LMFDB - Embedded newform 4025.2.a.x.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4025,2,Mod(1,4025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4025, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4025 = 5^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4025.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:	$32.1397868136$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} - 14 x^{10} + 26 x^{9} + 71 x^{8} - 120 x^{7} - 162 x^{6} + 244 x^{5} + 170 x^{4} + \cdots + 17 $ x^12 - 2x^11 - 14x^10 + 26x^9 + 71x^8 - 120x^7 - 162x^6 + 244x^5 + 170x^4 - 210x^3 - 81x^2 + 58*x + 17
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 805)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.31562$ of defining polynomial
Character	$\chi$	$=$	4025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.31562 q^{2} -2.16083 q^{3} -0.269134 q^{4} +2.84283 q^{6} +1.00000 q^{7} +2.98533 q^{8} +1.66917 q^{9} +O(q^{10})$	\(q-1.31562 q^{2} -2.16083 q^{3} -0.269134 q^{4} +2.84283 q^{6} +1.00000 q^{7} +2.98533 q^{8} +1.66917 q^{9} +2.63904 q^{11} +0.581551 q^{12} +6.78772 q^{13} -1.31562 q^{14} -3.38930 q^{16} -3.67083 q^{17} -2.19600 q^{18} -3.70794 q^{19} -2.16083 q^{21} -3.47198 q^{22} -1.00000 q^{23} -6.45077 q^{24} -8.93009 q^{26} +2.87570 q^{27} -0.269134 q^{28} -2.75368 q^{29} -8.90550 q^{31} -1.51161 q^{32} -5.70250 q^{33} +4.82943 q^{34} -0.449229 q^{36} +8.36214 q^{37} +4.87825 q^{38} -14.6671 q^{39} -4.73744 q^{41} +2.84283 q^{42} -11.2674 q^{43} -0.710254 q^{44} +1.31562 q^{46} +8.82064 q^{47} +7.32369 q^{48} +1.00000 q^{49} +7.93203 q^{51} -1.82680 q^{52} +0.435340 q^{53} -3.78333 q^{54} +2.98533 q^{56} +8.01220 q^{57} +3.62281 q^{58} +1.16132 q^{59} -3.72077 q^{61} +11.7163 q^{62} +1.66917 q^{63} +8.76731 q^{64} +7.50235 q^{66} -14.4255 q^{67} +0.987944 q^{68} +2.16083 q^{69} +0.347878 q^{71} +4.98301 q^{72} +10.4436 q^{73} -11.0014 q^{74} +0.997930 q^{76} +2.63904 q^{77} +19.2964 q^{78} +4.15078 q^{79} -11.2214 q^{81} +6.23269 q^{82} -6.34437 q^{83} +0.581551 q^{84} +14.8237 q^{86} +5.95022 q^{87} +7.87839 q^{88} +9.99263 q^{89} +6.78772 q^{91} +0.269134 q^{92} +19.2432 q^{93} -11.6046 q^{94} +3.26632 q^{96} +1.79036 q^{97} -1.31562 q^{98} +4.40500 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} + 8 q^{4} - 6 q^{6} + 12 q^{7} - 6 q^{8} + 8 q^{9}+O(q^{10}) $ 12 * q - 2 * q^2 + 8 * q^4 - 6 * q^6 + 12 * q^7 - 6 * q^8 + 8 * q^9	$ 12 q - 2 q^{2} + 8 q^{4} - 6 q^{6} + 12 q^{7} - 6 q^{8} + 8 q^{9} - 8 q^{11} + 12 q^{12} - 2 q^{13} - 2 q^{14} - 4 q^{16} + 8 q^{17} - 20 q^{18} - 26 q^{19} - 4 q^{22} - 12 q^{23} - 12 q^{24} - 22 q^{26} - 12 q^{27} + 8 q^{28} - 12 q^{29} - 50 q^{31} - 14 q^{32} - 4 q^{33} - 28 q^{34} - 18 q^{36} - 8 q^{37} + 4 q^{38} - 26 q^{39} - 4 q^{41} - 6 q^{42} - 26 q^{43} - 10 q^{44} + 2 q^{46} - 16 q^{47} + 40 q^{48} + 12 q^{49} - 32 q^{51} - 10 q^{52} + 18 q^{53} - 10 q^{54} - 6 q^{56} + 10 q^{57} + 18 q^{58} - 18 q^{59} + 8 q^{61} + 54 q^{62} + 8 q^{63} + 12 q^{64} - 2 q^{66} - 38 q^{67} + 36 q^{68} - 24 q^{71} - 18 q^{72} + 14 q^{73} + 36 q^{74} - 56 q^{76} - 8 q^{77} + 26 q^{78} - 44 q^{79} - 16 q^{81} + 44 q^{82} + 14 q^{83} + 12 q^{84} - 32 q^{86} - 16 q^{87} - 32 q^{88} - 10 q^{89} - 2 q^{91} - 8 q^{92} - 26 q^{93} + 18 q^{94} - 38 q^{96} + 4 q^{97} - 2 q^{98} - 56 q^{99}+O(q^{100}) $ 12 * q - 2 * q^2 + 8 * q^4 - 6 * q^6 + 12 * q^7 - 6 * q^8 + 8 * q^9 - 8 * q^11 + 12 * q^12 - 2 * q^13 - 2 * q^14 - 4 * q^16 + 8 * q^17 - 20 * q^18 - 26 * q^19 - 4 * q^22 - 12 * q^23 - 12 * q^24 - 22 * q^26 - 12 * q^27 + 8 * q^28 - 12 * q^29 - 50 * q^31 - 14 * q^32 - 4 * q^33 - 28 * q^34 - 18 * q^36 - 8 * q^37 + 4 * q^38 - 26 * q^39 - 4 * q^41 - 6 * q^42 - 26 * q^43 - 10 * q^44 + 2 * q^46 - 16 * q^47 + 40 * q^48 + 12 * q^49 - 32 * q^51 - 10 * q^52 + 18 * q^53 - 10 * q^54 - 6 * q^56 + 10 * q^57 + 18 * q^58 - 18 * q^59 + 8 * q^61 + 54 * q^62 + 8 * q^63 + 12 * q^64 - 2 * q^66 - 38 * q^67 + 36 * q^68 - 24 * q^71 - 18 * q^72 + 14 * q^73 + 36 * q^74 - 56 * q^76 - 8 * q^77 + 26 * q^78 - 44 * q^79 - 16 * q^81 + 44 * q^82 + 14 * q^83 + 12 * q^84 - 32 * q^86 - 16 * q^87 - 32 * q^88 - 10 * q^89 - 2 * q^91 - 8 * q^92 - 26 * q^93 + 18 * q^94 - 38 * q^96 + 4 * q^97 - 2 * q^98 - 56 * 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 $

$2$	−1.31562	−0.930287	−0.465143	−	0.885235i	$-0.653997\pi$
$2$	−1.31562	−0.930287	−0.465143	+	0.885235i	$0.653997\pi$
$3$	−2.16083	−1.24755	−0.623777	−	0.781603i	$-0.714403\pi$
$3$	−2.16083	−1.24755	−0.623777	+	0.781603i	$0.714403\pi$
$4$	−0.269134	−0.134567
$5$	0	0
$5$	0	0
$6$	2.84283	1.16058
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	2.98533	1.05547
$9$	1.66917	0.556389
$10$	0	0
$11$	2.63904	0.795700	0.397850	−	0.917450i	$-0.369756\pi$
$11$	2.63904	0.795700	0.397850	+	0.917450i	$0.369756\pi$
$12$	0.581551	0.167879
$13$	6.78772	1.88257	0.941287	−	0.337606i	$-0.109617\pi$
$13$	6.78772	1.88257	0.941287	+	0.337606i	$0.109617\pi$
$14$	−1.31562	−0.351615
$15$	0	0
$16$	−3.38930	−0.847325
$17$	−3.67083	−0.890307	−0.445154	−	0.895454i	$-0.646851\pi$
$17$	−3.67083	−0.890307	−0.445154	+	0.895454i	$0.646851\pi$
$18$	−2.19600	−0.517602
$19$	−3.70794	−0.850659	−0.425329	−	0.905039i	$-0.639842\pi$
$19$	−3.70794	−0.850659	−0.425329	+	0.905039i	$0.639842\pi$
$20$	0	0
$21$	−2.16083	−0.471531
$22$	−3.47198	−0.740229
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−6.45077	−1.31676
$25$	0	0
$26$	−8.93009	−1.75133
$27$	2.87570	0.553428
$28$	−0.269134	−0.0508615
$29$	−2.75368	−0.511345	−0.255673	−	0.966763i	$-0.582297\pi$
$29$	−2.75368	−0.511345	−0.255673	+	0.966763i	$0.582297\pi$
$30$	0	0
$31$	−8.90550	−1.59947	−0.799737	−	0.600350i	$-0.795028\pi$
$31$	−8.90550	−1.59947	−0.799737	+	0.600350i	$0.795028\pi$
