LMFDB - Embedded newform 3025.2.a.bd.1.2

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:	4.4.725.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 3x^{2} + x + 1 $ x^4 - x^3 - 3*x^2 + x + 1
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			1.2
Root			$-0.477260$ 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)

$f(q)$	$=$	$q-0.477260 q^{2} -0.323071 q^{3} -1.77222 q^{4} +0.154189 q^{6} -2.68522 q^{7} +1.80033 q^{8} -2.89563 q^{9} +O(q^{10})$	\(q-0.477260 q^{2} -0.323071 q^{3} -1.77222 q^{4} +0.154189 q^{6} -2.68522 q^{7} +1.80033 q^{8} -2.89563 q^{9} +0.572554 q^{12} +4.66785 q^{13} +1.28155 q^{14} +2.68522 q^{16} +4.62632 q^{17} +1.38197 q^{18} -4.34044 q^{19} +0.867517 q^{21} -2.77222 q^{23} -0.581635 q^{24} -2.22778 q^{26} +1.90471 q^{27} +4.75881 q^{28} -3.01341 q^{29} +2.38630 q^{31} -4.88221 q^{32} -2.20796 q^{34} +5.13169 q^{36} +10.6429 q^{37} +2.07152 q^{38} -1.50805 q^{39} -2.21041 q^{41} -0.414031 q^{42} +7.06719 q^{43} +1.32307 q^{46} -4.36215 q^{47} -0.867517 q^{48} +0.210405 q^{49} -1.49463 q^{51} -8.27247 q^{52} +6.33404 q^{53} -0.909040 q^{54} -4.83428 q^{56} +1.40227 q^{57} +1.43818 q^{58} +11.7473 q^{59} -3.98263 q^{61} -1.13889 q^{62} +7.77539 q^{63} -3.04036 q^{64} -7.31984 q^{67} -8.19888 q^{68} +0.895625 q^{69} +1.19571 q^{71} -5.21308 q^{72} -1.02171 q^{73} -5.07943 q^{74} +7.69223 q^{76} +0.719730 q^{78} +3.50213 q^{79} +8.07152 q^{81} +1.05494 q^{82} -11.1158 q^{83} -1.53743 q^{84} -3.37289 q^{86} +0.973547 q^{87} +2.76978 q^{89} -12.5342 q^{91} +4.91300 q^{92} -0.770945 q^{93} +2.08188 q^{94} +1.57730 q^{96} -18.5342 q^{97} -0.100418 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - q^{4} - q^{6} + 3 q^{7} + 3 q^{8}+O(q^{10}) $ 4 * q + q^2 - q^4 - q^6 + 3 * q^7 + 3 * q^8	$ 4 q + q^{2} - q^{4} - q^{6} + 3 q^{7} + 3 q^{8} - 8 q^{12} + q^{13} + 2 q^{14} - 3 q^{16} - q^{17} + 10 q^{18} - 20 q^{19} - 10 q^{21} - 5 q^{23} - 11 q^{24} - 15 q^{26} + 15 q^{27} + 13 q^{28} - 12 q^{29} - 5 q^{31} - 8 q^{32} + 2 q^{34} - 7 q^{37} - 20 q^{38} - 7 q^{39} - 11 q^{41} - 12 q^{42} + 19 q^{43} + 4 q^{46} - 5 q^{47} + 10 q^{48} + 3 q^{49} - 7 q^{51} - 11 q^{52} + 11 q^{53} + 8 q^{54} + 11 q^{56} - 5 q^{57} + 14 q^{58} + 9 q^{59} - 12 q^{61} - 35 q^{62} - 5 q^{63} - 3 q^{64} + 19 q^{67} - 3 q^{68} - 8 q^{69} + 5 q^{71} - 25 q^{72} + 11 q^{73} + 8 q^{78} - 34 q^{79} + 4 q^{81} + 6 q^{82} - 11 q^{83} - 11 q^{84} + q^{86} - 19 q^{87} - 8 q^{89} - 8 q^{91} + 12 q^{92} + 5 q^{93} + q^{94} + 34 q^{96} - 32 q^{97} - 8 q^{98}+O(q^{100}) $ 4 * q + q^2 - q^4 - q^6 + 3 * q^7 + 3 * q^8 - 8 * q^12 + q^13 + 2 * q^14 - 3 * q^16 - q^17 + 10 * q^18 - 20 * q^19 - 10 * q^21 - 5 * q^23 - 11 * q^24 - 15 * q^26 + 15 * q^27 + 13 * q^28 - 12 * q^29 - 5 * q^31 - 8 * q^32 + 2 * q^34 - 7 * q^37 - 20 * q^38 - 7 * q^39 - 11 * q^41 - 12 * q^42 + 19 * q^43 + 4 * q^46 - 5 * q^47 + 10 * q^48 + 3 * q^49 - 7 * q^51 - 11 * q^52 + 11 * q^53 + 8 * q^54 + 11 * q^56 - 5 * q^57 + 14 * q^58 + 9 * q^59 - 12 * q^61 - 35 * q^62 - 5 * q^63 - 3 * q^64 + 19 * q^67 - 3 * q^68 - 8 * q^69 + 5 * q^71 - 25 * q^72 + 11 * q^73 + 8 * q^78 - 34 * q^79 + 4 * q^81 + 6 * q^82 - 11 * q^83 - 11 * q^84 + q^86 - 19 * q^87 - 8 * q^89 - 8 * q^91 + 12 * q^92 + 5 * q^93 + q^94 + 34 * q^96 - 32 * q^97 - 8 * 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 $

$2$	−0.477260	−0.337474	−0.168737	−	0.985661i	$-0.553969\pi$
$2$	−0.477260	−0.337474	−0.168737	+	0.985661i	$0.553969\pi$
$3$	−0.323071	−0.186525	−0.0932626	−	0.995642i	$-0.529730\pi$
$3$	−0.323071	−0.186525	−0.0932626	+	0.995642i	$0.529730\pi$
$4$	−1.77222	−0.886111
$5$	0	0
$5$	0	0
$6$	0.154189	0.0629474
$7$	−2.68522	−1.01492	−0.507459	−	0.861676i	$-0.669415\pi$
$7$	−2.68522	−1.01492	−0.507459	+	0.861676i	$0.669415\pi$
$8$	1.80033	0.636513
$9$	−2.89563	−0.965208
$10$	0	0
$11$	0	0
$11$	0	0
$12$	0.572554	0.165282
$13$	4.66785	1.29463	0.647314	−	0.762223i	$-0.275892\pi$
$13$	4.66785	1.29463	0.647314	+	0.762223i	$0.275892\pi$
$14$	1.28155	0.342508
$15$	0	0
$16$	2.68522	0.671305
$17$	4.62632	1.12205	0.561024	−	0.827799i	$-0.310407\pi$
$17$	4.62632	1.12205	0.561024	+	0.827799i	$0.310407\pi$
$18$	1.38197	0.325733
$19$	−4.34044	−0.995766	−0.497883	−	0.867244i	$-0.665889\pi$
$19$	−4.34044	−0.995766	−0.497883	+	0.867244i	$0.665889\pi$
$20$	0	0
$21$	0.867517	0.189308
$22$	0	0
$23$	−2.77222	−0.578048	−0.289024	−	0.957322i	$-0.593331\pi$
$23$	−2.77222	−0.578048	−0.289024	+	0.957322i	$0.593331\pi$
$24$	−0.581635	−0.118726
$25$	0	0
$26$	−2.22778	−0.436903
$27$	1.90471	0.366561
$28$	4.75881	0.899330
$29$	−3.01341	−0.559577	−0.279789	−	0.960062i	$-0.590264\pi$
$29$	−3.01341	−0.559577	−0.279789	+	0.960062i	$0.590264\pi$
$30$	0	0
$31$	2.38630	0.428592	0.214296	−	0.976769i	$-0.431254\pi$
$31$	2.38630	0.428592	0.214296	+	0.976769i	$0.431254\pi$
$32$	−4.88221	−0.863061
$33$	0	0
$34$	−2.20796	−0.378662
$35$	0	0
$36$	5.13169	0.855282
$37$	10.6429	1.74968	0.874842	−	0.484409i	$-0.160965\pi$
$37$	10.6429	1.74968	0.874842	+	0.484409i	$0.160965\pi$
$38$	2.07152	0.336045
$39$	−1.50805	−0.241481
$40$	0	0
$41$	−2.21041	−0.345207	−0.172604	−	0.984991i	$-0.555218\pi$
$41$	−2.21041	−0.345207	−0.172604	+	0.984991i	$0.555218\pi$
$42$	−0.414031	−0.0638864
$43$	7.06719	1.07774	0.538868	−	0.842390i	$-0.318852\pi$
$43$	7.06719	1.07774	0.538868	+	0.842390i	$0.318852\pi$
$44$	0	0
$45$	0	0
$46$	1.32307	0.195076
$47$	−4.36215	−0.636285	−0.318142	−	0.948043i	$-0.603059\pi$
$47$	−4.36215	−0.636285	−0.318142	+	0.948043i	$0.603059\pi$
$48$	−0.867517	−0.125215
$49$	0.210405	0.0300579
$50$	0	0
$51$	−1.49463	−0.209290
$52$	−8.27247	−1.14718
