LMFDB - Embedded newform 3025.2.a.v.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3025,2,Mod(1,3025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3025, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("3025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3025 = 5^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3025.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:	$24.1547466114$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.2525.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 4x^{2} + 5x + 5 $ x^4 - 2x^3 - 4x^2 + 5*x + 5
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.46673$ of defining polynomial
Character	$\chi$	$=$	3025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.52452 q^{2} +2.46673 q^{3} +4.37322 q^{4} -6.22732 q^{6} -2.09351 q^{7} -5.99126 q^{8} +3.08477 q^{9} +O(q^{10})$	\(q-2.52452 q^{2} +2.46673 q^{3} +4.37322 q^{4} -6.22732 q^{6} -2.09351 q^{7} -5.99126 q^{8} +3.08477 q^{9} +10.7876 q^{12} -1.28846 q^{13} +5.28512 q^{14} +6.37863 q^{16} +2.99126 q^{17} -7.78757 q^{18} +2.15130 q^{19} -5.16413 q^{21} -8.77882 q^{23} -14.7788 q^{24} +3.25274 q^{26} +0.209094 q^{27} -9.15538 q^{28} -0.612630 q^{29} -3.64501 q^{31} -4.12048 q^{32} -7.55150 q^{34} +13.4904 q^{36} +1.87077 q^{37} -5.43101 q^{38} -3.17828 q^{39} -5.10684 q^{41} +13.0370 q^{42} -5.17287 q^{43} +22.1623 q^{46} +7.30669 q^{47} +15.7344 q^{48} -2.61722 q^{49} +7.37863 q^{51} -5.63470 q^{52} +2.94221 q^{53} -0.527864 q^{54} +12.5428 q^{56} +5.30669 q^{57} +1.54660 q^{58} -6.49421 q^{59} -0.502449 q^{61} +9.20191 q^{62} -6.45799 q^{63} -2.35499 q^{64} +7.80964 q^{67} +13.0814 q^{68} -21.6550 q^{69} -11.3042 q^{71} -18.4816 q^{72} +11.1171 q^{73} -4.72281 q^{74} +9.40812 q^{76} +8.02363 q^{78} +5.35907 q^{79} -8.73852 q^{81} +12.8923 q^{82} -10.8454 q^{83} -22.5839 q^{84} +13.0590 q^{86} -1.51119 q^{87} -4.32336 q^{89} +2.69740 q^{91} -38.3917 q^{92} -8.99126 q^{93} -18.4459 q^{94} -10.1641 q^{96} +0.351653 q^{97} +6.60723 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 3 q^{2} + 2 q^{3} + 7 q^{4} - q^{6} - 11 q^{7} - 9 q^{8}+O(q^{10}) $ 4 * q - 3 * q^2 + 2 * q^3 + 7 * q^4 - q^6 - 11 * q^7 - 9 * q^8	$ 4 q - 3 q^{2} + 2 q^{3} + 7 q^{4} - q^{6} - 11 q^{7} - 9 q^{8} + 14 q^{12} - 7 q^{13} - 2 q^{14} + 5 q^{16} - 3 q^{17} - 2 q^{18} + 12 q^{19} - 6 q^{21} + 9 q^{23} - 15 q^{24} + 13 q^{26} + 5 q^{27} - 7 q^{28} - 8 q^{29} + 3 q^{31} - 6 q^{32} - 10 q^{34} + 8 q^{36} + 3 q^{37} - 12 q^{38} - 3 q^{39} - 7 q^{41} - 2 q^{42} - 21 q^{43} + 12 q^{46} + 3 q^{47} + 2 q^{48} + 15 q^{49} + 9 q^{51} - 27 q^{52} + 11 q^{53} - 20 q^{54} + 15 q^{56} - 5 q^{57} - 2 q^{58} - 7 q^{59} + 4 q^{61} - 11 q^{62} - 3 q^{63} - 27 q^{64} + q^{67} + 15 q^{68} - 28 q^{69} - 15 q^{71} - 13 q^{72} + 9 q^{73} - 36 q^{74} + 8 q^{76} - 6 q^{78} + 6 q^{79} - 20 q^{81} + 44 q^{82} - 15 q^{83} - 47 q^{84} - 3 q^{86} - 15 q^{87} + 4 q^{91} - 18 q^{92} - 21 q^{93} - 11 q^{94} - 26 q^{96} - 6 q^{97} + 42 q^{98}+O(q^{100}) $ 4 * q - 3 * q^2 + 2 * q^3 + 7 * q^4 - q^6 - 11 * q^7 - 9 * q^8 + 14 * q^12 - 7 * q^13 - 2 * q^14 + 5 * q^16 - 3 * q^17 - 2 * q^18 + 12 * q^19 - 6 * q^21 + 9 * q^23 - 15 * q^24 + 13 * q^26 + 5 * q^27 - 7 * q^28 - 8 * q^29 + 3 * q^31 - 6 * q^32 - 10 * q^34 + 8 * q^36 + 3 * q^37 - 12 * q^38 - 3 * q^39 - 7 * q^41 - 2 * q^42 - 21 * q^43 + 12 * q^46 + 3 * q^47 + 2 * q^48 + 15 * q^49 + 9 * q^51 - 27 * q^52 + 11 * q^53 - 20 * q^54 + 15 * q^56 - 5 * q^57 - 2 * q^58 - 7 * q^59 + 4 * q^61 - 11 * q^62 - 3 * q^63 - 27 * q^64 + q^67 + 15 * q^68 - 28 * q^69 - 15 * q^71 - 13 * q^72 + 9 * q^73 - 36 * q^74 + 8 * q^76 - 6 * q^78 + 6 * q^79 - 20 * q^81 + 44 * q^82 - 15 * q^83 - 47 * q^84 - 3 * q^86 - 15 * q^87 + 4 * q^91 - 18 * q^92 - 21 * q^93 - 11 * q^94 - 26 * q^96 - 6 * q^97 + 42 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.52452	−1.78511	−0.892554	−	0.450940i	$-0.851089\pi$
$2$	−2.52452	−1.78511	−0.892554	+	0.450940i	$0.851089\pi$
$3$	2.46673	1.42417	0.712084	−	0.702094i	$-0.247751\pi$
$3$	2.46673	1.42417	0.712084	+	0.702094i	$0.247751\pi$
$4$	4.37322	2.18661
$5$	0	0
$5$	0	0
$6$	−6.22732	−2.54229
$7$	−2.09351	−0.791272	−0.395636	−	0.918407i	$-0.629476\pi$
$7$	−2.09351	−0.791272	−0.395636	+	0.918407i	$0.629476\pi$
$8$	−5.99126	−2.11823
$9$	3.08477	1.02826
$10$	0	0
$11$	0	0
$11$	0	0
$12$	10.7876	3.11410
$13$	−1.28846	−0.357353	−0.178677	−	0.983908i	$-0.557182\pi$
$13$	−1.28846	−0.357353	−0.178677	+	0.983908i	$0.557182\pi$
$14$	5.28512	1.41251
$15$	0	0
$16$	6.37863	1.59466
$17$	2.99126	0.725486	0.362743	−	0.931889i	$-0.381840\pi$
$17$	2.99126	0.725486	0.362743	+	0.931889i	$0.381840\pi$
$18$	−7.78757	−1.83555
$19$	2.15130	0.493543	0.246771	−	0.969074i	$-0.420630\pi$
$19$	2.15130	0.493543	0.246771	+	0.969074i	$0.420630\pi$
$20$	0	0
$21$	−5.16413	−1.12690
$22$	0	0
$23$	−8.77882	−1.83051	−0.915255	−	0.402874i	$-0.868011\pi$
$23$	−8.77882	−1.83051	−0.915255	+	0.402874i	$0.868011\pi$
$24$	−14.7788	−3.01671
$25$	0	0
$26$	3.25274	0.637915
$27$	0.209094	0.0402403
$28$	−9.15538	−1.73020
$29$	−0.612630	−0.113763	−0.0568813	−	0.998381i	$-0.518116\pi$
$29$	−0.612630	−0.113763	−0.0568813	+	0.998381i	$0.518116\pi$
$30$	0	0
$31$	−3.64501	−0.654663	−0.327331	−	0.944910i	$-0.606149\pi$
$31$	−3.64501	−0.654663	−0.327331	+	0.944910i	$0.606149\pi$
$32$	−4.12048	−0.728405
$33$	0	0
$34$	−7.55150	−1.29507
$35$	0	0
$36$	13.4904	2.24839
$37$	1.87077	0.307553	0.153777	−	0.988106i	$-0.450856\pi$
$37$	1.87077	0.307553	0.153777	+	0.988106i	$0.450856\pi$
$38$	−5.43101	−0.881027
$39$	−3.17828	−0.508931
$40$	0	0
$41$	−5.10684	−0.797554	−0.398777	−	0.917048i	$-0.630565\pi$
