LMFDB - Embedded newform 864.2.y.c.97.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(97,864)]

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, 0, 4]))

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

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

chi := DirichletCharacter("864.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.y (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$54$
Relative dimension:	$9$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			97.2
Character	$\chi$	$=$	864.97
Dual form			864.2.y.c.481.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.53630 - 0.799856i) q^{3} +(-1.92089 - 0.699146i) q^{5} +(-0.00661950 + 0.0375410i) q^{7} +(1.72046 + 2.45764i) q^{9} +O(q^{10})$	\(q+(-1.53630 - 0.799856i) q^{3} +(-1.92089 - 0.699146i) q^{5} +(-0.00661950 + 0.0375410i) q^{7} +(1.72046 + 2.45764i) q^{9} +(-5.36298 + 1.95197i) q^{11} +(1.96898 - 1.65217i) q^{13} +(2.39185 + 2.61053i) q^{15} +(0.997944 + 1.72849i) q^{17} +(1.93731 - 3.35552i) q^{19} +(0.0401970 - 0.0523798i) q^{21} +(1.27263 + 7.21744i) q^{23} +(-0.629218 - 0.527976i) q^{25} +(-0.677388 - 5.15181i) q^{27} +(6.23526 + 5.23200i) q^{29} +(-0.693158 - 3.93110i) q^{31} +(9.80047 + 1.29080i) q^{33} +(0.0389620 - 0.0674841i) q^{35} +(2.51087 + 4.34896i) q^{37} +(-4.34644 + 0.963334i) q^{39} +(8.96178 - 7.51983i) q^{41} +(-0.100025 + 0.0364061i) q^{43} +(-1.58656 - 5.92371i) q^{45} +(0.0551956 - 0.313030i) q^{47} +(6.57648 + 2.39364i) q^{49} +(-0.150602 - 3.45370i) q^{51} +3.69075 q^{53} +11.6664 q^{55} +(-5.66023 + 3.60553i) q^{57} +(-0.773278 - 0.281450i) q^{59} +(-1.23537 + 7.00614i) q^{61} +(-0.103651 + 0.0483195i) q^{63} +(-4.93729 + 1.79703i) q^{65} +(5.70526 - 4.78728i) q^{67} +(3.81777 - 12.1061i) q^{69} +(4.18112 + 7.24192i) q^{71} +(2.32294 - 4.02346i) q^{73} +(0.544364 + 1.31442i) q^{75} +(-0.0377786 - 0.214253i) q^{77} +(9.74225 + 8.17472i) q^{79} +(-3.08003 + 8.45656i) q^{81} +(9.00400 + 7.55525i) q^{83} +(-0.708471 - 4.01794i) q^{85} +(-5.39440 - 13.0253i) q^{87} +(-2.92897 + 5.07312i) q^{89} +(0.0489905 + 0.0848540i) q^{91} +(-2.07941 + 6.59379i) q^{93} +(-6.06736 + 5.09112i) q^{95} +(-8.56104 + 3.11596i) q^{97} +(-14.0240 - 9.82203i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q+O(q^{10}) $ 54 * q	$ 54 q + 9 q^{11} + 12 q^{17} - 18 q^{19} + 12 q^{21} + 21 q^{27} + 6 q^{29} - 36 q^{31} - 9 q^{33} - 24 q^{39} + 3 q^{41} + 21 q^{43} + 42 q^{45} - 18 q^{49} - 24 q^{51} + 36 q^{53} + 72 q^{55} + 39 q^{57} - 18 q^{59} - 18 q^{61} + 30 q^{63} + 48 q^{65} + 27 q^{67} + 24 q^{69} + 84 q^{75} + 36 q^{77} - 72 q^{79} + 36 q^{81} - 6 q^{87} + 33 q^{89} - 36 q^{91} + 72 q^{93} - 36 q^{95} + 9 q^{97} - 