LMFDB - Embedded newform 512.2.i.a.161.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [512,2,Mod(33,512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(512, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 15]))

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

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

chi := DirichletCharacter("512.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 512 = 2^{9} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	512.i (of order $16$, degree $8$, not 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:	$4.08834058349$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 64)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			161.6
Character	$\chi$	$=$	512.161
Dual form			512.2.i.a.353.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.93660 + 0.385213i) q^{3} +(0.787711 - 1.17889i) q^{5} +(2.16489 - 0.896725i) q^{7} +(0.830380 + 0.343954i) q^{9} +O(q^{10})$	\(q+(1.93660 + 0.385213i) q^{3} +(0.787711 - 1.17889i) q^{5} +(2.16489 - 0.896725i) q^{7} +(0.830380 + 0.343954i) q^{9} +(-1.08337 - 5.44648i) q^{11} +(-1.49710 - 2.24057i) q^{13} +(1.97960 - 1.97960i) q^{15} +(3.43875 + 3.43875i) q^{17} +(-1.24019 + 0.828669i) q^{19} +(4.53794 - 0.902653i) q^{21} +(-2.14281 + 5.17319i) q^{23} +(1.14412 + 2.76214i) q^{25} +(-3.44969 - 2.30501i) q^{27} +(-1.63164 + 8.20281i) q^{29} -5.17816i q^{31} -10.9650i q^{33} +(0.648162 - 3.25853i) q^{35} +(6.79044 + 4.53723i) q^{37} +(-2.03618 - 4.91578i) q^{39} +(-2.24634 + 5.42314i) q^{41} +(4.16031 - 0.827538i) q^{43} +(1.05958 - 0.707992i) q^{45} +(0.733603 + 0.733603i) q^{47} +(-1.06713 + 1.06713i) q^{49} +(5.33482 + 7.98413i) q^{51} +(-0.575078 - 2.89111i) q^{53} +(-7.27421 - 3.01307i) q^{55} +(-2.72096 + 1.12706i) q^{57} +(-3.31738 + 4.96481i) q^{59} +(-0.382794 - 0.0761424i) q^{61} +2.10611 q^{63} -3.82067 q^{65} +(1.67538 + 0.333253i) q^{67} +(-6.14253 + 9.19295i) q^{69} +(0.843458 - 0.349372i) q^{71} +(11.9774 + 4.96122i) q^{73} +(1.15168 + 5.78989i) q^{75} +(-7.22938 - 10.8195i) q^{77} +(5.30583 - 5.30583i) q^{79} +(-7.69937 - 7.69937i) q^{81} +(-1.28800 + 0.860615i) q^{83} +(6.76266 - 1.34518i) q^{85} +(-6.31966 + 15.2570i) q^{87} +(-3.98900 - 9.63030i) q^{89} +(-5.25023 - 3.50809i) q^{91} +(1.99470 - 10.0280i) q^{93} +2.11480i q^{95} -4.23236i q^{97} +(0.973732 - 4.89528i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{3} + 8 q^{5} + 8 q^{7} - 8 q^{9}+O(q^{10}) $ 56 * q - 8 * q^3 + 8 * q^5 + 8 * q^7 - 8 * q^9	$ 56 q - 8 q^{3} + 8 q^{5} + 8 q^{7} - 8 q^{9} - 8 q^{11} + 8 q^{13} + 8 q^{15} - 8 q^{17} - 8 q^{19} + 8 q^{21} + 8 q^{23} - 8 q^{25} - 8 q^{27} + 8 q^{29} - 8 q^{35} + 8 q^{37} + 8 q^{39} - 8 q^{41} - 8 q^{43} + 8 q^{45} + 8 q^{47} - 8 q^{49} + 24 q^{51} + 8 q^{53} - 56 q^{55} - 8 q^{57} + 56 q^{59} + 8 q^{61} - 64 q^{63} - 16 q^{65} + 72 q^{67} + 8 q^{69} - 56 q^{71} - 8 q^{73} + 56 q^{75} + 8 q^{77} - 24 q^{79} - 8 q^{81} - 8 q^{83} + 8 q^{85} + 8 q^{87} - 8 q^{89} - 8 q^{91} - 16 q^{93} + 16 q^{99}+O(q^{100}) $ 56 * q - 8 * q^3 + 8 * q^5 + 8 * q^7 - 8 * q^9 - 8 * q^11 + 8 * q^13 + 8 * q^15 - 8 * q^17 - 8 * q^19 + 8 * q^21 + 8 * q^23 - 8 * q^25 - 8 * q^27 + 8 * q^29 - 8 * q^35 + 8 * q^37 + 8 * q^39 - 8 * q^41 - 8 * q^43 + 8 * q^45 + 8 * q^47 - 8 * q^49 + 24 * q^51 + 8 * q^53 - 56 * q^55 - 8 * q^57 + 56 * q^59 + 8 * q^61 - 64 * q^63 - 16 * q^65 + 72 * q^67 + 8 * q^69 - 56 * q^71 - 8 * q^73 + 56 * q^75 + 8 * q^77 - 24 * q^79 - 8 * q^81 - 8 * q^83 + 8 * q^85 + 8 * q^87 - 8 * q^89 - 8 * q^91 - 16 * q^93 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/512\mathbb{Z}\right)^\times$.

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{11}{16}\right)$	$1$

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
$3$	1.93660	+	0.385213i	1.11809	+	0.222403i	0.719342	−	0.694656i	$-0.244443\pi$
$3$	1.93660	+	0.385213i	1.11809	+	0.222403i	0.398752	+	0.917059i	$0.369443\pi$
$4$		0			0
$5$	0.787711	−	1.17889i	0.352275	−	0.527217i	−0.612439	−	0.790518i	$-0.709811\pi$
$5$	0.787711	−	1.17889i	0.352275	−	0.527217i	0.964714	+	0.263301i	$0.0848113\pi$
$6$		0			0
$7$	2.16489	−	0.896725i	0.818250	−	0.338930i	0.0660095	−	0.997819i	$-0.478973\pi$
$7$	2.16489	−	0.896725i	0.818250	−	0.338930i	0.752240	+	0.658889i	$0.228973\pi$
$8$		0			0
$9$	0.830380	+	0.343954i	0.276793	+	0.114651i
$10$		0			0
$11$	−1.08337	−	5.44648i	−0.326649	−	1.64218i	−0.699752	−	0.714386i	$-0.746706\pi$
$11$	−1.08337	−	5.44648i	−0.326649	−	1.64218i	0.373102	−	0.927790i	$-0.378294\pi$
$12$		0			0
$13$	−1.49710	−	2.24057i	−0.415221	−	0.621422i	0.563623	−	0.826032i	$-0.309407\pi$
$13$	−1.49710	−	2.24057i	−0.415221	−	0.621422i	−0.978843	+	0.204610i	$0.934407\pi$
$14$		0			0
$15$	1.97960	−	1.97960i	0.511132	−	0.511132i
$16$		0			0
$17$	3.43875	+	3.43875i	0.834020	+	0.834020i	0.988064	−	0.154044i	$-0.0492299\pi$
$17$	3.43875	+	3.43875i	0.834020	+	0.834020i	−0.154044	+	0.988064i	$0.549230\pi$
$18$		0			0
$19$	−1.24019	+	0.828669i	−0.284519	+	0.190110i	−0.689638	−	0.724154i	$-0.742230\pi$
$19$	−1.24019	+	0.828669i	−0.284519	+	0.190110i	0.405118	+	0.914264i	$0.367230\pi$
$20$		0			0
$21$	4.53794	−	0.902653i	0.990260	−	0.196975i
$22$		0			0
$23$	−2.14281	+	5.17319i	−0.446806	+	1.07868i	0.526706	+	0.850048i	$0.323427\pi$
$23$	−2.14281	+	5.17319i	−0.446806	+	1.07868i	−0.973512	+	0.228637i	$0.926573\pi$
$24$		0			0
$25$	1.14412	+	2.76214i	0.228823	+	0.552429i
$26$		0			0
$27$	−3.44969	−	2.30501i	−0.663893	−	0.443599i
$28$		0			0
$29$	−1.63164	+	8.20281i	−0.302988	+	1.52322i	0.466476	+	0.884534i	$0.345524\pi$
$29$	−1.63164	+	8.20281i	−0.302988	+	1.52322i	−0.769464	+	0.638690i	$0.779476\pi$
$30$		0			0
$31$		−	5.17816i		−	0.930026i	−0.885304	−	0.465013i	$-0.846050\pi$
$31$		−	5.17816i		−	0.930026i	0.885304	−	0.465013i	$-0.153950\pi$
$32$		0			0
$33$		−	10.9650i		−	1.90876i
$34$		0			0
$35$	0.648162	−	3.25853i	0.109559	−	0.550792i
$36$		0			0
$37$	6.79044	+	4.53723i	1.11634	+	0.745916i	0.969948	−	0.243310i	$-0.0782334\pi$
$37$	6.79044	+	4.53723i	1.11634	+	0.745916i	0.146394	+	0.989226i	$0.453233\pi$
$38$		0			0
$39$	−2.03618	−	4.91578i	−0.326050	−	0.787155i
$40$		0			0
$41$	−2.24634	+	5.42314i	−0.350819	+	0.846952i	0.645701	+	0.763591i	$0.276565\pi$
$41$	−2.24634	+	5.42314i	−0.350819	+	0.846952i	−0.996519	+	0.0833609i	$0.973435\pi$
$42$		0			0
$43$	4.16031	−	0.827538i	0.634442	−	0.126198i	0.132617	−	0.991167i	$-0.457662\pi$
$43$	4.16031	−	0.827538i	0.634442	−	0.126198i	0.501825	+	0.864969i	$0.332662\pi$
$44$		0			0
$45$	1.05958	−	0.707992i	0.157954	−	0.105541i
$46$		0			0
$47$	0.733603	+	0.733603i	0.107007	+	0.107007i	0.758583	−	0.651576i	$-0.225892\pi$
$47$	0.733603	+	0.733603i	0.107007	+	0.107007i	−0.651576	+	0.758583i	$0.725892\pi$
$48$		0			0
$49$	−1.06713	+	1.06713i	−0.152448	+	0.152448i
$50$		0			0
$51$	5.33482	+	7.98413i	0.747025	+	1.11800i
$52$		0			0
$53$	−0.575078	−	2.89111i	−0.0789930	−	0.397125i	−0.999972	−	0.00751192i	$-0.997609\pi$
$53$	−0.575078	−	2.89111i	−0.0789930	−	0.397125i	0.920979	−	0.389613i	$-0.127391\pi$
$54$		0			0
$55$	−7.27421	−	3.01307i	−0.980854	−	0.406283i
