LMFDB - Embedded newform 864.2.bf.a.49.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(49,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 9, 14]))

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

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

chi := DirichletCharacter("864.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bf (of order $18$, degree $6$, 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:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			49.17
Character	$\chi$	$=$	864.49
Dual form			864.2.bf.a.529.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.123826 - 1.72762i) q^{3} +(0.608623 + 1.67218i) q^{5} +(-0.408085 - 2.31436i) q^{7} +(-2.96933 + 0.427848i) q^{9} +O(q^{10})$	\(q+(-0.123826 - 1.72762i) q^{3} +(0.608623 + 1.67218i) q^{5} +(-0.408085 - 2.31436i) q^{7} +(-2.96933 + 0.427848i) q^{9} +(0.860398 - 2.36392i) q^{11} +(0.359719 - 0.428697i) q^{13} +(2.81352 - 1.25853i) q^{15} +(1.49770 - 2.59409i) q^{17} +(-6.64437 + 3.83613i) q^{19} +(-3.94781 + 0.991593i) q^{21} +(1.12812 - 6.39788i) q^{23} +(1.40447 - 1.17849i) q^{25} +(1.10684 + 5.07690i) q^{27} +(-5.22169 - 6.22297i) q^{29} +(0.643875 - 3.65160i) q^{31} +(-4.19050 - 1.19372i) q^{33} +(3.62166 - 2.09096i) q^{35} +(4.07450 + 2.35241i) q^{37} +(-0.785167 - 0.568374i) q^{39} +(-5.67863 - 4.76494i) q^{41} +(-0.928888 + 2.55210i) q^{43} +(-2.52264 - 4.70485i) q^{45} +(-0.0919295 - 0.521358i) q^{47} +(1.38810 - 0.505226i) q^{49} +(-4.66705 - 2.26623i) q^{51} +6.39371i q^{53} +4.47656 q^{55} +(7.45011 + 11.0039i) q^{57} +(-2.87131 - 7.88886i) q^{59} +(0.716954 - 0.126418i) q^{61} +(2.20194 + 6.69753i) q^{63} +(0.935790 + 0.340600i) q^{65} +(-3.68574 + 4.39249i) q^{67} +(-11.1928 - 1.15674i) q^{69} +(-7.38597 + 12.7929i) q^{71} +(-5.98642 - 10.3688i) q^{73} +(-2.20989 - 2.28046i) q^{75} +(-5.82210 - 1.02659i) q^{77} +(8.94860 - 7.50876i) q^{79} +(8.63389 - 2.54084i) q^{81} +(-4.81848 - 5.74244i) q^{83} +(5.24930 + 0.925594i) q^{85} +(-10.1043 + 9.79165i) q^{87} +(-1.16774 - 2.02259i) q^{89} +(-1.13896 - 0.657577i) q^{91} +(-6.38830 - 0.660209i) q^{93} +(-10.4586 - 8.77580i) q^{95} +(13.8915 + 5.05610i) q^{97} +(-1.54341 + 7.38740i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q + 12 q^{7} - 12 q^{9}+O(q^{10}) $ 204 * q + 12 * q^7 - 12 * q^9	$ 204 q + 12 q^{7} - 12 q^{9} + 12 q^{15} - 6 q^{17} + 12 q^{23} - 12 q^{25} + 12 q^{31} + 12 q^{39} - 24 q^{41} + 12 q^{47} - 12 q^{49} + 24 q^{55} - 30 q^{57} + 72 q^{63} - 12 q^{65} + 90 q^{71} - 6 q^{73} + 12 q^{79} - 12 q^{81} + 48 q^{87} - 6 q^{89} + 42 q^{95} - 12 q^{97}+O(q^{100}) $ 204 * q + 12 * q^7 - 12 * q^9 + 12 * q^15 - 6 * q^17 + 12 * q^23 - 12 * q^25 + 12 * q^31 + 12 * q^39 - 24 * q^41 + 12 * q^47 - 12 * q^49 + 24 * q^55 - 30 * q^57 + 72 * q^63 - 12 * q^65 + 90 * q^71 - 6 * q^73 + 12 * q^79 - 12 * q^81 + 48 * q^87 - 6 * q^89 + 42 * q^95 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$-1$	$e\left(\frac{7}{9}\right)$	$1$

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
$3$	−0.123826	−	1.72762i	−0.0714909	−	0.997441i
$3$	−0.123826	−	1.72762i	−0.0714909	−	0.997441i
$4$		0			0
$5$	0.608623	+	1.67218i	0.272184	+	0.747820i	0.998190	+	0.0601320i	$0.0191521\pi$
$5$	0.608623	+	1.67218i	0.272184	+	0.747820i	−0.726006	+	0.687688i	$0.758626\pi$
$6$		0			0
$7$	−0.408085	−	2.31436i	−0.154242	−	0.874748i	−0.959476	−	0.281791i	$-0.909072\pi$
$7$	−0.408085	−	2.31436i	−0.154242	−	0.874748i	0.805234	−	0.592957i	$-0.202040\pi$
$8$		0			0
$9$	−2.96933	+	0.427848i	−0.989778	+	0.142616i
$10$		0			0
$11$	0.860398	−	2.36392i	0.259420	−	0.712750i	−0.739784	−	0.672845i	$-0.765072\pi$
$11$	0.860398	−	2.36392i	0.259420	−	0.712750i	0.999203	−	0.0399051i	$-0.0127056\pi$
$12$		0			0
$13$	0.359719	−	0.428697i	0.0997682	−	0.118899i	−0.713850	−	0.700299i	$-0.753050\pi$
$13$	0.359719	−	0.428697i	0.0997682	−	0.118899i	0.813618	+	0.581399i	$0.197495\pi$
$14$		0			0
$15$	2.81352	−	1.25853i	0.726448	−	0.324950i
$16$		0			0
$17$	1.49770	−	2.59409i	0.363245	−	0.629158i	−0.625248	−	0.780426i	$-0.715002\pi$
$17$	1.49770	−	2.59409i	0.363245	−	0.629158i	0.988493	+	0.151268i	$0.0483356\pi$
$18$		0			0
$19$	−6.64437	+	3.83613i	−1.52432	+	0.880068i	−0.524737	+	0.851264i	$0.675836\pi$
$19$	−6.64437	+	3.83613i	−1.52432	+	0.880068i	−0.999585	+	0.0288032i	$0.990830\pi$
$20$		0			0
$21$	−3.94781	+	0.991593i	−0.861483	+	0.216383i
$22$		0			0
$23$	1.12812	−	6.39788i	0.235229	−	1.33405i	−0.606902	−	0.794777i	$-0.707588\pi$
$23$	1.12812	−	6.39788i	0.235229	−	1.33405i	0.842131	−	0.539273i	$-0.181301\pi$
$24$		0			0
$25$	1.40447	−	1.17849i	0.280894	−	0.235698i
$26$		0			0
$27$	1.10684	+	5.07690i	0.213011	+	0.977050i
$28$		0			0
$29$	−5.22169	−	6.22297i	−0.969643	−	1.15558i	−0.987798	−	0.155741i	$-0.950224\pi$
$29$	−5.22169	−	6.22297i	−0.969643	−	1.15558i	0.0181545	−	0.999835i	$-0.494221\pi$
$30$		0			0
$31$	0.643875	−	3.65160i	0.115643	−	0.655846i	−0.870786	−	0.491662i	$-0.836390\pi$
$31$	0.643875	−	3.65160i	0.115643	−	0.655846i	0.986430	−	0.164184i	$-0.0524992\pi$
$32$		0			0
$33$	−4.19050	−	1.19372i	−0.729472	−	0.207801i
$34$		0			0
$35$	3.62166	−	2.09096i	0.612172	−	0.353438i
$36$		0			0
$37$	4.07450	+	2.35241i	0.669843	+	0.386734i	0.796017	−	0.605274i	$-0.206936\pi$
$37$	4.07450	+	2.35241i	0.669843	+	0.386734i	−0.126174	+	0.992008i	$0.540270\pi$
$38$		0			0
$39$	−0.785167	−	0.568374i	−0.125727	−	0.0910127i
$40$		0			0
$41$	−5.67863	−	4.76494i	−0.886853	−	0.744158i	0.0807232	−	0.996737i	$-0.474277\pi$
$41$	−5.67863	−	4.76494i	−0.886853	−	0.744158i	−0.967576	+	0.252578i	$0.918721\pi$
$42$		0			0
$43$	−0.928888	+	2.55210i	−0.141654	+	0.389191i	−0.990150	−	0.140011i	$-0.955286\pi$
$43$	−0.928888	+	2.55210i	−0.141654	+	0.389191i	0.848496	+	0.529202i	$0.177509\pi$
$44$		0			0
$45$	−2.52264	−	4.70485i	−0.376053	−	0.701358i
$46$		0			0
$47$	−0.0919295	−	0.521358i	−0.0134093	−	0.0760479i	0.977369	−	0.211543i	$-0.0678487\pi$
$47$	−0.0919295	−	0.521358i	−0.0134093	−	0.0760479i	−0.990778	+	0.135495i	$0.956738\pi$
$48$		0			0
$49$	1.38810	−	0.505226i	0.198300	−	0.0721751i
$50$		0			0
$51$	−4.66705	−	2.26623i	−0.653517	−	0.317336i
$52$		0			0
$53$			6.39371i			0.878244i	0.898427	+	0.439122i	$0.144710\pi$
$53$			6.39371i			0.878244i	−0.898427	+	0.439122i	$0.855290\pi$
$54$		0			0
$55$	4.47656			0.603619
$56$		0			0
$57$	7.45011	+	11.0039i	0.986791	+	1.45750i
$58$		0			0
$59$	−2.87131	−	7.88886i	−0.373813	−	1.02704i	−0.973874	−	0.227088i	$-0.927079\pi$
$59$	−2.87131	−	7.88886i	−0.373813	−	1.02704i	0.600061	−	0.799954i	$-0.295143\pi$
$60$		0			0
$61$	0.716954	−	0.126418i	0.0917966	−	0.0161862i	−0.127561	−	0.991831i	$-0.540715\pi$
$61$	0.716954	−	0.126418i	0.0917966	−	0.0161862i	0.219358	+	0.975644i	$0.429604\pi$
$62$		0			0
$63$	2.20194	+	6.69753i	0.277418	+	0.843809i
$64$		0			0
$65$	0.935790	+	0.340600i	0.116070	+	0.0422462i
$66$		0			0
$67$	−3.68574	+	4.39249i	−0.450285	+	0.536628i	−0.942660	−	0.333755i	$-0.891684\pi$
$67$	−3.68574	+	4.39249i	−0.450285	+	0.536628i	0.492375	+	0.870383i	$0.336129\pi$