120 q^{99}+O(q^{100}) $ 54 * q + 9 * q^11 + 12 * q^17 - 18 * q^19 + 12 * q^21 + 21 * q^27 + 6 * q^29 - 36 * q^31 - 9 * q^33 - 24 * q^39 + 3 * q^41 + 21 * q^43 + 42 * q^45 - 18 * q^49 - 24 * q^51 + 36 * q^53 + 72 * q^55 + 39 * q^57 - 18 * q^59 - 18 * q^61 + 30 * q^63 + 48 * q^65 + 27 * q^67 + 24 * q^69 + 84 * q^75 + 36 * q^77 - 72 * q^79 + 36 * q^81 - 6 * q^87 + 33 * q^89 - 36 * q^91 + 72 * q^93 - 36 * q^95 + 9 * q^97 - 120 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$353$	$703$
$\chi(n)$	$1$	$e\left(\frac{2}{9}\right)$	$1$

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
$3$	−1.53630	−	0.799856i	−0.886986	−	0.461797i
$3$	−1.53630	−	0.799856i	−0.886986	−	0.461797i
$4$		0			0
$5$	−1.92089	−	0.699146i	−0.859047	−	0.312668i	−0.125324	−	0.992116i	$-0.539997\pi$
$5$	−1.92089	−	0.699146i	−0.859047	−	0.312668i	−0.733723	+	0.679448i	$0.762219\pi$
$6$		0			0
$7$	−0.00661950	+	0.0375410i	−0.00250194	+	0.0141892i	−0.986033	−	0.166549i	$-0.946738\pi$
$7$	−0.00661950	+	0.0375410i	−0.00250194	+	0.0141892i	0.983531	+	0.180738i	$0.0578487\pi$
$8$		0			0
$9$	1.72046	+	2.45764i	0.573487	+	0.819215i
$10$		0			0
$11$	−5.36298	+	1.95197i	−1.61700	+	0.588540i	−0.982807	−	0.184635i	$-0.940890\pi$
$11$	−5.36298	+	1.95197i	−1.61700	+	0.588540i	−0.634193	+	0.773175i	$0.718668\pi$
$12$		0			0
$13$	1.96898	−	1.65217i	0.546096	−	0.458229i	−0.327521	−	0.944844i	$-0.606213\pi$
$13$	1.96898	−	1.65217i	0.546096	−	0.458229i	0.873616	+	0.486615i	$0.161769\pi$
$14$		0			0
$15$	2.39185	+	2.61053i	0.617573	+	0.674037i
$16$		0			0
$17$	0.997944	+	1.72849i	0.242037	+	0.419220i	0.961294	−	0.275523i	$-0.0888512\pi$
$17$	0.997944	+	1.72849i	0.242037	+	0.419220i	−0.719257	+	0.694744i	$0.755518\pi$
$18$		0			0
$19$	1.93731	−	3.35552i	0.444450	−	0.769809i	−0.553564	−	0.832807i	$-0.686733\pi$
$19$	1.93731	−	3.35552i	0.444450	−	0.769809i	0.998014	+	0.0629973i	$0.0200660\pi$
$20$		0			0
$21$	0.0401970	−	0.0523798i	0.00877170	−	0.0114302i
$22$		0			0
$23$	1.27263	+	7.21744i	0.265361	+	1.50494i	0.768004	+	0.640445i	$0.221250\pi$
$23$	1.27263	+	7.21744i	0.265361	+	1.50494i	−0.502642	+	0.864494i	$0.667639\pi$
$24$		0			0
$25$	−0.629218	−	0.527976i	−0.125844	−	0.105595i
$26$		0			0
$27$	−0.677388	−	5.15181i	−0.130363	−	0.991466i
$28$		0			0
$29$	6.23526	+	5.23200i	1.15786	+	0.971559i	0.999874	−	0.0158828i	$-0.00505586\pi$
$29$	6.23526	+	5.23200i	1.15786	+	0.971559i	0.157985	+	0.987442i	$0.449500\pi$
$30$		0			0
$31$	−0.693158	−	3.93110i	−0.124495	−	0.706046i	−0.981607	−	0.190915i	$-0.938854\pi$
$31$	−0.693158	−	3.93110i	−0.124495	−	0.706046i	0.857112	−	0.515131i	$-0.172257\pi$
$32$		0			0
$33$	9.80047	+	1.29080i	1.70604	+	0.224700i
$34$		0			0
