LMFDB - Embedded newform 891.2.n.e.379.1

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			379.1
Root			$-1.50964 - 0.320883i$ of defining polynomial
Character	$\chi$	$=$	891.379
Dual form			891.2.n.e.757.1

$q$-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 $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{3}\right)$

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	$-0.617055\pi$
$2$	−1.50964	−	0.320883i	−1.06747	−	0.226899i	−0.707968	+	0.706244i	$0.750388\pi$
$3$		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	$-0.454510\pi$
$5$	1.50964	−	0.320883i	0.675130	−	0.143503i	0.532703	+	0.846302i	$0.321176\pi$
$6$		0			0
$7$	−0.0246758	−	0.234775i	−0.00932658	−	0.0887365i	0.988868	−	0.148793i	$-0.0475387\pi$
$7$	−0.0246758	−	0.234775i	−0.00932658	−	0.0887365i	−0.998195	+	0.0600561i	$0.980872\pi$
$8$	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	−0.994477	−	0.104957i	$-0.966530\pi$
$13$	−2.83448	+	3.14801i	−0.786144	+	0.873101i	0.208333	+	0.978058i	$0.433196\pi$
$14$	−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	−0.435785	−	0.900051i	$-0.643529\pi$
$17$	1.83812	−	5.65714i	0.445809	−	1.37206i	0.881594	−	0.472008i	$-0.156471\pi$
$18$		0			0
$19$	3.73607	+	2.71441i	0.857113	+	0.622729i	0.927098	−	0.374819i	$-0.122295\pi$
$19$	3.73607	+	2.71441i	0.857113	+	0.622729i	−0.0699852	+	0.997548i	$0.522295\pi$
$20$	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	0.931326	+	0.364185i	$0.118653\pi$
$23$	3.74582	+	6.48795i	0.781057	+	1.35283i	−0.150269	+	0.988645i	$0.548014\pi$
$24$		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	0.997311	+	0.0732795i	$0.0233465\pi$
$29$	0.199409	+	1.89725i	0.0370293	+	0.352310i	−0.960282	+	0.279031i	$0.909987\pi$
$30$		0			0
$31$	−1.59385	+	1.77015i	−0.286263	+	0.317928i	−0.869076	−	0.494679i	$-0.835286\pi$
$31$	−1.59385	+	1.77015i	−0.286263	+	0.317928i	0.582812	+	0.812607i	$0.301952\pi$
$32$	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	−0.919391	−	0.393344i	$-0.871318\pi$
$37$	−5.04508	+	3.66547i	−0.829407	+	0.602599i	0.0899846	+	0.995943i	$0.471318\pi$
$38$	−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	−0.849423	−	0.527712i	$-0.823050\pi$
$41$	0.583680	−	5.55335i	0.0911555	−	0.867287i	0.940579	−	0.339575i	$-0.110283\pi$
$42$		0			0
$43$	5.35410	−	9.27358i	0.816493	−	1.41421i	−0.0917581	−	0.995781i	$-0.529249\pi$
$43$	5.35410	−	9.27358i	0.816493	−	1.41421i	0.908251	−	0.418426i	$-0.137418\pi$
$44$	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	$-0.655495\pi$
$47$	−0.871385	+	0.387966i	−0.127105	+	0.0565906i	0.342199	+	0.939628i	$0.388828\pi$
$48$		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	0.937558	+	0.347829i	$0.113081\pi$
$53$	2.79197	+	8.59279i	0.383506	+	1.18031i	−0.554052	+	0.832482i	$0.686919\pi$
$54$		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	$-0.181388\pi$
$59$	7.71534	+	3.43509i	1.00445	+	0.447210i	0.162468	+	0.986714i	$0.448055\pi$
$60$		0			0
$61$	2.89482	+	3.21502i	0.370643	+	0.411641i	0.899396	−	0.437135i	$-0.144007\pi$
$61$	2.89482	+	3.21502i	0.370643	+	0.411641i	−0.528753	+	0.848776i	$0.677340\pi$
$62$	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	0.723970	−	0.689832i	$-0.242315\pi$
$67$	−1.92705	−	3.33775i	−0.235427	−	0.407771i	−0.959397	+	0.282061i	$0.908982\pi$
$68$	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	−0.703987	−	0.710213i	$-0.748599\pi$
$71$	2.38463	−	7.33912i	0.283003	−	0.870994i	0.986990	−	0.160781i	$-0.0514012\pi$
$72$		0			0
$73$	5.23607	−	3.80423i	0.612835	−	0.445251i	−0.237576	−	0.971369i	$-0.576353\pi$
$73$	5.23607	−	3.80423i	0.612835	−	0.445251i	0.850412	+	0.526118i	$0.176353\pi$
