LMFDB - Embedded newform 1666.2.a.ba.1.1

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			1.1
Root			$-3.12631$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -3.12631 q^{3} +1.00000 q^{4} +3.94425 q^{5} -3.12631 q^{6} +1.00000 q^{8} +6.77382 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.12631 q^{3} +1.00000 q^{4} +3.94425 q^{5} -3.12631 q^{6} +1.00000 q^{8} +6.77382 q^{9} +3.94425 q^{10} +5.12631 q^{11} -3.12631 q^{12} +0.304523 q^{13} -12.3310 q^{15} +1.00000 q^{16} +1.00000 q^{17} +6.77382 q^{18} -1.30452 q^{19} +3.94425 q^{20} +5.12631 q^{22} +0.474955 q^{23} -3.12631 q^{24} +10.5571 q^{25} +0.304523 q^{26} -11.7981 q^{27} +0.189836 q^{29} -12.3310 q^{30} -4.07835 q^{31} +1.00000 q^{32} -16.0264 q^{33} +1.00000 q^{34} +6.77382 q^{36} -1.94425 q^{37} -1.30452 q^{38} -0.952034 q^{39} +3.94425 q^{40} -8.07835 q^{41} -3.13794 q^{43} +5.12631 q^{44} +26.7177 q^{45} +0.474955 q^{46} +4.44246 q^{47} -3.12631 q^{48} +10.5571 q^{50} -3.12631 q^{51} +0.304523 q^{52} -0.746982 q^{53} -11.7981 q^{54} +20.2195 q^{55} +4.07835 q^{57} +0.189836 q^{58} -6.40971 q^{59} -12.3310 q^{60} +14.5836 q^{61} -4.07835 q^{62} +1.00000 q^{64} +1.20112 q^{65} -16.0264 q^{66} -5.19303 q^{67} +1.00000 q^{68} -1.48486 q^{69} +4.65136 q^{71} +6.77382 q^{72} +12.0783 q^{73} -1.94425 q^{74} -33.0049 q^{75} -1.30452 q^{76} -0.952034 q^{78} -6.76220 q^{79} +3.94425 q^{80} +16.5632 q^{81} -8.07835 q^{82} -9.27946 q^{83} +3.94425 q^{85} -3.13794 q^{86} -0.593487 q^{87} +5.12631 q^{88} +12.9901 q^{89} +26.7177 q^{90} +0.474955 q^{92} +12.7502 q^{93} +4.44246 q^{94} -5.14537 q^{95} -3.12631 q^{96} +7.46930 q^{97} +34.7247 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−3.12631	−1.80498	−0.902488	−	0.430714i	$-0.858262\pi$
$3$	−3.12631	−1.80498	−0.902488	+	0.430714i	$0.858262\pi$
$4$	1.00000	0.500000
$5$	3.94425	1.76392	0.881962	−	0.471320i	$-0.156222\pi$
$5$	3.94425	1.76392	0.881962	+	0.471320i	$0.156222\pi$
$6$	−3.12631	−1.27631
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	6.77382	2.25794
$10$	3.94425	1.24728
$11$	5.12631	1.54564	0.772821	−	0.634625i	$-0.218845\pi$
$11$	5.12631	1.54564	0.772821	+	0.634625i	$0.218845\pi$
$12$	−3.12631	−0.902488
$13$	0.304523	0.0844596	0.0422298	−	0.999108i	$-0.486554\pi$
$13$	0.304523	0.0844596	0.0422298	+	0.999108i	$0.486554\pi$
$14$	0	0
$15$	−12.3310	−3.18384
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	6.77382	1.59661
$19$	−1.30452	−0.299278	−0.149639	−	0.988741i	$-0.547811\pi$
$19$	−1.30452	−0.299278	−0.149639	+	0.988741i	$0.547811\pi$
$20$	3.94425	0.881962
$21$	0	0
$22$	5.12631	1.09293
$23$	0.474955	0.0990351	0.0495175	−	0.998773i	$-0.484232\pi$
$23$	0.474955	0.0990351	0.0495175	+	0.998773i	$0.484232\pi$
$24$	−3.12631	−0.638156
$25$	10.5571	2.11143
$26$	0.304523	0.0597219
$27$	−11.7981	−2.27055
$28$	0	0
$29$	0.189836	0.0352517	0.0176259	−	0.999845i	$-0.494389\pi$
$29$	0.189836	0.0352517	0.0176259	+	0.999845i	$0.494389\pi$
$30$	−12.3310	−2.25132
$31$	−4.07835	−0.732493	−0.366246	−	0.930518i	$-0.619357\pi$
$31$	−4.07835	−0.732493	−0.366246	+	0.930518i	$0.619357\pi$
$32$	1.00000	0.176777
$33$	−16.0264	−2.78985
$34$	1.00000	0.171499
$35$	0	0
$36$	6.77382	1.12897
$37$	−1.94425	−0.319634	−0.159817	−	0.987147i	$-0.551090\pi$
$37$	−1.94425	−0.319634	−0.159817	+	0.987147i	$0.551090\pi$
$38$	−1.30452	−0.211622
$39$	−0.952034	−0.152448
$40$	3.94425	0.623641
$41$	−8.07835	−1.26163	−0.630813	−	0.775935i	$-0.717278\pi$
$41$	−8.07835	−1.26163	−0.630813	+	0.775935i	$0.717278\pi$
$42$	0	0
$43$	−3.13794	−0.478531	−0.239265	−	0.970954i	$-0.576907\pi$
$43$	−3.13794	−0.478531	−0.239265	+	0.970954i	$0.576907\pi$
$44$	5.12631	0.772821
$45$	26.7177	3.98284
$46$	0.474955	0.0700284
$47$	4.44246	0.647999	0.324000	−	0.946057i	$-0.394972\pi$
$47$	4.44246	0.647999	0.324000	+	0.946057i	$0.394972\pi$
$48$	−3.12631	−0.451244
$49$	0	0
$50$	10.5571	1.49301
$51$	−3.12631	−0.437771
$52$	0.304523	0.0422298
$53$	−0.746982	−0.102606	−0.0513029	−	0.998683i	$-0.516337\pi$
$53$	−0.746982	−0.102606	−0.0513029	+	0.998683i	$0.516337\pi$
$54$	−11.7981	−1.60552
$55$	20.2195	2.72639
$56$	0	0
$57$	4.07835	0.540190
$58$	0.189836	0.0249267
$59$	−6.40971	−0.834473	−0.417237	−	0.908798i	$-0.637001\pi$
$59$	−6.40971	−0.834473	−0.417237	+	0.908798i	$0.637001\pi$
$60$	−12.3310	−1.59192
$61$	14.5836	1.86724	0.933619	−	0.358268i	$-0.116633\pi$
$61$	14.5836	1.86724	0.933619	+	0.358268i	$0.116633\pi$
$62$	−4.07835	−0.517950
$63$	0	0
$64$	1.00000	0.125000
$65$	1.20112	0.148980
$66$	−16.0264	−1.97272
$67$	−5.19303	−0.634430	−0.317215	−	0.948354i	$-0.602748\pi$
$67$	−5.19303	−0.634430	−0.317215	+	0.948354i	$0.602748\pi$
$68$	1.00000	0.121268
$69$	−1.48486	−0.178756
$70$	0	0
$71$	4.65136	0.552014	0.276007	−	0.961156i	$-0.410989\pi$
$71$	4.65136	0.552014	0.276007	+	0.961156i	$0.410989\pi$
$72$	6.77382	0.798303
$73$	12.0783	1.41366	0.706832	−	0.707382i	$-0.250124\pi$
$73$	12.0783	1.41366	0.706832	+	0.707382i	$0.250124\pi$
$74$	−1.94425	−0.226015
$75$	−33.0049	−3.81108
$76$	−1.30452	−0.149639
$77$	0	0
$78$	−0.952034	−0.107797
$79$	−6.76220	−0.760807	−0.380403	−	0.924821i	$-0.624215\pi$
$79$	−6.76220	−0.760807	−0.380403	+	0.924821i	$0.624215\pi$
$80$	3.94425	0.440981
$81$	16.5632	1.84036
