LMFDB - Embedded newform 891.2.n.e.784.1

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			784.1
Root			$-0.224628 - 2.13719i$ of defining polynomial
Character	$\chi$	$=$	891.784
Dual form			891.2.n.e.433.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.224628 - 2.13719i) q^{2} +(-2.56082 + 0.544320i) q^{4} +(0.224628 - 2.13719i) q^{5} +(-2.83448 - 3.14801i) q^{7} +(0.410415 + 1.26313i) q^{8} -4.61803 q^{10} +(0.935653 - 3.18191i) q^{11} +(0.215659 + 0.0960175i) q^{13} +(-6.09119 + 6.76496i) q^{14} +(-2.17603 + 0.968833i) q^{16} +(4.96199 + 3.60510i) q^{17} +(-0.736068 - 2.26538i) q^{19} +(0.588083 + 5.59523i) q^{20} +(-7.01052 - 1.28492i) q^{22} +(-1.99220 - 3.45059i) q^{23} +(0.373619 + 0.0794152i) q^{25} +(0.156765 - 0.482472i) q^{26} +(8.97214 + 6.51864i) q^{28} +(4.65326 + 5.16797i) q^{29} +(-4.21878 - 1.87832i) q^{31} +(3.88751 + 6.73336i) q^{32} +(6.59017 - 11.4145i) q^{34} +(-7.36460 + 5.35069i) q^{35} +(0.545085 - 1.67760i) q^{37} +(-4.67621 + 2.08198i) q^{38} +(2.79173 - 0.593401i) q^{40} +(-1.98718 + 2.20699i) q^{41} +(-1.35410 + 2.34537i) q^{43} +(-0.664066 + 8.65761i) q^{44} +(-6.92705 + 5.03280i) q^{46} +(-3.40111 - 0.722928i) q^{47} +(-1.14399 + 10.8843i) q^{49} +(0.0858001 - 0.816334i) q^{50} +(-0.604528 - 0.128496i) q^{52} +(1.48490 - 1.07884i) q^{53} +(-6.59017 - 2.71441i) q^{55} +(2.81303 - 4.87231i) q^{56} +(9.99967 - 11.1058i) q^{58} +(7.29843 - 1.55133i) q^{59} +(-10.3470 + 4.60680i) q^{61} +(-3.06668 + 9.43826i) q^{62} +(9.66312 - 7.02067i) q^{64} +(0.253650 - 0.439335i) q^{65} +(1.42705 + 2.47172i) q^{67} +(-14.6691 - 6.53110i) q^{68} +(13.0897 + 14.5376i) q^{70} +(-8.69273 - 6.31564i) q^{71} +(0.763932 - 2.35114i) q^{73} +(-3.70779 - 0.788114i) q^{74} +(3.11803 + 5.40059i) q^{76} +(-12.6688 + 6.07362i) q^{77} +(0.990108 + 9.42025i) q^{79} +(1.58178 + 4.86822i) q^{80} +(5.16312 + 3.75123i) q^{82} +(7.56627 - 3.36872i) q^{83} +(8.81937 - 9.79490i) q^{85} +(5.31667 + 2.36714i) q^{86} +(4.40317 - 0.124055i) q^{88} +8.90937 q^{89} +(-0.309017 - 0.951057i) q^{91} +(6.97989 + 7.75195i) q^{92} +(-0.781051 + 7.43120i) q^{94} +(-5.00690 + 1.06425i) q^{95} +(-1.23327 - 11.7337i) q^{97} +23.5188 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.224628	−	2.13719i	−0.158836	−	1.51122i	−0.726045	−	0.687647i	$-0.758644\pi$
$2$	−0.224628	−	2.13719i	−0.158836	−	1.51122i	0.567209	−	0.823574i	$-0.308023\pi$
$3$		0			0
$3$		0			0
$4$	−2.56082	+	0.544320i	−1.28041	+	0.272160i
$5$	0.224628	−	2.13719i	0.100457	−	0.955780i	−0.821950	−	0.569560i	$-0.807114\pi$
$5$	0.224628	−	2.13719i	0.100457	−	0.955780i	0.922407	−	0.386220i	$-0.126220\pi$
$6$		0			0
$7$	−2.83448	−	3.14801i	−1.07133	−	1.18984i	−0.981017	−	0.193924i	$-0.937879\pi$
$7$	−2.83448	−	3.14801i	−1.07133	−	1.18984i	−0.0903171	−	0.995913i	$-0.528788\pi$
$8$	0.410415	+	1.26313i	0.145104	+	0.446583i
$9$		0			0
$10$	−4.61803			−1.46035
$11$	0.935653	−	3.18191i	0.282110	−	0.959382i
$11$	0.935653	−	3.18191i	0.282110	−	0.959382i
$12$		0			0
$13$	0.215659	+	0.0960175i	0.0598130	+	0.0266305i	0.436425	−	0.899741i	$-0.356244\pi$
$13$	0.215659	+	0.0960175i	0.0598130	+	0.0266305i	−0.376612	+	0.926371i	$0.622911\pi$
$14$	−6.09119	+	6.76496i	−1.62794	+	1.80801i
$15$		0			0
$16$	−2.17603	+	0.968833i	−0.544009	+	0.242208i
$17$	4.96199	+	3.60510i	1.20346	+	0.874364i	0.994620	−	0.103586i	$-0.0330318\pi$
$17$	4.96199	+	3.60510i	1.20346	+	0.874364i	0.208838	+	0.977950i	$0.433032\pi$
$18$		0			0
$19$	−0.736068	−	2.26538i	−0.168866	−	0.519715i	0.830435	−	0.557116i	$-0.188092\pi$
$19$	−0.736068	−	2.26538i	−0.168866	−	0.519715i	−0.999300	+	0.0374011i	$0.988092\pi$
$20$	0.588083	+	5.59523i	0.131499	+	1.25113i
$21$		0			0
$22$	−7.01052	−	1.28492i	−1.49465	−	0.273946i
$23$	−1.99220	−	3.45059i	−0.415402	−	0.719497i	0.580069	−	0.814567i	$-0.303026\pi$
$23$	−1.99220	−	3.45059i	−0.415402	−	0.719497i	−0.995471	+	0.0950706i	$0.969692\pi$
$24$		0			0
$25$	0.373619	+	0.0794152i	0.0747238	+	0.0158830i
$26$	0.156765	−	0.482472i	0.0307441	−	0.0946205i
$27$		0			0
$28$	8.97214	+	6.51864i	1.69557	+	1.23191i
$29$	4.65326	+	5.16797i	0.864088	+	0.959667i	0.999516	−	0.0311201i	$-0.00990742\pi$
$29$	4.65326	+	5.16797i	0.864088	+	0.959667i	−0.135427	+	0.990787i	$0.543241\pi$
$30$		0			0
$31$	−4.21878	−	1.87832i	−0.757716	−	0.337357i	−0.00874681	−	0.999962i	$-0.502784\pi$
$31$	−4.21878	−	1.87832i	−0.757716	−	0.337357i	−0.748969	+	0.662605i	$0.769451\pi$
$32$	3.88751	+	6.73336i	0.687221	+	1.19030i
$33$		0			0
$34$	6.59017	−	11.4145i	1.13020	−	1.95757i
$35$	−7.36460	+	5.35069i	−1.24484	+	0.904432i
$36$		0			0
$37$	0.545085	−	1.67760i	0.0896114	−	0.275796i	−0.896201	−	0.443649i	$-0.853684\pi$
$37$	0.545085	−	1.67760i	0.0896114	−	0.275796i	0.985812	+	0.167854i	$0.0536836\pi$
$38$	−4.67621	+	2.08198i	−0.758582	+	0.337742i
$39$		0			0
$40$	2.79173	−	0.593401i	0.441412	−	0.0938250i
$41$	−1.98718	+	2.20699i	−0.310345	+	0.344673i	−0.878059	−	0.478553i	$-0.841161\pi$
$41$	−1.98718	+	2.20699i	−0.310345	+	0.344673i	0.567714	+	0.823226i	$0.307828\pi$
$42$		0			0
$43$	−1.35410	+	2.34537i	−0.206499	+	0.357666i	−0.950609	−	0.310390i	$-0.899540\pi$
$43$	−1.35410	+	2.34537i	−0.206499	+	0.357666i	0.744111	+	0.668056i	$0.232874\pi$
$44$	−0.664066	+	8.65761i	−0.100112	+	1.30518i
$45$		0			0
$46$	−6.92705	+	5.03280i	−1.02134	+	0.742045i
$47$	−3.40111	−	0.722928i	−0.496103	−	0.105450i	−0.0469361	−	0.998898i	$-0.514946\pi$
$47$	−3.40111	−	0.722928i	−0.496103	−	0.105450i	−0.449167	+	0.893448i	$0.648279\pi$
$48$		0			0
$49$	−1.14399	+	10.8843i	−0.163427	+	1.55490i
$50$	0.0858001	−	0.816334i	0.0121340	−	0.115447i
$51$		0			0
$52$	−0.604528	−	0.128496i	−0.0838330	−	0.0178193i
$53$	1.48490	−	1.07884i	0.203966	−	0.148190i	−0.481113	−	0.876658i	$-0.659767\pi$
$53$	1.48490	−	1.07884i	0.203966	−	0.148190i	0.685079	+	0.728468i	$0.259767\pi$
$54$		0			0
$55$	−6.59017	−	2.71441i	−0.888618	−	0.366011i
$56$	2.81303	−	4.87231i	0.375906	−	0.651089i
$57$		0			0
$58$	9.99967	−	11.1058i	1.31302	−	1.45826i
$59$	7.29843	−	1.55133i	0.950175	−	0.201966i	0.293347	−	0.956006i	$-0.405231\pi$
$59$	7.29843	−	1.55133i	0.950175	−	0.201966i	0.656828	+	0.754040i	$0.271898\pi$
$60$		0			0
$61$	−10.3470	+	4.60680i	−1.32480	+	0.589840i	−0.942503	−	0.334199i	$-0.891534\pi$
$61$	−10.3470	+	4.60680i	−1.32480	+	0.589840i	−0.382299	+	0.924039i	$0.624868\pi$
$62$	−3.06668	+	9.43826i	−0.389468	+	1.19866i
$63$		0			0
$64$	9.66312	−	7.02067i	1.20789	−	0.877583i
$65$	0.253650	−	0.439335i	0.0314615	−	0.0544929i
$66$		0			0
$67$	1.42705	+	2.47172i	0.174342	+	0.301969i	0.939933	−	0.341358i	$-0.110887\pi$
$67$	1.42705	+	2.47172i	0.174342	+	0.301969i	−0.765591	+	0.643327i	$0.777553\pi$
$68$	−14.6691	−	6.53110i	−1.77889	−	0.792013i
$69$		0			0
$70$	13.0897	+	14.5376i	1.56452	+	1.73758i
$71$	−8.69273	−	6.31564i	−1.03164	−	0.749528i	−0.0630016	−	0.998013i	$-0.520067\pi$
$71$	−8.69273	−	6.31564i	−1.03164	−	0.749528i	−0.968636	+	0.248485i	$0.920067\pi$
$72$		0			0
$73$	0.763932	−	2.35114i	0.0894115	−	0.275180i	−0.896346	−	0.443356i	$-0.853788\pi$
$73$	0.763932	−	2.35114i	0.0894115	−	0.275180i	0.985757	+	0.168176i	$0.0537877\pi$
$74$	−3.70779	−	0.788114i	−0.431022	−	0.0916164i
$75$		0			0
$76$	3.11803	+	5.40059i	0.357663	+	0.619491i
$77$	−12.6688	+	6.07362i	−1.44374	+	0.692154i
$78$		0			0
$79$	0.990108	+	9.42025i	0.111396	+	1.05986i	0.897272	+	0.441477i	$0.145545\pi$
$79$	0.990108	+	9.42025i	0.111396	+	1.05986i	−0.785877	+	0.618383i	$0.787788\pi$
$80$	1.58178	+	4.86822i	0.176849	+	0.544284i
$81$		0			0
$82$	5.16312	+	3.75123i	0.570171	+	0.414254i
$83$	7.56627	−	3.36872i	0.830506	−	0.369765i	0.0529644	−	0.998596i	$-0.483133\pi$
