LMFDB - Embedded newform 891.2.n.e.433.1

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			433.1
Root			$-0.224628 + 2.13719i$ of defining polynomial
Character	$\chi$	$=$	891.433
Dual form			891.2.n.e.784.1

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.224628	+	2.13719i	−0.158836	+	1.51122i	0.567209	+	0.823574i	$0.308023\pi$
$2$	−0.224628	+	2.13719i	−0.158836	+	1.51122i	−0.726045	+	0.687647i	$0.758644\pi$
$3$		0			0
$3$		0			0
$4$	−2.56082	−	0.544320i	−1.28041	−	0.272160i
$5$	0.224628	+	2.13719i	0.100457	+	0.955780i	0.922407	+	0.386220i	$0.126220\pi$
$5$	0.224628	+	2.13719i	0.100457	+	0.955780i	−0.821950	+	0.569560i	$0.807114\pi$
$6$		0			0
$7$	−2.83448	+	3.14801i	−1.07133	+	1.18984i	−0.0903171	+	0.995913i	$0.528788\pi$
$7$	−2.83448	+	3.14801i	−1.07133	+	1.18984i	−0.981017	+	0.193924i	$0.937879\pi$
$8$	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	−0.376612	−	0.926371i	$-0.622911\pi$
$13$	0.215659	−	0.0960175i	0.0598130	−	0.0266305i	0.436425	+	0.899741i	$0.356244\pi$
$14$	−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	0.208838	−	0.977950i	$-0.433032\pi$
$17$	4.96199	−	3.60510i	1.20346	−	0.874364i	0.994620	+	0.103586i	$0.0330318\pi$
$18$		0			0
$19$	−0.736068	+	2.26538i	−0.168866	+	0.519715i	−0.999300	−	0.0374011i	$-0.988092\pi$
$19$	−0.736068	+	2.26538i	−0.168866	+	0.519715i	0.830435	+	0.557116i	$0.188092\pi$
$20$	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	−0.995471	−	0.0950706i	$-0.969692\pi$
$23$	−1.99220	+	3.45059i	−0.415402	+	0.719497i	0.580069	+	0.814567i	$0.303026\pi$
$24$		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	−0.135427	−	0.990787i	$-0.543241\pi$
$29$	4.65326	−	5.16797i	0.864088	−	0.959667i	0.999516	+	0.0311201i	$0.00990742\pi$
$30$		0			0
$31$	−4.21878	+	1.87832i	−0.757716	+	0.337357i	−0.748969	−	0.662605i	$-0.769451\pi$
$31$	−4.21878	+	1.87832i	−0.757716	+	0.337357i	−0.00874681	+	0.999962i	$0.502784\pi$
$32$	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	0.985812	−	0.167854i	$-0.0536836\pi$
$37$	0.545085	+	1.67760i	0.0896114	+	0.275796i	−0.896201	+	0.443649i	$0.853684\pi$
$38$	−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	0.567714	−	0.823226i	$-0.307828\pi$
$41$	−1.98718	−	2.20699i	−0.310345	−	0.344673i	−0.878059	+	0.478553i	$0.841161\pi$
$42$		0			0
$43$	−1.35410	−	2.34537i	−0.206499	−	0.357666i	0.744111	−	0.668056i	$-0.232874\pi$
$43$	−1.35410	−	2.34537i	−0.206499	−	0.357666i	−0.950609	+	0.310390i	$0.899540\pi$
$44$	−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	−0.449167	−	0.893448i	$-0.648279\pi$
$47$	−3.40111	+	0.722928i	−0.496103	+	0.105450i	−0.0469361	+	0.998898i	$0.514946\pi$
$48$		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	0.685079	−	0.728468i	$-0.259767\pi$
$53$	1.48490	+	1.07884i	0.203966	+	0.148190i	−0.481113	+	0.876658i	$0.659767\pi$
$54$		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	0.656828	−	0.754040i	$-0.271898\pi$
$59$	7.29843	+	1.55133i	0.950175	+	0.201966i	0.293347	+	0.956006i	$0.405231\pi$
$60$		0			0
$61$	−10.3470	−	4.60680i	−1.32480	−	0.589840i	−0.382299	−	0.924039i	$-0.624868\pi$
$61$	−10.3470	−	4.60680i	−1.32480	−	0.589840i	−0.942503	+	0.334199i	$0.891534\pi$
$62$	−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	−0.765591	−	0.643327i	$-0.777553\pi$
$67$	1.42705	−	2.47172i	0.174342	−	0.301969i	0.939933	+	0.341358i	$0.110887\pi$
$68$	−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	−0.968636	−	0.248485i	$-0.920067\pi$
$71$	−8.69273	+	6.31564i	−1.03164	+	0.749528i	−0.0630016	+	0.998013i	$0.520067\pi$
$72$		0			0
$73$	0.763932	+	2.35114i	0.0894115	+	0.275180i	0.985757	−	0.168176i	$-0.0537877\pi$
$73$	0.763932	+	2.35114i	0.0894115	+	0.275180i	−0.896346	+	0.443356i	$0.853788\pi$
