LMFDB - Embedded newform 3381.2.a.o.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3381,2,Mod(1,3381)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3381, 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("3381.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3381 = 3 \cdot 7^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3381.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:	$26.9974209234$
Analytic rank:	$1$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 483)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	3381.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.61803 q^{2} -1.00000 q^{3} +0.618034 q^{4} -1.38197 q^{5} +1.61803 q^{6} +2.23607 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.61803 q^{2} -1.00000 q^{3} +0.618034 q^{4} -1.38197 q^{5} +1.61803 q^{6} +2.23607 q^{8} +1.00000 q^{9} +2.23607 q^{10} +1.00000 q^{11} -0.618034 q^{12} +1.61803 q^{13} +1.38197 q^{15} -4.85410 q^{16} -3.47214 q^{17} -1.61803 q^{18} +0.236068 q^{19} -0.854102 q^{20} -1.61803 q^{22} +1.00000 q^{23} -2.23607 q^{24} -3.09017 q^{25} -2.61803 q^{26} -1.00000 q^{27} +6.23607 q^{29} -2.23607 q^{30} -4.70820 q^{31} +3.38197 q^{32} -1.00000 q^{33} +5.61803 q^{34} +0.618034 q^{36} -4.23607 q^{37} -0.381966 q^{38} -1.61803 q^{39} -3.09017 q^{40} -5.47214 q^{41} +2.85410 q^{43} +0.618034 q^{44} -1.38197 q^{45} -1.61803 q^{46} +1.70820 q^{47} +4.85410 q^{48} +5.00000 q^{50} +3.47214 q^{51} +1.00000 q^{52} +11.0902 q^{53} +1.61803 q^{54} -1.38197 q^{55} -0.236068 q^{57} -10.0902 q^{58} +1.38197 q^{59} +0.854102 q^{60} +1.14590 q^{61} +7.61803 q^{62} +4.23607 q^{64} -2.23607 q^{65} +1.61803 q^{66} +3.09017 q^{67} -2.14590 q^{68} -1.00000 q^{69} +5.32624 q^{71} +2.23607 q^{72} -6.23607 q^{73} +6.85410 q^{74} +3.09017 q^{75} +0.145898 q^{76} +2.61803 q^{78} -9.76393 q^{79} +6.70820 q^{80} +1.00000 q^{81} +8.85410 q^{82} +0.0557281 q^{83} +4.79837 q^{85} -4.61803 q^{86} -6.23607 q^{87} +2.23607 q^{88} +6.56231 q^{89} +2.23607 q^{90} +0.618034 q^{92} +4.70820 q^{93} -2.76393 q^{94} -0.326238 q^{95} -3.38197 q^{96} +6.70820 q^{97} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - 2 q^{3} - q^{4} - 5 q^{5} + q^{6} + 2 q^{9}+O(q^{10}) $ 2 * q - q^2 - 2 * q^3 - q^4 - 5 * q^5 + q^6 + 2 * q^9	$ 2 q - q^{2} - 2 q^{3} - q^{4} - 5 q^{5} + q^{6} + 2 q^{9} + 2 q^{11} + q^{12} + q^{13} + 5 q^{15} - 3 q^{16} + 2 q^{17} - q^{18} - 4 q^{19} + 5 q^{20} - q^{22} + 2 q^{23} + 5 q^{25} - 3 q^{26} - 2 q^{27} + 8 q^{29} + 4 q^{31} + 9 q^{32} - 2 q^{33} + 9 q^{34} - q^{36} - 4 q^{37} - 3 q^{38} - q^{39} + 5 q^{40} - 2 q^{41} - q^{43} - q^{44} - 5 q^{45} - q^{46} - 10 q^{47} + 3 q^{48} + 10 q^{50} - 2 q^{51} + 2 q^{52} + 11 q^{53} + q^{54} - 5 q^{55} + 4 q^{57} - 9 q^{58} + 5 q^{59} - 5 q^{60} + 9 q^{61} + 13 q^{62} + 4 q^{64} + q^{66} - 5 q^{67} - 11 q^{68} - 2 q^{69} - 5 q^{71} - 8 q^{73} + 7 q^{74} - 5 q^{75} + 7 q^{76} + 3 q^{78} - 24 q^{79} + 2 q^{81} + 11 q^{82} + 18 q^{83} - 15 q^{85} - 7 q^{86} - 8 q^{87} - 7 q^{89} - q^{92} - 4 q^{93} - 10 q^{94} + 15 q^{95} - 9 q^{96} + 2 q^{99}+O(q^{100}) $ 2 * q - q^2 - 2 * q^3 - q^4 - 5 * q^5 + q^6 + 2 * q^9 + 2 * q^11 + q^12 + q^13 + 5 * q^15 - 3 * q^16 + 2 * q^17 - q^18 - 4 * q^19 + 5 * q^20 - q^22 + 2 * q^23 + 5 * q^25 - 3 * q^26 - 2 * q^27 + 8 * q^29 + 4 * q^31 + 9 * q^32 - 2 * q^33 + 9 * q^34 - q^36 - 4 * q^37 - 3 * q^38 - q^39 + 5 * q^40 - 2 * q^41 - q^43 - q^44 - 5 * q^45 - q^46 - 10 * q^47 + 3 * q^48 + 10 * q^50 - 2 * q^51 + 2 * q^52 + 11 * q^53 + q^54 - 5 * q^55 + 4 * q^57 - 9 * q^58 + 5 * q^59 - 5 * q^60 + 9 * q^61 + 13 * q^62 + 4 * q^64 + q^66 - 5 * q^67 - 11 * q^68 - 2 * q^69 - 5 * q^71 - 8 * q^73 + 7 * q^74 - 5 * q^75 + 7 * q^76 + 3 * q^78 - 24 * q^79 + 2 * q^81 + 11 * q^82 + 18 * q^83 - 15 * q^85 - 7 * q^86 - 8 * q^87 - 7 * q^89 - q^92 - 4 * q^93 - 10 * q^94 + 15 * q^95 - 9 * q^96 + 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.61803	−1.14412	−0.572061	−	0.820211i	$-0.693856\pi$
$2$	−1.61803	−1.14412	−0.572061	+	0.820211i	$0.693856\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.618034	0.309017
$5$	−1.38197	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$5$	−1.38197	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$6$	1.61803	0.660560
$7$	0	0
$7$	0	0
$8$	2.23607	0.790569
$9$	1.00000	0.333333
$10$	2.23607	0.707107
$11$	1.00000	0.301511	0.150756	−	0.988571i	$-0.451829\pi$
$11$	1.00000	0.301511	0.150756	+	0.988571i	$0.451829\pi$
$12$	−0.618034	−0.178411
$13$	1.61803	0.448762	0.224381	−	0.974502i	$-0.427964\pi$
$13$	1.61803	0.448762	0.224381	+	0.974502i	$0.427964\pi$
$14$	0	0
$15$	1.38197	0.356822
$16$	−4.85410	−1.21353
$17$	−3.47214	−0.842117	−0.421058	−	0.907034i	$-0.638341\pi$
$17$	−3.47214	−0.842117	−0.421058	+	0.907034i	$0.638341\pi$
$18$	−1.61803	−0.381374
$19$	0.236068	0.0541577	0.0270789	−	0.999633i	$-0.491379\pi$
$19$	0.236068	0.0541577	0.0270789	+	0.999633i	$0.491379\pi$
$20$	−0.854102	−0.190983
$21$	0	0
$22$	−1.61803	−0.344966
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−2.23607	−0.456435
$25$	−3.09017	−0.618034
$26$	−2.61803	−0.513439
$27$	−1.00000	−0.192450
$28$	0	0
$29$	6.23607	1.15801	0.579004	−	0.815324i	$-0.303441\pi$
$29$	6.23607	1.15801	0.579004	+	0.815324i	$0.303441\pi$
$30$	−2.23607	−0.408248
$31$	−4.70820	−0.845618	−0.422809	−	0.906219i	$-0.638956\pi$
$31$	−4.70820	−0.845618	−0.422809	+	0.906219i	$0.638956\pi$
$32$	3.38197	0.597853
$33$	−1.00000	−0.174078
$34$	5.61803	0.963485
$35$	0	0
$36$	0.618034	0.103006
$37$	−4.23607	−0.696405	−0.348203	−	0.937419i	$-0.613208\pi$
$37$	−4.23607	−0.696405	−0.348203	+	0.937419i	$0.613208\pi$
$38$	−0.381966	−0.0619631
$39$	−1.61803	−0.259093
$40$	−3.09017	−0.488599
$41$	−5.47214	−0.854604	−0.427302	−	0.904109i	$-0.640536\pi$
