LMFDB - Embedded newform 504.2.cx.a.185.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(185,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5, 1]))

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

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

chi := DirichletCharacter("504.185");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cx (of order $6$, degree $2$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			185.6
Character	$\chi$	$=$	504.185
Dual form			504.2.cx.a.425.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.14647 - 1.29831i) q^{3} -0.0525740 q^{5} +(2.44149 - 1.01937i) q^{7} +(-0.371197 + 2.97695i) q^{9} +O(q^{10})$	\(q+(-1.14647 - 1.29831i) q^{3} -0.0525740 q^{5} +(2.44149 - 1.01937i) q^{7} +(-0.371197 + 2.97695i) q^{9} -2.48476i q^{11} +(2.51752 + 1.45349i) q^{13} +(0.0602747 + 0.0682572i) q^{15} +(2.88651 - 4.99959i) q^{17} +(-2.92807 + 1.69052i) q^{19} +(-4.12256 - 2.00113i) q^{21} -8.63028i q^{23} -4.99724 q^{25} +(4.29056 - 2.93106i) q^{27} +(-6.23728 + 3.60109i) q^{29} +(8.59189 - 4.96053i) q^{31} +(-3.22598 + 2.84871i) q^{33} +(-0.128359 + 0.0535922i) q^{35} +(-0.770828 - 1.33511i) q^{37} +(-0.999195 - 4.93490i) q^{39} +(0.392450 - 0.679743i) q^{41} +(-2.03075 - 3.51736i) q^{43} +(0.0195153 - 0.156510i) q^{45} +(0.657760 - 1.13927i) q^{47} +(4.92179 - 4.97755i) q^{49} +(-9.80031 + 1.98432i) q^{51} +(0.710864 + 0.410417i) q^{53} +0.130634i q^{55} +(5.55176 + 1.86339i) q^{57} +(-2.32075 - 4.01965i) q^{59} +(4.87064 + 2.81207i) q^{61} +(2.12832 + 7.64658i) q^{63} +(-0.132356 - 0.0764159i) q^{65} +(6.95059 + 12.0388i) q^{67} +(-11.2047 + 9.89439i) q^{69} -3.51362i q^{71} +(6.75829 + 3.90190i) q^{73} +(5.72920 + 6.48794i) q^{75} +(-2.53288 - 6.06653i) q^{77} +(-7.50070 + 12.9916i) q^{79} +(-8.72443 - 2.21007i) q^{81} +(-3.14086 - 5.44013i) q^{83} +(-0.151756 + 0.262848i) q^{85} +(11.8262 + 3.96934i) q^{87} +(7.93120 + 13.7372i) q^{89} +(7.62815 + 0.982418i) q^{91} +(-16.2907 - 5.46779i) q^{93} +(0.153940 - 0.0888775i) q^{95} +(1.57451 - 0.909044i) q^{97} +(7.39700 + 0.922336i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 2 q^{9}+O(q^{10}) $ 48 * q + 2 * q^9	$ 48 q + 2 q^{9} + 8 q^{15} - 10 q^{21} + 48 q^{25} + 18 q^{27} + 18 q^{29} + 18 q^{31} + 12 q^{33} - 4 q^{39} - 6 q^{41} - 6 q^{43} - 18 q^{45} + 18 q^{47} - 12 q^{49} + 6 q^{51} - 12 q^{53} + 4 q^{57} + 18 q^{61} - 32 q^{63} - 36 q^{65} - 12 q^{77} + 6 q^{79} + 6 q^{81} - 54 q^{87} - 18 q^{89} + 6 q^{91} + 4 q^{93} - 54 q^{95} - 64 q^{99}+O(q^{100}) $ 48 * q + 2 * q^9 + 8 * q^15 - 10 * q^21 + 48 * q^25 + 18 * q^27 + 18 * q^29 + 18 * q^31 + 12 * q^33 - 4 * q^39 - 6 * q^41 - 6 * q^43 - 18 * q^45 + 18 * q^47 - 12 * q^49 + 6 * q^51 - 12 * q^53 + 4 * q^57 + 18 * q^61 - 32 * q^63 - 36 * q^65 - 12 * q^77 + 6 * q^79 + 6 * q^81 - 54 * q^87 - 18 * q^89 + 6 * q^91 + 4 * q^93 - 54 * q^95 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.14647	−	1.29831i	−0.661917	−	0.749577i
$3$	−1.14647	−	1.29831i	−0.661917	−	0.749577i
$4$		0			0
$5$	−0.0525740			−0.0235118			−0.0117559	−	0.999931i	$-0.503742\pi$
$5$	−0.0525740			−0.0235118			−0.0117559	+	0.999931i	$0.503742\pi$
$6$		0			0
$7$	2.44149	−	1.01937i	0.922798	−	0.385284i
$7$	2.44149	−	1.01937i	0.922798	−	0.385284i
$8$		0			0
$9$	−0.371197	+	2.97695i	−0.123732	+	0.992316i
$10$		0			0
$11$		−	2.48476i		−	0.749184i	−0.927190	−	0.374592i	$-0.877783\pi$
$11$		−	2.48476i		−	0.749184i	0.927190	−	0.374592i	$-0.122217\pi$
$12$		0			0
$13$	2.51752	+	1.45349i	0.698235	+	0.403126i	0.806690	−	0.590975i	$-0.201257\pi$
$13$	2.51752	+	1.45349i	0.698235	+	0.403126i	−0.108455	+	0.994101i	$0.534590\pi$
$14$		0			0
$15$	0.0602747	+	0.0682572i	0.0155629	+	0.0176239i
$16$		0			0
$17$	2.88651	−	4.99959i	0.700082	−	1.21258i	−0.268355	−	0.963320i	$-0.586480\pi$
$17$	2.88651	−	4.99959i	0.700082	−	1.21258i	0.968437	−	0.249258i	$-0.0801867\pi$
$18$		0			0
$19$	−2.92807	+	1.69052i	−0.671745	+	0.387832i	−0.796737	−	0.604326i	$-0.793443\pi$
$19$	−2.92807	+	1.69052i	−0.671745	+	0.387832i	0.124993	+	0.992158i	$0.460109\pi$
$20$		0			0
$21$	−4.12256	−	2.00113i	−0.899616	−	0.436683i
$22$		0			0
$23$		−	8.63028i		−	1.79954i	−0.436367	−	0.899769i	$-0.643735\pi$
$23$		−	8.63028i		−	1.79954i	0.436367	−	0.899769i	$-0.356265\pi$
$24$		0			0
$25$	−4.99724			−0.999447
$26$		0			0
$27$	4.29056	−	2.93106i	0.825718	−	0.564083i
$28$		0			0
$29$	−6.23728	+	3.60109i	−1.15823	+	0.668706i	−0.950880	−	0.309560i	$-0.899818\pi$
$29$	−6.23728	+	3.60109i	−1.15823	+	0.668706i	−0.207353	+	0.978266i	$0.566485\pi$
$30$		0			0
$31$	8.59189	−	4.96053i	1.54315	−	0.890938i	0.544512	−	0.838753i	$-0.316715\pi$
$31$	8.59189	−	4.96053i	1.54315	−	0.890938i	0.998637	−	0.0521852i	$-0.0166186\pi$
$32$		0			0
$33$	−3.22598	+	2.84871i	−0.561571	+	0.495897i
$34$		0			0
$35$	−0.128359	+	0.0535922i	−0.0216967	+	0.00905873i
$36$		0			0
$37$	−0.770828	−	1.33511i	−0.126723	−	0.219491i	0.795682	−	0.605715i	$-0.207113\pi$
$37$	−0.770828	−	1.33511i	−0.126723	−	0.219491i	−0.922405	+	0.386223i	$0.873779\pi$
$38$		0			0
$39$	−0.999195	−	4.93490i	−0.159999	−	0.790217i
$40$		0			0
$41$	0.392450	−	0.679743i	0.0612904	−	0.106158i	−0.833752	−	0.552139i	$-0.813812\pi$
$41$	0.392450	−	0.679743i	0.0612904	−	0.106158i	0.895042	+	0.445981i	$0.147145\pi$
$42$		0			0
$43$	−2.03075	−	3.51736i	−0.309686	−	0.536392i	0.668608	−	0.743615i	$-0.266891\pi$
$43$	−2.03075	−	3.51736i	−0.309686	−	0.536392i	−0.978294	+	0.207223i	$0.933557\pi$
$44$		0			0
$45$	0.0195153	−	0.156510i	0.00290917	−	0.0233312i
$46$		0			0
$47$	0.657760	−	1.13927i	0.0959441	−	0.166180i	−0.814058	−	0.580783i	$-0.802746\pi$
$47$	0.657760	−	1.13927i	0.0959441	−	0.166180i	0.910002	+	0.414603i	$0.136080\pi$
$48$		0			0
$49$	4.92179	−	4.97755i	0.703113	−	0.711078i
$50$		0			0
$51$	−9.80031	+	1.98432i	−1.37232	+	0.277860i
$52$		0			0
$53$	0.710864	+	0.410417i	0.0976447	+	0.0563752i	0.548027	−	0.836461i	$-0.315379\pi$
$53$	0.710864	+	0.410417i	0.0976447	+	0.0563752i	−0.450382	+	0.892836i	$0.648712\pi$
$54$		0			0
$55$			0.130634i			0.0176147i
$56$		0			0
$57$	5.55176	+	1.86339i	0.735349	+	0.246812i
$58$		0			0
$59$	−2.32075	−	4.01965i	−0.302136	−	0.523314i	0.674484	−	0.738290i	$-0.264366\pi$
$59$	−2.32075	−	4.01965i	−0.302136	−	0.523314i	−0.976619	+	0.214975i	$0.931033\pi$
$60$		0			0
$61$	4.87064	+	2.81207i	0.623622	+	0.360048i	0.778278	−	0.627920i	$-0.216094\pi$
$61$	4.87064	+	2.81207i	0.623622	+	0.360048i	−0.154656	+	0.987968i	$0.549427\pi$
$62$		0			0
$63$	2.12832	+	7.64658i	0.268143	+	0.963379i
$64$		0			0
$65$	−0.132356	−	0.0764159i	−0.0164168	−	0.00947823i
$66$		0			0
$67$	6.95059	+	12.0388i	0.849149	+	1.47077i	0.881968	+	0.471309i	$0.156218\pi$
$67$	6.95059	+	12.0388i	0.849149	+	1.47077i	−0.0328189	+	0.999461i	$0.510448\pi$
$68$		0			0
$69$	−11.2047	+	9.89439i	−1.34889	+	1.19114i
