LMFDB - Embedded newform 504.2.bm.c.107.2

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			107.2
Character	$\chi$	$=$	504.107
Dual form			504.2.bm.c.179.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33462 - 0.467740i) q^{2} +(1.56244 + 1.24851i) q^{4} +(-0.316953 + 0.548978i) q^{5} +(2.06297 - 1.65655i) q^{7} +(-1.50129 - 2.39711i) q^{8} +O(q^{10})$	\(q+(-1.33462 - 0.467740i) q^{2} +(1.56244 + 1.24851i) q^{4} +(-0.316953 + 0.548978i) q^{5} +(2.06297 - 1.65655i) q^{7} +(-1.50129 - 2.39711i) q^{8} +(0.679792 - 0.584428i) q^{10} +(-0.424494 + 0.245082i) q^{11} -3.13261i q^{13} +(-3.52812 + 1.24593i) q^{14} +(0.882427 + 3.90145i) q^{16} +(0.987137 - 0.569924i) q^{17} +(-0.591155 + 1.02391i) q^{19} +(-1.18063 + 0.462025i) q^{20} +(0.681175 - 0.128539i) q^{22} +(2.80489 - 4.85822i) q^{23} +(2.29908 + 3.98213i) q^{25} +(-1.46525 + 4.18085i) q^{26} +(5.29149 - 0.0126068i) q^{28} +4.05920 q^{29} +(5.40346 - 3.11969i) q^{31} +(0.647158 - 5.61971i) q^{32} +(-1.58403 + 0.298910i) q^{34} +(0.255545 + 1.65757i) q^{35} +(-6.53184 - 3.77116i) q^{37} +(1.26789 - 1.09003i) q^{38} +(1.79180 - 0.0644029i) q^{40} +4.06598i q^{41} +4.65556 q^{43} +(-0.969234 - 0.147062i) q^{44} +(-6.01586 + 5.17193i) q^{46} +(4.80492 - 8.32236i) q^{47} +(1.51170 - 6.83482i) q^{49} +(-1.20581 - 6.39001i) q^{50} +(3.91111 - 4.89451i) q^{52} +(1.10444 + 1.91294i) q^{53} -0.310718i q^{55} +(-7.06804 - 2.45822i) q^{56} +(-5.41750 - 1.89865i) q^{58} +(9.12119 - 5.26612i) q^{59} +(-10.1718 - 5.87267i) q^{61} +(-8.67078 + 1.63619i) q^{62} +(-3.49228 + 7.19750i) q^{64} +(1.71973 + 0.992889i) q^{65} +(3.11964 + 5.40338i) q^{67} +(2.25390 + 0.341983i) q^{68} +(0.434258 - 2.33177i) q^{70} +5.48681 q^{71} +(-5.35648 - 9.27769i) q^{73} +(6.95363 + 8.08829i) q^{74} +(-2.20201 + 0.861731i) q^{76} +(-0.469729 + 1.20879i) q^{77} +(2.49304 + 1.43936i) q^{79} +(-2.42150 - 0.752143i) q^{80} +(1.90182 - 5.42656i) q^{82} +14.1254i q^{83} +0.722556i q^{85} +(-6.21342 - 2.17759i) q^{86} +(1.22478 + 0.649622i) q^{88} +(-9.12417 - 5.26784i) q^{89} +(-5.18932 - 6.46248i) q^{91} +(10.4480 - 4.08872i) q^{92} +(-10.3055 + 8.85976i) q^{94} +(-0.374736 - 0.649062i) q^{95} +2.17624 q^{97} +(-5.21447 + 8.41483i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.33462	−	0.467740i	−0.943721	−	0.330742i
$2$	−1.33462	−	0.467740i	−0.943721	−	0.330742i
$3$		0			0
$3$		0			0
$4$	1.56244	+	1.24851i	0.781219	+	0.624257i
$5$	−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
$10$	0.679792	−	0.584428i	0.214969	−	0.184812i
$11$	−0.424494	+	0.245082i	−0.127990	+	0.0738950i	−0.562628	−	0.826710i	$-0.690210\pi$
$11$	−0.424494	+	0.245082i	−0.127990	+	0.0738950i	0.434638	+	0.900605i	$0.356876\pi$
$12$		0			0
$13$		−	3.13261i		−	0.868830i	−0.900713	−	0.434415i	$-0.856955\pi$
$13$		−	3.13261i		−	0.868830i	0.900713	−	0.434415i	$-0.143045\pi$
$14$	−3.52812	+	1.24593i	−0.942930	+	0.332990i
$15$		0			0
$16$	0.882427	+	3.90145i	0.220607	+	0.975363i
$17$	0.987137	−	0.569924i	0.239416	−	0.138227i	−0.375492	−	0.926825i	$-0.622526\pi$
$17$	0.987137	−	0.569924i	0.239416	−	0.138227i	0.614908	+	0.788599i	$0.289193\pi$
$18$		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
$26$	−1.46525	+	4.18085i	−0.287359	+	0.819933i
$27$		0			0
$28$	5.29149	−	0.0126068i	0.999997	−	0.00238247i
$29$	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	0.0711043	−	0.997469i	$-0.477348\pi$
$31$	5.40346	−	3.11969i	0.970490	−	0.560313i	0.899386	+	0.437156i	$0.144014\pi$
$32$	0.647158	−	5.61971i	0.114402	−	0.993434i
$33$		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	−0.144604	−	0.989490i	$-0.546191\pi$
$37$	−6.53184	−	3.77116i	−1.07383	−	0.619975i	−0.929225	+	0.369514i	$0.879524\pi$
$38$	1.26789	−	1.09003i	0.205679	−	0.176826i
$39$		0			0
$40$	1.79180	−	0.0644029i	0.283308	−	0.0101830i
$41$			4.06598i			0.635000i	0.948258	+	0.317500i	$0.102843\pi$
$41$			4.06598i			0.635000i	−0.948258	+	0.317500i	$0.897157\pi$
$42$		0			0
$43$	4.65556			0.709966			0.354983	−	0.934873i	$-0.384487\pi$
$43$	4.65556			0.709966			0.354983	+	0.934873i	$0.384487\pi$
$44$	−0.969234	−	0.147062i	−0.146118	−	0.0221704i
$45$		0			0
$46$	−6.01586	+	5.17193i	−0.886990	+	0.762560i
$47$	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
$52$	3.91111	−	4.89451i	0.542373	−	0.678746i
$53$	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
$56$	−7.06804	−	2.45822i	−0.944506	−	0.328493i
$57$		0			0
$58$	−5.41750	−	1.89865i	−0.711353	−	0.249305i
$59$	9.12119	−	5.26612i	1.18748	−	0.685591i	0.229745	−	0.973251i	$-0.426211\pi$
$59$	9.12119	−	5.26612i	1.18748	−	0.685591i	0.957733	+	0.287660i	$0.0928774\pi$
$60$		0			0
$61$	−10.1718	−	5.87267i	−1.30236	−	0.751918i	−0.321552	−	0.946892i	$-0.604204\pi$
$61$	−10.1718	−	5.87267i	−1.30236	−	0.751918i	−0.980808	+	0.194974i	$0.937538\pi$
$62$	−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	$0.708870\pi$
$68$	2.25390	+	0.341983i	0.273325	+	0.0414716i
$69$		0			0
$70$	0.434258	−	2.33177i	0.0519038	−	0.278699i
