LMFDB - Embedded newform 504.2.ch.b.341.19

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			341.19
Character	$\chi$	$=$	504.341
Dual form			504.2.ch.b.269.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.593556 + 1.28362i) q^{2} +(-1.29538 + 1.52381i) q^{4} +(1.87230 + 1.08097i) q^{5} +(2.55958 - 0.669737i) q^{7} +(-2.72488 - 0.758320i) q^{8} +O(q^{10})$	\(q+(0.593556 + 1.28362i) q^{2} +(-1.29538 + 1.52381i) q^{4} +(1.87230 + 1.08097i) q^{5} +(2.55958 - 0.669737i) q^{7} +(-2.72488 - 0.758320i) q^{8} +(-0.276248 + 3.04495i) q^{10} +(1.67157 + 2.89525i) q^{11} -1.74247 q^{13} +(2.37895 + 2.88801i) q^{14} +(-0.643969 - 3.94782i) q^{16} +(0.283937 + 0.491793i) q^{17} +(0.270105 - 0.467836i) q^{19} +(-4.07254 + 1.45275i) q^{20} +(-2.72424 + 3.86416i) q^{22} +(5.21616 + 3.01155i) q^{23} +(-0.162997 - 0.282319i) q^{25} +(-1.03425 - 2.23667i) q^{26} +(-2.29509 + 4.76787i) q^{28} +1.77912 q^{29} +(-6.56726 + 3.79161i) q^{31} +(4.68529 - 3.16987i) q^{32} +(-0.462745 + 0.656375i) q^{34} +(5.51627 + 1.51289i) q^{35} +(-9.60029 - 5.54273i) q^{37} +(0.760849 + 0.0690267i) q^{38} +(-4.28206 - 4.36532i) q^{40} -7.77201 q^{41} +1.80152i q^{43} +(-6.57712 - 1.20330i) q^{44} +(-0.769617 + 8.48312i) q^{46} +(-0.679499 + 1.17693i) q^{47} +(6.10291 - 3.42849i) q^{49} +(0.265644 - 0.376799i) q^{50} +(2.25716 - 2.65518i) q^{52} +(1.46832 + 2.54321i) q^{53} +7.22769i q^{55} +(-7.48242 - 0.116030i) q^{56} +(1.05601 + 2.28372i) q^{58} +(9.84763 - 5.68553i) q^{59} +(5.60858 - 9.71434i) q^{61} +(-8.76504 - 6.17936i) q^{62} +(6.84990 + 4.13265i) q^{64} +(-3.26242 - 1.88356i) q^{65} +(10.7563 - 6.21014i) q^{67} +(-1.11720 - 0.204395i) q^{68} +(1.33223 + 7.97880i) q^{70} +7.79753i q^{71} +(7.56066 - 4.36515i) q^{73} +(1.41647 - 15.6131i) q^{74} +(0.363002 + 1.01761i) q^{76} +(6.21757 + 6.29110i) q^{77} +(-4.77913 + 8.27770i) q^{79} +(3.06178 - 8.08762i) q^{80} +(-4.61312 - 9.97633i) q^{82} -15.9958i q^{83} +1.22771i q^{85} +(-2.31248 + 1.06931i) q^{86} +(-2.35930 - 9.15677i) q^{88} +(6.30930 - 10.9280i) q^{89} +(-4.45999 + 1.16699i) q^{91} +(-11.3459 + 4.04731i) q^{92} +(-1.91405 - 0.173649i) q^{94} +(1.01144 - 0.583953i) q^{95} -16.4013i q^{97} +(8.02331 + 5.79884i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.593556	+	1.28362i	0.419708	+	0.907659i
$2$	0.593556	+	1.28362i	0.419708	+	0.907659i
$3$		0			0
$3$		0			0
$4$	−1.29538	+	1.52381i	−0.647691	+	0.761903i
$5$	1.87230	+	1.08097i	0.837318	+	0.483426i	0.856352	−	0.516393i	$-0.172726\pi$
$5$	1.87230	+	1.08097i	0.837318	+	0.483426i	−0.0190339	+	0.999819i	$0.506059\pi$
$6$		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
$10$	−0.276248	+	3.04495i	−0.0873572	+	0.962897i
$11$	1.67157	+	2.89525i	0.503998	+	0.872949i	0.999989	+	0.00462217i	$0.00147129\pi$
$11$	1.67157	+	2.89525i	0.503998	+	0.872949i	−0.495992	+	0.868327i	$0.665195\pi$
$12$		0			0
$13$	−1.74247			−0.483274			−0.241637	−	0.970367i	$-0.577684\pi$
$13$	−1.74247			−0.483274			−0.241637	+	0.970367i	$0.577684\pi$
$14$	2.37895	+	2.88801i	0.635800	+	0.771854i
$15$		0			0
$16$	−0.643969	−	3.94782i	−0.160992	−	0.986956i
$17$	0.283937	+	0.491793i	0.0688648	+	0.119277i	0.898402	−	0.439174i	$-0.144729\pi$
$17$	0.283937	+	0.491793i	0.0688648	+	0.119277i	−0.829537	+	0.558452i	$0.811396\pi$
$18$		0			0
$19$	0.270105	−	0.467836i	0.0619664	−	0.107329i	−0.833378	−	0.552704i	$-0.813596\pi$
$19$	0.270105	−	0.467836i	0.0619664	−	0.107329i	0.895344	+	0.445375i	$0.146929\pi$
$20$	−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	$-0.117227\pi$
$23$	5.21616	+	3.01155i	1.08764	+	0.627952i	0.154696	+	0.987962i	$0.450560\pi$
$24$		0			0
$25$	−0.162997	−	0.282319i	−0.0325994	−	0.0564638i
$26$	−1.03425	−	2.23667i	−0.202834	−	0.438648i
$27$		0			0
$28$	−2.29509	+	4.76787i	−0.433731	+	0.901043i
$29$	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	−0.955902	−	0.293685i	$-0.905118\pi$
$31$	−6.56726	+	3.79161i	−1.17952	+	0.680993i	−0.223613	+	0.974678i	$0.571785\pi$
$32$	4.68529	−	3.16987i	0.828250	−	0.560359i
$33$		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	−0.995100	−	0.0988741i	$-0.968476\pi$
$37$	−9.60029	−	5.54273i	−1.57828	−	0.911219i	−0.583177	−	0.812345i	$-0.698191\pi$
$38$	0.760849	+	0.0690267i	0.123426	+	0.0111976i
$39$		0			0
$40$	−4.28206	−	4.36532i	−0.677053	−	0.690217i
$41$	−7.77201			−1.21378			−0.606892	−	0.794785i	$-0.707584\pi$
$41$	−7.77201			−1.21378			−0.606892	+	0.794785i	$0.707584\pi$
$42$		0			0
$43$			1.80152i			0.274730i	0.990521	+	0.137365i	$0.0438633\pi$
$43$			1.80152i			0.274730i	−0.990521	+	0.137365i	$0.956137\pi$
$44$	−6.57712	−	1.20330i	−0.991538	−	0.181404i
$45$		0			0
$46$	−0.769617	+	8.48312i	−0.113474	+	1.25077i
$47$	−0.679499	+	1.17693i	−0.0991151	+	0.171672i	−0.911319	−	0.411702i	$-0.864935\pi$
$47$	−0.679499	+	1.17693i	−0.0991151	+	0.171672i	0.812204	+	0.583374i	$0.198268\pi$
$48$		0			0
$49$	6.10291	−	3.42849i	0.871844	−	0.489784i
$50$	0.265644	−	0.376799i	0.0375677	−	0.0532874i
$51$		0			0
$52$	2.25716	−	2.65518i	0.313012	−	0.368208i
$53$	1.46832	+	2.54321i	0.201689	+	0.349336i	0.949073	−	0.315057i	$-0.102023\pi$
$53$	1.46832	+	2.54321i	0.201689	+	0.349336i	−0.747383	+	0.664393i	$0.768690\pi$
$54$		0			0
$55$			7.22769i			0.974581i
$56$	−7.48242	−	0.116030i	−0.999880	−	0.0155052i
$57$		0			0
$58$	1.05601	+	2.28372i	0.138661	+	0.299867i
$59$	9.84763	−	5.68553i	1.28205	−	0.740194i	0.304830	−	0.952407i	$-0.401401\pi$
$59$	9.84763	−	5.68553i	1.28205	−	0.740194i	0.977223	+	0.212213i	$0.0680672\pi$
$60$		0			0
$61$	5.60858	−	9.71434i	0.718105	−	1.24379i	−0.243645	−	0.969864i	$-0.578343\pi$
$61$	5.60858	−	9.71434i	0.718105	−	1.24379i	0.961750	−	0.273929i	$-0.0883234\pi$
$62$	−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	$-0.392507\pi$
$67$	10.7563	−	6.21014i	1.31409	−	0.758689i	0.982770	+	0.184830i	$0.0591736\pi$
$68$	−1.11720	−	0.204395i	−0.135481	−	0.0247866i
$69$		0			0
$70$	1.33223	+	7.97880i	0.159232	+	0.953649i
$71$			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	0.0126348	−	0.999920i	$-0.495978\pi$
$73$	7.56066	−	4.36515i	0.884909	−	0.510902i	0.872274	+	0.489018i	$0.162645\pi$
