LMFDB - Embedded newform 1666.2.a.ba.1.5

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			1.5
Root			$3.40920$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +3.40920 q^{3} +1.00000 q^{4} +0.364940 q^{5} +3.40920 q^{6} +1.00000 q^{8} +8.62267 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +3.40920 q^{3} +1.00000 q^{4} +0.364940 q^{5} +3.40920 q^{6} +1.00000 q^{8} +8.62267 q^{9} +0.364940 q^{10} -1.40920 q^{11} +3.40920 q^{12} -2.04841 q^{13} +1.24415 q^{15} +1.00000 q^{16} +1.00000 q^{17} +8.62267 q^{18} +1.04841 q^{19} +0.364940 q^{20} -1.40920 q^{22} -7.30614 q^{23} +3.40920 q^{24} -4.86682 q^{25} -2.04841 q^{26} +19.1688 q^{27} +6.84437 q^{29} +1.24415 q^{30} -3.57425 q^{31} +1.00000 q^{32} -4.80426 q^{33} +1.00000 q^{34} +8.62267 q^{36} +1.63506 q^{37} +1.04841 q^{38} -6.98346 q^{39} +0.364940 q^{40} -7.57425 q^{41} +0.925620 q^{43} -1.40920 q^{44} +3.14675 q^{45} -7.30614 q^{46} -1.97403 q^{47} +3.40920 q^{48} -4.86682 q^{50} +3.40920 q^{51} -2.04841 q^{52} +8.02245 q^{53} +19.1688 q^{54} -0.514274 q^{55} +3.57425 q^{57} +6.84437 q^{58} -14.1710 q^{59} +1.24415 q^{60} -12.0626 q^{61} -3.57425 q^{62} +1.00000 q^{64} -0.747547 q^{65} -4.80426 q^{66} +4.31853 q^{67} +1.00000 q^{68} -24.9081 q^{69} +5.89694 q^{71} +8.62267 q^{72} +11.5743 q^{73} +1.63506 q^{74} -16.5920 q^{75} +1.04841 q^{76} -6.98346 q^{78} -6.13908 q^{79} +0.364940 q^{80} +39.4824 q^{81} -7.57425 q^{82} -6.82671 q^{83} +0.364940 q^{85} +0.925620 q^{86} +23.3339 q^{87} -1.40920 q^{88} +10.2713 q^{89} +3.14675 q^{90} -7.30614 q^{92} -12.1854 q^{93} -1.97403 q^{94} +0.382608 q^{95} +3.40920 q^{96} +11.6711 q^{97} -12.1511 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	3.40920	1.96830	0.984152	−	0.177326i	$-0.0567447\pi$
$3$	3.40920	1.96830	0.984152	+	0.177326i	$0.0567447\pi$
$4$	1.00000	0.500000
$5$	0.364940	0.163206	0.0816030	−	0.996665i	$-0.473996\pi$
$5$	0.364940	0.163206	0.0816030	+	0.996665i	$0.473996\pi$
$6$	3.40920	1.39180
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	8.62267	2.87422
$10$	0.364940	0.115404
$11$	−1.40920	−0.424891	−0.212445	−	0.977173i	$-0.568143\pi$
$11$	−1.40920	−0.424891	−0.212445	+	0.977173i	$0.568143\pi$
$12$	3.40920	0.984152
$13$	−2.04841	−0.568128	−0.284064	−	0.958805i	$-0.591683\pi$
$13$	−2.04841	−0.568128	−0.284064	+	0.958805i	$0.591683\pi$
$14$	0	0
$15$	1.24415	0.321239
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	8.62267	2.03238
$19$	1.04841	0.240522	0.120261	−	0.992742i	$-0.461627\pi$
$19$	1.04841	0.240522	0.120261	+	0.992742i	$0.461627\pi$
$20$	0.364940	0.0816030
$21$	0	0
$22$	−1.40920	−0.300443
$23$	−7.30614	−1.52344	−0.761718	−	0.647909i	$-0.775644\pi$
$23$	−7.30614	−1.52344	−0.761718	+	0.647909i	$0.775644\pi$
$24$	3.40920	0.695901
$25$	−4.86682	−0.973364
$26$	−2.04841	−0.401727
$27$	19.1688	3.68904
$28$	0	0
$29$	6.84437	1.27097	0.635484	−	0.772114i	$-0.280801\pi$
$29$	6.84437	1.27097	0.635484	+	0.772114i	$0.280801\pi$
$30$	1.24415	0.227150
$31$	−3.57425	−0.641955	−0.320977	−	0.947087i	$-0.604011\pi$
$31$	−3.57425	−0.641955	−0.320977	+	0.947087i	$0.604011\pi$
$32$	1.00000	0.176777
$33$	−4.80426	−0.836314
$34$	1.00000	0.171499
$35$	0	0
$36$	8.62267	1.43711
$37$	1.63506	0.268802	0.134401	−	0.990927i	$-0.457089\pi$
$37$	1.63506	0.268802	0.134401	+	0.990927i	$0.457089\pi$
$38$	1.04841	0.170075
$39$	−6.98346	−1.11825
$40$	0.364940	0.0577020
$41$	−7.57425	−1.18290	−0.591450	−	0.806342i	$-0.701444\pi$
$41$	−7.57425	−1.18290	−0.591450	+	0.806342i	$0.701444\pi$
$42$	0	0
$43$	0.925620	0.141156	0.0705779	−	0.997506i	$-0.477516\pi$
$43$	0.925620	0.141156	0.0705779	+	0.997506i	$0.477516\pi$
$44$	−1.40920	−0.212445
$45$	3.14675	0.469090
$46$	−7.30614	−1.07723
$47$	−1.97403	−0.287942	−0.143971	−	0.989582i	$-0.545987\pi$
$47$	−1.97403	−0.287942	−0.143971	+	0.989582i	$0.545987\pi$
$48$	3.40920	0.492076
$49$	0	0
$50$	−4.86682	−0.688272
$51$	3.40920	0.477384
$52$	−2.04841	−0.284064
$53$	8.02245	1.10197	0.550984	−	0.834516i	$-0.314253\pi$
$53$	8.02245	1.10197	0.550984	+	0.834516i	$0.314253\pi$
$54$	19.1688	2.60854
$55$	−0.514274	−0.0693447
$56$	0	0
$57$	3.57425	0.473421
$58$	6.84437	0.898710
$59$	−14.1710	−1.84490	−0.922450	−	0.386116i	$-0.873817\pi$
$59$	−14.1710	−1.84490	−0.922450	+	0.386116i	$0.873817\pi$
$60$	1.24415	0.160620
$61$	−12.0626	−1.54445	−0.772226	−	0.635348i	$-0.780857\pi$
$61$	−12.0626	−1.54445	−0.772226	+	0.635348i	$0.780857\pi$
$62$	−3.57425	−0.453931
$63$	0	0
$64$	1.00000	0.125000
$65$	−0.747547	−0.0927218
$66$	−4.80426	−0.591363
$67$	4.31853	0.527593	0.263796	−	0.964578i	$-0.415025\pi$
$67$	4.31853	0.527593	0.263796	+	0.964578i	$0.415025\pi$
$68$	1.00000	0.121268
$69$	−24.9081	−2.99858
$70$	0	0
$71$	5.89694	0.699837	0.349919	−	0.936780i	$-0.386209\pi$
$71$	5.89694	0.699837	0.349919	+	0.936780i	$0.386209\pi$
$72$	8.62267	1.01619
$73$	11.5743	1.35466	0.677332	−	0.735678i	$-0.263136\pi$
$73$	11.5743	1.35466	0.677332	+	0.735678i	$0.263136\pi$
$74$	1.63506	0.190072
$75$	−16.5920	−1.91588
$76$	1.04841	0.120261
$77$	0	0
$78$	−6.98346	−0.790721
$79$	−6.13908	−0.690701	−0.345350	−	0.938474i	$-0.612240\pi$
$79$	−6.13908	−0.690701	−0.345350	+	0.938474i	$0.612240\pi$
$80$	0.364940	0.0408015
$81$	39.4824	4.38693
$82$	−7.57425	−0.836436
