LMFDB - Embedded newform 891.2.n.e.757.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [891,2,Mod(136,891)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(891, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 6]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("891.136");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.n (of order $15$, degree $8$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{14} - 15x^{12} + 116x^{10} + 69x^{8} - 814x^{6} + 2420x^{4} - 7986x^{2} + 14641 $ x^16 - x^14 - 15x^12 + 116x^10 + 69x^8 - 814x^6 + 2420x^4 - 7986x^2 + 14641
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			757.2
Root			$1.50964 - 0.320883i$ of defining polynomial
Character	$\chi$	$=$	891.757
Dual form			891.2.n.e.379.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.50964 - 0.320883i) q^{2} +(0.348943 - 0.155360i) q^{4} +(-1.50964 - 0.320883i) q^{5} +(-0.0246758 + 0.234775i) q^{7} +(-2.02029 + 1.46782i) q^{8} -2.38197 q^{10} +(-3.21432 - 0.817391i) q^{11} +(-2.83448 - 3.14801i) q^{13} +(0.0380837 + 0.362342i) q^{14} +(-3.09007 + 3.43187i) q^{16} +(-1.83812 - 5.65714i) q^{17} +(3.73607 - 2.71441i) q^{19} +(-0.576630 + 0.122566i) q^{20} +(-5.11474 - 0.202541i) q^{22} +(-3.74582 + 6.48795i) q^{23} +(-2.39169 - 1.06485i) q^{25} +(-5.28918 - 3.84281i) q^{26} +(0.0278640 + 0.0857567i) q^{28} +(-0.199409 + 1.89725i) q^{29} +(-1.59385 - 1.77015i) q^{31} +(-1.06644 + 1.84712i) q^{32} +(-4.59017 - 7.95041i) q^{34} +(0.112587 - 0.346506i) q^{35} +(-5.04508 - 3.66547i) q^{37} +(4.76909 - 5.29661i) q^{38} +(3.52090 - 1.56760i) q^{40} +(-0.583680 - 5.55335i) q^{41} +(5.35410 + 9.27358i) q^{43} +(-1.24861 + 0.214153i) q^{44} +(-3.57295 + 10.9964i) q^{46} +(0.871385 + 0.387966i) q^{47} +(6.79252 + 1.44380i) q^{49} +(-3.95228 - 0.840083i) q^{50} +(-1.47815 - 0.658114i) q^{52} +(-2.79197 + 8.59279i) q^{53} +(4.59017 + 2.26538i) q^{55} +(-0.294756 - 0.510532i) q^{56} +(0.307760 + 2.92814i) q^{58} +(-7.71534 + 3.43509i) q^{59} +(2.89482 - 3.21502i) q^{61} +(-2.97414 - 2.16084i) q^{62} +(1.83688 - 5.65334i) q^{64} +(3.26889 + 5.66189i) q^{65} +(-1.92705 + 3.33775i) q^{67} +(-1.52029 - 1.68845i) q^{68} +(0.0587770 - 0.559226i) q^{70} +(-2.38463 - 7.33912i) q^{71} +(5.23607 + 3.80423i) q^{73} +(-8.79243 - 3.91464i) q^{74} +(0.881966 - 1.52761i) q^{76} +(0.271219 - 0.734472i) q^{77} +(0.516329 - 0.109749i) q^{79} +(5.76611 - 4.18932i) q^{80} +(-2.66312 - 8.19624i) q^{82} +(2.94746 - 3.27349i) q^{83} +(0.959607 + 9.13005i) q^{85} +(11.0585 + 12.2817i) q^{86} +(7.69364 - 3.06670i) q^{88} -16.7518 q^{89} +(0.809017 - 0.587785i) q^{91} +(-0.299113 + 2.84587i) q^{92} +(1.43997 + 0.306074i) q^{94} +(-6.51111 + 2.89893i) q^{95} +(12.5187 - 2.66093i) q^{97} +10.7175 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{4} + 6 q^{7} - 56 q^{10} + 6 q^{13} - 2 q^{16} + 24 q^{19} - 28 q^{22} - 8 q^{25} + 72 q^{28} - 12 q^{31} + 16 q^{34} - 36 q^{37} + 16 q^{40} + 32 q^{43} - 84 q^{46} + 44 q^{49} - 6 q^{52} - 16 q^{55}+ \cdots + 54 q^{97}+O(q^{100}) $ 16 * q - 2 * q^4 + 6 * q^7 - 56 * q^10 + 6 * q^13 - 2 * q^16 + 24 * q^19 - 28 * q^22 - 8 * q^25 + 72 * q^28 - 12 * q^31 + 16 * q^34 - 36 * q^37 + 16 * q^40 + 32 * q^43 - 84 * q^46 + 44 * q^49 - 6 * q^52 - 16 * q^55 - 28 * q^58 - 42 * q^61 + 92 * q^64 - 4 * q^67 - 26 * q^70 + 48 * q^73 + 32 * q^76 - 30 * q^79 + 20 * q^82 - 46 * q^85 + 14 * q^88 + 4 * q^91 + 26 * q^94 + 54 * q^97

Character values

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

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.50964	−	0.320883i	1.06747	−	0.226899i	0.359506	−	0.933143i	$-0.382945\pi$
$2$	1.50964	−	0.320883i	1.06747	−	0.226899i	0.707968	+	0.706244i	$0.249612\pi$
$3$		0			0
$3$		0			0
$4$	0.348943	−	0.155360i	0.174472	−	0.0776798i
$5$	−1.50964	−	0.320883i	−0.675130	−	0.143503i	−0.142426	−	0.989805i	$-0.545490\pi$
$5$	−1.50964	−	0.320883i	−0.675130	−	0.143503i	−0.532703	+	0.846302i	$0.678824\pi$
$6$		0			0
$7$	−0.0246758	+	0.234775i	−0.00932658	+	0.0887365i	−0.998195	−	0.0600561i	$-0.980872\pi$
$7$	−0.0246758	+	0.234775i	−0.00932658	+	0.0887365i	0.988868	+	0.148793i	$0.0475387\pi$
$8$	−2.02029	+	1.46782i	−0.714279	+	0.518954i
$9$		0			0
$10$	−2.38197			−0.753244
$11$	−3.21432	−	0.817391i	−0.969155	−	0.246453i
$11$	−3.21432	−	0.817391i	−0.969155	−	0.246453i
$12$		0			0
$13$	−2.83448	−	3.14801i	−0.786144	−	0.873101i	0.208333	−	0.978058i	$-0.433196\pi$
$13$	−2.83448	−	3.14801i	−0.786144	−	0.873101i	−0.994477	+	0.104957i	$0.966530\pi$
$14$	0.0380837	+	0.362342i	0.0101783	+	0.0968401i
$15$		0			0
$16$	−3.09007	+	3.43187i	−0.772517	+	0.857967i
$17$	−1.83812	−	5.65714i	−0.445809	−	1.37206i	−0.881594	−	0.472008i	$-0.843529\pi$
$17$	−1.83812	−	5.65714i	−0.445809	−	1.37206i	0.435785	−	0.900051i	$-0.356471\pi$
$18$		0			0
$19$	3.73607	−	2.71441i	0.857113	−	0.622729i	−0.0699852	−	0.997548i	$-0.522295\pi$
$19$	3.73607	−	2.71441i	0.857113	−	0.622729i	0.927098	+	0.374819i	$0.122295\pi$
$20$	−0.576630	+	0.122566i	−0.128938	+	0.0274067i
$21$		0			0
$22$	−5.11474	−	0.202541i	−1.09047	−	0.0431819i
$23$	−3.74582	+	6.48795i	−0.781057	+	1.35283i	0.150269	+	0.988645i	$0.451986\pi$
$23$	−3.74582	+	6.48795i	−0.781057	+	1.35283i	−0.931326	+	0.364185i	$0.881347\pi$
$24$		0			0
$25$	−2.39169	−	1.06485i	−0.478339	−	0.212970i
$26$	−5.28918	−	3.84281i	−1.03729	−	0.753638i
$27$		0			0
$28$	0.0278640	+	0.0857567i	0.00526581	+	0.0162065i
$29$	−0.199409	+	1.89725i	−0.0370293	+	0.352310i	0.960282	+	0.279031i	$0.0900132\pi$
$29$	−0.199409	+	1.89725i	−0.0370293	+	0.352310i	−0.997311	+	0.0732795i	$0.976653\pi$
$30$		0			0
$31$	−1.59385	−	1.77015i	−0.286263	−	0.317928i	0.582812	−	0.812607i	$-0.301952\pi$
$31$	−1.59385	−	1.77015i	−0.286263	−	0.317928i	−0.869076	+	0.494679i	$0.835286\pi$
$32$	−1.06644	+	1.84712i	−0.188521	+	0.326528i
$33$		0			0
$34$	−4.59017	−	7.95041i	−0.787208	−	1.36348i
$35$	0.112587	−	0.346506i	0.0190306	−	0.0585703i
$36$		0			0
$37$	−5.04508	−	3.66547i	−0.829407	−	0.602599i	0.0899846	−	0.995943i	$-0.471318\pi$
$37$	−5.04508	−	3.66547i	−0.829407	−	0.602599i	−0.919391	+	0.393344i	$0.871318\pi$
$38$	4.76909	−	5.29661i	0.773649	−	0.859224i
$39$		0			0
$40$	3.52090	−	1.56760i	0.556703	−	0.247860i
$41$	−0.583680	−	5.55335i	−0.0911555	−	0.867287i	−0.940579	−	0.339575i	$-0.889717\pi$
$41$	−0.583680	−	5.55335i	−0.0911555	−	0.867287i	0.849423	−	0.527712i	$-0.176950\pi$
$42$		0			0
$43$	5.35410	+	9.27358i	0.816493	+	1.41421i	0.908251	+	0.418426i	$0.137418\pi$
$43$	5.35410	+	9.27358i	0.816493	+	1.41421i	−0.0917581	+	0.995781i	$0.529249\pi$
$44$	−1.24861	+	0.214153i	−0.188234	+	0.0322847i
$45$		0			0
$46$	−3.57295	+	10.9964i	−0.526803	+	1.62133i
$47$	0.871385	+	0.387966i	0.127105	+	0.0565906i	0.469304	−	0.883037i	$-0.344505\pi$
$47$	0.871385	+	0.387966i	0.127105	+	0.0565906i	−0.342199	+	0.939628i	$0.611172\pi$
$48$		0			0
$49$	6.79252	+	1.44380i	0.970360	+	0.206256i
$50$	−3.95228	−	0.840083i	−0.558936	−	0.118806i
$51$		0			0
$52$	−1.47815	−	0.658114i	−0.204982	−	0.0912640i
$53$	−2.79197	+	8.59279i	−0.383506	+	1.18031i	0.554052	+	0.832482i	$0.313081\pi$
$53$	−2.79197	+	8.59279i	−0.383506	+	1.18031i	−0.937558	+	0.347829i	$0.886919\pi$
$54$		0			0
$55$	4.59017	+	2.26538i	0.618938	+	0.305464i
$56$	−0.294756	−	0.510532i	−0.0393884	−	0.0682227i
$57$		0			0
$58$	0.307760	+	2.92814i	0.0404109	+	0.384484i
$59$	−7.71534	+	3.43509i	−1.00445	+	0.447210i	−0.841983	−	0.539503i	$-0.818612\pi$
$59$	−7.71534	+	3.43509i	−1.00445	+	0.447210i	−0.162468	+	0.986714i	$0.551945\pi$
$60$		0			0
$61$	2.89482	−	3.21502i	0.370643	−	0.411641i	−0.528753	−	0.848776i	$-0.677340\pi$
$61$	2.89482	−	3.21502i	0.370643	−	0.411641i	0.899396	+	0.437135i	$0.144007\pi$
$62$	−2.97414	−	2.16084i	−0.377716	−	0.274427i
$63$		0			0
$64$	1.83688	−	5.65334i	0.229610	−	0.706667i
$65$	3.26889	+	5.66189i	0.405456	+	0.702271i
$66$		0			0
$67$	−1.92705	+	3.33775i	−0.235427	+	0.407771i	−0.959397	−	0.282061i	$-0.908982\pi$