$71$	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	$-0.382355\pi$
$74$	6.95363	+	8.08829i	0.808343	+	0.940244i
$75$		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	0.633645	−	0.773624i	$-0.281558\pi$
$79$	2.49304	+	1.43936i	0.280489	+	0.161940i	−0.353156	+	0.935564i	$0.614891\pi$
$80$	−2.42150	−	0.752143i	−0.270732	−	0.0840921i
$81$		0			0
$82$	1.90182	−	5.42656i	0.210021	−	0.599263i
$83$			14.1254i			1.55047i	0.631674	+	0.775234i	$0.282368\pi$
$83$			14.1254i			1.55047i	−0.631674	+	0.775234i	$0.717632\pi$
$84$		0			0
$85$			0.722556i			0.0783722i
$86$	−6.21342	−	2.17759i	−0.670010	−	0.234816i
$87$		0			0
$88$	1.22478	+	0.649622i	0.130562	+	0.0692499i
$89$	−9.12417	−	5.26784i	−0.967160	−	0.558390i	−0.0687909	−	0.997631i	$-0.521914\pi$
$89$	−9.12417	−	5.26784i	−0.967160	−	0.558390i	−0.898369	+	0.439241i	$0.855247\pi$
$90$		0			0
$91$	−5.18932	−	6.46248i	−0.543988	−	0.677452i
$92$	10.4480	−	4.08872i	1.08928	−	0.426278i
$93$		0			0
$94$	−10.3055	+	8.85976i	−1.06293	+	0.913814i
$95$	−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	$0.464761\pi$
$98$	−5.21447	+	8.41483i	−0.526741	+	0.850026i
$99$		0			0
$100$	−1.37957	+	9.09226i	−0.137957	+	0.909226i
$101$	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	0.938414	−	0.345513i	$-0.112295\pi$
$103$	11.2490	+	6.49462i	1.10840	+	0.639934i	0.169984	+	0.985447i	$0.445628\pi$
$104$	−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	0.498470	−	0.866907i	$-0.333895\pi$
$107$	−0.0316330	−	0.0182633i	−0.00305808	−	0.00176558i	−0.501528	+	0.865141i	$0.667229\pi$
$108$		0			0
$109$	−14.8136	+	8.55264i	−1.41889	+	0.819195i	−0.996201	−	0.0870820i	$-0.972246\pi$
$109$	−14.8136	+	8.55264i	−1.41889	+	0.819195i	−0.422685	+	0.906276i	$0.638912\pi$
$110$	−0.145335	+	0.414691i	−0.0138572	+	0.0395392i
$111$		0			0
$112$	8.28336	+	6.58680i	0.782704	+	0.622394i
$113$			7.98162i			0.750848i	0.926853	+	0.375424i	$0.122503\pi$
$113$			7.98162i			0.750848i	−0.926853	+	0.375424i	$0.877497\pi$
$114$		0			0
$115$	1.77804	+	3.07965i	0.165803	+	0.287179i
$116$	6.34225	+	5.06797i	0.588863	+	0.470549i
$117$		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
$122$	10.8286	+	12.5955i	0.980374	+	1.14035i
$123$		0			0
$124$	12.3375	+	1.87197i	1.10794	+	0.168108i
$125$	−6.08433			−0.544199
$126$		0			0
$127$			7.35098i			0.652294i	0.945319	+	0.326147i	$0.105750\pi$
$127$			7.35098i			0.652294i	−0.945319	+	0.326147i	$0.894250\pi$
$128$	8.02743	−	7.97247i	0.709532	−	0.704674i
$129$		0			0
$130$	−1.83078	−	2.12952i	−0.160570	−	0.186771i
$131$	−17.8525	−	10.3071i	−1.55978	−	0.900540i	−0.997277	−	0.0737443i	$-0.976505\pi$
$131$	−17.8525	−	10.3071i	−1.55978	−	0.900540i	−0.562503	−	0.826795i	$-0.690162\pi$
$132$		0			0
$133$	0.476621	+	3.09157i	0.0413283	+	0.268073i
$134$	−1.63617	−	8.67065i	−0.141344	−	0.749031i
$135$		0			0
$136$	−2.84815	−	1.51066i	−0.244226	−	0.129538i
$137$	0.0286513	−	0.0165418i	0.00244784	−	0.00141326i	−0.498776	−	0.866731i	$-0.666217\pi$
$137$	0.0286513	−	0.0165418i	0.00244784	−	0.00141326i	0.501223	+	0.865318i	$0.332883\pi$
$138$		0			0
$139$	−17.8470			−1.51376			−0.756882	−	0.653551i	$-0.773278\pi$
$139$	−17.8470			−1.51376			−0.756882	+	0.653551i	$0.773278\pi$
$140$	−1.67023	+	2.90891i	−0.141160	+	0.245848i
$141$		0			0
$142$	−7.32282	−	2.56640i	−0.614517	−	0.215367i
$143$	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	−0.444584	−	0.895737i	$-0.646649\pi$
$151$	1.33762	−	0.772277i	0.108854	−	0.0628470i	0.553439	+	0.832890i	$0.313315\pi$
$152$	3.34192	−	0.120119i	0.271065	−	0.00974293i
$153$		0			0
$154$	1.19231	−	1.39357i	0.0960793	−	0.112297i
$155$			3.95518i			0.317687i
$156$		0			0
$157$	−0.912293	+	0.526713i	−0.0728089	+	0.0420362i	−0.535963	−	0.844242i	$-0.680051\pi$
$157$	−0.912293	+	0.526713i	−0.0728089	+	0.0420362i	0.463154	+	0.886278i	$0.346718\pi$
$158$	−2.65402	−	3.08709i	−0.211143	−	0.245596i
$159$		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	$0.104663\pi$
$164$	−5.07644	+	6.35285i	−0.396403	+	0.496074i
$165$		0			0
$166$	6.60703	−	18.8521i	0.512805	−	1.46321i
$167$	−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
$170$	0.337968	−	0.964340i	0.0259210	−	0.0739615i
$171$		0			0
$172$	7.27402	+	5.81253i	0.554639	+	0.443201i
$173$	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
$178$	9.71335	+	11.2983i	0.728046	+	0.846845i
$179$	−2.84235	+	1.64103i	−0.212447	+	0.122656i	−0.602448	−	0.798158i	$-0.705808\pi$
$179$	−2.84235	+	1.64103i	−0.212447	+	0.122656i	0.390001	+	0.920814i	$0.372475\pi$
$180$		0			0
$181$		−	1.67052i		−	0.124169i	−0.998071	−	0.0620845i	$-0.980225\pi$
$181$		−	1.67052i		−	0.124169i	0.998071	−	0.0620845i	$-0.0197748\pi$
$182$	3.90302	+	11.0522i	0.289311	+	0.819246i
$183$		0			0
$184$	−15.8566	+	0.569937i	−1.16897	+	0.0420163i
$185$	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	$0.662955\pi$
$194$	−2.90446	−	1.01792i	−0.208528	−	0.0730821i
$195$		0			0
$196$	10.8953	−	8.79161i	0.778236	−	0.627972i
