LMFDB - Embedded newform 512.2.k.a.17.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [512,2,Mod(17,512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(512, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 7]))

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

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

chi := DirichletCharacter("512.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 512 = 2^{9} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	512.k (of order $32$, degree $16$, 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:	$240$
Relative dimension:	$15$ over $\Q(\zeta_{32})$
Twist minimal:	no (minimal twist has level 128)
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			17.3
Character	$\chi$	$=$	512.17
Dual form			512.2.k.a.241.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.995218 + 1.86192i) q^{3} +(-1.80486 - 1.48121i) q^{5} +(-0.154904 - 0.103503i) q^{7} +(-0.809586 - 1.21163i) q^{9} +O(q^{10})$	\(q+(-0.995218 + 1.86192i) q^{3} +(-1.80486 - 1.48121i) q^{5} +(-0.154904 - 0.103503i) q^{7} +(-0.809586 - 1.21163i) q^{9} +(1.36000 - 4.48334i) q^{11} +(-2.82091 - 3.43729i) q^{13} +(4.55412 - 1.88638i) q^{15} +(6.10980 + 2.53076i) q^{17} +(5.18669 + 0.510845i) q^{19} +(0.346878 - 0.185410i) q^{21} +(1.63598 + 0.325416i) q^{23} +(0.0880816 + 0.442816i) q^{25} +(-3.24146 + 0.319256i) q^{27} +(0.579898 - 0.175910i) q^{29} +(-1.03030 + 1.03030i) q^{31} +(6.99412 + 6.99412i) q^{33} +(0.126269 + 0.416253i) q^{35} +(-0.664297 - 6.74472i) q^{37} +(9.20740 - 1.83147i) q^{39} +(1.30788 - 6.57518i) q^{41} +(1.83276 + 3.42885i) q^{43} +(-0.333491 + 3.38599i) q^{45} +(2.82164 - 6.81205i) q^{47} +(-2.66550 - 6.43509i) q^{49} +(-10.7927 + 8.85731i) q^{51} +(9.65045 + 2.92743i) q^{53} +(-9.09537 + 6.07733i) q^{55} +(-6.11305 + 9.14882i) q^{57} +(3.24335 - 3.95204i) q^{59} +(7.18403 + 3.83994i) q^{61} +0.271481i q^{63} +10.3822i q^{65} +(-12.0271 - 6.42859i) q^{67} +(-2.23405 + 2.72220i) q^{69} +(1.85934 - 2.78269i) q^{71} +(-6.86335 + 4.58594i) q^{73} +(-0.912150 - 0.276698i) q^{75} +(-0.674709 + 0.553720i) q^{77} +(-5.99200 - 14.4660i) q^{79} +(4.30449 - 10.3920i) q^{81} +(-1.23471 + 12.5362i) q^{83} +(-7.27873 - 13.6175i) q^{85} +(-0.249594 + 1.25479i) q^{87} +(3.64255 - 0.724548i) q^{89} +(0.0811986 + 0.824423i) q^{91} +(-0.892966 - 2.94371i) q^{93} +(-8.60458 - 8.60458i) q^{95} +(1.83881 - 1.83881i) q^{97} +(-6.53319 + 1.98182i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9}+O(q^{10}) $ 240 * q + 16 * q^3 - 16 * q^5 + 16 * q^7 - 16 * q^9	$ 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9} + 16 q^{11} - 16 q^{13} + 16 q^{15} - 16 q^{17} + 16 q^{19} - 16 q^{21} + 16 q^{23} - 16 q^{25} + 16 q^{27} - 16 q^{29} + 16 q^{31} - 16 q^{33} + 16 q^{35} - 16 q^{37} + 16 q^{39} - 16 q^{41} + 16 q^{43} - 16 q^{45} + 16 q^{47} - 16 q^{49} + 16 q^{51} - 16 q^{53} + 16 q^{55} - 16 q^{57} + 16 q^{59} - 16 q^{61} + 16 q^{67} - 16 q^{69} + 16 q^{71} - 16 q^{73} + 16 q^{75} - 16 q^{77} + 16 q^{79} - 16 q^{81} + 16 q^{83} - 16 q^{85} + 16 q^{87} - 16 q^{89} + 16 q^{91} - 16 q^{93} + 16 q^{95} - 16 q^{97} + 16 q^{99}+O(q^{100}) $ 240 * q + 16 * q^3 - 16 * q^5 + 16 * q^7 - 16 * q^9 + 16 * q^11 - 16 * q^13 + 16 * q^15 - 16 * q^17 + 16 * q^19 - 16 * q^21 + 16 * q^23 - 16 * q^25 + 16 * q^27 - 16 * q^29 + 16 * q^31 - 16 * q^33 + 16 * q^35 - 16 * q^37 + 16 * q^39 - 16 * q^41 + 16 * q^43 - 16 * q^45 + 16 * q^47 - 16 * q^49 + 16 * q^51 - 16 * q^53 + 16 * q^55 - 16 * q^57 + 16 * q^59 - 16 * q^61 + 16 * q^67 - 16 * q^69 + 16 * q^71 - 16 * q^73 + 16 * q^75 - 16 * q^77 + 16 * q^79 - 16 * q^81 + 16 * q^83 - 16 * q^85 + 16 * q^87 - 16 * q^89 + 16 * q^91 - 16 * q^93 + 16 * q^95 - 16 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{7}{32}\right)$	$1$

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
$3$	−0.995218	+	1.86192i	−0.574590	+	1.07498i	0.411911	+	0.911224i	$0.364861\pi$
$3$	−0.995218	+	1.86192i	−0.574590	+	1.07498i	−0.986501	+	0.163758i	$0.947639\pi$
$4$		0			0
$5$	−1.80486	−	1.48121i	−0.807157	−	0.662417i	0.137491	−	0.990503i	$-0.456096\pi$
$5$	−1.80486	−	1.48121i	−0.807157	−	0.662417i	−0.944648	+	0.328086i	$0.893596\pi$
$6$		0			0
$7$	−0.154904	−	0.103503i	−0.0585480	−	0.0391205i	0.525952	−	0.850514i	$-0.323709\pi$
$7$	−0.154904	−	0.103503i	−0.0585480	−	0.0391205i	−0.584500	+	0.811394i	$0.698709\pi$
$8$		0			0
$9$	−0.809586	−	1.21163i	−0.269862	−	0.403877i
$10$		0			0
$11$	1.36000	−	4.48334i	0.410057	−	1.35178i	−0.472400	−	0.881384i	$-0.656612\pi$
$11$	1.36000	−	4.48334i	0.410057	−	1.35178i	0.882457	−	0.470392i	$-0.155888\pi$
$12$		0			0
$13$	−2.82091	−	3.43729i	−0.782381	−	0.953334i	0.217360	−	0.976091i	$-0.430255\pi$
$13$	−2.82091	−	3.43729i	−0.782381	−	0.953334i	−0.999741	+	0.0227576i	$0.992755\pi$
$14$		0			0
$15$	4.55412	−	1.88638i	1.17587	−	0.487061i
$16$		0			0
$17$	6.10980	+	2.53076i	1.48184	+	0.613800i	0.969524	−	0.244995i	$-0.0787865\pi$
$17$	6.10980	+	2.53076i	1.48184	+	0.613800i	0.512319	+	0.858795i	$0.328786\pi$
$18$		0			0
$19$	5.18669	+	0.510845i	1.18991	+	0.117196i	0.673527	−	0.739163i	$-0.264778\pi$
$19$	5.18669	+	0.510845i	1.18991	+	0.117196i	0.516382	+	0.856358i	$0.327278\pi$
$20$		0			0
$21$	0.346878	−	0.185410i	0.0756950	−	0.0404598i
$22$		0			0
$23$	1.63598	+	0.325416i	0.341125	+	0.0678539i	0.362680	−	0.931914i	$-0.381862\pi$
$23$	1.63598	+	0.325416i	0.341125	+	0.0678539i	−0.0215553	+	0.999768i	$0.506862\pi$
$24$		0			0
$25$	0.0880816	+	0.442816i	0.0176163	+	0.0885632i
$26$		0			0
$27$	−3.24146	+	0.319256i	−0.623819	+	0.0614408i
$28$		0			0
$29$	0.579898	−	0.175910i	0.107684	−	0.0326657i	−0.235983	−	0.971757i	$-0.575831\pi$
$29$	0.579898	−	0.175910i	0.107684	−	0.0326657i	0.343667	+	0.939092i	$0.388331\pi$
$30$		0			0
$31$	−1.03030	+	1.03030i	−0.185047	+	0.185047i	−0.793551	−	0.608504i	$-0.791770\pi$
$31$	−1.03030	+	1.03030i	−0.185047	+	0.185047i	0.608504	+	0.793551i	$0.291770\pi$
$32$		0			0
$33$	6.99412	+	6.99412i	1.21752	+	1.21752i
$34$		0			0
$35$	0.126269	+	0.416253i	0.0213434	+	0.0703596i
$36$		0			0
$37$	−0.664297	−	6.74472i	−0.109210	−	1.10883i	−0.881055	−	0.473014i	$-0.843166\pi$
$37$	−0.664297	−	6.74472i	−0.109210	−	1.10883i	0.771845	−	0.635811i	$-0.219334\pi$
$38$		0			0
$39$	9.20740	−	1.83147i	1.47436	−	0.293269i
$40$		0			0
$41$	1.30788	−	6.57518i	0.204257	−	1.02687i	−0.733529	−	0.679658i	$-0.762128\pi$
$41$	1.30788	−	6.57518i	0.204257	−	1.02687i	0.937787	−	0.347212i	$-0.112872\pi$
$42$		0			0
$43$	1.83276	+	3.42885i	0.279493	+	0.522895i	0.982023	−	0.188759i	$-0.0604464\pi$
$43$	1.83276	+	3.42885i	0.279493	+	0.522895i	−0.702530	+	0.711654i	$0.747946\pi$
$44$		0			0
$45$	−0.333491	+	3.38599i	−0.0497138	+	0.504753i
$46$		0			0
$47$	2.82164	−	6.81205i	0.411579	−	0.993640i	−0.573135	−	0.819461i	$-0.694273\pi$
$47$	2.82164	−	6.81205i	0.411579	−	0.993640i	0.984714	−	0.174179i	$-0.0557271\pi$
$48$		0			0
$49$	−2.66550	−	6.43509i	−0.380786	−	0.919299i
$50$		0			0
$51$	−10.7927	+	8.85731i	−1.51128	+	1.24027i
$52$		0			0
$53$	9.65045	+	2.92743i	1.32559	+	0.402114i	0.872179	−	0.489187i	$-0.162706\pi$
$53$	9.65045	+	2.92743i	1.32559	+	0.402114i	0.453412	+	0.891301i	$0.350206\pi$
