LMFDB - Embedded newform 6762.2.a.cb.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6762,2,Mod(1,6762)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6762, 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("6762.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6762.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:	$53.9948418468$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 138)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	6762.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.23607 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.23607 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +3.23607 q^{10} -0.763932 q^{11} -1.00000 q^{12} +4.47214 q^{13} -3.23607 q^{15} +1.00000 q^{16} +4.00000 q^{17} +1.00000 q^{18} +7.70820 q^{19} +3.23607 q^{20} -0.763932 q^{22} +1.00000 q^{23} -1.00000 q^{24} +5.47214 q^{25} +4.47214 q^{26} -1.00000 q^{27} +4.47214 q^{29} -3.23607 q^{30} -6.47214 q^{31} +1.00000 q^{32} +0.763932 q^{33} +4.00000 q^{34} +1.00000 q^{36} +6.76393 q^{37} +7.70820 q^{38} -4.47214 q^{39} +3.23607 q^{40} +2.00000 q^{41} -9.23607 q^{43} -0.763932 q^{44} +3.23607 q^{45} +1.00000 q^{46} -4.00000 q^{47} -1.00000 q^{48} +5.47214 q^{50} -4.00000 q^{51} +4.47214 q^{52} +0.763932 q^{53} -1.00000 q^{54} -2.47214 q^{55} -7.70820 q^{57} +4.47214 q^{58} -8.94427 q^{59} -3.23607 q^{60} -5.23607 q^{61} -6.47214 q^{62} +1.00000 q^{64} +14.4721 q^{65} +0.763932 q^{66} -3.70820 q^{67} +4.00000 q^{68} -1.00000 q^{69} -8.94427 q^{71} +1.00000 q^{72} -4.47214 q^{73} +6.76393 q^{74} -5.47214 q^{75} +7.70820 q^{76} -4.47214 q^{78} -4.47214 q^{79} +3.23607 q^{80} +1.00000 q^{81} +2.00000 q^{82} -8.76393 q^{83} +12.9443 q^{85} -9.23607 q^{86} -4.47214 q^{87} -0.763932 q^{88} +1.52786 q^{89} +3.23607 q^{90} +1.00000 q^{92} +6.47214 q^{93} -4.00000 q^{94} +24.9443 q^{95} -1.00000 q^{96} +8.47214 q^{97} -0.763932 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 6 q^{11} - 2 q^{12} - 2 q^{15} + 2 q^{16} + 8 q^{17} + 2 q^{18} + 2 q^{19} + 2 q^{20} - 6 q^{22} + 2 q^{23} - 2 q^{24} + 2 q^{25} - 2 q^{27} - 2 q^{30} - 4 q^{31} + 2 q^{32} + 6 q^{33} + 8 q^{34} + 2 q^{36} + 18 q^{37} + 2 q^{38} + 2 q^{40} + 4 q^{41} - 14 q^{43} - 6 q^{44} + 2 q^{45} + 2 q^{46} - 8 q^{47} - 2 q^{48} + 2 q^{50} - 8 q^{51} + 6 q^{53} - 2 q^{54} + 4 q^{55} - 2 q^{57} - 2 q^{60} - 6 q^{61} - 4 q^{62} + 2 q^{64} + 20 q^{65} + 6 q^{66} + 6 q^{67} + 8 q^{68} - 2 q^{69} + 2 q^{72} + 18 q^{74} - 2 q^{75} + 2 q^{76} + 2 q^{80} + 2 q^{81} + 4 q^{82} - 22 q^{83} + 8 q^{85} - 14 q^{86} - 6 q^{88} + 12 q^{89} + 2 q^{90} + 2 q^{92} + 4 q^{93} - 8 q^{94} + 32 q^{95} - 2 q^{96} + 8 q^{97} - 6 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 - 6 * q^11 - 2 * q^12 - 2 * q^15 + 2 * q^16 + 8 * q^17 + 2 * q^18 + 2 * q^19 + 2 * q^20 - 6 * q^22 + 2 * q^23 - 2 * q^24 + 2 * q^25 - 2 * q^27 - 2 * q^30 - 4 * q^31 + 2 * q^32 + 6 * q^33 + 8 * q^34 + 2 * q^36 + 18 * q^37 + 2 * q^38 + 2 * q^40 + 4 * q^41 - 14 * q^43 - 6 * q^44 + 2 * q^45 + 2 * q^46 - 8 * q^47 - 2 * q^48 + 2 * q^50 - 8 * q^51 + 6 * q^53 - 2 * q^54 + 4 * q^55 - 2 * q^57 - 2 * q^60 - 6 * q^61 - 4 * q^62 + 2 * q^64 + 20 * q^65 + 6 * q^66 + 6 * q^67 + 8 * q^68 - 2 * q^69 + 2 * q^72 + 18 * q^74 - 2 * q^75 + 2 * q^76 + 2 * q^80 + 2 * q^81 + 4 * q^82 - 22 * q^83 + 8 * q^85 - 14 * q^86 - 6 * q^88 + 12 * q^89 + 2 * q^90 + 2 * q^92 + 4 * q^93 - 8 * q^94 + 32 * q^95 - 2 * q^96 + 8 * q^97 - 6 * 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
$5$	3.23607	1.44721	0.723607	−	0.690212i	$-0.242483\pi$
$5$	3.23607	1.44721	0.723607	+	0.690212i	$0.242483\pi$
$6$	−1.00000	−0.408248
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	3.23607	1.02333
$11$	−0.763932	−0.230334	−0.115167	−	0.993346i	$-0.536740\pi$
$11$	−0.763932	−0.230334	−0.115167	+	0.993346i	$0.536740\pi$
$12$	−1.00000	−0.288675
$13$	4.47214	1.24035	0.620174	−	0.784465i	$-0.287062\pi$
$13$	4.47214	1.24035	0.620174	+	0.784465i	$0.287062\pi$
$14$	0	0
$15$	−3.23607	−0.835549
$16$	1.00000	0.250000
$17$	4.00000	0.970143	0.485071	−	0.874475i	$-0.338794\pi$
$17$	4.00000	0.970143	0.485071	+	0.874475i	$0.338794\pi$
$18$	1.00000	0.235702
$19$	7.70820	1.76838	0.884192	−	0.467124i	$-0.154710\pi$
$19$	7.70820	1.76838	0.884192	+	0.467124i	$0.154710\pi$
$20$	3.23607	0.723607
$21$	0	0
$22$	−0.763932	−0.162871
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−1.00000	−0.204124
$25$	5.47214	1.09443
$26$	4.47214	0.877058
$27$	−1.00000	−0.192450
$28$	0	0
$29$	4.47214	0.830455	0.415227	−	0.909718i	$-0.363702\pi$
$29$	4.47214	0.830455	0.415227	+	0.909718i	$0.363702\pi$
$30$	−3.23607	−0.590822
$31$	−6.47214	−1.16243	−0.581215	−	0.813750i	$-0.697422\pi$
$31$	−6.47214	−1.16243	−0.581215	+	0.813750i	$0.697422\pi$
$32$	1.00000	0.176777
$33$	0.763932	0.132983
$34$	4.00000	0.685994
$35$	0	0
$36$	1.00000	0.166667
$37$	6.76393	1.11198	0.555992	−	0.831188i	$-0.312339\pi$
$37$	6.76393	1.11198	0.555992	+	0.831188i	$0.312339\pi$
$38$	7.70820	1.25044
$39$	−4.47214	−0.716115
$40$	3.23607	0.511667
$41$	2.00000	0.312348	0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000	0.312348	0.156174	+	0.987730i	$0.450084\pi$
$42$	0	0
$43$	−9.23607	−1.40849	−0.704244	−	0.709958i	$-0.748714\pi$
$43$	−9.23607	−1.40849	−0.704244	+	0.709958i	$0.748714\pi$
$44$	−0.763932	−0.115167
$45$	3.23607	0.482405
$46$	1.00000	0.147442
$47$	−4.00000	−0.583460	−0.291730	−	0.956501i	$-0.594231\pi$
$47$	−4.00000	−0.583460	−0.291730	+	0.956501i	$0.594231\pi$
$48$	−1.00000	−0.144338
$49$	0	0
$50$	5.47214	0.773877
$51$	−4.00000	−0.560112
$52$	4.47214	0.620174
$53$	0.763932	0.104934	0.0524671	−	0.998623i	$-0.483292\pi$
$53$	0.763932	0.104934	0.0524671	+	0.998623i	$0.483292\pi$
