LMFDB - Embedded newform 750.2.a.g.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(1,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("750.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.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:	$5.98878015160$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	750.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +1.61803 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +1.61803 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.618034 q^{11} +1.00000 q^{12} -1.85410 q^{13} +1.61803 q^{14} +1.00000 q^{16} +5.23607 q^{17} +1.00000 q^{18} -0.854102 q^{19} +1.61803 q^{21} +0.618034 q^{22} -1.85410 q^{23} +1.00000 q^{24} -1.85410 q^{26} +1.00000 q^{27} +1.61803 q^{28} -7.23607 q^{29} +6.47214 q^{31} +1.00000 q^{32} +0.618034 q^{33} +5.23607 q^{34} +1.00000 q^{36} +10.5623 q^{37} -0.854102 q^{38} -1.85410 q^{39} -11.6180 q^{41} +1.61803 q^{42} -7.70820 q^{43} +0.618034 q^{44} -1.85410 q^{46} -0.618034 q^{47} +1.00000 q^{48} -4.38197 q^{49} +5.23607 q^{51} -1.85410 q^{52} +7.61803 q^{53} +1.00000 q^{54} +1.61803 q^{56} -0.854102 q^{57} -7.23607 q^{58} -1.90983 q^{59} +3.70820 q^{61} +6.47214 q^{62} +1.61803 q^{63} +1.00000 q^{64} +0.618034 q^{66} +9.70820 q^{67} +5.23607 q^{68} -1.85410 q^{69} -12.4721 q^{71} +1.00000 q^{72} -4.94427 q^{73} +10.5623 q^{74} -0.854102 q^{76} +1.00000 q^{77} -1.85410 q^{78} -13.4164 q^{79} +1.00000 q^{81} -11.6180 q^{82} +2.94427 q^{83} +1.61803 q^{84} -7.70820 q^{86} -7.23607 q^{87} +0.618034 q^{88} -6.90983 q^{89} -3.00000 q^{91} -1.85410 q^{92} +6.47214 q^{93} -0.618034 q^{94} +1.00000 q^{96} -3.70820 q^{97} -4.38197 q^{98} +0.618034 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{6} + q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^6 + q^7 + 2 * q^8 + 2 * q^9	$ 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{6} + q^{7} + 2 q^{8} + 2 q^{9} - q^{11} + 2 q^{12} + 3 q^{13} + q^{14} + 2 q^{16} + 6 q^{17} + 2 q^{18} + 5 q^{19} + q^{21} - q^{22} + 3 q^{23} + 2 q^{24} + 3 q^{26} + 2 q^{27} + q^{28} - 10 q^{29} + 4 q^{31} + 2 q^{32} - q^{33} + 6 q^{34} + 2 q^{36} + q^{37} + 5 q^{38} + 3 q^{39} - 21 q^{41} + q^{42} - 2 q^{43} - q^{44} + 3 q^{46} + q^{47} + 2 q^{48} - 11 q^{49} + 6 q^{51} + 3 q^{52} + 13 q^{53} + 2 q^{54} + q^{56} + 5 q^{57} - 10 q^{58} - 15 q^{59} - 6 q^{61} + 4 q^{62} + q^{63} + 2 q^{64} - q^{66} + 6 q^{67} + 6 q^{68} + 3 q^{69} - 16 q^{71} + 2 q^{72} + 8 q^{73} + q^{74} + 5 q^{76} + 2 q^{77} + 3 q^{78} + 2 q^{81} - 21 q^{82} - 12 q^{83} + q^{84} - 2 q^{86} - 10 q^{87} - q^{88} - 25 q^{89} - 6 q^{91} + 3 q^{92} + 4 q^{93} + q^{94} + 2 q^{96} + 6 q^{97} - 11 q^{98} - q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^6 + q^7 + 2 * q^8 + 2 * q^9 - q^11 + 2 * q^12 + 3 * q^13 + q^14 + 2 * q^16 + 6 * q^17 + 2 * q^18 + 5 * q^19 + q^21 - q^22 + 3 * q^23 + 2 * q^24 + 3 * q^26 + 2 * q^27 + q^28 - 10 * q^29 + 4 * q^31 + 2 * q^32 - q^33 + 6 * q^34 + 2 * q^36 + q^37 + 5 * q^38 + 3 * q^39 - 21 * q^41 + q^42 - 2 * q^43 - q^44 + 3 * q^46 + q^47 + 2 * q^48 - 11 * q^49 + 6 * q^51 + 3 * q^52 + 13 * q^53 + 2 * q^54 + q^56 + 5 * q^57 - 10 * q^58 - 15 * q^59 - 6 * q^61 + 4 * q^62 + q^63 + 2 * q^64 - q^66 + 6 * q^67 + 6 * q^68 + 3 * q^69 - 16 * q^71 + 2 * q^72 + 8 * q^73 + q^74 + 5 * q^76 + 2 * q^77 + 3 * q^78 + 2 * q^81 - 21 * q^82 - 12 * q^83 + q^84 - 2 * q^86 - 10 * q^87 - q^88 - 25 * q^89 - 6 * q^91 + 3 * q^92 + 4 * q^93 + q^94 + 2 * q^96 + 6 * q^97 - 11 * q^98 - 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
$5$	0	0
$5$	0	0
$6$	1.00000	0.408248
$7$	1.61803	0.611559	0.305780	−	0.952102i	$-0.401083\pi$
$7$	1.61803	0.611559	0.305780	+	0.952102i	$0.401083\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	0.618034	0.186344	0.0931721	−	0.995650i	$-0.470299\pi$
$11$	0.618034	0.186344	0.0931721	+	0.995650i	$0.470299\pi$
$12$	1.00000	0.288675
$13$	−1.85410	−0.514235	−0.257118	−	0.966380i	$-0.582773\pi$
$13$	−1.85410	−0.514235	−0.257118	+	0.966380i	$0.582773\pi$
$14$	1.61803	0.432438
$15$	0	0
$16$	1.00000	0.250000
$17$	5.23607	1.26993	0.634967	−	0.772540i	$-0.281014\pi$
$17$	5.23607	1.26993	0.634967	+	0.772540i	$0.281014\pi$
$18$	1.00000	0.235702
$19$	−0.854102	−0.195944	−0.0979722	−	0.995189i	$-0.531236\pi$
$19$	−0.854102	−0.195944	−0.0979722	+	0.995189i	$0.531236\pi$
$20$	0	0
$21$	1.61803	0.353084
$22$	0.618034	0.131765
$23$	−1.85410	−0.386607	−0.193303	−	0.981139i	$-0.561920\pi$
$23$	−1.85410	−0.386607	−0.193303	+	0.981139i	$0.561920\pi$
$24$	1.00000	0.204124
$25$	0	0
$26$	−1.85410	−0.363619
$27$	1.00000	0.192450
$28$	1.61803	0.305780
$29$	−7.23607	−1.34370	−0.671852	−	0.740685i	$-0.734501\pi$
$29$	−7.23607	−1.34370	−0.671852	+	0.740685i	$0.734501\pi$
$30$	0	0
$31$	6.47214	1.16243	0.581215	−	0.813750i	$-0.302578\pi$
$31$	6.47214	1.16243	0.581215	+	0.813750i	$0.302578\pi$
$32$	1.00000	0.176777
$33$	0.618034	0.107586
$34$	5.23607	0.897978
$35$	0	0
$36$	1.00000	0.166667
$37$	10.5623	1.73643	0.868216	−	0.496186i	$-0.165267\pi$
$37$	10.5623	1.73643	0.868216	+	0.496186i	$0.165267\pi$
$38$	−0.854102	−0.138554
$39$	−1.85410	−0.296894
$40$	0	0
$41$	−11.6180	−1.81443	−0.907216	−	0.420665i	$-0.861797\pi$
$41$	−11.6180	−1.81443	−0.907216	+	0.420665i	$0.861797\pi$
$42$	1.61803	0.249668
$43$	−7.70820	−1.17549	−0.587745	−	0.809046i	$-0.699984\pi$
$43$	−7.70820	−1.17549	−0.587745	+	0.809046i	$0.699984\pi$
$44$	0.618034	0.0931721
$45$	0	0
$46$	−1.85410	−0.273372
$47$	−0.618034	−0.0901495	−0.0450748	−	0.998984i	$-0.514353\pi$
$47$	−0.618034	−0.0901495	−0.0450748	+	0.998984i	$0.514353\pi$
$48$	1.00000	0.144338
$49$	−4.38197	−0.625995
$50$	0	0
$51$	5.23607	0.733196
