LMFDB - Embedded newform 825.4.a.r.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,4,Mod(1,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("825.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	825.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:	$48.6765757547$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.47528.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 26x - 22 $ x^3 - x^2 - 26*x - 22
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 165)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-4.06484$ of defining polynomial
Character	$\chi$	$=$	825.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.06484 q^{2} -3.00000 q^{3} +17.6526 q^{4} -15.1945 q^{6} -27.4348 q^{7} +48.8887 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+5.06484 q^{2} -3.00000 q^{3} +17.6526 q^{4} -15.1945 q^{6} -27.4348 q^{7} +48.8887 q^{8} +9.00000 q^{9} +11.0000 q^{11} -52.9577 q^{12} -22.6949 q^{13} -138.953 q^{14} +106.392 q^{16} +41.1755 q^{17} +45.5835 q^{18} -142.128 q^{19} +82.3044 q^{21} +55.7132 q^{22} -176.166 q^{23} -146.666 q^{24} -114.946 q^{26} -27.0000 q^{27} -484.295 q^{28} +76.2044 q^{29} +197.373 q^{31} +147.751 q^{32} -33.0000 q^{33} +208.547 q^{34} +158.873 q^{36} -367.297 q^{37} -719.856 q^{38} +68.0846 q^{39} -238.279 q^{41} +416.858 q^{42} -30.2905 q^{43} +194.178 q^{44} -892.254 q^{46} -137.390 q^{47} -319.177 q^{48} +409.668 q^{49} -123.526 q^{51} -400.623 q^{52} -638.665 q^{53} -136.751 q^{54} -1341.25 q^{56} +426.385 q^{57} +385.963 q^{58} +103.146 q^{59} +605.596 q^{61} +999.662 q^{62} -246.913 q^{63} -102.804 q^{64} -167.140 q^{66} +704.925 q^{67} +726.852 q^{68} +528.499 q^{69} -782.162 q^{71} +439.998 q^{72} +243.132 q^{73} -1860.30 q^{74} -2508.93 q^{76} -301.783 q^{77} +344.837 q^{78} -532.874 q^{79} +81.0000 q^{81} -1206.84 q^{82} -1204.91 q^{83} +1452.88 q^{84} -153.416 q^{86} -228.613 q^{87} +537.775 q^{88} +1058.49 q^{89} +622.629 q^{91} -3109.79 q^{92} -592.119 q^{93} -695.857 q^{94} -443.254 q^{96} +85.1964 q^{97} +2074.90 q^{98} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 2 q^{2} - 9 q^{3} + 30 q^{4} - 6 q^{6} - 10 q^{7} - 18 q^{8} + 27 q^{9}+O(q^{10}) $ 3 * q + 2 * q^2 - 9 * q^3 + 30 * q^4 - 6 * q^6 - 10 * q^7 - 18 * q^8 + 27 * q^9	$ 3 q + 2 q^{2} - 9 q^{3} + 30 q^{4} - 6 q^{6} - 10 q^{7} - 18 q^{8} + 27 q^{9} + 33 q^{11} - 90 q^{12} - 114 q^{13} - 68 q^{14} + 178 q^{16} + 104 q^{17} + 18 q^{18} - 58 q^{19} + 30 q^{21} + 22 q^{22} - 120 q^{23} + 54 q^{24} - 120 q^{26} - 81 q^{27} - 676 q^{28} - 220 q^{29} + 248 q^{31} + 258 q^{32} - 99 q^{33} - 80 q^{34} + 270 q^{36} - 838 q^{37} - 600 q^{38} + 342 q^{39} + 156 q^{41} + 204 q^{42} - 122 q^{43} + 330 q^{44} - 1256 q^{46} - 504 q^{47} - 534 q^{48} + 279 q^{49} - 312 q^{51} - 520 q^{52} - 282 q^{53} - 54 q^{54} - 1644 q^{56} + 174 q^{57} + 1644 q^{58} + 548 q^{59} + 414 q^{61} + 2448 q^{62} - 90 q^{63} - 58 q^{64} - 66 q^{66} + 428 q^{67} + 1704 q^{68} + 360 q^{69} - 912 q^{71} - 162 q^{72} - 618 q^{73} - 1612 q^{74} - 2752 q^{76} - 110 q^{77} + 360 q^{78} - 542 q^{79} + 243 q^{81} - 3372 q^{82} + 2028 q^{84} - 1548 q^{86} + 660 q^{87} - 198 q^{88} + 790 q^{89} - 772 q^{91} - 1912 q^{92} - 744 q^{93} - 424 q^{94} - 774 q^{96} - 2074 q^{97} + 3978 q^{98} + 297 q^{99}+O(q^{100}) $ 3 * q + 2 * q^2 - 9 * q^3 + 30 * q^4 - 6 * q^6 - 10 * q^7 - 18 * q^8 + 27 * q^9 + 33 * q^11 - 90 * q^12 - 114 * q^13 - 68 * q^14 + 178 * q^16 + 104 * q^17 + 18 * q^18 - 58 * q^19 + 30 * q^21 + 22 * q^22 - 120 * q^23 + 54 * q^24 - 120 * q^26 - 81 * q^27 - 676 * q^28 - 220 * q^29 + 248 * q^31 + 258 * q^32 - 99 * q^33 - 80 * q^34 + 270 * q^36 - 838 * q^37 - 600 * q^38 + 342 * q^39 + 156 * q^41 + 204 * q^42 - 122 * q^43 + 330 * q^44 - 1256 * q^46 - 504 * q^47 - 534 * q^48 + 279 * q^49 - 312 * q^51 - 520 * q^52 - 282 * q^53 - 54 * q^54 - 1644 * q^56 + 174 * q^57 + 1644 * q^58 + 548 * q^59 + 414 * q^61 + 2448 * q^62 - 90 * q^63 - 58 * q^64 - 66 * q^66 + 428 * q^67 + 1704 * q^68 + 360 * q^69 - 912 * q^71 - 162 * q^72 - 618 * q^73 - 1612 * q^74 - 2752 * q^76 - 110 * q^77 + 360 * q^78 - 542 * q^79 + 243 * q^81 - 3372 * q^82 + 2028 * q^84 - 1548 * q^86 + 660 * q^87 - 198 * q^88 + 790 * q^89 - 772 * q^91 - 1912 * q^92 - 744 * q^93 - 424 * q^94 - 774 * q^96 - 2074 * q^97 + 3978 * q^98 + 297 * 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 $

$2$	5.06484	1.79069	0.895345	−	0.445373i	$-0.146929\pi$
$2$	5.06484	1.79069	0.895345	+	0.445373i	$0.146929\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	17.6526	2.20657
$5$	0	0
$5$	0	0
$6$	−15.1945	−1.03386
$7$	−27.4348	−1.48134	−0.740670	−	0.671869i	$-0.765492\pi$
$7$	−27.4348	−1.48134	−0.740670	+	0.671869i	$0.765492\pi$
$8$	48.8887	2.16059
$9$	9.00000	0.333333
$10$	0	0
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−52.9577	−1.27396
$13$	−22.6949	−0.484187	−0.242093	−	0.970253i	$-0.577834\pi$
$13$	−22.6949	−0.484187	−0.242093	+	0.970253i	$0.577834\pi$
$14$	−138.953	−2.65262
$15$	0	0
$16$	106.392	1.66238
$17$	41.1755	0.587442	0.293721	−	0.955891i	$-0.405106\pi$
$17$	41.1755	0.587442	0.293721	+	0.955891i	$0.405106\pi$
$18$	45.5835	0.596897
$19$	−142.128	−1.71613	−0.858064	−	0.513542i	$-0.828333\pi$
$19$	−142.128	−1.71613	−0.858064	+	0.513542i	$0.828333\pi$
$20$	0	0
$21$	82.3044	0.855252
$22$	55.7132	0.539913
$23$	−176.166	−1.59710	−0.798548	−	0.601931i	$-0.794398\pi$
$23$	−176.166	−1.59710	−0.798548	+	0.601931i	$0.794398\pi$
$24$	−146.666	−1.24742
$25$	0	0
$26$	−114.946	−0.867028
$27$	−27.0000	−0.192450
$28$	−484.295	−3.26868
$29$	76.2044	0.487959	0.243979	−	0.969780i	$-0.421547\pi$
$29$	76.2044	0.487959	0.243979	+	0.969780i	$0.421547\pi$
$30$	0	0
$31$	197.373	1.14352	0.571762	−	0.820420i	$-0.306260\pi$