$41$	−5.47214	−0.854604	−0.427302	+	0.904109i	$0.640536\pi$
$42$	0	0
$43$	2.85410	0.435246	0.217623	−	0.976033i	$-0.430170\pi$
$43$	2.85410	0.435246	0.217623	+	0.976033i	$0.430170\pi$
$44$	0.618034	0.0931721
$45$	−1.38197	−0.206011
$46$	−1.61803	−0.238566
$47$	1.70820	0.249167	0.124584	−	0.992209i	$-0.460241\pi$
$47$	1.70820	0.249167	0.124584	+	0.992209i	$0.460241\pi$
$48$	4.85410	0.700629
$49$	0	0
$50$	5.00000	0.707107
$51$	3.47214	0.486196
$52$	1.00000	0.138675
$53$	11.0902	1.52335	0.761676	−	0.647958i	$-0.224377\pi$
$53$	11.0902	1.52335	0.761676	+	0.647958i	$0.224377\pi$
$54$	1.61803	0.220187
$55$	−1.38197	−0.186344
$56$	0	0
$57$	−0.236068	−0.0312680
$58$	−10.0902	−1.32490
$59$	1.38197	0.179917	0.0899583	−	0.995946i	$-0.471327\pi$
$59$	1.38197	0.179917	0.0899583	+	0.995946i	$0.471327\pi$
$60$	0.854102	0.110264
$61$	1.14590	0.146717	0.0733586	−	0.997306i	$-0.476628\pi$
$61$	1.14590	0.146717	0.0733586	+	0.997306i	$0.476628\pi$
$62$	7.61803	0.967491
$63$	0	0
$64$	4.23607	0.529508
$65$	−2.23607	−0.277350
$66$	1.61803	0.199166
$67$	3.09017	0.377524	0.188762	−	0.982023i	$-0.439552\pi$
$67$	3.09017	0.377524	0.188762	+	0.982023i	$0.439552\pi$
$68$	−2.14590	−0.260228
$69$	−1.00000	−0.120386
$70$	0	0
$71$	5.32624	0.632108	0.316054	−	0.948741i	$-0.397642\pi$
$71$	5.32624	0.632108	0.316054	+	0.948741i	$0.397642\pi$
$72$	2.23607	0.263523
$73$	−6.23607	−0.729877	−0.364938	−	0.931032i	$-0.618910\pi$
$73$	−6.23607	−0.729877	−0.364938	+	0.931032i	$0.618910\pi$
$74$	6.85410	0.796773
$75$	3.09017	0.356822
$76$	0.145898	0.0167357
$77$	0	0
$78$	2.61803	0.296434
$79$	−9.76393	−1.09853	−0.549264	−	0.835649i	$-0.685092\pi$
$79$	−9.76393	−1.09853	−0.549264	+	0.835649i	$0.685092\pi$
$80$	6.70820	0.750000
$81$	1.00000	0.111111
$82$	8.85410	0.977772
$83$	0.0557281	0.00611695	0.00305848	−	0.999995i	$-0.499026\pi$
$83$	0.0557281	0.00611695	0.00305848	+	0.999995i	$0.499026\pi$
$84$	0	0
$85$	4.79837	0.520457
$86$	−4.61803	−0.497975
$87$	−6.23607	−0.668577
$88$	2.23607	0.238366
$89$	6.56231	0.695603	0.347802	−	0.937568i	$-0.386928\pi$
$89$	6.56231	0.695603	0.347802	+	0.937568i	$0.386928\pi$
$90$	2.23607	0.235702
$91$	0	0
$92$	0.618034	0.0644345
$93$	4.70820	0.488218
$94$	−2.76393	−0.285078
$95$	−0.326238	−0.0334713
$96$	−3.38197	−0.345170
$97$	6.70820	0.681115	0.340557	−	0.940224i	$-0.389384\pi$
$97$	6.70820	0.681115	0.340557	+	0.940224i	$0.389384\pi$
$98$	0	0
$99$	1.00000	0.100504
$100$	−1.90983	−0.190983
$101$	9.09017	0.904506	0.452253	−	0.891890i	$-0.350620\pi$
$101$	9.09017	0.904506	0.452253	+	0.891890i	$0.350620\pi$
$102$	−5.61803	−0.556268
$103$	9.52786	0.938808	0.469404	−	0.882983i	$-0.344469\pi$
$103$	9.52786	0.938808	0.469404	+	0.882983i	$0.344469\pi$
$104$	3.61803	0.354777
$105$	0	0
$106$	−17.9443	−1.74290
$107$	−14.0902	−1.36215	−0.681074	−	0.732215i	$-0.738487\pi$
$107$	−14.0902	−1.36215	−0.681074	+	0.732215i	$0.738487\pi$
$108$	−0.618034	−0.0594703
$109$	4.61803	0.442327	0.221164	−	0.975237i	$-0.429014\pi$
$109$	4.61803	0.442327	0.221164	+	0.975237i	$0.429014\pi$
$110$	2.23607	0.213201
$111$	4.23607	0.402070
$112$	0	0
$113$	2.90983	0.273734	0.136867	−	0.990589i	$-0.456297\pi$
$113$	2.90983	0.273734	0.136867	+	0.990589i	$0.456297\pi$
$114$	0.381966	0.0357744
$115$	−1.38197	−0.128869
$116$	3.85410	0.357844
$117$	1.61803	0.149587
$118$	−2.23607	−0.205847
$119$	0	0
$120$	3.09017	0.282093
$121$	−10.0000	−0.909091
$122$	−1.85410	−0.167863
$123$	5.47214	0.493406
$124$	−2.90983	−0.261310
$125$	11.1803	1.00000
$126$	0	0
$127$	−1.14590	−0.101682	−0.0508410	−	0.998707i	$-0.516190\pi$
$127$	−1.14590	−0.101682	−0.0508410	+	0.998707i	$0.516190\pi$
$128$	−13.6180	−1.20368
$129$	−2.85410	−0.251290
$130$	3.61803	0.317323
$131$	16.7082	1.45980	0.729901	−	0.683553i	$-0.239566\pi$
$131$	16.7082	1.45980	0.729901	+	0.683553i	$0.239566\pi$
$132$	−0.618034	−0.0537930
$133$	0	0
$134$	−5.00000	−0.431934
$135$	1.38197	0.118941
$136$	−7.76393	−0.665752
$137$	−7.18034	−0.613458	−0.306729	−	0.951797i	$-0.599235\pi$
$137$	−7.18034	−0.613458	−0.306729	+	0.951797i	$0.599235\pi$
$138$	1.61803	0.137736
$139$	8.03444	0.681472	0.340736	−	0.940159i	$-0.389324\pi$
$139$	8.03444	0.681472	0.340736	+	0.940159i	$0.389324\pi$
$140$	0	0
$141$	−1.70820	−0.143857
$142$	−8.61803	−0.723209
$143$	1.61803	0.135307
$144$	−4.85410	−0.404508
$145$	−8.61803	−0.715689
$146$	10.0902	0.835068
$147$	0	0
$148$	−2.61803	−0.215201
$149$	−9.70820	−0.795327	−0.397664	−	0.917531i	$-0.630179\pi$
$149$	−9.70820	−0.795327	−0.397664	+	0.917531i	$0.630179\pi$
$150$	−5.00000	−0.408248
$151$	−22.6525	−1.84343	−0.921716	−	0.387865i	$-0.873213\pi$
$151$	−22.6525	−1.84343	−0.921716	+	0.387865i	$0.873213\pi$
$152$	0.527864	0.0428154
$153$	−3.47214	−0.280706
$154$	0	0
$155$	6.50658	0.522621
$156$	−1.00000	−0.0800641
$157$	−13.2361	−1.05635	−0.528177	−	0.849135i	$-0.677124\pi$
$157$	−13.2361	−1.05635	−0.528177	+	0.849135i	$0.677124\pi$
$158$	15.7984	1.25685
$159$	−11.0902	−0.879508
$160$	−4.67376	−0.369493
$161$	0	0
$162$	−1.61803	−0.127125
$163$	13.2705	1.03943	0.519713	−	0.854341i	$-0.326039\pi$
$163$	13.2705	1.03943	0.519713	+	0.854341i	$0.326039\pi$
$164$	−3.38197	−0.264087
$165$	1.38197	0.107586
$166$	−0.0901699	−0.00699854
$167$	2.70820	0.209567	0.104784	−	0.994495i	$-0.466585\pi$
$167$	2.70820	0.209567	0.104784	+	0.994495i	$0.466585\pi$
$168$	0	0
$169$	−10.3820	−0.798613
$170$	−7.76393	−0.595466
$171$	0.236068	0.0180526
$172$	1.76393	0.134499
$173$	−20.4164	−1.55223	−0.776115	−	0.630591i	$-0.782813\pi$
$173$	−20.4164	−1.55223	−0.776115	+	0.630591i	$0.782813\pi$
$174$	10.0902	0.764934
$175$	0	0
$176$	−4.85410	−0.365892
$177$	−1.38197	−0.103875
$178$	−10.6180	−0.795855
$179$	10.7984	0.807108	0.403554	−	0.914956i	$-0.367775\pi$
$179$	10.7984	0.807108	0.403554	+	0.914956i	$0.367775\pi$