$197$	−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	−0.691053	−	0.722804i	$-0.742853\pi$
$199$	−5.79242	+	3.34425i	−0.410614	+	0.237068i	0.280440	+	0.959872i	$0.409520\pi$
$200$	6.09402	−	11.4895i	0.430912	−	0.812428i
$201$		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
$206$	−11.9754	−	13.9295i	−0.834365	−	0.970513i
$207$		0			0
$208$	12.2217	−	2.76430i	0.847424	−	0.191670i
$209$		−	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	$0.316416\pi$
$212$	−0.662718	+	4.36775i	−0.0455157	+	0.299979i
$213$		0			0
$214$	0.0336756	+	0.0391707i	0.00230202	+	0.00267765i
$215$	−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
$220$	0.387935	−	0.485477i	0.0261546	−	0.0327309i
$221$	−1.78535	−	3.09231i	−0.120096	−	0.208012i
$222$		0			0
$223$		−	5.00823i		−	0.335376i	−0.985840	−	0.167688i	$-0.946370\pi$
$223$		−	5.00823i		−	0.335376i	0.985840	−	0.167688i	$-0.0536301\pi$
$224$	−7.97426	−	12.6654i	−0.532803	−	0.846240i
$225$		0			0
$226$	3.73333	−	10.6525i	0.248337	−	0.708591i
$227$	22.1014	−	12.7603i	1.46692	−	0.846928i	0.467607	−	0.883936i	$-0.345116\pi$
$227$	22.1014	−	12.7603i	1.46692	−	0.846928i	0.999315	+	0.0370085i	$0.0117829\pi$
$228$		0			0
$229$	21.0883	+	12.1753i	1.39355	+	0.804568i	0.993707	−	0.112014i	$-0.0357303\pi$
$229$	21.0883	+	12.1753i	1.39355	+	0.804568i	0.399846	+	0.916582i	$0.369064\pi$
$230$	−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	0.971919	−	0.235317i	$-0.0756130\pi$
$233$	19.1428	+	11.0521i	1.25409	+	0.724047i	0.282168	+	0.959365i	$0.408946\pi$
$234$		0			0
$235$	3.04586	+	5.27559i	0.198690	+	0.344141i
$236$	20.8261	+	3.15994i	1.35567	+	0.205695i
$237$		0			0
$238$	−2.77265	+	3.24067i	−0.179724	+	0.210061i
$239$	−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	$-0.380459\pi$
$242$	11.5386	−	9.91992i	0.741729	−	0.637676i
$243$		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
$248$	−15.5904	−	8.26914i	−0.989990	−	0.525091i
$249$		0			0
$250$	8.12029	+	2.84589i	0.513572	+	0.179990i
$251$			2.04696i			0.129203i	0.997911	+	0.0646015i	$0.0205776\pi$
$251$			2.04696i			0.129203i	−0.997911	+	0.0646015i	$0.979422\pi$
$252$		0			0
$253$			2.74971i			0.172873i
$254$	3.43835	−	9.81078i	0.215741	−	0.615583i
$255$		0			0
$256$	−14.4426	+	6.88549i	−0.902665	+	0.430343i
$257$	−18.7909	−	10.8489i	−1.17214	−	0.676738i	−0.217960	−	0.975958i	$-0.569940\pi$
$257$	−18.7909	−	10.8489i	−1.17214	−	0.676738i	−0.954184	+	0.299220i	$0.903274\pi$
$258$		0			0
$259$	−19.7221	+	3.04052i	−1.22547	+	0.188929i
$260$	1.44734	+	3.69844i	0.0897604	+	0.229368i
$261$		0			0
$262$	19.0053	+	22.1065i	1.17415	+	1.36574i
$263$	−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
$266$	0.809943	−	4.34902i	0.0496608	−	0.266655i
$267$		0			0
$268$	−1.87194	+	12.3374i	−0.114347	+	0.753624i
$269$	−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	0.0539891	−	0.998542i	$-0.482806\pi$
$271$	−12.9026	−	7.44933i	−0.783779	−	0.452515i	−0.837768	+	0.546027i	$0.816140\pi$
$272$	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	−0.275805	−	0.961213i	$-0.588945\pi$
$277$	6.96901	−	4.02356i	0.418727	−	0.241752i	0.694533	+	0.719461i	$0.255611\pi$
$278$	23.8190	+	8.34777i	1.42857	+	0.500666i
$279$		0			0
$280$	3.58974	−	3.10106i	0.214528	−	0.185324i
$281$			17.7045i			1.05616i	0.849195	+	0.528080i	$0.177088\pi$
$281$			17.7045i			1.05616i	−0.849195	+	0.528080i	$0.822912\pi$
$282$		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	$0.578142\pi$
$284$	8.57280	+	6.85035i	0.508702	+	0.406494i
$285$		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
$290$	2.75941	−	2.37231i	0.162038	−	0.139307i
$291$		0			0
$292$	3.21416	−	21.1835i	0.188094	−	1.23967i
$293$	−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
$296$	0.766277	+	21.3191i	0.0445389	+	1.23915i
$297$		0			0
$298$	19.8147	−	17.0350i	1.14783	−	0.986810i
$299$	−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
$304$	−4.51638	−	1.40284i	−0.259032	−	0.0804581i
$305$	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	$0.605766\pi$
$308$	−2.24312	+	1.30220i	−0.127813	+	0.0741997i
$309$		0			0
$310$	1.84999	−	5.27867i	0.105073	−	0.299808i
$311$	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
$320$	−2.84438	−	4.19845i	−0.159006	−	0.234701i
$321$		0			0
$322$	−3.84299	+	20.6351i	−0.214162	+	1.14995i
$323$			1.34765i			0.0749854i
$324$		0			0
$325$	12.4744	−	7.20213i	0.691958	−	0.399502i
$326$	−5.30024	+	4.55670i	−0.293553	+	0.252372i
$327$		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	$-0.193601\pi$
$332$	−17.6358	+	22.0701i	−0.967890	+	1.21126i
$333$		0			0
$334$	20.0628	+	7.03133i	1.09779	+	0.384737i
$335$	−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	$0.457138\pi$
$338$	−4.25312	−	1.49057i	−0.231339	−	0.0810766i
$339$		0			0
$340$	−0.902121	+	1.12895i	−0.0489244	+	0.0612259i
$341$	−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
$346$	−10.2366	+	8.80059i	−0.550325	+	0.473123i