$53$	6.33404	0.870047	0.435024	−	0.900419i	$-0.356740\pi$
$53$	6.33404	0.870047	0.435024	+	0.900419i	$0.356740\pi$
$54$	−0.909040	−0.123705
$55$	0	0
$56$	−4.83428	−0.646008
$57$	1.40227	0.185735
$58$	1.43818	0.188843
$59$	11.7473	1.52937	0.764683	−	0.644407i	$-0.222896\pi$
$59$	11.7473	1.52937	0.764683	+	0.644407i	$0.222896\pi$
$60$	0	0
$61$	−3.98263	−0.509923	−0.254962	−	0.966951i	$-0.582063\pi$
$61$	−3.98263	−0.509923	−0.254962	+	0.966951i	$0.582063\pi$
$62$	−1.13889	−0.144639
$63$	7.77539	0.979607
$64$	−3.04036	−0.380044
$65$	0	0
$66$	0	0
$67$	−7.31984	−0.894260	−0.447130	−	0.894469i	$-0.647554\pi$
$67$	−7.31984	−0.894260	−0.447130	+	0.894469i	$0.647554\pi$
$68$	−8.19888	−0.994260
$69$	0.895625	0.107821
$70$	0	0
$71$	1.19571	0.141905	0.0709525	−	0.997480i	$-0.477396\pi$
$71$	1.19571	0.141905	0.0709525	+	0.997480i	$0.477396\pi$
$72$	−5.21308	−0.614368
$73$	−1.02171	−0.119582	−0.0597908	−	0.998211i	$-0.519043\pi$
$73$	−1.02171	−0.119582	−0.0597908	+	0.998211i	$0.519043\pi$
$74$	−5.07943	−0.590472
$75$	0	0
$76$	7.69223	0.882360
$77$	0	0
$78$	0.719730	0.0814934
$79$	3.50213	0.394021	0.197010	−	0.980401i	$-0.436877\pi$
$79$	3.50213	0.394021	0.197010	+	0.980401i	$0.436877\pi$
$80$	0	0
$81$	8.07152	0.896836
$82$	1.05494	0.116498
$83$	−11.1158	−1.22012	−0.610061	−	0.792355i	$-0.708855\pi$
$83$	−11.1158	−1.22012	−0.610061	+	0.792355i	$0.708855\pi$
$84$	−1.53743	−0.167748
$85$	0	0
$86$	−3.37289	−0.363708
$87$	0.973547	0.104375
$88$	0	0
$89$	2.76978	0.293596	0.146798	−	0.989167i	$-0.453103\pi$
$89$	2.76978	0.293596	0.146798	+	0.989167i	$0.453103\pi$
$90$	0	0
$91$	−12.5342	−1.31394
$92$	4.91300	0.512215
$93$	−0.770945	−0.0799432
$94$	2.08188	0.214729
$95$	0	0
$96$	1.57730	0.160983
$97$	−18.5342	−1.88186	−0.940931	−	0.338597i	$-0.890048\pi$
$97$	−18.5342	−1.88186	−0.940931	+	0.338597i	$0.890048\pi$
$98$	−0.100418	−0.0101438
$99$	0	0
$100$	0	0
$101$	−7.11455	−0.707925	−0.353962	−	0.935260i	$-0.615166\pi$
$101$	−7.11455	−0.707925	−0.353962	+	0.935260i	$0.615166\pi$
$102$	0.713328	0.0706300
$103$	−7.52835	−0.741791	−0.370895	−	0.928675i	$-0.620949\pi$
$103$	−7.52835	−0.741791	−0.370895	+	0.928675i	$0.620949\pi$
$104$	8.40367	0.824048
$105$	0	0
$106$	−3.02298	−0.293618
$107$	−18.0292	−1.74295	−0.871475	−	0.490441i	$-0.836836\pi$
$107$	−18.0292	−1.74295	−0.871475	+	0.490441i	$0.836836\pi$
$108$	−3.37556	−0.324814
$109$	−16.3653	−1.56751	−0.783756	−	0.621068i	$-0.786699\pi$
$109$	−16.3653	−1.56751	−0.783756	+	0.621068i	$0.786699\pi$
$110$	0	0
$111$	−3.43842	−0.326360
$112$	−7.21041	−0.681319
$113$	2.05377	0.193203	0.0966013	−	0.995323i	$-0.469203\pi$
$113$	2.05377	0.193203	0.0966013	+	0.995323i	$0.469203\pi$
$114$	−0.669248	−0.0626808
$115$	0	0
$116$	5.34044	0.495848
$117$	−13.5163	−1.24959
$118$	−5.60651	−0.516121
$119$	−12.4227	−1.13879
$120$	0	0
$121$	0	0
$122$	1.90075	0.172086
$123$	0.714118	0.0643899
$124$	−4.22906	−0.379780
$125$	0	0
$126$	−3.71088	−0.330592
$127$	0.0762667	0.00676758	0.00338379	−	0.999994i	$-0.498923\pi$
$127$	0.0762667	0.00676758	0.00338379	+	0.999994i	$0.498923\pi$
$128$	11.2155	0.991316
$129$	−2.28320	−0.201025
$130$	0	0
$131$	−11.4831	−1.00328	−0.501642	−	0.865075i	$-0.667270\pi$
$131$	−11.4831	−1.00328	−0.501642	+	0.865075i	$0.667270\pi$
$132$	0	0
$133$	11.6550	1.01062
$134$	3.49346	0.301789
$135$	0	0
$136$	8.32892	0.714199
$137$	18.3293	1.56598	0.782989	−	0.622036i	$-0.213694\pi$
$137$	18.3293	1.56598	0.782989	+	0.622036i	$0.213694\pi$
$138$	−0.427446	−0.0363866
$139$	−23.1874	−1.96673	−0.983363	−	0.181653i	$-0.941855\pi$
$139$	−23.1874	−1.96673	−0.983363	+	0.181653i	$0.941855\pi$
$140$	0	0
$141$	1.40928	0.118683
$142$	−0.570666	−0.0478892
$143$	0	0
$144$	−7.77539	−0.647949
$145$	0	0
$146$	0.487619	0.0403557
$147$	−0.0679759	−0.00560655
$148$	−18.8616	−1.55041
$149$	14.6646	1.20137	0.600686	−	0.799485i	$-0.294894\pi$
$149$	14.6646	1.20137	0.600686	+	0.799485i	$0.294894\pi$
$150$	0	0
$151$	−7.51902	−0.611889	−0.305944	−	0.952049i	$-0.598972\pi$
$151$	−7.51902	−0.611889	−0.305944	+	0.952049i	$0.598972\pi$
$152$	−7.81423	−0.633818
$153$	−13.3961	−1.08301
$154$	0	0
$155$	0	0
$156$	2.67259	0.213979
$157$	13.3819	1.06799	0.533996	−	0.845487i	$-0.320690\pi$
$157$	13.3819	1.06799	0.533996	+	0.845487i	$0.320690\pi$
$158$	−1.67143	−0.132972
$159$	−2.04635	−0.162286
$160$	0	0
$161$	7.44403	0.586672
$162$	−3.85221	−0.302658
$163$	0.771990	0.0604669	0.0302335	−	0.999543i	$-0.490375\pi$
$163$	0.771990	0.0604669	0.0302335	+	0.999543i	$0.490375\pi$
$164$	3.91733	0.305892
$165$	0	0
$166$	5.30514	0.411759
$167$	8.48232	0.656381	0.328191	−	0.944612i	$-0.393561\pi$
$167$	8.48232	0.656381	0.328191	+	0.944612i	$0.393561\pi$
$168$	1.56182	0.120497
$169$	8.78880	0.676062
$170$	0	0
$171$	12.5683	0.961122
$172$	−12.5246	−0.954994
$173$	−5.07871	−0.386127	−0.193064	−	0.981186i	$-0.561842\pi$
$173$	−5.07871	−0.386127	−0.193064	+	0.981186i	$0.561842\pi$
$174$	−0.464635	−0.0352239
$175$	0	0
$176$	0	0
$177$	−3.79521	−0.285265
$178$	−1.32190	−0.0990809
$179$	−11.3170	−0.845876	−0.422938	−	0.906159i	$-0.639001\pi$
$179$	−11.3170	−0.845876	−0.422938	+	0.906159i	$0.639001\pi$
$180$	0	0
$181$	7.40006	0.550042	0.275021	−	0.961438i	$-0.411315\pi$
$181$	7.40006	0.550042	0.275021	+	0.961438i	$0.411315\pi$
$182$	5.98207	0.443421
$183$	1.28667	0.0951135
$184$	−4.99092	−0.367935
$185$	0	0
$186$	0.367941	0.0269787
$187$	0	0
$188$	7.73070	0.563819
$189$	−5.11455	−0.372029
$190$	0	0
$191$	−5.15608	−0.373081	−0.186540	−	0.982447i	$-0.559728\pi$
$191$	−5.15608	−0.373081	−0.186540	+	0.982447i	$0.559728\pi$
$192$	0.982251	0.0708879
$193$	4.03230	0.290251	0.145126	−	0.989413i	$-0.453641\pi$
