LMFDB - Embedded newform 925.2.d.f.924.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [925,2,Mod(924,925)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(925, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("925.924"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.d (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,2,0,18,0,0,0,6,-22,0,2,0,20,0,0,30,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(17)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 21x^{10} + 162x^{8} + 574x^{6} + 985x^{4} + 765x^{2} + 196 $ x^12 + 21x^10 + 162x^8 + 574x^6 + 985x^4 + 765*x^2 + 196
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	no (minimal twist has level 185)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			924.11
Root			$2.75497i$ of defining polynomial
Character	$\chi$	$=$	925.924
Dual form			925.2.d.f.924.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.75497 q^{2} -2.91885i q^{3} +5.58988 q^{4} -8.04135i q^{6} +1.45148i q^{7} +9.89002 q^{8} -5.51969 q^{9} -4.49421 q^{11} -16.3160i q^{12} +3.36753 q^{13} +3.99878i q^{14} +16.0670 q^{16} +0.0254774 q^{17} -15.2066 q^{18} -2.32897i q^{19} +4.23665 q^{21} -12.3814 q^{22} -1.90433 q^{23} -28.8675i q^{24} +9.27746 q^{26} +7.35459i q^{27} +8.11358i q^{28} +3.20167i q^{29} +2.69930i q^{31} +24.4840 q^{32} +13.1179i q^{33} +0.0701894 q^{34} -30.8544 q^{36} +(-4.72950 + 3.82516i) q^{37} -6.41626i q^{38} -9.82932i q^{39} -0.472939 q^{41} +11.6718 q^{42} -5.60561 q^{43} -25.1221 q^{44} -5.24639 q^{46} +7.56842i q^{47} -46.8971i q^{48} +4.89321 q^{49} -0.0743646i q^{51} +18.8241 q^{52} +7.83626i q^{53} +20.2617i q^{54} +14.3551i q^{56} -6.79792 q^{57} +8.82053i q^{58} +8.97610i q^{59} -8.05367i q^{61} +7.43650i q^{62} -8.01170i q^{63} +35.3190 q^{64} +36.1395i q^{66} -3.88363i q^{67} +0.142415 q^{68} +5.55846i q^{69} +3.31202 q^{71} -54.5898 q^{72} +1.34593i q^{73} +(-13.0296 + 10.5382i) q^{74} -13.0187i q^{76} -6.52324i q^{77} -27.0795i q^{78} -16.9128i q^{79} +4.90789 q^{81} -1.30294 q^{82} +14.1496i q^{83} +23.6823 q^{84} -15.4433 q^{86} +9.34521 q^{87} -44.4478 q^{88} -10.7092i q^{89} +4.88790i q^{91} -10.6450 q^{92} +7.87886 q^{93} +20.8508i q^{94} -71.4653i q^{96} +7.87010 q^{97} +13.4807 q^{98} +24.8066 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} + 18 q^{4} + 6 q^{8} - 22 q^{9} + 2 q^{11} + 20 q^{13} + 30 q^{16} + 12 q^{17} - 26 q^{18} - 6 q^{21} - 28 q^{22} - 16 q^{23} - 12 q^{26} + 14 q^{32} - 4 q^{34} - 22 q^{36} - 14 q^{37} - 10 q^{41}+ \cdots + 84 q^{99}+O(q^{100}) $ 12 * q + 2 * q^2 + 18 * q^4 + 6 * q^8 - 22 * q^9 + 2 * q^11 + 20 * q^13 + 30 * q^16 + 12 * q^17 - 26 * q^18 - 6 * q^21 - 28 * q^22 - 16 * q^23 - 12 * q^26 + 14 * q^32 - 4 * q^34 - 22 * q^36 - 14 * q^37 - 10 * q^41 + 72 * q^42 - 12 * q^43 - 44 * q^44 - 24 * q^46 - 30 * q^49 + 80 * q^52 - 32 * q^57 + 126 * q^64 - 40 * q^68 + 42 * q^71 - 178 * q^72 - 50 * q^74 - 12 * q^81 + 96 * q^82 + 84 * q^84 - 64 * q^86 - 56 * q^87 - 72 * q^88 + 16 * q^92 + 76 * q^93 - 28 * q^97 + 118 * q^98 + 84 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	2.75497			1.94806			0.974030	−	0.226419i	$-0.0727017\pi$
$2$	2.75497			1.94806			0.974030	+	0.226419i	$0.0727017\pi$
$3$		−	2.91885i		−	1.68520i	−0.538541	−	0.842600i	$-0.681024\pi$
$3$		−	2.91885i		−	1.68520i	0.538541	−	0.842600i	$-0.318976\pi$
$4$	5.58988			2.79494
$5$		0			0
$5$		0			0
$6$		−	8.04135i		−	3.28287i
$7$			1.45148i			0.548607i	0.961643	+	0.274303i	$0.0884473\pi$
$7$			1.45148i			0.548607i	−0.961643	+	0.274303i	$0.911553\pi$
$8$	9.89002			3.49665
$9$	−5.51969			−1.83990
$10$		0			0
$11$	−4.49421			−1.35506			−0.677528	−	0.735497i	$-0.736949\pi$
$11$	−4.49421			−1.35506			−0.677528	+	0.735497i	$0.736949\pi$
$12$		−	16.3160i		−	4.71003i
$13$	3.36753			0.933985			0.466993	−	0.884261i	$-0.345337\pi$
$13$	3.36753			0.933985			0.466993	+	0.884261i	$0.345337\pi$
$14$			3.99878i			1.06872i
$15$		0			0
$16$	16.0670			4.01674
$17$	0.0254774			0.00617917			0.00308958	−	0.999995i	$-0.499017\pi$
$17$	0.0254774			0.00617917			0.00308958	+	0.999995i	$0.499017\pi$
$18$	−15.2066			−3.58423
$19$		−	2.32897i		−	0.534303i	−0.963655	−	0.267152i	$-0.913918\pi$
$19$		−	2.32897i		−	0.534303i	0.963655	−	0.267152i	$-0.0860824\pi$
$20$		0			0
$21$	4.23665			0.924512
$22$	−12.3814			−2.63973
$23$	−1.90433			−0.397081			−0.198540	−	0.980093i	$-0.563620\pi$
$23$	−1.90433			−0.397081			−0.198540	+	0.980093i	$0.563620\pi$
$24$		−	28.8675i		−	5.89255i
$25$		0			0
$26$	9.27746			1.81946
$27$			7.35459i			1.41539i
$28$			8.11358i			1.53332i
$29$			3.20167i			0.594536i	0.954794	+	0.297268i	$0.0960755\pi$
$29$			3.20167i			0.594536i	−0.954794	+	0.297268i	$0.903925\pi$
$30$		0			0
$31$			2.69930i			0.484809i	0.970175	+	0.242404i	$0.0779361\pi$
$31$			2.69930i			0.484809i	−0.970175	+	0.242404i	$0.922064\pi$
$32$	24.4840			4.32821
$33$			13.1179i			2.28354i
$34$	0.0701894			0.0120374
$35$		0			0
$36$	−30.8544			−5.14240
$37$	−4.72950	+	3.82516i	−0.777524	+	0.628853i
$37$	−4.72950	+	3.82516i	−0.777524	+	0.628853i
$38$		−	6.41626i		−	1.04085i
$39$		−	9.82932i		−	1.57395i
$40$		0			0
$41$	−0.472939			−0.0738607			−0.0369304	−	0.999318i	$-0.511758\pi$
$41$	−0.472939			−0.0738607			−0.0369304	+	0.999318i	$0.511758\pi$
$42$	11.6718			1.80100
$43$	−5.60561			−0.854848			−0.427424	−	0.904051i	$-0.640579\pi$
$43$	−5.60561			−0.854848			−0.427424	+	0.904051i	$0.640579\pi$
$44$	−25.1221			−3.78730
$45$		0			0
$46$	−5.24639			−0.773538
$47$			7.56842i			1.10397i	0.833855	+	0.551983i	$0.186129\pi$
$47$			7.56842i			1.10397i	−0.833855	+	0.551983i	$0.813871\pi$
$48$		−	46.8971i		−	6.76901i
$49$	4.89321			0.699030
$50$		0			0
$51$		−	0.0743646i		−	0.0104131i
$52$	18.8241			2.61043
$53$			7.83626i			1.07639i	0.842819	+	0.538197i	$0.180894\pi$
$53$			7.83626i			1.07639i	−0.842819	+	0.538197i	$0.819106\pi$
$54$			20.2617i			2.75727i
$55$		0			0
$56$			14.3551i			1.91829i
$57$	−6.79792			−0.900407
$58$			8.82053i			1.15819i
$59$			8.97610i			1.16859i	0.811542	+	0.584294i	$0.198629\pi$
$59$			8.97610i			1.16859i	−0.811542	+	0.584294i	$0.801371\pi$
$60$		0			0
