LMFDB - Embedded newform 1666.2.a.z.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1666,2,Mod(1,1666)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1666, 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("1666.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1666 = 2 \cdot 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1666.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:	$13.3030769767$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.23949216.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 13x^{3} - 2x^{2} + 24x - 4 $ x^5 - 13x^3 - 2x^2 + 24*x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 238)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.72247$ of defining polynomial
Character	$\chi$	$=$	1666.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.72247 q^{3} +1.00000 q^{4} +2.42127 q^{5} +1.72247 q^{6} +1.00000 q^{8} -0.0331027 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.72247 q^{3} +1.00000 q^{4} +2.42127 q^{5} +1.72247 q^{6} +1.00000 q^{8} -0.0331027 q^{9} +2.42127 q^{10} +3.72247 q^{11} +1.72247 q^{12} +6.58239 q^{13} +4.17056 q^{15} +1.00000 q^{16} -1.00000 q^{17} -0.0331027 q^{18} -5.58239 q^{19} +2.42127 q^{20} +3.72247 q^{22} -5.97056 q^{23} +1.72247 q^{24} +0.862543 q^{25} +6.58239 q^{26} -5.22442 q^{27} -0.772958 q^{29} +4.17056 q^{30} -9.61550 q^{31} +1.00000 q^{32} +6.41183 q^{33} -1.00000 q^{34} -0.0331027 q^{36} +4.42127 q^{37} -5.58239 q^{38} +11.3380 q^{39} +2.42127 q^{40} -5.61550 q^{41} -6.25437 q^{43} +3.72247 q^{44} -0.0801505 q^{45} -5.97056 q^{46} -0.671979 q^{47} +1.72247 q^{48} +0.862543 q^{50} -1.72247 q^{51} +6.58239 q^{52} +9.91041 q^{53} -5.22442 q^{54} +9.01310 q^{55} -9.61550 q^{57} -0.772958 q^{58} -10.3206 q^{59} +4.17056 q^{60} +4.72562 q^{61} -9.61550 q^{62} +1.00000 q^{64} +15.9377 q^{65} +6.41183 q^{66} +14.4249 q^{67} -1.00000 q^{68} -10.2841 q^{69} +9.69303 q^{71} -0.0331027 q^{72} +1.61550 q^{73} +4.42127 q^{74} +1.48570 q^{75} -5.58239 q^{76} +11.3380 q^{78} +4.56501 q^{79} +2.42127 q^{80} -8.89960 q^{81} -5.61550 q^{82} +10.3222 q^{83} -2.42127 q^{85} -6.25437 q^{86} -1.33140 q^{87} +3.72247 q^{88} +4.39423 q^{89} -0.0801505 q^{90} -5.97056 q^{92} -16.5624 q^{93} -0.671979 q^{94} -13.5165 q^{95} +1.72247 q^{96} -7.54929 q^{97} -0.123224 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 5 q^{2} + 5 q^{4} - q^{5} + 5 q^{8} + 11 q^{9}+O(q^{10}) $ 5 * q + 5 * q^2 + 5 * q^4 - q^5 + 5 * q^8 + 11 * q^9	$ 5 q + 5 q^{2} + 5 q^{4} - q^{5} + 5 q^{8} + 11 q^{9} - q^{10} + 10 q^{11} + 2 q^{13} - 4 q^{15} + 5 q^{16} - 5 q^{17} + 11 q^{18} + 3 q^{19} - q^{20} + 10 q^{22} + 3 q^{23} + 18 q^{25} + 2 q^{26} - 6 q^{27} + 12 q^{29} - 4 q^{30} - 6 q^{31} + 5 q^{32} + 26 q^{33} - 5 q^{34} + 11 q^{36} + 9 q^{37} + 3 q^{38} + 6 q^{39} - q^{40} + 14 q^{41} + q^{43} + 10 q^{44} - 37 q^{45} + 3 q^{46} - 2 q^{47} + 18 q^{50} + 2 q^{52} + 20 q^{53} - 6 q^{54} - 6 q^{55} - 6 q^{57} + 12 q^{58} + 3 q^{59} - 4 q^{60} + 16 q^{61} - 6 q^{62} + 5 q^{64} + 2 q^{65} + 26 q^{66} + 15 q^{67} - 5 q^{68} + 4 q^{69} + 7 q^{71} + 11 q^{72} - 34 q^{73} + 9 q^{74} + 46 q^{75} + 3 q^{76} + 6 q^{78} - 12 q^{79} - q^{80} + 53 q^{81} + 14 q^{82} + 16 q^{83} + q^{85} + q^{86} - 20 q^{87} + 10 q^{88} + q^{89} - 37 q^{90} + 3 q^{92} - 12 q^{93} - 2 q^{94} - 3 q^{95} - 18 q^{97} + 16 q^{99}+O(q^{100}) $ 5 * q + 5 * q^2 + 5 * q^4 - q^5 + 5 * q^8 + 11 * q^9 - q^10 + 10 * q^11 + 2 * q^13 - 4 * q^15 + 5 * q^16 - 5 * q^17 + 11 * q^18 + 3 * q^19 - q^20 + 10 * q^22 + 3 * q^23 + 18 * q^25 + 2 * q^26 - 6 * q^27 + 12 * q^29 - 4 * q^30 - 6 * q^31 + 5 * q^32 + 26 * q^33 - 5 * q^34 + 11 * q^36 + 9 * q^37 + 3 * q^38 + 6 * q^39 - q^40 + 14 * q^41 + q^43 + 10 * q^44 - 37 * q^45 + 3 * q^46 - 2 * q^47 + 18 * q^50 + 2 * q^52 + 20 * q^53 - 6 * q^54 - 6 * q^55 - 6 * q^57 + 12 * q^58 + 3 * q^59 - 4 * q^60 + 16 * q^61 - 6 * q^62 + 5 * q^64 + 2 * q^65 + 26 * q^66 + 15 * q^67 - 5 * q^68 + 4 * q^69 + 7 * q^71 + 11 * q^72 - 34 * q^73 + 9 * q^74 + 46 * q^75 + 3 * q^76 + 6 * q^78 - 12 * q^79 - q^80 + 53 * q^81 + 14 * q^82 + 16 * q^83 + q^85 + q^86 - 20 * q^87 + 10 * q^88 + q^89 - 37 * q^90 + 3 * q^92 - 12 * q^93 - 2 * q^94 - 3 * q^95 - 18 * q^97 + 16 * 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
$3$	1.72247	0.994468	0.497234	−	0.867617i	$-0.334349\pi$
$3$	1.72247	0.994468	0.497234	+	0.867617i	$0.334349\pi$
$4$	1.00000	0.500000
$5$	2.42127	1.08282	0.541412	−	0.840757i	$-0.317890\pi$
$5$	2.42127	1.08282	0.541412	+	0.840757i	$0.317890\pi$
$6$	1.72247	0.703195
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	−0.0331027	−0.0110342
$10$	2.42127	0.765672
$11$	3.72247	1.12237	0.561183	−	0.827692i	$-0.310346\pi$
$11$	3.72247	1.12237	0.561183	+	0.827692i	$0.310346\pi$
$12$	1.72247	0.497234
$13$	6.58239	1.82563	0.912814	−	0.408376i	$-0.133905\pi$
$13$	6.58239	1.82563	0.912814	+	0.408376i	$0.133905\pi$
$14$	0	0
$15$	4.17056	1.07683
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−0.0331027	−0.00780238
$19$	−5.58239	−1.28069	−0.640344	−	0.768088i	$-0.721208\pi$
$19$	−5.58239	−1.28069	−0.640344	+	0.768088i	$0.721208\pi$
$20$	2.42127	0.541412
$21$	0	0
$22$	3.72247	0.793633
$23$	−5.97056	−1.24495	−0.622474	−	0.782641i	$-0.713872\pi$
$23$	−5.97056	−1.24495	−0.622474	+	0.782641i	$0.713872\pi$
$24$	1.72247	0.351597
$25$	0.862543	0.172509
$26$	6.58239	1.29091
$27$	−5.22442	−1.00544
$28$	0	0
$29$	−0.772958	−0.143535	−0.0717674	−	0.997421i	$-0.522864\pi$
$29$	−0.772958	−0.143535	−0.0717674	+	0.997421i	$0.522864\pi$
$30$	4.17056	0.761436
$31$	−9.61550	−1.72699	−0.863497	−	0.504354i	$-0.831731\pi$
$31$	−9.61550	−1.72699	−0.863497	+	0.504354i	$0.831731\pi$
$32$	1.00000	0.176777
$33$	6.41183	1.11616
$34$	−1.00000	−0.171499
$35$	0	0
$36$	−0.0331027	−0.00551711
$37$	4.42127	0.726852	0.363426	−	0.931623i	$-0.381607\pi$
