LMFDB - Embedded newform 3822.2.a.bj.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3822,2,Mod(1,3822)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3822, 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("3822.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3822.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:	$30.5188236525$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.41421$ of defining polynomial
Character	$\chi$	$=$	3822.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +2.41421 q^{11} -1.00000 q^{12} -1.00000 q^{13} -1.00000 q^{15} +1.00000 q^{16} -0.414214 q^{17} -1.00000 q^{18} +3.82843 q^{19} +1.00000 q^{20} -2.41421 q^{22} -8.65685 q^{23} +1.00000 q^{24} -4.00000 q^{25} +1.00000 q^{26} -1.00000 q^{27} +2.65685 q^{29} +1.00000 q^{30} -4.24264 q^{31} -1.00000 q^{32} -2.41421 q^{33} +0.414214 q^{34} +1.00000 q^{36} -3.24264 q^{37} -3.82843 q^{38} +1.00000 q^{39} -1.00000 q^{40} +6.82843 q^{41} -7.00000 q^{43} +2.41421 q^{44} +1.00000 q^{45} +8.65685 q^{46} +7.65685 q^{47} -1.00000 q^{48} +4.00000 q^{50} +0.414214 q^{51} -1.00000 q^{52} -13.6569 q^{53} +1.00000 q^{54} +2.41421 q^{55} -3.82843 q^{57} -2.65685 q^{58} -9.89949 q^{59} -1.00000 q^{60} -5.58579 q^{61} +4.24264 q^{62} +1.00000 q^{64} -1.00000 q^{65} +2.41421 q^{66} +1.41421 q^{67} -0.414214 q^{68} +8.65685 q^{69} +5.07107 q^{71} -1.00000 q^{72} -11.8284 q^{73} +3.24264 q^{74} +4.00000 q^{75} +3.82843 q^{76} -1.00000 q^{78} +10.2426 q^{79} +1.00000 q^{80} +1.00000 q^{81} -6.82843 q^{82} +11.6569 q^{83} -0.414214 q^{85} +7.00000 q^{86} -2.65685 q^{87} -2.41421 q^{88} +0.585786 q^{89} -1.00000 q^{90} -8.65685 q^{92} +4.24264 q^{93} -7.65685 q^{94} +3.82843 q^{95} +1.00000 q^{96} +7.31371 q^{97} +2.41421 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} - 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 - 2 * q^8 + 2 * q^9	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} - 2 q^{8} + 2 q^{9} - 2 q^{10} + 2 q^{11} - 2 q^{12} - 2 q^{13} - 2 q^{15} + 2 q^{16} + 2 q^{17} - 2 q^{18} + 2 q^{19} + 2 q^{20} - 2 q^{22} - 6 q^{23} + 2 q^{24} - 8 q^{25} + 2 q^{26} - 2 q^{27} - 6 q^{29} + 2 q^{30} - 2 q^{32} - 2 q^{33} - 2 q^{34} + 2 q^{36} + 2 q^{37} - 2 q^{38} + 2 q^{39} - 2 q^{40} + 8 q^{41} - 14 q^{43} + 2 q^{44} + 2 q^{45} + 6 q^{46} + 4 q^{47} - 2 q^{48} + 8 q^{50} - 2 q^{51} - 2 q^{52} - 16 q^{53} + 2 q^{54} + 2 q^{55} - 2 q^{57} + 6 q^{58} - 2 q^{60} - 14 q^{61} + 2 q^{64} - 2 q^{65} + 2 q^{66} + 2 q^{68} + 6 q^{69} - 4 q^{71} - 2 q^{72} - 18 q^{73} - 2 q^{74} + 8 q^{75} + 2 q^{76} - 2 q^{78} + 12 q^{79} + 2 q^{80} + 2 q^{81} - 8 q^{82} + 12 q^{83} + 2 q^{85} + 14 q^{86} + 6 q^{87} - 2 q^{88} + 4 q^{89} - 2 q^{90} - 6 q^{92} - 4 q^{94} + 2 q^{95} + 2 q^{96} - 8 q^{97} + 2 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 - 2 * q^8 + 2 * q^9 - 2 * q^10 + 2 * q^11 - 2 * q^12 - 2 * q^13 - 2 * q^15 + 2 * q^16 + 2 * q^17 - 2 * q^18 + 2 * q^19 + 2 * q^20 - 2 * q^22 - 6 * q^23 + 2 * q^24 - 8 * q^25 + 2 * q^26 - 2 * q^27 - 6 * q^29 + 2 * q^30 - 2 * q^32 - 2 * q^33 - 2 * q^34 + 2 * q^36 + 2 * q^37 - 2 * q^38 + 2 * q^39 - 2 * q^40 + 8 * q^41 - 14 * q^43 + 2 * q^44 + 2 * q^45 + 6 * q^46 + 4 * q^47 - 2 * q^48 + 8 * q^50 - 2 * q^51 - 2 * q^52 - 16 * q^53 + 2 * q^54 + 2 * q^55 - 2 * q^57 + 6 * q^58 - 2 * q^60 - 14 * q^61 + 2 * q^64 - 2 * q^65 + 2 * q^66 + 2 * q^68 + 6 * q^69 - 4 * q^71 - 2 * q^72 - 18 * q^73 - 2 * q^74 + 8 * q^75 + 2 * q^76 - 2 * q^78 + 12 * q^79 + 2 * q^80 + 2 * q^81 - 8 * q^82 + 12 * q^83 + 2 * q^85 + 14 * q^86 + 6 * q^87 - 2 * q^88 + 4 * q^89 - 2 * q^90 - 6 * q^92 - 4 * q^94 + 2 * q^95 + 2 * q^96 - 8 * q^97 + 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
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	1.00000	0.447214	0.223607	−	0.974679i	$-0.428217\pi$
$5$	1.00000	0.447214	0.223607	+	0.974679i	$0.428217\pi$
$6$	1.00000	0.408248
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−1.00000	−0.316228
$11$	2.41421	0.727913	0.363956	−	0.931416i	$-0.381426\pi$
$11$	2.41421	0.727913	0.363956	+	0.931416i	$0.381426\pi$
$12$	−1.00000	−0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0	0
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	−0.414214	−0.100462	−0.0502308	−	0.998738i	$-0.515996\pi$
$17$	−0.414214	−0.100462	−0.0502308	+	0.998738i	$0.515996\pi$
$18$	−1.00000	−0.235702
$19$	3.82843	0.878301	0.439151	−	0.898413i	$-0.355279\pi$
$19$	3.82843	0.878301	0.439151	+	0.898413i	$0.355279\pi$
$20$	1.00000	0.223607
$21$	0	0
$22$	−2.41421	−0.514712
$23$	−8.65685	−1.80508	−0.902539	−	0.430607i	$-0.858299\pi$
$23$	−8.65685	−1.80508	−0.902539	+	0.430607i	$0.858299\pi$
$24$	1.00000	0.204124
$25$	−4.00000	−0.800000
$26$	1.00000	0.196116
$27$	−1.00000	−0.192450
$28$	0	0
$29$	2.65685	0.493365	0.246683	−	0.969096i	$-0.420659\pi$
$29$	2.65685	0.493365	0.246683	+	0.969096i	$0.420659\pi$
$30$	1.00000	0.182574
$31$	−4.24264	−0.762001	−0.381000	−	0.924575i	$-0.624420\pi$
$31$	−4.24264	−0.762001	−0.381000	+	0.924575i	$0.624420\pi$
$32$	−1.00000	−0.176777
$33$	−2.41421	−0.420261
$34$	0.414214	0.0710370
$35$	0	0
$36$	1.00000	0.166667
$37$	−3.24264	−0.533087	−0.266543	−	0.963823i	$-0.585882\pi$
$37$	−3.24264	−0.533087	−0.266543	+	0.963823i	$0.585882\pi$
$38$	−3.82843	−0.621053
$39$	1.00000	0.160128
$40$	−1.00000	−0.158114
$41$	6.82843	1.06642	0.533211	−	0.845983i	$-0.320985\pi$
$41$	6.82843	1.06642	0.533211	+	0.845983i	$0.320985\pi$
$42$	0	0
$43$	−7.00000	−1.06749	−0.533745	−	0.845645i	$-0.679216\pi$
$43$	−7.00000	−1.06749	−0.533745	+	0.845645i	$0.679216\pi$
$44$	2.41421	0.363956
$45$	1.00000	0.149071
$46$	8.65685	1.27638
$47$	7.65685	1.11687	0.558433	−	0.829549i	$-0.311403\pi$