$61$		−	8.05367i		−	1.03117i	−0.856839	−	0.515584i	$-0.827575\pi$
$61$		−	8.05367i		−	1.03117i	0.856839	−	0.515584i	$-0.172425\pi$
$62$			7.43650i			0.944437i
$63$		−	8.01170i		−	1.00938i
$64$	35.3190			4.41487
$65$		0			0
$66$			36.1395i			4.44847i
$67$		−	3.88363i		−	0.474461i	−0.971453	−	0.237231i	$-0.923760\pi$
$67$		−	3.88363i		−	0.474461i	0.971453	−	0.237231i	$-0.0762397\pi$
$68$	0.142415			0.0172704
$69$			5.55846i			0.669160i
$70$		0			0
$71$	3.31202			0.393064			0.196532	−	0.980497i	$-0.437032\pi$
$71$	3.31202			0.393064			0.196532	+	0.980497i	$0.437032\pi$
$72$	−54.5898			−6.43347
$73$			1.34593i			0.157529i	0.996893	+	0.0787645i	$0.0250975\pi$
$73$			1.34593i			0.157529i	−0.996893	+	0.0787645i	$0.974902\pi$
$74$	−13.0296	+	10.5382i	−1.51466	+	1.22504i
$75$		0			0
$76$		−	13.0187i		−	1.49334i
$77$		−	6.52324i		−	0.743393i
$78$		−	27.0795i		−	3.06615i
$79$		−	16.9128i		−	1.90284i	−0.307892	−	0.951421i	$-0.599623\pi$
$79$		−	16.9128i		−	1.90284i	0.307892	−	0.951421i	$-0.400377\pi$
$80$		0			0
$81$	4.90789			0.545321
$82$	−1.30294			−0.143885
$83$			14.1496i			1.55312i	0.630046	+	0.776558i	$0.283036\pi$
$83$			14.1496i			1.55312i	−0.630046	+	0.776558i	$0.716964\pi$
$84$	23.6823			2.58395
$85$		0			0
$86$	−15.4433			−1.66530
$87$	9.34521			1.00191
$88$	−44.4478			−4.73815
$89$		−	10.7092i		−	1.13517i	−0.823314	−	0.567586i	$-0.807878\pi$
$89$		−	10.7092i		−	1.13517i	0.823314	−	0.567586i	$-0.192122\pi$
$90$		0			0
$91$			4.88790i			0.512391i
$92$	−10.6450			−1.10982
$93$	7.87886			0.816999
$94$			20.8508i			2.15059i
$95$		0			0
$96$		−	71.4653i		−	7.29389i
$97$	7.87010			0.799088			0.399544	−	0.916714i	$-0.369168\pi$
$97$	7.87010			0.799088			0.399544	+	0.916714i	$0.369168\pi$
$98$	13.4807			1.36175
$99$	24.8066			2.49316
$100$		0			0
$101$	13.4202			1.33536			0.667680	−	0.744448i	$-0.267287\pi$
$101$	13.4202			1.33536			0.667680	+	0.744448i	$0.267287\pi$
$102$		−	0.204872i		−	0.0202854i
$103$	−5.00106			−0.492769			−0.246384	−	0.969172i	$-0.579243\pi$
$103$	−5.00106			−0.492769			−0.246384	+	0.969172i	$0.579243\pi$
$104$	33.3049			3.26582
$105$		0			0
$106$			21.5887i			2.09688i
$107$		−	9.77780i		−	0.945255i	−0.881262	−	0.472628i	$-0.843306\pi$
$107$		−	9.77780i		−	0.945255i	0.881262	−	0.472628i	$-0.156694\pi$
$108$			41.1113i			3.95593i
$109$		−	15.7550i		−	1.50905i	−0.656271	−	0.754525i	$-0.727867\pi$
$109$		−	15.7550i		−	1.50905i	0.656271	−	0.754525i	$-0.272133\pi$
$110$		0			0
$111$	11.1651	+	13.8047i	1.05974	+	1.31028i
$112$			23.3208i			2.20361i
$113$	4.59824			0.432566			0.216283	−	0.976331i	$-0.430607\pi$
$113$	4.59824			0.432566			0.216283	+	0.976331i	$0.430607\pi$
$114$	−18.7281			−1.75405
$115$		0			0
$116$			17.8970i			1.66169i
$117$	−18.5877			−1.71844
$118$			24.7289i			2.27648i
$119$			0.0369798i			0.00338993i
$120$		0			0
$121$	9.19793			0.836175
$122$		−	22.1877i		−	2.00878i
$123$			1.38044i			0.124470i
$124$			15.0888i			1.35501i
$125$		0			0
$126$		−	22.0720i		−	1.96633i
$127$		−	11.5549i		−	1.02533i	−0.858589	−	0.512665i	$-0.828658\pi$
$127$		−	11.5549i		−	1.02533i	0.858589	−	0.512665i	$-0.171342\pi$
$128$	48.3347			4.27222
$129$			16.3619i			1.44059i
$130$		0			0
$131$		−	7.28288i		−	0.636308i	−0.948039	−	0.318154i	$-0.896937\pi$
$131$		−	7.28288i		−	0.636308i	0.948039	−	0.318154i	$-0.103063\pi$
$132$			73.3276i			6.38235i
$133$	3.38045			0.293122
$134$		−	10.6993i		−	0.924279i
$135$		0			0
$136$	0.251971			0.0216064
$137$			10.7116i			0.915156i	0.889170	+	0.457578i	$0.151283\pi$
$137$			10.7116i			0.915156i	−0.889170	+	0.457578i	$0.848717\pi$
$138$			15.3134i			1.30356i
$139$	−13.6631			−1.15889			−0.579444	−	0.815012i	$-0.696730\pi$
$139$	−13.6631			−1.15889			−0.579444	+	0.815012i	$0.696730\pi$
$140$		0			0
$141$	22.0911			1.86040
$142$	9.12452			0.765713
$143$	−15.1344			−1.26560
$144$	−88.6847			−7.39039
$145$		0			0
$146$			3.70799i			0.306876i
$147$		−	14.2826i		−	1.17801i
$148$	−26.4373	+	21.3822i	−2.17313	+	1.75761i
$149$	−10.4783			−0.858415			−0.429207	−	0.903206i	$-0.641207\pi$
$149$	−10.4783			−0.858415			−0.429207	+	0.903206i	$0.641207\pi$
$150$		0			0
$151$	−5.32975			−0.433729			−0.216864	−	0.976202i	$-0.569583\pi$
$151$	−5.32975			−0.433729			−0.216864	+	0.976202i	$0.569583\pi$
$152$		−	23.0336i		−	1.86827i
$153$	−0.140627			−0.0113690
$154$		−	17.9714i		−	1.44817i
$155$		0			0
$156$		−	54.9447i		−	4.39910i
$157$		−	8.49980i		−	0.678358i	−0.940722	−	0.339179i	$-0.889851\pi$
$157$		−	8.49980i		−	0.678358i	0.940722	−	0.339179i	$-0.110149\pi$
$158$		−	46.5944i		−	3.70685i
$159$	22.8729			1.81394
$160$		0			0
$161$		−	2.76410i		−	0.217841i
$162$	13.5211			1.06232
$163$	−18.4771			−1.44724			−0.723619	−	0.690200i	$-0.757523\pi$
$163$	−18.4771			−1.44724			−0.723619	+	0.690200i	$0.757523\pi$
$164$	−2.64367			−0.206436
$165$		0			0
$166$			38.9817i			3.02556i
$167$	−7.79299			−0.603040			−0.301520	−	0.953460i	$-0.597494\pi$
$167$	−7.79299			−0.603040			−0.301520	+	0.953460i	$0.597494\pi$
$168$	41.9005			3.23269
$169$	−1.65973			−0.127672
$170$		0			0
$171$			12.8552i			0.983062i
$172$	−31.3347			−2.38925
$173$			2.22137i			0.168888i	0.996428	+	0.0844438i	$0.0269113\pi$
$173$			2.22137i			0.168888i	−0.996428	+	0.0844438i	$0.973089\pi$
$174$	25.7458			1.95178
$175$		0			0
$176$	−72.2084			−5.44291
$177$	26.1999			1.96930
$178$		−	29.5035i		−	2.21138i
$179$			25.8707i			1.93366i	0.255411	+	0.966832i	$0.417789\pi$
$179$			25.8707i			1.93366i	−0.255411	+	0.966832i	$0.582211\pi$
$180$		0			0
$181$	5.69629			0.423402			0.211701	−	0.977335i	$-0.432100\pi$
$181$	5.69629			0.423402			0.211701	+	0.977335i	$0.432100\pi$
$182$			13.4660i			0.998168i
$183$	−23.5075			−1.73772
$184$	−18.8339			−1.38845
$185$		0			0
$186$	21.7060			1.59156
$187$	−0.114501			−0.00837311
$188$			42.3065i			3.08552i
$189$	−10.6750			−0.776494
$190$		0			0
$191$		−	23.2172i		−	1.67993i	−0.542637	−	0.839967i	$-0.682574\pi$
$191$		−	23.2172i		−	1.67993i	0.542637	−	0.839967i	$-0.317426\pi$
$192$		−	103.091i		−	7.43993i
$193$	16.5508			1.19136			0.595678	−	0.803223i	$-0.296883\pi$
$193$	16.5508			1.19136			0.595678	+	0.803223i	$0.296883\pi$