$68$		0			0
$69$	−11.1928	−	1.15674i	−1.34745	−	0.139255i
$70$		0			0
$71$	−7.38597	+	12.7929i	−0.876553	+	1.51823i	−0.0214546	+	0.999770i	$0.506830\pi$
$71$	−7.38597	+	12.7929i	−0.876553	+	1.51823i	−0.855099	+	0.518465i	$0.826504\pi$
$72$		0			0
$73$	−5.98642	−	10.3688i	−0.700657	−	1.21357i	−0.968236	−	0.250038i	$-0.919557\pi$
$73$	−5.98642	−	10.3688i	−0.700657	−	1.21357i	0.267579	−	0.963536i	$-0.413776\pi$
$74$		0			0
$75$	−2.20989	−	2.28046i	−0.255176	−	0.263325i
$76$		0			0
$77$	−5.82210	−	1.02659i	−0.663490	−	0.116991i
$78$		0			0
$79$	8.94860	−	7.50876i	1.00680	−	0.844802i	0.0188843	−	0.999822i	$-0.493989\pi$
$79$	8.94860	−	7.50876i	1.00680	−	0.844802i	0.987911	+	0.155020i	$0.0495441\pi$
$80$		0			0
$81$	8.63389	−	2.54084i	0.959321	−	0.282316i
$82$		0			0
$83$	−4.81848	−	5.74244i	−0.528897	−	0.630315i	0.433764	−	0.901027i	$-0.357185\pi$
$83$	−4.81848	−	5.74244i	−0.528897	−	0.630315i	−0.962660	+	0.270712i	$0.912741\pi$
$84$		0			0
$85$	5.24930	+	0.925594i	0.569367	+	0.100395i
$86$		0			0
$87$	−10.1043	+	9.79165i	−1.08330	+	1.04978i
$88$		0			0
$89$	−1.16774	−	2.02259i	−0.123780	−	0.214394i	0.797475	−	0.603352i	$-0.206168\pi$
$89$	−1.16774	−	2.02259i	−0.123780	−	0.214394i	−0.921255	+	0.388958i	$0.872835\pi$
$90$		0			0
$91$	−1.13896	−	0.657577i	−0.119395	−	0.0689328i
$92$		0			0
$93$	−6.38830	−	0.660209i	−0.662435	−	0.0684605i
$94$		0			0
$95$	−10.4586	−	8.77580i	−1.07303	−	0.900378i
$96$		0			0
$97$	13.8915	+	5.05610i	1.41047	+	0.513369i	0.931268	−	0.364336i	$-0.118704\pi$
$97$	13.8915	+	5.05610i	1.41047	+	0.513369i	0.479202	+	0.877705i	$0.340926\pi$
$98$		0			0
$99$	−1.54341	+	7.38740i	−0.155119	+	0.742461i
$100$		0			0
$101$	12.0747	−	2.12910i	1.20148	−	0.211853i	0.463142	−	0.886284i	$-0.346722\pi$
$101$	12.0747	−	2.12910i	1.20148	−	0.211853i	0.738338	+	0.674431i	$0.235611\pi$
$102$		0			0
$103$	−10.8828	+	3.96103i	−1.07232	+	0.390292i	−0.817043	−	0.576576i	$-0.804388\pi$
$103$	−10.8828	+	3.96103i	−1.07232	+	0.390292i	−0.255276	+	0.966868i	$0.582166\pi$
$104$		0			0
$105$	−4.06085	−	5.99793i	−0.396298	−	0.585338i
$106$		0			0
$107$		−	3.95255i		−	0.382107i	−0.981580	−	0.191054i	$-0.938810\pi$
$107$		−	3.95255i		−	0.382107i	0.981580	−	0.191054i	$-0.0611904\pi$
$108$		0			0
$109$		−	5.12938i		−	0.491305i	−0.969358	−	0.245653i	$-0.920998\pi$
$109$		−	5.12938i		−	0.491305i	0.969358	−	0.245653i	$-0.0790023\pi$
$110$		0			0
$111$	3.55954	−	7.33047i	0.337857	−	0.695777i
$112$		0			0
$113$	−9.37151	+	3.41095i	−0.881597	+	0.320875i	−0.742854	−	0.669453i	$-0.766528\pi$
$113$	−9.37151	+	3.41095i	−0.881597	+	0.320875i	−0.138743	+	0.990328i	$0.544306\pi$
$114$		0			0
$115$	11.3850	−	2.00748i	1.06165	−	0.187198i
$116$		0			0
$117$	−0.884710	+	1.42685i	−0.0817915	+	0.131912i
$118$		0			0
$119$	−6.61485	−	2.40761i	−0.606382	−	0.220705i
$120$		0			0
$121$	3.57864	+	3.00283i	0.325331	+	0.272985i
$122$		0			0
$123$	−7.52884	+	10.4005i	−0.678852	+	0.937785i
$124$		0			0
$125$	10.5309	+	6.08000i	0.941909	+	0.543812i
$126$		0			0
$127$	10.0971	+	17.4887i	0.895973	+	1.55187i	0.832596	+	0.553880i	$0.186853\pi$
$127$	10.0971	+	17.4887i	0.895973	+	1.55187i	0.0633763	+	0.997990i	$0.479813\pi$
$128$		0			0
$129$	4.52407	+	1.28875i	0.398322	+	0.113468i
$130$		0			0
$131$	13.3484	+	2.35368i	1.16625	+	0.205642i	0.723060	−	0.690785i	$-0.242735\pi$
$131$	13.3484	+	2.35368i	1.16625	+	0.205642i	0.443192	+	0.896427i	$0.353846\pi$
$132$		0			0
$133$	11.5897	+	13.8120i	1.00495	+	1.19765i
$134$		0			0
$135$	−7.81583	+	4.94074i	−0.672679	+	0.425232i
$136$		0			0
$137$	6.18657	−	5.19115i	0.528555	−	0.443510i	−0.339047	−	0.940769i	$-0.610105\pi$
$137$	6.18657	−	5.19115i	0.528555	−	0.443510i	0.867602	+	0.497259i	$0.165660\pi$
$138$		0			0
$139$	18.8808	+	3.32919i	1.60145	+	0.282378i	0.901814	−	0.432124i	$-0.142236\pi$
$139$	18.8808	+	3.32919i	1.60145	+	0.282378i	0.699633	+	0.714502i	$0.253347\pi$
$140$		0			0
$141$	−0.889325	+	0.223377i	−0.0748947	+	0.0188117i
$142$		0			0
$143$	−0.703905	−	1.21920i	−0.0588635	−	0.101955i
$144$		0			0
$145$	7.22786	−	12.5190i	0.600241	−	1.03965i
$146$		0			0
$147$	−1.04472	−	2.33554i	−0.0861670	−	0.192632i
$148$		0			0
$149$	0.614187	−	0.731960i	0.0503162	−	0.0599645i	−0.740299	−	0.672277i	$-0.765316\pi$
$149$	0.614187	−	0.731960i	0.0503162	−	0.0599645i	0.790616	+	0.612313i	$0.209761\pi$
$150$		0			0
$151$	1.04563	+	0.380578i	0.0850921	+	0.0309710i	0.384215	−	0.923243i	$-0.374472\pi$
$151$	1.04563	+	0.380578i	0.0850921	+	0.0309710i	−0.299123	+	0.954214i	$0.596694\pi$
$152$		0			0
$153$	−3.33729	+	8.34349i	−0.269804	+	0.674532i
$154$		0			0
$155$	6.49799	−	1.14577i	0.521931	−	0.0920306i
$156$		0			0
$157$	2.45899	+	6.75603i	0.196249	+	0.539190i	0.998314	−	0.0580471i	$-0.0184873\pi$
$157$	2.45899	+	6.75603i	0.196249	+	0.539190i	−0.802065	+	0.597237i	$0.796265\pi$
$158$		0			0
$159$	11.0459	−	0.791707i	0.875997	−	0.0627864i
$160$		0			0
$161$	−15.2674			−1.20324
$162$		0			0
$163$		−	0.783193i		−	0.0613444i	−0.999529	−	0.0306722i	$-0.990235\pi$
$163$		−	0.783193i		−	0.0613444i	0.999529	−	0.0306722i	$-0.00976480\pi$
$164$		0			0
$165$	−0.554313	−	7.73378i	−0.0431532	−	0.602074i
$166$		0			0
$167$	13.3409	−	4.85570i	1.03235	−	0.375745i	0.230376	−	0.973102i	$-0.426004\pi$
$167$	13.3409	−	4.85570i	1.03235	−	0.375745i	0.801976	+	0.597356i	$0.203782\pi$
$168$		0			0
$169$	2.20304	+	12.4941i	0.169465	+	0.961083i
$170$		0			0
$171$	18.0881	−	14.2335i	1.38323	−	1.08846i
$172$		0			0
$173$	4.11676	−	11.3107i	0.312991	−	0.859937i	−0.679058	−	0.734085i	$-0.737611\pi$
$173$	4.11676	−	11.3107i	0.312991	−	0.859937i	0.992049	−	0.125852i	$-0.0401664\pi$
$174$		0			0
$175$	−3.30060	−	2.76953i	−0.249502	−	0.209357i
$176$		0			0
$177$	−13.2734	+	5.93737i	−0.997690	+	0.446280i
$178$		0			0
$179$	6.41741	+	3.70509i	0.479660	+	0.276932i	0.720275	−	0.693689i	$-0.244016\pi$
$179$	6.41741	+	3.70509i	0.479660	+	0.276932i	−0.240615	+	0.970621i	$0.577349\pi$
$180$		0			0
$181$	−12.0116	+	6.93490i	−0.892815	+	0.515467i	−0.874862	−	0.484372i	$-0.839048\pi$
$181$	−12.0116	+	6.93490i	−0.892815	+	0.515467i	−0.0179527	+	0.999839i	$0.505715\pi$
$182$		0			0
$183$	−0.307180	−	1.22297i	−0.0227074	−	0.0904045i
$184$		0			0
$185$	−1.45382	+	8.24501i	−0.106887	+	0.606185i
$186$		0			0
$187$	−4.84361	−	5.77239i	−0.354200	−	0.422119i
$188$		0			0
$189$	11.2981	−	4.63343i	0.821817	−	0.337033i
$190$		0			0
$191$	6.35332	−	5.33107i	0.459710	−	0.385743i	−0.383314	−	0.923618i	$-0.625217\pi$
$191$	6.35332	−	5.33107i	0.459710	−	0.385743i	0.843024	+	0.537875i	$0.180773\pi$
$192$		0			0
$193$	1.66122	−	9.42126i	0.119577	−	0.678157i	−0.864804	−	0.502109i	$-0.832558\pi$
$193$	1.66122	−	9.42126i	0.119577	−	0.678157i	0.984382	−	0.176048i	$-0.0563314\pi$
$194$		0			0
$195$	0.472552	−	1.65886i	0.0338401	−	0.118794i
$196$		0			0
$197$	12.5364	−	7.23789i	0.893181	−	0.515678i	0.0181995	−	0.999834i	$-0.494207\pi$
$197$	12.5364	−	7.23789i	0.893181	−	0.515678i	0.874982	+	0.484156i	$0.160873\pi$
$198$		0			0
