LMFDB - Embedded newform 8025.2.a.bf.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8025,2,Mod(1,8025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8025, 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("8025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8025 = 3 \cdot 5^{2} \cdot 107 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8025.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:	$64.0799476221$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 15 x^{10} + 49 x^{9} + 71 x^{8} - 278 x^{7} - 92 x^{6} + 649 x^{5} - 127 x^{4} + \cdots - 6 $ x^12 - 3x^11 - 15x^10 + 49x^9 + 71x^8 - 278x^7 - 92x^6 + 649x^5 - 127x^4 - 529x^3 + 267x^2 + 15*x - 6
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1605)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.36308$ of defining polynomial
Character	$\chi$	$=$	8025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.36308 q^{2} -1.00000 q^{3} +3.58415 q^{4} +2.36308 q^{6} +1.44739 q^{7} -3.74348 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.36308 q^{2} -1.00000 q^{3} +3.58415 q^{4} +2.36308 q^{6} +1.44739 q^{7} -3.74348 q^{8} +1.00000 q^{9} +4.67457 q^{11} -3.58415 q^{12} +0.873126 q^{13} -3.42031 q^{14} +1.67784 q^{16} -2.24884 q^{17} -2.36308 q^{18} -5.64861 q^{19} -1.44739 q^{21} -11.0464 q^{22} -5.37771 q^{23} +3.74348 q^{24} -2.06327 q^{26} -1.00000 q^{27} +5.18767 q^{28} +2.30410 q^{29} -1.09517 q^{31} +3.52208 q^{32} -4.67457 q^{33} +5.31420 q^{34} +3.58415 q^{36} +6.05796 q^{37} +13.3481 q^{38} -0.873126 q^{39} +10.1973 q^{41} +3.42031 q^{42} +4.88520 q^{43} +16.7544 q^{44} +12.7080 q^{46} -0.209041 q^{47} -1.67784 q^{48} -4.90506 q^{49} +2.24884 q^{51} +3.12942 q^{52} +8.83811 q^{53} +2.36308 q^{54} -5.41829 q^{56} +5.64861 q^{57} -5.44477 q^{58} +2.79345 q^{59} -8.08566 q^{61} +2.58797 q^{62} +1.44739 q^{63} -11.6786 q^{64} +11.0464 q^{66} -10.5805 q^{67} -8.06019 q^{68} +5.37771 q^{69} -15.7811 q^{71} -3.74348 q^{72} -0.698172 q^{73} -14.3154 q^{74} -20.2455 q^{76} +6.76594 q^{77} +2.06327 q^{78} -11.6878 q^{79} +1.00000 q^{81} -24.0971 q^{82} -14.4572 q^{83} -5.18767 q^{84} -11.5441 q^{86} -2.30410 q^{87} -17.4992 q^{88} +2.10490 q^{89} +1.26376 q^{91} -19.2745 q^{92} +1.09517 q^{93} +0.493981 q^{94} -3.52208 q^{96} +3.68546 q^{97} +11.5910 q^{98} +4.67457 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} - 12 q^{3} + 15 q^{4} + 3 q^{6} - 7 q^{7} - 3 q^{8} + 12 q^{9}+O(q^{10}) $ 12 * q - 3 * q^2 - 12 * q^3 + 15 * q^4 + 3 * q^6 - 7 * q^7 - 3 * q^8 + 12 * q^9	$ 12 q - 3 q^{2} - 12 q^{3} + 15 q^{4} + 3 q^{6} - 7 q^{7} - 3 q^{8} + 12 q^{9} + 4 q^{11} - 15 q^{12} - 13 q^{13} + 4 q^{14} + 13 q^{16} + 4 q^{17} - 3 q^{18} + 14 q^{19} + 7 q^{21} - 15 q^{22} - 11 q^{23} + 3 q^{24} - 8 q^{26} - 12 q^{27} - 16 q^{28} - 7 q^{29} + 4 q^{31} - 4 q^{32} - 4 q^{33} + q^{34} + 15 q^{36} - 24 q^{37} + 11 q^{38} + 13 q^{39} + 13 q^{41} - 4 q^{42} - 25 q^{43} + 10 q^{44} - 22 q^{46} - 19 q^{47} - 13 q^{48} + 9 q^{49} - 4 q^{51} - 20 q^{52} - 11 q^{53} + 3 q^{54} - 37 q^{56} - 14 q^{57} + 2 q^{58} + 8 q^{59} + 7 q^{61} + 11 q^{62} - 7 q^{63} - 19 q^{64} + 15 q^{66} - 33 q^{67} + 24 q^{68} + 11 q^{69} - 3 q^{72} - 34 q^{73} - 27 q^{74} - 9 q^{76} + 29 q^{77} + 8 q^{78} + 12 q^{81} - q^{82} + 24 q^{83} + 16 q^{84} - 36 q^{86} + 7 q^{87} + 6 q^{88} - 10 q^{89} + 30 q^{91} + 28 q^{92} - 4 q^{93} - 8 q^{94} + 4 q^{96} - 16 q^{97} + 36 q^{98} + 4 q^{99}+O(q^{100}) $ 12 * q - 3 * q^2 - 12 * q^3 + 15 * q^4 + 3 * q^6 - 7 * q^7 - 3 * q^8 + 12 * q^9 + 4 * q^11 - 15 * q^12 - 13 * q^13 + 4 * q^14 + 13 * q^16 + 4 * q^17 - 3 * q^18 + 14 * q^19 + 7 * q^21 - 15 * q^22 - 11 * q^23 + 3 * q^24 - 8 * q^26 - 12 * q^27 - 16 * q^28 - 7 * q^29 + 4 * q^31 - 4 * q^32 - 4 * q^33 + q^34 + 15 * q^36 - 24 * q^37 + 11 * q^38 + 13 * q^39 + 13 * q^41 - 4 * q^42 - 25 * q^43 + 10 * q^44 - 22 * q^46 - 19 * q^47 - 13 * q^48 + 9 * q^49 - 4 * q^51 - 20 * q^52 - 11 * q^53 + 3 * q^54 - 37 * q^56 - 14 * q^57 + 2 * q^58 + 8 * q^59 + 7 * q^61 + 11 * q^62 - 7 * q^63 - 19 * q^64 + 15 * q^66 - 33 * q^67 + 24 * q^68 + 11 * q^69 - 3 * q^72 - 34 * q^73 - 27 * q^74 - 9 * q^76 + 29 * q^77 + 8 * q^78 + 12 * q^81 - q^82 + 24 * q^83 + 16 * q^84 - 36 * q^86 + 7 * q^87 + 6 * q^88 - 10 * q^89 + 30 * q^91 + 28 * q^92 - 4 * q^93 - 8 * q^94 + 4 * q^96 - 16 * q^97 + 36 * q^98 + 4 * 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 $

$2$	−2.36308	−1.67095	−0.835475	−	0.549528i	$-0.814808\pi$
$2$	−2.36308	−1.67095	−0.835475	+	0.549528i	$0.814808\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.58415	1.79208
$5$	0	0
$5$	0	0
$6$	2.36308	0.964724
$7$	1.44739	0.547063	0.273531	−	0.961863i	$-0.411808\pi$
$7$	1.44739	0.547063	0.273531	+	0.961863i	$0.411808\pi$
$8$	−3.74348	−1.32352
$9$	1.00000	0.333333
$10$	0	0
$11$	4.67457	1.40944	0.704718	−	0.709487i	$-0.251073\pi$
$11$	4.67457	1.40944	0.704718	+	0.709487i	$0.251073\pi$
$12$	−3.58415	−1.03466
$13$	0.873126	0.242161	0.121081	−	0.992643i	$-0.461364\pi$
$13$	0.873126	0.242161	0.121081	+	0.992643i	$0.461364\pi$
$14$	−3.42031	−0.914115
$15$	0	0
$16$	1.67784	0.419461
$17$	−2.24884	−0.545424	−0.272712	−	0.962096i	$-0.587921\pi$
$17$	−2.24884	−0.545424	−0.272712	+	0.962096i	$0.587921\pi$
$18$	−2.36308	−0.556984
$19$	−5.64861	−1.29588	−0.647940	−	0.761691i	$-0.724369\pi$
$19$	−5.64861	−1.29588	−0.647940	+	0.761691i	$0.724369\pi$
$20$	0	0
$21$	−1.44739	−0.315847
$22$	−11.0464	−2.35510
$23$	−5.37771	−1.12133	−0.560665	−	0.828043i	$-0.689454\pi$
$23$	−5.37771	−1.12133	−0.560665	+	0.828043i	$0.689454\pi$
$24$	3.74348	0.764135
$25$	0	0
$26$	−2.06327	−0.404640
$27$	−1.00000	−0.192450
$28$	5.18767	0.980378
$29$	2.30410	0.427860	0.213930	−	0.976849i	$-0.431374\pi$