$35$	0.0389620	−	0.0674841i	0.00658578	−	0.0114069i
$36$		0			0
$37$	2.51087	+	4.34896i	0.412785	+	0.714964i	0.995193	−	0.0979322i	$-0.0312228\pi$
$37$	2.51087	+	4.34896i	0.412785	+	0.714964i	−0.582408	+	0.812896i	$0.697889\pi$
$38$		0			0
$39$	−4.34644	+	0.963334i	−0.695988	+	0.154257i
$40$		0			0
$41$	8.96178	−	7.51983i	1.39959	−	1.17440i	0.438316	−	0.898821i	$-0.355575\pi$
$41$	8.96178	−	7.51983i	1.39959	−	1.17440i	0.961278	−	0.275579i	$-0.0888695\pi$
$42$		0			0
$43$	−0.100025	+	0.0364061i	−0.0152536	+	0.00555187i	−0.349636	−	0.936886i	$-0.613695\pi$
$43$	−0.100025	+	0.0364061i	−0.0152536	+	0.00555187i	0.334382	+	0.942438i	$0.391472\pi$
$44$		0			0
$45$	−1.58656	−	5.92371i	−0.236510	−	0.883055i
$46$		0			0
$47$	0.0551956	−	0.313030i	0.00805110	−	0.0456601i	−0.980518	−	0.196432i	$-0.937065\pi$
$47$	0.0551956	−	0.313030i	0.00805110	−	0.0456601i	0.988569	+	0.150771i	$0.0481758\pi$
$48$		0			0
$49$	6.57648	+	2.39364i	0.939498	+	0.341949i
$50$		0			0
$51$	−0.150602	−	3.45370i	−0.0210885	−	0.483614i
$52$		0			0
$53$	3.69075			0.506964			0.253482	−	0.967340i	$-0.418424\pi$
$53$	3.69075			0.506964			0.253482	+	0.967340i	$0.418424\pi$
$54$		0			0
$55$	11.6664			1.57310
$56$		0			0
$57$	−5.66023	+	3.60553i	−0.749716	+	0.477564i
$58$		0			0
$59$	−0.773278	−	0.281450i	−0.100672	−	0.0366417i	0.291193	−	0.956664i	$-0.405948\pi$
$59$	−0.773278	−	0.281450i	−0.100672	−	0.0366417i	−0.391865	+	0.920023i	$0.628170\pi$
$60$		0			0
$61$	−1.23537	+	7.00614i	−0.158173	+	0.897045i	0.797654	+	0.603115i	$0.206074\pi$
$61$	−1.23537	+	7.00614i	−0.158173	+	0.897045i	−0.955827	+	0.293929i	$0.905037\pi$
$62$		0			0
$63$	−0.103651	+	0.0483195i	−0.0130588	+	0.00608768i
$64$		0			0
$65$	−4.93729	+	1.79703i	−0.612395	+	0.222894i
$66$		0			0
$67$	5.70526	−	4.78728i	0.697008	−	0.584859i	−0.223912	−	0.974609i	$-0.571883\pi$
$67$	5.70526	−	4.78728i	0.697008	−	0.584859i	0.920921	+	0.389750i	$0.127439\pi$
$68$		0			0
$69$	3.81777	−	12.1061i	0.459605	−	1.45740i
$70$		0			0
$71$	4.18112	+	7.24192i	0.496208	+	0.859458i	0.999990	−	0.00437304i	$-0.00139199\pi$
$71$	4.18112	+	7.24192i	0.496208	+	0.859458i	−0.503782	+	0.863831i	$0.668059\pi$
$72$		0			0
$73$	2.32294	−	4.02346i	0.271880	−	0.470910i	−0.697463	−	0.716621i	$-0.745688\pi$
$73$	2.32294	−	4.02346i	0.271880	−	0.470910i	0.969343	+	0.245710i	$0.0790213\pi$
$74$		0			0
$75$	0.544364	+	1.31442i	0.0628578	+	0.151776i
$76$		0			0
$77$	−0.0377786	−	0.214253i	−0.00430527	−	0.0244164i
$78$		0			0
$79$	9.74225	+	8.17472i	1.09609	+	0.919728i	0.997156	−	0.0753661i	$-0.0240125\pi$
$79$	9.74225	+	8.17472i	1.09609	+	0.919728i	0.0989332	+	0.995094i	$0.468457\pi$
$80$		0			0
$81$	−3.08003	+	8.45656i	−0.342226	+	0.939618i
$82$		0			0
