LMFDB - Embedded newform 4025.2.a.v.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("4025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$32.1397868136$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 10x^{6} + 9x^{5} + 28x^{4} - 22x^{3} - 16x^{2} + 7x + 3 $ x^8 - x^7 - 10x^6 + 9x^5 + 28x^4 - 22x^3 - 16x^2 + 7x + 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-0.333224$ 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)

$f(q)$	$=$	$q-0.333224 q^{2} +0.161242 q^{3} -1.88896 q^{4} -0.0537298 q^{6} -1.00000 q^{7} +1.29590 q^{8} -2.97400 q^{9} +O(q^{10})$	\(q-0.333224 q^{2} +0.161242 q^{3} -1.88896 q^{4} -0.0537298 q^{6} -1.00000 q^{7} +1.29590 q^{8} -2.97400 q^{9} -2.18897 q^{11} -0.304580 q^{12} -5.74105 q^{13} +0.333224 q^{14} +3.34610 q^{16} -2.10691 q^{17} +0.991009 q^{18} -3.09494 q^{19} -0.161242 q^{21} +0.729419 q^{22} +1.00000 q^{23} +0.208953 q^{24} +1.91306 q^{26} -0.963261 q^{27} +1.88896 q^{28} -3.06986 q^{29} -4.44457 q^{31} -3.70679 q^{32} -0.352955 q^{33} +0.702072 q^{34} +5.61777 q^{36} -7.57953 q^{37} +1.03131 q^{38} -0.925700 q^{39} +9.26196 q^{41} +0.0537298 q^{42} -2.82670 q^{43} +4.13489 q^{44} -0.333224 q^{46} +6.45023 q^{47} +0.539533 q^{48} +1.00000 q^{49} -0.339722 q^{51} +10.8446 q^{52} +1.24851 q^{53} +0.320982 q^{54} -1.29590 q^{56} -0.499035 q^{57} +1.02295 q^{58} -10.5283 q^{59} -4.56579 q^{61} +1.48104 q^{62} +2.97400 q^{63} -5.45701 q^{64} +0.117613 q^{66} +8.55226 q^{67} +3.97986 q^{68} +0.161242 q^{69} +8.44306 q^{71} -3.85400 q^{72} -3.73397 q^{73} +2.52568 q^{74} +5.84623 q^{76} +2.18897 q^{77} +0.308466 q^{78} -15.2435 q^{79} +8.76668 q^{81} -3.08631 q^{82} +2.53961 q^{83} +0.304580 q^{84} +0.941924 q^{86} -0.494991 q^{87} -2.83668 q^{88} +7.33480 q^{89} +5.74105 q^{91} -1.88896 q^{92} -0.716652 q^{93} -2.14937 q^{94} -0.597692 q^{96} +6.34692 q^{97} -0.333224 q^{98} +6.51001 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + 4 q^{3} + 5 q^{4} - q^{6} - 8 q^{7}+O(q^{10}) $ 8 * q + q^2 + 4 * q^3 + 5 * q^4 - q^6 - 8 * q^7	$ 8 q + q^{2} + 4 q^{3} + 5 q^{4} - q^{6} - 8 q^{7} + 3 q^{11} + 9 q^{12} + 5 q^{13} - q^{14} - q^{16} + 5 q^{17} + 2 q^{18} - 2 q^{19} - 4 q^{21} + 21 q^{22} + 8 q^{23} - 6 q^{24} + 18 q^{26} + 7 q^{27} - 5 q^{28} - 9 q^{29} - 3 q^{31} + 6 q^{32} + 4 q^{33} - 10 q^{34} + 16 q^{36} + 6 q^{37} + 4 q^{38} - 2 q^{39} - 7 q^{41} + q^{42} + 8 q^{43} + 4 q^{44} + q^{46} + 22 q^{47} + 9 q^{48} + 8 q^{49} - 12 q^{51} + 11 q^{52} + 21 q^{53} - 15 q^{54} + 8 q^{57} + 16 q^{58} + 14 q^{59} + 8 q^{61} + 12 q^{62} - 40 q^{64} + 55 q^{66} + 21 q^{67} + 3 q^{68} + 4 q^{69} + 11 q^{71} - q^{72} + 26 q^{73} - 41 q^{74} + 21 q^{76} - 3 q^{77} + 17 q^{78} - 16 q^{79} - 20 q^{81} - q^{82} + 20 q^{83} - 9 q^{84} + 14 q^{86} - 29 q^{87} + 32 q^{88} + 15 q^{89} - 5 q^{91} + 5 q^{92} + 19 q^{93} + 21 q^{94} + 52 q^{96} + q^{97} + q^{98} + 15 q^{99}+O(q^{100}) $ 8 * q + q^2 + 4 * q^3 + 5 * q^4 - q^6 - 8 * q^7 + 3 * q^11 + 9 * q^12 + 5 * q^13 - q^14 - q^16 + 5 * q^17 + 2 * q^18 - 2 * q^19 - 4 * q^21 + 21 * q^22 + 8 * q^23 - 6 * q^24 + 18 * q^26 + 7 * q^27 - 5 * q^28 - 9 * q^29 - 3 * q^31 + 6 * q^32 + 4 * q^33 - 10 * q^34 + 16 * q^36 + 6 * q^37 + 4 * q^38 - 2 * q^39 - 7 * q^41 + q^42 + 8 * q^43 + 4 * q^44 + q^46 + 22 * q^47 + 9 * q^48 + 8 * q^49 - 12 * q^51 + 11 * q^52 + 21 * q^53 - 15 * q^54 + 8 * q^57 + 16 * q^58 + 14 * q^59 + 8 * q^61 + 12 * q^62 - 40 * q^64 + 55 * q^66 + 21 * q^67 + 3 * q^68 + 4 * q^69 + 11 * q^71 - q^72 + 26 * q^73 - 41 * q^74 + 21 * q^76 - 3 * q^77 + 17 * q^78 - 16 * q^79 - 20 * q^81 - q^82 + 20 * q^83 - 9 * q^84 + 14 * q^86 - 29 * q^87 + 32 * q^88 + 15 * q^89 - 5 * q^91 + 5 * q^92 + 19 * q^93 + 21 * q^94 + 52 * q^96 + q^97 + q^98 + 15 * 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 $

$2$	−0.333224	−0.235625	−0.117813	−	0.993036i	$-0.537588\pi$
$2$	−0.333224	−0.235625	−0.117813	+	0.993036i	$0.537588\pi$
$3$	0.161242	0.0930933	0.0465466	−	0.998916i	$-0.485178\pi$
$3$	0.161242	0.0930933	0.0465466	+	0.998916i	$0.485178\pi$
$4$	−1.88896	−0.944481
$5$	0	0
$5$	0	0
$6$	−0.0537298	−0.0219351
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.29590	0.458168
$9$	−2.97400	−0.991334
$10$	0	0
$11$	−2.18897	−0.660000	−0.330000	−	0.943981i	$-0.607049\pi$
$11$	−2.18897	−0.660000	−0.330000	+	0.943981i	$0.607049\pi$
$12$	−0.304580	−0.0879248
$13$	−5.74105	−1.59228	−0.796141	−	0.605111i	$-0.793129\pi$
$13$	−5.74105	−1.59228	−0.796141	+	0.605111i	$0.793129\pi$
$14$	0.333224	0.0890579
$15$	0	0
$16$	3.34610	0.836525
$17$	−2.10691	−0.511000	−0.255500	−	0.966809i	$-0.582240\pi$
$17$	−2.10691	−0.511000	−0.255500	+	0.966809i	$0.582240\pi$
$18$	0.991009	0.233583
$19$	−3.09494	−0.710029	−0.355014	−	0.934861i	$-0.615524\pi$
$19$	−3.09494	−0.710029	−0.355014	+	0.934861i	$0.615524\pi$
$20$	0	0
$21$	−0.161242	−0.0351859
$22$	0.729419	0.155513
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	0.208953	0.0426524
$25$	0	0
$26$	1.91306	0.375181
$27$	−0.963261	−0.185380
$28$	1.88896	0.356980
$29$	−3.06986	−0.570058	−0.285029	−	0.958519i	$-0.592003\pi$
$29$	−3.06986	−0.570058	−0.285029	+	0.958519i	$0.592003\pi$
$30$	0	0
$31$	−4.44457	−0.798268	−0.399134	−	0.916893i	$-0.630689\pi$
$31$	−4.44457	−0.798268	−0.399134	+	0.916893i	$0.630689\pi$
$32$	−3.70679	−0.655275
$33$	−0.352955	−0.0614416
$34$	0.702072	0.120404
$35$	0	0
$36$	5.61777	0.936296
$37$	−7.57953	−1.24607	−0.623034	−	0.782195i	$-0.714100\pi$
$37$	−7.57953	−1.24607	−0.623034	+	0.782195i	$0.714100\pi$
$38$	1.03131	0.167300
$39$	−0.925700	−0.148231
$40$	0	0
$41$	9.26196	1.44647	0.723237	−	0.690600i	$-0.242653\pi$
$41$	9.26196	1.44647	0.723237	+	0.690600i	$0.242653\pi$