$37$	4.42127	0.726852	0.363426	+	0.931623i	$0.381607\pi$
$38$	−5.58239	−0.905584
$39$	11.3380	1.81553
$40$	2.42127	0.382836
$41$	−5.61550	−0.876993	−0.438497	−	0.898733i	$-0.644489\pi$
$41$	−5.61550	−0.876993	−0.438497	+	0.898733i	$0.644489\pi$
$42$	0	0
$43$	−6.25437	−0.953783	−0.476891	−	0.878962i	$-0.658237\pi$
$43$	−6.25437	−0.953783	−0.476891	+	0.878962i	$0.658237\pi$
$44$	3.72247	0.561183
$45$	−0.0801505	−0.0119481
$46$	−5.97056	−0.880311
$47$	−0.671979	−0.0980182	−0.0490091	−	0.998798i	$-0.515606\pi$
$47$	−0.671979	−0.0980182	−0.0490091	+	0.998798i	$0.515606\pi$
$48$	1.72247	0.248617
$49$	0	0
$50$	0.862543	0.121982
$51$	−1.72247	−0.241194
$52$	6.58239	0.912814
$53$	9.91041	1.36130	0.680650	−	0.732609i	$-0.261697\pi$
$53$	9.91041	1.36130	0.680650	+	0.732609i	$0.261697\pi$
$54$	−5.22442	−0.710954
$55$	9.01310	1.21533
$56$	0	0
$57$	−9.61550	−1.27360
$58$	−0.772958	−0.101494
$59$	−10.3206	−1.34362	−0.671812	−	0.740721i	$-0.734484\pi$
$59$	−10.3206	−1.34362	−0.671812	+	0.740721i	$0.734484\pi$
$60$	4.17056	0.538417
$61$	4.72562	0.605054	0.302527	−	0.953141i	$-0.402170\pi$
$61$	4.72562	0.605054	0.302527	+	0.953141i	$0.402170\pi$
$62$	−9.61550	−1.22117
$63$	0	0
$64$	1.00000	0.125000
$65$	15.9377	1.97683
$66$	6.41183	0.789242
$67$	14.4249	1.76229	0.881143	−	0.472850i	$-0.156775\pi$
$67$	14.4249	1.76229	0.881143	+	0.472850i	$0.156775\pi$
$68$	−1.00000	−0.121268
$69$	−10.2841	−1.23806
$70$	0	0
$71$	9.69303	1.15035	0.575175	−	0.818030i	$-0.304934\pi$
$71$	9.69303	1.15035	0.575175	+	0.818030i	$0.304934\pi$
$72$	−0.0331027	−0.00390119
$73$	1.61550	0.189080	0.0945398	−	0.995521i	$-0.469862\pi$
$73$	1.61550	0.189080	0.0945398	+	0.995521i	$0.469862\pi$
$74$	4.42127	0.513962
$75$	1.48570	0.171554
$76$	−5.58239	−0.640344
$77$	0	0
$78$	11.3380	1.28377
$79$	4.56501	0.513603	0.256802	−	0.966464i	$-0.417331\pi$
$79$	4.56501	0.513603	0.256802	+	0.966464i	$0.417331\pi$
$80$	2.42127	0.270706
$81$	−8.89960	−0.988844
$82$	−5.61550	−0.620128
$83$	10.3222	1.13301	0.566507	−	0.824057i	$-0.308294\pi$
$83$	10.3222	1.13301	0.566507	+	0.824057i	$0.308294\pi$
$84$	0	0
$85$	−2.42127	−0.262623
$86$	−6.25437	−0.674426
$87$	−1.33140	−0.142741
$88$	3.72247	0.396816
$89$	4.39423	0.465787	0.232894	−	0.972502i	$-0.425181\pi$
$89$	4.39423	0.465787	0.232894	+	0.972502i	$0.425181\pi$
$90$	−0.0801505	−0.00844860
$91$	0	0
$92$	−5.97056	−0.622474
$93$	−16.5624	−1.71744
$94$	−0.671979	−0.0693093
$95$	−13.5165	−1.38676
$96$	1.72247	0.175799
$97$	−7.54929	−0.766514	−0.383257	−	0.923642i	$-0.625198\pi$
$97$	−7.54929	−0.766514	−0.383257	+	0.923642i	$0.625198\pi$
$98$	0	0
$99$	−0.123224	−0.0123844
$100$	0.862543	0.0862543
$101$	−12.3885	−1.23270	−0.616349	−	0.787473i	$-0.711389\pi$
$101$	−12.3885	−1.23270	−0.616349	+	0.787473i	$0.711389\pi$
$102$	−1.72247	−0.170550
$103$	4.10435	0.404414	0.202207	−	0.979343i	$-0.435189\pi$
$103$	4.10435	0.404414	0.202207	+	0.979343i	$0.435189\pi$
$104$	6.58239	0.645457
$105$	0	0
$106$	9.91041	0.962585
$107$	6.49880	0.628263	0.314131	−	0.949380i	$-0.398287\pi$
$107$	6.49880	0.628263	0.314131	+	0.949380i	$0.398287\pi$
$108$	−5.22442	−0.502720
$109$	6.35169	0.608381	0.304191	−	0.952611i	$-0.401614\pi$
$109$	6.35169	0.608381	0.304191	+	0.952611i	$0.401614\pi$
$110$	9.01310	0.859365
$111$	7.61550	0.722831
$112$	0	0
$113$	4.84254	0.455548	0.227774	−	0.973714i	$-0.426855\pi$
$113$	4.84254	0.455548	0.227774	+	0.973714i	$0.426855\pi$
$114$	−9.61550	−0.900574
$115$	−14.4563	−1.34806
$116$	−0.772958	−0.0717674
$117$	−0.217895	−0.0201444
$118$	−10.3206	−0.950086
$119$	0	0
$120$	4.17056	0.380718
$121$	2.85677	0.259706
$122$	4.72562	0.427838
$123$	−9.67251	−0.872141
$124$	−9.61550	−0.863497
$125$	−10.0179	−0.896028
$126$	0	0
$127$	−9.51452	−0.844277	−0.422138	−	0.906531i	$-0.638720\pi$
$127$	−9.51452	−0.844277	−0.422138	+	0.906531i	$0.638720\pi$
$128$	1.00000	0.0883883
$129$	−10.7730	−0.948506
$130$	15.9377	1.39783
$131$	−5.66621	−0.495059	−0.247529	−	0.968880i	$-0.579619\pi$
$131$	−5.66621	−0.495059	−0.247529	+	0.968880i	$0.579619\pi$
$132$	6.41183	0.558079
$133$	0	0
$134$	14.4249	1.24612
$135$	−12.6497	−1.08872
$136$	−1.00000	−0.0857493
$137$	−18.1773	−1.55300	−0.776498	−	0.630120i	$-0.783006\pi$
$137$	−18.1773	−1.55300	−0.776498	+	0.630120i	$0.783006\pi$
$138$	−10.2841	−0.875441
$139$	−16.1143	−1.36680	−0.683398	−	0.730046i	$-0.739499\pi$
$139$	−16.1143	−1.36680	−0.683398	+	0.730046i	$0.739499\pi$
$140$	0	0
$141$	−1.15746	−0.0974759
$142$	9.69303	0.813421
$143$	24.5028	2.04902
$144$	−0.0331027	−0.00275856
$145$	−1.87154	−0.155423
$146$	1.61550	0.133699
$147$	0	0
$148$	4.42127	0.363426
$149$	0.361124	0.0295844	0.0147922	−	0.999891i	$-0.495291\pi$
$149$	0.361124	0.0295844	0.0147922	+	0.999891i	$0.495291\pi$
$150$	1.48570	0.121307
$151$	−14.2841	−1.16242	−0.581212	−	0.813752i	$-0.697421\pi$
$151$	−14.2841	−1.16242	−0.581212	+	0.813752i	$0.697421\pi$
$152$	−5.58239	−0.452792
$153$	0.0331027	0.00267619
$154$	0	0
$155$	−23.2817	−1.87003
$156$	11.3380	0.907764
$157$	5.13746	0.410014	0.205007	−	0.978761i	$-0.434278\pi$
$157$	5.13746	0.410014	0.205007	+	0.978761i	$0.434278\pi$
$158$	4.56501	0.363172
$159$	17.0704	1.35377
$160$	2.42127	0.191418
$161$	0	0
$162$	−8.89960	−0.699218
$163$	1.61550	0.126535	0.0632677	−	0.997997i	$-0.479848\pi$
$163$	1.61550	0.126535	0.0632677	+	0.997997i	$0.479848\pi$
$164$	−5.61550	−0.438497
$165$	15.5248	1.20860
$166$	10.3222	0.801162
$167$	−0.477531	−0.0369525	−0.0184762	−	0.999829i	$-0.505882\pi$
$167$	−0.477531	−0.0369525	−0.0184762	+	0.999829i	$0.505882\pi$
$168$	0	0
$169$	30.3279	2.33292
$170$	−2.42127	−0.185703
$171$	0.184792	0.0141314
$172$	−6.25437	−0.476891
$173$	6.79423	0.516556	0.258278	−	0.966071i	$-0.416845\pi$
$173$	6.79423	0.516556	0.258278	+	0.966071i	$0.416845\pi$
$174$	−1.33140	−0.100933
$175$	0	0
$176$	3.72247	0.280592
$177$	−17.7769	−1.33619
