LMFDB - Embedded newform 3822.2.a.bl.1.1

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			1.1
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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -0.414214 q^{11} +1.00000 q^{12} +1.00000 q^{13} -1.00000 q^{15} +1.00000 q^{16} -2.41421 q^{17} -1.00000 q^{18} +1.82843 q^{19} -1.00000 q^{20} +0.414214 q^{22} +2.65685 q^{23} -1.00000 q^{24} -4.00000 q^{25} -1.00000 q^{26} +1.00000 q^{27} -8.65685 q^{29} +1.00000 q^{30} -4.24264 q^{31} -1.00000 q^{32} -0.414214 q^{33} +2.41421 q^{34} +1.00000 q^{36} +5.24264 q^{37} -1.82843 q^{38} +1.00000 q^{39} +1.00000 q^{40} -1.17157 q^{41} -7.00000 q^{43} -0.414214 q^{44} -1.00000 q^{45} -2.65685 q^{46} +3.65685 q^{47} +1.00000 q^{48} +4.00000 q^{50} -2.41421 q^{51} +1.00000 q^{52} -2.34315 q^{53} -1.00000 q^{54} +0.414214 q^{55} +1.82843 q^{57} +8.65685 q^{58} -9.89949 q^{59} -1.00000 q^{60} +8.41421 q^{61} +4.24264 q^{62} +1.00000 q^{64} -1.00000 q^{65} +0.414214 q^{66} -1.41421 q^{67} -2.41421 q^{68} +2.65685 q^{69} -9.07107 q^{71} -1.00000 q^{72} +6.17157 q^{73} -5.24264 q^{74} -4.00000 q^{75} +1.82843 q^{76} -1.00000 q^{78} +1.75736 q^{79} -1.00000 q^{80} +1.00000 q^{81} +1.17157 q^{82} -0.343146 q^{83} +2.41421 q^{85} +7.00000 q^{86} -8.65685 q^{87} +0.414214 q^{88} -3.41421 q^{89} +1.00000 q^{90} +2.65685 q^{92} -4.24264 q^{93} -3.65685 q^{94} -1.82843 q^{95} -1.00000 q^{96} +15.3137 q^{97} -0.414214 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.571783\pi$
$5$	−1.00000	−0.447214	−0.223607	+	0.974679i	$0.571783\pi$
$6$	−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
$11$	−0.414214	−0.124890	−0.0624450	−	0.998048i	$-0.519890\pi$
$11$	−0.414214	−0.124890	−0.0624450	+	0.998048i	$0.519890\pi$
$12$	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
$17$	−2.41421	−0.585533	−0.292766	−	0.956184i	$-0.594576\pi$
$17$	−2.41421	−0.585533	−0.292766	+	0.956184i	$0.594576\pi$
$18$	−1.00000	−0.235702
$19$	1.82843	0.419470	0.209735	−	0.977758i	$-0.432740\pi$
$19$	1.82843	0.419470	0.209735	+	0.977758i	$0.432740\pi$
$20$	−1.00000	−0.223607
$21$	0	0
$22$	0.414214	0.0883106
$23$	2.65685	0.553992	0.276996	−	0.960871i	$-0.410661\pi$
$23$	2.65685	0.553992	0.276996	+	0.960871i	$0.410661\pi$
$24$	−1.00000	−0.204124
$25$	−4.00000	−0.800000
$26$	−1.00000	−0.196116
$27$	1.00000	0.192450
$28$	0	0
$29$	−8.65685	−1.60754	−0.803769	−	0.594942i	$-0.797175\pi$
$29$	−8.65685	−1.60754	−0.803769	+	0.594942i	$0.797175\pi$
$30$	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
$33$	−0.414214	−0.0721053
$34$	2.41421	0.414034
$35$	0	0
$36$	1.00000	0.166667
$37$	5.24264	0.861885	0.430942	−	0.902379i	$-0.358181\pi$
$37$	5.24264	0.861885	0.430942	+	0.902379i	$0.358181\pi$
$38$	−1.82843	−0.296610
$39$	1.00000	0.160128
$40$	1.00000	0.158114
$41$	−1.17157	−0.182969	−0.0914845	−	0.995807i	$-0.529161\pi$
$41$	−1.17157	−0.182969	−0.0914845	+	0.995807i	$0.529161\pi$
$42$	0	0
$43$	−7.00000	−1.06749	−0.533745	−	0.845645i	$-0.679216\pi$
$43$	−7.00000	−1.06749	−0.533745	+	0.845645i	$0.679216\pi$
$44$	−0.414214	−0.0624450
$45$	−1.00000	−0.149071
$46$	−2.65685	−0.391732
$47$	3.65685	0.533407	0.266704	−	0.963779i	$-0.414066\pi$
$47$	3.65685	0.533407	0.266704	+	0.963779i	$0.414066\pi$
$48$	1.00000	0.144338
$49$	0	0
$50$	4.00000	0.565685
$51$	−2.41421	−0.338058
$52$	1.00000	0.138675
$53$	−2.34315	−0.321856	−0.160928	−	0.986966i	$-0.551449\pi$
$53$	−2.34315	−0.321856	−0.160928	+	0.986966i	$0.551449\pi$
$54$	−1.00000	−0.136083
$55$	0.414214	0.0558525
$56$	0	0
$57$	1.82843	0.242181
$58$	8.65685	1.13670
$59$	−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
$61$	8.41421	1.07733	0.538665	−	0.842520i	$-0.318929\pi$
$61$	8.41421	1.07733	0.538665	+	0.842520i	$0.318929\pi$
$62$	4.24264	0.538816
$63$	0	0
$64$	1.00000	0.125000
$65$	−1.00000	−0.124035
$66$	0.414214	0.0509862
$67$	−1.41421	−0.172774	−0.0863868	−	0.996262i	$-0.527532\pi$
$67$	−1.41421	−0.172774	−0.0863868	+	0.996262i	$0.527532\pi$
$68$	−2.41421	−0.292766
$69$	2.65685	0.319848
$70$	0	0
$71$	−9.07107	−1.07654	−0.538269	−	0.842773i	$-0.680921\pi$
$71$	−9.07107	−1.07654	−0.538269	+	0.842773i	$0.680921\pi$
$72$	−1.00000	−0.117851
$73$	6.17157	0.722328	0.361164	−	0.932502i	$-0.382379\pi$
$73$	6.17157	0.722328	0.361164	+	0.932502i	$0.382379\pi$
$74$	−5.24264	−0.609445
$75$	−4.00000	−0.461880
$76$	1.82843	0.209735
$77$	0	0
$78$	−1.00000	−0.113228
$79$	1.75736	0.197718	0.0988592	−	0.995101i	$-0.468481\pi$
$79$	1.75736	0.197718	0.0988592	+	0.995101i	$0.468481\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	1.17157	0.129379
$83$	−0.343146	−0.0376651	−0.0188326	−	0.999823i	$-0.505995\pi$
$83$	−0.343146	−0.0376651	−0.0188326	+	0.999823i	$0.505995\pi$
$84$	0	0
$85$	2.41421	0.261858
$86$	7.00000	0.754829
$87$	−8.65685	−0.928112
$88$	0.414214	0.0441553
$89$	−3.41421	−0.361906	−0.180953	−	0.983492i	$-0.557918\pi$
$89$	−3.41421	−0.361906	−0.180953	+	0.983492i	$0.557918\pi$
$90$	1.00000	0.105409
$91$	0	0
$92$	2.65685	0.276996
$93$	−4.24264	−0.439941
$94$	−3.65685	−0.377176
$95$	−1.82843	−0.187593
$96$	−1.00000	−0.102062
$97$	15.3137	1.55487	0.777436	−	0.628962i	$-0.216520\pi$