$194$	21.6819			1.55667
$195$		0			0
$196$	27.3525			1.95375
$197$			12.4656i			0.888135i	0.895993	+	0.444068i	$0.146465\pi$
$197$			12.4656i			0.888135i	−0.895993	+	0.444068i	$0.853535\pi$
$198$	68.3416			4.85683
$199$			15.6109i			1.10663i	0.832973	+	0.553314i	$0.186637\pi$
$199$			15.6109i			1.10663i	−0.832973	+	0.553314i	$0.813363\pi$
$200$		0			0
$201$	−11.3357			−0.799561
$202$	36.9723			2.60136
$203$	−4.64716			−0.326167
$204$		−	0.415689i		−	0.0291041i
$205$		0			0
$206$	−13.7778			−0.959944
$207$	10.5113			0.730588
$208$	54.1060			3.75158
$209$			10.4669i			0.724010i
$210$		0			0
$211$	−23.3395			−1.60676			−0.803379	−	0.595469i	$-0.796966\pi$
$211$	−23.3395			−1.60676			−0.803379	+	0.595469i	$0.796966\pi$
$212$			43.8038i			3.00845i
$213$		−	9.66729i		−	0.662392i
$214$		−	26.9376i		−	1.84141i
$215$		0			0
$216$			72.7370i			4.94913i
$217$	−3.91797			−0.265969
$218$		−	43.4045i		−	2.93972i
$219$	3.92856			0.265468
$220$		0			0
$221$	0.0857958			0.00577125
$222$	30.7595	+	38.0316i	2.06444	+	2.55251i
$223$		−	10.1496i		−	0.679665i	−0.940486	−	0.339832i	$-0.889630\pi$
$223$		−	10.1496i		−	0.679665i	0.940486	−	0.339832i	$-0.110370\pi$
$224$			35.5380i			2.37449i
$225$		0			0
$226$	12.6680			0.842665
$227$	1.96484			0.130411			0.0652055	−	0.997872i	$-0.479230\pi$
$227$	1.96484			0.130411			0.0652055	+	0.997872i	$0.479230\pi$
$228$	−37.9996			−2.51658
$229$	−24.4562			−1.61611			−0.808055	−	0.589107i	$-0.799480\pi$
$229$	−24.4562			−1.61611			−0.808055	+	0.589107i	$0.799480\pi$
$230$		0			0
$231$	−19.0404			−1.25276
$232$			31.6646i			2.07888i
$233$			8.99797i			0.589477i	0.955578	+	0.294738i	$0.0952325\pi$
$233$			8.99797i			0.589477i	−0.955578	+	0.294738i	$0.904767\pi$
$234$	−51.2087			−3.34762
$235$		0			0
$236$			50.1753i			3.26613i
$237$	−49.3660			−3.20667
$238$			0.101878i			0.00660380i
$239$		−	15.7417i		−	1.01825i	−0.860693	−	0.509124i	$-0.829969\pi$
$239$		−	15.7417i		−	1.01825i	0.860693	−	0.509124i	$-0.170031\pi$
$240$		0			0
$241$		−	6.84560i		−	0.440964i	−0.975391	−	0.220482i	$-0.929237\pi$
$241$		−	6.84560i		−	0.440964i	0.975391	−	0.220482i	$-0.0707631\pi$
$242$	25.3400			1.62892
$243$			7.73838i			0.496417i
$244$		−	45.0191i		−	2.88205i
$245$		0			0
$246$			3.80307i			0.242475i
$247$		−	7.84289i		−	0.499031i
$248$			26.6961i			1.69521i
$249$	41.3004			2.61731
$250$		0			0
$251$			8.89502i			0.561449i	0.959788	+	0.280724i	$0.0905747\pi$
$251$			8.89502i			0.561449i	−0.959788	+	0.280724i	$0.909425\pi$
$252$		−	44.7844i		−	2.82115i
$253$	8.55847			0.538067
$254$		−	31.8334i		−	1.99740i
$255$		0			0
$256$	62.5228			3.90768
$257$	24.1717			1.50779			0.753896	−	0.656994i	$-0.228172\pi$
$257$	24.1717			1.50779			0.753896	+	0.656994i	$0.228172\pi$
$258$			45.0767i			2.80635i
$259$	−5.55214	−	6.86476i	−0.344993	−	0.426555i
$260$		0			0
$261$		−	17.6722i		−	1.09388i
$262$		−	20.0641i		−	1.23957i
$263$		−	8.85085i		−	0.545767i	−0.962047	−	0.272883i	$-0.912023\pi$
$263$		−	8.85085i		−	0.545767i	0.962047	−	0.272883i	$-0.0879773\pi$
$264$			129.737i			7.98473i
$265$		0			0
$266$	9.31305			0.571020
$267$	−31.2585			−1.91299
$268$		−	21.7090i		−	1.32609i
$269$	−9.11977			−0.556042			−0.278021	−	0.960575i	$-0.589678\pi$
$269$	−9.11977			−0.556042			−0.278021	+	0.960575i	$0.589678\pi$
$270$		0			0
$271$	23.6107			1.43425			0.717124	−	0.696946i	$-0.245458\pi$
$271$	23.6107			1.43425			0.717124	+	0.696946i	$0.245458\pi$
$272$	0.409344			0.0248201
$273$	14.2670			0.863480
$274$			29.5102i			1.78278i
$275$		0			0
$276$			31.0711i			1.87026i
$277$	6.08750			0.365763			0.182881	−	0.983135i	$-0.441458\pi$
$277$	6.08750			0.365763			0.182881	+	0.983135i	$0.441458\pi$
$278$	−37.6415			−2.25758
$279$		−	14.8993i		−	0.891998i
$280$		0			0
$281$			3.06829i			0.183039i	0.995803	+	0.0915195i	$0.0291724\pi$
$281$			3.06829i			0.183039i	−0.995803	+	0.0915195i	$0.970828\pi$
$282$	60.8603			3.62418
$283$	14.1136			0.838966			0.419483	−	0.907763i	$-0.362211\pi$
$283$	14.1136			0.838966			0.419483	+	0.907763i	$0.362211\pi$
$284$	18.5138			1.09859
$285$		0			0
$286$	−41.6948			−2.46547
$287$		−	0.686461i		−	0.0405205i
$288$	−135.144			−7.96345
$289$	−16.9994			−0.999962
$290$		0			0
$291$		−	22.9717i		−	1.34662i
$292$			7.52357i			0.440284i
$293$			11.0541i			0.645789i	0.946435	+	0.322894i	$0.104656\pi$
$293$			11.0541i			0.645789i	−0.946435	+	0.322894i	$0.895344\pi$
$294$		−	39.3481i		−	2.29483i
$295$		0			0
$296$	−46.7748	+	37.8309i	−2.71873	+	2.19888i
$297$		−	33.0531i		−	1.91793i
$298$	−28.8674			−1.67224
$299$	−6.41290			−0.370868
$300$		0			0
$301$		−	8.13642i		−	0.468976i
$302$	−14.6833			−0.844929
$303$		−	39.1716i		−	2.25035i
$304$		−	37.4195i		−	2.14616i
$305$		0			0
$306$	−0.387424			−0.0221475
$307$		−	7.86166i		−	0.448689i	−0.974510	−	0.224344i	$-0.927976\pi$
$307$		−	7.86166i		−	0.448689i	0.974510	−	0.224344i	$-0.0720240\pi$
$308$		−	36.4641i		−	2.07774i
$309$			14.5973i			0.830414i
$310$		0			0
$311$		−	25.8719i		−	1.46706i	−0.679656	−	0.733531i	$-0.737871\pi$
$311$		−	25.8719i		−	1.46706i	0.679656	−	0.733531i	$-0.262129\pi$
$312$		−	97.2121i		−	5.50355i
$313$	−6.62741			−0.374603			−0.187302	−	0.982302i	$-0.559974\pi$
$313$	−6.62741			−0.374603			−0.187302	+	0.982302i	$0.559974\pi$
$314$		−	23.4167i		−	1.32148i
$315$		0			0
$316$		−	94.5407i		−	5.31833i
$317$		−	15.4948i		−	0.870273i	−0.900365	−	0.435136i	$-0.856700\pi$
$317$		−	15.4948i		−	0.870273i	0.900365	−	0.435136i	$-0.143300\pi$
$318$	63.0142			3.53366
$319$		−	14.3890i		−	0.805629i
$320$		0			0
$321$	−28.5399			−1.59294
$322$		−	7.61501i		−	0.424368i
$323$		−	0.0593361i		−	0.00330155i
$324$	27.4345			1.52414
$325$		0			0
$326$	−50.9039			−2.81931
$327$	−45.9864			−2.54305
$328$	−4.67738			−0.258265
$329$	−10.9854			−0.605644
$330$		0			0
$331$		−	18.5660i		−	1.02048i	−0.860032	−	0.510240i	$-0.829557\pi$
$331$		−	18.5660i		−	1.02048i	0.860032	−	0.510240i	$-0.170443\pi$
$332$			79.0943i			4.34086i
$333$	26.1053	−	21.1137i	1.43056	−	1.15702i
$334$	−21.4695			−1.17476
$335$		0			0
$336$	68.0701			3.71353
$337$			29.0093i			1.58024i	0.612954	+	0.790119i	$0.289981\pi$