$180$	−0.854102	−0.0636610
$181$	−19.1803	−1.42566	−0.712832	−	0.701335i	$-0.752588\pi$
$181$	−19.1803	−1.42566	−0.712832	+	0.701335i	$0.752588\pi$
$182$	0	0
$183$	−1.14590	−0.0847072
$184$	2.23607	0.164845
$185$	5.85410	0.430402
$186$	−7.61803	−0.558581
$187$	−3.47214	−0.253908
$188$	1.05573	0.0769969
$189$	0	0
$190$	0.527864	0.0382953
$191$	−8.18034	−0.591909	−0.295954	−	0.955202i	$-0.595638\pi$
$191$	−8.18034	−0.591909	−0.295954	+	0.955202i	$0.595638\pi$
$192$	−4.23607	−0.305712
$193$	5.23607	0.376900	0.188450	−	0.982083i	$-0.439654\pi$
$193$	5.23607	0.376900	0.188450	+	0.982083i	$0.439654\pi$
$194$	−10.8541	−0.779279
$195$	2.23607	0.160128
$196$	0	0
$197$	−8.56231	−0.610039	−0.305020	−	0.952346i	$-0.598663\pi$
$197$	−8.56231	−0.610039	−0.305020	+	0.952346i	$0.598663\pi$
$198$	−1.61803	−0.114989
$199$	−21.5623	−1.52851	−0.764256	−	0.644913i	$-0.776893\pi$
$199$	−21.5623	−1.52851	−0.764256	+	0.644913i	$0.776893\pi$
$200$	−6.90983	−0.488599
$201$	−3.09017	−0.217964
$202$	−14.7082	−1.03487
$203$	0	0
$204$	2.14590	0.150243
$205$	7.56231	0.528174
$206$	−15.4164	−1.07411
$207$	1.00000	0.0695048
$208$	−7.85410	−0.544584
$209$	0.236068	0.0163292
$210$	0	0
$211$	−26.8885	−1.85108	−0.925542	−	0.378645i	$-0.876390\pi$
$211$	−26.8885	−1.85108	−0.925542	+	0.378645i	$0.876390\pi$
$212$	6.85410	0.470742
$213$	−5.32624	−0.364948
$214$	22.7984	1.55846
$215$	−3.94427	−0.268997
$216$	−2.23607	−0.152145
$217$	0	0
$218$	−7.47214	−0.506077
$219$	6.23607	0.421394
$220$	−0.854102	−0.0575835
$221$	−5.61803	−0.377910
$222$	−6.85410	−0.460017
$223$	0.618034	0.0413866	0.0206933	−	0.999786i	$-0.493413\pi$
$223$	0.618034	0.0413866	0.0206933	+	0.999786i	$0.493413\pi$
$224$	0	0
$225$	−3.09017	−0.206011
$226$	−4.70820	−0.313185
$227$	22.9787	1.52515	0.762575	−	0.646899i	$-0.223935\pi$
$227$	22.9787	1.52515	0.762575	+	0.646899i	$0.223935\pi$
$228$	−0.145898	−0.00966233
$229$	−3.20163	−0.211569	−0.105785	−	0.994389i	$-0.533735\pi$
$229$	−3.20163	−0.211569	−0.105785	+	0.994389i	$0.533735\pi$
$230$	2.23607	0.147442
$231$	0	0
$232$	13.9443	0.915486
$233$	24.3262	1.59366	0.796832	−	0.604200i	$-0.206507\pi$
$233$	24.3262	1.59366	0.796832	+	0.604200i	$0.206507\pi$
$234$	−2.61803	−0.171146
$235$	−2.36068	−0.153994
$236$	0.854102	0.0555973
$237$	9.76393	0.634236
$238$	0	0
$239$	−8.79837	−0.569119	−0.284560	−	0.958658i	$-0.591847\pi$
$239$	−8.79837	−0.569119	−0.284560	+	0.958658i	$0.591847\pi$
$240$	−6.70820	−0.433013
$241$	16.7082	1.07627	0.538135	−	0.842859i	$-0.319129\pi$
$241$	16.7082	1.07627	0.538135	+	0.842859i	$0.319129\pi$
$242$	16.1803	1.04011
$243$	−1.00000	−0.0641500
$244$	0.708204	0.0453381
$245$	0	0
$246$	−8.85410	−0.564517
$247$	0.381966	0.0243039
$248$	−10.5279	−0.668520
$249$	−0.0557281	−0.00353162
$250$	−18.0902	−1.14412
$251$	−4.29180	−0.270896	−0.135448	−	0.990784i	$-0.543247\pi$
$251$	−4.29180	−0.270896	−0.135448	+	0.990784i	$0.543247\pi$
$252$	0	0
$253$	1.00000	0.0628695
$254$	1.85410	0.116337
$255$	−4.79837	−0.300486
$256$	13.5623	0.847644
$257$	−10.2918	−0.641985	−0.320992	−	0.947082i	$-0.604016\pi$
$257$	−10.2918	−0.641985	−0.320992	+	0.947082i	$0.604016\pi$
$258$	4.61803	0.287506
$259$	0	0
$260$	−1.38197	−0.0857059
$261$	6.23607	0.386003
$262$	−27.0344	−1.67019
$263$	−9.65248	−0.595197	−0.297599	−	0.954691i	$-0.596186\pi$
$263$	−9.65248	−0.595197	−0.297599	+	0.954691i	$0.596186\pi$
$264$	−2.23607	−0.137620
$265$	−15.3262	−0.941483
$266$	0	0
$267$	−6.56231	−0.401607
$268$	1.90983	0.116661
$269$	26.7426	1.63053	0.815264	−	0.579090i	$-0.196592\pi$
$269$	26.7426	1.63053	0.815264	+	0.579090i	$0.196592\pi$
$270$	−2.23607	−0.136083
$271$	6.52786	0.396540	0.198270	−	0.980147i	$-0.436468\pi$
$271$	6.52786	0.396540	0.198270	+	0.980147i	$0.436468\pi$
$272$	16.8541	1.02193
$273$	0	0
$274$	11.6180	0.701871
$275$	−3.09017	−0.186344
$276$	−0.618034	−0.0372013
$277$	−8.67376	−0.521156	−0.260578	−	0.965453i	$-0.583913\pi$
$277$	−8.67376	−0.521156	−0.260578	+	0.965453i	$0.583913\pi$
$278$	−13.0000	−0.779688
$279$	−4.70820	−0.281873
$280$	0	0
$281$	16.6525	0.993403	0.496702	−	0.867921i	$-0.334544\pi$
$281$	16.6525	0.993403	0.496702	+	0.867921i	$0.334544\pi$
$282$	2.76393	0.164590
$283$	−9.67376	−0.575045	−0.287523	−	0.957774i	$-0.592832\pi$
$283$	−9.67376	−0.575045	−0.287523	+	0.957774i	$0.592832\pi$
$284$	3.29180	0.195332
$285$	0.326238	0.0193247
$286$	−2.61803	−0.154808
$287$	0	0
$288$	3.38197	0.199284
$289$	−4.94427	−0.290840
$290$	13.9443	0.818836
$291$	−6.70820	−0.393242
$292$	−3.85410	−0.225544
$293$	−30.8328	−1.80127	−0.900636	−	0.434574i	$-0.856899\pi$
$293$	−30.8328	−1.80127	−0.900636	+	0.434574i	$0.856899\pi$
$294$	0	0
$295$	−1.90983	−0.111195
$296$	−9.47214	−0.550557
$297$	−1.00000	−0.0580259
$298$	15.7082	0.909952
$299$	1.61803	0.0935733
$300$	1.90983	0.110264
$301$	0	0
$302$	36.6525	2.10911
$303$	−9.09017	−0.522217
$304$	−1.14590	−0.0657218
$305$	−1.58359	−0.0906762
$306$	5.61803	0.321162
$307$	−6.12461	−0.349550	−0.174775	−	0.984608i	$-0.555920\pi$
$307$	−6.12461	−0.349550	−0.174775	+	0.984608i	$0.555920\pi$
$308$	0	0
$309$	−9.52786	−0.542021
$310$	−10.5279	−0.597942
$311$	−27.5066	−1.55975	−0.779877	−	0.625932i	$-0.784719\pi$
$311$	−27.5066	−1.55975	−0.779877	+	0.625932i	$0.784719\pi$
$312$	−3.61803	−0.204831
$313$	1.88854	0.106747	0.0533734	−	0.998575i	$-0.483003\pi$
$313$	1.88854	0.106747	0.0533734	+	0.998575i	$0.483003\pi$
$314$	21.4164	1.20860
$315$	0	0
$316$	−6.03444	−0.339464
$317$	11.0902	0.622886	0.311443	−	0.950265i	$-0.399188\pi$
$317$	11.0902	0.622886	0.311443	+	0.950265i	$0.399188\pi$
$318$	17.9443	1.00626
$319$	6.23607	0.349153
$320$	−5.85410	−0.327254
$321$	14.0902	0.786437
$322$	0	0
$323$	−0.819660	−0.0456071
$324$	0.618034	0.0343352
$325$	−5.00000	−0.277350