$97$	15.3137	1.55487	0.777436	+	0.628962i	$0.216520\pi$
$98$	0	0
$99$	−0.414214	−0.0416300
$100$	−4.00000	−0.400000
$101$	−13.0711	−1.30062	−0.650310	−	0.759669i	$-0.725361\pi$
$101$	−13.0711	−1.30062	−0.650310	+	0.759669i	$0.725361\pi$
$102$	2.41421	0.239043
$103$	−6.07107	−0.598200	−0.299100	−	0.954222i	$-0.596686\pi$
$103$	−6.07107	−0.598200	−0.299100	+	0.954222i	$0.596686\pi$
$104$	−1.00000	−0.0980581
$105$	0	0
$106$	2.34315	0.227586
$107$	7.41421	0.716759	0.358380	−	0.933576i	$-0.383329\pi$
$107$	7.41421	0.716759	0.358380	+	0.933576i	$0.383329\pi$
$108$	1.00000	0.0962250
$109$	−2.41421	−0.231240	−0.115620	−	0.993294i	$-0.536885\pi$
$109$	−2.41421	−0.231240	−0.115620	+	0.993294i	$0.536885\pi$
$110$	−0.414214	−0.0394937
$111$	5.24264	0.497609
$112$	0	0
$113$	−9.75736	−0.917895	−0.458948	−	0.888463i	$-0.651773\pi$
$113$	−9.75736	−0.917895	−0.458948	+	0.888463i	$0.651773\pi$
$114$	−1.82843	−0.171248
$115$	−2.65685	−0.247753
$116$	−8.65685	−0.803769
$117$	1.00000	0.0924500
$118$	9.89949	0.911322
$119$	0	0
$120$	1.00000	0.0912871
$121$	−10.8284	−0.984402
$122$	−8.41421	−0.761787
$123$	−1.17157	−0.105637
$124$	−4.24264	−0.381000
$125$	9.00000	0.804984
$126$	0	0
$127$	−17.0711	−1.51481	−0.757406	−	0.652944i	$-0.773534\pi$
$127$	−17.0711	−1.51481	−0.757406	+	0.652944i	$0.773534\pi$
$128$	−1.00000	−0.0883883
$129$	−7.00000	−0.616316
$130$	1.00000	0.0877058
$131$	−8.75736	−0.765134	−0.382567	−	0.923928i	$-0.624960\pi$
$131$	−8.75736	−0.765134	−0.382567	+	0.923928i	$0.624960\pi$
$132$	−0.414214	−0.0360527
$133$	0	0
$134$	1.41421	0.122169
$135$	−1.00000	−0.0860663
$136$	2.41421	0.207017
$137$	1.24264	0.106166	0.0530830	−	0.998590i	$-0.483095\pi$
$137$	1.24264	0.106166	0.0530830	+	0.998590i	$0.483095\pi$
$138$	−2.65685	−0.226166
$139$	1.17157	0.0993715	0.0496858	−	0.998765i	$-0.484178\pi$
$139$	1.17157	0.0993715	0.0496858	+	0.998765i	$0.484178\pi$
$140$	0	0
$141$	3.65685	0.307963
$142$	9.07107	0.761227
$143$	−0.414214	−0.0346383
$144$	1.00000	0.0833333
$145$	8.65685	0.718913
$146$	−6.17157	−0.510763
$147$	0	0
$148$	5.24264	0.430942
$149$	2.82843	0.231714	0.115857	−	0.993266i	$-0.463039\pi$
$149$	2.82843	0.231714	0.115857	+	0.993266i	$0.463039\pi$
$150$	4.00000	0.326599
$151$	−4.75736	−0.387148	−0.193574	−	0.981086i	$-0.562008\pi$
$151$	−4.75736	−0.387148	−0.193574	+	0.981086i	$0.562008\pi$
$152$	−1.82843	−0.148305
$153$	−2.41421	−0.195178
$154$	0	0
$155$	4.24264	0.340777
$156$	1.00000	0.0800641
$157$	−16.8995	−1.34873	−0.674363	−	0.738400i	$-0.735582\pi$
$157$	−16.8995	−1.34873	−0.674363	+	0.738400i	$0.735582\pi$
$158$	−1.75736	−0.139808
$159$	−2.34315	−0.185824
$160$	1.00000	0.0790569
$161$	0	0
$162$	−1.00000	−0.0785674
$163$	−0.343146	−0.0268772	−0.0134386	−	0.999910i	$-0.504278\pi$
$163$	−0.343146	−0.0268772	−0.0134386	+	0.999910i	$0.504278\pi$
$164$	−1.17157	−0.0914845
$165$	0.414214	0.0322465
$166$	0.343146	0.0266333
$167$	−8.17157	−0.632335	−0.316168	−	0.948703i	$-0.602396\pi$
$167$	−8.17157	−0.632335	−0.316168	+	0.948703i	$0.602396\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	−2.41421	−0.185162
$171$	1.82843	0.139823
$172$	−7.00000	−0.533745
$173$	−7.75736	−0.589781	−0.294891	−	0.955531i	$-0.595283\pi$
$173$	−7.75736	−0.589781	−0.294891	+	0.955531i	$0.595283\pi$
$174$	8.65685	0.656274
$175$	0	0
$176$	−0.414214	−0.0312225
$177$	−9.89949	−0.744092
$178$	3.41421	0.255906
$179$	11.5563	0.863762	0.431881	−	0.901931i	$-0.357850\pi$
$179$	11.5563	0.863762	0.431881	+	0.901931i	$0.357850\pi$
$180$	−1.00000	−0.0745356
$181$	10.1421	0.753859	0.376930	−	0.926242i	$-0.376980\pi$
$181$	10.1421	0.753859	0.376930	+	0.926242i	$0.376980\pi$
$182$	0	0
$183$	8.41421	0.621997
$184$	−2.65685	−0.195866
$185$	−5.24264	−0.385447
$186$	4.24264	0.311086
$187$	1.00000	0.0731272
$188$	3.65685	0.266704
$189$	0	0
$190$	1.82843	0.132648
$191$	−11.4853	−0.831046	−0.415523	−	0.909583i	$-0.636401\pi$
$191$	−11.4853	−0.831046	−0.415523	+	0.909583i	$0.636401\pi$
$192$	1.00000	0.0721688
$193$	−24.3848	−1.75525	−0.877627	−	0.479344i	$-0.840875\pi$
$193$	−24.3848	−1.75525	−0.877627	+	0.479344i	$0.840875\pi$
$194$	−15.3137	−1.09946
$195$	−1.00000	−0.0716115
$196$	0	0
$197$	−9.07107	−0.646287	−0.323143	−	0.946350i	$-0.604740\pi$
$197$	−9.07107	−0.646287	−0.323143	+	0.946350i	$0.604740\pi$
$198$	0.414214	0.0294369
$199$	4.07107	0.288590	0.144295	−	0.989535i	$-0.453909\pi$
$199$	4.07107	0.288590	0.144295	+	0.989535i	$0.453909\pi$
$200$	4.00000	0.282843
$201$	−1.41421	−0.0997509
$202$	13.0711	0.919677
$203$	0	0
$204$	−2.41421	−0.169029
$205$	1.17157	0.0818262
$206$	6.07107	0.422991
$207$	2.65685	0.184664
$208$	1.00000	0.0693375
$209$	−0.757359	−0.0523876
$210$	0	0
$211$	6.31371	0.434654	0.217327	−	0.976099i	$-0.430266\pi$
$211$	6.31371	0.434654	0.217327	+	0.976099i	$0.430266\pi$
$212$	−2.34315	−0.160928
$213$	−9.07107	−0.621539
$214$	−7.41421	−0.506825
$215$	7.00000	0.477396
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	2.41421	0.163511
$219$	6.17157	0.417036
$220$	0.414214	0.0279263
$221$	−2.41421	−0.162398
$222$	−5.24264	−0.351863
$223$	4.34315	0.290839	0.145419	−	0.989370i	$-0.453547\pi$