$337$			29.0093i			1.58024i	−0.612954	+	0.790119i	$0.710019\pi$
$338$	−4.57252			−0.248713
$339$		−	13.4216i		−	0.728960i
$340$		0			0
$341$		−	12.1312i		−	0.656943i
$342$			35.4157i			1.91506i
$343$			17.2627i			0.932100i
$344$	−55.4396			−2.98910
$345$		0			0
$346$			6.11981i			0.329003i
$347$	−31.1104			−1.67009			−0.835046	−	0.550180i	$-0.814559\pi$
$347$	−31.1104			−1.67009			−0.835046	+	0.550180i	$0.814559\pi$
$348$	52.2386			2.80028
$349$	−11.8632			−0.635021			−0.317511	−	0.948255i	$-0.602847\pi$
$349$	−11.8632			−0.635021			−0.317511	+	0.948255i	$0.602847\pi$
$350$		0			0
$351$			24.7668i			1.32195i
$352$	−110.036			−5.86496
$353$	33.7605			1.79689			0.898446	−	0.439083i	$-0.144697\pi$
$353$	33.7605			1.79689			0.898446	+	0.439083i	$0.144697\pi$
$354$	72.1800			3.83632
$355$		0			0
$356$		−	59.8630i		−	3.17273i
$357$	0.107939			0.00571271
$358$			71.2730i			3.76690i
$359$	−9.24876			−0.488131			−0.244065	−	0.969759i	$-0.578481\pi$
$359$	−9.24876			−0.488131			−0.244065	+	0.969759i	$0.578481\pi$
$360$		0			0
$361$	13.5759			0.714520
$362$	15.6931			0.824812
$363$		−	26.8474i		−	1.40912i
$364$			27.3227i			1.43210i
$365$		0			0
$366$	−64.7625			−3.38519
$367$		−	7.38718i		−	0.385608i	−0.981237	−	0.192804i	$-0.938242\pi$
$367$		−	7.38718i		−	0.385608i	0.981237	−	0.192804i	$-0.0617581\pi$
$368$	−30.5969			−1.59497
$369$	2.61048			0.135896
$370$		0			0
$371$	−11.3742			−0.590517
$372$	44.0418			2.28346
$373$		−	15.3033i		−	0.792374i	−0.918170	−	0.396187i	$-0.870333\pi$
$373$		−	15.3033i		−	0.792374i	0.918170	−	0.396187i	$-0.129667\pi$
$374$	−0.315446			−0.0163113
$375$		0			0
$376$			74.8517i			3.86018i
$377$			10.7817i			0.555288i
$378$	−29.4094			−1.51266
$379$	14.8574			0.763173			0.381587	−	0.924333i	$-0.375378\pi$
$379$	14.8574			0.763173			0.381587	+	0.924333i	$0.375378\pi$
$380$		0			0
$381$	−33.7270			−1.72788
$382$		−	63.9626i		−	3.27261i
$383$	−11.0996			−0.567164			−0.283582	−	0.958948i	$-0.591523\pi$
$383$	−11.0996			−0.567164			−0.283582	+	0.958948i	$0.591523\pi$
$384$		−	141.082i		−	7.19954i
$385$		0			0
$386$	45.5971			2.32083
$387$	30.9412			1.57283
$388$	43.9929			2.23340
$389$		−	7.50355i		−	0.380445i	−0.981741	−	0.190223i	$-0.939079\pi$
$389$		−	7.50355i		−	0.380445i	0.981741	−	0.190223i	$-0.0609210\pi$
$390$		0			0
$391$	−0.0485174			−0.00245363
$392$	48.3940			2.44426
$393$	−21.2576			−1.07231
$394$			34.3423i			1.73014i
$395$		0			0
$396$	138.666			6.96823
$397$			12.5602i			0.630378i	0.949029	+	0.315189i	$0.102068\pi$
$397$			12.5602i			0.630378i	−0.949029	+	0.315189i	$0.897932\pi$
$398$			43.0077i			2.15578i
$399$		−	9.86703i		−	0.493970i
$400$		0			0
$401$		−	11.4360i		−	0.571086i	−0.958366	−	0.285543i	$-0.907826\pi$
$401$		−	11.4360i		−	0.571086i	0.958366	−	0.285543i	$-0.0921739\pi$
$402$	−31.2297			−1.55759
$403$			9.08998i			0.452804i
$404$	75.0173			3.73225
$405$		0			0
$406$	−12.8028			−0.635392
$407$	21.2553	−	17.1911i	1.05359	−	0.852130i
$408$		−	0.735467i		−	0.0364110i
$409$		−	32.2880i		−	1.59654i	−0.602302	−	0.798268i	$-0.705750\pi$
$409$		−	32.2880i		−	1.59654i	0.602302	−	0.798268i	$-0.294250\pi$
$410$		0			0
$411$	31.2656			1.54222
$412$	−27.9553			−1.37726
$413$	−13.0286			−0.641096
$414$	28.9584			1.42323
$415$		0			0
$416$	82.4508			4.04248
$417$			39.8805i			1.95296i
$418$			28.8360i			1.41042i
$419$	24.2662			1.18548			0.592741	−	0.805393i	$-0.298046\pi$
$419$	24.2662			1.18548			0.592741	+	0.805393i	$0.298046\pi$
$420$		0			0
$421$			35.5190i			1.73109i	0.500832	+	0.865545i	$0.333027\pi$
$421$			35.5190i			1.73109i	−0.500832	+	0.865545i	$0.666973\pi$
$422$	−64.2997			−3.13006
$423$		−	41.7753i		−	2.03118i
$424$			77.5008i			3.76377i
$425$		0			0
$426$		−	26.6331i		−	1.29038i
$427$	11.6897			0.565706
$428$		−	54.6567i		−	2.64193i
$429$			44.1750i			2.13279i
$430$		0			0
$431$			14.5051i			0.698686i	0.936995	+	0.349343i	$0.113595\pi$
$431$			14.5051i			0.698686i	−0.936995	+	0.349343i	$0.886405\pi$
$432$			118.166i			5.68527i
$433$			24.7197i			1.18795i	0.804482	+	0.593977i	$0.202443\pi$
$433$			24.7197i			1.18795i	−0.804482	+	0.593977i	$0.797557\pi$
$434$	−10.7939			−0.518124
$435$		0			0
$436$		−	88.0683i		−	4.21770i
$437$			4.43514i			0.212162i
$438$	10.8231			0.517147
$439$			8.13962i			0.388483i	0.980954	+	0.194241i	$0.0622245\pi$
$439$			8.13962i			0.388483i	−0.980954	+	0.194241i	$0.937775\pi$
$440$		0			0
$441$	−27.0090			−1.28614
$442$	0.236365			0.0112427
$443$		−	5.50085i		−	0.261353i	−0.991425	−	0.130677i	$-0.958285\pi$
$443$		−	5.50085i		−	0.261353i	0.991425	−	0.130677i	$-0.0417150\pi$
$444$	62.4114	+	77.1665i	2.96191	+	3.66216i
$445$		0			0
$446$		−	27.9618i		−	1.32403i
$447$			30.5845i			1.44660i
$448$			51.2647i			2.42203i
$449$		−	7.73218i		−	0.364904i	−0.983215	−	0.182452i	$-0.941597\pi$
$449$		−	7.73218i		−	0.364904i	0.983215	−	0.182452i	$-0.0584034\pi$
$450$		0			0
$451$	2.12549			0.100085
$452$	25.7036			1.20900
$453$			15.5567i			0.730919i
$454$	5.41308			0.254048
$455$		0			0
$456$	−67.2316			−3.14841
$457$	−0.793718			−0.0371286			−0.0185643	−	0.999828i	$-0.505910\pi$
$457$	−0.793718			−0.0371286			−0.0185643	+	0.999828i	$0.505910\pi$
$458$	−67.3761			−3.14828
$459$			0.187376i			0.00874594i
$460$		0			0
$461$			1.34291i			0.0625456i	0.999511	+	0.0312728i	$0.00995606\pi$
$461$			1.34291i			0.0625456i	−0.999511	+	0.0312728i	$0.990044\pi$
$462$	−52.4557			−2.44046
$463$	34.5602			1.60615			0.803075	−	0.595878i	$-0.203196\pi$
$463$	34.5602			1.60615			0.803075	+	0.595878i	$0.203196\pi$
$464$			51.4412i			2.38810i
$465$		0			0
$466$			24.7892i			1.14834i
$467$	−15.0666			−0.697200			−0.348600	−	0.937272i	$-0.613343\pi$
$467$	−15.0666			−0.697200			−0.348600	+	0.937272i	$0.613343\pi$
$468$	−103.903			−4.80292
$469$	5.63700			0.260293
$470$		0			0
$471$	−24.8097			−1.14317
$472$			88.7738i			4.08614i
$473$	25.1928			1.15837
$474$	−136.002			−6.24678
$475$		0			0
$476$			0.206713i			0.00947466i
$477$		−	43.2537i		−	1.98045i
$478$		−	43.3681i		−	1.98361i
$479$		−	20.1293i		−	0.919731i	−0.887989	−	0.459865i	$-0.847898\pi$
$479$		−	20.1293i		−	0.919731i	0.887989	−	0.459865i	$-0.152102\pi$