$67$	−1.92705	+	3.33775i	−0.235427	+	0.407771i	0.723970	+	0.689832i	$0.242315\pi$
$68$	−1.52029	−	1.68845i	−0.184362	−	0.204755i
$69$		0			0
$70$	0.0587770	−	0.559226i	0.00702519	−	0.0668402i
$71$	−2.38463	−	7.33912i	−0.283003	−	0.870994i	−0.986990	−	0.160781i	$-0.948599\pi$
$71$	−2.38463	−	7.33912i	−0.283003	−	0.870994i	0.703987	−	0.710213i	$-0.251401\pi$
$72$		0			0
$73$	5.23607	+	3.80423i	0.612835	+	0.445251i	0.850412	−	0.526118i	$-0.176353\pi$
$73$	5.23607	+	3.80423i	0.612835	+	0.445251i	−0.237576	+	0.971369i	$0.576353\pi$
$74$	−8.79243	−	3.91464i	−1.02210	−	0.455068i
$75$		0			0
$76$	0.881966	−	1.52761i	0.101168	−	0.175229i
$77$	0.271219	−	0.734472i	0.0309083	−	0.0837009i
$78$		0			0
$79$	0.516329	−	0.109749i	0.0580915	−	0.0123477i	−0.178774	−	0.983890i	$-0.557213\pi$
$79$	0.516329	−	0.109749i	0.0580915	−	0.0123477i	0.236866	+	0.971542i	$0.423880\pi$
$80$	5.76611	−	4.18932i	0.644670	−	0.468380i
$81$		0			0
$82$	−2.66312	−	8.19624i	−0.294092	−	0.905123i
$83$	2.94746	−	3.27349i	0.323526	−	0.359312i	−0.559339	−	0.828939i	$-0.688945\pi$
$83$	2.94746	−	3.27349i	0.323526	−	0.359312i	0.882865	+	0.469627i	$0.155612\pi$
$84$		0			0
$85$	0.959607	+	9.13005i	0.104084	+	0.990293i
$86$	11.0585	+	12.2817i	1.19247	+	1.32437i
$87$		0			0
$88$	7.69364	−	3.06670i	0.820145	−	0.326911i
$89$	−16.7518			−1.77569			−0.887844	−	0.460145i	$-0.847798\pi$
$89$	−16.7518			−1.77569			−0.887844	+	0.460145i	$0.847798\pi$
$90$		0			0
$91$	0.809017	−	0.587785i	0.0848080	−	0.0616166i
$92$	−0.299113	+	2.84587i	−0.0311847	+	0.296703i
$93$		0			0
$94$	1.43997	+	0.306074i	0.148521	+	0.0315692i
$95$	−6.51111	+	2.89893i	−0.668026	+	0.297424i
$96$		0			0
$97$	12.5187	−	2.66093i	1.27108	−	0.270177i	0.477495	−	0.878634i	$-0.341545\pi$
$97$	12.5187	−	2.66093i	1.27108	−	0.270177i	0.793586	+	0.608458i	$0.208212\pi$
$98$	10.7175			1.08263
$99$		0			0
$100$	−1.00000			−0.100000
$101$	−10.3472	+	2.19936i	−1.02958	+	0.218845i	−0.691580	−	0.722300i	$-0.743085\pi$
$101$	−10.3472	+	2.19936i	−1.02958	+	0.218845i	−0.338004	+	0.941145i	$0.609752\pi$
$102$		0			0
$103$	6.34391	−	2.82449i	0.625084	−	0.278305i	−0.0696508	−	0.997571i	$-0.522188\pi$
$103$	6.34391	−	2.82449i	0.625084	−	0.278305i	0.694735	+	0.719266i	$0.255522\pi$
$104$	10.3472	+	2.19936i	1.01463	+	0.215665i
$105$		0			0
$106$	−1.45757	+	13.8679i	−0.141572	+	1.34697i
$107$	7.60422	−	5.52479i	0.735128	−	0.534102i	−0.156054	−	0.987749i	$-0.549877\pi$
$107$	7.60422	−	5.52479i	0.735128	−	0.534102i	0.891182	+	0.453647i	$0.149877\pi$
$108$		0			0
$109$	−0.291796			−0.0279490			−0.0139745	−	0.999902i	$-0.504448\pi$
$109$	−0.291796			−0.0279490			−0.0139745	+	0.999902i	$0.504448\pi$
$110$	7.65641	+	1.94700i	0.730010	+	0.185639i
$111$		0			0
$112$	−0.729466	−	0.810154i	−0.0689281	−	0.0765524i
$113$	−1.18191	−	11.2451i	−0.111184	−	1.05785i	−0.897799	−	0.440405i	$-0.854835\pi$
$113$	−1.18191	−	11.2451i	−0.111184	−	1.05785i	0.786615	−	0.617444i	$-0.211832\pi$
$114$		0			0
$115$	7.73669	−	8.59247i	0.721450	−	0.801252i
$116$	0.225173	+	0.693013i	0.0209068	+	0.0643446i
$117$		0			0
$118$	−10.5451	+	7.66145i	−0.970754	+	0.705294i
$119$	1.37351	−	0.291949i	0.125910	−	0.0267629i
$120$		0			0
$121$	9.66374	+	5.25472i	0.878522	+	0.477702i
$122$	3.33848	−	5.78241i	0.302251	−	0.523515i
$123$		0			0
$124$	−0.831171	−	0.370061i	−0.0746414	−	0.0332325i
$125$	9.51192	+	6.91082i	0.850772	+	0.618122i
$126$		0			0
$127$	−2.23607	−	6.88191i	−0.198419	−	0.610671i	−0.999920	−	0.0126769i	$-0.995965\pi$
$127$	−2.23607	−	6.88191i	−0.198419	−	0.610671i	0.801501	−	0.597994i	$-0.204035\pi$
$128$	1.40485	−	13.3663i	0.124173	−	1.18142i
$129$		0			0
$130$	6.75164	+	7.49846i	0.592158	+	0.657658i
$131$	6.06086	−	10.4977i	0.529540	−	0.917190i	−0.469866	−	0.882738i	$-0.655698\pi$
$131$	6.06086	−	10.4977i	0.529540	−	0.917190i	0.999406	−	0.0344525i	$-0.0109687\pi$
$132$		0			0
$133$	0.545085	+	0.944115i	0.0472649	+	0.0818651i
$134$	−1.83812	+	5.65714i	−0.158789	+	0.488703i
$135$		0			0
$136$	12.0172	+	8.73102i	1.03047	+	0.748679i
$137$	−7.07830	+	7.86125i	−0.604740	+	0.671632i	−0.965312	−	0.261099i	$-0.915915\pi$
$137$	−7.07830	+	7.86125i	−0.604740	+	0.671632i	0.360572	+	0.932732i	$0.382582\pi$
$138$		0			0
$139$	−12.4407	+	5.53895i	−1.05521	+	0.469808i	−0.859649	−	0.510885i	$-0.829318\pi$
$139$	−12.4407	+	5.53895i	−1.05521	+	0.469808i	−0.195556	+	0.980692i	$0.562651\pi$
$140$	−0.0145467	−	0.138402i	−0.00122942	−	0.0116971i
$141$		0			0
$142$	−5.95492	−	10.3142i	−0.499725	−	0.865550i
$143$	6.53779	+	12.4356i	0.546717	+	1.03992i
$144$		0			0
$145$	0.909830	−	2.80017i	0.0755573	−	0.232541i
$146$	9.12527	+	4.06283i	0.755212	+	0.336242i
$147$		0			0
$148$	−2.32991	−	0.495239i	−0.191518	−	0.0407084i
$149$	−13.3665	−	2.84113i	−1.09502	−	0.232754i	−0.375223	−	0.926935i	$-0.622434\pi$
$149$	−13.3665	−	2.84113i	−1.09502	−	0.232754i	−0.719801	+	0.694180i	$0.755767\pi$
$150$		0			0
$151$	−8.00625	−	3.56461i	−0.651539	−	0.290084i	0.0542270	−	0.998529i	$-0.482731\pi$
$151$	−8.00625	−	3.56461i	−0.651539	−	0.290084i	−0.705766	+	0.708445i	$0.749397\pi$
$152$	−3.56365	+	10.9678i	−0.289050	+	0.889605i
$153$		0			0
$154$	0.173762	−	1.19581i	0.0140021	−	0.0963615i
$155$	1.83812	+	3.18371i	0.147641	+	0.255722i
$156$		0			0
$157$	−1.11349	−	10.5941i	−0.0888659	−	0.845503i	−0.944630	−	0.328137i	$-0.893579\pi$
$157$	−1.11349	−	10.5941i	−0.0888659	−	0.845503i	0.855764	−	0.517366i	$-0.173087\pi$
$158$	0.744252	−	0.331362i	0.0592095	−	0.0263618i
$159$		0			0
$160$	2.20264	−	2.44628i	0.174134	−	0.193396i
$161$	−1.43078	−	1.03952i	−0.112761	−	0.0819256i
$162$		0			0
$163$	1.11803	−	3.44095i	0.0875712	−	0.269516i	−0.897675	−	0.440657i	$-0.854745\pi$
$163$	1.11803	−	3.44095i	0.0875712	−	0.269516i	0.985247	+	0.171141i	$0.0547454\pi$
$164$	−1.06644	−	1.84712i	−0.0832747	−	0.144236i
$165$		0			0
$166$	3.39919	−	5.88756i	0.263828	−	0.456964i
$167$	5.16355	+	5.73471i	0.399568	+	0.443765i	0.909032	−	0.416727i	$-0.136823\pi$
$167$	5.16355	+	5.73471i	0.399568	+	0.443765i	−0.509464	+	0.860492i	$0.670156\pi$
$168$		0			0
$169$	−0.516817	+	4.91719i	−0.0397552	+	0.378245i
$170$	4.37833	+	13.4751i	0.335803	+	1.03350i
$171$		0			0
$172$	3.30902	+	2.40414i	0.252310	+	0.183314i
$173$	2.48702	+	1.10729i	0.189085	+	0.0841860i	0.499095	−	0.866547i	$-0.333666\pi$
$173$	2.48702	+	1.10729i	0.189085	+	0.0841860i	−0.310010	+	0.950733i	$0.600332\pi$
$174$		0			0
$175$	0.309017	−	0.535233i	0.0233595	−	0.0404598i
$176$	12.7377	−	8.50534i	0.960137	−	0.641114i
$177$		0			0
$178$	−25.2891	+	5.37537i	−1.89550	+	0.402901i
$179$	15.0959	−	10.9678i	1.12832	−	0.819771i	0.142868	−	0.989742i	$-0.454367\pi$
$179$	15.0959	−	10.9678i	1.12832	−	0.819771i	0.985449	+	0.169971i	$0.0543674\pi$
$180$		0			0
$181$	2.39919	+	7.38394i	0.178330	+	0.548844i	0.999770	−	0.0214515i	$-0.00682876\pi$
$181$	2.39919	+	7.38394i	0.178330	+	0.548844i	−0.821440	+	0.570295i	$0.806829\pi$
$182$	1.03271	−	1.14694i	0.0765496	−	0.0850170i
$183$		0			0
$184$	−1.95554	−	18.6057i	−0.144164	−	1.37163i
$185$	6.44005	+	7.15240i	0.473482	+	0.525855i
$186$		0			0
$187$	1.28420	+	19.6864i	0.0939103	+	1.43961i
$188$	0.364338			0.0265721
$189$		0			0
$190$	−8.89919	+	6.46564i	−0.645615	+	0.469067i
$191$	−0.384271	+	3.65610i	−0.0278049	+	0.264546i	0.971784	+	0.235873i	$0.0757949\pi$
$191$	−0.384271	+	3.65610i	−0.0278049	+	0.264546i	−0.999589	+	0.0286731i	$0.990872\pi$
$192$		0			0
$193$	−9.40786	−	1.99970i	−0.677192	−	0.143942i	−0.143539	−	0.989645i	$-0.545848\pi$
$193$	−9.40786	−	1.99970i	−0.677192	−	0.143942i	−0.533654	+	0.845703i	$0.679181\pi$
$194$	18.0448	−	8.03407i	1.29554	−	0.576813i
$195$		0			0
$196$	2.59451	−	0.551481i	0.185322	−	0.0393915i
$197$	12.1217			0.863637			0.431818	−	0.901961i	$-0.357872\pi$
$197$	12.1217			0.863637			0.431818	+	0.901961i	$0.357872\pi$
$198$		0			0
$199$	−26.4164			−1.87261			−0.936305	−	0.351189i	$-0.885778\pi$
