LMFDB - Embedded newform 675.2.r.a.91.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(46,675)] 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("675.46"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(675, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([20, 18])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.r (of order $15$, degree $8$, 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:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 225)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			91.11
Character	$\chi$	$=$	675.91
Dual form			675.2.r.a.586.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.111376 + 1.05967i) q^{2} +(0.845797 + 0.179780i) q^{4} +(-0.223355 - 2.22488i) q^{5} +(-0.798426 - 1.38291i) q^{7} +(-0.943229 + 2.90296i) q^{8} +(2.38252 + 0.0111154i) q^{10} +(0.498219 - 4.74023i) q^{11} +(-0.103450 - 0.984265i) q^{13} +(1.55436 - 0.692046i) q^{14} +(-1.39126 - 0.619428i) q^{16} +(-0.0927524 + 0.285463i) q^{17} +(0.468623 - 1.44227i) q^{19} +(0.211076 - 1.92195i) q^{20} +(4.96760 + 1.05590i) q^{22} +(5.22312 - 2.32548i) q^{23} +(-4.90022 + 0.993880i) q^{25} +1.05452 q^{26} +(-0.426686 - 1.31321i) q^{28} +(3.96038 - 4.39845i) q^{29} +(-1.82684 - 2.02891i) q^{31} +(-2.24101 + 3.88154i) q^{32} +(-0.292166 - 0.130081i) q^{34} +(-2.89849 + 2.08529i) q^{35} +(1.92560 - 1.39903i) q^{37} +(1.47614 + 0.657221i) q^{38} +(6.66943 + 1.45018i) q^{40} +(-1.17806 - 11.2085i) q^{41} +(3.80449 + 6.58957i) q^{43} +(1.27359 - 3.91970i) q^{44} +(1.88252 + 5.79380i) q^{46} +(-3.89898 + 4.33025i) q^{47} +(2.22503 - 3.85387i) q^{49} +(-0.507419 - 5.30332i) q^{50} +(0.0894527 - 0.851086i) q^{52} +(-0.598625 - 1.84238i) q^{53} +(-10.6578 - 0.0497227i) q^{55} +(4.76765 - 1.01339i) q^{56} +(4.21982 + 4.68659i) q^{58} +(0.607997 + 5.78470i) q^{59} +(-1.39066 + 13.2313i) q^{61} +(2.35344 - 1.70988i) q^{62} +(-6.32771 - 4.59735i) q^{64} +(-2.16677 + 0.450006i) q^{65} +(-0.700631 - 0.778129i) q^{67} +(-0.129770 + 0.224768i) q^{68} +(-1.88690 - 3.30370i) q^{70} +(5.09100 + 15.6685i) q^{71} +(7.42742 + 5.39634i) q^{73} +(1.26805 + 2.19633i) q^{74} +(0.655651 - 1.13562i) q^{76} +(-6.95313 + 3.09573i) q^{77} +(7.48863 - 8.31697i) q^{79} +(-1.06741 + 3.23374i) q^{80} +12.0085 q^{82} +(5.82164 - 1.23743i) q^{83} +(0.655838 + 0.142604i) q^{85} +(-7.40651 + 3.29759i) q^{86} +(13.2908 + 5.91743i) q^{88} +(-1.01962 - 0.740795i) q^{89} +(-1.27856 + 0.928926i) q^{91} +(4.83578 - 1.02788i) q^{92} +(-4.15439 - 4.61392i) q^{94} +(-3.31356 - 0.720493i) q^{95} +(-1.28347 + 1.42544i) q^{97} +(3.83602 + 2.78703i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28}+ \cdots - 146 q^{98}+O(q^{100}) $ 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8 - 20 * q^10 + 11 * q^11 - 3 * q^13 - q^14 + 23 * q^16 + 24 * q^17 - 12 * q^19 - q^20 - 11 * q^22 - q^23 - 16 * q^25 + 136 * q^26 + 4 * q^28 + 15 * q^29 + 3 * q^31 - 12 * q^32 + q^34 - 14 * q^35 - 24 * q^37 - 55 * q^38 + q^40 + 19 * q^41 - 8 * q^43 - 4 * q^44 - 20 * q^46 + 10 * q^47 - 72 * q^49 + 3 * q^50 - 25 * q^52 + 12 * q^53 - 20 * q^55 + 60 * q^56 - 23 * q^58 + 30 * q^59 - 3 * q^61 + 44 * q^62 - 44 * q^64 - 51 * q^65 - 12 * q^67 + 156 * q^68 - 16 * q^70 - 42 * q^71 - 12 * q^73 - 90 * q^74 - 8 * q^76 - 31 * q^77 - 15 * q^79 - 298 * q^80 + 8 * q^82 - 59 * q^83 - 11 * q^85 - 9 * q^86 - 23 * q^88 - 106 * q^89 + 30 * q^91 - 11 * q^92 + 25 * q^94 - 7 * q^95 - 21 * q^97 - 146 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−0.111376	+	1.05967i	−0.0787547	+	0.749301i	0.881878	+	0.471478i	$0.156279\pi$
$2$	−0.111376	+	1.05967i	−0.0787547	+	0.749301i	−0.960632	+	0.277823i	$0.910387\pi$
$3$		0			0
$3$		0			0
$4$	0.845797	+	0.179780i	0.422898	+	0.0898898i
$5$	−0.223355	−	2.22488i	−0.0998875	−	0.994999i
$5$	−0.223355	−	2.22488i	−0.0998875	−	0.994999i
$6$		0			0
$7$	−0.798426	−	1.38291i	−0.301777	−	0.522693i	0.674762	−	0.738036i	$-0.264246\pi$
$7$	−0.798426	−	1.38291i	−0.301777	−	0.522693i	−0.976538	+	0.215343i	$0.930913\pi$
$8$	−0.943229	+	2.90296i	−0.333482	+	1.02635i
$9$		0			0
$10$	2.38252	+	0.0111154i	0.753420	+	0.00351501i
$11$	0.498219	−	4.74023i	0.150219	−	1.42923i	−0.616553	−	0.787314i	$-0.711471\pi$
$11$	0.498219	−	4.74023i	0.150219	−	1.42923i	0.766771	−	0.641921i	$-0.221862\pi$
$12$		0			0
$13$	−0.103450	−	0.984265i	−0.0286920	−	0.272986i	−0.999457	−	0.0329536i	$-0.989509\pi$
$13$	−0.103450	−	0.984265i	−0.0286920	−	0.272986i	0.970765	−	0.240032i	$-0.0771580\pi$
$14$	1.55436	−	0.692046i	0.415420	−	0.184957i
$15$		0			0
$16$	−1.39126	−	0.619428i	−0.347815	−	0.154857i
$17$	−0.0927524	+	0.285463i	−0.0224958	+	0.0692348i	−0.961674	−	0.274195i	$-0.911589\pi$
$17$	−0.0927524	+	0.285463i	−0.0224958	+	0.0692348i	0.939178	+	0.343430i	$0.111589\pi$
$18$		0			0
$19$	0.468623	−	1.44227i	0.107510	−	0.330880i	−0.882802	−	0.469746i	$-0.844346\pi$
$19$	0.468623	−	1.44227i	0.107510	−	0.330880i	0.990311	+	0.138866i	$0.0443456\pi$
$20$	0.211076	−	1.92195i	0.0471980	−	0.429762i
$21$		0			0
$22$	4.96760	+	1.05590i	1.05910	+	0.225118i
$23$	5.22312	−	2.32548i	1.08910	−	0.484897i	0.217970	−	0.975955i	$-0.430056\pi$
$23$	5.22312	−	2.32548i	1.08910	−	0.484897i	0.871127	+	0.491058i	$0.163390\pi$
$24$		0			0
$25$	−4.90022	+	0.993880i	−0.980045	+	0.198776i
$26$	1.05452			0.206808
$27$		0			0
$28$	−0.426686	−	1.31321i	−0.0806361	−	0.248173i
$29$	3.96038	−	4.39845i	0.735425	−	0.816772i	−0.253162	−	0.967424i	$-0.581471\pi$
$29$	3.96038	−	4.39845i	0.735425	−	0.816772i	0.988587	+	0.150652i	$0.0481373\pi$
$30$		0			0
$31$	−1.82684	−	2.02891i	−0.328110	−	0.364403i	0.556408	−	0.830909i	$-0.312179\pi$
$31$	−1.82684	−	2.02891i	−0.328110	−	0.364403i	−0.884518	+	0.466506i	$0.845513\pi$
$32$	−2.24101	+	3.88154i	−0.396158	+	0.686166i
$33$		0			0
$34$	−0.292166	−	0.130081i	−0.0501061	−	0.0223087i
$35$	−2.89849	+	2.08529i	−0.489935	+	0.352478i
$36$		0			0
$37$	1.92560	−	1.39903i	0.316567	−	0.230000i	−0.418142	−	0.908382i	$-0.637319\pi$
$37$	1.92560	−	1.39903i	0.316567	−	0.230000i	0.734709	+	0.678382i	$0.237319\pi$
$38$	1.47614	+	0.657221i	0.239462	+	0.106615i
$39$		0			0
$40$	6.66943	+	1.45018i	1.05453	+	0.229294i
$41$	−1.17806	−	11.2085i	−0.183981	−	1.75047i	−0.564262	−	0.825596i	$-0.690839\pi$
$41$	−1.17806	−	11.2085i	−0.183981	−	1.75047i	0.380280	−	0.924871i	$-0.375827\pi$
$42$		0			0
$43$	3.80449	+	6.58957i	0.580179	+	1.00490i	0.995458	+	0.0952056i	$0.0303508\pi$
$43$	3.80449	+	6.58957i	0.580179	+	1.00490i	−0.415278	+	0.909694i	$0.636316\pi$
$44$	1.27359	−	3.91970i	0.192001	−	0.590918i
$45$		0			0
$46$	1.88252	+	5.79380i	0.277562	+	0.854249i
$47$	−3.89898	+	4.33025i	−0.568724	+	0.631632i	−0.957061	−	0.289885i	$-0.906383\pi$
$47$	−3.89898	+	4.33025i	−0.568724	+	0.631632i	0.388337	+	0.921517i	$0.373050\pi$
$48$		0			0
$49$	2.22503	−	3.85387i	0.317862	−	0.550552i
$50$	−0.507419	−	5.30332i	−0.0717598	−	0.750003i
$51$		0			0
$52$	0.0894527	−	0.851086i	0.0124049	−	0.118024i
$53$	−0.598625	−	1.84238i	−0.0822275	−	0.253070i	0.901488	−	0.432805i	$-0.142476\pi$
$53$	−0.598625	−	1.84238i	−0.0822275	−	0.253070i	−0.983715	+	0.179735i	$0.942476\pi$
$54$		0			0
$55$	−10.6578	−	0.0497227i	−1.43709	−	0.00670461i
$56$	4.76765	−	1.01339i	0.637103	−	0.135421i
$57$		0			0
$58$	4.21982	+	4.68659i	0.554090	+	0.615379i
$59$	0.607997	+	5.78470i	0.0791544	+	0.753104i	0.960057	+	0.279806i	$0.0902701\pi$
$59$	0.607997	+	5.78470i	0.0791544	+	0.753104i	−0.880902	+	0.473298i	$0.843063\pi$
$60$		0			0
$61$	−1.39066	+	13.2313i	−0.178056	+	1.69409i	0.432111	+	0.901820i	$0.357769\pi$
$61$	−1.39066	+	13.2313i	−0.178056	+	1.69409i	−0.610167	+	0.792273i	$0.708898\pi$
$62$	2.35344	−	1.70988i	0.298888	−	0.217155i
$63$		0			0
$64$	−6.32771	−	4.59735i	−0.790963	−	0.574668i
$65$	−2.16677	+	0.450006i	−0.268755	+	0.0558164i
$66$		0			0
$67$	−0.700631	−	0.778129i	−0.0855957	−	0.0950636i	0.698825	−	0.715292i	$-0.253706\pi$
