LMFDB - Embedded newform 735.2.g.b.734.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,2,Mod(734,735)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(735, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1]))

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

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

chi := DirichletCharacter("735.734");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.g (of order $2$, degree $1$, 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:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			734.16
Character	$\chi$	$=$	735.734
Dual form			735.2.g.b.734.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.644806 q^{2} +(0.536966 + 1.64671i) q^{3} -1.58423 q^{4} +(2.15203 + 0.607270i) q^{5} +(0.346239 + 1.06181i) q^{6} -2.31113 q^{8} +(-2.42334 + 1.76846i) q^{9} +O(q^{10})$	\(q+0.644806 q^{2} +(0.536966 + 1.64671i) q^{3} -1.58423 q^{4} +(2.15203 + 0.607270i) q^{5} +(0.346239 + 1.06181i) q^{6} -2.31113 q^{8} +(-2.42334 + 1.76846i) q^{9} +(1.38764 + 0.391571i) q^{10} +4.05350i q^{11} +(-0.850674 - 2.60877i) q^{12} -4.21339 q^{13} +(0.155565 + 3.86986i) q^{15} +1.67822 q^{16} -2.17659i q^{17} +(-1.56258 + 1.14031i) q^{18} +4.47601i q^{19} +(-3.40930 - 0.962052i) q^{20} +2.61372i q^{22} -0.644806 q^{23} +(-1.24100 - 3.80577i) q^{24} +(4.26245 + 2.61372i) q^{25} -2.71682 q^{26} +(-4.21339 - 3.04094i) q^{27} +1.16875i q^{29} +(0.100309 + 2.49531i) q^{30} -0.391571i q^{31} +5.70439 q^{32} +(-6.67496 + 2.17659i) q^{33} -1.40348i q^{34} +(3.83911 - 2.80164i) q^{36} +4.26357i q^{37} +2.88616i q^{38} +(-2.26245 - 6.93825i) q^{39} +(-4.97361 - 1.40348i) q^{40} +2.27971 q^{41} +6.54419i q^{43} -6.42166i q^{44} +(-6.28902 + 2.33415i) q^{45} -0.415775 q^{46} -7.80140i q^{47} +(0.901147 + 2.76355i) q^{48} +(2.74845 + 1.68534i) q^{50} +(3.58423 - 1.16875i) q^{51} +6.67496 q^{52} -7.20148 q^{53} +(-2.71682 - 1.96082i) q^{54} +(-2.46157 + 8.72325i) q^{55} +(-7.37071 + 2.40346i) q^{57} +0.753620i q^{58} +11.3249 q^{59} +(-0.246450 - 6.13073i) q^{60} -6.99120i q^{61} -0.252487i q^{62} +0.321779 q^{64} +(-9.06734 - 2.55867i) q^{65} +(-4.30406 + 1.40348i) q^{66} +8.73739i q^{67} +3.44821i q^{68} +(-0.346239 - 1.06181i) q^{69} +8.13766i q^{71} +(5.60064 - 4.08713i) q^{72} -5.23685 q^{73} +2.74917i q^{74} +(-2.01527 + 8.42251i) q^{75} -7.09101i q^{76} +(-1.45884 - 4.47383i) q^{78} +3.75268 q^{79} +(3.61158 + 1.01913i) q^{80} +(2.74511 - 8.57113i) q^{81} +1.46997 q^{82} -5.27461i q^{83} +(1.32178 - 4.68409i) q^{85} +4.21973i q^{86} +(-1.92461 + 0.627581i) q^{87} -9.36817i q^{88} +0.894758 q^{89} +(-4.05520 + 1.50507i) q^{90} +1.02152 q^{92} +(0.644806 - 0.210260i) q^{93} -5.03039i q^{94} +(-2.71815 + 9.63250i) q^{95} +(3.06306 + 9.39349i) q^{96} +3.89968 q^{97} +(-7.16845 - 9.82300i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{4} + 12 q^{9}+O(q^{10}) $ 24 * q + 24 * q^4 + 12 * q^9	$ 24 q + 24 q^{4} + 12 q^{9} - 24 q^{15} + 24 q^{16} + 24 q^{25} - 36 q^{30} + 84 q^{36} + 24 q^{39} - 72 q^{46} + 24 q^{51} - 24 q^{60} + 24 q^{64} - 96 q^{79} + 12 q^{81} + 48 q^{85} - 48 q^{99}+O(q^{100}) $ 24 * q + 24 * q^4 + 12 * q^9 - 24 * q^15 + 24 * q^16 + 24 * q^25 - 36 * q^30 + 84 * q^36 + 24 * q^39 - 72 * q^46 + 24 * q^51 - 24 * q^60 + 24 * q^64 - 96 * q^79 + 12 * q^81 + 48 * q^85 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	0.644806			0.455947			0.227973	−	0.973667i	$-0.426790\pi$
$2$	0.644806			0.455947			0.227973	+	0.973667i	$0.426790\pi$
$3$	0.536966	+	1.64671i	0.310017	+	0.950731i
$3$	0.536966	+	1.64671i	0.310017	+	0.950731i
$4$	−1.58423			−0.792113
$5$	2.15203	+	0.607270i	0.962416	+	0.271579i
$5$	2.15203	+	0.607270i	0.962416	+	0.271579i
$6$	0.346239	+	1.06181i	0.141351	+	0.433483i
$7$		0			0
$7$		0			0
$8$	−2.31113			−0.817108
$9$	−2.42334	+	1.76846i	−0.807779	+	0.589486i
$10$	1.38764	+	0.391571i	0.438810	+	0.123826i
$11$			4.05350i			1.22218i	0.791562	+	0.611089i	$0.209268\pi$
$11$			4.05350i			1.22218i	−0.791562	+	0.611089i	$0.790732\pi$
$12$	−0.850674	−	2.60877i	−0.245569	−	0.753086i
$13$	−4.21339			−1.16858			−0.584292	−	0.811543i	$-0.698628\pi$
$13$	−4.21339			−1.16858			−0.584292	+	0.811543i	$0.698628\pi$
$14$		0			0
$15$	0.155565	+	3.86986i	0.0401666	+	0.999193i
$16$	1.67822			0.419555
$17$		−	2.17659i		−	0.527901i	−0.964536	−	0.263951i	$-0.914974\pi$
$17$		−	2.17659i		−	0.527901i	0.964536	−	0.263951i	$-0.0850256\pi$
$18$	−1.56258	+	1.14031i	−0.368304	+	0.268774i
$19$			4.47601i			1.02687i	0.858129	+	0.513434i	$0.171627\pi$
$19$			4.47601i			1.02687i	−0.858129	+	0.513434i	$0.828373\pi$
$20$	−3.40930	−	0.962052i	−0.762342	−	0.215121i
$21$		0			0
$22$			2.61372i			0.557248i
$23$	−0.644806			−0.134451			−0.0672257	−	0.997738i	$-0.521415\pi$
$23$	−0.644806			−0.134451			−0.0672257	+	0.997738i	$0.521415\pi$
$24$	−1.24100	−	3.80577i	−0.253317	−	0.776850i
$25$	4.26245	+	2.61372i	0.852489	+	0.522745i
$26$	−2.71682			−0.532812
$27$	−4.21339	−	3.04094i	−0.810868	−	0.585229i
$28$		0			0
$29$			1.16875i			0.217032i	0.994095	+	0.108516i	$0.0346099\pi$
$29$			1.16875i			0.217032i	−0.994095	+	0.108516i	$0.965390\pi$
$30$	0.100309	+	2.49531i	0.0183138	+	0.455579i
$31$		−	0.391571i		−	0.0703283i	−0.999382	−	0.0351641i	$-0.988805\pi$
$31$		−	0.391571i		−	0.0703283i	0.999382	−	0.0351641i	$-0.0111954\pi$
$32$	5.70439			1.00840
$33$	−6.67496	+	2.17659i	−1.16196	+	0.378896i
$34$		−	1.40348i		−	0.240695i
$35$		0			0
$36$	3.83911	−	2.80164i	0.639852	−	0.466939i
$37$			4.26357i			0.700926i	0.936577	+	0.350463i	$0.113976\pi$
$37$			4.26357i			0.700926i	−0.936577	+	0.350463i	$0.886024\pi$
$38$			2.88616i			0.468197i
$39$	−2.26245	−	6.93825i	−0.362281	−	1.11101i
$40$	−4.97361	−	1.40348i	−0.786398	−	0.221910i
$41$	2.27971			0.356031			0.178016	−	0.984028i	$-0.443032\pi$
$41$	2.27971			0.356031			0.178016	+	0.984028i	$0.443032\pi$
$42$		0			0
$43$			6.54419i			0.997980i	0.866608	+	0.498990i	$0.166295\pi$
$43$			6.54419i			0.997980i	−0.866608	+	0.498990i	$0.833705\pi$
$44$		−	6.42166i		−	0.968102i
$45$	−6.28902	+	2.33415i	−0.937511	+	0.347955i
$46$	−0.415775			−0.0613026
$47$		−	7.80140i		−	1.13795i	−0.822355	−	0.568975i	$-0.807340\pi$
$47$		−	7.80140i		−	1.13795i	0.822355	−	0.568975i	$-0.192660\pi$
$48$	0.901147	+	2.76355i	0.130069	+	0.398884i
$49$		0			0
$50$	2.74845	+	1.68534i	0.388690	+	0.238344i
$51$	3.58423	−	1.16875i	0.501892	−	0.163658i
$52$	6.67496			0.925651
$53$	−7.20148			−0.989200			−0.494600	−	0.869121i	$-0.664685\pi$
$53$	−7.20148			−0.989200			−0.494600	+	0.869121i	$0.664685\pi$
$54$	−2.71682	−	1.96082i	−0.369712	−	0.266833i
$55$	−2.46157	+	8.72325i	−0.331918	+	1.17624i
$56$		0			0
$57$	−7.37071	+	2.40346i	−0.976274	+	0.318346i
$58$			0.753620i			0.0989552i
$59$	11.3249			1.47438			0.737190	−	0.675685i	$-0.236152\pi$
$59$	11.3249			1.47438			0.737190	+	0.675685i	$0.236152\pi$
$60$	−0.246450	−	6.13073i	−0.0318165	−	0.791473i
$61$		−	6.99120i		−	0.895132i	−0.894251	−	0.447566i	$-0.852291\pi$
$61$		−	6.99120i		−	0.895132i	0.894251	−	0.447566i	$-0.147709\pi$
$62$		−	0.252487i		−	0.0320659i
$63$		0			0
$64$	0.321779			0.0402224
$65$	−9.06734	−	2.55867i	−1.12466	−	0.317364i
$66$	−4.30406	+	1.40348i	−0.529793	+	0.172756i
$67$			8.73739i			1.06744i	0.845660	+	0.533721i	$0.179207\pi$
$67$			8.73739i			1.06744i	−0.845660	+	0.533721i	$0.820793\pi$
$68$			3.44821i			0.418157i
$69$	−0.346239	−	1.06181i	−0.0416822	−	0.127827i
$70$		0			0
$71$			8.13766i			0.965762i	0.875686	+	0.482881i	$0.160410\pi$
