LMFDB - Embedded newform 1666.2.a.o.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1666,2,Mod(1,1666)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1666, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1666.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1666 = 2 \cdot 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1666.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:	$13.3030769767$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 238)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	1666.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.23607 q^{3} +1.00000 q^{4} -3.23607 q^{5} -1.23607 q^{6} -1.00000 q^{8} -1.47214 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.23607 q^{3} +1.00000 q^{4} -3.23607 q^{5} -1.23607 q^{6} -1.00000 q^{8} -1.47214 q^{9} +3.23607 q^{10} +0.763932 q^{11} +1.23607 q^{12} -6.47214 q^{13} -4.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.47214 q^{18} -0.472136 q^{19} -3.23607 q^{20} -0.763932 q^{22} +8.00000 q^{23} -1.23607 q^{24} +5.47214 q^{25} +6.47214 q^{26} -5.52786 q^{27} +7.70820 q^{29} +4.00000 q^{30} +10.4721 q^{31} -1.00000 q^{32} +0.944272 q^{33} +1.00000 q^{34} -1.47214 q^{36} +1.23607 q^{37} +0.472136 q^{38} -8.00000 q^{39} +3.23607 q^{40} +12.4721 q^{41} -6.47214 q^{43} +0.763932 q^{44} +4.76393 q^{45} -8.00000 q^{46} -6.47214 q^{47} +1.23607 q^{48} -5.47214 q^{50} -1.23607 q^{51} -6.47214 q^{52} +4.47214 q^{53} +5.52786 q^{54} -2.47214 q^{55} -0.583592 q^{57} -7.70820 q^{58} +6.00000 q^{59} -4.00000 q^{60} +3.23607 q^{61} -10.4721 q^{62} +1.00000 q^{64} +20.9443 q^{65} -0.944272 q^{66} -10.4721 q^{67} -1.00000 q^{68} +9.88854 q^{69} +6.47214 q^{71} +1.47214 q^{72} +13.4164 q^{73} -1.23607 q^{74} +6.76393 q^{75} -0.472136 q^{76} +8.00000 q^{78} -1.52786 q^{79} -3.23607 q^{80} -2.41641 q^{81} -12.4721 q^{82} -2.00000 q^{83} +3.23607 q^{85} +6.47214 q^{86} +9.52786 q^{87} -0.763932 q^{88} -2.00000 q^{89} -4.76393 q^{90} +8.00000 q^{92} +12.9443 q^{93} +6.47214 q^{94} +1.52786 q^{95} -1.23607 q^{96} -0.472136 q^{97} -1.12461 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{8} + 6 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 + 6 * q^9	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{8} + 6 q^{9} + 2 q^{10} + 6 q^{11} - 2 q^{12} - 4 q^{13} - 8 q^{15} + 2 q^{16} - 2 q^{17} - 6 q^{18} + 8 q^{19} - 2 q^{20} - 6 q^{22} + 16 q^{23} + 2 q^{24} + 2 q^{25} + 4 q^{26} - 20 q^{27} + 2 q^{29} + 8 q^{30} + 12 q^{31} - 2 q^{32} - 16 q^{33} + 2 q^{34} + 6 q^{36} - 2 q^{37} - 8 q^{38} - 16 q^{39} + 2 q^{40} + 16 q^{41} - 4 q^{43} + 6 q^{44} + 14 q^{45} - 16 q^{46} - 4 q^{47} - 2 q^{48} - 2 q^{50} + 2 q^{51} - 4 q^{52} + 20 q^{54} + 4 q^{55} - 28 q^{57} - 2 q^{58} + 12 q^{59} - 8 q^{60} + 2 q^{61} - 12 q^{62} + 2 q^{64} + 24 q^{65} + 16 q^{66} - 12 q^{67} - 2 q^{68} - 16 q^{69} + 4 q^{71} - 6 q^{72} + 2 q^{74} + 18 q^{75} + 8 q^{76} + 16 q^{78} - 12 q^{79} - 2 q^{80} + 22 q^{81} - 16 q^{82} - 4 q^{83} + 2 q^{85} + 4 q^{86} + 28 q^{87} - 6 q^{88} - 4 q^{89} - 14 q^{90} + 16 q^{92} + 8 q^{93} + 4 q^{94} + 12 q^{95} + 2 q^{96} + 8 q^{97} + 38 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 + 6 * q^9 + 2 * q^10 + 6 * q^11 - 2 * q^12 - 4 * q^13 - 8 * q^15 + 2 * q^16 - 2 * q^17 - 6 * q^18 + 8 * q^19 - 2 * q^20 - 6 * q^22 + 16 * q^23 + 2 * q^24 + 2 * q^25 + 4 * q^26 - 20 * q^27 + 2 * q^29 + 8 * q^30 + 12 * q^31 - 2 * q^32 - 16 * q^33 + 2 * q^34 + 6 * q^36 - 2 * q^37 - 8 * q^38 - 16 * q^39 + 2 * q^40 + 16 * q^41 - 4 * q^43 + 6 * q^44 + 14 * q^45 - 16 * q^46 - 4 * q^47 - 2 * q^48 - 2 * q^50 + 2 * q^51 - 4 * q^52 + 20 * q^54 + 4 * q^55 - 28 * q^57 - 2 * q^58 + 12 * q^59 - 8 * q^60 + 2 * q^61 - 12 * q^62 + 2 * q^64 + 24 * q^65 + 16 * q^66 - 12 * q^67 - 2 * q^68 - 16 * q^69 + 4 * q^71 - 6 * q^72 + 2 * q^74 + 18 * q^75 + 8 * q^76 + 16 * q^78 - 12 * q^79 - 2 * q^80 + 22 * q^81 - 16 * q^82 - 4 * q^83 + 2 * q^85 + 4 * q^86 + 28 * q^87 - 6 * q^88 - 4 * q^89 - 14 * q^90 + 16 * q^92 + 8 * q^93 + 4 * q^94 + 12 * q^95 + 2 * q^96 + 8 * q^97 + 38 * 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
$3$	1.23607	0.713644	0.356822	−	0.934172i	$-0.383860\pi$
$3$	1.23607	0.713644	0.356822	+	0.934172i	$0.383860\pi$
$4$	1.00000	0.500000
$5$	−3.23607	−1.44721	−0.723607	−	0.690212i	$-0.757517\pi$
$5$	−3.23607	−1.44721	−0.723607	+	0.690212i	$0.757517\pi$
$6$	−1.23607	−0.504623
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	−1.47214	−0.490712
$10$	3.23607	1.02333
$11$	0.763932	0.230334	0.115167	−	0.993346i	$-0.463260\pi$
$11$	0.763932	0.230334	0.115167	+	0.993346i	$0.463260\pi$
$12$	1.23607	0.356822
$13$	−6.47214	−1.79505	−0.897524	−	0.440966i	$-0.854636\pi$
$13$	−6.47214	−1.79505	−0.897524	+	0.440966i	$0.854636\pi$
$14$	0	0
$15$	−4.00000	−1.03280
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.47214	0.346986
$19$	−0.472136	−0.108315	−0.0541577	−	0.998532i	$-0.517247\pi$
$19$	−0.472136	−0.108315	−0.0541577	+	0.998532i	$0.517247\pi$
$20$	−3.23607	−0.723607
$21$	0	0
$22$	−0.763932	−0.162871
$23$	8.00000	1.66812	0.834058	−	0.551677i	$-0.186012\pi$
$23$	8.00000	1.66812	0.834058	+	0.551677i	$0.186012\pi$
$24$	−1.23607	−0.252311
$25$	5.47214	1.09443
$26$	6.47214	1.26929
$27$	−5.52786	−1.06384
$28$	0	0
$29$	7.70820	1.43138	0.715689	−	0.698419i	$-0.246113\pi$
$29$	7.70820	1.43138	0.715689	+	0.698419i	$0.246113\pi$
$30$	4.00000	0.730297
$31$	10.4721	1.88085	0.940426	−	0.340000i	$-0.110427\pi$
$31$	10.4721	1.88085	0.940426	+	0.340000i	$0.110427\pi$
$32$	−1.00000	−0.176777
$33$	0.944272	0.164377
$34$	1.00000	0.171499
$35$	0	0
$36$	−1.47214	−0.245356
$37$	1.23607	0.203208	0.101604	−	0.994825i	$-0.467602\pi$
$37$	1.23607	0.203208	0.101604	+	0.994825i	$0.467602\pi$
$38$	0.472136	0.0765906
$39$	−8.00000	−1.28103
$40$	3.23607	0.511667
$41$	12.4721	1.94782	0.973910	−	0.226934i	$-0.0728701\pi$
