LMFDB - Embedded newform 750.2.a.f.1.1

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:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.61803$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -3.23607 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -3.23607 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.61803 q^{11} -1.00000 q^{12} +3.85410 q^{13} -3.23607 q^{14} +1.00000 q^{16} -1.85410 q^{17} +1.00000 q^{18} +6.00000 q^{19} +3.23607 q^{21} +3.61803 q^{22} +8.09017 q^{23} -1.00000 q^{24} +3.85410 q^{26} -1.00000 q^{27} -3.23607 q^{28} -6.32624 q^{29} +8.85410 q^{31} +1.00000 q^{32} -3.61803 q^{33} -1.85410 q^{34} +1.00000 q^{36} -1.14590 q^{37} +6.00000 q^{38} -3.85410 q^{39} +1.23607 q^{41} +3.23607 q^{42} -6.85410 q^{43} +3.61803 q^{44} +8.09017 q^{46} +4.14590 q^{47} -1.00000 q^{48} +3.47214 q^{49} +1.85410 q^{51} +3.85410 q^{52} -1.23607 q^{53} -1.00000 q^{54} -3.23607 q^{56} -6.00000 q^{57} -6.32624 q^{58} +8.61803 q^{59} -13.4164 q^{61} +8.85410 q^{62} -3.23607 q^{63} +1.00000 q^{64} -3.61803 q^{66} -4.61803 q^{67} -1.85410 q^{68} -8.09017 q^{69} +8.94427 q^{71} +1.00000 q^{72} -12.0000 q^{73} -1.14590 q^{74} +6.00000 q^{76} -11.7082 q^{77} -3.85410 q^{78} -7.85410 q^{79} +1.00000 q^{81} +1.23607 q^{82} +14.1803 q^{83} +3.23607 q^{84} -6.85410 q^{86} +6.32624 q^{87} +3.61803 q^{88} -4.76393 q^{89} -12.4721 q^{91} +8.09017 q^{92} -8.85410 q^{93} +4.14590 q^{94} -1.00000 q^{96} +4.18034 q^{97} +3.47214 q^{98} +3.61803 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{6} - 2 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 - 2 * q^7 + 2 * q^8 + 2 * q^9	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{6} - 2 q^{7} + 2 q^{8} + 2 q^{9} + 5 q^{11} - 2 q^{12} + q^{13} - 2 q^{14} + 2 q^{16} + 3 q^{17} + 2 q^{18} + 12 q^{19} + 2 q^{21} + 5 q^{22} + 5 q^{23} - 2 q^{24} + q^{26} - 2 q^{27} - 2 q^{28} + 3 q^{29} + 11 q^{31} + 2 q^{32} - 5 q^{33} + 3 q^{34} + 2 q^{36} - 9 q^{37} + 12 q^{38} - q^{39} - 2 q^{41} + 2 q^{42} - 7 q^{43} + 5 q^{44} + 5 q^{46} + 15 q^{47} - 2 q^{48} - 2 q^{49} - 3 q^{51} + q^{52} + 2 q^{53} - 2 q^{54} - 2 q^{56} - 12 q^{57} + 3 q^{58} + 15 q^{59} + 11 q^{62} - 2 q^{63} + 2 q^{64} - 5 q^{66} - 7 q^{67} + 3 q^{68} - 5 q^{69} + 2 q^{72} - 24 q^{73} - 9 q^{74} + 12 q^{76} - 10 q^{77} - q^{78} - 9 q^{79} + 2 q^{81} - 2 q^{82} + 6 q^{83} + 2 q^{84} - 7 q^{86} - 3 q^{87} + 5 q^{88} - 14 q^{89} - 16 q^{91} + 5 q^{92} - 11 q^{93} + 15 q^{94} - 2 q^{96} - 14 q^{97} - 2 q^{98} + 5 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^6 - 2 * q^7 + 2 * q^8 + 2 * q^9 + 5 * q^11 - 2 * q^12 + q^13 - 2 * q^14 + 2 * q^16 + 3 * q^17 + 2 * q^18 + 12 * q^19 + 2 * q^21 + 5 * q^22 + 5 * q^23 - 2 * q^24 + q^26 - 2 * q^27 - 2 * q^28 + 3 * q^29 + 11 * q^31 + 2 * q^32 - 5 * q^33 + 3 * q^34 + 2 * q^36 - 9 * q^37 + 12 * q^38 - q^39 - 2 * q^41 + 2 * q^42 - 7 * q^43 + 5 * q^44 + 5 * q^46 + 15 * q^47 - 2 * q^48 - 2 * q^49 - 3 * q^51 + q^52 + 2 * q^53 - 2 * q^54 - 2 * q^56 - 12 * q^57 + 3 * q^58 + 15 * q^59 + 11 * q^62 - 2 * q^63 + 2 * q^64 - 5 * q^66 - 7 * q^67 + 3 * q^68 - 5 * q^69 + 2 * q^72 - 24 * q^73 - 9 * q^74 + 12 * q^76 - 10 * q^77 - q^78 - 9 * q^79 + 2 * q^81 - 2 * q^82 + 6 * q^83 + 2 * q^84 - 7 * q^86 - 3 * q^87 + 5 * q^88 - 14 * q^89 - 16 * q^91 + 5 * q^92 - 11 * q^93 + 15 * q^94 - 2 * q^96 - 14 * q^97 - 2 * q^98 + 5 * 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
$7$	−3.23607	−1.22312	−0.611559	−	0.791199i	$-0.709457\pi$
$7$	−3.23607	−1.22312	−0.611559	+	0.791199i	$0.709457\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	3.61803	1.09088	0.545439	−	0.838150i	$-0.316363\pi$
$11$	3.61803	1.09088	0.545439	+	0.838150i	$0.316363\pi$
$12$	−1.00000	−0.288675
$13$	3.85410	1.06894	0.534468	−	0.845189i	$-0.320512\pi$
$13$	3.85410	1.06894	0.534468	+	0.845189i	$0.320512\pi$
$14$	−3.23607	−0.864876
$15$	0	0
$16$	1.00000	0.250000
$17$	−1.85410	−0.449686	−0.224843	−	0.974395i	$-0.572187\pi$
$17$	−1.85410	−0.449686	−0.224843	+	0.974395i	$0.572187\pi$
$18$	1.00000	0.235702
$19$	6.00000	1.37649	0.688247	−	0.725476i	$-0.258380\pi$
$19$	6.00000	1.37649	0.688247	+	0.725476i	$0.258380\pi$
$20$	0	0
$21$	3.23607	0.706168
$22$	3.61803	0.771367
$23$	8.09017	1.68692	0.843459	−	0.537194i	$-0.180516\pi$
$23$	8.09017	1.68692	0.843459	+	0.537194i	$0.180516\pi$
$24$	−1.00000	−0.204124
$25$	0	0
$26$	3.85410	0.755852
$27$	−1.00000	−0.192450
$28$	−3.23607	−0.611559
$29$	−6.32624	−1.17475	−0.587376	−	0.809314i	$-0.699839\pi$
$29$	−6.32624	−1.17475	−0.587376	+	0.809314i	$0.699839\pi$
$30$	0	0
$31$	8.85410	1.59024	0.795122	−	0.606450i	$-0.207407\pi$
$31$	8.85410	1.59024	0.795122	+	0.606450i	$0.207407\pi$
$32$	1.00000	0.176777
$33$	−3.61803	−0.629819
$34$	−1.85410	−0.317976
$35$	0	0
$36$	1.00000	0.166667
$37$	−1.14590	−0.188384	−0.0941922	−	0.995554i	$-0.530027\pi$
$37$	−1.14590	−0.188384	−0.0941922	+	0.995554i	$0.530027\pi$
$38$	6.00000	0.973329
$39$	−3.85410	−0.617150
$40$	0	0
$41$	1.23607	0.193041	0.0965207	−	0.995331i	$-0.469229\pi$
$41$	1.23607	0.193041	0.0965207	+	0.995331i	$0.469229\pi$
$42$	3.23607	0.499336
$43$	−6.85410	−1.04524	−0.522620	−	0.852566i	$-0.675045\pi$
$43$	−6.85410	−1.04524	−0.522620	+	0.852566i	$0.675045\pi$
$44$	3.61803	0.545439
$45$	0	0
$46$	8.09017	1.19283
$47$	4.14590	0.604741	0.302371	−	0.953190i	$-0.402222\pi$
$47$	4.14590	0.604741	0.302371	+	0.953190i	$0.402222\pi$
$48$	−1.00000	−0.144338
$49$	3.47214	0.496019
$50$	0	0
$51$	1.85410	0.259626
$52$	3.85410	0.534468
$53$	−1.23607	−0.169787	−0.0848935	−	0.996390i	$-0.527055\pi$