$71$			8.13766i			0.965762i	−0.875686	+	0.482881i	$0.839590\pi$
$72$	5.60064	−	4.08713i	0.660042	−	0.481673i
$73$	−5.23685			−0.612927			−0.306464	−	0.951882i	$-0.599146\pi$
$73$	−5.23685			−0.612927			−0.306464	+	0.951882i	$0.599146\pi$
$74$			2.74917i			0.319585i
$75$	−2.01527	+	8.42251i	−0.232703	+	0.972548i
$76$		−	7.09101i		−	0.813394i
$77$		0			0
$78$	−1.45884	−	4.47383i	−0.165181	−	0.506561i
$79$	3.75268			0.422209			0.211105	−	0.977463i	$-0.432294\pi$
$79$	3.75268			0.422209			0.211105	+	0.977463i	$0.432294\pi$
$80$	3.61158	+	1.01913i	0.403787	+	0.113943i
$81$	2.74511	−	8.57113i	0.305013	−	0.952348i
$82$	1.46997			0.162331
$83$		−	5.27461i		−	0.578964i	−0.957183	−	0.289482i	$-0.906517\pi$
$83$		−	5.27461i		−	0.578964i	0.957183	−	0.289482i	$-0.0934831\pi$
$84$		0			0
$85$	1.32178	−	4.68409i	0.143367	−	0.508061i
$86$			4.21973i			0.455025i
$87$	−1.92461	+	0.627581i	−0.206339	+	0.0672838i
$88$		−	9.36817i		−	0.998651i
$89$	0.894758			0.0948442			0.0474221	−	0.998875i	$-0.484899\pi$
$89$	0.894758			0.0948442			0.0474221	+	0.998875i	$0.484899\pi$
$90$	−4.05520	+	1.50507i	−0.427455	+	0.158649i
$91$		0			0
$92$	1.02152			0.106501
$93$	0.644806	−	0.210260i	0.0668632	−	0.0218030i
$94$		−	5.03039i		−	0.518845i
$95$	−2.71815	+	9.63250i	−0.278876	+	0.988273i
$96$	3.06306	+	9.39349i	0.312622	+	0.958719i
$97$	3.89968			0.395953			0.197976	−	0.980207i	$-0.436563\pi$
$97$	3.89968			0.395953			0.197976	+	0.980207i	$0.436563\pi$
$98$		0			0
$99$	−7.16845	−	9.82300i	−0.720456	−	0.987249i
$100$	−6.75268	−	4.14073i	−0.675268	−	0.414073i
$101$	6.58377			0.655109			0.327555	−	0.944832i	$-0.393775\pi$
$101$	6.58377			0.655109			0.327555	+	0.944832i	$0.393775\pi$
$102$	2.31113	−	0.753620i	0.228836	−	0.0746195i
$103$	9.81443			0.967044			0.483522	−	0.875332i	$-0.339357\pi$
$103$	9.81443			0.967044			0.483522	+	0.875332i	$0.339357\pi$
$104$	9.73770			0.954860
$105$		0			0
$106$	−4.64356			−0.451022
$107$	18.7795			1.81548			0.907740	−	0.419532i	$-0.137806\pi$
$107$	18.7795			1.81548			0.907740	+	0.419532i	$0.137806\pi$
$108$	6.67496	+	4.81754i	0.642299	+	0.463568i
$109$	0.906004			0.0867795			0.0433897	−	0.999058i	$-0.486184\pi$
$109$	0.906004			0.0867795			0.0433897	+	0.999058i	$0.486184\pi$
$110$	−1.58724	+	5.62480i	−0.151337	+	0.536304i
$111$	−7.02088	+	2.28939i	−0.666392	+	0.217299i
$112$		0			0
$113$	8.82955			0.830614			0.415307	−	0.909681i	$-0.363674\pi$
$113$	8.82955			0.830614			0.415307	+	0.909681i	$0.363674\pi$
$114$	−4.75268	+	1.54977i	−0.445129	+	0.145149i
$115$	−1.38764	−	0.391571i	−0.129398	−	0.0365142i
$116$		−	1.85157i		−	0.171914i
$117$	10.2105	−	7.45121i	0.943958	−	0.688864i
$118$	7.30238			0.672239
$119$		0			0
$120$	−0.359530	−	8.94374i	−0.0328205	−	0.816448i
$121$	−5.43090			−0.493718
$122$		−	4.50797i		−	0.408132i
$123$	1.22413	+	3.75404i	0.110376	+	0.338490i
$124$			0.620337i			0.0557079i
$125$	7.58567	+	8.21326i	0.678483	+	0.734616i
$126$		0			0
$127$		−	15.8249i		−	1.40424i	−0.712060	−	0.702118i	$-0.752238\pi$
$127$		−	15.8249i		−	1.40424i	0.712060	−	0.702118i	$-0.247762\pi$
$128$	−11.2013			−0.990063
$129$	−10.7764	+	3.51400i	−0.948810	+	0.309391i
$130$	−5.84667	−	1.64984i	−0.512787	−	0.144701i
$131$	16.5563			1.44653			0.723265	−	0.690571i	$-0.242641\pi$
$131$	16.5563			1.44653			0.723265	+	0.690571i	$0.242641\pi$
$132$	10.5746	−	3.44821i	0.920405	−	0.300128i
$133$		0			0
$134$			5.63392i			0.486697i
$135$	−7.22067	−	9.10286i	−0.621456	−	0.783449i
$136$			5.03039i			0.431352i
$137$	19.8616			1.69689			0.848446	−	0.529282i	$-0.177539\pi$
$137$	19.8616			1.69689			0.848446	+	0.529282i	$0.177539\pi$
$138$	−0.223257	−	0.684662i	−0.0190049	−	0.0582823i
$139$		−	0.228766i		−	0.0194037i	−0.999953	−	0.00970183i	$-0.996912\pi$
$139$		−	0.228766i		−	0.0194037i	0.999953	−	0.00970183i	$-0.00308824\pi$
$140$		0			0
$141$	12.8467	−	4.18908i	1.08188	−	0.352784i
$142$			5.24721i			0.440336i
$143$		−	17.0790i		−	1.42822i
$144$	−4.06689	+	2.96786i	−0.338908	+	0.247322i
$145$	−0.709750	+	2.51519i	−0.0589415	+	0.208875i
$146$	−3.37675			−0.279462
$147$		0			0
$148$		−	6.75445i		−	0.555212i
$149$			9.95858i			0.815839i	0.913018	+	0.407919i	$0.133746\pi$
$149$			9.95858i			0.815839i	−0.913018	+	0.407919i	$0.866254\pi$
$150$	−1.29946	+	5.43088i	−0.106100	+	0.443430i
$151$	−5.07446			−0.412953			−0.206477	−	0.978452i	$-0.566200\pi$
$151$	−5.07446			−0.412953			−0.206477	+	0.978452i	$0.566200\pi$
$152$		−	10.3446i		−	0.839061i
$153$	3.84921	+	5.27461i	0.311190	+	0.426427i
$154$		0			0
$155$	0.237789	−	0.842672i	0.0190997	−	0.0676850i
$156$	3.58423	+	10.9918i	0.286968	+	0.880045i
$157$	−16.8536			−1.34506			−0.672531	−	0.740069i	$-0.734793\pi$
$157$	−16.8536			−1.34506			−0.672531	+	0.740069i	$0.734793\pi$
$158$	2.41975			0.192505
$159$	−3.86695	−	11.8588i	−0.306669	−	0.940463i
$160$	12.2760	+	3.46410i	0.970503	+	0.273861i
$161$		0			0
$162$	1.77007	−	5.52672i	0.139070	−	0.434220i
$163$		−	4.80693i		−	0.376508i	−0.982120	−	0.188254i	$-0.939717\pi$
$163$		−	4.80693i		−	0.376508i	0.982120	−	0.188254i	$-0.0602827\pi$
$164$	−3.61158			−0.282017
$165$	−15.6865	+	0.630582i	−1.22119	+	0.0490908i
$166$		−	3.40110i		−	0.263977i
$167$		−	4.45089i		−	0.344420i	−0.985060	−	0.172210i	$-0.944909\pi$
$167$		−	4.45089i		−	0.344420i	0.985060	−	0.172210i	$-0.0550908\pi$
$168$		0			0
$169$	4.75268			0.365590
$170$	0.852291	−	3.02033i	0.0653677	−	0.231648i
$171$	−7.91563	−	10.8469i	−0.605324	−	0.829481i
$172$		−	10.3675i		−	0.790512i
$173$			11.4542i			0.870847i	0.900226	+	0.435423i	$0.143401\pi$
$173$			11.4542i			0.870847i	−0.900226	+	0.435423i	$0.856599\pi$
$174$	−1.24100	+	0.404668i	−0.0940797	+	0.0306778i
$175$		0			0
$176$			6.80268i			0.512771i
$177$	6.08110	+	18.6489i	0.457083	+	1.40174i
$178$	0.576945			0.0432439
$179$			10.4445i			0.780660i	0.920675	+	0.390330i	$0.127639\pi$
$179$			10.4445i			0.780660i	−0.920675	+	0.390330i	$0.872361\pi$
$180$	9.96322	−	3.69782i	0.742615	−	0.275619i
$181$		−	11.9616i		−	0.889095i	−0.895755	−	0.444548i	$-0.853364\pi$
$181$		−	11.9616i		−	0.889095i	0.895755	−	0.444548i	$-0.146636\pi$
$182$		0			0
$183$	11.5125	−	3.75404i	0.851030	−	0.277506i
$184$	1.49023			0.109861
$185$	−2.58914	+	9.17531i	−0.190357	+	0.674582i
$186$	0.415775	−	0.135577i	0.0304861	−	0.00994099i
$187$	8.82283			0.645189
$188$			12.3592i			0.901385i
$189$		0			0
$190$	−1.75268	+	6.21109i	−0.127153	+	0.450600i
$191$		−	14.1477i		−	1.02369i	−0.859078	−	0.511844i	$-0.828962\pi$
$191$		−	14.1477i		−	1.02369i	0.859078	−	0.511844i	$-0.171038\pi$
$192$	0.172784	+	0.529878i	0.0124696	+	0.0382406i
$193$			6.19133i			0.445661i	0.974857	+	0.222831i	$0.0715297\pi$
$193$			6.19133i			0.445661i	−0.974857	+	0.222831i	$0.928470\pi$
$194$	2.51454			0.180533
$195$	−0.655455	−	16.3052i	−0.0469381	−	1.16764i
$196$		0			0
$197$	−13.0751			−0.931562			−0.465781	−	0.884900i	$-0.654227\pi$
$197$	−13.0751			−0.931562			−0.465781	+	0.884900i	$0.654227\pi$
$198$	−4.62226	−	6.33393i	−0.328490	−	0.450133i
$199$			16.9522i			1.20171i	0.799359	+	0.600854i	$0.205173\pi$
$199$			16.9522i			1.20171i	−0.799359	+	0.600854i	$0.794827\pi$
$200$	−9.85107	−	6.04065i	−0.696576	−	0.427139i
$201$	−14.3880	+	4.69168i	−1.01485	+	0.330926i
$202$	4.24525			0.298695
$203$		0			0
$204$	−5.67822	+	1.85157i	−0.397555	+	0.129636i
$205$	4.90600	+	1.38440i	0.342650	+	0.0966907i
$206$	6.32840			0.440920
$207$	1.56258	−	1.14031i	0.108607	−	0.0792572i
$208$	−7.07100			−0.490286
$209$	−18.1435			−1.25501
$210$		0			0
