LMFDB - Embedded newform 4025.2.a.z.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("4025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.1397868136$
Analytic rank:	$1$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 3 x^{13} - 18 x^{12} + 58 x^{11} + 111 x^{10} - 414 x^{9} - 244 x^{8} + 1330 x^{7} - 27 x^{6} + \cdots - 9 $ x^14 - 3x^13 - 18x^12 + 58x^11 + 111x^10 - 414x^9 - 244x^8 + 1330x^7 - 27x^6 - 1853x^5 + 539x^4 + 891x^3 - 218x^2 - 133*x - 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$1.29908$ of defining polynomial
Character	$\chi$	$=$	4025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.29908 q^{2} +2.64602 q^{3} -0.312383 q^{4} -3.43741 q^{6} -1.00000 q^{7} +3.00398 q^{8} +4.00145 q^{9} +O(q^{10})$	\(q-1.29908 q^{2} +2.64602 q^{3} -0.312383 q^{4} -3.43741 q^{6} -1.00000 q^{7} +3.00398 q^{8} +4.00145 q^{9} +6.40014 q^{11} -0.826572 q^{12} -2.78730 q^{13} +1.29908 q^{14} -3.27765 q^{16} -6.09215 q^{17} -5.19821 q^{18} -5.24833 q^{19} -2.64602 q^{21} -8.31432 q^{22} -1.00000 q^{23} +7.94860 q^{24} +3.62093 q^{26} +2.64985 q^{27} +0.312383 q^{28} -6.51629 q^{29} -6.15279 q^{31} -1.75001 q^{32} +16.9349 q^{33} +7.91420 q^{34} -1.24998 q^{36} +6.68122 q^{37} +6.81802 q^{38} -7.37526 q^{39} +0.0209156 q^{41} +3.43741 q^{42} +1.88922 q^{43} -1.99929 q^{44} +1.29908 q^{46} -11.2724 q^{47} -8.67275 q^{48} +1.00000 q^{49} -16.1200 q^{51} +0.870704 q^{52} -11.1841 q^{53} -3.44238 q^{54} -3.00398 q^{56} -13.8872 q^{57} +8.46520 q^{58} -8.49239 q^{59} -7.39589 q^{61} +7.99298 q^{62} -4.00145 q^{63} +8.82872 q^{64} -21.9999 q^{66} -13.4801 q^{67} +1.90308 q^{68} -2.64602 q^{69} +11.5814 q^{71} +12.0203 q^{72} +11.8020 q^{73} -8.67946 q^{74} +1.63949 q^{76} -6.40014 q^{77} +9.58108 q^{78} +3.18791 q^{79} -4.99277 q^{81} -0.0271711 q^{82} +4.72902 q^{83} +0.826572 q^{84} -2.45426 q^{86} -17.2423 q^{87} +19.2259 q^{88} +11.2199 q^{89} +2.78730 q^{91} +0.312383 q^{92} -16.2804 q^{93} +14.6437 q^{94} -4.63058 q^{96} +14.9683 q^{97} -1.29908 q^{98} +25.6098 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 3 q^{2} - 4 q^{3} + 17 q^{4} - 4 q^{6} - 14 q^{7} - 3 q^{8} + 18 q^{9}+O(q^{10}) $ 14 * q - 3 * q^2 - 4 * q^3 + 17 * q^4 - 4 * q^6 - 14 * q^7 - 3 * q^8 + 18 * q^9	$ 14 q - 3 q^{2} - 4 q^{3} + 17 q^{4} - 4 q^{6} - 14 q^{7} - 3 q^{8} + 18 q^{9} + 5 q^{11} - 17 q^{12} - 11 q^{13} + 3 q^{14} + 23 q^{16} - 3 q^{17} - 15 q^{18} - 2 q^{19} + 4 q^{21} - 23 q^{22} - 14 q^{23} - 12 q^{24} - 9 q^{26} - 25 q^{27} - 17 q^{28} + 7 q^{29} - 3 q^{31} - 24 q^{32} - 6 q^{33} - 14 q^{34} + 13 q^{36} - 22 q^{37} - 20 q^{38} - 10 q^{39} - 17 q^{41} + 4 q^{42} - 18 q^{43} + 28 q^{44} + 3 q^{46} - 30 q^{47} - 8 q^{48} + 14 q^{49} + 4 q^{51} - 8 q^{52} - 11 q^{53} + 20 q^{54} + 3 q^{56} - 18 q^{57} - 38 q^{58} - 22 q^{59} - 8 q^{61} + 22 q^{62} - 18 q^{63} + 29 q^{64} - 9 q^{66} - 39 q^{67} - q^{68} + 4 q^{69} - 5 q^{71} + 24 q^{72} - 18 q^{73} + 35 q^{74} - 41 q^{76} - 5 q^{77} + 22 q^{78} + 10 q^{79} + 2 q^{81} + 8 q^{82} - 24 q^{83} + 17 q^{84} - 26 q^{86} - 5 q^{87} - 58 q^{88} + 25 q^{89} + 11 q^{91} - 17 q^{92} - 47 q^{93} - 2 q^{94} - 117 q^{96} - 43 q^{97} - 3 q^{98} + 55 q^{99}+O(q^{100}) $ 14 * q - 3 * q^2 - 4 * q^3 + 17 * q^4 - 4 * q^6 - 14 * q^7 - 3 * q^8 + 18 * q^9 + 5 * q^11 - 17 * q^12 - 11 * q^13 + 3 * q^14 + 23 * q^16 - 3 * q^17 - 15 * q^18 - 2 * q^19 + 4 * q^21 - 23 * q^22 - 14 * q^23 - 12 * q^24 - 9 * q^26 - 25 * q^27 - 17 * q^28 + 7 * q^29 - 3 * q^31 - 24 * q^32 - 6 * q^33 - 14 * q^34 + 13 * q^36 - 22 * q^37 - 20 * q^38 - 10 * q^39 - 17 * q^41 + 4 * q^42 - 18 * q^43 + 28 * q^44 + 3 * q^46 - 30 * q^47 - 8 * q^48 + 14 * q^49 + 4 * q^51 - 8 * q^52 - 11 * q^53 + 20 * q^54 + 3 * q^56 - 18 * q^57 - 38 * q^58 - 22 * q^59 - 8 * q^61 + 22 * q^62 - 18 * q^63 + 29 * q^64 - 9 * q^66 - 39 * q^67 - q^68 + 4 * q^69 - 5 * q^71 + 24 * q^72 - 18 * q^73 + 35 * q^74 - 41 * q^76 - 5 * q^77 + 22 * q^78 + 10 * q^79 + 2 * q^81 + 8 * q^82 - 24 * q^83 + 17 * q^84 - 26 * q^86 - 5 * q^87 - 58 * q^88 + 25 * q^89 + 11 * q^91 - 17 * q^92 - 47 * q^93 - 2 * q^94 - 117 * q^96 - 43 * q^97 - 3 * q^98 + 55 * 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 $

$2$	−1.29908	−0.918591	−0.459295	−	0.888284i	$-0.651898\pi$
$2$	−1.29908	−0.918591	−0.459295	+	0.888284i	$0.651898\pi$
$3$	2.64602	1.52768	0.763842	−	0.645404i	$-0.223311\pi$
$3$	2.64602	1.52768	0.763842	+	0.645404i	$0.223311\pi$
$4$	−0.312383	−0.156191
$5$	0	0
$5$	0	0
$6$	−3.43741	−1.40332
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	3.00398	1.06207
$9$	4.00145	1.33382
$10$	0	0
$11$	6.40014	1.92972	0.964858	−	0.262772i	$-0.0846366\pi$
$11$	6.40014	1.92972	0.964858	+	0.262772i	$0.0846366\pi$
$12$	−0.826572	−0.238611
$13$	−2.78730	−0.773058	−0.386529	−	0.922277i	$-0.626326\pi$
$13$	−2.78730	−0.773058	−0.386529	+	0.922277i	$0.626326\pi$
$14$	1.29908	0.347195
$15$	0	0
$16$	−3.27765	−0.819413
$17$	−6.09215	−1.47756	−0.738781	−	0.673945i	$-0.764598\pi$
$17$	−6.09215	−1.47756	−0.738781	+	0.673945i	$0.764598\pi$
$18$	−5.19821	−1.22523
$19$	−5.24833	−1.20405	−0.602025	−	0.798477i	$-0.705639\pi$
$19$	−5.24833	−1.20405	−0.602025	+	0.798477i	$0.705639\pi$
$20$	0	0
$21$	−2.64602	−0.577410
$22$	−8.31432	−1.77262
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	7.94860	1.62250
$25$	0	0
$26$	3.62093	0.710124
$27$	2.64985	0.509964
$28$	0.312383	0.0590348
$29$	−6.51629	−1.21004	−0.605022	−	0.796209i	$-0.706836\pi$
$29$	−6.51629	−1.21004	−0.605022	+	0.796209i	$0.706836\pi$
$30$	0	0
$31$	−6.15279	−1.10507	−0.552537	−	0.833489i	$-0.686340\pi$
$31$	−6.15279	−1.10507	−0.552537	+	0.833489i	$0.686340\pi$
$32$	−1.75001	−0.309361
$33$	16.9349	2.94799
$34$	7.91420	1.35727