$82$	−8.07835	−0.892104
$83$	−9.27946	−1.01855	−0.509277	−	0.860603i	$-0.670087\pi$
$83$	−9.27946	−1.01855	−0.509277	+	0.860603i	$0.670087\pi$
$84$	0	0
$85$	3.94425	0.427814
$86$	−3.13794	−0.338372
$87$	−0.593487	−0.0636285
$88$	5.12631	0.546467
$89$	12.9901	1.37695	0.688474	−	0.725261i	$-0.258281\pi$
$89$	12.9901	1.37695	0.688474	+	0.725261i	$0.258281\pi$
$90$	26.7177	2.81629
$91$	0	0
$92$	0.474955	0.0495175
$93$	12.7502	1.32213
$94$	4.44246	0.458205
$95$	−5.14537	−0.527904
$96$	−3.12631	−0.319078
$97$	7.46930	0.758392	0.379196	−	0.925316i	$-0.376201\pi$
$97$	7.46930	0.758392	0.379196	+	0.925316i	$0.376201\pi$
$98$	0	0
$99$	34.7247	3.48997
$100$	10.5571	1.05571
$101$	−2.26818	−0.225693	−0.112846	−	0.993612i	$-0.535997\pi$
$101$	−2.26818	−0.225693	−0.112846	+	0.993612i	$0.535997\pi$
$102$	−3.12631	−0.309551
$103$	−1.21668	−0.119883	−0.0599414	−	0.998202i	$-0.519091\pi$
$103$	−1.21668	−0.119883	−0.0599414	+	0.998202i	$0.519091\pi$
$104$	0.304523	0.0298610
$105$	0	0
$106$	−0.746982	−0.0725533
$107$	8.78545	0.849321	0.424661	−	0.905353i	$-0.360393\pi$
$107$	8.78545	0.849321	0.424661	+	0.905353i	$0.360393\pi$
$108$	−11.7981	−1.13528
$109$	11.7544	1.12587	0.562935	−	0.826501i	$-0.309672\pi$
$109$	11.7544	1.12587	0.562935	+	0.826501i	$0.309672\pi$
$110$	20.2195	1.92785
$111$	6.07835	0.576931
$112$	0	0
$113$	−7.88851	−0.742089	−0.371044	−	0.928615i	$-0.621000\pi$
$113$	−7.88851	−0.742089	−0.371044	+	0.928615i	$0.621000\pi$
$114$	4.07835	0.381972
$115$	1.87335	0.174690
$116$	0.189836	0.0176259
$117$	2.06279	0.190705
$118$	−6.40971	−0.590062
$119$	0	0
$120$	−12.3310	−1.12566
$121$	15.2791	1.38901
$122$	14.5836	1.32034
$123$	25.2554	2.27720
$124$	−4.07835	−0.366246
$125$	21.9188	1.96048
$126$	0	0
$127$	−0.553949	−0.0491551	−0.0245775	−	0.999698i	$-0.507824\pi$
$127$	−0.553949	−0.0491551	−0.0245775	+	0.999698i	$0.507824\pi$
$128$	1.00000	0.0883883
$129$	9.81016	0.863737
$130$	1.20112	0.105345
$131$	12.1644	1.06281	0.531403	−	0.847119i	$-0.321665\pi$
$131$	12.1644	1.06281	0.531403	+	0.847119i	$0.321665\pi$
$132$	−16.0264	−1.39492
$133$	0	0
$134$	−5.19303	−0.448610
$135$	−46.5349	−4.00509
$136$	1.00000	0.0857493
$137$	−13.8694	−1.18494	−0.592470	−	0.805593i	$-0.701847\pi$
$137$	−13.8694	−1.18494	−0.592470	+	0.805593i	$0.701847\pi$
$138$	−1.48486	−0.126400
$139$	4.70710	0.399251	0.199626	−	0.979872i	$-0.436027\pi$
$139$	4.70710	0.399251	0.199626	+	0.979872i	$0.436027\pi$
$140$	0	0
$141$	−13.8885	−1.16962
$142$	4.65136	0.390333
$143$	1.56108	0.130544
$144$	6.77382	0.564485
$145$	0.748762	0.0621813
$146$	12.0783	0.999611
$147$	0	0
$148$	−1.94425	−0.159817
$149$	−10.2163	−0.836950	−0.418475	−	0.908228i	$-0.637435\pi$
$149$	−10.2163	−0.836950	−0.418475	+	0.908228i	$0.637435\pi$
$150$	−33.0049	−2.69484
$151$	−2.51514	−0.204679	−0.102340	−	0.994750i	$-0.532633\pi$
$151$	−2.51514	−0.204679	−0.102340	+	0.994750i	$0.532633\pi$
$152$	−1.30452	−0.105811
$153$	6.77382	0.547631
$154$	0	0
$155$	−16.0860	−1.29206
$156$	−0.952034	−0.0762238
$157$	4.55715	0.363700	0.181850	−	0.983326i	$-0.441791\pi$
$157$	4.55715	0.363700	0.181850	+	0.983326i	$0.441791\pi$
$158$	−6.76220	−0.537972
$159$	2.33530	0.185201
$160$	3.94425	0.311821
$161$	0	0
$162$	16.5632	1.30133
$163$	−12.0783	−0.946049	−0.473025	−	0.881049i	$-0.656838\pi$
$163$	−12.0783	−0.946049	−0.473025	+	0.881049i	$0.656838\pi$
$164$	−8.07835	−0.630813
$165$	−63.2124	−4.92108
$166$	−9.27946	−0.720226
$167$	−10.9823	−0.849838	−0.424919	−	0.905231i	$-0.639697\pi$
$167$	−10.9823	−0.849838	−0.424919	+	0.905231i	$0.639697\pi$
$168$	0	0
$169$	−12.9073	−0.992867
$170$	3.94425	0.302511
$171$	−8.83661	−0.675752
$172$	−3.13794	−0.239265
$173$	−19.5779	−1.48848	−0.744241	−	0.667911i	$-0.767189\pi$
$173$	−19.5779	−1.48848	−0.744241	+	0.667911i	$0.767189\pi$
$174$	−0.593487	−0.0449921
$175$	0	0
$176$	5.12631	0.386410
$177$	20.0387	1.50620
$178$	12.9901	0.973649
$179$	−5.32777	−0.398216	−0.199108	−	0.979978i	$-0.563805\pi$
$179$	−5.32777	−0.398216	−0.199108	+	0.979978i	$0.563805\pi$
$180$	26.7177	1.99142
$181$	18.9802	1.41079	0.705394	−	0.708816i	$-0.250770\pi$
$181$	18.9802	1.41079	0.705394	+	0.708816i	$0.250770\pi$
$182$	0	0
$183$	−45.5928	−3.37032
$184$	0.474955	0.0350142
$185$	−7.66864	−0.563809
$186$	12.7502	0.934888
$187$	5.12631	0.374873
$188$	4.44246	0.324000
$189$	0	0
$190$	−5.14537	−0.373285
$191$	22.2039	1.60662	0.803310	−	0.595562i	$-0.203070\pi$
$191$	22.2039	1.60662	0.803310	+	0.595562i	$0.203070\pi$
$192$	−3.12631	−0.225622
$193$	−18.0529	−1.29948	−0.649738	−	0.760158i	$-0.725121\pi$
$193$	−18.0529	−1.29948	−0.649738	+	0.760158i	$0.725121\pi$
$194$	7.46930	0.536264
$195$	−3.75507	−0.268906
$196$	0	0
$197$	−20.3380	−1.44902	−0.724512	−	0.689263i	$-0.757935\pi$
$197$	−20.3380	−1.44902	−0.724512	+	0.689263i	$0.757935\pi$
$198$	34.7247	2.46778
$199$	11.2273	0.795879	0.397940	−	0.917412i	$-0.369725\pi$
$199$	11.2273	0.795879	0.397940	+	0.917412i	$0.369725\pi$
$200$	10.5571	0.746503
$201$	16.2350	1.14513
$202$	−2.26818	−0.159589
$203$	0	0
$204$	−3.12631	−0.218886
$205$	−31.8631	−2.22541
$206$	−1.21668	−0.0847699
$207$	3.21726	0.223615
$208$	0.304523	0.0211149
$209$	−6.68739	−0.462577
$210$	0	0
$211$	24.3211	1.67433	0.837166	−	0.546949i	$-0.184211\pi$