$199$	13.2319	−	22.9183i	0.937983	−	1.62463i	0.168758	−	0.985658i	$-0.446024\pi$
$199$	13.2319	−	22.9183i	0.937983	−	1.62463i	0.769225	−	0.638977i	$-0.220642\pi$
$200$		0			0
$201$	8.04494	+	5.82365i	0.567446	+	0.410768i
$202$		0			0
$203$	−12.2713	+	14.6244i	−0.861278	+	1.02643i
$204$		0			0
$205$	4.51167	−	12.3957i	0.315109	−	0.865755i
$206$		0			0
$207$	−0.612444	+	19.4801i	−0.0425678	+	1.35396i
$208$		0			0
$209$	3.35151	+	19.0074i	0.231829	+	1.31477i
$210$		0			0
$211$	6.13970	+	16.8687i	0.422674	+	1.16129i	0.950170	+	0.311731i	$0.100909\pi$
$211$	6.13970	+	16.8687i	0.422674	+	1.16129i	−0.527496	+	0.849558i	$0.676869\pi$
$212$		0			0
$213$	23.0158	+	11.1761i	1.57702	+	0.765771i
$214$		0			0
$215$	−4.83290			−0.329601
$216$		0			0
$217$	−8.71388			−0.591537
$218$		0			0
$219$	−17.1720	+	11.6262i	−1.16038	+	0.785624i
$220$		0			0
$221$	−0.573326	−	1.57520i	−0.0385661	−	0.105959i
$222$		0			0
$223$	3.13816	+	17.7974i	0.210147	+	1.19180i	0.889132	+	0.457651i	$0.151309\pi$
$223$	3.13816	+	17.7974i	0.210147	+	1.19180i	−0.678985	+	0.734152i	$0.737580\pi$
$224$		0			0
$225$	−3.66612	+	4.10023i	−0.244408	+	0.273348i
$226$		0			0
$227$	2.07372	−	5.69750i	0.137638	−	0.378156i	−0.851655	−	0.524103i	$-0.824401\pi$
$227$	2.07372	−	5.69750i	0.137638	−	0.378156i	0.989292	+	0.145947i	$0.0466229\pi$
$228$		0			0
$229$	−14.8939	+	17.7498i	−0.984215	+	1.17294i	0.000716763		1.00000i	$0.499772\pi$
$229$	−14.8939	+	17.7498i	−0.984215	+	1.17294i	−0.984932	+	0.172942i	$0.944673\pi$
$230$		0			0
$231$	−1.05264	+	10.1855i	−0.0692583	+	0.670156i
$232$		0			0
$233$	4.63643	−	8.03053i	0.303742	−	0.526097i	−0.673238	−	0.739426i	$-0.735097\pi$
$233$	4.63643	−	8.03053i	0.303742	−	0.526097i	0.976981	+	0.213328i	$0.0684305\pi$
$234$		0			0
$235$	0.815853	−	0.471033i	0.0532204	−	0.0307268i
$236$		0			0
$237$	−14.0803	−	14.5300i	−0.914617	−	0.943824i
$238$		0			0
$239$	1.63200	−	9.25552i	0.105565	−	0.598690i	−0.885428	−	0.464777i	$-0.846135\pi$
$239$	1.63200	−	9.25552i	0.105565	−	0.598690i	0.990993	−	0.133913i	$-0.0427543\pi$
$240$		0			0
$241$	−20.4723	+	17.1783i	−1.31873	+	1.10655i	−0.332163	+	0.943222i	$0.607778\pi$
$241$	−20.4723	+	17.1783i	−1.31873	+	1.10655i	−0.986572	+	0.163328i	$0.947777\pi$
$242$		0			0
$243$	−5.45871	−	14.6015i	−0.350176	−	0.936684i
$244$		0			0
$245$	1.68965	+	2.01365i	0.107948	+	0.128647i
$246$		0			0
$247$	−0.745572	+	4.22835i	−0.0474396	+	0.269043i
$248$		0			0
$249$	−9.32409	+	9.03556i	−0.590890	+	0.572605i
$250$		0			0
$251$	0.101849	−	0.0588028i	0.00642868	−	0.00371160i	−0.496782	−	0.867875i	$-0.665485\pi$
$251$	0.101849	−	0.0588028i	0.00642868	−	0.00371160i	0.503211	+	0.864164i	$0.332152\pi$
$252$		0			0
$253$	−14.1535	−	8.17150i	−0.889821	−	0.513738i
$254$		0			0
$255$	0.949074	−	9.18341i	0.0594333	−	0.575087i
$256$		0			0
$257$	−7.73634	−	6.49156i	−0.482580	−	0.404932i	0.368778	−	0.929517i	$-0.379776\pi$
$257$	−7.73634	−	6.49156i	−0.482580	−	0.404932i	−0.851358	+	0.524585i	$0.824221\pi$
$258$		0			0
$259$	3.78160	−	10.3899i	0.234977	−	0.645594i
$260$		0			0
$261$	18.1674	+	16.2440i	1.12454	+	1.00548i
$262$		0			0
$263$	1.42729	+	8.09455i	0.0880104	+	0.499132i	0.996666	+	0.0815860i	$0.0259985\pi$
$263$	1.42729	+	8.09455i	0.0880104	+	0.499132i	−0.908656	+	0.417546i	$0.862890\pi$
$264$		0			0
$265$	−10.6914	+	3.89136i	−0.656769	+	0.239044i
$266$		0			0
$267$	−3.34966	+	2.26786i	−0.204996	+	0.138791i
$268$		0			0
$269$		−	16.5496i		−	1.00905i	−0.863398	−	0.504524i	$-0.831668\pi$
$269$		−	16.5496i		−	1.00905i	0.863398	−	0.504524i	$-0.168332\pi$
$270$		0			0
$271$	−8.76275			−0.532299			−0.266150	−	0.963932i	$-0.585751\pi$
$271$	−8.76275			−0.532299			−0.266150	+	0.963932i	$0.585751\pi$
$272$		0			0
$273$	−0.995010	+	2.04911i	−0.0602208	+	0.124018i
$274$		0			0
$275$	−1.57746	−	4.33403i	−0.0951242	−	0.261352i
$276$		0			0
$277$	5.89916	−	1.04018i	0.354446	−	0.0624985i	0.00640991	−	0.999979i	$-0.497960\pi$
$277$	5.89916	−	1.04018i	0.354446	−	0.0624985i	0.348036	+	0.937481i	$0.386849\pi$
$278$		0			0
$279$	−0.349553	+	11.1183i	−0.0209272	+	0.665635i
$280$		0			0
$281$	10.4464	+	3.80217i	0.623179	+	0.226819i	0.634260	−	0.773120i	$-0.281305\pi$
$281$	10.4464	+	3.80217i	0.623179	+	0.226819i	−0.0110807	+	0.999939i	$0.503527\pi$
$282$		0			0
$283$	−8.16295	+	9.72822i	−0.485237	+	0.578283i	−0.951999	−	0.306100i	$-0.900976\pi$
$283$	−8.16295	+	9.72822i	−0.485237	+	0.578283i	0.466763	+	0.884383i	$0.345420\pi$
$284$		0			0
$285$	−13.8662	+	19.1551i	−0.821363	+	1.13465i
$286$		0			0
$287$	−8.71044	+	15.0869i	−0.514161	+	0.890553i
$288$		0			0
$289$	4.01381	+	6.95213i	0.236107	+	0.408949i
$290$		0			0
$291$	7.01488	−	24.6253i	0.411220	−	1.44356i
$292$		0			0
$293$	−26.3005	−	4.63749i	−1.53649	−	0.270925i	−0.659601	−	0.751616i	$-0.729275\pi$
$293$	−26.3005	−	4.63749i	−1.53649	−	0.270925i	−0.876890	+	0.480691i	$0.840386\pi$
$294$		0			0
$295$	11.4440	−	9.60268i	0.666297	−	0.559089i
$296$		0			0
$297$	12.9537	+	1.75167i	0.751651	+	0.101642i
$298$		0			0
$299$	−2.33694	−	2.78506i	−0.135149	−	0.161064i
$300$		0			0
$301$	6.28555	+	1.10831i	0.362293	+	0.0638821i
$302$		0			0
$303$	−5.17343	−	20.5969i	−0.297206	−	1.18326i
$304$		0			0
$305$	0.647748	+	1.12193i	0.0370900	+	0.0642417i
$306$		0			0
$307$	4.31774	+	2.49285i	0.246426	+	0.142274i	0.618127	−	0.786078i	$-0.287892\pi$
$307$	4.31774	+	2.49285i	0.246426	+	0.142274i	−0.371700	+	0.928353i	$0.621225\pi$
$308$		0			0
$309$	8.19073	+	18.3109i	0.465955	+	1.04167i
$310$		0			0
$311$	12.4172	+	10.4193i	0.704116	+	0.590824i	0.922941	−	0.384940i	$-0.125778\pi$
$311$	12.4172	+	10.4193i	0.704116	+	0.590824i	−0.218825	+	0.975764i	$0.570222\pi$
$312$		0			0
$313$	12.8980	+	4.69448i	0.729037	+	0.265348i	0.679757	−	0.733437i	$-0.262085\pi$
$313$	12.8980	+	4.69448i	0.729037	+	0.265348i	0.0492798	+	0.998785i	$0.484307\pi$
$314$		0			0
$315$	−9.85930	+	7.75829i	−0.555508	+	0.437130i
$316$		0			0
$317$	−5.48493	+	0.967141i	−0.308064	+	0.0543200i	−0.325543	−	0.945527i	$-0.605547\pi$
$317$	−5.48493	+	0.967141i	−0.308064	+	0.0543200i	0.0174789	+	0.999847i	$0.494436\pi$
$318$		0			0
$319$	−19.2033	+	6.98945i	−1.07518	+	0.391334i
$320$		0			0
$321$	−6.82850	+	0.489427i	−0.381129	+	0.0273172i
$322$		0			0
$323$			22.9814i			1.27872i
$324$		0			0
$325$		−	1.02602i		−	0.0569132i
$326$		0			0
$327$	−8.86161	+	0.635149i	−0.490048	+	0.0351238i
$328$		0			0
$329$	−1.16910	+	0.425517i	−0.0644545	+	0.0234595i
$330$		0			0
$331$	22.7828	−	4.01723i	1.25226	−	0.220807i	0.492097	−	0.870541i	$-0.336231\pi$
$331$	22.7828	−	4.01723i	1.25226	−	0.220807i	0.760162	+	0.649734i	$0.225120\pi$
$332$		0			0
$333$	−13.1050	−	5.24184i	−0.718151	−	0.287251i
$334$		0			0
$335$	−9.58825	−	3.48984i	−0.523862	−	0.190670i
$336$		0			0
$337$	3.50303	+	2.93939i	0.190822	+	0.160119i	0.733194	−	0.680020i	$-0.238029\pi$
$337$	3.50303	+	2.93939i	0.190822	+	0.160119i	−0.542371	+	0.840139i	$0.682473\pi$
$338$		0			0
$339$	7.05326	+	15.7680i	0.383080	+	0.856402i
$340$		0			0
$341$	−8.07811	−	4.66390i	−0.437454	−	0.252564i
$342$		0			0