$178$	4.39423	0.329361
$179$	−7.48141	−0.559187	−0.279594	−	0.960118i	$-0.590200\pi$
$179$	−7.48141	−0.559187	−0.279594	+	0.960118i	$0.590200\pi$
$180$	−0.0801505	−0.00597406
$181$	−6.91931	−0.514309	−0.257154	−	0.966370i	$-0.582785\pi$
$181$	−6.91931	−0.514309	−0.257154	+	0.966370i	$0.582785\pi$
$182$	0	0
$183$	8.13974	0.601707
$184$	−5.97056	−0.440155
$185$	10.7051	0.787053
$186$	−16.5624	−1.21441
$187$	−3.72247	−0.272214
$188$	−0.671979	−0.0490091
$189$	0	0
$190$	−13.5165	−0.980588
$191$	4.82029	0.348784	0.174392	−	0.984676i	$-0.444204\pi$
$191$	4.82029	0.348784	0.174392	+	0.984676i	$0.444204\pi$
$192$	1.72247	0.124308
$193$	1.17633	0.0846742	0.0423371	−	0.999103i	$-0.486520\pi$
$193$	1.17633	0.0846742	0.0423371	+	0.999103i	$0.486520\pi$
$194$	−7.54929	−0.542007
$195$	27.4523	1.96590
$196$	0	0
$197$	4.37393	0.311630	0.155815	−	0.987786i	$-0.450200\pi$
$197$	4.37393	0.311630	0.155815	+	0.987786i	$0.450200\pi$
$198$	−0.123224	−0.00875712
$199$	23.9298	1.69634	0.848169	−	0.529726i	$-0.177705\pi$
$199$	23.9298	1.69634	0.848169	+	0.529726i	$0.177705\pi$
$200$	0.862543	0.0609910
$201$	24.8465	1.75254
$202$	−12.3885	−0.871649
$203$	0	0
$204$	−1.72247	−0.120597
$205$	−13.5966	−0.949630
$206$	4.10435	0.285964
$207$	0.197641	0.0137370
$208$	6.58239	0.456407
$209$	−20.7803	−1.43740
$210$	0	0
$211$	−9.56479	−0.658467	−0.329234	−	0.944249i	$-0.606790\pi$
$211$	−9.56479	−0.658467	−0.329234	+	0.944249i	$0.606790\pi$
$212$	9.91041	0.680650
$213$	16.6959	1.14399
$214$	6.49880	0.444249
$215$	−15.1435	−1.03278
$216$	−5.22442	−0.355477
$217$	0	0
$218$	6.35169	0.430191
$219$	2.78264	0.188033
$220$	9.01310	0.607663
$221$	−6.58239	−0.442780
$222$	7.61550	0.511119
$223$	12.2338	0.819238	0.409619	−	0.912257i	$-0.365662\pi$
$223$	12.2338	0.819238	0.409619	+	0.912257i	$0.365662\pi$
$224$	0	0
$225$	−0.0285525	−0.00190350
$226$	4.84254	0.322121
$227$	5.92780	0.393442	0.196721	−	0.980460i	$-0.436971\pi$
$227$	5.92780	0.393442	0.196721	+	0.980460i	$0.436971\pi$
$228$	−9.61550	−0.636802
$229$	18.8932	1.24850	0.624250	−	0.781224i	$-0.285404\pi$
$229$	18.8932	1.24850	0.624250	+	0.781224i	$0.285404\pi$
$230$	−14.4563	−0.953222
$231$	0	0
$232$	−0.772958	−0.0507472
$233$	23.3039	1.52669	0.763346	−	0.645990i	$-0.223555\pi$
$233$	23.3039	1.52669	0.763346	+	0.645990i	$0.223555\pi$
$234$	−0.217895	−0.0142442
$235$	−1.62704	−0.106136
$236$	−10.3206	−0.671812
$237$	7.86308	0.510762
$238$	0	0
$239$	−19.6228	−1.26929	−0.634647	−	0.772802i	$-0.718855\pi$
$239$	−19.6228	−1.26929	−0.634647	+	0.772802i	$0.718855\pi$
$240$	4.17056	0.269208
$241$	−6.70338	−0.431803	−0.215901	−	0.976415i	$-0.569269\pi$
$241$	−6.70338	−0.431803	−0.215901	+	0.976415i	$0.569269\pi$
$242$	2.85677	0.183640
$243$	0.343997	0.0220674
$244$	4.72562	0.302527
$245$	0	0
$246$	−9.67251	−0.616697
$247$	−36.7455	−2.33806
$248$	−9.61550	−0.610585
$249$	17.7797	1.12675
$250$	−10.0179	−0.633587
$251$	0.983528	0.0620798	0.0310399	−	0.999518i	$-0.490118\pi$
$251$	0.983528	0.0620798	0.0310399	+	0.999518i	$0.490118\pi$
$252$	0	0
$253$	−22.2252	−1.39729
$254$	−9.51452	−0.596994
$255$	−4.17056	−0.261171
$256$	1.00000	0.0625000
$257$	−19.3348	−1.20607	−0.603036	−	0.797714i	$-0.706043\pi$
$257$	−19.3348	−1.20607	−0.603036	+	0.797714i	$0.706043\pi$
$258$	−10.7730	−0.670695
$259$	0	0
$260$	15.9377	0.988417
$261$	0.0255870	0.00158379
$262$	−5.66621	−0.350059
$263$	8.67930	0.535189	0.267594	−	0.963532i	$-0.413771\pi$
$263$	8.67930	0.535189	0.267594	+	0.963532i	$0.413771\pi$
$264$	6.41183	0.394621
$265$	23.9958	1.47405
$266$	0	0
$267$	7.56892	0.463210
$268$	14.4249	0.881143
$269$	−22.4793	−1.37059	−0.685294	−	0.728267i	$-0.740326\pi$
$269$	−22.4793	−1.37059	−0.685294	+	0.728267i	$0.740326\pi$
$270$	−12.6497	−0.769838
$271$	9.27100	0.563173	0.281587	−	0.959536i	$-0.409139\pi$
$271$	9.27100	0.563173	0.281587	+	0.959536i	$0.409139\pi$
$272$	−1.00000	−0.0606339
$273$	0	0
$274$	−18.1773	−1.09813
$275$	3.21079	0.193618
$276$	−10.2841	−0.619030
$277$	−12.3918	−0.744553	−0.372276	−	0.928122i	$-0.621423\pi$
$277$	−12.3918	−0.744553	−0.372276	+	0.928122i	$0.621423\pi$
$278$	−16.1143	−0.966471
$279$	0.318299	0.0190560
$280$	0	0
$281$	16.0479	0.957336	0.478668	−	0.877996i	$-0.341120\pi$
$281$	16.0479	0.957336	0.478668	+	0.877996i	$0.341120\pi$
$282$	−1.15746	−0.0689259
$283$	−6.94951	−0.413106	−0.206553	−	0.978435i	$-0.566225\pi$
$283$	−6.94951	−0.413106	−0.206553	+	0.978435i	$0.566225\pi$
$284$	9.69303	0.575175
$285$	−23.2817	−1.37909
$286$	24.5028	1.44888
$287$	0	0
$288$	−0.0331027	−0.00195059
$289$	1.00000	0.0588235
$290$	−1.87154	−0.109901
$291$	−13.0034	−0.762274
$292$	1.61550	0.0945398
$293$	0.0862108	0.00503649	0.00251825	−	0.999997i	$-0.499198\pi$
$293$	0.0862108	0.00503649	0.00251825	+	0.999997i	$0.499198\pi$
$294$	0	0
$295$	−24.9889	−1.45491
$296$	4.42127	0.256981
$297$	−19.4478	−1.12847
$298$	0.361124	0.0209194
$299$	−39.3006	−2.27281
$300$	1.48570	0.0857771
$301$	0	0
$302$	−14.2841	−0.821958
$303$	−21.3387	−1.22588
$304$	−5.58239	−0.320172
$305$	11.4420	0.655167
$306$	0.0331027	0.00189235
$307$	−21.1317	−1.20605	−0.603024	−	0.797723i	$-0.706038\pi$
$307$	−21.1317	−1.20605	−0.603024	+	0.797723i	$0.706038\pi$
$308$	0	0
$309$	7.06962	0.402177
$310$	−23.2817	−1.32231
$311$	−10.6399	−0.603335	−0.301667	−	0.953413i	$-0.597543\pi$
$311$	−10.6399	−0.603335	−0.301667	+	0.953413i	$0.597543\pi$
$312$	11.3380	0.641886
$313$	20.6634	1.16796	0.583981	−	0.811767i	$-0.301494\pi$
$313$	20.6634	1.16796	0.583981	+	0.811767i	$0.301494\pi$
$314$	5.13746	0.289923
$315$	0	0
$316$	4.56501	0.256802
$317$	−8.67394	−0.487177	−0.243588	−	0.969879i	$-0.578325\pi$
$317$	−8.67394	−0.487177	−0.243588	+	0.969879i	$0.578325\pi$
$318$	17.0704	0.957259
$319$	−2.87731	−0.161099
$320$	2.42127	0.135353
$321$	11.1940	0.624787
$322$	0	0
$323$	5.58239	0.310613
