LMFDB - Embedded newform 775.2.a.j.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [775,2,Mod(1,775)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(775, 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("775.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 775 = 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	775.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:	$6.18840615665$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.205225.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 6x^{3} + 3x^{2} + 7x - 3 $ x^5 - x^4 - 6x^3 + 3x^2 + 7*x - 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.54180$ of defining polynomial
Character	$\chi$	$=$	775.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.54180 q^{2} -0.124960 q^{3} +0.377151 q^{4} +0.192664 q^{6} +4.01817 q^{7} +2.50211 q^{8} -2.98438 q^{9} +O(q^{10})$	\(q-1.54180 q^{2} -0.124960 q^{3} +0.377151 q^{4} +0.192664 q^{6} +4.01817 q^{7} +2.50211 q^{8} -2.98438 q^{9} +0.974257 q^{11} -0.0471288 q^{12} -2.01817 q^{13} -6.19522 q^{14} -4.61206 q^{16} +7.68493 q^{17} +4.60133 q^{18} +1.11162 q^{19} -0.502111 q^{21} -1.50211 q^{22} -2.43501 q^{23} -0.312664 q^{24} +3.11162 q^{26} +0.747809 q^{27} +1.51546 q^{28} -6.25474 q^{29} +1.00000 q^{31} +2.10666 q^{32} -0.121743 q^{33} -11.8486 q^{34} -1.12556 q^{36} -9.60294 q^{37} -1.71389 q^{38} +0.252191 q^{39} +8.36409 q^{41} +0.774155 q^{42} +11.1752 q^{43} +0.367442 q^{44} +3.75430 q^{46} +11.6479 q^{47} +0.576323 q^{48} +9.14568 q^{49} -0.960310 q^{51} -0.761154 q^{52} +4.09345 q^{53} -1.15297 q^{54} +10.0539 q^{56} -0.138908 q^{57} +9.64357 q^{58} +9.85762 q^{59} -4.17918 q^{61} -1.54180 q^{62} -11.9918 q^{63} +5.97607 q^{64} +0.187704 q^{66} -7.41349 q^{67} +2.89838 q^{68} +0.304279 q^{69} +6.02299 q^{71} -7.46726 q^{72} +4.20279 q^{73} +14.8058 q^{74} +0.419247 q^{76} +3.91473 q^{77} -0.388828 q^{78} -2.19313 q^{79} +8.85971 q^{81} -12.8958 q^{82} +9.70215 q^{83} -0.189371 q^{84} -17.2300 q^{86} +0.781594 q^{87} +2.43770 q^{88} +3.96300 q^{89} -8.10935 q^{91} -0.918366 q^{92} -0.124960 q^{93} -17.9588 q^{94} -0.263248 q^{96} +16.5915 q^{97} -14.1008 q^{98} -2.90756 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 4 q^{2} + q^{3} + 6 q^{4} - q^{6} + 6 q^{7} + 15 q^{8} + 2 q^{9}+O(q^{10}) $ 5 * q + 4 * q^2 + q^3 + 6 * q^4 - q^6 + 6 * q^7 + 15 * q^8 + 2 * q^9	$ 5 q + 4 q^{2} + q^{3} + 6 q^{4} - q^{6} + 6 q^{7} + 15 q^{8} + 2 q^{9} - 11 q^{12} + 4 q^{13} + 2 q^{14} + 20 q^{16} + 11 q^{17} + 19 q^{18} - 4 q^{19} - 5 q^{21} - 10 q^{22} + 12 q^{23} - 26 q^{24} + 6 q^{26} - 2 q^{27} + 18 q^{28} - 6 q^{29} + 5 q^{31} + 29 q^{32} + 21 q^{33} - 5 q^{34} + 23 q^{36} - 2 q^{37} - 6 q^{38} + 7 q^{39} - 2 q^{41} - 24 q^{42} + 7 q^{43} - 28 q^{44} + 27 q^{46} + 8 q^{47} - 39 q^{48} - q^{49} - 19 q^{51} - 6 q^{52} + 25 q^{53} - 18 q^{54} + 35 q^{56} + 20 q^{57} - q^{58} + 4 q^{59} - 17 q^{61} + 4 q^{62} + 10 q^{63} + 27 q^{64} + 27 q^{66} - 13 q^{67} + 18 q^{68} - 10 q^{69} - 6 q^{71} + 26 q^{72} + 7 q^{73} + 6 q^{74} - 5 q^{76} + 7 q^{77} + 22 q^{78} + 12 q^{79} - 11 q^{81} - 21 q^{82} - 4 q^{83} - 63 q^{84} - 41 q^{86} + q^{87} - 49 q^{88} - 3 q^{89} - 22 q^{91} + 34 q^{92} + q^{93} - 34 q^{94} - 64 q^{96} + 25 q^{97} - 22 q^{98} + 5 q^{99}+O(q^{100}) $ 5 * q + 4 * q^2 + q^3 + 6 * q^4 - q^6 + 6 * q^7 + 15 * q^8 + 2 * q^9 - 11 * q^12 + 4 * q^13 + 2 * q^14 + 20 * q^16 + 11 * q^17 + 19 * q^18 - 4 * q^19 - 5 * q^21 - 10 * q^22 + 12 * q^23 - 26 * q^24 + 6 * q^26 - 2 * q^27 + 18 * q^28 - 6 * q^29 + 5 * q^31 + 29 * q^32 + 21 * q^33 - 5 * q^34 + 23 * q^36 - 2 * q^37 - 6 * q^38 + 7 * q^39 - 2 * q^41 - 24 * q^42 + 7 * q^43 - 28 * q^44 + 27 * q^46 + 8 * q^47 - 39 * q^48 - q^49 - 19 * q^51 - 6 * q^52 + 25 * q^53 - 18 * q^54 + 35 * q^56 + 20 * q^57 - q^58 + 4 * q^59 - 17 * q^61 + 4 * q^62 + 10 * q^63 + 27 * q^64 + 27 * q^66 - 13 * q^67 + 18 * q^68 - 10 * q^69 - 6 * q^71 + 26 * q^72 + 7 * q^73 + 6 * q^74 - 5 * q^76 + 7 * q^77 + 22 * q^78 + 12 * q^79 - 11 * q^81 - 21 * q^82 - 4 * q^83 - 63 * q^84 - 41 * q^86 + q^87 - 49 * q^88 - 3 * q^89 - 22 * q^91 + 34 * q^92 + q^93 - 34 * q^94 - 64 * q^96 + 25 * q^97 - 22 * q^98 + 5 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.54180	−1.09022	−0.545109	−	0.838365i	$-0.683512\pi$
$2$	−1.54180	−1.09022	−0.545109	+	0.838365i	$0.683512\pi$
$3$	−0.124960	−0.0721457	−0.0360729	−	0.999349i	$-0.511485\pi$
$3$	−0.124960	−0.0721457	−0.0360729	+	0.999349i	$0.511485\pi$
$4$	0.377151	0.188575
$5$	0	0
$5$	0	0
$6$	0.192664	0.0786546
$7$	4.01817	1.51873	0.759363	−	0.650668i	$-0.225511\pi$
$7$	4.01817	1.51873	0.759363	+	0.650668i	$0.225511\pi$
$8$	2.50211	0.884630
$9$	−2.98438	−0.994795
$10$	0	0
$11$	0.974257	0.293750	0.146875	−	0.989155i	$-0.453079\pi$
$11$	0.974257	0.293750	0.146875	+	0.989155i	$0.453079\pi$
$12$	−0.0471288	−0.0136049
$13$	−2.01817	−0.559739	−0.279870	−	0.960038i	$-0.590291\pi$
$13$	−2.01817	−0.559739	−0.279870	+	0.960038i	$0.590291\pi$
$14$	−6.19522	−1.65574
$15$	0	0
$16$	−4.61206	−1.15301
$17$	7.68493	1.86387	0.931935	−	0.362626i	$-0.118120\pi$
$17$	7.68493	1.86387	0.931935	+	0.362626i	$0.118120\pi$
$18$	4.60133	1.08454
$19$	1.11162	0.255022	0.127511	−	0.991837i	$-0.459301\pi$
$19$	1.11162	0.255022	0.127511	+	0.991837i	$0.459301\pi$
$20$	0	0
$21$	−0.502111	−0.109570
$22$	−1.50211	−0.320251
$23$	−2.43501	−0.507735	−0.253867	−	0.967239i	$-0.581703\pi$
$23$	−2.43501	−0.507735	−0.253867	+	0.967239i	$0.581703\pi$
$24$	−0.312664	−0.0638223
$25$	0	0
$26$	3.11162	0.610238
$27$	0.747809	0.143916
$28$	1.51546	0.286394
$29$	−6.25474	−1.16148	−0.580738	−	0.814090i	$-0.697236\pi$
$29$	−6.25474	−1.16148	−0.580738	+	0.814090i	$0.697236\pi$
$30$	0	0
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	2.10666	0.372408
