LMFDB - Embedded newform 4025.2.a.l.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("4025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$32.1397868136$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.2777.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} + x + 2 $ x^4 - x^3 - 4*x^2 + x + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 805)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.679643$ of defining polynomial
Character	$\chi$	$=$	4025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.67964 q^{2} -3.26308 q^{3} +0.821201 q^{4} +5.48081 q^{6} +1.00000 q^{7} +1.97996 q^{8} +7.64767 q^{9} +O(q^{10})$	\(q-1.67964 q^{2} -3.26308 q^{3} +0.821201 q^{4} +5.48081 q^{6} +1.00000 q^{7} +1.97996 q^{8} +7.64767 q^{9} +2.67964 q^{11} -2.67964 q^{12} +4.80116 q^{13} -1.67964 q^{14} -4.96803 q^{16} +3.20580 q^{17} -12.8454 q^{18} +2.76223 q^{19} -3.26308 q^{21} -4.50084 q^{22} +1.00000 q^{23} -6.46077 q^{24} -8.06424 q^{26} -15.1657 q^{27} +0.821201 q^{28} -7.60233 q^{29} -8.00696 q^{31} +4.38460 q^{32} -8.74388 q^{33} -5.38460 q^{34} +6.28028 q^{36} -7.56340 q^{37} -4.63957 q^{38} -15.6666 q^{39} +8.18576 q^{41} +5.48081 q^{42} +5.22300 q^{43} +2.20053 q^{44} -1.67964 q^{46} -7.00527 q^{47} +16.2111 q^{48} +1.00000 q^{49} -10.4608 q^{51} +3.94272 q^{52} +0.178799 q^{53} +25.4730 q^{54} +1.97996 q^{56} -9.01338 q^{57} +12.7692 q^{58} -8.96972 q^{59} +7.14041 q^{61} +13.4488 q^{62} +7.64767 q^{63} +2.57150 q^{64} +14.6866 q^{66} -9.06806 q^{67} +2.63261 q^{68} -3.26308 q^{69} -6.29008 q^{71} +15.1421 q^{72} -2.44570 q^{73} +12.7038 q^{74} +2.26835 q^{76} +2.67964 q^{77} +26.3142 q^{78} -7.74219 q^{79} +26.5439 q^{81} -13.7492 q^{82} +4.71046 q^{83} -2.67964 q^{84} -8.77278 q^{86} +24.8070 q^{87} +5.30559 q^{88} -10.8320 q^{89} +4.80116 q^{91} +0.821201 q^{92} +26.1273 q^{93} +11.7664 q^{94} -14.3073 q^{96} +3.73409 q^{97} -1.67964 q^{98} +20.4930 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 3 q^{2} - 6 q^{3} + 3 q^{4} + 4 q^{6} + 4 q^{7} - 6 q^{8} + 6 q^{9}+O(q^{10}) $ 4 * q - 3 * q^2 - 6 * q^3 + 3 * q^4 + 4 * q^6 + 4 * q^7 - 6 * q^8 + 6 * q^9	$ 4 q - 3 q^{2} - 6 q^{3} + 3 q^{4} + 4 q^{6} + 4 q^{7} - 6 q^{8} + 6 q^{9} + 7 q^{11} - 7 q^{12} + 5 q^{13} - 3 q^{14} + q^{16} - 5 q^{17} - 2 q^{18} + 8 q^{19} - 6 q^{21} - 14 q^{22} + 4 q^{23} + 6 q^{24} - 11 q^{26} - 15 q^{27} + 3 q^{28} - 2 q^{29} - 10 q^{33} - 4 q^{34} + q^{36} - 13 q^{37} + 13 q^{38} - 13 q^{39} + q^{41} + 4 q^{42} - 14 q^{43} + 15 q^{44} - 3 q^{46} - 4 q^{47} + 23 q^{48} + 4 q^{49} - 10 q^{51} + 5 q^{52} + q^{53} + 14 q^{54} - 6 q^{56} - 19 q^{57} + 16 q^{58} - 7 q^{59} - 7 q^{61} + 15 q^{62} + 6 q^{63} + 23 q^{66} - 15 q^{67} + 11 q^{68} - 6 q^{69} + 17 q^{72} - 3 q^{73} - 2 q^{74} - 22 q^{76} + 7 q^{77} + 31 q^{78} - 14 q^{79} + 28 q^{81} - 6 q^{82} - 3 q^{83} - 7 q^{84} + 16 q^{86} + 14 q^{87} - 13 q^{88} - 11 q^{89} + 5 q^{91} + 3 q^{92} + 23 q^{93} - 19 q^{94} - 15 q^{96} - 9 q^{97} - 3 q^{98} + 8 q^{99}+O(q^{100}) $ 4 * q - 3 * q^2 - 6 * q^3 + 3 * q^4 + 4 * q^6 + 4 * q^7 - 6 * q^8 + 6 * q^9 + 7 * q^11 - 7 * q^12 + 5 * q^13 - 3 * q^14 + q^16 - 5 * q^17 - 2 * q^18 + 8 * q^19 - 6 * q^21 - 14 * q^22 + 4 * q^23 + 6 * q^24 - 11 * q^26 - 15 * q^27 + 3 * q^28 - 2 * q^29 - 10 * q^33 - 4 * q^34 + q^36 - 13 * q^37 + 13 * q^38 - 13 * q^39 + q^41 + 4 * q^42 - 14 * q^43 + 15 * q^44 - 3 * q^46 - 4 * q^47 + 23 * q^48 + 4 * q^49 - 10 * q^51 + 5 * q^52 + q^53 + 14 * q^54 - 6 * q^56 - 19 * q^57 + 16 * q^58 - 7 * q^59 - 7 * q^61 + 15 * q^62 + 6 * q^63 + 23 * q^66 - 15 * q^67 + 11 * q^68 - 6 * q^69 + 17 * q^72 - 3 * q^73 - 2 * q^74 - 22 * q^76 + 7 * q^77 + 31 * q^78 - 14 * q^79 + 28 * q^81 - 6 * q^82 - 3 * q^83 - 7 * q^84 + 16 * q^86 + 14 * q^87 - 13 * q^88 - 11 * q^89 + 5 * q^91 + 3 * q^92 + 23 * q^93 - 19 * q^94 - 15 * q^96 - 9 * q^97 - 3 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.67964	−1.18769	−0.593844	−	0.804581i	$-0.702390\pi$
$2$	−1.67964	−1.18769	−0.593844	+	0.804581i	$0.702390\pi$
$3$	−3.26308	−1.88394	−0.941969	−	0.335699i	$-0.891028\pi$
$3$	−3.26308	−1.88394	−0.941969	+	0.335699i	$0.891028\pi$
$4$	0.821201	0.410601
$5$	0	0
$5$	0	0
$6$	5.48081	2.23753
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.97996	0.700022
$9$	7.64767	2.54922
$10$	0	0
$11$	2.67964	0.807943	0.403971	−	0.914772i	$-0.367630\pi$
$11$	2.67964	0.807943	0.403971	+	0.914772i	$0.367630\pi$
$12$	−2.67964	−0.773546
$13$	4.80116	1.33160	0.665801	−	0.746129i	$-0.268090\pi$
$13$	4.80116	1.33160	0.665801	+	0.746129i	$0.268090\pi$
$14$	−1.67964	−0.448904
$15$	0	0
$16$	−4.96803	−1.24201
$17$	3.20580	0.777520	0.388760	−	0.921339i	$-0.372903\pi$
$17$	3.20580	0.777520	0.388760	+	0.921339i	$0.372903\pi$
$18$	−12.8454	−3.02768
$19$	2.76223	0.633700	0.316850	−	0.948476i	$-0.397375\pi$
$19$	2.76223	0.633700	0.316850	+	0.948476i	$0.397375\pi$
$20$	0	0
$21$	−3.26308	−0.712062
$22$	−4.50084	−0.959583
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−6.46077	−1.31880
$25$	0	0
$26$	−8.06424	−1.58153
$27$	−15.1657	−2.91864
$28$	0.821201	0.155192
$29$	−7.60233	−1.41172	−0.705858	−	0.708353i	$-0.749438\pi$
$29$	−7.60233	−1.41172	−0.705858	+	0.708353i	$0.749438\pi$
$30$	0	0
$31$	−8.00696	−1.43809	−0.719046	−	0.694962i	$-0.755421\pi$
$31$	−8.00696	−1.43809	−0.719046	+	0.694962i	$0.755421\pi$
$32$	4.38460	0.775095
$33$	−8.74388	−1.52211
$34$	−5.38460	−0.923451
$35$	0	0
$36$	6.28028	1.04671
$37$	−7.56340	−1.24341	−0.621707	−	0.783250i	$-0.713561\pi$
$37$	−7.56340	−1.24341	−0.621707	+	0.783250i	$0.713561\pi$
$38$	−4.63957	−0.752637
$39$	−15.6666	−2.50866
$40$	0	0