$54$	−1.00000	−0.136083
$55$	−2.47214	−0.333343
$56$	0	0
$57$	−7.70820	−1.02098
$58$	4.47214	0.587220
$59$	−8.94427	−1.16445	−0.582223	−	0.813029i	$-0.697817\pi$
$59$	−8.94427	−1.16445	−0.582223	+	0.813029i	$0.697817\pi$
$60$	−3.23607	−0.417775
$61$	−5.23607	−0.670410	−0.335205	−	0.942145i	$-0.608806\pi$
$61$	−5.23607	−0.670410	−0.335205	+	0.942145i	$0.608806\pi$
$62$	−6.47214	−0.821962
$63$	0	0
$64$	1.00000	0.125000
$65$	14.4721	1.79505
$66$	0.763932	0.0940335
$67$	−3.70820	−0.453029	−0.226515	−	0.974008i	$-0.572733\pi$
$67$	−3.70820	−0.453029	−0.226515	+	0.974008i	$0.572733\pi$
$68$	4.00000	0.485071
$69$	−1.00000	−0.120386
$70$	0	0
$71$	−8.94427	−1.06149	−0.530745	−	0.847532i	$-0.678088\pi$
$71$	−8.94427	−1.06149	−0.530745	+	0.847532i	$0.678088\pi$
$72$	1.00000	0.117851
$73$	−4.47214	−0.523424	−0.261712	−	0.965146i	$-0.584287\pi$
$73$	−4.47214	−0.523424	−0.261712	+	0.965146i	$0.584287\pi$
$74$	6.76393	0.786291
$75$	−5.47214	−0.631868
$76$	7.70820	0.884192
$77$	0	0
$78$	−4.47214	−0.506370
$79$	−4.47214	−0.503155	−0.251577	−	0.967837i	$-0.580949\pi$
$79$	−4.47214	−0.503155	−0.251577	+	0.967837i	$0.580949\pi$
$80$	3.23607	0.361803
$81$	1.00000	0.111111
$82$	2.00000	0.220863
$83$	−8.76393	−0.961967	−0.480983	−	0.876730i	$-0.659720\pi$
$83$	−8.76393	−0.961967	−0.480983	+	0.876730i	$0.659720\pi$
$84$	0	0
$85$	12.9443	1.40400
$86$	−9.23607	−0.995951
$87$	−4.47214	−0.479463
$88$	−0.763932	−0.0814354
$89$	1.52786	0.161953	0.0809766	−	0.996716i	$-0.474196\pi$
$89$	1.52786	0.161953	0.0809766	+	0.996716i	$0.474196\pi$
$90$	3.23607	0.341112
$91$	0	0
$92$	1.00000	0.104257
$93$	6.47214	0.671129
$94$	−4.00000	−0.412568
$95$	24.9443	2.55923
$96$	−1.00000	−0.102062
$97$	8.47214	0.860215	0.430108	−	0.902778i	$-0.358476\pi$
$97$	8.47214	0.860215	0.430108	+	0.902778i	$0.358476\pi$
$98$	0	0
$99$	−0.763932	−0.0767781
$100$	5.47214	0.547214
$101$	4.47214	0.444994	0.222497	−	0.974933i	$-0.428579\pi$
$101$	4.47214	0.444994	0.222497	+	0.974933i	$0.428579\pi$
$102$	−4.00000	−0.396059
$103$	6.00000	0.591198	0.295599	−	0.955312i	$-0.404481\pi$
$103$	6.00000	0.591198	0.295599	+	0.955312i	$0.404481\pi$
$104$	4.47214	0.438529
$105$	0	0
$106$	0.763932	0.0741996
$107$	18.6525	1.80320	0.901601	−	0.432568i	$-0.142392\pi$
$107$	18.6525	1.80320	0.901601	+	0.432568i	$0.142392\pi$
$108$	−1.00000	−0.0962250
$109$	9.23607	0.884655	0.442327	−	0.896854i	$-0.354153\pi$
$109$	9.23607	0.884655	0.442327	+	0.896854i	$0.354153\pi$
$110$	−2.47214	−0.235709
$111$	−6.76393	−0.642004
$112$	0	0
$113$	−14.4721	−1.36142	−0.680712	−	0.732551i	$-0.738329\pi$
$113$	−14.4721	−1.36142	−0.680712	+	0.732551i	$0.738329\pi$
$114$	−7.70820	−0.721939
$115$	3.23607	0.301765
$116$	4.47214	0.415227
$117$	4.47214	0.413449
$118$	−8.94427	−0.823387
$119$	0	0
$120$	−3.23607	−0.295411
$121$	−10.4164	−0.946946
$122$	−5.23607	−0.474051
$123$	−2.00000	−0.180334
$124$	−6.47214	−0.581215
$125$	1.52786	0.136656
$126$	0	0
$127$	−4.00000	−0.354943	−0.177471	−	0.984126i	$-0.556792\pi$
$127$	−4.00000	−0.354943	−0.177471	+	0.984126i	$0.556792\pi$
$128$	1.00000	0.0883883
$129$	9.23607	0.813190
$130$	14.4721	1.26929
$131$	18.4721	1.61392	0.806959	−	0.590607i	$-0.201112\pi$
$131$	18.4721	1.61392	0.806959	+	0.590607i	$0.201112\pi$
$132$	0.763932	0.0664917
$133$	0	0
$134$	−3.70820	−0.320340
$135$	−3.23607	−0.278516
$136$	4.00000	0.342997
$137$	20.9443	1.78939	0.894695	−	0.446678i	$-0.147393\pi$
$137$	20.9443	1.78939	0.894695	+	0.446678i	$0.147393\pi$
$138$	−1.00000	−0.0851257
$139$	−0.944272	−0.0800921	−0.0400460	−	0.999198i	$-0.512750\pi$
$139$	−0.944272	−0.0800921	−0.0400460	+	0.999198i	$0.512750\pi$
$140$	0	0
$141$	4.00000	0.336861
$142$	−8.94427	−0.750587
$143$	−3.41641	−0.285694
$144$	1.00000	0.0833333
$145$	14.4721	1.20185
$146$	−4.47214	−0.370117
$147$	0	0
$148$	6.76393	0.555992
$149$	1.70820	0.139942	0.0699708	−	0.997549i	$-0.477709\pi$
$149$	1.70820	0.139942	0.0699708	+	0.997549i	$0.477709\pi$
$150$	−5.47214	−0.446798
$151$	−5.52786	−0.449851	−0.224926	−	0.974376i	$-0.572214\pi$
$151$	−5.52786	−0.449851	−0.224926	+	0.974376i	$0.572214\pi$
$152$	7.70820	0.625218
$153$	4.00000	0.323381
$154$	0	0
$155$	−20.9443	−1.68228
$156$	−4.47214	−0.358057
$157$	−24.6525	−1.96748	−0.983741	−	0.179594i	$-0.942522\pi$
$157$	−24.6525	−1.96748	−0.983741	+	0.179594i	$0.942522\pi$
$158$	−4.47214	−0.355784
$159$	−0.763932	−0.0605838
$160$	3.23607	0.255834
$161$	0	0
$162$	1.00000	0.0785674
$163$	6.47214	0.506937	0.253468	−	0.967344i	$-0.418429\pi$
$163$	6.47214	0.506937	0.253468	+	0.967344i	$0.418429\pi$
$164$	2.00000	0.156174
$165$	2.47214	0.192456
$166$	−8.76393	−0.680213
$167$	0.944272	0.0730700	0.0365350	−	0.999332i	$-0.488368\pi$
$167$	0.944272	0.0730700	0.0365350	+	0.999332i	$0.488368\pi$
$168$	0	0
$169$	7.00000	0.538462
$170$	12.9443	0.992780
$171$	7.70820	0.589461
$172$	−9.23607	−0.704244
$173$	−9.41641	−0.715916	−0.357958	−	0.933738i	$-0.616527\pi$
$173$	−9.41641	−0.715916	−0.357958	+	0.933738i	$0.616527\pi$
$174$	−4.47214	−0.339032
$175$	0	0
$176$	−0.763932	−0.0575835
$177$	8.94427	0.672293
$178$	1.52786	0.114518
$179$	−7.41641	−0.554328	−0.277164	−	0.960823i	$-0.589395\pi$
$179$	−7.41641	−0.554328	−0.277164	+	0.960823i	$0.589395\pi$
$180$	3.23607	0.241202
$181$	6.76393	0.502759	0.251380	−	0.967889i	$-0.419116\pi$
$181$	6.76393	0.502759	0.251380	+	0.967889i	$0.419116\pi$
$182$	0	0
$183$	5.23607	0.387061
$184$	1.00000	0.0737210
$185$	21.8885	1.60928
$186$	6.47214	0.474560
$187$	−3.05573	−0.223457
$188$	−4.00000	−0.291730
$189$	0	0
$190$	24.9443	1.80965
$191$	−2.47214	−0.178877	−0.0894387	−	0.995992i	$-0.528507\pi$
$191$	−2.47214	−0.178877	−0.0894387	+	0.995992i	$0.528507\pi$
$192$	−1.00000	−0.0721688