$74$	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	0.236866	−	0.971542i	$-0.423880\pi$
$79$	0.516329	+	0.109749i	0.0580915	+	0.0123477i	−0.178774	+	0.983890i	$0.557213\pi$
$80$	−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	$-0.311055\pi$
$83$	−2.94746	−	3.27349i	−0.323526	−	0.359312i	−0.882865	+	0.469627i	$0.844388\pi$
$84$		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	$-0.152202\pi$
$89$	16.7518			1.77569			0.887844	+	0.460145i	$0.152202\pi$
$90$		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	0.793586	−	0.608458i	$-0.208212\pi$
$97$	12.5187	+	2.66093i	1.27108	+	0.270177i	0.477495	+	0.878634i	$0.341545\pi$
$98$	−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	$-0.256915\pi$
$101$	10.3472	+	2.19936i	1.02958	+	0.218845i	0.338004	+	0.941145i	$0.390248\pi$
$102$		0			0
$103$	6.34391	+	2.82449i	0.625084	+	0.278305i	0.694735	−	0.719266i	$-0.255522\pi$
$103$	6.34391	+	2.82449i	0.625084	+	0.278305i	−0.0696508	+	0.997571i	$0.522188\pi$
$104$	−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	$-0.450123\pi$
$107$	−7.60422	−	5.52479i	−0.735128	−	0.534102i	−0.891182	+	0.453647i	$0.850123\pi$
$108$		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	−0.786615	−	0.617444i	$-0.788168\pi$
$113$	1.18191	−	11.2451i	0.111184	−	1.05785i	0.897799	−	0.440405i	$-0.145165\pi$
$114$		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	0.801501	+	0.597994i	$0.204035\pi$
$127$	−2.23607	+	6.88191i	−0.198419	+	0.610671i	−0.999920	+	0.0126769i	$0.995965\pi$
$128$	−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	−0.999406	−	0.0344525i	$-0.989031\pi$
$131$	−6.06086	−	10.4977i	−0.529540	−	0.917190i	0.469866	−	0.882738i	$-0.344302\pi$
$132$		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	$-0.0840850\pi$
$137$	7.07830	+	7.86125i	0.604740	+	0.671632i	−0.360572	+	0.932732i	$0.617418\pi$
$138$		0			0
$139$	−12.4407	−	5.53895i	−1.05521	−	0.469808i	−0.195556	−	0.980692i	$-0.562651\pi$
$139$	−12.4407	−	5.53895i	−1.05521	−	0.469808i	−0.859649	+	0.510885i	$0.829318\pi$
$140$	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	$-0.377566\pi$
$149$	13.3665	−	2.84113i	1.09502	−	0.232754i	0.719801	+	0.694180i	$0.244233\pi$
$150$		0			0
$151$	−8.00625	+	3.56461i	−0.651539	+	0.290084i	−0.705766	−	0.708445i	$-0.749397\pi$
$151$	−8.00625	+	3.56461i	−0.651539	+	0.290084i	0.0542270	+	0.998529i	$0.482731\pi$
$152$	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	0.855764	+	0.517366i	$0.173087\pi$
$157$	−1.11349	+	10.5941i	−0.0888659	+	0.845503i	−0.944630	+	0.328137i	$0.893579\pi$
$158$	−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	0.985247	−	0.171141i	$-0.0547454\pi$
$163$	1.11803	+	3.44095i	0.0875712	+	0.269516i	−0.897675	+	0.440657i	$0.854745\pi$
$164$	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	$-0.863177\pi$
$167$	−5.16355	+	5.73471i	−0.399568	+	0.443765i	0.509464	+	0.860492i	$0.329844\pi$
$168$		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	$-0.666334\pi$
$173$	−2.48702	+	1.10729i	−0.189085	+	0.0841860i	0.310010	+	0.950733i	$0.399668\pi$
$174$		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	$-0.545633\pi$
$179$	−15.0959	−	10.9678i	−1.12832	−	0.819771i	−0.985449	+	0.169971i	$0.945633\pi$
$180$		0			0
$181$	2.39919	−	7.38394i	0.178330	−	0.548844i	−0.821440	−	0.570295i	$-0.806829\pi$
$181$	2.39919	−	7.38394i	0.178330	−	0.548844i	0.999770	+	0.0214515i	$0.00682876\pi$
$182$	−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	0.999589	+	0.0286731i	$0.00912819\pi$
$191$	0.384271	+	3.65610i	0.0278049	+	0.264546i	−0.971784	+	0.235873i	$0.924205\pi$
$192$		0			0
$193$	−9.40786	+	1.99970i	−0.677192	+	0.143942i	−0.533654	−	0.845703i	$-0.679181\pi$