$83$	9.00400	+	7.55525i	0.988317	+	0.829297i	0.985323	−	0.170699i	$-0.0546025\pi$
$83$	9.00400	+	7.55525i	0.988317	+	0.829297i	0.00299409	+	0.999996i	$0.499047\pi$
$84$		0			0
$85$	−0.708471	−	4.01794i	−0.0768445	−	0.435807i
$86$		0			0
$87$	−5.39440	−	13.0253i	−0.578341	−	1.39645i
$88$		0			0
$89$	−2.92897	+	5.07312i	−0.310470	+	0.537749i	−0.978464	−	0.206417i	$-0.933820\pi$
$89$	−2.92897	+	5.07312i	−0.310470	+	0.537749i	0.667994	+	0.744166i	$0.267153\pi$
$90$		0			0
$91$	0.0489905	+	0.0848540i	0.00513560	+	0.00889511i
$92$		0			0
$93$	−2.07941	+	6.59379i	−0.215625	+	0.683744i
$94$		0			0
$95$	−6.06736	+	5.09112i	−0.622497	+	0.522337i
$96$		0			0
$97$	−8.56104	+	3.11596i	−0.869242	+	0.316378i	−0.737860	−	0.674954i	$-0.764164\pi$
$97$	−8.56104	+	3.11596i	−0.869242	+	0.316378i	−0.131382	+	0.991332i	$0.541941\pi$
$98$		0			0
$99$	−14.0240	−	9.82203i	−1.40947	−	0.987151i
$100$		0			0
$101$	−0.602270	+	3.41564i	−0.0599281	+	0.339869i	−0.999999	−	0.00110883i	$-0.999647\pi$
$101$	−0.602270	+	3.41564i	−0.0599281	+	0.339869i	0.940071	+	0.340978i	$0.110758\pi$
$102$		0			0
$103$	6.45386	+	2.34901i	0.635917	+	0.231455i	0.639805	−	0.768537i	$-0.279015\pi$
$103$	6.45386	+	2.34901i	0.635917	+	0.231455i	−0.00388743	+	0.999992i	$0.501237\pi$
$104$		0			0
$105$	−0.113835	+	0.0725122i	−0.0111092	+	0.00707646i
$106$		0			0
$107$	−5.39529			−0.521583			−0.260791	−	0.965395i	$-0.583983\pi$
$107$	−5.39529			−0.521583			−0.260791	+	0.965395i	$0.583983\pi$
$108$		0			0
$109$	−14.4830			−1.38722			−0.693610	−	0.720351i	$-0.743981\pi$
$109$	−14.4830			−1.38722			−0.693610	+	0.720351i	$0.743981\pi$
$110$		0			0
$111$	−0.378922	−	8.68966i	−0.0359657	−	0.824786i
$112$		0			0
$113$	−19.8106	−	7.21047i	−1.86362	−	0.678304i	−0.976013	−	0.217711i	$-0.930141\pi$
$113$	−19.8106	−	7.21047i	−1.86362	−	0.678304i	−0.887611	−	0.460593i	$-0.847637\pi$
$114$		0			0
$115$	2.60146	−	14.7536i	0.242588	−	1.37578i
$116$		0			0
$117$	7.44799	+	1.99656i	0.688567	+	0.184582i
$118$		0			0
$119$	−0.0714952	+	0.0260221i	−0.00655395	+	0.00238544i
$120$		0			0
$121$	16.5249	−	13.8661i	1.50227	−	1.26055i
$122$		0			0
$123$	−19.7828	+	4.38460i	−1.78375	+	0.395346i
$124$		0			0
$125$	5.94994	+	10.3056i	0.532179	+	0.921761i
$126$		0			0
$127$	−6.50303	+	11.2636i	−0.577050	+	0.999481i	0.418765	+	0.908095i	$0.362463\pi$
$127$	−6.50303	+	11.2636i	−0.577050	+	0.999481i	−0.995816	+	0.0913860i	$0.970870\pi$
$128$		0			0
$129$	0.182788	+	0.0240747i	0.0160936	+	0.00211966i
$130$		0			0
$131$	−1.07737	−	6.11005i	−0.0941299	−	0.533837i	−0.995010	−	0.0997703i	$-0.968189\pi$
$131$	−1.07737	−	6.11005i	−0.0941299	−	0.533837i	0.900881	−	0.434067i	$-0.142922\pi$
$132$		0			0