$33$	−0.121743	−0.0211928
$34$	−11.8486	−2.03202
$35$	0	0
$36$	−1.12556	−0.187594
$37$	−9.60294	−1.57871	−0.789356	−	0.613935i	$-0.789586\pi$
$37$	−9.60294	−1.57871	−0.789356	+	0.613935i	$0.789586\pi$
$38$	−1.71389	−0.278030
$39$	0.252191	0.0403828
$40$	0	0
$41$	8.36409	1.30625	0.653126	−	0.757250i	$-0.273457\pi$
$41$	8.36409	1.30625	0.653126	+	0.757250i	$0.273457\pi$
$42$	0.774155	0.119455
$43$	11.1752	1.70421	0.852105	−	0.523372i	$-0.175326\pi$
$43$	11.1752	1.70421	0.852105	+	0.523372i	$0.175326\pi$
$44$	0.367442	0.0553939
$45$	0	0
$46$	3.75430	0.553542
$47$	11.6479	1.69903	0.849513	−	0.527568i	$-0.176896\pi$
$47$	11.6479	1.69903	0.849513	+	0.527568i	$0.176896\pi$
$48$	0.576323	0.0831851
$49$	9.14568	1.30653
$50$	0	0
$51$	−0.960310	−0.134470
$52$	−0.761154	−0.105553
$53$	4.09345	0.562278	0.281139	−	0.959667i	$-0.409288\pi$
$53$	4.09345	0.562278	0.281139	+	0.959667i	$0.409288\pi$
$54$	−1.15297	−0.156900
$55$	0	0
$56$	10.0539	1.34351
$57$	−0.138908	−0.0183988
$58$	9.64357	1.26626
$59$	9.85762	1.28335	0.641677	−	0.766975i	$-0.278239\pi$
$59$	9.85762	1.28335	0.641677	+	0.766975i	$0.278239\pi$
$60$	0	0
$61$	−4.17918	−0.535090	−0.267545	−	0.963545i	$-0.586212\pi$
$61$	−4.17918	−0.535090	−0.267545	+	0.963545i	$0.586212\pi$
$62$	−1.54180	−0.195809
$63$	−11.9918	−1.51082
$64$	5.97607	0.747009
$65$	0	0
$66$	0.187704	0.0231048
$67$	−7.41349	−0.905702	−0.452851	−	0.891586i	$-0.649593\pi$
$67$	−7.41349	−0.905702	−0.452851	+	0.891586i	$0.649593\pi$
$68$	2.89838	0.351480
$69$	0.304279	0.0366309
$70$	0	0
$71$	6.02299	0.714798	0.357399	−	0.933952i	$-0.383664\pi$
$71$	6.02299	0.714798	0.357399	+	0.933952i	$0.383664\pi$
$72$	−7.46726	−0.880025
$73$	4.20279	0.491900	0.245950	−	0.969283i	$-0.420900\pi$
$73$	4.20279	0.491900	0.245950	+	0.969283i	$0.420900\pi$
$74$	14.8058	1.72114
$75$	0	0
$76$	0.419247	0.0480909
$77$	3.91473	0.446125
$78$	−0.388828	−0.0440261
$79$	−2.19313	−0.246747	−0.123373	−	0.992360i	$-0.539371\pi$
$79$	−2.19313	−0.246747	−0.123373	+	0.992360i	$0.539371\pi$
$80$	0	0
$81$	8.85971	0.984412
$82$	−12.8958	−1.42410
$83$	9.70215	1.06495	0.532475	−	0.846446i	$-0.321262\pi$
$83$	9.70215	1.06495	0.532475	+	0.846446i	$0.321262\pi$
$84$	−0.189371	−0.0206621
$85$	0	0
$86$	−17.2300	−1.85796
$87$	0.781594	0.0837956
$88$	2.43770	0.259860
$89$	3.96300	0.420077	0.210039	−	0.977693i	$-0.432641\pi$
$89$	3.96300	0.420077	0.210039	+	0.977693i	$0.432641\pi$
$90$	0	0
$91$	−8.10935	−0.850090
$92$	−0.918366	−0.0957463
$93$	−0.124960	−0.0129578
$94$	−17.9588	−1.85231
$95$	0	0
$96$	−0.263248	−0.0268676
$97$	16.5915	1.68462	0.842308	−	0.538997i	$-0.181196\pi$
$97$	16.5915	1.68462	0.842308	+	0.538997i	$0.181196\pi$
$98$	−14.1008	−1.42440
$99$	−2.90756	−0.292221
$100$	0	0
$101$	−3.84399	−0.382492	−0.191246	−	0.981542i	$-0.561253\pi$
$101$	−3.84399	−0.382492	−0.191246	+	0.981542i	$0.561253\pi$
$102$	1.48061	0.146602
$103$	7.09628	0.699218	0.349609	−	0.936896i	$-0.386314\pi$
$103$	7.09628	0.699218	0.349609	+	0.936896i	$0.386314\pi$
$104$	−5.04968	−0.495162
$105$	0	0
$106$	−6.31128	−0.613006
$107$	3.85157	0.372345	0.186173	−	0.982517i	$-0.440392\pi$
$107$	3.85157	0.372345	0.186173	+	0.982517i	$0.440392\pi$
$108$	0.282037	0.0271390
$109$	−6.76598	−0.648063	−0.324032	−	0.946046i	$-0.605038\pi$
$109$	−6.76598	−0.648063	−0.324032	+	0.946046i	$0.605038\pi$
$110$	0	0
$111$	1.19998	0.113897
$112$	−18.5320	−1.75111
$113$	0.167507	0.0157577	0.00787886	−	0.999969i	$-0.497492\pi$
$113$	0.167507	0.0157577	0.00787886	+	0.999969i	$0.497492\pi$
$114$	0.214168	0.0200587
$115$	0	0
$116$	−2.35898	−0.219026
$117$	6.02299	0.556826
$118$	−15.1985	−1.39913
$119$	30.8794	2.83071
$120$	0	0
$121$	−10.0508	−0.913711
$122$	6.44347	0.583364
$123$	−1.04518	−0.0942405
$124$	0.377151	0.0338691
$125$	0	0
$126$	18.4889	1.64712
$127$	−7.60692	−0.675005	−0.337502	−	0.941325i	$-0.609582\pi$
$127$	−7.60692	−0.675005	−0.337502	+	0.941325i	$0.609582\pi$
$128$	−13.4272	−1.18681
$129$	−1.39646	−0.122951
$130$	0	0
$131$	−1.50111	−0.131152	−0.0655761	−	0.997848i	$-0.520889\pi$
$131$	−1.50111	−0.131152	−0.0655761	+	0.997848i	$0.520889\pi$
$132$	−0.0459156	−0.00399644
$133$	4.46666	0.387308
$134$	11.4301	0.987412
$135$	0	0
$136$	19.2285	1.64883
$137$	2.49306	0.212997	0.106498	−	0.994313i	$-0.466036\pi$
$137$	2.49306	0.212997	0.106498	+	0.994313i	$0.466036\pi$
$138$	−0.469138	−0.0399357
$139$	11.2843	0.957122	0.478561	−	0.878054i	$-0.341158\pi$
$139$	11.2843	0.957122	0.478561	+	0.878054i	$0.341158\pi$
$140$	0	0
$141$	−1.45553	−0.122577
$142$	−9.28626	−0.779286
$143$	−1.96622	−0.164423
$144$	13.7642	1.14701
$145$	0	0
$146$	−6.47987	−0.536278
$147$	−1.14285	−0.0942603
$148$	−3.62175	−0.297706
$149$	−19.1735	−1.57075	−0.785377	−	0.619017i	$-0.787531\pi$
$149$	−19.1735	−1.57075	−0.785377	+	0.619017i	$0.787531\pi$
$150$	0	0
$151$	−7.47088	−0.607972	−0.303986	−	0.952677i	$-0.598318\pi$
$151$	−7.47088	−0.607972	−0.303986	+	0.952677i	$0.598318\pi$
$152$	2.78139	0.225600
$153$	−22.9348	−1.85417
$154$	−6.03574	−0.486373
$155$	0	0
$156$	0.0951139	0.00761521
$157$	2.58643	0.206420	0.103210	−	0.994660i	$-0.467089\pi$
$157$	2.58643	0.206420	0.103210	+	0.994660i	$0.467089\pi$
$158$	3.38137	0.269008
$159$	−0.511517	−0.0405660
$160$	0	0
$161$	−9.78428	−0.771110
$162$	−13.6599	−1.07322
$163$	−17.0673	−1.33682	−0.668408	−	0.743795i	$-0.733024\pi$
$163$	−17.0673	−1.33682	−0.668408	+	0.743795i	$0.733024\pi$
$164$	3.15452	0.246327
$165$	0	0
$166$	−14.9588	−1.16103
$167$	−23.5812	−1.82477	−0.912385	−	0.409334i	$-0.865761\pi$
$167$	−23.5812	−1.82477	−0.912385	+	0.409334i	$0.865761\pi$
$168$	−1.25634	−0.0969285
$169$	−8.92699	−0.686692
$170$	0	0
$171$	−3.31749	−0.253695
$172$	4.21475	0.321372
$173$	15.2369	1.15844	0.579218	−	0.815172i	$-0.303358\pi$
$173$	15.2369	1.15844	0.579218	+	0.815172i	$0.303358\pi$
