LMFDB - Embedded newform 927.2.ba.b.28.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [927,2,Mod(19,927)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(927, base_ring=CyclotomicField(102))

chi = DirichletCharacter(H, H._module([0, 80]))

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

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

chi := DirichletCharacter("927.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 927 = 3^{2} \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	927.ba (of order $51$, degree $32$, 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:	$7.40213226737$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$8$ over $\Q(\zeta_{51})$
Twist minimal:	no (minimal twist has level 309)
Sato-Tate group:	$\mathrm{SU}(2)[C_{51}]$

Embedding invariants

Embedding label			28.1
Character	$\chi$	$=$	927.28
Dual form			927.2.ba.b.298.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.06654 + 1.60956i) q^{2} +(-0.673627 - 1.59151i) q^{4} +(-2.28349 + 0.726431i) q^{5} +(-0.823820 + 2.33783i) q^{7} +(-0.515877 - 0.0964341i) q^{8} +O(q^{10})$	\(q+(-1.06654 + 1.60956i) q^{2} +(-0.673627 - 1.59151i) q^{4} +(-2.28349 + 0.726431i) q^{5} +(-0.823820 + 2.33783i) q^{7} +(-0.515877 - 0.0964341i) q^{8} +(1.26619 - 4.45019i) q^{10} +(0.453444 + 0.0279674i) q^{11} +(-3.37263 + 0.630454i) q^{13} +(-2.88426 - 3.81937i) q^{14} +(3.11153 - 3.20887i) q^{16} +(2.94304 + 1.35402i) q^{17} +(-5.23345 - 2.81031i) q^{19} +(2.69434 + 3.14485i) q^{20} +(-0.528629 + 0.700018i) q^{22} +(0.410137 - 0.823667i) q^{23} +(0.605651 - 0.428732i) q^{25} +(2.58228 - 6.10087i) q^{26} +(4.27562 - 0.263711i) q^{28} +(-0.570120 + 2.60325i) q^{29} +(-1.46654 - 5.15434i) q^{31} +(1.62178 + 7.40526i) q^{32} +(-5.31824 + 3.29291i) q^{34} +(0.182913 - 5.93687i) q^{35} +(4.90908 - 1.90179i) q^{37} +(10.1050 - 5.42629i) q^{38} +(1.24805 - 0.154542i) q^{40} +(-0.0157621 - 0.00501428i) q^{41} +(1.19648 + 7.70783i) q^{43} +(-0.260941 - 0.740498i) q^{44} +(0.888318 + 1.53861i) q^{46} +(3.93077 - 6.80829i) q^{47} +(0.666787 + 0.536561i) q^{49} +(0.0441223 + 1.43209i) q^{50} +(3.27527 + 4.94287i) q^{52} +(-0.126880 - 4.11819i) q^{53} +(-1.05575 + 0.265532i) q^{55} +(0.650436 - 1.12659i) q^{56} +(-3.58204 - 3.69410i) q^{58} +(-0.865460 - 2.45600i) q^{59} +(-1.32546 - 14.3040i) q^{61} +(9.86035 + 3.13680i) q^{62} +(-5.31313 - 2.05832i) q^{64} +(7.24340 - 3.88962i) q^{65} +(-1.65765 + 1.93482i) q^{67} +(0.172410 - 5.59597i) q^{68} +(9.36069 + 6.62630i) q^{70} +(-1.98264 - 9.05301i) q^{71} +(6.47676 - 5.90434i) q^{73} +(-2.17466 + 9.92980i) q^{74} +(-0.947223 + 10.2222i) q^{76} +(-0.438939 + 1.03703i) q^{77} +(8.07662 + 7.36281i) q^{79} +(-4.77413 + 9.58775i) q^{80} +(0.0248816 - 0.0200222i) q^{82} +(-3.95041 - 4.61093i) q^{83} +(-7.70402 - 0.953964i) q^{85} +(-13.6823 - 6.29487i) q^{86} +(-0.231224 - 0.0581552i) q^{88} +(-6.23039 - 8.25037i) q^{89} +(1.30455 - 8.40403i) q^{91} +(-1.58715 - 0.0978920i) q^{92} +(6.76607 + 13.5881i) q^{94} +(13.9920 + 2.61557i) q^{95} +(11.3234 - 5.20961i) q^{97} +(-1.57478 + 0.500974i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q + q^{2} + 3 q^{4} + q^{5} - 4 q^{7} - 57 q^{8}+O(q^{10}) $ 256 * q + q^2 + 3 * q^4 + q^5 - 4 * q^7 - 57 * q^8	$ 256 q + q^{2} + 3 q^{4} + q^{5} - 4 q^{7} - 57 q^{8} - 58 q^{10} + 32 q^{11} + 10 q^{13} - 57 q^{14} - 7 q^{16} - 15 q^{19} - 46 q^{20} + 54 q^{22} + 21 q^{23} - 27 q^{25} - 14 q^{26} - 49 q^{28} - 2 q^{29} - 92 q^{31} - 8 q^{32} - 35 q^{34} - 58 q^{35} + 4 q^{37} + 51 q^{38} + 41 q^{40} + 216 q^{41} + 3 q^{43} + 133 q^{44} - 36 q^{46} - 2 q^{47} + 26 q^{49} + 60 q^{50} + 62 q^{52} + 7 q^{53} + 16 q^{55} - 19 q^{56} - 32 q^{58} - 73 q^{59} - 58 q^{61} + 20 q^{62} - 269 q^{64} - 41 q^{65} - 10 q^{67} + 8 q^{68} + 89 q^{70} + 178 q^{71} - 84 q^{73} + 239 q^{74} + 58 q^{76} - 33 q^{77} - 42 q^{79} + 24 q^{80} - 198 q^{82} - 31 q^{83} + 130 q^{85} + 86 q^{86} + 66 q^{88} - 73 q^{89} - 27 q^{91} - 146 q^{92} - 446 q^{94} - 48 q^{95} + 100 q^{97} - 363 q^{98}+O(q^{100}) $ 256 * q + q^2 + 3 * q^4 + q^5 - 4 * q^7 - 57 * q^8 - 58 * q^10 + 32 * q^11 + 10 * q^13 - 57 * q^14 - 7 * q^16 - 15 * q^19 - 46 * q^20 + 54 * q^22 + 21 * q^23 - 27 * q^25 - 14 * q^26 - 49 * q^28 - 2 * q^29 - 92 * q^31 - 8 * q^32 - 35 * q^34 - 58 * q^35 + 4 * q^37 + 51 * q^38 + 41 * q^40 + 216 * q^41 + 3 * q^43 + 133 * q^44 - 36 * q^46 - 2 * q^47 + 26 * q^49 + 60 * q^50 + 62 * q^52 + 7 * q^53 + 16 * q^55 - 19 * q^56 - 32 * q^58 - 73 * q^59 - 58 * q^61 + 20 * q^62 - 269 * q^64 - 41 * q^65 - 10 * q^67 + 8 * q^68 + 89 * q^70 + 178 * q^71 - 84 * q^73 + 239 * q^74 + 58 * q^76 - 33 * q^77 - 42 * q^79 + 24 * q^80 - 198 * q^82 - 31 * q^83 + 130 * q^85 + 86 * q^86 + 66 * q^88 - 73 * q^89 - 27 * q^91 - 146 * q^92 - 446 * q^94 - 48 * q^95 + 100 * q^97 - 363 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/927\mathbb{Z}\right)^\times$.

$n$	$722$	$829$
$\chi(n)$	$1$	$e\left(\frac{46}{51}\right)$

Coefficient data

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

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

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

$2$	−1.06654	+	1.60956i	−0.754155	+	1.13813i	0.232066	+	0.972700i	$0.425451\pi$
$2$	−1.06654	+	1.60956i	−0.754155	+	1.13813i	−0.986221	+	0.165434i	$0.947098\pi$
$3$		0			0
$3$		0			0
$4$	−0.673627	−	1.59151i	−0.336813	−	0.795753i
$5$	−2.28349	+	0.726431i	−1.02121	+	0.324870i	−0.766566	−	0.642165i	$-0.778036\pi$
$5$	−2.28349	+	0.726431i	−1.02121	+	0.324870i	−0.254643	+	0.967035i	$0.581958\pi$
$6$		0			0
$7$	−0.823820	+	2.33783i	−0.311375	+	0.883617i	0.677587	+	0.735443i	$0.263026\pi$
$7$	−0.823820	+	2.33783i	−0.311375	+	0.883617i	−0.988961	+	0.148174i	$0.952660\pi$
$8$	−0.515877	−	0.0964341i	−0.182390	−	0.0340946i
$9$		0			0
$10$	1.26619	−	4.45019i	0.400404	−	1.40727i
$11$	0.453444	+	0.0279674i	0.136718	+	0.00843250i	0.129776	−	0.991543i	$-0.458574\pi$
$11$	0.453444	+	0.0279674i	0.136718	+	0.00843250i	0.00694285	+	0.999976i	$0.497790\pi$
$12$		0			0
$13$	−3.37263	+	0.630454i	−0.935400	+	0.174857i	−0.629317	−	0.777148i	$-0.716665\pi$
$13$	−3.37263	+	0.630454i	−0.935400	+	0.174857i	−0.306083	+	0.952005i	$0.599018\pi$
$14$	−2.88426	−	3.81937i	−0.770850	−	1.02077i
$15$		0			0
$16$	3.11153	−	3.20887i	0.777883	−	0.802218i
$17$	2.94304	+	1.35402i	0.713793	+	0.328397i	0.741253	−	0.671226i	$-0.234232\pi$
$17$	2.94304	+	1.35402i	0.713793	+	0.328397i	−0.0274597	+	0.999623i	$0.508742\pi$
$18$		0			0
$19$	−5.23345	−	2.81031i	−1.20064	−	0.644728i	−0.254054	−	0.967190i	$-0.581764\pi$
$19$	−5.23345	−	2.81031i	−1.20064	−	0.644728i	−0.946583	+	0.322462i	$0.895490\pi$
$20$	2.69434	+	3.14485i	0.602473	+	0.703209i
$21$		0			0
$22$	−0.528629	+	0.700018i	−0.112704	+	0.149244i
$23$	0.410137	−	0.823667i	0.0855195	−	0.171746i	−0.848275	−	0.529556i	$-0.822359\pi$
$23$	0.410137	−	0.823667i	0.0855195	−	0.171746i	0.933795	+	0.357809i	$0.116476\pi$
$24$		0			0
$25$	0.605651	−	0.428732i	0.121130	−	0.0857463i
$26$	2.58228	−	6.10087i	0.506426	−	1.19648i
$27$		0			0
$28$	4.27562	−	0.263711i	0.808016	−	0.0498367i
$29$	−0.570120	+	2.60325i	−0.105869	+	0.483411i	0.893539	+	0.448986i	$0.148215\pi$
$29$	−0.570120	+	2.60325i	−0.105869	+	0.483411i	−0.999407	+	0.0344245i	$0.989040\pi$
$30$		0			0
$31$	−1.46654	−	5.15434i	−0.263398	−	0.925747i	−0.974822	−	0.222984i	$-0.928420\pi$
$31$	−1.46654	−	5.15434i	−0.263398	−	0.925747i	0.711425	−	0.702763i	$-0.248050\pi$
$32$	1.62178	+	7.40526i	0.286692	+	1.30908i
$33$		0			0
$34$	−5.31824	+	3.29291i	−0.912070	+	0.564730i
$35$	0.182913	−	5.93687i	0.0309179	−	1.00351i
$36$		0			0
$37$	4.90908	−	1.90179i	0.807047	−	0.312652i	0.0778585	−	0.996964i	$-0.475192\pi$
$37$	4.90908	−	1.90179i	0.807047	−	0.312652i	0.729189	+	0.684313i	$0.239898\pi$
$38$	10.1050	−	5.42629i	1.63925	−	0.880260i
$39$		0			0
$40$	1.24805	−	0.154542i	0.197335	−	0.0244353i
$41$	−0.0157621	−	0.00501428i	−0.00246162	−	0.000783099i	0.301922	−	0.953333i	$-0.402372\pi$
$41$	−0.0157621	−	0.00501428i	−0.00246162	−	0.000783099i	−0.304383	+	0.952550i	$0.598450\pi$
$42$		0			0
$43$	1.19648	+	7.70783i	0.182461	+	1.17543i	0.885624	+	0.464404i	$0.153731\pi$
$43$	1.19648	+	7.70783i	0.182461	+	1.17543i	−0.703163	+	0.711029i	$0.748229\pi$