$193$	−9.40786	+	1.99970i	−0.677192	+	0.143942i	−0.143539	+	0.989645i	$0.545848\pi$
$194$	−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	$-0.642128\pi$
$197$	−12.1217			−0.863637			−0.431818	+	0.901961i	$0.642128\pi$
$198$		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	−0.433304	−	0.901248i	$-0.642652\pi$
$211$	7.38348	−	8.20019i	0.508300	−	0.564524i	0.941603	+	0.336724i	$0.109319\pi$
$212$	−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	−0.898461	−	0.439054i	$-0.855314\pi$
$223$	−17.5221	+	7.80135i	−1.17337	+	0.522417i	−0.274907	+	0.961471i	$0.588647\pi$
$224$	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	0.977506	+	0.210906i	$0.0676414\pi$
$227$	0.982498	+	9.34785i	0.0652107	+	0.620438i	−0.912296	+	0.409532i	$0.865692\pi$
$228$		0			0
$229$	−6.37539	+	7.08058i	−0.421297	+	0.467898i	−0.916008	−	0.401160i	$-0.868607\pi$
$229$	−6.37539	+	7.08058i	−0.421297	+	0.467898i	0.494711	+	0.869058i	$0.335274\pi$
$230$	−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	$-0.143718\pi$
$233$	−1.29161	−	3.97517i	−0.0846162	−	0.260422i	−0.984409	+	0.175896i	$0.943718\pi$
$234$		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	−0.798351	−	0.602193i	$-0.794294\pi$
$239$	1.66588	−	15.8498i	0.107757	−	1.02524i	0.906108	−	0.423047i	$-0.139039\pi$
$240$		0			0
$241$	−7.00000	+	12.1244i	−0.450910	+	0.780998i	−0.998443	−	0.0557856i	$-0.982234\pi$
$241$	−7.00000	+	12.1244i	−0.450910	+	0.780998i	0.547533	+	0.836784i	$0.315567\pi$
$242$	−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	0.985528	+	0.169513i	$0.0542195\pi$
$251$	4.56050	+	14.0358i	0.287856	+	0.885931i	−0.697672	+	0.716418i	$0.745780\pi$
$252$		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	$-0.530666\pi$
$257$	−14.4322	−	6.42561i	−0.900253	−	0.400818i	−0.804063	+	0.594545i	$0.797332\pi$
$258$		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	$-0.787738\pi$
$263$	2.31504	−	4.00977i	0.142752	−	0.247253i	0.928532	+	0.371253i	$0.121072\pi$
$264$		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	0.291882	+	0.956454i	$0.405719\pi$
$269$	−8.30632	+	25.5642i	−0.506445	+	1.55868i	−0.798327	+	0.602224i	$0.794281\pi$
$270$		0			0
$271$	24.2984	−	17.6538i	1.47602	−	1.07239i	0.497209	−	0.867631i	$-0.334358\pi$
$271$	24.2984	−	17.6538i	1.47602	−	1.07239i	0.978812	−	0.204761i	$-0.0656418\pi$
$272$	−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	−0.477162	−	0.878815i	$-0.658335\pi$
$277$	−21.1456	−	4.49464i	−1.27052	−	0.270057i	−0.793356	+	0.608758i	$0.791668\pi$
$278$	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	$-0.148696\pi$
$281$	5.89492	+	6.54698i	0.351662	+	0.390560i	−0.541198	+	0.840895i	$0.682029\pi$
$282$		0			0
$283$	−0.725874	+	6.90623i	−0.0431487	+	0.410533i	0.951534	+	0.307544i	$0.0995072\pi$
$283$	−0.725874	+	6.90623i	−0.0431487	+	0.410533i	−0.994683	+	0.102989i	$0.967159\pi$
$284$	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	$-0.161526\pi$
$293$	18.7891	+	8.36544i	1.09767	+	0.488714i	0.223682	+	0.974662i	$0.428192\pi$
$294$		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	−0.654595	−	0.755979i	$-0.727161\pi$
$311$	2.51958	−	23.9722i	0.142872	−	1.35934i	0.797468	−	0.603361i	$-0.206172\pi$
$312$		0			0
$313$	0.232539	+	0.258261i	0.0131439	+	0.0145978i	0.749681	−	0.661799i	$-0.230207\pi$
$313$	0.232539	+	0.258261i	0.0131439	+	0.0145978i	−0.736537	+	0.676397i	$0.763540\pi$
$314$	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	$-0.337324\pi$
$317$	10.3472	+	2.19936i	0.581157	+	0.123529i	0.0920526	+	0.995754i	$0.470657\pi$
$318$		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	0.427541	+	0.903996i	$0.359380\pi$
$331$	−10.3541	+	17.9338i	−0.569113	+	0.985732i	−0.996654	+	0.0817366i	$0.973953\pi$