$29$	2.30410	0.427860	0.213930	+	0.976849i	$0.431374\pi$
$30$	0	0
$31$	−1.09517	−0.196698	−0.0983491	−	0.995152i	$-0.531356\pi$
$31$	−1.09517	−0.196698	−0.0983491	+	0.995152i	$0.531356\pi$
$32$	3.52208	0.622622
$33$	−4.67457	−0.813739
$34$	5.31420	0.911377
$35$	0	0
$36$	3.58415	0.597359
$37$	6.05796	0.995922	0.497961	−	0.867199i	$-0.334082\pi$
$37$	6.05796	0.995922	0.497961	+	0.867199i	$0.334082\pi$
$38$	13.3481	2.16535
$39$	−0.873126	−0.139812
$40$	0	0
$41$	10.1973	1.59255	0.796277	−	0.604933i	$-0.206800\pi$
$41$	10.1973	1.59255	0.796277	+	0.604933i	$0.206800\pi$
$42$	3.42031	0.527765
$43$	4.88520	0.744987	0.372493	−	0.928035i	$-0.378503\pi$
$43$	4.88520	0.744987	0.372493	+	0.928035i	$0.378503\pi$
$44$	16.7544	2.52582
$45$	0	0
$46$	12.7080	1.87369
$47$	−0.209041	−0.0304918	−0.0152459	−	0.999884i	$-0.504853\pi$
$47$	−0.209041	−0.0304918	−0.0152459	+	0.999884i	$0.504853\pi$
$48$	−1.67784	−0.242176
$49$	−4.90506	−0.700722
$50$	0	0
$51$	2.24884	0.314901
$52$	3.12942	0.433972
$53$	8.83811	1.21401	0.607004	−	0.794699i	$-0.292371\pi$
$53$	8.83811	1.21401	0.607004	+	0.794699i	$0.292371\pi$
$54$	2.36308	0.321575
$55$	0	0
$56$	−5.41829	−0.724049
$57$	5.64861	0.748177
$58$	−5.44477	−0.714933
$59$	2.79345	0.363677	0.181838	−	0.983328i	$-0.441795\pi$
$59$	2.79345	0.363677	0.181838	+	0.983328i	$0.441795\pi$
$60$	0	0
$61$	−8.08566	−1.03526	−0.517631	−	0.855604i	$-0.673186\pi$
$61$	−8.08566	−1.03526	−0.517631	+	0.855604i	$0.673186\pi$
$62$	2.58797	0.328673
$63$	1.44739	0.182354
$64$	−11.6786	−1.45983
$65$	0	0
$66$	11.0464	1.35972
$67$	−10.5805	−1.29262	−0.646308	−	0.763077i	$-0.723688\pi$
$67$	−10.5805	−1.29262	−0.646308	+	0.763077i	$0.723688\pi$
$68$	−8.06019	−0.977442
$69$	5.37771	0.647400
$70$	0	0
$71$	−15.7811	−1.87287	−0.936437	−	0.350837i	$-0.885897\pi$
$71$	−15.7811	−1.87287	−0.936437	+	0.350837i	$0.885897\pi$
$72$	−3.74348	−0.441173
$73$	−0.698172	−0.0817149	−0.0408574	−	0.999165i	$-0.513009\pi$
$73$	−0.698172	−0.0817149	−0.0408574	+	0.999165i	$0.513009\pi$
$74$	−14.3154	−1.66414
$75$	0	0
$76$	−20.2455	−2.32232
$77$	6.76594	0.771051
$78$	2.06327	0.233619
$79$	−11.6878	−1.31498	−0.657488	−	0.753465i	$-0.728381\pi$
$79$	−11.6878	−1.31498	−0.657488	+	0.753465i	$0.728381\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−24.0971	−2.66108
$83$	−14.4572	−1.58688	−0.793441	−	0.608647i	$-0.791713\pi$
$83$	−14.4572	−1.58688	−0.793441	+	0.608647i	$0.791713\pi$
$84$	−5.18767	−0.566022
$85$	0	0
$86$	−11.5441	−1.24484
$87$	−2.30410	−0.247025
$88$	−17.4992	−1.86542
$89$	2.10490	0.223119	0.111559	−	0.993758i	$-0.464415\pi$
$89$	2.10490	0.223119	0.111559	+	0.993758i	$0.464415\pi$
$90$	0	0
$91$	1.26376	0.132478
$92$	−19.2745	−2.00951
$93$	1.09517	0.113564
$94$	0.493981	0.0509503
$95$	0	0
$96$	−3.52208	−0.359471
$97$	3.68546	0.374201	0.187101	−	0.982341i	$-0.440091\pi$
$97$	3.68546	0.374201	0.187101	+	0.982341i	$0.440091\pi$
$98$	11.5910	1.17087
$99$	4.67457	0.469812
$100$	0	0
$101$	−0.924119	−0.0919533	−0.0459767	−	0.998943i	$-0.514640\pi$
$101$	−0.924119	−0.0919533	−0.0459767	+	0.998943i	$0.514640\pi$
$102$	−5.31420	−0.526184
$103$	−17.7880	−1.75271	−0.876354	−	0.481668i	$-0.840031\pi$
$103$	−17.7880	−1.75271	−0.876354	+	0.481668i	$0.840031\pi$
$104$	−3.26853	−0.320506
$105$	0	0
$106$	−20.8852	−2.02855
$107$	−1.00000	−0.0966736
$107$	−1.00000	−0.0966736
$108$	−3.58415	−0.344885
$109$	−5.32028	−0.509590	−0.254795	−	0.966995i	$-0.582008\pi$
$109$	−5.32028	−0.509590	−0.254795	+	0.966995i	$0.582008\pi$
$110$	0	0
$111$	−6.05796	−0.574996
$112$	2.42850	0.229471
$113$	−1.33883	−0.125947	−0.0629734	−	0.998015i	$-0.520058\pi$
$113$	−1.33883	−0.125947	−0.0629734	+	0.998015i	$0.520058\pi$
$114$	−13.3481	−1.25017
$115$	0	0
$116$	8.25823	0.766758
$117$	0.873126	0.0807205
$118$	−6.60116	−0.607686
$119$	−3.25496	−0.298381
$120$	0	0
$121$	10.8516	0.986512
$122$	19.1071	1.72987
$123$	−10.1973	−0.919461
$124$	−3.92525	−0.352498
$125$	0	0
$126$	−3.42031	−0.304705
$127$	19.6810	1.74641	0.873203	−	0.487357i	$-0.162039\pi$
$127$	19.6810	1.74641	0.873203	+	0.487357i	$0.162039\pi$
$128$	20.5534	1.81668
$129$	−4.88520	−0.430118
$130$	0	0
$131$	−2.85846	−0.249745	−0.124872	−	0.992173i	$-0.539852\pi$
$131$	−2.85846	−0.249745	−0.124872	+	0.992173i	$0.539852\pi$
$132$	−16.7544	−1.45828
$133$	−8.17575	−0.708928
$134$	25.0026	2.15990
$135$	0	0
$136$	8.41850	0.721880
$137$	16.2725	1.39026	0.695129	−	0.718885i	$-0.255347\pi$
$137$	16.2725	1.39026	0.695129	+	0.718885i	$0.255347\pi$
$138$	−12.7080	−1.08177
$139$	−12.1709	−1.03233	−0.516163	−	0.856490i	$-0.672640\pi$
$139$	−12.1709	−1.03233	−0.516163	+	0.856490i	$0.672640\pi$
$140$	0	0
$141$	0.209041	0.0176044
$142$	37.2920	3.12948
$143$	4.08149	0.341311
$144$	1.67784	0.139820
$145$	0	0
$146$	1.64984	0.136542
$147$	4.90506	0.404562
$148$	21.7126	1.78477
$149$	−7.27573	−0.596051	−0.298026	−	0.954558i	$-0.596328\pi$
$149$	−7.27573	−0.596051	−0.298026	+	0.954558i	$0.596328\pi$
$150$	0	0
$151$	−0.767327	−0.0624442	−0.0312221	−	0.999512i	$-0.509940\pi$
$151$	−0.767327	−0.0624442	−0.0312221	+	0.999512i	$0.509940\pi$
$152$	21.1455	1.71512
$153$	−2.24884	−0.181808
$154$	−15.9885	−1.28839
$155$	0	0
$156$	−3.12942	−0.250554
$157$	−12.9677	−1.03493	−0.517466	−	0.855704i	$-0.673125\pi$
$157$	−12.9677	−1.03493	−0.517466	+	0.855704i	$0.673125\pi$
$158$	27.6191	2.19726
$159$	−8.83811	−0.700908
$160$	0	0
$161$	−7.78366	−0.613438
$162$	−2.36308	−0.185661
$163$	−5.60955	−0.439374	−0.219687	−	0.975570i	$-0.570504\pi$
$163$	−5.60955	−0.439374	−0.219687	+	0.975570i	$0.570504\pi$
$164$	36.5487	2.85398
$165$	0	0
$166$	34.1635	2.65160
$167$	16.0465	1.24172	0.620859	−	0.783923i	$-0.286784\pi$
$167$	16.0465	1.24172	0.620859	+	0.783923i	$0.286784\pi$
$168$	5.41829	0.418030
$169$	−12.2377	−0.941358