$56$		0			0
$57$	−2.72096	+	1.12706i	−0.360401	+	0.149283i
$58$		0			0
$59$	−3.31738	+	4.96481i	−0.431886	+	0.646363i	−0.982034	−	0.188704i	$-0.939571\pi$
$59$	−3.31738	+	4.96481i	−0.431886	+	0.646363i	0.550148	+	0.835067i	$0.314571\pi$
$60$		0			0
$61$	−0.382794	−	0.0761424i	−0.0490117	−	0.00974904i	0.170524	−	0.985354i	$-0.445454\pi$
$61$	−0.382794	−	0.0761424i	−0.0490117	−	0.00974904i	−0.219535	+	0.975605i	$0.570454\pi$
$62$		0			0
$63$	2.10611			0.265345
$64$		0			0
$65$	−3.82067			−0.473896
$66$		0			0
$67$	1.67538	+	0.333253i	0.204680	+	0.0407133i	0.296365	−	0.955075i	$-0.404225\pi$
$67$	1.67538	+	0.333253i	0.204680	+	0.0407133i	−0.0916855	+	0.995788i	$0.529225\pi$
$68$		0			0
$69$	−6.14253	+	9.19295i	−0.739474	+	1.10670i
$70$		0			0
$71$	0.843458	−	0.349372i	0.100100	−	0.0414628i	−0.332071	−	0.943254i	$-0.607748\pi$
$71$	0.843458	−	0.349372i	0.100100	−	0.0414628i	0.432172	+	0.901791i	$0.357748\pi$
$72$		0			0
$73$	11.9774	+	4.96122i	1.40185	+	0.580667i	0.950232	−	0.311543i	$-0.100846\pi$
$73$	11.9774	+	4.96122i	1.40185	+	0.580667i	0.451622	+	0.892210i	$0.350846\pi$
$74$		0			0
$75$	1.15168	+	5.78989i	0.132985	+	0.668559i
$76$		0			0
$77$	−7.22938	−	10.8195i	−0.823864	−	1.23300i
$78$		0			0
$79$	5.30583	−	5.30583i	0.596952	−	0.596952i	−0.342548	−	0.939500i	$-0.611290\pi$
$79$	5.30583	−	5.30583i	0.596952	−	0.596952i	0.939500	+	0.342548i	$0.111290\pi$
$80$		0			0
$81$	−7.69937	−	7.69937i	−0.855486	−	0.855486i
$82$		0			0
$83$	−1.28800	+	0.860615i	−0.141376	+	0.0944647i	−0.624247	−	0.781227i	$-0.714594\pi$
$83$	−1.28800	+	0.860615i	−0.141376	+	0.0944647i	0.482871	+	0.875692i	$0.339594\pi$
$84$		0			0
$85$	6.76266	−	1.34518i	0.733514	−	0.145905i
$86$		0			0
$87$	−6.31966	+	15.2570i	−0.677539	+	1.63572i
$88$		0			0
$89$	−3.98900	−	9.63030i	−0.422833	−	1.02081i	−0.981508	−	0.191422i	$-0.938690\pi$
$89$	−3.98900	−	9.63030i	−0.422833	−	1.02081i	0.558675	−	0.829387i	$-0.311310\pi$
$90$		0			0
$91$	−5.25023	−	3.50809i	−0.550373	−	0.367748i
$92$		0			0
$93$	1.99470	−	10.0280i	0.206840	−	1.03986i
$94$		0			0
$95$			2.11480i			0.216974i
$96$		0			0
$97$		−	4.23236i		−	0.429731i	−0.976644	−	0.214866i	$-0.931069\pi$
$97$		−	4.23236i		−	0.429731i	0.976644	−	0.214866i	$-0.0689313\pi$
$98$		0			0
$99$	0.973732	−	4.89528i	0.0978637	−	0.491994i
$100$		0			0
$101$	−12.6885	−	8.47818i	−1.26255	−	0.843610i	−0.269697	−	0.962945i	$-0.586924\pi$
$101$	−12.6885	−	8.47818i	−1.26255	−	0.843610i	−0.992854	+	0.119335i	$0.961924\pi$
$102$		0			0
$103$	1.63698	+	3.95201i	0.161296	+	0.389404i	0.983779	−	0.179387i	$-0.0574115\pi$
$103$	1.63698	+	3.95201i	0.161296	+	0.389404i	−0.822482	+	0.568791i	$0.807411\pi$
$104$		0			0
$105$	2.51046	−	6.06078i	0.244995	−	0.591471i
$106$		0			0
$107$	6.49362	−	1.29166i	0.627762	−	0.124870i	0.129051	−	0.991638i	$-0.458807\pi$
$107$	6.49362	−	1.29166i	0.627762	−	0.124870i	0.498711	+	0.866768i	$0.333807\pi$
$108$		0			0
$109$	−9.55062	+	6.38152i	−0.914783	+	0.611239i	−0.921348	−	0.388740i	$-0.872911\pi$
$109$	−9.55062	+	6.38152i	−0.914783	+	0.611239i	0.00656414	+	0.999978i	$0.497911\pi$
$110$		0			0
$111$	11.4026	+	11.4026i	1.08228	+	1.08228i
$112$		0			0
$113$	−5.02130	+	5.02130i	−0.472365	+	0.472365i	−0.902679	−	0.430314i	$-0.858403\pi$
$113$	−5.02130	+	5.02130i	−0.472365	+	0.472365i	0.430314	+	0.902679i	$0.358403\pi$
$114$		0			0
$115$	4.41073	+	6.60112i	0.411302	+	0.615558i
$116$		0			0
$117$	−0.472508	−	2.37546i	−0.0436834	−	0.219611i
$118$		0			0
$119$	10.5281	+	4.36089i	0.965111	+	0.399762i
$120$		0			0
$121$	−18.3278	+	7.59162i	−1.66616	+	0.690148i
$122$		0			0
$123$	−6.43931	+	9.63711i	−0.580613	+	0.868949i
$124$		0			0
$125$	11.1105	+	2.21002i	0.993753	+	0.197670i
$126$		0			0
$127$	−14.0495			−1.24669			−0.623345	−	0.781947i	$-0.714227\pi$
$127$	−14.0495			−1.24669			−0.623345	+	0.781947i	$0.714227\pi$
$128$		0			0
$129$	8.37563			0.737433
$130$		0			0
$131$	−15.6501	−	3.11300i	−1.36736	−	0.271984i	−0.543799	−	0.839216i	$-0.683015\pi$
$131$	−15.6501	−	3.11300i	−1.36736	−	0.271984i	−0.823559	+	0.567231i	$0.808015\pi$
$132$		0			0
$133$	−1.94178	+	2.90608i	−0.168374	+	0.251989i
$134$		0			0
$135$	−5.43472	+	2.25113i	−0.467746	+	0.193747i
$136$		0			0
$137$	−5.39532	−	2.23482i	−0.460953	−	0.190933i	0.140108	−	0.990136i	$-0.455255\pi$
$137$	−5.39532	−	2.23482i	−0.460953	−	0.190933i	−0.601061	+	0.799203i	$0.705255\pi$
$138$		0			0
$139$	−0.198971	−	1.00029i	−0.0168765	−	0.0848438i	0.971429	−	0.237330i	$-0.0762721\pi$
$139$	−0.198971	−	1.00029i	−0.0168765	−	0.0848438i	−0.988306	+	0.152486i	$0.951272\pi$
$140$		0			0
$141$	1.13810	+	1.70329i	0.0958452	+	0.143443i
$142$		0			0
$143$	−10.5813	+	10.5813i	−0.884853	+	0.884853i
$144$		0			0
$145$	8.38498	+	8.38498i	0.696335	+	0.696335i
$146$		0			0
$147$	−2.47768	+	1.65553i	−0.204356	+	0.136546i
$148$		0			0
$149$	−0.0445180	+	0.00885518i	−0.00364705	+	0.000725444i	−0.196914	−	0.980421i	$-0.563092\pi$
$149$	−0.0445180	+	0.00885518i	−0.00364705	+	0.000725444i	0.193266	+	0.981146i	$0.438092\pi$
$150$		0			0
$151$	7.79199	−	18.8115i	0.634103	−	1.53086i	−0.200316	−	0.979731i	$-0.564197\pi$
$151$	7.79199	−	18.8115i	0.634103	−	1.53086i	0.834419	−	0.551130i	$-0.185803\pi$
$152$		0			0
$153$	1.67269	+	4.03824i	0.135229	+	0.326473i
$154$		0			0
$155$	−6.10450	−	4.07890i	−0.490325	−	0.327625i
$156$		0			0
$157$	−2.88193	+	14.4885i	−0.230003	+	1.15631i	0.677260	+	0.735743i	$0.263167\pi$
$157$	−2.88193	+	14.4885i	−0.230003	+	1.15631i	−0.907264	+	0.420562i	$0.861833\pi$
$158$		0			0
$159$		−	5.82044i		−	0.461591i
$160$		0			0
$161$			13.1209i			1.03407i
$162$		0			0
$163$	0.0805216	−	0.404809i	0.00630694	−	0.0317071i	−0.977504	−	0.210918i	$-0.932355\pi$
$163$	0.0805216	−	0.404809i	0.00630694	−	0.0317071i	0.983811	+	0.179211i	$0.0573546\pi$
$164$		0			0
$165$	−12.9265	−	8.63723i	−1.00633	−	0.672407i
$166$		0			0
$167$	1.88280	+	4.54548i	0.145695	+	0.351740i	0.979833	−	0.199816i	$-0.0640344\pi$
$167$	1.88280	+	4.54548i	0.145695	+	0.351740i	−0.834138	+	0.551556i	$0.814034\pi$
$168$		0			0
$169$	2.19604	−	5.30172i	0.168926	−	0.407825i
$170$		0			0
$171$	−1.31485	+	0.261541i	−0.100549	+	0.0200005i
$172$		0			0
$173$	2.58681	−	1.72845i	0.196672	−	0.131412i	−0.453335	−	0.891340i	$-0.649766\pi$
$173$	2.58681	−	1.72845i	0.196672	−	0.131412i	0.650007	+	0.759928i	$0.274766\pi$
$174$		0			0
$175$	4.95377	+	4.95377i	0.374469	+	0.374469i
$176$		0			0
$177$	−8.33693	+	8.33693i	−0.626642	+	0.626642i
$178$		0			0
$179$	−2.10987	−	3.15764i	−0.157699	−	0.236013i	0.744204	−	0.667953i	$-0.232829\pi$
$179$	−2.10987	−	3.15764i	−0.157699	−	0.236013i	−0.901902	+	0.431940i	$0.857829\pi$
$180$		0			0
$181$	0.219878	+	1.10540i	0.0163434	+	0.0821639i	0.988096	−	0.153837i	$-0.0491631\pi$
$181$	0.219878	+	1.10540i	0.0163434	+	0.0821639i	−0.971753	+	0.236001i	$0.924163\pi$
$182$		0			0
$183$	−0.711986	−	0.294914i	−0.0526315	−	0.0218007i
$184$		0			0
$185$	10.6978	−	4.43118i	0.786519	−	0.325787i
$186$		0			0
$187$	15.0036	−	22.4545i	1.09718	−	1.64204i
$188$		0			0
$189$	−9.53514	−	1.89666i	−0.693579	−	0.137961i