$223$	4.34315	0.290839	0.145419	+	0.989370i	$0.453547\pi$
$224$	0	0
$225$	−4.00000	−0.266667
$226$	9.75736	0.649050
$227$	−9.07107	−0.602068	−0.301034	−	0.953613i	$-0.597332\pi$
$227$	−9.07107	−0.602068	−0.301034	+	0.953613i	$0.597332\pi$
$228$	1.82843	0.121091
$229$	4.10051	0.270969	0.135485	−	0.990779i	$-0.456741\pi$
$229$	4.10051	0.270969	0.135485	+	0.990779i	$0.456741\pi$
$230$	2.65685	0.175188
$231$	0	0
$232$	8.65685	0.568350
$233$	−5.17157	−0.338801	−0.169401	−	0.985547i	$-0.554183\pi$
$233$	−5.17157	−0.338801	−0.169401	+	0.985547i	$0.554183\pi$
$234$	−1.00000	−0.0653720
$235$	−3.65685	−0.238547
$236$	−9.89949	−0.644402
$237$	1.75736	0.114153
$238$	0	0
$239$	−10.7279	−0.693932	−0.346966	−	0.937878i	$-0.612788\pi$
$239$	−10.7279	−0.693932	−0.346966	+	0.937878i	$0.612788\pi$
$240$	−1.00000	−0.0645497
$241$	23.6569	1.52387	0.761936	−	0.647652i	$-0.224249\pi$
$241$	23.6569	1.52387	0.761936	+	0.647652i	$0.224249\pi$
$242$	10.8284	0.696078
$243$	1.00000	0.0641500
$244$	8.41421	0.538665
$245$	0	0
$246$	1.17157	0.0746968
$247$	1.82843	0.116340
$248$	4.24264	0.269408
$249$	−0.343146	−0.0217460
$250$	−9.00000	−0.569210
$251$	−6.41421	−0.404862	−0.202431	−	0.979297i	$-0.564884\pi$
$251$	−6.41421	−0.404862	−0.202431	+	0.979297i	$0.564884\pi$
$252$	0	0
$253$	−1.10051	−0.0691882
$254$	17.0711	1.07113
$255$	2.41421	0.151184
$256$	1.00000	0.0625000
$257$	−10.8284	−0.675459	−0.337729	−	0.941243i	$-0.609659\pi$
$257$	−10.8284	−0.675459	−0.337729	+	0.941243i	$0.609659\pi$
$258$	7.00000	0.435801
$259$	0	0
$260$	−1.00000	−0.0620174
$261$	−8.65685	−0.535846
$262$	8.75736	0.541031
$263$	−1.65685	−0.102166	−0.0510830	−	0.998694i	$-0.516267\pi$
$263$	−1.65685	−0.102166	−0.0510830	+	0.998694i	$0.516267\pi$
$264$	0.414214	0.0254931
$265$	2.34315	0.143938
$266$	0	0
$267$	−3.41421	−0.208946
$268$	−1.41421	−0.0863868
$269$	−8.72792	−0.532151	−0.266075	−	0.963952i	$-0.585727\pi$
$269$	−8.72792	−0.532151	−0.266075	+	0.963952i	$0.585727\pi$
$270$	1.00000	0.0608581
$271$	5.75736	0.349735	0.174867	−	0.984592i	$-0.444050\pi$
$271$	5.75736	0.349735	0.174867	+	0.984592i	$0.444050\pi$
$272$	−2.41421	−0.146383
$273$	0	0
$274$	−1.24264	−0.0750707
$275$	1.65685	0.0999121
$276$	2.65685	0.159924
$277$	−19.4142	−1.16649	−0.583244	−	0.812297i	$-0.698217\pi$
$277$	−19.4142	−1.16649	−0.583244	+	0.812297i	$0.698217\pi$
$278$	−1.17157	−0.0702663
$279$	−4.24264	−0.254000
$280$	0	0
$281$	−21.3137	−1.27147	−0.635735	−	0.771908i	$-0.719303\pi$
$281$	−21.3137	−1.27147	−0.635735	+	0.771908i	$0.719303\pi$
$282$	−3.65685	−0.217763
$283$	5.17157	0.307418	0.153709	−	0.988116i	$-0.450878\pi$
$283$	5.17157	0.307418	0.153709	+	0.988116i	$0.450878\pi$
$284$	−9.07107	−0.538269
$285$	−1.82843	−0.108307
$286$	0.414214	0.0244930
$287$	0	0
$288$	−1.00000	−0.0589256
$289$	−11.1716	−0.657151
$290$	−8.65685	−0.508348
$291$	15.3137	0.897705
$292$	6.17157	0.361164
$293$	22.1421	1.29356	0.646779	−	0.762678i	$-0.276116\pi$
$293$	22.1421	1.29356	0.646779	+	0.762678i	$0.276116\pi$
$294$	0	0
$295$	9.89949	0.576371
$296$	−5.24264	−0.304722
$297$	−0.414214	−0.0240351
$298$	−2.82843	−0.163846
$299$	2.65685	0.153650
$300$	−4.00000	−0.230940
$301$	0	0
$302$	4.75736	0.273755
$303$	−13.0711	−0.750913
$304$	1.82843	0.104867
$305$	−8.41421	−0.481796
$306$	2.41421	0.138011
$307$	0.343146	0.0195844	0.00979218	−	0.999952i	$-0.496883\pi$
$307$	0.343146	0.0195844	0.00979218	+	0.999952i	$0.496883\pi$
$308$	0	0
$309$	−6.07107	−0.345371
$310$	−4.24264	−0.240966
$311$	17.7990	1.00929	0.504644	−	0.863328i	$-0.331624\pi$
$311$	17.7990	1.00929	0.504644	+	0.863328i	$0.331624\pi$
$312$	−1.00000	−0.0566139
$313$	6.92893	0.391646	0.195823	−	0.980639i	$-0.437262\pi$
$313$	6.92893	0.391646	0.195823	+	0.980639i	$0.437262\pi$
$314$	16.8995	0.953694
$315$	0	0
$316$	1.75736	0.0988592
$317$	−30.0416	−1.68731	−0.843653	−	0.536889i	$-0.819599\pi$
$317$	−30.0416	−1.68731	−0.843653	+	0.536889i	$0.819599\pi$
$318$	2.34315	0.131397
$319$	3.58579	0.200765
$320$	−1.00000	−0.0559017
$321$	7.41421	0.413821
$322$	0	0
$323$	−4.41421	−0.245613
$324$	1.00000	0.0555556
$325$	−4.00000	−0.221880
$326$	0.343146	0.0190051
$327$	−2.41421	−0.133506
$328$	1.17157	0.0646893
$329$	0	0
$330$	−0.414214	−0.0228017
$331$	−10.1005	−0.555174	−0.277587	−	0.960701i	$-0.589535\pi$
$331$	−10.1005	−0.555174	−0.277587	+	0.960701i	$0.589535\pi$
$332$	−0.343146	−0.0188326
$333$	5.24264	0.287295
$334$	8.17157	0.447129
$335$	1.41421	0.0772667
$336$	0	0
$337$	−0.514719	−0.0280385	−0.0140193	−	0.999902i	$-0.504463\pi$
$337$	−0.514719	−0.0280385	−0.0140193	+	0.999902i	$0.504463\pi$
$338$	−1.00000	−0.0543928
$339$	−9.75736	−0.529947
$340$	2.41421	0.130929
$341$	1.75736	0.0951663
$342$	−1.82843	−0.0988700
$343$	0	0
$344$	7.00000	0.377415
$345$	−2.65685	−0.143040
$346$	7.75736	0.417038
$347$	−25.4142	−1.36431	−0.682153	−	0.731209i	$-0.738956\pi$
$347$	−25.4142	−1.36431	−0.682153	+	0.731209i	$0.738956\pi$
$348$	−8.65685	−0.464056
$349$	10.7279	0.574253	0.287126	−	0.957893i	$-0.407300\pi$
$349$	10.7279	0.574253	0.287126	+	0.957893i	$0.407300\pi$
$350$	0	0
$351$	1.00000	0.0533761
$352$	0.414214	0.0220777