$343$	−9.96098	−	17.2529i	−0.537842	−	0.931570i
$344$		0			0
$345$	−4.87791	−	19.4203i	−0.262618	−	1.04556i
$346$		0			0
$347$	−17.5663	−	3.09741i	−0.943008	−	0.166278i	−0.319052	−	0.947737i	$-0.603364\pi$
$347$	−17.5663	−	3.09741i	−0.943008	−	0.166278i	−0.623956	+	0.781459i	$0.714476\pi$
$348$		0			0
$349$	−11.1052	−	13.2347i	−0.594449	−	0.708436i	0.382006	−	0.924160i	$-0.375233\pi$
$349$	−11.1052	−	13.2347i	−0.594449	−	0.708436i	−0.976454	+	0.215724i	$0.930789\pi$
$350$		0			0
$351$	2.57460	+	1.35176i	0.137422	+	0.0721517i
$352$		0			0
$353$	21.4608	−	18.0078i	1.14225	−	0.958458i	0.142736	−	0.989761i	$-0.454410\pi$
$353$	21.4608	−	18.0078i	1.14225	−	0.958458i	0.999510	+	0.0313029i	$0.00996565\pi$
$354$		0			0
$355$	−25.8872	−	4.56461i	−1.37395	−	0.242265i
$356$		0			0
$357$	−3.34034	+	11.7261i	−0.176790	+	0.620609i
$358$		0			0
$359$	11.9164	+	20.6398i	0.628922	+	1.08932i	0.987768	+	0.155928i	$0.0498369\pi$
$359$	11.9164	+	20.6398i	0.628922	+	1.08932i	−0.358846	+	0.933397i	$0.616830\pi$
$360$		0			0
$361$	19.9317	−	34.5228i	1.04904	−	1.81699i
$362$		0			0
$363$	4.74463	−	6.55435i	0.249028	−	0.344014i
$364$		0			0
$365$	13.6950	−	16.3210i	0.716827	−	0.854281i
$366$		0			0
$367$	0.313629	+	0.114152i	0.0163713	+	0.00595866i	0.350193	−	0.936678i	$-0.386116\pi$
$367$	0.313629	+	0.114152i	0.0163713	+	0.00595866i	−0.333822	+	0.942636i	$0.608338\pi$
$368$		0			0
$369$	18.9004	+	11.7191i	0.983917	+	0.610072i
$370$		0			0
$371$	14.7974	−	2.60918i	0.768242	−	0.135462i
$372$		0			0
$373$	1.23868	+	3.40324i	0.0641364	+	0.176213i	0.967621	−	0.252407i	$-0.0812221\pi$
$373$	1.23868	+	3.40324i	0.0641364	+	0.176213i	−0.903485	+	0.428620i	$0.859000\pi$
$374$		0			0
$375$	9.19993	−	18.9462i	0.475082	−	0.978377i
$376$		0			0
$377$	−4.54611			−0.234137
$378$		0			0
$379$		−	31.7219i		−	1.62944i	−0.579852	−	0.814722i	$-0.696890\pi$
$379$		−	31.7219i		−	1.62944i	0.579852	−	0.814722i	$-0.303110\pi$
$380$		0			0
$381$	28.9635	−	19.6095i	1.48385	−	1.00462i
$382$		0			0
$383$	−15.3087	+	5.57190i	−0.782237	+	0.284711i	−0.702105	−	0.712073i	$-0.747756\pi$
$383$	−15.3087	+	5.57190i	−0.782237	+	0.284711i	−0.0801320	+	0.996784i	$0.525534\pi$
$384$		0			0
$385$	−1.82681	−	10.3604i	−0.0931031	−	0.528014i
$386$		0			0
$387$	1.66627	−	7.97545i	0.0847012	−	0.405415i
$388$		0			0
$389$	−0.814629	+	2.23818i	−0.0413034	+	0.113480i	−0.958630	−	0.284656i	$-0.908121\pi$
$389$	−0.814629	+	2.23818i	−0.0413034	+	0.113480i	0.917326	+	0.398136i	$0.130343\pi$
$390$		0			0
$391$	−14.9071	−	12.5085i	−0.753883	−	0.632583i
$392$		0			0
$393$	2.41339	−	23.3523i	0.121739	−	1.17797i
$394$		0			0
$395$	18.0023	+	10.3936i	0.905794	+	0.522960i
$396$		0			0
$397$	−14.7658	+	8.52506i	−0.741076	+	0.427860i	−0.822460	−	0.568822i	$-0.807399\pi$
$397$	−14.7658	+	8.52506i	−0.741076	+	0.427860i	0.0813844	+	0.996683i	$0.474066\pi$
$398$		0			0
$399$	22.4268	−	21.7328i	1.12274	−	1.08800i
$400$		0			0
$401$	6.89131	−	39.0826i	0.344136	−	1.95169i	0.0395068	−	0.999219i	$-0.487421\pi$
$401$	6.89131	−	39.0826i	0.344136	−	1.95169i	0.304629	−	0.952471i	$-0.401468\pi$
$402$		0			0
$403$	−1.33381	−	1.58958i	−0.0664420	−	0.0791825i
$404$		0			0
$405$	9.50352	+	12.8910i	0.472234	+	0.640558i
$406$		0			0
$407$	9.06661	−	7.60779i	0.449415	−	0.377104i
$408$		0			0
$409$	−1.68450	+	9.55328i	−0.0832932	+	0.472379i	0.914419	+	0.404770i	$0.132648\pi$
$409$	−1.68450	+	9.55328i	−0.0832932	+	0.472379i	−0.997712	+	0.0676096i	$0.978463\pi$
$410$		0			0
$411$	−9.73439	−	10.0452i	−0.480162	−	0.495495i
$412$		0			0
$413$	−17.0860	+	9.86459i	−0.840745	+	0.485405i
$414$		0			0
$415$	6.66974	−	11.5523i	0.327405	−	0.567081i
$416$		0			0
$417$	3.41365	−	33.0310i	0.167167	−	1.61754i
$418$		0			0
$419$	−21.3004	+	25.3848i	−1.04059	+	1.24013i	−0.0704699	+	0.997514i	$0.522450\pi$
$419$	−21.3004	+	25.3848i	−1.04059	+	1.24013i	−0.970122	+	0.242616i	$0.921995\pi$
$420$		0			0
$421$	10.7589	−	29.5598i	0.524355	−	1.44065i	−0.341271	−	0.939965i	$-0.610857\pi$
$421$	10.7589	−	29.5598i	0.524355	−	1.44065i	0.865627	−	0.500690i	$-0.166920\pi$
$422$		0			0
$423$	0.496031	+	1.50875i	0.0241179	+	0.0733582i
$424$		0			0
$425$	−0.953635	−	5.40833i	−0.0462581	−	0.262343i
$426$		0			0
$427$	−0.585156	−	1.60770i	−0.0283177	−	0.0778022i
$428$		0			0
$429$	−2.01915	+	1.36705i	−0.0974854	+	0.0660017i
$430$		0			0
$431$	−9.66850			−0.465715			−0.232858	−	0.972511i	$-0.574808\pi$
$431$	−9.66850			−0.465715			−0.232858	+	0.972511i	$0.574808\pi$
$432$		0			0
$433$	−20.0283			−0.962501			−0.481250	−	0.876583i	$-0.659817\pi$
$433$	−20.0283			−0.962501			−0.481250	+	0.876583i	$0.659817\pi$
$434$		0			0
$435$	−22.5231	−	10.9368i	−1.07990	−	0.524380i
$436$		0			0
$437$	17.0474	+	46.8374i	0.815489	+	2.24054i
$438$		0			0
$439$	−0.0379532	−	0.215244i	−0.00181141	−	0.0102730i	0.983889	−	0.178782i	$-0.0572158\pi$
$439$	−0.0379532	−	0.215244i	−0.00181141	−	0.0102730i	−0.985700	+	0.168509i	$0.946105\pi$
$440$		0			0
$441$	−3.90556	+	2.09408i	−0.185979	+	0.0997180i
$442$		0			0
$443$	−3.15720	+	8.67435i	−0.150003	+	0.412131i	−0.991822	−	0.127630i	$-0.959263\pi$
$443$	−3.15720	+	8.67435i	−0.150003	+	0.412131i	0.841819	+	0.539761i	$0.181485\pi$
$444$		0			0
$445$	2.67141	−	3.18366i	0.126637	−	0.150920i
$446$		0			0
$447$	−1.34060	−	0.970446i	−0.0634082	−	0.0459005i
$448$		0			0
$449$	−20.7878	+	36.0055i	−0.981036	+	1.69920i	−0.322661	+	0.946514i	$0.604578\pi$
$449$	−20.7878	+	36.0055i	−0.981036	+	1.69920i	−0.658375	+	0.752690i	$0.728756\pi$
$450$		0			0
$451$	−16.1498	+	9.32411i	−0.760466	+	0.439055i
$452$		0			0
$453$	0.528018	−	1.85357i	0.0248084	−	0.0870885i
$454$		0			0
$455$	0.406390	−	2.30475i	0.0190519	−	0.108049i
$456$		0			0
$457$	1.23132	−	1.03320i	0.0575986	−	0.0483309i	−0.613534	−	0.789668i	$-0.710253\pi$
$457$	1.23132	−	1.03320i	0.0575986	−	0.0483309i	0.671132	+	0.741337i	$0.265808\pi$
$458$		0			0
$459$	14.8276	+	4.73242i	0.692094	+	0.220891i
$460$		0			0
$461$	−16.0349	−	19.1096i	−0.746819	−	0.890024i	0.250120	−	0.968215i	$-0.419530\pi$
$461$	−16.0349	−	19.1096i	−0.746819	−	0.890024i	−0.996938	+	0.0781909i	$0.975086\pi$
$462$		0			0
$463$	−6.29923	+	35.7247i	−0.292750	+	1.66027i	0.383458	+	0.923558i	$0.374733\pi$
$463$	−6.29923	+	35.7247i	−0.292750	+	1.66027i	−0.676208	+	0.736711i	$0.736378\pi$
$464$		0			0
$465$	−2.78408	−	11.0842i	−0.129108	−	0.514016i
$466$		0			0
$467$	−6.88704	+	3.97623i	−0.318694	+	0.183998i	−0.650810	−	0.759240i	$-0.725571\pi$
$467$	−6.88704	+	3.97623i	−0.318694	+	0.183998i	0.332116	+	0.943238i	$0.392237\pi$
$468$		0			0
$469$	11.6699	+	6.73763i	0.538867	+	0.311115i
$470$		0			0
$471$	11.3674	−	5.08478i	0.523780	−	0.234294i
$472$		0			0
$473$	5.23375	+	4.39164i	0.240648	+	0.201928i
$474$		0			0
$475$	−4.81097	+	13.2180i	−0.220742	+	0.606485i
$476$		0			0
$477$	−2.73553	−	18.9851i	−0.125252	−	0.869267i
$478$		0			0
$479$	−2.84409	−	16.1296i	−0.129950	−	0.736982i	−0.978244	−	0.207457i	$-0.933481\pi$
$479$	−2.84409	−	16.1296i	−0.129950	−	0.736982i	0.848294	−	0.529525i	$-0.177630\pi$