$41$	−5.10684	−0.797554	−0.398777	+	0.917048i	$0.630565\pi$
$42$	13.0370	2.01165
$43$	−5.17287	−0.788856	−0.394428	−	0.918927i	$-0.629057\pi$
$43$	−5.17287	−0.788856	−0.394428	+	0.918927i	$0.629057\pi$
$44$	0	0
$45$	0	0
$46$	22.1623	3.26766
$47$	7.30669	1.06579	0.532895	−	0.846181i	$-0.321104\pi$
$47$	7.30669	1.06579	0.532895	+	0.846181i	$0.321104\pi$
$48$	15.7344	2.27106
$49$	−2.61722	−0.373888
$50$	0	0
$51$	7.37863	1.03321
$52$	−5.63470	−0.781393
$53$	2.94221	0.404143	0.202072	−	0.979371i	$-0.435233\pi$
$53$	2.94221	0.404143	0.202072	+	0.979371i	$0.435233\pi$
$54$	−0.527864	−0.0718332
$55$	0	0
$56$	12.5428	1.67610
$57$	5.30669	0.702888
$58$	1.54660	0.203078
$59$	−6.49421	−0.845474	−0.422737	−	0.906252i	$-0.638931\pi$
$59$	−6.49421	−0.845474	−0.422737	+	0.906252i	$0.638931\pi$
$60$	0	0
$61$	−0.502449	−0.0643321	−0.0321660	−	0.999483i	$-0.510241\pi$
$61$	−0.502449	−0.0643321	−0.0321660	+	0.999483i	$0.510241\pi$
$62$	9.20191	1.16864
$63$	−6.45799	−0.813630
$64$	−2.35499	−0.294374
$65$	0	0
$66$	0	0
$67$	7.80964	0.954099	0.477050	−	0.878876i	$-0.341706\pi$
$67$	7.80964	0.954099	0.477050	+	0.878876i	$0.341706\pi$
$68$	13.0814	1.58636
$69$	−21.6550	−2.60696
$70$	0	0
$71$	−11.3042	−1.34156	−0.670779	−	0.741658i	$-0.734040\pi$
$71$	−11.3042	−1.34156	−0.670779	+	0.741658i	$0.734040\pi$
$72$	−18.4816	−2.17808
$73$	11.1171	1.30116	0.650582	−	0.759436i	$-0.274525\pi$
$73$	11.1171	1.30116	0.650582	+	0.759436i	$0.274525\pi$
$74$	−4.72281	−0.549016
$75$	0	0
$76$	9.40812	1.07919
$77$	0	0
$78$	8.02363	0.908498
$79$	5.35907	0.602943	0.301471	−	0.953475i	$-0.402522\pi$
$79$	5.35907	0.602943	0.301471	+	0.953475i	$0.402522\pi$
$80$	0	0
$81$	−8.73852	−0.970946
$82$	12.8923	1.42372
$83$	−10.8454	−1.19043	−0.595216	−	0.803565i	$-0.702934\pi$
$83$	−10.8454	−1.19043	−0.595216	+	0.803565i	$0.702934\pi$
$84$	−22.5839	−2.46410
$85$	0	0
$86$	13.0590	1.40819
$87$	−1.51119	−0.162017
$88$	0	0
$89$	−4.32336	−0.458275	−0.229137	−	0.973394i	$-0.573591\pi$
$89$	−4.32336	−0.458275	−0.229137	+	0.973394i	$0.573591\pi$
$90$	0	0
$91$	2.69740	0.282764
$92$	−38.3917	−4.00262
$93$	−8.99126	−0.932350
$94$	−18.4459	−1.90255
$95$	0	0
$96$	−10.1641	−1.03737
$97$	0.351653	0.0357049	0.0178525	−	0.999841i	$-0.494317\pi$
$97$	0.351653	0.0357049	0.0178525	+	0.999841i	$0.494317\pi$
$98$	6.60723	0.667431
$99$	0	0
$100$	0	0
$101$	−15.6995	−1.56215	−0.781077	−	0.624434i	$-0.785330\pi$
$101$	−15.6995	−1.56215	−0.781077	+	0.624434i	$0.785330\pi$
$102$	−18.6275	−1.84440
$103$	−6.67991	−0.658191	−0.329095	−	0.944297i	$-0.606744\pi$
$103$	−6.67991	−0.658191	−0.329095	+	0.944297i	$0.606744\pi$
$104$	7.71947	0.756956
$105$	0	0
$106$	−7.42767	−0.721439
$107$	−15.6080	−1.50888	−0.754440	−	0.656370i	$-0.772091\pi$
$107$	−15.6080	−1.50888	−0.754440	+	0.656370i	$0.772091\pi$
$108$	0.914417	0.0879898
$109$	11.5070	1.10217	0.551087	−	0.834448i	$-0.314213\pi$
$109$	11.5070	1.10217	0.551087	+	0.834448i	$0.314213\pi$
$110$	0	0
$111$	4.61469	0.438007
$112$	−13.3537	−1.26181
$113$	−9.04823	−0.851186	−0.425593	−	0.904915i	$-0.639934\pi$
$113$	−9.04823	−0.851186	−0.425593	+	0.904915i	$0.639934\pi$
$114$	−13.3969	−1.25473
$115$	0	0
$116$	−2.67917	−0.248754
$117$	−3.97459	−0.367451
$118$	16.3948	1.50926
$119$	−6.26222	−0.574057
$120$	0	0
$121$	0	0
$122$	1.26845	0.114840
$123$	−12.5972	−1.13585
$124$	−15.9404	−1.43149
$125$	0	0
$126$	16.3033	1.45242
$127$	−18.8341	−1.67126	−0.835628	−	0.549296i	$-0.814896\pi$
$127$	−18.8341	−1.67126	−0.835628	+	0.549296i	$0.814896\pi$
$128$	14.1862	1.25389
$129$	−12.7601	−1.12346
$130$	0	0
$131$	−20.0997	−1.75612	−0.878058	−	0.478555i	$-0.841161\pi$
$131$	−20.0997	−1.75612	−0.878058	+	0.478555i	$0.841161\pi$
$132$	0	0
$133$	−4.50377	−0.390527
$134$	−19.7156	−1.70317
$135$	0	0
$136$	−17.9214	−1.53675
$137$	17.9712	1.53539	0.767694	−	0.640817i	$-0.221404\pi$
$137$	17.9712	1.53539	0.767694	+	0.640817i	$0.221404\pi$
$138$	54.6686	4.65370
$139$	16.8631	1.43031	0.715154	−	0.698967i	$-0.246357\pi$
$139$	16.8631	1.43031	0.715154	+	0.698967i	$0.246357\pi$
$140$	0	0
$141$	18.0236	1.51786
$142$	28.5376	2.39482
$143$	0	0
$144$	19.6766	1.63971
$145$	0	0
$146$	−28.0655	−2.32272
$147$	−6.45597	−0.532479
$148$	8.18130	0.672499
$149$	2.33366	0.191181	0.0955904	−	0.995421i	$-0.469526\pi$
$149$	2.33366	0.191181	0.0955904	+	0.995421i	$0.469526\pi$
$150$	0	0
$151$	−3.93887	−0.320541	−0.160270	−	0.987073i	$-0.551237\pi$
$151$	−3.93887	−0.320541	−0.160270	+	0.987073i	$0.551237\pi$
$152$	−12.8890	−1.04544
$153$	9.22732	0.745985
$154$	0	0
$155$	0	0
$156$	−13.8993	−1.11284
$157$	4.88108	0.389552	0.194776	−	0.980848i	$-0.437602\pi$
$157$	4.88108	0.389552	0.194776	+	0.980848i	$0.437602\pi$
$158$	−13.5291	−1.07632
$159$	7.25764	0.575568
$160$	0	0
$161$	18.3785	1.44843
$162$	22.0606	1.73324
$163$	7.03572	0.551080	0.275540	−	0.961290i	$-0.411143\pi$
$163$	7.03572	0.551080	0.275540	+	0.961290i	$0.411143\pi$
$164$	−22.3333	−1.74394
$165$	0	0
$166$	27.3794	2.12505
$167$	−10.7195	−0.829498	−0.414749	−	0.909936i	$-0.636131\pi$
$167$	−10.7195	−0.829498	−0.414749	+	0.909936i	$0.636131\pi$
$168$	30.9396	2.38704
$169$	−11.3399	−0.872299
$170$	0	0
$171$	6.63626	0.507488
$172$	−22.6221	−1.72492
$173$	−8.41182	−0.639539	−0.319769	−	0.947495i	$-0.603605\pi$
$173$	−8.41182	−0.639539	−0.319769	+	0.947495i	$0.603605\pi$
$174$	3.81504	0.289218
$175$	0	0
$176$	0	0
$177$	−16.0195	−1.20410
$178$	10.9144	0.818070
$179$	21.0365	1.57234	0.786169	−	0.618011i	$-0.212061\pi$
$179$	21.0365	1.57234	0.786169	+	0.618011i	$0.212061\pi$
$180$	0	0
$181$	−1.74310	−0.129564	−0.0647819	−	0.997899i	$-0.520635\pi$
$181$	−1.74310	−0.129564	−0.0647819	+	0.997899i	$0.520635\pi$
$182$	−6.80964	−0.504764