$70$		0			0
$71$		−	3.51362i		−	0.416990i	−0.978023	−	0.208495i	$-0.933143\pi$
$71$		−	3.51362i		−	0.416990i	0.978023	−	0.208495i	$-0.0668565\pi$
$72$		0			0
$73$	6.75829	+	3.90190i	0.790998	+	0.456683i	0.840314	−	0.542100i	$-0.182371\pi$
$73$	6.75829	+	3.90190i	0.790998	+	0.456683i	−0.0493159	+	0.998783i	$0.515704\pi$
$74$		0			0
$75$	5.72920	+	6.48794i	0.661551	+	0.749163i
$76$		0			0
$77$	−2.53288	−	6.06653i	−0.288648	−	0.691345i
$78$		0			0
$79$	−7.50070	+	12.9916i	−0.843895	+	1.46167i	0.0426820	+	0.999089i	$0.486410\pi$
$79$	−7.50070	+	12.9916i	−0.843895	+	1.46167i	−0.886577	+	0.462581i	$0.846924\pi$
$80$		0			0
$81$	−8.72443	−	2.21007i	−0.969381	−	0.245563i
$82$		0			0
$83$	−3.14086	−	5.44013i	−0.344754	−	0.597132i	0.640555	−	0.767912i	$-0.278704\pi$
$83$	−3.14086	−	5.44013i	−0.344754	−	0.597132i	−0.985309	+	0.170781i	$0.945371\pi$
$84$		0			0
$85$	−0.151756	+	0.262848i	−0.0164602	+	0.0285099i
$86$		0			0
$87$	11.8262	+	3.96934i	1.26790	+	0.425557i
$88$		0			0
$89$	7.93120	+	13.7372i	0.840706	+	1.45615i	0.889299	+	0.457326i	$0.151193\pi$
$89$	7.93120	+	13.7372i	0.840706	+	1.45615i	−0.0485931	+	0.998819i	$0.515474\pi$
$90$		0			0
$91$	7.62815	+	0.982418i	0.799648	+	0.102985i
$92$		0			0
$93$	−16.2907	−	5.46779i	−1.68926	−	0.566983i
$94$		0			0
$95$	0.153940	−	0.0888775i	0.0157939	−	0.00911863i
$96$		0			0
$97$	1.57451	−	0.909044i	0.159867	−	0.0922995i	−0.417932	−	0.908478i	$-0.637245\pi$
$97$	1.57451	−	0.909044i	0.159867	−	0.0922995i	0.577799	+	0.816179i	$0.303912\pi$
$98$		0			0
$99$	7.39700	+	0.922336i	0.743427	+	0.0926982i
$100$		0			0
$101$	1.33589			0.132926			0.0664632	−	0.997789i	$-0.478828\pi$
$101$	1.33589			0.132926			0.0664632	+	0.997789i	$0.478828\pi$
$102$		0			0
$103$			7.65387i			0.754158i	0.926181	+	0.377079i	$0.123072\pi$
$103$			7.65387i			0.754158i	−0.926181	+	0.377079i	$0.876928\pi$
$104$		0			0
$105$	0.216739	+	0.105208i	0.0211516	+	0.0102672i
$106$		0			0
$107$	−10.9289	+	6.30978i	−1.05653	+	0.609989i	−0.924471	−	0.381252i	$-0.875493\pi$
$107$	−10.9289	+	6.30978i	−1.05653	+	0.609989i	−0.132062	+	0.991242i	$0.542160\pi$
$108$		0			0
$109$	5.12613	−	8.87871i	0.490994	−	0.850426i	−0.508952	−	0.860795i	$-0.669967\pi$
$109$	5.12613	−	8.87871i	0.490994	−	0.850426i	0.999946	+	0.0103684i	$0.00330042\pi$
$110$		0			0
$111$	−0.849651	+	2.53144i	−0.0806453	+	0.240274i
$112$		0			0
$113$	13.4379	+	7.75836i	1.26413	+	0.729845i	0.973871	−	0.227104i	$-0.0729257\pi$
$113$	13.4379	+	7.75836i	1.26413	+	0.729845i	0.290258	+	0.956949i	$0.406259\pi$
$114$		0			0
$115$			0.453729i			0.0423104i
$116$		0			0
$117$	−5.26146	+	6.95500i	−0.486422	+	0.642990i
$118$		0			0
$119$	1.95100	−	15.1489i	0.178848	−	1.38870i
$120$		0			0
$121$	4.82596			0.438723
$122$		0			0
$123$	−1.33245	+	0.269788i	−0.120143	+	0.0243259i
$124$		0			0
$125$	0.525595			0.0470107
$126$		0			0
$127$	−7.05269			−0.625825			−0.312912	−	0.949782i	$-0.601305\pi$
$127$	−7.05269			−0.625825			−0.312912	+	0.949782i	$0.601305\pi$
$128$		0			0
$129$	−2.23841	+	6.66909i	−0.197081	+	0.587181i
$130$		0			0
$131$	−3.69917			−0.323198			−0.161599	−	0.986857i	$-0.551665\pi$
$131$	−3.69917			−0.323198			−0.161599	+	0.986857i	$0.551665\pi$
$132$		0			0
$133$	−5.42560	+	7.11216i	−0.470459	+	0.616703i
$134$		0			0
$135$	−0.225572	+	0.154098i	−0.0194141	+	0.0132626i
$136$		0			0
$137$			4.09294i			0.349684i	0.984597	+	0.174842i	$0.0559414\pi$
$137$			4.09294i			0.349684i	−0.984597	+	0.174842i	$0.944059\pi$
$138$		0			0
$139$	12.1602	+	7.02072i	1.03142	+	0.595489i	0.917391	−	0.397988i	$-0.130292\pi$
$139$	12.1602	+	7.02072i	1.03142	+	0.595489i	0.114027	+	0.993478i	$0.463625\pi$
$140$		0			0
$141$	−2.23323	+	0.452173i	−0.188072	+	0.0380799i
$142$		0			0
$143$	3.61158	−	6.25544i	0.302016	−	0.523106i
$144$		0			0
$145$	0.327919	−	0.189324i	0.0272322	−	0.0157225i
$146$		0			0
$147$	−12.1051	−	0.683359i	−0.998410	−	0.0563625i
$148$		0			0
$149$		−	7.57383i		−	0.620473i	−0.950659	−	0.310236i	$-0.899592\pi$
$149$		−	7.57383i		−	0.620473i	0.950659	−	0.310236i	$-0.100408\pi$
$150$		0			0
$151$	−12.6883			−1.03256			−0.516278	−	0.856421i	$-0.672683\pi$
$151$	−12.6883			−1.03256			−0.516278	+	0.856421i	$0.672683\pi$
$152$		0			0
$153$	13.8120	+	10.4488i	1.11664	+	0.844738i
$154$		0			0
$155$	−0.451711	+	0.260795i	−0.0362823	+	0.0209476i
$156$		0			0
$157$	0.949094	−	0.547960i	0.0757459	−	0.0437319i	−0.461649	−	0.887063i	$-0.652742\pi$
$157$	0.949094	−	0.547960i	0.0757459	−	0.0437319i	0.537395	+	0.843331i	$0.319409\pi$
$158$		0			0
$159$	−0.282139	−	1.39345i	−0.0223751	−	0.110508i
$160$		0			0
$161$	−8.79741	−	21.0708i	−0.693333	−	1.66061i
$162$		0			0
$163$	4.43585	+	7.68311i	0.347442	+	0.601788i	0.985794	−	0.167957i	$-0.0537169\pi$
$163$	4.43585	+	7.68311i	0.347442	+	0.601788i	−0.638352	+	0.769745i	$0.720384\pi$
$164$		0			0
$165$	0.169603	−	0.149768i	0.0132036	−	0.0116595i
$166$		0			0
$167$	−4.68302	+	8.11124i	−0.362383	+	0.627666i	−0.988353	−	0.152181i	$-0.951370\pi$
$167$	−4.68302	+	8.11124i	−0.362383	+	0.627666i	0.625969	+	0.779848i	$0.284704\pi$
$168$		0			0
$169$	−2.27472	−	3.93994i	−0.174979	−	0.303072i
$170$		0			0
$171$	−3.94570	−	9.34421i	−0.301735	−	0.714570i
$172$		0			0
$173$	−11.4675	+	19.8624i	−0.871861	+	1.51011i	−0.0117920	+	0.999930i	$0.503754\pi$
$173$	−11.4675	+	19.8624i	−0.871861	+	1.51011i	−0.860069	+	0.510177i	$0.829580\pi$
$174$		0			0
$175$	−12.2007	+	5.09401i	−0.922288	+	0.385071i
$176$		0			0
$177$	−2.55806	+	7.62147i	−0.192276	+	0.572865i
$178$		0			0
$179$	10.5254	+	6.07685i	0.786706	+	0.454205i	0.838802	−	0.544437i	$-0.183257\pi$
$179$	10.5254	+	6.07685i	0.786706	+	0.454205i	−0.0520958	+	0.998642i	$0.516590\pi$
$180$		0			0
$181$		−	24.1883i		−	1.79790i	−0.438048	−	0.898952i	$-0.644330\pi$
$181$		−	24.1883i		−	1.79790i	0.438048	−	0.898952i	$-0.355670\pi$
$182$		0			0
$183$	−1.93314	−	9.54755i	−0.142902	−	0.705775i
$184$		0			0
$185$	0.0405255	+	0.0701923i	0.00297950	+	0.00516064i
$186$		0			0
$187$	−12.4228	−	7.17230i	−0.908444	−	0.524490i
$188$		0			0
$189$	7.48754	−	11.5298i	0.544639	−	0.838671i
$190$		0			0
$191$	−10.8543	−	6.26673i	−0.785389	−	0.453445i	0.0529477	−	0.998597i	$-0.483138\pi$
$191$	−10.8543	−	6.26673i	−0.785389	−	0.453445i	−0.838337	+	0.545153i	$0.816472\pi$
$192$		0			0
$193$	1.48867	+	2.57845i	0.107157	+	0.185601i	0.914617	−	0.404321i	$-0.132492\pi$
$193$	1.48867	+	2.57845i	0.107157	+	0.185601i	−0.807461	+	0.589921i	$0.799159\pi$
$194$		0			0
$195$	0.0525317	+	0.259448i	0.00376187	+	0.0185794i
$196$		0			0
$197$			8.95974i			0.638355i	0.947695	+	0.319178i	$0.103407\pi$
$197$			8.95974i			0.638355i	−0.947695	+	0.319178i	$0.896593\pi$
$198$		0			0
$199$	−5.95927	−	3.44059i	−0.422442	−	0.243897i	0.273680	−	0.961821i	$-0.411759\pi$
$199$	−5.95927	−	3.44059i	−0.422442	−	0.243897i	−0.696121	+	0.717924i	$0.745092\pi$