$74$	−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	−0.785877	−	0.618383i	$-0.787788\pi$
$79$	0.990108	−	9.42025i	0.111396	−	1.05986i	0.897272	−	0.441477i	$-0.145545\pi$
$80$	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	0.777542	−	0.628831i	$-0.216466\pi$
$83$	7.56627	+	3.36872i	0.830506	+	0.369765i	0.0529644	+	0.998596i	$0.483133\pi$
$84$		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	0.733774	+	0.679394i	$0.237757\pi$
$97$	−1.23327	+	11.7337i	−0.125219	+	1.19138i	−0.858993	+	0.511987i	$0.828910\pi$
$98$	23.5188			2.37576
$99$		0			0
$100$	−1.00000			−0.100000
$101$	0.0327727	−	0.311812i	0.00326101	−	0.0310264i	−0.992770	−	0.120029i	$-0.961701\pi$
$101$	0.0327727	−	0.311812i	0.00326101	−	0.0310264i	0.996031	+	0.0890025i	$0.0283679\pi$
$102$		0			0
$103$	10.7051	+	2.27544i	1.05481	+	0.224206i	0.702504	−	0.711680i	$-0.252065\pi$
$103$	10.7051	+	2.27544i	1.05481	+	0.224206i	0.352303	+	0.935886i	$0.385399\pi$
$104$	−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	0.643855	+	0.765147i	$0.277334\pi$
$107$	−3.38021	+	10.4032i	−0.326777	+	1.00572i	−0.970632	+	0.240569i	$0.922666\pi$
$108$		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	0.964512	+	0.264041i	$0.0850554\pi$
$113$	11.9726	+	13.2969i	1.12629	+	1.25087i	0.161775	+	0.986828i	$0.448278\pi$
$114$		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	−0.484139	−	0.874991i	$-0.660867\pi$
$127$	2.23607	−	1.62460i	0.198419	−	0.144160i	0.682558	+	0.730831i	$0.260867\pi$
$128$	−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	−0.914787	−	0.403936i	$-0.867642\pi$
$131$	−1.23125	+	2.13258i	−0.107574	+	0.186324i	0.807213	+	0.590261i	$0.200975\pi$
$132$		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	0.418936	−	0.908016i	$-0.362403\pi$
$137$	0.286423	+	0.127524i	0.0244708	+	0.0108951i	−0.394465	+	0.918911i	$0.629070\pi$
$138$		0			0
$139$	11.1332	+	2.36644i	0.944309	+	0.200719i	0.654240	−	0.756287i	$-0.272988\pi$
$139$	11.1332	+	2.36644i	0.944309	+	0.200719i	0.290069	+	0.957006i	$0.406322\pi$
$140$	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	0.996363	+	0.0852109i	$0.0271564\pi$
$149$	0.482028	+	4.58619i	0.0394893	+	0.375715i	−0.956874	+	0.290504i	$0.906177\pi$
$150$		0			0
$151$	12.9468	−	2.75193i	1.05360	−	0.223949i	0.351616	−	0.936144i	$-0.385632\pi$
$151$	12.9468	−	2.75193i	1.05360	−	0.223949i	0.701982	+	0.712195i	$0.252299\pi$
$152$	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	−0.972371	−	0.233441i	$-0.925002\pi$
$157$	−13.8192	−	15.3478i	−1.10289	−	1.22489i	−0.130521	−	0.991445i	$-0.541665\pi$
$158$	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	0.543138	−	0.839643i	$-0.317236\pi$
$163$	−1.11803	−	0.812299i	−0.0875712	−	0.0636242i	−0.630709	+	0.776019i	$0.717236\pi$
$164$	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	−0.749710	−	0.661767i	$-0.769807\pi$
$167$	−9.81587	+	4.37031i	−0.759575	+	0.338184i	−0.00986504	+	0.999951i	$0.503140\pi$
$168$		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	0.319390	−	0.947623i	$-0.396522\pi$
$173$	13.1082	−	2.78624i	0.996600	−	0.211834i	0.677210	+	0.735790i	$0.263189\pi$
$174$		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	−0.925935	−	0.377684i	$-0.876721\pi$
$179$	0.604187	−	1.85950i	0.0451590	−	0.138985i	0.971094	+	0.238698i	$0.0767207\pi$
$180$		0			0
$181$	−9.89919	+	7.19218i	−0.735801	+	0.534591i	−0.891393	−	0.453231i	$-0.850271\pi$
$181$	−9.89919	+	7.19218i	−0.735801	+	0.534591i	0.155592	+	0.987821i	$0.450271\pi$
$182$	−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	−0.933837	−	0.357699i	$-0.883561\pi$
$191$	−6.64044	+	7.37495i	−0.480485	+	0.533633i	0.453352	+	0.891332i	$0.350228\pi$
$192$		0			0
$193$	−0.771626	−	7.34153i	−0.0555428	−	0.528455i	−0.986551	−	0.163456i	$-0.947736\pi$