$52$	−1.85410	−0.257118
$53$	7.61803	1.04642	0.523209	−	0.852205i	$-0.324735\pi$
$53$	7.61803	1.04642	0.523209	+	0.852205i	$0.324735\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	1.61803	0.216219
$57$	−0.854102	−0.113129
$58$	−7.23607	−0.950142
$59$	−1.90983	−0.248639	−0.124319	−	0.992242i	$-0.539675\pi$
$59$	−1.90983	−0.248639	−0.124319	+	0.992242i	$0.539675\pi$
$60$	0	0
$61$	3.70820	0.474787	0.237393	−	0.971414i	$-0.423707\pi$
$61$	3.70820	0.474787	0.237393	+	0.971414i	$0.423707\pi$
$62$	6.47214	0.821962
$63$	1.61803	0.203853
$64$	1.00000	0.125000
$65$	0	0
$66$	0.618034	0.0760747
$67$	9.70820	1.18605	0.593023	−	0.805186i	$-0.297934\pi$
$67$	9.70820	1.18605	0.593023	+	0.805186i	$0.297934\pi$
$68$	5.23607	0.634967
$69$	−1.85410	−0.223208
$70$	0	0
$71$	−12.4721	−1.48017	−0.740085	−	0.672513i	$-0.765215\pi$
$71$	−12.4721	−1.48017	−0.740085	+	0.672513i	$0.765215\pi$
$72$	1.00000	0.117851
$73$	−4.94427	−0.578683	−0.289342	−	0.957226i	$-0.593436\pi$
$73$	−4.94427	−0.578683	−0.289342	+	0.957226i	$0.593436\pi$
$74$	10.5623	1.22784
$75$	0	0
$76$	−0.854102	−0.0979722
$77$	1.00000	0.113961
$78$	−1.85410	−0.209936
$79$	−13.4164	−1.50946	−0.754732	−	0.656033i	$-0.772233\pi$
$79$	−13.4164	−1.50946	−0.754732	+	0.656033i	$0.772233\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−11.6180	−1.28300
$83$	2.94427	0.323176	0.161588	−	0.986858i	$-0.448338\pi$
$83$	2.94427	0.323176	0.161588	+	0.986858i	$0.448338\pi$
$84$	1.61803	0.176542
$85$	0	0
$86$	−7.70820	−0.831197
$87$	−7.23607	−0.775788
$88$	0.618034	0.0658826
$89$	−6.90983	−0.732441	−0.366220	−	0.930528i	$-0.619348\pi$
$89$	−6.90983	−0.732441	−0.366220	+	0.930528i	$0.619348\pi$
$90$	0	0
$91$	−3.00000	−0.314485
$92$	−1.85410	−0.193303
$93$	6.47214	0.671129
$94$	−0.618034	−0.0637453
$95$	0	0
$96$	1.00000	0.102062
$97$	−3.70820	−0.376511	−0.188256	−	0.982120i	$-0.560283\pi$
$97$	−3.70820	−0.376511	−0.188256	+	0.982120i	$0.560283\pi$
$98$	−4.38197	−0.442645
$99$	0.618034	0.0621148
$100$	0	0
$101$	−18.6525	−1.85599	−0.927995	−	0.372592i	$-0.878469\pi$
$101$	−18.6525	−1.85599	−0.927995	+	0.372592i	$0.878469\pi$
$102$	5.23607	0.518448
$103$	11.5623	1.13927	0.569634	−	0.821899i	$-0.307085\pi$
$103$	11.5623	1.13927	0.569634	+	0.821899i	$0.307085\pi$
$104$	−1.85410	−0.181810
$105$	0	0
$106$	7.61803	0.739929
$107$	−10.9443	−1.05802	−0.529011	−	0.848615i	$-0.677437\pi$
$107$	−10.9443	−1.05802	−0.529011	+	0.848615i	$0.677437\pi$
$108$	1.00000	0.0962250
$109$	16.1803	1.54980	0.774898	−	0.632087i	$-0.217801\pi$
$109$	16.1803	1.54980	0.774898	+	0.632087i	$0.217801\pi$
$110$	0	0
$111$	10.5623	1.00253
$112$	1.61803	0.152890
$113$	1.23607	0.116279	0.0581397	−	0.998308i	$-0.481483\pi$
$113$	1.23607	0.116279	0.0581397	+	0.998308i	$0.481483\pi$
$114$	−0.854102	−0.0799940
$115$	0	0
$116$	−7.23607	−0.671852
$117$	−1.85410	−0.171412
$118$	−1.90983	−0.175814
$119$	8.47214	0.776639
$120$	0	0
$121$	−10.6180	−0.965276
$122$	3.70820	0.335725
$123$	−11.6180	−1.04756
$124$	6.47214	0.581215
$125$	0	0
$126$	1.61803	0.144146
$127$	−15.4164	−1.36798	−0.683992	−	0.729489i	$-0.739758\pi$
$127$	−15.4164	−1.36798	−0.683992	+	0.729489i	$0.739758\pi$
$128$	1.00000	0.0883883
$129$	−7.70820	−0.678670
$130$	0	0
$131$	15.0902	1.31843	0.659217	−	0.751953i	$-0.270888\pi$
$131$	15.0902	1.31843	0.659217	+	0.751953i	$0.270888\pi$
$132$	0.618034	0.0537930
$133$	−1.38197	−0.119832
$134$	9.70820	0.838661
$135$	0	0
$136$	5.23607	0.448989
$137$	−20.9443	−1.78939	−0.894695	−	0.446678i	$-0.852607\pi$
$137$	−20.9443	−1.78939	−0.894695	+	0.446678i	$0.852607\pi$
$138$	−1.85410	−0.157832
$139$	−7.56231	−0.641426	−0.320713	−	0.947176i	$-0.603923\pi$
$139$	−7.56231	−0.641426	−0.320713	+	0.947176i	$0.603923\pi$
$140$	0	0
$141$	−0.618034	−0.0520479
$142$	−12.4721	−1.04664
$143$	−1.14590	−0.0958248
$144$	1.00000	0.0833333
$145$	0	0
$146$	−4.94427	−0.409191
$147$	−4.38197	−0.361418
$148$	10.5623	0.868216
$149$	13.4164	1.09911	0.549557	−	0.835456i	$-0.314796\pi$
$149$	13.4164	1.09911	0.549557	+	0.835456i	$0.314796\pi$
$150$	0	0
$151$	23.7082	1.92935	0.964673	−	0.263450i	$-0.0848603\pi$
$151$	23.7082	1.92935	0.964673	+	0.263450i	$0.0848603\pi$
$152$	−0.854102	−0.0692768
$153$	5.23607	0.423311
$154$	1.00000	0.0805823
$155$	0	0
$156$	−1.85410	−0.148447
$157$	6.94427	0.554213	0.277107	−	0.960839i	$-0.410624\pi$
$157$	6.94427	0.554213	0.277107	+	0.960839i	$0.410624\pi$
$158$	−13.4164	−1.06735
$159$	7.61803	0.604149
$160$	0	0
$161$	−3.00000	−0.236433
$162$	1.00000	0.0785674
$163$	12.9443	1.01387	0.506937	−	0.861983i	$-0.330778\pi$
$163$	12.9443	1.01387	0.506937	+	0.861983i	$0.330778\pi$
$164$	−11.6180	−0.907216
$165$	0	0
$166$	2.94427	0.228520
$167$	−1.14590	−0.0886723	−0.0443361	−	0.999017i	$-0.514117\pi$
$167$	−1.14590	−0.0886723	−0.0443361	+	0.999017i	$0.514117\pi$
$168$	1.61803	0.124834
$169$	−9.56231	−0.735562
$170$	0	0
$171$	−0.854102	−0.0653148
$172$	−7.70820	−0.587745
$173$	−12.3820	−0.941383	−0.470692	−	0.882298i	$-0.655996\pi$
$173$	−12.3820	−0.941383	−0.470692	+	0.882298i	$0.655996\pi$
$174$	−7.23607	−0.548565
$175$	0	0
$176$	0.618034	0.0465861
$177$	−1.90983	−0.143552
$178$	−6.90983	−0.517914
$179$	−7.03444	−0.525779	−0.262889	−	0.964826i	$-0.584675\pi$
$179$	−7.03444	−0.525779	−0.262889	+	0.964826i	$0.584675\pi$
$180$	0	0
$181$	−1.41641	−0.105281	−0.0526404	−	0.998614i	$-0.516764\pi$
$181$	−1.41641	−0.105281	−0.0526404	+	0.998614i	$0.516764\pi$
$182$	−3.00000	−0.222375
$183$	3.70820	0.274118
$184$	−1.85410	−0.136686
$185$	0	0
$186$	6.47214	0.474560
$187$	3.23607	0.236645
$188$	−0.618034	−0.0450748
$189$	1.61803	0.117695
$190$	0	0
$191$	0.944272	0.0683251	0.0341626	−	0.999416i	$-0.489124\pi$
