LMFDB - Embedded newform 735.2.g.b.734.9

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			734.9
Character	$\chi$	$=$	735.734
Dual form			735.2.g.b.734.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.644806 q^{2} +(-0.536966 - 1.64671i) q^{3} -1.58423 q^{4} +(2.15203 - 0.607270i) q^{5} +(0.346239 + 1.06181i) q^{6} +2.31113 q^{8} +(-2.42334 + 1.76846i) q^{9} +O(q^{10})$	\(q-0.644806 q^{2} +(-0.536966 - 1.64671i) q^{3} -1.58423 q^{4} +(2.15203 - 0.607270i) q^{5} +(0.346239 + 1.06181i) q^{6} +2.31113 q^{8} +(-2.42334 + 1.76846i) q^{9} +(-1.38764 + 0.391571i) q^{10} +4.05350i q^{11} +(0.850674 + 2.60877i) q^{12} +4.21339 q^{13} +(-2.15556 - 3.21769i) q^{15} +1.67822 q^{16} +2.17659i q^{17} +(1.56258 - 1.14031i) q^{18} +4.47601i q^{19} +(-3.40930 + 0.962052i) q^{20} -2.61372i q^{22} +0.644806 q^{23} +(-1.24100 - 3.80577i) q^{24} +(4.26245 - 2.61372i) q^{25} -2.71682 q^{26} +(4.21339 + 3.04094i) q^{27} +1.16875i q^{29} +(1.38992 + 2.07479i) q^{30} -0.391571i q^{31} -5.70439 q^{32} +(6.67496 - 2.17659i) q^{33} -1.40348i q^{34} +(3.83911 - 2.80164i) q^{36} -4.26357i q^{37} -2.88616i q^{38} +(-2.26245 - 6.93825i) q^{39} +(4.97361 - 1.40348i) q^{40} +2.27971 q^{41} -6.54419i q^{43} -6.42166i q^{44} +(-4.14116 + 5.27739i) q^{45} -0.415775 q^{46} +7.80140i q^{47} +(-0.901147 - 2.76355i) q^{48} +(-2.74845 + 1.68534i) q^{50} +(3.58423 - 1.16875i) q^{51} -6.67496 q^{52} +7.20148 q^{53} +(-2.71682 - 1.96082i) q^{54} +(2.46157 + 8.72325i) q^{55} +(7.37071 - 2.40346i) q^{57} -0.753620i q^{58} +11.3249 q^{59} +(3.41490 + 5.09755i) q^{60} -6.99120i q^{61} +0.252487i q^{62} +0.321779 q^{64} +(9.06734 - 2.55867i) q^{65} +(-4.30406 + 1.40348i) q^{66} -8.73739i q^{67} -3.44821i q^{68} +(-0.346239 - 1.06181i) q^{69} +8.13766i q^{71} +(-5.60064 + 4.08713i) q^{72} +5.23685 q^{73} +2.74917i q^{74} +(-6.59284 - 5.61555i) q^{75} -7.09101i q^{76} +(1.45884 + 4.47383i) q^{78} +3.75268 q^{79} +(3.61158 - 1.01913i) q^{80} +(2.74511 - 8.57113i) q^{81} -1.46997 q^{82} +5.27461i q^{83} +(1.32178 + 4.68409i) q^{85} +4.21973i q^{86} +(1.92461 - 0.627581i) q^{87} +9.36817i q^{88} +0.894758 q^{89} +(2.67024 - 3.40289i) q^{90} -1.02152 q^{92} +(-0.644806 + 0.210260i) q^{93} -5.03039i q^{94} +(2.71815 + 9.63250i) q^{95} +(3.06306 + 9.39349i) q^{96} -3.89968 q^{97} +(-7.16845 - 9.82300i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.573210\pi$
$2$	−0.644806			−0.455947			−0.227973	+	0.973667i	$0.573210\pi$
$3$	−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	$-0.301372\pi$
$13$	4.21339			1.16858			0.584292	+	0.811543i	$0.301372\pi$
$14$		0			0
$15$	−2.15556	−	3.21769i	−0.556564	−	0.830804i
$16$	1.67822			0.419555
$17$			2.17659i			0.527901i	0.964536	+	0.263951i	$0.0850256\pi$
$17$			2.17659i			0.527901i	−0.964536	+	0.263951i	$0.914974\pi$
$18$	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	$-0.478585\pi$
$23$	0.644806			0.134451			0.0672257	+	0.997738i	$0.478585\pi$
$24$	−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	$0.965390\pi$
$30$	1.38992	+	2.07479i	0.253764	+	0.378802i
$31$		−	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	$-0.886024\pi$
$37$		−	4.26357i		−	0.700926i	0.936577	−	0.350463i	$-0.113976\pi$
$38$		−	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	$-0.833705\pi$
$43$		−	6.54419i		−	0.997980i	0.866608	−	0.498990i	$-0.166295\pi$
$44$		−	6.42166i		−	0.968102i
$45$	−4.14116	+	5.27739i	−0.617327	+	0.786707i
$46$	−0.415775			−0.0613026
$47$			7.80140i			1.13795i	0.822355	+	0.568975i	$0.192660\pi$