$324$	−8.89960	−0.494422
$325$	5.67760	0.314937
$326$	1.61550	0.0894740
$327$	10.9406	0.605016
$328$	−5.61550	−0.310064
$329$	0	0
$330$	15.5248	0.854611
$331$	5.68675	0.312572	0.156286	−	0.987712i	$-0.450048\pi$
$331$	5.68675	0.312572	0.156286	+	0.987712i	$0.450048\pi$
$332$	10.3222	0.566507
$333$	−0.146356	−0.00802025
$334$	−0.477531	−0.0261293
$335$	34.9266	1.90825
$336$	0	0
$337$	14.9972	0.816947	0.408474	−	0.912770i	$-0.366061\pi$
$337$	14.9972	0.816947	0.408474	+	0.912770i	$0.366061\pi$
$338$	30.3279	1.64962
$339$	8.34112	0.453027
$340$	−2.42127	−0.131312
$341$	−35.7934	−1.93832
$342$	0.184792	0.00999242
$343$	0	0
$344$	−6.25437	−0.337213
$345$	−24.9006	−1.34060
$346$	6.79423	0.365260
$347$	25.6006	1.37431	0.687155	−	0.726510i	$-0.258859\pi$
$347$	25.6006	1.37431	0.687155	+	0.726510i	$0.258859\pi$
$348$	−1.33140	−0.0713703
$349$	8.72225	0.466891	0.233446	−	0.972370i	$-0.425000\pi$
$349$	8.72225	0.466891	0.233446	+	0.972370i	$0.425000\pi$
$350$	0	0
$351$	−34.3892	−1.83556
$352$	3.72247	0.198408
$353$	27.4938	1.46335	0.731674	−	0.681654i	$-0.238739\pi$
$353$	27.4938	1.46335	0.731674	+	0.681654i	$0.238739\pi$
$354$	−17.7769	−0.944830
$355$	23.4694	1.24563
$356$	4.39423	0.232894
$357$	0	0
$358$	−7.48141	−0.395405
$359$	−14.3958	−0.759780	−0.379890	−	0.925032i	$-0.624038\pi$
$359$	−14.3958	−0.759780	−0.379890	+	0.925032i	$0.624038\pi$
$360$	−0.0801505	−0.00422430
$361$	12.1631	0.640164
$362$	−6.91931	−0.363671
$363$	4.92070	0.258270
$364$	0	0
$365$	3.91155	0.204740
$366$	8.13974	0.425471
$367$	−13.0839	−0.682973	−0.341486	−	0.939887i	$-0.610930\pi$
$367$	−13.0839	−0.682973	−0.341486	+	0.939887i	$0.610930\pi$
$368$	−5.97056	−0.311237
$369$	0.185888	0.00967694
$370$	10.7051	0.556531
$371$	0	0
$372$	−16.5624	−0.858720
$373$	28.8202	1.49225	0.746126	−	0.665805i	$-0.231912\pi$
$373$	28.8202	1.49225	0.746126	+	0.665805i	$0.231912\pi$
$374$	−3.72247	−0.192484
$375$	−17.2555	−0.891071
$376$	−0.671979	−0.0346547
$377$	−5.08791	−0.262041
$378$	0	0
$379$	−25.8274	−1.32666	−0.663332	−	0.748325i	$-0.730858\pi$
$379$	−25.8274	−1.32666	−0.663332	+	0.748325i	$0.730858\pi$
$380$	−13.5165	−0.693381
$381$	−16.3885	−0.839606
$382$	4.82029	0.246628
$383$	1.61887	0.0827204	0.0413602	−	0.999144i	$-0.486831\pi$
$383$	1.61887	0.0827204	0.0413602	+	0.999144i	$0.486831\pi$
$384$	1.72247	0.0878993
$385$	0	0
$386$	1.17633	0.0598737
$387$	0.207036	0.0105243
$388$	−7.54929	−0.383257
$389$	−22.2486	−1.12805	−0.564024	−	0.825758i	$-0.690748\pi$
$389$	−22.2486	−1.12805	−0.564024	+	0.825758i	$0.690748\pi$
$390$	27.4523	1.39010
$391$	5.97056	0.301944
$392$	0	0
$393$	−9.75986	−0.492320
$394$	4.37393	0.220356
$395$	11.0531	0.556142
$396$	−0.123224	−0.00619222
$397$	−25.5827	−1.28396	−0.641979	−	0.766722i	$-0.721886\pi$
$397$	−25.5827	−1.28396	−0.641979	+	0.766722i	$0.721886\pi$
$398$	23.9298	1.19949
$399$	0	0
$400$	0.862543	0.0431272
$401$	8.06621	0.402807	0.201404	−	0.979508i	$-0.435450\pi$
$401$	8.06621	0.402807	0.201404	+	0.979508i	$0.435450\pi$
$402$	24.8465	1.23923
$403$	−63.2930	−3.15285
$404$	−12.3885	−0.616349
$405$	−21.5483	−1.07074
$406$	0	0
$407$	16.4580	0.815794
$408$	−1.72247	−0.0852749
$409$	−7.15970	−0.354024	−0.177012	−	0.984209i	$-0.556643\pi$
$409$	−7.15970	−0.354024	−0.177012	+	0.984209i	$0.556643\pi$
$410$	−13.5966	−0.671490
$411$	−31.3099	−1.54440
$412$	4.10435	0.202207
$413$	0	0
$414$	0.197641	0.00971355
$415$	24.9929	1.22686
$416$	6.58239	0.322728
$417$	−27.7564	−1.35924
$418$	−20.7803	−1.01640
$419$	8.56501	0.418428	0.209214	−	0.977870i	$-0.432909\pi$
$419$	8.56501	0.418428	0.209214	+	0.977870i	$0.432909\pi$
$420$	0	0
$421$	9.98508	0.486643	0.243322	−	0.969946i	$-0.421763\pi$
$421$	9.98508	0.486643	0.243322	+	0.969946i	$0.421763\pi$
$422$	−9.56479	−0.465606
$423$	0.0222443	0.00108155
$424$	9.91041	0.481292
$425$	−0.862543	−0.0418395
$426$	16.6959	0.808921
$427$	0	0
$428$	6.49880	0.314131
$429$	42.2052	2.03769
$430$	−15.1435	−0.730285
$431$	14.2258	0.685235	0.342617	−	0.939475i	$-0.388687\pi$
$431$	14.2258	0.685235	0.342617	+	0.939475i	$0.388687\pi$
$432$	−5.22442	−0.251360
$433$	7.58763	0.364638	0.182319	−	0.983239i	$-0.441640\pi$
$433$	7.58763	0.364638	0.182319	+	0.983239i	$0.441640\pi$
$434$	0	0
$435$	−3.22367	−0.154563
$436$	6.35169	0.304191
$437$	33.3300	1.59439
$438$	2.78264	0.132960
$439$	12.4882	0.596031	0.298015	−	0.954561i	$-0.403675\pi$
$439$	12.4882	0.596031	0.298015	+	0.954561i	$0.403675\pi$
$440$	9.01310	0.429683
$441$	0	0
$442$	−6.58239	−0.313093
$443$	31.3496	1.48946	0.744732	−	0.667364i	$-0.232577\pi$
$443$	31.3496	1.48946	0.744732	+	0.667364i	$0.232577\pi$
$444$	7.61550	0.361415
$445$	10.6396	0.504366
$446$	12.2338	0.579289
$447$	0.622025	0.0294208
$448$	0	0
$449$	26.3918	1.24551	0.622754	−	0.782418i	$-0.286014\pi$
$449$	26.3918	1.24551	0.622754	+	0.782418i	$0.286014\pi$
$450$	−0.0285525	−0.00134598
$451$	−20.9035	−0.984308
$452$	4.84254	0.227774
$453$	−24.6039	−1.15599
$454$	5.92780	0.278206
$455$	0	0
$456$	−9.61550	−0.450287
$457$	−24.2177	−1.13286	−0.566429	−	0.824111i	$-0.691675\pi$
$457$	−24.2177	−1.13286	−0.566429	+	0.824111i	$0.691675\pi$
$458$	18.8932	0.882824
$459$	5.22442	0.243855
$460$	−14.4563	−0.674030
$461$	−20.3684	−0.948653	−0.474327	−	0.880349i	$-0.657308\pi$
$461$	−20.3684	−0.948653	−0.474327	+	0.880349i	$0.657308\pi$
$462$	0	0
$463$	−10.7382	−0.499044	−0.249522	−	0.968369i	$-0.580274\pi$
$463$	−10.7382	−0.499044	−0.249522	+	0.968369i	$0.580274\pi$
$464$	−0.772958	−0.0358837
$465$	−40.1020	−1.85969
$466$	23.3039	1.07953
$467$	−1.30748	−0.0605030	−0.0302515	−	0.999542i	$-0.509631\pi$
$467$	−1.30748	−0.0605030	−0.0302515	+	0.999542i	$0.509631\pi$
$468$	−0.217895	−0.0100722
$469$	0	0
$470$	−1.62704	−0.0750498
$471$	8.84911	0.407745
$472$	−10.3206	−0.475043
$473$	−23.2817	−1.07049
$474$	7.86308	0.361163
$475$	−4.81506	−0.220930
$476$	0	0