$211$	24.3211	1.67433	0.837166	+	0.546949i	$0.184211\pi$
$212$	−0.746982	−0.0513029
$213$	−14.5416	−0.996373
$214$	8.78545	0.600561
$215$	−12.3768	−0.844092
$216$	−11.7981	−0.802762
$217$	0	0
$218$	11.7544	0.796110
$219$	−37.7607	−2.55163
$220$	20.2195	1.36320
$221$	0.304523	0.0204845
$222$	6.07835	0.407952
$223$	−25.3902	−1.70025	−0.850126	−	0.526580i	$-0.823474\pi$
$223$	−25.3902	−1.70025	−0.850126	+	0.526580i	$0.823474\pi$
$224$	0	0
$225$	71.5122	4.76748
$226$	−7.88851	−0.524736
$227$	0.289307	0.0192020	0.00960099	−	0.999954i	$-0.496944\pi$
$227$	0.289307	0.0192020	0.00960099	+	0.999954i	$0.496944\pi$
$228$	4.07835	0.270095
$229$	−26.3542	−1.74154	−0.870768	−	0.491694i	$-0.836378\pi$
$229$	−26.3542	−1.74154	−0.870768	+	0.491694i	$0.836378\pi$
$230$	1.87335	0.123525
$231$	0	0
$232$	0.189836	0.0124634
$233$	−14.0064	−0.917589	−0.458795	−	0.888542i	$-0.651719\pi$
$233$	−14.0064	−0.917589	−0.458795	+	0.888542i	$0.651719\pi$
$234$	2.06279	0.134849
$235$	17.5222	1.14302
$236$	−6.40971	−0.417237
$237$	21.1407	1.37324
$238$	0	0
$239$	20.5759	1.33094	0.665472	−	0.746423i	$-0.268230\pi$
$239$	20.5759	1.33094	0.665472	+	0.746423i	$0.268230\pi$
$240$	−12.3310	−0.795961
$241$	17.5088	1.12784	0.563922	−	0.825828i	$-0.309292\pi$
$241$	17.5088	1.12784	0.563922	+	0.825828i	$0.309292\pi$
$242$	15.2791	0.982176
$243$	−16.3873	−1.05125
$244$	14.5836	0.933619
$245$	0	0
$246$	25.2554	1.61023
$247$	−0.397258	−0.0252769
$248$	−4.07835	−0.258975
$249$	29.0105	1.83847
$250$	21.9188	1.38627
$251$	−28.3705	−1.79073	−0.895365	−	0.445333i	$-0.853085\pi$
$251$	−28.3705	−1.79073	−0.895365	+	0.445333i	$0.853085\pi$
$252$	0	0
$253$	2.43477	0.153073
$254$	−0.553949	−0.0347579
$255$	−12.3310	−0.772195
$256$	1.00000	0.0625000
$257$	27.7579	1.73149	0.865744	−	0.500487i	$-0.166846\pi$
$257$	27.7579	1.73149	0.865744	+	0.500487i	$0.166846\pi$
$258$	9.81016	0.610754
$259$	0	0
$260$	1.20112	0.0744901
$261$	1.28592	0.0795963
$262$	12.1644	0.751518
$263$	−14.0551	−0.866674	−0.433337	−	0.901232i	$-0.642664\pi$
$263$	−14.0551	−0.866674	−0.433337	+	0.901232i	$0.642664\pi$
$264$	−16.0264	−0.986360
$265$	−2.94629	−0.180989
$266$	0	0
$267$	−40.6111	−2.48536
$268$	−5.19303	−0.317215
$269$	9.80092	0.597572	0.298786	−	0.954320i	$-0.403418\pi$
$269$	9.80092	0.597572	0.298786	+	0.954320i	$0.403418\pi$
$270$	−46.5349	−2.83202
$271$	−26.7346	−1.62401	−0.812006	−	0.583649i	$-0.801625\pi$
$271$	−26.7346	−1.62401	−0.812006	+	0.583649i	$0.801625\pi$
$272$	1.00000	0.0606339
$273$	0	0
$274$	−13.8694	−0.837879
$275$	54.1192	3.26351
$276$	−1.48486	−0.0893780
$277$	0.419210	0.0251879	0.0125940	−	0.999921i	$-0.495991\pi$
$277$	0.419210	0.0251879	0.0125940	+	0.999921i	$0.495991\pi$
$278$	4.70710	0.282313
$279$	−27.6260	−1.65392
$280$	0	0
$281$	−4.30413	−0.256763	−0.128381	−	0.991725i	$-0.540978\pi$
$281$	−4.30413	−0.256763	−0.128381	+	0.991725i	$0.540978\pi$
$282$	−13.8885	−0.827049
$283$	9.31615	0.553787	0.276894	−	0.960901i	$-0.410695\pi$
$283$	9.31615	0.553787	0.276894	+	0.960901i	$0.410695\pi$
$284$	4.65136	0.276007
$285$	16.0860	0.952854
$286$	1.56108	0.0923087
$287$	0	0
$288$	6.77382	0.399151
$289$	1.00000	0.0588235
$290$	0.748762	0.0439688
$291$	−23.3514	−1.36888
$292$	12.0783	0.706832
$293$	−8.89801	−0.519827	−0.259914	−	0.965632i	$-0.583694\pi$
$293$	−8.89801	−0.519827	−0.259914	+	0.965632i	$0.583694\pi$
$294$	0	0
$295$	−25.2815	−1.47195
$296$	−1.94425	−0.113008
$297$	−60.4810	−3.50946
$298$	−10.2163	−0.591813
$299$	0.144635	0.00836446
$300$	−33.0049	−1.90554
$301$	0	0
$302$	−2.51514	−0.144730
$303$	7.09104	0.407370
$304$	−1.30452	−0.0748195
$305$	57.5214	3.29367
$306$	6.77382	0.387234
$307$	14.1648	0.808426	0.404213	−	0.914665i	$-0.367545\pi$
$307$	14.1648	0.808426	0.404213	+	0.914665i	$0.367545\pi$
$308$	0	0
$309$	3.80371	0.216386
$310$	−16.0860	−0.913625
$311$	−10.0205	−0.568209	−0.284105	−	0.958793i	$-0.591696\pi$
$311$	−10.0205	−0.568209	−0.284105	+	0.958793i	$0.591696\pi$
$312$	−0.952034	−0.0538983
$313$	13.3825	0.756422	0.378211	−	0.925719i	$-0.376539\pi$
$313$	13.3825	0.756422	0.378211	+	0.925719i	$0.376539\pi$
$314$	4.55715	0.257175
$315$	0	0
$316$	−6.76220	−0.380403
$317$	−13.0339	−0.732056	−0.366028	−	0.930604i	$-0.619283\pi$
$317$	−13.0339	−0.732056	−0.366028	+	0.930604i	$0.619283\pi$
$318$	2.33530	0.130957
$319$	0.973160	0.0544865
$320$	3.94425	0.220491
$321$	−27.4660	−1.53300
$322$	0	0
$323$	−1.30452	−0.0725856
$324$	16.5632	0.920178
$325$	3.21490	0.178330
$326$	−12.0783	−0.668958
$327$	−36.7480	−2.03217
$328$	−8.07835	−0.446052
$329$	0	0
$330$	−63.2124	−3.47973
$331$	−4.08785	−0.224688	−0.112344	−	0.993669i	$-0.535836\pi$
$331$	−4.08785	−0.224688	−0.112344	+	0.993669i	$0.535836\pi$
$332$	−9.27946	−0.509277
$333$	−13.1700	−0.721714
$334$	−10.9823	−0.600926
$335$	−20.4826	−1.11909
$336$	0	0
$337$	−25.5469	−1.39163	−0.695813	−	0.718223i	$-0.744956\pi$
$337$	−25.5469	−1.39163	−0.695813	+	0.718223i	$0.744956\pi$
$338$	−12.9073	−0.702063
$339$	24.6619	1.33945
$340$	3.94425	0.213907
$341$	−20.9069	−1.13217
$342$	−8.83661	−0.477829
$343$	0	0
$344$	−3.13794	−0.169186
$345$	−5.85666	−0.315312
$346$	−19.5779	−1.05252
$347$	15.5165	0.832971	0.416485	−	0.909142i	$-0.363262\pi$
$347$	15.5165	0.832971	0.416485	+	0.909142i	$0.363262\pi$
$348$	−0.593487	−0.0318142