$200$		0			0
$201$	7.66134	−	22.8261i	0.540390	−	1.61003i
$202$		0			0
$203$	−11.5574	+	15.1501i	−0.811174	+	1.06333i
$204$		0			0
$205$	−0.0206327	+	0.0357369i	−0.00144105	+	0.00249597i
$206$		0			0
$207$	25.6919	+	3.20353i	1.78571	+	0.222661i
$208$		0			0
$209$	4.20054	+	7.27555i	0.290557	+	0.503260i
$210$		0			0
$211$	5.51329	−	9.54930i	0.379550	−	0.657401i	−0.611446	−	0.791286i	$-0.709412\pi$
$211$	5.51329	−	9.54930i	0.379550	−	0.657401i	0.990997	+	0.133885i	$0.0427453\pi$
$212$		0			0
$213$	−4.56175	+	4.02827i	−0.312566	+	0.276013i
$214$		0			0
$215$	0.106765	+	0.184922i	0.00728128	+	0.0126116i
$216$		0			0
$217$	15.9205	−	20.8694i	1.08075	−	1.41671i
$218$		0			0
$219$	−2.68234	−	13.2478i	−0.181256	−	0.895200i
$220$		0			0
$221$	14.5337	−	8.39105i	0.977644	−	0.564443i
$222$		0			0
$223$	5.55863	−	3.20928i	0.372234	−	0.214909i	−0.302200	−	0.953244i	$-0.597721\pi$
$223$	5.55863	−	3.20928i	0.372234	−	0.214909i	0.674434	+	0.738335i	$0.264388\pi$
$224$		0			0
$225$	1.85496	−	14.8765i	0.123664	−	0.991767i
$226$		0			0
$227$	24.2167			1.60732			0.803658	−	0.595091i	$-0.202884\pi$
$227$	24.2167			1.60732			0.803658	+	0.595091i	$0.202884\pi$
$228$		0			0
$229$			10.9925i			0.726407i	0.931710	+	0.363203i	$0.118317\pi$
$229$			10.9925i			0.726407i	−0.931710	+	0.363203i	$0.881683\pi$
$230$		0			0
$231$	−4.97233	+	10.2436i	−0.327156	+	0.673978i
$232$		0			0
$233$	18.3691	−	10.6054i	1.20340	−	0.694783i	0.242090	−	0.970254i	$-0.422167\pi$
$233$	18.3691	−	10.6054i	1.20340	−	0.694783i	0.961309	+	0.275471i	$0.0888338\pi$
$234$		0			0
$235$	−0.0345811	+	0.0598962i	−0.00225582	+	0.00390720i
$236$		0			0
$237$	25.4664	−	5.15632i	1.65422	−	0.334939i
$238$		0			0
$239$	−1.14539	−	0.661293i	−0.0740893	−	0.0427755i	0.462498	−	0.886620i	$-0.346953\pi$
$239$	−1.14539	−	0.661293i	−0.0740893	−	0.0427755i	−0.536587	+	0.843845i	$0.680287\pi$
$240$		0			0
$241$			3.70074i			0.238386i	0.992871	+	0.119193i	$0.0380307\pi$
$241$			3.70074i			0.238386i	−0.992871	+	0.119193i	$0.961969\pi$
$242$		0			0
$243$	7.13298	+	13.8608i	0.457581	+	0.889168i
$244$		0			0
$245$	−0.258758	+	0.261690i	−0.0165315	+	0.0167188i
$246$		0			0
$247$	−9.82863			−0.625381
$248$		0			0
$249$	−3.46204	+	10.3148i	−0.219398	+	0.653671i
$250$		0			0
$251$	−26.6932			−1.68486			−0.842429	−	0.538807i	$-0.818875\pi$
$251$	−26.6932			−1.68486			−0.842429	+	0.538807i	$0.818875\pi$
$252$		0			0
$253$	−21.4442			−1.34818
$254$		0			0
$255$	0.515242	−	0.104324i	0.0322657	−	0.00653300i
$256$		0			0
$257$	1.77792			0.110903			0.0554517	−	0.998461i	$-0.482340\pi$
$257$	1.77792			0.110903			0.0554517	+	0.998461i	$0.482340\pi$
$258$		0			0
$259$	−3.24294	−	2.47391i	−0.201506	−	0.153722i
$260$		0			0
$261$	−8.40501	−	19.9048i	−0.520257	−	1.23207i
$262$		0			0
$263$			18.9777i			1.17022i	0.810955	+	0.585109i	$0.198948\pi$
$263$			18.9777i			1.17022i	−0.810955	+	0.585109i	$0.801052\pi$
$264$		0			0
$265$	−0.0373730	−	0.0215773i	−0.00229580	−	0.00132548i
$266$		0			0
$267$	8.74223	−	26.0465i	0.535016	−	1.59402i
$268$		0			0
$269$	−7.17800	+	12.4327i	−0.437651	+	0.758033i	−0.997508	−	0.0705560i	$-0.977523\pi$
$269$	−7.17800	+	12.4327i	−0.437651	+	0.758033i	0.559857	+	0.828589i	$0.310856\pi$
$270$		0			0
$271$	−11.0202	+	6.36254i	−0.669432	+	0.386497i	−0.795861	−	0.605479i	$-0.792982\pi$
$271$	−11.0202	+	6.36254i	−0.669432	+	0.386497i	0.126429	+	0.991976i	$0.459648\pi$
$272$		0			0
$273$	−7.47000	−	11.0300i	−0.452105	−	0.667566i
$274$		0			0
$275$			12.4169i			0.748770i
$276$		0			0
$277$	−24.9525			−1.49925			−0.749625	−	0.661862i	$-0.769766\pi$
$277$	−24.9525			−1.49925			−0.749625	+	0.661862i	$0.769766\pi$
$278$		0			0
$279$	11.5780	+	27.4189i	0.693154	+	1.64153i
$280$		0			0
$281$	9.13275	−	5.27279i	0.544814	−	0.314549i	−0.202214	−	0.979341i	$-0.564814\pi$
$281$	9.13275	−	5.27279i	0.544814	−	0.314549i	0.747028	+	0.664793i	$0.231480\pi$
$282$		0			0
$283$	13.2881	−	7.67190i	0.789897	−	0.456047i	−0.0500293	−	0.998748i	$-0.515931\pi$
$283$	13.2881	−	7.67190i	0.789897	−	0.456047i	0.839926	+	0.542701i	$0.182598\pi$
$284$		0			0
$285$	−0.291879	−	0.0979659i	−0.0172894	−	0.00580300i
$286$		0			0
$287$	0.265258	−	2.05964i	0.0156577	−	0.121577i
$288$		0			0
$289$	−8.16392	−	14.1403i	−0.480230	−	0.831783i
$290$		0			0
$291$	−2.98535	−	1.00200i	−0.175004	−	0.0587384i
$292$		0			0
$293$	−1.55166	+	2.68756i	−0.0906490	+	0.157009i	−0.907784	−	0.419437i	$-0.862227\pi$
$293$	−1.55166	+	2.68756i	−0.0906490	+	0.157009i	0.817135	+	0.576446i	$0.195561\pi$
$294$		0			0
$295$	0.122011	+	0.211329i	0.00710376	+	0.0123041i
$296$		0			0
$297$	−7.28300	−	10.6610i	−0.422602	−	0.618614i
$298$		0			0
$299$	12.5440	−	21.7269i	0.725440	−	1.25650i
$300$		0			0
$301$	−8.54353	−	6.51754i	−0.492441	−	0.375664i
$302$		0			0
$303$	−1.53157	−	1.73440i	−0.0879862	−	0.0996386i
$304$		0			0
$305$	−0.256069	−	0.147842i	−0.0146625	−	0.00846539i
$306$		0			0
$307$		−	22.1272i		−	1.26286i	−0.775431	−	0.631432i	$-0.782467\pi$
$307$		−	22.1272i		−	1.26286i	0.775431	−	0.631432i	$-0.217533\pi$
$308$		0			0
$309$	9.93707	−	8.77496i	0.565300	−	0.499190i
$310$		0			0
$311$	−4.16625	−	7.21616i	−0.236246	−	0.409191i	0.723388	−	0.690442i	$-0.242584\pi$
$311$	−4.16625	−	7.21616i	−0.236246	−	0.409191i	−0.959634	+	0.281251i	$0.909251\pi$
$312$		0			0
$313$	20.4395	+	11.8007i	1.15531	+	0.667017i	0.950175	−	0.311718i	$-0.100904\pi$
$313$	20.4395	+	11.8007i	1.15531	+	0.667017i	0.205132	+	0.978734i	$0.434238\pi$
$314$		0			0
$315$	−0.111894	−	0.402012i	−0.00630454	−	0.0226508i
$316$		0			0
$317$	14.7979	+	8.54356i	0.831132	+	0.479854i	0.854240	−	0.519879i	$-0.174023\pi$
$317$	14.7979	+	8.54356i	0.831132	+	0.479854i	−0.0231082	+	0.999733i	$0.507356\pi$
$318$		0			0
$319$	8.94786	+	15.4982i	0.500984	+	0.867730i
$320$		0			0
$321$	20.7217	+	6.95501i	1.15657	+	0.388191i
$322$		0			0
$323$			19.5188i			1.08606i
$324$		0			0
$325$	−12.5806	−	7.26344i	−0.697849	−	0.402903i
$326$		0			0
$327$	−17.4043	+	3.52393i	−0.962457	+	0.194874i
$328$		0			0
$329$	0.444581	−	3.45203i	0.0245105	−	0.190316i
$330$		0			0
$331$	−9.68403	+	16.7732i	−0.532283	+	0.921941i	0.467007	+	0.884254i	$0.345332\pi$
$331$	−9.68403	+	16.7732i	−0.532283	+	0.921941i	−0.999290	+	0.0376870i	$0.988001\pi$
$332$		0			0
$333$	4.26069	−	1.79912i	0.233484	−	0.0985914i
$334$		0			0
$335$	−0.365420	−	0.632927i	−0.0199651	−	0.0345805i
$336$		0			0
$337$	4.58170	−	7.93573i	0.249581	−	0.432287i	−0.713829	−	0.700320i	$-0.753040\pi$
$337$	4.58170	−	7.93573i	0.249581	−	0.432287i	0.963410	+	0.268033i	$0.0863738\pi$
$338$		0			0
$339$	−5.33344	−	26.3412i	−0.289673	−	1.43066i
$340$		0			0
$341$	−12.3257	−	21.3488i	−0.667476	−	1.15610i
$342$		0			0
$343$	6.94258	−	17.1698i	0.374864	−	0.927080i
$344$		0			0
$345$	0.589079	−	0.520188i	0.0317149	−	0.0280060i
$346$		0			0
