LMFDB - Embedded newform 504.2.bm.c.107.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(107,504)]

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([3, 3, 3, 2]))

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

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

chi := DirichletCharacter("504.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.bm (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			107.4
Character	$\chi$	$=$	504.107
Dual form			504.2.bm.c.179.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23551 + 0.688125i) q^{2} +(1.05297 - 1.70037i) q^{4} +(0.317795 - 0.550436i) q^{5} +(-2.11900 - 1.58425i) q^{7} +(-0.130884 + 2.82540i) q^{8} +O(q^{10})$	\(q+(-1.23551 + 0.688125i) q^{2} +(1.05297 - 1.70037i) q^{4} +(0.317795 - 0.550436i) q^{5} +(-2.11900 - 1.58425i) q^{7} +(-0.130884 + 2.82540i) q^{8} +(-0.0138692 + 0.898752i) q^{10} +(-3.16457 + 1.82707i) q^{11} -4.15869i q^{13} +(3.70820 + 0.499220i) q^{14} +(-1.78252 - 3.58087i) q^{16} +(-3.01908 + 1.74306i) q^{17} +(-1.99238 + 3.45090i) q^{19} +(-0.601318 - 1.11996i) q^{20} +(2.65261 - 4.43498i) q^{22} +(-1.47015 + 2.54638i) q^{23} +(2.29801 + 3.98028i) q^{25} +(2.86170 + 5.13810i) q^{26} +(-4.92505 + 1.93492i) q^{28} -6.35746 q^{29} +(-5.20467 + 3.00492i) q^{31} +(4.66640 + 3.19760i) q^{32} +(2.53065 - 4.23107i) q^{34} +(-1.54543 + 0.662908i) q^{35} +(-1.59870 - 0.923007i) q^{37} +(0.0869514 - 5.63463i) q^{38} +(1.51361 + 0.969939i) q^{40} -10.4931i q^{41} -2.83895 q^{43} +(-0.225503 + 7.30479i) q^{44} +(0.0641605 - 4.15773i) q^{46} +(4.61494 - 7.99332i) q^{47} +(1.98031 + 6.71404i) q^{49} +(-5.57814 - 3.33635i) q^{50} +(-7.07132 - 4.37897i) q^{52} +(-2.99666 - 5.19038i) q^{53} +2.32253i q^{55} +(4.75348 - 5.77966i) q^{56} +(7.85470 - 4.37473i) q^{58} +(-9.10070 + 5.25429i) q^{59} +(-1.72447 - 0.995622i) q^{61} +(4.36266 - 7.29407i) q^{62} +(-7.96574 - 0.739601i) q^{64} +(-2.28909 - 1.32161i) q^{65} +(-8.01122 - 13.8758i) q^{67} +(-0.215135 + 6.96894i) q^{68} +(1.45324 - 1.88248i) q^{70} -0.737952 q^{71} +(2.13696 + 3.70132i) q^{73} +(2.61035 + 0.0402819i) q^{74} +(3.76990 + 7.02147i) q^{76} +(9.60025 + 1.14192i) q^{77} +(7.74900 + 4.47389i) q^{79} +(-2.53752 - 0.156819i) q^{80} +(7.22055 + 12.9643i) q^{82} +3.67740i q^{83} +2.21574i q^{85} +(3.50755 - 1.95355i) q^{86} +(-4.74800 - 9.18031i) q^{88} +(4.63483 + 2.67592i) q^{89} +(-6.58841 + 8.81226i) q^{91} +(2.78177 + 5.18107i) q^{92} +(-0.201405 + 13.0515i) q^{94} +(1.26633 + 2.19335i) q^{95} +17.6696 q^{97} +(-7.06679 - 6.93257i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q - 8 q^{10} - 28 q^{16} - 32 q^{19} + 32 q^{22} + 4 q^{28} + 112 q^{34} - 36 q^{40} - 160 q^{43} + 40 q^{46} + 56 q^{49} - 36 q^{52} + 12 q^{58} - 24 q^{64} + 92 q^{70} + 16 q^{73} - 120 q^{76} + 20 q^{82} - 100 q^{88} - 32 q^{91} - 20 q^{94} + 240 q^{97}+O(q^{100}) $ 48 * q - 8 * q^10 - 28 * q^16 - 32 * q^19 + 32 * q^22 + 4 * q^28 + 112 * q^34 - 36 * q^40 - 160 * q^43 + 40 * q^46 + 56 * q^49 - 36 * q^52 + 12 * q^58 - 24 * q^64 + 92 * q^70 + 16 * q^73 - 120 * q^76 + 20 * q^82 - 100 * q^88 - 32 * q^91 - 20 * q^94 + 240 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$-1$	$-1$

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 $

$2$	−1.23551	+	0.688125i	−0.873637	+	0.486578i
$2$	−1.23551	+	0.688125i	−0.873637	+	0.486578i
$3$		0			0
$3$		0			0
$4$	1.05297	−	1.70037i	0.526484	−	0.850185i
$5$	0.317795	−	0.550436i	0.142122	−	0.246163i	−0.786173	−	0.618006i	$-0.787941\pi$
$5$	0.317795	−	0.550436i	0.142122	−	0.246163i	0.928296	+	0.371843i	$0.121274\pi$
$6$		0			0
$7$	−2.11900	−	1.58425i	−0.800906	−	0.598790i
$7$	−2.11900	−	1.58425i	−0.800906	−	0.598790i
$8$	−0.130884	+	2.82540i	−0.0462746	+	0.998929i
$9$		0			0
$10$	−0.0138692	+	0.898752i	−0.00438582	+	0.284210i
$11$	−3.16457	+	1.82707i	−0.954155	+	0.550881i	−0.894369	−	0.447330i	$-0.852375\pi$
$11$	−3.16457	+	1.82707i	−0.954155	+	0.550881i	−0.0597855	+	0.998211i	$0.519042\pi$
$12$		0			0
$13$		−	4.15869i		−	1.15341i	−0.816951	−	0.576707i	$-0.804338\pi$
$13$		−	4.15869i		−	1.15341i	0.816951	−	0.576707i	$-0.195662\pi$
$14$	3.70820	+	0.499220i	0.991059	+	0.133422i
$15$		0			0
$16$	−1.78252	−	3.58087i	−0.445629	−	0.895218i
$17$	−3.01908	+	1.74306i	−0.732233	+	0.422755i	−0.819239	−	0.573453i	$-0.805604\pi$
$17$	−3.01908	+	1.74306i	−0.732233	+	0.422755i	0.0870053	+	0.996208i	$0.472270\pi$
$18$		0			0
$19$	−1.99238	+	3.45090i	−0.457083	+	0.791691i	−0.998805	−	0.0488665i	$-0.984439\pi$
$19$	−1.99238	+	3.45090i	−0.457083	+	0.791691i	0.541722	+	0.840558i	$0.317772\pi$
$20$	−0.601318	−	1.11996i	−0.134459	−	0.250431i
$21$		0			0
$22$	2.65261	−	4.43498i	0.565538	−	0.945541i
$23$	−1.47015	+	2.54638i	−0.306548	+	0.530957i	−0.977605	−	0.210449i	$-0.932507\pi$
$23$	−1.47015	+	2.54638i	−0.306548	+	0.530957i	0.671056	+	0.741406i	$0.265841\pi$
$24$		0			0
$25$	2.29801	+	3.98028i	0.459603	+	0.796055i
$26$	2.86170	+	5.13810i	0.561226	+	1.00767i
$27$		0			0
$28$	−4.92505	+	1.93492i	−0.930746	+	0.365665i
$29$	−6.35746			−1.18055			−0.590275	−	0.807202i	$-0.700981\pi$
$29$	−6.35746			−1.18055			−0.590275	+	0.807202i	$0.700981\pi$
$30$		0			0
$31$	−5.20467	+	3.00492i	−0.934787	+	0.539699i	−0.888322	−	0.459221i	$-0.848129\pi$
$31$	−5.20467	+	3.00492i	−0.934787	+	0.539699i	−0.0464645	+	0.998920i	$0.514795\pi$
$32$	4.66640	+	3.19760i	0.824911	+	0.565262i
$33$		0			0
$34$	2.53065	−	4.23107i	0.434003	−	0.725623i
$35$	−1.54543	+	0.662908i	−0.261226	+	0.112052i
$36$		0			0
$37$	−1.59870	−	0.923007i	−0.262824	−	0.151741i	0.362798	−	0.931868i	$-0.381821\pi$
$37$	−1.59870	−	0.923007i	−0.262824	−	0.151741i	−0.625622	+	0.780126i	$0.715155\pi$
$38$	0.0869514	−	5.63463i	0.0141054	−	0.914057i
$39$		0			0
$40$	1.51361	+	0.969939i	0.239322	+	0.153361i
$41$		−	10.4931i		−	1.63874i	−0.573262	−	0.819372i	$-0.694322\pi$
$41$		−	10.4931i		−	1.63874i	0.573262	−	0.819372i	$-0.305678\pi$
$42$		0			0
$43$	−2.83895			−0.432935			−0.216468	−	0.976290i	$-0.569454\pi$
$43$	−2.83895			−0.432935			−0.216468	+	0.976290i	$0.569454\pi$
$44$	−0.225503	+	7.30479i	−0.0339959	+	1.10124i
$45$		0			0
$46$	0.0641605	−	4.15773i	0.00945995	−	0.613024i
$47$	4.61494	−	7.99332i	0.673159	−	1.16595i	−0.303845	−	0.952722i	$-0.598270\pi$
$47$	4.61494	−	7.99332i	0.673159	−	1.16595i	0.977003	−	0.213224i	$-0.0683963\pi$
$48$		0			0
$49$	1.98031	+	6.71404i	0.282901	+	0.959149i
$50$	−5.57814	−	3.33635i	−0.788869	−	0.471831i
$51$		0			0
$52$	−7.07132	−	4.37897i	−0.980615	−	0.607254i
$53$	−2.99666	−	5.19038i	−0.411624	−	0.712953i	0.583444	−	0.812153i	$-0.301705\pi$
$53$	−2.99666	−	5.19038i	−0.411624	−	0.712953i	−0.995067	+	0.0992005i	$0.968371\pi$
$54$		0			0
$55$			2.32253i			0.313170i
$56$	4.75348	−	5.77966i	0.635210	−	0.772339i
$57$		0			0
$58$	7.85470	−	4.37473i	1.03137	−	0.574430i
$59$	−9.10070	+	5.25429i	−1.18481	+	0.684050i	−0.957122	−	0.289684i	$-0.906450\pi$
$59$	−9.10070	+	5.25429i	−1.18481	+	0.684050i	−0.227688	+	0.973734i	$0.573117\pi$
$60$		0			0
$61$	−1.72447	−	0.995622i	−0.220795	−	0.127476i	0.385523	−	0.922698i	$-0.374021\pi$
$61$	−1.72447	−	0.995622i	−0.220795	−	0.127476i	−0.606319	+	0.795222i	$0.707354\pi$
$62$	4.36266	−	7.29407i	0.554059	−	0.926348i
$63$		0			0
$64$	−7.96574	−	0.739601i	−0.995717	−	0.0924501i
$65$	−2.28909	−	1.32161i	−0.283927	−	0.163925i
$66$		0			0
$67$	−8.01122	−	13.8758i	−0.978726	−	1.69520i	−0.667048	−	0.745015i	$-0.732442\pi$
$67$	−8.01122	−	13.8758i	−0.978726	−	1.69520i	−0.311678	−	0.950188i	$-0.600891\pi$
$68$	−0.215135	+	6.96894i	−0.0260890	+	0.845108i
$69$		0			0
$70$	1.45324	−	1.88248i	0.173695	−	0.225000i