$347$	−14.0594	+	8.11720i	−0.754749	+	0.435754i	−0.827407	−	0.561603i	$-0.810185\pi$
$347$	−14.0594	+	8.11720i	−0.754749	+	0.435754i	0.0726585	+	0.997357i	$0.476852\pi$
$348$		0			0
$349$			8.62152i			0.461499i	0.973013	+	0.230750i	$0.0741178\pi$
$349$			8.62152i			0.461499i	−0.973013	+	0.230750i	$0.925882\pi$
$350$	−13.0729	−	11.1849i	−0.698776	−	0.597860i
$351$		0			0
$352$	1.10258	+	2.54414i	0.0587675	+	0.135603i
$353$	−14.7933	+	8.54090i	−0.787367	+	0.454586i	−0.839035	−	0.544078i	$-0.816880\pi$
$353$	−14.7933	+	8.54090i	−0.787367	+	0.454586i	0.0516680	+	0.998664i	$0.483546\pi$
$354$		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
$362$	−0.781371	+	2.22952i	−0.0410679	+	0.117181i
$363$		0			0
$364$	−0.0394923	−	16.5762i	−0.00206996	−	0.868827i
$365$	6.79100			0.355457
$366$		0			0
$367$	−16.9496	+	9.78583i	−0.884760	+	0.510816i	−0.872225	−	0.489105i	$-0.837323\pi$
$367$	−16.9496	+	9.78583i	−0.884760	+	0.510816i	−0.0125348	+	0.999921i	$0.503990\pi$
$368$	21.4292	+	6.65613i	1.11708	+	0.346975i
$369$		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	$0.0212344\pi$
$373$	30.0203	+	17.3322i	1.55439	+	0.897429i	0.556617	+	0.830769i	$0.312099\pi$
$374$	0.599155	−	0.515103i	0.0309816	−	0.0266353i
$375$		0			0
$376$	−27.1632	+	0.976329i	−1.40083	+	0.0503503i
$377$		−	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	$0.278203\pi$
$380$	0.224861	−	1.48198i	0.0115351	−	0.0760241i
$381$		0			0
$382$	0.727507	−	0.625449i	0.0372225	−	0.0320008i
$383$	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
$388$	3.40024	+	2.71707i	0.172621	+	0.137938i
$389$	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
$392$	−18.6533	+	6.63732i	−0.942134	+	0.335235i
$393$		0			0
$394$	28.8018	+	10.0941i	1.45101	+	0.508531i
$395$	−1.58035	+	0.912416i	−0.0795161	+	0.0459086i
$396$		0			0
$397$	−15.4930	−	8.94489i	−0.777571	−	0.448931i	0.0579974	−	0.998317i	$-0.481528\pi$
$397$	−15.4930	−	8.94489i	−0.777571	−	0.448931i	−0.835569	+	0.549386i	$0.814862\pi$
$398$	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	0.956025	−	0.293285i	$-0.0947485\pi$
$401$	23.6304	+	13.6430i	1.18005	+	0.681299i	0.224020	+	0.974585i	$0.428082\pi$
$402$		0			0
$403$	−9.77276	−	16.9269i	−0.486816	−	0.843190i
$404$	−4.82665	+	31.8109i	−0.240135	+	1.58265i
$405$		0			0
$406$	−14.3214	+	5.05749i	−0.710757	+	0.250999i
$407$	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	$0.999500\pi$
$410$	2.37627	+	2.76402i	0.117356	+	0.136505i
$411$		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
$416$	−17.6044	−	2.02729i	−0.863125	−	0.0993962i
$417$		0			0
$418$	−0.271067	+	0.773448i	−0.0132583	+	0.0378306i
$419$			13.2211i			0.645895i	0.946417	+	0.322947i	$0.104674\pi$
$419$			13.2211i			0.645895i	−0.946417	+	0.322947i	$0.895326\pi$
$420$		0			0
$421$			4.11935i			0.200765i	0.994949	+	0.100382i	$0.0320066\pi$
$421$			4.11935i			0.200765i	−0.994949	+	0.100382i	$0.967993\pi$
$422$	−21.1430	−	7.40989i	−1.02922	−	0.360708i
$423$		0			0
$424$	2.92745	−	5.51933i	0.142170	−	0.268042i
$425$	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
$430$	3.16481	−	2.72084i	0.152621	−	0.131210i
$431$	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	$0.275337\pi$
$434$	−15.1771	+	17.7390i	−0.728526	+	0.851499i
$435$		0			0
$436$	−33.8234	−	5.13202i	−1.61985	−	0.245779i
$437$	3.31625	+	5.74392i	0.158638	+	0.274769i
$438$		0			0
$439$	−24.9138	−	14.3840i	−1.18907	−	0.686510i	−0.230975	−	0.972960i	$-0.574191\pi$
$439$	−24.9138	−	14.3840i	−1.18907	−	0.686510i	−0.958095	+	0.286450i	$0.907525\pi$
$440$	−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	0.454817	−	0.890585i	$-0.349705\pi$
$443$	−1.87416	−	1.08205i	−0.0890442	−	0.0514097i	−0.543861	+	0.839175i	$0.683038\pi$
$444$		0			0
$445$	5.78386	−	3.33932i	0.274181	−	0.158299i
$446$	−2.34255	+	6.68410i	−0.110923	+	0.316501i
$447$		0			0
$448$	4.71854	+	20.6334i	0.222930	+	0.974834i
$449$			18.0886i			0.853652i	0.904334	+	0.426826i	$0.140368\pi$
$449$			18.0886i			0.853652i	−0.904334	+	0.426826i	$0.859632\pi$
$450$		0			0
$451$	−0.996499	−	1.72599i	−0.0469233	−	0.0812736i
$452$	−9.96517	+	12.4708i	−0.468722	+	0.586577i
$453$		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	$0.129714\pi$
$458$	−22.4500	−	26.1133i	−1.04902	−	1.22019i
$459$		0			0
$460$	−1.06691	+	7.03167i	−0.0497451	+	0.327853i
$461$	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	$0.0281268\pi$
$463$			3.79774i			0.176496i	−0.996099	+	0.0882479i	$0.971873\pi$
$464$	3.58195	+	15.8368i	0.166288	+	0.735204i
$465$		0			0
$466$	−20.3789	−	23.7043i	−0.944035	−	1.09808i
$467$	−1.07261	−	0.619273i	−0.0496346	−	0.0286565i	0.474977	−	0.879998i	$-0.342456\pi$
$467$	−1.07261	−	0.619273i	−0.0496346	−	0.0286565i	−0.524612	+	0.851341i	$0.675790\pi$
$468$		0			0
$469$	15.3867	+	5.97917i	0.710491	+	0.276093i
$470$	−1.59747	−	8.46560i	−0.0736860	−	0.390489i
$471$		0			0
$472$	−26.3170	−	13.9585i	−1.21134	−	0.642494i
$473$	−1.97626	+	1.14099i	−0.0908684	+	0.0524629i
$474$		0			0
$475$	−5.43645			−0.249441