$47$			7.80140i			1.13795i	−0.822355	+	0.568975i	$0.807340\pi$
$48$	−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	$-0.335315\pi$
$53$	7.20148			0.989200			0.494600	+	0.869121i	$0.335315\pi$
$54$	−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	$0.236152\pi$
$60$	3.41490	+	5.09755i	0.440862	+	0.658091i
$61$		−	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	$-0.820793\pi$
$67$		−	8.73739i		−	1.06744i	0.845660	−	0.533721i	$-0.179207\pi$
$68$		−	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	$-0.400854\pi$
$73$	5.23685			0.612927			0.306464	+	0.951882i	$0.400854\pi$
$74$			2.74917i			0.319585i
$75$	−6.59284	−	5.61555i	−0.761276	−	0.648428i
$76$		−	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	$0.0934831\pi$
$83$			5.27461i			0.578964i	−0.957183	+	0.289482i	$0.906517\pi$
$84$		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	$0.484899\pi$
$90$	2.67024	−	3.40289i	0.281468	−	0.358696i
$91$		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	$-0.563437\pi$
$97$	−3.89968			−0.395953			−0.197976	+	0.980207i	$0.563437\pi$
$98$		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	$-0.660643\pi$
$103$	−9.81443			−0.967044			−0.483522	+	0.875332i	$0.660643\pi$
$104$	9.73770			0.954860
$105$		0			0
$106$	−4.64356			−0.451022
$107$	−18.7795			−1.81548			−0.907740	−	0.419532i	$-0.862194\pi$
$107$	−18.7795			−1.81548			−0.907740	+	0.419532i	$0.862194\pi$
$108$	−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	$-0.636326\pi$
$113$	−8.82955			−0.830614			−0.415307	+	0.909681i	$0.636326\pi$
$114$	−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
$120$	−4.98179	−	7.43650i	−0.454773	−	0.678857i
$121$	−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	$0.247762\pi$
$127$			15.8249i			1.40424i	−0.712060	+	0.702118i	$0.752238\pi$
$128$	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
$135$	10.9140	+	3.98552i	0.939328	+	0.343019i
$136$			5.03039i			0.431352i
$137$	−19.8616			−1.69689			−0.848446	−	0.529282i	$-0.822461\pi$
$137$	−19.8616			−1.69689			−0.848446	+	0.529282i	$0.822461\pi$
$138$	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	$0.866254\pi$
$150$	4.25110	+	3.62094i	0.347101	+	0.295649i
$151$	−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	$-0.265207\pi$
$157$	16.8536			1.34506			0.672531	+	0.740069i	$0.265207\pi$
$158$	−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	$0.0602827\pi$
$163$			4.80693i			0.376508i	−0.982120	+	0.188254i	$0.939717\pi$
$164$	−3.61158			−0.282017
$165$	13.0429	−	8.73759i	1.01539	−	0.680221i
$166$		−	3.40110i		−	0.263977i
$167$			4.45089i			0.344420i	0.985060	+	0.172210i	$0.0550908\pi$
$167$			4.45089i			0.344420i	−0.985060	+	0.172210i	$0.944909\pi$
$168$		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	$-0.856599\pi$
$173$		−	11.4542i		−	0.870847i	0.900226	−	0.435423i	$-0.143401\pi$
$174$	−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	$0.872361\pi$
$180$	6.56052	−	8.36057i	0.488993	−	0.623160i
$181$		−	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	$-0.928470\pi$
$193$		−	6.19133i		−	0.445661i	0.974857	−	0.222831i	$-0.0715297\pi$
$194$	2.51454			0.180533
$195$	−9.08224	−	13.5574i	−0.650393	−	0.970865i
$196$		0			0
$197$	13.0751			0.931562			0.465781	−	0.884900i	$-0.345773\pi$
$197$	13.0751			0.931562			0.465781	+	0.884900i	$0.345773\pi$
$198$	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	$-0.493313\pi$
$223$	0.627418			0.0420150			0.0210075	+	0.999779i	$0.493313\pi$