$53$	−1.23607	−0.169787	−0.0848935	+	0.996390i	$0.527055\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	−3.23607	−0.432438
$57$	−6.00000	−0.794719
$58$	−6.32624	−0.830676
$59$	8.61803	1.12197	0.560986	−	0.827825i	$-0.310422\pi$
$59$	8.61803	1.12197	0.560986	+	0.827825i	$0.310422\pi$
$60$	0	0
$61$	−13.4164	−1.71780	−0.858898	−	0.512148i	$-0.828850\pi$
$61$	−13.4164	−1.71780	−0.858898	+	0.512148i	$0.828850\pi$
$62$	8.85410	1.12447
$63$	−3.23607	−0.407706
$64$	1.00000	0.125000
$65$	0	0
$66$	−3.61803	−0.445349
$67$	−4.61803	−0.564183	−0.282091	−	0.959388i	$-0.591028\pi$
$67$	−4.61803	−0.564183	−0.282091	+	0.959388i	$0.591028\pi$
$68$	−1.85410	−0.224843
$69$	−8.09017	−0.973942
$70$	0	0
$71$	8.94427	1.06149	0.530745	−	0.847532i	$-0.321912\pi$
$71$	8.94427	1.06149	0.530745	+	0.847532i	$0.321912\pi$
$72$	1.00000	0.117851
$73$	−12.0000	−1.40449	−0.702247	−	0.711934i	$-0.747820\pi$
$73$	−12.0000	−1.40449	−0.702247	+	0.711934i	$0.747820\pi$
$74$	−1.14590	−0.133208
$75$	0	0
$76$	6.00000	0.688247
$77$	−11.7082	−1.33427
$78$	−3.85410	−0.436391
$79$	−7.85410	−0.883656	−0.441828	−	0.897100i	$-0.645670\pi$
$79$	−7.85410	−0.883656	−0.441828	+	0.897100i	$0.645670\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	1.23607	0.136501
$83$	14.1803	1.55649	0.778247	−	0.627958i	$-0.216109\pi$
$83$	14.1803	1.55649	0.778247	+	0.627958i	$0.216109\pi$
$84$	3.23607	0.353084
$85$	0	0
$86$	−6.85410	−0.739097
$87$	6.32624	0.678244
$88$	3.61803	0.385684
$89$	−4.76393	−0.504976	−0.252488	−	0.967600i	$-0.581249\pi$
$89$	−4.76393	−0.504976	−0.252488	+	0.967600i	$0.581249\pi$
$90$	0	0
$91$	−12.4721	−1.30744
$92$	8.09017	0.843459
$93$	−8.85410	−0.918128
$94$	4.14590	0.427617
$95$	0	0
$96$	−1.00000	−0.102062
$97$	4.18034	0.424449	0.212225	−	0.977221i	$-0.431929\pi$
$97$	4.18034	0.424449	0.212225	+	0.977221i	$0.431929\pi$
$98$	3.47214	0.350739
$99$	3.61803	0.363626
$100$	0	0
$101$	13.3262	1.32601	0.663005	−	0.748615i	$-0.269281\pi$
$101$	13.3262	1.32601	0.663005	+	0.748615i	$0.269281\pi$
$102$	1.85410	0.183583
$103$	4.00000	0.394132	0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000	0.394132	0.197066	+	0.980390i	$0.436859\pi$
$104$	3.85410	0.377926
$105$	0	0
$106$	−1.23607	−0.120058
$107$	−14.1803	−1.37087	−0.685433	−	0.728136i	$-0.740387\pi$
$107$	−14.1803	−1.37087	−0.685433	+	0.728136i	$0.740387\pi$
$108$	−1.00000	−0.0962250
$109$	13.4164	1.28506	0.642529	−	0.766261i	$-0.277885\pi$
$109$	13.4164	1.28506	0.642529	+	0.766261i	$0.277885\pi$
$110$	0	0
$111$	1.14590	0.108764
$112$	−3.23607	−0.305780
$113$	3.32624	0.312906	0.156453	−	0.987685i	$-0.449994\pi$
$113$	3.32624	0.312906	0.156453	+	0.987685i	$0.449994\pi$
$114$	−6.00000	−0.561951
$115$	0	0
$116$	−6.32624	−0.587376
$117$	3.85410	0.356312
$118$	8.61803	0.793354
$119$	6.00000	0.550019
$120$	0	0
$121$	2.09017	0.190015
$122$	−13.4164	−1.21466
$123$	−1.23607	−0.111452
$124$	8.85410	0.795122
$125$	0	0
$126$	−3.23607	−0.288292
$127$	−13.4164	−1.19051	−0.595257	−	0.803535i	$-0.702950\pi$
$127$	−13.4164	−1.19051	−0.595257	+	0.803535i	$0.702950\pi$
$128$	1.00000	0.0883883
$129$	6.85410	0.603470
$130$	0	0
$131$	−17.8885	−1.56293	−0.781465	−	0.623949i	$-0.785527\pi$
$131$	−17.8885	−1.56293	−0.781465	+	0.623949i	$0.785527\pi$
$132$	−3.61803	−0.314909
$133$	−19.4164	−1.68362
$134$	−4.61803	−0.398937
$135$	0	0
$136$	−1.85410	−0.158988
$137$	−2.38197	−0.203505	−0.101753	−	0.994810i	$-0.532445\pi$
$137$	−2.38197	−0.203505	−0.101753	+	0.994810i	$0.532445\pi$
$138$	−8.09017	−0.688681
$139$	−16.7639	−1.42190	−0.710949	−	0.703243i	$-0.751734\pi$
$139$	−16.7639	−1.42190	−0.710949	+	0.703243i	$0.751734\pi$
$140$	0	0
$141$	−4.14590	−0.349148
$142$	8.94427	0.750587
$143$	13.9443	1.16608
$144$	1.00000	0.0833333
$145$	0	0
$146$	−12.0000	−0.993127
$147$	−3.47214	−0.286377
$148$	−1.14590	−0.0941922
$149$	−11.5279	−0.944399	−0.472200	−	0.881492i	$-0.656540\pi$
$149$	−11.5279	−0.944399	−0.472200	+	0.881492i	$0.656540\pi$
$150$	0	0
$151$	−11.1459	−0.907040	−0.453520	−	0.891246i	$-0.649832\pi$
$151$	−11.1459	−0.907040	−0.453520	+	0.891246i	$0.649832\pi$
$152$	6.00000	0.486664
$153$	−1.85410	−0.149895
$154$	−11.7082	−0.943474
$155$	0	0
$156$	−3.85410	−0.308575
$157$	20.5623	1.64105	0.820525	−	0.571610i	$-0.193681\pi$
$157$	20.5623	1.64105	0.820525	+	0.571610i	$0.193681\pi$
$158$	−7.85410	−0.624839
$159$	1.23607	0.0980266
$160$	0	0
$161$	−26.1803	−2.06330
$162$	1.00000	0.0785674
$163$	13.2705	1.03943	0.519713	−	0.854341i	$-0.326039\pi$
$163$	13.2705	1.03943	0.519713	+	0.854341i	$0.326039\pi$
$164$	1.23607	0.0965207
$165$	0	0
$166$	14.1803	1.10061
$167$	11.9098	0.921610	0.460805	−	0.887501i	$-0.347561\pi$
$167$	11.9098	0.921610	0.460805	+	0.887501i	$0.347561\pi$
$168$	3.23607	0.249668
$169$	1.85410	0.142623
$170$	0	0
$171$	6.00000	0.458831
$172$	−6.85410	−0.522620
$173$	4.76393	0.362195	0.181098	−	0.983465i	$-0.442035\pi$
$173$	4.76393	0.362195	0.181098	+	0.983465i	$0.442035\pi$
$174$	6.32624	0.479591
$175$	0	0
$176$	3.61803	0.272720
$177$	−8.61803	−0.647771
$178$	−4.76393	−0.357072
$179$	−19.4164	−1.45125	−0.725625	−	0.688090i	$-0.758449\pi$
$179$	−19.4164	−1.45125	−0.725625	+	0.688090i	$0.758449\pi$
$180$	0	0
$181$	−19.4164	−1.44321	−0.721605	−	0.692305i	$-0.756595\pi$
$181$	−19.4164	−1.44321	−0.721605	+	0.692305i	$0.756595\pi$
$182$	−12.4721	−0.924496
$183$	13.4164	0.991769
$184$	8.09017	0.596415
$185$	0	0
$186$	−8.85410	−0.649214
$187$	−6.70820	−0.490552
$188$	4.14590	0.302371
$189$	3.23607	0.235389
$190$	0	0
$191$	6.00000	0.434145	0.217072	−	0.976156i	$-0.430349\pi$
$191$	6.00000	0.434145	0.217072	+	0.976156i	$0.430349\pi$
$192$	−1.00000	−0.0721688
