LMFDB - Embedded newform 891.2.bb.a.800.19

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			800.19
Character	$\chi$	$=$	891.800
Dual form			891.2.bb.a.656.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.385357 + 0.372135i) q^{2} +(-0.0597834 - 1.71197i) q^{4} +(1.95609 - 0.487708i) q^{5} +(2.18603 + 1.70792i) q^{7} +(1.33097 - 1.47819i) q^{8} +(0.935288 + 0.539989i) q^{10} +(-0.121142 + 3.31441i) q^{11} +(6.36211 - 3.10301i) q^{13} +(0.206828 + 1.47166i) q^{14} +(-2.35470 + 0.164657i) q^{16} +(-3.40153 + 1.51446i) q^{17} +(-1.25300 - 1.12820i) q^{19} +(-0.951885 - 3.31962i) q^{20} +(-1.28009 + 1.23215i) q^{22} +(1.79865 + 4.94174i) q^{23} +(-0.826304 + 0.439353i) q^{25} +(3.60642 + 1.17180i) q^{26} +(2.79322 - 3.84453i) q^{28} +(-5.76336 - 0.809987i) q^{29} +(4.20577 - 6.23530i) q^{31} +(-4.01615 - 3.36995i) q^{32} +(-1.87439 - 0.682222i) q^{34} +(5.10905 + 2.27469i) q^{35} +(2.74029 + 3.04340i) q^{37} +(-0.0630073 - 0.901046i) q^{38} +(1.88257 - 3.54059i) q^{40} +(2.44256 - 0.343279i) q^{41} +(-0.620430 - 0.739399i) q^{43} +(5.68142 + 0.00924481i) q^{44} +(-1.14587 + 2.57367i) q^{46} +(9.37069 + 0.327232i) q^{47} +(0.168311 + 0.675059i) q^{49} +(-0.481921 - 0.138189i) q^{50} +(-5.69261 - 10.7062i) q^{52} +(-2.90818 - 4.00277i) q^{53} +(1.37950 + 6.54237i) q^{55} +(5.43416 - 0.958189i) q^{56} +(-1.91953 - 2.45688i) q^{58} +(-4.57361 - 7.31930i) q^{59} +(-1.51556 + 1.02226i) q^{61} +(3.94110 - 0.837706i) q^{62} +(0.199893 + 1.90185i) q^{64} +(10.9315 - 9.17262i) q^{65} +(-0.347986 + 1.97353i) q^{67} +(2.79607 + 5.73279i) q^{68} +(1.12231 + 2.77783i) q^{70} +(3.24593 + 7.29048i) q^{71} +(-2.83955 - 13.3590i) q^{73} +(-0.0765657 + 2.19256i) q^{74} +(-1.85654 + 2.21254i) q^{76} +(-5.92556 + 7.03852i) q^{77} +(-11.0348 + 11.4268i) q^{79} +(-4.52571 + 1.47049i) q^{80} +(1.06900 + 0.776676i) q^{82} +(2.67558 - 5.48576i) q^{83} +(-5.91509 + 4.62138i) q^{85} +(0.0360694 - 0.515817i) q^{86} +(4.73809 + 4.59044i) q^{88} +(-9.25241 + 5.34188i) q^{89} +(19.2075 + 4.08267i) q^{91} +(8.35259 - 3.37466i) q^{92} +(3.48929 + 3.61327i) q^{94} +(-3.00121 - 1.59577i) q^{95} +(-0.613324 + 2.45991i) q^{97} +(-0.186353 + 0.322773i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{17}{18}\right)$

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 $

$2$	0.385357	+	0.372135i	0.272489	+	0.263139i	0.818329	−	0.574750i	$-0.194901\pi$
$2$	0.385357	+	0.372135i	0.272489	+	0.263139i	−0.545840	+	0.837889i	$0.683790\pi$
$3$		0			0
$3$		0			0
$4$	−0.0597834	−	1.71197i	−0.0298917	−	0.855986i
$5$	1.95609	−	0.487708i	0.874791	−	0.218110i	0.221448	−	0.975172i	$-0.428922\pi$
$5$	1.95609	−	0.487708i	0.874791	−	0.218110i	0.653343	+	0.757062i	$0.273366\pi$
$6$		0			0
$7$	2.18603	+	1.70792i	0.826243	+	0.645532i	0.937394	−	0.348272i	$-0.113231\pi$
$7$	2.18603	+	1.70792i	0.826243	+	0.645532i	−0.111150	+	0.993804i	$0.535454\pi$
$8$	1.33097	−	1.47819i	0.470568	−	0.522618i
$9$		0			0
$10$	0.935288	+	0.539989i	0.295764	+	0.170759i
$11$	−0.121142	+	3.31441i	−0.0365257	+	0.999333i
$11$	−0.121142	+	3.31441i	−0.0365257	+	0.999333i
$12$		0			0
$13$	6.36211	−	3.10301i	1.76453	−	0.860620i	0.798585	−	0.601883i	$-0.205583\pi$
$13$	6.36211	−	3.10301i	1.76453	−	0.860620i	0.965948	−	0.258737i	$-0.0833064\pi$
$14$	0.206828	+	1.47166i	0.0552771	+	0.393317i
$15$		0			0
$16$	−2.35470	+	0.164657i	−0.588675	+	0.0411642i
$17$	−3.40153	+	1.51446i	−0.824993	+	0.367310i	−0.775409	−	0.631459i	$-0.782456\pi$
$17$	−3.40153	+	1.51446i	−0.824993	+	0.367310i	−0.0495840	+	0.998770i	$0.515790\pi$
$18$		0			0
$19$	−1.25300	−	1.12820i	−0.287457	−	0.258828i	0.512768	−	0.858527i	$-0.328620\pi$
$19$	−1.25300	−	1.12820i	−0.287457	−	0.258828i	−0.800225	+	0.599700i	$0.795287\pi$
$20$	−0.951885	−	3.31962i	−0.212848	−	0.742289i
$21$		0			0
$22$	−1.28009	+	1.23215i	−0.272917	+	0.262696i
$23$	1.79865	+	4.94174i	0.375044	+	1.03042i	0.973384	+	0.229181i	$0.0736049\pi$
$23$	1.79865	+	4.94174i	0.375044	+	1.03042i	−0.598340	+	0.801242i	$0.704173\pi$
$24$		0			0
$25$	−0.826304	+	0.439353i	−0.165261	+	0.0878707i
$26$	3.60642	+	1.17180i	0.707278	+	0.229809i
$27$		0			0
$28$	2.79322	−	3.84453i	0.527868	−	0.726548i
$29$	−5.76336	−	0.809987i	−1.07023	−	0.150411i	−0.418010	−	0.908442i	$-0.637272\pi$
$29$	−5.76336	−	0.809987i	−1.07023	−	0.150411i	−0.652218	+	0.758031i	$0.726161\pi$
$30$		0			0
$31$	4.20577	−	6.23530i	0.755378	−	1.11989i	−0.233672	−	0.972315i	$-0.575074\pi$
$31$	4.20577	−	6.23530i	0.755378	−	1.11989i	0.989050	−	0.147578i	$-0.0471479\pi$
$32$	−4.01615	−	3.36995i	−0.709962	−	0.595729i
$33$		0			0
$34$	−1.87439	−	0.682222i	−0.321455	−	0.117000i
$35$	5.10905	+	2.27469i	0.863587	+	0.384494i
$36$		0			0
$37$	2.74029	+	3.04340i	0.450501	+	0.500332i	0.925023	−	0.379912i	$-0.124046\pi$
$37$	2.74029	+	3.04340i	0.450501	+	0.500332i	−0.474522	+	0.880244i	$0.657379\pi$
$38$	−0.0630073	−	0.901046i	−0.0102211	−	0.146169i
$39$		0			0
$40$	1.88257	−	3.54059i	0.297660	−	0.559817i
$41$	2.44256	−	0.343279i	0.381463	−	0.0536112i	0.0541644	−	0.998532i	$-0.482750\pi$
$41$	2.44256	−	0.343279i	0.381463	−	0.0536112i	0.327299	+	0.944921i	$0.393862\pi$
$42$		0			0
$43$	−0.620430	−	0.739399i	−0.0946146	−	0.112757i	0.716660	−	0.697423i	$-0.245670\pi$
$43$	−0.620430	−	0.739399i	−0.0946146	−	0.112757i	−0.811274	+	0.584666i	$0.801226\pi$
$44$	5.68142	+	0.00924481i	0.856506	+	0.00139371i
$45$		0			0
$46$	−1.14587	+	2.57367i	−0.168950	+	0.379468i
$47$	9.37069	+	0.327232i	1.36686	+	0.0477317i	0.708892	−	0.705317i	$-0.249195\pi$
$47$	9.37069	+	0.327232i	1.36686	+	0.0477317i	0.657965	+	0.753049i	$0.271418\pi$
$48$		0			0
$49$	0.168311	+	0.675059i	0.0240444	+	0.0964370i
$50$	−0.481921	−	0.138189i	−0.0681539	−	0.0195428i
$51$		0			0
$52$	−5.69261	−	10.7062i	−0.789423	−	1.48469i
$53$	−2.90818	−	4.00277i	−0.399469	−	0.549822i	0.561141	−	0.827720i	$-0.310362\pi$
$53$	−2.90818	−	4.00277i	−0.399469	−	0.549822i	−0.960611	+	0.277898i	$0.910362\pi$
$54$		0			0
$55$	1.37950	+	6.54237i	0.186012	+	0.882174i
$56$	5.43416	−	0.958189i	0.726170	−	0.128043i
$57$		0			0
$58$	−1.91953	−	2.45688i	−0.252046	−	0.322604i
$59$	−4.57361	−	7.31930i	−0.595433	−	0.952892i	−0.999275	−	0.0380633i	$-0.987881\pi$
$59$	−4.57361	−	7.31930i	−0.595433	−	0.952892i	0.403842	−	0.914829i	$-0.367674\pi$
$60$		0			0
$61$	−1.51556	+	1.02226i	−0.194048	+	0.130887i	−0.652374	−	0.757897i	$-0.726227\pi$
$61$	−1.51556	+	1.02226i	−0.194048	+	0.130887i	0.458326	+	0.888784i	$0.348449\pi$
$62$	3.94110	−	0.837706i	0.500520	−	0.106389i
$63$		0			0
$64$	0.199893	+	1.90185i	0.0249866	+	0.237732i
$65$	10.9315	−	9.17262i	1.35589	−	1.13772i
$66$		0			0
$67$	−0.347986	+	1.97353i	−0.0425132	+	0.241105i	−0.998658	−	0.0517899i	$-0.983507\pi$
$67$	−0.347986	+	1.97353i	−0.0425132	+	0.241105i	0.956145	+	0.292895i	$0.0946185\pi$
$68$	2.79607	+	5.73279i	0.339073	+	0.695203i
$69$		0			0
$70$	1.12231	+	2.77783i	0.134142	+	0.332014i
$71$	3.24593	+	7.29048i	0.385221	+	0.865221i	0.997231	+	0.0743705i	$0.0236948\pi$
$71$	3.24593	+	7.29048i	0.385221	+	0.865221i	−0.612009	+	0.790850i	$0.709639\pi$
$72$		0			0
$73$	−2.83955	−	13.3590i	−0.332344	−	1.56355i	−0.754047	−	0.656821i	$-0.771901\pi$
$73$	−2.83955	−	13.3590i	−0.332344	−	1.56355i	0.421703	−	0.906734i	$-0.361432\pi$
$74$	−0.0765657	+	2.19256i	−0.00890059	+	0.254879i
$75$		0			0
$76$	−1.85654	+	2.21254i	−0.212960	+	0.253796i
$77$	−5.92556	+	7.03852i	−0.675280	+	0.802113i
$78$		0			0
$79$	−11.0348	+	11.4268i	−1.24151	+	1.28562i	−0.297883	+	0.954602i	$0.596280\pi$