$224$		0			0
$225$	−5.70708	+	13.8719i	−0.380472	+	0.924792i
$226$	5.69334			0.378716
$227$		−	5.42940i		−	0.360362i	−0.983633	−	0.180181i	$-0.942332\pi$
$227$		−	5.42940i		−	0.360362i	0.983633	−	0.180181i	$-0.0576683\pi$
$228$	−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	$-0.410941\pi$
$233$	8.43048			0.552299			0.276150	+	0.961115i	$0.410941\pi$
$234$	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	$0.971977\pi$
$240$	−3.61751	−	5.40000i	−0.233510	−	0.348568i
$241$		−	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
$255$	7.00360	−	4.69179i	0.438583	−	0.293811i
$256$	−7.86621			−0.491638
$257$			20.1035i			1.25402i	0.779011	+	0.627011i	$0.215722\pi$
$257$			20.1035i			1.25402i	−0.779011	+	0.627011i	$0.784278\pi$
$258$	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	$-0.412957\pi$
$263$	8.75919			0.540115			0.270057	+	0.962844i	$0.412957\pi$
$264$	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	$0.676248\pi$
$270$	−7.03742	−	2.56989i	−0.428284	−	0.156398i
$271$		−	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	$-0.870089\pi$
$277$		−	13.2112i		−	0.793785i	0.917865	−	0.396893i	$-0.129911\pi$
$278$			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	$-0.655727\pi$
$283$	−15.8115			−0.939896			−0.469948	+	0.882694i	$0.655727\pi$
$284$		−	12.8919i		−	0.764993i
$285$	14.4024	−	9.64833i	0.853126	−	0.571518i
$286$		−	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	$0.207620\pi$
$293$			20.7797i			1.21396i	−0.794716	+	0.606982i	$0.792380\pi$
$294$		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
$300$	10.4445	+	8.89630i	0.603016	+	0.513628i
$301$		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	$-0.379163\pi$
$307$	12.9857			0.741136			0.370568	+	0.928805i	$0.379163\pi$
$308$		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	$-0.213159\pi$
$313$	27.7419			1.56807			0.784033	+	0.620719i	$0.213159\pi$
$314$	−10.8673			−0.613276
$315$		0			0
$316$	−5.94509			−0.334437
$317$	4.52339			0.254059			0.127030	−	0.991899i	$-0.459456\pi$
$317$	4.52339			0.254059			0.127030	+	0.991899i	$0.459456\pi$
$318$	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
$330$	−8.41016	+	5.63405i	−0.462964	+	0.310144i
$331$	−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	$-0.675715\pi$
$337$		−	31.2616i		−	1.70293i	0.524413	−	0.851464i	$-0.324285\pi$
$338$	−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
$345$	−1.38992	−	2.07479i	−0.0748308	−	0.111703i
$346$			7.38573i			0.397060i
$347$	−2.78671			−0.149598			−0.0747992	−	0.997199i	$-0.523832\pi$
$347$	−2.78671			−0.149598			−0.0747992	+	0.997199i	$0.523832\pi$
$348$	−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	$-0.972206\pi$
$353$		−	3.27697i		−	0.174416i	0.996190	−	0.0872078i	$-0.0277944\pi$
$354$	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	$0.851855\pi$
$360$	−9.57075	+	12.1967i	−0.504423	+	0.642824i
$361$	−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	$-0.647417\pi$
$367$	−17.1168			−0.893490			−0.446745	+	0.894661i	$0.647417\pi$
$368$	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	$-0.730756\pi$
$373$		−	28.9133i		−	1.49708i	0.663092	−	0.748538i	$-0.269244\pi$
$374$	5.68901			0.294172
$375$	−17.5981	−	8.08119i	−0.908764	−	0.417311i
$376$			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	$0.0309390\pi$
$383$			3.79840i			0.194089i	−0.995280	+	0.0970447i	$0.969061\pi$
$384$	−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	$0.925821\pi$