$193$	−0.771626	−	7.34153i	−0.0555428	−	0.528455i	0.931008	−	0.364999i	$-0.118931\pi$
$194$	−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	−0.885981	−	0.463722i	$-0.846514\pi$
$211$	−16.4753	+	7.33527i	−1.13421	+	0.504981i	−0.248224	+	0.968703i	$0.579847\pi$
$212$	−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	−0.310888	−	0.950446i	$-0.600626\pi$
$223$	−3.11084	+	0.661230i	−0.208317	+	0.0442792i	0.102571	+	0.994726i	$0.467293\pi$
$224$	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	−0.449551	−	0.893255i	$-0.648416\pi$
$227$	7.31934	−	8.12895i	0.485801	−	0.539537i	0.935352	+	0.353718i	$0.115083\pi$
$228$		0			0
$229$	−16.8751	+	7.51329i	−1.11514	+	0.496492i	−0.879763	−	0.475412i	$-0.842299\pi$
$229$	−16.8751	+	7.51329i	−1.11514	+	0.496492i	−0.235377	+	0.971904i	$0.575632\pi$
$230$	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	−0.223552	−	0.974692i	$-0.571765\pi$
$233$	−18.6167	−	13.5258i	−1.21962	−	0.886106i	−0.996069	+	0.0885854i	$0.971765\pi$
$234$		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	0.938053	−	0.346492i	$-0.112627\pi$
$239$	7.65879	+	8.50595i	0.495406	+	0.550204i	−0.442647	+	0.896696i	$0.645961\pi$
$240$		0			0
$241$	−7.00000	−	12.1244i	−0.450910	−	0.780998i	0.547533	−	0.836784i	$-0.315567\pi$
$241$	−7.00000	−	12.1244i	−0.450910	−	0.780998i	−0.998443	+	0.0557856i	$0.982234\pi$
$242$	−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	0.989660	−	0.143436i	$-0.0458150\pi$
$251$	18.3631	+	13.3415i	1.15907	+	0.842111i	0.169406	+	0.985546i	$0.445815\pi$
$252$		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	0.569651	−	0.821886i	$-0.307078\pi$
$257$	12.1158	+	2.57529i	0.755762	+	0.160642i	0.186111	+	0.982529i	$0.440412\pi$
$258$		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	0.948129	−	0.317887i	$-0.102973\pi$
$263$	3.22344	+	5.58316i	0.198766	+	0.344273i	−0.749363	+	0.662160i	$0.769640\pi$
$264$		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	−0.961690	−	0.274138i	$-0.911608\pi$
$269$	−16.3709	+	11.8941i	−0.998149	+	0.725198i	−0.0364584	+	0.999335i	$0.511608\pi$
$270$		0			0
$271$	−0.298374	−	0.918300i	−0.0181249	−	0.0557828i	0.941585	−	0.336775i	$-0.109336\pi$
$271$	−0.298374	−	0.918300i	−0.0181249	−	0.0557828i	−0.959710	+	0.280993i	$0.909336\pi$
$272$	−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	0.747674	+	0.664066i	$0.231171\pi$
$277$	−2.02597	+	19.2758i	−0.121729	+	1.15817i	−0.869403	+	0.494104i	$0.835496\pi$
$278$	−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	−0.0977427	−	0.995212i	$-0.531162\pi$
$281$	−15.1325	−	6.73744i	−0.902732	−	0.401922i	−0.804989	+	0.593290i	$0.797829\pi$
$282$		0			0
$283$	−7.32315	−	8.13318i	−0.435316	−	0.483467i	0.485072	−	0.874474i	$-0.338793\pi$
$283$	−7.32315	−	8.13318i	−0.435316	−	0.483467i	−0.920388	+	0.391007i	$0.872127\pi$
$284$	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	0.348514	−	0.937303i	$-0.386686\pi$
$293$	4.88975	+	1.03935i	0.285663	+	0.0607194i	−0.0628519	+	0.998023i	$0.520020\pi$
$294$		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	−0.975837	−	0.218499i	$-0.929884\pi$
$311$	−19.2424	−	21.3709i	−1.09114	−	1.21183i	−0.115300	−	0.993331i	$-0.536783\pi$
$312$		0			0
$313$	28.9160	+	12.8742i	1.63443	+	0.727694i	0.999010	−	0.0444751i	$-0.0141615\pi$
$313$	28.9160	+	12.8742i	1.63443	+	0.727694i	0.635417	+	0.772169i	$0.280828\pi$
$314$	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	−0.993563	−	0.113281i	$-0.963864\pi$
$317$	0.0327727	−	0.311812i	0.00184070	−	0.0175131i	0.995404	+	0.0957679i	$0.0305306\pi$
$318$		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	0.748260	−	0.663406i	$-0.230890\pi$
$331$	−3.64590	−	6.31488i	−0.200397	−	0.347097i	−0.948656	+	0.316309i	$0.897556\pi$