$31$	197.373	1.14352	0.571762	+	0.820420i	$0.306260\pi$
$32$	147.751	0.816218
$33$	−33.0000	−0.174078
$34$	208.547	1.05193
$35$	0	0
$36$	158.873	0.735523
$37$	−367.297	−1.63198	−0.815989	−	0.578067i	$-0.803807\pi$
$37$	−367.297	−1.63198	−0.815989	+	0.578067i	$0.803807\pi$
$38$	−719.856	−3.07305
$39$	68.0846	0.279545
$40$	0	0
$41$	−238.279	−0.907633	−0.453817	−	0.891095i	$-0.649938\pi$
$41$	−238.279	−0.907633	−0.453817	+	0.891095i	$0.649938\pi$
$42$	416.858	1.53149
$43$	−30.2905	−0.107425	−0.0537123	−	0.998556i	$-0.517105\pi$
$43$	−30.2905	−0.107425	−0.0537123	+	0.998556i	$0.517105\pi$
$44$	194.178	0.665306
$45$	0	0
$46$	−892.254	−2.85990
$47$	−137.390	−0.426391	−0.213195	−	0.977010i	$-0.568387\pi$
$47$	−137.390	−0.426391	−0.213195	+	0.977010i	$0.568387\pi$
$48$	−319.177	−0.959777
$49$	409.668	1.19437
$50$	0	0
$51$	−123.526	−0.339160
$52$	−400.623	−1.06839
$53$	−638.665	−1.65523	−0.827617	−	0.561293i	$-0.810304\pi$
$53$	−638.665	−1.65523	−0.827617	+	0.561293i	$0.810304\pi$
$54$	−136.751	−0.344618
$55$	0	0
$56$	−1341.25	−3.20057
$57$	426.385	0.990807
$58$	385.963	0.873783
$59$	103.146	0.227601	0.113800	−	0.993504i	$-0.463698\pi$
$59$	103.146	0.227601	0.113800	+	0.993504i	$0.463698\pi$
$60$	0	0
$61$	605.596	1.27113	0.635563	−	0.772049i	$-0.280768\pi$
$61$	605.596	1.27113	0.635563	+	0.772049i	$0.280768\pi$
$62$	999.662	2.04770
$63$	−246.913	−0.493780
$64$	−102.804	−0.200789
$65$	0	0
$66$	−167.140	−0.311719
$67$	704.925	1.28538	0.642688	−	0.766128i	$-0.277819\pi$
$67$	704.925	1.28538	0.642688	+	0.766128i	$0.277819\pi$
$68$	726.852	1.29623
$69$	528.499	0.922084
$70$	0	0
$71$	−782.162	−1.30740	−0.653701	−	0.756753i	$-0.726785\pi$
$71$	−782.162	−1.30740	−0.653701	+	0.756753i	$0.726785\pi$
$72$	439.998	0.720198
$73$	243.132	0.389814	0.194907	−	0.980822i	$-0.437560\pi$
$73$	243.132	0.389814	0.194907	+	0.980822i	$0.437560\pi$
$74$	−1860.30	−2.92237
$75$	0	0
$76$	−2508.93	−3.78676
$77$	−301.783	−0.446641
$78$	344.837	0.500579
$79$	−532.874	−0.758899	−0.379449	−	0.925212i	$-0.623887\pi$
$79$	−532.874	−0.758899	−0.379449	+	0.925212i	$0.623887\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	−1206.84	−1.62529
$83$	−1204.91	−1.59344	−0.796722	−	0.604345i	$-0.793435\pi$
$83$	−1204.91	−1.59344	−0.796722	+	0.604345i	$0.793435\pi$
$84$	1452.88	1.88717
$85$	0	0
$86$	−153.416	−0.192364
$87$	−228.613	−0.281723
$88$	537.775	0.651443
$89$	1058.49	1.26067	0.630337	−	0.776322i	$-0.282917\pi$
$89$	1058.49	1.26067	0.630337	+	0.776322i	$0.282917\pi$
$90$	0	0
$91$	622.629	0.717245
$92$	−3109.79	−3.52411
$93$	−592.119	−0.660214
$94$	−695.857	−0.763533
$95$	0	0
$96$	−443.254	−0.471244
$97$	85.1964	0.0891792	0.0445896	−	0.999005i	$-0.485802\pi$
$97$	85.1964	0.0891792	0.0445896	+	0.999005i	$0.485802\pi$
$98$	2074.90	2.13874
$99$	99.0000	0.100504
$100$	0	0
$101$	−7.81823	−0.00770241	−0.00385120	−	0.999993i	$-0.501226\pi$
$101$	−7.81823	−0.00770241	−0.00385120	+	0.999993i	$0.501226\pi$
$102$	−625.641	−0.607330
$103$	−12.4770	−0.0119359	−0.00596794	−	0.999982i	$-0.501900\pi$
$103$	−12.4770	−0.0119359	−0.00596794	+	0.999982i	$0.501900\pi$
$104$	−1109.52	−1.04613
$105$	0	0
$106$	−3234.73	−2.96401
$107$	1376.81	1.24393	0.621967	−	0.783043i	$-0.286334\pi$
$107$	1376.81	1.24393	0.621967	+	0.783043i	$0.286334\pi$
$108$	−476.619	−0.424655
$109$	610.189	0.536197	0.268099	−	0.963391i	$-0.413605\pi$
$109$	610.189	0.536197	0.268099	+	0.963391i	$0.413605\pi$
$110$	0	0
$111$	1101.89	0.942223
$112$	−2918.86	−2.46255
$113$	36.7727	0.0306132	0.0153066	−	0.999883i	$-0.495128\pi$
$113$	36.7727	0.0306132	0.0153066	+	0.999883i	$0.495128\pi$
$114$	2159.57	1.77423
$115$	0	0
$116$	1345.20	1.07672
$117$	−204.254	−0.161396
$118$	522.416	0.407562
$119$	−1129.64	−0.870201
$120$	0	0
$121$	121.000	0.0909091
$122$	3067.25	2.27619
$123$	714.838	0.524022
$124$	3484.14	2.52326
$125$	0	0
$126$	−1250.57	−0.884207
$127$	54.5310	0.0381011	0.0190506	−	0.999819i	$-0.493936\pi$
$127$	54.5310	0.0381011	0.0190506	+	0.999819i	$0.493936\pi$
$128$	−1702.69	−1.17577
$129$	90.8715	0.0620216
$130$	0	0
$131$	2377.83	1.58589	0.792947	−	0.609290i	$-0.208546\pi$
$131$	2377.83	1.58589	0.792947	+	0.609290i	$0.208546\pi$
$132$	−582.535	−0.384115
$133$	3899.26	2.54217
$134$	3570.33	2.30171
$135$	0	0
$136$	2013.01	1.26922
$137$	3078.41	1.91976	0.959878	−	0.280417i	$-0.0904729\pi$
$137$	3078.41	1.91976	0.959878	+	0.280417i	$0.0904729\pi$
$138$	2676.76	1.65117
$139$	−1197.18	−0.730530	−0.365265	−	0.930904i	$-0.619022\pi$
$139$	−1197.18	−0.730530	−0.365265	+	0.930904i	$0.619022\pi$
$140$	0	0
$141$	412.169	0.246177
$142$	−3961.52	−2.34115
$143$	−249.644	−0.145988
$144$	957.532	0.554128
$145$	0	0
$146$	1231.42	0.698035
$147$	−1229.00	−0.689569
$148$	−6483.73	−3.60108
$149$	−749.456	−0.412066	−0.206033	−	0.978545i	$-0.566055\pi$
$149$	−749.456	−0.412066	−0.206033	+	0.978545i	$0.566055\pi$
$150$	0	0
$151$	−2645.72	−1.42586	−0.712931	−	0.701234i	$-0.752633\pi$
$151$	−2645.72	−1.42586	−0.712931	+	0.701234i	$0.752633\pi$
$152$	−6948.46	−3.70786
$153$	370.579	0.195814
$154$	−1528.48	−0.799795
$155$	0	0
$156$	1201.87	0.616836
$157$	3475.74	1.76684	0.883422	−	0.468578i	$-0.155233\pi$
$157$	3475.74	1.76684	0.883422	+	0.468578i	$0.155233\pi$
$158$	−2698.92	−1.35895
$159$	1916.00	0.955650
$160$	0	0
$161$	4833.09	2.36584
$162$	410.252	0.198966
$163$	−3518.89	−1.69092	−0.845462	−	0.534035i	$-0.820675\pi$
$163$	−3518.89	−1.69092	−0.845462	+	0.534035i	$0.820675\pi$
$164$	−4206.24	−2.00276
$165$	0	0
$166$	−6102.67	−2.85337
$167$	−250.304	−0.115983	−0.0579914	−	0.998317i	$-0.518470\pi$
$167$	−250.304	−0.115983	−0.0579914	+	0.998317i	$0.518470\pi$
$168$	4023.75	1.84785
$169$	−1681.94	−0.765563
$170$	0	0
$171$	−1279.15	−0.572043
$172$	−534.705	−0.237040
$173$	−941.985	−0.413976	−0.206988	−	0.978344i	$-0.566366\pi$