$211$	−18.4309			−1.26884			−0.634418	−	0.772990i	$-0.718760\pi$
$211$	−18.4309			−1.26884			−0.634418	+	0.772990i	$0.718760\pi$
$212$	11.4088			0.783558
$213$	−13.4004	+	4.36964i	−0.918180	+	0.299403i
$214$	12.1091			0.827762
$215$	−3.97409	+	14.0833i	−0.271031	+	0.960472i
$216$	9.73770	+	7.02801i	0.662566	+	0.478195i
$217$		0			0
$218$	0.584197			0.0395668
$219$	−2.81201	−	8.62360i	−0.190018	−	0.582729i
$220$	3.89968	−	13.8196i	0.262917	−	0.931717i
$221$			9.17084i			0.616897i
$222$	−4.52710	+	1.47621i	−0.303839	+	0.0990768i
$223$	−0.627418			−0.0420150			−0.0210075	−	0.999779i	$-0.506687\pi$
$223$	−0.627418			−0.0420150			−0.0210075	+	0.999779i	$0.506687\pi$
$224$		0			0
$225$	−14.9516	+	1.20403i	−0.996773	+	0.0802685i
$226$	5.69334			0.378716
$227$			5.42940i			0.360362i	0.983633	+	0.180181i	$0.0576683\pi$
$227$			5.42940i			0.360362i	−0.983633	+	0.180181i	$0.942332\pi$
$228$	11.6769	−	3.80763i	0.773319	−	0.252166i
$229$			14.3740i			0.949859i	0.880024	+	0.474930i	$0.157526\pi$
$229$			14.3740i			0.949859i	−0.880024	+	0.474930i	$0.842474\pi$
$230$	−0.894758	−	0.252487i	−0.0589986	−	0.0166485i
$231$		0			0
$232$		−	2.70114i		−	0.177339i
$233$	−8.43048			−0.552299			−0.276150	−	0.961115i	$-0.589059\pi$
$233$	−8.43048			−0.552299			−0.276150	+	0.961115i	$0.589059\pi$
$234$	6.58377	−	4.80458i	0.430394	−	0.314085i
$235$	4.73755	−	16.7888i	0.309044	−	1.09518i
$236$	−17.9412			−1.16788
$237$	2.01506	+	6.17959i	0.130892	+	0.401407i
$238$		0			0
$239$			2.71852i			0.175847i	0.996127	+	0.0879233i	$0.0280230\pi$
$239$			2.71852i			0.175847i	−0.996127	+	0.0879233i	$0.971977\pi$
$240$	0.261072	+	6.49448i	0.0168521	+	0.419217i
$241$		−	1.52948i		−	0.0985224i	−0.998786	−	0.0492612i	$-0.984313\pi$
$241$		−	1.52948i		−	0.0985224i	0.998786	−	0.0492612i	$-0.0156867\pi$
$242$	−3.50187			−0.225109
$243$	15.5882	−	0.0819839i	0.999986	−	0.00525927i
$244$			11.0756i			0.709045i
$245$		0			0
$246$	0.789324	+	2.42062i	0.0503255	+	0.154333i
$247$		−	18.8592i		−	1.19998i
$248$			0.904972i			0.0574658i
$249$	8.68578	−	2.83229i	0.550439	−	0.179489i
$250$	4.89128	+	5.29596i	0.309352	+	0.334946i
$251$	8.81039			0.556107			0.278054	−	0.960566i	$-0.410311\pi$
$251$	8.81039			0.556107			0.278054	+	0.960566i	$0.410311\pi$
$252$		0			0
$253$		−	2.61372i		−	0.164323i
$254$		−	10.2040i		−	0.640257i
$255$	8.42310	−	0.338601i	0.527475	−	0.0212040i
$256$	−7.86621			−0.491638
$257$		−	20.1035i		−	1.25402i	−0.779011	−	0.627011i	$-0.784278\pi$
$257$		−	20.1035i		−	1.25402i	0.779011	−	0.627011i	$-0.215722\pi$
$258$	−6.94869	+	2.26585i	−0.432607	+	0.141066i
$259$		0			0
$260$	14.3647	+	4.05350i	0.890861	+	0.251388i
$261$	−2.06689	−	2.83229i	−0.127938	−	0.175314i
$262$	10.6756			0.659540
$263$	−8.75919			−0.540115			−0.270057	−	0.962844i	$-0.587043\pi$
$263$	−8.75919			−0.540115			−0.270057	+	0.962844i	$0.587043\pi$
$264$	15.4267	−	5.03039i	0.949448	−	0.309599i
$265$	−15.4978	−	4.37324i	−0.952022	−	0.268646i
$266$		0			0
$267$	0.480454	+	1.47341i	0.0294033	+	0.0901713i
$268$		−	13.8420i		−	0.845535i
$269$	−17.2488			−1.05168			−0.525838	−	0.850585i	$-0.676248\pi$
$269$	−17.2488			−1.05168			−0.525838	+	0.850585i	$0.676248\pi$
$270$	−4.65593	−	5.86957i	−0.283351	−	0.357211i
$271$		−	22.6456i		−	1.37562i	−0.725889	−	0.687812i	$-0.758571\pi$
$271$		−	22.6456i		−	1.37562i	0.725889	−	0.687812i	$-0.241429\pi$
$272$		−	3.65280i		−	0.221484i
$273$		0			0
$274$	12.8069			0.773692
$275$	−10.5947	+	17.2778i	−0.638887	+	1.04189i
$276$	0.548520	+	1.68215i	0.0330170	+	0.101253i
$277$			13.2112i			0.793785i	0.917865	+	0.396893i	$0.129911\pi$
$277$			13.2112i			0.793785i	−0.917865	+	0.396893i	$0.870089\pi$
$278$		−	0.147510i		−	0.00884703i
$279$	0.692477	+	0.948908i	0.0414575	+	0.0568097i
$280$		0			0
$281$		−	32.8703i		−	1.96088i	−0.196817	−	0.980440i	$-0.563060\pi$
$281$		−	32.8703i		−	1.96088i	0.196817	−	0.980440i	$-0.436940\pi$
$282$	8.28361	−	2.70114i	0.493282	−	0.160851i
$283$	15.8115			0.939896			0.469948	−	0.882694i	$-0.344273\pi$
$283$	15.8115			0.939896			0.469948	+	0.882694i	$0.344273\pi$
$284$		−	12.8919i		−	0.764993i
$285$	−17.3215	+	0.696309i	−1.02604	+	0.0412458i
$286$		−	11.0126i		−	0.651191i
$287$		0			0
$288$	−13.8236	+	10.0880i	−0.814566	+	0.594439i
$289$	12.2624			0.721320
$290$	−0.457651	+	1.62181i	−0.0268742	+	0.0952360i
$291$	2.09400	+	6.42166i	0.122752	+	0.376445i
$292$	8.29635			0.485507
$293$		−	20.7797i		−	1.21396i	−0.794716	−	0.606982i	$-0.792380\pi$
$293$		−	20.7797i		−	1.21396i	0.794716	−	0.606982i	$-0.207620\pi$
$294$		0			0
$295$	24.3716	+	6.87729i	1.41897	+	0.400411i
$296$		−	9.85365i		−	0.572732i
$297$	12.3265	−	17.0790i	0.715254	−	0.991024i
$298$			6.42135i			0.371979i
$299$	2.71682			0.157118
$300$	3.19264	−	13.3432i	0.184327	−	0.770367i
$301$		0			0
$302$	−3.27204			−0.188285
$303$	3.53526	+	10.8416i	0.203095	+	0.622833i
$304$			7.51173i			0.430828i
$305$	4.24555	−	15.0453i	0.243099	−	0.861489i
$306$	2.48199	+	3.40110i	0.141886	+	0.194428i
$307$	−12.9857			−0.741136			−0.370568	−	0.928805i	$-0.620837\pi$
$307$	−12.9857			−0.741136			−0.370568	+	0.928805i	$0.620837\pi$
$308$		0			0
$309$	5.27001	+	16.1616i	0.299800	+	0.919399i
$310$	0.153328	−	0.543360i	0.00870844	−	0.0308608i
$311$	−0.457651			−0.0259510			−0.0129755	−	0.999916i	$-0.504130\pi$
$311$	−0.457651			−0.0259510			−0.0129755	+	0.999916i	$0.504130\pi$
$312$	5.22881	+	16.0352i	0.296023	+	0.907815i
$313$	−27.7419			−1.56807			−0.784033	−	0.620719i	$-0.786841\pi$
$313$	−27.7419			−1.56807			−0.784033	+	0.620719i	$0.786841\pi$
$314$	−10.8673			−0.613276
$315$		0			0
$316$	−5.94509			−0.334437
$317$	−4.52339			−0.254059			−0.127030	−	0.991899i	$-0.540544\pi$
$317$	−4.52339			−0.254059			−0.127030	+	0.991899i	$0.540544\pi$
$318$	−2.49343	−	7.64661i	−0.139825	−	0.428801i
$319$	−4.73755			−0.265252
$320$	0.692477	+	0.195407i	0.0387106	+	0.0109236i
$321$	10.0839	+	30.9244i	0.562830	+	1.72603i
$322$		0			0
$323$	9.74245			0.542084
$324$	−4.34888	+	13.5786i	−0.241604	+	0.754367i
$325$	−17.9594	−	11.0126i	−0.996206	−	0.610871i
$326$		−	3.09953i		−	0.171667i
$327$	0.486493	+	1.49193i	0.0269031	+	0.0825039i
$328$	−5.26871			−0.290916
$329$		0			0
$330$	−10.1147	+	0.406603i	−0.556798	+	0.0223828i
$331$	−22.8965			−1.25850			−0.629252	−	0.777202i	$-0.716638\pi$
$331$	−22.8965			−1.25850			−0.629252	+	0.777202i	$0.716638\pi$
$332$			8.35618i			0.458605i
$333$	−7.53994	−	10.3321i	−0.413186	−	0.566193i
$334$		−	2.86996i		−	0.157037i
$335$	−5.30596	+	18.8031i	−0.289895	+	1.02732i
$336$		0			0
$337$			31.2616i			1.70293i	0.524413	+	0.851464i	$0.324285\pi$
$337$			31.2616i			1.70293i	−0.524413	+	0.851464i	$0.675715\pi$
$338$	3.06455			0.166690
$339$	4.74116	+	14.5397i	0.257505	+	0.789690i
$340$	−2.09400	+	7.42065i	−0.113563	+	0.402441i
$341$	1.58724			0.0859536
$342$	−5.10405	−	6.99413i	−0.275995	−	0.378199i
$343$		0			0
$344$		−	15.1245i		−	0.815457i
$345$	−0.100309	−	2.49531i	−0.00540046	−	0.134343i
$346$			7.38573i			0.397060i
$347$	2.78671			0.149598			0.0747992	−	0.997199i	$-0.476168\pi$
$347$	2.78671			0.149598			0.0747992	+	0.997199i	$0.476168\pi$
$348$	3.04901	−	0.994230i	0.163444	−	0.0532963i
$349$			16.5636i			0.886627i	0.896367	+	0.443314i	$0.146197\pi$
$349$			16.5636i			0.886627i	−0.896367	+	0.443314i	$0.853803\pi$
$350$		0			0
$351$	17.7527	+	12.8127i	0.947568	+	0.683890i
$352$			23.1228i			1.23245i
$353$			3.27697i			0.174416i	0.996190	+	0.0872078i	$0.0277944\pi$