$332$	−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	0.853059	−	0.521814i	$-0.174745\pi$
$337$	26.0701	+	5.54136i	1.42013	+	0.301857i	0.567067	+	0.823671i	$0.308078\pi$
$338$	−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	−0.804057	−	0.594553i	$-0.797329\pi$
$347$	−2.62999	−	25.0226i	−0.141185	−	1.34329i	0.662872	−	0.748733i	$-0.269338\pi$
$348$		0			0
$349$	−8.97973	+	1.90870i	−0.480674	+	0.102170i	−0.441875	−	0.897077i	$-0.645686\pi$
$349$	−8.97973	+	1.90870i	−0.480674	+	0.102170i	−0.0387989	+	0.999247i	$0.512353\pi$
$350$	−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	0.829624	+	0.558323i	$0.188555\pi$
$353$	16.8782	+	29.2338i	0.898334	+	1.55596i	0.0687102	+	0.997637i	$0.478112\pi$
$354$		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	0.966239	−	0.257646i	$-0.0829468\pi$
$359$	0.627058	+	1.92989i	0.0330949	+	0.101856i	−0.933145	+	0.359501i	$0.882947\pi$
$360$		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	−0.191572	−	0.981479i	$-0.561359\pi$
$367$	15.4131	−	17.1179i	0.804555	−	0.893548i	0.996127	+	0.0879301i	$0.0280252\pi$
$368$	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	−0.616833	−	0.787094i	$-0.711585\pi$
$373$	7.20820	−	12.4850i	0.373227	−	0.646448i	0.990060	+	0.140646i	$0.0449180\pi$
$374$	−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	−0.709772	−	0.704432i	$-0.751202\pi$
$379$	−5.04508	+	3.66547i	−0.259149	+	0.188282i	0.450623	+	0.892714i	$0.351202\pi$
$380$	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	−0.995413	−	0.0956673i	$-0.969502\pi$
$383$	−31.1244	+	13.8575i	−1.59038	+	0.708083i	−0.594967	+	0.803750i	$0.702835\pi$
$384$		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	−0.234405	−	0.972139i	$-0.575314\pi$
$389$	14.9286	−	16.5799i	0.756910	−	0.840634i	0.991315	+	0.131505i	$0.0419810\pi$
$390$		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	0.924780	+	0.380503i	$0.124249\pi$
$401$	1.98888	+	18.9229i	0.0993197	+	0.944964i	−0.825460	+	0.564461i	$0.809084\pi$
$402$		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	−0.517735	−	0.855541i	$-0.673225\pi$
$409$	−4.61864	+	2.05635i	−0.228377	+	0.101680i	0.289358	+	0.957221i	$0.406558\pi$
$410$	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	−0.00853378	−	0.999964i	$-0.502716\pi$
$419$	17.6391	−	30.5518i	0.861727	−	1.49255i	0.870261	−	0.492591i	$-0.163950\pi$
$420$		0			0
$421$	28.5764	−	6.07409i	1.39273	−	0.296033i	0.550355	−	0.834930i	$-0.314492\pi$
$421$	28.5764	−	6.07409i	1.39273	−	0.296033i	0.842372	+	0.538897i	$0.181159\pi$
$422$	−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	0.996190	+	0.0872135i	$0.0277962\pi$
$431$	28.7943	+	20.9203i	1.38697	+	1.00770i	0.390785	+	0.920482i	$0.372204\pi$
$432$		0			0
$433$	−0.819660	−	2.52265i	−0.0393904	−	0.121231i	0.929428	−	0.369004i	$-0.120301\pi$
$433$	−0.819660	−	2.52265i	−0.0393904	−	0.121231i	−0.968818	+	0.247773i	$0.920301\pi$
$434$	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	0.993320	+	0.115392i	$0.0368124\pi$
$439$	12.5000	+	21.6506i	0.596592	+	1.03333i	−0.396728	+	0.917936i	$0.629854\pi$
$440$	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	−0.685979	−	0.727622i	$-0.740626\pi$
$443$	−21.3991	+	4.54852i	−1.01670	+	0.216107i	−0.330722	+	0.943728i	$0.607292\pi$
$444$		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	−0.139800	−	0.990180i	$-0.544646\pi$
$449$	−23.8323	−	17.3152i	−1.12472	−	0.817155i	−0.984918	+	0.173024i	$0.944646\pi$
$450$		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	0.982148	−	0.188112i	$-0.0602368\pi$
$457$	32.0565	+	14.2725i	1.49954	+	0.667637i	0.517391	+	0.855749i	$0.326903\pi$
$458$	−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	0.847761	−	0.530379i	$-0.177950\pi$
$461$	−0.760951	−	1.31801i	−0.0354410	−	0.0613857i	−0.883202	+	0.468993i	$0.844617\pi$