$170$	0	0
$171$	−5.64861	−0.431960
$172$	17.5093	1.33507
$173$	−3.75154	−0.285225	−0.142612	−	0.989779i	$-0.545550\pi$
$173$	−3.75154	−0.285225	−0.142612	+	0.989779i	$0.545550\pi$
$174$	5.44477	0.412767
$175$	0	0
$176$	7.84320	0.591204
$177$	−2.79345	−0.209969
$178$	−4.97405	−0.372821
$179$	4.26811	0.319014	0.159507	−	0.987197i	$-0.449010\pi$
$179$	4.26811	0.319014	0.159507	+	0.987197i	$0.449010\pi$
$180$	0	0
$181$	8.56462	0.636603	0.318301	−	0.947990i	$-0.396888\pi$
$181$	8.56462	0.636603	0.318301	+	0.947990i	$0.396888\pi$
$182$	−2.98636	−0.221363
$183$	8.08566	0.597709
$184$	20.1314	1.48410
$185$	0	0
$186$	−2.58797	−0.189759
$187$	−10.5124	−0.768741
$188$	−0.749235	−0.0546436
$189$	−1.44739	−0.105282
$190$	0	0
$191$	20.6622	1.49507	0.747533	−	0.664224i	$-0.231238\pi$
$191$	20.6622	1.49507	0.747533	+	0.664224i	$0.231238\pi$
$192$	11.6786	0.842834
$193$	−2.01647	−0.145149	−0.0725744	−	0.997363i	$-0.523121\pi$
$193$	−2.01647	−0.145149	−0.0725744	+	0.997363i	$0.523121\pi$
$194$	−8.70903	−0.625272
$195$	0	0
$196$	−17.5805	−1.25575
$197$	−16.0640	−1.14451	−0.572257	−	0.820075i	$-0.693932\pi$
$197$	−16.0640	−1.14451	−0.572257	+	0.820075i	$0.693932\pi$
$198$	−11.0464	−0.785033
$199$	−3.08539	−0.218718	−0.109359	−	0.994002i	$-0.534880\pi$
$199$	−3.08539	−0.218718	−0.109359	+	0.994002i	$0.534880\pi$
$200$	0	0
$201$	10.5805	0.746292
$202$	2.18377	0.153649
$203$	3.33493	0.234066
$204$	8.06019	0.564326
$205$	0	0
$206$	42.0346	2.92869
$207$	−5.37771	−0.373777
$208$	1.46497	0.101577
$209$	−26.4048	−1.82646
$210$	0	0
$211$	−11.1915	−0.770453	−0.385226	−	0.922822i	$-0.625877\pi$
$211$	−11.1915	−0.770453	−0.385226	+	0.922822i	$0.625877\pi$
$212$	31.6771	2.17559
$213$	15.7811	1.08130
$214$	2.36308	0.161537
$215$	0	0
$216$	3.74348	0.254712
$217$	−1.58514	−0.107606
$218$	12.5722	0.851500
$219$	0.698172	0.0471781
$220$	0	0
$221$	−1.96352	−0.132081
$222$	14.3154	0.960790
$223$	−11.7627	−0.787691	−0.393846	−	0.919177i	$-0.628856\pi$
$223$	−11.7627	−0.787691	−0.393846	+	0.919177i	$0.628856\pi$
$224$	5.09783	0.340613
$225$	0	0
$226$	3.16377	0.210451
$227$	−7.91558	−0.525375	−0.262688	−	0.964881i	$-0.584609\pi$
$227$	−7.91558	−0.525375	−0.262688	+	0.964881i	$0.584609\pi$
$228$	20.2455	1.34079
$229$	5.70800	0.377195	0.188598	−	0.982054i	$-0.439606\pi$
$229$	5.70800	0.377195	0.188598	+	0.982054i	$0.439606\pi$
$230$	0	0
$231$	−6.76594	−0.445166
$232$	−8.62534	−0.566281
$233$	13.5436	0.887272	0.443636	−	0.896207i	$-0.353688\pi$
$233$	13.5436	0.887272	0.443636	+	0.896207i	$0.353688\pi$
$234$	−2.06327	−0.134880
$235$	0	0
$236$	10.0122	0.651736
$237$	11.6878	0.759202
$238$	7.69173	0.498581
$239$	−3.96445	−0.256439	−0.128220	−	0.991746i	$-0.540926\pi$
$239$	−3.96445	−0.256439	−0.128220	+	0.991746i	$0.540926\pi$
$240$	0	0
$241$	15.7066	1.01175	0.505876	−	0.862606i	$-0.331169\pi$
$241$	15.7066	1.01175	0.505876	+	0.862606i	$0.331169\pi$
$242$	−25.6433	−1.64841
$243$	−1.00000	−0.0641500
$244$	−28.9802	−1.85527
$245$	0	0
$246$	24.0971	1.53637
$247$	−4.93195	−0.313812
$248$	4.09975	0.260334
$249$	14.4572	0.916187
$250$	0	0
$251$	28.2574	1.78359	0.891795	−	0.452440i	$-0.149446\pi$
$251$	28.2574	1.78359	0.891795	+	0.452440i	$0.149446\pi$
$252$	5.18767	0.326793
$253$	−25.1385	−1.58044
$254$	−46.5078	−2.91816
$255$	0	0
$256$	−25.2121	−1.57576
$257$	−26.0172	−1.62291	−0.811454	−	0.584416i	$-0.801324\pi$
$257$	−26.0172	−1.62291	−0.811454	+	0.584416i	$0.801324\pi$
$258$	11.5441	0.718706
$259$	8.76824	0.544832
$260$	0	0
$261$	2.30410	0.142620
$262$	6.75477	0.417311
$263$	−30.8359	−1.90142	−0.950712	−	0.310074i	$-0.899646\pi$
$263$	−30.8359	−1.90142	−0.950712	+	0.310074i	$0.899646\pi$
$264$	17.4992	1.07700
$265$	0	0
$266$	19.3200	1.18458
$267$	−2.10490	−0.128818
$268$	−37.9222	−2.31646
$269$	11.4911	0.700623	0.350311	−	0.936633i	$-0.386076\pi$
$269$	11.4911	0.700623	0.350311	+	0.936633i	$0.386076\pi$
$270$	0	0
$271$	−1.84758	−0.112233	−0.0561164	−	0.998424i	$-0.517872\pi$
$271$	−1.84758	−0.112233	−0.0561164	+	0.998424i	$0.517872\pi$
$272$	−3.77320	−0.228784
$273$	−1.26376	−0.0764860
$274$	−38.4533	−2.32305
$275$	0	0
$276$	19.2745	1.16019
$277$	−1.59420	−0.0957863	−0.0478932	−	0.998852i	$-0.515251\pi$
$277$	−1.59420	−0.0957863	−0.0478932	+	0.998852i	$0.515251\pi$
$278$	28.7609	1.72497
$279$	−1.09517	−0.0655661
$280$	0	0
$281$	−11.4596	−0.683624	−0.341812	−	0.939768i	$-0.611041\pi$
$281$	−11.4596	−0.683624	−0.341812	+	0.939768i	$0.611041\pi$
$282$	−0.493981	−0.0294162
$283$	21.9390	1.30414	0.652068	−	0.758160i	$-0.273902\pi$
$283$	21.9390	1.30414	0.652068	+	0.758160i	$0.273902\pi$
$284$	−56.5619	−3.35633
$285$	0	0
$286$	−9.64489	−0.570314
$287$	14.7595	0.871227
$288$	3.52208	0.207541
$289$	−11.9427	−0.702512
$290$	0	0
$291$	−3.68546	−0.216045
$292$	−2.50236	−0.146439
$293$	27.9899	1.63519	0.817594	−	0.575796i	$-0.195308\pi$
$293$	27.9899	1.63519	0.817594	+	0.575796i	$0.195308\pi$
$294$	−11.5910	−0.676003
$295$	0	0
$296$	−22.6778	−1.31812
$297$	−4.67457	−0.271246
$298$	17.1931	0.995972
$299$	−4.69542	−0.271543
$300$	0	0
$301$	7.07081	0.407555
$302$	1.81326	0.104341
$303$	0.924119	0.0530893
$304$	−9.47748	−0.543571
$305$	0	0
$306$	5.31420	0.303792
$307$	−11.6608	−0.665514	−0.332757	−	0.943013i	$-0.607979\pi$
$307$	−11.6608	−0.665514	−0.332757	+	0.943013i	$0.607979\pi$
$308$	24.2502	1.38178
$309$	17.7880	1.01193
$310$	0	0
$311$	28.9140	1.63957	0.819783	−	0.572675i	$-0.194094\pi$
$311$	28.9140	1.63957	0.819783	+	0.572675i	$0.194094\pi$
$312$	3.26853	0.185044
$313$	17.3774	0.982230	0.491115	−	0.871095i	$-0.336590\pi$
$313$	17.3774	0.982230	0.491115	+	0.871095i	$0.336590\pi$
$314$	30.6436	1.72932
$315$	0	0
$316$	−41.8907	−2.35654
$317$	−21.6442	−1.21566	−0.607829	−	0.794068i	$-0.707959\pi$
