LMFDB - Embedded newform 4025.2.a.j.1.3

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:	$3$
Coefficient field:	3.3.148.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 3x + 1 $ x^3 - x^2 - 3*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 161)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.17009$ 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)

$f(q)$	$=$	$q+2.70928 q^{2} +1.17009 q^{3} +5.34017 q^{4} +3.17009 q^{6} +1.00000 q^{7} +9.04945 q^{8} -1.63090 q^{9} +O(q^{10})$	\(q+2.70928 q^{2} +1.17009 q^{3} +5.34017 q^{4} +3.17009 q^{6} +1.00000 q^{7} +9.04945 q^{8} -1.63090 q^{9} +3.70928 q^{11} +6.24846 q^{12} -4.34017 q^{13} +2.70928 q^{14} +13.8371 q^{16} -3.17009 q^{17} -4.41855 q^{18} +5.26180 q^{19} +1.17009 q^{21} +10.0494 q^{22} -1.00000 q^{23} +10.5886 q^{24} -11.7587 q^{26} -5.41855 q^{27} +5.34017 q^{28} +0.630898 q^{29} +9.32684 q^{31} +19.3896 q^{32} +4.34017 q^{33} -8.58864 q^{34} -8.70928 q^{36} +3.07838 q^{37} +14.2557 q^{38} -5.07838 q^{39} +2.68035 q^{41} +3.17009 q^{42} +8.49693 q^{43} +19.8082 q^{44} -2.70928 q^{46} -6.09171 q^{47} +16.1906 q^{48} +1.00000 q^{49} -3.70928 q^{51} -23.1773 q^{52} -4.15676 q^{53} -14.6803 q^{54} +9.04945 q^{56} +6.15676 q^{57} +1.70928 q^{58} -8.40522 q^{59} -6.92881 q^{61} +25.2690 q^{62} -1.63090 q^{63} +24.8576 q^{64} +11.7587 q^{66} -9.86603 q^{67} -16.9288 q^{68} -1.17009 q^{69} +10.8371 q^{71} -14.7587 q^{72} +13.0205 q^{73} +8.34017 q^{74} +28.0989 q^{76} +3.70928 q^{77} -13.7587 q^{78} -4.38962 q^{79} -1.44748 q^{81} +7.26180 q^{82} -14.6537 q^{83} +6.24846 q^{84} +23.0205 q^{86} +0.738205 q^{87} +33.5669 q^{88} -6.77205 q^{89} -4.34017 q^{91} -5.34017 q^{92} +10.9132 q^{93} -16.5041 q^{94} +22.6875 q^{96} -8.58864 q^{97} +2.70928 q^{98} -6.04945 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + q^{2} - 2 q^{3} + 5 q^{4} + 4 q^{6} + 3 q^{7} + 9 q^{8} - q^{9}+O(q^{10}) $ 3 * q + q^2 - 2 * q^3 + 5 * q^4 + 4 * q^6 + 3 * q^7 + 9 * q^8 - q^9	$ 3 q + q^{2} - 2 q^{3} + 5 q^{4} + 4 q^{6} + 3 q^{7} + 9 q^{8} - q^{9} + 4 q^{11} + 10 q^{12} - 2 q^{13} + q^{14} + 13 q^{16} - 4 q^{17} + q^{18} + 8 q^{19} - 2 q^{21} + 12 q^{22} - 3 q^{23} + 12 q^{24} - 10 q^{26} - 2 q^{27} + 5 q^{28} - 2 q^{29} + 16 q^{31} + 29 q^{32} + 2 q^{33} - 6 q^{34} - 19 q^{36} + 6 q^{37} - 12 q^{39} - 14 q^{41} + 4 q^{42} + 8 q^{43} + 16 q^{44} - q^{46} - 16 q^{47} + 10 q^{48} + 3 q^{49} - 4 q^{51} - 30 q^{52} - 6 q^{53} - 22 q^{54} + 9 q^{56} + 12 q^{57} - 2 q^{58} - 10 q^{59} + 10 q^{61} + 34 q^{62} - q^{63} + 13 q^{64} + 10 q^{66} - 16 q^{67} - 20 q^{68} + 2 q^{69} + 4 q^{71} - 19 q^{72} + 6 q^{73} + 14 q^{74} + 48 q^{76} + 4 q^{77} - 16 q^{78} + 16 q^{79} - 5 q^{81} + 14 q^{82} - 20 q^{83} + 10 q^{84} + 36 q^{86} + 10 q^{87} + 32 q^{88} + 4 q^{89} - 2 q^{91} - 5 q^{92} - 12 q^{93} + 2 q^{94} + 12 q^{96} - 6 q^{97} + q^{98}+O(q^{100}) $ 3 * q + q^2 - 2 * q^3 + 5 * q^4 + 4 * q^6 + 3 * q^7 + 9 * q^8 - q^9 + 4 * q^11 + 10 * q^12 - 2 * q^13 + q^14 + 13 * q^16 - 4 * q^17 + q^18 + 8 * q^19 - 2 * q^21 + 12 * q^22 - 3 * q^23 + 12 * q^24 - 10 * q^26 - 2 * q^27 + 5 * q^28 - 2 * q^29 + 16 * q^31 + 29 * q^32 + 2 * q^33 - 6 * q^34 - 19 * q^36 + 6 * q^37 - 12 * q^39 - 14 * q^41 + 4 * q^42 + 8 * q^43 + 16 * q^44 - q^46 - 16 * q^47 + 10 * q^48 + 3 * q^49 - 4 * q^51 - 30 * q^52 - 6 * q^53 - 22 * q^54 + 9 * q^56 + 12 * q^57 - 2 * q^58 - 10 * q^59 + 10 * q^61 + 34 * q^62 - q^63 + 13 * q^64 + 10 * q^66 - 16 * q^67 - 20 * q^68 + 2 * q^69 + 4 * q^71 - 19 * q^72 + 6 * q^73 + 14 * q^74 + 48 * q^76 + 4 * q^77 - 16 * q^78 + 16 * q^79 - 5 * q^81 + 14 * q^82 - 20 * q^83 + 10 * q^84 + 36 * q^86 + 10 * q^87 + 32 * q^88 + 4 * q^89 - 2 * q^91 - 5 * q^92 - 12 * q^93 + 2 * q^94 + 12 * q^96 - 6 * q^97 + q^98

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 $

$2$	2.70928	1.91575	0.957873	−	0.287190i	$-0.0927213\pi$
$2$	2.70928	1.91575	0.957873	+	0.287190i	$0.0927213\pi$
$3$	1.17009	0.675550	0.337775	−	0.941227i	$-0.390326\pi$
$3$	1.17009	0.675550	0.337775	+	0.941227i	$0.390326\pi$
$4$	5.34017	2.67009
$5$	0	0
$5$	0	0
$6$	3.17009	1.29418
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	9.04945	3.19946
$9$	−1.63090	−0.543633
$10$	0	0
$11$	3.70928	1.11839	0.559194	−	0.829037i	$-0.311111\pi$
$11$	3.70928	1.11839	0.559194	+	0.829037i	$0.311111\pi$
$12$	6.24846	1.80378
$13$	−4.34017	−1.20375	−0.601874	−	0.798591i	$-0.705579\pi$
$13$	−4.34017	−1.20375	−0.601874	+	0.798591i	$0.705579\pi$
$14$	2.70928	0.724084
$15$	0	0
$16$	13.8371	3.45928
$17$	−3.17009	−0.768859	−0.384429	−	0.923154i	$-0.625602\pi$
$17$	−3.17009	−0.768859	−0.384429	+	0.923154i	$0.625602\pi$
$18$	−4.41855	−1.04146
$19$	5.26180	1.20714	0.603569	−	0.797311i	$-0.293745\pi$
$19$	5.26180	1.20714	0.603569	+	0.797311i	$0.293745\pi$
$20$	0	0
$21$	1.17009	0.255334
$22$	10.0494	2.14255
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	10.5886	2.16140
$25$	0	0
$26$	−11.7587	−2.30608
$27$	−5.41855	−1.04280
$28$	5.34017	1.00920
$29$	0.630898	0.117155	0.0585774	−	0.998283i	$-0.481344\pi$
$29$	0.630898	0.117155	0.0585774	+	0.998283i	$0.481344\pi$
$30$	0	0
$31$	9.32684	1.67515	0.837575	−	0.546322i	$-0.183973\pi$
$31$	9.32684	1.67515	0.837575	+	0.546322i	$0.183973\pi$
$32$	19.3896	3.42763
$33$	4.34017	0.755527
$34$	−8.58864	−1.47294
$35$	0	0
$36$	−8.70928	−1.45155
$37$	3.07838	0.506082	0.253041	−	0.967456i	$-0.418569\pi$
$37$	3.07838	0.506082	0.253041	+	0.967456i	$0.418569\pi$
$38$	14.2557	2.31257
$39$	−5.07838	−0.813191
$40$	0	0
$41$	2.68035	0.418600	0.209300	−	0.977852i	$-0.432882\pi$
$41$	2.68035	0.418600	0.209300	+	0.977852i	$0.432882\pi$
$42$	3.17009	0.489155