$133$	0.113146	+	0.0949405i	0.00981098	+	0.00823239i
$134$		0			0
$135$	−2.30068	+	10.3696i	−0.198011	+	0.892477i
$136$		0			0
$137$	−11.9235	−	10.0050i	−1.01869	−	0.854786i	−0.0292319	−	0.999573i	$-0.509306\pi$
$137$	−11.9235	−	10.0050i	−1.01869	−	0.854786i	−0.989463	+	0.144786i	$0.953751\pi$
$138$		0			0
$139$	2.19123	+	12.4271i	0.185858	+	1.05405i	0.924848	+	0.380336i	$0.124192\pi$
$139$	2.19123	+	12.4271i	0.185858	+	1.05405i	−0.738991	+	0.673716i	$0.764697\pi$
$140$		0			0
$141$	−0.335176	+	0.436760i	−0.0282269	+	0.0367818i
$142$		0			0
$143$	−7.33461	+	12.7039i	−0.613351	+	1.06236i
$144$		0			0
$145$	−8.31930	−	14.4094i	−0.690880	−	1.19664i
$146$		0			0
$147$	−8.18891	−	8.93761i	−0.675410	−	0.737161i
$148$		0			0
$149$	13.5689	−	11.3857i	1.11161	−	0.932752i	0.113460	−	0.993543i	$-0.463807\pi$
$149$	13.5689	−	11.3857i	1.11161	−	0.932752i	0.998151	+	0.0607906i	$0.0193622\pi$
$150$		0			0
$151$	12.7839	−	4.65295i	1.04034	−	0.378652i	0.235330	−	0.971916i	$-0.424383\pi$
$151$	12.7839	−	4.65295i	1.04034	−	0.378652i	0.805008	+	0.593264i	$0.202161\pi$
$152$		0			0
$153$	−2.53109	+	5.42639i	−0.204626	+	0.438697i
$154$		0			0
$155$	−1.41693	+	8.03581i	−0.113811	+	0.645452i
$156$		0			0
$157$	9.36404	+	3.40823i	0.747332	+	0.272007i	0.687483	−	0.726201i	$-0.258716\pi$
$157$	9.36404	+	3.40823i	0.747332	+	0.272007i	0.0598494	+	0.998207i	$0.480938\pi$
$158$		0			0
$159$	−5.67012	−	2.95207i	−0.449669	−	0.234114i
$160$		0			0
$161$	−0.279374			−0.0220178
$162$		0			0
$163$	0.778736			0.0609953			0.0304977	−	0.999535i	$-0.490291\pi$
$163$	0.778736			0.0609953			0.0304977	+	0.999535i	$0.490291\pi$
$164$		0			0
$165$	−17.9231	−	9.33144i	−1.39531	−	0.726452i
$166$		0			0
$167$	4.94525	+	1.79992i	0.382675	+	0.139282i	0.526192	−	0.850366i	$-0.323619\pi$
$167$	4.94525	+	1.79992i	0.382675	+	0.139282i	−0.143518	+	0.989648i	$0.545841\pi$
$168$		0			0
$169$	−1.11021	+	6.29634i	−0.0854011	+	0.484334i
$170$		0			0
$171$	11.5797	−	1.01182i	0.885525	−	0.0773757i
$172$		0			0
$173$	−9.50167	+	3.45832i	−0.722398	+	0.262931i	−0.676944	−	0.736035i	$-0.736696\pi$
$173$	−9.50167	+	3.45832i	−0.722398	+	0.262931i	−0.0454547	+	0.998966i	$0.514474\pi$
$174$		0			0
$175$	0.0239859	−	0.0201265i	0.00181316	−	0.00152142i
$176$		0			0
$177$	0.962870	+	1.05090i	0.0723738	+	0.0789908i
$178$		0			0
$179$	0.325314	+	0.563460i	0.0243151	+	0.0421150i	0.877927	−	0.478795i	$-0.158926\pi$
$179$	0.325314	+	0.563460i	0.0243151	+	0.0421150i	−0.853612	+	0.520910i	$0.825593\pi$
$180$		0			0
$181$	−3.55904	+	6.16443i	−0.264541	+	0.458199i	−0.967443	−	0.253088i	$-0.918554\pi$
$181$	−3.55904	+	6.16443i	−0.264541	+	0.458199i	0.702902	+	0.711286i	$0.251887\pi$
$182$		0			0
$183$	7.50181	−	9.77545i	0.554550	−	0.722622i