$54$		0			0
$55$	−9.09537	+	6.07733i	−1.22642	+	0.819467i
$56$		0			0
$57$	−6.11305	+	9.14882i	−0.809693	+	1.21179i
$58$		0			0
$59$	3.24335	−	3.95204i	0.422248	−	0.514511i	−0.517823	−	0.855488i	$-0.673258\pi$
$59$	3.24335	−	3.95204i	0.422248	−	0.514511i	0.940072	+	0.340976i	$0.110758\pi$
$60$		0			0
$61$	7.18403	+	3.83994i	0.919821	+	0.491655i	0.862134	−	0.506680i	$-0.169127\pi$
$61$	7.18403	+	3.83994i	0.919821	+	0.491655i	0.0576869	+	0.998335i	$0.481627\pi$
$62$		0			0
$63$			0.271481i			0.0342033i
$64$		0			0
$65$			10.3822i			1.28775i
$66$		0			0
$67$	−12.0271	−	6.42859i	−1.46934	−	0.785378i	−0.473881	−	0.880589i	$-0.657147\pi$
$67$	−12.0271	−	6.42859i	−1.46934	−	0.785378i	−0.995457	+	0.0952113i	$0.969647\pi$
$68$		0			0
$69$	−2.23405	+	2.72220i	−0.268948	+	0.327715i
$70$		0			0
$71$	1.85934	−	2.78269i	0.220663	−	0.330245i	−0.704577	−	0.709627i	$-0.748863\pi$
$71$	1.85934	−	2.78269i	0.220663	−	0.330245i	0.925240	+	0.379382i	$0.123863\pi$
$72$		0			0
$73$	−6.86335	+	4.58594i	−0.803294	+	0.536744i	−0.888098	−	0.459654i	$-0.847973\pi$
$73$	−6.86335	+	4.58594i	−0.803294	+	0.536744i	0.0848043	+	0.996398i	$0.472973\pi$
$74$		0			0
$75$	−0.912150	−	0.276698i	−0.105326	−	0.0319503i
$76$		0			0
$77$	−0.674709	+	0.553720i	−0.0768903	+	0.0631022i
$78$		0			0
$79$	−5.99200	−	14.4660i	−0.674153	−	1.62755i	−0.774483	−	0.632594i	$-0.781990\pi$
$79$	−5.99200	−	14.4660i	−0.674153	−	1.62755i	0.100330	−	0.994954i	$-0.468010\pi$
$80$		0			0
$81$	4.30449	−	10.3920i	0.478276	−	1.15466i
$82$		0			0
$83$	−1.23471	+	12.5362i	−0.135527	+	1.37603i	0.651285	+	0.758834i	$0.274230\pi$
$83$	−1.23471	+	12.5362i	−0.135527	+	1.37603i	−0.786811	+	0.617194i	$0.788270\pi$
$84$		0			0
$85$	−7.27873	−	13.6175i	−0.789489	−	1.47703i
$86$		0			0
$87$	−0.249594	+	1.25479i	−0.0267593	+	0.134528i
$88$		0			0
$89$	3.64255	−	0.724548i	0.386109	−	0.0768019i	0.00178105	−	0.999998i	$-0.499433\pi$
$89$	3.64255	−	0.724548i	0.386109	−	0.0768019i	0.384328	+	0.923196i	$0.374433\pi$
$90$		0			0
$91$	0.0811986	+	0.824423i	0.00851192	+	0.0864230i
$92$		0			0
$93$	−0.892966	−	2.94371i	−0.0925963	−	0.305249i
$94$		0			0
$95$	−8.60458	−	8.60458i	−0.882811	−	0.882811i
$96$		0			0
$97$	1.83881	−	1.83881i	0.186703	−	0.186703i	−0.607566	−	0.794269i	$-0.707854\pi$
$97$	1.83881	−	1.83881i	0.186703	−	0.186703i	0.794269	+	0.607566i	$0.207854\pi$
$98$		0			0
$99$	−6.53319	+	1.98182i	−0.656610	+	0.199181i
$100$		0			0
$101$	−11.7696	+	1.15921i	−1.17112	+	0.115345i	−0.664815	−	0.747008i	$-0.731490\pi$
$101$	−11.7696	+	1.15921i	−1.17112	+	0.115345i	−0.506307	+	0.862354i	$0.668990\pi$
$102$		0			0
$103$	1.54840	+	7.78434i	0.152569	+	0.767014i	0.978981	+	0.203949i	$0.0653777\pi$
$103$	1.54840	+	7.78434i	0.152569	+	0.767014i	−0.826413	+	0.563065i	$0.809622\pi$
$104$		0			0
$105$	−0.900696	−	0.179160i	−0.0878990	−	0.0174842i
$106$		0			0
$107$	0.942270	−	0.503654i	0.0910927	−	0.0486900i	−0.425221	−	0.905089i	$-0.639804\pi$
$107$	0.942270	−	0.503654i	0.0910927	−	0.0486900i	0.516314	+	0.856399i	$0.327304\pi$
$108$		0			0
$109$	−15.9511	−	1.57104i	−1.52783	−	0.150478i	−0.701096	−	0.713067i	$-0.747306\pi$
$109$	−15.9511	−	1.57104i	−1.52783	−	0.150478i	−0.826737	+	0.562588i	$0.809806\pi$
$110$		0			0
$111$	13.2193	+	5.47560i	1.25472	+	0.519721i
$112$		0			0
$113$	−5.12218	+	2.12168i	−0.481854	+	0.199591i	−0.610369	−	0.792117i	$-0.708979\pi$
$113$	−5.12218	+	2.12168i	−0.481854	+	0.199591i	0.128515	+	0.991708i	$0.458979\pi$
$114$		0			0
$115$	−2.47070	−	3.01055i	−0.230394	−	0.280735i
$116$		0			0
$117$	−1.88096	+	6.20069i	−0.173895	+	0.573254i
$118$		0			0
$119$	−0.684487	−	1.02441i	−0.0627468	−	0.0939073i
$120$		0			0
$121$	−9.10452	−	6.08344i	−0.827683	−	0.553040i
$122$		0			0
$123$	10.9408	+	8.97892i	0.986503	+	0.809602i
$124$		0			0
$125$	−5.00626	+	9.36605i	−0.447773	+	0.837725i
$126$		0			0
$127$	−0.563554			−0.0500074			−0.0250037	−	0.999687i	$-0.507960\pi$
$127$	−0.563554			−0.0500074			−0.0250037	+	0.999687i	$0.507960\pi$
$128$		0			0
$129$	−8.20826			−0.722697
$130$		0			0
$131$	2.77652	−	5.19451i	0.242586	−	0.453847i	−0.730934	−	0.682448i	$-0.760915\pi$
$131$	2.77652	−	5.19451i	0.242586	−	0.453847i	0.973520	+	0.228602i	$0.0734153\pi$
$132$		0			0
$133$	−0.750563	−	0.615971i	−0.0650821	−	0.0534115i
$134$		0			0
$135$	6.32326	+	4.22507i	0.544220	+	0.363636i
$136$		0			0
$137$	3.51003	+	5.25313i	0.299882	+	0.448805i	0.950557	−	0.310552i	$-0.100514\pi$
$137$	3.51003	+	5.25313i	0.299882	+	0.448805i	−0.650675	+	0.759357i	$0.725514\pi$
$138$		0			0
$139$	−3.44075	+	11.3426i	−0.291841	+	0.962070i	0.681328	+	0.731978i	$0.261403\pi$
$139$	−3.44075	+	11.3426i	−0.291841	+	0.962070i	−0.973169	+	0.230092i	$0.926097\pi$
$140$		0			0
$141$	9.87536	+	12.0332i	0.831656	+	1.01338i
$142$		0			0
$143$	−19.2470	+	7.97237i	−1.60952	+	0.666683i
$144$		0			0
$145$	−1.30719	−	0.541457i	−0.108557	−	0.0449656i
$146$		0			0
$147$	14.6344	+	1.44136i	1.20702	+	0.118882i
$148$		0			0
$149$	15.1211	−	8.08238i	1.23877	−	0.662134i	0.283810	−	0.958881i	$-0.408402\pi$
$149$	15.1211	−	8.08238i	1.23877	−	0.662134i	0.954956	+	0.296746i	$0.0959016\pi$
$150$		0			0
$151$	14.9898	+	2.98166i	1.21985	+	0.242644i	0.762705	−	0.646747i	$-0.223871\pi$
$151$	14.9898	+	2.98166i	1.21985	+	0.242644i	0.457148	+	0.889391i	$0.348871\pi$
$152$		0			0
$153$	−1.88006	−	9.45169i	−0.151994	−	0.764124i
$154$		0			0
$155$	3.38564	−	0.333456i	0.271941	−	0.0267838i
$156$		0			0
$157$	−2.10790	+	0.639424i	−0.168229	+	0.0510316i	−0.373275	−	0.927721i	$-0.621765\pi$
$157$	−2.10790	+	0.639424i	−0.168229	+	0.0510316i	0.205047	+	0.978752i	$0.434265\pi$
$158$		0			0
$159$	−15.0550	+	15.0550i	−1.19394	+	1.19394i
$160$		0			0
$161$	−0.219737	−	0.219737i	−0.0173177	−	0.0173177i
$162$		0			0
$163$	−1.86284	−	6.14095i	−0.145909	−	0.480997i	0.853272	−	0.521466i	$-0.174615\pi$
$163$	−1.86284	−	6.14095i	−0.145909	−	0.480997i	−0.999181	+	0.0404694i	$0.987115\pi$
$164$		0			0
$165$	−2.26364	−	22.9832i	−0.176224	−	1.78924i
$166$		0			0
$167$	7.09085	−	1.41046i	0.548706	−	0.109144i	0.0870509	−	0.996204i	$-0.472256\pi$
$167$	7.09085	−	1.41046i	0.548706	−	0.109144i	0.461655	+	0.887059i	$0.347256\pi$
$168$		0			0
$169$	−1.32126	+	6.64242i	−0.101635	+	0.510955i
$170$		0			0
$171$	−3.58012	−	6.69793i	−0.273778	−	0.512204i
$172$		0			0
$173$	−2.24018	+	22.7449i	−0.170318	+	1.72927i	0.407591	+	0.913164i	$0.366369\pi$
$173$	−2.24018	+	22.7449i	−0.170318	+	1.72927i	−0.577909	+	0.816101i	$0.696131\pi$
$174$		0			0
$175$	0.0321888	−	0.0777105i	0.00243324	−	0.00587436i
$176$		0			0
$177$	4.13054	+	9.97201i	0.310471	+	0.749542i
$178$		0			0
$179$	5.76523	−	4.73140i	0.430913	−	0.353641i	−0.393796	−	0.919198i	$-0.628839\pi$
$179$	5.76523	−	4.73140i	0.430913	−	0.353641i	0.824710	+	0.565556i	$0.191339\pi$
$180$		0			0
$181$	20.3751	+	6.18073i	1.51447	+	0.459410i	0.934720	−	0.355384i	$-0.115650\pi$
$181$	20.3751	+	6.18073i	1.51447	+	0.459410i	0.579751	+	0.814794i	$0.303150\pi$
$182$		0			0
$183$	−14.2994	+	9.55453i	−1.05704	+	0.706291i
$184$		0			0
$185$	−8.79138	+	13.1572i	−0.646355	+	0.967338i
$186$		0			0
$187$	19.6556	−	23.9504i	1.43736	−	1.75143i
$188$		0			0
$189$	0.535158	+	0.286048i	0.0389270	+	0.0208069i