$183$	−1.23941	−0.0916197
$184$	52.5962	3.87744
$185$	0	0
$186$	22.6986	1.66435
$187$	0	0
$188$	31.9538	2.33047
$189$	−0.437741	−0.0318410
$190$	0	0
$191$	0.0249566	0.00180579	0.000902896	−	1.00000i	$-0.499713\pi$
$191$	0.0249566	0.00180579	0.000902896		1.00000i	$0.499713\pi$
$192$	−5.80913	−0.419238
$193$	−1.45725	−0.104895	−0.0524474	−	0.998624i	$-0.516702\pi$
$193$	−1.45725	−0.104895	−0.0524474	+	0.998624i	$0.516702\pi$
$194$	−0.887755	−0.0637371
$195$	0	0
$196$	−11.4457	−0.817548
$197$	−22.7027	−1.61750	−0.808751	−	0.588151i	$-0.799856\pi$
$197$	−22.7027	−1.61750	−0.808751	+	0.588151i	$0.799856\pi$
$198$	0	0
$199$	−6.62834	−0.469870	−0.234935	−	0.972011i	$-0.575488\pi$
$199$	−6.62834	−0.469870	−0.234935	+	0.972011i	$0.575488\pi$
$200$	0	0
$201$	19.2643	1.35880
$202$	39.6337	2.78861
$203$	1.28255	0.0900171
$204$	32.2684	2.25924
$205$	0	0
$206$	16.8636	1.17494
$207$	−27.0806	−1.88223
$208$	−8.21858	−0.569856
$209$	0	0
$210$	0	0
$211$	5.65760	0.389485	0.194743	−	0.980854i	$-0.437613\pi$
$211$	5.65760	0.389485	0.194743	+	0.980854i	$0.437613\pi$
$212$	12.8669	0.883704
$213$	−27.8843	−1.91060
$214$	39.4027	2.69351
$215$	0	0
$216$	−1.25274	−0.0852381
$217$	7.63086	0.518016
$218$	−29.0498	−1.96750
$219$	27.4230	1.85308
$220$	0	0
$221$	−3.85410	−0.259255
$222$	−11.6499	−0.781891
$223$	−7.88442	−0.527980	−0.263990	−	0.964525i	$-0.585039\pi$
$223$	−7.88442	−0.527980	−0.263990	+	0.964525i	$0.585039\pi$
$224$	8.62627	0.576367
$225$	0	0
$226$	22.8425	1.51946
$227$	11.2114	0.744126	0.372063	−	0.928207i	$-0.378650\pi$
$227$	11.2114	0.744126	0.372063	+	0.928207i	$0.378650\pi$
$228$	23.2073	1.53694
$229$	26.9907	1.78360	0.891799	−	0.452433i	$-0.149444\pi$
$229$	26.9907	1.78360	0.891799	+	0.452433i	$0.149444\pi$
$230$	0	0
$231$	0	0
$232$	3.67042	0.240975
$233$	10.8508	0.710857	0.355429	−	0.934703i	$-0.384335\pi$
$233$	10.8508	0.710857	0.355429	+	0.934703i	$0.384335\pi$
$234$	10.0339	0.655939
$235$	0	0
$236$	−28.4006	−1.84872
$237$	13.2194	0.858692
$238$	15.8091	1.02475
$239$	−11.4663	−0.741692	−0.370846	−	0.928694i	$-0.620932\pi$
$239$	−11.4663	−0.741692	−0.370846	+	0.928694i	$0.620932\pi$
$240$	0	0
$241$	12.7542	0.821572	0.410786	−	0.911732i	$-0.365254\pi$
$241$	12.7542	0.821572	0.410786	+	0.911732i	$0.365254\pi$
$242$	0	0
$243$	−22.1829	−1.42303
$244$	−2.19732	−0.140669
$245$	0	0
$246$	31.8019	2.02762
$247$	−2.77186	−0.176369
$248$	21.8382	1.38673
$249$	−26.7526	−1.69538
$250$	0	0
$251$	−12.2016	−0.770158	−0.385079	−	0.922884i	$-0.625826\pi$
$251$	−12.2016	−0.770158	−0.385079	+	0.922884i	$0.625826\pi$
$252$	−28.2422	−1.77909
$253$	0	0
$254$	47.5471	2.98337
$255$	0	0
$256$	−31.1034	−1.94396
$257$	5.89604	0.367785	0.183892	−	0.982946i	$-0.441130\pi$
$257$	5.89604	0.367785	0.183892	+	0.982946i	$0.441130\pi$
$258$	32.2131	2.00550
$259$	−3.91648	−0.243358
$260$	0	0
$261$	−1.88982	−0.116977
$262$	50.7421	3.13486
$263$	21.7305	1.33996	0.669980	−	0.742379i	$-0.266302\pi$
$263$	21.7305	1.33996	0.669980	+	0.742379i	$0.266302\pi$
$264$	0	0
$265$	0	0
$266$	11.3699	0.697132
$267$	−10.6646	−0.652660
$268$	34.1533	2.08624
$269$	−4.52452	−0.275865	−0.137933	−	0.990442i	$-0.544046\pi$
$269$	−4.52452	−0.275865	−0.137933	+	0.990442i	$0.544046\pi$
$270$	0	0
$271$	−21.7608	−1.32188	−0.660938	−	0.750440i	$-0.729841\pi$
$271$	−21.7608	−1.32188	−0.660938	+	0.750440i	$0.729841\pi$
$272$	19.0801	1.15690
$273$	6.65375	0.402703
$274$	−45.3688	−2.74083
$275$	0	0
$276$	−94.7021	−5.70040
$277$	13.0346	0.783172	0.391586	−	0.920141i	$-0.371926\pi$
$277$	13.0346	0.783172	0.391586	+	0.920141i	$0.371926\pi$
$278$	−42.5713	−2.55325
$279$	−11.2440	−0.673160
$280$	0	0
$281$	9.38559	0.559897	0.279949	−	0.960015i	$-0.409683\pi$
$281$	9.38559	0.559897	0.279949	+	0.960015i	$0.409683\pi$
$282$	−45.5011	−2.70955
$283$	−13.9397	−0.828628	−0.414314	−	0.910134i	$-0.635979\pi$
$283$	−13.9397	−0.828628	−0.414314	+	0.910134i	$0.635979\pi$
$284$	−49.4356	−2.93346
$285$	0	0
$286$	0	0
$287$	10.6912	0.631083
$288$	−12.7107	−0.748987
$289$	−8.05239	−0.473670
$290$	0	0
$291$	0.867433	0.0508498
$292$	48.6177	2.84514
$293$	−30.4700	−1.78008	−0.890039	−	0.455884i	$-0.849323\pi$
$293$	−30.4700	−1.78008	−0.890039	+	0.455884i	$0.849323\pi$
$294$	16.2983	0.950533
$295$	0	0
$296$	−11.2083	−0.651468
$297$	0	0
$298$	−5.89138	−0.341278
$299$	11.3111	0.654139
$300$	0	0
$301$	10.8295	0.624200
$302$	9.94377	0.572199
$303$	−38.7264	−2.22477
$304$	13.7224	0.787031
$305$	0	0
$306$	−23.2946	−1.33166
$307$	−5.08609	−0.290278	−0.145139	−	0.989411i	$-0.546363\pi$
$307$	−5.08609	−0.290278	−0.145139	+	0.989411i	$0.546363\pi$
$308$	0	0
$309$	−16.4775	−0.937375
$310$	0	0
$311$	13.7613	0.780334	0.390167	−	0.920744i	$-0.372417\pi$
$311$	13.7613	0.780334	0.390167	+	0.920744i	$0.372417\pi$
$312$	19.0419	1.07803
$313$	−15.9527	−0.901700	−0.450850	−	0.892600i	$-0.648879\pi$
$313$	−15.9527	−0.901700	−0.450850	+	0.892600i	$0.648879\pi$
$314$	−12.3224	−0.695393
$315$	0	0
$316$	23.4364	1.31840
$317$	−10.7074	−0.601387	−0.300693	−	0.953721i	$-0.597218\pi$
$317$	−10.7074	−0.601387	−0.300693	+	0.953721i	$0.597218\pi$
$318$	−18.3221	−1.02745
$319$	0	0
$320$	0	0
$321$	−38.5007	−2.14890
$322$	−46.3971	−2.58561
$323$	6.43510	0.358058
$324$	−38.2155	−2.12308
$325$	0	0
$326$	−17.7618	−0.983737
$327$	28.3848	1.56968
$328$	30.5964	1.68940
$329$	−15.2966	−0.843330
$330$	0	0
$331$	−8.84618	−0.486230	−0.243115	−	0.969997i	$-0.578169\pi$
$331$	−8.84618	−0.486230	−0.243115	+	0.969997i	$0.578169\pi$
$332$	−47.4292	−2.60301
$333$	5.77090	0.316243
$334$	27.0616	1.48074
$335$	0	0
$336$	−32.9400	−1.79703
$337$	11.5897	0.631333	0.315667	−	0.948870i	$-0.397772\pi$
$337$	11.5897	0.631333	0.315667	+	0.948870i	$0.397772\pi$