$44$	−0.260941	−	0.740498i	−0.0393384	−	0.111634i
$45$		0			0
$46$	0.888318	+	1.53861i	0.130975	+	0.226856i
$47$	3.93077	−	6.80829i	0.573361	−	0.993091i	−0.422856	−	0.906197i	$-0.638972\pi$
$47$	3.93077	−	6.80829i	0.573361	−	0.993091i	0.996218	−	0.0868942i	$-0.0276942\pi$
$48$		0			0
$49$	0.666787	+	0.536561i	0.0952552	+	0.0766516i
$50$	0.0441223	+	1.43209i	0.00623984	+	0.202528i
$51$		0			0
$52$	3.27527	+	4.94287i	0.454198	+	0.685453i
$53$	−0.126880	−	4.11819i	−0.0174283	−	0.565676i	−0.967387	−	0.253302i	$-0.918483\pi$
$53$	−0.126880	−	4.11819i	−0.0174283	−	0.565676i	0.949959	−	0.312375i	$-0.101124\pi$
$54$		0			0
$55$	−1.05575	+	0.265532i	−0.142358	+	0.0358044i
$56$	0.650436	−	1.12659i	0.0869182	−	0.150547i
$57$		0			0
$58$	−3.58204	−	3.69410i	−0.470345	−	0.485059i
$59$	−0.865460	−	2.45600i	−0.112673	−	0.319744i	0.873169	−	0.487417i	$-0.162061\pi$
$59$	−0.865460	−	2.45600i	−0.112673	−	0.319744i	−0.985843	+	0.167673i	$0.946375\pi$
$60$		0			0
$61$	−1.32546	−	14.3040i	−0.169708	−	1.83144i	−0.475930	−	0.879483i	$-0.657888\pi$
$61$	−1.32546	−	14.3040i	−0.169708	−	1.83144i	0.306222	−	0.951960i	$-0.400935\pi$
$62$	9.86035	+	3.13680i	1.25227	+	0.398375i
$63$		0			0
$64$	−5.31313	−	2.05832i	−0.664142	−	0.257290i
$65$	7.24340	−	3.88962i	0.898433	−	0.482448i
$66$		0			0
$67$	−1.65765	+	1.93482i	−0.202514	+	0.236376i	−0.851409	−	0.524503i	$-0.824251\pi$
$67$	−1.65765	+	1.93482i	−0.202514	+	0.236376i	0.648895	+	0.760878i	$0.275232\pi$
$68$	0.172410	−	5.59597i	0.0209078	−	0.678611i
$69$		0			0
$70$	9.36069	+	6.62630i	1.11882	+	0.791994i
$71$	−1.98264	−	9.05301i	−0.235296	−	1.07439i	−0.933523	−	0.358518i	$-0.883282\pi$
$71$	−1.98264	−	9.05301i	−0.235296	−	1.07439i	0.698227	−	0.715877i	$-0.253973\pi$
$72$		0			0
$73$	6.47676	−	5.90434i	0.758047	−	0.691051i	−0.199317	−	0.979935i	$-0.563872\pi$
$73$	6.47676	−	5.90434i	0.758047	−	0.691051i	0.957364	+	0.288884i	$0.0932841\pi$
$74$	−2.17466	+	9.92980i	−0.252799	+	1.15432i
$75$		0			0
$76$	−0.947223	+	10.2222i	−0.108654	+	1.17256i
$77$	−0.438939	+	1.03703i	−0.0500218	+	0.118181i
$78$		0			0
$79$	8.07662	+	7.36281i	0.908691	+	0.828381i	0.985676	−	0.168651i	$-0.0539412\pi$
$79$	8.07662	+	7.36281i	0.908691	+	0.828381i	−0.0769852	+	0.997032i	$0.524529\pi$
$80$	−4.77413	+	9.58775i	−0.533764	+	1.07194i
$81$		0			0
$82$	0.0248816	−	0.0200222i	0.00274772	−	0.00221108i
$83$	−3.95041	−	4.61093i	−0.433613	−	0.506116i	0.499194	−	0.866490i	$-0.333629\pi$
$83$	−3.95041	−	4.61093i	−0.433613	−	0.506116i	−0.932808	+	0.360374i	$0.882649\pi$
$84$		0			0
$85$	−7.70402	−	0.953964i	−0.835618	−	0.103472i
$86$	−13.6823	−	6.29487i	−1.47540	−	0.678793i
$87$		0			0
$88$	−0.231224	−	0.0581552i	−0.0246486	−	0.00619936i
$89$	−6.23039	−	8.25037i	−0.660420	−	0.874537i	0.337344	−	0.941382i	$-0.390472\pi$
$89$	−6.23039	−	8.25037i	−0.660420	−	0.874537i	−0.997763	+	0.0668445i	$0.978707\pi$
$90$		0			0
$91$	1.30455	−	8.40403i	0.136754	−	0.880982i
$92$	−1.58715	−	0.0978920i	−0.165472	−	0.0102060i
$93$		0			0
$94$	6.76607	+	13.5881i	0.697867	+	1.40151i
$95$	13.9920	+	2.61557i	1.43555	+	0.268352i
$96$		0			0
$97$	11.3234	−	5.20961i	1.14972	−	0.528956i	0.251222	−	0.967929i	$-0.419168\pi$
$97$	11.3234	−	5.20961i	1.14972	−	0.528956i	0.898500	+	0.438973i	$0.144658\pi$
$98$	−1.57478	+	0.500974i	−0.159077	+	0.0506060i
$99$		0			0
$100$	−1.09031	−	0.675093i	−0.109031	−	0.0675093i
$101$	−9.38204	+	14.1589i	−0.933548	+	1.40886i	−0.0210521	+	0.999778i	$0.506702\pi$
$101$	−9.38204	+	14.1589i	−0.933548	+	1.40886i	−0.912496	+	0.409086i	$0.865847\pi$
$102$		0			0
$103$	4.78508	+	8.95003i	0.471488	+	0.881872i
$103$	4.78508	+	8.95003i	0.471488	+	0.881872i
$104$	1.80066			0.176569
$105$		0			0
$106$	6.76381	+	4.18797i	0.656959	+	0.406772i
$107$	3.52551	+	8.32934i	0.340824	+	0.805227i	0.998644	+	0.0520529i	$0.0165764\pi$
$107$	3.52551	+	8.32934i	0.340824	+	0.805227i	−0.657821	+	0.753174i	$0.728522\pi$
$108$		0			0
$109$	−15.3710	+	7.07176i	−1.47227	+	0.677352i	−0.981063	−	0.193690i	$-0.937954\pi$
$109$	−15.3710	+	7.07176i	−1.47227	+	0.677352i	−0.491208	+	0.871042i	$0.663445\pi$
$110$	0.698606	−	1.98250i	0.0666095	−	0.189024i
$111$		0			0
$112$	4.93846	+	9.91777i	0.466641	+	0.937141i
$113$	0.407696	−	1.43290i	0.0383528	−	0.134796i	−0.940285	−	0.340388i	$-0.889441\pi$
$113$	0.407696	−	1.43290i	0.0383528	−	0.134796i	0.978638	+	0.205592i	$0.0659120\pi$
$114$		0			0
$115$	−0.338208	+	2.17877i	−0.0315381	+	0.203172i
$116$	4.52713	−	0.846267i	0.420333	−	0.0785739i
$117$		0			0
$118$	4.87613	+	1.22640i	0.448884	+	0.112899i
$119$	−5.59000	+	5.76488i	−0.512434	+	0.528465i
$120$		0			0
$121$	−10.7118	−	1.32641i	−0.973800	−	0.120583i
$122$	24.4369	+	13.1223i	2.21241	+	1.18804i
$123$		0			0
$124$	−7.21526	+	5.80610i	−0.647950	+	0.521403i
$125$	6.14878	−	8.14230i	0.549963	−	0.728269i
$126$		0			0
$127$	−13.5623	−	12.3637i	−1.20346	−	1.09710i	−0.992830	−	0.119533i	$-0.961860\pi$
$127$	−13.5623	−	12.3637i	−1.20346	−	1.09710i	−0.210630	−	0.977566i	$-0.567551\pi$
$128$	−3.39516	+	2.40338i	−0.300092	+	0.212431i
$129$		0			0
$130$	−1.46475	+	15.8071i	−0.128467	+	1.38638i
$131$	−0.661000	+	0.0407691i	−0.0577518	+	0.00356201i	−0.0904110	−	0.995905i	$-0.528818\pi$
$131$	−0.661000	+	0.0407691i	−0.0577518	+	0.00356201i	0.0326592	+	0.999467i	$0.489602\pi$
$132$		0			0
$133$	10.8814	−	9.91975i	0.943541	−	0.860151i
$134$	−1.34627	−	4.73165i	−0.116300	−	0.408752i
$135$		0			0
$136$	−1.38767	−	0.982315i	−0.118992	−	0.0842328i
$137$	−6.56414	+	4.06434i	−0.560812	+	0.347240i	−0.777384	−	0.629027i	$-0.783454\pi$
$137$	−6.56414	+	4.06434i	−0.560812	+	0.347240i	0.216572	+	0.976267i	$0.430512\pi$
$138$		0			0
$139$	7.08348	−	8.26787i	0.600813	−	0.701272i	−0.373204	−	0.927749i	$-0.621741\pi$
$139$	7.08348	−	8.26787i	0.600813	−	0.701272i	0.974016	+	0.226478i	$0.0727211\pi$
$140$	−9.57178	+	3.70813i	−0.808963	+	0.313394i
$141$		0			0
$142$	16.6860	+	6.46417i	1.40025	+	0.542461i
$143$	−1.54693	+	0.191552i	−0.129361	+	0.0160183i
$144$		0			0
$145$	−0.589215	−	6.35864i	−0.0489317	−	0.528057i
$146$	2.59573	+	16.7220i	0.214824	+	1.38392i
$147$		0			0
$148$	−6.33359	−	6.53173i	−0.520618	−	0.536905i
$149$	7.07398	+	12.2525i	0.579523	+	1.00376i	0.995534	+	0.0944036i	$0.0300944\pi$
$149$	7.07398	+	12.2525i	0.579523	+	1.00376i	−0.416011	+	0.909360i	$0.636572\pi$
$150$		0			0
$151$	0.819562	−	0.206128i	0.0666950	−	0.0167745i	−0.210422	−	0.977611i	$-0.567484\pi$
$151$	0.819562	−	0.206128i	0.0666950	−	0.0167745i	0.277117	+	0.960836i	$0.410621\pi$
$152$	2.42881	+	1.95445i	0.197002	+	0.158527i
$153$		0			0
$154$	−1.20103	−	1.81254i	−0.0967817	−	0.146058i
$155$	7.09310	+	10.7046i	0.569731	+	0.859811i
$156$		0			0
$157$	−13.7324	−	11.0504i	−1.09596	−	0.881918i	−0.102348	−	0.994749i	$-0.532636\pi$
$157$	−13.7324	−	11.0504i	−1.09596	−	0.881918i	−0.993614	+	0.112831i	$0.964008\pi$
$158$	−20.4649	+	5.14713i	−1.62810	+	0.409484i
$159$		0			0
$160$	−9.08273	−	15.7318i	−0.718053	−	1.24370i
$161$	1.58771	+	1.63739i	0.125129	+	0.129044i
$162$		0			0
$163$	−0.302089	−	1.94609i	−0.0236614	−	0.152429i	0.973391	−	0.229149i	$-0.0735945\pi$
$163$	−0.302089	−	1.94609i	−0.0236614	−	0.152429i	−0.997053	+	0.0767200i	$0.975555\pi$
$164$	0.00263751	+	0.0284632i	0.000205955	+	0.00222260i
$165$		0			0
$166$	11.6348	−	1.44071i	0.903039	−	0.111820i
$167$	6.38520	+	2.47364i	0.494102	+	0.191416i	0.595383	−	0.803442i	$-0.297000\pi$
$167$	6.38520	+	2.47364i	0.494102	+	0.191416i	−0.101282	+	0.994858i	$0.532294\pi$
$168$		0			0
$169$	−1.14496	+	0.443560i	−0.0880738	+	0.0341200i
$170$	9.75208	−	11.3827i	0.747950	−	0.873012i
$171$		0			0
$172$	11.4611	−	7.09640i	0.873899	−	0.541095i
$173$	−6.60374	−	4.67469i	−0.502073	−	0.355410i	0.298730	−	0.954338i	$-0.403437\pi$
$173$	−6.60374	−	4.67469i	−0.502073	−	0.355410i	−0.800803	+	0.598927i	$0.795594\pi$
$174$		0			0
$175$	0.503355	+	1.76911i	0.0380500	+	0.133732i
$176$	1.50065	−	1.36802i	0.113116	−	0.103118i
$177$		0			0
$178$	19.9244	−	1.22890i	1.49340	−	0.0921097i
$179$	1.20839	−	13.0406i	0.0903194	−	0.974702i	−0.823158	−	0.567812i	$-0.807790\pi$
$179$	1.20839	−	13.0406i	0.0903194	−	0.974702i	0.913477	−	0.406889i	$-0.133387\pi$
$180$		0			0
$181$	−13.0242	+	9.21966i	−0.968083	+	0.685292i	−0.949247	−	0.314531i	$-0.898153\pi$