$193$	−23.1246	−1.66455	−0.832273	−	0.554366i	$-0.812961\pi$
$193$	−23.1246	−1.66455	−0.832273	+	0.554366i	$0.812961\pi$
$194$	4.18034	0.300131
$195$	0	0
$196$	3.47214	0.248010
$197$	10.4721	0.746109	0.373054	−	0.927809i	$-0.378310\pi$
$197$	10.4721	0.746109	0.373054	+	0.927809i	$0.378310\pi$
$198$	3.61803	0.257122
$199$	−13.3820	−0.948622	−0.474311	−	0.880357i	$-0.657303\pi$
$199$	−13.3820	−0.948622	−0.474311	+	0.880357i	$0.657303\pi$
$200$	0	0
$201$	4.61803	0.325731
$202$	13.3262	0.937631
$203$	20.4721	1.43686
$204$	1.85410	0.129813
$205$	0	0
$206$	4.00000	0.278693
$207$	8.09017	0.562306
$208$	3.85410	0.267234
$209$	21.7082	1.50159
$210$	0	0
$211$	−23.4164	−1.61205	−0.806026	−	0.591880i	$-0.798386\pi$
$211$	−23.4164	−1.61205	−0.806026	+	0.591880i	$0.798386\pi$
$212$	−1.23607	−0.0848935
$213$	−8.94427	−0.612851
$214$	−14.1803	−0.969348
$215$	0	0
$216$	−1.00000	−0.0680414
$217$	−28.6525	−1.94506
$218$	13.4164	0.908674
$219$	12.0000	0.810885
$220$	0	0
$221$	−7.14590	−0.480685
$222$	1.14590	0.0769076
$223$	8.29180	0.555260	0.277630	−	0.960688i	$-0.410451\pi$
$223$	8.29180	0.555260	0.277630	+	0.960688i	$0.410451\pi$
$224$	−3.23607	−0.216219
$225$	0	0
$226$	3.32624	0.221258
$227$	7.52786	0.499642	0.249821	−	0.968292i	$-0.419628\pi$
$227$	7.52786	0.499642	0.249821	+	0.968292i	$0.419628\pi$
$228$	−6.00000	−0.397360
$229$	11.7082	0.773700	0.386850	−	0.922143i	$-0.373563\pi$
$229$	11.7082	0.773700	0.386850	+	0.922143i	$0.373563\pi$
$230$	0	0
$231$	11.7082	0.770343
$232$	−6.32624	−0.415338
$233$	8.32624	0.545470	0.272735	−	0.962089i	$-0.412072\pi$
$233$	8.32624	0.545470	0.272735	+	0.962089i	$0.412072\pi$
$234$	3.85410	0.251951
$235$	0	0
$236$	8.61803	0.560986
$237$	7.85410	0.510179
$238$	6.00000	0.388922
$239$	4.65248	0.300944	0.150472	−	0.988614i	$-0.451921\pi$
$239$	4.65248	0.300944	0.150472	+	0.988614i	$0.451921\pi$
$240$	0	0
$241$	−11.0902	−0.714381	−0.357190	−	0.934032i	$-0.616265\pi$
$241$	−11.0902	−0.714381	−0.357190	+	0.934032i	$0.616265\pi$
$242$	2.09017	0.134361
$243$	−1.00000	−0.0641500
$244$	−13.4164	−0.858898
$245$	0	0
$246$	−1.23607	−0.0788088
$247$	23.1246	1.47138
$248$	8.85410	0.562236
$249$	−14.1803	−0.898643
$250$	0	0
$251$	19.0902	1.20496	0.602480	−	0.798134i	$-0.294179\pi$
$251$	19.0902	1.20496	0.602480	+	0.798134i	$0.294179\pi$
$252$	−3.23607	−0.203853
$253$	29.2705	1.84022
$254$	−13.4164	−0.841820
$255$	0	0
$256$	1.00000	0.0625000
$257$	14.5066	0.904895	0.452448	−	0.891791i	$-0.350551\pi$
$257$	14.5066	0.904895	0.452448	+	0.891791i	$0.350551\pi$
$258$	6.85410	0.426718
$259$	3.70820	0.230417
$260$	0	0
$261$	−6.32624	−0.391584
$262$	−17.8885	−1.10516
$263$	−30.9787	−1.91023	−0.955115	−	0.296236i	$-0.904268\pi$
$263$	−30.9787	−1.91023	−0.955115	+	0.296236i	$0.904268\pi$
$264$	−3.61803	−0.222675
$265$	0	0
$266$	−19.4164	−1.19050
$267$	4.76393	0.291548
$268$	−4.61803	−0.282091
$269$	20.3820	1.24271	0.621355	−	0.783529i	$-0.286582\pi$
$269$	20.3820	1.24271	0.621355	+	0.783529i	$0.286582\pi$
$270$	0	0
$271$	11.5623	0.702360	0.351180	−	0.936308i	$-0.385781\pi$
$271$	11.5623	0.702360	0.351180	+	0.936308i	$0.385781\pi$
$272$	−1.85410	−0.112421
$273$	12.4721	0.754848
$274$	−2.38197	−0.143900
$275$	0	0
$276$	−8.09017	−0.486971
$277$	30.3607	1.82420	0.912098	−	0.409972i	$-0.134461\pi$
$277$	30.3607	1.82420	0.912098	+	0.409972i	$0.134461\pi$
$278$	−16.7639	−1.00543
$279$	8.85410	0.530081
$280$	0	0
$281$	13.5279	0.807005	0.403502	−	0.914979i	$-0.367793\pi$
$281$	13.5279	0.807005	0.403502	+	0.914979i	$0.367793\pi$
$282$	−4.14590	−0.246885
$283$	9.90983	0.589078	0.294539	−	0.955639i	$-0.404834\pi$
$283$	9.90983	0.589078	0.294539	+	0.955639i	$0.404834\pi$
$284$	8.94427	0.530745
$285$	0	0
$286$	13.9443	0.824542
$287$	−4.00000	−0.236113
$288$	1.00000	0.0589256
$289$	−13.5623	−0.797783
$290$	0	0
$291$	−4.18034	−0.245056
$292$	−12.0000	−0.702247
$293$	−33.5967	−1.96274	−0.981371	−	0.192120i	$-0.938464\pi$
$293$	−33.5967	−1.96274	−0.981371	+	0.192120i	$0.938464\pi$
$294$	−3.47214	−0.202499
$295$	0	0
$296$	−1.14590	−0.0666040
$297$	−3.61803	−0.209940
$298$	−11.5279	−0.667791
$299$	31.1803	1.80321
$300$	0	0
$301$	22.1803	1.27845
$302$	−11.1459	−0.641374
$303$	−13.3262	−0.765572
$304$	6.00000	0.344124
$305$	0	0
$306$	−1.85410	−0.105992
$307$	21.9098	1.25046	0.625230	−	0.780441i	$-0.285005\pi$
$307$	21.9098	1.25046	0.625230	+	0.780441i	$0.285005\pi$
$308$	−11.7082	−0.667137
$309$	−4.00000	−0.227552
$310$	0	0
$311$	4.47214	0.253592	0.126796	−	0.991929i	$-0.459531\pi$
$311$	4.47214	0.253592	0.126796	+	0.991929i	$0.459531\pi$
$312$	−3.85410	−0.218196
$313$	−13.0557	−0.737953	−0.368977	−	0.929439i	$-0.620292\pi$
$313$	−13.0557	−0.737953	−0.368977	+	0.929439i	$0.620292\pi$
$314$	20.5623	1.16040
$315$	0	0
$316$	−7.85410	−0.441828
$317$	3.70820	0.208273	0.104137	−	0.994563i	$-0.466792\pi$
$317$	3.70820	0.208273	0.104137	+	0.994563i	$0.466792\pi$
$318$	1.23607	0.0693153
$319$	−22.8885	−1.28151
$320$	0	0
$321$	14.1803	0.791469
$322$	−26.1803	−1.45897
$323$	−11.1246	−0.618990
$324$	1.00000	0.0555556
$325$	0	0
$326$	13.2705	0.734986
$327$	−13.4164	−0.741929
$328$	1.23607	0.0682504
$329$	−13.4164	−0.739671
$330$	0	0
$331$	5.41641	0.297713	0.148856	−	0.988859i	$-0.452441\pi$
$331$	5.41641	0.297713	0.148856	+	0.988859i	$0.452441\pi$
$332$	14.1803	0.778247
$333$	−1.14590	−0.0627948
$334$	11.9098	0.651677
$335$	0	0
$336$	3.23607	0.176542
$337$	−4.94427	−0.269332	−0.134666	−	0.990891i	$-0.542996\pi$
$337$	−4.94427	−0.269332	−0.134666	+	0.990891i	$0.542996\pi$
$338$	1.85410	0.100850
$339$	−3.32624	−0.180656
$340$	0	0