$41$	8.18576	1.27840	0.639200	−	0.769040i	$-0.279265\pi$
$41$	8.18576	1.27840	0.639200	+	0.769040i	$0.279265\pi$
$42$	5.48081	0.845707
$43$	5.22300	0.796500	0.398250	−	0.917277i	$-0.369618\pi$
$43$	5.22300	0.796500	0.398250	+	0.917277i	$0.369618\pi$
$44$	2.20053	0.331742
$45$	0	0
$46$	−1.67964	−0.247650
$47$	−7.00527	−1.02182	−0.510912	−	0.859633i	$-0.670692\pi$
$47$	−7.00527	−1.02182	−0.510912	+	0.859633i	$0.670692\pi$
$48$	16.2111	2.33987
$49$	1.00000	0.142857
$50$	0	0
$51$	−10.4608	−1.46480
$52$	3.94272	0.546757
$53$	0.178799	0.0245599	0.0122799	−	0.999925i	$-0.496091\pi$
$53$	0.178799	0.0245599	0.0122799	+	0.999925i	$0.496091\pi$
$54$	25.4730	3.46644
$55$	0	0
$56$	1.97996	0.264583
$57$	−9.01338	−1.19385
$58$	12.7692	1.67668
$59$	−8.96972	−1.16776	−0.583879	−	0.811841i	$-0.698466\pi$
$59$	−8.96972	−1.16776	−0.583879	+	0.811841i	$0.698466\pi$
$60$	0	0
$61$	7.14041	0.914236	0.457118	−	0.889406i	$-0.348882\pi$
$61$	7.14041	0.914236	0.457118	+	0.889406i	$0.348882\pi$
$62$	13.4488	1.70800
$63$	7.64767	0.963516
$64$	2.57150	0.321438
$65$	0	0
$66$	14.6866	1.80780
$67$	−9.06806	−1.10784	−0.553920	−	0.832570i	$-0.686869\pi$
$67$	−9.06806	−1.10784	−0.553920	+	0.832570i	$0.686869\pi$
$68$	2.63261	0.319250
$69$	−3.26308	−0.392828
$70$	0	0
$71$	−6.29008	−0.746495	−0.373247	−	0.927732i	$-0.621756\pi$
$71$	−6.29008	−0.746495	−0.373247	+	0.927732i	$0.621756\pi$
$72$	15.1421	1.78451
$73$	−2.44570	−0.286247	−0.143124	−	0.989705i	$-0.545715\pi$
$73$	−2.44570	−0.286247	−0.143124	+	0.989705i	$0.545715\pi$
$74$	12.7038	1.47679
$75$	0	0
$76$	2.26835	0.260197
$77$	2.67964	0.305374
$78$	26.3142	2.97950
$79$	−7.74219	−0.871065	−0.435532	−	0.900173i	$-0.643440\pi$
$79$	−7.74219	−0.871065	−0.435532	+	0.900173i	$0.643440\pi$
$80$	0	0
$81$	26.5439	2.94932
$82$	−13.7492	−1.51834
$83$	4.71046	0.517041	0.258520	−	0.966006i	$-0.416765\pi$
$83$	4.71046	0.517041	0.258520	+	0.966006i	$0.416765\pi$
$84$	−2.67964	−0.292373
$85$	0	0
$86$	−8.77278	−0.945993
$87$	24.8070	2.65959
$88$	5.30559	0.565578
$89$	−10.8320	−1.14819	−0.574094	−	0.818789i	$-0.694646\pi$
$89$	−10.8320	−1.14819	−0.574094	+	0.818789i	$0.694646\pi$
$90$	0	0
$91$	4.80116	0.503299
$92$	0.821201	0.0856161
$93$	26.1273	2.70928
$94$	11.7664	1.21361
$95$	0	0
$96$	−14.3073	−1.46023
$97$	3.73409	0.379139	0.189569	−	0.981867i	$-0.439291\pi$
$97$	3.73409	0.379139	0.189569	+	0.981867i	$0.439291\pi$
$98$	−1.67964	−0.169670
$99$	20.4930	2.05963
$100$	0	0
$101$	−15.1576	−1.50824	−0.754119	−	0.656737i	$-0.771936\pi$
$101$	−15.1576	−1.50824	−0.754119	+	0.656737i	$0.771936\pi$
$102$	17.5704	1.73972
$103$	−11.3020	−1.11362	−0.556810	−	0.830640i	$-0.687975\pi$
$103$	−11.3020	−1.11362	−0.556810	+	0.830640i	$0.687975\pi$
$104$	9.50612	0.932151
$105$	0	0
$106$	−0.300318	−0.0291695
$107$	−11.3526	−1.09750	−0.548750	−	0.835987i	$-0.684896\pi$
$107$	−11.3526	−1.09750	−0.548750	+	0.835987i	$0.684896\pi$
$108$	−12.4541	−1.19840
$109$	−1.10263	−0.105613	−0.0528063	−	0.998605i	$-0.516817\pi$
$109$	−1.10263	−0.105613	−0.0528063	+	0.998605i	$0.516817\pi$
$110$	0	0
$111$	24.6799	2.34252
$112$	−4.96803	−0.469435
$113$	−8.17880	−0.769397	−0.384698	−	0.923042i	$-0.625695\pi$
$113$	−8.17880	−0.769397	−0.384698	+	0.923042i	$0.625695\pi$
$114$	15.1393	1.41792
$115$	0	0
$116$	−6.24304	−0.579652
$117$	36.7177	3.39456
$118$	15.0659	1.38693
$119$	3.20580	0.293875
$120$	0	0
$121$	−3.81951	−0.347228
$122$	−11.9933	−1.08583
$123$	−26.7108	−2.40843
$124$	−6.57533	−0.590482
$125$	0	0
$126$	−12.8454	−1.14436
$127$	−6.04704	−0.536588	−0.268294	−	0.963337i	$-0.586460\pi$
$127$	−6.04704	−0.536588	−0.268294	+	0.963337i	$0.586460\pi$
$128$	−13.0884	−1.15686
$129$	−17.0431	−1.50056
$130$	0	0
$131$	12.0779	1.05525	0.527624	−	0.849478i	$-0.323083\pi$
$131$	12.0779	1.05525	0.527624	+	0.849478i	$0.323083\pi$
$132$	−7.18049	−0.624981
$133$	2.76223	0.239516
$134$	15.2311	1.31577
$135$	0	0
$136$	6.34736	0.544281
$137$	−12.1351	−1.03677	−0.518387	−	0.855146i	$-0.673467\pi$
$137$	−12.1351	−1.03677	−0.518387	+	0.855146i	$0.673467\pi$
$138$	5.48081	0.466557
$139$	−6.37122	−0.540400	−0.270200	−	0.962804i	$-0.587090\pi$
$139$	−6.37122	−0.540400	−0.270200	+	0.962804i	$0.587090\pi$
$140$	0	0
$141$	22.8587	1.92505
$142$	10.5651	0.886602
$143$	12.8654	1.07586
$144$	−37.9939	−3.16616
$145$	0	0
$146$	4.10790	0.339972
$147$	−3.26308	−0.269134
$148$	−6.21107	−0.510547
$149$	21.7297	1.78016	0.890081	−	0.455802i	$-0.150647\pi$
$149$	21.7297	1.78016	0.890081	+	0.455802i	$0.150647\pi$
$150$	0	0
$151$	−14.8026	−1.20462	−0.602310	−	0.798262i	$-0.705753\pi$
$151$	−14.8026	−1.20462	−0.602310	+	0.798262i	$0.705753\pi$
$152$	5.46911	0.443604
$153$	24.5169	1.98207
$154$	−4.50084	−0.362688
$155$	0	0
$156$	−12.8654	−1.03006
$157$	−14.7783	−1.17944	−0.589718	−	0.807609i	$-0.700761\pi$
$157$	−14.7783	−1.17944	−0.589718	+	0.807609i	$0.700761\pi$
$158$	13.0041	1.03455
$159$	−0.583434	−0.0462693
$160$	0	0
$161$	1.00000	0.0788110
$162$	−44.5843	−3.50287
$163$	9.84536	0.771148	0.385574	−	0.922677i	$-0.374003\pi$
$163$	9.84536	0.771148	0.385574	+	0.922677i	$0.374003\pi$
$164$	6.72216	0.524912
$165$	0	0
$166$	−7.91190	−0.614082
$167$	10.1351	0.784281	0.392140	−	0.919905i	$-0.371735\pi$
$167$	10.1351	0.784281	0.392140	+	0.919905i	$0.371735\pi$
$168$	−6.46077	−0.498459
$169$	10.0512	0.773166
$170$	0	0
$171$	21.1247	1.61544
$172$	4.28913	0.327043
$173$	22.6902	1.72510	0.862551	−	0.505969i	$-0.168865\pi$
$173$	22.6902	1.72510	0.862551	+	0.505969i	$0.168865\pi$
$174$	−41.6669	−3.15876
$175$	0	0
$176$	−13.3126	−1.00347
$177$	29.2689	2.19998
$178$	18.1939	1.36369
$179$	−4.80475	−0.359124	−0.179562	−	0.983747i	$-0.557468\pi$