$332$	−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	0.519221	−	0.854640i	$-0.326222\pi$
$337$	4.25025	+	1.89233i	0.231526	+	0.103082i	−0.287695	+	0.957722i	$0.592889\pi$
$338$	−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	$-0.544123\pi$
$347$	2.57877	−	0.548134i	0.138435	−	0.0294254i	0.276608	+	0.960983i	$0.410790\pi$
$348$		0			0
$349$	−12.0408	+	5.36093i	−0.644531	+	0.286964i	−0.702854	−	0.711334i	$-0.748091\pi$
$349$	−12.0408	+	5.36093i	−0.644531	+	0.286964i	0.0583229	+	0.998298i	$0.481425\pi$
$350$	−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	$-0.803327\pi$
$353$	1.76854	−	3.06319i	0.0941296	−	0.163037i	0.909245	+	0.416261i	$0.136660\pi$
$354$		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	$-0.457566\pi$
$359$	21.1567	−	15.3713i	1.11661	−	0.811264i	0.983692	+	0.179863i	$0.0575655\pi$
$360$		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	0.998573	+	0.0534110i	$0.0170093\pi$
$367$	0.630771	+	6.00138i	0.0329260	+	0.313270i	−0.965647	+	0.259859i	$0.916324\pi$
$368$	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	0.659339	−	0.751846i	$-0.270836\pi$
$373$	−6.20820	−	10.7529i	−0.321449	−	0.556765i	−0.980787	+	0.195081i	$0.937503\pi$
$374$	−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	−0.936080	−	0.351786i	$-0.885574\pi$
$379$	0.545085	−	1.67760i	0.0279991	−	0.0861725i	0.964080	+	0.265613i	$0.0855745\pi$
$380$	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	$-0.884106\pi$
$383$	−9.44507	+	10.4898i	−0.482620	+	0.536004i	0.451827	+	0.892106i	$0.350772\pi$
$384$		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	−0.916478	−	0.400084i	$-0.868981\pi$
$389$	−2.03561	−	19.3675i	−0.103209	−	0.981972i	0.813269	−	0.581888i	$-0.197686\pi$
$390$		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	$-0.540314\pi$
$401$	3.23952	−	0.688582i	0.161774	−	0.0343862i	0.288087	+	0.957604i	$0.406981\pi$
$402$		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	−0.991580	−	0.129498i	$-0.958663\pi$
$409$	−15.3527	+	17.0509i	−0.759143	+	0.843114i	0.232437	+	0.972611i	$0.425330\pi$
$410$	−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	$-0.295122\pi$
$419$	−8.03814	−	13.9225i	−0.392689	−	0.680157i	−0.992803	+	0.119757i	$0.961788\pi$
$420$		0			0
$421$	20.2942	−	9.03557i	0.989079	−	0.440367i	0.152554	−	0.988295i	$-0.451250\pi$
$421$	20.2942	−	9.03557i	0.989079	−	0.440367i	0.836525	+	0.547929i	$0.184583\pi$
$422$	−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	$-0.0577275\pi$
$431$	1.69895	+	5.22884i	0.0818357	+	0.251864i	−0.901764	+	0.432228i	$0.857728\pi$
$432$		0			0
$433$	−23.1803	+	16.8415i	−1.11398	+	0.809351i	−0.983285	−	0.182072i	$-0.941720\pi$
$433$	−23.1803	+	16.8415i	−1.11398	+	0.809351i	−0.130691	+	0.991423i	$0.541720\pi$
$434$	−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	−0.396728	−	0.917936i	$-0.629854\pi$
$439$	12.5000	−	21.6506i	0.596592	−	1.03333i	0.993320	−	0.115392i	$-0.0368124\pi$
$440$	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	$-0.780690\pi$
$443$	−17.1734	+	7.64611i	−0.815935	+	0.363278i	−0.0440416	+	0.999030i	$0.514023\pi$
$444$		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	$-0.0966174\pi$
$449$	0.139165	+	0.428305i	0.00656760	+	0.0202130i	−0.947719	+	0.319106i	$0.896617\pi$
$450$		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	0.990274	−	0.139132i	$-0.0444312\pi$
$457$	15.9988	+	17.7685i	0.748392	+	0.831174i	−0.241882	+	0.970306i	$0.577765\pi$
$458$	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	$-0.682349\pi$
$461$	9.80668	−	16.9857i	0.456743	−	0.791101i	0.998787	+	0.0492488i	$0.0156827\pi$
$462$		0			0
$463$	0.718847	+	1.24508i	0.0334077	+	0.0578638i	0.882246	−	0.470789i	$-0.156031\pi$