$341$	32.0344	1.73476
$342$	6.00000	0.324443
$343$	11.4164	0.616428
$344$	−6.85410	−0.369548
$345$	0	0
$346$	4.76393	0.256111
$347$	20.3607	1.09302	0.546509	−	0.837453i	$-0.315956\pi$
$347$	20.3607	1.09302	0.546509	+	0.837453i	$0.315956\pi$
$348$	6.32624	0.339122
$349$	0	0		−	1.00000i	$-0.5\pi$
$349$	0	0			1.00000i	$0.5\pi$
$350$	0	0
$351$	−3.85410	−0.205717
$352$	3.61803	0.192842
$353$	−25.7984	−1.37311	−0.686554	−	0.727078i	$-0.740878\pi$
$353$	−25.7984	−1.37311	−0.686554	+	0.727078i	$0.740878\pi$
$354$	−8.61803	−0.458043
$355$	0	0
$356$	−4.76393	−0.252488
$357$	−6.00000	−0.317554
$358$	−19.4164	−1.02619
$359$	−11.8885	−0.627453	−0.313727	−	0.949513i	$-0.601578\pi$
$359$	−11.8885	−0.627453	−0.313727	+	0.949513i	$0.601578\pi$
$360$	0	0
$361$	17.0000	0.894737
$362$	−19.4164	−1.02050
$363$	−2.09017	−0.109705
$364$	−12.4721	−0.653718
$365$	0	0
$366$	13.4164	0.701287
$367$	−23.7082	−1.23756	−0.618779	−	0.785565i	$-0.712372\pi$
$367$	−23.7082	−1.23756	−0.618779	+	0.785565i	$0.712372\pi$
$368$	8.09017	0.421729
$369$	1.23607	0.0643471
$370$	0	0
$371$	4.00000	0.207670
$372$	−8.85410	−0.459064
$373$	−9.74265	−0.504455	−0.252228	−	0.967668i	$-0.581163\pi$
$373$	−9.74265	−0.504455	−0.252228	+	0.967668i	$0.581163\pi$
$374$	−6.70820	−0.346873
$375$	0	0
$376$	4.14590	0.213808
$377$	−24.3820	−1.25574
$378$	3.23607	0.166445
$379$	3.23607	0.166226	0.0831128	−	0.996540i	$-0.473514\pi$
$379$	3.23607	0.166226	0.0831128	+	0.996540i	$0.473514\pi$
$380$	0	0
$381$	13.4164	0.687343
$382$	6.00000	0.306987
$383$	17.8885	0.914062	0.457031	−	0.889451i	$-0.348913\pi$
$383$	17.8885	0.914062	0.457031	+	0.889451i	$0.348913\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−23.1246	−1.17701
$387$	−6.85410	−0.348414
$388$	4.18034	0.212225
$389$	−15.2705	−0.774246	−0.387123	−	0.922028i	$-0.626531\pi$
$389$	−15.2705	−0.774246	−0.387123	+	0.922028i	$0.626531\pi$
$390$	0	0
$391$	−15.0000	−0.758583
$392$	3.47214	0.175369
$393$	17.8885	0.902358
$394$	10.4721	0.527579
$395$	0	0
$396$	3.61803	0.181813
$397$	−23.5279	−1.18083	−0.590415	−	0.807100i	$-0.701036\pi$
$397$	−23.5279	−1.18083	−0.590415	+	0.807100i	$0.701036\pi$
$398$	−13.3820	−0.670777
$399$	19.4164	0.972036
$400$	0	0
$401$	−1.52786	−0.0762979	−0.0381489	−	0.999272i	$-0.512146\pi$
$401$	−1.52786	−0.0762979	−0.0381489	+	0.999272i	$0.512146\pi$
$402$	4.61803	0.230327
$403$	34.1246	1.69987
$404$	13.3262	0.663005
$405$	0	0
$406$	20.4721	1.01602
$407$	−4.14590	−0.205505
$408$	1.85410	0.0917917
$409$	−6.56231	−0.324485	−0.162243	−	0.986751i	$-0.551873\pi$
$409$	−6.56231	−0.324485	−0.162243	+	0.986751i	$0.551873\pi$
$410$	0	0
$411$	2.38197	0.117494
$412$	4.00000	0.197066
$413$	−27.8885	−1.37231
$414$	8.09017	0.397610
$415$	0	0
$416$	3.85410	0.188963
$417$	16.7639	0.820933
$418$	21.7082	1.06178
$419$	8.94427	0.436956	0.218478	−	0.975842i	$-0.429891\pi$
$419$	8.94427	0.436956	0.218478	+	0.975842i	$0.429891\pi$
$420$	0	0
$421$	5.52786	0.269412	0.134706	−	0.990886i	$-0.456991\pi$
$421$	5.52786	0.269412	0.134706	+	0.990886i	$0.456991\pi$
$422$	−23.4164	−1.13989
$423$	4.14590	0.201580
$424$	−1.23607	−0.0600288
$425$	0	0
$426$	−8.94427	−0.433351
$427$	43.4164	2.10107
$428$	−14.1803	−0.685433
$429$	−13.9443	−0.673236
$430$	0	0
$431$	−8.29180	−0.399402	−0.199701	−	0.979857i	$-0.563997\pi$
$431$	−8.29180	−0.399402	−0.199701	+	0.979857i	$0.563997\pi$
$432$	−1.00000	−0.0481125
$433$	−22.1803	−1.06592	−0.532960	−	0.846141i	$-0.678920\pi$
$433$	−22.1803	−1.06592	−0.532960	+	0.846141i	$0.678920\pi$
$434$	−28.6525	−1.37536
$435$	0	0
$436$	13.4164	0.642529
$437$	48.5410	2.32203
$438$	12.0000	0.573382
$439$	12.6738	0.604886	0.302443	−	0.953168i	$-0.402198\pi$
$439$	12.6738	0.604886	0.302443	+	0.953168i	$0.402198\pi$
$440$	0	0
$441$	3.47214	0.165340
$442$	−7.14590	−0.339896
$443$	−1.34752	−0.0640228	−0.0320114	−	0.999488i	$-0.510191\pi$
$443$	−1.34752	−0.0640228	−0.0320114	+	0.999488i	$0.510191\pi$
$444$	1.14590	0.0543819
$445$	0	0
$446$	8.29180	0.392628
$447$	11.5279	0.545249
$448$	−3.23607	−0.152890
$449$	−14.9443	−0.705264	−0.352632	−	0.935762i	$-0.614713\pi$
$449$	−14.9443	−0.705264	−0.352632	+	0.935762i	$0.614713\pi$
$450$	0	0
$451$	4.47214	0.210585
$452$	3.32624	0.156453
$453$	11.1459	0.523680
$454$	7.52786	0.353300
$455$	0	0
$456$	−6.00000	−0.280976
$457$	5.05573	0.236497	0.118248	−	0.992984i	$-0.462272\pi$
$457$	5.05573	0.236497	0.118248	+	0.992984i	$0.462272\pi$
$458$	11.7082	0.547088
$459$	1.85410	0.0865421
$460$	0	0
$461$	30.9787	1.44282	0.721411	−	0.692507i	$-0.243494\pi$
$461$	30.9787	1.44282	0.721411	+	0.692507i	$0.243494\pi$
$462$	11.7082	0.544715
$463$	15.7082	0.730022	0.365011	−	0.931003i	$-0.381065\pi$
$463$	15.7082	0.730022	0.365011	+	0.931003i	$0.381065\pi$
$464$	−6.32624	−0.293688
$465$	0	0
$466$	8.32624	0.385706
$467$	−15.7082	−0.726889	−0.363444	−	0.931616i	$-0.618399\pi$
$467$	−15.7082	−0.726889	−0.363444	+	0.931616i	$0.618399\pi$
$468$	3.85410	0.178156
$469$	14.9443	0.690062
$470$	0	0
$471$	−20.5623	−0.947461
$472$	8.61803	0.396677
$473$	−24.7984	−1.14023
$474$	7.85410	0.360751
$475$	0	0
$476$	6.00000	0.275010
$477$	−1.23607	−0.0565957
$478$	4.65248	0.212799
$479$	−24.6525	−1.12640	−0.563200	−	0.826320i	$-0.690430\pi$
$479$	−24.6525	−1.12640	−0.563200	+	0.826320i	$0.690430\pi$
$480$	0	0
$481$	−4.41641	−0.201371
$482$	−11.0902	−0.505143
$483$	26.1803	1.19125
$484$	2.09017	0.0950077
$485$	0	0
$486$	−1.00000	−0.0453609
$487$	−31.5967	−1.43179	−0.715893	−	0.698210i	$-0.753980\pi$
$487$	−31.5967	−1.43179	−0.715893	+	0.698210i	$0.753980\pi$
$488$	−13.4164	−0.607332
$489$	−13.2705	−0.600113
$490$	0	0