$190$		0			0
$191$			14.6009i			1.05648i	0.849094	+	0.528242i	$0.177149\pi$
$191$			14.6009i			1.05648i	−0.849094	+	0.528242i	$0.822851\pi$
$192$		0			0
$193$		−	3.18826i		−	0.229496i	−0.993395	−	0.114748i	$-0.963394\pi$
$193$		−	3.18826i		−	0.229496i	0.993395	−	0.114748i	$-0.0366061\pi$
$194$		0			0
$195$	−19.3308	−	10.3325i	−1.38431	−	0.739929i
$196$		0			0
$197$	−2.78078	+	3.38840i	−0.198123	+	0.241413i	−0.862589	−	0.505905i	$-0.831159\pi$
$197$	−2.78078	+	3.38840i	−0.198123	+	0.241413i	0.664467	+	0.747318i	$0.268659\pi$
$198$		0			0
$199$	−8.01656	+	11.9976i	−0.568279	+	0.850489i	−0.998638	−	0.0521684i	$-0.983387\pi$
$199$	−8.01656	+	11.9976i	−0.568279	+	0.850489i	0.430360	+	0.902657i	$0.358387\pi$
$200$		0			0
$201$	23.9391	−	15.9956i	1.68853	−	1.12824i
$202$		0			0
$203$	−0.108036	−	0.0327722i	−0.00758261	−	0.00230016i
$204$		0			0
$205$	−12.0998	+	9.93001i	−0.845084	+	0.693542i
$206$		0			0
$207$	−0.930180	−	2.24565i	−0.0646519	−	0.156084i
$208$		0			0
$209$	9.34422	−	22.5589i	0.646353	−	1.56043i
$210$		0			0
$211$	1.30891	−	13.2895i	0.0901088	−	0.914890i	−0.838765	−	0.544493i	$-0.816722\pi$
$211$	1.30891	−	13.2895i	0.0901088	−	0.914890i	0.928874	−	0.370396i	$-0.120778\pi$
$212$		0			0
$213$	3.33071	+	6.23133i	0.228217	+	0.426963i
$214$		0			0
$215$	1.77098	−	8.90329i	0.120780	−	0.607200i
$216$		0			0
$217$	0.266237	−	0.0529578i	0.0180733	−	0.00359501i
$218$		0			0
$219$	−1.70814	−	17.3430i	−0.115425	−	1.17193i
$220$		0			0
$221$	−8.53625	−	28.1402i	−0.574210	−	1.89292i
$222$		0			0
$223$	−0.847730	−	0.847730i	−0.0567682	−	0.0567682i	0.678153	−	0.734921i	$-0.262781\pi$
$223$	−0.847730	−	0.847730i	−0.0567682	−	0.0567682i	−0.734921	+	0.678153i	$0.762781\pi$
$224$		0			0
$225$	0.465220	−	0.465220i	0.0310147	−	0.0310147i
$226$		0			0
$227$	26.5262	−	8.04665i	1.76061	−	0.534075i	0.766479	−	0.642270i	$-0.222007\pi$
$227$	26.5262	−	8.04665i	1.76061	−	0.534075i	0.994130	+	0.108195i	$0.0345071\pi$
$228$		0			0
$229$	18.0313	−	1.77593i	1.19154	−	0.117357i	0.517259	−	0.855829i	$-0.326953\pi$
$229$	18.0313	−	1.77593i	1.19154	−	0.117357i	0.674284	+	0.738472i	$0.264453\pi$
$230$		0			0
$231$	−0.359500	−	1.80733i	−0.0236534	−	0.118913i
$232$		0			0
$233$	20.1081	+	3.99975i	1.31732	+	0.262032i	0.803213	−	0.595691i	$-0.203122\pi$
$233$	20.1081	+	3.99975i	1.31732	+	0.262032i	0.514111	+	0.857724i	$0.328122\pi$
$234$		0			0
$235$	−15.1827	+	8.11534i	−0.990413	+	0.529387i
$236$		0			0
$237$	32.8979	+	3.24016i	2.13695	+	0.210471i
$238$		0			0
$239$	−18.0518	−	7.47728i	−1.16767	−	0.483665i	−0.287249	−	0.957856i	$-0.592741\pi$
$239$	−18.0518	−	7.47728i	−1.16767	−	0.483665i	−0.880422	+	0.474191i	$0.842741\pi$
$240$		0			0
$241$	−7.63834	+	3.16390i	−0.492029	+	0.203805i	−0.614881	−	0.788620i	$-0.710796\pi$
$241$	−7.63834	+	3.16390i	−0.492029	+	0.203805i	0.122852	+	0.992425i	$0.460796\pi$
$242$		0			0
$243$	8.86618	+	10.8035i	0.568766	+	0.693043i
$244$		0			0
$245$	−4.72086	+	15.5626i	−0.301605	+	0.994257i
$246$		0			0
$247$	−12.8753	−	19.2692i	−0.819235	−	1.22607i
$248$		0			0
$249$	−22.1126	−	14.7752i	−1.40133	−	0.936340i
$250$		0			0
$251$	10.3147	+	8.46509i	0.651061	+	0.534312i	0.900928	−	0.433968i	$-0.142887\pi$
$251$	10.3147	+	8.46509i	0.651061	+	0.534312i	−0.249867	+	0.968280i	$0.580387\pi$
$252$		0			0
$253$	3.68389	−	6.89206i	0.231604	−	0.433300i
$254$		0			0
$255$	32.5987			2.04141
$256$		0			0
$257$	−14.0628			−0.877211			−0.438606	−	0.898680i	$-0.644527\pi$
$257$	−14.0628			−0.877211			−0.438606	+	0.898680i	$0.644527\pi$
$258$		0			0
$259$	−0.595198	+	1.11354i	−0.0369838	+	0.0691919i
$260$		0			0
$261$	−0.682615	−	0.560208i	−0.0422528	−	0.0346760i
$262$		0			0
$263$	−6.06785	−	4.05441i	−0.374160	−	0.250006i	0.354245	−	0.935153i	$-0.384738\pi$
$263$	−6.06785	−	4.05441i	−0.374160	−	0.250006i	−0.728405	+	0.685147i	$0.759738\pi$
$264$		0			0
$265$	−13.0816	−	19.5779i	−0.803594	−	1.20266i
$266$		0			0
$267$	−2.27608	+	7.50323i	−0.139294	+	0.459190i
$268$		0			0
$269$	−9.65655	−	11.7665i	−0.588770	−	0.717418i	0.390358	−	0.920663i	$-0.372351\pi$
$269$	−9.65655	−	11.7665i	−0.588770	−	0.717418i	−0.979128	+	0.203245i	$0.934851\pi$
$270$		0			0
$271$	5.31415	−	2.20119i	0.322812	−	0.133713i	−0.215392	−	0.976528i	$-0.569103\pi$
$271$	5.31415	−	2.20119i	0.322812	−	0.133713i	0.538204	+	0.842815i	$0.319103\pi$
$272$		0			0
$273$	−1.61582	−	0.669295i	−0.0977940	−	0.0405076i
$274$		0			0
$275$	2.10509	+	0.207333i	0.126941	+	0.0125026i
$276$		0			0
$277$	−10.7096	+	5.72441i	−0.643478	+	0.343946i	−0.760647	−	0.649166i	$-0.775118\pi$
$277$	−10.7096	+	5.72441i	−0.643478	+	0.343946i	0.117169	+	0.993112i	$0.462618\pi$
$278$		0			0
$279$	2.08246	+	0.414227i	0.124674	+	0.0247991i
$280$		0			0
$281$	−1.70438	−	8.56849i	−0.101675	−	0.511153i	−0.997738	−	0.0672264i	$-0.978585\pi$
$281$	−1.70438	−	8.56849i	−0.101675	−	0.511153i	0.896063	−	0.443927i	$-0.146415\pi$
$282$		0			0
$283$	−7.85803	+	0.773949i	−0.467112	+	0.0460065i	−0.328835	−	0.944387i	$-0.606656\pi$
$283$	−7.85803	+	0.773949i	−0.467112	+	0.0460065i	−0.138276	+	0.990394i	$0.544156\pi$
$284$		0			0
$285$	24.5845	−	7.45762i	1.45626	−	0.441752i
$286$		0			0
$287$	−0.883148	+	0.883148i	−0.0521306	+	0.0521306i
$288$		0			0
$289$	18.9041	+	18.9041i	1.11200	+	1.11200i
$290$		0			0
$291$	1.59371	+	5.25375i	0.0934249	+	0.307980i
$292$		0			0
$293$	2.67911	+	27.2014i	0.156515	+	1.58912i	0.677477	+	0.735544i	$0.263074\pi$
$293$	2.67911	+	27.2014i	0.156515	+	1.58912i	−0.520961	+	0.853580i	$0.674426\pi$
$294$		0			0
$295$	−11.7076	+	2.32878i	−0.681642	+	0.135587i
$296$		0			0
$297$	−2.97707	+	14.9667i	−0.172747	+	0.868458i
$298$		0			0
$299$	−3.49640	−	6.54130i	−0.202202	−	0.378293i
$300$		0			0
$301$	0.0709964	−	0.720838i	0.00409216	−	0.0415484i
$302$		0			0
$303$	9.55500	−	23.0678i	0.548920	−	1.32521i
$304$		0			0
$305$	−7.27840	−	17.5716i	−0.416760	−	1.00615i
$306$		0			0
$307$	−16.5272	+	13.5635i	−0.943257	+	0.774111i	−0.974264	−	0.225408i	$-0.927628\pi$
$307$	−16.5272	+	13.5635i	−0.943257	+	0.774111i	0.0310073	+	0.999519i	$0.490128\pi$
$308$		0			0
$309$	−16.0348	−	4.86411i	−0.912190	−	0.276710i
$310$		0			0
$311$	−1.40726	+	0.940302i	−0.0797985	+	0.0533196i	−0.594829	−	0.803852i	$-0.702780\pi$
$311$	−1.40726	+	0.940302i	−0.0797985	+	0.0533196i	0.515031	+	0.857172i	$0.327780\pi$
$312$		0			0
$313$	0.509816	−	0.762993i	0.0288165	−	0.0431269i	−0.816782	−	0.576947i	$-0.804244\pi$
$313$	0.509816	−	0.762993i	0.0288165	−	0.0431269i	0.845598	+	0.533820i	$0.179244\pi$
$314$		0			0
$315$	0.402120	−	0.489984i	0.0226569	−	0.0276075i
$316$		0			0
$317$	16.5566	+	8.84968i	0.929911	+	0.497048i	0.865519	−	0.500877i	$-0.166989\pi$
$317$	16.5566	+	8.84968i	0.929911	+	0.497048i	0.0643925	+	0.997925i	$0.479489\pi$
$318$		0			0
$319$		−	2.83912i		−	0.158960i
$320$		0			0
$321$			2.25568i			0.125900i
$322$		0			0
$323$	30.3968	+	16.2474i	1.69132	+	0.904032i
$324$		0			0
$325$	1.27362	−	1.55191i	0.0706477	−	0.0860844i
$326$		0			0
$327$	18.7999	−	28.1361i	1.03964	−	1.55593i
$328$		0			0
$329$	−1.14215	+	0.763162i	−0.0629689	+	0.0420745i
$330$		0			0
$331$	−10.7266	−	3.25387i	−0.589585	−	0.178849i	−0.0186251	−	0.999827i	$-0.505929\pi$
