LMFDB - Embedded newform 504.2.bm.c.107.19

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			107.19
Character	$\chi$	$=$	504.107
Dual form			504.2.bm.c.179.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.07239 + 0.921948i) q^{2} +(0.300025 + 1.97737i) q^{4} +(-0.316953 + 0.548978i) q^{5} +(-2.06297 + 1.65655i) q^{7} +(-1.50129 + 2.39711i) q^{8} +O(q^{10})$	\(q+(1.07239 + 0.921948i) q^{2} +(0.300025 + 1.97737i) q^{4} +(-0.316953 + 0.548978i) q^{5} +(-2.06297 + 1.65655i) q^{7} +(-1.50129 + 2.39711i) q^{8} +(-0.846025 + 0.296503i) q^{10} +(0.424494 - 0.245082i) q^{11} +3.13261i q^{13} +(-3.73955 - 0.125491i) q^{14} +(-3.81997 + 1.18652i) q^{16} +(-0.987137 + 0.569924i) q^{17} +(-0.591155 + 1.02391i) q^{19} +(-1.18063 - 0.462025i) q^{20} +(0.681175 + 0.128539i) q^{22} +(2.80489 - 4.85822i) q^{23} +(2.29908 + 3.98213i) q^{25} +(-2.88810 + 3.35937i) q^{26} +(-3.89455 - 3.58225i) q^{28} +4.05920 q^{29} +(-5.40346 + 3.11969i) q^{31} +(-5.19039 - 2.24940i) q^{32} +(-1.58403 - 0.298910i) q^{34} +(-0.255545 - 1.65757i) q^{35} +(6.53184 + 3.77116i) q^{37} +(-1.57794 + 0.553013i) q^{38} +(-0.840125 - 1.58394i) q^{40} -4.06598i q^{41} +4.65556 q^{43} +(0.611976 + 0.765851i) q^{44} +(7.48695 - 2.62392i) q^{46} +(4.80492 - 8.32236i) q^{47} +(1.51170 - 6.83482i) q^{49} +(-1.20581 + 6.39001i) q^{50} +(-6.19432 + 0.939863i) q^{52} +(1.10444 + 1.91294i) q^{53} +0.310718i q^{55} +(-0.873819 - 7.43212i) q^{56} +(4.35303 + 3.74237i) q^{58} +(-9.12119 + 5.26612i) q^{59} +(10.1718 + 5.87267i) q^{61} +(-8.67078 - 1.63619i) q^{62} +(-3.49228 - 7.19750i) q^{64} +(-1.71973 - 0.992889i) q^{65} +(3.11964 + 5.40338i) q^{67} +(-1.42312 - 1.78094i) q^{68} +(1.25415 - 2.01316i) q^{70} +5.48681 q^{71} +(-5.35648 - 9.27769i) q^{73} +(3.52785 + 10.0662i) q^{74} +(-2.20201 - 0.861731i) q^{76} +(-0.469729 + 1.20879i) q^{77} +(-2.49304 - 1.43936i) q^{79} +(0.559375 - 2.47315i) q^{80} +(3.74862 - 4.36031i) q^{82} -14.1254i q^{83} -0.722556i q^{85} +(4.99256 + 4.29218i) q^{86} +(-0.0497991 + 1.38550i) q^{88} +(9.12417 + 5.26784i) q^{89} +(-5.18932 - 6.46248i) q^{91} +(10.4480 + 4.08872i) q^{92} +(12.8255 - 4.49490i) q^{94} +(-0.374736 - 0.649062i) q^{95} +2.17624 q^{97} +(7.92247 - 5.93586i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.07239	+	0.921948i	0.758292	+	0.651915i
$2$	1.07239	+	0.921948i	0.758292	+	0.651915i
$3$		0			0
$3$		0			0
$4$	0.300025	+	1.97737i	0.150013	+	0.988684i
$5$	−0.316953	+	0.548978i	−0.141746	+	0.245511i	−0.928154	−	0.372196i	$-0.878605\pi$
$5$	−0.316953	+	0.548978i	−0.141746	+	0.245511i	0.786408	+	0.617707i	$0.211938\pi$
$6$		0			0
$7$	−2.06297	+	1.65655i	−0.779730	+	0.626116i
$7$	−2.06297	+	1.65655i	−0.779730	+	0.626116i
$8$	−1.50129	+	2.39711i	−0.530785	+	0.847507i
$9$		0			0
$10$	−0.846025	+	0.296503i	−0.267537	+	0.0937625i
$11$	0.424494	−	0.245082i	0.127990	−	0.0738950i	−0.434638	−	0.900605i	$-0.643124\pi$
$11$	0.424494	−	0.245082i	0.127990	−	0.0738950i	0.562628	+	0.826710i	$0.309790\pi$
$12$		0			0
$13$			3.13261i			0.868830i	0.900713	+	0.434415i	$0.143045\pi$
$13$			3.13261i			0.868830i	−0.900713	+	0.434415i	$0.856955\pi$
$14$	−3.73955	−	0.125491i	−0.999437	−	0.0335389i
$15$		0			0
$16$	−3.81997	+	1.18652i	−0.954992	+	0.296630i
$17$	−0.987137	+	0.569924i	−0.239416	+	0.138227i	−0.614908	−	0.788599i	$-0.710807\pi$
$17$	−0.987137	+	0.569924i	−0.239416	+	0.138227i	0.375492	+	0.926825i	$0.377474\pi$
$18$		0			0
$19$	−0.591155	+	1.02391i	−0.135620	+	0.234901i	−0.925834	−	0.377930i	$-0.876636\pi$
$19$	−0.591155	+	1.02391i	−0.135620	+	0.234901i	0.790214	+	0.612831i	$0.209969\pi$
$20$	−1.18063	−	0.462025i	−0.263996	−	0.103312i
$21$		0			0
$22$	0.681175	+	0.128539i	0.145227	+	0.0274046i
$23$	2.80489	−	4.85822i	0.584861	−	1.01301i	−0.410032	−	0.912071i	$-0.634482\pi$
$23$	2.80489	−	4.85822i	0.584861	−	1.01301i	0.994893	−	0.100938i	$-0.0321842\pi$
$24$		0			0
$25$	2.29908	+	3.98213i	0.459816	+	0.796425i
$26$	−2.88810	+	3.35937i	−0.566403	+	0.658826i
$27$		0			0
$28$	−3.89455	−	3.58225i	−0.736001	−	0.676981i
$29$	4.05920			0.753775			0.376887	−	0.926259i	$-0.376994\pi$
$29$	4.05920			0.753775			0.376887	+	0.926259i	$0.376994\pi$
$30$		0			0
$31$	−5.40346	+	3.11969i	−0.970490	+	0.560313i	−0.899386	−	0.437156i	$-0.855986\pi$
$31$	−5.40346	+	3.11969i	−0.970490	+	0.560313i	−0.0711043	+	0.997469i	$0.522652\pi$
$32$	−5.19039	−	2.24940i	−0.917541	−	0.397642i
$33$		0			0
$34$	−1.58403	−	0.298910i	−0.271659	−	0.0512626i
$35$	−0.255545	−	1.65757i	−0.0431949	−	0.280181i
$36$		0			0
$37$	6.53184	+	3.77116i	1.07383	+	0.619975i	0.929225	−	0.369514i	$-0.120476\pi$
$37$	6.53184	+	3.77116i	1.07383	+	0.619975i	0.144604	+	0.989490i	$0.453809\pi$
$38$	−1.57794	+	0.553013i	−0.255975	+	0.0897106i
$39$		0			0
$40$	−0.840125	−	1.58394i	−0.132835	−	0.250444i
$41$		−	4.06598i		−	0.635000i	−0.948258	−	0.317500i	$-0.897157\pi$
$41$		−	4.06598i		−	0.635000i	0.948258	−	0.317500i	$-0.102843\pi$
$42$		0			0
$43$	4.65556			0.709966			0.354983	−	0.934873i	$-0.384487\pi$
$43$	4.65556			0.709966			0.354983	+	0.934873i	$0.384487\pi$
$44$	0.611976	+	0.765851i	0.0922589	+	0.115456i
$45$		0			0
$46$	7.48695	−	2.62392i	1.10389	−	0.386876i
$47$	4.80492	−	8.32236i	0.700869	−	1.21394i	−0.267293	−	0.963615i	$-0.586129\pi$
$47$	4.80492	−	8.32236i	0.700869	−	1.21394i	0.968162	−	0.250325i	$-0.0805375\pi$
$48$		0			0
$49$	1.51170	−	6.83482i	0.215957	−	0.976403i
$50$	−1.20581	+	6.39001i	−0.170527	+	0.903684i
$51$		0			0
$52$	−6.19432	+	0.939863i	−0.858998	+	0.130335i
$53$	1.10444	+	1.91294i	0.151706	+	0.262762i	0.931855	−	0.362832i	$-0.118190\pi$
$53$	1.10444	+	1.91294i	0.151706	+	0.262762i	−0.780149	+	0.625594i	$0.784857\pi$
$54$		0			0
$55$			0.310718i			0.0418971i
$56$	−0.873819	−	7.43212i	−0.116769	−	0.993159i
$57$		0			0
$58$	4.35303	+	3.74237i	0.571581	+	0.491397i
$59$	−9.12119	+	5.26612i	−1.18748	+	0.685591i	−0.957733	−	0.287660i	$-0.907123\pi$
$59$	−9.12119	+	5.26612i	−1.18748	+	0.685591i	−0.229745	+	0.973251i	$0.573789\pi$
$60$		0			0
$61$	10.1718	+	5.87267i	1.30236	+	0.751918i	0.980808	−	0.194974i	$-0.0624623\pi$
$61$	10.1718	+	5.87267i	1.30236	+	0.751918i	0.321552	+	0.946892i	$0.395796\pi$
$62$	−8.67078	−	1.63619i	−1.10119	−	0.207797i
$63$		0			0
$64$	−3.49228	−	7.19750i	−0.436535	−	0.899687i
$65$	−1.71973	−	0.992889i	−0.213307	−	0.123153i
$66$		0			0
$67$	3.11964	+	5.40338i	0.381125	+	0.660128i	0.991223	−	0.132198i	$-0.0422035\pi$
$67$	3.11964	+	5.40338i	0.381125	+	0.660128i	−0.610098	+	0.792326i	$0.708870\pi$
$68$	−1.42312	−	1.78094i	−0.172578	−	0.215971i
$69$		0			0
$70$	1.25415	−	2.01316i	0.149900	−	0.240618i
$71$	5.48681			0.651164			0.325582	−	0.945514i	$-0.394440\pi$
$71$	5.48681			0.651164			0.325582	+	0.945514i	$0.394440\pi$
$72$		0			0
$73$	−5.35648	−	9.27769i	−0.626928	−	1.08587i	−0.988165	−	0.153397i	$-0.950979\pi$
$73$	−5.35648	−	9.27769i	−0.626928	−	1.08587i	0.361237	−	0.932474i	$-0.382355\pi$
$74$	3.52785	+	10.0662i	0.410104	+	1.17017i
$75$		0			0
$76$	−2.20201	−	0.861731i	−0.252588	−	0.0988474i
$77$	−0.469729	+	1.20879i	−0.0535306	+	0.137755i
$78$		0			0
$79$	−2.49304	−	1.43936i	−0.280489	−	0.161940i	0.353156	−	0.935564i	$-0.385109\pi$
$79$	−2.49304	−	1.43936i	−0.280489	−	0.161940i	−0.633645	+	0.773624i	$0.718442\pi$
$80$	0.559375	−	2.47315i	0.0625401	−	0.276507i
$81$		0			0
$82$	3.74862	−	4.36031i	0.413966	−	0.481515i
$83$		−	14.1254i		−	1.55047i	−0.631674	−	0.775234i	$-0.717632\pi$