$353$	31.4558	1.67423	0.837113	−	0.547030i	$-0.184242\pi$
$353$	31.4558	1.67423	0.837113	+	0.547030i	$0.184242\pi$
$354$	9.89949	0.526152
$355$	9.07107	0.481442
$356$	−3.41421	−0.180953
$357$	0	0
$358$	−11.5563	−0.610772
$359$	21.4558	1.13240	0.566198	−	0.824269i	$-0.308414\pi$
$359$	21.4558	1.13240	0.566198	+	0.824269i	$0.308414\pi$
$360$	1.00000	0.0527046
$361$	−15.6569	−0.824045
$362$	−10.1421	−0.533059
$363$	−10.8284	−0.568345
$364$	0	0
$365$	−6.17157	−0.323035
$366$	−8.41421	−0.439818
$367$	−4.00000	−0.208798	−0.104399	−	0.994535i	$-0.533292\pi$
$367$	−4.00000	−0.208798	−0.104399	+	0.994535i	$0.533292\pi$
$368$	2.65685	0.138498
$369$	−1.17157	−0.0609896
$370$	5.24264	0.272552
$371$	0	0
$372$	−4.24264	−0.219971
$373$	−4.24264	−0.219676	−0.109838	−	0.993950i	$-0.535033\pi$
$373$	−4.24264	−0.219676	−0.109838	+	0.993950i	$0.535033\pi$
$374$	−1.00000	−0.0517088
$375$	9.00000	0.464758
$376$	−3.65685	−0.188588
$377$	−8.65685	−0.445851
$378$	0	0
$379$	12.3848	0.636163	0.318082	−	0.948063i	$-0.396961\pi$
$379$	12.3848	0.636163	0.318082	+	0.948063i	$0.396961\pi$
$380$	−1.82843	−0.0937963
$381$	−17.0711	−0.874577
$382$	11.4853	0.587638
$383$	22.6569	1.15771	0.578856	−	0.815430i	$-0.303499\pi$
$383$	22.6569	1.15771	0.578856	+	0.815430i	$0.303499\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	24.3848	1.24115
$387$	−7.00000	−0.355830
$388$	15.3137	0.777436
$389$	−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
$391$	−6.41421	−0.324381
$392$	0	0
$393$	−8.75736	−0.441750
$394$	9.07107	0.456994
$395$	−1.75736	−0.0884223
$396$	−0.414214	−0.0208150
$397$	29.3137	1.47121	0.735606	−	0.677409i	$-0.236897\pi$
$397$	29.3137	1.47121	0.735606	+	0.677409i	$0.236897\pi$
$398$	−4.07107	−0.204064
$399$	0	0
$400$	−4.00000	−0.200000
$401$	29.4558	1.47095	0.735477	−	0.677549i	$-0.236958\pi$
$401$	29.4558	1.47095	0.735477	+	0.677549i	$0.236958\pi$
$402$	1.41421	0.0705346
$403$	−4.24264	−0.211341
$404$	−13.0711	−0.650310
$405$	−1.00000	−0.0496904
$406$	0	0
$407$	−2.17157	−0.107641
$408$	2.41421	0.119521
$409$	0.0294373	0.00145558	0.000727789	−	1.00000i	$-0.499768\pi$
$409$	0.0294373	0.00145558	0.000727789		1.00000i	$0.499768\pi$
$410$	−1.17157	−0.0578599
$411$	1.24264	0.0612949
$412$	−6.07107	−0.299100
$413$	0	0
$414$	−2.65685	−0.130577
$415$	0.343146	0.0168444
$416$	−1.00000	−0.0490290
$417$	1.17157	0.0573722
$418$	0.757359	0.0370437
$419$	−20.5563	−1.00424	−0.502122	−	0.864797i	$-0.667447\pi$
$419$	−20.5563	−1.00424	−0.502122	+	0.864797i	$0.667447\pi$
$420$	0	0
$421$	29.1127	1.41887	0.709433	−	0.704773i	$-0.248951\pi$
$421$	29.1127	1.41887	0.709433	+	0.704773i	$0.248951\pi$
$422$	−6.31371	−0.307347
$423$	3.65685	0.177802
$424$	2.34315	0.113793
$425$	9.65685	0.468426
$426$	9.07107	0.439495
$427$	0	0
$428$	7.41421	0.358380
$429$	−0.414214	−0.0199984
$430$	−7.00000	−0.337570
$431$	20.8284	1.00327	0.501635	−	0.865079i	$-0.332732\pi$
$431$	20.8284	1.00327	0.501635	+	0.865079i	$0.332732\pi$
$432$	1.00000	0.0481125
$433$	−18.6274	−0.895177	−0.447588	−	0.894240i	$-0.647717\pi$
$433$	−18.6274	−0.895177	−0.447588	+	0.894240i	$0.647717\pi$
$434$	0	0
$435$	8.65685	0.415064
$436$	−2.41421	−0.115620
$437$	4.85786	0.232383
$438$	−6.17157	−0.294889
$439$	4.21320	0.201085	0.100543	−	0.994933i	$-0.467942\pi$
$439$	4.21320	0.201085	0.100543	+	0.994933i	$0.467942\pi$
$440$	−0.414214	−0.0197469
$441$	0	0
$442$	2.41421	0.114832
$443$	−4.82843	−0.229405	−0.114703	−	0.993400i	$-0.536592\pi$
$443$	−4.82843	−0.229405	−0.114703	+	0.993400i	$0.536592\pi$
$444$	5.24264	0.248805
$445$	3.41421	0.161849
$446$	−4.34315	−0.205654
$447$	2.82843	0.133780
$448$	0	0
$449$	−12.5563	−0.592571	−0.296285	−	0.955099i	$-0.595748\pi$
$449$	−12.5563	−0.592571	−0.296285	+	0.955099i	$0.595748\pi$
$450$	4.00000	0.188562
$451$	0.485281	0.0228510
$452$	−9.75736	−0.458948
$453$	−4.75736	−0.223520
$454$	9.07107	0.425726
$455$	0	0
$456$	−1.82843	−0.0856239
$457$	−13.7574	−0.643542	−0.321771	−	0.946818i	$-0.604278\pi$
$457$	−13.7574	−0.643542	−0.321771	+	0.946818i	$0.604278\pi$
$458$	−4.10051	−0.191604
$459$	−2.41421	−0.112686
$460$	−2.65685	−0.123876
$461$	6.51472	0.303421	0.151710	−	0.988425i	$-0.451522\pi$
$461$	6.51472	0.303421	0.151710	+	0.988425i	$0.451522\pi$
$462$	0	0
$463$	−21.8701	−1.01639	−0.508194	−	0.861243i	$-0.669687\pi$
$463$	−21.8701	−1.01639	−0.508194	+	0.861243i	$0.669687\pi$
$464$	−8.65685	−0.401884
$465$	4.24264	0.196748
$466$	5.17157	0.239568
$467$	−28.8995	−1.33731	−0.668655	−	0.743573i	$-0.733129\pi$
$467$	−28.8995	−1.33731	−0.668655	+	0.743573i	$0.733129\pi$
$468$	1.00000	0.0462250
$469$	0	0
$470$	3.65685	0.168678
$471$	−16.8995	−0.778688
$472$	9.89949	0.455661
$473$	2.89949	0.133319
$474$	−1.75736	−0.0807182
$475$	−7.31371	−0.335576
$476$	0	0
$477$	−2.34315	−0.107285
$478$	10.7279	0.490684
$479$	−7.48528	−0.342011	−0.171006	−	0.985270i	$-0.554702\pi$
$479$	−7.48528	−0.342011	−0.171006	+	0.985270i	$0.554702\pi$
$480$	1.00000	0.0456435
$481$	5.24264	0.239044
$482$	−23.6569	−1.07754
$483$	0	0
$484$	−10.8284	−0.492201
$485$	−15.3137	−0.695360
$486$	−1.00000	−0.0453609
$487$	−41.5980	−1.88498	−0.942492	−	0.334228i	$-0.891524\pi$