$35$	0	0
$36$	−1.24998	−0.208330
$37$	6.68122	1.09839	0.549193	−	0.835695i	$-0.314935\pi$
$37$	6.68122	1.09839	0.549193	+	0.835695i	$0.314935\pi$
$38$	6.81802	1.10603
$39$	−7.37526	−1.18099
$40$	0	0
$41$	0.0209156	0.00326647	0.00163323	−	0.999999i	$-0.499480\pi$
$41$	0.0209156	0.00326647	0.00163323	+	0.999999i	$0.499480\pi$
$42$	3.43741	0.530403
$43$	1.88922	0.288104	0.144052	−	0.989570i	$-0.453987\pi$
$43$	1.88922	0.288104	0.144052	+	0.989570i	$0.453987\pi$
$44$	−1.99929	−0.301405
$45$	0	0
$46$	1.29908	0.191539
$47$	−11.2724	−1.64424	−0.822121	−	0.569313i	$-0.807209\pi$
$47$	−11.2724	−1.64424	−0.822121	+	0.569313i	$0.807209\pi$
$48$	−8.67275	−1.25180
$49$	1.00000	0.142857
$50$	0	0
$51$	−16.1200	−2.25725
$52$	0.870704	0.120745
$53$	−11.1841	−1.53625	−0.768125	−	0.640300i	$-0.778810\pi$
$53$	−11.1841	−1.53625	−0.768125	+	0.640300i	$0.778810\pi$
$54$	−3.44238	−0.468448
$55$	0	0
$56$	−3.00398	−0.401423
$57$	−13.8872	−1.83941
$58$	8.46520	1.11154
$59$	−8.49239	−1.10562	−0.552808	−	0.833309i	$-0.686444\pi$
$59$	−8.49239	−1.10562	−0.552808	+	0.833309i	$0.686444\pi$
$60$	0	0
$61$	−7.39589	−0.946947	−0.473473	−	0.880808i	$-0.657000\pi$
$61$	−7.39589	−0.946947	−0.473473	+	0.880808i	$0.657000\pi$
$62$	7.99298	1.01511
$63$	−4.00145	−0.504135
$64$	8.82872	1.10359
$65$	0	0
$66$	−21.9999	−2.70800
$67$	−13.4801	−1.64686	−0.823429	−	0.567419i	$-0.807942\pi$
$67$	−13.4801	−1.64686	−0.823429	+	0.567419i	$0.807942\pi$
$68$	1.90308	0.230782
$69$	−2.64602	−0.318544
$70$	0	0
$71$	11.5814	1.37446	0.687228	−	0.726441i	$-0.258827\pi$
$71$	11.5814	1.37446	0.687228	+	0.726441i	$0.258827\pi$
$72$	12.0203	1.41660
$73$	11.8020	1.38132	0.690658	−	0.723182i	$-0.257321\pi$
$73$	11.8020	1.38132	0.690658	+	0.723182i	$0.257321\pi$
$74$	−8.67946	−1.00897
$75$	0	0
$76$	1.63949	0.188062
$77$	−6.40014	−0.729364
$78$	9.58108	1.08484
$79$	3.18791	0.358668	0.179334	−	0.983788i	$-0.442606\pi$
$79$	3.18791	0.358668	0.179334	+	0.983788i	$0.442606\pi$
$80$	0	0
$81$	−4.99277	−0.554752
$82$	−0.0271711	−0.00300055
$83$	4.72902	0.519078	0.259539	−	0.965733i	$-0.416429\pi$
$83$	4.72902	0.519078	0.259539	+	0.965733i	$0.416429\pi$
$84$	0.826572	0.0901864
$85$	0	0
$86$	−2.45426	−0.264649
$87$	−17.2423	−1.84856
$88$	19.2259	2.04949
$89$	11.2199	1.18931	0.594654	−	0.803982i	$-0.297289\pi$
$89$	11.2199	1.18931	0.594654	+	0.803982i	$0.297289\pi$
$90$	0	0
$91$	2.78730	0.292188
$92$	0.312383	0.0325681
$93$	−16.2804	−1.68820
$94$	14.6437	1.51039
$95$	0	0
$96$	−4.63058	−0.472606
$97$	14.9683	1.51980	0.759898	−	0.650043i	$-0.225249\pi$
$97$	14.9683	1.51980	0.759898	+	0.650043i	$0.225249\pi$
$98$	−1.29908	−0.131227
$99$	25.6098	2.57389
$100$	0	0
$101$	−0.968093	−0.0963288	−0.0481644	−	0.998839i	$-0.515337\pi$
$101$	−0.968093	−0.0963288	−0.0481644	+	0.998839i	$0.515337\pi$
$102$	20.9412	2.07349
$103$	−18.2000	−1.79330	−0.896650	−	0.442740i	$-0.854006\pi$
$103$	−18.2000	−1.79330	−0.896650	+	0.442740i	$0.854006\pi$
$104$	−8.37299	−0.821039
$105$	0	0
$106$	14.5290	1.41118
$107$	−8.65155	−0.836377	−0.418189	−	0.908360i	$-0.637335\pi$
$107$	−8.65155	−0.836377	−0.418189	+	0.908360i	$0.637335\pi$
$108$	−0.827768	−0.0796520
$109$	5.06176	0.484829	0.242414	−	0.970173i	$-0.422061\pi$
$109$	5.06176	0.484829	0.242414	+	0.970173i	$0.422061\pi$
$110$	0	0
$111$	17.6787	1.67799
$112$	3.27765	0.309709
$113$	−20.7022	−1.94750	−0.973749	−	0.227624i	$-0.926904\pi$
$113$	−20.7022	−1.94750	−0.973749	+	0.227624i	$0.926904\pi$
$114$	18.0407	1.68966
$115$	0	0
$116$	2.03558	0.188998
$117$	−11.1532	−1.03112
$118$	11.0323	1.01561
$119$	6.09215	0.558466
$120$	0	0
$121$	29.9618	2.72380
$122$	9.60788	0.869856
$123$	0.0553432	0.00499013
$124$	1.92202	0.172603
$125$	0	0
$126$	5.19821	0.463094
$127$	9.11452	0.808783	0.404392	−	0.914586i	$-0.367483\pi$
$127$	9.11452	0.808783	0.404392	+	0.914586i	$0.367483\pi$
$128$	−7.96921	−0.704385
$129$	4.99893	0.440131
$130$	0	0
$131$	4.81558	0.420739	0.210370	−	0.977622i	$-0.432533\pi$
$131$	4.81558	0.420739	0.210370	+	0.977622i	$0.432533\pi$
$132$	−5.29018	−0.460451
$133$	5.24833	0.455088
$134$	17.5118	1.51279
$135$	0	0
$136$	−18.3007	−1.56927
$137$	1.92093	0.164116	0.0820582	−	0.996628i	$-0.473851\pi$
$137$	1.92093	0.164116	0.0820582	+	0.996628i	$0.473851\pi$
$138$	3.43741	0.292611
$139$	2.44741	0.207587	0.103793	−	0.994599i	$-0.466902\pi$
$139$	2.44741	0.207587	0.103793	+	0.994599i	$0.466902\pi$
$140$	0	0
$141$	−29.8269	−2.51188
$142$	−15.0452	−1.26256
$143$	−17.8391	−1.49178
$144$	−13.1153	−1.09295
$145$	0	0
$146$	−15.3317	−1.26886
$147$	2.64602	0.218240
$148$	−2.08710	−0.171558
$149$	17.5812	1.44031	0.720153	−	0.693815i	$-0.244072\pi$
$149$	17.5812	1.44031	0.720153	+	0.693815i	$0.244072\pi$
$150$	0	0
$151$	−5.27359	−0.429159	−0.214580	−	0.976707i	$-0.568838\pi$
$151$	−5.27359	−0.429159	−0.214580	+	0.976707i	$0.568838\pi$
$152$	−15.7659	−1.27878
$153$	−24.3774	−1.97080
$154$	8.31432	0.669987
$155$	0	0
$156$	2.30390	0.184460
$157$	1.64870	0.131580	0.0657902	−	0.997833i	$-0.479043\pi$
$157$	1.64870	0.131580	0.0657902	+	0.997833i	$0.479043\pi$
$158$	−4.14136	−0.329469
$159$	−29.5933	−2.34690
$160$	0	0
$161$	1.00000	0.0788110
$162$	6.48602	0.509590
$163$	16.1443	1.26452	0.632258	−	0.774758i	$-0.282128\pi$
$163$	16.1443	1.26452	0.632258	+	0.774758i	$0.282128\pi$
$164$	−0.00653367	−0.000510194 0
$165$	0	0
$166$	−6.14339	−0.476820
$167$	0.881909	0.0682442	0.0341221	−	0.999418i	$-0.489136\pi$
$167$	0.881909	0.0682442	0.0341221	+	0.999418i	$0.489136\pi$
$168$	−7.94860	−0.613248
$169$	−5.23096	−0.402381
$170$	0	0
$171$	−21.0009	−1.60598
$172$	−0.590160	−0.0449993
$173$	−12.9823	−0.987024	−0.493512	−	0.869739i	$-0.664287\pi$
$173$	−12.9823	−0.987024	−0.493512	+	0.869739i	$0.664287\pi$