$326$	−21.4721	−1.18923
$327$	−4.61803	−0.255378
$328$	−12.2361	−0.675624
$329$	0	0
$330$	−2.23607	−0.123091
$331$	−27.8885	−1.53289	−0.766447	−	0.642308i	$-0.777977\pi$
$331$	−27.8885	−1.53289	−0.766447	+	0.642308i	$0.777977\pi$
$332$	0.0344419	0.00189024
$333$	−4.23607	−0.232135
$334$	−4.38197	−0.239771
$335$	−4.27051	−0.233323
$336$	0	0
$337$	−19.0344	−1.03687	−0.518436	−	0.855116i	$-0.673486\pi$
$337$	−19.0344	−1.03687	−0.518436	+	0.855116i	$0.673486\pi$
$338$	16.7984	0.913711
$339$	−2.90983	−0.158040
$340$	2.96556	0.160830
$341$	−4.70820	−0.254964
$342$	−0.381966	−0.0206544
$343$	0	0
$344$	6.38197	0.344093
$345$	1.38197	0.0744025
$346$	33.0344	1.77594
$347$	−20.7082	−1.11167	−0.555837	−	0.831291i	$-0.687602\pi$
$347$	−20.7082	−1.11167	−0.555837	+	0.831291i	$0.687602\pi$
$348$	−3.85410	−0.206602
$349$	−4.79837	−0.256851	−0.128426	−	0.991719i	$-0.540992\pi$
$349$	−4.79837	−0.256851	−0.128426	+	0.991719i	$0.540992\pi$
$350$	0	0
$351$	−1.61803	−0.0863643
$352$	3.38197	0.180259
$353$	20.4164	1.08666	0.543328	−	0.839521i	$-0.317164\pi$
$353$	20.4164	1.08666	0.543328	+	0.839521i	$0.317164\pi$
$354$	2.23607	0.118846
$355$	−7.36068	−0.390664
$356$	4.05573	0.214953
$357$	0	0
$358$	−17.4721	−0.923431
$359$	−11.5623	−0.610235	−0.305118	−	0.952315i	$-0.598696\pi$
$359$	−11.5623	−0.610235	−0.305118	+	0.952315i	$0.598696\pi$
$360$	−3.09017	−0.162866
$361$	−18.9443	−0.997067
$362$	31.0344	1.63113
$363$	10.0000	0.524864
$364$	0	0
$365$	8.61803	0.451089
$366$	1.85410	0.0969155
$367$	20.2705	1.05811	0.529056	−	0.848587i	$-0.322546\pi$
$367$	20.2705	1.05811	0.529056	+	0.848587i	$0.322546\pi$
$368$	−4.85410	−0.253038
$369$	−5.47214	−0.284868
$370$	−9.47214	−0.492433
$371$	0	0
$372$	2.90983	0.150868
$373$	−6.12461	−0.317120	−0.158560	−	0.987349i	$-0.550685\pi$
$373$	−6.12461	−0.317120	−0.158560	+	0.987349i	$0.550685\pi$
$374$	5.61803	0.290502
$375$	−11.1803	−0.577350
$376$	3.81966	0.196984
$377$	10.0902	0.519670
$378$	0	0
$379$	−34.4721	−1.77071	−0.885357	−	0.464911i	$-0.846086\pi$
$379$	−34.4721	−1.77071	−0.885357	+	0.464911i	$0.846086\pi$
$380$	−0.201626	−0.0103432
$381$	1.14590	0.0587061
$382$	13.2361	0.677216
$383$	−13.9443	−0.712519	−0.356260	−	0.934387i	$-0.615948\pi$
$383$	−13.9443	−0.712519	−0.356260	+	0.934387i	$0.615948\pi$
$384$	13.6180	0.694942
$385$	0	0
$386$	−8.47214	−0.431220
$387$	2.85410	0.145082
$388$	4.14590	0.210476
$389$	−2.05573	−0.104230	−0.0521148	−	0.998641i	$-0.516596\pi$
$389$	−2.05573	−0.104230	−0.0521148	+	0.998641i	$0.516596\pi$
$390$	−3.61803	−0.183206
$391$	−3.47214	−0.175593
$392$	0	0
$393$	−16.7082	−0.842817
$394$	13.8541	0.697960
$395$	13.4934	0.678928
$396$	0.618034	0.0310574
$397$	0.180340	0.00905100	0.00452550	−	0.999990i	$-0.498559\pi$
$397$	0.180340	0.00905100	0.00452550	+	0.999990i	$0.498559\pi$
$398$	34.8885	1.74880
$399$	0	0
$400$	15.0000	0.750000
$401$	−5.00000	−0.249688	−0.124844	−	0.992176i	$-0.539843\pi$
$401$	−5.00000	−0.249688	−0.124844	+	0.992176i	$0.539843\pi$
$402$	5.00000	0.249377
$403$	−7.61803	−0.379481
$404$	5.61803	0.279508
$405$	−1.38197	−0.0686704
$406$	0	0
$407$	−4.23607	−0.209974
$408$	7.76393	0.384372
$409$	−10.8885	−0.538404	−0.269202	−	0.963084i	$-0.586760\pi$
$409$	−10.8885	−0.538404	−0.269202	+	0.963084i	$0.586760\pi$
$410$	−12.2361	−0.604296
$411$	7.18034	0.354180
$412$	5.88854	0.290108
$413$	0	0
$414$	−1.61803	−0.0795220
$415$	−0.0770143	−0.00378048
$416$	5.47214	0.268294
$417$	−8.03444	−0.393448
$418$	−0.381966	−0.0186826
$419$	−25.0902	−1.22574	−0.612868	−	0.790186i	$-0.709984\pi$
$419$	−25.0902	−1.22574	−0.612868	+	0.790186i	$0.709984\pi$
$420$	0	0
$421$	−9.43769	−0.459965	−0.229983	−	0.973195i	$-0.573867\pi$
$421$	−9.43769	−0.459965	−0.229983	+	0.973195i	$0.573867\pi$
$422$	43.5066	2.11787
$423$	1.70820	0.0830557
$424$	24.7984	1.20432
$425$	10.7295	0.520457
$426$	8.61803	0.417545
$427$	0	0
$428$	−8.70820	−0.420927
$429$	−1.61803	−0.0781194
$430$	6.38197	0.307766
$431$	−22.2705	−1.07273	−0.536366	−	0.843985i	$-0.680203\pi$
$431$	−22.2705	−1.07273	−0.536366	+	0.843985i	$0.680203\pi$
$432$	4.85410	0.233543
$433$	−25.2361	−1.21277	−0.606384	−	0.795172i	$-0.707381\pi$
$433$	−25.2361	−1.21277	−0.606384	+	0.795172i	$0.707381\pi$
$434$	0	0
$435$	8.61803	0.413203
$436$	2.85410	0.136687
$437$	0.236068	0.0112927
$438$	−10.0902	−0.482127
$439$	13.1803	0.629063	0.314532	−	0.949247i	$-0.398153\pi$
$439$	13.1803	0.629063	0.314532	+	0.949247i	$0.398153\pi$
$440$	−3.09017	−0.147318
$441$	0	0
$442$	9.09017	0.432375
$443$	26.8328	1.27487	0.637433	−	0.770506i	$-0.279996\pi$
$443$	26.8328	1.27487	0.637433	+	0.770506i	$0.279996\pi$
$444$	2.61803	0.124246
$445$	−9.06888	−0.429906
$446$	−1.00000	−0.0473514
$447$	9.70820	0.459182
$448$	0	0
$449$	6.72949	0.317584	0.158792	−	0.987312i	$-0.449240\pi$
$449$	6.72949	0.317584	0.158792	+	0.987312i	$0.449240\pi$
$450$	5.00000	0.235702
$451$	−5.47214	−0.257673
$452$	1.79837	0.0845884
$453$	22.6525	1.06431
$454$	−37.1803	−1.74496
$455$	0	0
$456$	−0.527864	−0.0247195
$457$	39.7426	1.85908	0.929541	−	0.368718i	$-0.120203\pi$
$457$	39.7426	1.85908	0.929541	+	0.368718i	$0.120203\pi$
$458$	5.18034	0.242061
$459$	3.47214	0.162065
$460$	−0.854102	−0.0398227
$461$	−10.3262	−0.480941	−0.240470	−	0.970656i	$-0.577302\pi$
$461$	−10.3262	−0.480941	−0.240470	+	0.970656i	$0.577302\pi$
$462$	0	0
$463$	−26.1246	−1.21411	−0.607057	−	0.794658i	$-0.707650\pi$
$463$	−26.1246	−1.21411	−0.607057	+	0.794658i	$0.707650\pi$
$464$	−30.2705	−1.40527
$465$	−6.50658	−0.301735
$466$	−39.3607	−1.82335
$467$	−2.88854	−0.133666	−0.0668329	−	0.997764i	$-0.521289\pi$
$467$	−2.88854	−0.133666	−0.0668329	+	0.997764i	$0.521289\pi$
$468$	1.00000	0.0462250
$469$	0	0
$470$	3.81966	0.176188
$471$	13.2361	0.609886
$472$	3.09017	0.142237
$473$	2.85410	0.131232