$83$		−	14.1254i		−	1.55047i	0.631674	−	0.775234i	$-0.282368\pi$
$84$		0			0
$85$		−	0.722556i		−	0.0783722i
$86$	4.99256	+	4.29218i	0.538361	+	0.462838i
$87$		0			0
$88$	−0.0497991	+	1.38550i	−0.00530860	+	0.147695i
$89$	9.12417	+	5.26784i	0.967160	+	0.558390i	0.898369	−	0.439241i	$-0.144753\pi$
$89$	9.12417	+	5.26784i	0.967160	+	0.558390i	0.0687909	+	0.997631i	$0.478086\pi$
$90$		0			0
$91$	−5.18932	−	6.46248i	−0.543988	−	0.677452i
$92$	10.4480	+	4.08872i	1.08928	+	0.426278i
$93$		0			0
$94$	12.8255	−	4.49490i	1.32285	−	0.463614i
$95$	−0.374736	−	0.649062i	−0.0384471	−	0.0665924i
$96$		0			0
$97$	2.17624			0.220964			0.110482	−	0.993878i	$-0.464761\pi$
$97$	2.17624			0.220964			0.110482	+	0.993878i	$0.464761\pi$
$98$	7.92247	−	5.93586i	0.800290	−	0.599613i
$99$		0			0
$100$	−7.18435	+	5.74087i	−0.718435	+	0.574087i
$101$	8.04374	+	13.9322i	0.800382	+	1.38630i	0.919365	+	0.393406i	$0.128703\pi$
$101$	8.04374	+	13.9322i	0.800382	+	1.38630i	−0.118982	+	0.992896i	$0.537963\pi$
$102$		0			0
$103$	−11.2490	−	6.49462i	−1.10840	−	0.639934i	−0.169984	−	0.985447i	$-0.554372\pi$
$103$	−11.2490	−	6.49462i	−1.10840	−	0.639934i	−0.938414	+	0.345513i	$0.887705\pi$
$104$	−7.50921	−	4.70294i	−0.736339	−	0.461162i
$105$		0			0
$106$	−0.579248	+	3.06964i	−0.0562615	+	0.298150i
$107$	0.0316330	+	0.0182633i	0.00305808	+	0.00176558i	0.501528	−	0.865141i	$-0.332771\pi$
$107$	0.0316330	+	0.0182633i	0.00305808	+	0.00176558i	−0.498470	+	0.866907i	$0.666105\pi$
$108$		0			0
$109$	14.8136	−	8.55264i	1.41889	−	0.819195i	0.422685	−	0.906276i	$-0.361088\pi$
$109$	14.8136	−	8.55264i	1.41889	−	0.819195i	0.996201	+	0.0870820i	$0.0277542\pi$
$110$	−0.286465	+	0.333209i	−0.0273134	+	0.0317703i
$111$		0			0
$112$	5.91496	−	8.77572i	0.558911	−	0.829228i
$113$		−	7.98162i		−	0.750848i	−0.926853	−	0.375424i	$-0.877497\pi$
$113$		−	7.98162i		−	0.750848i	0.926853	−	0.375424i	$-0.122503\pi$
$114$		0			0
$115$	1.77804	+	3.07965i	0.165803	+	0.287179i
$116$	1.21786	+	8.02653i	0.113076	+	0.745245i
$117$		0			0
$118$	−14.6365	−	2.76194i	−1.34740	−	0.254257i
$119$	1.09233	−	2.81098i	0.100134	−	0.257682i
$120$		0			0
$121$	−5.37987	+	9.31821i	−0.489079	+	0.847110i
$122$	5.49376	+	15.6756i	0.497382	+	1.41920i
$123$		0			0
$124$	−7.78995	−	9.74864i	−0.699558	−	0.875454i
$125$	−6.08433			−0.544199
$126$		0			0
$127$		−	7.35098i		−	0.652294i	−0.945319	−	0.326147i	$-0.894250\pi$
$127$		−	7.35098i		−	0.652294i	0.945319	−	0.326147i	$-0.105750\pi$
$128$	2.89064	−	10.9382i	0.255499	−	0.966809i
$129$		0			0
$130$	−0.928828	−	2.65027i	−0.0814636	−	0.232444i
$131$	17.8525	+	10.3071i	1.55978	+	0.900540i	0.997277	+	0.0737443i	$0.0234949\pi$
$131$	17.8525	+	10.3071i	1.55978	+	0.900540i	0.562503	+	0.826795i	$0.309838\pi$
$132$		0			0
$133$	−0.476621	−	3.09157i	−0.0413283	−	0.268073i
$134$	−1.63617	+	8.67065i	−0.141344	+	0.749031i
$135$		0			0
$136$	0.115805	−	3.22190i	0.00993020	−	0.276275i
$137$	−0.0286513	+	0.0165418i	−0.00244784	+	0.00141326i	−0.501223	−	0.865318i	$-0.667117\pi$
$137$	−0.0286513	+	0.0165418i	−0.00244784	+	0.00141326i	0.498776	+	0.866731i	$0.333783\pi$
$138$		0			0
$139$	−17.8470			−1.51376			−0.756882	−	0.653551i	$-0.773278\pi$
$139$	−17.8470			−1.51376			−0.756882	+	0.653551i	$0.773278\pi$
$140$	3.20096	−	1.00262i	0.270531	−	0.0847369i
$141$		0			0
$142$	5.88398	+	5.05855i	0.493772	+	0.424504i
$143$	0.767746	+	1.32977i	0.0642021	+	0.111201i
$144$		0			0
$145$	−1.28658	+	2.22841i	−0.106844	+	0.185060i
$146$	2.80933	−	14.8877i	0.232502	−	1.23211i
$147$		0			0
$148$	−5.49726	+	14.0473i	−0.451872	+	1.15468i
$149$	−9.23859	+	16.0017i	−0.756854	+	1.31091i	0.187593	+	0.982247i	$0.439932\pi$
$149$	−9.23859	+	16.0017i	−0.756854	+	1.31091i	−0.944447	+	0.328663i	$0.893402\pi$
$150$		0			0
$151$	−1.33762	+	0.772277i	−0.108854	+	0.0628470i	−0.553439	−	0.832890i	$-0.686685\pi$
$151$	−1.33762	+	0.772277i	−0.108854	+	0.0628470i	0.444584	+	0.895737i	$0.353351\pi$
$152$	−1.56693	−	2.95424i	−0.127095	−	0.239621i
$153$		0			0
$154$	−1.61817	+	0.863226i	−0.130396	+	0.0695608i
$155$		−	3.95518i		−	0.317687i
$156$		0			0
$157$	0.912293	−	0.526713i	0.0728089	−	0.0420362i	−0.463154	−	0.886278i	$-0.653282\pi$
$157$	0.912293	−	0.526713i	0.0728089	−	0.0420362i	0.535963	+	0.844242i	$0.319949\pi$
$158$	−1.34649	−	3.84200i	−0.107121	−	0.305653i
$159$		0			0
$160$	2.87998	−	2.13646i	0.227683	−	0.168902i
$161$	2.26146	+	14.6688i	0.178228	+	1.15606i
$162$		0			0
$163$	2.47123	−	4.28030i	0.193562	−	0.335259i	−0.752866	−	0.658174i	$-0.771329\pi$
$163$	2.47123	−	4.28030i	0.193562	−	0.335259i	0.946428	+	0.322914i	$0.104663\pi$
$164$	8.03995	−	1.21990i	0.627814	−	0.0952581i
$165$		0			0
$166$	13.0229	−	15.1479i	1.01077	−	1.17571i
$167$	−15.0325			−1.16325			−0.581627	−	0.813456i	$-0.697584\pi$
$167$	−15.0325			−1.16325			−0.581627	+	0.813456i	$0.697584\pi$
$168$		0			0
$169$	3.18676			0.245135
$170$	0.666159	−	0.774859i	0.0510920	−	0.0594290i
$171$		0			0
$172$	1.39679	+	9.20575i	0.106504	+	0.701932i
$173$	4.77283	−	8.26678i	0.362871	−	0.628511i	−0.625561	−	0.780175i	$-0.715130\pi$
$173$	4.77283	−	8.26678i	0.362871	−	0.628511i	0.988432	+	0.151664i	$0.0484631\pi$
$174$		0			0
$175$	−11.3395	−	4.40647i	−0.857187	−	0.333098i
$176$	−1.33076	+	1.43988i	−0.100310	+	0.108535i
$177$		0			0
$178$	4.92796	+	14.0612i	0.369366	+	1.05393i
$179$	2.84235	−	1.64103i	0.212447	−	0.122656i	−0.390001	−	0.920814i	$-0.627525\pi$
$179$	2.84235	−	1.64103i	0.212447	−	0.122656i	0.602448	+	0.798158i	$0.294192\pi$
$180$		0			0
$181$			1.67052i			0.124169i	0.998071	+	0.0620845i	$0.0197748\pi$
$181$			1.67052i			0.124169i	−0.998071	+	0.0620845i	$0.980225\pi$
$182$	0.393115	−	11.7146i	0.0291396	−	0.868341i
$183$		0			0
$184$	7.43474	+	14.0172i	0.548096	+	1.03336i
$185$	−4.14057	+	2.39056i	−0.304421	+	0.175758i
$186$		0			0
$187$	−0.279356	+	0.483859i	−0.0204285	+	0.0353833i
$188$	17.8980	+	7.00417i	1.30534	+	0.510831i
$189$		0			0
$190$	0.196539	−	1.04153i	0.0142585	−	0.0755607i
$191$	−0.339200	+	0.587512i	−0.0245436	+	0.0425108i	−0.878036	−	0.478594i	$-0.841147\pi$
$191$	−0.339200	+	0.587512i	−0.0245436	+	0.0425108i	0.853493	+	0.521105i	$0.174480\pi$
$192$		0			0
$193$	7.08605	+	12.2734i	0.510065	+	0.883458i	0.999932	+	0.0116611i	$0.00371192\pi$
$193$	7.08605	+	12.2734i	0.510065	+	0.883458i	−0.489867	+	0.871797i	$0.662955\pi$
$194$	2.33377	+	2.00638i	0.167555	+	0.144050i
$195$		0			0
$196$	13.9685	+	0.938561i	0.997750	+	0.0670401i
$197$	−21.5805			−1.53755			−0.768773	−	0.639522i	$-0.779132\pi$
$197$	−21.5805			−1.53755			−0.768773	+	0.639522i	$0.779132\pi$
$198$		0			0
$199$	5.79242	−	3.34425i	0.410614	−	0.237068i	−0.280440	−	0.959872i	$-0.590480\pi$
$199$	5.79242	−	3.34425i	0.410614	−	0.237068i	0.691053	+	0.722804i	$0.257147\pi$
$200$	−12.9972	−	0.467159i	−0.919039	−	0.0330331i
$201$		0			0
$202$	−4.21873	+	22.3566i	−0.296829	+	1.57300i
$203$	−8.37401	+	6.72426i	−0.587740	+	0.471951i
$204$		0			0
$205$	2.23214	+	1.28873i	0.155899	+	0.0900085i
$206$	−6.07559	−	17.3357i	−0.423306	−	1.20784i
$207$		0			0
$208$	−3.71691	−	11.9665i	−0.257721	−	0.829726i
$209$			0.579525i			0.0400866i
$210$		0			0
$211$	15.8419			1.09060			0.545301	−	0.838241i	$-0.316416\pi$
$211$	15.8419			1.09060			0.545301	+	0.838241i	$0.316416\pi$
$212$	−3.45123	+	2.75781i	−0.237031	+	0.189407i
$213$		0			0
$214$	0.0170850	+	0.0487493i	0.00116790	+	0.00333243i
$215$	−1.47559	+	2.55580i	−0.100635	+	0.174304i
$216$		0			0
$217$	5.97926	−	15.3869i	0.405899	−	1.04453i