$331$	−10.7266	−	3.25387i	−0.589585	−	0.178849i	−0.570960	+	0.820978i	$0.693429\pi$
$332$		0			0
$333$	−7.63431	+	6.26531i	−0.418357	+	0.343337i
$334$		0			0
$335$	12.1850	+	29.4173i	0.665739	+	1.60724i
$336$		0			0
$337$	−7.10862	+	17.1617i	−0.387231	+	0.934859i	0.603293	+	0.797520i	$0.293855\pi$
$337$	−7.10862	+	17.1617i	−0.387231	+	0.934859i	−0.990524	+	0.137339i	$0.956145\pi$
$338$		0			0
$339$	1.14729	−	11.6486i	0.0623123	−	0.632667i
$340$		0			0
$341$	3.21797	+	6.02040i	0.174263	+	0.326023i
$342$		0			0
$343$	−0.507576	+	2.55175i	−0.0274065	+	0.137782i
$344$		0			0
$345$	8.06430	−	1.60409i	0.434167	−	0.0863612i
$346$		0			0
$347$	−0.513362	−	5.21225i	−0.0275587	−	0.279808i	−0.999081	−	0.0428603i	$-0.986353\pi$
$347$	−0.513362	−	5.21225i	−0.0275587	−	0.279808i	0.971522	−	0.236948i	$-0.0761471\pi$
$348$		0			0
$349$	−4.25903	−	14.0401i	−0.227981	−	0.751552i	−0.994063	−	0.108809i	$-0.965296\pi$
$349$	−4.25903	−	14.0401i	−0.227981	−	0.751552i	0.766082	−	0.642743i	$-0.222204\pi$
$350$		0			0
$351$	10.2413	+	10.2413i	0.546638	+	0.546638i
$352$		0			0
$353$	21.1183	−	21.1183i	1.12402	−	1.12402i	0.132884	−	0.991132i	$-0.457576\pi$
$353$	21.1183	−	21.1183i	1.12402	−	1.12402i	0.991132	−	0.132884i	$-0.0424239\pi$
$354$		0			0
$355$	−7.47759	+	2.26830i	−0.396869	+	0.120389i
$356$		0			0
$357$	2.58858	−	0.254953i	0.137002	−	0.0134935i
$358$		0			0
$359$	6.47561	+	32.5551i	0.341770	+	1.71819i	0.644060	+	0.764975i	$0.277249\pi$
$359$	6.47561	+	32.5551i	0.341770	+	1.71819i	−0.302290	+	0.953216i	$0.597751\pi$
$360$		0			0
$361$	8.00590	+	1.59247i	0.421363	+	0.0838144i
$362$		0			0
$363$	20.3879	−	10.8976i	1.07009	−	0.571973i
$364$		0			0
$365$	19.1801	+	1.88908i	1.00393	+	0.0988787i
$366$		0			0
$367$	−7.75304	−	3.21142i	−0.404706	−	0.167635i	0.171039	−	0.985264i	$-0.445288\pi$
$367$	−7.75304	−	3.21142i	−0.404706	−	0.167635i	−0.575744	+	0.817630i	$0.695288\pi$
$368$		0			0
$369$	−9.02553	+	3.73850i	−0.469850	+	0.194618i
$370$		0			0
$371$	−1.19189	−	1.45232i	−0.0618799	−	0.0754008i
$372$		0			0
$373$	0.613400	−	2.02211i	0.0317607	−	0.104701i	−0.939627	−	0.342200i	$-0.888828\pi$
$373$	0.613400	−	2.02211i	0.0317607	−	0.104701i	0.971388	+	0.237500i	$0.0763278\pi$
$374$		0			0
$375$	−12.4565	−	18.6425i	−0.643253	−	0.962696i
$376$		0			0
$377$	−2.24050	−	1.49705i	−0.115392	−	0.0771021i
$378$		0			0
$379$	6.69609	+	5.49534i	0.343955	+	0.282276i	0.790471	−	0.612499i	$-0.209836\pi$
$379$	6.69609	+	5.49534i	0.343955	+	0.282276i	−0.446517	+	0.894775i	$0.647336\pi$
$380$		0			0
$381$	0.560860	−	1.04929i	0.0287337	−	0.0537570i
$382$		0			0
$383$	0.146828			0.00750254			0.00375127	−	0.999993i	$-0.498806\pi$
$383$	0.146828			0.00750254			0.00375127	+	0.999993i	$0.498806\pi$
$384$		0			0
$385$	2.03793			0.103862
$386$		0			0
$387$	2.67073	−	4.99658i	0.135761	−	0.253990i
$388$		0			0
$389$	3.65612	+	3.00050i	0.185372	+	0.152131i	0.722503	−	0.691368i	$-0.242992\pi$
$389$	3.65612	+	3.00050i	0.185372	+	0.152131i	−0.537130	+	0.843499i	$0.680492\pi$
$390$		0			0
$391$	9.17194	+	6.12849i	0.463845	+	0.309931i
$392$		0			0
$393$	6.90853	+	10.3393i	0.348489	+	0.521551i
$394$		0			0
$395$	−10.6124	+	34.9844i	−0.533968	+	1.76026i
$396$		0			0
$397$	−15.7867	−	19.2361i	−0.792310	−	0.965433i	0.207608	−	0.978212i	$-0.433432\pi$
$397$	−15.7867	−	19.2361i	−0.792310	−	0.965433i	−0.999918	+	0.0127792i	$0.995932\pi$
$398$		0			0
$399$	1.89386	−	0.784465i	0.0948118	−	0.0392723i
$400$		0			0
$401$	−22.7524	−	9.42434i	−1.13620	−	0.470629i	−0.266316	−	0.963886i	$-0.585806\pi$
$401$	−22.7524	−	9.42434i	−1.13620	−	0.470629i	−0.869884	+	0.493257i	$0.835806\pi$
$402$		0			0
$403$	6.44784	+	0.635056i	0.321190	+	0.0316344i
$404$		0			0
$405$	−23.1616	+	12.3802i	−1.15091	+	0.615175i
$406$		0			0
$407$	−31.1423	−	6.19459i	−1.54367	−	0.307054i
$408$		0			0
$409$	4.50171	+	22.6316i	0.222595	+	1.11906i	0.916819	+	0.399302i	$0.130748\pi$
$409$	4.50171	+	22.6316i	0.222595	+	1.11906i	−0.694224	+	0.719759i	$0.744252\pi$
$410$		0			0
$411$	−13.2742	+	1.30739i	−0.654766	+	0.0644888i
$412$		0			0
$413$	−0.911455	+	0.276487i	−0.0448498	+	0.0136050i
$414$		0			0
$415$	20.7972	−	20.7972i	1.02089	−	1.02089i
$416$		0			0
$417$	−17.6948	−	17.6948i	−0.866519	−	0.866519i
$418$		0			0
$419$	7.67078	+	25.2872i	0.374742	+	1.23536i	0.918266	+	0.395965i	$0.129590\pi$
$419$	7.67078	+	25.2872i	0.374742	+	1.23536i	−0.543524	+	0.839394i	$0.682910\pi$
$420$		0			0
$421$	−0.958023	−	9.72697i	−0.0466912	−	0.474063i	−0.989890	−	0.141835i	$-0.954700\pi$
$421$	−0.958023	−	9.72697i	−0.0466912	−	0.474063i	0.943199	−	0.332228i	$-0.107800\pi$
$422$		0			0
$423$	−10.5381	+	2.09615i	−0.512378	+	0.101918i
$424$		0			0
$425$	−0.582501	+	2.92843i	−0.0282555	+	0.142050i
$426$		0			0
$427$	−0.715385	−	1.33839i	−0.0346199	−	0.0647693i
$428$		0			0
$429$	4.31104	−	43.7707i	0.208139	−	2.11327i
$430$		0			0
$431$	5.77223	−	13.9354i	0.278039	−	0.671245i	−0.721743	−	0.692162i	$-0.756659\pi$
$431$	5.77223	−	13.9354i	0.278039	−	0.671245i	0.999781	+	0.0209170i	$0.00665858\pi$
$432$		0			0
$433$	7.41556	+	17.9028i	0.356369	+	0.860352i	0.995804	+	0.0915066i	$0.0291682\pi$
$433$	7.41556	+	17.9028i	0.356369	+	0.860352i	−0.639435	+	0.768845i	$0.720832\pi$
$434$		0			0
$435$	2.30909	−	1.89502i	0.110713	−	0.0908595i
$436$		0			0
$437$	8.31907	+	2.52356i	0.397955	+	0.120718i
$438$		0			0
$439$	6.67049	−	4.45708i	0.318365	−	0.212725i	−0.386111	−	0.922452i	$-0.626182\pi$
$439$	6.67049	−	4.45708i	0.318365	−	0.212725i	0.704476	+	0.709728i	$0.251182\pi$
$440$		0			0
$441$	−5.63900	+	8.43936i	−0.268524	+	0.401874i
$442$		0			0
$443$	−13.7641	+	16.7716i	−0.653953	+	0.796844i	−0.989400	−	0.145215i	$-0.953612\pi$
$443$	−13.7641	+	16.7716i	−0.653953	+	0.796844i	0.335447	+	0.942059i	$0.391112\pi$
$444$		0			0
$445$	−7.64749	−	4.08767i	−0.362526	−	0.193774i
$446$		0			0
$447$			36.1980i			1.71211i
$448$		0			0
$449$		−	17.5545i		−	0.828450i	−0.910174	−	0.414225i	$-0.864053\pi$
$449$		−	17.5545i		−	0.828450i	0.910174	−	0.414225i	$-0.135947\pi$
$450$		0			0
$451$	−27.7000	−	14.8060i	−1.30434	−	0.697185i
$452$		0			0
$453$	−20.4697	+	24.9424i	−0.961752	+	1.17190i
$454$		0			0
$455$	1.07459	−	1.60824i	0.0503776	−	0.0753954i
$456$		0			0
$457$	−1.50164	+	1.00337i	−0.0702439	+	0.0469354i	−0.590196	−	0.807260i	$-0.700950\pi$
$457$	−1.50164	+	1.00337i	−0.0702439	+	0.0469354i	0.519952	+	0.854195i	$0.325950\pi$
$458$		0			0
$459$	−20.6126	−	6.25277i	−0.962115	−	0.291854i
$460$		0			0
$461$	−18.9347	+	15.5393i	−0.881879	+	0.723739i	−0.962001	−	0.273046i	$-0.911969\pi$
$461$	−18.9347	+	15.5393i	−0.881879	+	0.723739i	0.0801223	+	0.996785i	$0.474469\pi$
$462$		0			0
$463$	8.99668	+	21.7199i	0.418111	+	1.00941i	0.982894	+	0.184170i	$0.0589597\pi$
$463$	8.99668	+	21.7199i	0.418111	+	1.00941i	−0.564783	+	0.825239i	$0.691040\pi$
$464$		0			0
$465$	−2.74858	+	6.63565i	−0.127462	+	0.307721i
$466$		0			0
$467$	1.03187	−	10.4768i	0.0477494	−	0.484808i	−0.941337	−	0.337469i	$-0.890429\pi$
$467$	1.03187	−	10.4768i	0.0477494	−	0.484808i	0.989086	−	0.147339i	$-0.0470708\pi$
$468$		0			0
$469$	1.19765	+	2.24065i	0.0553025	+	0.103464i
$470$		0			0
$471$	0.907261	−	4.56111i	0.0418044	−	0.210165i