$47$	7.65685	1.11687	0.558433	+	0.829549i	$0.311403\pi$
$48$	−1.00000	−0.144338
$49$	0	0
$50$	4.00000	0.565685
$51$	0.414214	0.0580015
$52$	−1.00000	−0.138675
$53$	−13.6569	−1.87591	−0.937957	−	0.346753i	$-0.887284\pi$
$53$	−13.6569	−1.87591	−0.937957	+	0.346753i	$0.887284\pi$
$54$	1.00000	0.136083
$55$	2.41421	0.325532
$56$	0	0
$57$	−3.82843	−0.507088
$58$	−2.65685	−0.348862
$59$	−9.89949	−1.28880	−0.644402	−	0.764687i	$-0.722894\pi$
$59$	−9.89949	−1.28880	−0.644402	+	0.764687i	$0.722894\pi$
$60$	−1.00000	−0.129099
$61$	−5.58579	−0.715187	−0.357593	−	0.933877i	$-0.616403\pi$
$61$	−5.58579	−0.715187	−0.357593	+	0.933877i	$0.616403\pi$
$62$	4.24264	0.538816
$63$	0	0
$64$	1.00000	0.125000
$65$	−1.00000	−0.124035
$66$	2.41421	0.297169
$67$	1.41421	0.172774	0.0863868	−	0.996262i	$-0.472468\pi$
$67$	1.41421	0.172774	0.0863868	+	0.996262i	$0.472468\pi$
$68$	−0.414214	−0.0502308
$69$	8.65685	1.04216
$70$	0	0
$71$	5.07107	0.601825	0.300913	−	0.953652i	$-0.402709\pi$
$71$	5.07107	0.601825	0.300913	+	0.953652i	$0.402709\pi$
$72$	−1.00000	−0.117851
$73$	−11.8284	−1.38441	−0.692206	−	0.721700i	$-0.743361\pi$
$73$	−11.8284	−1.38441	−0.692206	+	0.721700i	$0.743361\pi$
$74$	3.24264	0.376949
$75$	4.00000	0.461880
$76$	3.82843	0.439151
$77$	0	0
$78$	−1.00000	−0.113228
$79$	10.2426	1.15239	0.576194	−	0.817313i	$-0.304537\pi$
$79$	10.2426	1.15239	0.576194	+	0.817313i	$0.304537\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	−6.82843	−0.754074
$83$	11.6569	1.27951	0.639753	−	0.768581i	$-0.279037\pi$
$83$	11.6569	1.27951	0.639753	+	0.768581i	$0.279037\pi$
$84$	0	0
$85$	−0.414214	−0.0449278
$86$	7.00000	0.754829
$87$	−2.65685	−0.284845
$88$	−2.41421	−0.257356
$89$	0.585786	0.0620932	0.0310466	−	0.999518i	$-0.490116\pi$
$89$	0.585786	0.0620932	0.0310466	+	0.999518i	$0.490116\pi$
$90$	−1.00000	−0.105409
$91$	0	0
$92$	−8.65685	−0.902539
$93$	4.24264	0.439941
$94$	−7.65685	−0.789744
$95$	3.82843	0.392788
$96$	1.00000	0.102062
$97$	7.31371	0.742595	0.371297	−	0.928514i	$-0.378913\pi$
$97$	7.31371	0.742595	0.371297	+	0.928514i	$0.378913\pi$
$98$	0	0
$99$	2.41421	0.242638
$100$	−4.00000	−0.400000
$101$	−1.07107	−0.106575	−0.0532876	−	0.998579i	$-0.516970\pi$
$101$	−1.07107	−0.106575	−0.0532876	+	0.998579i	$0.516970\pi$
$102$	−0.414214	−0.0410133
$103$	−8.07107	−0.795266	−0.397633	−	0.917545i	$-0.630168\pi$
$103$	−8.07107	−0.795266	−0.397633	+	0.917545i	$0.630168\pi$
$104$	1.00000	0.0980581
$105$	0	0
$106$	13.6569	1.32647
$107$	4.58579	0.443325	0.221662	−	0.975123i	$-0.428852\pi$
$107$	4.58579	0.443325	0.221662	+	0.975123i	$0.428852\pi$
$108$	−1.00000	−0.0962250
$109$	0.414214	0.0396745	0.0198372	−	0.999803i	$-0.493685\pi$
$109$	0.414214	0.0396745	0.0198372	+	0.999803i	$0.493685\pi$
$110$	−2.41421	−0.230186
$111$	3.24264	0.307778
$112$	0	0
$113$	−18.2426	−1.71612	−0.858062	−	0.513547i	$-0.828331\pi$
$113$	−18.2426	−1.71612	−0.858062	+	0.513547i	$0.828331\pi$
$114$	3.82843	0.358565
$115$	−8.65685	−0.807256
$116$	2.65685	0.246683
$117$	−1.00000	−0.0924500
$118$	9.89949	0.911322
$119$	0	0
$120$	1.00000	0.0912871
$121$	−5.17157	−0.470143
$122$	5.58579	0.505713
$123$	−6.82843	−0.615699
$124$	−4.24264	−0.381000
$125$	−9.00000	−0.804984
$126$	0	0
$127$	−2.92893	−0.259901	−0.129950	−	0.991521i	$-0.541482\pi$
$127$	−2.92893	−0.259901	−0.129950	+	0.991521i	$0.541482\pi$
$128$	−1.00000	−0.0883883
$129$	7.00000	0.616316
$130$	1.00000	0.0877058
$131$	17.2426	1.50650	0.753248	−	0.657736i	$-0.228486\pi$
$131$	17.2426	1.50650	0.753248	+	0.657736i	$0.228486\pi$
$132$	−2.41421	−0.210130
$133$	0	0
$134$	−1.41421	−0.122169
$135$	−1.00000	−0.0860663
$136$	0.414214	0.0355185
$137$	−7.24264	−0.618781	−0.309390	−	0.950935i	$-0.600125\pi$
$137$	−7.24264	−0.618781	−0.309390	+	0.950935i	$0.600125\pi$
$138$	−8.65685	−0.736920
$139$	−6.82843	−0.579180	−0.289590	−	0.957151i	$-0.593519\pi$
$139$	−6.82843	−0.579180	−0.289590	+	0.957151i	$0.593519\pi$
$140$	0	0
$141$	−7.65685	−0.644823
$142$	−5.07107	−0.425555
$143$	−2.41421	−0.201887
$144$	1.00000	0.0833333
$145$	2.65685	0.220640
$146$	11.8284	0.978928
$147$	0	0
$148$	−3.24264	−0.266543
$149$	−2.82843	−0.231714	−0.115857	−	0.993266i	$-0.536961\pi$
$149$	−2.82843	−0.231714	−0.115857	+	0.993266i	$0.536961\pi$
$150$	−4.00000	−0.326599
$151$	−13.2426	−1.07767	−0.538835	−	0.842411i	$-0.681136\pi$
$151$	−13.2426	−1.07767	−0.538835	+	0.842411i	$0.681136\pi$
$152$	−3.82843	−0.310526
$153$	−0.414214	−0.0334872
$154$	0	0
$155$	−4.24264	−0.340777
$156$	1.00000	0.0800641
$157$	−2.89949	−0.231405	−0.115702	−	0.993284i	$-0.536912\pi$
$157$	−2.89949	−0.231405	−0.115702	+	0.993284i	$0.536912\pi$
$158$	−10.2426	−0.814861
$159$	13.6569	1.08306
$160$	−1.00000	−0.0790569
$161$	0	0
$162$	−1.00000	−0.0785674
$163$	−11.6569	−0.913035	−0.456518	−	0.889714i	$-0.650903\pi$
$163$	−11.6569	−0.913035	−0.456518	+	0.889714i	$0.650903\pi$
$164$	6.82843	0.533211
$165$	−2.41421	−0.187946
$166$	−11.6569	−0.904747
$167$	13.8284	1.07008	0.535038	−	0.844828i	$-0.320297\pi$
$167$	13.8284	1.07008	0.535038	+	0.844828i	$0.320297\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	0.414214	0.0317687
$171$	3.82843	0.292767
$172$	−7.00000	−0.533745
$173$	16.2426	1.23491	0.617453	−	0.786608i	$-0.288165\pi$
$173$	16.2426	1.23491	0.617453	+	0.786608i	$0.288165\pi$
$174$	2.65685	0.201416
$175$	0	0
$176$	2.41421	0.181978
$177$	9.89949	0.744092
$178$	−0.585786	−0.0439065
$179$	−19.5563	−1.46171	−0.730855	−	0.682533i	$-0.760878\pi$
$179$	−19.5563	−1.46171	−0.730855	+	0.682533i	$0.760878\pi$
$180$	1.00000	0.0745356
$181$	18.1421	1.34849	0.674247	−	0.738506i	$-0.264468\pi$
$181$	18.1421	1.34849	0.674247	+	0.738506i	$0.264468\pi$
$182$	0	0
$183$	5.58579	0.412913