$463$	0.718847	+	1.24508i	0.0334077	+	0.0578638i	−0.848838	+	0.528653i	$0.822697\pi$
$464$	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	$-0.864166\pi$
$467$	1.50036	−	4.61763i	0.0694283	−	0.213678i	0.979751	+	0.200222i	$0.0641663\pi$
$468$		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	−0.964771	−	0.263090i	$-0.915258\pi$
$479$	−24.6344	−	27.3593i	−1.12557	−	1.25008i	−0.160802	−	0.986987i	$-0.551408\pi$
$480$		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	0.852619	−	0.522533i	$-0.175013\pi$
$487$	13.6631	+	9.92684i	0.619135	+	0.449828i	−0.233484	+	0.972361i	$0.575013\pi$
$488$	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	$-0.120870\pi$
$491$	28.2472	+	12.5765i	1.27478	+	0.567568i	0.346010	+	0.938231i	$0.387536\pi$
$492$		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	0.197731	−	0.980256i	$-0.436643\pi$
$499$	−8.90035	−	3.96269i	−0.398434	−	0.177394i	−0.596165	+	0.802862i	$0.703310\pi$
$500$	−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	$-0.380094\pi$
$503$	−9.03500	−	6.56431i	−0.402851	−	0.292688i	−0.770701	+	0.637197i	$0.780094\pi$
$504$		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	0.958284	+	0.285819i	$0.0922657\pi$
$509$	−0.868247	+	8.26082i	−0.0384844	+	0.366154i	−0.996768	+	0.0803351i	$0.974401\pi$
$510$		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	$-0.661945\pi$
$521$	4.40491	−	3.20036i	0.192983	−	0.140210i	0.680081	+	0.733137i	$0.261945\pi$
$522$		0			0
$523$	5.70163	−	17.5478i	0.249315	−	0.767312i	−0.745582	−	0.666414i	$-0.767828\pi$
$523$	5.70163	−	17.5478i	0.249315	−	0.767312i	0.994897	−	0.100898i	$-0.0321716\pi$
$524$	−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	−0.761276	−	0.648428i	$-0.775427\pi$
$541$	−12.2467	−	37.6915i	−0.526527	−	1.62048i	0.234749	−	0.972056i	$-0.424573\pi$
$542$	−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	−0.575522	−	0.817786i	$-0.695201\pi$
$547$	−8.25337	+	3.67464i	−0.352889	+	0.157116i	0.222634	+	0.974902i	$0.428535\pi$
$548$	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	$-0.822394\pi$
$557$	−14.3242	+	10.4071i	−0.606935	+	0.440964i	0.241399	+	0.970426i	$0.422394\pi$
$558$		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	−0.185521	+	0.982640i	$0.559397\pi$
$563$	−27.1298	+	30.1307i	−1.14339	+	1.26986i	−0.957865	+	0.287219i	$0.907269\pi$
$564$		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	$-0.419533\pi$
$569$	27.1215	−	12.0753i	1.13699	−	0.506222i	0.886883	+	0.461995i	$0.152866\pi$
$570$		0			0
$571$	17.4894	+	30.2925i	0.731907	+	1.26770i	0.956067	+	0.293148i	$0.0947027\pi$
$571$	17.4894	+	30.2925i	0.731907	+	1.26770i	−0.224160	+	0.974552i	$0.571964\pi$
$572$	−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	0.487587	+	0.873074i	$0.337877\pi$
$577$	−10.0902	+	31.0543i	−0.420059	+	1.29281i	−0.907647	+	0.419735i	$0.862123\pi$
$578$	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	−0.996420	−	0.0845410i	$-0.973058\pi$
$587$	−0.953405	−	9.07104i	−0.0393512	−	0.374402i	0.957069	−	0.289861i	$-0.0936091\pi$
$588$		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	$-0.507144\pi$
$593$	−1.09301			−0.0448847			−0.0224424	+	0.999748i	$0.507144\pi$
$594$		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	$-0.647834\pi$
$599$	−12.0771	+	2.56706i	−0.493456	+	0.104887i	−0.0455394	+	0.998963i	$0.514501\pi$
$600$		0			0
$601$	−3.69620	−	35.1670i	−0.150771	−	1.43449i	−0.764322	−	0.644835i	$-0.776926\pi$
$601$	−3.69620	−	35.1670i	−0.150771	−	1.43449i	0.613551	−	0.789655i	$-0.289741\pi$
$602$	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	−0.985913	−	0.167261i	$-0.946508\pi$