$71$	−0.737952			−0.0875788			−0.0437894	−	0.999041i	$-0.513943\pi$
$71$	−0.737952			−0.0875788			−0.0437894	+	0.999041i	$0.513943\pi$
$72$		0			0
$73$	2.13696	+	3.70132i	0.250112	+	0.433207i	0.963557	−	0.267505i	$-0.0861991\pi$
$73$	2.13696	+	3.70132i	0.250112	+	0.433207i	−0.713444	+	0.700712i	$0.752866\pi$
$74$	2.61035	+	0.0402819i	0.303447	+	0.00468267i
$75$		0			0
$76$	3.76990	+	7.02147i	0.432437	+	0.805418i
$77$	9.60025	+	1.14192i	1.09405	+	0.130134i
$78$		0			0
$79$	7.74900	+	4.47389i	0.871830	+	0.503351i	0.867956	−	0.496641i	$-0.165433\pi$
$79$	7.74900	+	4.47389i	0.871830	+	0.503351i	0.00387425	+	0.999992i	$0.498767\pi$
$80$	−2.53752	−	0.156819i	−0.283703	−	0.0175328i
$81$		0			0
$82$	7.22055	+	12.9643i	0.797377	+	1.43167i
$83$			3.67740i			0.403647i	0.979422	+	0.201823i	$0.0646867\pi$
$83$			3.67740i			0.403647i	−0.979422	+	0.201823i	$0.935313\pi$
$84$		0			0
$85$			2.21574i			0.240331i
$86$	3.50755	−	1.95355i	0.378229	−	0.210657i
$87$		0			0
$88$	−4.74800	−	9.18031i	−0.506138	−	0.978624i
$89$	4.63483	+	2.67592i	0.491291	+	0.283647i	0.725110	−	0.688633i	$-0.241789\pi$
$89$	4.63483	+	2.67592i	0.491291	+	0.283647i	−0.233819	+	0.972280i	$0.575122\pi$
$90$		0			0
$91$	−6.58841	+	8.81226i	−0.690653	+	0.923776i
$92$	2.78177	+	5.18107i	0.290019	+	0.540163i
$93$		0			0
$94$	−0.201405	+	13.0515i	−0.0207734	+	1.34616i
$95$	1.26633	+	2.19335i	0.129923	+	0.225033i
$96$		0			0
$97$	17.6696			1.79407			0.897036	−	0.441958i	$-0.145716\pi$
$97$	17.6696			1.79407			0.897036	+	0.441958i	$0.145716\pi$
$98$	−7.06679	−	6.93257i	−0.713854	−	0.700295i
$99$		0			0
$100$	9.18768	+	0.283629i	0.918768	+	0.0283629i
$101$	−6.12560	−	10.6099i	−0.609520	−	1.05572i	−0.991320	−	0.131475i	$-0.958029\pi$
$101$	−6.12560	−	10.6099i	−0.609520	−	1.05572i	0.381799	−	0.924245i	$-0.375305\pi$
$102$		0			0
$103$	−2.71030	−	1.56479i	−0.267054	−	0.154184i	0.360494	−	0.932761i	$-0.382608\pi$
$103$	−2.71030	−	1.56479i	−0.267054	−	0.154184i	−0.627548	+	0.778578i	$0.715941\pi$
$104$	11.7500	+	0.544308i	1.15218	+	0.0533738i
$105$		0			0
$106$	7.27404	+	4.35068i	0.706517	+	0.422575i
$107$	−5.64238	−	3.25763i	−0.545470	−	0.314927i	0.201823	−	0.979422i	$-0.435313\pi$
$107$	−5.64238	−	3.25763i	−0.545470	−	0.314927i	−0.747293	+	0.664495i	$0.768647\pi$
$108$		0			0
$109$	1.23586	−	0.713527i	0.118374	−	0.0683435i	−0.439644	−	0.898172i	$-0.644895\pi$
$109$	1.23586	−	0.713527i	0.118374	−	0.0683435i	0.558018	+	0.829829i	$0.311562\pi$
$110$	−1.59819	−	2.86950i	−0.152381	−	0.273597i
$111$		0			0
$112$	−1.89584	+	10.4118i	−0.179140	+	0.983824i
$113$		−	3.27992i		−	0.308549i	−0.988028	−	0.154275i	$-0.950696\pi$
$113$		−	3.27992i		−	0.308549i	0.988028	−	0.154275i	$-0.0493040\pi$
$114$		0			0
$115$	0.934414	+	1.61845i	0.0871346	+	0.150922i
$116$	−6.69420	+	10.8100i	−0.621541	+	1.00369i
$117$		0			0
$118$	7.62839	−	12.7541i	0.702250	−	1.17411i
$119$	9.15886	+	1.08942i	0.839592	+	0.0998669i
$120$		0			0
$121$	1.17635	−	2.03749i	0.106941	−	0.185226i
$122$	2.81571	+	0.0434509i	0.254922	+	0.00393386i
$123$		0			0
$124$	−0.370878	+	12.0140i	−0.0333058	+	1.07888i
$125$	6.09913			0.545523
$126$		0			0
$127$			19.0629i			1.69156i	0.533535	+	0.845778i	$0.320863\pi$
$127$			19.0629i			1.69156i	−0.533535	+	0.845778i	$0.679137\pi$
$128$	10.3507	−	4.56764i	0.914880	−	0.403726i
$129$		0			0
$130$	3.73763	+	0.0576777i	0.327812	+	0.00505867i
$131$	11.2577	+	6.49965i	0.983591	+	0.567877i	0.903352	−	0.428899i	$-0.141098\pi$
$131$	11.2577	+	6.49965i	0.983591	+	0.567877i	0.0802388	+	0.996776i	$0.474432\pi$
$132$		0			0
$133$	9.68893	−	4.15603i	0.840137	−	0.360373i
$134$	19.4462	+	11.6310i	1.67990	+	1.00477i
$135$		0			0
$136$	−4.52970	−	8.75823i	−0.388418	−	0.751012i
$137$	1.17651	−	0.679257i	0.100516	−	0.0580329i	−0.448899	−	0.893582i	$-0.648184\pi$
$137$	1.17651	−	0.679257i	0.100516	−	0.0580329i	0.549415	+	0.835549i	$0.314851\pi$
$138$		0			0
$139$	−3.06037			−0.259577			−0.129788	−	0.991542i	$-0.541430\pi$
$139$	−3.06037			−0.259577			−0.129788	+	0.991542i	$0.541430\pi$
$140$	−0.500104	+	3.32583i	−0.0422665	+	0.281084i
$141$		0			0
$142$	0.911747	−	0.507803i	0.0765121	−	0.0426139i
$143$	7.59821	+	13.1605i	0.635394	+	1.10053i
$144$		0			0
$145$	−2.02037	+	3.49938i	−0.167782	+	0.290607i
$146$	−5.18721	−	3.10253i	−0.429297	−	0.256767i
$147$		0			0
$148$	−3.25283	+	1.74648i	−0.267381	+	0.143560i
$149$	−8.15986	+	14.1333i	−0.668481	+	1.15784i	0.309847	+	0.950786i	$0.399722\pi$
$149$	−8.15986	+	14.1333i	−0.668481	+	1.15784i	−0.978329	+	0.207057i	$0.933611\pi$
$150$		0			0
$151$	−7.81057	+	4.50943i	−0.635615	+	0.366972i	−0.782923	−	0.622118i	$-0.786272\pi$
$151$	−7.81057	+	4.50943i	−0.635615	+	0.366972i	0.147309	+	0.989091i	$0.452939\pi$
$152$	−9.48939	−	6.08093i	−0.769692	−	0.493229i
$153$		0			0
$154$	−12.6470	+	5.19532i	−1.01912	+	0.418651i
$155$			3.81979i			0.306813i
$156$		0			0
$157$	20.0104	−	11.5530i	1.59700	−	0.922031i	0.604944	−	0.796268i	$-0.293196\pi$
$157$	20.0104	−	11.5530i	1.59700	−	0.922031i	0.992060	−	0.125763i	$-0.0401378\pi$
$158$	−12.6526	−	0.195249i	−1.00658	−	0.0155332i
$159$		0			0
$160$	3.24304	−	1.55238i	0.256384	−	0.122726i
$161$	7.14936	−	3.06669i	0.563449	−	0.241689i
$162$		0			0
$163$	6.10214	−	10.5692i	0.477956	−	0.827845i	−0.521724	−	0.853114i	$-0.674711\pi$
$163$	6.10214	−	10.5692i	0.477956	−	0.827845i	0.999681	+	0.0252693i	$0.00804434\pi$
$164$	−17.8421	−	11.0489i	−1.39324	−	0.862773i
$165$		0			0
$166$	−2.53051	−	4.54346i	−0.196406	−	0.352641i
$167$	−3.33534			−0.258096			−0.129048	−	0.991638i	$-0.541192\pi$
$167$	−3.33534			−0.258096			−0.129048	+	0.991638i	$0.541192\pi$
$168$		0			0
$169$	−4.29472			−0.330363
$170$	−1.52471	−	2.73757i	−0.116940	−	0.209962i
$171$		0			0
$172$	−2.98932	+	4.82726i	−0.227934	+	0.368075i
$173$	4.79217	−	8.30028i	0.364342	−	0.631058i	−0.624329	−	0.781162i	$-0.714627\pi$
$173$	4.79217	−	8.30028i	0.364342	−	0.631058i	0.988670	+	0.150104i	$0.0479607\pi$
$174$		0			0
$175$	1.43626	−	12.0748i	0.108571	−	0.912771i
$176$	12.1834	+	8.07514i	0.918358	+	0.608687i
$177$		0			0
$178$	−7.56774	−	0.116782i	−0.567226	−	0.00875321i
$179$	0.0283182	−	0.0163495i	0.00211660	−	0.00122202i	−0.498941	−	0.866636i	$-0.666278\pi$
$179$	0.0283182	−	0.0163495i	0.00211660	−	0.00122202i	0.501058	+	0.865414i	$0.332944\pi$
$180$		0			0
$181$			19.3654i			1.43942i	0.694277	+	0.719708i	$0.255724\pi$
$181$			19.3654i			1.43942i	−0.694277	+	0.719708i	$0.744276\pi$
$182$	2.07610	−	15.4213i	0.153891	−	1.14310i
$183$		0			0
$184$	−7.00212	−	4.48705i	−0.516203	−	0.330790i
$185$	−1.01611	+	0.586653i	−0.0747061	+	0.0431316i
$186$		0			0
$187$	6.36939	−	11.0321i	0.465776	−	0.806747i
$188$	−8.73221	−	16.2638i	−0.636862	−	1.18616i
$189$		0			0
$190$	−3.07387	−	1.83851i	−0.223002	−	0.133380i
$191$	1.50826	−	2.61239i	0.109134	−	0.189026i	−0.806286	−	0.591526i	$-0.798526\pi$
$191$	1.50826	−	2.61239i	0.109134	−	0.189026i	0.915420	+	0.402501i	$0.131859\pi$
$192$		0			0
$193$	−10.9565	−	18.9772i	−0.788666	−	1.36601i	−0.926785	−	0.375593i	$-0.877439\pi$
$193$	−10.9565	−	18.9772i	−0.788666	−	1.36601i	0.138119	−	0.990416i	$-0.455894\pi$
$194$	−21.8309	+	12.1589i	−1.56737	+	0.872955i
$195$		0			0
$196$	13.5016	+	3.70242i	0.964397	+	0.264458i
$197$	−15.2950			−1.08972			−0.544860	−	0.838527i	$-0.683417\pi$
$197$	−15.2950			−1.08972			−0.544860	+	0.838527i	$0.683417\pi$
$198$		0			0
$199$	2.77706	−	1.60334i	0.196861	−	0.113658i	−0.398330	−	0.917242i	$-0.630410\pi$
$199$	2.77706	−	1.60334i	0.196861	−	0.113658i	0.595190	+	0.803585i	$0.297077\pi$
$200$	−11.5466	+	5.97184i	−0.816470	+	0.422273i
$201$		0			0
$202$	14.8691	+	8.89340i	1.04619	+	0.625737i