$338$	28.6278	1.55715
$339$	−22.3196	−1.21223
$340$	0	0
$341$	0	0
$342$	−16.7534	−0.905920
$343$	20.1337	1.08712
$344$	30.9920	1.67098
$345$	0	0
$346$	21.2358	1.14165
$347$	4.88900	0.262455	0.131228	−	0.991352i	$-0.458108\pi$
$347$	4.88900	0.262455	0.131228	+	0.991352i	$0.458108\pi$
$348$	−6.60878	−0.354268
$349$	0.953521	0.0510408	0.0255204	−	0.999674i	$-0.491876\pi$
$349$	0.953521	0.0510408	0.0255204	+	0.999674i	$0.491876\pi$
$350$	0	0
$351$	−0.269409	−0.0143800
$352$	0	0
$353$	15.5166	0.825865	0.412933	−	0.910762i	$-0.364505\pi$
$353$	15.5166	0.825865	0.412933	+	0.910762i	$0.364505\pi$
$354$	40.4416	2.14944
$355$	0	0
$356$	−18.9070	−1.00207
$357$	−15.4472	−0.817554
$358$	−53.1070	−2.80679
$359$	20.2550	1.06902	0.534510	−	0.845162i	$-0.320496\pi$
$359$	20.2550	1.06902	0.534510	+	0.845162i	$0.320496\pi$
$360$	0	0
$361$	−14.3719	−0.756416
$362$	4.40051	0.231286
$363$	0	0
$364$	11.7963	0.618295
$365$	0	0
$366$	3.12892	0.163551
$367$	−35.6550	−1.86118	−0.930588	−	0.366069i	$-0.880704\pi$
$367$	−35.6550	−1.86118	−0.930588	+	0.366069i	$0.880704\pi$
$368$	−55.9968	−2.91904
$369$	−15.7534	−0.820090
$370$	0	0
$371$	−6.15954	−0.319787
$372$	−39.3208	−2.03869
$373$	−12.1358	−0.628370	−0.314185	−	0.949362i	$-0.601731\pi$
$373$	−12.1358	−0.628370	−0.314185	+	0.949362i	$0.601731\pi$
$374$	0	0
$375$	0	0
$376$	−43.7762	−2.25759
$377$	0.789347	0.0406534
$378$	1.10509	0.0568396
$379$	7.14412	0.366969	0.183484	−	0.983023i	$-0.441262\pi$
$379$	7.14412	0.366969	0.183484	+	0.983023i	$0.441262\pi$
$380$	0	0
$381$	−46.4587	−2.38015
$382$	−0.0630034	−0.00322354
$383$	−15.9630	−0.815669	−0.407835	−	0.913056i	$-0.633716\pi$
$383$	−15.9630	−0.815669	−0.407835	+	0.913056i	$0.633716\pi$
$384$	34.9936	1.78576
$385$	0	0
$386$	3.67885	0.187249
$387$	−15.9571	−0.811145
$388$	1.53785	0.0780727
$389$	−25.0904	−1.27213	−0.636067	−	0.771634i	$-0.719440\pi$
$389$	−25.0904	−1.27213	−0.636067	+	0.771634i	$0.719440\pi$
$390$	0	0
$391$	−26.2597	−1.32801
$392$	15.6804	0.791980
$393$	−49.5805	−2.50100
$394$	57.3136	2.88742
$395$	0	0
$396$	0	0
$397$	−3.57490	−0.179419	−0.0897094	−	0.995968i	$-0.528594\pi$
$397$	−3.57490	−0.179419	−0.0897094	+	0.995968i	$0.528594\pi$
$398$	16.7334	0.838769
$399$	−11.1096	−0.556176
$400$	0	0
$401$	28.8838	1.44239	0.721195	−	0.692732i	$-0.243593\pi$
$401$	28.8838	1.44239	0.721195	+	0.692732i	$0.243593\pi$
$402$	−48.6332	−2.42560
$403$	4.69643	0.233946
$404$	−68.6572	−3.41582
$405$	0	0
$406$	−3.23782	−0.160690
$407$	0	0
$408$	−44.2072	−2.18858
$409$	9.61904	0.475631	0.237816	−	0.971310i	$-0.423569\pi$
$409$	9.61904	0.475631	0.237816	+	0.971310i	$0.423569\pi$
$410$	0	0
$411$	44.3302	2.18665
$412$	−29.2127	−1.43921
$413$	13.5957	0.669000
$414$	68.3656	3.35999
$415$	0	0
$416$	5.30906	0.260298
$417$	41.5967	2.03700
$418$	0	0
$419$	−30.6537	−1.49753	−0.748765	−	0.662836i	$-0.769353\pi$
$419$	−30.6537	−1.49753	−0.748765	+	0.662836i	$0.769353\pi$
$420$	0	0
$421$	−6.94963	−0.338704	−0.169352	−	0.985556i	$-0.554168\pi$
$421$	−6.94963	−0.338704	−0.169352	+	0.985556i	$0.554168\pi$
$422$	−14.2827	−0.695273
$423$	22.5394	1.09590
$424$	−17.6275	−0.856068
$425$	0	0
$426$	70.3947	3.41063
$427$	1.05188	0.0509042
$428$	−68.2571	−3.29933
$429$	0	0
$430$	0	0
$431$	−3.23400	−0.155776	−0.0778882	−	0.996962i	$-0.524818\pi$
$431$	−3.23400	−0.155776	−0.0778882	+	0.996962i	$0.524818\pi$
$432$	1.33374	0.0641694
$433$	30.3919	1.46054	0.730270	−	0.683158i	$-0.239394\pi$
$433$	30.3919	1.46054	0.730270	+	0.683158i	$0.239394\pi$
$434$	−19.2643	−0.924715
$435$	0	0
$436$	50.3228	2.41003
$437$	−18.8859	−0.903435
$438$	−69.2301	−3.30794
$439$	36.5311	1.74353	0.871767	−	0.489921i	$-0.162974\pi$
$439$	36.5311	1.74353	0.871767	+	0.489921i	$0.162974\pi$
$440$	0	0
$441$	−8.07350	−0.384452
$442$	9.72977	0.462798
$443$	2.16153	0.102697	0.0513487	−	0.998681i	$-0.483648\pi$
$443$	2.16153	0.102697	0.0513487	+	0.998681i	$0.483648\pi$
$444$	20.1811	0.957752
$445$	0	0
$446$	19.9044	0.942501
$447$	5.75651	0.272274
$448$	4.93020	0.232930
$449$	−11.5217	−0.543742	−0.271871	−	0.962334i	$-0.587642\pi$
$449$	−11.5217	−0.543742	−0.271871	+	0.962334i	$0.587642\pi$
$450$	0	0
$451$	0	0
$452$	−39.5699	−1.86121
$453$	−9.71613	−0.456504
$454$	−28.3034	−1.32835
$455$	0	0
$456$	−31.7937	−1.48888
$457$	15.9314	0.745242	0.372621	−	0.927984i	$-0.378459\pi$
$457$	15.9314	0.745242	0.372621	+	0.927984i	$0.378459\pi$
$458$	−68.1387	−3.18391
$459$	0.625455	0.0291937
$460$	0	0
$461$	1.52527	0.0710387	0.0355193	−	0.999369i	$-0.488691\pi$
$461$	1.52527	0.0710387	0.0355193	+	0.999369i	$0.488691\pi$
$462$	0	0
$463$	−14.2073	−0.660268	−0.330134	−	0.943934i	$-0.607094\pi$
$463$	−14.2073	−0.660268	−0.330134	+	0.943934i	$0.607094\pi$
$464$	−3.90774	−0.181412
$465$	0	0
$466$	−27.3930	−1.26896
$467$	6.05697	0.280283	0.140142	−	0.990131i	$-0.455244\pi$
$467$	6.05697	0.280283	0.140142	+	0.990131i	$0.455244\pi$
$468$	−17.3817	−0.803471
$469$	−16.3496	−0.754952
$470$	0	0
$471$	12.0403	0.554788
$472$	38.9085	1.79091
$473$	0	0
$474$	−33.3727	−1.53286
$475$	0	0
$476$	−27.3861	−1.25524
$477$	9.07602	0.415562
$478$	28.9469	1.32400
$479$	−17.6084	−0.804549	−0.402275	−	0.915519i	$-0.631780\pi$
$479$	−17.6084	−0.804549	−0.402275	+	0.915519i	$0.631780\pi$
$480$	0	0
$481$	−2.41041	−0.109905
$482$	−32.1983	−1.46659
$483$	45.3350	2.06281
$484$	0	0
$485$	0	0
$486$	56.0012	2.54026
$487$	−6.78341	−0.307386	−0.153693	−	0.988119i	$-0.549117\pi$
$487$	−6.78341	−0.307386	−0.153693	+	0.988119i	$0.549117\pi$
$488$	3.01030	0.136270
$489$	17.3552	0.784831
$490$	0	0
$491$	0.518615	0.0234047	0.0117024	−	0.999932i	$-0.496275\pi$
$491$	0.518615	0.0234047	0.0117024	+	0.999932i	$0.496275\pi$