$390$	5.85628	+	8.74189i	0.296544	+	0.442663i
$391$			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	$-0.291875\pi$
$397$	24.2383			1.21648			0.608242	+	0.793751i	$0.291875\pi$
$398$		−	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
$405$	0.702572	−	20.1123i	0.0349111	−	0.999390i
$406$		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	$-0.522648\pi$
$433$	−2.95856			−0.142179			−0.0710896	+	0.997470i	$0.522648\pi$
$434$		0			0
$435$	3.76069	−	2.51933i	0.180311	−	0.120792i
$436$	−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	$-0.772503\pi$
$443$	−31.7940			−1.51058			−0.755288	+	0.655392i	$0.772503\pi$
$444$	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	$-0.0225112\pi$
$450$	3.67996	−	8.94467i	0.173475	−	0.421656i
$451$			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	$-0.933974\pi$
$457$		−	8.80505i		−	0.411883i	0.978564	−	0.205941i	$-0.0660256\pi$
$458$		−	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	$0.0515943\pi$
$463$			6.94495i			0.322759i	−0.986892	+	0.161380i	$0.948406\pi$
$464$			1.96143i			0.0910571i
$465$	−1.25996	+	0.844057i	−0.0584290	+	0.0391422i
$466$	−5.43603			−0.251819
$467$		−	24.4731i		−	1.13248i	−0.824240	−	0.566241i	$-0.808397\pi$
$467$		−	24.4731i		−	1.13248i	0.824240	−	0.566241i	$-0.191603\pi$
$468$	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	$0.687252\pi$
$480$	12.2962	+	18.3550i	0.561241	+	0.837785i
$481$		−	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	$0.0709496\pi$
$487$			9.75645i			0.442107i	−0.975262	+	0.221054i	$0.929050\pi$
$488$		−	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
$495$	−21.3919	−	16.7862i	−0.961495	−	0.754483i
$496$		−	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	$0.122642\pi$
$503$			16.8580i			0.751659i	−0.926689	+	0.375830i	$0.877358\pi$
$504$		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	$0.520837\pi$
$510$	−4.51596	+	3.02529i	−0.199970	+	0.133962i
$511$		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	$-0.659407\pi$
$523$	−21.9600			−0.960243			−0.480122	+	0.877202i	$0.659407\pi$
$524$	−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
$540$	−17.2903	−	6.31397i	−0.744054	−	0.271710i
$541$	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	$0.103540\pi$
$547$			14.9485i			0.639151i	−0.947561	+	0.319575i	$0.896460\pi$
$548$	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
$555$	−13.7188	+	9.19039i	−0.582332	+	0.390110i
$556$			0.362417i			0.0153699i
$557$	−1.22900			−0.0520745			−0.0260373	−	0.999661i	$-0.508289\pi$
$557$	−1.22900			−0.0520745			−0.0260373	+	0.999661i	$0.508289\pi$
$558$	−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	$-0.971740\pi$
$563$		−	4.20758i		−	0.177329i	0.996062	−	0.0886643i	$-0.0282598\pi$
$564$	−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	$-0.181606\pi$
$570$	−9.28676	+	6.22130i	−0.388980	+	0.260582i
$571$	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	$-0.538082\pi$
$577$	−5.73384			−0.238703			−0.119351	+	0.992852i	$0.538082\pi$
$578$	−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
$585$	−17.4483	+	22.2357i	−0.721399	+	0.919333i
$586$		−	13.3989i		−	0.553502i
$587$		−	31.0435i		−	1.28130i	−0.767832	−	0.640652i	$-0.778664\pi$
$587$		−	31.0435i		−	1.28130i	0.767832	−	0.640652i	$-0.221336\pi$
$588$		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	$0.233228\pi$
$593$			32.5768i			1.33777i	−0.743366	+	0.668885i	$0.766772\pi$
$594$	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	$-0.270652\pi$
