 * q^37 - 7 * q^38 - 4 * q^39 + 2 * q^40 - 10 * q^41 + q^42 + 7 * q^43 + 7 * q^44 + 2 * q^45 + q^46 - 2 * q^47 + 2 * q^48 + 3 * q^49 + 2 * q^50 + 2 * q^51 - 4 * q^52 - 3 * q^53 + 2 * q^54 + 7 * q^55 + q^56 - 7 * q^57 - 6 * q^58 - 6 * q^59 + 2 * q^60 - 2 * q^62 + q^63 + 2 * q^64 - 4 * q^65 + 7 * q^66 + 10 * q^67 + 2 * q^68 + q^69 + q^70 + q^71 + 2 * q^72 + q^73 + 10 * q^74 + 2 * q^75 - 7 * q^76 - 13 * q^77 - 4 * q^78 - 15 * q^79 + 2 * q^80 + 2 * q^81 - 10 * q^82 - 24 * q^83 + q^84 + 2 * q^85 + 7 * q^86 - 6 * q^87 + 7 * q^88 + 3 * q^89 + 2 * q^90 - 2 * q^91 + q^92 - 2 * q^93 - 2 * q^94 - 7 * q^95 + 2 * q^96 + 4 * q^97 + 3 * q^98 + 7 * q^99

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