LMFDB - Embedded newform 891.2.bb.a.8.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [891,2,Mod(8,891)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("891.8"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(891, base_ring=CyclotomicField(90)) chi = DirichletCharacter(H, H._module([5, 27])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.bb (of order $90$, degree $24$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$816$
Relative dimension:	$34$ over $\Q(\zeta_{90})$
Twist minimal:	no (minimal twist has level 297)
Sato-Tate group:	$\mathrm{SU}(2)[C_{90}]$

Embedding invariants

Embedding label			8.19
Character	$\chi$	$=$	891.8
Dual form			891.2.bb.a.557.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.234840 + 0.481493i) q^{2} +(1.05464 - 1.34987i) q^{4} +(0.140627 + 2.01106i) q^{5} +(2.77243 - 0.0968153i) q^{7} +(1.94563 + 0.413557i) q^{8} +(-0.935288 + 0.539989i) q^{10} +(3.28509 - 0.456240i) q^{11} +(-4.91714 + 5.09185i) q^{13} +(0.697692 + 1.31217i) q^{14} +(-0.571045 - 2.29034i) q^{16} +(-0.389206 + 3.70304i) q^{17} +(-0.350554 + 1.64923i) q^{19} +(2.86299 + 1.93111i) q^{20} +(0.991147 + 1.47461i) q^{22} +(1.79865 - 4.94174i) q^{23} +(0.926739 - 0.130245i) q^{25} +(-3.60642 - 1.17180i) q^{26} +(2.79322 - 3.84453i) q^{28} +(-5.13875 - 2.73232i) q^{29} +(7.22978 - 2.07311i) q^{31} +(4.01615 - 3.36995i) q^{32} +(-1.87439 + 0.682222i) q^{34} +(0.584581 + 5.56191i) q^{35} +(-4.00581 + 0.851461i) q^{37} +(-0.876416 + 0.218515i) q^{38} +(-0.558080 + 3.97095i) q^{40} +(2.17784 - 1.15798i) q^{41} +(0.620430 - 0.739399i) q^{43} +(2.84872 - 4.91563i) q^{44} +(2.80180 - 0.294481i) q^{46} +(-7.38871 + 5.77269i) q^{47} +(0.694030 - 0.0485313i) q^{49} +(0.280347 + 0.415631i) q^{50} +(1.68755 + 12.0076i) q^{52} +(2.90818 + 4.00277i) q^{53} +(1.37950 + 6.54237i) q^{55} +(5.43416 + 0.958189i) q^{56} +(0.108811 - 3.11593i) q^{58} +(8.00230 - 3.23314i) q^{59} +(-0.503892 + 1.75728i) q^{61} +(2.69602 + 2.99424i) q^{62} +(-1.74700 - 0.777815i) q^{64} +(-10.9315 - 9.17262i) q^{65} +(-0.347986 - 1.97353i) q^{67} +(4.58817 + 4.43075i) q^{68} +(-2.54074 + 1.58763i) q^{70} +(7.93671 + 0.834182i) q^{71} +(-10.1495 + 9.13863i) q^{73} +(-1.35070 - 1.72881i) q^{74} +(1.85654 + 2.21254i) q^{76} +(9.06351 - 1.58294i) q^{77} +(14.2775 - 6.96360i) q^{79} +(4.52571 - 1.47049i) q^{80} +(1.06900 + 0.776676i) q^{82} +(4.39047 - 4.23982i) q^{83} +(-7.50179 - 0.261968i) q^{85} +(0.501717 + 0.125092i) q^{86} +(6.58026 + 0.470898i) q^{88} +(-9.25241 - 5.34188i) q^{89} +(-13.1394 + 14.5928i) q^{91} +(-4.77381 - 7.63969i) q^{92} +(-4.51467 - 2.20195i) q^{94} +(-3.36600 - 0.473061i) q^{95} +(-2.52904 - 0.176848i) q^{97} +(0.186353 + 0.322773i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 816 q + 30 q^{2} - 18 q^{4} + 21 q^{5} - 30 q^{7} + 45 q^{8} + 33 q^{11} - 30 q^{13} + 18 q^{14} - 30 q^{16} + 45 q^{17} - 15 q^{19} + 60 q^{20} - 15 q^{22} + 84 q^{23} - 27 q^{25} - 60 q^{28} - 60 q^{29}+ \cdots - 81 q^{97}+O(q^{100}) $ 816 * q + 30 * q^2 - 18 * q^4 + 21 * q^5 - 30 * q^7 + 45 * q^8 + 33 * q^11 - 30 * q^13 + 18 * q^14 - 30 * q^16 + 45 * q^17 - 15 * q^19 + 60 * q^20 - 15 * q^22 + 84 * q^23 - 27 * q^25 - 60 * q^28 - 60 * q^29 - 9 * q^31 - 42 * q^34 + 45 * q^35 - 9 * q^37 + 18 * q^38 - 90 * q^40 + 30 * q^41 + 108 * q^44 - 15 * q^46 + 6 * q^47 - 18 * q^49 + 105 * q^50 - 30 * q^52 - 48 * q^55 - 54 * q^56 - 18 * q^58 - 81 * q^59 - 30 * q^61 + 45 * q^62 + 51 * q^64 + 6 * q^67 + 225 * q^68 - 93 * q^70 + 27 * q^71 - 15 * q^73 + 30 * q^74 + 141 * q^77 - 30 * q^79 - 36 * q^82 - 15 * q^83 - 30 * q^85 - 93 * q^86 - 108 * q^88 - 54 * q^89 - 9 * q^91 - 276 * q^92 - 30 * q^94 - 90 * q^95 - 81 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{18}\right)$

Coefficient data

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

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

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

$2$	0.234840	+	0.481493i	0.166057	+	0.340467i	0.965554	−	0.260203i	$-0.0837895\pi$
$2$	0.234840	+	0.481493i	0.166057	+	0.340467i	−0.799497	+	0.600670i	$0.794901\pi$
$3$		0			0
$3$		0			0
$4$	1.05464	−	1.34987i	0.527319	−	0.674937i
$5$	0.140627	+	2.01106i	0.0628904	+	0.899375i	0.921903	+	0.387421i	$0.126634\pi$
$5$	0.140627	+	2.01106i	0.0628904	+	0.899375i	−0.859013	+	0.511954i	$0.828922\pi$
$6$		0			0
$7$	2.77243	−	0.0968153i	1.04788	−	0.0365927i	0.494220	−	0.869337i	$-0.335454\pi$
$7$	2.77243	−	0.0968153i	1.04788	−	0.0365927i	0.553658	+	0.832744i	$0.313231\pi$
$8$	1.94563	+	0.413557i	0.687885	+	0.146214i
$9$		0			0
$10$	−0.935288	+	0.539989i	−0.295764	+	0.170759i
$11$	3.28509	−	0.456240i	0.990493	−	0.137562i
$11$	3.28509	−	0.456240i	0.990493	−	0.137562i
$12$		0			0
$13$	−4.91714	+	5.09185i	−1.36377	+	1.41222i	−0.544568	+	0.838717i	$0.683306\pi$
$13$	−4.91714	+	5.09185i	−1.36377	+	1.41222i	−0.819201	+	0.573507i	$0.805583\pi$
$14$	0.697692	+	1.31217i	0.186466	+	0.350691i
$15$		0			0
$16$	−0.571045	−	2.29034i	−0.142761	−	0.572584i
$17$	−0.389206	+	3.70304i	−0.0943962	+	0.898120i	0.840168	+	0.542326i	$0.182456\pi$
$17$	−0.389206	+	3.70304i	−0.0943962	+	0.898120i	−0.934564	+	0.355794i	$0.884210\pi$
$18$		0			0
$19$	−0.350554	+	1.64923i	−0.0804227	+	0.378359i	−0.999890	−	0.0148065i	$-0.995287\pi$
$19$	−0.350554	+	1.64923i	−0.0804227	+	0.378359i	0.919468	+	0.393166i	$0.128620\pi$
$20$	2.86299	+	1.93111i	0.640185	+	0.431810i
$21$		0			0
$22$	0.991147	+	1.47461i	0.211313	+	0.314387i
$23$	1.79865	−	4.94174i	0.375044	−	1.03042i	−0.598340	−	0.801242i	$-0.704173\pi$
$23$	1.79865	−	4.94174i	0.375044	−	1.03042i	0.973384	−	0.229181i	$-0.0736049\pi$
$24$		0			0
$25$	0.926739	−	0.130245i	0.185348	−	0.0260489i
$26$	−3.60642	−	1.17180i	−0.707278	−	0.229809i
$27$		0			0
$28$	2.79322	−	3.84453i	0.527868	−	0.726548i
$29$	−5.13875	−	2.73232i	−0.954242	−	0.507380i	−0.0820957	−	0.996624i	$-0.526161\pi$
$29$	−5.13875	−	2.73232i	−0.954242	−	0.507380i	−0.872146	+	0.489245i	$0.837272\pi$
$30$		0			0
$31$	7.22978	−	2.07311i	1.29851	−	0.372341i	0.445989	−	0.895039i	$-0.352852\pi$
$31$	7.22978	−	2.07311i	1.29851	−	0.372341i	0.852518	+	0.522698i	$0.175074\pi$
$32$	4.01615	−	3.36995i	0.709962	−	0.595729i
$33$		0			0
$34$	−1.87439	+	0.682222i	−0.321455	+	0.117000i
$35$	0.584581	+	5.56191i	0.0988122	+	0.940135i
$36$		0			0
$37$	−4.00581	+	0.851461i	−0.658551	+	0.139979i	−0.525053	−	0.851070i	$-0.675954\pi$
$37$	−4.00581	+	0.851461i	−0.658551	+	0.139979i	−0.133498	+	0.991049i	$0.542621\pi$
$38$	−0.876416	+	0.218515i	−0.142173	+	0.0354478i
$39$		0			0
$40$	−0.558080	+	3.97095i	−0.0882402	+	0.627862i
$41$	2.17784	−	1.15798i	0.340122	−	0.180846i	−0.290620	−	0.956839i	$-0.593862\pi$
$41$	2.17784	−	1.15798i	0.340122	−	0.180846i	0.630742	+	0.775992i	$0.282750\pi$
$42$		0			0
$43$	0.620430	−	0.739399i	0.0946146	−	0.112757i	−0.716660	−	0.697423i	$-0.754330\pi$
$43$	0.620430	−	0.739399i	0.0946146	−	0.112757i	0.811274	+	0.584666i	$0.198774\pi$
$44$	2.84872	−	4.91563i	0.429460	−	0.741059i
$45$		0			0
$46$	2.80180	−	0.294481i	0.413103	−	0.0434189i
$47$	−7.38871	+	5.77269i	−1.07775	+	0.842034i	−0.988081	−	0.153937i	$-0.950805\pi$
$47$	−7.38871	+	5.77269i	−1.07775	+	0.842034i	−0.0896734	+	0.995971i	$0.528582\pi$
$48$		0			0
$49$	0.694030	−	0.0485313i	0.0991472	−	0.00693305i
$50$	0.280347	+	0.415631i	0.0396470	+	0.0587792i
$51$		0			0
$52$	1.68755	+	12.0076i	0.234022	+	1.66515i
$53$	2.90818	+	4.00277i	0.399469	+	0.549822i	0.960611	−	0.277898i	$-0.0896376\pi$
$53$	2.90818	+	4.00277i	0.399469	+	0.549822i	−0.561141	+	0.827720i	$0.689638\pi$
$54$		0			0
$55$	1.37950	+	6.54237i	0.186012	+	0.882174i
$56$	5.43416	+	0.958189i	0.726170	+	0.128043i
$57$		0			0
$58$	0.108811	−	3.11593i	0.0142875	−	0.409141i
$59$	8.00230	−	3.23314i	1.04181	−	0.420919i	0.211007	−	0.977484i	$-0.432326\pi$
$59$	8.00230	−	3.23314i	1.04181	−	0.420919i	0.830804	+	0.556565i	$0.187881\pi$
$60$		0			0
$61$	−0.503892	+	1.75728i	−0.0645168	+	0.224997i	−0.986914	−	0.161245i	$-0.948449\pi$
$61$	−0.503892	+	1.75728i	−0.0645168	+	0.224997i	0.922398	+	0.386242i	$0.126227\pi$
