LMFDB - Embedded newform 756.2.bo.a.169.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(85,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 2, 0]))

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

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

chi := DirichletCharacter("756.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bo (of order $9$, degree $6$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$54$
Relative dimension:	$9$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			169.6
Character	$\chi$	$=$	756.169
Dual form			756.2.bo.a.85.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.195914 - 1.72094i) q^{3} +(0.348691 + 1.97752i) q^{5} +(0.766044 + 0.642788i) q^{7} +(-2.92324 + 0.674312i) q^{9} +O(q^{10})$	\(q+(-0.195914 - 1.72094i) q^{3} +(0.348691 + 1.97752i) q^{5} +(0.766044 + 0.642788i) q^{7} +(-2.92324 + 0.674312i) q^{9} +(-0.745510 + 4.22800i) q^{11} +(-0.448439 - 0.163218i) q^{13} +(3.33488 - 0.987499i) q^{15} +(0.588542 + 1.01939i) q^{17} +(-2.40419 + 4.16419i) q^{19} +(0.956117 - 1.44424i) q^{21} +(-5.57617 + 4.67896i) q^{23} +(0.909450 - 0.331013i) q^{25} +(1.73315 + 4.89859i) q^{27} +(0.403765 - 0.146958i) q^{29} +(-1.84553 + 1.54858i) q^{31} +(7.42217 + 0.454649i) q^{33} +(-1.00401 + 1.73900i) q^{35} +(-1.55274 - 2.68943i) q^{37} +(-0.193033 + 0.803711i) q^{39} +(6.98140 + 2.54102i) q^{41} +(1.04268 - 5.91334i) q^{43} +(-2.35277 - 5.54564i) q^{45} +(3.59503 + 3.01659i) q^{47} +(0.173648 + 0.984808i) q^{49} +(1.63899 - 1.21256i) q^{51} +4.80720 q^{53} -8.62092 q^{55} +(7.63731 + 3.32164i) q^{57} +(-0.610826 - 3.46417i) q^{59} +(7.53216 + 6.32023i) q^{61} +(-2.67277 - 1.36247i) q^{63} +(0.166402 - 0.943711i) q^{65} +(-5.66718 - 2.06268i) q^{67} +(9.14465 + 8.67955i) q^{69} +(5.71692 + 9.90200i) q^{71} +(0.839416 - 1.45391i) q^{73} +(-0.747826 - 1.50026i) q^{75} +(-3.28880 + 2.75963i) q^{77} +(-1.03675 + 0.377347i) q^{79} +(8.09061 - 3.94234i) q^{81} +(-1.09003 + 0.396737i) q^{83} +(-1.81064 + 1.51931i) q^{85} +(-0.332009 - 0.666062i) q^{87} +(-1.94332 + 3.36593i) q^{89} +(-0.238609 - 0.413283i) q^{91} +(3.02657 + 2.87264i) q^{93} +(-9.07309 - 3.30234i) q^{95} +(2.32975 - 13.2127i) q^{97} +(-0.671688 - 12.8621i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q - 3 q^{3} - 3 q^{5} + 3 q^{9}+O(q^{10}) $ 54 * q - 3 * q^3 - 3 * q^5 + 3 * q^9	$ 54 q - 3 q^{3} - 3 q^{5} + 3 q^{9} - 9 q^{13} + 3 q^{15} - 3 q^{21} - 45 q^{25} + 15 q^{27} + 6 q^{29} - 9 q^{31} + 6 q^{33} + 6 q^{35} + 30 q^{39} + 9 q^{41} + 9 q^{43} - 21 q^{45} - 27 q^{47} - 108 q^{51} - 84 q^{53} - 57 q^{57} - 66 q^{59} + 3 q^{63} + 30 q^{65} + 63 q^{67} + 42 q^{69} + 42 q^{71} + 3 q^{75} - 9 q^{77} + 36 q^{79} + 3 q^{81} + 12 q^{83} + 18 q^{85} + 39 q^{87} + 12 q^{89} + 21 q^{93} + 120 q^{95} + 18 q^{97} + 39 q^{99}+O(q^{100}) $ 54 * q - 3 * q^3 - 3 * q^5 + 3 * q^9 - 9 * q^13 + 3 * q^15 - 3 * q^21 - 45 * q^25 + 15 * q^27 + 6 * q^29 - 9 * q^31 + 6 * q^33 + 6 * q^35 + 30 * q^39 + 9 * q^41 + 9 * q^43 - 21 * q^45 - 27 * q^47 - 108 * q^51 - 84 * q^53 - 57 * q^57 - 66 * q^59 + 3 * q^63 + 30 * q^65 + 63 * q^67 + 42 * q^69 + 42 * q^71 + 3 * q^75 - 9 * q^77 + 36 * q^79 + 3 * q^81 + 12 * q^83 + 18 * q^85 + 39 * q^87 + 12 * q^89 + 21 * q^93 + 120 * q^95 + 18 * q^97 + 39 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$1$	$1$

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			0
$2$		0			0
$3$	−0.195914	−	1.72094i	−0.113111	−	0.993582i
$3$	−0.195914	−	1.72094i	−0.113111	−	0.993582i
$4$		0			0
$5$	0.348691	+	1.97752i	0.155939	+	0.884375i	0.957922	+	0.287028i	$0.0926674\pi$
$5$	0.348691	+	1.97752i	0.155939	+	0.884375i	−0.801983	+	0.597347i	$0.796222\pi$
$6$		0			0
$7$	0.766044	+	0.642788i	0.289538	+	0.242951i
$7$	0.766044	+	0.642788i	0.289538	+	0.242951i
$8$		0			0
$9$	−2.92324	+	0.674312i	−0.974412	+	0.224771i
$10$		0			0
$11$	−0.745510	+	4.22800i	−0.224780	+	1.27479i	0.638326	+	0.769766i	$0.279627\pi$
$11$	−0.745510	+	4.22800i	−0.224780	+	1.27479i	−0.863106	+	0.505023i	$0.831484\pi$
$12$		0			0
$13$	−0.448439	−	0.163218i	−0.124375	−	0.0452686i	0.279083	−	0.960267i	$-0.409970\pi$
$13$	−0.448439	−	0.163218i	−0.124375	−	0.0452686i	−0.403458	+	0.914998i	$0.632192\pi$
$14$		0			0
$15$	3.33488	−	0.987499i	0.861061	−	0.254971i
$16$		0			0
$17$	0.588542	+	1.01939i	0.142742	+	0.247237i	0.928528	−	0.371261i	$-0.121075\pi$
$17$	0.588542	+	1.01939i	0.142742	+	0.247237i	−0.785786	+	0.618499i	$0.787741\pi$
$18$		0			0
$19$	−2.40419	+	4.16419i	−0.551560	+	0.955330i	0.446602	+	0.894733i	$0.352634\pi$
$19$	−2.40419	+	4.16419i	−0.551560	+	0.955330i	−0.998162	+	0.0605972i	$0.980699\pi$
$20$		0			0
$21$	0.956117	−	1.44424i	0.208642	−	0.315160i
$22$		0			0
$23$	−5.57617	+	4.67896i	−1.16271	+	0.975631i	−0.999939	−	0.0110321i	$-0.996488\pi$
$23$	−5.57617	+	4.67896i	−1.16271	+	0.975631i	−0.162773	+	0.986664i	$0.552044\pi$
$24$		0			0
$25$	0.909450	−	0.331013i	0.181890	−	0.0662026i
$26$		0			0
$27$	1.73315	+	4.89859i	0.333545	+	0.942734i
$28$		0			0
$29$	0.403765	−	0.146958i	0.0749773	−	0.0272895i	−0.304259	−	0.952589i	$-0.598409\pi$
$29$	0.403765	−	0.146958i	0.0749773	−	0.0272895i	0.379236	+	0.925300i	$0.376187\pi$
$30$		0			0
$31$	−1.84553	+	1.54858i	−0.331467	+	0.278133i	−0.793297	−	0.608835i	$-0.791637\pi$
$31$	−1.84553	+	1.54858i	−0.331467	+	0.278133i	0.461831	+	0.886968i	$0.347193\pi$
$32$		0			0
$33$	7.42217	+	0.454649i	1.29203	+	0.0791443i
$34$		0			0
$35$	−1.00401	+	1.73900i	−0.169709	+	0.293945i
$36$		0			0
$37$	−1.55274	−	2.68943i	−0.255270	−	0.442140i	0.709699	−	0.704505i	$-0.248831\pi$
$37$	−1.55274	−	2.68943i	−0.255270	−	0.442140i	−0.964969	+	0.262365i	$0.915498\pi$
$38$		0			0
$39$	−0.193033	+	0.803711i	−0.0309099	+	0.128697i
$40$		0			0
$41$	6.98140	+	2.54102i	1.09031	+	0.396841i	0.823736	−	0.566973i	$-0.191886\pi$
$41$	6.98140	+	2.54102i	1.09031	+	0.396841i	0.266575	+	0.963814i	$0.414108\pi$
$42$		0			0
$43$	1.04268	−	5.91334i	0.159007	−	0.901776i	−0.796023	−	0.605267i	$-0.793066\pi$
$43$	1.04268	−	5.91334i	0.159007	−	0.901776i	0.955030	−	0.296509i	$-0.0958225\pi$
$44$		0			0
$45$	−2.35277	−	5.54564i	−0.350731	−	0.826695i
$46$		0			0
$47$	3.59503	+	3.01659i	0.524389	+	0.440015i	0.866159	−	0.499769i	$-0.166582\pi$
$47$	3.59503	+	3.01659i	0.524389	+	0.440015i	−0.341770	+	0.939784i	$0.611026\pi$
$48$		0			0
$49$	0.173648	+	0.984808i	0.0248069	+	0.140687i
$50$		0			0
$51$	1.63899	−	1.21256i	0.229505	−	0.169792i
$52$		0			0
$53$	4.80720			0.660320			0.330160	−	0.943925i	$-0.392897\pi$
$53$	4.80720			0.660320			0.330160	+	0.943925i	$0.392897\pi$
$54$		0			0
$55$	−8.62092			−1.16244
$56$		0			0
$57$	7.63731	+	3.32164i	1.01159	+	0.439962i
$58$		0			0
$59$	−0.610826	−	3.46417i	−0.0795228	−	0.450996i	−0.998405	−	0.0564635i	$-0.982018\pi$
$59$	−0.610826	−	3.46417i	−0.0795228	−	0.450996i	0.918882	−	0.394533i	$-0.129094\pi$
$60$		0			0
$61$	7.53216	+	6.32023i	0.964394	+	0.809223i	0.981662	−	0.190628i	$-0.0610525\pi$
$61$	7.53216	+	6.32023i	0.964394	+	0.809223i	−0.0172684	+	0.999851i	$0.505497\pi$