$41$	12.4721	1.94782	0.973910	+	0.226934i	$0.0728701\pi$
$42$	0	0
$43$	−6.47214	−0.986991	−0.493496	−	0.869748i	$-0.664281\pi$
$43$	−6.47214	−0.986991	−0.493496	+	0.869748i	$0.664281\pi$
$44$	0.763932	0.115167
$45$	4.76393	0.710165
$46$	−8.00000	−1.17954
$47$	−6.47214	−0.944058	−0.472029	−	0.881583i	$-0.656478\pi$
$47$	−6.47214	−0.944058	−0.472029	+	0.881583i	$0.656478\pi$
$48$	1.23607	0.178411
$49$	0	0
$50$	−5.47214	−0.773877
$51$	−1.23607	−0.173084
$52$	−6.47214	−0.897524
$53$	4.47214	0.614295	0.307148	−	0.951662i	$-0.400625\pi$
$53$	4.47214	0.614295	0.307148	+	0.951662i	$0.400625\pi$
$54$	5.52786	0.752247
$55$	−2.47214	−0.333343
$56$	0	0
$57$	−0.583592	−0.0772987
$58$	−7.70820	−1.01214
$59$	6.00000	0.781133	0.390567	−	0.920575i	$-0.372279\pi$
$59$	6.00000	0.781133	0.390567	+	0.920575i	$0.372279\pi$
$60$	−4.00000	−0.516398
$61$	3.23607	0.414336	0.207168	−	0.978305i	$-0.433575\pi$
$61$	3.23607	0.414336	0.207168	+	0.978305i	$0.433575\pi$
$62$	−10.4721	−1.32996
$63$	0	0
$64$	1.00000	0.125000
$65$	20.9443	2.59782
$66$	−0.944272	−0.116232
$67$	−10.4721	−1.27938	−0.639688	−	0.768635i	$-0.720936\pi$
$67$	−10.4721	−1.27938	−0.639688	+	0.768635i	$0.720936\pi$
$68$	−1.00000	−0.121268
$69$	9.88854	1.19044
$70$	0	0
$71$	6.47214	0.768101	0.384051	−	0.923312i	$-0.374529\pi$
$71$	6.47214	0.768101	0.384051	+	0.923312i	$0.374529\pi$
$72$	1.47214	0.173493
$73$	13.4164	1.57027	0.785136	−	0.619324i	$-0.212593\pi$
$73$	13.4164	1.57027	0.785136	+	0.619324i	$0.212593\pi$
$74$	−1.23607	−0.143690
$75$	6.76393	0.781032
$76$	−0.472136	−0.0541577
$77$	0	0
$78$	8.00000	0.905822
$79$	−1.52786	−0.171898	−0.0859491	−	0.996300i	$-0.527392\pi$
$79$	−1.52786	−0.171898	−0.0859491	+	0.996300i	$0.527392\pi$
$80$	−3.23607	−0.361803
$81$	−2.41641	−0.268490
$82$	−12.4721	−1.37732
$83$	−2.00000	−0.219529	−0.109764	−	0.993958i	$-0.535010\pi$
$83$	−2.00000	−0.219529	−0.109764	+	0.993958i	$0.535010\pi$
$84$	0	0
$85$	3.23607	0.351001
$86$	6.47214	0.697908
$87$	9.52786	1.02149
$88$	−0.763932	−0.0814354
$89$	−2.00000	−0.212000	−0.106000	−	0.994366i	$-0.533804\pi$
$89$	−2.00000	−0.212000	−0.106000	+	0.994366i	$0.533804\pi$
$90$	−4.76393	−0.502163
$91$	0	0
$92$	8.00000	0.834058
$93$	12.9443	1.34226
$94$	6.47214	0.667550
$95$	1.52786	0.156756
$96$	−1.23607	−0.126156
$97$	−0.472136	−0.0479381	−0.0239691	−	0.999713i	$-0.507630\pi$
$97$	−0.472136	−0.0479381	−0.0239691	+	0.999713i	$0.507630\pi$
$98$	0	0
$99$	−1.12461	−0.113028
$100$	5.47214	0.547214
$101$	−2.47214	−0.245987	−0.122993	−	0.992407i	$-0.539249\pi$
$101$	−2.47214	−0.245987	−0.122993	+	0.992407i	$0.539249\pi$
$102$	1.23607	0.122389
$103$	4.00000	0.394132	0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000	0.394132	0.197066	+	0.980390i	$0.436859\pi$
$104$	6.47214	0.634645
$105$	0	0
$106$	−4.47214	−0.434372
$107$	3.23607	0.312842	0.156421	−	0.987690i	$-0.450004\pi$
$107$	3.23607	0.312842	0.156421	+	0.987690i	$0.450004\pi$
$108$	−5.52786	−0.531919
$109$	−10.1803	−0.975100	−0.487550	−	0.873095i	$-0.662109\pi$
$109$	−10.1803	−0.975100	−0.487550	+	0.873095i	$0.662109\pi$
$110$	2.47214	0.235709
$111$	1.52786	0.145018
$112$	0	0
$113$	−13.4164	−1.26211	−0.631055	−	0.775738i	$-0.717378\pi$
$113$	−13.4164	−1.26211	−0.631055	+	0.775738i	$0.717378\pi$
$114$	0.583592	0.0546584
$115$	−25.8885	−2.41412
$116$	7.70820	0.715689
$117$	9.52786	0.880851
$118$	−6.00000	−0.552345
$119$	0	0
$120$	4.00000	0.365148
$121$	−10.4164	−0.946946
$122$	−3.23607	−0.292980
$123$	15.4164	1.39005
$124$	10.4721	0.940426
$125$	−1.52786	−0.136656
$126$	0	0
$127$	12.0000	1.06483	0.532414	−	0.846484i	$-0.321285\pi$
$127$	12.0000	1.06483	0.532414	+	0.846484i	$0.321285\pi$
$128$	−1.00000	−0.0883883
$129$	−8.00000	−0.704361
$130$	−20.9443	−1.83693
$131$	11.7082	1.02295	0.511475	−	0.859298i	$-0.329099\pi$
$131$	11.7082	1.02295	0.511475	+	0.859298i	$0.329099\pi$
$132$	0.944272	0.0821883
$133$	0	0
$134$	10.4721	0.904655
$135$	17.8885	1.53960
$136$	1.00000	0.0857493
$137$	12.4721	1.06557	0.532783	−	0.846252i	$-0.321146\pi$
$137$	12.4721	1.06557	0.532783	+	0.846252i	$0.321146\pi$
$138$	−9.88854	−0.841769
$139$	−10.1803	−0.863485	−0.431743	−	0.901997i	$-0.642101\pi$
$139$	−10.1803	−0.863485	−0.431743	+	0.901997i	$0.642101\pi$
$140$	0	0
$141$	−8.00000	−0.673722
$142$	−6.47214	−0.543130
$143$	−4.94427	−0.413461
$144$	−1.47214	−0.122678
$145$	−24.9443	−2.07151
$146$	−13.4164	−1.11035
$147$	0	0
$148$	1.23607	0.101604
$149$	1.05573	0.0864886	0.0432443	−	0.999065i	$-0.486231\pi$
$149$	1.05573	0.0864886	0.0432443	+	0.999065i	$0.486231\pi$
$150$	−6.76393	−0.552273
$151$	4.00000	0.325515	0.162758	−	0.986666i	$-0.447961\pi$
$151$	4.00000	0.325515	0.162758	+	0.986666i	$0.447961\pi$
$152$	0.472136	0.0382953
$153$	1.47214	0.119015
$154$	0	0
$155$	−33.8885	−2.72199
$156$	−8.00000	−0.640513
$157$	−3.05573	−0.243874	−0.121937	−	0.992538i	$-0.538911\pi$
$157$	−3.05573	−0.243874	−0.121937	+	0.992538i	$0.538911\pi$
$158$	1.52786	0.121550
$159$	5.52786	0.438388
$160$	3.23607	0.255834
$161$	0	0
$162$	2.41641	0.189851
$163$	−13.7082	−1.07371	−0.536855	−	0.843675i	$-0.680388\pi$
$163$	−13.7082	−1.07371	−0.536855	+	0.843675i	$0.680388\pi$
$164$	12.4721	0.973910
$165$	−3.05573	−0.237888
$166$	2.00000	0.155230
$167$	5.52786	0.427759	0.213879	−	0.976860i	$-0.431390\pi$
$167$	5.52786	0.427759	0.213879	+	0.976860i	$0.431390\pi$
$168$	0	0
$169$	28.8885	2.22220
$170$	−3.23607	−0.248195
$171$	0.695048	0.0531517
$172$	−6.47214	−0.493496
$173$	10.6525	0.809893	0.404946	−	0.914340i	$-0.367290\pi$
$173$	10.6525	0.809893	0.404946	+	0.914340i	$0.367290\pi$
$174$	−9.52786	−0.722306
$175$	0	0
$176$	0.763932	0.0575835
$177$	7.41641	0.557451
$178$	2.00000	0.149906
$179$	8.94427	0.668526	0.334263	−	0.942480i	$-0.391513\pi$
$179$	8.94427	0.668526	0.334263	+	0.942480i	$0.391513\pi$