$62$	2.69602	+	2.99424i	0.342395	+	0.380269i
$63$		0			0
$64$	−1.74700	−	0.777815i	−0.218375	−	0.0972269i
$65$	−10.9315	−	9.17262i	−1.35589	−	1.13772i
$66$		0			0
$67$	−0.347986	−	1.97353i	−0.0425132	−	0.241105i	0.956145	−	0.292895i	$-0.0946185\pi$
$67$	−0.347986	−	1.97353i	−0.0425132	−	0.241105i	−0.998658	+	0.0517899i	$0.983507\pi$
$68$	4.58817	+	4.43075i	0.556398	+	0.537307i
$69$		0			0
$70$	−2.54074	+	1.58763i	−0.303676	+	0.189758i
$71$	7.93671	+	0.834182i	0.941914	+	0.0989991i	0.563022	−	0.826442i	$-0.309639\pi$
$71$	7.93671	+	0.834182i	0.941914	+	0.0989991i	0.378892	+	0.925441i	$0.376305\pi$
$72$		0			0
$73$	−10.1495	+	9.13863i	−1.18791	+	1.06960i	−0.191800	+	0.981434i	$0.561432\pi$
$73$	−10.1495	+	9.13863i	−1.18791	+	1.06960i	−0.996106	+	0.0881613i	$0.971901\pi$
$74$	−1.35070	−	1.72881i	−0.157015	−	0.200970i
$75$		0			0
$76$	1.85654	+	2.21254i	0.212960	+	0.253796i
$77$	9.06351	−	1.58294i	1.03288	−	0.180393i
$78$		0			0
$79$	14.2775	−	6.96360i	1.60634	−	0.783466i	0.606412	−	0.795151i	$-0.292608\pi$
$79$	14.2775	−	6.96360i	1.60634	−	0.783466i	0.999932	+	0.0116849i	$0.00371951\pi$
$80$	4.52571	−	1.47049i	0.505989	−	0.164406i
$81$		0			0
$82$	1.06900	+	0.776676i	0.118052	+	0.0857696i
$83$	4.39047	−	4.23982i	0.481916	−	0.465381i	−0.413569	−	0.910473i	$-0.635718\pi$
$83$	4.39047	−	4.23982i	0.481916	−	0.465381i	0.895485	+	0.445092i	$0.146829\pi$
$84$		0			0
$85$	−7.50179	−	0.261968i	−0.813683	−	0.0284144i
$86$	0.501717	+	0.125092i	0.0541015	+	0.0134890i
$87$		0			0
$88$	6.58026	+	0.470898i	0.701459	+	0.0501979i
$89$	−9.25241	−	5.34188i	−0.980753	−	0.566238i	−0.0782556	−	0.996933i	$-0.524935\pi$
$89$	−9.25241	−	5.34188i	−0.980753	−	0.566238i	−0.902497	+	0.430695i	$0.858268\pi$
$90$		0			0
$91$	−13.1394	+	14.5928i	−1.37739	+	1.52974i
$92$	−4.77381	−	7.63969i	−0.497704	−	0.796493i
$93$		0			0
$94$	−4.51467	−	2.20195i	−0.465653	−	0.227114i
$95$	−3.36600	−	0.473061i	−0.345345	−	0.0485350i
$96$		0			0
$97$	−2.52904	−	0.176848i	−0.256785	−	0.0179562i	−0.0592163	−	0.998245i	$-0.518860\pi$
$97$	−2.52904	−	0.176848i	−0.256785	−	0.0179562i	−0.197569	+	0.980289i	$0.563305\pi$
$98$	0.186353	+	0.322773i	0.0188245	+	0.0326050i
$99$		0			0
$100$	0.801560	−	1.38834i	0.0801560	−	0.138834i
$101$	2.01728	−	2.99074i	0.200727	−	0.297589i	−0.715212	−	0.698907i	$-0.753670\pi$
$101$	2.01728	−	2.99074i	0.200727	−	0.297589i	0.915939	+	0.401318i	$0.131448\pi$
$102$		0			0
$103$	−5.59182	−	13.8402i	−0.550978	−	1.36372i	−0.903770	−	0.428017i	$-0.859212\pi$
$103$	−5.59182	−	13.8402i	−0.550978	−	1.36372i	0.352792	−	0.935702i	$-0.385232\pi$
$104$	−11.6727	+	7.87334i	−1.14460	+	0.772044i
$105$		0			0
$106$	−1.24435	+	2.34028i	−0.120862	+	0.227308i
$107$	−1.23480	−	3.80034i	−0.119373	−	0.367392i	0.873461	−	0.486894i	$-0.161870\pi$
$107$	−1.23480	−	3.80034i	−0.119373	−	0.367392i	−0.992834	+	0.119502i	$0.961870\pi$
$108$		0			0
$109$			1.29557i			0.124093i	0.998073	+	0.0620467i	$0.0197628\pi$
$109$			1.29557i			0.124093i	−0.998073	+	0.0620467i	$0.980237\pi$
$110$	−2.82614	+	2.20063i	−0.269462	+	0.209822i
$111$		0			0
$112$	−1.80492	−	6.29450i	−0.170549	−	0.594775i
$113$	0.552449	−	0.884104i	0.0519701	−	0.0831695i	−0.821043	−	0.570867i	$-0.806607\pi$
$113$	0.552449	−	0.884104i	0.0519701	−	0.0831695i	0.873013	+	0.487697i	$0.162163\pi$
$114$		0			0
$115$	10.1911	+	2.92225i	0.950324	+	0.272501i
$116$	−9.10781	+	4.05506i	−0.845639	+	0.376503i
$117$		0			0
$118$	3.43599	+	3.09378i	0.316309	+	0.284806i
$119$	−0.720533	+	10.3041i	−0.0660511	+	0.944575i
$120$		0			0
$121$	10.5837	−	2.99758i	0.962154	−	0.272508i
$122$	−0.964452	+	0.170059i	−0.0873174	+	0.0153964i
$123$		0			0
$124$	4.82636	−	11.9457i	0.433420	−	1.07275i
$125$	2.48798	+	11.7050i	0.222532	+	1.04693i
$126$		0			0
$127$	−4.60832	−	10.3504i	−0.408922	−	0.918454i	−0.994193	−	0.107616i	$-0.965678\pi$
$127$	−4.60832	−	10.3504i	−0.408922	−	0.918454i	0.585271	−	0.810838i	$-0.300988\pi$
$128$	−0.401689	−	11.5029i	−0.0355046	−	1.01672i
$129$		0			0
$130$	1.84940	−	7.41754i	0.162203	−	0.650561i
$131$	2.64267	+	0.961854i	0.230891	+	0.0840376i	0.454875	−	0.890555i	$-0.349684\pi$
$131$	2.64267	+	0.961854i	0.230891	+	0.0840376i	−0.223984	+	0.974593i	$0.571906\pi$
$132$		0			0
$133$	−0.812216	+	4.60631i	−0.0704281	+	0.399417i
$134$	0.868517	−	0.631015i	0.0750285	−	0.0545114i
$135$		0			0
$136$	−2.28867	+	7.04380i	−0.196252	+	0.604001i
$137$	−7.11240	−	7.36510i	−0.607653	−	0.629243i	0.343061	−	0.939313i	$-0.388536\pi$
$137$	−7.11240	−	7.36510i	−0.607653	−	0.629243i	−0.950714	+	0.310070i	$0.899647\pi$
$138$		0			0
$139$	−10.1013	−	7.89198i	−0.856778	−	0.669389i	0.0883493	−	0.996090i	$-0.471841\pi$
$139$	−10.1013	−	7.89198i	−0.856778	−	0.669389i	−0.945128	+	0.326701i	$0.894063\pi$
$140$	8.12440	+	5.07669i	0.686637	+	0.429059i
$141$		0			0
$142$	1.46220	+	4.01737i	0.122705	+	0.337130i
$143$	−13.8302	+	18.9706i	−1.15654	+	1.58640i
$144$		0			0
$145$	4.77223	−	10.7186i	0.396312	−	0.890131i
$146$	−6.78368	−	2.74078i	−0.561421	−	0.226829i
$147$		0			0
$148$	−3.07531	+	6.30532i	−0.252789	+	0.518294i
$149$	−8.44232	+	17.3093i	−0.691622	+	1.41804i	0.206570	+	0.978432i	$0.433770\pi$
$149$	−8.44232	+	17.3093i	−0.691622	+	1.41804i	−0.898192	+	0.439604i	$0.855119\pi$
$150$		0			0
$151$	−14.2673	−	5.76437i	−1.16106	−	0.469098i	−0.288438	−	0.957498i	$-0.593136\pi$
$151$	−14.2673	−	5.76437i	−1.16106	−	0.469098i	−0.872620	+	0.488401i	$0.837580\pi$
$152$	−1.36410	+	3.06382i	−0.110643	+	0.248508i
$153$		0			0
$154$	2.89065	+	3.99228i	0.232935	+	0.321707i
$155$	5.18585	+	14.2480i	0.416538	+	1.14443i
$156$		0			0
$157$	−0.313197	−	0.195707i	−0.0249958	−	0.0156191i	0.517364	−	0.855766i	$-0.326913\pi$
$157$	−0.313197	−	0.195707i	−0.0249958	−	0.0156191i	−0.542360	+	0.840146i	$0.682469\pi$
$158$	6.70584	+	5.23918i	0.533488	+	0.416807i
$159$		0			0
$160$	7.34197	+	7.60283i	0.580433	+	0.601056i
$161$	4.50818	−	13.8747i	0.355294	−	1.09348i
$162$		0			0
$163$	−20.1301	+	14.6254i	−1.57671	+	1.14555i	−0.656364	+	0.754444i	$0.727906\pi$
$163$	−20.1301	+	14.6254i	−1.57671	+	1.14555i	−0.920347	+	0.391103i	$0.872094\pi$
$164$	0.733708	−	4.16107i	0.0572930	−	0.324925i
$165$		0			0
$166$	3.07250	+	1.11830i	0.238472	+	0.0867968i
$167$	0.641737	−	2.57386i	0.0496591	−	0.199172i	−0.940342	−	0.340230i	$-0.889495\pi$
$167$	0.641737	−	2.57386i	0.0496591	−	0.199172i	0.990001	+	0.141059i	$0.0450506\pi$
$168$		0			0
$169$	−1.29495	−	37.0825i	−0.0996116	−	2.85250i
$170$	−1.63558	−	3.67358i	−0.125443	−	0.281751i
$171$		0			0
$172$	−0.343768	−	1.61730i	−0.0262120	−	0.123318i
$173$	−0.415449	+	1.02827i	−0.0315860	+	0.0781782i	−0.942153	−	0.335184i	$-0.891201\pi$
$173$	−0.415449	+	1.02827i	−0.0315860	+	0.0781782i	0.910566	+	0.413363i	$0.135646\pi$
$174$		0			0
$175$	2.55671	−	0.450816i	0.193269	−	0.0340785i
$176$	−2.92088	−	7.26344i	−0.220170	−	0.547502i
$177$		0			0
$178$	0.399244	−	5.70945i	0.0299246	−	0.427941i
$179$	−16.9439	−	15.2564i	−1.26645	−	1.14031i	−0.983447	−	0.181195i	$-0.942004\pi$
$179$	−16.9439	−	15.2564i	−1.26645	−	1.14031i	−0.283001	−	0.959120i	$-0.591330\pi$
$180$		0			0
$181$	10.2699	−	4.57245i	0.763355	−	0.339867i	0.0121409	−	0.999926i	$-0.496135\pi$
$181$	10.2699	−	4.57245i	0.763355	−	0.339867i	0.751214	+	0.660059i	$0.229469\pi$
$182$	−10.1120	−	2.89957i	−0.749551	−	0.214930i
$183$		0			0
$184$	5.54319	−	8.87096i	0.408649	−	0.653976i
$185$	−2.27567	−	7.93620i	−0.167310	−	0.583481i
$186$		0			0
$187$	0.410900	+	12.3424i	0.0300480	+	0.902567i
$188$			16.0619i			1.17144i
$189$		0			0
$190$	−0.562696	−	1.73180i	−0.0408222	−	0.125638i
$191$	5.52129	−	10.3840i	0.399506	−	0.751362i	−0.599284	−	0.800537i	$-0.704548\pi$
$191$	5.52129	−	10.3840i	0.399506	−	0.751362i	0.998790	+	0.0491744i	$0.0156590\pi$
$192$		0			0
$193$	−1.26331	+	0.852112i	−0.0909349	+	0.0613364i	−0.603819	−	0.797122i	$-0.706355\pi$
$193$	−1.26331	+	0.852112i	−0.0909349	+	0.0613364i	0.512884	+	0.858458i	$0.328577\pi$
$194$	−0.508768	−	1.25925i	−0.0365274	−	0.0904085i
$195$		0			0
$196$	0.666439	−	0.988037i	0.0476028	−	0.0705741i