$179$	−4.80475	−0.359124	−0.179562	+	0.983747i	$0.557468\pi$
$180$	0	0
$181$	11.1636	0.829783	0.414891	−	0.909871i	$-0.363820\pi$
$181$	11.1636	0.829783	0.414891	+	0.909871i	$0.363820\pi$
$182$	−8.06424	−0.597761
$183$	−23.2997	−1.72236
$184$	1.97996	0.145965
$185$	0	0
$186$	−43.8846	−3.21777
$187$	8.59039	0.628192
$188$	−5.75274	−0.419562
$189$	−15.1657	−1.10314
$190$	0	0
$191$	26.1982	1.89564	0.947819	−	0.318810i	$-0.103283\pi$
$191$	26.1982	1.89564	0.947819	+	0.318810i	$0.103283\pi$
$192$	−8.39102	−0.605569
$193$	−24.7210	−1.77946	−0.889729	−	0.456490i	$-0.849106\pi$
$193$	−24.7210	−1.77946	−0.889729	+	0.456490i	$0.849106\pi$
$194$	−6.27193	−0.450298
$195$	0	0
$196$	0.821201	0.0586572
$197$	−3.38673	−0.241295	−0.120647	−	0.992695i	$-0.538497\pi$
$197$	−3.38673	−0.241295	−0.120647	+	0.992695i	$0.538497\pi$
$198$	−34.4210	−2.44619
$199$	−18.3782	−1.30279	−0.651397	−	0.758737i	$-0.725817\pi$
$199$	−18.3782	−1.30279	−0.651397	+	0.758737i	$0.725817\pi$
$200$	0	0
$201$	29.5898	2.08710
$202$	25.4594	1.79132
$203$	−7.60233	−0.533579
$204$	−8.59039	−0.601448
$205$	0	0
$206$	18.9833	1.32263
$207$	7.64767	0.531550
$208$	−23.8523	−1.65386
$209$	7.40180	0.511993
$210$	0	0
$211$	−0.550480	−0.0378966	−0.0189483	−	0.999820i	$-0.506032\pi$
$211$	−0.550480	−0.0378966	−0.0189483	+	0.999820i	$0.506032\pi$
$212$	0.146830	0.0100843
$213$	20.5250	1.40635
$214$	19.0684	1.30349
$215$	0	0
$216$	−30.0275	−2.04312
$217$	−8.00696	−0.543548
$218$	1.85202	0.125435
$219$	7.98050	0.539272
$220$	0	0
$221$	15.3916	1.03535
$222$	−41.4535	−2.78218
$223$	−27.0856	−1.81378	−0.906892	−	0.421364i	$-0.861552\pi$
$223$	−27.0856	−1.81378	−0.906892	+	0.421364i	$0.861552\pi$
$224$	4.38460	0.292958
$225$	0	0
$226$	13.7375	0.913802
$227$	−2.35500	−0.156307	−0.0781534	−	0.996941i	$-0.524902\pi$
$227$	−2.35500	−0.156307	−0.0781534	+	0.996941i	$0.524902\pi$
$228$	−7.40180	−0.490196
$229$	−27.6107	−1.82457	−0.912284	−	0.409557i	$-0.865683\pi$
$229$	−27.6107	−1.82457	−0.912284	+	0.409557i	$0.865683\pi$
$230$	0	0
$231$	−8.74388	−0.575305
$232$	−15.0523	−0.988233
$233$	−3.68820	−0.241622	−0.120811	−	0.992676i	$-0.538549\pi$
$233$	−3.68820	−0.241622	−0.120811	+	0.992676i	$0.538549\pi$
$234$	−61.6727	−4.03167
$235$	0	0
$236$	−7.36594	−0.479482
$237$	25.2634	1.64103
$238$	−5.38460	−0.349032
$239$	−10.8041	−0.698857	−0.349428	−	0.936963i	$-0.613624\pi$
$239$	−10.8041	−0.698857	−0.349428	+	0.936963i	$0.613624\pi$
$240$	0	0
$241$	17.2161	1.10899	0.554494	−	0.832187i	$-0.312912\pi$
$241$	17.2161	1.10899	0.554494	+	0.832187i	$0.312912\pi$
$242$	6.41542	0.412399
$243$	−41.1176	−2.63770
$244$	5.86371	0.375386
$245$	0	0
$246$	44.8646	2.86046
$247$	13.2619	0.843836
$248$	−15.8535	−1.00670
$249$	−15.3706	−0.974073
$250$	0	0
$251$	−12.9605	−0.818057	−0.409029	−	0.912522i	$-0.634132\pi$
$251$	−12.9605	−0.818057	−0.409029	+	0.912522i	$0.634132\pi$
$252$	6.28028	0.395620
$253$	2.67964	0.168468
$254$	10.1569	0.637298
$255$	0	0
$256$	16.8408	1.05255
$257$	1.80758	0.112754	0.0563769	−	0.998410i	$-0.482045\pi$
$257$	1.80758	0.112754	0.0563769	+	0.998410i	$0.482045\pi$
$258$	28.6262	1.78219
$259$	−7.56340	−0.469967
$260$	0	0
$261$	−58.1401	−3.59878
$262$	−20.2865	−1.25330
$263$	−1.70894	−0.105378	−0.0526888	−	0.998611i	$-0.516779\pi$
$263$	−1.70894	−0.105378	−0.0526888	+	0.998611i	$0.516779\pi$
$264$	−17.3126	−1.06551
$265$	0	0
$266$	−4.63957	−0.284470
$267$	35.3456	2.16312
$268$	−7.44670	−0.454880
$269$	−1.46574	−0.0893676	−0.0446838	−	0.999001i	$-0.514228\pi$
$269$	−1.46574	−0.0893676	−0.0446838	+	0.999001i	$0.514228\pi$
$270$	0	0
$271$	−9.91548	−0.602323	−0.301161	−	0.953573i	$-0.597374\pi$
$271$	−9.91548	−0.602323	−0.301161	+	0.953573i	$0.597374\pi$
$272$	−15.9265	−0.965686
$273$	−15.6666	−0.948184
$274$	20.3827	1.23136
$275$	0	0
$276$	−2.67964	−0.161296
$277$	−19.2414	−1.15611	−0.578053	−	0.815999i	$-0.696187\pi$
$277$	−19.2414	−1.15611	−0.578053	+	0.815999i	$0.696187\pi$
$278$	10.7014	0.641826
$279$	−61.2346	−3.66602
$280$	0	0
$281$	−23.9218	−1.42705	−0.713527	−	0.700628i	$-0.752903\pi$
$281$	−23.9218	−1.42705	−0.713527	+	0.700628i	$0.752903\pi$
$282$	−38.3945	−2.28636
$283$	−2.51919	−0.149751	−0.0748753	−	0.997193i	$-0.523856\pi$
$283$	−2.51919	−0.149751	−0.0748753	+	0.997193i	$0.523856\pi$
$284$	−5.16542	−0.306511
$285$	0	0
$286$	−21.6093	−1.27778
$287$	8.18576	0.483190
$288$	33.5320	1.97589
$289$	−6.72286	−0.395462
$290$	0	0
$291$	−12.1846	−0.714275
$292$	−2.00841	−0.117533
$293$	24.8657	1.45267	0.726335	−	0.687341i	$-0.241222\pi$
$293$	24.8657	1.45267	0.726335	+	0.687341i	$0.241222\pi$
$294$	5.48081	0.319647
$295$	0	0
$296$	−14.9752	−0.870418
$297$	−40.6387	−2.35810
$298$	−36.4981	−2.11428
$299$	4.80116	0.277658
$300$	0	0
$301$	5.22300	0.301049
$302$	24.8631	1.43071
$303$	49.4605	2.84143
$304$	−13.7229	−0.787060
$305$	0	0
$306$	−41.1796	−2.35408
$307$	−9.38101	−0.535403	−0.267701	−	0.963502i	$-0.586264\pi$
$307$	−9.38101	−0.535403	−0.267701	+	0.963502i	$0.586264\pi$
$308$	2.20053	0.125387
$309$	36.8793	2.09799
$310$	0	0
$311$	23.8487	1.35234	0.676169	−	0.736747i	$-0.263639\pi$
$311$	23.8487	1.35234	0.676169	+	0.736747i	$0.263639\pi$
$312$	−31.0192	−1.75612
$313$	25.3661	1.43378	0.716888	−	0.697188i	$-0.245566\pi$
$313$	25.3661	1.43378	0.716888	+	0.697188i	$0.245566\pi$
$314$	24.8222	1.40080
$315$	0	0
$316$	−6.35790	−0.357660
$317$	−34.5102	−1.93829	−0.969144	−	0.246495i	$-0.920721\pi$
$317$	−34.5102	−1.93829	−0.969144	+	0.246495i	$0.920721\pi$
$318$	0.979961	0.0549535
$319$	−20.3715	−1.14059
$320$	0	0
$321$	37.0445	2.06762
$322$	−1.67964	−0.0936029
$323$	8.85516	0.492714