$190$		0			0
$191$	−22.3207			−1.61507			−0.807533	−	0.589822i	$-0.799198\pi$
$191$	−22.3207			−1.61507			−0.807533	+	0.589822i	$0.799198\pi$
$192$		0			0
$193$	2.10778			0.151721			0.0758605	−	0.997118i	$-0.475830\pi$
$193$	2.10778			0.151721			0.0758605	+	0.997118i	$0.475830\pi$
$194$		0			0
$195$	−7.39911	−	1.47177i	−0.529861	−	0.105396i
$196$		0			0
$197$	3.12154	−	4.67172i	0.222401	−	0.332846i	−0.703444	−	0.710751i	$-0.748355\pi$
$197$	3.12154	−	4.67172i	0.222401	−	0.332846i	0.925845	+	0.377905i	$0.123355\pi$
$198$		0			0
$199$	14.6371	−	6.06290i	1.03760	−	0.429787i	0.202149	−	0.979355i	$-0.435207\pi$
$199$	14.6371	−	6.06290i	1.03760	−	0.429787i	0.835449	+	0.549567i	$0.185207\pi$
$200$		0			0
$201$	3.11615	+	1.29075i	0.219796	+	0.0910427i
$202$		0			0
$203$	3.82335	+	19.2213i	0.268347	+	1.34907i
$204$		0			0
$205$	4.62383	+	6.92006i	0.322943	+	0.483318i
$206$		0			0
$207$	−3.55868	+	3.55868i	−0.247346	+	0.247346i
$208$		0			0
$209$	5.85692	+	5.85692i	0.405132	+	0.405132i
$210$		0			0
$211$	2.41276	−	1.61216i	0.166102	−	0.110986i	−0.469741	−	0.882804i	$-0.655653\pi$
$211$	2.41276	−	1.61216i	0.166102	−	0.110986i	0.635843	+	0.771819i	$0.280653\pi$
$212$		0			0
$213$	1.76802	−	0.351681i	0.121143	−	0.0240968i
$214$		0			0
$215$	2.30155	−	5.55642i	0.156964	−	0.378945i
$216$		0			0
$217$	−4.64339	−	11.2101i	−0.315214	−	0.760993i
$218$		0			0
$219$	21.2844	+	14.2217i	1.43826	+	0.961017i
$220$		0			0
$221$	2.55660	−	12.8529i	0.171976	−	0.864581i
$222$		0			0
$223$		−	1.84279i		−	0.123403i	−0.998095	−	0.0617013i	$-0.980347\pi$
$223$		−	1.84279i		−	0.123403i	0.998095	−	0.0617013i	$-0.0196526\pi$
$224$		0			0
$225$			2.68715i			0.179143i
$226$		0			0
$227$	−0.293813	+	1.47710i	−0.0195011	+	0.0980385i	−0.989310	−	0.145827i	$-0.953416\pi$
$227$	−0.293813	+	1.47710i	−0.0195011	+	0.0980385i	0.969809	+	0.243866i	$0.0784156\pi$
$228$		0			0
$229$	16.7852	+	11.2155i	1.10920	+	0.741142i	0.968526	−	0.248914i	$-0.0800736\pi$
$229$	16.7852	+	11.2155i	1.10920	+	0.741142i	0.140672	+	0.990056i	$0.455074\pi$
$230$		0			0
$231$	−9.83256	−	23.7379i	−0.646935	−	1.56184i
$232$		0			0
$233$	9.18563	−	22.1761i	0.601771	−	1.45280i	−0.269986	−	0.962864i	$-0.587019\pi$
$233$	9.18563	−	22.1761i	0.601771	−	1.45280i	0.871757	−	0.489939i	$-0.162981\pi$
$234$		0			0
$235$	1.44271	−	0.286972i	0.0941118	−	0.0187200i
$236$		0			0
$237$	12.3191	−	8.23137i	0.800213	−	0.534685i
$238$		0			0
$239$	−6.58253	−	6.58253i	−0.425788	−	0.425788i	0.461403	−	0.887191i	$-0.347346\pi$
$239$	−6.58253	−	6.58253i	−0.425788	−	0.425788i	−0.887191	+	0.461403i	$0.847346\pi$
$240$		0			0
$241$	13.5889	−	13.5889i	0.875335	−	0.875335i	−0.117712	−	0.993048i	$-0.537556\pi$
$241$	13.5889	−	13.5889i	0.875335	−	0.875335i	0.993048	+	0.117712i	$0.0375561\pi$
$242$		0			0
$243$	−5.02966	−	7.52741i	−0.322653	−	0.482884i
$244$		0			0
$245$	0.417443	+	2.09863i	0.0266695	+	0.134076i
$246$		0			0
$247$	3.71338	+	1.53813i	0.236277	+	0.0978691i
$248$		0			0
$249$	−2.82586	+	1.17051i	−0.179081	+	0.0741780i
$250$		0			0
$251$	−8.95890	+	13.4079i	−0.565481	+	0.846302i	−0.998481	−	0.0550918i	$-0.982455\pi$
$251$	−8.95890	+	13.4079i	−0.565481	+	0.846302i	0.433000	+	0.901394i	$0.357455\pi$
$252$		0			0
$253$	30.4972	+	6.06626i	1.91734	+	0.381383i
$254$		0			0
$255$	13.6147			0.852587
$256$		0			0
$257$	−13.3833			−0.834824			−0.417412	−	0.908717i	$-0.637063\pi$
$257$	−13.3833			−0.834824			−0.417412	+	0.908717i	$0.637063\pi$
$258$		0			0
$259$	18.7692	+	3.73342i	1.16626	+	0.231984i
$260$		0			0
$261$	−4.17628	+	6.25024i	−0.258505	+	0.386880i
$262$		0			0
$263$	19.9818	−	8.27672i	1.23213	−	0.510364i	0.330883	−	0.943672i	$-0.392654\pi$
$263$	19.9818	−	8.27672i	1.23213	−	0.510364i	0.901246	+	0.433308i	$0.142654\pi$
$264$		0			0
$265$	−3.86131	−	1.59941i	−0.237198	−	0.0982507i
$266$		0			0
$267$	−4.01537	−	20.1866i	−0.245737	−	1.23540i
$268$		0			0
$269$	10.3945	+	15.5564i	0.633762	+	0.948493i	0.999840	+	0.0179081i	$0.00570062\pi$
$269$	10.3945	+	15.5564i	0.633762	+	0.948493i	−0.366077	+	0.930584i	$0.619299\pi$
$270$		0			0
$271$	6.71687	−	6.71687i	0.408021	−	0.408021i	−0.473027	−	0.881048i	$-0.656839\pi$
$271$	6.71687	−	6.71687i	0.408021	−	0.408021i	0.881048	+	0.473027i	$0.156839\pi$
$272$		0			0
$273$	−8.81621	−	8.81621i	−0.533581	−	0.533581i
$274$		0			0
$275$	13.8045	−	9.22385i	0.832440	−	0.556219i
$276$		0			0
$277$	−7.75914	+	1.54339i	−0.466201	+	0.0927332i	−0.422601	−	0.906316i	$-0.638883\pi$
$277$	−7.75914	+	1.54339i	−0.466201	+	0.0927332i	−0.0436004	+	0.999049i	$0.513883\pi$
$278$		0			0
$279$	1.78105	−	4.29984i	0.106629	−	0.257425i
$280$		0			0
$281$	−1.28145	−	3.09369i	−0.0764447	−	0.184554i	0.881037	−	0.473047i	$-0.156846\pi$
$281$	−1.28145	−	3.09369i	−0.0764447	−	0.184554i	−0.957482	+	0.288493i	$0.906846\pi$
$282$		0			0
$283$	−5.54432	−	3.70460i	−0.329576	−	0.220216i	0.379762	−	0.925084i	$-0.376006\pi$
$283$	−5.54432	−	3.70460i	−0.329576	−	0.220216i	−0.709338	+	0.704869i	$0.751006\pi$
$284$		0			0
$285$	−0.814650	+	4.09552i	−0.0482557	+	0.242598i
$286$		0			0
$287$			13.7548i			0.811921i
$288$		0			0
$289$			6.65002i			0.391177i
$290$		0			0
$291$	1.63036	−	8.19637i	0.0955734	−	0.480480i
$292$		0			0
$293$	−9.61191	−	6.42248i	−0.561534	−	0.375205i	0.242170	−	0.970234i	$-0.422141\pi$
$293$	−9.61191	−	6.42248i	−0.561534	−	0.375205i	−0.803704	+	0.595029i	$0.797141\pi$
$294$		0			0
$295$	3.23984	+	7.82167i	0.188631	+	0.455395i
$296$		0			0
$297$	−8.81689	+	21.2858i	−0.511608	+	1.23513i
$298$		0			0
$299$	14.7989	−	2.94368i	0.855842	−	0.170238i
$300$		0			0
$301$	8.26453	−	5.52218i	0.476359	−	0.318293i
$302$		0			0
$303$	−21.3066	−	21.3066i	−1.22403	−	1.22403i
$304$		0			0
$305$	−0.391295	+	0.391295i	−0.0224055	+	0.0224055i
$306$		0			0
$307$	−17.9541	−	26.8702i	−1.02469	−	1.53356i	−0.833889	−	0.551933i	$-0.813891\pi$
$307$	−17.9541	−	26.8702i	−1.02469	−	1.53356i	−0.190804	−	0.981628i	$-0.561109\pi$
$308$		0			0
$309$	1.64780	+	8.28404i	0.0937400	+	0.471263i
$310$		0			0
$311$	−17.5995	−	7.28996i	−0.997978	−	0.413376i	−0.176923	−	0.984225i	$-0.556614\pi$
$311$	−17.5995	−	7.28996i	−0.997978	−	0.413376i	−0.821055	+	0.570849i	$0.806614\pi$
$312$		0			0
$313$	27.5944	−	11.4300i	1.55973	−	0.646060i	0.574685	−	0.818375i	$-0.305125\pi$
$313$	27.5944	−	11.4300i	1.55973	−	0.646060i	0.985042	+	0.172315i	$0.0551246\pi$
$314$		0			0
$315$	1.65901	−	2.48288i	0.0934744	−	0.139894i
$316$		0			0
$317$	−13.5672	−	2.69867i	−0.762007	−	0.151573i	−0.201235	−	0.979543i	$-0.564496\pi$
$317$	−13.5672	−	2.69867i	−0.762007	−	0.151573i	−0.560772	+	0.827970i	$0.689496\pi$
$318$		0			0
$319$	46.4442			2.60037
$320$		0			0
$321$	13.0731			0.729669
$322$		0			0
$323$	−7.11430	−	1.41512i	−0.395850	−	0.0787395i
$324$		0			0
$325$	4.47591	−	6.69868i	0.248279	−	0.371576i
$326$		0			0
$327$	−20.9539	+	8.67941i	−1.15876	+	0.479972i
$328$		0			0
$329$	2.24601	+	0.930326i	0.123826	+	0.0512905i
$330$		0			0
$331$	1.95265	+	9.81665i	0.107328	+	0.539572i	0.996614	+	0.0822216i	$0.0262015\pi$
$331$	1.95265	+	9.81665i	0.107328	+	0.539572i	−0.889287	+	0.457351i	$0.848798\pi$