$184$	8.65685	0.638192
$185$	−3.24264	−0.238404
$186$	−4.24264	−0.311086
$187$	−1.00000	−0.0731272
$188$	7.65685	0.558433
$189$	0	0
$190$	−3.82843	−0.277743
$191$	5.48528	0.396901	0.198451	−	0.980111i	$-0.436409\pi$
$191$	5.48528	0.396901	0.198451	+	0.980111i	$0.436409\pi$
$192$	−1.00000	−0.0721688
$193$	12.3848	0.891476	0.445738	−	0.895164i	$-0.352941\pi$
$193$	12.3848	0.891476	0.445738	+	0.895164i	$0.352941\pi$
$194$	−7.31371	−0.525094
$195$	1.00000	0.0716115
$196$	0	0
$197$	5.07107	0.361299	0.180649	−	0.983548i	$-0.442180\pi$
$197$	5.07107	0.361299	0.180649	+	0.983548i	$0.442180\pi$
$198$	−2.41421	−0.171571
$199$	10.0711	0.713919	0.356960	−	0.934120i	$-0.383813\pi$
$199$	10.0711	0.713919	0.356960	+	0.934120i	$0.383813\pi$
$200$	4.00000	0.282843
$201$	−1.41421	−0.0997509
$202$	1.07107	0.0753601
$203$	0	0
$204$	0.414214	0.0290008
$205$	6.82843	0.476918
$206$	8.07107	0.562338
$207$	−8.65685	−0.601693
$208$	−1.00000	−0.0693375
$209$	9.24264	0.639327
$210$	0	0
$211$	−16.3137	−1.12308	−0.561541	−	0.827449i	$-0.689791\pi$
$211$	−16.3137	−1.12308	−0.561541	+	0.827449i	$0.689791\pi$
$212$	−13.6569	−0.937957
$213$	−5.07107	−0.347464
$214$	−4.58579	−0.313478
$215$	−7.00000	−0.477396
$216$	1.00000	0.0680414
$217$	0	0
$218$	−0.414214	−0.0280541
$219$	11.8284	0.799291
$220$	2.41421	0.162766
$221$	0.414214	0.0278630
$222$	−3.24264	−0.217632
$223$	−15.6569	−1.04846	−0.524230	−	0.851577i	$-0.675647\pi$
$223$	−15.6569	−1.04846	−0.524230	+	0.851577i	$0.675647\pi$
$224$	0	0
$225$	−4.00000	−0.266667
$226$	18.2426	1.21348
$227$	−5.07107	−0.336579	−0.168289	−	0.985738i	$-0.553824\pi$
$227$	−5.07107	−0.336579	−0.168289	+	0.985738i	$0.553824\pi$
$228$	−3.82843	−0.253544
$229$	−23.8995	−1.57932	−0.789662	−	0.613543i	$-0.789744\pi$
$229$	−23.8995	−1.57932	−0.789662	+	0.613543i	$0.789744\pi$
$230$	8.65685	0.570816
$231$	0	0
$232$	−2.65685	−0.174431
$233$	−10.8284	−0.709394	−0.354697	−	0.934981i	$-0.615416\pi$
$233$	−10.8284	−0.709394	−0.354697	+	0.934981i	$0.615416\pi$
$234$	1.00000	0.0653720
$235$	7.65685	0.499478
$236$	−9.89949	−0.644402
$237$	−10.2426	−0.665331
$238$	0	0
$239$	14.7279	0.952670	0.476335	−	0.879264i	$-0.341965\pi$
$239$	14.7279	0.952670	0.476335	+	0.879264i	$0.341965\pi$
$240$	−1.00000	−0.0645497
$241$	−12.3431	−0.795092	−0.397546	−	0.917582i	$-0.630138\pi$
$241$	−12.3431	−0.795092	−0.397546	+	0.917582i	$0.630138\pi$
$242$	5.17157	0.332441
$243$	−1.00000	−0.0641500
$244$	−5.58579	−0.357593
$245$	0	0
$246$	6.82843	0.435365
$247$	−3.82843	−0.243597
$248$	4.24264	0.269408
$249$	−11.6569	−0.738723
$250$	9.00000	0.569210
$251$	3.58579	0.226333	0.113166	−	0.993576i	$-0.463901\pi$
$251$	3.58579	0.226333	0.113166	+	0.993576i	$0.463901\pi$
$252$	0	0
$253$	−20.8995	−1.31394
$254$	2.92893	0.183778
$255$	0.414214	0.0259391
$256$	1.00000	0.0625000
$257$	5.17157	0.322594	0.161297	−	0.986906i	$-0.448432\pi$
$257$	5.17157	0.322594	0.161297	+	0.986906i	$0.448432\pi$
$258$	−7.00000	−0.435801
$259$	0	0
$260$	−1.00000	−0.0620174
$261$	2.65685	0.164455
$262$	−17.2426	−1.06525
$263$	9.65685	0.595467	0.297734	−	0.954649i	$-0.403769\pi$
$263$	9.65685	0.595467	0.297734	+	0.954649i	$0.403769\pi$
$264$	2.41421	0.148585
$265$	−13.6569	−0.838934
$266$	0	0
$267$	−0.585786	−0.0358495
$268$	1.41421	0.0863868
$269$	−16.7279	−1.01992	−0.509960	−	0.860198i	$-0.670340\pi$
$269$	−16.7279	−1.01992	−0.509960	+	0.860198i	$0.670340\pi$
$270$	1.00000	0.0608581
$271$	−14.2426	−0.865179	−0.432589	−	0.901591i	$-0.642400\pi$
$271$	−14.2426	−0.865179	−0.432589	+	0.901591i	$0.642400\pi$
$272$	−0.414214	−0.0251154
$273$	0	0
$274$	7.24264	0.437544
$275$	−9.65685	−0.582330
$276$	8.65685	0.521081
$277$	−16.5858	−0.996543	−0.498272	−	0.867021i	$-0.666032\pi$
$277$	−16.5858	−0.996543	−0.498272	+	0.867021i	$0.666032\pi$
$278$	6.82843	0.409542
$279$	−4.24264	−0.254000
$280$	0	0
$281$	1.31371	0.0783693	0.0391846	−	0.999232i	$-0.487524\pi$
$281$	1.31371	0.0783693	0.0391846	+	0.999232i	$0.487524\pi$
$282$	7.65685	0.455959
$283$	−10.8284	−0.643683	−0.321842	−	0.946794i	$-0.604302\pi$
$283$	−10.8284	−0.643683	−0.321842	+	0.946794i	$0.604302\pi$
$284$	5.07107	0.300913
$285$	−3.82843	−0.226776
$286$	2.41421	0.142755
$287$	0	0
$288$	−1.00000	−0.0589256
$289$	−16.8284	−0.989907
$290$	−2.65685	−0.156016
$291$	−7.31371	−0.428737
$292$	−11.8284	−0.692206
$293$	6.14214	0.358827	0.179414	−	0.983774i	$-0.442580\pi$
$293$	6.14214	0.358827	0.179414	+	0.983774i	$0.442580\pi$
$294$	0	0
$295$	−9.89949	−0.576371
$296$	3.24264	0.188475
$297$	−2.41421	−0.140087
$298$	2.82843	0.163846
$299$	8.65685	0.500639
$300$	4.00000	0.230940
$301$	0	0
$302$	13.2426	0.762028
$303$	1.07107	0.0615312
$304$	3.82843	0.219575
$305$	−5.58579	−0.319841
$306$	0.414214	0.0236790
$307$	−11.6569	−0.665292	−0.332646	−	0.943052i	$-0.607941\pi$
$307$	−11.6569	−0.665292	−0.332646	+	0.943052i	$0.607941\pi$
$308$	0	0
$309$	8.07107	0.459147
$310$	4.24264	0.240966
$311$	21.7990	1.23611	0.618054	−	0.786136i	$-0.287921\pi$
$311$	21.7990	1.23611	0.618054	+	0.786136i	$0.287921\pi$
$312$	−1.00000	−0.0566139
$313$	−21.0711	−1.19101	−0.595504	−	0.803353i	$-0.703047\pi$
$313$	−21.0711	−1.19101	−0.595504	+	0.803353i	$0.703047\pi$
$314$	2.89949	0.163628
$315$	0	0
$316$	10.2426	0.576194
$317$	18.0416	1.01332	0.506659	−	0.862146i	$-0.330880\pi$
$317$	18.0416	1.01332	0.506659	+	0.862146i	$0.330880\pi$
$318$	−13.6569	−0.765838
$319$	6.41421	0.359127
$320$	1.00000	0.0559017
$321$	−4.58579	−0.255954
$322$	0	0
$323$	−1.58579	−0.0882355
$324$	1.00000	0.0555556
$325$	4.00000	0.221880
$326$	11.6569	0.645613
$327$	−0.414214	−0.0229061
$328$	−6.82843	−0.377037
$329$	0	0
$330$	2.41421	0.132898
$331$	−29.8995	−1.64342	−0.821712	−	0.569902i	$-0.806981\pi$