$607$	−17.6530	+	19.6056i	−0.716512	+	0.795768i	0.269400	+	0.963028i	$0.413175\pi$
$608$	−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	−0.994262	−	0.106972i	$-0.965885\pi$
$613$	−34.7426	−	25.2420i	−1.40324	−	1.01952i	−0.408980	−	0.912543i	$-0.634115\pi$
$614$	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	$-0.178001\pi$
$617$	−0.884268	−	1.53160i	−0.0355993	−	0.0616598i	−0.883276	+	0.468853i	$0.844667\pi$
$618$		0			0
$619$	−26.3910	+	11.7500i	−1.06074	+	0.472274i	−0.861543	−	0.507685i	$-0.830501\pi$
$619$	−26.3910	+	11.7500i	−1.06074	+	0.472274i	−0.199201	+	0.979959i	$0.563835\pi$
$620$	−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	−0.225205	−	0.974311i	$-0.572305\pi$
$631$	15.8713	−	11.5312i	0.631827	−	0.459049i	0.857033	+	0.515262i	$0.172305\pi$
$632$	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	$-0.555485\pi$
$641$	11.2009	−	4.98695i	0.442408	−	0.196973i	0.615837	+	0.787874i	$0.288818\pi$
$642$		0			0
$643$	−27.5437	+	5.85460i	−1.08622	+	0.230883i	−0.716027	−	0.698073i	$-0.754041\pi$
$643$	−27.5437	+	5.85460i	−1.08622	+	0.230883i	−0.370191	+	0.928956i	$0.620708\pi$
$644$	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	−0.840084	−	0.542456i	$-0.817494\pi$
$647$	−12.1913	−	37.5210i	−0.479290	−	1.47510i	0.360794	−	0.932645i	$-0.382506\pi$
$648$		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	$-0.671625\pi$
$653$	−38.1953	−	17.0056i	−1.49470	−	0.665482i	−0.981268	+	0.192650i	$0.938292\pi$
$654$		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	$-0.811387\pi$
$659$	1.76854	−	3.06319i	0.0688924	−	0.119325i	0.898414	+	0.439150i	$0.144720\pi$
$660$		0			0
$661$	−11.2812	−	19.5395i	−0.438786	−	0.760000i	0.558810	−	0.829296i	$-0.311258\pi$
$661$	−11.2812	−	19.5395i	−0.438786	−	0.760000i	−0.997596	+	0.0692960i	$0.977925\pi$
$662$	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	−0.0590208	−	0.998257i	$-0.518798\pi$
$673$	−13.4632	−	2.86168i	−0.518967	−	0.110310i	−0.459946	+	0.887947i	$0.652131\pi$
$674$	−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	$-0.271184\pi$
$677$	−4.13084	−	4.58777i	−0.158761	−	0.176322i	−0.817278	+	0.576244i	$0.804518\pi$
$678$		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	$-0.707689\pi$
$683$	−31.7351			−1.21431			−0.607155	+	0.794584i	$0.707689\pi$
$684$		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	0.432057	−	0.901846i	$-0.357788\pi$
$691$	12.0906	+	2.56993i	0.459947	+	0.0977647i	0.0278899	+	0.999611i	$0.491121\pi$
$692$	−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	$-0.0416543\pi$
$701$	31.0760	+	22.5780i	1.17372	+	0.852760i	0.182274	+	0.983248i	$0.441654\pi$
$702$		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	−0.993846	−	0.110768i	$-0.964669\pi$
$709$	−26.6303	−	29.5760i	−1.00012	−	1.11075i	−0.00627600	−	0.999980i	$-0.501998\pi$
$710$	−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	$-0.930677\pi$
$719$	−28.7609	+	20.8960i	−1.07260	+	0.779291i	−0.0962240	+	0.995360i	$0.530677\pi$
$720$		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	−0.860765	−	0.509003i	$-0.830014\pi$
$727$	0.281153	−	0.486971i	0.0104274	−	0.0180608i	0.871192	+	0.490942i	$0.163347\pi$
$728$	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	0.667973	−	0.744185i	$-0.267162\pi$
$733$	15.2128	+	6.77317i	0.561897	+	0.250173i	−0.106076	+	0.994358i	$0.533829\pi$
$734$	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	0.998306	−	0.0581840i	$-0.0185310\pi$
$739$	4.25329	+	13.0903i	0.156460	+	0.481534i	−0.841846	+	0.539718i	$0.818531\pi$
$740$	−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	$-0.866444\pi$
$743$	−43.1187	+	9.16516i	−1.58187	+	0.336237i	−0.668610	+	0.743613i	$0.733111\pi$