$480$		0			0
$481$	−15.9267	+	12.8814i	−0.726196	+	0.587339i
$482$		−	18.8595i		−	0.859025i
$483$	−8.06798			−0.367106
$484$	51.4153			2.33706
$485$		0			0
$486$			21.3190i			0.967051i
$487$	−3.16807			−0.143559			−0.0717795	−	0.997421i	$-0.522868\pi$
$487$	−3.16807			−0.143559			−0.0717795	+	0.997421i	$0.522868\pi$
$488$		−	79.6510i		−	3.60563i
$489$			53.9319i			2.43888i
$490$		0			0
$491$	8.17507			0.368936			0.184468	−	0.982839i	$-0.440944\pi$
$491$	8.17507			0.368936			0.184468	+	0.982839i	$0.440944\pi$
$492$			7.71649i			0.347886i
$493$			0.0815702i			0.00367374i
$494$		−	21.6070i		−	0.972143i
$495$		0			0
$496$			43.3696i			1.94735i
$497$			4.80732i			0.215638i
$498$	113.782			5.09868
$499$			19.6941i			0.881630i	0.897598	+	0.440815i	$0.145310\pi$
$499$			19.6941i			0.881630i	−0.897598	+	0.440815i	$0.854690\pi$
$500$		0			0
$501$			22.7466i			1.01624i
$502$			24.5055i			1.09374i
$503$	−3.14419			−0.140193			−0.0700964	−	0.997540i	$-0.522331\pi$
$503$	−3.14419			−0.140193			−0.0700964	+	0.997540i	$0.522331\pi$
$504$		−	79.2359i		−	3.52945i
$505$		0			0
$506$	23.5784			1.04819
$507$			4.84452i			0.215153i
$508$		−	64.5903i		−	2.86573i
$509$	35.1772			1.55920			0.779601	−	0.626277i	$-0.215422\pi$
$509$	35.1772			1.55920			0.779601	+	0.626277i	$0.215422\pi$
$510$		0			0
$511$	−1.95358			−0.0864215
$512$	75.5793			3.34017
$513$	17.1286			0.756248
$514$	66.5925			2.93727
$515$		0			0
$516$			91.4613i			4.02636i
$517$		−	34.0141i		−	1.49594i
$518$	−15.2960	−	18.9122i	−0.672067	−	0.830955i
$519$	6.48384			0.284609
$520$		0			0
$521$	6.18006			0.270753			0.135377	−	0.990794i	$-0.456776\pi$
$521$	6.18006			0.270753			0.135377	+	0.990794i	$0.456776\pi$
$522$		−	48.6866i		−	2.13095i
$523$	−22.8302			−0.998295			−0.499148	−	0.866517i	$-0.666353\pi$
$523$	−22.8302			−0.998295			−0.499148	+	0.866517i	$0.666353\pi$
$524$		−	40.7104i		−	1.77844i
$525$		0			0
$526$		−	24.3839i		−	1.06319i
$527$			0.0687711i			0.00299571i
$528$			210.765i			9.17239i
$529$	−19.3735			−0.842327
$530$		0			0
$531$		−	49.5453i		−	2.15008i
$532$	18.8963			0.819259
$533$	−1.59264			−0.0689848
$534$	−86.1163			−3.72662
$535$		0			0
$536$		−	38.4092i		−	1.65902i
$537$	75.5126			3.25861
$538$	−25.1247			−1.08320
$539$	−21.9911			−0.947225
$540$		0			0
$541$			11.5724i			0.497534i	0.968563	+	0.248767i	$0.0800254\pi$
$541$			11.5724i			0.497534i	−0.968563	+	0.248767i	$0.919975\pi$
$542$	65.0469			2.79400
$543$		−	16.6266i		−	0.713516i
$544$	0.623789			0.0267447
$545$		0			0
$546$	39.3053			1.68211
$547$	24.6075			1.05214			0.526071	−	0.850440i	$-0.323664\pi$
$547$	24.6075			1.05214			0.526071	+	0.850440i	$0.323664\pi$
$548$			59.8766i			2.55780i
$549$			44.4538i			1.89724i
$550$		0			0
$551$	7.45661			0.317662
$552$			54.9733i			2.33982i
$553$	24.5486			1.04391
$554$	16.7709			0.712528
$555$		0			0
$556$	−76.3750			−3.23902
$557$	12.6204			0.534744			0.267372	−	0.963593i	$-0.413845\pi$
$557$	12.6204			0.534744			0.267372	+	0.963593i	$0.413845\pi$
$558$		−	41.0472i		−	1.73767i
$559$	−18.8771			−0.798415
$560$		0			0
$561$			0.334210i			0.0141104i
$562$			8.45307i			0.356571i
$563$	45.9241			1.93547			0.967734	−	0.251973i	$-0.0810795\pi$
$563$	45.9241			1.93547			0.967734	+	0.251973i	$0.0810795\pi$
$564$	123.486			5.19971
$565$		0			0
$566$	38.8826			1.63436
$567$			7.12369i			0.299167i
$568$	32.7559			1.37441
$569$		−	0.838147i		−	0.0351370i	−0.999846	−	0.0175685i	$-0.994407\pi$
$569$		−	0.838147i		−	0.0351370i	0.999846	−	0.0175685i	$-0.00559251\pi$
$570$		0			0
$571$	−7.23047			−0.302586			−0.151293	−	0.988489i	$-0.548344\pi$
$571$	−7.23047			−0.302586			−0.151293	+	0.988489i	$0.548344\pi$
$572$	−84.5994			−3.53728
$573$	−67.7674			−2.83102
$574$		−	1.89118i		−	0.0789364i
$575$		0			0
$576$	−194.950			−8.12290
$577$	20.4356			0.850746			0.425373	−	0.905018i	$-0.360143\pi$
$577$	20.4356			0.850746			0.425373	+	0.905018i	$0.360143\pi$
$578$	−46.8328			−1.94799
$579$		−	48.3094i		−	2.00767i
$580$		0			0
$581$	−20.5378			−0.852050
$582$		−	63.2863i		−	2.62330i
$583$		−	35.2178i		−	1.45857i
$584$			13.3112i			0.550823i
$585$		0			0
$586$			30.4538i			1.25804i
$587$	−13.3566			−0.551286			−0.275643	−	0.961260i	$-0.588891\pi$
$587$	−13.3566			−0.551286			−0.275643	+	0.961260i	$0.588891\pi$
$588$		−	79.8377i		−	3.29245i
$589$	6.28660			0.259035
$590$		0			0
$591$	36.3852			1.49669
$592$	−75.9887	+	61.4588i	−3.12312	+	2.52594i
$593$			36.0953i			1.48226i	0.671363	+	0.741129i	$0.265709\pi$
$593$			36.0953i			1.48226i	−0.671363	+	0.741129i	$0.734291\pi$
$594$		−	91.0604i		−	3.73625i
$595$		0			0
$596$	−58.5723			−2.39922
$597$	45.5659			1.86489
$598$	−17.6674			−0.722473
$599$	−6.63975			−0.271293			−0.135646	−	0.990757i	$-0.543311\pi$
$599$	−6.63975			−0.271293			−0.135646	+	0.990757i	$0.543311\pi$
$600$		0			0
$601$	40.7974			1.66416			0.832080	−	0.554656i	$-0.187150\pi$
$601$	40.7974			1.66416			0.832080	+	0.554656i	$0.187150\pi$
$602$		−	22.4156i		−	0.913593i
$603$			21.4364i			0.872959i
$604$	−29.7926			−1.21224
$605$		0			0
$606$		−	107.917i		−	4.38381i
$607$	11.0949			0.450327			0.225164	−	0.974321i	$-0.427708\pi$
$607$	11.0949			0.450327			0.225164	+	0.974321i	$0.427708\pi$
$608$		−	57.0227i		−	2.31258i
$609$			13.5644i			0.549656i
$610$		0			0
$611$			25.4869i			1.03109i
$612$	−0.786088			−0.0317757
$613$		−	22.9251i		−	0.925935i	−0.886375	−	0.462968i	$-0.846785\pi$
$613$		−	22.9251i		−	0.925935i	0.886375	−	0.462968i	$-0.153215\pi$
$614$		−	21.6587i		−	0.874072i
$615$		0			0
$616$		−	64.5150i		−	2.59938i
$617$			13.1796i			0.530589i	0.964167	+	0.265294i	$0.0854692\pi$
$617$			13.1796i			0.530589i	−0.964167	+	0.265294i	$0.914531\pi$
$618$			40.2153i			1.61770i
$619$	−18.1736			−0.730460			−0.365230	−	0.930917i	$-0.619010\pi$
$619$	−18.1736			−0.730460			−0.365230	+	0.930917i	$0.619010\pi$
$620$		0			0
$621$		−	14.0056i		−	0.562025i
$622$		−	71.2764i		−	2.85792i
$623$	15.5441			0.622763
$624$		−	157.927i		−	6.32216i
$625$		0			0
$626$	−18.2583			−0.729750
$627$	30.5513			1.22010
$628$		−	47.5129i		−	1.89597i
$629$	−0.120495	+	0.0974550i	−0.00480445	+	0.00388579i