$184$		0			0
$185$	−1.78255	−	10.1093i	−0.131055	−	0.743252i
$186$		0			0
$187$	−8.72591	−	7.32191i	−0.638102	−	0.535431i
$188$		0			0
$189$	0.197888	+	0.00867256i	0.0143943	+	0.000630836i
$190$		0			0
$191$	6.78845	+	5.69619i	0.491195	+	0.412162i	0.854454	−	0.519526i	$-0.173892\pi$
$191$	6.78845	+	5.69619i	0.491195	+	0.412162i	−0.363259	+	0.931688i	$0.618336\pi$
$192$		0			0
$193$	0.337268	+	1.91274i	0.0242771	+	0.137682i	0.994537	−	0.104382i	$-0.0332865\pi$
$193$	0.337268	+	1.91274i	0.0242771	+	0.137682i	−0.970260	+	0.242065i	$0.922175\pi$
$194$		0			0
$195$	9.02254	+	1.18834i	0.646118	+	0.0850990i
$196$		0			0
$197$	1.30183	−	2.25484i	0.0927516	−	0.160650i	−0.815916	−	0.578170i	$-0.803767\pi$
$197$	1.30183	−	2.25484i	0.0927516	−	0.160650i	0.908668	+	0.417519i	$0.137100\pi$
$198$		0			0
$199$	−13.6508	−	23.6439i	−0.967681	−	1.67607i	−0.702234	−	0.711947i	$-0.747814\pi$
$199$	−13.6508	−	23.6439i	−0.967681	−	1.67607i	−0.265447	−	0.964125i	$-0.585520\pi$
$200$		0			0
$201$	−12.5941	+	2.79133i	−0.888323	+	0.196885i
$202$		0			0
$203$	−0.237689	+	0.199445i	−0.0166825	+	0.0139983i
$204$		0			0
$205$	−22.4720	+	8.17915i	−1.56951	+	0.571257i
$206$		0			0
$207$	−15.5484	+	15.5450i	−1.08069	+	1.08045i
$208$		0			0
$209$	−3.83990	+	21.7772i	−0.265612	+	1.50636i
$210$		0			0
$211$	20.0187	+	7.28622i	1.37815	+	0.501604i	0.921615	−	0.388104i	$-0.126870\pi$
$211$	20.0187	+	7.28622i	1.37815	+	0.501604i	0.456530	+	0.889708i	$0.349092\pi$
$212$		0			0
$213$	−0.630984	−	14.4701i	−0.0432343	−	0.991474i
$214$		0			0
$215$	0.217590			0.0148395
$216$		0			0
$217$	0.152166			0.0103297
$218$		0			0
$219$	−6.78694	+	4.32323i	−0.458619	+	0.292137i
$220$		0			0
$221$	4.82068	+	1.75458i	0.324274	+	0.118026i
$222$		0			0
$223$	−0.585935	+	3.32300i	−0.0392371	+	0.222525i	−0.998121	−	0.0612740i	$-0.980484\pi$
$223$	−0.585935	+	3.32300i	−0.0392371	+	0.222525i	0.958884	+	0.283799i	$0.0915948\pi$
$224$		0			0
$225$	0.215034	−	2.45476i	0.0143356	−	0.163650i
$226$		0			0
$227$	−19.7280	+	7.18041i	−1.30939	+	0.476580i	−0.900045	−	0.435797i	$-0.856466\pi$
$227$	−19.7280	+	7.18041i	−1.30939	+	0.476580i	−0.409349	+	0.912378i	$0.634244\pi$
$228$		0			0
$229$	−14.7273	+	12.3577i	−0.973210	+	0.816621i	−0.983051	−	0.183331i	$-0.941312\pi$
$229$	−14.7273	+	12.3577i	−0.973210	+	0.816621i	0.00984076	+	0.999952i	$0.496868\pi$
$230$		0			0
$231$	−0.113332	+	0.359375i	−0.00745671	+	0.0236452i
$232$		0			0
$233$	0.180026	+	0.311815i	0.0117939	+	0.0204277i	0.871862	−	0.489751i	$-0.162912\pi$
$233$	0.180026	+	0.311815i	0.0117939	+	0.0204277i	−0.860068	+	0.510179i	$0.829579\pi$
$234$		0			0
$235$	−0.324878	+	0.562705i	−0.0211927	+	0.0367068i
$236$		0			0