$197$	−5.57501	+	9.65620i	−0.397203	+	0.687976i	−0.993380	−	0.114878i	$-0.963352\pi$
$197$	−5.57501	+	9.65620i	−0.397203	+	0.687976i	0.596177	+	0.802853i	$0.296686\pi$
$198$		0			0
$199$	−0.596514	−	1.03319i	−0.0422857	−	0.0732410i	0.844108	−	0.536173i	$-0.180131\pi$
$199$	−0.596514	−	1.03319i	−0.0422857	−	0.0732410i	−0.886394	+	0.462932i	$0.846797\pi$
$200$	1.85696	+	0.129851i	0.131307	+	0.00918186i
$201$		0			0
$202$	1.91375	+	0.268961i	0.134651	+	0.0189240i
$203$	−14.5113	−	7.07765i	−1.01850	−	0.496754i
$204$		0			0
$205$	2.63504	+	4.21694i	0.184039	+	0.294524i
$206$	5.35079	−	5.94266i	0.372807	−	0.414044i
$207$		0			0
$208$	14.4699	+	8.35422i	1.00331	+	0.579261i
$209$	−0.399160	+	5.57781i	−0.0276105	+	0.385825i
$210$		0			0
$211$	−5.16358	−	1.28742i	−0.355475	−	0.0886299i	0.0600909	−	0.998193i	$-0.480861\pi$
$211$	−5.16358	−	1.28742i	−0.355475	−	0.0886299i	−0.415566	+	0.909563i	$0.636417\pi$
$212$	8.47031	+	0.295790i	0.581743	+	0.0203149i
$213$		0			0
$214$	1.53985	−	1.48702i	0.105262	−	0.101651i
$215$	1.57423	+	1.14374i	0.107361	+	0.0780027i
$216$		0			0
$217$	19.8433	−	6.44749i	1.34705	−	0.437684i
$218$	−0.623809	+	0.304252i	−0.0422496	+	0.0206065i
$219$		0			0
$220$	10.2863	+	5.03768i	0.693499	+	0.339640i
$221$	−16.9415	−	20.1902i	−1.13961	−	1.35814i
$222$		0			0
$223$	−0.921016	−	1.17885i	−0.0616758	−	0.0789414i	0.756184	−	0.654359i	$-0.227062\pi$
$223$	−0.921016	−	1.17885i	−0.0616758	−	0.0789414i	−0.817859	+	0.575418i	$0.804839\pi$
$224$	10.8082	−	9.73177i	0.722155	−	0.650231i
$225$		0			0
$226$	0.555426	+	0.0583777i	0.0369464	+	0.00388322i
$227$	−2.67466	+	1.67131i	−0.177523	+	0.110929i	−0.615770	−	0.787926i	$-0.711155\pi$
$227$	−2.67466	+	1.67131i	−0.177523	+	0.110929i	0.438247	+	0.898855i	$0.355600\pi$
$228$		0			0
$229$	−13.4308	−	12.9699i	−0.887530	−	0.857078i	0.102957	−	0.994686i	$-0.467170\pi$
$229$	−13.4308	−	12.9699i	−0.887530	−	0.857078i	−0.990487	+	0.137608i	$0.956059\pi$
$230$	0.986231	+	5.59319i	0.0650301	+	0.368804i
$231$		0			0
$232$	−8.86815	−	7.44126i	−0.582222	−	0.488542i
$233$	−1.77131	−	0.788640i	−0.116043	−	0.0516655i	0.347894	−	0.937534i	$-0.386897\pi$
$233$	−1.77131	−	0.788640i	−0.116043	−	0.0516655i	−0.463937	+	0.885868i	$0.653564\pi$
$234$		0			0
$235$	−12.6483	−	14.0474i	−0.825085	−	0.916349i
$236$	4.07520	−	14.2119i	0.265273	−	0.925116i
$237$		0			0
$238$	−5.13056	+	2.07288i	−0.332565	+	0.134365i
$239$	−0.296285	+	8.48450i	−0.0191651	+	0.548817i	0.951397	+	0.307966i	$0.0996485\pi$
$239$	−0.296285	+	8.48450i	−0.0191651	+	0.548817i	−0.970562	+	0.240850i	$0.922574\pi$
$240$		0			0
$241$	7.30698	+	1.28842i	0.470684	+	0.0829943i	0.403959	−	0.914777i	$-0.367634\pi$
$241$	7.30698	+	1.28842i	0.470684	+	0.0829943i	0.0667250	+	0.997771i	$0.478745\pi$
$242$	3.92878	+	4.39202i	0.252552	+	0.282330i
$243$		0			0
$244$	1.84069	+	2.53349i	0.117838	+	0.162190i
$245$	0.195199	+	1.38891i	0.0124708	+	0.0887345i
$246$		0			0
$247$	−6.67389	−	9.89446i	−0.424650	−	0.629569i
$248$	14.9238	−	1.04358i	0.947665	−	0.0662672i
$249$		0			0
$250$	−5.05160	+	3.94675i	−0.319492	+	0.249614i
$251$	2.21172	−	0.232461i	0.139602	−	0.0146728i	−0.0344695	−	0.999406i	$-0.510974\pi$
$251$	2.21172	−	0.232461i	0.139602	−	0.0146728i	0.174072	+	0.984733i	$0.444307\pi$
$252$		0			0
$253$	3.65410	−	17.0547i	0.229731	−	1.07222i
$254$	3.90145	−	4.64956i	0.244799	−	0.291740i
$255$		0			0
$256$	2.06724	−	1.09917i	0.129202	−	0.0686981i
$257$	4.01814	−	28.5905i	0.250644	−	1.78343i	−0.305348	−	0.952241i	$-0.598773\pi$
$257$	4.01814	−	28.5905i	0.250644	−	1.78343i	0.555992	−	0.831187i	$-0.312338\pi$
$258$		0			0
$259$	−11.0234	+	2.74844i	−0.684960	+	0.170780i
$260$	−23.9107	+	5.08237i	−1.48288	+	0.315195i
$261$		0			0
$262$	0.157479	+	1.49831i	0.00972906	+	0.0925658i
$263$	−5.01185	+	1.82416i	−0.309044	+	0.112483i	−0.491886	−	0.870659i	$-0.663692\pi$
$263$	−5.01185	+	1.82416i	−0.309044	+	0.112483i	0.182842	+	0.983142i	$0.441470\pi$
$264$		0			0
$265$	−7.64085	+	6.41143i	−0.469374	+	0.393851i
$266$	−2.40864	+	0.690667i	−0.147683	+	0.0423475i
$267$		0			0
$268$	−3.03101	−	1.61162i	−0.185148	−	0.0984452i
$269$	−11.6256	+	16.0013i	−0.708828	+	0.975617i	0.290994	+	0.956725i	$0.406014\pi$
$269$	−11.6256	+	16.0013i	−0.708828	+	0.975617i	−0.999822	+	0.0188926i	$0.993986\pi$
$270$		0			0
$271$	−12.0019	−	3.89964i	−0.729061	−	0.236886i	−0.0791140	−	0.996866i	$-0.525209\pi$
$271$	−12.0019	−	3.89964i	−0.729061	−	0.236886i	−0.649947	+	0.759979i	$0.725209\pi$
$272$	8.70347	−	1.22319i	0.527725	−	0.0741669i
$273$		0			0
$274$	1.87597	−	5.15418i	0.113331	−	0.311376i
$275$	2.98500	−	0.850682i	0.180002	−	0.0512980i
$276$		0			0
$277$	25.0436	+	16.8921i	1.50472	+	1.01495i	0.987237	+	0.159256i	$0.0509097\pi$
$277$	25.0436	+	16.8921i	1.50472	+	1.01495i	0.517486	+	0.855692i	$0.326868\pi$
$278$	1.42775	−	6.71704i	0.0856308	−	0.402861i
$279$		0			0
$280$	−1.16279	+	11.0632i	−0.0694899	+	0.661152i
$281$	4.09352	+	16.4182i	0.244199	+	0.979430i	0.959747	+	0.280866i	$0.0906216\pi$
$281$	4.09352	+	16.4182i	0.244199	+	0.979430i	−0.715548	+	0.698564i	$0.753823\pi$
$282$		0			0
$283$	−8.20240	−	15.4265i	−0.487582	−	0.917008i	−0.998357	−	0.0572940i	$-0.981753\pi$
$283$	−8.20240	−	15.4265i	−0.487582	−	0.917008i	0.510775	−	0.859714i	$-0.329358\pi$
$284$	9.49639	−	9.83380i	0.563507	−	0.583529i
$285$		0			0
$286$	−12.3821	−	2.20407i	−0.732167	−	0.130330i
$287$	5.92580	−	3.42127i	0.349789	−	0.201951i
$288$		0			0
$289$	3.06746	+	0.652008i	0.180439	+	0.0383534i
$290$	6.28163	−	0.219359i	0.368870	−	0.0128812i
$291$		0			0
$292$	1.63198	+	23.3385i	0.0955046	+	1.36578i
$293$	0.997875	−	1.27722i	0.0582965	−	0.0746161i	−0.757979	−	0.652279i	$-0.773813\pi$
$293$	0.997875	−	1.27722i	0.0582965	−	0.0746161i	0.816275	+	0.577663i	$0.196035\pi$
$294$		0			0
$295$	7.62739	+	15.6385i	0.444084	+	0.910507i
$296$	−8.14596			−0.473474
$297$		0			0
$298$	−10.3169			−0.597642
$299$	16.3184	+	33.4576i	0.943716	+	1.93490i
$300$		0			0
$301$	1.64851	−	2.11000i	0.0950186	−	0.121618i
$302$	−0.575030	−	8.22331i	−0.0330893	−	0.473198i
$303$		0			0
$304$	3.97747	−	0.138896i	0.228124	−	0.00796625i
$305$	−3.60487	−	0.766238i	−0.206414	−	0.0438747i
$306$		0			0
$307$	−3.84384	+	2.21924i	−0.219379	+	0.126659i	−0.605663	−	0.795721i	$-0.707092\pi$
$307$	−3.84384	+	2.21924i	−0.219379	+	0.126659i	0.386283	+	0.922380i	$0.373759\pi$
$308$	7.42195	−	13.9040i	0.422905	−	0.792256i
$309$		0			0
$310$	−5.64247	+	5.84295i	−0.320471	+	0.331857i
$311$	12.1985	+	22.9420i	0.691712	+	1.30092i	0.942930	+	0.332990i	$0.108058\pi$
$311$	12.1985	+	22.9420i	0.691712	+	1.30092i	−0.251218	+	0.967930i	$0.580831\pi$
$312$		0			0
$313$	0.297865	+	1.19467i	0.0168363	+	0.0675268i	0.978126	−	0.208012i	$-0.0666993\pi$
$313$	0.297865	+	1.19467i	0.0168363	+	0.0675268i	−0.961290	+	0.275539i	$0.911144\pi$
$314$	0.0206805	−	0.196762i	0.00116707	−	0.0111039i
$315$		0			0
$316$	5.65759	−	26.6169i	0.318265	−	1.49732i
$317$	−9.96177	−	6.71930i	−0.559509	−	0.377394i	0.246639	−	0.969107i	$-0.420674\pi$
$317$	−9.96177	−	6.71930i	−0.559509	−	0.377394i	−0.806148	+	0.591714i	$0.798452\pi$
$318$		0			0
$319$	−18.1279	−	6.63143i	−1.01497	−	0.371289i
$320$	1.31856	−	3.62271i	0.0737097	−	0.202516i
$321$		0			0
$322$	7.73929	−	1.08769i	0.431294	−	0.0606144i
$323$	−5.97073	−	1.94001i	−0.332220	−	0.107945i
$324$		0			0
$325$	−3.89372	+	5.35924i	−0.215985	+	0.297277i
$326$	−11.7694	−	6.25788i	−0.651844	−	0.346592i
$327$		0			0
$328$	4.71617	−	1.35234i	0.260407	−	0.0746705i
$329$	−19.9258	+	16.7197i	−1.09854	+	0.921787i
$330$		0			0
$331$	22.6014	−	8.22625i	1.24229	−	0.452155i	0.364499	−	0.931204i	$-0.381240\pi$
$331$	22.6014	−	8.22625i	1.24229	−	0.452155i	0.877788	+	0.479048i	$0.159018\pi$
$332$	−1.09288	−	10.3981i	−0.0599796	−	0.570667i
$333$		0			0
$334$	1.39000	−	0.295454i	0.0760575	−	0.0161665i
$335$	3.91995	−	0.977353i	0.214170	−	0.0533985i
$336$		0			0
$337$	0.528559	−	3.76090i	0.0287925	−	0.204869i	−0.970560	−	0.240861i	$-0.922570\pi$
$337$	0.528559	−	3.76090i	0.0287925	−	0.204869i	0.999352	+	0.0359920i	$0.0114591\pi$