$32$	−1.51161	−0.267217
$33$	−5.70250	−0.992678
$34$	4.82943	0.828241
$35$	0	0
$36$	−0.449229	−0.0748715
$37$	8.36214	1.37473	0.687363	−	0.726314i	$-0.258768\pi$
$37$	8.36214	1.37473	0.687363	+	0.726314i	$0.258768\pi$
$38$	4.87825	0.791356
$39$	−14.6671	−2.34861
$40$	0	0
$41$	−4.73744	−0.739863	−0.369932	−	0.929059i	$-0.620619\pi$
$41$	−4.73744	−0.739863	−0.369932	+	0.929059i	$0.620619\pi$
$42$	2.84283	0.438659
$43$	−11.2674	−1.71826	−0.859132	−	0.511754i	$-0.828996\pi$
$43$	−11.2674	−1.71826	−0.859132	+	0.511754i	$0.828996\pi$
$44$	−0.710254	−0.107075
$45$	0	0
$46$	1.31562	0.193978
$47$	8.82064	1.28662	0.643311	−	0.765605i	$-0.277560\pi$
$47$	8.82064	1.28662	0.643311	+	0.765605i	$0.277560\pi$
$48$	7.32369	1.05708
$49$	1.00000	0.142857
$50$	0	0
$51$	7.93203	1.11071
$52$	−1.82680	−0.253332
$53$	0.435340	0.0597985	0.0298992	−	0.999553i	$-0.490481\pi$
$53$	0.435340	0.0597985	0.0298992	+	0.999553i	$0.490481\pi$
$54$	−3.78333	−0.514847
$55$	0	0
$56$	2.98533	0.398931
$57$	8.01220	1.06124
$58$	3.62281	0.475698
$59$	1.16132	0.151190	0.0755952	−	0.997139i	$-0.475914\pi$
$59$	1.16132	0.151190	0.0755952	+	0.997139i	$0.475914\pi$
$60$	0	0
$61$	−3.72077	−0.476396	−0.238198	−	0.971217i	$-0.576557\pi$
$61$	−3.72077	−0.476396	−0.238198	+	0.971217i	$0.576557\pi$
$62$	11.7163	1.48797
$63$	1.66917	0.210295
$64$	8.76731	1.09591
$65$	0	0
$66$	7.50235	0.923475
$67$	−14.4255	−1.76236	−0.881178	−	0.472785i	$-0.843249\pi$
$67$	−14.4255	−1.76236	−0.881178	+	0.472785i	$0.843249\pi$
$68$	0.987944	0.119806
$69$	2.16083	0.260133
$70$	0	0
$71$	0.347878	0.0412855	0.0206427	−	0.999787i	$-0.493429\pi$
$71$	0.347878	0.0412855	0.0206427	+	0.999787i	$0.493429\pi$
$72$	4.98301	0.587254
$73$	10.4436	1.22233	0.611166	−	0.791502i	$-0.290701\pi$
$73$	10.4436	1.22233	0.611166	+	0.791502i	$0.290701\pi$
$74$	−11.0014	−1.27889
$75$	0	0
$76$	0.997930	0.114470
$77$	2.63904	0.300746
$78$	19.2964	2.18488
$79$	4.15078	0.466999	0.233500	−	0.972357i	$-0.424982\pi$
$79$	4.15078	0.466999	0.233500	+	0.972357i	$0.424982\pi$
$80$	0	0
$81$	−11.2214	−1.24682
$82$	6.23269	0.688285
$83$	−6.34437	−0.696385	−0.348193	−	0.937423i	$-0.613204\pi$
$83$	−6.34437	−0.696385	−0.348193	+	0.937423i	$0.613204\pi$
$84$	0.581551	0.0634524
$85$	0	0
$86$	14.8237	1.59848
$87$	5.95022	0.637931
$88$	7.87839	0.839839
$89$	9.99263	1.05922	0.529608	−	0.848242i	$-0.322339\pi$
$89$	9.99263	1.05922	0.529608	+	0.848242i	$0.322339\pi$
$90$	0	0
$91$	6.78772	0.711546
$92$	0.269134	0.0280591
$93$	19.2432	1.99543
$94$	−11.6046	−1.19693
$95$	0	0
$96$	3.26632	0.333368
$97$	1.79036	0.181783	0.0908917	−	0.995861i	$-0.471028\pi$
$97$	1.79036	0.181783	0.0908917	+	0.995861i	$0.471028\pi$
$98$	−1.31562	−0.132898
$99$	4.40500	0.442719
$100$	0	0
$101$	0.231900	0.0230749	0.0115375	−	0.999933i	$-0.496327\pi$
$101$	0.231900	0.0230749	0.0115375	+	0.999933i	$0.496327\pi$
$102$	−10.4356	−1.03327
$103$	9.12191	0.898808	0.449404	−	0.893329i	$-0.351636\pi$
$103$	9.12191	0.898808	0.449404	+	0.893329i	$0.351636\pi$
$104$	20.2636	1.98701
$105$	0	0
$106$	−0.572743	−0.0556297
$107$	18.2051	1.75995	0.879975	−	0.475021i	$-0.157559\pi$
$107$	18.2051	1.75995	0.879975	+	0.475021i	$0.157559\pi$
$108$	−0.773946	−0.0744730
$109$	−11.9105	−1.14081	−0.570407	−	0.821362i	$-0.693215\pi$
$109$	−11.9105	−1.14081	−0.570407	+	0.821362i	$0.693215\pi$
$110$	0	0
$111$	−18.0691	−1.71504
$112$	−3.38930	−0.320259
$113$	−0.442983	−0.0416723	−0.0208362	−	0.999783i	$-0.506633\pi$
$113$	−0.442983	−0.0416723	−0.0208362	+	0.999783i	$0.506633\pi$
$114$	−10.5410	−0.987259
$115$	0	0
$116$	0.741107	0.0688101
$117$	11.3298	1.04744
$118$	−1.52785	−0.140650
$119$	−3.67083	−0.336505
$120$	0	0
$121$	−4.03547	−0.366861
$122$	4.89513	0.443185
$123$	10.2368	0.923019
$124$	2.39677	0.215236
$125$	0	0
$126$	−2.19600	−0.195635
$127$	−20.9821	−1.86186	−0.930930	−	0.365197i	$-0.881002\pi$
$127$	−20.9821	−1.86186	−0.930930	+	0.365197i	$0.881002\pi$
$128$	−8.51126	−0.752297
$129$	24.3469	2.14363
$130$	0	0
$131$	−16.7588	−1.46422	−0.732112	−	0.681184i	$-0.761465\pi$
$131$	−16.7588	−1.46422	−0.732112	+	0.681184i	$0.761465\pi$
$132$	1.53474	0.133582
$133$	−3.70794	−0.321519
$134$	18.9785	1.63950
$135$	0	0
$136$	−10.9586	−0.939695
$137$	2.44580	0.208959	0.104479	−	0.994527i	$-0.466682\pi$
$137$	2.44580	0.208959	0.104479	+	0.994527i	$0.466682\pi$
$138$	−2.84283	−0.241998
$139$	5.90685	0.501013	0.250506	−	0.968115i	$-0.419403\pi$
$139$	5.90685	0.501013	0.250506	+	0.968115i	$0.419403\pi$
$140$	0	0
$141$	−19.0599	−1.60513
$142$	−0.457676	−0.0384073
$143$	17.9131	1.49797
$144$	−5.65731	−0.471443
$145$	0	0
$146$	−13.7399	−1.13712
$147$	−2.16083	−0.178222
$148$	−2.25053	−0.184993
$149$	−7.25098	−0.594024	−0.297012	−	0.954874i	$-0.595990\pi$
$149$	−7.25098	−0.594024	−0.297012	+	0.954874i	$0.595990\pi$
$150$	0	0
$151$	14.3288	1.16606	0.583032	−	0.812449i	$-0.301866\pi$
$151$	14.3288	1.16606	0.583032	+	0.812449i	$0.301866\pi$
$152$	−11.0694	−0.897847
$153$	−6.12723	−0.495358
$154$	−3.47198	−0.279780
$155$	0	0
$156$	3.94740	0.316045
$157$	−13.3485	−1.06533	−0.532664	−	0.846327i	$-0.678809\pi$
$157$	−13.3485	−1.06533	−0.532664	+	0.846327i	$0.678809\pi$
$158$	−5.46087	−0.434443
$159$	−0.940693	−0.0746018
$160$	0	0
$161$	−1.00000	−0.0788110
$162$	14.7631	1.15990
$163$	−1.78440	−0.139765	−0.0698823	−	0.997555i	$-0.522262\pi$
$163$	−1.78440	−0.139765	−0.0698823	+	0.997555i	$0.522262\pi$
$164$	1.27500	0.0995610
$165$	0	0
$166$	8.34681	0.647838
$167$	10.2165	0.790578	0.395289	−	0.918557i	$-0.370644\pi$
$167$	10.2165	0.790578	0.395289	+	0.918557i	$0.370644\pi$
$168$	−6.45077	−0.497688
$169$	33.0731	2.54409
$170$	0	0
$171$	−6.18917	−0.473297
$172$	3.03244	0.231221
$173$	0.674341	0.0512692	0.0256346	−	0.999671i	$-0.491839\pi$