$324$	21.7979	1.21099
$325$	0	0
$326$	−16.5367	−0.915883
$327$	3.59796	0.198968
$328$	16.2075	0.894909
$329$	−7.00527	−0.386213
$330$	0	0
$331$	20.4556	1.12434	0.562170	−	0.827022i	$-0.309967\pi$
$331$	20.4556	1.12434	0.562170	+	0.827022i	$0.309967\pi$
$332$	3.86824	0.212297
$333$	−57.8424	−3.16974
$334$	−17.0234	−0.931480
$335$	0	0
$336$	16.2111	0.884386
$337$	10.7728	0.586831	0.293415	−	0.955985i	$-0.405208\pi$
$337$	10.7728	0.586831	0.293415	+	0.955985i	$0.405208\pi$
$338$	−16.8824	−0.918280
$339$	26.6881	1.44950
$340$	0	0
$341$	−21.4558	−1.16190
$342$	−35.4819	−1.91864
$343$	1.00000	0.0539949
$344$	10.3413	0.557568
$345$	0	0
$346$	−38.1114	−2.04888
$347$	−19.8084	−1.06337	−0.531684	−	0.846943i	$-0.678441\pi$
$347$	−19.8084	−1.06337	−0.531684	+	0.846943i	$0.678441\pi$
$348$	20.3715	1.09203
$349$	−7.80498	−0.417791	−0.208896	−	0.977938i	$-0.566987\pi$
$349$	−7.80498	−0.417791	−0.208896	+	0.977938i	$0.566987\pi$
$350$	0	0
$351$	−72.8131	−3.88648
$352$	11.7492	0.626232
$353$	27.9409	1.48714	0.743572	−	0.668656i	$-0.233130\pi$
$353$	27.9409	1.48714	0.743572	+	0.668656i	$0.233130\pi$
$354$	−49.1613	−2.61289
$355$	0	0
$356$	−8.89524	−0.471447
$357$	−10.4608	−0.553643
$358$	8.07026	0.426526
$359$	−22.4839	−1.18666	−0.593329	−	0.804960i	$-0.702187\pi$
$359$	−22.4839	−1.18666	−0.593329	+	0.804960i	$0.702187\pi$
$360$	0	0
$361$	−11.3701	−0.598425
$362$	−18.7508	−0.985522
$363$	12.4634	0.654157
$364$	3.94272	0.206655
$365$	0	0
$366$	39.1352	2.04563
$367$	17.4355	0.910127	0.455063	−	0.890459i	$-0.349617\pi$
$367$	17.4355	0.910127	0.455063	+	0.890459i	$0.349617\pi$
$368$	−4.96803	−0.258977
$369$	62.6020	3.25893
$370$	0	0
$371$	0.178799	0.00928277
$372$	21.4558	1.11243
$373$	−2.03991	−0.105623	−0.0528114	−	0.998605i	$-0.516818\pi$
$373$	−2.03991	−0.105623	−0.0528114	+	0.998605i	$0.516818\pi$
$374$	−14.4288	−0.746095
$375$	0	0
$376$	−13.8702	−0.715299
$377$	−36.5000	−1.87985
$378$	25.4730	1.31019
$379$	4.97399	0.255497	0.127748	−	0.991807i	$-0.459225\pi$
$379$	4.97399	0.255497	0.127748	+	0.991807i	$0.459225\pi$
$380$	0	0
$381$	19.7320	1.01090
$382$	−44.0037	−2.25142
$383$	−35.6475	−1.82150	−0.910752	−	0.412954i	$-0.864497\pi$
$383$	−35.6475	−1.82150	−0.910752	+	0.412954i	$0.864497\pi$
$384$	42.7085	2.17946
$385$	0	0
$386$	41.5225	2.11344
$387$	39.9438	2.03046
$388$	3.06644	0.155675
$389$	32.7559	1.66079	0.830394	−	0.557176i	$-0.188115\pi$
$389$	32.7559	1.66079	0.830394	+	0.557176i	$0.188115\pi$
$390$	0	0
$391$	3.20580	0.162124
$392$	1.97996	0.100003
$393$	−39.4110	−1.98802
$394$	5.68850	0.286582
$395$	0	0
$396$	16.8289	0.845684
$397$	9.09094	0.456261	0.228131	−	0.973631i	$-0.426739\pi$
$397$	9.09094	0.456261	0.228131	+	0.973631i	$0.426739\pi$
$398$	30.8688	1.54731
$399$	−9.01338	−0.451233
$400$	0	0
$401$	−35.3045	−1.76302	−0.881512	−	0.472161i	$-0.843474\pi$
$401$	−35.3045	−1.76302	−0.881512	+	0.472161i	$0.843474\pi$
$402$	−49.7003	−2.47882
$403$	−38.4427	−1.91497
$404$	−12.4474	−0.619284
$405$	0	0
$406$	12.7692	0.633724
$407$	−20.2672	−1.00461
$408$	−20.7119	−1.02539
$409$	22.5988	1.11744	0.558719	−	0.829357i	$-0.311293\pi$
$409$	22.5988	1.11744	0.558719	+	0.829357i	$0.311293\pi$
$410$	0	0
$411$	39.5979	1.95322
$412$	−9.28122	−0.457253
$413$	−8.96972	−0.441371
$414$	−12.8454	−0.631315
$415$	0	0
$416$	21.0512	1.03212
$417$	20.7898	1.01808
$418$	−12.4324	−0.608088
$419$	26.9997	1.31902	0.659511	−	0.751695i	$-0.270764\pi$
$419$	26.9997	1.31902	0.659511	+	0.751695i	$0.270764\pi$
$420$	0	0
$421$	4.61571	0.224956	0.112478	−	0.993654i	$-0.464121\pi$
$421$	4.61571	0.224956	0.112478	+	0.993654i	$0.464121\pi$
$422$	0.924610	0.0450093
$423$	−53.5740	−2.60486
$424$	0.354015	0.0171925
$425$	0	0
$426$	−34.4747	−1.67030
$427$	7.14041	0.345549
$428$	−9.32279	−0.450634
$429$	−41.9808	−2.02685
$430$	0	0
$431$	12.5937	0.606616	0.303308	−	0.952893i	$-0.401909\pi$
$431$	12.5937	0.606616	0.303308	+	0.952893i	$0.401909\pi$
$432$	75.3438	3.62498
$433$	24.7452	1.18918	0.594589	−	0.804030i	$-0.297315\pi$
$433$	24.7452	1.18918	0.594589	+	0.804030i	$0.297315\pi$
$434$	13.4488	0.645565
$435$	0	0
$436$	−0.905480	−0.0433646
$437$	2.76223	0.132136
$438$	−13.4044	−0.640487
$439$	−22.3702	−1.06767	−0.533835	−	0.845589i	$-0.679250\pi$
$439$	−22.3702	−1.06767	−0.533835	+	0.845589i	$0.679250\pi$
$440$	0	0
$441$	7.64767	0.364175
$442$	−25.8523	−1.22967
$443$	−15.3963	−0.731500	−0.365750	−	0.930713i	$-0.619187\pi$
$443$	−15.3963	−0.731500	−0.365750	+	0.930713i	$0.619187\pi$
$444$	20.2672	0.961839
$445$	0	0
$446$	45.4941	2.15421
$447$	−70.9056	−3.35372
$448$	2.57150	0.121492
$449$	26.9712	1.27285	0.636424	−	0.771339i	$-0.280413\pi$
$449$	26.9712	1.27285	0.636424	+	0.771339i	$0.280413\pi$
$450$	0	0
$451$	21.9349	1.03287
$452$	−6.71644	−0.315915
$453$	48.3021	2.26943
$454$	3.95556	0.185644
$455$	0	0
$456$	−17.8461	−0.835722
$457$	12.4710	0.583369	0.291685	−	0.956515i	$-0.405784\pi$
$457$	12.4710	0.583369	0.291685	+	0.956515i	$0.405784\pi$
$458$	46.3762	2.16702
$459$	−48.6182	−2.26930
$460$	0	0
$461$	1.29603	0.0603622	0.0301811	−	0.999544i	$-0.490392\pi$
$461$	1.29603	0.0603622	0.0301811	+	0.999544i	$0.490392\pi$
$462$	14.6866	0.683283
$463$	−41.6886	−1.93743	−0.968717	−	0.248169i	$-0.920171\pi$
$463$	−41.6886	−1.93743	−0.968717	+	0.248169i	$0.920171\pi$
$464$	37.7686	1.75336
$465$	0	0
$466$	6.19485	0.286971
$467$	30.3134	1.40274	0.701368	−	0.712799i	$-0.252573\pi$
$467$	30.3134	1.40274	0.701368	+	0.712799i	$0.252573\pi$
$468$	30.1526	1.39381
$469$	−9.06806	−0.418724
$470$	0	0
$471$	48.2227	2.22198
$472$	−17.7597	−0.817456
$473$	13.9958	0.643526
$474$	−42.4335	−1.94903
$475$	0	0