$203$	13.4715	+	10.0718i	0.945510	+	0.706902i
$204$		0			0
$205$	−5.77577	−	3.33464i	−0.403398	−	0.232902i
$206$	4.42538	+	0.0682907i	0.308330	+	0.00475804i
$207$		0			0
$208$	−14.8917	+	7.41294i	−1.03256	+	0.513995i
$209$		−	14.5608i		−	1.00719i
$210$		0			0
$211$	−16.7059			−1.15008			−0.575040	−	0.818125i	$-0.695014\pi$
$211$	−16.7059			−1.15008			−0.575040	+	0.818125i	$0.695014\pi$
$212$	−11.9810	−	0.369859i	−0.822855	−	0.0254020i
$213$		0			0
$214$	9.21287	+	0.142169i	0.629779	+	0.00971851i
$215$	−0.902202	+	1.56266i	−0.0615297	+	0.106573i
$216$		0			0
$217$	15.7892	+	1.87808i	1.07184	+	0.127492i
$218$	−1.03593	+	1.73200i	−0.0701618	+	0.117306i
$219$		0			0
$220$	3.94916	+	2.44555i	0.266252	+	0.164879i
$221$	7.24887	+	12.5554i	0.487611	+	0.844568i
$222$		0			0
$223$		−	19.1547i		−	1.28270i	−0.767250	−	0.641348i	$-0.778375\pi$
$223$		−	19.1547i		−	1.28270i	0.767250	−	0.641348i	$-0.221625\pi$
$224$	−4.82230	−	14.1685i	−0.322203	−	0.946670i
$225$		0			0
$226$	2.25700	+	4.05237i	0.150133	+	0.269560i
$227$	14.4962	−	8.36938i	0.962147	−	0.555496i	0.0653135	−	0.997865i	$-0.479195\pi$
$227$	14.4962	−	8.36938i	0.962147	−	0.555496i	0.896833	+	0.442369i	$0.145862\pi$
$228$		0			0
$229$	−17.5029	−	10.1053i	−1.15662	−	0.667777i	−0.206131	−	0.978524i	$-0.566087\pi$
$229$	−17.5029	−	10.1053i	−1.15662	−	0.667777i	−0.950492	+	0.310747i	$0.899421\pi$
$230$	−2.26818	−	1.35662i	−0.149559	−	0.0894529i
$231$		0			0
$232$	0.832093	−	17.9624i	0.0546296	−	1.17929i
$233$	17.3998	+	10.0458i	1.13990	+	0.658122i	0.946406	−	0.322979i	$-0.104684\pi$
$233$	17.3998	+	10.0458i	1.13990	+	0.658122i	0.193495	+	0.981101i	$0.438018\pi$
$234$		0			0
$235$	−2.93321	−	5.08047i	−0.191341	−	0.331413i
$236$	−0.648503	+	21.0072i	−0.0422140	+	1.36745i
$237$		0			0
$238$	−12.0655	+	4.95646i	−0.782091	+	0.321279i
$239$	−13.2312			−0.855855			−0.427928	−	0.903813i	$-0.640756\pi$
$239$	−13.2312			−0.855855			−0.427928	+	0.903813i	$0.640756\pi$
$240$		0			0
$241$	−5.90444	−	10.2268i	−0.380338	−	0.658765i	0.610772	−	0.791806i	$-0.290859\pi$
$241$	−5.90444	−	10.2268i	−0.380338	−	0.658765i	−0.991111	+	0.133041i	$0.957526\pi$
$242$	−0.0513381	+	3.32681i	−0.00330014	+	0.213856i
$243$		0			0
$244$	−3.50873	+	1.88388i	−0.224624	+	0.120603i
$245$	4.32498	+	1.04365i	0.276313	+	0.0666766i
$246$		0			0
$247$	14.3512	+	8.28569i	0.913147	+	0.527206i
$248$	−7.80888	−	15.0986i	−0.495864	−	0.958760i
$249$		0			0
$250$	−7.53553	+	4.19696i	−0.476589	+	0.265439i
$251$		−	18.9939i		−	1.19888i	−0.800419	−	0.599441i	$-0.795390\pi$
$251$		−	18.9939i		−	1.19888i	0.800419	−	0.599441i	$-0.204610\pi$
$252$		0			0
$253$		−	10.7443i		−	0.675487i
$254$	−13.1176	−	23.5524i	−0.823074	−	1.47781i
$255$		0			0
$256$	−9.64526	+	12.7659i	−0.602829	+	0.797871i
$257$	22.5458	+	13.0168i	1.40637	+	0.811966i	0.995036	−	0.0995204i	$-0.0317308\pi$
$257$	22.5458	+	13.0168i	1.40637	+	0.811966i	0.411331	+	0.911486i	$0.365064\pi$
$258$		0			0
$259$	1.92536	+	4.48858i	0.119636	+	0.278907i
$260$	−4.65757	+	2.50070i	−0.288850	+	0.155087i
$261$		0			0
$262$	−18.3816	−	0.283658i	−1.13562	−	0.0175244i
$263$	−13.3095	−	23.0527i	−0.820698	−	1.42149i	−0.905163	−	0.425064i	$-0.860251\pi$
$263$	−13.3095	−	23.0527i	−0.820698	−	1.42149i	0.0844650	−	0.996426i	$-0.473082\pi$
$264$		0			0
$265$	−3.80929			−0.234003
$266$	−9.11090	+	11.8020i	−0.558625	+	0.723628i
$267$		0			0
$268$	−32.0296	−	0.988772i	−1.95652	−	0.0603989i
$269$	12.6453	+	21.9022i	0.770995	+	1.33540i	0.937018	+	0.349281i	$0.113574\pi$
$269$	12.6453	+	21.9022i	0.770995	+	1.33540i	−0.166022	+	0.986122i	$0.553092\pi$
$270$		0			0
$271$	−14.4561	−	8.34622i	−0.878145	−	0.506997i	−0.00809834	−	0.999967i	$-0.502578\pi$
$271$	−14.4561	−	8.34622i	−0.878145	−	0.506997i	−0.870046	+	0.492970i	$0.835911\pi$
$272$	11.6232	+	7.70387i	0.704762	+	0.467116i
$273$		0			0
$274$	−0.986173	+	1.64881i	−0.0595769	+	0.0996085i
$275$	−14.5445	−	8.39725i	−0.877064	−	0.506373i
$276$		0			0
$277$	−23.0279	+	13.2952i	−1.38361	+	0.798830i	−0.992585	−	0.121549i	$-0.961214\pi$
$277$	−23.0279	+	13.2952i	−1.38361	+	0.798830i	−0.391029	+	0.920379i	$0.627881\pi$
$278$	3.78111	−	2.10591i	0.226776	−	0.126304i
$279$		0			0
$280$	−1.67070	−	4.45323i	−0.0998437	−	0.266131i
$281$		−	8.11615i		−	0.484169i	−0.970255	−	0.242085i	$-0.922169\pi$
$281$		−	8.11615i		−	0.484169i	0.970255	−	0.242085i	$-0.0778311\pi$
$282$		0			0
$283$	4.12929	+	7.15214i	0.245461	+	0.425150i	0.962261	−	0.272128i	$-0.0877274\pi$
$283$	4.12929	+	7.15214i	0.245461	+	0.425150i	−0.716800	+	0.697278i	$0.754394\pi$
$284$	−0.777040	+	1.25479i	−0.0461088	+	0.0744582i
$285$		0			0
$286$	−18.4437	−	11.0314i	−1.09060	−	0.652299i
$287$	−16.6237	+	22.2348i	−0.981264	+	1.31248i
$288$		0			0
$289$	−2.42346	+	4.19755i	−0.142556	+	0.246915i
$290$	0.0881728	−	5.71378i	0.00517769	−	0.335525i
$291$		0			0
$292$	8.54377	+	0.263751i	0.499987	+	0.0154349i
$293$	−20.9952			−1.22655			−0.613277	−	0.789868i	$-0.710149\pi$
$293$	−20.9952			−1.22655			−0.613277	+	0.789868i	$0.710149\pi$
$294$		0			0
$295$			6.67914i			0.388875i
$296$	2.81711	−	4.39614i	0.163741	−	0.255521i
$297$		0			0
$298$	0.356112	−	23.0768i	0.0206290	−	1.33680i
$299$	10.5896	+	6.11392i	0.612414	+	0.353577i
$300$		0			0
$301$	6.01572	+	4.49760i	0.346741	+	0.259237i
$302$	6.54698	−	10.9461i	0.376736	−	0.629877i
$303$		0			0
$304$	15.9087	+	0.983157i	0.912425	+	0.0563879i
$305$	−1.09605	+	0.632806i	−0.0627598	+	0.0362344i
$306$		0			0
$307$	18.1231			1.03434			0.517170	−	0.855882i	$-0.326985\pi$
$307$	18.1231			1.03434			0.517170	+	0.855882i	$0.326985\pi$
$308$	12.0504	−	15.1216i	0.686638	−	0.861632i
$309$		0			0
$310$	−2.62849	−	4.71938i	−0.149288	−	0.268043i
$311$	15.4208	+	26.7096i	0.874433	+	1.51456i	0.857366	+	0.514707i	$0.172099\pi$
$311$	15.4208	+	26.7096i	0.874433	+	1.51456i	0.0170667	+	0.999854i	$0.494567\pi$
$312$		0			0
$313$	0.521916	−	0.903984i	0.0295004	−	0.0510962i	−0.850898	−	0.525330i	$-0.823942\pi$
$313$	0.521916	−	0.903984i	0.0295004	−	0.0510962i	0.880399	+	0.474234i	$0.157275\pi$
$314$	−16.7731	+	28.0435i	−0.946562	+	1.58259i
$315$		0			0
$316$	15.7667	−	8.46531i	0.886946	−	0.476211i
$317$	−5.12901	+	8.88370i	−0.288074	+	0.498958i	−0.973350	−	0.229325i	$-0.926348\pi$
$317$	−5.12901	+	8.88370i	−0.288074	+	0.498958i	0.685276	+	0.728283i	$0.259681\pi$
$318$		0			0
$319$	20.1186	−	11.6155i	1.12643	−	0.650344i
$320$	−2.93857	+	4.14959i	−0.164271	+	0.231969i
$321$		0			0
$322$	−6.72284	+	8.70858i	−0.374649	+	0.485310i
$323$		−	13.8914i		−	0.772937i
$324$		0			0
$325$	16.5527	−	9.55673i	0.918181	−	0.530112i
$326$	−0.266310	+	17.2574i	−0.0147495	+	0.955799i
$327$		0			0
$328$	29.6471	+	1.37338i	1.63699	+	0.0758323i
$329$	−22.4425	+	9.62660i	−1.23729	+	0.530732i
$330$		0			0
$331$	2.31756	−	4.01414i	0.127385	−	0.220637i	−0.795278	−	0.606245i	$-0.792675\pi$
$331$	2.31756	−	4.01414i	0.127385	−	0.220637i	0.922663	+	0.385608i	$0.126008\pi$
$332$	6.25293	+	3.87218i	0.343174	+	0.212513i
$333$		0			0
$334$	4.12085	−	2.29513i	0.225483	−	0.125584i
$335$	−10.1837			−0.556394
$336$		0			0
$337$	−33.0263			−1.79906			−0.899528	−	0.436863i	$-0.856089\pi$
$337$	−33.0263			−1.79906			−0.899528	+	0.436863i	$0.856089\pi$
$338$	5.30616	−	2.95530i	0.288617	−	0.160747i
$339$		0			0
$340$	3.76759	+	2.33311i	0.204326	+	0.126531i
$341$	10.9804	−	19.0186i	0.594621	−	1.02991i
$342$		0			0
$343$	6.44045	−	17.3643i	0.347752	−	0.937587i
$344$	0.371574	−	8.02115i	0.0200339	−	0.432472i
$345$		0			0
$346$	−0.209140	+	13.5527i	−0.0112434	+	0.728597i
$347$	3.47551	−	2.00659i	0.186575	−	0.107719i	−0.403803	−	0.914846i	$-0.632312\pi$