$174$	−1.20506	−0.0913555
$175$	0	0
$176$	−4.49333	−0.338698
$177$	−1.23181	−0.0925885
$178$	−6.11016	−0.457976
$179$	13.0654	0.976556	0.488278	−	0.872688i	$-0.337625\pi$
$179$	13.0654	0.976556	0.488278	+	0.872688i	$0.337625\pi$
$180$	0	0
$181$	−3.18491	−0.236732	−0.118366	−	0.992970i	$-0.537766\pi$
$181$	−3.18491	−0.236732	−0.118366	+	0.992970i	$0.537766\pi$
$182$	12.5030	0.926784
$183$	0.522231	0.0386044
$184$	−6.09267	−0.449157
$185$	0	0
$186$	0.192664	0.0141268
$187$	7.48710	0.547511
$188$	4.39303	0.320394
$189$	3.00482	0.218569
$190$	0	0
$191$	8.90808	0.644566	0.322283	−	0.946643i	$-0.395550\pi$
$191$	8.90808	0.644566	0.322283	+	0.946643i	$0.395550\pi$
$192$	−0.746771	−0.0538935
$193$	−11.6069	−0.835484	−0.417742	−	0.908566i	$-0.637178\pi$
$193$	−11.6069	−0.835484	−0.417742	+	0.908566i	$0.637178\pi$
$194$	−25.5809	−1.83660
$195$	0	0
$196$	3.44930	0.246379
$197$	17.4802	1.24541	0.622705	−	0.782457i	$-0.286034\pi$
$197$	17.4802	1.24541	0.622705	+	0.782457i	$0.286034\pi$
$198$	4.48288	0.318584
$199$	8.10058	0.574235	0.287118	−	0.957895i	$-0.407303\pi$
$199$	8.10058	0.574235	0.287118	+	0.957895i	$0.407303\pi$
$200$	0	0
$201$	0.926390	0.0653425
$202$	5.92667	0.416999
$203$	−25.1326	−1.76396
$204$	−0.362182	−0.0253578
$205$	0	0
$206$	−10.9411	−0.762300
$207$	7.26701	0.505092
$208$	9.30791	0.645388
$209$	1.08300	0.0749126
$210$	0	0
$211$	−23.5086	−1.61840	−0.809201	−	0.587533i	$-0.800099\pi$
$211$	−23.5086	−1.61840	−0.809201	+	0.587533i	$0.800099\pi$
$212$	1.54385	0.106032
$213$	−0.752634	−0.0515696
$214$	−5.93835	−0.405937
$215$	0	0
$216$	1.87110	0.127312
$217$	4.01817	0.272771
$218$	10.4318	0.706530
$219$	−0.525181	−0.0354885
$220$	0	0
$221$	−15.5095	−1.04328
$222$	−1.85014	−0.124173
$223$	−12.5050	−0.837396	−0.418698	−	0.908126i	$-0.637513\pi$
$223$	−12.5050	−0.837396	−0.418698	+	0.908126i	$0.637513\pi$
$224$	8.46490	0.565585
$225$	0	0
$226$	−0.258262	−0.0171793
$227$	0.196602	0.0130489	0.00652445	−	0.999979i	$-0.497923\pi$
$227$	0.196602	0.0130489	0.00652445	+	0.999979i	$0.497923\pi$
$228$	−0.0523891	−0.00346955
$229$	11.3917	0.752782	0.376391	−	0.926461i	$-0.377165\pi$
$229$	11.3917	0.752782	0.376391	+	0.926461i	$0.377165\pi$
$230$	0	0
$231$	−0.489185	−0.0321860
$232$	−15.6501	−1.02748
$233$	16.8575	1.10437	0.552185	−	0.833722i	$-0.313794\pi$
$233$	16.8575	1.10437	0.552185	+	0.833722i	$0.313794\pi$
$234$	−9.28626	−0.607062
$235$	0	0
$236$	3.71781	0.242009
$237$	0.274054	0.0178017
$238$	−47.6098	−3.08609
$239$	−10.0140	−0.647752	−0.323876	−	0.946100i	$-0.604986\pi$
$239$	−10.0140	−0.647752	−0.323876	+	0.946100i	$0.604986\pi$
$240$	0	0
$241$	22.4527	1.44630	0.723152	−	0.690689i	$-0.242693\pi$
$241$	22.4527	1.44630	0.723152	+	0.690689i	$0.242693\pi$
$242$	15.4964	0.996144
$243$	−3.35054	−0.214937
$244$	−1.57618	−0.100905
$245$	0	0
$246$	1.61146	0.102743
$247$	−2.24343	−0.142746
$248$	2.50211	0.158884
$249$	−1.21238	−0.0768316
$250$	0	0
$251$	−17.5228	−1.10603	−0.553014	−	0.833172i	$-0.686522\pi$
$251$	−17.5228	−1.10603	−0.553014	+	0.833172i	$0.686522\pi$
$252$	−4.52270	−0.284903
$253$	−2.37233	−0.149147
$254$	11.7284	0.735902
$255$	0	0
$256$	8.74997	0.546873
$257$	−6.03459	−0.376428	−0.188214	−	0.982128i	$-0.560270\pi$
$257$	−6.03459	−0.376428	−0.188214	+	0.982128i	$0.560270\pi$
$258$	2.15306	0.134044
$259$	−38.5862	−2.39763
$260$	0	0
$261$	18.6666	1.15543
$262$	2.31441	0.142985
$263$	1.00685	0.0620852	0.0310426	−	0.999518i	$-0.490117\pi$
$263$	1.00685	0.0620852	0.0310426	+	0.999518i	$0.490117\pi$
$264$	−0.304615	−0.0187478
$265$	0	0
$266$	−6.88670	−0.422251
$267$	−0.495217	−0.0303068
$268$	−2.79600	−0.170793
$269$	−24.4383	−1.49003	−0.745014	−	0.667049i	$-0.767557\pi$
$269$	−24.4383	−1.49003	−0.745014	+	0.667049i	$0.767557\pi$
$270$	0	0
$271$	−12.7290	−0.773233	−0.386617	−	0.922241i	$-0.626356\pi$
$271$	−12.7290	−0.773233	−0.386617	+	0.922241i	$0.626356\pi$
$272$	−35.4434	−2.14907
$273$	1.01334	0.0613304
$274$	−3.84381	−0.232213
$275$	0	0
$276$	0.114759	0.00690769
$277$	9.10164	0.546864	0.273432	−	0.961891i	$-0.411841\pi$
$277$	9.10164	0.546864	0.273432	+	0.961891i	$0.411841\pi$
$278$	−17.3982	−1.04347
$279$	−2.98438	−0.178670
$280$	0	0
$281$	−6.01273	−0.358689	−0.179345	−	0.983786i	$-0.557398\pi$
$281$	−6.01273	−0.358689	−0.179345	+	0.983786i	$0.557398\pi$
$282$	2.24413	0.133636
$283$	18.3763	1.09236	0.546179	−	0.837669i	$-0.316082\pi$
$283$	18.3763	1.09236	0.546179	+	0.837669i	$0.316082\pi$
$284$	2.27158	0.134793
$285$	0	0
$286$	3.03151	0.179257
$287$	33.6083	1.98384
$288$	−6.28707	−0.370469
$289$	42.0582	2.47401
$290$	0	0
$291$	−2.07328	−0.121538
$292$	1.58509	0.0927601
$293$	2.49415	0.145710	0.0728548	−	0.997343i	$-0.476789\pi$
$293$	2.49415	0.145710	0.0728548	+	0.997343i	$0.476789\pi$
$294$	1.76204	0.102764
$295$	0	0
$296$	−24.0276	−1.39658
$297$	0.728559	0.0422753
$298$	29.5617	1.71246
$299$	4.91426	0.284199
$300$	0	0
$301$	44.9040	2.58823
$302$	11.5186	0.662822
$303$	0.480346	0.0275951
$304$	−5.12684	−0.294044
$305$	0	0
$306$	35.3609	2.02145
$307$	−26.2749	−1.49959	−0.749795	−	0.661670i	$-0.769848\pi$
$307$	−26.2749	−1.49959	−0.749795	+	0.661670i	$0.769848\pi$
$308$	1.47644	0.0841282
$309$	−0.886752	−0.0504456
$310$	0	0
$311$	16.3590	0.927634	0.463817	−	0.885931i	$-0.346479\pi$
$311$	16.3590	0.927634	0.463817	+	0.885931i	$0.346479\pi$
$312$	0.631009	0.0357238
$313$	16.9532	0.958249	0.479124	−	0.877747i	$-0.340954\pi$
$313$	16.9532	0.958249	0.479124	+	0.877747i	$0.340954\pi$
$314$	−3.98777	−0.225043
$315$	0	0
$316$	−0.827141	−0.0465303
$317$	−8.88323	−0.498932	−0.249466	−	0.968384i	$-0.580255\pi$
$317$	−8.88323	−0.498932	−0.249466	+	0.968384i	$0.580255\pi$
$318$	0.788658	0.0442258
$319$	−6.09373	−0.341183
$320$	0	0
$321$	−0.481292	−0.0268631