$83$	7.56627	−	3.36872i	0.830506	−	0.369765i	0.777542	+	0.628831i	$0.216466\pi$
$84$		0			0
$85$	8.81937	−	9.79490i	0.956595	−	1.06241i
$86$	5.31667	+	2.36714i	0.573312	+	0.255255i
$87$		0			0
$88$	4.40317	−	0.124055i	0.469379	−	0.0132243i
$89$	8.90937			0.944392			0.472196	−	0.881494i	$-0.343462\pi$
$89$	8.90937			0.944392			0.472196	+	0.881494i	$0.343462\pi$
$90$		0			0
$91$	−0.309017	−	0.951057i	−0.0323938	−	0.0996978i
$92$	6.97989	+	7.75195i	0.727703	+	0.808197i
$93$		0			0
$94$	−0.781051	+	7.43120i	−0.0805592	+	0.766470i
$95$	−5.00690	+	1.06425i	−0.513697	+	0.109190i
$96$		0			0
$97$	−1.23327	−	11.7337i	−0.125219	−	1.19138i	−0.858993	−	0.511987i	$-0.828910\pi$
$97$	−1.23327	−	11.7337i	−0.125219	−	1.19138i	0.733774	−	0.679394i	$-0.237757\pi$
$98$	23.5188			2.37576
$99$		0			0
$100$	−1.00000			−0.100000
$101$	0.0327727	+	0.311812i	0.00326101	+	0.0310264i	0.996031	−	0.0890025i	$-0.0283679\pi$
$101$	0.0327727	+	0.311812i	0.00326101	+	0.0310264i	−0.992770	+	0.120029i	$0.961701\pi$
$102$		0			0
$103$	10.7051	−	2.27544i	1.05481	−	0.224206i	0.352303	−	0.935886i	$-0.385399\pi$
$103$	10.7051	−	2.27544i	1.05481	−	0.224206i	0.702504	+	0.711680i	$0.252065\pi$
$104$	−0.0327727	+	0.311812i	−0.00321363	+	0.0305756i
$105$		0			0
$106$	−2.63923	−	2.93117i	−0.256345	−	0.284700i
$107$	−3.38021	−	10.4032i	−0.326777	−	1.00572i	−0.970632	−	0.240569i	$-0.922666\pi$
$107$	−3.38021	−	10.4032i	−0.326777	−	1.00572i	0.643855	−	0.765147i	$-0.277334\pi$
$108$		0			0
$109$	−13.7082			−1.31301			−0.656504	−	0.754323i	$-0.727965\pi$
$109$	−13.7082			−1.31301			−0.656504	+	0.754323i	$0.727965\pi$
$110$	−4.32088	+	14.6942i	−0.411980	+	1.40103i
$111$		0			0
$112$	9.21783	+	4.10404i	0.871003	+	0.387796i
$113$	11.9726	−	13.2969i	1.12629	−	1.25087i	0.161775	−	0.986828i	$-0.448278\pi$
$113$	11.9726	−	13.2969i	1.12629	−	1.25087i	0.964512	−	0.264041i	$-0.0850554\pi$
$114$		0			0
$115$	−7.82206	+	3.48260i	−0.729410	+	0.324754i
$116$	−14.7292	−	10.7014i	−1.36757	−	0.993599i
$117$		0			0
$118$	−4.95492	−	15.2497i	−0.456137	−	1.40385i
$119$	−2.71579	−	25.8390i	−0.248956	−	2.36866i
$120$		0			0
$121$	−9.24911	−	5.95433i	−0.840828	−	0.541303i
$122$	12.1698	+	21.0788i	1.10180	+	1.90838i
$123$		0			0
$124$	11.8260	+	2.51369i	1.06200	+	0.225736i
$125$	3.57398	−	10.9996i	0.319666	−	0.983832i
$126$		0			0
$127$	2.23607	+	1.62460i	0.198419	+	0.144160i	0.682558	−	0.730831i	$-0.260867\pi$
$127$	2.23607	+	1.62460i	0.198419	+	0.144160i	−0.484139	+	0.874991i	$0.660867\pi$
$128$	−6.77009	−	7.51895i	−0.598397	−	0.664588i
$129$		0			0
$130$	−0.995920	−	0.443412i	−0.0873479	−	0.0388898i
$131$	−1.23125	−	2.13258i	−0.107574	−	0.186324i	0.807213	−	0.590261i	$-0.200975\pi$
$131$	−1.23125	−	2.13258i	−0.107574	−	0.186324i	−0.914787	+	0.403936i	$0.867642\pi$
$132$		0			0
$133$	−5.04508	+	8.73834i	−0.437464	+	0.757710i
$134$	4.96199	−	3.60510i	0.428650	−	0.311433i
$135$		0			0
$136$	−2.51722	+	7.74721i	−0.215850	+	0.664318i
$137$	0.286423	−	0.127524i	0.0244708	−	0.0108951i	−0.394465	−	0.918911i	$-0.629070\pi$
$137$	0.286423	−	0.127524i	0.0244708	−	0.0108951i	0.418936	+	0.908016i	$0.362403\pi$
$138$		0			0
$139$	11.1332	−	2.36644i	0.944309	−	0.200719i	0.290069	−	0.957006i	$-0.406322\pi$
$139$	11.1332	−	2.36644i	0.944309	−	0.200719i	0.654240	+	0.756287i	$0.272988\pi$
$140$	15.9470	−	17.7109i	1.34776	−	1.49684i
$141$		0			0
$142$	−11.5451	+	19.9967i	−0.968842	+	1.67808i
$143$	0.507301	−	0.596368i	0.0424226	−	0.0498708i
$144$		0			0
$145$	12.0902	−	8.78402i	1.00403	−	0.729473i
$146$	−5.19643	−	1.10454i	−0.430060	−	0.0914120i
$147$		0			0
$148$	−0.482716	+	4.59274i	−0.0396790	+	0.377521i
$149$	0.482028	−	4.58619i	0.0394893	−	0.375715i	−0.956874	−	0.290504i	$-0.906177\pi$
$149$	0.482028	−	4.58619i	0.0394893	−	0.375715i	0.996363	−	0.0852109i	$-0.0271564\pi$
$150$		0			0
$151$	12.9468	+	2.75193i	1.05360	+	0.223949i	0.701982	−	0.712195i	$-0.252299\pi$
$151$	12.9468	+	2.75193i	1.05360	+	0.223949i	0.351616	+	0.936144i	$0.385632\pi$
$152$	2.55938	−	1.85950i	0.207593	−	0.150825i
$153$		0			0
$154$	15.8262	+	25.7113i	1.27531	+	2.07187i
$155$	−4.96199	+	8.59441i	−0.398556	+	0.690320i
$156$		0			0
$157$	−13.8192	+	15.3478i	−1.10289	+	1.22489i	−0.130521	+	0.991445i	$0.541665\pi$
$157$	−13.8192	+	15.3478i	−1.10289	+	1.22489i	−0.972371	+	0.233441i	$0.925002\pi$
$158$	19.9104	−	4.23209i	1.58399	−	0.336687i
$159$		0			0
$160$	15.2637	−	6.79584i	1.20670	−	0.537258i
$161$	−5.21564	+	16.0521i	−0.411050	+	1.26508i
$162$		0			0
$163$	−1.11803	+	0.812299i	−0.0875712	+	0.0636242i	−0.630709	−	0.776019i	$-0.717236\pi$
$163$	−1.11803	+	0.812299i	−0.0875712	+	0.0636242i	0.543138	+	0.839643i	$0.317236\pi$
$164$	3.88751	−	6.73336i	0.303563	−	0.525787i
$165$		0			0
$166$	−8.89919	−	15.4138i	−0.690711	−	1.19635i
$167$	−9.81587	−	4.37031i	−0.759575	−	0.338184i	−0.00986504	−	0.999951i	$-0.503140\pi$
$167$	−9.81587	−	4.37031i	−0.759575	−	0.338184i	−0.749710	+	0.661767i	$0.769807\pi$
$168$		0			0
$169$	−8.66141	−	9.61947i	−0.666262	−	0.739959i
$170$	−22.9146	−	16.6485i	−1.75747	−	1.27688i
$171$		0			0
$172$	2.19098	−	6.74315i	0.167061	−	0.514161i
$173$	13.1082	+	2.78624i	0.996600	+	0.211834i	0.677210	−	0.735790i	$-0.263189\pi$
$173$	13.1082	+	2.78624i	0.996600	+	0.211834i	0.319390	+	0.947623i	$0.396522\pi$
$174$		0			0
$175$	−0.809017	−	1.40126i	−0.0611559	−	0.105925i
$176$	1.04673	+	7.83044i	0.0789000	+	0.590241i
$177$		0			0
$178$	−2.00129	−	19.0410i	−0.150003	−	1.42718i
$179$	0.604187	+	1.85950i	0.0451590	+	0.138985i	0.971094	−	0.238698i	$-0.0767207\pi$
$179$	0.604187	+	1.85950i	0.0451590	+	0.138985i	−0.925935	+	0.377684i	$0.876721\pi$
$180$		0			0
$181$	−9.89919	−	7.19218i	−0.735801	−	0.534591i	0.155592	−	0.987821i	$-0.450271\pi$
$181$	−9.89919	−	7.19218i	−0.735801	−	0.534591i	−0.891393	+	0.453231i	$0.850271\pi$
$182$	−1.96317	+	0.874061i	−0.145520	+	0.0647897i
$183$		0			0
$184$	3.54090	−	3.93257i	0.261039	−	0.289913i
$185$	−3.46290	−	1.54178i	−0.254598	−	0.113354i
$186$		0			0
$187$	16.1138	−	12.4155i	1.17836	−	0.907910i
$188$	9.10315			0.663915
$189$		0			0
$190$	3.39919	+	10.4616i	0.246603	+	0.758966i
$191$	−6.64044	−	7.37495i	−0.480485	−	0.533633i	0.453352	−	0.891332i	$-0.350228\pi$
$191$	−6.64044	−	7.37495i	−0.480485	−	0.533633i	−0.933837	+	0.357699i	$0.883561\pi$
$192$		0			0
$193$	−0.771626	+	7.34153i	−0.0555428	+	0.528455i	0.931008	+	0.364999i	$0.118931\pi$
$193$	−0.771626	+	7.34153i	−0.0555428	+	0.528455i	−0.986551	+	0.163456i	$0.947736\pi$
$194$	−24.8002	+	5.27144i	−1.78055	+	0.378468i
$195$		0			0
$196$	−2.99500	−	28.4955i	−0.213929	−	2.03539i
$197$	−2.46249			−0.175445			−0.0877226	−	0.996145i	$-0.527959\pi$
$197$	−2.46249			−0.175445			−0.0877226	+	0.996145i	$0.527959\pi$
$198$		0			0
$199$	0.416408			0.0295184			0.0147592	−	0.999891i	$-0.495302\pi$
$199$	0.416408			0.0295184			0.0147592	+	0.999891i	$0.495302\pi$
$200$	0.0530274	+	0.504522i	0.00374960	+	0.0356751i
$201$		0			0
$202$	0.659039	−	0.140083i	0.0463698	−	0.00985621i
$203$	3.07924	−	29.2970i	0.216120	−	2.05625i
$204$		0			0
$205$	4.27037	+	4.74273i	0.298255	+	0.331246i
$206$	−7.26771	−	22.3677i	−0.506366	−	1.55843i
$207$		0			0
$208$	−0.562306			−0.0389889
$209$	−7.89695	+	0.222489i	−0.546244	+	0.0153899i
$210$		0			0
$211$	−16.4753	−	7.33527i	−1.13421	−	0.504981i	−0.248224	−	0.968703i	$-0.579847\pi$
$211$	−16.4753	−	7.33527i	−1.13421	−	0.504981i	−0.885981	+	0.463722i	$0.846514\pi$
$212$	−3.21532	+	3.57098i	−0.220829	+	0.245256i
$213$		0			0
$214$	−21.4743	+	9.56099i	−1.46795	+	0.653576i
$215$	4.70834	+	3.42081i	0.321106	+	0.233297i
$216$		0			0
$217$	6.04508	+	18.6049i	0.410367	+	1.26298i