$67$	−0.700631	−	0.778129i	−0.0855957	−	0.0950636i	−0.784421	+	0.620229i	$0.787040\pi$
$68$	−0.129770	+	0.224768i	−0.0157369	+	0.0272572i
$69$		0			0
$70$	−1.88690	−	3.30370i	−0.225527	−	0.394868i
$71$	5.09100	+	15.6685i	0.604191	+	1.85951i	0.502260	+	0.864716i	$0.332502\pi$
$71$	5.09100	+	15.6685i	0.604191	+	1.85951i	0.101930	+	0.994792i	$0.467498\pi$
$72$		0			0
$73$	7.42742	+	5.39634i	0.869314	+	0.631594i	0.930403	−	0.366539i	$-0.119457\pi$
$73$	7.42742	+	5.39634i	0.869314	+	0.631594i	−0.0610888	+	0.998132i	$0.519457\pi$
$74$	1.26805	+	2.19633i	0.147408	+	0.255318i
$75$		0			0
$76$	0.655651	−	1.13562i	0.0752084	−	0.130265i
$77$	−6.95313	+	3.09573i	−0.792383	+	0.352791i
$78$		0			0
$79$	7.48863	−	8.31697i	0.842537	−	0.935732i	−0.156109	−	0.987740i	$-0.549895\pi$
$79$	7.48863	−	8.31697i	0.842537	−	0.935732i	0.998647	+	0.0520074i	$0.0165619\pi$
$80$	−1.06741	+	3.23374i	−0.119340	+	0.361544i
$81$		0			0
$82$	12.0085			1.32612
$83$	5.82164	−	1.23743i	0.639008	−	0.135825i	0.122997	−	0.992407i	$-0.460750\pi$
$83$	5.82164	−	1.23743i	0.639008	−	0.135825i	0.516011	+	0.856582i	$0.327416\pi$
$84$		0			0
$85$	0.655838	+	0.142604i	0.0711356	+	0.0154676i
$86$	−7.40651	+	3.29759i	−0.798664	+	0.355588i
$87$		0			0
$88$	13.2908	+	5.91743i	1.41680	+	0.630801i
$89$	−1.01962	−	0.740795i	−0.108079	−	0.0785241i	0.532433	−	0.846472i	$-0.321278\pi$
$89$	−1.01962	−	0.740795i	−0.108079	−	0.0785241i	−0.640512	+	0.767948i	$0.721278\pi$
$90$		0			0
$91$	−1.27856	+	0.928926i	−0.134029	+	0.0973779i
$92$	4.83578	−	1.02788i	0.504165	−	0.107163i
$93$		0			0
$94$	−4.15439	−	4.61392i	−0.428493	−	0.475889i
$95$	−3.31356	−	0.720493i	−0.339964	−	0.0739210i
$96$		0			0
$97$	−1.28347	+	1.42544i	−0.130317	+	0.144731i	−0.804771	−	0.593585i	$-0.797712\pi$
$97$	−1.28347	+	1.42544i	−0.130317	+	0.144731i	0.674455	+	0.738316i	$0.264379\pi$
$98$	3.83602	+	2.78703i	0.387496	+	0.281533i
$99$		0			0
$100$	−4.32327	−	0.0403405i	−0.432327	−	0.00403405i
$101$	2.94567	+	5.10205i	0.293105	+	0.507673i	0.974542	−	0.224204i	$-0.0719781\pi$
$101$	2.94567	+	5.10205i	0.293105	+	0.507673i	−0.681437	+	0.731877i	$0.738645\pi$
$102$		0			0
$103$	−12.5571	−	2.66910i	−1.23729	−	0.262994i	−0.457598	−	0.889159i	$-0.651290\pi$
$103$	−12.5571	−	2.66910i	−1.23729	−	0.262994i	−0.779691	+	0.626165i	$0.784624\pi$
$104$	2.95486	+	0.628075i	0.289748	+	0.0615878i
$105$		0			0
$106$	2.01899	−	0.429149i	0.196102	−	0.0416827i
$107$	−19.9558			−1.92920			−0.964600	−	0.263716i	$-0.915052\pi$
$107$	−19.9558			−1.92920			−0.964600	+	0.263716i	$0.915052\pi$
$108$		0			0
$109$	6.54028	−	4.75180i	0.626446	−	0.455139i	−0.228721	−	0.973492i	$-0.573454\pi$
$109$	6.54028	−	4.75180i	0.626446	−	0.455139i	0.855167	+	0.518353i	$0.173454\pi$
$110$	1.23971	−	11.2882i	0.118201	−	1.07629i
$111$		0			0
$112$	0.254201	+	2.41856i	0.0240197	+	0.228532i
$113$	1.36211	+	12.9596i	0.128136	+	1.21914i	0.849880	+	0.526976i	$0.176674\pi$
$113$	1.36211	+	12.9596i	0.128136	+	1.21914i	−0.721744	+	0.692161i	$0.756659\pi$
$114$		0			0
$115$	−6.34055	−	11.1014i	−0.591259	−	1.03521i
$116$	4.14043	−	3.00820i	0.384429	−	0.279304i
$117$		0			0
$118$	−6.19760			−0.570535
$119$	0.468826	−	0.0996521i	0.0429772	−	0.00913509i
$120$		0			0
$121$	−11.4620	−	2.43632i	−1.04200	−	0.221483i
$122$	−13.8659	−	2.94729i	−1.25536	−	0.266835i
$123$		0			0
$124$	−1.18038	−	2.04447i	−0.106001	−	0.183599i
$125$	3.30576	+	10.6804i	0.295676	+	0.955288i
$126$		0			0
$127$	−8.64345	−	6.27983i	−0.766982	−	0.557245i	0.134062	−	0.990973i	$-0.457198\pi$
$127$	−8.64345	−	6.27983i	−0.766982	−	0.557245i	−0.901044	+	0.433728i	$0.857198\pi$
$128$	−0.421682	+	0.468326i	−0.0372718	+	0.0413945i
$129$		0			0
$130$	−0.235532	−	2.34618i	−0.0206576	−	0.205774i
$131$	−11.8657	−	13.1782i	−1.03671	−	1.15138i	−0.988295	−	0.152557i	$-0.951249\pi$
$131$	−11.8657	−	13.1782i	−1.03671	−	1.15138i	−0.0484165	−	0.998827i	$-0.515417\pi$
$132$		0			0
$133$	−2.36870	+	0.503483i	−0.205393	+	0.0436575i
$134$	0.902595	−	0.655773i	0.0779723	−	0.0566502i
$135$		0			0
$136$	−0.741200	−	0.538513i	−0.0635574	−	0.0461771i
$137$	15.7282	+	7.00264i	1.34375	+	0.598276i	0.947467	−	0.319852i	$-0.103633\pi$
$137$	15.7282	+	7.00264i	1.34375	+	0.598276i	0.396283	+	0.918128i	$0.370300\pi$
$138$		0			0
$139$	−7.86352	+	3.50106i	−0.666975	+	0.296956i	−0.712155	−	0.702022i	$-0.752281\pi$
$139$	−7.86352	+	3.50106i	−0.666975	+	0.296956i	0.0451798	+	0.998979i	$0.485614\pi$
$140$	−2.82643	+	1.24264i	−0.238877	+	0.105022i
$141$		0			0
$142$	−17.1705	+	3.64970i	−1.44091	+	0.306276i
$143$	−4.71719			−0.394471
$144$		0			0
$145$	−10.6706	−	7.82898i	−0.886147	−	0.650161i
$146$	−6.54558	+	7.26960i	−0.541716	+	0.601637i
$147$		0			0
$148$	1.88019	−	0.837114i	0.154550	−	0.0688103i
$149$	4.79551	−	8.30607i	0.392863	−	0.680460i	−0.599962	−	0.800028i	$-0.704818\pi$
$149$	4.79551	−	8.30607i	0.392863	−	0.680460i	0.992826	+	0.119569i	$0.0381512\pi$
$150$		0			0
$151$	−7.37063	−	12.7663i	−0.599814	−	1.03891i	−0.992848	−	0.119384i	$-0.961908\pi$
$151$	−7.37063	−	12.7663i	−0.599814	−	1.03891i	0.393034	−	0.919524i	$-0.371425\pi$
$152$	3.74484	+	2.72079i	0.303747	+	0.220685i
$153$		0			0
$154$	−2.50605	−	7.71282i	−0.201943	−	0.621517i
$155$	−4.10606	+	4.51768i	−0.329807	+	0.362868i
$156$		0			0
$157$	−6.76957	+	11.7252i	−0.540270	+	0.935775i	0.458618	+	0.888634i	$0.348345\pi$
$157$	−6.76957	+	11.7252i	−0.540270	+	0.935775i	−0.998888	+	0.0471419i	$0.984989\pi$
$158$	7.97920	+	8.86180i	0.634791	+	0.705007i
$159$		0			0
$160$	9.13653	+	4.11903i	0.722306	+	0.325638i
$161$	−7.38623	−	5.36641i	−0.582116	−	0.422932i
$162$		0			0
$163$	2.23732	−	1.62551i	0.175240	−	0.127320i	−0.496708	−	0.867918i	$-0.665458\pi$
$163$	2.23732	−	1.62551i	0.175240	−	0.127320i	0.671948	+	0.740598i	$0.265458\pi$
$164$	1.01866	−	9.69187i	0.0795437	−	0.756808i
$165$		0			0
$166$	0.662876	+	6.30684i	0.0514492	+	0.489506i
$167$	−1.98603	−	2.20571i	−0.153683	−	0.170683i	0.661387	−	0.750045i	$-0.269968\pi$
$167$	−1.98603	−	2.20571i	−0.153683	−	0.170683i	−0.815070	+	0.579362i	$0.803302\pi$
$168$		0			0
$169$	11.7578	−	2.49921i	0.904450	−	0.192247i
$170$	−0.224158	+	0.679090i	−0.0171921	+	0.0520838i
$171$		0			0
$172$	2.03315	+	6.25741i	0.155027	+	0.477123i
$173$	−1.30925	+	12.4567i	−0.0995404	+	0.947064i	0.824782	+	0.565451i	$0.191298\pi$
$173$	−1.30925	+	12.4567i	−0.0995404	+	0.947064i	−0.924322	+	0.381613i	$0.875369\pi$
$174$		0			0
$175$	5.28692	+	5.98305i	0.399653	+	0.452276i
$176$	−3.62939	+	6.28628i	−0.273575	+	0.473846i
$177$		0			0
$178$	0.898560	−	0.997952i	0.0673499	−	0.0747996i
$179$	3.60018	+	11.0802i	0.269090	+	0.828174i	0.990723	+	0.135898i	$0.0433919\pi$
$179$	3.60018	+	11.0802i	0.269090	+	0.828174i	−0.721633	+	0.692276i	$0.756608\pi$
$180$		0			0
$181$	−6.84051	+	21.0529i	−0.508451	+	1.56485i	0.286440	+	0.958098i	$0.407528\pi$
$181$	−6.84051	+	21.0529i	−0.508451	+	1.56485i	−0.794891	+	0.606752i	$0.792472\pi$
$182$	−0.841955	−	1.45831i	−0.0624099	−	0.108097i
$183$		0			0
$184$	1.82419	+	17.3560i	0.134481	+	1.27950i
$185$	−3.54278	−	3.97177i	−0.260471	−	0.292010i
$186$		0			0
$187$	1.30695	+	0.581891i	0.0955735	+	0.0425521i
$188$	−4.07623	+	2.96156i	−0.297290	+	0.215994i
$189$		0			0
$190$	1.13254	−	3.43104i	0.0821629	−	0.248914i
$191$	−10.4328	−	4.64499i	−0.754893	−	0.336100i	−0.00704931	−	0.999975i	$-0.502244\pi$
$191$	−10.4328	−	4.64499i	−0.754893	−	0.336100i	−0.747843	+	0.663875i	$0.768911\pi$
$192$		0			0
$193$	8.87230	−	15.3673i	0.638642	−	1.10616i	−0.347089	−	0.937832i	$-0.612830\pi$
$193$	8.87230	−	15.3673i	0.638642	−	1.10616i	0.985731	−	0.168328i	$-0.0538369\pi$
$194$	−1.36755	−	1.51882i	−0.0981842	−	0.109045i
$195$		0			0
$196$	2.57477	−	2.85957i	0.183912	−	0.204255i
$197$	2.97775	+	9.16457i	0.212156	+	0.652948i	0.999343	+	0.0362347i	$0.0115364\pi$
$197$	2.97775	+	9.16457i	0.212156	+	0.652948i	−0.787187	+	0.616714i	$0.788464\pi$