$173$	0.674341	0.0512692	0.0256346	+	0.999671i	$0.491839\pi$
$174$	−7.82825	−0.593458
$175$	0	0
$176$	−8.94449	−0.674217
$177$	−2.50940	−0.188618
$178$	−13.1465	−0.985375
$179$	−25.1419	−1.87920	−0.939598	−	0.342280i	$-0.888801\pi$
$179$	−25.1419	−1.87920	−0.939598	+	0.342280i	$0.888801\pi$
$180$	0	0
$181$	8.08590	0.601020	0.300510	−	0.953779i	$-0.402843\pi$
$181$	8.08590	0.601020	0.300510	+	0.953779i	$0.402843\pi$
$182$	−8.93009	−0.661942
$183$	8.03993	0.594329
$184$	−2.98533	−0.220081
$185$	0	0
$186$	−25.3169	−1.85632
$187$	−9.68747	−0.708418
$188$	−2.37393	−0.173137
$189$	2.87570	0.209176
$190$	0	0
$191$	−24.3693	−1.76330	−0.881651	−	0.471902i	$-0.843568\pi$
$191$	−24.3693	−1.76330	−0.881651	+	0.471902i	$0.843568\pi$
$192$	−18.9446	−1.36721
$193$	−10.1896	−0.733465	−0.366732	−	0.930326i	$-0.619524\pi$
$193$	−10.1896	−0.733465	−0.366732	+	0.930326i	$0.619524\pi$
$194$	−2.35544	−0.169111
$195$	0	0
$196$	−0.269134	−0.0192238
$197$	8.37443	0.596654	0.298327	−	0.954464i	$-0.403571\pi$
$197$	8.37443	0.596654	0.298327	+	0.954464i	$0.403571\pi$
$198$	−5.79532	−0.411856
$199$	−7.54893	−0.535129	−0.267565	−	0.963540i	$-0.586219\pi$
$199$	−7.54893	−0.535129	−0.267565	+	0.963540i	$0.586219\pi$
$200$	0	0
$201$	31.1710	2.19863
$202$	−0.305093	−0.0214663
$203$	−2.75368	−0.193270
$204$	−2.13478	−0.149464
$205$	0	0
$206$	−12.0010	−0.836149
$207$	−1.66917	−0.116015
$208$	−23.0056	−1.59515
$209$	−9.78539	−0.676869
$210$	0	0
$211$	24.3405	1.67567	0.837835	−	0.545924i	$-0.183821\pi$
$211$	24.3405	1.67567	0.837835	+	0.545924i	$0.183821\pi$
$212$	−0.117165	−0.00804689
$213$	−0.751703	−0.0515058
$214$	−23.9510	−1.63726
$215$	0	0
$216$	8.58489	0.584128
$217$	−8.90550	−0.604545
$218$	15.6697	1.06128
$219$	−22.5668	−1.52492
$220$	0	0
$221$	−24.9166	−1.67607
$222$	23.7722	1.59548
$223$	−2.75082	−0.184208	−0.0921041	−	0.995749i	$-0.529359\pi$
$223$	−2.75082	−0.184208	−0.0921041	+	0.995749i	$0.529359\pi$
$224$	−1.51161	−0.100999
$225$	0	0
$226$	0.582799	0.0387672
$227$	−11.9484	−0.793045	−0.396522	−	0.918025i	$-0.629783\pi$
$227$	−11.9484	−0.793045	−0.396522	+	0.918025i	$0.629783\pi$
$228$	−2.15635	−0.142808
$229$	0.371756	0.0245663	0.0122832	−	0.999925i	$-0.496090\pi$
$229$	0.371756	0.0245663	0.0122832	+	0.999925i	$0.496090\pi$
$230$	0	0
$231$	−5.70250	−0.375197
$232$	−8.22063	−0.539711
$233$	−22.3735	−1.46574	−0.732870	−	0.680369i	$-0.761820\pi$
$233$	−22.3735	−1.46574	−0.732870	+	0.680369i	$0.761820\pi$
$234$	−14.9058	−0.974424
$235$	0	0
$236$	−0.312549	−0.0203452
$237$	−8.96911	−0.582607
$238$	4.82943	0.313046
$239$	16.7231	1.08172	0.540862	−	0.841111i	$-0.318098\pi$
$239$	16.7231	1.08172	0.540862	+	0.841111i	$0.318098\pi$
$240$	0	0
$241$	−17.8844	−1.15203	−0.576017	−	0.817438i	$-0.695394\pi$
$241$	−17.8844	−1.15203	−0.576017	+	0.817438i	$0.695394\pi$
$242$	5.30917	0.341286
$243$	15.6204	1.00205
$244$	1.00138	0.0641070
$245$	0	0
$246$	−13.4677	−0.858672
$247$	−25.1684	−1.60143
$248$	−26.5858	−1.68820
$249$	13.7091	0.868778
$250$	0	0
$251$	11.2555	0.710443	0.355222	−	0.934782i	$-0.384405\pi$
$251$	11.2555	0.710443	0.355222	+	0.934782i	$0.384405\pi$
$252$	−0.449229	−0.0282988
$253$	−2.63904	−0.165915
$254$	27.6046	1.73206
$255$	0	0
$256$	−6.33700	−0.396062
$257$	−2.18094	−0.136043	−0.0680217	−	0.997684i	$-0.521669\pi$
$257$	−2.18094	−0.136043	−0.0680217	+	0.997684i	$0.521669\pi$
$258$	−32.0314	−1.99419
$259$	8.36214	0.519598
$260$	0	0
$261$	−4.59635	−0.284507
$262$	22.0483	1.36215
$263$	19.2362	1.18615	0.593076	−	0.805146i	$-0.297913\pi$
$263$	19.2362	1.18615	0.593076	+	0.805146i	$0.297913\pi$
$264$	−17.0238	−1.04774
$265$	0	0
$266$	4.87825	0.299105
$267$	−21.5923	−1.32143
$268$	3.88239	0.237155
$269$	16.8579	1.02784	0.513922	−	0.857837i	$-0.328192\pi$
$269$	16.8579	1.02784	0.513922	+	0.857837i	$0.328192\pi$
$270$	0	0
$271$	−2.11030	−0.128191	−0.0640957	−	0.997944i	$-0.520416\pi$
$271$	−2.11030	−0.128191	−0.0640957	+	0.997944i	$0.520416\pi$
$272$	12.4415	0.754380
$273$	−14.6671	−0.887692
$274$	−3.21775	−0.194392
$275$	0	0
$276$	−0.581551	−0.0350052
$277$	18.0610	1.08518	0.542590	−	0.839998i	$-0.317444\pi$
$277$	18.0610	1.08518	0.542590	+	0.839998i	$0.317444\pi$
$278$	−7.77120	−0.466085
$279$	−14.8648	−0.889931
$280$	0	0
$281$	6.27404	0.374278	0.187139	−	0.982333i	$-0.440078\pi$
$281$	6.27404	0.374278	0.187139	+	0.982333i	$0.440078\pi$
$282$	25.0756	1.49323
$283$	−14.3849	−0.855096	−0.427548	−	0.903993i	$-0.640622\pi$
$283$	−14.3849	−0.855096	−0.427548	+	0.903993i	$0.640622\pi$
$284$	−0.0936255	−0.00555565
$285$	0	0
$286$	−23.5668	−1.39354
$287$	−4.73744	−0.279642
$288$	−2.52313	−0.148677
$289$	−3.52500	−0.207353
$290$	0	0
$291$	−3.86866	−0.226785
$292$	−2.81073	−0.164485
$293$	15.5922	0.910909	0.455454	−	0.890259i	$-0.349477\pi$
$293$	15.5922	0.910909	0.455454	+	0.890259i	$0.349477\pi$
$294$	2.84283	0.165797
$295$	0	0
$296$	24.9637	1.45099
$297$	7.58907	0.440363
$298$	9.53957	0.552612
$299$	−6.78772	−0.392544
$300$	0	0
$301$	−11.2674	−0.649443
$302$	−18.8514	−1.08477
$303$	−0.501096	−0.0287872
$304$	12.5673	0.720784
$305$	0	0
$306$	8.06114	0.460825
$307$	5.08058	0.289964	0.144982	−	0.989434i	$-0.453688\pi$
$307$	5.08058	0.289964	0.144982	+	0.989434i	$0.453688\pi$
$308$	−0.710254	−0.0404705
$309$	−19.7109	−1.12131
$310$	0	0
$311$	14.9405	0.847197	0.423598	−	0.905850i	$-0.360767\pi$
$311$	14.9405	0.847197	0.423598	+	0.905850i	$0.360767\pi$
$312$	−43.7860	−2.47890
$313$	7.47141	0.422309	0.211155	−	0.977453i	$-0.432278\pi$
$313$	7.47141	0.422309	0.211155	+	0.977453i	$0.432278\pi$
$314$	17.5616	0.991060
$315$	0	0
$316$	−1.11711	−0.0628426
$317$	9.54120	0.535887	0.267943	−	0.963435i	$-0.413656\pi$
$317$	9.54120	0.535887	0.267943	+	0.963435i	$0.413656\pi$