$42$	0.0537298	0.00829069
$43$	−2.82670	−0.431068	−0.215534	−	0.976496i	$-0.569149\pi$
$43$	−2.82670	−0.431068	−0.215534	+	0.976496i	$0.569149\pi$
$44$	4.13489	0.623358
$45$	0	0
$46$	−0.333224	−0.0491312
$47$	6.45023	0.940863	0.470431	−	0.882437i	$-0.344098\pi$
$47$	6.45023	0.940863	0.470431	+	0.882437i	$0.344098\pi$
$48$	0.539533	0.0778748
$49$	1.00000	0.142857
$50$	0	0
$51$	−0.339722	−0.0475706
$52$	10.8446	1.50388
$53$	1.24851	0.171496	0.0857482	−	0.996317i	$-0.472672\pi$
$53$	1.24851	0.171496	0.0857482	+	0.996317i	$0.472672\pi$
$54$	0.320982	0.0436801
$55$	0	0
$56$	−1.29590	−0.173171
$57$	−0.499035	−0.0660989
$58$	1.02295	0.134320
$59$	−10.5283	−1.37066	−0.685331	−	0.728232i	$-0.740342\pi$
$59$	−10.5283	−1.37066	−0.685331	+	0.728232i	$0.740342\pi$
$60$	0	0
$61$	−4.56579	−0.584590	−0.292295	−	0.956328i	$-0.594419\pi$
$61$	−4.56579	−0.584590	−0.292295	+	0.956328i	$0.594419\pi$
$62$	1.48104	0.188092
$63$	2.97400	0.374689
$64$	−5.45701	−0.682126
$65$	0	0
$66$	0.117613	0.0144772
$67$	8.55226	1.04482	0.522412	−	0.852693i	$-0.325032\pi$
$67$	8.55226	1.04482	0.522412	+	0.852693i	$0.325032\pi$
$68$	3.97986	0.482630
$69$	0.161242	0.0194113
$70$	0	0
$71$	8.44306	1.00201	0.501003	−	0.865445i	$-0.332964\pi$
$71$	8.44306	1.00201	0.501003	+	0.865445i	$0.332964\pi$
$72$	−3.85400	−0.454198
$73$	−3.73397	−0.437028	−0.218514	−	0.975834i	$-0.570121\pi$
$73$	−3.73397	−0.437028	−0.218514	+	0.975834i	$0.570121\pi$
$74$	2.52568	0.293605
$75$	0	0
$76$	5.84623	0.670608
$77$	2.18897	0.249457
$78$	0.308466	0.0349269
$79$	−15.2435	−1.71503	−0.857516	−	0.514457i	$-0.827994\pi$
$79$	−15.2435	−1.71503	−0.857516	+	0.514457i	$0.827994\pi$
$80$	0	0
$81$	8.76668	0.974076
$82$	−3.08631	−0.340826
$83$	2.53961	0.278759	0.139379	−	0.990239i	$-0.455489\pi$
$83$	2.53961	0.278759	0.139379	+	0.990239i	$0.455489\pi$
$84$	0.304580	0.0332324
$85$	0	0
$86$	0.941924	0.101570
$87$	−0.494991	−0.0530686
$88$	−2.83668	−0.302391
$89$	7.33480	0.777487	0.388743	−	0.921346i	$-0.372909\pi$
$89$	7.33480	0.777487	0.388743	+	0.921346i	$0.372909\pi$
$90$	0	0
$91$	5.74105	0.601826
$92$	−1.88896	−0.196938
$93$	−0.716652	−0.0743134
$94$	−2.14937	−0.221691
$95$	0	0
$96$	−0.597692	−0.0610016
$97$	6.34692	0.644432	0.322216	−	0.946666i	$-0.395572\pi$
$97$	6.34692	0.644432	0.322216	+	0.946666i	$0.395572\pi$
$98$	−0.333224	−0.0336607
$99$	6.51001	0.654280
$100$	0	0
$101$	−5.89204	−0.586280	−0.293140	−	0.956070i	$-0.594700\pi$
$101$	−5.89204	−0.586280	−0.293140	+	0.956070i	$0.594700\pi$
$102$	0.113204	0.0112088
$103$	13.9097	1.37056	0.685282	−	0.728278i	$-0.259679\pi$
$103$	13.9097	1.37056	0.685282	+	0.728278i	$0.259679\pi$
$104$	−7.43981	−0.729533
$105$	0	0
$106$	−0.416034	−0.0404088
$107$	−11.4433	−1.10627	−0.553133	−	0.833093i	$-0.686568\pi$
$107$	−11.4433	−1.10627	−0.553133	+	0.833093i	$0.686568\pi$
$108$	1.81956	0.175088
$109$	11.0765	1.06093	0.530467	−	0.847706i	$-0.322017\pi$
$109$	11.0765	1.06093	0.530467	+	0.847706i	$0.322017\pi$
$110$	0	0
$111$	−1.22214	−0.116000
$112$	−3.34610	−0.316177
$113$	8.65304	0.814010	0.407005	−	0.913426i	$-0.366573\pi$
$113$	8.65304	0.814010	0.407005	+	0.913426i	$0.366573\pi$
$114$	0.166291	0.0155745
$115$	0	0
$116$	5.79884	0.538409
$117$	17.0739	1.57848
$118$	3.50827	0.322962
$119$	2.10691	0.193140
$120$	0	0
$121$	−6.20840	−0.564400
$122$	1.52143	0.137744
$123$	1.49342	0.134657
$124$	8.39562	0.753949
$125$	0	0
$126$	−0.991009	−0.0882861
$127$	7.41735	0.658183	0.329092	−	0.944298i	$-0.393258\pi$
$127$	7.41735	0.658183	0.329092	+	0.944298i	$0.393258\pi$
$128$	9.23199	0.816000
$129$	−0.455783	−0.0401295
$130$	0	0
$131$	4.00302	0.349746	0.174873	−	0.984591i	$-0.444049\pi$
$131$	4.00302	0.349746	0.174873	+	0.984591i	$0.444049\pi$
$132$	0.666718	0.0580304
$133$	3.09494	0.268366
$134$	−2.84982	−0.246187
$135$	0	0
$136$	−2.73033	−0.234124
$137$	−3.64882	−0.311739	−0.155870	−	0.987778i	$-0.549818\pi$
$137$	−3.64882	−0.311739	−0.155870	+	0.987778i	$0.549818\pi$
$138$	−0.0537298	−0.00457378
$139$	−23.4946	−1.99278	−0.996391	−	0.0848807i	$-0.972949\pi$
$139$	−23.4946	−1.99278	−0.996391	+	0.0848807i	$0.972949\pi$
$140$	0	0
$141$	1.04005	0.0875880
$142$	−2.81343	−0.236098
$143$	12.5670	1.05091
$144$	−9.95130	−0.829275
$145$	0	0
$146$	1.24425	0.102975
$147$	0.161242	0.0132990
$148$	14.3174	1.17689
$149$	−9.06658	−0.742763	−0.371382	−	0.928480i	$-0.621116\pi$
$149$	−9.06658	−0.742763	−0.371382	+	0.928480i	$0.621116\pi$
$150$	0	0
$151$	−19.7667	−1.60859	−0.804297	−	0.594227i	$-0.797458\pi$
$151$	−19.7667	−1.60859	−0.804297	+	0.594227i	$0.797458\pi$
$152$	−4.01072	−0.325313
$153$	6.26594	0.506571
$154$	−0.729419	−0.0587782
$155$	0	0
$156$	1.74861	0.140001
$157$	21.2569	1.69649	0.848244	−	0.529606i	$-0.177660\pi$
$157$	21.2569	1.69649	0.848244	+	0.529606i	$0.177660\pi$
$158$	5.07952	0.404105
$159$	0.201313	0.0159652
$160$	0	0
$161$	−1.00000	−0.0788110
$162$	−2.92127	−0.229517
$163$	5.64045	0.441794	0.220897	−	0.975297i	$-0.429102\pi$
$163$	5.64045	0.441794	0.220897	+	0.975297i	$0.429102\pi$
$164$	−17.4955	−1.36617
$165$	0	0
$166$	−0.846260	−0.0656825
$167$	7.24196	0.560400	0.280200	−	0.959942i	$-0.409599\pi$
$167$	7.24196	0.560400	0.280200	+	0.959942i	$0.409599\pi$
$168$	−0.208953	−0.0161211
$169$	19.9597	1.53536
$170$	0	0
$171$	9.20436	0.703875
$172$	5.33953	0.407135
$173$	4.61440	0.350826	0.175413	−	0.984495i	$-0.443874\pi$
$173$	4.61440	0.350826	0.175413	+	0.984495i	$0.443874\pi$
$174$	0.164943	0.0125043
$175$	0	0
$176$	−7.32452	−0.552107
$177$	−1.69760	−0.127599
$178$	−2.44413	−0.183195
$179$	−6.75800	−0.505116	−0.252558	−	0.967582i	$-0.581272\pi$
$179$	−6.75800	−0.505116	−0.252558	+	0.967582i	$0.581272\pi$