$477$	−0.328061	−0.0150209
$478$	−19.6228	−0.897527
$479$	17.9198	0.818779	0.409389	−	0.912360i	$-0.365742\pi$
$479$	17.9198	0.818779	0.409389	+	0.912360i	$0.365742\pi$
$480$	4.17056	0.190359
$481$	29.1025	1.32696
$482$	−6.70338	−0.305331
$483$	0	0
$484$	2.85677	0.129853
$485$	−18.2789	−0.830000
$486$	0.343997	0.0156040
$487$	8.03415	0.364062	0.182031	−	0.983293i	$-0.441733\pi$
$487$	8.03415	0.364062	0.182031	+	0.983293i	$0.441733\pi$
$488$	4.72562	0.213919
$489$	2.78264	0.125835
$490$	0	0
$491$	29.9897	1.35342	0.676708	−	0.736251i	$-0.263406\pi$
$491$	29.9897	1.35342	0.676708	+	0.736251i	$0.263406\pi$
$492$	−9.67251	−0.436071
$493$	0.772958	0.0348123
$494$	−36.7455	−1.65326
$495$	−0.298358	−0.0134102
$496$	−9.61550	−0.431749
$497$	0	0
$498$	17.7797	0.796730
$499$	−23.6236	−1.05754	−0.528768	−	0.848766i	$-0.677346\pi$
$499$	−23.6236	−1.05754	−0.528768	+	0.848766i	$0.677346\pi$
$500$	−10.0179	−0.448014
$501$	−0.822532	−0.0367480
$502$	0.983528	0.0438970
$503$	−18.4187	−0.821247	−0.410624	−	0.911805i	$-0.634689\pi$
$503$	−18.4187	−0.821247	−0.410624	+	0.911805i	$0.634689\pi$
$504$	0	0
$505$	−29.9958	−1.33479
$506$	−22.2252	−0.988032
$507$	52.2389	2.32001
$508$	−9.51452	−0.422138
$509$	30.3924	1.34712	0.673560	−	0.739133i	$-0.264764\pi$
$509$	30.3924	1.34712	0.673560	+	0.739133i	$0.264764\pi$
$510$	−4.17056	−0.184675
$511$	0	0
$512$	1.00000	0.0441942
$513$	29.1648	1.28766
$514$	−19.3348	−0.852822
$515$	9.93774	0.437909
$516$	−10.7730	−0.474253
$517$	−2.50142	−0.110012
$518$	0	0
$519$	11.7028	0.513698
$520$	15.9377	0.698916
$521$	−23.9532	−1.04941	−0.524705	−	0.851284i	$-0.675824\pi$
$521$	−23.9532	−1.04941	−0.524705	+	0.851284i	$0.675824\pi$
$522$	0.0255870	0.00111991
$523$	−20.4358	−0.893595	−0.446797	−	0.894635i	$-0.647435\pi$
$523$	−20.4358	−0.893595	−0.446797	+	0.894635i	$0.647435\pi$
$524$	−5.66621	−0.247529
$525$	0	0
$526$	8.67930	0.378436
$527$	9.61550	0.418858
$528$	6.41183	0.279039
$529$	12.6476	0.549895
$530$	23.9958	1.04231
$531$	0.341639	0.0148259
$532$	0	0
$533$	−36.9634	−1.60106
$534$	7.56892	0.327539
$535$	15.7353	0.680298
$536$	14.4249	0.623062
$537$	−12.8865	−0.556093
$538$	−22.4793	−0.969152
$539$	0	0
$540$	−12.6497	−0.544358
$541$	−41.3011	−1.77568	−0.887838	−	0.460157i	$-0.847793\pi$
$541$	−41.3011	−1.77568	−0.887838	+	0.460157i	$0.847793\pi$
$542$	9.27100	0.398224
$543$	−11.9183	−0.511463
$544$	−1.00000	−0.0428746
$545$	15.3791	0.658770
$546$	0	0
$547$	41.2956	1.76567	0.882836	−	0.469681i	$-0.155631\pi$
$547$	41.2956	1.76567	0.882836	+	0.469681i	$0.155631\pi$
$548$	−18.1773	−0.776498
$549$	−0.156431	−0.00667630
$550$	3.21079	0.136909
$551$	4.31496	0.183823
$552$	−10.2841	−0.437720
$553$	0	0
$554$	−12.3918	−0.526478
$555$	18.4392	0.782699
$556$	−16.1143	−0.683398
$557$	28.6452	1.21374	0.606869	−	0.794802i	$-0.292425\pi$
$557$	28.6452	1.21374	0.606869	+	0.794802i	$0.292425\pi$
$558$	0.318299	0.0134747
$559$	−41.1687	−1.74125
$560$	0	0
$561$	−6.41183	−0.270708
$562$	16.0479	0.676939
$563$	−7.90758	−0.333265	−0.166632	−	0.986019i	$-0.553289\pi$
$563$	−7.90758	−0.333265	−0.166632	+	0.986019i	$0.553289\pi$
$564$	−1.15746	−0.0487379
$565$	11.7251	0.493278
$566$	−6.94951	−0.292110
$567$	0	0
$568$	9.69303	0.406710
$569$	33.4146	1.40081	0.700407	−	0.713743i	$-0.253002\pi$
$569$	33.4146	1.40081	0.700407	+	0.713743i	$0.253002\pi$
$570$	−23.2817	−0.975163
$571$	−27.4682	−1.14951	−0.574754	−	0.818326i	$-0.694902\pi$
$571$	−27.4682	−1.14951	−0.574754	+	0.818326i	$0.694902\pi$
$572$	24.5028	1.02451
$573$	8.30280	0.346855
$574$	0	0
$575$	−5.14987	−0.214764
$576$	−0.0331027	−0.00137928
$577$	18.2568	0.760039	0.380020	−	0.924978i	$-0.375917\pi$
$577$	18.2568	0.760039	0.380020	+	0.924978i	$0.375917\pi$
$578$	1.00000	0.0415945
$579$	2.02619	0.0842058
$580$	−1.87154	−0.0777114
$581$	0	0
$582$	−13.0034	−0.539009
$583$	36.8912	1.52788
$584$	1.61550	0.0668497
$585$	−0.527582	−0.0218128
$586$	0.0862108	0.00356134
$587$	−10.7176	−0.442364	−0.221182	−	0.975232i	$-0.570992\pi$
$587$	−10.7176	−0.442364	−0.221182	+	0.975232i	$0.570992\pi$
$588$	0	0
$589$	53.6775	2.21174
$590$	−24.9889	−1.02878
$591$	7.53396	0.309906
$592$	4.42127	0.181713
$593$	−24.1927	−0.993473	−0.496737	−	0.867901i	$-0.665468\pi$
$593$	−24.1927	−0.993473	−0.496737	+	0.867901i	$0.665468\pi$
$594$	−19.4478	−0.797951
$595$	0	0
$596$	0.361124	0.0147922
$597$	41.2183	1.68695
$598$	−39.3006	−1.60712
$599$	27.7653	1.13446	0.567230	−	0.823559i	$-0.308015\pi$
$599$	27.7653	1.13446	0.567230	+	0.823559i	$0.308015\pi$
$600$	1.48570	0.0606536
$601$	43.5383	1.77597	0.887983	−	0.459877i	$-0.152107\pi$
$601$	43.5383	1.77597	0.887983	+	0.459877i	$0.152107\pi$
$602$	0	0
$603$	−0.477504	−0.0194455
$604$	−14.2841	−0.581212
$605$	6.91701	0.281216
$606$	−21.3387	−0.866826
$607$	4.91568	0.199521	0.0997606	−	0.995011i	$-0.468192\pi$
$607$	4.91568	0.199521	0.0997606	+	0.995011i	$0.468192\pi$
$608$	−5.58239	−0.226396
$609$	0	0
$610$	11.4420	0.463273
$611$	−4.42323	−0.178945
$612$	0.0331027	0.00133810
$613$	48.0420	1.94040	0.970199	−	0.242311i	$-0.0779054\pi$
$613$	48.0420	1.94040	0.970199	+	0.242311i	$0.0779054\pi$
$614$	−21.1317	−0.852805
$615$	−23.4198	−0.944376
$616$	0	0
$617$	−8.21941	−0.330901	−0.165450	−	0.986218i	$-0.552908\pi$
$617$	−8.21941	−0.330901	−0.165450	+	0.986218i	$0.552908\pi$
$618$	7.06962	0.284382
$619$	−31.7771	−1.27723	−0.638615	−	0.769526i	$-0.720492\pi$
$619$	−31.7771	−1.27723	−0.638615	+	0.769526i	$0.720492\pi$
$620$	−23.2817	−0.935016
$621$	31.1927	1.25172
$622$	−10.6399	−0.426622
$623$	0	0
$624$	11.3380	0.453882
$625$	−28.5687	−1.14275
$626$	20.6634	0.825874
$627$	−35.7934	−1.42945
$628$	5.13746	0.205007
$629$	−4.42127	−0.176288
$630$	0	0
$631$	−28.2493	−1.12459	−0.562294	−	0.826937i	$-0.690081\pi$
$631$	−28.2493	−1.12459	−0.562294	+	0.826937i	$0.690081\pi$
$632$	4.56501	0.181586