$630$		0			0
$631$			6.22219i			0.247701i	0.992301	+	0.123851i	$0.0395244\pi$
$631$			6.22219i			0.247701i	−0.992301	+	0.123851i	$0.960476\pi$
$632$		−	167.268i		−	6.65357i
$633$			68.1245i			2.70771i
$634$		−	42.6877i		−	1.69534i
$635$		0			0
$636$	127.857			5.06984
$637$	16.4780			0.652884
$638$		−	39.6413i		−	1.56941i
$639$	−18.2813			−0.723197
$640$		0			0
$641$	−9.36090			−0.369733			−0.184867	−	0.982764i	$-0.559185\pi$
$641$	−9.36090			−0.369733			−0.184867	+	0.982764i	$0.559185\pi$
$642$	−78.6267			−3.10315
$643$	−18.6445			−0.735267			−0.367634	−	0.929971i	$-0.619832\pi$
$643$	−18.6445			−0.735267			−0.367634	+	0.929971i	$0.619832\pi$
$644$		−	15.4510i		−	0.608853i
$645$		0			0
$646$		−	0.163469i		−	0.00643161i
$647$	−26.2257			−1.03104			−0.515518	−	0.856878i	$-0.672401\pi$
$647$	−26.2257			−1.03104			−0.515518	+	0.856878i	$0.672401\pi$
$648$	48.5391			1.90680
$649$		−	40.3405i		−	1.58350i
$650$		0			0
$651$			11.4360i			0.448211i
$652$	−103.285			−4.04494
$653$	12.3086			0.481672			0.240836	−	0.970566i	$-0.422578\pi$
$653$	12.3086			0.481672			0.240836	+	0.970566i	$0.422578\pi$
$654$	−126.691			−4.95402
$655$		0			0
$656$	−7.59870			−0.296680
$657$		−	7.42910i		−	0.289837i
$658$	−30.2644			−1.17983
$659$	38.3036			1.49209			0.746047	−	0.665893i	$-0.231949\pi$
$659$	38.3036			1.49209			0.746047	+	0.665893i	$0.231949\pi$
$660$		0			0
$661$		−	6.34290i		−	0.246710i	−0.992363	−	0.123355i	$-0.960635\pi$
$661$		−	6.34290i		−	0.246710i	0.992363	−	0.123355i	$-0.0393654\pi$
$662$		−	51.1488i		−	1.98796i
$663$		−	0.250425i		−	0.00972571i
$664$			139.939i			5.43070i
$665$		0			0
$666$	71.9195	−	58.1677i	2.78682	−	2.25395i
$667$		−	6.09706i		−	0.236079i
$668$	−43.5619			−1.68546
$669$	−29.6250			−1.14537
$670$		0			0
$671$			36.1949i			1.39729i
$672$	103.730			4.00148
$673$		−	13.2262i		−	0.509834i	−0.966963	−	0.254917i	$-0.917952\pi$
$673$		−	13.2262i		−	0.509834i	0.966963	−	0.254917i	$-0.0820481\pi$
$674$			79.9199i			3.07840i
$675$		0			0
$676$	−9.27771			−0.356835
$677$		−	38.0754i		−	1.46336i	−0.681650	−	0.731679i	$-0.738737\pi$
$677$		−	38.0754i		−	1.46336i	0.681650	−	0.731679i	$-0.261263\pi$
$678$		−	36.9761i		−	1.42006i
$679$			11.4233i			0.438385i
$680$		0			0
$681$		−	5.73507i		−	0.219768i
$682$		−	33.4212i		−	1.27976i
$683$	−30.6935			−1.17445			−0.587226	−	0.809423i	$-0.699780\pi$
$683$	−30.6935			−1.17445			−0.587226	+	0.809423i	$0.699780\pi$
$684$			71.8590i			2.74760i
$685$		0			0
$686$			47.5584i			1.81579i
$687$			71.3839i			2.72347i
$688$	−90.0652			−3.43371
$689$			26.3889i			1.00534i
$690$		0			0
$691$	7.67193			0.291854			0.145927	−	0.989295i	$-0.453384\pi$
$691$	7.67193			0.291854			0.145927	+	0.989295i	$0.453384\pi$
$692$			12.4172i			0.472030i
$693$			36.0063i			1.36777i
$694$	−85.7082			−3.25344
$695$		0			0
$696$	92.4243			3.50333
$697$	−0.0120492			−0.000456398
$698$	−32.6827			−1.23706
$699$	26.2637			0.993386
$700$		0			0
$701$		−	8.14310i		−	0.307561i	−0.988105	−	0.153780i	$-0.950855\pi$
$701$		−	8.14310i		−	0.307561i	0.988105	−	0.153780i	$-0.0491448\pi$
$702$			68.2319i			2.57525i
$703$	8.90870	+	11.0149i	0.335998	+	0.415434i
$704$	−158.731			−5.98239
$705$		0			0
$706$	93.0094			3.50046
$707$			19.4791i			0.732588i
$708$	146.454			5.50409
$709$			27.4696i			1.03164i	0.856696	+	0.515821i	$0.172513\pi$
$709$			27.4696i			1.03164i	−0.856696	+	0.515821i	$0.827487\pi$
$710$		0			0
$711$			93.3536i			3.50103i
$712$		−	105.914i		−	3.96929i
$713$		−	5.14037i		−	0.192508i
$714$	0.297368			0.0111287
$715$		0			0
$716$			144.614i			5.40447i
$717$	−45.9478			−1.71595
$718$	−25.4801			−0.950908
$719$	20.5876			0.767787			0.383893	−	0.923377i	$-0.374583\pi$
$719$	20.5876			0.767787			0.383893	+	0.923377i	$0.374583\pi$
$720$		0			0
$721$		−	7.25892i		−	0.270336i
$722$	37.4012			1.39193
$723$	−19.9813			−0.743112
$724$	31.8415			1.18338
$725$		0			0
$726$		−	73.9638i		−	2.74505i
$727$	50.8446			1.88572			0.942862	−	0.333185i	$-0.108123\pi$
$727$	50.8446			1.88572			0.942862	+	0.333185i	$0.108123\pi$
$728$			48.3414i			1.79165i
$729$	37.3108			1.38188
$730$		0			0
$731$	−0.142816			−0.00528225
$732$	−131.404			−4.85683
$733$			38.4050i			1.41852i	0.704946	+	0.709261i	$0.250971\pi$
$733$			38.4050i			1.41852i	−0.704946	+	0.709261i	$0.749029\pi$
$734$		−	20.3515i		−	0.751187i
$735$		0			0
$736$	−46.6258			−1.71865
$737$			17.4539i			0.642921i
$738$	7.19180			0.264734
$739$	18.6887			0.687475			0.343737	−	0.939066i	$-0.388307\pi$
$739$	18.6887			0.687475			0.343737	+	0.939066i	$0.388307\pi$
$740$		0			0
$741$	−22.8922			−0.840967
$742$	−31.3355			−1.15036
$743$		−	16.0098i		−	0.587343i	−0.955906	−	0.293672i	$-0.905123\pi$
$743$		−	16.0098i		−	0.587343i	0.955906	−	0.293672i	$-0.0948772\pi$
$744$	77.9220			2.85676
$745$		0			0
$746$		−	42.1601i		−	1.54359i
$747$		−	78.1012i		−	2.85757i
$748$	−0.640044			−0.0234023
$749$	14.1922			0.518573
$750$		0			0
$751$	−0.921894			−0.0336404			−0.0168202	−	0.999859i	$-0.505354\pi$
$751$	−0.921894			−0.0336404			−0.0168202	+	0.999859i	$0.505354\pi$
$752$			121.602i			4.43435i
$753$	25.9632			0.946153
$754$			29.7034i			1.08173i
$755$		0			0
$756$	−59.6721			−2.17025
$757$	−32.1248			−1.16760			−0.583798	−	0.811899i	$-0.698434\pi$
$757$	−32.1248			−1.16760			−0.583798	+	0.811899i	$0.698434\pi$
$758$	40.9317			1.48671
$759$		−	24.9809i		−	0.906749i
$760$		0			0
$761$	10.7066			0.388113			0.194056	−	0.980990i	$-0.437836\pi$
$761$	10.7066			0.388113			0.194056	+	0.980990i	$0.437836\pi$
$762$	−92.9169			−3.36602
$763$	22.8680			0.827876
$764$		−	129.781i		−	4.69531i
$765$		0			0
$766$	−30.5791			−1.10487
$767$			30.2273i			1.09144i
$768$		−	182.495i		−	6.58521i
$769$		−	50.6597i		−	1.82683i	−0.407025	−	0.913417i	$-0.633434\pi$
$769$		−	50.6597i		−	1.82683i	0.407025	−	0.913417i	$-0.366566\pi$
$770$		0			0
$771$		−	70.5537i		−	2.54093i
$772$	92.5172			3.32977
$773$			39.2085i			1.41023i	0.709092	+	0.705116i	$0.249105\pi$
$773$			39.2085i			1.41023i	−0.709092	+	0.705116i	$0.750895\pi$
$774$	85.2423			3.06397
$775$		0			0
$776$	77.8355			2.79413