$474$	−15.7984	−0.725643
$475$	−0.729490	−0.0334713
$476$	0	0
$477$	11.0902	0.507784
$478$	14.2361	0.651143
$479$	9.29180	0.424553	0.212276	−	0.977210i	$-0.431912\pi$
$479$	9.29180	0.424553	0.212276	+	0.977210i	$0.431912\pi$
$480$	4.67376	0.213327
$481$	−6.85410	−0.312520
$482$	−27.0344	−1.23139
$483$	0	0
$484$	−6.18034	−0.280925
$485$	−9.27051	−0.420952
$486$	1.61803	0.0733955
$487$	10.1246	0.458790	0.229395	−	0.973333i	$-0.426325\pi$
$487$	10.1246	0.458790	0.229395	+	0.973333i	$0.426325\pi$
$488$	2.56231	0.115990
$489$	−13.2705	−0.600113
$490$	0	0
$491$	−22.5623	−1.01822	−0.509111	−	0.860701i	$-0.670026\pi$
$491$	−22.5623	−1.01822	−0.509111	+	0.860701i	$0.670026\pi$
$492$	3.38197	0.152471
$493$	−21.6525	−0.975178
$494$	−0.618034	−0.0278067
$495$	−1.38197	−0.0621148
$496$	22.8541	1.02618
$497$	0	0
$498$	0.0901699	0.00404061
$499$	−3.56231	−0.159471	−0.0797354	−	0.996816i	$-0.525408\pi$
$499$	−3.56231	−0.159471	−0.0797354	+	0.996816i	$0.525408\pi$
$500$	6.90983	0.309017
$501$	−2.70820	−0.120994
$502$	6.94427	0.309938
$503$	−34.6869	−1.54661	−0.773307	−	0.634032i	$-0.781399\pi$
$503$	−34.6869	−1.54661	−0.773307	+	0.634032i	$0.781399\pi$
$504$	0	0
$505$	−12.5623	−0.559015
$506$	−1.61803	−0.0719304
$507$	10.3820	0.461079
$508$	−0.708204	−0.0314215
$509$	−35.2361	−1.56181	−0.780906	−	0.624649i	$-0.785242\pi$
$509$	−35.2361	−1.56181	−0.780906	+	0.624649i	$0.785242\pi$
$510$	7.76393	0.343793
$511$	0	0
$512$	5.29180	0.233867
$513$	−0.236068	−0.0104227
$514$	16.6525	0.734509
$515$	−13.1672	−0.580215
$516$	−1.76393	−0.0776528
$517$	1.70820	0.0751267
$518$	0	0
$519$	20.4164	0.896181
$520$	−5.00000	−0.219265
$521$	−5.41641	−0.237297	−0.118649	−	0.992936i	$-0.537856\pi$
$521$	−5.41641	−0.237297	−0.118649	+	0.992936i	$0.537856\pi$
$522$	−10.0902	−0.441635
$523$	37.4164	1.63611	0.818053	−	0.575143i	$-0.195054\pi$
$523$	37.4164	1.63611	0.818053	+	0.575143i	$0.195054\pi$
$524$	10.3262	0.451104
$525$	0	0
$526$	15.6180	0.680979
$527$	16.3475	0.712109
$528$	4.85410	0.211248
$529$	1.00000	0.0434783
$530$	24.7984	1.07717
$531$	1.38197	0.0599722
$532$	0	0
$533$	−8.85410	−0.383514
$534$	10.6180	0.459487
$535$	19.4721	0.841854
$536$	6.90983	0.298459
$537$	−10.7984	−0.465984
$538$	−43.2705	−1.86552
$539$	0	0
$540$	0.854102	0.0367547
$541$	−2.29180	−0.0985320	−0.0492660	−	0.998786i	$-0.515688\pi$
$541$	−2.29180	−0.0985320	−0.0492660	+	0.998786i	$0.515688\pi$
$542$	−10.5623	−0.453690
$543$	19.1803	0.823107
$544$	−11.7426	−0.503462
$545$	−6.38197	−0.273373
$546$	0	0
$547$	−32.1459	−1.37446	−0.687230	−	0.726440i	$-0.741173\pi$
$547$	−32.1459	−1.37446	−0.687230	+	0.726440i	$0.741173\pi$
$548$	−4.43769	−0.189569
$549$	1.14590	0.0489057
$550$	5.00000	0.213201
$551$	1.47214	0.0627151
$552$	−2.23607	−0.0951734
$553$	0	0
$554$	14.0344	0.596266
$555$	−5.85410	−0.248493
$556$	4.96556	0.210587
$557$	17.2361	0.730316	0.365158	−	0.930946i	$-0.381015\pi$
$557$	17.2361	0.730316	0.365158	+	0.930946i	$0.381015\pi$
$558$	7.61803	0.322497
$559$	4.61803	0.195322
$560$	0	0
$561$	3.47214	0.146594
$562$	−26.9443	−1.13658
$563$	15.2148	0.641227	0.320613	−	0.947210i	$-0.396111\pi$
$563$	15.2148	0.641227	0.320613	+	0.947210i	$0.396111\pi$
$564$	−1.05573	−0.0444542
$565$	−4.02129	−0.169177
$566$	15.6525	0.657923
$567$	0	0
$568$	11.9098	0.499725
$569$	−9.88854	−0.414549	−0.207275	−	0.978283i	$-0.566459\pi$
$569$	−9.88854	−0.414549	−0.207275	+	0.978283i	$0.566459\pi$
$570$	−0.527864	−0.0221098
$571$	24.5967	1.02934	0.514671	−	0.857388i	$-0.327914\pi$
$571$	24.5967	1.02934	0.514671	+	0.857388i	$0.327914\pi$
$572$	1.00000	0.0418121
$573$	8.18034	0.341739
$574$	0	0
$575$	−3.09017	−0.128869
$576$	4.23607	0.176503
$577$	−40.2492	−1.67560	−0.837799	−	0.545979i	$-0.816158\pi$
$577$	−40.2492	−1.67560	−0.837799	+	0.545979i	$0.816158\pi$
$578$	8.00000	0.332756
$579$	−5.23607	−0.217604
$580$	−5.32624	−0.221160
$581$	0	0
$582$	10.8541	0.449917
$583$	11.0902	0.459308
$584$	−13.9443	−0.577018
$585$	−2.23607	−0.0924500
$586$	49.8885	2.06088
$587$	−20.2016	−0.833810	−0.416905	−	0.908950i	$-0.636885\pi$
$587$	−20.2016	−0.833810	−0.416905	+	0.908950i	$0.636885\pi$
$588$	0	0
$589$	−1.11146	−0.0457968
$590$	3.09017	0.127220
$591$	8.56231	0.352206
$592$	20.5623	0.845106
$593$	4.87539	0.200208	0.100104	−	0.994977i	$-0.468082\pi$
$593$	4.87539	0.200208	0.100104	+	0.994977i	$0.468082\pi$
$594$	1.61803	0.0663887
$595$	0	0
$596$	−6.00000	−0.245770
$597$	21.5623	0.882486
$598$	−2.61803	−0.107059
$599$	−9.61803	−0.392982	−0.196491	−	0.980506i	$-0.562955\pi$
$599$	−9.61803	−0.392982	−0.196491	+	0.980506i	$0.562955\pi$
$600$	6.90983	0.282093
$601$	28.6869	1.17016	0.585082	−	0.810974i	$-0.301062\pi$
$601$	28.6869	1.17016	0.585082	+	0.810974i	$0.301062\pi$
$602$	0	0
$603$	3.09017	0.125841
$604$	−14.0000	−0.569652
$605$	13.8197	0.561849
$606$	14.7082	0.597480
$607$	31.5066	1.27881	0.639406	−	0.768869i	$-0.279180\pi$
$607$	31.5066	1.27881	0.639406	+	0.768869i	$0.279180\pi$
$608$	0.798374	0.0323783
$609$	0	0
$610$	2.56231	0.103745
$611$	2.76393	0.111817
$612$	−2.14590	−0.0867428
$613$	31.8328	1.28572	0.642858	−	0.765986i	$-0.277749\pi$
$613$	31.8328	1.28572	0.642858	+	0.765986i	$0.277749\pi$
$614$	9.90983	0.399928
$615$	−7.56231	−0.304942
$616$	0	0
$617$	34.7426	1.39869	0.699343	−	0.714786i	$-0.253476\pi$
$617$	34.7426	1.39869	0.699343	+	0.714786i	$0.253476\pi$
$618$	15.4164	0.620139
$619$	−16.0902	−0.646719	−0.323359	−	0.946276i	$-0.604812\pi$
$619$	−16.0902	−0.646719	−0.323359	+	0.946276i	$0.604812\pi$
$620$	4.02129	0.161499
$621$	−1.00000	−0.0401286
$622$	44.5066	1.78455
$623$	0	0
$624$	7.85410	0.314416
$625$	0	0
$626$	−3.05573	−0.122131
$627$	−0.236068	−0.00942765
$628$	−8.18034	−0.326431
$629$	14.7082	0.586454
$630$	0	0
$631$	5.00000	0.199047	0.0995234	−	0.995035i	$-0.468268\pi$