$349$	12.4326	0.665500	0.332750	−	0.943015i	$-0.392024\pi$
$349$	12.4326	0.665500	0.332750	+	0.943015i	$0.392024\pi$
$350$	0	0
$351$	−3.59281	−0.191770
$352$	5.12631	0.273233
$353$	−24.8707	−1.32374	−0.661868	−	0.749620i	$-0.730236\pi$
$353$	−24.8707	−1.32374	−0.661868	+	0.749620i	$0.730236\pi$
$354$	20.0387	1.06505
$355$	18.3461	0.973712
$356$	12.9901	0.688474
$357$	0	0
$358$	−5.32777	−0.281581
$359$	26.7657	1.41264	0.706321	−	0.707892i	$-0.250354\pi$
$359$	26.7657	1.41264	0.706321	+	0.707892i	$0.250354\pi$
$360$	26.7177	1.40815
$361$	−17.2982	−0.910433
$362$	18.9802	0.997577
$363$	−47.7671	−2.50712
$364$	0	0
$365$	47.6401	2.49360
$366$	−45.5928	−2.38318
$367$	−11.1877	−0.583994	−0.291997	−	0.956419i	$-0.594320\pi$
$367$	−11.1877	−0.583994	−0.291997	+	0.956419i	$0.594320\pi$
$368$	0.474955	0.0247588
$369$	−54.7213	−2.84868
$370$	−7.66864	−0.398673
$371$	0	0
$372$	12.7502	0.661066
$373$	6.73911	0.348938	0.174469	−	0.984663i	$-0.444179\pi$
$373$	6.73911	0.348938	0.174469	+	0.984663i	$0.444179\pi$
$374$	5.12631	0.265075
$375$	−68.5250	−3.53862
$376$	4.44246	0.229102
$377$	0.0578095	0.00297734
$378$	0	0
$379$	5.85251	0.300623	0.150312	−	0.988639i	$-0.451972\pi$
$379$	5.85251	0.300623	0.150312	+	0.988639i	$0.451972\pi$
$380$	−5.14537	−0.263952
$381$	1.73182	0.0887237
$382$	22.2039	1.13605
$383$	10.2294	0.522697	0.261348	−	0.965245i	$-0.415833\pi$
$383$	10.2294	0.522697	0.261348	+	0.965245i	$0.415833\pi$
$384$	−3.12631	−0.159539
$385$	0	0
$386$	−18.0529	−0.918868
$387$	−21.2558	−1.08049
$388$	7.46930	0.379196
$389$	−21.8599	−1.10834	−0.554169	−	0.832404i	$-0.686964\pi$
$389$	−21.8599	−1.10834	−0.554169	+	0.832404i	$0.686964\pi$
$390$	−3.75507	−0.190145
$391$	0.474955	0.0240195
$392$	0	0
$393$	−38.0296	−1.91834
$394$	−20.3380	−1.02461
$395$	−26.6718	−1.34201
$396$	34.7247	1.74498
$397$	3.59773	0.180565	0.0902824	−	0.995916i	$-0.471223\pi$
$397$	3.59773	0.180565	0.0902824	+	0.995916i	$0.471223\pi$
$398$	11.2273	0.562772
$399$	0	0
$400$	10.5571	0.527857
$401$	−5.54765	−0.277036	−0.138518	−	0.990360i	$-0.544234\pi$
$401$	−5.54765	−0.277036	−0.138518	+	0.990360i	$0.544234\pi$
$402$	16.2350	0.809730
$403$	−1.24195	−0.0618660
$404$	−2.26818	−0.112846
$405$	65.3295	3.24625
$406$	0	0
$407$	−9.96686	−0.494039
$408$	−3.12631	−0.154775
$409$	−32.6496	−1.61442	−0.807209	−	0.590266i	$-0.799023\pi$
$409$	−32.6496	−1.61442	−0.807209	+	0.590266i	$0.799023\pi$
$410$	−31.8631	−1.57360
$411$	43.3599	2.13879
$412$	−1.21668	−0.0599414
$413$	0	0
$414$	3.21726	0.158120
$415$	−36.6006	−1.79665
$416$	0.304523	0.0149305
$417$	−14.7159	−0.720639
$418$	−6.68739	−0.327091
$419$	2.76220	0.134942	0.0674711	−	0.997721i	$-0.478507\pi$
$419$	2.76220	0.134942	0.0674711	+	0.997721i	$0.478507\pi$
$420$	0	0
$421$	13.5949	0.662574	0.331287	−	0.943530i	$-0.392517\pi$
$421$	13.5949	0.662574	0.331287	+	0.943530i	$0.392517\pi$
$422$	24.3211	1.18393
$423$	30.0924	1.46314
$424$	−0.746982	−0.0362767
$425$	10.5571	0.512097
$426$	−14.5416	−0.704542
$427$	0	0
$428$	8.78545	0.424661
$429$	−4.88043	−0.235629
$430$	−12.3768	−0.596863
$431$	36.4912	1.75772	0.878859	−	0.477082i	$-0.158306\pi$
$431$	36.4912	1.75772	0.878859	+	0.477082i	$0.158306\pi$
$432$	−11.7981	−0.567638
$433$	−36.6714	−1.76232	−0.881158	−	0.472821i	$-0.843236\pi$
$433$	−36.6714	−1.76232	−0.881158	+	0.472821i	$0.843236\pi$
$434$	0	0
$435$	−2.34086	−0.112236
$436$	11.7544	0.562935
$437$	−0.619590	−0.0296390
$438$	−37.7607	−1.80427
$439$	23.6309	1.12784	0.563921	−	0.825829i	$-0.309292\pi$
$439$	23.6309	1.12784	0.563921	+	0.825829i	$0.309292\pi$
$440$	20.2195	0.963926
$441$	0	0
$442$	0.304523	0.0144847
$443$	26.2276	1.24611	0.623055	−	0.782178i	$-0.285891\pi$
$443$	26.2276	1.24611	0.623055	+	0.782178i	$0.285891\pi$
$444$	6.07835	0.288466
$445$	51.2363	2.42883
$446$	−25.3902	−1.20226
$447$	31.9393	1.51068
$448$	0	0
$449$	13.5808	0.640917	0.320459	−	0.947263i	$-0.396163\pi$
$449$	13.5808	0.640917	0.320459	+	0.947263i	$0.396163\pi$
$450$	71.5122	3.37112
$451$	−41.4121	−1.95002
$452$	−7.88851	−0.371044
$453$	7.86311	0.369441
$454$	0.289307	0.0135779
$455$	0	0
$456$	4.07835	0.190986
$457$	21.9044	1.02464	0.512322	−	0.858793i	$-0.328785\pi$
$457$	21.9044	1.02464	0.512322	+	0.858793i	$0.328785\pi$
$458$	−26.3542	−1.23145
$459$	−11.7981	−0.550690
$460$	1.87335	0.0873452
$461$	−16.7138	−0.778441	−0.389221	−	0.921145i	$-0.627256\pi$
$461$	−16.7138	−0.778441	−0.389221	+	0.921145i	$0.627256\pi$
$462$	0	0
$463$	−30.4242	−1.41393	−0.706966	−	0.707248i	$-0.749937\pi$
$463$	−30.4242	−1.41393	−0.706966	+	0.707248i	$0.749937\pi$
$464$	0.189836	0.00881293
$465$	50.2900	2.33214
$466$	−14.0064	−0.648834
$467$	13.8098	0.639040	0.319520	−	0.947580i	$-0.396478\pi$
$467$	13.8098	0.639040	0.319520	+	0.947580i	$0.396478\pi$
$468$	2.06279	0.0953523
$469$	0	0
$470$	17.5222	0.808238
$471$	−14.2471	−0.656470
$472$	−6.40971	−0.295031
$473$	−16.0860	−0.739637
$474$	21.1407	0.971026
$475$	−13.7720	−0.631905
$476$	0	0
$477$	−5.05992	−0.231678
$478$	20.5759	0.941120
$479$	8.71768	0.398321	0.199161	−	0.979967i	$-0.436178\pi$
$479$	8.71768	0.398321	0.199161	+	0.979967i	$0.436178\pi$
$480$	−12.3310	−0.562829
$481$	−0.592071	−0.0269961
$482$	17.5088	0.797506
$483$	0	0
$484$	15.2791	0.694503