$331$	−29.8995	−1.64342	−0.821712	+	0.569902i	$0.806981\pi$
$332$	11.6569	0.639753
$333$	−3.24264	−0.177696
$334$	−13.8284	−0.756658
$335$	1.41421	0.0772667
$336$	0	0
$337$	−17.4853	−0.952484	−0.476242	−	0.879314i	$-0.658001\pi$
$337$	−17.4853	−0.952484	−0.476242	+	0.879314i	$0.658001\pi$
$338$	−1.00000	−0.0543928
$339$	18.2426	0.990804
$340$	−0.414214	−0.0224639
$341$	−10.2426	−0.554670
$342$	−3.82843	−0.207018
$343$	0	0
$344$	7.00000	0.377415
$345$	8.65685	0.466069
$346$	−16.2426	−0.873210
$347$	−22.5858	−1.21247	−0.606234	−	0.795286i	$-0.707321\pi$
$347$	−22.5858	−1.21247	−0.606234	+	0.795286i	$0.707321\pi$
$348$	−2.65685	−0.142422
$349$	14.7279	0.788368	0.394184	−	0.919032i	$-0.371027\pi$
$349$	14.7279	0.788368	0.394184	+	0.919032i	$0.371027\pi$
$350$	0	0
$351$	1.00000	0.0533761
$352$	−2.41421	−0.128678
$353$	19.4558	1.03553	0.517765	−	0.855523i	$-0.326764\pi$
$353$	19.4558	1.03553	0.517765	+	0.855523i	$0.326764\pi$
$354$	−9.89949	−0.526152
$355$	5.07107	0.269144
$356$	0.585786	0.0310466
$357$	0	0
$358$	19.5563	1.03359
$359$	−29.4558	−1.55462	−0.777310	−	0.629118i	$-0.783416\pi$
$359$	−29.4558	−1.55462	−0.777310	+	0.629118i	$0.783416\pi$
$360$	−1.00000	−0.0527046
$361$	−4.34315	−0.228587
$362$	−18.1421	−0.953529
$363$	5.17157	0.271437
$364$	0	0
$365$	−11.8284	−0.619128
$366$	−5.58579	−0.291974
$367$	4.00000	0.208798	0.104399	−	0.994535i	$-0.466708\pi$
$367$	4.00000	0.208798	0.104399	+	0.994535i	$0.466708\pi$
$368$	−8.65685	−0.451270
$369$	6.82843	0.355474
$370$	3.24264	0.168577
$371$	0	0
$372$	4.24264	0.219971
$373$	4.24264	0.219676	0.109838	−	0.993950i	$-0.464967\pi$
$373$	4.24264	0.219676	0.109838	+	0.993950i	$0.464967\pi$
$374$	1.00000	0.0517088
$375$	9.00000	0.464758
$376$	−7.65685	−0.394872
$377$	−2.65685	−0.136835
$378$	0	0
$379$	−24.3848	−1.25256	−0.626281	−	0.779597i	$-0.715424\pi$
$379$	−24.3848	−1.25256	−0.626281	+	0.779597i	$0.715424\pi$
$380$	3.82843	0.196394
$381$	2.92893	0.150054
$382$	−5.48528	−0.280651
$383$	−11.3431	−0.579608	−0.289804	−	0.957086i	$-0.593590\pi$
$383$	−11.3431	−0.579608	−0.289804	+	0.957086i	$0.593590\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−12.3848	−0.630369
$387$	−7.00000	−0.355830
$388$	7.31371	0.371297
$389$	−8.00000	−0.405616	−0.202808	−	0.979219i	$-0.565007\pi$
$389$	−8.00000	−0.405616	−0.202808	+	0.979219i	$0.565007\pi$
$390$	−1.00000	−0.0506370
$391$	3.58579	0.181341
$392$	0	0
$393$	−17.2426	−0.869776
$394$	−5.07107	−0.255477
$395$	10.2426	0.515363
$396$	2.41421	0.121319
$397$	−6.68629	−0.335575	−0.167788	−	0.985823i	$-0.553662\pi$
$397$	−6.68629	−0.335575	−0.167788	+	0.985823i	$0.553662\pi$
$398$	−10.0711	−0.504817
$399$	0	0
$400$	−4.00000	−0.200000
$401$	−21.4558	−1.07145	−0.535727	−	0.844391i	$-0.679962\pi$
$401$	−21.4558	−1.07145	−0.535727	+	0.844391i	$0.679962\pi$
$402$	1.41421	0.0705346
$403$	4.24264	0.211341
$404$	−1.07107	−0.0532876
$405$	1.00000	0.0496904
$406$	0	0
$407$	−7.82843	−0.388041
$408$	−0.414214	−0.0205066
$409$	−33.9706	−1.67974	−0.839868	−	0.542791i	$-0.817368\pi$
$409$	−33.9706	−1.67974	−0.839868	+	0.542791i	$0.817368\pi$
$410$	−6.82843	−0.337232
$411$	7.24264	0.357253
$412$	−8.07107	−0.397633
$413$	0	0
$414$	8.65685	0.425461
$415$	11.6569	0.572212
$416$	1.00000	0.0490290
$417$	6.82843	0.334390
$418$	−9.24264	−0.452072
$419$	−10.5563	−0.515711	−0.257856	−	0.966183i	$-0.583016\pi$
$419$	−10.5563	−0.515711	−0.257856	+	0.966183i	$0.583016\pi$
$420$	0	0
$421$	−33.1127	−1.61381	−0.806907	−	0.590678i	$-0.798860\pi$
$421$	−33.1127	−1.61381	−0.806907	+	0.590678i	$0.798860\pi$
$422$	16.3137	0.794139
$423$	7.65685	0.372289
$424$	13.6569	0.663235
$425$	1.65685	0.0803692
$426$	5.07107	0.245694
$427$	0	0
$428$	4.58579	0.221662
$429$	2.41421	0.116559
$430$	7.00000	0.337570
$431$	15.1716	0.730789	0.365394	−	0.930853i	$-0.380934\pi$
$431$	15.1716	0.730789	0.365394	+	0.930853i	$0.380934\pi$
$432$	−1.00000	−0.0481125
$433$	−26.6274	−1.27963	−0.639816	−	0.768528i	$-0.720989\pi$
$433$	−26.6274	−1.27963	−0.639816	+	0.768528i	$0.720989\pi$
$434$	0	0
$435$	−2.65685	−0.127386
$436$	0.414214	0.0198372
$437$	−33.1421	−1.58540
$438$	−11.8284	−0.565184
$439$	38.2132	1.82382	0.911908	−	0.410394i	$-0.134609\pi$
$439$	38.2132	1.82382	0.911908	+	0.410394i	$0.134609\pi$
$440$	−2.41421	−0.115093
$441$	0	0
$442$	−0.414214	−0.0197021
$443$	0.828427	0.0393598	0.0196799	−	0.999806i	$-0.493735\pi$
$443$	0.828427	0.0393598	0.0196799	+	0.999806i	$0.493735\pi$
$444$	3.24264	0.153889
$445$	0.585786	0.0277689
$446$	15.6569	0.741374
$447$	2.82843	0.133780
$448$	0	0
$449$	18.5563	0.875728	0.437864	−	0.899041i	$-0.355735\pi$
$449$	18.5563	0.875728	0.437864	+	0.899041i	$0.355735\pi$
$450$	4.00000	0.188562
$451$	16.4853	0.776262
$452$	−18.2426	−0.858062
$453$	13.2426	0.622194
$454$	5.07107	0.237997
$455$	0	0
$456$	3.82843	0.179283
$457$	−22.2426	−1.04047	−0.520233	−	0.854024i	$-0.674155\pi$
$457$	−22.2426	−1.04047	−0.520233	+	0.854024i	$0.674155\pi$
$458$	23.8995	1.11675
$459$	0.414214	0.0193338
$460$	−8.65685	−0.403628
$461$	−23.4853	−1.09382	−0.546909	−	0.837192i	$-0.684196\pi$
$461$	−23.4853	−1.09382	−0.546909	+	0.837192i	$0.684196\pi$
$462$	0	0
$463$	31.8701	1.48113	0.740564	−	0.671986i	$-0.234559\pi$
$463$	31.8701	1.48113	0.740564	+	0.671986i	$0.234559\pi$
$464$	2.65685	0.123341
$465$	4.24264	0.196748
$466$	10.8284	0.501617
$467$	9.10051	0.421121	0.210561	−	0.977581i	$-0.432471\pi$
$467$	9.10051	0.421121	0.210561	+	0.977581i	$0.432471\pi$
$468$	−1.00000	−0.0462250
$469$	0	0
$470$	−7.65685	−0.353184
$471$	2.89949	0.133602
$472$	9.89949	0.455661
$473$	−16.8995	−0.777040
$474$	10.2426	0.470460
$475$	−15.3137	−0.702641
$476$	0	0