$198$		0			0
$199$	3.11193			0.220599			0.110299	−	0.993898i	$-0.464819\pi$
$199$	3.11193			0.220599			0.110299	+	0.993898i	$0.464819\pi$
$200$	1.73684	−	15.1626i	0.122813	−	1.07216i
$201$		0			0
$202$	−5.73457	+	2.55320i	−0.403483	+	0.179642i
$203$	−9.24476	−	1.96503i	−0.648855	−	0.137918i
$204$		0			0
$205$	−24.6744	+	5.12451i	−1.72334	+	0.357911i
$206$	4.22692	−	13.0091i	0.294504	−	0.906389i
$207$		0			0
$208$	−0.465755	+	1.43345i	−0.0322943	+	0.0993917i
$209$	−6.60324	−	2.93995i	−0.456755	−	0.203361i
$210$		0			0
$211$	7.83831	−	3.48984i	0.539611	−	0.240250i	−0.118787	−	0.992920i	$-0.537901\pi$
$211$	7.83831	−	3.48984i	0.539611	−	0.240250i	0.658399	+	0.752669i	$0.271234\pi$
$212$	−0.175093	−	1.66590i	−0.0120254	−	0.114414i
$213$		0			0
$214$	2.22260	−	21.1466i	0.151934	−	1.44555i
$215$	13.8113	−	9.93637i	0.941921	−	0.677655i
$216$		0			0
$217$	−1.34721	+	4.14630i	−0.0914549	+	0.281469i
$218$	4.30691	+	7.45979i	0.291701	+	0.505241i
$219$		0			0
$220$	−9.00535	−	1.95810i	−0.607141	−	0.132015i
$221$	0.290566	+	0.0617617i	0.0195456	+	0.00415454i
$222$		0			0
$223$	1.24525	−	11.8478i	0.0833880	−	0.793384i	−0.870287	−	0.492545i	$-0.836067\pi$
$223$	1.24525	−	11.8478i	0.0833880	−	0.793384i	0.953675	−	0.300839i	$-0.0972667\pi$
$224$	7.15712			0.478205
$225$		0			0
$226$	−13.8846			−0.923591
$227$	−2.31541	+	22.0296i	−0.153679	+	1.46216i	0.597400	+	0.801944i	$0.296201\pi$
$227$	−2.31541	+	22.0296i	−0.153679	+	1.46216i	−0.751078	+	0.660213i	$0.770466\pi$
$228$		0			0
$229$	14.8741	+	3.16158i	0.982906	+	0.208923i	0.671217	−	0.741261i	$-0.265772\pi$
$229$	14.8741	+	3.16158i	0.982906	+	0.208923i	0.311689	+	0.950184i	$0.399105\pi$
$230$	12.4701	−	5.48246i	0.822252	−	0.361503i
$231$		0			0
$232$	9.03298	+	15.6456i	0.593044	+	1.02718i
$233$	4.57150	−	14.0696i	0.299489	−	0.921732i	−0.682188	−	0.731177i	$-0.738971\pi$
$233$	4.57150	−	14.0696i	0.299489	−	0.921732i	0.981677	−	0.190555i	$-0.0610288\pi$
$234$		0			0
$235$	10.5052	+	7.70759i	0.685282	+	0.502788i
$236$	−0.525730	+	5.00199i	−0.0342221	+	0.325602i
$237$		0			0
$238$	0.0533825	+	0.507901i	0.00346027	+	0.0329223i
$239$	4.63845	−	2.06517i	0.300037	−	0.133585i	−0.251197	−	0.967936i	$-0.580824\pi$
$239$	4.63845	−	2.06517i	0.300037	−	0.133585i	0.551233	+	0.834351i	$0.314157\pi$
$240$		0			0
$241$	12.2409	+	5.44999i	0.788504	+	0.351064i	0.761162	−	0.648562i	$-0.224629\pi$
$241$	12.2409	+	5.44999i	0.788504	+	0.351064i	0.0273416	+	0.999626i	$0.491296\pi$
$242$	3.85828	−	11.8746i	0.248020	−	0.763326i
$243$		0			0
$244$	−3.55494	+	10.9410i	−0.227581	+	0.700424i
$245$	−9.07138	−	4.08966i	−0.579549	−	0.261279i
$246$		0			0
$247$	−1.46806	−	0.312045i	−0.0934103	−	0.0198550i
$248$	7.61298	−	3.38952i	0.483424	−	0.215234i
$249$		0			0
$250$	−11.6859	+	2.31347i	−0.739084	+	0.146317i
$251$	−25.6881			−1.62142			−0.810709	−	0.585450i	$-0.800918\pi$
$251$	−25.6881			−1.62142			−0.810709	+	0.585450i	$0.800918\pi$
$252$		0			0
$253$	−8.42108	−	25.9174i	−0.529429	−	1.62941i
$254$	7.61723	−	8.45979i	0.477947	−	0.530814i
$255$		0			0
$256$	−10.9165	−	12.1240i	−0.682280	−	0.757749i
$257$	9.78552	−	16.9490i	0.610404	−	1.05725i	−0.380768	−	0.924670i	$-0.624340\pi$
$257$	9.78552	−	16.9490i	0.610404	−	1.05725i	0.991172	−	0.132580i	$-0.0423262\pi$
$258$		0			0
$259$	−3.47220	−	1.54592i	−0.215752	−	0.0960589i
$260$	−1.91355	−	0.00892748i	−0.118673	−	0.000553659i
$261$		0			0
$262$	15.2861	−	11.1060i	0.944379	−	0.686131i
$263$	6.81087	+	3.03239i	0.419976	+	0.186985i	0.605834	−	0.795591i	$-0.292840\pi$
$263$	6.81087	+	3.03239i	0.419976	+	0.186985i	−0.185858	+	0.982577i	$0.559506\pi$
$264$		0			0
$265$	−3.96538	+	1.74338i	−0.243591	+	0.107095i
$266$	−0.269710	−	2.56612i	−0.0165370	−	0.157339i
$267$		0			0
$268$	−0.452699	−	0.784098i	−0.0276530	−	0.0478964i
$269$	1.24097	−	3.81931i	0.0756631	−	0.232867i	−0.906071	−	0.423126i	$-0.860933\pi$
$269$	1.24097	−	3.81931i	0.0756631	−	0.232867i	0.981734	+	0.190259i	$0.0609327\pi$
$270$		0			0
$271$	7.44164	+	22.9030i	0.452047	+	1.39126i	0.874567	+	0.484905i	$0.161146\pi$
$271$	7.44164	+	22.9030i	0.452047	+	1.39126i	−0.422519	+	0.906354i	$0.638854\pi$
$272$	0.305866	−	0.339699i	0.0185459	−	0.0205973i
$273$		0			0
$274$	−9.17224	+	15.8868i	−0.554115	+	0.959756i
$275$	2.26984	+	23.7234i	0.136876	+	1.43057i
$276$		0			0
$277$	−1.93044	+	18.3669i	−0.115989	+	1.10356i	0.769418	+	0.638746i	$0.220546\pi$
$277$	−1.93044	+	18.3669i	−0.115989	+	1.10356i	−0.885407	+	0.464817i	$0.846120\pi$
$278$	−2.83417	−	8.72268i	−0.169982	−	0.523152i
$279$		0			0
$280$	−3.31956	−	10.3811i	−0.198382	−	0.620390i
$281$	−6.38904	+	1.35803i	−0.381138	+	0.0810134i	−0.394497	−	0.918897i	$-0.629081\pi$
$281$	−6.38904	+	1.35803i	−0.381138	+	0.0810134i	0.0133585	+	0.999911i	$0.495748\pi$
$282$		0			0
$283$	−16.6428	−	18.4837i	−0.989313	−	1.09874i	−0.995111	−	0.0987608i	$-0.968512\pi$
$283$	−16.6428	−	18.4837i	−0.989313	−	1.09874i	0.00579771	−	0.999983i	$-0.498155\pi$
$284$	1.48908	+	14.1676i	0.0883604	+	0.840693i
$285$		0			0
$286$	0.525381	−	4.99867i	0.0310664	−	0.295577i
$287$	−14.5598	+	10.5783i	−0.859435	+	0.624416i
$288$		0			0
$289$	13.6804	+	9.93939i	0.804730	+	0.584670i
$290$	9.48459	−	10.4354i	0.556955	−	0.612787i
$291$		0			0
$292$	5.31194	+	5.89950i	0.310858	+	0.345242i
$293$	−3.51196	+	6.08289i	−0.205171	+	0.355366i	−0.950187	−	0.311680i	$-0.899108\pi$
$293$	−3.51196	+	6.08289i	−0.205171	+	0.355366i	0.745016	+	0.667046i	$0.232442\pi$
$294$		0			0
$295$	12.7345	−	2.64477i	0.741431	−	0.153984i
$296$	2.24505	+	6.90956i	0.130491	+	0.401610i
$297$		0			0
$298$	8.26760	+	6.00676i	0.478929	+	0.347962i
$299$	−2.82923	−	4.90036i	−0.163618	−	0.283395i
$300$		0			0
$301$	6.07521	−	10.5226i	0.350169	−	0.606511i
$302$	14.3490	−	6.38859i	0.825693	−	0.367622i
$303$		0			0
$304$	−1.54536	+	1.71630i	−0.0886326	+	0.0984364i
$305$	29.7487	+	0.138790i	1.70341	+	0.00794708i
$306$		0			0
$307$	20.8173			1.18810			0.594052	−	0.804427i	$-0.297527\pi$
$307$	20.8173			1.18810			0.594052	+	0.804427i	$0.297527\pi$
$308$	−6.43748	+	1.36833i	−0.366810	+	0.0779678i
$309$		0			0
$310$	−4.32993	−	4.85423i	−0.245924	−	0.275702i
$311$	6.24230	−	2.77925i	0.353968	−	0.157597i	−0.222047	−	0.975036i	$-0.571274\pi$
$311$	6.24230	−	2.77925i	0.353968	−	0.157597i	0.576015	+	0.817439i	$0.304607\pi$
$312$		0			0
$313$	28.9759	+	12.9009i	1.63781	+	0.729202i	0.999187	−	0.0403151i	$-0.0128362\pi$
$313$	28.9759	+	12.9009i	1.63781	+	0.729202i	0.638627	+	0.769517i	$0.279503\pi$
$314$	−11.6709	−	8.47942i	−0.658628	−	0.478522i
$315$		0			0
$316$	7.82908	−	5.68816i	0.440420	−	0.319984i
$317$	7.64125	−	1.62420i	0.429176	−	0.0912241i	0.0117410	−	0.999931i	$-0.496263\pi$
$317$	7.64125	−	1.62420i	0.429176	−	0.0912241i	0.417435	+	0.908707i	$0.362929\pi$
$318$		0			0
$319$	−18.8765	−	20.9645i	−1.05688	−	1.17379i
$320$	−8.81524	+	15.1053i	−0.492787	+	0.844410i
$321$		0			0
$322$	6.50928	−	7.22928i	0.362748	−	0.402872i
$323$	0.368249	+	0.267549i	0.0204899	+	0.0148868i
$324$		0			0
$325$	1.48517	+	4.72030i	0.0823825	+	0.261835i
$326$	1.47332	+	2.55186i	0.0815996	+	0.141335i
$327$		0			0
$328$	33.6489	+	7.15229i	1.85795	+	0.394919i
$329$	9.10142	+	1.93457i	0.501777	+	0.106656i
$330$		0			0
$331$	21.0076	−	4.46530i	1.15468	−	0.245435i	0.409509	−	0.912306i	$-0.365700\pi$
$331$	21.0076	−	4.46530i	1.15468	−	0.245435i	0.745173	+	0.666871i	$0.232367\pi$
$332$	5.14639			0.282445
$333$		0			0
$334$	2.55852	−	1.85887i	0.139996	−	0.101713i
$335$	−1.57476	+	1.73262i	−0.0860382	+	0.0946632i
$336$		0			0
$337$	1.79489	+	17.0772i	0.0977737	+	0.930254i	0.927938	+	0.372735i	$0.121580\pi$
$337$	1.79489	+	17.0772i	0.0977737	+	0.930254i	−0.830164	+	0.557519i	$0.811753\pi$
$338$	1.33880	+	12.7378i	0.0728209	+	0.692845i
$339$		0			0
$340$	0.529068	+	0.238520i	0.0286928	+	0.0129356i
$341$	−10.5277	+	7.64880i	−0.570106	+	0.414206i
$342$		0			0
$343$	−18.2841			−0.987246