$318$	1.23760	0.0694011
$319$	−7.26706	−0.406878
$320$	0	0
$321$	−39.3380	−2.19563
$322$	1.31562	0.0733169
$323$	13.6112	0.757348
$324$	3.02005	0.167781
$325$	0	0
$326$	2.34759	0.130021
$327$	25.7364	1.42323
$328$	−14.1428	−0.780905
$329$	8.82064	0.486298
$330$	0	0
$331$	−16.8124	−0.924096	−0.462048	−	0.886855i	$-0.652885\pi$
$331$	−16.8124	−0.924096	−0.462048	+	0.886855i	$0.652885\pi$
$332$	1.70748	0.0937103
$333$	13.9578	0.764883
$334$	−13.4411	−0.735464
$335$	0	0
$336$	7.32369	0.399540
$337$	−19.6042	−1.06791	−0.533954	−	0.845513i	$-0.679295\pi$
$337$	−19.6042	−1.06791	−0.533954	+	0.845513i	$0.679295\pi$
$338$	−43.5118	−2.36673
$339$	0.957209	0.0519884
$340$	0	0
$341$	−23.5020	−1.27270
$342$	8.14262	0.440302
$343$	1.00000	0.0539949
$344$	−33.6369	−1.81358
$345$	0	0
$346$	−0.887180	−0.0476951
$347$	−30.7135	−1.64879	−0.824393	−	0.566018i	$-0.808483\pi$
$347$	−30.7135	−1.64879	−0.824393	+	0.566018i	$0.808483\pi$
$348$	−1.60140	−0.0858443
$349$	−22.3643	−1.19713	−0.598566	−	0.801074i	$-0.704263\pi$
$349$	−22.3643	−1.19713	−0.598566	+	0.801074i	$0.704263\pi$
$350$	0	0
$351$	19.5194	1.04187
$352$	−3.98919	−0.212625
$353$	−7.03401	−0.374383	−0.187191	−	0.982323i	$-0.559938\pi$
$353$	−7.03401	−0.374383	−0.187191	+	0.982323i	$0.559938\pi$
$354$	3.30143	0.175469
$355$	0	0
$356$	−2.68935	−0.142535
$357$	7.93203	0.419807
$358$	33.0773	1.74819
$359$	14.9025	0.786524	0.393262	−	0.919426i	$-0.371346\pi$
$359$	14.9025	0.786524	0.393262	+	0.919426i	$0.371346\pi$
$360$	0	0
$361$	−5.25121	−0.276380
$362$	−10.6380	−0.559121
$363$	8.71996	0.457679
$364$	−1.82680	−0.0957505
$365$	0	0
$366$	−10.5775	−0.552896
$367$	−31.7700	−1.65838	−0.829190	−	0.558966i	$-0.811198\pi$
$367$	−31.7700	−1.65838	−0.829190	+	0.558966i	$0.811198\pi$
$368$	3.38930	0.176679
$369$	−7.90758	−0.411652
$370$	0	0
$371$	0.435340	0.0226017
$372$	−5.17900	−0.268519
$373$	28.0416	1.45194	0.725968	−	0.687728i	$-0.241392\pi$
$373$	28.0416	1.45194	0.725968	+	0.687728i	$0.241392\pi$
$374$	12.7451	0.659032
$375$	0	0
$376$	26.3325	1.35799
$377$	−18.6912	−0.962646
$378$	−3.78333	−0.194594
$379$	−6.39099	−0.328283	−0.164142	−	0.986437i	$-0.552485\pi$
$379$	−6.39099	−0.328283	−0.164142	+	0.986437i	$0.552485\pi$
$380$	0	0
$381$	45.3387	2.32277
$382$	32.0609	1.64038
$383$	−28.1787	−1.43986	−0.719931	−	0.694045i	$-0.755827\pi$
$383$	−28.1787	−1.43986	−0.719931	+	0.694045i	$0.755827\pi$
$384$	18.3914	0.938530
$385$	0	0
$386$	13.4057	0.682333
$387$	−18.8072	−0.956024
$388$	−0.481846	−0.0244620
$389$	13.4896	0.683949	0.341974	−	0.939709i	$-0.388904\pi$
$389$	13.4896	0.683949	0.341974	+	0.939709i	$0.388904\pi$
$390$	0	0
$391$	3.67083	0.185642
$392$	2.98533	0.150782
$393$	36.2129	1.82670
$394$	−11.0176	−0.555059
$395$	0	0
$396$	−1.18553	−0.0595753
$397$	−28.7899	−1.44493	−0.722463	−	0.691410i	$-0.756990\pi$
$397$	−28.7899	−1.44493	−0.722463	+	0.691410i	$0.756990\pi$
$398$	9.93155	0.497824
$399$	8.01220	0.401112
$400$	0	0
$401$	−10.0533	−0.502040	−0.251020	−	0.967982i	$-0.580766\pi$
$401$	−10.0533	−0.502040	−0.251020	+	0.967982i	$0.580766\pi$
$402$	−41.0093	−2.04536
$403$	−60.4480	−3.01113
$404$	−0.0624121	−0.00310512
$405$	0	0
$406$	3.62281	0.179797
$407$	22.0680	1.09387
$408$	23.6797	1.17232
$409$	2.27018	0.112253	0.0561266	−	0.998424i	$-0.482125\pi$
$409$	2.27018	0.112253	0.0561266	+	0.998424i	$0.482125\pi$
$410$	0	0
$411$	−5.28495	−0.260687
$412$	−2.45501	−0.120950
$413$	1.16132	0.0571446
$414$	2.19600	0.107927
$415$	0	0
$416$	−10.2604	−0.503056
$417$	−12.7637	−0.625040
$418$	12.8739	0.629682
$419$	−6.86466	−0.335361	−0.167680	−	0.985841i	$-0.553628\pi$
$419$	−6.86466	−0.335361	−0.167680	+	0.985841i	$0.553628\pi$
$420$	0	0
$421$	−3.99851	−0.194876	−0.0974378	−	0.995242i	$-0.531065\pi$
$421$	−3.99851	−0.194876	−0.0974378	+	0.995242i	$0.531065\pi$
$422$	−32.0230	−1.55885
$423$	14.7231	0.715863
$424$	1.29963	0.0631157
$425$	0	0
$426$	0.988958	0.0479152
$427$	−3.72077	−0.180061
$428$	−4.89959	−0.236831
$429$	−38.7070	−1.86879
$430$	0	0
$431$	−19.7551	−0.951570	−0.475785	−	0.879562i	$-0.657836\pi$
$431$	−19.7551	−0.951570	−0.475785	+	0.879562i	$0.657836\pi$
$432$	−9.74660	−0.468933
$433$	20.8948	1.00414	0.502071	−	0.864826i	$-0.332572\pi$
$433$	20.8948	1.00414	0.502071	+	0.864826i	$0.332572\pi$
$434$	11.7163	0.562400
$435$	0	0
$436$	3.20550	0.153516
$437$	3.70794	0.177375
$438$	29.6895	1.41862
$439$	−24.4876	−1.16873	−0.584364	−	0.811492i	$-0.698656\pi$
$439$	−24.4876	−1.16873	−0.584364	+	0.811492i	$0.698656\pi$
$440$	0	0
$441$	1.66917	0.0794842
$442$	32.7808	1.55923
$443$	−34.7057	−1.64892	−0.824459	−	0.565922i	$-0.808520\pi$
$443$	−34.7057	−1.64892	−0.824459	+	0.565922i	$0.808520\pi$
$444$	4.86301	0.230788
$445$	0	0
$446$	3.61904	0.171366
$447$	15.6681	0.741076
$448$	8.76731	0.414216
$449$	−30.8263	−1.45478	−0.727391	−	0.686223i	$-0.759267\pi$
$449$	−30.8263	−1.45478	−0.727391	+	0.686223i	$0.759267\pi$
$450$	0	0
$451$	−12.5023	−0.588709
$452$	0.119222	0.00560771
$453$	−30.9621	−1.45473
$454$	15.7196	0.737759
$455$	0	0
$456$	23.9190	1.12011
$457$	−8.90389	−0.416506	−0.208253	−	0.978075i	$-0.566778\pi$
$457$	−8.90389	−0.416506	−0.208253	+	0.978075i	$0.566778\pi$
$458$	−0.489091	−0.0228537
$459$	−10.5562	−0.492721
$460$	0	0
$461$	−9.05632	−0.421795	−0.210897	−	0.977508i	$-0.567639\pi$
$461$	−9.05632	−0.421795	−0.210897	+	0.977508i	$0.567639\pi$
$462$	7.50235	0.349041
$463$	0.794567	0.0369267	0.0184633	−	0.999830i	$-0.494123\pi$
$463$	0.794567	0.0369267	0.0184633	+	0.999830i	$0.494123\pi$
$464$	9.33304	0.433276
$465$	0	0
$466$	29.4352	1.36356
$467$	19.8666	0.919315	0.459658	−	0.888096i	$-0.347972\pi$
$467$	19.8666	0.919315	0.459658	+	0.888096i	$0.347972\pi$
$468$	−3.04924	−0.140951
$469$	−14.4255	−0.666108