$181$	−13.0242	+	9.21966i	−0.968083	+	0.685292i	−0.0188360	+	0.999823i	$0.505996\pi$
$182$	12.1355	+	11.0630i	0.899542	+	0.820040i
$183$		0			0
$184$	−0.291010	+	0.385359i	−0.0214535	+	0.0284091i
$185$	−9.82832	+	7.90882i	−0.722593	+	0.581468i
$186$		0			0
$187$	1.29664	+	0.696279i	0.0948195	+	0.0509170i
$188$	−13.4833	−	1.66959i	−0.983371	−	0.121768i
$189$		0			0
$190$	−19.1329	+	19.7315i	−1.38805	+	1.43147i
$191$	−24.0046	−	6.03741i	−1.73692	−	0.436852i	−0.759903	−	0.650036i	$-0.774754\pi$
$191$	−24.0046	−	6.03741i	−1.73692	−	0.436852i	−0.977012	+	0.213185i	$0.931616\pi$
$192$		0			0
$193$	7.23906	−	1.35322i	0.521079	−	0.0974066i	0.0833621	−	0.996519i	$-0.473434\pi$
$193$	7.23906	−	1.35322i	0.521079	−	0.0974066i	0.437717	+	0.899113i	$0.355787\pi$
$194$	−3.69166	+	23.7821i	−0.265046	+	1.70745i
$195$		0			0
$196$	0.404775	−	1.42264i	0.0289125	−	0.101617i
$197$	−10.0635	−	20.2103i	−0.716996	−	1.43992i	−0.890451	−	0.455079i	$-0.849611\pi$
$197$	−10.0635	−	20.2103i	−0.716996	−	1.43992i	0.173455	−	0.984842i	$-0.444507\pi$
$198$		0			0
$199$	1.71536	−	4.86782i	0.121598	−	0.345071i	−0.866440	−	0.499282i	$-0.833597\pi$
$199$	1.71536	−	4.86782i	0.121598	−	0.345071i	0.988038	+	0.154211i	$0.0492835\pi$
$200$	−0.353786	+	0.162767i	−0.0250164	+	0.0115094i
$201$		0			0
$202$	−12.7834	−	30.2020i	−0.899437	−	2.12500i
$203$	−5.61627	−	3.47745i	−0.394185	−	0.244069i
$204$		0			0
$205$	0.0396351			0.00276824
$206$	−19.5091	−	1.84363i	−1.35926	−	0.128452i
$207$		0			0
$208$	−8.47100	+	12.7840i	−0.587358	+	0.886413i
$209$	−2.29448	−	1.42068i	−0.158712	−	0.0982706i
$210$		0			0
$211$	−9.01342	+	2.86738i	−0.620510	+	0.197398i	−0.596891	−	0.802323i	$-0.703597\pi$
$211$	−9.01342	+	2.86738i	−0.620510	+	0.197398i	−0.0236192	+	0.999721i	$0.507519\pi$
$212$	−6.46865	+	2.97605i	−0.444269	+	0.204396i
$213$		0			0
$214$	−17.1667	−	3.20901i	−1.17349	−	0.219363i
$215$	−8.33135	−	16.7316i	−0.568194	−	1.14109i
$216$		0			0
$217$	13.2581	+	0.817734i	0.900021	+	0.0555114i
$218$	5.01122	−	32.2828i	0.339403	−	2.18647i
$219$		0			0
$220$	1.13378	+	1.50137i	0.0764393	+	0.101222i
$221$	−10.7795	−	2.71114i	−0.725104	−	0.182371i
$222$		0			0
$223$	−21.4133	−	9.85168i	−1.43394	−	0.659718i	−0.460292	−	0.887768i	$-0.652255\pi$
$223$	−21.4133	−	9.85168i	−1.43394	−	0.659718i	−0.973649	+	0.228050i	$0.926765\pi$
$224$	−18.6483	−	2.30916i	−1.24599	−	0.154287i
$225$		0			0
$226$	1.87153	+	2.18446i	0.124492	+	0.145308i
$227$	−15.6025	+	12.5553i	−1.03558	+	0.833326i	−0.986217	−	0.165455i	$-0.947091\pi$
$227$	−15.6025	+	12.5553i	−1.03558	+	0.833326i	−0.0493601	+	0.998781i	$0.515718\pi$
$228$		0			0
$229$	−3.74961	+	7.53022i	−0.247781	+	0.497611i	−0.983782	−	0.179369i	$-0.942594\pi$
$229$	−3.74961	+	7.53022i	−0.247781	+	0.497611i	0.736001	+	0.676981i	$0.236712\pi$
$230$	−3.14616	−	2.86811i	−0.207452	−	0.189117i
$231$		0			0
$232$	0.545153	−	1.28797i	0.0357910	−	0.0845597i
$233$	−1.18299	+	12.7665i	−0.0775003	+	0.836361i	0.864915	+	0.501918i	$0.167372\pi$
$233$	−1.18299	+	12.7665i	−0.0775003	+	0.836361i	−0.942416	+	0.334444i	$0.891452\pi$
$234$		0			0
$235$	−4.03012	+	18.4021i	−0.262896	+	1.20042i
$236$	−3.32574	+	3.03181i	−0.216487	+	0.197354i
$237$		0			0
$238$	−3.31701	−	15.1459i	−0.215010	−	0.981764i
$239$	−11.6080	−	8.21714i	−0.750860	−	0.531522i	0.137594	−	0.990489i	$-0.456063\pi$
$239$	−11.6080	−	8.21714i	−0.750860	−	0.531522i	−0.888454	+	0.458966i	$0.848220\pi$
$240$		0			0
$241$	0.790367	−	25.6532i	0.0509120	−	1.65247i	−0.537028	−	0.843564i	$-0.680453\pi$
$241$	0.790367	−	25.6532i	0.0509120	−	1.65247i	0.587940	−	0.808904i	$-0.299939\pi$
$242$	13.5595	−	15.8267i	0.871635	−	1.01738i
$243$		0			0
$244$	−21.8721	+	11.7451i	−1.40022	+	0.751900i
$245$	−1.91238	−	0.740859i	−0.122177	−	0.0473317i
$246$		0			0
$247$	19.4223	+	6.17867i	1.23581	+	0.393140i
$248$	0.259498	+	2.80043i	0.0164781	+	0.177827i
$249$		0			0
$250$	6.54766	+	18.5809i	0.414110	+	1.17516i
$251$	1.88966	+	1.94878i	0.119275	+	0.123006i	0.774910	−	0.632072i	$-0.217795\pi$
$251$	1.88966	+	1.94878i	0.119275	+	0.123006i	−0.655635	+	0.755078i	$0.727599\pi$
$252$		0			0
$253$	0.209010	−	0.362016i	0.0131403	−	0.0227597i
$254$	34.3648	−	8.64310i	2.15624	−	0.542316i
$255$		0			0
$256$	−0.598275	−	19.4184i	−0.0373922	−	1.21365i
$257$	3.37521	+	5.09371i	0.210540	+	0.317737i	0.923594	−	0.383373i	$-0.125237\pi$
$257$	3.37521	+	5.09371i	0.210540	+	0.317737i	−0.713054	+	0.701109i	$0.752688\pi$
$258$		0			0
$259$	0.401861	+	13.0433i	0.0249704	+	0.810473i
$260$	−11.0697	−	8.90776i	−0.686514	−	0.552436i
$261$		0			0
$262$	0.639360	−	1.10740i	0.0394998	−	0.0684156i
$263$	−11.4829	−	19.8889i	−0.708065	−	1.22640i	−0.965574	−	0.260129i	$-0.916235\pi$
$263$	−11.4829	−	19.8889i	−0.708065	−	1.22640i	0.257509	−	0.966276i	$-0.417098\pi$
$264$		0			0
$265$	3.28131	+	9.31168i	0.201569	+	0.572012i
$266$	4.36102	+	28.0942i	0.267391	+	1.72256i
$267$		0			0
$268$	4.19591	+	1.33482i	0.256306	+	0.0815368i
$269$	7.68150	−	0.951176i	0.468350	−	0.0579942i	0.114757	−	0.993394i	$-0.463391\pi$
$269$	7.68150	−	0.951176i	0.468350	−	0.0579942i	0.353593	+	0.935399i	$0.384960\pi$
$270$		0			0
$271$	5.06448	−	2.71957i	0.307645	−	0.165202i	−0.312004	−	0.950081i	$-0.601000\pi$
$271$	5.06448	−	2.71957i	0.307645	−	0.165202i	0.619649	+	0.784879i	$0.287275\pi$
$272$	13.5022	−	5.23079i	0.818693	−	0.317163i
$273$		0			0
$274$	0.459069	−	14.9002i	0.0277334	−	0.900152i
$275$	0.286619	−	0.177467i	0.0172838	−	0.0107017i
$276$		0			0
$277$	4.73711	+	21.6303i	0.284626	+	1.29964i	0.871673	+	0.490088i	$0.163035\pi$
$277$	4.73711	+	21.6303i	0.284626	+	1.29964i	−0.587048	+	0.809552i	$0.699710\pi$
$278$	5.75289	+	20.2193i	0.345035	+	1.21267i
$279$		0			0
$280$	−0.666877	+	3.04505i	−0.0398535	+	0.181977i
$281$	2.52018	−	0.155439i	0.150341	−	0.00927273i	0.0137846	−	0.999905i	$-0.495612\pi$
$281$	2.52018	−	0.155439i	0.150341	−	0.00927273i	0.136557	+	0.990632i	$0.456396\pi$
$282$		0			0
$283$	−2.54571	+	6.01448i	−0.151327	+	0.357524i	−0.979052	−	0.203610i	$-0.934733\pi$
$283$	−2.54571	+	6.01448i	−0.151327	+	0.357524i	0.827725	+	0.561134i	$0.189635\pi$
$284$	−13.0724	+	9.25373i	−0.775702	+	0.549108i
$285$		0			0
$286$	1.34154	−	2.69418i	0.0793271	−	0.159310i
$287$	0.0247077	−	0.0327182i	0.00145845	−	0.00193130i
$288$		0			0
$289$	−4.23236	−	4.94003i	−0.248962	−	0.290590i
$290$	10.8631	+	5.83334i	0.637901	+	0.342546i
$291$		0			0
$292$	−13.7597	−	6.33047i	−0.805226	−	0.370463i
$293$	−4.18666	+	4.31763i	−0.244587	+	0.252239i	−0.829041	−	0.559188i	$-0.811113\pi$
$293$	−4.18666	+	4.31763i	−0.244587	+	0.252239i	0.584454	+	0.811427i	$0.301309\pi$
$294$		0			0
$295$	3.76039	+	4.97956i	0.218938	+	0.289921i
$296$	−2.71588	+	0.507685i	−0.157857	+	0.0295086i
$297$		0			0
$298$	−27.2658	−	1.68170i	−1.57947	−	0.0974182i
$299$	−0.863958	+	3.03650i	−0.0499640	+	0.175605i
$300$		0			0
$301$	−19.0053	−	3.55270i	−1.09545	−	0.204774i
$302$	−0.542316	+	1.53898i	−0.0312068	+	0.0885583i
$303$		0			0
$304$	−25.3020	+	8.04913i	−1.45117	+	0.461649i
$305$	13.4176	+	31.7003i	0.768288	+	1.81515i
$306$		0			0
$307$	11.8967	−	17.9539i	0.678979	−	1.02468i	−0.318082	−	0.948063i	$-0.603039\pi$
$307$	11.8967	−	17.9539i	0.678979	−	1.02468i	0.997060	−	0.0766184i	$-0.0244123\pi$
$308$	1.94613			0.110891
$309$		0			0
$310$	−24.7947			−1.40825
$311$	18.5227	−	27.9535i	1.05032	−	1.58510i	0.266786	−	0.963756i	$-0.414038\pi$
$311$	18.5227	−	27.9535i	1.05032	−	1.58510i	0.783538	−	0.621343i	$-0.213413\pi$
$312$		0			0
$313$	11.0066	+	26.0041i	0.622129	+	1.46984i	0.866007	+	0.500031i	$0.166678\pi$
$313$	11.0066	+	26.0041i	0.622129	+	1.46984i	−0.243879	+	0.969806i	$0.578420\pi$
$314$	32.4324	−	10.3175i	1.83027	−	0.582250i
$315$		0			0
$316$	6.27733	−	17.8138i	0.353127	−	1.00210i
$317$	−26.8451	−	5.01821i	−1.50777	−	0.281851i	−0.635969	−	0.771714i	$-0.719400\pi$
$317$	−26.8451	−	5.01821i	−1.50777	−	0.281851i	−0.871799	+	0.489864i	$0.837047\pi$
$318$		0			0
$319$	−0.331323	+	1.16448i	−0.0185505	+	0.0651984i
$320$	13.6277	+	0.840529i	0.761813	+	0.0469870i
$321$		0			0
$322$	−4.32883	+	0.809199i	−0.241236	+	0.0450949i
$323$	−11.5971	−	15.3570i	−0.645279	−	0.854488i
$324$		0			0
$325$	−1.77234	+	1.82779i	−0.0983119	+	0.101388i
$326$	3.45455	+	1.58934i	0.191330	+	0.0880256i
$327$		0			0