$477$	−13.6569	−0.625304
$478$	−14.7279	−0.673639
$479$	−9.48528	−0.433394	−0.216697	−	0.976239i	$-0.569528\pi$
$479$	−9.48528	−0.433394	−0.216697	+	0.976239i	$0.569528\pi$
$480$	1.00000	0.0456435
$481$	3.24264	0.147852
$482$	12.3431	0.562215
$483$	0	0
$484$	−5.17157	−0.235071
$485$	7.31371	0.332098
$486$	1.00000	0.0453609
$487$	37.5980	1.70373	0.851864	−	0.523764i	$-0.175473\pi$
$487$	37.5980	1.70373	0.851864	+	0.523764i	$0.175473\pi$
$488$	5.58579	0.252857
$489$	11.6569	0.527141
$490$	0	0
$491$	34.7696	1.56913	0.784564	−	0.620048i	$-0.212887\pi$
$491$	34.7696	1.56913	0.784564	+	0.620048i	$0.212887\pi$
$492$	−6.82843	−0.307849
$493$	−1.10051	−0.0495643
$494$	3.82843	0.172249
$495$	2.41421	0.108511
$496$	−4.24264	−0.190500
$497$	0	0
$498$	11.6569	0.522356
$499$	22.7279	1.01744	0.508721	−	0.860932i	$-0.330119\pi$
$499$	22.7279	1.01744	0.508721	+	0.860932i	$0.330119\pi$
$500$	−9.00000	−0.402492
$501$	−13.8284	−0.617809
$502$	−3.58579	−0.160041
$503$	−11.0711	−0.493635	−0.246817	−	0.969062i	$-0.579385\pi$
$503$	−11.0711	−0.493635	−0.246817	+	0.969062i	$0.579385\pi$
$504$	0	0
$505$	−1.07107	−0.0476619
$506$	20.8995	0.929096
$507$	−1.00000	−0.0444116
$508$	−2.92893	−0.129950
$509$	−5.14214	−0.227921	−0.113961	−	0.993485i	$-0.536354\pi$
$509$	−5.14214	−0.227921	−0.113961	+	0.993485i	$0.536354\pi$
$510$	−0.414214	−0.0183417
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	−3.82843	−0.169029
$514$	−5.17157	−0.228108
$515$	−8.07107	−0.355654
$516$	7.00000	0.308158
$517$	18.4853	0.812982
$518$	0	0
$519$	−16.2426	−0.712973
$520$	1.00000	0.0438529
$521$	−10.5563	−0.462482	−0.231241	−	0.972896i	$-0.574279\pi$
$521$	−10.5563	−0.462482	−0.231241	+	0.972896i	$0.574279\pi$
$522$	−2.65685	−0.116287
$523$	−5.27208	−0.230532	−0.115266	−	0.993335i	$-0.536772\pi$
$523$	−5.27208	−0.230532	−0.115266	+	0.993335i	$0.536772\pi$
$524$	17.2426	0.753248
$525$	0	0
$526$	−9.65685	−0.421059
$527$	1.75736	0.0765518
$528$	−2.41421	−0.105065
$529$	51.9411	2.25831
$530$	13.6569	0.593216
$531$	−9.89949	−0.429601
$532$	0	0
$533$	−6.82843	−0.295772
$534$	0.585786	0.0253495
$535$	4.58579	0.198261
$536$	−1.41421	−0.0610847
$537$	19.5563	0.843919
$538$	16.7279	0.721192
$539$	0	0
$540$	−1.00000	−0.0430331
$541$	−25.3848	−1.09138	−0.545688	−	0.837988i	$-0.683732\pi$
$541$	−25.3848	−1.09138	−0.545688	+	0.837988i	$0.683732\pi$
$542$	14.2426	0.611774
$543$	−18.1421	−0.778554
$544$	0.414214	0.0177593
$545$	0.414214	0.0177430
$546$	0	0
$547$	−25.7990	−1.10309	−0.551543	−	0.834147i	$-0.685961\pi$
$547$	−25.7990	−1.10309	−0.551543	+	0.834147i	$0.685961\pi$
$548$	−7.24264	−0.309390
$549$	−5.58579	−0.238396
$550$	9.65685	0.411770
$551$	10.1716	0.433324
$552$	−8.65685	−0.368460
$553$	0	0
$554$	16.5858	0.704663
$555$	3.24264	0.137642
$556$	−6.82843	−0.289590
$557$	−8.48528	−0.359533	−0.179766	−	0.983709i	$-0.557534\pi$
$557$	−8.48528	−0.359533	−0.179766	+	0.983709i	$0.557534\pi$
$558$	4.24264	0.179605
$559$	7.00000	0.296068
$560$	0	0
$561$	1.00000	0.0422200
$562$	−1.31371	−0.0554154
$563$	8.41421	0.354617	0.177308	−	0.984155i	$-0.443261\pi$
$563$	8.41421	0.354617	0.177308	+	0.984155i	$0.443261\pi$
$564$	−7.65685	−0.322412
$565$	−18.2426	−0.767474
$566$	10.8284	0.455153
$567$	0	0
$568$	−5.07107	−0.212777
$569$	−18.4853	−0.774943	−0.387472	−	0.921882i	$-0.626651\pi$
$569$	−18.4853	−0.774943	−0.387472	+	0.921882i	$0.626651\pi$
$570$	3.82843	0.160355
$571$	30.2843	1.26736	0.633679	−	0.773596i	$-0.281544\pi$
$571$	30.2843	1.26736	0.633679	+	0.773596i	$0.281544\pi$
$572$	−2.41421	−0.100943
$573$	−5.48528	−0.229151
$574$	0	0
$575$	34.6274	1.44406
$576$	1.00000	0.0416667
$577$	21.1716	0.881384	0.440692	−	0.897658i	$-0.354733\pi$
$577$	21.1716	0.881384	0.440692	+	0.897658i	$0.354733\pi$
$578$	16.8284	0.699970
$579$	−12.3848	−0.514694
$580$	2.65685	0.110320
$581$	0	0
$582$	7.31371	0.303163
$583$	−32.9706	−1.36550
$584$	11.8284	0.489464
$585$	−1.00000	−0.0413449
$586$	−6.14214	−0.253729
$587$	−37.1127	−1.53180	−0.765902	−	0.642957i	$-0.777707\pi$
$587$	−37.1127	−1.53180	−0.765902	+	0.642957i	$0.777707\pi$
$588$	0	0
$589$	−16.2426	−0.669266
$590$	9.89949	0.407556
$591$	−5.07107	−0.208596
$592$	−3.24264	−0.133272
$593$	7.41421	0.304465	0.152233	−	0.988345i	$-0.451354\pi$
$593$	7.41421	0.304465	0.152233	+	0.988345i	$0.451354\pi$
$594$	2.41421	0.0990564
$595$	0	0
$596$	−2.82843	−0.115857
$597$	−10.0711	−0.412181
$598$	−8.65685	−0.354005
$599$	20.5147	0.838209	0.419104	−	0.907938i	$-0.362344\pi$
$599$	20.5147	0.838209	0.419104	+	0.907938i	$0.362344\pi$
$600$	−4.00000	−0.163299
$601$	−29.4558	−1.20153	−0.600764	−	0.799426i	$-0.705137\pi$
$601$	−29.4558	−1.20153	−0.600764	+	0.799426i	$0.705137\pi$
$602$	0	0
$603$	1.41421	0.0575912
$604$	−13.2426	−0.538835
$605$	−5.17157	−0.210254
$606$	−1.07107	−0.0435092
$607$	35.1838	1.42807	0.714033	−	0.700113i	$-0.246867\pi$
$607$	35.1838	1.42807	0.714033	+	0.700113i	$0.246867\pi$
$608$	−3.82843	−0.155263
$609$	0	0
$610$	5.58579	0.226162
$611$	−7.65685	−0.309763
$612$	−0.414214	−0.0167436
$613$	6.07107	0.245208	0.122604	−	0.992456i	$-0.460875\pi$
$613$	6.07107	0.245208	0.122604	+	0.992456i	$0.460875\pi$
$614$	11.6569	0.470432
$615$	−6.82843	−0.275349
$616$	0	0
$617$	−25.5858	−1.03004	−0.515022	−	0.857177i	$-0.672216\pi$
$617$	−25.5858	−1.03004	−0.515022	+	0.857177i	$0.672216\pi$
$618$	−8.07107	−0.324666
$619$	21.2843	0.855487	0.427744	−	0.903900i	$-0.359309\pi$
$619$	21.2843	0.855487	0.427744	+	0.903900i	$0.359309\pi$
$620$	−4.24264	−0.170389
$621$	8.65685	0.347388
$622$	−21.7990	−0.874060
$623$	0	0
$624$	1.00000	0.0400320
$625$	11.0000	0.440000
$626$	21.0711	0.842169
$627$	−9.24264	−0.369116
$628$	−2.89949	−0.115702