$332$		0			0
$333$	4.07805	+	6.10323i	0.223476	+	0.334455i
$334$		0			0
$335$	1.71258	−	1.71258i	0.0935683	−	0.0935683i
$336$		0			0
$337$	19.8896	+	19.8896i	1.08346	+	1.08346i	0.996184	+	0.0872738i	$0.0278155\pi$
$337$	19.8896	+	19.8896i	1.08346	+	1.08346i	0.0872738	+	0.996184i	$0.472184\pi$
$338$		0			0
$339$	−11.6585	+	7.78997i	−0.633204	+	0.423093i
$340$		0			0
$341$	−28.2028	+	5.60988i	−1.52727	+	0.303792i
$342$		0			0
$343$	−7.63037	+	18.4213i	−0.412001	+	0.994659i
$344$		0			0
$345$	5.99896	+	14.4828i	0.322973	+	0.779727i
$346$		0			0
$347$	20.0723	+	13.4119i	1.07754	+	0.719988i	0.961927	−	0.273306i	$-0.0881171\pi$
$347$	20.0723	+	13.4119i	1.07754	+	0.719988i	0.115612	+	0.993294i	$0.463117\pi$
$348$		0			0
$349$	2.58414	−	12.9913i	0.138326	−	0.695410i	−0.847920	−	0.530124i	$-0.822145\pi$
$349$	2.58414	−	12.9913i	0.138326	−	0.695410i	0.986246	−	0.165286i	$-0.0528547\pi$
$350$		0			0
$351$			11.1801i			0.596749i
$352$		0			0
$353$			6.93502i			0.369114i	0.982822	+	0.184557i	$0.0590850\pi$
$353$			6.93502i			0.369114i	−0.982822	+	0.184557i	$0.940915\pi$
$354$		0			0
$355$	0.252529	−	1.26955i	0.0134029	−	0.0673808i
$356$		0			0
$357$	18.7088	+	12.5009i	0.990177	+	0.661615i
$358$		0			0
$359$	5.35824	+	12.9359i	0.282797	+	0.682732i	0.999899	−	0.0142363i	$-0.00453170\pi$
$359$	5.35824	+	12.9359i	0.282797	+	0.682732i	−0.717102	+	0.696969i	$0.754532\pi$
$360$		0			0
$361$	−6.41960	+	15.4983i	−0.337874	+	0.815700i
$362$		0			0
$363$	−38.4180	+	7.64181i	−2.01642	+	0.401091i
$364$		0			0
$365$	15.2835	−	10.2121i	0.799976	−	0.534527i
$366$		0			0
$367$	−9.38352	−	9.38352i	−0.489816	−	0.489816i	0.418432	−	0.908248i	$-0.362580\pi$
$367$	−9.38352	−	9.38352i	−0.489816	−	0.489816i	−0.908248	+	0.418432i	$0.862580\pi$
$368$		0			0
$369$	−3.73062	+	3.73062i	−0.194209	+	0.194209i
$370$		0			0
$371$	−3.83751	−	5.74324i	−0.199234	−	0.298174i
$372$		0			0
$373$	−1.64789	−	8.28453i	−0.0853248	−	0.428956i	−0.999709	−	0.0241098i	$-0.992325\pi$
$373$	−1.64789	−	8.28453i	−0.0853248	−	0.428956i	0.914385	−	0.404847i	$-0.132675\pi$
$374$		0			0
$375$	20.6652	+	8.55982i	1.06715	+	0.442027i
$376$		0			0
$377$	20.8217	−	8.62463i	1.07237	−	0.444191i
$378$		0			0
$379$	2.04578	−	3.06172i	0.105085	−	0.157270i	−0.775201	−	0.631715i	$-0.782351\pi$
$379$	2.04578	−	3.06172i	0.105085	−	0.157270i	0.880285	+	0.474445i	$0.157351\pi$
$380$		0			0
$381$	−27.2082	−	5.41204i	−1.39392	−	0.277267i
$382$		0			0
$383$	−12.3567			−0.631396			−0.315698	−	0.948860i	$-0.602239\pi$
$383$	−12.3567			−0.631396			−0.315698	+	0.948860i	$0.602239\pi$
$384$		0			0
$385$	−18.4497			−0.940285
$386$		0			0
$387$	3.73927	+	0.743788i	0.190078	+	0.0378089i
$388$		0			0
$389$	2.74278	−	4.10486i	0.139065	−	0.208125i	−0.755400	−	0.655264i	$-0.772557\pi$
$389$	2.74278	−	4.10486i	0.139065	−	0.208125i	0.894464	+	0.447140i	$0.147557\pi$
$390$		0			0
$391$	−25.1579	+	10.4207i	−1.27229	+	0.526999i
$392$		0			0
$393$	−29.1088	−	12.0573i	−1.46835	−	0.608208i
$394$		0			0
$395$	−2.07554	−	10.4345i	−0.104432	−	0.525015i
$396$		0			0
$397$	−19.4770	−	29.1493i	−0.977521	−	1.46296i	−0.884078	−	0.467339i	$-0.845213\pi$
$397$	−19.4770	−	29.1493i	−0.977521	−	1.46296i	−0.0934430	−	0.995625i	$-0.529787\pi$
$398$		0			0
$399$	−4.87991	+	4.87991i	−0.244301	+	0.244301i
$400$		0			0
$401$	−23.0145	−	23.0145i	−1.14929	−	1.14929i	−0.986692	−	0.162599i	$-0.948012\pi$
$401$	−23.0145	−	23.0145i	−1.14929	−	1.14929i	−0.162599	−	0.986692i	$-0.551988\pi$
$402$		0			0
$403$	−11.6020	+	7.75223i	−0.577939	+	0.386166i
$404$		0			0
$405$	−15.1416	+	3.01185i	−0.752393	+	0.149660i
$406$		0			0
$407$	17.3554	−	41.8995i	0.860273	−	2.07688i
$408$		0			0
$409$	13.4728	+	32.5262i	0.666187	+	1.60832i	0.787936	+	0.615757i	$0.211150\pi$
$409$	13.4728	+	32.5262i	0.666187	+	1.60832i	−0.121749	+	0.992561i	$0.538850\pi$
$410$		0			0
$411$	−9.58768	−	6.40628i	−0.472925	−	0.315999i
$412$		0			0
$413$	−2.72968	+	13.7230i	−0.134319	+	0.675266i
$414$		0			0
$415$			2.19633i			0.107814i
$416$		0			0
$417$		−	2.01381i		−	0.0986167i
$418$		0			0
$419$	−3.73506	+	18.7774i	−0.182470	+	0.917337i	0.775692	+	0.631111i	$0.217401\pi$
$419$	−3.73506	+	18.7774i	−0.182470	+	0.917337i	−0.958162	+	0.286226i	$0.907599\pi$
$420$		0			0
$421$	15.5376	+	10.3819i	0.757256	+	0.505982i	0.873253	−	0.487267i	$-0.162006\pi$
$421$	15.5376	+	10.3819i	0.757256	+	0.505982i	−0.115997	+	0.993250i	$0.537006\pi$
$422$		0			0
$423$	0.356843	+	0.861495i	0.0173503	+	0.0418873i
$424$		0			0
$425$	−5.56399	+	13.4327i	−0.269893	+	0.651580i
$426$		0			0
$427$	−0.896984	+	0.178421i	−0.0434081	+	0.00863440i
$428$		0			0
$429$	−24.5678	+	16.4157i	−1.18614	+	0.792556i
$430$		0			0
$431$	10.1766	+	10.1766i	0.490192	+	0.490192i	0.908367	−	0.418175i	$-0.137330\pi$
$431$	10.1766	+	10.1766i	0.490192	+	0.490192i	−0.418175	+	0.908367i	$0.637330\pi$
$432$		0			0
$433$	7.09854	−	7.09854i	0.341134	−	0.341134i	−0.515660	−	0.856794i	$-0.672453\pi$
$433$	7.09854	−	7.09854i	0.341134	−	0.341134i	0.856794	+	0.515660i	$0.172453\pi$
$434$		0			0
$435$	13.0083	+	19.4683i	0.623701	+	0.933435i
$436$		0			0
$437$	−1.62938	−	8.19142i	−0.0779436	−	0.391849i
$438$		0			0
$439$	−21.2594	−	8.80592i	−1.01465	−	0.420284i	−0.187504	−	0.982264i	$-0.560040\pi$
$439$	−21.2594	−	8.80592i	−1.01465	−	0.420284i	−0.827151	+	0.561980i	$0.810040\pi$
$440$		0			0
$441$	−1.25317	+	0.519080i	−0.0596748	+	0.0247181i
$442$		0			0
$443$	−1.49883	+	2.24316i	−0.0712115	+	0.106576i	−0.865366	−	0.501140i	$-0.832914\pi$
$443$	−1.49883	+	2.24316i	−0.0712115	+	0.106576i	0.794155	+	0.607716i	$0.207914\pi$
$444$		0			0
$445$	−14.4953	−	2.88329i	−0.687142	−	0.136681i
$446$		0			0
$447$	−0.0896245			−0.00423909
$448$		0			0
$449$	8.51822			0.402000			0.201000	−	0.979591i	$-0.435581\pi$
$449$	8.51822			0.402000			0.201000	+	0.979591i	$0.435581\pi$
$450$		0			0
$451$	31.9706	+	6.35936i	1.50544	+	0.299450i
$452$		0			0
$453$	22.3364	−	33.4288i	1.04946	−	1.57062i
$454$		0			0
$455$	−8.27132	+	3.42609i	−0.387766	+	0.160618i
$456$		0			0
$457$	−11.6115	−	4.80963i	−0.543162	−	0.224985i	0.0941951	−	0.995554i	$-0.469972\pi$
$457$	−11.6115	−	4.80963i	−0.543162	−	0.224985i	−0.637357	+	0.770569i	$0.719972\pi$
$458$		0			0
$459$	−3.93627	−	19.7890i	−0.183729	−	0.923670i
$460$		0			0
$461$	11.2805	+	16.8825i	0.525388	+	0.786298i	0.995343	−	0.0963919i	$-0.0307302\pi$
$461$	11.2805	+	16.8825i	0.525388	+	0.786298i	−0.469956	+	0.882690i	$0.655730\pi$
$462$		0			0
$463$	−12.9581	+	12.9581i	−0.602214	+	0.602214i	−0.940899	−	0.338686i	$-0.890018\pi$
$463$	−12.9581	+	12.9581i	−0.602214	+	0.602214i	0.338686	+	0.940899i	$0.390018\pi$
$464$		0			0
$465$	−10.2507	−	10.2507i	−0.475366	−	0.475366i
$466$		0			0
$467$	9.64631	−	6.44546i	0.446378	−	0.298260i	−0.311992	−	0.950085i	$-0.600996\pi$
$467$	9.64631	−	6.44546i	0.446378	−	0.298260i	0.758370	+	0.651824i	$0.225996\pi$
$468$		0			0
$469$	3.92583	−	0.780897i	0.181278	−	0.0360585i
$470$		0			0
$471$	−11.1623	+	26.9482i	−0.514331	+	1.24171i
$472$		0			0
$473$	−9.01434	−	21.7625i	−0.414480	−	1.00064i
$474$		0			0