$199$	−26.4164			−1.87261			−0.936305	+	0.351189i	$0.885778\pi$
$200$	6.39492	−	1.35928i	0.452189	−	0.0961158i
$201$		0			0
$202$	−14.9148	+	6.64048i	−1.04940	+	0.467222i
$203$	−0.440506	−	0.0936324i	−0.0309174	−	0.00657171i
$204$		0			0
$205$	−0.900830	+	8.57082i	−0.0629167	+	0.598612i
$206$	8.67066	−	6.29960i	0.604113	−	0.438914i
$207$		0			0
$208$	19.5623			1.35640
$209$	−14.2277	+	5.67117i	−0.984148	+	0.392283i
$210$		0			0
$211$	7.38348	+	8.20019i	0.508300	+	0.564524i	0.941603	−	0.336724i	$-0.109319\pi$
$211$	7.38348	+	8.20019i	0.508300	+	0.564524i	−0.433304	+	0.901248i	$0.642652\pi$
$212$	0.360734	+	3.43216i	0.0247753	+	0.235722i
$213$		0			0
$214$	9.70680	−	10.7805i	0.663543	−	0.736939i
$215$	−5.10701	−	15.7178i	−0.348295	−	1.07194i
$216$		0			0
$217$	0.454915	−	0.330515i	0.0308816	−	0.0224368i
$218$	−0.440506	+	0.0936324i	−0.0298348	+	0.00634159i
$219$		0			0
$220$	1.95366	+	0.0773639i	0.131716	+	0.00521587i
$221$	−12.5986	+	21.8215i	−0.847477	+	1.46787i
$222$		0			0
$223$	−17.5221	−	7.80135i	−1.17337	−	0.522417i	−0.274907	−	0.961471i	$-0.588647\pi$
$223$	−17.5221	−	7.80135i	−1.17337	−	0.522417i	−0.898461	+	0.439054i	$0.855314\pi$
$224$	−0.407343	−	0.295952i	−0.0272167	−	0.0197741i
$225$		0			0
$226$	−5.39261	−	16.5967i	−0.358711	−	1.10400i
$227$	−0.982498	+	9.34785i	−0.0652107	+	0.620438i	0.912296	+	0.409532i	$0.134308\pi$
$227$	−0.982498	+	9.34785i	−0.0652107	+	0.620438i	−0.977506	+	0.210906i	$0.932359\pi$
$228$		0			0
$229$	−6.37539	−	7.08058i	−0.421297	−	0.467898i	0.494711	−	0.869058i	$-0.335274\pi$
$229$	−6.37539	−	7.08058i	−0.421297	−	0.467898i	−0.916008	+	0.401160i	$0.868607\pi$
$230$	8.92241	−	15.4541i	0.588326	−	1.01901i
$231$		0			0
$232$	−2.38197	−	4.12569i	−0.156384	−	0.270865i
$233$	1.29161	−	3.97517i	0.0846162	−	0.260422i	−0.899793	−	0.436318i	$-0.856282\pi$
$233$	1.29161	−	3.97517i	0.0846162	−	0.260422i	0.984409	+	0.175896i	$0.0562823\pi$
$234$		0			0
$235$	−1.19098	−	0.865300i	−0.0776912	−	0.0564459i
$236$	−2.15854	+	2.39730i	−0.140509	+	0.156051i
$237$		0			0
$238$	1.97982	−	0.881473i	0.128333	−	0.0571374i
$239$	−1.66588	−	15.8498i	−0.107757	−	1.02524i	−0.906108	−	0.423047i	$-0.860961\pi$
$239$	−1.66588	−	15.8498i	−0.107757	−	1.02524i	0.798351	−	0.602193i	$-0.205706\pi$
$240$		0			0
$241$	−7.00000	−	12.1244i	−0.450910	−	0.780998i	0.547533	−	0.836784i	$-0.315567\pi$
$241$	−7.00000	−	12.1244i	−0.450910	−	0.780998i	−0.998443	+	0.0557856i	$0.982234\pi$
$242$	16.2749	+	4.83178i	1.04619	+	0.310598i
$243$		0			0
$244$	0.510643	−	1.57160i	0.0326906	−	0.100611i
$245$	−9.79095	−	4.35921i	−0.625521	−	0.278500i
$246$		0			0
$247$	−19.1348	−	4.06723i	−1.21752	−	0.258792i
$248$	5.81829	+	1.23672i	0.369462	+	0.0785315i
$249$		0			0
$250$	16.5771	+	7.38060i	1.04843	+	0.466790i
$251$	−4.56050	+	14.0358i	−0.287856	+	0.885931i	0.697672	+	0.716418i	$0.254220\pi$
$251$	−4.56050	+	14.0358i	−0.287856	+	0.885931i	−0.985528	+	0.169513i	$0.945780\pi$
$252$		0			0
$253$	17.3435	−	17.7926i	1.09037	−	1.11861i
$254$	−5.58394	−	9.67166i	−0.350367	−	0.606854i
$255$		0			0
$256$	−0.925506	−	8.80560i	−0.0578441	−	0.550350i
$257$	14.4322	−	6.42561i	0.900253	−	0.400818i	0.0961902	−	0.995363i	$-0.469334\pi$
$257$	14.4322	−	6.42561i	0.900253	−	0.400818i	0.804063	+	0.594545i	$0.202668\pi$
$258$		0			0
$259$	0.985051	−	1.09401i	0.0612081	−	0.0679785i
$260$	2.02029	+	1.46782i	0.125293	+	0.0910306i
$261$		0			0
$262$	5.78115	−	17.7926i	0.357161	−	1.09923i
$263$	−2.31504	−	4.00977i	−0.142752	−	0.247253i	0.785780	−	0.618506i	$-0.212262\pi$
$263$	−2.31504	−	4.00977i	−0.142752	−	0.247253i	−0.928532	+	0.371253i	$0.878928\pi$
$264$		0			0
$265$	6.97214	−	12.0761i	0.428295	−	0.741829i
$266$	1.12583	+	1.25036i	0.0690291	+	0.0766646i
$267$		0			0
$268$	−0.153880	+	1.46407i	−0.00939972	+	0.0894324i
$269$	8.30632	+	25.5642i	0.506445	+	1.55868i	0.798327	+	0.602224i	$0.205719\pi$
$269$	8.30632	+	25.5642i	0.506445	+	1.55868i	−0.291882	+	0.956454i	$0.594281\pi$
$270$		0			0
$271$	24.2984	+	17.6538i	1.47602	+	1.07239i	0.978812	+	0.204761i	$0.0656418\pi$
$271$	24.2984	+	17.6538i	1.47602	+	1.07239i	0.497209	+	0.867631i	$0.334358\pi$
$272$	25.0945	+	11.1728i	1.52158	+	0.677450i
$273$		0			0
$274$	−8.16312	+	14.1389i	−0.493152	+	0.854164i
$275$	6.81727	+	5.37772i	0.411097	+	0.324289i
$276$		0			0
$277$	−21.1456	+	4.49464i	−1.27052	+	0.270057i	−0.793356	−	0.608758i	$-0.791668\pi$
$277$	−21.1456	+	4.49464i	−1.27052	+	0.270057i	−0.477162	+	0.878815i	$0.658335\pi$
$278$	−17.0036	+	12.3538i	−1.01981	+	0.740932i
$279$		0			0
$280$	0.281153	+	0.865300i	0.0168021	+	0.0517116i
$281$	−5.89492	+	6.54698i	−0.351662	+	0.390560i	−0.892859	−	0.450336i	$-0.851304\pi$
$281$	−5.89492	+	6.54698i	−0.351662	+	0.390560i	0.541198	+	0.840895i	$0.317971\pi$
$282$		0			0
$283$	−0.725874	−	6.90623i	−0.0431487	−	0.410533i	−0.994683	−	0.102989i	$-0.967159\pi$
$283$	−0.725874	−	6.90623i	−0.0431487	−	0.410533i	0.951534	−	0.307544i	$-0.0995072\pi$
$284$	−1.97230	−	2.19046i	−0.117035	−	0.129980i
$285$		0			0
$286$	13.8601	+	16.6754i	0.819562	+	0.986036i
$287$	1.31819			0.0778102
$288$		0			0
$289$	−14.8713	+	10.8046i	−0.874784	+	0.635568i
$290$	0.474985	−	4.51918i	0.0278921	−	0.265376i
$291$		0			0
$292$	2.41811	+	0.513986i	0.141509	+	0.0300788i
$293$	−18.7891	+	8.36544i	−1.09767	+	0.488714i	−0.873988	−	0.485948i	$-0.838474\pi$
$293$	−18.7891	+	8.36544i	−1.09767	+	0.488714i	−0.223682	+	0.974662i	$0.571808\pi$
$294$		0			0
$295$	12.7496	−	2.71001i	0.742311	−	0.157783i
$296$	15.5728			0.905150
$297$		0			0
$298$	−21.0902			−1.22172
$299$	31.0416	−	6.59809i	1.79518	−	0.381578i
$300$		0			0
$301$	−2.30932	+	1.02817i	−0.133107	+	0.0592630i
$302$	−13.2303	−	2.81220i	−0.761321	−	0.161824i
$303$		0			0
$304$	−2.22920	+	21.2094i	−0.127853	+	1.21644i
$305$	−5.40177	+	3.92461i	−0.309304	+	0.224723i
$306$		0			0
$307$	−16.2705			−0.928607			−0.464304	−	0.885676i	$-0.653695\pi$
$307$	−16.2705			−0.928607			−0.464304	+	0.885676i	$0.653695\pi$
$308$	−0.0194673	−	0.298426i	−0.00110925	−	0.0170044i
$309$		0			0
$310$	3.79649	+	4.21643i	0.215626	+	0.239477i
$311$	−2.51958	−	23.9722i	−0.142872	−	1.35934i	−0.797468	−	0.603361i	$-0.793828\pi$
$311$	−2.51958	−	23.9722i	−0.142872	−	1.35934i	0.654595	−	0.755979i	$-0.272839\pi$
$312$		0			0
$313$	0.232539	−	0.258261i	0.0131439	−	0.0145978i	−0.736537	−	0.676397i	$-0.763540\pi$
$313$	0.232539	−	0.258261i	0.0131439	−	0.0145978i	0.749681	+	0.661799i	$0.230207\pi$
$314$	−5.08043	−	15.6360i	−0.286705	−	0.882389i
$315$		0			0
$316$	0.163119	−	0.118513i	0.00917616	−	0.00666687i
$317$	−10.3472	+	2.19936i	−0.581157	+	0.123529i	−0.489104	−	0.872226i	$-0.662676\pi$
$317$	−10.3472	+	2.19936i	−0.581157	+	0.123529i	−0.0920526	+	0.995754i	$0.529343\pi$
$318$		0			0
$319$	2.19176	−	5.93538i	0.122715	−	0.332317i
$320$	−4.58708	+	7.94506i	−0.256426	+	0.444142i
$321$		0			0
$322$	−2.49351	−	1.11018i	−0.138958	−	0.0618681i
$323$	−22.2232	−	16.1461i	−1.23653	−	0.898391i
$324$		0			0
$325$	3.42705	+	10.5474i	0.190099	+	0.585063i
$326$	0.583680	−	5.55335i	0.0323271	−	0.307571i
$327$		0			0
$328$	9.33054	+	10.3626i	0.515193	+	0.572180i
$329$	−0.112587	+	0.195006i	−0.00620711	+	0.0107510i
$330$		0			0
$331$	−10.3541	−	17.9338i	−0.569113	−	0.985732i	−0.996654	−	0.0817366i	$-0.973953\pi$
$331$	−10.3541	−	17.9338i	−0.569113	−	0.985732i	0.427541	−	0.903996i	$-0.359380\pi$
$332$	0.519929	−	1.60018i	0.0285348	−	0.0878212i
$333$		0			0
$334$	9.63525	+	7.00042i	0.527218	+	0.383046i
$335$	3.98017	−	4.42043i	0.217460	−	0.241514i
$336$		0			0
$337$	4.25025	−	1.89233i	0.231526	−	0.103082i	−0.287695	−	0.957722i	$-0.592889\pi$
$337$	4.25025	−	1.89233i	0.231526	−	0.103082i	0.519221	+	0.854640i	$0.326222\pi$
$338$	0.797636	+	7.58900i	0.0433857	+	0.412787i
$339$		0			0
$340$	1.75329	+	3.03679i	0.0950854	+	0.164693i
$341$	3.67624	+	6.99262i	0.199079	+	0.378671i
$342$		0			0
$343$	−1.01722	+	3.13068i	−0.0549248	+	0.169041i