$328$	0.00764775	+	0.00410675i	0.000422276	+	0.000226758i
$329$	12.6784	+	14.7983i	0.698982	+	0.815855i
$330$		0			0
$331$	4.33562	−	5.74129i	0.238307	−	0.315570i	−0.663109	−	0.748523i	$-0.730764\pi$
$331$	4.33562	−	5.74129i	0.238307	−	0.315570i	0.901417	+	0.432953i	$0.142528\pi$
$332$	−4.67723	+	9.39314i	−0.256696	+	0.515516i
$333$		0			0
$334$	−10.7915	+	7.63917i	−0.590486	+	0.417997i
$335$	2.37972	−	5.62231i	0.130018	−	0.307180i
$336$		0			0
$337$	8.97033	−	0.553271i	0.488645	−	0.0301386i	0.184635	−	0.982807i	$-0.440890\pi$
$337$	8.97033	−	0.553271i	0.488645	−	0.0301386i	0.304011	+	0.952669i	$0.401674\pi$
$338$	0.507203	−	2.31596i	0.0275882	−	0.125972i
$339$		0			0
$340$	3.67139	+	12.9036i	0.199109	+	0.699796i
$341$	−0.520838	−	2.37822i	−0.0282049	−	0.128788i
$342$		0			0
$343$	−16.5560	+	10.2510i	−0.893937	+	0.553503i
$344$	0.126063	−	4.09167i	0.00679686	−	0.220608i
$345$		0			0
$346$	14.5673	−	5.64342i	0.783145	−	0.303392i
$347$	7.94180	−	4.26466i	0.426338	−	0.228939i	−0.245867	−	0.969304i	$-0.579073\pi$
$347$	7.94180	−	4.26466i	0.426338	−	0.228939i	0.672205	+	0.740365i	$0.265347\pi$
$348$		0			0
$349$	−18.0256	+	2.23206i	−0.964889	+	0.119479i	−0.589835	−	0.807524i	$-0.700807\pi$
$349$	−18.0256	+	2.23206i	−0.964889	+	0.119479i	−0.375054	+	0.927003i	$0.622376\pi$
$350$	−3.38434	−	1.07664i	−0.180901	−	0.0575486i
$351$		0			0
$352$	0.528278	+	3.40323i	0.0281573	+	0.181393i
$353$	11.8914	+	33.7452i	0.632913	+	1.79608i	0.604672	+	0.796475i	$0.293304\pi$
$353$	11.8914	+	33.7452i	0.632913	+	1.79608i	0.0282412	+	0.999601i	$0.491009\pi$
$354$		0			0
$355$	11.1037	+	19.2322i	0.589325	+	1.02074i
$356$	−8.93355	+	15.4734i	−0.473477	+	0.820087i
$357$		0			0
$358$	19.7009	+	15.8533i	1.04123	+	0.837872i
$359$	−0.703709	−	22.8405i	−0.0371403	−	1.20548i	−0.815915	−	0.578172i	$-0.803766\pi$
$359$	−0.703709	−	22.8405i	−0.0371403	−	1.20548i	0.778774	−	0.627304i	$-0.215842\pi$
$360$		0			0
$361$	8.99629	+	13.5768i	0.473489	+	0.714567i
$362$	−0.948828	−	30.7964i	−0.0498693	−	1.61862i
$363$		0			0
$364$	−14.2538	+	3.58498i	−0.747104	+	0.187904i
$365$	−10.5005	+	18.1874i	−0.549623	+	0.951974i
$366$		0			0
$367$	19.2711	+	19.8740i	1.00594	+	1.03741i	0.999299	+	0.0374363i	$0.0119191\pi$
$367$	19.2711	+	19.8740i	1.00594	+	1.03741i	0.00664508	+	0.999978i	$0.497885\pi$
$368$	−1.36689	−	3.87894i	−0.0712539	−	0.202204i
$369$		0			0
$370$	−2.24750	−	24.2544i	−0.116842	−	1.26092i
$371$	9.73215	+	3.09602i	0.505268	+	0.160737i
$372$		0			0
$373$	−1.84017	−	0.712884i	−0.0952802	−	0.0369117i	0.313130	−	0.949710i	$-0.398623\pi$
$373$	−1.84017	−	0.712884i	−0.0952802	−	0.0369117i	−0.408410	+	0.912799i	$0.633917\pi$
$374$	−2.50362	+	1.34441i	−0.129459	+	0.0695180i
$375$		0			0
$376$	−2.68434	+	3.13318i	−0.138434	+	0.161581i
$377$	0.281577	−	9.13923i	0.0145019	−	0.470694i
$378$		0			0
$379$	−22.9653	−	16.2568i	−1.17965	−	0.835056i	−0.190459	−	0.981695i	$-0.560998\pi$
$379$	−22.9653	−	16.2568i	−1.17965	−	0.835056i	−0.989190	+	0.146639i	$0.953154\pi$
$380$	−5.26273	−	24.0303i	−0.269972	−	1.23273i
$381$		0			0
$382$	35.3194	−	32.1979i	1.80710	−	1.64739i
$383$	3.80145	−	17.3579i	0.194245	−	0.886949i	−0.773258	−	0.634091i	$-0.781374\pi$
$383$	3.80145	−	17.3579i	0.194245	−	0.886949i	0.967503	−	0.252858i	$-0.0813707\pi$
$384$		0			0
$385$	0.248980	−	2.68692i	0.0126892	−	0.136938i
$386$	−5.54263	+	13.0950i	−0.282113	+	0.666517i
$387$		0			0
$388$	−15.9189	−	14.5120i	−0.808160	−	0.736735i
$389$	−5.62761	+	11.3018i	−0.285331	+	0.573022i	−0.990739	−	0.135780i	$-0.956646\pi$
$389$	−5.62761	+	11.3018i	−0.285331	+	0.573022i	0.705408	+	0.708801i	$0.250764\pi$
$390$		0			0
$391$	2.32231	−	1.86876i	0.117444	−	0.0945070i
$392$	−0.292237	−	0.341100i	−0.0147602	−	0.0172282i
$393$		0			0
$394$	43.2628	+	5.35710i	2.17955	+	0.269887i
$395$	−23.7915	−	10.9458i	−1.19708	−	0.550744i
$396$		0			0
$397$	−2.34007	−	0.588551i	−0.117445	−	0.0295385i	0.184744	−	0.982787i	$-0.440854\pi$
$397$	−2.34007	−	0.588551i	−0.117445	−	0.0295385i	−0.302188	+	0.953248i	$0.597717\pi$
$398$	6.00559	+	7.95268i	0.301033	+	0.398632i
$399$		0			0
$400$	0.508757	−	3.27747i	0.0254379	−	0.163873i
$401$	21.3316	+	1.31569i	1.06525	+	0.0657023i	0.584687	−	0.811259i	$-0.301217\pi$
$401$	21.3316	+	1.31569i	1.06525	+	0.0657023i	0.480562	+	0.876961i	$0.340433\pi$
$402$		0			0
$403$	8.19566	+	16.4591i	0.408255	+	0.819887i
$404$	28.8540	+	5.39375i	1.43554	+	0.268349i
$405$		0			0
$406$	11.5871	−	5.33093i	0.575060	−	0.264570i
$407$	2.27918	−	0.725059i	0.112975	−	0.0359398i
$408$		0			0
$409$	−4.33410	−	2.68356i	−0.214307	−	0.132693i	0.415081	−	0.909785i	$-0.363753\pi$
$409$	−4.33410	−	2.68356i	−0.214307	−	0.132693i	−0.629388	+	0.777091i	$0.716694\pi$
$410$	−0.0422723	+	0.0637953i	−0.00208768	+	0.00315063i
$411$		0			0
$412$	11.0207	−	13.6445i	0.542949	−	0.672214i
$413$	6.45469			0.317615
$414$		0			0
$415$	12.3702	+	7.65933i	0.607232	+	0.375982i
$416$	−10.1383	−	23.9528i	−0.497073	−	1.17438i
$417$		0			0
$418$	4.73382	−	2.17790i	0.231539	−	0.106525i
$419$	−2.23404	+	6.33974i	−0.109140	+	0.309717i	−0.984924	−	0.172986i	$-0.944658\pi$
$419$	−2.23404	+	6.33974i	−0.109140	+	0.309717i	0.875784	+	0.482703i	$0.160345\pi$
$420$		0			0
$421$	0.229574	+	0.461046i	0.0111887	+	0.0224700i	0.900687	−	0.434468i	$-0.143064\pi$
$421$	0.229574	+	0.461046i	0.0111887	+	0.0224700i	−0.889498	+	0.456938i	$0.848946\pi$
$422$	4.99791	−	17.5658i	0.243295	−	0.855092i
$423$		0			0
$424$	−0.331679	+	2.13671i	−0.0161078	+	0.103768i
$425$	2.36297	−	0.441715i	0.114621	−	0.0214263i
$426$		0			0
$427$	34.5324	+	8.68524i	1.67114	+	0.420308i
$428$	10.8813	−	11.2217i	0.525968	−	0.542423i
$429$		0			0
$430$	35.8163	+	4.43502i	1.72722	+	0.213876i
$431$	21.2097	+	11.3894i	1.02164	+	0.548607i	0.896273	−	0.443504i	$-0.146265\pi$
$431$	21.2097	+	11.3894i	1.02164	+	0.548607i	0.125364	+	0.992111i	$0.459990\pi$
$432$		0			0
$433$	18.1917	−	14.6388i	0.874237	−	0.703496i	−0.0818290	−	0.996646i	$-0.526076\pi$
$433$	18.1917	−	14.6388i	0.874237	−	0.703496i	0.956066	+	0.293150i	$0.0947036\pi$
$434$	−15.4565	+	20.4677i	−0.741935	+	0.982480i
$435$		0			0
$436$	21.6090	+	19.6992i	1.03489	+	0.943423i
$437$	−4.46119	+	3.15801i	−0.213408	+	0.151068i
$438$		0			0
$439$	−0.0835765	+	0.901934i	−0.00398889	+	0.0430469i	−0.997496	−	0.0707233i	$-0.977469\pi$
$439$	−0.0835765	+	0.901934i	−0.00398889	+	0.0430469i	0.993507	+	0.113770i	$0.0362928\pi$
$440$	0.570244	−	0.0351714i	0.0271853	−	0.00167673i
$441$		0			0
$442$	15.8604	−	14.4587i	0.754404	−	0.687730i
$443$	6.43793	+	22.6270i	0.305875	+	1.07504i	0.950547	+	0.310581i	$0.100524\pi$
$443$	6.43793	+	22.6270i	0.305875	+	1.07504i	−0.644671	+	0.764460i	$0.723006\pi$
$444$		0			0
$445$	20.2204	+	14.3137i	0.958537	+	0.678535i
$446$	38.6950	−	23.9589i	1.83226	−	1.13449i
$447$		0			0
$448$	9.18907	−	10.7255i	0.434143	−	0.506733i
$449$	−2.40218	+	0.930608i	−0.113366	+	0.0439181i	−0.417256	−	0.908789i	$-0.637008\pi$
$449$	−2.40218	+	0.930608i	−0.113366	+	0.0439181i	0.303891	+	0.952707i	$0.401714\pi$
$450$		0			0
$451$	−0.00700698	−	0.00271452i	−0.000329946	−	0.000127822i
$452$	−2.55511	+	0.316391i	−0.120182	+	0.0148818i
$453$		0			0
$454$	−3.56792	−	38.5040i	−0.167451	−	1.80708i
$455$	3.12603	+	20.1382i	0.146550	+	0.944093i
$456$		0			0
$457$	17.0654	+	17.5993i	0.798287	+	0.823261i	0.987325	−	0.158709i	$-0.0507331\pi$
$457$	17.0654	+	17.5993i	0.798287	+	0.823261i	−0.189038	+	0.981970i	$0.560537\pi$
$458$	−8.12129	−	14.0665i	−0.379483	−	0.657284i
$459$		0			0
$460$	3.69536	−	0.929419i	0.172297	−	0.0433344i
$461$	15.4935	+	12.4675i	0.721602	+	0.580671i	0.916444	−	0.400164i	$-0.131047\pi$
$461$	15.4935	+	12.4675i	0.721602	+	0.580671i	−0.194841	+	0.980835i	$0.562419\pi$
$462$		0			0
$463$	−11.7338	−	17.7081i	−0.545316	−	0.822965i	0.452307	−	0.891862i	$-0.350601\pi$
$463$	−11.7338	−	17.7081i	−0.545316	−	0.822965i	−0.997624	+	0.0688971i	$0.978052\pi$
$464$	6.57954	+	9.92952i	0.305447	+	0.460966i
$465$		0			0
$466$	−19.2868	−	15.5200i	−0.893444	−	0.718952i
$467$	9.32433	−	2.34516i	0.431478	−	0.108521i	−0.0220626	−	0.999757i	$-0.507023\pi$
$467$	9.32433	−	2.34516i	0.431478	−	0.108521i	0.453541	+	0.891235i	$0.350161\pi$
$468$		0			0
$469$	−3.15767	−	5.46925i	−0.145808	−	0.252546i