$218$	3.07924	+	29.2970i	0.208553	+	1.98424i
$219$		0			0
$220$	18.3538	+	3.36397i	1.23741	+	0.226799i
$221$	0.723944	+	1.25391i	0.0486978	+	0.0843470i
$222$		0			0
$223$	−3.11084	−	0.661230i	−0.208317	−	0.0442792i	0.102571	−	0.994726i	$-0.467293\pi$
$223$	−3.11084	−	0.661230i	−0.208317	−	0.0442792i	−0.310888	+	0.950446i	$0.600626\pi$
$224$	10.1776	−	31.3235i	0.680021	−	2.09289i
$225$		0			0
$226$	−31.1074	−	22.6008i	−2.06923	−	1.50339i
$227$	7.31934	+	8.12895i	0.485801	+	0.539537i	0.935352	−	0.353718i	$-0.115083\pi$
$227$	7.31934	+	8.12895i	0.485801	+	0.539537i	−0.449551	+	0.893255i	$0.648416\pi$
$228$		0			0
$229$	−16.8751	−	7.51329i	−1.11514	−	0.496492i	−0.235377	−	0.971904i	$-0.575632\pi$
$229$	−16.8751	−	7.51329i	−1.11514	−	0.496492i	−0.879763	+	0.475412i	$0.842299\pi$
$230$	9.20003	+	15.9349i	0.606632	+	1.05072i
$231$		0			0
$232$	−4.61803	+	7.99867i	−0.303189	+	0.525138i
$233$	−18.6167	+	13.5258i	−1.21962	+	0.886106i	−0.996069	−	0.0885854i	$-0.971765\pi$
$233$	−18.6167	+	13.5258i	−1.21962	+	0.886106i	−0.223552	+	0.974692i	$0.571765\pi$
$234$		0			0
$235$	−2.30902	+	7.10642i	−0.150624	+	0.463572i
$236$	−17.8456	+	7.94537i	−1.16165	+	0.517199i
$237$		0			0
$238$	−54.6127	+	11.6083i	−3.54002	+	0.752454i
$239$	7.65879	−	8.50595i	0.495406	−	0.550204i	−0.442647	−	0.896696i	$-0.645961\pi$
$239$	7.65879	−	8.50595i	0.495406	−	0.550204i	0.938053	+	0.346492i	$0.112627\pi$
$240$		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	$0.315567\pi$
$242$	−10.6479	+	21.1046i	−0.684474	+	1.35665i
$243$		0			0
$244$	23.9894	−	17.4293i	1.53576	−	1.11580i
$245$	23.0049	+	4.88984i	1.46973	+	0.312400i
$246$		0			0
$247$	0.0587770	−	0.559226i	0.00373989	−	0.0355827i
$248$	0.641110	−	6.09976i	0.0407105	−	0.387335i
$249$		0			0
$250$	−24.3110	−	5.16746i	−1.53756	−	0.326819i
$251$	18.3631	−	13.3415i	1.15907	−	0.842111i	0.169406	−	0.985546i	$-0.445815\pi$
$251$	18.3631	−	13.3415i	1.15907	−	0.842111i	0.989660	+	0.143436i	$0.0458150\pi$
$252$		0			0
$253$	−12.8435	+	3.11044i	−0.807461	+	0.195552i
$254$	2.96979	−	5.14383i	0.186341	−	0.322753i
$255$		0			0
$256$	1.43589	−	1.59471i	0.0897429	−	0.0996696i
$257$	12.1158	−	2.57529i	0.755762	−	0.160642i	0.186111	−	0.982529i	$-0.440412\pi$
$257$	12.1158	−	2.57529i	0.755762	−	0.160642i	0.569651	+	0.821886i	$0.307078\pi$
$258$		0			0
$259$	−6.82614	+	3.03919i	−0.424155	+	0.188846i
$260$	−0.410415	+	1.26313i	−0.0254529	+	0.0783359i
$261$		0			0
$262$	−4.28115	+	3.11044i	−0.264491	+	0.192164i
$263$	3.22344	−	5.58316i	0.198766	−	0.344273i	−0.749363	−	0.662160i	$-0.769640\pi$
$263$	3.22344	−	5.58316i	0.198766	−	0.344273i	0.948129	+	0.317887i	$0.102973\pi$
$264$		0			0
$265$	−1.97214	−	3.41584i	−0.121147	−	0.209833i
$266$	19.8088	+	8.81943i	1.21455	+	0.540754i
$267$		0			0
$268$	−4.99983	−	5.55288i	−0.305414	−	0.339196i
$269$	−16.3709	−	11.8941i	−0.998149	−	0.725198i	−0.0364584	−	0.999335i	$-0.511608\pi$
$269$	−16.3709	−	11.8941i	−0.998149	−	0.725198i	−0.961690	+	0.274138i	$0.911608\pi$
$270$		0			0
$271$	−0.298374	+	0.918300i	−0.0181249	+	0.0557828i	−0.959710	−	0.280993i	$-0.909336\pi$
$271$	−0.298374	+	0.918300i	−0.0181249	+	0.0557828i	0.941585	+	0.336775i	$0.109336\pi$
$272$	−14.2902	−	3.03747i	−0.866470	−	0.184174i
$273$		0			0
$274$	−0.336881	−	0.583495i	−0.0203517	−	0.0352502i
$275$	0.602270	−	1.11452i	0.0363182	−	0.0672079i
$276$		0			0
$277$	−2.02597	−	19.2758i	−0.121729	−	1.15817i	−0.869403	−	0.494104i	$-0.835496\pi$
$277$	−2.02597	−	19.2758i	−0.121729	−	1.15817i	0.747674	−	0.664066i	$-0.231171\pi$
$278$	−7.55837	−	23.2623i	−0.453321	−	1.39518i
$279$		0			0
$280$	−9.78115	−	7.10642i	−0.584536	−	0.424690i
$281$	−15.1325	+	6.73744i	−0.902732	+	0.401922i	−0.804989	−	0.593290i	$-0.797829\pi$
$281$	−15.1325	+	6.73744i	−0.902732	+	0.401922i	−0.0977427	+	0.995212i	$0.531162\pi$
$282$		0			0
$283$	−7.32315	+	8.13318i	−0.435316	+	0.483467i	−0.920388	−	0.391007i	$-0.872127\pi$
$283$	−7.32315	+	8.13318i	−0.435316	+	0.483467i	0.485072	+	0.874474i	$0.338793\pi$
$284$	25.6983	+	11.4416i	1.52491	+	0.678935i
$285$		0			0
$286$	−1.38850	−	0.950237i	−0.0821040	−	0.0561887i
$287$	12.5802			0.742588
$288$		0			0
$289$	6.37132	+	19.6089i	0.374784	+	1.15347i
$290$	−21.4889	−	23.8658i	−1.26187	−	1.40145i
$291$		0			0
$292$	−0.676522	+	6.43668i	−0.0395905	+	0.376678i
$293$	4.88975	−	1.03935i	0.285663	−	0.0607194i	−0.0628519	−	0.998023i	$-0.520020\pi$
$293$	4.88975	−	1.03935i	0.285663	−	0.0607194i	0.348514	+	0.937303i	$0.386686\pi$
$294$		0			0
$295$	−1.67606	−	15.9466i	−0.0975837	−	0.928447i
$296$	2.34273			0.136169
$297$		0			0
$298$	−9.90983			−0.574061
$299$	−0.0983182	−	0.935435i	−0.00568589	−	0.0540976i
$300$		0			0
$301$	11.2214	−	2.38519i	0.646793	−	0.137480i
$302$	2.97319	−	28.2880i	0.171088	−	1.62779i
$303$		0			0
$304$	3.79649	+	4.21643i	0.217744	+	0.241829i
$305$	7.52136	+	23.1484i	0.430672	+	1.32547i
$306$		0			0
$307$	17.2705			0.985680			0.492840	−	0.870120i	$-0.335959\pi$
$307$	17.2705			0.985680			0.492840	+	0.870120i	$0.335959\pi$
$308$	29.1365	−	22.4493i	1.66021	−	1.27917i
$309$		0			0
$310$	19.4825	+	8.67416i	1.10653	+	0.492659i
$311$	−19.2424	+	21.3709i	−1.09114	+	1.21183i	−0.115300	+	0.993331i	$0.536783\pi$
$311$	−19.2424	+	21.3709i	−1.09114	+	1.21183i	−0.975837	+	0.218499i	$0.929884\pi$
$312$		0			0
$313$	28.9160	−	12.8742i	1.63443	−	0.727694i	0.635417	−	0.772169i	$-0.280828\pi$
$313$	28.9160	−	12.8742i	1.63443	−	0.727694i	0.999010	+	0.0444751i	$0.0141615\pi$
$314$	35.9053	+	26.0867i	2.02625	+	1.47216i
$315$		0			0
$316$	−7.66312	−	23.5847i	−0.431084	−	1.32674i
$317$	0.0327727	+	0.311812i	0.00184070	+	0.0175131i	0.995404	−	0.0957679i	$-0.0305306\pi$
$317$	0.0327727	+	0.311812i	0.00184070	+	0.0175131i	−0.993563	+	0.113281i	$0.963864\pi$
$318$		0			0
$319$	20.7978	−	9.97082i	1.16446	−	0.558259i
$320$	−12.8339	−	22.2289i	−0.717436	−	1.24264i
$321$		0			0
$322$	35.4779	+	7.54106i	1.97711	+	0.420247i
$323$	4.51457	−	13.8944i	0.251197	−	0.773105i
$324$		0			0
$325$	0.0729490	+	0.0530006i	0.00404648	+	0.00293994i
$326$	1.98718	+	2.20699i	0.110060	+	0.122234i
$327$		0			0
$328$	−3.60327	−	1.60428i	−0.198957	−	0.0885815i
$329$	7.36460	+	12.7559i	0.406024	+	0.703253i
$330$		0			0
$331$	−3.64590	+	6.31488i	−0.200397	+	0.347097i	−0.948656	−	0.316309i	$-0.897556\pi$
$331$	−3.64590	+	6.31488i	−0.200397	+	0.347097i	0.748260	+	0.663406i	$0.230890\pi$
$332$	−17.5422	+	12.7452i	−0.962755	+	0.699482i
$333$		0			0
$334$	−7.13525	+	21.9601i	−0.390424	+	1.20160i
$335$	5.60310	−	2.49466i	0.306130	−	0.136298i
$336$		0			0
$337$	26.0701	−	5.54136i	1.42013	−	0.301857i	0.567067	−	0.823671i	$-0.308078\pi$
$337$	26.0701	−	5.54136i	1.42013	−	0.301857i	0.853059	+	0.521814i	$0.174745\pi$
$338$	−18.6130	+	20.6719i	−1.01242	+	1.12440i
$339$		0			0
$340$	−17.2533	+	29.8836i	−0.935691	+	1.62066i
$341$	−9.92398	+	11.6663i	−0.537413	+	0.631767i
$342$		0			0
$343$	13.5172	−	9.82084i	0.729861	−	0.530275i
$344$	−3.51825	−	0.747827i	−0.189691	−	0.0403201i
$345$		0			0
$346$	3.01025	−	28.6406i	0.161832	−	1.53973i
$347$	−2.62999	+	25.0226i	−0.141185	+	1.34329i	0.662872	+	0.748733i	$0.269338\pi$
$347$	−2.62999	+	25.0226i	−0.141185	+	1.34329i	−0.804057	+	0.594553i	$0.797329\pi$
$348$		0			0
$349$	−8.97973	−	1.90870i	−0.480674	−	0.102170i	−0.0387989	−	0.999247i	$-0.512353\pi$
$349$	−8.97973	−	1.90870i	−0.480674	−	0.102170i	−0.441875	+	0.897077i	$0.645686\pi$
$350$	−2.81303	+	2.04378i	−0.150363	+	0.109245i
$351$		0			0
$352$	25.0623	−	6.06961i	1.33583	−	0.323511i
$353$	16.8782	−	29.2338i	0.898334	−	1.55596i	0.0687102	−	0.997637i	$-0.478112\pi$