$353$			3.27697i			0.174416i	−0.996190	+	0.0872078i	$0.972206\pi$
$354$	3.92113	+	12.0249i	0.208406	+	0.639118i
$355$	−4.94176	+	17.5125i	−0.262281	+	0.929465i
$356$	−1.41750			−0.0751273
$357$		0			0
$358$			6.73469i			0.355939i
$359$			17.0067i			0.897579i	0.893638	+	0.448789i	$0.148145\pi$
$359$			17.0067i			0.897579i	−0.893638	+	0.448789i	$0.851855\pi$
$360$	14.5347	−	5.39453i	0.766048	−	0.284316i
$361$	−1.03466			−0.0544560
$362$		−	7.71288i		−	0.405380i
$363$	−2.91620	−	8.94314i	−0.153061	−	0.469393i
$364$		0			0
$365$	−11.2698	−	3.18018i	−0.589891	−	0.166458i
$366$	7.42334	−	2.42062i	0.388024	−	0.126528i
$367$	17.1168			0.893490			0.446745	−	0.894661i	$-0.352583\pi$
$367$	17.1168			0.893490			0.446745	+	0.894661i	$0.352583\pi$
$368$	−1.08213			−0.0564098
$369$	−5.52451	+	4.03157i	−0.287594	+	0.209875i
$370$	−1.66949	+	5.91630i	−0.0867926	+	0.307574i
$371$		0			0
$372$	−1.02152	+	0.333100i	−0.0529632	+	0.0172704i
$373$			28.9133i			1.49708i	0.663092	+	0.748538i	$0.269244\pi$
$373$			28.9133i			1.49708i	−0.663092	+	0.748538i	$0.730756\pi$
$374$	5.68901			0.294172
$375$	−9.45165	+	16.9017i	−0.488081	+	0.872798i
$376$			18.0300i			0.929828i
$377$		−	4.92442i		−	0.253621i
$378$		0			0
$379$	−0.559557			−0.0287425			−0.0143712	−	0.999897i	$-0.504575\pi$
$379$	−0.559557			−0.0287425			−0.0143712	+	0.999897i	$0.504575\pi$
$380$	4.30616	−	15.2600i	0.220901	−	0.782824i
$381$	26.0592	−	8.49745i	1.33505	−	0.435337i
$382$		−	9.12249i		−	0.466747i
$383$		−	3.79840i		−	0.194089i	−0.995280	−	0.0970447i	$-0.969061\pi$
$383$		−	3.79840i		−	0.194089i	0.995280	−	0.0970447i	$-0.0309390\pi$
$384$	−6.01470	−	18.4453i	−0.306937	−	0.941284i
$385$		0			0
$386$			3.99220i			0.203198i
$387$	−11.5731	−	15.8588i	−0.588295	−	0.806147i
$388$	−6.17798			−0.313639
$389$			9.10954i			0.461872i	0.972969	+	0.230936i	$0.0741788\pi$
$389$			9.10954i			0.461872i	−0.972969	+	0.230936i	$0.925821\pi$
$390$	−0.422641	−	10.5137i	−0.0214013	−	0.532382i
$391$			1.40348i			0.0709770i
$392$		0			0
$393$	8.89016	+	27.2635i	0.448449	+	1.37526i
$394$	−8.43090			−0.424742
$395$	8.07586	+	2.27889i	0.406341	+	0.114663i
$396$	11.3564	+	15.5619i	0.570683	+	0.782012i
$397$	−24.2383			−1.21648			−0.608242	−	0.793751i	$-0.708125\pi$
$397$	−24.2383			−1.21648			−0.608242	+	0.793751i	$0.708125\pi$
$398$			10.9309i			0.547914i
$399$		0			0
$400$	7.15333	+	4.38641i	0.357666	+	0.219320i
$401$			30.1955i			1.50789i	0.656938	+	0.753944i	$0.271851\pi$
$401$			30.1955i			1.50789i	−0.656938	+	0.753944i	$0.728149\pi$
$402$	−9.27746	+	3.02522i	−0.462718	+	0.150884i
$403$			1.64984i			0.0821845i
$404$	−10.4302			−0.518920
$405$	11.1126	−	16.7783i	0.552187	−	0.833720i
$406$		0			0
$407$	−17.2824			−0.856656
$408$	−8.28361	+	2.70114i	−0.410100	+	0.133727i
$409$		−	24.6665i		−	1.21968i	−0.792525	−	0.609839i	$-0.791234\pi$
$409$		−	24.6665i		−	1.21968i	0.792525	−	0.609839i	$-0.208766\pi$
$410$	3.16342	+	0.892670i	0.156230	+	0.0440858i
$411$	10.6650	+	32.7064i	0.526066	+	1.61329i
$412$	−15.5483			−0.766008
$413$		0			0
$414$	1.00756	−	0.735280i	0.0495189	−	0.0361370i
$415$	3.20311	−	11.3511i	0.157235	−	0.557204i
$416$	−24.0348			−1.17840
$417$	0.376712	−	0.122839i	0.0184477	−	0.00601547i
$418$	−11.6991			−0.572219
$419$	39.4615			1.92782			0.963911	−	0.266226i	$-0.0857766\pi$
$419$	39.4615			1.92782			0.963911	+	0.266226i	$0.0857766\pi$
$420$		0			0
$421$	−30.9363			−1.50774			−0.753870	−	0.657023i	$-0.771815\pi$
$421$	−30.9363			−1.50774			−0.753870	+	0.657023i	$0.771815\pi$
$422$	−11.8844			−0.578521
$423$	13.7964	+	18.9054i	0.670806	+	0.919212i
$424$	16.6436			0.808283
$425$	5.68901	−	9.27761i	0.275957	−	0.450030i
$426$	−8.64066	+	2.81757i	−0.418641	+	0.136512i
$427$		0			0
$428$	−29.7509			−1.43807
$429$	28.1242	−	9.17084i	1.35785	−	0.442772i
$430$	−2.56252	+	9.08098i	−0.123575	+	0.437924i
$431$		−	30.7427i		−	1.48082i	−0.672154	−	0.740412i	$-0.734631\pi$
$431$		−	30.7427i		−	1.48082i	0.672154	−	0.740412i	$-0.265369\pi$
$432$	−7.07100	−	5.10337i	−0.340204	−	0.245536i
$433$	2.95856			0.142179			0.0710896	−	0.997470i	$-0.477352\pi$
$433$	2.95856			0.142179			0.0710896	+	0.997470i	$0.477352\pi$
$434$		0			0
$435$	−4.52292	+	0.181817i	−0.216857	+	0.00871746i
$436$	−1.43532			−0.0687391
$437$		−	2.88616i		−	0.138064i
$438$	−1.81320	−	5.56055i	−0.0866380	−	0.265693i
$439$		−	17.4097i		−	0.830920i	−0.909612	−	0.415460i	$-0.863621\pi$
$439$		−	17.4097i		−	0.830920i	0.909612	−	0.415460i	$-0.136379\pi$
$440$	5.68901	−	20.1606i	0.271213	−	0.961117i
$441$		0			0
$442$			5.91341i			0.281272i
$443$	31.7940			1.51058			0.755288	−	0.655392i	$-0.227497\pi$
$443$	31.7940			1.51058			0.755288	+	0.655392i	$0.227497\pi$
$444$	11.1226	−	3.62691i	0.527858	−	0.172125i
$445$	1.92554	+	0.543360i	0.0912796	+	0.0257577i
$446$	−0.404563			−0.0191566
$447$	−16.3989	+	5.34741i	−0.775643	+	0.252924i
$448$		0			0
$449$		−	2.99461i		−	0.141324i	−0.997500	−	0.0706621i	$-0.977489\pi$
$449$		−	2.99461i		−	0.141324i	0.997500	−	0.0706621i	$-0.0225112\pi$
$450$	−9.64088	+	0.776363i	−0.454475	+	0.0365981i
$451$			9.24082i			0.435133i
$452$	−13.9880			−0.657940
$453$	−2.72481	−	8.35618i	−0.128023	−	0.392607i
$454$			3.50091i			0.164306i
$455$		0			0
$456$	17.0347	−	5.55471i	0.797721	−	0.260123i
$457$			8.80505i			0.411883i	0.978564	+	0.205941i	$0.0660256\pi$
$457$			8.80505i			0.411883i	−0.978564	+	0.205941i	$0.933974\pi$
$458$			9.26842i			0.433085i
$459$	−6.61889	+	9.17084i	−0.308943	+	0.428058i
$460$	2.19833	+	0.620337i	0.102498	+	0.0289234i
$461$	−31.9710			−1.48904			−0.744519	−	0.667602i	$-0.767321\pi$
$461$	−31.9710			−1.48904			−0.744519	+	0.667602i	$0.767321\pi$
$462$		0			0
$463$		−	6.94495i		−	0.322759i	−0.986892	−	0.161380i	$-0.948406\pi$
$463$		−	6.94495i		−	0.322759i	0.986892	−	0.161380i	$-0.0515943\pi$
$464$			1.96143i			0.0910571i
$465$	1.51532	−	0.0609147i	0.0702715	−	0.00282485i
$466$	−5.43603			−0.251819
$467$			24.4731i			1.13248i	0.824240	+	0.566241i	$0.191603\pi$
$467$			24.4731i			1.13248i	−0.824240	+	0.566241i	$0.808397\pi$
$468$	−16.1757	+	11.8044i	−0.747721	+	0.545658i
$469$		0			0
$470$	3.05480	−	10.8255i	0.140908	−	0.499344i
$471$	−9.04979	−	27.7530i	−0.416992	−	1.27879i
$472$	−26.1734			−1.20473
$473$	−26.5269			−1.21971
$474$	1.29932	+	3.98463i	0.0596798	+	0.183020i
$475$	−11.6991	+	19.0788i	−0.536789	+	0.875393i
$476$		0			0
$477$	17.4516	−	12.7355i	0.799054	−	0.583119i
$478$			1.75292i			0.0801766i
$479$	−24.2902			−1.10985			−0.554923	−	0.831901i	$-0.687252\pi$
$479$	−24.2902			−1.10985			−0.554923	+	0.831901i	$0.687252\pi$
$480$	0.887401	+	22.0752i	0.0405041	+	1.00759i
$481$		−	17.9641i		−	0.819091i
$482$		−	0.986217i		−	0.0449209i
$483$		0			0
$484$	8.60377			0.391080
$485$	8.39223	+	2.36816i	0.381071	+	0.107533i
$486$	10.0514	−	0.0528637i	0.455940	−	0.00239795i
$487$		−	9.75645i		−	0.442107i	−0.975262	−	0.221054i	$-0.929050\pi$
$487$		−	9.75645i		−	0.442107i	0.975262	−	0.221054i	$-0.0709496\pi$
$488$			16.1576i			0.731419i
$489$	7.91563	−	2.58115i	0.357957	−	0.116724i
$490$		0			0
$491$			23.6689i			1.06816i	0.845434	+	0.534080i	$0.179342\pi$
$491$			23.6689i			1.06816i	−0.845434	+	0.534080i	$0.820658\pi$
$492$	−1.93929	−	5.94724i	−0.0874301	−	0.268122i
$493$	2.54390			0.114572
$494$		−	12.1605i		−	0.547127i
$495$	−9.46149	−	25.4926i	−0.425262	−	1.14581i
$496$		−	0.657143i		−	0.0295066i
$497$		0			0
$498$	5.60064	−	1.82627i	0.250971	−	0.0818373i
$499$	−11.4707			−0.513499			−0.256749	−	0.966478i	$-0.582651\pi$