$485$	29.4608	1.33775
$486$	−16.3873	−0.743343
$487$	−30.0106	−1.35991	−0.679955	−	0.733254i	$-0.738001\pi$
$487$	−30.0106	−1.35991	−0.679955	+	0.733254i	$0.738001\pi$
$488$	14.5836	0.660168
$489$	37.7607	1.70760
$490$	0	0
$491$	−23.5141	−1.06118	−0.530588	−	0.847630i	$-0.678029\pi$
$491$	−23.5141	−1.06118	−0.530588	+	0.847630i	$0.678029\pi$
$492$	25.2554	1.13860
$493$	0.189836	0.00854979
$494$	−0.397258	−0.0178735
$495$	136.963	6.15604
$496$	−4.07835	−0.183123
$497$	0	0
$498$	29.0105	1.29999
$499$	32.7149	1.46452	0.732260	−	0.681025i	$-0.238465\pi$
$499$	32.7149	1.46452	0.732260	+	0.681025i	$0.238465\pi$
$500$	21.9188	0.980239
$501$	34.3342	1.53394
$502$	−28.3705	−1.26624
$503$	−5.93224	−0.264505	−0.132253	−	0.991216i	$-0.542221\pi$
$503$	−5.93224	−0.264505	−0.132253	+	0.991216i	$0.542221\pi$
$504$	0	0
$505$	−8.94629	−0.398105
$506$	2.43477	0.108239
$507$	40.3521	1.79210
$508$	−0.553949	−0.0245775
$509$	12.6147	0.559137	0.279569	−	0.960126i	$-0.409809\pi$
$509$	12.6147	0.559137	0.279569	+	0.960126i	$0.409809\pi$
$510$	−12.3310	−0.546024
$511$	0	0
$512$	1.00000	0.0441942
$513$	15.3910	0.679527
$514$	27.7579	1.22435
$515$	−4.79888	−0.211464
$516$	9.81016	0.431868
$517$	22.7734	1.00157
$518$	0	0
$519$	61.2067	2.68668
$520$	1.20112	0.0526725
$521$	−24.5893	−1.07727	−0.538637	−	0.842538i	$-0.681061\pi$
$521$	−24.5893	−1.07727	−0.538637	+	0.842538i	$0.681061\pi$
$522$	1.28592	0.0562831
$523$	24.1256	1.05494	0.527469	−	0.849574i	$-0.323141\pi$
$523$	24.1256	1.05494	0.527469	+	0.849574i	$0.323141\pi$
$524$	12.1644	0.531403
$525$	0	0
$526$	−14.0551	−0.612831
$527$	−4.07835	−0.177656
$528$	−16.0264	−0.697462
$529$	−22.7744	−0.990192
$530$	−2.94629	−0.127979
$531$	−43.4182	−1.88419
$532$	0	0
$533$	−2.46004	−0.106556
$534$	−40.6111	−1.75741
$535$	34.6520	1.49814
$536$	−5.19303	−0.224305
$537$	16.6563	0.718771
$538$	9.80092	0.422547
$539$	0	0
$540$	−46.5349	−2.00254
$541$	28.0509	1.20600	0.603000	−	0.797741i	$-0.293972\pi$
$541$	28.0509	1.20600	0.603000	+	0.797741i	$0.293972\pi$
$542$	−26.7346	−1.14835
$543$	−59.3380	−2.54644
$544$	1.00000	0.0428746
$545$	46.3624	1.98595
$546$	0	0
$547$	−2.77007	−0.118440	−0.0592198	−	0.998245i	$-0.518861\pi$
$547$	−2.77007	−0.118440	−0.0592198	+	0.998245i	$0.518861\pi$
$548$	−13.8694	−0.592470
$549$	98.7867	4.21611
$550$	54.1192	2.30765
$551$	−0.247646	−0.0105501
$552$	−1.48486	−0.0631998
$553$	0	0
$554$	0.419210	0.0178105
$555$	23.9745	1.01766
$556$	4.70710	0.199626
$557$	6.29886	0.266891	0.133446	−	0.991056i	$-0.457396\pi$
$557$	6.29886	0.266891	0.133446	+	0.991056i	$0.457396\pi$
$558$	−27.6260	−1.16950
$559$	−0.955574	−0.0404165
$560$	0	0
$561$	−16.0264	−0.676637
$562$	−4.30413	−0.181559
$563$	−43.2938	−1.82462	−0.912309	−	0.409503i	$-0.865702\pi$
$563$	−43.2938	−1.82462	−0.912309	+	0.409503i	$0.865702\pi$
$564$	−13.8885	−0.584812
$565$	−31.1143	−1.30899
$566$	9.31615	0.391587
$567$	0	0
$568$	4.65136	0.195167
$569$	−39.7071	−1.66461	−0.832305	−	0.554318i	$-0.812979\pi$
$569$	−39.7071	−1.66461	−0.832305	+	0.554318i	$0.812979\pi$
$570$	16.0860	0.673770
$571$	−15.0824	−0.631181	−0.315590	−	0.948896i	$-0.602203\pi$
$571$	−15.0824	−0.631181	−0.315590	+	0.948896i	$0.602203\pi$
$572$	1.56108	0.0652721
$573$	−69.4164	−2.89991
$574$	0	0
$575$	5.01417	0.209106
$576$	6.77382	0.282243
$577$	−10.5670	−0.439912	−0.219956	−	0.975510i	$-0.570591\pi$
$577$	−10.5670	−0.439912	−0.219956	+	0.975510i	$0.570591\pi$
$578$	1.00000	0.0415945
$579$	56.4390	2.34552
$580$	0.748762	0.0310907
$581$	0	0
$582$	−23.3514	−0.967945
$583$	−3.82926	−0.158592
$584$	12.0783	0.499806
$585$	8.13616	0.336389
$586$	−8.89801	−0.367573
$587$	17.1470	0.707734	0.353867	−	0.935296i	$-0.384867\pi$
$587$	17.1470	0.707734	0.353867	+	0.935296i	$0.384867\pi$
$588$	0	0
$589$	5.32030	0.219219
$590$	−25.2815	−1.04082
$591$	63.5830	2.61545
$592$	−1.94425	−0.0799084
$593$	−32.3588	−1.32882	−0.664409	−	0.747369i	$-0.731317\pi$
$593$	−32.3588	−1.32882	−0.664409	+	0.747369i	$0.731317\pi$
$594$	−60.4810	−2.48156
$595$	0	0
$596$	−10.2163	−0.418475
$597$	−35.0999	−1.43654
$598$	0.144635	0.00591456
$599$	−4.59490	−0.187743	−0.0938713	−	0.995584i	$-0.529924\pi$
$599$	−4.59490	−0.187743	−0.0938713	+	0.995584i	$0.529924\pi$
$600$	−33.0049	−1.34742
$601$	−18.7176	−0.763509	−0.381754	−	0.924264i	$-0.624680\pi$
$601$	−18.7176	−0.763509	−0.381754	+	0.924264i	$0.624680\pi$
$602$	0	0
$603$	−35.1767	−1.43251
$604$	−2.51514	−0.102340
$605$	60.2645	2.45010
$606$	7.09104	0.288054
$607$	15.9300	0.646580	0.323290	−	0.946300i	$-0.395211\pi$
$607$	15.9300	0.646580	0.323290	+	0.946300i	$0.395211\pi$
$608$	−1.30452	−0.0529054
$609$	0	0
$610$	57.5214	2.32897
$611$	1.35283	0.0547297
$612$	6.77382	0.273816
$613$	−9.04701	−0.365405	−0.182703	−	0.983168i	$-0.558485\pi$
$613$	−9.04701	−0.365405	−0.182703	+	0.983168i	$0.558485\pi$
$614$	14.1648	0.571644
$615$	99.6138	4.01682
$616$	0	0
$617$	22.2152	0.894352	0.447176	−	0.894446i	$-0.352430\pi$
$617$	22.2152	0.894352	0.447176	+	0.894446i	$0.352430\pi$
$618$	3.80371	0.153008
$619$	25.0225	1.00574	0.502870	−	0.864362i	$-0.332278\pi$
$619$	25.0225	1.00574	0.502870	+	0.864362i	$0.332278\pi$
$620$	−16.0860	−0.646031
$621$	−5.60359	−0.224864
$622$	−10.0205	−0.401785
$623$	0	0
$624$	−0.952034	−0.0381119