$353$	16.8782	−	29.2338i	0.898334	−	1.55596i	0.829624	−	0.558323i	$-0.188555\pi$
$354$		0			0
$355$	−15.4503	+	17.1593i	−0.820019	+	0.910723i
$356$	−22.8153	+	4.84955i	−1.20921	+	0.257026i
$357$		0			0
$358$	3.83838	−	1.70896i	0.202864	−	0.0903211i
$359$	0.627058	−	1.92989i	0.0330949	−	0.101856i	−0.933145	−	0.359501i	$-0.882947\pi$
$359$	0.627058	−	1.92989i	0.0330949	−	0.101856i	0.966239	+	0.257646i	$0.0829468\pi$
$360$		0			0
$361$	10.7812	−	7.83297i	0.567429	−	0.412261i
$362$	−13.1474	+	22.7720i	−0.691013	+	1.19687i
$363$		0			0
$364$	1.30902	+	2.26728i	0.0686111	+	0.118838i
$365$	−4.85323	−	2.16080i	−0.254030	−	0.113101i
$366$		0			0
$367$	15.4131	+	17.1179i	0.804555	+	0.893548i	0.996127	−	0.0879301i	$-0.0280252\pi$
$367$	15.4131	+	17.1179i	0.804555	+	0.893548i	−0.191572	+	0.981479i	$0.561359\pi$
$368$	7.67813	+	5.57849i	0.400250	+	0.290799i
$369$		0			0
$370$	−2.51722	+	7.74721i	−0.130864	+	0.402758i
$371$	−7.60511	−	1.61652i	−0.394838	−	0.0839253i
$372$		0			0
$373$	7.20820	+	12.4850i	0.373227	+	0.646448i	0.990060	−	0.140646i	$-0.0449180\pi$
$373$	7.20820	+	12.4850i	0.373227	+	0.646448i	−0.616833	+	0.787094i	$0.711585\pi$
$374$	−30.1538	−	31.6494i	−1.55922	−	1.63655i
$375$		0			0
$376$	−0.482716	−	4.59274i	−0.0248942	−	0.236852i
$377$	0.507301	+	1.56131i	0.0261273	+	0.0804116i
$378$		0			0
$379$	−5.04508	−	3.66547i	−0.259149	−	0.188282i	0.450623	−	0.892714i	$-0.351202\pi$
$379$	−5.04508	−	3.66547i	−0.259149	−	0.188282i	−0.709772	+	0.704432i	$0.751202\pi$
$380$	12.2425	−	5.45071i	0.628026	−	0.279615i
$381$		0			0
$382$	−14.2700	+	15.8485i	−0.730119	+	0.810879i
$383$	−31.1244	−	13.8575i	−1.59038	−	0.708083i	−0.594967	−	0.803750i	$-0.702835\pi$
$383$	−31.1244	−	13.8575i	−1.59038	−	0.708083i	−0.995413	+	0.0956673i	$0.969502\pi$
$384$		0			0
$385$	10.1347	+	28.4399i	0.516513	+	1.44943i
$386$	15.8636			0.807434
$387$		0			0
$388$	9.54508	+	29.3768i	0.484578	+	1.49138i
$389$	14.9286	+	16.5799i	0.756910	+	0.840634i	0.991315	−	0.131505i	$-0.0419810\pi$
$389$	14.9286	+	16.5799i	0.756910	+	0.840634i	−0.234405	+	0.972139i	$0.575314\pi$
$390$		0			0
$391$	2.55443	−	24.3038i	0.129183	−	1.22910i
$392$	−14.2178	+	3.02209i	−0.718107	+	0.152638i
$393$		0			0
$394$	0.553143	+	5.26281i	0.0278670	+	0.265136i
$395$	20.3553			1.02418
$396$		0			0
$397$	24.4164			1.22542			0.612712	−	0.790306i	$-0.290078\pi$
$397$	24.4164			1.22542			0.612712	+	0.790306i	$0.290078\pi$
$398$	−0.0935367	−	0.889942i	−0.00468857	−	0.0446088i
$399$		0			0
$400$	−0.889948	+	0.189164i	−0.0444974	+	0.00945822i
$401$	1.98888	−	18.9229i	0.0993197	−	0.944964i	−0.825460	−	0.564461i	$-0.809084\pi$
$401$	1.98888	−	18.9229i	0.0993197	−	0.944964i	0.924780	−	0.380503i	$-0.124249\pi$
$402$		0			0
$403$	−0.729466	−	0.810154i	−0.0363373	−	0.0403567i
$404$	−0.253650	−	0.780656i	−0.0126196	−	0.0388391i
$405$		0			0
$406$	−63.3050			−3.14177
$407$	−4.82796	−	3.30406i	−0.239313	−	0.163776i
$408$		0			0
$409$	−4.61864	−	2.05635i	−0.228377	−	0.101680i	0.289358	−	0.957221i	$-0.406558\pi$
$409$	−4.61864	−	2.05635i	−0.228377	−	0.101680i	−0.517735	+	0.855541i	$0.673225\pi$
$410$	9.17686	−	10.1919i	0.453213	−	0.503344i
$411$		0			0
$412$	−26.1753	+	11.6540i	−1.28957	+	0.574152i
$413$	−25.5709	−	18.5783i	−1.25826	−	0.914180i
$414$		0			0
$415$	−5.50000	−	16.9273i	−0.269984	−	0.830926i
$416$	0.191855	+	1.82538i	0.00940646	+	0.0894965i
$417$		0			0
$418$	2.24937	+	16.8273i	0.110020	+	0.823050i
$419$	17.6391	+	30.5518i	0.861727	+	1.49255i	0.870261	+	0.492591i	$0.163950\pi$
$419$	17.6391	+	30.5518i	0.861727	+	1.49255i	−0.00853378	+	0.999964i	$0.502716\pi$
$420$		0			0
$421$	28.5764	+	6.07409i	1.39273	+	0.296033i	0.842372	−	0.538897i	$-0.181159\pi$
$421$	28.5764	+	6.07409i	1.39273	+	0.296033i	0.550355	+	0.834930i	$0.314492\pi$
$422$	−11.9761	+	36.8585i	−0.582985	+	1.79424i
$423$		0			0
$424$	1.97214	+	1.43284i	0.0957754	+	0.0695849i
$425$	1.56759	+	1.74099i	0.0760395	+	0.0844504i
$426$		0			0
$427$	43.8307	+	19.5147i	2.12112	+	0.944383i
$428$	14.3188	+	24.8009i	0.692125	+	1.19879i
$429$		0			0
$430$	6.25329	−	10.8310i	0.301560	−	0.522318i
$431$	28.7943	−	20.9203i	1.38697	−	1.00770i	0.390785	−	0.920482i	$-0.372204\pi$
$431$	28.7943	−	20.9203i	1.38697	−	1.00770i	0.996190	−	0.0872135i	$-0.0277962\pi$
$432$		0			0
$433$	−0.819660	+	2.52265i	−0.0393904	+	0.121231i	−0.968818	−	0.247773i	$-0.920301\pi$
$433$	−0.819660	+	2.52265i	−0.0393904	+	0.121231i	0.929428	+	0.369004i	$0.120301\pi$
$434$	38.4042	−	17.0987i	1.84346	−	0.820762i
$435$		0			0
$436$	35.1043	−	7.46165i	1.68119	−	0.357348i
$437$	−6.35051	+	7.05296i	−0.303786	+	0.337389i
$438$		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	$-0.0368124\pi$
$440$	0.723944	−	9.43826i	0.0345127	−	0.449951i
$441$		0			0
$442$	2.51722	−	1.82887i	0.119732	−	0.0869904i
$443$	−21.3991	−	4.54852i	−1.01670	−	0.216107i	−0.330722	−	0.943728i	$-0.607292\pi$
$443$	−21.3991	−	4.54852i	−1.01670	−	0.216107i	−0.685979	+	0.727622i	$0.740626\pi$
$444$		0			0
$445$	2.00129	−	19.0410i	0.0948703	−	0.902631i
$446$	−0.714392	+	6.79699i	−0.0338274	+	0.321847i
$447$		0			0
$448$	−49.4911	−	10.5197i	−2.33823	−	0.497007i
$449$	−23.8323	+	17.3152i	−1.12472	+	0.817155i	−0.984918	−	0.173024i	$-0.944646\pi$
$449$	−23.8323	+	17.3152i	−1.12472	+	0.817155i	−0.139800	+	0.990180i	$0.544646\pi$
$450$		0			0
$451$	5.16312	+	8.38800i	0.243122	+	0.394975i
$452$	−23.4219	+	40.5680i	−1.10167	+	1.90816i
$453$		0			0
$454$	15.7290	−	17.4688i	0.738197	−	0.819851i
$455$	−2.10200	+	0.446794i	−0.0985433	+	0.0209460i
$456$		0			0
$457$	32.0565	−	14.2725i	1.49954	−	0.667637i	0.517391	−	0.855749i	$-0.326903\pi$
$457$	32.0565	−	14.2725i	1.49954	−	0.667637i	0.982148	+	0.188112i	$0.0602368\pi$
$458$	−12.2667	+	37.7530i	−0.573186	+	1.76408i
$459$		0			0
$460$	18.1353	−	13.1760i	0.845561	−	0.614336i
$461$	−0.760951	+	1.31801i	−0.0354410	+	0.0613857i	−0.883202	−	0.468993i	$-0.844617\pi$
$461$	−0.760951	+	1.31801i	−0.0354410	+	0.0613857i	0.847761	+	0.530379i	$0.177950\pi$
$462$		0			0
$463$	10.7812	+	18.6735i	0.501043	+	0.867831i	0.999999	+	0.00120439i	$0.000383369\pi$
$463$	10.7812	+	18.6735i	0.501043	+	0.867831i	−0.498957	+	0.866627i	$0.666283\pi$
$464$	−15.1325	−	6.73744i	−0.702511	−	0.312778i
$465$		0			0
$466$	33.0891	+	36.7491i	1.53282	+	1.70237i
$467$	−17.1318	−	12.4470i	−0.792766	−	0.575978i	0.116017	−	0.993247i	$-0.462987\pi$
$467$	−17.1318	−	12.4470i	−0.792766	−	0.575978i	−0.908783	+	0.417269i	$0.862987\pi$
$468$		0			0
$469$	3.73607	−	11.4984i	0.172516	−	0.530948i
$470$	15.7064	+	3.33851i	0.724484	+	0.153994i
$471$		0			0
$472$	4.95492	+	8.58216i	0.228068	+	0.395026i
$473$	6.19580	+	6.50309i	0.284883	+	0.299012i
$474$		0			0
$475$	−0.0951031	−	0.904846i	−0.00436363	−	0.0415172i
$476$	21.0193	+	64.6908i	0.963419	+	2.96510i
$477$		0			0
$478$	−19.8992	−	14.4576i	−0.910168	−	0.661275i
$479$	−33.6604	+	14.9866i	−1.53798	+	0.684754i	−0.988565	−	0.150795i	$-0.951817\pi$
$479$	−33.6604	+	14.9866i	−1.53798	+	0.684754i	−0.549417	+	0.835548i	$0.685150\pi$
$480$		0			0
$481$	0.278631	−	0.309451i	0.0127045	−	0.0141098i
$482$	27.4844	+	12.2369i	1.25188	+	0.557374i
$483$		0			0
$484$	26.9264	+	10.2135i	1.22393	+	0.464251i
$485$	−25.3542			−1.15128
$486$		0			0
$487$	5.83688	+	17.9641i	0.264494	+	0.814030i	0.991809	+	0.127726i	$0.0407679\pi$
$487$	5.83688	+	17.9641i	0.264494	+	0.814030i	−0.727315	+	0.686304i	$0.759232\pi$
$488$	−10.0655	−	11.1789i	−0.455646	−	0.506046i
$489$		0			0
$490$	5.28298	−	50.2642i	0.238660	−	2.27070i
$491$	18.9904	−	4.03654i	0.857025	−	0.182166i	0.241614	−	0.970372i	$-0.422323\pi$
$491$	18.9904	−	4.03654i	0.857025	−	0.182166i	0.615411	+	0.788206i	$0.288990\pi$