$462$		0			0
$463$	10.7812	−	18.6735i	0.501043	−	0.867831i	−0.498957	−	0.866627i	$-0.666283\pi$
$463$	10.7812	−	18.6735i	0.501043	−	0.867831i	0.999999	−	0.00120439i	$-0.000383369\pi$
$464$	−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	−0.908783	−	0.417269i	$-0.862987\pi$
$467$	−17.1318	+	12.4470i	−0.792766	+	0.575978i	0.116017	+	0.993247i	$0.462987\pi$
$468$		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	−0.549417	−	0.835548i	$-0.685150\pi$
$479$	−33.6604	−	14.9866i	−1.53798	−	0.684754i	−0.988565	+	0.150795i	$0.951817\pi$
$480$		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	−0.727315	−	0.686304i	$-0.759232\pi$
$487$	5.83688	−	17.9641i	0.264494	−	0.814030i	0.991809	−	0.127726i	$-0.0407679\pi$
$488$	−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	0.615411	−	0.788206i	$-0.288990\pi$
$491$	18.9904	+	4.03654i	0.857025	+	0.182166i	0.241614	+	0.970372i	$0.422323\pi$
$492$		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	−0.575412	−	0.817864i	$-0.695158\pi$
$499$	−32.0271	−	6.80758i	−1.43373	−	0.304749i	−0.858320	+	0.513115i	$0.828492\pi$
$500$	−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	−0.901763	−	0.432231i	$-0.857726\pi$
$503$	1.83543	−	5.64888i	0.0818379	−	0.251871i	0.983601	+	0.180360i	$0.0577264\pi$
$504$		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	0.935278	−	0.353915i	$-0.115150\pi$
$509$	10.9542	+	12.1659i	0.485538	+	0.539245i	−0.449739	+	0.893160i	$0.648483\pi$
$510$		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	−0.951313	−	0.308225i	$-0.900265\pi$
$521$	−8.28232	−	25.4903i	−0.362855	−	1.11675i	0.588459	−	0.808527i	$-0.299735\pi$
$522$		0			0
$523$	30.2984	−	22.0131i	1.32486	−	0.962564i	0.324997	−	0.945715i	$-0.394637\pi$
$523$	30.2984	−	22.0131i	1.32486	−	0.962564i	0.999858	−	0.0168489i	$-0.00536341\pi$
$524$	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	−0.999300	−	0.0374146i	$-0.988088\pi$
$541$	−31.2533	−	22.7068i	−1.34368	−	0.976243i	−0.344384	−	0.938829i	$-0.611912\pi$
$542$	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	−0.606822	−	0.794838i	$-0.707556\pi$
$547$	−19.5966	+	4.16539i	−0.837892	+	0.178099i	−0.231070	+	0.972937i	$0.574223\pi$
$548$	−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	0.980301	−	0.197510i	$-0.0632855\pi$
$557$	1.67867	+	5.16641i	0.0711274	+	0.218908i	−0.909173	+	0.416418i	$0.863285\pi$
$558$		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	−0.0832865	−	0.996526i	$-0.526542\pi$
$563$	14.2733	−	6.35487i	0.601547	−	0.267826i	0.684833	+	0.728700i	$0.259875\pi$
$564$		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	−0.805773	−	0.592224i	$-0.798250\pi$
$569$	−31.0338	+	6.59644i	−1.30100	+	0.276537i	−0.495231	+	0.868761i	$0.664917\pi$
$570$		0			0
$571$	−5.98936	+	10.3739i	−0.250647	+	0.434133i	−0.963704	−	0.266973i	$-0.913977\pi$
$571$	−5.98936	+	10.3739i	−0.250647	+	0.434133i	0.713057	+	0.701106i	$0.247310\pi$
$572$	−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	−0.564862	−	0.825186i	$-0.691071\pi$
$577$	1.09017	−	0.792055i	0.0453844	−	0.0329737i	0.610246	+	0.792212i	$0.291071\pi$
$578$	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	0.0223656	−	0.999750i	$-0.492880\pi$
$587$	24.5746	−	27.2928i	1.01430	−	1.12650i	0.991935	−	0.126745i	$-0.0404531\pi$
$588$		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	−0.967877	−	0.251423i	$-0.919101\pi$
$599$	−1.79702	−	17.0975i	−0.0734243	−	0.698585i	0.894453	−	0.447162i	$-0.147565\pi$
$600$		0			0
$601$	−6.26352	+	6.95634i	−0.255494	+	0.283755i	−0.857223	−	0.514945i	$-0.827812\pi$
$601$	−6.26352	+	6.95634i	−0.255494	+	0.283755i	0.601729	+	0.798701i	$0.294479\pi$
$602$	−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	−0.861680	−	0.507451i	$-0.830588\pi$