$744$		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	0.672178	+	0.740390i	$0.265359\pi$
$751$	−3.81598	+	36.3066i	−0.139247	+	1.32485i	−0.811425	+	0.584457i	$0.801308\pi$
$752$	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	0.918240	−	0.396024i	$-0.129610\pi$
$757$	−1.57953	−	4.86128i	−0.0574089	−	0.176686i	−0.975649	+	0.219338i	$0.929610\pi$
$758$	−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	$-0.807402\pi$
$761$	−4.71154	+	5.23270i	−0.170793	+	0.189685i	0.651671	+	0.758502i	$0.274068\pi$
$762$		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	0.746349	−	0.665555i	$-0.231805\pi$
$769$	−5.63525	−	9.76055i	−0.203212	−	0.351974i	−0.949562	+	0.313580i	$0.898472\pi$
$770$	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	0.993773	+	0.111426i	$0.0355417\pi$
$773$	39.1141	+	28.4181i	1.40684	+	1.02213i	0.413065	+	0.910702i	$0.364458\pi$
$774$		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	0.633148	−	0.774031i	$-0.281762\pi$
$787$	42.8205	−	9.10177i	1.52638	−	0.324443i	0.893236	+	0.449588i	$0.148429\pi$
$788$	−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	$-0.584077\pi$
$797$	−3.01927	+	0.641766i	−0.106948	+	0.0227325i	0.154127	+	0.988051i	$0.450744\pi$
$798$		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	0.707648	+	0.706565i	$0.249756\pi$
$809$	−7.96856	+	24.5247i	−0.280160	+	0.862243i	−0.987808	+	0.155678i	$0.950244\pi$
$810$		0			0
$811$	−5.83688	−	4.24074i	−0.204961	−	0.148913i	0.480570	−	0.876956i	$-0.340430\pi$
$811$	−5.83688	−	4.24074i	−0.204961	−	0.148913i	−0.685531	+	0.728044i	$0.740430\pi$
$812$	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	0.901140	+	0.433528i	$0.142732\pi$
$821$	3.14690	+	29.9408i	0.109828	+	1.04494i	−0.791312	+	0.611412i	$0.790602\pi$
$822$		0			0
$823$	36.7276	−	40.7901i	1.28024	−	1.42185i	0.423681	−	0.905811i	$-0.360738\pi$
$823$	36.7276	−	40.7901i	1.28024	−	1.42185i	0.856562	−	0.516044i	$-0.172596\pi$
$824$	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	−0.955907	−	0.293669i	$-0.905124\pi$
$827$	−10.2140	−	31.4355i	−0.355176	−	1.09312i	0.600731	−	0.799451i	$-0.294876\pi$
$828$		0			0
$829$	7.30902	−	5.31031i	0.253853	−	0.184435i	−0.453580	−	0.891216i	$-0.649853\pi$
$829$	7.30902	−	5.31031i	0.253853	−	0.184435i	0.707433	+	0.706781i	$0.249853\pi$
$830$	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	$-0.316252\pi$
$839$	44.4221	−	19.7780i	1.53362	−	0.682812i	0.987891	+	0.155149i	$0.0495856\pi$
$840$		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	0.935197	−	0.354128i	$-0.115222\pi$
$853$	14.1724	+	15.7401i	0.485254	+	0.538929i	−0.449943	+	0.893057i	$0.648556\pi$
$854$	−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	0.268216	+	0.963359i	$0.413566\pi$
$857$	−20.4976	+	35.5029i	−0.700186	+	1.21276i	−0.968401	+	0.249398i	$0.919767\pi$
$858$		0			0
$859$	−7.79180	−	13.4958i	−0.265853	−	0.460470i	0.701934	−	0.712242i	$-0.252320\pi$
$859$	−7.79180	−	13.4958i	−0.265853	−	0.460470i	−0.967787	+	0.251772i	$0.918987\pi$
$860$	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	0.733100	+	0.680121i	$0.238073\pi$
$863$	−7.63080	+	23.4852i	−0.259755	+	0.799445i	−0.992855	+	0.119324i	$0.961927\pi$
$864$		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	−0.998077	−	0.0619871i	$-0.980256\pi$
$877$	−0.264234	+	2.51402i	−0.00892254	+	0.0848923i	0.989154	+	0.146879i	$0.0469229\pi$
$878$	−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	$-0.798051\pi$
$881$	−47.8114			−1.61081			−0.805403	+	0.592728i	$0.798051\pi$
$882$		0			0
$883$	40.3607	+	29.3238i	1.35825	+	0.986823i	0.998554	+	0.0537512i	$0.0171178\pi$
$883$	40.3607	+	29.3238i	1.35825	+	0.986823i	0.359691	+	0.933072i	$0.382882\pi$