$344$	−22.7178	+	4.82881i	−1.22486	+	0.260352i
$345$		0			0
$346$	−13.0542	−	2.77475i	−0.701796	−	0.149171i
$347$	18.2151	+	3.87175i	0.977840	+	0.207846i	0.668996	−	0.743266i	$-0.266724\pi$
$347$	18.2151	+	3.87175i	0.977840	+	0.207846i	0.308844	+	0.951113i	$0.400058\pi$
$348$		0			0
$349$	−8.55166	−	14.8119i	−0.457760	−	0.792863i	0.541083	−	0.840969i	$-0.318015\pi$
$349$	−8.55166	−	14.8119i	−0.457760	−	0.792863i	−0.998842	+	0.0481065i	$0.984681\pi$
$350$	−6.92891	+	4.93603i	−0.370366	+	0.263842i
$351$		0			0
$352$	17.2829	+	12.5568i	0.921182	+	0.669278i
$353$	13.4404	−	14.9271i	0.715359	−	0.794487i	−0.270383	−	0.962753i	$-0.587150\pi$
$353$	13.4404	−	14.9271i	0.715359	−	0.794487i	0.985742	+	0.168266i	$0.0538168\pi$
$354$		0			0
$355$	33.7235	−	14.8265i	1.78986	−	0.786911i
$356$	−0.729209	−	0.809868i	−0.0386480	−	0.0429229i
$357$		0			0
$358$	−12.1424	+	2.58094i	−0.641743	+	0.136407i
$359$	3.71885	−	2.70190i	0.196273	−	0.142601i	−0.485308	−	0.874343i	$-0.661293\pi$
$359$	3.71885	−	2.70190i	0.196273	−	0.142601i	0.681581	+	0.731742i	$0.261293\pi$
$360$		0			0
$361$	13.5108	+	9.81615i	0.711094	+	0.516640i
$362$	−21.5473	−	9.59347i	−1.13250	−	0.504222i
$363$		0			0
$364$	−1.24840	+	0.555824i	−0.0654340	+	0.0291331i
$365$	10.3473	−	17.7305i	0.541601	−	0.928055i
$366$		0			0
$367$	−17.2316	+	3.66269i	−0.899483	+	0.191191i	−0.634373	−	0.773027i	$-0.718742\pi$
$367$	−17.2316	+	3.66269i	−0.899483	+	0.191191i	−0.265110	+	0.964218i	$0.585408\pi$
$368$	−8.70719			−0.453894
$369$		0			0
$370$	4.60335	−	3.31183i	0.239317	−	0.172174i
$371$	−2.06990	+	2.29885i	−0.107464	+	0.119350i
$372$		0			0
$373$	9.22942	−	4.10920i	0.477881	−	0.212766i	−0.153637	−	0.988127i	$-0.549099\pi$
$373$	9.22942	−	4.10920i	0.477881	−	0.212766i	0.631518	+	0.775361i	$0.282432\pi$
$374$	−0.762176	+	1.32013i	−0.0394112	+	0.0682621i
$375$		0			0
$376$	−8.89292	−	15.4030i	−0.458618	−	0.794349i
$377$	−4.73894	−	3.44304i	−0.244068	−	0.177326i
$378$		0			0
$379$	6.82808	+	21.0147i	0.350735	+	1.07945i	0.958442	+	0.285289i	$0.0920896\pi$
$379$	6.82808	+	21.0147i	0.350735	+	1.07945i	−0.607707	+	0.794162i	$0.707910\pi$
$380$	−2.67307	−	1.20510i	−0.137126	−	0.0618204i
$381$		0			0
$382$	6.08413	−	10.5380i	0.311291	−	0.539172i
$383$	−5.20039	−	5.77562i	−0.265727	−	0.295120i	0.595484	−	0.803367i	$-0.296960\pi$
$383$	−5.20039	−	5.77562i	−0.265727	−	0.295120i	−0.861211	+	0.508247i	$0.830294\pi$
$384$		0			0
$385$	8.44067	+	14.7785i	0.430176	+	0.753180i
$386$	15.2961	+	11.1133i	0.778551	+	0.565650i
$387$		0			0
$388$	−1.34182	+	0.974889i	−0.0681205	+	0.0494925i
$389$	−1.30925	+	12.4567i	−0.0663816	+	0.631579i	0.909863	+	0.414908i	$0.136186\pi$
$389$	−1.30925	+	12.4567i	−0.0663816	+	0.631579i	−0.976245	+	0.216670i	$0.930480\pi$
$390$		0			0
$391$	0.179381	+	1.70670i	0.00907171	+	0.0863116i
$392$	9.08891	+	10.0943i	0.459059	+	0.509837i
$393$		0			0
$394$	−10.0431	+	2.13472i	−0.505963	+	0.107546i
$395$	−20.1769	−	14.8037i	−1.01521	−	0.744855i
$396$		0			0
$397$	−8.80399	−	27.0959i	−0.441859	−	1.35990i	−0.885891	−	0.463893i	$-0.846452\pi$
$397$	−8.80399	−	27.0959i	−0.441859	−	1.35990i	0.444032	−	0.896011i	$-0.353548\pi$
$398$	−0.346594	+	3.29762i	−0.0173732	+	0.165295i
$399$		0			0
$400$	7.43312	+	1.65259i	0.371656	+	0.0826297i
$401$	−4.38488	+	7.59484i	−0.218971	+	0.379268i	−0.954494	−	0.298232i	$-0.903603\pi$
$401$	−4.38488	+	7.59484i	−0.218971	+	0.379268i	0.735523	+	0.677500i	$0.236937\pi$
$402$		0			0
$403$	−1.80800	+	2.00799i	−0.0900628	+	0.100025i
$404$	1.57419	+	4.84487i	0.0783190	+	0.241041i
$405$		0			0
$406$	3.11193	−	9.57755i	0.154443	−	0.475326i
$407$	−5.67237	−	9.82484i	−0.281169	−	0.486999i
$408$		0			0
$409$	1.21205	+	11.5319i	0.0599320	+	0.570214i	0.982745	+	0.184966i	$0.0592175\pi$
$409$	1.21205	+	11.5319i	0.0599320	+	0.570214i	−0.922813	+	0.385248i	$0.874116\pi$
$410$	−2.68216	−	26.7175i	−0.132462	−	1.31948i
$411$		0			0
$412$	−10.1409	−	4.51503i	−0.499607	−	0.222439i
$413$	7.51431	−	5.45947i	0.369755	−	0.268643i
$414$		0			0
$415$	−4.05343	−	12.6761i	−0.198975	−	0.622245i
$416$	4.05230	+	1.80420i	0.198680	+	0.0884582i
$417$		0			0
$418$	3.85082	−	6.66982i	0.188350	−	0.326232i
$419$	19.1565	+	21.2755i	0.935858	+	1.03938i	0.999143	+	0.0413804i	$0.0131756\pi$
$419$	19.1565	+	21.2755i	0.935858	+	1.03938i	−0.0632852	+	0.997995i	$0.520158\pi$
$420$		0			0
$421$	−9.31495	+	10.3453i	−0.453983	+	0.504199i	−0.926069	−	0.377353i	$-0.876834\pi$
$421$	−9.31495	+	10.3453i	−0.453983	+	0.504199i	0.472087	+	0.881552i	$0.343501\pi$
$422$	2.82508	+	8.69471i	0.137523	+	0.423252i
$423$		0			0
$424$	5.91300			0.287160
$425$	0.170792	−	1.49102i	0.00828464	−	0.0723249i
$426$		0			0
$427$	19.4081	−	8.64104i	0.939223	−	0.418169i
$428$	−16.8786	−	3.58765i	−0.815856	−	0.173416i
$429$		0			0
$430$	8.99104	+	15.7421i	0.433586	+	0.759151i
$431$	3.32930	−	10.2465i	0.160367	−	0.493559i	−0.838298	−	0.545212i	$-0.816449\pi$
$431$	3.32930	−	10.2465i	0.160367	−	0.493559i	0.998665	+	0.0516534i	$0.0164491\pi$
$432$		0			0
$433$	−3.22740	+	9.93293i	−0.155099	+	0.477346i	−0.998171	−	0.0604550i	$-0.980745\pi$
$433$	−3.22740	+	9.93293i	−0.155099	+	0.477346i	0.843072	+	0.537801i	$0.180745\pi$
$434$	−4.24367	−	1.88940i	−0.203703	−	0.0906942i
$435$		0			0
$436$	6.38603	−	2.84324i	0.305835	−	0.136167i
$437$	−0.906309	−	8.62295i	−0.0433546	−	0.412492i
$438$		0			0
$439$	−2.75093	+	26.1733i	−0.131294	+	1.24918i	0.708277	+	0.705935i	$0.249473\pi$
$439$	−2.75093	+	26.1733i	−0.131294	+	1.24918i	−0.839572	+	0.543249i	$0.817194\pi$
$440$	10.1970	−	30.8921i	0.486125	−	1.47272i
$441$		0			0
$442$	−0.0978092	+	0.301026i	−0.00465231	+	0.0143183i
$443$	1.09162	+	1.89074i	0.0518643	+	0.0898316i	0.890792	−	0.454411i	$-0.150150\pi$
$443$	1.09162	+	1.89074i	0.0518643	+	0.0898316i	−0.838928	+	0.544243i	$0.816817\pi$
$444$		0			0
$445$	−1.42045	+	2.43399i	−0.0673356	+	0.115382i
$446$	12.4160	+	2.63911i	0.587916	+	0.124965i
$447$		0			0
$448$	−1.30553	+	12.4213i	−0.0616806	+	0.586852i
$449$	32.5364			1.53549			0.767743	−	0.640758i	$-0.221380\pi$
$449$	32.5364			1.53549			0.767743	+	0.640758i	$0.221380\pi$
$450$		0			0
$451$	−53.7176			−2.52946
$452$	−1.17781	+	11.2061i	−0.0553993	+	0.527089i
$453$		0			0
$454$	−23.0863	−	4.90714i	−1.08349	−	0.230303i
$455$	2.35233	+	2.63716i	0.110279	+	0.123632i
$456$		0			0
$457$	−10.4827	−	18.1566i	−0.490360	−	0.849328i	0.509579	−	0.860424i	$-0.329801\pi$
$457$	−10.4827	−	18.1566i	−0.490360	−	0.849328i	−0.999938	+	0.0110963i	$0.996468\pi$
$458$	−5.00685	+	15.4095i	−0.233955	+	0.720038i
$459$		0			0
$460$	−3.36700	−	10.5295i	−0.156987	−	0.490939i
$461$	1.52962	−	14.5533i	0.0712413	−	0.677816i	−0.899374	−	0.437180i	$-0.855977\pi$
$461$	1.52962	−	14.5533i	0.0712413	−	0.677816i	0.970615	−	0.240636i	$-0.0773560\pi$
$462$		0			0
$463$	2.76908	+	26.3460i	0.128690	+	1.22440i	0.848107	+	0.529825i	$0.177743\pi$
$463$	2.76908	+	26.3460i	0.128690	+	1.22440i	−0.719417	+	0.694579i	$0.755591\pi$
$464$	−8.23445	+	3.66621i	−0.382275	+	0.170200i
$465$		0			0
$466$	14.4000	+	6.41131i	0.667068	+	0.296998i
$467$	6.73062	−	20.7147i	0.311456	−	0.958562i	−0.665733	−	0.746190i	$-0.731881\pi$
$467$	6.73062	−	20.7147i	0.311456	−	0.958562i	0.977189	−	0.212372i	$-0.0681189\pi$
$468$		0			0
$469$	−0.516684	+	1.59019i	−0.0238583	+	0.0734282i
$470$	−9.33753	+	10.2736i	−0.430708	+	0.473885i
$471$		0			0
$472$	−17.3662	−	3.69131i	−0.799346	−	0.169906i
$473$	33.1316	−	14.7511i	1.52339	−	0.678257i
$474$		0			0
$475$	−0.862912	+	7.53322i	−0.0395931	+	0.345648i
$476$	0.414447			0.0189962
$477$		0			0
$478$	1.67179	+	5.14524i	0.0764660	+	0.235338i
$479$	−4.23484	+	4.70327i	−0.193495	+	0.214898i	−0.832083	−	0.554651i	$-0.812852\pi$
$479$	−4.23484	+	4.70327i	−0.193495	+	0.214898i	0.638589	+	0.769548i	$0.279519\pi$
$480$		0			0
$481$	−1.57622	−	1.75057i	−0.0718696	−	0.0798193i
$482$	−7.13853	+	12.3643i	−0.325151	+	0.563178i