$218$	23.7710	+	4.48563i	1.60998	+	0.303805i
$219$		0			0
$220$	−0.614403	+	0.0932232i	−0.0414230	+	0.00628511i
$221$	−1.78535	−	3.09231i	−0.120096	−	0.208012i
$222$		0			0
$223$			5.00823i			0.335376i	0.985840	+	0.167688i	$0.0536301\pi$
$223$			5.00823i			0.335376i	−0.985840	+	0.167688i	$0.946370\pi$
$224$	14.4339	−	3.95769i	0.964404	−	0.264434i
$225$		0			0
$226$	7.35864	−	8.55939i	0.489489	−	0.569362i
$227$	−22.1014	+	12.7603i	−1.46692	+	0.846928i	−0.999315	−	0.0370085i	$-0.988217\pi$
$227$	−22.1014	+	12.7603i	−1.46692	+	0.846928i	−0.467607	+	0.883936i	$0.654884\pi$
$228$		0			0
$229$	−21.0883	−	12.1753i	−1.39355	−	0.804568i	−0.399846	−	0.916582i	$-0.630936\pi$
$229$	−21.0883	−	12.1753i	−1.39355	−	0.804568i	−0.993707	+	0.112014i	$0.964270\pi$
$230$	−0.932534	+	4.94184i	−0.0614895	+	0.325855i
$231$		0			0
$232$	−6.09402	+	9.73035i	−0.400092	+	0.638829i
$233$	−19.1428	−	11.0521i	−1.25409	−	0.724047i	−0.282168	−	0.959365i	$-0.591054\pi$
$233$	−19.1428	−	11.0521i	−1.25409	−	0.724047i	−0.971919	+	0.235317i	$0.924387\pi$
$234$		0			0
$235$	3.04586	+	5.27559i	0.198690	+	0.344141i
$236$	−13.1497	−	16.4560i	−0.855969	−	1.07119i
$237$		0			0
$238$	3.76297	−	2.00738i	0.243917	−	0.130119i
$239$	−21.8072			−1.41059			−0.705295	−	0.708914i	$-0.749185\pi$
$239$	−21.8072			−1.41059			−0.705295	+	0.708914i	$0.749185\pi$
$240$		0			0
$241$	−9.66034	−	16.7322i	−0.622277	−	1.07782i	−0.989061	−	0.147510i	$-0.952874\pi$
$241$	−9.66034	−	16.7322i	−0.622277	−	1.07782i	0.366783	−	0.930306i	$-0.380459\pi$
$242$	−14.3602	+	5.03276i	−0.923109	+	0.323518i
$243$		0			0
$244$	−8.56064	+	21.8753i	−0.548039	+	1.40042i
$245$	3.27303	+	2.99620i	0.209106	+	0.191420i
$246$		0			0
$247$	−3.20751	−	1.85186i	−0.204089	−	0.117831i
$248$	0.633901	−	17.6362i	0.0402528	−	1.11990i
$249$		0			0
$250$	−6.52475	−	5.60943i	−0.412662	−	0.354772i
$251$		−	2.04696i		−	0.129203i	−0.997911	−	0.0646015i	$-0.979422\pi$
$251$		−	2.04696i		−	0.129203i	0.997911	−	0.0646015i	$-0.0205776\pi$
$252$		0			0
$253$		−	2.74971i		−	0.172873i
$254$	6.77721	−	7.88309i	0.425240	−	0.494629i
$255$		0			0
$256$	13.1843	−	9.06495i	0.824021	−	0.566560i
$257$	18.7909	+	10.8489i	1.17214	+	0.676738i	0.954184	−	0.299220i	$-0.0967264\pi$
$257$	18.7909	+	10.8489i	1.17214	+	0.676738i	0.217960	+	0.975958i	$0.430060\pi$
$258$		0			0
$259$	−19.7221	+	3.04052i	−1.22547	+	0.188929i
$260$	1.44734	−	3.69844i	0.0897604	−	0.229368i
$261$		0			0
$262$	9.64213	+	27.5123i	0.595693	+	1.69972i
$263$	−6.40425	−	11.0925i	−0.394903	−	0.683991i	0.598186	−	0.801357i	$-0.295888\pi$
$263$	−6.40425	−	11.0925i	−0.394903	−	0.683991i	−0.993089	+	0.117366i	$0.962555\pi$
$264$		0			0
$265$	−1.40022			−0.0860146
$266$	2.33915	−	3.75478i	0.143422	−	0.230220i
$267$		0			0
$268$	−9.74849	+	7.78983i	−0.595484	+	0.475840i
$269$	−13.4541	−	23.3033i	−0.820314	−	1.42082i	−0.905449	−	0.424455i	$-0.860466\pi$
$269$	−13.4541	−	23.3033i	−0.820314	−	1.42082i	0.0851352	−	0.996369i	$-0.472868\pi$
$270$		0			0
$271$	12.9026	+	7.44933i	0.783779	+	0.452515i	0.837768	−	0.546027i	$-0.183860\pi$
$271$	12.9026	+	7.44933i	0.783779	+	0.452515i	−0.0539891	+	0.998542i	$0.517194\pi$
$272$	3.09461	−	3.34835i	0.187638	−	0.203024i
$273$		0			0
$274$	−0.0459760	−	0.00867575i	−0.00277751	−	0.000524121i
$275$	1.95189	+	1.12693i	0.117704	+	0.0679562i
$276$		0			0
$277$	−6.96901	+	4.02356i	−0.418727	+	0.241752i	−0.694533	−	0.719461i	$-0.744389\pi$
$277$	−6.96901	+	4.02356i	−0.418727	+	0.241752i	0.275805	+	0.961213i	$0.411055\pi$
$278$	−19.1389	−	16.4540i	−1.14787	−	0.986846i
$279$		0			0
$280$	4.35703	+	1.87592i	0.260383	+	0.112108i
$281$		−	17.7045i		−	1.05616i	−0.849195	−	0.528080i	$-0.822912\pi$
$281$		−	17.7045i		−	1.05616i	0.849195	−	0.528080i	$-0.177088\pi$
$282$		0			0
$283$	12.0878	+	20.9367i	0.718545	+	1.24456i	0.961576	+	0.274538i	$0.0885249\pi$
$283$	12.0878	+	20.9367i	0.718545	+	1.24456i	−0.243031	+	0.970018i	$0.578142\pi$
$284$	1.64618	+	10.8494i	0.0976829	+	0.643796i
$285$		0			0
$286$	−0.402662	+	2.13385i	−0.0238099	+	0.126177i
$287$	6.73550	+	8.38801i	0.397584	+	0.495128i
$288$		0			0
$289$	−7.85037	+	13.5972i	−0.461787	+	0.799838i
$290$	−3.43419	+	1.20357i	−0.201662	+	0.0706758i
$291$		0			0
$292$	16.7383	−	13.3753i	0.979536	−	0.782728i
$293$	−3.79788			−0.221874			−0.110937	−	0.993827i	$-0.535385\pi$
$293$	−3.79788			−0.221874			−0.110937	+	0.993827i	$0.535385\pi$
$294$		0			0
$295$		−	6.67645i		−	0.388718i
$296$	−18.8461	+	9.99596i	−1.09541	+	0.581003i
$297$		0			0
$298$	−24.6601	+	8.64252i	−1.42852	+	0.500647i
$299$	15.2189	+	8.78664i	0.880132	+	0.508144i
$300$		0			0
$301$	−9.60428	+	7.71216i	−0.553581	+	0.444521i
$302$	−2.14645	−	0.405039i	−0.123514	−	0.0233074i
$303$		0			0
$304$	1.04330	−	4.61272i	0.0598374	−	0.264558i
$305$	−6.44793	+	3.72272i	−0.369208	+	0.213162i
$306$		0			0
$307$	−11.4307			−0.652387			−0.326193	−	0.945303i	$-0.605766\pi$
$307$	−11.4307			−0.652387			−0.326193	+	0.945303i	$0.605766\pi$
$308$	−2.53116	−	0.566159i	−0.144226	−	0.0322599i
$309$		0			0
$310$	3.64646	−	4.24148i	0.207105	−	0.240900i
$311$	7.73439	+	13.3964i	0.438577	+	0.759638i	0.997580	−	0.0695277i	$-0.0221492\pi$
$311$	7.73439	+	13.3964i	0.438577	+	0.759638i	−0.559003	+	0.829166i	$0.688816\pi$
$312$		0			0
$313$	−8.64467	+	14.9730i	−0.488626	+	0.846325i	−0.999914	−	0.0130845i	$-0.995835\pi$
$313$	−8.64467	+	14.9730i	−0.488626	+	0.846325i	0.511289	+	0.859409i	$0.329168\pi$
$314$	1.46393	+	0.276247i	0.0826145	+	0.0155895i
$315$		0			0
$316$	2.09816	−	5.36150i	0.118031	−	0.301608i
$317$	6.94130	−	12.0227i	0.389863	−	0.675262i	−0.602568	−	0.798067i	$-0.705856\pi$
$317$	6.94130	−	12.0227i	0.389863	−	0.675262i	0.992431	+	0.122806i	$0.0391892\pi$
$318$		0			0
$319$	1.72311	−	0.994837i	0.0964755	−	0.0557002i
$320$	5.05816	+	0.364082i	0.282760	+	0.0203528i
$321$		0			0
$322$	−11.0987	+	17.8156i	−0.618507	+	0.992823i
$323$		−	1.34765i		−	0.0749854i
$324$		0			0
$325$	−12.4744	+	7.20213i	−0.691958	+	0.399502i
$326$	6.59633	−	2.31179i	0.365337	−	0.128038i
$327$		0			0
$328$	9.74661	+	6.10421i	0.538167	+	0.337048i
$329$	3.87399	+	25.1284i	0.213580	+	1.38537i
$330$		0			0
$331$	16.4684	−	28.5241i	0.905185	−	1.56783i	0.0845160	−	0.996422i	$-0.473066\pi$
$331$	16.4684	−	28.5241i	0.905185	−	1.56783i	0.820669	−	0.571404i	$-0.193601\pi$
$332$	27.9312	−	4.23799i	1.53292	−	0.232590i
$333$		0			0
$334$	−16.1207	−	13.8592i	−0.882086	−	0.758343i
$335$	−3.95512			−0.216091
$336$		0			0
$337$	4.92898			0.268499			0.134249	−	0.990948i	$-0.457138\pi$
$337$	4.92898			0.268499			0.134249	+	0.990948i	$0.457138\pi$
$338$	3.41744	+	2.93802i	0.185884	+	0.159807i
$339$		0			0
$340$	1.42876	−	0.216785i	0.0774853	−	0.0117568i
$341$	−1.52916	+	2.64858i	−0.0828086	+	0.143429i
$342$		0			0
$343$	8.20362	+	16.6042i	0.442954	+	0.896544i
$344$	−6.98933	+	11.1599i	−0.376839	+	0.601701i
$345$		0			0
$346$	12.7398	−	4.46488i	0.684898	−	0.240034i
$347$	14.0594	−	8.11720i	0.754749	−	0.435754i	−0.0726585	−	0.997357i	$-0.523148\pi$
$347$	14.0594	−	8.11720i	0.754749	−	0.435754i	0.827407	+	0.561603i	$0.189815\pi$
$348$		0			0
$349$		−	8.62152i		−	0.461499i	−0.973013	−	0.230750i	$-0.925882\pi$
$349$		−	8.62152i		−	0.461499i	0.973013	−	0.230750i	$-0.0741178\pi$
$350$	−8.09782	−	15.1799i	−0.432846	−	0.811399i
$351$		0			0
$352$	−2.75458	+	0.317213i	−0.146820	+	0.0169075i
$353$	14.7933	−	8.54090i	0.787367	−	0.454586i	−0.0516680	−	0.998664i	$-0.516454\pi$
