LMFDB - Embedded newform 504.2.ch.b.269.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(269,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 3, 3, 1]))

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

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

chi := DirichletCharacter("504.269");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.ch (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:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			269.2
Character	$\chi$	$=$	504.269
Dual form			504.2.ch.b.341.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40843 - 0.127777i) q^{2} +(1.96735 + 0.359931i) q^{4} +(1.87230 - 1.08097i) q^{5} +(2.55958 + 0.669737i) q^{7} +(-2.72488 - 0.758320i) q^{8} +O(q^{10})$	\(q+(-1.40843 - 0.127777i) q^{2} +(1.96735 + 0.359931i) q^{4} +(1.87230 - 1.08097i) q^{5} +(2.55958 + 0.669737i) q^{7} +(-2.72488 - 0.758320i) q^{8} +(-2.77512 + 1.28324i) q^{10} +(1.67157 - 2.89525i) q^{11} +1.74247 q^{13} +(-3.51941 - 1.27033i) q^{14} +(3.74090 + 1.41622i) q^{16} +(-0.283937 + 0.491793i) q^{17} +(-0.270105 - 0.467836i) q^{19} +(4.07254 - 1.45275i) q^{20} +(-2.72424 + 3.86416i) q^{22} +(-5.21616 + 3.01155i) q^{23} +(-0.162997 + 0.282319i) q^{25} +(-2.45414 - 0.222648i) q^{26} +(4.79452 + 2.23888i) q^{28} +1.77912 q^{29} +(-6.56726 - 3.79161i) q^{31} +(-5.08783 - 2.47264i) q^{32} +(0.462745 - 0.656375i) q^{34} +(5.51627 - 1.51289i) q^{35} +(9.60029 - 5.54273i) q^{37} +(0.320645 + 0.693428i) q^{38} +(-5.92151 + 1.52571i) q^{40} +7.77201 q^{41} +1.80152i q^{43} +(4.33065 - 5.09430i) q^{44} +(7.73140 - 3.57505i) q^{46} +(0.679499 + 1.17693i) q^{47} +(6.10291 + 3.42849i) q^{49} +(0.265644 - 0.376799i) q^{50} +(3.42804 + 0.627168i) q^{52} +(1.46832 - 2.54321i) q^{53} -7.22769i q^{55} +(-6.46667 - 3.76593i) q^{56} +(-2.50576 - 0.227331i) q^{58} +(9.84763 + 5.68553i) q^{59} +(-5.60858 - 9.71434i) q^{61} +(8.76504 + 6.17936i) q^{62} +(6.84990 + 4.13265i) q^{64} +(3.26242 - 1.88356i) q^{65} +(-10.7563 - 6.21014i) q^{67} +(-0.735613 + 0.865329i) q^{68} +(-7.96259 + 1.42594i) q^{70} +7.79753i q^{71} +(7.56066 + 4.36515i) q^{73} +(-14.2296 + 6.57984i) q^{74} +(-0.363002 - 1.01761i) q^{76} +(6.21757 - 6.29110i) q^{77} +(-4.77913 - 8.27770i) q^{79} +(8.53498 - 1.39223i) q^{80} +(-10.9463 - 0.993087i) q^{82} +15.9958i q^{83} +1.22771i q^{85} +(0.230194 - 2.53732i) q^{86} +(-6.75035 + 6.62160i) q^{88} +(-6.30930 - 10.9280i) q^{89} +(4.45999 + 1.16699i) q^{91} +(-11.3459 + 4.04731i) q^{92} +(-0.806641 - 1.74444i) q^{94} +(-1.01144 - 0.583953i) q^{95} +16.4013i q^{97} +(-8.15743 - 5.60860i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{4} - 20 q^{7}+O(q^{10}) $ 56 * q - 8 * q^4 - 20 * q^7	$ 56 q - 8 q^{4} - 20 q^{7} + 20 q^{16} - 16 q^{22} + 8 q^{25} + 36 q^{28} - 36 q^{31} + 60 q^{40} - 8 q^{46} - 28 q^{49} + 36 q^{52} - 44 q^{58} + 40 q^{64} - 60 q^{70} + 72 q^{73} - 12 q^{79} - 36 q^{82} + 4 q^{88} - 180 q^{94}+O(q^{100}) $ 56 * q - 8 * q^4 - 20 * q^7 + 20 * q^16 - 16 * q^22 + 8 * q^25 + 36 * q^28 - 36 * q^31 + 60 * q^40 - 8 * q^46 - 28 * q^49 + 36 * q^52 - 44 * q^58 + 40 * q^64 - 60 * q^70 + 72 * q^73 - 12 * q^79 - 36 * q^82 + 4 * q^88 - 180 * q^94

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.40843	−	0.127777i	−0.995910	−	0.0903523i
$2$	−1.40843	−	0.127777i	−0.995910	−	0.0903523i
$3$		0			0
$3$		0			0
$4$	1.96735	+	0.359931i	0.983673	+	0.179965i
$5$	1.87230	−	1.08097i	0.837318	−	0.483426i	−0.0190339	−	0.999819i	$-0.506059\pi$
$5$	1.87230	−	1.08097i	0.837318	−	0.483426i	0.856352	+	0.516393i	$0.172726\pi$
$6$		0			0
$7$	2.55958	+	0.669737i	0.967431	+	0.253137i
$7$	2.55958	+	0.669737i	0.967431	+	0.253137i
$8$	−2.72488	−	0.758320i	−0.963389	−	0.268107i
$9$		0			0
$10$	−2.77512	+	1.28324i	−0.877572	+	0.405795i
$11$	1.67157	−	2.89525i	0.503998	−	0.872949i	−0.495992	−	0.868327i	$-0.665195\pi$
$11$	1.67157	−	2.89525i	0.503998	−	0.872949i	0.999989	−	0.00462217i	$-0.00147129\pi$
$12$		0			0
$13$	1.74247			0.483274			0.241637	−	0.970367i	$-0.422316\pi$
$13$	1.74247			0.483274			0.241637	+	0.970367i	$0.422316\pi$
$14$	−3.51941	−	1.27033i	−0.940602	−	0.339511i
$15$		0			0
$16$	3.74090	+	1.41622i	0.935225	+	0.354054i
$17$	−0.283937	+	0.491793i	−0.0688648	+	0.119277i	−0.898402	−	0.439174i	$-0.855271\pi$
$17$	−0.283937	+	0.491793i	−0.0688648	+	0.119277i	0.829537	+	0.558452i	$0.188604\pi$
$18$		0			0
$19$	−0.270105	−	0.467836i	−0.0619664	−	0.107329i	0.833378	−	0.552704i	$-0.186404\pi$
$19$	−0.270105	−	0.467836i	−0.0619664	−	0.107329i	−0.895344	+	0.445375i	$0.853071\pi$
$20$	4.07254	−	1.45275i	0.910647	−	0.324844i
$21$		0			0
$22$	−2.72424	+	3.86416i	−0.580809	+	0.823842i
$23$	−5.21616	+	3.01155i	−1.08764	+	0.627952i	−0.932948	−	0.360010i	$-0.882773\pi$
$23$	−5.21616	+	3.01155i	−1.08764	+	0.627952i	−0.154696	+	0.987962i	$0.549440\pi$
$24$		0			0
$25$	−0.162997	+	0.282319i	−0.0325994	+	0.0564638i
$26$	−2.45414	−	0.222648i	−0.481297	−	0.0436649i
$27$		0			0
$28$	4.79452	+	2.23888i	0.906079	+	0.423108i
$29$	1.77912			0.330374			0.165187	−	0.986262i	$-0.447177\pi$
$29$	1.77912			0.330374			0.165187	+	0.986262i	$0.447177\pi$
$30$		0			0
$31$	−6.56726	−	3.79161i	−1.17952	−	0.680993i	−0.223613	−	0.974678i	$-0.571785\pi$
$31$	−6.56726	−	3.79161i	−1.17952	−	0.680993i	−0.955902	+	0.293685i	$0.905118\pi$
$32$	−5.08783	−	2.47264i	−0.899410	−	0.437106i
$33$		0			0
$34$	0.462745	−	0.656375i	0.0793601	−	0.112567i
$35$	5.51627	−	1.51289i	0.932419	−	0.255725i
$36$		0			0
$37$	9.60029	−	5.54273i	1.57828	−	0.911219i	0.583177	−	0.812345i	$-0.301809\pi$
$37$	9.60029	−	5.54273i	1.57828	−	0.911219i	0.995100	−	0.0988741i	$-0.0315241\pi$
$38$	0.320645	+	0.693428i	0.0520156	+	0.112489i
$39$		0			0
$40$	−5.92151	+	1.52571i	−0.936272	+	0.241237i
$41$	7.77201			1.21378			0.606892	−	0.794785i	$-0.292416\pi$
$41$	7.77201			1.21378			0.606892	+	0.794785i	$0.292416\pi$
$42$		0			0
$43$			1.80152i			0.274730i	0.990521	+	0.137365i	$0.0438633\pi$
$43$			1.80152i			0.274730i	−0.990521	+	0.137365i	$0.956137\pi$
$44$	4.33065	−	5.09430i	0.652870	−	0.767995i
$45$		0			0
$46$	7.73140	−	3.57505i	1.13993	−	0.527112i
$47$	0.679499	+	1.17693i	0.0991151	+	0.171672i	0.911319	−	0.411702i	$-0.135065\pi$
$47$	0.679499	+	1.17693i	0.0991151	+	0.171672i	−0.812204	+	0.583374i	$0.801732\pi$
$48$		0			0
$49$	6.10291	+	3.42849i	0.871844	+	0.489784i
$50$	0.265644	−	0.376799i	0.0375677	−	0.0532874i
$51$		0			0
$52$	3.42804	+	0.627168i	0.475383	+	0.0869726i
$53$	1.46832	−	2.54321i	0.201689	−	0.349336i	−0.747383	−	0.664393i	$-0.768690\pi$
$53$	1.46832	−	2.54321i	0.201689	−	0.349336i	0.949073	+	0.315057i	$0.102023\pi$
$54$		0			0
$55$		−	7.22769i		−	0.974581i
$56$	−6.46667	−	3.76593i	−0.864145	−	0.503244i
$57$		0			0
$58$	−2.50576	−	0.227331i	−0.329023	−	0.0298501i
$59$	9.84763	+	5.68553i	1.28205	+	0.740194i	0.977223	−	0.212213i	$-0.0680672\pi$
$59$	9.84763	+	5.68553i	1.28205	+	0.740194i	0.304830	+	0.952407i	$0.401401\pi$
$60$		0			0
$61$	−5.60858	−	9.71434i	−0.718105	−	1.24379i	−0.961750	−	0.273929i	$-0.911677\pi$
$61$	−5.60858	−	9.71434i	−0.718105	−	1.24379i	0.243645	−	0.969864i	$-0.421657\pi$
$62$	8.76504	+	6.17936i	1.11316	+	0.784780i
$63$		0			0
$64$	6.84990	+	4.13265i	0.856238	+	0.516582i
$65$	3.26242	−	1.88356i	0.404654	−	0.233627i
$66$		0			0
$67$	−10.7563	−	6.21014i	−1.31409	−	0.758689i	−0.331317	−	0.943519i	$-0.607493\pi$
$67$	−10.7563	−	6.21014i	−1.31409	−	0.758689i	−0.982770	+	0.184830i	$0.940826\pi$
$68$	−0.735613	+	0.865329i	−0.0892062	+	0.104937i
$69$		0			0
$70$	−7.96259	+	1.42594i	−0.951711	+	0.170433i
$71$			7.79753i			0.925397i	0.886516	+	0.462698i	$0.153119\pi$