$193$	−11.8885	−0.855756	−0.427878	−	0.903836i	$-0.640739\pi$
$193$	−11.8885	−0.855756	−0.427878	+	0.903836i	$0.640739\pi$
$194$	8.47214	0.608264
$195$	−14.4721	−1.03637
$196$	0	0
$197$	−14.9443	−1.06474	−0.532368	−	0.846513i	$-0.678698\pi$
$197$	−14.9443	−1.06474	−0.532368	+	0.846513i	$0.678698\pi$
$198$	−0.763932	−0.0542903
$199$	9.41641	0.667511	0.333756	−	0.942660i	$-0.391684\pi$
$199$	9.41641	0.667511	0.333756	+	0.942660i	$0.391684\pi$
$200$	5.47214	0.386938
$201$	3.70820	0.261557
$202$	4.47214	0.314658
$203$	0	0
$204$	−4.00000	−0.280056
$205$	6.47214	0.452034
$206$	6.00000	0.418040
$207$	1.00000	0.0695048
$208$	4.47214	0.310087
$209$	−5.88854	−0.407319
$210$	0	0
$211$	3.41641	0.235195	0.117598	−	0.993061i	$-0.462481\pi$
$211$	3.41641	0.235195	0.117598	+	0.993061i	$0.462481\pi$
$212$	0.763932	0.0524671
$213$	8.94427	0.612851
$214$	18.6525	1.27506
$215$	−29.8885	−2.03838
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	9.23607	0.625545
$219$	4.47214	0.302199
$220$	−2.47214	−0.166671
$221$	17.8885	1.20331
$222$	−6.76393	−0.453965
$223$	7.41641	0.496639	0.248320	−	0.968678i	$-0.420122\pi$
$223$	7.41641	0.496639	0.248320	+	0.968678i	$0.420122\pi$
$224$	0	0
$225$	5.47214	0.364809
$226$	−14.4721	−0.962672
$227$	4.76393	0.316193	0.158097	−	0.987424i	$-0.449464\pi$
$227$	4.76393	0.316193	0.158097	+	0.987424i	$0.449464\pi$
$228$	−7.70820	−0.510488
$229$	−4.29180	−0.283610	−0.141805	−	0.989895i	$-0.545291\pi$
$229$	−4.29180	−0.283610	−0.141805	+	0.989895i	$0.545291\pi$
$230$	3.23607	0.213380
$231$	0	0
$232$	4.47214	0.293610
$233$	−15.8885	−1.04089	−0.520447	−	0.853894i	$-0.674235\pi$
$233$	−15.8885	−1.04089	−0.520447	+	0.853894i	$0.674235\pi$
$234$	4.47214	0.292353
$235$	−12.9443	−0.844391
$236$	−8.94427	−0.582223
$237$	4.47214	0.290496
$238$	0	0
$239$	12.9443	0.837295	0.418648	−	0.908149i	$-0.362504\pi$
$239$	12.9443	0.837295	0.418648	+	0.908149i	$0.362504\pi$
$240$	−3.23607	−0.208887
$241$	3.52786	0.227250	0.113625	−	0.993524i	$-0.463754\pi$
$241$	3.52786	0.227250	0.113625	+	0.993524i	$0.463754\pi$
$242$	−10.4164	−0.669592
$243$	−1.00000	−0.0641500
$244$	−5.23607	−0.335205
$245$	0	0
$246$	−2.00000	−0.127515
$247$	34.4721	2.19341
$248$	−6.47214	−0.410981
$249$	8.76393	0.555392
$250$	1.52786	0.0966306
$251$	6.29180	0.397135	0.198567	−	0.980087i	$-0.436371\pi$
$251$	6.29180	0.397135	0.198567	+	0.980087i	$0.436371\pi$
$252$	0	0
$253$	−0.763932	−0.0480280
$254$	−4.00000	−0.250982
$255$	−12.9443	−0.810602
$256$	1.00000	0.0625000
$257$	−23.8885	−1.49013	−0.745063	−	0.666994i	$-0.767581\pi$
$257$	−23.8885	−1.49013	−0.745063	+	0.666994i	$0.767581\pi$
$258$	9.23607	0.575012
$259$	0	0
$260$	14.4721	0.897524
$261$	4.47214	0.276818
$262$	18.4721	1.14121
$263$	7.05573	0.435075	0.217537	−	0.976052i	$-0.430198\pi$
$263$	7.05573	0.435075	0.217537	+	0.976052i	$0.430198\pi$
$264$	0.763932	0.0470168
$265$	2.47214	0.151862
$266$	0	0
$267$	−1.52786	−0.0935038
$268$	−3.70820	−0.226515
$269$	30.9443	1.88671	0.943353	−	0.331791i	$-0.107653\pi$
$269$	30.9443	1.88671	0.943353	+	0.331791i	$0.107653\pi$
$270$	−3.23607	−0.196941
$271$	−0.944272	−0.0573604	−0.0286802	−	0.999589i	$-0.509130\pi$
$271$	−0.944272	−0.0573604	−0.0286802	+	0.999589i	$0.509130\pi$
$272$	4.00000	0.242536
$273$	0	0
$274$	20.9443	1.26529
$275$	−4.18034	−0.252084
$276$	−1.00000	−0.0601929
$277$	−11.5279	−0.692642	−0.346321	−	0.938116i	$-0.612569\pi$
$277$	−11.5279	−0.692642	−0.346321	+	0.938116i	$0.612569\pi$
$278$	−0.944272	−0.0566337
$279$	−6.47214	−0.387477
$280$	0	0
$281$	−22.4721	−1.34058	−0.670288	−	0.742101i	$-0.733829\pi$
$281$	−22.4721	−1.34058	−0.670288	+	0.742101i	$0.733829\pi$
$282$	4.00000	0.238197
$283$	26.1803	1.55626	0.778130	−	0.628103i	$-0.216169\pi$
$283$	26.1803	1.55626	0.778130	+	0.628103i	$0.216169\pi$
$284$	−8.94427	−0.530745
$285$	−24.9443	−1.47757
$286$	−3.41641	−0.202016
$287$	0	0
$288$	1.00000	0.0589256
$289$	−1.00000	−0.0588235
$290$	14.4721	0.849833
$291$	−8.47214	−0.496645
$292$	−4.47214	−0.261712
$293$	−13.7082	−0.800842	−0.400421	−	0.916331i	$-0.631136\pi$
$293$	−13.7082	−0.800842	−0.400421	+	0.916331i	$0.631136\pi$
$294$	0	0
$295$	−28.9443	−1.68520
$296$	6.76393	0.393146
$297$	0.763932	0.0443278
$298$	1.70820	0.0989536
$299$	4.47214	0.258630
$300$	−5.47214	−0.315934
$301$	0	0
$302$	−5.52786	−0.318093
$303$	−4.47214	−0.256917
$304$	7.70820	0.442096
$305$	−16.9443	−0.970226
$306$	4.00000	0.228665
$307$	11.4164	0.651569	0.325784	−	0.945444i	$-0.394372\pi$
$307$	11.4164	0.651569	0.325784	+	0.945444i	$0.394372\pi$
$308$	0	0
$309$	−6.00000	−0.341328
$310$	−20.9443	−1.18955
$311$	3.05573	0.173274	0.0866372	−	0.996240i	$-0.472388\pi$
$311$	3.05573	0.173274	0.0866372	+	0.996240i	$0.472388\pi$
$312$	−4.47214	−0.253185
$313$	−24.4721	−1.38325	−0.691623	−	0.722258i	$-0.743104\pi$
$313$	−24.4721	−1.38325	−0.691623	+	0.722258i	$0.743104\pi$
$314$	−24.6525	−1.39122
$315$	0	0
$316$	−4.47214	−0.251577
$317$	28.4721	1.59915	0.799577	−	0.600563i	$-0.205057\pi$
$317$	28.4721	1.59915	0.799577	+	0.600563i	$0.205057\pi$
$318$	−0.763932	−0.0428392
$319$	−3.41641	−0.191282
$320$	3.23607	0.180902
$321$	−18.6525	−1.04108
$322$	0	0
$323$	30.8328	1.71558
$324$	1.00000	0.0555556
$325$	24.4721	1.35747
$326$	6.47214	0.358458
$327$	−9.23607	−0.510756
$328$	2.00000	0.110432
$329$	0	0
$330$	2.47214	0.136087
$331$	−1.52786	−0.0839790	−0.0419895	−	0.999118i	$-0.513370\pi$
$331$	−1.52786	−0.0839790	−0.0419895	+	0.999118i	$0.513370\pi$
$332$	−8.76393	−0.480983
$333$	6.76393	0.370661
$334$	0.944272	0.0516683
$335$	−12.0000	−0.655630
$336$	0	0
$337$	15.8885	0.865504	0.432752	−	0.901513i	$-0.357543\pi$
$337$	15.8885	0.865504	0.432752	+	0.901513i	$0.357543\pi$
$338$	7.00000	0.380750