$317$	−21.6442	−1.21566	−0.607829	+	0.794068i	$0.707959\pi$
$318$	20.8852	1.17118
$319$	10.7707	0.603041
$320$	0	0
$321$	1.00000	0.0558146
$322$	18.3934	1.02502
$323$	12.7028	0.706804
$324$	3.58415	0.199120
$325$	0	0
$326$	13.2558	0.734172
$327$	5.32028	0.294212
$328$	−38.1735	−2.10778
$329$	−0.302565	−0.0166809
$330$	0	0
$331$	11.2133	0.616336	0.308168	−	0.951332i	$-0.400284\pi$
$331$	11.2133	0.616336	0.308168	+	0.951332i	$0.400284\pi$
$332$	−51.8168	−2.84381
$333$	6.05796	0.331974
$334$	−37.9192	−2.07485
$335$	0	0
$336$	−2.42850	−0.132485
$337$	−1.11702	−0.0608482	−0.0304241	−	0.999537i	$-0.509686\pi$
$337$	−1.11702	−0.0608482	−0.0304241	+	0.999537i	$0.509686\pi$
$338$	28.9186	1.57296
$339$	1.33883	0.0727155
$340$	0	0
$341$	−5.11945	−0.277234
$342$	13.3481	0.721784
$343$	−17.2313	−0.930402
$344$	−18.2877	−0.986005
$345$	0	0
$346$	8.86520	0.476596
$347$	−14.5839	−0.782907	−0.391454	−	0.920198i	$-0.628028\pi$
$347$	−14.5839	−0.782907	−0.391454	+	0.920198i	$0.628028\pi$
$348$	−8.25823	−0.442688
$349$	−27.2044	−1.45622	−0.728109	−	0.685461i	$-0.759601\pi$
$349$	−27.2044	−1.45622	−0.728109	+	0.685461i	$0.759601\pi$
$350$	0	0
$351$	−0.873126	−0.0466040
$352$	16.4642	0.877546
$353$	4.59066	0.244336	0.122168	−	0.992509i	$-0.461015\pi$
$353$	4.59066	0.244336	0.122168	+	0.992509i	$0.461015\pi$
$354$	6.60116	0.350848
$355$	0	0
$356$	7.54428	0.399846
$357$	3.25496	0.172271
$358$	−10.0859	−0.533056
$359$	−0.640646	−0.0338120	−0.0169060	−	0.999857i	$-0.505382\pi$
$359$	−0.640646	−0.0338120	−0.0169060	+	0.999857i	$0.505382\pi$
$360$	0	0
$361$	12.9068	0.679305
$362$	−20.2389	−1.06373
$363$	−10.8516	−0.569563
$364$	4.52949	0.237410
$365$	0	0
$366$	−19.1071	−0.998742
$367$	20.2023	1.05455	0.527276	−	0.849694i	$-0.323213\pi$
$367$	20.2023	1.05455	0.527276	+	0.849694i	$0.323213\pi$
$368$	−9.02295	−0.470354
$369$	10.1973	0.530851
$370$	0	0
$371$	12.7922	0.664139
$372$	3.92525	0.203515
$373$	−37.2391	−1.92817	−0.964085	−	0.265594i	$-0.914432\pi$
$373$	−37.2391	−1.92817	−0.964085	+	0.265594i	$0.914432\pi$
$374$	24.8416	1.28453
$375$	0	0
$376$	0.782542	0.0403565
$377$	2.01177	0.103611
$378$	3.42031	0.175922
$379$	−16.1652	−0.830350	−0.415175	−	0.909742i	$-0.636280\pi$
$379$	−16.1652	−0.830350	−0.415175	+	0.909742i	$0.636280\pi$
$380$	0	0
$381$	−19.6810	−1.00829
$382$	−48.8265	−2.49818
$383$	22.5153	1.15048	0.575239	−	0.817986i	$-0.304909\pi$
$383$	22.5153	1.15048	0.575239	+	0.817986i	$0.304909\pi$
$384$	−20.5534	−1.04886
$385$	0	0
$386$	4.76509	0.242536
$387$	4.88520	0.248329
$388$	13.2092	0.670598
$389$	−34.8276	−1.76583	−0.882914	−	0.469534i	$-0.844422\pi$
$389$	−34.8276	−1.76583	−0.882914	+	0.469534i	$0.844422\pi$
$390$	0	0
$391$	12.0936	0.611601
$392$	18.3620	0.927420
$393$	2.85846	0.144190
$394$	37.9606	1.91243
$395$	0	0
$396$	16.7544	0.841939
$397$	4.98338	0.250109	0.125054	−	0.992150i	$-0.460089\pi$
$397$	4.98338	0.250109	0.125054	+	0.992150i	$0.460089\pi$
$398$	7.29103	0.365466
$399$	8.17575	0.409300
$400$	0	0
$401$	−18.6735	−0.932513	−0.466256	−	0.884650i	$-0.654398\pi$
$401$	−18.6735	−0.932513	−0.466256	+	0.884650i	$0.654398\pi$
$402$	−25.0026	−1.24702
$403$	−0.956220	−0.0476327
$404$	−3.31218	−0.164787
$405$	0	0
$406$	−7.88071	−0.391113
$407$	28.3184	1.40369
$408$	−8.41850	−0.416778
$409$	25.8370	1.27756	0.638779	−	0.769391i	$-0.279440\pi$
$409$	25.8370	1.27756	0.638779	+	0.769391i	$0.279440\pi$
$410$	0	0
$411$	−16.2725	−0.802666
$412$	−63.7550	−3.14099
$413$	4.04322	0.198954
$414$	12.7080	0.624562
$415$	0	0
$416$	3.07522	0.150775
$417$	12.1709	0.596014
$418$	62.3968	3.05193
$419$	20.3519	0.994253	0.497127	−	0.867678i	$-0.334388\pi$
$419$	20.3519	0.994253	0.497127	+	0.867678i	$0.334388\pi$
$420$	0	0
$421$	11.0249	0.537320	0.268660	−	0.963235i	$-0.413419\pi$
$421$	11.0249	0.537320	0.268660	+	0.963235i	$0.413419\pi$
$422$	26.4464	1.28739
$423$	−0.209041	−0.0101639
$424$	−33.0853	−1.60676
$425$	0	0
$426$	−37.2920	−1.80681
$427$	−11.7031	−0.566353
$428$	−3.58415	−0.173247
$429$	−4.08149	−0.197056
$430$	0	0
$431$	4.18429	0.201550	0.100775	−	0.994909i	$-0.467868\pi$
$431$	4.18429	0.201550	0.100775	+	0.994909i	$0.467868\pi$
$432$	−1.67784	−0.0807253
$433$	1.66788	0.0801530	0.0400765	−	0.999197i	$-0.487240\pi$
$433$	1.66788	0.0801530	0.0400765	+	0.999197i	$0.487240\pi$
$434$	3.74581	0.179805
$435$	0	0
$436$	−19.0687	−0.913224
$437$	30.3766	1.45311
$438$	−1.64984	−0.0788323
$439$	0.146208	0.00697812	0.00348906	−	0.999994i	$-0.498889\pi$
$439$	0.146208	0.00697812	0.00348906	+	0.999994i	$0.498889\pi$
$440$	0	0
$441$	−4.90506	−0.233574
$442$	4.63996	0.220700
$443$	−1.57764	−0.0749561	−0.0374780	−	0.999297i	$-0.511932\pi$
$443$	−1.57764	−0.0749561	−0.0374780	+	0.999297i	$0.511932\pi$
$444$	−21.7126	−1.03044
$445$	0	0
$446$	27.7963	1.31619
$447$	7.27573	0.344130
$448$	−16.9036	−0.798619
$449$	−12.7601	−0.602185	−0.301093	−	0.953595i	$-0.597351\pi$
$449$	−12.7601	−0.602185	−0.301093	+	0.953595i	$0.597351\pi$
$450$	0	0
$451$	47.6681	2.24460
$452$	−4.79858	−0.225706
$453$	0.767327	0.0360522
$454$	18.7051	0.877876
$455$	0	0
$456$	−21.1455	−0.990227
$457$	−26.7828	−1.25285	−0.626424	−	0.779483i	$-0.715482\pi$
$457$	−26.7828	−1.25285	−0.626424	+	0.779483i	$0.715482\pi$
$458$	−13.4885	−0.630274
$459$	2.24884	0.104967
$460$	0	0
$461$	−8.95079	−0.416880	−0.208440	−	0.978035i	$-0.566839\pi$
$461$	−8.95079	−0.416880	−0.208440	+	0.978035i	$0.566839\pi$
$462$	15.9885	0.743851
$463$	−41.2338	−1.91630	−0.958148	−	0.286274i	$-0.907583\pi$
$463$	−41.2338	−1.91630	−0.958148	+	0.286274i	$0.907583\pi$
$464$	3.86591	0.179470
$465$	0	0
$466$	−32.0047	−1.48259
$467$	32.0527	1.48322	0.741611	−	0.670831i	$-0.234062\pi$
$467$	32.0527	1.48322	0.741611	+	0.670831i	$0.234062\pi$