$483$		0			0
$484$	−9.25650	−	4.12126i	−0.420750	−	0.187330i
$485$	3.45810	+	2.53719i	0.157024	+	0.115208i
$486$		0			0
$487$	−18.7250	+	13.6045i	−0.848512	+	0.616480i	−0.924735	−	0.380611i	$-0.875714\pi$
$487$	−18.7250	+	13.6045i	−0.848512	+	0.616480i	0.0762233	+	0.997091i	$0.475714\pi$
$488$	−37.0982	−	16.5172i	−1.67936	−	0.747698i
$489$		0			0
$490$	5.34403	−	9.15719i	0.241418	−	0.413680i
$491$	1.05910	+	10.0766i	0.0477963	+	0.454752i	0.992079	+	0.125616i	$0.0400907\pi$
$491$	1.05910	+	10.0766i	0.0477963	+	0.454752i	−0.944283	+	0.329136i	$0.893243\pi$
$492$		0			0
$493$	0.888258	+	1.53851i	0.0400051	+	0.0692909i
$494$	0.494172	−	1.52090i	0.0222338	−	0.0684287i
$495$		0			0
$496$	1.28484	+	3.95434i	0.0576911	+	0.177555i
$497$	17.6034	−	19.5506i	0.789620	−	0.876962i
$498$		0			0
$499$	2.03652	−	3.52736i	0.0911674	−	0.157906i	−0.816835	−	0.576871i	$-0.804274\pi$
$499$	2.03652	−	3.52736i	0.0911674	−	0.157906i	0.908003	+	0.418965i	$0.137607\pi$
$500$	0.875873	+	9.62780i	0.0391702	+	0.430568i
$501$		0			0
$502$	2.86103	−	27.2209i	0.127694	−	1.21493i
$503$	−6.77990	−	20.8664i	−0.302301	−	0.930386i	−0.980671	−	0.195666i	$-0.937313\pi$
$503$	−6.77990	−	20.8664i	−0.302301	−	0.930386i	0.678370	−	0.734721i	$-0.262687\pi$
$504$		0			0
$505$	10.6935	−	7.69334i	0.475856	−	0.342349i
$506$	28.4019	−	6.03700i	1.26262	−	0.268377i
$507$		0			0
$508$	−6.18161	−	6.86538i	−0.274265	−	0.304602i
$509$	−1.17263	−	11.1568i	−0.0519760	−	0.494518i	−0.989283	−	0.146013i	$-0.953356\pi$
$509$	−1.17263	−	11.1568i	−0.0519760	−	0.494518i	0.937307	−	0.348506i	$-0.113311\pi$
$510$		0			0
$511$	1.53243	−	14.5801i	0.0677906	−	0.644984i
$512$	13.0436	−	9.47672i	0.576451	−	0.418816i
$513$		0			0
$514$	16.8705	+	12.2571i	0.744126	+	0.540639i
$515$	−3.13373	+	28.5343i	−0.138089	+	1.25737i
$516$		0			0
$517$	18.5839	+	20.6395i	0.817318	+	0.907723i
$518$	2.02489	−	3.50721i	0.0889685	−	0.154098i
$519$		0			0
$520$	0.737410	−	6.71450i	0.0323376	−	0.294450i
$521$	0.276314	+	0.850408i	0.0121056	+	0.0372571i	0.956927	−	0.290329i	$-0.0937648\pi$
$521$	0.276314	+	0.850408i	0.0121056	+	0.0372571i	−0.944821	+	0.327586i	$0.893765\pi$
$522$		0			0
$523$	−9.65472	−	7.01456i	−0.422171	−	0.306725i	0.356340	−	0.934357i	$-0.384025\pi$
$523$	−9.65472	−	7.01456i	−0.422171	−	0.306725i	−0.778511	+	0.627631i	$0.784025\pi$
$524$	−7.66680	−	13.2793i	−0.334926	−	0.580108i
$525$		0			0
$526$	−3.97191	+	6.87955i	−0.173183	+	0.299962i
$527$	0.748622	−	0.333308i	0.0326105	−	0.0145191i
$528$		0			0
$529$	6.48314	−	7.20026i	0.281876	−	0.313055i
$530$	−1.40576	−	4.39617i	−0.0610623	−	0.190957i
$531$		0			0
$532$	−2.09396			−0.0907845
$533$	−10.9102	+	2.31904i	−0.472574	+	0.100449i
$534$		0			0
$535$	4.45724	+	44.3994i	0.192703	+	1.91955i
$536$	2.91973	−	1.29995i	0.126113	−	0.0561492i
$537$		0			0
$538$	3.90899	+	1.74040i	0.168529	+	0.0750338i
$539$	−17.1597	−	12.4672i	−0.739120	−	0.537002i
$540$		0			0
$541$	24.7363	−	17.9720i	1.06350	−	0.772675i	0.0887638	−	0.996053i	$-0.471708\pi$
$541$	24.7363	−	17.9720i	1.06350	−	0.772675i	0.974732	+	0.223378i	$0.0717084\pi$
$542$	−25.0985	+	5.33485i	−1.07807	+	0.229151i
$543$		0			0
$544$	−0.900176	−	0.999747i	−0.0385947	−	0.0428638i
$545$	−12.0330	−	13.4900i	−0.515437	−	0.577850i
$546$		0			0
$547$	0.275835	−	0.306346i	0.0117939	−	0.0130984i	−0.737219	−	0.675654i	$-0.763861\pi$
$547$	0.275835	−	0.306346i	0.0117939	−	0.0130984i	0.749013	+	0.662555i	$0.230528\pi$
$548$	12.0439	+	8.75042i	0.514491	+	0.373799i
$549$		0			0
$550$	−25.3918	−	0.236931i	−1.08271	−	0.0101028i
$551$	−4.48784	−	7.77317i	−0.191189	−	0.331148i
$552$		0			0
$553$	−17.4808	−	3.71566i	−0.743359	−	0.158006i
$554$	−19.2479	−	4.09127i	−0.817765	−	0.173821i
$555$		0			0
$556$	−7.28036	+	1.54749i	−0.308756	+	0.0656281i
$557$	11.0413			0.467833			0.233917	−	0.972257i	$-0.424846\pi$
$557$	11.0413			0.467833			0.233917	+	0.972257i	$0.424846\pi$
$558$		0			0
$559$	6.09230	−	4.42632i	0.257677	−	0.187213i
$560$	5.32424	−	1.10577i	0.224990	−	0.0467272i
$561$		0			0
$562$	−0.727483	−	6.92153i	−0.0306870	−	0.291967i
$563$	−3.22430	−	30.6772i	−0.135888	−	1.29289i	−0.823711	−	0.567011i	$-0.808100\pi$
$563$	−3.22430	−	30.6772i	−0.135888	−	1.29289i	0.687822	−	0.725879i	$-0.258567\pi$
$564$		0			0
$565$	28.5294	−	5.92513i	1.20024	−	0.249272i
$566$	21.4403	−	15.5773i	0.901203	−	0.654762i
$567$		0			0
$568$	−50.2870			−2.11000
$569$	6.98129	−	1.48392i	0.292671	−	0.0622091i	−0.0592364	−	0.998244i	$-0.518867\pi$
$569$	6.98129	−	1.48392i	0.292671	−	0.0622091i	0.351907	+	0.936035i	$0.385533\pi$
$570$		0			0
$571$	−0.820617	−	0.174427i	−0.0343417	−	0.00729956i	0.190709	−	0.981647i	$-0.438921\pi$
$571$	−0.820617	−	0.174427i	−0.0343417	−	0.00729956i	−0.225051	+	0.974347i	$0.572255\pi$
$572$	−3.98978	−	0.848054i	−0.166821	−	0.0354589i
$573$		0			0
$574$	−9.58789	−	16.6067i	−0.400191	−	0.693151i
$575$	−23.2832	+	16.5866i	−0.970978	+	0.691707i
$576$		0			0
$577$	−21.7584	−	15.8084i	−0.905813	−	0.658112i	0.0341394	−	0.999417i	$-0.489131\pi$
$577$	−21.7584	−	15.8084i	−0.905813	−	0.658112i	−0.939952	+	0.341305i	$0.889131\pi$
$578$	−12.0562	+	13.3897i	−0.501470	+	0.556939i
$579$		0			0
$580$	−7.61768	−	8.54008i	−0.316307	−	0.354608i
$581$	−6.35941	−	7.06284i	−0.263833	−	0.293016i
$582$		0			0
$583$	−9.03156	+	1.91972i	−0.374049	+	0.0795065i
$584$	−22.6711	+	16.4715i	−0.938137	+	0.681597i
$585$		0			0
$586$	−6.05471	−	4.39901i	−0.250118	−	0.181721i
$587$	−0.830983	−	0.369978i	−0.0342984	−	0.0152706i	0.389516	−	0.921020i	$-0.372642\pi$
$587$	−0.830983	−	0.369978i	−0.0342984	−	0.0152706i	−0.423814	+	0.905749i	$0.639309\pi$
$588$		0			0
$589$	−3.78234	+	1.68401i	−0.155849	+	0.0693883i
$590$	1.38427	+	13.7889i	0.0569894	+	0.567682i
$591$		0			0
$592$	−3.54562	+	0.753644i	−0.145724	+	0.0309746i
$593$	−35.9174			−1.47495			−0.737476	−	0.675373i	$-0.763983\pi$
$593$	−35.9174			−1.47495			−0.737476	+	0.675373i	$0.763983\pi$
$594$		0			0
$595$	−0.326429	−	1.02083i	−0.0133823	−	0.0418498i
$596$	5.54929	−	6.16311i	0.227308	−	0.252451i
$597$		0			0
$598$	5.50788	−	2.45227i	0.225234	−	0.100281i
$599$	−21.6849	+	37.5593i	−0.886020	+	1.53463i	−0.0414800	+	0.999139i	$0.513207\pi$
$599$	−21.6849	+	37.5593i	−0.886020	+	1.53463i	−0.844540	+	0.535492i	$0.820126\pi$
$600$		0			0
$601$	−9.27357	−	16.0623i	−0.378277	−	0.655195i	0.612535	−	0.790444i	$-0.290150\pi$
$601$	−9.27357	−	16.0623i	−0.378277	−	0.655195i	−0.990812	+	0.135249i	$0.956817\pi$
$602$	10.4738	+	7.60968i	0.426882	+	0.310148i
$603$		0			0
$604$	−3.93893	−	12.1228i	−0.160273	−	0.493270i
$605$	−2.86043	+	26.0457i	−0.116293	+	1.05891i
$606$		0			0
$607$	−10.0739	+	17.4485i	−0.408886	+	0.708212i	−0.994765	−	0.102187i	$-0.967416\pi$
$607$	−10.0739	+	17.4485i	−0.408886	+	0.708212i	0.585879	+	0.810398i	$0.300749\pi$
$608$	4.54806	+	5.05113i	0.184448	+	0.204850i
$609$		0			0
$610$	−3.46036	+	31.5084i	−0.140106	+	1.27574i
$611$	4.66547	+	3.38966i	0.188745	+	0.137131i
$612$		0			0
$613$	6.07494	−	4.41370i	0.245365	−	0.178268i	−0.458305	−	0.888795i	$-0.651543\pi$
$613$	6.07494	−	4.41370i	0.245365	−	0.178268i	0.703670	+	0.710527i	$0.251543\pi$
$614$	−2.31854	+	22.0595i	−0.0935688	+	0.890247i
$615$		0			0
$616$	−2.42840	−	23.1046i	−0.0978429	−	0.930913i
$617$	6.56579	+	7.29205i	0.264329	+	0.293567i	0.860669	−	0.509165i	$-0.170046\pi$
$617$	6.56579	+	7.29205i	0.264329	+	0.293567i	−0.596340	+	0.802732i	$0.703379\pi$
$618$		0			0
$619$	−1.51584	+	0.322202i	−0.0609267	+	0.0129504i	−0.238274	−	0.971198i	$-0.576582\pi$
$619$	−1.51584	+	0.322202i	−0.0609267	+	0.0129504i	0.177347	+	0.984148i	$0.443248\pi$
$620$	−4.28508	+	3.08285i	−0.172093	+	0.123810i
$621$		0			0
$622$	2.24985	+	6.92432i	0.0902107	+	0.277640i
$623$	−0.210367	+	2.00151i	−0.00842820	+	0.0801889i
$624$		0			0
$625$	23.0244	−	9.74047i	0.920976	−	0.389619i
$626$	−16.8979	+	29.2681i	−0.675377	+	1.16979i