$173$	−941.985	−0.413976	−0.206988	+	0.978344i	$0.566366\pi$
$174$	−1157.89	−0.504479
$175$	0	0
$176$	1170.32	0.501227
$177$	−309.437	−0.131405
$178$	5361.09	2.25748
$179$	336.037	0.140316	0.0701582	−	0.997536i	$-0.477650\pi$
$179$	336.037	0.140316	0.0701582	+	0.997536i	$0.477650\pi$
$180$	0	0
$181$	1107.45	0.454784	0.227392	−	0.973803i	$-0.426980\pi$
$181$	1107.45	0.454784	0.227392	+	0.973803i	$0.426980\pi$
$182$	3153.52	1.28436
$183$	−1816.79	−0.733885
$184$	−8612.53	−3.45068
$185$	0	0
$186$	−2998.98	−1.18224
$187$	452.930	0.177120
$188$	−2425.28	−0.940861
$189$	740.740	0.285084
$190$	0	0
$191$	−4243.01	−1.60740	−0.803700	−	0.595035i	$-0.797138\pi$
$191$	−4243.01	−1.60740	−0.803700	+	0.595035i	$0.797138\pi$
$192$	308.411	0.115925
$193$	3324.23	1.23981	0.619905	−	0.784677i	$-0.287171\pi$
$193$	3324.23	1.23981	0.619905	+	0.784677i	$0.287171\pi$
$194$	431.506	0.159692
$195$	0	0
$196$	7231.69	2.63546
$197$	−2677.14	−0.968213	−0.484107	−	0.875009i	$-0.660855\pi$
$197$	−2677.14	−0.968213	−0.484107	+	0.875009i	$0.660855\pi$
$198$	501.419	0.179971
$199$	2779.90	0.990261	0.495131	−	0.868819i	$-0.335120\pi$
$199$	2779.90	0.990261	0.495131	+	0.868819i	$0.335120\pi$
$200$	0	0
$201$	−2114.77	−0.742113
$202$	−39.5981	−0.0137926
$203$	−2090.65	−0.722833
$204$	−2180.56	−0.748380
$205$	0	0
$206$	−63.1940	−0.0213735
$207$	−1585.50	−0.532365
$208$	−2414.56	−0.804903
$209$	−1563.41	−0.517432
$210$	0	0
$211$	3056.15	0.997129	0.498564	−	0.866853i	$-0.333861\pi$
$211$	3056.15	0.997129	0.498564	+	0.866853i	$0.333861\pi$
$212$	−11274.1	−3.65239
$213$	2346.49	0.754829
$214$	6973.30	2.22750
$215$	0	0
$216$	−1319.99	−0.415806
$217$	−5414.89	−1.69395
$218$	3090.51	0.960163
$219$	−729.395	−0.225059
$220$	0	0
$221$	−934.472	−0.284432
$222$	5580.89	1.68723
$223$	−571.375	−0.171579	−0.0857895	−	0.996313i	$-0.527341\pi$
$223$	−571.375	−0.171579	−0.0857895	+	0.996313i	$0.527341\pi$
$224$	−4053.53	−1.20910
$225$	0	0
$226$	186.248	0.0548187
$227$	1094.40	0.319989	0.159995	−	0.987118i	$-0.448852\pi$
$227$	1094.40	0.319989	0.159995	+	0.987118i	$0.448852\pi$
$228$	7526.78	2.18629
$229$	−645.240	−0.186195	−0.0930975	−	0.995657i	$-0.529677\pi$
$229$	−645.240	−0.186195	−0.0930975	+	0.995657i	$0.529677\pi$
$230$	0	0
$231$	905.348	0.257868
$232$	3725.53	1.05428
$233$	2337.39	0.657201	0.328600	−	0.944469i	$-0.393423\pi$
$233$	2337.39	0.657201	0.328600	+	0.944469i	$0.393423\pi$
$234$	−1034.51	−0.289009
$235$	0	0
$236$	1820.79	0.502217
$237$	1598.62	0.438151
$238$	−5721.44	−1.55826
$239$	−3656.91	−0.989733	−0.494866	−	0.868969i	$-0.664783\pi$
$239$	−3656.91	−0.989733	−0.494866	+	0.868969i	$0.664783\pi$
$240$	0	0
$241$	−389.034	−0.103983	−0.0519914	−	0.998648i	$-0.516557\pi$
$241$	−389.034	−0.103983	−0.0519914	+	0.998648i	$0.516557\pi$
$242$	612.845	0.162790
$243$	−243.000	−0.0641500
$244$	10690.3	2.80483
$245$	0	0
$246$	3620.53	0.938361
$247$	3225.58	0.830927
$248$	9649.30	2.47069
$249$	3614.73	0.919976
$250$	0	0
$251$	2299.55	0.578271	0.289135	−	0.957288i	$-0.406632\pi$
$251$	2299.55	0.578271	0.289135	+	0.957288i	$0.406632\pi$
$252$	−4358.65	−1.08956
$253$	−1937.83	−0.481543
$254$	276.191	0.0682273
$255$	0	0
$256$	−7801.44	−1.90465
$257$	−4921.61	−1.19456	−0.597279	−	0.802033i	$-0.703752\pi$
$257$	−4921.61	−1.19456	−0.597279	+	0.802033i	$0.703752\pi$
$258$	460.249	0.111062
$259$	10076.7	2.41752
$260$	0	0
$261$	685.840	0.162653
$262$	12043.3	2.83985
$263$	2575.61	0.603875	0.301938	−	0.953328i	$-0.402367\pi$
$263$	2575.61	0.603875	0.301938	+	0.953328i	$0.402367\pi$
$264$	−1613.33	−0.376111
$265$	0	0
$266$	19749.1	4.55224
$267$	−3175.48	−0.727850
$268$	12443.7	2.83627
$269$	−4794.97	−1.08682	−0.543410	−	0.839468i	$-0.682867\pi$
$269$	−4794.97	−1.08682	−0.543410	+	0.839468i	$0.682867\pi$
$270$	0	0
$271$	2729.47	0.611821	0.305910	−	0.952060i	$-0.401039\pi$
$271$	2729.47	0.611821	0.305910	+	0.952060i	$0.401039\pi$
$272$	4380.76	0.976553
$273$	−1867.89	−0.414102
$274$	15591.7	3.43769
$275$	0	0
$276$	9329.36	2.03464
$277$	3761.45	0.815898	0.407949	−	0.913005i	$-0.366244\pi$
$277$	3761.45	0.815898	0.407949	+	0.913005i	$0.366244\pi$
$278$	−6063.53	−1.30815
$279$	1776.36	0.381174
$280$	0	0
$281$	−6434.87	−1.36609	−0.683046	−	0.730375i	$-0.739345\pi$
$281$	−6434.87	−1.36609	−0.683046	+	0.730375i	$0.739345\pi$
$282$	2087.57	0.440826
$283$	−3335.65	−0.700649	−0.350325	−	0.936628i	$-0.613929\pi$
$283$	−3335.65	−0.700649	−0.350325	+	0.936628i	$0.613929\pi$
$284$	−13807.2	−2.88487
$285$	0	0
$286$	−1264.40	−0.261419
$287$	6537.14	1.34451
$288$	1329.76	0.272073
$289$	−3217.58	−0.654912
$290$	0	0
$291$	−255.589	−0.0514876
$292$	4291.89	0.860151
$293$	2878.93	0.574023	0.287012	−	0.957927i	$-0.407338\pi$
$293$	2878.93	0.574023	0.287012	+	0.957927i	$0.407338\pi$
$294$	−6224.71	−1.23480
$295$	0	0
$296$	−17956.6	−3.52604
$297$	−297.000	−0.0580259
$298$	−3795.87	−0.737883
$299$	3998.07	0.773293
$300$	0	0
$301$	831.014	0.159132
$302$	−13400.1	−2.55328
$303$	23.4547	0.00444699
$304$	−15121.4	−2.85286
$305$	0	0
$306$	1876.92	0.350642
$307$	8154.28	1.51593	0.757963	−	0.652297i	$-0.226195\pi$
$307$	8154.28	1.51593	0.757963	+	0.652297i	$0.226195\pi$
$308$	−5327.24	−0.985544
$309$	37.4310	0.00689119
$310$	0	0
$311$	3818.24	0.696182	0.348091	−	0.937461i	$-0.386830\pi$
$311$	3818.24	0.696182	0.348091	+	0.937461i	$0.386830\pi$
$312$	3328.57	0.603984
$313$	−2527.23	−0.456381	−0.228191	−	0.973616i	$-0.573281\pi$
$313$	−2527.23	−0.456381	−0.228191	+	0.973616i	$0.573281\pi$
$314$	17604.1	3.16387
$315$	0	0
$316$	−9406.59	−1.67456
$317$	11084.7	1.96398	0.981989	−	0.188937i	$-0.0605042\pi$
$317$	11084.7	1.96398	0.981989	+	0.188937i	$0.0605042\pi$
$318$	9704.20	1.71127
$319$	838.249	0.147125
$320$	0	0
$321$	−4130.42	−0.718186
$322$	24478.8	4.23649