$180$	4.76393	0.355083
$181$	7.23607	0.537853	0.268926	−	0.963161i	$-0.413331\pi$
$181$	7.23607	0.537853	0.268926	+	0.963161i	$0.413331\pi$
$182$	0	0
$183$	4.00000	0.295689
$184$	−8.00000	−0.589768
$185$	−4.00000	−0.294086
$186$	−12.9443	−0.949120
$187$	−0.763932	−0.0558642
$188$	−6.47214	−0.472029
$189$	0	0
$190$	−1.52786	−0.110843
$191$	−4.94427	−0.357755	−0.178877	−	0.983871i	$-0.557247\pi$
$191$	−4.94427	−0.357755	−0.178877	+	0.983871i	$0.557247\pi$
$192$	1.23607	0.0892055
$193$	23.8885	1.71954	0.859768	−	0.510686i	$-0.170608\pi$
$193$	23.8885	1.71954	0.859768	+	0.510686i	$0.170608\pi$
$194$	0.472136	0.0338974
$195$	25.8885	1.85392
$196$	0	0
$197$	8.29180	0.590766	0.295383	−	0.955379i	$-0.404553\pi$
$197$	8.29180	0.590766	0.295383	+	0.955379i	$0.404553\pi$
$198$	1.12461	0.0799227
$199$	−5.52786	−0.391860	−0.195930	−	0.980618i	$-0.562773\pi$
$199$	−5.52786	−0.391860	−0.195930	+	0.980618i	$0.562773\pi$
$200$	−5.47214	−0.386938
$201$	−12.9443	−0.913019
$202$	2.47214	0.173939
$203$	0	0
$204$	−1.23607	−0.0865421
$205$	−40.3607	−2.81891
$206$	−4.00000	−0.278693
$207$	−11.7771	−0.818564
$208$	−6.47214	−0.448762
$209$	−0.360680	−0.0249487
$210$	0	0
$211$	−14.2918	−0.983888	−0.491944	−	0.870627i	$-0.663713\pi$
$211$	−14.2918	−0.983888	−0.491944	+	0.870627i	$0.663713\pi$
$212$	4.47214	0.307148
$213$	8.00000	0.548151
$214$	−3.23607	−0.221213
$215$	20.9443	1.42839
$216$	5.52786	0.376124
$217$	0	0
$218$	10.1803	0.689500
$219$	16.5836	1.12062
$220$	−2.47214	−0.166671
$221$	6.47214	0.435363
$222$	−1.52786	−0.102544
$223$	−10.4721	−0.701266	−0.350633	−	0.936513i	$-0.614034\pi$
$223$	−10.4721	−0.701266	−0.350633	+	0.936513i	$0.614034\pi$
$224$	0	0
$225$	−8.05573	−0.537049
$226$	13.4164	0.892446
$227$	21.5967	1.43343	0.716713	−	0.697368i	$-0.245646\pi$
$227$	21.5967	1.43343	0.716713	+	0.697368i	$0.245646\pi$
$228$	−0.583592	−0.0386493
$229$	−12.9443	−0.855382	−0.427691	−	0.903925i	$-0.640673\pi$
$229$	−12.9443	−0.855382	−0.427691	+	0.903925i	$0.640673\pi$
$230$	25.8885	1.70704
$231$	0	0
$232$	−7.70820	−0.506068
$233$	−15.8885	−1.04089	−0.520447	−	0.853894i	$-0.674235\pi$
$233$	−15.8885	−1.04089	−0.520447	+	0.853894i	$0.674235\pi$
$234$	−9.52786	−0.622856
$235$	20.9443	1.36625
$236$	6.00000	0.390567
$237$	−1.88854	−0.122674
$238$	0	0
$239$	12.9443	0.837295	0.418648	−	0.908149i	$-0.362504\pi$
$239$	12.9443	0.837295	0.418648	+	0.908149i	$0.362504\pi$
$240$	−4.00000	−0.258199
$241$	23.8885	1.53880	0.769398	−	0.638769i	$-0.220556\pi$
$241$	23.8885	1.53880	0.769398	+	0.638769i	$0.220556\pi$
$242$	10.4164	0.669592
$243$	13.5967	0.872232
$244$	3.23607	0.207168
$245$	0	0
$246$	−15.4164	−0.982914
$247$	3.05573	0.194431
$248$	−10.4721	−0.664981
$249$	−2.47214	−0.156665
$250$	1.52786	0.0966306
$251$	−14.0000	−0.883672	−0.441836	−	0.897096i	$-0.645673\pi$
$251$	−14.0000	−0.883672	−0.441836	+	0.897096i	$0.645673\pi$
$252$	0	0
$253$	6.11146	0.384224
$254$	−12.0000	−0.752947
$255$	4.00000	0.250490
$256$	1.00000	0.0625000
$257$	2.00000	0.124757	0.0623783	−	0.998053i	$-0.480131\pi$
$257$	2.00000	0.124757	0.0623783	+	0.998053i	$0.480131\pi$
$258$	8.00000	0.498058
$259$	0	0
$260$	20.9443	1.29891
$261$	−11.3475	−0.702394
$262$	−11.7082	−0.723335
$263$	24.9443	1.53813	0.769065	−	0.639171i	$-0.220722\pi$
$263$	24.9443	1.53813	0.769065	+	0.639171i	$0.220722\pi$
$264$	−0.944272	−0.0581159
$265$	−14.4721	−0.889016
$266$	0	0
$267$	−2.47214	−0.151292
$268$	−10.4721	−0.639688
$269$	13.7082	0.835804	0.417902	−	0.908492i	$-0.362766\pi$
$269$	13.7082	0.835804	0.417902	+	0.908492i	$0.362766\pi$
$270$	−17.8885	−1.08866
$271$	7.41641	0.450515	0.225257	−	0.974299i	$-0.427678\pi$
$271$	7.41641	0.450515	0.225257	+	0.974299i	$0.427678\pi$
$272$	−1.00000	−0.0606339
$273$	0	0
$274$	−12.4721	−0.753469
$275$	4.18034	0.252084
$276$	9.88854	0.595220
$277$	8.65248	0.519877	0.259938	−	0.965625i	$-0.416298\pi$
$277$	8.65248	0.519877	0.259938	+	0.965625i	$0.416298\pi$
$278$	10.1803	0.610576
$279$	−15.4164	−0.922956
$280$	0	0
$281$	12.4721	0.744025	0.372013	−	0.928228i	$-0.378668\pi$
$281$	12.4721	0.744025	0.372013	+	0.928228i	$0.378668\pi$
$282$	8.00000	0.476393
$283$	−23.7082	−1.40931	−0.704653	−	0.709552i	$-0.748897\pi$
$283$	−23.7082	−1.40931	−0.704653	+	0.709552i	$0.748897\pi$
$284$	6.47214	0.384051
$285$	1.88854	0.111868
$286$	4.94427	0.292361
$287$	0	0
$288$	1.47214	0.0867464
$289$	1.00000	0.0588235
$290$	24.9443	1.46478
$291$	−0.583592	−0.0342108
$292$	13.4164	0.785136
$293$	28.0000	1.63578	0.817889	−	0.575376i	$-0.195144\pi$
$293$	28.0000	1.63578	0.817889	+	0.575376i	$0.195144\pi$
$294$	0	0
$295$	−19.4164	−1.13047
$296$	−1.23607	−0.0718450
$297$	−4.22291	−0.245038
$298$	−1.05573	−0.0611567
$299$	−51.7771	−2.99435
$300$	6.76393	0.390516
$301$	0	0
$302$	−4.00000	−0.230174
$303$	−3.05573	−0.175547
$304$	−0.472136	−0.0270789
$305$	−10.4721	−0.599633
$306$	−1.47214	−0.0841564
$307$	12.4721	0.711822	0.355911	−	0.934520i	$-0.384171\pi$
$307$	12.4721	0.711822	0.355911	+	0.934520i	$0.384171\pi$
$308$	0	0
$309$	4.94427	0.281270
$310$	33.8885	1.92474
$311$	3.05573	0.173274	0.0866372	−	0.996240i	$-0.472388\pi$
$311$	3.05573	0.173274	0.0866372	+	0.996240i	$0.472388\pi$
$312$	8.00000	0.452911
$313$	−21.4164	−1.21053	−0.605263	−	0.796025i	$-0.706932\pi$
$313$	−21.4164	−1.21053	−0.605263	+	0.796025i	$0.706932\pi$
$314$	3.05573	0.172445
$315$	0	0
$316$	−1.52786	−0.0859491
$317$	−5.81966	−0.326865	−0.163432	−	0.986555i	$-0.552257\pi$
$317$	−5.81966	−0.326865	−0.163432	+	0.986555i	$0.552257\pi$
$318$	−5.52786	−0.309987
$319$	5.88854	0.329695
$320$	−3.23607	−0.180902
$321$	4.00000	0.223258
$322$	0	0
$323$	0.472136	0.0262703
$324$	−2.41641	−0.134245
$325$	−35.4164	−1.96455
$326$	13.7082	0.759227
$327$	−12.5836	−0.695874
$328$	−12.4721	−0.688659
$329$	0	0
$330$	3.05573	0.168212
$331$	24.3607	1.33898	0.669492	−	0.742819i	$-0.266512\pi$