$347$	3.47551	−	2.00659i	0.186575	−	0.107719i	0.590378	+	0.807127i	$0.298979\pi$
$348$		0			0
$349$			10.4671i			0.560291i	0.959958	+	0.280145i	$0.0903826\pi$
$349$			10.4671i			0.560291i	−0.959958	+	0.280145i	$0.909617\pi$
$350$	6.53447	+	15.9069i	0.349282	+	0.850259i
$351$		0			0
$352$	−20.6094	−	1.59322i	−1.09849	−	0.0849188i
$353$	−15.3486	+	8.86154i	−0.816925	+	0.471652i	−0.849355	−	0.527822i	$-0.823009\pi$
$353$	−15.3486	+	8.86154i	−0.816925	+	0.471652i	0.0324298	+	0.999474i	$0.489675\pi$
$354$		0			0
$355$	−0.234517	+	0.406196i	−0.0124469	+	0.0215586i
$356$	9.43037	−	5.06326i	0.499809	−	0.268352i
$357$		0			0
$358$	−0.0237369	+	0.0396865i	−0.00125453	+	0.00209750i
$359$	6.52933	−	11.3091i	0.344605	−	0.596873i	−0.640677	−	0.767811i	$-0.721346\pi$
$359$	6.52933	−	11.3091i	0.344605	−	0.596873i	0.985282	+	0.170937i	$0.0546795\pi$
$360$		0			0
$361$	1.56085	+	2.70348i	0.0821503	+	0.142288i
$362$	−13.3258	−	23.9261i	−0.700388	−	1.25753i
$363$		0			0
$364$	8.04673	+	20.4818i	0.421763	+	1.07354i
$365$	2.71646			0.142186
$366$		0			0
$367$	−19.3899	+	11.1948i	−1.01215	+	0.584363i	−0.911819	−	0.410592i	$-0.865322\pi$
$367$	−19.3899	+	11.1948i	−1.01215	+	0.584363i	−0.100327	+	0.994955i	$0.531989\pi$
$368$	11.7388	+	0.725461i	0.611929	+	0.0378173i
$369$		0			0
$370$	0.851727	−	1.42403i	0.0442792	−	0.0740317i
$371$	−1.87292	+	15.7459i	−0.0972373	+	0.817484i
$372$		0			0
$373$	−3.83798	−	2.21586i	−0.198723	−	0.114733i	0.397337	−	0.917673i	$-0.369935\pi$
$373$	−3.83798	−	2.21586i	−0.198723	−	0.114733i	−0.596060	+	0.802940i	$0.703268\pi$
$374$	−0.277973	+	18.0132i	−0.0143736	+	0.931441i
$375$		0			0
$376$	21.9803	+	14.0853i	1.13355	+	0.726391i
$377$			26.4387i			1.36166i
$378$		0			0
$379$	28.8901			1.48399			0.741993	−	0.670407i	$-0.233881\pi$
$379$	28.8901			1.48399			0.741993	+	0.670407i	$0.233881\pi$
$380$	5.06292	+	0.156295i	0.259723	+	0.00801779i
$381$		0			0
$382$	−0.0658237	+	4.26551i	−0.00336783	+	0.218242i
$383$	16.3811	−	28.3729i	0.837037	−	1.44979i	−0.0553247	−	0.998468i	$-0.517619\pi$
$383$	16.3811	−	28.3729i	0.837037	−	1.44979i	0.892361	−	0.451322i	$-0.149047\pi$
$384$		0			0
$385$	3.67946	−	4.92143i	0.187523	−	0.250819i
$386$	26.5955	+	15.9071i	1.35368	+	0.809649i
$387$		0			0
$388$	18.6055	−	30.0448i	0.944550	−	1.52529i
$389$	−6.24881	−	10.8233i	−0.316827	−	0.548761i	0.662997	−	0.748622i	$-0.269284\pi$
$389$	−6.24881	−	10.8233i	−0.316827	−	0.548761i	−0.979824	+	0.199861i	$0.935951\pi$
$390$		0			0
$391$		−	10.2503i		−	0.518380i
$392$	−19.2290	+	4.71639i	−0.971213	+	0.238214i
$393$		0			0
$394$	18.8971	−	10.5248i	0.952020	−	0.530234i
$395$	4.92518	−	2.84355i	0.247813	−	0.143075i
$396$		0			0
$397$	−6.09678	−	3.51998i	−0.305989	−	0.176663i	0.339141	−	0.940735i	$-0.389863\pi$
$397$	−6.09678	−	3.51998i	−0.305989	−	0.176663i	−0.645130	+	0.764073i	$0.723197\pi$
$398$	−2.32779	+	3.89191i	−0.116682	+	0.195084i
$399$		0			0
$400$	10.1566	−	15.3238i	0.507830	−	0.766190i
$401$	−25.7480	−	14.8656i	−1.28579	−	0.742353i	−0.307893	−	0.951421i	$-0.599624\pi$
$401$	−25.7480	−	14.8656i	−1.28579	−	0.742353i	−0.977901	+	0.209068i	$0.932957\pi$
$402$		0			0
$403$	12.4965	+	21.6446i	0.622497	+	1.07820i
$404$	−24.4907	−	0.756043i	−1.21846	−	0.0376146i
$405$		0			0
$406$	−23.5748	−	3.17377i	−1.17000	−	0.157512i
$407$	6.74558			0.334366
$408$		0			0
$409$	−16.6222	−	28.7905i	−0.821914	−	1.42360i	−0.904255	−	0.426993i	$-0.859573\pi$
$409$	−16.6222	−	28.7905i	−0.821914	−	1.42360i	0.0823411	−	0.996604i	$-0.473760\pi$
$410$	9.43068	+	0.145531i	0.465748	+	0.00718724i
$411$		0			0
$412$	−5.51459	+	2.96084i	−0.271684	+	0.145870i
$413$	27.6085	+	3.28394i	1.35852	+	0.161592i
$414$		0			0
$415$	2.02417	+	1.16866i	0.0993627	+	0.0573671i
$416$	13.2979	−	19.4061i	0.651981	−	0.951464i
$417$		0			0
$418$	10.0197	+	17.9901i	0.490078	+	0.879922i
$419$			8.95024i			0.437248i	0.975809	+	0.218624i	$0.0701568\pi$
$419$			8.95024i			0.437248i	−0.975809	+	0.218624i	$0.929843\pi$
$420$		0			0
$421$			26.3473i			1.28409i	0.766667	+	0.642044i	$0.221914\pi$
$421$			26.3473i			1.28409i	−0.766667	+	0.642044i	$0.778086\pi$
$422$	20.6403	−	11.4957i	1.00475	−	0.559604i
$423$		0			0
$424$	15.0571	−	7.78743i	0.731237	−	0.378191i
$425$	−13.8758	−	8.01117i	−0.673073	−	0.388599i
$426$		0			0
$427$	2.07683	+	4.84171i	0.100505	+	0.234307i
$428$	−11.4804	+	6.16396i	−0.554927	+	0.297946i
$429$		0			0
$430$	0.0393739	−	2.55151i	0.00189878	−	0.123045i
$431$	−7.97354	−	13.8106i	−0.384072	−	0.665232i	0.607568	−	0.794268i	$-0.292145\pi$
$431$	−7.97354	−	13.8106i	−0.384072	−	0.665232i	−0.991640	+	0.129036i	$0.958812\pi$
$432$		0			0
$433$	12.5058			0.600991			0.300496	−	0.953783i	$-0.402848\pi$
$433$	12.5058			0.600991			0.300496	+	0.953783i	$0.402848\pi$
$434$	−20.8001	+	8.54458i	−0.998437	+	0.410153i
$435$		0			0
$436$	0.0880660	−	2.85275i	0.00421760	−	0.136622i
$437$	−5.85821	−	10.1467i	−0.280236	−	0.485383i
$438$		0			0
$439$	14.0552	+	8.11479i	0.670820	+	0.387298i	0.796387	−	0.604787i	$-0.206742\pi$
$439$	14.0552	+	8.11479i	0.670820	+	0.387298i	−0.125568	+	0.992085i	$0.540075\pi$
$440$	−6.56206	−	0.303983i	−0.312834	−	0.0144918i
$441$		0			0
$442$	−17.5957	−	10.5242i	−0.836944	−	0.500585i
$443$	5.80303	+	3.35038i	0.275710	+	0.159181i	0.631480	−	0.775392i	$-0.282448\pi$
$443$	5.80303	+	3.35038i	0.275710	+	0.159181i	−0.355769	+	0.934574i	$0.615781\pi$
$444$		0			0
$445$	2.94584	−	1.70078i	0.139646	−	0.0806249i
$446$	13.1809	+	23.6659i	0.624132	+	1.12061i
$447$		0			0
$448$	15.7077	+	14.1869i	0.742118	+	0.670269i
$449$			26.1155i			1.23246i	0.787565	+	0.616232i	$0.211342\pi$
$449$			26.1155i			1.23246i	−0.787565	+	0.616232i	$0.788658\pi$
$450$		0			0
$451$	19.1716	+	33.2061i	0.902754	+	1.56362i
$452$	−5.57708	−	3.45365i	−0.262324	−	0.162446i
$453$		0			0
$454$	−12.1510	+	20.3157i	−0.570275	+	0.953461i
$455$	2.75683	+	6.42699i	0.129242	+	0.301302i
$456$		0			0
$457$	−16.0328	+	27.7697i	−0.749984	+	1.29901i	0.197846	+	0.980233i	$0.436606\pi$
$457$	−16.0328	+	27.7697i	−0.749984	+	1.29901i	−0.947830	+	0.318777i	$0.896728\pi$
$458$	28.5787	+	0.441015i	1.33539	+	0.0206073i
$459$		0			0
$460$	3.73588	+	0.115329i	0.174186	+	0.00537723i
$461$	39.2781			1.82936			0.914682	−	0.404175i	$-0.132441\pi$
$461$	39.2781			1.82936			0.914682	+	0.404175i	$0.132441\pi$
$462$		0			0
$463$		−	2.26863i		−	0.105432i	−0.998610	−	0.0527161i	$-0.983212\pi$
$463$		−	2.26863i		−	0.105432i	0.998610	−	0.0527161i	$-0.0167878\pi$
$464$	11.3323	+	22.7652i	0.526088	+	1.05685i
$465$		0			0
$466$	−28.4104	−	0.438419i	−1.31609	−	0.0203094i
$467$	−20.8867	−	12.0590i	−0.966522	−	0.558022i	−0.0683480	−	0.997662i	$-0.521773\pi$
$467$	−20.8867	−	12.0590i	−0.966522	−	0.558022i	−0.898174	+	0.439640i	$0.855106\pi$
$468$		0			0
$469$	−5.00703	+	42.0946i	−0.231203	+	1.94375i
$470$	7.12000	+	4.25855i	0.328421	+	0.196432i
$471$		0			0
$472$	−13.6543	−	26.4008i	−0.628491	−	1.21519i
$473$	8.98406	−	5.18695i	0.413087	−	0.238496i
$474$		0			0
$475$	−18.3141			−0.840306
$476$	11.4964	−	14.4263i	0.526937	−	0.661230i
$477$		0			0
$478$	16.3473	−	9.10472i	0.747707	−	0.416440i
$479$	6.19574	+	10.7313i	0.283091	+	0.490328i	0.972144	−	0.234383i	$-0.0753069\pi$
$479$	6.19574	+	10.7313i	0.283091	+	0.490328i	−0.689054	+	0.724710i	$0.741974\pi$
$480$		0			0
$481$	−3.83850	+	6.64848i	−0.175021	+	0.303145i
$482$	14.3323	+	8.57230i	0.652818	+	0.390458i
$483$		0			0
$484$	−2.22583	−	4.14564i	−0.101174	−	0.188438i
$485$	5.61529	−	9.72596i	0.254977	−	0.441633i
$486$		0			0
$487$	−10.1179	+	5.84159i	−0.458487	+	0.264708i	−0.711408	−	0.702779i	$-0.751942\pi$
$487$	−10.1179	+	5.84159i	−0.458487	+	0.264708i	0.252921	+	0.967487i	$0.418609\pi$