$339$	14.4721	0.786019
$340$	12.9443	0.702002
$341$	4.94427	0.267747
$342$	7.70820	0.416812
$343$	0	0
$344$	−9.23607	−0.497975
$345$	−3.23607	−0.174224
$346$	−9.41641	−0.506229
$347$	21.5279	1.15568	0.577838	−	0.816151i	$-0.303896\pi$
$347$	21.5279	1.15568	0.577838	+	0.816151i	$0.303896\pi$
$348$	−4.47214	−0.239732
$349$	31.8885	1.70695	0.853477	−	0.521130i	$-0.174489\pi$
$349$	31.8885	1.70695	0.853477	+	0.521130i	$0.174489\pi$
$350$	0	0
$351$	−4.47214	−0.238705
$352$	−0.763932	−0.0407177
$353$	−31.8885	−1.69726	−0.848628	−	0.528990i	$-0.822571\pi$
$353$	−31.8885	−1.69726	−0.848628	+	0.528990i	$0.822571\pi$
$354$	8.94427	0.475383
$355$	−28.9443	−1.53620
$356$	1.52786	0.0809766
$357$	0	0
$358$	−7.41641	−0.391969
$359$	−33.3050	−1.75777	−0.878884	−	0.477035i	$-0.841711\pi$
$359$	−33.3050	−1.75777	−0.878884	+	0.477035i	$0.841711\pi$
$360$	3.23607	0.170556
$361$	40.4164	2.12718
$362$	6.76393	0.355504
$363$	10.4164	0.546720
$364$	0	0
$365$	−14.4721	−0.757506
$366$	5.23607	0.273694
$367$	17.4164	0.909129	0.454565	−	0.890714i	$-0.349795\pi$
$367$	17.4164	0.909129	0.454565	+	0.890714i	$0.349795\pi$
$368$	1.00000	0.0521286
$369$	2.00000	0.104116
$370$	21.8885	1.13793
$371$	0	0
$372$	6.47214	0.335565
$373$	13.5967	0.704013	0.352006	−	0.935998i	$-0.385500\pi$
$373$	13.5967	0.704013	0.352006	+	0.935998i	$0.385500\pi$
$374$	−3.05573	−0.158008
$375$	−1.52786	−0.0788986
$376$	−4.00000	−0.206284
$377$	20.0000	1.03005
$378$	0	0
$379$	0.291796	0.0149886	0.00749428	−	0.999972i	$-0.497614\pi$
$379$	0.291796	0.0149886	0.00749428	+	0.999972i	$0.497614\pi$
$380$	24.9443	1.27961
$381$	4.00000	0.204926
$382$	−2.47214	−0.126485
$383$	−24.9443	−1.27459	−0.637296	−	0.770619i	$-0.719947\pi$
$383$	−24.9443	−1.27459	−0.637296	+	0.770619i	$0.719947\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−11.8885	−0.605111
$387$	−9.23607	−0.469496
$388$	8.47214	0.430108
$389$	10.2918	0.521815	0.260907	−	0.965364i	$-0.415978\pi$
$389$	10.2918	0.521815	0.260907	+	0.965364i	$0.415978\pi$
$390$	−14.4721	−0.732825
$391$	4.00000	0.202289
$392$	0	0
$393$	−18.4721	−0.931796
$394$	−14.9443	−0.752882
$395$	−14.4721	−0.728172
$396$	−0.763932	−0.0383890
$397$	−9.05573	−0.454494	−0.227247	−	0.973837i	$-0.572972\pi$
$397$	−9.05573	−0.454494	−0.227247	+	0.973837i	$0.572972\pi$
$398$	9.41641	0.472002
$399$	0	0
$400$	5.47214	0.273607
$401$	−8.94427	−0.446656	−0.223328	−	0.974743i	$-0.571692\pi$
$401$	−8.94427	−0.446656	−0.223328	+	0.974743i	$0.571692\pi$
$402$	3.70820	0.184948
$403$	−28.9443	−1.44182
$404$	4.47214	0.222497
$405$	3.23607	0.160802
$406$	0	0
$407$	−5.16718	−0.256128
$408$	−4.00000	−0.198030
$409$	0.111456	0.00551115	0.00275558	−	0.999996i	$-0.499123\pi$
$409$	0.111456	0.00551115	0.00275558	+	0.999996i	$0.499123\pi$
$410$	6.47214	0.319636
$411$	−20.9443	−1.03310
$412$	6.00000	0.295599
$413$	0	0
$414$	1.00000	0.0491473
$415$	−28.3607	−1.39217
$416$	4.47214	0.219265
$417$	0.944272	0.0462412
$418$	−5.88854	−0.288018
$419$	30.0689	1.46896	0.734481	−	0.678630i	$-0.237426\pi$
$419$	30.0689	1.46896	0.734481	+	0.678630i	$0.237426\pi$
$420$	0	0
$421$	−5.23607	−0.255190	−0.127595	−	0.991826i	$-0.540726\pi$
$421$	−5.23607	−0.255190	−0.127595	+	0.991826i	$0.540726\pi$
$422$	3.41641	0.166308
$423$	−4.00000	−0.194487
$424$	0.763932	0.0370998
$425$	21.8885	1.06175
$426$	8.94427	0.433351
$427$	0	0
$428$	18.6525	0.901601
$429$	3.41641	0.164946
$430$	−29.8885	−1.44135
$431$	3.41641	0.164563	0.0822813	−	0.996609i	$-0.473779\pi$
$431$	3.41641	0.164563	0.0822813	+	0.996609i	$0.473779\pi$
$432$	−1.00000	−0.0481125
$433$	−5.41641	−0.260296	−0.130148	−	0.991495i	$-0.541545\pi$
$433$	−5.41641	−0.260296	−0.130148	+	0.991495i	$0.541545\pi$
$434$	0	0
$435$	−14.4721	−0.693886
$436$	9.23607	0.442327
$437$	7.70820	0.368733
$438$	4.47214	0.213687
$439$	−36.9443	−1.76325	−0.881627	−	0.471947i	$-0.843551\pi$
$439$	−36.9443	−1.76325	−0.881627	+	0.471947i	$0.843551\pi$
$440$	−2.47214	−0.117854
$441$	0	0
$442$	17.8885	0.850871
$443$	−32.9443	−1.56523	−0.782615	−	0.622506i	$-0.786115\pi$
$443$	−32.9443	−1.56523	−0.782615	+	0.622506i	$0.786115\pi$
$444$	−6.76393	−0.321002
$445$	4.94427	0.234381
$446$	7.41641	0.351177
$447$	−1.70820	−0.0807953
$448$	0	0
$449$	−19.8885	−0.938598	−0.469299	−	0.883039i	$-0.655493\pi$
$449$	−19.8885	−0.938598	−0.469299	+	0.883039i	$0.655493\pi$
$450$	5.47214	0.257959
$451$	−1.52786	−0.0719443
$452$	−14.4721	−0.680712
$453$	5.52786	0.259722
$454$	4.76393	0.223582
$455$	0	0
$456$	−7.70820	−0.360970
$457$	36.4721	1.70609	0.853047	−	0.521834i	$-0.174752\pi$
$457$	36.4721	1.70609	0.853047	+	0.521834i	$0.174752\pi$
$458$	−4.29180	−0.200542
$459$	−4.00000	−0.186704
$460$	3.23607	0.150882
$461$	−22.0000	−1.02464	−0.512321	−	0.858794i	$-0.671214\pi$
$461$	−22.0000	−1.02464	−0.512321	+	0.858794i	$0.671214\pi$
$462$	0	0
$463$	24.0000	1.11537	0.557687	−	0.830051i	$-0.311689\pi$
$463$	24.0000	1.11537	0.557687	+	0.830051i	$0.311689\pi$
$464$	4.47214	0.207614
$465$	20.9443	0.971267
$466$	−15.8885	−0.736023
$467$	40.1803	1.85932	0.929662	−	0.368413i	$-0.120099\pi$
$467$	40.1803	1.85932	0.929662	+	0.368413i	$0.120099\pi$
$468$	4.47214	0.206725
$469$	0	0
$470$	−12.9443	−0.597075
$471$	24.6525	1.13593
$472$	−8.94427	−0.411693
$473$	7.05573	0.324423
$474$	4.47214	0.205412
$475$	42.1803	1.93537
$476$	0	0
$477$	0.763932	0.0349780
$478$	12.9443	0.592057
$479$	11.0557	0.505149	0.252575	−	0.967577i	$-0.418723\pi$
$479$	11.0557	0.505149	0.252575	+	0.967577i	$0.418723\pi$
$480$	−3.23607	−0.147706
$481$	30.2492	1.37925
$482$	3.52786	0.160690
$483$	0	0
$484$	−10.4164	−0.473473
$485$	27.4164	1.24491
$486$	−1.00000	−0.0453609
$487$	−25.8885	−1.17312	−0.586561	−	0.809905i	$-0.699519\pi$