$492$		0			0
$493$	4.45840	+	42.4188i	0.200796	+	1.91045i
$494$	−1.20837			−0.0543673
$495$		0			0
$496$	11.0000			0.493915
$497$	4.75769	+	45.2664i	0.213412	+	2.03047i
$498$		0			0
$499$	−32.0271	+	6.80758i	−1.43373	+	0.304749i	−0.858320	−	0.513115i	$-0.828492\pi$
$499$	−32.0271	+	6.80758i	−1.43373	+	0.304749i	−0.575412	+	0.817864i	$0.695158\pi$
$500$	−3.16504	+	30.1134i	−0.141545	+	1.34671i
$501$		0			0
$502$	−32.6382	−	36.2484i	−1.45672	−	1.61785i
$503$	1.83543	+	5.64888i	0.0818379	+	0.251871i	0.983601	−	0.180360i	$-0.0577264\pi$
$503$	1.83543	+	5.64888i	0.0818379	+	0.251871i	−0.901763	+	0.432231i	$0.857726\pi$
$504$		0			0
$505$	0.673762			0.0299820
$506$	9.53259	+	26.7502i	0.423775	+	1.18919i
$507$		0			0
$508$	−6.61048	−	2.94317i	−0.293292	−	0.130582i
$509$	10.9542	−	12.1659i	0.485538	−	0.539245i	−0.449739	−	0.893160i	$-0.648483\pi$
$509$	10.9542	−	12.1659i	0.485538	−	0.539245i	0.935278	+	0.353915i	$0.115150\pi$
$510$		0			0
$511$	−9.56677	+	4.25940i	−0.423209	+	0.188425i
$512$	−20.1016	−	14.6047i	−0.888374	−	0.645441i
$513$		0			0
$514$	−8.22542	−	25.3153i	−0.362808	−	1.11661i
$515$	−2.45839	−	23.3900i	−0.108329	−	1.03069i
$516$		0			0
$517$	−5.48255	+	10.1456i	−0.241122	+	0.446204i
$518$	8.02866	+	13.9061i	0.352759	+	0.610997i
$519$		0			0
$520$	0.659039	+	0.140083i	0.0289008	+	0.00614305i
$521$	−8.28232	+	25.4903i	−0.362855	+	1.11675i	0.588459	+	0.808527i	$0.299735\pi$
$521$	−8.28232	+	25.4903i	−0.362855	+	1.11675i	−0.951313	+	0.308225i	$0.900265\pi$
$522$		0			0
$523$	30.2984	+	22.0131i	1.32486	+	0.962564i	0.999858	+	0.0168489i	$0.00536341\pi$
$523$	30.2984	+	22.0131i	1.32486	+	0.962564i	0.324997	+	0.945715i	$0.394637\pi$
$524$	4.31381	+	4.79097i	0.188450	+	0.209294i
$525$		0			0
$526$	−12.6564	−	5.63497i	−0.551843	−	0.245696i
$527$	−14.1620	−	24.5293i	−0.616907	−	1.06851i
$528$		0			0
$529$	3.56231	−	6.17009i	0.154883	−	0.268265i
$530$	−6.85730	+	4.98212i	−0.297862	+	0.216409i
$531$		0			0
$532$	8.16312	−	25.1235i	0.353916	−	1.08924i
$533$	−0.640462	+	0.285152i	−0.0277415	+	0.0123513i
$534$		0			0
$535$	−22.9929	+	4.88729i	−0.994070	+	0.211296i
$536$	−2.53642	+	2.81698i	−0.109557	+	0.121675i
$537$		0			0
$538$	−21.7426	+	37.6594i	−0.937392	+	1.62361i
$539$	33.5625	+	13.8240i	1.44564	+	0.595442i
$540$		0			0
$541$	−31.2533	+	22.7068i	−1.34368	+	0.976243i	−0.344384	+	0.938829i	$0.611912\pi$
$541$	−31.2533	+	22.7068i	−1.34368	+	0.976243i	−0.999300	+	0.0374146i	$0.988088\pi$
$542$	2.02960	+	0.431406i	0.0871790	+	0.0185305i
$543$		0			0
$544$	−4.98464	+	47.4257i	−0.213715	+	2.03336i
$545$	−3.07924	+	29.2970i	−0.131900	+	1.25495i
$546$		0			0
$547$	−19.5966	−	4.16539i	−0.837892	−	0.178099i	−0.231070	−	0.972937i	$-0.574223\pi$
$547$	−19.5966	−	4.16539i	−0.837892	−	0.178099i	−0.606822	+	0.794838i	$0.707556\pi$
$548$	−0.664066	+	0.482472i	−0.0283675	+	0.0206102i
$549$		0			0
$550$	−2.51722	−	1.03681i	−0.107335	−	0.0442099i
$551$	8.28232	−	14.3454i	0.352838	−	0.611134i
$552$		0			0
$553$	26.8486	−	29.8184i	1.14172	−	1.26801i
$554$	−40.7409	+	8.65975i	−1.73092	+	0.367917i
$555$		0			0
$556$	−27.2222	+	12.1201i	−1.15448	+	0.514006i
$557$	1.67867	−	5.16641i	0.0711274	−	0.218908i	−0.909173	−	0.416418i	$-0.863285\pi$
$557$	1.67867	−	5.16641i	0.0711274	−	0.218908i	0.980301	+	0.197510i	$0.0632855\pi$
$558$		0			0
$559$	−0.517221	+	0.375783i	−0.0218761	+	0.0158939i
$560$	10.8417	−	18.7784i	0.458145	−	0.793531i
$561$		0			0
$562$	17.7984	+	30.8277i	0.750779	+	1.30039i
$563$	14.2733	+	6.35487i	0.601547	+	0.267826i	0.684833	−	0.728700i	$-0.259875\pi$
$563$	14.2733	+	6.35487i	0.601547	+	0.267826i	−0.0832865	+	0.996526i	$0.526542\pi$
$564$		0			0
$565$	−25.7286	−	28.5746i	−1.08241	−	1.20214i
$566$	19.0271	+	13.8240i	0.799770	+	0.581067i
$567$		0			0
$568$	4.40983	−	13.5721i	0.185032	−	0.569471i
$569$	−31.0338	−	6.59644i	−1.30100	−	0.276537i	−0.495231	−	0.868761i	$-0.664917\pi$
$569$	−31.0338	−	6.59644i	−1.30100	−	0.276537i	−0.805773	+	0.592224i	$0.798250\pi$
$570$		0			0
$571$	−5.98936	−	10.3739i	−0.250647	−	0.434133i	0.713057	−	0.701106i	$-0.247310\pi$
$571$	−5.98936	−	10.3739i	−0.250647	−	0.434133i	−0.963704	+	0.266973i	$0.913977\pi$
$572$	−0.974493	+	1.80333i	−0.0407456	+	0.0754009i
$573$		0			0
$574$	−2.82587	−	26.8863i	−0.117949	−	1.12221i
$575$	−0.470294	−	1.44742i	−0.0196126	−	0.0603614i
$576$		0			0
$577$	1.09017	+	0.792055i	0.0453844	+	0.0329737i	0.610246	−	0.792212i	$-0.291071\pi$
$577$	1.09017	+	0.792055i	0.0453844	+	0.0329737i	−0.564862	+	0.825186i	$0.691071\pi$
$578$	40.4768	−	18.0214i	1.68361	−	0.749592i
$579$		0			0
$580$	−26.1795	+	29.0753i	−1.08704	+	1.20728i
$581$	−32.0512	−	14.2701i	−1.32971	−	0.592025i
$582$		0			0
$583$	−2.04342	−	5.73422i	−0.0846300	−	0.237487i
$584$	3.28332			0.135865
$585$		0			0
$586$	−3.31966	−	10.2169i	−0.137134	−	0.422055i
$587$	24.5746	+	27.2928i	1.01430	+	1.12650i	0.991935	+	0.126745i	$0.0404531\pi$
$587$	24.5746	+	27.2928i	1.01430	+	1.12650i	0.0223656	+	0.999750i	$0.492880\pi$
$588$		0			0
$589$	−1.14981	+	10.9397i	−0.0473772	+	0.450764i
$590$	−33.7044	+	7.16409i	−1.38759	+	0.294941i
$591$		0			0
$592$	0.439190	+	4.17861i	0.0180506	+	0.171740i
$593$	27.3094			1.12146			0.560732	−	0.827997i	$-0.310520\pi$
$593$	27.3094			1.12146			0.560732	+	0.827997i	$0.310520\pi$
$594$		0			0
$595$	−55.8328			−2.28892
$596$	1.26197	+	12.0068i	0.0516921	+	0.491818i
$597$		0			0
$598$	−1.97712	+	0.420249i	−0.0808503	+	0.0171853i
$599$	−1.79702	+	17.0975i	−0.0734243	+	0.698585i	0.894453	+	0.447162i	$0.147565\pi$
$599$	−1.79702	+	17.0975i	−0.0734243	+	0.698585i	−0.967877	+	0.251423i	$0.919101\pi$
$600$		0			0
$601$	−6.26352	−	6.95634i	−0.255494	−	0.283755i	0.601729	−	0.798701i	$-0.294479\pi$
$601$	−6.26352	−	6.95634i	−0.255494	−	0.283755i	−0.857223	+	0.514945i	$0.827812\pi$
$602$	−7.61825	−	23.4466i	−0.310497	−	0.955611i
$603$		0			0
$604$	−34.6525			−1.40999
$605$	−14.8031	+	18.4296i	−0.601833	+	0.749269i
$606$		0			0
$607$	−26.1439	−	11.6400i	−1.06115	−	0.472453i	−0.199467	−	0.979905i	$-0.563921\pi$
$607$	−26.1439	−	11.6400i	−1.06115	−	0.472453i	−0.861680	+	0.507451i	$0.830588\pi$
$608$	12.3922	−	13.7629i	0.502569	−	0.558160i
$609$		0			0
$610$	47.7830	−	21.2743i	1.93468	−	0.861373i
$611$	−0.664066	−	0.482472i	−0.0268652	−	0.0195187i
$612$		0			0
$613$	7.74265	+	23.8294i	0.312723	+	0.962461i	0.976682	+	0.214692i	$0.0688748\pi$
$613$	7.74265	+	23.8294i	0.312723	+	0.962461i	−0.663959	+	0.747769i	$0.731125\pi$
$614$	−3.87943	−	36.9103i	−0.156561	−	1.48958i
$615$		0			0
$616$	−12.8712	−	13.5096i	−0.518596	−	0.544317i
$617$	−8.43908	−	14.6169i	−0.339745	−	0.588455i	0.644640	−	0.764486i	$-0.277007\pi$
$617$	−8.43908	−	14.6169i	−0.339745	−	0.588455i	−0.984385	+	0.176031i	$0.943674\pi$
$618$		0			0
$619$	−6.73801	−	1.43221i	−0.270824	−	0.0575653i	0.0704980	−	0.997512i	$-0.477541\pi$
$619$	−6.73801	−	1.43221i	−0.270824	−	0.0575653i	−0.341322	+	0.939947i	$0.610875\pi$
$620$	8.02866	−	24.7097i	0.322439	−	0.992365i
$621$		0			0
$622$	49.9959	+	36.3242i	2.00465	+	1.45647i
$623$	−25.2535	−	28.0468i	−1.01176	−	1.12367i
$624$		0			0
$625$	−20.9606	−	9.33228i	−0.838425	−	0.373291i
$626$	−34.0100	−	58.9070i	−1.35931	−	2.35440i
$627$		0			0
$628$	27.0344	−	46.8250i	1.07879	−	1.86852i
$629$	8.75261	−	6.35914i	0.348989	−	0.253556i
$630$		0			0
$631$	−5.37132	+	16.5312i	−0.213829	+	0.658098i	0.785406	+	0.618981i	$0.212454\pi$
$631$	−5.37132	+	16.5312i	−0.213829	+	0.658098i	−0.999235	+	0.0391166i	$0.987546\pi$
$632$	−11.4926	+	5.11684i	−0.457152	+	0.203537i
$633$		0			0
$634$	0.659039	−	0.140083i	0.0261738	−	0.00556341i
$635$	3.97436	−	4.41397i	0.157718	−	0.175163i