$71$			7.79753i			0.925397i	−0.886516	+	0.462698i	$0.846881\pi$
$72$		0			0
$73$	7.56066	+	4.36515i	0.884909	+	0.510902i	0.872274	−	0.489018i	$-0.162645\pi$
$73$	7.56066	+	4.36515i	0.884909	+	0.510902i	0.0126348	+	0.999920i	$0.495978\pi$
$74$	−14.2296	+	6.57984i	−1.65415	+	0.764891i
$75$		0			0
$76$	−0.363002	−	1.01761i	−0.0416392	−	0.116728i
$77$	6.21757	−	6.29110i	0.708558	−	0.716938i
$78$		0			0
$79$	−4.77913	−	8.27770i	−0.537694	−	0.931314i	−0.999028	−	0.0440870i	$-0.985962\pi$
$79$	−4.77913	−	8.27770i	−0.537694	−	0.931314i	0.461333	−	0.887227i	$-0.347371\pi$
$80$	8.53498	−	1.39223i	0.954239	−	0.155656i
$81$		0			0
$82$	−10.9463	−	0.993087i	−1.20882	−	0.109668i
$83$			15.9958i			1.75577i	0.478875	+	0.877883i	$0.341045\pi$
$83$			15.9958i			1.75577i	−0.478875	+	0.877883i	$0.658955\pi$
$84$		0			0
$85$			1.22771i			0.133164i
$86$	0.230194	−	2.53732i	0.0248225	−	0.273606i
$87$		0			0
$88$	−6.75035	+	6.62160i	−0.719589	+	0.705865i
$89$	−6.30930	−	10.9280i	−0.668784	−	1.15837i	−0.978244	−	0.207456i	$-0.933482\pi$
$89$	−6.30930	−	10.9280i	−0.668784	−	1.15837i	0.309460	−	0.950912i	$-0.399852\pi$
$90$		0			0
$91$	4.45999	+	1.16699i	0.467534	+	0.122334i
$92$	−11.3459	+	4.04731i	−1.18290	+	0.421961i
$93$		0			0
$94$	−0.806641	−	1.74444i	−0.0831987	−	0.179925i
$95$	−1.01144	−	0.583953i	−0.103771	−	0.0599123i
$96$		0			0
$97$			16.4013i			1.66530i	0.553802	+	0.832649i	$0.313177\pi$
$97$			16.4013i			1.66530i	−0.553802	+	0.832649i	$0.686823\pi$
$98$	−8.15743	−	5.60860i	−0.824025	−	0.566554i
$99$		0			0
$100$	−0.422287	+	0.496752i	−0.0422287	+	0.0496752i
$101$	−13.4514	−	7.76615i	−1.33846	−	0.772761i	−0.351882	−	0.936044i	$-0.614458\pi$
$101$	−13.4514	−	7.76615i	−1.33846	−	0.772761i	−0.986579	+	0.163283i	$0.947792\pi$
$102$		0			0
$103$	−4.69281	+	2.70939i	−0.462396	+	0.266964i	−0.713051	−	0.701112i	$-0.752687\pi$
$103$	−4.69281	+	2.70939i	−0.462396	+	0.266964i	0.250655	+	0.968076i	$0.419354\pi$
$104$	−4.74801	−	1.32135i	−0.465581	−	0.129569i
$105$		0			0
$106$	−2.39299	+	3.39431i	−0.232428	+	0.329684i
$107$	−1.85983	−	3.22131i	−0.179796	−	0.311416i	0.762014	−	0.647560i	$-0.224210\pi$
$107$	−1.85983	−	3.22131i	−0.179796	−	0.311416i	−0.941811	+	0.336144i	$0.890877\pi$
$108$		0			0
$109$	−5.72483	−	3.30523i	−0.548340	−	0.316584i	0.200112	−	0.979773i	$-0.435869\pi$
$109$	−5.72483	−	3.30523i	−0.548340	−	0.316584i	−0.748452	+	0.663189i	$0.769203\pi$
$110$	−0.923536	+	10.1797i	−0.0880557	+	0.970595i
$111$		0			0
$112$	8.62664	+	6.13034i	0.815141	+	0.579263i
$113$			4.32161i			0.406543i	0.979122	+	0.203272i	$0.0651575\pi$
$113$			4.32161i			0.406543i	−0.979122	+	0.203272i	$0.934843\pi$
$114$		0			0
$115$	−6.51081	+	11.2771i	−0.607136	+	1.05159i
$116$	3.50014	+	0.640360i	0.324980	+	0.0594560i
$117$		0			0
$118$	−13.1432	−	9.26598i	−1.20993	−	0.853002i
$119$	−1.05613	+	1.06862i	−0.0968154	+	0.0979603i
$120$		0			0
$121$	−0.0882982	−	0.152937i	−0.00802711	−	0.0139034i
$122$	6.65801	+	14.3986i	0.602788	+	1.30359i
$123$		0			0
$124$	−11.5554	−	9.82317i	−1.03770	−	0.882147i
$125$			11.5145i			1.02989i
$126$		0			0
$127$	6.96976			0.618467			0.309233	−	0.950986i	$-0.399928\pi$
$127$	6.96976			0.618467			0.309233	+	0.950986i	$0.399928\pi$
$128$	−9.11954	−	6.69582i	−0.806061	−	0.591832i
$129$		0			0
$130$	−4.83557	+	2.23600i	−0.424107	+	0.196110i
$131$	−7.62582	+	4.40277i	−0.666271	+	0.384672i	−0.794662	−	0.607052i	$-0.792352\pi$
$131$	−7.62582	+	4.40277i	−0.666271	+	0.384672i	0.128391	+	0.991724i	$0.459019\pi$
$132$		0			0
$133$	−0.378029	−	1.37836i	−0.0327793	−	0.119519i
$134$	14.3559	+	10.1209i	1.24016	+	0.874317i
$135$		0			0
$136$	1.14663	−	1.12476i	0.0983226	−	0.0964474i
$137$	14.5256	+	8.38635i	1.24100	+	0.716494i	0.969299	−	0.245887i	$-0.0790791\pi$
$137$	14.5256	+	8.38635i	1.24100	+	0.716494i	0.271705	+	0.962381i	$0.412412\pi$
$138$		0			0
$139$	−10.3308			−0.876249			−0.438124	−	0.898914i	$-0.644357\pi$
$139$	−10.3308			−0.876249			−0.438124	+	0.898914i	$0.644357\pi$
$140$	11.3969	−	0.990899i	0.963217	−	0.0837463i
$141$		0			0
$142$	0.996349	−	10.9823i	0.0836117	−	0.921612i
$143$	2.91266	−	5.04487i	0.243569	−	0.421873i
$144$		0			0
$145$	3.33105	−	1.92318i	0.276628	−	0.159711i
$146$	−10.0909	−	7.11409i	−0.835128	−	0.588766i
$147$		0			0
$148$	20.8821	−	7.44902i	1.71650	−	0.612306i
$149$	−2.10661	−	3.64876i	−0.172580	−	0.298918i	0.766741	−	0.641957i	$-0.221877\pi$
$149$	−2.10661	−	3.64876i	−0.172580	−	0.298918i	−0.939321	+	0.343039i	$0.888544\pi$
$150$		0			0
$151$	−3.10493	+	5.37790i	−0.252676	+	0.437647i	−0.964262	−	0.264952i	$-0.914644\pi$
$151$	−3.10493	+	5.37790i	−0.252676	+	0.437647i	0.711586	+	0.702599i	$0.247977\pi$
$152$	0.381234	+	1.47962i	0.0309222	+	0.120013i
$153$		0			0
$154$	−9.56087	+	8.06611i	−0.770437	+	0.649985i
$155$	−16.3945			−1.31684
$156$		0			0
$157$	−10.3210	+	17.8764i	−0.823702	+	1.42669i	0.0792057	+	0.996858i	$0.474762\pi$
$157$	−10.3210	+	17.8764i	−0.823702	+	1.42669i	−0.902907	+	0.429835i	$0.858572\pi$
$158$	5.67337	+	12.2692i	0.451349	+	0.976087i
$159$		0			0
$160$	−12.1988	+	0.870275i	−0.964400	+	0.0688013i
$161$	−15.3681	+	4.21486i	−1.21118	+	0.332177i
$162$		0			0
$163$	3.56609	−	2.05888i	0.279317	−	0.161264i	−0.353797	−	0.935322i	$-0.615110\pi$
$163$	3.56609	−	2.05888i	0.279317	−	0.161264i	0.633114	+	0.774058i	$0.281776\pi$
$164$	15.2902	+	2.79739i	1.19397	+	0.218439i
$165$		0			0
$166$	2.04390	−	22.5289i	0.158637	−	1.74858i
$167$	−13.2654			−1.02651			−0.513253	−	0.858237i	$-0.671560\pi$
$167$	−13.2654			−1.02651			−0.513253	+	0.858237i	$0.671560\pi$
$168$		0			0
$169$	−9.96381			−0.766447
$170$	0.156874	−	1.72914i	0.0120317	−	0.132619i
$171$		0			0
$172$	−0.648424	+	3.54422i	−0.0494419	+	0.270244i
$173$	−19.4886	+	11.2517i	−1.48169	+	0.855453i	−0.999784	−	0.0207720i	$-0.993388\pi$
$173$	−19.4886	+	11.2517i	−1.48169	+	0.855453i	−0.481903	+	0.876225i	$0.660054\pi$
$174$		0			0
$175$	−0.606283	+	0.613453i	−0.0458307	+	0.0463727i
$176$	10.3535	−	8.46352i	0.780423	−	0.637961i
$177$		0			0
$178$	7.48985	+	16.1975i	0.561388	+	1.21406i
$179$	9.63774	−	16.6931i	0.720358	−	1.24770i	−0.240498	−	0.970650i	$-0.577311\pi$
$179$	9.63774	−	16.6931i	0.720358	−	1.24770i	0.960856	−	0.277048i	$-0.0893560\pi$
$180$		0			0
$181$	22.3500			1.66126			0.830631	−	0.556823i	$-0.187980\pi$
$181$	22.3500			1.66126			0.830631	+	0.556823i	$0.187980\pi$
$182$	−6.13246	−	2.21352i	−0.454568	−	0.164077i
$183$		0			0
$184$	16.4971	−	4.25059i	1.21618	−	0.313358i
$185$	11.9831	−	20.7553i	0.881013	−	1.52596i
$186$		0			0
$187$	0.949241	+	1.64413i	0.0694154	+	0.120231i
$188$	0.913197	+	2.55999i	0.0666017	+	0.186707i
$189$		0			0
$190$	1.34992	+	0.951695i	0.0979335	+	0.0690432i
$191$	−5.69175	+	3.28613i	−0.411841	+	0.237776i	−0.691580	−	0.722300i	$-0.743085\pi$
$191$	−5.69175	+	3.28613i	−0.411841	+	0.237776i	0.279740	+	0.960076i	$0.409752\pi$
$192$		0			0
$193$	3.70334	−	6.41438i	0.266572	−	0.461717i	−0.701402	−	0.712766i	$-0.747442\pi$
$193$	3.70334	−	6.41438i	0.266572	−	0.461717i	0.967974	+	0.251049i	$0.0807755\pi$
$194$	2.09571	−	23.1000i	0.150463	−	1.65849i
$195$		0			0
$196$	10.7725	+	8.94165i	0.769465	+	0.638689i
$197$	1.80322			0.128474			0.0642371	−	0.997935i	$-0.479539\pi$
$197$	1.80322			0.128474			0.0642371	+	0.997935i	$0.479539\pi$
$198$		0			0
$199$	−7.72728	−	4.46135i	−0.547772	−	0.316257i	0.200451	−	0.979704i	$-0.435759\pi$
$199$	−7.72728	−	4.46135i	−0.547772	−	0.316257i	−0.748223	+	0.663447i	$0.769093\pi$
$200$	0.658235	−	0.645681i	0.0465442	−	0.0456565i
$201$		0			0
$202$	17.9530	+	12.6569i	1.26317	+	0.890534i
$203$	4.55380	+	1.19154i	0.319614	+	0.0836299i