$600$	−15.2369	−	12.9783i	−0.622044	−	0.529836i
$601$		−	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	$-0.611793\pi$
$607$	−16.9521			−0.688066			−0.344033	+	0.938958i	$0.611793\pi$
$608$		−	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	$0.247013\pi$
$613$			34.6841i			1.40088i	−0.713712	+	0.700439i	$0.752987\pi$
$614$	−8.37328			−0.337918
$615$	−4.91407	−	7.33541i	−0.198154	−	0.295792i
$616$		0			0
$617$	−45.7116			−1.84028			−0.920140	−	0.391590i	$-0.871925\pi$
$617$	−45.7116			−1.84028			−0.920140	+	0.391590i	$0.871925\pi$
$618$	−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	$-0.671737\pi$
$643$	−26.0538			−1.02746			−0.513731	+	0.857951i	$0.671737\pi$
$644$		0			0
$645$	−21.0572	+	14.1064i	−0.829126	+	0.555440i
$646$	6.28199			0.247161
$647$		−	40.8426i		−	1.60569i	−0.596190	−	0.802844i	$-0.703319\pi$
$647$		−	40.8426i		−	1.60569i	0.596190	−	0.802844i	$-0.296681\pi$
$648$	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	$-0.655659\pi$
$653$	−24.0083			−0.939517			−0.469758	+	0.882795i	$0.655659\pi$
$654$	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	$-0.272142\pi$
$660$	−20.6629	+	13.8423i	−0.804304	+	0.538811i
$661$			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	$0.0204553\pi$
$673$			3.33192i			0.128436i	−0.997936	+	0.0642181i	$0.979545\pi$
$674$			20.1577i			0.776444i
$675$	25.9075	+	1.94921i	0.997182	+	0.0750250i
$676$	−7.52931			−0.289589
$677$		−	32.3722i		−	1.24417i	−0.782951	−	0.622083i	$-0.786287\pi$
$677$		−	32.3722i		−	1.24417i	0.782951	−	0.622083i	$-0.213713\pi$
$678$	−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	$-0.636769\pi$
$683$	−21.7737			−0.833146			−0.416573	+	0.909102i	$0.636769\pi$
$684$	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
$690$	0.896229	+	1.33783i	0.0341189	+	0.0509305i
$691$		−	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
$705$	25.1025	−	16.8164i	0.945415	−	0.633343i
$706$			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	$0.329141\pi$
$720$	−6.94977	+	8.85663i	−0.259003	+	0.330067i
$721$		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	$-0.536358\pi$
$727$	−6.14612			−0.227947			−0.113973	+	0.993484i	$0.536358\pi$
$728$		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	$-0.600633\pi$
$733$	−16.8350			−0.621813			−0.310907	+	0.950440i	$0.600633\pi$
$734$	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	$-0.756740\pi$
$743$	−39.3563			−1.44384			−0.721920	+	0.691976i	$0.756740\pi$
$744$	−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
$750$	11.3474	+	5.21080i	0.414348	+	0.190271i
$751$	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	$0.259607\pi$
$757$			40.0667i			1.45625i	−0.685446	+	0.728124i	$0.740393\pi$
$758$	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
$765$	−11.4867	−	9.01361i	−0.415303	−	0.325888i
$766$		−	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	$0.106071\pi$
$773$			18.1886i			0.654197i	−0.944990	+	0.327099i	$0.893929\pi$
$774$	−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
$780$	14.3883	+	21.4780i	0.515184	+	0.769035i
$781$	−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	$-0.492973\pi$
$787$	1.23859			0.0441511			0.0220756	+	0.999756i	$0.492973\pi$
$788$	−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
$795$	−15.5233	−	23.1722i	−0.550553	−	0.821831i
$796$		−	26.8561i		−	0.951888i
$797$		−	51.4416i		−	1.82216i	−0.412235	−	0.911078i	$-0.635252\pi$
$797$		−	51.4416i		−	1.82216i	0.412235	−	0.911078i	$-0.364748\pi$