$62$		0			0
$63$	−2.67277	−	1.36247i	−0.336737	−	0.171655i
$64$		0			0
$65$	0.166402	−	0.943711i	0.0206396	−	0.117053i
$66$		0			0
$67$	−5.66718	−	2.06268i	−0.692356	−	0.251997i	−0.0282123	−	0.999602i	$-0.508981\pi$
$67$	−5.66718	−	2.06268i	−0.692356	−	0.251997i	−0.664144	+	0.747605i	$0.731204\pi$
$68$		0			0
$69$	9.14465	+	8.67955i	1.10089	+	1.04490i
$70$		0			0
$71$	5.71692	+	9.90200i	0.678474	+	1.17515i	0.975440	+	0.220263i	$0.0706917\pi$
$71$	5.71692	+	9.90200i	0.678474	+	1.17515i	−0.296967	+	0.954888i	$0.595975\pi$
$72$		0			0
$73$	0.839416	−	1.45391i	0.0982462	−	0.170167i	−0.812713	−	0.582665i	$-0.802010\pi$
$73$	0.839416	−	1.45391i	0.0982462	−	0.170167i	0.910959	+	0.412497i	$0.135343\pi$
$74$		0			0
$75$	−0.747826	−	1.50026i	−0.0863515	−	0.173235i
$76$		0			0
$77$	−3.28880	+	2.75963i	−0.374794	+	0.314489i
$78$		0			0
$79$	−1.03675	+	0.377347i	−0.116644	+	0.0424548i	−0.399683	−	0.916654i	$-0.630880\pi$
$79$	−1.03675	+	0.377347i	−0.116644	+	0.0424548i	0.283039	+	0.959108i	$0.408657\pi$
$80$		0			0
$81$	8.09061	−	3.94234i	0.898956	−	0.438038i
$82$		0			0
$83$	−1.09003	+	0.396737i	−0.119646	+	0.0435476i	−0.401149	−	0.916013i	$-0.631389\pi$
$83$	−1.09003	+	0.396737i	−0.119646	+	0.0435476i	0.281503	+	0.959560i	$0.409167\pi$
$84$		0			0
$85$	−1.81064	+	1.51931i	−0.196391	+	0.164792i
$86$		0			0
$87$	−0.332009	−	0.666062i	−0.0355951	−	0.0714093i
$88$		0			0
$89$	−1.94332	+	3.36593i	−0.205992	+	0.356788i	−0.950448	−	0.310883i	$-0.899375\pi$
$89$	−1.94332	+	3.36593i	−0.205992	+	0.356788i	0.744457	+	0.667671i	$0.232709\pi$
$90$		0			0
$91$	−0.238609	−	0.413283i	−0.0250130	−	0.0433239i
$92$		0			0
$93$	3.02657	+	2.87264i	0.313841	+	0.297879i
$94$		0			0
$95$	−9.07309	−	3.30234i	−0.930880	−	0.338813i
$96$		0			0
$97$	2.32975	−	13.2127i	0.236551	−	1.34155i	−0.602773	−	0.797913i	$-0.705937\pi$
$97$	2.32975	−	13.2127i	0.236551	−	1.34155i	0.839323	−	0.543632i	$-0.182951\pi$
$98$		0			0
$99$	−0.671688	−	12.8621i	−0.0675072	−	1.29269i
$100$		0			0
$101$	−4.16800	−	3.49737i	−0.414731	−	0.348001i	0.411423	−	0.911444i	$-0.365032\pi$
$101$	−4.16800	−	3.49737i	−0.414731	−	0.348001i	−0.826155	+	0.563443i	$0.809476\pi$
$102$		0			0
$103$	−0.218299	−	1.23803i	−0.0215096	−	0.121987i	0.972162	−	0.234308i	$-0.0752825\pi$
$103$	−0.218299	−	1.23803i	−0.0215096	−	0.121987i	−0.993672	+	0.112321i	$0.964171\pi$
$104$		0			0
$105$	3.18942	+	1.38715i	0.311255	+	0.135372i
$106$		0			0
$107$	12.2741			1.18658			0.593292	−	0.804987i	$-0.297828\pi$
$107$	12.2741			1.18658			0.593292	+	0.804987i	$0.297828\pi$
$108$		0			0
$109$	−16.1410			−1.54603			−0.773013	−	0.634390i	$-0.781252\pi$
$109$	−16.1410			−1.54603			−0.773013	+	0.634390i	$0.781252\pi$
$110$		0			0
$111$	−4.32413	+	3.19907i	−0.410428	+	0.303642i
$112$		0			0
$113$	−1.32882	−	7.53613i	−0.125005	−	0.708939i	−0.981305	−	0.192460i	$-0.938353\pi$
$113$	−1.32882	−	7.53613i	−0.125005	−	0.708939i	0.856300	−	0.516479i	$-0.172758\pi$
$114$		0			0
$115$	−11.1971	−	9.39550i	−1.04414	−	0.876135i
$116$		0			0
$117$	1.42095	+	0.174738i	0.131367	+	0.0161545i
$118$		0			0
$119$	−0.204399	+	1.15920i	−0.0187372	+	0.106264i
$120$		0			0
$121$	−6.98357	−	2.54181i	−0.634870	−	0.231074i
$122$		0			0
$123$	3.00518	−	12.5124i	0.270968	−	1.12820i
$124$		0			0
$125$	5.99178	+	10.3781i	0.535921	+	0.928242i
$126$		0			0
$127$	7.65461	−	13.2582i	0.679237	−	1.17647i	−0.295974	−	0.955196i	$-0.595644\pi$
$127$	7.65461	−	13.2582i	0.679237	−	1.17647i	0.975211	−	0.221277i	$-0.0710224\pi$
$128$		0			0
$129$	−10.3808	−	0.635879i	−0.913974	−	0.0559860i
$130$		0			0
$131$	−13.6278	+	11.4350i	−1.19066	+	0.999085i	−0.190815	+	0.981626i	$0.561113\pi$
$131$	−13.6278	+	11.4350i	−1.19066	+	0.999085i	−0.999848	+	0.0174586i	$0.994442\pi$
$132$		0			0
$133$	−4.51841	+	1.64457i	−0.391796	+	0.142602i
$134$		0			0
$135$	−9.08274	+	5.13544i	−0.781718	+	0.441988i
$136$		0			0
$137$	−6.32219	+	2.30109i	−0.540141	+	0.196595i	−0.597661	−	0.801749i	$-0.703903\pi$
$137$	−6.32219	+	2.30109i	−0.540141	+	0.196595i	0.0575198	+	0.998344i	$0.481681\pi$
$138$		0			0
$139$	−13.5431	+	11.3640i	−1.14871	+	0.963884i	−0.999689	−	0.0249495i	$-0.992057\pi$
$139$	−13.5431	+	11.3640i	−1.14871	+	0.963884i	−0.149024	+	0.988834i	$0.547613\pi$
$140$		0			0
$141$	4.48703	−	6.77781i	0.377876	−	0.570794i
$142$		0			0
$143$	1.02440	−	1.77432i	0.0856649	−	0.148376i
$144$		0			0
$145$	0.431403	+	0.747212i	0.0358261	+	0.0620525i
$146$		0			0
$147$	1.66077	−	0.491775i	0.136978	−	0.0405609i
$148$		0			0
$149$	−2.36657	−	0.861361i	−0.193877	−	0.0705654i	0.243257	−	0.969962i	$-0.421784\pi$
$149$	−2.36657	−	0.861361i	−0.193877	−	0.0705654i	−0.437134	+	0.899396i	$0.644006\pi$
$150$		0			0
$151$	3.95102	−	22.4073i	0.321529	−	1.82348i	−0.211490	−	0.977380i	$-0.567832\pi$
$151$	3.95102	−	22.4073i	0.321529	−	1.82348i	0.533019	−	0.846103i	$-0.321057\pi$
$152$		0			0
$153$	−2.40783	−	2.58304i	−0.194662	−	0.208827i
$154$		0			0
$155$	−3.70587	−	3.10960i	−0.297663	−	0.249769i
$156$		0			0
$157$	3.43714	+	19.4930i	0.274313	+	1.55571i	0.741135	+	0.671356i	$0.234288\pi$
$157$	3.43714	+	19.4930i	0.274313	+	1.55571i	−0.466822	+	0.884352i	$0.654601\pi$
$158$		0			0
$159$	−0.941800	−	8.27288i	−0.0746896	−	0.656082i
$160$		0			0
$161$	−7.27918			−0.573679
$162$		0			0
$163$	−16.8575			−1.32038			−0.660190	−	0.751099i	$-0.729524\pi$
$163$	−16.8575			−1.32038			−0.660190	+	0.751099i	$0.729524\pi$
$164$		0			0
$165$	1.68896	+	14.8360i	0.131486	+	1.15498i
$166$		0			0
$167$	2.00667	+	11.3804i	0.155281	+	0.880643i	0.958528	+	0.284997i	$0.0919927\pi$
$167$	2.00667	+	11.3804i	0.155281	+	0.880643i	−0.803247	+	0.595646i	$0.796896\pi$
$168$		0			0
$169$	−9.78412	−	8.20985i	−0.752625	−	0.631527i
$170$		0			0
$171$	4.22006	−	13.7941i	0.322716	−	1.05486i
$172$		0			0
$173$	−0.776997	+	4.40657i	−0.0590740	+	0.335025i	−0.999994	−	0.00360509i	$-0.998852\pi$
$173$	−0.776997	+	4.40657i	−0.0590740	+	0.335025i	0.940920	+	0.338630i	$0.109964\pi$
$174$		0			0
$175$	0.909450	+	0.331013i	0.0687480	+	0.0250222i
$176$		0			0
$177$	−5.84194	+	1.72987i	−0.439107	+	0.130025i
$178$		0			0
$179$	−1.60181	−	2.77442i	−0.119725	−	0.207370i	0.799934	−	0.600088i	$-0.204868\pi$
$179$	−1.60181	−	2.77442i	−0.119725	−	0.207370i	−0.919659	+	0.392719i	$0.871535\pi$
$180$		0			0
$181$	2.36606	−	4.09814i	0.175868	−	0.304612i	−0.764593	−	0.644513i	$-0.777060\pi$
$181$	2.36606	−	4.09814i	0.175868	−	0.304612i	0.940461	+	0.339901i	$0.110393\pi$
$182$		0			0
$183$	9.40105	−	14.2006i	0.694945	−	1.04974i
$184$		0			0
$185$	4.77699	−	4.00837i	0.351211	−	0.294701i
$186$		0			0
$187$	−4.74872	+	1.72839i	−0.347261	+	0.126393i
$188$		0			0
$189$	−1.82108	+	4.86659i	−0.132464	+	0.353992i
$190$		0			0
$191$	21.9770	−	7.99898i	1.59020	−	0.578786i	0.612811	−	0.790230i	$-0.290039\pi$
$191$	21.9770	−	7.99898i	1.59020	−	0.578786i	0.977390	+	0.211444i	$0.0678165\pi$
$192$		0			0
$193$	11.7785	−	9.88331i	0.847833	−	0.711416i	−0.111478	−	0.993767i	$-0.535559\pi$