$491$	0.381966	0.0172379	0.00861894	−	0.999963i	$-0.497256\pi$
$491$	0.381966	0.0172379	0.00861894	+	0.999963i	$0.497256\pi$
$492$	−1.23607	−0.0557262
$493$	11.7295	0.528270
$494$	23.1246	1.04043
$495$	0	0
$496$	8.85410	0.397561
$497$	−28.9443	−1.29833
$498$	−14.1803	−0.635436
$499$	8.76393	0.392327	0.196164	−	0.980571i	$-0.437152\pi$
$499$	8.76393	0.392327	0.196164	+	0.980571i	$0.437152\pi$
$500$	0	0
$501$	−11.9098	−0.532092
$502$	19.0902	0.852036
$503$	1.52786	0.0681241	0.0340620	−	0.999420i	$-0.489156\pi$
$503$	1.52786	0.0681241	0.0340620	+	0.999420i	$0.489156\pi$
$504$	−3.23607	−0.144146
$505$	0	0
$506$	29.2705	1.30123
$507$	−1.85410	−0.0823436
$508$	−13.4164	−0.595257
$509$	−14.9443	−0.662393	−0.331197	−	0.943562i	$-0.607452\pi$
$509$	−14.9443	−0.662393	−0.331197	+	0.943562i	$0.607452\pi$
$510$	0	0
$511$	38.8328	1.71786
$512$	1.00000	0.0441942
$513$	−6.00000	−0.264906
$514$	14.5066	0.639858
$515$	0	0
$516$	6.85410	0.301735
$517$	15.0000	0.659699
$518$	3.70820	0.162929
$519$	−4.76393	−0.209113
$520$	0	0
$521$	14.1803	0.621252	0.310626	−	0.950532i	$-0.399461\pi$
$521$	14.1803	0.621252	0.310626	+	0.950532i	$0.399461\pi$
$522$	−6.32624	−0.276892
$523$	−23.0902	−1.00966	−0.504831	−	0.863218i	$-0.668445\pi$
$523$	−23.0902	−1.00966	−0.504831	+	0.863218i	$0.668445\pi$
$524$	−17.8885	−0.781465
$525$	0	0
$526$	−30.9787	−1.35074
$527$	−16.4164	−0.715110
$528$	−3.61803	−0.157455
$529$	42.4508	1.84569
$530$	0	0
$531$	8.61803	0.373991
$532$	−19.4164	−0.841808
$533$	4.76393	0.206349
$534$	4.76393	0.206156
$535$	0	0
$536$	−4.61803	−0.199469
$537$	19.4164	0.837880
$538$	20.3820	0.878729
$539$	12.5623	0.541097
$540$	0	0
$541$	−1.70820	−0.0734414	−0.0367207	−	0.999326i	$-0.511691\pi$
$541$	−1.70820	−0.0734414	−0.0367207	+	0.999326i	$0.511691\pi$
$542$	11.5623	0.496644
$543$	19.4164	0.833238
$544$	−1.85410	−0.0794940
$545$	0	0
$546$	12.4721	0.533758
$547$	25.5623	1.09297	0.546483	−	0.837470i	$-0.315966\pi$
$547$	25.5623	1.09297	0.546483	+	0.837470i	$0.315966\pi$
$548$	−2.38197	−0.101753
$549$	−13.4164	−0.572598
$550$	0	0
$551$	−37.9574	−1.61704
$552$	−8.09017	−0.344340
$553$	25.4164	1.08082
$554$	30.3607	1.28990
$555$	0	0
$556$	−16.7639	−0.710949
$557$	34.3607	1.45591	0.727954	−	0.685626i	$-0.240471\pi$
$557$	34.3607	1.45591	0.727954	+	0.685626i	$0.240471\pi$
$558$	8.85410	0.374824
$559$	−26.4164	−1.11730
$560$	0	0
$561$	6.70820	0.283221
$562$	13.5279	0.570639
$563$	−18.6525	−0.786108	−0.393054	−	0.919515i	$-0.628581\pi$
$563$	−18.6525	−0.786108	−0.393054	+	0.919515i	$0.628581\pi$
$564$	−4.14590	−0.174574
$565$	0	0
$566$	9.90983	0.416541
$567$	−3.23607	−0.135902
$568$	8.94427	0.375293
$569$	−30.9443	−1.29725	−0.648626	−	0.761108i	$-0.724656\pi$
$569$	−30.9443	−1.29725	−0.648626	+	0.761108i	$0.724656\pi$
$570$	0	0
$571$	−32.3607	−1.35425	−0.677126	−	0.735867i	$-0.736775\pi$
$571$	−32.3607	−1.35425	−0.677126	+	0.735867i	$0.736775\pi$
$572$	13.9443	0.583039
$573$	−6.00000	−0.250654
$574$	−4.00000	−0.166957
$575$	0	0
$576$	1.00000	0.0416667
$577$	−39.8885	−1.66058	−0.830291	−	0.557330i	$-0.811826\pi$
$577$	−39.8885	−1.66058	−0.830291	+	0.557330i	$0.811826\pi$
$578$	−13.5623	−0.564118
$579$	23.1246	0.961026
$580$	0	0
$581$	−45.8885	−1.90378
$582$	−4.18034	−0.173281
$583$	−4.47214	−0.185217
$584$	−12.0000	−0.496564
$585$	0	0
$586$	−33.5967	−1.38787
$587$	12.6525	0.522224	0.261112	−	0.965309i	$-0.415911\pi$
$587$	12.6525	0.522224	0.261112	+	0.965309i	$0.415911\pi$
$588$	−3.47214	−0.143188
$589$	53.1246	2.18896
$590$	0	0
$591$	−10.4721	−0.430766
$592$	−1.14590	−0.0470961
$593$	−10.2016	−0.418931	−0.209465	−	0.977816i	$-0.567172\pi$
$593$	−10.2016	−0.418931	−0.209465	+	0.977816i	$0.567172\pi$
$594$	−3.61803	−0.148450
$595$	0	0
$596$	−11.5279	−0.472200
$597$	13.3820	0.547687
$598$	31.1803	1.27506
$599$	3.88854	0.158882	0.0794408	−	0.996840i	$-0.474687\pi$
$599$	3.88854	0.158882	0.0794408	+	0.996840i	$0.474687\pi$
$600$	0	0
$601$	−19.6869	−0.803046	−0.401523	−	0.915849i	$-0.631519\pi$
$601$	−19.6869	−0.803046	−0.401523	+	0.915849i	$0.631519\pi$
$602$	22.1803	0.904003
$603$	−4.61803	−0.188061
$604$	−11.1459	−0.453520
$605$	0	0
$606$	−13.3262	−0.541341
$607$	20.5836	0.835462	0.417731	−	0.908571i	$-0.362825\pi$
$607$	20.5836	0.835462	0.417731	+	0.908571i	$0.362825\pi$
$608$	6.00000	0.243332
$609$	−20.4721	−0.829573
$610$	0	0
$611$	15.9787	0.646430
$612$	−1.85410	−0.0749476
$613$	33.7771	1.36424	0.682122	−	0.731239i	$-0.261057\pi$
$613$	33.7771	1.36424	0.682122	+	0.731239i	$0.261057\pi$
$614$	21.9098	0.884209
$615$	0	0
$616$	−11.7082	−0.471737
$617$	−31.3050	−1.26029	−0.630145	−	0.776478i	$-0.717005\pi$
$617$	−31.3050	−1.26029	−0.630145	+	0.776478i	$0.717005\pi$
$618$	−4.00000	−0.160904
$619$	−34.2918	−1.37830	−0.689152	−	0.724617i	$-0.742017\pi$
$619$	−34.2918	−1.37830	−0.689152	+	0.724617i	$0.742017\pi$
$620$	0	0
$621$	−8.09017	−0.324647
$622$	4.47214	0.179316
$623$	15.4164	0.617645
$624$	−3.85410	−0.154288
$625$	0	0
$626$	−13.0557	−0.521812
$627$	−21.7082	−0.866942
$628$	20.5623	0.820525
$629$	2.12461	0.0847138
$630$	0	0
$631$	14.0344	0.558702	0.279351	−	0.960189i	$-0.409881\pi$
$631$	14.0344	0.558702	0.279351	+	0.960189i	$0.409881\pi$
$632$	−7.85410	−0.312419
$633$	23.4164	0.930719
$634$	3.70820	0.147272
$635$	0	0
$636$	1.23607	0.0490133
$637$	13.3820	0.530213
$638$	−22.8885	−0.906166
$639$	8.94427	0.353830
$640$	0	0
$641$	0.652476	0.0257712	0.0128856	−	0.999917i	$-0.495898\pi$
$641$	0.652476	0.0257712	0.0128856	+	0.999917i	$0.495898\pi$
$642$	14.1803	0.559653
$643$	11.4377	0.451059	0.225529	−	0.974236i	$-0.427589\pi$