$798$		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	$-0.0158054\pi$
$810$	−0.453022	+	12.9686i	−0.0159176	+	0.455669i
$811$		−	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	$0.232099\pi$
$823$			38.2263i			1.33249i	−0.745735	+	0.666243i	$0.767901\pi$
$824$	−22.6824			−0.790179
$825$	22.7627	−	26.7241i	0.792494	−	0.930414i
$826$		0			0
$827$	7.13112			0.247973			0.123987	−	0.992284i	$-0.460432\pi$
$827$	7.13112			0.247973			0.123987	+	0.992284i	$0.460432\pi$
$828$	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	$-0.623450\pi$
$853$	−22.0904			−0.756362			−0.378181	+	0.925732i	$0.623450\pi$
$854$		0			0
$855$	−23.6216	−	18.5359i	−0.807843	−	0.633913i
$856$	−43.4018			−1.48344
$857$			14.3312i			0.489544i	0.969581	+	0.244772i	$0.0787130\pi$
$857$			14.3312i			0.489544i	−0.969581	+	0.244772i	$0.921287\pi$
$858$	−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	$-0.589046\pi$
$863$	−16.2226			−0.552224			−0.276112	+	0.961125i	$0.589046\pi$
$864$	−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
$870$	−2.42492	+	1.62448i	−0.0822124	+	0.0550749i
$871$		−	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	$0.270527\pi$
$877$			44.4926i			1.50241i	−0.660070	+	0.751204i	$0.729473\pi$
$878$			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	$-0.663400\pi$
$883$		−	51.7706i		−	1.74222i	0.491088	−	0.871110i	$-0.336600\pi$
$884$		−	14.5287i		−	0.488652i
$885$	−24.4116	−	36.4401i	−0.820588	−	1.22492i
$886$	20.5009			0.688742
$887$		−	55.9733i		−	1.87940i	−0.342000	−	0.939700i	$-0.611104\pi$
$887$		−	55.9733i		−	1.87940i	0.342000	−	0.939700i	$-0.388896\pi$
$888$	−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
$900$	9.04130	−	21.9762i	0.301377	−	0.732540i
$901$			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	$0.205670\pi$
$907$			36.2663i			1.20420i	−0.798419	+	0.602102i	$0.794330\pi$
$908$			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
$915$	−22.4955	+	15.0700i	−0.743679	+	0.498199i
$916$		−	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	$0.535571\pi$
$930$	0.812427	−	0.544253i	0.0266405	−	0.0178468i
$931$		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	$-0.243739\pi$
$937$	44.1327			1.44175			0.720877	+	0.693063i	$0.243739\pi$
$938$		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	$-0.304382\pi$
$947$	35.4874			1.15319			0.576593	+	0.817031i	$0.304382\pi$
$948$	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	$-0.443652\pi$
$953$	10.8726			0.352198			0.176099	+	0.984373i	$0.443652\pi$
$954$	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
$960$	−0.693615	−	1.03539i	−0.0223863	−	0.0334169i
$961$	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	$-0.888267\pi$
$967$		−	21.3855i		−	0.687711i	0.939023	−	0.343855i	$-0.111733\pi$
$968$	−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
$975$	−27.7782	−	23.6605i	−0.889615	−	0.757743i
$976$		−	11.7328i		−	0.375557i
$977$	0.731073			0.0233891			0.0116945	−	0.999932i	$-0.496277\pi$
$977$	0.731073			0.0233891			0.0116945	+	0.999932i	$0.496277\pi$
$978$	−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	$0.0189565\pi$
$983$			3.73214i			0.119037i	−0.998227	+	0.0595184i	$0.981044\pi$
$984$	−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
$990$	13.7936	+	10.8238i	0.438390	+	0.344004i
$991$	−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	$-0.474406\pi$
$997$	5.07219			0.160638			0.0803189	+	0.996769i	$0.474406\pi$
$998$	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.734.9		24