$633$	−16.4750	−0.654824
$634$	−8.67394	−0.344486
$635$	−23.0372	−0.914204
$636$	17.0704	0.676884
$637$	0	0
$638$	−2.87731	−0.113914
$639$	−0.320865	−0.0126932
$640$	2.42127	0.0957091
$641$	13.0986	0.517363	0.258681	−	0.965963i	$-0.416712\pi$
$641$	13.0986	0.517363	0.258681	+	0.965963i	$0.416712\pi$
$642$	11.1940	0.441791
$643$	−19.3602	−0.763492	−0.381746	−	0.924267i	$-0.624677\pi$
$643$	−19.3602	−0.763492	−0.381746	+	0.924267i	$0.624677\pi$
$644$	0	0
$645$	−26.0842	−1.02707
$646$	5.58239	0.219636
$647$	33.6262	1.32198	0.660991	−	0.750394i	$-0.270136\pi$
$647$	33.6262	1.32198	0.660991	+	0.750394i	$0.270136\pi$
$648$	−8.89960	−0.349609
$649$	−38.4180	−1.50804
$650$	5.67760	0.222694
$651$	0	0
$652$	1.61550	0.0632677
$653$	−23.5605	−0.921992	−0.460996	−	0.887402i	$-0.652508\pi$
$653$	−23.5605	−0.921992	−0.460996	+	0.887402i	$0.652508\pi$
$654$	10.9406	0.427811
$655$	−13.7194	−0.536062
$656$	−5.61550	−0.219248
$657$	−0.0534772	−0.00208635
$658$	0	0
$659$	−10.7974	−0.420609	−0.210304	−	0.977636i	$-0.567446\pi$
$659$	−10.7974	−0.420609	−0.210304	+	0.977636i	$0.567446\pi$
$660$	15.5248	0.604301
$661$	11.0290	0.428978	0.214489	−	0.976726i	$-0.431191\pi$
$661$	11.0290	0.428978	0.214489	+	0.976726i	$0.431191\pi$
$662$	5.68675	0.221022
$663$	−11.3380	−0.440330
$664$	10.3222	0.400581
$665$	0	0
$666$	−0.146356	−0.00567117
$667$	4.61499	0.178693
$668$	−0.477531	−0.0184762
$669$	21.0724	0.814706
$670$	34.9266	1.34933
$671$	17.5910	0.679092
$672$	0	0
$673$	−46.4316	−1.78981	−0.894903	−	0.446260i	$-0.852756\pi$
$673$	−46.4316	−1.78981	−0.894903	+	0.446260i	$0.852756\pi$
$674$	14.9972	0.577669
$675$	−4.50629	−0.173447
$676$	30.3279	1.16646
$677$	−21.7653	−0.836509	−0.418255	−	0.908330i	$-0.637358\pi$
$677$	−21.7653	−0.836509	−0.418255	+	0.908330i	$0.637358\pi$
$678$	8.34112	0.320339
$679$	0	0
$680$	−2.42127	−0.0928514
$681$	10.2105	0.391265
$682$	−35.7934	−1.37060
$683$	18.8776	0.722330	0.361165	−	0.932502i	$-0.382379\pi$
$683$	18.8776	0.722330	0.361165	+	0.932502i	$0.382379\pi$
$684$	0.184792	0.00706570
$685$	−44.0122	−1.68162
$686$	0	0
$687$	32.5430	1.24159
$688$	−6.25437	−0.238446
$689$	65.2342	2.48523
$690$	−24.9006	−0.947949
$691$	−7.74396	−0.294594	−0.147297	−	0.989092i	$-0.547057\pi$
$691$	−7.74396	−0.294594	−0.147297	+	0.989092i	$0.547057\pi$
$692$	6.79423	0.258278
$693$	0	0
$694$	25.6006	0.971785
$695$	−39.0170	−1.48000
$696$	−1.33140	−0.0504664
$697$	5.61550	0.212702
$698$	8.72225	0.330142
$699$	40.1403	1.51825
$700$	0	0
$701$	37.0878	1.40079	0.700393	−	0.713758i	$-0.253008\pi$
$701$	37.0878	1.40079	0.700393	+	0.713758i	$0.253008\pi$
$702$	−34.3892	−1.29794
$703$	−24.6813	−0.930871
$704$	3.72247	0.140296
$705$	−2.80253	−0.105549
$706$	27.4938	1.03474
$707$	0	0
$708$	−17.7769	−0.668096
$709$	−38.9224	−1.46176	−0.730881	−	0.682505i	$-0.760891\pi$
$709$	−38.9224	−1.46176	−0.730881	+	0.682505i	$0.760891\pi$
$710$	23.4694	0.880792
$711$	−0.151114	−0.00566721
$712$	4.39423	0.164681
$713$	57.4099	2.15002
$714$	0	0
$715$	59.3278	2.21873
$716$	−7.48141	−0.279594
$717$	−33.7997	−1.26227
$718$	−14.3958	−0.537246
$719$	−16.9061	−0.630492	−0.315246	−	0.949010i	$-0.602087\pi$
$719$	−16.9061	−0.630492	−0.315246	+	0.949010i	$0.602087\pi$
$720$	−0.0801505	−0.00298703
$721$	0	0
$722$	12.1631	0.452664
$723$	−11.5464	−0.429414
$724$	−6.91931	−0.257154
$725$	−0.666710	−0.0247610
$726$	4.92070	0.182624
$727$	−9.55267	−0.354289	−0.177144	−	0.984185i	$-0.556686\pi$
$727$	−9.55267	−0.354289	−0.177144	+	0.984185i	$0.556686\pi$
$728$	0	0
$729$	27.2913	1.01079
$730$	3.91155	0.144773
$731$	6.25437	0.231326
$732$	8.13974	0.300853
$733$	−26.2704	−0.970319	−0.485160	−	0.874426i	$-0.661239\pi$
$733$	−26.2704	−0.970319	−0.485160	+	0.874426i	$0.661239\pi$
$734$	−13.0839	−0.482935
$735$	0	0
$736$	−5.97056	−0.220078
$737$	53.6964	1.97793
$738$	0.185888	0.00684263
$739$	16.3172	0.600238	0.300119	−	0.953902i	$-0.402974\pi$
$739$	16.3172	0.600238	0.300119	+	0.953902i	$0.402974\pi$
$740$	10.7051	0.393527
$741$	−63.2930	−2.32513
$742$	0	0
$743$	45.3294	1.66297	0.831486	−	0.555545i	$-0.187490\pi$
$743$	45.3294	1.66297	0.831486	+	0.555545i	$0.187490\pi$
$744$	−16.5624	−0.607207
$745$	0.874378	0.0320347
$746$	28.8202	1.05518
$747$	−0.341694	−0.0125019
$748$	−3.72247	−0.136107
$749$	0	0
$750$	−17.2555	−0.630082
$751$	−10.5664	−0.385573	−0.192787	−	0.981241i	$-0.561752\pi$
$751$	−10.5664	−0.385573	−0.192787	+	0.981241i	$0.561752\pi$
$752$	−0.671979	−0.0245045
$753$	1.69410	0.0617363
$754$	−5.08791	−0.185291
$755$	−34.5856	−1.25870
$756$	0	0
$757$	36.3965	1.32285	0.661427	−	0.750010i	$-0.269951\pi$
$757$	36.3965	1.32285	0.661427	+	0.750010i	$0.269951\pi$
$758$	−25.8274	−0.938093
$759$	−38.2822	−1.38956
$760$	−13.5165	−0.490294
$761$	50.6461	1.83592	0.917960	−	0.396674i	$-0.129836\pi$
$761$	50.6461	1.83592	0.917960	+	0.396674i	$0.129836\pi$
$762$	−16.3885	−0.593691
$763$	0	0
$764$	4.82029	0.174392
$765$	0.0801505	0.00289785
$766$	1.61887	0.0584922
$767$	−67.9341	−2.45296
$768$	1.72247	0.0621542
$769$	−17.6097	−0.635023	−0.317511	−	0.948254i	$-0.602847\pi$
$769$	−17.6097	−0.635023	−0.317511	+	0.948254i	$0.602847\pi$
$770$	0	0
$771$	−33.3036	−1.19940
$772$	1.17633	0.0423371
$773$	3.31956	0.119396	0.0596982	−	0.998216i	$-0.480986\pi$
$773$	3.31956	0.119396	0.0596982	+	0.998216i	$0.480986\pi$
$774$	0.207036	0.00744177
$775$	−8.29378	−0.297921
$776$	−7.54929	−0.271004
$777$	0	0
$778$	−22.2486	−0.797651
$779$	31.3479	1.12316
$780$	27.4523	0.982949
$781$	36.0820	1.29112
$782$	5.97056	0.213507
$783$	4.03826	0.144316
$784$	0	0
$785$	12.4392	0.443973
$786$	−9.75986	−0.348123
$787$	3.22029	0.114791	0.0573955	−	0.998352i	$-0.481720\pi$
$787$	3.22029	0.114791	0.0573955	+	0.998352i	$0.481720\pi$
$788$	4.37393	0.155815
$789$	14.9498	0.532228
$790$	11.0531	0.393252
$791$	0	0
$792$	−0.123224	−0.00437856
$793$	31.1059	1.10460