$487$	−25.8885	−1.17312	−0.586561	+	0.809905i	$0.699519\pi$
$488$	−5.23607	−0.237026
$489$	−6.47214	−0.292680
$490$	0	0
$491$	−33.3050	−1.50303	−0.751516	−	0.659715i	$-0.770677\pi$
$491$	−33.3050	−1.50303	−0.751516	+	0.659715i	$0.770677\pi$
$492$	−2.00000	−0.0901670
$493$	17.8885	0.805659
$494$	34.4721	1.55097
$495$	−2.47214	−0.111114
$496$	−6.47214	−0.290607
$497$	0	0
$498$	8.76393	0.392721
$499$	27.4164	1.22733	0.613663	−	0.789568i	$-0.289695\pi$
$499$	27.4164	1.22733	0.613663	+	0.789568i	$0.289695\pi$
$500$	1.52786	0.0683282
$501$	−0.944272	−0.0421870
$502$	6.29180	0.280817
$503$	−1.52786	−0.0681241	−0.0340620	−	0.999420i	$-0.510844\pi$
$503$	−1.52786	−0.0681241	−0.0340620	+	0.999420i	$0.510844\pi$
$504$	0	0
$505$	14.4721	0.644002
$506$	−0.763932	−0.0339609
$507$	−7.00000	−0.310881
$508$	−4.00000	−0.177471
$509$	6.58359	0.291813	0.145906	−	0.989298i	$-0.453390\pi$
$509$	6.58359	0.291813	0.145906	+	0.989298i	$0.453390\pi$
$510$	−12.9443	−0.573182
$511$	0	0
$512$	1.00000	0.0441942
$513$	−7.70820	−0.340326
$514$	−23.8885	−1.05368
$515$	19.4164	0.855589
$516$	9.23607	0.406595
$517$	3.05573	0.134391
$518$	0	0
$519$	9.41641	0.413334
$520$	14.4721	0.634645
$521$	−16.0000	−0.700973	−0.350486	−	0.936568i	$-0.613984\pi$
$521$	−16.0000	−0.700973	−0.350486	+	0.936568i	$0.613984\pi$
$522$	4.47214	0.195740
$523$	−12.2918	−0.537483	−0.268741	−	0.963212i	$-0.586608\pi$
$523$	−12.2918	−0.537483	−0.268741	+	0.963212i	$0.586608\pi$
$524$	18.4721	0.806959
$525$	0	0
$526$	7.05573	0.307644
$527$	−25.8885	−1.12772
$528$	0.763932	0.0332459
$529$	1.00000	0.0434783
$530$	2.47214	0.107383
$531$	−8.94427	−0.388148
$532$	0	0
$533$	8.94427	0.387419
$534$	−1.52786	−0.0661171
$535$	60.3607	2.60962
$536$	−3.70820	−0.160170
$537$	7.41641	0.320042
$538$	30.9443	1.33410
$539$	0	0
$540$	−3.23607	−0.139258
$541$	43.8885	1.88692	0.943458	−	0.331492i	$-0.107552\pi$
$541$	43.8885	1.88692	0.943458	+	0.331492i	$0.107552\pi$
$542$	−0.944272	−0.0405600
$543$	−6.76393	−0.290268
$544$	4.00000	0.171499
$545$	29.8885	1.28028
$546$	0	0
$547$	−21.3050	−0.910934	−0.455467	−	0.890253i	$-0.650528\pi$
$547$	−21.3050	−0.910934	−0.455467	+	0.890253i	$0.650528\pi$
$548$	20.9443	0.894695
$549$	−5.23607	−0.223470
$550$	−4.18034	−0.178250
$551$	34.4721	1.46856
$552$	−1.00000	−0.0425628
$553$	0	0
$554$	−11.5279	−0.489772
$555$	−21.8885	−0.929117
$556$	−0.944272	−0.0400460
$557$	25.1246	1.06456	0.532282	−	0.846567i	$-0.321335\pi$
$557$	25.1246	1.06456	0.532282	+	0.846567i	$0.321335\pi$
$558$	−6.47214	−0.273987
$559$	−41.3050	−1.74701
$560$	0	0
$561$	3.05573	0.129013
$562$	−22.4721	−0.947930
$563$	6.65248	0.280368	0.140184	−	0.990125i	$-0.455231\pi$
$563$	6.65248	0.280368	0.140184	+	0.990125i	$0.455231\pi$
$564$	4.00000	0.168430
$565$	−46.8328	−1.97027
$566$	26.1803	1.10044
$567$	0	0
$568$	−8.94427	−0.375293
$569$	20.0000	0.838444	0.419222	−	0.907884i	$-0.362303\pi$
$569$	20.0000	0.838444	0.419222	+	0.907884i	$0.362303\pi$
$570$	−24.9443	−1.04480
$571$	−27.7082	−1.15955	−0.579776	−	0.814776i	$-0.696860\pi$
$571$	−27.7082	−1.15955	−0.579776	+	0.814776i	$0.696860\pi$
$572$	−3.41641	−0.142847
$573$	2.47214	0.103275
$574$	0	0
$575$	5.47214	0.228204
$576$	1.00000	0.0416667
$577$	−10.3607	−0.431321	−0.215660	−	0.976468i	$-0.569190\pi$
$577$	−10.3607	−0.431321	−0.215660	+	0.976468i	$0.569190\pi$
$578$	−1.00000	−0.0415945
$579$	11.8885	0.494071
$580$	14.4721	0.600923
$581$	0	0
$582$	−8.47214	−0.351181
$583$	−0.583592	−0.0241699
$584$	−4.47214	−0.185058
$585$	14.4721	0.598349
$586$	−13.7082	−0.566281
$587$	2.47214	0.102036	0.0510180	−	0.998698i	$-0.483753\pi$
$587$	2.47214	0.102036	0.0510180	+	0.998698i	$0.483753\pi$
$588$	0	0
$589$	−49.8885	−2.05562
$590$	−28.9443	−1.19162
$591$	14.9443	0.614725
$592$	6.76393	0.277996
$593$	37.7771	1.55132	0.775660	−	0.631152i	$-0.217417\pi$
$593$	37.7771	1.55132	0.775660	+	0.631152i	$0.217417\pi$
$594$	0.763932	0.0313445
$595$	0	0
$596$	1.70820	0.0699708
$597$	−9.41641	−0.385388
$598$	4.47214	0.182879
$599$	−1.88854	−0.0771638	−0.0385819	−	0.999255i	$-0.512284\pi$
$599$	−1.88854	−0.0771638	−0.0385819	+	0.999255i	$0.512284\pi$
$600$	−5.47214	−0.223399
$601$	−34.3607	−1.40160	−0.700801	−	0.713357i	$-0.747174\pi$
$601$	−34.3607	−1.40160	−0.700801	+	0.713357i	$0.747174\pi$
$602$	0	0
$603$	−3.70820	−0.151010
$604$	−5.52786	−0.224926
$605$	−33.7082	−1.37043
$606$	−4.47214	−0.181668
$607$	26.4721	1.07447	0.537235	−	0.843432i	$-0.319469\pi$
$607$	26.4721	1.07447	0.537235	+	0.843432i	$0.319469\pi$
$608$	7.70820	0.312609
$609$	0	0
$610$	−16.9443	−0.686054
$611$	−17.8885	−0.723693
$612$	4.00000	0.161690
$613$	15.1246	0.610877	0.305439	−	0.952212i	$-0.401197\pi$
$613$	15.1246	0.610877	0.305439	+	0.952212i	$0.401197\pi$
$614$	11.4164	0.460729
$615$	−6.47214	−0.260982
$616$	0	0
$617$	−24.3607	−0.980724	−0.490362	−	0.871519i	$-0.663135\pi$
$617$	−24.3607	−0.980724	−0.490362	+	0.871519i	$0.663135\pi$
$618$	−6.00000	−0.241355
$619$	−31.7082	−1.27446	−0.637230	−	0.770674i	$-0.719920\pi$
$619$	−31.7082	−1.27446	−0.637230	+	0.770674i	$0.719920\pi$
$620$	−20.9443	−0.841142
$621$	−1.00000	−0.0401286
$622$	3.05573	0.122524
$623$	0	0
$624$	−4.47214	−0.179029
$625$	−22.4164	−0.896656
$626$	−24.4721	−0.978103
$627$	5.88854	0.235166
$628$	−24.6525	−0.983741
$629$	27.0557	1.07878
$630$	0	0
$631$	−6.00000	−0.238856	−0.119428	−	0.992843i	$-0.538106\pi$
$631$	−6.00000	−0.238856	−0.119428	+	0.992843i	$0.538106\pi$
$632$	−4.47214	−0.177892
$633$	−3.41641	−0.135790
$634$	28.4721	1.13077
$635$	−12.9443	−0.513678
$636$	−0.763932	−0.0302919
$637$	0	0
$638$	−3.41641	−0.135257
$639$	−8.94427	−0.353830
$640$	3.23607	0.127917
$641$	4.00000	0.157991	0.0789953	−	0.996875i	$-0.474829\pi$