$322$	15.0854	0.840677
$323$	8.54269	0.475328
$324$	3.34145	0.185636
$325$	0	0
$326$	26.3144	1.45742
$327$	0.845477	0.0467550
$328$	20.9279	1.15555
$329$	46.8034	2.58035
$330$	0	0
$331$	−26.2669	−1.44376	−0.721880	−	0.692018i	$-0.756722\pi$
$331$	−26.2669	−1.44376	−0.721880	+	0.692018i	$0.756722\pi$
$332$	3.65917	0.200823
$333$	28.6589	1.57050
$334$	36.3576	1.98940
$335$	0	0
$336$	2.31576	0.126335
$337$	−21.0537	−1.14687	−0.573435	−	0.819251i	$-0.694389\pi$
$337$	−21.0537	−1.14687	−0.573435	+	0.819251i	$0.694389\pi$
$338$	13.7636	0.748644
$339$	−0.0209317	−0.00113685
$340$	0	0
$341$	0.974257	0.0527590
$342$	5.11491	0.276583
$343$	8.62172	0.465529
$344$	27.9617	1.50759
$345$	0	0
$346$	−23.4922	−1.26295
$347$	17.1853	0.922553	0.461276	−	0.887256i	$-0.347392\pi$
$347$	17.1853	0.922553	0.461276	+	0.887256i	$0.347392\pi$
$348$	0.294779	0.0158018
$349$	−0.312213	−0.0167124	−0.00835619	−	0.999965i	$-0.502660\pi$
$349$	−0.312213	−0.0167124	−0.00835619	+	0.999965i	$0.502660\pi$
$350$	0	0
$351$	−1.50921	−0.0805554
$352$	2.05242	0.109395
$353$	29.6247	1.57676	0.788381	−	0.615187i	$-0.210919\pi$
$353$	29.6247	1.57676	0.788381	+	0.615187i	$0.210919\pi$
$354$	1.89921	0.100942
$355$	0	0
$356$	1.49465	0.0792162
$357$	−3.85869	−0.204223
$358$	−20.1443	−1.06466
$359$	0.528002	0.0278669	0.0139334	−	0.999903i	$-0.495565\pi$
$359$	0.528002	0.0278669	0.0139334	+	0.999903i	$0.495565\pi$
$360$	0	0
$361$	−17.7643	−0.934964
$362$	4.91049	0.258090
$363$	1.25595	0.0659204
$364$	−3.05845	−0.160306
$365$	0	0
$366$	−0.805177	−0.0420873
$367$	−23.7635	−1.24044	−0.620221	−	0.784427i	$-0.712957\pi$
$367$	−23.7635	−1.24044	−0.620221	+	0.784427i	$0.712957\pi$
$368$	11.2304	0.585426
$369$	−24.9617	−1.29945
$370$	0	0
$371$	16.4482	0.853946
$372$	−0.0471288	−0.00244351
$373$	36.2286	1.87585	0.937923	−	0.346842i	$-0.112746\pi$
$373$	36.2286	1.87585	0.937923	+	0.346842i	$0.112746\pi$
$374$	−11.5436	−0.596906
$375$	0	0
$376$	29.1444	1.50301
$377$	12.6231	0.650124
$378$	−4.63284	−0.238288
$379$	−17.4756	−0.897663	−0.448831	−	0.893616i	$-0.648160\pi$
$379$	−17.4756	−0.897663	−0.448831	+	0.893616i	$0.648160\pi$
$380$	0	0
$381$	0.950561	0.0486987
$382$	−13.7345	−0.702718
$383$	−29.4077	−1.50266	−0.751332	−	0.659924i	$-0.770588\pi$
$383$	−29.4077	−1.50266	−0.751332	+	0.659924i	$0.770588\pi$
$384$	1.67787	0.0856233
$385$	0	0
$386$	17.8956	0.910860
$387$	−33.3512	−1.69534
$388$	6.25751	0.317677
$389$	5.64351	0.286138	0.143069	−	0.989713i	$-0.454303\pi$
$389$	5.64351	0.286138	0.143069	+	0.989713i	$0.454303\pi$
$390$	0	0
$391$	−18.7129	−0.946351
$392$	22.8835	1.15579
$393$	0.187578	0.00946208
$394$	−26.9509	−1.35777
$395$	0	0
$396$	−1.09659	−0.0551056
$397$	−11.3962	−0.571957	−0.285979	−	0.958236i	$-0.592319\pi$
$397$	−11.3962	−0.571957	−0.285979	+	0.958236i	$0.592319\pi$
$398$	−12.4895	−0.626041
$399$	−0.558154	−0.0279427
$400$	0	0
$401$	−32.2236	−1.60917	−0.804585	−	0.593838i	$-0.797612\pi$
$401$	−32.2236	−1.60917	−0.804585	+	0.593838i	$0.797612\pi$
$402$	−1.42831	−0.0712376
$403$	−2.01817	−0.100532
$404$	−1.44977	−0.0721285
$405$	0	0
$406$	38.7495	1.92311
$407$	−9.35573	−0.463746
$408$	−2.40280	−0.118956
$409$	−25.9199	−1.28166	−0.640828	−	0.767684i	$-0.721409\pi$
$409$	−25.9199	−1.28166	−0.640828	+	0.767684i	$0.721409\pi$
$410$	0	0
$411$	−0.311534	−0.0153668
$412$	2.67637	0.131855
$413$	39.6096	1.94906
$414$	−11.2043	−0.550660
$415$	0	0
$416$	−4.25159	−0.208451
$417$	−1.41009	−0.0690523
$418$	−1.66977	−0.0816711
$419$	−34.4106	−1.68107	−0.840534	−	0.541759i	$-0.817759\pi$
$419$	−34.4106	−1.68107	−0.840534	+	0.541759i	$0.817759\pi$
$420$	0	0
$421$	39.0522	1.90329	0.951645	−	0.307200i	$-0.0993920\pi$
$421$	39.0522	1.90329	0.951645	+	0.307200i	$0.0993920\pi$
$422$	36.2456	1.76441
$423$	−34.7619	−1.69018
$424$	10.2423	0.497408
$425$	0	0
$426$	1.16041	0.0562221
$427$	−16.7927	−0.812654
$428$	1.45262	0.0702151
$429$	0.245699	0.0118624
$430$	0	0
$431$	23.3062	1.12262	0.561311	−	0.827605i	$-0.310297\pi$
$431$	23.3062	1.12262	0.561311	+	0.827605i	$0.310297\pi$
$432$	−3.44894	−0.165937
$433$	36.6195	1.75982	0.879910	−	0.475141i	$-0.157603\pi$
$433$	36.6195	1.75982	0.879910	+	0.475141i	$0.157603\pi$
$434$	−6.19522	−0.297380
$435$	0	0
$436$	−2.55179	−0.122209
$437$	−2.70680	−0.129484
$438$	0.809725	0.0386902
$439$	11.5431	0.550921	0.275460	−	0.961312i	$-0.411170\pi$
$439$	11.5431	0.550921	0.275460	+	0.961312i	$0.411170\pi$
$440$	0	0
$441$	−27.2942	−1.29973
$442$	23.9125	1.13740
$443$	9.73233	0.462397	0.231198	−	0.972907i	$-0.425735\pi$
$443$	9.73233	0.462397	0.231198	+	0.972907i	$0.425735\pi$
$444$	0.452575	0.0214782
$445$	0	0
$446$	19.2802	0.912944
$447$	2.39592	0.113323
$448$	24.0129	1.13450
$449$	−13.8787	−0.654979	−0.327489	−	0.944855i	$-0.606203\pi$
$449$	−13.8787	−0.654979	−0.327489	+	0.944855i	$0.606203\pi$
$450$	0	0
$451$	8.14877	0.383711
$452$	0.0631753	0.00297152
$453$	0.933562	0.0438626
$454$	−0.303121	−0.0142262
$455$	0	0
$456$	−0.347562	−0.0162761
$457$	−14.7404	−0.689526	−0.344763	−	0.938690i	$-0.612041\pi$
$457$	−14.7404	−0.689526	−0.344763	+	0.938690i	$0.612041\pi$
$458$	−17.5637	−0.820697
$459$	5.74686	0.268241
$460$	0	0
$461$	−13.5967	−0.633262	−0.316631	−	0.948549i	$-0.602552\pi$
$461$	−13.5967	−0.633262	−0.316631	+	0.948549i	$0.602552\pi$
$462$	0.754226	0.0350898
$463$	−31.1824	−1.44917	−0.724584	−	0.689186i	$-0.757968\pi$
$463$	−31.1824	−1.44917	−0.724584	+	0.689186i	$0.757968\pi$
$464$	28.8473	1.33920
$465$	0	0
$466$	−25.9909	−1.20400
$467$	23.6269	1.09332	0.546662	−	0.837354i	$-0.315898\pi$
$467$	23.6269	1.09332	0.546662	+	0.837354i	$0.315898\pi$
$468$	2.27158	0.105004
$469$	−29.7887	−1.37551
$470$	0	0
$471$	−0.323201	−0.0148923
$472$	24.6649	1.13529
$473$	10.8876	0.500611
$474$	−0.422537	−0.0194078
$475$	0	0
$476$	11.6462	0.533801