$476$	2.63261	0.120665
$477$	1.36739	0.0626087
$478$	18.1470	0.830023
$479$	18.8138	0.859626	0.429813	−	0.902918i	$-0.358579\pi$
$479$	18.8138	0.859626	0.429813	+	0.902918i	$0.358579\pi$
$480$	0	0
$481$	−36.3131	−1.65573
$482$	−28.9170	−1.31713
$483$	−3.26308	−0.148475
$484$	−3.13659	−0.142572
$485$	0	0
$486$	69.0629	3.13276
$487$	−25.0431	−1.13481	−0.567405	−	0.823439i	$-0.692052\pi$
$487$	−25.0431	−1.13481	−0.567405	+	0.823439i	$0.692052\pi$
$488$	14.1377	0.639985
$489$	−32.1262	−1.45280
$490$	0	0
$491$	−6.72080	−0.303306	−0.151653	−	0.988434i	$-0.548460\pi$
$491$	−6.72080	−0.303306	−0.151653	+	0.988434i	$0.548460\pi$
$492$	−21.9349	−0.988902
$493$	−24.3715	−1.09764
$494$	−22.2753	−1.00221
$495$	0	0
$496$	39.7788	1.78612
$497$	−6.29008	−0.282148
$498$	25.8171	1.15689
$499$	−29.0096	−1.29865	−0.649325	−	0.760511i	$-0.724948\pi$
$499$	−29.0096	−1.29865	−0.649325	+	0.760511i	$0.724948\pi$
$500$	0	0
$501$	−33.0717	−1.47754
$502$	21.7690	0.971596
$503$	−9.75253	−0.434844	−0.217422	−	0.976078i	$-0.569765\pi$
$503$	−9.75253	−0.434844	−0.217422	+	0.976078i	$0.569765\pi$
$504$	15.1421	0.674483
$505$	0	0
$506$	−4.50084	−0.200087
$507$	−32.7977	−1.45660
$508$	−4.96583	−0.220323
$509$	26.9981	1.19667	0.598336	−	0.801245i	$-0.295829\pi$
$509$	26.9981	1.19667	0.598336	+	0.801245i	$0.295829\pi$
$510$	0	0
$511$	−2.44570	−0.108191
$512$	−2.10979	−0.0932406
$513$	−41.8913	−1.84954
$514$	−3.03609	−0.133916
$515$	0	0
$516$	−13.9958	−0.616130
$517$	−18.7716	−0.825575
$518$	12.7038	0.558173
$519$	−74.0398	−3.24999
$520$	0	0
$521$	13.4672	0.590008	0.295004	−	0.955496i	$-0.404679\pi$
$521$	13.4672	0.590008	0.295004	+	0.955496i	$0.404679\pi$
$522$	97.6546	4.27423
$523$	25.4845	1.11436	0.557179	−	0.830392i	$-0.311884\pi$
$523$	25.4845	1.11436	0.557179	+	0.830392i	$0.311884\pi$
$524$	9.91835	0.433285
$525$	0	0
$526$	2.87041	0.125156
$527$	−25.6687	−1.11815
$528$	43.4399	1.89048
$529$	1.00000	0.0434783
$530$	0	0
$531$	−68.5975	−2.97688
$532$	2.26835	0.0983454
$533$	39.3012	1.70232
$534$	−59.3680	−2.56910
$535$	0	0
$536$	−17.9544	−0.775512
$537$	15.6783	0.676567
$538$	2.46191	0.106141
$539$	2.67964	0.115420
$540$	0	0
$541$	−16.4540	−0.707413	−0.353707	−	0.935356i	$-0.615079\pi$
$541$	−16.4540	−0.707413	−0.353707	+	0.935356i	$0.615079\pi$
$542$	16.6545	0.715371
$543$	−36.4277	−1.56326
$544$	14.0561	0.602652
$545$	0	0
$546$	26.3142	1.12615
$547$	20.6818	0.884289	0.442144	−	0.896944i	$-0.354218\pi$
$547$	20.6818	0.884289	0.442144	+	0.896944i	$0.354218\pi$
$548$	−9.96539	−0.425700
$549$	54.6075	2.33059
$550$	0	0
$551$	−20.9994	−0.894604
$552$	−6.46077	−0.274989
$553$	−7.74219	−0.329232
$554$	32.3188	1.37309
$555$	0	0
$556$	−5.23205	−0.221888
$557$	−18.1276	−0.768093	−0.384046	−	0.923314i	$-0.625470\pi$
$557$	−18.1276	−0.768093	−0.384046	+	0.923314i	$0.625470\pi$
$558$	102.852	4.35409
$559$	25.0765	1.06062
$560$	0	0
$561$	−28.0311	−1.18347
$562$	40.1800	1.69489
$563$	−27.5014	−1.15905	−0.579523	−	0.814956i	$-0.696761\pi$
$563$	−27.5014	−1.15905	−0.579523	+	0.814956i	$0.696761\pi$
$564$	18.7716	0.790428
$565$	0	0
$566$	4.23135	0.177857
$567$	26.5439	1.11474
$568$	−12.4541	−0.522563
$569$	34.0356	1.42685	0.713424	−	0.700732i	$-0.247143\pi$
$569$	34.0356	1.42685	0.713424	+	0.700732i	$0.247143\pi$
$570$	0	0
$571$	−39.3673	−1.64747	−0.823736	−	0.566974i	$-0.808114\pi$
$571$	−39.3673	−1.64747	−0.823736	+	0.566974i	$0.808114\pi$
$572$	10.5651	0.441748
$573$	−85.4869	−3.57126
$574$	−13.7492	−0.573879
$575$	0	0
$576$	19.6660	0.819418
$577$	22.6021	0.940937	0.470469	−	0.882417i	$-0.344085\pi$
$577$	22.6021	0.940937	0.470469	+	0.882417i	$0.344085\pi$
$578$	11.2920	0.469685
$579$	80.6666	3.35239
$580$	0	0
$581$	4.71046	0.195423
$582$	20.4658	0.848335
$583$	0.479117	0.0198430
$584$	−4.84239	−0.200379
$585$	0	0
$586$	−41.7655	−1.72532
$587$	32.7051	1.34988	0.674942	−	0.737871i	$-0.264169\pi$
$587$	32.7051	1.34988	0.674942	+	0.737871i	$0.264169\pi$
$588$	−2.67964	−0.110507
$589$	−22.1171	−0.911319
$590$	0	0
$591$	11.0512	0.454584
$592$	37.5752	1.54433
$593$	−26.2375	−1.07744	−0.538722	−	0.842484i	$-0.681093\pi$
$593$	−26.2375	−1.07744	−0.538722	+	0.842484i	$0.681093\pi$
$594$	68.2585	2.80068
$595$	0	0
$596$	17.8444	0.730936
$597$	59.9694	2.45438
$598$	−8.06424	−0.329771
$599$	11.9920	0.489979	0.244990	−	0.969526i	$-0.421215\pi$
$599$	11.9920	0.489979	0.244990	+	0.969526i	$0.421215\pi$
$600$	0	0
$601$	−4.63520	−0.189074	−0.0945369	−	0.995521i	$-0.530137\pi$
$601$	−4.63520	−0.189074	−0.0945369	+	0.995521i	$0.530137\pi$
$602$	−8.77278	−0.357552
$603$	−69.3496	−2.82413
$604$	−12.1559	−0.494618
$605$	0	0
$606$	−83.0759	−3.37473
$607$	12.7869	0.519003	0.259502	−	0.965743i	$-0.416442\pi$
$607$	12.7869	0.519003	0.259502	+	0.965743i	$0.416442\pi$
$608$	12.1113	0.491177
$609$	24.8070	1.00523
$610$	0	0
$611$	−33.6334	−1.36066
$612$	20.1333	0.813841
$613$	19.3148	0.780117	0.390058	−	0.920790i	$-0.372455\pi$
$613$	19.3148	0.780117	0.390058	+	0.920790i	$0.372455\pi$
$614$	15.7568	0.635891
$615$	0	0
$616$	5.30559	0.213768
$617$	−24.5587	−0.988697	−0.494349	−	0.869264i	$-0.664593\pi$
$617$	−24.5587	−0.988697	−0.494349	+	0.869264i	$0.664593\pi$
$618$	−61.9441	−2.49176
$619$	16.7349	0.672632	0.336316	−	0.941749i	$-0.390819\pi$
$619$	16.7349	0.672632	0.336316	+	0.941749i	$0.390819\pi$
$620$	0	0
$621$	−15.1657	−0.608579
$622$	−40.0574	−1.60615
$623$	−10.8320	−0.433974
$624$	77.8320	3.11577
$625$	0	0
$626$	−42.6060	−1.70288
$627$	−24.1526	−0.964564
$628$	−12.1359	−0.484277
$629$	−24.2467	−0.966780
$630$	0	0
$631$	−12.8320	−0.510833	−0.255417	−	0.966831i	$-0.582213\pi$