$338$	17.5509	−	9.33196i	0.954641	−	0.507592i
$339$		0			0
$340$	−8.26529	+	9.85019i	−0.448248	+	0.534202i
$341$	22.8047	−	10.1089i	1.23494	−	0.547426i
$342$		0			0
$343$	−17.3930	+	1.82808i	−0.939133	+	0.0987069i
$344$	1.51291	−	1.18202i	0.0815707	−	0.0637300i
$345$		0			0
$346$	−0.592670	+	0.0414435i	−0.0318621	+	0.00222802i
$347$	14.6589	+	21.7327i	0.786931	+	1.16667i	0.982551	+	0.185993i	$0.0595502\pi$
$347$	14.6589	+	21.7327i	0.786931	+	1.16667i	−0.195620	+	0.980680i	$0.562672\pi$
$348$		0			0
$349$	−0.688164	−	4.89654i	−0.0368366	−	0.262106i	0.963140	−	0.269002i	$-0.0866938\pi$
$349$	−0.688164	−	4.89654i	−0.0368366	−	0.262106i	−0.999976	+	0.00689607i	$0.997805\pi$
$350$	0.817481	+	1.12517i	0.0436962	+	0.0601427i
$351$		0			0
$352$	11.6559	−	12.9029i	0.621263	−	0.687729i
$353$	−15.1849	−	2.67750i	−0.808210	−	0.142509i	−0.245749	−	0.969333i	$-0.579034\pi$
$353$	−15.1849	−	2.67750i	−0.808210	−	0.142509i	−0.562460	+	0.826824i	$0.690145\pi$
$354$		0			0
$355$	−0.561475	+	16.0785i	−0.0298000	+	0.853360i
$356$	−16.9688	+	6.85584i	−0.899345	+	0.363359i
$357$		0			0
$358$	3.36673	−	11.7412i	0.177937	−	0.620540i
$359$	22.8289	+	25.3540i	1.20486	+	1.33813i	0.925871	+	0.377840i	$0.123333\pi$
$359$	22.8289	+	25.3540i	1.20486	+	1.33813i	0.278990	+	0.960294i	$0.410000\pi$
$360$		0			0
$361$	14.7603	+	6.57171i	0.776858	+	0.345879i
$362$	4.61338	+	3.87108i	0.242474	+	0.203460i
$363$		0			0
$364$	5.84114	+	33.1267i	0.306159	+	1.73631i
$365$	−19.8057	−	19.1261i	−1.03668	−	1.00111i
$366$		0			0
$367$	−13.9701	+	8.72948i	−0.729233	+	0.455675i	−0.843056	−	0.537826i	$-0.819246\pi$
$367$	−13.9701	+	8.72948i	−0.729233	+	0.455675i	0.113823	+	0.993501i	$0.463690\pi$
$368$	−12.3453	−	1.29755i	−0.643546	−	0.0676394i
$369$		0			0
$370$	3.28680	−	2.95945i	0.170873	−	0.153855i
$371$	8.45025	+	10.8158i	0.438715	+	0.561530i
$372$		0			0
$373$	20.2914	+	24.1824i	1.05065	+	1.25212i	0.966772	+	0.255639i	$0.0822859\pi$
$373$	20.2914	+	24.1824i	1.05065	+	1.25212i	0.0838773	+	0.996476i	$0.473270\pi$
$374$	−5.84629	+	3.09633i	−0.302304	+	0.160108i
$375$		0			0
$376$	−16.7630	+	8.17588i	−0.864488	+	0.421639i
$377$	39.1805	−	12.7305i	2.01790	−	0.655655i
$378$		0			0
$379$	1.71682	+	1.24734i	0.0881871	+	0.0640717i	0.631005	−	0.775779i	$-0.282643\pi$
$379$	1.71682	+	1.24734i	0.0881871	+	0.0640717i	−0.542818	+	0.839850i	$0.682643\pi$
$380$	−4.18848	+	4.04477i	−0.214865	+	0.207492i
$381$		0			0
$382$	6.29645	+	0.219877i	0.322155	+	0.0112499i
$383$	−15.6027	−	3.89019i	−0.797261	−	0.198779i	−0.178068	−	0.984018i	$-0.556985\pi$
$383$	−15.6027	−	3.89019i	−0.797261	−	0.198779i	−0.619193	+	0.785239i	$0.712540\pi$
$384$		0			0
$385$	4.45797	+	18.0047i	0.227199	+	0.917604i
$386$	−0.706961	−	0.408164i	−0.0359834	−	0.0207750i
$387$		0			0
$388$	−2.90594	+	3.22738i	−0.147527	+	0.163845i
$389$	−10.1715	−	16.2779i	−0.515718	−	0.825321i	0.483017	−	0.875611i	$-0.339541\pi$
$389$	−10.1715	−	16.2779i	−0.515718	−	0.825321i	−0.998735	+	0.0502902i	$0.983985\pi$
$390$		0			0
$391$	17.5994	+	8.58382i	0.890041	+	0.434102i
$392$	1.37040	+	0.192597i	0.0692155	+	0.00972761i
$393$		0			0
$394$	−5.95862	−	0.416667i	−0.300191	−	0.0209914i
$395$	16.0120	+	27.7337i	0.805653	+	1.39543i
$396$		0			0
$397$	−8.27264	+	14.3286i	−0.415192	+	0.719133i	−0.995449	−	0.0953004i	$-0.969619\pi$
$397$	−8.27264	+	14.3286i	−0.415192	+	0.719133i	0.580257	+	0.814434i	$0.302952\pi$
$398$	0.357389	−	0.529851i	0.0179143	−	0.0265590i
$399$		0			0
$400$	−0.827514	−	2.04817i	−0.0413757	−	0.102408i
$401$	21.6552	−	14.6066i	1.08141	−	0.729420i	0.116815	−	0.993154i	$-0.462732\pi$
$401$	21.6552	−	14.6066i	1.08141	−	0.729420i	0.964596	+	0.263733i	$0.0849539\pi$
$402$		0			0
$403$	−24.9939	+	47.0067i	−1.24503	+	2.34157i
$404$	−1.90962	−	5.87721i	−0.0950073	−	0.292402i
$405$		0			0
$406$		−	8.64922i		−	0.429254i
$407$	−12.7710	+	4.62474i	−0.633035	+	0.229240i
$408$		0			0
$409$	5.22271	+	18.2137i	0.258246	+	0.900612i	0.978387	+	0.206784i	$0.0662996\pi$
$409$	5.22271	+	18.2137i	0.258246	+	0.900612i	−0.720140	+	0.693828i	$0.755923\pi$
$410$	−1.41161	+	2.25906i	−0.0697147	+	0.111567i
$411$		0			0
$412$	−24.5799	−	7.04818i	−1.21097	−	0.347239i
$413$	21.8728	−	9.73839i	1.07629	−	0.479195i
$414$		0			0
$415$	9.14397	+	8.23327i	0.448860	+	0.404155i
$416$	−2.58870	+	37.0201i	−0.126921	+	1.81506i
$417$		0			0
$418$	−2.77941	+	1.11770i	−0.135946	+	0.0546684i
$419$	−6.95358	+	1.22610i	−0.339704	+	0.0598991i	−0.340898	−	0.940100i	$-0.610731\pi$
$419$	−6.95358	+	1.22610i	−0.339704	+	0.0598991i	0.00119373	+	0.999999i	$0.499620\pi$
$420$		0			0
$421$	4.92679	−	12.1942i	0.240117	−	0.594310i	−0.758217	−	0.652002i	$-0.773929\pi$
$421$	4.92679	−	12.1942i	0.240117	−	0.594310i	0.998334	+	0.0576913i	$0.0183739\pi$
$422$	−0.592727	−	2.78856i	−0.0288535	−	0.135745i
$423$		0			0
$424$	4.00288	+	8.99061i	0.194397	+	0.436622i
$425$	0.121610	+	3.48245i	0.00589894	+	0.168924i
$426$		0			0
$427$	−1.22687	+	4.92072i	−0.0593726	+	0.238130i
$428$	−6.43225	−	2.34115i	−0.310914	−	0.113164i
$429$		0			0
$430$	−0.181013	+	1.02658i	−0.00872922	+	0.0495059i
$431$	−28.8671	+	20.9732i	−1.39048	+	1.01024i	−0.394668	+	0.918824i	$0.629140\pi$
$431$	−28.8671	+	20.9732i	−1.39048	+	1.01024i	−0.995812	+	0.0914192i	$0.970860\pi$
$432$		0			0
$433$	3.21010	−	9.87967i	0.154267	−	0.474786i	−0.843818	−	0.536629i	$-0.819698\pi$
$433$	3.21010	−	9.87967i	0.154267	−	0.474786i	0.998086	+	0.0618423i	$0.0196976\pi$
$434$	7.76442	+	8.04029i	0.372704	+	0.385946i
$435$		0			0
$436$	1.74886	+	1.36636i	0.0837552	+	0.0654367i
$437$	7.51954	+	4.69873i	0.359708	+	0.224771i
$438$		0			0
$439$	−5.31252	−	14.5960i	−0.253553	−	0.696631i	−0.999530	−	0.0306592i	$-0.990239\pi$
$439$	−5.31252	−	14.5960i	−0.253553	−	0.696631i	0.745977	−	0.665972i	$-0.231983\pi$
$440$	−0.0216410	+	13.2996i	−0.00103170	+	0.634031i
$441$		0			0
$442$	5.74286	−	12.8987i	0.273160	−	0.613528i
$443$	2.93354	+	1.18523i	0.139377	+	0.0563118i	0.443235	−	0.896405i	$-0.353831\pi$
$443$	2.93354	+	1.18523i	0.139377	+	0.0563118i	−0.303859	+	0.952717i	$0.598275\pi$
$444$		0			0
$445$	9.44172	−	19.3584i	0.447580	−	0.917676i
$446$	0.351315	−	0.720302i	0.0166352	−	0.0341073i
$447$		0			0
$448$	−4.91874	−	1.98730i	−0.232389	−	0.0938911i
$449$	1.94037	−	4.35815i	0.0915720	−	0.205674i	−0.861953	−	0.506988i	$-0.830759\pi$
$449$	1.94037	−	4.35815i	0.0915720	−	0.205674i	0.953525	+	0.301314i	$0.0974254\pi$
$450$		0			0
$451$	6.62611	−	4.79770i	0.312011	−	0.225915i
$452$	−0.610795	−	1.67815i	−0.0287294	−	0.0789333i
$453$		0			0
$454$	−1.43284	−	0.895339i	−0.0672466	−	0.0420203i
$455$	−31.1949	−	24.3721i	−1.46244	−	1.14258i
$456$		0			0
$457$	−6.09014	−	6.30652i	−0.284885	−	0.295007i	0.561612	−	0.827401i	$-0.310181\pi$
$457$	−6.09014	−	6.30652i	−0.284885	−	0.295007i	−0.846497	+	0.532394i	$0.821292\pi$
$458$	3.09085	−	9.51267i	0.144426	−	0.444498i
$459$		0			0
$460$	14.6926	−	10.6748i	0.685045	−	0.497714i
$461$	−0.392501	+	2.22598i	−0.0182806	+	0.103674i	−0.992583	−	0.121570i	$-0.961207\pi$
$461$	−0.392501	+	2.22598i	−0.0182806	+	0.103674i	0.974302	+	0.225245i	$0.0723181\pi$
$462$		0			0
$463$	12.9450	+	4.71161i	0.601607	+	0.218967i	0.624827	−	0.780763i	$-0.285170\pi$
$463$	12.9450	+	4.71161i	0.601607	+	0.218967i	−0.0232198	+	0.999730i	$0.507392\pi$
$464$	−3.32348	+	13.3297i	−0.154289	+	0.618818i
$465$		0			0
$466$	−0.0362505	−	1.03808i	−0.00167927	−	0.0480881i
$467$	−11.1151	−	24.9650i	−0.514347	−	1.15524i	−0.964930	−	0.262508i	$-0.915451\pi$
$467$	−11.1151	−	24.9650i	−0.514347	−	1.15524i	0.450583	−	0.892735i	$-0.351216\pi$
$468$		0			0
$469$	−1.15583	−	5.43777i	−0.0533714	−	0.251093i
$470$	3.79338	−	9.38895i	0.174976	−	0.433080i
$471$		0			0
$472$	16.9066	−	2.98109i	0.778190	−	0.137216i
$473$	1.70083	−	2.71206i	0.0782041	−	0.124701i
$474$		0			0
$475$	−0.110069	+	1.57406i	−0.00505032	+	0.0722230i
$476$	13.1493	+	11.8397i	0.602699	+	0.542673i
$477$		0			0
$478$	−4.15480	+	1.84984i	−0.190036	+	0.0846096i
$479$	−8.07532	−	2.31556i	−0.368971	−	0.105801i	0.0860279	−	0.996293i	$-0.472583\pi$