$470$	−25.3211	−	26.1133i	−1.16798	−	1.20451i
$471$		0			0
$472$	0.209629	+	1.35045i	0.00964895	+	0.0621596i
$473$	0.326966	+	3.52853i	0.0150339	+	0.162242i
$474$		0			0
$475$	−4.37452	+	0.541682i	−0.200717	+	0.0248541i
$476$	12.9404	+	5.01314i	0.593123	+	0.229777i
$477$		0			0
$478$	25.6064	−	9.91996i	1.17121	−	0.453728i
$479$	−13.1044	+	15.2955i	−0.598753	+	0.698868i	−0.973611	−	0.228215i	$-0.926711\pi$
$479$	−13.1044	+	15.2955i	−0.598753	+	0.698868i	0.374858	+	0.927082i	$0.377692\pi$
$480$		0			0
$481$	−15.3575	+	9.50898i	−0.700243	+	0.433572i
$482$	40.4475	+	28.6322i	1.84233	+	1.30416i
$483$		0			0
$484$	5.10477	+	17.9414i	0.232035	+	0.815518i
$485$	−22.0726	+	20.1218i	−1.00226	+	0.913685i
$486$		0			0
$487$	−10.8722	+	0.670577i	−0.492668	+	0.0303867i	−0.305991	−	0.952034i	$-0.598988\pi$
$487$	−10.8722	+	0.670577i	−0.492668	+	0.0303867i	−0.186678	+	0.982421i	$0.559772\pi$
$488$	−0.695620	+	7.50694i	−0.0314892	+	0.339823i
$489$		0			0
$490$	3.23208	−	2.28794i	0.146010	−	0.103359i
$491$	6.71012	+	6.11708i	0.302823	+	0.276060i	0.810816	−	0.585302i	$-0.199024\pi$
$491$	6.71012	+	6.11708i	0.302823	+	0.276060i	−0.507992	+	0.861362i	$0.669612\pi$
$492$		0			0
$493$	−5.20272	+	6.88952i	−0.234319	+	0.310288i
$494$	−30.6595	+	24.6716i	−1.37944	+	1.11003i
$495$		0			0
$496$	−21.1028	−	11.3320i	−0.947543	−	0.508820i
$497$	22.7978	+	2.82297i	1.02262	+	0.126628i
$498$		0			0
$499$	12.4788	−	12.8692i	0.558628	−	0.576105i	−0.378275	−	0.925693i	$-0.623483\pi$
$499$	12.4788	−	12.8692i	0.558628	−	0.576105i	0.936903	+	0.349589i	$0.113679\pi$
$500$	−17.1005	−	4.30095i	−0.764757	−	0.192344i
$501$		0			0
$502$	−5.15208	+	0.963091i	−0.229949	+	0.0429849i
$503$	4.50280	−	29.0075i	0.200770	−	1.29338i	−0.646785	−	0.762673i	$-0.723887\pi$
$503$	4.50280	−	29.0075i	0.200770	−	1.29338i	0.847555	−	0.530708i	$-0.178074\pi$
$504$		0			0
$505$	11.1383	−	39.1472i	0.495649	−	1.74203i
$506$	0.359771	+	0.722518i	0.0159938	+	0.0321198i
$507$		0			0
$508$	−10.5409	+	29.9130i	−0.467678	+	1.32717i
$509$	−23.2882	+	10.7143i	−1.03223	+	0.474901i	−0.860075	−	0.510168i	$-0.829583\pi$
$509$	−23.2882	+	10.7143i	−1.03223	+	0.474901i	−0.172156	+	0.985070i	$0.555073\pi$
$510$		0			0
$511$	8.46768	+	20.0057i	0.374588	+	0.884999i
$512$	24.8199	+	15.3678i	1.09690	+	0.679169i
$513$		0			0
$514$	−11.7984			−0.520407
$515$	−17.4283	−	16.9613i	−0.767982	−	0.747404i
$516$		0			0
$517$	1.97279	−	2.97724i	0.0867633	−	0.130939i
$518$	−21.4227	−	13.2644i	−0.941258	−	0.582802i
$519$		0			0
$520$	−4.11179	+	1.30806i	−0.180314	+	0.0573620i
$521$	10.4170	−	4.79260i	0.456379	−	0.209967i	−0.176371	−	0.984324i	$-0.556436\pi$
$521$	10.4170	−	4.79260i	0.456379	−	0.209967i	0.632750	+	0.774356i	$0.281926\pi$
$522$		0			0
$523$	9.08325	+	1.69795i	0.397183	+	0.0742463i	0.378552	−	0.925580i	$-0.376422\pi$
$523$	9.08325	+	1.69795i	0.397183	+	0.0742463i	0.0186309	+	0.999826i	$0.494069\pi$
$524$	0.510151	+	1.02452i	0.0222861	+	0.0447564i
$525$		0			0
$526$	44.2594	+	2.72983i	1.92980	+	0.119026i
$527$	2.66297	−	17.1552i	0.116001	−	0.747290i
$528$		0			0
$529$	13.3504	+	17.6788i	0.580451	+	0.768642i
$530$	−18.4874	−	4.64976i	−0.803040	−	0.201973i
$531$		0			0
$532$	−23.1174	−	10.6357i	−1.00227	−	0.461115i
$533$	0.0563210	+	0.00697405i	0.00243953	+	0.000302080i
$534$		0			0
$535$	−14.1012	−	16.4589i	−0.609646	−	0.711582i
$536$	1.04173	−	0.838273i	0.0449957	−	0.0362079i
$537$		0			0
$538$	−6.66162	+	13.3783i	−0.287203	+	0.576781i
$539$	0.287344	+	0.261949i	0.0123768	+	0.0112829i
$540$		0			0
$541$	2.65060	−	6.26229i	0.113958	−	0.269237i	−0.854034	−	0.520217i	$-0.825851\pi$
$541$	2.65060	−	6.26229i	0.113958	−	0.269237i	0.967992	+	0.250980i	$0.0807530\pi$
$542$	−1.02413	+	11.0521i	−0.0439901	+	0.474729i
$543$		0			0
$544$	−5.25388	+	23.9899i	−0.225258	+	1.02856i
$545$	29.9623	−	27.3143i	1.28345	−	1.17001i
$546$		0			0
$547$	−2.18527	−	9.97824i	−0.0934353	−	0.426639i	−0.999990	−	0.00454960i	$-0.998552\pi$
$547$	−2.18527	−	9.97824i	−0.0934353	−	0.426639i	0.906554	−	0.422089i	$-0.138703\pi$
$548$	10.8902	+	7.70901i	0.465206	+	0.329313i
$549$		0			0
$550$	−0.0200450	+	0.650607i	−0.000854722	+	0.0277420i
$551$	10.2996	−	12.0218i	0.438778	−	0.512144i
$552$		0			0
$553$	−23.8667	+	12.8161i	−1.01492	+	0.544998i
$554$	−39.8677	−	15.4448i	−1.69382	−	0.656188i
$555$		0			0
$556$	−17.9300	−	5.70394i	−0.760401	−	0.241901i
$557$	3.94245	+	42.5458i	0.167047	+	1.80272i	0.506649	+	0.862153i	$0.330884\pi$
$557$	3.94245	+	42.5458i	0.167047	+	1.80272i	−0.339602	+	0.940569i	$0.610292\pi$
$558$		0			0
$559$	−8.89471	−	25.2414i	−0.376206	−	1.06760i
$560$	−18.4815	−	19.0597i	−0.780987	−	0.805419i
$561$		0			0
$562$	−2.43767	+	4.22217i	−0.102827	+	0.178102i
$563$	31.0447	−	7.80806i	1.30838	−	0.329071i	0.474128	−	0.880456i	$-0.342763\pi$
$563$	31.0447	−	7.80806i	1.30838	−	0.329071i	0.834251	+	0.551385i	$0.185901\pi$
$564$		0			0
$565$	0.109935	+	3.56819i	0.00462499	+	0.150115i
$566$	−6.96560	−	10.5122i	−0.292786	−	0.441859i
$567$		0			0
$568$	0.149779	+	4.86143i	0.00628459	+	0.203981i
$569$	−25.1230	−	20.2164i	−1.05321	−	0.847515i	−0.0645844	−	0.997912i	$-0.520572\pi$
$569$	−25.1230	−	20.2164i	−1.05321	−	0.847515i	−0.988626	+	0.150397i	$0.951945\pi$
$570$		0			0
$571$	11.1989	−	19.3971i	0.468659	−	0.811742i	−0.530699	−	0.847560i	$-0.678071\pi$
$571$	11.1989	−	19.3971i	0.468659	−	0.811742i	0.999358	+	0.0358187i	$0.0114039\pi$
$572$	1.34691	+	2.33292i	0.0563171	+	0.0975441i
$573$		0			0
$574$	0.0263105	+	0.0746638i	0.00109818	+	0.00311641i
$575$	−0.104732	−	0.674694i	−0.00436762	−	0.0281367i
$576$		0			0
$577$	29.2306	+	9.29892i	1.21689	+	0.387119i	0.841759	−	0.539854i	$-0.181521\pi$
$577$	29.2306	+	9.29892i	1.21689	+	0.387119i	0.375127	+	0.926973i	$0.377599\pi$
$578$	12.4653	−	1.54353i	0.518486	−	0.0642025i
$579$		0			0
$580$	−9.72291	+	5.22109i	−0.403722	+	0.216794i
$581$	14.0340	−	5.43680i	0.582229	−	0.225557i
$582$		0			0
$583$	0.0576422	−	1.87091i	0.00238730	−	0.0774853i
$584$	−3.91059	+	2.42133i	−0.161821	+	0.100195i
$585$		0			0
$586$	−2.48429	−	11.3436i	−0.102625	−	0.468600i
$587$	−7.32244	−	25.7357i	−0.302229	−	1.06223i	−0.953005	−	0.302956i	$-0.902027\pi$
$587$	−7.32244	−	25.7357i	−0.302229	−	1.06223i	0.650775	−	0.759270i	$-0.274444\pi$
$588$		0			0
$589$	−6.81022	+	31.0964i	−0.280610	+	1.28131i
$590$	−12.0255	+	0.741708i	−0.495082	+	0.0305356i
$591$		0			0
$592$	9.17215	−	21.6701i	0.376973	−	0.890634i
$593$	29.1865	−	20.6607i	1.19854	−	0.848432i	0.207018	−	0.978337i	$-0.433624\pi$
$593$	29.1865	−	20.6607i	1.19854	−	0.848432i	0.991526	+	0.129905i	$0.0414673\pi$
$594$		0			0
$595$	8.57693	−	17.2248i	0.351620	−	0.706148i
$596$	14.7347	−	19.5119i	0.603556	−	0.799238i
$597$		0			0
$598$	−3.96600	−	4.62913i	−0.162182	−	0.189299i
$599$	21.0643	+	11.3113i	0.860663	+	0.462166i	0.843149	−	0.537680i	$-0.180699\pi$
$599$	21.0643	+	11.3113i	0.860663	+	0.462166i	0.0175145	+	0.999847i	$0.494425\pi$
$600$		0			0
$601$	−41.9280	−	19.2899i	−1.71028	−	0.786853i	−0.996230	−	0.0867561i	$-0.972350\pi$
$601$	−41.9280	−	19.2899i	−1.71028	−	0.786853i	−0.714048	−	0.700097i	$-0.753140\pi$
$602$	25.9881	−	26.8011i	1.05920	−	1.09233i
$603$		0			0
$604$	−0.880132	−	1.16548i	−0.0358121	−	0.0474229i
$605$	25.4239	−	4.75254i	1.03363	−	0.193218i
$606$		0			0
$607$	−42.4044	−	2.61542i	−1.72114	−	0.106156i	−0.829387	−	0.558674i	$-0.811310\pi$
$607$	−42.4044	−	2.61542i	−1.72114	−	0.106156i	−0.891755	+	0.452518i	$0.850526\pi$
$608$	12.3236	−	43.3128i	0.499786	−	1.75657i
$609$		0			0
$610$	−65.3340	−	12.2130i	−2.64530	−	0.494491i
$611$	−8.96472	+	25.4400i	−0.362674	+	1.02919i
$612$		0			0
$613$	−25.6062	+	8.14591i	−1.03422	+	0.329010i	−0.771748	−	0.635929i	$-0.780617\pi$
$613$	−25.6062	+	8.14591i	−1.03422	+	0.329010i	−0.262475	+	0.964939i	$0.584539\pi$
$614$	16.2097	+	38.2969i	0.654170	+	1.54554i
$615$		0			0
$616$	0.326444	−	0.492653i	0.0131528	−	0.0198496i
$617$	−41.1691			−1.65741			−0.828703	−	0.559688i	$-0.810921\pi$
$617$	−41.1691			−1.65741			−0.828703	+	0.559688i	$0.810921\pi$
$618$		0			0
$619$	−32.8500			−1.32035			−0.660176	−	0.751111i	$-0.729519\pi$
$619$	−32.8500			−1.32035			−0.660176	+	0.751111i	$0.729519\pi$
$620$	12.2583	−	18.4996i	0.492304	−	0.742961i
$621$		0			0
$622$	25.2379	+	59.6269i	1.01195	+	2.39082i