$631$	5.00000	0.199047	0.0995234	+	0.995035i	$0.468268\pi$
$632$	−21.8328	−0.868463
$633$	26.8885	1.06872
$634$	−17.9443	−0.712658
$635$	1.58359	0.0628429
$636$	−6.85410	−0.271783
$637$	0	0
$638$	−10.0902	−0.399474
$639$	5.32624	0.210703
$640$	18.8197	0.743912
$641$	−0.201626	−0.00796375	−0.00398188	−	0.999992i	$-0.501267\pi$
$641$	−0.201626	−0.00796375	−0.00398188	+	0.999992i	$0.501267\pi$
$642$	−22.7984	−0.899780
$643$	−33.0344	−1.30275	−0.651376	−	0.758755i	$-0.725808\pi$
$643$	−33.0344	−1.30275	−0.651376	+	0.758755i	$0.725808\pi$
$644$	0	0
$645$	3.94427	0.155306
$646$	1.32624	0.0521801
$647$	−6.72949	−0.264564	−0.132282	−	0.991212i	$-0.542230\pi$
$647$	−6.72949	−0.264564	−0.132282	+	0.991212i	$0.542230\pi$
$648$	2.23607	0.0878410
$649$	1.38197	0.0542469
$650$	8.09017	0.317323
$651$	0	0
$652$	8.20163	0.321200
$653$	−7.09017	−0.277460	−0.138730	−	0.990330i	$-0.544302\pi$
$653$	−7.09017	−0.277460	−0.138730	+	0.990330i	$0.544302\pi$
$654$	7.47214	0.292184
$655$	−23.0902	−0.902208
$656$	26.5623	1.03708
$657$	−6.23607	−0.243292
$658$	0	0
$659$	−18.0557	−0.703351	−0.351676	−	0.936122i	$-0.614388\pi$
$659$	−18.0557	−0.703351	−0.351676	+	0.936122i	$0.614388\pi$
$660$	0.854102	0.0332459
$661$	7.65248	0.297647	0.148823	−	0.988864i	$-0.452451\pi$
$661$	7.65248	0.297647	0.148823	+	0.988864i	$0.452451\pi$
$662$	45.1246	1.75382
$663$	5.61803	0.218186
$664$	0.124612	0.00483588
$665$	0	0
$666$	6.85410	0.265591
$667$	6.23607	0.241462
$668$	1.67376	0.0647598
$669$	−0.618034	−0.0238946
$670$	6.90983	0.266950
$671$	1.14590	0.0442369
$672$	0	0
$673$	−7.58359	−0.292326	−0.146163	−	0.989261i	$-0.546692\pi$
$673$	−7.58359	−0.292326	−0.146163	+	0.989261i	$0.546692\pi$
$674$	30.7984	1.18631
$675$	3.09017	0.118941
$676$	−6.41641	−0.246785
$677$	−18.6738	−0.717691	−0.358845	−	0.933397i	$-0.616830\pi$
$677$	−18.6738	−0.717691	−0.358845	+	0.933397i	$0.616830\pi$
$678$	4.70820	0.180817
$679$	0	0
$680$	10.7295	0.411457
$681$	−22.9787	−0.880546
$682$	7.61803	0.291710
$683$	−26.1246	−0.999630	−0.499815	−	0.866132i	$-0.666599\pi$
$683$	−26.1246	−0.999630	−0.499815	+	0.866132i	$0.666599\pi$
$684$	0.145898	0.00557855
$685$	9.92299	0.379138
$686$	0	0
$687$	3.20163	0.122150
$688$	−13.8541	−0.528183
$689$	17.9443	0.683622
$690$	−2.23607	−0.0851257
$691$	18.3820	0.699283	0.349641	−	0.936884i	$-0.386303\pi$
$691$	18.3820	0.699283	0.349641	+	0.936884i	$0.386303\pi$
$692$	−12.6180	−0.479666
$693$	0	0
$694$	33.5066	1.27189
$695$	−11.1033	−0.421173
$696$	−13.9443	−0.528556
$697$	19.0000	0.719676
$698$	7.76393	0.293869
$699$	−24.3262	−0.920103
$700$	0	0
$701$	−3.09017	−0.116714	−0.0583571	−	0.998296i	$-0.518586\pi$
$701$	−3.09017	−0.116714	−0.0583571	+	0.998296i	$0.518586\pi$
$702$	2.61803	0.0988113
$703$	−1.00000	−0.0377157
$704$	4.23607	0.159653
$705$	2.36068	0.0889083
$706$	−33.0344	−1.24327
$707$	0	0
$708$	−0.854102	−0.0320991
$709$	42.2705	1.58750	0.793751	−	0.608243i	$-0.208125\pi$
$709$	42.2705	1.58750	0.793751	+	0.608243i	$0.208125\pi$
$710$	11.9098	0.446968
$711$	−9.76393	−0.366176
$712$	14.6738	0.549922
$713$	−4.70820	−0.176324
$714$	0	0
$715$	−2.23607	−0.0836242
$716$	6.67376	0.249410
$717$	8.79837	0.328581
$718$	18.7082	0.698184
$719$	2.88854	0.107725	0.0538623	−	0.998548i	$-0.482847\pi$
$719$	2.88854	0.107725	0.0538623	+	0.998548i	$0.482847\pi$
$720$	6.70820	0.250000
$721$	0	0
$722$	30.6525	1.14077
$723$	−16.7082	−0.621385
$724$	−11.8541	−0.440554
$725$	−19.2705	−0.715689
$726$	−16.1803	−0.600509
$727$	15.5410	0.576385	0.288192	−	0.957573i	$-0.406946\pi$
$727$	15.5410	0.576385	0.288192	+	0.957573i	$0.406946\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−13.9443	−0.516101
$731$	−9.90983	−0.366528
$732$	−0.708204	−0.0261760
$733$	−42.7639	−1.57952	−0.789761	−	0.613415i	$-0.789795\pi$
$733$	−42.7639	−1.57952	−0.789761	+	0.613415i	$0.789795\pi$
$734$	−32.7984	−1.21061
$735$	0	0
$736$	3.38197	0.124661
$737$	3.09017	0.113828
$738$	8.85410	0.325924
$739$	−22.5279	−0.828701	−0.414350	−	0.910117i	$-0.635991\pi$
$739$	−22.5279	−0.828701	−0.414350	+	0.910117i	$0.635991\pi$
$740$	3.61803	0.133002
$741$	−0.381966	−0.0140319
$742$	0	0
$743$	13.3820	0.490937	0.245468	−	0.969405i	$-0.421058\pi$
$743$	13.3820	0.490937	0.245468	+	0.969405i	$0.421058\pi$
$744$	10.5279	0.385970
$745$	13.4164	0.491539
$746$	9.90983	0.362825
$747$	0.0557281	0.00203898
$748$	−2.14590	−0.0784618
$749$	0	0
$750$	18.0902	0.660560
$751$	−45.4508	−1.65853	−0.829263	−	0.558859i	$-0.811239\pi$
$751$	−45.4508	−1.65853	−0.829263	+	0.558859i	$0.811239\pi$
$752$	−8.29180	−0.302371
$753$	4.29180	0.156402
$754$	−16.3262	−0.594567
$755$	31.3050	1.13930
$756$	0	0
$757$	22.3475	0.812235	0.406117	−	0.913821i	$-0.366882\pi$
$757$	22.3475	0.812235	0.406117	+	0.913821i	$0.366882\pi$
$758$	55.7771	2.02592
$759$	−1.00000	−0.0362977
$760$	−0.729490	−0.0264614
$761$	−6.11146	−0.221540	−0.110770	−	0.993846i	$-0.535332\pi$
$761$	−6.11146	−0.221540	−0.110770	+	0.993846i	$0.535332\pi$
$762$	−1.85410	−0.0671670
$763$	0	0
$764$	−5.05573	−0.182910
$765$	4.79837	0.173486
$766$	22.5623	0.815209
$767$	2.23607	0.0807397
$768$	−13.5623	−0.489388
$769$	−20.6525	−0.744747	−0.372374	−	0.928083i	$-0.621456\pi$
$769$	−20.6525	−0.744747	−0.372374	+	0.928083i	$0.621456\pi$
$770$	0	0
$771$	10.2918	0.370650
$772$	3.23607	0.116469
$773$	−28.5967	−1.02855	−0.514277	−	0.857624i	$-0.671940\pi$
$773$	−28.5967	−1.02855	−0.514277	+	0.857624i	$0.671940\pi$
$774$	−4.61803	−0.165992
$775$	14.5492	0.522621
$776$	15.0000	0.538469
$777$	0	0
$778$	3.32624	0.119251
$779$	−1.29180	−0.0462834
$780$	1.38197	0.0494823
$781$	5.32624	0.190588
$782$	5.61803	0.200900
$783$	−6.23607	−0.222859
$784$	0	0
$785$	18.2918	0.652862
$786$	27.0344	0.964287
$787$	10.7984	0.384920	0.192460	−	0.981305i	$-0.438353\pi$