$492$	−55.0904	−2.48367
$493$	−1.83253	−0.0825331
$494$	6.99762	0.314838
$495$	0	0
$496$	−23.2501	−1.04396
$497$	23.6654	1.06154
$498$	67.5376	3.02643
$499$	21.8608	0.978622	0.489311	−	0.872109i	$-0.337248\pi$
$499$	21.8608	0.978622	0.489311	+	0.872109i	$0.337248\pi$
$500$	0	0
$501$	−26.4421	−1.18134
$502$	30.8032	1.37482
$503$	−3.01667	−0.134507	−0.0672533	−	0.997736i	$-0.521424\pi$
$503$	−3.01667	−0.134507	−0.0672533	+	0.997736i	$0.521424\pi$
$504$	38.6915	1.72345
$505$	0	0
$506$	0	0
$507$	−27.9724	−1.24230
$508$	−82.3657	−3.65439
$509$	−25.7079	−1.13948	−0.569741	−	0.821824i	$-0.692957\pi$
$509$	−25.7079	−1.13948	−0.569741	+	0.821824i	$0.692957\pi$
$510$	0	0
$511$	−23.2738	−1.02957
$512$	50.1489	2.21629
$513$	0.449825	0.0198603
$514$	−14.8847	−0.656536
$515$	0	0
$516$	−55.8027	−2.45658
$517$	0	0
$518$	9.88725	0.434421
$519$	−20.7497	−0.910811
$520$	0	0
$521$	11.1326	0.487729	0.243864	−	0.969809i	$-0.421585\pi$
$521$	11.1326	0.487729	0.243864	+	0.969809i	$0.421585\pi$
$522$	4.77090	0.208816
$523$	6.53840	0.285904	0.142952	−	0.989730i	$-0.454340\pi$
$523$	6.53840	0.285904	0.142952	+	0.989730i	$0.454340\pi$
$524$	−87.9003	−3.83994
$525$	0	0
$526$	−54.8592	−2.39198
$527$	−10.9032	−0.474949
$528$	0	0
$529$	54.0677	2.35077
$530$	0	0
$531$	−20.0331	−0.869363
$532$	−19.6960	−0.853930
$533$	6.57994	0.285009
$534$	26.9229	1.16507
$535$	0	0
$536$	−46.7896	−2.02100
$537$	51.8913	2.23927
$538$	11.4223	0.492449
$539$	0	0
$540$	0	0
$541$	41.7400	1.79454	0.897271	−	0.441479i	$-0.145546\pi$
$541$	41.7400	1.79454	0.897271	+	0.441479i	$0.145546\pi$
$542$	54.9357	2.35969
$543$	−4.29977	−0.184521
$544$	−12.3254	−0.528448
$545$	0	0
$546$	−16.7976	−0.718869
$547$	4.45616	0.190532	0.0952658	−	0.995452i	$-0.469630\pi$
$547$	4.45616	0.190532	0.0952658	+	0.995452i	$0.469630\pi$
$548$	78.5922	3.35729
$549$	−1.54994	−0.0661498
$550$	0	0
$551$	−1.31795	−0.0561466
$552$	129.741	5.52213
$553$	−11.2193	−0.477092
$554$	−32.9061	−1.39805
$555$	0	0
$556$	73.7460	3.12753
$557$	−19.3714	−0.820791	−0.410396	−	0.911908i	$-0.634609\pi$
$557$	−19.3714	−0.820791	−0.410396	+	0.911908i	$0.634609\pi$
$558$	28.3857	1.20166
$559$	6.66502	0.281900
$560$	0	0
$561$	0	0
$562$	−23.6941	−0.999477
$563$	−20.7432	−0.874220	−0.437110	−	0.899408i	$-0.643998\pi$
$563$	−20.7432	−0.874220	−0.437110	+	0.899408i	$0.643998\pi$
$564$	78.8213	3.31898
$565$	0	0
$566$	35.1911	1.47919
$567$	18.2942	0.768283
$568$	67.7261	2.84173
$569$	−42.3747	−1.77644	−0.888220	−	0.459418i	$-0.848058\pi$
$569$	−42.3747	−1.77644	−0.888220	+	0.459418i	$0.848058\pi$
$570$	0	0
$571$	−5.03980	−0.210909	−0.105455	−	0.994424i	$-0.533630\pi$
$571$	−5.03980	−0.210909	−0.105455	+	0.994424i	$0.533630\pi$
$572$	0	0
$573$	0.0615611	0.00257175
$574$	−26.9902	−1.12655
$575$	0	0
$576$	−7.26460	−0.302692
$577$	−34.8419	−1.45049	−0.725245	−	0.688491i	$-0.758273\pi$
$577$	−34.8419	−1.45049	−0.725245	+	0.688491i	$0.758273\pi$
$578$	20.3284	0.845552
$579$	−3.59464	−0.149388
$580$	0	0
$581$	22.7049	0.941956
$582$	−2.18985	−0.0907724
$583$	0	0
$584$	−66.6057	−2.75616
$585$	0	0
$586$	76.9224	3.17763
$587$	13.7783	0.568690	0.284345	−	0.958722i	$-0.408224\pi$
$587$	13.7783	0.568690	0.284345	+	0.958722i	$0.408224\pi$
$588$	−28.2334	−1.16433
$589$	−7.84151	−0.323104
$590$	0	0
$591$	−56.0015	−2.30360
$592$	11.9330	0.490442
$593$	25.1595	1.03318	0.516588	−	0.856234i	$-0.327202\pi$
$593$	25.1595	1.03318	0.516588	+	0.856234i	$0.327202\pi$
$594$	0	0
$595$	0	0
$596$	10.2056	0.418038
$597$	−16.3503	−0.669174
$598$	−28.5552	−1.16771
$599$	−16.5063	−0.674429	−0.337214	−	0.941428i	$-0.609485\pi$
$599$	−16.5063	−0.674429	−0.337214	+	0.941428i	$0.609485\pi$
$600$	0	0
$601$	39.6449	1.61715	0.808574	−	0.588395i	$-0.200240\pi$
$601$	39.6449	1.61715	0.808574	+	0.588395i	$0.200240\pi$
$602$	−27.3392	−1.11426
$603$	24.0909	0.981058
$604$	−17.2255	−0.700897
$605$	0	0
$606$	97.7656	3.97146
$607$	−14.1895	−0.575933	−0.287966	−	0.957641i	$-0.592979\pi$
$607$	−14.1895	−0.575933	−0.287966	+	0.957641i	$0.592979\pi$
$608$	−8.86440	−0.359499
$609$	3.16370	0.128200
$610$	0	0
$611$	−9.41434	−0.380864
$612$	40.3531	1.63118
$613$	−30.1543	−1.21792	−0.608961	−	0.793200i	$-0.708414\pi$
$613$	−30.1543	−1.21792	−0.608961	+	0.793200i	$0.708414\pi$
$614$	12.8400	0.518178
$615$	0	0
$616$	0	0
$617$	31.3844	1.26349	0.631744	−	0.775177i	$-0.282339\pi$
$617$	31.3844	1.26349	0.631744	+	0.775177i	$0.282339\pi$
$618$	41.5979	1.67331
$619$	35.2332	1.41614	0.708070	−	0.706142i	$-0.249566\pi$
$619$	35.2332	1.41614	0.708070	+	0.706142i	$0.249566\pi$
$620$	0	0
$621$	−1.83560	−0.0736602
$622$	−34.7408	−1.39298
$623$	9.05099	0.362620
$624$	−20.2730	−0.811571
$625$	0	0
$626$	40.2730	1.60963
$627$	0	0
$628$	21.3460	0.851799
$629$	5.59596	0.223126
$630$	0	0
$631$	5.73472	0.228296	0.114148	−	0.993464i	$-0.463586\pi$
$631$	5.73472	0.228296	0.114148	+	0.993464i	$0.463586\pi$
$632$	−32.1076	−1.27717
$633$	13.9558	0.554692
$634$	27.0311	1.07354
$635$	0	0
$636$	31.7393	1.25854
$637$	3.37217	0.133610
$638$	0	0
$639$	−34.8707	−1.37946
$640$	0	0
$641$	−7.12476	−0.281411	−0.140706	−	0.990051i	$-0.544937\pi$
$641$	−7.12476	−0.281411	−0.140706	+	0.990051i	$0.544937\pi$
$642$	97.1959	3.83601
$643$	21.1895	0.835634	0.417817	−	0.908531i	$-0.362795\pi$
$643$	21.1895	0.835634	0.417817	+	0.908531i	$0.362795\pi$
$644$	80.3735	3.16716
$645$	0	0
$646$	−16.2456	−0.639173
$647$	5.64974	0.222114	0.111057	−	0.993814i	$-0.464576\pi$
$647$	5.64974	0.222114	0.111057	+	0.993814i	$0.464576\pi$
$648$	52.3547	2.05669
$649$	0	0
$650$	0	0
$651$	18.8233	0.737743
$652$	30.7688	1.20500
$653$	15.7131	0.614903	0.307452	−	0.951564i	$-0.400524\pi$