3.2	odd	2	inner	735.2.g.b.734.14		24
5.4	even	2	inner	735.2.g.b.734.16		24
7.2	even	3		735.2.p.f.374.8		24
7.3	odd	6		735.2.p.f.509.7		24
7.4	even	3		105.2.p.a.89.8	yes	24
7.5	odd	6		105.2.p.a.59.7	yes	24
7.6	odd	2	inner	735.2.g.b.734.12		24
15.14	odd	2	inner	735.2.g.b.734.11		24
21.2	odd	6		735.2.p.f.374.6		24
21.5	even	6		105.2.p.a.59.5	✓	24
21.11	odd	6		105.2.p.a.89.6	yes	24
21.17	even	6		735.2.p.f.509.5		24
21.20	even	2	inner	735.2.g.b.734.15		24
35.4	even	6		105.2.p.a.89.5	yes	24
35.9	even	6		735.2.p.f.374.5		24
35.12	even	12		525.2.t.j.101.6		24
35.18	odd	12		525.2.t.j.26.5		24
35.19	odd	6		105.2.p.a.59.6	yes	24
35.24	odd	6		735.2.p.f.509.6		24
35.32	odd	12		525.2.t.j.26.8		24
35.33	even	12		525.2.t.j.101.7		24
35.34	odd	2	inner	735.2.g.b.734.13		24
105.32	even	12		525.2.t.j.26.6		24
105.44	odd	6		735.2.p.f.374.7		24
105.47	odd	12		525.2.t.j.101.8		24
105.53	even	12		525.2.t.j.26.7		24
105.59	even	6		735.2.p.f.509.8		24
105.68	odd	12		525.2.t.j.101.5		24
105.74	odd	6		105.2.p.a.89.7	yes	24
105.89	even	6		105.2.p.a.59.8	yes	24
105.104	even	2	inner	735.2.g.b.734.10		24

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

\(f(q)\)	\(=\)	\(q-0.644806 q^{2} +(-0.536966 - 1.64671i) q^{3} -1.58423 q^{4} +(2.15203 - 0.607270i) q^{5} +(0.346239 + 1.06181i) q^{6} +2.31113 q^{8} +(-2.42334 + 1.76846i) q^{9} +O(q^{10})\)	\(q-0.644806 q^{2} +(-0.536966 - 1.64671i) q^{3} -1.58423 q^{4} +(2.15203 - 0.607270i) q^{5} +(0.346239 + 1.06181i) q^{6} +2.31113 q^{8} +(-2.42334 + 1.76846i) q^{9} +(-1.38764 + 0.391571i) q^{10} +4.05350i q^{11} +(0.850674 + 2.60877i) q^{12} +4.21339 q^{13} +(-2.15556 - 3.21769i) q^{15} +1.67822 q^{16} +2.17659i q^{17} +(1.56258 - 1.14031i) q^{18} +4.47601i q^{19} +(-3.40930 + 0.962052i) q^{20} -2.61372i q^{22} +0.644806 q^{23} +(-1.24100 - 3.80577i) q^{24} +(4.26245 - 2.61372i) q^{25} -2.71682 q^{26} +(4.21339 + 3.04094i) q^{27} +1.16875i q^{29} +(1.38992 + 2.07479i) q^{30} -0.391571i q^{31} -5.70439 q^{32} +(6.67496 - 2.17659i) q^{33} -1.40348i q^{34} +(3.83911 - 2.80164i) q^{36} -4.26357i q^{37} -2.88616i q^{38} +(-2.26245 - 6.93825i) q^{39} +(4.97361 - 1.40348i) q^{40} +2.27971 q^{41} -6.54419i q^{43} -6.42166i q^{44} +(-4.14116 + 5.27739i) q^{45} -0.415775 q^{46} +7.80140i q^{47} +(-0.901147 - 2.76355i) q^{48} +(-2.74845 + 1.68534i) q^{50} +(3.58423 - 1.16875i) q^{51} -6.67496 q^{52} +7.20148 q^{53} +(-2.71682 - 1.96082i) q^{54} +(2.46157 + 8.72325i) q^{55} +(7.37071 - 2.40346i) q^{57} -0.753620i q^{58} +11.3249 q^{59} +(3.41490 + 5.09755i) q^{60} -6.99120i q^{61} +0.252487i q^{62} +0.321779 q^{64} +(9.06734 - 2.55867i) q^{65} +(-4.30406 + 1.40348i) q^{66} -8.73739i q^{67} -3.44821i q^{68} +(-0.346239 - 1.06181i) q^{69} +8.13766i q^{71} +(-5.60064 + 4.08713i) q^{72} +5.23685 q^{73} +2.74917i q^{74} +(-6.59284 - 5.61555i) q^{75} -7.09101i q^{76} +(1.45884 + 4.47383i) q^{78} +3.75268 q^{79} +(3.61158 - 1.01913i) q^{80} +(2.74511 - 8.57113i) q^{81} -1.46997 q^{82} +5.27461i q^{83} +(1.32178 + 4.68409i) q^{85} +4.21973i q^{86} +(1.92461 - 0.627581i) q^{87} +9.36817i q^{88} +0.894758 q^{89} +(2.67024 - 3.40289i) q^{90} -1.02152 q^{92} +(-0.644806 + 0.210260i) q^{93} -5.03039i q^{94} +(2.71815 + 9.63250i) q^{95} +(3.06306 + 9.39349i) q^{96} -3.89968 q^{97} +(-7.16845 - 9.82300i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{4} + 12 q^{9}+O(q^{10}) \) 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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