$487$	−41.5980	−1.88498	−0.942492	+	0.334228i	$0.891524\pi$
$488$	−8.41421	−0.380894
$489$	−0.343146	−0.0155176
$490$	0	0
$491$	−38.7696	−1.74965	−0.874823	−	0.484443i	$-0.839022\pi$
$491$	−38.7696	−1.74965	−0.874823	+	0.484443i	$0.839022\pi$
$492$	−1.17157	−0.0528186
$493$	20.8995	0.941266
$494$	−1.82843	−0.0822648
$495$	0.414214	0.0186175
$496$	−4.24264	−0.190500
$497$	0	0
$498$	0.343146	0.0153767
$499$	−2.72792	−0.122119	−0.0610593	−	0.998134i	$-0.519448\pi$
$499$	−2.72792	−0.122119	−0.0610593	+	0.998134i	$0.519448\pi$
$500$	9.00000	0.402492
$501$	−8.17157	−0.365079
$502$	6.41421	0.286280
$503$	−3.07107	−0.136932	−0.0684661	−	0.997653i	$-0.521810\pi$
$503$	−3.07107	−0.136932	−0.0684661	+	0.997653i	$0.521810\pi$
$504$	0	0
$505$	13.0711	0.581655
$506$	1.10051	0.0489234
$507$	1.00000	0.0444116
$508$	−17.0711	−0.757406
$509$	−23.1421	−1.02576	−0.512879	−	0.858461i	$-0.671421\pi$
$509$	−23.1421	−1.02576	−0.512879	+	0.858461i	$0.671421\pi$
$510$	−2.41421	−0.106903
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	1.82843	0.0807270
$514$	10.8284	0.477621
$515$	6.07107	0.267523
$516$	−7.00000	−0.308158
$517$	−1.51472	−0.0666172
$518$	0	0
$519$	−7.75736	−0.340510
$520$	1.00000	0.0438529
$521$	−20.5563	−0.900590	−0.450295	−	0.892880i	$-0.648681\pi$
$521$	−20.5563	−0.900590	−0.450295	+	0.892880i	$0.648681\pi$
$522$	8.65685	0.378900
$523$	30.7279	1.34364	0.671819	−	0.740715i	$-0.265513\pi$
$523$	30.7279	1.34364	0.671819	+	0.740715i	$0.265513\pi$
$524$	−8.75736	−0.382567
$525$	0	0
$526$	1.65685	0.0722423
$527$	10.2426	0.446176
$528$	−0.414214	−0.0180263
$529$	−15.9411	−0.693092
$530$	−2.34315	−0.101780
$531$	−9.89949	−0.429601
$532$	0	0
$533$	−1.17157	−0.0507465
$534$	3.41421	0.147747
$535$	−7.41421	−0.320544
$536$	1.41421	0.0610847
$537$	11.5563	0.498693
$538$	8.72792	0.376287
$539$	0	0
$540$	−1.00000	−0.0430331
$541$	11.3848	0.489470	0.244735	−	0.969590i	$-0.421299\pi$
$541$	11.3848	0.489470	0.244735	+	0.969590i	$0.421299\pi$
$542$	−5.75736	−0.247300
$543$	10.1421	0.435241
$544$	2.41421	0.103509
$545$	2.41421	0.103414
$546$	0	0
$547$	13.7990	0.590002	0.295001	−	0.955497i	$-0.404680\pi$
$547$	13.7990	0.590002	0.295001	+	0.955497i	$0.404680\pi$
$548$	1.24264	0.0530830
$549$	8.41421	0.359110
$550$	−1.65685	−0.0706485
$551$	−15.8284	−0.674314
$552$	−2.65685	−0.113083
$553$	0	0
$554$	19.4142	0.824831
$555$	−5.24264	−0.222538
$556$	1.17157	0.0496858
$557$	8.48528	0.359533	0.179766	−	0.983709i	$-0.442466\pi$
$557$	8.48528	0.359533	0.179766	+	0.983709i	$0.442466\pi$
$558$	4.24264	0.179605
$559$	−7.00000	−0.296068
$560$	0	0
$561$	1.00000	0.0422200
$562$	21.3137	0.899065
$563$	−5.58579	−0.235413	−0.117706	−	0.993048i	$-0.537554\pi$
$563$	−5.58579	−0.235413	−0.117706	+	0.993048i	$0.537554\pi$
$564$	3.65685	0.153981
$565$	9.75736	0.410495
$566$	−5.17157	−0.217377
$567$	0	0
$568$	9.07107	0.380614
$569$	−1.51472	−0.0635003	−0.0317502	−	0.999496i	$-0.510108\pi$
$569$	−1.51472	−0.0635003	−0.0317502	+	0.999496i	$0.510108\pi$
$570$	1.82843	0.0765844
$571$	−26.2843	−1.09996	−0.549981	−	0.835177i	$-0.685365\pi$
$571$	−26.2843	−1.09996	−0.549981	+	0.835177i	$0.685365\pi$
$572$	−0.414214	−0.0173191
$573$	−11.4853	−0.479805
$574$	0	0
$575$	−10.6274	−0.443194
$576$	1.00000	0.0416667
$577$	−26.8284	−1.11688	−0.558441	−	0.829544i	$-0.688600\pi$
$577$	−26.8284	−1.11688	−0.558441	+	0.829544i	$0.688600\pi$
$578$	11.1716	0.464676
$579$	−24.3848	−1.01340
$580$	8.65685	0.359456
$581$	0	0
$582$	−15.3137	−0.634774
$583$	0.970563	0.0401966
$584$	−6.17157	−0.255382
$585$	−1.00000	−0.0413449
$586$	−22.1421	−0.914683
$587$	−25.1127	−1.03651	−0.518256	−	0.855226i	$-0.673419\pi$
$587$	−25.1127	−1.03651	−0.518256	+	0.855226i	$0.673419\pi$
$588$	0	0
$589$	−7.75736	−0.319636
$590$	−9.89949	−0.407556
$591$	−9.07107	−0.373134
$592$	5.24264	0.215471
$593$	−4.58579	−0.188316	−0.0941578	−	0.995557i	$-0.530016\pi$
$593$	−4.58579	−0.188316	−0.0941578	+	0.995557i	$0.530016\pi$
$594$	0.414214	0.0169954
$595$	0	0
$596$	2.82843	0.115857
$597$	4.07107	0.166618
$598$	−2.65685	−0.108647
$599$	37.4853	1.53161	0.765804	−	0.643075i	$-0.222341\pi$
$599$	37.4853	1.53161	0.765804	+	0.643075i	$0.222341\pi$
$600$	4.00000	0.163299
$601$	−21.4558	−0.875202	−0.437601	−	0.899169i	$-0.644172\pi$
$601$	−21.4558	−0.875202	−0.437601	+	0.899169i	$0.644172\pi$
$602$	0	0
$603$	−1.41421	−0.0575912
$604$	−4.75736	−0.193574
$605$	10.8284	0.440238
$606$	13.0711	0.530976
$607$	41.1838	1.67160	0.835799	−	0.549036i	$-0.185005\pi$
$607$	41.1838	1.67160	0.835799	+	0.549036i	$0.185005\pi$
$608$	−1.82843	−0.0741525
$609$	0	0
$610$	8.41421	0.340682
$611$	3.65685	0.147940
$612$	−2.41421	−0.0975888
$613$	−8.07107	−0.325987	−0.162994	−	0.986627i	$-0.552115\pi$
$613$	−8.07107	−0.325987	−0.162994	+	0.986627i	$0.552115\pi$
$614$	−0.343146	−0.0138482
$615$	1.17157	0.0472424
$616$	0	0
$617$	−28.4142	−1.14391	−0.571957	−	0.820284i	$-0.693815\pi$
$617$	−28.4142	−1.14391	−0.571957	+	0.820284i	$0.693815\pi$
$618$	6.07107	0.244214
$619$	35.2843	1.41819	0.709097	−	0.705111i	$-0.249103\pi$
$619$	35.2843	1.41819	0.709097	+	0.705111i	$0.249103\pi$