$74$	1.41647	−	15.6131i	0.164661	−	1.81498i
$75$		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	0.461333	+	0.887227i	$0.347371\pi$
$79$	−4.77913	+	8.27770i	−0.537694	+	0.931314i	−0.999028	+	0.0440870i	$0.985962\pi$
$80$	3.06178	−	8.08762i	0.342318	−	0.904223i
$81$		0			0
$82$	−4.61312	−	9.97633i	−0.509434	−	1.10170i
$83$		−	15.9958i		−	1.75577i	−0.478875	−	0.877883i	$-0.658955\pi$
$83$		−	15.9958i		−	1.75577i	0.478875	−	0.877883i	$-0.341045\pi$
$84$		0			0
$85$			1.22771i			0.133164i
$86$	−2.31248	+	1.06931i	−0.249361	+	0.115306i
$87$		0			0
$88$	−2.35930	−	9.15677i	−0.251502	−	0.976115i
$89$	6.30930	−	10.9280i	0.668784	−	1.15837i	−0.309460	−	0.950912i	$-0.600148\pi$
$89$	6.30930	−	10.9280i	0.668784	−	1.15837i	0.978244	−	0.207456i	$-0.0665184\pi$
$90$		0			0
$91$	−4.45999	+	1.16699i	−0.467534	+	0.122334i
$92$	−11.3459	+	4.04731i	−1.18290	+	0.421961i
$93$		0			0
$94$	−1.91405	−	0.173649i	−0.197419	−	0.0179106i
$95$	1.01144	−	0.583953i	0.103771	−	0.0599123i
$96$		0			0
$97$		−	16.4013i		−	1.66530i	−0.553802	−	0.832649i	$-0.686823\pi$
$97$		−	16.4013i		−	1.66530i	0.553802	−	0.832649i	$-0.313177\pi$
$98$	8.02331	+	5.79884i	0.810477	+	0.585771i
$99$		0			0
$100$	0.641343	+	0.117335i	0.0641343	+	0.0117335i
$101$	−13.4514	+	7.76615i	−1.33846	+	0.772761i	−0.986579	−	0.163283i	$-0.947792\pi$
$101$	−13.4514	+	7.76615i	−1.33846	+	0.772761i	−0.351882	+	0.936044i	$0.614458\pi$
$102$		0			0
$103$	−4.69281	−	2.70939i	−0.462396	−	0.266964i	0.250655	−	0.968076i	$-0.419354\pi$
$103$	−4.69281	−	2.70939i	−0.462396	−	0.266964i	−0.713051	+	0.701112i	$0.752687\pi$
$104$	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	−0.941811	−	0.336144i	$-0.890877\pi$
$107$	−1.85983	+	3.22131i	−0.179796	+	0.311416i	0.762014	+	0.647560i	$0.224210\pi$
$108$		0			0
$109$	5.72483	−	3.30523i	0.548340	−	0.316584i	−0.200112	−	0.979773i	$-0.564131\pi$
$109$	5.72483	−	3.30523i	0.548340	−	0.316584i	0.748452	+	0.663189i	$0.230797\pi$
$110$	−9.27764	+	4.29004i	−0.884588	+	0.409039i
$111$		0			0
$112$	−4.29229	−	9.67348i	−0.405584	−	0.914058i
$113$			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
$116$	−2.30464	+	2.71103i	−0.213981	+	0.251713i
$117$		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
$122$	15.7986	+	1.43330i	1.43033	+	0.129765i
$123$		0			0
$124$	2.72944	−	14.9188i	0.245111	−	1.33975i
$125$		−	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	$0.399928\pi$
$128$	−1.23897	+	11.2457i	−0.109511	+	0.993986i
$129$		0			0
$130$	0.481353	−	5.30572i	0.0422174	−	0.465343i
$131$	−7.62582	−	4.40277i	−0.666271	−	0.384672i	0.128391	−	0.991724i	$-0.459019\pi$
$131$	−7.62582	−	4.40277i	−0.666271	−	0.384672i	−0.794662	+	0.607052i	$0.792352\pi$
$132$		0			0
$133$	0.378029	−	1.37836i	0.0327793	−	0.119519i
$134$	14.3559	+	10.1209i	1.24016	+	0.874317i
$135$		0			0
$136$	−0.400756	−	1.55539i	−0.0343646	−	0.133374i
$137$	−14.5256	+	8.38635i	−1.24100	+	0.716494i	−0.969299	−	0.245887i	$-0.920921\pi$
$137$	−14.5256	+	8.38635i	−1.24100	+	0.716494i	−0.271705	+	0.962381i	$0.587588\pi$
$138$		0			0
$139$	10.3308			0.876249			0.438124	−	0.898914i	$-0.355643\pi$
$139$	10.3308			0.876249			0.438124	+	0.898914i	$0.355643\pi$
$140$	−9.45102	+	6.44595i	−0.798757	+	0.544782i
$141$		0			0
$142$	−10.0091	+	4.62827i	−0.839945	+	0.388396i
$143$	−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	−0.939321	−	0.343039i	$-0.888544\pi$
$149$	−2.10661	+	3.64876i	−0.172580	+	0.298918i	0.766741	+	0.641957i	$0.221877\pi$
$150$		0			0
$151$	−3.10493	−	5.37790i	−0.252676	−	0.437647i	0.711586	−	0.702599i	$-0.247977\pi$
$151$	−3.10493	−	5.37790i	−0.252676	−	0.437647i	−0.964262	+	0.264952i	$0.914644\pi$
$152$	−1.09077	+	1.06997i	−0.0884734	+	0.0867860i
$153$		0			0
$154$	−4.38493	+	11.7151i	−0.353348	+	0.944034i
$155$	−16.3945			−1.31684
$156$		0			0
$157$	10.3210	+	17.8764i	0.823702	+	1.42669i	0.902907	+	0.429835i	$0.141428\pi$
$157$	10.3210	+	17.8764i	0.823702	+	1.42669i	−0.0792057	+	0.996858i	$0.525238\pi$
$158$	−13.4621	−	1.22133i	−1.07099	−	0.0971638i
$159$		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	$-0.384890\pi$
$163$	−3.56609	−	2.05888i	−0.279317	−	0.161264i	−0.633114	+	0.774058i	$0.718224\pi$
$164$	10.0677	−	11.8430i	0.786157	−	0.924785i
$165$		0			0
$166$	20.5326	−	9.49440i	1.59364	−	0.736908i
$167$	13.2654			1.02651			0.513253	−	0.858237i	$-0.328440\pi$
$167$	13.2654			1.02651			0.513253	+	0.858237i	$0.328440\pi$
$168$		0			0
$169$	−9.96381			−0.766447
$170$	−1.57592	+	0.728716i	−0.120868	+	0.0558899i
$171$		0			0
$172$	−2.74517	−	2.33366i	−0.209317	−	0.177940i
$173$	−19.4886	−	11.2517i	−1.48169	−	0.855453i	−0.481903	−	0.876225i	$-0.660054\pi$
$173$	−19.4886	−	11.2517i	−1.48169	−	0.855453i	−0.999784	+	0.0207720i	$0.993388\pi$
$174$		0			0
$175$	−0.606283	−	0.613453i	−0.0458307	−	0.0463727i
$176$	10.3535	−	8.46352i	0.780423	−	0.637961i
$177$		0			0
$178$	17.7724	+	1.61237i	1.33210	+	0.120852i
$179$	9.63774	+	16.6931i	0.720358	+	1.24770i	0.960856	+	0.277048i	$0.0893560\pi$
$179$	9.63774	+	16.6931i	0.720358	+	1.24770i	−0.240498	+	0.970650i	$0.577311\pi$
$180$		0			0
$181$	−22.3500			−1.66126			−0.830631	−	0.556823i	$-0.812020\pi$
$181$	−22.3500			−1.66126			−0.830631	+	0.556823i	$0.812020\pi$
$182$	−4.14524	−	5.03227i	−0.307265	−	0.373017i
$183$		0			0
$184$	−11.9297	−	12.1616i	−0.879467	−	0.896567i
$185$	−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	$-0.256915\pi$
$191$	5.69175	+	3.28613i	0.411841	+	0.237776i	−0.279740	+	0.960076i	$0.590248\pi$
$192$		0			0
$193$	3.70334	+	6.41438i	0.266572	+	0.461717i	0.967974	−	0.251049i	$-0.0807755\pi$
$193$	3.70334	+	6.41438i	0.266572	+	0.461717i	−0.701402	+	0.712766i	$0.747442\pi$
$194$	21.0531	−	9.73508i	1.51152	−	0.698938i
$195$		0			0
$196$	−2.68124	+	13.7408i	−0.191517	+	0.981489i
$197$	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	−0.748223	−	0.663447i	$-0.769093\pi$
$199$	−7.72728	+	4.46135i	−0.547772	+	0.316257i	0.200451	+	0.979704i	$0.435759\pi$
$200$	0.230059	+	0.892888i	0.0162676	+	0.0631367i
$201$		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