$475$	−3.70783	−	2.47749i	−0.170127	−	0.113675i
$476$		0			0
$477$	0.516878	−	2.59852i	0.0236662	−	0.118978i
$478$		0			0
$479$			12.0889i			0.552355i	0.961107	+	0.276178i	$0.0890678\pi$
$479$			12.0889i			0.552355i	−0.961107	+	0.276178i	$0.910932\pi$
$480$		0			0
$481$		−	22.0071i		−	1.00344i
$482$		0			0
$483$	−5.05433	+	25.4098i	−0.229980	+	1.15619i
$484$		0			0
$485$	−4.98950	−	3.33388i	−0.226562	−	0.151384i
$486$		0			0
$487$	13.3448	+	32.2172i	0.604711	+	1.45990i	0.868682	+	0.495370i	$0.164968\pi$
$487$	13.3448	+	32.2172i	0.604711	+	1.45990i	−0.263971	+	0.964531i	$0.585032\pi$
$488$		0			0
$489$	0.311876	−	0.752935i	0.0141035	−	0.0340489i
$490$		0			0
$491$	−26.1410	+	5.19977i	−1.17973	+	0.234662i	−0.745727	−	0.666251i	$-0.767898\pi$
$491$	−26.1410	+	5.19977i	−1.17973	+	0.234662i	−0.433999	+	0.900913i	$0.642898\pi$
$492$		0			0
$493$	−33.8182	+	22.5966i	−1.52310	+	1.01770i
$494$		0			0
$495$	−5.00399	−	5.00399i	−0.224913	−	0.224913i
$496$		0			0
$497$	1.51270	−	1.51270i	0.0678539	−	0.0678539i
$498$		0			0
$499$	1.56309	+	2.33933i	0.0699736	+	0.104723i	0.864806	−	0.502106i	$-0.167441\pi$
$499$	1.56309	+	2.33933i	0.0699736	+	0.104723i	−0.794832	+	0.606829i	$0.792441\pi$
$500$		0			0
$501$	1.89525	+	9.52804i	0.0846733	+	0.425682i
$502$		0			0
$503$	36.9205	+	15.2930i	1.64620	+	0.681880i	0.996902	−	0.0786507i	$-0.0250612\pi$
$503$	36.9205	+	15.2930i	1.64620	+	0.681880i	0.649302	+	0.760531i	$0.275061\pi$
$504$		0			0
$505$	−19.9897	+	8.28001i	−0.889531	+	0.368456i
$506$		0			0
$507$	6.29514	−	9.42135i	0.279577	−	0.418417i
$508$		0			0
$509$	3.51571	+	0.699318i	0.155831	+	0.0309967i	0.272389	−	0.962187i	$-0.412186\pi$
$509$	3.51571	+	0.699318i	0.155831	+	0.0309967i	−0.116558	+	0.993184i	$0.537186\pi$
$510$		0			0
$511$	30.3786			1.34387
$512$		0			0
$513$	6.18836			0.273223
$514$		0			0
$515$	5.94847	+	1.18322i	0.262121	+	0.0521391i
$516$		0			0
$517$	3.20079	−	4.79032i	0.140771	−	0.210678i
$518$		0			0
$519$	5.67543	−	2.35084i	0.249124	−	0.103190i
$520$		0			0
$521$	−13.4480	−	5.57034i	−0.589168	−	0.244041i	0.0681249	−	0.997677i	$-0.478298\pi$
$521$	−13.4480	−	5.57034i	−0.589168	−	0.244041i	−0.657292	+	0.753636i	$0.728298\pi$
$522$		0			0
$523$	−0.274054	−	1.37776i	−0.0119835	−	0.0602453i	0.974331	−	0.225121i	$-0.0722777\pi$
$523$	−0.274054	−	1.37776i	−0.0119835	−	0.0602453i	−0.986314	+	0.164876i	$0.947278\pi$
$524$		0			0
$525$	7.68519	+	11.5017i	0.335409	+	0.501975i
$526$		0			0
$527$	17.8064	−	17.8064i	0.775660	−	0.775660i
$528$		0			0
$529$	−5.90683	−	5.90683i	−0.256819	−	0.256819i
$530$		0			0
$531$	−4.46235	+	2.98165i	−0.193650	+	0.129392i
$532$		0			0
$533$	15.5139	−	3.08591i	0.671982	−	0.133665i
$534$		0			0
$535$	3.59237	−	8.67274i	0.155312	−	0.374955i
$536$		0			0
$537$	−2.86960	−	6.92782i	−0.123832	−	0.298958i
$538$		0			0
$539$	6.96822	+	4.65602i	0.300143	+	0.200549i
$540$		0			0
$541$	8.09775	−	40.7102i	0.348150	−	1.75027i	−0.268736	−	0.963214i	$-0.586606\pi$
$541$	8.09775	−	40.7102i	0.348150	−	1.75027i	0.616886	−	0.787053i	$-0.288394\pi$
$542$		0			0
$543$			2.22542i			0.0955018i
$544$		0			0
$545$			16.2860i			0.697614i
$546$		0			0
$547$	−8.11081	+	40.7758i	−0.346793	+	1.74345i	0.276090	+	0.961132i	$0.410961\pi$
$547$	−8.11081	+	40.7758i	−0.346793	+	1.74345i	−0.622883	+	0.782315i	$0.714039\pi$
$548$		0			0
$549$	−0.291675	−	0.194891i	−0.0124484	−	0.00831773i
$550$		0			0
$551$	−4.77387	−	11.5251i	−0.203374	−	0.490988i
$552$		0			0
$553$	6.72864	−	16.2444i	0.286131	−	0.690781i
$554$		0			0
$555$	22.4243	−	4.46047i	0.951859	−	0.189337i
$556$		0			0
$557$	0.577961	−	0.386181i	0.0244890	−	0.0163630i	−0.543265	−	0.839561i	$-0.682812\pi$
$557$	0.577961	−	0.386181i	0.0244890	−	0.0163630i	0.567754	+	0.823198i	$0.307812\pi$
$558$		0			0
$559$	−8.08256	−	8.08256i	−0.341856	−	0.341856i
$560$		0			0
$561$	37.7058	−	37.7058i	1.59194	−	1.59194i
$562$		0			0
$563$	−1.19920	−	1.79474i	−0.0505404	−	0.0756391i	0.805339	−	0.592815i	$-0.201983\pi$
$563$	−1.19920	−	1.79474i	−0.0505404	−	0.0756391i	−0.855879	+	0.517176i	$0.826983\pi$
$564$		0			0
$565$	1.96424	+	9.87492i	0.0826364	+	0.415441i
$566$		0			0
$567$	−23.5725	−	9.76404i	−0.989951	−	0.410051i
$568$		0			0
$569$	−17.7585	+	7.35583i	−0.744477	+	0.308372i	−0.722486	−	0.691386i	$-0.757001\pi$
$569$	−17.7585	+	7.35583i	−0.744477	+	0.308372i	−0.0219910	+	0.999758i	$0.507001\pi$
$570$		0			0
$571$	15.2733	−	22.8580i	0.639166	−	0.956579i	−0.360550	−	0.932740i	$-0.617411\pi$
$571$	15.2733	−	22.8580i	0.639166	−	0.956579i	0.999716	−	0.0238392i	$-0.00758897\pi$
$572$		0			0
$573$	−43.2261	−	8.59821i	−1.80580	−	0.359195i
$574$		0			0
$575$	−16.7407			−0.698136
$576$		0			0
$577$	−33.2616			−1.38470			−0.692350	−	0.721562i	$-0.743425\pi$
$577$	−33.2616			−1.38470			−0.692350	+	0.721562i	$0.743425\pi$
$578$		0			0
$579$	4.08191	+	0.811943i	0.169638	+	0.0337432i
$580$		0			0
$581$	−2.01664	+	3.01811i	−0.0836643	+	0.125213i
$582$		0			0
$583$	−15.1234	+	6.26430i	−0.626346	+	0.259441i
$584$		0			0
$585$	−3.17261	−	1.31414i	−0.131171	−	0.0543329i
$586$		0			0
$587$	7.71743	+	38.7981i	0.318532	+	1.60137i	0.725697	+	0.688015i	$0.241518\pi$
$587$	7.71743	+	38.7981i	0.318532	+	1.60137i	−0.407164	+	0.913355i	$0.633482\pi$
$588$		0			0
$589$	4.29099	+	6.42191i	0.176807	+	0.264610i
$590$		0			0
$591$	7.84478	−	7.84478i	0.322691	−	0.322691i
$592$		0			0
$593$	−18.9653	−	18.9653i	−0.778811	−	0.778811i	0.200817	−	0.979629i	$-0.435640\pi$
$593$	−18.9653	−	18.9653i	−0.778811	−	0.778811i	−0.979629	+	0.200817i	$0.935640\pi$
$594$		0			0
$595$	13.4341	−	8.97640i	0.550746	−	0.367997i
$596$		0			0
$597$	30.6817	−	6.10297i	1.25572	−	0.249778i
$598$		0			0
$599$	−7.92904	+	19.1424i	−0.323972	+	0.782137i	0.675044	+	0.737777i	$0.264125\pi$
$599$	−7.92904	+	19.1424i	−0.323972	+	0.782137i	−0.999016	+	0.0443592i	$0.985875\pi$
$600$		0			0
$601$	9.15574	+	22.1039i	0.373471	+	0.901638i	0.993157	+	0.116788i	$0.0372598\pi$
$601$	9.15574	+	22.1039i	0.373471	+	0.901638i	−0.619686	+	0.784850i	$0.712740\pi$
$602$		0			0
$603$	1.27657	+	0.852979i	0.0519861	+	0.0347360i
$604$		0			0
$605$	−5.48730	+	27.5865i	−0.223091	+	1.12155i
$606$		0			0
$607$		−	47.2885i		−	1.91938i	−0.281061	−	0.959690i	$-0.590686\pi$
$607$		−	47.2885i		−	1.91938i	0.281061	−	0.959690i	$-0.409314\pi$
$608$		0			0
$609$			38.6967i			1.56807i
$610$		0			0
$611$	0.545411	−	2.74196i	0.0220649	−	0.110928i
$612$		0			0
$613$	−26.9337	−	17.9965i	−1.08784	−	0.726873i	−0.123717	−	0.992318i	$-0.539481\pi$
$613$	−26.9337	−	17.9965i	−1.08784	−	0.726873i	−0.964126	+	0.265444i	$0.914481\pi$
$614$		0			0
$615$	6.28881	+	15.1825i	0.253589	+	0.612218i
$616$		0			0
$617$	−2.14483	+	5.17808i	−0.0863476	+	0.208462i	−0.961155	−	0.276009i	$-0.910988\pi$
$617$	−2.14483	+	5.17808i	−0.0863476	+	0.208462i	0.874807	+	0.484471i	$0.160988\pi$
$618$		0			0
$619$	−42.0718	+	8.36860i	−1.69101	+	0.336363i	−0.944374	−	0.328872i	$-0.893331\pi$
$619$	−42.0718	+	8.36860i	−1.69101	+	0.336363i	−0.746634	+	0.665235i	$0.768331\pi$
$620$		0			0
$621$	19.3163	−	12.9067i	0.775135	−	0.517928i
$622$		0			0