$477$	−12.2164	−0.559351
$478$	15.4396	0.706191
$479$	10.7106	0.489380	0.244690	−	0.969601i	$-0.421314\pi$
$479$	10.7106	0.489380	0.244690	+	0.969601i	$0.421314\pi$
$480$	0	0
$481$	19.3803	0.883668
$482$	−34.6175	−1.57679
$483$	1.22265	0.0556323
$484$	−3.79068	−0.172303
$485$	0	0
$486$	5.16586	0.234328
$487$	6.17246	0.279701	0.139850	−	0.990173i	$-0.455338\pi$
$487$	6.17246	0.279701	0.139850	+	0.990173i	$0.455338\pi$
$488$	−10.4568	−0.473356
$489$	2.13273	0.0964456
$490$	0	0
$491$	−22.5638	−1.01829	−0.509145	−	0.860681i	$-0.670038\pi$
$491$	−22.5638	−1.01829	−0.509145	+	0.860681i	$0.670038\pi$
$492$	−0.394189	−0.0177714
$493$	−48.0673	−2.16484
$494$	3.45892	0.155624
$495$	0	0
$496$	−4.61206	−0.207088
$497$	24.2014	1.08558
$498$	1.86925	0.0837632
$499$	19.4201	0.869361	0.434681	−	0.900585i	$-0.356861\pi$
$499$	19.4201	0.869361	0.434681	+	0.900585i	$0.356861\pi$
$500$	0	0
$501$	2.94671	0.131649
$502$	27.0166	1.20581
$503$	−12.7360	−0.567869	−0.283934	−	0.958844i	$-0.591640\pi$
$503$	−12.7360	−0.567869	−0.283934	+	0.958844i	$0.591640\pi$
$504$	−30.0047	−1.33652
$505$	0	0
$506$	3.65766	0.162603
$507$	1.11552	0.0495419
$508$	−2.86895	−0.127289
$509$	32.2162	1.42796	0.713979	−	0.700167i	$-0.246891\pi$
$509$	32.2162	1.42796	0.713979	+	0.700167i	$0.246891\pi$
$510$	0	0
$511$	16.8875	0.747060
$512$	13.3637	0.590600
$513$	0.831276	0.0367018
$514$	9.30414	0.410388
$515$	0	0
$516$	−0.526676	−0.0231856
$517$	11.3481	0.499088
$518$	59.4923	2.61394
$519$	−1.90400	−0.0835763
$520$	0	0
$521$	13.5007	0.591476	0.295738	−	0.955269i	$-0.404435\pi$
$521$	13.5007	0.591476	0.295738	+	0.955269i	$0.404435\pi$
$522$	−28.7801	−1.25967
$523$	−4.87610	−0.213217	−0.106609	−	0.994301i	$-0.533999\pi$
$523$	−4.87610	−0.213217	−0.106609	+	0.994301i	$0.533999\pi$
$524$	−0.566143	−0.0247321
$525$	0	0
$526$	−1.55237	−0.0676864
$527$	7.68493	0.334761
$528$	0.561487	0.0244356
$529$	−17.0707	−0.742205
$530$	0	0
$531$	−29.4189	−1.27667
$532$	1.68460	0.0730368
$533$	−16.8801	−0.731160
$534$	0.763526	0.0330410
$535$	0	0
$536$	−18.5494	−0.801211
$537$	−1.63266	−0.0704544
$538$	37.6789	1.62445
$539$	8.91025	0.383792
$540$	0	0
$541$	−2.41921	−0.104010	−0.0520050	−	0.998647i	$-0.516561\pi$
$541$	−2.41921	−0.104010	−0.0520050	+	0.998647i	$0.516561\pi$
$542$	19.6256	0.842993
$543$	0.397986	0.0170792
$544$	16.1895	0.694119
$545$	0	0
$546$	−1.56238	−0.0668635
$547$	−4.06006	−0.173596	−0.0867978	−	0.996226i	$-0.527663\pi$
$547$	−4.06006	−0.173596	−0.0867978	+	0.996226i	$0.527663\pi$
$548$	0.940261	0.0401660
$549$	12.4723	0.532305
$550$	0	0
$551$	−6.95287	−0.296202
$552$	0.761340	0.0324048
$553$	−8.81237	−0.374740
$554$	−14.0329	−0.596201
$555$	0	0
$556$	4.25588	0.180490
$557$	−27.4132	−1.16153	−0.580767	−	0.814070i	$-0.697247\pi$
$557$	−27.4132	−1.16153	−0.580767	+	0.814070i	$0.697247\pi$
$558$	4.60133	0.194790
$559$	−22.5535	−0.953913
$560$	0	0
$561$	−0.935589	−0.0395006
$562$	9.27044	0.391050
$563$	−28.6883	−1.20907	−0.604533	−	0.796580i	$-0.706640\pi$
$563$	−28.6883	−1.20907	−0.604533	+	0.796580i	$0.706640\pi$
$564$	−0.548953	−0.0231151
$565$	0	0
$566$	−28.3326	−1.19091
$567$	35.5998	1.49505
$568$	15.0702	0.632331
$569$	−21.1119	−0.885059	−0.442529	−	0.896754i	$-0.645919\pi$
$569$	−21.1119	−0.885059	−0.442529	+	0.896754i	$0.645919\pi$
$570$	0	0
$571$	6.30304	0.263774	0.131887	−	0.991265i	$-0.457896\pi$
$571$	6.30304	0.263774	0.131887	+	0.991265i	$0.457896\pi$
$572$	−0.741560	−0.0310062
$573$	−1.11316	−0.0465027
$574$	−51.8174	−2.16281
$575$	0	0
$576$	−17.8349	−0.743121
$577$	−26.8157	−1.11635	−0.558175	−	0.829723i	$-0.688498\pi$
$577$	−26.8157	−1.11635	−0.558175	+	0.829723i	$0.688498\pi$
$578$	−64.8453	−2.69721
$579$	1.45040	0.0602766
$580$	0	0
$581$	38.9849	1.61737
$582$	3.19659	0.132503
$583$	3.98807	0.165169
$584$	10.5158	0.435149
$585$	0	0
$586$	−3.84548	−0.158855
$587$	−13.7041	−0.565628	−0.282814	−	0.959175i	$-0.591268\pi$
$587$	−13.7041	−0.565628	−0.282814	+	0.959175i	$0.591268\pi$
$588$	−0.431025	−0.0177752
$589$	1.11162	0.0458033
$590$	0	0
$591$	−2.18432	−0.0898510
$592$	44.2893	1.82028
$593$	−24.5447	−1.00793	−0.503966	−	0.863724i	$-0.668126\pi$
$593$	−24.5447	−1.00793	−0.503966	+	0.863724i	$0.668126\pi$
$594$	−1.12329	−0.0460893
$595$	0	0
$596$	−7.23130	−0.296206
$597$	−1.01225	−0.0414286
$598$	−7.57682	−0.309839
$599$	−9.77735	−0.399492	−0.199746	−	0.979848i	$-0.564012\pi$
$599$	−9.77735	−0.399492	−0.199746	+	0.979848i	$0.564012\pi$
$600$	0	0
$601$	16.0052	0.652865	0.326433	−	0.945220i	$-0.394153\pi$
$601$	16.0052	0.652865	0.326433	+	0.945220i	$0.394153\pi$
$602$	−69.2331	−2.82173
$603$	22.1247	0.900988
$604$	−2.81765	−0.114648
$605$	0	0
$606$	−0.740598	−0.0300847
$607$	−5.91480	−0.240074	−0.120037	−	0.992769i	$-0.538301\pi$
$607$	−5.91480	−0.240074	−0.120037	+	0.992769i	$0.538301\pi$
$608$	2.34179	0.0949722
$609$	3.14058	0.127263
$610$	0	0
$611$	−23.5075	−0.951011
$612$	−8.64987	−0.349650
$613$	−34.0802	−1.37649	−0.688243	−	0.725481i	$-0.741618\pi$
$613$	−34.0802	−1.37649	−0.688243	+	0.725481i	$0.741618\pi$
$614$	40.5107	1.63488
$615$	0	0
$616$	9.79509	0.394655
$617$	40.0176	1.61105	0.805525	−	0.592562i	$-0.201883\pi$
$617$	40.0176	1.61105	0.805525	+	0.592562i	$0.201883\pi$
$618$	1.36720	0.0549967
$619$	45.5214	1.82966	0.914830	−	0.403840i	$-0.132325\pi$
$619$	45.5214	1.82966	0.914830	+	0.403840i	$0.132325\pi$
$620$	0	0
$621$	−1.82092	−0.0730711
$622$	−25.2223	−1.01132
$623$	15.9240	0.637982
$624$	−1.16312	−0.0465620
$625$	0	0
$626$	−26.1384	−1.04470
$627$	−0.135332	−0.00540463
$628$	0.975476	0.0389257
$629$	−73.7979	−2.94251
$630$	0	0
$631$	35.9670	1.43182	0.715912	−	0.698190i	$-0.246011\pi$
$631$	35.9670	1.43182	0.715912	+	0.698190i	$0.246011\pi$
$632$	−5.48746	−0.218279
$633$	2.93764	0.116761