$641$	4.00000	0.157991	0.0789953	+	0.996875i	$0.474829\pi$
$642$	−18.6525	−0.736155
$643$	−34.5410	−1.36216	−0.681082	−	0.732207i	$-0.738490\pi$
$643$	−34.5410	−1.36216	−0.681082	+	0.732207i	$0.738490\pi$
$644$	0	0
$645$	29.8885	1.17686
$646$	30.8328	1.21310
$647$	4.94427	0.194379	0.0971897	−	0.995266i	$-0.469015\pi$
$647$	4.94427	0.194379	0.0971897	+	0.995266i	$0.469015\pi$
$648$	1.00000	0.0392837
$649$	6.83282	0.268211
$650$	24.4721	0.959876
$651$	0	0
$652$	6.47214	0.253468
$653$	−17.4164	−0.681557	−0.340778	−	0.940144i	$-0.610691\pi$
$653$	−17.4164	−0.681557	−0.340778	+	0.940144i	$0.610691\pi$
$654$	−9.23607	−0.361159
$655$	59.7771	2.33568
$656$	2.00000	0.0780869
$657$	−4.47214	−0.174475
$658$	0	0
$659$	−1.34752	−0.0524921	−0.0262460	−	0.999656i	$-0.508355\pi$
$659$	−1.34752	−0.0524921	−0.0262460	+	0.999656i	$0.508355\pi$
$660$	2.47214	0.0962278
$661$	−26.1803	−1.01830	−0.509149	−	0.860679i	$-0.670040\pi$
$661$	−26.1803	−1.01830	−0.509149	+	0.860679i	$0.670040\pi$
$662$	−1.52786	−0.0593821
$663$	−17.8885	−0.694733
$664$	−8.76393	−0.340107
$665$	0	0
$666$	6.76393	0.262097
$667$	4.47214	0.173162
$668$	0.944272	0.0365350
$669$	−7.41641	−0.286735
$670$	−12.0000	−0.463600
$671$	4.00000	0.154418
$672$	0	0
$673$	−4.47214	−0.172388	−0.0861941	−	0.996278i	$-0.527471\pi$
$673$	−4.47214	−0.172388	−0.0861941	+	0.996278i	$0.527471\pi$
$674$	15.8885	0.612004
$675$	−5.47214	−0.210623
$676$	7.00000	0.269231
$677$	21.1246	0.811885	0.405942	−	0.913899i	$-0.366943\pi$
$677$	21.1246	0.811885	0.405942	+	0.913899i	$0.366943\pi$
$678$	14.4721	0.555799
$679$	0	0
$680$	12.9443	0.496390
$681$	−4.76393	−0.182554
$682$	4.94427	0.189326
$683$	5.52786	0.211518	0.105759	−	0.994392i	$-0.466273\pi$
$683$	5.52786	0.211518	0.105759	+	0.994392i	$0.466273\pi$
$684$	7.70820	0.294731
$685$	67.7771	2.58963
$686$	0	0
$687$	4.29180	0.163742
$688$	−9.23607	−0.352122
$689$	3.41641	0.130155
$690$	−3.23607	−0.123195
$691$	−43.4164	−1.65164	−0.825819	−	0.563935i	$-0.809287\pi$
$691$	−43.4164	−1.65164	−0.825819	+	0.563935i	$0.809287\pi$
$692$	−9.41641	−0.357958
$693$	0	0
$694$	21.5279	0.817187
$695$	−3.05573	−0.115910
$696$	−4.47214	−0.169516
$697$	8.00000	0.303022
$698$	31.8885	1.20700
$699$	15.8885	0.600960
$700$	0	0
$701$	37.1246	1.40218	0.701089	−	0.713074i	$-0.252698\pi$
$701$	37.1246	1.40218	0.701089	+	0.713074i	$0.252698\pi$
$702$	−4.47214	−0.168790
$703$	52.1378	1.96641
$704$	−0.763932	−0.0287918
$705$	12.9443	0.487509
$706$	−31.8885	−1.20014
$707$	0	0
$708$	8.94427	0.336146
$709$	−41.0132	−1.54028	−0.770141	−	0.637874i	$-0.779814\pi$
$709$	−41.0132	−1.54028	−0.770141	+	0.637874i	$0.779814\pi$
$710$	−28.9443	−1.08626
$711$	−4.47214	−0.167718
$712$	1.52786	0.0572591
$713$	−6.47214	−0.242383
$714$	0	0
$715$	−11.0557	−0.413461
$716$	−7.41641	−0.277164
$717$	−12.9443	−0.483413
$718$	−33.3050	−1.24293
$719$	20.9443	0.781090	0.390545	−	0.920584i	$-0.372287\pi$
$719$	20.9443	0.781090	0.390545	+	0.920584i	$0.372287\pi$
$720$	3.23607	0.120601
$721$	0	0
$722$	40.4164	1.50414
$723$	−3.52786	−0.131203
$724$	6.76393	0.251380
$725$	24.4721	0.908872
$726$	10.4164	0.386589
$727$	−43.3050	−1.60609	−0.803046	−	0.595917i	$-0.796789\pi$
$727$	−43.3050	−1.60609	−0.803046	+	0.595917i	$0.796789\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−14.4721	−0.535638
$731$	−36.9443	−1.36643
$732$	5.23607	0.193531
$733$	8.29180	0.306264	0.153132	−	0.988206i	$-0.451064\pi$
$733$	8.29180	0.306264	0.153132	+	0.988206i	$0.451064\pi$
$734$	17.4164	0.642851
$735$	0	0
$736$	1.00000	0.0368605
$737$	2.83282	0.104348
$738$	2.00000	0.0736210
$739$	−15.0557	−0.553834	−0.276917	−	0.960894i	$-0.589313\pi$
$739$	−15.0557	−0.553834	−0.276917	+	0.960894i	$0.589313\pi$
$740$	21.8885	0.804639
$741$	−34.4721	−1.26637
$742$	0	0
$743$	−4.00000	−0.146746	−0.0733729	−	0.997305i	$-0.523376\pi$
$743$	−4.00000	−0.146746	−0.0733729	+	0.997305i	$0.523376\pi$
$744$	6.47214	0.237280
$745$	5.52786	0.202525
$746$	13.5967	0.497812
$747$	−8.76393	−0.320656
$748$	−3.05573	−0.111728
$749$	0	0
$750$	−1.52786	−0.0557897
$751$	−18.0000	−0.656829	−0.328415	−	0.944534i	$-0.606514\pi$
$751$	−18.0000	−0.656829	−0.328415	+	0.944534i	$0.606514\pi$
$752$	−4.00000	−0.145865
$753$	−6.29180	−0.229286
$754$	20.0000	0.728357
$755$	−17.8885	−0.651031
$756$	0	0
$757$	−32.6525	−1.18677	−0.593387	−	0.804917i	$-0.702210\pi$
$757$	−32.6525	−1.18677	−0.593387	+	0.804917i	$0.702210\pi$
$758$	0.291796	0.0105985
$759$	0.763932	0.0277290
$760$	24.9443	0.904824
$761$	22.9443	0.831729	0.415865	−	0.909427i	$-0.363479\pi$
$761$	22.9443	0.831729	0.415865	+	0.909427i	$0.363479\pi$
$762$	4.00000	0.144905
$763$	0	0
$764$	−2.47214	−0.0894387
$765$	12.9443	0.468001
$766$	−24.9443	−0.901273
$767$	−40.0000	−1.44432
$768$	−1.00000	−0.0360844
$769$	−3.52786	−0.127218	−0.0636090	−	0.997975i	$-0.520261\pi$
$769$	−3.52786	−0.127218	−0.0636090	+	0.997975i	$0.520261\pi$
$770$	0	0
$771$	23.8885	0.860325
$772$	−11.8885	−0.427878
$773$	15.8197	0.568994	0.284497	−	0.958677i	$-0.408173\pi$
$773$	15.8197	0.568994	0.284497	+	0.958677i	$0.408173\pi$
$774$	−9.23607	−0.331984
$775$	−35.4164	−1.27219
$776$	8.47214	0.304132
$777$	0	0
$778$	10.2918	0.368979
$779$	15.4164	0.552350
$780$	−14.4721	−0.518186
$781$	6.83282	0.244497
$782$	4.00000	0.143040
$783$	−4.47214	−0.159821
$784$	0	0
$785$	−79.7771	−2.84737
$786$	−18.4721	−0.658879
$787$	−30.7639	−1.09662	−0.548308	−	0.836277i	$-0.684728\pi$
$787$	−30.7639	−1.09662	−0.548308	+	0.836277i	$0.684728\pi$
$788$	−14.9443	−0.532368
$789$	−7.05573	−0.251191
$790$	−14.4721	−0.514895
$791$	0	0
$792$	−0.763932	−0.0271451
$793$	−23.4164	−0.831541
$794$	−9.05573	−0.321376
$795$	−2.47214	−0.0876776
$796$	9.41641	0.333756
$797$	7.59675	0.269091	0.134545	−	0.990907i	$-0.457043\pi$