$204$		0			0
$205$	14.5515	−	8.40132i	1.01632	−	0.586774i
$206$	6.95568	−	3.21635i	0.484625	−	0.224094i
$207$		0			0
$208$	6.51840	+	2.46771i	0.451969	+	0.171105i
$209$	−1.80600			−0.124924
$210$		0			0
$211$			11.3878i			0.783969i	0.919972	+	0.391985i	$0.128211\pi$
$211$			11.3878i			0.783969i	−0.919972	+	0.391985i	$0.871789\pi$
$212$	3.80408	−	4.47487i	0.261265	−	0.307336i
$213$		0			0
$214$	2.20782	+	4.77464i	0.150924	+	0.326387i
$215$	1.94740	+	3.37299i	0.132811	+	0.230036i
$216$		0			0
$217$	−14.2701	−	14.1033i	−0.968715	−	0.957393i
$218$	7.64069	+	5.38669i	0.517493	+	0.364833i
$219$		0			0
$220$	2.60147	−	14.2194i	0.175391	−	0.958669i
$221$	−0.494751	+	0.856933i	−0.0332805	+	0.0576436i
$222$		0			0
$223$		−	4.90035i		−	0.328151i	−0.986448	−	0.164076i	$-0.947536\pi$
$223$		−	4.90035i		−	0.328151i	0.986448	−	0.164076i	$-0.0524641\pi$
$224$	−11.3667	−	9.73644i	−0.759469	−	0.650543i
$225$		0			0
$226$	0.552205	−	6.08669i	0.0367321	−	0.404880i
$227$	−18.4585	−	10.6570i	−1.22514	−	0.707332i	−0.259127	−	0.965843i	$-0.583435\pi$
$227$	−18.4585	−	10.6570i	−1.22514	−	0.707332i	−0.966008	+	0.258511i	$0.916768\pi$
$228$		0			0
$229$	1.59915	+	2.76981i	0.105675	+	0.183034i	0.914014	−	0.405683i	$-0.132966\pi$
$229$	1.59915	+	2.76981i	0.105675	+	0.183034i	−0.808339	+	0.588717i	$0.799633\pi$
$230$	10.6110	−	15.0510i	0.699667	−	0.992433i
$231$		0			0
$232$	−4.84788	−	1.34914i	−0.318279	−	0.0885755i
$233$	3.35808	−	1.93879i	0.219995	−	0.127014i	−0.385953	−	0.922518i	$-0.626127\pi$
$233$	3.35808	−	1.93879i	0.219995	−	0.127014i	0.605948	+	0.795504i	$0.292794\pi$
$234$		0			0
$235$	2.54445	+	1.46904i	0.165982	+	0.0958295i
$236$	17.3273	+	14.7299i	1.12791	+	0.958834i
$237$		0			0
$238$	1.62403	−	1.37013i	0.105270	−	0.0888121i
$239$		−	22.1432i		−	1.43233i	−0.697933	−	0.716163i	$-0.745897\pi$
$239$		−	22.1432i		−	1.43233i	0.697933	−	0.716163i	$-0.254103\pi$
$240$		0			0
$241$	6.23397	+	3.59918i	0.401565	+	0.231844i	0.687159	−	0.726507i	$-0.258858\pi$
$241$	6.23397	+	3.59918i	0.401565	+	0.231844i	−0.285594	+	0.958351i	$0.592191\pi$
$242$	0.104820	+	0.226684i	0.00673808	+	0.0145718i
$243$		0			0
$244$	−7.53752	−	21.1302i	−0.482540	−	1.35272i
$245$	15.1326	−	0.177912i	0.966784	−	0.0113664i
$246$		0			0
$247$	−0.470650	−	0.815190i	−0.0299467	−	0.0518693i
$248$	15.0197	+	15.3118i	0.953754	+	0.972298i
$249$		0			0
$250$	1.47129	−	16.2174i	0.0930528	−	1.02568i
$251$			9.58773i			0.605172i	0.953122	+	0.302586i	$0.0978500\pi$
$251$			9.58773i			0.605172i	−0.953122	+	0.302586i	$0.902150\pi$
$252$		0			0
$253$			20.1361i			1.26595i
$254$	−9.81642	−	0.890579i	−0.615937	−	0.0558799i
$255$		0			0
$256$	11.9887	+	10.5959i	0.749291	+	0.662241i
$257$	4.33124	+	7.50192i	0.270175	+	0.467957i	0.968907	−	0.247427i	$-0.0795851\pi$
$257$	4.33124	+	7.50192i	0.270175	+	0.467957i	−0.698731	+	0.715384i	$0.746252\pi$
$258$		0			0
$259$	28.2849	−	7.75739i	1.75754	−	0.482021i
$260$	7.09626	−	2.53137i	0.440092	−	0.156989i
$261$		0			0
$262$	11.3030	−	5.22658i	0.698302	−	0.322899i
$263$	5.39801	+	3.11654i	0.332855	+	0.192174i	0.657108	−	0.753796i	$-0.271780\pi$
$263$	5.39801	+	3.11654i	0.332855	+	0.192174i	−0.324253	+	0.945970i	$0.605113\pi$
$264$		0			0
$265$		−	6.34886i		−	0.390007i
$266$	0.356304	+	1.98963i	0.0218464	+	0.121992i
$267$		0			0
$268$	−18.9261	−	16.0890i	−1.15609	−	0.982792i
$269$	−9.46950	−	5.46722i	−0.577366	−	0.333342i	0.182720	−	0.983165i	$-0.441510\pi$
$269$	−9.46950	−	5.46722i	−0.577366	−	0.333342i	−0.760086	+	0.649823i	$0.774843\pi$
$270$		0			0
$271$	−18.1322	+	10.4687i	−1.10145	+	0.635925i	−0.936603	−	0.350393i	$-0.886048\pi$
$271$	−18.1322	+	10.4687i	−1.10145	+	0.635925i	−0.164852	+	0.986318i	$0.552715\pi$
$272$	−1.75866	+	1.43763i	−0.106635	+	0.0871692i
$273$		0			0
$274$	−19.3867	−	13.6676i	−1.17119	−	0.825691i
$275$	0.544922	+	0.943833i	0.0328600	+	0.0569152i
$276$		0			0
$277$	−3.80313	−	2.19574i	−0.228508	−	0.131929i	0.381376	−	0.924420i	$-0.375450\pi$
$277$	−3.80313	−	2.19574i	−0.228508	−	0.131929i	−0.609884	+	0.792491i	$0.708784\pi$
$278$	14.5502	+	1.32005i	0.872665	+	0.0791711i
$279$		0			0
$280$	−16.1784	−	0.0606607i	−0.966844	−	0.00362517i
$281$		−	7.93386i		−	0.473295i	−0.971596	−	0.236647i	$-0.923951\pi$
$281$		−	7.93386i		−	0.473295i	0.971596	−	0.236647i	$-0.0760486\pi$
$282$		0			0
$283$	−15.1600	+	26.2580i	−0.901171	+	1.56087i	−0.0751951	+	0.997169i	$0.523958\pi$
$283$	−15.1600	+	26.2580i	−0.901171	+	1.56087i	−0.825976	+	0.563705i	$0.809375\pi$
$284$	−2.80657	+	15.3404i	−0.166540	+	0.910288i
$285$		0			0
$286$	−4.74689	+	6.73317i	−0.280690	+	0.398141i
$287$	19.8931	+	5.20520i	1.17425	+	0.307253i
$288$		0			0
$289$	8.33876	+	14.4432i	0.490515	+	0.849597i
$290$	−4.93728	+	2.28303i	−0.289927	+	0.134064i
$291$		0			0
$292$	13.3033	+	11.3091i	0.778516	+	0.661814i
$293$		−	4.34894i		−	0.254068i	−0.991898	−	0.127034i	$-0.959454\pi$
$293$		−	4.34894i		−	0.254068i	0.991898	−	0.127034i	$-0.0405457\pi$
$294$		0			0
$295$	24.5836			1.43131
$296$	−30.3628	+	7.82316i	−1.76480	+	0.454712i
$297$		0			0
$298$	2.50078	+	5.40819i	0.144867	+	0.313288i
$299$	−9.08899	+	5.24753i	−0.525630	+	0.303473i
$300$		0			0
$301$	−1.20655	+	4.61115i	−0.0695442	+	0.265782i
$302$	5.06025	−	7.17764i	0.291184	−	0.413027i
$303$		0			0
$304$	−0.347879	−	2.13266i	−0.0199522	−	0.122316i
$305$	−21.0019	−	12.1254i	−1.20256	−	0.694300i
$306$		0			0
$307$	4.81287			0.274685			0.137343	−	0.990524i	$-0.456144\pi$
$307$	4.81287			0.274685			0.137343	+	0.990524i	$0.456144\pi$
$308$	14.4965	−	10.1389i	0.826014	−	0.577716i
$309$		0			0
$310$	23.0905	+	2.09485i	1.31145	+	0.118979i
$311$	3.96879	−	6.87414i	0.225049	−	0.389797i	−0.731285	−	0.682072i	$-0.761079\pi$
$311$	3.96879	−	6.87414i	0.225049	−	0.389797i	0.956334	+	0.292275i	$0.0944123\pi$
$312$		0			0
$313$	1.95587	−	1.12922i	0.110552	−	0.0638273i	−0.443704	−	0.896173i	$-0.646336\pi$
$313$	1.95587	−	1.12922i	0.110552	−	0.0638273i	0.554257	+	0.832346i	$0.313003\pi$
$314$	16.8205	−	23.8589i	0.949238	−	1.34643i
$315$		0			0
$316$	−6.42280	−	18.0053i	−0.361311	−	1.01287i
$317$	−3.72820	−	6.45744i	−0.209397	−	0.362686i	0.742128	−	0.670258i	$-0.233817\pi$
$317$	−3.72820	−	6.45744i	−0.209397	−	0.362686i	−0.951525	+	0.307572i	$0.900483\pi$
$318$		0			0
$319$	2.97393	−	5.15099i	0.166508	−	0.288400i
$320$	17.2924	+	0.333011i	0.966672	+	0.0186159i
$321$		0			0
$322$	22.1835	−	3.97262i	1.23624	−	0.221386i
$323$	0.306771			0.0170692
$324$		0			0
$325$	−0.284017	+	0.491932i	−0.0157544	+	0.0272875i
$326$	−5.28566	+	2.44412i	−0.292745	+	0.135367i
$327$		0			0
$328$	−21.1778	−	5.89366i	−1.16935	−	0.325423i
$329$	0.951001	+	3.46752i	0.0524304	+	0.191171i
$330$		0			0
$331$	19.5260	−	11.2733i	1.07325	−	0.619639i	0.144180	−	0.989551i	$-0.453946\pi$
$331$	19.5260	−	11.2733i	1.07325	−	0.619639i	0.929067	+	0.369912i	$0.120612\pi$
$332$	−5.75738	+	31.4692i	−0.315977	+	1.72710i
$333$		0			0
$334$	18.6834	+	1.69502i	1.02231	+	0.0927472i
$335$	−26.8519			−1.46708
$336$		0			0
$337$	−25.9907			−1.41580			−0.707901	−	0.706312i	$-0.750358\pi$
$337$	−25.9907			−1.41580			−0.707901	+	0.706312i	$0.750358\pi$
$338$	14.0333	+	1.27315i	0.763312	+	0.0692502i
$339$		0			0
$340$	−0.441891	+	2.41533i	−0.0239649	+	0.130990i
$341$	−21.9553	+	12.6759i	−1.18895	+	0.686438i
$342$		0			0
$343$	13.3247	+	12.8628i	0.719466	+	0.694528i
$344$	1.36613	−	4.90893i	0.0736568	−	0.264672i
$345$		0			0
$346$	28.8860	−	13.3571i	1.55292	−	0.718080i
$347$	7.86526	−	13.6230i	0.422229	−	0.731322i	−0.573928	−	0.818906i	$-0.694581\pi$
$347$	7.86526	−	13.6230i	0.422229	−	0.731322i	0.996157	+	0.0875835i	$0.0279144\pi$