$331$	24.3607	1.33898	0.669492	+	0.742819i	$0.266512\pi$
$332$	−2.00000	−0.109764
$333$	−1.81966	−0.0997168
$334$	−5.52786	−0.302471
$335$	33.8885	1.85153
$336$	0	0
$337$	−11.5279	−0.627963	−0.313981	−	0.949429i	$-0.601663\pi$
$337$	−11.5279	−0.627963	−0.313981	+	0.949429i	$0.601663\pi$
$338$	−28.8885	−1.57133
$339$	−16.5836	−0.900697
$340$	3.23607	0.175500
$341$	8.00000	0.433224
$342$	−0.695048	−0.0375839
$343$	0	0
$344$	6.47214	0.348954
$345$	−32.0000	−1.72282
$346$	−10.6525	−0.572681
$347$	−26.6525	−1.43078	−0.715390	−	0.698725i	$-0.753751\pi$
$347$	−26.6525	−1.43078	−0.715390	+	0.698725i	$0.753751\pi$
$348$	9.52786	0.510747
$349$	30.4721	1.63114	0.815568	−	0.578661i	$-0.196425\pi$
$349$	30.4721	1.63114	0.815568	+	0.578661i	$0.196425\pi$
$350$	0	0
$351$	35.7771	1.90964
$352$	−0.763932	−0.0407177
$353$	−23.8885	−1.27146	−0.635729	−	0.771912i	$-0.719301\pi$
$353$	−23.8885	−1.27146	−0.635729	+	0.771912i	$0.719301\pi$
$354$	−7.41641	−0.394178
$355$	−20.9443	−1.11161
$356$	−2.00000	−0.106000
$357$	0	0
$358$	−8.94427	−0.472719
$359$	−30.8328	−1.62729	−0.813647	−	0.581359i	$-0.802521\pi$
$359$	−30.8328	−1.62729	−0.813647	+	0.581359i	$0.802521\pi$
$360$	−4.76393	−0.251081
$361$	−18.7771	−0.988268
$362$	−7.23607	−0.380319
$363$	−12.8754	−0.675783
$364$	0	0
$365$	−43.4164	−2.27252
$366$	−4.00000	−0.209083
$367$	11.0557	0.577104	0.288552	−	0.957464i	$-0.406826\pi$
$367$	11.0557	0.577104	0.288552	+	0.957464i	$0.406826\pi$
$368$	8.00000	0.417029
$369$	−18.3607	−0.955819
$370$	4.00000	0.207950
$371$	0	0
$372$	12.9443	0.671129
$373$	−13.4164	−0.694675	−0.347338	−	0.937740i	$-0.612914\pi$
$373$	−13.4164	−0.694675	−0.347338	+	0.937740i	$0.612914\pi$
$374$	0.763932	0.0395020
$375$	−1.88854	−0.0975240
$376$	6.47214	0.333775
$377$	−49.8885	−2.56939
$378$	0	0
$379$	31.5967	1.62302	0.811508	−	0.584341i	$-0.198647\pi$
$379$	31.5967	1.62302	0.811508	+	0.584341i	$0.198647\pi$
$380$	1.52786	0.0783778
$381$	14.8328	0.759908
$382$	4.94427	0.252971
$383$	−8.94427	−0.457031	−0.228515	−	0.973540i	$-0.573387\pi$
$383$	−8.94427	−0.457031	−0.228515	+	0.973540i	$0.573387\pi$
$384$	−1.23607	−0.0630778
$385$	0	0
$386$	−23.8885	−1.21589
$387$	9.52786	0.484329
$388$	−0.472136	−0.0239691
$389$	26.0000	1.31825	0.659126	−	0.752032i	$-0.270926\pi$
$389$	26.0000	1.31825	0.659126	+	0.752032i	$0.270926\pi$
$390$	−25.8885	−1.31092
$391$	−8.00000	−0.404577
$392$	0	0
$393$	14.4721	0.730023
$394$	−8.29180	−0.417735
$395$	4.94427	0.248773
$396$	−1.12461	−0.0565139
$397$	4.18034	0.209805	0.104903	−	0.994482i	$-0.466547\pi$
$397$	4.18034	0.209805	0.104903	+	0.994482i	$0.466547\pi$
$398$	5.52786	0.277087
$399$	0	0
$400$	5.47214	0.273607
$401$	−14.9443	−0.746281	−0.373141	−	0.927775i	$-0.621719\pi$
$401$	−14.9443	−0.746281	−0.373141	+	0.927775i	$0.621719\pi$
$402$	12.9443	0.645602
$403$	−67.7771	−3.37622
$404$	−2.47214	−0.122993
$405$	7.81966	0.388562
$406$	0	0
$407$	0.944272	0.0468058
$408$	1.23607	0.0611945
$409$	2.94427	0.145585	0.0727924	−	0.997347i	$-0.476809\pi$
$409$	2.94427	0.145585	0.0727924	+	0.997347i	$0.476809\pi$
$410$	40.3607	1.99327
$411$	15.4164	0.760435
$412$	4.00000	0.197066
$413$	0	0
$414$	11.7771	0.578812
$415$	6.47214	0.317705
$416$	6.47214	0.317323
$417$	−12.5836	−0.616221
$418$	0.360680	0.0176414
$419$	−28.0689	−1.37125	−0.685627	−	0.727953i	$-0.740472\pi$
$419$	−28.0689	−1.37125	−0.685627	+	0.727953i	$0.740472\pi$
$420$	0	0
$421$	−24.4721	−1.19270	−0.596349	−	0.802725i	$-0.703383\pi$
$421$	−24.4721	−1.19270	−0.596349	+	0.802725i	$0.703383\pi$
$422$	14.2918	0.695714
$423$	9.52786	0.463261
$424$	−4.47214	−0.217186
$425$	−5.47214	−0.265438
$426$	−8.00000	−0.387601
$427$	0	0
$428$	3.23607	0.156421
$429$	−6.11146	−0.295064
$430$	−20.9443	−1.01002
$431$	4.94427	0.238157	0.119079	−	0.992885i	$-0.462006\pi$
$431$	4.94427	0.238157	0.119079	+	0.992885i	$0.462006\pi$
$432$	−5.52786	−0.265959
$433$	6.94427	0.333720	0.166860	−	0.985981i	$-0.446637\pi$
$433$	6.94427	0.333720	0.166860	+	0.985981i	$0.446637\pi$
$434$	0	0
$435$	−30.8328	−1.47832
$436$	−10.1803	−0.487550
$437$	−3.77709	−0.180683
$438$	−16.5836	−0.792395
$439$	20.9443	0.999616	0.499808	−	0.866136i	$-0.333404\pi$
$439$	20.9443	0.999616	0.499808	+	0.866136i	$0.333404\pi$
$440$	2.47214	0.117854
$441$	0	0
$442$	−6.47214	−0.307848
$443$	36.3607	1.72755	0.863774	−	0.503879i	$-0.168094\pi$
$443$	36.3607	1.72755	0.863774	+	0.503879i	$0.168094\pi$
$444$	1.52786	0.0725092
$445$	6.47214	0.306809
$446$	10.4721	0.495870
$447$	1.30495	0.0617221
$448$	0	0
$449$	−17.4164	−0.821931	−0.410966	−	0.911651i	$-0.634808\pi$
$449$	−17.4164	−0.821931	−0.410966	+	0.911651i	$0.634808\pi$
$450$	8.05573	0.379751
$451$	9.52786	0.448650
$452$	−13.4164	−0.631055
$453$	4.94427	0.232302
$454$	−21.5967	−1.01359
$455$	0	0
$456$	0.583592	0.0273292
$457$	−19.8885	−0.930347	−0.465173	−	0.885220i	$-0.654008\pi$
$457$	−19.8885	−0.930347	−0.465173	+	0.885220i	$0.654008\pi$
$458$	12.9443	0.604846
$459$	5.52786	0.258019
$460$	−25.8885	−1.20706
$461$	14.4721	0.674035	0.337017	−	0.941498i	$-0.390582\pi$
$461$	14.4721	0.674035	0.337017	+	0.941498i	$0.390582\pi$
$462$	0	0
$463$	15.0557	0.699699	0.349850	−	0.936806i	$-0.386233\pi$
$463$	15.0557	0.699699	0.349850	+	0.936806i	$0.386233\pi$
$464$	7.70820	0.357844
$465$	−41.8885	−1.94253
$466$	15.8885	0.736023
$467$	−34.3607	−1.59002	−0.795011	−	0.606595i	$-0.792535\pi$
$467$	−34.3607	−1.59002	−0.795011	+	0.606595i	$0.792535\pi$
$468$	9.52786	0.440426
$469$	0	0
$470$	−20.9443	−0.966087
$471$	−3.77709	−0.174039
$472$	−6.00000	−0.276172
$473$	−4.94427	−0.227338
$474$	1.88854	0.0867437
$475$	−2.58359	−0.118543
$476$	0	0
$477$	−6.58359	−0.301442
$478$	−12.9443	−0.592057
$479$	−7.41641	−0.338864	−0.169432	−	0.985542i	$-0.554193\pi$
$479$	−7.41641	−0.338864	−0.169432	+	0.985542i	$0.554193\pi$
$480$	4.00000	0.182574