$623$	24.4207	−	7.76878i	0.978394	−	0.311250i
$624$		0			0
$625$	−9.35897	+	26.5588i	−0.374359	+	1.06235i
$626$	−53.5941	−	10.0185i	−2.14205	−	0.400419i
$627$		0			0
$628$	−8.33628	+	29.2990i	−0.332654	+	1.16916i
$629$	17.0227	+	1.04992i	0.678739	+	0.0418632i
$630$		0			0
$631$	−32.8361	+	6.13813i	−1.30718	+	0.244355i	−0.790838	−	0.612025i	$-0.790355\pi$
$631$	−32.8361	+	6.13813i	−1.30718	+	0.244355i	−0.516346	+	0.856380i	$0.672708\pi$
$632$	−3.45651	−	4.57716i	−0.137493	−	0.182070i
$633$		0			0
$634$	36.7084	−	37.8567i	1.45787	−	1.50348i
$635$	39.9508	+	18.3803i	1.58540	+	0.729399i
$636$		0			0
$637$	−2.58710	−	1.38925i	−0.102505	−	0.0550439i
$638$	−1.52094	−	1.77525i	−0.0602145	−	0.0702827i
$639$		0			0
$640$	6.00693	−	7.95446i	0.237445	−	0.314427i
$641$	−7.98794	+	16.0419i	−0.315504	+	0.633618i	−0.994979	−	0.100080i	$-0.968090\pi$
$641$	−7.98794	+	16.0419i	−0.315504	+	0.633618i	0.679475	+	0.733699i	$0.262208\pi$
$642$		0			0
$643$	35.4840	−	25.1186i	1.39935	−	0.990582i	0.402171	−	0.915564i	$-0.368256\pi$
$643$	35.4840	−	25.1186i	1.39935	−	0.990582i	0.997182	−	0.0750173i	$-0.0239012\pi$
$644$	1.53638	−	3.62984i	0.0605419	−	0.143036i
$645$		0			0
$646$	37.0868	−	2.28744i	1.45916	−	0.0899981i
$647$	−7.74977	+	35.3865i	−0.304675	+	1.39119i	0.533507	+	0.845796i	$0.320874\pi$
$647$	−7.74977	+	35.3865i	−0.304675	+	1.39119i	−0.838181	+	0.545392i	$0.816381\pi$
$648$		0			0
$649$	−0.323749	−	1.13786i	−0.0127083	−	0.0446650i
$650$	−1.05168	−	4.80211i	−0.0412502	−	0.188354i
$651$		0			0
$652$	−2.89372	+	1.79171i	−0.113327	+	0.0701689i
$653$	1.07498	−	34.8911i	0.0420674	−	1.36540i	−0.709018	−	0.705190i	$-0.750862\pi$
$653$	1.07498	−	34.8911i	0.0420674	−	1.36540i	0.751086	−	0.660205i	$-0.229531\pi$
$654$		0			0
$655$	1.47977	−	0.573267i	0.0578195	−	0.0223994i
$656$	−0.0651344	+	0.0349764i	−0.00254307	+	0.00136560i
$657$		0			0
$658$	−37.3407	+	4.62379i	−1.45569	+	0.180254i
$659$	−18.5834	−	5.91180i	−0.723906	−	0.230291i	−0.0815194	−	0.996672i	$-0.525977\pi$
$659$	−18.5834	−	5.91180i	−0.723906	−	0.230291i	−0.642387	+	0.766381i	$0.722056\pi$
$660$		0			0
$661$	−1.35907	−	8.75529i	−0.0528618	−	0.340541i	−0.999816	−	0.0191733i	$-0.993897\pi$
$661$	−1.35907	−	8.75529i	−0.0528618	−	0.340541i	0.946954	−	0.321368i	$-0.104143\pi$
$662$	4.61688	+	13.1018i	0.179440	+	0.509214i
$663$		0			0
$664$	1.59327	+	2.75963i	0.0618309	+	0.107094i
$665$	−17.6417	+	30.5563i	−0.684115	+	1.18492i
$666$		0			0
$667$	1.91038	+	1.53728i	0.0739702	+	0.0595236i
$668$	−0.364429	−	11.8284i	−0.0141002	−	0.457654i
$669$		0			0
$670$	6.51141	+	9.82671i	0.251558	+	0.379639i
$671$	−0.200976	−	6.52314i	−0.00775859	−	0.251823i
$672$		0			0
$673$	−25.2846	+	6.35932i	−0.974648	+	0.245134i	−0.698206	−	0.715897i	$-0.746018\pi$
$673$	−25.2846	+	6.35932i	−0.974648	+	0.245134i	−0.276442	+	0.961031i	$0.589155\pi$
$674$	−8.67666	+	15.0284i	−0.334212	+	0.578873i
$675$		0			0
$676$	1.47720	+	1.52342i	0.0568155	+	0.0585930i
$677$	14.4126	+	40.9000i	0.553922	+	1.57192i	0.798315	+	0.602240i	$0.205725\pi$
$677$	14.4126	+	40.9000i	0.553922	+	1.57192i	−0.244394	+	0.969676i	$0.578589\pi$
$678$		0			0
$679$	2.85071	+	30.7641i	0.109400	+	1.18062i
$680$	3.88233	+	1.23506i	0.148881	+	0.0473623i
$681$		0			0
$682$	4.38339	+	1.69813i	0.167849	+	0.0650249i
$683$	0.893975	−	0.480055i	0.0342070	−	0.0183688i	−0.455901	−	0.890031i	$-0.650683\pi$
$683$	0.893975	−	0.480055i	0.0342070	−	0.0183688i	0.490108	+	0.871662i	$0.336957\pi$
$684$		0			0
$685$	12.0367	−	14.0493i	0.459898	−	0.536796i
$686$	1.15786	−	37.5809i	0.0442072	−	1.43485i
$687$		0			0
$688$	28.4563	+	20.1438i	1.08489	+	0.767975i
$689$	3.02425	+	13.8091i	0.115215	+	0.526086i
$690$		0			0
$691$	10.0399	−	9.15261i	0.381937	−	0.348182i	−0.459845	−	0.887999i	$-0.652095\pi$
$691$	10.0399	−	9.15261i	0.381937	−	0.348182i	0.841782	+	0.539818i	$0.181507\pi$
$692$	−2.99134	+	13.6589i	−0.113714	+	0.519233i
$693$		0			0
$694$	−1.60598	+	17.3313i	−0.0609621	+	0.657885i
$695$	−10.1690	+	24.0253i	−0.385733	+	0.911331i
$696$		0			0
$697$	−0.0395991	−	0.0360994i	−0.00149992	−	0.00136736i
$698$	15.6323	−	31.3940i	0.591693	−	1.18828i
$699$		0			0
$700$	2.47647	−	1.99281i	0.0936019	−	0.0753212i
$701$	9.00628	+	10.5122i	0.340162	+	0.397039i	0.903079	−	0.429474i	$-0.141301\pi$
$701$	9.00628	+	10.5122i	0.340162	+	0.397039i	−0.562917	+	0.826514i	$0.690321\pi$
$702$		0			0
$703$	−31.0360	−	3.84309i	−1.17055	−	0.144945i
$704$	−2.35164	−	1.08193i	−0.0886308	−	0.0407766i
$705$		0			0
$706$	−66.9976	−	16.8506i	−2.52149	−	0.634180i
$707$	−25.3721	−	33.5980i	−0.954214	−	1.26358i
$708$		0			0
$709$	0.0177246	−	0.114184i	0.000665662	−	0.00428826i	−0.987830	−	0.155535i	$-0.950290\pi$
$709$	0.0177246	−	0.114184i	0.000665662	−	0.00428826i	0.988496	+	0.151247i	$0.0483289\pi$
$710$	−42.7980	−	2.63969i	−1.60618	−	0.0990659i
$711$		0			0
$712$	2.41850	+	4.85699i	0.0906369	+	0.182024i
$713$	−4.84694	−	0.906050i	−0.181519	−	0.0339318i
$714$		0			0
$715$	3.39326	−	1.56115i	0.126901	−	0.0583835i
$716$	−21.5682	+	6.86135i	−0.806042	+	0.256421i
$717$		0			0
$718$	37.5138	+	23.2276i	1.40000	+	0.866845i
$719$	−18.4747	+	27.8811i	−0.688990	+	1.03979i	0.307120	+	0.951671i	$0.400635\pi$
$719$	−18.4747	+	27.8811i	−0.688990	+	1.03979i	−0.996110	+	0.0881198i	$0.971914\pi$
$720$		0			0
$721$	−24.8657	+	3.81350i	−0.926047	+	0.142022i
$722$	−31.4475			−1.17036
$723$		0			0
$724$	23.4466	+	14.5175i	0.871387	+	0.539540i
$725$	0.770800	+	1.82109i	0.0286268	+	0.0676335i
$726$		0			0
$727$	16.2378	−	7.47056i	0.602226	−	0.277068i	−0.0932209	−	0.995645i	$-0.529716\pi$
$727$	16.2378	−	7.47056i	0.602226	−	0.277068i	0.695447	+	0.718578i	$0.255206\pi$
$728$	−1.48342	+	4.20964i	−0.0549792	+	0.156020i
$729$		0			0
$730$	−18.0747	−	36.2988i	−0.668974	−	1.34348i
$731$	−6.91524	+	24.3045i	−0.255769	+	0.898936i
$732$		0			0
$733$	−1.80296	+	11.6149i	−0.0665939	+	0.429005i	0.931306	+	0.364237i	$0.118670\pi$
$733$	−1.80296	+	11.6149i	−0.0665939	+	0.429005i	−0.997900	+	0.0647685i	$0.979369\pi$
$734$	−52.5418	+	9.82177i	−1.93935	+	0.362528i
$735$		0			0
$736$	6.76462	+	1.70137i	0.249347	+	0.0627133i
$737$	−0.805763	+	0.830970i	−0.0296807	+	0.0306092i
$738$		0			0
$739$	16.0437	+	1.98664i	0.590178	+	0.0730798i	0.412419	−	0.910994i	$-0.364684\pi$
$739$	16.0437	+	1.98664i	0.590178	+	0.0730798i	0.177759	+	0.984074i	$0.443115\pi$
$740$	19.2076	+	10.3142i	0.706084	+	0.379159i
$741$		0			0
$742$	−15.3629	+	12.3625i	−0.563991	+	0.453842i
$743$	24.9869	−	33.0880i	0.916680	−	1.21388i	−0.0597869	−	0.998211i	$-0.519042\pi$
$743$	24.9869	−	33.0880i	0.916680	−	1.21388i	0.976467	−	0.215669i	$-0.0691932\pi$
$744$		0			0
$745$	−25.0540	−	22.8397i	−0.917906	−	0.836782i
$746$	3.11004	−	2.20155i	0.113867	−	0.0806044i
$747$		0			0
$748$	0.234683	−	2.53264i	0.00858087	−	0.0926024i
$749$	−22.3770	+	1.38016i	−0.817637	+	0.0504301i
$750$		0			0
$751$	−9.73485	+	8.87449i	−0.355230	+	0.323835i	−0.831563	−	0.555430i	$-0.812554\pi$
$751$	−9.73485	+	8.87449i	−0.355230	+	0.323835i	0.476334	+	0.879265i	$0.341965\pi$
$752$	−9.61623	−	33.7975i	−0.350668	−	1.23247i
$753$		0			0
$754$	14.4099	+	10.2005i	0.524776	+	0.371481i
$755$	−1.72172	+	1.06605i	−0.0626600	+	0.0387974i
$756$		0			0
$757$	8.39701	−	9.80103i	0.305195	−	0.356225i	−0.585625	−	0.810582i	$-0.699151\pi$
$757$	8.39701	−	9.80103i	0.305195	−	0.356225i	0.890819	+	0.454358i	$0.150131\pi$
$758$	50.6597	−	19.6257i	1.84004	−	0.712837i
$759$		0			0
$760$	−6.96594	−	2.69862i	−0.252681	−	0.0978892i
$761$	19.3989	−	2.40211i	0.703210	−	0.0870763i	0.236688	−	0.971586i	$-0.423938\pi$
$761$	19.3989	−	2.40211i	0.703210	−	0.0870763i	0.466522	+	0.884509i	$0.345507\pi$
$762$		0			0
$763$	−3.86969	−	41.7606i	−0.140092	−	1.51183i
$764$	6.56159	+	42.2705i	0.237390	+	1.52929i
$765$		0			0
$766$	23.8843	+	24.6315i	0.862976	+	0.889974i
$767$	4.46727	+	7.73755i	0.161304	+	0.279387i
$768$		0			0
$769$	−23.6232	+	5.94147i	−0.851874	+	0.214255i	−0.645066	−	0.764127i	$-0.723170\pi$
$769$	−23.6232	+	5.94147i	−0.851874	+	0.214255i	−0.206808	+	0.978382i	$0.566308\pi$
$770$	4.05923	+	3.26645i	0.146284	+	0.117715i
$771$		0			0
$772$	−7.03008	−	10.6094i	−0.253018	−	0.381842i
$773$	−21.6567	−	32.6833i	−0.778938	−	1.17554i	−0.980588	−	0.196078i	$-0.937180\pi$