$180$	0	0
$181$	−5.71982	−0.425151	−0.212575	−	0.977145i	$-0.568185\pi$
$181$	−5.71982	−0.425151	−0.212575	+	0.977145i	$0.568185\pi$
$182$	−1.91306	−0.141805
$183$	−0.736199	−0.0544214
$184$	1.29590	0.0955347
$185$	0	0
$186$	0.238806	0.0175101
$187$	4.61196	0.337260
$188$	−12.1842	−0.888627
$189$	0.963261	0.0700670
$190$	0	0
$191$	8.38714	0.606872	0.303436	−	0.952852i	$-0.401866\pi$
$191$	8.38714	0.606872	0.303436	+	0.952852i	$0.401866\pi$
$192$	−0.879900	−0.0635013
$193$	−13.3919	−0.963969	−0.481985	−	0.876180i	$-0.660084\pi$
$193$	−13.3919	−0.963969	−0.481985	+	0.876180i	$0.660084\pi$
$194$	−2.11495	−0.151844
$195$	0	0
$196$	−1.88896	−0.134926
$197$	−12.5678	−0.895419	−0.447709	−	0.894179i	$-0.647760\pi$
$197$	−12.5678	−0.895419	−0.447709	+	0.894179i	$0.647760\pi$
$198$	−2.16929	−0.154165
$199$	−1.01087	−0.0716587	−0.0358294	−	0.999358i	$-0.511407\pi$
$199$	−1.01087	−0.0716587	−0.0358294	+	0.999358i	$0.511407\pi$
$200$	0	0
$201$	1.37899	0.0972661
$202$	1.96337	0.138142
$203$	3.06986	0.215462
$204$	0.641722	0.0449296
$205$	0	0
$206$	−4.63505	−0.322939
$207$	−2.97400	−0.206707
$208$	−19.2101	−1.33198
$209$	6.77475	0.468619
$210$	0	0
$211$	−4.71229	−0.324407	−0.162204	−	0.986757i	$-0.551860\pi$
$211$	−4.71229	−0.324407	−0.162204	+	0.986757i	$0.551860\pi$
$212$	−2.35839	−0.161975
$213$	1.36138	0.0932801
$214$	3.81319	0.260664
$215$	0	0
$216$	−1.24829	−0.0849351
$217$	4.44457	0.301717
$218$	−3.69095	−0.249983
$219$	−0.602073	−0.0406843
$220$	0	0
$221$	12.0959	0.813656
$222$	0.407247	0.0273326
$223$	13.5367	0.906483	0.453242	−	0.891388i	$-0.350267\pi$
$223$	13.5367	0.906483	0.453242	+	0.891388i	$0.350267\pi$
$224$	3.70679	0.247670
$225$	0	0
$226$	−2.88340	−0.191801
$227$	−12.5383	−0.832197	−0.416099	−	0.909320i	$-0.636603\pi$
$227$	−12.5383	−0.832197	−0.416099	+	0.909320i	$0.636603\pi$
$228$	0.942659	0.0624291
$229$	1.46874	0.0970569	0.0485285	−	0.998822i	$-0.484547\pi$
$229$	1.46874	0.0970569	0.0485285	+	0.998822i	$0.484547\pi$
$230$	0	0
$231$	0.352955	0.0232227
$232$	−3.97821	−0.261183
$233$	23.8444	1.56210	0.781049	−	0.624470i	$-0.214685\pi$
$233$	23.8444	1.56210	0.781049	+	0.624470i	$0.214685\pi$
$234$	−5.68943	−0.371930
$235$	0	0
$236$	19.8875	1.29456
$237$	−2.45790	−0.159658
$238$	−0.702072	−0.0455086
$239$	20.1489	1.30332	0.651662	−	0.758509i	$-0.274072\pi$
$239$	20.1489	1.30332	0.651662	+	0.758509i	$0.274072\pi$
$240$	0	0
$241$	−21.0524	−1.35610	−0.678052	−	0.735014i	$-0.737175\pi$
$241$	−21.0524	−1.35610	−0.678052	+	0.735014i	$0.737175\pi$
$242$	2.06879	0.132987
$243$	4.30334	0.276060
$244$	8.62461	0.552134
$245$	0	0
$246$	−0.497643	−0.0317286
$247$	17.7682	1.13057
$248$	−5.75970	−0.365741
$249$	0.409493	0.0259505
$250$	0	0
$251$	11.9137	0.751986	0.375993	−	0.926622i	$-0.377302\pi$
$251$	11.9137	0.751986	0.375993	+	0.926622i	$0.377302\pi$
$252$	−5.61777	−0.353886
$253$	−2.18897	−0.137620
$254$	−2.47164	−0.155084
$255$	0	0
$256$	7.83769	0.489856
$257$	29.6832	1.85159	0.925793	−	0.378030i	$-0.123398\pi$
$257$	29.6832	1.85159	0.925793	+	0.378030i	$0.123398\pi$
$258$	0.151878	0.00945551
$259$	7.57953	0.470969
$260$	0	0
$261$	9.12976	0.565118
$262$	−1.33390	−0.0824088
$263$	28.2320	1.74086	0.870430	−	0.492292i	$-0.163841\pi$
$263$	28.2320	1.74086	0.870430	+	0.492292i	$0.163841\pi$
$264$	−0.457393	−0.0281506
$265$	0	0
$266$	−1.03131	−0.0632336
$267$	1.18268	0.0723788
$268$	−16.1549	−0.986817
$269$	−11.7617	−0.717122	−0.358561	−	0.933506i	$-0.616733\pi$
$269$	−11.7617	−0.717122	−0.358561	+	0.933506i	$0.616733\pi$
$270$	0	0
$271$	13.6610	0.829849	0.414924	−	0.909856i	$-0.363808\pi$
$271$	13.6610	0.829849	0.414924	+	0.909856i	$0.363808\pi$
$272$	−7.04992	−0.427464
$273$	0.925700	0.0560259
$274$	1.21587	0.0734536
$275$	0	0
$276$	−0.304580	−0.0183336
$277$	11.5075	0.691419	0.345709	−	0.938342i	$-0.387638\pi$
$277$	11.5075	0.691419	0.345709	+	0.938342i	$0.387638\pi$
$278$	7.82895	0.469549
$279$	13.2181	0.791350
$280$	0	0
$281$	23.1677	1.38207	0.691034	−	0.722823i	$-0.257156\pi$
$281$	23.1677	1.38207	0.691034	+	0.722823i	$0.257156\pi$
$282$	−0.346570	−0.0206379
$283$	11.0849	0.658928	0.329464	−	0.944168i	$-0.393132\pi$
$283$	11.0849	0.658928	0.329464	+	0.944168i	$0.393132\pi$
$284$	−15.9486	−0.946376
$285$	0	0
$286$	−4.18763	−0.247620
$287$	−9.26196	−0.546716
$288$	11.0240	0.649596
$289$	−12.5609	−0.738879
$290$	0	0
$291$	1.02339	0.0599923
$292$	7.05332	0.412764
$293$	−28.6938	−1.67631	−0.838156	−	0.545430i	$-0.816366\pi$
$293$	−28.6938	−1.67631	−0.838156	+	0.545430i	$0.816366\pi$
$294$	−0.0537298	−0.00313359
$295$	0	0
$296$	−9.82228	−0.570909
$297$	2.10855	0.122351
$298$	3.02120	0.175014
$299$	−5.74105	−0.332014
$300$	0	0
$301$	2.82670	0.162928
$302$	6.58676	0.379025
$303$	−0.950046	−0.0545787
$304$	−10.3560	−0.593957
$305$	0	0
$306$	−2.08796	−0.119361
$307$	−3.08371	−0.175997	−0.0879984	−	0.996121i	$-0.528047\pi$
$307$	−3.08371	−0.175997	−0.0879984	+	0.996121i	$0.528047\pi$
$308$	−4.13489	−0.235607
$309$	2.24283	0.127590
$310$	0	0
$311$	1.72641	0.0978958	0.0489479	−	0.998801i	$-0.484413\pi$
$311$	1.72641	0.0978958	0.0489479	+	0.998801i	$0.484413\pi$
$312$	−1.19961	−0.0679146
$313$	−15.0076	−0.848278	−0.424139	−	0.905597i	$-0.639423\pi$
$313$	−15.0076	−0.848278	−0.424139	+	0.905597i	$0.639423\pi$
$314$	−7.08332	−0.399735
$315$	0	0
$316$	28.7945	1.61982
$317$	29.3777	1.65002	0.825008	−	0.565121i	$-0.191171\pi$
$317$	29.3777	1.65002	0.825008	+	0.565121i	$0.191171\pi$
$318$	−0.0670823	−0.00376179
$319$	6.71983	0.376238
$320$	0	0
$321$	−1.84515	−0.102986
$322$	0.333224	0.0185699
$323$	6.52075	0.362824
$324$	−16.5599	−0.919996
$325$	0	0
$326$	−1.87953	−0.104098