$323$	−5852.19	−1.00813
$324$	1429.86	0.245174
$325$	0	0
$326$	−17822.6	−3.02792
$327$	−1830.57	−0.309574
$328$	−11649.1	−1.96103
$329$	3769.26	0.631629
$330$	0	0
$331$	−9417.70	−1.56388	−0.781939	−	0.623355i	$-0.785769\pi$
$331$	−9417.70	−1.56388	−0.781939	+	0.623355i	$0.785769\pi$
$332$	−21269.7	−3.51605
$333$	−3305.67	−0.543993
$334$	−1267.75	−0.207689
$335$	0	0
$336$	8756.57	1.42176
$337$	11263.2	1.82061	0.910305	−	0.413938i	$-0.135847\pi$
$337$	11263.2	1.82061	0.910305	+	0.413938i	$0.135847\pi$
$338$	−8518.76	−1.37089
$339$	−110.318	−0.0176745
$340$	0	0
$341$	2171.10	0.344785
$342$	−6478.70	−1.02435
$343$	−1829.03	−0.287925
$344$	−1480.86	−0.232101
$345$	0	0
$346$	−4771.00	−0.741302
$347$	4213.25	0.651814	0.325907	−	0.945402i	$-0.394330\pi$
$347$	4213.25	0.651814	0.325907	+	0.945402i	$0.394330\pi$
$348$	−4035.61	−0.621642
$349$	4987.07	0.764905	0.382452	−	0.923975i	$-0.375080\pi$
$349$	4987.07	0.764905	0.382452	+	0.923975i	$0.375080\pi$
$350$	0	0
$351$	612.762	0.0931817
$352$	1625.26	0.246099
$353$	7633.47	1.15096	0.575480	−	0.817816i	$-0.304815\pi$
$353$	7633.47	1.15096	0.575480	+	0.817816i	$0.304815\pi$
$354$	−1567.25	−0.235306
$355$	0	0
$356$	18685.1	2.78177
$357$	3388.92	0.502411
$358$	1701.97	0.251263
$359$	−3114.76	−0.457913	−0.228957	−	0.973437i	$-0.573531\pi$
$359$	−3114.76	−0.457913	−0.228957	+	0.973437i	$0.573531\pi$
$360$	0	0
$361$	13341.4	1.94510
$362$	5609.04	0.814378
$363$	−363.000	−0.0524864
$364$	10991.0	1.58265
$365$	0	0
$366$	−9201.74	−1.31416
$367$	−5931.48	−0.843653	−0.421827	−	0.906677i	$-0.638611\pi$
$367$	−5931.48	−0.843653	−0.421827	+	0.906677i	$0.638611\pi$
$368$	−18742.8	−2.65499
$369$	−2144.51	−0.302544
$370$	0	0
$371$	17521.7	2.45196
$372$	−10452.4	−1.45681
$373$	−13918.9	−1.93215	−0.966073	−	0.258267i	$-0.916848\pi$
$373$	−13918.9	−1.93215	−0.966073	+	0.258267i	$0.916848\pi$
$374$	2294.02	0.317168
$375$	0	0
$376$	−6716.80	−0.921257
$377$	−1729.45	−0.236263
$378$	3751.72	0.510497
$379$	−12267.3	−1.66261	−0.831303	−	0.555820i	$-0.812404\pi$
$379$	−12267.3	−1.66261	−0.831303	+	0.555820i	$0.812404\pi$
$380$	0	0
$381$	−163.593	−0.0219977
$382$	−21490.1	−2.87835
$383$	6935.04	0.925233	0.462616	−	0.886559i	$-0.346911\pi$
$383$	6935.04	0.925233	0.462616	+	0.886559i	$0.346911\pi$
$384$	5108.08	0.678830
$385$	0	0
$386$	16836.7	2.22012
$387$	−272.615	−0.0358082
$388$	1503.93	0.196780
$389$	2775.18	0.361715	0.180858	−	0.983509i	$-0.442113\pi$
$389$	2775.18	0.361715	0.180858	+	0.983509i	$0.442113\pi$
$390$	0	0
$391$	−7253.73	−0.938202
$392$	20028.1	2.58054
$393$	−7133.50	−0.915617
$394$	−13559.3	−1.73377
$395$	0	0
$396$	1747.60	0.221769
$397$	−10539.5	−1.33240	−0.666198	−	0.745775i	$-0.732079\pi$
$397$	−10539.5	−1.33240	−0.666198	+	0.745775i	$0.732079\pi$
$398$	14079.7	1.77325
$399$	−11697.8	−1.46772
$400$	0	0
$401$	−12295.3	−1.53117	−0.765585	−	0.643334i	$-0.777550\pi$
$401$	−12295.3	−1.53117	−0.765585	+	0.643334i	$0.777550\pi$
$402$	−10711.0	−1.32889
$403$	−4479.35	−0.553679
$404$	−138.012	−0.0169959
$405$	0	0
$406$	−10588.8	−1.29437
$407$	−4040.26	−0.492060
$408$	−6039.04	−0.732787
$409$	−11545.7	−1.39584	−0.697918	−	0.716178i	$-0.745890\pi$
$409$	−11545.7	−1.39584	−0.697918	+	0.716178i	$0.745890\pi$
$410$	0	0
$411$	−9235.24	−1.10837
$412$	−220.251	−0.0263374
$413$	−2829.78	−0.337154
$414$	−8030.28	−0.953301
$415$	0	0
$416$	−3353.20	−0.395202
$417$	3591.55	0.421772
$418$	−7918.42	−0.926561
$419$	1851.51	0.215876	0.107938	−	0.994158i	$-0.465575\pi$
$419$	1851.51	0.215876	0.107938	+	0.994158i	$0.465575\pi$
$420$	0	0
$421$	−1303.60	−0.150911	−0.0754557	−	0.997149i	$-0.524041\pi$
$421$	−1303.60	−0.150911	−0.0754557	+	0.997149i	$0.524041\pi$
$422$	15478.9	1.78555
$423$	−1236.51	−0.142130
$424$	−31223.5	−3.57629
$425$	0	0
$426$	11884.6	1.35166
$427$	−16614.4	−1.88297
$428$	24304.2	2.74483
$429$	748.931	0.0842861
$430$	0	0
$431$	8228.85	0.919652	0.459826	−	0.888009i	$-0.347912\pi$
$431$	8228.85	0.919652	0.459826	+	0.888009i	$0.347912\pi$
$432$	−2872.60	−0.319926
$433$	−5830.21	−0.647072	−0.323536	−	0.946216i	$-0.604872\pi$
$433$	−5830.21	−0.647072	−0.323536	+	0.946216i	$0.604872\pi$
$434$	−27425.5	−3.03333
$435$	0	0
$436$	10771.4	1.18316
$437$	25038.2	2.74082
$438$	−3694.26	−0.403011
$439$	14261.0	1.55044	0.775218	−	0.631694i	$-0.217640\pi$
$439$	14261.0	1.55044	0.775218	+	0.631694i	$0.217640\pi$
$440$	0	0
$441$	3687.01	0.398123
$442$	−4732.95	−0.509329
$443$	−12025.7	−1.28975	−0.644875	−	0.764288i	$-0.723090\pi$
$443$	−12025.7	−1.28975	−0.644875	+	0.764288i	$0.723090\pi$
$444$	19451.2	2.07908
$445$	0	0
$446$	−2893.92	−0.307245
$447$	2248.37	0.237907
$448$	2820.40	0.297436
$449$	−7073.28	−0.743449	−0.371725	−	0.928343i	$-0.621233\pi$
$449$	−7073.28	−0.743449	−0.371725	+	0.928343i	$0.621233\pi$
$450$	0	0
$451$	−2621.07	−0.273662
$452$	649.133	0.0675501
$453$	7937.15	0.823222
$454$	5542.93	0.573001
$455$	0	0
$456$	20845.4	2.14073
$457$	−2732.31	−0.279677	−0.139838	−	0.990174i	$-0.544658\pi$
$457$	−2732.31	−0.279677	−0.139838	+	0.990174i	$0.544658\pi$
$458$	−3268.04	−0.333418
$459$	−1111.74	−0.113053
$460$	0	0
$461$	−332.708	−0.0336134	−0.0168067	−	0.999859i	$-0.505350\pi$
$461$	−332.708	−0.0336134	−0.0168067	+	0.999859i	$0.505350\pi$
$462$	4585.44	0.461762
$463$	−8248.39	−0.827937	−0.413969	−	0.910291i	$-0.635858\pi$
$463$	−8248.39	−0.827937	−0.413969	+	0.910291i	$0.635858\pi$
$464$	8107.58	0.811174
$465$	0	0
$466$	11838.5	1.17684
$467$	−7359.35	−0.729229	−0.364615	−	0.931158i	$-0.618799\pi$
$467$	−7359.35	−0.729229	−0.364615	+	0.931158i	$0.618799\pi$
$468$	−3605.60	−0.356131
$469$	−19339.5	−1.90408
$470$	0	0
$471$	−10427.2	−1.02009
$472$	5042.66	0.491752
$473$	−333.196	−0.0323897
$474$	8096.76	0.784592
$475$	0	0
$476$	−19941.0	−1.92016
$477$	−5747.99	−0.551745