$627$		0			0
$628$	−7.83363	+	8.70013i	−0.312596	+	0.347173i
$629$	0.220767	+	0.679452i	0.00880257	+	0.0270915i
$630$		0			0
$631$	3.50012	−	10.7722i	0.139337	−	0.428836i	−0.856902	−	0.515479i	$-0.827614\pi$
$631$	3.50012	−	10.7722i	0.139337	−	0.428836i	0.996239	+	0.0866429i	$0.0276139\pi$
$632$	17.0803	+	29.5840i	0.679419	+	1.17679i
$633$		0			0
$634$	0.870065	+	8.27811i	0.0345547	+	0.328766i
$635$	−12.0413	+	20.6333i	−0.477846	+	0.818808i
$636$		0			0
$637$	−4.02341	−	1.79134i	−0.159413	−	0.0709753i
$638$	24.3179	−	17.6680i	0.962755	−	0.699483i
$639$		0			0
$640$	1.13616	+	0.833592i	0.0449105	+	0.0329506i
$641$	16.7627	+	7.46323i	0.662087	+	0.294780i	0.710135	−	0.704065i	$-0.248634\pi$
$641$	16.7627	+	7.46323i	0.662087	+	0.294780i	−0.0480489	+	0.998845i	$0.515300\pi$
$642$		0			0
$643$	6.43258	−	11.1415i	0.253676	−	0.439380i	−0.710859	−	0.703334i	$-0.751694\pi$
$643$	6.43258	−	11.1415i	0.253676	−	0.439380i	0.964535	+	0.263955i	$0.0850270\pi$
$644$	−5.28248	−	5.86678i	−0.208159	−	0.231184i
$645$		0			0
$646$	−0.324528	+	0.360425i	−0.0127684	+	0.0141807i
$647$	−5.33164	−	16.4091i	−0.209608	−	0.645108i	−0.999493	−	0.0318523i	$-0.989859\pi$
$647$	−5.33164	−	16.4091i	−0.209608	−	0.645108i	0.789884	−	0.613256i	$-0.210141\pi$
$648$		0			0
$649$	27.7238			1.08825
$650$	−5.16738	+	1.04806i	−0.202681	+	0.0411085i
$651$		0			0
$652$	2.18455	−	0.972624i	0.0855536	−	0.0380909i
$653$	−27.6443	−	5.87598i	−1.08181	−	0.229945i	−0.367673	−	0.929955i	$-0.619845\pi$
$653$	−27.6443	−	5.87598i	−1.08181	−	0.229945i	−0.714133	+	0.700010i	$0.753179\pi$
$654$		0			0
$655$	−26.6697	+	29.3432i	−1.04207	+	1.14654i
$656$	−5.30386	+	16.3236i	−0.207081	+	0.637329i
$657$		0			0
$658$	−3.06368	+	9.42904i	−0.119435	+	0.367582i
$659$	19.3379	+	8.60978i	0.753297	+	0.335390i	0.747207	−	0.664592i	$-0.231395\pi$
$659$	19.3379	+	8.60978i	0.753297	+	0.335390i	0.00609079	+	0.999981i	$0.498061\pi$
$660$		0			0
$661$	−40.2135	+	17.9042i	−1.56412	+	0.696392i	−0.992285	−	0.123975i	$-0.960436\pi$
$661$	−40.2135	+	17.9042i	−1.56412	+	0.696392i	−0.571837	+	0.820367i	$0.693769\pi$
$662$	2.39201	+	22.7585i	0.0929682	+	0.884533i
$663$		0			0
$664$	−1.89894	+	18.0672i	−0.0736930	+	0.701142i
$665$	1.64925	+	5.15763i	0.0639553	+	0.200004i
$666$		0			0
$667$	10.4570	−	32.1835i	0.404898	−	1.24615i
$668$	−1.28323	−	2.22263i	−0.0496498	−	0.0859960i
$669$		0			0
$670$	−1.66062	−	1.86170i	−0.0641553	−	0.0719237i
$671$	62.0265	+	13.1841i	2.39451	+	0.508968i
$672$		0			0
$673$	−0.959818	+	9.13206i	−0.0369983	+	0.352015i	0.960324	+	0.278886i	$0.0899652\pi$
$673$	−0.959818	+	9.13206i	−0.0369983	+	0.352015i	−0.997322	+	0.0731291i	$0.976702\pi$
$674$	−18.2961			−0.704740
$675$		0			0
$676$	10.3941			0.399771
$677$	2.28459	−	21.7364i	0.0878040	−	0.835399i	−0.858650	−	0.512562i	$-0.828697\pi$
$677$	2.28459	−	21.7364i	0.0878040	−	0.835399i	0.946454	−	0.322837i	$-0.104637\pi$
$678$		0			0
$679$	2.99601	+	0.636822i	0.114976	+	0.0244390i
$680$	−1.03258	+	1.76936i	−0.0395976	+	0.0678520i
$681$		0			0
$682$	−6.93269	−	12.0078i	−0.265466	−	0.459801i
$683$	1.01224	−	3.11535i	0.0387322	−	0.119206i	−0.929821	−	0.368012i	$-0.880038\pi$
$683$	1.01224	−	3.11535i	0.0387322	−	0.119206i	0.968553	+	0.248807i	$0.0800384\pi$
$684$		0			0
$685$	12.0671	−	36.5575i	0.461060	−	1.39679i
$686$	2.03640	−	19.3751i	0.0777503	−	0.739744i
$687$		0			0
$688$	−1.21126	−	11.5244i	−0.0461790	−	0.439364i
$689$	−1.75146	+	0.779801i	−0.0667254	+	0.0297080i
$690$		0			0
$691$	17.3374	+	7.71909i	0.659544	+	0.293648i	0.709084	−	0.705124i	$-0.249109\pi$
$691$	17.3374	+	7.71909i	0.659544	+	0.293648i	−0.0495396	+	0.998772i	$0.515775\pi$
$692$	−3.34682	+	10.3004i	−0.127227	+	0.391564i
$693$		0			0
$694$	−6.13151	+	18.8708i	−0.232749	+	0.716327i
$695$	9.54582	+	16.7134i	0.362094	+	0.633977i
$696$		0			0
$697$	3.30886	+	0.703320i	0.125332	+	0.0266402i
$698$	16.6482	−	7.41225i	0.630143	−	0.280558i
$699$		0			0
$700$	3.39603	+	6.01093i	0.128358	+	0.227192i
$701$	−26.6440			−1.00633			−0.503164	−	0.864191i	$-0.667831\pi$
$701$	−26.6440			−1.00633			−0.503164	+	0.864191i	$0.667831\pi$
$702$		0			0
$703$	−1.11541	−	3.43287i	−0.0420684	−	0.129473i
$704$	−24.9451	+	27.7043i	−0.940153	+	1.04415i
$705$		0			0
$706$	14.3208	+	15.9049i	0.538972	+	0.598589i
$707$	4.70380	−	8.14722i	0.176905	−	0.306408i
$708$		0			0
$709$	−15.0470	−	6.69934i	−0.565101	−	0.251599i	0.104243	−	0.994552i	$-0.466758\pi$
$709$	−15.0470	−	6.69934i	−0.565101	−	0.251599i	−0.669344	+	0.742953i	$0.733425\pi$
$710$	11.9553	+	37.3871i	0.448673	+	1.40311i
$711$		0			0
$712$	3.11223	−	2.26117i	0.116636	−	0.0847408i
$713$	−14.2600	−	6.34897i	−0.534042	−	0.237771i
$714$		0			0
$715$	1.05361	+	10.4952i	0.0394027	+	0.392498i
$716$	1.05302	+	10.0188i	0.0393533	+	0.374422i
$717$		0			0
$718$	2.44894	+	4.24168i	0.0913935	+	0.158298i
$719$	8.80843	−	27.1096i	0.328499	−	1.01102i	−0.641337	−	0.767259i	$-0.721620\pi$
$719$	8.80843	−	27.1096i	0.328499	−	1.01102i	0.969836	−	0.243757i	$-0.0783800\pi$
$720$		0			0
$721$	6.33479	+	19.4965i	0.235920	+	0.726087i
$722$	−11.9067	+	13.2237i	−0.443120	+	0.492135i
$723$		0			0
$724$	−9.57056	+	16.5767i	−0.355687	+	0.616068i
$725$	−15.0352	+	25.4895i	−0.558395	+	0.946658i
$726$		0			0
$727$	2.51719	−	23.9495i	0.0933575	−	0.888237i	−0.843171	−	0.537645i	$-0.819314\pi$
$727$	2.51719	−	23.9495i	0.0933575	−	0.888237i	0.936529	−	0.350591i	$-0.114019\pi$
$728$	−1.49066	−	4.58779i	−0.0552476	−	0.170035i
$729$		0			0
$730$	17.6360	+	12.9395i	0.652738	+	0.478911i
$731$	−2.23395	+	0.474841i	−0.0826257	+	0.0175626i
$732$		0			0
$733$	1.35468	+	1.50453i	0.0500364	+	0.0555710i	0.767643	−	0.640877i	$-0.221429\pi$
$733$	1.35468	+	1.50453i	0.0500364	+	0.0555710i	−0.717607	+	0.696448i	$0.754763\pi$
$734$	−1.96206	−	18.6678i	−0.0724211	−	0.689041i
$735$		0			0
$736$	−2.67860	+	25.4852i	−0.0987347	+	0.939397i
$737$	−4.03758	+	2.93347i	−0.148726	+	0.108056i
$738$		0			0
$739$	−32.8526	−	23.8688i	−1.20850	−	0.878028i	−0.213408	−	0.976963i	$-0.568456\pi$
$739$	−32.8526	−	23.8688i	−1.20850	−	0.878028i	−0.995094	+	0.0989355i	$0.968456\pi$
$740$	−2.28243	−	3.99623i	−0.0839038	−	0.146904i
$741$		0			0
$742$	−2.20549	−	2.44945i	−0.0809661	−	0.0899220i
$743$	−4.58729	+	7.94543i	−0.168292	+	0.291489i	−0.937819	−	0.347124i	$-0.887158\pi$
$743$	−4.58729	+	7.94543i	−0.168292	+	0.291489i	0.769528	+	0.638613i	$0.220492\pi$
$744$		0			0
$745$	−19.5511	−	8.81425i	−0.716299	−	0.322929i
$746$	3.32647	+	10.2378i	0.121791	+	0.374833i
$747$		0			0
$748$	1.00080	+	0.727124i	0.0365929	+	0.0265863i
$749$	15.9332	+	27.5972i	0.582188	+	1.00838i
$750$		0			0
$751$	−7.16746	+	12.4144i	−0.261544	+	0.453008i	−0.966652	−	0.256092i	$-0.917565\pi$
$751$	−7.16746	+	12.4144i	−0.261544	+	0.453008i	0.705108	+	0.709100i	$0.250898\pi$
$752$	8.10677	−	3.60937i	0.295623	−	0.131620i
$753$		0			0
$754$	4.17630	−	4.63825i	0.152092	−	0.168915i
$755$	−26.7573	+	19.2502i	−0.973798	+	0.700588i
$756$		0			0
$757$	−7.98963			−0.290388			−0.145194	−	0.989403i	$-0.546381\pi$
$757$	−7.98963			−0.290388			−0.145194	+	0.989403i	$0.546381\pi$
$758$	−23.0291	+	4.89499i	−0.836455	+	0.177794i
$759$		0			0
$760$	5.21701	−	8.93955i	0.189241	−	0.324272i
$761$	0.311204	−	0.138557i	0.0112812	−	0.00502269i	−0.401088	−	0.916039i	$-0.631368\pi$
$761$	0.311204	−	0.138557i	0.0112812	−	0.00502269i	0.412369	+	0.911017i	$0.364701\pi$
$762$		0			0
$763$	−11.7933	−	5.25070i	−0.426945	−	0.190088i
$764$	−7.98897	−	5.80433i	−0.289031	−	0.209993i
$765$		0			0
$766$	6.69945	−	4.86744i	0.242061	−	0.175868i
$767$	5.63078	−	1.19686i	0.203316	−	0.0432161i
$768$		0			0
$769$	−1.20218	−	1.33516i	−0.0433517	−	0.0481469i	0.721079	−	0.692853i	$-0.243646\pi$
$769$	−1.20218	−	1.33516i	−0.0433517	−	0.0481469i	−0.764431	+	0.644706i	$0.776980\pi$
$770$	−16.6004	+	7.29837i	−0.598237	+	0.263015i
$771$		0			0
$772$	10.2669	−	11.4025i	0.369513	−	0.410386i