$191$	0.944272	0.0683251	0.0341626	+	0.999416i	$0.489124\pi$
$192$	1.00000	0.0721688
$193$	−17.7082	−1.27466	−0.637332	−	0.770589i	$-0.719962\pi$
$193$	−17.7082	−1.27466	−0.637332	+	0.770589i	$0.719962\pi$
$194$	−3.70820	−0.266234
$195$	0	0
$196$	−4.38197	−0.312998
$197$	−10.9443	−0.779747	−0.389874	−	0.920868i	$-0.627481\pi$
$197$	−10.9443	−0.779747	−0.389874	+	0.920868i	$0.627481\pi$
$198$	0.618034	0.0439218
$199$	16.1803	1.14699	0.573497	−	0.819208i	$-0.305586\pi$
$199$	16.1803	1.14699	0.573497	+	0.819208i	$0.305586\pi$
$200$	0	0
$201$	9.70820	0.684764
$202$	−18.6525	−1.31238
$203$	−11.7082	−0.821755
$204$	5.23607	0.366598
$205$	0	0
$206$	11.5623	0.805584
$207$	−1.85410	−0.128869
$208$	−1.85410	−0.128559
$209$	−0.527864	−0.0365131
$210$	0	0
$211$	16.2705	1.12011	0.560054	−	0.828456i	$-0.310780\pi$
$211$	16.2705	1.12011	0.560054	+	0.828456i	$0.310780\pi$
$212$	7.61803	0.523209
$213$	−12.4721	−0.854577
$214$	−10.9443	−0.748135
$215$	0	0
$216$	1.00000	0.0680414
$217$	10.4721	0.710895
$218$	16.1803	1.09587
$219$	−4.94427	−0.334103
$220$	0	0
$221$	−9.70820	−0.653044
$222$	10.5623	0.708896
$223$	24.0000	1.60716	0.803579	−	0.595198i	$-0.202926\pi$
$223$	24.0000	1.60716	0.803579	+	0.595198i	$0.202926\pi$
$224$	1.61803	0.108109
$225$	0	0
$226$	1.23607	0.0822220
$227$	−5.81966	−0.386264	−0.193132	−	0.981173i	$-0.561865\pi$
$227$	−5.81966	−0.386264	−0.193132	+	0.981173i	$0.561865\pi$
$228$	−0.854102	−0.0565643
$229$	−11.7082	−0.773700	−0.386850	−	0.922143i	$-0.626437\pi$
$229$	−11.7082	−0.773700	−0.386850	+	0.922143i	$0.626437\pi$
$230$	0	0
$231$	1.00000	0.0657952
$232$	−7.23607	−0.475071
$233$	7.41641	0.485865	0.242933	−	0.970043i	$-0.421891\pi$
$233$	7.41641	0.485865	0.242933	+	0.970043i	$0.421891\pi$
$234$	−1.85410	−0.121206
$235$	0	0
$236$	−1.90983	−0.124319
$237$	−13.4164	−0.871489
$238$	8.47214	0.549167
$239$	−8.94427	−0.578557	−0.289278	−	0.957245i	$-0.593415\pi$
$239$	−8.94427	−0.578557	−0.289278	+	0.957245i	$0.593415\pi$
$240$	0	0
$241$	−13.8541	−0.892421	−0.446211	−	0.894928i	$-0.647227\pi$
$241$	−13.8541	−0.892421	−0.446211	+	0.894928i	$0.647227\pi$
$242$	−10.6180	−0.682553
$243$	1.00000	0.0641500
$244$	3.70820	0.237393
$245$	0	0
$246$	−11.6180	−0.740739
$247$	1.58359	0.100762
$248$	6.47214	0.410981
$249$	2.94427	0.186586
$250$	0	0
$251$	3.05573	0.192876	0.0964379	−	0.995339i	$-0.469255\pi$
$251$	3.05573	0.192876	0.0964379	+	0.995339i	$0.469255\pi$
$252$	1.61803	0.101927
$253$	−1.14590	−0.0720420
$254$	−15.4164	−0.967311
$255$	0	0
$256$	1.00000	0.0625000
$257$	22.4721	1.40177	0.700887	−	0.713273i	$-0.252788\pi$
$257$	22.4721	1.40177	0.700887	+	0.713273i	$0.252788\pi$
$258$	−7.70820	−0.479892
$259$	17.0902	1.06193
$260$	0	0
$261$	−7.23607	−0.447901
$262$	15.0902	0.932274
$263$	−12.3820	−0.763505	−0.381752	−	0.924265i	$-0.624679\pi$
$263$	−12.3820	−0.763505	−0.381752	+	0.924265i	$0.624679\pi$
$264$	0.618034	0.0380374
$265$	0	0
$266$	−1.38197	−0.0847338
$267$	−6.90983	−0.422875
$268$	9.70820	0.593023
$269$	13.4164	0.818013	0.409006	−	0.912532i	$-0.365875\pi$
$269$	13.4164	0.818013	0.409006	+	0.912532i	$0.365875\pi$
$270$	0	0
$271$	−1.41641	−0.0860407	−0.0430203	−	0.999074i	$-0.513698\pi$
$271$	−1.41641	−0.0860407	−0.0430203	+	0.999074i	$0.513698\pi$
$272$	5.23607	0.317483
$273$	−3.00000	−0.181568
$274$	−20.9443	−1.26529
$275$	0	0
$276$	−1.85410	−0.111604
$277$	−6.14590	−0.369271	−0.184636	−	0.982807i	$-0.559110\pi$
$277$	−6.14590	−0.369271	−0.184636	+	0.982807i	$0.559110\pi$
$278$	−7.56231	−0.453557
$279$	6.47214	0.387477
$280$	0	0
$281$	5.09017	0.303654	0.151827	−	0.988407i	$-0.451484\pi$
$281$	5.09017	0.303654	0.151827	+	0.988407i	$0.451484\pi$
$282$	−0.618034	−0.0368034
$283$	7.81966	0.464831	0.232415	−	0.972617i	$-0.425337\pi$
$283$	7.81966	0.464831	0.232415	+	0.972617i	$0.425337\pi$
$284$	−12.4721	−0.740085
$285$	0	0
$286$	−1.14590	−0.0677584
$287$	−18.7984	−1.10963
$288$	1.00000	0.0589256
$289$	10.4164	0.612730
$290$	0	0
$291$	−3.70820	−0.217379
$292$	−4.94427	−0.289342
$293$	10.9098	0.637359	0.318680	−	0.947863i	$-0.396761\pi$
$293$	10.9098	0.637359	0.318680	+	0.947863i	$0.396761\pi$
$294$	−4.38197	−0.255561
$295$	0	0
$296$	10.5623	0.613922
$297$	0.618034	0.0358620
$298$	13.4164	0.777192
$299$	3.43769	0.198807
$300$	0	0
$301$	−12.4721	−0.718882
$302$	23.7082	1.36425
$303$	−18.6525	−1.07156
$304$	−0.854102	−0.0489861
$305$	0	0
$306$	5.23607	0.299326
$307$	25.2361	1.44030	0.720149	−	0.693819i	$-0.244073\pi$
$307$	25.2361	1.44030	0.720149	+	0.693819i	$0.244073\pi$
$308$	1.00000	0.0569803
$309$	11.5623	0.657757
$310$	0	0
$311$	12.0000	0.680458	0.340229	−	0.940343i	$-0.389495\pi$
$311$	12.0000	0.680458	0.340229	+	0.940343i	$0.389495\pi$
$312$	−1.85410	−0.104968
$313$	15.7082	0.887880	0.443940	−	0.896056i	$-0.353580\pi$
$313$	15.7082	0.887880	0.443940	+	0.896056i	$0.353580\pi$
$314$	6.94427	0.391888
$315$	0	0
$316$	−13.4164	−0.754732
$317$	−7.85410	−0.441130	−0.220565	−	0.975372i	$-0.570790\pi$
$317$	−7.85410	−0.441130	−0.220565	+	0.975372i	$0.570790\pi$
$318$	7.61803	0.427198
$319$	−4.47214	−0.250392
$320$	0	0
$321$	−10.9443	−0.610850
$322$	−3.00000	−0.167183
$323$	−4.47214	−0.248836
$324$	1.00000	0.0555556
$325$	0	0
$326$	12.9443	0.716917
$327$	16.1803	0.894775
$328$	−11.6180	−0.641499
$329$	−1.00000	−0.0551318
$330$	0	0
$331$	6.47214	0.355741	0.177870	−	0.984054i	$-0.443079\pi$
$331$	6.47214	0.355741	0.177870	+	0.984054i	$0.443079\pi$
$332$	2.94427	0.161588
$333$	10.5623	0.578811
$334$	−1.14590	−0.0627008
$335$	0	0
$336$	1.61803	0.0882710
$337$	15.8885	0.865504	0.432752	−	0.901513i	$-0.357543\pi$
$337$	15.8885	0.865504	0.432752	+	0.901513i	$0.357543\pi$