$468$	3.12942	0.144657
$469$	−15.3142	−0.707142
$470$	0	0
$471$	12.9677	0.597518
$472$	−10.4572	−0.481333
$473$	22.8362	1.05001
$474$	−27.6191	−1.26859
$475$	0	0
$476$	−11.6663	−0.534722
$477$	8.83811	0.404669
$478$	9.36833	0.428497
$479$	4.32250	0.197500	0.0987500	−	0.995112i	$-0.468516\pi$
$479$	4.32250	0.197500	0.0987500	+	0.995112i	$0.468516\pi$
$480$	0	0
$481$	5.28936	0.241174
$482$	−37.1160	−1.69059
$483$	7.78366	0.354169
$484$	38.8939	1.76790
$485$	0	0
$486$	2.36308	0.107192
$487$	4.78685	0.216913	0.108456	−	0.994101i	$-0.465409\pi$
$487$	4.78685	0.216913	0.108456	+	0.994101i	$0.465409\pi$
$488$	30.2685	1.37019
$489$	5.60955	0.253672
$490$	0	0
$491$	2.84131	0.128226	0.0641132	−	0.997943i	$-0.479578\pi$
$491$	2.84131	0.128226	0.0641132	+	0.997943i	$0.479578\pi$
$492$	−36.5487	−1.64774
$493$	−5.18155	−0.233365
$494$	11.6546	0.524365
$495$	0	0
$496$	−1.83752	−0.0825072
$497$	−22.8415	−1.02458
$498$	−34.1635	−1.53090
$499$	−4.14553	−0.185579	−0.0927897	−	0.995686i	$-0.529578\pi$
$499$	−4.14553	−0.185579	−0.0927897	+	0.995686i	$0.529578\pi$
$500$	0	0
$501$	−16.0465	−0.716906
$502$	−66.7745	−2.98029
$503$	−19.5052	−0.869692	−0.434846	−	0.900505i	$-0.643197\pi$
$503$	−19.5052	−0.869692	−0.434846	+	0.900505i	$0.643197\pi$
$504$	−5.41829	−0.241350
$505$	0	0
$506$	59.4043	2.64084
$507$	12.2377	0.543493
$508$	70.5397	3.12969
$509$	11.2511	0.498698	0.249349	−	0.968414i	$-0.419783\pi$
$509$	11.2511	0.498698	0.249349	+	0.968414i	$0.419783\pi$
$510$	0	0
$511$	−1.01053	−0.0447032
$512$	18.4714	0.816330
$513$	5.64861	0.249392
$514$	61.4808	2.71180
$515$	0	0
$516$	−17.5093	−0.770805
$517$	−0.977178	−0.0429762
$518$	−20.7201	−0.910387
$519$	3.75154	0.164675
$520$	0	0
$521$	2.34748	0.102845	0.0514224	−	0.998677i	$-0.483625\pi$
$521$	2.34748	0.102845	0.0514224	+	0.998677i	$0.483625\pi$
$522$	−5.44477	−0.238311
$523$	−29.0453	−1.27006	−0.635032	−	0.772486i	$-0.719013\pi$
$523$	−29.0453	−1.27006	−0.635032	+	0.772486i	$0.719013\pi$
$524$	−10.2451	−0.447561
$525$	0	0
$526$	72.8678	3.17719
$527$	2.46286	0.107284
$528$	−7.84320	−0.341332
$529$	5.91976	0.257381
$530$	0	0
$531$	2.79345	0.121226
$532$	−29.3032	−1.27045
$533$	8.90354	0.385655
$534$	4.97405	0.215248
$535$	0	0
$536$	39.6079	1.71080
$537$	−4.26811	−0.184183
$538$	−27.1543	−1.17071
$539$	−22.9290	−0.987624
$540$	0	0
$541$	−28.2067	−1.21270	−0.606351	−	0.795197i	$-0.707367\pi$
$541$	−28.2067	−1.21270	−0.606351	+	0.795197i	$0.707367\pi$
$542$	4.36599	0.187535
$543$	−8.56462	−0.367543
$544$	−7.92060	−0.339593
$545$	0	0
$546$	2.98636	0.127804
$547$	−11.6167	−0.496694	−0.248347	−	0.968671i	$-0.579887\pi$
$547$	−11.6167	−0.496694	−0.248347	+	0.968671i	$0.579887\pi$
$548$	58.3233	2.49145
$549$	−8.08566	−0.345087
$550$	0	0
$551$	−13.0149	−0.554455
$552$	−20.1314	−0.856847
$553$	−16.9168	−0.719375
$554$	3.76723	0.160054
$555$	0	0
$556$	−43.6225	−1.85001
$557$	11.7725	0.498815	0.249408	−	0.968399i	$-0.419764\pi$
$557$	11.7725	0.498815	0.249408	+	0.968399i	$0.419764\pi$
$558$	2.58797	0.109558
$559$	4.26540	0.180407
$560$	0	0
$561$	10.5124	0.443833
$562$	27.0800	1.14230
$563$	−9.33586	−0.393460	−0.196730	−	0.980458i	$-0.563032\pi$
$563$	−9.33586	−0.393460	−0.196730	+	0.980458i	$0.563032\pi$
$564$	0.749235	0.0315485
$565$	0	0
$566$	−51.8436	−2.17915
$567$	1.44739	0.0607848
$568$	59.0763	2.47879
$569$	−10.8231	−0.453729	−0.226864	−	0.973926i	$-0.572847\pi$
$569$	−10.8231	−0.453729	−0.226864	+	0.973926i	$0.572847\pi$
$570$	0	0
$571$	35.8249	1.49923	0.749613	−	0.661876i	$-0.230239\pi$
$571$	35.8249	1.49923	0.749613	+	0.661876i	$0.230239\pi$
$572$	14.6287	0.611656
$573$	−20.6622	−0.863177
$574$	−34.8779	−1.45578
$575$	0	0
$576$	−11.6786	−0.486610
$577$	0.290697	0.0121019	0.00605093	−	0.999982i	$-0.498074\pi$
$577$	0.290697	0.0121019	0.00605093	+	0.999982i	$0.498074\pi$
$578$	28.2216	1.17386
$579$	2.01647	0.0838017
$580$	0	0
$581$	−20.9252	−0.868125
$582$	8.70903	0.361001
$583$	41.3144	1.71107
$584$	2.61359	0.108151
$585$	0	0
$586$	−66.1424	−2.73232
$587$	−1.59450	−0.0658119	−0.0329059	−	0.999458i	$-0.510476\pi$
$587$	−1.59450	−0.0658119	−0.0329059	+	0.999458i	$0.510476\pi$
$588$	17.5805	0.725006
$589$	6.18618	0.254897
$590$	0	0
$591$	16.0640	0.660785
$592$	10.1643	0.417750
$593$	9.88819	0.406059	0.203030	−	0.979173i	$-0.434921\pi$
$593$	9.88819	0.406059	0.203030	+	0.979173i	$0.434921\pi$
$594$	11.0464	0.453239
$595$	0	0
$596$	−26.0773	−1.06817
$597$	3.08539	0.126277
$598$	11.0956	0.453735
$599$	−38.6178	−1.57788	−0.788940	−	0.614470i	$-0.789370\pi$
$599$	−38.6178	−1.57788	−0.788940	+	0.614470i	$0.789370\pi$
$600$	0	0
$601$	47.5013	1.93762	0.968810	−	0.247805i	$-0.0797092\pi$
$601$	47.5013	1.93762	0.968810	+	0.247805i	$0.0797092\pi$
$602$	−16.7089	−0.681004
$603$	−10.5805	−0.430872
$604$	−2.75022	−0.111905
$605$	0	0
$606$	−2.18377	−0.0887095
$607$	−21.8153	−0.885454	−0.442727	−	0.896656i	$-0.645989\pi$
$607$	−21.8153	−0.885454	−0.442727	+	0.896656i	$0.645989\pi$
$608$	−19.8949	−0.806843
$609$	−3.33493	−0.135138
$610$	0	0
$611$	−0.182519	−0.00738394
$612$	−8.06019	−0.325814
$613$	−20.6800	−0.835256	−0.417628	−	0.908618i	$-0.637139\pi$
$613$	−20.6800	−0.835256	−0.417628	+	0.908618i	$0.637139\pi$
$614$	27.5553	1.11204
$615$	0	0
$616$	−25.3282	−1.02050
$617$	−17.3073	−0.696764	−0.348382	−	0.937353i	$-0.613269\pi$
$617$	−17.3073	−0.696764	−0.348382	+	0.937353i	$0.613269\pi$
$618$	−42.0346	−1.69088
$619$	−36.6184	−1.47182	−0.735909	−	0.677081i	$-0.763245\pi$
$619$	−36.6184	−1.47182	−0.735909	+	0.677081i	$0.763245\pi$
$620$	0	0
$621$	5.37771	0.215800
$622$	−68.3262	−2.73963
$623$	3.04662	0.122060
$624$	−1.46497	−0.0586457
$625$	0	0
$626$	−41.0642	−1.64126
$627$	26.4048	1.05451
$628$	−46.4781	−1.85468
$629$	−13.6234	−0.543200