$174$	22.3991	1.69807
$175$	0	0
$176$	−20.9774	−1.58123
$177$	−22.4711	−1.68903
$178$	−14.5756	−1.09249
$179$	13.0020	0.971812	0.485906	−	0.874011i	$-0.338490\pi$
$179$	13.0020	0.971812	0.485906	+	0.874011i	$0.338490\pi$
$180$	0	0
$181$	−9.78156	−0.727057	−0.363529	−	0.931583i	$-0.618428\pi$
$181$	−9.78156	−0.727057	−0.363529	+	0.931583i	$0.618428\pi$
$182$	−3.62093	−0.268402
$183$	−19.5697	−1.44663
$184$	−3.00398	−0.221456
$185$	0	0
$186$	21.1496	1.55077
$187$	−38.9906	−2.85128
$188$	3.52129	0.256816
$189$	−2.64985	−0.192748
$190$	0	0
$191$	−1.65321	−0.119622	−0.0598110	−	0.998210i	$-0.519050\pi$
$191$	−1.65321	−0.119622	−0.0598110	+	0.998210i	$0.519050\pi$
$192$	23.3610	1.68593
$193$	−20.8656	−1.50194	−0.750969	−	0.660338i	$-0.770413\pi$
$193$	−20.8656	−1.50194	−0.750969	+	0.660338i	$0.770413\pi$
$194$	−19.4450	−1.39607
$195$	0	0
$196$	−0.312383	−0.0223130
$197$	16.7618	1.19423	0.597116	−	0.802155i	$-0.296313\pi$
$197$	16.7618	1.19423	0.597116	+	0.802155i	$0.296313\pi$
$198$	−33.2693	−2.36435
$199$	−19.4476	−1.37860	−0.689300	−	0.724476i	$-0.742082\pi$
$199$	−19.4476	−1.37860	−0.689300	+	0.724476i	$0.742082\pi$
$200$	0	0
$201$	−35.6687	−2.51588
$202$	1.25763	0.0884868
$203$	6.51629	0.457354
$204$	5.03560	0.352562
$205$	0	0
$206$	23.6433	1.64731
$207$	−4.00145	−0.278120
$208$	9.13580	0.633454
$209$	−33.5901	−2.32347
$210$	0	0
$211$	24.0917	1.65854	0.829271	−	0.558846i	$-0.188756\pi$
$211$	24.0917	1.65854	0.829271	+	0.558846i	$0.188756\pi$
$212$	3.49371	0.239949
$213$	30.6446	2.09973
$214$	11.2391	0.768288
$215$	0	0
$216$	7.96010	0.541616
$217$	6.15279	0.417678
$218$	−6.57565	−0.445359
$219$	31.2283	2.11021
$220$	0	0
$221$	16.9806	1.14224
$222$	−22.9661	−1.54138
$223$	−15.6877	−1.05053	−0.525263	−	0.850940i	$-0.676033\pi$
$223$	−15.6877	−1.05053	−0.525263	+	0.850940i	$0.676033\pi$
$224$	1.75001	0.116928
$225$	0	0
$226$	26.8939	1.78895
$227$	−1.37858	−0.0914997	−0.0457498	−	0.998953i	$-0.514568\pi$
$227$	−1.37858	−0.0914997	−0.0457498	+	0.998953i	$0.514568\pi$
$228$	4.33813	0.287299
$229$	−11.8583	−0.783621	−0.391811	−	0.920046i	$-0.628151\pi$
$229$	−11.8583	−0.783621	−0.391811	+	0.920046i	$0.628151\pi$
$230$	0	0
$231$	−16.9349	−1.11424
$232$	−19.5748	−1.28515
$233$	0.376209	0.0246462	0.0123231	−	0.999924i	$-0.496077\pi$
$233$	0.376209	0.0246462	0.0123231	+	0.999924i	$0.496077\pi$
$234$	14.4890	0.947174
$235$	0	0
$236$	2.65288	0.172688
$237$	8.43529	0.547931
$238$	−7.91420	−0.513002
$239$	15.7120	1.01633	0.508163	−	0.861261i	$-0.330325\pi$
$239$	15.7120	1.01633	0.508163	+	0.861261i	$0.330325\pi$
$240$	0	0
$241$	−16.5635	−1.06695	−0.533473	−	0.845817i	$-0.679113\pi$
$241$	−16.5635	−1.06695	−0.533473	+	0.845817i	$0.679113\pi$
$242$	−38.9229	−2.50206
$243$	−21.1605	−1.35745
$244$	2.31035	0.147905
$245$	0	0
$246$	−0.0718954	−0.00458389
$247$	14.6287	0.930801
$248$	−18.4828	−1.17366
$249$	12.5131	0.792986
$250$	0	0
$251$	16.9440	1.06949	0.534747	−	0.845012i	$-0.320407\pi$
$251$	16.9440	1.06949	0.534747	+	0.845012i	$0.320407\pi$
$252$	1.24998	0.0787415
$253$	−6.40014	−0.402374
$254$	−11.8405	−0.742941
$255$	0	0
$256$	−7.30476	−0.456548
$257$	−19.2135	−1.19850	−0.599252	−	0.800561i	$-0.704535\pi$
$257$	−19.2135	−1.19850	−0.599252	+	0.800561i	$0.704535\pi$
$258$	−6.49402	−0.404300
$259$	−6.68122	−0.415151
$260$	0	0
$261$	−26.0746	−1.61398
$262$	−6.25584	−0.386487
$263$	−13.0466	−0.804486	−0.402243	−	0.915533i	$-0.631769\pi$
$263$	−13.0466	−0.804486	−0.402243	+	0.915533i	$0.631769\pi$
$264$	50.8722	3.13097
$265$	0	0
$266$	−6.81802	−0.418040
$267$	29.6881	1.81688
$268$	4.21095	0.257225
$269$	−16.9023	−1.03055	−0.515274	−	0.857025i	$-0.672310\pi$
$269$	−16.9023	−1.03055	−0.515274	+	0.857025i	$0.672310\pi$
$270$	0	0
$271$	4.09308	0.248637	0.124319	−	0.992242i	$-0.460326\pi$
$271$	4.09308	0.248637	0.124319	+	0.992242i	$0.460326\pi$
$272$	19.9679	1.21073
$273$	7.37526	0.446371
$274$	−2.49545	−0.150756
$275$	0	0
$276$	0.826572	0.0497538
$277$	−2.42111	−0.145470	−0.0727351	−	0.997351i	$-0.523173\pi$
$277$	−2.42111	−0.145470	−0.0727351	+	0.997351i	$0.523173\pi$
$278$	−3.17939	−0.190687
$279$	−24.6200	−1.47396
$280$	0	0
$281$	−17.3045	−1.03230	−0.516150	−	0.856498i	$-0.672635\pi$
$281$	−17.3045	−1.03230	−0.516150	+	0.856498i	$0.672635\pi$
$282$	38.7477	2.30739
$283$	23.8571	1.41816	0.709079	−	0.705129i	$-0.249111\pi$
$283$	23.8571	1.41816	0.709079	+	0.705129i	$0.249111\pi$
$284$	−3.61782	−0.214678
$285$	0	0
$286$	23.1745	1.37034
$287$	−0.0209156	−0.00123461
$288$	−7.00258	−0.412631
$289$	20.1142	1.18319
$290$	0	0
$291$	39.6064	2.32177
$292$	−3.68673	−0.215750
$293$	8.43245	0.492629	0.246315	−	0.969190i	$-0.420780\pi$
$293$	8.43245	0.492629	0.246315	+	0.969190i	$0.420780\pi$
$294$	−3.43741	−0.200474
$295$	0	0
$296$	20.0702	1.16656
$297$	16.9594	0.984086
$298$	−22.8394	−1.32305
$299$	2.78730	0.161194
$300$	0	0
$301$	−1.88922	−0.108893
$302$	6.85084	0.394221
$303$	−2.56160	−0.147160
$304$	17.2022	0.986614
$305$	0	0
$306$	31.6683	1.81035
$307$	−5.69436	−0.324994	−0.162497	−	0.986709i	$-0.551955\pi$
$307$	−5.69436	−0.324994	−0.162497	+	0.986709i	$0.551955\pi$
$308$	1.99929	0.113920
$309$	−48.1577	−2.73959
$310$	0	0
$311$	11.2164	0.636023	0.318012	−	0.948087i	$-0.396985\pi$
$311$	11.2164	0.636023	0.318012	+	0.948087i	$0.396985\pi$
$312$	−22.1551	−1.25429
$313$	−4.07427	−0.230291	−0.115146	−	0.993349i	$-0.536733\pi$
$313$	−4.07427	−0.230291	−0.115146	+	0.993349i	$0.536733\pi$
$314$	−2.14180	−0.120869
$315$	0	0
$316$	−0.995849	−0.0560209
$317$	−7.42575	−0.417072	−0.208536	−	0.978015i	$-0.566870\pi$
$317$	−7.42575	−0.417072	−0.208536	+	0.978015i	$0.566870\pi$
$318$	38.4442	2.15584
$319$	−41.7052	−2.33504