$79$	−11.0348	+	11.4268i	−1.24151	+	1.28562i	−0.943625	+	0.331017i	$0.892608\pi$
$80$	−4.52571	+	1.47049i	−0.505989	+	0.164406i
$81$		0			0
$82$	1.06900	+	0.776676i	0.118052	+	0.0857696i
$83$	2.67558	−	5.48576i	0.293683	−	0.602140i	−0.700028	−	0.714116i	$-0.746829\pi$
$83$	2.67558	−	5.48576i	0.293683	−	0.602140i	0.993711	+	0.111976i	$0.0357179\pi$
$84$		0			0
$85$	−5.91509	+	4.62138i	−0.641582	+	0.501259i
$86$	0.0360694	−	0.515817i	0.00388946	−	0.0556219i
$87$		0			0
$88$	4.73809	+	4.59044i	0.505082	+	0.489343i
$89$	−9.25241	+	5.34188i	−0.980753	+	0.566238i	−0.902497	−	0.430695i	$-0.858268\pi$
$89$	−9.25241	+	5.34188i	−0.980753	+	0.566238i	−0.0782556	+	0.996933i	$0.524935\pi$
$90$		0			0
$91$	19.2075	+	4.08267i	2.01349	+	0.427981i
$92$	8.35259	−	3.37466i	0.870817	−	0.351833i
$93$		0			0
$94$	3.48929	+	3.61327i	0.359893	+	0.372680i
$95$	−3.00121	−	1.59577i	−0.307918	−	0.163723i
$96$		0			0
$97$	−0.613324	+	2.45991i	−0.0622736	+	0.249766i	−0.993362	−	0.115027i	$-0.963305\pi$
$97$	−0.613324	+	2.45991i	−0.0622736	+	0.249766i	0.931089	+	0.364793i	$0.118860\pi$
$98$	−0.186353	+	0.322773i	−0.0188245	+	0.0326050i
$99$		0			0
$100$	0.801560	+	1.38834i	0.0801560	+	0.138834i
$101$	−3.46773	+	0.994356i	−0.345052	+	0.0989422i	−0.443688	−	0.896181i	$-0.646330\pi$
$101$	−3.46773	+	0.994356i	−0.345052	+	0.0989422i	0.0986353	+	0.995124i	$0.468552\pi$
$102$		0			0
$103$	12.6590	−	7.91020i	1.24732	−	0.779415i	0.264577	−	0.964365i	$-0.414768\pi$
$103$	12.6590	−	7.91020i	1.24732	−	0.779415i	0.982748	+	0.184950i	$0.0592122\pi$
$104$	3.88093	−	13.5344i	0.380556	−	1.32716i
$105$		0			0
$106$	0.368882	−	2.62473i	0.0358290	−	0.254936i
$107$	1.23480	+	3.80034i	0.119373	+	0.367392i	0.992834	−	0.119502i	$-0.0381297\pi$
$107$	1.23480	+	3.80034i	0.119373	+	0.367392i	−0.873461	+	0.486894i	$0.838130\pi$
$108$		0			0
$109$			1.29557i			0.124093i	0.998073	+	0.0620467i	$0.0197628\pi$
$109$			1.29557i			0.124093i	−0.998073	+	0.0620467i	$0.980237\pi$
$110$	−1.90305	+	3.03451i	−0.181448	+	0.289329i
$111$		0			0
$112$	−5.42868	−	3.66169i	−0.512962	−	0.345997i
$113$	−0.966604	−	0.390533i	−0.0909304	−	0.0367383i	0.328691	−	0.944438i	$-0.393393\pi$
$113$	−0.966604	−	0.390533i	−0.0909304	−	0.0367383i	−0.419621	+	0.907699i	$0.637837\pi$
$114$		0			0
$115$	5.92844	+	8.78928i	0.552830	+	0.819604i
$116$	−1.04212	+	9.91513i	−0.0967586	+	0.920596i
$117$		0			0
$118$	0.961297	−	4.52255i	0.0884945	−	0.416334i
$119$	−10.0224	−	2.49887i	−0.918755	−	0.229071i
$120$		0			0
$121$	−10.9706	−	0.803028i	−0.997332	−	0.0730026i
$122$	−0.964452	−	0.170059i	−0.0873174	−	0.0153964i
$123$		0			0
$124$	−10.9261	−	6.82738i	−0.981193	−	0.613117i
$125$	−8.89285	+	8.00716i	−0.795401	+	0.716182i
$126$		0			0
$127$	11.2679	+	1.18430i	0.999865	+	0.105090i	0.590294	−	0.807188i	$-0.299012\pi$
$127$	11.2679	+	1.18430i	0.999865	+	0.105090i	0.409571	+	0.912278i	$0.365678\pi$
$128$	−7.08619	+	9.06991i	−0.626337	+	0.801674i
$129$		0			0
$130$	7.62599	+	0.533261i	0.668844	+	0.0467701i
$131$	−2.64267	+	0.961854i	−0.230891	+	0.0840376i	−0.454875	−	0.890555i	$-0.650316\pi$
$131$	−2.64267	+	0.961854i	−0.230891	+	0.0840376i	0.223984	+	0.974593i	$0.428094\pi$
$132$		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
$137$	−9.20248	−	4.48835i	−0.786221	−	0.383466i	0.00110751	−	0.999999i	$-0.499647\pi$
$137$	−9.20248	−	4.48835i	−0.786221	−	0.383466i	−0.787328	+	0.616534i	$0.788536\pi$
$138$		0			0
$139$	−12.8109	+	0.447366i	−1.08661	+	0.0379451i	−0.572595	−	0.819839i	$-0.694063\pi$
$139$	−12.8109	+	0.447366i	−1.08661	+	0.0379451i	−0.514011	+	0.857784i	$0.671841\pi$
$140$	3.58878	−	8.88253i	0.303307	−	0.750711i
$141$		0			0
$142$	−1.46220	+	4.01737i	−0.122705	+	0.337130i
$143$	9.51393	+	21.4626i	0.795595	+	1.79479i
$144$		0			0
$145$	−11.6687	+	1.22643i	−0.969032	+	0.101849i
$146$	3.87712	−	6.20469i	0.320873	−	0.513504i
$147$		0			0
$148$	5.04639	−	4.87325i	0.414811	−	0.400578i
$149$	−13.8533	+	13.3780i	−1.13491	+	1.09597i	−0.140531	+	0.990076i	$0.544881\pi$
$149$	−13.8533	+	13.3780i	−1.13491	+	1.09597i	−0.994378	+	0.105892i	$0.966230\pi$
$150$		0			0
$151$	−8.15429	+	13.0496i	−0.663587	+	1.06196i	0.329452	+	0.944172i	$0.393136\pi$
$151$	−8.15429	+	13.0496i	−0.663587	+	1.06196i	−0.993039	+	0.117789i	$0.962420\pi$
$152$	−3.33539	+	0.350564i	−0.270536	+	0.0284345i
$153$		0			0
$154$	−4.90274	+	0.507234i	−0.395074	+	0.0408741i
$155$	5.18585	−	14.2480i	0.416538	−	1.14443i
$156$		0			0
$157$	0.138348	−	0.342423i	0.0110413	−	0.0273283i	−0.921562	−	0.388230i	$-0.873087\pi$
$157$	0.138348	−	0.342423i	0.0110413	−	0.0273283i	0.932604	+	0.360902i	$0.117531\pi$
$158$	−8.50465	+	0.296989i	−0.676594	+	0.0236272i
$159$		0			0
$160$	−9.49951	−	4.63322i	−0.751002	−	0.366288i
$161$	−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
$167$	−2.64620	−	0.185040i	−0.204769	−	0.0143188i	−0.0329964	−	0.999455i	$-0.510505\pi$
$167$	−2.64620	−	0.185040i	−0.204769	−	0.0143188i	−0.171773	+	0.985137i	$0.554949\pi$
$168$		0			0
$169$	22.8442	−	29.2392i	1.75725	−	2.24917i
$170$	−3.99920	−	0.420333i	−0.306725	−	0.0322381i
$171$		0			0
$172$	−1.22874	+	1.10636i	−0.0936905	+	0.0843593i
$173$	−0.940509	−	0.587695i	−0.0715056	−	0.0446817i	0.493695	−	0.869635i	$-0.335646\pi$
$173$	−0.940509	−	0.587695i	−0.0715056	−	0.0446817i	−0.565201	+	0.824953i	$0.691201\pi$
$174$		0			0
$175$	−2.55671	−	0.450816i	−0.193269	−	0.0340785i
$176$	−0.260487	−	7.82440i	−0.0196350	−	0.589786i
$177$		0			0
$178$	−5.55338	−	1.38461i	−0.416244	−	0.103781i
$179$	4.74045	−	22.3020i	0.354318	−	1.66693i	−0.334804	−	0.942288i	$-0.608670\pi$
$179$	4.74045	−	22.3020i	0.354318	−	1.66693i	0.689122	−	0.724646i	$-0.257996\pi$
$180$		0			0
$181$	−1.17509	+	11.1802i	−0.0873436	+	0.831018i	0.859891	+	0.510477i	$0.170531\pi$
$181$	−1.17509	+	11.1802i	−0.0873436	+	0.831018i	−0.947235	+	0.320541i	$0.896135\pi$
$182$	5.88243	+	8.72107i	0.436035	+	0.646448i
$183$		0			0
$184$	9.69875	+	3.91855i	0.715002	+	0.288879i
$185$	6.84455	+	4.61671i	0.503222	+	0.339427i
$186$		0			0
$187$	−4.60748	−	11.4575i	−0.336932	−	0.837859i
$188$		−	16.0619i		−	1.17144i
$189$		0			0
$190$	−0.562696	−	1.73180i	−0.0408222	−	0.125638i
$191$	1.63677	−	11.6462i	0.118432	−	0.842689i	−0.836942	−	0.547291i	$-0.815659\pi$
$191$	1.63677	−	11.6462i	0.118432	−	0.842689i	0.955374	−	0.295398i	$-0.0954521\pi$
$192$		0			0
$193$	−0.420023	+	1.46479i	−0.0302339	+	0.105438i	−0.974932	−	0.222503i	$-0.928577\pi$
$193$	−0.420023	+	1.46479i	−0.0302339	+	0.105438i	0.944698	+	0.327942i	$0.106355\pi$
$194$	−1.15177	+	0.719704i	−0.0826921	+	0.0516718i
$195$		0			0
$196$	1.14562	−	0.328501i	0.0818300	−	0.0234644i
$197$	5.57501	+	9.65620i	0.397203	+	0.687976i	0.993380	−	0.114878i	$-0.0366476\pi$
$197$	5.57501	+	9.65620i	0.397203	+	0.687976i	−0.596177	+	0.802853i	$0.703314\pi$
$198$		0			0
$199$	−0.596514	+	1.03319i	−0.0422857	+	0.0732410i	−0.886394	−	0.462932i	$-0.846797\pi$
$199$	−0.596514	+	1.03319i	−0.0422857	+	0.0732410i	0.844108	+	0.536173i	$0.180131\pi$
$200$	−0.450335	+	1.80620i	−0.0318435	+	0.127717i
$201$		0			0
$202$	−1.70635	−	0.907283i	−0.120058	−	0.0638362i
$203$	−11.2155	−	11.6140i	−0.787174	−	0.815142i
$204$		0			0
$205$	4.61044	−	1.86274i	0.322007	−	0.130099i
$206$	7.82189	+	1.66259i	0.544977	+	0.115838i
$207$		0			0
$208$	−14.4699	+	8.35422i	−1.00331	+	0.579261i
$209$	3.89112	−	4.01628i	0.269155	−	0.277812i
$210$		0			0
$211$	0.371220	−	5.30869i	0.0255558	−	0.365465i	−0.967907	−	0.251309i	$-0.919139\pi$