$43$	8.49693	1.29577	0.647885	−	0.761738i	$-0.275654\pi$
$43$	8.49693	1.29577	0.647885	+	0.761738i	$0.275654\pi$
$44$	19.8082	2.98619
$45$	0	0
$46$	−2.70928	−0.399461
$47$	−6.09171	−0.888567	−0.444284	−	0.895886i	$-0.646542\pi$
$47$	−6.09171	−0.888567	−0.444284	+	0.895886i	$0.646542\pi$
$48$	16.1906	2.33691
$49$	1.00000	0.142857
$50$	0	0
$51$	−3.70928	−0.519402
$52$	−23.1773	−3.21411
$53$	−4.15676	−0.570974	−0.285487	−	0.958383i	$-0.592155\pi$
$53$	−4.15676	−0.570974	−0.285487	+	0.958383i	$0.592155\pi$
$54$	−14.6803	−1.99774
$55$	0	0
$56$	9.04945	1.20928
$57$	6.15676	0.815482
$58$	1.70928	0.224439
$59$	−8.40522	−1.09427	−0.547133	−	0.837046i	$-0.684281\pi$
$59$	−8.40522	−1.09427	−0.547133	+	0.837046i	$0.684281\pi$
$60$	0	0
$61$	−6.92881	−0.887143	−0.443572	−	0.896239i	$-0.646289\pi$
$61$	−6.92881	−0.887143	−0.443572	+	0.896239i	$0.646289\pi$
$62$	25.2690	3.20916
$63$	−1.63090	−0.205474
$64$	24.8576	3.10720
$65$	0	0
$66$	11.7587	1.44740
$67$	−9.86603	−1.20533	−0.602664	−	0.797995i	$-0.705894\pi$
$67$	−9.86603	−1.20533	−0.602664	+	0.797995i	$0.705894\pi$
$68$	−16.9288	−2.05292
$69$	−1.17009	−0.140862
$70$	0	0
$71$	10.8371	1.28613	0.643064	−	0.765813i	$-0.277663\pi$
$71$	10.8371	1.28613	0.643064	+	0.765813i	$0.277663\pi$
$72$	−14.7587	−1.73933
$73$	13.0205	1.52394	0.761968	−	0.647614i	$-0.224233\pi$
$73$	13.0205	1.52394	0.761968	+	0.647614i	$0.224233\pi$
$74$	8.34017	0.969525
$75$	0	0
$76$	28.0989	3.22316
$77$	3.70928	0.422711
$78$	−13.7587	−1.55787
$79$	−4.38962	−0.493871	−0.246935	−	0.969032i	$-0.579424\pi$
$79$	−4.38962	−0.493871	−0.246935	+	0.969032i	$0.579424\pi$
$80$	0	0
$81$	−1.44748	−0.160831
$82$	7.26180	0.801931
$83$	−14.6537	−1.60845	−0.804225	−	0.594324i	$-0.797420\pi$
$83$	−14.6537	−1.60845	−0.804225	+	0.594324i	$0.797420\pi$
$84$	6.24846	0.681763
$85$	0	0
$86$	23.0205	2.48237
$87$	0.738205	0.0791439
$88$	33.5669	3.57824
$89$	−6.77205	−0.717836	−0.358918	−	0.933369i	$-0.616854\pi$
$89$	−6.77205	−0.717836	−0.358918	+	0.933369i	$0.616854\pi$
$90$	0	0
$91$	−4.34017	−0.454974
$92$	−5.34017	−0.556752
$93$	10.9132	1.13165
$94$	−16.5041	−1.70227
$95$	0	0
$96$	22.6875	2.31554
$97$	−8.58864	−0.872044	−0.436022	−	0.899936i	$-0.643613\pi$
$97$	−8.58864	−0.872044	−0.436022	+	0.899936i	$0.643613\pi$
$98$	2.70928	0.273678
$99$	−6.04945	−0.607992
$100$	0	0
$101$	−4.92162	−0.489720	−0.244860	−	0.969558i	$-0.578742\pi$
$101$	−4.92162	−0.489720	−0.244860	+	0.969558i	$0.578742\pi$
$102$	−10.0494	−0.995044
$103$	−16.6803	−1.64356	−0.821782	−	0.569803i	$-0.807020\pi$
$103$	−16.6803	−1.64356	−0.821782	+	0.569803i	$0.807020\pi$
$104$	−39.2762	−3.85135
$105$	0	0
$106$	−11.2618	−1.09384
$107$	15.3340	1.48240	0.741198	−	0.671286i	$-0.234258\pi$
$107$	15.3340	1.48240	0.741198	+	0.671286i	$0.234258\pi$
$108$	−28.9360	−2.78437
$109$	−11.1773	−1.07059	−0.535294	−	0.844666i	$-0.679799\pi$
$109$	−11.1773	−1.07059	−0.535294	+	0.844666i	$0.679799\pi$
$110$	0	0
$111$	3.60197	0.341884
$112$	13.8371	1.30748
$113$	−13.5174	−1.27161	−0.635807	−	0.771848i	$-0.719333\pi$
$113$	−13.5174	−1.27161	−0.635807	+	0.771848i	$0.719333\pi$
$114$	16.6803	1.56226
$115$	0	0
$116$	3.36910	0.312813
$117$	7.07838	0.654396
$118$	−22.7721	−2.09634
$119$	−3.17009	−0.290601
$120$	0	0
$121$	2.75872	0.250793
$122$	−18.7721	−1.69954
$123$	3.13624	0.282785
$124$	49.8069	4.47280
$125$	0	0
$126$	−4.41855	−0.393636
$127$	−2.92162	−0.259252	−0.129626	−	0.991563i	$-0.541378\pi$
$127$	−2.92162	−0.259252	−0.129626	+	0.991563i	$0.541378\pi$
$128$	28.5669	2.52498
$129$	9.94214	0.875357
$130$	0	0
$131$	−6.27513	−0.548260	−0.274130	−	0.961693i	$-0.588390\pi$
$131$	−6.27513	−0.548260	−0.274130	+	0.961693i	$0.588390\pi$
$132$	23.1773	2.01732
$133$	5.26180	0.456256
$134$	−26.7298	−2.30910
$135$	0	0
$136$	−28.6875	−2.45994
$137$	−7.75872	−0.662873	−0.331436	−	0.943478i	$-0.607533\pi$
$137$	−7.75872	−0.662873	−0.331436	+	0.943478i	$0.607533\pi$
$138$	−3.17009	−0.269856
$139$	−2.92881	−0.248418	−0.124209	−	0.992256i	$-0.539639\pi$
$139$	−2.92881	−0.248418	−0.124209	+	0.992256i	$0.539639\pi$
$140$	0	0
$141$	−7.12783	−0.600271
$142$	29.3607	2.46389
$143$	−16.0989	−1.34626
$144$	−22.5669	−1.88057
$145$	0	0
$146$	35.2762	2.91948
$147$	1.17009	0.0965071
$148$	16.4391	1.35128
$149$	0.837101	0.0685780	0.0342890	−	0.999412i	$-0.489083\pi$
$149$	0.837101	0.0685780	0.0342890	+	0.999412i	$0.489083\pi$
$150$	0	0
$151$	15.9155	1.29518	0.647592	−	0.761988i	$-0.275776\pi$
$151$	15.9155	1.29518	0.647592	+	0.761988i	$0.275776\pi$
$152$	47.6163	3.86220
$153$	5.17009	0.417977
$154$	10.0494	0.809808
$155$	0	0
$156$	−27.1194	−2.17129
$157$	11.1701	0.891470	0.445735	−	0.895165i	$-0.352942\pi$
$157$	11.1701	0.891470	0.445735	+	0.895165i	$0.352942\pi$
$158$	−11.8927	−0.946132
$159$	−4.86376	−0.385722
$160$	0	0
$161$	−1.00000	−0.0788110
$162$	−3.92162	−0.308112
$163$	−14.6225	−1.14532	−0.572661	−	0.819792i	$-0.694089\pi$
$163$	−14.6225	−1.14532	−0.572661	+	0.819792i	$0.694089\pi$
$164$	14.3135	1.11770
$165$	0	0
$166$	−39.7009	−3.08138
$167$	−6.00719	−0.464850	−0.232425	−	0.972614i	$-0.574666\pi$
$167$	−6.00719	−0.464850	−0.232425	+	0.972614i	$0.574666\pi$
$168$	10.5886	0.816931
$169$	5.83710	0.449008
$170$	0	0
$171$	−8.58145	−0.656240
$172$	45.3751	3.45982
$173$	−14.0989	−1.07192	−0.535960	−	0.844244i	$-0.680050\pi$
$173$	−14.0989	−1.07192	−0.535960	+	0.844244i	$0.680050\pi$
$174$	2.00000	0.151620
$175$	0	0
$176$	51.3256	3.86881
$177$	−9.83483	−0.739231
$178$	−18.3474	−1.37519
$179$	−18.1256	−1.35477	−0.677384	−	0.735630i	$-0.736886\pi$
$179$	−18.1256	−1.35477	−0.677384	+	0.735630i	$0.736886\pi$
$180$	0	0