$83$	−6.82671	−0.749328	−0.374664	−	0.927161i	$-0.622242\pi$
$83$	−6.82671	−0.749328	−0.374664	+	0.927161i	$0.622242\pi$
$84$	0	0
$85$	0.364940	0.0395833
$86$	0.925620	0.0998122
$87$	23.3339	2.50165
$88$	−1.40920	−0.150222
$89$	10.2713	1.08876	0.544378	−	0.838840i	$-0.316766\pi$
$89$	10.2713	1.08876	0.544378	+	0.838840i	$0.316766\pi$
$90$	3.14675	0.331697
$91$	0	0
$92$	−7.30614	−0.761718
$93$	−12.1854	−1.26356
$94$	−1.97403	−0.203606
$95$	0.382608	0.0392547
$96$	3.40920	0.347950
$97$	11.6711	1.18502	0.592509	−	0.805564i	$-0.298137\pi$
$97$	11.6711	1.18502	0.592509	+	0.805564i	$0.298137\pi$
$98$	0	0
$99$	−12.1511	−1.22123
$100$	−4.86682	−0.486682
$101$	−8.41863	−0.837685	−0.418842	−	0.908059i	$-0.637564\pi$
$101$	−8.41863	−0.837685	−0.418842	+	0.908059i	$0.637564\pi$
$102$	3.40920	0.337561
$103$	−18.4895	−1.82182	−0.910912	−	0.412602i	$-0.864620\pi$
$103$	−18.4895	−1.82182	−0.910912	+	0.412602i	$0.864620\pi$
$104$	−2.04841	−0.200863
$105$	0	0
$106$	8.02245	0.779209
$107$	13.1062	1.26703	0.633514	−	0.773731i	$-0.281612\pi$
$107$	13.1062	1.26703	0.633514	+	0.773731i	$0.281612\pi$
$108$	19.1688	1.84452
$109$	1.52057	0.145644	0.0728219	−	0.997345i	$-0.476800\pi$
$109$	1.52057	0.145644	0.0728219	+	0.997345i	$0.476800\pi$
$110$	−0.514274	−0.0490341
$111$	5.57425	0.529085
$112$	0	0
$113$	−0.729879	−0.0686613	−0.0343306	−	0.999411i	$-0.510930\pi$
$113$	−0.729879	−0.0686613	−0.0343306	+	0.999411i	$0.510930\pi$
$114$	3.57425	0.334759
$115$	−2.66630	−0.248634
$116$	6.84437	0.635484
$117$	−17.6628	−1.63292
$118$	−14.1710	−1.30454
$119$	0	0
$120$	1.24415	0.113575
$121$	−9.01415	−0.819468
$122$	−12.0626	−1.09209
$123$	−25.8222	−2.32831
$124$	−3.57425	−0.320977
$125$	−3.60079	−0.322065
$126$	0	0
$127$	−1.29609	−0.115009	−0.0575046	−	0.998345i	$-0.518314\pi$
$127$	−1.29609	−0.115009	−0.0575046	+	0.998345i	$0.518314\pi$
$128$	1.00000	0.0883883
$129$	3.15563	0.277837
$130$	−0.747547	−0.0655642
$131$	−3.12136	−0.272715	−0.136357	−	0.990660i	$-0.543540\pi$
$131$	−3.12136	−0.272715	−0.136357	+	0.990660i	$0.543540\pi$
$132$	−4.80426	−0.418157
$133$	0	0
$134$	4.31853	0.373064
$135$	6.99546	0.602073
$136$	1.00000	0.0857493
$137$	18.1851	1.55366	0.776829	−	0.629712i	$-0.216827\pi$
$137$	18.1851	1.55366	0.776829	+	0.629712i	$0.216827\pi$
$138$	−24.9081	−2.12032
$139$	9.53200	0.808493	0.404247	−	0.914650i	$-0.367534\pi$
$139$	9.53200	0.808493	0.404247	+	0.914650i	$0.367534\pi$
$140$	0	0
$141$	−6.72988	−0.566758
$142$	5.89694	0.494860
$143$	2.88663	0.241392
$144$	8.62267	0.718555
$145$	2.49778	0.207430
$146$	11.5743	0.957892
$147$	0	0
$148$	1.63506	0.134401
$149$	−5.64863	−0.462754	−0.231377	−	0.972864i	$-0.574323\pi$
$149$	−5.64863	−0.462754	−0.231377	+	0.972864i	$0.574323\pi$
$150$	−16.5920	−1.35473
$151$	20.9081	1.70148	0.850739	−	0.525589i	$-0.176155\pi$
$151$	20.9081	1.70148	0.850739	+	0.525589i	$0.176155\pi$
$152$	1.04841	0.0850375
$153$	8.62267	0.697101
$154$	0	0
$155$	−1.30439	−0.104771
$156$	−6.98346	−0.559124
$157$	−10.8668	−0.867267	−0.433633	−	0.901089i	$-0.642769\pi$
$157$	−10.8668	−0.867267	−0.433633	+	0.901089i	$0.642769\pi$
$158$	−6.13908	−0.488399
$159$	27.3501	2.16901
$160$	0.364940	0.0288510
$161$	0	0
$162$	39.4824	3.10203
$163$	−11.5743	−0.906565	−0.453283	−	0.891367i	$-0.649747\pi$
$163$	−11.5743	−0.906565	−0.453283	+	0.891367i	$0.649747\pi$
$164$	−7.57425	−0.591450
$165$	−1.75327	−0.136491
$166$	−6.82671	−0.529855
$167$	1.34722	0.104251	0.0521254	−	0.998641i	$-0.483400\pi$
$167$	1.34722	0.104251	0.0521254	+	0.998641i	$0.483400\pi$
$168$	0	0
$169$	−8.80400	−0.677231
$170$	0.364940	0.0279896
$171$	9.04011	0.691315
$172$	0.925620	0.0705779
$173$	−4.91466	−0.373654	−0.186827	−	0.982393i	$-0.559820\pi$
$173$	−4.91466	−0.373654	−0.186827	+	0.982393i	$0.559820\pi$
$174$	23.3339	1.76894
$175$	0	0
$176$	−1.40920	−0.106223
$177$	−48.3116	−3.63133
$178$	10.2713	0.769866
$179$	−7.91875	−0.591875	−0.295938	−	0.955207i	$-0.595632\pi$
$179$	−7.91875	−0.591875	−0.295938	+	0.955207i	$0.595632\pi$
$180$	3.14675	0.234545
$181$	−14.9430	−1.11070	−0.555350	−	0.831616i	$-0.687416\pi$
$181$	−14.9430	−1.11070	−0.555350	+	0.831616i	$0.687416\pi$
$182$	0	0
$183$	−41.1237	−3.03995
$184$	−7.30614	−0.538616
$185$	0.596698	0.0438701
$186$	−12.1854	−0.893473
$187$	−1.40920	−0.103051
$188$	−1.97403	−0.143971
$189$	0	0
$190$	0.382608	0.0277573
$191$	−17.7513	−1.28444	−0.642220	−	0.766521i	$-0.721986\pi$
$191$	−17.7513	−1.28444	−0.642220	+	0.766521i	$0.721986\pi$
$192$	3.40920	0.246038
$193$	4.39148	0.316106	0.158053	−	0.987431i	$-0.449478\pi$
$193$	4.39148	0.316106	0.158053	+	0.987431i	$0.449478\pi$
$194$	11.6711	0.837935
$195$	−2.54854	−0.182505
$196$	0	0
$197$	16.5420	1.17857	0.589284	−	0.807926i	$-0.299410\pi$
$197$	16.5420	1.17857	0.589284	+	0.807926i	$0.299410\pi$
$198$	−12.1511	−0.863540
$199$	0.104242	0.00738950	0.00369475	−	0.999993i	$-0.498824\pi$
$199$	0.104242	0.00738950	0.00369475	+	0.999993i	$0.498824\pi$
$200$	−4.86682	−0.344136
$201$	14.7228	1.03846
$202$	−8.41863	−0.592332
$203$	0	0
$204$	3.40920	0.238692
$205$	−2.76415	−0.193056
$206$	−18.4895	−1.28822
$207$	−62.9984	−4.37869
$208$	−2.04841	−0.142032
$209$	−1.47743	−0.102196
$210$	0	0
$211$	8.02714	0.552611	0.276306	−	0.961070i	$-0.410890\pi$