$797$	7.59675	0.269091	0.134545	+	0.990907i	$0.457043\pi$
$798$	0	0
$799$	−16.0000	−0.566039
$800$	5.47214	0.193469
$801$	1.52786	0.0539844
$802$	−8.94427	−0.315833
$803$	3.41641	0.120562
$804$	3.70820	0.130778
$805$	0	0
$806$	−28.9443	−1.01952
$807$	−30.9443	−1.08929
$808$	4.47214	0.157329
$809$	25.0557	0.880912	0.440456	−	0.897774i	$-0.354817\pi$
$809$	25.0557	0.880912	0.440456	+	0.897774i	$0.354817\pi$
$810$	3.23607	0.113704
$811$	21.3050	0.748118	0.374059	−	0.927405i	$-0.377966\pi$
$811$	21.3050	0.748118	0.374059	+	0.927405i	$0.377966\pi$
$812$	0	0
$813$	0.944272	0.0331171
$814$	−5.16718	−0.181110
$815$	20.9443	0.733646
$816$	−4.00000	−0.140028
$817$	−71.1935	−2.49075
$818$	0.111456	0.00389697
$819$	0	0
$820$	6.47214	0.226017
$821$	48.4721	1.69169	0.845845	−	0.533429i	$-0.179097\pi$
$821$	48.4721	1.69169	0.845845	+	0.533429i	$0.179097\pi$
$822$	−20.9443	−0.730515
$823$	−7.63932	−0.266290	−0.133145	−	0.991097i	$-0.542508\pi$
$823$	−7.63932	−0.266290	−0.133145	+	0.991097i	$0.542508\pi$
$824$	6.00000	0.209020
$825$	4.18034	0.145541
$826$	0	0
$827$	27.5967	0.959633	0.479816	−	0.877369i	$-0.340703\pi$
$827$	27.5967	0.959633	0.479816	+	0.877369i	$0.340703\pi$
$828$	1.00000	0.0347524
$829$	6.00000	0.208389	0.104194	−	0.994557i	$-0.466774\pi$
$829$	6.00000	0.208389	0.104194	+	0.994557i	$0.466774\pi$
$830$	−28.3607	−0.984414
$831$	11.5279	0.399897
$832$	4.47214	0.155043
$833$	0	0
$834$	0.944272	0.0326975
$835$	3.05573	0.105748
$836$	−5.88854	−0.203660
$837$	6.47214	0.223710
$838$	30.0689	1.03871
$839$	10.1115	0.349086	0.174543	−	0.984650i	$-0.444155\pi$
$839$	10.1115	0.349086	0.174543	+	0.984650i	$0.444155\pi$
$840$	0	0
$841$	−9.00000	−0.310345
$842$	−5.23607	−0.180447
$843$	22.4721	0.773981
$844$	3.41641	0.117598
$845$	22.6525	0.779269
$846$	−4.00000	−0.137523
$847$	0	0
$848$	0.763932	0.0262335
$849$	−26.1803	−0.898507
$850$	21.8885	0.750771
$851$	6.76393	0.231865
$852$	8.94427	0.306426
$853$	26.0000	0.890223	0.445112	−	0.895475i	$-0.353164\pi$
$853$	26.0000	0.890223	0.445112	+	0.895475i	$0.353164\pi$
$854$	0	0
$855$	24.9443	0.853076
$856$	18.6525	0.637528
$857$	22.0000	0.751506	0.375753	−	0.926720i	$-0.377384\pi$
$857$	22.0000	0.751506	0.375753	+	0.926720i	$0.377384\pi$
$858$	3.41641	0.116634
$859$	20.0000	0.682391	0.341196	−	0.939992i	$-0.389168\pi$
$859$	20.0000	0.682391	0.341196	+	0.939992i	$0.389168\pi$
$860$	−29.8885	−1.01919
$861$	0	0
$862$	3.41641	0.116363
$863$	−38.8328	−1.32188	−0.660942	−	0.750437i	$-0.729843\pi$
$863$	−38.8328	−1.32188	−0.660942	+	0.750437i	$0.729843\pi$
$864$	−1.00000	−0.0340207
$865$	−30.4721	−1.03608
$866$	−5.41641	−0.184057
$867$	1.00000	0.0339618
$868$	0	0
$869$	3.41641	0.115894
$870$	−14.4721	−0.490651
$871$	−16.5836	−0.561914
$872$	9.23607	0.312773
$873$	8.47214	0.286738
$874$	7.70820	0.260734
$875$	0	0
$876$	4.47214	0.151099
$877$	32.2492	1.08898	0.544489	−	0.838768i	$-0.316723\pi$
$877$	32.2492	1.08898	0.544489	+	0.838768i	$0.316723\pi$
$878$	−36.9443	−1.24681
$879$	13.7082	0.462366
$880$	−2.47214	−0.0833357
$881$	−12.5836	−0.423952	−0.211976	−	0.977275i	$-0.567990\pi$
$881$	−12.5836	−0.423952	−0.211976	+	0.977275i	$0.567990\pi$
$882$	0	0
$883$	22.4721	0.756248	0.378124	−	0.925755i	$-0.376569\pi$
$883$	22.4721	0.756248	0.378124	+	0.925755i	$0.376569\pi$
$884$	17.8885	0.601657
$885$	28.9443	0.972951
$886$	−32.9443	−1.10678
$887$	−0.944272	−0.0317055	−0.0158528	−	0.999874i	$-0.505046\pi$
$887$	−0.944272	−0.0317055	−0.0158528	+	0.999874i	$0.505046\pi$
$888$	−6.76393	−0.226983
$889$	0	0
$890$	4.94427	0.165732
$891$	−0.763932	−0.0255927
$892$	7.41641	0.248320
$893$	−30.8328	−1.03178
$894$	−1.70820	−0.0571309
$895$	−24.0000	−0.802232
$896$	0	0
$897$	−4.47214	−0.149320
$898$	−19.8885	−0.663689
$899$	−28.9443	−0.965346
$900$	5.47214	0.182405
$901$	3.05573	0.101801
$902$	−1.52786	−0.0508723
$903$	0	0
$904$	−14.4721	−0.481336
$905$	21.8885	0.727600
$906$	5.52786	0.183651
$907$	−18.1803	−0.603668	−0.301834	−	0.953360i	$-0.597599\pi$
$907$	−18.1803	−0.603668	−0.301834	+	0.953360i	$0.597599\pi$
$908$	4.76393	0.158097
$909$	4.47214	0.148331
$910$	0	0
$911$	43.4164	1.43845	0.719225	−	0.694777i	$-0.244497\pi$
$911$	43.4164	1.43845	0.719225	+	0.694777i	$0.244497\pi$
$912$	−7.70820	−0.255244
$913$	6.69505	0.221574
$914$	36.4721	1.20639
$915$	16.9443	0.560160
$916$	−4.29180	−0.141805
$917$	0	0
$918$	−4.00000	−0.132020
$919$	−7.52786	−0.248321	−0.124161	−	0.992262i	$-0.539624\pi$
$919$	−7.52786	−0.248321	−0.124161	+	0.992262i	$0.539624\pi$
$920$	3.23607	0.106690
$921$	−11.4164	−0.376183
$922$	−22.0000	−0.724531
$923$	−40.0000	−1.31662
$924$	0	0
$925$	37.0132	1.21699
$926$	24.0000	0.788689
$927$	6.00000	0.197066
$928$	4.47214	0.146805
$929$	−28.8328	−0.945974	−0.472987	−	0.881069i	$-0.656824\pi$
$929$	−28.8328	−0.945974	−0.472987	+	0.881069i	$0.656824\pi$
$930$	20.9443	0.686790
$931$	0	0
$932$	−15.8885	−0.520447
$933$	−3.05573	−0.100040
$934$	40.1803	1.31474
$935$	−9.88854	−0.323390
$936$	4.47214	0.146176
$937$	30.0000	0.980057	0.490029	−	0.871706i	$-0.336986\pi$
$937$	30.0000	0.980057	0.490029	+	0.871706i	$0.336986\pi$
$938$	0	0
$939$	24.4721	0.798618
$940$	−12.9443	−0.422196
$941$	−15.8197	−0.515706	−0.257853	−	0.966184i	$-0.583015\pi$
$941$	−15.8197	−0.515706	−0.257853	+	0.966184i	$0.583015\pi$
$942$	24.6525	0.803221
$943$	2.00000	0.0651290
$944$	−8.94427	−0.291111
$945$	0	0
$946$	7.05573	0.229402
$947$	51.1935	1.66357	0.831783	−	0.555102i	$-0.187321\pi$
$947$	51.1935	1.66357	0.831783	+	0.555102i	$0.187321\pi$
$948$	4.47214	0.145248
$949$	−20.0000	−0.649227
$950$	42.1803	1.36851
$951$	−28.4721	−0.923272
$952$	0	0
$953$	23.7771	0.770215	0.385108	−	0.922872i	$-0.374164\pi$