$193$	11.7785	−	9.88331i	0.847833	−	0.711416i	0.959311	+	0.282350i	$0.0911141\pi$
$194$		0			0
$195$	−1.65667	−	0.101480i	−0.118636	−	0.00726713i
$196$		0			0
$197$	6.90090	−	11.9527i	0.491669	−	0.851596i	−0.508285	−	0.861189i	$-0.669720\pi$
$197$	6.90090	−	11.9527i	0.491669	−	0.851596i	0.999954	+	0.00959318i	$0.00305365\pi$
$198$		0			0
$199$	6.57498	+	11.3882i	0.466088	+	0.807288i	0.999250	−	0.0387254i	$-0.0123298\pi$
$199$	6.57498	+	11.3882i	0.466088	+	0.807288i	−0.533162	+	0.846013i	$0.678996\pi$
$200$		0			0
$201$	−2.43946	+	10.1570i	−0.172067	+	0.716416i
$202$		0			0
$203$	0.403765	+	0.146958i	0.0283387	+	0.0103145i
$204$		0			0
$205$	−2.59058	+	14.6919i	−0.180934	+	1.02613i
$206$		0			0
$207$	13.1454	−	17.4378i	0.913667	−	1.21201i
$208$		0			0
$209$	−15.8138	−	13.2694i	−1.09387	−	0.917862i
$210$		0			0
$211$	−2.28498	−	12.9588i	−0.157305	−	0.892119i	−0.956648	−	0.291245i	$-0.905930\pi$
$211$	−2.28498	−	12.9588i	−0.157305	−	0.892119i	0.799344	−	0.600874i	$-0.205181\pi$
$212$		0			0
$213$	15.9207	−	11.7784i	1.09087	−	0.807042i
$214$		0			0
$215$	12.0573			0.822304
$216$		0			0
$217$	−2.40917			−0.163545
$218$		0			0
$219$	−2.66654	−	1.15974i	−0.180188	−	0.0783678i
$220$		0			0
$221$	−0.0975428	−	0.553193i	−0.00656144	−	0.0372118i
$222$		0			0
$223$	−4.99820	−	4.19399i	−0.334704	−	0.280850i	0.459909	−	0.887966i	$-0.347882\pi$
$223$	−4.99820	−	4.19399i	−0.334704	−	0.280850i	−0.794613	+	0.607116i	$0.792326\pi$
$224$		0			0
$225$	−2.43533	+	1.58088i	−0.162355	+	0.105392i
$226$		0			0
$227$	3.98301	−	22.5888i	0.264362	−	1.49927i	−0.506484	−	0.862249i	$-0.669055\pi$
$227$	3.98301	−	22.5888i	0.264362	−	1.49927i	0.770846	−	0.637021i	$-0.219834\pi$
$228$		0			0
$229$	24.4474	+	8.89813i	1.61553	+	0.588005i	0.982523	−	0.186140i	$-0.0595979\pi$
$229$	24.4474	+	8.89813i	1.61553	+	0.588005i	0.633008	+	0.774146i	$0.281820\pi$
$230$		0			0
$231$	5.39347	+	5.11916i	0.354864	+	0.336816i
$232$		0			0
$233$	5.02552	+	8.70446i	0.329233	+	0.570248i	0.982360	−	0.187000i	$-0.0598765\pi$
$233$	5.02552	+	8.70446i	0.329233	+	0.570248i	−0.653127	+	0.757249i	$0.726543\pi$
$234$		0			0
$235$	−4.71182	+	8.16111i	−0.307365	+	0.532372i
$236$		0			0
$237$	0.852504	+	1.71026i	0.0553761	+	0.111093i
$238$		0			0
$239$	−17.6103	+	14.7768i	−1.13912	+	0.955831i	−0.999409	−	0.0343621i	$-0.989060\pi$
$239$	−17.6103	+	14.7768i	−1.13912	+	0.955831i	−0.139706	+	0.990193i	$0.544616\pi$
$240$		0			0
$241$	28.9002	−	10.5188i	1.86162	−	0.677575i	0.883900	−	0.467675i	$-0.154908\pi$
$241$	28.9002	−	10.5188i	1.86162	−	0.677575i	0.977723	−	0.209900i	$-0.0673140\pi$
$242$		0			0
$243$	−8.36958	−	13.1510i	−0.536909	−	0.843640i
$244$		0			0
$245$	−1.88693	+	0.686787i	−0.120552	+	0.0438772i
$246$		0			0
$247$	1.75780	−	1.47497i	0.111846	−	0.0938503i
$248$		0			0
$249$	0.896311	+	1.79814i	0.0568014	+	0.113952i
$250$		0			0
$251$	−13.4163	+	23.2378i	−0.846831	+	1.46675i	0.0371911	+	0.999308i	$0.488159\pi$
$251$	−13.4163	+	23.2378i	−0.846831	+	1.46675i	−0.884022	+	0.467446i	$0.845174\pi$
$252$		0			0
$253$	−15.6256	−	27.0643i	−0.982371	−	1.70152i
$254$		0			0
$255$	2.96936	+	2.81834i	0.185948	+	0.176491i
$256$		0			0
$257$	−3.55000	−	1.29210i	−0.221443	−	0.0805987i	0.228916	−	0.973446i	$-0.426482\pi$
$257$	−3.55000	−	1.29210i	−0.221443	−	0.0805987i	−0.450359	+	0.892847i	$0.648704\pi$
$258$		0			0
$259$	0.539262	−	3.05831i	0.0335081	−	0.190034i
$260$		0			0
$261$	−1.08120	+	0.701858i	−0.0669249	+	0.0434439i
$262$		0			0
$263$	−0.553163	−	0.464158i	−0.0341095	−	0.0286212i	0.625574	−	0.780165i	$-0.284865\pi$
$263$	−0.553163	−	0.464158i	−0.0341095	−	0.0286212i	−0.659683	+	0.751544i	$0.729309\pi$
$264$		0			0
$265$	1.67623	+	9.50635i	0.102970	+	0.583970i
$266$		0			0
$267$	6.17328	+	2.68490i	0.377798	+	0.164313i
$268$		0			0
$269$	−0.596397			−0.0363630			−0.0181815	−	0.999835i	$-0.505788\pi$
$269$	−0.596397			−0.0363630			−0.0181815	+	0.999835i	$0.505788\pi$
$270$		0			0
$271$	−21.5071			−1.30647			−0.653233	−	0.757157i	$-0.726588\pi$
$271$	−21.5071			−1.30647			−0.653233	+	0.757157i	$0.726588\pi$
$272$		0			0
$273$	−0.664487	+	0.491599i	−0.0402166	+	0.0297529i
$274$		0			0
$275$	0.721518	+	4.09193i	0.0435091	+	0.246753i
$276$		0			0
$277$	17.4327	+	14.6278i	1.04743	+	0.878897i	0.992821	−	0.119611i	$-0.0381649\pi$
$277$	17.4327	+	14.6278i	1.04743	+	0.878897i	0.0546073	+	0.998508i	$0.482609\pi$
$278$		0			0
$279$	4.35068	−	5.77133i	0.260469	−	0.345520i
$280$		0			0
$281$	3.69264	−	20.9420i	0.220284	−	1.24929i	−0.651214	−	0.758894i	$-0.725740\pi$
$281$	3.69264	−	20.9420i	0.220284	−	1.24929i	0.871498	−	0.490399i	$-0.163149\pi$
$282$		0			0
$283$	22.8004	+	8.29868i	1.35535	+	0.493305i	0.914612	−	0.404332i	$-0.132496\pi$
$283$	22.8004	+	8.29868i	1.35535	+	0.493305i	0.440734	+	0.897638i	$0.354718\pi$
$284$		0			0
$285$	−3.90556	+	16.2612i	−0.231345	+	0.963229i
$286$		0			0
$287$	3.71472	+	6.43409i	0.219273	+	0.379792i
$288$		0			0
$289$	7.80724	−	13.5225i	0.459249	−	0.795443i
$290$		0			0
$291$	−23.1946	−	1.42080i	−1.35969	−	0.0832887i
$292$		0			0
$293$	−7.06118	+	5.92504i	−0.412519	+	0.346144i	−0.825309	−	0.564682i	$-0.808999\pi$
$293$	−7.06118	+	5.92504i	−0.412519	+	0.346144i	0.412790	+	0.910826i	$0.364554\pi$
$294$		0			0
$295$	6.63748	−	2.41585i	0.386449	−	0.140656i
$296$		0			0
$297$	−22.0033	+	3.67581i	−1.27676	+	0.213292i
$298$		0			0
$299$	3.26426	−	1.18809i	0.188777	−	0.0687093i
$300$		0			0
$301$	4.59976	−	3.85966i	0.265126	−	0.222467i
$302$		0			0
$303$	−5.20217	+	7.85804i	−0.298857	+	0.451433i
$304$		0			0
$305$	−9.87201	+	17.0988i	−0.565270	+	0.979076i
$306$		0			0
$307$	4.17281	+	7.22753i	0.238155	+	0.412497i	0.960185	−	0.279365i	$-0.0901240\pi$
$307$	4.17281	+	7.22753i	0.238155	+	0.412497i	−0.722030	+	0.691862i	$0.756791\pi$
$308$		0			0
$309$	−2.08781	+	0.618226i	−0.118771	+	0.0351697i
$310$		0			0
$311$	21.4486	+	7.80665i	1.21624	+	0.442675i	0.868864	−	0.495052i	$-0.164851\pi$
$311$	21.4486	+	7.80665i	1.21624	+	0.442675i	0.347375	+	0.937726i	$0.387073\pi$
$312$		0			0
$313$	−1.43574	+	8.14249i	−0.0811529	+	0.460241i	0.916968	+	0.398961i	$0.130629\pi$
$313$	−1.43574	+	8.14249i	−0.0811529	+	0.460241i	−0.998121	+	0.0612796i	$0.980482\pi$
$314$		0			0
$315$	1.76234	−	5.76054i	0.0992966	−	0.324570i
$316$		0			0
$317$	−2.18218	−	1.83106i	−0.122563	−	0.102843i	0.579446	−	0.815011i	$-0.303269\pi$
$317$	−2.18218	−	1.83106i	−0.122563	−	0.102843i	−0.702009	+	0.712168i	$0.747713\pi$
$318$		0			0
$319$	0.320329	+	1.81668i	0.0179350	+	0.101714i
$320$		0			0
$321$	−2.40468	−	21.1230i	−0.134216	−	1.17897i
$322$		0			0
$323$	−5.65988			−0.314924
$324$		0			0
$325$	−0.461860			−0.0256194
$326$		0			0
$327$	3.16225	+	27.7776i	0.174873	+	1.53611i
$328$		0			0
$329$	0.814927	+	4.62168i	0.0449284	+	0.254802i
$330$		0			0
$331$	16.6988	+	14.0119i	0.917848	+	0.770166i	0.973596	−	0.228279i	$-0.0733099\pi$
$331$	16.6988	+	14.0119i	0.917848	+	0.770166i	−0.0557480	+	0.998445i	$0.517754\pi$
$332$		0			0
$333$	6.35255	+	6.81481i	0.348118	+	0.373449i