$181$	12.4319	0.924054	0.462027	−	0.886866i	$-0.347122\pi$
$181$	12.4319	0.924054	0.462027	+	0.886866i	$0.347122\pi$
$182$	−11.7587	−0.871615
$183$	−8.10731	−0.599309
$184$	−9.04945	−0.667134
$185$	0	0
$186$	29.5669	2.16795
$187$	−11.7587	−0.859883
$188$	−32.5308	−2.37255
$189$	−5.41855	−0.394142
$190$	0	0
$191$	−4.86376	−0.351930	−0.175965	−	0.984396i	$-0.556304\pi$
$191$	−4.86376	−0.351930	−0.175965	+	0.984396i	$0.556304\pi$
$192$	29.0856	2.09907
$193$	17.2351	1.24061	0.620306	−	0.784360i	$-0.287008\pi$
$193$	17.2351	1.24061	0.620306	+	0.784360i	$0.287008\pi$
$194$	−23.2690	−1.67062
$195$	0	0
$196$	5.34017	0.381441
$197$	12.5236	0.892269	0.446134	−	0.894966i	$-0.352800\pi$
$197$	12.5236	0.892269	0.446134	+	0.894966i	$0.352800\pi$
$198$	−16.3896	−1.16476
$199$	1.16290	0.0824357	0.0412178	−	0.999150i	$-0.486876\pi$
$199$	1.16290	0.0824357	0.0412178	+	0.999150i	$0.486876\pi$
$200$	0	0
$201$	−11.5441	−0.814259
$202$	−13.3340	−0.938179
$203$	0.630898	0.0442803
$204$	−19.8082	−1.38685
$205$	0	0
$206$	−45.1917	−3.14865
$207$	1.63090	0.113355
$208$	−60.0554	−4.16409
$209$	19.5174	1.35005
$210$	0	0
$211$	4.76487	0.328027	0.164013	−	0.986458i	$-0.447556\pi$
$211$	4.76487	0.328027	0.164013	+	0.986458i	$0.447556\pi$
$212$	−22.1978	−1.52455
$213$	12.6803	0.868843
$214$	41.5441	2.83990
$215$	0	0
$216$	−49.0349	−3.33640
$217$	9.32684	0.633147
$218$	−30.2823	−2.05098
$219$	15.2351	1.02949
$220$	0	0
$221$	13.7587	0.925512
$222$	9.75872	0.654963
$223$	21.3679	1.43090	0.715450	−	0.698664i	$-0.246222\pi$
$223$	21.3679	1.43090	0.715450	+	0.698664i	$0.246222\pi$
$224$	19.3896	1.29552
$225$	0	0
$226$	−36.6225	−2.43609
$227$	5.84324	0.387830	0.193915	−	0.981018i	$-0.437881\pi$
$227$	5.84324	0.387830	0.193915	+	0.981018i	$0.437881\pi$
$228$	32.8781	2.17741
$229$	2.85658	0.188768	0.0943839	−	0.995536i	$-0.469912\pi$
$229$	2.85658	0.188768	0.0943839	+	0.995536i	$0.469912\pi$
$230$	0	0
$231$	4.34017	0.285562
$232$	5.70928	0.374832
$233$	13.5259	0.886108	0.443054	−	0.896495i	$-0.353895\pi$
$233$	13.5259	0.886108	0.443054	+	0.896495i	$0.353895\pi$
$234$	19.1773	1.25366
$235$	0	0
$236$	−44.8853	−2.92179
$237$	−5.13624	−0.333634
$238$	−8.58864	−0.556719
$239$	4.76487	0.308214	0.154107	−	0.988054i	$-0.450750\pi$
$239$	4.76487	0.308214	0.154107	+	0.988054i	$0.450750\pi$
$240$	0	0
$241$	24.4775	1.57673	0.788366	−	0.615207i	$-0.210928\pi$
$241$	24.4775	1.57673	0.788366	+	0.615207i	$0.210928\pi$
$242$	7.47414	0.480456
$243$	14.5620	0.934151
$244$	−37.0010	−2.36875
$245$	0	0
$246$	8.49693	0.541744
$247$	−22.8371	−1.45309
$248$	84.4028	5.35958
$249$	−17.1461	−1.08659
$250$	0	0
$251$	−26.2557	−1.65724	−0.828621	−	0.559810i	$-0.810874\pi$
$251$	−26.2557	−1.65724	−0.828621	+	0.559810i	$0.810874\pi$
$252$	−8.70928	−0.548633
$253$	−3.70928	−0.233200
$254$	−7.91548	−0.496661
$255$	0	0
$256$	27.6803	1.73002
$257$	−7.84324	−0.489248	−0.244624	−	0.969618i	$-0.578665\pi$
$257$	−7.84324	−0.489248	−0.244624	+	0.969618i	$0.578665\pi$
$258$	26.9360	1.67696
$259$	3.07838	0.191281
$260$	0	0
$261$	−1.02893	−0.0636891
$262$	−17.0010	−1.05033
$263$	−10.9132	−0.672937	−0.336469	−	0.941695i	$-0.609233\pi$
$263$	−10.9132	−0.672937	−0.336469	+	0.941695i	$0.609233\pi$
$264$	39.2762	2.41728
$265$	0	0
$266$	14.2557	0.874070
$267$	−7.92389	−0.484934
$268$	−52.6863	−3.21833
$269$	−3.57531	−0.217990	−0.108995	−	0.994042i	$-0.534763\pi$
$269$	−3.57531	−0.217990	−0.108995	+	0.994042i	$0.534763\pi$
$270$	0	0
$271$	−5.98053	−0.363291	−0.181646	−	0.983364i	$-0.558142\pi$
$271$	−5.98053	−0.363291	−0.181646	+	0.983364i	$0.558142\pi$
$272$	−43.8648	−2.65969
$273$	−5.07838	−0.307357
$274$	−21.0205	−1.26990
$275$	0	0
$276$	−6.24846	−0.376113
$277$	13.3112	0.799795	0.399898	−	0.916560i	$-0.369046\pi$
$277$	13.3112	0.799795	0.399898	+	0.916560i	$0.369046\pi$
$278$	−7.93495	−0.475907
$279$	−15.2111	−0.910666
$280$	0	0
$281$	−2.13009	−0.127071	−0.0635354	−	0.997980i	$-0.520238\pi$
$281$	−2.13009	−0.127071	−0.0635354	+	0.997980i	$0.520238\pi$
$282$	−19.3112	−1.14997
$283$	−13.6742	−0.812847	−0.406423	−	0.913685i	$-0.633224\pi$
$283$	−13.6742	−0.812847	−0.406423	+	0.913685i	$0.633224\pi$
$284$	57.8720	3.43407
$285$	0	0
$286$	−43.6163	−2.57909
$287$	2.68035	0.158216
$288$	−31.6225	−1.86337
$289$	−6.95055	−0.408856
$290$	0	0
$291$	−10.0494	−0.589109
$292$	69.5318	4.06904
$293$	13.2690	0.775182	0.387591	−	0.921831i	$-0.373307\pi$
$293$	13.2690	0.775182	0.387591	+	0.921831i	$0.373307\pi$
$294$	3.17009	0.184883
$295$	0	0
$296$	27.8576	1.61919
$297$	−20.0989	−1.16626
$298$	2.26794	0.131378
$299$	4.34017	0.250999
$300$	0	0
$301$	8.49693	0.489755
$302$	43.1194	2.48124
$303$	−5.75872	−0.330830
$304$	72.8080	4.17582
$305$	0	0
$306$	14.0072	0.800738
$307$	17.5103	0.999363	0.499682	−	0.866209i	$-0.333450\pi$
$307$	17.5103	0.999363	0.499682	+	0.866209i	$0.333450\pi$
$308$	19.8082	1.12868
$309$	−19.5174	−1.11031
$310$	0	0
$311$	2.03385	0.115329	0.0576645	−	0.998336i	$-0.481635\pi$
$311$	2.03385	0.115329	0.0576645	+	0.998336i	$0.481635\pi$
$312$	−45.9565	−2.60178
$313$	−12.3786	−0.699677	−0.349839	−	0.936810i	$-0.613764\pi$
$313$	−12.3786	−0.699677	−0.349839	+	0.936810i	$0.613764\pi$
$314$	30.2628	1.70783
$315$	0	0
$316$	−23.4413	−1.31868
$317$	20.1483	1.13164	0.565822	−	0.824527i	$-0.308559\pi$
$317$	20.1483	1.13164	0.565822	+	0.824527i	$0.308559\pi$
$318$	−13.1773	−0.738945
$319$	2.34017	0.131025
$320$	0	0
$321$	17.9421	1.00143
$322$	−2.70928	−0.150982
$323$	−16.6803	−0.928119
$324$	−7.72979	−0.429433
$325$	0	0
$326$	−39.6163	−2.19415
$327$	−13.0784	−0.723236
$328$	24.2557	1.33929
$329$	−6.09171	−0.335847
$330$	0	0
$331$	−6.70701	−0.368650	−0.184325	−	0.982865i	$-0.559010\pi$