$620$	4.24264	0.170389
$621$	2.65685	0.106616
$622$	−17.7990	−0.713674
$623$	0	0
$624$	1.00000	0.0400320
$625$	11.0000	0.440000
$626$	−6.92893	−0.276936
$627$	−0.757359	−0.0302460
$628$	−16.8995	−0.674363
$629$	−12.6569	−0.504662
$630$	0	0
$631$	37.3848	1.48826	0.744132	−	0.668032i	$-0.232863\pi$
$631$	37.3848	1.48826	0.744132	+	0.668032i	$0.232863\pi$
$632$	−1.75736	−0.0699040
$633$	6.31371	0.250947
$634$	30.0416	1.19311
$635$	17.0711	0.677445
$636$	−2.34315	−0.0929118
$637$	0	0
$638$	−3.58579	−0.141963
$639$	−9.07107	−0.358846
$640$	1.00000	0.0395285
$641$	22.5269	0.889760	0.444880	−	0.895590i	$-0.353246\pi$
$641$	22.5269	0.889760	0.444880	+	0.895590i	$0.353246\pi$
$642$	−7.41421	−0.292616
$643$	−38.3137	−1.51095	−0.755473	−	0.655180i	$-0.772593\pi$
$643$	−38.3137	−1.51095	−0.755473	+	0.655180i	$0.772593\pi$
$644$	0	0
$645$	7.00000	0.275625
$646$	4.41421	0.173675
$647$	44.9706	1.76798	0.883988	−	0.467510i	$-0.154849\pi$
$647$	44.9706	1.76798	0.883988	+	0.467510i	$0.154849\pi$
$648$	−1.00000	−0.0392837
$649$	4.10051	0.160959
$650$	4.00000	0.156893
$651$	0	0
$652$	−0.343146	−0.0134386
$653$	−4.51472	−0.176675	−0.0883373	−	0.996091i	$-0.528155\pi$
$653$	−4.51472	−0.176675	−0.0883373	+	0.996091i	$0.528155\pi$
$654$	2.41421	0.0944032
$655$	8.75736	0.342178
$656$	−1.17157	−0.0457422
$657$	6.17157	0.240776
$658$	0	0
$659$	39.4558	1.53698	0.768491	−	0.639861i	$-0.221008\pi$
$659$	39.4558	1.53698	0.768491	+	0.639861i	$0.221008\pi$
$660$	0.414214	0.0161232
$661$	−1.02944	−0.0400405	−0.0200202	−	0.999800i	$-0.506373\pi$
$661$	−1.02944	−0.0400405	−0.0200202	+	0.999800i	$0.506373\pi$
$662$	10.1005	0.392567
$663$	−2.41421	−0.0937603
$664$	0.343146	0.0133166
$665$	0	0
$666$	−5.24264	−0.203148
$667$	−23.0000	−0.890564
$668$	−8.17157	−0.316168
$669$	4.34315	0.167916
$670$	−1.41421	−0.0546358
$671$	−3.48528	−0.134548
$672$	0	0
$673$	−24.1127	−0.929476	−0.464738	−	0.885448i	$-0.653852\pi$
$673$	−24.1127	−0.929476	−0.464738	+	0.885448i	$0.653852\pi$
$674$	0.514719	0.0198262
$675$	−4.00000	−0.153960
$676$	1.00000	0.0384615
$677$	34.7696	1.33630	0.668151	−	0.744025i	$-0.267086\pi$
$677$	34.7696	1.33630	0.668151	+	0.744025i	$0.267086\pi$
$678$	9.75736	0.374729
$679$	0	0
$680$	−2.41421	−0.0925809
$681$	−9.07107	−0.347604
$682$	−1.75736	−0.0672928
$683$	26.4142	1.01071	0.505356	−	0.862911i	$-0.331361\pi$
$683$	26.4142	1.01071	0.505356	+	0.862911i	$0.331361\pi$
$684$	1.82843	0.0699117
$685$	−1.24264	−0.0474789
$686$	0	0
$687$	4.10051	0.156444
$688$	−7.00000	−0.266872
$689$	−2.34315	−0.0892667
$690$	2.65685	0.101145
$691$	28.8284	1.09669	0.548343	−	0.836254i	$-0.315259\pi$
$691$	28.8284	1.09669	0.548343	+	0.836254i	$0.315259\pi$
$692$	−7.75736	−0.294891
$693$	0	0
$694$	25.4142	0.964710
$695$	−1.17157	−0.0444403
$696$	8.65685	0.328137
$697$	2.82843	0.107134
$698$	−10.7279	−0.406058
$699$	−5.17157	−0.195607
$700$	0	0
$701$	29.1716	1.10180	0.550898	−	0.834573i	$-0.314285\pi$
$701$	29.1716	1.10180	0.550898	+	0.834573i	$0.314285\pi$
$702$	−1.00000	−0.0377426
$703$	9.58579	0.361535
$704$	−0.414214	−0.0156113
$705$	−3.65685	−0.137725
$706$	−31.4558	−1.18386
$707$	0	0
$708$	−9.89949	−0.372046
$709$	35.1716	1.32090	0.660448	−	0.750872i	$-0.270366\pi$
$709$	35.1716	1.32090	0.660448	+	0.750872i	$0.270366\pi$
$710$	−9.07107	−0.340431
$711$	1.75736	0.0659061
$712$	3.41421	0.127953
$713$	−11.2721	−0.422143
$714$	0	0
$715$	0.414214	0.0154907
$716$	11.5563	0.431881
$717$	−10.7279	−0.400642
$718$	−21.4558	−0.800725
$719$	−13.4142	−0.500266	−0.250133	−	0.968212i	$-0.580474\pi$
$719$	−13.4142	−0.500266	−0.250133	+	0.968212i	$0.580474\pi$
$720$	−1.00000	−0.0372678
$721$	0	0
$722$	15.6569	0.582688
$723$	23.6569	0.879808
$724$	10.1421	0.376930
$725$	34.6274	1.28603
$726$	10.8284	0.401881
$727$	−50.2132	−1.86230	−0.931152	−	0.364630i	$-0.881195\pi$
$727$	−50.2132	−1.86230	−0.931152	+	0.364630i	$0.881195\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	6.17157	0.228420
$731$	16.8995	0.625050
$732$	8.41421	0.310998
$733$	−40.7279	−1.50432	−0.752160	−	0.658980i	$-0.770988\pi$
$733$	−40.7279	−1.50432	−0.752160	+	0.658980i	$0.770988\pi$
$734$	4.00000	0.147643
$735$	0	0
$736$	−2.65685	−0.0979329
$737$	0.585786	0.0215777
$738$	1.17157	0.0431262
$739$	−22.2843	−0.819740	−0.409870	−	0.912144i	$-0.634426\pi$
$739$	−22.2843	−0.819740	−0.409870	+	0.912144i	$0.634426\pi$
$740$	−5.24264	−0.192723
$741$	1.82843	0.0671689
$742$	0	0
$743$	7.37258	0.270474	0.135237	−	0.990813i	$-0.456820\pi$
$743$	7.37258	0.270474	0.135237	+	0.990813i	$0.456820\pi$
$744$	4.24264	0.155543
$745$	−2.82843	−0.103626
$746$	4.24264	0.155334
$747$	−0.343146	−0.0125550
$748$	1.00000	0.0365636
$749$	0	0
$750$	−9.00000	−0.328634
$751$	47.5563	1.73536	0.867678	−	0.497127i	$-0.165612\pi$
$751$	47.5563	1.73536	0.867678	+	0.497127i	$0.165612\pi$
$752$	3.65685	0.133352
$753$	−6.41421	−0.233747
$754$	8.65685	0.315264
$755$	4.75736	0.173138
$756$	0	0
$757$	9.07107	0.329694	0.164847	−	0.986319i	$-0.447287\pi$
$757$	9.07107	0.329694	0.164847	+	0.986319i	$0.447287\pi$
$758$	−12.3848	−0.449835
$759$	−1.10051	−0.0399458
$760$	1.82843	0.0663240