$327$	1.78600	0.0987658
$328$	12.0025	0.662729
$329$	−6.45023	−0.355613
$330$	0	0
$331$	−6.04710	−0.332379	−0.166189	−	0.986094i	$-0.553146\pi$
$331$	−6.04710	−0.332379	−0.166189	+	0.986094i	$0.553146\pi$
$332$	−4.79723	−0.263282
$333$	22.5415	1.23527
$334$	−2.41320	−0.132044
$335$	0	0
$336$	−0.539533	−0.0294339
$337$	17.8996	0.975052	0.487526	−	0.873108i	$-0.337899\pi$
$337$	17.8996	0.975052	0.487526	+	0.873108i	$0.337899\pi$
$338$	−6.65105	−0.361770
$339$	1.39524	0.0757788
$340$	0	0
$341$	9.72904	0.526857
$342$	−3.06712	−0.165851
$343$	−1.00000	−0.0539949
$344$	−3.66311	−0.197502
$345$	0	0
$346$	−1.53763	−0.0826634
$347$	−36.5879	−1.96414	−0.982070	−	0.188517i	$-0.939632\pi$
$347$	−36.5879	−1.96414	−0.982070	+	0.188517i	$0.939632\pi$
$348$	0.935018	0.0501222
$349$	25.7509	1.37841	0.689206	−	0.724566i	$-0.257960\pi$
$349$	25.7509	1.37841	0.689206	+	0.724566i	$0.257960\pi$
$350$	0	0
$351$	5.53013	0.295177
$352$	8.11407	0.432481
$353$	−9.70263	−0.516419	−0.258210	−	0.966089i	$-0.583132\pi$
$353$	−9.70263	−0.516419	−0.258210	+	0.966089i	$0.583132\pi$
$354$	0.565681	0.0300656
$355$	0	0
$356$	−13.8551	−0.734321
$357$	0.339722	0.0179800
$358$	2.25193	0.119018
$359$	18.0326	0.951723	0.475862	−	0.879520i	$-0.342136\pi$
$359$	18.0326	0.951723	0.475862	+	0.879520i	$0.342136\pi$
$360$	0	0
$361$	−9.42133	−0.495860
$362$	1.90598	0.100176
$363$	−1.00106	−0.0525418
$364$	−10.8446	−0.568413
$365$	0	0
$366$	0.245319	0.0128230
$367$	−11.5865	−0.604809	−0.302405	−	0.953180i	$-0.597789\pi$
$367$	−11.5865	−0.604809	−0.302405	+	0.953180i	$0.597789\pi$
$368$	3.34610	0.174428
$369$	−27.5451	−1.43394
$370$	0	0
$371$	−1.24851	−0.0648195
$372$	1.35373	0.0701876
$373$	3.82651	0.198129	0.0990645	−	0.995081i	$-0.468415\pi$
$373$	3.82651	0.198129	0.0990645	+	0.995081i	$0.468415\pi$
$374$	−1.53682	−0.0794669
$375$	0	0
$376$	8.35883	0.431074
$377$	17.6242	0.907693
$378$	−0.320982	−0.0165095
$379$	−27.1851	−1.39640	−0.698201	−	0.715901i	$-0.746016\pi$
$379$	−27.1851	−1.39640	−0.698201	+	0.715901i	$0.746016\pi$
$380$	0	0
$381$	1.19599	0.0612724
$382$	−2.79480	−0.142994
$383$	−17.2252	−0.880168	−0.440084	−	0.897957i	$-0.645051\pi$
$383$	−17.2252	−0.880168	−0.440084	+	0.897957i	$0.645051\pi$
$384$	1.48859	0.0759641
$385$	0	0
$386$	4.46250	0.227135
$387$	8.40661	0.427332
$388$	−11.9891	−0.608654
$389$	12.0516	0.611041	0.305520	−	0.952186i	$-0.401170\pi$
$389$	12.0516	0.611041	0.305520	+	0.952186i	$0.401170\pi$
$390$	0	0
$391$	−2.10691	−0.106551
$392$	1.29590	0.0654526
$393$	0.645456	0.0325590
$394$	4.18789	0.210983
$395$	0	0
$396$	−12.2972	−0.617955
$397$	−20.1013	−1.00885	−0.504427	−	0.863454i	$-0.668296\pi$
$397$	−20.1013	−1.00885	−0.504427	+	0.863454i	$0.668296\pi$
$398$	0.336847	0.0168846
$399$	0.499035	0.0249830
$400$	0	0
$401$	−5.24998	−0.262171	−0.131086	−	0.991371i	$-0.541846\pi$
$401$	−5.24998	−0.262171	−0.131086	+	0.991371i	$0.541846\pi$
$402$	−0.459511	−0.0229183
$403$	25.5165	1.27107
$404$	11.1298	0.553730
$405$	0	0
$406$	−1.02295	−0.0507682
$407$	16.5914	0.822405
$408$	−0.440245	−0.0217954
$409$	−0.124465	−0.00615441	−0.00307721	−	0.999995i	$-0.500980\pi$
$409$	−0.124465	−0.00615441	−0.00307721	+	0.999995i	$0.500980\pi$
$410$	0	0
$411$	−0.588343	−0.0290208
$412$	−26.2749	−1.29447
$413$	10.5283	0.518061
$414$	0.991009	0.0487054
$415$	0	0
$416$	21.2809	1.04338
$417$	−3.78832	−0.185515
$418$	−2.25751	−0.110418
$419$	3.40812	0.166497	0.0832487	−	0.996529i	$-0.473470\pi$
$419$	3.40812	0.166497	0.0832487	+	0.996529i	$0.473470\pi$
$420$	0	0
$421$	−0.589915	−0.0287507	−0.0143753	−	0.999897i	$-0.504576\pi$
$421$	−0.589915	−0.0287507	−0.0143753	+	0.999897i	$0.504576\pi$
$422$	1.57025	0.0764385
$423$	−19.1830	−0.932709
$424$	1.61794	0.0785742
$425$	0	0
$426$	−0.453644	−0.0219791
$427$	4.56579	0.220954
$428$	21.6160	1.04485
$429$	2.02633	0.0978323
$430$	0	0
$431$	−30.4802	−1.46818	−0.734090	−	0.679052i	$-0.762391\pi$
$431$	−30.4802	−1.46818	−0.734090	+	0.679052i	$0.762391\pi$
$432$	−3.22317	−0.155075
$433$	25.9106	1.24519	0.622593	−	0.782546i	$-0.286079\pi$
$433$	25.9106	1.24519	0.622593	+	0.782546i	$0.286079\pi$
$434$	−1.48104	−0.0710921
$435$	0	0
$436$	−20.9230	−1.00203
$437$	−3.09494	−0.148051
$438$	0.200625	0.00958624
$439$	25.2408	1.20468	0.602339	−	0.798240i	$-0.294236\pi$
$439$	25.2408	1.20468	0.602339	+	0.798240i	$0.294236\pi$
$440$	0	0
$441$	−2.97400	−0.141619
$442$	−4.03063	−0.191718
$443$	32.1455	1.52728	0.763640	−	0.645642i	$-0.223410\pi$
$443$	32.1455	1.52728	0.763640	+	0.645642i	$0.223410\pi$
$444$	2.30858	0.109560
$445$	0	0
$446$	−4.51075	−0.213590
$447$	−1.46192	−0.0691463
$448$	5.45701	0.257819
$449$	36.1660	1.70678	0.853390	−	0.521273i	$-0.174543\pi$
$449$	36.1660	1.70678	0.853390	+	0.521273i	$0.174543\pi$
$450$	0	0
$451$	−20.2742	−0.954673
$452$	−16.3453	−0.768817
$453$	−3.18723	−0.149749
$454$	4.17807	0.196086
$455$	0	0
$456$	−0.646698	−0.0302844
$457$	−4.09273	−0.191450	−0.0957250	−	0.995408i	$-0.530517\pi$
$457$	−4.09273	−0.191450	−0.0957250	+	0.995408i	$0.530517\pi$
$458$	−0.489419	−0.0228690
$459$	2.02950	0.0947290
$460$	0	0
$461$	−4.39372	−0.204636	−0.102318	−	0.994752i	$-0.532626\pi$
$461$	−4.39372	−0.204636	−0.102318	+	0.994752i	$0.532626\pi$
$462$	−0.117613	−0.00547186
$463$	4.52158	0.210136	0.105068	−	0.994465i	$-0.466494\pi$
$463$	4.52158	0.210136	0.105068	+	0.994465i	$0.466494\pi$
$464$	−10.2720	−0.476868
$465$	0	0
$466$	−7.94553	−0.368069
$467$	20.9134	0.967758	0.483879	−	0.875135i	$-0.339228\pi$
$467$	20.9134	0.967758	0.483879	+	0.875135i	$0.339228\pi$
$468$	−32.2519	−1.49085
$469$	−8.55226	−0.394907
$470$	0	0
$471$	3.42751	0.157932
$472$	−13.6435	−0.627994
$473$	6.18757	0.284505