$777$	−20.0372	+	16.2059i	−0.718830	+	0.581382i
$778$		−	20.6721i		−	0.741130i
$779$			1.10146i			0.0394640i
$780$		0			0
$781$	−14.8849			−0.532624
$782$	−0.133664			−0.00477982
$783$	−23.5470			−0.841502
$784$	78.6191			2.80783
$785$		0			0
$786$	−58.5642			−2.08892
$787$		−	20.7482i		−	0.739592i	−0.929113	−	0.369796i	$-0.879428\pi$
$787$		−	20.7482i		−	0.739592i	0.929113	−	0.369796i	$-0.120572\pi$
$788$			69.6810i			2.48228i
$789$	−25.8343			−0.919726
$790$		0			0
$791$			6.67424i			0.237309i
$792$	245.338			8.71771
$793$		−	27.1210i		−	0.963095i
$794$			34.6030i			1.22801i
$795$		0			0
$796$			87.2631i			3.09296i
$797$	−33.9237			−1.20164			−0.600819	−	0.799385i	$-0.705159\pi$
$797$	−33.9237			−1.20164			−0.600819	+	0.799385i	$0.705159\pi$
$798$		−	27.1834i		−	0.962282i
$799$			0.192823i			0.00682160i
$800$		0			0
$801$			59.1114i			2.08860i
$802$		−	31.5058i		−	1.11251i
$803$		−	6.04888i		−	0.213460i
$804$	−63.3654			−2.23473
$805$		0			0
$806$			25.0427i			0.882090i
$807$			26.6192i			0.937041i
$808$	132.726			4.66929
$809$		−	11.3402i		−	0.398701i	−0.979928	−	0.199350i	$-0.936117\pi$
$809$		−	11.3402i		−	0.398701i	0.979928	−	0.199350i	$-0.0638832\pi$
$810$		0			0
$811$	5.91038			0.207541			0.103771	−	0.994601i	$-0.466909\pi$
$811$	5.91038			0.207541			0.103771	+	0.994601i	$0.466909\pi$
$812$	−25.9770			−0.911616
$813$		−	68.9161i		−	2.41699i
$814$	58.5579	−	47.3610i	2.05245	−	1.66000i
$815$		0			0
$816$		−	1.19481i		−	0.0418269i
$817$			13.0553i			0.456748i
$818$		−	88.9524i		−	3.11015i
$819$		−	26.9797i		−	0.942745i
$820$		0			0
$821$	−52.3144			−1.82579			−0.912893	−	0.408200i	$-0.866157\pi$
$821$	−52.3144			−1.82579			−0.912893	+	0.408200i	$0.866157\pi$
$822$	86.1359			3.00434
$823$		−	0.226046i		−	0.00787948i	−0.999992	−	0.00393974i	$-0.998746\pi$
$823$		−	0.226046i		−	0.00787948i	0.999992	−	0.00393974i	$-0.00125406\pi$
$824$	−49.4606			−1.72304
$825$		0			0
$826$	−35.8935			−1.24889
$827$	18.6949			0.650084			0.325042	−	0.945700i	$-0.394621\pi$
$827$	18.6949			0.650084			0.325042	+	0.945700i	$0.394621\pi$
$828$	58.7570			2.04195
$829$			8.63683i			0.299969i	0.988688	+	0.149985i	$0.0479224\pi$
$829$			8.63683i			0.299969i	−0.988688	+	0.149985i	$0.952078\pi$
$830$		0			0
$831$		−	17.7685i		−	0.616383i
$832$	118.938			4.12342
$833$	0.124666			0.00431943
$834$			109.870i			3.80448i
$835$		0			0
$836$			58.5087i			2.02356i
$837$	−19.8523			−0.686194
$838$	66.8528			2.30939
$839$	26.0271			0.898554			0.449277	−	0.893393i	$-0.351682\pi$
$839$	26.0271			0.898554			0.449277	+	0.893393i	$0.351682\pi$
$840$		0			0
$841$	18.7493			0.646527
$842$			97.8538i			3.37227i
$843$	8.95589			0.308457
$844$	−130.465			−4.49079
$845$		0			0
$846$		−	115.090i		−	3.95687i
$847$			13.3506i			0.458732i
$848$			125.905i			4.32360i
$849$		−	41.1955i		−	1.41382i
$850$		0			0
$851$	9.00654	−	7.28438i	0.308740	−	0.249705i
$852$		−	54.0389i		−	1.85134i
$853$	−0.625659			−0.0214222			−0.0107111	−	0.999943i	$-0.503410\pi$
$853$	−0.625659			−0.0214222			−0.0107111	+	0.999943i	$0.503410\pi$
$854$	32.2049			1.10203
$855$		0			0
$856$		−	96.7025i		−	3.30523i
$857$	−33.7157			−1.15171			−0.575853	−	0.817553i	$-0.695330\pi$
$857$	−33.7157			−1.15171			−0.575853	+	0.817553i	$0.695330\pi$
$858$			121.701i			4.15480i
$859$		−	40.4148i		−	1.37894i	−0.724316	−	0.689468i	$-0.757845\pi$
$859$		−	40.4148i		−	1.37894i	0.724316	−	0.689468i	$-0.242155\pi$
$860$		0			0
$861$	−2.00368			−0.0682851
$862$			39.9611i			1.36108i
$863$			48.2173i			1.64134i	0.571406	+	0.820668i	$0.306398\pi$
$863$			48.2173i			1.64134i	−0.571406	+	0.820668i	$0.693602\pi$
$864$			180.070i			6.12611i
$865$		0			0
$866$			68.1022i			2.31421i
$867$			49.6186i			1.68513i
$868$	−21.9010			−0.743368
$869$			76.0099i			2.57846i
$870$		0			0
$871$		−	13.0783i		−	0.443140i
$872$		−	155.817i		−	5.27662i
$873$	−43.4405			−1.47024
$874$			12.2187i			0.413303i
$875$		0			0
$876$	21.9602			0.741966
$877$		−	41.7183i		−	1.40873i	−0.709839	−	0.704364i	$-0.751232\pi$
$877$		−	41.7183i		−	1.40873i	0.709839	−	0.704364i	$-0.248768\pi$
$878$			22.4244i			0.756788i
$879$	32.2653			1.08828
$880$		0			0
$881$	−26.5652			−0.895004			−0.447502	−	0.894283i	$-0.647686\pi$
$881$	−26.5652			−0.895004			−0.447502	+	0.894283i	$0.647686\pi$
$882$	−74.4091			−2.50548
$883$	−25.2500			−0.849729			−0.424864	−	0.905257i	$-0.639678\pi$
$883$	−25.2500			−0.849729			−0.424864	+	0.905257i	$0.639678\pi$
$884$	0.479588			0.0161303
$885$		0			0
$886$		−	15.1547i		−	0.509132i
$887$			44.1343i			1.48188i	0.671569	+	0.740942i	$0.265621\pi$
$887$			44.1343i			1.48188i	−0.671569	+	0.740942i	$0.734379\pi$
$888$	110.423	+	136.529i	3.70555	+	4.58160i
$889$	16.7716			0.562503
$890$		0			0
$891$	−22.0571			−0.738940
$892$		−	56.7348i		−	1.89962i
$893$	17.6266			0.589853
$894$			84.2596i			2.81806i
$895$		0			0
$896$			70.1567i			2.34377i
$897$			18.7183i			0.624986i
$898$		−	21.3019i		−	0.710855i
$899$	−8.64228			−0.288236
$900$		0			0
$901$			0.199647i			0.00665122i
$902$	5.85566			0.194972
$903$	−23.7490			−0.790317
$904$	45.4767			1.51253
$905$		0			0
$906$			42.8584i			1.42387i
$907$	13.5822			0.450989			0.225494	−	0.974244i	$-0.427600\pi$
$907$	13.5822			0.450989			0.225494	+	0.974244i	$0.427600\pi$
$908$	10.9832			0.364491
$909$	−74.0753			−2.45692
$910$		0			0
$911$		−	10.9249i		−	0.361958i	−0.983487	−	0.180979i	$-0.942073\pi$
$911$		−	10.9249i		−	0.361958i	0.983487	−	0.180979i	$-0.0579265\pi$
$912$	−109.222			−3.61670
$913$		−	63.5911i		−	2.10456i
$914$	−2.18667			−0.0723287
$915$		0			0
$916$	−136.707			−4.51693
$917$	10.5709			0.349083
$918$			0.516215i			0.0170376i
$919$		−	19.8094i		−	0.653452i	−0.945119	−	0.326726i	$-0.894055\pi$
$919$		−	19.8094i		−	0.653452i	0.945119	−	0.326726i	$-0.105945\pi$
$920$		0			0
$921$	−22.9470			−0.756130
$922$			3.69968i			0.121843i
$923$	11.1533			0.367116
$924$	−106.433			−3.50140
$925$		0			0
$926$	95.2125			3.12888
$927$	27.6043			0.906644
$928$			78.3900i			2.57328i
$929$	−45.0292			−1.47736			−0.738680	−	0.674056i	$-0.764551\pi$
$929$	−45.0292			−1.47736			−0.738680	+	0.674056i	$0.764551\pi$
$930$		0			0