$353$	14.7933	−	8.54090i	0.787367	−	0.454586i	0.839035	+	0.544078i	$0.183120\pi$
$354$		0			0
$355$	−1.73906	+	3.01214i	−0.0922997	+	0.159868i
$356$	−7.67898	+	19.6223i	−0.406985	+	1.03998i
$357$		0			0
$358$	4.56104	+	0.860678i	0.241059	+	0.0454882i
$359$	−12.6622	+	21.9316i	−0.668285	+	1.15750i	0.310099	+	0.950704i	$0.399638\pi$
$359$	−12.6622	+	21.9316i	−0.668285	+	1.15750i	−0.978383	+	0.206799i	$0.933695\pi$
$360$		0			0
$361$	8.80107	+	15.2439i	0.463214	+	0.802311i
$362$	−1.54013	+	1.79145i	−0.0809477	+	0.0941563i
$363$		0			0
$364$	11.2218	−	12.2001i	0.588181	−	0.639459i
$365$	6.79100			0.355457
$366$		0			0
$367$	16.9496	−	9.78583i	0.884760	−	0.510816i	0.0125348	−	0.999921i	$-0.496010\pi$
$367$	16.9496	−	9.78583i	0.884760	−	0.510816i	0.872225	+	0.489105i	$0.162677\pi$
$368$	−4.95023	+	21.8863i	−0.258048	+	1.14090i
$369$		0			0
$370$	−6.64427	−	1.25379i	−0.345419	−	0.0651812i
$371$	−5.44730	−	2.11679i	−0.282810	−	0.109898i
$372$		0			0
$373$	−30.0203	−	17.3322i	−1.55439	−	0.897429i	−0.997776	−	0.0666604i	$-0.978766\pi$
$373$	−30.0203	−	17.3322i	−1.55439	−	0.897429i	−0.556617	−	0.830769i	$-0.687901\pi$
$374$	−0.745670	+	0.261332i	−0.0385577	+	0.0135132i
$375$		0			0
$376$	12.7361	+	24.0122i	0.656812	+	1.23833i
$377$			12.7159i			0.654902i
$378$		0			0
$379$	24.9877			1.28353			0.641765	−	0.766901i	$-0.278203\pi$
$379$	24.9877			1.28353			0.641765	+	0.766901i	$0.278203\pi$
$380$	1.17100	−	0.935727i	0.0600713	−	0.0480018i
$381$		0			0
$382$	−0.905408	+	0.317315i	−0.0463247	+	0.0162352i
$383$	1.70505	−	2.95323i	0.0871239	−	0.150903i	−0.819170	−	0.573550i	$-0.805566\pi$
$383$	1.70505	−	2.95323i	0.0871239	−	0.150903i	0.906294	+	0.422647i	$0.138899\pi$
$384$		0			0
$385$	−0.514719	−	0.641001i	−0.0262325	−	0.0326684i
$386$	−3.71644	+	19.6948i	−0.189162	+	1.00244i
$387$		0			0
$388$	0.652928	+	4.30323i	0.0331474	+	0.218463i
$389$	7.12599	+	12.3426i	0.361302	+	0.625794i	0.988175	−	0.153328i	$-0.0489990\pi$
$389$	7.12599	+	12.3426i	0.361302	+	0.625794i	−0.626873	+	0.779121i	$0.715666\pi$
$390$		0			0
$391$			6.39430i			0.323374i
$392$	14.1143	+	13.8847i	0.712881	+	0.701285i
$393$		0			0
$394$	−23.1426	−	19.8961i	−1.16591	−	1.00235i
$395$	1.58035	−	0.912416i	0.0795161	−	0.0459086i
$396$		0			0
$397$	15.4930	+	8.94489i	0.777571	+	0.448931i	0.835569	−	0.549386i	$-0.185138\pi$
$397$	15.4930	+	8.94489i	0.777571	+	0.448931i	−0.0579974	+	0.998317i	$0.518472\pi$
$398$	9.29494	+	1.75397i	0.465913	+	0.0879187i
$399$		0			0
$400$	−13.5073	−	12.4837i	−0.675365	−	0.624185i
$401$	−23.6304	−	13.6430i	−1.18005	−	0.681299i	−0.224020	−	0.974585i	$-0.571918\pi$
$401$	−23.6304	−	13.6430i	−1.18005	−	0.681299i	−0.956025	+	0.293285i	$0.905251\pi$
$402$		0			0
$403$	−9.77276	−	16.9269i	−0.486816	−	0.843190i
$404$	−25.1357	+	20.0854i	−1.25055	+	0.999288i
$405$		0			0
$406$	−15.1796	−	0.509394i	−0.753351	−	0.0252808i
$407$	3.69697			0.183252
$408$		0			0
$409$	−10.0843	−	17.4666i	−0.498638	−	0.863667i	0.501360	−	0.865239i	$-0.332833\pi$
$409$	−10.0843	−	17.4666i	−0.498638	−	0.863667i	−0.999999	+	0.00157143i	$0.999500\pi$
$410$	1.20558	+	3.43993i	0.0595392	+	0.169886i
$411$		0			0
$412$	9.46726	−	24.1920i	0.466418	−	1.19185i
$413$	10.0932	−	25.9735i	0.496652	−	1.27807i
$414$		0			0
$415$	7.75456	+	4.47710i	0.380656	+	0.219772i
$416$	7.04650	−	16.2595i	0.345483	−	0.797186i
$417$		0			0
$418$	−0.534292	+	0.621475i	−0.0261331	+	0.0303973i
$419$		−	13.2211i		−	0.645895i	−0.946417	−	0.322947i	$-0.895326\pi$
$419$		−	13.2211i		−	0.645895i	0.946417	−	0.322947i	$-0.104674\pi$
$420$		0			0
$421$		−	4.11935i		−	0.200765i	−0.994949	−	0.100382i	$-0.967993\pi$
$421$		−	4.11935i		−	0.200765i	0.994949	−	0.100382i	$-0.0320066\pi$
$422$	16.9886	+	14.6054i	0.826994	+	0.710980i
$423$		0			0
$424$	−6.24360	−	0.224415i	−0.303216	−	0.0108985i
$425$	−4.53902	−	2.62060i	−0.220175	−	0.127118i
$426$		0			0
$427$	−30.7124	+	4.73487i	−1.48628	+	0.229136i
$428$	−0.0266226	+	0.0680295i	−0.00128685	+	0.00328833i
$429$		0			0
$430$	−3.93872	+	1.38039i	−0.189942	+	0.0665682i
$431$	18.6205	+	32.2516i	0.896916	+	1.55350i	0.831415	+	0.555652i	$0.187531\pi$
$431$	18.6205	+	32.2516i	0.896916	+	1.55350i	0.0655008	+	0.997853i	$0.479136\pi$
$432$		0			0
$433$	26.9948			1.29729			0.648644	−	0.761092i	$-0.275337\pi$
$433$	26.9948			1.29729			0.648644	+	0.761092i	$0.275337\pi$
$434$	20.5980	−	10.9882i	0.988736	−	0.527448i
$435$		0			0
$436$	21.3562	+	26.7260i	1.02278	+	1.27994i
$437$	3.31625	+	5.74392i	0.158638	+	0.274769i
$438$		0			0
$439$	24.9138	+	14.3840i	1.18907	+	0.686510i	0.958095	−	0.286450i	$-0.0924752\pi$
$439$	24.9138	+	14.3840i	1.18907	+	0.686510i	0.230975	+	0.972960i	$0.425809\pi$
$440$	−0.744824	−	0.466476i	−0.0355081	−	0.0222384i
$441$		0			0
$442$	0.936368	−	4.96215i	0.0445385	−	0.236026i
$443$	1.87416	+	1.08205i	0.0890442	+	0.0514097i	0.543861	−	0.839175i	$-0.316962\pi$
$443$	1.87416	+	1.08205i	0.0890442	+	0.0514097i	−0.454817	+	0.890585i	$0.650295\pi$
$444$		0			0
$445$	−5.78386	+	3.33932i	−0.274181	+	0.158299i
$446$	−4.61732	+	5.37076i	−0.218637	+	0.254313i
$447$		0			0
$448$	19.1275	+	9.06310i	0.903688	+	0.428191i
$449$		−	18.0886i		−	0.853652i	−0.904334	−	0.426826i	$-0.859632\pi$
$449$		−	18.0886i		−	0.853652i	0.904334	−	0.426826i	$-0.140368\pi$
$450$		0			0
$451$	−0.996499	−	1.72599i	−0.0469233	−	0.0812736i
$452$	15.7826	−	2.39469i	0.742352	−	0.112637i
$453$		0			0
$454$	−35.4655	−	6.69242i	−1.66448	−	0.314091i
$455$	5.19253	−	0.800522i	0.243430	−	0.0375290i
$456$		0			0
$457$	2.47619	−	4.28888i	0.115831	−	0.200625i	−0.802281	−	0.596947i	$-0.796380\pi$
$457$	2.47619	−	4.28888i	0.115831	−	0.200625i	0.918112	+	0.396322i	$0.129714\pi$
$458$	−11.3898	−	32.4989i	−0.532209	−	1.51858i
$459$		0			0
$460$	−5.55615	+	4.43981i	−0.259057	+	0.207007i
$461$	33.3858			1.55493			0.777465	−	0.628926i	$-0.216505\pi$
$461$	33.3858			1.55493			0.777465	+	0.628926i	$0.216505\pi$
$462$		0			0
$463$		−	3.79774i		−	0.176496i	−0.996099	−	0.0882479i	$-0.971873\pi$
$463$		−	3.79774i		−	0.176496i	0.996099	−	0.0882479i	$-0.0281268\pi$
$464$	−15.5060	+	4.81633i	−0.719849	+	0.223592i
$465$		0			0
$466$	−10.3390	−	29.5008i	−0.478946	−	1.36660i
$467$	1.07261	+	0.619273i	0.0496346	+	0.0286565i	0.524612	−	0.851341i	$-0.324210\pi$
$467$	1.07261	+	0.619273i	0.0496346	+	0.0286565i	−0.474977	+	0.879998i	$0.657544\pi$
$468$		0			0
$469$	−15.3867	−	5.97917i	−0.710491	−	0.276093i
$470$	−1.59747	+	8.46560i	−0.0736860	+	0.390489i
$471$		0			0
$472$	1.07004	−	29.7705i	0.0492527	−	1.37030i
$473$	1.97626	−	1.14099i	0.0908684	−	0.0524629i
$474$		0			0
$475$	−5.43645			−0.249441
$476$	5.88606	+	1.31657i	0.269787	+	0.0603449i
$477$		0			0
$478$	−23.3857	−	20.1051i	−1.06964	−	0.919585i
$479$	−2.76851	−	4.79520i	−0.126497	−	0.219098i	0.795820	−	0.605533i	$-0.207040\pi$
$479$	−2.76851	−	4.79520i	−0.126497	−	0.219098i	−0.922317	+	0.386434i	$0.873707\pi$
$480$		0			0
$481$	−11.8136	+	20.4617i	−0.538653	+	0.932974i
$482$	5.06659	−	26.8497i	0.230777	−	1.22297i
$483$		0			0
$484$	−20.0396	−	7.84228i	−0.910892	−	0.356467i
$485$	−0.689766	+	1.19471i	−0.0313206	+	0.0542489i
$486$		0			0
$487$	26.5146	−	15.3082i	1.20149	−	0.693681i	0.240604	−	0.970623i	$-0.422655\pi$
$487$	26.5146	−	15.3082i	1.20149	−	0.693681i	0.960886	+	0.276943i	$0.0893212\pi$
$488$	−29.3482	+	15.5663i	−1.32853	+	0.704652i
$489$		0			0
$490$	0.747612	+	6.23065i	0.0337737	+	0.281472i
$491$		−	23.4948i		−	1.06030i	−0.847903	−	0.530152i	$-0.822135\pi$