$773$	34.6828	+	25.1985i	1.24745	+	0.906328i	0.998071	−	0.0620773i	$-0.0197725\pi$
$773$	34.6828	+	25.1985i	1.24745	+	0.906328i	0.249382	+	0.968405i	$0.419773\pi$
$774$		0			0
$775$	10.9684	+	8.12646i	0.393997	+	0.291911i
$776$	−2.92738	−	5.07038i	−0.105087	−	0.182016i
$777$		0			0
$778$	−13.0542	−	2.77475i	−0.468015	−	0.0994796i
$779$	−16.7177	−	3.55346i	−0.598975	−	0.127316i
$780$		0			0
$781$	76.8087	−	16.3262i	2.74843	−	0.584197i
$782$	−1.82852			−0.0653878
$783$		0			0
$784$	−5.48279	+	3.98348i	−0.195814	+	0.142267i
$785$	27.5993	+	12.4426i	0.985062	+	0.444096i
$786$		0			0
$787$	−1.14814	−	10.9238i	−0.0409266	−	0.389391i	−0.995741	−	0.0921896i	$-0.970613\pi$
$787$	−1.14814	−	10.9238i	−0.0409266	−	0.389391i	0.954815	−	0.297201i	$-0.0960533\pi$
$788$	0.870967	+	8.28670i	0.0310269	+	0.295201i
$789$		0			0
$790$	17.9343	−	19.7321i	0.638073	−	0.702038i
$791$	16.8345	−	12.2310i	0.598565	−	0.434883i
$792$		0			0
$793$	13.1670			0.467572
$794$	29.6933	−	6.31150i	1.05378	−	0.223987i
$795$		0			0
$796$	2.63206	+	0.559462i	0.0932909	+	0.0198296i
$797$	−33.4366	−	7.10716i	−1.18438	−	0.251749i	−0.426714	−	0.904387i	$-0.640329\pi$
$797$	−33.4366	−	7.10716i	−1.18438	−	0.251749i	−0.757670	+	0.652638i	$0.773662\pi$
$798$		0			0
$799$	−0.874486	−	1.51465i	−0.0309371	−	0.0535846i
$800$	7.12367	−	21.2477i	0.251860	−	0.751221i
$801$		0			0
$802$	−7.55966	−	5.49242i	−0.266941	−	0.193944i
$803$	29.2804	−	32.5192i	1.03328	−	1.14758i
$804$		0			0
$805$	−10.2899	+	17.6321i	−0.362671	+	0.621451i
$806$	−1.92644	−	2.13952i	−0.0678558	−	0.0753615i
$807$		0			0
$808$	−17.5895	+	3.73876i	−0.618796	+	0.131529i
$809$	6.42510	−	4.66811i	0.225894	−	0.164122i	−0.469082	−	0.883155i	$-0.655415\pi$
$809$	6.42510	−	4.66811i	0.225894	−	0.164122i	0.694976	+	0.719033i	$0.255415\pi$
$810$		0			0
$811$	−6.94724	−	5.04746i	−0.243951	−	0.177240i	0.459091	−	0.888389i	$-0.348175\pi$
$811$	−6.94724	−	5.04746i	−0.243951	−	0.177240i	−0.703041	+	0.711149i	$0.748175\pi$
$812$	−7.46591	−	3.32404i	−0.262002	−	0.116651i
$813$		0			0
$814$	11.0429	−	4.91660i	0.387052	−	0.172327i
$815$	−4.11628	−	4.61471i	−0.144187	−	0.161646i
$816$		0			0
$817$	11.2868	−	2.39909i	0.394876	−	0.0839336i
$818$	−12.3550			−0.431982
$819$		0			0
$820$	−21.7908	−	0.101663i	−0.760968	−	0.00355022i
$821$	−1.13356	+	1.25895i	−0.0395616	+	0.0439376i	−0.762601	−	0.646869i	$-0.776078\pi$
$821$	−1.13356	+	1.25895i	−0.0395616	+	0.0439376i	0.723039	+	0.690807i	$0.242745\pi$
$822$		0			0
$823$	−3.98222	+	1.77300i	−0.138811	+	0.0618028i	−0.474967	−	0.880004i	$-0.657540\pi$
$823$	−3.98222	+	1.77300i	−0.138811	+	0.0618028i	0.336155	+	0.941807i	$0.390873\pi$
$824$	19.5925	−	33.9352i	0.682538	−	1.18219i
$825$		0			0
$826$	4.94833	+	8.57075i	0.172174	+	0.298215i
$827$	−21.8549	−	15.8785i	−0.759968	−	0.552149i	0.138933	−	0.990302i	$-0.455633\pi$
$827$	−21.8549	−	15.8785i	−0.759968	−	0.552149i	−0.898901	+	0.438153i	$0.855633\pi$
$828$		0			0
$829$	16.9452	+	52.1521i	0.588533	+	1.81132i	0.584595	+	0.811326i	$0.301254\pi$
$829$	16.9452	+	52.1521i	0.588533	+	1.81132i	0.00393824	+	0.999992i	$0.498746\pi$
$830$	13.8839	−	2.88349i	0.481919	−	0.100087i
$831$		0			0
$832$	−3.87040	+	6.70373i	−0.134182	+	0.232410i
$833$	0.893758	+	0.992619i	0.0309669	+	0.0343922i
$834$		0			0
$835$	−4.46385	+	4.91134i	−0.154478	+	0.169964i
$836$	−5.05645	−	3.67373i	−0.174881	−	0.127059i
$837$		0			0
$838$	−24.6786	+	17.9301i	−0.852508	+	0.619384i
$839$	−2.22063	+	21.1279i	−0.0766648	+	0.729417i	0.886904	+	0.461955i	$0.152852\pi$
$839$	−2.22063	+	21.1279i	−0.0766648	+	0.729417i	−0.963568	+	0.267462i	$0.913815\pi$
$840$		0			0
$841$	−0.630412	−	5.99797i	−0.0217383	−	0.206827i
$842$	−9.92515	−	11.0230i	−0.342043	−	0.379878i
$843$		0			0
$844$	7.25702	−	1.54253i	0.249797	−	0.0530960i
$845$	−8.18662	−	25.6016i	−0.281628	−	0.880723i
$846$		0			0
$847$	5.78232	+	17.7961i	0.198683	+	0.611483i
$848$	−0.308379	+	2.93403i	−0.0105898	+	0.100755i
$849$		0			0
$850$	1.56096	+	0.347047i	0.0535406	+	0.0119036i
$851$	6.80424	−	11.7853i	0.233246	−	0.403995i
$852$		0			0
$853$	9.71608	−	10.7908i	0.332672	−	0.369470i	−0.553481	−	0.832862i	$-0.686701\pi$
$853$	9.71608	−	10.7908i	0.332672	−	0.369470i	0.886154	+	0.463392i	$0.153368\pi$
$854$	6.99506	+	21.5286i	0.239366	+	0.736693i
$855$		0			0
$856$	18.8229	−	57.9309i	0.643353	−	1.98004i
$857$	−27.2809	−	47.2519i	−0.931897	−	1.61409i	−0.780075	−	0.625686i	$-0.784819\pi$
$857$	−27.2809	−	47.2519i	−0.931897	−	1.61409i	−0.151822	−	0.988408i	$-0.548514\pi$
$858$		0			0
$859$	−2.38237	−	22.6667i	−0.0812854	−	0.773379i	−0.956910	−	0.290386i	$-0.906216\pi$
$859$	−2.38237	−	22.6667i	−0.0812854	−	0.773379i	0.875624	−	0.482993i	$-0.160450\pi$
$860$	13.4679	−	5.92116i	0.459251	−	0.201910i
$861$		0			0
$862$	10.4872	+	4.66919i	0.357194	+	0.159033i
$863$	35.8456	−	26.0434i	1.22020	−	0.886526i	0.224082	−	0.974570i	$-0.428062\pi$
$863$	35.8456	−	26.0434i	1.22020	−	0.886526i	0.996117	+	0.0880440i	$0.0280616\pi$
$864$		0			0
$865$	28.0071	+	0.130664i	0.952270	+	0.00444272i
$866$	−10.1662	−	4.52628i	−0.345461	−	0.153809i
$867$		0			0
$868$	−1.88489	+	3.26472i	−0.0639773	+	0.110812i
$869$	−35.6934	−	39.6415i	−1.21082	−	1.34475i
$870$		0			0
$871$	−0.693405	+	0.770104i	−0.0234951	+	0.0260940i
$872$	7.62529	+	23.4682i	0.258225	+	0.794734i
$873$		0			0
$874$	9.23843			0.312495
$875$	12.1307	−	13.0991i	0.410094	−	0.442831i
$876$		0			0
$877$	−17.4459	+	7.76743i	−0.589107	+	0.262287i	−0.679568	−	0.733613i	$-0.737833\pi$
$877$	−17.4459	+	7.76743i	−0.589107	+	0.262287i	0.0904608	+	0.995900i	$0.471166\pi$
$878$	−27.4287	−	5.83015i	−0.925674	−	0.196758i
$879$		0			0
$880$	14.7969	+	6.67089i	0.498803	+	0.224876i
$881$	8.53041	−	26.2539i	0.287397	−	0.884517i	−0.698273	−	0.715832i	$-0.746048\pi$
$881$	8.53041	−	26.2539i	0.287397	−	0.884517i	0.985670	−	0.168685i	$-0.0539522\pi$
$882$		0			0
$883$	−15.3512	+	47.2463i	−0.516610	+	1.58996i	0.263722	+	0.964599i	$0.415050\pi$
$883$	−15.3512	+	47.2463i	−0.516610	+	1.58996i	−0.780333	+	0.625365i	$0.784950\pi$
$884$	0.234656	+	0.104476i	0.00789234	+	0.00351390i
$885$		0			0
$886$	−2.12514	+	0.946173i	−0.0713955	+	0.0317873i
$887$	−0.735487	−	6.99769i	−0.0246952	−	0.234960i	−0.999906	−	0.0136832i	$-0.995644\pi$
$887$	−0.735487	−	6.99769i	−0.0246952	−	0.234960i	0.975211	−	0.221276i	$-0.0710223\pi$
$888$		0			0
$889$	−1.78332	+	16.9671i	−0.0598106	+	0.569059i
$890$	−2.42103	−	1.77629i	−0.0811530	−	0.0595415i
$891$		0			0
$892$	3.18321	−	9.79692i	0.106582	−	0.328025i
$893$	4.41826	+	7.65265i	0.147851	+	0.256086i
$894$		0			0
$895$	23.8481	−	10.4848i	0.797153	−	0.350468i
$896$	0.984337	+	0.209227i	0.0328844	+	0.00698979i
$897$		0			0
$898$	−3.62377	+	34.4778i	−0.120927	+	1.15054i
$899$	−16.1590			−0.538934
$900$		0			0
$901$	0.581454			0.0193711
$902$	5.98285	−	56.9230i	0.199207	−	1.89533i
$903$		0			0
$904$	−38.9060	−	8.26972i	−1.29399	−	0.275047i
$905$	48.3682	+	10.5171i	1.60781	+	0.349599i
$906$		0			0
$907$	−24.0868	−	41.7196i	−0.799789	−	1.38528i	−0.919753	−	0.392497i	$-0.871611\pi$
$907$	−24.0868	−	41.7196i	−0.799789	−	1.38528i	0.119964	−	0.992778i	$-0.461722\pi$
$908$	−5.91884	+	18.2163i	−0.196424	+	0.604529i
$909$		0			0
$910$	−3.05652	+	2.19898i	−0.101323	+	0.0728953i
$911$	−5.52265	+	52.5445i	−0.182974	+	1.74088i	0.389563	+	0.921000i	$0.372626\pi$
$911$	−5.52265	+	52.5445i	−0.182974	+	1.74088i	−0.572537	+	0.819879i	$0.694041\pi$
$912$		0			0
$913$	−2.96525	−	28.2124i	−0.0981354	−	0.933696i
$914$	20.4075	−	9.08600i	0.675020	−	0.300538i
$915$		0			0
$916$	12.0120	+	5.34811i	0.396889	+	0.176706i
$917$	−8.75044	+	26.9311i	−0.288965	+	0.889342i
$918$		0			0
$919$	−5.29882	+	16.3081i	−0.174792	+	0.537954i	−0.999624	−	0.0274237i	$-0.991270\pi$
$919$	−5.29882	+	16.3081i	−0.174792	+	0.537954i	0.824832	+	0.565378i	$0.191270\pi$
$920$	38.2076	−	7.93516i	1.25967	−	0.261614i