$474$	0.819033	0.0376194
$475$	0	0
$476$	−3.97986	−0.182417
$477$	−3.71308	−0.170010
$478$	−6.71410	−0.307096
$479$	−22.4902	−1.02761	−0.513803	−	0.857908i	$-0.671764\pi$
$479$	−22.4902	−1.02761	−0.513803	+	0.857908i	$0.671764\pi$
$480$	0	0
$481$	43.5145	1.98409
$482$	7.01516	0.319532
$483$	−0.161242	−0.00733678
$484$	11.7274	0.533065
$485$	0	0
$486$	−1.43398	−0.0650466
$487$	−19.2579	−0.872660	−0.436330	−	0.899787i	$-0.643722\pi$
$487$	−19.2579	−0.872660	−0.436330	+	0.899787i	$0.643722\pi$
$488$	−5.91679	−0.267841
$489$	0.909479	0.0411281
$490$	0	0
$491$	1.74890	0.0789269	0.0394634	−	0.999221i	$-0.487435\pi$
$491$	1.74890	0.0789269	0.0394634	+	0.999221i	$0.487435\pi$
$492$	−2.82101	−0.127181
$493$	6.46790	0.291300
$494$	−5.92080	−0.266390
$495$	0	0
$496$	−14.8720	−0.667771
$497$	−8.44306	−0.378723
$498$	−0.136453	−0.00611460
$499$	−1.01500	−0.0454376	−0.0227188	−	0.999742i	$-0.507232\pi$
$499$	−1.01500	−0.0454376	−0.0227188	+	0.999742i	$0.507232\pi$
$500$	0	0
$501$	1.16771	0.0521695
$502$	−3.96993	−0.177187
$503$	7.03616	0.313727	0.156863	−	0.987620i	$-0.449862\pi$
$503$	7.03616	0.313727	0.156863	+	0.987620i	$0.449862\pi$
$504$	3.85400	0.171671
$505$	0	0
$506$	0.729419	0.0324266
$507$	3.21835	0.142932
$508$	−14.0111	−0.621641
$509$	−31.1088	−1.37887	−0.689437	−	0.724346i	$-0.742142\pi$
$509$	−31.1088	−1.37887	−0.689437	+	0.724346i	$0.742142\pi$
$510$	0	0
$511$	3.73397	0.165181
$512$	−21.0757	−0.931423
$513$	2.98124	0.131625
$514$	−9.89115	−0.436280
$515$	0	0
$516$	0.860957	0.0379015
$517$	−14.1194	−0.620970
$518$	−2.52568	−0.110972
$519$	0.744036	0.0326595
$520$	0	0
$521$	−37.3301	−1.63546	−0.817731	−	0.575601i	$-0.804768\pi$
$521$	−37.3301	−1.63546	−0.817731	+	0.575601i	$0.804768\pi$
$522$	−3.04225	−0.133156
$523$	−5.31573	−0.232441	−0.116220	−	0.993223i	$-0.537078\pi$
$523$	−5.31573	−0.232441	−0.116220	+	0.993223i	$0.537078\pi$
$524$	−7.56156	−0.330328
$525$	0	0
$526$	−9.40758	−0.410190
$527$	9.36429	0.407915
$528$	−1.18102	−0.0513974
$529$	1.00000	0.0434783
$530$	0	0
$531$	31.3110	1.35878
$532$	−5.84623	−0.253466
$533$	−53.1734	−2.30319
$534$	−0.394097	−0.0170542
$535$	0	0
$536$	11.0828	0.478706
$537$	−1.08967	−0.0470229
$538$	3.91927	0.168972
$539$	−2.18897	−0.0942857
$540$	0	0
$541$	−37.4481	−1.61002	−0.805009	−	0.593262i	$-0.797840\pi$
$541$	−37.4481	−1.61002	−0.805009	+	0.593262i	$0.797840\pi$
$542$	−4.55219	−0.195533
$543$	−0.922276	−0.0395787
$544$	7.80986	0.334845
$545$	0	0
$546$	−0.308466	−0.0132011
$547$	12.8705	0.550305	0.275152	−	0.961401i	$-0.411272\pi$
$547$	12.8705	0.550305	0.275152	+	0.961401i	$0.411272\pi$
$548$	6.89247	0.294432
$549$	13.5787	0.579524
$550$	0	0
$551$	9.50103	0.404757
$552$	0.208953	0.00889364
$553$	15.2435	0.648221
$554$	−3.83458	−0.162916
$555$	0	0
$556$	44.3803	1.88214
$557$	−19.0160	−0.805733	−0.402867	−	0.915259i	$-0.631986\pi$
$557$	−19.0160	−0.805733	−0.402867	+	0.915259i	$0.631986\pi$
$558$	−4.40461	−0.186462
$559$	16.2282	0.686381
$560$	0	0
$561$	0.743643	0.0313966
$562$	−7.72003	−0.325650
$563$	−33.1773	−1.39826	−0.699129	−	0.714996i	$-0.746429\pi$
$563$	−33.1773	−1.39826	−0.699129	+	0.714996i	$0.746429\pi$
$564$	−1.96461	−0.0827252
$565$	0	0
$566$	−3.69375	−0.155260
$567$	−8.76668	−0.368166
$568$	10.9413	0.459088
$569$	11.5203	0.482958	0.241479	−	0.970406i	$-0.422368\pi$
$569$	11.5203	0.482958	0.241479	+	0.970406i	$0.422368\pi$
$570$	0	0
$571$	−38.6494	−1.61743	−0.808713	−	0.588203i	$-0.799836\pi$
$571$	−38.6494	−1.61743	−0.808713	+	0.588203i	$0.799836\pi$
$572$	−23.7386	−0.992561
$573$	1.35236	0.0564957
$574$	3.08631	0.128820
$575$	0	0
$576$	16.2291	0.676214
$577$	6.67944	0.278069	0.139034	−	0.990288i	$-0.455600\pi$
$577$	6.67944	0.278069	0.139034	+	0.990288i	$0.455600\pi$
$578$	4.18561	0.174098
$579$	−2.15934	−0.0897390
$580$	0	0
$581$	−2.53961	−0.105361
$582$	−0.341019	−0.0141357
$583$	−2.73296	−0.113188
$584$	−4.83883	−0.200232
$585$	0	0
$586$	9.56148	0.394981
$587$	15.7340	0.649412	0.324706	−	0.945815i	$-0.394735\pi$
$587$	15.7340	0.649412	0.324706	+	0.945815i	$0.394735\pi$
$588$	−0.304580	−0.0125607
$589$	13.7557	0.566793
$590$	0	0
$591$	−2.02646	−0.0833574
$592$	−25.3619	−1.04237
$593$	−17.5142	−0.719222	−0.359611	−	0.933102i	$-0.617091\pi$
$593$	−17.5142	−0.719222	−0.359611	+	0.933102i	$0.617091\pi$
$594$	−0.702621	−0.0288289
$595$	0	0
$596$	17.1264	0.701526
$597$	−0.162995	−0.00667094
$598$	1.91306	0.0782307
$599$	28.6611	1.17106	0.585531	−	0.810650i	$-0.300886\pi$
$599$	28.6611	1.17106	0.585531	+	0.810650i	$0.300886\pi$
$600$	0	0
$601$	−12.3972	−0.505693	−0.252846	−	0.967506i	$-0.581367\pi$
$601$	−12.3972	−0.505693	−0.252846	+	0.967506i	$0.581367\pi$
$602$	−0.941924	−0.0383900
$603$	−25.4344	−1.03577
$604$	37.3386	1.51929
$605$	0	0
$606$	0.316578	0.0128601
$607$	13.6311	0.553268	0.276634	−	0.960975i	$-0.410781\pi$
$607$	13.6311	0.553268	0.276634	+	0.960975i	$0.410781\pi$
$608$	11.4723	0.465264
$609$	0.494991	0.0200580
$610$	0	0
$611$	−37.0311	−1.49812
$612$	−11.8361	−0.478447
$613$	−14.2334	−0.574882	−0.287441	−	0.957798i	$-0.592805\pi$
$613$	−14.2334	−0.574882	−0.287441	+	0.957798i	$0.592805\pi$
$614$	1.02757	0.0414693
$615$	0	0
$616$	2.83668	0.114293
$617$	−6.53605	−0.263132	−0.131566	−	0.991307i	$-0.542000\pi$
$617$	−6.53605	−0.263132	−0.131566	+	0.991307i	$0.542000\pi$
$618$	−0.747366	−0.0300635
$619$	17.1383	0.688847	0.344424	−	0.938814i	$-0.388074\pi$
$619$	17.1383	0.688847	0.344424	+	0.938814i	$0.388074\pi$
$620$	0	0
$621$	−0.963261	−0.0386543
$622$	−0.575282	−0.0230667
$623$	−7.33480	−0.293862
$624$	−3.09749	−0.123999
$625$	0	0
$626$	5.00088	0.199876
$627$	1.09238	0.0436253
$628$	−40.1535	−1.60230