$338$	−9.56231	−0.520121
$339$	1.23607	0.0671340
$340$	0	0
$341$	4.00000	0.216612
$342$	−0.854102	−0.0461845
$343$	−18.4164	−0.994393
$344$	−7.70820	−0.415599
$345$	0	0
$346$	−12.3820	−0.665659
$347$	32.0689	1.72155	0.860774	−	0.508987i	$-0.169980\pi$
$347$	32.0689	1.72155	0.860774	+	0.508987i	$0.169980\pi$
$348$	−7.23607	−0.387894
$349$	26.8328	1.43633	0.718164	−	0.695874i	$-0.244983\pi$
$349$	26.8328	1.43633	0.718164	+	0.695874i	$0.244983\pi$
$350$	0	0
$351$	−1.85410	−0.0989646
$352$	0.618034	0.0329413
$353$	2.29180	0.121980	0.0609900	−	0.998138i	$-0.480574\pi$
$353$	2.29180	0.121980	0.0609900	+	0.998138i	$0.480574\pi$
$354$	−1.90983	−0.101506
$355$	0	0
$356$	−6.90983	−0.366220
$357$	8.47214	0.448393
$358$	−7.03444	−0.371782
$359$	−4.47214	−0.236030	−0.118015	−	0.993012i	$-0.537653\pi$
$359$	−4.47214	−0.236030	−0.118015	+	0.993012i	$0.537653\pi$
$360$	0	0
$361$	−18.2705	−0.961606
$362$	−1.41641	−0.0744447
$363$	−10.6180	−0.557302
$364$	−3.00000	−0.157243
$365$	0	0
$366$	3.70820	0.193831
$367$	31.4164	1.63992	0.819962	−	0.572419i	$-0.193995\pi$
$367$	31.4164	1.63992	0.819962	+	0.572419i	$0.193995\pi$
$368$	−1.85410	−0.0966517
$369$	−11.6180	−0.604811
$370$	0	0
$371$	12.3262	0.639946
$372$	6.47214	0.335565
$373$	−7.50658	−0.388676	−0.194338	−	0.980935i	$-0.562256\pi$
$373$	−7.50658	−0.388676	−0.194338	+	0.980935i	$0.562256\pi$
$374$	3.23607	0.167333
$375$	0	0
$376$	−0.618034	−0.0318727
$377$	13.4164	0.690980
$378$	1.61803	0.0832227
$379$	30.9787	1.59127	0.795635	−	0.605777i	$-0.207137\pi$
$379$	30.9787	1.59127	0.795635	+	0.605777i	$0.207137\pi$
$380$	0	0
$381$	−15.4164	−0.789807
$382$	0.944272	0.0483132
$383$	25.9098	1.32393	0.661965	−	0.749535i	$-0.269723\pi$
$383$	25.9098	1.32393	0.661965	+	0.749535i	$0.269723\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−17.7082	−0.901324
$387$	−7.70820	−0.391830
$388$	−3.70820	−0.188256
$389$	17.2361	0.873903	0.436952	−	0.899485i	$-0.356058\pi$
$389$	17.2361	0.873903	0.436952	+	0.899485i	$0.356058\pi$
$390$	0	0
$391$	−9.70820	−0.490965
$392$	−4.38197	−0.221323
$393$	15.0902	0.761198
$394$	−10.9443	−0.551364
$395$	0	0
$396$	0.618034	0.0310574
$397$	−16.2705	−0.816593	−0.408297	−	0.912849i	$-0.633877\pi$
$397$	−16.2705	−0.816593	−0.408297	+	0.912849i	$0.633877\pi$
$398$	16.1803	0.811047
$399$	−1.38197	−0.0691848
$400$	0	0
$401$	−13.3262	−0.665481	−0.332740	−	0.943019i	$-0.607973\pi$
$401$	−13.3262	−0.665481	−0.332740	+	0.943019i	$0.607973\pi$
$402$	9.70820	0.484201
$403$	−12.0000	−0.597763
$404$	−18.6525	−0.927995
$405$	0	0
$406$	−11.7082	−0.581068
$407$	6.52786	0.323574
$408$	5.23607	0.259224
$409$	−20.8541	−1.03117	−0.515584	−	0.856839i	$-0.672425\pi$
$409$	−20.8541	−1.03117	−0.515584	+	0.856839i	$0.672425\pi$
$410$	0	0
$411$	−20.9443	−1.03310
$412$	11.5623	0.569634
$413$	−3.09017	−0.152057
$414$	−1.85410	−0.0911241
$415$	0	0
$416$	−1.85410	−0.0909048
$417$	−7.56231	−0.370328
$418$	−0.527864	−0.0258187
$419$	28.9443	1.41402	0.707010	−	0.707203i	$-0.250044\pi$
$419$	28.9443	1.41402	0.707010	+	0.707203i	$0.250044\pi$
$420$	0	0
$421$	−4.18034	−0.203737	−0.101869	−	0.994798i	$-0.532482\pi$
$421$	−4.18034	−0.203737	−0.101869	+	0.994798i	$0.532482\pi$
$422$	16.2705	0.792036
$423$	−0.618034	−0.0300498
$424$	7.61803	0.369964
$425$	0	0
$426$	−12.4721	−0.604277
$427$	6.00000	0.290360
$428$	−10.9443	−0.529011
$429$	−1.14590	−0.0553245
$430$	0	0
$431$	38.1803	1.83908	0.919541	−	0.392994i	$-0.128561\pi$
$431$	38.1803	1.83908	0.919541	+	0.392994i	$0.128561\pi$
$432$	1.00000	0.0481125
$433$	−9.41641	−0.452524	−0.226262	−	0.974067i	$-0.572651\pi$
$433$	−9.41641	−0.452524	−0.226262	+	0.974067i	$0.572651\pi$
$434$	10.4721	0.502679
$435$	0	0
$436$	16.1803	0.774898
$437$	1.58359	0.0757535
$438$	−4.94427	−0.236246
$439$	−11.7082	−0.558802	−0.279401	−	0.960174i	$-0.590136\pi$
$439$	−11.7082	−0.558802	−0.279401	+	0.960174i	$0.590136\pi$
$440$	0	0
$441$	−4.38197	−0.208665
$442$	−9.70820	−0.461772
$443$	−35.5967	−1.69125	−0.845626	−	0.533775i	$-0.820773\pi$
$443$	−35.5967	−1.69125	−0.845626	+	0.533775i	$0.820773\pi$
$444$	10.5623	0.501265
$445$	0	0
$446$	24.0000	1.13643
$447$	13.4164	0.634574
$448$	1.61803	0.0764449
$449$	−23.2148	−1.09557	−0.547787	−	0.836618i	$-0.684529\pi$
$449$	−23.2148	−1.09557	−0.547787	+	0.836618i	$0.684529\pi$
$450$	0	0
$451$	−7.18034	−0.338109
$452$	1.23607	0.0581397
$453$	23.7082	1.11391
$454$	−5.81966	−0.273130
$455$	0	0
$456$	−0.854102	−0.0399970
$457$	14.8328	0.693850	0.346925	−	0.937893i	$-0.387226\pi$
$457$	14.8328	0.693850	0.346925	+	0.937893i	$0.387226\pi$
$458$	−11.7082	−0.547088
$459$	5.23607	0.244399
$460$	0	0
$461$	15.8197	0.736795	0.368398	−	0.929668i	$-0.379907\pi$
$461$	15.8197	0.736795	0.368398	+	0.929668i	$0.379907\pi$
$462$	1.00000	0.0465242
$463$	39.7771	1.84860	0.924299	−	0.381669i	$-0.124651\pi$
$463$	39.7771	1.84860	0.924299	+	0.381669i	$0.124651\pi$
$464$	−7.23607	−0.335926
$465$	0	0
$466$	7.41641	0.343558
$467$	10.7639	0.498095	0.249048	−	0.968491i	$-0.419882\pi$
$467$	10.7639	0.498095	0.249048	+	0.968491i	$0.419882\pi$
$468$	−1.85410	−0.0857059
$469$	15.7082	0.725337
$470$	0	0
$471$	6.94427	0.319975
$472$	−1.90983	−0.0879071
$473$	−4.76393	−0.219046
$474$	−13.4164	−0.616236
$475$	0	0
$476$	8.47214	0.388320
$477$	7.61803	0.348806
$478$	−8.94427	−0.409101
$479$	21.7082	0.991873	0.495937	−	0.868359i	$-0.334825\pi$
$479$	21.7082	0.991873	0.495937	+	0.868359i	$0.334825\pi$
$480$	0	0
$481$	−19.5836	−0.892935
$482$	−13.8541	−0.631037
$483$	−3.00000	−0.136505
$484$	−10.6180	−0.482638
$485$	0	0
$486$	1.00000	0.0453609
$487$	−1.67376	−0.0758454	−0.0379227	−	0.999281i	$-0.512074\pi$