$629$	1.34315	0.0535547
$630$	0	0
$631$	0.615224	0.0244917	0.0122458	−	0.999925i	$-0.496102\pi$
$631$	0.615224	0.0244917	0.0122458	+	0.999925i	$0.496102\pi$
$632$	−10.2426	−0.407430
$633$	16.3137	0.648412
$634$	−18.0416	−0.716525
$635$	−2.92893	−0.116231
$636$	13.6569	0.541529
$637$	0	0
$638$	−6.41421	−0.253941
$639$	5.07107	0.200608
$640$	−1.00000	−0.0395285
$641$	−42.5269	−1.67971	−0.839856	−	0.542809i	$-0.817361\pi$
$641$	−42.5269	−1.67971	−0.839856	+	0.542809i	$0.817361\pi$
$642$	4.58579	0.180987
$643$	15.6863	0.618607	0.309303	−	0.950963i	$-0.399904\pi$
$643$	15.6863	0.618607	0.309303	+	0.950963i	$0.399904\pi$
$644$	0	0
$645$	7.00000	0.275625
$646$	1.58579	0.0623919
$647$	−11.0294	−0.433612	−0.216806	−	0.976215i	$-0.569564\pi$
$647$	−11.0294	−0.433612	−0.216806	+	0.976215i	$0.569564\pi$
$648$	−1.00000	−0.0392837
$649$	−23.8995	−0.938137
$650$	−4.00000	−0.156893
$651$	0	0
$652$	−11.6569	−0.456518
$653$	−21.4853	−0.840784	−0.420392	−	0.907343i	$-0.638107\pi$
$653$	−21.4853	−0.840784	−0.420392	+	0.907343i	$0.638107\pi$
$654$	0.414214	0.0161970
$655$	17.2426	0.673726
$656$	6.82843	0.266605
$657$	−11.8284	−0.461471
$658$	0	0
$659$	−11.4558	−0.446256	−0.223128	−	0.974789i	$-0.571627\pi$
$659$	−11.4558	−0.446256	−0.223128	+	0.974789i	$0.571627\pi$
$660$	−2.41421	−0.0939731
$661$	34.9706	1.36020	0.680099	−	0.733121i	$-0.261937\pi$
$661$	34.9706	1.36020	0.680099	+	0.733121i	$0.261937\pi$
$662$	29.8995	1.16208
$663$	−0.414214	−0.0160867
$664$	−11.6569	−0.452374
$665$	0	0
$666$	3.24264	0.125650
$667$	−23.0000	−0.890564
$668$	13.8284	0.535038
$669$	15.6569	0.605329
$670$	−1.41421	−0.0546358
$671$	−13.4853	−0.520594
$672$	0	0
$673$	38.1127	1.46914	0.734568	−	0.678535i	$-0.237385\pi$
$673$	38.1127	1.46914	0.734568	+	0.678535i	$0.237385\pi$
$674$	17.4853	0.673508
$675$	4.00000	0.153960
$676$	1.00000	0.0384615
$677$	38.7696	1.49003	0.745017	−	0.667045i	$-0.232441\pi$
$677$	38.7696	1.49003	0.745017	+	0.667045i	$0.232441\pi$
$678$	−18.2426	−0.700604
$679$	0	0
$680$	0.414214	0.0158844
$681$	5.07107	0.194324
$682$	10.2426	0.392211
$683$	23.5858	0.902485	0.451243	−	0.892401i	$-0.350981\pi$
$683$	23.5858	0.902485	0.451243	+	0.892401i	$0.350981\pi$
$684$	3.82843	0.146384
$685$	−7.24264	−0.276727
$686$	0	0
$687$	23.8995	0.911823
$688$	−7.00000	−0.266872
$689$	13.6569	0.520285
$690$	−8.65685	−0.329561
$691$	−23.1716	−0.881488	−0.440744	−	0.897633i	$-0.645285\pi$
$691$	−23.1716	−0.881488	−0.440744	+	0.897633i	$0.645285\pi$
$692$	16.2426	0.617453
$693$	0	0
$694$	22.5858	0.857345
$695$	−6.82843	−0.259017
$696$	2.65685	0.100708
$697$	−2.82843	−0.107134
$698$	−14.7279	−0.557460
$699$	10.8284	0.409569
$700$	0	0
$701$	34.8284	1.31545	0.657726	−	0.753257i	$-0.271519\pi$
$701$	34.8284	1.31545	0.657726	+	0.753257i	$0.271519\pi$
$702$	−1.00000	−0.0377426
$703$	−12.4142	−0.468211
$704$	2.41421	0.0909891
$705$	−7.65685	−0.288374
$706$	−19.4558	−0.732230
$707$	0	0
$708$	9.89949	0.372046
$709$	40.8284	1.53334	0.766672	−	0.642039i	$-0.221911\pi$
$709$	40.8284	1.53334	0.766672	+	0.642039i	$0.221911\pi$
$710$	−5.07107	−0.190314
$711$	10.2426	0.384129
$712$	−0.585786	−0.0219533
$713$	36.7279	1.37547
$714$	0	0
$715$	−2.41421	−0.0902865
$716$	−19.5563	−0.730855
$717$	−14.7279	−0.550024
$718$	29.4558	1.09928
$719$	10.5858	0.394783	0.197392	−	0.980325i	$-0.436753\pi$
$719$	10.5858	0.394783	0.197392	+	0.980325i	$0.436753\pi$
$720$	1.00000	0.0372678
$721$	0	0
$722$	4.34315	0.161635
$723$	12.3431	0.459047
$724$	18.1421	0.674247
$725$	−10.6274	−0.394692
$726$	−5.17157	−0.191935
$727$	7.78680	0.288796	0.144398	−	0.989520i	$-0.453875\pi$
$727$	7.78680	0.288796	0.144398	+	0.989520i	$0.453875\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	11.8284	0.437790
$731$	2.89949	0.107242
$732$	5.58579	0.206457
$733$	15.2721	0.564087	0.282044	−	0.959402i	$-0.408988\pi$
$733$	15.2721	0.564087	0.282044	+	0.959402i	$0.408988\pi$
$734$	−4.00000	−0.147643
$735$	0	0
$736$	8.65685	0.319096
$737$	3.41421	0.125764
$738$	−6.82843	−0.251358
$739$	34.2843	1.26117	0.630584	−	0.776121i	$-0.282816\pi$
$739$	34.2843	1.26117	0.630584	+	0.776121i	$0.282816\pi$
$740$	−3.24264	−0.119202
$741$	3.82843	0.140641
$742$	0	0
$743$	52.6274	1.93071	0.965356	−	0.260935i	$-0.0840309\pi$
$743$	52.6274	1.93071	0.965356	+	0.260935i	$0.0840309\pi$
$744$	−4.24264	−0.155543
$745$	−2.82843	−0.103626
$746$	−4.24264	−0.155334
$747$	11.6569	0.426502
$748$	−1.00000	−0.0365636
$749$	0	0
$750$	−9.00000	−0.328634
$751$	16.4437	0.600037	0.300019	−	0.953933i	$-0.403007\pi$
$751$	16.4437	0.600037	0.300019	+	0.953933i	$0.403007\pi$
$752$	7.65685	0.279217
$753$	−3.58579	−0.130673
$754$	2.65685	0.0967569
$755$	−13.2426	−0.481949
$756$	0	0
$757$	−5.07107	−0.184311	−0.0921555	−	0.995745i	$-0.529376\pi$
$757$	−5.07107	−0.184311	−0.0921555	+	0.995745i	$0.529376\pi$
$758$	24.3848	0.885695
$759$	20.8995	0.758604
$760$	−3.82843	−0.138872
$761$	6.82843	0.247530	0.123765	−	0.992312i	$-0.460503\pi$
$761$	6.82843	0.247530	0.123765	+	0.992312i	$0.460503\pi$
$762$	−2.92893	−0.106104
$763$	0	0
$764$	5.48528	0.198451
$765$	−0.414214	−0.0149759
$766$	11.3431	0.409845
$767$	9.89949	0.357450
$768$	−1.00000	−0.0360844
$769$	−0.857864	−0.0309354	−0.0154677	−	0.999880i	$-0.504924\pi$
$769$	−0.857864	−0.0309354	−0.0154677	+	0.999880i	$0.504924\pi$
$770$	0	0
$771$	−5.17157	−0.186250
$772$	12.3848	0.445738
$773$	−8.02944	−0.288799	−0.144399	−	0.989519i	$-0.546125\pi$
$773$	−8.02944	−0.288799	−0.144399	+	0.989519i	$0.546125\pi$
$774$	7.00000	0.251610
$775$	16.9706	0.609601
$776$	−7.31371	−0.262547
$777$	0	0
$778$	8.00000	0.286814
$779$	26.1421	0.936639
$780$	1.00000	0.0358057
$781$	12.2426	0.438076
$782$	−3.58579	−0.128227