$643$	11.4377	0.451059	0.225529	+	0.974236i	$0.427589\pi$
$644$	−26.1803	−1.03165
$645$	0	0
$646$	−11.1246	−0.437692
$647$	−10.3820	−0.408157	−0.204079	−	0.978955i	$-0.565420\pi$
$647$	−10.3820	−0.408157	−0.204079	+	0.978955i	$0.565420\pi$
$648$	1.00000	0.0392837
$649$	31.1803	1.22394
$650$	0	0
$651$	28.6525	1.12298
$652$	13.2705	0.519713
$653$	−25.8885	−1.01310	−0.506549	−	0.862211i	$-0.669079\pi$
$653$	−25.8885	−1.01310	−0.506549	+	0.862211i	$0.669079\pi$
$654$	−13.4164	−0.524623
$655$	0	0
$656$	1.23607	0.0482603
$657$	−12.0000	−0.468165
$658$	−13.4164	−0.523026
$659$	48.9787	1.90794	0.953970	−	0.299902i	$-0.0969541\pi$
$659$	48.9787	1.90794	0.953970	+	0.299902i	$0.0969541\pi$
$660$	0	0
$661$	−7.70820	−0.299814	−0.149907	−	0.988700i	$-0.547897\pi$
$661$	−7.70820	−0.299814	−0.149907	+	0.988700i	$0.547897\pi$
$662$	5.41641	0.210515
$663$	7.14590	0.277524
$664$	14.1803	0.550304
$665$	0	0
$666$	−1.14590	−0.0444026
$667$	−51.1803	−1.98171
$668$	11.9098	0.460805
$669$	−8.29180	−0.320579
$670$	0	0
$671$	−48.5410	−1.87391
$672$	3.23607	0.124834
$673$	15.3050	0.589963	0.294981	−	0.955503i	$-0.404687\pi$
$673$	15.3050	0.589963	0.294981	+	0.955503i	$0.404687\pi$
$674$	−4.94427	−0.190446
$675$	0	0
$676$	1.85410	0.0713116
$677$	−26.7639	−1.02862	−0.514311	−	0.857604i	$-0.671952\pi$
$677$	−26.7639	−1.02862	−0.514311	+	0.857604i	$0.671952\pi$
$678$	−3.32624	−0.127743
$679$	−13.5279	−0.519152
$680$	0	0
$681$	−7.52786	−0.288468
$682$	32.0344	1.22666
$683$	−15.2361	−0.582992	−0.291496	−	0.956572i	$-0.594153\pi$
$683$	−15.2361	−0.582992	−0.291496	+	0.956572i	$0.594153\pi$
$684$	6.00000	0.229416
$685$	0	0
$686$	11.4164	0.435880
$687$	−11.7082	−0.446696
$688$	−6.85410	−0.261310
$689$	−4.76393	−0.181491
$690$	0	0
$691$	31.2361	1.18828	0.594138	−	0.804363i	$-0.297493\pi$
$691$	31.2361	1.18828	0.594138	+	0.804363i	$0.297493\pi$
$692$	4.76393	0.181098
$693$	−11.7082	−0.444758
$694$	20.3607	0.772881
$695$	0	0
$696$	6.32624	0.239795
$697$	−2.29180	−0.0868080
$698$	0	0
$699$	−8.32624	−0.314927
$700$	0	0
$701$	−39.2148	−1.48112	−0.740561	−	0.671989i	$-0.765440\pi$
$701$	−39.2148	−1.48112	−0.740561	+	0.671989i	$0.765440\pi$
$702$	−3.85410	−0.145464
$703$	−6.87539	−0.259310
$704$	3.61803	0.136360
$705$	0	0
$706$	−25.7984	−0.970935
$707$	−43.1246	−1.62187
$708$	−8.61803	−0.323886
$709$	−47.1246	−1.76980	−0.884901	−	0.465779i	$-0.845774\pi$
$709$	−47.1246	−1.76980	−0.884901	+	0.465779i	$0.845774\pi$
$710$	0	0
$711$	−7.85410	−0.294552
$712$	−4.76393	−0.178536
$713$	71.6312	2.68261
$714$	−6.00000	−0.224544
$715$	0	0
$716$	−19.4164	−0.725625
$717$	−4.65248	−0.173750
$718$	−11.8885	−0.443677
$719$	−2.76393	−0.103077	−0.0515386	−	0.998671i	$-0.516413\pi$
$719$	−2.76393	−0.103077	−0.0515386	+	0.998671i	$0.516413\pi$
$720$	0	0
$721$	−12.9443	−0.482070
$722$	17.0000	0.632674
$723$	11.0902	0.412448
$724$	−19.4164	−0.721605
$725$	0	0
$726$	−2.09017	−0.0775735
$727$	38.6525	1.43354	0.716770	−	0.697309i	$-0.245620\pi$
$727$	38.6525	1.43354	0.716770	+	0.697309i	$0.245620\pi$
$728$	−12.4721	−0.462248
$729$	1.00000	0.0370370
$730$	0	0
$731$	12.7082	0.470030
$732$	13.4164	0.495885
$733$	−25.6869	−0.948768	−0.474384	−	0.880318i	$-0.657329\pi$
$733$	−25.6869	−0.948768	−0.474384	+	0.880318i	$0.657329\pi$
$734$	−23.7082	−0.875086
$735$	0	0
$736$	8.09017	0.298208
$737$	−16.7082	−0.615455
$738$	1.23607	0.0455003
$739$	−22.6525	−0.833285	−0.416642	−	0.909070i	$-0.636793\pi$
$739$	−22.6525	−0.833285	−0.416642	+	0.909070i	$0.636793\pi$
$740$	0	0
$741$	−23.1246	−0.849504
$742$	4.00000	0.146845
$743$	−17.3820	−0.637682	−0.318841	−	0.947808i	$-0.603294\pi$
$743$	−17.3820	−0.637682	−0.318841	+	0.947808i	$0.603294\pi$
$744$	−8.85410	−0.324607
$745$	0	0
$746$	−9.74265	−0.356704
$747$	14.1803	0.518832
$748$	−6.70820	−0.245276
$749$	45.8885	1.67673
$750$	0	0
$751$	−16.5836	−0.605144	−0.302572	−	0.953127i	$-0.597845\pi$
$751$	−16.5836	−0.605144	−0.302572	+	0.953127i	$0.597845\pi$
$752$	4.14590	0.151185
$753$	−19.0902	−0.695684
$754$	−24.3820	−0.887939
$755$	0	0
$756$	3.23607	0.117695
$757$	−48.8328	−1.77486	−0.887429	−	0.460944i	$-0.847511\pi$
$757$	−48.8328	−1.77486	−0.887429	+	0.460944i	$0.847511\pi$
$758$	3.23607	0.117539
$759$	−29.2705	−1.06245
$760$	0	0
$761$	−1.34752	−0.0488477	−0.0244239	−	0.999702i	$-0.507775\pi$
$761$	−1.34752	−0.0488477	−0.0244239	+	0.999702i	$0.507775\pi$
$762$	13.4164	0.486025
$763$	−43.4164	−1.57178
$764$	6.00000	0.217072
$765$	0	0
$766$	17.8885	0.646339
$767$	33.2148	1.19932
$768$	−1.00000	−0.0360844
$769$	41.9230	1.51178	0.755891	−	0.654698i	$-0.227204\pi$
$769$	41.9230	1.51178	0.755891	+	0.654698i	$0.227204\pi$
$770$	0	0
$771$	−14.5066	−0.522442
$772$	−23.1246	−0.832273
$773$	2.47214	0.0889166	0.0444583	−	0.999011i	$-0.485844\pi$
$773$	2.47214	0.0889166	0.0444583	+	0.999011i	$0.485844\pi$
$774$	−6.85410	−0.246366
$775$	0	0
$776$	4.18034	0.150065
$777$	−3.70820	−0.133031
$778$	−15.2705	−0.547474
$779$	7.41641	0.265720
$780$	0	0
$781$	32.3607	1.15796
$782$	−15.0000	−0.536399
$783$	6.32624	0.226081
$784$	3.47214	0.124005
$785$	0	0
$786$	17.8885	0.638063
$787$	−18.4377	−0.657233	−0.328616	−	0.944463i	$-0.606582\pi$
$787$	−18.4377	−0.657233	−0.328616	+	0.944463i	$0.606582\pi$
$788$	10.4721	0.373054
$789$	30.9787	1.10287
$790$	0	0
$791$	−10.7639	−0.382721
$792$	3.61803	0.128561
$793$	−51.7082	−1.83621
$794$	−23.5279	−0.834973
$795$	0	0
$796$	−13.3820	−0.474311
$797$	25.5279	0.904243	0.452122	−	0.891956i	$-0.350667\pi$
$797$	25.5279	0.904243	0.452122	+	0.891956i	$0.350667\pi$
$798$	19.4164	0.687333
$799$	−7.68692	−0.271944
$800$	0	0
$801$	−4.76393	−0.168325