$478$	−18521.7	−1.77230
$479$	−10327.6	−0.985140	−0.492570	−	0.870273i	$-0.663942\pi$
$479$	−10327.6	−0.985140	−0.492570	+	0.870273i	$0.663942\pi$
$480$	0	0
$481$	8335.75	0.790182
$482$	−1970.39	−0.186201
$483$	−14499.3	−1.36592
$484$	2135.96	0.200597
$485$	0	0
$486$	−1230.76	−0.114873
$487$	−9622.57	−0.895360	−0.447680	−	0.894194i	$-0.647750\pi$
$487$	−9622.57	−0.895360	−0.447680	+	0.894194i	$0.647750\pi$
$488$	29606.8	2.74639
$489$	10556.7	0.976256
$490$	0	0
$491$	−8993.59	−0.826629	−0.413315	−	0.910588i	$-0.635629\pi$
$491$	−8993.59	−0.826629	−0.413315	+	0.910588i	$0.635629\pi$
$492$	12618.7	1.15629
$493$	3137.75	0.286648
$494$	16337.0	1.48793
$495$	0	0
$496$	20999.0	1.90097
$497$	21458.5	1.93671
$498$	18308.0	1.64739
$499$	2623.70	0.235377	0.117688	−	0.993051i	$-0.462452\pi$
$499$	2623.70	0.235377	0.117688	+	0.993051i	$0.462452\pi$
$500$	0	0
$501$	750.912	0.0669627
$502$	11646.8	1.03550
$503$	−13234.5	−1.17316	−0.586579	−	0.809892i	$-0.699526\pi$
$503$	−13234.5	−1.17316	−0.586579	+	0.809892i	$0.699526\pi$
$504$	−12071.3	−1.06686
$505$	0	0
$506$	−9814.79	−0.862294
$507$	5045.83	0.441998
$508$	962.612	0.0840728
$509$	−12810.3	−1.11553	−0.557765	−	0.829999i	$-0.688341\pi$
$509$	−12810.3	−1.11553	−0.557765	+	0.829999i	$0.688341\pi$
$510$	0	0
$511$	−6670.26	−0.577446
$512$	−25891.5	−2.23487
$513$	3837.46	0.330269
$514$	−24927.1	−2.13908
$515$	0	0
$516$	1604.12	0.136855
$517$	−1511.29	−0.128562
$518$	51036.9	4.32902
$519$	2825.95	0.239009
$520$	0	0
$521$	1151.47	0.0968268	0.0484134	−	0.998827i	$-0.484584\pi$
$521$	1151.47	0.0968268	0.0484134	+	0.998827i	$0.484584\pi$
$522$	3473.67	0.291261
$523$	17319.1	1.44801	0.724005	−	0.689794i	$-0.242299\pi$
$523$	17319.1	1.44801	0.724005	+	0.689794i	$0.242299\pi$
$524$	41974.8	3.49939
$525$	0	0
$526$	13045.1	1.08135
$527$	8126.92	0.671754
$528$	−3510.95	−0.289384
$529$	18867.6	1.55072
$530$	0	0
$531$	928.312	0.0758669
$532$	68831.9	5.60948
$533$	5407.72	0.439464
$534$	−16083.3	−1.30335
$535$	0	0
$536$	34462.8	2.77718
$537$	−1008.11	−0.0810117
$538$	−24285.7	−1.94616
$539$	4506.35	0.360115
$540$	0	0
$541$	−7190.73	−0.571449	−0.285724	−	0.958312i	$-0.592234\pi$
$541$	−7190.73	−0.571449	−0.285724	+	0.958312i	$0.592234\pi$
$542$	13824.3	1.09558
$543$	−3322.34	−0.262570
$544$	6083.73	0.479481
$545$	0	0
$546$	−9460.55	−0.741527
$547$	−18670.5	−1.45940	−0.729701	−	0.683766i	$-0.760341\pi$
$547$	−18670.5	−1.45940	−0.729701	+	0.683766i	$0.760341\pi$
$548$	54341.9	4.23608
$549$	5450.37	0.423709
$550$	0	0
$551$	−10830.8	−0.837400
$552$	25837.6	1.99225
$553$	14619.3	1.12419
$554$	19051.1	1.46102
$555$	0	0
$556$	−21133.3	−1.61197
$557$	5510.44	0.419183	0.209591	−	0.977789i	$-0.432787\pi$
$557$	5510.44	0.419183	0.209591	+	0.977789i	$0.432787\pi$
$558$	8996.95	0.682565
$559$	687.439	0.0520136
$560$	0	0
$561$	−1358.79	−0.102261
$562$	−32591.5	−2.44625
$563$	−3576.57	−0.267734	−0.133867	−	0.990999i	$-0.542740\pi$
$563$	−3576.57	−0.267734	−0.133867	+	0.990999i	$0.542740\pi$
$564$	7275.84	0.543206
$565$	0	0
$566$	−16894.5	−1.25465
$567$	−2222.22	−0.164593
$568$	−38238.8	−2.82476
$569$	12285.2	0.905138	0.452569	−	0.891729i	$-0.350508\pi$
$569$	12285.2	0.905138	0.452569	+	0.891729i	$0.350508\pi$
$570$	0	0
$571$	13889.5	1.01797	0.508983	−	0.860777i	$-0.330022\pi$
$571$	13889.5	1.01797	0.508983	+	0.860777i	$0.330022\pi$
$572$	−4406.85	−0.322132
$573$	12729.0	0.928032
$574$	33109.5	2.40761
$575$	0	0
$576$	−925.234	−0.0669296
$577$	−11579.4	−0.835457	−0.417728	−	0.908572i	$-0.637174\pi$
$577$	−11579.4	−0.835457	−0.417728	+	0.908572i	$0.637174\pi$
$578$	−16296.5	−1.17274
$579$	−9972.69	−0.715805
$580$	0	0
$581$	33056.4	2.36043
$582$	−1294.52	−0.0921984
$583$	−7025.32	−0.499072
$584$	11886.4	0.842229
$585$	0	0
$586$	14581.3	1.02790
$587$	−26468.0	−1.86107	−0.930537	−	0.366199i	$-0.880659\pi$
$587$	−26468.0	−1.86107	−0.930537	+	0.366199i	$0.880659\pi$
$588$	−21695.1	−1.52158
$589$	−28052.3	−1.96243
$590$	0	0
$591$	8031.41	0.558998
$592$	−39077.6	−2.71297
$593$	−1059.52	−0.0733716	−0.0366858	−	0.999327i	$-0.511680\pi$
$593$	−1059.52	−0.0733716	−0.0366858	+	0.999327i	$0.511680\pi$
$594$	−1504.26	−0.103906
$595$	0	0
$596$	−13229.8	−0.909253
$597$	−8339.70	−0.571728
$598$	20249.6	1.38473
$599$	−17858.7	−1.21817	−0.609086	−	0.793104i	$-0.708464\pi$
$599$	−17858.7	−1.21817	−0.609086	+	0.793104i	$0.708464\pi$
$600$	0	0
$601$	−9650.91	−0.655023	−0.327511	−	0.944847i	$-0.606210\pi$
$601$	−9650.91	−0.655023	−0.327511	+	0.944847i	$0.606210\pi$
$602$	4208.95	0.284957
$603$	6344.32	0.428459
$604$	−46703.7	−3.14627
$605$	0	0
$606$	118.794	0.00796318
$607$	−22754.9	−1.52157	−0.760786	−	0.649002i	$-0.775187\pi$
$607$	−22754.9	−1.52157	−0.760786	+	0.649002i	$0.775187\pi$
$608$	−20999.6	−1.40074
$609$	6271.96	0.417328
$610$	0	0
$611$	3118.04	0.206453
$612$	6541.67	0.432077
$613$	−13074.5	−0.861459	−0.430729	−	0.902481i	$-0.641744\pi$
$613$	−13074.5	−0.861459	−0.430729	+	0.902481i	$0.641744\pi$
$614$	41300.1	2.71455
$615$	0	0
$616$	−14753.8	−0.965009
$617$	13393.0	0.873878	0.436939	−	0.899491i	$-0.356063\pi$
$617$	13393.0	0.873878	0.436939	+	0.899491i	$0.356063\pi$
$618$	189.582	0.0123400
$619$	−15965.3	−1.03667	−0.518336	−	0.855177i	$-0.673448\pi$
$619$	−15965.3	−1.03667	−0.518336	+	0.855177i	$0.673448\pi$
$620$	0	0
$621$	4756.49	0.307361
$622$	19338.8	1.24665
$623$	−29039.5	−1.86749
$624$	7243.69	0.464711
$625$	0	0
$626$	−12800.0	−0.817237
$627$	4690.23	0.298740
$628$	61355.8	3.89867
$629$	−15123.6	−0.958693
$630$	0	0
$631$	17698.3	1.11657	0.558287	−	0.829648i	$-0.311459\pi$
$631$	17698.3	1.11657	0.558287	+	0.829648i	$0.311459\pi$
$632$	−26051.5	−1.63967
$633$	−9168.45	−0.575693
$634$	56142.4	3.51688
$635$	0	0
$636$	33822.2	2.10871
$637$	−9297.37	−0.578297
$638$	4245.59	0.263455