$787$	10.7984	0.384920	0.192460	+	0.981305i	$0.438353\pi$
$788$	−5.29180	−0.188512
$789$	9.65248	0.343637
$790$	−21.8328	−0.776777
$791$	0	0
$792$	2.23607	0.0794552
$793$	1.85410	0.0658411
$794$	−0.291796	−0.0103555
$795$	15.3262	0.543566
$796$	−13.3262	−0.472336
$797$	33.1246	1.17333	0.586667	−	0.809828i	$-0.300440\pi$
$797$	33.1246	1.17333	0.586667	+	0.809828i	$0.300440\pi$
$798$	0	0
$799$	−5.93112	−0.209828
$800$	−10.4508	−0.369493
$801$	6.56231	0.231868
$802$	8.09017	0.285674
$803$	−6.23607	−0.220066
$804$	−1.90983	−0.0673545
$805$	0	0
$806$	12.3262	0.434173
$807$	−26.7426	−0.941386
$808$	20.3262	0.715075
$809$	−40.2705	−1.41584	−0.707918	−	0.706295i	$-0.750365\pi$
$809$	−40.2705	−1.41584	−0.707918	+	0.706295i	$0.750365\pi$
$810$	2.23607	0.0785674
$811$	−50.3050	−1.76645	−0.883223	−	0.468953i	$-0.844631\pi$
$811$	−50.3050	−1.76645	−0.883223	+	0.468953i	$0.844631\pi$
$812$	0	0
$813$	−6.52786	−0.228942
$814$	6.85410	0.240236
$815$	−18.3394	−0.642401
$816$	−16.8541	−0.590012
$817$	0.673762	0.0235720
$818$	17.6180	0.616000
$819$	0	0
$820$	4.67376	0.163215
$821$	36.5410	1.27529	0.637645	−	0.770330i	$-0.279909\pi$
$821$	36.5410	1.27529	0.637645	+	0.770330i	$0.279909\pi$
$822$	−11.6180	−0.405225
$823$	−8.21478	−0.286349	−0.143175	−	0.989697i	$-0.545731\pi$
$823$	−8.21478	−0.286349	−0.143175	+	0.989697i	$0.545731\pi$
$824$	21.3050	0.742193
$825$	3.09017	0.107586
$826$	0	0
$827$	5.85410	0.203567	0.101784	−	0.994807i	$-0.467545\pi$
$827$	5.85410	0.203567	0.101784	+	0.994807i	$0.467545\pi$
$828$	0.618034	0.0214782
$829$	32.7771	1.13840	0.569198	−	0.822201i	$-0.307254\pi$
$829$	32.7771	1.13840	0.569198	+	0.822201i	$0.307254\pi$
$830$	0.124612	0.00432534
$831$	8.67376	0.300889
$832$	6.85410	0.237623
$833$	0	0
$834$	13.0000	0.450153
$835$	−3.74265	−0.129520
$836$	0.145898	0.00504599
$837$	4.70820	0.162739
$838$	40.5967	1.40239
$839$	−45.9787	−1.58736	−0.793681	−	0.608335i	$-0.791838\pi$
$839$	−45.9787	−1.58736	−0.793681	+	0.608335i	$0.791838\pi$
$840$	0	0
$841$	9.88854	0.340984
$842$	15.2705	0.526257
$843$	−16.6525	−0.573542
$844$	−16.6180	−0.572016
$845$	14.3475	0.493570
$846$	−2.76393	−0.0950259
$847$	0	0
$848$	−53.8328	−1.84863
$849$	9.67376	0.332003
$850$	−17.3607	−0.595466
$851$	−4.23607	−0.145211
$852$	−3.29180	−0.112775
$853$	36.0689	1.23498	0.617488	−	0.786581i	$-0.288151\pi$
$853$	36.0689	1.23498	0.617488	+	0.786581i	$0.288151\pi$
$854$	0	0
$855$	−0.326238	−0.0111571
$856$	−31.5066	−1.07687
$857$	39.1246	1.33647	0.668236	−	0.743950i	$-0.267050\pi$
$857$	39.1246	1.33647	0.668236	+	0.743950i	$0.267050\pi$
$858$	2.61803	0.0893782
$859$	46.3607	1.58181	0.790903	−	0.611942i	$-0.209611\pi$
$859$	46.3607	1.58181	0.790903	+	0.611942i	$0.209611\pi$
$860$	−2.43769	−0.0831247
$861$	0	0
$862$	36.0344	1.22734
$863$	30.1803	1.02735	0.513675	−	0.857985i	$-0.328284\pi$
$863$	30.1803	1.02735	0.513675	+	0.857985i	$0.328284\pi$
$864$	−3.38197	−0.115057
$865$	28.2148	0.959331
$866$	40.8328	1.38756
$867$	4.94427	0.167916
$868$	0	0
$869$	−9.76393	−0.331219
$870$	−13.9443	−0.472755
$871$	5.00000	0.169419
$872$	10.3262	0.349691
$873$	6.70820	0.227038
$874$	−0.381966	−0.0129202
$875$	0	0
$876$	3.85410	0.130218
$877$	20.0000	0.675352	0.337676	−	0.941262i	$-0.390359\pi$
$877$	20.0000	0.675352	0.337676	+	0.941262i	$0.390359\pi$
$878$	−21.3262	−0.719726
$879$	30.8328	1.03997
$880$	6.70820	0.226134
$881$	47.7082	1.60733	0.803665	−	0.595082i	$-0.202880\pi$
$881$	47.7082	1.60733	0.803665	+	0.595082i	$0.202880\pi$
$882$	0	0
$883$	16.0902	0.541477	0.270739	−	0.962653i	$-0.412732\pi$
$883$	16.0902	0.541477	0.270739	+	0.962653i	$0.412732\pi$
$884$	−3.47214	−0.116781
$885$	1.90983	0.0641982
$886$	−43.4164	−1.45860
$887$	−49.9787	−1.67812	−0.839060	−	0.544038i	$-0.816895\pi$
$887$	−49.9787	−1.67812	−0.839060	+	0.544038i	$0.816895\pi$
$888$	9.47214	0.317864
$889$	0	0
$890$	14.6738	0.491866
$891$	1.00000	0.0335013
$892$	0.381966	0.0127892
$893$	0.403252	0.0134943
$894$	−15.7082	−0.525361
$895$	−14.9230	−0.498820
$896$	0	0
$897$	−1.61803	−0.0540246
$898$	−10.8885	−0.363355
$899$	−29.3607	−0.979233
$900$	−1.90983	−0.0636610
$901$	−38.5066	−1.28284
$902$	8.85410	0.294809
$903$	0	0
$904$	6.50658	0.216406
$905$	26.5066	0.881108
$906$	−36.6525	−1.21770
$907$	31.2705	1.03832	0.519160	−	0.854677i	$-0.326245\pi$
$907$	31.2705	1.03832	0.519160	+	0.854677i	$0.326245\pi$
$908$	14.2016	0.471298
$909$	9.09017	0.301502
$910$	0	0
$911$	35.0132	1.16004	0.580019	−	0.814603i	$-0.303045\pi$
$911$	35.0132	1.16004	0.580019	+	0.814603i	$0.303045\pi$
$912$	1.14590	0.0379445
$913$	0.0557281	0.00184433
$914$	−64.3050	−2.12702
$915$	1.58359	0.0523519
$916$	−1.97871	−0.0653785
$917$	0	0
$918$	−5.61803	−0.185423
$919$	56.1935	1.85365	0.926826	−	0.375491i	$-0.122526\pi$
$919$	56.1935	1.85365	0.926826	+	0.375491i	$0.122526\pi$
$920$	−3.09017	−0.101880
$921$	6.12461	0.201813
$922$	16.7082	0.550255
$923$	8.61803	0.283666
$924$	0	0
$925$	13.0902	0.430402
$926$	42.2705	1.38910
$927$	9.52786	0.312936
$928$	21.0902	0.692319
$929$	−29.9230	−0.981741	−0.490871	−	0.871232i	$-0.663321\pi$
$929$	−29.9230	−0.981741	−0.490871	+	0.871232i	$0.663321\pi$
$930$	10.5279	0.345222
$931$	0	0
$932$	15.0344	0.492470
$933$	27.5066	0.900525
$934$	4.67376	0.152930
$935$	4.79837	0.156924
$936$	3.61803	0.118259
$937$	23.3607	0.763160	0.381580	−	0.924336i	$-0.375380\pi$
$937$	23.3607	0.763160	0.381580	+	0.924336i	$0.375380\pi$
$938$	0	0
$939$	−1.88854	−0.0616303
$940$	−1.45898	−0.0475867
$941$	−44.3607	−1.44612	−0.723058	−	0.690787i	$-0.757264\pi$
$941$	−44.3607	−1.44612	−0.723058	+	0.690787i	$0.757264\pi$
$942$	−21.4164	−0.697784
$943$	−5.47214	−0.178197
$944$	−6.70820	−0.218333
$945$	0	0
$946$	−4.61803	−0.150145
$947$	−53.4164	−1.73580	−0.867900	−	0.496739i	$-0.834531\pi$