$344$	−24.4288	−	10.8764i	−1.31711	−	0.586416i
$345$		0			0
$346$	4.10981	+	0.873567i	0.220945	+	0.0469633i
$347$	−2.57877	−	0.548134i	−0.138435	−	0.0294254i	0.138173	−	0.990408i	$-0.455877\pi$
$347$	−2.57877	−	0.548134i	−0.138435	−	0.0294254i	−0.276608	+	0.960983i	$0.589210\pi$
$348$		0			0
$349$	−12.0408	−	5.36093i	−0.644531	−	0.286964i	0.0583229	−	0.998298i	$-0.481425\pi$
$349$	−12.0408	−	5.36093i	−0.644531	−	0.286964i	−0.702854	+	0.711334i	$0.748091\pi$
$350$	0.294756	−	0.907165i	0.0157554	−	0.0484900i
$351$		0			0
$352$	4.93769	−	5.06555i	0.263180	−	0.269995i
$353$	−1.76854	−	3.06319i	−0.0941296	−	0.163037i	0.815115	−	0.579299i	$-0.196673\pi$
$353$	−1.76854	−	3.06319i	−0.0941296	−	0.163037i	−0.909245	+	0.416261i	$0.863340\pi$
$354$		0			0
$355$	1.24492	+	11.8446i	0.0660733	+	0.628645i
$356$	−5.84543	+	2.60255i	−0.309807	+	0.137935i
$357$		0			0
$358$	19.2699	−	21.4014i	1.01844	−	1.13110i
$359$	−21.1567	−	15.3713i	−1.11661	−	0.811264i	−0.132917	−	0.991127i	$-0.542434\pi$
$359$	−21.1567	−	15.3713i	−1.11661	−	0.811264i	−0.983692	+	0.179863i	$0.942434\pi$
$360$		0			0
$361$	0.718847	−	2.21238i	0.0378341	−	0.116441i
$362$	5.99128	+	10.3772i	0.314895	+	0.545413i
$363$		0			0
$364$	0.190983	−	0.330792i	0.0100102	−	0.0173382i
$365$	−6.68384	−	7.42316i	−0.349848	−	0.388546i
$366$		0			0
$367$	0.630771	−	6.00138i	0.0329260	−	0.313270i	−0.965647	−	0.259859i	$-0.916324\pi$
$367$	0.630771	−	6.00138i	0.0329260	−	0.313270i	0.998573	−	0.0534110i	$-0.0170093\pi$
$368$	−10.6909	−	32.9034i	−0.557304	−	1.71521i
$369$		0			0
$370$	12.0172	+	8.73102i	0.624746	+	0.453904i
$371$	−1.94848	−	0.867518i	−0.101160	−	0.0450393i
$372$		0			0
$373$	−6.20820	+	10.7529i	−0.321449	+	0.556765i	−0.980787	−	0.195081i	$-0.937503\pi$
$373$	−6.20820	+	10.7529i	−0.321449	+	0.556765i	0.659339	+	0.751846i	$0.270836\pi$
$374$	8.25570	+	29.3071i	0.426892	+	1.51544i
$375$		0			0
$376$	−2.32991	+	0.495239i	−0.120156	+	0.0255400i
$377$	6.53779	−	4.74998i	0.336713	−	0.244636i
$378$		0			0
$379$	0.545085	+	1.67760i	0.0279991	+	0.0861725i	0.964080	−	0.265613i	$-0.0855745\pi$
$379$	0.545085	+	1.67760i	0.0279991	+	0.0861725i	−0.936080	+	0.351786i	$0.885574\pi$
$380$	−1.82163	+	2.02313i	−0.0934477	+	0.103784i
$381$		0			0
$382$	0.593070	+	5.64268i	0.0303441	+	0.288705i
$383$	9.44507	+	10.4898i	0.482620	+	0.536004i	0.934447	−	0.356101i	$-0.115894\pi$
$383$	9.44507	+	10.4898i	0.482620	+	0.536004i	−0.451827	+	0.892106i	$0.649228\pi$
$384$		0			0
$385$	−0.645121	+	1.02176i	−0.0328784	+	0.0520735i
$386$	−14.8441			−0.755545
$387$		0			0
$388$	3.95492	−	2.87341i	0.200780	−	0.145875i
$389$	2.03561	−	19.3675i	0.103209	−	0.981972i	−0.813269	−	0.581888i	$-0.802314\pi$
$389$	2.03561	−	19.3675i	0.103209	−	0.981972i	0.916478	−	0.400084i	$-0.131019\pi$
$390$		0			0
$391$	43.5885	+	9.26502i	2.20437	+	0.468552i
$392$	−15.8421	+	7.05335i	−0.800146	+	0.356248i
$393$		0			0
$394$	18.2994	−	3.88965i	0.921910	−	0.195958i
$395$	−0.814685			−0.0409913
$396$		0			0
$397$	−2.41641			−0.121276			−0.0606380	−	0.998160i	$-0.519314\pi$
$397$	−2.41641			−0.121276			−0.0606380	+	0.998160i	$0.519314\pi$
$398$	−39.8792	+	8.47658i	−1.99896	+	0.424892i
$399$		0			0
$400$	11.0449	−	4.91752i	0.552246	−	0.245876i
$401$	−3.23952	−	0.688582i	−0.161774	−	0.0343862i	0.126313	−	0.991990i	$-0.459686\pi$
$401$	−3.23952	−	0.688582i	−0.161774	−	0.0343862i	−0.288087	+	0.957604i	$0.593019\pi$
$402$		0			0
$403$	−1.05471	+	10.0349i	−0.0525388	+	0.499874i
$404$	−3.26889	+	2.37499i	−0.162634	+	0.118160i
$405$		0			0
$406$	−0.695048			−0.0344947
$407$	13.2204	+	15.9058i	0.655311	+	0.788422i
$408$		0			0
$409$	−15.3527	−	17.0509i	−0.759143	−	0.843114i	0.232437	−	0.972611i	$-0.425330\pi$
$409$	−15.3527	−	17.0509i	−0.759143	−	0.843114i	−0.991580	+	0.129498i	$0.958663\pi$
$410$	1.39031	+	13.2279i	0.0686623	+	0.653279i
$411$		0			0
$412$	1.77485	−	1.97117i	0.0874407	−	0.0971128i
$413$	−0.616090	−	1.89613i	−0.0303158	−	0.0933024i
$414$		0			0
$415$	−5.50000	+	3.99598i	−0.269984	+	0.196155i
$416$	8.83756	−	1.87848i	0.433297	−	0.0921001i
$417$		0			0
$418$	−19.6588	+	13.1268i	−0.961544	+	0.642054i
$419$	8.03814	−	13.9225i	0.392689	−	0.680157i	−0.600114	−	0.799914i	$-0.704878\pi$
$419$	8.03814	−	13.9225i	0.392689	−	0.680157i	0.992803	+	0.119757i	$0.0382115\pi$
$420$		0			0
$421$	20.2942	+	9.03557i	0.989079	+	0.440367i	0.836525	−	0.547929i	$-0.184583\pi$
$421$	20.2942	+	9.03557i	0.989079	+	0.440367i	0.152554	+	0.988295i	$0.451250\pi$
$422$	13.7777	+	10.0101i	0.670687	+	0.487282i
$423$		0			0
$424$	−6.97214	−	21.4580i	−0.338597	−	1.04209i
$425$	−1.62780	+	15.4875i	−0.0789599	+	0.751253i
$426$		0			0
$427$	0.683374	+	0.758964i	0.0330708	+	0.0367288i
$428$	1.79511	−	3.10923i	0.0867701	−	0.150290i
$429$		0			0
$430$	−12.7533	−	22.0893i	−0.615018	−	1.06524i
$431$	−1.69895	+	5.22884i	−0.0818357	+	0.251864i	−0.983600	−	0.180364i	$-0.942272\pi$
$431$	−1.69895	+	5.22884i	−0.0818357	+	0.251864i	0.901764	+	0.432228i	$0.142272\pi$
$432$		0			0
$433$	−23.1803	−	16.8415i	−1.11398	−	0.809351i	−0.130691	−	0.991423i	$-0.541720\pi$
$433$	−23.1803	−	16.8415i	−1.11398	−	0.809351i	−0.983285	+	0.182072i	$0.941720\pi$
$434$	0.580699	−	0.644932i	0.0278745	−	0.0309577i
$435$		0			0
$436$	−0.101820	+	0.0453333i	−0.00487631	+	0.00217107i
$437$	3.61633	+	34.4071i	0.172993	+	1.64592i
$438$		0			0
$439$	12.5000	+	21.6506i	0.596592	+	1.03333i	0.993320	+	0.115392i	$0.0368124\pi$
$439$	12.5000	+	21.6506i	0.596592	+	1.03333i	−0.396728	+	0.917936i	$0.629854\pi$
$440$	−12.5986	+	2.16084i	−0.600617	+	0.103014i
$441$		0			0
$442$	−12.0172	+	36.9852i	−0.571601	+	1.75921i
$443$	17.1734	+	7.64611i	0.815935	+	0.363278i	0.771893	−	0.635752i	$-0.219310\pi$
$443$	17.1734	+	7.64611i	0.815935	+	0.363278i	0.0440416	+	0.999030i	$0.485977\pi$
$444$		0			0
$445$	25.2891	+	5.37537i	1.19882	+	0.254817i
$446$	−28.9553	−	6.15464i	−1.37107	−	0.291431i
$447$		0			0
$448$	1.28193	+	0.570754i	0.0605657	+	0.0269656i
$449$	−0.139165	+	0.428305i	−0.00656760	+	0.0202130i	−0.954287	−	0.298893i	$-0.903383\pi$
$449$	−0.139165	+	0.428305i	−0.00656760	+	0.0202130i	0.947719	+	0.319106i	$0.103383\pi$
$450$		0			0
$451$	−2.66312	+	18.3273i	−0.125401	+	0.863001i
$452$	−2.15945	−	3.74028i	−0.101572	−	0.175928i
$453$		0			0
$454$	1.51635	+	14.4271i	0.0711658	+	0.677098i
$455$	−1.40993	+	0.627742i	−0.0660986	+	0.0294290i
$456$		0			0
$457$	15.9988	−	17.7685i	0.748392	−	0.831174i	−0.241882	−	0.970306i	$-0.577765\pi$
$457$	15.9988	−	17.7685i	0.748392	−	0.831174i	0.990274	+	0.139132i	$0.0444312\pi$
$458$	−11.8965	−	8.64335i	−0.555889	−	0.403877i
$459$		0			0
$460$	1.36475	−	4.20025i	0.0636316	−	0.195838i
$461$	−9.80668	−	16.9857i	−0.456743	−	0.791101i	0.542044	−	0.840350i	$-0.317651\pi$
$461$	−9.80668	−	16.9857i	−0.456743	−	0.791101i	−0.998787	+	0.0492488i	$0.984317\pi$
$462$		0			0
$463$	0.718847	−	1.24508i	0.0334077	−	0.0578638i	−0.848838	−	0.528653i	$-0.822697\pi$
$463$	0.718847	−	1.24508i	0.0334077	−	0.0578638i	0.882246	+	0.470789i	$0.156031\pi$
$464$	−5.89492	−	6.54698i	−0.273665	−	0.303936i
$465$		0			0
$466$	0.674297	−	6.41551i	0.0312362	−	0.297193i
$467$	−1.50036	−	4.61763i	−0.0694283	−	0.213678i	0.910322	−	0.413900i	$-0.135834\pi$
$467$	−1.50036	−	4.61763i	−0.0694283	−	0.213678i	−0.979751	+	0.200222i	$0.935834\pi$
$468$		0			0
$469$	−0.736068	−	0.534785i	−0.0339885	−	0.0246941i
$470$	−2.07561	−	0.924121i	−0.0957408	−	0.0426265i
$471$		0			0
$472$	10.5451	−	18.2646i	0.485377	−	0.840697i
$473$	−9.62967	−	34.1847i	−0.442773	−	1.57181i
$474$		0			0
$475$	−11.8260	+	2.51369i	−0.542613	+	0.115336i
$476$	0.433921	−	0.315262i	0.0198887	−	0.0144500i
$477$		0			0
$478$	−7.60081	−	23.3929i	−0.347653	−	1.06997i
$479$	24.6344	−	27.3593i	1.12557	−	1.25008i	0.160802	−	0.986987i	$-0.448592\pi$
$479$	24.6344	−	27.3593i	1.12557	−	1.25008i	0.964771	−	0.263090i	$-0.0847415\pi$
$480$		0			0
$481$	2.76127	+	26.2717i	0.125903	+	1.19789i