$607$	−26.1439	+	11.6400i	−1.06115	+	0.472453i	−0.199467	+	0.979905i	$0.563921\pi$
$608$	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	−0.663959	−	0.747769i	$-0.731125\pi$
$613$	7.74265	−	23.8294i	0.312723	−	0.962461i	0.976682	−	0.214692i	$-0.0688748\pi$
$614$	−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	−0.984385	−	0.176031i	$-0.943674\pi$
$617$	−8.43908	+	14.6169i	−0.339745	+	0.588455i	0.644640	+	0.764486i	$0.277007\pi$
$618$		0			0
$619$	−6.73801	+	1.43221i	−0.270824	+	0.0575653i	−0.341322	−	0.939947i	$-0.610875\pi$
$619$	−6.73801	+	1.43221i	−0.270824	+	0.0575653i	0.0704980	+	0.997512i	$0.477541\pi$
$620$	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	−0.999235	−	0.0391166i	$-0.987546\pi$
$631$	−5.37132	−	16.5312i	−0.213829	−	0.658098i	0.785406	−	0.618981i	$-0.212454\pi$
$632$	−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	0.224318	−	0.974516i	$-0.427985\pi$
$641$	20.9029	−	4.44304i	0.825614	−	0.175490i	0.601296	+	0.799026i	$0.294651\pi$
$642$		0			0
$643$	4.30229	+	40.9336i	0.169666	+	1.61426i	0.665877	+	0.746061i	$0.268057\pi$
$643$	4.30229	+	40.9336i	0.169666	+	1.61426i	−0.496212	+	0.868202i	$0.665276\pi$
$644$	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	0.757900	−	0.652371i	$-0.226225\pi$
$647$	9.45368	+	6.86850i	0.371663	+	0.270029i	−0.386237	+	0.922399i	$0.626225\pi$
$648$		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	0.808891	−	0.587959i	$-0.200068\pi$
$653$	33.4425	+	7.10842i	1.30871	+	0.278174i	0.499814	+	0.866133i	$0.333402\pi$
$654$		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	0.981266	+	0.192658i	$0.0617108\pi$
$659$	16.8782	+	29.2338i	0.657480	+	1.13879i	−0.323786	+	0.946130i	$0.604956\pi$
$660$		0			0
$661$	−1.21885	+	2.11111i	−0.0474077	+	0.0821125i	−0.888755	−	0.458382i	$-0.848429\pi$
$661$	−1.21885	+	2.11111i	−0.0474077	+	0.0821125i	0.841348	+	0.540494i	$0.181763\pi$
$662$	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	0.894330	+	0.447408i	$0.147653\pi$
$673$	−1.90619	+	18.1362i	−0.0734782	+	0.699098i	−0.967808	+	0.251690i	$0.919014\pi$
$674$	−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	0.250248	−	0.968182i	$-0.419488\pi$
$677$	−7.85269	−	3.49624i	−0.301804	−	0.134372i	−0.552051	+	0.833810i	$0.686155\pi$
$678$		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	0.719456	+	0.694538i	$0.244391\pi$
$691$	−3.38261	+	32.1834i	−0.128681	+	1.22431i	−0.848137	+	0.529777i	$0.822276\pi$
$692$	−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	−0.716616	−	0.697468i	$-0.754310\pi$
$701$	7.23071	−	22.2538i	0.273100	−	0.840515i	0.989716	−	0.143047i	$-0.0456901\pi$
$702$		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	0.129038	−	0.991640i	$-0.458811\pi$
$709$	−13.8874	−	6.18306i	−0.521551	−	0.232210i	−0.650589	+	0.759430i	$0.725478\pi$
$710$	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	0.848110	−	0.529820i	$-0.177741\pi$
$719$	−4.00726	−	12.3331i	−0.149446	−	0.459947i	−0.997556	+	0.0698732i	$0.977741\pi$
$720$		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	0.625652	−	0.780103i	$-0.284833\pi$
$727$	−9.78115	−	16.9415i	−0.362763	−	0.628324i	−0.988414	+	0.151779i	$0.951500\pi$
$728$	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	0.464842	−	0.885393i	$-0.346111\pi$
$733$	14.3323	+	3.04642i	0.529375	+	0.112522i	0.0645326	+	0.997916i	$0.479444\pi$
$734$	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	0.282381	−	0.959302i	$-0.408876\pi$
$739$	−14.7533	−	10.7189i	−0.542709	−	0.394301i	−0.825090	+	0.565001i	$0.808876\pi$
$740$	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	−0.972667	−	0.232205i	$-0.925406\pi$
$743$	−1.89534	−	18.0329i	−0.0695332	−	0.661565i	0.903134	−	0.429360i	$-0.141261\pi$