$347$	−11.1297	+	6.42571i	−0.597471	+	0.344950i	−0.768046	−	0.640395i	$-0.778771\pi$
$347$	−11.1297	+	6.42571i	−0.597471	+	0.344950i	0.170575	+	0.985345i	$0.445438\pi$
$348$		0			0
$349$	17.3111	−	9.99458i	0.926643	−	0.534998i	0.0408947	−	0.999163i	$-0.486979\pi$
$349$	17.3111	−	9.99458i	0.926643	−	0.534998i	0.885748	+	0.464166i	$0.153646\pi$
$350$		0			0
$351$	15.0618	−	1.14273i	0.803942	−	0.0609944i
$352$		0			0
$353$	−7.05824			−0.375672			−0.187836	−	0.982200i	$-0.560147\pi$
$353$	−7.05824			−0.375672			−0.187836	+	0.982200i	$0.560147\pi$
$354$		0			0
$355$			0.184725i			0.00980420i
$356$		0			0
$357$	−21.9046	+	14.8348i	−1.15932	+	0.785140i
$358$		0			0
$359$	24.3683	−	14.0690i	1.28611	−	0.742536i	0.308151	−	0.951337i	$-0.400290\pi$
$359$	24.3683	−	14.0690i	1.28611	−	0.742536i	0.977958	+	0.208802i	$0.0669563\pi$
$360$		0			0
$361$	−3.78428	+	6.55457i	−0.199173	+	0.344978i
$362$		0			0
$363$	−5.53283	−	6.26557i	−0.290398	−	0.328857i
$364$		0			0
$365$	−0.355310	−	0.205139i	−0.0185978	−	0.0107374i
$366$		0			0
$367$			36.0898i			1.88387i	0.335793	+	0.941936i	$0.390996\pi$
$367$			36.0898i			1.88387i	−0.335793	+	0.941936i	$0.609004\pi$
$368$		0			0
$369$	1.87788	+	1.42062i	0.0977587	+	0.0739546i
$370$		0			0
$371$	2.15394	+	0.277402i	0.111827	+	0.0144020i
$372$		0			0
$373$	−7.19622			−0.372606			−0.186303	−	0.982492i	$-0.559651\pi$
$373$	−7.19622			−0.372606			−0.186303	+	0.982492i	$0.559651\pi$
$374$		0			0
$375$	−0.602581	−	0.682383i	−0.0311171	−	0.0352381i
$376$		0			0
$377$	−20.9366			−1.07829
$378$		0			0
$379$	−28.1915			−1.44810			−0.724051	−	0.689746i	$-0.757722\pi$
$379$	−28.1915			−1.44810			−0.724051	+	0.689746i	$0.757722\pi$
$380$		0			0
$381$	8.08572	+	9.15654i	0.414244	+	0.469104i
$382$		0			0
$383$	4.41653			0.225674			0.112837	−	0.993614i	$-0.464006\pi$
$383$	4.41653			0.225674			0.112837	+	0.993614i	$0.464006\pi$
$384$		0			0
$385$	0.133164	+	0.318942i	0.00678665	+	0.0162548i
$386$		0			0
$387$	11.2248	−	4.73980i	0.570588	−	0.240937i
$388$		0			0
$389$		−	12.3060i		−	0.623939i	−0.950092	−	0.311970i	$-0.899011\pi$
$389$		−	12.3060i		−	0.623939i	0.950092	−	0.311970i	$-0.100989\pi$
$390$		0			0
$391$	−43.1478	−	24.9114i	−2.18208	−	1.25982i
$392$		0			0
$393$	4.24100	+	4.80265i	0.213930	+	0.242262i
$394$		0			0
$395$	0.394342	−	0.683021i	0.0198415	−	0.0343665i
$396$		0			0
$397$	−0.201000	+	0.116048i	−0.0100879	+	0.00582426i	−0.505035	−	0.863099i	$-0.668521\pi$
$397$	−0.201000	+	0.116048i	−0.0100879	+	0.00582426i	0.494948	+	0.868923i	$0.335187\pi$
$398$		0			0
$399$	15.4541	−	1.10982i	0.773671	−	0.0555605i
$400$		0			0
$401$			34.8761i			1.74163i	0.491609	+	0.870816i	$0.336409\pi$
$401$			34.8761i			1.74163i	−0.491609	+	0.870816i	$0.663591\pi$
$402$		0			0
$403$	28.8404			1.43664
$404$		0			0
$405$	0.458678	+	0.116192i	0.0227919	+	0.00577363i
$406$		0			0
$407$	−3.31744	+	1.91532i	−0.164439	+	0.0949390i
$408$		0			0
$409$	−5.78383	+	3.33930i	−0.285992	+	0.165118i	−0.636133	−	0.771579i	$-0.719467\pi$
$409$	−5.78383	+	3.33930i	−0.285992	+	0.165118i	0.350141	+	0.936697i	$0.386134\pi$
$410$		0			0
$411$	5.31389	−	4.69245i	0.262115	−	0.231462i
$412$		0			0
$413$	−9.76359	−	7.44827i	−0.480435	−	0.366505i
$414$		0			0
$415$	0.165128	+	0.286009i	0.00810580	+	0.0140397i
$416$		0			0
$417$	−4.82635	−	23.8368i	−0.236347	−	1.16729i
$418$		0			0
$419$	−14.8635	+	25.7443i	−0.726128	+	1.25769i	0.232380	+	0.972625i	$0.425349\pi$
$419$	−14.8635	+	25.7443i	−0.726128	+	1.25769i	−0.958508	+	0.285066i	$0.907985\pi$
$420$		0			0
$421$	−15.2147	−	26.3526i	−0.741518	−	1.28435i	−0.951804	−	0.306707i	$-0.900773\pi$
$421$	−15.2147	−	26.3526i	−0.741518	−	1.28435i	0.210286	−	0.977640i	$-0.432560\pi$
$422$		0			0
$423$	3.14740	+	2.38101i	0.153032	+	0.115769i
$424$		0			0
$425$	−14.4246	+	24.9841i	−0.699695	+	1.21191i
$426$		0			0
$427$	14.7582	+	1.90068i	0.714198	+	0.0919804i
$428$		0			0
$429$	−12.2621	+	2.48276i	−0.592018	+	0.119869i
$430$		0			0
$431$	21.8782	+	12.6314i	1.05384	+	0.608432i	0.923721	−	0.383066i	$-0.125132\pi$
$431$	21.8782	+	12.6314i	1.05384	+	0.608432i	0.130115	+	0.991499i	$0.458465\pi$
$432$		0			0
$433$			20.7303i			0.996234i	0.867110	+	0.498117i	$0.165975\pi$
$433$			20.7303i			0.996234i	−0.867110	+	0.498117i	$0.834025\pi$
$434$		0			0
$435$	−0.621751	−	0.208684i	−0.0298107	−	0.0100056i
$436$		0			0
$437$	14.5897	+	25.2700i	0.697918	+	1.20883i
$438$		0			0
$439$	−31.1782	−	18.0007i	−1.48805	−	0.859128i	−0.488146	−	0.872762i	$-0.662327\pi$
$439$	−31.1782	−	18.0007i	−1.48805	−	0.859128i	−0.999907	+	0.0136341i	$0.995660\pi$
$440$		0			0
$441$	12.9909	+	16.4996i	0.618617	+	0.785693i
$442$		0			0
$443$	2.03807	+	1.17668i	0.0968315	+	0.0559057i	0.547634	−	0.836718i	$-0.315529\pi$
$443$	2.03807	+	1.17668i	0.0968315	+	0.0559057i	−0.450802	+	0.892624i	$0.648862\pi$
$444$		0			0
$445$	−0.416975	−	0.722222i	−0.0197665	−	0.0342366i
$446$		0			0
$447$	−9.83315	+	8.68320i	−0.465092	+	0.410701i
$448$		0			0
$449$			31.3789i			1.48086i	0.672132	+	0.740431i	$0.265379\pi$
$449$			31.3789i			1.48086i	−0.672132	+	0.740431i	$0.734621\pi$
$450$		0			0
$451$	−1.68900	−	0.975145i	−0.0795319	−	0.0459178i
$452$		0			0
$453$	14.5467	+	16.4732i	0.683466	+	0.773980i
$454$		0			0
$455$	−0.401043	−	0.0516497i	−0.0188012	−	0.00242137i
$456$		0			0
$457$	−8.99106	+	15.5730i	−0.420584	+	0.728473i	−0.995997	−	0.0893902i	$-0.971508\pi$
$457$	−8.99106	+	15.5730i	−0.420584	+	0.728473i	0.575413	+	0.817863i	$0.304842\pi$
$458$		0			0
$459$	−2.26937	−	29.9116i	−0.105925	−	1.39615i
$460$		0			0
$461$	2.53192	+	4.38541i	0.117923	+	0.204249i	0.918945	−	0.394387i	$-0.129043\pi$
$461$	2.53192	+	4.38541i	0.117923	+	0.204249i	−0.801021	+	0.598636i	$0.795710\pi$
$462$		0			0
$463$	−12.8461	+	22.2501i	−0.597008	+	1.03405i	0.396252	+	0.918142i	$0.370311\pi$
$463$	−12.8461	+	22.2501i	−0.597008	+	1.03405i	−0.993260	+	0.115906i	$0.963023\pi$
$464$		0			0
$465$	0.856466	+	0.287464i	0.0397177	+	0.0133308i
$466$		0			0
$467$	19.1382	+	33.1484i	0.885612	+	1.53392i	0.845011	+	0.534749i	$0.179594\pi$
$467$	19.1382	+	33.1484i	0.885612	+	1.53392i	0.0406007	+	0.999175i	$0.487073\pi$
$468$		0			0
$469$	29.2417	+	22.3074i	1.35026	+	1.03006i
$470$		0			0
$471$	−1.79953	−	0.603993i	−0.0829180	−	0.0278305i
$472$		0			0
$473$	−8.73980	+	5.04592i	−0.401856	+	0.232012i
$474$		0			0
$475$	14.6322	−	8.44793i	0.671373	−	0.387617i
$476$		0			0
$477$	−1.48566	+	1.96386i	−0.0680238	+	0.0899189i
$478$		0			0
$479$	−9.80062			−0.447802			−0.223901	−	0.974612i	$-0.571879\pi$
$479$	−9.80062			−0.447802			−0.223901	+	0.974612i	$0.571879\pi$
$480$		0			0
$481$		−	4.48157i		−	0.204342i
$482$		0			0
$483$	−17.2703	+	35.5788i	−0.785827	+	1.61889i
$484$		0			0
$485$	−0.0827784	+	0.0477921i	−0.00375877	+	0.00217013i
$486$		0			0