$211$	8.02714	0.552611	0.276306	+	0.961070i	$0.410890\pi$
$212$	8.02245	0.550984
$213$	20.1039	1.37749
$214$	13.1062	0.895925
$215$	0.337796	0.0230375
$216$	19.1688	1.30427
$217$	0	0
$218$	1.52057	0.102986
$219$	39.4590	2.66639
$220$	−0.514274	−0.0346724
$221$	−2.04841	−0.137791
$222$	5.57425	0.374119
$223$	13.5849	0.909711	0.454855	−	0.890565i	$-0.349691\pi$
$223$	13.5849	0.909711	0.454855	+	0.890565i	$0.349691\pi$
$224$	0	0
$225$	−41.9650	−2.79766
$226$	−0.729879	−0.0485509
$227$	−10.2099	−0.677658	−0.338829	−	0.940848i	$-0.610031\pi$
$227$	−10.2099	−0.677658	−0.338829	+	0.940848i	$0.610031\pi$
$228$	3.57425	0.236711
$229$	−17.7230	−1.17117	−0.585585	−	0.810611i	$-0.699135\pi$
$229$	−17.7230	−1.17117	−0.585585	+	0.810611i	$0.699135\pi$
$230$	−2.66630	−0.175811
$231$	0	0
$232$	6.84437	0.449355
$233$	18.3258	1.20056	0.600282	−	0.799788i	$-0.295055\pi$
$233$	18.3258	1.20056	0.600282	+	0.799788i	$0.295055\pi$
$234$	−17.6628	−1.15465
$235$	−0.720403	−0.0469939
$236$	−14.1710	−0.922450
$237$	−20.9294	−1.35951
$238$	0	0
$239$	8.20731	0.530886	0.265443	−	0.964126i	$-0.414482\pi$
$239$	8.20731	0.530886	0.265443	+	0.964126i	$0.414482\pi$
$240$	1.24415	0.0803098
$241$	−2.95887	−0.190597	−0.0952987	−	0.995449i	$-0.530381\pi$
$241$	−2.95887	−0.190597	−0.0952987	+	0.995449i	$0.530381\pi$
$242$	−9.01415	−0.579451
$243$	77.0970	4.94577
$244$	−12.0626	−0.772226
$245$	0	0
$246$	−25.8222	−1.64636
$247$	−2.14758	−0.136647
$248$	−3.57425	−0.226965
$249$	−23.2736	−1.47491
$250$	−3.60079	−0.227734
$251$	9.87410	0.623248	0.311624	−	0.950206i	$-0.399127\pi$
$251$	9.87410	0.623248	0.311624	+	0.950206i	$0.399127\pi$
$252$	0	0
$253$	10.2958	0.647293
$254$	−1.29609	−0.0813238
$255$	1.24415	0.0779119
$256$	1.00000	0.0625000
$257$	−11.4552	−0.714557	−0.357278	−	0.933998i	$-0.616295\pi$
$257$	−11.4552	−0.714557	−0.357278	+	0.933998i	$0.616295\pi$
$258$	3.15563	0.196461
$259$	0	0
$260$	−0.747547	−0.0463609
$261$	59.0167	3.65304
$262$	−3.12136	−0.192838
$263$	−8.60709	−0.530736	−0.265368	−	0.964147i	$-0.585493\pi$
$263$	−8.60709	−0.530736	−0.265368	+	0.964147i	$0.585493\pi$
$264$	−4.80426	−0.295682
$265$	2.92771	0.179848
$266$	0	0
$267$	35.0169	2.14300
$268$	4.31853	0.263796
$269$	9.45490	0.576475	0.288238	−	0.957559i	$-0.406931\pi$
$269$	9.45490	0.576475	0.288238	+	0.957559i	$0.406931\pi$
$270$	6.99546	0.425730
$271$	17.4224	1.05833	0.529167	−	0.848518i	$-0.322504\pi$
$271$	17.4224	1.05833	0.529167	+	0.848518i	$0.322504\pi$
$272$	1.00000	0.0606339
$273$	0	0
$274$	18.1851	1.09860
$275$	6.85834	0.413573
$276$	−24.9081	−1.49929
$277$	−10.9412	−0.657393	−0.328696	−	0.944436i	$-0.606609\pi$
$277$	−10.9412	−0.657393	−0.328696	+	0.944436i	$0.606609\pi$
$278$	9.53200	0.571691
$279$	−30.8196	−1.84512
$280$	0	0
$281$	19.8893	1.18649	0.593247	−	0.805020i	$-0.297846\pi$
$281$	19.8893	1.18649	0.593247	+	0.805020i	$0.297846\pi$
$282$	−6.72988	−0.400758
$283$	9.43517	0.560863	0.280431	−	0.959874i	$-0.409523\pi$
$283$	9.43517	0.560863	0.280431	+	0.959874i	$0.409523\pi$
$284$	5.89694	0.349919
$285$	1.30439	0.0772652
$286$	2.88663	0.170690
$287$	0	0
$288$	8.62267	0.508095
$289$	1.00000	0.0588235
$290$	2.49778	0.146675
$291$	39.7891	2.33248
$292$	11.5743	0.677332
$293$	17.3823	1.01548	0.507742	−	0.861509i	$-0.330480\pi$
$293$	17.3823	1.01548	0.507742	+	0.861509i	$0.330480\pi$
$294$	0	0
$295$	−5.17154	−0.301099
$296$	1.63506	0.0950359
$297$	−27.0127	−1.56744
$298$	−5.64863	−0.327216
$299$	14.9660	0.865505
$300$	−16.5920	−0.957938
$301$	0	0
$302$	20.9081	1.20313
$303$	−28.7008	−1.64882
$304$	1.04841	0.0601306
$305$	−4.40211	−0.252064
$306$	8.62267	0.492925
$307$	20.7195	1.18252	0.591262	−	0.806480i	$-0.298630\pi$
$307$	20.7195	1.18252	0.591262	+	0.806480i	$0.298630\pi$
$308$	0	0
$309$	−63.0344	−3.58590
$310$	−1.30439	−0.0740842
$311$	15.6565	0.887801	0.443900	−	0.896076i	$-0.353594\pi$
$311$	15.6565	0.887801	0.443900	+	0.896076i	$0.353594\pi$
$312$	−6.98346	−0.395360
$313$	−11.3150	−0.639562	−0.319781	−	0.947491i	$-0.603609\pi$
$313$	−11.3150	−0.639562	−0.319781	+	0.947491i	$0.603609\pi$
$314$	−10.8668	−0.613250
$315$	0	0
$316$	−6.13908	−0.345350
$317$	−0.347272	−0.0195047	−0.00975237	−	0.999952i	$-0.503104\pi$
$317$	−0.347272	−0.0195047	−0.00975237	+	0.999952i	$0.503104\pi$
$318$	27.3501	1.53372
$319$	−9.64511	−0.540023
$320$	0.364940	0.0204008
$321$	44.6819	2.49390
$322$	0	0
$323$	1.04841	0.0583353
$324$	39.4824	2.19346
$325$	9.96925	0.552995
$326$	−11.5743	−0.641039
$327$	5.18392	0.286671
$328$	−7.57425	−0.418218
$329$	0	0
$330$	−1.75327	−0.0965141
$331$	15.5379	0.854040	0.427020	−	0.904242i	$-0.359563\pi$
$331$	15.5379	0.854040	0.427020	+	0.904242i	$0.359563\pi$
$332$	−6.82671	−0.374664
$333$	14.0986	0.772597
$334$	1.34722	0.0737165
$335$	1.57600	0.0861063
$336$	0	0
$337$	14.4364	0.786399	0.393200	−	0.919453i	$-0.371368\pi$
$337$	14.4364	0.786399	0.393200	+	0.919453i	$0.371368\pi$
$338$	−8.80400	−0.478875
$339$	−2.48831	−0.135146
$340$	0.364940	0.0197916
$341$	5.03685	0.272761
$342$	9.04011	0.488833
$343$	0	0
$344$	0.925620	0.0499061
$345$	−9.08996	−0.489387
$346$	−4.91466	−0.264214
$347$	−19.2287	−1.03225	−0.516126	−	0.856513i	$-0.672626\pi$
$347$	−19.2287	−1.03225	−0.516126	+	0.856513i	$0.672626\pi$
$348$	23.3339	1.25083