$482$	−14.4579	−	16.0572i	−0.658542	−	0.731385i
$483$		0			0
$484$	4.18847	+	0.332243i	0.190385	+	0.0151020i
$485$	−19.7525			−0.896916
$486$		0			0
$487$	13.6631	−	9.92684i	0.619135	−	0.449828i	−0.233484	−	0.972361i	$-0.575013\pi$
$487$	13.6631	−	9.92684i	0.619135	−	0.449828i	0.852619	+	0.522533i	$0.175013\pi$
$488$	−1.12928	+	10.7444i	−0.0511200	+	0.486374i
$489$		0			0
$490$	−16.1796	−	3.43907i	−0.730918	−	0.155361i
$491$	−28.2472	+	12.5765i	−1.27478	+	0.567568i	−0.928767	−	0.370663i	$-0.879130\pi$
$491$	−28.2472	+	12.5765i	−1.27478	+	0.567568i	−0.346010	+	0.938231i	$0.612464\pi$
$492$		0			0
$493$	11.0996	−	2.35928i	0.499899	−	0.106257i
$494$	−30.1917			−1.35839
$495$		0			0
$496$	11.0000			0.493915
$497$	1.78188	−	0.378751i	0.0799284	−	0.0169893i
$498$		0			0
$499$	−8.90035	+	3.96269i	−0.398434	+	0.177394i	−0.596165	−	0.802862i	$-0.703310\pi$
$499$	−8.90035	+	3.96269i	−0.398434	+	0.177394i	0.197731	+	0.980256i	$0.436643\pi$
$500$	4.39278	+	0.933715i	0.196451	+	0.0417570i
$501$		0			0
$502$	−2.38085	+	22.6523i	−0.106263	+	1.01102i
$503$	9.03500	−	6.56431i	0.402851	−	0.292688i	−0.367850	−	0.929885i	$-0.619906\pi$
$503$	9.03500	−	6.56431i	0.402851	−	0.292688i	0.770701	+	0.637197i	$0.219906\pi$
$504$		0			0
$505$	16.3262			0.726508
$506$	20.4730	−	32.4255i	0.910135	−	1.44149i
$507$		0			0
$508$	−1.84943	−	2.05400i	−0.0820553	−	0.0911316i
$509$	0.868247	+	8.26082i	0.0384844	+	0.366154i	0.996768	+	0.0803351i	$0.0255990\pi$
$509$	0.868247	+	8.26082i	0.0384844	+	0.366154i	−0.958284	+	0.285819i	$0.907734\pi$
$510$		0			0
$511$	−1.02234	+	1.13542i	−0.0452257	+	0.0502282i
$512$	4.08358	+	12.5680i	0.180470	+	0.555431i
$513$		0			0
$514$	19.7254	−	14.3314i	0.870051	−	0.632129i
$515$	−10.4833	+	2.22830i	−0.461950	+	0.0981906i
$516$		0			0
$517$	−2.48379	−	1.95931i	−0.109237	−	0.0861704i
$518$	1.13602	−	1.96764i	0.0499138	−	0.0864533i
$519$		0			0
$520$	−14.9148	−	6.64048i	−0.654056	−	0.291204i
$521$	−4.40491	−	3.20036i	−0.192983	−	0.140210i	0.487098	−	0.873347i	$-0.338055\pi$
$521$	−4.40491	−	3.20036i	−0.192983	−	0.140210i	−0.680081	+	0.733137i	$0.738055\pi$
$522$		0			0
$523$	5.70163	+	17.5478i	0.249315	+	0.767312i	0.994897	+	0.100898i	$0.0321716\pi$
$523$	5.70163	+	17.5478i	0.249315	+	0.767312i	−0.745582	+	0.666414i	$0.767828\pi$
$524$	0.483976	−	4.60472i	0.0211426	−	0.201158i
$525$		0			0
$526$	−4.78154	−	5.31044i	−0.208485	−	0.231546i
$527$	−7.08429	+	12.2704i	−0.308597	+	0.534505i
$528$		0			0
$529$	−16.5623	−	28.6868i	−0.720100	−	1.24725i
$530$	6.65037	−	20.4677i	0.288874	−	0.889062i
$531$		0			0
$532$	0.336881	+	0.244758i	0.0146056	+	0.0106116i
$533$	−15.8276	+	17.5783i	−0.685568	+	0.761401i
$534$		0			0
$535$	−13.2524	+	5.90036i	−0.572952	+	0.255095i
$536$	−1.00604	−	9.57179i	−0.0434541	−	0.413438i
$537$		0			0
$538$	20.7426	+	35.9273i	0.894279	+	1.54894i
$539$	−20.6532	−	10.1930i	−0.889597	−	0.439042i
$540$		0			0
$541$	−12.2467	+	37.6915i	−0.526527	+	1.62048i	0.234749	+	0.972056i	$0.424573\pi$
$541$	−12.2467	+	37.6915i	−0.526527	+	1.62048i	−0.761276	+	0.648428i	$0.775427\pi$
$542$	42.3465	+	18.8539i	1.81894	+	0.809843i
$543$		0			0
$544$	12.4097	+	2.63776i	0.532061	+	0.113093i
$545$	0.440506	+	0.0936324i	0.0188692	+	0.00401077i
$546$		0			0
$547$	−8.25337	−	3.67464i	−0.352889	−	0.157116i	0.222634	−	0.974902i	$-0.428535\pi$
$547$	−8.25337	−	3.67464i	−0.352889	−	0.157116i	−0.575522	+	0.817786i	$0.695201\pi$
$548$	−1.24861	+	3.84281i	−0.0533378	+	0.164157i
$549$		0			0
$550$	12.0172	+	5.93085i	0.512416	+	0.252892i
$551$	4.40491	+	7.62953i	0.187656	+	0.325029i
$552$		0			0
$553$	0.0130255	+	0.123929i	0.000553900	+	0.00527000i
$554$	−30.4799	+	13.5705i	−1.29497	+	0.576557i
$555$		0			0
$556$	−3.48057	+	3.86556i	−0.147609	+	0.163936i
$557$	14.3242	+	10.4071i	0.606935	+	0.440964i	0.848334	−	0.529462i	$-0.177606\pi$
$557$	14.3242	+	10.4071i	0.606935	+	0.440964i	−0.241399	+	0.970426i	$0.577606\pi$
$558$		0			0
$559$	14.0172	−	43.1406i	0.592865	−	1.82465i
$560$	0.841263	+	1.45711i	0.0355499	+	0.0615742i
$561$		0			0
$562$	−6.79837	+	11.7751i	−0.286772	+	0.496704i
$563$	27.1298	+	30.1307i	1.14339	+	1.26986i	0.957865	+	0.287219i	$0.0927307\pi$
$563$	27.1298	+	30.1307i	1.14339	+	1.26986i	0.185521	+	0.982640i	$0.440603\pi$
$564$		0			0
$565$	−1.82411	+	17.3553i	−0.0767409	+	0.730141i
$566$	−3.31190	−	10.1930i	−0.139209	−	0.428443i
$567$		0			0
$568$	15.5902	+	11.3269i	0.654149	+	0.475267i
$569$	−27.1215	−	12.0753i	−1.13699	−	0.506222i	−0.250111	−	0.968217i	$-0.580467\pi$
$569$	−27.1215	−	12.0753i	−1.13699	−	0.506222i	−0.886883	+	0.461995i	$0.847134\pi$
$570$		0			0
$571$	17.4894	−	30.2925i	0.731907	−	1.26770i	−0.224160	−	0.974552i	$-0.571964\pi$
$571$	17.4894	−	30.2925i	0.731907	−	1.26770i	0.956067	−	0.293148i	$-0.0947027\pi$
$572$	4.21331	+	3.32361i	0.176167	+	0.138967i
$573$		0			0
$574$	1.98998	−	0.422984i	0.0830603	−	0.0176550i
$575$	15.8675	−	11.5284i	0.661722	−	0.480769i
$576$		0			0
$577$	−10.0902	−	31.0543i	−0.420059	−	1.29281i	−0.907647	−	0.419735i	$-0.862123\pi$
$577$	−10.0902	−	31.0543i	−0.420059	−	1.29281i	0.487587	−	0.873074i	$-0.337877\pi$
$578$	−18.9833	+	21.0830i	−0.789599	+	0.876939i
$579$		0			0
$580$	−0.117554	−	1.11845i	−0.00488116	−	0.0464412i
$581$	0.695801	+	0.772766i	0.0288667	+	0.0320597i
$582$		0			0
$583$	15.9980	−	25.3379i	0.662568	−	1.04939i
$584$	−16.1623			−0.668801
$585$		0			0
$586$	−25.6803	+	18.6579i	−1.06085	+	0.770749i
$587$	0.953405	−	9.07104i	0.0393512	−	0.374402i	−0.957069	−	0.289861i	$-0.906391\pi$
$587$	0.953405	−	9.07104i	0.0393512	−	0.374402i	0.996420	−	0.0845410i	$-0.0269424\pi$
$588$		0			0
$589$	−10.7596	−	2.28703i	−0.443343	−	0.0942354i
$590$	18.3777	−	8.18226i	0.756597	−	0.336859i
$591$		0			0
$592$	28.1691	−	5.98752i	1.15774	−	0.246085i
$593$	1.09301			0.0448847			0.0224424	−	0.999748i	$-0.492856\pi$
$593$	1.09301			0.0448847			0.0224424	+	0.999748i	$0.492856\pi$
$594$		0			0
$595$	−2.16718			−0.0888459
$596$	−5.10554	+	1.08522i	−0.209131	+	0.0444522i
$597$		0			0
$598$	44.7443	−	19.9214i	1.82973	−	0.814648i
$599$	12.0771	+	2.56706i	0.493456	+	0.104887i	0.447917	−	0.894075i	$-0.352166\pi$
$599$	12.0771	+	2.56706i	0.493456	+	0.104887i	0.0455394	+	0.998963i	$0.485499\pi$
$600$		0			0
$601$	−3.69620	+	35.1670i	−0.150771	+	1.43449i	0.613551	+	0.789655i	$0.289741\pi$
$601$	−3.69620	+	35.1670i	−0.150771	+	1.43449i	−0.764322	+	0.644835i	$0.776926\pi$
$602$	−3.15631	+	2.29319i	−0.128641	+	0.0934635i
$603$		0			0
$604$	−3.34752			−0.136209
$605$	−12.9026	−	11.0336i	−0.524565	−	0.448581i
$606$		0			0
$607$	−17.6530	−	19.6056i	−0.716512	−	0.795768i	0.269400	−	0.963028i	$-0.413175\pi$
$607$	−17.6530	−	19.6056i	−0.716512	−	0.795768i	−0.985913	+	0.167261i	$0.946508\pi$
$608$	1.02957	+	9.79573i	0.0417547	+	0.397269i
$609$		0			0
$610$	−6.89536	+	7.65807i	−0.279185	+	0.310066i
$611$	−1.24861	−	3.84281i	−0.0505132	−	0.155464i
$612$		0			0
$613$	−34.7426	+	25.2420i	−1.40324	+	1.01952i	−0.408980	+	0.912543i	$0.634115\pi$
$613$	−34.7426	+	25.2420i	−1.40324	+	1.01952i	−0.994262	+	0.106972i	$0.965885\pi$
$614$	−24.5625	+	5.22093i	−0.991264	+	0.210700i
$615$		0			0
$616$	0.530136	+	1.88195i	0.0213598	+	0.0758258i
$617$	0.884268	−	1.53160i	0.0355993	−	0.0616598i	−0.847677	−	0.530513i	$-0.821999\pi$
$617$	0.884268	−	1.53160i	0.0355993	−	0.0616598i	0.883276	+	0.468853i	$0.155333\pi$
$618$		0			0
$619$	−26.3910	−	11.7500i	−1.06074	−	0.472274i	−0.199201	−	0.979959i	$-0.563835\pi$
$619$	−26.3910	−	11.7500i	−1.06074	−	0.472274i	−0.861543	+	0.507685i	$0.830501\pi$
$620$	1.13602	+	0.825366i	0.0456236	+	0.0331475i
$621$		0			0
$622$	−11.4959	−	35.3808i	−0.460945	−	1.41864i
$623$	0.413365	−	3.93290i	0.0165611	−	0.157568i
$624$		0			0
$625$	−3.38294	−	3.75714i	−0.135318	−	0.150286i
$626$	0.268178	−	0.464498i	0.0107185	−	0.0185651i
$627$		0			0
$628$	−2.03444	−	3.52376i	−0.0811831	−	0.140613i
$629$	−11.4626	+	35.2783i	−0.457045	+	1.40664i