$193$	4.03230	0.290251	0.145126	+	0.989413i	$0.453641\pi$
$194$	8.84563	0.635079
$195$	0	0
$196$	−0.372885	−0.0266346
$197$	−11.4176	−0.813469	−0.406734	−	0.913547i	$-0.633333\pi$
$197$	−11.4176	−0.813469	−0.406734	+	0.913547i	$0.633333\pi$
$198$	0	0
$199$	−7.16644	−0.508015	−0.254008	−	0.967202i	$-0.581749\pi$
$199$	−7.16644	−0.508015	−0.254008	+	0.967202i	$0.581749\pi$
$200$	0	0
$201$	2.36483	0.166802
$202$	3.39549	0.238906
$203$	8.09168	0.567925
$204$	2.64882	0.185455
$205$	0	0
$206$	3.59298	0.250335
$207$	8.02732	0.557937
$208$	12.5342	0.869090
$209$	0	0
$210$	0	0
$211$	3.48359	0.239820	0.119910	−	0.992785i	$-0.461739\pi$
$211$	3.48359	0.239820	0.119910	+	0.992785i	$0.461739\pi$
$212$	−11.2253	−0.770959
$213$	−0.386300	−0.0264688
$214$	8.60462	0.588200
$215$	0	0
$216$	3.42910	0.233321
$217$	−6.40774	−0.434986
$218$	7.81051	0.528995
$219$	0.330084	0.0223050
$220$	0	0
$221$	21.5950	1.45264
$222$	1.64102	0.110138
$223$	−10.5449	−0.706141	−0.353071	−	0.935597i	$-0.614862\pi$
$223$	−10.5449	−0.706141	−0.353071	+	0.935597i	$0.614862\pi$
$224$	13.1098	0.875936
$225$	0	0
$226$	−0.980183	−0.0652008
$227$	−0.216018	−0.0143376	−0.00716880	−	0.999974i	$-0.502282\pi$
$227$	−0.216018	−0.0143376	−0.00716880	+	0.999974i	$0.502282\pi$
$228$	−2.48514	−0.164582
$229$	−0.0757097	−0.00500304	−0.00250152	−	0.999997i	$-0.500796\pi$
$229$	−0.0757097	−0.00500304	−0.00250152	+	0.999997i	$0.500796\pi$
$230$	0	0
$231$	0	0
$232$	−5.42514	−0.356178
$233$	−15.1201	−0.990548	−0.495274	−	0.868737i	$-0.664932\pi$
$233$	−15.1201	−0.990548	−0.495274	+	0.868737i	$0.664932\pi$
$234$	6.45081	0.421702
$235$	0	0
$236$	−20.8188	−1.35519
$237$	−1.13144	−0.0734948
$238$	5.92886	0.384311
$239$	−23.1646	−1.49839	−0.749197	−	0.662347i	$-0.769561\pi$
$239$	−23.1646	−1.49839	−0.749197	+	0.662347i	$0.769561\pi$
$240$	0	0
$241$	−21.3349	−1.37430	−0.687151	−	0.726515i	$-0.741139\pi$
$241$	−21.3349	−1.37430	−0.687151	+	0.726515i	$0.741139\pi$
$242$	0	0
$243$	−8.32179	−0.533843
$244$	7.05810	0.451849
$245$	0	0
$246$	−0.340820	−0.0217299
$247$	−20.2605	−1.28915
$248$	4.29613	0.272805
$249$	3.59120	0.227583
$250$	0	0
$251$	−6.22186	−0.392721	−0.196360	−	0.980532i	$-0.562912\pi$
$251$	−6.22186	−0.392721	−0.196360	+	0.980532i	$0.562912\pi$
$252$	−13.7797	−0.868041
$253$	0	0
$254$	−0.0363991	−0.00228388
$255$	0	0
$256$	0.728021	0.0455013
$257$	14.2903	0.891406	0.445703	−	0.895181i	$-0.352954\pi$
$257$	14.2903	0.891406	0.445703	+	0.895181i	$0.352954\pi$
$258$	1.08968	0.0678406
$259$	−28.5785	−1.77578
$260$	0	0
$261$	8.72572	0.540108
$262$	5.48043	0.338582
$263$	−4.13132	−0.254748	−0.127374	−	0.991855i	$-0.540655\pi$
$263$	−4.13132	−0.254748	−0.127374	+	0.991855i	$0.540655\pi$
$264$	0	0
$265$	0	0
$266$	−5.56249	−0.341058
$267$	−0.894835	−0.0547630
$268$	12.9724	0.792414
$269$	−1.68394	−0.102672	−0.0513359	−	0.998681i	$-0.516348\pi$
$269$	−1.68394	−0.102672	−0.0513359	+	0.998681i	$0.516348\pi$
$270$	0	0
$271$	−18.4310	−1.11960	−0.559801	−	0.828627i	$-0.689123\pi$
$271$	−18.4310	−1.11960	−0.559801	+	0.828627i	$0.689123\pi$
$272$	12.4227	0.753237
$273$	4.04944	0.245083
$274$	−8.74784	−0.528476
$275$	0	0
$276$	−1.58725	−0.0955411
$277$	3.42745	0.205935	0.102968	−	0.994685i	$-0.467166\pi$
$277$	3.42745	0.205935	0.102968	+	0.994685i	$0.467166\pi$
$278$	11.0664	0.663718
$279$	−6.90983	−0.413681
$280$	0	0
$281$	−22.8217	−1.36143	−0.680715	−	0.732548i	$-0.738331\pi$
$281$	−22.8217	−1.36143	−0.680715	+	0.732548i	$0.738331\pi$
$282$	−0.672595	−0.0400524
$283$	29.0991	1.72976	0.864880	−	0.501978i	$-0.167394\pi$
$283$	29.0991	1.72976	0.864880	+	0.501978i	$0.167394\pi$
$284$	−2.11907	−0.125744
$285$	0	0
$286$	0	0
$287$	5.93542	0.350357
$288$	14.1371	0.833034
$289$	4.40288	0.258993
$290$	0	0
$291$	5.98786	0.351015
$292$	1.81069	0.105963
$293$	−21.2136	−1.23931	−0.619655	−	0.784874i	$-0.712727\pi$
$293$	−21.2136	−1.23931	−0.619655	+	0.784874i	$0.712727\pi$
$294$	0.0324422	0.00189207
$295$	0	0
$296$	19.1608	1.11370
$297$	0	0
$298$	−6.99883	−0.405432
$299$	−12.9403	−0.748358
$300$	0	0
$301$	−18.9769	−1.09381
$302$	3.58853	0.206496
$303$	2.29851	0.132046
$304$	−11.6550	−0.668463
$305$	0	0
$306$	6.39342	0.365488
$307$	6.87520	0.392388	0.196194	−	0.980565i	$-0.437142\pi$
$307$	6.87520	0.392388	0.196194	+	0.980565i	$0.437142\pi$
$308$	0	0
$309$	2.43219	0.138363
$310$	0	0
$311$	25.1577	1.42656	0.713280	−	0.700879i	$-0.247209\pi$
$311$	25.1577	1.42656	0.713280	+	0.700879i	$0.247209\pi$
$312$	−2.71498	−0.153706
$313$	11.5793	0.654503	0.327251	−	0.944937i	$-0.393878\pi$
$313$	11.5793	0.654503	0.327251	+	0.944937i	$0.393878\pi$
$314$	−6.38664	−0.360419
$315$	0	0
$316$	−6.20656	−0.349146
$317$	−20.7413	−1.16495	−0.582473	−	0.812850i	$-0.697915\pi$
$317$	−20.7413	−1.16495	−0.582473	+	0.812850i	$0.697915\pi$
$318$	0.976639	0.0547672
$319$	0	0
$320$	0	0
$321$	5.82472	0.325104
$322$	−3.55274	−0.197986
$323$	−20.0803	−1.11730
$324$	−14.3045	−0.794696
$325$	0	0
$326$	−0.368440	−0.0204060
$327$	5.28716	0.292381
$328$	−3.97946	−0.219729
$329$	11.7133	0.645777
$330$	0	0
$331$	−32.1415	−1.76665	−0.883327	−	0.468757i	$-0.844702\pi$
$331$	−32.1415	−1.76665	−0.883327	+	0.468757i	$0.844702\pi$
$332$	19.6997	1.08116
$333$	−30.8179	−1.68881
$334$	−4.04827	−0.221511
$335$	0	0
$336$	2.32947	0.127083
$337$	17.9964	0.980326	0.490163	−	0.871631i	$-0.336937\pi$
$337$	17.9964	0.980326	0.490163	+	0.871631i	$0.336937\pi$
$338$	−4.19454	−0.228153
$339$	−0.663514	−0.0360371
$340$	0	0
$341$	0	0
$342$	−5.99834	−0.324353
$343$	18.2316	0.984411
$344$	12.7233	0.685993
$345$	0	0
$346$	2.42387	0.130308
$347$	8.04981	0.432137	0.216068	−	0.976378i	$-0.430677\pi$