$623$	−17.2715	−	17.2715i	−0.691966	−	0.691966i
$624$		0			0
$625$	0.786975	−	0.786975i	0.0314790	−	0.0314790i
$626$		0			0
$627$	9.08633	+	13.5987i	0.362873	+	0.543078i
$628$		0			0
$629$	7.74824	+	38.9530i	0.308943	+	1.55316i
$630$		0			0
$631$	−20.3573	−	8.43229i	−0.810413	−	0.335684i	−0.0612942	−	0.998120i	$-0.519523\pi$
$631$	−20.3573	−	8.43229i	−0.810413	−	0.335684i	−0.749119	+	0.662436i	$0.769523\pi$
$632$		0			0
$633$	5.29358	−	2.19267i	0.210401	−	0.0871509i
$634$		0			0
$635$	−11.0669	+	16.5628i	−0.439178	+	0.657276i
$636$		0			0
$637$	3.98859	+	0.793380i	0.158034	+	0.0314349i
$638$		0			0
$639$	0.820558			0.0324608
$640$		0			0
$641$	24.2418			0.957494			0.478747	−	0.877953i	$-0.341091\pi$
$641$	24.2418			0.957494			0.478747	+	0.877953i	$0.341091\pi$
$642$		0			0
$643$	−9.42785	−	1.87532i	−0.371798	−	0.0739552i	0.00565492	−	0.999984i	$-0.498200\pi$
$643$	−9.42785	−	1.87532i	−0.371798	−	0.0739552i	−0.377453	+	0.926029i	$0.623200\pi$
$644$		0			0
$645$	6.59758	−	9.87397i	0.259779	−	0.388787i
$646$		0			0
$647$	−31.3004	+	12.9650i	−1.23055	+	0.509709i	−0.900748	−	0.434343i	$-0.856981\pi$
$647$	−31.3004	+	12.9650i	−1.23055	+	0.509709i	−0.329798	+	0.944052i	$0.606981\pi$
$648$		0			0
$649$	30.6347	+	12.6893i	1.20252	+	0.498099i
$650$		0			0
$651$	−4.67408	−	23.4982i	−0.183192	−	0.920967i
$652$		0			0
$653$	9.43917	+	14.1267i	0.369383	+	0.552821i	0.968872	−	0.247562i	$-0.0796295\pi$
$653$	9.43917	+	14.1267i	0.369383	+	0.552821i	−0.599489	+	0.800383i	$0.704629\pi$
$654$		0			0
$655$	−15.9977	+	15.9977i	−0.625081	+	0.625081i
$656$		0			0
$657$	8.23939	+	8.23939i	0.321449	+	0.321449i
$658$		0			0
$659$	15.6666	−	10.4681i	0.610286	−	0.407780i	−0.211662	−	0.977343i	$-0.567888\pi$
$659$	15.6666	−	10.4681i	0.610286	−	0.407780i	0.821948	+	0.569563i	$0.192888\pi$
$660$		0			0
$661$	−8.02511	+	1.59629i	−0.312140	+	0.0620886i	−0.348675	−	0.937244i	$-0.613368\pi$
$661$	−8.02511	+	1.59629i	−0.312140	+	0.0620886i	0.0365342	+	0.999332i	$0.488368\pi$
$662$		0			0
$663$	9.90222	−	23.9061i	0.384570	−	0.928435i
$664$		0			0
$665$	1.89640	+	4.57831i	0.0735392	+	0.177539i
$666$		0			0
$667$	−38.9384	−	26.0178i	−1.50770	−	1.00741i
$668$		0			0
$669$	0.709869	−	3.56875i	0.0274451	−	0.137976i
$670$		0			0
$671$			2.16737i			0.0836704i
$672$		0			0
$673$		−	15.1387i		−	0.583554i	−0.956486	−	0.291777i	$-0.905753\pi$
$673$		−	15.1387i		−	0.583554i	0.956486	−	0.291777i	$-0.0942465\pi$
$674$		0			0
$675$	2.41991	−	12.1657i	0.0931425	−	0.468259i
$676$		0			0
$677$	17.6776	+	11.8118i	0.679406	+	0.453964i	0.846790	−	0.531927i	$-0.178532\pi$
$677$	17.6776	+	11.8118i	0.679406	+	0.453964i	−0.167384	+	0.985892i	$0.553532\pi$
$678$		0			0
$679$	−3.79526	−	9.16258i	−0.145649	−	0.351627i
$680$		0			0
$681$	−1.13800	+	2.74736i	−0.0436081	+	0.105279i
$682$		0			0
$683$	3.48191	−	0.692594i	0.133231	−	0.0265014i	−0.128024	−	0.991771i	$-0.540863\pi$
$683$	3.48191	−	0.692594i	0.133231	−	0.0265014i	0.261256	+	0.965270i	$0.415863\pi$
$684$		0			0
$685$	−6.88456	+	4.60012i	−0.263046	+	0.175761i
$686$		0			0
$687$	28.1858	+	28.1858i	1.07536	+	1.07536i
$688$		0			0
$689$	−5.61679	+	5.61679i	−0.213982	+	0.213982i
$690$		0			0
$691$	2.86419	+	4.28656i	0.108959	+	0.163069i	0.881942	−	0.471358i	$-0.156236\pi$
$691$	2.86419	+	4.28656i	0.108959	+	0.163069i	−0.772983	+	0.634427i	$0.781236\pi$
$692$		0			0
$693$	−2.28170	−	11.4709i	−0.0866747	−	0.435743i
$694$		0			0
$695$	−1.33597	−	0.553377i	−0.0506762	−	0.0209908i
$696$		0			0
$697$	−26.3734	+	10.9242i	−0.998964	+	0.413784i
$698$		0			0
$699$	26.3314	−	39.4077i	0.995944	−	1.49054i
$700$		0			0
$701$	24.9906	+	4.97093i	0.943881	+	0.187750i	0.642960	−	0.765900i	$-0.277706\pi$
$701$	24.9906	+	4.97093i	0.943881	+	0.187750i	0.300920	+	0.953649i	$0.402706\pi$
$702$		0			0
$703$	−12.1813			−0.459427
$704$		0			0
$705$	2.90449			0.109389
$706$		0			0
$707$	−35.0717	−	6.97620i	−1.31901	−	0.262367i
$708$		0			0
$709$	−27.8695	+	41.7097i	−1.04666	+	1.56644i	−0.244213	+	0.969722i	$0.578530\pi$
$709$	−27.8695	+	41.7097i	−1.04666	+	1.56644i	−0.802450	+	0.596720i	$0.796470\pi$
$710$		0			0
$711$	6.23081	−	2.58089i	0.233674	−	0.0967908i
$712$		0			0
$713$	26.7876	+	11.0958i	1.00320	+	0.415541i
$714$		0			0
$715$	4.13921	+	20.8092i	0.154798	+	0.778221i
$716$		0			0
$717$	−10.2120	−	15.2834i	−0.381375	−	0.570768i
$718$		0			0
$719$	17.1962	−	17.1962i	0.641311	−	0.641311i	−0.309567	−	0.950878i	$-0.600184\pi$
$719$	17.1962	−	17.1962i	0.641311	−	0.641311i	0.950878	+	0.309567i	$0.100184\pi$
$720$		0			0
$721$	7.08774	+	7.08774i	0.263961	+	0.263961i
$722$		0			0
$723$	31.5508	−	21.0815i	1.17339	−	0.784031i
$724$		0			0
$725$	−24.5241	+	4.87815i	−0.910804	+	0.181170i
$726$		0			0
$727$	7.53130	−	18.1822i	0.279320	−	0.674339i	−0.720497	−	0.693458i	$-0.756086\pi$
$727$	7.53130	−	18.1822i	0.279320	−	0.674339i	0.999817	+	0.0191193i	$0.00608624\pi$
$728$		0			0
$729$	5.65985	+	13.6641i	0.209624	+	0.506077i
$730$		0			0
$731$	17.1520	+	11.4606i	0.634389	+	0.423885i
$732$		0			0
$733$	2.30717	−	11.5989i	0.0852174	−	0.428417i	−0.914499	−	0.404589i	$-0.867415\pi$
$733$	2.30717	−	11.5989i	0.0852174	−	0.428417i	0.999716	−	0.0238279i	$-0.00758537\pi$
$734$		0			0
$735$			4.22500i			0.155842i
$736$		0			0
$737$		−	9.48594i		−	0.349419i
$738$		0			0
$739$	3.47244	−	17.4572i	0.127736	−	0.642172i	−0.862870	−	0.505426i	$-0.831336\pi$
$739$	3.47244	−	17.4572i	0.127736	−	0.642172i	0.990606	−	0.136746i	$-0.0436645\pi$
$740$		0			0
$741$	6.59881	+	4.40919i	0.242413	+	0.161976i
$742$		0			0
$743$	−16.7416	−	40.4177i	−0.614188	−	1.48278i	−0.858359	−	0.513049i	$-0.828516\pi$
$743$	−16.7416	−	40.4177i	−0.614188	−	1.48278i	0.244171	−	0.969732i	$-0.421484\pi$
$744$		0			0
$745$	−0.0246280	+	0.0594573i	−0.000902300	+	0.00217835i
$746$		0			0
$747$	−1.36554	+	0.271623i	−0.0499626	+	0.00993817i
$748$		0			0
$749$	12.8997	−	8.61929i	0.471344	−	0.314942i
$750$		0			0
$751$	33.9816	+	33.9816i	1.24001	+	1.24001i	0.959998	+	0.280008i	$0.0903371\pi$
$751$	33.9816	+	33.9816i	1.24001	+	1.24001i	0.280008	+	0.959998i	$0.409663\pi$
$752$		0			0
$753$	−22.5147	+	22.5147i	−0.820481	+	0.820481i
$754$		0			0
$755$	−16.0390	−	24.0040i	−0.583717	−	0.873595i
$756$		0			0
$757$	−7.87408	−	39.5857i	−0.286188	−	1.43877i	−0.809749	−	0.586777i	$-0.800396\pi$
$757$	−7.87408	−	39.5857i	−0.286188	−	1.43877i	0.523560	−	0.851989i	$-0.324604\pi$
$758$		0			0
$759$	56.7239	+	23.4958i	2.05895	+	0.852844i
$760$		0			0
$761$	40.6579	−	16.8410i	1.47385	−	0.610488i	0.506114	−	0.862466i	$-0.331081\pi$
$761$	40.6579	−	16.8410i	1.47385	−	0.610488i	0.967733	+	0.251979i	$0.0810813\pi$
$762$		0			0
$763$	−14.9535	+	22.3795i	−0.541354	+	0.810194i
$764$		0			0
$765$	6.07826	+	1.20904i	0.219760	+	0.0437129i
$766$		0			0
$767$	16.0904			0.580992
$768$		0			0
$769$	9.57488			0.345279			0.172639	−	0.984985i	$-0.444770\pi$
$769$	9.57488			0.345279			0.172639	+	0.984985i	$0.444770\pi$
$770$		0			0
$771$	−25.9180	−	5.15540i	−0.933413	−	0.185667i
$772$		0			0
$773$	8.88263	−	13.2938i	0.319486	−	0.478145i	−0.636615	−	0.771182i	$-0.719666\pi$