$488$	3.03873	−	4.74199i	0.137557	−	0.214660i
$489$		0			0
$490$	−6.06172	+	1.68669i	−0.273841	+	0.0761967i
$491$		−	42.8926i		−	1.93572i	−0.251498	−	0.967858i	$-0.580923\pi$
$491$		−	42.8926i		−	1.93572i	0.251498	−	0.967858i	$-0.419077\pi$
$492$		0			0
$493$	19.1937	−	11.0815i	0.864439	−	0.499084i
$494$	−23.4327	−	0.361604i	−1.05429	−	0.0162693i
$495$		0			0
$496$	20.0376	+	13.2809i	0.899717	+	0.596332i
$497$	1.56372	+	1.16910i	0.0701424	+	0.0524413i
$498$		0			0
$499$	−4.49173	+	7.77991i	−0.201078	+	0.348277i	−0.948876	−	0.315649i	$-0.897778\pi$
$499$	−4.49173	+	7.77991i	−0.201078	+	0.348277i	0.747798	+	0.663926i	$0.231111\pi$
$500$	6.42219	−	10.3708i	0.287209	−	0.463795i
$501$		0			0
$502$	13.0702	+	23.4671i	0.583349	+	1.04739i
$503$	−43.5055			−1.93981			−0.969907	−	0.243476i	$-0.921712\pi$
$503$	−43.5055			−1.93981			−0.969907	+	0.243476i	$0.921712\pi$
$504$		0			0
$505$	−7.78673			−0.346505
$506$	7.39341	+	13.2747i	0.328677	+	0.590131i
$507$		0			0
$508$	32.4139	+	20.0726i	1.43814	+	0.890577i
$509$	5.45911	−	9.45546i	0.241971	−	0.419106i	−0.719305	−	0.694695i	$-0.755540\pi$
$509$	5.45911	−	9.45546i	0.241971	−	0.419106i	0.961276	+	0.275589i	$0.0888728\pi$
$510$		0			0
$511$	1.33561	−	11.2286i	0.0590837	−	0.496723i
$512$	3.13226	−	22.4096i	0.138428	−	0.990373i
$513$		0			0
$514$	−36.8127	−	0.568079i	−1.62374	−	0.0250569i
$515$	−1.72264	+	0.994565i	−0.0759085	+	0.0438258i
$516$		0			0
$517$			33.7272i			1.48332i
$518$	−5.46750	−	4.22080i	−0.240228	−	0.185451i
$519$		0			0
$520$	4.03368	−	6.29462i	0.176889	−	0.276038i
$521$	−19.4185	+	11.2113i	−0.850739	+	0.491174i	−0.860900	−	0.508774i	$-0.830099\pi$
$521$	−19.4185	+	11.2113i	−0.850739	+	0.491174i	0.0101612	+	0.999948i	$0.496766\pi$
$522$		0			0
$523$	−0.483187	+	0.836904i	−0.0211283	+	0.0365953i	−0.876396	−	0.481591i	$-0.840059\pi$
$523$	−0.483187	+	0.836904i	−0.0211283	+	0.0365953i	0.855268	+	0.518186i	$0.173393\pi$
$524$	22.9058	−	12.2984i	1.00065	−	0.537257i
$525$		0			0
$526$	32.3071	+	19.3232i	1.40866	+	0.842534i
$527$	10.4755	−	18.1442i	0.456321	−	0.790372i
$528$		0			0
$529$	7.17729	+	12.4314i	0.312056	+	0.540497i
$530$	4.70642	−	2.62127i	0.204434	−	0.113861i
$531$		0			0
$532$	3.13535	−	20.8509i	0.135935	−	0.904003i
$533$	−43.6375			−1.89015
$534$		0			0
$535$	−3.58624	+	2.07051i	−0.155046	+	0.0895161i
$536$	40.2533	−	20.8187i	1.73868	−	0.899232i
$537$		0			0
$538$	−30.6948	−	18.3589i	−1.32335	−	0.791509i
$539$	−18.5338	−	17.6289i	−0.798309	−	0.759332i
$540$		0			0
$541$	−32.5318	−	18.7823i	−1.39865	−	0.807512i	−0.404400	−	0.914582i	$-0.632520\pi$
$541$	−32.5318	−	18.7823i	−1.39865	−	0.807512i	−0.994251	+	0.107070i	$0.965853\pi$
$542$	23.6039	+	0.364246i	1.01387	+	0.0156457i
$543$		0			0
$544$	−19.6619	−	1.51997i	−0.842995	−	0.0651681i
$545$		−	0.907020i		−	0.0388525i
$546$		0			0
$547$	13.8253			0.591126			0.295563	−	0.955323i	$-0.404493\pi$
$547$	13.8253			0.591126			0.295563	+	0.955323i	$0.404493\pi$
$548$	0.0838363	−	2.71574i	0.00358131	−	0.116010i
$549$		0			0
$550$	23.7482	+	0.366473i	1.01263	+	0.0156264i
$551$	12.6665	−	21.9390i	0.539610	−	0.934632i
$552$		0			0
$553$	−9.33236	−	21.7565i	−0.396852	−	0.925180i
$554$	19.3025	−	32.2724i	0.820084	−	1.37112i
$555$		0			0
$556$	−3.22247	+	5.20376i	−0.136663	+	0.220688i
$557$	2.15732	+	3.73659i	0.0914087	+	0.158325i	0.908104	−	0.418744i	$-0.137530\pi$
$557$	2.15732	+	3.73659i	0.0914087	+	0.158325i	−0.816695	+	0.577069i	$0.804196\pi$
$558$		0			0
$559$			11.8063i			0.499354i
$560$	5.12855	+	4.35236i	0.216721	+	0.183921i
$561$		0			0
$562$	5.58493	+	10.0276i	0.235586	+	0.422988i
$563$	5.35371	−	3.09097i	0.225632	−	0.130269i	−0.382923	−	0.923780i	$-0.625083\pi$
$563$	5.35371	−	3.09097i	0.225632	−	0.130269i	0.608555	+	0.793511i	$0.291749\pi$
$564$		0			0
$565$	−1.80539	−	1.04234i	−0.0759532	−	0.0438516i
$566$	−10.0233	−	5.99507i	−0.421312	−	0.251991i
$567$		0			0
$568$	0.0965865	−	2.08501i	0.00405268	−	0.0874850i
$569$	−5.65848	−	3.26692i	−0.237216	−	0.136957i	0.376681	−	0.926343i	$-0.377065\pi$
$569$	−5.65848	−	3.26692i	−0.237216	−	0.136957i	−0.613896	+	0.789387i	$0.710399\pi$
$570$		0			0
$571$	−6.00146	−	10.3948i	−0.251153	−	0.435011i	0.712690	−	0.701479i	$-0.247477\pi$
$571$	−6.00146	−	10.3948i	−0.251153	−	0.435011i	−0.963844	+	0.266468i	$0.914143\pi$
$572$	30.3784	+	0.937798i	1.27018	+	0.0392113i
$573$		0			0
$574$	5.23835	−	38.9105i	0.218645	−	1.62409i
$575$	−13.5137			−0.563562
$576$		0			0
$577$	1.42990	+	2.47666i	0.0595276	+	0.103105i	0.894253	−	0.447561i	$-0.147707\pi$
$577$	1.42990	+	2.47666i	0.0595276	+	0.103105i	−0.834726	+	0.550666i	$0.814374\pi$
$578$	0.105764	−	6.85375i	0.00439922	−	0.285079i
$579$		0			0
$580$	3.82286	+	7.12010i	0.158735	+	0.295646i
$581$	5.82591	−	7.79240i	0.241700	−	0.323283i
$582$		0			0
$583$	18.9663	+	10.9502i	0.785505	+	0.453512i
$584$	−10.7374	+	5.55332i	−0.444317	+	0.229798i
$585$		0			0
$586$	25.9398	−	14.4473i	1.07156	−	0.596814i
$587$			30.3998i			1.25473i	0.778723	+	0.627367i	$0.215868\pi$
$587$			30.3998i			1.25473i	−0.778723	+	0.627367i	$0.784132\pi$
$588$		0			0
$589$		−	23.9477i		−	0.986750i
$590$	−4.59608	−	8.25214i	−0.189218	−	0.339735i
$591$		0			0
$592$	−0.455466	+	7.37000i	−0.0187195	+	0.302905i
$593$	−1.46791	−	0.847496i	−0.0602797	−	0.0348025i	0.469557	−	0.882902i	$-0.344414\pi$
$593$	−1.46791	−	0.847496i	−0.0602797	−	0.0348025i	−0.529837	+	0.848100i	$0.677747\pi$
$594$		0			0
$595$	3.51029	−	4.69516i	0.143908	−	0.192483i
$596$	15.4398	+	28.7567i	0.632437	+	1.17792i
$597$		0			0
$598$	−17.2907	−	0.266824i	−0.707070	−	0.0109112i
$599$	−2.00010	−	3.46428i	−0.0817219	−	0.141547i	0.822268	−	0.569101i	$-0.192709\pi$
$599$	−2.00010	−	3.46428i	−0.0817219	−	0.141547i	−0.903990	+	0.427554i	$0.859375\pi$
$600$		0			0
$601$	−33.9144			−1.38340			−0.691699	−	0.722186i	$-0.743138\pi$
$601$	−33.9144			−1.38340			−0.691699	+	0.722186i	$0.743138\pi$
$602$	−10.5274	−	1.41726i	−0.429065	−	0.0577631i
$603$		0			0
$604$	−0.556570	+	18.0291i	−0.0226465	+	0.733595i
$605$	−0.747673	−	1.29501i	−0.0303972	−	0.0526495i
$606$		0			0
$607$	−2.15442	−	1.24386i	−0.0874452	−	0.0504865i	0.455640	−	0.890164i	$-0.349411\pi$
$607$	−2.15442	−	1.24386i	−0.0874452	−	0.0504865i	−0.543085	+	0.839678i	$0.682744\pi$
$608$	−20.3319	+	9.73246i	−0.824566	+	0.394703i
$609$		0			0
$610$	0.918734	−	1.53606i	0.0371984	−	0.0621932i
$611$	−33.2417	−	19.1921i	−1.34482	−	0.776431i
$612$		0			0
$613$	−26.9572	+	15.5638i	−1.08879	+	0.628614i	−0.933255	−	0.359216i	$-0.883044\pi$
$613$	−26.9572	+	15.5638i	−1.08879	+	0.628614i	−0.155537	+	0.987830i	$0.549711\pi$
$614$	−22.3913	+	12.4710i	−0.903639	+	0.503287i
$615$		0			0
$616$	−4.48290	+	26.9751i	−0.180621	+	1.08686i
$617$		−	8.23255i		−	0.331430i	−0.986174	−	0.165715i	$-0.947007\pi$
$617$		−	8.23255i		−	0.331430i	0.986174	−	0.165715i	$-0.0529932\pi$
$618$		0			0
$619$	18.6796	+	32.3540i	0.750796	+	1.30042i	0.947437	+	0.319941i	$0.103663\pi$
$619$	18.6796	+	32.3540i	0.750796	+	1.30042i	−0.196641	+	0.980475i	$0.563003\pi$
$620$	6.49505	+	4.02211i	0.260848	+	0.161532i
$621$		0			0
$622$	−37.4321	−	22.3885i	−1.50089	−	0.897698i
$623$	−5.58187	−	13.0130i	−0.223633	−	0.521354i
$624$		0			0
$625$	−9.55180	+	16.5442i	−0.382072	+	0.661768i
$626$	−0.0227774	+	1.47602i	−0.000910370	+	0.0589938i
$627$		0			0
$628$	1.42591	−	46.1900i	0.0569001	−	1.84318i
$629$	6.43544			0.256598
$630$		0			0
$631$			1.68550i			0.0670986i	0.999437	+	0.0335493i	$0.0106811\pi$
$631$			1.68550i			0.0670986i	−0.999437	+	0.0335493i	$0.989319\pi$
$632$	−13.6547	+	21.3084i	−0.543156	+	0.847604i
$633$		0			0