$761$	−1.17157	−0.0424695	−0.0212347	−	0.999775i	$-0.506760\pi$
$761$	−1.17157	−0.0424695	−0.0212347	+	0.999775i	$0.506760\pi$
$762$	17.0711	0.618420
$763$	0	0
$764$	−11.4853	−0.415523
$765$	2.41421	0.0872861
$766$	−22.6569	−0.818625
$767$	−9.89949	−0.357450
$768$	1.00000	0.0360844
$769$	29.1421	1.05089	0.525446	−	0.850827i	$-0.323898\pi$
$769$	29.1421	1.05089	0.525446	+	0.850827i	$0.323898\pi$
$770$	0	0
$771$	−10.8284	−0.389976
$772$	−24.3848	−0.877627
$773$	41.9706	1.50958	0.754788	−	0.655969i	$-0.227740\pi$
$773$	41.9706	1.50958	0.754788	+	0.655969i	$0.227740\pi$
$774$	7.00000	0.251610
$775$	16.9706	0.609601
$776$	−15.3137	−0.549730
$777$	0	0
$778$	8.00000	0.286814
$779$	−2.14214	−0.0767500
$780$	−1.00000	−0.0358057
$781$	3.75736	0.134449
$782$	6.41421	0.229372
$783$	−8.65685	−0.309371
$784$	0	0
$785$	16.8995	0.603169
$786$	8.75736	0.312365
$787$	15.8284	0.564222	0.282111	−	0.959382i	$-0.408965\pi$
$787$	15.8284	0.564222	0.282111	+	0.959382i	$0.408965\pi$
$788$	−9.07107	−0.323143
$789$	−1.65685	−0.0589856
$790$	1.75736	0.0625240
$791$	0	0
$792$	0.414214	0.0147184
$793$	8.41421	0.298797
$794$	−29.3137	−1.04030
$795$	2.34315	0.0831028
$796$	4.07107	0.144295
$797$	18.7279	0.663377	0.331689	−	0.943389i	$-0.392382\pi$
$797$	18.7279	0.663377	0.331689	+	0.943389i	$0.392382\pi$
$798$	0	0
$799$	−8.82843	−0.312327
$800$	4.00000	0.141421
$801$	−3.41421	−0.120635
$802$	−29.4558	−1.04012
$803$	−2.55635	−0.0902116
$804$	−1.41421	−0.0498755
$805$	0	0
$806$	4.24264	0.149441
$807$	−8.72792	−0.307237
$808$	13.0711	0.459839
$809$	17.5563	0.617248	0.308624	−	0.951184i	$-0.400131\pi$
$809$	17.5563	0.617248	0.308624	+	0.951184i	$0.400131\pi$
$810$	1.00000	0.0351364
$811$	−32.6569	−1.14674	−0.573369	−	0.819298i	$-0.694364\pi$
$811$	−32.6569	−1.14674	−0.573369	+	0.819298i	$0.694364\pi$
$812$	0	0
$813$	5.75736	0.201919
$814$	2.17157	0.0761136
$815$	0.343146	0.0120199
$816$	−2.41421	−0.0845144
$817$	−12.7990	−0.447780
$818$	−0.0294373	−0.00102925
$819$	0	0
$820$	1.17157	0.0409131
$821$	11.5147	0.401866	0.200933	−	0.979605i	$-0.435603\pi$
$821$	11.5147	0.401866	0.200933	+	0.979605i	$0.435603\pi$
$822$	−1.24264	−0.0433421
$823$	44.5269	1.55211	0.776055	−	0.630665i	$-0.217218\pi$
$823$	44.5269	1.55211	0.776055	+	0.630665i	$0.217218\pi$
$824$	6.07107	0.211496
$825$	1.65685	0.0576843
$826$	0	0
$827$	−37.5269	−1.30494	−0.652469	−	0.757815i	$-0.726267\pi$
$827$	−37.5269	−1.30494	−0.652469	+	0.757815i	$0.726267\pi$
$828$	2.65685	0.0923321
$829$	−13.5269	−0.469809	−0.234905	−	0.972018i	$-0.575478\pi$
$829$	−13.5269	−0.469809	−0.234905	+	0.972018i	$0.575478\pi$
$830$	−0.343146	−0.0119108
$831$	−19.4142	−0.673472
$832$	1.00000	0.0346688
$833$	0	0
$834$	−1.17157	−0.0405683
$835$	8.17157	0.282789
$836$	−0.757359	−0.0261938
$837$	−4.24264	−0.146647
$838$	20.5563	0.710107
$839$	11.3726	0.392625	0.196313	−	0.980541i	$-0.437103\pi$
$839$	11.3726	0.392625	0.196313	+	0.980541i	$0.437103\pi$
$840$	0	0
$841$	45.9411	1.58418
$842$	−29.1127	−1.00329
$843$	−21.3137	−0.734083
$844$	6.31371	0.217327
$845$	−1.00000	−0.0344010
$846$	−3.65685	−0.125725
$847$	0	0
$848$	−2.34315	−0.0804640
$849$	5.17157	0.177488
$850$	−9.65685	−0.331227
$851$	13.9289	0.477478
$852$	−9.07107	−0.310770
$853$	22.3431	0.765015	0.382507	−	0.923952i	$-0.375061\pi$
$853$	22.3431	0.765015	0.382507	+	0.923952i	$0.375061\pi$
$854$	0	0
$855$	−1.82843	−0.0625309
$856$	−7.41421	−0.253413
$857$	−39.1716	−1.33808	−0.669038	−	0.743228i	$-0.733294\pi$
$857$	−39.1716	−1.33808	−0.669038	+	0.743228i	$0.733294\pi$
$858$	0.414214	0.0141410
$859$	−15.0294	−0.512798	−0.256399	−	0.966571i	$-0.582536\pi$
$859$	−15.0294	−0.512798	−0.256399	+	0.966571i	$0.582536\pi$
$860$	7.00000	0.238698
$861$	0	0
$862$	−20.8284	−0.709419
$863$	22.9706	0.781927	0.390964	−	0.920406i	$-0.372142\pi$
$863$	22.9706	0.781927	0.390964	+	0.920406i	$0.372142\pi$
$864$	−1.00000	−0.0340207
$865$	7.75736	0.263758
$866$	18.6274	0.632985
$867$	−11.1716	−0.379407
$868$	0	0
$869$	−0.727922	−0.0246931
$870$	−8.65685	−0.293495
$871$	−1.41421	−0.0479188
$872$	2.41421	0.0817556
$873$	15.3137	0.518291
$874$	−4.85786	−0.164320
$875$	0	0
$876$	6.17157	0.208518
$877$	8.48528	0.286528	0.143264	−	0.989685i	$-0.454240\pi$
$877$	8.48528	0.286528	0.143264	+	0.989685i	$0.454240\pi$
$878$	−4.21320	−0.142189
$879$	22.1421	0.746836
$880$	0.414214	0.0139631
$881$	4.61522	0.155491	0.0777454	−	0.996973i	$-0.475228\pi$
$881$	4.61522	0.155491	0.0777454	+	0.996973i	$0.475228\pi$
$882$	0	0
$883$	55.9706	1.88356	0.941780	−	0.336231i	$-0.109152\pi$
$883$	55.9706	1.88356	0.941780	+	0.336231i	$0.109152\pi$
$884$	−2.41421	−0.0811988
$885$	9.89949	0.332768
$886$	4.82843	0.162214
$887$	3.11270	0.104514	0.0522571	−	0.998634i	$-0.483358\pi$
$887$	3.11270	0.104514	0.0522571	+	0.998634i	$0.483358\pi$
$888$	−5.24264	−0.175932
$889$	0	0
$890$	−3.41421	−0.114445
$891$	−0.414214	−0.0138767
$892$	4.34315	0.145419
$893$	6.68629	0.223748
$894$	−2.82843	−0.0945968
$895$	−11.5563	−0.386286
$896$	0	0
$897$	2.65685	0.0887098
$898$	12.5563	0.419011
$899$	36.7279	1.22494
$900$	−4.00000	−0.133333
$901$	5.65685	0.188457
$902$	−0.485281	−0.0161581
$903$	0	0