$630$		0			0
$631$	15.8713	+	11.5312i	0.631827	+	0.459049i	0.857033	−	0.515262i	$-0.172305\pi$
$631$	15.8713	+	11.5312i	0.631827	+	0.459049i	−0.225205	+	0.974311i	$0.572305\pi$
$632$	−0.882040	+	0.979605i	−0.0350857	+	0.0389666i
$633$		0			0
$634$	−14.9148	+	6.64048i	−0.592341	+	0.263727i
$635$	1.16736	+	11.1067i	0.0463253	+	0.440756i
$636$		0			0
$637$	−14.7082	−	25.4754i	−0.582760	−	1.00937i
$638$	1.40420	−	9.66356i	0.0555927	−	0.382584i
$639$		0			0
$640$	−6.40983	+	19.7274i	−0.253371	+	0.779795i
$641$	−11.2009	−	4.98695i	−0.442408	−	0.196973i	0.173429	−	0.984846i	$-0.444515\pi$
$641$	−11.2009	−	4.98695i	−0.442408	−	0.196973i	−0.615837	+	0.787874i	$0.711182\pi$
$642$		0			0
$643$	−27.5437	−	5.85460i	−1.08622	−	0.230883i	−0.370191	−	0.928956i	$-0.620708\pi$
$643$	−27.5437	−	5.85460i	−1.08622	−	0.230883i	−0.716027	+	0.698073i	$0.754041\pi$
$644$	−0.660759	−	0.140449i	−0.0260375	−	0.00553445i
$645$		0			0
$646$	−38.7299	−	17.2436i	−1.52381	−	0.678442i
$647$	12.1913	−	37.5210i	0.479290	−	1.47510i	−0.360794	−	0.932645i	$-0.617494\pi$
$647$	12.1913	−	37.5210i	0.479290	−	1.47510i	0.840084	−	0.542456i	$-0.182506\pi$
$648$		0			0
$649$	27.6074	−	4.73504i	1.08368	−	0.185867i
$650$	8.55807	+	14.8230i	0.335675	+	0.581407i
$651$		0			0
$652$	−0.144455	−	1.37440i	−0.00565729	−	0.0538255i
$653$	38.1953	−	17.0056i	1.49470	−	0.665482i	0.513429	−	0.858132i	$-0.328375\pi$
$653$	38.1953	−	17.0056i	1.49470	−	0.665482i	0.981268	+	0.192650i	$0.0617082\pi$
$654$		0			0
$655$	−12.5182	+	13.9029i	−0.489128	+	0.543231i
$656$	20.8620	+	15.1571i	0.814523	+	0.591785i
$657$		0			0
$658$	−0.107391	+	0.330515i	−0.00418653	+	0.0128848i
$659$	−1.76854	−	3.06319i	−0.0688924	−	0.119325i	0.829522	−	0.558475i	$-0.188613\pi$
$659$	−1.76854	−	3.06319i	−0.0688924	−	0.119325i	−0.898414	+	0.439150i	$0.855280\pi$
$660$		0			0
$661$	−11.2812	+	19.5395i	−0.438786	+	0.760000i	−0.997596	−	0.0692960i	$-0.977925\pi$
$661$	−11.2812	+	19.5395i	−0.438786	+	0.760000i	0.558810	+	0.829296i	$0.311258\pi$
$662$	−21.3856	−	23.7511i	−0.831174	−	0.923113i
$663$		0			0
$664$	−1.14981	+	10.9397i	−0.0446214	+	0.424544i
$665$	−0.519929	−	1.60018i	−0.0201620	−	0.0620522i
$666$		0			0
$667$	−11.5623	−	8.40051i	−0.447694	−	0.325269i
$668$	2.69273	+	1.19888i	0.104185	+	0.0463861i
$669$		0			0
$670$	4.59017	−	7.95041i	0.177334	−	0.307151i
$671$	−11.9328	+	7.96792i	−0.460661	+	0.307598i
$672$		0			0
$673$	−13.4632	+	2.86168i	−0.518967	+	0.110310i	−0.459946	−	0.887947i	$-0.652131\pi$
$673$	−13.4632	+	2.86168i	−0.518967	+	0.110310i	−0.0590208	+	0.998257i	$0.518798\pi$
$674$	5.80911	−	4.22056i	0.223759	−	0.162570i
$675$		0			0
$676$	0.583592	+	1.79611i	0.0224459	+	0.0690812i
$677$	4.13084	−	4.58777i	0.158761	−	0.176322i	−0.658516	−	0.752566i	$-0.728816\pi$
$677$	4.13084	−	4.58777i	0.158761	−	0.176322i	0.817278	+	0.576244i	$0.195482\pi$
$678$		0			0
$679$	0.315810	+	3.00474i	0.0121197	+	0.115311i
$680$	−15.3400	−	17.0368i	−0.588262	−	0.653331i
$681$		0			0
$682$	7.79359	+	9.37666i	0.298432	+	0.359051i
$683$	31.7351			1.21431			0.607155	−	0.794584i	$-0.292311\pi$
$683$	31.7351			1.21431			0.607155	+	0.794584i	$0.292311\pi$
$684$		0			0
$685$	13.2082	−	9.59632i	0.504660	−	0.366657i
$686$	−0.531050	+	5.05260i	−0.0202756	+	0.192909i
$687$		0			0
$688$	−48.3702	−	10.2814i	−1.84410	−	0.391975i
$689$	34.9640	−	15.5670i	1.33202	−	0.593055i
$690$		0			0
$691$	12.0906	−	2.56993i	0.459947	−	0.0977647i	0.0278899	−	0.999611i	$-0.491121\pi$
$691$	12.0906	−	2.56993i	0.459947	−	0.0977647i	0.432057	+	0.901846i	$0.357788\pi$
$692$	1.03986			0.0395295
$693$		0			0
$694$	−4.06888			−0.154453
$695$	20.5583	−	4.36980i	0.779820	−	0.165756i
$696$		0			0
$697$	−30.3432	+	13.5097i	−1.14933	+	0.511715i
$698$	−19.8975	−	4.22935i	−0.753132	−	0.160083i
$699$		0			0
$700$	0.0246758	−	0.234775i	0.000932658	−	0.00887365i
$701$	−31.0760	+	22.5780i	−1.17372	+	0.852760i	−0.991450	−	0.130488i	$-0.958346\pi$
$701$	−31.0760	+	22.5780i	−1.17372	+	0.852760i	−0.182274	+	0.983248i	$0.558346\pi$
$702$		0			0
$703$	−28.7984			−1.08615
$704$	−10.5253	+	16.6702i	−0.396688	+	0.628282i
$705$		0			0
$706$	−3.65277	−	4.05681i	−0.137474	−	0.152680i
$707$	−0.261030	−	2.48353i	−0.00981703	−	0.0934028i
$708$		0			0
$709$	−26.6303	+	29.5760i	−1.00012	+	1.11075i	−0.00627600	+	0.999980i	$0.501998\pi$
$709$	−26.6303	+	29.5760i	−1.00012	+	1.11075i	−0.993846	+	0.110768i	$0.964669\pi$
$710$	5.68010	+	17.4815i	0.213170	+	0.656070i
$711$		0			0
$712$	33.8435	−	24.5887i	1.26834	−	0.921501i
$713$	17.4549	−	3.71015i	0.653690	−	0.138946i
$714$		0			0
$715$	−5.87930	−	20.8711i	−0.219873	−	0.780535i
$716$	3.56365	−	6.17242i	0.133180	−	0.230674i
$717$		0			0
$718$	−36.8713	−	16.4162i	−1.37603	−	0.612646i
$719$	28.7609	+	20.8960i	1.07260	+	0.779291i	0.976378	−	0.216069i	$-0.0693235\pi$
$719$	28.7609	+	20.8960i	1.07260	+	0.779291i	0.0962240	+	0.995360i	$0.469323\pi$
$720$		0			0
$721$	0.506578	+	1.55909i	0.0188659	+	0.0580634i
$722$	0.375281	−	3.57056i	0.0139665	−	0.132882i
$723$		0			0
$724$	1.98435	+	2.20384i	0.0737476	+	0.0819050i
$725$	2.49721	−	4.32530i	0.0927441	−	0.160638i
$726$		0			0
$727$	0.281153	+	0.486971i	0.0104274	+	0.0180608i	0.871192	−	0.490942i	$-0.163347\pi$
$727$	0.281153	+	0.486971i	0.0104274	+	0.0180608i	−0.860765	+	0.509003i	$0.830014\pi$
$728$	−0.771681	+	2.37499i	−0.0286004	+	0.0880230i
$729$		0			0
$730$	−12.4721	−	9.06154i	−0.461614	−	0.335383i
$731$	42.6205	−	47.3349i	1.57638	−	1.75074i
$732$		0			0
$733$	15.2128	−	6.77317i	0.561897	−	0.250173i	−0.106076	−	0.994358i	$-0.533829\pi$
$733$	15.2128	−	6.77317i	0.561897	−	0.250173i	0.667973	+	0.744185i	$0.267162\pi$
$734$	−0.973508	−	9.26231i	−0.0359328	−	0.341878i
$735$		0			0
$736$	−7.98936	−	13.8380i	−0.294492	−	0.510074i
$737$	8.92241	−	9.15345i	0.328661	−	0.337172i
$738$		0			0
$739$	4.25329	−	13.0903i	0.156460	−	0.481534i	−0.841846	−	0.539718i	$-0.818531\pi$
$739$	4.25329	−	13.0903i	0.156460	−	0.481534i	0.998306	+	0.0581840i	$0.0185310\pi$
$740$	3.35841	+	1.49526i	0.123458	+	0.0549668i
$741$		0			0
$742$	−3.21986	−	0.684403i	−0.118205	−	0.0251252i
$743$	43.1187	+	9.16516i	1.58187	+	0.336237i	0.913261	−	0.407376i	$-0.133556\pi$
$743$	43.1187	+	9.16516i	1.58187	+	0.336237i	0.668610	+	0.743613i	$0.266889\pi$
$744$		0			0
$745$	19.2668	+	8.57814i	0.705882	+	0.314279i
$746$	−5.92170	+	18.2251i	−0.216809	+	0.667269i
$747$		0			0
$748$	3.50658	+	6.66991i	0.128213	+	0.243876i
$749$	1.10944	+	1.92161i	0.0405381	+	0.0702140i
$750$		0			0
$751$	−3.81598	−	36.3066i	−0.139247	−	1.32485i	−0.811425	−	0.584457i	$-0.801308\pi$
$751$	−3.81598	−	36.3066i	−0.139247	−	1.32485i	0.672178	−	0.740390i	$-0.265359\pi$
$752$	−4.02409	+	1.79164i	−0.146743	+	0.0653344i
$753$		0			0
$754$	8.34549	−	9.26860i	0.303925	−	0.337543i
$755$	10.9427	+	7.95034i	0.398246	+	0.289342i
$756$		0			0
$757$	−1.57953	+	4.86128i	−0.0574089	+	0.176686i	−0.975649	−	0.219338i	$-0.929610\pi$
$757$	−1.57953	+	4.86128i	−0.0574089	+	0.176686i	0.918240	+	0.396024i	$0.129610\pi$
$758$	1.36119	+	2.35766i	0.0494407	+	0.0856339i
$759$		0			0
$760$	8.89919	−	15.4138i	0.322807	−	0.559119i
$761$	4.71154	+	5.23270i	0.170793	+	0.189685i	0.822465	−	0.568816i	$-0.192598\pi$
$761$	4.71154	+	5.23270i	0.170793	+	0.189685i	−0.651671	+	0.758502i	$0.725932\pi$
$762$		0			0
$763$	0.00720031	−	0.0685064i	0.000260669	−	0.00248010i
$764$	0.433921	+	1.33547i	0.0156987	+	0.0483156i
$765$		0			0
$766$	17.6246	+	12.8050i	0.636803	+	0.462665i
$767$	32.6827	+	14.5513i	1.18010	+	0.525416i
$768$		0			0
$769$	−5.63525	+	9.76055i	−0.203212	+	0.351974i	−0.949562	−	0.313580i	$-0.898472\pi$
$769$	−5.63525	+	9.76055i	−0.203212	+	0.351974i	0.746349	+	0.665555i	$0.231805\pi$
$770$	−0.646034	+	1.74949i	−0.0232815	+	0.0630472i
$771$		0			0
$772$	−3.59348	+	0.763818i	−0.129332	+	0.0274904i
$773$	−39.1141	+	28.4181i	−1.40684	+	1.02213i	−0.413065	+	0.910702i	$0.635542\pi$