$349$	3.29726	0.176499	0.0882493	−	0.996098i	$-0.471873\pi$
$349$	3.29726	0.176499	0.0882493	+	0.996098i	$0.471873\pi$
$350$	0	0
$351$	−39.2656	−2.09584
$352$	−1.40920	−0.0751108
$353$	18.5057	0.984960	0.492480	−	0.870324i	$-0.336090\pi$
$353$	18.5057	0.984960	0.492480	+	0.870324i	$0.336090\pi$
$354$	−48.3116	−2.56774
$355$	2.15203	0.114218
$356$	10.2713	0.544378
$357$	0	0
$358$	−7.91875	−0.418519
$359$	21.0517	1.11107	0.555533	−	0.831495i	$-0.312514\pi$
$359$	21.0517	1.11107	0.555533	+	0.831495i	$0.312514\pi$
$360$	3.14675	0.165848
$361$	−17.9008	−0.942149
$362$	−14.9430	−0.785384
$363$	−30.7311	−1.61296
$364$	0	0
$365$	4.22390	0.221089
$366$	−41.1237	−2.14957
$367$	−24.7342	−1.29111	−0.645557	−	0.763712i	$-0.723375\pi$
$367$	−24.7342	−1.29111	−0.645557	+	0.763712i	$0.723375\pi$
$368$	−7.30614	−0.380859
$369$	−65.3102	−3.39992
$370$	0.596698	0.0310209
$371$	0	0
$372$	−12.1854	−0.631781
$373$	−35.5293	−1.83964	−0.919820	−	0.392341i	$-0.871665\pi$
$373$	−35.5293	−1.83964	−0.919820	+	0.392341i	$0.871665\pi$
$374$	−1.40920	−0.0728682
$375$	−12.2758	−0.633922
$376$	−1.97403	−0.101803
$377$	−14.0201	−0.722072
$378$	0	0
$379$	18.2724	0.938591	0.469296	−	0.883041i	$-0.344508\pi$
$379$	18.2724	0.938591	0.469296	+	0.883041i	$0.344508\pi$
$380$	0.382608	0.0196274
$381$	−4.41863	−0.226373
$382$	−17.7513	−0.908236
$383$	−7.78557	−0.397824	−0.198912	−	0.980017i	$-0.563741\pi$
$383$	−7.78557	−0.397824	−0.198912	+	0.980017i	$0.563741\pi$
$384$	3.40920	0.173975
$385$	0	0
$386$	4.39148	0.223521
$387$	7.98131	0.405713
$388$	11.6711	0.592509
$389$	−8.92705	−0.452620	−0.226310	−	0.974055i	$-0.572666\pi$
$389$	−8.92705	−0.452620	−0.226310	+	0.974055i	$0.572666\pi$
$390$	−2.54854	−0.129050
$391$	−7.30614	−0.369487
$392$	0	0
$393$	−10.6414	−0.536785
$394$	16.5420	0.833374
$395$	−2.24040	−0.112727
$396$	−12.1511	−0.610615
$397$	−5.62794	−0.282458	−0.141229	−	0.989977i	$-0.545105\pi$
$397$	−5.62794	−0.282458	−0.141229	+	0.989977i	$0.545105\pi$
$398$	0.104242	0.00522516
$399$	0	0
$400$	−4.86682	−0.243341
$401$	−9.24533	−0.461690	−0.230845	−	0.972991i	$-0.574149\pi$
$401$	−9.24533	−0.461690	−0.230845	+	0.972991i	$0.574149\pi$
$402$	14.7228	0.734304
$403$	7.32154	0.364712
$404$	−8.41863	−0.418842
$405$	14.4087	0.715973
$406$	0	0
$407$	−2.30413	−0.114212
$408$	3.40920	0.168781
$409$	29.8882	1.47788	0.738939	−	0.673772i	$-0.235327\pi$
$409$	29.8882	1.47788	0.738939	+	0.673772i	$0.235327\pi$
$410$	−2.76415	−0.136511
$411$	61.9967	3.05807
$412$	−18.4895	−0.910912
$413$	0	0
$414$	−62.9984	−3.09620
$415$	−2.49134	−0.122295
$416$	−2.04841	−0.100432
$417$	32.4965	1.59136
$418$	−1.47743	−0.0722633
$419$	2.13908	0.104501	0.0522505	−	0.998634i	$-0.483361\pi$
$419$	2.13908	0.104501	0.0522505	+	0.998634i	$0.483361\pi$
$420$	0	0
$421$	−21.6545	−1.05537	−0.527687	−	0.849439i	$-0.676941\pi$
$421$	−21.6545	−1.05537	−0.527687	+	0.849439i	$0.676941\pi$
$422$	8.02714	0.390755
$423$	−17.0214	−0.827610
$424$	8.02245	0.389604
$425$	−4.86682	−0.236075
$426$	20.1039	0.974035
$427$	0	0
$428$	13.1062	0.633514
$429$	9.84111	0.475133
$430$	0.337796	0.0162899
$431$	3.69392	0.177930	0.0889648	−	0.996035i	$-0.471644\pi$
$431$	3.69392	0.177930	0.0889648	+	0.996035i	$0.471644\pi$
$432$	19.1688	0.922260
$433$	9.60046	0.461369	0.230684	−	0.973029i	$-0.425904\pi$
$433$	9.60046	0.461369	0.230684	+	0.973029i	$0.425904\pi$
$434$	0	0
$435$	8.51545	0.408285
$436$	1.52057	0.0728219
$437$	−7.65985	−0.366420
$438$	39.4590	1.88542
$439$	−18.0740	−0.862624	−0.431312	−	0.902203i	$-0.641949\pi$
$439$	−18.0740	−0.862624	−0.431312	+	0.902203i	$0.641949\pi$
$440$	−0.514274	−0.0245171
$441$	0	0
$442$	−2.04841	−0.0974331
$443$	13.0567	0.620343	0.310172	−	0.950681i	$-0.399614\pi$
$443$	13.0567	0.620343	0.310172	+	0.950681i	$0.399614\pi$
$444$	5.57425	0.264542
$445$	3.74840	0.177691
$446$	13.5849	0.643263
$447$	−19.2573	−0.910841
$448$	0	0
$449$	24.9412	1.17705	0.588524	−	0.808480i	$-0.299709\pi$
$449$	24.9412	1.17705	0.588524	+	0.808480i	$0.299709\pi$
$450$	−41.9650	−1.97825
$451$	10.6737	0.502603
$452$	−0.729879	−0.0343306
$453$	71.2800	3.34903
$454$	−10.2099	−0.479176
$455$	0	0
$456$	3.57425	0.167380
$457$	−36.7081	−1.71713	−0.858566	−	0.512703i	$-0.828644\pi$
$457$	−36.7081	−1.71713	−0.858566	+	0.512703i	$0.828644\pi$
$458$	−17.7230	−0.828142
$459$	19.1688	0.894723
$460$	−2.66630	−0.124317
$461$	−0.281686	−0.0131194	−0.00655971	−	0.999978i	$-0.502088\pi$
$461$	−0.281686	−0.0131194	−0.00655971	+	0.999978i	$0.502088\pi$
$462$	0	0
$463$	−13.4161	−0.623500	−0.311750	−	0.950164i	$-0.600915\pi$
$463$	−13.4161	−0.623500	−0.311750	+	0.950164i	$0.600915\pi$
$464$	6.84437	0.317742
$465$	−4.44692	−0.206221
$466$	18.3258	0.848927
$467$	−14.6852	−0.679551	−0.339776	−	0.940507i	$-0.610351\pi$
$467$	−14.6852	−0.679551	−0.339776	+	0.940507i	$0.610351\pi$
$468$	−17.6628	−0.816462
$469$	0	0
$470$	−0.720403	−0.0332297
$471$	−37.0472	−1.70704
$472$	−14.1710	−0.652271
$473$	−1.30439	−0.0599758
$474$	−20.9294	−0.961318
$475$	−5.10244	−0.234116
$476$	0	0
$477$	69.1749	3.16730
$478$	8.20731	0.375393
$479$	−14.8532	−0.678662	−0.339331	−	0.940667i	$-0.610201\pi$
$479$	−14.8532	−0.678662	−0.339331	+	0.940667i	$0.610201\pi$
$480$	1.24415	0.0567876
$481$	−3.34928	−0.152714
$482$	−2.95887	−0.134773
$483$	0	0