$320$	0	0
$321$	−22.8922	−1.27772
$322$	−1.29908	−0.0723951
$323$	31.9736	1.77906
$324$	1.55965	0.0866474
$325$	0	0
$326$	−20.9727	−1.16157
$327$	13.3936	0.740665
$328$	0.0628300	0.00346921
$329$	11.2724	0.621465
$330$	0	0
$331$	2.93039	0.161069	0.0805343	−	0.996752i	$-0.474337\pi$
$331$	2.93039	0.161069	0.0805343	+	0.996752i	$0.474337\pi$
$332$	−1.47726	−0.0810754
$333$	26.7346	1.46504
$334$	−1.14567	−0.0626884
$335$	0	0
$336$	8.67275	0.473137
$337$	−0.555694	−0.0302706	−0.0151353	−	0.999885i	$-0.504818\pi$
$337$	−0.555694	−0.0302706	−0.0151353	+	0.999885i	$0.504818\pi$
$338$	6.79545	0.369624
$339$	−54.7785	−2.97516
$340$	0	0
$341$	−39.3787	−2.13248
$342$	27.2819	1.47524
$343$	−1.00000	−0.0539949
$344$	5.67518	0.305985
$345$	0	0
$346$	16.8651	0.906671
$347$	7.98054	0.428418	0.214209	−	0.976788i	$-0.431283\pi$
$347$	7.98054	0.428418	0.214209	+	0.976788i	$0.431283\pi$
$348$	5.38618	0.288730
$349$	20.7706	1.11182	0.555912	−	0.831241i	$-0.312369\pi$
$349$	20.7706	1.11182	0.555912	+	0.831241i	$0.312369\pi$
$350$	0	0
$351$	−7.38593	−0.394232
$352$	−11.2003	−0.596980
$353$	−20.1432	−1.07211	−0.536056	−	0.844182i	$-0.680087\pi$
$353$	−20.1432	−1.07211	−0.536056	+	0.844182i	$0.680087\pi$
$354$	29.1918	1.55153
$355$	0	0
$356$	−3.50490	−0.185759
$357$	16.1200	0.853159
$358$	−16.8906	−0.892697
$359$	9.31581	0.491670	0.245835	−	0.969312i	$-0.420938\pi$
$359$	9.31581	0.491670	0.245835	+	0.969312i	$0.420938\pi$
$360$	0	0
$361$	8.54500	0.449737
$362$	12.7071	0.667868
$363$	79.2798	4.16111
$364$	−0.870704	−0.0456373
$365$	0	0
$366$	25.4227	1.32886
$367$	12.0757	0.630346	0.315173	−	0.949034i	$-0.397938\pi$
$367$	12.0757	0.630346	0.315173	+	0.949034i	$0.397938\pi$
$368$	3.27765	0.170859
$369$	0.0836927	0.00435687
$370$	0	0
$371$	11.1841	0.580648
$372$	5.08572	0.263682
$373$	−13.9857	−0.724152	−0.362076	−	0.932149i	$-0.617932\pi$
$373$	−13.9857	−0.724152	−0.362076	+	0.932149i	$0.617932\pi$
$374$	50.6520	2.61915
$375$	0	0
$376$	−33.8619	−1.74629
$377$	18.1628	0.935434
$378$	3.44238	0.177057
$379$	−11.2622	−0.578501	−0.289251	−	0.957253i	$-0.593406\pi$
$379$	−11.2622	−0.578501	−0.289251	+	0.957253i	$0.593406\pi$
$380$	0	0
$381$	24.1173	1.23556
$382$	2.14766	0.109884
$383$	−27.7466	−1.41779	−0.708893	−	0.705316i	$-0.750805\pi$
$383$	−27.7466	−1.41779	−0.708893	+	0.705316i	$0.750805\pi$
$384$	−21.0867	−1.07608
$385$	0	0
$386$	27.1061	1.37967
$387$	7.55962	0.384277
$388$	−4.67582	−0.237379
$389$	−27.9704	−1.41815	−0.709077	−	0.705131i	$-0.750888\pi$
$389$	−27.9704	−1.41815	−0.709077	+	0.705131i	$0.750888\pi$
$390$	0	0
$391$	6.09215	0.308093
$392$	3.00398	0.151724
$393$	12.7421	0.642756
$394$	−21.7750	−1.09701
$395$	0	0
$396$	−8.00007	−0.402019
$397$	−25.0885	−1.25915	−0.629577	−	0.776938i	$-0.716772\pi$
$397$	−25.0885	−1.25915	−0.629577	+	0.776938i	$0.716772\pi$
$398$	25.2640	1.26637
$399$	13.8872	0.695230
$400$	0	0
$401$	33.0007	1.64798	0.823989	−	0.566605i	$-0.191744\pi$
$401$	33.0007	1.64798	0.823989	+	0.566605i	$0.191744\pi$
$402$	46.3366	2.31106
$403$	17.1497	0.854285
$404$	0.302415	0.0150457
$405$	0	0
$406$	−8.46520	−0.420121
$407$	42.7608	2.11957
$408$	−48.4240	−2.39735
$409$	−0.663295	−0.0327978	−0.0163989	−	0.999866i	$-0.505220\pi$
$409$	−0.663295	−0.0327978	−0.0163989	+	0.999866i	$0.505220\pi$
$410$	0	0
$411$	5.08283	0.250718
$412$	5.68537	0.280098
$413$	8.49239	0.417883
$414$	5.19821	0.255478
$415$	0	0
$416$	4.87781	0.239154
$417$	6.47591	0.317127
$418$	43.6363	2.13432
$419$	26.0294	1.27162	0.635810	−	0.771845i	$-0.280666\pi$
$419$	26.0294	1.27162	0.635810	+	0.771845i	$0.280666\pi$
$420$	0	0
$421$	−0.904809	−0.0440977	−0.0220488	−	0.999757i	$-0.507019\pi$
$421$	−0.904809	−0.0440977	−0.0220488	+	0.999757i	$0.507019\pi$
$422$	−31.2972	−1.52352
$423$	−45.1057	−2.19312
$424$	−33.5967	−1.63160
$425$	0	0
$426$	−39.8099	−1.92880
$427$	7.39589	0.357912
$428$	2.70260	0.130635
$429$	−47.2028	−2.27897
$430$	0	0
$431$	22.3619	1.07714	0.538568	−	0.842582i	$-0.318965\pi$
$431$	22.3619	1.07714	0.538568	+	0.842582i	$0.318965\pi$
$432$	−8.68529	−0.417871
$433$	−10.7492	−0.516575	−0.258287	−	0.966068i	$-0.583158\pi$
$433$	−10.7492	−0.516575	−0.258287	+	0.966068i	$0.583158\pi$
$434$	−7.99298	−0.383675
$435$	0	0
$436$	−1.58121	−0.0757261
$437$	5.24833	0.251062
$438$	−40.5682	−1.93842
$439$	12.4548	0.594437	0.297218	−	0.954809i	$-0.403941\pi$
$439$	12.4548	0.594437	0.297218	+	0.954809i	$0.403941\pi$
$440$	0	0
$441$	4.00145	0.190545
$442$	−22.0593	−1.04925
$443$	−33.8071	−1.60622	−0.803111	−	0.595829i	$-0.796824\pi$
$443$	−33.8071	−1.60622	−0.803111	+	0.595829i	$0.796824\pi$
$444$	−5.52251	−0.262087
$445$	0	0
$446$	20.3796	0.965003
$447$	46.5202	2.20033
$448$	−8.82872	−0.417118
$449$	5.98643	0.282517	0.141258	−	0.989973i	$-0.454885\pi$
$449$	5.98643	0.282517	0.141258	+	0.989973i	$0.454885\pi$
$450$	0	0
$451$	0.133863	0.00630336
$452$	6.46701	0.304182
$453$	−13.9541	−0.655619
$454$	1.79089	0.0840507
$455$	0	0
$456$	−41.7169	−1.95357
$457$	19.6283	0.918172	0.459086	−	0.888392i	$-0.348177\pi$
$457$	19.6283	0.918172	0.459086	+	0.888392i	$0.348177\pi$
$458$	15.4050	0.719827
$459$	−16.1433	−0.753504
$460$	0	0
$461$	5.23147	0.243654	0.121827	−	0.992551i	$-0.461125\pi$
$461$	5.23147	0.243654	0.121827	+	0.992551i	$0.461125\pi$
$462$	21.9999	1.02353
$463$	−34.2446	−1.59148	−0.795741	−	0.605637i	$-0.792918\pi$
$463$	−34.2446	−1.59148	−0.795741	+	0.605637i	$0.792918\pi$
$464$	21.3581	0.991526
$465$	0	0
$466$	−0.488726	−0.0226398
$467$	13.0142	0.602227	0.301114	−	0.953588i	$-0.402642\pi$
$467$	13.0142	0.602227	0.301114	+	0.953588i	$0.402642\pi$
$468$	3.48408	0.161051
$469$	13.4801	0.622454
$470$	0	0
$471$	4.36250	0.201013
$472$	−25.5110	−1.17424