$773$	−39.1141	+	28.4181i	−1.40684	+	1.02213i	−0.993773	+	0.111426i	$0.964458\pi$
$774$		0			0
$775$	1.92705	+	5.93085i	0.0692217	+	0.213043i
$776$	−21.3856	+	23.7511i	−0.767698	+	0.852615i
$777$		0			0
$778$	−3.14168	−	29.8911i	−0.112635	−	1.07165i
$779$	−17.2547	−	19.1633i	−0.618215	−	0.686598i
$780$		0			0
$781$	1.66602	+	25.5395i	0.0596150	+	0.913874i
$782$	68.7758			2.45942
$783$		0			0
$784$	−25.9443	+	18.8496i	−0.926581	+	0.673201i
$785$	−1.71851	+	16.3506i	−0.0613364	+	0.583577i
$786$		0			0
$787$	42.8205	+	9.10177i	1.52638	+	0.324443i	0.893236	−	0.449588i	$-0.148429\pi$
$787$	42.8205	+	9.10177i	1.52638	+	0.324443i	0.633148	+	0.774031i	$0.281762\pi$
$788$	4.22979	−	1.88323i	0.150680	−	0.0670871i
$789$		0			0
$790$	−1.22988	+	0.261419i	−0.0437571	+	0.00930086i
$791$	2.66923			0.0949069
$792$		0			0
$793$	−18.3262			−0.650784
$794$	−3.64790	+	0.775384i	−0.129459	+	0.0275174i
$795$		0			0
$796$	−9.21783	+	4.10404i	−0.326717	+	0.145464i
$797$	3.01927	+	0.641766i	0.106948	+	0.0227325i	0.261075	−	0.965319i	$-0.415923\pi$
$797$	3.01927	+	0.641766i	0.106948	+	0.0227325i	−0.154127	+	0.988051i	$0.549256\pi$
$798$		0			0
$799$	0.593070	−	5.64268i	0.0209813	−	0.199624i
$800$	4.51750	−	3.28216i	0.159718	−	0.116042i
$801$		0			0
$802$	−5.11146			−0.180492
$803$	−13.7209	−	16.5079i	−0.484199	−	0.582552i
$804$		0			0
$805$	1.82639	+	2.02841i	0.0643716	+	0.0714919i
$806$	1.62780	+	15.4875i	0.0573368	+	0.545523i
$807$		0			0
$808$	17.6760	−	19.6312i	0.621840	−	0.690624i
$809$	7.96856	+	24.5247i	0.280160	+	0.862243i	0.987808	+	0.155678i	$0.0497562\pi$
$809$	7.96856	+	24.5247i	0.280160	+	0.862243i	−0.707648	+	0.706565i	$0.750244\pi$
$810$		0			0
$811$	−5.83688	+	4.24074i	−0.204961	+	0.148913i	−0.685531	−	0.728044i	$-0.740430\pi$
$811$	−5.83688	+	4.24074i	−0.204961	+	0.148913i	0.480570	+	0.876956i	$0.340430\pi$
$812$	−0.168258	+	0.0357644i	−0.00590471	+	0.00125508i
$813$		0			0
$814$	25.0619	+	19.7698i	0.878419	+	0.692930i
$815$	−2.79197	+	4.83583i	−0.0977984	+	0.169392i
$816$		0			0
$817$	45.1756	+	20.1135i	1.58049	+	0.703681i
$818$	−28.6484	−	20.8142i	−1.00167	−	0.727753i
$819$		0			0
$820$	1.01722	+	3.13068i	0.0355229	+	0.109328i
$821$	−3.14690	+	29.9408i	−0.109828	+	1.04494i	0.791312	+	0.611412i	$0.209398\pi$
$821$	−3.14690	+	29.9408i	−0.109828	+	1.04494i	−0.901140	+	0.433528i	$0.857268\pi$
$822$		0			0
$823$	36.7276	+	40.7901i	1.28024	+	1.42185i	0.856562	+	0.516044i	$0.172596\pi$
$823$	36.7276	+	40.7901i	1.28024	+	1.42185i	0.423681	+	0.905811i	$0.360738\pi$
$824$	−8.67066	+	15.0180i	−0.302057	+	0.523178i
$825$		0			0
$826$	−1.53851	−	2.66477i	−0.0535315	−	0.0927193i
$827$	10.2140	−	31.4355i	0.355176	−	1.09312i	−0.600731	−	0.799451i	$-0.705124\pi$
$827$	10.2140	−	31.4355i	0.355176	−	1.09312i	0.955907	−	0.293669i	$-0.0948763\pi$
$828$		0			0
$829$	7.30902	+	5.31031i	0.253853	+	0.184435i	0.707433	−	0.706781i	$-0.249853\pi$
$829$	7.30902	+	5.31031i	0.253853	+	0.184435i	−0.453580	+	0.891216i	$0.649853\pi$
$830$	−7.02075	+	7.79734i	−0.243694	+	0.270650i
$831$		0			0
$832$	−23.0034	+	10.2418i	−0.797499	+	0.355069i
$833$	−4.31770	−	41.0802i	−0.149599	−	1.42334i
$834$		0			0
$835$	−5.95492	−	10.3142i	−0.206078	−	0.356938i
$836$	−4.08358	+	4.18932i	−0.141234	+	0.144891i
$837$		0			0
$838$	7.66718	−	23.5972i	0.264858	−	0.815151i
$839$	−44.4221	−	19.7780i	−1.53362	−	0.682812i	−0.545730	−	0.837961i	$-0.683748\pi$
$839$	−44.4221	−	19.7780i	−1.53362	−	0.682812i	−0.987891	+	0.155149i	$0.950414\pi$
$840$		0			0
$841$	24.8065	+	5.27278i	0.855396	+	0.181820i
$842$	33.5362	+	7.12835i	1.15573	+	0.245659i
$843$		0			0
$844$	3.85039	+	1.71431i	0.132536	+	0.0590089i
$845$	2.35805	−	7.25732i	0.0811193	−	0.249660i
$846$		0			0
$847$	−1.47214	+	2.13914i	−0.0505832	+	0.0735017i
$848$	−20.8620	−	36.1340i	−0.716403	−	1.24085i
$849$		0			0
$850$	2.51228	+	23.9028i	0.0861706	+	0.819859i
$851$	42.6793	−	19.0021i	1.46303	−	0.651382i
$852$		0			0
$853$	14.1724	−	15.7401i	0.485254	−	0.538929i	−0.449943	−	0.893057i	$-0.648556\pi$
$853$	14.1724	−	15.7401i	0.485254	−	0.538929i	0.935197	+	0.354128i	$0.115222\pi$
$854$	1.27518	+	0.926476i	0.0436359	+	0.0317033i
$855$		0			0
$856$	−7.25329	+	22.3233i	−0.247912	+	0.762996i
$857$	20.4976	+	35.5029i	0.700186	+	1.21276i	0.968401	+	0.249398i	$0.0802327\pi$
$857$	20.4976	+	35.5029i	0.700186	+	1.21276i	−0.268216	+	0.963359i	$0.586434\pi$
$858$		0			0
$859$	−7.79180	+	13.4958i	−0.265853	+	0.460470i	−0.967787	−	0.251772i	$-0.918987\pi$
$859$	−7.79180	+	13.4958i	−0.265853	+	0.460470i	0.701934	+	0.712242i	$0.252320\pi$
$860$	−4.22396	−	4.69119i	−0.144036	−	0.159968i
$861$		0			0
$862$	−0.886954	+	8.43881i	−0.0302098	+	0.287427i
$863$	7.63080	+	23.4852i	0.259755	+	0.799445i	0.992855	+	0.119324i	$0.0380728\pi$
$863$	7.63080	+	23.4852i	0.259755	+	0.799445i	−0.733100	+	0.680121i	$0.761927\pi$
$864$		0			0
$865$	−3.39919	−	2.46965i	−0.115576	−	0.0839708i
$866$	−40.3980	−	17.9864i	−1.37278	−	0.611201i
$867$		0			0
$868$	0.107391	−	0.186006i	0.00364508	−	0.00631347i
$869$	−1.74936	−	0.0692736i	−0.0593428	−	0.00234995i
$870$		0			0
$871$	15.9695	−	3.39442i	0.541105	−	0.115015i
$872$	0.589512	−	0.428305i	0.0199634	−	0.0145043i
$873$		0			0
$874$	16.5000	+	50.7818i	0.558121	+	1.71772i
$875$	−1.85720	+	2.06263i	−0.0627848	+	0.0697296i
$876$		0			0
$877$	−0.264234	−	2.51402i	−0.00892254	−	0.0848923i	0.989154	−	0.146879i	$-0.0469229\pi$
$877$	−0.264234	−	2.51402i	−0.00892254	−	0.0848923i	−0.998077	+	0.0619871i	$0.980256\pi$
$878$	25.8178	+	28.6735i	0.871307	+	0.967685i
$879$		0			0
$880$	−21.9584	+	8.75267i	−0.740219	+	0.295052i
$881$	47.8114			1.61081			0.805403	−	0.592728i	$-0.201949\pi$
$881$	47.8114			1.61081			0.805403	+	0.592728i	$0.201949\pi$
$882$		0			0
$883$	40.3607	−	29.3238i	1.35825	−	0.986823i	0.359691	−	0.933072i	$-0.382882\pi$
$883$	40.3607	−	29.3238i	1.35825	−	0.986823i	0.998554	−	0.0537512i	$-0.0171178\pi$
$884$	−1.00604	+	9.57179i	−0.0338366	+	0.321934i
$885$		0			0
$886$	28.3791	+	6.03217i	0.953416	+	0.202655i
$887$	15.0493	−	6.70037i	0.505305	−	0.224976i	−0.138220	−	0.990402i	$-0.544138\pi$
$887$	15.0493	−	6.70037i	0.505305	−	0.224976i	0.643525	+	0.765425i	$0.277471\pi$
$888$		0			0
$889$	1.67088	−	0.355156i	0.0560394	−	0.0119115i
$890$	39.9022			1.33753
$891$		0			0
$892$	−7.32624			−0.245301
$893$	4.30865	−	0.915833i	0.144184	−	0.0306472i
$894$		0			0
$895$	−26.3086	+	11.7134i	−0.879400	+	0.391534i
$896$	3.10340	+	0.659648i	0.103677	+	0.0220373i
$897$		0			0
$898$	−0.0726523	+	0.691241i	−0.00242444	+	0.0230670i
$899$	3.67624	−	2.67094i	0.122609	−	0.0890809i
$900$		0			0
$901$	53.7426			1.79043
$902$	1.86059	+	28.5222i	0.0619510	+	0.949684i
$903$		0			0
$904$	18.8936	+	20.9835i	0.628392	+	0.697900i
$905$	−1.25252	−	11.9169i	−0.0416351	−	0.396132i
$906$		0			0
$907$	31.3603	−	34.8292i	1.04130	−	1.15648i	0.0538526	−	0.998549i	$-0.482850\pi$
$907$	31.3603	−	34.8292i	1.04130	−	1.15648i	0.987450	−	0.157934i	$-0.0504834\pi$
$908$	1.10944	+	3.41451i	0.0368181	+	0.113314i
$909$		0			0
$910$	−1.92705	+	1.40008i	−0.0638811	+	0.0464123i
$911$	37.0801	−	7.88163i	1.22852	−	0.261130i	0.452457	−	0.891786i	$-0.350547\pi$
$911$	37.0801	−	7.88163i	1.22852	−	0.261130i	0.776062	+	0.630656i	$0.217214\pi$
$912$		0			0
$913$	−12.1498	+	8.11282i	−0.402100	+	0.268495i
$914$	18.4508	−	31.9577i	0.610297	−	1.05707i
$915$		0			0
$916$	−3.32468	−	1.48024i	−0.109851	−	0.0489087i
$917$	2.31504	+	1.68198i	0.0764495	+	0.0555438i
$918$		0			0
$919$	−0.871323	−	2.68166i	−0.0287423	−	0.0884597i	0.935656	−	0.352912i	$-0.114809\pi$
$919$	−0.871323	−	2.68166i	−0.0287423	−	0.0884597i	−0.964399	+	0.264453i	$0.914809\pi$
$920$	−3.01811	+	28.7154i	−0.0995040	+	0.946717i
$921$		0			0
$922$	−20.2549	−	22.4954i	−0.667060	−	0.740846i
$923$	−16.3445	+	28.3094i	−0.537985	+	0.931817i
$924$		0			0
$925$	8.16312	+	14.1389i	0.268402	+	0.464885i
$926$	0.685672	−	2.11028i	0.0225326	−	0.0693482i