$499$	−11.4707			−0.513499			−0.256749	+	0.966478i	$0.582651\pi$
$500$	−12.0174	−	13.0117i	−0.537435	−	0.581899i
$501$	7.32934	−	2.38997i	0.327451	−	0.106776i
$502$	5.68099			0.253555
$503$		−	16.8580i		−	0.751659i	−0.926689	−	0.375830i	$-0.877358\pi$
$503$		−	16.8580i		−	0.751659i	0.926689	−	0.375830i	$-0.122642\pi$
$504$		0			0
$505$	14.1685	+	3.99812i	0.630488	+	0.177914i
$506$		−	1.68534i		−	0.0749227i
$507$	2.55202	+	7.82630i	0.113339	+	0.347578i
$508$			25.0703i			1.11231i
$509$	−2.95165			−0.130829			−0.0654147	−	0.997858i	$-0.520837\pi$
$509$	−2.95165			−0.130829			−0.0654147	+	0.997858i	$0.520837\pi$
$510$	5.43127	−	0.218332i	0.240500	−	0.00966790i
$511$		0			0
$512$	17.3304			0.765902
$513$	13.6113	−	18.8592i	0.600953	−	0.832653i
$514$		−	12.9628i		−	0.571767i
$515$	21.1209	+	5.96000i	0.930699	+	0.262629i
$516$	17.0723	−	5.56698i	0.751565	−	0.245072i
$517$	31.6230			1.39078
$518$		0			0
$519$	−18.8618	+	6.15051i	−0.827941	+	0.269977i
$520$	20.9558	+	5.91341i	0.918972	+	0.259320i
$521$	−15.8313			−0.693580			−0.346790	−	0.937943i	$-0.612728\pi$
$521$	−15.8313			−0.693580			−0.346790	+	0.937943i	$0.612728\pi$
$522$	−1.33275	−	1.82627i	−0.0583327	−	0.0799339i
$523$	21.9600			0.960243			0.480122	−	0.877202i	$-0.340593\pi$
$523$	21.9600			0.960243			0.480122	+	0.877202i	$0.340593\pi$
$524$	−26.2289			−1.14581
$525$		0			0
$526$	−5.64798			−0.246263
$527$	−0.852291			−0.0371264
$528$	−11.2021	+	3.65280i	−0.487507	+	0.158968i
$529$	−22.5842			−0.981923
$530$	−9.99306	−	2.81989i	−0.434071	−	0.122488i
$531$	−27.4441	+	20.0277i	−1.19097	+	0.869126i
$532$		0			0
$533$	−9.60532			−0.416053
$534$	0.309800	+	0.950064i	0.0134063	+	0.0411133i
$535$	40.4140	+	11.4042i	1.74725	+	0.493047i
$536$		−	20.1932i		−	0.872215i
$537$	−17.1991	+	5.60835i	−0.742198	+	0.242018i
$538$	−11.1221			−0.479508
$539$		0			0
$540$	11.4392	+	14.4210i	0.492263	+	0.620580i
$541$	4.69334			0.201783			0.100891	−	0.994897i	$-0.467831\pi$
$541$	4.69334			0.201783			0.100891	+	0.994897i	$0.467831\pi$
$542$		−	14.6020i		−	0.627211i
$543$	19.6973	−	6.42294i	0.845290	−	0.275635i
$544$		−	12.4161i		−	0.532337i
$545$	1.94975	+	0.550189i	0.0835180	+	0.0235675i
$546$		0			0
$547$		−	14.9485i		−	0.639151i	−0.947561	−	0.319575i	$-0.896460\pi$
$547$		−	14.9485i		−	0.639151i	0.947561	−	0.319575i	$-0.103540\pi$
$548$	−31.4653			−1.34413
$549$	12.3636	+	16.9420i	0.527668	+	0.723068i
$550$	−6.83155	+	11.1409i	−0.291298	+	0.475048i
$551$	−5.23136			−0.222863
$552$	0.800202	+	2.45398i	0.0340589	+	0.104448i
$553$		0			0
$554$			8.51867i			0.361924i
$555$	−16.4994	+	0.663261i	−0.700360	+	0.0281538i
$556$			0.362417i			0.0153699i
$557$	1.22900			0.0520745			0.0260373	−	0.999661i	$-0.491711\pi$
$557$	1.22900			0.0520745			0.0260373	+	0.999661i	$0.491711\pi$
$558$	0.446513	+	0.611862i	0.0189024	+	0.0259022i
$559$		−	27.5732i		−	1.16622i
$560$		0			0
$561$	4.73755	+	14.5287i	0.200020	+	0.613401i
$562$		−	21.1950i		−	0.894057i
$563$			4.20758i			0.177329i	0.996062	+	0.0886643i	$0.0282598\pi$
$563$			4.20758i			0.177329i	−0.996062	+	0.0886643i	$0.971740\pi$
$564$	−20.3520	+	6.63645i	−0.856975	+	0.279445i
$565$	19.0014	+	5.36192i	0.799396	+	0.225578i
$566$	10.1953			0.428542
$567$		0			0
$568$		−	18.8072i		−	0.789132i
$569$		−	25.7659i		−	1.08016i	−0.841613	−	0.540081i	$-0.818394\pi$
$569$		−	25.7659i		−	1.08016i	0.841613	−	0.540081i	$-0.181606\pi$
$570$	−11.1690	+	0.448984i	−0.467819	+	0.0188059i
$571$	24.6838			1.03298			0.516492	−	0.856292i	$-0.327237\pi$
$571$	24.6838			1.03298			0.516492	+	0.856292i	$0.327237\pi$
$572$			27.0570i			1.13131i
$573$	23.2972	−	7.59681i	0.973253	−	0.317361i
$574$		0			0
$575$	−2.74845	−	1.68534i	−0.114618	−	0.0702837i
$576$	−0.779778	+	0.569052i	−0.0324908	+	0.0237105i
$577$	5.73384			0.238703			0.119351	−	0.992852i	$-0.461918\pi$
$577$	5.73384			0.238703			0.119351	+	0.992852i	$0.461918\pi$
$578$	7.90690			0.328884
$579$	−10.1953	+	3.32453i	−0.423704	+	0.138163i
$580$	1.12440	−	3.98463i	0.0466883	−	0.165453i
$581$		0			0
$582$	1.35022	+	4.14073i	0.0559684	+	0.171639i
$583$		−	29.1912i		−	1.20898i
$584$	12.1030			0.500827
$585$	26.4981	−	9.83469i	1.09556	−	0.406615i
$586$		−	13.3989i		−	0.553502i
$587$			31.0435i			1.28130i	0.767832	+	0.640652i	$0.221336\pi$
$587$			31.0435i			1.28130i	−0.767832	+	0.640652i	$0.778664\pi$
$588$		0			0
$589$	1.75268			0.0722178
$590$	15.7149	+	4.43452i	0.646973	+	0.182566i
$591$	−7.02088	−	21.5309i	−0.288800	−	0.885665i
$592$			7.15521i			0.294077i
$593$		−	32.5768i		−	1.33777i	−0.743366	−	0.668885i	$-0.766772\pi$
$593$		−	32.5768i		−	1.33777i	0.743366	−	0.668885i	$-0.233228\pi$
$594$	7.94818	−	11.0126i	0.326118	−	0.451854i
$595$		0			0
$596$		−	15.7766i		−	0.646236i
$597$	−27.9154	+	9.10273i	−1.14250	+	0.372550i
$598$	1.75182			0.0716373
$599$		−	36.7833i		−	1.50293i	−0.659775	−	0.751463i	$-0.729348\pi$
$599$		−	36.7833i		−	1.50293i	0.659775	−	0.751463i	$-0.270652\pi$
$600$	4.65755	−	19.4655i	0.190144	−	0.794676i
$601$		−	42.5075i		−	1.73392i	−0.498380	−	0.866959i	$-0.666071\pi$
$601$		−	42.5075i		−	1.73392i	0.498380	−	0.866959i	$-0.333929\pi$
$602$		0			0
$603$	−15.4517	−	21.1736i	−0.629242	−	0.862257i
$604$	8.03908			0.327106
$605$	−11.6874	−	3.29802i	−0.475162	−	0.134084i
$606$	2.27955	+	6.99072i	0.0926006	+	0.283978i
$607$	16.9521			0.688066			0.344033	−	0.938958i	$-0.388207\pi$
$607$	16.9521			0.688066			0.344033	+	0.938958i	$0.388207\pi$
$608$			25.5329i			1.03550i
$609$		0			0
$610$	2.73755	−	9.70127i	0.110840	−	0.392793i
$611$			32.8703i			1.32979i
$612$	−6.09802	−	8.35618i	−0.246498	−	0.337778i
$613$		−	34.6841i		−	1.40088i	−0.713712	−	0.700439i	$-0.752987\pi$
$613$		−	34.6841i		−	1.40088i	0.713712	−	0.700439i	$-0.247013\pi$
$614$	−8.37328			−0.337918
$615$	0.354643	+	8.82216i	0.0143006	+	0.355744i
$616$		0			0
$617$	45.7116			1.84028			0.920140	−	0.391590i	$-0.128075\pi$
$617$	45.7116			1.84028			0.920140	+	0.391590i	$0.128075\pi$
$618$	3.39813	+	10.4211i	0.136693	+	0.419197i
$619$		−	39.5318i		−	1.58892i	−0.607318	−	0.794459i	$-0.707754\pi$
$619$		−	39.5318i		−	1.58892i	0.607318	−	0.794459i	$-0.292246\pi$
$620$	−0.376712	+	1.33498i	−0.0151291	+	0.0536142i
$621$	2.71682	+	1.96082i	0.109022	+	0.0786849i
$622$	−0.295096			−0.0118323
$623$		0			0
$624$	−3.79689	−	11.6439i	−0.151997	−	0.466130i
$625$	11.3369	+	22.2817i	0.453476	+	0.891268i
$626$	−17.8882			−0.714954
$627$	−9.74245	−	29.8772i	−0.389076	−	1.19318i
$628$	26.6999			1.06544
$629$	9.28004			0.370020
$630$		0			0
$631$	−21.1685			−0.842703			−0.421351	−	0.906897i	$-0.638444\pi$
$631$	−21.1685			−0.842703			−0.421351	+	0.906897i	$0.638444\pi$
$632$	−8.67292			−0.344990
$633$	−9.89676	−	30.3504i	−0.393361	−	1.20632i
$634$	−2.91671			−0.115837
$635$	9.61001	−	34.0557i	0.381362	−	1.35146i
$636$	6.12612	+	18.7870i	0.242916	+	0.744952i
$637$		0			0
$638$	−3.05480			−0.120941
$639$	−14.3911	−	19.7203i	−0.569303	−	0.780122i
$640$	−24.1055	−	6.80220i	−0.952853	−	0.268881i
$641$			35.3434i			1.39598i	0.716107	+	0.697991i	$0.245922\pi$
$641$			35.3434i			1.39598i	−0.716107	+	0.697991i	$0.754078\pi$
$642$	6.50218	+	19.9403i	0.256621	+	0.786979i
$643$	26.0538			1.02746			0.513731	−	0.857951i	$-0.328263\pi$
$643$	26.0538			1.02746			0.513731	+	0.857951i	$0.328263\pi$
$644$		0			0
$645$	−25.3251	+	1.01805i	−0.997174	+	0.0400855i
$646$	6.28199			0.247161
$647$			40.8426i			1.60569i	0.596190	+	0.802844i	$0.296681\pi$
$647$			40.8426i			1.60569i	−0.596190	+	0.802844i	$0.703319\pi$