$653$	15.7131	0.614903	0.307452	+	0.951564i	$0.400524\pi$
$654$	−71.6580	−2.80205
$655$	0	0
$656$	−32.5746	−1.27183
$657$	34.2938	1.33793
$658$	38.6167	1.50543
$659$	−41.7884	−1.62784	−0.813922	−	0.580975i	$-0.802671\pi$
$659$	−41.7884	−1.62784	−0.813922	+	0.580975i	$0.802671\pi$
$660$	0	0
$661$	15.8742	0.617435	0.308717	−	0.951154i	$-0.400100\pi$
$661$	15.8742	0.617435	0.308717	+	0.951154i	$0.400100\pi$
$662$	22.3324	0.867973
$663$	−9.50704	−0.369223
$664$	64.9773	2.52161
$665$	0	0
$666$	−14.5688	−0.564528
$667$	5.37817	0.208243
$668$	−46.8786	−1.81379
$669$	−19.4487	−0.751932
$670$	0	0
$671$	0	0
$672$	21.2787	0.820844
$673$	−32.2446	−1.24294	−0.621469	−	0.783439i	$-0.713464\pi$
$673$	−32.2446	−1.24294	−0.621469	+	0.783439i	$0.713464\pi$
$674$	−29.2586	−1.12700
$675$	0	0
$676$	−49.5918	−1.90738
$677$	−17.5625	−0.674983	−0.337492	−	0.941329i	$-0.609578\pi$
$677$	−17.5625	−0.674983	−0.337492	+	0.941329i	$0.609578\pi$
$678$	56.3463	2.16397
$679$	−0.736188	−0.0282523
$680$	0	0
$681$	27.6555	1.05976
$682$	0	0
$683$	5.93856	0.227233	0.113616	−	0.993525i	$-0.463757\pi$
$683$	5.93856	0.227233	0.113616	+	0.993525i	$0.463757\pi$
$684$	29.0219	1.10968
$685$	0	0
$686$	−50.8281	−1.94063
$687$	66.5789	2.54014
$688$	−32.9958	−1.25795
$689$	−3.79091	−0.144422
$690$	0	0
$691$	21.9356	0.834469	0.417235	−	0.908799i	$-0.362999\pi$
$691$	21.9356	0.834469	0.417235	+	0.908799i	$0.362999\pi$
$692$	−36.7868	−1.39842
$693$	0	0
$694$	−12.3424	−0.468511
$695$	0	0
$696$	9.05395	0.343189
$697$	−15.2759	−0.578615
$698$	−2.40719	−0.0911134
$699$	26.7659	1.01238
$700$	0	0
$701$	32.4209	1.22452	0.612260	−	0.790657i	$-0.290261\pi$
$701$	32.4209	1.22452	0.612260	+	0.790657i	$0.290261\pi$
$702$	0.680130	0.0256698
$703$	4.02460	0.151791
$704$	0	0
$705$	0	0
$706$	−39.1720	−1.47426
$707$	32.8670	1.23609
$708$	−70.0567	−2.63289
$709$	−16.1005	−0.604666	−0.302333	−	0.953202i	$-0.597765\pi$
$709$	−16.1005	−0.604666	−0.302333	+	0.953202i	$0.597765\pi$
$710$	0	0
$711$	16.5315	0.619979
$712$	25.9023	0.970731
$713$	31.9989	1.19837
$714$	38.9969	1.45942
$715$	0	0
$716$	91.9971	3.43809
$717$	−28.2842	−1.05629
$718$	−51.1343	−1.90832
$719$	−7.81216	−0.291345	−0.145672	−	0.989333i	$-0.546534\pi$
$719$	−7.81216	−0.291345	−0.145672	+	0.989333i	$0.546534\pi$
$720$	0	0
$721$	13.9845	0.520808
$722$	36.2822	1.35028
$723$	31.4613	1.17006
$724$	−7.62298	−0.283306
$725$	0	0
$726$	0	0
$727$	49.1218	1.82183	0.910914	−	0.412597i	$-0.135378\pi$
$727$	49.1218	1.82183	0.910914	+	0.412597i	$0.135378\pi$
$728$	−16.1608	−0.598959
$729$	−28.5036	−1.05569
$730$	0	0
$731$	−15.4734	−0.572304
$732$	−5.42021	−0.200337
$733$	0.667947	0.0246712	0.0123356	−	0.999924i	$-0.496073\pi$
$733$	0.667947	0.0246712	0.0123356	+	0.999924i	$0.496073\pi$
$734$	90.0119	3.32240
$735$	0	0
$736$	36.1730	1.33335
$737$	0	0
$738$	39.7699	1.46395
$739$	38.0939	1.40131	0.700654	−	0.713501i	$-0.252892\pi$
$739$	38.0939	1.40131	0.700654	+	0.713501i	$0.252892\pi$
$740$	0	0
$741$	−6.83743	−0.251179
$742$	15.5499	0.570855
$743$	31.3356	1.14959	0.574797	−	0.818296i	$-0.305081\pi$
$743$	31.3356	1.14959	0.574797	+	0.818296i	$0.305081\pi$
$744$	53.8689	1.97493
$745$	0	0
$746$	30.6372	1.12171
$747$	−33.4554	−1.22407
$748$	0	0
$749$	32.6754	1.19393
$750$	0	0
$751$	−37.1874	−1.35699	−0.678494	−	0.734606i	$-0.737367\pi$
$751$	−37.1874	−1.35699	−0.678494	+	0.734606i	$0.737367\pi$
$752$	46.6066	1.69957
$753$	−30.0981	−1.09683
$754$	−1.99272	−0.0725708
$755$	0	0
$756$	−1.91434	−0.0696239
$757$	−6.68068	−0.242813	−0.121407	−	0.992603i	$-0.538741\pi$
$757$	−6.68068	−0.242813	−0.121407	+	0.992603i	$0.538741\pi$
$758$	−18.0355	−0.655079
$759$	0	0
$760$	0	0
$761$	−22.8936	−0.829894	−0.414947	−	0.909846i	$-0.636200\pi$
$761$	−22.8936	−0.829894	−0.414947	+	0.909846i	$0.636200\pi$
$762$	117.286	4.24882
$763$	−24.0901	−0.872120
$764$	0.109141	0.00394857
$765$	0	0
$766$	40.2989	1.45606
$767$	8.36751	0.302133
$768$	−76.7238	−2.76853
$769$	−13.1946	−0.475808	−0.237904	−	0.971289i	$-0.576460\pi$
$769$	−13.1946	−0.475808	−0.237904	+	0.971289i	$0.576460\pi$
$770$	0	0
$771$	14.5440	0.523788
$772$	−6.37286	−0.229364
$773$	12.4209	0.446749	0.223374	−	0.974733i	$-0.428293\pi$
$773$	12.4209	0.446749	0.223374	+	0.974733i	$0.428293\pi$
$774$	40.2841	1.44798
$775$	0	0
$776$	−2.10684	−0.0756312
$777$	−9.66091	−0.346583
$778$	63.3413	2.27090
$779$	−10.9864	−0.393627
$780$	0	0
$781$	0	0
$782$	66.2932	2.37064
$783$	−0.128098	−0.00457783
$784$	−16.6942	−0.596223
$785$	0	0
$786$	125.167	4.46456
$787$	−21.4851	−0.765861	−0.382931	−	0.923777i	$-0.625085\pi$
$787$	−21.4851	−0.765861	−0.382931	+	0.923777i	$0.625085\pi$
$788$	−99.2840	−3.53685
$789$	53.6034	1.90833
$790$	0	0
$791$	18.9426	0.673520
$792$	0	0
$793$	0.647384	0.0229893
$794$	9.02491	0.320282
$795$	0	0
$796$	−28.9872	−1.02742
$797$	−2.12930	−0.0754238	−0.0377119	−	0.999289i	$-0.512007\pi$
$797$	−2.12930	−0.0754238	−0.0377119	+	0.999289i	$0.512007\pi$
$798$	28.0464	0.992834
$799$	21.8562	0.773216
$800$	0	0
$801$	−13.3365	−0.471224
$802$	−72.9179	−2.57482
$803$	0	0
$804$	84.2470	2.97116
$805$	0	0
$806$	−11.8563	−0.417619
$807$	−11.1608	−0.392878
$808$	94.0595	3.30900
$809$	−5.36232	−0.188529	−0.0942645	−	0.995547i	$-0.530050\pi$
$809$	−5.36232	−0.188529	−0.0942645	+	0.995547i	$0.530050\pi$
$810$	0	0
$811$	19.5797	0.687538	0.343769	−	0.939054i	$-0.388296\pi$
$811$	19.5797	0.687538	0.343769	+	0.939054i	$0.388296\pi$
$812$	5.60886	0.196832
$813$	−53.6781	−1.88257
$814$	0	0
$815$	0	0
$816$	47.0655	1.64762
$817$	−11.1284	−0.389334
$818$	−24.2835	−0.849053
$819$	8.32083	0.290753
$820$	0	0
$821$	−16.6365	−0.580616	−0.290308	−	0.956933i	$-0.593758\pi$