$476$	5.21624	−	3.02819i	0.239086	−	0.138797i
$477$		0			0
$478$	29.1044	+	10.2001i	1.33120	+	0.466542i
$479$	−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	−0.960886	−	0.276943i	$-0.910679\pi$
$487$	−26.5146	+	15.3082i	−1.20149	+	0.693681i	−0.240604	+	0.970623i	$0.577345\pi$
$488$	1.19329	+	33.1994i	0.0540177	+	1.50287i
$489$		0			0
$490$	−2.96682	−	5.52973i	−0.134027	−	0.249808i
$491$			23.4948i			1.06030i	0.847903	+	0.530152i	$0.177865\pi$
$491$			23.4948i			1.06030i	−0.847903	+	0.530152i	$0.822135\pi$
$492$		0			0
$493$	4.00699	−	2.31344i	0.180466	−	0.104192i
$494$	−3.41463	−	3.97181i	−0.153631	−	0.178700i
$495$		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	$-0.0150021\pi$
$500$	−9.50639	−	7.59637i	−0.425139	−	0.339720i
$501$		0			0
$502$	0.957446	−	2.73192i	0.0427329	−	0.121932i
$503$	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
$506$	1.28615	−	3.66983i	0.0571764	−	0.163144i
$507$		0			0
$508$	−9.17779	+	11.4854i	−0.407199	+	0.509584i
$509$	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
$514$	20.0043	+	23.2685i	0.882351	+	1.02633i
$515$	−7.13081	+	4.11697i	−0.314221	+	0.181416i
$516$		0			0
$517$			4.71039i			0.207163i
$518$	27.7438	+	5.16688i	1.21899	+	0.227020i
$519$		0			0
$520$	−0.201749	−	5.61301i	−0.00884728	−	0.246147i
$521$	−22.8772	+	13.2082i	−1.00227	+	0.578660i	−0.908918	−	0.416974i	$-0.863091\pi$
$521$	−22.8772	+	13.2082i	−1.00227	+	0.578660i	−0.0933493	+	0.995633i	$0.529757\pi$
$522$		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
$530$	1.86876	+	0.654938i	0.0811738	+	0.0284487i
$531$		0			0
$532$	−3.11518	+	5.42546i	−0.135060	+	0.235223i
$533$	12.7371			0.551707
$534$		0			0
$535$	0.0200523	−	0.0115772i	0.000866938	−	0.000500527i
$536$	8.26902	−	15.5901i	0.357167	−	0.673392i
$537$		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	−0.0184329	−	0.999830i	$-0.505868\pi$
$541$	−20.7829	−	11.9990i	−0.893528	−	0.515878i	−0.875095	+	0.483952i	$0.839201\pi$
$542$	13.7358	+	15.9771i	0.590003	+	0.686277i
$543$		0			0
$544$	−2.56398	−	5.91626i	−0.109930	−	0.253657i
$545$		−	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	$0.393278\pi$
$548$	0.0654186	+	0.00992594i	0.00279454	+	0.000424015i
$549$		0			0
$550$	2.07793	+	2.41700i	0.0886034	+	0.103061i
$551$	−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
$556$	−27.8849	−	22.2822i	−1.18258	−	0.944978i
$557$	−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
$560$	−6.24144	+	2.45968i	−0.263749	+	0.103941i
$561$		0			0
$562$	8.28109	−	23.6288i	0.349317	−	0.996720i
$563$	29.9610	−	17.2980i	1.26271	−	0.729024i	0.289109	−	0.957296i	$-0.406641\pi$
$563$	29.9610	−	17.2980i	1.26271	−	0.729024i	0.973597	+	0.228273i	$0.0733078\pi$
$564$		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	0.626727	−	0.779239i	$-0.284394\pi$
$569$	6.32717	+	3.65299i	0.265249	+	0.153141i	−0.361478	+	0.932381i	$0.617728\pi$
$570$		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	$0.917936\pi$
$572$	−0.460687	+	3.03623i	−0.0192623	+	0.126951i
$573$		0			0
$574$	−5.06595	−	14.3453i	−0.211448	−	0.598761i
$575$	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	$-0.465456\pi$
$578$	16.8373	−	14.4753i	0.700338	−	0.602092i
$579$		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
$584$	−14.1980	+	26.7685i	−0.587519	+	1.10769i
$585$		0			0
$586$	5.06873	+	1.77642i	0.209387	+	0.0733832i
$587$			8.75340i			0.361291i	0.983548	+	0.180646i	$0.0578187\pi$
$587$			8.75340i			0.361291i	−0.983548	+	0.180646i	$0.942181\pi$
$588$		0			0
$589$			7.37687i			0.303959i
$590$	3.12284	−	8.91054i	0.128565	−	0.366841i
$591$		0			0
$592$	8.94913	−	28.8115i	0.367807	−	1.18414i
$593$	20.9557	+	12.0988i	0.860547	+	0.496837i	0.864195	−	0.503156i	$-0.167828\pi$
$593$	20.9557	+	12.0988i	0.860547	+	0.496837i	−0.00364837	+	0.999993i	$0.501161\pi$
$594$		0			0
$595$	1.19695	+	1.49061i	0.0490701	+	0.0611091i
$596$	−34.4131	+	13.4672i	−1.40961	+	0.551637i
$597$		0			0
$598$	16.2016	+	18.8453i	0.662534	+	0.770643i
$599$	−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	$0.214825\pi$
$602$	−16.4254	+	5.80051i	−0.669449	+	0.236411i
$603$		0			0
$604$	3.05415	+	0.463405i	0.124272	+	0.0188557i
$605$	−3.41033	−	5.90686i	−0.138650	−	0.240148i
$606$		0			0
$607$	−4.12752	−	2.38303i	−0.167531	−	0.0967240i	0.413890	−	0.910327i	$-0.364170\pi$
$607$	−4.12752	−	2.38303i	−0.167531	−	0.0967240i	−0.581421	+	0.813603i	$0.697503\pi$
$608$	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	0.0760723	−	0.997102i	$-0.475762\pi$
$613$	24.2048	−	13.9747i	0.977624	−	0.564432i	0.901552	+	0.432671i	$0.142429\pi$
$614$	15.2557	+	5.34662i	0.615671	+	0.215772i
$615$		0			0
$616$	3.60281	−	0.688750i	0.145161	−	0.0277505i
$617$			25.6270i			1.03171i	0.856677	+	0.515853i	$0.172525\pi$
$617$			25.6270i			1.03171i	−0.856677	+	0.515853i	$0.827475\pi$
$618$		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	$0.571527\pi$
$620$	−4.93809	+	6.17972i	−0.198319	+	0.248183i