$639$	−7039.46	−0.435801
$640$	0	0
$641$	18264.8	1.12546	0.562728	−	0.826642i	$-0.309752\pi$
$641$	18264.8	1.12546	0.562728	+	0.826642i	$0.309752\pi$
$642$	−20919.9	−1.28605
$643$	15730.5	0.964778	0.482389	−	0.875957i	$-0.339769\pi$
$643$	15730.5	0.964778	0.482389	+	0.875957i	$0.339769\pi$
$644$	85316.4	5.22040
$645$	0	0
$646$	−29640.4	−1.80524
$647$	−21176.6	−1.28676	−0.643382	−	0.765545i	$-0.722469\pi$
$647$	−21176.6	−1.28676	−0.643382	+	0.765545i	$0.722469\pi$
$648$	3959.98	0.240066
$649$	1134.60	0.0686242
$650$	0	0
$651$	16244.7	0.978001
$652$	−62117.4	−3.73114
$653$	28293.6	1.69558	0.847791	−	0.530331i	$-0.177932\pi$
$653$	28293.6	1.69558	0.847791	+	0.530331i	$0.177932\pi$
$654$	−9271.52	−0.554350
$655$	0	0
$656$	−25351.1	−1.50883
$657$	2188.18	0.129938
$658$	19090.7	1.13105
$659$	−3894.19	−0.230191	−0.115096	−	0.993354i	$-0.536717\pi$
$659$	−3894.19	−0.230191	−0.115096	+	0.993354i	$0.536717\pi$
$660$	0	0
$661$	−6063.63	−0.356805	−0.178402	−	0.983958i	$-0.557093\pi$
$661$	−6063.63	−0.356805	−0.178402	+	0.983958i	$0.557093\pi$
$662$	−47699.1	−2.80042
$663$	2803.42	0.164217
$664$	−58906.4	−3.44279
$665$	0	0
$666$	−16742.7	−0.974123
$667$	−13424.7	−0.779317
$668$	−4418.51	−0.255924
$669$	1714.13	0.0990612
$670$	0	0
$671$	6661.56	0.383259
$672$	12160.6	0.698072
$673$	−17297.1	−0.990719	−0.495360	−	0.868688i	$-0.664964\pi$
$673$	−17297.1	−0.990719	−0.495360	+	0.868688i	$0.664964\pi$
$674$	57046.3	3.26015
$675$	0	0
$676$	−29690.6	−1.68927
$677$	4640.36	0.263432	0.131716	−	0.991287i	$-0.457951\pi$
$677$	4640.36	0.263432	0.131716	+	0.991287i	$0.457951\pi$
$678$	−558.744	−0.0316496
$679$	−2337.35	−0.132105
$680$	0	0
$681$	−3283.19	−0.184746
$682$	10996.3	0.617404
$683$	14694.9	0.823256	0.411628	−	0.911352i	$-0.364960\pi$
$683$	14694.9	0.823256	0.411628	+	0.911352i	$0.364960\pi$
$684$	−22580.3	−1.26225
$685$	0	0
$686$	−9263.73	−0.515584
$687$	1935.72	0.107500
$688$	−3222.68	−0.178581
$689$	14494.4	0.801442
$690$	0	0
$691$	−9905.09	−0.545307	−0.272654	−	0.962112i	$-0.587901\pi$
$691$	−9905.09	−0.545307	−0.272654	+	0.962112i	$0.587901\pi$
$692$	−16628.4	−0.913466
$693$	−2716.05	−0.148880
$694$	21339.4	1.16720
$695$	0	0
$696$	−11176.6	−0.608689
$697$	−9811.25	−0.533182
$698$	25258.7	1.36971
$699$	−7012.18	−0.379435
$700$	0	0
$701$	−947.946	−0.0510748	−0.0255374	−	0.999674i	$-0.508130\pi$
$701$	−947.946	−0.0510748	−0.0255374	+	0.999674i	$0.508130\pi$
$702$	3103.54	0.166860
$703$	52203.2	2.80069
$704$	−1130.84	−0.0605401
$705$	0	0
$706$	38662.3	2.06101
$707$	214.492	0.0114099
$708$	−5462.36	−0.289955
$709$	−3310.76	−0.175371	−0.0876855	−	0.996148i	$-0.527947\pi$
$709$	−3310.76	−0.175371	−0.0876855	+	0.996148i	$0.527947\pi$
$710$	0	0
$711$	−4795.87	−0.252966
$712$	51748.3	2.72380
$713$	−34770.5	−1.82632
$714$	17164.3	0.899662
$715$	0	0
$716$	5931.92	0.309618
$717$	10970.7	0.571423
$718$	−15775.8	−0.819981
$719$	3061.15	0.158778	0.0793892	−	0.996844i	$-0.474703\pi$
$719$	3061.15	0.158778	0.0793892	+	0.996844i	$0.474703\pi$
$720$	0	0
$721$	342.304	0.0176811
$722$	67572.1	3.48307
$723$	1167.10	0.0600345
$724$	19549.3	1.00351
$725$	0	0
$726$	−1838.54	−0.0939868
$727$	7405.09	0.377771	0.188886	−	0.981999i	$-0.439512\pi$
$727$	7405.09	0.377771	0.188886	+	0.981999i	$0.439512\pi$
$728$	30439.5	1.54967
$729$	729.000	0.0370370
$730$	0	0
$731$	−1247.23	−0.0631057
$732$	−32071.0	−1.61937
$733$	−29791.4	−1.50119	−0.750593	−	0.660765i	$-0.770232\pi$
$733$	−29791.4	−1.50119	−0.750593	+	0.660765i	$0.770232\pi$
$734$	−30042.0	−1.51072
$735$	0	0
$736$	−26028.8	−1.30358
$737$	7754.17	0.387556
$738$	−10861.6	−0.541763
$739$	−7150.93	−0.355955	−0.177978	−	0.984035i	$-0.556955\pi$
$739$	−7150.93	−0.355955	−0.177978	+	0.984035i	$0.556955\pi$
$740$	0	0
$741$	−9676.75	−0.479736
$742$	88744.3	4.39071
$743$	1940.69	0.0958239	0.0479120	−	0.998852i	$-0.484743\pi$
$743$	1940.69	0.0958239	0.0479120	+	0.998852i	$0.484743\pi$
$744$	−28947.9	−1.42645
$745$	0	0
$746$	−70496.7	−3.45988
$747$	−10844.2	−0.531148
$748$	7995.38	0.390829
$749$	−37772.4	−1.84269
$750$	0	0
$751$	−29491.2	−1.43295	−0.716476	−	0.697611i	$-0.754246\pi$
$751$	−29491.2	−1.43295	−0.716476	+	0.697611i	$0.754246\pi$
$752$	−14617.2	−0.708824
$753$	−6898.64	−0.333865
$754$	−8759.38	−0.423074
$755$	0	0
$756$	13076.0	0.629058
$757$	−3542.54	−0.170087	−0.0850436	−	0.996377i	$-0.527103\pi$
$757$	−3542.54	−0.170087	−0.0850436	+	0.996377i	$0.527103\pi$
$758$	−62131.7	−2.97721
$759$	5813.49	0.278019
$760$	0	0
$761$	8552.86	0.407412	0.203706	−	0.979032i	$-0.434701\pi$
$761$	8552.86	0.407412	0.203706	+	0.979032i	$0.434701\pi$
$762$	−828.572	−0.0393911
$763$	−16740.4	−0.794290
$764$	−74900.0	−3.54684
$765$	0	0
$766$	35124.9	1.65680
$767$	−2340.88	−0.110201
$768$	23404.3	1.09965
$769$	−3128.73	−0.146716	−0.0733582	−	0.997306i	$-0.523372\pi$
$769$	−3128.73	−0.146716	−0.0733582	+	0.997306i	$0.523372\pi$
$770$	0	0
$771$	14764.8	0.689679
$772$	58681.2	2.73573
$773$	5364.51	0.249609	0.124805	−	0.992181i	$-0.460170\pi$
$773$	5364.51	0.249609	0.124805	+	0.992181i	$0.460170\pi$
$774$	−1380.75	−0.0641214
$775$	0	0
$776$	4165.14	0.192680
$777$	−30230.1	−1.39575
$778$	14055.8	0.647719
$779$	33866.2	1.55762
$780$	0	0
$781$	−8603.78	−0.394197
$782$	−36738.9	−1.68003
$783$	−2057.52	−0.0939077
$784$	43585.6	1.98550
$785$	0	0
$786$	−36130.0	−1.63959
$787$	−12160.9	−0.550813	−0.275406	−	0.961328i	$-0.588812\pi$
$787$	−12160.9	−0.550813	−0.275406	+	0.961328i	$0.588812\pi$
$788$	−47258.3	−2.13643
$789$	−7726.84	−0.348648
$790$	0	0
$791$	−1008.85	−0.0453485
$792$	4839.98	0.217148
$793$	−13743.9	−0.615462
$794$	−53380.7	−2.38591
$795$	0	0
$796$	49072.4	2.18508
$797$	581.179	0.0258299	0.0129149	−	0.999917i	$-0.495889\pi$
$797$	581.179	0.0258299	0.0129149	+	0.999917i	$0.495889\pi$