$821$	−16.6365	−0.580616	−0.290308	+	0.956933i	$0.593758\pi$
$822$	−111.913	−3.90341
$823$	18.2929	0.637650	0.318825	−	0.947814i	$-0.396712\pi$
$823$	18.2929	0.637650	0.318825	+	0.947814i	$0.396712\pi$
$824$	40.0210	1.39420
$825$	0	0
$826$	−34.3227	−1.19424
$827$	38.0184	1.32203	0.661014	−	0.750373i	$-0.270126\pi$
$827$	38.0184	1.32203	0.661014	+	0.750373i	$0.270126\pi$
$828$	−118.430	−4.11571
$829$	51.7002	1.79562	0.897811	−	0.440382i	$-0.145157\pi$
$829$	51.7002	1.79562	0.897811	+	0.440382i	$0.145157\pi$
$830$	0	0
$831$	32.1528	1.11537
$832$	3.03430	0.105196
$833$	−7.82876	−0.271251
$834$	−105.012	−3.63626
$835$	0	0
$836$	0	0
$837$	−0.762151	−0.0263438
$838$	77.3859	2.67325
$839$	38.6025	1.33271	0.666354	−	0.745636i	$-0.267854\pi$
$839$	38.6025	1.33271	0.666354	+	0.745636i	$0.267854\pi$
$840$	0	0
$841$	−28.6247	−0.987058
$842$	17.5445	0.604624
$843$	23.1517	0.797388
$844$	24.7419	0.851652
$845$	0	0
$846$	−56.9013	−1.95631
$847$	0	0
$848$	18.7672	0.644470
$849$	−34.3855	−1.18011
$850$	0	0
$851$	−16.4232	−0.562979
$852$	−121.944	−4.17775
$853$	−33.9058	−1.16091	−0.580456	−	0.814292i	$-0.697126\pi$
$853$	−33.9058	−1.16091	−0.580456	+	0.814292i	$0.697126\pi$
$854$	−2.65550	−0.0908695
$855$	0	0
$856$	93.5113	3.19615
$857$	56.7117	1.93723	0.968617	−	0.248558i	$-0.0799568\pi$
$857$	56.7117	1.93723	0.968617	+	0.248558i	$0.0799568\pi$
$858$	0	0
$859$	−25.7505	−0.878597	−0.439298	−	0.898341i	$-0.644773\pi$
$859$	−25.7505	−0.878597	−0.439298	+	0.898341i	$0.644773\pi$
$860$	0	0
$861$	26.3724	0.898768
$862$	8.16432	0.278078
$863$	−35.7650	−1.21746	−0.608728	−	0.793379i	$-0.708320\pi$
$863$	−35.7650	−1.21746	−0.608728	+	0.793379i	$0.708320\pi$
$864$	−0.861570	−0.0293112
$865$	0	0
$866$	−76.7250	−2.60722
$867$	−19.8631	−0.674586
$868$	33.3714	1.13270
$869$	0	0
$870$	0	0
$871$	−10.0624	−0.340951
$872$	−68.9416	−2.33466
$873$	1.08477	0.0367138
$874$	47.6779	1.61273
$875$	0	0
$876$	119.927	4.05195
$877$	−17.3101	−0.584522	−0.292261	−	0.956339i	$-0.594408\pi$
$877$	−17.3101	−0.584522	−0.292261	+	0.956339i	$0.594408\pi$
$878$	−92.2236	−3.11240
$879$	−75.1614	−2.53513
$880$	0	0
$881$	−4.15822	−0.140094	−0.0700470	−	0.997544i	$-0.522315\pi$
$881$	−4.15822	−0.140094	−0.0700470	+	0.997544i	$0.522315\pi$
$882$	20.3817	0.686289
$883$	41.2704	1.38886	0.694430	−	0.719560i	$-0.255656\pi$
$883$	41.2704	1.38886	0.694430	+	0.719560i	$0.255656\pi$
$884$	−16.8548	−0.566890
$885$	0	0
$886$	−5.45683	−0.183326
$887$	−30.4790	−1.02339	−0.511693	−	0.859169i	$-0.670981\pi$
$887$	−30.4790	−1.02339	−0.511693	+	0.859169i	$0.670981\pi$
$888$	−27.6478	−0.927800
$889$	39.4294	1.32242
$890$	0	0
$891$	0	0
$892$	−34.4803	−1.15449
$893$	15.7189	0.526013
$894$	−14.5325	−0.486038
$895$	0	0
$896$	−29.6990	−0.992172
$897$	27.9015	0.931604
$898$	29.0868	0.970639
$899$	2.23304	0.0744761
$900$	0	0
$901$	8.80090	0.293200
$902$	0	0
$903$	26.7134	0.888965
$904$	54.2103	1.80301
$905$	0	0
$906$	24.5286	0.814908
$907$	−11.2895	−0.374861	−0.187430	−	0.982278i	$-0.560016\pi$
$907$	−11.2895	−0.374861	−0.187430	+	0.982278i	$0.560016\pi$
$908$	49.0299	1.62711
$909$	−48.4292	−1.60629
$910$	0	0
$911$	50.6067	1.67667	0.838337	−	0.545152i	$-0.183528\pi$
$911$	50.6067	1.67667	0.838337	+	0.545152i	$0.183528\pi$
$912$	33.8494	1.12086
$913$	0	0
$914$	−40.2193	−1.33034
$915$	0	0
$916$	118.036	3.90003
$917$	42.0788	1.38957
$918$	−1.57898	−0.0521140
$919$	−27.2180	−0.897837	−0.448919	−	0.893573i	$-0.648191\pi$
$919$	−27.2180	−0.897837	−0.448919	+	0.893573i	$0.648191\pi$
$920$	0	0
$921$	−12.5460	−0.413405
$922$	−3.85057	−0.126812
$923$	14.5649	0.479410
$924$	0	0
$925$	0	0
$926$	35.8666	1.17865
$927$	−20.6059	−0.676788
$928$	2.52433	0.0828652
$929$	−23.2104	−0.761508	−0.380754	−	0.924676i	$-0.624336\pi$
$929$	−23.2104	−0.761508	−0.380754	+	0.924676i	$0.624336\pi$
$930$	0	0
$931$	−5.63042	−0.184530
$932$	47.4528	1.55437
$933$	33.9455	1.11133
$934$	−15.2910	−0.500336
$935$	0	0
$936$	23.8128	0.778344
$937$	42.2117	1.37900	0.689498	−	0.724287i	$-0.257831\pi$
$937$	42.2117	1.37900	0.689498	+	0.724287i	$0.257831\pi$
$938$	41.2749	1.34767
$939$	−39.3510	−1.28417
$940$	0	0
$941$	−29.2128	−0.952310	−0.476155	−	0.879361i	$-0.657970\pi$
$941$	−29.2128	−0.952310	−0.476155	+	0.879361i	$0.657970\pi$
$942$	−30.3960	−0.990356
$943$	44.8320	1.45993
$944$	−41.4241	−1.34824
$945$	0	0
$946$	0	0
$947$	−9.63809	−0.313196	−0.156598	−	0.987662i	$-0.550053\pi$
$947$	−9.63809	−0.313196	−0.156598	+	0.987662i	$0.550053\pi$
$948$	57.8114	1.87763
$949$	−14.3240	−0.464975
$950$	0	0
$951$	−26.4123	−0.856476
$952$	37.5186	1.21598
$953$	−5.22149	−0.169141	−0.0845703	−	0.996418i	$-0.526952\pi$
$953$	−5.22149	−0.169141	−0.0845703	+	0.996418i	$0.526952\pi$
$954$	−22.9126	−0.741824
$955$	0	0
$956$	−50.1446	−1.62179
$957$	0	0
$958$	44.4529	1.43621
$959$	−37.6230	−1.21491
$960$	0	0
$961$	−17.7139	−0.571417
$962$	6.08513	0.196193
$963$	−48.1469	−1.55151
$964$	55.7771	1.79646
$965$	0	0
$966$	−114.449	−3.68234
$967$	−38.4583	−1.23674	−0.618368	−	0.785889i	$-0.712206\pi$
$967$	−38.4583	−1.23674	−0.618368	+	0.785889i	$0.712206\pi$
$968$	0	0
$969$	15.8737	0.509935
$970$	0	0
$971$	43.6637	1.40124	0.700618	−	0.713536i	$-0.252908\pi$
$971$	43.6637	1.40124	0.700618	+	0.713536i	$0.252908\pi$
$972$	−97.0106	−3.11162
$973$	−35.3030	−1.13176
$974$	17.1249	0.548716
$975$	0	0
$976$	−3.20494	−0.102588
$977$	11.7467	0.375811	0.187906	−	0.982187i	$-0.439830\pi$
$977$	11.7467	0.375811	0.187906	+	0.982187i	$0.439830\pi$
$978$	−43.8137	−1.40101
$979$	0	0
$980$	0	0
$981$	35.4965	1.13332
$982$	−1.30926	−0.0417800
$983$	−9.35189	−0.298279	−0.149139	−	0.988816i	$-0.547650\pi$
$983$	−9.35189	−0.298279	−0.149139	+	0.988816i	$0.547650\pi$