$487$	−1.67376	−0.0758454	−0.0379227	+	0.999281i	$0.512074\pi$
$488$	3.70820	0.167863
$489$	12.9443	0.585360
$490$	0	0
$491$	27.9787	1.26266	0.631331	−	0.775514i	$-0.282509\pi$
$491$	27.9787	1.26266	0.631331	+	0.775514i	$0.282509\pi$
$492$	−11.6180	−0.523781
$493$	−37.8885	−1.70641
$494$	1.58359	0.0712492
$495$	0	0
$496$	6.47214	0.290607
$497$	−20.1803	−0.905212
$498$	2.94427	0.131936
$499$	−39.2705	−1.75799	−0.878995	−	0.476831i	$-0.841785\pi$
$499$	−39.2705	−1.75799	−0.878995	+	0.476831i	$0.841785\pi$
$500$	0	0
$501$	−1.14590	−0.0511949
$502$	3.05573	0.136384
$503$	16.0344	0.714940	0.357470	−	0.933925i	$-0.383639\pi$
$503$	16.0344	0.714940	0.357470	+	0.933925i	$0.383639\pi$
$504$	1.61803	0.0720730
$505$	0	0
$506$	−1.14590	−0.0509414
$507$	−9.56231	−0.424677
$508$	−15.4164	−0.683992
$509$	−0.652476	−0.0289205	−0.0144602	−	0.999895i	$-0.504603\pi$
$509$	−0.652476	−0.0289205	−0.0144602	+	0.999895i	$0.504603\pi$
$510$	0	0
$511$	−8.00000	−0.353899
$512$	1.00000	0.0441942
$513$	−0.854102	−0.0377095
$514$	22.4721	0.991203
$515$	0	0
$516$	−7.70820	−0.339335
$517$	−0.381966	−0.0167988
$518$	17.0902	0.750899
$519$	−12.3820	−0.543508
$520$	0	0
$521$	17.4508	0.764536	0.382268	−	0.924052i	$-0.375143\pi$
$521$	17.4508	0.764536	0.382268	+	0.924052i	$0.375143\pi$
$522$	−7.23607	−0.316714
$523$	38.4721	1.68227	0.841135	−	0.540826i	$-0.181888\pi$
$523$	38.4721	1.68227	0.841135	+	0.540826i	$0.181888\pi$
$524$	15.0902	0.659217
$525$	0	0
$526$	−12.3820	−0.539879
$527$	33.8885	1.47621
$528$	0.618034	0.0268965
$529$	−19.5623	−0.850535
$530$	0	0
$531$	−1.90983	−0.0828796
$532$	−1.38197	−0.0599158
$533$	21.5410	0.933045
$534$	−6.90983	−0.299018
$535$	0	0
$536$	9.70820	0.419331
$537$	−7.03444	−0.303559
$538$	13.4164	0.578422
$539$	−2.70820	−0.116651
$540$	0	0
$541$	18.5836	0.798971	0.399486	−	0.916740i	$-0.369189\pi$
$541$	18.5836	0.798971	0.399486	+	0.916740i	$0.369189\pi$
$542$	−1.41641	−0.0608399
$543$	−1.41641	−0.0607839
$544$	5.23607	0.224495
$545$	0	0
$546$	−3.00000	−0.128388
$547$	−17.1246	−0.732196	−0.366098	−	0.930576i	$-0.619306\pi$
$547$	−17.1246	−0.732196	−0.366098	+	0.930576i	$0.619306\pi$
$548$	−20.9443	−0.894695
$549$	3.70820	0.158262
$550$	0	0
$551$	6.18034	0.263291
$552$	−1.85410	−0.0789158
$553$	−21.7082	−0.923127
$554$	−6.14590	−0.261114
$555$	0	0
$556$	−7.56231	−0.320713
$557$	9.38197	0.397527	0.198763	−	0.980048i	$-0.436307\pi$
$557$	9.38197	0.397527	0.198763	+	0.980048i	$0.436307\pi$
$558$	6.47214	0.273987
$559$	14.2918	0.604479
$560$	0	0
$561$	3.23607	0.136627
$562$	5.09017	0.214716
$563$	−14.9443	−0.629826	−0.314913	−	0.949121i	$-0.601975\pi$
$563$	−14.9443	−0.629826	−0.314913	+	0.949121i	$0.601975\pi$
$564$	−0.618034	−0.0260239
$565$	0	0
$566$	7.81966	0.328685
$567$	1.61803	0.0679510
$568$	−12.4721	−0.523319
$569$	−30.3262	−1.27134	−0.635671	−	0.771960i	$-0.719277\pi$
$569$	−30.3262	−1.27134	−0.635671	+	0.771960i	$0.719277\pi$
$570$	0	0
$571$	25.2148	1.05521	0.527603	−	0.849491i	$-0.323091\pi$
$571$	25.2148	1.05521	0.527603	+	0.849491i	$0.323091\pi$
$572$	−1.14590	−0.0479124
$573$	0.944272	0.0394475
$574$	−18.7984	−0.784629
$575$	0	0
$576$	1.00000	0.0416667
$577$	−20.2918	−0.844759	−0.422379	−	0.906419i	$-0.638805\pi$
$577$	−20.2918	−0.844759	−0.422379	+	0.906419i	$0.638805\pi$
$578$	10.4164	0.433265
$579$	−17.7082	−0.735928
$580$	0	0
$581$	4.76393	0.197641
$582$	−3.70820	−0.153710
$583$	4.70820	0.194994
$584$	−4.94427	−0.204595
$585$	0	0
$586$	10.9098	0.450681
$587$	−38.1803	−1.57587	−0.787936	−	0.615758i	$-0.788850\pi$
$587$	−38.1803	−1.57587	−0.787936	+	0.615758i	$0.788850\pi$
$588$	−4.38197	−0.180709
$589$	−5.52786	−0.227772
$590$	0	0
$591$	−10.9443	−0.450187
$592$	10.5623	0.434108
$593$	46.3607	1.90380	0.951902	−	0.306401i	$-0.0991249\pi$
$593$	46.3607	1.90380	0.951902	+	0.306401i	$0.0991249\pi$
$594$	0.618034	0.0253582
$595$	0	0
$596$	13.4164	0.549557
$597$	16.1803	0.662217
$598$	3.43769	0.140578
$599$	−18.5410	−0.757566	−0.378783	−	0.925486i	$-0.623657\pi$
$599$	−18.5410	−0.757566	−0.378783	+	0.925486i	$0.623657\pi$
$600$	0	0
$601$	1.27051	0.0518252	0.0259126	−	0.999664i	$-0.491751\pi$
$601$	1.27051	0.0518252	0.0259126	+	0.999664i	$0.491751\pi$
$602$	−12.4721	−0.508326
$603$	9.70820	0.395349
$604$	23.7082	0.964673
$605$	0	0
$606$	−18.6525	−0.757705
$607$	−39.6869	−1.61084	−0.805421	−	0.592703i	$-0.798061\pi$
$607$	−39.6869	−1.61084	−0.805421	+	0.592703i	$0.798061\pi$
$608$	−0.854102	−0.0346384
$609$	−11.7082	−0.474440
$610$	0	0
$611$	1.14590	0.0463581
$612$	5.23607	0.211656
$613$	−24.6180	−0.994313	−0.497157	−	0.867661i	$-0.665623\pi$
$613$	−24.6180	−0.994313	−0.497157	+	0.867661i	$0.665623\pi$
$614$	25.2361	1.01844
$615$	0	0
$616$	1.00000	0.0402911
$617$	−33.3050	−1.34081	−0.670403	−	0.741997i	$-0.733879\pi$
$617$	−33.3050	−1.34081	−0.670403	+	0.741997i	$0.733879\pi$
$618$	11.5623	0.465104
$619$	−6.90983	−0.277730	−0.138865	−	0.990311i	$-0.544345\pi$
$619$	−6.90983	−0.277730	−0.138865	+	0.990311i	$0.544345\pi$
$620$	0	0
$621$	−1.85410	−0.0744025
$622$	12.0000	0.481156
$623$	−11.1803	−0.447931
$624$	−1.85410	−0.0742235
$625$	0	0
$626$	15.7082	0.627826
$627$	−0.527864	−0.0210809
$628$	6.94427	0.277107
$629$	55.3050	2.20515
$630$	0	0
$631$	−24.1803	−0.962604	−0.481302	−	0.876555i	$-0.659836\pi$
$631$	−24.1803	−0.962604	−0.481302	+	0.876555i	$0.659836\pi$
$632$	−13.4164	−0.533676
$633$	16.2705	0.646695
$634$	−7.85410	−0.311926
$635$	0	0
$636$	7.61803	0.302075
$637$	8.12461	0.321909
$638$	−4.47214	−0.177054
$639$	−12.4721	−0.493390
$640$	0	0
$641$	40.7426	1.60924	0.804619	−	0.593792i	$-0.202370\pi$
$641$	40.7426	1.60924	0.804619	+	0.593792i	$0.202370\pi$