$331$	−6.70701	−0.368650	−0.184325	+	0.982865i	$0.559010\pi$
$332$	−78.2532	−4.29470
$333$	−5.02052	−0.275123
$334$	−16.2751	−0.890535
$335$	0	0
$336$	16.1906	0.883270
$337$	29.0205	1.58085	0.790424	−	0.612560i	$-0.209860\pi$
$337$	29.0205	1.58085	0.790424	+	0.612560i	$0.209860\pi$
$338$	15.8143	0.860185
$339$	−15.8166	−0.859039
$340$	0	0
$341$	34.5958	1.87347
$342$	−23.2495	−1.25719
$343$	1.00000	0.0539949
$344$	76.8925	4.14577
$345$	0	0
$346$	−38.1978	−2.05353
$347$	18.2413	0.979243	0.489622	−	0.871935i	$-0.337135\pi$
$347$	18.2413	0.979243	0.489622	+	0.871935i	$0.337135\pi$
$348$	3.94214	0.211321
$349$	−8.35455	−0.447209	−0.223604	−	0.974680i	$-0.571782\pi$
$349$	−8.35455	−0.447209	−0.223604	+	0.974680i	$0.571782\pi$
$350$	0	0
$351$	23.5174	1.25527
$352$	71.9214	3.83343
$353$	31.5897	1.68135	0.840675	−	0.541541i	$-0.182159\pi$
$353$	31.5897	1.68135	0.840675	+	0.541541i	$0.182159\pi$
$354$	−26.6453	−1.41618
$355$	0	0
$356$	−36.1639	−1.91669
$357$	−3.70928	−0.196316
$358$	−49.1071	−2.59539
$359$	−4.48852	−0.236895	−0.118447	−	0.992960i	$-0.537792\pi$
$359$	−4.48852	−0.236895	−0.118447	+	0.992960i	$0.537792\pi$
$360$	0	0
$361$	8.68649	0.457184
$362$	33.6814	1.77025
$363$	3.22795	0.169423
$364$	−23.1773	−1.21482
$365$	0	0
$366$	−21.9649	−1.14813
$367$	18.7526	0.978877	0.489438	−	0.872038i	$-0.337202\pi$
$367$	18.7526	0.978877	0.489438	+	0.872038i	$0.337202\pi$
$368$	−13.8371	−0.721309
$369$	−4.37137	−0.227564
$370$	0	0
$371$	−4.15676	−0.215808
$372$	58.2784	3.02160
$373$	−22.5113	−1.16559	−0.582796	−	0.812619i	$-0.698041\pi$
$373$	−22.5113	−1.16559	−0.582796	+	0.812619i	$0.698041\pi$
$374$	−31.8576	−1.64732
$375$	0	0
$376$	−55.1266	−2.84294
$377$	−2.73820	−0.141025
$378$	−14.6803	−0.755076
$379$	−22.3318	−1.14711	−0.573553	−	0.819169i	$-0.694435\pi$
$379$	−22.3318	−1.14711	−0.573553	+	0.819169i	$0.694435\pi$
$380$	0	0
$381$	−3.41855	−0.175138
$382$	−13.1773	−0.674208
$383$	−15.2351	−0.778479	−0.389239	−	0.921137i	$-0.627262\pi$
$383$	−15.2351	−0.778479	−0.389239	+	0.921137i	$0.627262\pi$
$384$	33.4257	1.70575
$385$	0	0
$386$	46.6947	2.37670
$387$	−13.8576	−0.704422
$388$	−45.8648	−2.32843
$389$	21.3874	1.08438	0.542191	−	0.840255i	$-0.317595\pi$
$389$	21.3874	1.08438	0.542191	+	0.840255i	$0.317595\pi$
$390$	0	0
$391$	3.17009	0.160318
$392$	9.04945	0.457066
$393$	−7.34244	−0.370377
$394$	33.9299	1.70936
$395$	0	0
$396$	−32.3051	−1.62339
$397$	−20.6537	−1.03658	−0.518289	−	0.855205i	$-0.673431\pi$
$397$	−20.6537	−1.03658	−0.518289	+	0.855205i	$0.673431\pi$
$398$	3.15061	0.157926
$399$	6.15676	0.308223
$400$	0	0
$401$	24.3402	1.21549	0.607745	−	0.794132i	$-0.292074\pi$
$401$	24.3402	1.21549	0.607745	+	0.794132i	$0.292074\pi$
$402$	−31.2762	−1.55991
$403$	−40.4801	−2.01646
$404$	−26.2823	−1.30759
$405$	0	0
$406$	1.70928	0.0848299
$407$	11.4186	0.565997
$408$	−33.5669	−1.66181
$409$	17.2885	0.854859	0.427430	−	0.904049i	$-0.359419\pi$
$409$	17.2885	0.854859	0.427430	+	0.904049i	$0.359419\pi$
$410$	0	0
$411$	−9.07838	−0.447803
$412$	−89.0759	−4.38846
$413$	−8.40522	−0.413594
$414$	4.41855	0.217160
$415$	0	0
$416$	−84.1543	−4.12600
$417$	−3.42696	−0.167819
$418$	52.8781	2.58635
$419$	−3.05172	−0.149086	−0.0745430	−	0.997218i	$-0.523750\pi$
$419$	−3.05172	−0.149086	−0.0745430	+	0.997218i	$0.523750\pi$
$420$	0	0
$421$	13.8843	0.676679	0.338339	−	0.941024i	$-0.390135\pi$
$421$	13.8843	0.676679	0.338339	+	0.941024i	$0.390135\pi$
$422$	12.9093	0.628417
$423$	9.93495	0.483054
$424$	−37.6163	−1.82681
$425$	0	0
$426$	34.3545	1.66448
$427$	−6.92881	−0.335309
$428$	81.8864	3.95813
$429$	−18.8371	−0.909464
$430$	0	0
$431$	15.2039	0.732348	0.366174	−	0.930546i	$-0.380668\pi$
$431$	15.2039	0.732348	0.366174	+	0.930546i	$0.380668\pi$
$432$	−74.9770	−3.60733
$433$	−12.8566	−0.617848	−0.308924	−	0.951087i	$-0.599969\pi$
$433$	−12.8566	−0.617848	−0.308924	+	0.951087i	$0.599969\pi$
$434$	25.2690	1.21295
$435$	0	0
$436$	−59.6886	−2.85856
$437$	−5.26180	−0.251706
$438$	41.2762	1.97225
$439$	14.5620	0.695005	0.347503	−	0.937679i	$-0.387030\pi$
$439$	14.5620	0.695005	0.347503	+	0.937679i	$0.387030\pi$
$440$	0	0
$441$	−1.63090	−0.0776618
$442$	37.2762	1.77305
$443$	30.2557	1.43749	0.718745	−	0.695274i	$-0.244717\pi$
$443$	30.2557	1.43749	0.718745	+	0.695274i	$0.244717\pi$
$444$	19.2351	0.912859
$445$	0	0
$446$	57.8915	2.74124
$447$	0.979481	0.0463279
$448$	24.8576	1.17441
$449$	−4.68422	−0.221062	−0.110531	−	0.993873i	$-0.535255\pi$
$449$	−4.68422	−0.221062	−0.110531	+	0.993873i	$0.535255\pi$
$450$	0	0
$451$	9.94214	0.468157
$452$	−72.1855	−3.39532
$453$	18.6225	0.874961
$454$	15.8310	0.742984
$455$	0	0
$456$	55.7152	2.60911
$457$	−23.4596	−1.09739	−0.548697	−	0.836022i	$-0.684876\pi$
$457$	−23.4596	−1.09739	−0.548697	+	0.836022i	$0.684876\pi$
$458$	7.73925	0.361631
$459$	17.1773	0.801767
$460$	0	0
$461$	6.58145	0.306529	0.153264	−	0.988185i	$-0.451021\pi$
$461$	6.58145	0.306529	0.153264	+	0.988185i	$0.451021\pi$
$462$	11.7587	0.547065
$463$	−20.0144	−0.930147	−0.465073	−	0.885272i	$-0.653972\pi$
$463$	−20.0144	−0.930147	−0.465073	+	0.885272i	$0.653972\pi$
$464$	8.72979	0.405271
$465$	0	0
$466$	36.6453	1.69756
$467$	−21.4596	−0.993031	−0.496516	−	0.868028i	$-0.665387\pi$
$467$	−21.4596	−0.993031	−0.496516	+	0.868028i	$0.665387\pi$
$468$	37.7998	1.74729
$469$	−9.86603	−0.455571
$470$	0	0
$471$	13.0700	0.602232
$472$	−76.0626	−3.50107
$473$	31.5174	1.44917
$474$	−13.9155	−0.639159
$475$	0	0
$476$	−16.9288	−0.775931
$477$	6.77924	0.310400
$478$	12.9093	0.590459
$479$	−14.3090	−0.653794	−0.326897	−	0.945060i	$-0.606003\pi$