$484$	−9.01415	−0.409734
$485$	4.25924	0.193402
$486$	77.0970	3.49719
$487$	−1.61476	−0.0731716	−0.0365858	−	0.999331i	$-0.511648\pi$
$487$	−1.61476	−0.0731716	−0.0365858	+	0.999331i	$0.511648\pi$
$488$	−12.0626	−0.546046
$489$	−39.4590	−1.78440
$490$	0	0
$491$	2.29139	0.103409	0.0517045	−	0.998662i	$-0.483535\pi$
$491$	2.29139	0.103409	0.0517045	+	0.998662i	$0.483535\pi$
$492$	−25.8222	−1.16415
$493$	6.84437	0.308255
$494$	−2.14758	−0.0966243
$495$	−4.43441	−0.199312
$496$	−3.57425	−0.160489
$497$	0	0
$498$	−23.2736	−1.04292
$499$	−21.4770	−0.961440	−0.480720	−	0.876874i	$-0.659625\pi$
$499$	−21.4770	−0.961440	−0.480720	+	0.876874i	$0.659625\pi$
$500$	−3.60079	−0.161032
$501$	4.59294	0.205197
$502$	9.87410	0.440703
$503$	21.9595	0.979125	0.489563	−	0.871968i	$-0.337156\pi$
$503$	21.9595	0.979125	0.489563	+	0.871968i	$0.337156\pi$
$504$	0	0
$505$	−3.07229	−0.136715
$506$	10.2958	0.457706
$507$	−30.0146	−1.33300
$508$	−1.29609	−0.0575046
$509$	24.4115	1.08202	0.541010	−	0.841016i	$-0.318042\pi$
$509$	24.4115	1.08202	0.541010	+	0.841016i	$0.318042\pi$
$510$	1.24415	0.0550920
$511$	0	0
$512$	1.00000	0.0441942
$513$	20.0968	0.887297
$514$	−11.4552	−0.505268
$515$	−6.74755	−0.297332
$516$	3.15563	0.138919
$517$	2.78181	0.122344
$518$	0	0
$519$	−16.7551	−0.735466
$520$	−0.747547	−0.0327821
$521$	−14.4458	−0.632881	−0.316440	−	0.948612i	$-0.602488\pi$
$521$	−14.4458	−0.632881	−0.316440	+	0.948612i	$0.602488\pi$
$522$	59.0167	2.58309
$523$	−15.3256	−0.670140	−0.335070	−	0.942193i	$-0.608760\pi$
$523$	−15.3256	−0.670140	−0.335070	+	0.942193i	$0.608760\pi$
$524$	−3.12136	−0.136357
$525$	0	0
$526$	−8.60709	−0.375287
$527$	−3.57425	−0.155697
$528$	−4.80426	−0.209079
$529$	30.3797	1.32085
$530$	2.92771	0.127172
$531$	−122.191	−5.30265
$532$	0	0
$533$	15.5152	0.672038
$534$	35.0169	1.51533
$535$	4.78299	0.206787
$536$	4.31853	0.186532
$537$	−26.9966	−1.16499
$538$	9.45490	0.407630
$539$	0	0
$540$	6.99546	0.301037
$541$	36.3867	1.56439	0.782194	−	0.623036i	$-0.214101\pi$
$541$	36.3867	1.56439	0.782194	+	0.623036i	$0.214101\pi$
$542$	17.4224	0.748355
$543$	−50.9436	−2.18620
$544$	1.00000	0.0428746
$545$	0.554915	0.0237700
$546$	0	0
$547$	−35.6460	−1.52411	−0.762056	−	0.647511i	$-0.775810\pi$
$547$	−35.6460	−1.52411	−0.762056	+	0.647511i	$0.775810\pi$
$548$	18.1851	0.776829
$549$	−104.011	−4.43910
$550$	6.85834	0.292440
$551$	7.17573	0.305696
$552$	−24.9081	−1.06016
$553$	0	0
$554$	−10.9412	−0.464847
$555$	2.03427	0.0863498
$556$	9.53200	0.404247
$557$	−12.5567	−0.532046	−0.266023	−	0.963967i	$-0.585710\pi$
$557$	−12.5567	−0.532046	−0.266023	+	0.963967i	$0.585710\pi$
$558$	−30.8196	−1.30470
$559$	−1.89605	−0.0801945
$560$	0	0
$561$	−4.80426	−0.202836
$562$	19.8893	0.838978
$563$	5.45882	0.230062	0.115031	−	0.993362i	$-0.463303\pi$
$563$	5.45882	0.230062	0.115031	+	0.993362i	$0.463303\pi$
$564$	−6.72988	−0.283379
$565$	−0.266362	−0.0112059
$566$	9.43517	0.396590
$567$	0	0
$568$	5.89694	0.247430
$569$	−4.39008	−0.184042	−0.0920208	−	0.995757i	$-0.529333\pi$
$569$	−4.39008	−0.184042	−0.0920208	+	0.995757i	$0.529333\pi$
$570$	1.30439	0.0546347
$571$	5.37356	0.224876	0.112438	−	0.993659i	$-0.464134\pi$
$571$	5.37356	0.224876	0.112438	+	0.993659i	$0.464134\pi$
$572$	2.88663	0.120696
$573$	−60.5178	−2.52817
$574$	0	0
$575$	35.5577	1.48286
$576$	8.62267	0.359278
$577$	2.13812	0.0890110	0.0445055	−	0.999009i	$-0.485829\pi$
$577$	2.13812	0.0890110	0.0445055	+	0.999009i	$0.485829\pi$
$578$	1.00000	0.0415945
$579$	14.9715	0.622192
$580$	2.49778	0.103715
$581$	0	0
$582$	39.7891	1.64931
$583$	−11.3053	−0.468216
$584$	11.5743	0.478946
$585$	−6.44585	−0.266503
$586$	17.3823	0.718055
$587$	−27.8786	−1.15067	−0.575337	−	0.817917i	$-0.695129\pi$
$587$	−27.8786	−1.15067	−0.575337	+	0.817917i	$0.695129\pi$
$588$	0	0
$589$	−3.74729	−0.154404
$590$	−5.17154	−0.212909
$591$	56.3950	2.31978
$592$	1.63506	0.0672006
$593$	19.1230	0.785289	0.392644	−	0.919690i	$-0.371560\pi$
$593$	19.1230	0.785289	0.392644	+	0.919690i	$0.371560\pi$
$594$	−27.0127	−1.10835
$595$	0	0
$596$	−5.64863	−0.231377
$597$	0.355381	0.0145448
$598$	14.9660	0.612005
$599$	46.0170	1.88020	0.940102	−	0.340894i	$-0.110730\pi$
$599$	46.0170	1.88020	0.940102	+	0.340894i	$0.110730\pi$
$600$	−16.5920	−0.677365
$601$	17.9763	0.733268	0.366634	−	0.930365i	$-0.380510\pi$
$601$	17.9763	0.733268	0.366634	+	0.930365i	$0.380510\pi$
$602$	0	0
$603$	37.2373	1.51642
$604$	20.9081	0.850739
$605$	−3.28962	−0.133742
$606$	−28.7008	−1.16589
$607$	−28.9581	−1.17537	−0.587686	−	0.809089i	$-0.699961\pi$
$607$	−28.9581	−1.17537	−0.587686	+	0.809089i	$0.699961\pi$
$608$	1.04841	0.0425188
$609$	0	0
$610$	−4.40211	−0.178236
$611$	4.04363	0.163588
$612$	8.62267	0.348551
$613$	3.96390	0.160100	0.0800502	−	0.996791i	$-0.474492\pi$
$613$	3.96390	0.160100	0.0800502	+	0.996791i	$0.474492\pi$
$614$	20.7195	0.836171
$615$	−9.42353	−0.379994
$616$	0	0
$617$	−41.7057	−1.67901	−0.839505	−	0.543352i	$-0.817155\pi$
$617$	−41.7057	−1.67901	−0.839505	+	0.543352i	$0.817155\pi$
$618$	−63.0344	−2.53562
$619$	−2.94919	−0.118538	−0.0592690	−	0.998242i	$-0.518877\pi$
$619$	−2.94919	−0.118538	−0.0592690	+	0.998242i	$0.518877\pi$
$620$	−1.30439	−0.0523854
$621$	−140.050	−5.62001
$622$	15.6565	0.627770
$623$	0	0