$206$	0.692398	−	7.63197i	0.0482417	−	0.531745i
$207$		0			0
$208$	1.12210	+	6.87895i	0.0778034	+	0.476970i
$209$	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	$0.871789\pi$
$212$	−5.77739	−	1.05699i	−0.396793	−	0.0725943i
$213$		0			0
$214$	−5.23887	−	0.475288i	−0.358122	−	0.0324900i
$215$	−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
$220$	−11.0136	−	9.36262i	−0.742536	−	0.631228i
$221$	−0.494751	−	0.856933i	−0.0332805	−	0.0576436i
$222$		0			0
$223$			4.90035i			0.328151i	0.986448	+	0.164076i	$0.0524641\pi$
$223$			4.90035i			0.328151i	−0.986448	+	0.164076i	$0.947536\pi$
$224$	9.86940	−	11.2514i	0.659427	−	0.751769i
$225$		0			0
$226$	−5.54733	+	2.56512i	−0.369003	+	0.170629i
$227$	−18.4585	+	10.6570i	−1.22514	+	0.707332i	−0.966008	−	0.258511i	$-0.916768\pi$
$227$	−18.4585	+	10.6570i	−1.22514	+	0.707332i	−0.259127	+	0.965843i	$0.583435\pi$
$228$		0			0
$229$	−1.59915	+	2.76981i	−0.105675	+	0.183034i	−0.914014	−	0.405683i	$-0.867034\pi$
$229$	−1.59915	+	2.76981i	−0.105675	+	0.183034i	0.808339	+	0.588717i	$0.200367\pi$
$230$	−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	$-0.373873\pi$
$233$	−3.35808	−	1.93879i	−0.219995	−	0.127014i	−0.605948	+	0.795504i	$0.707206\pi$
$234$		0			0
$235$	−2.54445	+	1.46904i	−0.165982	+	0.0958295i
$236$	−4.09280	+	22.3708i	−0.266419	+	1.45622i
$237$		0			0
$238$	−0.744834	+	1.98996i	−0.0482804	+	0.128990i
$239$		−	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	−0.285594	−	0.958351i	$-0.592191\pi$
$241$	6.23397	−	3.59918i	0.401565	−	0.231844i	0.687159	+	0.726507i	$0.258858\pi$
$242$	−0.248724	−	0.0225650i	−0.0159886	−	0.00145054i
$243$		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
$248$	20.7702	−	5.35159i	1.31891	−	0.339826i
$249$		0			0
$250$	14.7803	−	6.83451i	0.934788	−	0.432252i
$251$		−	9.58773i		−	0.605172i	−0.953122	−	0.302586i	$-0.902150\pi$
$251$		−	9.58773i		−	0.605172i	0.953122	−	0.302586i	$-0.0978500\pi$
$252$		0			0
$253$			20.1361i			1.26595i
$254$	4.13695	+	8.94656i	0.259575	+	0.561357i
$255$		0			0
$256$	−15.1706	+	5.08455i	−0.948163	+	0.317785i
$257$	−4.33124	+	7.50192i	−0.270175	+	0.467957i	−0.968907	−	0.247427i	$-0.920415\pi$
$257$	−4.33124	+	7.50192i	−0.270175	+	0.467957i	0.698731	+	0.715384i	$0.253748\pi$
$258$		0			0
$259$	−28.2849	−	7.75739i	−1.75754	−	0.482021i
$260$	7.09626	−	2.53137i	0.440092	−	0.156989i
$261$		0			0
$262$	1.12515	−	12.4020i	0.0695120	−	0.766197i
$263$	−5.39801	+	3.11654i	−0.332855	+	0.192174i	−0.657108	−	0.753796i	$-0.728220\pi$
$263$	−5.39801	+	3.11654i	−0.332855	+	0.192174i	0.324253	+	0.945970i	$0.394887\pi$
$264$		0			0
$265$			6.34886i			0.390007i
$266$	1.99368	−	0.332889i	0.122241	−	0.0204107i
$267$		0			0
$268$	−4.47044	+	24.4350i	−0.273076	+	1.49260i
$269$	−9.46950	+	5.46722i	−0.577366	+	0.333342i	−0.760086	−	0.649823i	$-0.774843\pi$
$269$	−9.46950	+	5.46722i	−0.577366	+	0.333342i	0.182720	+	0.983165i	$0.441510\pi$
$270$		0			0
$271$	−18.1322	−	10.4687i	−1.10145	−	0.635925i	−0.164852	−	0.986318i	$-0.552715\pi$
$271$	−18.1322	−	10.4687i	−1.10145	−	0.635925i	−0.936603	+	0.350393i	$0.886048\pi$
$272$	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	$-0.624550\pi$
$277$	3.80313	−	2.19574i	0.228508	−	0.131929i	0.609884	+	0.792491i	$0.291216\pi$
$278$	6.13192	+	13.2609i	0.367768	+	0.795335i
$279$		0			0
$280$	−13.8839	−	8.30553i	−0.829721	−	0.496350i
$281$		−	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	0.825976	+	0.563705i	$0.190625\pi$
$283$	15.1600	+	26.2580i	0.901171	+	1.56087i	0.0751951	+	0.997169i	$0.476042\pi$
$284$	−11.8819	−	10.1008i	−0.705063	−	0.599371i
$285$		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
$290$	−0.491478	+	5.41733i	−0.0288606	+	0.318116i
$291$		0			0
$292$	−3.14231	+	17.1755i	−0.183890	+	1.00512i
$293$			4.34894i			0.254068i	0.991898	+	0.127034i	$0.0405457\pi$
$293$			4.34894i			0.254068i	−0.991898	+	0.127034i	$0.959454\pi$
$294$		0			0
$295$	24.5836			1.43131
$296$	21.9564	+	22.3833i	1.27619	+	1.30100i
$297$		0			0
$298$	−5.93403	−	0.538355i	−0.343749	−	0.0311861i
$299$	−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
$304$	−2.02087	−	0.765056i	−0.115905	−	0.0438790i
$305$	21.0019	−	12.1254i	1.20256	−	0.694300i
$306$		0			0
$307$	−4.81287			−0.274685			−0.137343	−	0.990524i	$-0.543856\pi$
$307$	−4.81287			−0.274685			−0.137343	+	0.990524i	$0.543856\pi$
$308$	−17.6406	+	1.32499i	−1.00516	+	0.0754985i
$309$		0			0
$310$	−9.73106	−	21.0444i	−0.552687	−	1.19524i
$311$	−3.96879	−	6.87414i	−0.225049	−	0.389797i	0.731285	−	0.682072i	$-0.238921\pi$
$311$	−3.96879	−	6.87414i	−0.225049	−	0.389797i	−0.956334	+	0.292275i	$0.905588\pi$
$312$		0			0
$313$	1.95587	+	1.12922i	0.110552	+	0.0638273i	0.554257	−	0.832346i	$-0.313003\pi$
$313$	1.95587	+	1.12922i	0.110552	+	0.0638273i	−0.443704	+	0.896173i	$0.646336\pi$
$314$	−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	−0.951525	−	0.307572i	$-0.900483\pi$
$317$	−3.72820	+	6.45744i	−0.209397	+	0.362686i	0.742128	+	0.670258i	$0.233817\pi$
$318$		0			0
$319$	2.97393	+	5.15099i	0.166508	+	0.288400i
$320$	8.35778	+	15.1421i	0.467214	+	0.846470i
$321$		0			0
$322$	3.71156	+	22.2287i	0.206837	+	1.23875i
$323$	0.306771			0.0170692
$324$		0			0
$325$	0.284017	+	0.491932i	0.0157544	+	0.0272875i
$326$	0.526157	−	5.79957i	0.0291411	−	0.321209i
$327$		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	$-0.546054\pi$
$331$	−19.5260	−	11.2733i	−1.07325	−	0.619639i	−0.929067	+	0.369912i	$0.879388\pi$
$332$	24.3745	+	20.7207i	1.33772	+	1.13719i
$333$		0			0
$334$	7.87375	+	17.0278i	0.430832	+	0.931718i
$335$	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	$0.750358\pi$
$338$	−5.91408	−	12.7898i	−0.321683	−	0.695672i
$339$		0			0
$340$	−1.87079	−	1.59036i	−0.101458	−	0.0862491i
$341$	−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
$346$	2.87543	−	31.6945i	0.154584	−	1.70391i
$347$	7.86526	+	13.6230i	0.422229	+	0.731322i	0.996157	−	0.0875835i	$-0.0279144\pi$
$347$	7.86526	+	13.6230i	0.422229	+	0.731322i	−0.573928	+	0.818906i	$0.694581\pi$
$348$		0			0
$349$	1.79135			0.0958889			0.0479444	−	0.998850i	$-0.484733\pi$