$480$		0			0
$481$	2.47415	−	0.900516i	0.112811	−	0.0410600i
$482$		0			0
$483$	1.89050	+	26.3762i	0.0860206	+	1.20016i
$484$		0			0
$485$			26.3063i			1.19451i
$486$		0			0
$487$	−4.24111			−0.192183			−0.0960914	−	0.995373i	$-0.530634\pi$
$487$	−4.24111			−0.192183			−0.0960914	+	0.995373i	$0.530634\pi$
$488$		0			0
$489$	−1.35306	+	0.0969795i	−0.0611875	+	0.00438557i
$490$		0			0
$491$	−4.31034	−	11.8426i	−0.194523	−	0.534447i	0.803635	−	0.595123i	$-0.202897\pi$
$491$	−4.31034	−	11.8426i	−0.194523	−	0.534447i	−0.998158	+	0.0606758i	$0.980674\pi$
$492$		0			0
$493$	−23.9634	+	4.22540i	−1.07926	+	0.190302i
$494$		0			0
$495$	−13.2924	+	1.91528i	−0.597448	+	0.0860856i
$496$		0			0
$497$	32.6215	+	11.8732i	1.46327	+	0.532588i
$498$		0			0
$499$	10.4544	−	12.4591i	0.468003	−	0.557744i	−0.479479	−	0.877553i	$-0.659174\pi$
$499$	10.4544	−	12.4591i	0.468003	−	0.557744i	0.947482	+	0.319809i	$0.103619\pi$
$500$		0			0
$501$	−10.0408	−	22.4468i	−0.448588	−	1.00285i
$502$		0			0
$503$	17.8227	−	30.8698i	0.794674	−	1.37642i	−0.128372	−	0.991726i	$-0.540975\pi$
$503$	17.8227	−	30.8698i	0.794674	−	1.37642i	0.923046	−	0.384690i	$-0.125692\pi$
$504$		0			0
$505$	10.9092	+	18.8953i	0.485452	+	0.840828i
$506$		0			0
$507$	21.3122	−	5.35311i	0.946509	−	0.237740i
$508$		0			0
$509$	−25.2257	−	4.44797i	−1.11811	−	0.197153i	−0.416099	−	0.909319i	$-0.636603\pi$
$509$	−25.2257	−	4.44797i	−1.11811	−	0.197153i	−0.702010	+	0.712167i	$0.747714\pi$
$510$		0			0
$511$	−21.5542	+	18.0861i	−0.953500	+	0.800082i
$512$		0			0
$513$	−26.8299	−	29.4868i	−1.18457	−	1.30187i
$514$		0			0
$515$	−13.2471	−	15.7873i	−0.583737	−	0.695670i
$516$		0			0
$517$	−1.31155	−	0.231261i	−0.0576818	−	0.0101709i
$518$		0			0
$519$	−20.0503	−	5.71163i	−0.880112	−	0.250713i
$520$		0			0
$521$	1.83496	+	3.17824i	0.0803909	+	0.139241i	0.903418	−	0.428761i	$-0.141050\pi$
$521$	1.83496	+	3.17824i	0.0803909	+	0.139241i	−0.823027	+	0.568002i	$0.807716\pi$
$522$		0			0
$523$	−6.27809	−	3.62466i	−0.274522	−	0.158495i	0.356419	−	0.934326i	$-0.383998\pi$
$523$	−6.27809	−	3.62466i	−0.274522	−	0.158495i	−0.630941	+	0.775831i	$0.717331\pi$
$524$		0			0
$525$	−4.37599	+	6.04511i	−0.190984	+	0.263830i
$526$		0			0
$527$	−8.50823	−	7.13925i	−0.370624	−	0.310991i
$528$		0			0
$529$	−18.0473	−	6.56866i	−0.784663	−	0.285594i
$530$		0			0
$531$	11.9011	+	22.1962i	0.516464	+	0.963232i
$532$		0			0
$533$	−4.08543	+	0.720371i	−0.176959	+	0.0312027i
$534$		0			0
$535$	6.60936	−	2.40561i	0.285747	−	0.104004i
$536$		0			0
$537$	5.60635	−	11.5456i	0.241932	−	0.498231i
$538$		0			0
$539$		−	3.71605i		−	0.160062i
$540$		0			0
$541$		−	45.0694i		−	1.93768i	−0.247679	−	0.968842i	$-0.579668\pi$
$541$		−	45.0694i		−	1.93768i	0.247679	−	0.968842i	$-0.420332\pi$
$542$		0			0
$543$	13.4682	+	19.8927i	0.577976	+	0.853679i
$544$		0			0
$545$	8.57723	−	3.12186i	0.367408	−	0.133726i
$546$		0			0
$547$	−14.7500	+	2.60083i	−0.630666	+	0.111203i	−0.479839	−	0.877357i	$-0.659305\pi$
$547$	−14.7500	+	2.60083i	−0.630666	+	0.111203i	−0.150827	+	0.988560i	$0.548194\pi$
$548$		0			0
$549$	−2.07479	+	0.682125i	−0.0885498	+	0.0291124i
$550$		0			0
$551$	58.5669	+	21.3166i	2.49503	+	0.908118i
$552$		0			0
$553$	−21.0298	−	17.6461i	−0.894278	−	0.750389i
$554$		0			0
$555$	14.4243	+	1.49070i	0.612276	+	0.0632766i
$556$		0			0
$557$	22.1699	+	12.7998i	0.939368	+	0.542344i	0.889762	−	0.456424i	$-0.150870\pi$
$557$	22.1699	+	12.7998i	0.939368	+	0.542344i	0.0496059	+	0.998769i	$0.484203\pi$
$558$		0			0
$559$	0.759937	+	1.31625i	0.0321419	+	0.0556714i
$560$		0			0
$561$	−9.37272	+	9.08268i	−0.395716	+	0.383471i
$562$		0			0
$563$	−8.77498	−	1.54727i	−0.369821	−	0.0652095i	−0.0143510	−	0.999897i	$-0.504568\pi$
$563$	−8.77498	−	1.54727i	−0.369821	−	0.0652095i	−0.355470	+	0.934688i	$0.615679\pi$
$564$		0			0
$565$	−11.4074	−	13.5948i	−0.479914	−	0.571939i
$566$		0			0
$567$	−9.40380	−	18.9451i	−0.394923	−	0.795619i
$568$		0			0
$569$	−16.0670	+	13.4818i	−0.673565	+	0.565188i	−0.914118	−	0.405448i	$-0.867116\pi$
$569$	−16.0670	+	13.4818i	−0.673565	+	0.565188i	0.240553	+	0.970636i	$0.422671\pi$
$570$		0			0
$571$	1.19314	+	0.210382i	0.0499312	+	0.00880422i	0.198558	−	0.980089i	$-0.436374\pi$
$571$	1.19314	+	0.210382i	0.0499312	+	0.00880422i	−0.148627	+	0.988893i	$0.547485\pi$
$572$		0			0
$573$	−9.99676	−	10.3160i	−0.417621	−	0.430957i
$574$		0			0
$575$	−5.95542	−	10.3151i	−0.248358	−	0.430169i
$576$		0			0
$577$	−8.95106	+	15.5037i	−0.372638	+	0.645427i	−0.989970	−	0.141275i	$-0.954880\pi$
$577$	−8.95106	+	15.5037i	−0.372638	+	0.645427i	0.617333	+	0.786702i	$0.288213\pi$
$578$		0			0
$579$	−16.4820	−	1.70336i	−0.684971	−	0.0707894i
$580$		0			0
$581$	−11.3238	+	13.4951i	−0.469788	+	0.559872i
$582$		0			0
$583$	15.1142	+	5.50114i	0.625968	+	0.227834i
$584$		0			0
$585$	−2.92440	−	0.610979i	−0.120909	−	0.0252609i
$586$		0			0
$587$	−4.19636	+	0.739932i	−0.173202	+	0.0305402i	−0.259577	−	0.965723i	$-0.583583\pi$
$587$	−4.19636	+	0.739932i	−0.173202	+	0.0305402i	0.0863743	+	0.996263i	$0.472472\pi$
$588$		0			0
$589$	9.72984	+	26.7325i	0.400911	+	1.10149i
$590$		0			0
$591$	−14.0566	−	20.7619i	−0.578213	−	0.854029i
$592$		0			0
$593$	14.8627			0.610340			0.305170	−	0.952298i	$-0.401287\pi$
$593$	14.8627			0.610340			0.305170	+	0.952298i	$0.401287\pi$
$594$		0			0
$595$		−	12.5265i		−	0.513537i
$596$		0			0
$597$	−41.2325	−	20.0218i	−1.68754	−	0.819437i
$598$		0			0
$599$	−4.35844	+	1.58634i	−0.178081	+	0.0648162i	−0.429522	−	0.903057i	$-0.641318\pi$
$599$	−4.35844	+	1.58634i	−0.178081	+	0.0648162i	0.251441	+	0.967873i	$0.419096\pi$
$600$		0			0
$601$	2.59673	+	14.7268i	0.105923	+	0.600718i	0.990848	+	0.134985i	$0.0430985\pi$
$601$	2.59673	+	14.7268i	0.105923	+	0.600718i	−0.884925	+	0.465734i	$0.845790\pi$
$602$		0			0
$603$	9.06487	−	14.6197i	0.369150	−	0.595361i
$604$		0			0
$605$	−2.84323	+	7.81171i	−0.115594	+	0.317591i
$606$		0			0
$607$	13.7989	+	11.5786i	0.560079	+	0.469962i	0.878337	−	0.478042i	$-0.158653\pi$
$607$	13.7989	+	11.5786i	0.560079	+	0.469962i	−0.318258	+	0.948004i	$0.603098\pi$
$608$		0			0
$609$	26.7849	+	19.3893i	1.08538	+	0.785694i
$610$		0			0
$611$	−0.256573	−	0.148133i	−0.0103798	−	0.00599281i
$612$		0			0
$613$	−26.2514	+	15.1562i	−1.06028	+	0.612155i	−0.925511	−	0.378722i	$-0.876364\pi$
$613$	−26.2514	+	15.1562i	−1.06028	+	0.612155i	−0.134772	+	0.990877i	$0.543030\pi$
$614$		0			0
$615$	−21.9737	−	6.25954i	−0.886067	−	0.252409i
$616$		0			0
$617$	−2.22018	+	12.5913i	−0.0893810	+	0.506905i	0.906944	+	0.421251i	$0.138409\pi$
$617$	−2.22018	+	12.5913i	−0.0893810	+	0.506905i	−0.996325	+	0.0856536i	$0.972702\pi$
$618$		0			0
$619$	−11.8907	−	14.1707i	−0.477926	−	0.569570i	0.472178	−	0.881503i	$-0.343468\pi$
$619$	−11.8907	−	14.1707i	−0.477926	−	0.569570i	−0.950104	+	0.311933i	$0.899023\pi$
$620$		0			0
$621$	33.7300	−	1.35407i	1.35354	−	0.0543369i
$622$		0			0
$623$	−4.20447	+	3.52797i	−0.168448	+	0.141345i
$624$		0			0
$625$	−2.16567	+	12.2821i	−0.0866269	+	0.491286i
$626$		0			0