$630$	0	0
$631$	21.4040	0.852079	0.426039	−	0.904705i	$-0.359909\pi$
$631$	21.4040	0.852079	0.426039	+	0.904705i	$0.359909\pi$
$632$	43.7529	1.74040
$633$	11.1915	0.444821
$634$	51.1469	2.03130
$635$	0	0
$636$	−31.6771	−1.25608
$637$	−4.28273	−0.169688
$638$	−25.4520	−1.00765
$639$	−15.7811	−0.624291
$640$	0	0
$641$	36.9750	1.46042	0.730212	−	0.683221i	$-0.239421\pi$
$641$	36.9750	1.46042	0.730212	+	0.683221i	$0.239421\pi$
$642$	−2.36308	−0.0932634
$643$	−11.1122	−0.438224	−0.219112	−	0.975700i	$-0.570316\pi$
$643$	−11.1122	−0.438224	−0.219112	+	0.975700i	$0.570316\pi$
$644$	−27.8978	−1.09933
$645$	0	0
$646$	−30.0178	−1.18104
$647$	−23.8168	−0.936336	−0.468168	−	0.883639i	$-0.655086\pi$
$647$	−23.8168	−0.936336	−0.468168	+	0.883639i	$0.655086\pi$
$648$	−3.74348	−0.147058
$649$	13.0582	0.512579
$650$	0	0
$651$	1.58514	0.0621265
$652$	−20.1055	−0.787391
$653$	48.0214	1.87922	0.939612	−	0.342241i	$-0.111186\pi$
$653$	48.0214	1.87922	0.939612	+	0.342241i	$0.111186\pi$
$654$	−12.5722	−0.491614
$655$	0	0
$656$	17.1095	0.668014
$657$	−0.698172	−0.0272383
$658$	0.714985	0.0278730
$659$	23.4923	0.915131	0.457565	−	0.889176i	$-0.348722\pi$
$659$	23.4923	0.915131	0.457565	+	0.889176i	$0.348722\pi$
$660$	0	0
$661$	5.94768	0.231338	0.115669	−	0.993288i	$-0.463099\pi$
$661$	5.94768	0.231338	0.115669	+	0.993288i	$0.463099\pi$
$662$	−26.4978	−1.02987
$663$	1.96352	0.0762569
$664$	54.1202	2.10027
$665$	0	0
$666$	−14.3154	−0.554712
$667$	−12.3908	−0.479772
$668$	57.5132	2.22525
$669$	11.7627	0.454774
$670$	0	0
$671$	−37.7970	−1.45914
$672$	−5.09783	−0.196653
$673$	−10.8664	−0.418868	−0.209434	−	0.977823i	$-0.567162\pi$
$673$	−10.8664	−0.418868	−0.209434	+	0.977823i	$0.567162\pi$
$674$	2.63962	0.101674
$675$	0	0
$676$	−43.8616	−1.68698
$677$	−27.9593	−1.07456	−0.537281	−	0.843403i	$-0.680549\pi$
$677$	−27.9593	−1.07456	−0.537281	+	0.843403i	$0.680549\pi$
$678$	−3.16377	−0.121504
$679$	5.33430	0.204712
$680$	0	0
$681$	7.91558	0.303326
$682$	12.0977	0.463244
$683$	−35.4747	−1.35740	−0.678700	−	0.734415i	$-0.737456\pi$
$683$	−35.4747	−1.35740	−0.678700	+	0.734415i	$0.737456\pi$
$684$	−20.2455	−0.774105
$685$	0	0
$686$	40.7189	1.55466
$687$	−5.70800	−0.217774
$688$	8.19661	0.312493
$689$	7.71678	0.293986
$690$	0	0
$691$	−10.2516	−0.389988	−0.194994	−	0.980804i	$-0.562469\pi$
$691$	−10.2516	−0.389988	−0.194994	+	0.980804i	$0.562469\pi$
$692$	−13.4461	−0.511144
$693$	6.76594	0.257017
$694$	34.4630	1.30820
$695$	0	0
$696$	8.62534	0.326943
$697$	−22.9322	−0.868617
$698$	64.2862	2.43327
$699$	−13.5436	−0.512267
$700$	0	0
$701$	−16.5070	−0.623462	−0.311731	−	0.950170i	$-0.600909\pi$
$701$	−16.5070	−0.623462	−0.311731	+	0.950170i	$0.600909\pi$
$702$	2.06327	0.0778730
$703$	−34.2190	−1.29060
$704$	−54.5927	−2.05754
$705$	0	0
$706$	−10.8481	−0.408274
$707$	−1.33756	−0.0503042
$708$	−10.0122	−0.376280
$709$	38.4846	1.44532	0.722659	−	0.691204i	$-0.242920\pi$
$709$	38.4846	1.44532	0.722659	+	0.691204i	$0.242920\pi$
$710$	0	0
$711$	−11.6878	−0.438325
$712$	−7.87965	−0.295303
$713$	5.88950	0.220564
$714$	−7.69173	−0.287856
$715$	0	0
$716$	15.2976	0.571697
$717$	3.96445	0.148055
$718$	1.51390	0.0564981
$719$	17.1250	0.638653	0.319327	−	0.947645i	$-0.396543\pi$
$719$	17.1250	0.638653	0.319327	+	0.947645i	$0.396543\pi$
$720$	0	0
$721$	−25.7463	−0.958841
$722$	−30.4998	−1.13509
$723$	−15.7066	−0.584136
$724$	30.6969	1.14084
$725$	0	0
$726$	25.6433	0.951712
$727$	19.1313	0.709542	0.354771	−	0.934953i	$-0.384559\pi$
$727$	19.1313	0.709542	0.354771	+	0.934953i	$0.384559\pi$
$728$	−4.73084	−0.175337
$729$	1.00000	0.0370370
$730$	0	0
$731$	−10.9861	−0.406334
$732$	28.9802	1.07114
$733$	35.0229	1.29360	0.646800	−	0.762660i	$-0.276107\pi$
$733$	35.0229	1.29360	0.646800	+	0.762660i	$0.276107\pi$
$734$	−47.7397	−1.76210
$735$	0	0
$736$	−18.9407	−0.698165
$737$	−49.4594	−1.82186
$738$	−24.0971	−0.887026
$739$	29.0459	1.06847	0.534235	−	0.845336i	$-0.320600\pi$
$739$	29.0459	1.06847	0.534235	+	0.845336i	$0.320600\pi$
$740$	0	0
$741$	4.93195	0.181180
$742$	−30.2290	−1.10974
$743$	1.22055	0.0447777	0.0223888	−	0.999749i	$-0.492873\pi$
$743$	1.22055	0.0447777	0.0223888	+	0.999749i	$0.492873\pi$
$744$	−4.09975	−0.150304
$745$	0	0
$746$	87.9991	3.22188
$747$	−14.4572	−0.528961
$748$	−37.6780	−1.37764
$749$	−1.44739	−0.0528866
$750$	0	0
$751$	−0.853157	−0.0311321	−0.0155661	−	0.999879i	$-0.504955\pi$
$751$	−0.853157	−0.0311321	−0.0155661	+	0.999879i	$0.504955\pi$
$752$	−0.350738	−0.0127901
$753$	−28.2574	−1.02976
$754$	−4.75396	−0.173129
$755$	0	0
$756$	−5.18767	−0.188674
$757$	31.4896	1.14451	0.572255	−	0.820076i	$-0.306069\pi$
$757$	31.4896	1.14451	0.572255	+	0.820076i	$0.306069\pi$
$758$	38.1997	1.38747
$759$	25.1385	0.912470
$760$	0	0
$761$	52.5069	1.90337	0.951687	−	0.307070i	$-0.0993487\pi$
$761$	52.5069	1.90337	0.951687	+	0.307070i	$0.0993487\pi$
$762$	46.5078	1.68480
$763$	−7.70053	−0.278778
$764$	74.0566	2.67927
$765$	0	0
$766$	−53.2054	−1.92239
$767$	2.43904	0.0880685
$768$	25.2121	0.909765
$769$	20.2190	0.729115	0.364557	−	0.931181i	$-0.381220\pi$
$769$	20.2190	0.729115	0.364557	+	0.931181i	$0.381220\pi$
$770$	0	0
$771$	26.0172	0.936987
$772$	−7.22734	−0.260118
$773$	−25.0425	−0.900715	−0.450357	−	0.892848i	$-0.648703\pi$
$773$	−25.0425	−0.900715	−0.450357	+	0.892848i	$0.648703\pi$
$774$	−11.5441	−0.414945
$775$	0	0
$776$	−13.7964	−0.495263
$777$	−8.76824	−0.314559
$778$	82.3004	2.95061
$779$	−57.6007	−2.06376
$780$	0	0
$781$	−73.7699	−2.63970
$782$	−28.5782	−1.02195
$783$	−2.30410	−0.0823417
$784$	−8.22991	−0.293926
$785$	0	0
$786$	−6.75477	−0.240935
$787$	1.40150	0.0499580	0.0249790	−	0.999688i	$-0.492048\pi$
$787$	1.40150	0.0499580	0.0249790	+	0.999688i	$0.492048\pi$
$788$	−57.5759	−2.05105