$479$	−8.07532	−	2.31556i	−0.368971	−	0.105801i	−0.454999	+	0.890492i	$0.650360\pi$
$480$		0			0
$481$	15.3616	−	24.5837i	0.700429	−	1.12092i
$482$	1.09560	+	3.82083i	0.0499034	+	0.174034i
$483$		0			0
$484$	7.11559	−	17.4480i	0.323436	−	0.793092i
$485$		−	5.11093i		−	0.232075i
$486$		0			0
$487$	8.33051	+	25.6387i	0.377491	+	1.16180i	0.941782	+	0.336223i	$0.109150\pi$
$487$	8.33051	+	25.6387i	0.377491	+	1.16180i	−0.564291	+	0.825576i	$0.690850\pi$
$488$	−1.70712	+	3.21063i	−0.0772779	+	0.145339i
$489$		0			0
$490$	−0.622912	+	0.420159i	−0.0281403	+	0.0189809i
$491$	−0.874339	−	2.16407i	−0.0394584	−	0.0976629i	0.906168	−	0.422918i	$-0.138994\pi$
$491$	−0.874339	−	2.16407i	−0.0394584	−	0.0976629i	−0.945626	+	0.325255i	$0.894550\pi$
$492$		0			0
$493$	12.1179	−	17.9656i	0.545765	−	0.809129i
$494$	3.19681	−	5.53704i	0.143831	−	0.249123i
$495$		0			0
$496$	−8.87664	−	15.3748i	−0.398573	−	0.690348i
$497$	22.0847	+	1.54431i	0.990634	+	0.0692719i
$498$		0			0
$499$	−4.52078	−	0.635355i	−0.202378	−	0.0284424i	0.0372556	−	0.999306i	$-0.488138\pi$
$499$	−4.52078	−	0.635355i	−0.202378	−	0.0284424i	−0.239634	+	0.970863i	$0.577027\pi$
$500$	18.4242	+	8.98609i	0.823956	+	0.401870i
$501$		0			0
$502$	0.631327	+	1.01033i	0.0281775	+	0.0450934i
$503$	17.9511	−	19.9367i	0.800400	−	0.888934i	−0.195378	−	0.980728i	$-0.562593\pi$
$503$	17.9511	−	19.9367i	0.800400	−	0.888934i	0.995778	+	0.0917939i	$0.0292601\pi$
$504$		0			0
$505$	6.29825	+	3.63629i	0.280268	+	0.161813i
$506$	9.06984	−	2.24569i	0.403203	−	0.0998333i
$507$		0			0
$508$	−18.8319	−	4.69532i	−0.835531	−	0.208321i
$509$	−31.7255	−	1.10788i	−1.40621	−	0.0491059i	−0.678302	−	0.734783i	$-0.737284\pi$
$509$	−31.7255	−	1.10788i	−1.40621	−	0.0491059i	−0.727906	+	0.685677i	$0.759506\pi$
$510$		0			0
$511$	−27.2539	+	26.3188i	−1.20564	+	1.16428i
$512$	−17.6087	−	12.7934i	−0.778200	−	0.565396i
$513$		0			0
$514$	14.7097	−	4.77949i	0.648819	−	0.210814i
$515$	27.0472	−	13.1918i	1.19184	−	0.581301i
$516$		0			0
$517$	−21.6389	+	22.3349i	−0.951677	+	0.982286i
$518$	−3.91208	−	4.66223i	−0.171887	−	0.204847i
$519$		0			0
$520$	−17.4753	−	22.3673i	−0.766342	−	0.980873i
$521$	20.9290	−	18.8445i	0.916915	−	0.825594i	−0.0681681	−	0.997674i	$-0.521715\pi$
$521$	20.9290	−	18.8445i	0.916915	−	0.825594i	0.985083	+	0.172080i	$0.0550488\pi$
$522$		0			0
$523$	25.8767	+	2.71975i	1.13151	+	0.118926i	0.651722	−	0.758458i	$-0.274047\pi$
$523$	25.8767	+	2.71975i	1.13151	+	0.118926i	0.479788	+	0.877384i	$0.340714\pi$
$524$	4.08544	−	2.55287i	0.178473	−	0.111523i
$525$		0			0
$526$	−2.05530	−	1.98478i	−0.0896154	−	0.0865406i
$527$	4.86293	+	27.5791i	0.211833	+	1.20136i
$528$		0			0
$529$	−3.56663	−	2.99276i	−0.155071	−	0.130120i
$530$	−4.88143	−	2.17335i	−0.212036	−	0.0944045i
$531$		0			0
$532$	5.36134	+	5.95437i	0.232444	+	0.258155i
$533$	−4.81250	+	16.7832i	−0.208453	+	0.726961i
$534$		0			0
$535$	7.46907	−	3.01770i	0.322916	−	0.130467i
$536$	0.139113	−	3.98367i	0.00600875	−	0.172068i
$537$		0			0
$538$	−10.4347	−	1.83991i	−0.449871	−	0.0793244i
$539$	2.25781	−	0.476074i	0.0972509	−	0.0205060i
$540$		0			0
$541$	−8.51340	−	11.7177i	−0.366020	−	0.503783i	0.585794	−	0.810460i	$-0.300783\pi$
$541$	−8.51340	−	11.7177i	−0.366020	−	0.503783i	−0.951814	+	0.306677i	$0.900783\pi$
$542$	−0.940865	−	6.69460i	−0.0404136	−	0.287558i
$543$		0			0
$544$	10.9160	+	16.1836i	0.468018	+	0.693866i
$545$	−2.60548	+	0.182193i	−0.111606	+	0.00780428i
$546$		0			0
$547$	30.6500	−	23.9464i	1.31050	−	1.02387i	0.313255	−	0.949669i	$-0.398581\pi$
$547$	30.6500	−	23.9464i	1.31050	−	1.02387i	0.997243	−	0.0742044i	$-0.0236417\pi$
$548$	−17.4430	+	1.83333i	−0.745126	+	0.0783159i
$549$		0			0
$550$	1.11059	+	1.23748i	0.0473559	+	0.0527665i
$551$	6.30764	−	7.51715i	0.268714	−	0.320241i
$552$		0			0
$553$	38.9091	−	20.6883i	1.65458	−	0.879758i
$554$	−2.25220	+	16.0252i	−0.0956868	+	0.680847i
$555$		0			0
$556$	−21.3064	+	5.31227i	−0.903591	+	0.225290i
$557$	−35.7215	+	7.59283i	−1.51357	+	0.321719i	−0.888509	−	0.458859i	$-0.848258\pi$
$557$	−35.7215	+	7.59283i	−1.51357	+	0.321719i	−0.625059	+	0.780578i	$0.714925\pi$
$558$		0			0
$559$	0.714169	+	6.79486i	0.0302061	+	0.287392i
$560$	12.4048	−	4.51499i	0.524200	−	0.190793i
$561$		0			0
$562$	−6.94394	+	5.82665i	−0.292912	+	0.245783i
$563$	5.99498	−	1.71903i	0.252658	−	0.0724486i	−0.146918	−	0.989149i	$-0.546935\pi$
$563$	5.99498	−	1.71903i	0.252658	−	0.0724486i	0.399576	+	0.916700i	$0.369157\pi$
$564$		0			0
$565$	1.85568	+	0.986681i	0.0780690	+	0.0415100i
$566$	5.50148	−	7.57214i	0.231245	−	0.318281i
$567$		0			0
$568$	15.0969	+	4.90529i	0.633453	+	0.205821i
$569$	3.94713	−	0.554733i	0.165472	−	0.0232556i	−0.0559503	−	0.998434i	$-0.517819\pi$
$569$	3.94713	−	0.554733i	0.165472	−	0.0232556i	0.221423	+	0.975178i	$0.428930\pi$
$570$		0			0
$571$	2.01549	−	5.53753i	0.0843458	−	0.231738i	−0.890349	−	0.455279i	$-0.849539\pi$
$571$	2.01549	−	5.53753i	0.0843458	−	0.231738i	0.974695	+	0.223541i	$0.0717617\pi$
$572$	11.0221	+	38.6761i	0.460857	+	1.61713i
$573$		0			0
$574$	3.03893	+	2.04978i	0.126842	+	0.0855563i
$575$	1.02324	−	4.81397i	0.0426721	−	0.200756i
$576$		0			0
$577$	−2.46434	+	23.4467i	−0.102592	+	0.976097i	0.815239	+	0.579125i	$0.196606\pi$
$577$	−2.46434	+	23.4467i	−0.102592	+	0.976097i	−0.917831	+	0.396972i	$0.870061\pi$
$578$	0.406423	+	1.63008i	0.0169050	+	0.0678022i
$579$		0			0
$580$	−9.43579	−	17.7461i	−0.391800	−	0.736868i
$581$	11.7618	−	12.1797i	0.487960	−	0.505298i
$582$		0			0
$583$	11.3799	+	11.8226i	0.471306	+	0.489644i
$584$	−23.5265	+	13.5830i	−0.973533	+	0.562069i
$585$		0			0
$586$	0.849313	+	0.180527i	0.0350848	+	0.00745751i
$587$	43.2690	−	1.51099i	1.78590	−	0.0623651i	0.877279	−	0.479981i	$-0.159356\pi$
$587$	43.2690	−	1.51099i	1.78590	−	0.0623651i	0.908624	+	0.417616i	$0.137134\pi$
$588$		0			0
$589$	0.884595	+	12.6503i	0.0364491	+	0.521247i
$590$	−5.73860	+	7.34507i	−0.236254	+	0.302392i
$591$		0			0
$592$	4.23763	+	8.68843i	0.174165	+	0.357092i
$593$	35.6507			1.46400			0.731998	−	0.681306i	$-0.238588\pi$
$593$	35.6507			1.46400			0.731998	+	0.681306i	$0.238588\pi$
$594$		0			0
$595$	−20.8235			−0.853681
$596$	14.4618	+	29.6511i	0.592380	+	1.21456i
$597$		0			0
$598$	−12.2774	+	15.7144i	−0.502060	+	0.642608i
$599$	2.64089	+	37.7666i	0.107904	+	1.54310i	0.686285	+	0.727333i	$0.259240\pi$
$599$	2.64089	+	37.7666i	0.107904	+	1.54310i	−0.578381	+	0.815767i	$0.696315\pi$
$600$		0			0
$601$	−1.32195	+	0.0461635i	−0.0539235	+	0.00188305i	−0.0618485	−	0.998086i	$-0.519700\pi$
$601$	−1.32195	+	0.0461635i	−0.0539235	+	0.00188305i	0.00792507	+	0.999969i	$0.497477\pi$
$602$	1.40308	+	0.298235i	0.0571854	+	0.0121551i
$603$		0			0
$604$	−22.8280	+	13.1798i	−0.928859	+	0.536277i
$605$	7.51669	+	20.8629i	0.305597	+	0.848199i
$606$		0			0
$607$	−0.854118	+	0.884465i	−0.0346676	+	0.0358993i	−0.736450	−	0.676492i	$-0.763499\pi$
$607$	−0.854118	+	0.884465i	−0.0346676	+	0.0358993i	0.701782	+	0.712392i	$0.252388\pi$
$608$	4.14994	+	7.80490i	0.168302	+	0.316531i
$609$		0			0
$610$	−0.477628	−	1.91566i	−0.0193386	−	0.0775628i
$611$	6.93765	−	66.0073i	0.280667	−	2.67037i
$612$		0			0
$613$	−8.25160	+	38.8207i	−0.333279	+	1.56795i	0.418298	+	0.908310i	$0.362627\pi$
$613$	−8.25160	+	38.8207i	−0.333279	+	1.56795i	−0.751577	+	0.659645i	$0.770707\pi$
$614$	−1.97123	−	1.32961i	−0.0795525	−	0.0536589i
$615$		0			0
$616$	18.2889	+	0.668460i	0.736880	+	0.0269330i
$617$	−7.43732	+	20.4339i	−0.299415	+	0.822636i	0.695183	+	0.718833i	$0.255323\pi$
$617$	−7.43732	+	20.4339i	−0.299415	+	0.822636i	−0.994598	+	0.103803i	$0.966899\pi$
$618$		0			0
$619$	−20.8890	+	2.93576i	−0.839600	+	0.117998i	−0.545849	−	0.837884i	$-0.683793\pi$
$619$	−20.8890	+	2.93576i	−0.839600	+	0.117998i	−0.293752	+	0.955882i	$0.594904\pi$
$620$	24.7022	+	8.02624i	0.992065	+	0.322342i
$621$		0			0
$622$	−8.18171	+	11.2612i	−0.328057	+	0.451531i
$623$	−26.1688	−	13.9142i	−1.04843	−	0.557460i
$624$		0			0
$625$	−18.6917	+	5.35976i	−0.747668	+	0.214390i
$626$	−0.505275	+	0.423976i	−0.0201949	+	0.0169455i