$631$	−12.8320	−0.510833	−0.255417	+	0.966831i	$0.582213\pi$
$632$	−15.3292	−0.609765
$633$	1.79626	0.0713949
$634$	57.9649	2.30208
$635$	0	0
$636$	−0.479117	−0.0189982
$637$	4.80116	0.190229
$638$	34.2169	1.35466
$639$	−48.1045	−1.90298
$640$	0	0
$641$	0.471994	0.0186426	0.00932132	−	0.999957i	$-0.497033\pi$
$641$	0.471994	0.0186426	0.00932132	+	0.999957i	$0.497033\pi$
$642$	−62.2215	−2.45569
$643$	19.6766	0.775969	0.387985	−	0.921666i	$-0.373171\pi$
$643$	19.6766	0.775969	0.387985	+	0.921666i	$0.373171\pi$
$644$	0.821201	0.0323599
$645$	0	0
$646$	−14.8735	−0.585190
$647$	3.28434	0.129121	0.0645604	−	0.997914i	$-0.479435\pi$
$647$	3.28434	0.129121	0.0645604	+	0.997914i	$0.479435\pi$
$648$	52.5559	2.06459
$649$	−24.0356	−0.943482
$650$	0	0
$651$	26.1273	1.02401
$652$	8.08502	0.316634
$653$	41.8409	1.63736	0.818681	−	0.574248i	$-0.194706\pi$
$653$	41.8409	1.63736	0.818681	+	0.574248i	$0.194706\pi$
$654$	−6.04329	−0.236311
$655$	0	0
$656$	−40.6671	−1.58778
$657$	−18.7039	−0.729709
$658$	11.7664	0.458700
$659$	28.8414	1.12350	0.561750	−	0.827307i	$-0.310128\pi$
$659$	28.8414	1.12350	0.561750	+	0.827307i	$0.310128\pi$
$660$	0	0
$661$	−31.5995	−1.22908	−0.614539	−	0.788886i	$-0.710658\pi$
$661$	−31.5995	−1.22908	−0.614539	+	0.788886i	$0.710658\pi$
$662$	−34.3580	−1.33536
$663$	−50.2238	−1.95053
$664$	9.32654	0.361940
$665$	0	0
$666$	97.1546	3.76466
$667$	−7.60233	−0.294363
$668$	8.32299	0.322026
$669$	88.3823	3.41706
$670$	0	0
$671$	19.1338	0.738650
$672$	−14.3073	−0.551915
$673$	29.1165	1.12236	0.561180	−	0.827694i	$-0.310347\pi$
$673$	29.1165	1.12236	0.561180	+	0.827694i	$0.310347\pi$
$674$	−18.0944	−0.696971
$675$	0	0
$676$	8.25403	0.317463
$677$	33.7943	1.29882	0.649410	−	0.760439i	$-0.275016\pi$
$677$	33.7943	1.29882	0.649410	+	0.760439i	$0.275016\pi$
$678$	−44.8264	−1.72155
$679$	3.73409	0.143301
$680$	0	0
$681$	7.68455	0.294472
$682$	36.0381	1.37997
$683$	−1.54422	−0.0590880	−0.0295440	−	0.999563i	$-0.509406\pi$
$683$	−1.54422	−0.0590880	−0.0295440	+	0.999563i	$0.509406\pi$
$684$	17.3476	0.663302
$685$	0	0
$686$	−1.67964	−0.0641291
$687$	90.0960	3.43738
$688$	−25.9480	−0.989259
$689$	0.858442	0.0327040
$690$	0	0
$691$	−14.5264	−0.552609	−0.276304	−	0.961070i	$-0.589110\pi$
$691$	−14.5264	−0.552609	−0.276304	+	0.961070i	$0.589110\pi$
$692$	18.6332	0.708328
$693$	20.4930	0.778466
$694$	33.2710	1.26295
$695$	0	0
$696$	49.1169	1.86177
$697$	26.2419	0.993982
$698$	13.1096	0.496205
$699$	12.0349	0.455201
$700$	0	0
$701$	15.7337	0.594254	0.297127	−	0.954838i	$-0.403972\pi$
$701$	15.7337	0.594254	0.297127	+	0.954838i	$0.403972\pi$
$702$	122.300	4.61592
$703$	−20.8919	−0.787951
$704$	6.89071	0.259704
$705$	0	0
$706$	−46.9307	−1.76626
$707$	−15.1576	−0.570061
$708$	24.0356	0.903315
$709$	−24.7380	−0.929055	−0.464528	−	0.885559i	$-0.653776\pi$
$709$	−24.7380	−0.929055	−0.464528	+	0.885559i	$0.653776\pi$
$710$	0	0
$711$	−59.2098	−2.22054
$712$	−21.4469	−0.803757
$713$	−8.00696	−0.299863
$714$	17.5704	0.657554
$715$	0	0
$716$	−3.94566	−0.147456
$717$	35.2545	1.31660
$718$	37.7650	1.40938
$719$	−2.75298	−0.102669	−0.0513344	−	0.998682i	$-0.516347\pi$
$719$	−2.75298	−0.102669	−0.0513344	+	0.998682i	$0.516347\pi$
$720$	0	0
$721$	−11.3020	−0.420909
$722$	19.0977	0.710741
$723$	−56.1776	−2.08927
$724$	9.16755	0.340709
$725$	0	0
$726$	−20.9340	−0.776934
$727$	−30.8834	−1.14540	−0.572700	−	0.819765i	$-0.694104\pi$
$727$	−30.8834	−1.14540	−0.572700	+	0.819765i	$0.694104\pi$
$728$	9.50612	0.352320
$729$	54.5383	2.01994
$730$	0	0
$731$	16.7439	0.619295
$732$	−19.1338	−0.707204
$733$	−10.0586	−0.371522	−0.185761	−	0.982595i	$-0.559475\pi$
$733$	−10.0586	−0.371522	−0.185761	+	0.982595i	$0.559475\pi$
$734$	−29.2855	−1.08095
$735$	0	0
$736$	4.38460	0.161618
$737$	−24.2992	−0.895071
$738$	−105.149	−3.87059
$739$	−16.9041	−0.621828	−0.310914	−	0.950438i	$-0.600635\pi$
$739$	−16.9041	−0.621828	−0.310914	+	0.950438i	$0.600635\pi$
$740$	0	0
$741$	−43.2747	−1.58974
$742$	−0.300318	−0.0110250
$743$	40.8918	1.50017	0.750087	−	0.661339i	$-0.230011\pi$
$743$	40.8918	1.50017	0.750087	+	0.661339i	$0.230011\pi$
$744$	51.7311	1.89655
$745$	0	0
$746$	3.42633	0.125447
$747$	36.0241	1.31805
$748$	7.05444	0.257936
$749$	−11.3526	−0.414816
$750$	0	0
$751$	14.1108	0.514910	0.257455	−	0.966290i	$-0.417116\pi$
$751$	14.1108	0.514910	0.257455	+	0.966290i	$0.417116\pi$
$752$	34.8024	1.26911
$753$	42.2910	1.54117
$754$	61.3070	2.23267
$755$	0	0
$756$	−12.4541	−0.452952
$757$	21.6387	0.786470	0.393235	−	0.919438i	$-0.371356\pi$
$757$	21.6387	0.786470	0.393235	+	0.919438i	$0.371356\pi$
$758$	−8.35452	−0.303450
$759$	−8.74388	−0.317383
$760$	0	0
$761$	−10.9224	−0.395936	−0.197968	−	0.980208i	$-0.563434\pi$
$761$	−10.9224	−0.395936	−0.197968	+	0.980208i	$0.563434\pi$
$762$	−33.1426	−1.20063
$763$	−1.10263	−0.0399178
$764$	21.5140	0.778350
$765$	0	0
$766$	59.8751	2.16338
$767$	−43.0651	−1.55499
$768$	−54.9530	−1.98294
$769$	−39.6918	−1.43132	−0.715662	−	0.698447i	$-0.753875\pi$
$769$	−39.6918	−1.43132	−0.715662	+	0.698447i	$0.753875\pi$
$770$	0	0
$771$	−5.89828	−0.212421
$772$	−20.3009	−0.730646
$773$	47.8917	1.72255	0.861273	−	0.508143i	$-0.169668\pi$
$773$	47.8917	1.72255	0.861273	+	0.508143i	$0.169668\pi$
$774$	−67.0913	−2.41155
$775$	0	0
$776$	7.39335	0.265406
$777$	24.6799	0.885388
$778$	−55.0182	−1.97250
$779$	22.6110	0.810122
$780$	0	0
$781$	−16.8552	−0.603125
$782$	−5.38460	−0.192553
$783$	115.295	4.12030
$784$	−4.96803	−0.177430
$785$	0	0
$786$	66.1964	2.36115
$787$	13.4304	0.478742	0.239371	−	0.970928i	$-0.423059\pi$
$787$	13.4304	0.478742	0.239371	+	0.970928i	$0.423059\pi$
$788$	−2.78119	−0.0990757