$470$	0	0
$471$	28.8438	1.32905
$472$	3.46691	0.159577
$473$	−29.7351	−1.36722
$474$	11.8000	0.541991
$475$	0	0
$476$	0.987944	0.0452823
$477$	0.726655	0.0332712
$478$	−22.0012	−1.00631
$479$	36.5784	1.67131	0.835655	−	0.549254i	$-0.185088\pi$
$479$	36.5784	1.67131	0.835655	+	0.549254i	$0.185088\pi$
$480$	0	0
$481$	56.7598	2.58803
$482$	23.5291	1.07172
$483$	2.16083	0.0983210
$484$	1.08608	0.0493673
$485$	0	0
$486$	−20.5505	−0.932191
$487$	−24.1588	−1.09474	−0.547369	−	0.836891i	$-0.684371\pi$
$487$	−24.1588	−1.09474	−0.547369	+	0.836891i	$0.684371\pi$
$488$	−11.1077	−0.502822
$489$	3.85577	0.174364
$490$	0	0
$491$	−1.45421	−0.0656275	−0.0328137	−	0.999461i	$-0.510447\pi$
$491$	−1.45421	−0.0656275	−0.0328137	+	0.999461i	$0.510447\pi$
$492$	−2.75506	−0.124208
$493$	10.1083	0.455255
$494$	33.1122	1.48979
$495$	0	0
$496$	30.1834	1.35527
$497$	0.347878	0.0156044
$498$	−18.0360	−0.808212
$499$	−24.5180	−1.09758	−0.548788	−	0.835961i	$-0.684911\pi$
$499$	−24.5180	−1.09758	−0.548788	+	0.835961i	$0.684911\pi$
$500$	0	0
$501$	−22.0761	−0.986289
$502$	−14.8081	−0.660916
$503$	−4.70190	−0.209647	−0.104824	−	0.994491i	$-0.533428\pi$
$503$	−4.70190	−0.209647	−0.104824	+	0.994491i	$0.533428\pi$
$504$	4.98301	0.221961
$505$	0	0
$506$	3.47198	0.154348
$507$	−71.4653	−3.17389
$508$	5.64699	0.250545
$509$	28.5444	1.26521	0.632603	−	0.774476i	$-0.281986\pi$
$509$	28.5444	1.26521	0.632603	+	0.774476i	$0.281986\pi$
$510$	0	0
$511$	10.4436	0.461998
$512$	25.3596	1.12075
$513$	−10.6629	−0.470778
$514$	2.86930	0.126559
$515$	0	0
$516$	−6.55257	−0.288461
$517$	23.2780	1.02377
$518$	−11.0014	−0.483375
$519$	−1.45713	−0.0639611
$520$	0	0
$521$	16.3836	0.717778	0.358889	−	0.933380i	$-0.383156\pi$
$521$	16.3836	0.717778	0.358889	+	0.933380i	$0.383156\pi$
$522$	6.04707	0.264673
$523$	−8.73120	−0.381789	−0.190894	−	0.981611i	$-0.561139\pi$
$523$	−8.73120	−0.381789	−0.190894	+	0.981611i	$0.561139\pi$
$524$	4.51036	0.197036
$525$	0	0
$526$	−25.3076	−1.10346
$527$	32.6906	1.42402
$528$	19.3275	0.841121
$529$	1.00000	0.0434783
$530$	0	0
$531$	1.93843	0.0841208
$532$	0.997930	0.0432658
$533$	−32.1564	−1.39285
$534$	28.4074	1.22931
$535$	0	0
$536$	−43.0648	−1.86012
$537$	54.3273	2.34440
$538$	−22.1786	−0.956189
$539$	2.63904	0.113671
$540$	0	0
$541$	−33.1645	−1.42585	−0.712927	−	0.701238i	$-0.752631\pi$
$541$	−33.1645	−1.42585	−0.712927	+	0.701238i	$0.752631\pi$
$542$	2.77636	0.119255
$543$	−17.4722	−0.749805
$544$	5.54886	0.237905
$545$	0	0
$546$	19.2964	0.825808
$547$	−20.0273	−0.856307	−0.428154	−	0.903706i	$-0.640836\pi$
$547$	−20.0273	−0.856307	−0.428154	+	0.903706i	$0.640836\pi$
$548$	−0.658247	−0.0281189
$549$	−6.21059	−0.265062
$550$	0	0
$551$	10.2105	0.434980
$552$	6.45077	0.274563
$553$	4.15078	0.176509
$554$	−23.7615	−1.00953
$555$	0	0
$556$	−1.58973	−0.0674197
$557$	−12.3335	−0.522588	−0.261294	−	0.965259i	$-0.584149\pi$
$557$	−12.3335	−0.522588	−0.261294	+	0.965259i	$0.584149\pi$
$558$	19.5565	0.827891
$559$	−76.4800	−3.23476
$560$	0	0
$561$	20.9329	0.883789
$562$	−8.25428	−0.348186
$563$	9.79580	0.412844	0.206422	−	0.978463i	$-0.433818\pi$
$563$	9.79580	0.412844	0.206422	+	0.978463i	$0.433818\pi$
$564$	5.12965	0.215997
$565$	0	0
$566$	18.9252	0.795484
$567$	−11.2214	−0.471254
$568$	1.03853	0.0435757
$569$	−23.0187	−0.964996	−0.482498	−	0.875897i	$-0.660270\pi$
$569$	−23.0187	−0.964996	−0.482498	+	0.875897i	$0.660270\pi$
$570$	0	0
$571$	6.65937	0.278686	0.139343	−	0.990244i	$-0.455501\pi$
$571$	6.65937	0.278686	0.139343	+	0.990244i	$0.455501\pi$
$572$	−4.82101	−0.201576
$573$	52.6579	2.19981
$574$	6.23269	0.260147
$575$	0	0
$576$	14.6341	0.609755
$577$	29.6758	1.23542	0.617709	−	0.786407i	$-0.288061\pi$
$577$	29.6758	1.23542	0.617709	+	0.786407i	$0.288061\pi$
$578$	4.63757	0.192897
$579$	22.0180	0.915037
$580$	0	0
$581$	−6.34437	−0.263209
$582$	5.08970	0.210975
$583$	1.14888	0.0475817
$584$	31.1776	1.29014
$585$	0	0
$586$	−20.5135	−0.847406
$587$	17.0649	0.704345	0.352173	−	0.935935i	$-0.385443\pi$
$587$	17.0649	0.704345	0.352173	+	0.935935i	$0.385443\pi$
$588$	0.581551	0.0239828
$589$	33.0210	1.36061
$590$	0	0
$591$	−18.0957	−0.744357
$592$	−28.3418	−1.16484
$593$	7.43780	0.305434	0.152717	−	0.988270i	$-0.451198\pi$
$593$	7.43780	0.305434	0.152717	+	0.988270i	$0.451198\pi$
$594$	−9.98437	−0.409664
$595$	0	0
$596$	1.95148	0.0799359
$597$	16.3119	0.667603
$598$	8.93009	0.365178
$599$	−34.6736	−1.41672	−0.708362	−	0.705849i	$-0.750566\pi$
$599$	−34.6736	−1.41672	−0.708362	+	0.705849i	$0.750566\pi$
$600$	0	0
$601$	−23.7157	−0.967383	−0.483691	−	0.875239i	$-0.660704\pi$
$601$	−23.7157	−0.967383	−0.483691	+	0.875239i	$0.660704\pi$
$602$	14.8237	0.604168
$603$	−24.0786	−0.980556
$604$	−3.85637	−0.156913
$605$	0	0
$606$	0.659253	0.0267803
$607$	33.3784	1.35479	0.677394	−	0.735620i	$-0.263109\pi$
$607$	33.3784	1.35479	0.677394	+	0.735620i	$0.263109\pi$
$608$	5.60495	0.227311
$609$	5.95022	0.241115
$610$	0	0
$611$	59.8720	2.42216
$612$	1.64904	0.0666587
$613$	4.22928	0.170819	0.0854094	−	0.996346i	$-0.472780\pi$
$613$	4.22928	0.170819	0.0854094	+	0.996346i	$0.472780\pi$
$614$	−6.68413	−0.269750
$615$	0	0
$616$	7.87839	0.317429
$617$	37.6911	1.51739	0.758694	−	0.651448i	$-0.225838\pi$
$617$	37.6911	1.51739	0.758694	+	0.651448i	$0.225838\pi$
$618$	25.9321	1.04314
$619$	−18.3528	−0.737661	−0.368831	−	0.929497i	$-0.620242\pi$
$619$	−18.3528	−0.737661	−0.368831	+	0.929497i	$0.620242\pi$
$620$	0	0
$621$	−2.87570	−0.115398
$622$	−19.6560	−0.788136
$623$	9.99263	0.400346
$624$	49.7111	1.99004
$625$	0	0
$626$	−9.82957	−0.392869
$627$	21.1445	0.844431
$628$	3.59254	0.143358
$629$	−30.6960	−1.22393
$630$	0	0
$631$	−1.02169	−0.0406728	−0.0203364	−	0.999793i	$-0.506474\pi$