$773$	8.88263	−	13.2938i	0.319486	−	0.478145i	0.956101	+	0.293037i	$0.0946659\pi$
$774$		0			0
$775$	14.3028	−	5.92443i	0.513773	−	0.212812i
$776$		0			0
$777$	34.9102	+	14.4603i	1.25240	+	0.518759i
$778$		0			0
$779$	−1.70810	−	8.58720i	−0.0611990	−	0.307668i
$780$		0			0
$781$	−2.81663	−	4.21538i	−0.100787	−	0.150838i
$782$		0			0
$783$	24.5362	−	24.5362i	0.876852	−	0.876852i
$784$		0			0
$785$	14.8102	+	14.8102i	0.528599	+	0.528599i
$786$		0			0
$787$	−12.1334	+	8.10728i	−0.432509	+	0.288993i	−0.752705	−	0.658358i	$-0.771251\pi$
$787$	−12.1334	+	8.10728i	−0.432509	+	0.288993i	0.320196	+	0.947351i	$0.396251\pi$
$788$		0			0
$789$	41.8849	−	8.33143i	1.49114	−	0.296607i
$790$		0			0
$791$	−6.36782	+	15.3733i	−0.226414	+	0.546611i
$792$		0			0
$793$	0.402478	+	0.971669i	0.0142924	+	0.0345050i
$794$		0			0
$795$	−6.86168	−	4.58483i	−0.243359	−	0.162607i
$796$		0			0
$797$	5.58966	−	28.1011i	0.197996	−	0.995393i	−0.746128	−	0.665803i	$-0.768089\pi$
$797$	5.58966	−	28.1011i	0.197996	−	0.995393i	0.944124	−	0.329591i	$-0.106911\pi$
$798$		0			0
$799$			5.04535i			0.178492i
$800$		0			0
$801$		−	9.36884i		−	0.331032i
$802$		0			0
$803$	14.0452	−	70.6098i	0.495643	−	2.49177i
$804$		0			0
$805$	15.4681	+	10.3355i	0.545179	+	0.364277i
$806$		0			0
$807$	14.1374	+	34.1306i	0.497659	+	1.20146i
$808$		0			0
$809$	2.83209	−	6.83727i	0.0995710	−	0.240386i	−0.866242	−	0.499624i	$-0.833472\pi$
$809$	2.83209	−	6.83727i	0.0995710	−	0.240386i	0.965813	+	0.259238i	$0.0834715\pi$
$810$		0			0
$811$	46.3896	−	9.22747i	1.62896	−	0.324020i	0.705792	−	0.708419i	$-0.250591\pi$
$811$	46.3896	−	9.22747i	1.62896	−	0.324020i	0.923167	+	0.384399i	$0.125591\pi$
$812$		0			0
$813$	15.5953	−	10.4204i	0.546951	−	0.365461i
$814$		0			0
$815$	−0.413799	−	0.413799i	−0.0144948	−	0.0144948i
$816$		0			0
$817$	−4.47383	+	4.47383i	−0.156519	+	0.156519i
$818$		0			0
$819$	−3.15306	−	4.71888i	−0.110177	−	0.164891i
$820$		0			0
$821$	3.86909	+	19.4512i	0.135032	+	0.678852i	0.987695	+	0.156391i	$0.0499859\pi$
$821$	3.86909	+	19.4512i	0.135032	+	0.678852i	−0.852663	+	0.522461i	$0.825014\pi$
$822$		0			0
$823$	−32.9693	−	13.6563i	−1.14924	−	0.476030i	−0.274960	−	0.961456i	$-0.588665\pi$
$823$	−32.9693	−	13.6563i	−1.14924	−	0.476030i	−0.874278	+	0.485426i	$0.838665\pi$
$824$		0			0
$825$	30.2868	−	12.5452i	1.05445	−	0.436768i
$826$		0			0
$827$	10.8849	−	16.2904i	0.378505	−	0.566473i	−0.592488	−	0.805579i	$-0.701854\pi$
$827$	10.8849	−	16.2904i	0.378505	−	0.566473i	0.970994	+	0.239106i	$0.0768543\pi$
$828$		0			0
$829$	39.3454	+	7.82628i	1.36652	+	0.271818i	0.823221	−	0.567721i	$-0.192175\pi$
$829$	39.3454	+	7.82628i	1.36652	+	0.271818i	0.543300	+	0.839539i	$0.317175\pi$
$830$		0			0
$831$	−15.6209			−0.541882
$832$		0			0
$833$	−7.33921			−0.254289
$834$		0			0
$835$	6.84174	+	1.36091i	0.236768	+	0.0470961i
$836$		0			0
$837$	−11.9357	+	17.8630i	−0.412558	+	0.617437i
$838$		0			0
$839$	37.2927	−	15.4471i	1.28749	−	0.533294i	0.369251	−	0.929330i	$-0.379614\pi$
$839$	37.2927	−	15.4471i	1.28749	−	0.533294i	0.918235	+	0.396035i	$0.129614\pi$
$840$		0			0
$841$	−37.8314	−	15.6703i	−1.30453	−	0.540355i
$842$		0			0
$843$	−1.28992	−	6.48485i	−0.0444271	−	0.223350i
$844$		0			0
$845$	−4.52031	−	6.76513i	−0.155503	−	0.232727i
$846$		0			0
$847$	−32.8700	+	32.8700i	−1.12943	+	1.12943i
$848$		0			0
$849$	−9.31006	−	9.31006i	−0.319520	−	0.319520i
$850$		0			0
$851$	−38.0226	+	25.4059i	−1.30340	+	0.870902i
$852$		0			0
$853$	4.15795	−	0.827067i	0.142365	−	0.0283182i	−0.123393	−	0.992358i	$-0.539378\pi$
$853$	4.15795	−	0.827067i	0.142365	−	0.0283182i	0.265759	+	0.964040i	$0.414378\pi$
$854$		0			0
$855$	−0.727397	+	1.75609i	−0.0248764	+	0.0600570i
$856$		0			0
$857$	−3.06475	−	7.39897i	−0.104690	−	0.252744i	0.862851	−	0.505459i	$-0.168677\pi$
$857$	−3.06475	−	7.39897i	−0.104690	−	0.252744i	−0.967541	+	0.252715i	$0.918677\pi$
$858$		0			0
$859$	25.3340	+	16.9276i	0.864385	+	0.577564i	0.906812	−	0.421536i	$-0.138509\pi$
$859$	25.3340	+	16.9276i	0.864385	+	0.577564i	−0.0424267	+	0.999100i	$0.513509\pi$
$860$		0			0
$861$	−5.29854	+	26.6375i	−0.180574	+	0.907805i
$862$		0			0
$863$		−	19.0711i		−	0.649189i	−0.945853	−	0.324595i	$-0.894772\pi$
$863$		−	19.0711i		−	0.649189i	0.945853	−	0.324595i	$-0.105228\pi$
$864$		0			0
$865$		−	4.41109i		−	0.149982i
$866$		0			0
$867$	−2.56167	+	12.8784i	−0.0869990	+	0.437373i
$868$		0			0
$869$	−34.6463	−	23.1499i	−1.17529	−	0.785307i
$870$		0			0
$871$	−1.76153	−	4.25271i	−0.0596871	−	0.144097i
$872$		0			0
$873$	1.45574	−	3.51447i	0.0492693	−	0.118947i
$874$		0			0
$875$	26.0347	−	5.17863i	0.880135	−	0.175070i
$876$		0			0
$877$	−18.3071	+	12.2324i	−0.618187	+	0.413060i	−0.824849	−	0.565353i	$-0.808740\pi$
$877$	−18.3071	+	12.2324i	−0.618187	+	0.413060i	0.206662	+	0.978412i	$0.433740\pi$
$878$		0			0
$879$	−16.1404	−	16.1404i	−0.544402	−	0.544402i
$880$		0			0
$881$	−5.72028	+	5.72028i	−0.192721	+	0.192721i	−0.796871	−	0.604150i	$-0.793513\pi$
$881$	−5.72028	+	5.72028i	−0.192721	+	0.192721i	0.604150	+	0.796871i	$0.293513\pi$
$882$		0			0
$883$	−14.0036	−	20.9579i	−0.471259	−	0.705289i	0.517353	−	0.855772i	$-0.326917\pi$
$883$	−14.0036	−	20.9579i	−0.471259	−	0.705289i	−0.988613	+	0.150483i	$0.951917\pi$
$884$		0			0
$885$	3.26126	+	16.3954i	0.109626	+	0.551127i
$886$		0			0
$887$	1.34482	+	0.557044i	0.0451548	+	0.0187037i	0.405147	−	0.914252i	$-0.367221\pi$
$887$	1.34482	+	0.557044i	0.0451548	+	0.0187037i	−0.359992	+	0.932955i	$0.617221\pi$
$888$		0			0
$889$	−30.4155	+	12.5985i	−1.02010	+	0.422541i
$890$		0			0
$891$	−33.5932	+	50.2758i	−1.12541	+	1.68430i
$892$		0			0
$893$	−1.51772	−	0.301894i	−0.0507886	−	0.0101025i
$894$		0			0
$895$	−5.38449			−0.179984
$896$		0			0
$897$	29.7934			0.994774
$898$		0			0
$899$	42.4755	+	8.44891i	1.41664	+	0.281787i
$900$		0			0
$901$	7.96426	−	11.9194i	0.265328	−	0.397091i
$902$		0			0
$903$	18.1323	−	7.51063i	0.603404	−	0.249938i
$904$		0			0
$905$	1.47635	+	0.611525i	0.0490756	+	0.0203278i
$906$		0			0
$907$	5.15594	+	25.9207i	0.171200	+	0.860681i	0.966932	+	0.255033i	$0.0820862\pi$
$907$	5.15594	+	25.9207i	0.171200	+	0.860681i	−0.795732	+	0.605648i	$0.792914\pi$
$908$		0			0
$909$	−7.62015	−	11.4044i	−0.252745	−	0.378259i
$910$		0			0
$911$	−9.32241	+	9.32241i	−0.308865	+	0.308865i	−0.844469	−	0.535604i	$-0.820084\pi$
$911$	−9.32241	+	9.32241i	−0.308865	+	0.308865i	0.535604	+	0.844469i	$0.320084\pi$
$912$		0			0
$913$	6.08271	+	6.08271i	0.201308	+	0.201308i
$914$		0			0
$915$	−0.908512	+	0.607048i	−0.0300345	+	0.0200684i
$916$		0			0
$917$	−36.6722	+	7.29456i	−1.21102	+	0.240888i
$918$		0			0
$919$	10.1895	−	24.5995i	0.336119	−	0.811464i	−0.661961	−	0.749538i	$-0.730276\pi$
$919$	10.1895	−	24.5995i	0.336119	−	0.811464i	0.998081	−	0.0619260i	$-0.0197243\pi$
$920$		0			0
$921$	−24.4191	−	58.9528i	−0.804635	−	1.94256i
$922$		0			0
$923$	−2.04553	−	1.36678i	−0.0673295	−	0.0449882i
$924$		0			0
$925$	−4.76341	+	23.9473i	−0.156620	+	0.787382i
$926$		0			0
$927$			3.84472i			0.126277i
$928$		0			0
$929$		−	1.73073i		−	0.0567835i	−0.999597	−	0.0283918i	$-0.990961\pi$