$347$	8.04981	0.432137	0.216068	+	0.976378i	$0.430677\pi$
$348$	−1.72534	−0.0924881
$349$	19.2294	1.02932	0.514662	−	0.857393i	$-0.327917\pi$
$349$	19.2294	1.02932	0.514662	+	0.857393i	$0.327917\pi$
$350$	0	0
$351$	8.89088	0.474560
$352$	0	0
$353$	−14.8497	−0.790371	−0.395186	−	0.918601i	$-0.629320\pi$
$353$	−14.8497	−0.790371	−0.395186	+	0.918601i	$0.629320\pi$
$354$	1.81130	0.0962695
$355$	0	0
$356$	−4.90866	−0.260159
$357$	4.01341	0.212412
$358$	5.40117	0.285461
$359$	10.2233	0.539563	0.269782	−	0.962922i	$-0.413048\pi$
$359$	10.2233	0.539563	0.269782	+	0.962922i	$0.413048\pi$
$360$	0	0
$361$	−0.160555	−0.00845028
$362$	−3.53175	−0.185625
$363$	0	0
$364$	22.2134	1.16430
$365$	0	0
$366$	−0.614077	−0.0320983
$367$	−14.1434	−0.738279	−0.369139	−	0.929374i	$-0.620347\pi$
$367$	−14.1434	−0.738279	−0.369139	+	0.929374i	$0.620347\pi$
$368$	−7.44403	−0.388047
$369$	6.40050	0.333197
$370$	0	0
$371$	−17.0083	−0.883026
$372$	1.36629	0.0708386
$373$	−12.4600	−0.645154	−0.322577	−	0.946543i	$-0.604549\pi$
$373$	−12.4600	−0.645154	−0.322577	+	0.946543i	$0.604549\pi$
$374$	0	0
$375$	0	0
$376$	−7.85331	−0.405004
$377$	−14.0662	−0.724444
$378$	2.44097	0.125550
$379$	16.3370	0.839174	0.419587	−	0.907715i	$-0.362175\pi$
$379$	16.3370	0.839174	0.419587	+	0.907715i	$0.362175\pi$
$380$	0	0
$381$	−0.0246396	−0.00126232
$382$	2.46079	0.125905
$383$	0.812648	0.0415244	0.0207622	−	0.999784i	$-0.493391\pi$
$383$	0.812648	0.0415244	0.0207622	+	0.999784i	$0.493391\pi$
$384$	−3.62339	−0.184905
$385$	0	0
$386$	−1.92445	−0.0979522
$387$	−20.4639	−1.04024
$388$	32.8467	1.66754
$389$	−30.3941	−1.54104	−0.770521	−	0.637414i	$-0.780004\pi$
$389$	−30.3941	−1.54104	−0.770521	+	0.637414i	$0.780004\pi$
$390$	0	0
$391$	−12.8252	−0.648598
$392$	0.378799	0.0191322
$393$	3.70986	0.187138
$394$	5.44915	0.274524
$395$	0	0
$396$	0	0
$397$	14.8996	0.747789	0.373894	−	0.927471i	$-0.378022\pi$
$397$	14.8996	0.747789	0.373894	+	0.927471i	$0.378022\pi$
$398$	3.42025	0.171442
$399$	−3.76541	−0.188506
$400$	0	0
$401$	12.1692	0.607700	0.303850	−	0.952720i	$-0.401728\pi$
$401$	12.1692	0.607700	0.303850	+	0.952720i	$0.401728\pi$
$402$	−1.12864	−0.0562913
$403$	11.1389	0.554867
$404$	12.6086	0.627300
$405$	0	0
$406$	−3.86184	−0.191660
$407$	0	0
$408$	−2.69083	−0.133216
$409$	−0.262108	−0.0129604	−0.00648020	−	0.999979i	$-0.502063\pi$
$409$	−0.262108	−0.0129604	−0.00648020	+	0.999979i	$0.502063\pi$
$410$	0	0
$411$	−5.92166	−0.292094
$412$	13.3419	0.657309
$413$	−31.5440	−1.55218
$414$	−3.83112	−0.188289
$415$	0	0
$416$	−22.7894	−1.11734
$417$	7.49116	0.366844
$418$	0	0
$419$	−1.26916	−0.0620023	−0.0310012	−	0.999519i	$-0.509870\pi$
$419$	−1.26916	−0.0620023	−0.0310012	+	0.999519i	$0.509870\pi$
$420$	0	0
$421$	−29.6655	−1.44581	−0.722903	−	0.690949i	$-0.757193\pi$
$421$	−29.6655	−1.44581	−0.722903	+	0.690949i	$0.757193\pi$
$422$	−1.66258	−0.0809331
$423$	12.6311	0.614147
$424$	11.4034	0.553797
$425$	0	0
$426$	0.184366	0.00893254
$427$	10.6942	0.517530
$428$	31.9518	1.54445
$429$	0	0
$430$	0	0
$431$	31.3549	1.51031	0.755156	−	0.655545i	$-0.227561\pi$
$431$	31.3549	1.51031	0.755156	+	0.655545i	$0.227561\pi$
$432$	5.11455	0.246074
$433$	26.0325	1.25104	0.625521	−	0.780207i	$-0.284886\pi$
$433$	26.0325	1.25104	0.625521	+	0.780207i	$0.284886\pi$
$434$	3.05816	0.146796
$435$	0	0
$436$	29.0030	1.38899
$437$	12.0327	0.575601
$438$	−0.157536	−0.00752735
$439$	14.4191	0.688185	0.344093	−	0.938936i	$-0.388187\pi$
$439$	14.4191	0.688185	0.344093	+	0.938936i	$0.388187\pi$
$440$	0	0
$441$	−0.609255	−0.0290121
$442$	−10.3064	−0.490226
$443$	0.330608	0.0157077	0.00785383	−	0.999969i	$-0.497500\pi$
$443$	0.330608	0.0157077	0.00785383	+	0.999969i	$0.497500\pi$
$444$	6.09364	0.289191
$445$	0	0
$446$	5.03268	0.238304
$447$	−4.73771	−0.224086
$448$	8.16402	0.385714
$449$	8.50828	0.401531	0.200765	−	0.979639i	$-0.435657\pi$
$449$	8.50828	0.401531	0.200765	+	0.979639i	$0.435657\pi$
$450$	0	0
$451$	0	0
$452$	−3.63974	−0.171199
$453$	2.42918	0.114133
$454$	0.103097	0.00483856
$455$	0	0
$456$	2.52455	0.118223
$457$	−1.13847	−0.0532555	−0.0266277	−	0.999645i	$-0.508477\pi$
$457$	−1.13847	−0.0532555	−0.0266277	+	0.999645i	$0.508477\pi$
$458$	0.0361332	0.00168839
$459$	8.81179	0.411299
$460$	0	0
$461$	14.5073	0.675670	0.337835	−	0.941205i	$-0.390305\pi$
$461$	14.5073	0.675670	0.337835	+	0.941205i	$0.390305\pi$
$462$	0	0
$463$	4.89739	0.227601	0.113801	−	0.993504i	$-0.463698\pi$
$463$	4.89739	0.227601	0.113801	+	0.993504i	$0.463698\pi$
$464$	−8.09168	−0.375647
$465$	0	0
$466$	7.21620	0.334284
$467$	−32.4230	−1.50036	−0.750180	−	0.661234i	$-0.770033\pi$
$467$	−32.4230	−1.50036	−0.750180	+	0.661234i	$0.770033\pi$
$468$	23.9540	1.10727
$469$	19.6554	0.907601
$470$	0	0
$471$	−4.32330	−0.199207
$472$	21.1490	0.973461
$473$	0	0
$474$	0.539990	0.0248026
$475$	0	0
$476$	22.0158	1.00909
$477$	−18.3410	−0.839777
$478$	11.0555	0.505669
$479$	17.7354	0.810352	0.405176	−	0.914239i	$-0.367210\pi$
$479$	17.7354	0.810352	0.405176	+	0.914239i	$0.367210\pi$
$480$	0	0
$481$	49.6795	2.26519
$482$	10.1823	0.463791
$483$	−2.40495	−0.109429
$484$	0	0
$485$	0	0
$486$	3.97166	0.180158
$487$	18.4603	0.836514	0.418257	−	0.908329i	$-0.362641\pi$
$487$	18.4603	0.836514	0.418257	+	0.908329i	$0.362641\pi$
$488$	−7.17005	−0.324573
$489$	−0.249408	−0.0112786
$490$	0	0
$491$	−11.4338	−0.516002	−0.258001	−	0.966145i	$-0.583064\pi$
$491$	−11.4338	−0.516002	−0.258001	+	0.966145i	$0.583064\pi$
$492$	−1.26558	−0.0570566
$493$	−13.9410	−0.627873
$494$	9.66954	0.435053
$495$	0	0
$496$	6.40774	0.287716
$497$	−3.21075	−0.144022
$498$	−1.71394	−0.0768034