$211$	0.371220	−	5.30869i	0.0255558	−	0.365465i	0.993463	−	0.114156i	$-0.0364165\pi$
$212$	−6.67876	+	5.21802i	−0.458699	+	0.358375i
$213$		0			0
$214$	−0.938398	+	1.92400i	−0.0641476	+	0.131522i
$215$	−1.57423	−	1.14374i	−0.107361	−	0.0780027i
$216$		0			0
$217$	19.8433	−	6.44749i	1.34705	−	0.437684i
$218$	−0.482128	+	0.499258i	−0.0326538	+	0.0338140i
$219$		0			0
$220$	11.1179	−	2.75279i	0.749568	−	0.185593i
$221$	−16.9415	+	20.1902i	−1.13961	+	1.35814i
$222$		0			0
$223$	0.0522089	−	1.49507i	0.00349616	−	0.100117i	−0.996388	−	0.0849142i	$-0.972938\pi$
$223$	0.0522089	−	1.49507i	0.00349616	−	0.100117i	0.999884	−	0.0152028i	$-0.00483940\pi$
$224$	−3.02385	−	14.2261i	−0.202039	−	0.950520i
$225$		0			0
$226$	−0.227157	−	0.510202i	−0.0151102	−	0.0339381i
$227$	−1.18147	−	2.92425i	−0.0784171	−	0.194089i	0.882883	−	0.469594i	$-0.155600\pi$
$227$	−1.18147	−	2.92425i	−0.0784171	−	0.194089i	−0.961300	+	0.275505i	$0.911155\pi$
$228$		0			0
$229$	8.18481	+	16.7813i	0.540867	+	1.10894i	0.977818	+	0.209457i	$0.0671696\pi$
$229$	8.18481	+	16.7813i	0.540867	+	1.10894i	−0.436950	+	0.899486i	$0.643941\pi$
$230$	−0.986231	+	5.59319i	−0.0650301	+	0.368804i
$231$		0			0
$232$	−8.86815	+	7.44126i	−0.582222	+	0.488542i
$233$	−0.202675	−	1.92832i	−0.0132777	−	0.126329i	0.985875	−	0.167482i	$-0.0535635\pi$
$233$	−0.202675	−	1.92832i	−0.0132777	−	0.126329i	−0.999153	+	0.0411531i	$0.986897\pi$
$234$		0			0
$235$	18.4895	−	3.93007i	1.20612	−	0.256370i
$236$	−12.2570	+	8.26746i	−0.797863	+	0.538166i
$237$		0			0
$238$	−2.93230	−	4.69266i	−0.190073	−	0.304180i
$239$	−5.22676	−	6.68995i	−0.338091	−	0.432737i	0.588678	−	0.808367i	$-0.299648\pi$
$239$	−5.22676	−	6.68995i	−0.338091	−	0.432737i	−0.926770	+	0.375630i	$0.877426\pi$
$240$		0			0
$241$	−7.30698	+	1.28842i	−0.470684	+	0.0829943i	−0.403959	−	0.914777i	$-0.632366\pi$
$241$	−7.30698	+	1.28842i	−0.470684	+	0.0829943i	−0.0667250	+	0.997771i	$0.521255\pi$
$242$	−3.92878	−	4.39202i	−0.252552	−	0.282330i
$243$		0			0
$244$	1.84069	+	2.53349i	0.117838	+	0.162190i
$245$	0.658464	+	1.23839i	0.0420677	+	0.0791179i
$246$		0			0
$247$	−11.4725	−	3.28970i	−0.729980	−	0.209318i
$248$	−3.61922	−	14.5159i	−0.229821	−	0.921760i
$249$		0			0
$250$	−6.40667	−	0.223726i	−0.405194	−	0.0141497i
$251$	0.904542	−	2.03163i	0.0570942	−	0.128236i	−0.882746	−	0.469851i	$-0.844307\pi$
$251$	0.904542	−	2.03163i	0.0570942	−	0.128236i	0.939840	+	0.341616i	$0.110974\pi$
$252$		0			0
$253$	−16.5968	+	5.36280i	−1.04343	+	0.337156i
$254$	3.90145	+	4.64956i	0.244799	+	0.291740i
$255$		0			0
$256$	−2.31851	+	0.325845i	−0.144907	+	0.0203653i
$257$	13.5544	−	25.4920i	0.845497	−	1.59015i	0.0387524	−	0.999249i	$-0.487662\pi$
$257$	13.5544	−	25.4920i	0.845497	−	1.59015i	0.806745	−	0.590900i	$-0.201227\pi$
$258$		0			0
$259$	0.792493	+	11.3332i	0.0492431	+	0.704209i
$260$	−16.3568	−	18.1661i	−1.01441	−	1.12661i
$261$		0			0
$262$	−1.37631	−	0.612774i	−0.0850289	−	0.0378573i
$263$	5.01185	+	1.82416i	0.309044	+	0.112483i	0.491886	−	0.870659i	$-0.336308\pi$
$263$	5.01185	+	1.82416i	0.309044	+	0.112483i	−0.182842	+	0.983142i	$0.558530\pi$
$264$		0			0
$265$	−7.64085	−	6.41143i	−0.469374	−	0.393851i
$266$	1.40118	−	2.07733i	0.0859116	−	0.127369i
$267$		0			0
$268$	3.39942	+	0.477758i	0.207653	+	0.0291837i
$269$	11.6256	−	16.0013i	0.708828	−	0.975617i	−0.290994	−	0.956725i	$-0.593986\pi$
$269$	11.6256	−	16.0013i	0.708828	−	0.975617i	0.999822	−	0.0188926i	$-0.00601405\pi$
$270$		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	$0.725209\pi$
$272$	7.76023	−	4.12619i	0.470533	−	0.250187i
$273$		0			0
$274$	−1.87597	−	5.15418i	−0.113331	−	0.311376i
$275$	−1.35610	−	2.79193i	−0.0817758	−	0.168360i
$276$		0			0
$277$	8.32646	+	29.0378i	0.500288	+	1.74471i	0.653899	+	0.756581i	$0.273132\pi$
$277$	8.32646	+	29.0378i	0.500288	+	1.74471i	−0.153611	+	0.988131i	$0.549090\pi$
$278$	−5.10325	−	4.59499i	−0.306073	−	0.275589i
$279$		0			0
$280$	10.1624	−	4.52459i	0.607319	−	0.270396i
$281$	−16.8796	+	1.18034i	−1.00695	+	0.0704131i	−0.563697	−	0.825981i	$-0.690622\pi$
$281$	−16.8796	+	1.18034i	−1.00695	+	0.0704131i	−0.443257	+	0.896394i	$0.646177\pi$
$282$		0			0
$283$	2.43157	+	17.3015i	0.144542	+	1.02847i	0.918553	+	0.395297i	$0.129358\pi$
$283$	2.43157	+	17.3015i	0.144542	+	1.02847i	−0.774011	+	0.633172i	$0.781753\pi$
$284$	12.2870	−	5.99279i	0.729102	−	0.355607i
$285$		0			0
$286$	−4.32071	+	11.8112i	−0.255489	+	0.698412i
$287$	5.92580	+	3.42127i	0.349789	+	0.201951i
$288$		0			0
$289$	−2.09838	+	2.33049i	−0.123434	+	0.137088i
$290$	−4.95301	−	3.86972i	−0.290851	−	0.227238i
$291$		0			0
$292$	−22.7005	+	5.65987i	−1.32845	+	0.331219i
$293$	0.0565657	+	1.61983i	0.00330460	+	0.0946315i	0.999922	+	0.0124554i	$0.00396477\pi$
$293$	0.0565657	+	1.61983i	0.00330460	+	0.0946315i	−0.996618	+	0.0821761i	$0.973813\pi$
$294$		0			0
$295$	−12.5161	−	12.0866i	−0.728714	−	0.703711i
$296$	8.14596			0.473474
$297$		0			0
$298$	−10.3169			−0.597642
$299$	26.7774	+	25.8587i	1.54858	+	1.49545i
$300$		0			0
$301$	−0.0934478	−	2.67599i	−0.00538624	−	0.154242i
$302$	−7.99853	+	1.99426i	−0.460264	+	0.114757i
$303$		0			0
$304$	3.13620	+	2.45027i	0.179873	+	0.140533i
$305$	−2.46601	+	2.73879i	−0.141204	+	0.156822i
$306$		0			0
$307$	3.84384	+	2.21924i	0.219379	+	0.126659i	0.605663	−	0.795721i	$-0.292908\pi$
$307$	3.84384	+	2.21924i	0.219379	+	0.126659i	−0.386283	+	0.922380i	$0.626241\pi$
$308$	12.4040	+	9.72360i	0.706783	+	0.554054i
$309$		0			0
$310$	7.30059	−	3.56074i	0.414646	−	0.202236i
$311$	3.61619	+	25.7305i	0.205055	+	1.45904i	0.772175	+	0.635410i	$0.219169\pi$
$311$	3.61619	+	25.7305i	0.205055	+	1.45904i	−0.567120	+	0.823635i	$0.691942\pi$
$312$		0			0
$313$	1.22825	−	0.0858873i	0.0694245	−	0.00485464i	−0.0350020	−	0.999387i	$-0.511144\pi$
$313$	1.22825	−	0.0858873i	0.0694245	−	0.00485464i	0.104427	+	0.994533i	$0.466699\pi$
$314$	0.180741	−	0.0804710i	0.0101998	−	0.00454124i
$315$		0			0
$316$	20.2221	+	18.2081i	1.13758	+	1.02428i
$317$	3.31208	+	11.5506i	0.186025	+	0.648746i	0.997892	+	0.0649029i	$0.0206738\pi$
$317$	3.31208	+	11.5506i	0.186025	+	0.648746i	−0.811867	+	0.583843i	$0.801548\pi$
$318$		0			0
$319$	3.38281	−	19.0040i	0.189401	−	1.06402i
$320$	1.31856	+	3.62271i	0.0737097	+	0.202516i
$321$		0			0
$322$	−6.90054	+	3.66908i	−0.384552	+	0.204470i
$323$	5.97073	+	1.94001i	0.332220	+	0.107945i
$324$		0			0
$325$	−3.89372	+	5.35924i	−0.215985	+	0.297277i
$326$	−13.1999	−	1.85512i	−0.731075	−	0.102746i
$327$		0			0
$328$	2.74353	−	4.06745i	0.151486	−	0.224587i
$329$	19.9258	+	16.7197i	1.09854	+	0.921787i
$330$		0			0
$331$	22.6014	+	8.22625i	1.24229	+	0.452155i	0.877788	−	0.479048i	$-0.159018\pi$
$331$	22.6014	+	8.22625i	1.24229	+	0.452155i	0.364499	+	0.931204i	$0.381240\pi$
$332$	−9.55142	−	4.25257i	−0.524202	−	0.233390i
$333$		0			0
$334$	−0.950872	−	1.05605i	−0.0520294	−	0.0577845i
$335$	0.281813	+	4.03011i	0.0153971	+	0.220189i
$336$		0			0
$337$	−1.78299	+	3.35331i	−0.0971254	+	0.182666i	−0.926774	−	0.375620i	$-0.877430\pi$
$337$	−1.78299	+	3.35331i	−0.0971254	+	0.182666i	0.829648	+	0.558286i	$0.188541\pi$
$338$	19.6841	−	2.76642i	1.07068	−	0.150474i
$339$		0			0
$340$	8.26529	+	9.85019i	0.448248	+	0.534202i
$341$	20.1569	+	14.6950i	1.09156	+	0.795779i
$342$		0			0
$343$	7.11333	−	15.9768i	0.384084	−	0.862667i
$344$	−1.91874	−	0.0670040i	−0.103452	−	0.00361261i
$345$		0			0
$346$	−0.143730	−	0.576469i	−0.00772697	−	0.0309912i