$625$	33.6676	1.34670
$626$	13.3825	0.534871
$627$	20.9069	0.834940
$628$	4.55715	0.181850
$629$	−1.94425	−0.0775225
$630$	0	0
$631$	−7.59979	−0.302543	−0.151271	−	0.988492i	$-0.548337\pi$
$631$	−7.59979	−0.302543	−0.151271	+	0.988492i	$0.548337\pi$
$632$	−6.76220	−0.268986
$633$	−76.0352	−3.02213
$634$	−13.0339	−0.517642
$635$	−2.18492	−0.0867058
$636$	2.33530	0.0926006
$637$	0	0
$638$	0.973160	0.0385278
$639$	31.5075	1.24642
$640$	3.94425	0.155910
$641$	12.9386	0.511044	0.255522	−	0.966803i	$-0.417753\pi$
$641$	12.9386	0.511044	0.255522	+	0.966803i	$0.417753\pi$
$642$	−27.4660	−1.08400
$643$	−23.0445	−0.908785	−0.454392	−	0.890802i	$-0.650144\pi$
$643$	−23.0445	−0.908785	−0.454392	+	0.890802i	$0.650144\pi$
$644$	0	0
$645$	38.6938	1.52357
$646$	−1.30452	−0.0513258
$647$	4.72693	0.185835	0.0929174	−	0.995674i	$-0.470381\pi$
$647$	4.72693	0.185835	0.0929174	+	0.995674i	$0.470381\pi$
$648$	16.5632	0.650664
$649$	−32.8582	−1.28980
$650$	3.21490	0.126099
$651$	0	0
$652$	−12.0783	−0.473025
$653$	−2.16078	−0.0845579	−0.0422790	−	0.999106i	$-0.513462\pi$
$653$	−2.16078	−0.0845579	−0.0422790	+	0.999106i	$0.513462\pi$
$654$	−36.7480	−1.43696
$655$	47.9794	1.87471
$656$	−8.07835	−0.315406
$657$	81.8166	3.19197
$658$	0	0
$659$	34.7886	1.35517	0.677586	−	0.735444i	$-0.263026\pi$
$659$	34.7886	1.35517	0.677586	+	0.735444i	$0.263026\pi$
$660$	−63.2124	−2.46054
$661$	−22.6373	−0.880488	−0.440244	−	0.897878i	$-0.645108\pi$
$661$	−22.6373	−0.880488	−0.440244	+	0.897878i	$0.645108\pi$
$662$	−4.08785	−0.158879
$663$	−0.952034	−0.0369740
$664$	−9.27946	−0.360113
$665$	0	0
$666$	−13.1700	−0.510329
$667$	0.0901638	0.00349115
$668$	−10.9823	−0.424919
$669$	79.3776	3.06891
$670$	−20.4826	−0.791314
$671$	74.7600	2.88608
$672$	0	0
$673$	0.457513	0.0176358	0.00881791	−	0.999961i	$-0.497193\pi$
$673$	0.457513	0.0176358	0.00881791	+	0.999961i	$0.497193\pi$
$674$	−25.5469	−0.984028
$675$	−124.555	−4.79411
$676$	−12.9073	−0.496433
$677$	−10.5949	−0.407195	−0.203598	−	0.979055i	$-0.565263\pi$
$677$	−10.5949	−0.407195	−0.203598	+	0.979055i	$0.565263\pi$
$678$	24.6619	0.947136
$679$	0	0
$680$	3.94425	0.151255
$681$	−0.904464	−0.0346591
$682$	−20.9069	−0.800565
$683$	46.0881	1.76351	0.881756	−	0.471706i	$-0.156362\pi$
$683$	46.0881	1.76351	0.881756	+	0.471706i	$0.156362\pi$
$684$	−8.83661	−0.337876
$685$	−54.7043	−2.09014
$686$	0	0
$687$	82.3915	3.14343
$688$	−3.13794	−0.119633
$689$	−0.227473	−0.00866605
$690$	−5.85666	−0.222959
$691$	−4.82711	−0.183632	−0.0918159	−	0.995776i	$-0.529267\pi$
$691$	−4.82711	−0.183632	−0.0918159	+	0.995776i	$0.529267\pi$
$692$	−19.5779	−0.744241
$693$	0	0
$694$	15.5165	0.588999
$695$	18.5660	0.704249
$696$	−0.593487	−0.0224961
$697$	−8.07835	−0.305989
$698$	12.4326	0.470579
$699$	43.7883	1.65623
$700$	0	0
$701$	22.1224	0.835551	0.417775	−	0.908550i	$-0.362810\pi$
$701$	22.1224	0.835551	0.417775	+	0.908550i	$0.362810\pi$
$702$	−3.59281	−0.135602
$703$	2.53633	0.0956593
$704$	5.12631	0.193205
$705$	−54.7798	−2.06313
$706$	−24.8707	−0.936023
$707$	0	0
$708$	20.0387	0.753102
$709$	−3.42893	−0.128776	−0.0643881	−	0.997925i	$-0.520510\pi$
$709$	−3.42893	−0.128776	−0.0643881	+	0.997925i	$0.520510\pi$
$710$	18.3461	0.688518
$711$	−45.8059	−1.71786
$712$	12.9901	0.486825
$713$	−1.93703	−0.0725424
$714$	0	0
$715$	6.15730	0.230270
$716$	−5.32777	−0.199108
$717$	−64.3267	−2.40232
$718$	26.7657	0.998888
$719$	−27.4241	−1.02275	−0.511374	−	0.859358i	$-0.670863\pi$
$719$	−27.4241	−1.02275	−0.511374	+	0.859358i	$0.670863\pi$
$720$	26.7177	0.995709
$721$	0	0
$722$	−17.2982	−0.643773
$723$	−54.7381	−2.03573
$724$	18.9802	0.705394
$725$	2.00413	0.0744315
$726$	−47.7671	−1.77280
$727$	11.3183	0.419771	0.209886	−	0.977726i	$-0.432691\pi$
$727$	11.3183	0.419771	0.209886	+	0.977726i	$0.432691\pi$
$728$	0	0
$729$	1.54219	0.0571182
$730$	47.6401	1.76324
$731$	−3.13794	−0.116061
$732$	−45.5928	−1.68516
$733$	−49.3503	−1.82280	−0.911398	−	0.411526i	$-0.864996\pi$
$733$	−49.3503	−1.82280	−0.911398	+	0.411526i	$0.864996\pi$
$734$	−11.1877	−0.412946
$735$	0	0
$736$	0.474955	0.0175071
$737$	−26.6211	−0.980601
$738$	−54.7213	−2.01432
$739$	−2.25868	−0.0830869	−0.0415435	−	0.999137i	$-0.513228\pi$
$739$	−2.25868	−0.0830869	−0.0415435	+	0.999137i	$0.513228\pi$
$740$	−7.66864	−0.281905
$741$	1.24195	0.0456242
$742$	0	0
$743$	−4.77697	−0.175250	−0.0876250	−	0.996154i	$-0.527928\pi$
$743$	−4.77697	−0.175250	−0.0876250	+	0.996154i	$0.527928\pi$
$744$	12.7502	0.467444
$745$	−40.2956	−1.47632
$746$	6.73911	0.246736
$747$	−62.8574	−2.29983
$748$	5.12631	0.187437
$749$	0	0
$750$	−68.5250	−2.50218
$751$	−30.0247	−1.09562	−0.547809	−	0.836604i	$-0.684538\pi$
$751$	−30.0247	−1.09562	−0.547809	+	0.836604i	$0.684538\pi$
$752$	4.44246	0.162000
$753$	88.6950	3.23223
$754$	0.0578095	0.00210530
$755$	−9.92036	−0.361039
$756$	0	0
$757$	−25.0258	−0.909578	−0.454789	−	0.890599i	$-0.650285\pi$
$757$	−25.0258	−0.909578	−0.454789	+	0.890599i	$0.650285\pi$
$758$	5.85251	0.212573
$759$	−7.61185	−0.276293
$760$	−5.14537	−0.186642
$761$	4.74608	0.172045	0.0860227	−	0.996293i	$-0.472584\pi$
$761$	4.74608	0.172045	0.0860227	+	0.996293i	$0.472584\pi$
$762$	1.73182	0.0627371
$763$	0	0
$764$	22.2039	0.803310
$765$	26.7177	0.965980