$487$	17.3631	−	30.0737i	0.786796	−	1.36277i	−0.141125	−	0.989992i	$-0.545072\pi$
$487$	17.3631	−	30.0737i	0.786796	−	1.36277i	0.927920	−	0.372778i	$-0.121595\pi$
$488$		0			0
$489$	4.88945	−	14.5676i	0.221109	−	0.658768i
$490$		0			0
$491$	23.3641	+	13.4893i	1.05441	+	0.608763i	0.923880	−	0.382682i	$-0.124999\pi$
$491$	23.3641	+	13.4893i	1.05441	+	0.608763i	0.130528	+	0.991445i	$0.458333\pi$
$492$		0			0
$493$			41.5784i			1.87260i
$494$		0			0
$495$	−0.388890	−	0.0484909i	−0.0174793	−	0.00217950i
$496$		0			0
$497$	−3.58166	−	8.57848i	−0.160660	−	0.384798i
$498$		0			0
$499$	4.94545			0.221389			0.110694	−	0.993854i	$-0.464693\pi$
$499$	4.94545			0.221389			0.110694	+	0.993854i	$0.464693\pi$
$500$		0			0
$501$	15.8998	−	3.21932i	0.710352	−	0.143829i
$502$		0			0
$503$	−15.0173			−0.669587			−0.334794	−	0.942291i	$-0.608667\pi$
$503$	−15.0173			−0.669587			−0.334794	+	0.942291i	$0.608667\pi$
$504$		0			0
$505$	−0.0702334			−0.00312534
$506$		0			0
$507$	−2.50733	+	7.47032i	−0.111355	+	0.331769i
$508$		0			0
$509$	24.8594			1.10188			0.550938	−	0.834546i	$-0.314270\pi$
$509$	24.8594			1.10188			0.550938	+	0.834546i	$0.314270\pi$
$510$		0			0
$511$	20.4778	+	2.63730i	0.905884	+	0.116667i
$512$		0			0
$513$	−7.60801	+	15.8356i	−0.335902	+	0.699160i
$514$		0			0
$515$		−	0.402395i		−	0.0177316i
$516$		0			0
$517$	−2.83082	−	1.63438i	−0.124499	−	0.0718798i
$518$		0			0
$519$	38.9347	−	7.88330i	1.70904	−	0.346038i
$520$		0			0
$521$	8.60577	−	14.9056i	0.377025	−	0.653027i	−0.613603	−	0.789615i	$-0.710280\pi$
$521$	8.60577	−	14.9056i	0.377025	−	0.653027i	0.990628	+	0.136588i	$0.0436136\pi$
$522$		0			0
$523$	23.4139	−	13.5180i	1.02382	−	0.591101i	0.108609	−	0.994085i	$-0.465360\pi$
$523$	23.4139	−	13.5180i	1.02382	−	0.591101i	0.915207	+	0.402984i	$0.132027\pi$
$524$		0			0
$525$	20.6014	+	10.0001i	0.899118	+	0.436441i
$526$		0			0
$527$		−	57.2746i		−	2.49492i
$528$		0			0
$529$	−51.4817			−2.23834
$530$		0			0
$531$	12.8277	−	5.41666i	0.556677	−	0.235063i
$532$		0			0
$533$	1.97600	−	1.14085i	0.0855902	−	0.0494155i
$534$		0			0
$535$	0.574574	−	0.331731i	0.0248410	−	0.0143420i
$536$		0			0
$537$	−4.17749	−	20.6321i	−0.180272	−	0.890343i
$538$		0			0
$539$	−12.3680	−	12.2295i	−0.532729	−	0.526761i
$540$		0			0
$541$	19.4779	+	33.7367i	0.837419	+	1.45045i	0.892045	+	0.451946i	$0.149270\pi$
$541$	19.4779	+	33.7367i	0.837419	+	1.45045i	−0.0546263	+	0.998507i	$0.517397\pi$
$542$		0			0
$543$	−31.4038	+	27.7313i	−1.34767	+	1.19006i
$544$		0			0
$545$	−0.269501	+	0.466790i	−0.0115442	+	0.0199951i
$546$		0			0
$547$	−1.14413	−	1.98170i	−0.0489196	−	0.0847313i	0.840529	−	0.541767i	$-0.182244\pi$
$547$	−1.14413	−	1.98170i	−0.0489196	−	0.0847313i	−0.889448	+	0.457036i	$0.848911\pi$
$548$		0			0
$549$	−10.1793	+	13.4558i	−0.434444	+	0.574280i
$550$		0			0
$551$	12.1754	−	21.0885i	0.518691	−	0.898400i
$552$		0			0
$553$	−5.06974	+	39.3649i	−0.215587	+	1.67396i
$554$		0			0
$555$	0.0446696	−	0.133088i	0.00189612	−	0.00564928i
$556$		0			0
$557$	−35.2838	−	20.3711i	−1.49502	−	0.863151i	−0.495038	−	0.868871i	$-0.664846\pi$
$557$	−35.2838	−	20.3711i	−1.49502	−	0.863151i	−0.999984	+	0.00572024i	$0.998179\pi$
$558$		0			0
$559$		−	11.8067i		−	0.499370i
$560$		0			0
$561$	4.93056	+	24.3514i	0.208168	+	1.02812i
$562$		0			0
$563$	−11.7144	−	20.2899i	−0.493701	−	0.855116i	0.506272	−	0.862374i	$-0.331023\pi$
$563$	−11.7144	−	20.2899i	−0.493701	−	0.855116i	−0.999974	+	0.00725772i	$0.997690\pi$
$564$		0			0
$565$	−0.706483	−	0.407888i	−0.0297220	−	0.0171600i
$566$		0			0
$567$	−23.5535	+	3.49751i	−0.989154	+	0.146882i
$568$		0			0
$569$	5.77724	+	3.33549i	0.242195	+	0.139831i	0.616185	−	0.787601i	$-0.288677\pi$
$569$	5.77724	+	3.33549i	0.242195	+	0.139831i	−0.373990	+	0.927433i	$0.622011\pi$
$570$		0			0
$571$	−1.34777	−	2.33441i	−0.0564026	−	0.0976921i	0.836446	−	0.548050i	$-0.184630\pi$
$571$	−1.34777	−	2.33441i	−0.0564026	−	0.0976921i	−0.892848	+	0.450358i	$0.851296\pi$
$572$		0			0
$573$	4.30803	+	21.2768i	0.179970	+	0.888852i
$574$		0			0
$575$			43.1275i			1.79854i
$576$		0			0
$577$	−27.9482	−	16.1359i	−1.16350	−	0.671747i	−0.211359	−	0.977408i	$-0.567789\pi$
$577$	−27.9482	−	16.1359i	−1.16350	−	0.671747i	−0.952140	+	0.305662i	$0.901122\pi$
$578$		0			0
$579$	1.64090	−	4.88887i	0.0681933	−	0.203174i
$580$		0			0
$581$	−13.2139	−	10.0804i	−0.548204	−	0.418204i
$582$		0			0
$583$	1.01979	−	1.76633i	0.0422354	−	0.0731538i
$584$		0			0
$585$	0.276616	−	0.365652i	0.0114367	−	0.0151179i
$586$		0			0
$587$	3.93933	+	6.82313i	0.162594	+	0.281621i	0.935798	−	0.352536i	$-0.114681\pi$
$587$	3.93933	+	6.82313i	0.162594	+	0.281621i	−0.773204	+	0.634157i	$0.781347\pi$
$588$		0			0
$589$	−16.7718	+	29.0495i	−0.691068	+	1.19697i
$590$		0			0
$591$	11.6325	−	10.2721i	0.478497	−	0.422538i
$592$		0			0
$593$	−10.7133	−	18.5559i	−0.439941	−	0.762001i	0.557743	−	0.830014i	$-0.311667\pi$
$593$	−10.7133	−	18.5559i	−0.439941	−	0.762001i	−0.997684	+	0.0680127i	$0.978334\pi$
$594$		0			0
$595$	−0.102572	+	0.796438i	−0.00420504	+	0.0326508i
$596$		0			0
$597$	2.36521	+	11.6815i	0.0968017	+	0.478092i
$598$		0			0
$599$	1.34694	−	0.777655i	0.0550344	−	0.0317741i	−0.472230	−	0.881475i	$-0.656551\pi$
$599$	1.34694	−	0.777655i	0.0550344	−	0.0317741i	0.527265	+	0.849701i	$0.323218\pi$
$600$		0			0
$601$	25.4367	−	14.6859i	1.03758	−	0.599050i	0.118436	−	0.992962i	$-0.462212\pi$
$601$	25.4367	−	14.6859i	1.03758	−	0.599050i	0.919148	+	0.393912i	$0.128879\pi$
$602$		0			0
$603$	−38.4188	+	16.2228i	−1.56454	+	0.660643i
$604$		0			0
$605$	−0.253720			−0.0103152
$606$		0			0
$607$		−	34.4600i		−	1.39869i	−0.714784	−	0.699345i	$-0.753475\pi$
$607$		−	34.4600i		−	1.39869i	0.714784	−	0.699345i	$-0.246525\pi$
$608$		0			0
$609$	32.9198	−	2.36410i	1.33398	−	0.0957983i
$610$		0			0
$611$	3.31185	−	1.91210i	0.133983	−	0.0773552i
$612$		0			0
$613$	−14.9007	+	25.8087i	−0.601832	+	1.04240i	0.390711	+	0.920513i	$0.372229\pi$
$613$	−14.9007	+	25.8087i	−0.601832	+	1.04240i	−0.992544	+	0.121891i	$0.961104\pi$
$614$		0			0
$615$	0.0700522	−	0.0141838i	0.00282478	−	0.000571947i
$616$		0			0
$617$	−10.9008	−	6.29358i	−0.438850	−	0.253370i	0.264260	−	0.964451i	$-0.414872\pi$
$617$	−10.9008	−	6.29358i	−0.438850	−	0.253370i	−0.703110	+	0.711082i	$0.748206\pi$
$618$		0			0
$619$		−	42.8309i		−	1.72152i	−0.509012	−	0.860759i	$-0.669989\pi$
$619$		−	42.8309i		−	1.72152i	0.509012	−	0.860759i	$-0.330011\pi$
$620$		0			0
$621$	−25.2959	−	37.0287i	−1.01509	−	1.48591i
$622$		0			0
$623$	33.3673	+	25.4546i	1.33683	+	1.01982i
$624$		0			0
$625$	24.9585			0.998342
$626$		0			0
$627$	4.63008	−	13.7948i	0.184908	−	0.550912i
$628$		0			0
$629$	−8.90002			−0.354867
$630$		0			0
$631$	21.2015			0.844018			0.422009	−	0.906592i	$-0.361325\pi$
$631$	21.2015			0.844018			0.422009	+	0.906592i	$0.361325\pi$
$632$		0			0