$347$	−25.1989	−	7.22566i	−1.35275	−	0.387894i	−0.480515	−	0.876987i	$-0.659550\pi$
$347$	−25.1989	−	7.22566i	−1.35275	−	0.387894i	−0.872232	+	0.489093i	$0.837328\pi$
$348$		0			0
$349$	2.32138	+	4.36588i	0.124261	+	0.233700i	0.937312	−	0.348492i	$-0.113306\pi$
$349$	2.32138	+	4.36588i	0.124261	+	0.233700i	−0.813051	+	0.582192i	$0.802195\pi$
$350$	−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	−0.562460	−	0.826824i	$-0.690145\pi$
$353$	−15.1849	+	2.67750i	−0.808210	+	0.142509i	−0.245749	+	0.969333i	$0.579034\pi$
$354$		0			0
$355$	9.90497	+	12.6778i	0.525701	+	0.672867i
$356$	9.69829	+	15.5205i	0.514008	+	0.822585i
$357$		0			0
$358$	10.1261	−	6.83017i	0.535183	−	0.360986i
$359$	33.3717	−	7.09336i	1.76129	−	0.374373i	0.790155	−	0.612908i	$-0.210000\pi$
$359$	33.3717	−	7.09336i	1.76129	−	0.374373i	0.971134	+	0.238534i	$0.0766669\pi$
$360$		0			0
$361$	−1.68888	−	16.0686i	−0.0888886	−	0.845718i
$362$	−4.61338	+	3.87108i	−0.242474	+	0.203460i
$363$		0			0
$364$	5.84114	−	33.1267i	0.306159	−	1.73631i
$365$	−12.0697	−	24.7466i	−0.631758	−	1.29530i
$366$		0			0
$367$	6.17098	+	15.2737i	0.322123	+	0.797282i	0.998173	+	0.0604258i	$0.0192459\pi$
$367$	6.17098	+	15.2737i	0.322123	+	0.797282i	−0.676050	+	0.736856i	$0.736310\pi$
$368$	−5.04896	−	11.3402i	−0.263195	−	0.591147i
$369$		0			0
$370$	0.919558	+	4.32618i	0.0478056	+	0.224907i
$371$	0.479012	−	13.7171i	0.0248691	−	0.712157i
$372$		0			0
$373$	−20.2914	+	24.1824i	−1.05065	+	1.25212i	−0.0838773	+	0.996476i	$0.526730\pi$
$373$	−20.2914	+	24.1824i	−1.05065	+	1.25212i	−0.966772	+	0.255639i	$0.917714\pi$
$374$	2.48823	−	6.12985i	0.128663	−	0.316967i
$375$		0			0
$376$	12.9558	−	13.4161i	0.668144	−	0.691883i
$377$	−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	$0.682643\pi$
$380$	−2.55249	+	5.23339i	−0.130940	+	0.268467i
$381$		0			0
$382$	4.96470	−	3.87885i	0.254016	−	0.198459i
$383$	−1.12171	+	16.0412i	−0.0573166	+	0.819666i	0.880831	+	0.473431i	$0.156985\pi$
$383$	−1.12171	+	16.0412i	−0.0573166	+	0.819666i	−0.938148	+	0.346235i	$0.887460\pi$
$384$		0			0
$385$	−8.15819	+	16.6579i	−0.415780	+	0.848967i
$386$	−0.706961	+	0.408164i	−0.0359834	+	0.0207750i
$387$		0			0
$388$	4.24796	+	0.902932i	0.215658	+	0.0458394i
$389$	17.7968	−	7.19039i	0.902336	−	0.364567i	0.123902	−	0.992294i	$-0.460459\pi$
$389$	17.7968	−	7.19039i	0.902336	−	0.364567i	0.778433	+	0.627727i	$0.216015\pi$
$390$		0			0
$391$	−13.6022	−	14.0855i	−0.687894	−	0.712335i
$392$	1.22188	+	0.649685i	0.0617143	+	0.0328141i
$393$		0			0
$394$	−1.44504	+	5.79574i	−0.0728001	+	0.291985i
$395$	−16.0120	+	27.7337i	−0.805653	+	1.39543i
$396$		0			0
$397$	−8.27264	−	14.3286i	−0.415192	−	0.719133i	0.580257	−	0.814434i	$-0.302952\pi$
$397$	−8.27264	−	14.3286i	−0.415192	−	0.719133i	−0.995449	+	0.0953004i	$0.969619\pi$
$398$	−0.614358	+	0.176164i	−0.0307950	+	0.00883032i
$399$		0			0
$400$	1.87336	−	1.17060i	0.0936678	−	0.0585301i
$401$	−7.19990	+	25.1090i	−0.359546	+	1.25389i	0.548902	+	0.835887i	$0.315046\pi$
$401$	−7.19990	+	25.1090i	−0.359546	+	1.25389i	−0.908448	+	0.417999i	$0.862732\pi$
$402$		0			0
$403$	7.40935	−	52.7202i	0.369086	−	2.62618i
$404$	1.90962	+	5.87721i	0.0950073	+	0.292402i
$405$		0			0
$406$		−	8.64922i		−	0.429254i
$407$	−10.4191	+	8.71377i	−0.516453	+	0.431926i
$408$		0			0
$409$	15.7084	+	10.5954i	0.776730	+	0.523911i	0.882406	−	0.470489i	$-0.155923\pi$
$409$	15.7084	+	10.5954i	0.776730	+	0.523911i	−0.105675	+	0.994401i	$0.533700\pi$
$410$	2.46986	+	0.997888i	0.121978	+	0.0492822i
$411$		0			0
$412$	−14.2988	−	21.1989i	−0.704453	−	1.04439i
$413$	2.50270	−	23.8116i	0.123150	−	1.17169i
$414$		0			0
$415$	2.55824	−	12.0355i	0.125579	−	0.590802i
$416$	−36.0082	−	8.97785i	−1.76545	−	0.440175i
$417$		0			0
$418$	2.99407	−	0.0996776i	0.146445	−	0.00487539i
$419$	−6.95358	−	1.22610i	−0.339704	−	0.0598991i	0.00119373	−	0.999999i	$-0.499620\pi$
$419$	−6.95358	−	1.22610i	−0.339704	−	0.0598991i	−0.340898	+	0.940100i	$0.610731\pi$
$420$		0			0
$421$	−11.1534	−	6.96945i	−0.543586	−	0.339670i	0.230174	−	0.973150i	$-0.426071\pi$
$421$	−11.1534	−	6.96945i	−0.543586	−	0.339670i	−0.773759	+	0.633480i	$0.781626\pi$
$422$	2.11860	−	1.90760i	0.103132	−	0.0928604i
$423$		0			0
$424$	−9.78753	−	1.02871i	−0.475325	−	0.0499586i
$425$	2.14532	−	2.74588i	0.104063	−	0.133195i
$426$		0			0
$427$	−5.05901	−	0.353760i	−0.244823	−	0.0171197i
$428$	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	$-0.370860\pi$
$431$	28.8671	−	20.9732i	1.39048	−	1.01024i	0.995812	−	0.0914192i	$-0.0291403\pi$
$432$		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	$0.0196976\pi$
$434$	10.0461	+	4.89981i	0.482229	+	0.235199i
$435$		0			0
$436$	2.21798	−	0.0774537i	0.106222	−	0.00370936i
$437$	3.32159	−	8.22122i	0.158893	−	0.393274i
$438$		0			0
$439$	5.31252	−	14.5960i	0.253553	−	0.696631i	−0.745977	−	0.665972i	$-0.768017\pi$
$439$	5.31252	−	14.5960i	0.253553	−	0.696631i	0.999530	−	0.0306592i	$-0.00976066\pi$
$440$	11.5069	+	6.66852i	0.548571	+	0.317909i
$441$		0			0
$442$	−14.0420	+	1.47588i	−0.667911	+	0.0702002i
$443$	−1.67662	+	2.68316i	−0.0796588	+	0.127481i	−0.885479	−	0.464680i	$-0.846169\pi$
$443$	−1.67662	+	2.68316i	−0.0796588	+	0.127481i	0.805820	+	0.592161i	$0.201725\pi$
$444$		0			0
$445$	−15.4933	+	14.9617i	−0.734452	+	0.709252i
$446$	0.576486	−	0.556706i	0.0272974	−	0.0263608i
$447$		0			0
$448$	−2.81124	+	4.49892i	−0.132818	+	0.212554i
$449$	4.74446	−	0.498663i	0.223905	−	0.0235334i	0.00808837	−	0.999967i	$-0.497425\pi$
$449$	4.74446	−	0.498663i	0.223905	−	0.0235334i	0.215817	+	0.976434i	$0.430759\pi$
$450$		0			0
$451$	0.841872	+	8.13723i	0.0396422	+	0.383167i
$452$	−0.610795	+	1.67815i	−0.0287294	+	0.0789333i
$453$		0			0
$454$	0.632926	−	1.56655i	0.0297047	−	0.0735217i
$455$	39.5627	−	1.38156i	1.85473	−	0.0647686i
$456$		0			0
$457$	7.87981	+	3.84324i	0.368602	+	0.179779i	0.613357	−	0.789806i	$-0.289819\pi$
$457$	7.87981	+	3.84324i	0.368602	+	0.179779i	−0.244755	+	0.969585i	$0.578708\pi$
$458$	−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	$-0.0387930\pi$
$461$	0.392501	+	2.22598i	0.0182806	+	0.103674i	−0.974302	+	0.225245i	$0.927682\pi$
$462$		0			0
$463$	12.9450	−	4.71161i	0.601607	−	0.218967i	−0.0232198	−	0.999730i	$-0.507392\pi$
$463$	12.9450	−	4.71161i	0.601607	−	0.218967i	0.624827	+	0.780763i	$0.285170\pi$
$464$	13.7044	+	0.958302i	0.636209	+	0.0444880i
$465$		0			0
$466$	0.639495	−	0.818516i	0.0296240	−	0.0379170i
$467$	−27.1779	−	2.85651i	−1.25764	−	0.132184i	−0.547839	−	0.836584i	$-0.684549\pi$
$467$	−27.1779	−	2.85651i	−1.25764	−	0.132184i	−0.709803	+	0.704400i	$0.751216\pi$
$468$		0			0
$469$	−4.13133	+	3.71986i	−0.190767	+	0.171767i
$470$	8.58759	+	5.36612i	0.396116	+	0.247521i
$471$		0			0
$472$	−16.9066	−	2.98109i	−0.778190	−	0.137216i
$473$	2.52583	−	1.96679i	0.116138	−	0.0904330i
$474$		0			0
$475$	1.53104	+	0.381730i	0.0702488	+	0.0175150i
$476$	−3.67883	+	17.3075i	−0.168619	+	0.793289i
$477$		0			0
$478$	0.475395	−	4.52308i	0.0217441	−	0.206881i
$479$	4.69764	+	6.96454i	0.214641	+	0.318218i	0.920947	−	0.389689i	$-0.127417\pi$
$479$	4.69764	+	6.96454i	0.214641	+	0.318218i	−0.706306	+	0.707907i	$0.749640\pi$
$480$		0			0
$481$	26.8777	+	10.8593i	1.22552	+	0.495142i
$482$	−3.29526	−	2.22268i	−0.150095	−	0.101240i
$483$		0			0
$484$	−0.718899	+	18.8294i	−0.0326772	+	0.855884i
$485$			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	$0.690850\pi$