$789$	5.57640	0.198525
$790$	0	0
$791$	−8.17880	−0.290805
$792$	40.5754	1.44178
$793$	34.2823	1.21740
$794$	−15.2695	−0.541895
$795$	0	0
$796$	−15.0922	−0.534928
$797$	4.64951	0.164694	0.0823470	−	0.996604i	$-0.473758\pi$
$797$	4.64951	0.164694	0.0823470	+	0.996604i	$0.473758\pi$
$798$	15.1393	0.535924
$799$	−22.4575	−0.794489
$800$	0	0
$801$	−82.8395	−2.92699
$802$	59.2990	2.09392
$803$	−6.55360	−0.231271
$804$	24.2992	0.856966
$805$	0	0
$806$	64.5701	2.27438
$807$	4.78281	0.168363
$808$	−30.0115	−1.05580
$809$	19.1296	0.672563	0.336281	−	0.941762i	$-0.390831\pi$
$809$	19.1296	0.672563	0.336281	+	0.941762i	$0.390831\pi$
$810$	0	0
$811$	−46.6536	−1.63823	−0.819116	−	0.573628i	$-0.805535\pi$
$811$	−46.6536	−1.63823	−0.819116	+	0.573628i	$0.805535\pi$
$812$	−6.24304	−0.219088
$813$	32.3550	1.13474
$814$	34.0417	1.19316
$815$	0	0
$816$	51.9694	1.81929
$817$	14.4271	0.504742
$818$	−37.9579	−1.32717
$819$	36.7177	1.28302
$820$	0	0
$821$	−8.23992	−0.287575	−0.143788	−	0.989609i	$-0.545928\pi$
$821$	−8.23992	−0.287575	−0.143788	+	0.989609i	$0.545928\pi$
$822$	−66.5103	−2.31981
$823$	−10.7290	−0.373990	−0.186995	−	0.982361i	$-0.559875\pi$
$823$	−10.7290	−0.373990	−0.186995	+	0.982361i	$0.559875\pi$
$824$	−22.3775	−0.779558
$825$	0	0
$826$	15.0659	0.524211
$827$	−6.55812	−0.228048	−0.114024	−	0.993478i	$-0.536374\pi$
$827$	−6.55812	−0.228048	−0.114024	+	0.993478i	$0.536374\pi$
$828$	6.28028	0.218255
$829$	−40.2596	−1.39827	−0.699136	−	0.714989i	$-0.746432\pi$
$829$	−40.2596	−1.39827	−0.699136	+	0.714989i	$0.746432\pi$
$830$	0	0
$831$	62.7863	2.17803
$832$	12.3462	0.428028
$833$	3.20580	0.111074
$834$	−34.9194	−1.20916
$835$	0	0
$836$	6.07837	0.210225
$837$	121.431	4.19728
$838$	−45.3499	−1.56658
$839$	−47.0571	−1.62459	−0.812295	−	0.583246i	$-0.801782\pi$
$839$	−47.0571	−1.62459	−0.812295	+	0.583246i	$0.801782\pi$
$840$	0	0
$841$	28.7953	0.992943
$842$	−7.75274	−0.267177
$843$	78.0586	2.68848
$844$	−0.452055	−0.0155604
$845$	0	0
$846$	89.9853	3.09376
$847$	−3.81951	−0.131240
$848$	−0.888278	−0.0305036
$849$	8.22033	0.282121
$850$	0	0
$851$	−7.56340	−0.259270
$852$	16.8552	0.577448
$853$	31.5132	1.07899	0.539495	−	0.841989i	$-0.318615\pi$
$853$	31.5132	1.07899	0.539495	+	0.841989i	$0.318615\pi$
$854$	−11.9933	−0.410404
$855$	0	0
$856$	−22.4778	−0.768274
$857$	41.9712	1.43371	0.716855	−	0.697222i	$-0.245581\pi$
$857$	41.9712	1.43371	0.716855	+	0.697222i	$0.245581\pi$
$858$	70.5128	2.40727
$859$	13.6155	0.464554	0.232277	−	0.972650i	$-0.425382\pi$
$859$	13.6155	0.464554	0.232277	+	0.972650i	$0.425382\pi$
$860$	0	0
$861$	−26.7108	−0.910300
$862$	−21.1529	−0.720470
$863$	−21.9714	−0.747915	−0.373958	−	0.927446i	$-0.621999\pi$
$863$	−21.9714	−0.747915	−0.373958	+	0.927446i	$0.621999\pi$
$864$	−66.4956	−2.26223
$865$	0	0
$866$	−41.5631	−1.41237
$867$	21.9372	0.745027
$868$	−6.57533	−0.223181
$869$	−20.7463	−0.703771
$870$	0	0
$871$	−43.5372	−1.47520
$872$	−2.18316	−0.0739312
$873$	28.5571	0.966510
$874$	−4.63957	−0.156936
$875$	0	0
$876$	6.55360	0.221426
$877$	21.4899	0.725662	0.362831	−	0.931855i	$-0.381810\pi$
$877$	21.4899	0.725662	0.362831	+	0.931855i	$0.381810\pi$
$878$	37.5739	1.26806
$879$	−81.1387	−2.73674
$880$	0	0
$881$	8.41612	0.283546	0.141773	−	0.989899i	$-0.454720\pi$
$881$	8.41612	0.283546	0.141773	+	0.989899i	$0.454720\pi$
$882$	−12.8454	−0.432526
$883$	10.5555	0.355221	0.177611	−	0.984101i	$-0.443163\pi$
$883$	10.5555	0.355221	0.177611	+	0.984101i	$0.443163\pi$
$884$	12.6396	0.425115
$885$	0	0
$886$	25.8603	0.868793
$887$	−33.8411	−1.13627	−0.568136	−	0.822934i	$-0.692335\pi$
$887$	−33.8411	−1.13627	−0.568136	+	0.822934i	$0.692335\pi$
$888$	48.8653	1.63981
$889$	−6.04704	−0.202811
$890$	0	0
$891$	71.1282	2.38288
$892$	−22.2427	−0.744741
$893$	−19.3502	−0.647530
$894$	119.096	3.98317
$895$	0	0
$896$	−13.0884	−0.437253
$897$	−15.6666	−0.523091
$898$	−45.3019	−1.51175
$899$	60.8715	2.03018
$900$	0	0
$901$	0.573193	0.0190958
$902$	−36.8428	−1.22673
$903$	−17.0431	−0.567157
$904$	−16.1937	−0.538595
$905$	0	0
$906$	−81.1302	−2.69537
$907$	−38.6329	−1.28278	−0.641392	−	0.767213i	$-0.721643\pi$
$907$	−38.6329	−1.28278	−0.641392	+	0.767213i	$0.721643\pi$
$908$	−1.93393	−0.0641797
$909$	−115.920	−3.84484
$910$	0	0
$911$	6.73296	0.223073	0.111536	−	0.993760i	$-0.464423\pi$
$911$	6.73296	0.223073	0.111536	+	0.993760i	$0.464423\pi$
$912$	44.7788	1.48277
$913$	12.6224	0.417739
$914$	−20.9468	−0.692860
$915$	0	0
$916$	−22.6740	−0.749169
$917$	12.0779	0.398846
$918$	81.6613	2.69522
$919$	−2.18234	−0.0719887	−0.0359944	−	0.999352i	$-0.511460\pi$
$919$	−2.18234	−0.0719887	−0.0359944	+	0.999352i	$0.511460\pi$
$920$	0	0
$921$	30.6110	1.00867
$922$	−2.17687	−0.0716914
$923$	−30.1997	−0.994035
$924$	−7.18049	−0.236221
$925$	0	0
$926$	70.0220	2.30106
$927$	−86.4341	−2.83887
$928$	−33.3331	−1.09421
$929$	20.4040	0.669432	0.334716	−	0.942319i	$-0.391360\pi$
$929$	20.4040	0.669432	0.334716	+	0.942319i	$0.391360\pi$
$930$	0	0
$931$	2.76223	0.0905285
$932$	−3.02875	−0.0992100
$933$	−77.8203	−2.54772
$934$	−50.9157	−1.66601
$935$	0	0
$936$	72.6997	2.37626
$937$	−38.4028	−1.25457	−0.627283	−	0.778791i	$-0.715833\pi$
$937$	−38.4028	−1.25457	−0.627283	+	0.778791i	$0.715833\pi$
$938$	15.2311	0.497313
$939$	−82.7715	−2.70115
$940$	0	0
$941$	−41.8317	−1.36368	−0.681838	−	0.731503i	$-0.738819\pi$
$941$	−41.8317	−1.36368	−0.681838	+	0.731503i	$0.738819\pi$
$942$	−80.9969	−2.63902
$943$	8.18576	0.266565
$944$	44.5618	1.45036
$945$	0	0
$946$	−23.5079	−0.764308
$947$	23.7548	0.771927	0.385964	−	0.922514i	$-0.373869\pi$
$947$	23.7548	0.771927	0.385964	+	0.922514i	$0.373869\pi$