$334$		0			0
$335$	2.10291	−	11.9262i	0.114894	−	0.651599i
$336$		0			0
$337$	11.6529	+	4.24129i	0.634771	+	0.231038i	0.639307	−	0.768952i	$-0.279221\pi$
$337$	11.6529	+	4.24129i	0.634771	+	0.231038i	−0.00453533	+	0.999990i	$0.501444\pi$
$338$		0			0
$339$	−12.7089	+	3.76325i	−0.690250	+	0.204392i
$340$		0			0
$341$	−5.17154	−	8.95737i	−0.280055	−	0.485069i
$342$		0			0
$343$	−0.500000	+	0.866025i	−0.0269975	+	0.0467610i
$344$		0			0
$345$	−13.9754	+	21.1102i	−0.752408	+	1.13654i
$346$		0			0
$347$	−19.5729	+	16.4236i	−1.05073	+	0.881668i	−0.993170	−	0.116674i	$-0.962777\pi$
$347$	−19.5729	+	16.4236i	−1.05073	+	0.881668i	−0.0575603	+	0.998342i	$0.518332\pi$
$348$		0			0
$349$	12.0047	−	4.36935i	0.642596	−	0.233886i	−0.000108307	−	1.00000i	$-0.500034\pi$
$349$	12.0047	−	4.36935i	0.642596	−	0.233886i	0.642705	+	0.766114i	$0.277812\pi$
$350$		0			0
$351$	0.0223280	−	2.47960i	0.00119178	−	0.132351i
$352$		0			0
$353$	20.6710	−	7.52362i	1.10020	−	0.400442i	0.272813	−	0.962067i	$-0.412046\pi$
$353$	20.6710	−	7.52362i	1.10020	−	0.400442i	0.827392	+	0.561625i	$0.189824\pi$
$354$		0			0
$355$	−17.5880	+	14.7581i	−0.933474	+	0.783278i
$356$		0			0
$357$	2.03496	+	0.124652i	0.107701	+	0.00659730i
$358$		0			0
$359$	12.2266	−	21.1771i	0.645296	−	1.11769i	−0.338937	−	0.940809i	$-0.610067\pi$
$359$	12.2266	−	21.1771i	0.645296	−	1.11769i	0.984233	−	0.176876i	$-0.0565993\pi$
$360$		0			0
$361$	−2.06030	−	3.56854i	−0.108437	−	0.187818i
$362$		0			0
$363$	−3.00611	+	12.5163i	−0.157780	+	0.656933i
$364$		0			0
$365$	3.16784	+	1.15300i	0.165812	+	0.0603507i
$366$		0			0
$367$	−4.73815	+	26.8714i	−0.247330	+	1.40268i	0.567690	+	0.823242i	$0.307837\pi$
$367$	−4.73815	+	26.8714i	−0.247330	+	1.40268i	−0.815020	+	0.579433i	$0.803274\pi$
$368$		0			0
$369$	−22.1217	−	2.72036i	−1.15161	−	0.141616i
$370$		0			0
$371$	3.68253	+	3.09001i	0.191187	+	0.160425i
$372$		0			0
$373$	6.70075	+	38.0018i	0.346952	+	1.96766i	0.217349	+	0.976094i	$0.430259\pi$
$373$	6.70075	+	38.0018i	0.346952	+	1.96766i	0.129603	+	0.991566i	$0.458630\pi$
$374$		0			0
$375$	16.6861	−	12.3447i	0.861666	−	0.637476i
$376$		0			0
$377$	−0.205050			−0.0105606
$378$		0			0
$379$	−27.1855			−1.39643			−0.698213	−	0.715890i	$-0.746021\pi$
$379$	−27.1855			−1.39643			−0.698213	+	0.715890i	$0.746021\pi$
$380$		0			0
$381$	−24.3161	−	10.5756i	−1.24575	−	0.541805i
$382$		0			0
$383$	−4.18402	−	23.7288i	−0.213793	−	1.21248i	−0.882988	−	0.469396i	$-0.844472\pi$
$383$	−4.18402	−	23.7288i	−0.213793	−	1.21248i	0.669194	−	0.743087i	$-0.266639\pi$
$384$		0			0
$385$	−6.60401	−	5.54142i	−0.336571	−	0.282417i
$386$		0			0
$387$	0.939432	+	17.9892i	0.0477540	+	0.914441i
$388$		0			0
$389$	0.893368	−	5.06654i	0.0452956	−	0.256884i	−0.953748	−	0.300607i	$-0.902811\pi$
$389$	0.893368	−	5.06654i	0.0452956	−	0.256884i	0.999044	+	0.0437230i	$0.0139219\pi$
$390$		0			0
$391$	−8.05148	−	2.93050i	−0.407181	−	0.148202i
$392$		0			0
$393$	22.3488	+	21.2122i	1.12735	+	1.07001i
$394$		0			0
$395$	−1.10772	−	1.91862i	−0.0557353	−	0.0965365i
$396$		0			0
$397$	−7.10440	+	12.3052i	−0.356560	+	0.617580i	−0.987384	−	0.158346i	$-0.949384\pi$
$397$	−7.10440	+	12.3052i	−0.356560	+	0.617580i	0.630824	+	0.775926i	$0.282717\pi$
$398$		0			0
$399$	3.71541	+	7.45369i	0.186003	+	0.373151i
$400$		0			0
$401$	−23.7019	+	19.8883i	−1.18362	+	0.993173i	−0.183669	+	0.982988i	$0.558797\pi$
$401$	−23.7019	+	19.8883i	−1.18362	+	0.993173i	−0.999948	+	0.0101843i	$0.996758\pi$
$402$		0			0
$403$	1.08036	−	0.393220i	0.0538167	−	0.0195877i
$404$		0			0
$405$	10.6172	+	14.6247i	0.527573	+	0.726707i
$406$		0			0
$407$	12.5285	−	4.56000i	0.621015	−	0.226031i
$408$		0			0
$409$	5.64810	−	4.73932i	0.279280	−	0.234344i	−0.492378	−	0.870382i	$-0.663872\pi$
$409$	5.64810	−	4.73932i	0.279280	−	0.234344i	0.771658	+	0.636038i	$0.219428\pi$
$410$		0			0
$411$	5.19863	+	10.4293i	0.256430	+	0.514437i
$412$		0			0
$413$	1.75880	−	3.04634i	0.0865451	−	0.149901i
$414$		0			0
$415$	−1.16464	−	2.01722i	−0.0571699	−	0.0990212i
$416$		0			0
$417$	22.2100	+	21.0805i	1.08763	+	1.03231i
$418$		0			0
$419$	−2.89893	−	1.05513i	−0.141622	−	0.0515462i	0.270237	−	0.962794i	$-0.412898\pi$
$419$	−2.89893	−	1.05513i	−0.141622	−	0.0515462i	−0.411859	+	0.911248i	$0.635120\pi$
$420$		0			0
$421$	1.95375	−	11.0803i	0.0952201	−	0.540020i	−0.899460	−	0.437004i	$-0.856040\pi$
$421$	1.95375	−	11.0803i	0.0952201	−	0.540020i	0.994680	−	0.103016i	$-0.0328493\pi$
$422$		0			0
$423$	−12.5432	−	6.39403i	−0.609873	−	0.310888i
$424$		0			0
$425$	0.872680	+	0.732265i	0.0423312	+	0.0355201i
$426$		0			0
$427$	1.70740	+	9.68315i	0.0826269	+	0.468601i
$428$		0			0
$429$	−3.25418	−	1.41532i	−0.157113	−	0.0683321i
$430$		0			0
$431$	20.2947			0.977561			0.488781	−	0.872407i	$-0.337442\pi$
$431$	20.2947			0.977561			0.488781	+	0.872407i	$0.337442\pi$
$432$		0			0
$433$	34.0859			1.63807			0.819033	−	0.573747i	$-0.194511\pi$
$433$	34.0859			1.63807			0.819033	+	0.573747i	$0.194511\pi$
$434$		0			0
$435$	1.20138	−	0.888806i	0.0576020	−	0.0426150i
$436$		0			0
$437$	−6.07788	−	34.4694i	−0.290744	−	1.64889i
$438$		0			0
$439$	−16.9141	−	14.1926i	−0.807266	−	0.677377i	0.142688	−	0.989768i	$-0.454426\pi$
$439$	−16.9141	−	14.1926i	−0.807266	−	0.677377i	−0.949954	+	0.312391i	$0.898870\pi$
$440$		0			0
$441$	−1.17168	−	2.76173i	−0.0557944	−	0.131511i
$442$		0			0
$443$	5.33970	−	30.2830i	0.253697	−	1.43879i	−0.545698	−	0.837982i	$-0.683736\pi$
$443$	5.33970	−	30.2830i	0.253697	−	1.43879i	0.799395	−	0.600805i	$-0.205153\pi$
$444$		0			0
$445$	−7.33383	−	2.66930i	−0.347657	−	0.126537i
$446$		0			0
$447$	−1.01870	+	4.24146i	−0.0481829	+	0.200614i
$448$		0			0
$449$	−10.3491	−	17.9252i	−0.488406	−	0.845943i	0.511506	−	0.859280i	$-0.329088\pi$
$449$	−10.3491	−	17.9252i	−0.488406	−	0.845943i	−0.999911	+	0.0133368i	$0.995755\pi$
$450$		0			0
$451$	−15.9481	+	27.6230i	−0.750969	+	1.30072i
$452$		0			0
$453$	−39.3356	−	2.40953i	−1.84815	−	0.113209i
$454$		0			0
$455$	0.734076	−	0.615963i	0.0344140	−	0.0288768i
$456$		0			0
$457$	21.3747	−	7.77976i	0.999867	−	0.363922i	0.210334	−	0.977630i	$-0.432545\pi$
$457$	21.3747	−	7.77976i	0.999867	−	0.363922i	0.789533	+	0.613708i	$0.210323\pi$
$458$		0			0
$459$	−3.97352	+	4.64978i	−0.185468	+	0.217033i
$460$		0			0
$461$	−22.4432	+	8.16867i	−1.04529	+	0.380453i	−0.806882	−	0.590713i	$-0.798847\pi$
$461$	−22.4432	+	8.16867i	−1.04529	+	0.380453i	−0.238404	+	0.971166i	$0.576624\pi$
$462$		0			0
$463$	10.9259	−	9.16794i	0.507771	−	0.426070i	−0.352573	−	0.935784i	$-0.614693\pi$
$463$	10.9259	−	9.16794i	0.507771	−	0.426070i	0.860344	+	0.509714i	$0.170249\pi$
$464$		0			0
$465$	−4.62538	+	6.98678i	−0.214497	+	0.324004i
$466$		0			0
$467$	5.41182	−	9.37355i	0.250429	−	0.433756i	−0.713215	−	0.700946i	$-0.752762\pi$
$467$	5.41182	−	9.37355i	0.250429	−	0.433756i	0.963644	+	0.267189i	$0.0860949\pi$
$468$		0			0
$469$	−3.01544	−	5.22290i	−0.139240	−	0.241171i
$470$		0			0
$471$	32.8727	−	9.73404i	1.51470	−	0.448521i