$633$	−18.7187	+	3.79008i	−0.744003	+	0.150642i
$634$		0			0
$635$	0.370788			0.0147143
$636$		0			0
$637$	19.6255	−	5.37731i	0.777592	−	0.213057i
$638$		0			0
$639$	10.4599	+	1.30424i	0.413786	+	0.0515951i
$640$		0			0
$641$		−	12.4565i		−	0.492004i	−0.969269	−	0.246002i	$-0.920883\pi$
$641$		−	12.4565i		−	0.492004i	0.969269	−	0.246002i	$-0.0791170\pi$
$642$		0			0
$643$	4.57692	+	2.64249i	0.180496	+	0.104209i	0.587526	−	0.809205i	$-0.300102\pi$
$643$	4.57692	+	2.64249i	0.180496	+	0.104209i	−0.407030	+	0.913415i	$0.633435\pi$
$644$		0			0
$645$	0.117682	−	0.350621i	0.00463373	−	0.0138057i
$646$		0			0
$647$	17.3799	−	30.1028i	0.683273	−	1.18346i	−0.290704	−	0.956813i	$-0.593889\pi$
$647$	17.3799	−	30.1028i	0.683273	−	1.18346i	0.973976	−	0.226650i	$-0.0727773\pi$
$648$		0			0
$649$	−9.98788	+	5.76651i	−0.392059	+	0.226355i
$650$		0			0
$651$	−45.3473	+	3.25657i	−1.77730	+	0.127635i
$652$		0			0
$653$		−	30.4261i		−	1.19067i	−0.803479	−	0.595333i	$-0.797020\pi$
$653$		−	30.4261i		−	1.19067i	0.803479	−	0.595333i	$-0.202980\pi$
$654$		0			0
$655$	0.194480			0.00759897
$656$		0			0
$657$	−14.1244	+	18.6707i	−0.551045	+	0.728413i
$658$		0			0
$659$	−33.3127	+	19.2331i	−1.29768	+	0.749215i	−0.980003	−	0.198984i	$-0.936236\pi$
$659$	−33.3127	+	19.2331i	−1.29768	+	0.749215i	−0.317676	+	0.948199i	$0.602903\pi$
$660$		0			0
$661$	38.0662	−	21.9775i	1.48060	−	0.854827i	0.480845	−	0.876806i	$-0.340330\pi$
$661$	38.0662	−	21.9775i	1.48060	−	0.854827i	0.999758	+	0.0219789i	$0.00699667\pi$
$662$		0			0
$663$	−27.5567	−	9.24910i	−1.07021	−	0.359205i
$664$		0			0
$665$	0.285246	−	0.373915i	0.0110614	−	0.0144998i
$666$		0			0
$667$	31.0784	+	53.8294i	1.20336	+	2.08428i
$668$		0			0
$669$	−10.5395	−	3.53745i	−0.407479	−	0.136766i
$670$		0			0
$671$	6.98732	−	12.1024i	0.269742	−	0.467208i
$672$		0			0
$673$	−4.65619	−	8.06477i	−0.179483	−	0.310874i	0.762221	−	0.647317i	$-0.224109\pi$
$673$	−4.65619	−	8.06477i	−0.179483	−	0.310874i	−0.941704	+	0.336444i	$0.890776\pi$
$674$		0			0
$675$	−21.4409	+	14.6472i	−0.825261	+	0.563772i
$676$		0			0
$677$	−2.77064	+	4.79889i	−0.106484	+	0.184436i	−0.914344	−	0.404939i	$-0.867293\pi$
$677$	−2.77064	+	4.79889i	−0.106484	+	0.184436i	0.807859	+	0.589375i	$0.200626\pi$
$678$		0			0
$679$	2.91751	−	3.82443i	0.111964	−	0.146768i
$680$		0			0
$681$	−27.7638	−	31.4406i	−1.06391	−	1.20481i
$682$		0			0
$683$	25.8479	+	14.9233i	0.989041	+	0.571023i	0.904988	−	0.425438i	$-0.139880\pi$
$683$	25.8479	+	14.9233i	0.989041	+	0.571023i	0.0840538	+	0.996461i	$0.473213\pi$
$684$		0			0
$685$		−	0.215183i		−	0.00822170i
$686$		0			0
$687$	14.2717	−	12.6026i	0.544498	−	0.480821i
$688$		0			0
$689$	1.19308	+	2.06647i	0.0454526	+	0.0787262i
$690$		0			0
$691$	27.9638	+	16.1449i	1.06379	+	0.614181i	0.926479	−	0.376347i	$-0.122820\pi$
$691$	27.9638	+	16.1449i	1.06379	+	0.614181i	0.137314	+	0.990528i	$0.456153\pi$
$692$		0			0
$693$	18.9999	−	5.28837i	0.721748	−	0.200889i
$694$		0			0
$695$	−0.639313	−	0.369107i	−0.0242505	−	0.0140010i
$696$		0			0
$697$	−2.26562	−	3.92418i	−0.0858167	−	0.148639i
$698$		0			0
$699$	−34.8287	−	11.6899i	−1.31734	−	0.442152i
$700$		0			0
$701$		−	27.6043i		−	1.04260i	−0.853373	−	0.521301i	$-0.825447\pi$
$701$		−	27.6043i		−	1.04260i	0.853373	−	0.521301i	$-0.174553\pi$
$702$		0			0
$703$	4.51407	+	2.60620i	0.170251	+	0.0982947i
$704$		0			0
$705$	0.117410	−	0.0237726i	0.00442191	−	0.000895327i
$706$		0			0
$707$	3.26158	−	1.36176i	0.122664	−	0.0512144i
$708$		0			0
$709$	19.7177	−	34.1520i	0.740514	−	1.28261i	−0.211748	−	0.977324i	$-0.567916\pi$
$709$	19.7177	−	34.1520i	0.740514	−	1.28261i	0.952262	−	0.305283i	$-0.0987510\pi$
$710$		0			0
$711$	−35.8911	−	27.1516i	−1.34602	−	1.01827i
$712$		0			0
$713$	−42.8108	−	74.1504i	−1.60328	−	2.77696i
$714$		0			0
$715$	−0.189875	+	0.328874i	−0.00710094	+	0.0122992i
$716$		0			0
$717$	0.454602	+	2.24522i	0.0169774	+	0.0838494i
$718$		0			0
$719$	−2.51750	−	4.36045i	−0.0938871	−	0.162617i	0.815257	−	0.579100i	$-0.196596\pi$
$719$	−2.51750	−	4.36045i	−0.0938871	−	0.162617i	−0.909144	+	0.416483i	$0.863263\pi$
$720$		0			0
$721$	7.80209	+	18.6869i	0.290565	+	0.695936i
$722$		0			0
$723$	4.80469	−	4.24280i	0.178688	−	0.157791i
$724$		0			0
$725$	31.1691	−	17.9955i	1.15759	−	0.668337i
$726$		0			0
$727$	15.3848	−	8.88245i	0.570592	−	0.329432i	−0.186793	−	0.982399i	$-0.559810\pi$
$727$	15.3848	−	8.88245i	0.570592	−	0.329432i	0.757386	+	0.652968i	$0.226476\pi$
$728$		0			0
$729$	9.81773	−	25.1518i	0.363620	−	0.931548i
$730$		0			0
$731$	−23.4471			−0.867223
$732$		0			0
$733$		−	12.2529i		−	0.452571i	−0.974061	−	0.226285i	$-0.927342\pi$
$733$		−	12.2529i		−	0.452571i	0.974061	−	0.226285i	$-0.0726582\pi$
$734$		0			0
$735$	0.636413	+	0.0359269i	0.0234744	+	0.00132519i
$736$		0			0
$737$	29.9135	−	17.2706i	1.10188	−	0.636169i
$738$		0			0
$739$	−4.09505	+	7.09284i	−0.150639	+	0.260914i	−0.931463	−	0.363837i	$-0.881466\pi$
$739$	−4.09505	+	7.09284i	−0.150639	+	0.260914i	0.780824	+	0.624752i	$0.214800\pi$
$740$		0			0
$741$	11.2683	+	12.7606i	0.413950	+	0.468771i
$742$		0			0
$743$	−20.9393	−	12.0893i	−0.768190	−	0.443514i	0.0640389	−	0.997947i	$-0.479602\pi$
$743$	−20.9393	−	12.0893i	−0.768190	−	0.443514i	−0.832228	+	0.554433i	$0.812935\pi$
$744$		0			0
$745$			0.398187i			0.0145884i
$746$		0			0
$747$	17.3608	−	7.33081i	0.635200	−	0.268220i
$748$		0			0
$749$	−20.2508	+	26.5458i	−0.739947	+	0.969962i
$750$		0			0
$751$	−12.3049			−0.449011			−0.224505	−	0.974473i	$-0.572077\pi$
$751$	−12.3049			−0.449011			−0.224505	+	0.974473i	$0.572077\pi$
$752$		0			0
$753$	30.6030	+	34.6559i	1.11524	+	1.26293i
$754$		0			0
$755$	0.667073			0.0242773
$756$		0			0
$757$	−29.3788			−1.06779			−0.533895	−	0.845551i	$-0.679272\pi$
$757$	−29.3788			−1.06779			−0.533895	+	0.845551i	$0.679272\pi$
$758$		0			0
$759$	24.5852	+	27.8411i	0.892386	+	1.01057i
$760$		0			0
$761$	−24.3381			−0.882254			−0.441127	−	0.897445i	$-0.645421\pi$
$761$	−24.3381			−0.882254			−0.441127	+	0.897445i	$0.645421\pi$
$762$		0			0
$763$	3.46476	−	26.9027i	0.125433	−	0.973944i
$764$		0			0
$765$	−0.726155	−	0.549337i	−0.0262542	−	0.0198613i
$766$		0			0
$767$		−	13.4928i		−	0.487195i
$768$		0			0
$769$	−16.0120	−	9.24453i	−0.577407	−	0.333366i	0.182695	−	0.983170i	$-0.441518\pi$
$769$	−16.0120	−	9.24453i	−0.577407	−	0.333366i	−0.760102	+	0.649803i	$0.774851\pi$
$770$		0			0
$771$	−2.03833	−	2.30828i	−0.0734088	−	0.0831306i
$772$		0			0
$773$	9.77378	−	16.9287i	0.351538	−	0.608882i	−0.634981	−	0.772528i	$-0.718992\pi$
$773$	9.77378	−	16.9287i	0.351538	−	0.608882i	0.986519	+	0.163646i	$0.0523253\pi$
$774$		0			0
$775$	−42.9357	+	24.7890i	−1.54230	+	0.890445i
$776$		0			0
$777$	0.506045	+	7.04660i	0.0181543	+	0.252796i
$778$		0			0
$779$			2.65378i			0.0950815i
$780$		0			0
$781$	−8.73051			−0.312402