$348$		0			0
$349$	−1.79135			−0.0958889			−0.0479444	−	0.998850i	$-0.515267\pi$
$349$	−1.79135			−0.0958889			−0.0479444	+	0.998850i	$0.515267\pi$
$350$	0.932293	−	0.786536i	0.0498331	−	0.0420421i
$351$		0			0
$352$	−15.6636	+	10.5973i	−0.834872	+	0.564839i
$353$	−13.0108	+	22.5353i	−0.692493	+	1.19943i	0.278526	+	0.960429i	$0.410154\pi$
$353$	−13.0108	+	22.5353i	−0.692493	+	1.19943i	−0.971019	+	0.239004i	$0.923179\pi$
$354$		0			0
$355$	8.42892	+	14.5993i	0.447361	+	0.774851i
$356$	−8.47924	−	23.7701i	−0.449399	−	1.25981i
$357$		0			0
$358$	−15.7071	+	22.2795i	−0.830144	+	1.17751i
$359$	14.8932	−	8.59857i	0.786031	−	0.453815i	−0.0525323	−	0.998619i	$-0.516729\pi$
$359$	14.8932	−	8.59857i	0.786031	−	0.453815i	0.838563	+	0.544804i	$0.183396\pi$
$360$		0			0
$361$	9.35409	−	16.2018i	0.492320	−	0.852724i
$362$	−31.4784	−	2.85582i	−1.65447	−	0.150099i
$363$		0			0
$364$	8.35430	+	3.90117i	0.437884	+	0.204477i
$365$	18.8744			0.987933
$366$		0			0
$367$	11.5047	+	6.64226i	0.600542	+	0.346723i	0.769255	−	0.638942i	$-0.220628\pi$
$367$	11.5047	+	6.64226i	0.600542	+	0.346723i	−0.168713	+	0.985665i	$0.553961\pi$
$368$	−23.7781	+	3.87870i	−1.23952	+	0.202191i
$369$		0			0
$370$	−19.5294	+	27.7012i	−1.01528	+	1.44012i
$371$	5.46157	−	5.52616i	0.283550	−	0.286904i
$372$		0			0
$373$	−32.2609	+	18.6259i	−1.67041	+	0.964410i	−0.702999	+	0.711191i	$0.748156\pi$
$373$	−32.2609	+	18.6259i	−1.67041	+	0.964410i	−0.967409	+	0.253219i	$0.918511\pi$
$374$	−1.12686	−	2.43694i	−0.0582683	−	0.126011i
$375$		0			0
$376$	−0.959064	−	3.72226i	−0.0494599	−	0.191961i
$377$	3.10006			0.159661
$378$		0			0
$379$		−	33.4030i		−	1.71580i	−0.513821	−	0.857898i	$-0.671770\pi$
$379$		−	33.4030i		−	1.71580i	0.513821	−	0.857898i	$-0.328230\pi$
$380$	−1.77966	−	1.51288i	−0.0912947	−	0.0776093i
$381$		0			0
$382$	8.43632	−	3.90101i	0.431640	−	0.199593i
$383$	10.1288	+	17.5435i	0.517556	+	0.896433i	0.999792	+	0.0203917i	$0.00649134\pi$
$383$	10.1288	+	17.5435i	0.517556	+	0.896433i	−0.482236	+	0.876041i	$0.660175\pi$
$384$		0			0
$385$	4.84065	−	18.4999i	0.246702	−	0.942840i
$386$	−6.03551	+	8.56099i	−0.307199	+	0.435743i
$387$		0			0
$388$	−5.90333	+	32.2670i	−0.299696	+	1.63811i
$389$	9.87868	−	17.1104i	0.500869	−	0.867530i	−0.499131	−	0.866527i	$-0.666347\pi$
$389$	9.87868	−	17.1104i	0.500869	−	0.867530i	0.999999	−	0.00100341i	$-0.000319396\pi$
$390$		0			0
$391$		−	3.42036i		−	0.172975i
$392$	−14.0298	−	13.9702i	−0.708610	−	0.705600i
$393$		0			0
$394$	−2.53971	−	0.230411i	−0.127949	−	0.0116079i
$395$	−17.8959	−	10.3322i	−0.900442	−	0.519870i
$396$		0			0
$397$	−6.15364	−	10.6584i	−0.308842	−	0.534930i	0.669267	−	0.743022i	$-0.266608\pi$
$397$	−6.15364	−	10.6584i	−0.308842	−	0.534930i	−0.978109	+	0.208092i	$0.933275\pi$
$398$	10.3133	+	7.27087i	0.516957	+	0.364456i
$399$		0			0
$400$	−1.00958	+	0.825288i	−0.0504790	+	0.0412644i
$401$	−29.5658	+	17.0698i	−1.47645	+	0.852427i	−0.999647	−	0.0265843i	$-0.991537\pi$
$401$	−29.5658	+	17.0698i	−1.47645	+	0.852427i	−0.476801	+	0.879011i	$0.658204\pi$
$402$		0			0
$403$	−11.4432	−	6.60676i	−0.570029	−	0.329106i
$404$	−23.6682	−	20.1203i	−1.17754	−	1.00102i
$405$		0			0
$406$	−6.26145	−	2.26008i	−0.310751	−	0.112166i
$407$		−	37.0603i		−	1.83701i
$408$		0			0
$409$	−23.4733	−	13.5523i	−1.16068	−	0.670119i	−0.209213	−	0.977870i	$-0.567090\pi$
$409$	−23.4733	−	13.5523i	−1.16068	−	0.670119i	−0.951467	+	0.307752i	$0.900423\pi$
$410$	−21.5683	+	9.97331i	−1.06518	+	0.492547i
$411$		0			0
$412$	−10.2076	+	3.64123i	−0.502891	+	0.179390i
$413$	21.3980	+	21.1479i	1.05293	+	1.04062i
$414$		0			0
$415$	17.2910	+	29.9489i	0.848782	+	1.47013i
$416$	−8.86538	−	4.30850i	−0.434661	−	0.211242i
$417$		0			0
$418$	2.54362	+	0.230766i	0.124413	+	0.0112871i
$419$			6.84933i			0.334612i	0.985905	+	0.167306i	$0.0535067\pi$
$419$			6.84933i			0.334612i	−0.985905	+	0.167306i	$0.946493\pi$
$420$		0			0
$421$			10.8560i			0.529089i	0.964374	+	0.264544i	$0.0852215\pi$
$421$			10.8560i			0.529089i	−0.964374	+	0.264544i	$0.914778\pi$
$422$	1.45511	−	16.0389i	0.0708334	−	0.780763i
$423$		0			0
$424$	−5.92956	+	5.81647i	−0.287965	+	0.282473i
$425$	−0.0925617	−	0.160322i	−0.00448990	−	0.00777674i
$426$		0			0
$427$	−7.84955	−	28.6209i	−0.379866	−	1.38506i
$428$	−2.49947	−	7.00685i	−0.120816	−	0.338689i
$429$		0			0
$430$	−2.31178	−	4.99945i	−0.111484	−	0.241095i
$431$	19.5579	+	11.2917i	0.942069	+	0.543904i	0.890608	−	0.454771i	$-0.150279\pi$
$431$	19.5579	+	11.2917i	0.942069	+	0.543904i	0.0514606	+	0.998675i	$0.483612\pi$
$432$		0			0
$433$			33.9522i			1.63164i	0.578307	+	0.815819i	$0.303713\pi$
$433$			33.9522i			1.63164i	−0.578307	+	0.815819i	$0.696287\pi$
$434$	18.2963	+	21.6869i	0.878250	+	1.04100i
$435$		0			0
$436$	−10.0731	−	8.56308i	−0.482413	−	0.410097i
$437$	2.81783	+	1.62687i	0.134795	+	0.0778239i
$438$		0			0
$439$	−21.4344	+	12.3752i	−1.02301	+	0.590634i	−0.914974	−	0.403513i	$-0.867789\pi$
$439$	−21.4344	+	12.3752i	−1.02301	+	0.590634i	−0.108034	+	0.994147i	$0.534456\pi$
$440$	−5.48090	+	19.6946i	−0.261292	+	0.938901i
$441$		0			0
$442$	0.806318	−	1.14371i	0.0383526	−	0.0544008i
$443$	9.24079	+	16.0055i	0.439043	+	0.760445i	0.997616	−	0.0690105i	$-0.0219842\pi$
$443$	9.24079	+	16.0055i	0.439043	+	0.760445i	−0.558573	+	0.829455i	$0.688651\pi$
$444$		0			0
$445$	−23.6258	−	13.6404i	−1.11997	−	0.646615i
$446$	−0.626154	+	6.90179i	−0.0296492	+	0.326809i
$447$		0			0
$448$	14.7651	+	15.1655i	0.697585	+	0.716502i
$449$			30.4888i			1.43886i	0.694567	+	0.719428i	$0.255596\pi$
$449$			30.4888i			1.43886i	−0.694567	+	0.719428i	$0.744404\pi$
$450$		0			0
$451$	12.9915	−	22.5019i	0.611744	−	1.05957i
$452$	−1.55548	+	8.50211i	−0.0731638	+	0.399906i
$453$		0			0
$454$	24.6358	+	17.3683i	1.15622	+	0.815133i
$455$	9.61192	−	2.63616i	0.450614	−	0.123585i
$456$		0			0
$457$	−13.2873	−	23.0142i	−0.621553	−	1.07656i	−0.989197	−	0.146594i	$-0.953169\pi$
$457$	−13.2873	−	23.0142i	−0.621553	−	1.07656i	0.367644	−	0.929967i	$-0.380165\pi$
$458$	−1.89837	−	4.10542i	−0.0887050	−	0.191833i
$459$		0			0
$460$	−16.8680	+	19.8424i	−0.786473	+	0.925158i
$461$		−	1.26742i		−	0.0590294i	−0.999564	−	0.0295147i	$-0.990604\pi$
$461$		−	1.26742i		−	0.0590294i	0.999564	−	0.0295147i	$-0.00939619\pi$
$462$		0			0
$463$	9.82295			0.456511			0.228256	−	0.973601i	$-0.426698\pi$
$463$	9.82295			0.456511			0.228256	+	0.973601i	$0.426698\pi$
$464$	6.65551	+	2.51962i	0.308974	+	0.116970i
$465$		0			0
$466$	−4.97735	+	2.30156i	−0.230571	+	0.106618i
$467$	18.5816	−	10.7281i	0.859855	−	0.496438i	−0.00410868	−	0.999992i	$-0.501308\pi$
$467$	18.5816	−	10.7281i	0.859855	−	0.496438i	0.863964	+	0.503554i	$0.167975\pi$
$468$		0			0
$469$	−23.3724	−	23.0992i	−1.07924	−	1.06662i
$470$	−3.39597	−	2.39416i	−0.156644	−	0.110434i
$471$		0			0
$472$	−22.5221	−	22.9600i	−1.03667	−	1.05682i
$473$	5.21585	+	3.01137i	0.239825	+	0.138463i
$474$		0			0
$475$	0.176105			0.00808027
$476$	−2.46240	+	1.72221i	−0.112864	+	0.0789375i
$477$		0			0
$478$	−2.82940	+	31.1872i	−0.129414	+	1.42647i
$479$	−13.5560	+	23.4798i	−0.619391	+	1.07282i	0.370206	+	0.928950i	$0.379287\pi$
$479$	−13.5560	+	23.4798i	−0.619391	+	1.07282i	−0.989597	+	0.143867i	$0.954046\pi$
$480$		0			0
$481$	16.7282	−	9.65803i	0.762740	−	0.440368i
$482$	−8.32021	−	5.86575i	−0.378975	−	0.267178i
$483$		0			0
$484$	−0.118666	−	0.332661i	−0.00539393	−	0.0151210i
$485$	17.7293	+	30.7081i	0.805047	+	1.39438i
$486$		0			0
$487$	4.06126	−	7.03430i	0.184033	−	0.318755i	−0.759217	−	0.650837i	$-0.774418\pi$