$481$	−8.00000	−0.364769
$482$	−23.8885	−1.08809
$483$	0	0
$484$	−10.4164	−0.473473
$485$	1.52786	0.0693767
$486$	−13.5967	−0.616761
$487$	20.9443	0.949076	0.474538	−	0.880235i	$-0.342615\pi$
$487$	20.9443	0.949076	0.474538	+	0.880235i	$0.342615\pi$
$488$	−3.23607	−0.146490
$489$	−16.9443	−0.766246
$490$	0	0
$491$	−15.0557	−0.679455	−0.339728	−	0.940524i	$-0.610335\pi$
$491$	−15.0557	−0.679455	−0.339728	+	0.940524i	$0.610335\pi$
$492$	15.4164	0.695025
$493$	−7.70820	−0.347160
$494$	−3.05573	−0.137484
$495$	3.63932	0.163575
$496$	10.4721	0.470213
$497$	0	0
$498$	2.47214	0.110779
$499$	−9.34752	−0.418453	−0.209226	−	0.977867i	$-0.567095\pi$
$499$	−9.34752	−0.418453	−0.209226	+	0.977867i	$0.567095\pi$
$500$	−1.52786	−0.0683282
$501$	6.83282	0.305268
$502$	14.0000	0.624851
$503$	4.94427	0.220454	0.110227	−	0.993906i	$-0.464842\pi$
$503$	4.94427	0.220454	0.110227	+	0.993906i	$0.464842\pi$
$504$	0	0
$505$	8.00000	0.355995
$506$	−6.11146	−0.271687
$507$	35.7082	1.58586
$508$	12.0000	0.532414
$509$	20.9443	0.928339	0.464169	−	0.885747i	$-0.346353\pi$
$509$	20.9443	0.928339	0.464169	+	0.885747i	$0.346353\pi$
$510$	−4.00000	−0.177123
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	2.60990	0.115230
$514$	−2.00000	−0.0882162
$515$	−12.9443	−0.570393
$516$	−8.00000	−0.352180
$517$	−4.94427	−0.217449
$518$	0	0
$519$	13.1672	0.577975
$520$	−20.9443	−0.918467
$521$	18.9443	0.829964	0.414982	−	0.909830i	$-0.363788\pi$
$521$	18.9443	0.829964	0.414982	+	0.909830i	$0.363788\pi$
$522$	11.3475	0.496668
$523$	25.0557	1.09561	0.547805	−	0.836606i	$-0.315463\pi$
$523$	25.0557	1.09561	0.547805	+	0.836606i	$0.315463\pi$
$524$	11.7082	0.511475
$525$	0	0
$526$	−24.9443	−1.08762
$527$	−10.4721	−0.456173
$528$	0.944272	0.0410942
$529$	41.0000	1.78261
$530$	14.4721	0.628629
$531$	−8.83282	−0.383312
$532$	0	0
$533$	−80.7214	−3.49643
$534$	2.47214	0.106980
$535$	−10.4721	−0.452750
$536$	10.4721	0.452327
$537$	11.0557	0.477090
$538$	−13.7082	−0.591003
$539$	0	0
$540$	17.8885	0.769800
$541$	−18.7639	−0.806724	−0.403362	−	0.915040i	$-0.632159\pi$
$541$	−18.7639	−0.806724	−0.403362	+	0.915040i	$0.632159\pi$
$542$	−7.41641	−0.318562
$543$	8.94427	0.383835
$544$	1.00000	0.0428746
$545$	32.9443	1.41118
$546$	0	0
$547$	−7.59675	−0.324813	−0.162407	−	0.986724i	$-0.551926\pi$
$547$	−7.59675	−0.324813	−0.162407	+	0.986724i	$0.551926\pi$
$548$	12.4721	0.532783
$549$	−4.76393	−0.203320
$550$	−4.18034	−0.178250
$551$	−3.63932	−0.155040
$552$	−9.88854	−0.420884
$553$	0	0
$554$	−8.65248	−0.367608
$555$	−4.94427	−0.209873
$556$	−10.1803	−0.431743
$557$	−10.3607	−0.438996	−0.219498	−	0.975613i	$-0.570442\pi$
$557$	−10.3607	−0.438996	−0.219498	+	0.975613i	$0.570442\pi$
$558$	15.4164	0.652629
$559$	41.8885	1.77170
$560$	0	0
$561$	−0.944272	−0.0398672
$562$	−12.4721	−0.526105
$563$	−20.8328	−0.877999	−0.438999	−	0.898487i	$-0.644667\pi$
$563$	−20.8328	−0.877999	−0.438999	+	0.898487i	$0.644667\pi$
$564$	−8.00000	−0.336861
$565$	43.4164	1.82654
$566$	23.7082	0.996530
$567$	0	0
$568$	−6.47214	−0.271565
$569$	−19.8885	−0.833771	−0.416886	−	0.908959i	$-0.636878\pi$
$569$	−19.8885	−0.833771	−0.416886	+	0.908959i	$0.636878\pi$
$570$	−1.88854	−0.0791024
$571$	−8.76393	−0.366759	−0.183380	−	0.983042i	$-0.558704\pi$
$571$	−8.76393	−0.366759	−0.183380	+	0.983042i	$0.558704\pi$
$572$	−4.94427	−0.206730
$573$	−6.11146	−0.255310
$574$	0	0
$575$	43.7771	1.82563
$576$	−1.47214	−0.0613390
$577$	−30.0000	−1.24892	−0.624458	−	0.781058i	$-0.714680\pi$
$577$	−30.0000	−1.24892	−0.624458	+	0.781058i	$0.714680\pi$
$578$	−1.00000	−0.0415945
$579$	29.5279	1.22714
$580$	−24.9443	−1.03575
$581$	0	0
$582$	0.583592	0.0241907
$583$	3.41641	0.141493
$584$	−13.4164	−0.555175
$585$	−30.8328	−1.27478
$586$	−28.0000	−1.15667
$587$	5.41641	0.223559	0.111780	−	0.993733i	$-0.464345\pi$
$587$	5.41641	0.223559	0.111780	+	0.993733i	$0.464345\pi$
$588$	0	0
$589$	−4.94427	−0.203725
$590$	19.4164	0.799361
$591$	10.2492	0.421597
$592$	1.23607	0.0508021
$593$	−14.9443	−0.613688	−0.306844	−	0.951760i	$-0.599273\pi$
$593$	−14.9443	−0.613688	−0.306844	+	0.951760i	$0.599273\pi$
$594$	4.22291	0.173268
$595$	0	0
$596$	1.05573	0.0432443
$597$	−6.83282	−0.279649
$598$	51.7771	2.11732
$599$	−39.7771	−1.62525	−0.812624	−	0.582789i	$-0.801962\pi$
$599$	−39.7771	−1.62525	−0.812624	+	0.582789i	$0.801962\pi$
$600$	−6.76393	−0.276136
$601$	−14.0000	−0.571072	−0.285536	−	0.958368i	$-0.592172\pi$
$601$	−14.0000	−0.571072	−0.285536	+	0.958368i	$0.592172\pi$
$602$	0	0
$603$	15.4164	0.627805
$604$	4.00000	0.162758
$605$	33.7082	1.37043
$606$	3.05573	0.124130
$607$	8.00000	0.324710	0.162355	−	0.986732i	$-0.448091\pi$
$607$	8.00000	0.324710	0.162355	+	0.986732i	$0.448091\pi$
$608$	0.472136	0.0191476
$609$	0	0
$610$	10.4721	0.424004
$611$	41.8885	1.69463
$612$	1.47214	0.0595076
$613$	8.83282	0.356754	0.178377	−	0.983962i	$-0.442915\pi$
$613$	8.83282	0.356754	0.178377	+	0.983962i	$0.442915\pi$
$614$	−12.4721	−0.503334
$615$	−49.8885	−2.01170
$616$	0	0
$617$	−34.3607	−1.38331	−0.691654	−	0.722229i	$-0.743118\pi$
$617$	−34.3607	−1.38331	−0.691654	+	0.722229i	$0.743118\pi$
$618$	−4.94427	−0.198888
$619$	−12.2918	−0.494049	−0.247024	−	0.969009i	$-0.579453\pi$
$619$	−12.2918	−0.494049	−0.247024	+	0.969009i	$0.579453\pi$
$620$	−33.8885	−1.36100
$621$	−44.2229	−1.77460
$622$	−3.05573	−0.122524
$623$	0	0
$624$	−8.00000	−0.320256
$625$	−22.4164	−0.896656
$626$	21.4164	0.855972
$627$	−0.445825	−0.0178045
$628$	−3.05573	−0.121937
$629$	−1.23607	−0.0492853
$630$	0	0
$631$	20.9443	0.833778	0.416889	−	0.908957i	$-0.363120\pi$
$631$	20.9443	0.833778	0.416889	+	0.908957i	$0.363120\pi$
$632$	1.52786	0.0607752
$633$	−17.6656	−0.702146
$634$	5.81966	0.231128
$635$	−38.8328	−1.54103
$636$	5.52786	0.219194
$637$	0	0
$638$	−5.88854	−0.233130
$639$	−9.52786	−0.376916