$789$	30.8359	1.09779
$790$	0	0
$791$	−1.93782	−0.0689009
$792$	−17.4992	−0.621806
$793$	−7.05979	−0.250701
$794$	−11.7761	−0.417919
$795$	0	0
$796$	−11.0585	−0.391959
$797$	−21.5005	−0.761587	−0.380794	−	0.924660i	$-0.624349\pi$
$797$	−21.5005	−0.761587	−0.380794	+	0.924660i	$0.624349\pi$
$798$	−19.3200	−0.683920
$799$	0.470101	0.0166310
$800$	0	0
$801$	2.10490	0.0743730
$802$	44.1271	1.55818
$803$	−3.26366	−0.115172
$804$	37.9222	1.33741
$805$	0	0
$806$	2.25963	0.0795919
$807$	−11.4911	−0.404505
$808$	3.45942	0.121702
$809$	−21.6260	−0.760331	−0.380165	−	0.924919i	$-0.624133\pi$
$809$	−21.6260	−0.760331	−0.380165	+	0.924919i	$0.624133\pi$
$810$	0	0
$811$	−38.6557	−1.35738	−0.678692	−	0.734423i	$-0.737453\pi$
$811$	−38.6557	−1.35738	−0.678692	+	0.734423i	$0.737453\pi$
$812$	11.9529	0.419465
$813$	1.84758	0.0647976
$814$	−66.9186	−2.34550
$815$	0	0
$816$	3.77320	0.132089
$817$	−27.5946	−0.965413
$818$	−61.0549	−2.13474
$819$	1.26376	0.0441592
$820$	0	0
$821$	−22.5086	−0.785555	−0.392777	−	0.919634i	$-0.628486\pi$
$821$	−22.5086	−0.785555	−0.392777	+	0.919634i	$0.628486\pi$
$822$	38.4533	1.34121
$823$	−2.92883	−0.102092	−0.0510462	−	0.998696i	$-0.516256\pi$
$823$	−2.92883	−0.102092	−0.0510462	+	0.998696i	$0.516256\pi$
$824$	66.5892	2.31974
$825$	0	0
$826$	−9.55447	−0.332442
$827$	−30.0926	−1.04642	−0.523211	−	0.852203i	$-0.675266\pi$
$827$	−30.0926	−1.04642	−0.523211	+	0.852203i	$0.675266\pi$
$828$	−19.2745	−0.669836
$829$	23.4175	0.813323	0.406661	−	0.913579i	$-0.366693\pi$
$829$	23.4175	0.813323	0.406661	+	0.913579i	$0.366693\pi$
$830$	0	0
$831$	1.59420	0.0553023
$832$	−10.1969	−0.353515
$833$	11.0307	0.382191
$834$	−28.7609	−0.995910
$835$	0	0
$836$	−94.6390	−3.27316
$837$	1.09517	0.0378546
$838$	−48.0931	−1.66135
$839$	−43.5906	−1.50491	−0.752457	−	0.658641i	$-0.771132\pi$
$839$	−43.5906	−1.50491	−0.752457	+	0.658641i	$0.771132\pi$
$840$	0	0
$841$	−23.6911	−0.816936
$842$	−26.0527	−0.897836
$843$	11.4596	0.394691
$844$	−40.1119	−1.38071
$845$	0	0
$846$	0.493981	0.0169834
$847$	15.7066	0.539684
$848$	14.8290	0.509229
$849$	−21.9390	−0.752943
$850$	0	0
$851$	−32.5779	−1.11676
$852$	56.5619	1.93778
$853$	12.6420	0.432855	0.216428	−	0.976299i	$-0.430559\pi$
$853$	12.6420	0.432855	0.216428	+	0.976299i	$0.430559\pi$
$854$	27.6554	0.946349
$855$	0	0
$856$	3.74348	0.127950
$857$	54.2198	1.85211	0.926056	−	0.377385i	$-0.123177\pi$
$857$	54.2198	1.85211	0.926056	+	0.377385i	$0.123177\pi$
$858$	9.64489	0.329271
$859$	−11.8641	−0.404798	−0.202399	−	0.979303i	$-0.564874\pi$
$859$	−11.8641	−0.404798	−0.202399	+	0.979303i	$0.564874\pi$
$860$	0	0
$861$	−14.7595	−0.503003
$862$	−9.88781	−0.336780
$863$	−32.9713	−1.12236	−0.561178	−	0.827695i	$-0.689652\pi$
$863$	−32.9713	−1.12236	−0.561178	+	0.827695i	$0.689652\pi$
$864$	−3.52208	−0.119824
$865$	0	0
$866$	−3.94133	−0.133932
$867$	11.9427	0.405596
$868$	−5.68138	−0.192839
$869$	−54.6353	−1.85338
$870$	0	0
$871$	−9.23812	−0.313022
$872$	19.9164	0.674453
$873$	3.68546	0.124734
$874$	−71.7823	−2.42807
$875$	0	0
$876$	2.50236	0.0845468
$877$	16.5623	0.559268	0.279634	−	0.960107i	$-0.409787\pi$
$877$	16.5623	0.559268	0.279634	+	0.960107i	$0.409787\pi$
$878$	−0.345501	−0.0116601
$879$	−27.9899	−0.944076
$880$	0	0
$881$	4.29022	0.144541	0.0722706	−	0.997385i	$-0.476975\pi$
$881$	4.29022	0.144541	0.0722706	+	0.997385i	$0.476975\pi$
$882$	11.5910	0.390291
$883$	−6.93590	−0.233412	−0.116706	−	0.993167i	$-0.537233\pi$
$883$	−6.93590	−0.233412	−0.116706	+	0.993167i	$0.537233\pi$
$884$	−7.03756	−0.236699
$885$	0	0
$886$	3.72810	0.125248
$887$	−34.1013	−1.14501	−0.572504	−	0.819902i	$-0.694028\pi$
$887$	−34.1013	−1.14501	−0.572504	+	0.819902i	$0.694028\pi$
$888$	22.6778	0.761019
$889$	28.4861	0.955394
$890$	0	0
$891$	4.67457	0.156604
$892$	−42.1594	−1.41160
$893$	1.18079	0.0395137
$894$	−17.1931	−0.575025
$895$	0	0
$896$	29.7489	0.993840
$897$	4.69542	0.156775
$898$	30.1531	1.00622
$899$	−2.52338	−0.0841593
$900$	0	0
$901$	−19.8755	−0.662149
$902$	−112.644	−3.75062
$903$	−7.07081	−0.235302
$904$	5.01190	0.166693
$905$	0	0
$906$	−1.81326	−0.0602414
$907$	−29.9049	−0.992975	−0.496488	−	0.868044i	$-0.665377\pi$
$907$	−29.9049	−0.992975	−0.496488	+	0.868044i	$0.665377\pi$
$908$	−28.3706	−0.941512
$909$	−0.924119	−0.0306511
$910$	0	0
$911$	16.1032	0.533524	0.266762	−	0.963762i	$-0.414046\pi$
$911$	16.1032	0.533524	0.266762	+	0.963762i	$0.414046\pi$
$912$	9.47748	0.313831
$913$	−67.5812	−2.23661
$914$	63.2900	2.09345
$915$	0	0
$916$	20.4583	0.675962
$917$	−4.13731	−0.136626
$918$	−5.31420	−0.175395
$919$	12.1131	0.399574	0.199787	−	0.979839i	$-0.435975\pi$
$919$	12.1131	0.399574	0.199787	+	0.979839i	$0.435975\pi$
$920$	0	0
$921$	11.6608	0.384235
$922$	21.1514	0.696585
$923$	−13.7789	−0.453538
$924$	−24.2502	−0.797772
$925$	0	0
$926$	97.4387	3.20204
$927$	−17.7880	−0.584236
$928$	8.11521	0.266395
$929$	−47.2640	−1.55068	−0.775340	−	0.631544i	$-0.782422\pi$
$929$	−47.2640	−1.55068	−0.775340	+	0.631544i	$0.782422\pi$
$930$	0	0
$931$	27.7067	0.908052
$932$	48.5424	1.59006
$933$	−28.9140	−0.946603
$934$	−75.7431	−2.47839
$935$	0	0
$936$	−3.26853	−0.106835
$937$	21.0685	0.688278	0.344139	−	0.938919i	$-0.388171\pi$
$937$	21.0685	0.688278	0.344139	+	0.938919i	$0.388171\pi$
$938$	36.1886	1.18160
$939$	−17.3774	−0.567091
$940$	0	0
$941$	−23.4389	−0.764086	−0.382043	−	0.924145i	$-0.624779\pi$
$941$	−23.4389	−0.764086	−0.382043	+	0.924145i	$0.624779\pi$
$942$	−30.6436	−0.998423
$943$	−54.8382	−1.78578
$944$	4.68698	0.152548
$945$	0	0
$946$	−53.9639	−1.75452
$947$	−15.4007	−0.500456	−0.250228	−	0.968187i	$-0.580506\pi$
$947$	−15.4007	−0.500456	−0.250228	+	0.968187i	$0.580506\pi$
$948$	41.8907	1.36055
$949$	−0.609592	−0.0197882