$487$	4.06126	−	7.03430i	0.184033	−	0.318755i	0.943250	+	0.332083i	$0.107751\pi$
$488$	7.91610	+	30.7235i	0.358345	+	1.39079i
$489$		0			0
$490$	−21.3359	−	1.68302i	−0.963857	−	0.0760313i
$491$	−6.11572			−0.275998			−0.137999	−	0.990432i	$-0.544067\pi$
$491$	−6.11572			−0.275998			−0.137999	+	0.990432i	$0.544067\pi$
$492$		0			0
$493$	−0.505158	+	0.874959i	−0.0227512	+	0.0394062i
$494$	0.558714	+	1.20828i	0.0251377	+	0.0543629i
$495$		0			0
$496$	−19.1977	−	23.4847i	−0.862003	−	1.05449i
$497$	−5.22229	+	19.9584i	−0.234252	+	0.895257i
$498$		0			0
$499$	−16.4251	+	9.48302i	−0.735287	+	0.424518i	−0.820353	−	0.571857i	$-0.806223\pi$
$499$	−16.4251	+	9.48302i	−0.735287	+	0.424518i	0.0850663	+	0.996375i	$0.472890\pi$
$500$	−4.14443	+	22.6530i	−0.185344	+	1.01307i
$501$		0			0
$502$	1.22510	−	13.5036i	0.0546787	−	0.602697i
$503$	24.6249			1.09797			0.548985	−	0.835832i	$-0.315015\pi$
$503$	24.6249			1.09797			0.548985	+	0.835832i	$0.315015\pi$
$504$		0			0
$505$	−33.5800			−1.49429
$506$	2.57294	−	28.3603i	0.114381	−	1.26077i
$507$		0			0
$508$	13.7119	+	2.50863i	0.608369	+	0.111303i
$509$	7.66857	−	4.42745i	0.339904	−	0.196243i	−0.320326	−	0.947307i	$-0.603792\pi$
$509$	7.66857	−	4.42745i	0.339904	−	0.196243i	0.660229	+	0.751064i	$0.270459\pi$
$510$		0			0
$511$	16.4286	+	16.2366i	0.726759	+	0.718265i
$512$	−15.5313	−	16.4554i	−0.686391	−	0.727232i
$513$		0			0
$514$	−5.14166	−	11.1194i	−0.226789	−	0.490454i
$515$	−5.85756	+	10.1456i	−0.258115	+	0.447068i
$516$		0			0
$517$	4.54332			0.199815
$518$	−40.8285	+	7.31157i	−1.79390	+	0.321252i
$519$		0			0
$520$	−10.3180	+	2.65851i	−0.452476	+	0.116583i
$521$	12.0185	−	20.8167i	0.526540	−	0.911995i	−0.472981	−	0.881072i	$-0.656822\pi$
$521$	12.0185	−	20.8167i	0.526540	−	0.911995i	0.999522	−	0.0309222i	$-0.00984441\pi$
$522$		0			0
$523$	1.89548	+	3.28306i	0.0828835	+	0.143558i	0.904487	−	0.426500i	$-0.140254\pi$
$523$	1.89548	+	3.28306i	0.0828835	+	0.143558i	−0.821604	+	0.570059i	$0.806920\pi$
$524$	−16.5873	+	5.91700i	−0.724621	+	0.258485i
$525$		0			0
$526$	−7.20449	−	5.07917i	−0.314130	−	0.221462i
$527$	3.72937	−	2.15316i	0.162454	−	0.0937929i
$528$		0			0
$529$	6.63889	−	11.4989i	0.288648	−	0.499952i
$530$	−0.811241	+	8.94192i	−0.0352381	+	0.388412i
$531$		0			0
$532$	−0.247599	−	2.84778i	−0.0107348	−	0.123467i
$533$	13.5425			0.586589
$534$		0			0
$535$	−6.96430	−	4.02084i	−0.301093	−	0.173836i
$536$	24.6002	+	25.0785i	1.06257	+	1.08323i
$537$		0			0
$538$	12.6385	+	8.91018i	0.544886	+	0.384145i
$539$	20.1278	−	11.9384i	0.866964	−	0.514225i
$540$		0			0
$541$	16.4954	−	9.52363i	0.709193	−	0.409453i	−0.101569	−	0.994828i	$-0.532386\pi$
$541$	16.4954	−	9.52363i	0.709193	−	0.409453i	0.810762	+	0.585376i	$0.199053\pi$
$542$	26.8756	−	12.4275i	1.15441	−	0.533805i
$543$		0			0
$544$	2.66065	−	1.80008i	0.114074	−	0.0771780i
$545$	−14.2915			−0.612179
$546$		0			0
$547$		−	46.3065i		−	1.97992i	−0.141342	−	0.989961i	$-0.545142\pi$
$547$		−	46.3065i		−	1.97992i	0.141342	−	0.989961i	$-0.454858\pi$
$548$	25.5583	+	21.7270i	1.09180	+	0.928133i
$549$		0			0
$550$	−0.646884	−	1.39895i	−0.0275832	−	0.0596514i
$551$	−0.480550	−	0.832337i	−0.0204721	−	0.0354587i
$552$		0			0
$553$	−6.68869	−	24.3882i	−0.284432	−	1.03709i
$554$	5.07587	+	3.57850i	0.215653	+	0.152036i
$555$		0			0
$556$	−20.3243	−	3.71838i	−0.861942	−	0.157695i
$557$	11.1463	−	19.3059i	0.472283	−	0.818019i	−0.527214	−	0.849733i	$-0.676763\pi$
$557$	11.1463	−	19.3059i	0.472283	−	0.818019i	0.999497	+	0.0317140i	$0.0100966\pi$
$558$		0			0
$559$			3.13910i			0.132770i
$560$	22.7784	+	2.15267i	0.962562	+	0.0909670i
$561$		0			0
$562$	−1.01377	+	11.1743i	−0.0427633	+	0.471359i
$563$	−2.42370	−	1.39932i	−0.102147	−	0.0589745i	0.448056	−	0.894005i	$-0.352116\pi$
$563$	−2.42370	−	1.39932i	−0.102147	−	0.0589745i	−0.550203	+	0.835031i	$0.685450\pi$
$564$		0			0
$565$	4.67155	+	8.09136i	0.196533	+	0.340406i
$566$	24.7070	−	35.0454i	1.03851	−	1.47307i
$567$		0			0
$568$	5.91302	−	21.2473i	0.248105	−	0.891517i
$569$	35.6988	−	20.6107i	1.49657	−	0.864046i	0.496579	−	0.867992i	$-0.334589\pi$
$569$	35.6988	−	20.6107i	1.49657	−	0.864046i	0.999992	+	0.00394571i	$0.00125596\pi$
$570$		0			0
$571$	24.3886	+	14.0808i	1.02063	+	0.589262i	0.914287	−	0.405068i	$-0.132752\pi$
$571$	24.3886	+	14.0808i	1.02063	+	0.589262i	0.106345	+	0.994329i	$0.466085\pi$
$572$	7.54601	−	8.87665i	0.315515	−	0.371151i
$573$		0			0
$574$	−27.3529	−	9.87304i	−1.14169	−	0.412093i
$575$		−	1.96350i		−	0.0818834i
$576$		0			0
$577$	8.23601	+	4.75506i	0.342870	+	0.197956i	0.661540	−	0.749910i	$-0.269903\pi$
$577$	8.23601	+	4.75506i	0.342870	+	0.197956i	−0.318671	+	0.947866i	$0.603236\pi$
$578$	−9.89904	−	21.4077i	−0.411746	−	0.890442i
$579$		0			0
$580$	7.24553	−	2.58461i	0.300854	−	0.107320i
$581$	−10.7130	+	40.9425i	−0.444449	+	1.69858i
$582$		0			0
$583$	−4.90881	−	8.50230i	−0.203302	−	0.352129i
$584$	−17.2917	−	17.6279i	−0.715535	−	0.729447i
$585$		0			0
$586$	−0.555697	+	6.12518i	−0.0229556	+	0.253029i
$587$			6.47220i			0.267136i	0.991040	+	0.133568i	$0.0426435\pi$
$587$			6.47220i			0.267136i	−0.991040	+	0.133568i	$0.957357\pi$
$588$		0			0
$589$			4.09654i			0.168795i
$590$	−34.6243	−	3.14123i	−1.42546	−	0.129323i
$591$		0			0
$592$	43.7634	−	7.13870i	1.79867	−	0.293399i
$593$	−14.5174	−	25.1449i	−0.596159	−	1.03258i	−0.993382	−	0.114855i	$-0.963360\pi$
$593$	−14.5174	−	25.1449i	−0.596159	−	1.03258i	0.397224	−	0.917722i	$-0.369974\pi$
$594$		0			0
$595$	−0.822243	+	3.14243i	−0.0337087	+	0.128827i
$596$	−2.83113	−	7.93660i	−0.115968	−	0.325096i
$597$		0			0
$598$	13.4717	−	6.22941i	0.550900	−	0.254740i
$599$	4.06979	+	2.34969i	0.166287	+	0.0960058i	0.580834	−	0.814022i	$-0.302727\pi$
$599$	4.06979	+	2.34969i	0.166287	+	0.0960058i	−0.414547	+	0.910028i	$0.636060\pi$
$600$		0			0
$601$			20.3259i			0.829111i	0.910024	+	0.414555i	$0.136063\pi$
$601$			20.3259i			0.829111i	−0.910024	+	0.414555i	$0.863937\pi$
$602$	2.28854	−	6.34030i	0.0932738	−	0.258411i
$603$		0			0
$604$	−8.04414	+	9.46262i	−0.327311	+	0.385029i
$605$	−0.330641	−	0.190896i	−0.0134425	−	0.00776102i
$606$		0			0
$607$	26.3222	−	15.1971i	1.06838	−	0.616832i	0.140645	−	0.990060i	$-0.455082\pi$
$607$	26.3222	−	15.1971i	1.06838	−	0.616832i	0.927740	+	0.373228i	$0.121749\pi$
$608$	0.217458	+	3.04815i	0.00881908	+	0.123619i
$609$		0			0
$610$	28.0303	+	19.7614i	1.13491	+	0.800115i
$611$	1.18400	+	2.05076i	0.0478997	+	0.0829647i
$612$		0			0
$613$	−24.4975	−	14.1436i	−0.989444	−	0.571256i	−0.0843357	−	0.996437i	$-0.526877\pi$
$613$	−24.4975	−	14.1436i	−0.989444	−	0.571256i	−0.905108	+	0.425182i	$0.860210\pi$
$614$	−6.77859	−	0.614976i	−0.273562	−	0.0248184i
$615$		0			0
$616$	−21.7128	+	12.4276i	−0.874833	+	0.500721i
$617$			21.3569i			0.859795i	0.902878	+	0.429898i	$0.141450\pi$
$617$			21.3569i			0.859795i	−0.902878	+	0.429898i	$0.858550\pi$
$618$		0			0
$619$	−10.6447	+	18.4372i	−0.427847	+	0.741053i	−0.996682	−	0.0813988i	$-0.974061\pi$
$619$	−10.6447	+	18.4372i	−0.427847	+	0.741053i	0.568834	+	0.822452i	$0.307395\pi$
$620$	−32.2537	−	5.90089i	−1.29534	−	0.236986i
$621$		0			0
$622$	−6.46812	+	9.17462i	−0.259348	+	0.367869i
$623$	−8.83026	−	32.1967i	−0.353777	−	1.28993i
$624$		0			0
$625$	11.6319	+	20.1470i	0.465275	+	0.805880i
$626$	−2.89899	+	1.34051i	−0.115867	+	0.0535776i
$627$		0			0
$628$	−26.7392	+	31.4543i	−1.06701	+	1.25516i
$629$			6.29514i			0.251004i
$630$		0			0
$631$	8.31457			0.330998			0.165499	−	0.986210i	$-0.447077\pi$
$631$	8.31457			0.330998			0.165499	+	0.986210i	$0.447077\pi$
$632$	6.74540	+	26.1798i	0.268318	+	1.04138i
$633$		0			0