$472$		0			0
$473$	24.2243	+	8.81691i	1.11383	+	0.405402i
$474$		0			0
$475$	−0.808096	+	4.58294i	−0.0370780	+	0.210280i
$476$		0			0
$477$	−14.0526	+	3.24155i	−0.643423	+	0.148420i
$478$		0			0
$479$	3.47062	+	2.91219i	0.158577	+	0.133062i	0.718624	−	0.695399i	$-0.244772\pi$
$479$	3.47062	+	2.91219i	0.158577	+	0.133062i	−0.560047	+	0.828461i	$0.689217\pi$
$480$		0			0
$481$	0.257346	+	1.45948i	0.0117340	+	0.0665466i
$482$		0			0
$483$	1.42609	+	12.5270i	0.0648896	+	0.569998i
$484$		0			0
$485$	26.9408			1.22332
$486$		0			0
$487$	18.5819			0.842025			0.421013	−	0.907055i	$-0.361675\pi$
$487$	18.5819			0.842025			0.421013	+	0.907055i	$0.361675\pi$
$488$		0			0
$489$	3.30262	+	29.0106i	0.149350	+	1.31191i
$490$		0			0
$491$	2.77586	+	15.7427i	0.125273	+	0.710457i	0.981145	+	0.193271i	$0.0619095\pi$
$491$	2.77586	+	15.7427i	0.125273	+	0.710457i	−0.855873	+	0.517186i	$0.826979\pi$
$492$		0			0
$493$	0.387440	+	0.325101i	0.0174494	+	0.0146418i
$494$		0			0
$495$	25.2010	−	5.81319i	1.13270	−	0.261283i
$496$		0			0
$497$	−1.98547	+	11.2601i	−0.0890603	+	0.505086i
$498$		0			0
$499$	11.9530	+	4.35054i	0.535091	+	0.194757i	0.595410	−	0.803422i	$-0.296990\pi$
$499$	11.9530	+	4.35054i	0.535091	+	0.194757i	−0.0603193	+	0.998179i	$0.519212\pi$
$500$		0			0
$501$	19.1918	−	5.68294i	0.857427	−	0.253895i
$502$		0			0
$503$	20.5567	+	35.6053i	0.916579	+	1.58756i	0.804572	+	0.593855i	$0.202395\pi$
$503$	20.5567	+	35.6053i	0.916579	+	1.58756i	0.112007	+	0.993707i	$0.464272\pi$
$504$		0			0
$505$	5.46278	−	9.46181i	0.243091	−	0.421045i
$506$		0			0
$507$	−12.2118	+	18.4463i	−0.542344	+	0.819227i
$508$		0			0
$509$	8.02271	−	6.73185i	0.355600	−	0.298384i	−0.447434	−	0.894317i	$-0.647662\pi$
$509$	8.02271	−	6.73185i	0.355600	−	0.298384i	0.803034	+	0.595933i	$0.203218\pi$
$510$		0			0
$511$	1.57759	−	0.574194i	0.0697883	−	0.0254009i
$512$		0			0
$513$	−24.5655	−	4.56000i	−1.08459	−	0.201329i
$514$		0			0
$515$	2.37212	−	0.863381i	0.104528	−	0.0380451i
$516$		0			0
$517$	−15.4343	+	12.9509i	−0.678798	+	0.569579i
$518$		0			0
$519$	7.73564	+	0.473851i	0.339557	+	0.0207998i
$520$		0			0
$521$	15.0299	−	26.0325i	0.658471	−	1.14051i	−0.322541	−	0.946556i	$-0.604537\pi$
$521$	15.0299	−	26.0325i	0.658471	−	1.14051i	0.981012	−	0.193950i	$-0.0621298\pi$
$522$		0			0
$523$	2.62857	+	4.55282i	0.114939	+	0.199081i	0.917755	−	0.397146i	$-0.129999\pi$
$523$	2.62857	+	4.55282i	0.114939	+	0.199081i	−0.802816	+	0.596227i	$0.796666\pi$
$524$		0			0
$525$	0.391477	−	1.62996i	0.0170855	−	0.0711371i
$526$		0			0
$527$	−2.66477	−	0.969898i	−0.116079	−	0.0422494i
$528$		0			0
$529$	5.20708	−	29.5308i	0.226395	−	1.28395i
$530$		0			0
$531$	4.12152	+	9.71469i	0.178859	+	0.421582i
$532$		0			0
$533$	−2.71599	−	2.27898i	−0.117642	−	0.0987138i
$534$		0			0
$535$	4.27987	+	24.2724i	0.185035	+	1.04939i
$536$		0			0
$537$	−4.46077	+	3.30016i	−0.192497	+	0.142412i
$538$		0			0
$539$	−4.29322			−0.184922
$540$		0			0
$541$	15.5679			0.669317			0.334658	−	0.942339i	$-0.391379\pi$
$541$	15.5679			0.669317			0.334658	+	0.942339i	$0.391379\pi$
$542$		0			0
$543$	−7.51618	−	3.26896i	−0.322550	−	0.140284i
$544$		0			0
$545$	−5.62821	−	31.9192i	−0.241086	−	1.36727i
$546$		0			0
$547$	17.3613	+	14.5679i	0.742316	+	0.622877i	0.933459	−	0.358685i	$-0.116775\pi$
$547$	17.3613	+	14.5679i	0.742316	+	0.622877i	−0.191143	+	0.981562i	$0.561219\pi$
$548$		0			0
$549$	−26.2801	−	13.3965i	−1.12161	−	0.571749i
$550$		0			0
$551$	−0.358767	+	2.03467i	−0.0152840	+	0.0866798i
$552$		0			0
$553$	−1.03675	−	0.377347i	−0.0440872	−	0.0160464i
$554$		0			0
$555$	−7.83402	−	7.43559i	−0.332536	−	0.315623i
$556$		0			0
$557$	−3.95740	−	6.85442i	−0.167681	−	0.290431i	0.769923	−	0.638136i	$-0.220294\pi$
$557$	−3.95740	−	6.85442i	−0.167681	−	0.290431i	−0.937604	+	0.347705i	$0.886961\pi$
$558$		0			0
$559$	−1.43274	+	2.48159i	−0.0605986	+	0.104960i
$560$		0			0
$561$	3.90480	+	7.83363i	0.164861	+	0.330736i
$562$		0			0
$563$	22.3471	−	18.7514i	0.941818	−	0.790279i	−0.0360829	−	0.999349i	$-0.511488\pi$
$563$	22.3471	−	18.7514i	0.941818	−	0.790279i	0.977901	+	0.209070i	$0.0670436\pi$
$564$		0			0
$565$	14.4395	−	5.25556i	0.607475	−	0.221103i
$566$		0			0
$567$	8.73185	+	2.18053i	0.366703	+	0.0915737i
$568$		0			0
$569$	−27.7847	+	10.1128i	−1.16479	+	0.423950i	−0.850808	−	0.525477i	$-0.823887\pi$
$569$	−27.7847	+	10.1128i	−1.16479	+	0.423950i	−0.313986	+	0.949427i	$0.601665\pi$
$570$		0			0
$571$	2.49631	−	2.09465i	0.104467	−	0.0876586i	−0.589058	−	0.808091i	$-0.700501\pi$
$571$	2.49631	−	2.09465i	0.104467	−	0.0876586i	0.693525	+	0.720432i	$0.256057\pi$
$572$		0			0
$573$	−18.0713	−	36.2539i	−0.754941	−	1.51453i
$574$		0			0
$575$	−3.52245	+	6.10107i	−0.146897	+	0.254432i
$576$		0			0
$577$	5.10231	+	8.83746i	0.212412	+	0.367908i	0.952469	−	0.304636i	$-0.0985348\pi$
$577$	5.10231	+	8.83746i	0.212412	+	0.367908i	−0.740057	+	0.672544i	$0.765201\pi$
$578$		0			0
$579$	−19.3161	−	18.3337i	−0.802750	−	0.761923i
$580$		0			0
$581$	−1.09003	−	0.396737i	−0.0452220	−	0.0164594i
$582$		0			0
$583$	−3.58382	+	20.3248i	−0.148427	+	0.841769i
$584$		0			0
$585$	0.149924	+	2.87089i	0.00619860	+	0.118697i
$586$		0			0
$587$	−19.5385	−	16.3948i	−0.806441	−	0.676684i	0.143315	−	0.989677i	$-0.454224\pi$
$587$	−19.5385	−	16.3948i	−0.806441	−	0.676684i	−0.949755	+	0.312993i	$0.898668\pi$
$588$		0			0
$589$	−2.01158	−	11.4082i	−0.0828855	−	0.470067i
$590$		0			0
$591$	−21.9218	−	9.53430i	−0.901744	−	0.392189i
$592$		0			0
$593$	−27.4240			−1.12617			−0.563085	−	0.826399i	$-0.690386\pi$
$593$	−27.4240			−1.12617			−0.563085	+	0.826399i	$0.690386\pi$
$594$		0			0
$595$	−2.36362			−0.0968990
$596$		0			0
$597$	18.3102	−	13.5462i	0.749387	−	0.554410i
$598$		0			0
$599$	−7.67240	−	43.5123i	−0.313486	−	1.77787i	−0.580588	−	0.814197i	$-0.697177\pi$
$599$	−7.67240	−	43.5123i	−0.313486	−	1.77787i	0.267103	−	0.963668i	$-0.413934\pi$
$600$		0			0
$601$	−0.268904	−	0.225638i	−0.0109688	−	0.00920395i	0.637287	−	0.770627i	$-0.280057\pi$
$601$	−0.268904	−	0.225638i	−0.0109688	−	0.00920395i	−0.648256	+	0.761423i	$0.724501\pi$
$602$		0			0
$603$	17.9574	+	2.20827i	0.731281	+	0.0899275i
$604$		0			0
$605$	2.59139	−	14.6965i	0.105355	−	0.597497i
$606$		0			0
$607$	34.7496	+	12.6478i	1.41044	+	0.513359i	0.931259	−	0.364357i	$-0.118711\pi$
$607$	34.7496	+	12.6478i	1.41044	+	0.513359i	0.479182	+	0.877716i	$0.340934\pi$
$608$		0			0
$609$	0.173803	−	0.723645i	0.00704284	−	0.0293236i
$610$		0			0
$611$	−1.11979	−	1.93953i	−0.0453018	−	0.0784650i
$612$		0			0
$613$	5.14331	−	8.90847i	0.207736	−	0.359810i	−0.743265	−	0.668997i	$-0.766724\pi$
$613$	5.14331	−	8.90847i	0.207736	−	0.359810i	0.951001	+	0.309188i	$0.100057\pi$
$614$		0			0
$615$	25.7914	+	1.57986i	1.04001	+	0.0637063i
$616$		0			0
$617$	−27.6797	+	23.2260i	−1.11434	+	0.935044i	−0.998305	−	0.0582010i	$-0.981464\pi$
$617$	−27.6797	+	23.2260i	−1.11434	+	0.935044i	−0.116037	+	0.993245i	$0.537019\pi$
$618$		0			0