$634$	13.6962	0.543945
$635$	0	0
$636$	−0.192919	−0.00764974
$637$	−18.4575	−0.731314
$638$	9.39532	0.371964
$639$	−17.9749	−0.711077
$640$	0	0
$641$	−19.5917	−0.773826	−0.386913	−	0.922116i	$-0.626459\pi$
$641$	−19.5917	−0.773826	−0.386913	+	0.922116i	$0.626459\pi$
$642$	0.742057	0.0292867
$643$	−24.4945	−0.965968	−0.482984	−	0.875629i	$-0.660447\pi$
$643$	−24.4945	−0.965968	−0.482984	+	0.875629i	$0.660447\pi$
$644$	−3.69015	−0.145412
$645$	0	0
$646$	−13.1711	−0.518211
$647$	−12.3849	−0.486900	−0.243450	−	0.969913i	$-0.578279\pi$
$647$	−12.3849	−0.486900	−0.243450	+	0.969913i	$0.578279\pi$
$648$	22.1680	0.870840
$649$	9.60386	0.376984
$650$	0	0
$651$	−0.502111	−0.0196793
$652$	−6.43695	−0.252091
$653$	22.3766	0.875666	0.437833	−	0.899056i	$-0.355746\pi$
$653$	22.3766	0.875666	0.437833	+	0.899056i	$0.355746\pi$
$654$	−1.30356	−0.0509732
$655$	0	0
$656$	−38.5757	−1.50613
$657$	−12.5427	−0.489339
$658$	−72.1615	−2.81315
$659$	−40.5978	−1.58147	−0.790733	−	0.612162i	$-0.790300\pi$
$659$	−40.5978	−1.58147	−0.790733	+	0.612162i	$0.790300\pi$
$660$	0	0
$661$	16.6473	0.647503	0.323752	−	0.946142i	$-0.395056\pi$
$661$	16.6473	0.647503	0.323752	+	0.946142i	$0.395056\pi$
$662$	40.4984	1.57401
$663$	1.93807	0.0752683
$664$	24.2759	0.942086
$665$	0	0
$666$	−44.1863	−1.71218
$667$	15.2304	0.589722
$668$	−8.89367	−0.344107
$669$	1.56262	0.0604145
$670$	0	0
$671$	−4.07160	−0.157182
$672$	−1.05777	−0.0408045
$673$	−1.10443	−0.0425728	−0.0212864	−	0.999773i	$-0.506776\pi$
$673$	−1.10443	−0.0425728	−0.0212864	+	0.999773i	$0.506776\pi$
$674$	32.4607	1.25034
$675$	0	0
$676$	−3.36682	−0.129493
$677$	7.44687	0.286207	0.143103	−	0.989708i	$-0.454292\pi$
$677$	7.44687	0.286207	0.143103	+	0.989708i	$0.454292\pi$
$678$	0.0322725	0.00123942
$679$	66.6676	2.55847
$680$	0	0
$681$	−0.0245674	−0.000941423 0
$682$	−1.50211	−0.0575188
$683$	−33.8310	−1.29451	−0.647254	−	0.762274i	$-0.724083\pi$
$683$	−33.8310	−1.29451	−0.647254	+	0.762274i	$0.724083\pi$
$684$	−1.25119	−0.0478406
$685$	0	0
$686$	−13.2930	−0.507528
$687$	−1.42350	−0.0543101
$688$	−51.5409	−1.96498
$689$	−8.26127	−0.314729
$690$	0	0
$691$	−25.3775	−0.965406	−0.482703	−	0.875784i	$-0.660345\pi$
$691$	−25.3775	−0.965406	−0.482703	+	0.875784i	$0.660345\pi$
$692$	5.74659	0.218453
$693$	−11.6831	−0.443803
$694$	−26.4962	−1.00578
$695$	0	0
$696$	1.95563	0.0741281
$697$	64.2774	2.43468
$698$	0.481371	0.0182201
$699$	−2.10651	−0.0796756
$700$	0	0
$701$	32.5936	1.23104	0.615521	−	0.788121i	$-0.288946\pi$
$701$	32.5936	1.23104	0.615521	+	0.788121i	$0.288946\pi$
$702$	2.32690	0.0878230
$703$	−10.6748	−0.402607
$704$	5.82223	0.219434
$705$	0	0
$706$	−45.6754	−1.71902
$707$	−15.4458	−0.580900
$708$	−0.464578	−0.0174599
$709$	−40.2936	−1.51326	−0.756630	−	0.653844i	$-0.773155\pi$
$709$	−40.2936	−1.51326	−0.756630	+	0.653844i	$0.773155\pi$
$710$	0	0
$711$	6.54515	0.245462
$712$	9.91586	0.371613
$713$	−2.43501	−0.0911918
$714$	5.94933	0.222648
$715$	0	0
$716$	4.92764	0.184154
$717$	1.25135	0.0467326
$718$	−0.814074	−0.0303810
$719$	−14.7979	−0.551870	−0.275935	−	0.961176i	$-0.588987\pi$
$719$	−14.7979	−0.551870	−0.275935	+	0.961176i	$0.588987\pi$
$720$	0	0
$721$	28.5141	1.06192
$722$	27.3890	1.01931
$723$	−2.80569	−0.104345
$724$	−1.20119	−0.0446419
$725$	0	0
$726$	−1.93643	−0.0718676
$727$	−6.03520	−0.223833	−0.111917	−	0.993718i	$-0.535699\pi$
$727$	−6.03520	−0.223833	−0.111917	+	0.993718i	$0.535699\pi$
$728$	−20.2905	−0.752015
$729$	−26.1604	−0.968905
$730$	0	0
$731$	85.8810	3.17642
$732$	0.196960	0.00727985
$733$	−33.4392	−1.23511	−0.617553	−	0.786529i	$-0.711876\pi$
$733$	−33.4392	−1.23511	−0.617553	+	0.786529i	$0.711876\pi$
$734$	36.6385	1.35235
$735$	0	0
$736$	−5.12973	−0.189084
$737$	−7.22265	−0.266050
$738$	38.4859	1.41669
$739$	31.7340	1.16735	0.583676	−	0.811986i	$-0.301614\pi$
$739$	31.7340	1.16735	0.583676	+	0.811986i	$0.301614\pi$
$740$	0	0
$741$	0.280339	0.0102985
$742$	−25.3598	−0.930987
$743$	42.3804	1.55479	0.777393	−	0.629015i	$-0.216542\pi$
$743$	42.3804	1.55479	0.777393	+	0.629015i	$0.216542\pi$
$744$	−0.312664	−0.0114628
$745$	0	0
$746$	−55.8573	−2.04508
$747$	−28.9550	−1.05941
$748$	2.82376	0.103247
$749$	15.4762	0.565490
$750$	0	0
$751$	−29.5302	−1.07757	−0.538787	−	0.842442i	$-0.681117\pi$
$751$	−29.5302	−1.07757	−0.538787	+	0.842442i	$0.681117\pi$
$752$	−53.7209	−1.95900
$753$	2.18965	0.0797952
$754$	−19.4624	−0.708777
$755$	0	0
$756$	1.13327	0.0412167
$757$	−47.8492	−1.73911	−0.869554	−	0.493837i	$-0.835594\pi$
$757$	−47.8492	−1.73911	−0.869554	+	0.493837i	$0.835594\pi$
$758$	26.9439	0.978648
$759$	0.296446	0.0107603
$760$	0	0
$761$	0.803690	0.0291337	0.0145669	−	0.999894i	$-0.495363\pi$
$761$	0.803690	0.0291337	0.0145669	+	0.999894i	$0.495363\pi$
$762$	−1.46558	−0.0530922
$763$	−27.1868	−0.984230
$764$	3.35969	0.121549
$765$	0	0
$766$	45.3409	1.63823
$767$	−19.8943	−0.718343
$768$	−1.09340	−0.0394546
$769$	44.3934	1.60087	0.800433	−	0.599423i	$-0.204603\pi$
$769$	44.3934	1.60087	0.800433	+	0.599423i	$0.204603\pi$
$770$	0	0
$771$	0.754084	0.0271577
$772$	−4.37756	−0.157552
$773$	−25.0855	−0.902263	−0.451131	−	0.892458i	$-0.648979\pi$
$773$	−25.0855	−0.902263	−0.451131	+	0.892458i	$0.648979\pi$
$774$	51.4210	1.84829
$775$	0	0
$776$	41.5139	1.49026
$777$	4.82174	0.172979
$778$	−8.70118	−0.311952
$779$	9.29765	0.333123
$780$	0	0
$781$	5.86794	0.209972
$782$	28.8515	1.03173
$783$	−4.67736	−0.167155
$784$	−42.1804	−1.50644
$785$	0	0
$786$	−0.289209	−0.0103157
$787$	3.15157	0.112341	0.0561707	−	0.998421i	$-0.482111\pi$
$787$	3.15157	0.112341	0.0561707	+	0.998421i	$0.482111\pi$
$788$	6.59265	0.234854
$789$	−0.125816	−0.00447918
$790$	0	0
$791$	0.673071	0.0239316
$792$	−7.27503	−0.258507
$793$	8.43430	0.299511
$794$	17.5706	0.623558
$795$	0	0