$640$	3.23607	0.127917
$641$	26.9443	1.06423	0.532117	−	0.846671i	$-0.321397\pi$
$641$	26.9443	1.06423	0.532117	+	0.846671i	$0.321397\pi$
$642$	−4.00000	−0.157867
$643$	27.1246	1.06969	0.534845	−	0.844950i	$-0.320370\pi$
$643$	27.1246	1.06969	0.534845	+	0.844950i	$0.320370\pi$
$644$	0	0
$645$	25.8885	1.01936
$646$	−0.472136	−0.0185759
$647$	24.3607	0.957717	0.478859	−	0.877892i	$-0.341051\pi$
$647$	24.3607	0.957717	0.478859	+	0.877892i	$0.341051\pi$
$648$	2.41641	0.0949255
$649$	4.58359	0.179922
$650$	35.4164	1.38915
$651$	0	0
$652$	−13.7082	−0.536855
$653$	41.5967	1.62781	0.813903	−	0.581000i	$-0.197339\pi$
$653$	41.5967	1.62781	0.813903	+	0.581000i	$0.197339\pi$
$654$	12.5836	0.492057
$655$	−37.8885	−1.48043
$656$	12.4721	0.486955
$657$	−19.7508	−0.770551
$658$	0	0
$659$	−3.05573	−0.119034	−0.0595171	−	0.998227i	$-0.518956\pi$
$659$	−3.05573	−0.119034	−0.0595171	+	0.998227i	$0.518956\pi$
$660$	−3.05573	−0.118944
$661$	−23.4164	−0.910793	−0.455396	−	0.890289i	$-0.650502\pi$
$661$	−23.4164	−0.910793	−0.455396	+	0.890289i	$0.650502\pi$
$662$	−24.3607	−0.946805
$663$	8.00000	0.310694
$664$	2.00000	0.0776151
$665$	0	0
$666$	1.81966	0.0705104
$667$	61.6656	2.38770
$668$	5.52786	0.213879
$669$	−12.9443	−0.500454
$670$	−33.8885	−1.30923
$671$	2.47214	0.0954358
$672$	0	0
$673$	39.3050	1.51509	0.757547	−	0.652780i	$-0.226398\pi$
$673$	39.3050	1.51509	0.757547	+	0.652780i	$0.226398\pi$
$674$	11.5279	0.444037
$675$	−30.2492	−1.16429
$676$	28.8885	1.11110
$677$	−11.8197	−0.454266	−0.227133	−	0.973864i	$-0.572935\pi$
$677$	−11.8197	−0.454266	−0.227133	+	0.973864i	$0.572935\pi$
$678$	16.5836	0.636889
$679$	0	0
$680$	−3.23607	−0.124098
$681$	26.6950	1.02296
$682$	−8.00000	−0.306336
$683$	23.8197	0.911434	0.455717	−	0.890125i	$-0.349383\pi$
$683$	23.8197	0.911434	0.455717	+	0.890125i	$0.349383\pi$
$684$	0.695048	0.0265758
$685$	−40.3607	−1.54210
$686$	0	0
$687$	−16.0000	−0.610438
$688$	−6.47214	−0.246748
$689$	−28.9443	−1.10269
$690$	32.0000	1.21822
$691$	3.34752	0.127346	0.0636729	−	0.997971i	$-0.479719\pi$
$691$	3.34752	0.127346	0.0636729	+	0.997971i	$0.479719\pi$
$692$	10.6525	0.404946
$693$	0	0
$694$	26.6525	1.01171
$695$	32.9443	1.24965
$696$	−9.52786	−0.361153
$697$	−12.4721	−0.472416
$698$	−30.4721	−1.15339
$699$	−19.6393	−0.742827
$700$	0	0
$701$	44.2492	1.67127	0.835635	−	0.549285i	$-0.185100\pi$
$701$	44.2492	1.67127	0.835635	+	0.549285i	$0.185100\pi$
$702$	−35.7771	−1.35032
$703$	−0.583592	−0.0220106
$704$	0.763932	0.0287918
$705$	25.8885	0.975019
$706$	23.8885	0.899057
$707$	0	0
$708$	7.41641	0.278726
$709$	25.5967	0.961306	0.480653	−	0.876911i	$-0.340400\pi$
$709$	25.5967	0.961306	0.480653	+	0.876911i	$0.340400\pi$
$710$	20.9443	0.786025
$711$	2.24922	0.0843525
$712$	2.00000	0.0749532
$713$	83.7771	3.13748
$714$	0	0
$715$	16.0000	0.598366
$716$	8.94427	0.334263
$717$	16.0000	0.597531
$718$	30.8328	1.15067
$719$	0.583592	0.0217643	0.0108822	−	0.999941i	$-0.496536\pi$
$719$	0.583592	0.0217643	0.0108822	+	0.999941i	$0.496536\pi$
$720$	4.76393	0.177541
$721$	0	0
$722$	18.7771	0.698811
$723$	29.5279	1.09815
$724$	7.23607	0.268926
$725$	42.1803	1.56654
$726$	12.8754	0.477850
$727$	46.4721	1.72356	0.861778	−	0.507285i	$-0.169351\pi$
$727$	46.4721	1.72356	0.861778	+	0.507285i	$0.169351\pi$
$728$	0	0
$729$	24.0557	0.890953
$730$	43.4164	1.60691
$731$	6.47214	0.239381
$732$	4.00000	0.147844
$733$	31.4164	1.16039	0.580196	−	0.814477i	$-0.302976\pi$
$733$	31.4164	1.16039	0.580196	+	0.814477i	$0.302976\pi$
$734$	−11.0557	−0.408074
$735$	0	0
$736$	−8.00000	−0.294884
$737$	−8.00000	−0.294684
$738$	18.3607	0.675866
$739$	−6.83282	−0.251349	−0.125675	−	0.992072i	$-0.540110\pi$
$739$	−6.83282	−0.251349	−0.125675	+	0.992072i	$0.540110\pi$
$740$	−4.00000	−0.147043
$741$	3.77709	0.138755
$742$	0	0
$743$	38.4721	1.41141	0.705703	−	0.708508i	$-0.250631\pi$
$743$	38.4721	1.41141	0.705703	+	0.708508i	$0.250631\pi$
$744$	−12.9443	−0.474560
$745$	−3.41641	−0.125167
$746$	13.4164	0.491210
$747$	2.94427	0.107725
$748$	−0.763932	−0.0279321
$749$	0	0
$750$	1.88854	0.0689599
$751$	11.0557	0.403429	0.201715	−	0.979444i	$-0.435349\pi$
$751$	11.0557	0.403429	0.201715	+	0.979444i	$0.435349\pi$
$752$	−6.47214	−0.236015
$753$	−17.3050	−0.630627
$754$	49.8885	1.81683
$755$	−12.9443	−0.471090
$756$	0	0
$757$	18.0000	0.654221	0.327111	−	0.944986i	$-0.393925\pi$
$757$	18.0000	0.654221	0.327111	+	0.944986i	$0.393925\pi$
$758$	−31.5967	−1.14765
$759$	7.55418	0.274199
$760$	−1.52786	−0.0554215
$761$	31.8885	1.15596	0.577979	−	0.816051i	$-0.303841\pi$
$761$	31.8885	1.15596	0.577979	+	0.816051i	$0.303841\pi$
$762$	−14.8328	−0.537336
$763$	0	0
$764$	−4.94427	−0.178877
$765$	−4.76393	−0.172240
$766$	8.94427	0.323170
$767$	−38.8328	−1.40217
$768$	1.23607	0.0446028
$769$	−48.8328	−1.76096	−0.880478	−	0.474087i	$-0.842778\pi$
$769$	−48.8328	−1.76096	−0.880478	+	0.474087i	$0.842778\pi$
$770$	0	0
$771$	2.47214	0.0890318
$772$	23.8885	0.859768
$773$	−4.00000	−0.143870	−0.0719350	−	0.997409i	$-0.522917\pi$
$773$	−4.00000	−0.143870	−0.0719350	+	0.997409i	$0.522917\pi$
$774$	−9.52786	−0.342472
$775$	57.3050	2.05845
$776$	0.472136	0.0169487
$777$	0	0
$778$	−26.0000	−0.932145
$779$	−5.88854	−0.210979
$780$	25.8885	0.926959
$781$	4.94427	0.176920
$782$	8.00000	0.286079
$783$	−42.6099	−1.52275
$784$	0	0
$785$	9.88854	0.352937
$786$	−14.4721	−0.516204
$787$	3.70820	0.132183	0.0660916	−	0.997814i	$-0.478947\pi$
$787$	3.70820	0.132183	0.0660916	+	0.997814i	$0.478947\pi$
$788$	8.29180	0.295383
$789$	30.8328	1.09768
$790$	−4.94427	−0.175909
$791$	0	0
$792$	1.12461	0.0399613
$793$	−20.9443	−0.743753
$794$	−4.18034	−0.148355
$795$	−17.8885	−0.634441
$796$	−5.52786	−0.195930
$797$	−12.5836	−0.445734	−0.222867	−	0.974849i	$-0.571542\pi$
$797$	−12.5836	−0.445734	−0.222867	+	0.974849i	$0.571542\pi$
$798$	0	0