$499$	10.8815	0.487125	0.243562	−	0.969885i	$-0.421684\pi$
$499$	10.8815	0.487125	0.243562	+	0.969885i	$0.421684\pi$
$500$	0	0
$501$	−2.74039	−0.122432
$502$	2.96945	0.132533
$503$	−44.7247	−1.99417	−0.997087	−	0.0762683i	$-0.975699\pi$
$503$	−44.7247	−1.99417	−0.997087	+	0.0762683i	$0.975699\pi$
$504$	13.9983	0.623533
$505$	0	0
$506$	0	0
$507$	−2.83941	−0.126103
$508$	−0.135162	−0.00599683
$509$	−13.8093	−0.612088	−0.306044	−	0.952017i	$-0.599006\pi$
$509$	−13.8093	−0.612088	−0.306044	+	0.952017i	$0.599006\pi$
$510$	0	0
$511$	2.74350	0.121365
$512$	−22.7784	−1.00667
$513$	−8.26727	−0.365009
$514$	−6.82020	−0.300826
$515$	0	0
$516$	4.04635	0.178130
$517$	0	0
$518$	13.6394	0.599281
$519$	1.64079	0.0720225
$520$	0	0
$521$	−3.64972	−0.159897	−0.0799486	−	0.996799i	$-0.525476\pi$
$521$	−3.64972	−0.159897	−0.0799486	+	0.996799i	$0.525476\pi$
$522$	−4.16444	−0.182272
$523$	4.98707	0.218069	0.109035	−	0.994038i	$-0.465224\pi$
$523$	4.98707	0.218069	0.109035	+	0.994038i	$0.465224\pi$
$524$	20.3506	0.889021
$525$	0	0
$526$	1.97171	0.0859707
$527$	11.0398	0.480901
$528$	0	0
$529$	−15.3148	−0.665860
$530$	0	0
$531$	−34.0157	−1.47616
$532$	−20.6553	−0.895522
$533$	−10.3178	−0.446915
$534$	0.427069	0.0184811
$535$	0	0
$536$	−13.1781	−0.569208
$537$	3.65621	0.157777
$538$	0.803678	0.0346490
$539$	0	0
$540$	0	0
$541$	0.247594	0.0106449	0.00532246	−	0.999986i	$-0.498306\pi$
$541$	0.247594	0.0106449	0.00532246	+	0.999986i	$0.498306\pi$
$542$	8.79637	0.377837
$543$	−2.39075	−0.102597
$544$	−22.5867	−0.968396
$545$	0	0
$546$	−1.93263	−0.0827091
$547$	25.3120	1.08226	0.541132	−	0.840938i	$-0.317996\pi$
$547$	25.3120	1.08226	0.541132	+	0.840938i	$0.317996\pi$
$548$	−32.4836	−1.38763
$549$	11.5322	0.492182
$550$	0	0
$551$	13.0796	0.557208
$552$	1.61242	0.0686292
$553$	−9.40400	−0.399899
$554$	−1.63578	−0.0694978
$555$	0	0
$556$	41.0932	1.74274
$557$	38.6671	1.63838	0.819190	−	0.573523i	$-0.194424\pi$
$557$	38.6671	1.63838	0.819190	+	0.573523i	$0.194424\pi$
$558$	3.29779	0.139606
$559$	32.9885	1.39527
$560$	0	0
$561$	0	0
$562$	10.8919	0.459447
$563$	−13.9362	−0.587341	−0.293671	−	0.955907i	$-0.594877\pi$
$563$	−13.9362	−0.587341	−0.293671	+	0.955907i	$0.594877\pi$
$564$	−2.49757	−0.105166
$565$	0	0
$566$	−13.8878	−0.583749
$567$	−21.6738	−0.910214
$568$	2.15268	0.0903243
$569$	27.9125	1.17015	0.585076	−	0.810979i	$-0.301065\pi$
$569$	27.9125	1.17015	0.585076	+	0.810979i	$0.301065\pi$
$570$	0	0
$571$	−31.4113	−1.31452	−0.657261	−	0.753663i	$-0.728285\pi$
$571$	−31.4113	−1.31452	−0.657261	+	0.753663i	$0.728285\pi$
$572$	0	0
$573$	1.66578	0.0695889
$574$	−2.83274	−0.118236
$575$	0	0
$576$	8.80373	0.366822
$577$	−20.7349	−0.863206	−0.431603	−	0.902064i	$-0.642052\pi$
$577$	−20.7349	−0.863206	−0.431603	+	0.902064i	$0.642052\pi$
$578$	−2.10132	−0.0874034
$579$	−1.30272	−0.0541392
$580$	0	0
$581$	29.8485	1.23832
$582$	−2.85777	−0.118458
$583$	0	0
$584$	−1.83941	−0.0761153
$585$	0	0
$586$	10.1244	0.418235
$587$	−15.2367	−0.628886	−0.314443	−	0.949276i	$-0.601818\pi$
$587$	−15.2367	−0.628886	−0.314443	+	0.949276i	$0.601818\pi$
$588$	0.120468	0.00496803
$589$	−10.3576	−0.426777
$590$	0	0
$591$	3.68869	0.151732
$592$	28.5785	1.17457
$593$	−27.5413	−1.13098	−0.565492	−	0.824754i	$-0.691314\pi$
$593$	−27.5413	−1.13098	−0.565492	+	0.824754i	$0.691314\pi$
$594$	0	0
$595$	0	0
$596$	−25.9890	−1.06455
$597$	2.31527	0.0947576
$598$	6.17589	0.252551
$599$	−26.7331	−1.09228	−0.546142	−	0.837693i	$-0.683904\pi$
$599$	−26.7331	−1.09228	−0.546142	+	0.837693i	$0.683904\pi$
$600$	0	0
$601$	2.40680	0.0981753	0.0490876	−	0.998794i	$-0.484369\pi$
$601$	2.40680	0.0981753	0.0490876	+	0.998794i	$0.484369\pi$
$602$	9.05694	0.369133
$603$	21.1955	0.863147
$604$	13.3254	0.542202
$605$	0	0
$606$	−1.09699	−0.0445620
$607$	−10.2929	−0.417774	−0.208887	−	0.977940i	$-0.566984\pi$
$607$	−10.2929	−0.417774	−0.208887	+	0.977940i	$0.566984\pi$
$608$	21.1910	0.859407
$609$	−2.61419	−0.105932
$610$	0	0
$611$	−20.3618	−0.823752
$612$	23.7409	0.959668
$613$	−27.8756	−1.12589	−0.562943	−	0.826496i	$-0.690331\pi$
$613$	−27.8756	−1.12589	−0.562943	+	0.826496i	$0.690331\pi$
$614$	−3.28126	−0.132421
$615$	0	0
$616$	0	0
$617$	28.7216	1.15629	0.578143	−	0.815935i	$-0.303778\pi$
$617$	28.7216	1.15629	0.578143	+	0.815935i	$0.303778\pi$
$618$	−1.16079	−0.0466938
$619$	22.6968	0.912261	0.456131	−	0.889913i	$-0.349235\pi$
$619$	22.6968	0.912261	0.456131	+	0.889913i	$0.349235\pi$
$620$	0	0
$621$	−5.28027	−0.211890
$622$	−12.0067	−0.481427
$623$	−7.43746	−0.297976
$624$	−4.04944	−0.162107
$625$	0	0
$626$	−5.52635	−0.220877
$627$	0	0
$628$	−23.7157	−0.946360
$629$	49.2375	1.96323
$630$	0	0
$631$	28.5364	1.13602	0.568008	−	0.823023i	$-0.307714\pi$
$631$	28.5364	1.13602	0.568008	+	0.823023i	$0.307714\pi$
$632$	6.30500	0.250799
$633$	−1.12545	−0.0447326
$634$	9.89897	0.393138
$635$	0	0
$636$	3.62658	0.143803
$637$	0.982140	0.0389138
$638$	0	0
$639$	−3.46233	−0.136968
$640$	0	0
$641$	2.37375	0.0937575	0.0468788	−	0.998901i	$-0.485073\pi$
$641$	2.37375	0.0937575	0.0468788	+	0.998901i	$0.485073\pi$
$642$	−2.77990	−0.109714
$643$	−11.3603	−0.448007	−0.224004	−	0.974588i	$-0.571913\pi$
$643$	−11.3603	−0.448007	−0.224004	+	0.974588i	$0.571913\pi$
$644$	−13.1925	−0.519856
$645$	0	0
$646$	9.58352	0.377059
$647$	48.4220	1.90366	0.951832	−	0.306621i	$-0.0991984\pi$
$647$	48.4220	1.90366	0.951832	+	0.306621i	$0.0991984\pi$
$648$	14.5314	0.570848
$649$	0	0
$650$	0	0
$651$	2.07016	0.0811358
$652$	−1.36814	−0.0535804
$653$	−29.7548	−1.16440	−0.582198	−	0.813047i	$-0.697807\pi$
$653$	−29.7548	−1.16440	−0.582198	+	0.813047i	$0.697807\pi$