$947$	−53.4164	−1.73580	−0.867900	+	0.496739i	$0.834531\pi$
$948$	6.03444	0.195990
$949$	−10.0902	−0.327541
$950$	1.18034	0.0382953
$951$	−11.0902	−0.359623
$952$	0	0
$953$	−33.9787	−1.10068	−0.550339	−	0.834941i	$-0.685502\pi$
$953$	−33.9787	−1.10068	−0.550339	+	0.834941i	$0.685502\pi$
$954$	−17.9443	−0.580967
$955$	11.3050	0.365820
$956$	−5.43769	−0.175868
$957$	−6.23607	−0.201583
$958$	−15.0344	−0.485741
$959$	0	0
$960$	5.85410	0.188940
$961$	−8.83282	−0.284930
$962$	11.0902	0.357561
$963$	−14.0902	−0.454049
$964$	10.3262	0.332586
$965$	−7.23607	−0.232937
$966$	0	0
$967$	−7.88854	−0.253678	−0.126839	−	0.991923i	$-0.540483\pi$
$967$	−7.88854	−0.253678	−0.126839	+	0.991923i	$0.540483\pi$
$968$	−22.3607	−0.718699
$969$	0.819660	0.0263313
$970$	15.0000	0.481621
$971$	−20.9656	−0.672817	−0.336408	−	0.941716i	$-0.609212\pi$
$971$	−20.9656	−0.672817	−0.336408	+	0.941716i	$0.609212\pi$
$972$	−0.618034	−0.0198234
$973$	0	0
$974$	−16.3820	−0.524912
$975$	5.00000	0.160128
$976$	−5.56231	−0.178045
$977$	39.2148	1.25459	0.627296	−	0.778781i	$-0.284162\pi$
$977$	39.2148	1.25459	0.627296	+	0.778781i	$0.284162\pi$
$978$	21.4721	0.686603
$979$	6.56231	0.209732
$980$	0	0
$981$	4.61803	0.147442
$982$	36.5066	1.16497
$983$	−5.00000	−0.159475	−0.0797376	−	0.996816i	$-0.525408\pi$
$983$	−5.00000	−0.159475	−0.0797376	+	0.996816i	$0.525408\pi$
$984$	12.2361	0.390072
$985$	11.8328	0.377025
$986$	35.0344	1.11572
$987$	0	0
$988$	0.236068	0.00751032
$989$	2.85410	0.0907552
$990$	2.23607	0.0710669
$991$	−48.3820	−1.53690	−0.768452	−	0.639908i	$-0.778973\pi$
$991$	−48.3820	−1.53690	−0.768452	+	0.639908i	$0.778973\pi$
$992$	−15.9230	−0.505555
$993$	27.8885	0.885016
$994$	0	0
$995$	29.7984	0.944672
$996$	−0.0344419	−0.00109133
$997$	22.3050	0.706405	0.353202	−	0.935547i	$-0.385093\pi$
$997$	22.3050	0.706405	0.353202	+	0.935547i	$0.385093\pi$
$998$	5.76393	0.182454
$999$	4.23607	0.134023

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3381.2.a.o.1.1		2
7.6	odd	2		483.2.a.e.1.1	✓	2
21.20	even	2		1449.2.a.g.1.2		2
28.27	even	2		7728.2.a.be.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.a.e.1.1	✓	2	7.6	odd	2
1449.2.a.g.1.2		2	21.20	even	2
3381.2.a.o.1.1		2	1.1	even	1	trivial
7728.2.a.be.1.1		2	28.27	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:	\( N \)	\(=\)	\( 3381 = 3 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3381.a (trivial)

\(f(q)\)	\(=\)	\(q-1.61803 q^{2} -1.00000 q^{3} +0.618034 q^{4} -1.38197 q^{5} +1.61803 q^{6} +2.23607 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.61803 q^{2} -1.00000 q^{3} +0.618034 q^{4} -1.38197 q^{5} +1.61803 q^{6} +2.23607 q^{8} +1.00000 q^{9} +2.23607 q^{10} +1.00000 q^{11} -0.618034 q^{12} +1.61803 q^{13} +1.38197 q^{15} -4.85410 q^{16} -3.47214 q^{17} -1.61803 q^{18} +0.236068 q^{19} -0.854102 q^{20} -1.61803 q^{22} +1.00000 q^{23} -2.23607 q^{24} -3.09017 q^{25} -2.61803 q^{26} -1.00000 q^{27} +6.23607 q^{29} -2.23607 q^{30} -4.70820 q^{31} +3.38197 q^{32} -1.00000 q^{33} +5.61803 q^{34} +0.618034 q^{36} -4.23607 q^{37} -0.381966 q^{38} -1.61803 q^{39} -3.09017 q^{40} -5.47214 q^{41} +2.85410 q^{43} +0.618034 q^{44} -1.38197 q^{45} -1.61803 q^{46} +1.70820 q^{47} +4.85410 q^{48} +5.00000 q^{50} +3.47214 q^{51} +1.00000 q^{52} +11.0902 q^{53} +1.61803 q^{54} -1.38197 q^{55} -0.236068 q^{57} -10.0902 q^{58} +1.38197 q^{59} +0.854102 q^{60} +1.14590 q^{61} +7.61803 q^{62} +4.23607 q^{64} -2.23607 q^{65} +1.61803 q^{66} +3.09017 q^{67} -2.14590 q^{68} -1.00000 q^{69} +5.32624 q^{71} +2.23607 q^{72} -6.23607 q^{73} +6.85410 q^{74} +3.09017 q^{75} +0.145898 q^{76} +2.61803 q^{78} -9.76393 q^{79} +6.70820 q^{80} +1.00000 q^{81} +8.85410 q^{82} +0.0557281 q^{83} +4.79837 q^{85} -4.61803 q^{86} -6.23607 q^{87} +2.23607 q^{88} +6.56231 q^{89} +2.23607 q^{90} +0.618034 q^{92} +4.70820 q^{93} -2.76393 q^{94} -0.326238 q^{95} -3.38197 q^{96} +6.70820 q^{97} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - 2 q^{3} - q^{4} - 5 q^{5} + q^{6} + 2 q^{9}+O(q^{10}) \) 2 * q - q^2 - 2 * q^3 - q^4 - 5 * q^5 + q^6 + 2 * q^9	\( 2 q - q^{2} - 2 q^{3} - q^{4} - 5 q^{5} + q^{6} + 2 q^{9} + 2 q^{11} + q^{12} + q^{13} + 5 q^{15} - 3 q^{16} + 2 q^{17} - q^{18} - 4 q^{19} + 5 q^{20} - q^{22} + 2 q^{23} + 5 q^{25} - 3 q^{26} - 2 q^{27} + 8 q^{29} + 4 q^{31} + 9 q^{32} - 2 q^{33} + 9 q^{34} - q^{36} - 4 q^{37} - 3 q^{38} - q^{39} + 5 q^{40} - 2 q^{41} - q^{43} - q^{44} - 5 q^{45} - q^{46} - 10 q^{47} + 3 q^{48} + 10 q^{50} - 2 q^{51} + 2 q^{52} + 11 q^{53} + q^{54} - 5 q^{55} + 4 q^{57} - 9 q^{58} + 5 q^{59} - 5 q^{60} + 9 q^{61} + 13 q^{62} + 4 q^{64} + q^{66} - 5 q^{67} - 11 q^{68} - 2 q^{69} - 5 q^{71} - 8 q^{73} + 7 q^{74} - 5 q^{75} + 7 q^{76} + 3 q^{78} - 24 q^{79} + 2 q^{81} + 11 q^{82} + 18 q^{83} - 15 q^{85} - 7 q^{86} - 8 q^{87} - 7 q^{89} - q^{92} - 4 q^{93} - 10 q^{94} + 15 q^{95} - 9 q^{96} + 2 q^{99}+O(q^{100}) \) 2 * q - q^2 - 2 * q^3 - q^4 - 5 * q^5 + q^6 + 2 * q^9 + 2 * q^11 + q^12 + q^13 + 5 * q^15 - 3 * q^16 + 2 * q^17 - q^18 - 4 * q^19 + 5 * q^20 - q^22 + 2 * q^23 + 5 * q^25 - 3 * q^26 - 2 * q^27 + 8 * q^29 + 4 * q^31 + 9 * q^32 - 2 * q^33 + 9 * q^34 - q^36 - 4 * q^37 - 3 * q^38 - q^39 + 5 * q^40 - 2 * q^41 - q^43 - q^44 - 5 * q^45 - q^46 - 10 * q^47 + 3 * q^48 + 10 * q^50 - 2 * q^51 + 2 * q^52 + 11 * q^53 + q^54 - 5 * q^55 + 4 * q^57 - 9 * q^58 + 5 * q^59 - 5 * q^60 + 9 * q^61 + 13 * q^62 + 4 * q^64 + q^66 - 5 * q^67 - 11 * q^68 - 2 * q^69 - 5 * q^71 - 8 * q^73 + 7 * q^74 - 5 * q^75 + 7 * q^76 + 3 * q^78 - 24 * q^79 + 2 * q^81 + 11 * q^82 + 18 * q^83 - 15 * q^85 - 7 * q^86 - 8 * q^87 - 7 * q^89 - q^92 - 4 * q^93 - 10 * q^94 + 15 * q^95 - 9 * q^96 + 2 * q^99

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