$479$	−14.3090	−0.653794	−0.326897	+	0.945060i	$0.606003\pi$
$480$	0	0
$481$	−13.3607	−0.609195
$482$	66.3162	3.02062
$483$	−1.17009	−0.0532408
$484$	14.7321	0.669639
$485$	0	0
$486$	39.4524	1.78960
$487$	5.36069	0.242916	0.121458	−	0.992597i	$-0.461243\pi$
$487$	5.36069	0.242916	0.121458	+	0.992597i	$0.461243\pi$
$488$	−62.7019	−2.83838
$489$	−17.1096	−0.773722
$490$	0	0
$491$	8.99386	0.405887	0.202944	−	0.979190i	$-0.434949\pi$
$491$	8.99386	0.405887	0.202944	+	0.979190i	$0.434949\pi$
$492$	16.7480	0.755060
$493$	−2.00000	−0.0900755
$494$	−61.8720	−2.78375
$495$	0	0
$496$	129.056	5.79481
$497$	10.8371	0.486110
$498$	−46.4534	−2.08163
$499$	2.02666	0.0907259	0.0453629	−	0.998971i	$-0.485556\pi$
$499$	2.02666	0.0907259	0.0453629	+	0.998971i	$0.485556\pi$
$500$	0	0
$501$	−7.02893	−0.314029
$502$	−71.1338	−3.17486
$503$	32.4124	1.44520	0.722599	−	0.691268i	$-0.242947\pi$
$503$	32.4124	1.44520	0.722599	+	0.691268i	$0.242947\pi$
$504$	−14.7587	−0.657406
$505$	0	0
$506$	−10.0494	−0.446752
$507$	6.82991	0.303327
$508$	−15.6020	−0.692225
$509$	−10.4826	−0.464631	−0.232315	−	0.972640i	$-0.574630\pi$
$509$	−10.4826	−0.464631	−0.232315	+	0.972640i	$0.574630\pi$
$510$	0	0
$511$	13.0205	0.575994
$512$	17.8599	0.789303
$513$	−28.5113	−1.25880
$514$	−21.2495	−0.937276
$515$	0	0
$516$	53.0928	2.33728
$517$	−22.5958	−0.993763
$518$	8.34017	0.366446
$519$	−16.4969	−0.724135
$520$	0	0
$521$	−24.6030	−1.07788	−0.538939	−	0.842345i	$-0.681175\pi$
$521$	−24.6030	−1.07788	−0.538939	+	0.842345i	$0.681175\pi$
$522$	−2.78765	−0.122012
$523$	−12.1978	−0.533372	−0.266686	−	0.963783i	$-0.585929\pi$
$523$	−12.1978	−0.533372	−0.266686	+	0.963783i	$0.585929\pi$
$524$	−33.5103	−1.46390
$525$	0	0
$526$	−29.5669	−1.28918
$527$	−29.5669	−1.28795
$528$	60.0554	2.61358
$529$	1.00000	0.0434783
$530$	0	0
$531$	13.7081	0.594879
$532$	28.0989	1.21824
$533$	−11.6332	−0.503888
$534$	−21.4680	−0.929011
$535$	0	0
$536$	−89.2821	−3.85640
$537$	−21.2085	−0.915213
$538$	−9.68649	−0.417614
$539$	3.70928	0.159770
$540$	0	0
$541$	17.5259	0.753495	0.376748	−	0.926316i	$-0.377042\pi$
$541$	17.5259	0.753495	0.376748	+	0.926316i	$0.377042\pi$
$542$	−16.2029	−0.695974
$543$	14.5464	0.624245
$544$	−61.4668	−2.63537
$545$	0	0
$546$	−13.7587	−0.588819
$547$	−12.5958	−0.538559	−0.269279	−	0.963062i	$-0.586785\pi$
$547$	−12.5958	−0.538559	−0.269279	+	0.963062i	$0.586785\pi$
$548$	−41.4329	−1.76993
$549$	11.3002	0.482280
$550$	0	0
$551$	3.31965	0.141422
$552$	−10.5886	−0.450682
$553$	−4.38962	−0.186666
$554$	36.0638	1.53221
$555$	0	0
$556$	−15.6404	−0.663299
$557$	26.5113	1.12332	0.561660	−	0.827368i	$-0.310163\pi$
$557$	26.5113	1.12332	0.561660	+	0.827368i	$0.310163\pi$
$558$	−41.2111	−1.74461
$559$	−36.8781	−1.55978
$560$	0	0
$561$	−13.7587	−0.580894
$562$	−5.77101	−0.243435
$563$	17.0472	0.718453	0.359227	−	0.933250i	$-0.383041\pi$
$563$	17.0472	0.718453	0.359227	+	0.933250i	$0.383041\pi$
$564$	−38.0638	−1.60278
$565$	0	0
$566$	−37.0472	−1.55721
$567$	−1.44748	−0.0607885
$568$	98.0698	4.11492
$569$	−25.1194	−1.05306	−0.526530	−	0.850156i	$-0.676507\pi$
$569$	−25.1194	−1.05306	−0.526530	+	0.850156i	$0.676507\pi$
$570$	0	0
$571$	−12.0144	−0.502786	−0.251393	−	0.967885i	$-0.580889\pi$
$571$	−12.0144	−0.502786	−0.251393	+	0.967885i	$0.580889\pi$
$572$	−85.9709	−3.59462
$573$	−5.69102	−0.237746
$574$	7.26180	0.303101
$575$	0	0
$576$	−40.5402	−1.68918
$577$	10.1133	0.421021	0.210511	−	0.977592i	$-0.432487\pi$
$577$	10.1133	0.421021	0.210511	+	0.977592i	$0.432487\pi$
$578$	−18.8310	−0.783265
$579$	20.1666	0.838095
$580$	0	0
$581$	−14.6537	−0.607937
$582$	−27.2267	−1.12858
$583$	−15.4186	−0.638571
$584$	117.829	4.87578
$585$	0	0
$586$	35.9493	1.48505
$587$	14.2485	0.588097	0.294049	−	0.955790i	$-0.404997\pi$
$587$	14.2485	0.588097	0.294049	+	0.955790i	$0.404997\pi$
$588$	6.24846	0.257682
$589$	49.0759	2.02214
$590$	0	0
$591$	14.6537	0.602772
$592$	42.5958	1.75068
$593$	20.2557	0.831800	0.415900	−	0.909410i	$-0.363467\pi$
$593$	20.2557	0.831800	0.415900	+	0.909410i	$0.363467\pi$
$594$	−54.4534	−2.23425
$595$	0	0
$596$	4.47027	0.183109
$597$	1.36069	0.0556894
$598$	11.7587	0.480850
$599$	−19.2351	−0.785926	−0.392963	−	0.919554i	$-0.628550\pi$
$599$	−19.2351	−0.785926	−0.392963	+	0.919554i	$0.628550\pi$
$600$	0	0
$601$	−21.4329	−0.874267	−0.437134	−	0.899397i	$-0.644006\pi$
$601$	−21.4329	−0.874267	−0.437134	+	0.899397i	$0.644006\pi$
$602$	23.0205	0.938246
$603$	16.0905	0.655255
$604$	84.9914	3.45825
$605$	0	0
$606$	−15.6020	−0.633787
$607$	37.7926	1.53395	0.766977	−	0.641675i	$-0.221760\pi$
$607$	37.7926	1.53395	0.766977	+	0.641675i	$0.221760\pi$
$608$	102.024	4.13763
$609$	0.738205	0.0299136
$610$	0	0
$611$	26.4391	1.06961
$612$	27.6092	1.11603
$613$	−14.6947	−0.593514	−0.296757	−	0.954953i	$-0.595905\pi$
$613$	−14.6947	−0.593514	−0.296757	+	0.954953i	$0.595905\pi$
$614$	47.4401	1.91453
$615$	0	0
$616$	33.5669	1.35245
$617$	−12.1256	−0.488157	−0.244078	−	0.969756i	$-0.578485\pi$
$617$	−12.1256	−0.488157	−0.244078	+	0.969756i	$0.578485\pi$
$618$	−52.8781	−2.12707
$619$	−12.0144	−0.482899	−0.241449	−	0.970413i	$-0.577623\pi$
$619$	−12.0144	−0.482899	−0.241449	+	0.970413i	$0.577623\pi$
$620$	0	0
$621$	5.41855	0.217439
$622$	5.51026	0.220941
$623$	−6.77205	−0.271317
$624$	−70.2700	−2.81305
$625$	0	0
$626$	−33.5369	−1.34040
$627$	22.8371	0.912026
$628$	59.6502	2.38030
$629$	−9.75872	−0.389106
$630$	0	0
$631$	10.9300	0.435118	0.217559	−	0.976047i	$-0.430191\pi$
$631$	10.9300	0.435118	0.217559	+	0.976047i	$0.430191\pi$
$632$	−39.7237	−1.58012
$633$	5.57531	0.221599
$634$	54.5874	2.16794
$635$	0	0
$636$	−25.9733	−1.02991