$798$	−59247.3	−2.62824
$799$	−5657.09	−0.250480
$800$	0	0
$801$	9526.43	0.420225
$802$	−62273.8	−2.74185
$803$	2674.45	0.117533
$804$	−37331.2	−1.63752
$805$	0	0
$806$	−22687.2	−0.991467
$807$	14384.9	0.627475
$808$	−382.223	−0.0166418
$809$	4763.37	0.207010	0.103505	−	0.994629i	$-0.466994\pi$
$809$	4763.37	0.207010	0.103505	+	0.994629i	$0.466994\pi$
$810$	0	0
$811$	−18055.4	−0.781762	−0.390881	−	0.920441i	$-0.627830\pi$
$811$	−18055.4	−0.781762	−0.390881	+	0.920441i	$0.627830\pi$
$812$	−36905.4	−1.59498
$813$	−8188.40	−0.353235
$814$	−20463.3	−0.881127
$815$	0	0
$816$	−13142.3	−0.563813
$817$	4305.14	0.184354
$818$	−58476.9	−2.49951
$819$	5603.66	0.239082
$820$	0	0
$821$	1128.04	0.0479522	0.0239761	−	0.999713i	$-0.492367\pi$
$821$	1128.04	0.0479522	0.0239761	+	0.999713i	$0.492367\pi$
$822$	−46775.0	−1.98475
$823$	32124.2	1.36061	0.680304	−	0.732930i	$-0.261848\pi$
$823$	32124.2	1.36061	0.680304	+	0.732930i	$0.261848\pi$
$824$	−609.984	−0.0257886
$825$	0	0
$826$	−14332.4	−0.603738
$827$	−11914.2	−0.500964	−0.250482	−	0.968121i	$-0.580589\pi$
$827$	−11914.2	−0.500964	−0.250482	+	0.968121i	$0.580589\pi$
$828$	−27988.1	−1.17470
$829$	−37721.6	−1.58037	−0.790185	−	0.612868i	$-0.790016\pi$
$829$	−37721.6	−1.58037	−0.790185	+	0.612868i	$0.790016\pi$
$830$	0	0
$831$	−11284.4	−0.471059
$832$	2333.12	0.0972192
$833$	16868.3	0.701622
$834$	18190.6	0.755262
$835$	0	0
$836$	−27598.2	−1.14175
$837$	−5329.07	−0.220071
$838$	9377.57	0.386567
$839$	−16550.5	−0.681034	−0.340517	−	0.940238i	$-0.610602\pi$
$839$	−16550.5	−0.681034	−0.340517	+	0.940238i	$0.610602\pi$
$840$	0	0
$841$	−18581.9	−0.761896
$842$	−6602.53	−0.270236
$843$	19304.6	0.788714
$844$	53948.9	2.20023
$845$	0	0
$846$	−6262.71	−0.254511
$847$	−3319.61	−0.134667
$848$	−67949.2	−2.75163
$849$	10006.9	0.404520
$850$	0	0
$851$	64705.3	2.60643
$852$	41421.5	1.66558
$853$	−1045.52	−0.0419672	−0.0209836	−	0.999780i	$-0.506680\pi$
$853$	−1045.52	−0.0419672	−0.0209836	+	0.999780i	$0.506680\pi$
$854$	−84149.3	−3.37181
$855$	0	0
$856$	67310.2	2.68764
$857$	14016.5	0.558688	0.279344	−	0.960191i	$-0.409883\pi$
$857$	14016.5	0.558688	0.279344	+	0.960191i	$0.409883\pi$
$858$	3793.21	0.150930
$859$	−20476.3	−0.813319	−0.406660	−	0.913580i	$-0.633306\pi$
$859$	−20476.3	−0.813319	−0.406660	+	0.913580i	$0.633306\pi$
$860$	0	0
$861$	−19611.4	−0.776255
$862$	41677.8	1.64681
$863$	−24083.0	−0.949936	−0.474968	−	0.880003i	$-0.657540\pi$
$863$	−24083.0	−0.949936	−0.474968	+	0.880003i	$0.657540\pi$
$864$	−3989.29	−0.157081
$865$	0	0
$866$	−29529.1	−1.15871
$867$	9652.75	0.378114
$868$	−95586.6	−3.73781
$869$	−5861.61	−0.228817
$870$	0	0
$871$	−15998.2	−0.622362
$872$	29831.3	1.15850
$873$	766.768	0.0297264
$874$	126814.	4.90796
$875$	0	0
$876$	−12875.7	−0.496608
$877$	−30432.5	−1.17176	−0.585879	−	0.810399i	$-0.699250\pi$
$877$	−30432.5	−1.17176	−0.585879	+	0.810399i	$0.699250\pi$
$878$	72229.7	2.77635
$879$	−8636.79	−0.331413
$880$	0	0
$881$	24559.2	0.939183	0.469592	−	0.882884i	$-0.344401\pi$
$881$	24559.2	0.939183	0.469592	+	0.882884i	$0.344401\pi$
$882$	18674.1	0.712914
$883$	−6013.88	−0.229200	−0.114600	−	0.993412i	$-0.536559\pi$
$883$	−6013.88	−0.229200	−0.114600	+	0.993412i	$0.536559\pi$
$884$	−16495.8	−0.627618
$885$	0	0
$886$	−60908.3	−2.30954
$887$	−13395.5	−0.507075	−0.253538	−	0.967325i	$-0.581594\pi$
$887$	−13395.5	−0.507075	−0.253538	+	0.967325i	$0.581594\pi$
$888$	53869.9	2.03576
$889$	−1496.05	−0.0564407
$890$	0	0
$891$	891.000	0.0335013
$892$	−10086.2	−0.378601
$893$	19527.0	0.731741
$894$	11387.6	0.426017
$895$	0	0
$896$	46713.1	1.74171
$897$	−11994.2	−0.446461
$898$	−35825.0	−1.33129
$899$	15040.7	0.557992
$900$	0	0
$901$	−26297.3	−0.972354
$902$	−13275.3	−0.490043
$903$	−2493.04	−0.0918751
$904$	1797.77	0.0661426
$905$	0	0
$906$	40200.3	1.47414
$907$	32078.9	1.17438	0.587189	−	0.809450i	$-0.300234\pi$
$907$	32078.9	1.17438	0.587189	+	0.809450i	$0.300234\pi$
$908$	19318.9	0.706079
$909$	−70.3641	−0.00256747
$910$	0	0
$911$	−15992.0	−0.581600	−0.290800	−	0.956784i	$-0.593921\pi$
$911$	−15992.0	−0.581600	−0.290800	+	0.956784i	$0.593921\pi$
$912$	45364.1	1.64710
$913$	−13254.0	−0.480442
$914$	−13838.7	−0.500814
$915$	0	0
$916$	−11390.1	−0.410852
$917$	−65235.4	−2.34925
$918$	−5630.77	−0.202443
$919$	33876.1	1.21596	0.607980	−	0.793952i	$-0.291980\pi$
$919$	33876.1	1.21596	0.607980	+	0.793952i	$0.291980\pi$
$920$	0	0
$921$	−24462.8	−0.875220
$922$	−1685.11	−0.0601912
$923$	17751.1	0.633026
$924$	15981.7	0.569004
$925$	0	0
$926$	−41776.7	−1.48258
$927$	−112.293	−0.00397863
$928$	11259.3	0.398281
$929$	21163.4	0.747416	0.373708	−	0.927546i	$-0.378086\pi$
$929$	21163.4	0.747416	0.373708	+	0.927546i	$0.378086\pi$
$930$	0	0
$931$	−58225.4	−2.04969
$932$	41261.0	1.45016
$933$	−11454.7	−0.401941
$934$	−37273.9	−1.30582
$935$	0	0
$936$	−9985.70	−0.348710
$937$	49771.9	1.73530	0.867650	−	0.497175i	$-0.165629\pi$
$937$	49771.9	1.73530	0.867650	+	0.497175i	$0.165629\pi$
$938$	−97951.2	−3.40962
$939$	7581.68	0.263492
$940$	0	0
$941$	32194.6	1.11532	0.557659	−	0.830070i	$-0.311700\pi$
$941$	32194.6	1.11532	0.557659	+	0.830070i	$0.311700\pi$
$942$	−52812.2	−1.82666
$943$	41976.8	1.44958
$944$	10973.9	0.378359
$945$	0	0
$946$	−1687.58	−0.0580000
$947$	30091.9	1.03258	0.516291	−	0.856413i	$-0.327312\pi$
$947$	30091.9	1.03258	0.516291	+	0.856413i	$0.327312\pi$
$948$	28219.8	0.966810
$949$	−5517.84	−0.188742
$950$	0	0
$951$	−33254.2	−1.13390
$952$	−55226.6	−1.88015
$953$	−5710.17	−0.194093	−0.0970465	−	0.995280i	$-0.530940\pi$
$953$	−5710.17	−0.194093	−0.0970465	+	0.995280i	$0.530940\pi$
$954$	−29112.6	−0.988004
$955$	0	0
$956$	−64553.9	−2.18392
$957$	−2514.75	−0.0849427
$958$	−52307.8	−1.76408
$959$	−84455.7	−2.84381
$960$	0	0
$961$	9165.07	0.307646