$473$	12.0913	0.555958
$474$	−10.9582	−0.503325
$475$	0	0
$476$	−1.90308	−0.0872276
$477$	−44.7524	−2.04907
$478$	−20.4112	−0.933588
$479$	17.3418	0.792369	0.396184	−	0.918171i	$-0.370334\pi$
$479$	17.3418	0.792369	0.396184	+	0.918171i	$0.370334\pi$
$480$	0	0
$481$	−18.6226	−0.849116
$482$	21.5173	0.980087
$483$	2.64602	0.120398
$484$	−9.35956	−0.425435
$485$	0	0
$486$	27.4893	1.24694
$487$	−35.7305	−1.61910	−0.809552	−	0.587048i	$-0.800290\pi$
$487$	−35.7305	−1.61910	−0.809552	+	0.587048i	$0.800290\pi$
$488$	−22.2171	−1.00572
$489$	42.7181	1.93178
$490$	0	0
$491$	−33.4450	−1.50935	−0.754677	−	0.656097i	$-0.772206\pi$
$491$	−33.4450	−1.50935	−0.754677	+	0.656097i	$0.772206\pi$
$492$	−0.0172883	−0.000779415 0
$493$	39.6982	1.78792
$494$	−19.0039	−0.855025
$495$	0	0
$496$	20.1667	0.905511
$497$	−11.5814	−0.519496
$498$	−16.2556	−0.728429
$499$	−7.34443	−0.328782	−0.164391	−	0.986395i	$-0.552566\pi$
$499$	−7.34443	−0.328782	−0.164391	+	0.986395i	$0.552566\pi$
$500$	0	0
$501$	2.33355	0.104255
$502$	−22.0116	−0.982426
$503$	30.0916	1.34172	0.670860	−	0.741584i	$-0.265925\pi$
$503$	30.0916	1.34172	0.670860	+	0.741584i	$0.265925\pi$
$504$	−12.0203	−0.535425
$505$	0	0
$506$	8.31432	0.369617
$507$	−13.8412	−0.614711
$508$	−2.84722	−0.126325
$509$	11.0144	0.488206	0.244103	−	0.969749i	$-0.421507\pi$
$509$	11.0144	0.488206	0.244103	+	0.969749i	$0.421507\pi$
$510$	0	0
$511$	−11.8020	−0.522088
$512$	25.4279	1.12377
$513$	−13.9073	−0.614022
$514$	24.9599	1.10093
$515$	0	0
$516$	−1.56158	−0.0687446
$517$	−72.1447	−3.17292
$518$	8.67946	0.381354
$519$	−34.3514	−1.50786
$520$	0	0
$521$	−18.6738	−0.818113	−0.409057	−	0.912509i	$-0.634142\pi$
$521$	−18.6738	−0.818113	−0.409057	+	0.912509i	$0.634142\pi$
$522$	33.8730	1.48258
$523$	−14.8714	−0.650280	−0.325140	−	0.945666i	$-0.605411\pi$
$523$	−14.8714	−0.650280	−0.325140	+	0.945666i	$0.605411\pi$
$524$	−1.50430	−0.0657158
$525$	0	0
$526$	16.9486	0.738993
$527$	37.4837	1.63281
$528$	−55.5068	−2.41562
$529$	1.00000	0.0434783
$530$	0	0
$531$	−33.9819	−1.47469
$532$	−1.63949	−0.0710808
$533$	−0.0582981	−0.00252517
$534$	−38.5674	−1.66897
$535$	0	0
$536$	−40.4940	−1.74907
$537$	34.4035	1.48462
$538$	21.9574	0.946652
$539$	6.40014	0.275674
$540$	0	0
$541$	−14.4279	−0.620305	−0.310153	−	0.950687i	$-0.600380\pi$
$541$	−14.4279	−0.620305	−0.310153	+	0.950687i	$0.600380\pi$
$542$	−5.31725	−0.228396
$543$	−25.8822	−1.11071
$544$	10.6613	0.457101
$545$	0	0
$546$	−9.58108	−0.410032
$547$	−31.9642	−1.36669	−0.683344	−	0.730096i	$-0.739475\pi$
$547$	−31.9642	−1.36669	−0.683344	+	0.730096i	$0.739475\pi$
$548$	−0.600066	−0.0256335
$549$	−29.5943	−1.26305
$550$	0	0
$551$	34.1996	1.45695
$552$	−7.94860	−0.338315
$553$	−3.18791	−0.135564
$554$	3.14522	0.133628
$555$	0	0
$556$	−0.764529	−0.0324233
$557$	31.4553	1.33281	0.666403	−	0.745592i	$-0.267833\pi$
$557$	31.4553	1.33281	0.666403	+	0.745592i	$0.267833\pi$
$558$	31.9835	1.35397
$559$	−5.26583	−0.222721
$560$	0	0
$561$	−103.170	−4.35585
$562$	22.4800	0.948261
$563$	−1.45678	−0.0613960	−0.0306980	−	0.999529i	$-0.509773\pi$
$563$	−1.45678	−0.0613960	−0.0306980	+	0.999529i	$0.509773\pi$
$564$	9.31742	0.392334
$565$	0	0
$566$	−30.9924	−1.30271
$567$	4.99277	0.209676
$568$	34.7902	1.45976
$569$	−5.19758	−0.217894	−0.108947	−	0.994048i	$-0.534748\pi$
$569$	−5.19758	−0.217894	−0.108947	+	0.994048i	$0.534748\pi$
$570$	0	0
$571$	23.8067	0.996278	0.498139	−	0.867097i	$-0.334017\pi$
$571$	23.8067	0.996278	0.498139	+	0.867097i	$0.334017\pi$
$572$	5.57263	0.233003
$573$	−4.37443	−0.182745
$574$	0.0271711	0.00113410
$575$	0	0
$576$	35.3276	1.47198
$577$	10.9988	0.457886	0.228943	−	0.973440i	$-0.426473\pi$
$577$	10.9988	0.457886	0.228943	+	0.973440i	$0.426473\pi$
$578$	−26.1301	−1.08687
$579$	−55.2108	−2.29448
$580$	0	0
$581$	−4.72902	−0.196193
$582$	−51.4520	−2.13275
$583$	−71.5796	−2.96452
$584$	35.4529	1.46705
$585$	0	0
$586$	−10.9545	−0.452525
$587$	−25.4268	−1.04947	−0.524737	−	0.851264i	$-0.675836\pi$
$587$	−25.4268	−1.04947	−0.524737	+	0.851264i	$0.675836\pi$
$588$	−0.826572	−0.0340873
$589$	32.2919	1.33056
$590$	0	0
$591$	44.3522	1.82441
$592$	−21.8987	−0.900032
$593$	45.0956	1.85185	0.925927	−	0.377702i	$-0.123286\pi$
$593$	45.0956	1.85185	0.925927	+	0.377702i	$0.123286\pi$
$594$	−22.0317	−0.903972
$595$	0	0
$596$	−5.49205	−0.224963
$597$	−51.4587	−2.10607
$598$	−3.62093	−0.148071
$599$	−10.3240	−0.421828	−0.210914	−	0.977505i	$-0.567644\pi$
$599$	−10.3240	−0.421828	−0.210914	+	0.977505i	$0.567644\pi$
$600$	0	0
$601$	−11.2231	−0.457802	−0.228901	−	0.973450i	$-0.573513\pi$
$601$	−11.2231	−0.457802	−0.228901	+	0.973450i	$0.573513\pi$
$602$	2.45426	0.100028
$603$	−53.9400	−2.19661
$604$	1.64738	0.0670309
$605$	0	0
$606$	3.32773	0.135180
$607$	6.42280	0.260693	0.130347	−	0.991468i	$-0.458391\pi$
$607$	6.42280	0.260693	0.130347	+	0.991468i	$0.458391\pi$
$608$	9.18465	0.372487
$609$	17.2423	0.698691
$610$	0	0
$611$	31.4194	1.27109
$612$	7.61507	0.307821
$613$	11.6218	0.469399	0.234700	−	0.972068i	$-0.424589\pi$
$613$	11.6218	0.469399	0.234700	+	0.972068i	$0.424589\pi$
$614$	7.39744	0.298537
$615$	0	0
$616$	−19.2259	−0.774633
$617$	16.6011	0.668335	0.334167	−	0.942514i	$-0.391545\pi$
$617$	16.6011	0.668335	0.334167	+	0.942514i	$0.391545\pi$
$618$	62.5608	2.51657
$619$	5.87879	0.236288	0.118144	−	0.992996i	$-0.462305\pi$
$619$	5.87879	0.236288	0.118144	+	0.992996i	$0.462305\pi$
$620$	0	0
$621$	−2.64985	−0.106335
$622$	−14.5710	−0.584245
$623$	−11.2199	−0.449516
$624$	24.1735	0.967716
$625$	0	0
$626$	5.29282	0.211544
$627$	−88.8802	−3.54953
$628$	−0.515025	−0.0205517
$629$	−40.7030	−1.62293
$630$	0	0
$631$	25.3002	1.00718	0.503592	−	0.863942i	$-0.332011\pi$