$621$		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
$626$	18.5409	−	15.9399i	0.741042	−	0.637085i
$627$		0			0
$628$	−2.08301	−	0.316054i	−0.0831211	−	0.0126119i
$629$	−8.59710			−0.342789
$630$		0			0
$631$		−	25.5148i		−	1.01573i	−0.861437	−	0.507864i	$-0.830435\pi$
$631$		−	25.5148i		−	1.01573i	0.861437	−	0.507864i	$-0.169565\pi$
$632$	−0.292468	−	8.13697i	−0.0116338	−	0.323671i
$633$		0			0
$634$	−14.8875	+	12.7990i	−0.591259	+	0.508315i
$635$	−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
$640$	1.83240	+	6.93379i	0.0724318	+	0.274082i
$641$	−14.3543	+	8.28743i	−0.566959	+	0.327334i	−0.755934	−	0.654648i	$-0.772817\pi$
$641$	−14.3543	+	8.28743i	−0.566959	+	0.327334i	0.188975	+	0.981982i	$0.439484\pi$
$642$		0			0
$643$	−1.84462			−0.0727446			−0.0363723	−	0.999338i	$-0.511580\pi$
$643$	−1.84462			−0.0727446			−0.0363723	+	0.999338i	$0.511580\pi$
$644$	14.7808	−	25.7426i	0.582446	−	1.01440i
$645$		0			0
$646$	0.630351	−	1.79861i	0.0248008	−	0.0707653i
$647$	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
$656$	−15.8632	+	3.58793i	−0.619355	+	0.140085i
$657$		0			0
$658$	−6.58323	+	35.3489i	−0.256641	+	1.37804i
$659$		−	25.6600i		−	0.999573i	−0.866148	−	0.499787i	$-0.833412\pi$
$659$		−	25.6600i		−	0.999573i	0.866148	−	0.499787i	$-0.166588\pi$
$660$		0			0
$661$	28.3071	−	16.3431i	1.10102	−	0.635674i	0.164531	−	0.986372i	$-0.447389\pi$
$661$	28.3071	−	16.3431i	1.10102	−	0.635674i	0.936489	+	0.350698i	$0.114056\pi$
$662$	−35.3210	+	30.3660i	−1.37279	+	1.18021i
$663$		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
$668$	−23.4874	−	18.7683i	−0.908756	−	0.726169i
$669$		0			0
$670$	5.27859	+	1.84997i	0.203930	+	0.0714705i
$671$	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	$0.618605\pi$
$674$	−6.57833	−	2.30548i	−0.253388	−	0.0888038i
$675$		0			0
$676$	4.97911	+	3.97871i	0.191504	+	0.153027i
$677$	−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
$682$	3.27970	−	2.81961i	0.125586	−	0.107968i
$683$	−7.14692	+	4.12627i	−0.273469	+	0.157887i	−0.630463	−	0.776219i	$-0.717135\pi$
$683$	−7.14692	+	4.12627i	−0.273469	+	0.157887i	0.356994	+	0.934107i	$0.383802\pi$
$684$		0			0
$685$			0.0209719i			0.000801296i
$686$	3.18228	+	25.9976i	0.121500	+	0.992591i
$687$		0			0
$688$	4.10819	+	18.1634i	0.156623	+	0.692474i
$689$	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
$698$	4.03263	−	11.5065i	0.152637	−	0.435527i
$699$		0			0
$700$	12.2158	+	21.0424i	0.461713	+	0.795328i
$701$	−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
$704$	−0.281525	−	3.91119i	−0.0106104	−	0.147409i
$705$		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	0.643343	−	0.765578i	$-0.277547\pi$
$709$	8.04150	+	4.64276i	0.302005	+	0.174363i	−0.341338	+	0.939940i	$0.610880\pi$
$710$	3.72989	−	3.20664i	0.139980	−	0.120343i
$711$		0			0
$712$	1.07039	+	29.7802i	0.0401147	+	1.11606i
$713$		−	35.0016i		−	1.31082i
$714$		0			0
$715$	−0.973357			−0.0364015
$716$	−6.48985	−	0.984703i	−0.242537	−	0.0368001i
$717$		0			0
$718$	27.1575	−	23.3477i	1.01351	−	0.871330i
$719$	−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
$724$	2.08567	−	2.61009i	0.0775134	−	0.0970032i
$725$	9.33244	+	16.1643i	0.346598	+	0.600325i
$726$		0			0
$727$			31.6181i			1.17265i	0.810075	+	0.586326i	$0.199426\pi$
$727$			31.6181i			1.17265i	−0.810075	+	0.586326i	$0.800574\pi$
$728$	−7.70063	+	22.1414i	−0.285404	+	0.820615i
$729$		0			0
$730$	−9.06343	−	3.17642i	−0.335452	−	0.117565i
$731$	4.59567	−	2.65331i	0.169977	−	0.0981363i
$732$		0			0
$733$	0.114112	+	0.0658825i	0.00421482	+	0.00243343i	0.502106	−	0.864806i	$-0.332559\pi$
$733$	0.114112	+	0.0658825i	0.00421482	+	0.00243343i	−0.497891	+	0.867240i	$0.665892\pi$
$734$	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	$0.881075\pi$
$740$	9.45404	+	1.43446i	0.347537	+	0.0527317i
$741$		0			0
$742$	−6.27998	−	5.37303i	−0.230545	−	0.197250i
$743$	−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
$746$	−31.9588	−	37.1737i	−1.17010	−	1.36103i
$747$		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	0.876215	−	0.481921i	$-0.160061\pi$
$751$	24.5808	+	14.1917i	0.896967	+	0.517864i	0.0207520	+	0.999785i	$0.493394\pi$
$752$	36.7093	+	11.4023i	1.33865	+	0.415798i
$753$		0			0
$754$	−5.94773	+	16.9709i	−0.216604	+	0.618045i
$755$			0.979101i			0.0356331i
$756$		0			0
$757$		−	8.94140i		−	0.324981i	−0.986710	−	0.162490i	$-0.948047\pi$
$757$		−	8.94140i		−	0.324981i	0.986710	−	0.162490i	$-0.0519526\pi$
$758$	−33.3491	−	11.6877i	−1.21129	−	0.424518i
$759$		0			0
$760$	−0.993287	+	1.87271i	−0.0360303	+	0.0679304i
$761$	−18.3315	−	10.5837i	−0.664515	−	0.383658i	0.129480	−	0.991582i	$-0.458669\pi$
$761$	−18.3315	−	10.5837i	−0.664515	−	0.383658i	−0.793995	+	0.607924i	$0.792002\pi$
$762$		0			0
$763$	−16.3922	+	42.1833i	−0.593437	+	1.52714i
$764$	−1.26350	+	0.494455i	−0.0457117	+	0.0178887i
$765$		0			0
$766$	−3.65694	+	3.14393i	−0.132131	+	0.113595i
$767$	−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	$0.414969\pi$