$648$	−6.34432	+	19.8090i	−0.249228	+	0.778171i
$649$			45.9057i			1.80195i
$650$	−11.5803	−	7.10102i	−0.454217	−	0.278525i
$651$		0			0
$652$			7.61525i			0.298236i
$653$	24.0083			0.939517			0.469758	−	0.882795i	$-0.344341\pi$
$653$	24.0083			0.939517			0.469758	+	0.882795i	$0.344341\pi$
$654$	0.313694	+	0.962005i	0.0122664	+	0.0376174i
$655$	35.6296	+	10.0541i	1.39216	+	0.392848i
$656$	3.82586			0.149375
$657$	12.6906	−	9.26115i	0.495109	−	0.361312i
$658$		0			0
$659$		−	38.7398i		−	1.50909i	−0.656248	−	0.754545i	$-0.727858\pi$
$659$		−	38.7398i		−	1.50909i	0.656248	−	0.754545i	$-0.272142\pi$
$660$	24.8509	−	0.998985i	0.967321	−	0.0388854i
$661$			50.9022i			1.97987i	0.141537	+	0.989933i	$0.454796\pi$
$661$			50.9022i			1.97987i	−0.141537	+	0.989933i	$0.545204\pi$
$662$	−14.7638			−0.573810
$663$	−15.1017	+	4.92442i	−0.586503	+	0.191249i
$664$			12.1903i			0.473076i
$665$		0			0
$666$	−4.86179	−	6.66217i	−0.188391	−	0.258154i
$667$		−	0.753620i		−	0.0291803i
$668$			7.05121i			0.272819i
$669$	−0.336902	−	1.03318i	−0.0130254	−	0.0399450i
$670$	−3.42131	+	12.1244i	−0.132177	+	0.468405i
$671$	28.3389			1.09401
$672$		0			0
$673$		−	3.33192i		−	0.128436i	−0.997936	−	0.0642181i	$-0.979545\pi$
$673$		−	3.33192i		−	0.128436i	0.997936	−	0.0642181i	$-0.0204553\pi$
$674$			20.1577i			0.776444i
$675$	−10.0112	−	23.9745i	−0.385331	−	0.922779i
$676$	−7.52931			−0.289589
$677$			32.3722i			1.24417i	0.782951	+	0.622083i	$0.213713\pi$
$677$			32.3722i			1.24417i	−0.782951	+	0.622083i	$0.786287\pi$
$678$	3.05713	+	9.37531i	0.117408	+	0.360057i
$679$		0			0
$680$	−3.05480	+	10.8255i	−0.117146	+	0.415140i
$681$	−8.94067	+	2.91540i	−0.342607	+	0.111718i
$682$	1.02346			0.0391903
$683$	21.7737			0.833146			0.416573	−	0.909102i	$-0.363231\pi$
$683$	21.7737			0.833146			0.416573	+	0.909102i	$0.363231\pi$
$684$	12.5401	+	17.1839i	0.479485	+	0.657043i
$685$	42.7427	+	12.0614i	1.63312	+	0.460841i
$686$		0			0
$687$	−23.6698	+	7.71833i	−0.903060	+	0.294473i
$688$			10.9826i			0.418708i
$689$	30.3427			1.15596
$690$	−0.0646799	−	1.60899i	−0.00246232	−	0.0612531i
$691$		−	5.95310i		−	0.226467i	−0.993568	−	0.113233i	$-0.963879\pi$
$691$		−	5.95310i		−	0.226467i	0.993568	−	0.113233i	$-0.0361208\pi$
$692$		−	18.1460i		−	0.689809i
$693$		0			0
$694$	1.79689			0.0682088
$695$	0.138923	−	0.492310i	0.00526963	−	0.0186744i
$696$	4.44801	−	1.45042i	0.168601	−	0.0549781i
$697$		−	4.96200i		−	0.187949i
$698$			10.6803i			0.404255i
$699$	−4.52688	−	13.8826i	−0.171222	−	0.525088i
$700$		0			0
$701$		−	19.3393i		−	0.730434i	−0.930922	−	0.365217i	$-0.880995\pi$
$701$		−	19.3393i		−	0.730434i	0.930922	−	0.365217i	$-0.119005\pi$
$702$	11.4470	+	8.26169i	0.432040	+	0.311817i
$703$	−19.0838			−0.719758
$704$			1.30433i			0.0491589i
$705$	30.1903	−	1.21362i	1.13703	−	0.0457077i
$706$			2.11301i			0.0795242i
$707$		0			0
$708$	−9.63383	−	29.5441i	−0.362061	−	1.11034i
$709$	−33.8025			−1.26948			−0.634739	−	0.772727i	$-0.718892\pi$
$709$	−33.8025			−1.26948			−0.634739	+	0.772727i	$0.718892\pi$
$710$	−3.18647	+	11.2921i	−0.119586	+	0.423787i
$711$	−9.09400	+	6.63645i	−0.341051	+	0.248886i
$712$	−2.06790			−0.0774979
$713$			0.252487i			0.00945573i
$714$		0			0
$715$	10.3716	−	36.7545i	0.387875	−	1.37454i
$716$		−	16.5465i		−	0.618371i
$717$	−4.47663	+	1.45975i	−0.167183	+	0.0545155i
$718$			10.9660i			0.409248i
$719$	27.4236			1.02273			0.511363	−	0.859365i	$-0.329141\pi$
$719$	27.4236			1.02273			0.511363	+	0.859365i	$0.329141\pi$
$720$	−10.5544	+	3.91722i	−0.393338	+	0.145986i
$721$		0			0
$722$	−0.667157			−0.0248290
$723$	2.51861	−	0.821277i	0.0936683	−	0.0305436i
$724$			18.9498i			0.704263i
$725$	−3.05480	+	4.98176i	−0.113453	+	0.185018i
$726$	−1.88039	−	5.76659i	−0.0697877	−	0.214018i
$727$	6.14612			0.227947			0.113973	−	0.993484i	$-0.463642\pi$
$727$	6.14612			0.227947			0.113973	+	0.993484i	$0.463642\pi$
$728$		0			0
$729$	8.50535	+	25.6254i	0.315013	+	0.949087i
$730$	−7.26686	−	2.05060i	−0.268959	−	0.0758961i
$731$	14.2440			0.526835
$732$	−18.2384	+	5.94724i	−0.674111	+	0.219816i
$733$	16.8350			0.621813			0.310907	−	0.950440i	$-0.399367\pi$
$733$	16.8350			0.621813			0.310907	+	0.950440i	$0.399367\pi$
$734$	11.0370			0.407384
$735$		0			0
$736$	−3.67822			−0.135581
$737$	−35.4171			−1.30460
$738$	−3.56224	+	2.59958i	−0.131128	+	0.0956920i
$739$	−38.6838			−1.42301			−0.711503	−	0.702683i	$-0.751985\pi$
$739$	−38.6838			−1.42301			−0.711503	+	0.702683i	$0.751985\pi$
$740$	4.10177	−	14.5358i	0.150784	−	0.534345i
$741$	31.0557	−	10.1267i	1.14086	−	0.372015i
$742$		0			0
$743$	39.3563			1.44384			0.721920	−	0.691976i	$-0.243260\pi$
$743$	39.3563			1.44384			0.721920	+	0.691976i	$0.243260\pi$
$744$	−1.49023	+	0.485939i	−0.0546345	+	0.0178154i
$745$	−6.04755	+	21.4311i	−0.221565	+	0.785176i
$746$			18.6435i			0.682586i
$747$	9.32793	+	12.7822i	0.341291	+	0.467675i
$748$	−13.9773			−0.511062
$749$		0			0
$750$	−6.09448	+	10.8983i	−0.222539	+	0.397949i
$751$	32.2831			1.17803			0.589014	−	0.808123i	$-0.299516\pi$
$751$	32.2831			1.17803			0.589014	+	0.808123i	$0.299516\pi$
$752$		−	13.0925i		−	0.477433i
$753$	4.73088	+	14.5082i	0.172403	+	0.528708i
$754$		−	3.17530i		−	0.115637i
$755$	−10.9204	−	3.08156i	−0.397433	−	0.112150i
$756$		0			0
$757$		−	40.0667i		−	1.45625i	−0.685446	−	0.728124i	$-0.740393\pi$
$757$		−	40.0667i		−	1.45625i	0.685446	−	0.728124i	$-0.259607\pi$
$758$	−0.360805			−0.0131050
$759$	4.30406	−	1.40348i	0.156227	−	0.0509431i
$760$	6.28199	−	22.2619i	0.227872	−	0.807526i
$761$	−13.1795			−0.477758			−0.238879	−	0.971049i	$-0.576780\pi$
$761$	−13.1795			−0.477758			−0.238879	+	0.971049i	$0.576780\pi$
$762$	16.8031	−	5.47920i	0.608712	−	0.198491i
$763$		0			0
$764$			22.4131i			0.810877i
$765$	5.08049	+	13.6886i	0.183686	+	0.494913i
$766$		−	2.44923i		−	0.0884944i
$767$	−47.7164			−1.72294
$768$	−4.22389	−	12.9534i	−0.152416	−	0.467416i
$769$			12.7709i			0.460530i	0.973128	+	0.230265i	$0.0739593\pi$
$769$			12.7709i			0.460530i	−0.973128	+	0.230265i	$0.926041\pi$
$770$		0			0
$771$	33.1047	−	10.7949i	1.19224	−	0.388768i
$772$		−	9.80846i		−	0.353014i
$773$		−	18.1886i		−	0.654197i	−0.944990	−	0.327099i	$-0.893929\pi$
$773$		−	18.1886i		−	0.654197i	0.944990	−	0.327099i	$-0.106071\pi$
$774$	−7.46242	−	10.2258i	−0.268231	−	0.367560i
$775$	1.02346	−	1.66905i	0.0367637	−	0.0599541i
$776$	−9.01267			−0.323536
$777$		0			0
$778$			5.87388i			0.210589i
$779$			10.2040i			0.365597i
$780$	1.03839	+	25.8312i	0.0371803	+	0.924904i
$781$	−32.9860			−1.18033
$782$			0.904972i			0.0323617i
$783$	3.55412	−	4.92442i	0.127014	−	0.175985i
$784$		0			0
$785$	−36.2693	−	10.2347i	−1.29451	−	0.365291i
$786$	5.73243	+	17.5797i	0.204469	+	0.627045i
$787$	−1.23859			−0.0441511			−0.0220756	−	0.999756i	$-0.507027\pi$
$787$	−1.23859			−0.0441511			−0.0220756	+	0.999756i	$0.507027\pi$
$788$	20.7139			0.737902
$789$	−4.70338	−	14.4239i	−0.167445	−	0.513504i
$790$	5.20736	+	1.46944i	0.185270	+	0.0522803i
$791$		0			0
$792$	16.5672	+	22.7022i	0.588690	+	0.806689i
$793$			29.4567i			1.04604i
$794$	−15.6290			−0.554652
$795$	−1.12030	−	27.8687i	−0.0397328	−	0.988401i
$796$		−	26.8561i		−	0.951888i
$797$			51.4416i			1.82216i	0.412235	+	0.911078i	$0.364748\pi$
$797$			51.4416i			1.82216i	−0.412235	+	0.911078i	$0.635252\pi$
$798$		0			0
$799$	−16.9805			−0.600725
$800$	24.3146	+	14.9097i	0.859652	+	0.527137i
$801$	−2.16830	+	1.58234i	−0.0766131	+	0.0559093i
$802$			19.4702i			0.687517i
$803$		−	21.2276i		−	0.749106i