$619$	2.05140	−	0.746648i	0.0824527	−	0.0300103i	−0.300465	−	0.953793i	$-0.597142\pi$
$619$	2.05140	−	0.746648i	0.0824527	−	0.0300103i	0.382917	+	0.923783i	$0.374919\pi$
$620$		0			0
$621$	−32.5847	−	19.2060i	−1.30758	−	0.770712i
$622$		0			0
$623$	−3.65225	+	1.32931i	−0.146324	+	0.0532577i
$624$		0			0
$625$	−14.7266	+	12.3571i	−0.589065	+	0.494284i
$626$		0			0
$627$	−19.7376	+	29.8142i	−0.788243	+	1.19067i
$628$		0			0
$629$	1.82771	−	3.16569i	0.0728756	−	0.126224i
$630$		0			0
$631$	5.42320	+	9.39326i	0.215894	+	0.373940i	0.953549	−	0.301239i	$-0.0974001\pi$
$631$	5.42320	+	9.39326i	0.215894	+	0.373940i	−0.737655	+	0.675178i	$0.764067\pi$
$632$		0			0
$633$	−21.8536	+	6.47112i	−0.868601	+	0.257204i
$634$		0			0
$635$	28.8874	+	10.5142i	1.14636	+	0.417242i
$636$		0			0
$637$	0.0828681	−	0.469968i	0.00328335	−	0.0186208i
$638$		0			0
$639$	−23.3889	−	25.0909i	−0.925252	−	0.992580i
$640$		0			0
$641$	5.40191	+	4.53274i	0.213363	+	0.179033i	0.743205	−	0.669063i	$-0.233305\pi$
$641$	5.40191	+	4.53274i	0.213363	+	0.179033i	−0.529843	+	0.848096i	$0.677749\pi$
$642$		0			0
$643$	−4.23085	−	23.9943i	−0.166848	−	0.946244i	−0.947138	−	0.320826i	$-0.896040\pi$
$643$	−4.23085	−	23.9943i	−0.166848	−	0.946244i	0.780290	−	0.625418i	$-0.215072\pi$
$644$		0			0
$645$	−2.36221	−	20.7499i	−0.0930118	−	0.817027i
$646$		0			0
$647$	16.0792			0.632137			0.316069	−	0.948736i	$-0.397637\pi$
$647$	16.0792			0.632137			0.316069	+	0.948736i	$0.397637\pi$
$648$		0			0
$649$	15.1019			0.592801
$650$		0			0
$651$	0.471990	+	4.14602i	0.0184987	+	0.162495i
$652$		0			0
$653$	−4.62160	−	26.2104i	−0.180857	−	1.02569i	−0.931164	−	0.364601i	$-0.881205\pi$
$653$	−4.62160	−	26.2104i	−0.180857	−	1.02569i	0.750307	−	0.661090i	$-0.229906\pi$
$654$		0			0
$655$	−27.3649	−	22.9619i	−1.06924	−	0.897196i
$656$		0			0
$657$	−1.47342	+	4.81615i	−0.0574836	+	0.187896i
$658$		0			0
$659$	−5.79620	+	32.8719i	−0.225788	+	1.28051i	0.635386	+	0.772195i	$0.280841\pi$
$659$	−5.79620	+	32.8719i	−0.225788	+	1.28051i	−0.861173	+	0.508311i	$0.830270\pi$
$660$		0			0
$661$	−20.9138	−	7.61200i	−0.813453	−	0.296073i	−0.0984034	−	0.995147i	$-0.531374\pi$
$661$	−20.9138	−	7.61200i	−0.813453	−	0.296073i	−0.715049	+	0.699074i	$0.753596\pi$
$662$		0			0
$663$	−0.932899	+	0.276243i	−0.0362308	+	0.0107284i
$664$		0			0
$665$	−4.82769	−	8.36181i	−0.187210	−	0.324257i
$666$		0			0
$667$	−1.56385	+	2.70867i	−0.0605525	+	0.104880i
$668$		0			0
$669$	−6.23836	+	9.42324i	−0.241189	+	0.364324i
$670$		0			0
$671$	−32.3372	+	27.1342i	−1.24836	+	1.04750i
$672$		0			0
$673$	4.26780	−	1.55335i	0.164512	−	0.0598773i	−0.258452	−	0.966024i	$-0.583212\pi$
$673$	4.26780	−	1.55335i	0.164512	−	0.0598773i	0.422963	+	0.906147i	$0.360990\pi$
$674$		0			0
$675$	3.19771	+	3.88133i	0.123080	+	0.149392i
$676$		0			0
$677$	7.80948	−	2.84242i	0.300143	−	0.109243i	−0.187559	−	0.982253i	$-0.560058\pi$
$677$	7.80948	−	2.84242i	0.300143	−	0.109243i	0.487702	+	0.873010i	$0.337835\pi$
$678$		0			0
$679$	10.2776	−	8.62397i	0.394420	−	0.330958i
$680$		0			0
$681$	−39.6542	−	2.42904i	−1.51955	−	0.0930809i
$682$		0			0
$683$	−18.7316	+	32.4441i	−0.716746	+	1.24144i	0.245537	+	0.969387i	$0.421036\pi$
$683$	−18.7316	+	32.4441i	−0.716746	+	1.24144i	−0.962282	+	0.272053i	$0.912297\pi$
$684$		0			0
$685$	−6.75494	−	11.6999i	−0.258093	−	0.447030i
$686$		0			0
$687$	10.5235	−	43.8157i	0.401497	−	1.67167i
$688$		0			0
$689$	−2.15573	−	0.784623i	−0.0821269	−	0.0298918i
$690$		0			0
$691$	6.54782	−	37.1345i	0.249091	−	1.41266i	−0.561707	−	0.827337i	$-0.689855\pi$
$691$	6.54782	−	37.1345i	0.249091	−	1.41266i	0.810797	−	0.585327i	$-0.199034\pi$
$692$		0			0
$693$	7.75308	−	10.2847i	0.294515	−	0.390684i
$694$		0			0
$695$	−27.1950	−	22.8193i	−1.03156	−	0.865585i
$696$		0			0
$697$	1.51857	+	8.61223i	0.0575199	+	0.326212i
$698$		0			0
$699$	13.9952	−	10.3539i	0.529349	−	0.391622i
$700$		0			0
$701$	−8.75590			−0.330706			−0.165353	−	0.986234i	$-0.552876\pi$
$701$	−8.75590			−0.330706			−0.165353	+	0.986234i	$0.552876\pi$
$702$		0			0
$703$	14.9324			0.563186
$704$		0			0
$705$	14.9679	+	6.50986i	0.563722	+	0.245175i
$706$		0			0
$707$	−0.944809	−	5.35828i	−0.0355332	−	0.201519i
$708$		0			0
$709$	30.0281	+	25.1966i	1.12773	+	0.946278i	0.998969	−	0.0453976i	$-0.0144555\pi$
$709$	30.0281	+	25.1966i	1.12773	+	0.946278i	0.128761	+	0.991676i	$0.458900\pi$
$710$		0			0
$711$	2.77622	−	1.80217i	0.104116	−	0.0675866i
$712$		0			0
$713$	3.04522	−	17.2703i	0.114044	−	0.646778i
$714$		0			0
$715$	3.86595	+	1.40709i	0.144578	+	0.0526223i
$716$		0			0
$717$	28.8800	+	27.4112i	1.07854	+	1.02369i
$718$		0			0
$719$	7.94097	+	13.7542i	0.296148	+	0.512944i	0.975251	−	0.221099i	$-0.0709644\pi$
$719$	7.94097	+	13.7542i	0.296148	+	0.512944i	−0.679103	+	0.734043i	$0.737631\pi$
$720$		0			0
$721$	0.628566	−	1.08871i	0.0234090	−	0.0405456i
$722$		0			0
$723$	−23.7641	−	47.6745i	−0.883797	−	1.77303i
$724$		0			0
$725$	0.318559	−	0.267303i	0.0118310	−	0.00992738i
$726$		0			0
$727$	38.5157	−	14.0186i	1.42847	−	0.519919i	0.491975	−	0.870609i	$-0.336275\pi$
$727$	38.5157	−	14.0186i	1.42847	−	0.519919i	0.936492	+	0.350690i	$0.114053\pi$
$728$		0			0
$729$	−20.9924	+	16.9800i	−0.777495	+	0.628889i
$730$		0			0
$731$	6.64163	−	2.41736i	0.245650	−	0.0894092i
$732$		0			0
$733$	0.546221	−	0.458334i	0.0201751	−	0.0169289i	−0.632644	−	0.774442i	$-0.718030\pi$
$733$	0.546221	−	0.458334i	0.0201751	−	0.0169289i	0.652819	+	0.757514i	$0.273586\pi$
$734$		0			0
$735$	1.55159	+	3.11273i	0.0572313	+	0.114815i
$736$		0			0
$737$	12.9460	−	22.4231i	0.476871	−	0.825964i
$738$		0			0
$739$	−8.81462	−	15.2674i	−0.324251	−	0.561619i	0.657109	−	0.753795i	$-0.271779\pi$
$739$	−8.81462	−	15.2674i	−0.324251	−	0.561619i	−0.981361	+	0.192176i	$0.938446\pi$
$740$		0			0
$741$	−2.88271	−	2.73610i	−0.105899	−	0.100513i
$742$		0			0
$743$	−20.1486	−	7.33349i	−0.739181	−	0.269040i	−0.0551351	−	0.998479i	$-0.517559\pi$
$743$	−20.1486	−	7.33349i	−0.739181	−	0.269040i	−0.684046	+	0.729439i	$0.739781\pi$
$744$		0			0
$745$	0.878160	−	4.98029i	0.0321733	−	0.182464i
$746$		0			0
$747$	2.91888	−	1.89478i	0.106796	−	0.0693262i
$748$		0			0
$749$	9.40253	+	7.88966i	0.343561	+	0.288282i
$750$		0			0
$751$	2.70460	+	15.3385i	0.0986922	+	0.559711i	0.993553	+	0.113366i	$0.0361634\pi$
$751$	2.70460	+	15.3385i	0.0986922	+	0.559711i	−0.894861	+	0.446345i	$0.852725\pi$
$752$		0			0
$753$	42.6191	+	18.5360i	1.55313	+	0.675490i
$754$		0			0
$755$	45.6887			1.66278
$756$		0			0
$757$	5.39440			0.196063			0.0980313	−	0.995183i	$-0.468745\pi$
$757$	5.39440			0.196063			0.0980313	+	0.995183i	$0.468745\pi$
$758$		0			0
$759$	−43.5146	+	32.1929i	−1.57948	+	1.16853i
$760$		0			0
$761$	−3.41138	−	19.3469i	−0.123662	−	0.701324i	−0.982093	−	0.188395i	$-0.939671\pi$
$761$	−3.41138	−	19.3469i	−0.123662	−	0.701324i	0.858431	−	0.512929i	$-0.171440\pi$
$762$		0			0
$763$	−12.3647	−	10.3752i	−0.447633	−	0.375609i
$764$		0			0
$765$	4.26844	−	5.66222i	0.154326	−	0.204718i
$766$		0			0