$799$	6.47214	0.228968
$800$	−5.47214	−0.193469
$801$	2.94427	0.104031
$802$	14.9443	0.527701
$803$	10.2492	0.361687
$804$	−12.9443	−0.456509
$805$	0	0
$806$	67.7771	2.38735
$807$	16.9443	0.596467
$808$	2.47214	0.0869694
$809$	18.9443	0.666045	0.333023	−	0.942919i	$-0.391931\pi$
$809$	18.9443	0.666045	0.333023	+	0.942919i	$0.391931\pi$
$810$	−7.81966	−0.274755
$811$	42.1803	1.48115	0.740576	−	0.671973i	$-0.234553\pi$
$811$	42.1803	1.48115	0.740576	+	0.671973i	$0.234553\pi$
$812$	0	0
$813$	9.16718	0.321507
$814$	−0.944272	−0.0330967
$815$	44.3607	1.55389
$816$	−1.23607	−0.0432710
$817$	3.05573	0.106906
$818$	−2.94427	−0.102944
$819$	0	0
$820$	−40.3607	−1.40946
$821$	33.0132	1.15217	0.576084	−	0.817391i	$-0.304580\pi$
$821$	33.0132	1.15217	0.576084	+	0.817391i	$0.304580\pi$
$822$	−15.4164	−0.537709
$823$	6.47214	0.225604	0.112802	−	0.993617i	$-0.464017\pi$
$823$	6.47214	0.225604	0.112802	+	0.993617i	$0.464017\pi$
$824$	−4.00000	−0.139347
$825$	5.16718	0.179898
$826$	0	0
$827$	11.5967	0.403258	0.201629	−	0.979462i	$-0.435376\pi$
$827$	11.5967	0.403258	0.201629	+	0.979462i	$0.435376\pi$
$828$	−11.7771	−0.409282
$829$	−23.0557	−0.800759	−0.400379	−	0.916350i	$-0.631122\pi$
$829$	−23.0557	−0.800759	−0.400379	+	0.916350i	$0.631122\pi$
$830$	−6.47214	−0.224651
$831$	10.6950	0.371007
$832$	−6.47214	−0.224381
$833$	0	0
$834$	12.5836	0.435734
$835$	−17.8885	−0.619059
$836$	−0.360680	−0.0124744
$837$	−57.8885	−2.00092
$838$	28.0689	0.969623
$839$	−52.3607	−1.80769	−0.903846	−	0.427859i	$-0.859268\pi$
$839$	−52.3607	−1.80769	−0.903846	+	0.427859i	$0.859268\pi$
$840$	0	0
$841$	30.4164	1.04884
$842$	24.4721	0.843365
$843$	15.4164	0.530969
$844$	−14.2918	−0.491944
$845$	−93.4853	−3.21599
$846$	−9.52786	−0.327575
$847$	0	0
$848$	4.47214	0.153574
$849$	−29.3050	−1.00574
$850$	5.47214	0.187693
$851$	9.88854	0.338975
$852$	8.00000	0.274075
$853$	16.7639	0.573986	0.286993	−	0.957933i	$-0.407344\pi$
$853$	16.7639	0.573986	0.286993	+	0.957933i	$0.407344\pi$
$854$	0	0
$855$	−2.24922	−0.0769218
$856$	−3.23607	−0.110607
$857$	12.4721	0.426040	0.213020	−	0.977048i	$-0.431670\pi$
$857$	12.4721	0.426040	0.213020	+	0.977048i	$0.431670\pi$
$858$	6.11146	0.208642
$859$	0.111456	0.00380284	0.00190142	−	0.999998i	$-0.499395\pi$
$859$	0.111456	0.00380284	0.00190142	+	0.999998i	$0.499395\pi$
$860$	20.9443	0.714194
$861$	0	0
$862$	−4.94427	−0.168403
$863$	−0.944272	−0.0321434	−0.0160717	−	0.999871i	$-0.505116\pi$
$863$	−0.944272	−0.0321434	−0.0160717	+	0.999871i	$0.505116\pi$
$864$	5.52786	0.188062
$865$	−34.4721	−1.17209
$866$	−6.94427	−0.235976
$867$	1.23607	0.0419791
$868$	0	0
$869$	−1.16718	−0.0395940
$870$	30.8328	1.04533
$871$	67.7771	2.29654
$872$	10.1803	0.344750
$873$	0.695048	0.0235238
$874$	3.77709	0.127762
$875$	0	0
$876$	16.5836	0.560308
$877$	−31.1246	−1.05100	−0.525502	−	0.850793i	$-0.676122\pi$
$877$	−31.1246	−1.05100	−0.525502	+	0.850793i	$0.676122\pi$
$878$	−20.9443	−0.706835
$879$	34.6099	1.16736
$880$	−2.47214	−0.0833357
$881$	29.0557	0.978912	0.489456	−	0.872028i	$-0.337195\pi$
$881$	29.0557	0.978912	0.489456	+	0.872028i	$0.337195\pi$
$882$	0	0
$883$	−23.4164	−0.788025	−0.394012	−	0.919105i	$-0.628913\pi$
$883$	−23.4164	−0.788025	−0.394012	+	0.919105i	$0.628913\pi$
$884$	6.47214	0.217681
$885$	−24.0000	−0.806751
$886$	−36.3607	−1.22156
$887$	−20.3607	−0.683645	−0.341822	−	0.939765i	$-0.611044\pi$
$887$	−20.3607	−0.683645	−0.341822	+	0.939765i	$0.611044\pi$
$888$	−1.52786	−0.0512718
$889$	0	0
$890$	−6.47214	−0.216946
$891$	−1.84597	−0.0618424
$892$	−10.4721	−0.350633
$893$	3.05573	0.102256
$894$	−1.30495	−0.0436441
$895$	−28.9443	−0.967500
$896$	0	0
$897$	−64.0000	−2.13690
$898$	17.4164	0.581193
$899$	80.7214	2.69221
$900$	−8.05573	−0.268524
$901$	−4.47214	−0.148988
$902$	−9.52786	−0.317243
$903$	0	0
$904$	13.4164	0.446223
$905$	−23.4164	−0.778388
$906$	−4.94427	−0.164262
$907$	−11.2361	−0.373088	−0.186544	−	0.982447i	$-0.559729\pi$
$907$	−11.2361	−0.373088	−0.186544	+	0.982447i	$0.559729\pi$
$908$	21.5967	0.716713
$909$	3.63932	0.120709
$910$	0	0
$911$	−32.3607	−1.07216	−0.536079	−	0.844168i	$-0.680095\pi$
$911$	−32.3607	−1.07216	−0.536079	+	0.844168i	$0.680095\pi$
$912$	−0.583592	−0.0193247
$913$	−1.52786	−0.0505649
$914$	19.8885	0.657855
$915$	−12.9443	−0.427924
$916$	−12.9443	−0.427691
$917$	0	0
$918$	−5.52786	−0.182447
$919$	−44.9443	−1.48257	−0.741287	−	0.671188i	$-0.765784\pi$
$919$	−44.9443	−1.48257	−0.741287	+	0.671188i	$0.765784\pi$
$920$	25.8885	0.853520
$921$	15.4164	0.507988
$922$	−14.4721	−0.476614
$923$	−41.8885	−1.37878
$924$	0	0
$925$	6.76393	0.222397
$926$	−15.0557	−0.494762
$927$	−5.88854	−0.193405
$928$	−7.70820	−0.253034
$929$	30.0000	0.984268	0.492134	−	0.870519i	$-0.336217\pi$
$929$	30.0000	0.984268	0.492134	+	0.870519i	$0.336217\pi$
$930$	41.8885	1.37358
$931$	0	0
$932$	−15.8885	−0.520447
$933$	3.77709	0.123656
$934$	34.3607	1.12432
$935$	2.47214	0.0808475
$936$	−9.52786	−0.311428
$937$	−55.8885	−1.82580	−0.912900	−	0.408184i	$-0.866162\pi$
$937$	−55.8885	−1.82580	−0.912900	+	0.408184i	$0.866162\pi$
$938$	0	0
$939$	−26.4721	−0.863886
$940$	20.9443	0.683127
$941$	−18.8754	−0.615320	−0.307660	−	0.951496i	$-0.599546\pi$
$941$	−18.8754	−0.615320	−0.307660	+	0.951496i	$0.599546\pi$
$942$	3.77709	0.123064
$943$	99.7771	3.24919
$944$	6.00000	0.195283
$945$	0	0
$946$	4.94427	0.160752
$947$	−6.87539	−0.223420	−0.111710	−	0.993741i	$-0.535633\pi$
$947$	−6.87539	−0.223420	−0.111710	+	0.993741i	$0.535633\pi$
$948$	−1.88854	−0.0613371
$949$	−86.8328	−2.81871
$950$	2.58359	0.0838228
$951$	−7.19350	−0.233265
$952$	0	0
$953$	22.9443	0.743238	0.371619	−	0.928385i	$-0.378803\pi$
$953$	22.9443	0.743238	0.371619	+	0.928385i	$0.378803\pi$
$954$	6.58359	0.213152
$955$	16.0000	0.517748
$956$	12.9443	0.418648
$957$	7.27864	0.235285
$958$	7.41641	0.239613