$629$	15.9694	0.636740
$630$	0	0
$631$	19.3648	0.770901	0.385451	−	0.922728i	$-0.374046\pi$
$631$	19.3648	0.770901	0.385451	+	0.922728i	$0.374046\pi$
$632$	−19.7540	−0.785774
$633$	−0.759820	−0.0302001
$634$	−9.78936	−0.388785
$635$	0	0
$636$	−0.380272	−0.0150788
$637$	−5.74105	−0.227469
$638$	−2.23921	−0.0886512
$639$	−25.1097	−0.993323
$640$	0	0
$641$	17.8243	0.704016	0.352008	−	0.935997i	$-0.385499\pi$
$641$	17.8243	0.704016	0.352008	+	0.935997i	$0.385499\pi$
$642$	0.614847	0.0242661
$643$	−10.0692	−0.397091	−0.198545	−	0.980092i	$-0.563622\pi$
$643$	−10.0692	−0.397091	−0.198545	+	0.980092i	$0.563622\pi$
$644$	1.88896	0.0744355
$645$	0	0
$646$	−2.17287	−0.0854905
$647$	−12.8025	−0.503319	−0.251659	−	0.967816i	$-0.580976\pi$
$647$	−12.8025	−0.503319	−0.251659	+	0.967816i	$0.580976\pi$
$648$	11.3607	0.446291
$649$	23.0461	0.904637
$650$	0	0
$651$	0.716652	0.0280878
$652$	−10.6546	−0.417266
$653$	−23.5198	−0.920401	−0.460200	−	0.887815i	$-0.652222\pi$
$653$	−23.5198	−0.920401	−0.460200	+	0.887815i	$0.652222\pi$
$654$	−0.595137	−0.0232717
$655$	0	0
$656$	30.9914	1.21001
$657$	11.1048	0.433240
$658$	2.14937	0.0837912
$659$	−40.7749	−1.58836	−0.794182	−	0.607679i	$-0.792101\pi$
$659$	−40.7749	−1.58836	−0.794182	+	0.607679i	$0.792101\pi$
$660$	0	0
$661$	21.2541	0.826688	0.413344	−	0.910575i	$-0.364361\pi$
$661$	21.2541	0.826688	0.413344	+	0.910575i	$0.364361\pi$
$662$	2.01504	0.0783167
$663$	1.95036	0.0757459
$664$	3.29107	0.127718
$665$	0	0
$666$	−7.51138	−0.291060
$667$	−3.06986	−0.118865
$668$	−13.6798	−0.529287
$669$	2.18268	0.0843875
$670$	0	0
$671$	9.99440	0.385829
$672$	0.597692	0.0230565
$673$	−36.4783	−1.40613	−0.703067	−	0.711123i	$-0.748187\pi$
$673$	−36.4783	−1.40613	−0.703067	+	0.711123i	$0.748187\pi$
$674$	−5.96457	−0.229747
$675$	0	0
$676$	−37.7031	−1.45012
$677$	34.3285	1.31935	0.659676	−	0.751550i	$-0.270694\pi$
$677$	34.3285	1.31935	0.659676	+	0.751550i	$0.270694\pi$
$678$	−0.464926	−0.0178554
$679$	−6.34692	−0.243572
$680$	0	0
$681$	−2.02171	−0.0774719
$682$	−3.24195	−0.124141
$683$	−26.1557	−1.00082	−0.500411	−	0.865788i	$-0.666818\pi$
$683$	−26.1557	−1.00082	−0.500411	+	0.865788i	$0.666818\pi$
$684$	−17.3867	−0.664797
$685$	0	0
$686$	0.333224	0.0127226
$687$	0.236823	0.00903535
$688$	−9.45842	−0.360599
$689$	−7.16778	−0.273071
$690$	0	0
$691$	38.3265	1.45801	0.729005	−	0.684508i	$-0.239983\pi$
$691$	38.3265	1.45801	0.729005	+	0.684508i	$0.239983\pi$
$692$	−8.71642	−0.331349
$693$	−6.51001	−0.247295
$694$	12.1920	0.462800
$695$	0	0
$696$	−0.641456	−0.0243143
$697$	−19.5141	−0.739148
$698$	−8.58081	−0.324788
$699$	3.84472	0.145421
$700$	0	0
$701$	−25.7969	−0.974337	−0.487168	−	0.873308i	$-0.661970\pi$
$701$	−25.7969	−0.974337	−0.487168	+	0.873308i	$0.661970\pi$
$702$	−1.84277	−0.0695510
$703$	23.4582	0.884743
$704$	11.9452	0.450203
$705$	0	0
$706$	3.23315	0.121681
$707$	5.89204	0.221593
$708$	3.20670	0.120515
$709$	−6.32648	−0.237596	−0.118798	−	0.992918i	$-0.537904\pi$
$709$	−6.32648	−0.237596	−0.118798	+	0.992918i	$0.537904\pi$
$710$	0	0
$711$	45.3343	1.70017
$712$	9.50513	0.356220
$713$	−4.44457	−0.166450
$714$	−0.113204	−0.00423654
$715$	0	0
$716$	12.7656	0.477073
$717$	3.24885	0.121331
$718$	−6.00889	−0.224250
$719$	0.677523	0.0252673	0.0126337	−	0.999920i	$-0.495978\pi$
$719$	0.677523	0.0252673	0.0126337	+	0.999920i	$0.495978\pi$
$720$	0	0
$721$	−13.9097	−0.518025
$722$	3.13941	0.116837
$723$	−3.39453	−0.126244
$724$	10.8045	0.401547
$725$	0	0
$726$	0.333576	0.0123802
$727$	−40.3617	−1.49693	−0.748467	−	0.663172i	$-0.769210\pi$
$727$	−40.3617	−1.49693	−0.748467	+	0.663172i	$0.769210\pi$
$728$	7.43981	0.275738
$729$	−25.6062	−0.948377
$730$	0	0
$731$	5.95559	0.220275
$732$	1.39065	0.0513999
$733$	−35.0872	−1.29597	−0.647987	−	0.761651i	$-0.724389\pi$
$733$	−35.0872	−1.29597	−0.647987	+	0.761651i	$0.724389\pi$
$734$	3.86089	0.142508
$735$	0	0
$736$	−3.70679	−0.136634
$737$	−18.7207	−0.689585
$738$	9.17868	0.337872
$739$	−2.22501	−0.0818484	−0.0409242	−	0.999162i	$-0.513030\pi$
$739$	−2.22501	−0.0818484	−0.0409242	+	0.999162i	$0.513030\pi$
$740$	0	0
$741$	2.86499	0.105248
$742$	0.416034	0.0152731
$743$	17.2182	0.631673	0.315837	−	0.948814i	$-0.397715\pi$
$743$	17.2182	0.631673	0.315837	+	0.948814i	$0.397715\pi$
$744$	−0.928706	−0.0340480
$745$	0	0
$746$	−1.27508	−0.0466842
$747$	−7.55281	−0.276343
$748$	−8.71182	−0.318536
$749$	11.4433	0.418130
$750$	0	0
$751$	−5.36076	−0.195617	−0.0978084	−	0.995205i	$-0.531183\pi$
$751$	−5.36076	−0.195617	−0.0978084	+	0.995205i	$0.531183\pi$
$752$	21.5831	0.787055
$753$	1.92099	0.0700048
$754$	−5.87281	−0.213875
$755$	0	0
$756$	−1.81956	−0.0661769
$757$	31.7514	1.15403	0.577013	−	0.816735i	$-0.304218\pi$
$757$	31.7514	1.15403	0.577013	+	0.816735i	$0.304218\pi$
$758$	9.05872	0.329027
$759$	−0.352955	−0.0128115
$760$	0	0
$761$	−18.0900	−0.655761	−0.327880	−	0.944719i	$-0.606334\pi$
$761$	−18.0900	−0.655761	−0.327880	+	0.944719i	$0.606334\pi$
$762$	−0.398533	−0.0144373
$763$	−11.0765	−0.400995
$764$	−15.8430	−0.573179
$765$	0	0
$766$	5.73986	0.207390
$767$	60.4433	2.18248
$768$	1.26377	0.0456023
$769$	38.9439	1.40435	0.702176	−	0.712003i	$-0.252212\pi$
$769$	38.9439	1.40435	0.702176	+	0.712003i	$0.252212\pi$
$770$	0	0
$771$	4.78618	0.172370
$772$	25.2968	0.910450
$773$	24.5341	0.882431	0.441216	−	0.897401i	$-0.354547\pi$
$773$	24.5341	0.882431	0.441216	+	0.897401i	$0.354547\pi$
$774$	−2.80128	−0.100690
$775$	0	0
$776$	8.22495	0.295258
$777$	1.22214	0.0438441
$778$	−4.01589	−0.143977
$779$	−28.6652	−1.02704
$780$	0	0
$781$	−18.4816	−0.661325
$782$	0.702072	0.0251060
$783$	2.95707	0.105677
$784$	3.34610	0.119504
$785$	0	0