$631$	−1.02169	−0.0406728	−0.0203364	+	0.999793i	$0.506474\pi$
$632$	12.3914	0.492905
$633$	−52.5956	−2.09049
$634$	−12.5526	−0.498528
$635$	0	0
$636$	0.253172	0.0100389
$637$	6.78772	0.268939
$638$	9.56072	0.378513
$639$	0.580666	0.0229708
$640$	0	0
$641$	16.8284	0.664680	0.332340	−	0.943160i	$-0.392162\pi$
$641$	16.8284	0.664680	0.332340	+	0.943160i	$0.392162\pi$
$642$	51.7540	2.04257
$643$	−35.1604	−1.38659	−0.693295	−	0.720654i	$-0.743842\pi$
$643$	−35.1604	−1.38659	−0.693295	+	0.720654i	$0.743842\pi$
$644$	0.269134	0.0106053
$645$	0	0
$646$	−17.9072	−0.704551
$647$	28.7775	1.13136	0.565681	−	0.824624i	$-0.308614\pi$
$647$	28.7775	1.13136	0.565681	+	0.824624i	$0.308614\pi$
$648$	−33.4995	−1.31598
$649$	3.06476	0.120302
$650$	0	0
$651$	19.2432	0.754202
$652$	0.480241	0.0188077
$653$	−29.5242	−1.15537	−0.577685	−	0.816260i	$-0.696044\pi$
$653$	−29.5242	−1.15537	−0.577685	+	0.816260i	$0.696044\pi$
$654$	−33.8595	−1.32401
$655$	0	0
$656$	16.0566	0.626905
$657$	17.4321	0.680093
$658$	−11.6046	−0.452396
$659$	2.27234	0.0885180	0.0442590	−	0.999020i	$-0.485907\pi$
$659$	2.27234	0.0885180	0.0442590	+	0.999020i	$0.485907\pi$
$660$	0	0
$661$	−0.297754	−0.0115813	−0.00579065	−	0.999983i	$-0.501843\pi$
$661$	−0.297754	−0.0115813	−0.00579065	+	0.999983i	$0.501843\pi$
$662$	22.1189	0.859674
$663$	53.8404	2.09099
$664$	−18.9400	−0.735015
$665$	0	0
$666$	−18.3632	−0.711561
$667$	2.75368	0.106623
$668$	−2.74961	−0.106386
$669$	5.94403	0.229810
$670$	0	0
$671$	−9.81926	−0.379068
$672$	3.26632	0.126001
$673$	−16.5962	−0.639736	−0.319868	−	0.947462i	$-0.603639\pi$
$673$	−16.5962	−0.639736	−0.319868	+	0.947462i	$0.603639\pi$
$674$	25.7917	0.993461
$675$	0	0
$676$	−8.90109	−0.342350
$677$	24.1590	0.928506	0.464253	−	0.885703i	$-0.346323\pi$
$677$	24.1590	0.928506	0.464253	+	0.885703i	$0.346323\pi$
$678$	−1.25933	−0.0483642
$679$	1.79036	0.0687077
$680$	0	0
$681$	25.8185	0.989366
$682$	30.9197	1.18398
$683$	2.88434	0.110366	0.0551832	−	0.998476i	$-0.482426\pi$
$683$	2.88434	0.110366	0.0551832	+	0.998476i	$0.482426\pi$
$684$	1.66571	0.0636901
$685$	0	0
$686$	−1.31562	−0.0502308
$687$	−0.803300	−0.0306478
$688$	38.1886	1.45593
$689$	2.95496	0.112575
$690$	0	0
$691$	−38.2681	−1.45579	−0.727893	−	0.685690i	$-0.759500\pi$
$691$	−38.2681	−1.45579	−0.727893	+	0.685690i	$0.759500\pi$
$692$	−0.181488	−0.00689914
$693$	4.40500	0.167332
$694$	40.4074	1.53384
$695$	0	0
$696$	17.7633	0.673318
$697$	17.3903	0.658706
$698$	29.4230	1.11368
$699$	48.3453	1.82859
$700$	0	0
$701$	45.1389	1.70487	0.852437	−	0.522830i	$-0.175124\pi$
$701$	45.1389	1.70487	0.852437	+	0.522830i	$0.175124\pi$
$702$	−25.6802	−0.969237
$703$	−31.0063	−1.16942
$704$	23.1373	0.872019
$705$	0	0
$706$	9.25412	0.348283
$707$	0.231900	0.00872150
$708$	0.675364	0.0253817
$709$	2.21497	0.0831849	0.0415925	−	0.999135i	$-0.486757\pi$
$709$	2.21497	0.0831849	0.0415925	+	0.999135i	$0.486757\pi$
$710$	0	0
$711$	6.92835	0.259833
$712$	29.8313	1.11797
$713$	8.90550	0.333514
$714$	−10.4356	−0.390541
$715$	0	0
$716$	6.76654	0.252877
$717$	−36.1356	−1.34951
$718$	−19.6061	−0.731693
$719$	−33.5434	−1.25096	−0.625478	−	0.780242i	$-0.715096\pi$
$719$	−33.5434	−1.25096	−0.625478	+	0.780242i	$0.715096\pi$
$720$	0	0
$721$	9.12191	0.339718
$722$	6.90862	0.257112
$723$	38.6450	1.43722
$724$	−2.17619	−0.0808774
$725$	0	0
$726$	−11.4722	−0.425773
$727$	−32.6123	−1.20952	−0.604762	−	0.796406i	$-0.706732\pi$
$727$	−32.6123	−1.20952	−0.604762	+	0.796406i	$0.706732\pi$
$728$	20.2636	0.751018
$729$	−0.0887395	−0.00328665
$730$	0	0
$731$	41.3608	1.52978
$732$	−2.16382	−0.0799770
$733$	6.40201	0.236464	0.118232	−	0.992986i	$-0.462277\pi$
$733$	6.40201	0.236464	0.118232	+	0.992986i	$0.462277\pi$
$734$	41.7974	1.54277
$735$	0	0
$736$	1.51161	0.0557186
$737$	−38.0695	−1.40231
$738$	10.4034	0.382954
$739$	−4.23247	−0.155694	−0.0778470	−	0.996965i	$-0.524805\pi$
$739$	−4.23247	−0.155694	−0.0778470	+	0.996965i	$0.524805\pi$
$740$	0	0
$741$	54.3846	1.99787
$742$	−0.572743	−0.0210261
$743$	22.4600	0.823976	0.411988	−	0.911189i	$-0.364835\pi$
$743$	22.4600	0.823976	0.411988	+	0.911189i	$0.364835\pi$
$744$	57.4473	2.10612
$745$	0	0
$746$	−36.8921	−1.35072
$747$	−10.5898	−0.387461
$748$	2.60722	0.0953295
$749$	18.2051	0.665198
$750$	0	0
$751$	34.3859	1.25476	0.627380	−	0.778713i	$-0.284127\pi$
$751$	34.3859	1.25476	0.627380	+	0.778713i	$0.284127\pi$
$752$	−29.8958	−1.09019
$753$	−24.3213	−0.886316
$754$	24.5906	0.895536
$755$	0	0
$756$	−0.773946	−0.0281482
$757$	3.05610	0.111076	0.0555380	−	0.998457i	$-0.482313\pi$
$757$	3.05610	0.111076	0.0555380	+	0.998457i	$0.482313\pi$
$758$	8.40815	0.305398
$759$	5.70250	0.206988
$760$	0	0
$761$	−6.52982	−0.236706	−0.118353	−	0.992972i	$-0.537761\pi$
$761$	−6.52982	−0.236706	−0.118353	+	0.992972i	$0.537761\pi$
$762$	−59.6486	−2.16084
$763$	−11.9105	−0.431188
$764$	6.55860	0.237282
$765$	0	0
$766$	37.0725	1.33948
$767$	7.88269	0.284627
$768$	13.6931	0.494109
$769$	12.3803	0.446444	0.223222	−	0.974768i	$-0.428342\pi$
$769$	12.3803	0.446444	0.223222	+	0.974768i	$0.428342\pi$
$770$	0	0
$771$	4.71264	0.169721
$772$	2.74237	0.0987000
$773$	53.5050	1.92444	0.962221	−	0.272271i	$-0.0877746\pi$
$773$	53.5050	1.92444	0.962221	+	0.272271i	$0.0877746\pi$
$774$	24.7432	0.889376
$775$	0	0
$776$	5.34481	0.191867
$777$	−18.0691	−0.648226
$778$	−17.7472	−0.636268
$779$	17.5661	0.629371
$780$	0	0
$781$	0.918062	0.0328509
$782$	−4.82943	−0.172700
$783$	−7.91874	−0.282993
$784$	−3.38930	−0.121046
$785$	0	0
$786$	−47.6425	−1.69935
$787$	−4.37159	−0.155830	−0.0779152	−	0.996960i	$-0.524826\pi$
$787$	−4.37159	−0.155830	−0.0779152	+	0.996960i	$0.524826\pi$
$788$	−2.25384	−0.0802898
$789$	−41.5660	−1.47979
$790$	0	0
$791$	−0.442983	−0.0157507