$654$	−2.52335	−0.0986708
$655$	0	0
$656$	−5.93542	−0.231739
$657$	2.95848	0.115421
$658$	−5.59030	−0.217933
$659$	−28.4931	−1.10993	−0.554966	−	0.831873i	$-0.687269\pi$
$659$	−28.4931	−1.10993	−0.554966	+	0.831873i	$0.687269\pi$
$660$	0	0
$661$	−1.02875	−0.0400139	−0.0200070	−	0.999800i	$-0.506369\pi$
$661$	−1.02875	−0.0400139	−0.0200070	+	0.999800i	$0.506369\pi$
$662$	15.3398	0.596200
$663$	−6.97671	−0.270953
$664$	−20.0122	−0.776623
$665$	0	0
$666$	14.7081	0.569929
$667$	8.35386	0.323463
$668$	−15.0326	−0.581627
$669$	3.40676	0.131713
$670$	0	0
$671$	0	0
$672$	−4.23540	−0.163384
$673$	−13.0369	−0.502536	−0.251268	−	0.967918i	$-0.580848\pi$
$673$	−13.0369	−0.502536	−0.251268	+	0.967918i	$0.580848\pi$
$674$	−8.58896	−0.330834
$675$	0	0
$676$	−15.5757	−0.599066
$677$	37.1064	1.42612	0.713058	−	0.701105i	$-0.247310\pi$
$677$	37.1064	1.42612	0.713058	+	0.701105i	$0.247310\pi$
$678$	0.316669	0.0121616
$679$	49.7684	1.90994
$680$	0	0
$681$	0.0697890	0.00267432
$682$	0	0
$683$	32.8992	1.25885	0.629426	−	0.777061i	$-0.283290\pi$
$683$	32.8992	1.25885	0.629426	+	0.777061i	$0.283290\pi$
$684$	−22.2738	−0.851661
$685$	0	0
$686$	−8.70119	−0.332213
$687$	0.0244596	0.000933193 0
$688$	18.9769	0.723489
$689$	29.5663	1.12639
$690$	0	0
$691$	36.6998	1.39613	0.698064	−	0.716035i	$-0.254045\pi$
$691$	36.6998	1.39613	0.698064	+	0.716035i	$0.254045\pi$
$692$	9.00061	0.342152
$693$	0	0
$694$	−3.84185	−0.145835
$695$	0	0
$696$	1.75271	0.0664362
$697$	−10.2261	−0.387339
$698$	−9.17741	−0.347370
$699$	4.88485	0.184762
$700$	0	0
$701$	−36.2497	−1.36913	−0.684566	−	0.728951i	$-0.740008\pi$
$701$	−36.2497	−1.36913	−0.684566	+	0.728951i	$0.740008\pi$
$702$	−4.24326	−0.160152
$703$	−46.1949	−1.74227
$704$	0	0
$705$	0	0
$706$	7.08718	0.266730
$707$	19.1041	0.718485
$708$	6.72595	0.252777
$709$	−18.6013	−0.698585	−0.349293	−	0.937014i	$-0.613578\pi$
$709$	−18.6013	−0.698585	−0.349293	+	0.937014i	$0.613578\pi$
$710$	0	0
$711$	−10.1409	−0.380312
$712$	4.98652	0.186878
$713$	−6.61536	−0.247747
$714$	−1.91544	−0.0716836
$715$	0	0
$716$	20.0563	0.749540
$717$	7.48382	0.279488
$718$	−4.87915	−0.182088
$719$	−37.4280	−1.39583	−0.697914	−	0.716181i	$-0.745888\pi$
$719$	−37.4280	−1.39583	−0.697914	+	0.716181i	$0.745888\pi$
$720$	0	0
$721$	20.2153	0.752856
$722$	0.0766267	0.00285175
$723$	6.89269	0.256342
$724$	−13.1146	−0.487399
$725$	0	0
$726$	0	0
$727$	−14.6011	−0.541526	−0.270763	−	0.962646i	$-0.587276\pi$
$727$	−14.6011	−0.541526	−0.270763	+	0.962646i	$0.587276\pi$
$728$	−22.5657	−0.836341
$729$	−21.5260	−0.797260
$730$	0	0
$731$	32.6951	1.20927
$732$	−2.28027	−0.0842812
$733$	−41.8369	−1.54528	−0.772640	−	0.634844i	$-0.781064\pi$
$733$	−41.8369	−1.54528	−0.772640	+	0.634844i	$0.781064\pi$
$734$	6.75007	0.249150
$735$	0	0
$736$	13.5346	0.498891
$737$	0	0
$738$	−3.05470	−0.112445
$739$	−11.9299	−0.438849	−0.219424	−	0.975630i	$-0.570418\pi$
$739$	−11.9299	−0.438849	−0.219424	+	0.975630i	$0.570418\pi$
$740$	0	0
$741$	6.54559	0.240458
$742$	8.11738	0.297998
$743$	−46.6803	−1.71253	−0.856267	−	0.516534i	$-0.827222\pi$
$743$	−46.6803	−1.71253	−0.856267	+	0.516534i	$0.827222\pi$
$744$	−1.38796	−0.0508849
$745$	0	0
$746$	5.94666	0.217723
$747$	32.1873	1.17767
$748$	0	0
$749$	48.4124	1.76895
$750$	0	0
$751$	14.4039	0.525607	0.262803	−	0.964849i	$-0.415353\pi$
$751$	14.4039	0.525607	0.262803	+	0.964849i	$0.415353\pi$
$752$	−11.7133	−0.427141
$753$	2.01010	0.0732523
$754$	6.71322	0.244481
$755$	0	0
$756$	9.06413	0.329659
$757$	16.0616	0.583768	0.291884	−	0.956454i	$-0.405718\pi$
$757$	16.0616	0.583768	0.291884	+	0.956454i	$0.405718\pi$
$758$	−7.79698	−0.283199
$759$	0	0
$760$	0	0
$761$	−38.8840	−1.40954	−0.704772	−	0.709433i	$-0.748951\pi$
$761$	−38.8840	−1.40954	−0.704772	+	0.709433i	$0.748951\pi$
$762$	0.0117595	0.000426001 0
$763$	43.9445	1.59090
$764$	9.13772	0.330591
$765$	0	0
$766$	−0.387844	−0.0140134
$767$	54.8345	1.97996
$768$	−0.235203	−0.00848714
$769$	43.0017	1.55068	0.775341	−	0.631543i	$-0.217578\pi$
$769$	43.0017	1.55068	0.775341	+	0.631543i	$0.217578\pi$
$770$	0	0
$771$	−4.61679	−0.166270
$772$	−7.14613	−0.257195
$773$	7.85462	0.282511	0.141256	−	0.989973i	$-0.454886\pi$
$773$	7.85462	0.282511	0.141256	+	0.989973i	$0.454886\pi$
$774$	9.76661	0.351054
$775$	0	0
$776$	−33.3677	−1.19783
$777$	9.23290	0.331228
$778$	14.5059	0.520061
$779$	9.59414	0.343746
$780$	0	0
$781$	0	0
$782$	6.12096	0.218885
$783$	−5.73967	−0.205119
$784$	0.564984	0.0201780
$785$	0	0
$786$	−1.77057	−0.0631541
$787$	11.4249	0.407253	0.203627	−	0.979049i	$-0.434727\pi$
$787$	11.4249	0.407253	0.203627	+	0.979049i	$0.434727\pi$
$788$	20.2345	0.720824
$789$	1.33471	0.0475169
$790$	0	0
$791$	−5.51483	−0.196085
$792$	0	0
$793$	−18.5903	−0.660161
$794$	−7.11097	−0.252359
$795$	0	0
$796$	12.7005	0.450158
$797$	4.28502	0.151783	0.0758915	−	0.997116i	$-0.475820\pi$
$797$	4.28502	0.151783	0.0758915	+	0.997116i	$0.475820\pi$
$798$	1.79708	0.0636159
$799$	−20.1807	−0.713942
$800$	0	0
$801$	−8.02024	−0.283381
$802$	−5.80787	−0.205083
$803$	0	0
$804$	−4.19100	−0.147805
$805$	0	0
$806$	−5.31614	−0.187253
$807$	0.544033	0.0191509
$808$	−12.8086	−0.450603
$809$	−19.8484	−0.697833	−0.348917	−	0.937154i	$-0.613450\pi$
$809$	−19.8484	−0.697833	−0.348917	+	0.937154i	$0.613450\pi$
$810$	0	0
$811$	−3.13836	−0.110203	−0.0551014	−	0.998481i	$-0.517548\pi$
$811$	−3.13836	−0.110203	−0.0551014	+	0.998481i	$0.517548\pi$
$812$	−14.3403	−0.503245
$813$	5.95452	0.208834
$814$	0	0
$815$	0	0
$816$	−4.01341	−0.140498
$817$	−30.6747	−1.07317
$818$	0.125094	0.00437379
$819$	36.2943	1.26823
$820$	0	0
$821$	23.4999	0.820151	0.410076	−	0.912052i	$-0.365502\pi$