$794$	−25.5827	−0.907895
$795$	41.3320	1.46589
$796$	23.9298	0.848169
$797$	1.39748	0.0495013	0.0247507	−	0.999694i	$-0.492121\pi$
$797$	1.39748	0.0495013	0.0247507	+	0.999694i	$0.492121\pi$
$798$	0	0
$799$	0.671979	0.0237729
$800$	0.862543	0.0304955
$801$	−0.145461	−0.00513960
$802$	8.06621	0.284828
$803$	6.01363	0.212216
$804$	24.8465	0.876268
$805$	0	0
$806$	−63.2930	−2.22940
$807$	−38.7199	−1.36300
$808$	−12.3885	−0.435824
$809$	48.5538	1.70706	0.853530	−	0.521044i	$-0.174457\pi$
$809$	48.5538	1.70706	0.853530	+	0.521044i	$0.174457\pi$
$810$	−21.5483	−0.757131
$811$	56.4439	1.98201	0.991006	−	0.133816i	$-0.0427232\pi$
$811$	56.4439	1.98201	0.991006	+	0.133816i	$0.0427232\pi$
$812$	0	0
$813$	15.9690	0.560058
$814$	16.4580	0.576854
$815$	3.91155	0.137016
$816$	−1.72247	−0.0602985
$817$	34.9144	1.22150
$818$	−7.15970	−0.250333
$819$	0	0
$820$	−13.5966	−0.474815
$821$	4.89422	0.170810	0.0854048	−	0.996346i	$-0.472782\pi$
$821$	4.89422	0.170810	0.0854048	+	0.996346i	$0.472782\pi$
$822$	−31.3099	−1.09206
$823$	−15.7036	−0.547393	−0.273697	−	0.961816i	$-0.588246\pi$
$823$	−15.7036	−0.547393	−0.273697	+	0.961816i	$0.588246\pi$
$824$	4.10435	0.142982
$825$	5.53049	0.192547
$826$	0	0
$827$	0.125810	0.00437485	0.00218743	−	0.999998i	$-0.499304\pi$
$827$	0.125810	0.00437485	0.00218743	+	0.999998i	$0.499304\pi$
$828$	0.197641	0.00686852
$829$	−36.9028	−1.28169	−0.640844	−	0.767671i	$-0.721415\pi$
$829$	−36.9028	−1.28169	−0.640844	+	0.767671i	$0.721415\pi$
$830$	24.9929	0.867518
$831$	−21.3445	−0.740434
$832$	6.58239	0.228203
$833$	0	0
$834$	−27.7564	−0.961124
$835$	−1.15623	−0.0400130
$836$	−20.7803	−0.718701
$837$	50.2354	1.73639
$838$	8.56501	0.295873
$839$	−19.4435	−0.671265	−0.335632	−	0.941993i	$-0.608950\pi$
$839$	−19.4435	−0.671265	−0.335632	+	0.941993i	$0.608950\pi$
$840$	0	0
$841$	−28.4025	−0.979398
$842$	9.98508	0.344109
$843$	27.6420	0.952039
$844$	−9.56479	−0.329234
$845$	73.4320	2.52614
$846$	0.0222443	0.000764775 0
$847$	0	0
$848$	9.91041	0.340325
$849$	−11.9703	−0.410820
$850$	−0.862543	−0.0295850
$851$	−26.3975	−0.904893
$852$	16.6959	0.571993
$853$	−6.78450	−0.232297	−0.116148	−	0.993232i	$-0.537055\pi$
$853$	−6.78450	−0.232297	−0.116148	+	0.993232i	$0.537055\pi$
$854$	0	0
$855$	0.447432	0.0153018
$856$	6.49880	0.222124
$857$	26.7547	0.913923	0.456961	−	0.889486i	$-0.348938\pi$
$857$	26.7547	0.913923	0.456961	+	0.889486i	$0.348938\pi$
$858$	42.2052	1.44086
$859$	42.9418	1.46516	0.732578	−	0.680683i	$-0.238317\pi$
$859$	42.9418	1.46516	0.732578	+	0.680683i	$0.238317\pi$
$860$	−15.1435	−0.516390
$861$	0	0
$862$	14.2258	0.484534
$863$	29.3141	0.997864	0.498932	−	0.866641i	$-0.333726\pi$
$863$	29.3141	0.997864	0.498932	+	0.866641i	$0.333726\pi$
$864$	−5.22442	−0.177738
$865$	16.4507	0.559339
$866$	7.58763	0.257838
$867$	1.72247	0.0584981
$868$	0	0
$869$	16.9931	0.576451
$870$	−3.22367	−0.109293
$871$	94.9506	3.21728
$872$	6.35169	0.215095
$873$	0.249902	0.00845789
$874$	33.3300	1.12740
$875$	0	0
$876$	2.78264	0.0940167
$877$	−34.8243	−1.17593	−0.587966	−	0.808886i	$-0.700071\pi$
$877$	−34.8243	−1.17593	−0.587966	+	0.808886i	$0.700071\pi$
$878$	12.4882	0.421457
$879$	0.148495	0.00500863
$880$	9.01310	0.303831
$881$	−33.4518	−1.12702	−0.563510	−	0.826109i	$-0.690549\pi$
$881$	−33.4518	−1.12702	−0.563510	+	0.826109i	$0.690549\pi$
$882$	0	0
$883$	−43.4476	−1.46213	−0.731064	−	0.682309i	$-0.760976\pi$
$883$	−43.4476	−1.46213	−0.731064	+	0.682309i	$0.760976\pi$
$884$	−6.58239	−0.221390
$885$	−43.0426	−1.44686
$886$	31.3496	1.05321
$887$	6.69786	0.224892	0.112446	−	0.993658i	$-0.464131\pi$
$887$	6.69786	0.224892	0.112446	+	0.993658i	$0.464131\pi$
$888$	7.61550	0.255559
$889$	0	0
$890$	10.6396	0.356640
$891$	−33.1285	−1.10985
$892$	12.2338	0.409619
$893$	3.75125	0.125531
$894$	0.622025	0.0208036
$895$	−18.1145	−0.605501
$896$	0	0
$897$	−67.6940	−2.26024
$898$	26.3918	0.880707
$899$	7.43238	0.247884
$900$	−0.0285525	−0.000951750 0
$901$	−9.91041	−0.330164
$902$	−20.9035	−0.696011
$903$	0	0
$904$	4.84254	0.161060
$905$	−16.7535	−0.556906
$906$	−24.6039	−0.817410
$907$	4.11297	0.136569	0.0682844	−	0.997666i	$-0.478247\pi$
$907$	4.11297	0.136569	0.0682844	+	0.997666i	$0.478247\pi$
$908$	5.92780	0.196721
$909$	0.410091	0.0136019
$910$	0	0
$911$	−24.3957	−0.808264	−0.404132	−	0.914701i	$-0.632426\pi$
$911$	−24.3957	−0.808264	−0.404132	+	0.914701i	$0.632426\pi$
$912$	−9.61550	−0.318401
$913$	38.4242	1.27166
$914$	−24.2177	−0.801051
$915$	19.7085	0.651543
$916$	18.8932	0.624250
$917$	0	0
$918$	5.22442	0.172432
$919$	−28.5117	−0.940513	−0.470257	−	0.882530i	$-0.655839\pi$
$919$	−28.5117	−0.940513	−0.470257	+	0.882530i	$0.655839\pi$
$920$	−14.4563	−0.476611
$921$	−36.3987	−1.19938
$922$	−20.3684	−0.670799
$923$	63.8033	2.10011
$924$	0	0
$925$	3.81354	0.125388
$926$	−10.7382	−0.352878
$927$	−0.135865	−0.00446240
$928$	−0.772958	−0.0253736
$929$	38.0152	1.24724	0.623620	−	0.781728i	$-0.285661\pi$
$929$	38.0152	1.24724	0.623620	+	0.781728i	$0.285661\pi$
$930$	−40.1020	−1.31500
$931$	0	0
$932$	23.3039	0.763346
$933$	−18.3269	−0.599997
$934$	−1.30748	−0.0427821
$935$	−9.01310	−0.294760
$936$	−0.217895	−0.00712212
$937$	−26.1085	−0.852927	−0.426464	−	0.904505i	$-0.640241\pi$
$937$	−26.1085	−0.852927	−0.426464	+	0.904505i	$0.640241\pi$
$938$	0	0
$939$	35.5920	1.16150
$940$	−1.62704	−0.0530682
$941$	−24.4179	−0.796001	−0.398000	−	0.917385i	$-0.630296\pi$
$941$	−24.4179	−0.796001	−0.398000	+	0.917385i	$0.630296\pi$
$942$	8.84911	0.288319
$943$	33.5277	1.09181
$944$	−10.3206	−0.335906
$945$	0	0
$946$	−23.2817	−0.756953
$947$	15.6506	0.508576	0.254288	−	0.967129i	$-0.418159\pi$
$947$	15.6506	0.508576	0.254288	+	0.967129i	$0.418159\pi$
$948$	7.86308	0.255381
$949$	10.6338	0.345189
$950$	−4.81506	−0.156221
$951$	−14.9406	−0.484482
$952$	0	0