$627$		0			0
$628$	−0.594489	+	0.216376i	−0.0237227	+	0.00863435i
$629$	−1.59391	−	15.1651i	−0.0635535	−	0.604671i
$630$		0			0
$631$	12.6347	−	2.68559i	0.502979	−	0.106911i	0.0505672	−	0.998721i	$-0.483897\pi$
$631$	12.6347	−	2.68559i	0.502979	−	0.106911i	0.452412	+	0.891809i	$0.350564\pi$
$632$	30.6586	−	7.64404i	1.21953	−	0.304064i
$633$		0			0
$634$	0.895875	−	6.37448i	0.0355797	−	0.253163i
$635$	20.1674	−	10.7232i	0.800317	−	0.425536i
$636$		0			0
$637$	−3.16553	+	3.77253i	−0.125423	+	0.149473i
$638$	−1.06416	−	10.2858i	−0.0421304	−	0.407217i
$639$		0			0
$640$	23.0765	−	2.42544i	0.912179	−	0.0958739i
$641$	−12.9048	+	10.0824i	−0.509710	+	0.398229i	−0.837429	−	0.546546i	$-0.815942\pi$
$641$	−12.9048	+	10.0824i	−0.509710	+	0.398229i	0.327719	+	0.944775i	$0.393720\pi$
$642$		0			0
$643$	−15.0896	+	1.05517i	−0.595075	+	0.0416117i	−0.364119	−	0.931352i	$-0.618630\pi$
$643$	−15.0896	+	1.05517i	−0.595075	+	0.0416117i	−0.230956	+	0.972964i	$0.574185\pi$
$644$	−13.9747	−	20.7183i	−0.550679	−	0.816415i
$645$		0			0
$646$	−0.468065	−	3.33045i	−0.0184158	−	0.131035i
$647$	−11.1748	−	15.3808i	−0.439326	−	0.604680i	0.530736	−	0.847537i	$-0.321915\pi$
$647$	−11.1748	−	15.3808i	−0.439326	−	0.604680i	−0.970062	+	0.242857i	$0.921915\pi$
$648$		0			0
$649$	24.8132	−	14.2721i	0.974005	−	0.560231i
$650$	−3.49484	−	0.616234i	−0.137079	−	0.0241707i
$651$		0			0
$652$	−1.48754	+	42.5976i	−0.0582566	+	1.66825i
$653$	15.1482	−	6.12028i	0.592796	−	0.239505i	−0.0585519	−	0.998284i	$-0.518648\pi$
$653$	15.1482	−	6.12028i	0.592796	−	0.239505i	0.651348	+	0.758779i	$0.274204\pi$
$654$		0			0
$655$	−1.56272	+	5.44985i	−0.0610604	+	0.212943i
$656$	−3.89581	−	4.32674i	−0.152106	−	0.168931i
$657$		0			0
$658$	−12.7298	−	5.66766i	−0.496258	−	0.220948i
$659$	5.34987	+	4.48907i	0.208401	+	0.174869i	0.741014	−	0.671490i	$-0.234345\pi$
$659$	5.34987	+	4.48907i	0.208401	+	0.174869i	−0.532613	+	0.846359i	$0.678790\pi$
$660$		0			0
$661$	8.74606	+	49.6014i	0.340182	+	1.92927i	0.368397	+	0.929669i	$0.379907\pi$
$661$	8.74606	+	49.6014i	0.340182	+	1.92927i	−0.0282147	+	0.999602i	$0.508982\pi$
$662$	9.26859	+	8.95057i	0.360234	+	0.347874i
$663$		0			0
$664$	10.2956	−	6.43343i	0.399548	−	0.249665i
$665$	−9.37780	−	0.985646i	−0.363655	−	0.0382217i
$666$		0			0
$667$	−22.7452	+	20.4799i	−0.880698	+	0.792984i
$668$	−2.79759	−	3.58076i	−0.108242	−	0.138544i
$669$		0			0
$670$	1.39115	+	1.65791i	0.0537447	+	0.0640505i
$671$	−0.853592	+	6.00273i	−0.0329525	+	0.231733i
$672$		0			0
$673$	17.7450	−	8.65481i	0.684019	−	0.333618i	−0.0633843	−	0.997989i	$-0.520189\pi$
$673$	17.7450	−	8.65481i	0.684019	−	0.333618i	0.747403	+	0.664371i	$0.231300\pi$
$674$	1.93497	−	0.628710i	0.0745323	−	0.0242170i
$675$		0			0
$676$	−51.4225	−	37.3606i	−1.97779	−	1.43695i
$677$	−7.38868	+	7.13516i	−0.283970	+	0.274227i	−0.822977	−	0.568075i	$-0.807688\pi$
$677$	−7.38868	+	7.13516i	−0.283970	+	0.274227i	0.539007	+	0.842301i	$0.318800\pi$
$678$		0			0
$679$	−7.02870	−	0.245448i	−0.269737	−	0.00941942i
$680$	−14.4874	−	3.61211i	−0.555566	−	0.138518i
$681$		0			0
$682$	10.2228	+	8.60632i	0.391451	+	0.329553i
$683$	1.16852	+	0.674647i	0.0447123	+	0.0258146i	0.522190	−	0.852829i	$-0.325115\pi$
$683$	1.16852	+	0.674647i	0.0447123	+	0.0258146i	−0.477477	+	0.878644i	$0.658449\pi$
$684$		0			0
$685$	13.8115	−	15.3392i	0.527710	−	0.586081i
$686$	−4.96477	−	7.94529i	−0.189556	−	0.303353i
$687$		0			0
$688$	−2.04777	−	0.998762i	−0.0780703	−	0.0380775i
$689$	−34.6814	−	4.87415i	−1.32126	−	0.185690i
$690$		0			0
$691$	2.89146	+	0.202191i	0.109996	+	0.00769169i	0.124649	−	0.992201i	$-0.460220\pi$
$691$	2.89146	+	0.202191i	0.109996	+	0.00769169i	−0.0146522	+	0.999893i	$0.504664\pi$
$692$	0.949891	+	1.64526i	0.0361094	+	0.0625434i
$693$		0			0
$694$	−7.02165	+	12.1619i	−0.266538	+	0.461658i
$695$	14.4508	−	21.4241i	0.548148	−	0.812663i
$696$		0			0
$697$	3.44042	+	8.51535i	0.130315	+	0.322542i
$698$	2.19604	−	1.48125i	0.0831213	−	0.0560661i
$699$		0			0
$700$	2.08785	−	3.92668i	0.0789134	−	0.148415i
$701$	2.68287	+	8.25702i	0.101330	+	0.311863i	0.988852	−	0.148904i	$-0.0475744\pi$
$701$	2.68287	+	8.25702i	0.101330	+	0.311863i	−0.887521	+	0.460767i	$0.847574\pi$
$702$		0			0
$703$		−	6.90498i		−	0.260426i
$704$	−6.09393	−	1.75814i	−0.229674	−	0.0662625i
$705$		0			0
$706$	−2.27681	−	7.94019i	−0.0856890	−	0.298833i
$707$	5.30321	−	8.48690i	0.199448	−	0.319183i
$708$		0			0
$709$	11.8213	+	3.38971i	0.443959	+	0.127303i	0.490167	−	0.871629i	$-0.336936\pi$
$709$	11.8213	+	3.38971i	0.443959	+	0.127303i	−0.0462077	+	0.998932i	$0.514714\pi$
$710$	−7.87355	+	3.50553i	−0.295489	+	0.131560i
$711$		0			0
$712$	−15.7926	−	14.2197i	−0.591853	−	0.532907i
$713$	2.75906	−	39.4565i	0.103328	−	1.47766i
$714$		0			0
$715$	−40.0960	−	25.1455i	−1.49950	−	0.940390i
$716$	−38.4639	+	6.78222i	−1.43746	+	0.253463i
$717$		0			0
$718$	−6.84665	+	16.9461i	−0.255515	+	0.632421i
$719$	−2.15672	−	10.1466i	−0.0804321	−	0.378403i	0.919459	−	0.393187i	$-0.128627\pi$
$719$	−2.15672	−	10.1466i	−0.0804321	−	0.378403i	−0.999891	+	0.0147834i	$0.995294\pi$
$720$		0			0
$721$	−16.8429	−	37.8297i	−0.627261	−	1.40885i
$722$	0.302074	+	8.65027i	0.0112420	+	0.321930i
$723$		0			0
$724$	4.65878	−	18.6853i	0.173142	−	0.694435i
$725$	−5.11815	−	1.86286i	−0.190083	−	0.0691847i
$726$		0			0
$727$	3.74787	−	21.2552i	0.139001	−	0.788312i	−0.832989	−	0.553289i	$-0.813372\pi$
$727$	3.74787	−	21.2552i	0.139001	−	0.788312i	0.971990	−	0.235023i	$-0.0755165\pi$
$728$	−31.5995	+	22.9584i	−1.17115	+	0.850893i
$729$		0			0
$730$	4.55792	−	14.0278i	0.168696	−	0.519194i
$731$	2.49655	+	2.58526i	0.0923384	+	0.0956192i
$732$		0			0
$733$	−5.01187	−	3.91570i	−0.185118	−	0.144630i	0.518841	−	0.854871i	$-0.326364\pi$
$733$	−5.01187	−	3.91570i	−0.185118	−	0.144630i	−0.703959	+	0.710241i	$0.748586\pi$
$734$	−7.48391	−	4.67647i	−0.276236	−	0.172612i
$735$		0			0
$736$	−9.42978	−	25.9081i	−0.347586	−	0.954986i
$737$	−2.04357	−	6.32445i	−0.0752758	−	0.232964i
$738$		0			0
$739$	14.1340	−	31.7455i	0.519928	−	1.16778i	−0.442631	−	0.896704i	$-0.645955\pi$
$739$	14.1340	−	31.7455i	0.519928	−	1.16778i	0.962559	−	0.271073i	$-0.0873785\pi$
$740$	−13.1129	−	5.29795i	−0.482039	−	0.194756i
$741$		0			0
$742$	−3.22329	+	6.60872i	−0.118331	+	0.242614i
$743$	−1.03011	+	2.11204i	−0.0377911	+	0.0774832i	−0.916854	−	0.399222i	$-0.869280\pi$
$743$	−1.03011	+	2.11204i	−0.0377911	+	0.0774832i	0.879063	+	0.476705i	$0.158169\pi$
$744$		0			0
$745$	−35.9974	−	14.5439i	−1.31884	−	0.532847i
$746$	−6.87840	+	15.4491i	−0.251836	+	0.565633i
$747$		0			0
$748$	17.0941	+	12.4621i	0.625021	+	0.455660i
$749$	−3.79134	−	10.4166i	−0.138532	−	0.380615i
$750$		0			0
$751$	23.1579	+	14.4706i	0.845043	+	0.528041i	0.881986	−	0.471276i	$-0.156206\pi$
$751$	23.1579	+	14.4706i	0.845043	+	0.528041i	−0.0369431	+	0.999317i	$0.511762\pi$
$752$	17.4407	+	13.6262i	0.635996	+	0.496895i
$753$		0			0
$754$	15.3308	+	15.8755i	0.558314	+	0.578151i
$755$	9.58614	−	29.5031i	0.348875	−	1.07373i
$756$		0			0
$757$	18.5897	−	13.5062i	0.675655	−	0.490892i	−0.196258	−	0.980552i	$-0.562879\pi$
$757$	18.5897	−	13.5062i	0.675655	−	0.490892i	0.871914	+	0.489660i	$0.162879\pi$
$758$	−0.197409	+	1.11956i	−0.00717021	+	0.0406643i
$759$		0			0
$760$	−6.35336	−	2.31244i	−0.230461	−	0.0838808i
$761$	4.44226	−	17.8169i	0.161032	−	0.645864i	−0.834464	−	0.551062i	$-0.814223\pi$
$761$	4.44226	−	17.8169i	0.161032	−	0.645864i	0.995496	−	0.0948017i	$-0.0302217\pi$
$762$		0			0
$763$	0.125431	+	3.59188i	0.00454091	+	0.130035i
$764$	−8.19418	−	18.4044i	−0.296455	−	0.665849i
$765$		0			0
$766$	−1.79103	−	8.42615i	−0.0647127	−	0.304449i
$767$	−22.8858	+	56.6443i	−0.826357	+	2.04531i
$768$		0			0
$769$	−4.66158	+	0.821963i	−0.168101	+	0.0296407i	−0.257065	−	0.966394i	$-0.582755\pi$
$769$	−4.66158	+	0.821963i	−0.168101	+	0.0296407i	0.0889641	+	0.996035i	$0.471644\pi$
$770$	−7.62222	+	6.37470i	−0.274686	+	0.229728i
$771$		0			0
$772$	−0.182088	+	2.60398i	−0.00655348	+	0.0937192i