$237$	−8.42846	−	20.3513i	−0.547487	−	1.32196i
$238$		0			0
$239$	0.224548	+	1.27348i	0.0145248	+	0.0823744i	0.991209	−	0.132309i	$-0.0422391\pi$
$239$	0.224548	+	1.27348i	0.0145248	+	0.0823744i	−0.976684	+	0.214683i	$0.931128\pi$
$240$		0			0
$241$	13.0556	+	10.9549i	0.840983	+	0.705669i	0.957785	−	0.287486i	$-0.0928196\pi$
$241$	13.0556	+	10.9549i	0.840983	+	0.705669i	−0.116801	+	0.993155i	$0.537264\pi$
$242$		0			0
$243$	11.4959	−	10.5283i	0.737462	−	0.675388i
$244$		0			0
$245$	−10.9592	−	9.19584i	−0.700156	−	0.587501i
$246$		0			0
$247$	−1.72936	−	9.80770i	−0.110037	−	0.624049i
$248$		0			0
$249$	−7.78977	−	18.8091i	−0.493656	−	1.19198i
$250$		0			0
$251$	−3.81263	+	6.60367i	−0.240651	+	0.416820i	−0.960900	−	0.276896i	$-0.910694\pi$
$251$	−3.81263	+	6.60367i	−0.240651	+	0.416820i	0.720249	+	0.693716i	$0.244028\pi$
$252$		0			0
$253$	−20.9133	−	36.2229i	−1.31481	−	2.27731i
$254$		0			0
$255$	−2.12535	+	6.73946i	−0.133094	+	0.422041i
$256$		0			0
$257$	−9.01084	+	7.56099i	−0.562081	+	0.471642i	−0.879007	−	0.476808i	$-0.841794\pi$
$257$	−9.01084	+	7.56099i	−0.562081	+	0.471642i	0.316927	+	0.948450i	$0.397349\pi$
$258$		0			0
$259$	−0.179885	+	0.0654728i	−0.0111775	+	0.00406828i
$260$		0			0
$261$	−2.13089	+	24.3255i	−0.131899	+	1.50571i
$262$		0			0
$263$	5.31836	−	30.1619i	0.327944	−	1.85986i	−0.160179	−	0.987088i	$-0.551207\pi$
$263$	5.31836	−	30.1619i	0.327944	−	1.85986i	0.488123	−	0.872775i	$-0.337682\pi$
$264$		0			0
$265$	−7.08952	−	2.58037i	−0.435506	−	0.158511i
$266$		0			0
$267$	8.55755	−	5.45110i	0.523713	−	0.333602i
$268$		0			0
$269$	29.7829			1.81590			0.907948	−	0.419084i	$-0.137649\pi$
$269$	29.7829			1.81590			0.907948	+	0.419084i	$0.137649\pi$
$270$		0			0
$271$	29.5350			1.79412			0.897060	−	0.441908i	$-0.145698\pi$
$271$	29.5350			1.79412			0.897060	+	0.441908i	$0.145698\pi$
$272$		0			0
$273$	−0.00739327	−	0.169547i	−0.000447461	−	0.0102614i
$274$		0			0
$275$	4.40508	+	1.60332i	0.265636	+	0.0966836i
$276$		0			0
$277$	−4.48813	+	25.4534i	−0.269666	+	1.52935i	0.485747	+	0.874100i	$0.338548\pi$
$277$	−4.48813	+	25.4534i	−0.269666	+	1.52935i	−0.755412	+	0.655250i	$0.772563\pi$
$278$		0			0
$279$	8.46869	−	8.46683i	0.507007	−	0.506896i
$280$		0			0
$281$	−15.1859	+	5.52720i	−0.905913	+	0.329725i	−0.752620	−	0.658455i	$-0.771210\pi$
$281$	−15.1859	+	5.52720i	−0.905913	+	0.329725i	−0.153293	+	0.988181i	$0.548988\pi$
$282$		0			0
$283$	7.29423	−	6.12058i	0.433597	−	0.363831i	−0.399710	−	0.916642i	$-0.630889\pi$
$283$	7.29423	−	6.12058i	0.433597	−	0.363831i	0.833307	+	0.552811i	$0.186445\pi$
$284$		0			0
$285$	13.3935	−	2.96849i	0.793360	−	0.175838i
$286$		0			0
$287$	0.222980	+	0.386212i	0.0131621	+	0.0227974i