$349$	1.79135			0.0958889			0.0479444	+	0.998850i	$0.484733\pi$
$350$	0.427580	−	1.14236i	0.0228551	−	0.0610617i
$351$		0			0
$352$	17.0093	+	8.26640i	0.906601	+	0.440601i
$353$	13.0108	+	22.5353i	0.692493	+	1.19943i	0.971019	+	0.239004i	$0.0768210\pi$
$353$	13.0108	+	22.5353i	0.692493	+	1.19943i	−0.278526	+	0.960429i	$0.589846\pi$
$354$		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	$-0.483271\pi$
$359$	−14.8932	−	8.59857i	−0.786031	−	0.453815i	−0.838563	+	0.544804i	$0.816604\pi$
$360$		0			0
$361$	9.35409	+	16.2018i	0.492320	+	0.852724i
$362$	−13.2660	−	28.6890i	−0.697244	−	1.50786i
$363$		0			0
$364$	3.99911	−	8.30786i	0.209611	−	0.435450i
$365$	18.8744			0.987933
$366$		0			0
$367$	11.5047	−	6.64226i	0.600542	−	0.346723i	−0.168713	−	0.985665i	$-0.553961\pi$
$367$	11.5047	−	6.64226i	0.600542	−	0.346723i	0.769255	+	0.638942i	$0.220628\pi$
$368$	8.53003	−	22.5318i	0.444658	−	1.17455i
$369$		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	0.967409	+	0.253219i	$0.0814895\pi$
$373$	32.2609	+	18.6259i	1.67041	+	0.964410i	0.702999	+	0.711191i	$0.251844\pi$
$374$	−2.67388	−	0.242583i	−0.138263	−	0.0125437i
$375$		0			0
$376$	2.74404	−	2.69170i	0.141513	−	0.138814i
$377$	−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	$-0.328230\pi$
$380$	−0.420365	+	2.29767i	−0.0215643	+	0.117868i
$381$		0			0
$382$	−0.839788	+	9.25658i	−0.0429673	+	0.473608i
$383$	−10.1288	+	17.5435i	−0.517556	+	0.896433i	0.482236	+	0.876041i	$0.339825\pi$
$383$	−10.1288	+	17.5435i	−0.517556	+	0.896433i	−0.999792	+	0.0203917i	$0.993509\pi$
$384$		0			0
$385$	4.84065	+	18.4999i	0.246702	+	0.942840i
$386$	−6.03551	+	8.56099i	−0.307199	+	0.435743i
$387$		0			0
$388$	24.9924	+	21.2459i	1.26879	+	1.07860i
$389$	9.87868	+	17.1104i	0.500869	+	0.867530i	0.999999	+	0.00100341i	$0.000319396\pi$
$389$	9.87868	+	17.1104i	0.500869	+	0.867530i	−0.499131	+	0.866527i	$0.666347\pi$
$390$		0			0
$391$			3.42036i			0.172975i
$392$	−19.2296	+	4.71426i	−0.971239	+	0.238106i
$393$		0			0
$394$	1.07031	+	2.31466i	0.0539216	+	0.116611i
$395$	−17.8959	+	10.3322i	−0.900442	+	0.519870i
$396$		0			0
$397$	6.15364	−	10.6584i	0.308842	−	0.534930i	−0.669267	−	0.743022i	$-0.733392\pi$
$397$	6.15364	−	10.6584i	0.308842	−	0.534930i	0.978109	+	0.208092i	$0.0667252\pi$
$398$	−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	$-0.00846305\pi$
$401$	29.5658	+	17.0698i	1.47645	+	0.852427i	0.476801	+	0.879011i	$0.341796\pi$
$402$		0			0
$403$	11.4432	−	6.60676i	0.570029	−	0.329106i
$404$	5.59056	−	30.5574i	0.278141	−	1.52029i
$405$		0			0
$406$	4.23243	+	5.13812i	0.210052	+	0.255001i
$407$		−	37.0603i		−	1.83701i
$408$		0			0
$409$	−23.4733	+	13.5523i	−1.16068	+	0.670119i	−0.951467	−	0.307752i	$-0.900423\pi$
$409$	−23.4733	+	13.5523i	−1.16068	+	0.670119i	−0.209213	+	0.977870i	$0.567090\pi$
$410$	2.14700	−	23.6653i	0.106033	−	1.16875i
$411$		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
$416$	−8.16396	+	5.52339i	−0.400271	+	0.270807i
$417$		0			0
$418$	1.07196	+	2.31823i	0.0524314	+	0.113388i
$419$		−	6.84933i		−	0.334612i	−0.985905	−	0.167306i	$-0.946493\pi$
$419$		−	6.84933i		−	0.334612i	0.985905	−	0.167306i	$-0.0535067\pi$
$420$		0			0
$421$			10.8560i			0.529089i	0.964374	+	0.264544i	$0.0852215\pi$
$421$			10.8560i			0.529089i	−0.964374	+	0.264544i	$0.914778\pi$
$422$	−14.6177	+	6.75930i	−0.711577	+	0.329038i
$423$		0			0
$424$	−2.07243	−	8.04338i	−0.100646	−	0.390621i
$425$	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
$430$	−5.48554	−	0.497667i	−0.264536	−	0.0239996i
$431$	−19.5579	+	11.2917i	−0.942069	+	0.543904i	−0.890608	−	0.454771i	$-0.849721\pi$
$431$	−19.5579	+	11.2917i	−0.942069	+	0.543904i	−0.0514606	+	0.998675i	$0.516388\pi$
$432$		0			0
$433$		−	33.9522i		−	1.63164i	−0.578307	−	0.815819i	$-0.696287\pi$
$433$		−	33.9522i		−	1.63164i	0.578307	−	0.815819i	$-0.303713\pi$
$434$	−26.5734	−	9.94631i	−1.27556	−	0.477438i
$435$		0			0
$436$	−2.37931	+	13.0051i	−0.113948	+	0.622830i
$437$	2.81783	−	1.62687i	0.134795	−	0.0778239i
$438$		0			0
$439$	−21.4344	−	12.3752i	−1.02301	−	0.590634i	−0.108034	−	0.994147i	$-0.534456\pi$
$439$	−21.4344	−	12.3752i	−1.02301	−	0.590634i	−0.914974	+	0.403513i	$0.867789\pi$
$440$	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	−0.558573	−	0.829455i	$-0.688651\pi$
$443$	9.24079	−	16.0055i	0.439043	−	0.760445i	0.997616	+	0.0690105i	$0.0219842\pi$
$444$		0			0
$445$	23.6258	−	13.6404i	1.11997	−	0.646615i
$446$	−6.29020	+	2.90863i	−0.297850	+	0.137728i
$447$		0			0
$448$	20.3007	+	5.99023i	0.959116	+	0.283012i
$449$			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
$452$	−6.58530	−	5.59814i	−0.309747	−	0.263314i
$453$		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	0.367644	+	0.929967i	$0.380165\pi$
$457$	−13.2873	+	23.0142i	−0.621553	+	1.07656i	−0.989197	+	0.146594i	$0.953169\pi$
$458$	−4.50458	−	0.408671i	−0.210485	−	0.0190959i
$459$		0			0
$460$	−25.6180	−	4.68688i	−1.19445	−	0.218527i
$461$			1.26742i			0.0590294i	0.999564	+	0.0295147i	$0.00939619\pi$
$461$			1.26742i			0.0590294i	−0.999564	+	0.0295147i	$0.990604\pi$
$462$		0			0
$463$	9.82295			0.456511			0.228256	−	0.973601i	$-0.426698\pi$
$463$	9.82295			0.456511			0.228256	+	0.973601i	$0.426698\pi$
$464$	−1.14570	−	7.02365i	−0.0531877	−	0.326065i
$465$		0			0
$466$	0.495467	−	5.46129i	0.0229521	−	0.252989i
$467$	18.5816	+	10.7281i	0.859855	+	0.496438i	0.863964	−	0.503554i	$-0.167975\pi$
$467$	18.5816	+	10.7281i	0.859855	+	0.496438i	−0.00410868	+	0.999992i	$0.501308\pi$
$468$		0			0
$469$	23.3724	−	23.0992i	1.07924	−	1.06662i
$470$	−3.39597	−	2.39416i	−0.156644	−	0.110434i
$471$		0			0
$472$	−31.1450	+	8.02472i	−1.43357	+	0.369368i
$473$	−5.21585	+	3.01137i	−0.239825	+	0.138463i
$474$		0			0
$475$	−0.176105			−0.00808027
$476$	−2.99646	+	0.225066i	−0.137343	+	0.0103159i
$477$		0			0
$478$	28.4236	−	13.1432i	1.30006	−	0.601158i
$479$	13.5560	+	23.4798i	0.619391	+	1.07282i	0.989597	+	0.143867i	$0.0459539\pi$
$479$	13.5560	+	23.4798i	0.619391	+	1.07282i	−0.370206	+	0.928950i	$0.620713\pi$