$984$	75.4731	2.40599
$985$	0	0
$986$	4.62627	0.147331
$987$	−37.7327	−1.20104
$988$	−12.1220	−0.385651
$989$	45.4117	1.44401
$990$	0	0
$991$	−32.3450	−1.02747	−0.513737	−	0.857948i	$-0.671739\pi$
$991$	−32.3450	−1.02747	−0.513737	+	0.857948i	$0.671739\pi$
$992$	15.0192	0.476860
$993$	−21.8211	−0.692473
$994$	−59.7438	−1.89496
$995$	0	0
$996$	−116.995	−3.70713
$997$	29.1174	0.922157	0.461078	−	0.887359i	$-0.347463\pi$
$997$	29.1174	0.922157	0.461078	+	0.887359i	$0.347463\pi$
$998$	−55.1880	−1.74695
$999$	0.391168	0.0123760

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3025.2.a.v.1.1		4
5.4	even	2		605.2.a.l.1.4		4
11.5	even	5		275.2.h.b.201.2		8
11.9	even	5		275.2.h.b.26.2		8
11.10	odd	2		3025.2.a.be.1.4		4
15.14	odd	2		5445.2.a.bg.1.1		4
20.19	odd	2		9680.2.a.cs.1.4		4
55.4	even	10		605.2.g.j.511.2		8
55.9	even	10		55.2.g.a.26.1	✓	8
55.14	even	10		605.2.g.j.251.2		8
55.19	odd	10		605.2.g.g.251.1		8
55.24	odd	10		605.2.g.n.81.2		8
55.27	odd	20		275.2.z.b.124.4		16
55.29	odd	10		605.2.g.g.511.1		8
55.38	odd	20		275.2.z.b.124.1		16
55.39	odd	10		605.2.g.n.366.2		8
55.42	odd	20		275.2.z.b.224.1		16
55.49	even	10		55.2.g.a.36.1	yes	8
55.53	odd	20		275.2.z.b.224.4		16
55.54	odd	2		605.2.a.i.1.1		4
165.104	odd	10		495.2.n.f.91.2		8
165.119	odd	10		495.2.n.f.136.2		8
165.164	even	2		5445.2.a.bu.1.4		4
220.119	odd	10		880.2.bo.e.81.2		8
220.159	odd	10		880.2.bo.e.641.2		8
220.219	even	2		9680.2.a.cv.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.g.a.26.1	✓	8	55.9	even	10
55.2.g.a.36.1	yes	8	55.49	even	10
275.2.h.b.26.2		8	11.9	even	5
275.2.h.b.201.2		8	11.5	even	5
275.2.z.b.124.1		16	55.38	odd	20
275.2.z.b.124.4		16	55.27	odd	20
275.2.z.b.224.1		16	55.42	odd	20
275.2.z.b.224.4		16	55.53	odd	20
495.2.n.f.91.2		8	165.104	odd	10
495.2.n.f.136.2		8	165.119	odd	10
605.2.a.i.1.1		4	55.54	odd	2
605.2.a.l.1.4		4	5.4	even	2
605.2.g.g.251.1		8	55.19	odd	10
605.2.g.g.511.1		8	55.29	odd	10
605.2.g.j.251.2		8	55.14	even	10
605.2.g.j.511.2		8	55.4	even	10
605.2.g.n.81.2		8	55.24	odd	10
605.2.g.n.366.2		8	55.39	odd	10
880.2.bo.e.81.2		8	220.119	odd	10
880.2.bo.e.641.2		8	220.159	odd	10
3025.2.a.v.1.1		4	1.1	even	1	trivial
3025.2.a.be.1.4		4	11.10	odd	2
5445.2.a.bg.1.1		4	15.14	odd	2
5445.2.a.bu.1.4		4	165.164	even	2
9680.2.a.cs.1.4		4	20.19	odd	2
9680.2.a.cv.1.4		4	220.219	even	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:	\( N \)	\(=\)	\( 3025 = 5^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3025.a (trivial)

\(f(q)\)	\(=\)	\(q-2.52452 q^{2} +2.46673 q^{3} +4.37322 q^{4} -6.22732 q^{6} -2.09351 q^{7} -5.99126 q^{8} +3.08477 q^{9} +O(q^{10})\)	\(q-2.52452 q^{2} +2.46673 q^{3} +4.37322 q^{4} -6.22732 q^{6} -2.09351 q^{7} -5.99126 q^{8} +3.08477 q^{9} +10.7876 q^{12} -1.28846 q^{13} +5.28512 q^{14} +6.37863 q^{16} +2.99126 q^{17} -7.78757 q^{18} +2.15130 q^{19} -5.16413 q^{21} -8.77882 q^{23} -14.7788 q^{24} +3.25274 q^{26} +0.209094 q^{27} -9.15538 q^{28} -0.612630 q^{29} -3.64501 q^{31} -4.12048 q^{32} -7.55150 q^{34} +13.4904 q^{36} +1.87077 q^{37} -5.43101 q^{38} -3.17828 q^{39} -5.10684 q^{41} +13.0370 q^{42} -5.17287 q^{43} +22.1623 q^{46} +7.30669 q^{47} +15.7344 q^{48} -2.61722 q^{49} +7.37863 q^{51} -5.63470 q^{52} +2.94221 q^{53} -0.527864 q^{54} +12.5428 q^{56} +5.30669 q^{57} +1.54660 q^{58} -6.49421 q^{59} -0.502449 q^{61} +9.20191 q^{62} -6.45799 q^{63} -2.35499 q^{64} +7.80964 q^{67} +13.0814 q^{68} -21.6550 q^{69} -11.3042 q^{71} -18.4816 q^{72} +11.1171 q^{73} -4.72281 q^{74} +9.40812 q^{76} +8.02363 q^{78} +5.35907 q^{79} -8.73852 q^{81} +12.8923 q^{82} -10.8454 q^{83} -22.5839 q^{84} +13.0590 q^{86} -1.51119 q^{87} -4.32336 q^{89} +2.69740 q^{91} -38.3917 q^{92} -8.99126 q^{93} -18.4459 q^{94} -10.1641 q^{96} +0.351653 q^{97} +6.60723 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3 q^{2} + 2 q^{3} + 7 q^{4} - q^{6} - 11 q^{7} - 9 q^{8}+O(q^{10}) \) 4 * q - 3 * q^2 + 2 * q^3 + 7 * q^4 - q^6 - 11 * q^7 - 9 * q^8	\( 4 q - 3 q^{2} + 2 q^{3} + 7 q^{4} - q^{6} - 11 q^{7} - 9 q^{8} + 14 q^{12} - 7 q^{13} - 2 q^{14} + 5 q^{16} - 3 q^{17} - 2 q^{18} + 12 q^{19} - 6 q^{21} + 9 q^{23} - 15 q^{24} + 13 q^{26} + 5 q^{27} - 7 q^{28} - 8 q^{29} + 3 q^{31} - 6 q^{32} - 10 q^{34} + 8 q^{36} + 3 q^{37} - 12 q^{38} - 3 q^{39} - 7 q^{41} - 2 q^{42} - 21 q^{43} + 12 q^{46} + 3 q^{47} + 2 q^{48} + 15 q^{49} + 9 q^{51} - 27 q^{52} + 11 q^{53} - 20 q^{54} + 15 q^{56} - 5 q^{57} - 2 q^{58} - 7 q^{59} + 4 q^{61} - 11 q^{62} - 3 q^{63} - 27 q^{64} + q^{67} + 15 q^{68} - 28 q^{69} - 15 q^{71} - 13 q^{72} + 9 q^{73} - 36 q^{74} + 8 q^{76} - 6 q^{78} + 6 q^{79} - 20 q^{81} + 44 q^{82} - 15 q^{83} - 47 q^{84} - 3 q^{86} - 15 q^{87} + 4 q^{91} - 18 q^{92} - 21 q^{93} - 11 q^{94} - 26 q^{96} - 6 q^{97} + 42 q^{98}+O(q^{100}) \) 4 * q - 3 * q^2 + 2 * q^3 + 7 * q^4 - q^6 - 11 * q^7 - 9 * q^8 + 14 * q^12 - 7 * q^13 - 2 * q^14 + 5 * q^16 - 3 * q^17 - 2 * q^18 + 12 * q^19 - 6 * q^21 + 9 * q^23 - 15 * q^24 + 13 * q^26 + 5 * q^27 - 7 * q^28 - 8 * q^29 + 3 * q^31 - 6 * q^32 - 10 * q^34 + 8 * q^36 + 3 * q^37 - 12 * q^38 - 3 * q^39 - 7 * q^41 - 2 * q^42 - 21 * q^43 + 12 * q^46 + 3 * q^47 + 2 * q^48 + 15 * q^49 + 9 * q^51 - 27 * q^52 + 11 * q^53 - 20 * q^54 + 15 * q^56 - 5 * q^57 - 2 * q^58 - 7 * q^59 + 4 * q^61 - 11 * q^62 - 3 * q^63 - 27 * q^64 + q^67 + 15 * q^68 - 28 * q^69 - 15 * q^71 - 13 * q^72 + 9 * q^73 - 36 * q^74 + 8 * q^76 - 6 * q^78 + 6 * q^79 - 20 * q^81 + 44 * q^82 - 15 * q^83 - 47 * q^84 - 3 * q^86 - 15 * q^87 + 4 * q^91 - 18 * q^92 - 21 * q^93 - 11 * q^94 - 26 * q^96 - 6 * q^97 + 42 * q^98

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