$786$	−0.215082	−0.00767171
$787$	36.1897	1.29002	0.645012	−	0.764172i	$-0.276852\pi$
$787$	36.1897	1.29002	0.645012	+	0.764172i	$0.276852\pi$
$788$	23.7401	0.845706
$789$	4.55219	0.162062
$790$	0	0
$791$	−8.65304	−0.307667
$792$	8.43629	0.299771
$793$	26.2125	0.930832
$794$	6.69823	0.237711
$795$	0	0
$796$	1.90950	0.0676803
$797$	−49.4289	−1.75086	−0.875430	−	0.483345i	$-0.839422\pi$
$797$	−49.4289	−1.75086	−0.875430	+	0.483345i	$0.839422\pi$
$798$	−0.166291	−0.00588663
$799$	−13.5900	−0.480781
$800$	0	0
$801$	−21.8137	−0.770749
$802$	1.74942	0.0617741
$803$	8.17355	0.288438
$804$	−2.60485	−0.0918660
$805$	0	0
$806$	−8.50271	−0.299495
$807$	−1.89648	−0.0667592
$808$	−7.63547	−0.268615
$809$	−26.6055	−0.935399	−0.467700	−	0.883887i	$-0.654917\pi$
$809$	−26.6055	−0.935399	−0.467700	+	0.883887i	$0.654917\pi$
$810$	0	0
$811$	42.7646	1.50167	0.750834	−	0.660490i	$-0.229652\pi$
$811$	42.7646	1.50167	0.750834	+	0.660490i	$0.229652\pi$
$812$	−5.79884	−0.203499
$813$	2.20274	0.0772533
$814$	−5.52865	−0.193779
$815$	0	0
$816$	−1.13674	−0.0397940
$817$	8.74847	0.306070
$818$	0.0414748	0.00145013
$819$	−17.0739	−0.596610
$820$	0	0
$821$	−30.9035	−1.07854	−0.539270	−	0.842133i	$-0.681300\pi$
$821$	−30.9035	−1.07854	−0.539270	+	0.842133i	$0.681300\pi$
$822$	0.196050	0.00683803
$823$	−19.8425	−0.691666	−0.345833	−	0.938296i	$-0.612404\pi$
$823$	−19.8425	−0.691666	−0.345833	+	0.938296i	$0.612404\pi$
$824$	18.0255	0.627949
$825$	0	0
$826$	−3.50827	−0.122068
$827$	3.18559	0.110774	0.0553869	−	0.998465i	$-0.482361\pi$
$827$	3.18559	0.110774	0.0553869	+	0.998465i	$0.482361\pi$
$828$	5.61777	0.195231
$829$	25.9914	0.902719	0.451359	−	0.892342i	$-0.350939\pi$
$829$	25.9914	0.902719	0.451359	+	0.892342i	$0.350939\pi$
$830$	0	0
$831$	1.85549	0.0643664
$832$	31.3290	1.08614
$833$	−2.10691	−0.0730000
$834$	1.26236	0.0437119
$835$	0	0
$836$	−12.7972	−0.442602
$837$	4.28128	0.147983
$838$	−1.13567	−0.0392309
$839$	41.2270	1.42332	0.711658	−	0.702526i	$-0.247945\pi$
$839$	41.2270	1.42332	0.711658	+	0.702526i	$0.247945\pi$
$840$	0	0
$841$	−19.5760	−0.675034
$842$	0.196574	0.00677438
$843$	3.73561	0.128661
$844$	8.90133	0.306397
$845$	0	0
$846$	6.39223	0.219770
$847$	6.20840	0.213323
$848$	4.17765	0.143461
$849$	1.78735	0.0613418
$850$	0	0
$851$	−7.57953	−0.259823
$852$	−2.57159	−0.0881012
$853$	16.6285	0.569350	0.284675	−	0.958624i	$-0.408114\pi$
$853$	16.6285	0.569350	0.284675	+	0.958624i	$0.408114\pi$
$854$	−1.52143	−0.0520623
$855$	0	0
$856$	−14.8293	−0.506856
$857$	15.8262	0.540613	0.270307	−	0.962774i	$-0.412875\pi$
$857$	15.8262	0.540613	0.270307	+	0.962774i	$0.412875\pi$
$858$	−0.675223	−0.0230517
$859$	49.3957	1.68536	0.842680	−	0.538415i	$-0.180977\pi$
$859$	49.3957	1.68536	0.842680	+	0.538415i	$0.180977\pi$
$860$	0	0
$861$	−1.49342	−0.0508956
$862$	10.1567	0.345940
$863$	−26.1044	−0.888604	−0.444302	−	0.895877i	$-0.646548\pi$
$863$	−26.1044	−0.888604	−0.444302	+	0.895877i	$0.646548\pi$
$864$	3.57061	0.121475
$865$	0	0
$866$	−8.63404	−0.293397
$867$	−2.02536	−0.0687847
$868$	−8.39562	−0.284966
$869$	33.3677	1.13192
$870$	0	0
$871$	−49.0990	−1.66366
$872$	14.3540	0.486086
$873$	−18.8757	−0.638847
$874$	1.03131	0.0348846
$875$	0	0
$876$	1.13729	0.0384256
$877$	−0.177280	−0.00598632	−0.00299316	−	0.999996i	$-0.500953\pi$
$877$	−0.177280	−0.00598632	−0.00299316	+	0.999996i	$0.500953\pi$
$878$	−8.41084	−0.283852
$879$	−4.62666	−0.156053
$880$	0	0
$881$	−32.7236	−1.10249	−0.551244	−	0.834344i	$-0.685846\pi$
$881$	−32.7236	−1.10249	−0.551244	+	0.834344i	$0.685846\pi$
$882$	0.991009	0.0333690
$883$	−11.2516	−0.378648	−0.189324	−	0.981915i	$-0.560630\pi$
$883$	−11.2516	−0.378648	−0.189324	+	0.981915i	$0.560630\pi$
$884$	−22.8486	−0.768482
$885$	0	0
$886$	−10.7117	−0.359865
$887$	−31.0613	−1.04294	−0.521468	−	0.853271i	$-0.674615\pi$
$887$	−31.0613	−1.04294	−0.521468	+	0.853271i	$0.674615\pi$
$888$	−1.58377	−0.0531477
$889$	−7.41735	−0.248770
$890$	0	0
$891$	−19.1900	−0.642890
$892$	−25.5703	−0.856156
$893$	−19.9631	−0.668039
$894$	0.487146	0.0162926
$895$	0	0
$896$	−9.23199	−0.308419
$897$	−0.925700	−0.0309082
$898$	−12.0514	−0.402160
$899$	13.6442	0.455059
$900$	0	0
$901$	−2.63050	−0.0876346
$902$	6.75584	0.224945
$903$	0.455783	0.0151675
$904$	11.2134	0.372953
$905$	0	0
$906$	1.06206	0.0352847
$907$	6.92099	0.229808	0.114904	−	0.993377i	$-0.463344\pi$
$907$	6.92099	0.229808	0.114904	+	0.993377i	$0.463344\pi$
$908$	23.6844	0.785994
$909$	17.5229	0.581199
$910$	0	0
$911$	16.6916	0.553018	0.276509	−	0.961011i	$-0.410822\pi$
$911$	16.6916	0.553018	0.276509	+	0.961011i	$0.410822\pi$
$912$	−1.66982	−0.0552933
$913$	−5.55914	−0.183981
$914$	1.36380	0.0451104
$915$	0	0
$916$	−2.77439	−0.0916684
$917$	−4.00302	−0.132191
$918$	−0.676279	−0.0223205
$919$	26.6252	0.878284	0.439142	−	0.898418i	$-0.355282\pi$
$919$	26.6252	0.878284	0.439142	+	0.898418i	$0.355282\pi$
$920$	0	0
$921$	−0.497225	−0.0163841
$922$	1.46409	0.0482174
$923$	−48.4720	−1.59548
$924$	−0.666718	−0.0219334
$925$	0	0
$926$	−1.50670	−0.0495132
$927$	−41.3675	−1.35869
$928$	11.3793	0.373545
$929$	−20.8889	−0.685343	−0.342672	−	0.939455i	$-0.611332\pi$
$929$	−20.8889	−0.685343	−0.342672	+	0.939455i	$0.611332\pi$
$930$	0	0
$931$	−3.09494	−0.101433
$932$	−45.0411	−1.47537
$933$	0.278370	0.00911344
$934$	−6.96886	−0.228028
$935$	0	0
$936$	22.1260	0.723211
$937$	38.0571	1.24327	0.621636	−	0.783306i	$-0.286468\pi$
$937$	38.0571	1.24327	0.621636	+	0.783306i	$0.286468\pi$
$938$	2.84982	0.0930499
$939$	−2.41985	−0.0789690
$940$	0	0
$941$	−59.4206	−1.93706	−0.968528	−	0.248905i	$-0.919929\pi$
$941$	−59.4206	−1.93706	−0.968528	+	0.248905i	$0.919929\pi$