$627$	32.4225	−	8.14374i	1.29483	−	0.325230i
$628$		0			0
$629$	12.2047	−	7.04640i	0.486634	−	0.280958i
$630$		0			0
$631$	−4.30167	+	7.45072i	−0.171247	+	0.296608i	−0.938856	−	0.344310i	$-0.888113\pi$
$631$	−4.30167	+	7.45072i	−0.171247	+	0.296608i	0.767609	+	0.640918i	$0.221446\pi$
$632$		0			0
$633$	28.3824	−	12.6958i	1.12810	−	0.504614i
$634$		0			0
$635$	−23.0989	+	27.5281i	−0.916650	+	1.09242i
$636$		0			0
$637$	0.282736	−	0.776812i	0.0112024	−	0.0307784i
$638$		0			0
$639$	16.4580	−	41.1464i	0.651069	−	1.62773i
$640$		0			0
$641$	−1.04346	−	5.91773i	−0.0412140	−	0.233736i	0.957242	−	0.289289i	$-0.0934189\pi$
$641$	−1.04346	−	5.91773i	−0.0412140	−	0.233736i	−0.998456	+	0.0555530i	$0.982308\pi$
$642$		0			0
$643$	−8.03942	−	22.0881i	−0.317044	−	0.871070i	−0.991187	−	0.132470i	$-0.957709\pi$
$643$	−8.03942	−	22.0881i	−0.317044	−	0.871070i	0.674143	−	0.738601i	$-0.264513\pi$
$644$		0			0
$645$	0.598438	+	8.34941i	0.0235635	+	0.328758i
$646$		0			0
$647$	10.6875			0.420169			0.210085	−	0.977683i	$-0.432626\pi$
$647$	10.6875			0.420169			0.210085	+	0.977683i	$0.432626\pi$
$648$		0			0
$649$	−21.1191			−0.828998
$650$		0			0
$651$	1.07900	+	15.0543i	0.0422895	+	0.590023i
$652$		0			0
$653$	7.40542	+	20.3462i	0.289796	+	0.796209i	0.996094	+	0.0882946i	$0.0281417\pi$
$653$	7.40542	+	20.3462i	0.289796	+	0.796209i	−0.706298	+	0.707915i	$0.749636\pi$
$654$		0			0
$655$	4.18835	+	23.7533i	0.163653	+	0.928120i
$656$		0			0
$657$	22.2119	+	28.2271i	0.866570	+	1.10124i
$658$		0			0
$659$	6.12164	−	16.8191i	0.238465	−	0.655177i	−0.761510	−	0.648153i	$-0.775542\pi$
$659$	6.12164	−	16.8191i	0.238465	−	0.655177i	0.999975	−	0.00702451i	$-0.00223599\pi$
$660$		0			0
$661$	15.6447	−	18.6447i	0.608510	−	0.725194i	−0.370539	−	0.928817i	$-0.620827\pi$
$661$	15.6447	−	18.6447i	0.608510	−	0.725194i	0.979049	+	0.203623i	$0.0652716\pi$
$662$		0			0
$663$	−2.65035	+	1.18554i	−0.102931	+	0.0460425i
$664$		0			0
$665$	−16.0424	+	27.7863i	−0.622098	+	1.07751i
$666$		0			0
$667$	−45.7045	+	26.3875i	−1.76968	+	1.02173i
$668$		0			0
$669$	30.3586	−	7.62533i	1.17373	−	0.294812i
$670$		0			0
$671$	0.318022	−	1.80359i	0.0122771	−	0.0696270i
$672$		0			0
$673$	7.83345	−	6.57304i	0.301957	−	0.253372i	−0.479201	−	0.877705i	$-0.659074\pi$
$673$	7.83345	−	6.57304i	0.301957	−	0.253372i	0.781158	+	0.624333i	$0.214629\pi$
$674$		0			0
$675$	7.53759	+	5.82595i	0.290122	+	0.224241i
$676$		0			0
$677$	18.4828	+	22.0270i	0.710352	+	0.846565i	0.993656	−	0.112465i	$-0.0358747\pi$
$677$	18.4828	+	22.0270i	0.710352	+	0.846565i	−0.283303	+	0.959030i	$0.591430\pi$
$678$		0			0
$679$	6.03274	−	34.2133i	0.231515	−	1.31299i
$680$		0			0
$681$	−10.0999	−	2.87710i	−0.387028	−	0.110251i
$682$		0			0
$683$	28.1049	−	16.2264i	1.07540	−	0.620885i	0.145751	−	0.989321i	$-0.453440\pi$
$683$	28.1049	−	16.2264i	1.07540	−	0.620885i	0.929653	+	0.368436i	$0.120107\pi$
$684$		0			0
$685$	12.4458	+	7.18559i	0.475530	+	0.274547i
$686$		0			0
$687$	32.5092	+	23.5331i	1.24030	+	0.897842i
$688$		0			0
$689$	2.74096	+	2.29994i	0.104422	+	0.0876208i
$690$		0			0
$691$	9.17035	−	25.1953i	0.348856	−	0.958475i	−0.633875	−	0.773436i	$-0.718537\pi$
$691$	9.17035	−	25.1953i	0.348856	−	0.958475i	0.982731	−	0.185039i	$-0.0592412\pi$
$692$		0			0
$693$	17.7270	+	0.557327i	0.673392	+	0.0211711i
$694$		0			0
$695$	5.92427	+	33.5982i	0.224721	+	1.27445i
$696$		0			0
$697$	−20.8655	+	7.59443i	−0.790338	+	0.287660i
$698$		0			0
$699$	−14.4478	−	7.01559i	−0.546466	−	0.265354i
$700$		0			0
$701$			26.7362i			1.00981i	0.863174	+	0.504907i	$0.168473\pi$
$701$			26.7362i			1.00981i	−0.863174	+	0.504907i	$0.831527\pi$
$702$		0			0
$703$	−36.0966			−1.36141
$704$		0			0
$705$	−0.914789	−	1.35116i	−0.0344529	−	0.0508875i
$706$		0			0
$707$	−9.85503	−	27.0765i	−0.370636	−	1.01832i
$708$		0			0
$709$	41.4005	−	7.30003i	1.55483	−	0.274158i	0.670817	−	0.741623i	$-0.265943\pi$
$709$	41.4005	−	7.30003i	1.55483	−	0.274158i	0.884012	+	0.467464i	$0.154832\pi$
$710$		0			0
$711$	−23.3588	+	26.1247i	−0.876022	+	0.979751i
$712$		0			0
$713$	−22.6361	−	8.23887i	−0.847729	−	0.308548i
$714$		0			0
$715$	1.61030	−	1.91908i	0.0602219	−	0.0717697i
$716$		0			0
$717$	−16.1921	−	1.67340i	−0.604705	−	0.0624942i
$718$		0			0
$719$	−7.75793	+	13.4371i	−0.289322	+	0.501121i	−0.973648	−	0.228056i	$-0.926763\pi$
$719$	−7.75793	+	13.4371i	−0.289322	+	0.501121i	0.684326	+	0.729176i	$0.260097\pi$
$720$		0			0
$721$	13.6084	+	23.5704i	0.506803	+	0.877809i
$722$		0			0
$723$	32.2125	+	33.2412i	1.19800	+	1.23625i
$724$		0			0
$725$	−14.6674	−	2.58626i	−0.544734	−	0.0960512i
$726$		0			0
$727$	6.76072	−	5.67292i	0.250741	−	0.210397i	−0.508750	−	0.860914i	$-0.669892\pi$
$727$	6.76072	−	5.67292i	0.250741	−	0.210397i	0.759491	+	0.650517i	$0.225448\pi$
$728$		0			0
$729$	−24.5498	+	11.2386i	−0.909253	+	0.416245i
$730$		0			0
$731$	5.22917	+	6.23188i	0.193408	+	0.230494i
$732$		0			0
$733$	−17.4479	−	3.07653i	−0.644452	−	0.113634i	−0.158136	−	0.987417i	$-0.550549\pi$
$733$	−17.4479	−	3.07653i	−0.644452	−	0.113634i	−0.486316	+	0.873783i	$0.661660\pi$
$734$		0			0
$735$	3.26960	−	3.16842i	0.120601	−	0.116869i
$736$		0			0
$737$	7.21231	+	12.4921i	0.265669	+	0.460152i
$738$		0			0
$739$	24.2476	+	13.9993i	0.891961	+	0.514974i	0.874583	−	0.484875i	$-0.161135\pi$
$739$	24.2476	+	13.9993i	0.891961	+	0.514974i	0.0173774	+	0.999849i	$0.494468\pi$
$740$		0			0
$741$	7.39729	+	0.764485i	0.271746	+	0.0280841i
$742$		0			0
$743$	0.976314	+	0.819225i	0.0358175	+	0.0300544i	0.660521	−	0.750808i	$-0.270336\pi$
$743$	0.976314	+	0.819225i	0.0358175	+	0.0300544i	−0.624703	+	0.780862i	$0.714780\pi$
$744$		0			0
$745$	1.59778	+	0.581543i	0.0585379	+	0.0213061i
$746$		0			0
$747$	16.7646	+	14.9896i	0.613383	+	0.548442i
$748$		0			0
$749$	−9.14764	+	1.61298i	−0.334247	+	0.0589368i
$750$		0			0
$751$	8.98866	−	3.27161i	0.328001	−	0.119383i	−0.172771	−	0.984962i	$-0.555272\pi$
$751$	8.98866	−	3.27161i	0.328001	−	0.119383i	0.500771	+	0.865580i	$0.333050\pi$
$752$		0			0
$753$	−0.114200	−	0.168676i	−0.00416169	−	0.00614689i
$754$		0			0
$755$			1.98011i			0.0720634i
$756$		0			0
$757$		−	5.24463i		−	0.190619i	−0.995448	−	0.0953096i	$-0.969616\pi$
$757$		−	5.24463i		−	0.190619i	0.995448	−	0.0953096i	$-0.0303841\pi$
$758$		0			0
$759$	−12.3647	+	25.4636i	−0.448810	+	0.924271i
$760$		0			0
$761$	27.2099	−	9.90361i	0.986360	−	0.359006i	0.202050	−	0.979375i	$-0.435240\pi$
$761$	27.2099	−	9.90361i	0.986360	−	0.359006i	0.784310	+	0.620370i	$0.213017\pi$
$762$		0			0
$763$	−11.8713	+	2.09322i	−0.429768	+	0.0757797i
$764$		0			0
$765$	−15.9829	−	0.502496i	−0.577865	−	0.0181678i
$766$		0			0
$767$	−4.41479	−	1.60685i	−0.159409	−	0.0580201i
$768$		0			0
$769$	−31.0584	−	26.0611i	−1.11999	−	0.939786i	−0.121389	−	0.992605i	$-0.538735\pi$
$769$	−31.0584	−	26.0611i	−1.11999	−	0.939786i	−0.998604	+	0.0528190i	$0.983179\pi$
$770$		0			0
$771$	−10.2570	+	14.1693i	−0.369396	+	0.510294i
$772$		0			0
$773$	−8.73768	−	5.04470i	−0.314273	−	0.181445i	0.334564	−	0.942373i	$-0.391411\pi$