$953$	49.6977	1.60987	0.804933	−	0.593366i	$-0.202201\pi$
$953$	49.6977	1.60987	0.804933	+	0.593366i	$0.202201\pi$
$954$	−0.328061	−0.0106214
$955$	11.6712	0.377672
$956$	−19.6228	−0.634647
$957$	−4.95608	−0.160207
$958$	17.9198	0.578964
$959$	0	0
$960$	4.17056	0.134604
$961$	61.4578	1.98251
$962$	29.1025	0.938303
$963$	−0.215128	−0.00693239
$964$	−6.70338	−0.215901
$965$	2.84822	0.0916873
$966$	0	0
$967$	−23.2765	−0.748521	−0.374260	−	0.927324i	$-0.622103\pi$
$967$	−23.2765	−0.748521	−0.374260	+	0.927324i	$0.622103\pi$
$968$	2.85677	0.0918201
$969$	9.61550	0.308894
$970$	−18.2789	−0.586899
$971$	−42.9492	−1.37830	−0.689152	−	0.724617i	$-0.742017\pi$
$971$	−42.9492	−1.37830	−0.689152	+	0.724617i	$0.742017\pi$
$972$	0.343997	0.0110337
$973$	0	0
$974$	8.03415	0.257431
$975$	9.77949	0.313194
$976$	4.72562	0.151263
$977$	−19.4124	−0.621058	−0.310529	−	0.950564i	$-0.600506\pi$
$977$	−19.4124	−0.621058	−0.310529	+	0.950564i	$0.600506\pi$
$978$	2.78264	0.0889790
$979$	16.3574	0.522784
$980$	0	0
$981$	−0.210258	−0.00671302
$982$	29.9897	0.957010
$983$	−1.75400	−0.0559438	−0.0279719	−	0.999609i	$-0.508905\pi$
$983$	−1.75400	−0.0559438	−0.0279719	+	0.999609i	$0.508905\pi$
$984$	−9.67251	−0.308348
$985$	10.5905	0.337440
$986$	0.772958	0.0246160
$987$	0	0
$988$	−36.7455	−1.16903
$989$	37.3421	1.18741
$990$	−0.298358	−0.00948243
$991$	0.131751	0.00418522	0.00209261	−	0.999998i	$-0.499334\pi$
$991$	0.131751	0.00418522	0.00209261	+	0.999998i	$0.499334\pi$
$992$	−9.61550	−0.305292
$993$	9.79524	0.310843
$994$	0	0
$995$	57.9405	1.83684
$996$	17.7797	0.563373
$997$	−24.0735	−0.762415	−0.381208	−	0.924489i	$-0.624492\pi$
$997$	−24.0735	−0.762415	−0.381208	+	0.924489i	$0.624492\pi$
$998$	−23.6236	−0.747791
$999$	−23.0986	−0.730807

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1666.2.a.z.1.4		5
7.2	even	3		238.2.e.f.137.2	✓	10
7.4	even	3		238.2.e.f.205.2	yes	10
7.6	odd	2		1666.2.a.ba.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
238.2.e.f.137.2	✓	10	7.2	even	3
238.2.e.f.205.2	yes	10	7.4	even	3
1666.2.a.z.1.4		5	1.1	even	1	trivial
1666.2.a.ba.1.2		5	7.6	odd	2

Overview	Random
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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:	\( N \)	\(=\)	\( 1666 = 2 \cdot 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1666.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.72247 q^{3} +1.00000 q^{4} +2.42127 q^{5} +1.72247 q^{6} +1.00000 q^{8} -0.0331027 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.72247 q^{3} +1.00000 q^{4} +2.42127 q^{5} +1.72247 q^{6} +1.00000 q^{8} -0.0331027 q^{9} +2.42127 q^{10} +3.72247 q^{11} +1.72247 q^{12} +6.58239 q^{13} +4.17056 q^{15} +1.00000 q^{16} -1.00000 q^{17} -0.0331027 q^{18} -5.58239 q^{19} +2.42127 q^{20} +3.72247 q^{22} -5.97056 q^{23} +1.72247 q^{24} +0.862543 q^{25} +6.58239 q^{26} -5.22442 q^{27} -0.772958 q^{29} +4.17056 q^{30} -9.61550 q^{31} +1.00000 q^{32} +6.41183 q^{33} -1.00000 q^{34} -0.0331027 q^{36} +4.42127 q^{37} -5.58239 q^{38} +11.3380 q^{39} +2.42127 q^{40} -5.61550 q^{41} -6.25437 q^{43} +3.72247 q^{44} -0.0801505 q^{45} -5.97056 q^{46} -0.671979 q^{47} +1.72247 q^{48} +0.862543 q^{50} -1.72247 q^{51} +6.58239 q^{52} +9.91041 q^{53} -5.22442 q^{54} +9.01310 q^{55} -9.61550 q^{57} -0.772958 q^{58} -10.3206 q^{59} +4.17056 q^{60} +4.72562 q^{61} -9.61550 q^{62} +1.00000 q^{64} +15.9377 q^{65} +6.41183 q^{66} +14.4249 q^{67} -1.00000 q^{68} -10.2841 q^{69} +9.69303 q^{71} -0.0331027 q^{72} +1.61550 q^{73} +4.42127 q^{74} +1.48570 q^{75} -5.58239 q^{76} +11.3380 q^{78} +4.56501 q^{79} +2.42127 q^{80} -8.89960 q^{81} -5.61550 q^{82} +10.3222 q^{83} -2.42127 q^{85} -6.25437 q^{86} -1.33140 q^{87} +3.72247 q^{88} +4.39423 q^{89} -0.0801505 q^{90} -5.97056 q^{92} -16.5624 q^{93} -0.671979 q^{94} -13.5165 q^{95} +1.72247 q^{96} -7.54929 q^{97} -0.123224 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{2} + 5 q^{4} - q^{5} + 5 q^{8} + 11 q^{9}+O(q^{10}) \) 5 * q + 5 * q^2 + 5 * q^4 - q^5 + 5 * q^8 + 11 * q^9	\( 5 q + 5 q^{2} + 5 q^{4} - q^{5} + 5 q^{8} + 11 q^{9} - q^{10} + 10 q^{11} + 2 q^{13} - 4 q^{15} + 5 q^{16} - 5 q^{17} + 11 q^{18} + 3 q^{19} - q^{20} + 10 q^{22} + 3 q^{23} + 18 q^{25} + 2 q^{26} - 6 q^{27} + 12 q^{29} - 4 q^{30} - 6 q^{31} + 5 q^{32} + 26 q^{33} - 5 q^{34} + 11 q^{36} + 9 q^{37} + 3 q^{38} + 6 q^{39} - q^{40} + 14 q^{41} + q^{43} + 10 q^{44} - 37 q^{45} + 3 q^{46} - 2 q^{47} + 18 q^{50} + 2 q^{52} + 20 q^{53} - 6 q^{54} - 6 q^{55} - 6 q^{57} + 12 q^{58} + 3 q^{59} - 4 q^{60} + 16 q^{61} - 6 q^{62} + 5 q^{64} + 2 q^{65} + 26 q^{66} + 15 q^{67} - 5 q^{68} + 4 q^{69} + 7 q^{71} + 11 q^{72} - 34 q^{73} + 9 q^{74} + 46 q^{75} + 3 q^{76} + 6 q^{78} - 12 q^{79} - q^{80} + 53 q^{81} + 14 q^{82} + 16 q^{83} + q^{85} + q^{86} - 20 q^{87} + 10 q^{88} + q^{89} - 37 q^{90} + 3 q^{92} - 12 q^{93} - 2 q^{94} - 3 q^{95} - 18 q^{97} + 16 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 + 5 * q^4 - q^5 + 5 * q^8 + 11 * q^9 - q^10 + 10 * q^11 + 2 * q^13 - 4 * q^15 + 5 * q^16 - 5 * q^17 + 11 * q^18 + 3 * q^19 - q^20 + 10 * q^22 + 3 * q^23 + 18 * q^25 + 2 * q^26 - 6 * q^27 + 12 * q^29 - 4 * q^30 - 6 * q^31 + 5 * q^32 + 26 * q^33 - 5 * q^34 + 11 * q^36 + 9 * q^37 + 3 * q^38 + 6 * q^39 - q^40 + 14 * q^41 + q^43 + 10 * q^44 - 37 * q^45 + 3 * q^46 - 2 * q^47 + 18 * q^50 + 2 * q^52 + 20 * q^53 - 6 * q^54 - 6 * q^55 - 6 * q^57 + 12 * q^58 + 3 * q^59 - 4 * q^60 + 16 * q^61 - 6 * q^62 + 5 * q^64 + 2 * q^65 + 26 * q^66 + 15 * q^67 - 5 * q^68 + 4 * q^69 + 7 * q^71 + 11 * q^72 - 34 * q^73 + 9 * q^74 + 46 * q^75 + 3 * q^76 + 6 * q^78 - 12 * q^79 - q^80 + 53 * q^81 + 14 * q^82 + 16 * q^83 + q^85 + q^86 - 20 * q^87 + 10 * q^88 + q^89 - 37 * q^90 + 3 * q^92 - 12 * q^93 - 2 * q^94 - 3 * q^95 - 18 * q^97 + 16 * q^99

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