$796$	3.05514	0.108287
$797$	−3.91118	−0.138541	−0.0692706	−	0.997598i	$-0.522067\pi$
$797$	−3.91118	−0.138541	−0.0692706	+	0.997598i	$0.522067\pi$
$798$	0.860563	0.0304636
$799$	89.5135	3.16676
$800$	0	0
$801$	−11.8271	−0.417891
$802$	49.6824	1.75435
$803$	4.09460	0.144495
$804$	0.349389	0.0123220
$805$	0	0
$806$	3.11162	0.109602
$807$	3.05381	0.107499
$808$	−9.61810	−0.338364
$809$	−37.3305	−1.31247	−0.656235	−	0.754556i	$-0.727852\pi$
$809$	−37.3305	−1.31247	−0.656235	+	0.754556i	$0.727852\pi$
$810$	0	0
$811$	−21.4907	−0.754641	−0.377321	−	0.926083i	$-0.623155\pi$
$811$	−21.4907	−0.754641	−0.377321	+	0.926083i	$0.623155\pi$
$812$	−9.47879	−0.332640
$813$	1.59062	0.0557855
$814$	14.4247	0.505585
$815$	0	0
$816$	4.42900	0.155046
$817$	12.4226	0.434611
$818$	39.9633	1.39728
$819$	24.2014	0.845666
$820$	0	0
$821$	−40.6754	−1.41958	−0.709790	−	0.704413i	$-0.751210\pi$
$821$	−40.6754	−1.41958	−0.709790	+	0.704413i	$0.751210\pi$
$822$	0.480323	0.0167532
$823$	−4.42152	−0.154124	−0.0770622	−	0.997026i	$-0.524554\pi$
$823$	−4.42152	−0.154124	−0.0770622	+	0.997026i	$0.524554\pi$
$824$	17.7557	0.618549
$825$	0	0
$826$	−61.0701	−2.12490
$827$	−48.1431	−1.67410	−0.837050	−	0.547126i	$-0.815722\pi$
$827$	−48.1431	−1.67410	−0.837050	+	0.547126i	$0.815722\pi$
$828$	2.74076	0.0952479
$829$	31.8748	1.10706	0.553529	−	0.832830i	$-0.313281\pi$
$829$	31.8748	1.10706	0.553529	+	0.832830i	$0.313281\pi$
$830$	0	0
$831$	−1.13734	−0.0394539
$832$	−12.0607	−0.418130
$833$	70.2839	2.43519
$834$	2.17408	0.0752821
$835$	0	0
$836$	0.408454	0.0141267
$837$	0.747809	0.0258481
$838$	53.0543	1.83273
$839$	7.93381	0.273906	0.136953	−	0.990578i	$-0.456269\pi$
$839$	7.93381	0.273906	0.136953	+	0.990578i	$0.456269\pi$
$840$	0	0
$841$	10.1218	0.349029
$842$	−60.2108	−2.07500
$843$	0.751351	0.0258779
$844$	−8.86630	−0.305191
$845$	0	0
$846$	53.5959	1.84267
$847$	−40.3859	−1.38768
$848$	−18.8792	−0.648315
$849$	−2.29630	−0.0788089
$850$	0	0
$851$	23.3832	0.801567
$852$	−0.283856	−0.00972476
$853$	−9.94107	−0.340376	−0.170188	−	0.985412i	$-0.554437\pi$
$853$	−9.94107	−0.340376	−0.170188	+	0.985412i	$0.554437\pi$
$854$	25.8910	0.885970
$855$	0	0
$856$	9.63705	0.329388
$857$	−16.3136	−0.557260	−0.278630	−	0.960398i	$-0.589880\pi$
$857$	−16.3136	−0.557260	−0.278630	+	0.960398i	$0.589880\pi$
$858$	−0.378818	−0.0129326
$859$	28.1621	0.960879	0.480439	−	0.877028i	$-0.340477\pi$
$859$	28.1621	0.960879	0.480439	+	0.877028i	$0.340477\pi$
$860$	0	0
$861$	−4.19970	−0.143125
$862$	−35.9336	−1.22390
$863$	−16.6900	−0.568135	−0.284067	−	0.958804i	$-0.591684\pi$
$863$	−16.6900	−0.568135	−0.284067	+	0.958804i	$0.591684\pi$
$864$	1.57538	0.0535954
$865$	0	0
$866$	−56.4599	−1.91859
$867$	−5.25559	−0.178489
$868$	1.51546	0.0514379
$869$	−2.13667	−0.0724817
$870$	0	0
$871$	14.9617	0.506957
$872$	−16.9292	−0.573296
$873$	−49.5156	−1.67585
$874$	4.17334	0.141165
$875$	0	0
$876$	−0.198072	−0.00669225
$877$	−1.82448	−0.0616082	−0.0308041	−	0.999525i	$-0.509807\pi$
$877$	−1.82448	−0.0616082	−0.0308041	+	0.999525i	$0.509807\pi$
$878$	−17.7971	−0.600624
$879$	−0.311669	−0.0105123
$880$	0	0
$881$	−0.107710	−0.00362883	−0.00181441	−	0.999998i	$-0.500578\pi$
$881$	−0.107710	−0.00362883	−0.00181441	+	0.999998i	$0.500578\pi$
$882$	42.0823	1.41698
$883$	3.70829	0.124794	0.0623970	−	0.998051i	$-0.480126\pi$
$883$	3.70829	0.124794	0.0623970	+	0.998051i	$0.480126\pi$
$884$	−5.84942	−0.196737
$885$	0	0
$886$	−15.0053	−0.504113
$887$	12.3923	0.416091	0.208046	−	0.978119i	$-0.433290\pi$
$887$	12.3923	0.416091	0.208046	+	0.978119i	$0.433290\pi$
$888$	3.00249	0.100757
$889$	−30.5659	−1.02515
$890$	0	0
$891$	8.63163	0.289171
$892$	−4.71626	−0.157912
$893$	12.9480	0.433289
$894$	−3.69404	−0.123547
$895$	0	0
$896$	−53.9529	−1.80244
$897$	−0.614087	−0.0205038
$898$	21.3983	0.714069
$899$	−6.25474	−0.208607
$900$	0	0
$901$	31.4579	1.04801
$902$	−12.5638	−0.418328
$903$	−5.61121	−0.186729
$904$	0.419121	0.0139397
$905$	0	0
$906$	−1.43937	−0.0478198
$907$	42.0580	1.39651	0.698257	−	0.715847i	$-0.253959\pi$
$907$	42.0580	1.39651	0.698257	+	0.715847i	$0.253959\pi$
$908$	0.0741484	0.00246070
$909$	11.4720	0.380501
$910$	0	0
$911$	−27.5936	−0.914217	−0.457109	−	0.889411i	$-0.651115\pi$
$911$	−27.5936	−0.914217	−0.457109	+	0.889411i	$0.651115\pi$
$912$	0.640650	0.0212140
$913$	9.45239	0.312829
$914$	22.7267	0.751734
$915$	0	0
$916$	4.29638	0.141956
$917$	−6.03170	−0.199184
$918$	−8.86052	−0.292441
$919$	−48.0391	−1.58466	−0.792332	−	0.610091i	$-0.791133\pi$
$919$	−48.0391	−1.58466	−0.792332	+	0.610091i	$0.791133\pi$
$920$	0	0
$921$	3.28332	0.108189
$922$	20.9634	0.690394
$923$	−12.1554	−0.400101
$924$	−0.184497	−0.00606949
$925$	0	0
$926$	48.0770	1.57991
$927$	−21.1780	−0.695578
$928$	−13.1766	−0.432543
$929$	1.86185	0.0610855	0.0305427	−	0.999533i	$-0.490276\pi$
$929$	1.86185	0.0610855	0.0305427	+	0.999533i	$0.490276\pi$
$930$	0	0
$931$	10.1665	0.333193
$932$	6.35781	0.208257
$933$	−2.04422	−0.0669249
$934$	−36.4280	−1.19196
$935$	0	0
$936$	15.0702	0.492585
$937$	30.3542	0.991628	0.495814	−	0.868429i	$-0.334870\pi$
$937$	30.3542	0.991628	0.495814	+	0.868429i	$0.334870\pi$
$938$	45.9282	1.49961
$939$	−2.11847	−0.0691336
$940$	0	0
$941$	4.24695	0.138447	0.0692233	−	0.997601i	$-0.477948\pi$
$941$	4.24695	0.138447	0.0692233	+	0.997601i	$0.477948\pi$
$942$	0.498312	0.0162359
$943$	−20.3666	−0.663229
$944$	−45.4639	−1.47972
$945$	0	0
$946$	−16.7865	−0.545775
$947$	23.1180	0.751235	0.375617	−	0.926775i	$-0.377431\pi$
$947$	23.1180	0.751235	0.375617	+	0.926775i	$0.377431\pi$
$948$	0.103360	0.00335696
$949$	−8.48194	−0.275336
$950$	0	0
$951$	1.11005	0.0359958
$952$	77.2636	2.50413
$953$	−19.3876	−0.628026	−0.314013	−	0.949419i	$-0.601674\pi$
$953$	−19.3876	−0.628026	−0.314013	+	0.949419i	$0.601674\pi$