$637$	−4.34017	−0.171964
$638$	6.34017	0.251010
$639$	−17.6742	−0.699181
$640$	0	0
$641$	−33.1194	−1.30814	−0.654069	−	0.756435i	$-0.726939\pi$
$641$	−33.1194	−1.30814	−0.654069	+	0.756435i	$0.726939\pi$
$642$	48.6102	1.91849
$643$	17.5297	0.691305	0.345653	−	0.938363i	$-0.387658\pi$
$643$	17.5297	0.691305	0.345653	+	0.938363i	$0.387658\pi$
$644$	−5.34017	−0.210432
$645$	0	0
$646$	−45.1917	−1.77804
$647$	6.88777	0.270786	0.135393	−	0.990792i	$-0.456770\pi$
$647$	6.88777	0.270786	0.135393	+	0.990792i	$0.456770\pi$
$648$	−13.0989	−0.514573
$649$	−31.1773	−1.22382
$650$	0	0
$651$	10.9132	0.427722
$652$	−78.0866	−3.05811
$653$	36.3545	1.42266	0.711332	−	0.702856i	$-0.248092\pi$
$653$	36.3545	1.42266	0.711332	+	0.702856i	$0.248092\pi$
$654$	−35.4329	−1.38554
$655$	0	0
$656$	37.0882	1.44805
$657$	−21.2351	−0.828461
$658$	−16.5041	−0.643397
$659$	−2.63931	−0.102813	−0.0514064	−	0.998678i	$-0.516370\pi$
$659$	−2.63931	−0.102813	−0.0514064	+	0.998678i	$0.516370\pi$
$660$	0	0
$661$	21.0010	0.816846	0.408423	−	0.912793i	$-0.366079\pi$
$661$	21.0010	0.816846	0.408423	+	0.912793i	$0.366079\pi$
$662$	−18.1711	−0.706241
$663$	16.0989	0.625229
$664$	−132.608	−5.14618
$665$	0	0
$666$	−13.6020	−0.527066
$667$	−0.630898	−0.0244285
$668$	−32.0794	−1.24119
$669$	25.0023	0.966644
$670$	0	0
$671$	−25.7009	−0.992171
$672$	22.6875	0.875191
$673$	51.2534	1.97567	0.987836	−	0.155497i	$-0.0496978\pi$
$673$	51.2534	1.97567	0.987836	+	0.155497i	$0.0496978\pi$
$674$	78.6246	3.02851
$675$	0	0
$676$	31.1711	1.19889
$677$	−41.4668	−1.59370	−0.796849	−	0.604179i	$-0.793501\pi$
$677$	−41.4668	−1.59370	−0.796849	+	0.604179i	$0.793501\pi$
$678$	−42.8515	−1.64570
$679$	−8.58864	−0.329602
$680$	0	0
$681$	6.83710	0.261998
$682$	93.7296	3.58909
$683$	26.2557	1.00464	0.502322	−	0.864680i	$-0.332479\pi$
$683$	26.2557	1.00464	0.502322	+	0.864680i	$0.332479\pi$
$684$	−45.8264	−1.75222
$685$	0	0
$686$	2.70928	0.103441
$687$	3.34244	0.127522
$688$	117.573	4.48242
$689$	18.0410	0.687309
$690$	0	0
$691$	−12.0338	−0.457789	−0.228895	−	0.973451i	$-0.573511\pi$
$691$	−12.0338	−0.457789	−0.228895	+	0.973451i	$0.573511\pi$
$692$	−75.2905	−2.86212
$693$	−6.04945	−0.229800
$694$	49.4206	1.87598
$695$	0	0
$696$	6.68035	0.253218
$697$	−8.49693	−0.321844
$698$	−22.6348	−0.856739
$699$	15.8264	0.598610
$700$	0	0
$701$	34.6491	1.30868	0.654340	−	0.756200i	$-0.272946\pi$
$701$	34.6491	1.30868	0.654340	+	0.756200i	$0.272946\pi$
$702$	63.7152	2.40478
$703$	16.1978	0.610911
$704$	92.2038	3.47506
$705$	0	0
$706$	85.5851	3.22104
$707$	−4.92162	−0.185097
$708$	−52.5197	−1.97381
$709$	7.65983	0.287671	0.143835	−	0.989602i	$-0.454056\pi$
$709$	7.65983	0.287671	0.143835	+	0.989602i	$0.454056\pi$
$710$	0	0
$711$	7.15902	0.268484
$712$	−61.2834	−2.29669
$713$	−9.32684	−0.349293
$714$	−10.0494	−0.376091
$715$	0	0
$716$	−96.7936	−3.61735
$717$	5.57531	0.208214
$718$	−12.1606	−0.453831
$719$	22.4196	0.836110	0.418055	−	0.908422i	$-0.362712\pi$
$719$	22.4196	0.836110	0.418055	+	0.908422i	$0.362712\pi$
$720$	0	0
$721$	−16.6803	−0.621209
$722$	23.5341	0.875848
$723$	28.6407	1.06516
$724$	66.3884	2.46731
$725$	0	0
$726$	8.74539	0.324572
$727$	−34.8371	−1.29204	−0.646018	−	0.763322i	$-0.723567\pi$
$727$	−34.8371	−1.29204	−0.646018	+	0.763322i	$0.723567\pi$
$728$	−39.2762	−1.45567
$729$	21.3812	0.791897
$730$	0	0
$731$	−26.9360	−0.996264
$732$	−43.2944	−1.60021
$733$	38.6752	1.42850	0.714251	−	0.699889i	$-0.246767\pi$
$733$	38.6752	1.42850	0.714251	+	0.699889i	$0.246767\pi$
$734$	50.8059	1.87528
$735$	0	0
$736$	−19.3896	−0.714711
$737$	−36.5958	−1.34802
$738$	−11.8432	−0.435956
$739$	−51.3484	−1.88888	−0.944441	−	0.328682i	$-0.893396\pi$
$739$	−51.3484	−1.88888	−0.944441	+	0.328682i	$0.893396\pi$
$740$	0	0
$741$	−26.7214	−0.981635
$742$	−11.2618	−0.413434
$743$	−8.00597	−0.293710	−0.146855	−	0.989158i	$-0.546915\pi$
$743$	−8.00597	−0.293710	−0.146855	+	0.989158i	$0.546915\pi$
$744$	98.7585	3.62066
$745$	0	0
$746$	−60.9893	−2.23298
$747$	23.8987	0.874406
$748$	−62.7936	−2.29596
$749$	15.3340	0.560293
$750$	0	0
$751$	23.3958	0.853724	0.426862	−	0.904317i	$-0.359619\pi$
$751$	23.3958	0.853724	0.426862	+	0.904317i	$0.359619\pi$
$752$	−84.2916	−3.07380
$753$	−30.7214	−1.11955
$754$	−7.41855	−0.270168
$755$	0	0
$756$	−28.9360	−1.05239
$757$	29.1194	1.05836	0.529182	−	0.848509i	$-0.322499\pi$
$757$	29.1194	1.05836	0.529182	+	0.848509i	$0.322499\pi$
$758$	−60.5029	−2.19756
$759$	−4.34017	−0.157538
$760$	0	0
$761$	−10.1834	−0.369149	−0.184574	−	0.982819i	$-0.559091\pi$
$761$	−10.1834	−0.369149	−0.184574	+	0.982819i	$0.559091\pi$
$762$	−9.26180	−0.335519
$763$	−11.1773	−0.404645
$764$	−25.9733	−0.939682
$765$	0	0
$766$	−41.2762	−1.49137
$767$	36.4801	1.31722
$768$	32.3884	1.16872
$769$	0.431882	0.0155741	0.00778703	−	0.999970i	$-0.497521\pi$
$769$	0.431882	0.0155741	0.00778703	+	0.999970i	$0.497521\pi$
$770$	0	0
$771$	−9.17727	−0.330511
$772$	92.0386	3.31254
$773$	0.0650468	0.00233957	0.00116978	−	0.999999i	$-0.499628\pi$
$773$	0.0650468	0.00233957	0.00116978	+	0.999999i	$0.499628\pi$
$774$	−37.5441	−1.34950
$775$	0	0
$776$	−77.7224	−2.79007
$777$	3.60197	0.129220
$778$	57.9442	2.07740
$779$	14.1034	0.505308
$780$	0	0
$781$	40.1978	1.43839
$782$	8.58864	0.307129
$783$	−3.41855	−0.122169
$784$	13.8371	0.494182
$785$	0	0
$786$	−19.8927	−0.709549
$787$	−31.5486	−1.12459	−0.562294	−	0.826937i	$-0.690081\pi$
$787$	−31.5486	−1.12459	−0.562294	+	0.826937i	$0.690081\pi$
$788$	66.8781	2.38244
$789$	−12.7694	−0.454603
$790$	0	0
$791$	−13.5174	−0.480625
$792$	−54.7442	−1.94525
$793$	30.0722	1.06790
$794$	−55.9565	−1.98582
$795$	0	0