$782$		0			0
$783$	−16.2063	+	33.7326i	−0.579168	+	1.20550i
$784$		0			0
$785$	−0.0498977	+	0.0288084i	−0.00178093	+	0.00102822i
$786$		0			0
$787$	16.7519	−	9.67174i	0.597142	−	0.344760i	−0.170774	−	0.985310i	$-0.554627\pi$
$787$	16.7519	−	9.67174i	0.597142	−	0.344760i	0.767916	+	0.640550i	$0.221294\pi$
$788$		0			0
$789$	24.6389	−	21.7575i	0.877168	−	0.774586i
$790$		0			0
$791$	40.7171	+	5.24389i	1.44773	+	0.186451i
$792$		0			0
$793$	8.17463	+	14.1589i	0.290290	+	0.502797i
$794$		0			0
$795$	0.0148332	+	0.0732594i	0.000526079	+	0.00259824i
$796$		0			0
$797$	−4.07573	+	7.05937i	−0.144370	+	0.250056i	−0.929138	−	0.369734i	$-0.879449\pi$
$797$	−4.07573	+	7.05937i	−0.144370	+	0.250056i	0.784768	+	0.619790i	$0.212782\pi$
$798$		0			0
$799$	−3.79726	−	6.57705i	−0.134338	−	0.232679i
$800$		0			0
$801$	−43.8391	+	18.5115i	−1.54898	+	0.654073i
$802$		0			0
$803$	9.69529	−	16.7927i	0.342139	−	0.592603i
$804$		0			0
$805$	0.462515	+	1.10778i	0.0163015	+	0.0390440i
$806$		0			0
$807$	24.3708	−	4.93448i	0.857893	−	0.173702i
$808$		0			0
$809$	5.27457	+	3.04527i	0.185444	+	0.107066i	0.589848	−	0.807514i	$-0.299188\pi$
$809$	5.27457	+	3.04527i	0.185444	+	0.107066i	−0.404404	+	0.914580i	$0.632521\pi$
$810$		0			0
$811$		−	0.909185i		−	0.0319258i	−0.999873	−	0.0159629i	$-0.994919\pi$
$811$		−	0.909185i		−	0.0319258i	0.999873	−	0.0159629i	$-0.00508137\pi$
$812$		0			0
$813$	20.8949	+	7.01316i	0.732817	+	0.245962i
$814$		0			0
$815$	−0.233210	−	0.403932i	−0.00816900	−	0.0141491i
$816$		0			0
$817$	11.8923	+	6.86604i	0.416060	+	0.240212i
$818$		0			0
$819$	−5.75615	+	22.3439i	−0.201136	+	0.780760i
$820$		0			0
$821$	31.0560	+	17.9302i	1.08386	+	0.625768i	0.931936	−	0.362624i	$-0.118119\pi$
$821$	31.0560	+	17.9302i	1.08386	+	0.625768i	0.151926	+	0.988392i	$0.451452\pi$
$822$		0			0
$823$	3.13221	+	5.42514i	0.109182	+	0.189109i	0.915439	−	0.402457i	$-0.131844\pi$
$823$	3.13221	+	5.42514i	0.109182	+	0.189109i	−0.806257	+	0.591565i	$0.798510\pi$
$824$		0			0
$825$	16.1210	−	14.2357i	0.561261	−	0.495623i
$826$		0			0
$827$		−	21.2516i		−	0.738990i	−0.929233	−	0.369495i	$-0.879531\pi$
$827$		−	21.2516i		−	0.738990i	0.929233	−	0.369495i	$-0.120469\pi$
$828$		0			0
$829$	21.3259	+	12.3125i	0.740678	+	0.427631i	0.822316	−	0.569031i	$-0.192682\pi$
$829$	21.3259	+	12.3125i	0.740678	+	0.427631i	−0.0816377	+	0.996662i	$0.526015\pi$
$830$		0			0
$831$	28.6074	+	32.3960i	0.992379	+	1.12380i
$832$		0			0
$833$	−10.6789	−	38.9747i	−0.370001	−	1.35039i
$834$		0			0
$835$	0.246205	−	0.426440i	0.00852029	−	0.0147576i
$836$		0			0
$837$	22.3244	−	46.4668i	0.771643	−	1.60613i
$838$		0			0
$839$	−6.92909	−	12.0015i	−0.239219	−	0.414339i	0.721272	−	0.692652i	$-0.243558\pi$
$839$	−6.92909	−	12.0015i	−0.239219	−	0.414339i	−0.960490	+	0.278313i	$0.910225\pi$
$840$		0			0
$841$	11.4358	−	19.8073i	0.394336	−	0.683011i
$842$		0			0
$843$	−17.3162	−	5.81198i	−0.596400	−	0.200175i
$844$		0			0
$845$	0.119591	+	0.207138i	0.00411407	+	0.00712578i
$846$		0			0
$847$	11.7825	−	4.91941i	0.404853	−	0.169033i
$848$		0			0
$849$	−25.1950	−	8.45642i	−0.864689	−	0.290224i
$850$		0			0
$851$	−11.5224	+	6.65246i	−0.394983	+	0.228043i
$852$		0			0
$853$	6.86165	−	3.96158i	0.234938	−	0.135642i	−0.377910	−	0.925842i	$-0.623357\pi$
$853$	6.86165	−	3.96158i	0.234938	−	0.135642i	0.612848	+	0.790201i	$0.290024\pi$
$854$		0			0
$855$	0.207441	+	0.491263i	0.00709434	+	0.0168008i
$856$		0			0
$857$	−43.7884			−1.49578			−0.747892	−	0.663820i	$-0.768934\pi$
$857$	−43.7884			−1.49578			−0.747892	+	0.663820i	$0.768934\pi$
$858$		0			0
$859$		−	50.4515i		−	1.72138i	−0.509127	−	0.860691i	$-0.670032\pi$
$859$		−	50.4515i		−	1.72138i	0.509127	−	0.860691i	$-0.329968\pi$
$860$		0			0
$861$	−2.97815	+	2.01694i	−0.101495	+	0.0687370i
$862$		0			0
$863$	17.5324	−	10.1223i	0.596810	−	0.344568i	−0.170976	−	0.985275i	$-0.554692\pi$
$863$	17.5324	−	10.1223i	0.596810	−	0.344568i	0.767786	+	0.640707i	$0.221359\pi$
$864$		0			0
$865$	0.602895	−	1.04424i	0.0204990	−	0.0355054i
$866$		0			0
$867$	−8.99874	+	26.8108i	−0.305613	+	0.910541i
$868$		0			0
$869$	32.2810	+	18.6375i	1.09506	+	0.632233i
$870$		0			0
$871$			40.4105i			1.36926i
$872$		0			0
$873$	2.12172	+	5.02467i	0.0718094	+	0.170059i
$874$		0			0
$875$	1.28324	−	0.535773i	0.0433813	−	0.0181124i
$876$		0			0
$877$	44.7832			1.51222			0.756111	−	0.654444i	$-0.227097\pi$
$877$	44.7832			1.51222			0.756111	+	0.654444i	$0.227097\pi$
$878$		0			0
$879$	5.26821	−	1.06668i	0.177692	−	0.0359782i
$880$		0			0
$881$	8.83016			0.297496			0.148748	−	0.988875i	$-0.452476\pi$
$881$	8.83016			0.297496			0.148748	+	0.988875i	$0.452476\pi$
$882$		0			0
$883$	12.5994			0.424005			0.212002	−	0.977269i	$-0.432002\pi$
$883$	12.5994			0.424005			0.212002	+	0.977269i	$0.432002\pi$
$884$		0			0
$885$	0.134488	−	0.400691i	0.00452076	−	0.0134691i
$886$		0			0
$887$	−18.9037			−0.634724			−0.317362	−	0.948304i	$-0.602797\pi$
$887$	−18.9037			−0.634724			−0.317362	+	0.948304i	$0.602797\pi$
$888$		0			0
$889$	−17.2191	+	7.18926i	−0.577510	+	0.241120i
$890$		0			0
$891$	−5.49149	+	21.6781i	−0.183972	+	0.726244i
$892$		0			0
$893$			4.44782i			0.148841i
$894$		0			0
$895$	−0.553363	−	0.319484i	−0.0184969	−	0.0106792i
$896$		0			0
$897$	−42.5896	+	8.62333i	−1.42202	+	0.287925i
$898$		0			0
$899$	−35.7267	+	61.8804i	−1.19155	+	2.06383i
$900$		0			0
$901$	4.10384	−	2.36935i	0.136719	−	0.0789345i
$902$		0			0
$903$	1.33318	+	18.5643i	0.0443654	+	0.617781i
$904$		0			0
$905$			1.27168i			0.0422720i
$906$		0			0
$907$	−12.6413			−0.419747			−0.209873	−	0.977729i	$-0.567305\pi$
$907$	−12.6413			−0.419747			−0.209873	+	0.977729i	$0.567305\pi$
$908$		0			0
$909$	−0.495880	+	3.97689i	−0.0164473	+	0.131905i
$910$		0			0
$911$	−9.36161	+	5.40493i	−0.310164	+	0.179073i	−0.647000	−	0.762490i	$-0.723977\pi$
$911$	−9.36161	+	5.40493i	−0.310164	+	0.179073i	0.336836	+	0.941563i	$0.390643\pi$
$912$		0			0
$913$	−13.5174	+	7.80429i	−0.447361	+	0.258284i
$914$		0			0
$915$	0.101633	+	0.501953i	0.00335988	+	0.0165941i
$916$		0			0
$917$	−9.03150	+	3.77080i	−0.298246	+	0.124523i
$918$		0			0
$919$	7.46198	+	12.9245i	0.246148	+	0.426341i	0.962454	−	0.271446i	$-0.0875017\pi$
$919$	7.46198	+	12.9245i	0.246148	+	0.426341i	−0.716306	+	0.697787i	$0.754168\pi$
$920$		0			0
$921$	−28.7278	+	25.3682i	−0.946615	+	0.835911i
$922$		0			0
$923$	5.10702	−	8.84561i	0.168100	−	0.291157i
$924$		0			0
$925$	3.85201	+	6.67187i	0.126653	+	0.219370i
$926$		0			0
$927$	−22.7852	−	2.84109i	−0.748363	−	0.0933137i
$928$		0			0
$929$	13.2620	−	22.9705i	0.435114	−	0.753639i	−0.562191	−	0.827007i	$-0.690042\pi$
$929$	13.2620	−	22.9705i	0.435114	−	0.753639i	0.997305	+	0.0733684i	$0.0233749\pi$
$930$		0			0
$931$	−5.99668	+	22.8950i	−0.196533	+	0.750353i
$932$		0			0
$933$	−4.59229	+	13.6822i	−0.150345	+	0.447935i