$480$		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	0.943250	−	0.332083i	$-0.107751\pi$
$487$	4.06126	+	7.03430i	0.184033	+	0.318755i	−0.759217	+	0.650837i	$0.774418\pi$
$488$	−22.6492	+	22.2173i	−1.02528	+	1.00573i
$489$		0			0
$490$	8.75366	+	19.5301i	0.395450	+	0.882281i
$491$	−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
$494$	−1.32575	−	0.120277i	−0.0596485	−	0.00541151i
$495$		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	$-0.193777\pi$
$499$	16.4251	+	9.48302i	0.735287	+	0.424518i	−0.0850663	+	0.996375i	$0.527110\pi$
$500$	17.5459	+	14.9157i	0.784675	+	0.667050i
$501$		0			0
$502$	12.3070	−	5.69086i	0.549290	−	0.253995i
$503$	−24.6249			−1.09797			−0.548985	−	0.835832i	$-0.684985\pi$
$503$	−24.6249			−1.09797			−0.548985	+	0.835832i	$0.684985\pi$
$504$		0			0
$505$	−33.5800			−1.49429
$506$	−25.8472	+	11.9519i	−1.14905	+	0.531327i
$507$		0			0
$508$	−9.02851	+	10.6206i	−0.400575	+	0.471211i
$509$	7.66857	+	4.42745i	0.339904	+	0.196243i	0.660229	−	0.751064i	$-0.270459\pi$
$509$	7.66857	+	4.42745i	0.339904	+	0.196243i	−0.320326	+	0.947307i	$0.603792\pi$
$510$		0			0
$511$	16.4286	−	16.2366i	0.726759	−	0.718265i
$512$	−15.5313	−	16.4554i	−0.686391	−	0.727232i
$513$		0			0
$514$	−12.2005	−	1.10687i	−0.538140	−	0.0488219i
$515$	−5.85756	−	10.1456i	−0.258115	−	0.447068i
$516$		0			0
$517$	−4.54332			−0.199815
$518$	−6.83108	−	40.9116i	−0.300141	−	1.79755i
$519$		0			0
$520$	7.46135	+	7.60643i	0.327202	+	0.333564i
$521$	−12.0185	−	20.8167i	−0.526540	−	0.911995i	−0.999522	−	0.0309222i	$-0.990156\pi$
$521$	−12.0185	−	20.8167i	−0.526540	−	0.911995i	0.472981	−	0.881072i	$-0.343178\pi$
$522$		0			0
$523$	−1.89548	+	3.28306i	−0.0828835	+	0.143558i	−0.904487	−	0.426500i	$-0.859746\pi$
$523$	−1.89548	+	3.28306i	−0.0828835	+	0.143558i	0.821604	+	0.570059i	$0.193080\pi$
$524$	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
$530$	−8.14955	+	3.76841i	−0.353994	+	0.163689i
$531$		0			0
$532$	1.61067	+	2.36155i	0.0698313	+	0.102386i
$533$	13.5425			0.586589
$534$		0			0
$535$	−6.96430	+	4.02084i	−0.301093	+	0.173836i
$536$	−34.0188	+	8.76516i	−1.46939	+	0.378597i
$537$		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	$-0.467614\pi$
$541$	−16.4954	−	9.52363i	−0.709193	−	0.409453i	−0.810762	+	0.585376i	$0.800947\pi$
$542$	2.67531	−	29.4887i	0.114915	−	1.26665i
$543$		0			0
$544$	2.88924	+	1.40415i	0.123875	+	0.0602024i
$545$	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	$-0.454858\pi$
$548$	6.03701	−	32.9977i	0.257888	−	1.40959i
$549$		0			0
$550$	1.53497	+	0.139257i	0.0654513	+	0.00593796i
$551$	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
$556$	−13.3824	+	15.7422i	−0.567539	+	0.667617i
$557$	11.1463	+	19.3059i	0.472283	+	0.818019i	0.999497	−	0.0317140i	$-0.0100966\pi$
$557$	11.1463	+	19.3059i	0.472283	+	0.818019i	−0.527214	+	0.849733i	$0.676763\pi$
$558$		0			0
$559$		−	3.13910i		−	0.132770i
$560$	2.42031	−	22.7515i	0.102277	−	0.961426i
$561$		0			0
$562$	10.1841	−	4.70919i	0.429590	−	0.198645i
$563$	−2.42370	+	1.39932i	−0.102147	+	0.0589745i	−0.550203	−	0.835031i	$-0.685450\pi$
$563$	−2.42370	+	1.39932i	−0.102147	+	0.0589745i	0.448056	+	0.894005i	$0.352116\pi$
$564$		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	$-0.665411\pi$
$569$	−35.6988	−	20.6107i	−1.49657	−	0.864046i	−0.999992	+	0.00394571i	$0.998744\pi$
$570$		0			0
$571$	−24.3886	+	14.0808i	−1.02063	+	0.589262i	−0.914287	−	0.405068i	$-0.867248\pi$
$571$	−24.3886	+	14.0808i	−1.02063	+	0.589262i	−0.106345	+	0.994329i	$0.533915\pi$
$572$	11.4604	+	2.09671i	0.479184	+	0.0876679i
$573$		0			0
$574$	−18.4892	−	22.4457i	−0.771723	−	0.936863i
$575$		−	1.96350i		−	0.0818834i
$576$		0			0
$577$	8.23601	−	4.75506i	0.342870	−	0.197956i	−0.318671	−	0.947866i	$-0.603236\pi$
$577$	8.23601	−	4.75506i	0.342870	−	0.197956i	0.661540	+	0.749910i	$0.269903\pi$
$578$	23.4891	+	2.13101i	0.977018	+	0.0886384i
$579$		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
$584$	−23.9120	+	6.16110i	−0.989488	+	0.254948i
$585$		0			0
$586$	−5.58241	+	2.58134i	−0.230607	+	0.106634i
$587$		−	6.47220i		−	0.267136i	−0.991040	−	0.133568i	$-0.957357\pi$
$587$		−	6.47220i		−	0.267136i	0.991040	−	0.133568i	$-0.0426435\pi$
$588$		0			0
$589$			4.09654i			0.168795i
$590$	14.5918	+	31.5561i	0.600733	+	1.29915i
$591$		0			0
$592$	−15.6994	+	41.4696i	−0.645242	+	1.70439i
$593$	14.5174	−	25.1449i	0.596159	−	1.03258i	−0.397224	−	0.917722i	$-0.630026\pi$
$593$	14.5174	−	25.1449i	0.596159	−	1.03258i	0.993382	−	0.114855i	$-0.0366404\pi$
$594$		0			0
$595$	0.822243	+	3.14243i	0.0337087	+	0.128827i
$596$	−2.83113	−	7.93660i	−0.115968	−	0.325096i
$597$		0			0
$598$	1.34103	−	14.7816i	0.0548389	−	0.604463i
$599$	−4.06979	+	2.34969i	−0.166287	+	0.0960058i	−0.580834	−	0.814022i	$-0.697273\pi$
$599$	−4.06979	+	2.34969i	−0.166287	+	0.0960058i	0.414547	+	0.910028i	$0.363940\pi$
$600$		0			0
$601$		−	20.3259i		−	0.829111i	−0.910024	−	0.414555i	$-0.863937\pi$
$601$		−	20.3259i		−	0.829111i	0.910024	−	0.414555i	$-0.136063\pi$
$602$	−5.20282	+	4.28573i	−0.212051	+	0.174673i
$603$		0			0
$604$	12.2169	+	2.23512i	0.497100	+	0.0909458i
$605$	−0.330641	+	0.190896i	−0.0134425	+	0.00776102i
$606$		0			0
$607$	26.3222	+	15.1971i	1.06838	+	0.616832i	0.927740	−	0.373228i	$-0.121749\pi$
$607$	26.3222	+	15.1971i	1.06838	+	0.616832i	0.140645	+	0.990060i	$0.455082\pi$
$608$	−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	$-0.473123\pi$
$613$	24.4975	−	14.1436i	0.989444	−	0.571256i	0.905108	+	0.425182i	$0.139790\pi$
$614$	−2.85671	−	6.17792i	−0.115287	−	0.249320i
$615$		0			0
$616$	−12.1715	−	21.8574i	−0.490402	−	0.880659i
$617$			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	$-0.0259388\pi$
$619$	10.6447	+	18.4372i	0.427847	+	0.741053i	−0.568834	+	0.822452i	$0.692605\pi$
$620$	21.2372	−	24.9821i	0.852905	−	1.00330i
$621$		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
$626$	−0.288578	+	3.18085i	−0.0115339	+	0.127133i
$627$		0			0
$628$	−40.6098	−	7.42966i	−1.62051	−	0.296476i
$629$		−	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	$0.447077\pi$
$632$	19.2997	−	18.9316i	0.767700	−	0.753058i