$472$		0			0
$473$	17.8653	−	3.55362i	0.821446	−	0.163396i
$474$		0			0
$475$	0.230642	+	2.34175i	0.0105826	+	0.107447i
$476$		0			0
$477$	−4.26590	−	14.0628i	−0.195322	−	0.643891i
$478$		0			0
$479$	−17.3081	−	17.3081i	−0.790828	−	0.790828i	0.190801	−	0.981629i	$-0.438892\pi$
$479$	−17.3081	−	17.3081i	−0.790828	−	0.790828i	−0.981629	+	0.190801i	$0.938892\pi$
$480$		0			0
$481$	−21.3097	+	21.3097i	−0.971637	+	0.971637i
$482$		0			0
$483$	0.627820	−	0.190447i	0.0285668	−	0.00866564i
$484$		0			0
$485$	−6.04247	+	0.595131i	−0.274374	+	0.0270235i
$486$		0			0
$487$	3.41086	+	17.1475i	0.154561	+	0.777029i	0.977834	+	0.209383i	$0.0671456\pi$
$487$	3.41086	+	17.1475i	0.154561	+	0.777029i	−0.823273	+	0.567646i	$0.807854\pi$
$488$		0			0
$489$	13.2879	+	2.64313i	0.600900	+	0.119526i
$490$		0			0
$491$	13.3084	−	7.11346i	0.600598	−	0.321026i	−0.142928	−	0.989733i	$-0.545652\pi$
$491$	13.3084	−	7.11346i	0.600598	−	0.321026i	0.743526	+	0.668707i	$0.233152\pi$
$492$		0			0
$493$	3.98825	+	0.392808i	0.179622	+	0.0176912i
$494$		0			0
$495$	14.7270	+	6.10011i	0.661928	+	0.274180i
$496$		0			0
$497$	−0.576035	+	0.238602i	−0.0258387	+	0.0107027i
$498$		0			0
$499$	−13.7049	−	16.6995i	−0.613517	−	0.747573i	0.369872	−	0.929083i	$-0.379401\pi$
$499$	−13.7049	−	16.6995i	−0.613517	−	0.747573i	−0.983389	+	0.181510i	$0.941901\pi$
$500$		0			0
$501$	−4.43078	+	14.6063i	−0.197953	+	0.652562i
$502$		0			0
$503$	8.02145	+	12.0049i	0.357659	+	0.535274i	0.966047	−	0.258365i	$-0.0831838\pi$
$503$	8.02145	+	12.0049i	0.357659	+	0.535274i	−0.608389	+	0.793639i	$0.708184\pi$
$504$		0			0
$505$	22.9595	+	15.3411i	1.02169	+	0.682669i
$506$		0			0
$507$	−11.0527	−	9.07074i	−0.490869	−	0.402846i
$508$		0			0
$509$	−0.684010	+	1.27969i	−0.0303182	+	0.0567214i	−0.896624	−	0.442792i	$-0.853988\pi$
$509$	−0.684010	+	1.27969i	−0.0303182	+	0.0567214i	0.866306	+	0.499514i	$0.166488\pi$
$510$		0			0
$511$	1.53782			0.0680290
$512$		0			0
$513$	−16.9755			−0.749489
$514$		0			0
$515$	8.73559	−	16.3431i	0.384936	−	0.720164i
$516$		0			0
$517$	−26.7033	−	21.9148i	−1.17441	−	0.963812i
$518$		0			0
$519$	−40.1198	−	26.8072i	−1.76107	−	1.17671i
$520$		0			0
$521$	−10.4516	−	15.6419i	−0.457894	−	0.685286i	0.528640	−	0.848846i	$-0.322702\pi$
$521$	−10.4516	−	15.6419i	−0.457894	−	0.685286i	−0.986533	+	0.163560i	$0.947702\pi$
$522$		0			0
$523$	−6.99755	+	23.0678i	−0.305982	+	1.00869i	0.660258	+	0.751039i	$0.270447\pi$
$523$	−6.99755	+	23.0678i	−0.305982	+	1.00869i	−0.966239	+	0.257647i	$0.917053\pi$
$524$		0			0
$525$	0.112656	+	0.137272i	0.00491672	+	0.00599104i
$526$		0			0
$527$	−8.90237	+	3.68748i	−0.387793	+	0.160629i
$528$		0			0
$529$	−18.6787	−	7.73697i	−0.812118	−	0.336390i
$530$		0			0
$531$	−7.41418	−	0.730233i	−0.321748	−	0.0316894i
$532$		0			0
$533$	−26.2902	+	14.0524i	−1.13876	+	0.608678i
$534$		0			0
$535$	−2.44668	−	0.486675i	−0.105779	−	0.0210408i
$536$		0			0
$537$	3.07184	+	15.4432i	0.132560	+	0.666422i
$538$		0			0
$539$	−32.4758	+	3.19858i	−1.39883	+	0.137773i
$540$		0			0
$541$	−10.7168	+	3.25091i	−0.460752	+	0.139767i	−0.512123	−	0.858912i	$-0.671141\pi$
$541$	−10.7168	+	3.25091i	−0.460752	+	0.139767i	0.0513713	+	0.998680i	$0.483641\pi$
$542$		0			0
$543$	−31.7857	+	31.7857i	−1.36406	+	1.36406i
$544$		0			0
$545$	26.4623	+	26.4623i	1.13352	+	1.13352i
$546$		0			0
$547$	1.63758	+	5.39837i	0.0700178	+	0.230818i	0.984964	−	0.172757i	$-0.0552675\pi$
$547$	1.63758	+	5.39837i	0.0700178	+	0.230818i	−0.914947	+	0.403575i	$0.867768\pi$
$548$		0			0
$549$	−1.16349	−	11.8132i	−0.0496567	−	0.504173i
$550$		0			0
$551$	3.09762	−	0.616154i	0.131963	−	0.0262491i
$552$		0			0
$553$	−0.569092	+	2.86102i	−0.0242003	+	0.121663i
$554$		0			0
$555$	−15.7484	−	29.4632i	−0.668482	−	1.25064i
$556$		0			0
$557$	1.03043	−	10.4622i	0.0436608	−	0.443296i	−0.948358	−	0.317203i	$-0.897256\pi$
$557$	1.03043	−	10.4622i	0.0436608	−	0.443296i	0.992018	−	0.126093i	$-0.0402437\pi$
$558$		0			0
$559$	6.61592	−	15.9722i	0.279824	−	0.675554i
$560$		0			0
$561$	25.0322	+	60.4331i	1.05686	+	2.55149i
$562$		0			0
$563$	10.1395	−	8.32127i	0.427329	−	0.350700i	−0.396014	−	0.918245i	$-0.629607\pi$
$563$	10.1395	−	8.32127i	0.427329	−	0.350700i	0.823342	+	0.567545i	$0.192107\pi$
$564$		0			0
$565$	12.3875	+	3.75770i	0.521144	+	0.158087i
$566$		0			0
$567$	−1.74238	+	1.16422i	−0.0731731	+	0.0488927i
$568$		0			0
$569$	4.34586	−	6.50405i	0.182188	−	0.272664i	−0.729123	−	0.684383i	$-0.760072\pi$
$569$	4.34586	−	6.50405i	0.182188	−	0.272664i	0.911311	+	0.411719i	$0.135072\pi$
$570$		0			0
$571$	−11.1096	+	13.5370i	−0.464921	+	0.566508i	−0.951705	−	0.307015i	$-0.900670\pi$
$571$	−11.1096	+	13.5370i	−0.464921	+	0.566508i	0.486784	+	0.873522i	$0.338170\pi$
$572$		0			0
$573$	−27.1857	−	14.5311i	−1.13570	−	0.607045i
$574$		0			0
$575$			0.753100i			0.0314064i
$576$		0			0
$577$			11.4472i			0.476552i	0.971198	+	0.238276i	$0.0765822\pi$
$577$			11.4472i			0.476552i	−0.971198	+	0.238276i	$0.923418\pi$
$578$		0			0
$579$	5.93629	+	3.17301i	0.246704	+	0.131866i
$580$		0			0
$581$	1.48880	−	1.81411i	0.0617658	−	0.0752618i
$582$		0			0
$583$	26.2493	−	39.2849i	1.08714	−	1.62701i
$584$		0			0
$585$	12.5794	−	8.40527i	0.520093	−	0.347515i
$586$		0			0
$587$	24.5270	+	7.44018i	1.01234	+	0.307089i	0.752520	−	0.658569i	$-0.228838\pi$
$587$	24.5270	+	7.44018i	1.01234	+	0.307089i	0.259816	+	0.965658i	$0.416338\pi$
$588$		0			0
$589$	−5.87018	+	4.81753i	−0.241876	+	0.198503i
$590$		0			0
$591$	−3.54144	−	8.54980i	−0.145676	−	0.351692i
$592$		0			0
$593$	14.3732	−	34.7001i	0.590238	−	1.42496i	−0.293034	−	0.956102i	$-0.594665\pi$
$593$	14.3732	−	34.7001i	0.590238	−	1.42496i	0.883273	−	0.468859i	$-0.155335\pi$
$594$		0			0
$595$	−0.281959	+	2.86278i	−0.0115592	+	0.117362i
$596$		0			0
$597$	−14.3604	−	26.8665i	−0.587733	−	1.09957i
$598$		0			0
$599$	5.45301	−	27.4141i	0.222804	−	1.12011i	−0.693755	−	0.720211i	$-0.744045\pi$
$599$	5.45301	−	27.4141i	0.222804	−	1.12011i	0.916559	−	0.399900i	$-0.130955\pi$
$600$		0			0
$601$	4.95314	−	0.985240i	0.202043	−	0.0401888i	−0.0930314	−	0.995663i	$-0.529656\pi$
$601$	4.95314	−	0.985240i	0.202043	−	0.0401888i	0.295074	+	0.955474i	$0.404656\pi$
$602$		0			0
$603$	1.94785	+	19.7768i	0.0793225	+	0.805375i
$604$		0			0
$605$	7.42151	+	24.4654i	0.301727	+	0.994662i
$606$		0			0
$607$	5.84253	+	5.84253i	0.237141	+	0.237141i	0.815665	−	0.578524i	$-0.196371\pi$
$607$	5.84253	+	5.84253i	0.237141	+	0.237141i	−0.578524	+	0.815665i	$0.696371\pi$
$608$		0			0
$609$	0.168538	−	0.168538i	0.00682952	−	0.00682952i
$610$		0			0
$611$	−31.3746	+	9.51740i	−1.26928	+	0.385033i
$612$		0			0
$613$	38.5449	−	3.79634i	1.55681	−	0.153333i	0.717336	−	0.696727i	$-0.245361\pi$
$613$	38.5449	−	3.79634i	1.55681	−	0.153333i	0.839478	+	0.543394i	$0.182861\pi$
$614$		0			0
$615$	−6.44702	−	32.4113i	−0.259969	−	1.30695i
$616$		0			0
$617$	7.84954	+	1.56137i	0.316011	+	0.0628584i	0.350547	−	0.936545i	$-0.385996\pi$
$617$	7.84954	+	1.56137i	0.316011	+	0.0628584i	−0.0345368	+	0.999403i	$0.510996\pi$
$618$		0			0
$619$	−9.50677	+	5.08148i	−0.382109	+	0.204242i	−0.651257	−	0.758857i	$-0.725758\pi$