$634$	4.42580	+	9.57122i	0.175771	+	0.380122i
$635$	13.0495	−	7.53412i	0.517853	−	0.298983i
$636$		0			0
$637$	10.6341	+	5.97403i	0.421339	+	0.236700i
$638$	−4.84674	+	6.87480i	−0.191884	+	0.272176i
$639$		0			0
$640$	−24.3125	−	2.67859i	−0.961036	−	0.105881i
$641$	4.98896	+	2.88038i	0.197052	+	0.113768i	0.595280	−	0.803519i	$-0.297041\pi$
$641$	4.98896	+	2.88038i	0.197052	+	0.113768i	−0.398228	+	0.917287i	$0.630375\pi$
$642$		0			0
$643$	−18.7692			−0.740184			−0.370092	−	0.928995i	$-0.620674\pi$
$643$	−18.7692			−0.740184			−0.370092	+	0.928995i	$0.620674\pi$
$644$	−31.7515	+	2.76061i	−1.25118	+	0.108783i
$645$		0			0
$646$	−0.432066	−	0.0391985i	−0.0169994	−	0.00154224i
$647$	−0.705648	+	1.22222i	−0.0277419	+	0.0480503i	−0.879563	−	0.475782i	$-0.842165\pi$
$647$	−0.705648	+	1.22222i	−0.0277419	+	0.0480503i	0.851821	+	0.523833i	$0.175498\pi$
$648$		0			0
$649$	32.9220	−	19.0075i	1.29230	−	0.746112i
$650$	0.462876	−	0.656560i	0.0181555	−	0.0257524i
$651$		0			0
$652$	7.75678	−	2.76699i	0.303779	−	0.108364i
$653$	−3.21537	−	5.56919i	−0.125827	−	0.217939i	0.796229	−	0.604996i	$-0.206825\pi$
$653$	−3.21537	−	5.56919i	−0.125827	−	0.217939i	−0.922056	+	0.387057i	$0.873492\pi$
$654$		0			0
$655$	−9.51855	+	16.4866i	−0.371920	+	0.644185i
$656$	29.0743	+	11.0068i	1.13516	+	0.429745i
$657$		0			0
$658$	−0.896346	−	5.00528i	−0.0349432	−	0.195126i
$659$	15.9229			0.620269			0.310134	−	0.950693i	$-0.399626\pi$
$659$	15.9229			0.620269			0.310134	+	0.950693i	$0.399626\pi$
$660$		0			0
$661$	13.8309	−	23.9557i	0.537958	−	0.931770i	−0.461056	−	0.887371i	$-0.652529\pi$
$661$	13.8309	−	23.9557i	0.537958	−	0.931770i	0.999014	−	0.0443993i	$-0.0141374\pi$
$662$	−28.9415	+	13.3827i	−1.12484	+	0.520134i
$663$		0			0
$664$	12.1299	−	43.5865i	0.470732	−	1.69149i
$665$	−2.19776	−	2.17207i	−0.0852254	−	0.0842293i
$666$		0			0
$667$	−9.28018	+	5.35791i	−0.359330	+	0.207459i
$668$	−26.0976	−	4.77462i	−1.00975	−	0.184736i
$669$		0			0
$670$	37.8191	+	3.43107i	1.46108	+	0.132554i
$671$	−37.5005			−1.44769
$672$		0			0
$673$	16.8132			0.648103			0.324052	−	0.946039i	$-0.394955\pi$
$673$	16.8132			0.648103			0.324052	+	0.946039i	$0.394955\pi$
$674$	36.6060	+	3.32102i	1.41001	+	0.127921i
$675$		0			0
$676$	−19.6023	−	3.58628i	−0.753933	−	0.137934i
$677$	33.3325	−	19.2445i	1.28107	−	0.739626i	0.304026	−	0.952664i	$-0.401669\pi$
$677$	33.3325	−	19.2445i	1.28107	−	0.739626i	0.977044	+	0.213037i	$0.0683356\pi$
$678$		0			0
$679$	−10.9845	+	41.9804i	−0.421548	+	1.61106i
$680$	0.930998	−	3.34536i	0.0357021	−	0.128289i
$681$		0			0
$682$	32.5422	−	15.0477i	1.24610	−	0.576207i
$683$	16.8564	−	29.1961i	0.644991	−	1.11716i	−0.339313	−	0.940674i	$-0.610194\pi$
$683$	16.8564	−	29.1961i	0.644991	−	1.11716i	0.984304	−	0.176483i	$-0.0564722\pi$
$684$		0			0
$685$	36.2616			1.38549
$686$	−17.1233	−	19.8190i	−0.653771	−	0.756693i
$687$		0			0
$688$	−2.55135	+	6.73932i	−0.0972693	+	0.256934i
$689$	2.55850	−	4.43146i	0.0974712	−	0.168825i
$690$		0			0
$691$	16.3070	+	28.2445i	0.620346	+	1.07447i	0.989421	+	0.145072i	$0.0463413\pi$
$691$	16.3070	+	28.2445i	0.620346	+	1.07447i	−0.369075	+	0.929400i	$0.620325\pi$
$692$	−42.3906	+	15.1215i	−1.61145	+	0.574833i
$693$		0			0
$694$	−12.8184	+	18.1821i	−0.486579	+	0.690182i
$695$	−19.3424	+	11.1673i	−0.733699	+	0.423601i
$696$		0			0
$697$	−2.20676	+	3.82222i	−0.0835869	+	0.144777i
$698$	2.52299	+	0.228894i	0.0954967	+	0.00866378i
$699$		0			0
$700$	−1.41357	+	0.988655i	−0.0534279	+	0.0373676i
$701$	−18.4784			−0.697919			−0.348959	−	0.937138i	$-0.613465\pi$
$701$	−18.4784			−0.697919			−0.348959	+	0.937138i	$0.613465\pi$
$702$		0			0
$703$	−5.18618	−	2.99424i	−0.195600	−	0.112930i
$704$	23.4151	−	12.9241i	0.882492	−	0.487096i
$705$		0			0
$706$	21.2042	−	30.0769i	0.798032	−	1.13196i
$707$	−29.2286	−	28.8870i	−1.09925	−	1.08641i
$708$		0			0
$709$	−0.277961	+	0.160481i	−0.0104390	+	0.00602697i	−0.505210	−	0.862996i	$-0.668585\pi$
$709$	−0.277961	+	0.160481i	−0.0104390	+	0.00602697i	0.494771	+	0.869023i	$0.335252\pi$
$710$	−10.0061	−	21.6391i	−0.375521	−	0.812102i
$711$		0			0
$712$	8.90512	+	34.5620i	0.333734	+	1.29527i
$713$	45.6745			1.71053
$714$		0			0
$715$		−	12.5940i		−	0.470989i
$716$	24.9691	−	29.3721i	0.933139	−	1.09769i
$717$		0			0
$718$	−22.0747	+	10.2075i	−0.823819	+	0.380939i
$719$	6.95557	+	12.0474i	0.259399	+	0.449292i	0.966081	−	0.258239i	$-0.0831422\pi$
$719$	6.95557	+	12.0474i	0.259399	+	0.449292i	−0.706682	+	0.707531i	$0.749809\pi$
$720$		0			0
$721$	−13.8262	+	3.79196i	−0.514914	+	0.141220i
$722$	−15.2448	+	21.6238i	−0.567352	+	0.804754i
$723$		0			0
$724$	43.9702	+	8.04445i	1.63414	+	0.298970i
$725$	−0.289991	+	0.502280i	−0.0107700	+	0.0186542i
$726$		0			0
$727$		−	42.1216i		−	1.56220i	−0.624403	−	0.781102i	$-0.714658\pi$
$727$		−	42.1216i		−	1.56220i	0.624403	−	0.781102i	$-0.285342\pi$
$728$	−11.2680	−	6.56201i	−0.417618	−	0.243204i
$729$		0			0
$730$	−26.5833	−	2.41173i	−0.983892	−	0.0892620i
$731$	−0.885977	−	0.511519i	−0.0327690	−	0.0189192i
$732$		0			0
$733$	4.20815	+	7.28873i	0.155432	+	0.269215i	0.933216	−	0.359316i	$-0.116990\pi$
$733$	4.20815	+	7.28873i	0.155432	+	0.269215i	−0.777785	+	0.628531i	$0.783657\pi$
$734$	−15.3549	−	10.8252i	−0.566759	−	0.399565i
$735$		0			0
$736$	33.9854	−	2.42456i	1.25272	−	0.0893704i
$737$	−35.9597	+	20.7614i	−1.32459	+	0.764755i
$738$		0			0
$739$	2.15443	+	1.24386i	0.0792519	+	0.0457561i	0.539102	−	0.842240i	$-0.318764\pi$
$739$	2.15443	+	1.24386i	0.0792519	+	0.0457561i	−0.459850	+	0.887996i	$0.652097\pi$
$740$	31.0453	−	36.5198i	1.14125	−	1.34249i
$741$		0			0
$742$	−8.39835	+	7.08533i	−0.308313	+	0.260111i
$743$			27.2694i			1.00042i	0.865904	+	0.500209i	$0.166744\pi$
$743$			27.2694i			1.00042i	−0.865904	+	0.500209i	$0.833256\pi$
$744$		0			0
$745$	−7.88841	−	4.55438i	−0.289009	−	0.166859i
$746$	47.8172	−	22.1110i	1.75071	−	0.809541i
$747$		0			0
$748$	1.27571	+	3.57624i	0.0466446	+	0.130760i
$749$	−2.60294	−	9.49080i	−0.0951094	−	0.346786i
$750$		0			0
$751$	−15.7789	−	27.3299i	−0.575781	−	0.997282i	−0.995956	−	0.0898389i	$-0.971365\pi$
$751$	−15.7789	−	27.3299i	−0.575781	−	0.997282i	0.420175	−	0.907443i	$-0.361969\pi$
$752$	0.875153	+	5.36508i	0.0319135	+	0.195644i
$753$		0			0
$754$	−4.36621	−	0.396118i	−0.159008	−	0.0144258i
$755$			13.4254i			0.488599i
$756$		0			0
$757$			36.9092i			1.34149i	0.741689	+	0.670744i	$0.234025\pi$
$757$			36.9092i			1.34149i	−0.741689	+	0.670744i	$0.765975\pi$
$758$	−4.26815	+	47.0457i	−0.155026	+	1.70878i
$759$		0			0
$760$	2.31322	+	2.35819i	0.0839091	+	0.0855406i
$761$	−9.14893	−	15.8464i	−0.331648	−	0.574432i	0.651187	−	0.758917i	$-0.274271\pi$
$761$	−9.14893	−	15.8464i	−0.331648	−	0.574432i	−0.982835	+	0.184486i	$0.940938\pi$
$762$		0			0
$763$	−12.4395	−	12.2941i	−0.450341	−	0.445078i
$764$	−12.3804	+	4.41633i	−0.447908	+	0.159777i
$765$		0			0
$766$	−12.0240	−	26.0031i	−0.434444	−	0.939529i
$767$	17.1592	+	9.90686i	0.619582	+	0.357716i
$768$		0			0
$769$			5.09495i			0.183729i	0.995772	+	0.0918644i	$0.0292826\pi$
$769$			5.09495i			0.183729i	−0.995772	+	0.0918644i	$0.970717\pi$
$770$	−9.18158	+	25.4372i	−0.330881	+	0.916693i
$771$		0			0
$772$	9.59449	−	11.2864i	0.345313	−	0.406205i
$773$	−27.0448	−	15.6143i	−0.972735	−	0.561609i	−0.0726659	−	0.997356i	$-0.523151\pi$
$773$	−27.0448	−	15.6143i	−0.972735	−	0.561609i	−0.900069	+	0.435748i	$0.856484\pi$
$774$		0			0
$775$	2.14089	−	1.23604i	0.0769030	−	0.0444000i
$776$	12.4374	−	44.6914i	0.446477	−	1.60433i
$777$		0			0
$778$	−16.0997	+	22.8365i	−0.577203	+	0.818727i
$779$	−2.09926	−	3.63603i	−0.0752138	−	0.130274i