$929$		−	1.73073i		−	0.0567835i	0.999597	−	0.0283918i	$-0.00903859\pi$
$930$		0			0
$931$	0.439149	−	2.20775i	0.0143925	−	0.0723561i
$932$		0			0
$933$	−31.2750	−	20.8973i	−1.02390	−	0.684147i
$934$		0			0
$935$	−14.6530	−	35.3754i	−0.479203	−	1.15690i
$936$		0			0
$937$	18.3095	−	44.2031i	0.598146	−	1.44405i	−0.277323	−	0.960777i	$-0.589447\pi$
$937$	18.3095	−	44.2031i	0.598146	−	1.44405i	0.875469	−	0.483275i	$-0.160553\pi$
$938$		0			0
$939$	57.8422	−	11.5055i	1.88761	−	0.375469i
$940$		0			0
$941$	2.21555	−	1.48039i	0.0722250	−	0.0482592i	−0.518933	−	0.854815i	$-0.673671\pi$
$941$	2.21555	−	1.48039i	0.0722250	−	0.0482592i	0.591158	+	0.806555i	$0.298671\pi$
$942$		0			0
$943$	−23.2415	−	23.2415i	−0.756846	−	0.756846i
$944$		0			0
$945$	−9.74689	+	9.74689i	−0.317066	+	0.317066i
$946$		0			0
$947$	14.3424	+	21.4649i	0.466065	+	0.697516i	0.987824	−	0.155578i	$-0.0497239\pi$
$947$	14.3424	+	21.4649i	0.466065	+	0.697516i	−0.521759	+	0.853093i	$0.674724\pi$
$948$		0			0
$949$	−6.81548	−	34.2637i	−0.221240	−	1.11225i
$950$		0			0
$951$	−25.2345	−	10.4525i	−0.818286	−	0.338945i
$952$		0			0
$953$	−24.3145	+	10.0714i	−0.787622	+	0.326244i	−0.739987	−	0.672621i	$-0.765169\pi$
$953$	−24.3145	+	10.0714i	−0.787622	+	0.326244i	−0.0476352	+	0.998865i	$0.515169\pi$
$954$		0			0
$955$	−17.5822	+	26.3137i	−0.568948	+	0.851490i
$956$		0			0
$957$	89.9436	+	17.8909i	2.90746	+	0.578331i
$958$		0			0
$959$	−13.6843			−0.441888
$960$		0			0
$961$	4.18662			0.135052
$962$		0			0
$963$	5.83644	+	1.16094i	0.188077	+	0.0374108i
$964$		0			0
$965$	1.66032	−	2.48484i	0.0534475	−	0.0799899i
$966$		0			0
$967$	8.02112	−	3.32246i	0.257942	−	0.106843i	−0.249965	−	0.968255i	$-0.580419\pi$
$967$	8.02112	−	3.32246i	0.257942	−	0.106843i	0.507907	+	0.861412i	$0.330419\pi$
$968$		0			0
$969$	−13.2324	−	5.48104i	−0.425086	−	0.176076i
$970$		0			0
$971$	−9.92238	−	49.8832i	−0.318424	−	1.60083i	−0.726026	−	0.687667i	$-0.758635\pi$
$971$	−9.92238	−	49.8832i	−0.318424	−	1.60083i	0.407602	−	0.913160i	$-0.366365\pi$
$972$		0			0
$973$	−1.32774	−	1.98710i	−0.0425653	−	0.0637034i
$974$		0			0
$975$	11.2485	−	11.2485i	0.360239	−	0.360239i
$976$		0			0
$977$	34.0542	+	34.0542i	1.08949	+	1.08949i	0.995581	+	0.0939094i	$0.0299364\pi$
$977$	34.0542	+	34.0542i	1.08949	+	1.08949i	0.0939094	+	0.995581i	$0.470064\pi$
$978$		0			0
$979$	−48.1297	+	32.1592i	−1.53823	+	1.02781i
$980$		0			0
$981$	−10.1256	+	2.01411i	−0.323285	+	0.0643054i
$982$		0			0
$983$	−21.4849	+	51.8692i	−0.685262	+	1.65437i	0.0688520	+	0.997627i	$0.478066\pi$
$983$	−21.4849	+	51.8692i	−0.685262	+	1.65437i	−0.754114	+	0.656743i	$0.771934\pi$
$984$		0			0
$985$	−3.04858	−	7.35993i	−0.0971360	−	0.234507i
$986$		0			0
$987$	3.99123	+	2.66686i	0.127042	+	0.0848870i
$988$		0			0
$989$	−4.63373	+	23.2953i	−0.147344	+	0.740749i
$990$		0			0
$991$			56.1598i			1.78397i	0.452061	+	0.891987i	$0.350689\pi$
$991$			56.1598i			1.78397i	−0.452061	+	0.891987i	$0.649311\pi$
$992$		0			0
$993$			19.7631i			0.627163i
$994$		0			0
$995$	4.38232	−	22.0314i	0.138929	−	0.698443i
$996$		0			0
$997$	19.4239	+	12.9787i	0.615162	+	0.411038i	0.823740	−	0.566968i	$-0.191884\pi$
$997$	19.4239	+	12.9787i	0.615162	+	0.411038i	−0.208578	+	0.978006i	$0.566884\pi$
$998$		0			0
$999$	−12.9666	−	31.3041i	−0.410244	−	0.990416i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.i.a.161.6		56
4.3	odd	2		512.2.i.b.161.2		56
8.3	odd	2		64.2.i.a.29.4	✓	56
8.5	even	2		256.2.i.a.209.2		56
24.11	even	2		576.2.bd.a.541.4		56
64.11	odd	16		512.2.i.b.353.2		56
64.21	even	16		256.2.i.a.49.2		56
64.43	odd	16		64.2.i.a.53.4	yes	56
64.53	even	16	inner	512.2.i.a.353.6		56
192.107	even	16		576.2.bd.a.181.4		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.29.4	✓	56	8.3	odd	2
64.2.i.a.53.4	yes	56	64.43	odd	16
256.2.i.a.49.2		56	64.21	even	16
256.2.i.a.209.2		56	8.5	even	2
512.2.i.a.161.6		56	1.1	even	1	trivial
512.2.i.a.353.6		56	64.53	even	16	inner
512.2.i.b.161.2		56	4.3	odd	2
512.2.i.b.353.2		56	64.11	odd	16
576.2.bd.a.181.4		56	192.107	even	16
576.2.bd.a.541.4		56	24.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 512 = 2^{9} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	512.i (of order \(16\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.93660 + 0.385213i) q^{3} +(0.787711 - 1.17889i) q^{5} +(2.16489 - 0.896725i) q^{7} +(0.830380 + 0.343954i) q^{9} +O(q^{10})\)	\(q+(1.93660 + 0.385213i) q^{3} +(0.787711 - 1.17889i) q^{5} +(2.16489 - 0.896725i) q^{7} +(0.830380 + 0.343954i) q^{9} +(-1.08337 - 5.44648i) q^{11} +(-1.49710 - 2.24057i) q^{13} +(1.97960 - 1.97960i) q^{15} +(3.43875 + 3.43875i) q^{17} +(-1.24019 + 0.828669i) q^{19} +(4.53794 - 0.902653i) q^{21} +(-2.14281 + 5.17319i) q^{23} +(1.14412 + 2.76214i) q^{25} +(-3.44969 - 2.30501i) q^{27} +(-1.63164 + 8.20281i) q^{29} -5.17816i q^{31} -10.9650i q^{33} +(0.648162 - 3.25853i) q^{35} +(6.79044 + 4.53723i) q^{37} +(-2.03618 - 4.91578i) q^{39} +(-2.24634 + 5.42314i) q^{41} +(4.16031 - 0.827538i) q^{43} +(1.05958 - 0.707992i) q^{45} +(0.733603 + 0.733603i) q^{47} +(-1.06713 + 1.06713i) q^{49} +(5.33482 + 7.98413i) q^{51} +(-0.575078 - 2.89111i) q^{53} +(-7.27421 - 3.01307i) q^{55} +(-2.72096 + 1.12706i) q^{57} +(-3.31738 + 4.96481i) q^{59} +(-0.382794 - 0.0761424i) q^{61} +2.10611 q^{63} -3.82067 q^{65} +(1.67538 + 0.333253i) q^{67} +(-6.14253 + 9.19295i) q^{69} +(0.843458 - 0.349372i) q^{71} +(11.9774 + 4.96122i) q^{73} +(1.15168 + 5.78989i) q^{75} +(-7.22938 - 10.8195i) q^{77} +(5.30583 - 5.30583i) q^{79} +(-7.69937 - 7.69937i) q^{81} +(-1.28800 + 0.860615i) q^{83} +(6.76266 - 1.34518i) q^{85} +(-6.31966 + 15.2570i) q^{87} +(-3.98900 - 9.63030i) q^{89} +(-5.25023 - 3.50809i) q^{91} +(1.99470 - 10.0280i) q^{93} +2.11480i q^{95} -4.23236i q^{97} +(0.973732 - 4.89528i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{3} + 8 q^{5} + 8 q^{7} - 8 q^{9}+O(q^{10}) \) 56 * q - 8 * q^3 + 8 * q^5 + 8 * q^7 - 8 * q^9	\( 56 q - 8 q^{3} + 8 q^{5} + 8 q^{7} - 8 q^{9} - 8 q^{11} + 8 q^{13} + 8 q^{15} - 8 q^{17} - 8 q^{19} + 8 q^{21} + 8 q^{23} - 8 q^{25} - 8 q^{27} + 8 q^{29} - 8 q^{35} + 8 q^{37} + 8 q^{39} - 8 q^{41} - 8 q^{43} + 8 q^{45} + 8 q^{47} - 8 q^{49} + 24 q^{51} + 8 q^{53} - 56 q^{55} - 8 q^{57} + 56 q^{59} + 8 q^{61} - 64 q^{63} - 16 q^{65} + 72 q^{67} + 8 q^{69} - 56 q^{71} - 8 q^{73} + 56 q^{75} + 8 q^{77} - 24 q^{79} - 8 q^{81} - 8 q^{83} + 8 q^{85} + 8 q^{87} - 8 q^{89} - 8 q^{91} - 16 q^{93} + 16 q^{99}+O(q^{100}) \) 56 * q - 8 * q^3 + 8 * q^5 + 8 * q^7 - 8 * q^9 - 8 * q^11 + 8 * q^13 + 8 * q^15 - 8 * q^17 - 8 * q^19 + 8 * q^21 + 8 * q^23 - 8 * q^25 - 8 * q^27 + 8 * q^29 - 8 * q^35 + 8 * q^37 + 8 * q^39 - 8 * q^41 - 8 * q^43 + 8 * q^45 + 8 * q^47 - 8 * q^49 + 24 * q^51 + 8 * q^53 - 56 * q^55 - 8 * q^57 + 56 * q^59 + 8 * q^61 - 64 * q^63 - 16 * q^65 + 72 * q^67 + 8 * q^69 - 56 * q^71 - 8 * q^73 + 56 * q^75 + 8 * q^77 - 24 * q^79 - 8 * q^81 - 8 * q^83 + 8 * q^85 + 8 * q^87 - 8 * q^89 - 8 * q^91 - 16 * q^93 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more