$792$	13.1504	0.467278
$793$	−25.2555	−0.896851
$794$	37.8767	1.34420
$795$	0	0
$796$	2.03167	0.0720107
$797$	−19.9786	−0.707677	−0.353838	−	0.935307i	$-0.615124\pi$
$797$	−19.9786	−0.707677	−0.353838	+	0.935307i	$0.615124\pi$
$798$	−10.5410	−0.373149
$799$	−32.3791	−1.14549
$800$	0	0
$801$	16.6794	0.589337
$802$	13.2264	0.467041
$803$	27.5611	0.972610
$804$	−8.38917	−0.295863
$805$	0	0
$806$	79.5269	2.80122
$807$	−36.4270	−1.28229
$808$	0.692297	0.0243549
$809$	−32.8637	−1.15543	−0.577714	−	0.816239i	$-0.696055\pi$
$809$	−32.8637	−1.15543	−0.577714	+	0.816239i	$0.696055\pi$
$810$	0	0
$811$	−26.8029	−0.941177	−0.470588	−	0.882353i	$-0.655958\pi$
$811$	−26.8029	−0.941177	−0.470588	+	0.882353i	$0.655958\pi$
$812$	0.741107	0.0260078
$813$	4.55999	0.159926
$814$	−29.0332	−1.01761
$815$	0	0
$816$	−26.8840	−0.941129
$817$	41.7788	1.46166
$818$	−2.98670	−0.104428
$819$	11.3298	0.395897
$820$	0	0
$821$	−17.4299	−0.608306	−0.304153	−	0.952623i	$-0.598373\pi$
$821$	−17.4299	−0.608306	−0.304153	+	0.952623i	$0.598373\pi$
$822$	6.95301	0.242514
$823$	−30.1134	−1.04969	−0.524844	−	0.851198i	$-0.675876\pi$
$823$	−30.1134	−1.04969	−0.524844	+	0.851198i	$0.675876\pi$
$824$	27.2319	0.948667
$825$	0	0
$826$	−1.52785	−0.0531609
$827$	−46.2535	−1.60839	−0.804197	−	0.594363i	$-0.797404\pi$
$827$	−46.2535	−1.60839	−0.804197	+	0.594363i	$0.797404\pi$
$828$	0.449229	0.0156118
$829$	18.7423	0.650946	0.325473	−	0.945551i	$-0.394476\pi$
$829$	18.7423	0.650946	0.325473	+	0.945551i	$0.394476\pi$
$830$	0	0
$831$	−39.0266	−1.35382
$832$	59.5100	2.06314
$833$	−3.67083	−0.127187
$834$	16.7922	0.581466
$835$	0	0
$836$	2.63358	0.0910841
$837$	−25.6095	−0.885194
$838$	9.03131	0.311981
$839$	3.28756	0.113499	0.0567495	−	0.998388i	$-0.481926\pi$
$839$	3.28756	0.113499	0.0567495	+	0.998388i	$0.481926\pi$
$840$	0	0
$841$	−21.4173	−0.738526
$842$	5.26054	0.181290
$843$	−13.5571	−0.466932
$844$	−6.55085	−0.225489
$845$	0	0
$846$	−19.3701	−0.665958
$847$	−4.03547	−0.138661
$848$	−1.47550	−0.0506688
$849$	31.0833	1.06678
$850$	0	0
$851$	−8.36214	−0.286650
$852$	0.202308	0.00693097
$853$	40.5821	1.38951	0.694753	−	0.719249i	$-0.255514\pi$
$853$	40.5821	1.38951	0.694753	+	0.719249i	$0.255514\pi$
$854$	4.89513	0.167508
$855$	0	0
$856$	54.3480	1.85758
$857$	49.2836	1.68350	0.841748	−	0.539871i	$-0.181527\pi$
$857$	49.2836	1.68350	0.841748	+	0.539871i	$0.181527\pi$
$858$	50.9239	1.73851
$859$	−21.9973	−0.750539	−0.375270	−	0.926916i	$-0.622450\pi$
$859$	−21.9973	−0.750539	−0.375270	+	0.926916i	$0.622450\pi$
$860$	0	0
$861$	10.2368	0.348868
$862$	25.9903	0.885232
$863$	6.12283	0.208423	0.104212	−	0.994555i	$-0.466768\pi$
$863$	6.12283	0.208423	0.104212	+	0.994555i	$0.466768\pi$
$864$	−4.34693	−0.147885
$865$	0	0
$866$	−27.4897	−0.934140
$867$	7.61690	0.258684
$868$	2.39677	0.0813516
$869$	10.9541	0.371591
$870$	0	0
$871$	−97.9163	−3.31777
$872$	−35.5566	−1.20410
$873$	2.98841	0.101142
$874$	−4.87825	−0.165009
$875$	0	0
$876$	6.07349	0.205204
$877$	−54.6162	−1.84426	−0.922129	−	0.386883i	$-0.873552\pi$
$877$	−54.6162	−1.84426	−0.922129	+	0.386883i	$0.873552\pi$
$878$	32.2164	1.08725
$879$	−33.6921	−1.13641
$880$	0	0
$881$	−52.9711	−1.78464	−0.892322	−	0.451400i	$-0.850925\pi$
$881$	−52.9711	−1.78464	−0.892322	+	0.451400i	$0.850925\pi$
$882$	−2.19600	−0.0739431
$883$	−14.2882	−0.480836	−0.240418	−	0.970669i	$-0.577284\pi$
$883$	−14.2882	−0.480836	−0.240418	+	0.970669i	$0.577284\pi$
$884$	6.70589	0.225543
$885$	0	0
$886$	45.6596	1.53397
$887$	−34.9490	−1.17347	−0.586736	−	0.809778i	$-0.699587\pi$
$887$	−34.9490	−1.17347	−0.586736	+	0.809778i	$0.699587\pi$
$888$	−53.9422	−1.81018
$889$	−20.9821	−0.703717
$890$	0	0
$891$	−29.6137	−0.992095
$892$	0.740337	0.0247883
$893$	−32.7064	−1.09448
$894$	−20.6133	−0.689413
$895$	0	0
$896$	−8.51126	−0.284341
$897$	14.6671	0.489720
$898$	40.5558	1.35336
$899$	24.5229	0.817884
$900$	0	0
$901$	−1.59806	−0.0532390
$902$	16.4483	0.547668
$903$	24.3469	0.810215
$904$	−1.32245	−0.0439840
$905$	0	0
$906$	40.7345	1.35331
$907$	21.2561	0.705798	0.352899	−	0.935661i	$-0.385196\pi$
$907$	21.2561	0.705798	0.352899	+	0.935661i	$0.385196\pi$
$908$	3.21572	0.106718
$909$	0.387080	0.0128386
$910$	0	0
$911$	23.2853	0.771476	0.385738	−	0.922608i	$-0.373947\pi$
$911$	23.2853	0.771476	0.385738	+	0.922608i	$0.373947\pi$
$912$	−27.1558	−0.899217
$913$	−16.7430	−0.554114
$914$	11.7142	0.387470
$915$	0	0
$916$	−0.100052	−0.00330581
$917$	−16.7588	−0.553425
$918$	13.8880	0.458372
$919$	−0.551712	−0.0181993	−0.00909966	−	0.999959i	$-0.502897\pi$
$919$	−0.551712	−0.0181993	−0.00909966	+	0.999959i	$0.502897\pi$
$920$	0	0
$921$	−10.9783	−0.361746
$922$	11.9147	0.392390
$923$	2.36130	0.0777230
$924$	1.53474	0.0504891
$925$	0	0
$926$	−1.04535	−0.0343524
$927$	15.2260	0.500087
$928$	4.16249	0.136640
$929$	−25.8329	−0.847551	−0.423775	−	0.905767i	$-0.639295\pi$
$929$	−25.8329	−0.847551	−0.423775	+	0.905767i	$0.639295\pi$
$930$	0	0
$931$	−3.70794	−0.121523
$932$	6.02147	0.197240
$933$	−32.2838	−1.05692
$934$	−26.1369	−0.855227
$935$	0	0
$936$	33.8233	1.10555
$937$	−41.7101	−1.36261	−0.681305	−	0.732000i	$-0.738587\pi$
$937$	−41.7101	−1.36261	−0.681305	+	0.732000i	$0.738587\pi$
$938$	18.9785	0.619671
$939$	−16.1444	−0.526853
$940$	0	0
$941$	39.1240	1.27541	0.637703	−	0.770282i	$-0.279885\pi$
$941$	39.1240	1.27541	0.637703	+	0.770282i	$0.279885\pi$
$942$	−37.9476	−1.23640
$943$	4.73744	0.154272
$944$	−3.93605	−0.128107
$945$	0	0
$946$	39.1203	1.27191
$947$	−40.5439	−1.31750	−0.658750	−	0.752362i	$-0.728914\pi$
$947$	−40.5439	−1.31750	−0.658750	+	0.752362i	$0.728914\pi$
$948$	2.41389	0.0783995
$949$	70.8883	2.30113
$950$	0	0
$951$	−20.6169	−0.668548
$952$	−10.9586	−0.355171