$780$		0			0
$781$	22.5758	+	13.0341i	0.807825	+	0.466398i
$782$	−0.437045	+	4.81734i	−0.0156287	+	0.172268i
$783$		0			0
$784$	17.9749	+	21.4687i	0.641960	+	0.766739i
$785$			44.6267i			1.59279i
$786$		0			0
$787$	9.96558	−	17.2609i	0.355235	−	0.615284i	−0.631923	−	0.775031i	$-0.717734\pi$
$787$	9.96558	−	17.2609i	0.355235	−	0.615284i	0.987158	+	0.159746i	$0.0510676\pi$
$788$	3.54756	+	0.649035i	0.126377	+	0.0231209i
$789$		0			0
$790$	23.8849	+	16.8389i	0.849787	+	0.599101i
$791$	−2.89434	+	11.0615i	−0.102911	+	0.393302i
$792$		0			0
$793$	−9.77276	−	16.9269i	−0.347041	−	0.601093i
$794$	7.30506	+	15.7979i	0.259247	+	0.560647i
$795$		0			0
$796$	−13.5965	−	11.5583i	−0.481914	−	0.409673i
$797$		−	46.5551i		−	1.64907i	−0.565813	−	0.824534i	$-0.691438\pi$
$797$		−	46.5551i		−	1.64907i	0.565813	−	0.824534i	$-0.308562\pi$
$798$		0			0
$799$	−0.771739			−0.0273022
$800$	1.52738	−	1.03336i	0.0540009	−	0.0365347i
$801$		0			0
$802$	43.8225	−	20.2638i	1.54743	−	0.715540i
$803$	25.2764	−	14.5933i	0.891984	−	0.514987i
$804$		0			0
$805$	−24.2176	+	24.5040i	−0.853558	+	0.863652i
$806$	15.2728	+	10.7673i	0.537962	+	0.379263i
$807$		0			0
$808$	30.7641	+	31.3622i	1.08228	+	1.10332i
$809$	−35.1771	−	20.3095i	−1.23676	−	0.714045i	−0.268331	−	0.963327i	$-0.586472\pi$
$809$	−35.1771	−	20.3095i	−1.23676	−	0.714045i	−0.968431	+	0.249282i	$0.919805\pi$
$810$		0			0
$811$	43.3104			1.52083			0.760417	−	0.649435i	$-0.224995\pi$
$811$	43.3104			1.52083			0.760417	+	0.649435i	$0.224995\pi$
$812$	8.53003	+	3.98323i	0.299345	+	0.139784i
$813$		0			0
$814$	−4.73546	+	52.1967i	−0.165978	+	1.82949i
$815$	4.45119	−	7.70968i	0.155918	−	0.270058i
$816$		0			0
$817$	0.842818	−	0.486601i	0.0294865	−	0.0170240i
$818$	31.3288	+	22.0868i	1.09539	+	0.772248i
$819$		0			0
$820$	31.6518	−	11.2908i	1.10533	−	0.394291i
$821$	−1.21375	−	2.10228i	−0.0423602	−	0.0733699i	0.844068	−	0.536236i	$-0.180154\pi$
$821$	−1.21375	−	2.10228i	−0.0423602	−	0.0733699i	−0.886428	+	0.462866i	$0.846821\pi$
$822$		0			0
$823$	−8.90145	+	15.4178i	−0.310285	+	0.537429i	−0.978424	−	0.206607i	$-0.933758\pi$
$823$	−8.90145	+	15.4178i	−0.310285	+	0.537429i	0.668139	+	0.744036i	$0.267091\pi$
$824$	14.8419	−	3.82411i	0.517042	−	0.133219i
$825$		0			0
$826$	−27.4353	−	32.5195i	−0.954598	−	1.13150i
$827$	−39.3153			−1.36713			−0.683564	−	0.729890i	$-0.739571\pi$
$827$	−39.3153			−1.36713			−0.683564	+	0.729890i	$0.739571\pi$
$828$		0			0
$829$	21.4409	−	37.1368i	0.744675	−	1.28981i	−0.205672	−	0.978621i	$-0.565938\pi$
$829$	21.4409	−	37.1368i	0.744675	−	1.28981i	0.950346	−	0.311194i	$-0.100729\pi$
$830$	−20.5264	−	44.3903i	−0.712481	−	1.54081i
$831$		0			0
$832$	11.9357	+	7.20102i	0.413797	+	0.249650i
$833$	−3.41895	+	2.02789i	−0.118459	+	0.0702623i
$834$		0			0
$835$	−24.8368	+	14.3395i	−0.859512	+	0.496239i
$836$	−3.55303	−	0.650036i	−0.122884	−	0.0224820i
$837$		0			0
$838$	0.875190	−	9.64679i	0.0302329	−	0.333243i
$839$	−4.03008			−0.139134			−0.0695668	−	0.997577i	$-0.522162\pi$
$839$	−4.03008			−0.139134			−0.0695668	+	0.997577i	$0.522162\pi$
$840$		0			0
$841$	−25.8347			−0.890853
$842$	1.38715	−	15.2899i	0.0478044	−	0.526925i
$843$		0			0
$844$	−4.09883	+	22.4038i	−0.141087	+	0.771169i
$845$	−18.6552	+	10.7706i	−0.641759	+	0.370520i
$846$		0			0
$847$	−0.123579	−	0.450591i	−0.00424622	−	0.0154825i
$848$	9.09458	−	7.43442i	0.312309	−	0.255299i
$849$		0			0
$850$	0.109881	+	0.237629i	0.00376889	+	0.00815060i
$851$	−33.3844	+	57.8235i	−1.14440	+	1.98217i
$852$		0			0
$853$	1.89394			0.0648474			0.0324237	−	0.999474i	$-0.489677\pi$
$853$	1.89394			0.0648474			0.0324237	+	0.999474i	$0.489677\pi$
$854$	7.39843	+	41.3135i	0.253169	+	1.41372i
$855$		0			0
$856$	2.62501	+	10.1880i	0.0897210	+	0.348219i
$857$	10.3144	−	17.8650i	0.352333	−	0.610258i	−0.634325	−	0.773066i	$-0.718722\pi$
$857$	10.3144	−	17.8650i	0.352333	−	0.610258i	0.986658	+	0.162808i	$0.0520552\pi$
$858$		0			0
$859$	25.2260	+	43.6928i	0.860701	+	1.49078i	0.871253	+	0.490833i	$0.163308\pi$
$859$	25.2260	+	43.6928i	0.860701	+	1.49078i	−0.0105526	+	0.999944i	$0.503359\pi$
$860$	2.61716	+	7.33677i	0.0892444	+	0.250182i
$861$		0			0
$862$	−26.1030	−	18.4027i	−0.889073	−	0.626797i
$863$	−1.95161	+	1.12676i	−0.0664336	+	0.0383554i	−0.532849	−	0.846210i	$-0.678879\pi$
$863$	−1.95161	+	1.12676i	−0.0664336	+	0.0383554i	0.466415	+	0.884566i	$0.345545\pi$
$864$		0			0
$865$	−24.3256	+	42.1332i	−0.827095	+	1.43257i
$866$	4.33832	−	47.8193i	0.147422	−	1.62496i
$867$		0			0
$868$	−22.9979	−	32.8823i	−0.780601	−	1.11610i
$869$	−31.9546			−1.08399
$870$		0			0
$871$	−18.7425	−	10.8210i	−0.635064	−	0.366654i
$872$	13.0930	+	13.3476i	0.443386	+	0.452007i
$873$		0			0
$874$	−3.76083	−	2.65139i	−0.127212	−	0.0896846i
$875$	−7.71169	+	29.4723i	−0.260703	+	0.996346i
$876$		0			0
$877$	−22.7244	+	13.1200i	−0.767350	+	0.443029i	−0.831928	−	0.554883i	$-0.812763\pi$
$877$	−22.7244	+	13.1200i	−0.767350	+	0.443029i	0.0645788	+	0.997913i	$0.479430\pi$
$878$	31.7701	−	14.6907i	1.07219	−	0.495787i
$879$		0			0
$880$	10.2360	−	27.0381i	0.345055	−	0.911453i
$881$	−13.9743			−0.470804			−0.235402	−	0.971898i	$-0.575641\pi$
$881$	−13.9743			−0.470804			−0.235402	+	0.971898i	$0.575641\pi$
$882$		0			0
$883$			40.0650i			1.34830i	0.738596	+	0.674148i	$0.235489\pi$
$883$			40.0650i			1.34830i	−0.738596	+	0.674148i	$0.764511\pi$
$884$	−1.28178	+	1.50781i	−0.0431110	+	0.0507131i
$885$		0			0
$886$	−10.9699	−	23.7234i	−0.368539	−	0.797003i
$887$	−22.9798	−	39.8022i	−0.771586	−	1.33643i	−0.936694	−	0.350150i	$-0.886131\pi$
$887$	−22.9798	−	39.8022i	−0.771586	−	1.33643i	0.165108	−	0.986275i	$-0.447203\pi$
$888$		0			0
$889$	17.8397	+	4.66791i	0.598323	+	0.156557i
$890$	31.5323	+	22.2303i	1.05697	+	0.745162i
$891$		0			0
$892$	1.76379	−	9.64067i	0.0590559	−	0.322794i
$893$	0.367073	−	0.635788i	0.0122836	−	0.0212758i
$894$		0			0
$895$		−	41.6725i		−	1.39296i
$896$	−18.8578	−	23.2462i	−0.629994	−	0.776600i
$897$		0			0
$898$	3.89578	−	42.9414i	0.130004	−	1.43297i
$899$	−11.6840	−	6.74573i	−0.389682	−	0.224983i
$900$		0			0
$901$	0.833821	+	1.44422i	0.0277786	+	0.0481140i
$902$	−21.1728	+	30.0323i	−0.704976	+	0.999965i
$903$		0			0
$904$	3.27717	−	11.7759i	0.108997	−	0.391659i
$905$	41.8459	−	24.1597i	1.39100	−	0.803096i
$906$		0			0
$907$	8.32291	+	4.80524i	0.276358	+	0.159555i	0.631773	−	0.775153i	$-0.282327\pi$
$907$	8.32291	+	4.80524i	0.276358	+	0.159555i	−0.355416	+	0.934708i	$0.615661\pi$
$908$	−32.4785	−	27.6099i	−1.07784	−	0.916266i
$909$		0			0
$910$	−13.8745	+	2.48466i	−0.459937	+	0.0823656i
$911$		−	55.0751i		−	1.82472i	−0.409390	−	0.912359i	$-0.634258\pi$
$911$		−	55.0751i		−	1.82472i	0.409390	−	0.912359i	$-0.365742\pi$
$912$		0			0
$913$	46.3117	+	26.7381i	1.53269	+	0.884902i
$914$	15.7735	+	34.1118i	0.521741	+	1.12832i
$915$		0			0
$916$	2.14914	+	6.02476i	0.0710096	+	0.199064i
$917$	−22.4676	+	6.16195i	−0.741946	+	0.203486i
$918$		0			0
$919$	−10.4392	−	18.0812i	−0.344357	−	0.596444i	0.640880	−	0.767641i	$-0.278570\pi$
$919$	−10.4392	−	18.0812i	−0.344357	−	0.596444i	−0.985237	+	0.171198i	$0.945236\pi$
$920$	26.2928	−	25.7913i	0.866847	−	0.850314i
$921$		0			0
$922$	−0.161947	+	1.78506i	−0.00533344	+	0.0587880i
$923$			13.5870i			0.447220i
$924$		0			0
$925$			3.61379i			0.118821i
$926$	−13.8349	−	1.25515i	−0.454644	−	0.0412468i
$927$		0			0
$928$	−9.05186	−	4.39913i	−0.297142	−	0.144409i
$929$	−19.3495	−	33.5143i	−0.634837	−	1.09957i	−0.986550	−	0.163462i	$-0.947734\pi$
$929$	−19.3495	−	33.5143i	−0.634837	−	1.09957i	0.351713	−	0.936108i	$-0.385599\pi$
$930$		0			0