$773$	−8.73768	−	5.04470i	−0.314273	−	0.181445i	−0.648837	+	0.760928i	$0.724744\pi$
$774$		0			0
$775$	−3.39906	−	5.88735i	−0.122098	−	0.211480i
$776$		0			0
$777$	−18.4180	−	5.24663i	−0.660741	−	0.188222i
$778$		0			0
$779$	56.0098	+	9.87604i	2.00676	+	0.353846i
$780$		0			0
$781$	23.8865	+	28.4668i	0.854726	+	1.01862i
$782$		0			0
$783$	25.8138	−	33.3978i	0.922511	−	1.19354i
$784$		0			0
$785$	−9.80068	+	8.22375i	−0.349801	+	0.293518i
$786$		0			0
$787$	14.0000	+	2.46858i	0.499046	+	0.0879952i	0.417505	−	0.908675i	$-0.362905\pi$
$787$	14.0000	+	2.46858i	0.499046	+	0.0879952i	0.0815410	+	0.996670i	$0.474016\pi$
$788$		0			0
$789$	13.8076	−	3.46813i	0.491563	−	0.123469i
$790$		0			0
$791$	11.7186	+	20.2971i	0.416664	+	0.721683i
$792$		0			0
$793$	0.203707	−	0.352831i	0.00723385	−	0.0125294i
$794$		0			0
$795$	8.04666	+	17.9888i	0.285386	+	0.637999i
$796$		0			0
$797$	14.0727	−	16.7712i	0.498482	−	0.594068i	−0.456871	−	0.889533i	$-0.651030\pi$
$797$	14.0727	−	16.7712i	0.498482	−	0.594068i	0.955354	+	0.295465i	$0.0954745\pi$
$798$		0			0
$799$	−1.49013	−	0.542363i	−0.0527170	−	0.0191874i
$800$		0			0
$801$	4.33277	+	5.50612i	0.153091	+	0.194549i
$802$		0			0
$803$	−29.6617	+	5.23016i	−1.04674	+	0.184568i
$804$		0			0
$805$	−9.29208	−	25.5298i	−0.327503	−	0.899806i
$806$		0			0
$807$	−28.5914	+	2.04927i	−1.00647	+	0.0721377i
$808$		0			0
$809$	40.9197			1.43866			0.719331	−	0.694668i	$-0.244449\pi$
$809$	40.9197			1.43866			0.719331	+	0.694668i	$0.244449\pi$
$810$		0			0
$811$		−	19.0286i		−	0.668185i	−0.942540	−	0.334093i	$-0.891570\pi$
$811$		−	19.0286i		−	0.668185i	0.942540	−	0.334093i	$-0.108430\pi$
$812$		0			0
$813$	1.08505	+	15.1387i	0.0380545	+	0.530937i
$814$		0			0
$815$	1.30964	−	0.476669i	0.0458746	−	0.0166970i
$816$		0			0
$817$	−3.61830	−	20.5204i	−0.126588	−	0.717918i
$818$		0			0
$819$	3.66329	+	1.46527i	0.128006	+	0.0512005i
$820$		0			0
$821$	4.35542	−	11.9664i	0.152005	−	0.417631i	−0.840195	−	0.542284i	$-0.817560\pi$
$821$	4.35542	−	11.9664i	0.152005	−	0.417631i	0.992200	+	0.124653i	$0.0397818\pi$
$822$		0			0
$823$	−11.3183	−	9.49719i	−0.394531	−	0.331051i	0.423844	−	0.905735i	$-0.360680\pi$
$823$	−11.3183	−	9.49719i	−0.394531	−	0.331051i	−0.818375	+	0.574684i	$0.805125\pi$
$824$		0			0
$825$	−7.29222	+	3.26191i	−0.253882	+	0.113565i
$826$		0			0
$827$	−18.0361	−	10.4132i	−0.627178	−	0.362101i	0.152481	−	0.988306i	$-0.451274\pi$
$827$	−18.0361	−	10.4132i	−0.627178	−	0.362101i	−0.779658	+	0.626205i	$0.784607\pi$
$828$		0			0
$829$	11.5499	−	6.66836i	0.401146	−	0.231602i	−0.285832	−	0.958280i	$-0.592270\pi$
$829$	11.5499	−	6.66836i	0.401146	−	0.231602i	0.686978	+	0.726678i	$0.258937\pi$
$830$		0			0
$831$	−2.52751	−	10.0627i	−0.0876782	−	0.349071i
$832$		0			0
$833$	0.768348	−	4.35752i	0.0266217	−	0.150979i
$834$		0			0
$835$	16.2392	+	19.3531i	0.561980	+	0.669742i
$836$		0			0
$837$	19.2515	−	0.772836i	0.665428	−	0.0267131i
$838$		0			0
$839$	9.48780	−	7.96121i	0.327555	−	0.274852i	−0.464148	−	0.885758i	$-0.653639\pi$
$839$	9.48780	−	7.96121i	0.327555	−	0.274852i	0.791703	+	0.610906i	$0.209195\pi$
$840$		0			0
$841$	−6.42348	+	36.4294i	−0.221499	+	1.25619i
$842$		0			0
$843$	5.27518	−	18.5182i	0.181687	−	0.637800i
$844$		0			0
$845$	−19.5515	+	11.2881i	−0.672592	+	0.388321i
$846$		0			0
$847$	5.48927	−	9.50769i	0.188613	−	0.326688i
$848$		0			0
$849$	17.8174	+	12.8979i	0.611493	+	0.442653i
$850$		0			0
$851$	19.6470	−	23.4143i	0.673489	−	0.802633i
$852$		0			0
$853$	−8.85840	+	24.3382i	−0.303306	+	0.833326i	0.690614	+	0.723223i	$0.257340\pi$
$853$	−8.85840	+	24.3382i	−0.303306	+	0.833326i	−0.993920	+	0.110103i	$0.964882\pi$
$854$		0			0
$855$	34.8098	+	21.5836i	1.19047	+	0.738144i
$856$		0			0
$857$	0.658395	+	3.73394i	0.0224903	+	0.127549i	0.993986	−	0.109509i	$-0.0349279\pi$
$857$	0.658395	+	3.73394i	0.0224903	+	0.127549i	−0.971495	+	0.237058i	$0.923817\pi$
$858$		0			0
$859$	12.7084	+	34.9159i	0.433603	+	1.19132i	0.943585	+	0.331130i	$0.107430\pi$
$859$	12.7084	+	34.9159i	0.433603	+	1.19132i	−0.509982	+	0.860185i	$0.670348\pi$
$860$		0			0
$861$	27.1430	+	13.1802i	0.925032	+	0.449179i
$862$		0			0
$863$	−14.8041			−0.503936			−0.251968	−	0.967736i	$-0.581078\pi$
$863$	−14.8041			−0.503936			−0.251968	+	0.967736i	$0.581078\pi$
$864$		0			0
$865$	21.4190			0.728269
$866$		0			0
$867$	11.5136	−	7.79519i	0.391023	−	0.264739i
$868$		0			0
$869$	−10.0508	−	27.6143i	−0.340950	−	0.936752i
$870$		0			0
$871$	0.557216	+	3.16013i	0.0188805	+	0.107077i
$872$		0			0
$873$	−43.4118	−	9.06979i	−1.46927	−	0.306966i
$874$		0			0
$875$	9.77385	−	26.8534i	0.330416	−	0.907811i
$876$		0			0
$877$	20.8616	−	24.8619i	0.704447	−	0.839527i	−0.288575	−	0.957457i	$-0.593182\pi$
$877$	20.8616	−	24.8619i	0.704447	−	0.839527i	0.993022	+	0.117931i	$0.0376260\pi$
$878$		0			0
$879$	−4.75513	+	46.0115i	−0.160387	+	1.55193i
$880$		0			0
$881$	9.60040	−	16.6284i	0.323446	−	0.560224i	−0.657751	−	0.753235i	$-0.728492\pi$
$881$	9.60040	−	16.6284i	0.323446	−	0.560224i	0.981197	+	0.193011i	$0.0618254\pi$
$882$		0			0
$883$	2.82855	−	1.63307i	0.0951884	−	0.0549571i	−0.451650	−	0.892195i	$-0.649164\pi$
$883$	2.82855	−	1.63307i	0.0951884	−	0.0549571i	0.546839	+	0.837238i	$0.315831\pi$
$884$		0			0
$885$	−18.0068	−	18.5819i	−0.605293	−	0.624622i
$886$		0			0
$887$	−4.93246	+	27.9734i	−0.165616	+	0.939255i	0.782811	+	0.622259i	$0.213785\pi$
$887$	−4.93246	+	27.9734i	−0.165616	+	0.939255i	−0.948427	+	0.316995i	$0.897326\pi$
$888$		0			0
$889$	36.3547	−	30.5052i	1.21930	−	1.02311i
$890$		0			0
$891$	1.42222	−	22.5960i	0.0476461	−	0.756994i
$892$		0			0
$893$	2.61081	+	3.11144i	0.0873674	+	0.104120i
$894$		0			0
$895$	−2.28979	+	12.9861i	−0.0765393	+	0.434076i
$896$		0			0
$897$	−4.52215	+	4.38221i	−0.150990	+	0.146318i
$898$		0			0
$899$	−26.0859	+	15.0607i	−0.870013	+	0.502302i
$900$		0			0
$901$	16.5858	+	9.57584i	0.552555	+	0.319018i
$902$		0			0
$903$	1.13643	−	10.9963i	0.0378180	−	0.365933i
$904$		0			0
$905$	−18.9069	−	15.8648i	−0.628487	−	0.527363i
$906$		0			0
$907$	−3.87326	+	10.6417i	−0.128609	+	0.353351i	−0.987239	−	0.159245i	$-0.949094\pi$
$907$	−3.87326	+	10.6417i	−0.128609	+	0.353351i	0.858630	+	0.512596i	$0.171316\pi$
$908$		0			0
$909$	−34.9430	+	11.4881i	−1.15898	+	0.381038i
$910$		0			0
$911$	1.07530	+	6.09830i	0.0356261	+	0.202046i	0.997426	−	0.0717092i	$-0.0228454\pi$
$911$	1.07530	+	6.09830i	0.0356261	+	0.202046i	−0.961799	+	0.273755i	$0.911734\pi$
$912$		0			0
$913$	−17.7205	+	6.44973i	−0.586463	+	0.213455i
$914$		0			0
$915$	1.85806	−	1.25799i	0.0614257	−	0.0415877i
$916$		0			0
$917$		−	31.8535i		−	1.05190i
$918$		0			0
$919$	−38.3693			−1.26569			−0.632844	−	0.774279i	$-0.718113\pi$
$919$	−38.3693			−1.26569			−0.632844	+	0.774279i	$0.718113\pi$
$920$		0			0
$921$	3.77204	−	7.76809i	0.124293	−	0.255967i
$922$		0			0
$923$	2.82739	+	7.76819i	0.0930646	+	0.255693i
$924$		0			0
$925$	8.49480	−	1.49786i	0.279307	−	0.0492494i
$926$		0			0
$927$	30.6201	−	16.4178i	1.00570	−	0.539232i