$636$		0			0
$637$	−1.29180	+	2.23746i	−0.0511828	+	0.0886513i
$638$	−25.9813	−	42.2092i	−1.02861	−	1.67108i
$639$		0			0
$640$	−17.5902	+	12.7800i	−0.695313	+	0.505174i
$641$	20.9029	+	4.44304i	0.825614	+	0.175490i	0.601296	−	0.799026i	$-0.294651\pi$
$641$	20.9029	+	4.44304i	0.825614	+	0.175490i	0.224318	+	0.974516i	$0.427985\pi$
$642$		0			0
$643$	4.30229	−	40.9336i	0.169666	−	1.61426i	−0.496212	−	0.868202i	$-0.665276\pi$
$643$	4.30229	−	40.9336i	0.169666	−	1.61426i	0.665877	−	0.746061i	$-0.268057\pi$
$644$	4.61886	−	43.9455i	0.182009	−	1.73170i
$645$		0			0
$646$	−30.7091	−	6.52741i	−1.20823	−	0.256818i
$647$	9.45368	−	6.86850i	0.371663	−	0.270029i	−0.386237	−	0.922399i	$-0.626225\pi$
$647$	9.45368	−	6.86850i	0.371663	−	0.270029i	0.757900	+	0.652371i	$0.226225\pi$
$648$		0			0
$649$	1.89261	−	24.6745i	0.0742914	−	0.968558i
$650$	0.0968859	−	0.167811i	0.00380018	−	0.00658210i
$651$		0			0
$652$	2.42094	−	2.68872i	0.0948112	−	0.105299i
$653$	33.4425	−	7.10842i	1.30871	−	0.278174i	0.499814	−	0.866133i	$-0.333402\pi$
$653$	33.4425	−	7.10842i	1.30871	−	0.278174i	0.808891	+	0.587959i	$0.200068\pi$
$654$		0			0
$655$	−4.83430	+	2.15237i	−0.188892	+	0.0841000i
$656$	2.18597	−	6.72772i	0.0853477	−	0.262673i
$657$		0			0
$658$	25.6074	−	18.6049i	0.998280	−	0.725293i
$659$	16.8782	−	29.2338i	0.657480	−	1.13879i	−0.323786	−	0.946130i	$-0.604956\pi$
$659$	16.8782	−	29.2338i	0.657480	−	1.13879i	0.981266	−	0.192658i	$-0.0617108\pi$
$660$		0			0
$661$	−1.21885	−	2.11111i	−0.0474077	−	0.0821125i	0.841348	−	0.540494i	$-0.181763\pi$
$661$	−1.21885	−	2.11111i	−0.0474077	−	0.0821125i	−0.888755	+	0.458382i	$0.848429\pi$
$662$	14.3151	+	6.37348i	0.556371	+	0.247712i
$663$		0			0
$664$	7.36044	+	8.17459i	0.285640	+	0.317236i
$665$	17.5422	+	12.7452i	0.680258	+	0.494237i
$666$		0			0
$667$	8.56231	−	26.3521i	0.331534	−	1.02036i
$668$	27.5156	+	5.84861i	1.06461	+	0.226290i
$669$		0			0
$670$	−6.59017	−	11.4145i	−0.254600	−	0.440981i
$671$	4.97718	+	37.2337i	0.192142	+	1.43739i
$672$		0			0
$673$	−1.90619	−	18.1362i	−0.0734782	−	0.699098i	−0.967808	−	0.251690i	$-0.919014\pi$
$673$	−1.90619	−	18.1362i	−0.0734782	−	0.699098i	0.894330	−	0.447408i	$-0.147653\pi$
$674$	−17.6990	−	54.4719i	−0.681740	−	2.09818i
$675$		0			0
$676$	27.4164	+	19.9192i	1.05448	+	0.766123i
$677$	−7.85269	+	3.49624i	−0.301804	+	0.134372i	−0.552051	−	0.833810i	$-0.686155\pi$
$677$	−7.85269	+	3.49624i	−0.301804	+	0.134372i	0.250248	+	0.968182i	$0.419488\pi$
$678$		0			0
$679$	−33.4423	+	37.1414i	−1.28340	+	1.42536i
$680$	15.9918	+	7.12001i	0.613258	+	0.273040i
$681$		0			0
$682$	27.1624	+	18.5888i	1.04010	+	0.711803i
$683$	−0.940588			−0.0359906			−0.0179953	−	0.999838i	$-0.505728\pi$
$683$	−0.940588			−0.0359906			−0.0179953	+	0.999838i	$0.505728\pi$
$684$		0			0
$685$	−0.208204	−	0.640786i	−0.00795506	−	0.0244832i
$686$	−24.0253	−	26.6828i	−0.917291	−	1.01875i
$687$		0			0
$688$	0.674297	−	6.41551i	0.0257073	−	0.244589i
$689$	0.423818	−	0.0900854i	0.0161462	−	0.00343198i
$690$		0			0
$691$	−3.38261	−	32.1834i	−0.128681	−	1.22431i	−0.848137	−	0.529777i	$-0.822276\pi$
$691$	−3.38261	−	32.1834i	−0.128681	−	1.22431i	0.719456	−	0.694538i	$-0.244391\pi$
$692$	−35.0845			−1.33371
$693$		0			0
$694$	54.0689			2.05243
$695$	−2.55670	−	24.3254i	−0.0969813	−	0.922715i
$696$		0			0
$697$	−17.8167	+	3.78707i	−0.674857	+	0.143445i
$698$	−2.06216	+	19.6201i	−0.0780538	+	0.742633i
$699$		0			0
$700$	2.83448	+	3.14801i	0.107133	+	0.118984i
$701$	7.23071	+	22.2538i	0.273100	+	0.840515i	0.989716	+	0.143047i	$0.0456901\pi$
$701$	7.23071	+	22.2538i	0.273100	+	0.840515i	−0.716616	+	0.697468i	$0.754310\pi$
$702$		0			0
$703$	−4.20163			−0.158467
$704$	−13.2978	−	37.3161i	−0.501180	−	1.40640i
$705$		0			0
$706$	−66.2695	−	29.5051i	−2.49409	−	1.11044i
$707$	0.888693	−	0.986994i	0.0334227	−	0.0371197i
$708$		0			0
$709$	−13.8874	+	6.18306i	−0.521551	+	0.232210i	−0.650589	−	0.759430i	$-0.725478\pi$
$709$	−13.8874	+	6.18306i	−0.521551	+	0.232210i	0.129038	+	0.991640i	$0.458811\pi$
$710$	40.1433	+	29.1658i	1.50655	+	1.09457i
$711$		0			0
$712$	3.65654	+	11.2537i	0.137035	+	0.421749i
$713$	1.92333	+	18.2993i	0.0720293	+	0.685313i
$714$		0			0
$715$	−1.16060	−	1.21816i	−0.0434039	−	0.0455565i
$716$	−2.55938	−	4.43297i	−0.0956484	−	0.165668i
$717$		0			0
$718$	−4.26539	−	0.906636i	−0.159183	−	0.0338354i
$719$	−4.00726	+	12.3331i	−0.149446	+	0.459947i	−0.997556	−	0.0698732i	$-0.977741\pi$
$719$	−4.00726	+	12.3331i	−0.149446	+	0.459947i	0.848110	+	0.529820i	$0.177741\pi$
$720$		0			0
$721$	−37.5066	−	27.2501i	−1.39682	−	1.01485i
$722$	−19.1623	−	21.2819i	−0.713146	−	0.792029i
$723$		0			0
$724$	29.2649	+	13.0296i	1.08762	+	0.484241i
$725$	1.32813	+	2.30039i	0.0493255	+	0.0854344i
$726$		0			0
$727$	−9.78115	+	16.9415i	−0.362763	+	0.628324i	−0.988414	−	0.151779i	$-0.951500\pi$
$727$	−9.78115	+	16.9415i	−0.362763	+	0.628324i	0.625652	+	0.780103i	$0.284833\pi$
$728$	1.07448	−	0.780656i	0.0398229	−	0.0289330i
$729$		0			0
$730$	−3.52786	+	10.8576i	−0.130572	+	0.401860i
$731$	−15.1743	+	6.75605i	−0.561243	+	0.249881i
$732$		0			0
$733$	14.3323	−	3.04642i	0.529375	−	0.112522i	0.0645326	−	0.997916i	$-0.479444\pi$
$733$	14.3323	−	3.04642i	0.529375	−	0.112522i	0.464842	+	0.885393i	$0.346111\pi$
$734$	33.1220	−	36.7858i	1.22256	−	1.35779i
$735$		0			0
$736$	15.4894	−	26.8284i	0.570945	−	0.988906i
$737$	9.20003	−	2.22807i	0.338888	−	0.0820721i
$738$		0			0
$739$	−14.7533	+	10.7189i	−0.542709	+	0.394301i	−0.825090	−	0.565001i	$-0.808876\pi$
$739$	−14.7533	+	10.7189i	−0.542709	+	0.394301i	0.282381	+	0.959302i	$0.408876\pi$
$740$	9.70711	+	2.06331i	0.356841	+	0.0758488i
$741$		0			0
$742$	−1.74648	+	16.6167i	−0.0641154	+	0.610017i
$743$	−1.89534	+	18.0329i	−0.0695332	+	0.661565i	0.903134	+	0.429360i	$0.141261\pi$
$743$	−1.89534	+	18.0329i	−0.0695332	+	0.661565i	−0.972667	+	0.232205i	$0.925406\pi$
$744$		0			0
$745$	−9.69328	−	2.06037i	−0.355134	−	0.0754861i
$746$	25.0636	−	18.2098i	0.917643	−	0.666707i
$747$		0			0
$748$	−34.5066	+	40.5649i	−1.26169	+	1.48320i
$749$	−23.1683	+	40.1286i	−0.846550	+	1.46627i
$750$		0			0
$751$	−1.00810	+	1.11961i	−0.0367860	+	0.0408550i	−0.761257	−	0.648450i	$-0.775417\pi$
$751$	−1.00810	+	1.11961i	−0.0367860	+	0.0408550i	0.724471	+	0.689305i	$0.242084\pi$
$752$	8.10133	−	1.72199i	0.295425	−	0.0627945i
$753$		0			0
$754$	3.22286	−	1.43491i	0.117370	−	0.0522564i
$755$	8.78962	−	27.0517i	0.319887	−	0.984511i
$756$		0			0
$757$	33.0795	−	24.0337i	1.20230	−	0.873519i	0.207787	−	0.978174i	$-0.433374\pi$
$757$	33.0795	−	24.0337i	1.20230	−	0.873519i	0.994509	+	0.104655i	$0.0333738\pi$
$758$	−6.70053	+	11.6057i	−0.243374	+	0.421537i
$759$		0			0
$760$	−3.39919	−	5.88756i	−0.123301	−	0.213564i
$761$	30.5515	+	13.6024i	1.10749	+	0.493087i	0.877244	−	0.480045i	$-0.159380\pi$
$761$	30.5515	+	13.6024i	1.10749	+	0.493087i	0.230248	+	0.973132i	$0.426046\pi$
$762$		0			0
$763$	38.8557	+	43.1536i	1.40667	+	1.56226i
$764$	21.0193	+	15.2714i	0.760452	+	0.552501i
$765$		0			0
$766$	−22.6246	+	69.6314i	−0.817460	+	2.51588i
$767$	1.72293	+	0.366219i	0.0622113	+	0.0132234i
$768$		0			0
$769$	11.1353	+	19.2868i	0.401548	+	0.695501i	0.993913	−	0.110169i	$-0.0351391\pi$
$769$	11.1353	+	19.2868i	0.401548	+	0.695501i	−0.592365	+	0.805669i	$0.701806\pi$
$770$	58.5049	−	28.0482i	2.10837	−	1.01079i
$771$		0			0
$772$	−2.02014	−	19.2204i	−0.0727065	−	0.691756i
$773$	−10.4084	−	32.0338i	−0.374364	−	1.15217i	−0.943907	−	0.330213i	$-0.892879\pi$
$773$	−10.4084	−	32.0338i	−0.374364	−	1.15217i	0.569542	−	0.821962i	$-0.307121\pi$
$774$		0			0