$962$	42219.2	1.41497
$963$	12391.3	0.414645
$964$	−6867.44	−0.229445
$965$	0	0
$966$	−73436.4	−2.44594
$967$	−29638.4	−0.985634	−0.492817	−	0.870133i	$-0.664033\pi$
$967$	−29638.4	−0.985634	−0.492817	+	0.870133i	$0.664033\pi$
$968$	5915.53	0.196418
$969$	17556.6	0.582042
$970$	0	0
$971$	21416.3	0.707808	0.353904	−	0.935282i	$-0.384854\pi$
$971$	21416.3	0.707808	0.353904	+	0.935282i	$0.384854\pi$
$972$	−4289.57	−0.141552
$973$	32844.5	1.08216
$974$	−48736.7	−1.60331
$975$	0	0
$976$	64430.9	2.11310
$977$	−1038.84	−0.0340177	−0.0170088	−	0.999855i	$-0.505414\pi$
$977$	−1038.84	−0.0340177	−0.0170088	+	0.999855i	$0.505414\pi$
$978$	53467.8	1.74817
$979$	11643.4	0.380107
$980$	0	0
$981$	5491.70	0.178732
$982$	−45551.1	−1.48024
$983$	44173.6	1.43329	0.716643	−	0.697440i	$-0.245678\pi$
$983$	44173.6	1.43329	0.716643	+	0.697440i	$0.245678\pi$
$984$	34947.4	1.13220
$985$	0	0
$986$	15892.2	0.513297
$987$	−11307.8	−0.364671
$988$	56939.8	1.83350
$989$	5336.17	0.171567
$990$	0	0
$991$	−23940.9	−0.767414	−0.383707	−	0.923455i	$-0.625353\pi$
$991$	−23940.9	−0.767414	−0.383707	+	0.923455i	$0.625353\pi$
$992$	29162.1	0.933365
$993$	28253.1	0.902905
$994$	108684.	3.46804
$995$	0	0
$996$	63809.2	2.02999
$997$	−13557.9	−0.430674	−0.215337	−	0.976540i	$-0.569085\pi$
$997$	−13557.9	−0.430674	−0.215337	+	0.976540i	$0.569085\pi$
$998$	13288.6	0.421487
$999$	9917.01	0.314074

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.4.a.r.1.3		3
3.2	odd	2		2475.4.a.t.1.1		3
5.2	odd	4		825.4.c.k.199.6		6
5.3	odd	4		825.4.c.k.199.1		6
5.4	even	2		165.4.a.e.1.1	✓	3
15.14	odd	2		495.4.a.k.1.3		3
55.54	odd	2		1815.4.a.r.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.4.a.e.1.1	✓	3	5.4	even	2
495.4.a.k.1.3		3	15.14	odd	2
825.4.a.r.1.3		3	1.1	even	1	trivial
825.4.c.k.199.1		6	5.3	odd	4
825.4.c.k.199.6		6	5.2	odd	4
1815.4.a.r.1.3		3	55.54	odd	2
2475.4.a.t.1.1		3	3.2	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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	825.a (trivial)

\(f(q)\)	\(=\)	\(q+5.06484 q^{2} -3.00000 q^{3} +17.6526 q^{4} -15.1945 q^{6} -27.4348 q^{7} +48.8887 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+5.06484 q^{2} -3.00000 q^{3} +17.6526 q^{4} -15.1945 q^{6} -27.4348 q^{7} +48.8887 q^{8} +9.00000 q^{9} +11.0000 q^{11} -52.9577 q^{12} -22.6949 q^{13} -138.953 q^{14} +106.392 q^{16} +41.1755 q^{17} +45.5835 q^{18} -142.128 q^{19} +82.3044 q^{21} +55.7132 q^{22} -176.166 q^{23} -146.666 q^{24} -114.946 q^{26} -27.0000 q^{27} -484.295 q^{28} +76.2044 q^{29} +197.373 q^{31} +147.751 q^{32} -33.0000 q^{33} +208.547 q^{34} +158.873 q^{36} -367.297 q^{37} -719.856 q^{38} +68.0846 q^{39} -238.279 q^{41} +416.858 q^{42} -30.2905 q^{43} +194.178 q^{44} -892.254 q^{46} -137.390 q^{47} -319.177 q^{48} +409.668 q^{49} -123.526 q^{51} -400.623 q^{52} -638.665 q^{53} -136.751 q^{54} -1341.25 q^{56} +426.385 q^{57} +385.963 q^{58} +103.146 q^{59} +605.596 q^{61} +999.662 q^{62} -246.913 q^{63} -102.804 q^{64} -167.140 q^{66} +704.925 q^{67} +726.852 q^{68} +528.499 q^{69} -782.162 q^{71} +439.998 q^{72} +243.132 q^{73} -1860.30 q^{74} -2508.93 q^{76} -301.783 q^{77} +344.837 q^{78} -532.874 q^{79} +81.0000 q^{81} -1206.84 q^{82} -1204.91 q^{83} +1452.88 q^{84} -153.416 q^{86} -228.613 q^{87} +537.775 q^{88} +1058.49 q^{89} +622.629 q^{91} -3109.79 q^{92} -592.119 q^{93} -695.857 q^{94} -443.254 q^{96} +85.1964 q^{97} +2074.90 q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 2 q^{2} - 9 q^{3} + 30 q^{4} - 6 q^{6} - 10 q^{7} - 18 q^{8} + 27 q^{9}+O(q^{10}) \) 3 * q + 2 * q^2 - 9 * q^3 + 30 * q^4 - 6 * q^6 - 10 * q^7 - 18 * q^8 + 27 * q^9	\( 3 q + 2 q^{2} - 9 q^{3} + 30 q^{4} - 6 q^{6} - 10 q^{7} - 18 q^{8} + 27 q^{9} + 33 q^{11} - 90 q^{12} - 114 q^{13} - 68 q^{14} + 178 q^{16} + 104 q^{17} + 18 q^{18} - 58 q^{19} + 30 q^{21} + 22 q^{22} - 120 q^{23} + 54 q^{24} - 120 q^{26} - 81 q^{27} - 676 q^{28} - 220 q^{29} + 248 q^{31} + 258 q^{32} - 99 q^{33} - 80 q^{34} + 270 q^{36} - 838 q^{37} - 600 q^{38} + 342 q^{39} + 156 q^{41} + 204 q^{42} - 122 q^{43} + 330 q^{44} - 1256 q^{46} - 504 q^{47} - 534 q^{48} + 279 q^{49} - 312 q^{51} - 520 q^{52} - 282 q^{53} - 54 q^{54} - 1644 q^{56} + 174 q^{57} + 1644 q^{58} + 548 q^{59} + 414 q^{61} + 2448 q^{62} - 90 q^{63} - 58 q^{64} - 66 q^{66} + 428 q^{67} + 1704 q^{68} + 360 q^{69} - 912 q^{71} - 162 q^{72} - 618 q^{73} - 1612 q^{74} - 2752 q^{76} - 110 q^{77} + 360 q^{78} - 542 q^{79} + 243 q^{81} - 3372 q^{82} + 2028 q^{84} - 1548 q^{86} + 660 q^{87} - 198 q^{88} + 790 q^{89} - 772 q^{91} - 1912 q^{92} - 744 q^{93} - 424 q^{94} - 774 q^{96} - 2074 q^{97} + 3978 q^{98} + 297 q^{99}+O(q^{100}) \) 3 * q + 2 * q^2 - 9 * q^3 + 30 * q^4 - 6 * q^6 - 10 * q^7 - 18 * q^8 + 27 * q^9 + 33 * q^11 - 90 * q^12 - 114 * q^13 - 68 * q^14 + 178 * q^16 + 104 * q^17 + 18 * q^18 - 58 * q^19 + 30 * q^21 + 22 * q^22 - 120 * q^23 + 54 * q^24 - 120 * q^26 - 81 * q^27 - 676 * q^28 - 220 * q^29 + 248 * q^31 + 258 * q^32 - 99 * q^33 - 80 * q^34 + 270 * q^36 - 838 * q^37 - 600 * q^38 + 342 * q^39 + 156 * q^41 + 204 * q^42 - 122 * q^43 + 330 * q^44 - 1256 * q^46 - 504 * q^47 - 534 * q^48 + 279 * q^49 - 312 * q^51 - 520 * q^52 - 282 * q^53 - 54 * q^54 - 1644 * q^56 + 174 * q^57 + 1644 * q^58 + 548 * q^59 + 414 * q^61 + 2448 * q^62 - 90 * q^63 - 58 * q^64 - 66 * q^66 + 428 * q^67 + 1704 * q^68 + 360 * q^69 - 912 * q^71 - 162 * q^72 - 618 * q^73 - 1612 * q^74 - 2752 * q^76 - 110 * q^77 + 360 * q^78 - 542 * q^79 + 243 * q^81 - 3372 * q^82 + 2028 * q^84 - 1548 * q^86 + 660 * q^87 - 198 * q^88 + 790 * q^89 - 772 * q^91 - 1912 * q^92 - 744 * q^93 - 424 * q^94 - 774 * q^96 - 2074 * q^97 + 3978 * q^98 + 297 * q^99

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