$934$		0			0
$935$	0.653116	+	0.377077i	0.0213592	+	0.0123317i
$936$		0			0
$937$			41.3437i			1.35064i	0.737525	+	0.675320i	$0.235994\pi$
$937$			41.3437i			1.35064i	−0.737525	+	0.675320i	$0.764006\pi$
$938$		0			0
$939$	−8.11235	−	40.0659i	−0.264736	−	1.30750i
$940$		0			0
$941$	−22.6487	−	39.2288i	−0.738328	−	1.27882i	−0.953248	−	0.302189i	$-0.902283\pi$
$941$	−22.6487	−	39.2288i	−0.738328	−	1.27882i	0.214920	−	0.976632i	$-0.431051\pi$
$942$		0			0
$943$	−5.86638	−	3.38695i	−0.191035	−	0.110294i
$944$		0			0
$945$	−0.393650	+	0.606169i	−0.0128054	+	0.0197187i
$946$		0			0
$947$	13.6198	+	7.86340i	0.442584	+	0.255526i	0.704693	−	0.709512i	$-0.251085\pi$
$947$	13.6198	+	7.86340i	0.442584	+	0.255526i	−0.262109	+	0.965038i	$0.584418\pi$
$948$		0			0
$949$	11.3428	+	19.6462i	0.368201	+	0.637744i
$950$		0			0
$951$	−5.87322	−	29.0071i	−0.190452	−	0.940621i
$952$		0			0
$953$			40.0501i			1.29735i	0.761065	+	0.648676i	$0.224677\pi$
$953$			40.0501i			1.29735i	−0.761065	+	0.648676i	$0.775323\pi$
$954$		0			0
$955$	0.570654	+	0.329467i	0.0184659	+	0.0106613i
$956$		0			0
$957$	9.86286	−	29.3853i	0.318821	−	0.949891i
$958$		0			0
$959$	4.17220	+	9.99290i	0.134727	+	0.322687i
$960$		0			0
$961$	33.7138	−	58.3940i	1.08754	−	1.88368i
$962$		0			0
$963$	−14.7271	−	34.8768i	−0.474575	−	1.12389i
$964$		0			0
$965$	−0.0782652	−	0.135559i	−0.00251945	−	0.00436381i
$966$		0			0
$967$	10.9257	−	18.9239i	0.351348	−	0.608553i	−0.635138	−	0.772399i	$-0.719057\pi$
$967$	10.9257	−	18.9239i	0.351348	−	0.608553i	0.986486	+	0.163846i	$0.0523900\pi$
$968$		0			0
$969$	25.3414	−	22.3778i	0.814084	−	0.718879i
$970$		0			0
$971$	−16.2295	−	28.1102i	−0.520828	−	0.902100i	−0.999707	−	0.0242194i	$-0.992290\pi$
$971$	−16.2295	−	28.1102i	−0.520828	−	0.902100i	0.478879	−	0.877881i	$-0.341043\pi$
$972$		0			0
$973$	36.8458	+	4.74531i	1.18122	+	0.152128i
$974$		0			0
$975$	4.99321	+	24.6609i	0.159911	+	0.789780i
$976$		0			0
$977$	46.9485	−	27.1057i	1.50202	−	0.867189i	0.502018	−	0.864857i	$-0.332591\pi$
$977$	46.9485	−	27.1057i	1.50202	−	0.867189i	0.999997	−	0.00233147i	$-0.000742130\pi$
$978$		0			0
$979$	34.1338	−	19.7071i	1.09092	−	0.629843i
$980$		0			0
$981$	24.5286	+	18.5560i	0.783139	+	0.592446i
$982$		0			0
$983$	17.0080			0.542470			0.271235	−	0.962513i	$-0.412568\pi$
$983$	17.0080			0.542470			0.271235	+	0.962513i	$0.412568\pi$
$984$		0			0
$985$		−	0.471050i		−	0.0150089i
$986$		0			0
$987$	−4.99149	+	3.38046i	−0.158881	+	0.107601i
$988$		0			0
$989$	−30.3558	+	17.5259i	−0.965258	+	0.557292i
$990$		0			0
$991$	5.21588	−	9.03416i	0.165688	−	0.286980i	−0.771212	−	0.636579i	$-0.780349\pi$
$991$	5.21588	−	9.03416i	0.165688	−	0.286980i	0.936899	+	0.349599i	$0.113682\pi$
$992$		0			0
$993$	32.8793	−	6.65724i	1.04339	−	0.211261i
$994$		0			0
$995$	0.313303	+	0.180886i	0.00993237	+	0.00573446i
$996$		0			0
$997$			18.0331i			0.571114i	0.958362	+	0.285557i	$0.0921785\pi$
$997$			18.0331i			0.571114i	−0.958362	+	0.285557i	$0.907821\pi$
$998$		0			0
$999$	−7.22058	−	3.46903i	−0.228449	−	0.109755i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cx.a.185.6	yes	48
3.2	odd	2		1512.2.cx.a.17.10		48
4.3	odd	2		1008.2.df.e.689.19		48
7.5	odd	6		504.2.bs.a.257.2	✓	48
9.2	odd	6		504.2.bs.a.353.2	yes	48
9.7	even	3		1512.2.bs.a.521.10		48
12.11	even	2		3024.2.df.e.17.10		48
21.5	even	6		1512.2.bs.a.1097.10		48
28.19	even	6		1008.2.ca.e.257.23		48
36.7	odd	6		3024.2.ca.e.2033.10		48
36.11	even	6		1008.2.ca.e.353.23		48
63.47	even	6	inner	504.2.cx.a.425.6	yes	48
63.61	odd	6		1512.2.cx.a.89.10		48
84.47	odd	6		3024.2.ca.e.2609.10		48
252.47	odd	6		1008.2.df.e.929.19		48
252.187	even	6		3024.2.df.e.1601.10		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.2	✓	48	7.5	odd	6
504.2.bs.a.353.2	yes	48	9.2	odd	6
504.2.cx.a.185.6	yes	48	1.1	even	1	trivial
504.2.cx.a.425.6	yes	48	63.47	even	6	inner
1008.2.ca.e.257.23		48	28.19	even	6
1008.2.ca.e.353.23		48	36.11	even	6
1008.2.df.e.689.19		48	4.3	odd	2
1008.2.df.e.929.19		48	252.47	odd	6
1512.2.bs.a.521.10		48	9.7	even	3
1512.2.bs.a.1097.10		48	21.5	even	6
1512.2.cx.a.17.10		48	3.2	odd	2
1512.2.cx.a.89.10		48	63.61	odd	6
3024.2.ca.e.2033.10		48	36.7	odd	6
3024.2.ca.e.2609.10		48	84.47	odd	6
3024.2.df.e.17.10		48	12.11	even	2
3024.2.df.e.1601.10		48	252.187	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cx (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.14647 - 1.29831i) q^{3} -0.0525740 q^{5} +(2.44149 - 1.01937i) q^{7} +(-0.371197 + 2.97695i) q^{9} +O(q^{10})\)	\(q+(-1.14647 - 1.29831i) q^{3} -0.0525740 q^{5} +(2.44149 - 1.01937i) q^{7} +(-0.371197 + 2.97695i) q^{9} -2.48476i q^{11} +(2.51752 + 1.45349i) q^{13} +(0.0602747 + 0.0682572i) q^{15} +(2.88651 - 4.99959i) q^{17} +(-2.92807 + 1.69052i) q^{19} +(-4.12256 - 2.00113i) q^{21} -8.63028i q^{23} -4.99724 q^{25} +(4.29056 - 2.93106i) q^{27} +(-6.23728 + 3.60109i) q^{29} +(8.59189 - 4.96053i) q^{31} +(-3.22598 + 2.84871i) q^{33} +(-0.128359 + 0.0535922i) q^{35} +(-0.770828 - 1.33511i) q^{37} +(-0.999195 - 4.93490i) q^{39} +(0.392450 - 0.679743i) q^{41} +(-2.03075 - 3.51736i) q^{43} +(0.0195153 - 0.156510i) q^{45} +(0.657760 - 1.13927i) q^{47} +(4.92179 - 4.97755i) q^{49} +(-9.80031 + 1.98432i) q^{51} +(0.710864 + 0.410417i) q^{53} +0.130634i q^{55} +(5.55176 + 1.86339i) q^{57} +(-2.32075 - 4.01965i) q^{59} +(4.87064 + 2.81207i) q^{61} +(2.12832 + 7.64658i) q^{63} +(-0.132356 - 0.0764159i) q^{65} +(6.95059 + 12.0388i) q^{67} +(-11.2047 + 9.89439i) q^{69} -3.51362i q^{71} +(6.75829 + 3.90190i) q^{73} +(5.72920 + 6.48794i) q^{75} +(-2.53288 - 6.06653i) q^{77} +(-7.50070 + 12.9916i) q^{79} +(-8.72443 - 2.21007i) q^{81} +(-3.14086 - 5.44013i) q^{83} +(-0.151756 + 0.262848i) q^{85} +(11.8262 + 3.96934i) q^{87} +(7.93120 + 13.7372i) q^{89} +(7.62815 + 0.982418i) q^{91} +(-16.2907 - 5.46779i) q^{93} +(0.153940 - 0.0888775i) q^{95} +(1.57451 - 0.909044i) q^{97} +(7.39700 + 0.922336i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{9}+O(q^{10}) \) 48 * q + 2 * q^9	\( 48 q + 2 q^{9} + 8 q^{15} - 10 q^{21} + 48 q^{25} + 18 q^{27} + 18 q^{29} + 18 q^{31} + 12 q^{33} - 4 q^{39} - 6 q^{41} - 6 q^{43} - 18 q^{45} + 18 q^{47} - 12 q^{49} + 6 q^{51} - 12 q^{53} + 4 q^{57} + 18 q^{61} - 32 q^{63} - 36 q^{65} - 12 q^{77} + 6 q^{79} + 6 q^{81} - 54 q^{87} - 18 q^{89} + 6 q^{91} + 4 q^{93} - 54 q^{95} - 64 q^{99}+O(q^{100}) \) 48 * q + 2 * q^9 + 8 * q^15 - 10 * q^21 + 48 * q^25 + 18 * q^27 + 18 * q^29 + 18 * q^31 + 12 * q^33 - 4 * q^39 - 6 * q^41 - 6 * q^43 - 18 * q^45 + 18 * q^47 - 12 * q^49 + 6 * q^51 - 12 * q^53 + 4 * q^57 + 18 * q^61 - 32 * q^63 - 36 * q^65 - 12 * q^77 + 6 * q^79 + 6 * q^81 - 54 * q^87 - 18 * q^89 + 6 * q^91 + 4 * q^93 - 54 * q^95 - 64 * q^99

Introduction

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