$619$	−9.50677	+	5.08148i	−0.382109	+	0.204242i	0.269148	+	0.963099i	$0.413258\pi$
$620$		0			0
$621$	−5.40684	−	0.532528i	−0.216969	−	0.0213696i
$622$		0			0
$623$	−0.639237	−	0.264780i	−0.0256105	−	0.0106082i
$624$		0			0
$625$	24.9943	−	10.3530i	0.999771	−	0.414119i
$626$		0			0
$627$	32.7035	+	39.8493i	1.30605	+	1.59143i
$628$		0			0
$629$	13.0106	−	42.8900i	0.518765	−	1.71014i
$630$		0			0
$631$	22.3341	+	33.4253i	0.889105	+	1.33064i	0.943242	+	0.332107i	$0.107759\pi$
$631$	22.3341	+	33.4253i	0.889105	+	1.33064i	−0.0541365	+	0.998534i	$0.517241\pi$
$632$		0			0
$633$	23.4415	+	15.6631i	0.931714	+	0.622551i
$634$		0			0
$635$	1.01714	+	0.834742i	0.0403638	+	0.0331257i
$636$		0			0
$637$	−14.6001	+	27.3150i	−0.578479	+	1.08226i
$638$		0			0
$639$	−4.87689			−0.192927
$640$		0			0
$641$	11.3614			0.448748			0.224374	−	0.974503i	$-0.427966\pi$
$641$	11.3614			0.448748			0.224374	+	0.974503i	$0.427966\pi$
$642$		0			0
$643$	3.96444	−	7.41694i	0.156342	−	0.292495i	−0.791540	−	0.611118i	$-0.790720\pi$
$643$	3.96444	−	7.41694i	0.156342	−	0.292495i	0.947882	+	0.318622i	$0.103220\pi$
$644$		0			0
$645$	14.8147	+	12.1581i	0.583330	+	0.478726i
$646$		0			0
$647$	−10.1354	−	6.77226i	−0.398464	−	0.266245i	0.340154	−	0.940370i	$-0.389521\pi$
$647$	−10.1354	−	6.77226i	−0.398464	−	0.266245i	−0.738617	+	0.674125i	$0.764521\pi$
$648$		0			0
$649$	−13.3073	−	19.9158i	−0.522358	−	0.781764i
$650$		0			0
$651$	−0.166360	+	0.548417i	−0.00652018	+	0.0214941i
$652$		0			0
$653$	−0.473095	−	0.576467i	−0.0185136	−	0.0225589i	0.763671	−	0.645605i	$-0.223395\pi$
$653$	−0.473095	−	0.576467i	−0.0185136	−	0.0225589i	−0.782185	+	0.623046i	$0.785895\pi$
$654$		0			0
$655$	−12.7054	+	5.26274i	−0.496441	+	0.205632i
$656$		0			0
$657$	11.1129	+	4.60313i	0.433557	+	0.179585i
$658$		0			0
$659$	−1.87363	−	0.184536i	−0.0729863	−	0.00718852i	0.0614581	−	0.998110i	$-0.480425\pi$
$659$	−1.87363	−	0.184536i	−0.0729863	−	0.00718852i	−0.134444	+	0.990921i	$0.542925\pi$
$660$		0			0
$661$	39.5857	−	21.1590i	1.53970	−	0.822989i	0.539880	−	0.841742i	$-0.318470\pi$
$661$	39.5857	−	21.1590i	1.53970	−	0.822989i	0.999824	+	0.0187535i	$0.00596978\pi$
$662$		0			0
$663$	60.8904	+	12.1118i	2.36479	+	0.470385i
$664$		0			0
$665$	0.442278	+	2.22348i	0.0171508	+	0.0862229i
$666$		0			0
$667$	1.00594	−	0.0990768i	0.0389503	−	0.00383627i
$668$		0			0
$669$	2.42208	−	0.734731i	0.0936432	−	0.0284064i
$670$		0			0
$671$	26.9861	−	26.9861i	1.04179	−	1.04179i
$672$		0			0
$673$	−19.4363	−	19.4363i	−0.749216	−	0.749216i	0.225116	−	0.974332i	$-0.427724\pi$
$673$	−19.4363	−	19.4363i	−0.749216	−	0.749216i	−0.974332	+	0.225116i	$0.927724\pi$
$674$		0			0
$675$	−0.426885	−	1.40725i	−0.0164308	−	0.0541651i
$676$		0			0
$677$	0.876869	+	8.90300i	0.0337008	+	0.342170i	0.997219	+	0.0745271i	$0.0237447\pi$
$677$	0.876869	+	8.90300i	0.0337008	+	0.342170i	−0.963518	+	0.267643i	$0.913755\pi$
$678$		0			0
$679$	−0.475162	+	0.0945156i	−0.0182350	+	0.00362718i
$680$		0			0
$681$	−11.4172	+	57.3980i	−0.437507	+	2.19950i
$682$		0			0
$683$	−9.78169	−	18.3002i	−0.374286	−	0.700239i	0.622302	−	0.782777i	$-0.286198\pi$
$683$	−9.78169	−	18.3002i	−0.374286	−	0.700239i	−0.996588	+	0.0825376i	$0.973698\pi$
$684$		0			0
$685$	1.44588	−	14.6802i	0.0552441	−	0.560903i
$686$		0			0
$687$	−14.6384	+	35.3403i	−0.558492	+	1.34832i
$688$		0			0
$689$	−17.1606	−	41.4295i	−0.653769	−	1.57834i
$690$		0			0
$691$	−6.36236	+	5.22146i	−0.242036	+	0.198634i	−0.747589	−	0.664162i	$-0.768789\pi$
$691$	−6.36236	+	5.22146i	−0.242036	+	0.198634i	0.505553	+	0.862796i	$0.331289\pi$
$692$		0			0
$693$	1.21714	+	0.369215i	0.0462353	+	0.0140253i
$694$		0			0
$695$	23.0109	−	15.3754i	0.872853	−	0.583222i
$696$		0			0
$697$	24.6311	−	36.8631i	0.932970	−	1.39629i
$698$		0			0
$699$	−27.4592	+	33.4591i	−1.03860	+	1.26554i
$700$		0			0
$701$	6.72543	+	3.59482i	0.254016	+	0.135774i	0.593491	−	0.804841i	$-0.297749\pi$
$701$	6.72543	+	3.59482i	0.254016	+	0.135774i	−0.339475	+	0.940615i	$0.610249\pi$
$702$		0			0
$703$		−	35.3221i		−	1.33220i
$704$		0			0
$705$		−	36.3456i		−	1.36886i
$706$		0			0
$707$	1.94314	+	1.03863i	0.0730792	+	0.0390617i
$708$		0			0
$709$	−26.5090	+	32.3013i	−0.995566	+	1.21310i	−0.0185737	+	0.999827i	$0.505913\pi$
$709$	−26.5090	+	32.3013i	−0.995566	+	1.21310i	−0.976993	+	0.213273i	$0.931587\pi$
$710$		0			0
$711$	−12.6764	+	18.9715i	−0.475401	+	0.711488i
$712$		0			0
$713$	−2.02082	+	1.35027i	−0.0756805	+	0.0505681i
$714$		0			0
$715$	46.5468	+	14.1198i	1.74075	+	0.528052i
$716$		0			0
$717$	31.8876	−	26.1695i	1.19086	−	0.977316i
$718$		0			0
$719$	11.8714	+	28.6600i	0.442728	+	1.06884i	0.974988	+	0.222258i	$0.0713428\pi$
$719$	11.8714	+	28.6600i	0.442728	+	1.06884i	−0.532260	+	0.846581i	$0.678657\pi$
$720$		0			0
$721$	0.565851	−	1.36609i	0.0210734	−	0.0508757i
$722$		0			0
$723$	1.71087	−	17.3708i	0.0636280	−	0.646026i
$724$		0			0
$725$	0.128974	+	0.241294i	0.00478998	+	0.00896143i
$726$		0			0
$727$	−2.00475	+	10.0786i	−0.0743522	+	0.373794i	−0.999989	−	0.00461855i	$-0.998530\pi$
$727$	−2.00475	+	10.0786i	−0.0743522	+	0.373794i	0.925637	+	0.378412i	$0.123530\pi$
$728$		0			0
$729$	4.15711	−	0.826900i	0.153967	−	0.0306259i
$730$		0			0
$731$	2.52019	+	25.5879i	0.0932124	+	0.946402i
$732$		0			0
$733$	14.0674	+	46.3740i	0.519592	+	1.71286i	0.686714	+	0.726928i	$0.259052\pi$
$733$	14.0674	+	46.3740i	0.519592	+	1.71286i	−0.167123	+	0.985936i	$0.553448\pi$
$734$		0			0
$735$	−24.2781	−	24.2781i	−0.895509	−	0.895509i
$736$		0			0
$737$	−45.1784	+	45.1784i	−1.66417	+	1.66417i
$738$		0			0
$739$	43.3530	−	13.1510i	1.59477	−	0.483767i	0.636892	−	0.770953i	$-0.280220\pi$
$739$	43.3530	−	13.1510i	1.59477	−	0.483767i	0.957875	+	0.287186i	$0.0927197\pi$
$740$		0			0
$741$	48.6916	−	4.79570i	1.78873	−	0.176174i
$742$		0			0
$743$	−7.11608	−	35.7749i	−0.261064	−	1.31246i	−0.859439	−	0.511239i	$-0.829187\pi$
$743$	−7.11608	−	35.7749i	−0.261064	−	1.31246i	0.598375	−	0.801216i	$-0.295813\pi$
$744$		0			0
$745$	−39.2631	−	7.80991i	−1.43849	−	0.286133i
$746$		0			0
$747$	16.1889	−	8.65312i	0.592319	−	0.316601i
$748$		0			0
$749$	−0.198091	−	0.0195102i	−0.00723808	−	0.000712888i
$750$		0			0
$751$	36.4747	+	15.1083i	1.33098	+	0.551310i	0.930935	−	0.365186i	$-0.118995\pi$
$751$	36.4747	+	15.1083i	1.33098	+	0.551310i	0.400045	+	0.916496i	$0.368995\pi$
$752$		0			0
$753$	−26.0268	+	10.7806i	−0.948468	+	0.392868i
$754$		0			0
$755$	−22.6380	−	27.5845i	−0.823881	−	1.00390i
$756$		0			0
$757$	−1.66167	+	5.47778i	−0.0603943	+	0.199093i	−0.981946	−	0.189163i	$-0.939423\pi$
$757$	−1.66167	+	5.47778i	−0.0603943	+	0.199093i	0.921551	+	0.388256i	$0.126923\pi$
$758$		0			0
$759$	9.16622	+	13.7182i	0.332713	+	0.497940i
$760$		0			0
$761$	11.6429	+	7.77955i	0.422056	+	0.282009i	0.748407	−	0.663240i	$-0.230819\pi$
$761$	11.6429	+	7.77955i	0.422056	+	0.282009i	−0.326351	+	0.945249i	$0.605819\pi$
$762$		0			0
$763$	2.30827	+	1.89435i	0.0835649	+	0.0685799i
$764$		0			0
$765$	−10.6067	+	19.8437i	−0.383485	+	0.717451i
$766$		0			0
$767$	−22.7335			−0.820860
$768$		0			0
$769$	−25.3820			−0.915300			−0.457650	−	0.889133i	$-0.651309\pi$
$769$	−25.3820			−0.915300			−0.457650	+	0.889133i	$0.651309\pi$