$959$	0	0
$960$	−4.00000	−0.129099
$961$	78.6656	2.53760
$962$	8.00000	0.257930
$963$	−4.76393	−0.153516
$964$	23.8885	0.769398
$965$	−77.3050	−2.48853
$966$	0	0
$967$	27.0557	0.870054	0.435027	−	0.900418i	$-0.356739\pi$
$967$	27.0557	0.870054	0.435027	+	0.900418i	$0.356739\pi$
$968$	10.4164	0.334796
$969$	0.583592	0.0187477
$970$	−1.52786	−0.0490568
$971$	28.8328	0.925289	0.462645	−	0.886544i	$-0.346901\pi$
$971$	28.8328	0.925289	0.462645	+	0.886544i	$0.346901\pi$
$972$	13.5967	0.436116
$973$	0	0
$974$	−20.9443	−0.671098
$975$	−43.7771	−1.40199
$976$	3.23607	0.103584
$977$	−41.0557	−1.31349	−0.656745	−	0.754113i	$-0.728067\pi$
$977$	−41.0557	−1.31349	−0.656745	+	0.754113i	$0.728067\pi$
$978$	16.9443	0.541818
$979$	−1.52786	−0.0488307
$980$	0	0
$981$	14.9868	0.478493
$982$	15.0557	0.480448
$983$	−45.5279	−1.45211	−0.726057	−	0.687635i	$-0.758649\pi$
$983$	−45.5279	−1.45211	−0.726057	+	0.687635i	$0.758649\pi$
$984$	−15.4164	−0.491457
$985$	−26.8328	−0.854965
$986$	7.70820	0.245479
$987$	0	0
$988$	3.05573	0.0972157
$989$	−51.7771	−1.64642
$990$	−3.63932	−0.115665
$991$	58.2492	1.85035	0.925174	−	0.379544i	$-0.123919\pi$
$991$	58.2492	1.85035	0.925174	+	0.379544i	$0.123919\pi$
$992$	−10.4721	−0.332491
$993$	30.1115	0.955558
$994$	0	0
$995$	17.8885	0.567105
$996$	−2.47214	−0.0783326
$997$	−37.4853	−1.18717	−0.593586	−	0.804771i	$-0.702288\pi$
$997$	−37.4853	−1.18717	−0.593586	+	0.804771i	$0.702288\pi$
$998$	9.34752	0.295891
$999$	−6.83282	−0.216181

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1666.2.a.o.1.2		2
7.6	odd	2		238.2.a.f.1.1	✓	2
21.20	even	2		2142.2.a.x.1.1		2
28.27	even	2		1904.2.a.f.1.2		2
35.34	odd	2		5950.2.a.x.1.2		2
56.13	odd	2		7616.2.a.n.1.2		2
56.27	even	2		7616.2.a.y.1.1		2
119.118	odd	2		4046.2.a.v.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
238.2.a.f.1.1	✓	2	7.6	odd	2
1666.2.a.o.1.2		2	1.1	even	1	trivial
1904.2.a.f.1.2		2	28.27	even	2
2142.2.a.x.1.1		2	21.20	even	2
4046.2.a.v.1.2		2	119.118	odd	2
5950.2.a.x.1.2		2	35.34	odd	2
7616.2.a.n.1.2		2	56.13	odd	2
7616.2.a.y.1.1		2	56.27	even	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:	\( N \)	\(=\)	\( 1666 = 2 \cdot 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1666.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.23607 q^{3} +1.00000 q^{4} -3.23607 q^{5} -1.23607 q^{6} -1.00000 q^{8} -1.47214 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.23607 q^{3} +1.00000 q^{4} -3.23607 q^{5} -1.23607 q^{6} -1.00000 q^{8} -1.47214 q^{9} +3.23607 q^{10} +0.763932 q^{11} +1.23607 q^{12} -6.47214 q^{13} -4.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.47214 q^{18} -0.472136 q^{19} -3.23607 q^{20} -0.763932 q^{22} +8.00000 q^{23} -1.23607 q^{24} +5.47214 q^{25} +6.47214 q^{26} -5.52786 q^{27} +7.70820 q^{29} +4.00000 q^{30} +10.4721 q^{31} -1.00000 q^{32} +0.944272 q^{33} +1.00000 q^{34} -1.47214 q^{36} +1.23607 q^{37} +0.472136 q^{38} -8.00000 q^{39} +3.23607 q^{40} +12.4721 q^{41} -6.47214 q^{43} +0.763932 q^{44} +4.76393 q^{45} -8.00000 q^{46} -6.47214 q^{47} +1.23607 q^{48} -5.47214 q^{50} -1.23607 q^{51} -6.47214 q^{52} +4.47214 q^{53} +5.52786 q^{54} -2.47214 q^{55} -0.583592 q^{57} -7.70820 q^{58} +6.00000 q^{59} -4.00000 q^{60} +3.23607 q^{61} -10.4721 q^{62} +1.00000 q^{64} +20.9443 q^{65} -0.944272 q^{66} -10.4721 q^{67} -1.00000 q^{68} +9.88854 q^{69} +6.47214 q^{71} +1.47214 q^{72} +13.4164 q^{73} -1.23607 q^{74} +6.76393 q^{75} -0.472136 q^{76} +8.00000 q^{78} -1.52786 q^{79} -3.23607 q^{80} -2.41641 q^{81} -12.4721 q^{82} -2.00000 q^{83} +3.23607 q^{85} +6.47214 q^{86} +9.52786 q^{87} -0.763932 q^{88} -2.00000 q^{89} -4.76393 q^{90} +8.00000 q^{92} +12.9443 q^{93} +6.47214 q^{94} +1.52786 q^{95} -1.23607 q^{96} -0.472136 q^{97} -1.12461 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{8} + 6 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^8 + 6 * q^9	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{8} + 6 q^{9} + 2 q^{10} + 6 q^{11} - 2 q^{12} - 4 q^{13} - 8 q^{15} + 2 q^{16} - 2 q^{17} - 6 q^{18} + 8 q^{19} - 2 q^{20} - 6 q^{22} + 16 q^{23} + 2 q^{24} + 2 q^{25} + 4 q^{26} - 20 q^{27} + 2 q^{29} + 8 q^{30} + 12 q^{31} - 2 q^{32} - 16 q^{33} + 2 q^{34} + 6 q^{36} - 2 q^{37} - 8 q^{38} - 16 q^{39} + 2 q^{40} + 16 q^{41} - 4 q^{43} + 6 q^{44} + 14 q^{45} - 16 q^{46} - 4 q^{47} - 2 q^{48} - 2 q^{50} + 2 q^{51} - 4 q^{52} + 20 q^{54} + 4 q^{55} - 28 q^{57} - 2 q^{58} + 12 q^{59} - 8 q^{60} + 2 q^{61} - 12 q^{62} + 2 q^{64} + 24 q^{65} + 16 q^{66} - 12 q^{67} - 2 q^{68} - 16 q^{69} + 4 q^{71} - 6 q^{72} + 2 q^{74} + 18 q^{75} + 8 q^{76} + 16 q^{78} - 12 q^{79} - 2 q^{80} + 22 q^{81} - 16 q^{82} - 4 q^{83} + 2 q^{85} + 4 q^{86} + 28 q^{87} - 6 q^{88} - 4 q^{89} - 14 q^{90} + 16 q^{92} + 8 q^{93} + 4 q^{94} + 12 q^{95} + 2 q^{96} + 8 q^{97} + 38 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^8 + 6 * q^9 + 2 * q^10 + 6 * q^11 - 2 * q^12 - 4 * q^13 - 8 * q^15 + 2 * q^16 - 2 * q^17 - 6 * q^18 + 8 * q^19 - 2 * q^20 - 6 * q^22 + 16 * q^23 + 2 * q^24 + 2 * q^25 + 4 * q^26 - 20 * q^27 + 2 * q^29 + 8 * q^30 + 12 * q^31 - 2 * q^32 - 16 * q^33 + 2 * q^34 + 6 * q^36 - 2 * q^37 - 8 * q^38 - 16 * q^39 + 2 * q^40 + 16 * q^41 - 4 * q^43 + 6 * q^44 + 14 * q^45 - 16 * q^46 - 4 * q^47 - 2 * q^48 - 2 * q^50 + 2 * q^51 - 4 * q^52 + 20 * q^54 + 4 * q^55 - 28 * q^57 - 2 * q^58 + 12 * q^59 - 8 * q^60 + 2 * q^61 - 12 * q^62 + 2 * q^64 + 24 * q^65 + 16 * q^66 - 12 * q^67 - 2 * q^68 - 16 * q^69 + 4 * q^71 - 6 * q^72 + 2 * q^74 + 18 * q^75 + 8 * q^76 + 16 * q^78 - 12 * q^79 - 2 * q^80 + 22 * q^81 - 16 * q^82 - 4 * q^83 + 2 * q^85 + 4 * q^86 + 28 * q^87 - 6 * q^88 - 4 * q^89 - 14 * q^90 + 16 * q^92 + 8 * q^93 + 4 * q^94 + 12 * q^95 + 2 * q^96 + 8 * q^97 + 38 * q^99

Introduction

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