$931$	−0.0444554	−	3.78121i	−0.00145697	−	0.123924i
$932$	7.30433	−	2.60559i	0.239261	−	0.0853489i
$933$		0			0
$934$	−27.5417	+	12.7355i	−0.901192	+	0.416717i
$935$	3.55453	+	2.05221i	0.116245	+	0.0671143i
$936$		0			0
$937$			2.23597i			0.0730458i	0.999333	+	0.0365229i	$0.0116282\pi$
$937$			2.23597i			0.0730458i	−0.999333	+	0.0365229i	$0.988372\pi$
$938$	29.9668	+	35.5201i	0.978451	+	1.15977i
$939$		0			0
$940$	4.47706	+	3.80593i	0.146026	+	0.124136i
$941$	8.23966	+	4.75717i	0.268605	+	0.155079i	0.628254	−	0.778009i	$-0.283770\pi$
$941$	8.23966	+	4.75717i	0.268605	+	0.155079i	−0.359648	+	0.933088i	$0.617103\pi$
$942$		0			0
$943$	−40.5400	+	23.4058i	−1.32017	+	0.762198i
$944$	28.7871	+	35.2154i	0.936939	+	1.14616i
$945$		0			0
$946$	−6.96138	−	4.90778i	−0.226334	−	0.159566i
$947$	19.3346	+	33.4885i	0.628290	+	1.08823i	0.987895	+	0.155126i	$0.0495782\pi$
$947$	19.3346	+	33.4885i	0.628290	+	1.08823i	−0.359605	+	0.933105i	$0.617088\pi$
$948$		0			0
$949$	13.1742	+	7.60613i	0.427653	+	0.246906i
$950$	−0.248032	−	0.0225023i	−0.00804722	−	0.000730071i
$951$		0			0
$952$	3.68818	−	2.11097i	0.119535	−	0.0684171i
$953$		−	31.5906i		−	1.02332i	−0.859188	−	0.511659i	$-0.829031\pi$
$953$		−	31.5906i		−	1.02332i	0.859188	−	0.511659i	$-0.170969\pi$
$954$		0			0
$955$	−7.10444	+	12.3053i	−0.229894	+	0.398189i
$956$	7.97003	−	43.5634i	0.257769	−	1.40894i
$957$		0			0
$958$	22.0929	−	31.3374i	0.713789	−	1.01247i
$959$	31.5627	+	31.1938i	1.01921	+	1.00730i
$960$		0			0
$961$	13.2526	+	22.9542i	0.427504	+	0.740459i
$962$	−24.7946	+	11.4652i	−0.799408	+	0.369652i
$963$		0			0
$964$	10.9689	+	9.32463i	0.353285	+	0.300326i
$965$		−	16.0128i		−	0.515472i
$966$		0			0
$967$	54.1994			1.74294			0.871468	−	0.490452i	$-0.163168\pi$
$967$	54.1994			1.74294			0.871468	+	0.490452i	$0.163168\pi$
$968$	0.124627	+	0.483693i	0.00400565	+	0.0155465i
$969$		0			0
$970$	−21.0467	−	45.5156i	−0.675769	−	1.46142i
$971$	−5.92025	+	3.41806i	−0.189990	+	0.109691i	−0.591978	−	0.805954i	$-0.701653\pi$
$971$	−5.92025	+	3.41806i	−0.189990	+	0.109691i	0.401988	+	0.915645i	$0.368319\pi$
$972$		0			0
$973$	−26.4426	−	6.91893i	−0.847710	−	0.221811i
$974$	−6.61882	+	9.38838i	−0.212081	+	0.300823i
$975$		0			0
$976$	−7.22350	−	44.2833i	−0.231219	−	1.41747i
$977$	19.1650	+	11.0649i	0.613144	+	0.353999i	0.774195	−	0.632947i	$-0.218155\pi$
$977$	19.1650	+	11.0649i	0.613144	+	0.353999i	−0.161051	+	0.986946i	$0.551488\pi$
$978$		0			0
$979$	−42.1858			−1.34826
$980$	29.8350	+	5.09667i	0.953045	+	0.162807i
$981$		0			0
$982$	8.61356	+	0.781451i	0.274870	+	0.0249371i
$983$	−3.18986	+	5.52499i	−0.101741	+	0.176220i	−0.912402	−	0.409296i	$-0.865775\pi$
$983$	−3.18986	+	5.52499i	−0.101741	+	0.176220i	0.810661	+	0.585515i	$0.199108\pi$
$984$		0			0
$985$	3.37617	−	1.94923i	0.107574	−	0.0621077i
$986$	0.823279	−	1.16777i	0.0262185	−	0.0371894i
$987$		0			0
$988$	−0.632519	−	1.77316i	−0.0201231	−	0.0564118i
$989$	−5.42538	−	9.39704i	−0.172517	−	0.298808i
$990$		0			0
$991$	5.49218	−	9.51273i	0.174465	−	0.302182i	−0.765511	−	0.643423i	$-0.777514\pi$
$991$	5.49218	−	9.51273i	0.174465	−	0.302182i	0.939976	+	0.341241i	$0.110847\pi$
$992$	24.0378	+	35.5296i	0.763202	+	1.12807i
$993$		0			0
$994$	9.90547	−	27.4427i	0.314182	−	0.870430i
$995$	−19.2904			−0.611546
$996$		0			0
$997$	3.65692	−	6.33397i	0.115816	−	0.200599i	−0.802290	−	0.596935i	$-0.796385\pi$
$997$	3.65692	−	6.33397i	0.115816	−	0.200599i	0.918106	+	0.396336i	$0.129718\pi$
$998$	24.3453	−	11.2574i	0.770636	−	0.356347i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.ch.b.269.2	✓	56
3.2	odd	2	inner	504.2.ch.b.269.27	yes	56
4.3	odd	2		2016.2.cp.b.17.23		56
7.5	odd	6	inner	504.2.ch.b.341.19	yes	56
8.3	odd	2		2016.2.cp.b.17.6		56
8.5	even	2	inner	504.2.ch.b.269.10	yes	56
12.11	even	2		2016.2.cp.b.17.5		56
21.5	even	6	inner	504.2.ch.b.341.10	yes	56
24.5	odd	2	inner	504.2.ch.b.269.19	yes	56
24.11	even	2		2016.2.cp.b.17.24		56
28.19	even	6		2016.2.cp.b.593.24		56
56.5	odd	6	inner	504.2.ch.b.341.27	yes	56
56.19	even	6		2016.2.cp.b.593.5		56
84.47	odd	6		2016.2.cp.b.593.6		56
168.5	even	6	inner	504.2.ch.b.341.2	yes	56
168.131	odd	6		2016.2.cp.b.593.23		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.ch.b.269.2	✓	56	1.1	even	1	trivial
504.2.ch.b.269.10	yes	56	8.5	even	2	inner
504.2.ch.b.269.19	yes	56	24.5	odd	2	inner
504.2.ch.b.269.27	yes	56	3.2	odd	2	inner
504.2.ch.b.341.2	yes	56	168.5	even	6	inner
504.2.ch.b.341.10	yes	56	21.5	even	6	inner
504.2.ch.b.341.19	yes	56	7.5	odd	6	inner
504.2.ch.b.341.27	yes	56	56.5	odd	6	inner
2016.2.cp.b.17.5		56	12.11	even	2
2016.2.cp.b.17.6		56	8.3	odd	2
2016.2.cp.b.17.23		56	4.3	odd	2
2016.2.cp.b.17.24		56	24.11	even	2
2016.2.cp.b.593.5		56	56.19	even	6
2016.2.cp.b.593.6		56	84.47	odd	6
2016.2.cp.b.593.23		56	168.131	odd	6
2016.2.cp.b.593.24		56	28.19	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.ch (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40843 - 0.127777i) q^{2} +(1.96735 + 0.359931i) q^{4} +(1.87230 - 1.08097i) q^{5} +(2.55958 + 0.669737i) q^{7} +(-2.72488 - 0.758320i) q^{8} +O(q^{10})\)	\(q+(-1.40843 - 0.127777i) q^{2} +(1.96735 + 0.359931i) q^{4} +(1.87230 - 1.08097i) q^{5} +(2.55958 + 0.669737i) q^{7} +(-2.72488 - 0.758320i) q^{8} +(-2.77512 + 1.28324i) q^{10} +(1.67157 - 2.89525i) q^{11} +1.74247 q^{13} +(-3.51941 - 1.27033i) q^{14} +(3.74090 + 1.41622i) q^{16} +(-0.283937 + 0.491793i) q^{17} +(-0.270105 - 0.467836i) q^{19} +(4.07254 - 1.45275i) q^{20} +(-2.72424 + 3.86416i) q^{22} +(-5.21616 + 3.01155i) q^{23} +(-0.162997 + 0.282319i) q^{25} +(-2.45414 - 0.222648i) q^{26} +(4.79452 + 2.23888i) q^{28} +1.77912 q^{29} +(-6.56726 - 3.79161i) q^{31} +(-5.08783 - 2.47264i) q^{32} +(0.462745 - 0.656375i) q^{34} +(5.51627 - 1.51289i) q^{35} +(9.60029 - 5.54273i) q^{37} +(0.320645 + 0.693428i) q^{38} +(-5.92151 + 1.52571i) q^{40} +7.77201 q^{41} +1.80152i q^{43} +(4.33065 - 5.09430i) q^{44} +(7.73140 - 3.57505i) q^{46} +(0.679499 + 1.17693i) q^{47} +(6.10291 + 3.42849i) q^{49} +(0.265644 - 0.376799i) q^{50} +(3.42804 + 0.627168i) q^{52} +(1.46832 - 2.54321i) q^{53} -7.22769i q^{55} +(-6.46667 - 3.76593i) q^{56} +(-2.50576 - 0.227331i) q^{58} +(9.84763 + 5.68553i) q^{59} +(-5.60858 - 9.71434i) q^{61} +(8.76504 + 6.17936i) q^{62} +(6.84990 + 4.13265i) q^{64} +(3.26242 - 1.88356i) q^{65} +(-10.7563 - 6.21014i) q^{67} +(-0.735613 + 0.865329i) q^{68} +(-7.96259 + 1.42594i) q^{70} +7.79753i q^{71} +(7.56066 + 4.36515i) q^{73} +(-14.2296 + 6.57984i) q^{74} +(-0.363002 - 1.01761i) q^{76} +(6.21757 - 6.29110i) q^{77} +(-4.77913 - 8.27770i) q^{79} +(8.53498 - 1.39223i) q^{80} +(-10.9463 - 0.993087i) q^{82} +15.9958i q^{83} +1.22771i q^{85} +(0.230194 - 2.53732i) q^{86} +(-6.75035 + 6.62160i) q^{88} +(-6.30930 - 10.9280i) q^{89} +(4.45999 + 1.16699i) q^{91} +(-11.3459 + 4.04731i) q^{92} +(-0.806641 - 1.74444i) q^{94} +(-1.01144 - 0.583953i) q^{95} +16.4013i q^{97} +(-8.15743 - 5.60860i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{4} - 20 q^{7}+O(q^{10}) \) 56 * q - 8 * q^4 - 20 * q^7	\( 56 q - 8 q^{4} - 20 q^{7} + 20 q^{16} - 16 q^{22} + 8 q^{25} + 36 q^{28} - 36 q^{31} + 60 q^{40} - 8 q^{46} - 28 q^{49} + 36 q^{52} - 44 q^{58} + 40 q^{64} - 60 q^{70} + 72 q^{73} - 12 q^{79} - 36 q^{82} + 4 q^{88} - 180 q^{94}+O(q^{100}) \) 56 * q - 8 * q^4 - 20 * q^7 + 20 * q^16 - 16 * q^22 + 8 * q^25 + 36 * q^28 - 36 * q^31 + 60 * q^40 - 8 * q^46 - 28 * q^49 + 36 * q^52 - 44 * q^58 + 40 * q^64 - 60 * q^70 + 72 * q^73 - 12 * q^79 - 36 * q^82 + 4 * q^88 - 180 * q^94

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