$488$	−0.506071	+	3.60088i	−0.0229087	+	0.163004i
$489$		0			0
$490$	−0.207105	+	0.722260i	−0.00935604	+	0.0326284i
$491$	−1.97936	+	1.23684i	−0.0893273	+	0.0558179i	−0.573847	−	0.818962i	$-0.694550\pi$
$491$	−1.97936	+	1.23684i	−0.0893273	+	0.0558179i	0.484520	+	0.874780i	$0.338994\pi$
$492$		0			0
$493$	20.8309	−	5.97317i	0.938178	−	0.269018i
$494$	−3.19681	−	5.53704i	−0.143831	−	0.249123i
$495$		0			0
$496$	−8.87664	+	15.3748i	−0.398573	+	0.690348i
$497$	−5.35582	+	21.4810i	−0.240241	+	0.963555i
$498$		0			0
$499$	4.03084	+	2.14324i	0.180445	+	0.0959444i	0.557237	−	0.830354i	$-0.311862\pi$
$499$	4.03084	+	2.14324i	0.180445	+	0.0959444i	−0.376792	+	0.926298i	$0.622973\pi$
$500$	14.2397	+	14.7456i	0.636818	+	0.659444i
$501$		0			0
$502$	1.10461	−	0.446293i	0.0493014	−	0.0199190i
$503$	26.2412	+	5.57775i	1.17004	+	0.248700i	0.751646	−	0.659566i	$-0.229260\pi$
$503$	26.2412	+	5.57775i	1.17004	+	0.248700i	0.418393	+	0.908266i	$0.362593\pi$
$504$		0			0
$505$	−6.29825	+	3.63629i	−0.280268	+	0.161813i
$506$	−8.39140	−	4.10968i	−0.373043	−	0.182697i
$507$		0			0
$508$	1.35386	−	19.3611i	0.0600679	−	0.859012i
$509$	25.0153	−	19.5441i	1.10878	−	0.866276i	0.116864	−	0.993148i	$-0.462716\pi$
$509$	25.0153	−	19.5441i	1.10878	−	0.866276i	0.991919	+	0.126872i	$0.0404937\pi$
$510$		0			0
$511$	16.6087	−	34.0530i	0.734728	−	1.50641i
$512$	17.6087	+	12.7934i	0.778200	+	0.565396i
$513$		0			0
$514$	14.7097	−	4.77949i	0.648819	−	0.210814i
$515$	20.9042	−	21.6470i	0.921150	−	0.953879i
$516$		0			0
$517$	−2.21976	+	31.0187i	−0.0976252	+	1.36420i
$518$	−3.91208	+	4.66223i	−0.171887	+	0.204847i
$519$		0			0
$520$	0.990607	−	28.3673i	0.0434410	−	1.24399i
$521$	−5.85536	−	27.5473i	−0.256528	−	1.20687i	−0.898095	−	0.439802i	$-0.855049\pi$
$521$	−5.85536	−	27.5473i	−0.256528	−	1.20687i	0.641567	−	0.767067i	$-0.278285\pi$
$522$		0			0
$523$	−10.5830	−	23.7698i	−0.462762	−	1.03938i	−0.982705	−	0.185179i	$-0.940714\pi$
$523$	−10.5830	−	23.7698i	−0.462762	−	1.03938i	0.519943	−	0.854201i	$-0.325953\pi$
$524$	1.80465	+	4.46668i	0.0788367	+	0.195128i
$525$		0			0
$526$	1.25252	+	2.56804i	0.0546123	+	0.111972i
$527$	−4.86293	+	27.5791i	−0.211833	+	1.20136i
$528$		0			0
$529$	−3.56663	+	2.99276i	−0.155071	+	0.130120i
$530$	−0.558537	−	5.31412i	−0.0242613	−	0.230831i
$531$		0			0
$532$	−7.83731	+	1.66587i	−0.339790	+	0.0722247i
$533$	14.4746	−	9.76326i	0.626966	−	0.422894i
$534$		0			0
$535$	4.26885	+	6.83158i	0.184558	+	0.295355i
$536$	2.45409	+	3.14109i	0.106000	+	0.135674i
$537$		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	$0.900783\pi$
$542$	−3.17381	−	5.96907i	−0.136327	−	0.256394i
$543$		0			0
$544$	18.7647	+	5.38070i	0.804531	+	0.230696i
$545$	0.631862	+	2.53426i	0.0270660	+	0.108556i
$546$		0			0
$547$	38.8717	+	1.35743i	1.66203	+	0.0580395i	0.850403	−	0.526132i	$-0.176358\pi$
$547$	38.8717	+	1.35743i	1.66203	+	0.0580395i	0.811630	+	0.584172i	$0.198581\pi$
$548$	−7.13377	+	16.0227i	−0.304740	+	0.684456i
$549$		0			0
$550$	0.516395	−	1.58054i	0.0220191	−	0.0673946i
$551$	6.30764	+	7.51715i	0.268714	+	0.320241i
$552$		0			0
$553$	−43.6384	+	6.13298i	−1.85570	+	0.260801i
$554$	−7.59733	+	14.2885i	−0.322780	+	0.607060i
$555$		0			0
$556$	1.53176	+	21.9051i	0.0649609	+	0.928984i
$557$	−24.4363	−	27.1393i	−1.03540	−	1.14993i	−0.988530	−	0.151028i	$-0.951742\pi$
$557$	−24.4363	−	27.1393i	−1.03540	−	1.14993i	−0.0468708	−	0.998901i	$-0.514925\pi$
$558$		0			0
$559$	−6.24161	−	2.77894i	−0.263992	−	0.117537i
$560$	−12.4048	−	4.51499i	−0.524200	−	0.190793i
$561$		0			0
$562$	−6.94394	−	5.82665i	−0.292912	−	0.245783i
$563$	−3.48745	+	5.17035i	−0.146978	+	0.217904i	−0.895336	−	0.445391i	$-0.853065\pi$
$563$	−3.48745	+	5.17035i	−0.146978	+	0.217904i	0.748358	+	0.663295i	$0.230843\pi$
$564$		0			0
$565$	−2.08123	−	0.292498i	−0.0875581	−	0.0123055i
$566$	−5.50148	+	7.57214i	−0.231245	+	0.318281i
$567$		0			0
$568$	15.0969	+	4.90529i	0.633453	+	0.205821i
$569$	3.51936	−	1.87128i	0.147539	−	0.0784480i	−0.394061	−	0.919084i	$-0.628930\pi$
$569$	3.51936	−	1.87128i	0.147539	−	0.0784480i	0.541600	+	0.840636i	$0.317819\pi$
$570$		0			0
$571$	−2.01549	−	5.53753i	−0.0843458	−	0.231738i	0.890349	−	0.455279i	$-0.150461\pi$
$571$	−2.01549	−	5.53753i	−0.0843458	−	0.231738i	−0.974695	+	0.223541i	$0.928238\pi$
$572$	36.1745	−	17.5707i	1.51253	−	0.734667i
$573$		0			0
$574$	1.01038	+	3.52361i	0.0421724	+	0.147073i
$575$	−3.65740	−	3.29314i	−0.152524	−	0.137333i
$576$		0			0
$577$	21.5376	−	9.58914i	0.896621	−	0.399201i	0.0939176	−	0.995580i	$-0.470061\pi$
$577$	21.5376	−	9.58914i	0.896621	−	0.399201i	0.802703	+	0.596379i	$0.203394\pi$
$578$	−1.67589	+	0.117189i	−0.0697077	+	0.00487443i
$579$		0			0
$580$	2.79720	+	19.9031i	0.116148	+	0.826433i
$581$	15.2181	−	7.42238i	0.631355	−	0.307932i
$582$		0			0
$583$	13.6191	−	9.15400i	0.564046	−	0.379120i
$584$	−23.5265	−	13.5830i	−0.973533	−	0.562069i
$585$		0			0
$586$	−0.580998	+	0.645263i	−0.0240008	+	0.0266556i
$587$	−34.1172	−	26.6553i	−1.40817	−	1.10018i	−0.980560	−	0.196218i	$-0.937134\pi$
$587$	−34.1172	−	26.6553i	−1.40817	−	1.10018i	−0.427608	−	0.903964i	$-0.640644\pi$
$588$		0			0
$589$	−12.3045	+	3.06786i	−0.506998	+	0.126409i
$590$	−0.325299	−	9.31535i	−0.0133924	−	0.383507i
$591$		0			0
$592$	−6.95369	−	6.71510i	−0.285795	−	0.275989i
$593$	−35.6507			−1.46400			−0.731998	−	0.681306i	$-0.761412\pi$
$593$	−35.6507			−1.46400			−0.731998	+	0.681306i	$0.761412\pi$
$594$		0			0
$595$	−20.8235			−0.853681
$596$	23.7310	+	22.9167i	0.972058	+	0.938705i
$597$		0			0
$598$	0.695959	+	19.9297i	0.0284599	+	0.814984i
$599$	36.7342	−	9.15887i	1.50092	−	0.374221i	0.597111	−	0.802159i	$-0.296315\pi$
$599$	36.7342	−	9.15887i	1.50092	−	0.374221i	0.903808	+	0.427938i	$0.140760\pi$
$600$		0			0
$601$	−1.04235	−	0.814370i	−0.0425182	−	0.0332188i	0.594178	−	0.804333i	$-0.297477\pi$
$601$	−1.04235	−	0.814370i	−0.0425182	−	0.0332188i	−0.636696	+	0.771115i	$0.719700\pi$
$602$	0.959821	−	1.06599i	0.0391194	−	0.0434465i
$603$		0			0
$604$	22.8280	+	13.1798i	0.928859	+	0.536277i
$605$	−21.8512	+	3.77968i	−0.888379	+	0.153666i
$606$		0			0
$607$	1.10511	−	0.539000i	0.0448552	−	0.0218773i	−0.415807	−	0.909453i	$-0.636501\pi$
$607$	1.10511	−	0.539000i	0.0448552	−	0.0218773i	0.460662	+	0.887576i	$0.347612\pi$
$608$	1.23023	+	8.75357i	0.0498926	+	0.355004i
$609$		0			0
$610$	−1.96950	+	0.137721i	−0.0797426	+	0.00557614i
$611$	60.6328	−	26.9955i	2.45294	−	1.09212i
$612$		0			0
$613$	−29.4939	−	26.5565i	−1.19125	−	1.07261i	−0.995768	−	0.0918981i	$-0.970707\pi$
$613$	−29.4939	−	26.5565i	−1.19125	−	1.07261i	−0.195481	−	0.980708i	$-0.562627\pi$
$614$	0.655393	+	2.28563i	0.0264495	+	0.0922404i
$615$		0			0
$616$	2.51753	+	18.1271i	0.101434	+	0.730362i
$617$	−7.43732	−	20.4339i	−0.299415	−	0.822636i	−0.994598	−	0.103803i	$-0.966899\pi$
$617$	−7.43732	−	20.4339i	−0.299415	−	0.822636i	0.695183	−	0.718833i	$-0.255323\pi$
$618$		0			0
$619$	18.6252	−	9.90317i	0.748609	−	0.398042i	−0.0508947	−	0.998704i	$-0.516207\pi$
$619$	18.6252	−	9.90317i	0.748609	−	0.398042i	0.799503	+	0.600662i	$0.205096\pi$
$620$	−24.7022	−	8.02624i	−0.992065	−	0.322342i
$621$		0			0
$622$	−8.18171	+	11.2612i	−0.328057	+	0.451531i
$623$	−29.3496	−	4.12481i	−1.17587	−	0.165257i
$624$		0			0
$625$	−10.8735	+	16.1206i	−0.434939	+	0.644824i
$626$	0.505275	+	0.423976i	0.0201949	+	0.0169455i
$627$		0			0
$628$	−0.594489	−	0.216376i	−0.0237227	−	0.00863435i
$629$	−13.9303	−	6.20217i	−0.555438	−	0.247297i