$633$		0			0
$634$	−10.5018	−	0.952760i	−0.417081	−	0.0378390i
$635$	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
$640$	−14.4760	+	19.7159i	−0.572213	+	0.779341i
$641$	−4.98896	+	2.88038i	−0.197052	+	0.113768i	−0.595280	−	0.803519i	$-0.702959\pi$
$641$	−4.98896	+	2.88038i	−0.197052	+	0.113768i	0.398228	+	0.917287i	$0.369625\pi$
$642$		0			0
$643$	18.7692			0.740184			0.370092	−	0.928995i	$-0.379326\pi$
$643$	18.7692			0.740184			0.370092	+	0.928995i	$0.379326\pi$
$644$	−26.3302	+	17.9582i	−1.03756	+	0.707652i
$645$		0			0
$646$	0.182086	+	0.393779i	0.00716408	+	0.0154930i
$647$	0.705648	+	1.22222i	0.0277419	+	0.0480503i	0.879563	−	0.475782i	$-0.157835\pi$
$647$	0.705648	+	1.22222i	0.0277419	+	0.0480503i	−0.851821	+	0.523833i	$0.824502\pi$
$648$		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	−0.922056	−	0.387057i	$-0.873492\pi$
$653$	−3.21537	+	5.56919i	−0.125827	+	0.217939i	0.796229	+	0.604996i	$0.206825\pi$
$654$		0			0
$655$	−9.51855	−	16.4866i	−0.371920	−	0.644185i
$656$	5.00493	+	30.6825i	0.195410	+	1.19795i
$657$		0			0
$658$	−5.01547	+	0.837442i	−0.195523	+	0.0326469i
$659$	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	−0.999014	−	0.0443993i	$-0.985863\pi$
$661$	−13.8309	−	23.9557i	−0.537958	−	0.931770i	0.461056	−	0.887371i	$-0.347471\pi$
$662$	2.88096	−	31.7554i	0.111972	−	1.23421i
$663$		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
$668$	−17.1837	+	20.2139i	−0.664859	+	0.782098i
$669$		0			0
$670$	15.9381	+	34.4678i	0.615744	+	1.33161i
$671$	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	$0.394955\pi$
$674$	−15.4269	−	33.3622i	−0.594223	−	1.28507i
$675$		0			0
$676$	12.9069	−	15.1829i	0.496421	−	0.583958i
$677$	33.3325	+	19.2445i	1.28107	+	0.739626i	0.977044	−	0.213037i	$-0.0683356\pi$
$677$	33.3325	+	19.2445i	1.28107	+	0.739626i	0.304026	+	0.952664i	$0.401669\pi$
$678$		0			0
$679$	−10.9845	−	41.9804i	−0.421548	−	1.61106i
$680$	0.930998	−	3.34536i	0.0357021	−	0.128289i
$681$		0			0
$682$	3.23939	−	35.7062i	0.124043	−	1.36726i
$683$	16.8564	+	29.1961i	0.644991	+	1.11716i	0.984304	+	0.176483i	$0.0564722\pi$
$683$	16.8564	+	29.1961i	0.644991	+	1.11716i	−0.339313	+	0.940674i	$0.610194\pi$
$684$		0			0
$685$	−36.2616			−1.38549
$686$	24.4200	+	9.46908i	0.932360	+	0.361531i
$687$		0			0
$688$	7.11210	−	1.16013i	0.271146	−	0.0442294i
$689$	−2.55850	−	4.43146i	−0.0974712	−	0.168825i
$690$		0			0
$691$	−16.3070	+	28.2445i	−0.620346	+	1.07447i	0.369075	+	0.929400i	$0.379675\pi$
$691$	−16.3070	+	28.2445i	−0.620346	+	1.07447i	−0.989421	+	0.145072i	$0.953659\pi$
$692$	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
$698$	1.06327	+	2.29942i	0.0402453	+	0.0870344i
$699$		0			0
$700$	1.72015	−	0.129202i	0.0650157	−	0.00488337i
$701$	−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
$704$	−0.514954	+	26.7402i	−0.0194081	+	1.00781i
$705$		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	$-0.331415\pi$
$709$	0.277961	+	0.160481i	0.0104390	+	0.00602697i	−0.494771	+	0.869023i	$0.664748\pi$
$710$	−23.7431	−	2.15405i	−0.891062	−	0.0808401i
$711$		0			0
$712$	−25.4790	+	24.9931i	−0.954866	+	0.936654i
$713$	−45.6745			−1.71053
$714$		0			0
$715$		−	12.5940i		−	0.470989i
$716$	−37.9215	−	6.93784i	−1.41719	−	0.259279i
$717$		0			0
$718$	2.19741	−	24.2210i	0.0820065	−	0.903918i
$719$	−6.95557	+	12.0474i	−0.259399	+	0.449292i	−0.966081	−	0.258239i	$-0.916858\pi$
$719$	−6.95557	+	12.0474i	−0.259399	+	0.449292i	0.706682	+	0.707531i	$0.250191\pi$
$720$		0			0
$721$	−13.8262	−	3.79196i	−0.514914	−	0.141220i
$722$	−15.2448	+	21.6238i	−0.567352	+	0.804754i
$723$		0			0
$724$	28.9518	−	34.0570i	1.07598	−	1.26572i
$725$	−0.289991	−	0.502280i	−0.0107700	−	0.0186542i
$726$		0			0
$727$			42.1216i			1.56220i	0.624403	+	0.781102i	$0.285342\pi$
$727$			42.1216i			1.56220i	−0.624403	+	0.781102i	$0.714658\pi$
$728$	13.0379	+	0.202179i	0.483216	+	0.00749326i
$729$		0			0
$730$	11.2030	+	24.2277i	0.414643	+	0.896706i
$731$	−0.885977	+	0.511519i	−0.0327690	+	0.0189192i
$732$		0			0
$733$	−4.20815	+	7.28873i	−0.155432	+	0.269215i	−0.933216	−	0.359316i	$-0.883010\pi$
$733$	−4.20815	+	7.28873i	−0.155432	+	0.269215i	0.777785	+	0.628531i	$0.216343\pi$
$734$	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	$-0.681236\pi$
$739$	−2.15443	+	1.24386i	−0.0792519	+	0.0457561i	0.459850	+	0.887996i	$0.347903\pi$
$740$	47.1497	+	8.62616i	1.73326	+	0.317104i
$741$		0			0
$742$	−3.85176	+	10.2907i	−0.141403	+	0.377783i
$743$			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
$746$	−4.75993	+	52.4664i	−0.174273	+	1.92093i
$747$		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	0.420175	+	0.907443i	$0.361969\pi$
$751$	−15.7789	+	27.3299i	−0.575781	+	0.997282i	−0.995956	+	0.0898389i	$0.971365\pi$
$752$	5.08387	+	1.92464i	0.185390	+	0.0701843i
$753$		0			0
$754$	−1.84006	−	3.97931i	−0.0670110	−	0.144918i
$755$		−	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	$0.765975\pi$
$758$	42.8769	−	19.8265i	1.55736	−	0.720132i
$759$		0			0
$760$	−3.19886	+	0.824208i	−0.116035	+	0.0298972i
$761$	9.14893	−	15.8464i	0.331648	−	0.574432i	−0.651187	−	0.758917i	$-0.725729\pi$
$761$	9.14893	−	15.8464i	0.331648	−	0.574432i	0.982835	+	0.184486i	$0.0590619\pi$
$762$		0			0
$763$	12.4395	−	12.2941i	0.450341	−	0.445078i
$764$	−12.3804	+	4.41633i	−0.447908	+	0.159777i
$765$		0			0
$766$	−28.5313	−	2.58846i	−1.03088	−	0.0935247i
$767$	−17.1592	+	9.90686i	−0.619582	+	0.357716i
$768$		0			0
$769$		−	5.09495i		−	0.183729i	−0.995772	−	0.0918644i	$-0.970717\pi$
$769$		−	5.09495i		−	0.183729i	0.995772	−	0.0918644i	$-0.0292826\pi$
$770$	−20.8737	+	17.1943i	−0.752234	+	0.619639i
$771$		0			0
$772$	−14.5715	−	2.66590i	−0.524440	−	0.0959477i
$773$	−27.0448	+	15.6143i	−0.972735	+	0.561609i	−0.900069	−	0.435748i	$-0.856484\pi$
$773$	−27.0448	+	15.6143i	−0.972735	+	0.561609i	−0.0726659	+	0.997356i	$0.523151\pi$
$774$		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
$782$	−4.39046	+	2.03018i	−0.157002	+	0.0725990i
$783$		0			0
$784$	−17.4652	−	21.8853i	−0.623756	−	0.781619i
$785$			44.6267i			1.59279i