$802$	−1.52786	−0.0539508
$803$	−43.4164	−1.53213
$804$	4.61803	0.162866
$805$	0	0
$806$	34.1246	1.20199
$807$	−20.3820	−0.717479
$808$	13.3262	0.468815
$809$	−38.4721	−1.35261	−0.676304	−	0.736623i	$-0.736419\pi$
$809$	−38.4721	−1.35261	−0.676304	+	0.736623i	$0.736419\pi$
$810$	0	0
$811$	−34.0000	−1.19390	−0.596951	−	0.802278i	$-0.703621\pi$
$811$	−34.0000	−1.19390	−0.596951	+	0.802278i	$0.703621\pi$
$812$	20.4721	0.718431
$813$	−11.5623	−0.405508
$814$	−4.14590	−0.145314
$815$	0	0
$816$	1.85410	0.0649066
$817$	−41.1246	−1.43877
$818$	−6.56231	−0.229446
$819$	−12.4721	−0.435812
$820$	0	0
$821$	−15.2148	−0.531000	−0.265500	−	0.964111i	$-0.585537\pi$
$821$	−15.2148	−0.531000	−0.265500	+	0.964111i	$0.585537\pi$
$822$	2.38197	0.0830806
$823$	−25.1246	−0.875789	−0.437894	−	0.899026i	$-0.644276\pi$
$823$	−25.1246	−0.875789	−0.437894	+	0.899026i	$0.644276\pi$
$824$	4.00000	0.139347
$825$	0	0
$826$	−27.8885	−0.970367
$827$	18.0000	0.625921	0.312961	−	0.949766i	$-0.398679\pi$
$827$	18.0000	0.625921	0.312961	+	0.949766i	$0.398679\pi$
$828$	8.09017	0.281153
$829$	11.8197	0.410514	0.205257	−	0.978708i	$-0.434197\pi$
$829$	11.8197	0.410514	0.205257	+	0.978708i	$0.434197\pi$
$830$	0	0
$831$	−30.3607	−1.05320
$832$	3.85410	0.133617
$833$	−6.43769	−0.223053
$834$	16.7639	0.580487
$835$	0	0
$836$	21.7082	0.750794
$837$	−8.85410	−0.306043
$838$	8.94427	0.308975
$839$	29.1246	1.00549	0.502747	−	0.864434i	$-0.332323\pi$
$839$	29.1246	1.00549	0.502747	+	0.864434i	$0.332323\pi$
$840$	0	0
$841$	11.0213	0.380044
$842$	5.52786	0.190503
$843$	−13.5279	−0.465924
$844$	−23.4164	−0.806026
$845$	0	0
$846$	4.14590	0.142539
$847$	−6.76393	−0.232411
$848$	−1.23607	−0.0424467
$849$	−9.90983	−0.340104
$850$	0	0
$851$	−9.27051	−0.317789
$852$	−8.94427	−0.306426
$853$	17.9098	0.613221	0.306610	−	0.951835i	$-0.400805\pi$
$853$	17.9098	0.613221	0.306610	+	0.951835i	$0.400805\pi$
$854$	43.4164	1.48568
$855$	0	0
$856$	−14.1803	−0.484674
$857$	3.32624	0.113622	0.0568111	−	0.998385i	$-0.481907\pi$
$857$	3.32624	0.113622	0.0568111	+	0.998385i	$0.481907\pi$
$858$	−13.9443	−0.476050
$859$	−2.29180	−0.0781951	−0.0390975	−	0.999235i	$-0.512448\pi$
$859$	−2.29180	−0.0781951	−0.0390975	+	0.999235i	$0.512448\pi$
$860$	0	0
$861$	4.00000	0.136320
$862$	−8.29180	−0.282420
$863$	−11.5623	−0.393585	−0.196793	−	0.980445i	$-0.563053\pi$
$863$	−11.5623	−0.393585	−0.196793	+	0.980445i	$0.563053\pi$
$864$	−1.00000	−0.0340207
$865$	0	0
$866$	−22.1803	−0.753719
$867$	13.5623	0.460600
$868$	−28.6525	−0.972528
$869$	−28.4164	−0.963961
$870$	0	0
$871$	−17.7984	−0.603075
$872$	13.4164	0.454337
$873$	4.18034	0.141483
$874$	48.5410	1.64192
$875$	0	0
$876$	12.0000	0.405442
$877$	47.3951	1.60042	0.800210	−	0.599720i	$-0.204721\pi$
$877$	47.3951	1.60042	0.800210	+	0.599720i	$0.204721\pi$
$878$	12.6738	0.427719
$879$	33.5967	1.13319
$880$	0	0
$881$	−22.9443	−0.773012	−0.386506	−	0.922287i	$-0.626318\pi$
$881$	−22.9443	−0.773012	−0.386506	+	0.922287i	$0.626318\pi$
$882$	3.47214	0.116913
$883$	−0.0212862	−0.000716339 0	−0.000358169	−	1.00000i	$-0.500114\pi$
$883$	−0.0212862	−0.000716339 0	−0.000358169		1.00000i	$0.500114\pi$
$884$	−7.14590	−0.240343
$885$	0	0
$886$	−1.34752	−0.0452710
$887$	−45.5279	−1.52868	−0.764338	−	0.644816i	$-0.776934\pi$
$887$	−45.5279	−1.52868	−0.764338	+	0.644816i	$0.776934\pi$
$888$	1.14590	0.0384538
$889$	43.4164	1.45614
$890$	0	0
$891$	3.61803	0.121209
$892$	8.29180	0.277630
$893$	24.8754	0.832423
$894$	11.5279	0.385549
$895$	0	0
$896$	−3.23607	−0.108109
$897$	−31.1803	−1.04108
$898$	−14.9443	−0.498697
$899$	−56.0132	−1.86814
$900$	0	0
$901$	2.29180	0.0763508
$902$	4.47214	0.148906
$903$	−22.1803	−0.738115
$904$	3.32624	0.110629
$905$	0	0
$906$	11.1459	0.370298
$907$	−29.8541	−0.991289	−0.495645	−	0.868525i	$-0.665068\pi$
$907$	−29.8541	−0.991289	−0.495645	+	0.868525i	$0.665068\pi$
$908$	7.52786	0.249821
$909$	13.3262	0.442003
$910$	0	0
$911$	46.4721	1.53969	0.769845	−	0.638231i	$-0.220333\pi$
$911$	46.4721	1.53969	0.769845	+	0.638231i	$0.220333\pi$
$912$	−6.00000	−0.198680
$913$	51.3050	1.69795
$914$	5.05573	0.167229
$915$	0	0
$916$	11.7082	0.386850
$917$	57.8885	1.91165
$918$	1.85410	0.0611945
$919$	−13.8885	−0.458141	−0.229070	−	0.973410i	$-0.573569\pi$
$919$	−13.8885	−0.458141	−0.229070	+	0.973410i	$0.573569\pi$
$920$	0	0
$921$	−21.9098	−0.721953
$922$	30.9787	1.02023
$923$	34.4721	1.13466
$924$	11.7082	0.385172
$925$	0	0
$926$	15.7082	0.516204
$927$	4.00000	0.131377
$928$	−6.32624	−0.207669
$929$	42.5410	1.39573	0.697863	−	0.716231i	$-0.254135\pi$
$929$	42.5410	1.39573	0.697863	+	0.716231i	$0.254135\pi$
$930$	0	0
$931$	20.8328	0.682768
$932$	8.32624	0.272735
$933$	−4.47214	−0.146411
$934$	−15.7082	−0.513988
$935$	0	0
$936$	3.85410	0.125975
$937$	0.583592	0.0190651	0.00953256	−	0.999955i	$-0.496966\pi$
$937$	0.583592	0.0190651	0.00953256	+	0.999955i	$0.496966\pi$
$938$	14.9443	0.487948
$939$	13.0557	0.426058
$940$	0	0
$941$	33.4508	1.09047	0.545233	−	0.838284i	$-0.316441\pi$
$941$	33.4508	1.09047	0.545233	+	0.838284i	$0.316441\pi$
$942$	−20.5623	−0.669956
$943$	10.0000	0.325645
$944$	8.61803	0.280493
$945$	0	0
$946$	−24.7984	−0.806265
$947$	−7.30495	−0.237379	−0.118690	−	0.992931i	$-0.537869\pi$
$947$	−7.30495	−0.237379	−0.118690	+	0.992931i	$0.537869\pi$
$948$	7.85410	0.255089
$949$	−46.2492	−1.50131
$950$	0	0
$951$	−3.70820	−0.120247
$952$	6.00000	0.194461
$953$	46.3607	1.50177	0.750885	−	0.660433i	$-0.229627\pi$
$953$	46.3607	1.50177	0.750885	+	0.660433i	$0.229627\pi$
$954$	−1.23607	−0.0400192
$955$	0	0
$956$	4.65248	0.150472
$957$	22.8885	0.739882