$770$	0.387133	+	1.09625i	0.0139513	+	0.0395061i
$771$		0			0
$772$	−4.25199	+	28.0234i	−0.153032	+	1.00859i
$773$	−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
$782$	−2.99087	+	8.53399i	−0.106953	+	0.305175i
$783$		0			0
$784$	27.9997	−	0.133418i	0.999989	−	0.00476492i
$785$		−	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	$0.735383\pi$
$788$	−33.7182	−	26.9435i	−1.20116	−	0.959823i
$789$		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
$794$	16.4934	+	19.1848i	0.585330	+	0.680842i
$795$		0			0
$796$	−13.2256	−	2.00672i	−0.468770	−	0.0711264i
$797$	−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
$800$	23.8663	−	10.3431i	0.843800	−	0.365684i
$801$		0			0
$802$	−25.1563	−	29.2612i	−0.888299	−	1.03325i
$803$	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
$808$	21.3210	−	40.1979i	0.750070	−	1.41416i
$809$	13.9845	−	8.07393i	0.491668	−	0.283864i	−0.233598	−	0.972333i	$-0.575050\pi$
$809$	13.9845	−	8.07393i	0.491668	−	0.283864i	0.725266	+	0.688469i	$0.241717\pi$
$810$		0			0
$811$	14.3851			0.505129			0.252565	−	0.967580i	$-0.418726\pi$
$811$	14.3851			0.505129			0.252565	+	0.967580i	$0.418726\pi$
$812$	21.4792	−	0.0511737i	0.753773	−	0.00179584i
$813$		0			0
$814$	−4.93407	−	1.72922i	−0.172939	−	0.0606092i
$815$	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	0.327254	−	0.944936i	$-0.393877\pi$
$823$	37.5589	−	21.6846i	1.30922	−	0.755878i	0.981966	+	0.189058i	$0.0605434\pi$
$824$	−1.31967	−	36.7154i	−0.0459728	−	1.27904i
$825$		0			0
$826$	−25.6194	+	29.9439i	−0.891414	+	1.04188i
$827$		−	9.52077i		−	0.331070i	−0.986204	−	0.165535i	$-0.947065\pi$
$827$		−	9.52077i		−	0.331070i	0.986204	−	0.165535i	$-0.0529350\pi$
$828$		0			0
$829$	−23.9717	+	13.8400i	−0.832570	+	0.480685i	−0.854732	−	0.519070i	$-0.826278\pi$
$829$	−23.9717	+	13.8400i	−0.832570	+	0.480685i	0.0221616	+	0.999754i	$0.492945\pi$
$830$	8.25530	+	9.60235i	0.286545	+	0.333303i
$831$		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
$836$	0.723545	−	0.905472i	0.0250243	−	0.0313164i
$837$		0			0
$838$	6.18406	−	17.6452i	0.213625	−	0.609544i
$839$	−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
$842$	1.92678	−	5.49777i	0.0664013	−	0.189466i
$843$		0			0
$844$	24.7520	+	19.7788i	0.851998	+	0.680815i
$845$	−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
$850$	−4.83212	−	5.62060i	−0.165740	−	0.192785i
$851$	−36.6423	+	21.1554i	−1.25608	+	0.725199i
$852$		0			0
$853$			31.9251i			1.09310i	0.837428	+	0.546548i	$0.184058\pi$
$853$			31.9251i			1.09310i	−0.837428	+	0.546548i	$0.815942\pi$
$854$	43.2042	+	8.04616i	1.47842	+	0.275334i
$855$		0			0
$856$	0.00371099	+	0.103246i	0.000126839	+	0.00352888i
$857$	−5.74550	+	3.31716i	−0.196262	+	0.113312i	−0.594911	−	0.803792i	$-0.702813\pi$
$857$	−5.74550	+	3.31716i	−0.196262	+	0.113312i	0.398649	+	0.917104i	$0.369479\pi$
$858$		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
$866$	−36.0279	−	12.6266i	−1.22428	−	0.429068i
$867$		0			0
$868$	28.5530	−	16.5759i	0.969152	−	0.562623i
$869$	−1.41104			−0.0478663
$870$		0			0
$871$	16.9267	−	9.77262i	0.573538	−	0.331133i
$872$	42.7411	+	22.6699i	1.44740	+	0.767700i
$873$		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	−0.375998	−	0.926620i	$-0.622700\pi$
$877$	−40.4670	−	23.3636i	−1.36647	−	0.788934i	−0.990476	+	0.137686i	$0.956033\pi$
$878$	26.5225	+	30.8504i	0.895093	+	1.04115i
$879$		0			0
$880$	1.21225	−	0.274186i	0.0408649	−	0.00924279i
$881$		−	14.0128i		−	0.472105i	−0.971740	−	0.236052i	$-0.924146\pi$
$881$		−	14.0128i		−	0.472105i	0.971740	−	0.236052i	$-0.0758537\pi$
$882$		0			0
$883$	−37.1955			−1.25173			−0.625864	−	0.779932i	$-0.715254\pi$
$883$	−37.1955			−1.25173			−0.625864	+	0.779932i	$0.715254\pi$
$884$	1.07130	−	7.06058i	0.0360317	−	0.237473i
$885$		0			0
$886$	1.99518	+	2.32075i	0.0670295	+	0.0779671i
$887$	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
$892$	6.25284	−	7.82505i	0.209361	−	0.262002i
$893$	5.68089	+	9.83960i	0.190104	+	0.329270i
$894$		0			0
$895$		−	2.08052i		−	0.0695441i
$896$	3.35358	−	29.7448i	0.112035	−	0.993704i
$897$		0			0
$898$	8.46075	−	24.1414i	0.282339	−	0.805610i
$899$	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	$-0.424674\pi$
$908$	50.4634	+	7.65680i	1.67469	+	0.254100i
$909$		0			0
$910$	−7.30451	−	1.36036i	−0.242142	−	0.0450955i
$911$	−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
$914$	−5.31086	+	4.56583i	−0.175668	+	0.151024i
$915$		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	0.371768	−	0.928326i	$-0.378752\pi$
$919$	−7.46664	−	4.31087i	−0.246302	−	0.142202i	−0.618070	+	0.786123i	$0.712085\pi$
$920$	4.71292	−	8.88559i	0.155380	−	0.292949i
$921$		0			0
$922$	−44.5574	−	15.6159i	−1.46742	−	0.514281i
$923$		−	17.1880i		−	0.565751i
$924$		0			0
$925$		−	34.6808i		−	1.14030i
$926$	1.77635	−	5.06855i	0.0583746	−	0.166563i
$927$		0			0
$928$	2.62694	−	22.8115i	0.0862337	−	0.748826i