$796$	6.21008	0.220110
$797$	−51.8336	−1.83604	−0.918020	−	0.396533i	$-0.870213\pi$
$797$	−51.8336	−1.83604	−0.918020	+	0.396533i	$0.870213\pi$
$798$	16.6803	0.590478
$799$	19.3112	0.683183
$800$	0	0
$801$	11.0445	0.390239
$802$	65.9442	2.32857
$803$	48.2967	1.70435
$804$	−61.6475	−2.17414
$805$	0	0
$806$	−109.672	−3.86302
$807$	−4.18342	−0.147263
$808$	−44.5380	−1.56684
$809$	44.4391	1.56239	0.781197	−	0.624284i	$-0.214609\pi$
$809$	44.4391	1.56239	0.781197	+	0.624284i	$0.214609\pi$
$810$	0	0
$811$	−23.6358	−0.829966	−0.414983	−	0.909829i	$-0.636212\pi$
$811$	−23.6358	−0.829966	−0.414983	+	0.909829i	$0.636212\pi$
$812$	3.36910	0.118232
$813$	−6.99773	−0.245421
$814$	30.9360	1.08431
$815$	0	0
$816$	−51.3256	−1.79676
$817$	44.7091	1.56417
$818$	46.8392	1.63769
$819$	7.07838	0.247339
$820$	0	0
$821$	−14.9399	−0.521405	−0.260703	−	0.965419i	$-0.583954\pi$
$821$	−14.9399	−0.521405	−0.260703	+	0.965419i	$0.583954\pi$
$822$	−24.5958	−0.857878
$823$	−30.7670	−1.07247	−0.536234	−	0.844069i	$-0.680154\pi$
$823$	−30.7670	−1.07247	−0.536234	+	0.844069i	$0.680154\pi$
$824$	−150.948	−5.25852
$825$	0	0
$826$	−22.7721	−0.792341
$827$	24.5113	0.852342	0.426171	−	0.904643i	$-0.359862\pi$
$827$	24.5113	0.852342	0.426171	+	0.904643i	$0.359862\pi$
$828$	8.70928	0.302668
$829$	43.8720	1.52374	0.761869	−	0.647731i	$-0.224282\pi$
$829$	43.8720	1.52374	0.761869	+	0.647731i	$0.224282\pi$
$830$	0	0
$831$	15.5753	0.540301
$832$	−107.886	−3.74029
$833$	−3.17009	−0.109837
$834$	−9.28458	−0.321499
$835$	0	0
$836$	104.227	3.60475
$837$	−50.5380	−1.74685
$838$	−8.26794	−0.285611
$839$	−5.39189	−0.186149	−0.0930743	−	0.995659i	$-0.529669\pi$
$839$	−5.39189	−0.186149	−0.0930743	+	0.995659i	$0.529669\pi$
$840$	0	0
$841$	−28.6020	−0.986275
$842$	37.6163	1.29634
$843$	−2.49239	−0.0858426
$844$	25.4452	0.875860
$845$	0	0
$846$	26.9165	0.925409
$847$	2.75872	0.0947909
$848$	−57.5174	−1.97516
$849$	−16.0000	−0.549119
$850$	0	0
$851$	−3.07838	−0.105525
$852$	67.7152	2.31989
$853$	1.33403	0.0456763	0.0228382	−	0.999739i	$-0.492730\pi$
$853$	1.33403	0.0456763	0.0228382	+	0.999739i	$0.492730\pi$
$854$	−18.7721	−0.642366
$855$	0	0
$856$	138.765	4.74287
$857$	−12.1034	−0.413445	−0.206723	−	0.978400i	$-0.566280\pi$
$857$	−12.1034	−0.413445	−0.206723	+	0.978400i	$0.566280\pi$
$858$	−51.0349	−1.74230
$859$	40.5718	1.38429	0.692146	−	0.721757i	$-0.256665\pi$
$859$	40.5718	1.38429	0.692146	+	0.721757i	$0.256665\pi$
$860$	0	0
$861$	3.13624	0.106883
$862$	41.1917	1.40299
$863$	−34.0944	−1.16059	−0.580293	−	0.814408i	$-0.697062\pi$
$863$	−34.0944	−1.16059	−0.580293	+	0.814408i	$0.697062\pi$
$864$	−105.064	−3.57434
$865$	0	0
$866$	−34.8320	−1.18364
$867$	−8.13275	−0.276203
$868$	49.8069	1.69056
$869$	−16.2823	−0.552340
$870$	0	0
$871$	42.8203	1.45091
$872$	−101.148	−3.42531
$873$	14.0072	0.474071
$874$	−14.2557	−0.482205
$875$	0	0
$876$	81.3582	2.74884
$877$	20.4163	0.689409	0.344704	−	0.938711i	$-0.387979\pi$
$877$	20.4163	0.689409	0.344704	+	0.938711i	$0.387979\pi$
$878$	39.4524	1.33145
$879$	15.5259	0.523674
$880$	0	0
$881$	−35.4668	−1.19491	−0.597453	−	0.801904i	$-0.703821\pi$
$881$	−35.4668	−1.19491	−0.597453	+	0.801904i	$0.703821\pi$
$882$	−4.41855	−0.148780
$883$	−7.91548	−0.266377	−0.133189	−	0.991091i	$-0.542522\pi$
$883$	−7.91548	−0.266377	−0.133189	+	0.991091i	$0.542522\pi$
$884$	73.4740	2.47120
$885$	0	0
$886$	81.9709	2.75387
$887$	8.10608	0.272176	0.136088	−	0.990697i	$-0.456547\pi$
$887$	8.10608	0.272176	0.136088	+	0.990697i	$0.456547\pi$
$888$	32.5958	1.09384
$889$	−2.92162	−0.0979881
$890$	0	0
$891$	−5.36910	−0.179872
$892$	114.108	3.82062
$893$	−32.0533	−1.07262
$894$	2.65368	0.0887525
$895$	0	0
$896$	28.5669	0.954353
$897$	5.07838	0.169562
$898$	−12.6908	−0.423499
$899$	5.88428	0.196252
$900$	0	0
$901$	13.1773	0.438999
$902$	26.9360	0.896871
$903$	9.94214	0.330854
$904$	−122.325	−4.06848
$905$	0	0
$906$	50.4534	1.67620
$907$	18.8371	0.625476	0.312738	−	0.949839i	$-0.398754\pi$
$907$	18.8371	0.625476	0.312738	+	0.949839i	$0.398754\pi$
$908$	31.2039	1.03554
$909$	8.02666	0.266228
$910$	0	0
$911$	33.6514	1.11492	0.557461	−	0.830203i	$-0.311776\pi$
$911$	33.6514	1.11492	0.557461	+	0.830203i	$0.311776\pi$
$912$	85.1917	2.82098
$913$	−54.3545	−1.79887
$914$	−63.5585	−2.10233
$915$	0	0
$916$	15.2546	0.504026
$917$	−6.27513	−0.207223
$918$	46.5380	1.53598
$919$	42.5464	1.40348	0.701738	−	0.712435i	$-0.252408\pi$
$919$	42.5464	1.40348	0.701738	+	0.712435i	$0.252408\pi$
$920$	0	0
$921$	20.4885	0.675120
$922$	17.8310	0.587231
$923$	−47.0349	−1.54817
$924$	23.1773	0.762476
$925$	0	0
$926$	−54.2245	−1.78193
$927$	27.2039	0.893495
$928$	12.2329	0.401563
$929$	36.3012	1.19100	0.595502	−	0.803354i	$-0.296953\pi$
$929$	36.3012	1.19100	0.595502	+	0.803354i	$0.296953\pi$
$930$	0	0
$931$	5.26180	0.172448
$932$	72.2304	2.36599
$933$	2.37978	0.0779105
$934$	−58.1399	−1.90240
$935$	0	0
$936$	64.0554	2.09372
$937$	−6.50412	−0.212480	−0.106240	−	0.994341i	$-0.533881\pi$
$937$	−6.50412	−0.212480	−0.106240	+	0.994341i	$0.533881\pi$
$938$	−26.7298	−0.872759
$939$	−14.4840	−0.472667
$940$	0	0
$941$	−2.35965	−0.0769223	−0.0384611	−	0.999260i	$-0.512246\pi$
$941$	−2.35965	−0.0769223	−0.0384611	+	0.999260i	$0.512246\pi$
$942$	35.4101	1.15372
$943$	−2.68035	−0.0872841
$944$	−116.304	−3.78537
$945$	0	0
$946$	85.3894	2.77625
$947$	−1.17727	−0.0382563	−0.0191281	−	0.999817i	$-0.506089\pi$
$947$	−1.17727	−0.0382563	−0.0191281	+	0.999817i	$0.506089\pi$
$948$	−27.4284	−0.890833
$949$	−56.5113	−1.83443
$950$	0	0
$951$	23.5753	0.764482
$952$	−28.6875	−0.929768
$953$	31.8264	1.03096	0.515479	−	0.856902i	$-0.327614\pi$