$744$		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	0.724471	−	0.689305i	$-0.242084\pi$
$751$	−1.00810	−	1.11961i	−0.0367860	−	0.0408550i	−0.761257	+	0.648450i	$0.775417\pi$
$752$	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	0.994509	−	0.104655i	$-0.0333738\pi$
$757$	33.0795	+	24.0337i	1.20230	+	0.873519i	0.207787	+	0.978174i	$0.433374\pi$
$758$	−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	0.230248	−	0.973132i	$-0.426046\pi$
$761$	30.5515	−	13.6024i	1.10749	−	0.493087i	0.877244	+	0.480045i	$0.159380\pi$
$762$		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	−0.592365	−	0.805669i	$-0.701806\pi$
$769$	11.1353	−	19.2868i	0.401548	−	0.695501i	0.993913	+	0.110169i	$0.0351391\pi$
$770$	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	0.569542	+	0.821962i	$0.307121\pi$
$773$	−10.4084	+	32.0338i	−0.374364	+	1.15217i	−0.943907	+	0.330213i	$0.892879\pi$
$774$		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	−0.915841	−	0.401541i	$-0.868475\pi$
$787$	−2.90350	−	27.6249i	−0.103498	−	0.984722i	0.812342	−	0.583181i	$-0.198192\pi$
$788$	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	0.983680	−	0.179928i	$-0.0575866\pi$
$797$	−0.449255	−	4.27438i	−0.0159134	−	0.151406i	−0.999593	+	0.0285221i	$0.990920\pi$
$798$		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	−0.482619	−	0.875830i	$-0.660314\pi$
$809$	5.72294	−	4.15796i	0.201208	−	0.146186i	0.683827	+	0.729644i	$0.260314\pi$
$810$		0			0
$811$	−13.6631	+	42.0508i	−0.479777	+	1.47660i	0.359628	+	0.933096i	$0.382904\pi$
$811$	−13.6631	+	42.0508i	−0.479777	+	1.47660i	−0.839405	+	0.543506i	$0.817096\pi$
$812$	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	−0.0706831	−	0.997499i	$-0.522518\pi$
$821$	26.6113	−	29.5548i	0.928740	−	1.03147i	0.999423	−	0.0339711i	$-0.0108154\pi$
$822$		0			0
$823$	17.4592	−	7.77333i	0.608589	−	0.270961i	−0.0792153	−	0.996858i	$-0.525241\pi$
$823$	17.4592	−	7.77333i	0.608589	−	0.270961i	0.687804	+	0.725896i	$0.258575\pi$
$824$	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	0.411898	−	0.911230i	$-0.364866\pi$
$827$	−9.41667	−	6.84161i	−0.327450	−	0.237906i	−0.739348	+	0.673324i	$0.764866\pi$
$828$		0			0
$829$	6.19098	+	19.0539i	0.215022	+	0.661769i	0.999152	+	0.0411726i	$0.0131094\pi$
$829$	6.19098	+	19.0539i	0.215022	+	0.661769i	−0.784130	+	0.620596i	$0.786891\pi$
$830$	−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	0.0343236	−	0.999411i	$-0.489072\pi$
$839$	13.6768	−	2.90710i	0.472177	−	0.100364i	0.437853	+	0.899047i	$0.355739\pi$
$840$		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	0.388194	−	0.921578i	$-0.373099\pi$
$853$	−1.07829	−	0.480087i	−0.0369201	−	0.0164379i	−0.425114	+	0.905140i	$0.639766\pi$
$854$	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	0.723359	−	0.690472i	$-0.242597\pi$
$857$	−6.91718	−	11.9809i	−0.236286	−	0.409260i	−0.959646	+	0.281212i	$0.909264\pi$
$858$		0			0
$859$	−21.2082	+	36.7337i	−0.723615	+	1.25334i	0.235927	+	0.971771i	$0.424187\pi$
$859$	−21.2082	+	36.7337i	−0.723615	+	1.25334i	−0.959542	+	0.281566i	$0.909146\pi$
$860$	−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	−0.00317717	−	0.999995i	$-0.501011\pi$
$863$	27.8167	−	20.2100i	0.946893	−	0.687958i	0.950070	+	0.312037i	$0.101011\pi$
$864$		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	0.858677	−	0.512517i	$-0.171287\pi$
$877$	7.67636	+	8.52546i	0.259212	+	0.287884i	−0.599465	+	0.800401i	$0.704620\pi$
$878$	−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	−0.997232	−	0.0743567i	$-0.976310\pi$
$883$	−4.36068	+	13.4208i	−0.146749	+	0.451646i	0.850483	+	0.526002i	$0.176310\pi$
$884$	−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	0.994086	−	0.108592i	$-0.0346343\pi$