$766$	10.2294	0.369602
$767$	−1.95191	−0.0704792
$768$	−3.12631	−0.112811
$769$	6.64358	0.239573	0.119787	−	0.992800i	$-0.461779\pi$
$769$	6.64358	0.239573	0.119787	+	0.992800i	$0.461779\pi$
$770$	0	0
$771$	−86.7797	−3.12530
$772$	−18.0529	−0.649738
$773$	28.3320	1.01903	0.509515	−	0.860462i	$-0.329825\pi$
$773$	28.3320	1.01903	0.509515	+	0.860462i	$0.329825\pi$
$774$	−21.2558	−0.764025
$775$	−43.0557	−1.54661
$776$	7.46930	0.268132
$777$	0	0
$778$	−21.8599	−0.783714
$779$	10.5384	0.377577
$780$	−3.75507	−0.134453
$781$	23.8443	0.853216
$782$	0.474955	0.0169844
$783$	−2.23972	−0.0800409
$784$	0	0
$785$	17.9745	0.641539
$786$	−38.0296	−1.35647
$787$	−0.491893	−0.0175341	−0.00876704	−	0.999962i	$-0.502791\pi$
$787$	−0.491893	−0.0175341	−0.00876704	+	0.999962i	$0.502791\pi$
$788$	−20.3380	−0.724512
$789$	43.9406	1.56433
$790$	−26.6718	−0.948941
$791$	0	0
$792$	34.7247	1.23389
$793$	4.44104	0.157706
$794$	3.59773	0.127679
$795$	9.21101	0.326681
$796$	11.2273	0.397940
$797$	53.6059	1.89882	0.949410	−	0.314040i	$-0.101682\pi$
$797$	53.6059	1.89882	0.949410	+	0.314040i	$0.101682\pi$
$798$	0	0
$799$	4.44246	0.157163
$800$	10.5571	0.373251
$801$	87.9927	3.10907
$802$	−5.54765	−0.195894
$803$	61.9174	2.18502
$804$	16.2350	0.572566
$805$	0	0
$806$	−1.24195	−0.0437459
$807$	−30.6407	−1.07860
$808$	−2.26818	−0.0797944
$809$	−18.5751	−0.653066	−0.326533	−	0.945186i	$-0.605880\pi$
$809$	−18.5751	−0.653066	−0.326533	+	0.945186i	$0.605880\pi$
$810$	65.3295	2.29544
$811$	−17.4890	−0.614122	−0.307061	−	0.951690i	$-0.599346\pi$
$811$	−17.4890	−0.614122	−0.307061	+	0.951690i	$0.599346\pi$
$812$	0	0
$813$	83.5807	2.93130
$814$	−9.96686	−0.349338
$815$	−47.6401	−1.66876
$816$	−3.12631	−0.109443
$817$	4.09351	0.143214
$818$	−32.6496	−1.14157
$819$	0	0
$820$	−31.8631	−1.11271
$821$	−31.5060	−1.09957	−0.549783	−	0.835307i	$-0.685290\pi$
$821$	−31.5060	−1.09957	−0.549783	+	0.835307i	$0.685290\pi$
$822$	43.3599	1.51235
$823$	−49.0677	−1.71039	−0.855196	−	0.518304i	$-0.826564\pi$
$823$	−49.0677	−1.71039	−0.855196	+	0.518304i	$0.826564\pi$
$824$	−1.21668	−0.0423849
$825$	−169.194	−5.89056
$826$	0	0
$827$	12.7926	0.444843	0.222422	−	0.974951i	$-0.428604\pi$
$827$	12.7926	0.444843	0.222422	+	0.974951i	$0.428604\pi$
$828$	3.21726	0.111808
$829$	−34.6814	−1.20454	−0.602268	−	0.798294i	$-0.705736\pi$
$829$	−34.6814	−1.20454	−0.602268	+	0.798294i	$0.705736\pi$
$830$	−36.6006	−1.27042
$831$	−1.31058	−0.0454636
$832$	0.304523	0.0105574
$833$	0	0
$834$	−14.7159	−0.509569
$835$	−43.3171	−1.49905
$836$	−6.68739	−0.231288
$837$	48.1169	1.66316
$838$	2.76220	0.0954186
$839$	20.9951	0.724830	0.362415	−	0.932017i	$-0.381952\pi$
$839$	20.9951	0.724830	0.362415	+	0.932017i	$0.381952\pi$
$840$	0	0
$841$	−28.9640	−0.998757
$842$	13.5949	0.468510
$843$	13.4560	0.463451
$844$	24.3211	0.837166
$845$	−50.9095	−1.75134
$846$	30.0924	1.03460
$847$	0	0
$848$	−0.746982	−0.0256515
$849$	−29.1252	−0.999574
$850$	10.5571	0.362107
$851$	−0.923434	−0.0316549
$852$	−14.5416	−0.498187
$853$	0.366320	0.0125426	0.00627128	−	0.999980i	$-0.498004\pi$
$853$	0.366320	0.0125426	0.00627128	+	0.999980i	$0.498004\pi$
$854$	0	0
$855$	−34.8538	−1.19198
$856$	8.78545	0.300280
$857$	1.97331	0.0674070	0.0337035	−	0.999432i	$-0.489270\pi$
$857$	1.97331	0.0674070	0.0337035	+	0.999432i	$0.489270\pi$
$858$	−4.88043	−0.166615
$859$	−9.79002	−0.334031	−0.167016	−	0.985954i	$-0.553413\pi$
$859$	−9.79002	−0.334031	−0.167016	+	0.985954i	$0.553413\pi$
$860$	−12.3768	−0.422046
$861$	0	0
$862$	36.4912	1.24289
$863$	44.0747	1.50032	0.750159	−	0.661257i	$-0.229977\pi$
$863$	44.0747	1.50032	0.750159	+	0.661257i	$0.229977\pi$
$864$	−11.7981	−0.401381
$865$	−77.2204	−2.62557
$866$	−36.6714	−1.24615
$867$	−3.12631	−0.106175
$868$	0	0
$869$	−34.6651	−1.17593
$870$	−2.34086	−0.0793627
$871$	−1.58140	−0.0535837
$872$	11.7544	0.398055
$873$	50.5957	1.71241
$874$	−0.619590	−0.0209580
$875$	0	0
$876$	−37.7607	−1.27581
$877$	5.67198	0.191529	0.0957646	−	0.995404i	$-0.469470\pi$
$877$	5.67198	0.191529	0.0957646	+	0.995404i	$0.469470\pi$
$878$	23.6309	0.797505
$879$	27.8180	0.938276
$880$	20.2195	0.681598
$881$	−35.3627	−1.19140	−0.595700	−	0.803207i	$-0.703125\pi$
$881$	−35.3627	−1.19140	−0.595700	+	0.803207i	$0.703125\pi$
$882$	0	0
$883$	46.4164	1.56204	0.781018	−	0.624508i	$-0.214701\pi$
$883$	46.4164	1.56204	0.781018	+	0.624508i	$0.214701\pi$
$884$	0.304523	0.0102422
$885$	79.0379	2.65683
$886$	26.2276	0.881132
$887$	−13.2603	−0.445236	−0.222618	−	0.974906i	$-0.571460\pi$
$887$	−13.2603	−0.445236	−0.222618	+	0.974906i	$0.571460\pi$
$888$	6.07835	0.203976
$889$	0	0
$890$	51.2363	1.71744
$891$	84.9081	2.84453
$892$	−25.3902	−0.850126
$893$	−5.79529	−0.193932
$894$	31.9393	1.06821
$895$	−21.0141	−0.702424
$896$	0	0
$897$	−0.452174	−0.0150977
$898$	13.5808	0.453197
$899$	−0.774218	−0.0258216
$900$	71.5122	2.38374
$901$	−0.746982	−0.0248856
$902$	−41.4121	−1.37887
$903$	0	0
$904$	−7.88851	−0.262368
$905$	74.8627	2.48852
$906$	7.86311	0.261234
$907$	39.0416	1.29636	0.648178	−	0.761489i	$-0.275531\pi$
$907$	39.0416	1.29636	0.648178	+	0.761489i	$0.275531\pi$
$908$	0.289307	0.00960099
$909$	−15.3643	−0.509600
$910$	0	0
$911$	−46.2992	−1.53396	−0.766980	−	0.641670i	$-0.778242\pi$