$953$	31.8264	1.03096	0.515479	+	0.856902i	$0.327614\pi$
$954$	18.3668	0.594648
$955$	0	0
$956$	25.4452	0.822957
$957$	2.73820	0.0885136
$958$	−38.7670	−1.25250
$959$	−7.75872	−0.250542
$960$	0	0
$961$	55.9900	1.80613
$962$	−36.1978	−1.16706
$963$	−25.0082	−0.805879
$964$	130.714	4.21001
$965$	0	0
$966$	−3.17009	−0.101996
$967$	−42.6225	−1.37065	−0.685323	−	0.728239i	$-0.740339\pi$
$967$	−42.6225	−1.37065	−0.685323	+	0.728239i	$0.740339\pi$
$968$	24.9649	0.802403
$969$	−19.5174	−0.626991
$970$	0	0
$971$	55.7998	1.79070	0.895350	−	0.445364i	$-0.146926\pi$
$971$	55.7998	1.79070	0.895350	+	0.445364i	$0.146926\pi$
$972$	77.7635	2.49426
$973$	−2.92881	−0.0938933
$974$	14.5236	0.465366
$975$	0	0
$976$	−95.8746	−3.06887
$977$	−52.2245	−1.67081	−0.835404	−	0.549636i	$-0.814766\pi$
$977$	−52.2245	−1.67081	−0.835404	+	0.549636i	$0.814766\pi$
$978$	−46.3545	−1.48226
$979$	−25.1194	−0.802820
$980$	0	0
$981$	18.2290	0.582007
$982$	24.3668	0.777577
$983$	16.7649	0.534716	0.267358	−	0.963597i	$-0.413849\pi$
$983$	16.7649	0.534716	0.267358	+	0.963597i	$0.413849\pi$
$984$	28.3812	0.904760
$985$	0	0
$986$	−5.41855	−0.172562
$987$	−7.12783	−0.226881
$988$	−121.954	−3.87988
$989$	−8.49693	−0.270187
$990$	0	0
$991$	−39.0349	−1.23998	−0.619992	−	0.784608i	$-0.712864\pi$
$991$	−39.0349	−1.23998	−0.619992	+	0.784608i	$0.712864\pi$
$992$	180.844	5.74180
$993$	−7.84778	−0.249042
$994$	29.3607	0.931265
$995$	0	0
$996$	−91.5630	−2.90129
$997$	11.2618	0.356665	0.178332	−	0.983970i	$-0.442930\pi$
$997$	11.2618	0.356665	0.178332	+	0.983970i	$0.442930\pi$
$998$	5.49079	0.173808
$999$	−16.6803	−0.527743

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.j.1.3		3
5.4	even	2		161.2.a.c.1.1	✓	3
15.14	odd	2		1449.2.a.m.1.3		3
20.19	odd	2		2576.2.a.v.1.3		3
35.34	odd	2		1127.2.a.f.1.1		3
115.114	odd	2		3703.2.a.c.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
161.2.a.c.1.1	✓	3	5.4	even	2
1127.2.a.f.1.1		3	35.34	odd	2
1449.2.a.m.1.3		3	15.14	odd	2
2576.2.a.v.1.3		3	20.19	odd	2
3703.2.a.c.1.1		3	115.114	odd	2
4025.2.a.j.1.3		3	1.1	even	1	trivial

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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)

\(f(q)\)	\(=\)	\(q+2.70928 q^{2} +1.17009 q^{3} +5.34017 q^{4} +3.17009 q^{6} +1.00000 q^{7} +9.04945 q^{8} -1.63090 q^{9} +O(q^{10})\)	\(q+2.70928 q^{2} +1.17009 q^{3} +5.34017 q^{4} +3.17009 q^{6} +1.00000 q^{7} +9.04945 q^{8} -1.63090 q^{9} +3.70928 q^{11} +6.24846 q^{12} -4.34017 q^{13} +2.70928 q^{14} +13.8371 q^{16} -3.17009 q^{17} -4.41855 q^{18} +5.26180 q^{19} +1.17009 q^{21} +10.0494 q^{22} -1.00000 q^{23} +10.5886 q^{24} -11.7587 q^{26} -5.41855 q^{27} +5.34017 q^{28} +0.630898 q^{29} +9.32684 q^{31} +19.3896 q^{32} +4.34017 q^{33} -8.58864 q^{34} -8.70928 q^{36} +3.07838 q^{37} +14.2557 q^{38} -5.07838 q^{39} +2.68035 q^{41} +3.17009 q^{42} +8.49693 q^{43} +19.8082 q^{44} -2.70928 q^{46} -6.09171 q^{47} +16.1906 q^{48} +1.00000 q^{49} -3.70928 q^{51} -23.1773 q^{52} -4.15676 q^{53} -14.6803 q^{54} +9.04945 q^{56} +6.15676 q^{57} +1.70928 q^{58} -8.40522 q^{59} -6.92881 q^{61} +25.2690 q^{62} -1.63090 q^{63} +24.8576 q^{64} +11.7587 q^{66} -9.86603 q^{67} -16.9288 q^{68} -1.17009 q^{69} +10.8371 q^{71} -14.7587 q^{72} +13.0205 q^{73} +8.34017 q^{74} +28.0989 q^{76} +3.70928 q^{77} -13.7587 q^{78} -4.38962 q^{79} -1.44748 q^{81} +7.26180 q^{82} -14.6537 q^{83} +6.24846 q^{84} +23.0205 q^{86} +0.738205 q^{87} +33.5669 q^{88} -6.77205 q^{89} -4.34017 q^{91} -5.34017 q^{92} +10.9132 q^{93} -16.5041 q^{94} +22.6875 q^{96} -8.58864 q^{97} +2.70928 q^{98} -6.04945 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + q^{2} - 2 q^{3} + 5 q^{4} + 4 q^{6} + 3 q^{7} + 9 q^{8} - q^{9}+O(q^{10}) \) 3 * q + q^2 - 2 * q^3 + 5 * q^4 + 4 * q^6 + 3 * q^7 + 9 * q^8 - q^9	\( 3 q + q^{2} - 2 q^{3} + 5 q^{4} + 4 q^{6} + 3 q^{7} + 9 q^{8} - q^{9} + 4 q^{11} + 10 q^{12} - 2 q^{13} + q^{14} + 13 q^{16} - 4 q^{17} + q^{18} + 8 q^{19} - 2 q^{21} + 12 q^{22} - 3 q^{23} + 12 q^{24} - 10 q^{26} - 2 q^{27} + 5 q^{28} - 2 q^{29} + 16 q^{31} + 29 q^{32} + 2 q^{33} - 6 q^{34} - 19 q^{36} + 6 q^{37} - 12 q^{39} - 14 q^{41} + 4 q^{42} + 8 q^{43} + 16 q^{44} - q^{46} - 16 q^{47} + 10 q^{48} + 3 q^{49} - 4 q^{51} - 30 q^{52} - 6 q^{53} - 22 q^{54} + 9 q^{56} + 12 q^{57} - 2 q^{58} - 10 q^{59} + 10 q^{61} + 34 q^{62} - q^{63} + 13 q^{64} + 10 q^{66} - 16 q^{67} - 20 q^{68} + 2 q^{69} + 4 q^{71} - 19 q^{72} + 6 q^{73} + 14 q^{74} + 48 q^{76} + 4 q^{77} - 16 q^{78} + 16 q^{79} - 5 q^{81} + 14 q^{82} - 20 q^{83} + 10 q^{84} + 36 q^{86} + 10 q^{87} + 32 q^{88} + 4 q^{89} - 2 q^{91} - 5 q^{92} - 12 q^{93} + 2 q^{94} + 12 q^{96} - 6 q^{97} + q^{98}+O(q^{100}) \) 3 * q + q^2 - 2 * q^3 + 5 * q^4 + 4 * q^6 + 3 * q^7 + 9 * q^8 - q^9 + 4 * q^11 + 10 * q^12 - 2 * q^13 + q^14 + 13 * q^16 - 4 * q^17 + q^18 + 8 * q^19 - 2 * q^21 + 12 * q^22 - 3 * q^23 + 12 * q^24 - 10 * q^26 - 2 * q^27 + 5 * q^28 - 2 * q^29 + 16 * q^31 + 29 * q^32 + 2 * q^33 - 6 * q^34 - 19 * q^36 + 6 * q^37 - 12 * q^39 - 14 * q^41 + 4 * q^42 + 8 * q^43 + 16 * q^44 - q^46 - 16 * q^47 + 10 * q^48 + 3 * q^49 - 4 * q^51 - 30 * q^52 - 6 * q^53 - 22 * q^54 + 9 * q^56 + 12 * q^57 - 2 * q^58 - 10 * q^59 + 10 * q^61 + 34 * q^62 - q^63 + 13 * q^64 + 10 * q^66 - 16 * q^67 - 20 * q^68 + 2 * q^69 + 4 * q^71 - 19 * q^72 + 6 * q^73 + 14 * q^74 + 48 * q^76 + 4 * q^77 - 16 * q^78 + 16 * q^79 - 5 * q^81 + 14 * q^82 - 20 * q^83 + 10 * q^84 + 36 * q^86 + 10 * q^87 + 32 * q^88 + 4 * q^89 - 2 * q^91 - 5 * q^92 - 12 * q^93 + 2 * q^94 + 12 * q^96 - 6 * q^97 + q^98

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