$642$	−10.9443	−0.431936
$643$	−24.9443	−0.983706	−0.491853	−	0.870678i	$-0.663680\pi$
$643$	−24.9443	−0.983706	−0.491853	+	0.870678i	$0.663680\pi$
$644$	−3.00000	−0.118217
$645$	0	0
$646$	−4.47214	−0.175954
$647$	6.09017	0.239429	0.119715	−	0.992808i	$-0.461802\pi$
$647$	6.09017	0.239429	0.119715	+	0.992808i	$0.461802\pi$
$648$	1.00000	0.0392837
$649$	−1.18034	−0.0463324
$650$	0	0
$651$	10.4721	0.410435
$652$	12.9443	0.506937
$653$	19.8541	0.776951	0.388476	−	0.921459i	$-0.373002\pi$
$653$	19.8541	0.776951	0.388476	+	0.921459i	$0.373002\pi$
$654$	16.1803	0.632701
$655$	0	0
$656$	−11.6180	−0.453608
$657$	−4.94427	−0.192894
$658$	−1.00000	−0.0389841
$659$	−43.7426	−1.70397	−0.851986	−	0.523565i	$-0.824602\pi$
$659$	−43.7426	−1.70397	−0.851986	+	0.523565i	$0.824602\pi$
$660$	0	0
$661$	−28.6525	−1.11445	−0.557226	−	0.830361i	$-0.688134\pi$
$661$	−28.6525	−1.11445	−0.557226	+	0.830361i	$0.688134\pi$
$662$	6.47214	0.251547
$663$	−9.70820	−0.377035
$664$	2.94427	0.114260
$665$	0	0
$666$	10.5623	0.409281
$667$	13.4164	0.519485
$668$	−1.14590	−0.0443361
$669$	24.0000	0.927894
$670$	0	0
$671$	2.29180	0.0884738
$672$	1.61803	0.0624170
$673$	−30.4721	−1.17461	−0.587307	−	0.809364i	$-0.699812\pi$
$673$	−30.4721	−1.17461	−0.587307	+	0.809364i	$0.699812\pi$
$674$	15.8885	0.612004
$675$	0	0
$676$	−9.56231	−0.367781
$677$	−1.14590	−0.0440404	−0.0220202	−	0.999758i	$-0.507010\pi$
$677$	−1.14590	−0.0440404	−0.0220202	+	0.999758i	$0.507010\pi$
$678$	1.23607	0.0474709
$679$	−6.00000	−0.230259
$680$	0	0
$681$	−5.81966	−0.223010
$682$	4.00000	0.153168
$683$	−7.05573	−0.269980	−0.134990	−	0.990847i	$-0.543100\pi$
$683$	−7.05573	−0.269980	−0.134990	+	0.990847i	$0.543100\pi$
$684$	−0.854102	−0.0326574
$685$	0	0
$686$	−18.4164	−0.703142
$687$	−11.7082	−0.446696
$688$	−7.70820	−0.293873
$689$	−14.1246	−0.538105
$690$	0	0
$691$	−8.00000	−0.304334	−0.152167	−	0.988355i	$-0.548625\pi$
$691$	−8.00000	−0.304334	−0.152167	+	0.988355i	$0.548625\pi$
$692$	−12.3820	−0.470692
$693$	1.00000	0.0379869
$694$	32.0689	1.21732
$695$	0	0
$696$	−7.23607	−0.274282
$697$	−60.8328	−2.30421
$698$	26.8328	1.01564
$699$	7.41641	0.280514
$700$	0	0
$701$	−20.7639	−0.784243	−0.392121	−	0.919913i	$-0.628259\pi$
$701$	−20.7639	−0.784243	−0.392121	+	0.919913i	$0.628259\pi$
$702$	−1.85410	−0.0699786
$703$	−9.02129	−0.340244
$704$	0.618034	0.0232930
$705$	0	0
$706$	2.29180	0.0862529
$707$	−30.1803	−1.13505
$708$	−1.90983	−0.0717758
$709$	−7.23607	−0.271756	−0.135878	−	0.990726i	$-0.543386\pi$
$709$	−7.23607	−0.271756	−0.135878	+	0.990726i	$0.543386\pi$
$710$	0	0
$711$	−13.4164	−0.503155
$712$	−6.90983	−0.258957
$713$	−12.0000	−0.449404
$714$	8.47214	0.317062
$715$	0	0
$716$	−7.03444	−0.262889
$717$	−8.94427	−0.334030
$718$	−4.47214	−0.166899
$719$	7.88854	0.294193	0.147097	−	0.989122i	$-0.453007\pi$
$719$	7.88854	0.294193	0.147097	+	0.989122i	$0.453007\pi$
$720$	0	0
$721$	18.7082	0.696730
$722$	−18.2705	−0.679958
$723$	−13.8541	−0.515240
$724$	−1.41641	−0.0526404
$725$	0	0
$726$	−10.6180	−0.394072
$727$	−43.1033	−1.59861	−0.799307	−	0.600923i	$-0.794800\pi$
$727$	−43.1033	−1.59861	−0.799307	+	0.600923i	$0.794800\pi$
$728$	−3.00000	−0.111187
$729$	1.00000	0.0370370
$730$	0	0
$731$	−40.3607	−1.49279
$732$	3.70820	0.137059
$733$	−15.6738	−0.578924	−0.289462	−	0.957190i	$-0.593476\pi$
$733$	−15.6738	−0.578924	−0.289462	+	0.957190i	$0.593476\pi$
$734$	31.4164	1.15960
$735$	0	0
$736$	−1.85410	−0.0683431
$737$	6.00000	0.221013
$738$	−11.6180	−0.427666
$739$	44.2705	1.62852	0.814259	−	0.580502i	$-0.197144\pi$
$739$	44.2705	1.62852	0.814259	+	0.580502i	$0.197144\pi$
$740$	0	0
$741$	1.58359	0.0581747
$742$	12.3262	0.452510
$743$	−1.85410	−0.0680204	−0.0340102	−	0.999421i	$-0.510828\pi$
$743$	−1.85410	−0.0680204	−0.0340102	+	0.999421i	$0.510828\pi$
$744$	6.47214	0.237280
$745$	0	0
$746$	−7.50658	−0.274835
$747$	2.94427	0.107725
$748$	3.23607	0.118322
$749$	−17.7082	−0.647044
$750$	0	0
$751$	1.59675	0.0582662	0.0291331	−	0.999576i	$-0.490725\pi$
$751$	1.59675	0.0582662	0.0291331	+	0.999576i	$0.490725\pi$
$752$	−0.618034	−0.0225374
$753$	3.05573	0.111357
$754$	13.4164	0.488597
$755$	0	0
$756$	1.61803	0.0588473
$757$	2.79837	0.101709	0.0508543	−	0.998706i	$-0.483806\pi$
$757$	2.79837	0.101709	0.0508543	+	0.998706i	$0.483806\pi$
$758$	30.9787	1.12520
$759$	−1.14590	−0.0415935
$760$	0	0
$761$	19.0344	0.689998	0.344999	−	0.938603i	$-0.387879\pi$
$761$	19.0344	0.689998	0.344999	+	0.938603i	$0.387879\pi$
$762$	−15.4164	−0.558478
$763$	26.1803	0.947792
$764$	0.944272	0.0341626
$765$	0	0
$766$	25.9098	0.936160
$767$	3.54102	0.127859
$768$	1.00000	0.0360844
$769$	−49.2705	−1.77674	−0.888370	−	0.459128i	$-0.848162\pi$
$769$	−49.2705	−1.77674	−0.888370	+	0.459128i	$0.848162\pi$
$770$	0	0
$771$	22.4721	0.809314
$772$	−17.7082	−0.637332
$773$	−14.9443	−0.537508	−0.268754	−	0.963209i	$-0.586612\pi$
$773$	−14.9443	−0.537508	−0.268754	+	0.963209i	$0.586612\pi$
$774$	−7.70820	−0.277066
$775$	0	0
$776$	−3.70820	−0.133117
$777$	17.0902	0.613106
$778$	17.2361	0.617943
$779$	9.92299	0.355528
$780$	0	0
$781$	−7.70820	−0.275821
$782$	−9.70820	−0.347165
$783$	−7.23607	−0.258596
$784$	−4.38197	−0.156499
$785$	0	0
$786$	15.0902	0.538249
$787$	1.41641	0.0504895	0.0252447	−	0.999681i	$-0.491963\pi$
$787$	1.41641	0.0504895	0.0252447	+	0.999681i	$0.491963\pi$
$788$	−10.9443	−0.389874
$789$	−12.3820	−0.440810
$790$	0	0
$791$	2.00000	0.0711118
$792$	0.618034	0.0219609
$793$	−6.87539	−0.244152
$794$	−16.2705	−0.577419
$795$	0	0
$796$	16.1803	0.573497
$797$	6.09017	0.215725	0.107862	−	0.994166i	$-0.465599\pi$
$797$	6.09017	0.215725	0.107862	+	0.994166i	$0.465599\pi$