$884$	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	$-0.455862\pi$
$887$	−15.0493	−	6.70037i	−0.505305	−	0.224976i	−0.643525	+	0.765425i	$0.722529\pi$
$888$		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	0.987450	+	0.157934i	$0.0504834\pi$
$907$	31.3603	+	34.8292i	1.04130	+	1.15648i	0.0538526	+	0.998549i	$0.482850\pi$
$908$	−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	$-0.649453\pi$
$911$	−37.0801	−	7.88163i	−1.22852	−	0.261130i	−0.776062	+	0.630656i	$0.782786\pi$
$912$		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	−0.964399	−	0.264453i	$-0.914809\pi$
$919$	−0.871323	+	2.68166i	−0.0287423	+	0.0884597i	0.935656	+	0.352912i	$0.114809\pi$
$920$	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	$-0.237865\pi$
$929$	−0.580699	−	0.644932i	−0.0190521	−	0.0211595i	−0.752596	+	0.658483i	$0.771198\pi$
$930$		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	0.966742	+	0.255755i	$0.0823241\pi$
$937$	10.2533	+	31.5564i	0.334960	+	1.03090i	−0.631781	+	0.775147i	$0.717676\pi$
$938$	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	$-0.830110\pi$
$941$	−44.1878	+	9.39241i	−1.44048	+	0.306184i	−0.579563	+	0.814927i	$0.696777\pi$
$942$		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	$-0.968385\pi$
$947$	−12.6682	+	21.9420i	−0.411662	+	0.713020i	0.583410	+	0.812178i	$0.301718\pi$
$948$		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	$-0.972084\pi$
$953$	−37.6834	+	27.3786i	−1.22068	+	0.886879i	−0.224527	+	0.974468i	$0.572084\pi$
$954$		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	−0.973008	−	0.230773i	$-0.925874\pi$
$967$	−21.3435	−	36.9680i	−0.686359	−	1.18881i	0.286648	−	0.958036i	$-0.407459\pi$
$968$	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	$-0.232716\pi$
$971$	10.5784	+	7.68563i	0.339476	+	0.246644i	−0.404965	+	0.914332i	$0.632716\pi$
$972$		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	$-0.615136\pi$
$977$	19.1695	−	21.2899i	0.613286	−	0.681124i	0.967160	+	0.254170i	$0.0818022\pi$
$978$		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	−0.838188	−	0.545381i	$-0.816385\pi$
$983$	−4.12940	−	39.2886i	−0.131707	−	1.25311i	0.706481	−	0.707732i	$-0.250282\pi$
$984$		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	0.998969	−	0.0454040i	$-0.0144575\pi$
$997$	0.391213	+	3.72214i	0.0123898	+	0.117881i	−0.986579	+	0.163285i	$0.947791\pi$
$998$	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.379.1		16
3.2	odd	2	inner	891.2.n.e.379.2		16
9.2	odd	6		99.2.f.c.82.1	yes	8
9.4	even	3	inner	891.2.n.e.676.2		16
9.5	odd	6	inner	891.2.n.e.676.1		16
9.7	even	3		99.2.f.c.82.2	yes	8
11.9	even	5	inner	891.2.n.e.460.2		16
33.20	odd	10	inner	891.2.n.e.460.1		16
99.20	odd	30		99.2.f.c.64.1	✓	8
99.25	even	15		1089.2.a.v.1.3		4
99.31	even	15	inner	891.2.n.e.757.1		16
99.47	odd	30		1089.2.a.v.1.2		4
99.52	odd	30		1089.2.a.w.1.2		4
99.74	even	30		1089.2.a.w.1.3		4
99.86	odd	30	inner	891.2.n.e.757.2		16
99.97	even	15		99.2.f.c.64.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.f.c.64.1	✓	8	99.20	odd	30
99.2.f.c.64.2	yes	8	99.97	even	15
99.2.f.c.82.1	yes	8	9.2	odd	6
99.2.f.c.82.2	yes	8	9.7	even	3
891.2.n.e.379.1		16	1.1	even	1	trivial
891.2.n.e.379.2		16	3.2	odd	2	inner
891.2.n.e.460.1		16	33.20	odd	10	inner
891.2.n.e.460.2		16	11.9	even	5	inner
891.2.n.e.676.1		16	9.5	odd	6	inner
891.2.n.e.676.2		16	9.4	even	3	inner
891.2.n.e.757.1		16	99.31	even	15	inner
891.2.n.e.757.2		16	99.86	odd	30	inner
1089.2.a.v.1.2		4	99.47	odd	30
1089.2.a.v.1.3		4	99.25	even	15
1089.2.a.w.1.2		4	99.52	odd	30
1089.2.a.w.1.3		4	99.74	even	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

Modular forms

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