$630$		0			0
$631$	−8.64313	−	9.59917i	−0.344078	−	0.382137i	0.546124	−	0.837705i	$-0.316103\pi$
$631$	−8.64313	−	9.59917i	−0.344078	−	0.382137i	−0.890201	+	0.455568i	$0.849436\pi$
$632$	2.20411	+	31.5202i	0.0876746	+	1.25381i
$633$		0			0
$634$	−3.02205	+	5.68364i	−0.120021	+	0.225726i
$635$	22.6187	−	3.17884i	0.897594	−	0.126149i
$636$		0			0
$637$	3.16553	+	3.77253i	0.125423	+	0.149473i
$638$	8.37565	−	6.06447i	0.331595	−	0.240095i
$639$		0			0
$640$	−9.43776	+	21.1976i	−0.373060	+	0.837907i
$641$	16.3665	+	0.571531i	0.646438	+	0.0225741i	0.356243	−	0.934393i	$-0.384058\pi$
$641$	16.3665	+	0.571531i	0.646438	+	0.0225741i	0.290195	+	0.956968i	$0.406280\pi$
$642$		0			0
$643$	−3.65942	−	14.6771i	−0.144313	−	0.578809i	−0.998288	−	0.0584942i	$-0.981370\pi$
$643$	−3.65942	−	14.6771i	−0.144313	−	0.578809i	0.853974	−	0.520315i	$-0.174185\pi$
$644$	24.0227	+	6.88839i	0.946626	+	0.271441i
$645$		0			0
$646$	1.57892	+	2.96951i	0.0621217	+	0.116834i
$647$	11.1748	+	15.3808i	0.439326	+	0.604680i	0.970062	−	0.242857i	$-0.0780845\pi$
$647$	11.1748	+	15.3808i	0.439326	+	0.604680i	−0.530736	+	0.847537i	$0.678085\pi$
$648$		0			0
$649$	24.8132	−	14.2721i	0.974005	−	0.560231i
$650$	−3.49484	+	0.616234i	−0.137079	+	0.0241707i
$651$		0			0
$652$	26.2417	+	33.5878i	1.02770	+	1.31540i
$653$	−8.65776	−	13.8553i	−0.338804	−	0.542200i	0.634146	−	0.773213i	$-0.281352\pi$
$653$	−8.65776	−	13.8553i	−0.338804	−	0.542200i	−0.972951	+	0.231013i	$0.925796\pi$
$654$		0			0
$655$	−4.70020	+	3.17033i	−0.183652	+	0.123875i
$656$	−5.69497	+	1.21050i	−0.222351	+	0.0472622i
$657$		0			0
$658$	1.45655	+	13.8581i	0.0567822	+	0.540247i
$659$	−5.34987	+	4.48907i	−0.208401	+	0.174869i	−0.741014	−	0.671490i	$-0.765655\pi$
$659$	−5.34987	+	4.48907i	−0.208401	+	0.174869i	0.532613	+	0.846359i	$0.321210\pi$
$660$		0			0
$661$	8.74606	−	49.6014i	0.340182	−	1.92927i	−0.0282147	−	0.999602i	$-0.508982\pi$
$661$	8.74606	−	49.6014i	0.340182	−	1.92927i	0.368397	−	0.929669i	$-0.379907\pi$
$662$	5.64835	+	11.5808i	0.219529	+	0.450102i
$663$		0			0
$664$	−4.54787	−	11.2564i	−0.176492	−	0.436832i
$665$	−3.83530	−	8.61423i	−0.148727	−	0.334046i
$666$		0			0
$667$	−6.36349	−	29.9379i	−0.246395	−	1.15920i
$668$	−0.158585	+	4.54128i	−0.00613584	+	0.175707i
$669$		0			0
$670$	−1.39115	+	1.65791i	−0.0537447	+	0.0640505i
$671$	−3.20459	−	5.14704i	−0.123712	−	0.198699i
$672$		0			0
$673$	−13.7147	+	14.2020i	−0.528663	+	0.547447i	−0.929557	−	0.368678i	$-0.879811\pi$
$673$	−13.7147	+	14.2020i	−0.528663	+	0.547447i	0.400894	+	0.916124i	$0.368700\pi$
$674$	−1.93497	+	0.628710i	−0.0745323	+	0.0242170i
$675$		0			0
$676$	−51.4225	−	37.3606i	−1.97779	−	1.43695i
$677$	−4.50272	+	9.23194i	−0.173053	+	0.354812i	−0.967638	−	0.252341i	$-0.918800\pi$
$677$	−4.50272	+	9.23194i	−0.173053	+	0.354812i	0.794585	+	0.607153i	$0.207688\pi$
$678$		0			0
$679$	−5.54207	+	4.32994i	−0.212685	+	0.166168i
$680$	−1.04153	+	14.8945i	−0.0399407	+	0.571179i
$681$		0			0
$682$	2.29907	+	13.1639i	0.0880360	+	0.504072i
$683$	1.16852	−	0.674647i	0.0447123	−	0.0258146i	−0.477477	−	0.878644i	$-0.658449\pi$
$683$	1.16852	−	0.674647i	0.0447123	−	0.0258146i	0.522190	+	0.852829i	$0.325115\pi$
$684$		0			0
$685$	−20.1899	−	4.29150i	−0.771416	−	0.163970i
$686$	8.68671	−	3.50966i	0.331660	−	0.133999i
$687$		0			0
$688$	1.58267	+	1.63891i	0.0603389	+	0.0624827i
$689$	−30.9228	−	16.4419i	−1.17806	−	0.626388i
$690$		0			0
$691$	0.701216	−	2.81242i	0.0266755	−	0.106990i	−0.955482	−	0.295049i	$-0.904664\pi$
$691$	0.701216	−	2.81242i	0.0266755	−	0.106990i	0.982158	+	0.188059i	$0.0602197\pi$
$692$	−0.949891	+	1.64526i	−0.0361094	+	0.0625434i
$693$		0			0
$694$	−7.02165	−	12.1619i	−0.266538	−	0.461658i
$695$	−24.8411	+	7.12307i	−0.942276	+	0.270193i
$696$		0			0
$697$	−7.78856	+	4.86683i	−0.295013	+	0.184344i
$698$	−0.730137	+	2.54629i	−0.0276361	+	0.0963785i
$699$		0			0
$700$	−0.618936	+	4.40396i	−0.0233936	+	0.166454i
$701$	−2.68287	−	8.25702i	−0.101330	−	0.311863i	0.887521	−	0.460767i	$-0.152426\pi$
$701$	−2.68287	−	8.25702i	−0.101330	−	0.311863i	−0.988852	+	0.148904i	$0.952426\pi$
$702$		0			0
$703$		−	6.90498i		−	0.260426i
$704$	−6.32775	+	0.432133i	−0.238486	+	0.0162866i
$705$		0			0
$706$	−6.84800	−	4.61903i	−0.257728	−	0.173840i
$707$	−9.27886	−	3.74890i	−0.348967	−	0.140992i
$708$		0			0
$709$	6.87680	+	10.1953i	0.258263	+	0.382891i	0.935762	−	0.352633i	$-0.114714\pi$
$709$	6.87680	+	10.1953i	0.258263	+	0.382891i	−0.677498	+	0.735524i	$0.736936\pi$
$710$	−0.900897	+	8.57146i	−0.0338101	+	0.321681i
$711$		0			0
$712$	−4.41834	+	20.7867i	−0.165584	+	0.779013i
$713$	38.3779	+	9.56869i	1.43726	+	0.358350i
$714$		0			0
$715$	29.0776	+	37.3427i	1.08744	+	1.39654i
$716$	−38.4639	−	6.78222i	−1.43746	−	0.253463i
$717$		0			0
$718$	15.4997	+	9.68529i	0.578444	+	0.361452i
$719$	7.70883	−	6.94106i	0.287491	−	0.258858i	−0.512748	−	0.858539i	$-0.671373\pi$
$719$	7.70883	−	6.94106i	0.287491	−	0.258858i	0.800239	+	0.599681i	$0.204706\pi$
$720$		0			0
$721$	41.1829	+	4.32850i	1.53373	+	0.161202i
$722$	5.32888	−	6.82066i	0.198321	−	0.253839i
$723$		0			0
$724$	19.2105	+	1.34333i	0.713951	+	0.0499243i
$725$	5.11815	−	1.86286i	0.190083	−	0.0691847i
$726$		0			0
$727$	3.74787	+	21.2552i	0.139001	+	0.788312i	0.971990	+	0.235023i	$0.0755165\pi$
$727$	3.74787	+	21.2552i	0.139001	+	0.788312i	−0.832989	+	0.553289i	$0.813372\pi$
$728$	31.5995	−	22.9584i	1.17115	−	0.850893i
$729$		0			0
$730$	4.55792	−	14.0278i	0.168696	−	0.519194i
$731$	3.23020	+	1.57548i	0.119473	+	0.0582711i
$732$		0			0
$733$	−6.35628	+	0.221966i	−0.234775	+	0.00819851i	−0.152045	−	0.988374i	$-0.548586\pi$
$733$	−6.35628	+	0.221966i	−0.234775	+	0.00819851i	−0.0827294	+	0.996572i	$0.526364\pi$
$734$	−3.30585	+	8.18228i	−0.122021	+	0.302013i
$735$		0			0
$736$	9.42978	−	25.9081i	0.347586	−	0.954986i
$737$	−6.49892	−	1.39245i	−0.239391	−	0.0512914i
$738$		0			0
$739$	−34.5594	+	3.63234i	−1.27129	+	0.133618i	−0.716036	−	0.698064i	$-0.754045\pi$
$739$	−34.5594	+	3.63234i	−1.27129	+	0.133618i	−0.555253	+	0.831682i	$0.687379\pi$
$740$	7.49449	−	11.9937i	0.275503	−	0.440897i
$741$		0			0
$742$	5.28921	−	5.10773i	0.194173	−	0.187511i
$743$	−1.69035	+	1.63235i	−0.0620128	+	0.0598851i	−0.725019	−	0.688729i	$-0.758169\pi$
$743$	−1.69035	+	1.63235i	−0.0620128	+	0.0598851i	0.663006	+	0.748614i	$0.269280\pi$
$744$		0			0
$745$	−20.5738	+	32.9250i	−0.753766	+	1.20628i
$746$	−16.8186	+	1.76770i	−0.615771	+	0.0647201i
$747$		0			0
$748$	−19.3395	+	8.57284i	−0.707124	+	0.313454i
$749$	−3.79134	+	10.4166i	−0.138532	+	0.380615i
$750$		0			0
$751$	−10.2295	+	25.3188i	−0.373279	+	0.923898i	0.617272	+	0.786750i	$0.288238\pi$
$751$	−10.2295	+	25.3188i	−0.373279	+	0.923898i	−0.990551	+	0.137148i	$0.956206\pi$
$752$	−22.1191	+	0.772415i	−0.806599	+	0.0281671i
$753$		0			0
$754$	−19.8360	−	9.67465i	−0.722383	−	0.352330i
$755$	−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
$761$	−18.3177	−	1.28090i	−0.664015	−	0.0464324i	−0.266228	−	0.963910i	$-0.585777\pi$
$761$	−18.3177	−	1.28090i	−0.664015	−	0.0464324i	−0.397787	+	0.917478i	$0.630222\pi$
$762$		0			0
$763$	−2.21273	+	2.83217i	−0.0801062	+	0.102531i
$764$	−20.0358	−	2.10585i	−0.724870	−	0.0761869i
$765$		0			0
$766$	−6.40175	+	5.76416i	−0.231305	+	0.208268i
$767$	−51.8097	−	32.3743i	−1.87074	−	1.16897i
$768$		0			0
$769$	4.66158	+	0.821963i	0.168101	+	0.0296407i	0.257065	−	0.966394i	$-0.417245\pi$