$491$		−	23.4948i		−	1.06030i	0.847903	−	0.530152i	$-0.177865\pi$
$492$		0			0
$493$	−4.00699	+	2.31344i	−0.180466	+	0.104192i
$494$	−1.73238	−	4.94306i	−0.0779432	−	0.222399i
$495$		0			0
$496$	16.9395	−	18.3284i	0.760605	−	0.822971i
$497$	−11.3191	+	9.08916i	−0.507732	+	0.407705i
$498$		0			0
$499$	12.0682	−	20.9027i	0.540246	−	0.935733i	−0.458644	−	0.888620i	$-0.651665\pi$
$499$	12.0682	−	20.9027i	0.540246	−	0.935733i	0.998890	−	0.0471131i	$-0.0150021\pi$
$500$	−1.82545	−	12.0310i	−0.0816368	−	0.538041i
$501$		0			0
$502$	1.88719	−	2.19513i	0.0842295	−	0.0979736i
$503$	36.3978			1.62290			0.811449	−	0.584424i	$-0.198679\pi$
$503$	36.3978			1.62290			0.811449	+	0.584424i	$0.198679\pi$
$504$		0			0
$505$	−10.1979			−0.453803
$506$	2.53509	−	2.94876i	0.112699	−	0.131088i
$507$		0			0
$508$	14.5356	−	2.20548i	0.644912	−	0.0978523i
$509$	19.9466	−	34.5486i	0.884119	−	1.53134i	0.0373991	−	0.999300i	$-0.488093\pi$
$509$	19.9466	−	34.5486i	0.884119	−	1.53134i	0.846720	−	0.532039i	$-0.178574\pi$
$510$		0			0
$511$	26.4192	+	10.2663i	1.16872	+	0.454156i
$512$	22.4961	+	2.43413i	0.994197	+	0.107574i
$513$		0			0
$514$	10.1490	+	28.9585i	0.447651	+	1.27730i
$515$	7.13081	−	4.11697i	0.314221	−	0.181416i
$516$		0			0
$517$		−	4.71039i		−	0.207163i
$518$	−23.9529	−	14.9221i	−1.05243	−	0.655642i
$519$		0			0
$520$	4.96188	−	2.63178i	0.217593	−	0.115411i
$521$	22.8772	−	13.2082i	1.00227	−	0.578660i	0.0933493	−	0.995633i	$-0.470243\pi$
$521$	22.8772	−	13.2082i	1.00227	−	0.578660i	0.908918	+	0.416974i	$0.136909\pi$
$522$		0			0
$523$	−2.15196	+	3.72730i	−0.0940986	+	0.162984i	−0.909232	−	0.416290i	$-0.863330\pi$
$523$	−2.15196	+	3.72730i	−0.0940986	+	0.162984i	0.815133	+	0.579273i	$0.196664\pi$
$524$	−15.0248	+	38.3934i	−0.656362	+	1.67722i
$525$		0			0
$526$	3.35886	−	17.7998i	0.146453	−	0.776108i
$527$	3.55597	−	6.15912i	0.154900	−	0.268295i
$528$		0			0
$529$	−4.23486	−	7.33500i	−0.184124	−	0.318913i
$530$	−1.50157	−	1.29093i	−0.0652242	−	0.0560743i
$531$		0			0
$532$	5.97018	−	1.87001i	0.258840	−	0.0810750i
$533$	12.7371			0.551707
$534$		0			0
$535$	−0.0200523	+	0.0115772i	−0.000866938	+	0.000500527i
$536$	−17.6360	−	0.633892i	−0.761758	−	0.0273800i
$537$		0			0
$538$	7.05634	−	37.3941i	0.304221	−	1.61217i
$539$	−1.03338	−	3.27183i	−0.0445110	−	0.140928i
$540$		0			0
$541$	20.7829	+	11.9990i	0.893528	+	0.515878i	0.875095	−	0.483952i	$-0.160799\pi$
$541$	20.7829	+	11.9990i	0.893528	+	0.515878i	0.0184329	+	0.999830i	$0.494132\pi$
$542$	6.96871	+	19.8841i	0.299332	+	0.854096i
$543$		0			0
$544$	6.40562	−	0.737662i	0.274639	−	0.0316270i
$545$			10.8431i			0.464469i
$546$		0			0
$547$	15.3907			0.658059			0.329030	−	0.944320i	$-0.393278\pi$
$547$	15.3907			0.658059			0.329030	+	0.944320i	$0.393278\pi$
$548$	−0.0413054	−	0.0516912i	−0.00176448	−	0.00220814i
$549$		0			0
$550$	1.05422	+	3.00804i	0.0449520	+	0.128263i
$551$	−2.39962	+	4.15626i	−0.102227	+	0.177062i
$552$		0			0
$553$	7.52743	−	1.16049i	0.320099	−	0.0493490i
$554$	−11.1830	−	2.11025i	−0.475119	−	0.0896559i
$555$		0			0
$556$	−5.35456	−	35.2901i	−0.227084	−	1.49663i
$557$	−22.6049	−	39.1528i	−0.957799	−	1.65896i	−0.727829	−	0.685759i	$-0.759470\pi$
$557$	−22.6049	−	39.1528i	−0.957799	−	1.65896i	−0.229970	−	0.973198i	$-0.573863\pi$
$558$		0			0
$559$			14.5840i			0.616839i
$560$	2.94292	+	6.02867i	0.124361	+	0.254758i
$561$		0			0
$562$	16.3226	−	18.9860i	0.688527	−	0.800877i
$563$	−29.9610	+	17.2980i	−1.26271	+	0.729024i	−0.973597	−	0.228273i	$-0.926692\pi$
$563$	−29.9610	+	17.2980i	−1.26271	+	0.729024i	−0.289109	+	0.957296i	$0.593359\pi$
$564$		0			0
$565$	4.38174	+	2.52980i	0.184341	+	0.106429i
$566$	−6.33973	+	33.5965i	−0.266479	+	1.41217i
$567$		0			0
$568$	−8.23727	+	13.1525i	−0.345628	+	0.551866i
$569$	−6.32717	−	3.65299i	−0.265249	−	0.153141i	0.361478	−	0.932381i	$-0.382272\pi$
$569$	−6.32717	−	3.65299i	−0.265249	−	0.153141i	−0.626727	+	0.779239i	$0.715606\pi$
$570$		0			0
$571$	−6.27659	−	10.8714i	−0.262667	−	0.454953i	0.704283	−	0.709920i	$-0.251269\pi$
$571$	−6.27659	−	10.8714i	−0.262667	−	0.454953i	−0.966950	+	0.254967i	$0.917936\pi$
$572$	−2.39911	+	1.91708i	−0.100312	+	0.0801572i
$573$		0			0
$574$	−0.510245	+	15.2050i	−0.0212972	+	0.634643i
$575$	25.7947			1.07571
$576$		0			0
$577$	−19.3794	−	33.5661i	−0.806775	−	1.39738i	−0.915086	−	0.403258i	$-0.867878\pi$
$577$	−19.3794	−	33.5661i	−0.806775	−	1.39738i	0.108311	−	0.994117i	$-0.465456\pi$
$578$	−20.9546	+	7.34387i	−0.871596	+	0.305465i
$579$		0			0
$580$	−4.79240	−	1.87545i	−0.198994	−	0.0778739i
$581$	23.3995	+	29.1404i	0.970773	+	1.20895i
$582$		0			0
$583$	0.937654	+	0.541355i	0.0388337	+	0.0224206i
$584$	30.2813	+	1.08840i	1.25305	+	0.0450384i
$585$		0			0
$586$	−4.07279	−	3.50144i	−0.168245	−	0.144643i
$587$		−	8.75340i		−	0.361291i	−0.983548	−	0.180646i	$-0.942181\pi$
$587$		−	8.75340i		−	0.361291i	0.983548	−	0.180646i	$-0.0578187\pi$
$588$		0			0
$589$		−	7.37687i		−	0.303959i
$590$	6.15534	−	7.15973i	0.253411	−	0.294762i
$591$		0			0
$592$	−29.4260	−	6.65555i	−1.20940	−	0.273541i
$593$	−20.9557	−	12.0988i	−0.860547	−	0.496837i	0.00364837	−	0.999993i	$-0.498839\pi$
$593$	−20.9557	−	12.0988i	−0.860547	−	0.496837i	−0.864195	+	0.503156i	$0.832172\pi$
$594$		0			0
$595$	1.19695	+	1.49061i	0.0490701	+	0.0611091i
$596$	−34.4131	−	13.4672i	−1.40961	−	0.551637i
$597$		0			0
$598$	8.21973	+	23.4537i	0.336130	+	0.959093i
$599$	−10.6813	−	18.5005i	−0.436426	−	0.755911i	0.560985	−	0.827826i	$-0.310422\pi$
$599$	−10.6813	−	18.5005i	−0.436426	−	0.755911i	−0.997411	+	0.0719145i	$0.977089\pi$
$600$		0			0
$601$	38.2818			1.56155			0.780773	−	0.624814i	$-0.214825\pi$
$601$	38.2818			1.56155			0.780773	+	0.624814i	$0.214825\pi$
$602$	−17.4097	−	0.584231i	−0.709567	−	0.0238115i
$603$		0			0
$604$	−1.92840	−	2.41327i	−0.0784653	−	0.0981946i
$605$	−3.41033	−	5.90686i	−0.138650	−	0.240148i
$606$		0			0
$607$	4.12752	+	2.38303i	0.167531	+	0.0967240i	0.581421	−	0.813603i	$-0.302497\pi$
$607$	4.12752	+	2.38303i	0.167531	+	0.0967240i	−0.413890	+	0.910327i	$0.635830\pi$
$608$	5.37151	−	3.98475i	0.217843	−	0.161603i
$609$		0			0
$610$	−10.3468	−	1.95247i	−0.418931	−	0.0790531i
$611$	26.0707	+	15.0519i	1.05471	+	0.608936i
$612$		0			0
$613$	−24.2048	+	13.9747i	−0.977624	+	0.564432i	−0.901552	−	0.432671i	$-0.857571\pi$
$613$	−24.2048	+	13.9747i	−0.977624	+	0.564432i	−0.0760723	+	0.997102i	$0.524238\pi$
$614$	−12.2582	−	10.5385i	−0.494700	−	0.425301i
$615$		0			0
$616$	−2.19241	−	2.94074i	−0.0883347	−	0.118486i
$617$		−	25.6270i		−	1.03171i	−0.856677	−	0.515853i	$-0.827475\pi$
$617$		−	25.6270i		−	1.03171i	0.856677	−	0.515853i	$-0.172525\pi$
$618$		0			0
$619$	18.2329	+	31.5803i	0.732842	+	1.26932i	0.955664	+	0.294460i	$0.0951397\pi$
$619$	18.2329	+	31.5803i	0.732842	+	1.26932i	−0.222822	+	0.974859i	$0.571527\pi$
$620$	7.82084	−	1.18665i	0.314092	−	0.0476572i
$621$		0			0
$622$	−4.05648	+	21.4968i	−0.162650	+	0.861942i
$623$	−27.5493	+	4.24722i	−1.10374	+	0.170161i
$624$		0			0
$625$	−9.56696	+	16.5705i	−0.382679	+	0.662819i
$626$	−23.0748	+	8.08692i	−0.922253	+	0.323218i
$627$		0			0
$628$	1.31522	+	1.64591i	0.0524828	+	0.0656790i
$629$	−8.59710			−0.342789
$630$		0			0
$631$			25.5148i			1.01573i	0.861437	+	0.507864i	$0.169565\pi$
$631$			25.5148i			1.01573i	−0.861437	+	0.507864i	$0.830435\pi$
$632$	7.19306	−	3.81520i	0.286125	−	0.151761i
$633$		0			0
$634$	18.5281	−	6.49345i	0.735843	−	0.257888i