$953$	−3.47933	−0.112707	−0.0563533	−	0.998411i	$-0.517947\pi$
$953$	−3.47933	−0.112707	−0.0563533	+	0.998411i	$0.517947\pi$
$954$	−0.956005	−0.0309518
$955$	0	0
$956$	−4.50074	−0.145564
$957$	15.7029	0.507601
$958$	−48.1234	−1.55480
$959$	2.44580	0.0789790
$960$	0	0
$961$	48.3079	1.55832
$962$	−74.6746	−2.40761
$963$	30.3873	0.979217
$964$	4.81329	0.155026
$965$	0	0
$966$	−2.84283	−0.0914667
$967$	24.5596	0.789783	0.394891	−	0.918728i	$-0.370782\pi$
$967$	24.5596	0.789783	0.394891	+	0.918728i	$0.370782\pi$
$968$	−12.0472	−0.387212
$969$	−29.4114	−0.944832
$970$	0	0
$971$	−30.0938	−0.965755	−0.482878	−	0.875688i	$-0.660408\pi$
$971$	−30.0938	−0.965755	−0.482878	+	0.875688i	$0.660408\pi$
$972$	−4.20396	−0.134842
$973$	5.90685	0.189365
$974$	31.7839	1.01842
$975$	0	0
$976$	12.6108	0.403662
$977$	50.2436	1.60743	0.803717	−	0.595011i	$-0.202852\pi$
$977$	50.2436	1.60743	0.803717	+	0.595011i	$0.202852\pi$
$978$	−5.07274	−0.162208
$979$	26.3709	0.842819
$980$	0	0
$981$	−19.8806	−0.634737
$982$	1.91319	0.0610524
$983$	36.5100	1.16449	0.582244	−	0.813014i	$-0.302175\pi$
$983$	36.5100	1.16449	0.582244	+	0.813014i	$0.302175\pi$
$984$	30.5601	0.974221
$985$	0	0
$986$	−13.2987	−0.423517
$987$	−19.0599	−0.606682
$988$	6.77367	0.215499
$989$	11.2674	0.358283
$990$	0	0
$991$	−32.6272	−1.03644	−0.518218	−	0.855249i	$-0.673404\pi$
$991$	−32.6272	−1.03644	−0.518218	+	0.855249i	$0.673404\pi$
$992$	13.4616	0.427407
$993$	36.3288	1.15286
$994$	−0.457676	−0.0145166
$995$	0	0
$996$	−3.68957	−0.116909
$997$	50.5714	1.60161	0.800806	−	0.598923i	$-0.204405\pi$
$997$	50.5714	1.60161	0.800806	+	0.598923i	$0.204405\pi$
$998$	32.2565	1.02106
$999$	24.0470	0.760812

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.x.1.4		12
5.2	odd	4		805.2.c.b.484.7	✓	24
5.3	odd	4		805.2.c.b.484.18	yes	24
5.4	even	2		4025.2.a.y.1.9		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.c.b.484.7	✓	24	5.2	odd	4
805.2.c.b.484.18	yes	24	5.3	odd	4
4025.2.a.x.1.4		12	1.1	even	1	trivial
4025.2.a.y.1.9		12	5.4	even	2

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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:	\( N \)	\(=\)	\( 4025 = 5^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4025.a (trivial)

\(f(q)\)	\(=\)	\(q-1.31562 q^{2} -2.16083 q^{3} -0.269134 q^{4} +2.84283 q^{6} +1.00000 q^{7} +2.98533 q^{8} +1.66917 q^{9} +O(q^{10})\)	\(q-1.31562 q^{2} -2.16083 q^{3} -0.269134 q^{4} +2.84283 q^{6} +1.00000 q^{7} +2.98533 q^{8} +1.66917 q^{9} +2.63904 q^{11} +0.581551 q^{12} +6.78772 q^{13} -1.31562 q^{14} -3.38930 q^{16} -3.67083 q^{17} -2.19600 q^{18} -3.70794 q^{19} -2.16083 q^{21} -3.47198 q^{22} -1.00000 q^{23} -6.45077 q^{24} -8.93009 q^{26} +2.87570 q^{27} -0.269134 q^{28} -2.75368 q^{29} -8.90550 q^{31} -1.51161 q^{32} -5.70250 q^{33} +4.82943 q^{34} -0.449229 q^{36} +8.36214 q^{37} +4.87825 q^{38} -14.6671 q^{39} -4.73744 q^{41} +2.84283 q^{42} -11.2674 q^{43} -0.710254 q^{44} +1.31562 q^{46} +8.82064 q^{47} +7.32369 q^{48} +1.00000 q^{49} +7.93203 q^{51} -1.82680 q^{52} +0.435340 q^{53} -3.78333 q^{54} +2.98533 q^{56} +8.01220 q^{57} +3.62281 q^{58} +1.16132 q^{59} -3.72077 q^{61} +11.7163 q^{62} +1.66917 q^{63} +8.76731 q^{64} +7.50235 q^{66} -14.4255 q^{67} +0.987944 q^{68} +2.16083 q^{69} +0.347878 q^{71} +4.98301 q^{72} +10.4436 q^{73} -11.0014 q^{74} +0.997930 q^{76} +2.63904 q^{77} +19.2964 q^{78} +4.15078 q^{79} -11.2214 q^{81} +6.23269 q^{82} -6.34437 q^{83} +0.581551 q^{84} +14.8237 q^{86} +5.95022 q^{87} +7.87839 q^{88} +9.99263 q^{89} +6.78772 q^{91} +0.269134 q^{92} +19.2432 q^{93} -11.6046 q^{94} +3.26632 q^{96} +1.79036 q^{97} -1.31562 q^{98} +4.40500 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} + 8 q^{4} - 6 q^{6} + 12 q^{7} - 6 q^{8} + 8 q^{9}+O(q^{10}) \) 12 * q - 2 * q^2 + 8 * q^4 - 6 * q^6 + 12 * q^7 - 6 * q^8 + 8 * q^9	\( 12 q - 2 q^{2} + 8 q^{4} - 6 q^{6} + 12 q^{7} - 6 q^{8} + 8 q^{9} - 8 q^{11} + 12 q^{12} - 2 q^{13} - 2 q^{14} - 4 q^{16} + 8 q^{17} - 20 q^{18} - 26 q^{19} - 4 q^{22} - 12 q^{23} - 12 q^{24} - 22 q^{26} - 12 q^{27} + 8 q^{28} - 12 q^{29} - 50 q^{31} - 14 q^{32} - 4 q^{33} - 28 q^{34} - 18 q^{36} - 8 q^{37} + 4 q^{38} - 26 q^{39} - 4 q^{41} - 6 q^{42} - 26 q^{43} - 10 q^{44} + 2 q^{46} - 16 q^{47} + 40 q^{48} + 12 q^{49} - 32 q^{51} - 10 q^{52} + 18 q^{53} - 10 q^{54} - 6 q^{56} + 10 q^{57} + 18 q^{58} - 18 q^{59} + 8 q^{61} + 54 q^{62} + 8 q^{63} + 12 q^{64} - 2 q^{66} - 38 q^{67} + 36 q^{68} - 24 q^{71} - 18 q^{72} + 14 q^{73} + 36 q^{74} - 56 q^{76} - 8 q^{77} + 26 q^{78} - 44 q^{79} - 16 q^{81} + 44 q^{82} + 14 q^{83} + 12 q^{84} - 32 q^{86} - 16 q^{87} - 32 q^{88} - 10 q^{89} - 2 q^{91} - 8 q^{92} - 26 q^{93} + 18 q^{94} - 38 q^{96} + 4 q^{97} - 2 q^{98} - 56 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 + 8 * q^4 - 6 * q^6 + 12 * q^7 - 6 * q^8 + 8 * q^9 - 8 * q^11 + 12 * q^12 - 2 * q^13 - 2 * q^14 - 4 * q^16 + 8 * q^17 - 20 * q^18 - 26 * q^19 - 4 * q^22 - 12 * q^23 - 12 * q^24 - 22 * q^26 - 12 * q^27 + 8 * q^28 - 12 * q^29 - 50 * q^31 - 14 * q^32 - 4 * q^33 - 28 * q^34 - 18 * q^36 - 8 * q^37 + 4 * q^38 - 26 * q^39 - 4 * q^41 - 6 * q^42 - 26 * q^43 - 10 * q^44 + 2 * q^46 - 16 * q^47 + 40 * q^48 + 12 * q^49 - 32 * q^51 - 10 * q^52 + 18 * q^53 - 10 * q^54 - 6 * q^56 + 10 * q^57 + 18 * q^58 - 18 * q^59 + 8 * q^61 + 54 * q^62 + 8 * q^63 + 12 * q^64 - 2 * q^66 - 38 * q^67 + 36 * q^68 - 24 * q^71 - 18 * q^72 + 14 * q^73 + 36 * q^74 - 56 * q^76 - 8 * q^77 + 26 * q^78 - 44 * q^79 - 16 * q^81 + 44 * q^82 + 14 * q^83 + 12 * q^84 - 32 * q^86 - 16 * q^87 - 32 * q^88 - 10 * q^89 - 2 * q^91 - 8 * q^92 - 26 * q^93 + 18 * q^94 - 38 * q^96 + 4 * q^97 - 2 * q^98 - 56 * q^99

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