$950$	0	0
$951$	21.6442	0.701860
$952$	12.1849	0.394914
$953$	34.2377	1.10907	0.554535	−	0.832161i	$-0.312896\pi$
$953$	34.2377	1.10907	0.554535	+	0.832161i	$0.312896\pi$
$954$	−20.8852	−0.676182
$955$	0	0
$956$	−14.2092	−0.459559
$957$	−10.7707	−0.348166
$958$	−10.2144	−0.330013
$959$	23.5528	0.760558
$960$	0	0
$961$	−29.8006	−0.961310
$962$	−12.4992	−0.402990
$963$	−1.00000	−0.0322245
$964$	56.2949	1.81314
$965$	0	0
$966$	−18.3934	−0.591798
$967$	54.3298	1.74713	0.873564	−	0.486709i	$-0.161803\pi$
$967$	54.3298	1.74713	0.873564	+	0.486709i	$0.161803\pi$
$968$	−40.6229	−1.30567
$969$	−12.7028	−0.408074
$970$	0	0
$971$	−40.4098	−1.29681	−0.648407	−	0.761294i	$-0.724564\pi$
$971$	−40.4098	−1.29681	−0.648407	+	0.761294i	$0.724564\pi$
$972$	−3.58415	−0.114962
$973$	−17.6161	−0.564747
$974$	−11.3117	−0.362451
$975$	0	0
$976$	−13.5665	−0.434252
$977$	33.3177	1.06593	0.532963	−	0.846138i	$-0.321078\pi$
$977$	33.3177	1.06593	0.532963	+	0.846138i	$0.321078\pi$
$978$	−13.2558	−0.423874
$979$	9.83951	0.314472
$980$	0	0
$981$	−5.32028	−0.169863
$982$	−6.71424	−0.214260
$983$	−3.45352	−0.110150	−0.0550751	−	0.998482i	$-0.517540\pi$
$983$	−3.45352	−0.110150	−0.0550751	+	0.998482i	$0.517540\pi$
$984$	38.1735	1.21693
$985$	0	0
$986$	12.2444	0.389942
$987$	0.302565	0.00963074
$988$	−17.6768	−0.562375
$989$	−26.2712	−0.835376
$990$	0	0
$991$	−5.35863	−0.170222	−0.0851112	−	0.996371i	$-0.527125\pi$
$991$	−5.35863	−0.170222	−0.0851112	+	0.996371i	$0.527125\pi$
$992$	−3.85728	−0.122469
$993$	−11.2133	−0.355842
$994$	53.9762	1.71202
$995$	0	0
$996$	51.8168	1.64188
$997$	60.5247	1.91684	0.958419	−	0.285365i	$-0.0921148\pi$
$997$	60.5247	1.91684	0.958419	+	0.285365i	$0.0921148\pi$
$998$	9.79623	0.310094
$999$	−6.05796	−0.191665

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8025.2.a.bf.1.3		12
5.4	even	2		1605.2.a.n.1.10	✓	12
15.14	odd	2		4815.2.a.u.1.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1605.2.a.n.1.10	✓	12	5.4	even	2
4815.2.a.u.1.3		12	15.14	odd	2
8025.2.a.bf.1.3		12	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8025 = 3 \cdot 5^{2} \cdot 107 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8025.a (trivial)

\(f(q)\)	\(=\)	\(q-2.36308 q^{2} -1.00000 q^{3} +3.58415 q^{4} +2.36308 q^{6} +1.44739 q^{7} -3.74348 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.36308 q^{2} -1.00000 q^{3} +3.58415 q^{4} +2.36308 q^{6} +1.44739 q^{7} -3.74348 q^{8} +1.00000 q^{9} +4.67457 q^{11} -3.58415 q^{12} +0.873126 q^{13} -3.42031 q^{14} +1.67784 q^{16} -2.24884 q^{17} -2.36308 q^{18} -5.64861 q^{19} -1.44739 q^{21} -11.0464 q^{22} -5.37771 q^{23} +3.74348 q^{24} -2.06327 q^{26} -1.00000 q^{27} +5.18767 q^{28} +2.30410 q^{29} -1.09517 q^{31} +3.52208 q^{32} -4.67457 q^{33} +5.31420 q^{34} +3.58415 q^{36} +6.05796 q^{37} +13.3481 q^{38} -0.873126 q^{39} +10.1973 q^{41} +3.42031 q^{42} +4.88520 q^{43} +16.7544 q^{44} +12.7080 q^{46} -0.209041 q^{47} -1.67784 q^{48} -4.90506 q^{49} +2.24884 q^{51} +3.12942 q^{52} +8.83811 q^{53} +2.36308 q^{54} -5.41829 q^{56} +5.64861 q^{57} -5.44477 q^{58} +2.79345 q^{59} -8.08566 q^{61} +2.58797 q^{62} +1.44739 q^{63} -11.6786 q^{64} +11.0464 q^{66} -10.5805 q^{67} -8.06019 q^{68} +5.37771 q^{69} -15.7811 q^{71} -3.74348 q^{72} -0.698172 q^{73} -14.3154 q^{74} -20.2455 q^{76} +6.76594 q^{77} +2.06327 q^{78} -11.6878 q^{79} +1.00000 q^{81} -24.0971 q^{82} -14.4572 q^{83} -5.18767 q^{84} -11.5441 q^{86} -2.30410 q^{87} -17.4992 q^{88} +2.10490 q^{89} +1.26376 q^{91} -19.2745 q^{92} +1.09517 q^{93} +0.493981 q^{94} -3.52208 q^{96} +3.68546 q^{97} +11.5910 q^{98} +4.67457 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - 12 q^{3} + 15 q^{4} + 3 q^{6} - 7 q^{7} - 3 q^{8} + 12 q^{9}+O(q^{10}) \) 12 * q - 3 * q^2 - 12 * q^3 + 15 * q^4 + 3 * q^6 - 7 * q^7 - 3 * q^8 + 12 * q^9	\( 12 q - 3 q^{2} - 12 q^{3} + 15 q^{4} + 3 q^{6} - 7 q^{7} - 3 q^{8} + 12 q^{9} + 4 q^{11} - 15 q^{12} - 13 q^{13} + 4 q^{14} + 13 q^{16} + 4 q^{17} - 3 q^{18} + 14 q^{19} + 7 q^{21} - 15 q^{22} - 11 q^{23} + 3 q^{24} - 8 q^{26} - 12 q^{27} - 16 q^{28} - 7 q^{29} + 4 q^{31} - 4 q^{32} - 4 q^{33} + q^{34} + 15 q^{36} - 24 q^{37} + 11 q^{38} + 13 q^{39} + 13 q^{41} - 4 q^{42} - 25 q^{43} + 10 q^{44} - 22 q^{46} - 19 q^{47} - 13 q^{48} + 9 q^{49} - 4 q^{51} - 20 q^{52} - 11 q^{53} + 3 q^{54} - 37 q^{56} - 14 q^{57} + 2 q^{58} + 8 q^{59} + 7 q^{61} + 11 q^{62} - 7 q^{63} - 19 q^{64} + 15 q^{66} - 33 q^{67} + 24 q^{68} + 11 q^{69} - 3 q^{72} - 34 q^{73} - 27 q^{74} - 9 q^{76} + 29 q^{77} + 8 q^{78} + 12 q^{81} - q^{82} + 24 q^{83} + 16 q^{84} - 36 q^{86} + 7 q^{87} + 6 q^{88} - 10 q^{89} + 30 q^{91} + 28 q^{92} - 4 q^{93} - 8 q^{94} + 4 q^{96} - 16 q^{97} + 36 q^{98} + 4 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 - 12 * q^3 + 15 * q^4 + 3 * q^6 - 7 * q^7 - 3 * q^8 + 12 * q^9 + 4 * q^11 - 15 * q^12 - 13 * q^13 + 4 * q^14 + 13 * q^16 + 4 * q^17 - 3 * q^18 + 14 * q^19 + 7 * q^21 - 15 * q^22 - 11 * q^23 + 3 * q^24 - 8 * q^26 - 12 * q^27 - 16 * q^28 - 7 * q^29 + 4 * q^31 - 4 * q^32 - 4 * q^33 + q^34 + 15 * q^36 - 24 * q^37 + 11 * q^38 + 13 * q^39 + 13 * q^41 - 4 * q^42 - 25 * q^43 + 10 * q^44 - 22 * q^46 - 19 * q^47 - 13 * q^48 + 9 * q^49 - 4 * q^51 - 20 * q^52 - 11 * q^53 + 3 * q^54 - 37 * q^56 - 14 * q^57 + 2 * q^58 + 8 * q^59 + 7 * q^61 + 11 * q^62 - 7 * q^63 - 19 * q^64 + 15 * q^66 - 33 * q^67 + 24 * q^68 + 11 * q^69 - 3 * q^72 - 34 * q^73 - 27 * q^74 - 9 * q^76 + 29 * q^77 + 8 * q^78 + 12 * q^81 - q^82 + 24 * q^83 + 16 * q^84 - 36 * q^86 + 7 * q^87 + 6 * q^88 - 10 * q^89 + 30 * q^91 + 28 * q^92 - 4 * q^93 - 8 * q^94 + 4 * q^96 - 16 * q^97 + 36 * q^98 + 4 * q^99

Introduction

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