$775$	−1.42705	−	1.03681i	−0.0512612	−	0.0372434i
$776$	14.3151	−	6.37348i	0.513881	−	0.228794i
$777$		0			0
$778$	32.0810	−	35.6295i	1.15016	−	1.27738i
$779$	6.46237	+	2.87723i	0.231538	+	0.103088i
$780$		0			0
$781$	−28.2292	+	21.7502i	−1.01012	+	0.778285i
$782$	−52.5157			−1.87796
$783$		0			0
$784$	−8.05573	−	24.7930i	−0.287705	−	0.885464i
$785$	29.6969	+	32.9818i	1.05993	+	1.17717i
$786$		0			0
$787$	−2.90350	+	27.6249i	−0.103498	+	0.984722i	0.812342	+	0.583181i	$0.198192\pi$
$787$	−2.90350	+	27.6249i	−0.103498	+	0.984722i	−0.915841	+	0.401541i	$0.868475\pi$
$788$	6.30600	−	1.34038i	0.224642	−	0.0477491i
$789$		0			0
$790$	−4.57235	−	43.5030i	−0.162677	−	1.54777i
$791$	−75.7950			−2.69496
$792$		0			0
$793$	−2.67376			−0.0949481
$794$	−5.48460	−	52.1825i	−0.194641	−	1.85189i
$795$		0			0
$796$	−1.06635	+	0.226659i	−0.0377957	+	0.00803372i
$797$	−0.449255	+	4.27438i	−0.0159134	+	0.151406i	−0.999593	−	0.0285221i	$-0.990920\pi$
$797$	−0.449255	+	4.27438i	−0.0159134	+	0.151406i	0.983680	+	0.179928i	$0.0575866\pi$
$798$		0			0
$799$	−14.2700	−	15.8485i	−0.504838	−	0.560679i
$800$	0.917716	+	2.82444i	0.0324462	+	0.0998590i
$801$		0			0
$802$	−40.8885			−1.44382
$803$	−6.76634	−	4.63062i	−0.238779	−	0.163411i
$804$		0			0
$805$	33.1348	+	14.7525i	1.16785	+	0.519959i
$806$	−1.56759	+	1.74099i	−0.0552162	+	0.0613237i
$807$		0			0
$808$	−0.380408	+	0.169368i	−0.0133827	+	0.00595836i
$809$	5.72294	+	4.15796i	0.201208	+	0.146186i	0.683827	−	0.729644i	$-0.260314\pi$
$809$	5.72294	+	4.15796i	0.201208	+	0.146186i	−0.482619	+	0.875830i	$0.660314\pi$
$810$		0			0
$811$	−13.6631	−	42.0508i	−0.479777	−	1.47660i	−0.839405	−	0.543506i	$-0.817096\pi$
$811$	−13.6631	−	42.0508i	−0.479777	−	1.47660i	0.359628	−	0.933096i	$-0.382904\pi$
$812$	8.06156	+	76.7006i	0.282905	+	2.69166i
$813$		0			0
$814$	−5.97691	+	11.0604i	−0.209491	+	0.387668i
$815$	1.48490	+	2.57191i	0.0520136	+	0.0900902i
$816$		0			0
$817$	6.30988	+	1.34121i	0.220755	+	0.0469229i
$818$	−3.35733	+	10.3328i	−0.117386	+	0.361278i
$819$		0			0
$820$	−13.5172	−	9.82084i	−0.472042	−	0.342958i
$821$	26.6113	+	29.5548i	0.928740	+	1.03147i	0.999423	+	0.0339711i	$0.0108154\pi$
$821$	26.6113	+	29.5548i	0.928740	+	1.03147i	−0.0706831	+	0.997499i	$0.522518\pi$
$822$		0			0
$823$	17.4592	+	7.77333i	0.608589	+	0.270961i	0.687804	−	0.725896i	$-0.258575\pi$
$823$	17.4592	+	7.77333i	0.608589	+	0.270961i	−0.0792153	+	0.996858i	$0.525241\pi$
$824$	7.26771	+	12.5880i	0.253183	+	0.438525i
$825$		0			0
$826$	−33.9615	+	58.8230i	−1.18167	+	2.04672i
$827$	−9.41667	+	6.84161i	−0.327450	+	0.237906i	−0.739348	−	0.673324i	$-0.764866\pi$
$827$	−9.41667	+	6.84161i	−0.327450	+	0.237906i	0.411898	+	0.911230i	$0.364866\pi$
$828$		0			0
$829$	6.19098	−	19.0539i	0.215022	−	0.661769i	−0.784130	−	0.620596i	$-0.786891\pi$
$829$	6.19098	−	19.0539i	0.215022	−	0.661769i	0.999152	−	0.0411726i	$-0.0131094\pi$
$830$	−34.9413	+	15.5569i	−1.21283	+	0.539987i
$831$		0			0
$832$	2.75804	−	0.586240i	0.0956180	−	0.0203242i
$833$	−44.9155	+	49.8837i	−1.55623	+	1.72837i
$834$		0			0
$835$	−11.5451	+	19.9967i	−0.399534	+	0.692013i
$836$	20.1016	−	4.86822i	0.695228	−	0.168371i
$837$		0			0
$838$	61.3328	−	44.5609i	2.11871	−	1.53933i
$839$	13.6768	+	2.90710i	0.472177	+	0.100364i	0.437853	−	0.899047i	$-0.355739\pi$
$839$	13.6768	+	2.90710i	0.472177	+	0.100364i	0.0343236	+	0.999411i	$0.489072\pi$
$840$		0			0
$841$	−2.02374	+	19.2546i	−0.0697842	+	0.663952i
$842$	6.56245	−	62.4375i	0.226157	−	2.15174i
$843$		0			0
$844$	46.1830	+	9.81651i	1.58969	+	0.337898i
$845$	−22.5042	+	16.3503i	−0.774168	+	0.562466i
$846$		0			0
$847$	7.47214	+	45.9937i	0.256746	+	1.58036i
$848$	−2.18597	+	3.78621i	−0.0750665	+	0.130019i
$849$		0			0
$850$	3.36870	−	3.74132i	0.115545	−	0.128326i
$851$	−6.87462	+	1.46124i	−0.235659	+	0.0500908i
$852$		0			0
$853$	−1.07829	+	0.480087i	−0.0369201	+	0.0164379i	−0.425114	−	0.905140i	$-0.639766\pi$
$853$	−1.07829	+	0.480087i	−0.0369201	+	0.0164379i	0.388194	+	0.921578i	$0.373099\pi$
$854$	31.8610	−	98.0581i	1.09026	−	3.35548i
$855$		0			0
$856$	11.7533	−	8.53926i	0.401719	−	0.291866i
$857$	−6.91718	+	11.9809i	−0.236286	+	0.409260i	−0.959646	−	0.281212i	$-0.909264\pi$
$857$	−6.91718	+	11.9809i	−0.236286	+	0.409260i	0.723359	+	0.690472i	$0.242597\pi$
$858$		0			0
$859$	−21.2082	−	36.7337i	−0.723615	−	1.25334i	−0.959542	−	0.281566i	$-0.909146\pi$
$859$	−21.2082	−	36.7337i	−0.723615	−	1.25334i	0.235927	−	0.971771i	$-0.424187\pi$
$860$	−13.9192	−	6.19724i	−0.474642	−	0.211324i
$861$		0			0
$862$	−51.1786	−	56.8396i	−1.74315	−	1.93597i
$863$	27.8167	+	20.2100i	0.946893	+	0.687958i	0.950070	−	0.312037i	$-0.101011\pi$
$863$	27.8167	+	20.2100i	0.946893	+	0.687958i	−0.00317717	+	0.999995i	$0.501011\pi$
$864$		0			0
$865$	8.89919	−	27.3889i	0.302581	−	0.931250i
$866$	5.57551	+	1.18511i	0.189463	+	0.0402717i
$867$		0			0
$868$	−25.6074	−	44.3533i	−0.869171	−	1.50545i
$869$	30.9008	+	5.66365i	1.04824	+	0.192126i
$870$		0			0
$871$	0.0704273	+	0.670071i	0.00238634	+	0.0227045i
$872$	−5.62605	−	17.3152i	−0.190522	−	0.586367i
$873$		0			0
$874$	16.5000	+	11.9880i	0.558121	+	0.405499i
$875$	−44.7572	+	19.9272i	−1.51307	+	0.673661i
$876$		0			0
$877$	7.67636	−	8.52546i	0.259212	−	0.287884i	−0.599465	−	0.800401i	$-0.704620\pi$
$877$	7.67636	−	8.52546i	0.259212	−	0.287884i	0.858677	+	0.512517i	$0.171287\pi$
$878$	−49.0793	−	21.8515i	−1.65635	−	0.737453i
$879$		0			0
$880$	16.9702	−	0.478119i	0.572067	−	0.0161174i
$881$	34.3376			1.15686			0.578432	−	0.815730i	$-0.303665\pi$
$881$	34.3376			1.15686			0.578432	+	0.815730i	$0.303665\pi$
$882$		0			0
$883$	−4.36068	−	13.4208i	−0.146749	−	0.451646i	0.850483	−	0.526002i	$-0.176310\pi$
$883$	−4.36068	−	13.4208i	−0.146749	−	0.451646i	−0.997232	+	0.0743567i	$0.976310\pi$
$884$	−2.53642	−	2.81698i	−0.0853091	−	0.0947453i
$885$		0			0
$886$	−4.91421	+	46.7556i	−0.165096	+	1.57079i
$887$	55.3378	−	11.7624i	1.85806	−	0.394943i	0.863975	−	0.503535i	$-0.167968\pi$
$887$	55.3378	−	11.7624i	1.85806	−	0.394943i	0.994086	+	0.108592i	$0.0346343\pi$
$888$		0			0
$889$	−1.22384	−	11.6441i	−0.0410463	−	0.390529i
$890$	−41.1438			−1.37914
$891$		0			0
$892$	8.32624			0.278783
$893$	0.865738	+	8.23694i	0.0289708	+	0.275639i
$894$		0			0
$895$	4.10981	−	0.873567i	0.137376	−	0.0292001i
$896$	−4.48003	+	42.6247i	−0.149667	+	1.42399i
$897$		0			0
$898$	42.3593	+	47.0447i	1.41355	+	1.56990i
$899$	−9.92398	−	30.5429i	−0.330983	−	1.01866i
$900$		0			0
$901$	11.2574			0.375037
$902$	16.7670	−	12.9187i	0.558278	−	0.430147i
$903$		0			0
$904$	21.7094	+	9.66566i	0.722045	+	0.321475i
$905$	−17.5947	+	19.5409i	−0.584867	+	0.649561i
$906$		0			0
$907$	−32.7664	+	14.5885i	−1.08799	+	0.484404i	−0.870756	−	0.491716i	$-0.836370\pi$
$907$	−32.7664	+	14.5885i	−1.08799	+	0.484404i	−0.217234	+	0.976120i	$0.569703\pi$
$908$	−23.1683	−	16.8327i	−0.768866	−	0.558614i
$909$		0			0
$910$	1.42705	+	4.39201i	0.0473063	+	0.145594i
$911$	−0.996829	−	9.48419i	−0.0330264	−	0.314225i	−0.998547	−	0.0538968i	$-0.982836\pi$
$911$	−0.996829	−	9.48419i	−0.0330264	−	0.314225i	0.965520	−	0.260328i	$-0.0838309\pi$
$912$		0			0
$913$	−3.63956	−	27.2272i	−0.120452	−	0.901087i
$914$	−37.7037	−	65.3047i	−1.24713	−	2.16009i
$915$		0			0
$916$	47.3039	+	10.0548i	1.56296	+	0.332218i
$917$	−3.22344	+	9.92073i	−0.106447	+	0.327611i
$918$		0			0
$919$	20.3713	+	14.8006i	0.671988	+	0.488228i	0.870690	−	0.491832i	$-0.163673\pi$
$919$	20.3713	+	14.8006i	0.671988	+	0.488228i	−0.198702	+	0.980060i	$0.563673\pi$
$920$	−7.60926	−	8.45094i	−0.250870	−	0.278619i
$921$		0			0
$922$	2.98776	+	1.33024i	0.0983966	+	0.0438090i