$804$	22.7938	−	7.43268i	0.803876	−	0.262130i
$805$		0			0
$806$			1.06383i			0.0374718i
$807$	−9.26199	−	28.4038i	−0.326038	−	0.999861i
$808$	−15.2159			−0.535295
$809$		−	2.82345i		−	0.0992672i	−0.998767	−	0.0496336i	$-0.984195\pi$
$809$		−	2.82345i		−	0.0992672i	0.998767	−	0.0496336i	$-0.0158054\pi$
$810$	7.16544	−	10.8187i	0.251768	−	0.380132i
$811$		−	0.162805i		−	0.00571687i	−0.999996	−	0.00285843i	$-0.999090\pi$
$811$		−	0.162805i		−	0.00571687i	0.999996	−	0.00285843i	$-0.000909869\pi$
$812$		0			0
$813$	37.2909	−	12.1599i	1.30785	−	0.426467i
$814$	−11.1438			−0.390589
$815$	2.91910	−	10.3446i	0.102252	−	0.362357i
$816$	6.01512	−	1.96143i	0.210571	−	0.0686638i
$817$	−29.2919			−1.02479
$818$		−	15.9051i		−	0.556108i
$819$		0			0
$820$	−7.77222	−	2.19320i	−0.271418	−	0.0765900i
$821$		−	50.0869i		−	1.74804i	−0.485886	−	0.874022i	$-0.661503\pi$
$821$		−	50.0869i		−	1.74804i	0.485886	−	0.874022i	$-0.338497\pi$
$822$	6.87685	+	21.0893i	0.239858	+	0.735573i
$823$		−	38.2263i		−	1.33249i	−0.745735	−	0.666243i	$-0.767901\pi$
$823$		−	38.2263i		−	1.33249i	0.745735	−	0.666243i	$-0.232099\pi$
$824$	−22.6824			−0.790179
$825$	−34.1407	−	8.16890i	−1.18863	−	0.284405i
$826$		0			0
$827$	−7.13112			−0.247973			−0.123987	−	0.992284i	$-0.539568\pi$
$827$	−7.13112			−0.247973			−0.123987	+	0.992284i	$0.539568\pi$
$828$	−2.47548	+	1.80651i	−0.0860289	+	0.0627806i
$829$			1.01191i			0.0351450i	0.999846	+	0.0175725i	$0.00559379\pi$
$829$			1.01191i			0.0351450i	−0.999846	+	0.0175725i	$0.994406\pi$
$830$	2.06539	−	7.31927i	0.0716906	−	0.254055i
$831$	−21.7551	+	7.09397i	−0.754676	+	0.246087i
$832$	−1.35578			−0.0470032
$833$		0			0
$834$	0.242906	−	0.0792075i	0.00841115	−	0.00274273i
$835$	2.70289	−	9.57843i	0.0935374	−	0.331475i
$836$	28.7434			0.994112
$837$	−1.19074	+	1.64984i	−0.0411582	+	0.0570269i
$838$	25.4450			0.878984
$839$	−29.5215			−1.01920			−0.509598	−	0.860412i	$-0.670206\pi$
$839$	−29.5215			−1.01920			−0.509598	+	0.860412i	$0.670206\pi$
$840$		0			0
$841$	27.6340			0.952897
$842$	−19.9479			−0.687449
$843$	54.1281	−	17.6502i	1.86427	−	0.607907i
$844$	29.1987			1.00506
$845$	10.2279	+	2.88616i	0.351850	+	0.0992868i
$846$	8.89603	+	12.1903i	0.305852	+	0.419112i
$847$		0			0
$848$	−12.0857			−0.415024
$849$	8.49023	+	26.0370i	0.291384	+	0.893588i
$850$	3.66831	−	5.98226i	0.125822	−	0.205190i
$851$		−	2.74917i		−	0.0942404i
$852$	21.2293	−	6.92250i	0.727302	−	0.237161i
$853$	22.0904			0.756362			0.378181	−	0.925732i	$-0.376550\pi$
$853$	22.0904			0.756362			0.378181	+	0.925732i	$0.376550\pi$
$854$		0			0
$855$	−10.4477	−	28.1497i	−0.357303	−	0.962700i
$856$	−43.4018			−1.48344
$857$		−	14.3312i		−	0.489544i	−0.969581	−	0.244772i	$-0.921287\pi$
$857$		−	14.3312i		−	0.489544i	0.969581	−	0.244772i	$-0.0787130\pi$
$858$	18.1347	−	5.91341i	0.619108	−	0.201880i
$859$		−	27.4705i		−	0.937280i	−0.883389	−	0.468640i	$-0.844744\pi$
$859$		−	27.4705i		−	0.937280i	0.883389	−	0.468640i	$-0.155256\pi$
$860$	6.29585	−	22.3111i	0.214687	−	0.760802i
$861$		0			0
$862$		−	19.8231i		−	0.675176i
$863$	16.2226			0.552224			0.276112	−	0.961125i	$-0.410954\pi$
$863$	16.2226			0.552224			0.276112	+	0.961125i	$0.410954\pi$
$864$	−24.0348	−	17.3467i	−0.817681	−	0.590147i
$865$	−6.95579	+	24.6498i	−0.236504	+	0.838117i
$866$	1.90769			0.0648261
$867$	6.58451	+	20.1927i	0.223622	+	0.685782i
$868$		0			0
$869$			15.2115i			0.516014i
$870$	−2.91640	+	0.117237i	−0.0988753	+	0.00397470i
$871$		−	36.8141i		−	1.24740i
$872$	−2.09389			−0.0709082
$873$	−9.45024	+	6.89643i	−0.319842	+	0.233409i
$874$		−	1.86101i		−	0.0629496i
$875$		0			0
$876$	4.45486	+	13.6617i	0.150516	+	0.461587i
$877$		−	44.4926i		−	1.50241i	−0.660070	−	0.751204i	$-0.729473\pi$
$877$		−	44.4926i		−	1.50241i	0.660070	−	0.751204i	$-0.270527\pi$
$878$		−	11.2259i		−	0.378855i
$879$	34.2182	−	11.1580i	1.15415	−	0.376350i
$880$	−4.13106	+	14.6395i	−0.139258	+	0.493499i
$881$	−0.841670			−0.0283566			−0.0141783	−	0.999899i	$-0.504513\pi$
$881$	−0.841670			−0.0283566			−0.0141783	+	0.999899i	$0.504513\pi$
$882$		0			0
$883$			51.7706i			1.74222i	0.491088	+	0.871110i	$0.336600\pi$
$883$			51.7706i			1.74222i	−0.491088	+	0.871110i	$0.663400\pi$
$884$		−	14.5287i		−	0.488652i
$885$	1.76176	+	43.8259i	0.0592209	+	1.47319i
$886$	20.5009			0.688742
$887$			55.9733i			1.87940i	0.342000	+	0.939700i	$0.388896\pi$
$887$			55.9733i			1.87940i	−0.342000	+	0.939700i	$0.611104\pi$
$888$	16.2262	−	5.29107i	0.544514	−	0.177557i
$889$		0			0
$890$	1.24160	+	0.350362i	0.0416186	+	0.0117441i
$891$	34.7431	+	11.1273i	1.16394	+	0.372780i
$892$	0.993971			0.0332806
$893$	34.9191			1.16852
$894$	−10.5741	+	3.44804i	−0.353652	+	0.115320i
$895$	−6.34264	+	22.4769i	−0.212011	+	0.751320i
$896$		0			0
$897$	1.45884	+	4.47383i	0.0487092	+	0.149377i
$898$		−	1.93094i		−	0.0644363i
$899$	0.457651			0.0152635
$900$	23.6867	−	1.90745i	0.789557	−	0.0635817i
$901$			15.6747i			0.522200i
$902$			5.95854i			0.198398i
$903$		0			0
$904$	−20.4062			−0.678701
$905$	7.26389	−	25.7416i	0.241460	−	0.855679i
$906$	−1.75697	−	5.38811i	−0.0583715	−	0.179008i
$907$		−	36.2663i		−	1.20420i	−0.798419	−	0.602102i	$-0.794330\pi$
$907$		−	36.2663i		−	1.20420i	0.798419	−	0.602102i	$-0.205670\pi$
$908$		−	8.60139i		−	0.285447i
$909$	−15.9547	+	11.6431i	−0.529183	+	0.386178i
$910$		0			0
$911$		−	5.35784i		−	0.177513i	−0.996053	−	0.0887565i	$-0.971711\pi$
$911$		−	5.35784i		−	0.177513i	0.996053	−	0.0887565i	$-0.0282893\pi$
$912$	−12.3697	+	4.03354i	−0.409601	+	0.133564i
$913$	21.3807			0.707597
$914$			5.67755i			0.187797i
$915$	27.0550	−	1.08758i	0.894409	−	0.0359544i
$916$		−	22.7716i		−	0.752396i
$917$		0			0
$918$	−4.26790	+	5.91341i	−0.140862	+	0.195172i
$919$	20.1142			0.663508			0.331754	−	0.943366i	$-0.392360\pi$
$919$	20.1142			0.663508			0.331754	+	0.943366i	$0.392360\pi$
$920$	3.20702	+	0.904972i	0.105732	+	0.0298360i
$921$	−6.97290	−	21.3838i	−0.229765	−	0.704621i
$922$	−20.6151			−0.678922
$923$		−	34.2872i		−	1.12858i
$924$		0			0
$925$	−11.1438	+	18.1732i	−0.366405	+	0.597532i
$926$		−	4.47814i		−	0.147161i
$927$	−23.7836	+	17.3564i	−0.781158	+	0.570059i
$928$			6.66703i			0.218856i
$929$	−6.79805			−0.223037			−0.111518	−	0.993762i	$-0.535571\pi$
$929$	−6.79805			−0.223037			−0.111518	+	0.993762i	$0.535571\pi$
$930$	0.977090	−	0.0392781i	0.0320401	−	0.00128798i
$931$		0			0
$932$	13.3558			0.437483
$933$	−0.245743	−	0.753620i	−0.00804525	−	0.0246724i
$934$			15.7804i			0.516351i
$935$	18.9870	+	5.35784i	0.620940	+	0.175220i
$936$	−23.5977	+	17.2207i	−0.771315	+	0.562876i
$937$	−44.1327			−1.44175			−0.720877	−	0.693063i	$-0.756261\pi$
$937$	−44.1327			−1.44175			−0.720877	+	0.693063i	$0.756261\pi$
$938$		0			0
$939$	−14.8965	−	45.6830i	−0.486128	−	1.49081i
$940$	−7.50535	+	26.5973i	−0.244798	+	0.867508i
$941$	9.06576			0.295535			0.147768	−	0.989022i	$-0.452791\pi$
$941$	9.06576			0.295535			0.147768	+	0.989022i	$0.452791\pi$
$942$	−5.83535	−	17.8953i	−0.190126	−	0.583061i
$943$	−1.46997			−0.0478689
$944$	19.0057			0.618584
$945$		0			0
$946$	−17.1047			−0.556122
$947$	−35.4874			−1.15319			−0.576593	−	0.817031i	$-0.695618\pi$
$947$	−35.4874			−1.15319			−0.576593	+	0.817031i	$0.695618\pi$
$948$	−3.19231	−	9.78986i	−0.103681	−	0.317960i
$949$	22.0649			0.716257
$950$	−7.54362	+	12.3021i	−0.244747	+	0.399133i
$951$	−2.42891	−	7.44873i	−0.0787627	−	0.241542i
$952$		0			0
$953$	−10.8726			−0.352198			−0.176099	−	0.984373i	$-0.556348\pi$