$786$		0			0
$787$	−9.96558	−	17.2609i	−0.355235	−	0.615284i	0.631923	−	0.775031i	$-0.282266\pi$
$787$	−9.96558	−	17.2609i	−0.355235	−	0.615284i	−0.987158	+	0.159746i	$0.948932\pi$
$788$	−2.33586	+	2.74776i	−0.0832116	+	0.0978849i
$789$		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
$794$	17.3339	+	1.57259i	0.615158	+	0.0558092i
$795$		0			0
$796$	3.21155	−	17.5540i	0.113831	−	0.622186i
$797$			46.5551i			1.64907i	0.565813	+	0.824534i	$0.308562\pi$
$797$			46.5551i			1.64907i	−0.565813	+	0.824534i	$0.691438\pi$
$798$		0			0
$799$	−0.771739			−0.0273022
$800$	−1.65860	−	0.806067i	−0.0586405	−	0.0284988i
$801$		0			0
$802$	−4.36228	+	48.0833i	−0.154037	+	1.69788i
$803$	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
$808$	42.5426	−	10.9614i	1.49664	−	0.385620i
$809$	35.1771	−	20.3095i	1.23676	−	0.714045i	0.268331	−	0.963327i	$-0.413528\pi$
$809$	35.1771	−	20.3095i	1.23676	−	0.714045i	0.968431	+	0.249282i	$0.0801946\pi$
$810$		0			0
$811$	−43.3104			−1.52083			−0.760417	−	0.649435i	$-0.775005\pi$
$811$	−43.3104			−1.52083			−0.760417	+	0.649435i	$0.775005\pi$
$812$	−4.08323	+	8.48261i	−0.143293	+	0.297681i
$813$		0			0
$814$	47.5714	−	21.9973i	1.66738	−	0.771006i
$815$	−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	−0.886428	−	0.462866i	$-0.846821\pi$
$821$	−1.21375	+	2.10228i	−0.0423602	+	0.0733699i	0.844068	+	0.536236i	$0.180154\pi$
$822$		0			0
$823$	−8.90145	−	15.4178i	−0.310285	−	0.537429i	0.668139	−	0.744036i	$-0.267091\pi$
$823$	−8.90145	−	15.4178i	−0.310285	−	0.537429i	−0.978424	+	0.206607i	$0.933758\pi$
$824$	10.7327	+	10.9414i	0.373892	+	0.381162i
$825$		0			0
$826$	39.8469	+	14.9145i	1.38645	+	0.518943i
$827$	−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	−0.950346	−	0.311194i	$-0.899271\pi$
$829$	−21.4409	−	37.1368i	−0.744675	−	1.28981i	0.205672	−	0.978621i	$-0.434062\pi$
$830$	48.7063	+	4.41880i	1.69062	+	0.153379i
$831$		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
$836$	−2.33946	+	2.75200i	−0.0809120	+	0.0951797i
$837$		0			0
$838$	8.79196	−	4.06546i	0.303713	−	0.140439i
$839$	4.03008			0.139134			0.0695668	−	0.997577i	$-0.477838\pi$
$839$	4.03008			0.139134			0.0695668	+	0.997577i	$0.477838\pi$
$840$		0			0
$841$	−25.8347			−0.890853
$842$	−13.9350	+	6.44364i	−0.480232	+	0.222062i
$843$		0			0
$844$	−17.3528	−	14.7516i	−0.597309	−	0.507770i
$845$	−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
$850$	0.260733	+	0.0236546i	0.00894307	+	0.000811346i
$851$	−33.3844	−	57.8235i	−1.14440	−	1.98217i
$852$		0			0
$853$	−1.89394			−0.0648474			−0.0324237	−	0.999474i	$-0.510323\pi$
$853$	−1.89394			−0.0648474			−0.0324237	+	0.999474i	$0.510323\pi$
$854$	41.3976	−	6.91224i	1.41660	−	0.236532i
$855$		0			0
$856$	7.51058	−	7.36734i	0.256706	−	0.251810i
$857$	−10.3144	−	17.8650i	−0.352333	−	0.610258i	0.634325	−	0.773066i	$-0.281278\pi$
$857$	−10.3144	−	17.8650i	−0.352333	−	0.610258i	−0.986658	+	0.162808i	$0.947945\pi$
$858$		0			0
$859$	−25.2260	+	43.6928i	−0.860701	+	1.49078i	0.0105526	+	0.999944i	$0.496641\pi$
$859$	−25.2260	+	43.6928i	−0.860701	+	1.49078i	−0.871253	+	0.490833i	$0.836692\pi$
$860$	−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	$-0.321121\pi$
$863$	1.95161	+	1.12676i	0.0664336	+	0.0383554i	−0.466415	+	0.884566i	$0.654455\pi$
$864$		0			0
$865$	−24.3256	−	42.1332i	−0.827095	−	1.43257i
$866$	43.5819	−	20.1525i	1.48097	−	0.684811i
$867$		0			0
$868$	−3.00547	−	40.0139i	−0.102012	−	1.35816i
$869$	−31.9546			−1.08399
$870$		0			0
$871$	−18.7425	+	10.8210i	−0.635064	+	0.366654i
$872$	−18.1059	+	4.66510i	−0.613143	+	0.157980i
$873$		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	$-0.187237\pi$
$877$	22.7244	+	13.1200i	0.767350	+	0.443029i	−0.0645788	+	0.997913i	$0.520570\pi$
$878$	3.16253	−	34.8591i	0.106730	−	1.17644i
$879$		0			0
$880$	28.5336	−	4.65441i	0.961869	−	0.156900i
$881$	13.9743			0.470804			0.235402	−	0.971898i	$-0.424359\pi$
$881$	13.9743			0.470804			0.235402	+	0.971898i	$0.424359\pi$
$882$		0			0
$883$			40.0650i			1.34830i	0.738596	+	0.674148i	$0.235489\pi$
$883$			40.0650i			1.34830i	−0.738596	+	0.674148i	$0.764511\pi$
$884$	1.94669	+	0.356152i	0.0654743	+	0.0119787i
$885$		0			0
$886$	26.0300	+	2.36153i	0.874495	+	0.0793371i
$887$	22.9798	−	39.8022i	0.771586	−	1.33643i	−0.165108	−	0.986275i	$-0.552797\pi$
$887$	22.9798	−	39.8022i	0.771586	−	1.33643i	0.936694	−	0.350150i	$-0.113869\pi$
$888$		0			0
$889$	17.8397	−	4.66791i	0.598323	−	0.156557i
$890$	31.5323	+	22.2303i	1.05697	+	0.745162i
$891$		0			0
$892$	−7.46718	−	6.34782i	−0.250020	−	0.212541i
$893$	0.367073	+	0.635788i	0.0122836	+	0.0212758i
$894$		0			0
$895$			41.6725i			1.39296i
$896$	4.36038	+	29.6140i	0.145670	+	0.989333i
$897$		0			0
$898$	−39.1362	+	18.0968i	−1.30599	+	0.603899i
$899$	−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	$-0.717673\pi$
$907$	−8.32291	+	4.80524i	−0.276358	+	0.159555i	0.355416	+	0.934708i	$0.384339\pi$
$908$	7.67159	−	41.9321i	0.254591	−	1.39157i
$909$		0			0
$910$	−2.32138	−	13.9028i	−0.0769528	−	0.460873i
$911$		−	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
$914$	−37.4284	−	3.39563i	−1.23802	−	0.112317i
$915$		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	−0.985237	−	0.171198i	$-0.945236\pi$
$919$	−10.4392	+	18.0812i	−0.344357	+	0.596444i	0.640880	+	0.767641i	$0.278570\pi$
$920$	−9.18954	−	35.6659i	−0.302970	−	1.17587i
$921$		0			0
$922$	−1.62688	+	0.752282i	−0.0535786	+	0.0247751i
$923$		−	13.5870i		−	0.447220i
$924$		0			0
$925$			3.61379i			0.118821i
$926$	5.83047	+	12.6090i	0.191601	+	0.414357i
$927$		0			0
$928$	8.33569	−	5.63958i	0.273632	−	0.185128i
$929$	19.3495	−	33.5143i	0.634837	−	1.09957i	−0.351713	−	0.936108i	$-0.614401\pi$
$929$	19.3495	−	33.5143i	0.634837	−	1.09957i	0.986550	−	0.163462i	$-0.0522660\pi$
$930$		0			0
$931$	0.0444554	−	3.78121i	0.00145697	−	0.123924i
$932$	7.30433	−	2.60559i	0.239261	−	0.0853489i
$933$		0			0
$934$	−2.74162	+	30.2196i	−0.0897085	+	0.988814i
$935$	−3.55453	+	2.05221i	−0.116245	+	0.0671143i
$936$		0			0
$937$		−	2.23597i		−	0.0730458i	−0.999333	−	0.0365229i	$-0.988372\pi$