$634$	0.223840	−	14.5053i	0.00888983	−	0.576079i
$635$	10.4929	+	6.05808i	0.416398	+	0.240407i
$636$		0			0
$637$	27.9216	−	8.23549i	1.10630	−	0.326302i
$638$	−16.8639	+	28.1952i	−0.667647	+	1.11626i
$639$		0			0
$640$	0.775196	−	7.14896i	0.0306423	−	0.282588i
$641$	−9.16827	+	5.29330i	−0.362125	+	0.209073i	−0.670012	−	0.742350i	$-0.733711\pi$
$641$	−9.16827	+	5.29330i	−0.362125	+	0.209073i	0.307888	+	0.951423i	$0.400378\pi$
$642$		0			0
$643$	−27.0154			−1.06538			−0.532692	−	0.846309i	$-0.678820\pi$
$643$	−27.0154			−1.06538			−0.532692	+	0.846309i	$0.678820\pi$
$644$	2.31354	−	15.3857i	0.0911663	−	0.606281i
$645$		0			0
$646$	9.55900	+	17.1629i	0.376094	+	0.675266i
$647$	1.31353	+	2.27510i	0.0516402	+	0.0894434i	0.890690	−	0.454611i	$-0.150222\pi$
$647$	1.31353	+	2.27510i	0.0516402	+	0.0894434i	−0.839050	+	0.544055i	$0.816888\pi$
$648$		0			0
$649$	19.1999	−	33.2552i	0.753661	−	1.30538i
$650$	−13.8748	+	23.1978i	−0.544216	+	0.909892i
$651$		0			0
$652$	−11.5462	−	21.5049i	−0.452185	−	0.842198i
$653$	−16.6027	+	28.7567i	−0.649712	+	1.12533i	0.333479	+	0.942757i	$0.391777\pi$
$653$	−16.6027	+	28.7567i	−0.649712	+	1.12533i	−0.983191	+	0.182577i	$0.941556\pi$
$654$		0			0
$655$	7.15528	−	4.13110i	0.279580	−	0.161416i
$656$	−37.5744	+	18.7041i	−1.46703	+	0.730273i
$657$		0			0
$658$	21.1036	−	27.3370i	0.822703	−	1.06571i
$659$		−	0.108371i		−	0.00422154i	−0.999998	−	0.00211077i	$-0.999328\pi$
$659$		−	0.108371i		−	0.00422154i	0.999998	−	0.00211077i	$-0.000671879\pi$
$660$		0			0
$661$	2.37028	−	1.36848i	0.0921932	−	0.0532278i	−0.453195	−	0.891412i	$-0.649716\pi$
$661$	2.37028	−	1.36848i	0.0921932	−	0.0532278i	0.545388	+	0.838184i	$0.316382\pi$
$662$	−0.101143	+	6.55428i	−0.00393104	+	0.254739i
$663$		0			0
$664$	−10.3901	−	0.481314i	−0.403214	−	0.0186786i
$665$	0.791462	−	6.65390i	0.0306916	−	0.258027i
$666$		0			0
$667$	9.34645	−	16.1885i	0.361896	−	0.626822i
$668$	−3.51201	+	5.67131i	−0.135884	+	0.219430i
$669$		0			0
$670$	12.5820	−	7.00765i	0.486086	−	0.270729i
$671$	7.27627			0.280897
$672$		0			0
$673$	15.7488			0.607071			0.303536	−	0.952820i	$-0.401833\pi$
$673$	15.7488			0.607071			0.303536	+	0.952820i	$0.401833\pi$
$674$	40.8043	−	22.7262i	1.57172	−	0.875381i
$675$		0			0
$676$	−4.52220	+	7.30261i	−0.173931	+	0.280870i
$677$	−19.1246	+	33.1248i	−0.735019	+	1.27309i	0.219696	+	0.975568i	$0.429493\pi$
$677$	−19.1246	+	33.1248i	−0.735019	+	1.27309i	−0.954715	+	0.297522i	$0.903840\pi$
$678$		0			0
$679$	−37.4418	−	27.9930i	−1.43688	−	1.07427i
$680$	−6.26036	−	0.290006i	−0.240074	−	0.0111212i
$681$		0			0
$682$	−0.479206	+	31.0535i	−0.0183497	+	1.18910i
$683$	3.06255	−	1.76816i	0.117185	−	0.0676569i	−0.440262	−	0.897869i	$-0.645114\pi$
$683$	3.06255	−	1.76816i	0.117185	−	0.0676569i	0.557447	+	0.830213i	$0.311781\pi$
$684$		0			0
$685$		−	0.863457i		−	0.0329910i
$686$	3.99160	+	25.8857i	0.152400	+	0.988319i
$687$		0			0
$688$	5.06047	+	10.1659i	0.192929	+	0.387571i
$689$	−21.5852	+	12.4622i	−0.822330	+	0.474772i
$690$		0			0
$691$	7.99597	−	13.8494i	0.304181	−	0.526857i	−0.672898	−	0.739736i	$-0.734951\pi$
$691$	7.99597	−	13.8494i	0.304181	−	0.526857i	0.977079	+	0.212879i	$0.0682839\pi$
$692$	−9.06754	−	16.8884i	−0.344696	−	0.642000i
$693$		0			0
$694$	−2.91324	+	4.87074i	−0.110585	+	0.184891i
$695$	−0.972568	+	1.68454i	−0.0368916	+	0.0638981i
$696$		0			0
$697$	18.2901	+	31.6794i	0.692788	+	1.19994i
$698$	−7.20267	−	12.9322i	−0.272625	−	0.489491i
$699$		0			0
$700$	−19.0193	−	15.1566i	−0.718863	−	0.572865i
$701$	42.7818			1.61585			0.807924	−	0.589287i	$-0.200591\pi$
$701$	42.7818			1.61585			0.807924	+	0.589287i	$0.200591\pi$
$702$		0			0
$703$	6.37041	−	3.67796i	0.240265	−	0.138717i
$704$	26.5595	−	12.2134i	1.00100	−	0.460310i
$705$		0			0
$706$	12.8655	−	21.5103i	0.484201	−	0.809550i
$707$	−3.82852	+	32.1867i	−0.143986	+	1.21051i
$708$		0			0
$709$	−17.0615	−	9.85048i	−0.640759	−	0.369943i	0.144148	−	0.989556i	$-0.453956\pi$
$709$	−17.0615	−	9.85048i	−0.640759	−	0.369943i	−0.784907	+	0.619614i	$0.787289\pi$
$710$	0.0102348	−	0.663236i	0.000384105	−	0.0248908i
$711$		0			0
$712$	−8.16716	+	12.7450i	−0.306077	+	0.477639i
$713$		−	17.6708i		−	0.661776i
$714$		0			0
$715$	9.65868			0.361214
$716$	0.00201792	−	0.0653670i	7.54131e−5	−	0.00244288i
$717$		0			0
$718$	−0.284953	+	18.4655i	−0.0106344	+	0.689128i
$719$	−5.14423	+	8.91007i	−0.191847	+	0.332290i	−0.945863	−	0.324568i	$-0.894781\pi$
$719$	−5.14423	+	8.91007i	−0.191847	+	0.332290i	0.754015	+	0.656857i	$0.228115\pi$
$720$		0			0
$721$	3.26410	+	7.60958i	0.121561	+	0.283396i
$722$	−3.78878	−	2.26611i	−0.141004	−	0.0843360i
$723$		0			0
$724$	32.9283	+	20.3911i	1.22377	+	0.757829i
$725$	−14.6095	−	25.3045i	−0.542584	−	0.939784i
$726$		0			0
$727$		−	40.0773i		−	1.48638i	−0.669078	−	0.743192i	$-0.733311\pi$
$727$		−	40.0773i		−	1.48638i	0.669078	−	0.743192i	$-0.266689\pi$
$728$	−24.0358	−	19.7682i	−0.890827	−	0.732660i
$729$		0			0
$730$	−3.35621	+	1.86926i	−0.124219	+	0.0691845i
$731$	8.57100	−	4.94847i	0.317010	−	0.183026i
$732$		0			0
$733$	−17.9716	−	10.3759i	−0.663795	−	0.383242i	0.129926	−	0.991524i	$-0.458526\pi$
$733$	−17.9716	−	10.3759i	−0.663795	−	0.383242i	−0.793721	+	0.608281i	$0.791859\pi$
$734$	16.2530	−	27.1740i	0.599910	−	1.00301i
$735$		0			0
$736$	−15.0027	+	7.18148i	−0.553005	+	0.264713i
$737$	50.7041	+	29.2741i	1.86771	+	1.07832i
$738$		0			0
$739$	8.47770	+	14.6838i	0.311857	+	0.540152i	0.978764	−	0.204988i	$-0.0657157\pi$
$739$	8.47770	+	14.6838i	0.311857	+	0.540152i	−0.666907	+	0.745141i	$0.732382\pi$
$740$	−0.0724068	+	2.34550i	−0.00266173	+	0.0862221i
$741$		0			0
$742$	−8.52111	−	20.7430i	−0.312820	−	0.761498i
$743$	5.45125			0.199987			0.0999935	−	0.994988i	$-0.468118\pi$
$743$	5.45125			0.199987			0.0999935	+	0.994988i	$0.468118\pi$
$744$		0			0
$745$	5.18631	+	8.98296i	0.190012	+	0.329110i
$746$	6.26665	+	0.0967045i	0.229438	+	0.00354060i
$747$		0			0
$748$	−12.0519	−	22.4468i	−0.440661	−	0.820735i
$749$	6.79530	+	15.8419i	0.248295	+	0.578849i
$750$		0			0
$751$	13.5551	+	7.82606i	0.494634	+	0.285577i	0.726495	−	0.687172i	$-0.241148\pi$
$751$	13.5551	+	7.82606i	0.494634	+	0.285577i	−0.231861	+	0.972749i	$0.574481\pi$
$752$	−36.8493	−	2.27729i	−1.34375	−	0.0830441i
$753$		0			0
$754$	−18.1931	−	32.6653i	−0.662555	−	1.18960i
$755$			5.73229i			0.208619i
$756$		0			0
$757$		−	9.16577i		−	0.333136i	−0.986030	−	0.166568i	$-0.946732\pi$
$757$		−	9.16577i		−	0.333136i	0.986030	−	0.166568i	$-0.0532685\pi$
$758$	−35.6940	+	19.8800i	−1.29647	+	0.722075i
$759$		0			0
$760$	−6.36284	+	3.29082i	−0.230805	+	0.119371i
$761$	1.73152	+	0.999696i	0.0627677	+	0.0362389i	0.531055	−	0.847337i	$-0.321796\pi$
$761$	1.73152	+	0.999696i	0.0627677	+	0.0362389i	−0.468288	+	0.883576i	$0.655129\pi$
$762$		0			0
$763$	−3.74920	−	0.445956i	−0.135730	−	0.0161447i
$764$	−2.85388	−	5.31537i	−0.103250	−	0.192303i
$765$		0			0
$766$	−0.714905	+	46.3273i	−0.0258306	+	1.67387i
$767$	21.8510	+	37.8470i	0.788993	+	1.36658i
$768$		0			0
$769$	2.48446			0.0895920			0.0447960	−	0.998996i	$-0.485736\pi$
$769$	2.48446			0.0895920			0.0447960	+	0.998996i	$0.485736\pi$
$770$	−1.15945	+	8.61241i	−0.0417837	+	0.310370i
$771$		0			0
$772$	−43.8051	−	1.35229i	−1.57658	−	0.0486700i
$773$	−26.3968	−	45.7206i	−0.949427	−	1.64446i	−0.746635	−	0.665234i	$-0.768332\pi$
$773$	−26.3968	−	45.7206i	−0.949427	−	1.64446i	−0.202792	−	0.979222i	$-0.565002\pi$
$774$		0			0
$775$	−23.9208	−	13.8107i	−0.859261	−	0.496095i
$776$	−2.31267	+	49.9235i	−0.0830200	+	1.79215i
$777$		0			0
$778$	15.1682	+	9.07228i	0.543807	+	0.325257i
$779$	36.2106	+	20.9062i	1.29738	+	0.749042i