$624$	−6.98346	−0.279562
$625$	23.0200	0.920801
$626$	−11.3150	−0.452239
$627$	−5.03685	−0.201152
$628$	−10.8668	−0.433633
$629$	1.63506	0.0651941
$630$	0	0
$631$	19.2831	0.767648	0.383824	−	0.923406i	$-0.374607\pi$
$631$	19.2831	0.767648	0.383824	+	0.923406i	$0.374607\pi$
$632$	−6.13908	−0.244200
$633$	27.3662	1.08771
$634$	−0.347272	−0.0137919
$635$	−0.472994	−0.0187702
$636$	27.3501	1.08450
$637$	0	0
$638$	−9.64511	−0.381854
$639$	50.8473	2.01149
$640$	0.364940	0.0144255
$641$	21.3422	0.842965	0.421482	−	0.906837i	$-0.361510\pi$
$641$	21.3422	0.842965	0.421482	+	0.906837i	$0.361510\pi$
$642$	44.6819	1.76345
$643$	18.0380	0.711348	0.355674	−	0.934610i	$-0.384251\pi$
$643$	18.0380	0.711348	0.355674	+	0.934610i	$0.384251\pi$
$644$	0	0
$645$	1.15161	0.0453447
$646$	1.04841	0.0412493
$647$	−25.1525	−0.988848	−0.494424	−	0.869221i	$-0.664621\pi$
$647$	−25.1525	−0.988848	−0.494424	+	0.869221i	$0.664621\pi$
$648$	39.4824	1.55101
$649$	19.9697	0.783881
$650$	9.96925	0.391026
$651$	0	0
$652$	−11.5743	−0.453283
$653$	47.2849	1.85040	0.925200	−	0.379481i	$-0.123897\pi$
$653$	47.2849	1.85040	0.925200	+	0.379481i	$0.123897\pi$
$654$	5.18392	0.202707
$655$	−1.13911	−0.0445087
$656$	−7.57425	−0.295725
$657$	99.8009	3.89360
$658$	0	0
$659$	12.1780	0.474387	0.237194	−	0.971462i	$-0.423772\pi$
$659$	12.1780	0.474387	0.237194	+	0.971462i	$0.423772\pi$
$660$	−1.75327	−0.0682457
$661$	−17.2277	−0.670078	−0.335039	−	0.942204i	$-0.608750\pi$
$661$	−17.2277	−0.670078	−0.335039	+	0.942204i	$0.608750\pi$
$662$	15.5379	0.603898
$663$	−6.98346	−0.271215
$664$	−6.82671	−0.264928
$665$	0	0
$666$	14.0986	0.546309
$667$	−50.0059	−1.93624
$668$	1.34722	0.0521254
$669$	46.3136	1.79059
$670$	1.57600	0.0608864
$671$	16.9986	0.656224
$672$	0	0
$673$	38.8888	1.49905	0.749526	−	0.661975i	$-0.230282\pi$
$673$	38.8888	1.49905	0.749526	+	0.661975i	$0.230282\pi$
$674$	14.4364	0.556068
$675$	−93.2911	−3.59078
$676$	−8.80400	−0.338616
$677$	40.0170	1.53798	0.768989	−	0.639262i	$-0.220760\pi$
$677$	40.0170	1.53798	0.768989	+	0.639262i	$0.220760\pi$
$678$	−2.48831	−0.0955629
$679$	0	0
$680$	0.364940	0.0139948
$681$	−34.8078	−1.33384
$682$	5.03685	0.192871
$683$	−39.6157	−1.51585	−0.757927	−	0.652340i	$-0.773788\pi$
$683$	−39.6157	−1.51585	−0.757927	+	0.652340i	$0.773788\pi$
$684$	9.04011	0.345657
$685$	6.63646	0.253566
$686$	0	0
$687$	−60.4213	−2.30522
$688$	0.925620	0.0352889
$689$	−16.4333	−0.626058
$690$	−9.08996	−0.346049
$691$	−6.07204	−0.230991	−0.115496	−	0.993308i	$-0.536846\pi$
$691$	−6.07204	−0.230991	−0.115496	+	0.993308i	$0.536846\pi$
$692$	−4.91466	−0.186827
$693$	0	0
$694$	−19.2287	−0.729913
$695$	3.47860	0.131951
$696$	23.3339	0.884468
$697$	−7.57425	−0.286895
$698$	3.29726	0.124803
$699$	62.4764	2.36308
$700$	0	0
$701$	−1.16265	−0.0439128	−0.0219564	−	0.999759i	$-0.506989\pi$
$701$	−1.16265	−0.0439128	−0.0219564	+	0.999759i	$0.506989\pi$
$702$	−39.2656	−1.48199
$703$	1.71422	0.0646530
$704$	−1.40920	−0.0531113
$705$	−2.45600	−0.0924983
$706$	18.5057	0.696472
$707$	0	0
$708$	−48.3116	−1.81566
$709$	24.5037	0.920256	0.460128	−	0.887853i	$-0.347803\pi$
$709$	24.5037	0.920256	0.460128	+	0.887853i	$0.347803\pi$
$710$	2.15203	0.0807641
$711$	−52.9353	−1.98523
$712$	10.2713	0.384933
$713$	26.1140	0.977976
$714$	0	0
$715$	1.05345	0.0393966
$716$	−7.91875	−0.295938
$717$	27.9804	1.04495
$718$	21.0517	0.785642
$719$	0.349225	0.0130239	0.00651194	−	0.999979i	$-0.497927\pi$
$719$	0.349225	0.0130239	0.00651194	+	0.999979i	$0.497927\pi$
$720$	3.14675	0.117273
$721$	0	0
$722$	−17.9008	−0.666200
$723$	−10.0874	−0.375154
$724$	−14.9430	−0.555350
$725$	−33.3103	−1.23711
$726$	−30.7311	−1.14054
$727$	33.0309	1.22505	0.612524	−	0.790452i	$-0.290154\pi$
$727$	33.0309	1.22505	0.612524	+	0.790452i	$0.290154\pi$
$728$	0	0
$729$	144.392	5.34786
$730$	4.22390	0.156334
$731$	0.925620	0.0342353
$732$	−41.1237	−1.51998
$733$	16.1724	0.597340	0.298670	−	0.954357i	$-0.403457\pi$
$733$	16.1724	0.597340	0.298670	+	0.954357i	$0.403457\pi$
$734$	−24.7342	−0.912955
$735$	0	0
$736$	−7.30614	−0.269308
$737$	−6.08569	−0.224169
$738$	−65.3102	−2.40410
$739$	−27.5308	−1.01274	−0.506368	−	0.862318i	$-0.669012\pi$
$739$	−27.5308	−1.01274	−0.506368	+	0.862318i	$0.669012\pi$
$740$	0.596698	0.0219351
$741$	−7.32154	−0.268964
$742$	0	0
$743$	20.3056	0.744940	0.372470	−	0.928044i	$-0.378511\pi$
$743$	20.3056	0.744940	0.372470	+	0.928044i	$0.378511\pi$
$744$	−12.1854	−0.446737
$745$	−2.06141	−0.0755242
$746$	−35.5293	−1.30082
$747$	−58.8644	−2.15374
$748$	−1.40920	−0.0515256
$749$	0	0
$750$	−12.2758	−0.448250
$751$	−47.5349	−1.73457	−0.867287	−	0.497808i	$-0.834138\pi$
$751$	−47.5349	−1.73457	−0.867287	+	0.497808i	$0.834138\pi$
$752$	−1.97403	−0.0719856
$753$	33.6628	1.22674
$754$	−14.0201	−0.510582
$755$	7.63020	0.277691
$756$	0	0
$757$	−33.2618	−1.20892	−0.604461	−	0.796635i	$-0.706611\pi$
$757$	−33.2618	−1.20892	−0.604461	+	0.796635i	$0.706611\pi$
$758$	18.2724	0.663684
$759$	35.1006	1.27407
$760$	0.382608	0.0138786
$761$	−0.237541	−0.00861086	−0.00430543	−	0.999991i	$-0.501370\pi$
$761$	−0.237541	−0.00861086	−0.00430543	+	0.999991i	$0.501370\pi$
$762$	−4.41863	−0.160070
$763$	0	0
$764$	−17.7513	−0.642220
$765$	3.14675	0.113771
$766$	−7.78557	−0.281304