$769$	4.66158	+	0.821963i	0.168101	+	0.0296407i	−0.0889641	+	0.996035i	$0.528356\pi$
$770$	−9.34282	+	3.38330i	−0.336692	+	0.121926i
$771$		0			0
$772$	2.53280	+	0.631497i	0.0911574	+	0.0227281i
$773$	−11.0189	+	51.8399i	−0.396322	+	1.86455i	0.0978725	+	0.995199i	$0.468796\pi$
$773$	−11.0189	+	51.8399i	−0.396322	+	1.86455i	−0.494195	+	0.869351i	$0.664537\pi$
$774$		0			0
$775$	−0.735737	+	7.00007i	−0.0264285	+	0.251450i
$776$	2.81989	+	4.18066i	0.101228	+	0.150077i
$777$		0			0
$778$	9.53394	+	3.85196i	0.341808	+	0.138100i
$779$	−3.44781	−	2.32557i	−0.123530	−	0.0833223i
$780$		0			0
$781$	−24.5569	+	9.87517i	−0.878714	+	0.353361i
$782$		−	10.4898i		−	0.375115i
$783$		0			0
$784$	−0.507475	−	1.56185i	−0.0181241	−	0.0557803i
$785$	0.103618	−	0.737283i	0.00369830	−	0.0263148i
$786$		0			0
$787$	1.98039	−	6.90643i	0.0705931	−	0.246187i	−0.918051	−	0.396462i	$-0.870238\pi$
$787$	1.98039	−	6.90643i	0.0705931	−	0.246187i	0.988644	+	0.150274i	$0.0480157\pi$
$788$	16.1978	−	10.1215i	0.577024	−	0.360565i
$789$		0			0
$790$	−16.4910	+	4.72873i	−0.586725	+	0.168241i
$791$	−1.44603	−	2.50460i	−0.0514149	−	0.0890533i
$792$		0			0
$793$	−6.47010	+	11.2065i	−0.229760	+	0.397956i
$794$	2.14427	−	8.60018i	0.0760971	−	0.305209i
$795$		0			0
$796$	1.80446	+	0.959447i	0.0639573	+	0.0340067i
$797$	−10.8747	−	11.2610i	−0.385200	−	0.398886i	0.498538	−	0.866868i	$-0.333870\pi$
$797$	−10.8747	−	11.2610i	−0.385200	−	0.398886i	−0.883738	+	0.467981i	$0.844981\pi$
$798$		0			0
$799$	−32.3703	+	13.0785i	−1.14518	+	0.462682i
$800$	4.79916	+	1.02009i	0.169676	+	0.0360657i
$801$		0			0
$802$	−12.1185	+	6.99661i	−0.427919	+	0.247059i
$803$	44.6213	−	7.79309i	1.57465	−	0.275012i
$804$		0			0
$805$	−2.05158	+	29.3389i	−0.0723087	+	1.03406i
$806$	22.4743	−	17.5588i	0.791623	−	0.618484i
$807$		0			0
$808$	−3.14559	+	6.44942i	−0.110661	+	0.226890i
$809$	18.7796	+	13.6442i	0.660255	+	0.479704i	0.866749	−	0.498744i	$-0.166205\pi$
$809$	18.7796	+	13.6442i	0.660255	+	0.479704i	−0.206494	+	0.978448i	$0.566205\pi$
$810$		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	$0.436277\pi$
$812$	−19.2123	+	19.8949i	−0.674220	+	0.698176i
$813$		0			0
$814$	−7.25776	−	0.519381i	−0.254384	−	0.0182043i
$815$	−32.2434	+	38.4262i	−1.12944	+	1.34601i
$816$		0			0
$817$	−0.0567964	+	1.62644i	−0.00198705	+	0.0569018i
$818$	2.11041	+	9.92868i	0.0737886	+	0.347148i
$819$		0			0
$820$	−3.46459	−	7.78159i	−0.120989	−	0.271745i
$821$	−12.6741	−	31.3694i	−0.442328	−	1.09480i	−0.969511	−	0.245048i	$-0.921196\pi$
$821$	−12.6741	−	31.3694i	−0.442328	−	1.09480i	0.527183	−	0.849752i	$-0.323248\pi$
$822$		0			0
$823$	1.53768	+	3.15271i	0.0536001	+	0.109896i	0.923913	−	0.382603i	$-0.124972\pi$
$823$	1.53768	+	3.15271i	0.0536001	+	0.109896i	−0.870313	+	0.492499i	$0.836083\pi$
$824$	5.15590	−	29.2405i	0.179614	−	1.01864i
$825$		0			0
$826$	9.82556	−	8.24462i	0.341875	−	0.286867i
$827$	1.02410	+	9.74368i	0.0356115	+	0.338821i	0.997792	+	0.0664098i	$0.0211545\pi$
$827$	1.02410	+	9.74368i	0.0356115	+	0.338821i	−0.962181	+	0.272411i	$0.912179\pi$
$828$		0			0
$829$	28.6907	−	6.09839i	0.996468	−	0.211806i	0.319315	−	0.947649i	$-0.396547\pi$
$829$	28.6907	−	6.09839i	0.996468	−	0.211806i	0.677152	+	0.735843i	$0.263214\pi$
$830$	5.46469	−	3.68598i	0.189682	−	0.127942i
$831$		0			0
$832$	7.17321	+	11.4795i	0.248686	+	0.397982i
$833$	−1.59487	−	2.04134i	−0.0552588	−	0.0707281i
$834$		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
$839$	−13.4064	−	25.2138i	−0.462842	−	0.870478i	−0.999642	−	0.0267689i	$-0.991478\pi$
$839$	−13.4064	−	25.2138i	−0.462842	−	0.870478i	0.536800	−	0.843709i	$-0.319633\pi$
$840$		0			0
$841$	4.68360	+	1.34300i	0.161503	+	0.0463104i
$842$	−1.70449	−	6.83632i	−0.0587404	−	0.235595i
$843$		0			0
$844$	−9.11052	−	0.318146i	−0.313597	−	0.0109510i
$845$	30.4251	−	68.3359i	1.04666	−	2.35083i
$846$		0			0
$847$	−22.6107	−	20.4924i	−0.776913	−	0.704127i
$848$	7.50698	+	8.94647i	0.257791	+	0.307223i
$849$		0			0
$850$	1.84855	−	0.259797i	0.0634048	−	0.00891096i
$851$	−10.1109	+	19.0158i	−0.346597	+	0.651853i
$852$		0			0
$853$	0.713662	+	10.2058i	0.0244353	+	0.349441i	0.994362	+	0.106042i	$0.0338179\pi$
$853$	0.713662	+	10.2058i	0.0244353	+	0.349441i	−0.969926	+	0.243399i	$0.921738\pi$
$854$	−1.81788	−	2.01896i	−0.0622065	−	0.0690874i
$855$		0			0
$856$	7.26110	+	3.23285i	0.248179	+	0.110496i
$857$	−20.3024	−	7.38948i	−0.693517	−	0.252420i	−0.0288769	−	0.999583i	$-0.509193\pi$
$857$	−20.3024	−	7.38948i	−0.693517	−	0.252420i	−0.664641	+	0.747163i	$0.731415\pi$
$858$		0			0
$859$	−19.4772	−	16.3433i	−0.664552	−	0.557626i	0.246895	−	0.969042i	$-0.420590\pi$
$859$	−19.4772	−	16.3433i	−0.664552	−	0.557626i	−0.911447	+	0.411417i	$0.865034\pi$
$860$	−1.86394	+	2.76341i	−0.0635600	+	0.0942315i
$861$		0			0
$862$	18.9290	+	2.66030i	0.644725	+	0.0906102i
$863$	8.84285	−	12.1711i	0.301014	−	0.414310i	−0.631539	−	0.775344i	$-0.717576\pi$
$863$	8.84285	−	12.1711i	0.301014	−	0.414310i	0.932553	+	0.361034i	$0.117576\pi$
$864$		0			0
$865$	−2.12635	−	0.690892i	−0.0722979	−	0.0234910i
$866$	4.91361	−	2.61261i	0.166971	−	0.0887801i
$867$		0			0
$868$	−12.2242	−	33.5858i	−0.414917	−	1.13998i
$869$	−36.5365	−	37.9580i	−1.23941	−	1.28764i
$870$		0			0
$871$	3.90994	+	13.6356i	0.132483	+	0.462025i
$872$	1.91510	+	1.72436i	0.0648535	+	0.0583943i
$873$		0			0
$874$	4.33940	−	1.93203i	0.146783	−	0.0653518i
$875$	−33.1156	+	2.31567i	−1.11951	+	0.0782840i
$876$		0			0
$877$	−3.15326	−	22.4366i	−0.106478	−	0.757629i	−0.968187	−	0.250227i	$-0.919495\pi$
$877$	−3.15326	−	22.4366i	−0.106478	−	0.757629i	0.861709	−	0.507402i	$-0.169394\pi$
$878$	7.47892	−	3.64771i	0.252401	−	0.123104i
$879$		0			0
$880$	−4.32556	−	15.1782i	−0.145815	−	0.511657i
$881$	−30.6507	−	17.6962i	−1.03265	−	0.596200i	−0.114906	−	0.993376i	$-0.536657\pi$
$881$	−30.6507	−	17.6962i	−1.03265	−	0.596200i	−0.917742	+	0.397176i	$0.869990\pi$
$882$		0			0
$883$	8.21701	−	9.12592i	0.276524	−	0.307112i	−0.588845	−	0.808246i	$-0.700417\pi$
$883$	8.21701	−	9.12592i	0.276524	−	0.307112i	0.865369	+	0.501134i	$0.167084\pi$
$884$	35.5778	+	27.7964i	1.19661	+	0.934895i
$885$		0			0
$886$	−1.64460	+	0.410044i	−0.0552513	+	0.0137757i
$887$	1.29883	+	37.1935i	0.0436103	+	1.24884i	0.802116	+	0.597168i	$0.203708\pi$
$887$	1.29883	+	37.1935i	0.0436103	+	1.24884i	−0.758506	+	0.651667i	$0.774070\pi$
$888$		0			0
$889$	22.6093	+	21.8336i	0.758293	+	0.732275i
$890$	−11.5382			−0.386762
$891$		0			0
$892$	−2.56263			−0.0858033
$893$	−11.3723	−	10.9821i	−0.380558	−	0.367501i
$894$		0			0
$895$	−1.60415	−	45.9368i	−0.0536208	−	1.53550i
$896$	−30.9813	+	7.72451i	−1.03501	+	0.258058i
$897$		0			0
$898$	2.01388	+	1.57342i	0.0672041	+	0.0525056i
$899$	−29.2898	+	32.5297i	−0.976871	+	1.08493i
$900$		0			0
$901$	15.9543	+	9.21122i	0.531515	+	0.306870i
$902$	−2.70373	+	3.44903i	−0.0900242	+	0.114840i
$903$		0			0
$904$	−1.86380	+	0.909035i	−0.0619890	+	0.0302341i
$905$	3.15410	+	22.4426i	0.104846	+	0.746018i
$906$		0			0
$907$	22.9035	−	1.60157i	0.760498	−	0.0531792i	0.315759	−	0.948839i	$-0.397741\pi$
$907$	22.9035	−	1.60157i	0.760498	−	0.0531792i	0.444739	+	0.895660i	$0.353297\pi$
$908$	−4.93559	+	2.19747i	−0.163793	+	0.0729255i
$909$		0			0
$910$	15.7599	+	14.1903i	0.522436	+	0.470404i
$911$	2.16952	+	7.56601i	0.0718794	+	0.250673i	0.988995	−	0.147948i	$-0.0472667\pi$
$911$	2.16952	+	7.56601i	0.0718794	+	0.250673i	−0.917116	+	0.398621i	$0.869489\pi$
$912$		0			0
$913$	17.8579	+	9.53254i	0.591011	+	0.315481i