$773$	39.3852	+	35.4626i	1.41659	+	1.27550i	0.910804	+	0.412839i	$0.135463\pi$
$773$	39.3852	+	35.4626i	1.41659	+	1.27550i	0.505783	+	0.862661i	$0.331204\pi$
$774$		0			0
$775$	6.43011	−	2.86287i	0.230976	−	0.102837i
$776$	−4.84744	−	1.38998i	−0.174013	−	0.0498974i
$777$		0			0
$778$	5.44899	−	8.72021i	0.195356	−	0.312635i
$779$	1.14632	+	3.99770i	0.0410712	+	0.143232i
$780$		0			0
$781$	26.4534	−	0.880679i	0.946578	−	0.0315132i
$782$			10.4898i			0.375115i
$783$		0			0
$784$	−0.507475	−	1.56185i	−0.0181241	−	0.0557803i
$785$	0.349535	−	0.657380i	0.0124754	−	0.0234629i
$786$		0			0
$787$	5.95643	−	4.01766i	0.212324	−	0.143214i	−0.448427	−	0.893819i	$-0.648016\pi$
$787$	5.95643	−	4.01766i	0.212324	−	0.143214i	0.660751	+	0.750605i	$0.270238\pi$
$788$	7.15504	+	17.7093i	0.254888	+	0.630869i
$789$		0			0
$790$	−9.59330	+	14.2226i	−0.341314	+	0.506019i
$791$	1.44603	−	2.50460i	0.0514149	−	0.0890533i
$792$		0			0
$793$	−6.47010	−	11.2065i	−0.229760	−	0.397956i
$794$	−8.84187	−	0.618284i	−0.313786	−	0.0219421i
$795$		0			0
$796$	−2.02378	−	0.284424i	−0.0717312	−	0.0100812i
$797$	−14.0703	−	6.86256i	−0.498397	−	0.243084i	0.171986	−	0.985099i	$-0.444981\pi$
$797$	−14.0703	−	6.86256i	−0.498397	−	0.243084i	−0.670383	+	0.742015i	$0.733870\pi$
$798$		0			0
$799$	−18.5008	−	29.6075i	−0.654511	−	1.04744i
$800$	3.28301	−	3.64615i	0.116072	−	0.128911i
$801$		0			0
$802$	12.1185	+	6.99661i	0.427919	+	0.247059i
$803$	−29.1726	+	34.6518i	−1.02948	+	1.22284i
$804$		0			0
$805$	28.5370	+	7.11507i	1.00580	+	0.250773i
$806$	−28.5029	−	0.995344i	−1.00397	−	0.0350595i
$807$		0			0
$808$	5.16172	−	4.98461i	0.181589	−	0.175358i
$809$	−18.7796	−	13.6442i	−0.660255	−	0.479704i	0.206494	−	0.978448i	$-0.433795\pi$
$809$	−18.7796	−	13.6442i	−0.660255	−	0.479704i	−0.866749	+	0.498744i	$0.833795\pi$
$810$		0			0
$811$	−6.16014	+	2.00155i	−0.216312	+	0.0702839i	−0.415168	−	0.909745i	$-0.636277\pi$
$811$	−6.16014	+	2.00155i	−0.216312	+	0.0702839i	0.198856	+	0.980029i	$0.436277\pi$
$812$	−24.8582	+	12.1241i	−0.872350	+	0.425474i
$813$		0			0
$814$	−5.22591	−	5.06307i	−0.183168	−	0.177460i
$815$	−32.2434	−	38.4262i	−1.12944	−	1.34601i
$816$		0			0
$817$	1.00194	+	1.28243i	0.0350536	+	0.0448666i
$818$	−7.54329	+	6.79201i	−0.263745	+	0.237477i
$819$		0			0
$820$	8.47135	+	0.890375i	0.295832	+	0.0310932i
$821$	−28.6920	+	17.9288i	−1.00136	+	0.625718i	−0.928387	−	0.371616i	$-0.878804\pi$
$821$	−28.6920	+	17.9288i	−1.00136	+	0.625718i	−0.0729718	+	0.997334i	$0.523248\pi$
$822$		0			0
$823$	−2.52323	−	2.43666i	−0.0879544	−	0.0849366i	0.649382	−	0.760463i	$-0.275028\pi$
$823$	−2.52323	−	2.43666i	−0.0879544	−	0.0849366i	−0.737336	+	0.675526i	$0.763917\pi$
$824$	−5.15590	−	29.2405i	−0.179614	−	1.01864i
$825$		0			0
$826$	9.82556	+	8.24462i	0.341875	+	0.286867i
$827$	8.95033	+	3.98494i	0.311233	+	0.138570i	0.556409	−	0.830909i	$-0.312179\pi$
$827$	8.95033	+	3.98494i	0.311233	+	0.138570i	−0.245175	+	0.969479i	$0.578846\pi$
$828$		0			0
$829$	−19.6267	−	21.7976i	−0.681663	−	0.757064i	0.298682	−	0.954353i	$-0.403453\pi$
$829$	−19.6267	−	21.7976i	−0.681663	−	0.757064i	−0.980345	+	0.197289i	$0.936786\pi$
$830$	−1.81689	+	6.33626i	−0.0630652	+	0.219935i
$831$		0			0
$832$	12.5508	−	5.07084i	0.435119	−	0.175800i
$833$	−0.0904068	+	2.58891i	−0.00313241	+	0.0897005i
$834$		0			0
$835$	5.26645	+	0.928617i	0.182253	+	0.0321361i
$836$	7.10837	+	6.42138i	0.245848	+	0.222088i
$837$		0			0
$838$	−2.22334	−	3.06016i	−0.0768038	−	0.105711i
$839$	−3.97429	−	28.2785i	−0.137208	−	0.976283i	−0.930200	−	0.367052i	$-0.880367\pi$
$839$	−3.97429	−	28.2785i	−0.137208	−	0.976283i	0.792993	−	0.609231i	$-0.208522\pi$
$840$		0			0
$841$	2.72458	+	4.03936i	0.0939511	+	0.139288i
$842$	7.02844	−	0.491476i	0.242216	−	0.0169374i
$843$		0			0
$844$	−7.18356	+	5.61241i	−0.247268	+	0.193187i
$845$	74.3932	−	7.81904i	2.55920	−	0.268983i
$846$		0			0
$847$	29.0523	−	9.33524i	0.998249	−	0.320763i
$848$	7.50698	−	8.94647i	0.257791	−	0.307223i
$849$		0			0
$850$	−1.64821	+	0.876371i	−0.0565333	+	0.0300593i
$851$	−2.99733	+	21.3271i	−0.102747	+	0.731085i
$852$		0			0
$853$	−9.92686	+	2.47504i	−0.339889	+	0.0847439i	−0.408127	−	0.912925i	$-0.633818\pi$
$853$	−9.92686	+	2.47504i	−0.339889	+	0.0847439i	0.0682377	+	0.997669i	$0.478262\pi$
$854$	−2.65741	+	0.564850i	−0.0909347	+	0.0193288i
$855$		0			0
$856$	−0.830819	−	7.90472i	−0.0283968	−	0.270178i
$857$	20.3024	−	7.38948i	0.693517	−	0.252420i	0.0288769	−	0.999583i	$-0.490807\pi$
$857$	20.3024	−	7.38948i	0.693517	−	0.252420i	0.664641	+	0.747163i	$0.268585\pi$
$858$		0			0
$859$	−19.4772	+	16.3433i	−0.664552	+	0.557626i	−0.911447	−	0.411417i	$-0.865034\pi$
$859$	−19.4772	+	16.3433i	−0.664552	+	0.557626i	0.246895	+	0.969042i	$0.420590\pi$
$860$	3.20415	−	0.918775i	0.109261	−	0.0313300i
$861$		0			0
$862$	−16.8776	−	8.97397i	−0.574853	−	0.305655i
$863$	−8.84285	+	12.1711i	−0.301014	+	0.414310i	−0.932553	−	0.361034i	$-0.882424\pi$
$863$	−8.84285	+	12.1711i	−0.301014	+	0.414310i	0.631539	+	0.775344i	$0.282424\pi$
$864$		0			0
$865$	−2.12635	−	0.690892i	−0.0722979	−	0.0234910i
$866$	5.51084	−	0.774499i	0.187266	−	0.0263185i
$867$		0			0
$868$	12.2242	−	33.5858i	0.414917	−	1.13998i
$869$	43.7258	−	29.3900i	1.48330	−	0.996989i
$870$		0			0
$871$	11.7600	+	7.93221i	0.398472	+	0.268773i
$872$	−0.535793	+	2.52071i	−0.0181442	+	0.0853619i
$873$		0			0
$874$	−0.496518	+	4.72405i	−0.0167950	+	0.159793i
$875$	8.03096	+	32.2104i	0.271496	+	1.08891i
$876$		0			0
$877$	10.6369	+	20.0050i	0.359181	+	0.675521i	0.995381	−	0.0960029i	$-0.0306058\pi$
$877$	10.6369	+	20.0050i	0.359181	+	0.675521i	−0.636200	+	0.771524i	$0.719495\pi$
$878$	5.78029	−	5.98567i	0.195075	−	0.202007i
$879$		0			0
$880$	14.1965	−	6.89551i	0.478563	−	0.232448i
$881$	−30.6507	+	17.6962i	−1.03265	+	0.596200i	−0.917742	−	0.397176i	$-0.869990\pi$
$881$	−30.6507	+	17.6962i	−1.03265	+	0.596200i	−0.114906	+	0.993376i	$0.536657\pi$
$882$		0			0
$883$	−12.0118	−	2.55318i	−0.404229	−	0.0859214i	0.00131049	−	0.999999i	$-0.499583\pi$
$883$	−12.0118	−	2.55318i	−0.404229	−	0.0859214i	−0.405539	+	0.914078i	$0.632916\pi$
$884$	−45.1214	+	1.57567i	−1.51760	+	0.0529956i
$885$		0			0
$886$	0.118233	+	1.69082i	0.00397213	+	0.0568041i
$887$	22.9126	−	29.3267i	0.769328	−	0.984695i	−0.230604	−	0.973048i	$-0.574070\pi$
$887$	22.9126	−	29.3267i	0.769328	−	0.984695i	0.999932	−	0.0116476i	$-0.00370762\pi$
$888$		0			0
$889$	−13.7783	−	28.2497i	−0.462109	−	0.947465i
$890$	11.5382			0.386762
$891$		0			0
$892$	−2.56263			−0.0858033
$893$	−6.93035	−	14.2093i	−0.231915	−	0.475497i
$894$		0			0
$895$	28.2988	−	36.2208i	0.945923	−	1.21073i
$896$	−2.22731	−	31.8520i	−0.0744091	−	1.06410i
$897$		0			0
$898$	2.55410	−	0.0891910i	0.0852313	−	0.00297634i
$899$	−42.8164	−	9.10091i	−1.42801	−	0.303532i
$900$		0			0
$901$	−15.9543	+	9.21122i	−0.531515	+	0.306870i
$902$	3.86613	+	2.06373i	0.128728	+	0.0687148i
$903$		0			0
$904$	1.44049	−	1.49167i	0.0479100	−	0.0496122i
$905$	10.6397	+	20.0104i	0.353676	+	0.665168i
$906$		0			0
$907$	5.55438	+	22.2774i	0.184430	+	0.739709i	0.989255	+	0.146197i	$0.0467035\pi$
$907$	5.55438	+	22.2774i	0.184430	+	0.739709i	−0.804825	+	0.593512i	$0.797741\pi$
$908$	−0.564734	+	5.37308i	−0.0187414	+	0.178312i
$909$		0			0
$910$	4.40919	−	20.7436i	0.146163	−	0.687645i
$911$	−6.52529	−	4.40136i	−0.216192	−	0.145824i	0.446323	−	0.894872i	$-0.352733\pi$
$911$	−6.52529	−	4.40136i	−0.216192	−	0.145824i	−0.662515	+	0.749048i	$0.730511\pi$
$912$		0			0
$913$	12.4887	−	15.9313i	0.413316	−	0.527250i
$914$	1.60634	−	4.41338i	0.0531329	−	0.145982i
$915$		0			0
$916$	−31.6724	+	4.45126i	−1.04648	+	0.147074i
$917$	7.41974	+	2.41082i	0.245021	+	0.0796123i
$918$		0			0
$919$	12.0930	−	16.6445i	0.398910	−	0.549053i	−0.561560	−	0.827436i	$-0.689799\pi$
$919$	12.0930	−	16.6445i	0.398910	−	0.549053i	0.960470	+	0.278383i	$0.0897986\pi$
$920$	18.6196	+	9.90021i	0.613870	+	0.326400i
$921$		0			0
$922$	−1.16397	+	0.333763i	−0.0383333	+	0.0109919i
$923$	−43.2734	+	36.3107i	−1.42436	+	1.19518i
$924$		0			0