$631$	25.3002	1.00718	0.503592	+	0.863942i	$0.332011\pi$
$632$	9.57642	0.380929
$633$	63.7473	2.53373
$634$	9.64666	0.383118
$635$	0	0
$636$	9.24444	0.366566
$637$	−2.78730	−0.110437
$638$	54.1785	2.14495
$639$	46.3423	1.83327
$640$	0	0
$641$	26.1388	1.03242	0.516210	−	0.856462i	$-0.327342\pi$
$641$	26.1388	1.03242	0.516210	+	0.856462i	$0.327342\pi$
$642$	29.7389	1.17370
$643$	43.2339	1.70498	0.852489	−	0.522745i	$-0.175092\pi$
$643$	43.2339	1.70498	0.852489	+	0.522745i	$0.175092\pi$
$644$	−0.312383	−0.0123096
$645$	0	0
$646$	−41.5364	−1.63423
$647$	2.23115	0.0877157	0.0438579	−	0.999038i	$-0.486035\pi$
$647$	2.23115	0.0877157	0.0438579	+	0.999038i	$0.486035\pi$
$648$	−14.9982	−0.589183
$649$	−54.3525	−2.13352
$650$	0	0
$651$	16.2804	0.638080
$652$	−5.04319	−0.197506
$653$	−6.57176	−0.257173	−0.128586	−	0.991698i	$-0.541044\pi$
$653$	−6.57176	−0.257173	−0.128586	+	0.991698i	$0.541044\pi$
$654$	−17.3993	−0.680368
$655$	0	0
$656$	−0.0685541	−0.00267659
$657$	47.2249	1.84242
$658$	−14.6437	−0.570872
$659$	3.30887	0.128895	0.0644476	−	0.997921i	$-0.479471\pi$
$659$	3.30887	0.128895	0.0644476	+	0.997921i	$0.479471\pi$
$660$	0	0
$661$	−7.40738	−0.288114	−0.144057	−	0.989569i	$-0.546015\pi$
$661$	−7.40738	−0.288114	−0.144057	+	0.989569i	$0.546015\pi$
$662$	−3.80682	−0.147956
$663$	44.9312	1.74498
$664$	14.2059	0.551295
$665$	0	0
$666$	−34.7304	−1.34578
$667$	6.51629	0.252312
$668$	−0.275493	−0.0106591
$669$	−41.5100	−1.60487
$670$	0	0
$671$	−47.3348	−1.82734
$672$	4.63058	0.178628
$673$	16.3153	0.628908	0.314454	−	0.949273i	$-0.398179\pi$
$673$	16.3153	0.628908	0.314454	+	0.949273i	$0.398179\pi$
$674$	0.721893	0.0278063
$675$	0	0
$676$	1.63406	0.0628485
$677$	−26.3862	−1.01411	−0.507053	−	0.861915i	$-0.669265\pi$
$677$	−26.3862	−1.01411	−0.507053	+	0.861915i	$0.669265\pi$
$678$	71.1618	2.73295
$679$	−14.9683	−0.574429
$680$	0	0
$681$	−3.64776	−0.139782
$682$	51.1562	1.95887
$683$	−14.2592	−0.545614	−0.272807	−	0.962069i	$-0.587952\pi$
$683$	−14.2592	−0.545614	−0.272807	+	0.962069i	$0.587952\pi$
$684$	6.56032	0.250840
$685$	0	0
$686$	1.29908	0.0495992
$687$	−31.3775	−1.19713
$688$	−6.19221	−0.236076
$689$	31.1733	1.18761
$690$	0	0
$691$	−14.2880	−0.543543	−0.271771	−	0.962362i	$-0.587609\pi$
$691$	−14.2880	−0.543543	−0.271771	+	0.962362i	$0.587609\pi$
$692$	4.05544	0.154165
$693$	−25.6098	−0.972837
$694$	−10.3674	−0.393541
$695$	0	0
$696$	−51.7953	−1.96330
$697$	−0.127421	−0.00482641
$698$	−26.9827	−1.02131
$699$	0.995457	0.0376516
$700$	0	0
$701$	17.6976	0.668430	0.334215	−	0.942497i	$-0.391529\pi$
$701$	17.6976	0.668430	0.334215	+	0.942497i	$0.391529\pi$
$702$	9.59494	0.362138
$703$	−35.0653	−1.32251
$704$	56.5051	2.12961
$705$	0	0
$706$	26.1677	0.984833
$707$	0.968093	0.0364089
$708$	7.01958	0.263812
$709$	10.0987	0.379265	0.189633	−	0.981855i	$-0.439270\pi$
$709$	10.0987	0.379265	0.189633	+	0.981855i	$0.439270\pi$
$710$	0	0
$711$	12.7563	0.478397
$712$	33.7043	1.26312
$713$	6.15279	0.230424
$714$	−20.9412	−0.783704
$715$	0	0
$716$	−4.06159	−0.151789
$717$	41.5744	1.55263
$718$	−12.1020	−0.451643
$719$	21.1603	0.789147	0.394574	−	0.918864i	$-0.370892\pi$
$719$	21.1603	0.789147	0.394574	+	0.918864i	$0.370892\pi$
$720$	0	0
$721$	18.2000	0.677804
$722$	−11.1007	−0.413124
$723$	−43.8273	−1.62996
$724$	3.05559	0.113560
$725$	0	0
$726$	−102.991	−3.82236
$727$	−47.2004	−1.75057	−0.875283	−	0.483611i	$-0.839325\pi$
$727$	−47.2004	−1.75057	−0.875283	+	0.483611i	$0.839325\pi$
$728$	8.37299	0.310324
$729$	−41.0130	−1.51900
$730$	0	0
$731$	−11.5094	−0.425691
$732$	6.11324	0.225952
$733$	9.09085	0.335778	0.167889	−	0.985806i	$-0.446305\pi$
$733$	9.09085	0.335778	0.167889	+	0.985806i	$0.446305\pi$
$734$	−15.6873	−0.579030
$735$	0	0
$736$	1.75001	0.0645063
$737$	−86.2747	−3.17797
$738$	−0.108724	−0.00400218
$739$	−14.8468	−0.546149	−0.273075	−	0.961993i	$-0.588041\pi$
$739$	−14.8468	−0.546149	−0.273075	+	0.961993i	$0.588041\pi$
$740$	0	0
$741$	38.7078	1.42197
$742$	−14.5290	−0.533377
$743$	46.8998	1.72059	0.860294	−	0.509798i	$-0.170280\pi$
$743$	46.8998	1.72059	0.860294	+	0.509798i	$0.170280\pi$
$744$	−48.9060	−1.79298
$745$	0	0
$746$	18.1686	0.665199
$747$	18.9229	0.692354
$748$	12.1800	0.445345
$749$	8.65155	0.316121
$750$	0	0
$751$	−45.1405	−1.64720	−0.823600	−	0.567171i	$-0.808038\pi$
$751$	−45.1405	−1.64720	−0.823600	+	0.567171i	$0.808038\pi$
$752$	36.9469	1.34731
$753$	44.8341	1.63385
$754$	−23.5950	−0.859281
$755$	0	0
$756$	0.827768	0.0301056
$757$	16.1423	0.586701	0.293351	−	0.956005i	$-0.405230\pi$
$757$	16.1423	0.586701	0.293351	+	0.956005i	$0.405230\pi$
$758$	14.6306	0.531406
$759$	−16.9349	−0.614699
$760$	0	0
$761$	−23.0502	−0.835571	−0.417785	−	0.908546i	$-0.637194\pi$
$761$	−23.0502	−0.835571	−0.417785	+	0.908546i	$0.637194\pi$
$762$	−31.3303	−1.13498
$763$	−5.06176	−0.183248
$764$	0.516434	0.0186839
$765$	0	0
$766$	36.0452	1.30236
$767$	23.6708	0.854705
$768$	−19.3286	−0.697460
$769$	−28.8802	−1.04145	−0.520723	−	0.853726i	$-0.674337\pi$
$769$	−28.8802	−1.04145	−0.520723	+	0.853726i	$0.674337\pi$
$770$	0	0
$771$	−50.8393	−1.83093
$772$	6.51805	0.234590
$773$	18.4978	0.665318	0.332659	−	0.943047i	$-0.392054\pi$
$773$	18.4978	0.665318	0.332659	+	0.943047i	$0.392054\pi$
$774$	−9.82057	−0.352993
$775$	0	0
$776$	44.9643	1.61412
$777$	−17.6787	−0.634219
$778$	36.3358	1.30270
$779$	−0.109772	−0.00393299
$780$	0	0
$781$	74.1225	2.65231
$782$	−7.91420	−0.283011
$783$	−17.2672	−0.617079
$784$	−3.27765	−0.117059
$785$	0	0
$786$	−16.5531	−0.590430
$787$	28.7684	1.02548	0.512742	−	0.858543i	$-0.328630\pi$
$787$	28.7684	1.02548	0.512742	+	0.858543i	$0.328630\pi$
$788$	−5.23611	−0.186529