$770$		0			0
$771$	13.9955	−	26.1838i	0.504036	−	0.942986i
$772$		0			0
$773$	−13.3305	−	10.9400i	−0.479464	−	0.393486i	0.363383	−	0.931640i	$-0.381622\pi$
$773$	−13.3305	−	10.9400i	−0.479464	−	0.393486i	−0.842846	+	0.538154i	$0.819122\pi$
$774$		0			0
$775$	−0.546984	−	0.365483i	−0.0196483	−	0.0131285i
$776$		0			0
$777$	−1.48097	−	2.21643i	−0.0531295	−	0.0795139i
$778$		0			0
$779$	10.1425	−	33.4353i	0.363392	−	1.19794i
$780$		0			0
$781$	−9.94704	−	12.1205i	−0.355933	−	0.433706i
$782$		0			0
$783$	−1.82356	+	0.755342i	−0.0651686	+	0.0269937i
$784$		0			0
$785$	4.75158	+	1.96817i	0.169591	+	0.0702469i
$786$		0			0
$787$	−31.0247	−	3.05566i	−1.10591	−	0.108923i	−0.471460	−	0.881887i	$-0.656273\pi$
$787$	−31.0247	−	3.05566i	−1.10591	−	0.108923i	−0.634449	+	0.772965i	$0.718773\pi$
$788$		0			0
$789$	13.5878	−	7.26285i	0.483740	−	0.258564i
$790$		0			0
$791$	1.01304	+	0.201507i	0.0360197	+	0.00716477i
$792$		0			0
$793$	−7.06652	−	35.5258i	−0.250939	−	1.26156i
$794$		0			0
$795$	49.4716	−	4.87253i	1.75458	−	0.172811i
$796$		0			0
$797$	1.59540	−	0.483958i	0.0565119	−	0.0171427i	−0.261902	−	0.965094i	$-0.584350\pi$
$797$	1.59540	−	0.483958i	0.0565119	−	0.0171427i	0.318414	+	0.947952i	$0.396850\pi$
$798$		0			0
$799$	34.4794	−	34.4794i	1.21979	−	1.21979i
$800$		0			0
$801$	−3.82684	−	3.82684i	−0.135215	−	0.135215i
$802$		0			0
$803$	11.2261	+	37.0076i	0.396161	+	1.30597i
$804$		0			0
$805$	0.0711177	+	0.722070i	0.00250657	+	0.0254496i
$806$		0			0
$807$	31.5188	−	6.26947i	1.10951	−	0.220696i
$808$		0			0
$809$	−0.437939	+	2.20167i	−0.0153971	+	0.0774065i	−0.987720	−	0.156235i	$-0.950064\pi$
$809$	−0.437939	+	2.20167i	−0.0153971	+	0.0774065i	0.972323	+	0.233642i	$0.0750642\pi$
$810$		0			0
$811$	13.9781	+	26.1512i	0.490838	+	0.918293i	0.998393	+	0.0566734i	$0.0180494\pi$
$811$	13.9781	+	26.1512i	0.490838	+	0.918293i	−0.507555	+	0.861619i	$0.669451\pi$
$812$		0			0
$813$	−1.19029	+	12.0852i	−0.0417453	+	0.423847i
$814$		0			0
$815$	−5.73388	+	13.8428i	−0.200849	+	0.484892i
$816$		0			0
$817$	7.75435	+	18.7207i	0.271291	+	0.654953i
$818$		0			0
$819$	0.933159	−	0.765824i	0.0326072	−	0.0267600i
$820$		0			0
$821$	−27.7462	−	8.41672i	−0.968349	−	0.293745i	−0.233787	−	0.972288i	$-0.575112\pi$
$821$	−27.7462	−	8.41672i	−0.968349	−	0.293745i	−0.734561	+	0.678542i	$0.762612\pi$
$822$		0			0
$823$	−22.3531	+	14.9359i	−0.779180	+	0.520631i	−0.880399	−	0.474233i	$-0.842725\pi$
$823$	−22.3531	+	14.9359i	−0.779180	+	0.520631i	0.101220	+	0.994864i	$0.467725\pi$
$824$		0			0
$825$	−2.48106	+	3.71316i	−0.0863793	+	0.129276i
$826$		0			0
$827$	12.5338	−	15.2725i	0.435843	−	0.531076i	−0.508050	−	0.861328i	$-0.669633\pi$
$827$	12.5338	−	15.2725i	0.435843	−	0.531076i	0.943893	+	0.330251i	$0.107133\pi$
$828$		0			0
$829$	3.41538	+	1.82556i	0.118621	+	0.0634042i	0.529640	−	0.848223i	$-0.322327\pi$
$829$	3.41538	+	1.82556i	0.118621	+	0.0634042i	−0.411019	+	0.911627i	$0.634827\pi$
$830$		0			0
$831$		−	25.6375i		−	0.889355i
$832$		0			0
$833$		−	46.0628i		−	1.59598i
$834$		0			0
$835$	−14.8872	−	7.95735i	−0.515191	−	0.275375i
$836$		0			0
$837$	3.01075	−	3.66861i	0.104067	−	0.126806i
$838$		0			0
$839$	−12.8715	+	19.2635i	−0.444373	+	0.665051i	−0.984268	−	0.176681i	$-0.943464\pi$
$839$	−12.8715	+	19.2635i	−0.444373	+	0.665051i	0.539895	+	0.841732i	$0.318464\pi$
$840$		0			0
$841$	−23.8073	+	15.9075i	−0.820941	+	0.548535i
$842$		0			0
$843$	17.6501	+	5.35410i	0.607901	+	0.184405i
$844$		0			0
$845$	12.2235	−	10.0316i	0.420501	−	0.345096i
$846$		0			0
$847$	0.780666	+	1.88469i	0.0268240	+	0.0647589i
$848$		0			0
$849$	6.37943	−	15.4013i	0.218941	−	0.528571i
$850$		0			0
$851$	1.10807	−	11.2504i	0.0379840	−	0.385658i
$852$		0			0
$853$	−7.65406	−	14.3197i	−0.262070	−	0.490298i	0.716129	−	0.697968i	$-0.245912\pi$
$853$	−7.65406	−	14.3197i	−0.262070	−	0.490298i	−0.978199	+	0.207670i	$0.933412\pi$
$854$		0			0
$855$	−3.45943	+	17.3917i	−0.118310	+	0.594784i
$856$		0			0
$857$	−11.0037	+	2.18876i	−0.375878	+	0.0747667i	−0.379414	−	0.925227i	$-0.623874\pi$
$857$	−11.0037	+	2.18876i	−0.375878	+	0.0747667i	0.00353634	+	0.999994i	$0.498874\pi$
$858$		0			0
$859$	−2.79178	−	28.3455i	−0.0952545	−	0.967135i	−0.917429	−	0.397899i	$-0.869739\pi$
$859$	−2.79178	−	28.3455i	−0.0952545	−	0.967135i	0.822175	−	0.569235i	$-0.192761\pi$
$860$		0			0
$861$	−0.765428	−	2.52328i	−0.0260857	−	0.0859931i
$862$		0			0
$863$	5.86840	+	5.86840i	0.199763	+	0.199763i	0.799898	−	0.600136i	$-0.204887\pi$
$863$	5.86840	+	5.86840i	0.199763	+	0.199763i	−0.600136	+	0.799898i	$0.704887\pi$
$864$		0			0
$865$	37.7332	−	37.7332i	1.28297	−	1.28297i
$866$		0			0
$867$	−54.0116	+	16.3842i	−1.83433	+	0.556437i
$868$		0			0
$869$	−73.0049	+	7.19036i	−2.47652	+	0.243916i
$870$		0			0
$871$	11.8303	+	59.4750i	0.400855	+	2.01523i
$872$		0			0
$873$	−3.71664	−	0.739286i	−0.125789	−	0.0250210i
$874$		0			0
$875$	1.74490	−	0.932670i	0.0589885	−	0.0315300i
$876$		0			0
$877$	43.2510	+	4.25986i	1.46048	+	0.143845i	0.796834	−	0.604198i	$-0.206506\pi$
$877$	43.2510	+	4.25986i	1.46048	+	0.143845i	0.663650	+	0.748043i	$0.269006\pi$
$878$		0			0
$879$	−53.3133	−	22.0831i	−1.79821	−	0.744844i
$880$		0			0
$881$	−10.8318	+	4.48669i	−0.364934	+	0.151160i	−0.557612	−	0.830101i	$-0.688282\pi$
$881$	−10.8318	+	4.48669i	−0.364934	+	0.151160i	0.192679	+	0.981262i	$0.438282\pi$
$882$		0			0
$883$	28.1407	+	34.2895i	0.947009	+	1.15393i	0.987950	+	0.154772i	$0.0494643\pi$
$883$	28.1407	+	34.2895i	0.947009	+	1.15393i	−0.0409414	+	0.999162i	$0.513036\pi$
$884$		0			0
$885$	7.31559	−	24.1163i	0.245911	−	0.810659i
$886$		0			0
$887$	4.97872	+	7.45117i	0.167169	+	0.250186i	0.905590	−	0.424154i	$-0.139428\pi$
$887$	4.97872	+	7.45117i	0.167169	+	0.250186i	−0.738421	+	0.674340i	$0.764428\pi$
$888$		0			0
$889$	0.0872966	+	0.0583297i	0.00292783	+	0.00195632i
$890$		0			0
$891$	−40.7365	−	33.4316i	−1.36472	−	1.12000i
$892$		0			0
$893$	18.1149	−	33.8906i	0.606192	−	1.13411i
$894$		0			0
$895$	−17.4136			−0.582073
$896$		0			0
$897$	15.6591			0.522842
$898$		0			0
$899$	−0.416229	+	0.778710i	−0.0138820	+	0.0259714i
$900$		0			0
$901$	51.5537	+	42.3090i	1.71750	+	1.40952i
$902$		0			0
$903$	1.27149	+	0.849581i	0.0423125	+	0.0282723i
$904$		0			0
$905$	−27.6193	−	41.3351i	−0.918095	−	1.37403i
$906$		0			0
$907$	15.4005	−	50.7688i	0.511367	−	1.68575i	−0.197413	−	0.980320i	$-0.563254\pi$
$907$	15.4005	−	50.7688i	0.511367	−	1.68575i	0.708779	−	0.705430i	$-0.249246\pi$
$908$		0			0
$909$	10.9331	+	13.3220i	0.362627	+	0.441862i
$910$		0			0
$911$	1.30602	−	0.540970i	0.0432703	−	0.0179231i	−0.360943	−	0.932588i	$-0.617545\pi$
$911$	1.30602	−	0.540970i	0.0432703	−	0.0179231i	0.404214	+	0.914665i	$0.367545\pi$
$912$		0			0
$913$	54.5248	+	22.5849i	1.80451	+	0.747451i
$914$		0			0
$915$	39.9606	+	3.93577i	1.32106	+	0.130113i
$916$		0			0
$917$	−0.967742	+	0.517269i	−0.0319577	+	0.0170817i
$918$		0			0
$919$	−23.3135	−	4.63735i	−0.769043	−	0.152972i	−0.205050	−	0.978752i	$-0.565736\pi$
$919$	−23.3135	−	4.63735i	−0.769043	−	0.152972i	−0.563993	+	0.825779i	$0.690736\pi$
$920$		0			0
$921$	−8.80606	−	44.2710i	−0.290169	−	1.45878i
$922$		0			0