$773$	−21.6567	−	32.6833i	−0.778938	−	1.17554i	0.201651	−	0.979458i	$-0.435369\pi$
$774$		0			0
$775$	−3.09804	−	2.49298i	−0.111285	−	0.0895505i
$776$	−6.34389	+	1.59555i	−0.227732	+	0.0572770i
$777$		0			0
$778$	−12.1889	−	21.1117i	−0.436992	−	0.756892i
$779$	0.0683985	+	0.0705383i	0.00245063	+	0.00252730i
$780$		0			0
$781$	−0.645826	−	4.16048i	−0.0231095	−	0.148874i
$782$	0.531056	+	5.73100i	0.0189905	+	0.204940i
$783$		0			0
$784$	3.79648	−	0.470107i	0.135589	−	0.0167895i
$785$	39.3851	+	15.2579i	1.40572	+	0.544577i
$786$		0			0
$787$	11.1022	−	4.30103i	0.395752	−	0.153315i	−0.155139	−	0.987893i	$-0.549582\pi$
$787$	11.1022	−	4.30103i	0.395752	−	0.153315i	0.550890	+	0.834578i	$0.314288\pi$
$788$	−25.3857	+	29.6303i	−0.904328	+	1.05554i
$789$		0			0
$790$	42.9925	−	26.6198i	1.52960	−	0.947090i
$791$	3.01402	+	2.13358i	0.107166	+	0.0758614i
$792$		0			0
$793$	13.4883	+	47.4066i	0.478985	+	1.68346i
$794$	3.44308	−	3.13878i	0.122190	−	0.111391i
$795$		0			0
$796$	−8.90268	+	0.549098i	−0.315547	+	0.0194623i
$797$	3.62950	−	39.1685i	0.128563	−	1.38742i	−0.650038	−	0.759901i	$-0.725247\pi$
$797$	3.62950	−	39.1685i	0.128563	−	1.38742i	0.778602	−	0.627518i	$-0.215929\pi$
$798$		0			0
$799$	20.7870	−	14.7148i	0.735389	−	0.520571i
$800$	4.15710	+	3.78970i	0.146976	+	0.133986i
$801$		0			0
$802$	−24.8686	+	32.9313i	−0.878141	+	1.16285i
$803$	3.10197	−	2.49615i	0.109466	−	0.0880872i
$804$		0			0
$805$	−4.81498	−	2.58559i	−0.169706	−	0.0911301i
$806$	−35.2330	−	4.36279i	−1.24103	−	0.153673i
$807$		0			0
$808$	6.20538	−	6.39951i	0.218304	−	0.225134i
$809$	9.65368	+	2.42800i	0.339405	+	0.0853638i	0.409853	−	0.912152i	$-0.365580\pi$
$809$	9.65368	+	2.42800i	0.339405	+	0.0853638i	−0.0704477	+	0.997515i	$0.522443\pi$
$810$		0			0
$811$	14.4796	−	2.70670i	0.508446	−	0.0950451i	0.0767253	−	0.997052i	$-0.475554\pi$
$811$	14.4796	−	2.70670i	0.508446	−	0.0950451i	0.431721	+	0.902007i	$0.357906\pi$
$812$	−1.75111	+	11.2808i	−0.0614519	+	0.395880i
$813$		0			0
$814$	−1.26380	+	4.44178i	−0.0442961	+	0.155684i
$815$	2.10352	+	4.22443i	0.0736830	+	0.147975i
$816$		0			0
$817$	15.3996	−	43.7010i	0.538766	−	1.52891i
$818$	8.94183	−	4.11390i	0.312644	−	0.143839i
$819$		0			0
$820$	−0.0266993	−	0.0630796i	−0.000932380	−	0.00220283i
$821$	−40.2318	−	24.9105i	−1.40410	−	0.869381i	−0.405107	−	0.914269i	$-0.632766\pi$
$821$	−40.2318	−	24.9105i	−1.40410	−	0.869381i	−0.998992	+	0.0448885i	$0.985707\pi$
$822$		0			0
$823$	−29.1989			−1.01781			−0.508905	−	0.860823i	$-0.669950\pi$
$823$	−29.1989			−1.01781			−0.508905	+	0.860823i	$0.669950\pi$
$824$	−1.60542	−	5.07856i	−0.0559276	−	0.176920i
$825$		0			0
$826$	−6.88416	+	10.3892i	−0.239531	+	0.361488i
$827$	−26.2155	−	16.2320i	−0.911604	−	0.564441i	−0.0114121	−	0.999935i	$-0.503633\pi$
$827$	−26.2155	−	16.2320i	−0.911604	−	0.564441i	−0.900192	+	0.435494i	$0.856574\pi$
$828$		0			0
$829$	17.7317	−	5.64087i	0.615849	−	0.195916i	0.0210344	−	0.999779i	$-0.493304\pi$
$829$	17.7317	−	5.64087i	0.615849	−	0.195916i	0.594814	+	0.803863i	$0.297226\pi$
$830$	−25.5215	+	11.7418i	−0.885864	+	0.407562i
$831$		0			0
$832$	19.2169	+	3.59226i	0.666227	+	0.124539i
$833$	1.23587	+	2.48196i	0.0428204	+	0.0859949i
$834$		0			0
$835$	−16.3775	−	1.01013i	−0.566766	−	0.0349570i
$836$	−0.715400	+	4.60869i	−0.0247426	+	0.159395i
$837$		0			0
$838$	−7.82154	−	10.3574i	−0.270191	−	0.357790i
$839$	39.6979	+	9.98442i	1.37052	+	0.344700i	0.857857	−	0.513888i	$-0.171795\pi$
$839$	39.6979	+	9.98442i	1.37052	+	0.344700i	0.512666	+	0.858588i	$0.328658\pi$
$840$		0			0
$841$	19.8936	+	9.15253i	0.685988	+	0.315604i
$842$	−0.986931	−	0.122209i	−0.0340119	−	0.00421159i
$843$		0			0
$844$	10.6351	+	12.4134i	0.366076	+	0.427286i
$845$	2.29229	−	1.84460i	0.0788572	−	0.0634562i
$846$		0			0
$847$	11.9255	−	23.9497i	0.409765	−	0.822920i
$848$	−13.6095	−	12.4067i	−0.467353	−	0.426049i
$849$		0			0
$850$	−1.80922	+	4.27445i	−0.0620558	+	0.146613i
$851$	0.446957	−	4.82344i	0.0153215	−	0.165345i
$852$		0			0
$853$	−11.6341	+	53.1230i	−0.398344	+	1.81890i	0.157390	+	0.987537i	$0.449692\pi$
$853$	−11.6341	+	53.1230i	−0.398344	+	1.81890i	−0.555734	+	0.831360i	$0.687563\pi$
$854$	−50.8095	+	46.3189i	−1.73866	+	1.58500i
$855$		0			0
$856$	−1.01549	−	4.63689i	−0.0347089	−	0.158486i
$857$	−36.7230	−	25.9956i	−1.25443	−	0.887994i	−0.257501	−	0.966278i	$-0.582899\pi$
$857$	−36.7230	−	25.9956i	−1.25443	−	0.887994i	−0.996931	+	0.0782837i	$0.975056\pi$
$858$		0			0
$859$	0.934942	−	30.3457i	0.0318998	−	1.03538i	−0.839063	−	0.544034i	$-0.816896\pi$
$859$	0.934942	−	30.3457i	0.0318998	−	1.03538i	0.870963	−	0.491349i	$-0.163496\pi$
$860$	−21.0162	+	24.5303i	−0.716648	+	0.836475i
$861$		0			0
$862$	−40.9529	+	21.9912i	−1.39486	+	0.749024i
$863$	−30.7718	−	11.9211i	−1.04749	−	0.405798i	−0.224866	−	0.974390i	$-0.572194\pi$
$863$	−30.7718	−	11.9211i	−1.04749	−	0.405798i	−0.822620	+	0.568592i	$0.807488\pi$
$864$		0			0
$865$	18.4754	+	5.87746i	0.628184	+	0.199840i
$866$	4.16000	+	44.8935i	0.141363	+	1.52554i
$867$		0			0
$868$	−7.62961	−	21.6513i	−0.258966	−	0.734891i
$869$	3.45637	+	3.56450i	0.117249	+	0.120917i
$870$		0			0
$871$	4.37083	−	7.57050i	0.148100	−	0.256517i
$872$	8.61148	−	2.16587i	0.291621	−	0.0733458i
$873$		0			0
$874$	−0.325002	−	10.5487i	−0.0109934	−	0.356815i
$875$	13.9698	+	21.0826i	0.472267	+	0.712722i
$876$		0			0
$877$	−0.513498	−	16.6668i	−0.0173396	−	0.562797i	−0.967767	−	0.251849i	$-0.918961\pi$
$877$	−0.513498	−	16.6668i	−0.0173396	−	0.562797i	0.950427	−	0.310948i	$-0.100646\pi$
$878$	−1.36258	−	1.09647i	−0.0459850	−	0.0370040i
$879$		0			0
$880$	−2.43294	+	4.21398i	−0.0820145	+	0.142053i
$881$	6.11424	+	10.5902i	0.205994	+	0.356792i	0.950449	−	0.310881i	$-0.100624\pi$
$881$	6.11424	+	10.5902i	0.205994	+	0.356792i	−0.744455	+	0.667673i	$0.767291\pi$
$882$		0			0
$883$	3.43604	+	9.75076i	0.115632	+	0.328139i	0.986590	−	0.163218i	$-0.0521873\pi$
$883$	3.43604	+	9.75076i	0.115632	+	0.328139i	−0.870958	+	0.491357i	$0.836501\pi$
$884$	2.94653	+	18.9819i	0.0991025	+	0.638429i
$885$		0			0
$886$	−43.2859	−	13.7702i	−1.45422	−	0.462620i
$887$	−5.38985	+	0.667408i	−0.180973	+	0.0224094i	−0.212863	−	0.977082i	$-0.568279\pi$
$887$	−5.38985	+	0.667408i	−0.180973	+	0.0224094i	0.0318897	+	0.999491i	$0.489847\pi$
$888$		0			0
$889$	40.0771	−	21.5209i	1.34414	−	0.721789i
$890$	−44.6046	+	17.2799i	−1.49515	+	0.579224i
$891$		0			0
$892$	−1.25444	+	40.7158i	−0.0420017	+	1.36326i
$893$	−39.7049	+	24.5842i	−1.32867	+	0.822679i
$894$		0			0
$895$	6.71376	+	30.6560i	0.224416	+	1.02472i
$896$	−2.82170	−	9.91726i	−0.0942665	−	0.331313i
$897$		0			0
$898$	1.06413	−	4.85899i	0.0355106	−	0.162146i
$899$	14.2541	−	0.879163i	0.475401	−	0.0293217i
$900$		0			0
$901$	5.20267	−	12.2918i	0.173326	−	0.409499i
$902$	0.0118424	−	0.00838306i	0.000394309	−	0.000279125i
$903$		0			0
$904$	−0.348502	+	0.699886i	−0.0115910	+	0.0232778i
$905$	23.0433	−	30.5142i	0.765985	−	1.01433i
$906$		0			0
$907$	8.55665	+	9.98736i	0.284119	+	0.331625i	0.883141	−	0.469107i	$-0.155424\pi$
$907$	8.55665	+	9.98736i	0.284119	+	0.331625i	−0.599022	+	0.800732i	$0.704444\pi$
$908$	30.4922	+	16.3739i	1.01192	+	0.543388i
$909$		0			0
$910$	−35.7478	−	16.4466i	−1.18503	−	0.545199i
$911$	34.4252	−	35.5021i	1.14056	−	1.17624i	0.158558	−	0.987350i	$-0.449316\pi$
$911$	34.4252	−	35.5021i	1.14056	−	1.17624i	0.981999	−	0.188888i	$-0.0604884\pi$
$912$		0			0
$913$	−1.66233	−	2.20128i	−0.0550151	−	0.0728518i
$914$	−46.5281	+	8.69761i	−1.53901	+	0.287692i
$915$		0			0
$916$	14.5102	+	0.894960i	0.479432	+	0.0295703i
$917$	0.449234	−	1.57889i	0.0148350	−	0.0521396i
$918$		0			0
$919$	−42.1943	−	7.88749i	−1.39186	−	0.260184i	−0.566163	−	0.824293i	$-0.691573\pi$
$919$	−42.1943	−	7.88749i	−1.39186	−	0.260184i	−0.825700	+	0.564109i	$0.809220\pi$
$920$	0.384582	−	1.09136i	0.0126793	−	0.0359812i
$921$		0			0
$922$	−36.5916	+	11.6406i	−1.20508	+	0.383364i
$923$	12.3942	+	29.2825i	0.407961	+	0.963846i
$924$		0			0
$925$	2.15783	−	3.25650i	0.0709491	−	0.107073i
$926$	41.0169			1.34790
$927$		0			0
$928$	−20.2023			−0.663174
$929$	−1.39234	+	2.10126i	−0.0456813	+	0.0689401i	−0.855730	−	0.517423i	$-0.826892\pi$
$929$	−1.39234	+	2.10126i	−0.0456813	+	0.0689401i	0.810049	+	0.586363i	$0.199441\pi$