$789$	−34.5215	−1.22900
$790$	0	0
$791$	20.7022	0.736085
$792$	76.9314	2.73364
$793$	20.6146	0.732045
$794$	32.5920	1.15665
$795$	0	0
$796$	6.07508	0.215326
$797$	−33.0925	−1.17219	−0.586097	−	0.810241i	$-0.699336\pi$
$797$	−33.0925	−1.17219	−0.586097	+	0.810241i	$0.699336\pi$
$798$	−18.0407	−0.638632
$799$	68.6728	2.42947
$800$	0	0
$801$	44.8958	1.58632
$802$	−42.8707	−1.51382
$803$	75.5343	2.66555
$804$	11.1423	0.392958
$805$	0	0
$806$	−22.2788	−0.784739
$807$	−44.7238	−1.57435
$808$	−2.90813	−0.102308
$809$	−12.1479	−0.427098	−0.213549	−	0.976932i	$-0.568502\pi$
$809$	−12.1479	−0.427098	−0.213549	+	0.976932i	$0.568502\pi$
$810$	0	0
$811$	−3.91279	−0.137397	−0.0686983	−	0.997637i	$-0.521885\pi$
$811$	−3.91279	−0.137397	−0.0686983	+	0.997637i	$0.521885\pi$
$812$	−2.03558	−0.0714347
$813$	10.8304	0.379839
$814$	−55.5498	−1.94702
$815$	0	0
$816$	52.8356	1.84962
$817$	−9.91526	−0.346891
$818$	0.861676	0.0301278
$819$	11.1532	0.389725
$820$	0	0
$821$	−45.7853	−1.59792	−0.798960	−	0.601385i	$-0.794616\pi$
$821$	−45.7853	−1.59792	−0.798960	+	0.601385i	$0.794616\pi$
$822$	−6.60303	−0.230307
$823$	51.6185	1.79931	0.899654	−	0.436604i	$-0.143819\pi$
$823$	51.6185	1.79931	0.899654	+	0.436604i	$0.143819\pi$
$824$	−54.6724	−1.90460
$825$	0	0
$826$	−11.0323	−0.383864
$827$	−16.8894	−0.587302	−0.293651	−	0.955913i	$-0.594870\pi$
$827$	−16.8894	−0.587302	−0.293651	+	0.955913i	$0.594870\pi$
$828$	1.24998	0.0434399
$829$	−7.28503	−0.253020	−0.126510	−	0.991965i	$-0.540378\pi$
$829$	−7.28503	−0.253020	−0.126510	+	0.991965i	$0.540378\pi$
$830$	0	0
$831$	−6.40631	−0.222232
$832$	−24.6083	−0.853139
$833$	−6.09215	−0.211080
$834$	−8.41275	−0.291310
$835$	0	0
$836$	10.4930	0.362907
$837$	−16.3040	−0.563548
$838$	−33.8144	−1.16810
$839$	−21.6946	−0.748981	−0.374490	−	0.927231i	$-0.622182\pi$
$839$	−21.6946	−0.748981	−0.374490	+	0.927231i	$0.622182\pi$
$840$	0	0
$841$	13.4620	0.464207
$842$	1.17542	0.0405077
$843$	−45.7881	−1.57703
$844$	−7.52584	−0.259050
$845$	0	0
$846$	58.5961	2.01458
$847$	−29.9618	−1.02950
$848$	36.6575	1.25882
$849$	63.1265	2.16649
$850$	0	0
$851$	−6.68122	−0.229029
$852$	−9.57285	−0.327960
$853$	10.7643	0.368561	0.184281	−	0.982874i	$-0.441004\pi$
$853$	10.7643	0.368561	0.184281	+	0.982874i	$0.441004\pi$
$854$	−9.60788	−0.328775
$855$	0	0
$856$	−25.9891	−0.888288
$857$	−51.0047	−1.74229	−0.871144	−	0.491028i	$-0.836621\pi$
$857$	−51.0047	−1.74229	−0.871144	+	0.491028i	$0.836621\pi$
$858$	61.3203	2.09344
$859$	−15.6036	−0.532387	−0.266194	−	0.963920i	$-0.585766\pi$
$859$	−15.6036	−0.532387	−0.266194	+	0.963920i	$0.585766\pi$
$860$	0	0
$861$	−0.0553432	−0.00188609
$862$	−29.0500	−0.989448
$863$	−2.96380	−0.100889	−0.0504444	−	0.998727i	$-0.516064\pi$
$863$	−2.96380	−0.100889	−0.0504444	+	0.998727i	$0.516064\pi$
$864$	−4.63727	−0.157763
$865$	0	0
$866$	13.9641	0.474521
$867$	53.2228	1.80754
$868$	−1.92202	−0.0652377
$869$	20.4031	0.692128
$870$	0	0
$871$	37.5731	1.27312
$872$	15.2054	0.514921
$873$	59.8947	2.02713
$874$	−6.81802	−0.230623
$875$	0	0
$876$	−9.75518	−0.329597
$877$	−17.4676	−0.589840	−0.294920	−	0.955522i	$-0.595293\pi$
$877$	−17.4676	−0.589840	−0.294920	+	0.955522i	$0.595293\pi$
$878$	−16.1799	−0.546044
$879$	22.3125	0.752581
$880$	0	0
$881$	54.1022	1.82275	0.911375	−	0.411578i	$-0.135022\pi$
$881$	54.1022	1.82275	0.911375	+	0.411578i	$0.135022\pi$
$882$	−5.19821	−0.175033
$883$	−16.3288	−0.549508	−0.274754	−	0.961515i	$-0.588596\pi$
$883$	−16.3288	−0.549508	−0.274754	+	0.961515i	$0.588596\pi$
$884$	−5.30446	−0.178408
$885$	0	0
$886$	43.9182	1.47546
$887$	−6.30682	−0.211762	−0.105881	−	0.994379i	$-0.533766\pi$
$887$	−6.30682	−0.211762	−0.105881	+	0.994379i	$0.533766\pi$
$888$	53.1064	1.78213
$889$	−9.11452	−0.305691
$890$	0	0
$891$	−31.9544	−1.07051
$892$	4.90056	0.164083
$893$	59.1611	1.97975
$894$	−60.4336	−2.02120
$895$	0	0
$896$	7.96921	0.266233
$897$	7.37526	0.246253
$898$	−7.77687	−0.259517
$899$	40.0933	1.33719
$900$	0	0
$901$	68.1349	2.26990
$902$	−0.173899	−0.00579020
$903$	−4.99893	−0.166354
$904$	−62.1889	−2.06837
$905$	0	0
$906$	18.1275	0.602245
$907$	30.2046	1.00293	0.501464	−	0.865178i	$-0.332795\pi$
$907$	30.2046	1.00293	0.501464	+	0.865178i	$0.332795\pi$
$908$	0.430645	0.0142915
$909$	−3.87377	−0.128485
$910$	0	0
$911$	−11.8550	−0.392775	−0.196387	−	0.980526i	$-0.562921\pi$
$911$	−11.8550	−0.392775	−0.196387	+	0.980526i	$0.562921\pi$
$912$	45.5175	1.50723
$913$	30.2664	1.00167
$914$	−25.4988	−0.843424
$915$	0	0
$916$	3.70434	0.122395
$917$	−4.81558	−0.159025
$918$	20.9715	0.692162
$919$	−6.46903	−0.213393	−0.106697	−	0.994292i	$-0.534027\pi$
$919$	−6.46903	−0.213393	−0.106697	+	0.994292i	$0.534027\pi$
$920$	0	0
$921$	−15.0674	−0.496488
$922$	−6.79611	−0.223818
$923$	−32.2808	−1.06253
$924$	5.29018	0.174034
$925$	0	0
$926$	44.4866	1.46192
$927$	−72.8263	−2.39193
$928$	11.4036	0.374341
$929$	12.8776	0.422500	0.211250	−	0.977432i	$-0.432247\pi$
$929$	12.8776	0.422500	0.211250	+	0.977432i	$0.432247\pi$
$930$	0	0
$931$	−5.24833	−0.172007
$932$	−0.117521	−0.00384953
$933$	29.6789	0.971642
$934$	−16.9066	−0.553200
$935$	0	0
$936$	−33.5041	−1.09511
$937$	45.6311	1.49070	0.745352	−	0.666671i	$-0.232281\pi$
$937$	45.6311	1.49070	0.745352	+	0.666671i	$0.232281\pi$
$938$	−17.5118	−0.571780
$939$	−10.7806	−0.351812
$940$	0	0
$941$	−26.4930	−0.863648	−0.431824	−	0.901958i	$-0.642130\pi$
$941$	−26.4930	−0.863648	−0.431824	+	0.901958i	$0.642130\pi$
$942$	−5.66725	−0.184649
$943$	−0.0209156	−0.000681106 0
$944$	27.8351	0.905956
$945$	0	0
$946$	−15.7076	−0.510698
$947$	41.8187	1.35893	0.679463	−	0.733710i	$-0.262213\pi$
$947$	41.8187	1.35893	0.679463	+	0.733710i	$0.262213\pi$
$948$	−2.63504	−0.0855821