$911$	−46.2992	−1.53396	−0.766980	+	0.641670i	$0.778242\pi$
$912$	4.07835	0.135048
$913$	−47.5694	−1.57432
$914$	21.9044	0.724533
$915$	−179.830	−5.94499
$916$	−26.3542	−0.870768
$917$	0	0
$918$	−11.7981	−0.389397
$919$	20.9929	0.692492	0.346246	−	0.938144i	$-0.387456\pi$
$919$	20.9929	0.692492	0.346246	+	0.938144i	$0.387456\pi$
$920$	1.87335	0.0617624
$921$	−44.2835	−1.45919
$922$	−16.7138	−0.550441
$923$	1.41645	0.0466229
$924$	0	0
$925$	−20.5258	−0.674884
$926$	−30.4242	−0.999801
$927$	−8.24155	−0.270688
$928$	0.189836	0.00623168
$929$	45.1906	1.48266	0.741328	−	0.671143i	$-0.234196\pi$
$929$	45.1906	1.48266	0.741328	+	0.671143i	$0.234196\pi$
$930$	50.2900	1.64907
$931$	0	0
$932$	−14.0064	−0.458795
$933$	31.3271	1.02560
$934$	13.8098	0.451869
$935$	20.2195	0.661248
$936$	2.06279	0.0674243
$937$	13.3080	0.434752	0.217376	−	0.976088i	$-0.430250\pi$
$937$	13.3080	0.434752	0.217376	+	0.976088i	$0.430250\pi$
$938$	0	0
$939$	−41.8378	−1.36532
$940$	17.5222	0.571511
$941$	16.2068	0.528326	0.264163	−	0.964478i	$-0.414904\pi$
$941$	16.2068	0.528326	0.264163	+	0.964478i	$0.414904\pi$
$942$	−14.2471	−0.464194
$943$	−3.83685	−0.124945
$944$	−6.40971	−0.208618
$945$	0	0
$946$	−16.0860	−0.523002
$947$	−50.4198	−1.63842	−0.819211	−	0.573492i	$-0.805588\pi$
$947$	−50.4198	−1.63842	−0.819211	+	0.573492i	$0.805588\pi$
$948$	21.1407	0.686619
$949$	3.67814	0.119397
$950$	−13.7720	−0.446824
$951$	40.7480	1.32134
$952$	0	0
$953$	42.2038	1.36711	0.683557	−	0.729897i	$-0.260432\pi$
$953$	42.2038	1.36711	0.683557	+	0.729897i	$0.260432\pi$
$954$	−5.05992	−0.163821
$955$	87.5779	2.83395
$956$	20.5759	0.665472
$957$	−3.04240	−0.0983468
$958$	8.71768	0.281656
$959$	0	0
$960$	−12.3310	−0.397980
$961$	−14.3671	−0.463455
$962$	−0.592071	−0.0190891
$963$	59.5111	1.91772
$964$	17.5088	0.563922
$965$	−71.2052	−2.29218
$966$	0	0
$967$	19.8899	0.639617	0.319808	−	0.947482i	$-0.396381\pi$
$967$	19.8899	0.639617	0.319808	+	0.947482i	$0.396381\pi$
$968$	15.2791	0.491088
$969$	4.07835	0.131015
$970$	29.4608	0.945930
$971$	−16.7075	−0.536170	−0.268085	−	0.963395i	$-0.586391\pi$
$971$	−16.7075	−0.536170	−0.268085	+	0.963395i	$0.586391\pi$
$972$	−16.3873	−0.525623
$973$	0	0
$974$	−30.0106	−0.961601
$975$	−10.0508	−0.321882
$976$	14.5836	0.466809
$977$	1.16905	0.0374014	0.0187007	−	0.999825i	$-0.494047\pi$
$977$	1.16905	0.0374014	0.0187007	+	0.999825i	$0.494047\pi$
$978$	37.7607	1.20745
$979$	66.5913	2.12827
$980$	0	0
$981$	79.6223	2.54215
$982$	−23.5141	−0.750365
$983$	−52.8723	−1.68636	−0.843181	−	0.537629i	$-0.819320\pi$
$983$	−52.8723	−1.68636	−0.843181	+	0.537629i	$0.819320\pi$
$984$	25.2554	0.805114
$985$	−80.2183	−2.55597
$986$	0.189836	0.00604562
$987$	0	0
$988$	−0.397258	−0.0126384
$989$	−1.49038	−0.0473913
$990$	136.963	4.35297
$991$	−44.4918	−1.41333	−0.706665	−	0.707548i	$-0.749801\pi$
$991$	−44.4918	−1.41333	−0.706665	+	0.707548i	$0.749801\pi$
$992$	−4.07835	−0.129488
$993$	12.7799	0.405557
$994$	0	0
$995$	44.2832	1.40387
$996$	29.0105	0.919233
$997$	13.4842	0.427048	0.213524	−	0.976938i	$-0.431506\pi$
$997$	13.4842	0.427048	0.213524	+	0.976938i	$0.431506\pi$
$998$	32.7149	1.03557
$999$	22.9386	0.725745

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1666.2.a.ba.1.1		5
7.3	odd	6		238.2.e.f.205.1	yes	10
7.5	odd	6		238.2.e.f.137.1	✓	10
7.6	odd	2		1666.2.a.z.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
238.2.e.f.137.1	✓	10	7.5	odd	6
238.2.e.f.205.1	yes	10	7.3	odd	6
1666.2.a.z.1.5		5	7.6	odd	2
1666.2.a.ba.1.1		5	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.12631 q^{3} +1.00000 q^{4} +3.94425 q^{5} -3.12631 q^{6} +1.00000 q^{8} +6.77382 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.12631 q^{3} +1.00000 q^{4} +3.94425 q^{5} -3.12631 q^{6} +1.00000 q^{8} +6.77382 q^{9} +3.94425 q^{10} +5.12631 q^{11} -3.12631 q^{12} +0.304523 q^{13} -12.3310 q^{15} +1.00000 q^{16} +1.00000 q^{17} +6.77382 q^{18} -1.30452 q^{19} +3.94425 q^{20} +5.12631 q^{22} +0.474955 q^{23} -3.12631 q^{24} +10.5571 q^{25} +0.304523 q^{26} -11.7981 q^{27} +0.189836 q^{29} -12.3310 q^{30} -4.07835 q^{31} +1.00000 q^{32} -16.0264 q^{33} +1.00000 q^{34} +6.77382 q^{36} -1.94425 q^{37} -1.30452 q^{38} -0.952034 q^{39} +3.94425 q^{40} -8.07835 q^{41} -3.13794 q^{43} +5.12631 q^{44} +26.7177 q^{45} +0.474955 q^{46} +4.44246 q^{47} -3.12631 q^{48} +10.5571 q^{50} -3.12631 q^{51} +0.304523 q^{52} -0.746982 q^{53} -11.7981 q^{54} +20.2195 q^{55} +4.07835 q^{57} +0.189836 q^{58} -6.40971 q^{59} -12.3310 q^{60} +14.5836 q^{61} -4.07835 q^{62} +1.00000 q^{64} +1.20112 q^{65} -16.0264 q^{66} -5.19303 q^{67} +1.00000 q^{68} -1.48486 q^{69} +4.65136 q^{71} +6.77382 q^{72} +12.0783 q^{73} -1.94425 q^{74} -33.0049 q^{75} -1.30452 q^{76} -0.952034 q^{78} -6.76220 q^{79} +3.94425 q^{80} +16.5632 q^{81} -8.07835 q^{82} -9.27946 q^{83} +3.94425 q^{85} -3.13794 q^{86} -0.593487 q^{87} +5.12631 q^{88} +12.9901 q^{89} +26.7177 q^{90} +0.474955 q^{92} +12.7502 q^{93} +4.44246 q^{94} -5.14537 q^{95} -3.12631 q^{96} +7.46930 q^{97} +34.7247 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{2} + 5 q^{4} + q^{5} + 5 q^{8} + 11 q^{9}+O(q^{10}) \) 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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