$635$	4.03553	+	2.32991i	0.160145	+	0.0924598i
$636$		0			0
$637$	21.4108	+	4.73556i	0.848328	+	0.187630i
$638$	2.76502	+	0.521765i	0.109468	+	0.0206569i
$639$		0			0
$640$	5.08864	+	5.05379i	0.201146	+	0.199769i
$641$	14.3543	−	8.28743i	0.566959	−	0.327334i	−0.188975	−	0.981982i	$-0.560516\pi$
$641$	14.3543	−	8.28743i	0.566959	−	0.327334i	0.755934	+	0.654648i	$0.227183\pi$
$642$		0			0
$643$	−1.84462			−0.0727446			−0.0363723	−	0.999338i	$-0.511580\pi$
$643$	−1.84462			−0.0727446			−0.0363723	+	0.999338i	$0.511580\pi$
$644$	−28.3271	+	8.87275i	−1.11625	+	0.349635i
$645$		0			0
$646$	1.24246	−	1.44520i	0.0488841	−	0.0568608i
$647$	8.78089	+	15.2090i	0.345212	+	0.597926i	0.985392	−	0.170300i	$-0.0544735\pi$
$647$	8.78089	+	15.2090i	0.345212	+	0.597926i	−0.640180	+	0.768225i	$0.721140\pi$
$648$		0			0
$649$	−2.58126	+	4.47088i	−0.101323	+	0.175497i
$650$	−20.0174	−	3.77732i	−0.785147	−	0.148159i
$651$		0			0
$652$	9.20517	+	3.60234i	0.360502	+	0.141079i
$653$	14.7739	−	25.5891i	0.578146	−	1.00138i	−0.417546	−	0.908656i	$-0.637110\pi$
$653$	14.7739	−	25.5891i	0.578146	−	1.00138i	0.995692	−	0.0927224i	$-0.0295569\pi$
$654$		0			0
$655$	−11.3168	+	6.53376i	−0.442184	+	0.255295i
$656$	4.82438	+	15.5319i	0.188360	+	0.606420i
$657$		0			0
$658$	−19.0126	+	30.5189i	−0.741189	+	1.18975i
$659$			25.6600i			0.999573i	0.866148	+	0.499787i	$0.166588\pi$
$659$			25.6600i			0.999573i	−0.866148	+	0.499787i	$0.833412\pi$
$660$		0			0
$661$	−28.3071	+	16.3431i	−1.10102	+	0.635674i	−0.936489	−	0.350698i	$-0.885944\pi$
$661$	−28.3071	+	16.3431i	−1.10102	+	0.635674i	−0.164531	+	0.986372i	$0.552611\pi$
$662$	43.9582	−	15.4059i	1.70848	−	0.598766i
$663$		0			0
$664$	33.8602	+	21.2063i	1.31403	+	0.822965i
$665$	1.84827	+	0.718228i	0.0716729	+	0.0278517i
$666$		0			0
$667$	11.3856	−	19.7205i	0.440853	−	0.763580i
$668$	−4.51015	−	29.7249i	−0.174503	−	1.15009i
$669$		0			0
$670$	−4.24141	−	3.64641i	−0.163860	−	0.140873i
$671$	5.75714			0.222252
$672$		0			0
$673$	−18.8884			−0.728092			−0.364046	−	0.931381i	$-0.618605\pi$
$673$	−18.8884			−0.728092			−0.364046	+	0.931381i	$0.618605\pi$
$674$	5.28577	+	4.54426i	0.203600	+	0.175038i
$675$		0			0
$676$	0.956109	+	6.30139i	0.0367734	+	0.242361i
$677$	−20.0840	+	34.7866i	−0.771893	+	1.33696i	0.164632	+	0.986355i	$0.447356\pi$
$677$	−20.0840	+	34.7866i	−0.771893	+	1.33696i	−0.936524	+	0.350602i	$0.885977\pi$
$678$		0			0
$679$	−4.48952	+	3.60505i	−0.172292	+	0.138349i
$680$	1.73205	+	1.08476i	0.0664209	+	0.0415988i
$681$		0			0
$682$	−4.08170	+	1.43050i	−0.156296	+	0.0547766i
$683$	7.14692	−	4.12627i	0.273469	−	0.157887i	−0.356994	−	0.934107i	$-0.616198\pi$
$683$	7.14692	−	4.12627i	0.273469	−	0.157887i	0.630463	+	0.776219i	$0.282865\pi$
$684$		0			0
$685$		−	0.0209719i		−	0.000801296i
$686$	−6.51078	+	25.3695i	−0.248583	+	0.968611i
$687$		0			0
$688$	−17.7841	+	5.52392i	−0.678012	+	0.210597i
$689$	−5.99249	+	3.45977i	−0.228296	+	0.131807i
$690$		0			0
$691$	−5.93733	+	10.2838i	−0.225867	+	0.391213i	−0.956579	−	0.291473i	$-0.905855\pi$
$691$	−5.93733	+	10.2838i	−0.225867	+	0.391213i	0.730712	+	0.682685i	$0.239188\pi$
$692$	17.7784	+	6.95739i	0.675835	+	0.264480i
$693$		0			0
$694$	22.5608	+	4.25726i	0.856395	+	0.161603i
$695$	5.65666	−	9.79763i	0.214569	−	0.371645i
$696$		0			0
$697$	2.31730	+	4.01368i	0.0877740	+	0.152029i
$698$	7.94859	−	9.24560i	0.300858	−	0.349951i
$699$		0			0
$700$	5.31107	−	23.7445i	0.200740	−	0.897456i
$701$	−19.5183			−0.737197			−0.368599	−	0.929589i	$-0.620162\pi$
$701$	−19.5183			−0.737197			−0.368599	+	0.929589i	$0.620162\pi$
$702$		0			0
$703$	−7.72266	+	4.45868i	−0.291266	+	0.168162i
$704$	−3.24643	−	2.19940i	−0.122354	−	0.0828931i
$705$		0			0
$706$	23.7384	+	4.47948i	0.893406	+	0.168587i
$707$	−39.6733	−	15.4168i	−1.49207	−	0.579809i
$708$		0			0
$709$	−8.04150	−	4.64276i	−0.302005	−	0.174363i	0.341338	−	0.939940i	$-0.389120\pi$
$709$	−8.04150	−	4.64276i	−0.302005	−	0.174363i	−0.643343	+	0.765578i	$0.722453\pi$
$710$	−4.64198	+	1.62686i	−0.174210	+	0.0610548i
$711$		0			0
$712$	−26.3256	+	13.9631i	−0.986593	+	0.523290i
$713$			35.0016i			1.31082i
$714$		0			0
$715$	−0.973357			−0.0364015
$716$	4.09770	+	5.12802i	0.153138	+	0.191643i
$717$		0			0
$718$	−33.7985	+	11.8452i	−1.26135	+	0.442060i
$719$	−2.64134	+	4.57494i	−0.0985054	+	0.170616i	−0.911066	−	0.412260i	$-0.864740\pi$
$719$	−2.64134	+	4.57494i	−0.0985054	+	0.170616i	0.812561	+	0.582876i	$0.198073\pi$
$720$		0			0
$721$	33.9650	−	5.23632i	1.26492	−	0.195011i
$722$	−4.61593	+	24.4615i	−0.171787	+	0.910362i
$723$		0			0
$724$	−3.30324	+	0.501199i	−0.122764	+	0.0186269i
$725$	9.33244	+	16.1643i	0.346598	+	0.600325i
$726$		0			0
$727$		−	31.6181i		−	1.17265i	−0.810075	−	0.586326i	$-0.800574\pi$
$727$		−	31.6181i		−	1.17265i	0.810075	−	0.586326i	$-0.199426\pi$
$728$	23.2819	−	2.73733i	0.862886	−	0.101452i
$729$		0			0
$730$	7.28258	+	6.26095i	0.269540	+	0.231728i
$731$	−4.59567	+	2.65331i	−0.169977	+	0.0981363i
$732$		0			0
$733$	−0.114112	−	0.0658825i	−0.00421482	−	0.00243343i	0.497891	−	0.867240i	$-0.334108\pi$
$733$	−0.114112	−	0.0658825i	−0.00421482	−	0.00243343i	−0.502106	+	0.864806i	$0.667441\pi$
$734$	27.1985	+	5.13241i	1.00391	+	0.189441i
$735$		0			0
$736$	−25.4866	+	18.9067i	−0.939448	+	0.696912i
$737$	2.64854	+	1.52914i	0.0975602	+	0.0563264i
$738$		0			0
$739$	−4.06197	−	7.03554i	−0.149422	−	0.258806i	0.781592	−	0.623790i	$-0.214408\pi$
$739$	−4.06197	−	7.03554i	−0.149422	−	0.258806i	−0.931014	+	0.364984i	$0.881075\pi$
$740$	−5.96930	−	7.47021i	−0.219436	−	0.274610i
$741$		0			0
$742$	−3.89004	−	7.29214i	−0.142808	−	0.267703i
$743$	−27.1897			−0.997493			−0.498746	−	0.866748i	$-0.666206\pi$
$743$	−27.1897			−0.997493			−0.498746	+	0.866748i	$0.666206\pi$
$744$		0			0
$745$	−5.85639	−	10.1436i	−0.214562	−	0.371632i
$746$	−16.2140	−	46.2640i	−0.593636	−	1.69385i
$747$		0			0
$748$	−1.04058	−	0.407220i	−0.0380474	−	0.0148894i
$749$	−0.0955120	+	0.0147249i	−0.00348993	+	0.000538036i
$750$		0			0
$751$	−24.5808	−	14.1917i	−0.896967	−	0.517864i	−0.0207520	−	0.999785i	$-0.506606\pi$
$751$	−24.5808	−	14.1917i	−0.896967	−	0.517864i	−0.876215	+	0.481921i	$0.839939\pi$
$752$	−8.47997	+	37.4923i	−0.309233	+	1.36720i
$753$		0			0
$754$	−11.7234	+	13.6363i	−0.426940	+	0.496607i
$755$		−	0.979101i		−	0.0356331i
$756$		0			0
$757$			8.94140i			0.324981i	0.986710	+	0.162490i	$0.0519526\pi$
$757$			8.94140i			0.324981i	−0.986710	+	0.162490i	$0.948047\pi$
$758$	26.7964	+	23.0373i	0.973290	+	0.836753i
$759$		0			0
$760$	2.11846	+	0.0761441i	0.0768446	+	0.00276204i
$761$	18.3315	+	10.5837i	0.664515	+	0.383658i	0.793995	−	0.607924i	$-0.207998\pi$
$761$	18.3315	+	10.5837i	0.664515	+	0.383658i	−0.129480	+	0.991582i	$0.541331\pi$
$762$		0			0
$763$	−16.3922	+	42.1833i	−0.593437	+	1.52714i
$764$	−1.26350	−	0.494455i	−0.0457117	−	0.0178887i
$765$		0			0
$766$	4.55120	−	1.59504i	0.164441	−	0.0576311i
$767$	−16.4967	−	28.5731i	−0.595661	−	1.03172i
$768$		0			0
$769$	14.6400			0.527933			0.263966	−	0.964532i	$-0.414969\pi$
$769$	14.6400			0.527933			0.263966	+	0.964532i	$0.414969\pi$
$770$	0.0389923	−	1.16194i	0.00140518	−	0.0418736i
$771$		0			0
$772$	−22.1430	+	17.6941i	−0.796945	+	0.636823i
$773$	−7.03780	−	12.1898i	−0.253132	−	0.438438i	0.711254	−	0.702935i	$-0.248127\pi$
$773$	−7.03780	−	12.1898i	−0.253132	−	0.438438i	−0.964386	+	0.264497i	$0.914794\pi$
$774$		0			0
$775$	−24.8460	−	14.3448i	−0.892494	−	0.515282i