$948$	20.7463	0.673809
$949$	−11.7422	−0.381168
$950$	0	0
$951$	112.610	3.65162
$952$	6.34736	0.205719
$953$	−15.6317	−0.506360	−0.253180	−	0.967419i	$-0.581476\pi$
$953$	−15.6317	−0.506360	−0.253180	+	0.967419i	$0.581476\pi$
$954$	−2.29674	−0.0743595
$955$	0	0
$956$	−8.87231	−0.286951
$957$	66.4738	2.14879
$958$	−31.6005	−1.02097
$959$	−12.1351	−0.391864
$960$	0	0
$961$	33.1114	1.06811
$962$	60.9930	1.96649
$963$	−86.8212	−2.79777
$964$	14.1379	0.455351
$965$	0	0
$966$	5.48081	0.176342
$967$	−48.8900	−1.57220	−0.786098	−	0.618102i	$-0.787902\pi$
$967$	−48.8900	−1.57220	−0.786098	+	0.618102i	$0.787902\pi$
$968$	−7.56249	−0.243068
$969$	−28.8951	−0.928244
$970$	0	0
$971$	7.46023	0.239410	0.119705	−	0.992810i	$-0.461805\pi$
$971$	7.46023	0.239410	0.119705	+	0.992810i	$0.461805\pi$
$972$	−33.7658	−1.08304
$973$	−6.37122	−0.204252
$974$	42.0634	1.34780
$975$	0	0
$976$	−35.4738	−1.13549
$977$	−1.29583	−0.0414572	−0.0207286	−	0.999785i	$-0.506599\pi$
$977$	−1.29583	−0.0414572	−0.0207286	+	0.999785i	$0.506599\pi$
$978$	53.9605	1.72547
$979$	−29.0259	−0.927670
$980$	0	0
$981$	−8.43254	−0.269230
$982$	11.2886	0.360232
$983$	−6.55833	−0.209178	−0.104589	−	0.994516i	$-0.533353\pi$
$983$	−6.55833	−0.209178	−0.104589	+	0.994516i	$0.533353\pi$
$984$	−52.8863	−1.68595
$985$	0	0
$986$	40.9355	1.30365
$987$	22.8587	0.727602
$988$	10.8907	0.346480
$989$	5.22300	0.166082
$990$	0	0
$991$	−4.91640	−0.156175	−0.0780874	−	0.996947i	$-0.524881\pi$
$991$	−4.91640	−0.156175	−0.0780874	+	0.996947i	$0.524881\pi$
$992$	−35.1073	−1.11466
$993$	−66.7481	−2.11819
$994$	10.5651	0.335104
$995$	0	0
$996$	−12.6224	−0.399955
$997$	−38.6696	−1.22468	−0.612340	−	0.790595i	$-0.709772\pi$
$997$	−38.6696	−1.22468	−0.612340	+	0.790595i	$0.709772\pi$
$998$	48.7258	1.54239
$999$	114.704	3.62908

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.l.1.2		4
5.4	even	2		805.2.a.j.1.3	✓	4
15.14	odd	2		7245.2.a.bc.1.2		4
35.34	odd	2		5635.2.a.w.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.a.j.1.3	✓	4	5.4	even	2
4025.2.a.l.1.2		4	1.1	even	1	trivial
5635.2.a.w.1.3		4	35.34	odd	2
7245.2.a.bc.1.2		4	15.14	odd	2

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)

\(f(q)\)	\(=\)	\(q-1.67964 q^{2} -3.26308 q^{3} +0.821201 q^{4} +5.48081 q^{6} +1.00000 q^{7} +1.97996 q^{8} +7.64767 q^{9} +O(q^{10})\)	\(q-1.67964 q^{2} -3.26308 q^{3} +0.821201 q^{4} +5.48081 q^{6} +1.00000 q^{7} +1.97996 q^{8} +7.64767 q^{9} +2.67964 q^{11} -2.67964 q^{12} +4.80116 q^{13} -1.67964 q^{14} -4.96803 q^{16} +3.20580 q^{17} -12.8454 q^{18} +2.76223 q^{19} -3.26308 q^{21} -4.50084 q^{22} +1.00000 q^{23} -6.46077 q^{24} -8.06424 q^{26} -15.1657 q^{27} +0.821201 q^{28} -7.60233 q^{29} -8.00696 q^{31} +4.38460 q^{32} -8.74388 q^{33} -5.38460 q^{34} +6.28028 q^{36} -7.56340 q^{37} -4.63957 q^{38} -15.6666 q^{39} +8.18576 q^{41} +5.48081 q^{42} +5.22300 q^{43} +2.20053 q^{44} -1.67964 q^{46} -7.00527 q^{47} +16.2111 q^{48} +1.00000 q^{49} -10.4608 q^{51} +3.94272 q^{52} +0.178799 q^{53} +25.4730 q^{54} +1.97996 q^{56} -9.01338 q^{57} +12.7692 q^{58} -8.96972 q^{59} +7.14041 q^{61} +13.4488 q^{62} +7.64767 q^{63} +2.57150 q^{64} +14.6866 q^{66} -9.06806 q^{67} +2.63261 q^{68} -3.26308 q^{69} -6.29008 q^{71} +15.1421 q^{72} -2.44570 q^{73} +12.7038 q^{74} +2.26835 q^{76} +2.67964 q^{77} +26.3142 q^{78} -7.74219 q^{79} +26.5439 q^{81} -13.7492 q^{82} +4.71046 q^{83} -2.67964 q^{84} -8.77278 q^{86} +24.8070 q^{87} +5.30559 q^{88} -10.8320 q^{89} +4.80116 q^{91} +0.821201 q^{92} +26.1273 q^{93} +11.7664 q^{94} -14.3073 q^{96} +3.73409 q^{97} -1.67964 q^{98} +20.4930 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3 q^{2} - 6 q^{3} + 3 q^{4} + 4 q^{6} + 4 q^{7} - 6 q^{8} + 6 q^{9}+O(q^{10}) \) 4 * q - 3 * q^2 - 6 * q^3 + 3 * q^4 + 4 * q^6 + 4 * q^7 - 6 * q^8 + 6 * q^9	\( 4 q - 3 q^{2} - 6 q^{3} + 3 q^{4} + 4 q^{6} + 4 q^{7} - 6 q^{8} + 6 q^{9} + 7 q^{11} - 7 q^{12} + 5 q^{13} - 3 q^{14} + q^{16} - 5 q^{17} - 2 q^{18} + 8 q^{19} - 6 q^{21} - 14 q^{22} + 4 q^{23} + 6 q^{24} - 11 q^{26} - 15 q^{27} + 3 q^{28} - 2 q^{29} - 10 q^{33} - 4 q^{34} + q^{36} - 13 q^{37} + 13 q^{38} - 13 q^{39} + q^{41} + 4 q^{42} - 14 q^{43} + 15 q^{44} - 3 q^{46} - 4 q^{47} + 23 q^{48} + 4 q^{49} - 10 q^{51} + 5 q^{52} + q^{53} + 14 q^{54} - 6 q^{56} - 19 q^{57} + 16 q^{58} - 7 q^{59} - 7 q^{61} + 15 q^{62} + 6 q^{63} + 23 q^{66} - 15 q^{67} + 11 q^{68} - 6 q^{69} + 17 q^{72} - 3 q^{73} - 2 q^{74} - 22 q^{76} + 7 q^{77} + 31 q^{78} - 14 q^{79} + 28 q^{81} - 6 q^{82} - 3 q^{83} - 7 q^{84} + 16 q^{86} + 14 q^{87} - 13 q^{88} - 11 q^{89} + 5 q^{91} + 3 q^{92} + 23 q^{93} - 19 q^{94} - 15 q^{96} - 9 q^{97} - 3 q^{98} + 8 q^{99}+O(q^{100}) \) 4 * q - 3 * q^2 - 6 * q^3 + 3 * q^4 + 4 * q^6 + 4 * q^7 - 6 * q^8 + 6 * q^9 + 7 * q^11 - 7 * q^12 + 5 * q^13 - 3 * q^14 + q^16 - 5 * q^17 - 2 * q^18 + 8 * q^19 - 6 * q^21 - 14 * q^22 + 4 * q^23 + 6 * q^24 - 11 * q^26 - 15 * q^27 + 3 * q^28 - 2 * q^29 - 10 * q^33 - 4 * q^34 + q^36 - 13 * q^37 + 13 * q^38 - 13 * q^39 + q^41 + 4 * q^42 - 14 * q^43 + 15 * q^44 - 3 * q^46 - 4 * q^47 + 23 * q^48 + 4 * q^49 - 10 * q^51 + 5 * q^52 + q^53 + 14 * q^54 - 6 * q^56 - 19 * q^57 + 16 * q^58 - 7 * q^59 - 7 * q^61 + 15 * q^62 + 6 * q^63 + 23 * q^66 - 15 * q^67 + 11 * q^68 - 6 * q^69 + 17 * q^72 - 3 * q^73 - 2 * q^74 - 22 * q^76 + 7 * q^77 + 31 * q^78 - 14 * q^79 + 28 * q^81 - 6 * q^82 - 3 * q^83 - 7 * q^84 + 16 * q^86 + 14 * q^87 - 13 * q^88 - 11 * q^89 + 5 * q^91 + 3 * q^92 + 23 * q^93 - 19 * q^94 - 15 * q^96 - 9 * q^97 - 3 * q^98 + 8 * q^99

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