$958$	−24.6525	−0.796485
$959$	7.70820	0.248911
$960$	0	0
$961$	47.3951	1.52887
$962$	−4.41641	−0.142391
$963$	−14.1803	−0.456955
$964$	−11.0902	−0.357190
$965$	0	0
$966$	26.1803	0.842339
$967$	37.0132	1.19026	0.595131	−	0.803628i	$-0.297100\pi$
$967$	37.0132	1.19026	0.595131	+	0.803628i	$0.297100\pi$
$968$	2.09017	0.0671806
$969$	11.1246	0.357374
$970$	0	0
$971$	40.9098	1.31286	0.656429	−	0.754387i	$-0.272066\pi$
$971$	40.9098	1.31286	0.656429	+	0.754387i	$0.272066\pi$
$972$	−1.00000	−0.0320750
$973$	54.2492	1.73915
$974$	−31.5967	−1.01243
$975$	0	0
$976$	−13.4164	−0.429449
$977$	−55.2837	−1.76868	−0.884341	−	0.466842i	$-0.845392\pi$
$977$	−55.2837	−1.76868	−0.884341	+	0.466842i	$0.845392\pi$
$978$	−13.2705	−0.424344
$979$	−17.2361	−0.550867
$980$	0	0
$981$	13.4164	0.428353
$982$	0.381966	0.0121890
$983$	−21.9787	−0.701012	−0.350506	−	0.936560i	$-0.613990\pi$
$983$	−21.9787	−0.701012	−0.350506	+	0.936560i	$0.613990\pi$
$984$	−1.23607	−0.0394044
$985$	0	0
$986$	11.7295	0.373543
$987$	13.4164	0.427049
$988$	23.1246	0.735692
$989$	−55.4508	−1.76323
$990$	0	0
$991$	51.6869	1.64189	0.820945	−	0.571008i	$-0.193447\pi$
$991$	51.6869	1.64189	0.820945	+	0.571008i	$0.193447\pi$
$992$	8.85410	0.281118
$993$	−5.41641	−0.171885
$994$	−28.9443	−0.918057
$995$	0	0
$996$	−14.1803	−0.449321
$997$	4.72949	0.149784	0.0748922	−	0.997192i	$-0.476139\pi$
$997$	4.72949	0.149784	0.0748922	+	0.997192i	$0.476139\pi$
$998$	8.76393	0.277417
$999$	1.14590	0.0362546

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.a.f.1.1	yes	2
3.2	odd	2		2250.2.a.c.1.1		2
4.3	odd	2		6000.2.a.y.1.2		2
5.2	odd	4		750.2.c.b.499.3		4
5.3	odd	4		750.2.c.b.499.2		4
5.4	even	2		750.2.a.c.1.2	✓	2
15.2	even	4		2250.2.c.b.1999.1		4
15.8	even	4		2250.2.c.b.1999.4		4
15.14	odd	2		2250.2.a.n.1.2		2
20.3	even	4		6000.2.f.a.1249.3		4
20.7	even	4		6000.2.f.a.1249.2		4
20.19	odd	2		6000.2.a.d.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
750.2.a.c.1.2	✓	2	5.4	even	2
750.2.a.f.1.1	yes	2	1.1	even	1	trivial
750.2.c.b.499.2		4	5.3	odd	4
750.2.c.b.499.3		4	5.2	odd	4
2250.2.a.c.1.1		2	3.2	odd	2
2250.2.a.n.1.2		2	15.14	odd	2
2250.2.c.b.1999.1		4	15.2	even	4
2250.2.c.b.1999.4		4	15.8	even	4
6000.2.a.d.1.1		2	20.19	odd	2
6000.2.a.y.1.2		2	4.3	odd	2
6000.2.f.a.1249.2		4	20.7	even	4
6000.2.f.a.1249.3		4	20.3	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -3.23607 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -3.23607 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.61803 q^{11} -1.00000 q^{12} +3.85410 q^{13} -3.23607 q^{14} +1.00000 q^{16} -1.85410 q^{17} +1.00000 q^{18} +6.00000 q^{19} +3.23607 q^{21} +3.61803 q^{22} +8.09017 q^{23} -1.00000 q^{24} +3.85410 q^{26} -1.00000 q^{27} -3.23607 q^{28} -6.32624 q^{29} +8.85410 q^{31} +1.00000 q^{32} -3.61803 q^{33} -1.85410 q^{34} +1.00000 q^{36} -1.14590 q^{37} +6.00000 q^{38} -3.85410 q^{39} +1.23607 q^{41} +3.23607 q^{42} -6.85410 q^{43} +3.61803 q^{44} +8.09017 q^{46} +4.14590 q^{47} -1.00000 q^{48} +3.47214 q^{49} +1.85410 q^{51} +3.85410 q^{52} -1.23607 q^{53} -1.00000 q^{54} -3.23607 q^{56} -6.00000 q^{57} -6.32624 q^{58} +8.61803 q^{59} -13.4164 q^{61} +8.85410 q^{62} -3.23607 q^{63} +1.00000 q^{64} -3.61803 q^{66} -4.61803 q^{67} -1.85410 q^{68} -8.09017 q^{69} +8.94427 q^{71} +1.00000 q^{72} -12.0000 q^{73} -1.14590 q^{74} +6.00000 q^{76} -11.7082 q^{77} -3.85410 q^{78} -7.85410 q^{79} +1.00000 q^{81} +1.23607 q^{82} +14.1803 q^{83} +3.23607 q^{84} -6.85410 q^{86} +6.32624 q^{87} +3.61803 q^{88} -4.76393 q^{89} -12.4721 q^{91} +8.09017 q^{92} -8.85410 q^{93} +4.14590 q^{94} -1.00000 q^{96} +4.18034 q^{97} +3.47214 q^{98} +3.61803 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{6} - 2 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^6 - 2 * q^7 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{6} - 2 q^{7} + 2 q^{8} + 2 q^{9} + 5 q^{11} - 2 q^{12} + q^{13} - 2 q^{14} + 2 q^{16} + 3 q^{17} + 2 q^{18} + 12 q^{19} + 2 q^{21} + 5 q^{22} + 5 q^{23} - 2 q^{24} + q^{26} - 2 q^{27} - 2 q^{28} + 3 q^{29} + 11 q^{31} + 2 q^{32} - 5 q^{33} + 3 q^{34} + 2 q^{36} - 9 q^{37} + 12 q^{38} - q^{39} - 2 q^{41} + 2 q^{42} - 7 q^{43} + 5 q^{44} + 5 q^{46} + 15 q^{47} - 2 q^{48} - 2 q^{49} - 3 q^{51} + q^{52} + 2 q^{53} - 2 q^{54} - 2 q^{56} - 12 q^{57} + 3 q^{58} + 15 q^{59} + 11 q^{62} - 2 q^{63} + 2 q^{64} - 5 q^{66} - 7 q^{67} + 3 q^{68} - 5 q^{69} + 2 q^{72} - 24 q^{73} - 9 q^{74} + 12 q^{76} - 10 q^{77} - q^{78} - 9 q^{79} + 2 q^{81} - 2 q^{82} + 6 q^{83} + 2 q^{84} - 7 q^{86} - 3 q^{87} + 5 q^{88} - 14 q^{89} - 16 q^{91} + 5 q^{92} - 11 q^{93} + 15 q^{94} - 2 q^{96} - 14 q^{97} - 2 q^{98} + 5 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^6 - 2 * q^7 + 2 * q^8 + 2 * q^9 + 5 * q^11 - 2 * q^12 + q^13 - 2 * q^14 + 2 * q^16 + 3 * q^17 + 2 * q^18 + 12 * q^19 + 2 * q^21 + 5 * q^22 + 5 * q^23 - 2 * q^24 + q^26 - 2 * q^27 - 2 * q^28 + 3 * q^29 + 11 * q^31 + 2 * q^32 - 5 * q^33 + 3 * q^34 + 2 * q^36 - 9 * q^37 + 12 * q^38 - q^39 - 2 * q^41 + 2 * q^42 - 7 * q^43 + 5 * q^44 + 5 * q^46 + 15 * q^47 - 2 * q^48 - 2 * q^49 - 3 * q^51 + q^52 + 2 * q^53 - 2 * q^54 - 2 * q^56 - 12 * q^57 + 3 * q^58 + 15 * q^59 + 11 * q^62 - 2 * q^63 + 2 * q^64 - 5 * q^66 - 7 * q^67 + 3 * q^68 - 5 * q^69 + 2 * q^72 - 24 * q^73 - 9 * q^74 + 12 * q^76 - 10 * q^77 - q^78 - 9 * q^79 + 2 * q^81 - 2 * q^82 + 6 * q^83 + 2 * q^84 - 7 * q^86 - 3 * q^87 + 5 * q^88 - 14 * q^89 - 16 * q^91 + 5 * q^92 - 11 * q^93 + 15 * q^94 - 2 * q^96 - 14 * q^97 - 2 * q^98 + 5 * q^99

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