$942$	−1.14213	−0.0372126
$943$	9.26196	0.301611
$944$	−35.2286	−1.14659
$945$	0	0
$946$	−2.06185	−0.0670364
$947$	19.4122	0.630810	0.315405	−	0.948957i	$-0.397860\pi$
$947$	19.4122	0.630810	0.315405	+	0.948957i	$0.397860\pi$
$948$	4.64288	0.150794
$949$	21.4369	0.695871
$950$	0	0
$951$	4.73693	0.153605
$952$	2.73033	0.0884905
$953$	−39.2294	−1.27077	−0.635383	−	0.772197i	$-0.719158\pi$
$953$	−39.2294	−1.27077	−0.635383	+	0.772197i	$0.719158\pi$
$954$	1.23729	0.0400586
$955$	0	0
$956$	−38.0605	−1.23096
$957$	1.08352	0.0350253
$958$	7.49429	0.242130
$959$	3.64882	0.117826
$960$	0	0
$961$	−11.2458	−0.362768
$962$	−14.5001	−0.467501
$963$	34.0324	1.09668
$964$	39.7672	1.28081
$965$	0	0
$966$	0.0537298	0.00172873
$967$	4.11249	0.132249	0.0661244	−	0.997811i	$-0.478937\pi$
$967$	4.11249	0.132249	0.0661244	+	0.997811i	$0.478937\pi$
$968$	−8.04544	−0.258590
$969$	1.05142	0.0337765
$970$	0	0
$971$	−19.3820	−0.621999	−0.310999	−	0.950410i	$-0.600664\pi$
$971$	−19.3820	−0.621999	−0.310999	+	0.950410i	$0.600664\pi$
$972$	−8.12885	−0.260733
$973$	23.4946	0.753201
$974$	6.41721	0.205621
$975$	0	0
$976$	−15.2776	−0.489024
$977$	−34.2480	−1.09569	−0.547845	−	0.836580i	$-0.684552\pi$
$977$	−34.2480	−1.09569	−0.547845	+	0.836580i	$0.684552\pi$
$978$	−0.303060	−0.00969080
$979$	−16.0557	−0.513141
$980$	0	0
$981$	−32.9414	−1.05174
$982$	−0.582776	−0.0185971
$983$	23.6638	0.754757	0.377379	−	0.926059i	$-0.376826\pi$
$983$	23.6638	0.754757	0.377379	+	0.926059i	$0.376826\pi$
$984$	1.93531	0.0616956
$985$	0	0
$986$	−2.15526	−0.0686375
$987$	−1.04005	−0.0331051
$988$	−33.5635	−1.06780
$989$	−2.82670	−0.0898838
$990$	0	0
$991$	−53.9874	−1.71497	−0.857483	−	0.514513i	$-0.827973\pi$
$991$	−53.9874	−1.71497	−0.857483	+	0.514513i	$0.827973\pi$
$992$	16.4751	0.523085
$993$	−0.975048	−0.0309422
$994$	2.81343	0.0892366
$995$	0	0
$996$	−0.773516	−0.0245098
$997$	29.6827	0.940060	0.470030	−	0.882651i	$-0.344243\pi$
$997$	29.6827	0.940060	0.470030	+	0.882651i	$0.344243\pi$
$998$	0.338222	0.0107062
$999$	7.30107	0.230996

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.v.1.4	yes	8
5.4	even	2		4025.2.a.u.1.5	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4025.2.a.u.1.5	✓	8	5.4	even	2
4025.2.a.v.1.4	yes	8	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-0.333224 q^{2} +0.161242 q^{3} -1.88896 q^{4} -0.0537298 q^{6} -1.00000 q^{7} +1.29590 q^{8} -2.97400 q^{9} +O(q^{10})\)	\(q-0.333224 q^{2} +0.161242 q^{3} -1.88896 q^{4} -0.0537298 q^{6} -1.00000 q^{7} +1.29590 q^{8} -2.97400 q^{9} -2.18897 q^{11} -0.304580 q^{12} -5.74105 q^{13} +0.333224 q^{14} +3.34610 q^{16} -2.10691 q^{17} +0.991009 q^{18} -3.09494 q^{19} -0.161242 q^{21} +0.729419 q^{22} +1.00000 q^{23} +0.208953 q^{24} +1.91306 q^{26} -0.963261 q^{27} +1.88896 q^{28} -3.06986 q^{29} -4.44457 q^{31} -3.70679 q^{32} -0.352955 q^{33} +0.702072 q^{34} +5.61777 q^{36} -7.57953 q^{37} +1.03131 q^{38} -0.925700 q^{39} +9.26196 q^{41} +0.0537298 q^{42} -2.82670 q^{43} +4.13489 q^{44} -0.333224 q^{46} +6.45023 q^{47} +0.539533 q^{48} +1.00000 q^{49} -0.339722 q^{51} +10.8446 q^{52} +1.24851 q^{53} +0.320982 q^{54} -1.29590 q^{56} -0.499035 q^{57} +1.02295 q^{58} -10.5283 q^{59} -4.56579 q^{61} +1.48104 q^{62} +2.97400 q^{63} -5.45701 q^{64} +0.117613 q^{66} +8.55226 q^{67} +3.97986 q^{68} +0.161242 q^{69} +8.44306 q^{71} -3.85400 q^{72} -3.73397 q^{73} +2.52568 q^{74} +5.84623 q^{76} +2.18897 q^{77} +0.308466 q^{78} -15.2435 q^{79} +8.76668 q^{81} -3.08631 q^{82} +2.53961 q^{83} +0.304580 q^{84} +0.941924 q^{86} -0.494991 q^{87} -2.83668 q^{88} +7.33480 q^{89} +5.74105 q^{91} -1.88896 q^{92} -0.716652 q^{93} -2.14937 q^{94} -0.597692 q^{96} +6.34692 q^{97} -0.333224 q^{98} +6.51001 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + 4 q^{3} + 5 q^{4} - q^{6} - 8 q^{7}+O(q^{10}) \) 8 * q + q^2 + 4 * q^3 + 5 * q^4 - q^6 - 8 * q^7	\( 8 q + q^{2} + 4 q^{3} + 5 q^{4} - q^{6} - 8 q^{7} + 3 q^{11} + 9 q^{12} + 5 q^{13} - q^{14} - q^{16} + 5 q^{17} + 2 q^{18} - 2 q^{19} - 4 q^{21} + 21 q^{22} + 8 q^{23} - 6 q^{24} + 18 q^{26} + 7 q^{27} - 5 q^{28} - 9 q^{29} - 3 q^{31} + 6 q^{32} + 4 q^{33} - 10 q^{34} + 16 q^{36} + 6 q^{37} + 4 q^{38} - 2 q^{39} - 7 q^{41} + q^{42} + 8 q^{43} + 4 q^{44} + q^{46} + 22 q^{47} + 9 q^{48} + 8 q^{49} - 12 q^{51} + 11 q^{52} + 21 q^{53} - 15 q^{54} + 8 q^{57} + 16 q^{58} + 14 q^{59} + 8 q^{61} + 12 q^{62} - 40 q^{64} + 55 q^{66} + 21 q^{67} + 3 q^{68} + 4 q^{69} + 11 q^{71} - q^{72} + 26 q^{73} - 41 q^{74} + 21 q^{76} - 3 q^{77} + 17 q^{78} - 16 q^{79} - 20 q^{81} - q^{82} + 20 q^{83} - 9 q^{84} + 14 q^{86} - 29 q^{87} + 32 q^{88} + 15 q^{89} - 5 q^{91} + 5 q^{92} + 19 q^{93} + 21 q^{94} + 52 q^{96} + q^{97} + q^{98} + 15 q^{99}+O(q^{100}) \) 8 * q + q^2 + 4 * q^3 + 5 * q^4 - q^6 - 8 * q^7 + 3 * q^11 + 9 * q^12 + 5 * q^13 - q^14 - q^16 + 5 * q^17 + 2 * q^18 - 2 * q^19 - 4 * q^21 + 21 * q^22 + 8 * q^23 - 6 * q^24 + 18 * q^26 + 7 * q^27 - 5 * q^28 - 9 * q^29 - 3 * q^31 + 6 * q^32 + 4 * q^33 - 10 * q^34 + 16 * q^36 + 6 * q^37 + 4 * q^38 - 2 * q^39 - 7 * q^41 + q^42 + 8 * q^43 + 4 * q^44 + q^46 + 22 * q^47 + 9 * q^48 + 8 * q^49 - 12 * q^51 + 11 * q^52 + 21 * q^53 - 15 * q^54 + 8 * q^57 + 16 * q^58 + 14 * q^59 + 8 * q^61 + 12 * q^62 - 40 * q^64 + 55 * q^66 + 21 * q^67 + 3 * q^68 + 4 * q^69 + 11 * q^71 - q^72 + 26 * q^73 - 41 * q^74 + 21 * q^76 - 3 * q^77 + 17 * q^78 - 16 * q^79 - 20 * q^81 - q^82 + 20 * q^83 - 9 * q^84 + 14 * q^86 - 29 * q^87 + 32 * q^88 + 15 * q^89 - 5 * q^91 + 5 * q^92 + 19 * q^93 + 21 * q^94 + 52 * q^96 + q^97 + q^98 + 15 * q^99

Introduction

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