$767$	29.0280	1.04814
$768$	3.40920	0.123019
$769$	−1.72158	−0.0620818	−0.0310409	−	0.999518i	$-0.509882\pi$
$769$	−1.72158	−0.0620818	−0.0310409	+	0.999518i	$0.509882\pi$
$770$	0	0
$771$	−39.0532	−1.40647
$772$	4.39148	0.158053
$773$	−18.4056	−0.662004	−0.331002	−	0.943630i	$-0.607387\pi$
$773$	−18.4056	−0.662004	−0.331002	+	0.943630i	$0.607387\pi$
$774$	7.98131	0.286882
$775$	17.3952	0.624855
$776$	11.6711	0.418967
$777$	0	0
$778$	−8.92705	−0.320050
$779$	−7.94094	−0.284514
$780$	−2.54854	−0.0912524
$781$	−8.30998	−0.297354
$782$	−7.30614	−0.261267
$783$	131.198	4.68865
$784$	0	0
$785$	−3.96573	−0.141543
$786$	−10.6414	−0.379564
$787$	27.8753	0.993646	0.496823	−	0.867852i	$-0.334500\pi$
$787$	27.8753	0.993646	0.496823	+	0.867852i	$0.334500\pi$
$788$	16.5420	0.589284
$789$	−29.3433	−1.04465
$790$	−2.24040	−0.0797097
$791$	0	0
$792$	−12.1511	−0.431770
$793$	24.7091	0.877446
$794$	−5.62794	−0.199728
$795$	9.98115	0.353995
$796$	0.104242	0.00369475
$797$	35.6895	1.26419	0.632094	−	0.774892i	$-0.282196\pi$
$797$	35.6895	1.26419	0.632094	+	0.774892i	$0.282196\pi$
$798$	0	0
$799$	−1.97403	−0.0698363
$800$	−4.86682	−0.172068
$801$	88.5660	3.12932
$802$	−9.24533	−0.326464
$803$	−16.3105	−0.575584
$804$	14.7228	0.519232
$805$	0	0
$806$	7.32154	0.257890
$807$	32.2337	1.13468
$808$	−8.41863	−0.296166
$809$	37.4744	1.31753	0.658765	−	0.752349i	$-0.271079\pi$
$809$	37.4744	1.31753	0.658765	+	0.752349i	$0.271079\pi$
$810$	14.4087	0.506269
$811$	−31.7256	−1.11404	−0.557019	−	0.830500i	$-0.688055\pi$
$811$	−31.7256	−1.11404	−0.557019	+	0.830500i	$0.688055\pi$
$812$	0	0
$813$	59.3964	2.08312
$814$	−2.30413	−0.0807598
$815$	−4.22390	−0.147957
$816$	3.40920	0.119346
$817$	0.970432	0.0339511
$818$	29.8882	1.04502
$819$	0	0
$820$	−2.76415	−0.0965282
$821$	14.9854	0.522994	0.261497	−	0.965204i	$-0.415784\pi$
$821$	14.9854	0.522994	0.261497	+	0.965204i	$0.415784\pi$
$822$	61.9967	2.16238
$823$	−12.9292	−0.450683	−0.225342	−	0.974280i	$-0.572350\pi$
$823$	−12.9292	−0.450683	−0.225342	+	0.974280i	$0.572350\pi$
$824$	−18.4895	−0.644112
$825$	23.3815	0.814038
$826$	0	0
$827$	28.4621	0.989726	0.494863	−	0.868971i	$-0.335218\pi$
$827$	28.4621	0.989726	0.494863	+	0.868971i	$0.335218\pi$
$828$	−62.9984	−2.18935
$829$	38.2483	1.32842	0.664210	−	0.747546i	$-0.268768\pi$
$829$	38.2483	1.32842	0.664210	+	0.747546i	$0.268768\pi$
$830$	−2.49134	−0.0864755
$831$	−37.3008	−1.29395
$832$	−2.04841	−0.0710159
$833$	0	0
$834$	32.4965	1.12526
$835$	0.491653	0.0170144
$836$	−1.47743	−0.0510979
$837$	−68.5142	−2.36820
$838$	2.13908	0.0738934
$839$	−15.8569	−0.547442	−0.273721	−	0.961809i	$-0.588254\pi$
$839$	−15.8569	−0.547442	−0.273721	+	0.961809i	$0.588254\pi$
$840$	0	0
$841$	17.8454	0.615360
$842$	−21.6545	−0.746263
$843$	67.8065	2.33538
$844$	8.02714	0.276306
$845$	−3.21293	−0.110528
$846$	−17.0214	−0.585209
$847$	0	0
$848$	8.02245	0.275492
$849$	32.1664	1.10395
$850$	−4.86682	−0.166931
$851$	−11.9460	−0.409503
$852$	20.1039	0.688747
$853$	11.4503	0.392050	0.196025	−	0.980599i	$-0.437197\pi$
$853$	11.4503	0.392050	0.196025	+	0.980599i	$0.437197\pi$
$854$	0	0
$855$	3.29910	0.112827
$856$	13.1062	0.447962
$857$	54.4942	1.86149	0.930743	−	0.365675i	$-0.119162\pi$
$857$	54.4942	1.86149	0.930743	+	0.365675i	$0.119162\pi$
$858$	9.84111	0.335970
$859$	−11.4021	−0.389035	−0.194518	−	0.980899i	$-0.562314\pi$
$859$	−11.4021	−0.389035	−0.194518	+	0.980899i	$0.562314\pi$
$860$	0.337796	0.0115187
$861$	0	0
$862$	3.69392	0.125815
$863$	−39.2570	−1.33632	−0.668162	−	0.744016i	$-0.732919\pi$
$863$	−39.2570	−1.33632	−0.668162	+	0.744016i	$0.732919\pi$
$864$	19.1688	0.652136
$865$	−1.79355	−0.0609827
$866$	9.60046	0.326237
$867$	3.40920	0.115783
$868$	0	0
$869$	8.65121	0.293472
$870$	8.51545	0.288701
$871$	−8.84614	−0.299740
$872$	1.52057	0.0514929
$873$	100.636	3.40601
$874$	−7.65985	−0.259098
$875$	0	0
$876$	39.4590	1.33320
$877$	44.3797	1.49860	0.749298	−	0.662234i	$-0.230391\pi$
$877$	44.3797	1.49860	0.749298	+	0.662234i	$0.230391\pi$
$878$	−18.0740	−0.609968
$879$	59.2597	1.99878
$880$	−0.514274	−0.0173362
$881$	−5.22758	−0.176122	−0.0880609	−	0.996115i	$-0.528067\pi$
$881$	−5.22758	−0.176122	−0.0880609	+	0.996115i	$0.528067\pi$
$882$	0	0
$883$	22.1553	0.745585	0.372792	−	0.927915i	$-0.378400\pi$
$883$	22.1553	0.745585	0.372792	+	0.927915i	$0.378400\pi$
$884$	−2.04841	−0.0688956
$885$	−17.6308	−0.592654
$886$	13.0567	0.438649
$887$	24.8536	0.834503	0.417251	−	0.908791i	$-0.362993\pi$
$887$	24.8536	0.834503	0.417251	+	0.908791i	$0.362993\pi$
$888$	5.57425	0.187060
$889$	0	0
$890$	3.74840	0.125647
$891$	−55.6387	−1.86397
$892$	13.5849	0.454855
$893$	−2.06960	−0.0692566
$894$	−19.2573	−0.644062
$895$	−2.88987	−0.0965976
$896$	0	0
$897$	51.0221	1.70358
$898$	24.9412	0.832299
$899$	−24.4635	−0.815904
$900$	−41.9650	−1.39883
$901$	8.02245	0.267266
$902$	10.6737	0.355394
$903$	0	0
$904$	−0.729879	−0.0242754
$905$	−5.45328	−0.181273
$906$	71.2800	2.36812
$907$	25.2004	0.836767	0.418383	−	0.908271i	$-0.362597\pi$
$907$	25.2004	0.836767	0.418383	+	0.908271i	$0.362597\pi$
$908$	−10.2099	−0.338829
$909$	−72.5910	−2.40769
$910$	0	0
$911$	14.7462	0.488563	0.244282	−	0.969704i	$-0.421448\pi$
$911$	14.7462	0.488563	0.244282	+	0.969704i	$0.421448\pi$