$767$	−0.291498	+	1.65316i	−0.0105254	+	0.0596923i
$768$		0			0
$769$	−37.8865	−	13.7896i	−1.36622	−	0.497264i	−0.448249	−	0.893909i	$-0.647952\pi$
$769$	−37.8865	−	13.7896i	−1.36622	−	0.497264i	−0.917972	+	0.396645i	$0.870174\pi$
$770$		0			0
$771$	−1.52812	+	6.36247i	−0.0550338	+	0.229139i
$772$		0			0
$773$	−12.5999	−	21.8237i	−0.453188	−	0.784944i	0.545394	−	0.838180i	$-0.316380\pi$
$773$	−12.5999	−	21.8237i	−0.453188	−	0.784944i	−0.998582	+	0.0532356i	$0.983047\pi$
$774$		0			0
$775$	−1.16582	+	2.01925i	−0.0418773	+	0.0725337i
$776$		0			0
$777$	−5.36880	−	0.328869i	−0.192605	−	0.0117981i
$778$		0			0
$779$	−27.3659	+	22.9627i	−0.980486	+	0.822725i
$780$		0			0
$781$	−46.1277	+	16.7891i	−1.65058	+	0.600761i
$782$		0			0
$783$	1.41967	+	1.72318i	0.0507350	+	0.0615814i
$784$		0			0
$785$	−37.3493	+	13.5940i	−1.33305	+	0.485192i
$786$		0			0
$787$	21.6306	−	18.1503i	0.771049	−	0.646987i	−0.169929	−	0.985456i	$-0.554354\pi$
$787$	21.6306	−	18.1503i	0.771049	−	0.646987i	0.940977	+	0.338470i	$0.109909\pi$
$788$		0			0
$789$	−0.690414	+	1.04289i	−0.0245794	+	0.0371279i
$790$		0			0
$791$	3.82619	−	6.62716i	0.136044	−	0.235635i
$792$		0			0
$793$	−2.34613	−	4.06362i	−0.0833136	−	0.144303i
$794$		0			0
$795$	16.0314	−	4.74711i	0.568576	−	0.168363i
$796$		0			0
$797$	16.6469	+	6.05899i	0.589665	+	0.214620i	0.619582	−	0.784932i	$-0.287302\pi$
$797$	16.6469	+	6.05899i	0.589665	+	0.214620i	−0.0299171	+	0.999552i	$0.509524\pi$
$798$		0			0
$799$	−0.959238	+	5.44011i	−0.0339354	+	0.192457i
$800$		0			0
$801$	3.41110	−	11.1498i	0.120525	−	0.393959i
$802$		0			0
$803$	5.52134	+	4.63295i	0.194844	+	0.163493i
$804$		0			0
$805$	−2.53818	−	14.3947i	−0.0894591	−	0.507348i
$806$		0			0
$807$	0.116843	+	1.02636i	0.00411306	+	0.0361296i
$808$		0			0
$809$	−31.3847			−1.10343			−0.551713	−	0.834034i	$-0.686026\pi$
$809$	−31.3847			−1.10343			−0.551713	+	0.834034i	$0.686026\pi$
$810$		0			0
$811$	−29.6782			−1.04214			−0.521071	−	0.853513i	$-0.674467\pi$
$811$	−29.6782			−1.04214			−0.521071	+	0.853513i	$0.674467\pi$
$812$		0			0
$813$	4.21356	+	37.0124i	0.147776	+	1.29808i
$814$		0			0
$815$	−5.87804	−	33.3360i	−0.205899	−	1.16771i
$816$		0			0
$817$	22.1174	+	18.5587i	0.773791	+	0.649288i
$818$		0			0
$819$	0.976193	+	1.04723i	0.0341109	+	0.0365931i
$820$		0			0
$821$	1.85541	−	10.5225i	0.0647542	−	0.367239i	−0.935161	−	0.354223i	$-0.884745\pi$
$821$	1.85541	−	10.5225i	0.0647542	−	0.367239i	0.999915	−	0.0130165i	$-0.00414341\pi$
$822$		0			0
$823$	−15.4490	−	5.62296i	−0.538517	−	0.196004i	0.0584203	−	0.998292i	$-0.481394\pi$
$823$	−15.4490	−	5.62296i	−0.538517	−	0.196004i	−0.596937	+	0.802288i	$0.703616\pi$
$824$		0			0
$825$	6.90059	−	2.04335i	0.240248	−	0.0711404i
$826$		0			0
$827$	17.1759	+	29.7495i	0.597265	+	1.03449i	0.993223	+	0.116224i	$0.0370792\pi$
$827$	17.1759	+	29.7495i	0.597265	+	1.03449i	−0.395958	+	0.918269i	$0.629588\pi$
$828$		0			0
$829$	−24.1791	+	41.8794i	−0.839775	+	1.45453i	0.0503077	+	0.998734i	$0.483980\pi$
$829$	−24.1791	+	41.8794i	−0.839775	+	1.45453i	−0.890083	+	0.455799i	$0.849354\pi$
$830$		0			0
$831$	21.7581	−	32.8663i	0.754780	−	1.14012i
$832$		0			0
$833$	−0.901699	+	0.756615i	−0.0312420	+	0.0262152i
$834$		0			0
$835$	−21.8053	+	7.93649i	−0.754604	+	0.274654i
$836$		0			0
$837$	−10.7844	−	6.35656i	−0.372765	−	0.219715i
$838$		0			0
$839$	29.2776	−	10.6562i	1.01078	−	0.367892i	0.217045	−	0.976162i	$-0.430358\pi$
$839$	29.2776	−	10.6562i	1.01078	−	0.367892i	0.793731	+	0.608269i	$0.208136\pi$
$840$		0			0
$841$	−22.0739	+	18.5222i	−0.761168	+	0.638695i
$842$		0			0
$843$	−36.7632	−	2.25195i	−1.26619	−	0.0775613i
$844$		0			0
$845$	12.8235	−	22.2110i	0.441143	−	0.764082i
$846$		0			0
$847$	−3.71588	−	6.43610i	−0.127679	−	0.221147i
$848$		0			0
$849$	9.81456	−	40.8639i	0.336835	−	1.40245i
$850$		0			0
$851$	21.2421	+	7.73150i	0.728171	+	0.265032i
$852$		0			0
$853$	−2.35528	+	13.3575i	−0.0806434	+	0.457352i	0.917569	+	0.397578i	$0.130149\pi$
$853$	−2.35528	+	13.3575i	−0.0806434	+	0.457352i	−0.998212	+	0.0597739i	$0.980962\pi$
$854$		0			0
$855$	28.7496	+	3.53541i	0.983215	+	0.120908i
$856$		0			0
$857$	26.7440	+	22.4409i	0.913559	+	0.766567i	0.972793	−	0.231677i	$-0.0744212\pi$
$857$	26.7440	+	22.4409i	0.913559	+	0.766567i	−0.0592336	+	0.998244i	$0.518866\pi$
$858$		0			0
$859$	−6.24893	−	35.4395i	−0.213211	−	1.20918i	−0.883984	−	0.467516i	$-0.845149\pi$
$859$	−6.24893	−	35.4395i	−0.213211	−	1.20918i	0.670774	−	0.741662i	$-0.265962\pi$
$860$		0			0
$861$	10.3449	−	7.65333i	0.352553	−	0.260825i
$862$		0			0
$863$	−15.1206			−0.514712			−0.257356	−	0.966317i	$-0.582851\pi$
$863$	−15.1206			−0.514712			−0.257356	+	0.966317i	$0.582851\pi$
$864$		0			0
$865$	−8.98502			−0.305500
$866$		0			0
$867$	−24.8009	−	10.7865i	−0.842284	−	0.366328i
$868$		0			0
$869$	−0.822513	−	4.66470i	−0.0279018	−	0.158239i
$870$		0			0
$871$	2.20471	+	1.84997i	0.0747039	+	0.0626840i
$872$		0			0
$873$	2.09905	+	40.1948i	0.0710422	+	1.36039i
$874$		0			0
$875$	−2.08092	+	11.8015i	−0.0703480	+	0.398963i
$876$		0			0
$877$	−36.4459	−	13.2652i	−1.23069	−	0.447934i	−0.356856	−	0.934159i	$-0.616151\pi$
$877$	−36.4459	−	13.2652i	−1.23069	−	0.447934i	−0.873834	+	0.486225i	$0.838373\pi$
$878$		0			0
$879$	11.5800	+	10.9910i	0.390583	+	0.370718i
$880$		0			0
$881$	−25.6919	−	44.4996i	−0.865581	−	1.49923i	−0.866469	−	0.499230i	$-0.833616\pi$
$881$	−25.6919	−	44.4996i	−0.865581	−	1.49923i	0.000888482	−	1.00000i	$-0.499717\pi$
$882$		0			0
$883$	−6.02719	+	10.4394i	−0.202831	+	0.351314i	−0.949440	−	0.313950i	$-0.898348\pi$
$883$	−6.02719	+	10.4394i	−0.202831	+	0.351314i	0.746608	+	0.665264i	$0.231681\pi$
$884$		0			0
$885$	−5.45789	−	10.9494i	−0.183465	−	0.368059i
$886$		0			0
$887$	5.23490	−	4.39261i	0.175771	−	0.147489i	−0.550658	−	0.834731i	$-0.685623\pi$
$887$	5.23490	−	4.39261i	0.175771	−	0.147489i	0.726429	+	0.687242i	$0.241179\pi$
$888$		0			0
$889$	14.3860	−	5.23606i	0.482490	−	0.175612i
$890$		0			0
$891$	10.6366	+	37.1461i	0.356339	+	1.24444i
$892$		0			0
$893$	−21.2048	+	7.71791i	−0.709591	+	0.258270i
$894$		0			0
$895$	4.92794	−	4.13503i	0.164723	−	0.138219i
$896$		0			0
$897$	−2.68415	−	5.38482i	−0.0896212	−	0.179794i
$898$		0			0
$899$	−0.517582	+	0.896479i	−0.0172623	+	0.0298992i
$900$		0			0
$901$	2.82924	+	4.90039i	0.0942557	+	0.163256i
$902$		0			0
$903$	−7.54338	−	7.15973i	−0.251028	−	0.238261i
$904$		0			0
$905$	8.92919	+	3.24996i	0.296816	+	0.108032i
$906$		0			0
$907$	8.92792	−	50.6327i	0.296447	−	1.68123i	−0.364818	−	0.931079i	$-0.618869\pi$
$907$	8.92792	−	50.6327i	0.296447	−	1.68123i	0.661264	−	0.750153i	$-0.270020\pi$
$908$		0			0
$909$	14.5424	+	7.41309i	0.482339	+	0.245877i
$910$		0			0
$911$	27.5772	+	23.1400i	0.913672	+	0.766662i	0.972814	−	0.231587i	$-0.0743919\pi$
$911$	27.5772	+	23.1400i	0.913672	+	0.766662i	−0.0591417	+	0.998250i	$0.518836\pi$
$912$		0			0
$913$	−0.864779	−	4.90441i	−0.0286200	−	0.162312i
$914$		0			0
$915$	31.3600	+	13.6392i	1.03673	+	0.450897i