$904$	9.75736	0.324525
$905$	−10.1421	−0.337136
$906$	4.75736	0.158053
$907$	56.8284	1.88696	0.943478	−	0.331434i	$-0.107532\pi$
$907$	56.8284	1.88696	0.943478	+	0.331434i	$0.107532\pi$
$908$	−9.07107	−0.301034
$909$	−13.0711	−0.433540
$910$	0	0
$911$	23.9706	0.794180	0.397090	−	0.917780i	$-0.370020\pi$
$911$	23.9706	0.794180	0.397090	+	0.917780i	$0.370020\pi$
$912$	1.82843	0.0605453
$913$	0.142136	0.00470400
$914$	13.7574	0.455053
$915$	−8.41421	−0.278165
$916$	4.10051	0.135485
$917$	0	0
$918$	2.41421	0.0796809
$919$	16.1421	0.532480	0.266240	−	0.963907i	$-0.414219\pi$
$919$	16.1421	0.532480	0.266240	+	0.963907i	$0.414219\pi$
$920$	2.65685	0.0875939
$921$	0.343146	0.0113070
$922$	−6.51472	−0.214551
$923$	−9.07107	−0.298578
$924$	0	0
$925$	−20.9706	−0.689508
$926$	21.8701	0.718695
$927$	−6.07107	−0.199400
$928$	8.65685	0.284175
$929$	30.1421	0.988931	0.494466	−	0.869197i	$-0.335364\pi$
$929$	30.1421	0.988931	0.494466	+	0.869197i	$0.335364\pi$
$930$	−4.24264	−0.139122
$931$	0	0
$932$	−5.17157	−0.169401
$933$	17.7990	0.582713
$934$	28.8995	0.945620
$935$	−1.00000	−0.0327035
$936$	−1.00000	−0.0326860
$937$	17.6985	0.578184	0.289092	−	0.957301i	$-0.406647\pi$
$937$	17.6985	0.578184	0.289092	+	0.957301i	$0.406647\pi$
$938$	0	0
$939$	6.92893	0.226117
$940$	−3.65685	−0.119273
$941$	−38.0000	−1.23876	−0.619382	−	0.785090i	$-0.712617\pi$
$941$	−38.0000	−1.23876	−0.619382	+	0.785090i	$0.712617\pi$
$942$	16.8995	0.550615
$943$	−3.11270	−0.101363
$944$	−9.89949	−0.322201
$945$	0	0
$946$	−2.89949	−0.0942707
$947$	12.7574	0.414558	0.207279	−	0.978282i	$-0.433539\pi$
$947$	12.7574	0.414558	0.207279	+	0.978282i	$0.433539\pi$
$948$	1.75736	0.0570764
$949$	6.17157	0.200338
$950$	7.31371	0.237288
$951$	−30.0416	−0.974167
$952$	0	0
$953$	−20.2843	−0.657072	−0.328536	−	0.944491i	$-0.606555\pi$
$953$	−20.2843	−0.657072	−0.328536	+	0.944491i	$0.606555\pi$
$954$	2.34315	0.0758621
$955$	11.4853	0.371655
$956$	−10.7279	−0.346966
$957$	3.58579	0.115912
$958$	7.48528	0.241838
$959$	0	0
$960$	−1.00000	−0.0322749
$961$	−13.0000	−0.419355
$962$	−5.24264	−0.169030
$963$	7.41421	0.238920
$964$	23.6569	0.761936
$965$	24.3848	0.784974
$966$	0	0
$967$	−4.41421	−0.141952	−0.0709758	−	0.997478i	$-0.522611\pi$
$967$	−4.41421	−0.141952	−0.0709758	+	0.997478i	$0.522611\pi$
$968$	10.8284	0.348039
$969$	−4.41421	−0.141805
$970$	15.3137	0.491694
$971$	48.4853	1.55597	0.777983	−	0.628285i	$-0.216243\pi$
$971$	48.4853	1.55597	0.777983	+	0.628285i	$0.216243\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	41.5980	1.33289
$975$	−4.00000	−0.128103
$976$	8.41421	0.269332
$977$	5.87006	0.187800	0.0938999	−	0.995582i	$-0.470067\pi$
$977$	5.87006	0.187800	0.0938999	+	0.995582i	$0.470067\pi$
$978$	0.343146	0.0109726
$979$	1.41421	0.0451985
$980$	0	0
$981$	−2.41421	−0.0770799
$982$	38.7696	1.23719
$983$	36.3137	1.15823	0.579114	−	0.815247i	$-0.303399\pi$
$983$	36.3137	1.15823	0.579114	+	0.815247i	$0.303399\pi$
$984$	1.17157	0.0373484
$985$	9.07107	0.289028
$986$	−20.8995	−0.665576
$987$	0	0
$988$	1.82843	0.0581700
$989$	−18.5980	−0.591381
$990$	−0.414214	−0.0131646
$991$	14.6863	0.466525	0.233263	−	0.972414i	$-0.425060\pi$
$991$	14.6863	0.466525	0.233263	+	0.972414i	$0.425060\pi$
$992$	4.24264	0.134704
$993$	−10.1005	−0.320530
$994$	0	0
$995$	−4.07107	−0.129062
$996$	−0.343146	−0.0108730
$997$	1.71573	0.0543377	0.0271688	−	0.999631i	$-0.491351\pi$
$997$	1.71573	0.0543377	0.0271688	+	0.999631i	$0.491351\pi$
$998$	2.72792	0.0863509
$999$	5.24264	0.165870

Twists

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

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

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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -0.414214 q^{11} +1.00000 q^{12} +1.00000 q^{13} -1.00000 q^{15} +1.00000 q^{16} -2.41421 q^{17} -1.00000 q^{18} +1.82843 q^{19} -1.00000 q^{20} +0.414214 q^{22} +2.65685 q^{23} -1.00000 q^{24} -4.00000 q^{25} -1.00000 q^{26} +1.00000 q^{27} -8.65685 q^{29} +1.00000 q^{30} -4.24264 q^{31} -1.00000 q^{32} -0.414214 q^{33} +2.41421 q^{34} +1.00000 q^{36} +5.24264 q^{37} -1.82843 q^{38} +1.00000 q^{39} +1.00000 q^{40} -1.17157 q^{41} -7.00000 q^{43} -0.414214 q^{44} -1.00000 q^{45} -2.65685 q^{46} +3.65685 q^{47} +1.00000 q^{48} +4.00000 q^{50} -2.41421 q^{51} +1.00000 q^{52} -2.34315 q^{53} -1.00000 q^{54} +0.414214 q^{55} +1.82843 q^{57} +8.65685 q^{58} -9.89949 q^{59} -1.00000 q^{60} +8.41421 q^{61} +4.24264 q^{62} +1.00000 q^{64} -1.00000 q^{65} +0.414214 q^{66} -1.41421 q^{67} -2.41421 q^{68} +2.65685 q^{69} -9.07107 q^{71} -1.00000 q^{72} +6.17157 q^{73} -5.24264 q^{74} -4.00000 q^{75} +1.82843 q^{76} -1.00000 q^{78} +1.75736 q^{79} -1.00000 q^{80} +1.00000 q^{81} +1.17157 q^{82} -0.343146 q^{83} +2.41421 q^{85} +7.00000 q^{86} -8.65685 q^{87} +0.414214 q^{88} -3.41421 q^{89} +1.00000 q^{90} +2.65685 q^{92} -4.24264 q^{93} -3.65685 q^{94} -1.82843 q^{95} -1.00000 q^{96} +15.3137 q^{97} -0.414214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 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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