$776$	−3.26716	+	5.21669i	−0.117284	+	0.187268i
$777$		0			0
$778$	−3.73739	+	19.8058i	−0.133992	+	0.710073i
$779$	4.16320	+	2.40363i	0.149162	+	0.0861188i
$780$		0			0
$781$	2.32912	−	1.34472i	0.0833424	−	0.0481178i
$782$	−5.89521	+	6.85717i	−0.210812	+	0.245212i
$783$		0			0
$784$	2.33503	+	27.9025i	0.0833938	+	0.996517i
$785$			0.667772i			0.0238338i
$786$		0			0
$787$	8.49706	+	14.7173i	0.302887	+	0.524616i	0.976789	−	0.214205i	$-0.0687160\pi$
$787$	8.49706	+	14.7173i	0.302887	+	0.524616i	−0.673901	+	0.738821i	$0.735383\pi$
$788$	−6.47469	−	42.6726i	−0.230651	−	1.52015i
$789$		0			0
$790$	2.53595	+	0.478538i	0.0902249	+	0.0170256i
$791$	13.2219	+	16.4659i	0.470118	+	0.585459i
$792$		0			0
$793$	−18.3968	+	31.8641i	−0.653289	+	1.13153i
$794$	8.36777	+	23.8761i	0.296961	+	0.847332i
$795$		0			0
$796$	8.35069	+	10.4504i	0.295982	+	0.370404i
$797$	−14.7667			−0.523063			−0.261531	−	0.965195i	$-0.584227\pi$
$797$	−14.7667			−0.523063			−0.261531	+	0.965195i	$0.584227\pi$
$798$		0			0
$799$			10.9537i			0.387516i
$800$	−2.97574	−	25.8404i	−0.105208	−	0.913595i
$801$		0			0
$802$	−12.7628	−	36.4166i	−0.450669	−	1.28591i
$803$	−4.54759	−	2.62555i	−0.160481	−	0.0926537i
$804$		0			0
$805$	−8.76963	−	3.40783i	−0.309089	−	0.120110i
$806$	5.12556	−	27.1622i	0.180540	−	0.956747i
$807$		0			0
$808$	−45.4729	−	1.63444i	−1.59973	−	0.0574994i
$809$	−13.9845	+	8.07393i	−0.491668	+	0.283864i	−0.725266	−	0.688469i	$-0.758283\pi$
$809$	−13.9845	+	8.07393i	−0.491668	+	0.283864i	0.233598	+	0.972333i	$0.424950\pi$
$810$		0			0
$811$	14.3851			0.505129			0.252565	−	0.967580i	$-0.418726\pi$
$811$	14.3851			0.505129			0.252565	+	0.967580i	$0.418726\pi$
$812$	−15.8088	−	14.5411i	−0.554779	−	0.510291i
$813$		0			0
$814$	3.96459	+	3.40842i	0.138959	+	0.119465i
$815$	1.56653	+	2.71331i	0.0548731	+	0.0950431i
$816$		0			0
$817$	−2.75215	+	4.76687i	−0.0962857	+	0.166772i
$818$	5.28897	−	28.0282i	0.184924	−	0.979982i
$819$		0			0
$820$	−1.87859	+	4.80041i	−0.0656031	+	0.167638i
$821$	−22.6789	+	39.2809i	−0.791498	+	1.37091i	0.133541	+	0.991043i	$0.457365\pi$
$821$	−22.6789	+	39.2809i	−0.791498	+	1.37091i	−0.925039	+	0.379871i	$0.875968\pi$
$822$		0			0
$823$	−37.5589	+	21.6846i	−1.30922	+	0.755878i	−0.981966	−	0.189058i	$-0.939457\pi$
$823$	−37.5589	+	21.6846i	−1.30922	+	0.755878i	−0.327254	+	0.944936i	$0.606123\pi$
$824$	32.4563	−	17.2148i	1.13067	−	0.599707i
$825$		0			0
$826$	34.7700	−	18.5483i	1.20980	−	0.645378i
$827$			9.52077i			0.331070i	0.986204	+	0.165535i	$0.0529350\pi$
$827$			9.52077i			0.331070i	−0.986204	+	0.165535i	$0.947065\pi$
$828$		0			0
$829$	23.9717	−	13.8400i	0.832570	−	0.480685i	−0.0221616	−	0.999754i	$-0.507055\pi$
$829$	23.9717	−	13.8400i	0.832570	−	0.480685i	0.854732	+	0.519070i	$0.173722\pi$
$830$	4.18824	+	11.9505i	0.145376	+	0.414807i
$831$		0			0
$832$	22.5470	−	10.9399i	0.781675	−	0.379274i
$833$	2.40308	+	7.60846i	0.0832616	+	0.263617i
$834$		0			0
$835$	4.76461	−	8.25254i	0.164886	−	0.285591i
$836$	−1.14593	+	0.173872i	−0.0396330	+	0.00601350i
$837$		0			0
$838$	12.1892	−	14.1782i	0.421069	−	0.489777i
$839$	−52.2255			−1.80303			−0.901513	−	0.432752i	$-0.857543\pi$
$839$	−52.2255			−1.80303			−0.901513	+	0.432752i	$0.857543\pi$
$840$		0			0
$841$	−12.5229			−0.431824
$842$	3.79782	−	4.41753i	0.130882	−	0.152238i
$843$		0			0
$844$	4.75297	+	31.3253i	0.163604	+	1.07826i
$845$	−1.01005	+	1.74946i	−0.0347468	+	0.0601833i
$846$		0			0
$847$	−4.33755	−	28.1352i	−0.149040	−	0.966737i
$848$	−6.48866	−	5.99693i	−0.222821	−	0.205936i
$849$		0			0
$850$	−2.45152	−	6.99504i	−0.0840865	−	0.239928i
$851$	36.6423	−	21.1554i	1.25608	−	0.725199i
$852$		0			0
$853$		−	31.9251i		−	1.09310i	−0.837428	−	0.546548i	$-0.815942\pi$
$853$		−	31.9251i		−	1.09310i	0.837428	−	0.546548i	$-0.184058\pi$
$854$	−37.3009	−	23.2376i	−1.27641	−	0.795175i
$855$		0			0
$856$	−0.0912694	+	0.0484093i	−0.00311952	+	0.00165460i
$857$	5.74550	−	3.31716i	0.196262	−	0.113312i	−0.398649	−	0.917104i	$-0.630521\pi$
$857$	5.74550	−	3.31716i	0.196262	−	0.113312i	0.594911	+	0.803792i	$0.297187\pi$
$858$		0			0
$859$	1.84968	−	3.20373i	0.0631102	−	0.109310i	−0.832744	−	0.553658i	$-0.813231\pi$
$859$	1.84968	−	3.20373i	0.0631102	−	0.109310i	0.895854	+	0.444348i	$0.146565\pi$
$860$	−5.49647	−	2.15098i	−0.187428	−	0.0733479i
$861$		0			0
$862$	−9.76594	+	51.7533i	−0.332629	+	1.76272i
$863$	10.9267	−	18.9256i	0.371949	−	0.644235i	−0.617916	−	0.786244i	$-0.712023\pi$
$863$	10.9267	−	18.9256i	0.371949	−	0.644235i	0.989865	+	0.142009i	$0.0453562\pi$
$864$		0			0
$865$	3.02552	+	5.24036i	0.102871	+	0.178177i
$866$	28.9489	+	24.8878i	0.983722	+	0.845722i
$867$		0			0
$868$	32.2195	+	7.20674i	1.09360	+	0.244613i
$869$	−1.41104			−0.0478663
$870$		0			0
$871$	−16.9267	+	9.77262i	−0.573538	+	0.331133i
$872$	−1.73784	+	48.3498i	−0.0588508	+	1.63733i
$873$		0			0
$874$	−1.73929	+	9.21711i	−0.0588322	+	0.311773i
$875$	12.5518	−	10.0790i	0.424328	−	0.340732i
$876$		0			0
$877$	40.4670	+	23.3636i	1.36647	+	0.788934i	0.990476	−	0.137686i	$-0.0439666\pi$
$877$	40.4670	+	23.3636i	1.36647	+	0.788934i	0.375998	+	0.926620i	$0.377300\pi$
$878$	13.4559	+	38.3944i	0.454116	+	1.29575i
$879$		0			0
$880$	−0.368673	−	1.18693i	−0.0124280	−	0.0400115i
$881$			14.0128i			0.472105i	0.971740	+	0.236052i	$0.0758537\pi$
$881$			14.0128i			0.472105i	−0.971740	+	0.236052i	$0.924146\pi$
$882$		0			0
$883$	−37.1955			−1.25173			−0.625864	−	0.779932i	$-0.715254\pi$
$883$	−37.1955			−1.25173			−0.625864	+	0.779932i	$0.715254\pi$
$884$	5.57899	−	4.45806i	0.187642	−	0.149941i
$885$		0			0
$886$	1.01224	+	2.88826i	0.0340067	+	0.0970328i
$887$	16.3122	−	28.2535i	0.547710	−	0.948661i	−0.450721	−	0.892665i	$-0.648833\pi$
$887$	16.3122	−	28.2535i	0.547710	−	0.948661i	0.998431	−	0.0559963i	$-0.0178335\pi$
$888$		0			0
$889$	12.1772	+	15.1648i	0.408412	+	0.508613i
$890$	−9.28121	−	1.75138i	−0.311107	−	0.0587065i
$891$		0			0
$892$	−9.90311	+	1.50260i	−0.331581	+	0.0503106i
$893$	5.68089	+	9.83960i	0.190104	+	0.329270i
$894$		0			0
$895$			2.08052i			0.0695441i
$896$	12.1563	+	27.3537i	0.406115	+	0.913822i
$897$		0			0
$898$	16.6767	−	19.3979i	0.556509	−	0.647318i
$899$	−21.9337	+	12.6634i	−0.731531	+	0.422349i
$900$		0			0
$901$	−2.18046	−	1.25889i	−0.0726417	−	0.0419397i
$902$	0.522637	−	2.76964i	0.0174019	−	0.0922191i
$903$		0			0
$904$	19.1328	+	11.9827i	0.636349	+	0.398539i
$905$	−0.917081	−	0.529477i	−0.0304848	−	0.0176004i
$906$		0			0
$907$	−21.8244	−	37.8010i	−0.724668	−	1.25516i	−0.959111	−	0.283032i	$-0.908660\pi$
$907$	−21.8244	−	37.8010i	−0.724668	−	1.25516i	0.234442	−	0.972130i	$-0.424674\pi$
$908$	−31.8627	−	39.8742i	−1.05740	−	1.32327i
$909$		0			0
$910$	6.30644	+	3.92877i	0.209056	+	0.130238i
$911$	−14.8830			−0.493096			−0.246548	−	0.969131i	$-0.579296\pi$
$911$	−14.8830			−0.493096			−0.246548	+	0.969131i	$0.579296\pi$
$912$		0			0
$913$	−3.46189	−	5.99617i	−0.114572	−	0.198444i
$914$	6.60955	−	2.31642i	0.218625	−	0.0766205i
$915$		0			0
$916$	17.7481	−	45.3522i	0.586413	−	1.49848i
$917$	−53.9035	+	8.31018i	−1.78005	+	0.274426i
$918$		0			0
$919$	7.46664	+	4.31087i	0.246302	+	0.142202i	0.618070	−	0.786123i	$-0.287915\pi$
$919$	7.46664	+	4.31087i	0.246302	+	0.142202i	−0.371768	+	0.928326i	$0.621248\pi$
$920$	−10.0516	−	0.361286i	−0.331392	−	0.0119113i
$921$		0			0
$922$	35.8025	+	30.7799i	1.17909	+	1.01368i
$923$			17.1880i			0.565751i
$924$		0			0