$783$	−2.65685	−0.0949482
$784$	0	0
$785$	−2.89949	−0.103487
$786$	17.2426	0.615025
$787$	−10.1716	−0.362577	−0.181289	−	0.983430i	$-0.558027\pi$
$787$	−10.1716	−0.362577	−0.181289	+	0.983430i	$0.558027\pi$
$788$	5.07107	0.180649
$789$	−9.65685	−0.343793
$790$	−10.2426	−0.364417
$791$	0	0
$792$	−2.41421	−0.0857853
$793$	5.58579	0.198357
$794$	6.68629	0.237288
$795$	13.6569	0.484359
$796$	10.0711	0.356960
$797$	6.72792	0.238315	0.119158	−	0.992875i	$-0.461981\pi$
$797$	6.72792	0.238315	0.119158	+	0.992875i	$0.461981\pi$
$798$	0	0
$799$	−3.17157	−0.112202
$800$	4.00000	0.141421
$801$	0.585786	0.0206977
$802$	21.4558	0.757632
$803$	−28.5563	−1.00773
$804$	−1.41421	−0.0498755
$805$	0	0
$806$	−4.24264	−0.149441
$807$	16.7279	0.588851
$808$	1.07107	0.0376800
$809$	−13.5563	−0.476616	−0.238308	−	0.971190i	$-0.576593\pi$
$809$	−13.5563	−0.476616	−0.238308	+	0.971190i	$0.576593\pi$
$810$	−1.00000	−0.0351364
$811$	21.3431	0.749459	0.374730	−	0.927134i	$-0.377736\pi$
$811$	21.3431	0.749459	0.374730	+	0.927134i	$0.377736\pi$
$812$	0	0
$813$	14.2426	0.499511
$814$	7.82843	0.274386
$815$	−11.6569	−0.408322
$816$	0.414214	0.0145004
$817$	−26.7990	−0.937578
$818$	33.9706	1.18775
$819$	0	0
$820$	6.82843	0.238459
$821$	28.4853	0.994143	0.497072	−	0.867710i	$-0.334409\pi$
$821$	28.4853	0.994143	0.497072	+	0.867710i	$0.334409\pi$
$822$	−7.24264	−0.252616
$823$	−20.5269	−0.715523	−0.357762	−	0.933813i	$-0.616460\pi$
$823$	−20.5269	−0.715523	−0.357762	+	0.933813i	$0.616460\pi$
$824$	8.07107	0.281169
$825$	9.65685	0.336209
$826$	0	0
$827$	27.5269	0.957205	0.478602	−	0.878032i	$-0.341144\pi$
$827$	27.5269	0.957205	0.478602	+	0.878032i	$0.341144\pi$
$828$	−8.65685	−0.300846
$829$	−51.5269	−1.78960	−0.894802	−	0.446464i	$-0.852683\pi$
$829$	−51.5269	−1.78960	−0.894802	+	0.446464i	$0.852683\pi$
$830$	−11.6569	−0.404615
$831$	16.5858	0.575355
$832$	−1.00000	−0.0346688
$833$	0	0
$834$	−6.82843	−0.236449
$835$	13.8284	0.478552
$836$	9.24264	0.319663
$837$	4.24264	0.146647
$838$	10.5563	0.364663
$839$	−56.6274	−1.95500	−0.977498	−	0.210946i	$-0.932346\pi$
$839$	−56.6274	−1.95500	−0.977498	+	0.210946i	$0.932346\pi$
$840$	0	0
$841$	−21.9411	−0.756591
$842$	33.1127	1.14114
$843$	−1.31371	−0.0452465
$844$	−16.3137	−0.561541
$845$	1.00000	0.0344010
$846$	−7.65685	−0.263248
$847$	0	0
$848$	−13.6569	−0.468978
$849$	10.8284	0.371631
$850$	−1.65685	−0.0568296
$851$	28.0711	0.962264
$852$	−5.07107	−0.173732
$853$	−33.6569	−1.15239	−0.576194	−	0.817313i	$-0.695463\pi$
$853$	−33.6569	−1.15239	−0.576194	+	0.817313i	$0.695463\pi$
$854$	0	0
$855$	3.82843	0.130929
$856$	−4.58579	−0.156739
$857$	44.8284	1.53131	0.765655	−	0.643252i	$-0.222415\pi$
$857$	44.8284	1.53131	0.765655	+	0.643252i	$0.222415\pi$
$858$	−2.41421	−0.0824199
$859$	48.9706	1.67085	0.835427	−	0.549601i	$-0.185220\pi$
$859$	48.9706	1.67085	0.835427	+	0.549601i	$0.185220\pi$
$860$	−7.00000	−0.238698
$861$	0	0
$862$	−15.1716	−0.516746
$863$	−10.9706	−0.373442	−0.186721	−	0.982413i	$-0.559786\pi$
$863$	−10.9706	−0.373442	−0.186721	+	0.982413i	$0.559786\pi$
$864$	1.00000	0.0340207
$865$	16.2426	0.552266
$866$	26.6274	0.904836
$867$	16.8284	0.571523
$868$	0	0
$869$	24.7279	0.838837
$870$	2.65685	0.0900758
$871$	−1.41421	−0.0479188
$872$	−0.414214	−0.0140270
$873$	7.31371	0.247532
$874$	33.1421	1.12105
$875$	0	0
$876$	11.8284	0.399646
$877$	−8.48528	−0.286528	−0.143264	−	0.989685i	$-0.545760\pi$
$877$	−8.48528	−0.286528	−0.143264	+	0.989685i	$0.545760\pi$
$878$	−38.2132	−1.28963
$879$	−6.14214	−0.207169
$880$	2.41421	0.0813831
$881$	−41.3848	−1.39429	−0.697144	−	0.716931i	$-0.745546\pi$
$881$	−41.3848	−1.39429	−0.697144	+	0.716931i	$0.745546\pi$
$882$	0	0
$883$	22.0294	0.741350	0.370675	−	0.928763i	$-0.379126\pi$
$883$	22.0294	0.741350	0.370675	+	0.928763i	$0.379126\pi$
$884$	0.414214	0.0139315
$885$	9.89949	0.332768
$886$	−0.828427	−0.0278316
$887$	59.1127	1.98481	0.992405	−	0.123013i	$-0.0392556\pi$
$887$	59.1127	1.98481	0.992405	+	0.123013i	$0.0392556\pi$
$888$	−3.24264	−0.108816
$889$	0	0
$890$	−0.585786	−0.0196356
$891$	2.41421	0.0808792
$892$	−15.6569	−0.524230
$893$	29.3137	0.980946
$894$	−2.82843	−0.0945968
$895$	−19.5563	−0.653697
$896$	0	0
$897$	−8.65685	−0.289044
$898$	−18.5563	−0.619233
$899$	−11.2721	−0.375945
$900$	−4.00000	−0.133333
$901$	5.65685	0.188457
$902$	−16.4853	−0.548900
$903$	0	0
$904$	18.2426	0.606741
$905$	18.1421	0.603065
$906$	−13.2426	−0.439957
$907$	51.1716	1.69912	0.849562	−	0.527489i	$-0.176866\pi$
$907$	51.1716	1.69912	0.849562	+	0.527489i	$0.176866\pi$
$908$	−5.07107	−0.168289
$909$	−1.07107	−0.0355251
$910$	0	0
$911$	−9.97056	−0.330339	−0.165170	−	0.986265i	$-0.552817\pi$
$911$	−9.97056	−0.330339	−0.165170	+	0.986265i	$0.552817\pi$
$912$	−3.82843	−0.126772
$913$	28.1421	0.931369
$914$	22.2426	0.735721
$915$	5.58579	0.184660
$916$	−23.8995	−0.789662
$917$	0	0
$918$	−0.414214	−0.0136711
$919$	−12.1421	−0.400532	−0.200266	−	0.979742i	$-0.564181\pi$
$919$	−12.1421	−0.400532	−0.200266	+	0.979742i	$0.564181\pi$
$920$	8.65685	0.285408
$921$	11.6569	0.384106
$922$	23.4853	0.773447
$923$	−5.07107	−0.166916
$924$	0	0
$925$	12.9706	0.426469
$926$	−31.8701	−1.04732
$927$	−8.07107	−0.265089
$928$	−2.65685	−0.0872155
$929$	−1.85786	−0.0609546	−0.0304773	−	0.999535i	$-0.509703\pi$
$929$	−1.85786	−0.0609546	−0.0304773	+	0.999535i	$0.509703\pi$
$930$	−4.24264	−0.139122
$931$	0	0
$932$	−10.8284	−0.354697
$933$	−21.7990	−0.713667
$934$	−9.10051	−0.297778
$935$	−1.00000	−0.0327035
$936$	1.00000	0.0326860
$937$	41.6985	1.36223	0.681115	−	0.732176i	$-0.261495\pi$
$937$	41.6985	1.36223	0.681115	+	0.732176i	$0.261495\pi$
$938$	0	0
$939$	21.0711	0.687628
$940$	7.65685	0.249739