$954$	18.8353	0.609815
$955$	0	0
$956$	−3.77679	−0.122150
$957$	0.761473	0.0246149
$958$	−16.5136	−0.533531
$959$	10.0176	0.323484
$960$	0	0
$961$	1.00000	0.0322581
$962$	−29.8806	−0.963391
$963$	−11.4946	−0.370407
$964$	8.46804	0.272737
$965$	0	0
$966$	−1.88508	−0.0606513
$967$	−29.6877	−0.954693	−0.477346	−	0.878715i	$-0.658401\pi$
$967$	−29.6877	−0.954693	−0.477346	+	0.878715i	$0.658401\pi$
$968$	−25.1483	−0.808296
$969$	−1.06750	−0.0342929
$970$	0	0
$971$	−4.37531	−0.140410	−0.0702051	−	0.997533i	$-0.522365\pi$
$971$	−4.37531	−0.140410	−0.0702051	+	0.997533i	$0.522365\pi$
$972$	−1.26366	−0.0405318
$973$	45.3423	1.45361
$974$	−9.51670	−0.304935
$975$	0	0
$976$	19.2746	0.616966
$977$	52.6283	1.68373	0.841865	−	0.539689i	$-0.181458\pi$
$977$	52.6283	1.68373	0.841865	+	0.539689i	$0.181458\pi$
$978$	−3.28825	−0.105147
$979$	3.86098	0.123397
$980$	0	0
$981$	20.1923	0.644690
$982$	34.7889	1.11016
$983$	41.9825	1.33903	0.669517	−	0.742797i	$-0.266501\pi$
$983$	41.9825	1.33903	0.669517	+	0.742797i	$0.266501\pi$
$984$	−2.61515	−0.0833679
$985$	0	0
$986$	74.1102	2.36015
$987$	−5.84855	−0.186161
$988$	−0.846111	−0.0269184
$989$	−27.2118	−0.865286
$990$	0	0
$991$	7.30861	0.232166	0.116083	−	0.993240i	$-0.462966\pi$
$991$	7.30861	0.232166	0.116083	+	0.993240i	$0.462966\pi$
$992$	2.10666	0.0668864
$993$	3.28232	0.104161
$994$	−37.3138	−1.18352
$995$	0	0
$996$	−0.457251	−0.0144885
$997$	5.88688	0.186439	0.0932197	−	0.995646i	$-0.470284\pi$
$997$	5.88688	0.186439	0.0932197	+	0.995646i	$0.470284\pi$
$998$	−29.9419	−0.947793
$999$	−7.18117	−0.227202

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	775.2.a.j.1.1	yes	5
3.2	odd	2		6975.2.a.bq.1.5		5
5.2	odd	4		775.2.b.h.249.3		10
5.3	odd	4		775.2.b.h.249.8		10
5.4	even	2		775.2.a.i.1.5	✓	5
15.14	odd	2		6975.2.a.bx.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
775.2.a.i.1.5	✓	5	5.4	even	2
775.2.a.j.1.1	yes	5	1.1	even	1	trivial
775.2.b.h.249.3		10	5.2	odd	4
775.2.b.h.249.8		10	5.3	odd	4
6975.2.a.bq.1.5		5	3.2	odd	2
6975.2.a.bx.1.1		5	15.14	odd	2

Overview	Random
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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:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.a (trivial)

\(f(q)\)	\(=\)	\(q-1.54180 q^{2} -0.124960 q^{3} +0.377151 q^{4} +0.192664 q^{6} +4.01817 q^{7} +2.50211 q^{8} -2.98438 q^{9} +O(q^{10})\)	\(q-1.54180 q^{2} -0.124960 q^{3} +0.377151 q^{4} +0.192664 q^{6} +4.01817 q^{7} +2.50211 q^{8} -2.98438 q^{9} +0.974257 q^{11} -0.0471288 q^{12} -2.01817 q^{13} -6.19522 q^{14} -4.61206 q^{16} +7.68493 q^{17} +4.60133 q^{18} +1.11162 q^{19} -0.502111 q^{21} -1.50211 q^{22} -2.43501 q^{23} -0.312664 q^{24} +3.11162 q^{26} +0.747809 q^{27} +1.51546 q^{28} -6.25474 q^{29} +1.00000 q^{31} +2.10666 q^{32} -0.121743 q^{33} -11.8486 q^{34} -1.12556 q^{36} -9.60294 q^{37} -1.71389 q^{38} +0.252191 q^{39} +8.36409 q^{41} +0.774155 q^{42} +11.1752 q^{43} +0.367442 q^{44} +3.75430 q^{46} +11.6479 q^{47} +0.576323 q^{48} +9.14568 q^{49} -0.960310 q^{51} -0.761154 q^{52} +4.09345 q^{53} -1.15297 q^{54} +10.0539 q^{56} -0.138908 q^{57} +9.64357 q^{58} +9.85762 q^{59} -4.17918 q^{61} -1.54180 q^{62} -11.9918 q^{63} +5.97607 q^{64} +0.187704 q^{66} -7.41349 q^{67} +2.89838 q^{68} +0.304279 q^{69} +6.02299 q^{71} -7.46726 q^{72} +4.20279 q^{73} +14.8058 q^{74} +0.419247 q^{76} +3.91473 q^{77} -0.388828 q^{78} -2.19313 q^{79} +8.85971 q^{81} -12.8958 q^{82} +9.70215 q^{83} -0.189371 q^{84} -17.2300 q^{86} +0.781594 q^{87} +2.43770 q^{88} +3.96300 q^{89} -8.10935 q^{91} -0.918366 q^{92} -0.124960 q^{93} -17.9588 q^{94} -0.263248 q^{96} +16.5915 q^{97} -14.1008 q^{98} -2.90756 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 4 q^{2} + q^{3} + 6 q^{4} - q^{6} + 6 q^{7} + 15 q^{8} + 2 q^{9}+O(q^{10}) \) 5 * q + 4 * q^2 + q^3 + 6 * q^4 - q^6 + 6 * q^7 + 15 * q^8 + 2 * q^9	\( 5 q + 4 q^{2} + q^{3} + 6 q^{4} - q^{6} + 6 q^{7} + 15 q^{8} + 2 q^{9} - 11 q^{12} + 4 q^{13} + 2 q^{14} + 20 q^{16} + 11 q^{17} + 19 q^{18} - 4 q^{19} - 5 q^{21} - 10 q^{22} + 12 q^{23} - 26 q^{24} + 6 q^{26} - 2 q^{27} + 18 q^{28} - 6 q^{29} + 5 q^{31} + 29 q^{32} + 21 q^{33} - 5 q^{34} + 23 q^{36} - 2 q^{37} - 6 q^{38} + 7 q^{39} - 2 q^{41} - 24 q^{42} + 7 q^{43} - 28 q^{44} + 27 q^{46} + 8 q^{47} - 39 q^{48} - q^{49} - 19 q^{51} - 6 q^{52} + 25 q^{53} - 18 q^{54} + 35 q^{56} + 20 q^{57} - q^{58} + 4 q^{59} - 17 q^{61} + 4 q^{62} + 10 q^{63} + 27 q^{64} + 27 q^{66} - 13 q^{67} + 18 q^{68} - 10 q^{69} - 6 q^{71} + 26 q^{72} + 7 q^{73} + 6 q^{74} - 5 q^{76} + 7 q^{77} + 22 q^{78} + 12 q^{79} - 11 q^{81} - 21 q^{82} - 4 q^{83} - 63 q^{84} - 41 q^{86} + q^{87} - 49 q^{88} - 3 q^{89} - 22 q^{91} + 34 q^{92} + q^{93} - 34 q^{94} - 64 q^{96} + 25 q^{97} - 22 q^{98} + 5 q^{99}+O(q^{100}) \) 5 * q + 4 * q^2 + q^3 + 6 * q^4 - q^6 + 6 * q^7 + 15 * q^8 + 2 * q^9 - 11 * q^12 + 4 * q^13 + 2 * q^14 + 20 * q^16 + 11 * q^17 + 19 * q^18 - 4 * q^19 - 5 * q^21 - 10 * q^22 + 12 * q^23 - 26 * q^24 + 6 * q^26 - 2 * q^27 + 18 * q^28 - 6 * q^29 + 5 * q^31 + 29 * q^32 + 21 * q^33 - 5 * q^34 + 23 * q^36 - 2 * q^37 - 6 * q^38 + 7 * q^39 - 2 * q^41 - 24 * q^42 + 7 * q^43 - 28 * q^44 + 27 * q^46 + 8 * q^47 - 39 * q^48 - q^49 - 19 * q^51 - 6 * q^52 + 25 * q^53 - 18 * q^54 + 35 * q^56 + 20 * q^57 - q^58 + 4 * q^59 - 17 * q^61 + 4 * q^62 + 10 * q^63 + 27 * q^64 + 27 * q^66 - 13 * q^67 + 18 * q^68 - 10 * q^69 - 6 * q^71 + 26 * q^72 + 7 * q^73 + 6 * q^74 - 5 * q^76 + 7 * q^77 + 22 * q^78 + 12 * q^79 - 11 * q^81 - 21 * q^82 - 4 * q^83 - 63 * q^84 - 41 * q^86 + q^87 - 49 * q^88 - 3 * q^89 - 22 * q^91 + 34 * q^92 + q^93 - 34 * q^94 - 64 * q^96 + 25 * q^97 - 22 * q^98 + 5 * q^99

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