$953$	−10.8726			−0.352198			−0.176099	+	0.984373i	$0.556348\pi$
$954$	11.2529	−	8.21194i	0.364326	−	0.265871i
$955$	8.59145	−	30.4462i	0.278013	−	0.985215i
$956$		−	4.30675i		−	0.139290i
$957$	−2.54390	−	7.80140i	−0.0822327	−	0.252183i
$958$	−15.6625			−0.506031
$959$		0			0
$960$	0.0500574	+	1.24524i	0.00161560	+	0.0401899i
$961$	30.8467			0.995054
$962$		−	11.5833i		−	0.373462i
$963$	−45.5090	+	33.2107i	−1.46651	+	1.07020i
$964$			2.42304i			0.0780408i
$965$	−3.75981	+	13.3239i	−0.121032	+	0.428912i
$966$		0			0
$967$			21.3855i			0.687711i	0.939023	+	0.343855i	$0.111733\pi$
$967$			21.3855i			0.687711i	−0.939023	+	0.343855i	$0.888267\pi$
$968$	12.5515			0.403421
$969$	5.23136	+	16.0430i	0.168055	+	0.515376i
$970$	5.41136	+	1.52700i	0.173748	+	0.0490291i
$971$	8.86348			0.284443			0.142221	−	0.989835i	$-0.454576\pi$
$971$	8.86348			0.284443			0.142221	+	0.989835i	$0.454576\pi$
$972$	−24.6953	+	0.129881i	−0.792102	+	0.00416593i
$973$		0			0
$974$		−	6.29102i		−	0.201577i
$975$	8.49112	−	35.4873i	0.271933	−	1.13650i
$976$		−	11.7328i		−	0.375557i
$977$	−0.731073			−0.0233891			−0.0116945	−	0.999932i	$-0.503723\pi$
$977$	−0.731073			−0.0233891			−0.0116945	+	0.999932i	$0.503723\pi$
$978$	5.10405	−	1.66434i	0.163209	−	0.0532198i
$979$			3.62691i			0.115916i
$980$		0			0
$981$	−2.19555	+	1.60223i	−0.0700986	+	0.0511553i
$982$			15.2618i			0.487024i
$983$		−	3.73214i		−	0.119037i	−0.998227	−	0.0595184i	$-0.981044\pi$
$983$		−	3.73214i		−	0.119037i	0.998227	−	0.0595184i	$-0.0189565\pi$
$984$	−2.82912	−	8.67606i	−0.0901889	−	0.276583i
$985$	−28.1380	−	7.94011i	−0.896550	−	0.252993i
$986$	1.64032			0.0522385
$987$		0			0
$988$			29.8772i			0.950520i
$989$		−	4.21973i		−	0.134180i
$990$	−6.10082	−	16.4378i	−0.193897	−	0.522426i
$991$	−5.48510			−0.174240			−0.0871200	−	0.996198i	$-0.527766\pi$
$991$	−5.48510			−0.174240			−0.0871200	+	0.996198i	$0.527766\pi$
$992$		−	2.23367i		−	0.0709192i
$993$	−12.2946	−	37.7039i	−0.390158	−	1.19650i
$994$		0			0
$995$	−10.2945	+	36.4815i	−0.326359	+	1.15654i
$996$	−13.7602	+	4.48698i	−0.436010	+	0.142175i
$997$	−5.07219			−0.160638			−0.0803189	−	0.996769i	$-0.525594\pi$
$997$	−5.07219			−0.160638			−0.0803189	+	0.996769i	$0.525594\pi$
$998$	−7.39637			−0.234128
$999$	12.9653	−	17.9641i	0.410202	−	0.568358i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.g.b.734.16		24
3.2	odd	2	inner	735.2.g.b.734.11		24
5.4	even	2	inner	735.2.g.b.734.9		24
7.2	even	3		735.2.p.f.374.5		24
7.3	odd	6		735.2.p.f.509.6		24
7.4	even	3		105.2.p.a.89.5	yes	24
7.5	odd	6		105.2.p.a.59.6	yes	24
7.6	odd	2	inner	735.2.g.b.734.13		24
15.14	odd	2	inner	735.2.g.b.734.14		24
21.2	odd	6		735.2.p.f.374.7		24
21.5	even	6		105.2.p.a.59.8	yes	24
21.11	odd	6		105.2.p.a.89.7	yes	24
21.17	even	6		735.2.p.f.509.8		24
21.20	even	2	inner	735.2.g.b.734.10		24
35.4	even	6		105.2.p.a.89.8	yes	24
35.9	even	6		735.2.p.f.374.8		24
35.12	even	12		525.2.t.j.101.7		24
35.18	odd	12		525.2.t.j.26.8		24
35.19	odd	6		105.2.p.a.59.7	yes	24
35.24	odd	6		735.2.p.f.509.7		24
35.32	odd	12		525.2.t.j.26.5		24
35.33	even	12		525.2.t.j.101.6		24
35.34	odd	2	inner	735.2.g.b.734.12		24
105.32	even	12		525.2.t.j.26.7		24
105.44	odd	6		735.2.p.f.374.6		24
105.47	odd	12		525.2.t.j.101.5		24
105.53	even	12		525.2.t.j.26.6		24
105.59	even	6		735.2.p.f.509.5		24
105.68	odd	12		525.2.t.j.101.8		24
105.74	odd	6		105.2.p.a.89.6	yes	24
105.89	even	6		105.2.p.a.59.5	✓	24
105.104	even	2	inner	735.2.g.b.734.15		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.p.a.59.5	✓	24	105.89	even	6
105.2.p.a.59.6	yes	24	7.5	odd	6
105.2.p.a.59.7	yes	24	35.19	odd	6
105.2.p.a.59.8	yes	24	21.5	even	6
105.2.p.a.89.5	yes	24	7.4	even	3
105.2.p.a.89.6	yes	24	105.74	odd	6
105.2.p.a.89.7	yes	24	21.11	odd	6
105.2.p.a.89.8	yes	24	35.4	even	6
525.2.t.j.26.5		24	35.32	odd	12
525.2.t.j.26.6		24	105.53	even	12
525.2.t.j.26.7		24	105.32	even	12
525.2.t.j.26.8		24	35.18	odd	12
525.2.t.j.101.5		24	105.47	odd	12
525.2.t.j.101.6		24	35.33	even	12
525.2.t.j.101.7		24	35.12	even	12
525.2.t.j.101.8		24	105.68	odd	12
735.2.g.b.734.9		24	5.4	even	2	inner
735.2.g.b.734.10		24	21.20	even	2	inner
735.2.g.b.734.11		24	3.2	odd	2	inner
735.2.g.b.734.12		24	35.34	odd	2	inner
735.2.g.b.734.13		24	7.6	odd	2	inner
735.2.g.b.734.14		24	15.14	odd	2	inner
735.2.g.b.734.15		24	105.104	even	2	inner
735.2.g.b.734.16		24	1.1	even	1	trivial
735.2.p.f.374.5		24	7.2	even	3
735.2.p.f.374.6		24	105.44	odd	6
735.2.p.f.374.7		24	21.2	odd	6
735.2.p.f.374.8		24	35.9	even	6
735.2.p.f.509.5		24	105.59	even	6
735.2.p.f.509.6		24	7.3	odd	6
735.2.p.f.509.7		24	35.24	odd	6
735.2.p.f.509.8		24	21.17	even	6

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:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.644806 q^{2} +(0.536966 + 1.64671i) q^{3} -1.58423 q^{4} +(2.15203 + 0.607270i) q^{5} +(0.346239 + 1.06181i) q^{6} -2.31113 q^{8} +(-2.42334 + 1.76846i) q^{9} +O(q^{10})\)	\(q+0.644806 q^{2} +(0.536966 + 1.64671i) q^{3} -1.58423 q^{4} +(2.15203 + 0.607270i) q^{5} +(0.346239 + 1.06181i) q^{6} -2.31113 q^{8} +(-2.42334 + 1.76846i) q^{9} +(1.38764 + 0.391571i) q^{10} +4.05350i q^{11} +(-0.850674 - 2.60877i) q^{12} -4.21339 q^{13} +(0.155565 + 3.86986i) q^{15} +1.67822 q^{16} -2.17659i q^{17} +(-1.56258 + 1.14031i) q^{18} +4.47601i q^{19} +(-3.40930 - 0.962052i) q^{20} +2.61372i q^{22} -0.644806 q^{23} +(-1.24100 - 3.80577i) q^{24} +(4.26245 + 2.61372i) q^{25} -2.71682 q^{26} +(-4.21339 - 3.04094i) q^{27} +1.16875i q^{29} +(0.100309 + 2.49531i) q^{30} -0.391571i q^{31} +5.70439 q^{32} +(-6.67496 + 2.17659i) q^{33} -1.40348i q^{34} +(3.83911 - 2.80164i) q^{36} +4.26357i q^{37} +2.88616i q^{38} +(-2.26245 - 6.93825i) q^{39} +(-4.97361 - 1.40348i) q^{40} +2.27971 q^{41} +6.54419i q^{43} -6.42166i q^{44} +(-6.28902 + 2.33415i) q^{45} -0.415775 q^{46} -7.80140i q^{47} +(0.901147 + 2.76355i) q^{48} +(2.74845 + 1.68534i) q^{50} +(3.58423 - 1.16875i) q^{51} +6.67496 q^{52} -7.20148 q^{53} +(-2.71682 - 1.96082i) q^{54} +(-2.46157 + 8.72325i) q^{55} +(-7.37071 + 2.40346i) q^{57} +0.753620i q^{58} +11.3249 q^{59} +(-0.246450 - 6.13073i) q^{60} -6.99120i q^{61} -0.252487i q^{62} +0.321779 q^{64} +(-9.06734 - 2.55867i) q^{65} +(-4.30406 + 1.40348i) q^{66} +8.73739i q^{67} +3.44821i q^{68} +(-0.346239 - 1.06181i) q^{69} +8.13766i q^{71} +(5.60064 - 4.08713i) q^{72} -5.23685 q^{73} +2.74917i q^{74} +(-2.01527 + 8.42251i) q^{75} -7.09101i q^{76} +(-1.45884 - 4.47383i) q^{78} +3.75268 q^{79} +(3.61158 + 1.01913i) q^{80} +(2.74511 - 8.57113i) q^{81} +1.46997 q^{82} -5.27461i q^{83} +(1.32178 - 4.68409i) q^{85} +4.21973i q^{86} +(-1.92461 + 0.627581i) q^{87} -9.36817i q^{88} +0.894758 q^{89} +(-4.05520 + 1.50507i) q^{90} +1.02152 q^{92} +(0.644806 - 0.210260i) q^{93} -5.03039i q^{94} +(-2.71815 + 9.63250i) q^{95} +(3.06306 + 9.39349i) q^{96} +3.89968 q^{97} +(-7.16845 - 9.82300i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{4} + 12 q^{9}+O(q^{10}) \) 24 * q + 24 * q^4 + 12 * q^9	\( 24 q + 24 q^{4} + 12 q^{9} - 24 q^{15} + 24 q^{16} + 24 q^{25} - 36 q^{30} + 84 q^{36} + 24 q^{39} - 72 q^{46} + 24 q^{51} - 24 q^{60} + 24 q^{64} - 96 q^{79} + 12 q^{81} + 48 q^{85} - 48 q^{99}+O(q^{100}) \) 24 * q + 24 * q^4 + 12 * q^9 - 24 * q^15 + 24 * q^16 + 24 * q^25 - 36 * q^30 + 84 * q^36 + 24 * q^39 - 72 * q^46 + 24 * q^51 - 24 * q^60 + 24 * q^64 - 96 * q^79 + 12 * q^81 + 48 * q^85 - 48 * q^99

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