$930$		0			0
$931$	−1.98170	−	4.68194i	−0.0649475	−	0.153444i
$932$	21.1149	−	6.71712i	0.691640	−	0.220027i
$933$		0			0
$934$	−6.17004	+	17.5093i	−0.201890	+	0.572922i
$935$	−3.46666	−	0.648031i	−0.113372	−	0.0211929i
$936$		0			0
$937$	−14.4072	+	50.6360i	−0.470662	+	1.65421i	0.255597	+	0.966784i	$0.417728\pi$
$937$	−14.4072	+	50.6360i	−0.470662	+	1.65421i	−0.726258	+	0.687422i	$0.758742\pi$
$938$	12.1709	+	0.750674i	0.397393	+	0.0245104i
$939$		0			0
$940$	32.0019	−	5.98218i	1.04379	−	0.195117i
$941$	−18.4868	−	24.4804i	−0.602651	−	0.798039i	0.389771	−	0.920912i	$-0.372554\pi$
$941$	−18.4868	−	24.4804i	−0.602651	−	0.798039i	−0.992422	+	0.122873i	$0.960789\pi$
$942$		0			0
$943$	−0.0105947	+	0.0109262i	−0.000345011	+	0.000355805i
$944$	−10.5739	−	4.86476i	−0.344151	−	0.158334i
$945$		0			0
$946$	−6.02812	−	3.23703i	−0.195991	−	0.105245i
$947$	23.1791	+	27.0548i	0.753221	+	0.879163i	0.995855	−	0.0909547i	$-0.0289919\pi$
$947$	23.1791	+	27.0548i	0.753221	+	0.879163i	−0.242634	+	0.970118i	$0.578011\pi$
$948$		0			0
$949$	−18.1213	+	23.9965i	−0.588242	+	0.778959i
$950$	3.79371	−	7.61879i	0.123084	−	0.247186i
$951$		0			0
$952$	3.43968	−	2.43490i	0.111481	−	0.0789155i
$953$	−8.68065	+	20.5088i	−0.281194	+	0.664346i	−0.999508	−	0.0313726i	$-0.990012\pi$
$953$	−8.68065	+	20.5088i	−0.281194	+	0.664346i	0.718314	+	0.695719i	$0.244914\pi$
$954$		0			0
$955$	59.2002	−	3.65134i	1.91567	−	0.118155i
$956$	−5.25816	+	24.0095i	−0.170061	+	0.776522i
$957$		0			0
$958$	−10.6428	−	37.4055i	−0.343852	−	1.20852i
$959$	−4.09408	−	18.6941i	−0.132205	−	0.603665i
$960$		0			0
$961$	1.94025	−	1.20135i	0.0625888	−	0.0387533i
$962$	1.07404	−	34.8606i	0.0346285	−	1.12395i
$963$		0			0
$964$	−41.3596	+	16.0228i	−1.33210	+	0.516060i
$965$	−15.5473	+	8.34874i	−0.500486	+	0.268755i
$966$		0			0
$967$	28.7542	−	3.56055i	0.924674	−	0.114499i	0.353599	−	0.935397i	$-0.384958\pi$
$967$	28.7542	−	3.56055i	0.924674	−	0.114499i	0.571075	+	0.820898i	$0.306527\pi$
$968$	5.39806	+	1.71724i	0.173500	+	0.0551943i
$969$		0			0
$970$	−8.84616	−	56.9879i	−0.284033	−	1.82977i
$971$	17.4514	+	49.5235i	0.560043	+	1.58929i	0.788040	+	0.615624i	$0.211096\pi$
$971$	17.4514	+	49.5235i	0.560043	+	1.58929i	−0.227997	+	0.973662i	$0.573218\pi$
$972$		0			0
$973$	13.4934	+	23.3712i	0.432578	+	0.749247i
$974$	10.5163	−	18.2148i	0.336964	−	0.583639i
$975$		0			0
$976$	−50.0240	−	40.2542i	−1.60123	−	1.28851i
$977$	0.519105	+	16.8488i	0.0166076	+	0.539039i	0.970806	+	0.239865i	$0.0771033\pi$
$977$	0.519105	+	16.8488i	0.0166076	+	0.539039i	−0.954199	+	0.299174i	$0.903289\pi$
$978$		0			0
$979$	−2.59439	−	3.91532i	−0.0829170	−	0.125134i
$980$	0.109147	+	3.54262i	0.00348657	+	0.113165i
$981$		0			0
$982$	−17.0024	+	4.27628i	−0.542569	+	0.136462i
$983$	21.6049	−	37.4208i	0.689090	−	1.19354i	−0.283042	−	0.959107i	$-0.591344\pi$
$983$	21.6049	−	37.4208i	0.689090	−	1.19354i	0.972133	−	0.234432i	$-0.0753230\pi$
$984$		0			0
$985$	37.6613	+	38.8395i	1.19999	+	1.23753i
$986$	−5.54023	−	15.7220i	−0.176437	−	0.500692i
$987$		0			0
$988$	−3.24997	−	35.0728i	−0.103395	−	1.11581i
$989$	6.83940	+	2.17577i	0.217480	+	0.0691855i
$990$		0			0
$991$	41.5878	+	16.1112i	1.32108	+	0.511789i	0.915517	−	0.402279i	$-0.131782\pi$
$991$	41.5878	+	16.1112i	1.32108	+	0.511789i	0.405562	+	0.914068i	$0.367076\pi$
$992$	35.7908	−	19.2193i	1.13636	−	0.610212i
$993$		0			0
$994$	−28.8584	+	33.6836i	−0.915332	+	1.06838i
$995$	−0.380861	+	12.3617i	−0.0120741	+	0.391893i
$996$		0			0
$997$	14.4475	+	10.2272i	0.457557	+	0.323898i	0.783391	−	0.621529i	$-0.213488\pi$
$997$	14.4475	+	10.2272i	0.457557	+	0.323898i	−0.325834	+	0.945427i	$0.605645\pi$
$998$	7.40471	+	33.8109i	0.234392	+	1.07027i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	927.2.ba.b.28.1		256
3.2	odd	2		309.2.m.a.28.8	✓	256
103.92	even	51	inner	927.2.ba.b.298.1		256
309.92	odd	102		309.2.m.a.298.8	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
309.2.m.a.28.8	✓	256	3.2	odd	2
309.2.m.a.298.8	yes	256	309.92	odd	102
927.2.ba.b.28.1		256	1.1	even	1	trivial
927.2.ba.b.298.1		256	103.92	even	51	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 927 = 3^{2} \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	927.ba (of order \(51\), degree \(32\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.06654 + 1.60956i) q^{2} +(-0.673627 - 1.59151i) q^{4} +(-2.28349 + 0.726431i) q^{5} +(-0.823820 + 2.33783i) q^{7} +(-0.515877 - 0.0964341i) q^{8} +O(q^{10})\)	\(q+(-1.06654 + 1.60956i) q^{2} +(-0.673627 - 1.59151i) q^{4} +(-2.28349 + 0.726431i) q^{5} +(-0.823820 + 2.33783i) q^{7} +(-0.515877 - 0.0964341i) q^{8} +(1.26619 - 4.45019i) q^{10} +(0.453444 + 0.0279674i) q^{11} +(-3.37263 + 0.630454i) q^{13} +(-2.88426 - 3.81937i) q^{14} +(3.11153 - 3.20887i) q^{16} +(2.94304 + 1.35402i) q^{17} +(-5.23345 - 2.81031i) q^{19} +(2.69434 + 3.14485i) q^{20} +(-0.528629 + 0.700018i) q^{22} +(0.410137 - 0.823667i) q^{23} +(0.605651 - 0.428732i) q^{25} +(2.58228 - 6.10087i) q^{26} +(4.27562 - 0.263711i) q^{28} +(-0.570120 + 2.60325i) q^{29} +(-1.46654 - 5.15434i) q^{31} +(1.62178 + 7.40526i) q^{32} +(-5.31824 + 3.29291i) q^{34} +(0.182913 - 5.93687i) q^{35} +(4.90908 - 1.90179i) q^{37} +(10.1050 - 5.42629i) q^{38} +(1.24805 - 0.154542i) q^{40} +(-0.0157621 - 0.00501428i) q^{41} +(1.19648 + 7.70783i) q^{43} +(-0.260941 - 0.740498i) q^{44} +(0.888318 + 1.53861i) q^{46} +(3.93077 - 6.80829i) q^{47} +(0.666787 + 0.536561i) q^{49} +(0.0441223 + 1.43209i) q^{50} +(3.27527 + 4.94287i) q^{52} +(-0.126880 - 4.11819i) q^{53} +(-1.05575 + 0.265532i) q^{55} +(0.650436 - 1.12659i) q^{56} +(-3.58204 - 3.69410i) q^{58} +(-0.865460 - 2.45600i) q^{59} +(-1.32546 - 14.3040i) q^{61} +(9.86035 + 3.13680i) q^{62} +(-5.31313 - 2.05832i) q^{64} +(7.24340 - 3.88962i) q^{65} +(-1.65765 + 1.93482i) q^{67} +(0.172410 - 5.59597i) q^{68} +(9.36069 + 6.62630i) q^{70} +(-1.98264 - 9.05301i) q^{71} +(6.47676 - 5.90434i) q^{73} +(-2.17466 + 9.92980i) q^{74} +(-0.947223 + 10.2222i) q^{76} +(-0.438939 + 1.03703i) q^{77} +(8.07662 + 7.36281i) q^{79} +(-4.77413 + 9.58775i) q^{80} +(0.0248816 - 0.0200222i) q^{82} +(-3.95041 - 4.61093i) q^{83} +(-7.70402 - 0.953964i) q^{85} +(-13.6823 - 6.29487i) q^{86} +(-0.231224 - 0.0581552i) q^{88} +(-6.23039 - 8.25037i) q^{89} +(1.30455 - 8.40403i) q^{91} +(-1.58715 - 0.0978920i) q^{92} +(6.76607 + 13.5881i) q^{94} +(13.9920 + 2.61557i) q^{95} +(11.3234 - 5.20961i) q^{97} +(-1.57478 + 0.500974i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q + q^{2} + 3 q^{4} + q^{5} - 4 q^{7} - 57 q^{8}+O(q^{10}) \) 256 * q + q^2 + 3 * q^4 + q^5 - 4 * q^7 - 57 * q^8	\( 256 q + q^{2} + 3 q^{4} + q^{5} - 4 q^{7} - 57 q^{8} - 58 q^{10} + 32 q^{11} + 10 q^{13} - 57 q^{14} - 7 q^{16} - 15 q^{19} - 46 q^{20} + 54 q^{22} + 21 q^{23} - 27 q^{25} - 14 q^{26} - 49 q^{28} - 2 q^{29} - 92 q^{31} - 8 q^{32} - 35 q^{34} - 58 q^{35} + 4 q^{37} + 51 q^{38} + 41 q^{40} + 216 q^{41} + 3 q^{43} + 133 q^{44} - 36 q^{46} - 2 q^{47} + 26 q^{49} + 60 q^{50} + 62 q^{52} + 7 q^{53} + 16 q^{55} - 19 q^{56} - 32 q^{58} - 73 q^{59} - 58 q^{61} + 20 q^{62} - 269 q^{64} - 41 q^{65} - 10 q^{67} + 8 q^{68} + 89 q^{70} + 178 q^{71} - 84 q^{73} + 239 q^{74} + 58 q^{76} - 33 q^{77} - 42 q^{79} + 24 q^{80} - 198 q^{82} - 31 q^{83} + 130 q^{85} + 86 q^{86} + 66 q^{88} - 73 q^{89} - 27 q^{91} - 146 q^{92} - 446 q^{94} - 48 q^{95} + 100 q^{97} - 363 q^{98}+O(q^{100}) \) 256 * q + q^2 + 3 * q^4 + q^5 - 4 * q^7 - 57 * q^8 - 58 * q^10 + 32 * q^11 + 10 * q^13 - 57 * q^14 - 7 * q^16 - 15 * q^19 - 46 * q^20 + 54 * q^22 + 21 * q^23 - 27 * q^25 - 14 * q^26 - 49 * q^28 - 2 * q^29 - 92 * q^31 - 8 * q^32 - 35 * q^34 - 58 * q^35 + 4 * q^37 + 51 * q^38 + 41 * q^40 + 216 * q^41 + 3 * q^43 + 133 * q^44 - 36 * q^46 - 2 * q^47 + 26 * q^49 + 60 * q^50 + 62 * q^52 + 7 * q^53 + 16 * q^55 - 19 * q^56 - 32 * q^58 - 73 * q^59 - 58 * q^61 + 20 * q^62 - 269 * q^64 - 41 * q^65 - 10 * q^67 + 8 * q^68 + 89 * q^70 + 178 * q^71 - 84 * q^73 + 239 * q^74 + 58 * q^76 - 33 * q^77 - 42 * q^79 + 24 * q^80 - 198 * q^82 - 31 * q^83 + 130 * q^85 + 86 * q^86 + 66 * q^88 - 73 * q^89 - 27 * q^91 - 146 * q^92 - 446 * q^94 - 48 * q^95 + 100 * q^97 - 363 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more