$927$		0			0
$928$	−3.29180	−	2.39163i	−0.108058	−	0.0785091i
$929$	0.580699	−	0.644932i	0.0190521	−	0.0211595i	−0.733543	−	0.679643i	$-0.762135\pi$
$929$	0.580699	−	0.644932i	0.0190521	−	0.0211595i	0.752596	+	0.658483i	$0.228802\pi$
$930$		0			0
$931$	29.2964	−	13.0436i	0.960150	−	0.427486i
$932$	−0.166882	−	1.58777i	−0.00546639	−	0.0520092i
$933$		0			0
$934$	−3.74671	−	6.48949i	−0.122596	−	0.212343i
$935$	4.37833	−	30.1313i	0.143187	−	0.985399i
$936$		0			0
$937$	10.2533	−	31.5564i	0.334960	−	1.03090i	−0.631781	−	0.775147i	$-0.717676\pi$
$937$	10.2533	−	31.5564i	0.334960	−	1.03090i	0.966742	−	0.255755i	$-0.0823241\pi$
$938$	−1.28280	−	0.571138i	−0.0418848	−	0.0186483i
$939$		0			0
$940$	−0.550018	−	0.116910i	−0.0179396	−	0.00381318i
$941$	44.1878	+	9.39241i	1.44048	+	0.306184i	0.860918	−	0.508743i	$-0.169890\pi$
$941$	44.1878	+	9.39241i	1.44048	+	0.306184i	0.579563	+	0.814927i	$0.303223\pi$
$942$		0			0
$943$	38.2162	+	17.0149i	1.24449	+	0.554083i
$944$	12.0521	−	37.0927i	0.392264	−	1.20726i
$945$		0			0
$946$	−25.5066	−	48.5164i	−0.829290	−	1.57740i
$947$	12.6682	+	21.9420i	0.411662	+	0.713020i	0.995072	−	0.0991584i	$-0.0316151\pi$
$947$	12.6682	+	21.9420i	0.411662	+	0.713020i	−0.583410	+	0.812178i	$0.698282\pi$
$948$		0			0
$949$	−2.86579	−	27.2662i	−0.0930276	−	0.885099i
$950$	−17.0463	+	7.58951i	−0.553055	+	0.246236i
$951$		0			0
$952$	−2.34636	+	2.60590i	−0.0760459	+	0.0844575i
$953$	37.6834	+	27.3786i	1.22068	+	0.886879i	0.996157	−	0.0875894i	$-0.0279163\pi$
$953$	37.6834	+	27.3786i	1.22068	+	0.886879i	0.224527	+	0.974468i	$0.427916\pi$
$954$		0			0
$955$	1.75329	−	5.39607i	0.0567351	−	0.174613i
$956$	−3.04372	−	5.27188i	−0.0984409	−	0.170505i
$957$		0			0
$958$	28.4098	−	49.2073i	0.917880	−	1.58981i
$959$	−1.67096	−	1.85579i	−0.0539581	−	0.0599266i
$960$		0			0
$961$	2.64731	−	25.1875i	0.0853972	−	0.812500i
$962$	12.5986	+	38.7746i	0.406197	+	1.25014i
$963$		0			0
$964$	−4.32624	−	3.14320i	−0.139339	−	0.101236i
$965$	13.5608	+	6.03764i	0.436537	+	0.194359i
$966$		0			0
$967$	−21.3435	+	36.9680i	−0.686359	+	1.18881i	0.286648	+	0.958036i	$0.407459\pi$
$967$	−21.3435	+	36.9680i	−0.686359	+	1.18881i	−0.973008	+	0.230773i	$0.925874\pi$
$968$	−27.2365	+	3.56864i	−0.875415	+	0.114700i
$969$		0			0
$970$	−29.8191	+	6.33825i	−0.957434	+	0.203509i
$971$	−10.5784	+	7.68563i	−0.339476	+	0.246644i	−0.744441	−	0.667689i	$-0.767284\pi$
$971$	−10.5784	+	7.68563i	−0.339476	+	0.246644i	0.404965	+	0.914332i	$0.367284\pi$
$972$		0			0
$973$	−0.993422	−	3.05744i	−0.0318477	−	0.0980170i
$974$	17.4410	−	19.3702i	0.558845	−	0.620660i
$975$		0			0
$976$	2.08834	+	19.8693i	0.0668463	+	0.636000i
$977$	−19.1695	−	21.2899i	−0.613286	−	0.681124i	0.353873	−	0.935293i	$-0.384864\pi$
$977$	−19.1695	−	21.2899i	−0.613286	−	0.681124i	−0.967160	+	0.254170i	$0.918198\pi$
$978$		0			0
$979$	53.8457	+	13.6928i	1.72092	+	0.437623i
$980$	−4.09373			−0.130769
$981$		0			0
$982$	−38.6074	+	28.0499i	−1.23201	+	0.895109i
$983$	4.12940	−	39.2886i	0.131707	−	1.25311i	−0.706481	−	0.707732i	$-0.749718\pi$
$983$	4.12940	−	39.2886i	0.131707	−	1.25311i	0.838188	−	0.545381i	$-0.183615\pi$
$984$		0			0
$985$	−18.2994	−	3.88965i	−0.583067	−	0.123935i
$986$	15.9992	−	7.12332i	0.509519	−	0.226853i
$987$		0			0
$988$	−7.30885	+	1.55354i	−0.232526	+	0.0494248i
$989$	−80.2220			−2.55091
$990$		0			0
$991$	−24.7295			−0.785558			−0.392779	−	0.919633i	$-0.628486\pi$
$991$	−24.7295			−0.785558			−0.392779	+	0.919633i	$0.628486\pi$
$992$	4.96941	−	1.05628i	0.157779	−	0.0335370i
$993$		0			0
$994$	2.56846	−	1.14355i	0.0814666	−	0.0362713i
$995$	39.8792	+	8.47658i	1.26425	+	0.268726i
$996$		0			0
$997$	0.391213	−	3.72214i	0.0123898	−	0.117881i	−0.986579	−	0.163285i	$-0.947791\pi$
$997$	0.391213	−	3.72214i	0.0123898	−	0.117881i	0.998969	+	0.0454040i	$0.0144575\pi$
$998$	−12.1647	+	8.83819i	−0.385068	+	0.279768i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.n.e.757.2		16
3.2	odd	2	inner	891.2.n.e.757.1		16
9.2	odd	6	inner	891.2.n.e.460.2		16
9.4	even	3		99.2.f.c.64.1	✓	8
9.5	odd	6		99.2.f.c.64.2	yes	8
9.7	even	3	inner	891.2.n.e.460.1		16
11.5	even	5	inner	891.2.n.e.676.1		16
33.5	odd	10	inner	891.2.n.e.676.2		16
99.4	even	15		1089.2.a.v.1.2		4
99.5	odd	30		99.2.f.c.82.2	yes	8
99.16	even	15	inner	891.2.n.e.379.2		16
99.38	odd	30	inner	891.2.n.e.379.1		16
99.40	odd	30		1089.2.a.w.1.3		4
99.49	even	15		99.2.f.c.82.1	yes	8
99.59	odd	30		1089.2.a.v.1.3		4
99.95	even	30		1089.2.a.w.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.f.c.64.1	✓	8	9.4	even	3
99.2.f.c.64.2	yes	8	9.5	odd	6
99.2.f.c.82.1	yes	8	99.49	even	15
99.2.f.c.82.2	yes	8	99.5	odd	30
891.2.n.e.379.1		16	99.38	odd	30	inner
891.2.n.e.379.2		16	99.16	even	15	inner
891.2.n.e.460.1		16	9.7	even	3	inner
891.2.n.e.460.2		16	9.2	odd	6	inner
891.2.n.e.676.1		16	11.5	even	5	inner
891.2.n.e.676.2		16	33.5	odd	10	inner
891.2.n.e.757.1		16	3.2	odd	2	inner
891.2.n.e.757.2		16	1.1	even	1	trivial
1089.2.a.v.1.2		4	99.4	even	15
1089.2.a.v.1.3		4	99.59	odd	30
1089.2.a.w.1.2		4	99.95	even	30
1089.2.a.w.1.3		4	99.40	odd	30

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.n (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.50964 - 0.320883i) q^{2} +(0.348943 - 0.155360i) q^{4} +(-1.50964 - 0.320883i) q^{5} +(-0.0246758 + 0.234775i) q^{7} +(-2.02029 + 1.46782i) q^{8} -2.38197 q^{10} +(-3.21432 - 0.817391i) q^{11} +(-2.83448 - 3.14801i) q^{13} +(0.0380837 + 0.362342i) q^{14} +(-3.09007 + 3.43187i) q^{16} +(-1.83812 - 5.65714i) q^{17} +(3.73607 - 2.71441i) q^{19} +(-0.576630 + 0.122566i) q^{20} +(-5.11474 - 0.202541i) q^{22} +(-3.74582 + 6.48795i) q^{23} +(-2.39169 - 1.06485i) q^{25} +(-5.28918 - 3.84281i) q^{26} +(0.0278640 + 0.0857567i) q^{28} +(-0.199409 + 1.89725i) q^{29} +(-1.59385 - 1.77015i) q^{31} +(-1.06644 + 1.84712i) q^{32} +(-4.59017 - 7.95041i) q^{34} +(0.112587 - 0.346506i) q^{35} +(-5.04508 - 3.66547i) q^{37} +(4.76909 - 5.29661i) q^{38} +(3.52090 - 1.56760i) q^{40} +(-0.583680 - 5.55335i) q^{41} +(5.35410 + 9.27358i) q^{43} +(-1.24861 + 0.214153i) q^{44} +(-3.57295 + 10.9964i) q^{46} +(0.871385 + 0.387966i) q^{47} +(6.79252 + 1.44380i) q^{49} +(-3.95228 - 0.840083i) q^{50} +(-1.47815 - 0.658114i) q^{52} +(-2.79197 + 8.59279i) q^{53} +(4.59017 + 2.26538i) q^{55} +(-0.294756 - 0.510532i) q^{56} +(0.307760 + 2.92814i) q^{58} +(-7.71534 + 3.43509i) q^{59} +(2.89482 - 3.21502i) q^{61} +(-2.97414 - 2.16084i) q^{62} +(1.83688 - 5.65334i) q^{64} +(3.26889 + 5.66189i) q^{65} +(-1.92705 + 3.33775i) q^{67} +(-1.52029 - 1.68845i) q^{68} +(0.0587770 - 0.559226i) q^{70} +(-2.38463 - 7.33912i) q^{71} +(5.23607 + 3.80423i) q^{73} +(-8.79243 - 3.91464i) q^{74} +(0.881966 - 1.52761i) q^{76} +(0.271219 - 0.734472i) q^{77} +(0.516329 - 0.109749i) q^{79} +(5.76611 - 4.18932i) q^{80} +(-2.66312 - 8.19624i) q^{82} +(2.94746 - 3.27349i) q^{83} +(0.959607 + 9.13005i) q^{85} +(11.0585 + 12.2817i) q^{86} +(7.69364 - 3.06670i) q^{88} -16.7518 q^{89} +(0.809017 - 0.587785i) q^{91} +(-0.299113 + 2.84587i) q^{92} +(1.43997 + 0.306074i) q^{94} +(-6.51111 + 2.89893i) q^{95} +(12.5187 - 2.66093i) q^{97} +10.7175 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{4} + 6 q^{7} - 56 q^{10} + 6 q^{13} - 2 q^{16} + 24 q^{19} - 28 q^{22} - 8 q^{25} + 72 q^{28} - 12 q^{31} + 16 q^{34} - 36 q^{37} + 16 q^{40} + 32 q^{43} - 84 q^{46} + 44 q^{49} - 6 q^{52} - 16 q^{55}+ \cdots + 54 q^{97}+O(q^{100}) \) 16 * q - 2 * q^4 + 6 * q^7 - 56 * q^10 + 6 * q^13 - 2 * q^16 + 24 * q^19 - 28 * q^22 - 8 * q^25 + 72 * q^28 - 12 * q^31 + 16 * q^34 - 36 * q^37 + 16 * q^40 + 32 * q^43 - 84 * q^46 + 44 * q^49 - 6 * q^52 - 16 * q^55 - 28 * q^58 - 42 * q^61 + 92 * q^64 - 4 * q^67 - 26 * q^70 + 48 * q^73 + 32 * q^76 - 30 * q^79 + 20 * q^82 - 46 * q^85 + 14 * q^88 + 4 * q^91 + 26 * q^94 + 54 * q^97

Introduction

L-functions

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