$929$	12.9536	+	7.47874i	0.424992	+	0.245369i	0.697211	−	0.716866i	$-0.254424\pi$
$929$	12.9536	+	7.47874i	0.424992	+	0.245369i	−0.272219	+	0.962235i	$0.587757\pi$
$930$		0			0
$931$	6.10459	+	5.58828i	0.200070	+	0.183148i
$932$	16.1108	+	41.1683i	0.527725	+	1.34851i
$933$		0			0
$934$	1.14187	+	1.32820i	0.0373633	+	0.0434600i
$935$	−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	$0.402260\pi$
$938$	−17.7387	−	15.1769i	−0.579190	−	0.495544i
$939$		0			0
$940$	−1.82767	+	12.0456i	−0.0596121	+	0.392884i
$941$	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	−0.309562	−	0.950879i	$-0.600182\pi$
$947$	−39.6308	−	22.8809i	−1.28783	−	0.743528i	−0.978267	+	0.207351i	$0.933516\pi$
$948$		0			0
$949$	−29.0634	+	16.7797i	−0.943437	+	0.544694i
$950$	7.25561	+	2.54285i	0.235403	+	0.0825008i
$951$		0			0
$952$	−8.37812	+	1.60165i	−0.271536	+	0.0519097i
$953$		−	42.0094i		−	1.36082i	−0.732832	−	0.680409i	$-0.761802\pi$
$953$		−	42.0094i		−	1.36082i	0.732832	−	0.680409i	$-0.238198\pi$
$954$		0			0
$955$	−0.215021	−	0.372427i	−0.00695791	−	0.0120515i
$956$	−34.0724	−	27.2266i	−1.10198	−	0.880570i
$957$		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
$962$	25.3374	−	21.7830i	0.816912	−	0.702312i
$963$		0			0
$964$	5.79670	−	38.2041i	0.186699	−	1.23047i
$965$	−8.98377			−0.289198
$966$		0			0
$967$			54.8008i			1.76227i	0.472860	+	0.881137i	$0.343222\pi$
$967$			54.8008i			1.76227i	−0.472860	+	0.881137i	$0.656778\pi$
$968$	30.4135	−	1.09316i	0.977527	−	0.0351354i
$969$		0			0
$970$	1.47939	−	1.27186i	0.0475004	−	0.0408368i
$971$	19.9522	+	11.5194i	0.640298	+	0.369676i	0.784729	−	0.619839i	$-0.212802\pi$
$971$	19.9522	+	11.5194i	0.640298	+	0.369676i	−0.144431	+	0.989515i	$0.546135\pi$
$972$		0			0
$973$	−36.8179	+	29.5644i	−1.18033	+	0.947792i
$974$	42.5472	−	8.02874i	1.36330	−	0.257258i
$975$		0			0
$976$	13.9361	−	44.8668i	0.446083	−	1.43615i
$977$	−5.56153	+	3.21095i	−0.177929	+	0.102727i	−0.586319	−	0.810080i	$-0.699424\pi$
$977$	−5.56153	+	3.21095i	−0.177929	+	0.102727i	0.408390	+	0.912807i	$0.366090\pi$
$978$		0			0
$979$	5.16421			0.165049
$980$	1.37311	+	8.76781i	0.0438623	+	0.280077i
$981$		0			0
$982$	10.9894	−	31.3567i	0.350687	−	1.00063i
$983$	−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	−0.287519	−	0.957775i	$-0.592830\pi$
$991$	12.5347	−	7.23693i	0.398179	−	0.229889i	0.685698	+	0.727886i	$0.259497\pi$
$992$	−14.0349	−	32.3848i	−0.445607	−	1.02822i
$993$		0			0
$994$	−19.3581	+	6.83620i	−0.614003	+	0.216831i
$995$		−	4.23988i		−	0.134413i
$996$		0			0
$997$	−13.8349	+	7.98761i	−0.438157	+	0.252970i	−0.702816	−	0.711372i	$-0.748074\pi$
$997$	−13.8349	+	7.98761i	−0.438157	+	0.252970i	0.264659	+	0.964342i	$0.414741\pi$
$998$	−25.8835	+	22.2525i	−0.819328	+	0.704389i
$999$		0			0

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-1.33462 - 0.467740i) q^{2} +(1.56244 + 1.24851i) q^{4} +(-0.316953 + 0.548978i) q^{5} +(2.06297 - 1.65655i) q^{7} +(-1.50129 - 2.39711i) q^{8} +O(q^{10})\)	\(q+(-1.33462 - 0.467740i) q^{2} +(1.56244 + 1.24851i) q^{4} +(-0.316953 + 0.548978i) q^{5} +(2.06297 - 1.65655i) q^{7} +(-1.50129 - 2.39711i) q^{8} +(0.679792 - 0.584428i) q^{10} +(-0.424494 + 0.245082i) q^{11} -3.13261i q^{13} +(-3.52812 + 1.24593i) q^{14} +(0.882427 + 3.90145i) q^{16} +(0.987137 - 0.569924i) q^{17} +(-0.591155 + 1.02391i) q^{19} +(-1.18063 + 0.462025i) q^{20} +(0.681175 - 0.128539i) q^{22} +(2.80489 - 4.85822i) q^{23} +(2.29908 + 3.98213i) q^{25} +(-1.46525 + 4.18085i) q^{26} +(5.29149 - 0.0126068i) q^{28} +4.05920 q^{29} +(5.40346 - 3.11969i) q^{31} +(0.647158 - 5.61971i) q^{32} +(-1.58403 + 0.298910i) q^{34} +(0.255545 + 1.65757i) q^{35} +(-6.53184 - 3.77116i) q^{37} +(1.26789 - 1.09003i) q^{38} +(1.79180 - 0.0644029i) q^{40} +4.06598i q^{41} +4.65556 q^{43} +(-0.969234 - 0.147062i) q^{44} +(-6.01586 + 5.17193i) q^{46} +(4.80492 - 8.32236i) q^{47} +(1.51170 - 6.83482i) q^{49} +(-1.20581 - 6.39001i) q^{50} +(3.91111 - 4.89451i) q^{52} +(1.10444 + 1.91294i) q^{53} -0.310718i q^{55} +(-7.06804 - 2.45822i) q^{56} +(-5.41750 - 1.89865i) q^{58} +(9.12119 - 5.26612i) q^{59} +(-10.1718 - 5.87267i) q^{61} +(-8.67078 + 1.63619i) q^{62} +(-3.49228 + 7.19750i) q^{64} +(1.71973 + 0.992889i) q^{65} +(3.11964 + 5.40338i) q^{67} +(2.25390 + 0.341983i) q^{68} +(0.434258 - 2.33177i) q^{70} +5.48681 q^{71} +(-5.35648 - 9.27769i) q^{73} +(6.95363 + 8.08829i) q^{74} +(-2.20201 + 0.861731i) q^{76} +(-0.469729 + 1.20879i) q^{77} +(2.49304 + 1.43936i) q^{79} +(-2.42150 - 0.752143i) q^{80} +(1.90182 - 5.42656i) q^{82} +14.1254i q^{83} +0.722556i q^{85} +(-6.21342 - 2.17759i) q^{86} +(1.22478 + 0.649622i) q^{88} +(-9.12417 - 5.26784i) q^{89} +(-5.18932 - 6.46248i) q^{91} +(10.4480 - 4.08872i) q^{92} +(-10.3055 + 8.85976i) q^{94} +(-0.374736 - 0.649062i) q^{95} +2.17624 q^{97} +(-5.21447 + 8.41483i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 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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