$780$		0			0
$781$	2.33530	−	1.34829i	0.0835637	−	0.0482455i
$782$	7.05348	+	12.6643i	0.252232	+	0.452876i
$783$		0			0
$784$	20.5122	−	19.0591i	0.732578	−	0.680683i
$785$		−	14.6859i		−	0.524164i
$786$		0			0
$787$	−20.0243	−	34.6831i	−0.713789	−	1.23632i	−0.963425	−	0.267979i	$-0.913644\pi$
$787$	−20.0243	−	34.6831i	−0.713789	−	1.23632i	0.249635	−	0.968340i	$-0.419689\pi$
$788$	−16.1051	+	26.0071i	−0.573720	+	0.926464i
$789$		0			0
$790$	−4.12838	+	6.90237i	−0.146881	+	0.245575i
$791$	−5.19621	+	6.95015i	−0.184756	+	0.247119i
$792$		0			0
$793$	−4.14048	+	7.17153i	−0.147033	+	0.254668i
$794$	9.95481	+	0.153619i	0.353283	+	0.00545173i
$795$		0			0
$796$	0.197890	−	6.41030i	0.00701401	−	0.227207i
$797$	23.9157			0.847139			0.423570	−	0.905864i	$-0.360777\pi$
$797$	23.9157			0.847139			0.423570	+	0.905864i	$0.360777\pi$
$798$		0			0
$799$			32.1766i			1.13833i
$800$	−2.00389	+	25.9217i	−0.0708481	+	0.916471i
$801$		0			0
$802$	42.0413	+	0.648765i	1.48453	+	0.0229087i
$803$	−13.5251	−	7.80874i	−0.477292	−	0.275564i
$804$		0			0
$805$	0.584011	−	4.90984i	0.0205837	−	0.173049i
$806$	−30.3338	−	18.1430i	−1.06846	−	0.639059i
$807$		0			0
$808$	30.7788	−	15.9186i	1.08279	−	0.560014i
$809$	23.2044	−	13.3971i	0.815824	−	0.471016i	−0.0331504	−	0.999450i	$-0.510554\pi$
$809$	23.2044	−	13.3971i	0.815824	−	0.471016i	0.848974	+	0.528434i	$0.177221\pi$
$810$		0			0
$811$	−43.7619			−1.53669			−0.768345	−	0.640036i	$-0.778919\pi$
$811$	−43.7619			−1.53669			−0.768345	+	0.640036i	$0.778919\pi$
$812$	31.3108	−	12.3012i	1.09879	−	0.431686i
$813$		0			0
$814$	−8.33423	+	4.64180i	−0.292115	+	0.162695i
$815$	−3.87845	−	6.71768i	−0.135856	−	0.235310i
$816$		0			0
$817$	5.65626	−	9.79693i	0.197887	−	0.342751i
$818$	40.3483	+	24.1328i	1.41075	+	0.843782i
$819$		0			0
$820$	−11.7518	+	6.30968i	−0.410392	+	0.220344i
$821$	−18.9005	+	32.7366i	−0.659632	+	1.14252i	0.321080	+	0.947052i	$0.395954\pi$
$821$	−18.9005	+	32.7366i	−0.659632	+	1.14252i	−0.980711	+	0.195463i	$0.937379\pi$
$822$		0			0
$823$	19.9129	−	11.4967i	0.694121	−	0.400751i	−0.111033	−	0.993817i	$-0.535416\pi$
$823$	19.9129	−	11.4967i	0.694121	−	0.400751i	0.805154	+	0.593066i	$0.202083\pi$
$824$	4.77590	−	7.45287i	0.166376	−	0.259633i
$825$		0			0
$826$	−36.3703	+	14.9407i	−1.26548	+	0.519855i
$827$			31.3424i			1.08988i	0.838474	+	0.544941i	$0.183448\pi$
$827$			31.3424i			1.08988i	−0.838474	+	0.544941i	$0.816552\pi$
$828$		0			0
$829$	35.5914	−	20.5487i	1.23614	−	0.713686i	0.267837	−	0.963464i	$-0.413691\pi$
$829$	35.5914	−	20.5487i	1.23614	−	0.713686i	0.968303	+	0.249779i	$0.0803579\pi$
$830$	−3.30507	−	0.0510025i	−0.114721	−	0.00177032i
$831$		0			0
$832$	−3.07577	+	33.1271i	−0.106633	+	1.14847i
$833$	−17.6817	−	16.8184i	−0.612635	−	0.582723i
$834$		0			0
$835$	−1.05995	+	1.83589i	−0.0366812	+	0.0635337i
$836$	−24.7588	−	15.3321i	−0.856301	−	0.530271i
$837$		0			0
$838$	−6.15889	−	11.0581i	−0.212755	−	0.381996i
$839$	−5.17046			−0.178504			−0.0892520	−	0.996009i	$-0.528448\pi$
$839$	−5.17046			−0.178504			−0.0892520	+	0.996009i	$0.528448\pi$
$840$		0			0
$841$	11.4173			0.393701
$842$	−18.1302	−	32.5523i	−0.624809	−	1.12183i
$843$		0			0
$844$	−17.5908	+	28.4062i	−0.605499	+	0.977781i
$845$	−1.36484	+	2.36397i	−0.0469518	+	0.0813230i
$846$		0			0
$847$	−5.72057	+	2.45381i	−0.196561	+	0.0843141i
$848$	−13.2445	+	19.9826i	−0.454816	+	0.686205i
$849$		0			0
$850$	22.6563	+	0.349623i	0.777105	+	0.0119920i
$851$	4.70066	−	2.71393i	0.161136	−	0.0930322i
$852$		0			0
$853$		−	23.8844i		−	0.817786i	−0.912582	−	0.408893i	$-0.865915\pi$
$853$		−	23.8844i		−	0.817786i	0.912582	−	0.408893i	$-0.134085\pi$
$854$	−5.89764	−	4.55286i	−0.201813	−	0.155796i
$855$		0			0
$856$	9.94260	−	15.5156i	0.339831	−	0.530312i
$857$	16.7053	−	9.64484i	0.570644	−	0.329461i	−0.186763	−	0.982405i	$-0.559800\pi$
$857$	16.7053	−	9.64484i	0.570644	−	0.329461i	0.757406	+	0.652944i	$0.226466\pi$
$858$		0			0
$859$	4.54550	−	7.87303i	0.155090	−	0.268624i	−0.778002	−	0.628262i	$-0.783766\pi$
$859$	4.54550	−	7.87303i	0.155090	−	0.268624i	0.933092	+	0.359638i	$0.117100\pi$
$860$	1.70711	+	3.17951i	0.0582120	+	0.108420i
$861$		0			0
$862$	19.3548	+	11.5763i	0.659226	+	0.394290i
$863$	−11.0104	+	19.0706i	−0.374799	+	0.649170i	−0.990297	−	0.138968i	$-0.955621\pi$
$863$	−11.0104	+	19.0706i	−0.374799	+	0.649170i	0.615498	+	0.788138i	$0.288955\pi$
$864$		0			0
$865$	−3.04585	−	5.27556i	−0.103562	−	0.179375i
$866$	−15.4511	+	8.60557i	−0.525048	+	0.292429i
$867$		0			0
$868$	19.8190	−	24.8700i	0.672700	−	0.844142i
$869$	−32.6964			−1.10915
$870$		0			0
$871$	−57.7053	+	33.3162i	−1.95527	+	1.12888i
$872$	1.85424	+	3.58520i	0.0627925	+	0.121410i
$873$		0			0
$874$	14.2201	+	8.50518i	0.481002	+	0.287692i
$875$	−12.9240	−	9.66254i	−0.436912	−	0.326654i
$876$		0			0
$877$	23.0512	+	13.3086i	0.778385	+	0.449401i	0.835858	−	0.548946i	$-0.184971\pi$
$877$	23.0512	+	13.3086i	0.778385	+	0.449401i	−0.0574726	+	0.998347i	$0.518304\pi$
$878$	−22.9494	−	0.354146i	−0.774504	−	0.0119518i
$879$		0			0
$880$	8.31667	−	4.13995i	0.280355	−	0.139558i
$881$			5.95975i			0.200789i	0.994948	+	0.100395i	$0.0320105\pi$
$881$			5.95975i			0.200789i	−0.994948	+	0.100395i	$0.967990\pi$
$882$		0			0
$883$	−8.91564			−0.300035			−0.150018	−	0.988683i	$-0.547933\pi$
$883$	−8.91564			−0.300035			−0.150018	+	0.988683i	$0.547933\pi$
$884$	28.9817	+	0.894681i	0.974759	+	0.0300914i
$885$		0			0
$886$	−9.47518	−	0.146217i	−0.318325	−	0.00491227i
$887$	−26.1142	+	45.2311i	−0.876829	+	1.51871i	−0.0220275	+	0.999757i	$0.507012\pi$
$887$	−26.1142	+	45.2311i	−0.876829	+	1.51871i	−0.854802	+	0.518955i	$0.826321\pi$
$888$		0			0
$889$	30.2003	−	40.3942i	1.01289	−	1.35478i
$890$	−2.46927	+	4.12844i	−0.0827700	+	0.138386i
$891$		0			0
$892$	−32.5702	−	20.1693i	−1.09053	−	0.675319i
$893$	18.3894	+	31.8514i	0.615379	+	1.06587i
$894$		0			0
$895$		−	0.0207832i		−	0.000694704i
$896$	−29.1694	−	6.71924i	−0.974480	−	0.224474i
$897$		0			0
$898$	−17.9707	−	32.2659i	−0.599690	−	1.07673i
$899$	33.0885	−	19.1037i	1.10356	−	0.637143i
$900$		0			0
$901$	18.0943	+	10.4468i	0.602809	+	0.348032i
$902$	−46.5366	−	27.8341i	−1.54950	−	0.926773i
$903$		0			0
$904$	9.26708	+	0.429291i	0.308219	+	0.0142780i
$905$	10.6594	+	6.15421i	0.354330	+	0.204573i
$906$		0			0
$907$	−8.71744	−	15.0990i	−0.289458	−	0.501355i	0.684223	−	0.729273i	$-0.260142\pi$
$907$	−8.71744	−	15.0990i	−0.289458	−	0.501355i	−0.973680	+	0.227918i	$0.926808\pi$
$908$	1.03298	−	33.4616i	0.0342806	−	1.11046i
$909$		0			0
$910$	−7.82866	−	6.04356i	−0.259517	−	0.200342i
$911$	39.1655			1.29761			0.648805	−	0.760954i	$-0.275269\pi$
$911$	39.1655			1.29761			0.648805	+	0.760954i	$0.275269\pi$
$912$		0			0
$913$	−6.71885	−	11.6374i	−0.222361	−	0.385141i
$914$	0.699705	−	45.3423i	0.0231442	−	1.49979i
$915$		0			0
$916$	−35.6127	+	19.1208i	−1.17668	+	0.631770i
$917$	−13.5580	−	31.6078i	−0.447725	−	1.04378i
$918$		0			0
$919$	35.0892	+	20.2588i	1.15749	+	0.668276i	0.950701	−	0.310110i	$-0.100366\pi$
$919$	35.0892	+	20.2588i	1.15749	+	0.668276i	0.206787	+	0.978386i	$0.433699\pi$
$920$	−4.69507	+	2.42826i	−0.154792	+	0.0800574i
$921$		0			0
$922$	−48.5285	+	27.0282i	−1.59820	+	0.890128i
$923$			3.06892i			0.101015i
$924$		0			0
$925$		−	8.48433i		−	0.278963i
$926$	1.56110	+	2.80292i	0.0513010	+	0.0921095i
$927$		0			0
$928$	−29.6665	−	20.3286i	−0.973850	−	0.667321i
$929$	−14.0117	−	8.08966i	−0.459709	−	0.265413i	0.252213	−	0.967672i	$-0.418842\pi$
$929$	−14.0117	−	8.08966i	−0.459709	−	0.265413i	−0.711922	+	0.702259i	$0.752175\pi$
$930$		0			0