$925$	−3.60144	+	1.31082i	−0.118415	+	0.0430994i
$926$	0.771404	+	7.33941i	0.0253499	+	0.241188i
$927$		0			0
$928$	−29.8458	+	6.34392i	−0.979736	+	0.208249i
$929$	1.74833	−	0.435909i	0.0573610	−	0.0143017i	−0.213136	−	0.977023i	$-0.568368\pi$
$929$	1.74833	−	0.435909i	0.0573610	−	0.0143017i	0.270497	+	0.962721i	$0.412812\pi$
$930$		0			0
$931$	−0.163256	+	1.16163i	−0.00535050	+	0.0380708i
$932$	−2.93266	+	1.55932i	−0.0960624	+	0.0510773i
$933$		0			0
$934$	9.41019	−	11.2146i	0.307911	−	0.366954i
$935$	−24.7636	+	2.56203i	−0.809857	+	0.0837872i
$936$		0			0
$937$	15.2491	−	1.60274i	0.498165	−	0.0523592i	0.147886	−	0.989004i	$-0.452753\pi$
$937$	15.2491	−	1.60274i	0.498165	−	0.0523592i	0.350279	+	0.936645i	$0.386087\pi$
$938$	2.34681	−	1.83353i	0.0766260	−	0.0598668i
$939$		0			0
$940$	−32.3016	+	2.25874i	−1.05356	+	0.0736721i
$941$	−22.9642	−	34.0458i	−0.748612	−	1.10986i	−0.990224	−	0.139490i	$-0.955454\pi$
$941$	−22.9642	−	34.0458i	−0.748612	−	1.10986i	0.241612	−	0.970373i	$-0.422324\pi$
$942$		0			0
$943$	−1.80527	−	12.8451i	−0.0587875	−	0.418295i
$944$	−11.9747	−	16.4817i	−0.389742	−	0.536433i
$945$		0			0
$946$	1.70526	+	0.182036i	0.0554428	+	0.00591850i
$947$	57.9533	+	10.2187i	1.88323	+	0.332064i	0.992477	−	0.122428i	$-0.0390682\pi$
$947$	57.9533	+	10.2187i	1.88323	+	0.332064i	0.890751	+	0.454492i	$0.150179\pi$
$948$		0			0
$949$	3.37389	−	96.6154i	0.109521	−	3.13627i
$950$	−0.783748	+	0.316655i	−0.0254282	+	0.0102736i
$951$		0			0
$952$	−5.66322	+	19.7500i	−0.183546	+	0.640101i
$953$	−9.65092	−	10.7184i	−0.312624	−	0.347204i	0.566271	−	0.824219i	$-0.308385\pi$
$953$	−9.65092	−	10.7184i	−0.312624	−	0.347204i	−0.878895	+	0.477015i	$0.841719\pi$
$954$		0			0
$955$	21.6594	+	9.64338i	0.700882	+	0.312053i
$956$	11.1405	+	9.34802i	0.360311	+	0.302337i
$957$		0			0
$958$	−0.781480	−	4.43200i	−0.0252485	−	0.143191i
$959$	−20.4317	−	19.7306i	−0.659773	−	0.637135i
$960$		0			0
$961$	21.6825	−	13.5487i	0.699434	−	0.437055i
$962$	15.4444	+	1.62327i	0.497947	+	0.0523364i
$963$		0			0
$964$	9.44541	−	8.50469i	0.304216	−	0.273918i
$965$	−1.89131	−	2.42076i	−0.0608834	−	0.0779271i
$966$		0			0
$967$	19.7776	+	23.5701i	0.636006	+	0.757962i	0.983734	−	0.179633i	$-0.0574911\pi$
$967$	19.7776	+	23.5701i	0.636006	+	0.757962i	−0.347728	+	0.937596i	$0.613047\pi$
$968$	21.8316	−	1.45524i	0.701695	−	0.0467731i
$969$		0			0
$970$	2.46088	−	1.20025i	0.0790139	−	0.0385377i
$971$	−46.8858	+	15.2341i	−1.50464	+	0.488886i	−0.941366	−	0.337386i	$-0.890457\pi$
$971$	−46.8858	+	15.2341i	−1.50464	+	0.488886i	−0.563271	+	0.826272i	$0.690457\pi$
$972$		0			0
$973$	−28.7691	−	20.9020i	−0.922295	−	0.670086i
$974$	−10.3885	+	10.0321i	−0.332869	+	0.321448i
$975$		0			0
$976$	4.31251	+	0.150596i	0.138040	+	0.00482047i
$977$	37.1269	+	9.25679i	1.18780	+	0.296151i	0.785209	−	0.619231i	$-0.212555\pi$
$977$	37.1269	+	9.25679i	1.18780	+	0.296151i	0.402587	+	0.915382i	$0.368111\pi$
$978$		0			0
$979$	−32.8322	−	13.3273i	−1.04932	−	0.425941i
$980$	2.08072	+	1.20131i	0.0664663	+	0.0383743i
$981$		0			0
$982$	0.836652	−	0.929196i	0.0266986	−	0.0296518i
$983$	−13.9760	−	22.3662i	−0.445764	−	0.713371i	0.546508	−	0.837454i	$-0.315957\pi$
$983$	−13.9760	−	22.3662i	−0.445764	−	0.713371i	−0.992272	+	0.124082i	$0.960401\pi$
$984$		0			0
$985$	−20.2032	−	9.85377i	−0.643728	−	0.313967i
$986$	11.4961	+	1.61567i	0.366109	+	0.0514533i
$987$		0			0
$988$	−20.3948	−	1.42614i	−0.648845	−	0.0453717i
$989$	−2.53798	−	4.39592i	−0.0807032	−	0.139782i
$990$		0			0
$991$	6.79604	−	11.7711i	0.215883	−	0.373921i	−0.737662	−	0.675170i	$-0.764070\pi$
$991$	6.79604	−	11.7711i	0.215883	−	0.373921i	0.953545	+	0.301249i	$0.0974036\pi$
$992$	22.0496	−	32.6899i	0.700076	−	1.03791i
$993$		0			0
$994$	4.44279	+	10.9963i	0.140917	+	0.348781i
$995$	1.99393	−	1.34492i	0.0632118	−	0.0426369i
$996$		0			0
$997$	1.25349	−	2.35747i	0.0396984	−	0.0746619i	−0.862309	−	0.506383i	$-0.830982\pi$
$997$	1.25349	−	2.35747i	0.0396984	−	0.0746619i	0.902007	+	0.431721i	$0.142093\pi$
$998$	−0.755740	−	2.32593i	−0.0239225	−	0.0736260i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.bb.a.8.19		816
3.2	odd	2		297.2.x.a.272.16	yes	816
11.7	odd	10	inner	891.2.bb.a.656.19		816
27.13	even	9		297.2.x.a.41.16	yes	816
27.14	odd	18	inner	891.2.bb.a.800.19		816
33.29	even	10		297.2.x.a.29.16	✓	816
297.40	odd	90		297.2.x.a.95.16	yes	816
297.95	even	90	inner	891.2.bb.a.557.19		816

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
297.2.x.a.29.16	✓	816	33.29	even	10
297.2.x.a.41.16	yes	816	27.13	even	9
297.2.x.a.95.16	yes	816	297.40	odd	90
297.2.x.a.272.16	yes	816	3.2	odd	2
891.2.bb.a.8.19		816	1.1	even	1	trivial
891.2.bb.a.557.19		816	297.95	even	90	inner
891.2.bb.a.656.19		816	11.7	odd	10	inner
891.2.bb.a.800.19		816	27.14	odd	18	inner

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:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.bb (of order \(90\), degree \(24\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.234840 + 0.481493i) q^{2} +(1.05464 - 1.34987i) q^{4} +(0.140627 + 2.01106i) q^{5} +(2.77243 - 0.0968153i) q^{7} +(1.94563 + 0.413557i) q^{8} +(-0.935288 + 0.539989i) q^{10} +(3.28509 - 0.456240i) q^{11} +(-4.91714 + 5.09185i) q^{13} +(0.697692 + 1.31217i) q^{14} +(-0.571045 - 2.29034i) q^{16} +(-0.389206 + 3.70304i) q^{17} +(-0.350554 + 1.64923i) q^{19} +(2.86299 + 1.93111i) q^{20} +(0.991147 + 1.47461i) q^{22} +(1.79865 - 4.94174i) q^{23} +(0.926739 - 0.130245i) q^{25} +(-3.60642 - 1.17180i) q^{26} +(2.79322 - 3.84453i) q^{28} +(-5.13875 - 2.73232i) q^{29} +(7.22978 - 2.07311i) q^{31} +(4.01615 - 3.36995i) q^{32} +(-1.87439 + 0.682222i) q^{34} +(0.584581 + 5.56191i) q^{35} +(-4.00581 + 0.851461i) q^{37} +(-0.876416 + 0.218515i) q^{38} +(-0.558080 + 3.97095i) q^{40} +(2.17784 - 1.15798i) q^{41} +(0.620430 - 0.739399i) q^{43} +(2.84872 - 4.91563i) q^{44} +(2.80180 - 0.294481i) q^{46} +(-7.38871 + 5.77269i) q^{47} +(0.694030 - 0.0485313i) q^{49} +(0.280347 + 0.415631i) q^{50} +(1.68755 + 12.0076i) q^{52} +(2.90818 + 4.00277i) q^{53} +(1.37950 + 6.54237i) q^{55} +(5.43416 + 0.958189i) q^{56} +(0.108811 - 3.11593i) q^{58} +(8.00230 - 3.23314i) q^{59} +(-0.503892 + 1.75728i) q^{61} +(2.69602 + 2.99424i) q^{62} +(-1.74700 - 0.777815i) q^{64} +(-10.9315 - 9.17262i) q^{65} +(-0.347986 - 1.97353i) q^{67} +(4.58817 + 4.43075i) q^{68} +(-2.54074 + 1.58763i) q^{70} +(7.93671 + 0.834182i) q^{71} +(-10.1495 + 9.13863i) q^{73} +(-1.35070 - 1.72881i) q^{74} +(1.85654 + 2.21254i) q^{76} +(9.06351 - 1.58294i) q^{77} +(14.2775 - 6.96360i) q^{79} +(4.52571 - 1.47049i) q^{80} +(1.06900 + 0.776676i) q^{82} +(4.39047 - 4.23982i) q^{83} +(-7.50179 - 0.261968i) q^{85} +(0.501717 + 0.125092i) q^{86} +(6.58026 + 0.470898i) q^{88} +(-9.25241 - 5.34188i) q^{89} +(-13.1394 + 14.5928i) q^{91} +(-4.77381 - 7.63969i) q^{92} +(-4.51467 - 2.20195i) q^{94} +(-3.36600 - 0.473061i) q^{95} +(-2.52904 - 0.176848i) q^{97} +(0.186353 + 0.322773i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 816 q + 30 q^{2} - 18 q^{4} + 21 q^{5} - 30 q^{7} + 45 q^{8} + 33 q^{11} - 30 q^{13} + 18 q^{14} - 30 q^{16} + 45 q^{17} - 15 q^{19} + 60 q^{20} - 15 q^{22} + 84 q^{23} - 27 q^{25} - 60 q^{28} - 60 q^{29}+ \cdots - 81 q^{97}+O(q^{100}) \) 816 * q + 30 * q^2 - 18 * q^4 + 21 * q^5 - 30 * q^7 + 45 * q^8 + 33 * q^11 - 30 * q^13 + 18 * q^14 - 30 * q^16 + 45 * q^17 - 15 * q^19 + 60 * q^20 - 15 * q^22 + 84 * q^23 - 27 * q^25 - 60 * q^28 - 60 * q^29 - 9 * q^31 - 42 * q^34 + 45 * q^35 - 9 * q^37 + 18 * q^38 - 90 * q^40 + 30 * q^41 + 108 * q^44 - 15 * q^46 + 6 * q^47 - 18 * q^49 + 105 * q^50 - 30 * q^52 - 48 * q^55 - 54 * q^56 - 18 * q^58 - 81 * q^59 - 30 * q^61 + 45 * q^62 + 51 * q^64 + 6 * q^67 + 225 * q^68 - 93 * q^70 + 27 * q^71 - 15 * q^73 + 30 * q^74 + 141 * q^77 - 30 * q^79 - 36 * q^82 - 15 * q^83 - 30 * q^85 - 93 * q^86 - 108 * q^88 - 54 * q^89 - 9 * q^91 - 276 * q^92 - 30 * q^94 - 90 * q^95 - 81 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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