$912$	3.57425	0.118355
$913$	9.62021	0.318383
$914$	−36.7081	−1.21420
$915$	−15.0077	−0.496138
$916$	−17.7230	−0.585585
$917$	0	0
$918$	19.1688	0.632665
$919$	−19.7325	−0.650914	−0.325457	−	0.945557i	$-0.605518\pi$
$919$	−19.7325	−0.650914	−0.325457	+	0.945557i	$0.605518\pi$
$920$	−2.66630	−0.0879053
$921$	70.6370	2.32757
$922$	−0.281686	−0.00927683
$923$	−12.0794	−0.397597
$924$	0	0
$925$	−7.95754	−0.261642
$926$	−13.4161	−0.440881
$927$	−159.429	−5.23632
$928$	6.84437	0.224678
$929$	44.6188	1.46390	0.731948	−	0.681361i	$-0.238611\pi$
$929$	44.6188	1.46390	0.731948	+	0.681361i	$0.238611\pi$
$930$	−4.44692	−0.145820
$931$	0	0
$932$	18.3258	0.600282
$933$	53.3763	1.74746
$934$	−14.6852	−0.480515
$935$	−0.514274	−0.0168186
$936$	−17.6628	−0.577326
$937$	−46.5097	−1.51941	−0.759704	−	0.650270i	$-0.774656\pi$
$937$	−46.5097	−1.51941	−0.759704	+	0.650270i	$0.774656\pi$
$938$	0	0
$939$	−38.5752	−1.25885
$940$	−0.720403	−0.0234970
$941$	2.27524	0.0741706	0.0370853	−	0.999312i	$-0.488193\pi$
$941$	2.27524	0.0741706	0.0370853	+	0.999312i	$0.488193\pi$
$942$	−37.0472	−1.20706
$943$	55.3385	1.80207
$944$	−14.1710	−0.461225
$945$	0	0
$946$	−1.30439	−0.0424093
$947$	26.7089	0.867922	0.433961	−	0.900932i	$-0.357116\pi$
$947$	26.7089	0.867922	0.433961	+	0.900932i	$0.357116\pi$
$948$	−20.9294	−0.679755
$949$	−23.7088	−0.769622
$950$	−5.10244	−0.165545
$951$	−1.18392	−0.0383913
$952$	0	0
$953$	−60.8906	−1.97244	−0.986220	−	0.165441i	$-0.947095\pi$
$953$	−60.8906	−1.97244	−0.986220	+	0.165441i	$0.947095\pi$
$954$	69.1749	2.23962
$955$	−6.47816	−0.209628
$956$	8.20731	0.265443
$957$	−32.8821	−1.06293
$958$	−14.8532	−0.479887
$959$	0	0
$960$	1.24415	0.0401549
$961$	−18.2247	−0.587894
$962$	−3.34928	−0.107985
$963$	113.011	3.64172
$964$	−2.95887	−0.0952987
$965$	1.60263	0.0515904
$966$	0	0
$967$	−13.9533	−0.448706	−0.224353	−	0.974508i	$-0.572027\pi$
$967$	−13.9533	−0.448706	−0.224353	+	0.974508i	$0.572027\pi$
$968$	−9.01415	−0.289726
$969$	3.57425	0.114822
$970$	4.25924	0.136756
$971$	−3.23093	−0.103685	−0.0518427	−	0.998655i	$-0.516509\pi$
$971$	−3.23093	−0.103685	−0.0518427	+	0.998655i	$0.516509\pi$
$972$	77.0970	2.47289
$973$	0	0
$974$	−1.61476	−0.0517402
$975$	33.9872	1.08846
$976$	−12.0626	−0.386113
$977$	35.5484	1.13730	0.568648	−	0.822581i	$-0.307467\pi$
$977$	35.5484	1.13730	0.568648	+	0.822581i	$0.307467\pi$
$978$	−39.4590	−1.26176
$979$	−14.4743	−0.462602
$980$	0	0
$981$	13.1113	0.418613
$982$	2.29139	0.0731212
$983$	−6.69953	−0.213682	−0.106841	−	0.994276i	$-0.534074\pi$
$983$	−6.69953	−0.213682	−0.106841	+	0.994276i	$0.534074\pi$
$984$	−25.8222	−0.823181
$985$	6.03683	0.192349
$986$	6.84437	0.217969
$987$	0	0
$988$	−2.14758	−0.0683237
$989$	−6.76271	−0.215042
$990$	−4.43441	−0.140935
$991$	−33.8449	−1.07512	−0.537560	−	0.843226i	$-0.680654\pi$
$991$	−33.8449	−1.07512	−0.537560	+	0.843226i	$0.680654\pi$
$992$	−3.57425	−0.113483
$993$	52.9718	1.68101
$994$	0	0
$995$	0.0380419	0.00120601
$996$	−23.2736	−0.737453
$997$	14.7571	0.467362	0.233681	−	0.972313i	$-0.424923\pi$
$997$	14.7571	0.467362	0.233681	+	0.972313i	$0.424923\pi$
$998$	−21.4770	−0.679841
$999$	31.3422	0.991622

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1666.2.a.ba.1.5		5
7.3	odd	6		238.2.e.f.205.5	yes	10
7.5	odd	6		238.2.e.f.137.5	✓	10
7.6	odd	2		1666.2.a.z.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
238.2.e.f.137.5	✓	10	7.5	odd	6
238.2.e.f.205.5	yes	10	7.3	odd	6
1666.2.a.z.1.1		5	7.6	odd	2
1666.2.a.ba.1.5		5	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +3.40920 q^{3} +1.00000 q^{4} +0.364940 q^{5} +3.40920 q^{6} +1.00000 q^{8} +8.62267 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +3.40920 q^{3} +1.00000 q^{4} +0.364940 q^{5} +3.40920 q^{6} +1.00000 q^{8} +8.62267 q^{9} +0.364940 q^{10} -1.40920 q^{11} +3.40920 q^{12} -2.04841 q^{13} +1.24415 q^{15} +1.00000 q^{16} +1.00000 q^{17} +8.62267 q^{18} +1.04841 q^{19} +0.364940 q^{20} -1.40920 q^{22} -7.30614 q^{23} +3.40920 q^{24} -4.86682 q^{25} -2.04841 q^{26} +19.1688 q^{27} +6.84437 q^{29} +1.24415 q^{30} -3.57425 q^{31} +1.00000 q^{32} -4.80426 q^{33} +1.00000 q^{34} +8.62267 q^{36} +1.63506 q^{37} +1.04841 q^{38} -6.98346 q^{39} +0.364940 q^{40} -7.57425 q^{41} +0.925620 q^{43} -1.40920 q^{44} +3.14675 q^{45} -7.30614 q^{46} -1.97403 q^{47} +3.40920 q^{48} -4.86682 q^{50} +3.40920 q^{51} -2.04841 q^{52} +8.02245 q^{53} +19.1688 q^{54} -0.514274 q^{55} +3.57425 q^{57} +6.84437 q^{58} -14.1710 q^{59} +1.24415 q^{60} -12.0626 q^{61} -3.57425 q^{62} +1.00000 q^{64} -0.747547 q^{65} -4.80426 q^{66} +4.31853 q^{67} +1.00000 q^{68} -24.9081 q^{69} +5.89694 q^{71} +8.62267 q^{72} +11.5743 q^{73} +1.63506 q^{74} -16.5920 q^{75} +1.04841 q^{76} -6.98346 q^{78} -6.13908 q^{79} +0.364940 q^{80} +39.4824 q^{81} -7.57425 q^{82} -6.82671 q^{83} +0.364940 q^{85} +0.925620 q^{86} +23.3339 q^{87} -1.40920 q^{88} +10.2713 q^{89} +3.14675 q^{90} -7.30614 q^{92} -12.1854 q^{93} -1.97403 q^{94} +0.382608 q^{95} +3.40920 q^{96} +11.6711 q^{97} -12.1511 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{2} + 5 q^{4} + q^{5} + 5 q^{8} + 11 q^{9}+O(q^{10}) \) 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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