$953$	23.7771	0.770215	0.385108	+	0.922872i	$0.374164\pi$
$954$	0.763932	0.0247332
$955$	−8.00000	−0.258874
$956$	12.9443	0.418648
$957$	3.41641	0.110437
$958$	11.0557	0.357194
$959$	0	0
$960$	−3.23607	−0.104444
$961$	10.8885	0.351243
$962$	30.2492	0.975274
$963$	18.6525	0.601068
$964$	3.52786	0.113625
$965$	−38.4721	−1.23846
$966$	0	0
$967$	−11.4164	−0.367127	−0.183563	−	0.983008i	$-0.558763\pi$
$967$	−11.4164	−0.367127	−0.183563	+	0.983008i	$0.558763\pi$
$968$	−10.4164	−0.334796
$969$	−30.8328	−0.990493
$970$	27.4164	0.880288
$971$	−21.1246	−0.677921	−0.338961	−	0.940801i	$-0.610075\pi$
$971$	−21.1246	−0.677921	−0.338961	+	0.940801i	$0.610075\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	−25.8885	−0.829522
$975$	−24.4721	−0.783736
$976$	−5.23607	−0.167602
$977$	54.8328	1.75426	0.877129	−	0.480256i	$-0.159456\pi$
$977$	54.8328	1.75426	0.877129	+	0.480256i	$0.159456\pi$
$978$	−6.47214	−0.206956
$979$	−1.16718	−0.0373034
$980$	0	0
$981$	9.23607	0.294885
$982$	−33.3050	−1.06280
$983$	−27.4164	−0.874448	−0.437224	−	0.899353i	$-0.644038\pi$
$983$	−27.4164	−0.874448	−0.437224	+	0.899353i	$0.644038\pi$
$984$	−2.00000	−0.0637577
$985$	−48.3607	−1.54090
$986$	17.8885	0.569687
$987$	0	0
$988$	34.4721	1.09670
$989$	−9.23607	−0.293690
$990$	−2.47214	−0.0785696
$991$	−1.52786	−0.0485342	−0.0242671	−	0.999706i	$-0.507725\pi$
$991$	−1.52786	−0.0485342	−0.0242671	+	0.999706i	$0.507725\pi$
$992$	−6.47214	−0.205491
$993$	1.52786	0.0484853
$994$	0	0
$995$	30.4721	0.966032
$996$	8.76393	0.277696
$997$	−22.9443	−0.726652	−0.363326	−	0.931662i	$-0.618359\pi$
$997$	−22.9443	−0.726652	−0.363326	+	0.931662i	$0.618359\pi$
$998$	27.4164	0.867851
$999$	−6.76393	−0.214001

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6762.2.a.cb.1.2		2
7.6	odd	2		138.2.a.d.1.1	✓	2
21.20	even	2		414.2.a.f.1.2		2
28.27	even	2		1104.2.a.j.1.1		2
35.13	even	4		3450.2.d.x.2899.1		4
35.27	even	4		3450.2.d.x.2899.4		4
35.34	odd	2		3450.2.a.be.1.1		2
56.13	odd	2		4416.2.a.bh.1.2		2
56.27	even	2		4416.2.a.bl.1.2		2
84.83	odd	2		3312.2.a.bc.1.2		2
161.160	even	2		3174.2.a.s.1.2		2
483.482	odd	2		9522.2.a.q.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.2.a.d.1.1	✓	2	7.6	odd	2
414.2.a.f.1.2		2	21.20	even	2
1104.2.a.j.1.1		2	28.27	even	2
3174.2.a.s.1.2		2	161.160	even	2
3312.2.a.bc.1.2		2	84.83	odd	2
3450.2.a.be.1.1		2	35.34	odd	2
3450.2.d.x.2899.1		4	35.13	even	4
3450.2.d.x.2899.4		4	35.27	even	4
4416.2.a.bh.1.2		2	56.13	odd	2
4416.2.a.bl.1.2		2	56.27	even	2
6762.2.a.cb.1.2		2	1.1	even	1	trivial
9522.2.a.q.1.1		2	483.482	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6762.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.23607 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.23607 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +3.23607 q^{10} -0.763932 q^{11} -1.00000 q^{12} +4.47214 q^{13} -3.23607 q^{15} +1.00000 q^{16} +4.00000 q^{17} +1.00000 q^{18} +7.70820 q^{19} +3.23607 q^{20} -0.763932 q^{22} +1.00000 q^{23} -1.00000 q^{24} +5.47214 q^{25} +4.47214 q^{26} -1.00000 q^{27} +4.47214 q^{29} -3.23607 q^{30} -6.47214 q^{31} +1.00000 q^{32} +0.763932 q^{33} +4.00000 q^{34} +1.00000 q^{36} +6.76393 q^{37} +7.70820 q^{38} -4.47214 q^{39} +3.23607 q^{40} +2.00000 q^{41} -9.23607 q^{43} -0.763932 q^{44} +3.23607 q^{45} +1.00000 q^{46} -4.00000 q^{47} -1.00000 q^{48} +5.47214 q^{50} -4.00000 q^{51} +4.47214 q^{52} +0.763932 q^{53} -1.00000 q^{54} -2.47214 q^{55} -7.70820 q^{57} +4.47214 q^{58} -8.94427 q^{59} -3.23607 q^{60} -5.23607 q^{61} -6.47214 q^{62} +1.00000 q^{64} +14.4721 q^{65} +0.763932 q^{66} -3.70820 q^{67} +4.00000 q^{68} -1.00000 q^{69} -8.94427 q^{71} +1.00000 q^{72} -4.47214 q^{73} +6.76393 q^{74} -5.47214 q^{75} +7.70820 q^{76} -4.47214 q^{78} -4.47214 q^{79} +3.23607 q^{80} +1.00000 q^{81} +2.00000 q^{82} -8.76393 q^{83} +12.9443 q^{85} -9.23607 q^{86} -4.47214 q^{87} -0.763932 q^{88} +1.52786 q^{89} +3.23607 q^{90} +1.00000 q^{92} +6.47214 q^{93} -4.00000 q^{94} +24.9443 q^{95} -1.00000 q^{96} +8.47214 q^{97} -0.763932 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{8} + 2 q^{9} + 2 q^{10} - 6 q^{11} - 2 q^{12} - 2 q^{15} + 2 q^{16} + 8 q^{17} + 2 q^{18} + 2 q^{19} + 2 q^{20} - 6 q^{22} + 2 q^{23} - 2 q^{24} + 2 q^{25} - 2 q^{27} - 2 q^{30} - 4 q^{31} + 2 q^{32} + 6 q^{33} + 8 q^{34} + 2 q^{36} + 18 q^{37} + 2 q^{38} + 2 q^{40} + 4 q^{41} - 14 q^{43} - 6 q^{44} + 2 q^{45} + 2 q^{46} - 8 q^{47} - 2 q^{48} + 2 q^{50} - 8 q^{51} + 6 q^{53} - 2 q^{54} + 4 q^{55} - 2 q^{57} - 2 q^{60} - 6 q^{61} - 4 q^{62} + 2 q^{64} + 20 q^{65} + 6 q^{66} + 6 q^{67} + 8 q^{68} - 2 q^{69} + 2 q^{72} + 18 q^{74} - 2 q^{75} + 2 q^{76} + 2 q^{80} + 2 q^{81} + 4 q^{82} - 22 q^{83} + 8 q^{85} - 14 q^{86} - 6 q^{88} + 12 q^{89} + 2 q^{90} + 2 q^{92} + 4 q^{93} - 8 q^{94} + 32 q^{95} - 2 q^{96} + 8 q^{97} - 6 q^{99}+O(q^{100}) \) 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 - 6 * q^11 - 2 * q^12 - 2 * q^15 + 2 * q^16 + 8 * q^17 + 2 * q^18 + 2 * q^19 + 2 * q^20 - 6 * q^22 + 2 * q^23 - 2 * q^24 + 2 * q^25 - 2 * q^27 - 2 * q^30 - 4 * q^31 + 2 * q^32 + 6 * q^33 + 8 * q^34 + 2 * q^36 + 18 * q^37 + 2 * q^38 + 2 * q^40 + 4 * q^41 - 14 * q^43 - 6 * q^44 + 2 * q^45 + 2 * q^46 - 8 * q^47 - 2 * q^48 + 2 * q^50 - 8 * q^51 + 6 * q^53 - 2 * q^54 + 4 * q^55 - 2 * q^57 - 2 * q^60 - 6 * q^61 - 4 * q^62 + 2 * q^64 + 20 * q^65 + 6 * q^66 + 6 * q^67 + 8 * q^68 - 2 * q^69 + 2 * q^72 + 18 * q^74 - 2 * q^75 + 2 * q^76 + 2 * q^80 + 2 * q^81 + 4 * q^82 - 22 * q^83 + 8 * q^85 - 14 * q^86 - 6 * q^88 + 12 * q^89 + 2 * q^90 + 2 * q^92 + 4 * q^93 - 8 * q^94 + 32 * q^95 - 2 * q^96 + 8 * q^97 - 6 * q^99

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