$941$	38.0000	1.23876	0.619382	−	0.785090i	$-0.287383\pi$
$941$	38.0000	1.23876	0.619382	+	0.785090i	$0.287383\pi$
$942$	−2.89949	−0.0944706
$943$	−59.1127	−1.92497
$944$	−9.89949	−0.322201
$945$	0	0
$946$	16.8995	0.549450
$947$	21.2426	0.690293	0.345147	−	0.938549i	$-0.387829\pi$
$947$	21.2426	0.690293	0.345147	+	0.938549i	$0.387829\pi$
$948$	−10.2426	−0.332666
$949$	11.8284	0.383967
$950$	15.3137	0.496842
$951$	−18.0416	−0.585040
$952$	0	0
$953$	36.2843	1.17536	0.587681	−	0.809092i	$-0.300041\pi$
$953$	36.2843	1.17536	0.587681	+	0.809092i	$0.300041\pi$
$954$	13.6569	0.442157
$955$	5.48528	0.177500
$956$	14.7279	0.476335
$957$	−6.41421	−0.207342
$958$	9.48528	0.306456
$959$	0	0
$960$	−1.00000	−0.0322749
$961$	−13.0000	−0.419355
$962$	−3.24264	−0.104547
$963$	4.58579	0.147775
$964$	−12.3431	−0.397546
$965$	12.3848	0.398680
$966$	0	0
$967$	−1.58579	−0.0509955	−0.0254977	−	0.999675i	$-0.508117\pi$
$967$	−1.58579	−0.0509955	−0.0254977	+	0.999675i	$0.508117\pi$
$968$	5.17157	0.166221
$969$	1.58579	0.0509428
$970$	−7.31371	−0.234829
$971$	−31.5147	−1.01136	−0.505678	−	0.862722i	$-0.668758\pi$
$971$	−31.5147	−1.01136	−0.505678	+	0.862722i	$0.668758\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	−37.5980	−1.20472
$975$	−4.00000	−0.128103
$976$	−5.58579	−0.178797
$977$	−47.8701	−1.53150	−0.765749	−	0.643139i	$-0.777632\pi$
$977$	−47.8701	−1.53150	−0.765749	+	0.643139i	$0.777632\pi$
$978$	−11.6569	−0.372745
$979$	1.41421	0.0451985
$980$	0	0
$981$	0.414214	0.0132248
$982$	−34.7696	−1.10954
$983$	−13.6863	−0.436525	−0.218262	−	0.975890i	$-0.570039\pi$
$983$	−13.6863	−0.436525	−0.218262	+	0.975890i	$0.570039\pi$
$984$	6.82843	0.217682
$985$	5.07107	0.161578
$986$	1.10051	0.0350472
$987$	0	0
$988$	−3.82843	−0.121798
$989$	60.5980	1.92690
$990$	−2.41421	−0.0767287
$991$	37.3137	1.18531	0.592655	−	0.805457i	$-0.298080\pi$
$991$	37.3137	1.18531	0.592655	+	0.805457i	$0.298080\pi$
$992$	4.24264	0.134704
$993$	29.8995	0.948832
$994$	0	0
$995$	10.0711	0.319274
$996$	−11.6569	−0.369362
$997$	−58.2843	−1.84588	−0.922941	−	0.384942i	$-0.874221\pi$
$997$	−58.2843	−1.84588	−0.922941	+	0.384942i	$0.874221\pi$
$998$	−22.7279	−0.719440
$999$	3.24264	0.102593

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3822.2.a.bj.1.2	✓	2
7.6	odd	2		3822.2.a.bl.1.2	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3822.2.a.bj.1.2	✓	2	1.1	even	1	trivial
3822.2.a.bl.1.2	yes	2	7.6	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:	\( N \)	\(=\)	\( 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3822.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +2.41421 q^{11} -1.00000 q^{12} -1.00000 q^{13} -1.00000 q^{15} +1.00000 q^{16} -0.414214 q^{17} -1.00000 q^{18} +3.82843 q^{19} +1.00000 q^{20} -2.41421 q^{22} -8.65685 q^{23} +1.00000 q^{24} -4.00000 q^{25} +1.00000 q^{26} -1.00000 q^{27} +2.65685 q^{29} +1.00000 q^{30} -4.24264 q^{31} -1.00000 q^{32} -2.41421 q^{33} +0.414214 q^{34} +1.00000 q^{36} -3.24264 q^{37} -3.82843 q^{38} +1.00000 q^{39} -1.00000 q^{40} +6.82843 q^{41} -7.00000 q^{43} +2.41421 q^{44} +1.00000 q^{45} +8.65685 q^{46} +7.65685 q^{47} -1.00000 q^{48} +4.00000 q^{50} +0.414214 q^{51} -1.00000 q^{52} -13.6569 q^{53} +1.00000 q^{54} +2.41421 q^{55} -3.82843 q^{57} -2.65685 q^{58} -9.89949 q^{59} -1.00000 q^{60} -5.58579 q^{61} +4.24264 q^{62} +1.00000 q^{64} -1.00000 q^{65} +2.41421 q^{66} +1.41421 q^{67} -0.414214 q^{68} +8.65685 q^{69} +5.07107 q^{71} -1.00000 q^{72} -11.8284 q^{73} +3.24264 q^{74} +4.00000 q^{75} +3.82843 q^{76} -1.00000 q^{78} +10.2426 q^{79} +1.00000 q^{80} +1.00000 q^{81} -6.82843 q^{82} +11.6569 q^{83} -0.414214 q^{85} +7.00000 q^{86} -2.65685 q^{87} -2.41421 q^{88} +0.585786 q^{89} -1.00000 q^{90} -8.65685 q^{92} +4.24264 q^{93} -7.65685 q^{94} +3.82843 q^{95} +1.00000 q^{96} +7.31371 q^{97} +2.41421 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} - 2 q^{8} + 2 q^{9} - 2 q^{10} + 2 q^{11} - 2 q^{12} - 2 q^{13} - 2 q^{15} + 2 q^{16} + 2 q^{17} - 2 q^{18} + 2 q^{19} + 2 q^{20} - 2 q^{22} - 6 q^{23} + 2 q^{24} - 8 q^{25} + 2 q^{26} - 2 q^{27} - 6 q^{29} + 2 q^{30} - 2 q^{32} - 2 q^{33} - 2 q^{34} + 2 q^{36} + 2 q^{37} - 2 q^{38} + 2 q^{39} - 2 q^{40} + 8 q^{41} - 14 q^{43} + 2 q^{44} + 2 q^{45} + 6 q^{46} + 4 q^{47} - 2 q^{48} + 8 q^{50} - 2 q^{51} - 2 q^{52} - 16 q^{53} + 2 q^{54} + 2 q^{55} - 2 q^{57} + 6 q^{58} - 2 q^{60} - 14 q^{61} + 2 q^{64} - 2 q^{65} + 2 q^{66} + 2 q^{68} + 6 q^{69} - 4 q^{71} - 2 q^{72} - 18 q^{73} - 2 q^{74} + 8 q^{75} + 2 q^{76} - 2 q^{78} + 12 q^{79} + 2 q^{80} + 2 q^{81} - 8 q^{82} + 12 q^{83} + 2 q^{85} + 14 q^{86} + 6 q^{87} - 2 q^{88} + 4 q^{89} - 2 q^{90} - 6 q^{92} - 4 q^{94} + 2 q^{95} + 2 q^{96} - 8 q^{97} + 2 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 - 2 * q^8 + 2 * q^9 - 2 * q^10 + 2 * q^11 - 2 * q^12 - 2 * q^13 - 2 * q^15 + 2 * q^16 + 2 * q^17 - 2 * q^18 + 2 * q^19 + 2 * q^20 - 2 * q^22 - 6 * q^23 + 2 * q^24 - 8 * q^25 + 2 * q^26 - 2 * q^27 - 6 * q^29 + 2 * q^30 - 2 * q^32 - 2 * q^33 - 2 * q^34 + 2 * q^36 + 2 * q^37 - 2 * q^38 + 2 * q^39 - 2 * q^40 + 8 * q^41 - 14 * q^43 + 2 * q^44 + 2 * q^45 + 6 * q^46 + 4 * q^47 - 2 * q^48 + 8 * q^50 - 2 * q^51 - 2 * q^52 - 16 * q^53 + 2 * q^54 + 2 * q^55 - 2 * q^57 + 6 * q^58 - 2 * q^60 - 14 * q^61 + 2 * q^64 - 2 * q^65 + 2 * q^66 + 2 * q^68 + 6 * q^69 - 4 * q^71 - 2 * q^72 - 18 * q^73 - 2 * q^74 + 8 * q^75 + 2 * q^76 - 2 * q^78 + 12 * q^79 + 2 * q^80 + 2 * q^81 - 8 * q^82 + 12 * q^83 + 2 * q^85 + 14 * q^86 + 6 * q^87 - 2 * q^88 + 4 * q^89 - 2 * q^90 - 6 * q^92 - 4 * q^94 + 2 * q^95 + 2 * q^96 - 8 * q^97 + 2 * q^99

Introduction

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