$916$		0			0
$917$	−17.7898			−0.587470
$918$		0			0
$919$	39.1299			1.29078			0.645388	−	0.763855i	$-0.276696\pi$
$919$	39.1299			1.29078			0.645388	+	0.763855i	$0.276696\pi$
$920$		0			0
$921$	11.6206	−	8.59712i	0.382911	−	0.283285i
$922$		0			0
$923$	−0.947501	−	5.37355i	−0.0311874	−	0.176872i
$924$		0			0
$925$	−2.30238	−	1.93193i	−0.0757018	−	0.0635214i
$926$		0			0
$927$	1.47296	+	3.47186i	0.0483783	+	0.114031i
$928$		0			0
$929$	1.11046	−	6.29772i	0.0364329	−	0.206621i	−0.961157	−	0.276001i	$-0.910991\pi$
$929$	1.11046	−	6.29772i	0.0364329	−	0.206621i	0.997590	+	0.0693793i	$0.0221019\pi$
$930$		0			0
$931$	−4.51841	−	1.64457i	−0.148085	−	0.0538985i
$932$		0			0
$933$	9.23265	−	38.4411i	0.302264	−	1.25850i
$934$		0			0
$935$	−5.07378	−	8.78804i	−0.165930	−	0.287400i
$936$		0			0
$937$	16.2199	−	28.0936i	0.529880	−	0.917779i	−0.469512	−	0.882926i	$-0.655570\pi$
$937$	16.2199	−	28.0936i	0.529880	−	0.917779i	0.999392	−	0.0348535i	$-0.0110965\pi$
$938$		0			0
$939$	14.2940	+	0.875586i	0.466466	+	0.0285737i
$940$		0			0
$941$	12.3761	−	10.3848i	0.403449	−	0.338534i	−0.418376	−	0.908274i	$-0.637401\pi$
$941$	12.3761	−	10.3848i	0.403449	−	0.338534i	0.821825	+	0.569740i	$0.192956\pi$
$942$		0			0
$943$	−50.8188	+	18.4965i	−1.65489	+	0.602330i
$944$		0			0
$945$	−10.2588	−	1.90430i	−0.333718	−	0.0619469i
$946$		0			0
$947$	32.4766	−	11.8205i	1.05535	−	0.384116i	0.244670	−	0.969606i	$-0.421320\pi$
$947$	32.4766	−	11.8205i	1.05535	−	0.384116i	0.810679	+	0.585491i	$0.199098\pi$
$948$		0			0
$949$	−0.613731	+	0.514982i	−0.0199226	+	0.0167170i
$950$		0			0
$951$	−2.72362	+	4.11412i	−0.0883196	+	0.133409i
$952$		0			0
$953$	−4.88131	+	8.45468i	−0.158121	+	0.273874i	−0.934191	−	0.356773i	$-0.883877\pi$
$953$	−4.88131	+	8.45468i	−0.158121	+	0.273874i	0.776070	+	0.630647i	$0.217210\pi$
$954$		0			0
$955$	23.4813	+	40.6709i	0.759839	+	1.31608i
$956$		0			0
$957$	3.06363	−	0.907179i	0.0990330	−	0.0293249i
$958$		0			0
$959$	−6.32219	−	2.30109i	−0.204154	−	0.0743060i
$960$		0			0
$961$	−4.37523	+	24.8131i	−0.141136	+	0.800424i
$962$		0			0
$963$	−35.8802	+	8.27659i	−1.15622	+	0.266709i
$964$		0			0
$965$	23.6515	+	19.8460i	0.761370	+	0.638865i
$966$		0			0
$967$	−0.949158	−	5.38294i	−0.0305229	−	0.173104i	0.965736	−	0.259528i	$-0.0835670\pi$
$967$	−0.949158	−	5.38294i	−0.0305229	−	0.173104i	−0.996258	+	0.0864243i	$0.972456\pi$
$968$		0			0
$969$	1.10885	+	9.74028i	0.0356214	+	0.312903i
$970$		0			0
$971$	−2.57872			−0.0827551			−0.0413775	−	0.999144i	$-0.513175\pi$
$971$	−2.57872			−0.0827551			−0.0413775	+	0.999144i	$0.513175\pi$
$972$		0			0
$973$	−17.6793			−0.566772
$974$		0			0
$975$	0.0904850	+	0.794831i	0.00289784	+	0.0254550i
$976$		0			0
$977$	9.20588	+	52.2091i	0.294522	+	1.67032i	0.669138	+	0.743138i	$0.266664\pi$
$977$	9.20588	+	52.2091i	0.294522	+	1.67032i	−0.374616	+	0.927180i	$0.622225\pi$
$978$		0			0
$979$	−12.7824	−	10.7257i	−0.408527	−	0.342795i
$980$		0			0
$981$	47.1839	−	10.8841i	1.50647	−	0.347501i
$982$		0			0
$983$	−7.95960	+	45.1412i	−0.253872	+	1.43978i	0.545080	+	0.838384i	$0.316499\pi$
$983$	−7.95960	+	45.1412i	−0.253872	+	1.43978i	−0.798952	+	0.601395i	$0.794612\pi$
$984$		0			0
$985$	26.0431	+	9.47890i	0.829801	+	0.302023i
$986$		0			0
$987$	7.79396	−	2.30789i	0.248084	−	0.0734610i
$988$		0			0
$989$	21.8541	+	37.8525i	0.694921	+	1.20364i
$990$		0			0
$991$	−7.70370	+	13.3432i	−0.244716	+	0.423860i	−0.962052	−	0.272867i	$-0.912028\pi$
$991$	−7.70370	+	13.3432i	−0.244716	+	0.423860i	0.717336	+	0.696728i	$0.245361\pi$
$992$		0			0
$993$	20.8421	−	31.4826i	0.661404	−	0.999072i
$994$		0			0
$995$	−20.2278	+	16.9731i	−0.641264	+	0.538084i
$996$		0			0
$997$	−29.1687	+	10.6166i	−0.923783	+	0.336230i	−0.759743	−	0.650224i	$-0.774675\pi$
$997$	−29.1687	+	10.6166i	−0.923783	+	0.336230i	−0.164041	+	0.986454i	$0.552453\pi$
$998$		0			0
$999$	10.4833	−	12.2674i	0.331676	−	0.388125i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bo.a.169.6	yes	54
27.4	even	9	inner	756.2.bo.a.85.6	✓	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bo.a.85.6	✓	54	27.4	even	9	inner
756.2.bo.a.169.6	yes	54	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bo (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.195914 - 1.72094i) q^{3} +(0.348691 + 1.97752i) q^{5} +(0.766044 + 0.642788i) q^{7} +(-2.92324 + 0.674312i) q^{9} +O(q^{10})\)	\(q+(-0.195914 - 1.72094i) q^{3} +(0.348691 + 1.97752i) q^{5} +(0.766044 + 0.642788i) q^{7} +(-2.92324 + 0.674312i) q^{9} +(-0.745510 + 4.22800i) q^{11} +(-0.448439 - 0.163218i) q^{13} +(3.33488 - 0.987499i) q^{15} +(0.588542 + 1.01939i) q^{17} +(-2.40419 + 4.16419i) q^{19} +(0.956117 - 1.44424i) q^{21} +(-5.57617 + 4.67896i) q^{23} +(0.909450 - 0.331013i) q^{25} +(1.73315 + 4.89859i) q^{27} +(0.403765 - 0.146958i) q^{29} +(-1.84553 + 1.54858i) q^{31} +(7.42217 + 0.454649i) q^{33} +(-1.00401 + 1.73900i) q^{35} +(-1.55274 - 2.68943i) q^{37} +(-0.193033 + 0.803711i) q^{39} +(6.98140 + 2.54102i) q^{41} +(1.04268 - 5.91334i) q^{43} +(-2.35277 - 5.54564i) q^{45} +(3.59503 + 3.01659i) q^{47} +(0.173648 + 0.984808i) q^{49} +(1.63899 - 1.21256i) q^{51} +4.80720 q^{53} -8.62092 q^{55} +(7.63731 + 3.32164i) q^{57} +(-0.610826 - 3.46417i) q^{59} +(7.53216 + 6.32023i) q^{61} +(-2.67277 - 1.36247i) q^{63} +(0.166402 - 0.943711i) q^{65} +(-5.66718 - 2.06268i) q^{67} +(9.14465 + 8.67955i) q^{69} +(5.71692 + 9.90200i) q^{71} +(0.839416 - 1.45391i) q^{73} +(-0.747826 - 1.50026i) q^{75} +(-3.28880 + 2.75963i) q^{77} +(-1.03675 + 0.377347i) q^{79} +(8.09061 - 3.94234i) q^{81} +(-1.09003 + 0.396737i) q^{83} +(-1.81064 + 1.51931i) q^{85} +(-0.332009 - 0.666062i) q^{87} +(-1.94332 + 3.36593i) q^{89} +(-0.238609 - 0.413283i) q^{91} +(3.02657 + 2.87264i) q^{93} +(-9.07309 - 3.30234i) q^{95} +(2.32975 - 13.2127i) q^{97} +(-0.671688 - 12.8621i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q - 3 q^{3} - 3 q^{5} + 3 q^{9}+O(q^{10}) \) 54 * q - 3 * q^3 - 3 * q^5 + 3 * q^9	\( 54 q - 3 q^{3} - 3 q^{5} + 3 q^{9} - 9 q^{13} + 3 q^{15} - 3 q^{21} - 45 q^{25} + 15 q^{27} + 6 q^{29} - 9 q^{31} + 6 q^{33} + 6 q^{35} + 30 q^{39} + 9 q^{41} + 9 q^{43} - 21 q^{45} - 27 q^{47} - 108 q^{51} - 84 q^{53} - 57 q^{57} - 66 q^{59} + 3 q^{63} + 30 q^{65} + 63 q^{67} + 42 q^{69} + 42 q^{71} + 3 q^{75} - 9 q^{77} + 36 q^{79} + 3 q^{81} + 12 q^{83} + 18 q^{85} + 39 q^{87} + 12 q^{89} + 21 q^{93} + 120 q^{95} + 18 q^{97} + 39 q^{99}+O(q^{100}) \) 54 * q - 3 * q^3 - 3 * q^5 + 3 * q^9 - 9 * q^13 + 3 * q^15 - 3 * q^21 - 45 * q^25 + 15 * q^27 + 6 * q^29 - 9 * q^31 + 6 * q^33 + 6 * q^35 + 30 * q^39 + 9 * q^41 + 9 * q^43 - 21 * q^45 - 27 * q^47 - 108 * q^51 - 84 * q^53 - 57 * q^57 - 66 * q^59 + 3 * q^63 + 30 * q^65 + 63 * q^67 + 42 * q^69 + 42 * q^71 + 3 * q^75 - 9 * q^77 + 36 * q^79 + 3 * q^81 + 12 * q^83 + 18 * q^85 + 39 * q^87 + 12 * q^89 + 21 * q^93 + 120 * q^95 + 18 * q^97 + 39 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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