$887$	55.3378	+	11.7624i	1.85806	+	0.394943i	0.863975	+	0.503535i	$0.167968\pi$
$888$		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	−0.217234	−	0.976120i	$-0.569703\pi$
$907$	−32.7664	−	14.5885i	−1.08799	−	0.484404i	−0.870756	+	0.491716i	$0.836370\pi$
$908$	−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	0.965520	+	0.260328i	$0.0838309\pi$
$911$	−0.996829	+	9.48419i	−0.0330264	+	0.314225i	−0.998547	+	0.0538968i	$0.982836\pi$
$912$		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	−0.198702	−	0.980060i	$-0.563673\pi$
$919$	20.3713	−	14.8006i	0.671988	−	0.488228i	0.870690	+	0.491832i	$0.163673\pi$
$920$	−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	0.924547	−	0.381068i	$-0.124444\pi$
$929$	38.4042	+	17.0987i	1.26000	+	0.560989i	0.335454	+	0.942057i	$0.391110\pi$
$930$		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	0.435554	−	0.900162i	$-0.356552\pi$
$937$	−8.75329	−	6.35964i	−0.285957	−	0.207760i	−0.721512	+	0.692402i	$0.756552\pi$
$938$	−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	0.998968	+	0.0454116i	$0.0144599\pi$
$941$	0.959274	+	9.12689i	0.0312715	+	0.297528i	−0.967697	+	0.252116i	$0.918873\pi$
$942$		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	0.988566	−	0.150786i	$-0.0481805\pi$
$947$	11.1922	+	19.3855i	0.363699	+	0.629944i	−0.624868	+	0.780731i	$0.714847\pi$
$948$		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	0.999259	−	0.0385025i	$-0.0122587\pi$
$953$	5.19277	+	15.9817i	0.168210	+	0.517698i	−0.831048	+	0.556200i	$0.812259\pi$
$954$		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	−0.688074	−	0.725641i	$-0.741543\pi$
$967$	8.84346	−	15.3173i	0.284386	−	0.492572i	0.972460	+	0.233069i	$0.0748768\pi$
$968$	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	−0.945900	−	0.324459i	$-0.894818\pi$
$971$	0.313529	−	0.964944i	0.0100616	−	0.0309665i	0.955961	+	0.293493i	$0.0948177\pi$
$972$		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	−0.455212	−	0.890383i	$-0.650436\pi$
$977$	−3.06708	+	1.36555i	−0.0981245	+	0.0436878i	0.357087	+	0.934071i	$0.383770\pi$
$978$		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	−0.103950	+	0.994583i	$0.533148\pi$
$983$	−33.9306	+	37.6838i	−1.08222	+	1.20193i	−0.978268	+	0.207343i	$0.933519\pi$
$984$		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	−0.176351	−	0.984327i	$-0.556429\pi$
$997$	25.9239	−	28.7914i	0.821018	−	0.911833i	0.997369	+	0.0724947i	$0.0230960\pi$
$998$	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.433.1		16
3.2	odd	2	inner	891.2.n.e.433.2		16
9.2	odd	6	inner	891.2.n.e.136.1		16
9.4	even	3		99.2.f.c.37.1	✓	8
9.5	odd	6		99.2.f.c.37.2	yes	8
9.7	even	3	inner	891.2.n.e.136.2		16
11.3	even	5	inner	891.2.n.e.190.2		16
33.14	odd	10	inner	891.2.n.e.190.1		16
99.5	odd	30		1089.2.a.v.1.1		4
99.14	odd	30		99.2.f.c.91.2	yes	8
99.25	even	15	inner	891.2.n.e.784.1		16
99.47	odd	30	inner	891.2.n.e.784.2		16
99.49	even	15		1089.2.a.v.1.4		4
99.50	even	30		1089.2.a.w.1.4		4
99.58	even	15		99.2.f.c.91.1	yes	8
99.94	odd	30		1089.2.a.w.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.f.c.37.1	✓	8	9.4	even	3
99.2.f.c.37.2	yes	8	9.5	odd	6
99.2.f.c.91.1	yes	8	99.58	even	15
99.2.f.c.91.2	yes	8	99.14	odd	30
891.2.n.e.136.1		16	9.2	odd	6	inner
891.2.n.e.136.2		16	9.7	even	3	inner
891.2.n.e.190.1		16	33.14	odd	10	inner
891.2.n.e.190.2		16	11.3	even	5	inner
891.2.n.e.433.1		16	1.1	even	1	trivial
891.2.n.e.433.2		16	3.2	odd	2	inner
891.2.n.e.784.1		16	99.25	even	15	inner
891.2.n.e.784.2		16	99.47	odd	30	inner
1089.2.a.v.1.1		4	99.5	odd	30
1089.2.a.v.1.4		4	99.49	even	15
1089.2.a.w.1.1		4	99.94	odd	30
1089.2.a.w.1.4		4	99.50	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

Modular forms

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