$928$		0			0
$929$	−24.3789	−	8.87320i	−0.799846	−	0.291120i	−0.0904233	−	0.995903i	$-0.528822\pi$
$929$	−24.3789	−	8.87320i	−0.799846	−	0.291120i	−0.709423	+	0.704783i	$0.751044\pi$
$930$		0			0
$931$	−7.28491	+	8.68182i	−0.238753	+	0.284535i
$932$		0			0
$933$	16.4630	−	22.7424i	0.538974	−	0.744553i
$934$		0			0
$935$	6.70452	−	11.6126i	0.219261	−	0.379772i
$936$		0			0
$937$	9.82408	+	17.0158i	0.320939	+	0.555882i	0.980682	−	0.195609i	$-0.0626684\pi$
$937$	9.82408	+	17.0158i	0.320939	+	0.555882i	−0.659743	+	0.751491i	$0.729335\pi$
$938$		0			0
$939$	6.51317	−	22.8641i	0.212549	−	0.746141i
$940$		0			0
$941$	13.6658	+	2.40964i	0.445491	+	0.0785520i	0.391894	−	0.920011i	$-0.371820\pi$
$941$	13.6658	+	2.40964i	0.445491	+	0.0785520i	0.0535973	+	0.998563i	$0.482931\pi$
$942$		0			0
$943$	−36.8917	+	30.9558i	−1.20136	+	1.00806i
$944$		0			0
$945$	14.6242	+	16.0724i	0.475725	+	0.522836i
$946$		0			0
$947$	22.0765	+	26.3098i	0.717391	+	0.854953i	0.994375	−	0.105921i	$-0.0337792\pi$
$947$	22.0765	+	26.3098i	0.717391	+	0.854953i	−0.276984	+	0.960875i	$0.589335\pi$
$948$		0			0
$949$	−6.59849	−	1.16349i	−0.214196	−	0.0377685i
$950$		0			0
$951$	2.35003	+	9.35611i	0.0762048	+	0.303393i
$952$		0			0
$953$	7.72473	+	13.3796i	0.250228	+	0.433408i	0.963589	−	0.267389i	$-0.0861609\pi$
$953$	7.72473	+	13.3796i	0.250228	+	0.433408i	−0.713360	+	0.700798i	$0.752828\pi$
$954$		0			0
$955$	12.7813	+	7.37926i	0.413592	+	0.238787i
$956$		0			0
$957$	14.4530	+	32.3106i	0.467198	+	1.04445i
$958$		0			0
$959$	−14.5389	−	12.1996i	−0.469484	−	0.393944i
$960$		0			0
$961$	16.2109	+	5.90028i	0.522932	+	0.190332i
$962$		0			0
$963$	1.69109	+	11.7364i	0.0544945	+	0.378201i
$964$		0			0
$965$	16.7651	−	2.95613i	0.539687	−	0.0951613i
$966$		0			0
$967$	23.1303	−	8.41874i	0.743820	−	0.270728i	0.0578171	−	0.998327i	$-0.481586\pi$
$967$	23.1303	−	8.41874i	0.743820	−	0.270728i	0.686003	+	0.727599i	$0.259364\pi$
$968$		0			0
$969$	39.7031	−	2.84569i	1.27545	−	0.0914168i
$970$		0			0
$971$			14.5202i			0.465977i	0.972480	+	0.232988i	$0.0748504\pi$
$971$			14.5202i			0.465977i	−0.972480	+	0.232988i	$0.925150\pi$
$972$		0			0
$973$		−	45.0556i		−	1.44442i
$974$		0			0
$975$	−1.77257	+	0.127047i	−0.0567675	+	0.00406877i
$976$		0			0
$977$	1.09977	−	0.400283i	0.0351847	−	0.0128062i	−0.324368	−	0.945931i	$-0.605152\pi$
$977$	1.09977	−	0.400283i	0.0351847	−	0.0128062i	0.359553	+	0.933125i	$0.382929\pi$
$978$		0			0
$979$	−5.78596	+	1.02022i	−0.184920	+	0.0326064i
$980$		0			0
$981$	2.19459	+	15.2308i	0.0700679	+	0.486283i
$982$		0			0
$983$	10.8380	+	3.94472i	0.345679	+	0.125817i	0.509025	−	0.860752i	$-0.330006\pi$
$983$	10.8380	+	3.94472i	0.345679	+	0.125817i	−0.163345	+	0.986569i	$0.552228\pi$
$984$		0			0
$985$	19.7330	+	16.5579i	0.628745	+	0.527579i
$986$		0			0
$987$	0.879896	+	1.96707i	0.0280074	+	0.0626124i
$988$		0			0
$989$	15.2801	+	8.82198i	0.485879	+	0.280523i
$990$		0			0
$991$	28.8387	+	49.9500i	0.916091	+	1.58672i	0.805297	+	0.592872i	$0.202006\pi$
$991$	28.8387	+	49.9500i	0.916091	+	1.58672i	0.110794	+	0.993843i	$0.464661\pi$
$992$		0			0
$993$	−9.76135	−	38.8626i	−0.309767	−	1.23327i
$994$		0			0
$995$	46.3767	+	8.17746i	1.47024	+	0.259243i
$996$		0			0
$997$	−1.71942	−	2.04913i	−0.0544547	−	0.0648966i	0.738130	−	0.674659i	$-0.235709\pi$
$997$	−1.71942	−	2.04913i	−0.0544547	−	0.0648966i	−0.792584	+	0.609762i	$0.791265\pi$
$998$		0			0
$999$	−7.43315	+	23.2896i	−0.235175	+	0.736849i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bf.a.49.17		204
4.3	odd	2		216.2.t.a.157.19	✓	204
8.3	odd	2		216.2.t.a.157.34	yes	204
8.5	even	2	inner	864.2.bf.a.49.18		204
12.11	even	2		648.2.t.a.37.16		204
24.11	even	2		648.2.t.a.37.1		204
27.16	even	9	inner	864.2.bf.a.529.18		204
108.11	even	18		648.2.t.a.613.1		204
108.43	odd	18		216.2.t.a.205.34	yes	204
216.11	even	18		648.2.t.a.613.16		204
216.43	odd	18		216.2.t.a.205.19	yes	204
216.205	even	18	inner	864.2.bf.a.529.17		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.157.19	✓	204	4.3	odd	2
216.2.t.a.157.34	yes	204	8.3	odd	2
216.2.t.a.205.19	yes	204	216.43	odd	18
216.2.t.a.205.34	yes	204	108.43	odd	18
648.2.t.a.37.1		204	24.11	even	2
648.2.t.a.37.16		204	12.11	even	2
648.2.t.a.613.1		204	108.11	even	18
648.2.t.a.613.16		204	216.11	even	18
864.2.bf.a.49.17		204	1.1	even	1	trivial
864.2.bf.a.49.18		204	8.5	even	2	inner
864.2.bf.a.529.17		204	216.205	even	18	inner
864.2.bf.a.529.18		204	27.16	even	9	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:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bf (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.123826 - 1.72762i) q^{3} +(0.608623 + 1.67218i) q^{5} +(-0.408085 - 2.31436i) q^{7} +(-2.96933 + 0.427848i) q^{9} +O(q^{10})\)	\(q+(-0.123826 - 1.72762i) q^{3} +(0.608623 + 1.67218i) q^{5} +(-0.408085 - 2.31436i) q^{7} +(-2.96933 + 0.427848i) q^{9} +(0.860398 - 2.36392i) q^{11} +(0.359719 - 0.428697i) q^{13} +(2.81352 - 1.25853i) q^{15} +(1.49770 - 2.59409i) q^{17} +(-6.64437 + 3.83613i) q^{19} +(-3.94781 + 0.991593i) q^{21} +(1.12812 - 6.39788i) q^{23} +(1.40447 - 1.17849i) q^{25} +(1.10684 + 5.07690i) q^{27} +(-5.22169 - 6.22297i) q^{29} +(0.643875 - 3.65160i) q^{31} +(-4.19050 - 1.19372i) q^{33} +(3.62166 - 2.09096i) q^{35} +(4.07450 + 2.35241i) q^{37} +(-0.785167 - 0.568374i) q^{39} +(-5.67863 - 4.76494i) q^{41} +(-0.928888 + 2.55210i) q^{43} +(-2.52264 - 4.70485i) q^{45} +(-0.0919295 - 0.521358i) q^{47} +(1.38810 - 0.505226i) q^{49} +(-4.66705 - 2.26623i) q^{51} +6.39371i q^{53} +4.47656 q^{55} +(7.45011 + 11.0039i) q^{57} +(-2.87131 - 7.88886i) q^{59} +(0.716954 - 0.126418i) q^{61} +(2.20194 + 6.69753i) q^{63} +(0.935790 + 0.340600i) q^{65} +(-3.68574 + 4.39249i) q^{67} +(-11.1928 - 1.15674i) q^{69} +(-7.38597 + 12.7929i) q^{71} +(-5.98642 - 10.3688i) q^{73} +(-2.20989 - 2.28046i) q^{75} +(-5.82210 - 1.02659i) q^{77} +(8.94860 - 7.50876i) q^{79} +(8.63389 - 2.54084i) q^{81} +(-4.81848 - 5.74244i) q^{83} +(5.24930 + 0.925594i) q^{85} +(-10.1043 + 9.79165i) q^{87} +(-1.16774 - 2.02259i) q^{89} +(-1.13896 - 0.657577i) q^{91} +(-6.38830 - 0.660209i) q^{93} +(-10.4586 - 8.77580i) q^{95} +(13.8915 + 5.05610i) q^{97} +(-1.54341 + 7.38740i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 12 q^{7} - 12 q^{9}+O(q^{10}) \) 204 * q + 12 * q^7 - 12 * q^9	\( 204 q + 12 q^{7} - 12 q^{9} + 12 q^{15} - 6 q^{17} + 12 q^{23} - 12 q^{25} + 12 q^{31} + 12 q^{39} - 24 q^{41} + 12 q^{47} - 12 q^{49} + 24 q^{55} - 30 q^{57} + 72 q^{63} - 12 q^{65} + 90 q^{71} - 6 q^{73} + 12 q^{79} - 12 q^{81} + 48 q^{87} - 6 q^{89} + 42 q^{95} - 12 q^{97}+O(q^{100}) \) 204 * q + 12 * q^7 - 12 * q^9 + 12 * q^15 - 6 * q^17 + 12 * q^23 - 12 * q^25 + 12 * q^31 + 12 * q^39 - 24 * q^41 + 12 * q^47 - 12 * q^49 + 24 * q^55 - 30 * q^57 + 72 * q^63 - 12 * q^65 + 90 * q^71 - 6 * q^73 + 12 * q^79 - 12 * q^81 + 48 * q^87 - 6 * q^89 + 42 * q^95 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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