$798$	−1.38197	−0.0489211
$799$	−3.23607	−0.114484
$800$	0	0
$801$	−6.90983	−0.244147
$802$	−13.3262	−0.470566
$803$	−3.05573	−0.107834
$804$	9.70820	0.342382
$805$	0	0
$806$	−12.0000	−0.422682
$807$	13.4164	0.472280
$808$	−18.6525	−0.656192
$809$	−30.9787	−1.08915	−0.544577	−	0.838711i	$-0.683310\pi$
$809$	−30.9787	−1.08915	−0.544577	+	0.838711i	$0.683310\pi$
$810$	0	0
$811$	−34.1033	−1.19753	−0.598765	−	0.800925i	$-0.704342\pi$
$811$	−34.1033	−1.19753	−0.598765	+	0.800925i	$0.704342\pi$
$812$	−11.7082	−0.410877
$813$	−1.41641	−0.0496756
$814$	6.52786	0.228802
$815$	0	0
$816$	5.23607	0.183299
$817$	6.58359	0.230331
$818$	−20.8541	−0.729147
$819$	−3.00000	−0.104828
$820$	0	0
$821$	0.944272	0.0329553	0.0164777	−	0.999864i	$-0.494755\pi$
$821$	0.944272	0.0329553	0.0164777	+	0.999864i	$0.494755\pi$
$822$	−20.9443	−0.730515
$823$	21.0344	0.733215	0.366607	−	0.930376i	$-0.380519\pi$
$823$	21.0344	0.733215	0.366607	+	0.930376i	$0.380519\pi$
$824$	11.5623	0.402792
$825$	0	0
$826$	−3.09017	−0.107521
$827$	−30.5410	−1.06202	−0.531008	−	0.847367i	$-0.678186\pi$
$827$	−30.5410	−1.06202	−0.531008	+	0.847367i	$0.678186\pi$
$828$	−1.85410	−0.0644345
$829$	40.2492	1.39791	0.698957	−	0.715164i	$-0.253648\pi$
$829$	40.2492	1.39791	0.698957	+	0.715164i	$0.253648\pi$
$830$	0	0
$831$	−6.14590	−0.213199
$832$	−1.85410	−0.0642794
$833$	−22.9443	−0.794972
$834$	−7.56231	−0.261861
$835$	0	0
$836$	−0.527864	−0.0182566
$837$	6.47214	0.223710
$838$	28.9443	0.999863
$839$	6.18034	0.213369	0.106685	−	0.994293i	$-0.465977\pi$
$839$	6.18034	0.213369	0.106685	+	0.994293i	$0.465977\pi$
$840$	0	0
$841$	23.3607	0.805541
$842$	−4.18034	−0.144064
$843$	5.09017	0.175315
$844$	16.2705	0.560054
$845$	0	0
$846$	−0.618034	−0.0212484
$847$	−17.1803	−0.590323
$848$	7.61803	0.261604
$849$	7.81966	0.268370
$850$	0	0
$851$	−19.5836	−0.671317
$852$	−12.4721	−0.427288
$853$	26.5623	0.909476	0.454738	−	0.890625i	$-0.349733\pi$
$853$	26.5623	0.909476	0.454738	+	0.890625i	$0.349733\pi$
$854$	6.00000	0.205316
$855$	0	0
$856$	−10.9443	−0.374068
$857$	14.1803	0.484391	0.242196	−	0.970227i	$-0.422132\pi$
$857$	14.1803	0.484391	0.242196	+	0.970227i	$0.422132\pi$
$858$	−1.14590	−0.0391203
$859$	−45.9787	−1.56877	−0.784387	−	0.620272i	$-0.787022\pi$
$859$	−45.9787	−1.56877	−0.784387	+	0.620272i	$0.787022\pi$
$860$	0	0
$861$	−18.7984	−0.640647
$862$	38.1803	1.30043
$863$	−14.0902	−0.479635	−0.239817	−	0.970818i	$-0.577088\pi$
$863$	−14.0902	−0.479635	−0.239817	+	0.970818i	$0.577088\pi$
$864$	1.00000	0.0340207
$865$	0	0
$866$	−9.41641	−0.319983
$867$	10.4164	0.353760
$868$	10.4721	0.355447
$869$	−8.29180	−0.281280
$870$	0	0
$871$	−18.0000	−0.609907
$872$	16.1803	0.547935
$873$	−3.70820	−0.125504
$874$	1.58359	0.0535658
$875$	0	0
$876$	−4.94427	−0.167051
$877$	−41.2705	−1.39361	−0.696803	−	0.717263i	$-0.745395\pi$
$877$	−41.2705	−1.39361	−0.696803	+	0.717263i	$0.745395\pi$
$878$	−11.7082	−0.395133
$879$	10.9098	0.367979
$880$	0	0
$881$	−42.2705	−1.42413	−0.712065	−	0.702114i	$-0.752240\pi$
$881$	−42.2705	−1.42413	−0.712065	+	0.702114i	$0.752240\pi$
$882$	−4.38197	−0.147548
$883$	29.5279	0.993692	0.496846	−	0.867839i	$-0.334491\pi$
$883$	29.5279	0.993692	0.496846	+	0.867839i	$0.334491\pi$
$884$	−9.70820	−0.326522
$885$	0	0
$886$	−35.5967	−1.19590
$887$	46.0902	1.54756	0.773778	−	0.633457i	$-0.218364\pi$
$887$	46.0902	1.54756	0.773778	+	0.633457i	$0.218364\pi$
$888$	10.5623	0.354448
$889$	−24.9443	−0.836604
$890$	0	0
$891$	0.618034	0.0207049
$892$	24.0000	0.803579
$893$	0.527864	0.0176643
$894$	13.4164	0.448712
$895$	0	0
$896$	1.61803	0.0540547
$897$	3.43769	0.114781
$898$	−23.2148	−0.774687
$899$	−46.8328	−1.56196
$900$	0	0
$901$	39.8885	1.32888
$902$	−7.18034	−0.239079
$903$	−12.4721	−0.415047
$904$	1.23607	0.0411110
$905$	0	0
$906$	23.7082	0.787652
$907$	−27.1246	−0.900658	−0.450329	−	0.892863i	$-0.648693\pi$
$907$	−27.1246	−0.900658	−0.450329	+	0.892863i	$0.648693\pi$
$908$	−5.81966	−0.193132
$909$	−18.6525	−0.618664
$910$	0	0
$911$	−0.111456	−0.00369271	−0.00184635	−	0.999998i	$-0.500588\pi$
$911$	−0.111456	−0.00369271	−0.00184635	+	0.999998i	$0.500588\pi$
$912$	−0.854102	−0.0282821
$913$	1.81966	0.0602220
$914$	14.8328	0.490626
$915$	0	0
$916$	−11.7082	−0.386850
$917$	24.4164	0.806301
$918$	5.23607	0.172816
$919$	19.5967	0.646437	0.323219	−	0.946324i	$-0.395235\pi$
$919$	19.5967	0.646437	0.323219	+	0.946324i	$0.395235\pi$
$920$	0	0
$921$	25.2361	0.831557
$922$	15.8197	0.520993
$923$	23.1246	0.761156
$924$	1.00000	0.0328976
$925$	0	0
$926$	39.7771	1.30716
$927$	11.5623	0.379756
$928$	−7.23607	−0.237536
$929$	25.4508	0.835015	0.417508	−	0.908673i	$-0.362904\pi$
$929$	25.4508	0.835015	0.417508	+	0.908673i	$0.362904\pi$
$930$	0	0
$931$	3.74265	0.122660
$932$	7.41641	0.242933
$933$	12.0000	0.392862
$934$	10.7639	0.352207
$935$	0	0
$936$	−1.85410	−0.0606032
$937$	13.1246	0.428762	0.214381	−	0.976750i	$-0.431227\pi$
$937$	13.1246	0.428762	0.214381	+	0.976750i	$0.431227\pi$
$938$	15.7082	0.512891
$939$	15.7082	0.512618
$940$	0	0
$941$	−23.1246	−0.753841	−0.376920	−	0.926246i	$-0.623017\pi$
$941$	−23.1246	−0.753841	−0.376920	+	0.926246i	$0.623017\pi$
$942$	6.94427	0.226257
$943$	21.5410	0.701472
$944$	−1.90983	−0.0621597
$945$	0	0
$946$	−4.76393	−0.154889
$947$	5.88854	0.191352	0.0956760	−	0.995413i	$-0.469499\pi$
$947$	5.88854	0.191352	0.0956760	+	0.995413i	$0.469499\pi$
$948$	−13.4164	−0.435745
$949$	9.16718	0.297579
$950$	0	0
$951$	−7.85410	−0.254687
$952$	8.47214	0.274584
$953$	37.8197	1.22510	0.612549	−	0.790432i	$-0.290144\pi$
$953$	37.8197	1.22510	0.612549	+	0.790432i	$0.290144\pi$
$954$	7.61803	0.246643
$955$	0	0