$914$	1.60634	+	4.41338i	0.0531329	+	0.145982i
$915$		0			0
$916$	28.2399	−	15.0154i	0.933072	−	0.496123i
$917$	−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	$0.0897986\pi$
$920$	20.8828	+	2.93488i	0.688484	+	0.0967602i
$921$		0			0
$922$	−0.677114	+	1.00386i	−0.0222996	+	0.0330605i
$923$	43.2734	+	36.3107i	1.42436	+	1.19518i
$924$		0			0
$925$	−3.60144	−	1.31082i	−0.118415	−	0.0430994i
$926$	6.74182	+	3.00165i	0.221550	+	0.0986404i
$927$		0			0
$928$	20.4169	+	22.6753i	0.670217	+	0.744352i
$929$	0.125691	+	1.79747i	0.00412379	+	0.0589730i	0.999190	−	0.0402395i	$-0.0128121\pi$
$929$	0.125691	+	1.79747i	0.00412379	+	0.0589730i	−0.995066	+	0.0992125i	$0.968368\pi$
$930$		0			0
$931$	0.550711	−	1.03574i	0.0180488	−	0.0339449i
$932$	−3.28912	+	0.462255i	−0.107739	+	0.0151417i
$933$		0			0
$934$	−9.41019	−	11.2146i	−0.307911	−	0.366954i
$935$	−14.6006	−	20.1649i	−0.477490	−	0.659463i
$936$		0			0
$937$	−6.23651	+	14.0074i	−0.203738	+	0.457603i	−0.986298	−	0.164972i	$-0.947247\pi$
$937$	−6.23651	+	14.0074i	−0.203738	+	0.457603i	0.782560	+	0.622575i	$0.213913\pi$
$938$	−2.97633	−	0.103936i	−0.0971806	−	0.00339362i
$939$		0			0
$940$	−7.83354	−	31.4186i	−0.255502	−	1.02476i
$941$	39.4758	+	11.3195i	1.28688	+	0.369006i	0.848217	−	0.529648i	$-0.177676\pi$
$941$	39.4758	+	11.3195i	1.28688	+	0.369006i	0.438658	+	0.898654i	$0.355454\pi$
$942$		0			0
$943$	6.08969	+	11.4530i	0.198308	+	0.372962i
$944$	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	0.890751	−	0.454492i	$-0.150179\pi$
$947$	57.9533	−	10.2187i	1.88323	−	0.332064i	0.992477	+	0.122428i	$0.0390682\pi$
$948$		0			0
$949$	−59.5187	−	76.1804i	−1.93206	−	2.47292i
$950$	0.447941	+	0.716855i	0.0145331	+	0.0232578i
$951$		0			0
$952$	−17.0333	+	11.4891i	−0.552054	+	0.372365i
$953$	−14.1079	+	2.99872i	−0.456999	+	0.0971382i	−0.430659	−	0.902515i	$-0.641719\pi$
$953$	−14.1079	+	2.99872i	−0.456999	+	0.0971382i	−0.0263405	+	0.999653i	$0.508385\pi$
$954$		0			0
$955$	−2.47828	−	23.5793i	−0.0801953	−	0.763007i
$956$	−11.1405	+	9.34802i	−0.360311	+	0.302337i
$957$		0			0
$958$	−0.781480	+	4.43200i	−0.0252485	+	0.143191i
$959$	−12.4512	−	25.5288i	−0.402070	−	0.824367i
$960$		0			0
$961$	−9.57775	−	23.7058i	−0.308960	−	0.764702i
$962$	6.31640	+	14.1869i	0.203649	+	0.457403i
$963$		0			0
$964$	2.64257	+	12.4323i	0.0851114	+	0.400418i
$965$	−0.107211	+	3.07012i	−0.00345124	+	0.0988307i
$966$		0			0
$967$	−19.7776	+	23.5701i	−0.636006	+	0.757962i	−0.983734	−	0.179633i	$-0.942509\pi$
$967$	−19.7776	+	23.5701i	−0.636006	+	0.757962i	0.347728	+	0.937596i	$0.386953\pi$
$968$	−15.7886	+	15.1479i	−0.507465	+	0.486871i
$969$		0			0
$970$	−1.90196	+	1.96953i	−0.0610682	+	0.0632379i
$971$	46.8858	−	15.2341i	1.50464	−	0.488886i	0.563271	−	0.826272i	$-0.309543\pi$
$971$	46.8858	−	15.2341i	1.50464	−	0.488886i	0.941366	+	0.337386i	$0.109543\pi$
$972$		0			0
$973$	−28.7691	−	20.9020i	−0.922295	−	0.670086i
$974$	−6.33083	+	12.9801i	−0.202853	+	0.415910i
$975$		0			0
$976$	3.40038	−	2.65667i	0.108843	−	0.0850378i
$977$	2.66913	−	38.1703i	0.0853930	−	1.22118i	−0.746173	−	0.665752i	$-0.768111\pi$
$977$	2.66913	−	38.1703i	0.0853930	−	1.22118i	0.831566	−	0.555425i	$-0.187445\pi$
$978$		0			0
$979$	−16.5843	−	31.3134i	−0.530038	−	1.00078i
$980$	2.08072	−	1.20131i	0.0664663	−	0.0383743i
$981$		0			0
$982$	−1.22303	−	0.259964i	−0.0390286	−	0.00829578i
$983$	24.4533	−	9.87978i	0.779940	−	0.315116i	0.0501088	−	0.998744i	$-0.484043\pi$
$983$	24.4533	−	9.87978i	0.779940	−	0.315116i	0.729831	+	0.683628i	$0.239599\pi$
$984$		0			0
$985$	15.6146	+	16.1694i	0.497524	+	0.515201i
$986$	10.2502	+	5.45012i	0.326432	+	0.173567i
$987$		0			0
$988$	−4.94600	+	19.8373i	−0.157353	+	0.631109i
$989$	2.53798	−	4.39592i	0.0807032	−	0.139782i
$990$		0			0
$991$	6.79604	+	11.7711i	0.215883	+	0.373921i	0.953545	−	0.301249i	$-0.0974036\pi$
$991$	6.79604	+	11.7711i	0.215883	+	0.373921i	−0.737662	+	0.675170i	$0.764070\pi$
$992$	−37.9037	+	10.8687i	−1.20344	+	0.345082i
$993$		0			0
$994$	−10.0577	+	6.28478i	−0.319012	+	0.199341i
$995$	−0.662939	+	2.31194i	−0.0210166	+	0.0732935i
$996$		0			0
$997$	−0.371593	+	2.64402i	−0.0117685	+	0.0837369i	−0.995267	−	0.0971802i	$-0.969018\pi$
$997$	−0.371593	+	2.64402i	−0.0117685	+	0.0837369i	0.983498	+	0.180917i	$0.0579066\pi$
$998$	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.800.19		816
3.2	odd	2		297.2.x.a.41.16	yes	816
11.7	odd	10	inner	891.2.bb.a.557.19		816
27.2	odd	18	inner	891.2.bb.a.8.19		816
27.25	even	9		297.2.x.a.272.16	yes	816
33.29	even	10		297.2.x.a.95.16	yes	816
297.29	even	90	inner	891.2.bb.a.656.19		816
297.106	odd	90		297.2.x.a.29.16	✓	816

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
297.2.x.a.29.16	✓	816	297.106	odd	90
297.2.x.a.41.16	yes	816	3.2	odd	2
297.2.x.a.95.16	yes	816	33.29	even	10
297.2.x.a.272.16	yes	816	27.25	even	9
891.2.bb.a.8.19		816	27.2	odd	18	inner
891.2.bb.a.557.19		816	11.7	odd	10	inner
891.2.bb.a.656.19		816	297.29	even	90	inner
891.2.bb.a.800.19		816	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(0.385357 + 0.372135i) q^{2} +(-0.0597834 - 1.71197i) q^{4} +(1.95609 - 0.487708i) q^{5} +(2.18603 + 1.70792i) q^{7} +(1.33097 - 1.47819i) q^{8} +(0.935288 + 0.539989i) q^{10} +(-0.121142 + 3.31441i) q^{11} +(6.36211 - 3.10301i) q^{13} +(0.206828 + 1.47166i) q^{14} +(-2.35470 + 0.164657i) q^{16} +(-3.40153 + 1.51446i) q^{17} +(-1.25300 - 1.12820i) q^{19} +(-0.951885 - 3.31962i) q^{20} +(-1.28009 + 1.23215i) q^{22} +(1.79865 + 4.94174i) q^{23} +(-0.826304 + 0.439353i) q^{25} +(3.60642 + 1.17180i) q^{26} +(2.79322 - 3.84453i) q^{28} +(-5.76336 - 0.809987i) q^{29} +(4.20577 - 6.23530i) q^{31} +(-4.01615 - 3.36995i) q^{32} +(-1.87439 - 0.682222i) q^{34} +(5.10905 + 2.27469i) q^{35} +(2.74029 + 3.04340i) q^{37} +(-0.0630073 - 0.901046i) q^{38} +(1.88257 - 3.54059i) q^{40} +(2.44256 - 0.343279i) q^{41} +(-0.620430 - 0.739399i) q^{43} +(5.68142 + 0.00924481i) q^{44} +(-1.14587 + 2.57367i) q^{46} +(9.37069 + 0.327232i) q^{47} +(0.168311 + 0.675059i) q^{49} +(-0.481921 - 0.138189i) q^{50} +(-5.69261 - 10.7062i) q^{52} +(-2.90818 - 4.00277i) q^{53} +(1.37950 + 6.54237i) q^{55} +(5.43416 - 0.958189i) q^{56} +(-1.91953 - 2.45688i) q^{58} +(-4.57361 - 7.31930i) q^{59} +(-1.51556 + 1.02226i) q^{61} +(3.94110 - 0.837706i) q^{62} +(0.199893 + 1.90185i) q^{64} +(10.9315 - 9.17262i) q^{65} +(-0.347986 + 1.97353i) q^{67} +(2.79607 + 5.73279i) q^{68} +(1.12231 + 2.77783i) q^{70} +(3.24593 + 7.29048i) q^{71} +(-2.83955 - 13.3590i) q^{73} +(-0.0765657 + 2.19256i) q^{74} +(-1.85654 + 2.21254i) q^{76} +(-5.92556 + 7.03852i) q^{77} +(-11.0348 + 11.4268i) q^{79} +(-4.52571 + 1.47049i) q^{80} +(1.06900 + 0.776676i) q^{82} +(2.67558 - 5.48576i) q^{83} +(-5.91509 + 4.62138i) q^{85} +(0.0360694 - 0.515817i) q^{86} +(4.73809 + 4.59044i) q^{88} +(-9.25241 + 5.34188i) q^{89} +(19.2075 + 4.08267i) q^{91} +(8.35259 - 3.37466i) q^{92} +(3.48929 + 3.61327i) q^{94} +(-3.00121 - 1.59577i) q^{95} +(-0.613324 + 2.45991i) q^{97} +(-0.186353 + 0.322773i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 816 q + 30 q^{2} - 18 q^{4} + 21 q^{5} - 30 q^{7} + 45 q^{8} + 33 q^{11} - 30 q^{13} + 18 q^{14} - 30 q^{16} + 45 q^{17} - 15 q^{19} + 60 q^{20} - 15 q^{22} + 84 q^{23} - 27 q^{25} - 60 q^{28} - 60 q^{29}+ \cdots - 81 q^{97}+O(q^{100}) \) 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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