$921$		0			0
$922$	15.2514	+	3.24178i	0.502277	+	0.106762i
$923$	14.8953	−	6.63180i	0.490284	−	0.218289i
$924$		0			0
$925$	−8.04542	+	8.76940i	−0.264532	+	0.288336i
$926$	−28.2265			−0.927582
$927$		0			0
$928$	8.19752	+	25.2294i	0.269097	+	0.828195i
$929$	26.6322	−	29.5781i	0.873775	−	0.970426i	−0.125991	−	0.992031i	$-0.540211\pi$
$929$	26.6322	−	29.5781i	0.873775	−	0.970426i	0.999767	+	0.0216056i	$0.00687783\pi$
$930$		0			0
$931$	−4.51563	−	5.01512i	−0.147994	−	0.164364i
$932$	6.39599	−	11.0782i	0.209508	−	0.362878i
$933$		0			0
$934$	21.2011	+	9.43936i	0.693723	+	0.308865i
$935$	1.00273	−	3.03778i	0.0327927	−	0.0993460i
$936$		0			0
$937$	−18.7168	+	13.5986i	−0.611453	+	0.444246i	−0.849926	−	0.526903i	$-0.823353\pi$
$937$	−18.7168	+	13.5986i	−0.611453	+	0.444246i	0.238473	+	0.971149i	$0.423353\pi$
$938$	−1.62753	−	0.724625i	−0.0531409	−	0.0236598i
$939$		0			0
$940$	7.49957	+	8.40767i	0.244609	+	0.274228i
$941$	−3.52098	−	33.4999i	−0.114781	−	1.09207i	−0.888607	−	0.458669i	$-0.848326\pi$
$941$	−3.52098	−	33.4999i	−0.114781	−	1.09207i	0.773826	−	0.633398i	$-0.218340\pi$
$942$		0			0
$943$	−32.2182	−	55.8036i	−1.04917	−	1.81722i
$944$	2.73733	−	8.42463i	0.0890924	−	0.274198i
$945$		0			0
$946$	11.9413	+	36.7515i	0.388245	+	1.19489i
$947$	27.4653	−	30.5034i	0.892504	−	0.991226i	−0.107492	−	0.994206i	$-0.534282\pi$
$947$	27.4653	−	30.5034i	0.892504	−	0.991226i	0.999996	+	0.00298011i	$0.000948599\pi$
$948$		0			0
$949$	4.54306	−	7.86880i	0.147474	−	0.255432i
$950$	−7.88663	−	1.75342i	−0.255876	−	0.0568885i
$951$		0			0
$952$	−0.152924	+	1.45498i	−0.00495631	+	0.0471561i
$953$	18.3625	+	56.5138i	0.594818	+	1.83066i	0.555629	+	0.831430i	$0.312478\pi$
$953$	18.3625	+	56.5138i	0.594818	+	1.83066i	0.0391893	+	0.999232i	$0.487522\pi$
$954$		0			0
$955$	−8.00435	+	24.2493i	−0.259015	+	0.784689i
$956$	4.29446	−	0.912816i	0.138893	−	0.0295226i
$957$		0			0
$958$	−4.51226	−	5.01137i	−0.145784	−	0.161910i
$959$	−2.87374	−	27.3418i	−0.0927980	−	0.882914i
$960$		0			0
$961$	2.46125	−	23.4172i	0.0793950	−	0.755393i
$962$	2.03059	−	1.47531i	0.0654687	−	0.0475658i
$963$		0			0
$964$	9.37349	+	6.81024i	0.301900	+	0.219343i
$965$	−36.1721	−	16.3075i	−1.16442	−	0.524957i
$966$		0			0
$967$	−4.12389	−	4.58005i	−0.132615	−	0.147284i	0.673179	−	0.739479i	$-0.264928\pi$
$967$	−4.12389	−	4.58005i	−0.132615	−	0.147284i	−0.805795	+	0.592195i	$0.798262\pi$
$968$	17.8838	−	30.9756i	0.574807	−	0.995595i
$969$		0			0
$970$	−3.07374	+	3.38187i	−0.0986918	+	0.108585i
$971$	13.0593	+	40.1925i	0.419094	+	1.28984i	0.908537	+	0.417804i	$0.137200\pi$
$971$	13.0593	+	40.1925i	0.419094	+	1.28984i	−0.489443	+	0.872036i	$0.662800\pi$
$972$		0			0
$973$	11.1201	+	8.07923i	0.356494	+	0.259008i
$974$	−12.3308	−	21.3576i	−0.395105	−	0.684341i
$975$		0			0
$976$	10.1306	−	17.5467i	0.324273	−	0.561657i
$977$	−10.7125	+	4.76952i	−0.342724	+	0.152591i	−0.570879	−	0.821034i	$-0.693397\pi$
$977$	−10.7125	+	4.76952i	−0.342724	+	0.152591i	0.228155	+	0.973625i	$0.426731\pi$
$978$		0			0
$979$	−4.01953	+	4.46414i	−0.128465	+	0.142675i
$980$	−6.93731	−	5.08987i	−0.221604	−	0.162590i
$981$		0			0
$982$	−10.7959			−0.344510
$983$	5.76471	−	1.22533i	0.183866	−	0.0390819i	−0.115058	−	0.993359i	$-0.536706\pi$
$983$	5.76471	−	1.22533i	0.183866	−	0.0390819i	0.298924	+	0.954277i	$0.403372\pi$
$984$		0			0
$985$	19.7250	−	8.67210i	0.628491	−	0.276316i
$986$	−1.72924	+	0.769909i	−0.0550703	+	0.0245189i
$987$		0			0
$988$	−1.18558	−	0.527854i	−0.0377183	−	0.0167933i
$989$	35.1953	+	25.5709i	1.11914	+	0.813106i
$990$		0			0
$991$	−6.01131	+	4.36747i	−0.190956	+	0.138737i	−0.679155	−	0.733995i	$-0.737654\pi$
$991$	−6.01131	+	4.36747i	−0.190956	+	0.138737i	0.488200	+	0.872732i	$0.337654\pi$
$992$	11.9693	−	2.54415i	0.380025	−	0.0807767i
$993$		0			0
$994$	18.7566	+	20.8313i	0.594922	+	0.660728i
$995$	−0.695066	−	6.92369i	−0.0220351	−	0.219496i
$996$		0			0
$997$	−1.21923	+	1.35409i	−0.0386133	+	0.0428844i	−0.762142	−	0.647410i	$-0.775852\pi$
$997$	−1.21923	+	1.35409i	−0.0386133	+	0.0428844i	0.723529	+	0.690294i	$0.242519\pi$
$998$	3.51103	+	2.55091i	0.111140	+	0.0807476i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.r.a.91.11		224
3.2	odd	2		225.2.q.a.166.18	yes	224
9.2	odd	6		225.2.q.a.16.11	✓	224
9.7	even	3	inner	675.2.r.a.316.18		224
25.11	even	5	inner	675.2.r.a.361.18		224
75.11	odd	10		225.2.q.a.211.11	yes	224
225.11	odd	30		225.2.q.a.61.18	yes	224
225.61	even	15	inner	675.2.r.a.586.11		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.16.11	✓	224	9.2	odd	6
225.2.q.a.61.18	yes	224	225.11	odd	30
225.2.q.a.166.18	yes	224	3.2	odd	2
225.2.q.a.211.11	yes	224	75.11	odd	10
675.2.r.a.91.11		224	1.1	even	1	trivial
675.2.r.a.316.18		224	9.7	even	3	inner
675.2.r.a.361.18		224	25.11	even	5	inner
675.2.r.a.586.11		224	225.61	even	15	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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.r (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.111376 + 1.05967i) q^{2} +(0.845797 + 0.179780i) q^{4} +(-0.223355 - 2.22488i) q^{5} +(-0.798426 - 1.38291i) q^{7} +(-0.943229 + 2.90296i) q^{8} +(2.38252 + 0.0111154i) q^{10} +(0.498219 - 4.74023i) q^{11} +(-0.103450 - 0.984265i) q^{13} +(1.55436 - 0.692046i) q^{14} +(-1.39126 - 0.619428i) q^{16} +(-0.0927524 + 0.285463i) q^{17} +(0.468623 - 1.44227i) q^{19} +(0.211076 - 1.92195i) q^{20} +(4.96760 + 1.05590i) q^{22} +(5.22312 - 2.32548i) q^{23} +(-4.90022 + 0.993880i) q^{25} +1.05452 q^{26} +(-0.426686 - 1.31321i) q^{28} +(3.96038 - 4.39845i) q^{29} +(-1.82684 - 2.02891i) q^{31} +(-2.24101 + 3.88154i) q^{32} +(-0.292166 - 0.130081i) q^{34} +(-2.89849 + 2.08529i) q^{35} +(1.92560 - 1.39903i) q^{37} +(1.47614 + 0.657221i) q^{38} +(6.66943 + 1.45018i) q^{40} +(-1.17806 - 11.2085i) q^{41} +(3.80449 + 6.58957i) q^{43} +(1.27359 - 3.91970i) q^{44} +(1.88252 + 5.79380i) q^{46} +(-3.89898 + 4.33025i) q^{47} +(2.22503 - 3.85387i) q^{49} +(-0.507419 - 5.30332i) q^{50} +(0.0894527 - 0.851086i) q^{52} +(-0.598625 - 1.84238i) q^{53} +(-10.6578 - 0.0497227i) q^{55} +(4.76765 - 1.01339i) q^{56} +(4.21982 + 4.68659i) q^{58} +(0.607997 + 5.78470i) q^{59} +(-1.39066 + 13.2313i) q^{61} +(2.35344 - 1.70988i) q^{62} +(-6.32771 - 4.59735i) q^{64} +(-2.16677 + 0.450006i) q^{65} +(-0.700631 - 0.778129i) q^{67} +(-0.129770 + 0.224768i) q^{68} +(-1.88690 - 3.30370i) q^{70} +(5.09100 + 15.6685i) q^{71} +(7.42742 + 5.39634i) q^{73} +(1.26805 + 2.19633i) q^{74} +(0.655651 - 1.13562i) q^{76} +(-6.95313 + 3.09573i) q^{77} +(7.48863 - 8.31697i) q^{79} +(-1.06741 + 3.23374i) q^{80} +12.0085 q^{82} +(5.82164 - 1.23743i) q^{83} +(0.655838 + 0.142604i) q^{85} +(-7.40651 + 3.29759i) q^{86} +(13.2908 + 5.91743i) q^{88} +(-1.01962 - 0.740795i) q^{89} +(-1.27856 + 0.928926i) q^{91} +(4.83578 - 1.02788i) q^{92} +(-4.15439 - 4.61392i) q^{94} +(-3.31356 - 0.720493i) q^{95} +(-1.28347 + 1.42544i) q^{97} +(3.83602 + 2.78703i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28}+ \cdots - 146 q^{98}+O(q^{100}) \) 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8 - 20 * q^10 + 11 * q^11 - 3 * q^13 - q^14 + 23 * q^16 + 24 * q^17 - 12 * q^19 - q^20 - 11 * q^22 - q^23 - 16 * q^25 + 136 * q^26 + 4 * q^28 + 15 * q^29 + 3 * q^31 - 12 * q^32 + q^34 - 14 * q^35 - 24 * q^37 - 55 * q^38 + q^40 + 19 * q^41 - 8 * q^43 - 4 * q^44 - 20 * q^46 + 10 * q^47 - 72 * q^49 + 3 * q^50 - 25 * q^52 + 12 * q^53 - 20 * q^55 + 60 * q^56 - 23 * q^58 + 30 * q^59 - 3 * q^61 + 44 * q^62 - 44 * q^64 - 51 * q^65 - 12 * q^67 + 156 * q^68 - 16 * q^70 - 42 * q^71 - 12 * q^73 - 90 * q^74 - 8 * q^76 - 31 * q^77 - 15 * q^79 - 298 * q^80 + 8 * q^82 - 59 * q^83 - 11 * q^85 - 9 * q^86 - 23 * q^88 - 106 * q^89 + 30 * q^91 - 11 * q^92 + 25 * q^94 - 7 * q^95 - 21 * q^97 - 146 * q^98

Introduction

L-functions

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