$821$	23.4999	0.820151	0.410076	+	0.912052i	$0.365502\pi$
$822$	2.82617	0.0985741
$823$	12.6564	0.441173	0.220586	−	0.975367i	$-0.429203\pi$
$823$	12.6564	0.441173	0.220586	+	0.975367i	$0.429203\pi$
$824$	−13.5535	−0.472159
$825$	0	0
$826$	15.0547	0.523820
$827$	−30.2236	−1.05098	−0.525488	−	0.850801i	$-0.676117\pi$
$827$	−30.2236	−1.05098	−0.525488	+	0.850801i	$0.676117\pi$
$828$	−14.2262	−0.494395
$829$	2.00166	0.0695204	0.0347602	−	0.999396i	$-0.488933\pi$
$829$	2.00166	0.0695204	0.0347602	+	0.999396i	$0.488933\pi$
$830$	0	0
$831$	−1.10731	−0.0384121
$832$	−14.1919	−0.492016
$833$	0.973403	0.0337264
$834$	−3.57523	−0.123800
$835$	0	0
$836$	0	0
$837$	4.54520	0.157105
$838$	0.605717	0.0209242
$839$	35.3744	1.22126	0.610629	−	0.791917i	$-0.290917\pi$
$839$	35.3744	1.22126	0.610629	+	0.791917i	$0.290917\pi$
$840$	0	0
$841$	−19.9193	−0.686873
$842$	14.1581	0.487922
$843$	7.37304	0.253941
$844$	−6.17370	−0.212508
$845$	0	0
$846$	−6.02834	−0.207259
$847$	0	0
$848$	17.0083	0.584067
$849$	−9.40107	−0.322644
$850$	0	0
$851$	−29.5045	−1.01140
$852$	0.684610	0.0234543
$853$	18.2034	0.623272	0.311636	−	0.950202i	$-0.399123\pi$
$853$	18.2034	0.623272	0.311636	+	0.950202i	$0.399123\pi$
$854$	−5.10393	−0.174653
$855$	0	0
$856$	−32.4585	−1.10941
$857$	29.2837	1.00031	0.500156	−	0.865935i	$-0.333276\pi$
$857$	29.2837	1.00031	0.500156	+	0.865935i	$0.333276\pi$
$858$	0	0
$859$	8.44030	0.287979	0.143990	−	0.989579i	$-0.454007\pi$
$859$	8.44030	0.287979	0.143990	+	0.989579i	$0.454007\pi$
$860$	0	0
$861$	−1.91756	−0.0653504
$862$	−14.9644	−0.509691
$863$	19.3487	0.658636	0.329318	−	0.944219i	$-0.393181\pi$
$863$	19.3487	0.658636	0.329318	+	0.944219i	$0.393181\pi$
$864$	−9.29918	−0.316364
$865$	0	0
$866$	−12.4243	−0.422194
$867$	−1.42244	−0.0483087
$868$	11.3559	0.385446
$869$	0	0
$870$	0	0
$871$	−34.1679	−1.15773
$872$	−29.4630	−0.997743
$873$	53.6681	1.81639
$874$	−5.74271	−0.194250
$875$	0	0
$876$	−0.584982	−0.0197647
$877$	−17.5140	−0.591405	−0.295702	−	0.955280i	$-0.595554\pi$
$877$	−17.5140	−0.591405	−0.295702	+	0.955280i	$0.595554\pi$
$878$	−6.88165	−0.232245
$879$	6.85349	0.231163
$880$	0	0
$881$	−20.0575	−0.675754	−0.337877	−	0.941190i	$-0.609709\pi$
$881$	−20.0575	−0.675754	−0.337877	+	0.941190i	$0.609709\pi$
$882$	0.290773	0.00979083
$883$	−26.8980	−0.905189	−0.452594	−	0.891717i	$-0.649501\pi$
$883$	−26.8980	−0.905189	−0.452594	+	0.891717i	$0.649501\pi$
$884$	−38.2711	−1.28720
$885$	0	0
$886$	−0.157786	−0.00530092
$887$	−6.80568	−0.228512	−0.114256	−	0.993451i	$-0.536448\pi$
$887$	−6.80568	−0.228512	−0.114256	+	0.993451i	$0.536448\pi$
$888$	−6.19029	−0.207732
$889$	−0.204793	−0.00686854
$890$	0	0
$891$	0	0
$892$	18.6880	0.625720
$893$	18.9337	0.633591
$894$	2.26112	0.0756232
$895$	0	0
$896$	−30.1160	−1.00610
$897$	4.18064	0.139588
$898$	−4.06066	−0.135506
$899$	−7.19091	−0.239830
$900$	0	0
$901$	29.3033	0.976235
$902$	0	0
$903$	6.13090	0.204024
$904$	3.69747	0.122976
$905$	0	0
$906$	−1.15935	−0.0385168
$907$	21.3313	0.708295	0.354148	−	0.935190i	$-0.384771\pi$
$907$	21.3313	0.708295	0.354148	+	0.935190i	$0.384771\pi$
$908$	0.382831	0.0127047
$909$	20.6011	0.683295
$910$	0	0
$911$	−27.5888	−0.914059	−0.457029	−	0.889452i	$-0.651087\pi$
$911$	−27.5888	−0.914059	−0.457029	+	0.889452i	$0.651087\pi$
$912$	3.76541	0.124685
$913$	0	0
$914$	0.543347	0.0179723
$915$	0	0
$916$	0.134174	0.00443325
$917$	30.8347	1.01825
$918$	−4.20551	−0.138803
$919$	−6.00889	−0.198215	−0.0991075	−	0.995077i	$-0.531599\pi$
$919$	−6.00889	−0.198215	−0.0991075	+	0.995077i	$0.531599\pi$
$920$	0	0
$921$	−2.22118	−0.0731903
$922$	−6.92373	−0.228021
$923$	5.58140	0.183714
$924$	0	0
$925$	0	0
$926$	−2.33733	−0.0768094
$927$	21.7993	0.715982
$928$	14.7121	0.482949
$929$	9.59739	0.314880	0.157440	−	0.987529i	$-0.449676\pi$
$929$	9.59739	0.314880	0.157440	+	0.987529i	$0.449676\pi$
$930$	0	0
$931$	−0.913252	−0.0299306
$932$	26.7961	0.877736
$933$	−8.12771	−0.266089
$934$	15.4742	0.506332
$935$	0	0
$936$	−24.3339	−0.795378
$937$	38.5917	1.26074	0.630369	−	0.776296i	$-0.282904\pi$
$937$	38.5917	1.26074	0.630369	+	0.776296i	$0.282904\pi$
$938$	−9.38072	−0.306291
$939$	−3.74095	−0.122081
$940$	0	0
$941$	−29.1846	−0.951391	−0.475695	−	0.879610i	$-0.657804\pi$
$941$	−29.1846	−0.951391	−0.475695	+	0.879610i	$0.657804\pi$
$942$	2.06334	0.0672273
$943$	6.12774	0.199547
$944$	31.5440	1.02667
$945$	0	0
$946$	0	0
$947$	−46.7623	−1.51957	−0.759785	−	0.650174i	$-0.774696\pi$
$947$	−46.7623	−1.51957	−0.759785	+	0.650174i	$0.774696\pi$
$948$	2.00516	0.0651246
$949$	−4.76917	−0.154814
$950$	0	0
$951$	6.70090	0.217292
$952$	−22.3650	−0.724853
$953$	6.15238	0.199295	0.0996475	−	0.995023i	$-0.468228\pi$
$953$	6.15238	0.199295	0.0996475	+	0.995023i	$0.468228\pi$
$954$	8.75343	0.283403
$955$	0	0
$956$	41.0529	1.32774
$957$	0	0
$958$	−8.46440	−0.273472
$959$	−49.2182	−1.58934
$960$	0	0
$961$	−25.3056	−0.816309
$962$	−23.7100	−0.764442
$963$	52.2058	1.68231
$964$	37.8102	1.21778
$965$	0	0
$966$	1.14779	0.0369294
$967$	−3.39625	−0.109216	−0.0546080	−	0.998508i	$-0.517391\pi$
$967$	−3.39625	−0.109216	−0.0546080	+	0.998508i	$0.517391\pi$
$968$	0	0
$969$	6.48736	0.208404
$970$	0	0
$971$	−9.39500	−0.301500	−0.150750	−	0.988572i	$-0.548169\pi$
$971$	−9.39500	−0.301500	−0.150750	+	0.988572i	$0.548169\pi$
$972$	14.7481	0.473045
$973$	62.2631	1.99606
$974$	−8.81035	−0.282302
$975$	0	0
$976$	−10.6942	−0.342314
$977$	16.5552	0.529649	0.264824	−	0.964297i	$-0.414686\pi$
$977$	16.5552	0.529649	0.264824	+	0.964297i	$0.414686\pi$
$978$	0.119032	0.00380623
$979$	0	0
$980$	0	0
$981$	47.3878	1.51298