$925$			34.6808i			1.14030i
$926$	3.50131	−	4.07264i	0.115060	−	0.133835i
$927$		0			0
$928$	−21.0689	−	9.13077i	−0.691619	−	0.299732i
$929$	−12.9536	−	7.47874i	−0.424992	−	0.245369i	0.272219	−	0.962235i	$-0.412243\pi$
$929$	−12.9536	−	7.47874i	−0.424992	−	0.245369i	−0.697211	+	0.716866i	$0.745576\pi$
$930$		0			0
$931$	6.10459	+	5.58828i	0.200070	+	0.183148i
$932$	16.1108	−	41.1683i	0.527725	−	1.34851i
$933$		0			0
$934$	0.579317	+	1.65299i	0.0189558	+	0.0540875i
$935$	−0.177085	−	0.306721i	−0.00579131	−	0.0100308i
$936$		0			0
$937$	18.5044			0.604513			0.302257	−	0.953227i	$-0.402260\pi$
$937$	18.5044			0.604513			0.302257	+	0.953227i	$0.402260\pi$
$938$	−10.9880	−	20.5977i	−0.358771	−	0.672539i
$939$		0			0
$940$	−9.51795	+	7.60560i	−0.310441	+	0.248067i
$941$	11.2163	+	19.4271i	0.365640	+	0.633307i	0.988879	−	0.148725i	$-0.0475169\pi$
$941$	11.2163	+	19.4271i	0.365640	+	0.633307i	−0.623239	+	0.782032i	$0.714184\pi$
$942$		0			0
$943$	−19.7534	−	11.4047i	−0.643261	−	0.371387i
$944$	28.5943	−	30.9389i	0.930665	−	1.00698i
$945$		0			0
$946$	3.17125	+	0.598421i	0.103106	+	0.0194563i
$947$	39.6308	+	22.8809i	1.28783	+	0.743528i	0.978267	−	0.207351i	$-0.0664842\pi$
$947$	39.6308	+	22.8809i	1.28783	+	0.743528i	0.309562	+	0.950879i	$0.399818\pi$
$948$		0			0
$949$	29.0634	−	16.7797i	0.943437	−	0.544694i
$950$	−5.82998	−	5.01212i	−0.189149	−	0.162615i
$951$		0			0
$952$	5.09832	+	6.83851i	0.165238	+	0.221637i
$953$			42.0094i			1.36082i	0.732832	+	0.680409i	$0.238198\pi$
$953$			42.0094i			1.36082i	−0.732832	+	0.680409i	$0.761802\pi$
$954$		0			0
$955$	−0.215021	−	0.372427i	−0.00695791	−	0.0120515i
$956$	−6.54271	−	43.1208i	−0.211606	−	1.39463i
$957$		0			0
$958$	1.45201	−	7.69473i	0.0469123	−	0.248606i
$959$	0.0317044	−	0.0815876i	0.00102379	−	0.00263460i
$960$		0			0
$961$	3.96491	−	6.86742i	0.127900	−	0.221530i
$962$	−31.5334	+	11.0514i	−1.01668	+	0.356310i
$963$		0			0
$964$	30.1874	−	24.1221i	0.972270	−	0.776922i
$965$	−8.98377			−0.289198
$966$		0			0
$967$		−	54.8008i		−	1.76227i	−0.472860	−	0.881137i	$-0.656778\pi$
$967$		−	54.8008i		−	1.76227i	0.472860	−	0.881137i	$-0.343222\pi$
$968$	−14.2600	−	26.8854i	−0.458335	−	0.864131i
$969$		0			0
$970$	−1.84115	+	0.645262i	−0.0591159	+	0.0207181i
$971$	−19.9522	−	11.5194i	−0.640298	−	0.369676i	0.144431	−	0.989515i	$-0.453865\pi$
$971$	−19.9522	−	11.5194i	−0.640298	−	0.369676i	−0.784729	+	0.619839i	$0.787198\pi$
$972$		0			0
$973$	36.8179	−	29.5644i	1.18033	−	0.947792i
$974$	42.5472	+	8.02874i	1.36330	+	0.257258i
$975$		0			0
$976$	−45.8239	−	10.3644i	−1.46679	−	0.331756i
$977$	5.56153	−	3.21095i	0.177929	−	0.102727i	−0.408390	−	0.912807i	$-0.633910\pi$
$977$	5.56153	−	3.21095i	0.177929	−	0.102727i	0.586319	+	0.810080i	$0.300576\pi$
$978$		0			0
$979$	5.16421			0.165049
$980$	−4.94261	+	7.37093i	−0.157886	+	0.235456i
$981$		0			0
$982$	21.6609	−	25.1955i	0.691228	−	0.804019i
$983$	−12.3211	−	21.3408i	−0.392982	−	0.680664i	0.599860	−	0.800105i	$-0.295223\pi$
$983$	−12.3211	−	21.3408i	−0.392982	−	0.680664i	−0.992841	+	0.119441i	$0.961890\pi$
$984$		0			0
$985$	6.83999	−	11.8472i	0.217940	−	0.377484i
$986$	−6.42991	−	1.21334i	−0.204770	−	0.0386405i
$987$		0			0
$988$	2.69947	−	6.89803i	0.0858815	−	0.219456i
$989$	13.0583	−	22.6177i	0.415231	−	0.719202i
$990$		0			0
$991$	−12.5347	+	7.23693i	−0.398179	+	0.229889i	−0.685698	−	0.727886i	$-0.740503\pi$
$991$	−12.5347	+	7.23693i	−0.398179	+	0.229889i	0.287519	+	0.957775i	$0.407170\pi$
$992$	35.0635	−	4.03786i	1.11327	−	0.128202i
$993$		0			0
$994$	−20.5182	−	0.688545i	−0.650798	−	0.0218393i
$995$			4.23988i			0.134413i
$996$		0			0
$997$	13.8349	−	7.98761i	0.438157	−	0.252970i	−0.264659	−	0.964342i	$-0.585259\pi$
$997$	13.8349	−	7.98761i	0.438157	−	0.252970i	0.702816	+	0.711372i	$0.251926\pi$
$998$	32.2129	−	11.2895i	1.01968	−	0.357364i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bm.c.107.19	yes	48
3.2	odd	2	inner	504.2.bm.c.107.6	yes	48
4.3	odd	2		2016.2.bu.c.1871.12		48
7.4	even	3	inner	504.2.bm.c.179.2	yes	48
8.3	odd	2	inner	504.2.bm.c.107.23	yes	48
8.5	even	2		2016.2.bu.c.1871.14		48
12.11	even	2		2016.2.bu.c.1871.13		48
21.11	odd	6	inner	504.2.bm.c.179.23	yes	48
24.5	odd	2		2016.2.bu.c.1871.11		48
24.11	even	2	inner	504.2.bm.c.107.2	✓	48
28.11	odd	6		2016.2.bu.c.431.11		48
56.11	odd	6	inner	504.2.bm.c.179.6	yes	48
56.53	even	6		2016.2.bu.c.431.13		48
84.11	even	6		2016.2.bu.c.431.14		48
168.11	even	6	inner	504.2.bm.c.179.19	yes	48
168.53	odd	6		2016.2.bu.c.431.12		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bm.c.107.2	✓	48	24.11	even	2	inner
504.2.bm.c.107.6	yes	48	3.2	odd	2	inner
504.2.bm.c.107.19	yes	48	1.1	even	1	trivial
504.2.bm.c.107.23	yes	48	8.3	odd	2	inner
504.2.bm.c.179.2	yes	48	7.4	even	3	inner
504.2.bm.c.179.6	yes	48	56.11	odd	6	inner
504.2.bm.c.179.19	yes	48	168.11	even	6	inner
504.2.bm.c.179.23	yes	48	21.11	odd	6	inner
2016.2.bu.c.431.11		48	28.11	odd	6
2016.2.bu.c.431.12		48	168.53	odd	6
2016.2.bu.c.431.13		48	56.53	even	6
2016.2.bu.c.431.14		48	84.11	even	6
2016.2.bu.c.1871.11		48	24.5	odd	2
2016.2.bu.c.1871.12		48	4.3	odd	2
2016.2.bu.c.1871.13		48	12.11	even	2
2016.2.bu.c.1871.14		48	8.5	even	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)

\(f(q)\)	\(=\)	\(q+(1.07239 + 0.921948i) q^{2} +(0.300025 + 1.97737i) q^{4} +(-0.316953 + 0.548978i) q^{5} +(-2.06297 + 1.65655i) q^{7} +(-1.50129 + 2.39711i) q^{8} +O(q^{10})\)	\(q+(1.07239 + 0.921948i) q^{2} +(0.300025 + 1.97737i) q^{4} +(-0.316953 + 0.548978i) q^{5} +(-2.06297 + 1.65655i) q^{7} +(-1.50129 + 2.39711i) q^{8} +(-0.846025 + 0.296503i) q^{10} +(0.424494 - 0.245082i) q^{11} +3.13261i q^{13} +(-3.73955 - 0.125491i) q^{14} +(-3.81997 + 1.18652i) q^{16} +(-0.987137 + 0.569924i) q^{17} +(-0.591155 + 1.02391i) q^{19} +(-1.18063 - 0.462025i) q^{20} +(0.681175 + 0.128539i) q^{22} +(2.80489 - 4.85822i) q^{23} +(2.29908 + 3.98213i) q^{25} +(-2.88810 + 3.35937i) q^{26} +(-3.89455 - 3.58225i) q^{28} +4.05920 q^{29} +(-5.40346 + 3.11969i) q^{31} +(-5.19039 - 2.24940i) q^{32} +(-1.58403 - 0.298910i) q^{34} +(-0.255545 - 1.65757i) q^{35} +(6.53184 + 3.77116i) q^{37} +(-1.57794 + 0.553013i) q^{38} +(-0.840125 - 1.58394i) q^{40} -4.06598i q^{41} +4.65556 q^{43} +(0.611976 + 0.765851i) q^{44} +(7.48695 - 2.62392i) q^{46} +(4.80492 - 8.32236i) q^{47} +(1.51170 - 6.83482i) q^{49} +(-1.20581 + 6.39001i) q^{50} +(-6.19432 + 0.939863i) q^{52} +(1.10444 + 1.91294i) q^{53} +0.310718i q^{55} +(-0.873819 - 7.43212i) q^{56} +(4.35303 + 3.74237i) q^{58} +(-9.12119 + 5.26612i) q^{59} +(10.1718 + 5.87267i) q^{61} +(-8.67078 - 1.63619i) q^{62} +(-3.49228 - 7.19750i) q^{64} +(-1.71973 - 0.992889i) q^{65} +(3.11964 + 5.40338i) q^{67} +(-1.42312 - 1.78094i) q^{68} +(1.25415 - 2.01316i) q^{70} +5.48681 q^{71} +(-5.35648 - 9.27769i) q^{73} +(3.52785 + 10.0662i) q^{74} +(-2.20201 - 0.861731i) q^{76} +(-0.469729 + 1.20879i) q^{77} +(-2.49304 - 1.43936i) q^{79} +(0.559375 - 2.47315i) q^{80} +(3.74862 - 4.36031i) q^{82} -14.1254i q^{83} -0.722556i q^{85} +(4.99256 + 4.29218i) q^{86} +(-0.0497991 + 1.38550i) q^{88} +(9.12417 + 5.26784i) q^{89} +(-5.18932 - 6.46248i) q^{91} +(10.4480 + 4.08872i) q^{92} +(12.8255 - 4.49490i) q^{94} +(-0.374736 - 0.649062i) q^{95} +2.17624 q^{97} +(7.92247 - 5.93586i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 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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