$923$	−1.26825	−	2.19668i	−0.0417450	−	0.0723045i
$924$		0			0
$925$	0.336881	−	0.583495i	0.0110766	−	0.0191852i
$926$	37.4871	−	27.2359i	1.23190	−	0.895029i
$927$		0			0
$928$	−16.7082	+	51.4226i	−0.548474	+	1.68803i
$929$	38.4042	−	17.0987i	1.26000	−	0.560989i	0.335454	−	0.942057i	$-0.391110\pi$
$929$	38.4042	−	17.0987i	1.26000	−	0.560989i	0.924547	+	0.381068i	$0.124444\pi$
$930$		0			0
$931$	25.4992	−	5.42003i	0.835703	−	0.177634i
$932$	40.3117	−	44.7707i	1.32045	−	1.46651i
$933$		0			0
$934$	−22.7533	+	39.4099i	−0.744510	+	1.28953i
$935$	−22.9146	−	37.2271i	−0.749388	−	1.21746i
$936$		0			0
$937$	−8.75329	+	6.35964i	−0.285957	+	0.207760i	−0.721512	−	0.692402i	$-0.756552\pi$
$937$	−8.75329	+	6.35964i	−0.285957	+	0.207760i	0.435554	+	0.900162i	$0.356552\pi$
$938$	−25.4136	−	5.40182i	−0.829782	−	0.176376i
$939$		0			0
$940$	2.04482	−	19.4551i	0.0666946	−	0.634557i
$941$	0.959274	−	9.12689i	0.0312715	−	0.297528i	−0.967697	−	0.252116i	$-0.918873\pi$
$941$	0.959274	−	9.12689i	0.0312715	−	0.297528i	0.998968	−	0.0454116i	$-0.0144599\pi$
$942$		0			0
$943$	11.5742	+	2.46018i	0.376909	+	0.0801145i
$944$	−14.3787	+	10.4467i	−0.467986	+	0.340011i
$945$		0			0
$946$	12.5066	−	14.7024i	0.406624	−	0.478015i
$947$	11.1922	−	19.3855i	0.363699	−	0.629944i	−0.624868	−	0.780731i	$-0.714847\pi$
$947$	11.1922	−	19.3855i	0.363699	−	0.629944i	0.988566	+	0.150786i	$0.0481805\pi$
$948$		0			0
$949$	0.390499	−	0.433693i	0.0126761	−	0.0140783i
$950$	−1.91246	+	0.406507i	−0.0620485	+	0.0131888i
$951$		0			0
$952$	31.5233	−	14.0351i	1.02168	−	0.454880i
$953$	5.19277	−	15.9817i	0.168210	−	0.517698i	−0.831048	−	0.556200i	$-0.812259\pi$
$953$	5.19277	−	15.9817i	0.168210	−	0.517698i	0.999259	+	0.0385025i	$0.0122587\pi$
$954$		0			0
$955$	−17.2533	+	12.5352i	−0.558303	+	0.405631i
$956$	−14.9828	+	25.9511i	−0.484580	+	0.839317i
$957$		0			0
$958$	39.5902	+	68.5722i	1.27910	+	2.21547i
$959$	−1.21331	−	0.540200i	−0.0391798	−	0.0174440i
$960$		0			0
$961$	−6.47301	−	7.18901i	−0.208807	−	0.231903i
$962$	−0.723944	−	0.525976i	−0.0233409	−	0.0169582i
$963$		0			0
$964$	11.3262	−	34.8586i	0.364794	−	1.12272i
$965$	15.5169	+	3.29822i	0.499507	+	0.106173i
$966$		0			0
$967$	8.84346	+	15.3173i	0.284386	+	0.492572i	0.972460	−	0.233069i	$-0.0748768\pi$
$967$	8.84346	+	15.3173i	0.284386	+	0.492572i	−0.688074	+	0.725641i	$0.741543\pi$
$968$	3.72510	−	14.1265i	0.119729	−	0.454044i
$969$		0			0
$970$	5.69526	+	54.1868i	0.182864	+	1.73983i
$971$	0.313529	+	0.964944i	0.0100616	+	0.0309665i	0.955961	−	0.293493i	$-0.0948177\pi$
$971$	0.313529	+	0.964944i	0.0100616	+	0.0309665i	−0.945900	+	0.324459i	$0.894818\pi$
$972$		0			0
$973$	−39.0066	−	28.3399i	−1.25049	−	0.908537i
$974$	37.0815	−	16.5097i	1.18817	−	0.529006i
$975$		0			0
$976$	18.0523	−	20.0491i	0.577840	−	0.641756i
$977$	−3.06708	−	1.36555i	−0.0981245	−	0.0436878i	0.357087	−	0.934071i	$-0.383770\pi$
$977$	−3.06708	−	1.36555i	−0.0981245	−	0.0436878i	−0.455212	+	0.890383i	$0.650436\pi$
$978$		0			0
$979$	8.33608	−	28.3488i	0.266422	−	0.906032i
$980$	−61.5731			−1.96688
$981$		0			0
$982$	−12.8926	−	39.6794i	−0.411420	−	1.26622i
$983$	−33.9306	−	37.6838i	−1.08222	−	1.20193i	−0.978268	−	0.207343i	$-0.933519\pi$
$983$	−33.9306	−	37.6838i	−1.08222	−	1.20193i	−0.103950	−	0.994583i	$-0.533148\pi$
$984$		0			0
$985$	−0.553143	+	5.26281i	−0.0176246	+	0.167687i
$986$	89.6556	−	19.0569i	2.85521	−	0.606895i
$987$		0			0
$988$	0.153880	+	1.46407i	0.00489558	+	0.0465783i
$989$	10.7905			0.343119
$990$		0			0
$991$	−58.2705			−1.85102			−0.925512	−	0.378719i	$-0.876365\pi$
$991$	−58.2705			−1.85102			−0.925512	+	0.378719i	$0.876365\pi$
$992$	−3.75312	−	35.7086i	−0.119162	−	1.13375i
$993$		0			0
$994$	95.6741	−	20.3362i	3.03460	−	0.645024i
$995$	0.0935367	−	0.889942i	0.00296531	−	0.0282131i
$996$		0			0
$997$	25.9239	+	28.7914i	0.821018	+	0.911833i	0.997369	−	0.0724947i	$-0.0230960\pi$
$997$	25.9239	+	28.7914i	0.821018	+	0.911833i	−0.176351	+	0.984327i	$0.556429\pi$
$998$	21.7433	+	66.9189i	0.688271	+	2.11828i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.n.e.784.1		16
3.2	odd	2	inner	891.2.n.e.784.2		16
9.2	odd	6		99.2.f.c.91.2	yes	8
9.4	even	3	inner	891.2.n.e.190.2		16
9.5	odd	6	inner	891.2.n.e.190.1		16
9.7	even	3		99.2.f.c.91.1	yes	8
11.4	even	5	inner	891.2.n.e.136.2		16
33.26	odd	10	inner	891.2.n.e.136.1		16
99.2	even	30		1089.2.a.w.1.4		4
99.4	even	15	inner	891.2.n.e.433.1		16
99.20	odd	30		1089.2.a.v.1.1		4
99.59	odd	30	inner	891.2.n.e.433.2		16
99.70	even	15		99.2.f.c.37.1	✓	8
99.79	odd	30		1089.2.a.w.1.1		4
99.92	odd	30		99.2.f.c.37.2	yes	8
99.97	even	15		1089.2.a.v.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.f.c.37.1	✓	8	99.70	even	15
99.2.f.c.37.2	yes	8	99.92	odd	30
99.2.f.c.91.1	yes	8	9.7	even	3
99.2.f.c.91.2	yes	8	9.2	odd	6
891.2.n.e.136.1		16	33.26	odd	10	inner
891.2.n.e.136.2		16	11.4	even	5	inner
891.2.n.e.190.1		16	9.5	odd	6	inner
891.2.n.e.190.2		16	9.4	even	3	inner
891.2.n.e.433.1		16	99.4	even	15	inner
891.2.n.e.433.2		16	99.59	odd	30	inner
891.2.n.e.784.1		16	1.1	even	1	trivial
891.2.n.e.784.2		16	3.2	odd	2	inner
1089.2.a.v.1.1		4	99.20	odd	30
1089.2.a.v.1.4		4	99.97	even	15
1089.2.a.w.1.1		4	99.79	odd	30
1089.2.a.w.1.4		4	99.2	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)

\(f(q)\)	\(=\)	\(q+(-0.224628 - 2.13719i) q^{2} +(-2.56082 + 0.544320i) q^{4} +(0.224628 - 2.13719i) q^{5} +(-2.83448 - 3.14801i) q^{7} +(0.410415 + 1.26313i) q^{8} -4.61803 q^{10} +(0.935653 - 3.18191i) q^{11} +(0.215659 + 0.0960175i) q^{13} +(-6.09119 + 6.76496i) q^{14} +(-2.17603 + 0.968833i) q^{16} +(4.96199 + 3.60510i) q^{17} +(-0.736068 - 2.26538i) q^{19} +(0.588083 + 5.59523i) q^{20} +(-7.01052 - 1.28492i) q^{22} +(-1.99220 - 3.45059i) q^{23} +(0.373619 + 0.0794152i) q^{25} +(0.156765 - 0.482472i) q^{26} +(8.97214 + 6.51864i) q^{28} +(4.65326 + 5.16797i) q^{29} +(-4.21878 - 1.87832i) q^{31} +(3.88751 + 6.73336i) q^{32} +(6.59017 - 11.4145i) q^{34} +(-7.36460 + 5.35069i) q^{35} +(0.545085 - 1.67760i) q^{37} +(-4.67621 + 2.08198i) q^{38} +(2.79173 - 0.593401i) q^{40} +(-1.98718 + 2.20699i) q^{41} +(-1.35410 + 2.34537i) q^{43} +(-0.664066 + 8.65761i) q^{44} +(-6.92705 + 5.03280i) q^{46} +(-3.40111 - 0.722928i) q^{47} +(-1.14399 + 10.8843i) q^{49} +(0.0858001 - 0.816334i) q^{50} +(-0.604528 - 0.128496i) q^{52} +(1.48490 - 1.07884i) q^{53} +(-6.59017 - 2.71441i) q^{55} +(2.81303 - 4.87231i) q^{56} +(9.99967 - 11.1058i) q^{58} +(7.29843 - 1.55133i) q^{59} +(-10.3470 + 4.60680i) q^{61} +(-3.06668 + 9.43826i) q^{62} +(9.66312 - 7.02067i) q^{64} +(0.253650 - 0.439335i) q^{65} +(1.42705 + 2.47172i) q^{67} +(-14.6691 - 6.53110i) q^{68} +(13.0897 + 14.5376i) q^{70} +(-8.69273 - 6.31564i) q^{71} +(0.763932 - 2.35114i) q^{73} +(-3.70779 - 0.788114i) q^{74} +(3.11803 + 5.40059i) q^{76} +(-12.6688 + 6.07362i) q^{77} +(0.990108 + 9.42025i) q^{79} +(1.58178 + 4.86822i) q^{80} +(5.16312 + 3.75123i) q^{82} +(7.56627 - 3.36872i) q^{83} +(8.81937 - 9.79490i) q^{85} +(5.31667 + 2.36714i) q^{86} +(4.40317 - 0.124055i) q^{88} +8.90937 q^{89} +(-0.309017 - 0.951057i) q^{91} +(6.97989 + 7.75195i) q^{92} +(-0.781051 + 7.43120i) q^{94} +(-5.00690 + 1.06425i) q^{95} +(-1.23327 - 11.7337i) q^{97} +23.5188 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{4} + 6 q^{7} - 56 q^{10} + 6 q^{13} - 2 q^{16} + 24 q^{19} - 28 q^{22} - 8 q^{25} + 72 q^{28} - 12 q^{31} + 16 q^{34} - 36 q^{37} + 16 q^{40} + 32 q^{43} - 84 q^{46} + 44 q^{49} - 6 q^{52} - 16 q^{55}+ \cdots + 54 q^{97}+O(q^{100}) \) 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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