$982$	5.45692	0.174137
$983$	−50.8180	−1.62084	−0.810421	−	0.585848i	$-0.800762\pi$
$983$	−50.8180	−1.62084	−0.810421	+	0.585848i	$0.800762\pi$
$984$	1.28565	0.0409850
$985$	0	0
$986$	6.65350	0.211891
$987$	−3.78424	−0.120454
$988$	35.9062	1.14233
$989$	−19.5918	−0.622983
$990$	0	0
$991$	11.3642	0.360996	0.180498	−	0.983575i	$-0.442229\pi$
$991$	11.3642	0.360996	0.180498	+	0.983575i	$0.442229\pi$
$992$	−11.6504	−0.369901
$993$	10.3840	0.329526
$994$	1.53236	0.0486036
$995$	0	0
$996$	−6.36441	−0.201664
$997$	29.1644	0.923647	0.461824	−	0.886972i	$-0.347195\pi$
$997$	29.1644	0.923647	0.461824	+	0.886972i	$0.347195\pi$
$998$	−5.19332	−0.164392
$999$	20.2716	0.641365

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3025.2.a.bd.1.2		4
5.4	even	2		605.2.a.j.1.3		4
11.3	even	5		275.2.h.a.251.1		8
11.4	even	5		275.2.h.a.126.1		8
11.10	odd	2		3025.2.a.w.1.3		4
15.14	odd	2		5445.2.a.bp.1.2		4
20.19	odd	2		9680.2.a.cn.1.3		4
55.3	odd	20		275.2.z.a.174.3		16
55.4	even	10		55.2.g.b.16.2	✓	8
55.9	even	10		605.2.g.m.81.1		8
55.14	even	10		55.2.g.b.31.2	yes	8
55.19	odd	10		605.2.g.k.251.1		8
55.24	odd	10		605.2.g.e.81.2		8
55.29	odd	10		605.2.g.k.511.1		8
55.37	odd	20		275.2.z.a.49.3		16
55.39	odd	10		605.2.g.e.366.2		8
55.47	odd	20		275.2.z.a.174.2		16
55.48	odd	20		275.2.z.a.49.2		16
55.49	even	10		605.2.g.m.366.1		8
55.54	odd	2		605.2.a.k.1.2		4
165.14	odd	10		495.2.n.e.361.1		8
165.59	odd	10		495.2.n.e.181.1		8
165.164	even	2		5445.2.a.bi.1.3		4
220.59	odd	10		880.2.bo.h.401.1		8
220.179	odd	10		880.2.bo.h.801.1		8
220.219	even	2		9680.2.a.cm.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.g.b.16.2	✓	8	55.4	even	10
55.2.g.b.31.2	yes	8	55.14	even	10
275.2.h.a.126.1		8	11.4	even	5
275.2.h.a.251.1		8	11.3	even	5
275.2.z.a.49.2		16	55.48	odd	20
275.2.z.a.49.3		16	55.37	odd	20
275.2.z.a.174.2		16	55.47	odd	20
275.2.z.a.174.3		16	55.3	odd	20
495.2.n.e.181.1		8	165.59	odd	10
495.2.n.e.361.1		8	165.14	odd	10
605.2.a.j.1.3		4	5.4	even	2
605.2.a.k.1.2		4	55.54	odd	2
605.2.g.e.81.2		8	55.24	odd	10
605.2.g.e.366.2		8	55.39	odd	10
605.2.g.k.251.1		8	55.19	odd	10
605.2.g.k.511.1		8	55.29	odd	10
605.2.g.m.81.1		8	55.9	even	10
605.2.g.m.366.1		8	55.49	even	10
880.2.bo.h.401.1		8	220.59	odd	10
880.2.bo.h.801.1		8	220.179	odd	10
3025.2.a.w.1.3		4	11.10	odd	2
3025.2.a.bd.1.2		4	1.1	even	1	trivial
5445.2.a.bi.1.3		4	165.164	even	2
5445.2.a.bp.1.2		4	15.14	odd	2
9680.2.a.cm.1.3		4	220.219	even	2
9680.2.a.cn.1.3		4	20.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3025 = 5^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3025.a (trivial)

\(f(q)\)	\(=\)	\(q-0.477260 q^{2} -0.323071 q^{3} -1.77222 q^{4} +0.154189 q^{6} -2.68522 q^{7} +1.80033 q^{8} -2.89563 q^{9} +O(q^{10})\)	\(q-0.477260 q^{2} -0.323071 q^{3} -1.77222 q^{4} +0.154189 q^{6} -2.68522 q^{7} +1.80033 q^{8} -2.89563 q^{9} +0.572554 q^{12} +4.66785 q^{13} +1.28155 q^{14} +2.68522 q^{16} +4.62632 q^{17} +1.38197 q^{18} -4.34044 q^{19} +0.867517 q^{21} -2.77222 q^{23} -0.581635 q^{24} -2.22778 q^{26} +1.90471 q^{27} +4.75881 q^{28} -3.01341 q^{29} +2.38630 q^{31} -4.88221 q^{32} -2.20796 q^{34} +5.13169 q^{36} +10.6429 q^{37} +2.07152 q^{38} -1.50805 q^{39} -2.21041 q^{41} -0.414031 q^{42} +7.06719 q^{43} +1.32307 q^{46} -4.36215 q^{47} -0.867517 q^{48} +0.210405 q^{49} -1.49463 q^{51} -8.27247 q^{52} +6.33404 q^{53} -0.909040 q^{54} -4.83428 q^{56} +1.40227 q^{57} +1.43818 q^{58} +11.7473 q^{59} -3.98263 q^{61} -1.13889 q^{62} +7.77539 q^{63} -3.04036 q^{64} -7.31984 q^{67} -8.19888 q^{68} +0.895625 q^{69} +1.19571 q^{71} -5.21308 q^{72} -1.02171 q^{73} -5.07943 q^{74} +7.69223 q^{76} +0.719730 q^{78} +3.50213 q^{79} +8.07152 q^{81} +1.05494 q^{82} -11.1158 q^{83} -1.53743 q^{84} -3.37289 q^{86} +0.973547 q^{87} +2.76978 q^{89} -12.5342 q^{91} +4.91300 q^{92} -0.770945 q^{93} +2.08188 q^{94} +1.57730 q^{96} -18.5342 q^{97} -0.100418 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - q^{4} - q^{6} + 3 q^{7} + 3 q^{8}+O(q^{10}) \) 4 * q + q^2 - q^4 - q^6 + 3 * q^7 + 3 * q^8	\( 4 q + q^{2} - q^{4} - q^{6} + 3 q^{7} + 3 q^{8} - 8 q^{12} + q^{13} + 2 q^{14} - 3 q^{16} - q^{17} + 10 q^{18} - 20 q^{19} - 10 q^{21} - 5 q^{23} - 11 q^{24} - 15 q^{26} + 15 q^{27} + 13 q^{28} - 12 q^{29} - 5 q^{31} - 8 q^{32} + 2 q^{34} - 7 q^{37} - 20 q^{38} - 7 q^{39} - 11 q^{41} - 12 q^{42} + 19 q^{43} + 4 q^{46} - 5 q^{47} + 10 q^{48} + 3 q^{49} - 7 q^{51} - 11 q^{52} + 11 q^{53} + 8 q^{54} + 11 q^{56} - 5 q^{57} + 14 q^{58} + 9 q^{59} - 12 q^{61} - 35 q^{62} - 5 q^{63} - 3 q^{64} + 19 q^{67} - 3 q^{68} - 8 q^{69} + 5 q^{71} - 25 q^{72} + 11 q^{73} + 8 q^{78} - 34 q^{79} + 4 q^{81} + 6 q^{82} - 11 q^{83} - 11 q^{84} + q^{86} - 19 q^{87} - 8 q^{89} - 8 q^{91} + 12 q^{92} + 5 q^{93} + q^{94} + 34 q^{96} - 32 q^{97} - 8 q^{98}+O(q^{100}) \) 4 * q + q^2 - q^4 - q^6 + 3 * q^7 + 3 * q^8 - 8 * q^12 + q^13 + 2 * q^14 - 3 * q^16 - q^17 + 10 * q^18 - 20 * q^19 - 10 * q^21 - 5 * q^23 - 11 * q^24 - 15 * q^26 + 15 * q^27 + 13 * q^28 - 12 * q^29 - 5 * q^31 - 8 * q^32 + 2 * q^34 - 7 * q^37 - 20 * q^38 - 7 * q^39 - 11 * q^41 - 12 * q^42 + 19 * q^43 + 4 * q^46 - 5 * q^47 + 10 * q^48 + 3 * q^49 - 7 * q^51 - 11 * q^52 + 11 * q^53 + 8 * q^54 + 11 * q^56 - 5 * q^57 + 14 * q^58 + 9 * q^59 - 12 * q^61 - 35 * q^62 - 5 * q^63 - 3 * q^64 + 19 * q^67 - 3 * q^68 - 8 * q^69 + 5 * q^71 - 25 * q^72 + 11 * q^73 + 8 * q^78 - 34 * q^79 + 4 * q^81 + 6 * q^82 - 11 * q^83 - 11 * q^84 + q^86 - 19 * q^87 - 8 * q^89 - 8 * q^91 + 12 * q^92 + 5 * q^93 + q^94 + 34 * q^96 - 32 * q^97 - 8 * q^98

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