$923$	−14.8100	+	1.45865i	−0.487476	+	0.0480122i
$924$		0			0
$925$	2.92816	−	0.888247i	0.0962773	−	0.0292054i
$926$		0			0
$927$	8.17818	−	8.17818i	0.268607	−	0.268607i
$928$		0			0
$929$	17.9121	+	17.9121i	0.587676	+	0.587676i	0.937001	−	0.349325i	$-0.113589\pi$
$929$	17.9121	+	17.9121i	0.587676	+	0.587676i	−0.349325	+	0.937001i	$0.613589\pi$
$930$		0			0
$931$	−10.5378	−	34.7385i	−0.345363	−	1.13851i
$932$		0			0
$933$	−0.350237	−	3.55602i	−0.0114662	−	0.116419i
$934$		0			0
$935$	−70.9511	+	14.1131i	−2.32035	+	0.461546i
$936$		0			0
$937$	10.3730	−	52.1488i	0.338873	−	1.70363i	−0.316725	−	0.948517i	$-0.602583\pi$
$937$	10.3730	−	52.1488i	0.338873	−	1.70363i	0.655598	−	0.755110i	$-0.272417\pi$
$938$		0			0
$939$	0.913256	+	1.70858i	0.0298030	+	0.0557575i
$940$		0			0
$941$	−0.837774	+	8.50607i	−0.0273107	+	0.277290i	0.971824	+	0.235706i	$0.0757403\pi$
$941$	−0.837774	+	8.50607i	−0.0273107	+	0.277290i	−0.999135	+	0.0415836i	$0.986760\pi$
$942$		0			0
$943$	4.27934	−	10.3312i	0.139354	−	0.336431i
$944$		0			0
$945$	−0.542187	−	1.30896i	−0.0176374	−	0.0425803i
$946$		0			0
$947$	−33.5911	+	27.5675i	−1.09157	+	0.895825i	−0.995037	−	0.0995055i	$-0.968274\pi$
$947$	−33.5911	+	27.5675i	−1.09157	+	0.895825i	−0.0965286	+	0.995330i	$0.530774\pi$
$948$		0			0
$949$	35.1241	+	10.6548i	1.14018	+	0.345869i
$950$		0			0
$951$	−32.9549	+	22.0197i	−1.06863	+	0.714039i
$952$		0			0
$953$	−15.3671	+	22.9985i	−0.497789	+	0.744994i	−0.992257	−	0.124202i	$-0.960363\pi$
$953$	−15.3671	+	22.9985i	−0.497789	+	0.744994i	0.494468	+	0.869196i	$0.335363\pi$
$954$		0			0
$955$	21.6270	−	26.3526i	0.699833	−	0.852748i
$956$		0			0
$957$	5.28622	+	2.82554i	0.170879	+	0.0913368i
$958$		0			0
$959$		−	1.17703i		−	0.0380082i
$960$		0			0
$961$			28.8770i			0.931515i
$962$		0			0
$963$	−1.37309	−	0.733932i	−0.0442472	−	0.0236506i
$964$		0			0
$965$	−4.72248	+	5.75436i	−0.152022	+	0.185239i
$966$		0			0
$967$	9.50331	−	14.2227i	0.305606	−	0.457372i	−0.646600	−	0.762830i	$-0.723810\pi$
$967$	9.50331	−	14.2227i	0.305606	−	0.457372i	0.952206	+	0.305458i	$0.0988096\pi$
$968$		0			0
$969$	−60.5029	+	40.4268i	−1.94363	+	1.29870i
$970$		0			0
$971$	−20.0906	−	6.09441i	−0.644738	−	0.195579i	−0.0490515	−	0.998796i	$-0.515620\pi$
$971$	−20.0906	−	6.09441i	−0.644738	−	0.195579i	−0.595686	+	0.803217i	$0.703120\pi$
$972$		0			0
$973$	1.70698	−	1.40089i	0.0547234	−	0.0449103i
$974$		0			0
$975$	1.62201	+	3.91587i	0.0519458	+	0.125408i
$976$		0			0
$977$	−12.3558	+	29.8296i	−0.395297	+	0.954332i	0.593468	+	0.804858i	$0.297758\pi$
$977$	−12.3558	+	29.8296i	−0.395297	+	0.954332i	−0.988766	+	0.149475i	$0.952242\pi$
$978$		0			0
$979$	1.70549	−	17.3162i	0.0545078	−	0.553427i
$980$		0			0
$981$	11.0102	+	20.5987i	0.351529	+	0.657665i
$982$		0			0
$983$	1.39742	−	7.02530i	0.0445708	−	0.224072i	−0.952080	−	0.305849i	$-0.901060\pi$
$983$	1.39742	−	7.02530i	0.0445708	−	0.224072i	0.996651	+	0.0817771i	$0.0260596\pi$
$984$		0			0
$985$	10.0378	−	1.99665i	0.319832	−	0.0636186i
$986$		0			0
$987$	−0.284257	−	2.88611i	−0.00904801	−	0.0918660i
$988$		0			0
$989$	1.88255	+	6.20593i	0.0598616	+	0.197337i
$990$		0			0
$991$	−7.41124	−	7.41124i	−0.235426	−	0.235426i	0.579527	−	0.814953i	$-0.303237\pi$
$991$	−7.41124	−	7.41124i	−0.235426	−	0.235426i	−0.814953	+	0.579527i	$0.803237\pi$
$992$		0			0
$993$	16.7337	−	16.7337i	0.531029	−	0.531029i
$994$		0			0
$995$	32.2397	−	9.77982i	1.02207	−	0.310041i
$996$		0			0
$997$	22.2676	−	2.19317i	0.705222	−	0.0694583i	0.260952	−	0.965352i	$-0.415963\pi$
$997$	22.2676	−	2.19317i	0.705222	−	0.0694583i	0.444269	+	0.895893i	$0.353463\pi$
$998$		0			0
$999$	4.30658	+	21.6507i	0.136254	+	0.684996i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.k.a.17.3		240
4.3	odd	2		128.2.k.a.45.13	yes	240
128.37	even	32	inner	512.2.k.a.241.3		240
128.91	odd	32		128.2.k.a.37.13	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
128.2.k.a.37.13	✓	240	128.91	odd	32
128.2.k.a.45.13	yes	240	4.3	odd	2
512.2.k.a.17.3		240	1.1	even	1	trivial
512.2.k.a.241.3		240	128.37	even	32	inner

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.k (of order \(32\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.995218 + 1.86192i) q^{3} +(-1.80486 - 1.48121i) q^{5} +(-0.154904 - 0.103503i) q^{7} +(-0.809586 - 1.21163i) q^{9} +O(q^{10})\)	\(q+(-0.995218 + 1.86192i) q^{3} +(-1.80486 - 1.48121i) q^{5} +(-0.154904 - 0.103503i) q^{7} +(-0.809586 - 1.21163i) q^{9} +(1.36000 - 4.48334i) q^{11} +(-2.82091 - 3.43729i) q^{13} +(4.55412 - 1.88638i) q^{15} +(6.10980 + 2.53076i) q^{17} +(5.18669 + 0.510845i) q^{19} +(0.346878 - 0.185410i) q^{21} +(1.63598 + 0.325416i) q^{23} +(0.0880816 + 0.442816i) q^{25} +(-3.24146 + 0.319256i) q^{27} +(0.579898 - 0.175910i) q^{29} +(-1.03030 + 1.03030i) q^{31} +(6.99412 + 6.99412i) q^{33} +(0.126269 + 0.416253i) q^{35} +(-0.664297 - 6.74472i) q^{37} +(9.20740 - 1.83147i) q^{39} +(1.30788 - 6.57518i) q^{41} +(1.83276 + 3.42885i) q^{43} +(-0.333491 + 3.38599i) q^{45} +(2.82164 - 6.81205i) q^{47} +(-2.66550 - 6.43509i) q^{49} +(-10.7927 + 8.85731i) q^{51} +(9.65045 + 2.92743i) q^{53} +(-9.09537 + 6.07733i) q^{55} +(-6.11305 + 9.14882i) q^{57} +(3.24335 - 3.95204i) q^{59} +(7.18403 + 3.83994i) q^{61} +0.271481i q^{63} +10.3822i q^{65} +(-12.0271 - 6.42859i) q^{67} +(-2.23405 + 2.72220i) q^{69} +(1.85934 - 2.78269i) q^{71} +(-6.86335 + 4.58594i) q^{73} +(-0.912150 - 0.276698i) q^{75} +(-0.674709 + 0.553720i) q^{77} +(-5.99200 - 14.4660i) q^{79} +(4.30449 - 10.3920i) q^{81} +(-1.23471 + 12.5362i) q^{83} +(-7.27873 - 13.6175i) q^{85} +(-0.249594 + 1.25479i) q^{87} +(3.64255 - 0.724548i) q^{89} +(0.0811986 + 0.824423i) q^{91} +(-0.892966 - 2.94371i) q^{93} +(-8.60458 - 8.60458i) q^{95} +(1.83881 - 1.83881i) q^{97} +(-6.53319 + 1.98182i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9}+O(q^{10}) \) 240 * q + 16 * q^3 - 16 * q^5 + 16 * q^7 - 16 * q^9	\( 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9} + 16 q^{11} - 16 q^{13} + 16 q^{15} - 16 q^{17} + 16 q^{19} - 16 q^{21} + 16 q^{23} - 16 q^{25} + 16 q^{27} - 16 q^{29} + 16 q^{31} - 16 q^{33} + 16 q^{35} - 16 q^{37} + 16 q^{39} - 16 q^{41} + 16 q^{43} - 16 q^{45} + 16 q^{47} - 16 q^{49} + 16 q^{51} - 16 q^{53} + 16 q^{55} - 16 q^{57} + 16 q^{59} - 16 q^{61} + 16 q^{67} - 16 q^{69} + 16 q^{71} - 16 q^{73} + 16 q^{75} - 16 q^{77} + 16 q^{79} - 16 q^{81} + 16 q^{83} - 16 q^{85} + 16 q^{87} - 16 q^{89} + 16 q^{91} - 16 q^{93} + 16 q^{95} - 16 q^{97} + 16 q^{99}+O(q^{100}) \) 240 * q + 16 * q^3 - 16 * q^5 + 16 * q^7 - 16 * q^9 + 16 * q^11 - 16 * q^13 + 16 * q^15 - 16 * q^17 + 16 * q^19 - 16 * q^21 + 16 * q^23 - 16 * q^25 + 16 * q^27 - 16 * q^29 + 16 * q^31 - 16 * q^33 + 16 * q^35 - 16 * q^37 + 16 * q^39 - 16 * q^41 + 16 * q^43 - 16 * q^45 + 16 * q^47 - 16 * q^49 + 16 * q^51 - 16 * q^53 + 16 * q^55 - 16 * q^57 + 16 * q^59 - 16 * q^61 + 16 * q^67 - 16 * q^69 + 16 * q^71 - 16 * q^73 + 16 * q^75 - 16 * q^77 + 16 * q^79 - 16 * q^81 + 16 * q^83 - 16 * q^85 + 16 * q^87 - 16 * q^89 + 16 * q^91 - 16 * q^93 + 16 * q^95 - 16 * q^97 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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