$956$	−8.94427	−0.289278
$957$	−4.47214	−0.144564
$958$	21.7082	0.701360
$959$	−33.8885	−1.09432
$960$	0	0
$961$	10.8885	0.351243
$962$	−19.5836	−0.631400
$963$	−10.9443	−0.352674
$964$	−13.8541	−0.446211
$965$	0	0
$966$	−3.00000	−0.0965234
$967$	−2.32624	−0.0748068	−0.0374034	−	0.999300i	$-0.511909\pi$
$967$	−2.32624	−0.0748068	−0.0374034	+	0.999300i	$0.511909\pi$
$968$	−10.6180	−0.341277
$969$	−4.47214	−0.143666
$970$	0	0
$971$	−48.9787	−1.57180	−0.785901	−	0.618353i	$-0.787800\pi$
$971$	−48.9787	−1.57180	−0.785901	+	0.618353i	$0.787800\pi$
$972$	1.00000	0.0320750
$973$	−12.2361	−0.392270
$974$	−1.67376	−0.0536308
$975$	0	0
$976$	3.70820	0.118697
$977$	31.4164	1.00510	0.502550	−	0.864548i	$-0.332395\pi$
$977$	31.4164	1.00510	0.502550	+	0.864548i	$0.332395\pi$
$978$	12.9443	0.413912
$979$	−4.27051	−0.136486
$980$	0	0
$981$	16.1803	0.516598
$982$	27.9787	0.892837
$983$	−31.4508	−1.00313	−0.501563	−	0.865121i	$-0.667242\pi$
$983$	−31.4508	−1.00313	−0.501563	+	0.865121i	$0.667242\pi$
$984$	−11.6180	−0.370369
$985$	0	0
$986$	−37.8885	−1.20662
$987$	−1.00000	−0.0318304
$988$	1.58359	0.0503808
$989$	14.2918	0.454453
$990$	0	0
$991$	42.0000	1.33417	0.667087	−	0.744980i	$-0.267541\pi$
$991$	42.0000	1.33417	0.667087	+	0.744980i	$0.267541\pi$
$992$	6.47214	0.205491
$993$	6.47214	0.205387
$994$	−20.1803	−0.640082
$995$	0	0
$996$	2.94427	0.0932928
$997$	28.8541	0.913819	0.456909	−	0.889513i	$-0.348956\pi$
$997$	28.8541	0.913819	0.456909	+	0.889513i	$0.348956\pi$
$998$	−39.2705	−1.24309
$999$	10.5623	0.334177

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.a.g.1.2	yes	2
3.2	odd	2		2250.2.a.e.1.2		2
4.3	odd	2		6000.2.a.f.1.1		2
5.2	odd	4		750.2.c.d.499.4		4
5.3	odd	4		750.2.c.d.499.1		4
5.4	even	2		750.2.a.b.1.1	✓	2
15.2	even	4		2250.2.c.d.1999.2		4
15.8	even	4		2250.2.c.d.1999.3		4
15.14	odd	2		2250.2.a.l.1.1		2
20.3	even	4		6000.2.f.h.1249.2		4
20.7	even	4		6000.2.f.h.1249.3		4
20.19	odd	2		6000.2.a.w.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
750.2.a.b.1.1	✓	2	5.4	even	2
750.2.a.g.1.2	yes	2	1.1	even	1	trivial
750.2.c.d.499.1		4	5.3	odd	4
750.2.c.d.499.4		4	5.2	odd	4
2250.2.a.e.1.2		2	3.2	odd	2
2250.2.a.l.1.1		2	15.14	odd	2
2250.2.c.d.1999.2		4	15.2	even	4
2250.2.c.d.1999.3		4	15.8	even	4
6000.2.a.f.1.1		2	4.3	odd	2
6000.2.a.w.1.2		2	20.19	odd	2
6000.2.f.h.1249.2		4	20.3	even	4
6000.2.f.h.1249.3		4	20.7	even	4

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:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +1.61803 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +1.61803 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.618034 q^{11} +1.00000 q^{12} -1.85410 q^{13} +1.61803 q^{14} +1.00000 q^{16} +5.23607 q^{17} +1.00000 q^{18} -0.854102 q^{19} +1.61803 q^{21} +0.618034 q^{22} -1.85410 q^{23} +1.00000 q^{24} -1.85410 q^{26} +1.00000 q^{27} +1.61803 q^{28} -7.23607 q^{29} +6.47214 q^{31} +1.00000 q^{32} +0.618034 q^{33} +5.23607 q^{34} +1.00000 q^{36} +10.5623 q^{37} -0.854102 q^{38} -1.85410 q^{39} -11.6180 q^{41} +1.61803 q^{42} -7.70820 q^{43} +0.618034 q^{44} -1.85410 q^{46} -0.618034 q^{47} +1.00000 q^{48} -4.38197 q^{49} +5.23607 q^{51} -1.85410 q^{52} +7.61803 q^{53} +1.00000 q^{54} +1.61803 q^{56} -0.854102 q^{57} -7.23607 q^{58} -1.90983 q^{59} +3.70820 q^{61} +6.47214 q^{62} +1.61803 q^{63} +1.00000 q^{64} +0.618034 q^{66} +9.70820 q^{67} +5.23607 q^{68} -1.85410 q^{69} -12.4721 q^{71} +1.00000 q^{72} -4.94427 q^{73} +10.5623 q^{74} -0.854102 q^{76} +1.00000 q^{77} -1.85410 q^{78} -13.4164 q^{79} +1.00000 q^{81} -11.6180 q^{82} +2.94427 q^{83} +1.61803 q^{84} -7.70820 q^{86} -7.23607 q^{87} +0.618034 q^{88} -6.90983 q^{89} -3.00000 q^{91} -1.85410 q^{92} +6.47214 q^{93} -0.618034 q^{94} +1.00000 q^{96} -3.70820 q^{97} -4.38197 q^{98} +0.618034 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{6} + q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^6 + q^7 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{6} + q^{7} + 2 q^{8} + 2 q^{9} - q^{11} + 2 q^{12} + 3 q^{13} + q^{14} + 2 q^{16} + 6 q^{17} + 2 q^{18} + 5 q^{19} + q^{21} - q^{22} + 3 q^{23} + 2 q^{24} + 3 q^{26} + 2 q^{27} + q^{28} - 10 q^{29} + 4 q^{31} + 2 q^{32} - q^{33} + 6 q^{34} + 2 q^{36} + q^{37} + 5 q^{38} + 3 q^{39} - 21 q^{41} + q^{42} - 2 q^{43} - q^{44} + 3 q^{46} + q^{47} + 2 q^{48} - 11 q^{49} + 6 q^{51} + 3 q^{52} + 13 q^{53} + 2 q^{54} + q^{56} + 5 q^{57} - 10 q^{58} - 15 q^{59} - 6 q^{61} + 4 q^{62} + q^{63} + 2 q^{64} - q^{66} + 6 q^{67} + 6 q^{68} + 3 q^{69} - 16 q^{71} + 2 q^{72} + 8 q^{73} + q^{74} + 5 q^{76} + 2 q^{77} + 3 q^{78} + 2 q^{81} - 21 q^{82} - 12 q^{83} + q^{84} - 2 q^{86} - 10 q^{87} - q^{88} - 25 q^{89} - 6 q^{91} + 3 q^{92} + 4 q^{93} + q^{94} + 2 q^{96} + 6 q^{97} - 11 q^{98} - q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^6 + q^7 + 2 * q^8 + 2 * q^9 - q^11 + 2 * q^12 + 3 * q^13 + q^14 + 2 * q^16 + 6 * q^17 + 2 * q^18 + 5 * q^19 + q^21 - q^22 + 3 * q^23 + 2 * q^24 + 3 * q^26 + 2 * q^27 + q^28 - 10 * q^29 + 4 * q^31 + 2 * q^32 - q^33 + 6 * q^34 + 2 * q^36 + q^37 + 5 * q^38 + 3 * q^39 - 21 * q^41 + q^42 - 2 * q^43 - q^44 + 3 * q^46 + q^47 + 2 * q^48 - 11 * q^49 + 6 * q^51 + 3 * q^52 + 13 * q^53 + 2 * q^54 + q^56 + 5 * q^57 - 10 * q^58 - 15 * q^59 - 6 * q^61 + 4 * q^62 + q^63 + 2 * q^64 - q^66 + 6 * q^67 + 6 * q^68 + 3 * q^69 - 16 * q^71 + 2 * q^72 + 8 * q^73 + q^74 + 5 * q^76 + 2 * q^77 + 3 * q^78 + 2 * q^81 - 21 * q^82 - 12 * q^83 + q^84 - 2 * q^86 - 10 * q^87 - q^88 - 25 * q^89 - 6 * q^91 + 3 * q^92 + 4 * q^93 + q^94 + 2 * q^96 + 6 * q^97 - 11 * q^98 - q^99

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