$931$	−27.1150	−	6.54307i	−0.888659	−	0.214441i
$932$	35.4030	−	19.0083i	1.15966	−	0.622636i
$933$		0			0
$934$	34.1038	+	0.526277i	1.11591	+	0.0172203i
$935$	−4.04831	−	7.01188i	−0.132394	−	0.229313i
$936$		0			0
$937$	7.65486			0.250073			0.125037	−	0.992152i	$-0.460095\pi$
$937$	7.65486			0.250073			0.125037	+	0.992152i	$0.460095\pi$
$938$	−22.7801	−	55.4538i	−0.743798	−	1.81063i
$939$		0			0
$940$	−11.7272	−	0.362027i	−0.382501	−	0.0118080i
$941$	−11.8841	−	20.5839i	−0.387411	−	0.671016i	0.604689	−	0.796462i	$-0.293297\pi$
$941$	−11.8841	−	20.5839i	−0.387411	−	0.671016i	−0.992101	+	0.125445i	$0.959964\pi$
$942$		0			0
$943$	26.7194	+	15.4265i	0.870104	+	0.502355i
$944$	35.0371	+	23.2226i	1.14036	+	0.755830i
$945$		0			0
$946$	−7.53062	+	12.5907i	−0.244842	+	0.409358i
$947$	35.2481	+	20.3505i	1.14541	+	0.661302i	0.947764	−	0.318972i	$-0.103338\pi$
$947$	35.2481	+	20.3505i	1.14541	+	0.661302i	0.197644	+	0.980274i	$0.436671\pi$
$948$		0			0
$949$	15.3927	−	8.88696i	0.499667	−	0.288483i
$950$	22.6272	−	12.6024i	0.734123	−	0.408874i
$951$		0			0
$952$	−4.27679	+	25.7348i	−0.138612	+	0.834071i
$953$			19.5679i			0.633867i	0.948448	+	0.316934i	$0.102653\pi$
$953$			19.5679i			0.633867i	−0.948448	+	0.316934i	$0.897347\pi$
$954$		0			0
$955$	−0.958636	−	1.66041i	−0.0310207	−	0.0537295i
$956$	−13.9320	+	22.4979i	−0.450594	+	0.727635i
$957$		0			0
$958$	−15.0394	−	8.99523i	−0.485901	−	0.290623i
$959$	−3.56913	−	0.424537i	−0.115253	−	0.0137090i
$960$		0			0
$961$	2.55908	−	4.43245i	0.0825509	−	0.142982i
$962$	0.167520	−	10.8556i	0.00540106	−	0.350000i
$963$		0			0
$964$	−23.6065	−	0.728746i	−0.760314	−	0.0234713i
$965$	−13.9277			−0.448347
$966$		0			0
$967$			24.6339i			0.792174i	0.918213	+	0.396087i	$0.129632\pi$
$967$			24.6339i			0.792174i	−0.918213	+	0.396087i	$0.870368\pi$
$968$	5.60276	+	3.59032i	0.180079	+	0.115397i
$969$		0			0
$970$	−0.245062	+	15.8805i	−0.00786848	+	0.509893i
$971$	−41.0803	−	23.7177i	−1.31833	−	0.761137i	−0.334869	−	0.942265i	$-0.608692\pi$
$971$	−41.0803	−	23.7177i	−1.31833	−	0.761137i	−0.983460	+	0.181128i	$0.942025\pi$
$972$		0			0
$973$	6.48491	+	4.84838i	0.207897	+	0.155432i
$974$	8.48106	−	14.1797i	0.271751	−	0.454348i
$975$		0			0
$976$	−0.491299	+	7.94981i	−0.0157261	+	0.254467i
$977$	48.9364	−	28.2534i	1.56561	−	0.903908i	0.568943	−	0.822377i	$-0.307352\pi$
$977$	48.9364	−	28.2534i	1.56561	−	0.903908i	0.996671	−	0.0815309i	$-0.0259809\pi$
$978$		0			0
$979$	−19.5563			−0.625023
$980$	6.32867	−	6.25514i	0.202162	−	0.199813i
$981$		0			0
$982$	29.5155	+	52.9942i	0.941876	+	1.69111i
$983$	18.0801	+	31.3156i	0.576665	+	0.998814i	0.995859	+	0.0909167i	$0.0289797\pi$
$983$	18.0801	+	31.3156i	0.576665	+	0.998814i	−0.419193	+	0.907897i	$0.637687\pi$
$984$		0			0
$985$	−4.86065	+	8.41890i	−0.154873	+	0.268248i
$986$	−16.0885	+	26.8989i	−0.512363	+	0.856635i
$987$		0			0
$988$	29.2001	−	15.6778i	0.928980	−	0.498779i
$989$	4.17369	−	7.22905i	0.132716	−	0.229870i
$990$		0			0
$991$	8.72687	−	5.03846i	0.277218	−	0.160052i	−0.354945	−	0.934887i	$-0.615500\pi$
$991$	8.72687	−	5.03846i	0.277218	−	0.160052i	0.632163	+	0.774835i	$0.282167\pi$
$992$	−33.8956	−	2.62032i	−1.07619	−	0.0831951i
$993$		0			0
$994$	−2.73648	−	0.368400i	−0.0867958	−	0.0116849i
$995$		−	2.03813i		−	0.0646130i
$996$		0			0
$997$	−14.5584	+	8.40532i	−0.461070	+	0.266199i	−0.712494	−	0.701678i	$-0.752435\pi$
$997$	−14.5584	+	8.40532i	−0.461070	+	0.266199i	0.251424	+	0.967877i	$0.419101\pi$
$998$	0.196028	−	12.7030i	0.00620516	−	0.402107i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bm.c.107.4	✓	48
3.2	odd	2	inner	504.2.bm.c.107.21	yes	48
4.3	odd	2		2016.2.bu.c.1871.16		48
7.4	even	3	inner	504.2.bm.c.179.13	yes	48
8.3	odd	2	inner	504.2.bm.c.107.12	yes	48
8.5	even	2		2016.2.bu.c.1871.10		48
12.11	even	2		2016.2.bu.c.1871.9		48
21.11	odd	6	inner	504.2.bm.c.179.12	yes	48
24.5	odd	2		2016.2.bu.c.1871.15		48
24.11	even	2	inner	504.2.bm.c.107.13	yes	48
28.11	odd	6		2016.2.bu.c.431.15		48
56.11	odd	6	inner	504.2.bm.c.179.21	yes	48
56.53	even	6		2016.2.bu.c.431.9		48
84.11	even	6		2016.2.bu.c.431.10		48
168.11	even	6	inner	504.2.bm.c.179.4	yes	48
168.53	odd	6		2016.2.bu.c.431.16		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bm.c.107.4	✓	48	1.1	even	1	trivial
504.2.bm.c.107.12	yes	48	8.3	odd	2	inner
504.2.bm.c.107.13	yes	48	24.11	even	2	inner
504.2.bm.c.107.21	yes	48	3.2	odd	2	inner
504.2.bm.c.179.4	yes	48	168.11	even	6	inner
504.2.bm.c.179.12	yes	48	21.11	odd	6	inner
504.2.bm.c.179.13	yes	48	7.4	even	3	inner
504.2.bm.c.179.21	yes	48	56.11	odd	6	inner
2016.2.bu.c.431.9		48	56.53	even	6
2016.2.bu.c.431.10		48	84.11	even	6
2016.2.bu.c.431.15		48	28.11	odd	6
2016.2.bu.c.431.16		48	168.53	odd	6
2016.2.bu.c.1871.9		48	12.11	even	2
2016.2.bu.c.1871.10		48	8.5	even	2
2016.2.bu.c.1871.15		48	24.5	odd	2
2016.2.bu.c.1871.16		48	4.3	odd	2

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.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.23551 + 0.688125i) q^{2} +(1.05297 - 1.70037i) q^{4} +(0.317795 - 0.550436i) q^{5} +(-2.11900 - 1.58425i) q^{7} +(-0.130884 + 2.82540i) q^{8} +O(q^{10})\)	\(q+(-1.23551 + 0.688125i) q^{2} +(1.05297 - 1.70037i) q^{4} +(0.317795 - 0.550436i) q^{5} +(-2.11900 - 1.58425i) q^{7} +(-0.130884 + 2.82540i) q^{8} +(-0.0138692 + 0.898752i) q^{10} +(-3.16457 + 1.82707i) q^{11} -4.15869i q^{13} +(3.70820 + 0.499220i) q^{14} +(-1.78252 - 3.58087i) q^{16} +(-3.01908 + 1.74306i) q^{17} +(-1.99238 + 3.45090i) q^{19} +(-0.601318 - 1.11996i) q^{20} +(2.65261 - 4.43498i) q^{22} +(-1.47015 + 2.54638i) q^{23} +(2.29801 + 3.98028i) q^{25} +(2.86170 + 5.13810i) q^{26} +(-4.92505 + 1.93492i) q^{28} -6.35746 q^{29} +(-5.20467 + 3.00492i) q^{31} +(4.66640 + 3.19760i) q^{32} +(2.53065 - 4.23107i) q^{34} +(-1.54543 + 0.662908i) q^{35} +(-1.59870 - 0.923007i) q^{37} +(0.0869514 - 5.63463i) q^{38} +(1.51361 + 0.969939i) q^{40} -10.4931i q^{41} -2.83895 q^{43} +(-0.225503 + 7.30479i) q^{44} +(0.0641605 - 4.15773i) q^{46} +(4.61494 - 7.99332i) q^{47} +(1.98031 + 6.71404i) q^{49} +(-5.57814 - 3.33635i) q^{50} +(-7.07132 - 4.37897i) q^{52} +(-2.99666 - 5.19038i) q^{53} +2.32253i q^{55} +(4.75348 - 5.77966i) q^{56} +(7.85470 - 4.37473i) q^{58} +(-9.10070 + 5.25429i) q^{59} +(-1.72447 - 0.995622i) q^{61} +(4.36266 - 7.29407i) q^{62} +(-7.96574 - 0.739601i) q^{64} +(-2.28909 - 1.32161i) q^{65} +(-8.01122 - 13.8758i) q^{67} +(-0.215135 + 6.96894i) q^{68} +(1.45324 - 1.88248i) q^{70} -0.737952 q^{71} +(2.13696 + 3.70132i) q^{73} +(2.61035 + 0.0402819i) q^{74} +(3.76990 + 7.02147i) q^{76} +(9.60025 + 1.14192i) q^{77} +(7.74900 + 4.47389i) q^{79} +(-2.53752 - 0.156819i) q^{80} +(7.22055 + 12.9643i) q^{82} +3.67740i q^{83} +2.21574i q^{85} +(3.50755 - 1.95355i) q^{86} +(-4.74800 - 9.18031i) q^{88} +(4.63483 + 2.67592i) q^{89} +(-6.58841 + 8.81226i) q^{91} +(2.78177 + 5.18107i) q^{92} +(-0.201405 + 13.0515i) q^{94} +(1.26633 + 2.19335i) q^{95} +17.6696 q^{97} +(-7.06679 - 6.93257i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q - 8 q^{10} - 28 q^{16} - 32 q^{19} + 32 q^{22} + 4 q^{28} + 112 q^{34} - 36 q^{40} - 160 q^{43} + 40 q^{46} + 56 q^{49} - 36 q^{52} + 12 q^{58} - 24 q^{64} + 92 q^{70} + 16 q^{73} - 120 q^{76} + 20 q^{82} - 100 q^{88} - 32 q^{91} - 20 q^{94} + 240 q^{97}+O(q^{100}) \) 48 * q - 8 * q^10 - 28 * q^16 - 32 * q^19 + 32 * q^22 + 4 * q^28 + 112 * q^34 - 36 * q^40 - 160 * q^43 + 40 * q^46 + 56 * q^49 - 36 * q^52 + 12 * q^58 - 24 * q^64 + 92 * q^70 + 16 * q^73 - 120 * q^76 + 20 * q^82 - 100 * q^88 - 32 * q^91 - 20 * q^94 + 240 * q^97

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