$937$		−	2.23597i		−	0.0730458i	0.999333	−	0.0365229i	$-0.0116282\pi$
$938$	43.5235	+	16.2907i	1.42109	+	0.531910i
$939$		0			0
$940$	1.05751	−	5.78022i	0.0344920	−	0.188530i
$941$	8.23966	−	4.75717i	0.268605	−	0.155079i	−0.359648	−	0.933088i	$-0.617103\pi$
$941$	8.23966	−	4.75717i	0.268605	−	0.155079i	0.628254	+	0.778009i	$0.283770\pi$
$942$		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	−0.359605	−	0.933105i	$-0.617088\pi$
$947$	19.3346	−	33.4885i	0.628290	−	1.08823i	0.987895	−	0.155126i	$-0.0495782\pi$
$948$		0			0
$949$	−13.1742	+	7.60613i	−0.427653	+	0.246906i
$950$	−0.104528	−	0.226053i	−0.00339135	−	0.00733413i
$951$		0			0
$952$	−2.06747	−	3.71274i	−0.0670071	−	0.120331i
$953$		−	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
$956$	33.7420	+	28.6839i	1.09129	+	0.927705i
$957$		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
$962$	−2.46816	+	27.2053i	−0.0795765	+	0.877134i
$963$		0			0
$964$	−2.59091	+	14.1617i	−0.0834477	+	0.456117i
$965$			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	$0.163168\pi$
$968$	0.356577	−	0.349776i	0.0114608	−	0.0112422i
$969$		0			0
$970$	49.9410	+	4.53082i	1.60351	+	0.145476i
$971$	−5.92025	−	3.41806i	−0.189990	−	0.109691i	0.401988	−	0.915645i	$-0.368319\pi$
$971$	−5.92025	−	3.41806i	−0.189990	−	0.109691i	−0.591978	+	0.805954i	$0.701653\pi$
$972$		0			0
$973$	26.4426	−	6.91893i	0.847710	−	0.221811i
$974$	−6.61882	+	9.38838i	−0.212081	+	0.300823i
$975$		0			0
$976$	−41.9622	−	15.8859i	−1.34318	−	0.508496i
$977$	−19.1650	+	11.0649i	−0.613144	+	0.353999i	−0.774195	−	0.632947i	$-0.781845\pi$
$977$	−19.1650	+	11.0649i	−0.613144	+	0.353999i	0.161051	+	0.986946i	$0.448512\pi$
$978$		0			0
$979$	42.1858			1.34826
$980$	−19.8736	+	22.8286i	−0.634838	+	0.729234i
$981$		0			0
$982$	−3.63002	−	7.85028i	−0.115839	−	0.250513i
$983$	3.18986	+	5.52499i	0.101741	+	0.176220i	0.912402	−	0.409296i	$-0.134225\pi$
$983$	3.18986	+	5.52499i	0.101741	+	0.176220i	−0.810661	+	0.585515i	$0.800892\pi$
$984$		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	0.939976	−	0.341241i	$-0.110847\pi$
$991$	5.49218	+	9.51273i	0.174465	+	0.302182i	−0.765511	+	0.643423i	$0.777514\pi$
$992$	−18.7506	+	38.5822i	−0.595333	+	1.22498i
$993$		0			0
$994$	−22.5194	+	18.5499i	−0.714271	+	0.588367i
$995$	−19.2904			−0.611546
$996$		0			0
$997$	−3.65692	−	6.33397i	−0.115816	−	0.200599i	0.802290	−	0.596935i	$-0.203615\pi$
$997$	−3.65692	−	6.33397i	−0.115816	−	0.200599i	−0.918106	+	0.396336i	$0.870282\pi$
$998$	−2.42343	+	26.7123i	−0.0767124	+	0.845563i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.ch.b.341.19	yes	56
3.2	odd	2	inner	504.2.ch.b.341.10	yes	56
4.3	odd	2		2016.2.cp.b.593.24		56
7.3	odd	6	inner	504.2.ch.b.269.2	✓	56
8.3	odd	2		2016.2.cp.b.593.5		56
8.5	even	2	inner	504.2.ch.b.341.27	yes	56
12.11	even	2		2016.2.cp.b.593.6		56
21.17	even	6	inner	504.2.ch.b.269.27	yes	56
24.5	odd	2	inner	504.2.ch.b.341.2	yes	56
24.11	even	2		2016.2.cp.b.593.23		56
28.3	even	6		2016.2.cp.b.17.23		56
56.3	even	6		2016.2.cp.b.17.6		56
56.45	odd	6	inner	504.2.ch.b.269.10	yes	56
84.59	odd	6		2016.2.cp.b.17.5		56
168.59	odd	6		2016.2.cp.b.17.24		56
168.101	even	6	inner	504.2.ch.b.269.19	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.ch.b.269.2	✓	56	7.3	odd	6	inner
504.2.ch.b.269.10	yes	56	56.45	odd	6	inner
504.2.ch.b.269.19	yes	56	168.101	even	6	inner
504.2.ch.b.269.27	yes	56	21.17	even	6	inner
504.2.ch.b.341.2	yes	56	24.5	odd	2	inner
504.2.ch.b.341.10	yes	56	3.2	odd	2	inner
504.2.ch.b.341.19	yes	56	1.1	even	1	trivial
504.2.ch.b.341.27	yes	56	8.5	even	2	inner
2016.2.cp.b.17.5		56	84.59	odd	6
2016.2.cp.b.17.6		56	56.3	even	6
2016.2.cp.b.17.23		56	28.3	even	6
2016.2.cp.b.17.24		56	168.59	odd	6
2016.2.cp.b.593.5		56	8.3	odd	2
2016.2.cp.b.593.6		56	12.11	even	2
2016.2.cp.b.593.23		56	24.11	even	2
2016.2.cp.b.593.24		56	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.593556 + 1.28362i) q^{2} +(-1.29538 + 1.52381i) q^{4} +(1.87230 + 1.08097i) q^{5} +(2.55958 - 0.669737i) q^{7} +(-2.72488 - 0.758320i) q^{8} +O(q^{10})\)	\(q+(0.593556 + 1.28362i) q^{2} +(-1.29538 + 1.52381i) q^{4} +(1.87230 + 1.08097i) q^{5} +(2.55958 - 0.669737i) q^{7} +(-2.72488 - 0.758320i) q^{8} +(-0.276248 + 3.04495i) q^{10} +(1.67157 + 2.89525i) q^{11} -1.74247 q^{13} +(2.37895 + 2.88801i) q^{14} +(-0.643969 - 3.94782i) q^{16} +(0.283937 + 0.491793i) q^{17} +(0.270105 - 0.467836i) q^{19} +(-4.07254 + 1.45275i) q^{20} +(-2.72424 + 3.86416i) q^{22} +(5.21616 + 3.01155i) q^{23} +(-0.162997 - 0.282319i) q^{25} +(-1.03425 - 2.23667i) q^{26} +(-2.29509 + 4.76787i) q^{28} +1.77912 q^{29} +(-6.56726 + 3.79161i) q^{31} +(4.68529 - 3.16987i) q^{32} +(-0.462745 + 0.656375i) q^{34} +(5.51627 + 1.51289i) q^{35} +(-9.60029 - 5.54273i) q^{37} +(0.760849 + 0.0690267i) q^{38} +(-4.28206 - 4.36532i) q^{40} -7.77201 q^{41} +1.80152i q^{43} +(-6.57712 - 1.20330i) q^{44} +(-0.769617 + 8.48312i) q^{46} +(-0.679499 + 1.17693i) q^{47} +(6.10291 - 3.42849i) q^{49} +(0.265644 - 0.376799i) q^{50} +(2.25716 - 2.65518i) q^{52} +(1.46832 + 2.54321i) q^{53} +7.22769i q^{55} +(-7.48242 - 0.116030i) q^{56} +(1.05601 + 2.28372i) q^{58} +(9.84763 - 5.68553i) q^{59} +(5.60858 - 9.71434i) q^{61} +(-8.76504 - 6.17936i) q^{62} +(6.84990 + 4.13265i) q^{64} +(-3.26242 - 1.88356i) q^{65} +(10.7563 - 6.21014i) q^{67} +(-1.11720 - 0.204395i) q^{68} +(1.33223 + 7.97880i) q^{70} +7.79753i q^{71} +(7.56066 - 4.36515i) q^{73} +(1.41647 - 15.6131i) q^{74} +(0.363002 + 1.01761i) q^{76} +(6.21757 + 6.29110i) q^{77} +(-4.77913 + 8.27770i) q^{79} +(3.06178 - 8.08762i) q^{80} +(-4.61312 - 9.97633i) q^{82} -15.9958i q^{83} +1.22771i q^{85} +(-2.31248 + 1.06931i) q^{86} +(-2.35930 - 9.15677i) q^{88} +(6.30930 - 10.9280i) q^{89} +(-4.45999 + 1.16699i) q^{91} +(-11.3459 + 4.04731i) q^{92} +(-1.91405 - 0.173649i) q^{94} +(1.01144 - 0.583953i) q^{95} -16.4013i q^{97} +(8.02331 + 5.79884i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{4} - 20 q^{7}+O(q^{10}) \) 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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