$931$		−	11.3962i		−	0.373494i
$932$			50.2976i			1.64755i
$933$	−75.5162			−2.47229
$934$	−41.5081			−1.35819
$935$		0			0
$936$	−183.833			−6.00876
$937$			7.84999i			0.256448i	0.991745	+	0.128224i	$0.0409276\pi$
$937$			7.84999i			0.256448i	−0.991745	+	0.128224i	$0.959072\pi$
$938$	15.5298			0.507066
$939$			19.3444i			0.631281i
$940$		0			0
$941$	25.0461			0.816479			0.408239	−	0.912875i	$-0.366143\pi$
$941$	25.0461			0.816479			0.408239	+	0.912875i	$0.366143\pi$
$942$	−68.3499			−2.22696
$943$	0.900634			0.0293287
$944$			144.219i			4.69392i
$945$		0			0
$946$	69.4055			2.25657
$947$	−0.776901			−0.0252459			−0.0126229	−	0.999920i	$-0.504018\pi$
$947$	−0.776901			−0.0252459			−0.0126229	+	0.999920i	$0.504018\pi$
$948$	−275.950			−8.96244
$949$			4.53245i			0.147130i
$950$		0			0
$951$	−45.2269			−1.46658
$952$			0.365731i			0.0118534i
$953$			6.91778i			0.224089i	0.993703	+	0.112045i	$0.0357399\pi$
$953$			6.91778i			0.224089i	−0.993703	+	0.112045i	$0.964260\pi$
$954$		−	119.163i		−	3.85804i
$955$		0			0
$956$		−	87.9944i		−	2.84594i
$957$	−41.9993			−1.35765
$958$		−	55.4557i		−	1.79169i
$959$	−15.5477			−0.502061
$960$		0			0
$961$	23.7138			0.764960
$962$	−43.8777	+	35.4878i	−1.41467	+	1.14417i
$963$			53.9704i			1.73917i
$964$		−	38.2661i		−	1.23247i
$965$		0			0
$966$	−22.2271			−0.715145
$967$	50.9043			1.63697			0.818486	−	0.574526i	$-0.194814\pi$
$967$	50.9043			1.63697			0.818486	+	0.574526i	$0.194814\pi$
$968$	90.9677			2.92381
$969$	−0.173193			−0.00556377
$970$		0			0
$971$	−27.7895			−0.891806			−0.445903	−	0.895081i	$-0.647117\pi$
$971$	−27.7895			−0.891806			−0.445903	+	0.895081i	$0.647117\pi$
$972$			43.2566i			1.38746i
$973$		−	19.8317i		−	0.635774i
$974$	−8.72795			−0.279662
$975$		0			0
$976$		−	129.398i		−	4.14193i
$977$	−25.9080			−0.828871			−0.414436	−	0.910079i	$-0.636021\pi$
$977$	−25.9080			−0.828871			−0.414436	+	0.910079i	$0.636021\pi$
$978$			148.581i			4.75109i
$979$			48.1293i			1.53822i
$980$		0			0
$981$			86.9624i			2.77650i
$982$	22.5221			0.718709
$983$			38.9012i			1.24076i	0.784303	+	0.620379i	$0.213021\pi$
$983$			38.9012i			1.24076i	−0.784303	+	0.620379i	$0.786979\pi$
$984$			13.6526i			0.435228i
$985$		0			0
$986$			0.224724i			0.00715666i
$987$			32.0647i			1.02063i
$988$		−	43.8408i		−	1.39476i
$989$	10.6750			0.339444
$990$		0			0
$991$		−	35.5867i		−	1.13045i	−0.824937	−	0.565225i	$-0.808789\pi$
$991$		−	35.5867i		−	1.13045i	0.824937	−	0.565225i	$-0.191211\pi$
$992$			66.0898i			2.09835i
$993$	−54.1914			−1.71971
$994$			13.2440i			0.420075i
$995$		0			0
$996$	230.864			7.31522
$997$	27.5414			0.872244			0.436122	−	0.899887i	$-0.356352\pi$
$997$	27.5414			0.872244			0.436122	+	0.899887i	$0.356352\pi$
$998$			54.2568i			1.71747i
$999$	−28.1325	−	34.7835i	−0.890073	−	1.10050i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.d.f.924.11		12
5.2	odd	4		925.2.c.c.776.12		12
5.3	odd	4		185.2.c.b.36.1	✓	12
5.4	even	2		925.2.d.e.924.2		12
15.8	even	4		1665.2.e.e.406.12		12
20.3	even	4		2960.2.p.h.961.1		12
37.36	even	2		925.2.d.e.924.1		12
185.43	even	4		6845.2.a.h.1.1		6
185.68	even	4		6845.2.a.i.1.6		6
185.73	odd	4		185.2.c.b.36.12	yes	12
185.147	odd	4		925.2.c.c.776.1		12
185.184	even	2	inner	925.2.d.f.924.12		12
555.443	even	4		1665.2.e.e.406.1		12
740.443	even	4		2960.2.p.h.961.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.c.b.36.1	✓	12	5.3	odd	4
185.2.c.b.36.12	yes	12	185.73	odd	4
925.2.c.c.776.1		12	185.147	odd	4
925.2.c.c.776.12		12	5.2	odd	4
925.2.d.e.924.1		12	37.36	even	2
925.2.d.e.924.2		12	5.4	even	2
925.2.d.f.924.11		12	1.1	even	1	trivial
925.2.d.f.924.12		12	185.184	even	2	inner
1665.2.e.e.406.1		12	555.443	even	4
1665.2.e.e.406.12		12	15.8	even	4
2960.2.p.h.961.1		12	20.3	even	4
2960.2.p.h.961.2		12	740.443	even	4
6845.2.a.h.1.1		6	185.43	even	4
6845.2.a.i.1.6		6	185.68	even	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+2.75497 q^{2} -2.91885i q^{3} +5.58988 q^{4} -8.04135i q^{6} +1.45148i q^{7} +9.89002 q^{8} -5.51969 q^{9} -4.49421 q^{11} -16.3160i q^{12} +3.36753 q^{13} +3.99878i q^{14} +16.0670 q^{16} +0.0254774 q^{17} -15.2066 q^{18} -2.32897i q^{19} +4.23665 q^{21} -12.3814 q^{22} -1.90433 q^{23} -28.8675i q^{24} +9.27746 q^{26} +7.35459i q^{27} +8.11358i q^{28} +3.20167i q^{29} +2.69930i q^{31} +24.4840 q^{32} +13.1179i q^{33} +0.0701894 q^{34} -30.8544 q^{36} +(-4.72950 + 3.82516i) q^{37} -6.41626i q^{38} -9.82932i q^{39} -0.472939 q^{41} +11.6718 q^{42} -5.60561 q^{43} -25.1221 q^{44} -5.24639 q^{46} +7.56842i q^{47} -46.8971i q^{48} +4.89321 q^{49} -0.0743646i q^{51} +18.8241 q^{52} +7.83626i q^{53} +20.2617i q^{54} +14.3551i q^{56} -6.79792 q^{57} +8.82053i q^{58} +8.97610i q^{59} -8.05367i q^{61} +7.43650i q^{62} -8.01170i q^{63} +35.3190 q^{64} +36.1395i q^{66} -3.88363i q^{67} +0.142415 q^{68} +5.55846i q^{69} +3.31202 q^{71} -54.5898 q^{72} +1.34593i q^{73} +(-13.0296 + 10.5382i) q^{74} -13.0187i q^{76} -6.52324i q^{77} -27.0795i q^{78} -16.9128i q^{79} +4.90789 q^{81} -1.30294 q^{82} +14.1496i q^{83} +23.6823 q^{84} -15.4433 q^{86} +9.34521 q^{87} -44.4478 q^{88} -10.7092i q^{89} +4.88790i q^{91} -10.6450 q^{92} +7.87886 q^{93} +20.8508i q^{94} -71.4653i q^{96} +7.87010 q^{97} +13.4807 q^{98} +24.8066 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} + 18 q^{4} + 6 q^{8} - 22 q^{9} + 2 q^{11} + 20 q^{13} + 30 q^{16} + 12 q^{17} - 26 q^{18} - 6 q^{21} - 28 q^{22} - 16 q^{23} - 12 q^{26} + 14 q^{32} - 4 q^{34} - 22 q^{36} - 14 q^{37} - 10 q^{41}+ \cdots + 84 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 + 18 * q^4 + 6 * q^8 - 22 * q^9 + 2 * q^11 + 20 * q^13 + 30 * q^16 + 12 * q^17 - 26 * q^18 - 6 * q^21 - 28 * q^22 - 16 * q^23 - 12 * q^26 + 14 * q^32 - 4 * q^34 - 22 * q^36 - 14 * q^37 - 10 * q^41 + 72 * q^42 - 12 * q^43 - 44 * q^44 - 24 * q^46 - 30 * q^49 + 80 * q^52 - 32 * q^57 + 126 * q^64 - 40 * q^68 + 42 * q^71 - 178 * q^72 - 50 * q^74 - 12 * q^81 + 96 * q^82 + 84 * q^84 - 64 * q^86 - 56 * q^87 - 72 * q^88 + 16 * q^92 + 76 * q^93 - 28 * q^97 + 118 * q^98 + 84 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more