$949$	−32.8956	−1.06784
$950$	0	0
$951$	−19.6487	−0.637153
$952$	18.3007	0.593128
$953$	47.2592	1.53088	0.765438	−	0.643510i	$-0.222523\pi$
$953$	47.2592	1.53088	0.765438	+	0.643510i	$0.222523\pi$
$954$	58.1371	1.88226
$955$	0	0
$956$	−4.90817	−0.158741
$957$	−110.353	−3.56720
$958$	−22.5285	−0.727862
$959$	−1.92093	−0.0620301
$960$	0	0
$961$	6.85678	0.221186
$962$	24.1923	0.779990
$963$	−34.6187	−1.11557
$964$	5.17414	0.166648
$965$	0	0
$966$	−3.43741	−0.110597
$967$	−4.16411	−0.133909	−0.0669544	−	0.997756i	$-0.521328\pi$
$967$	−4.16411	−0.133909	−0.0669544	+	0.997756i	$0.521328\pi$
$968$	90.0047	2.89286
$969$	84.6030	2.71784
$970$	0	0
$971$	−55.0441	−1.76645	−0.883224	−	0.468951i	$-0.844632\pi$
$971$	−55.0441	−1.76645	−0.883224	+	0.468951i	$0.844632\pi$
$972$	6.61019	0.212022
$973$	−2.44741	−0.0784604
$974$	46.4169	1.48729
$975$	0	0
$976$	24.2411	0.775940
$977$	33.0791	1.05830	0.529148	−	0.848530i	$-0.322512\pi$
$977$	33.0791	1.05830	0.529148	+	0.848530i	$0.322512\pi$
$978$	−55.4944	−1.77451
$979$	71.8090	2.29503
$980$	0	0
$981$	20.2544	0.646672
$982$	43.4479	1.38648
$983$	23.6958	0.755778	0.377889	−	0.925851i	$-0.376650\pi$
$983$	23.6958	0.755778	0.377889	+	0.925851i	$0.376650\pi$
$984$	0.166250	0.00529985
$985$	0	0
$986$	−51.5712	−1.64236
$987$	29.8269	0.949402
$988$	−4.56975	−0.145383
$989$	−1.88922	−0.0600737
$990$	0	0
$991$	−0.0169133	−0.000537269 0	−0.000268635	−	1.00000i	$-0.500086\pi$
$991$	−0.0169133	−0.000537269 0	−0.000268635		1.00000i	$0.500086\pi$
$992$	10.7675	0.341867
$993$	7.75388	0.246062
$994$	15.0452	0.477204
$995$	0	0
$996$	−3.90888	−0.123858
$997$	35.2510	1.11641	0.558206	−	0.829703i	$-0.311490\pi$
$997$	35.2510	1.11641	0.558206	+	0.829703i	$0.311490\pi$
$998$	9.54103	0.302016
$999$	17.7042	0.560138

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.z.1.6	✓	14
5.4	even	2		4025.2.a.bc.1.9	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4025.2.a.z.1.6	✓	14	1.1	even	1	trivial
4025.2.a.bc.1.9	yes	14	5.4	even	2

Overview	Random
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Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.29908 q^{2} +2.64602 q^{3} -0.312383 q^{4} -3.43741 q^{6} -1.00000 q^{7} +3.00398 q^{8} +4.00145 q^{9} +O(q^{10})\)	\(q-1.29908 q^{2} +2.64602 q^{3} -0.312383 q^{4} -3.43741 q^{6} -1.00000 q^{7} +3.00398 q^{8} +4.00145 q^{9} +6.40014 q^{11} -0.826572 q^{12} -2.78730 q^{13} +1.29908 q^{14} -3.27765 q^{16} -6.09215 q^{17} -5.19821 q^{18} -5.24833 q^{19} -2.64602 q^{21} -8.31432 q^{22} -1.00000 q^{23} +7.94860 q^{24} +3.62093 q^{26} +2.64985 q^{27} +0.312383 q^{28} -6.51629 q^{29} -6.15279 q^{31} -1.75001 q^{32} +16.9349 q^{33} +7.91420 q^{34} -1.24998 q^{36} +6.68122 q^{37} +6.81802 q^{38} -7.37526 q^{39} +0.0209156 q^{41} +3.43741 q^{42} +1.88922 q^{43} -1.99929 q^{44} +1.29908 q^{46} -11.2724 q^{47} -8.67275 q^{48} +1.00000 q^{49} -16.1200 q^{51} +0.870704 q^{52} -11.1841 q^{53} -3.44238 q^{54} -3.00398 q^{56} -13.8872 q^{57} +8.46520 q^{58} -8.49239 q^{59} -7.39589 q^{61} +7.99298 q^{62} -4.00145 q^{63} +8.82872 q^{64} -21.9999 q^{66} -13.4801 q^{67} +1.90308 q^{68} -2.64602 q^{69} +11.5814 q^{71} +12.0203 q^{72} +11.8020 q^{73} -8.67946 q^{74} +1.63949 q^{76} -6.40014 q^{77} +9.58108 q^{78} +3.18791 q^{79} -4.99277 q^{81} -0.0271711 q^{82} +4.72902 q^{83} +0.826572 q^{84} -2.45426 q^{86} -17.2423 q^{87} +19.2259 q^{88} +11.2199 q^{89} +2.78730 q^{91} +0.312383 q^{92} -16.2804 q^{93} +14.6437 q^{94} -4.63058 q^{96} +14.9683 q^{97} -1.29908 q^{98} +25.6098 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 3 q^{2} - 4 q^{3} + 17 q^{4} - 4 q^{6} - 14 q^{7} - 3 q^{8} + 18 q^{9}+O(q^{10}) \) 14 * q - 3 * q^2 - 4 * q^3 + 17 * q^4 - 4 * q^6 - 14 * q^7 - 3 * q^8 + 18 * q^9	\( 14 q - 3 q^{2} - 4 q^{3} + 17 q^{4} - 4 q^{6} - 14 q^{7} - 3 q^{8} + 18 q^{9} + 5 q^{11} - 17 q^{12} - 11 q^{13} + 3 q^{14} + 23 q^{16} - 3 q^{17} - 15 q^{18} - 2 q^{19} + 4 q^{21} - 23 q^{22} - 14 q^{23} - 12 q^{24} - 9 q^{26} - 25 q^{27} - 17 q^{28} + 7 q^{29} - 3 q^{31} - 24 q^{32} - 6 q^{33} - 14 q^{34} + 13 q^{36} - 22 q^{37} - 20 q^{38} - 10 q^{39} - 17 q^{41} + 4 q^{42} - 18 q^{43} + 28 q^{44} + 3 q^{46} - 30 q^{47} - 8 q^{48} + 14 q^{49} + 4 q^{51} - 8 q^{52} - 11 q^{53} + 20 q^{54} + 3 q^{56} - 18 q^{57} - 38 q^{58} - 22 q^{59} - 8 q^{61} + 22 q^{62} - 18 q^{63} + 29 q^{64} - 9 q^{66} - 39 q^{67} - q^{68} + 4 q^{69} - 5 q^{71} + 24 q^{72} - 18 q^{73} + 35 q^{74} - 41 q^{76} - 5 q^{77} + 22 q^{78} + 10 q^{79} + 2 q^{81} + 8 q^{82} - 24 q^{83} + 17 q^{84} - 26 q^{86} - 5 q^{87} - 58 q^{88} + 25 q^{89} + 11 q^{91} - 17 q^{92} - 47 q^{93} - 2 q^{94} - 117 q^{96} - 43 q^{97} - 3 q^{98} + 55 q^{99}+O(q^{100}) \) 14 * q - 3 * q^2 - 4 * q^3 + 17 * q^4 - 4 * q^6 - 14 * q^7 - 3 * q^8 + 18 * q^9 + 5 * q^11 - 17 * q^12 - 11 * q^13 + 3 * q^14 + 23 * q^16 - 3 * q^17 - 15 * q^18 - 2 * q^19 + 4 * q^21 - 23 * q^22 - 14 * q^23 - 12 * q^24 - 9 * q^26 - 25 * q^27 - 17 * q^28 + 7 * q^29 - 3 * q^31 - 24 * q^32 - 6 * q^33 - 14 * q^34 + 13 * q^36 - 22 * q^37 - 20 * q^38 - 10 * q^39 - 17 * q^41 + 4 * q^42 - 18 * q^43 + 28 * q^44 + 3 * q^46 - 30 * q^47 - 8 * q^48 + 14 * q^49 + 4 * q^51 - 8 * q^52 - 11 * q^53 + 20 * q^54 + 3 * q^56 - 18 * q^57 - 38 * q^58 - 22 * q^59 - 8 * q^61 + 22 * q^62 - 18 * q^63 + 29 * q^64 - 9 * q^66 - 39 * q^67 - q^68 + 4 * q^69 - 5 * q^71 + 24 * q^72 - 18 * q^73 + 35 * q^74 - 41 * q^76 - 5 * q^77 + 22 * q^78 + 10 * q^79 + 2 * q^81 + 8 * q^82 - 24 * q^83 + 17 * q^84 - 26 * q^86 - 5 * q^87 - 58 * q^88 + 25 * q^89 + 11 * q^91 - 17 * q^92 - 47 * q^93 - 2 * q^94 - 117 * q^96 - 43 * q^97 - 3 * q^98 + 55 * q^99

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