$288$		0			0
$289$	6.50822	−	11.2726i	0.382836	−	0.663092i
$290$		0			0
$291$	15.6447	+	2.06053i	0.917108	+	0.120791i
$292$		0			0
$293$	−3.91539	−	22.2053i	−0.228740	−	1.29725i	−0.855405	−	0.517959i	$-0.826692\pi$
$293$	−3.91539	−	22.2053i	−0.228740	−	1.29725i	0.626666	−	0.779288i	$-0.284419\pi$
$294$		0			0
$295$	1.28861	+	1.08127i	0.0750255	+	0.0629539i
$296$		0			0
$297$	13.6890	+	26.3068i	0.794315	+	1.52648i
$298$		0			0
$299$	14.4302	+	12.1084i	0.834520	+	0.700245i
$300$		0			0
$301$	−0.000704607	−	0.00399603i	−4.06129e−5	−	0.000230327i
$302$		0			0
$303$	3.65729	−	4.76574i	0.210106	−	0.273784i
$304$		0			0
$305$	7.27133	−	12.5943i	0.416355	−	0.721148i
$306$		0			0
$307$	5.79272	+	10.0333i	0.330608	+	0.572630i	0.982631	−	0.185569i	$-0.0594128\pi$
$307$	5.79272	+	10.0333i	0.330608	+	0.572630i	−0.652023	+	0.758199i	$0.726080\pi$
$308$		0			0
$309$	−8.03621	−	8.77095i	−0.457164	−	0.498962i
$310$		0			0
$311$	−10.2517	+	8.60218i	−0.581320	+	0.487785i	−0.885380	−	0.464868i	$-0.846102\pi$
$311$	−10.2517	+	8.60218i	−0.581320	+	0.487785i	0.304061	+	0.952653i	$0.401657\pi$
$312$		0			0
$313$	27.8372	−	10.1319i	1.57345	−	0.572690i	0.599685	−	0.800236i	$-0.295293\pi$
$313$	27.8372	−	10.1319i	1.57345	−	0.572690i	0.973767	+	0.227547i	$0.0730705\pi$
$314$		0			0
$315$	0.232885	−	0.0203491i	0.0131216	−	0.00114654i
$316$		0			0
$317$	−1.52636	+	8.65640i	−0.0857287	+	0.486192i	0.911468	+	0.411370i	$0.134950\pi$
$317$	−1.52636	+	8.65640i	−0.0857287	+	0.486192i	−0.997197	+	0.0748212i	$0.976161\pi$
$318$		0			0
$319$	−43.6523	−	15.8881i	−2.44406	−	0.889565i
$320$		0			0
$321$	8.28881	+	4.31546i	0.462636	+	0.240865i
$322$		0			0
$323$	7.73331			0.430293
$324$		0			0
$325$	−2.11122			−0.117109
$326$		0			0
$327$	22.2503	+	11.5843i	1.23044	+	0.640614i
$328$		0			0
$329$	0.0113861	+	0.00414420i	0.000627735	+	0.000228477i
$330$		0			0
$331$	−3.36785	+	19.1001i	−0.185114	+	1.04983i	0.740695	+	0.671842i	$0.234496\pi$
$331$	−3.36785	+	19.1001i	−0.185114	+	1.04983i	−0.925809	+	0.377992i	$0.876615\pi$
$332$		0			0
$333$	−6.36834	+	13.6530i	−0.348983	+	0.748182i
$334$		0			0
$335$	−14.3062	+	5.20702i	−0.781630	+	0.284490i
$336$		0			0
$337$	20.1687	−	16.9236i	1.09866	−	0.921886i	0.101326	−	0.994853i	$-0.467691\pi$
$337$	20.1687	−	16.9236i	1.09866	−	0.921886i	0.997334	+	0.0729676i	$0.0232470\pi$
$338$		0			0
$339$	24.6678	+	26.9231i	1.33977	+	1.46226i
$340$		0			0
$341$	11.3908	+	19.7294i	0.616844	+	1.06841i
$342$		0			0
$343$	−0.266814	+	0.462135i	−0.0144066	+	0.0249529i
$344$		0			0
$345$	−15.7974	+	20.5853i	−0.850505	+	1.10827i
$346$		0			0
$347$	2.24206	+	12.7154i	0.120360	+	0.682597i	0.983956	+	0.178412i	$0.0570959\pi$
$347$	2.24206	+	12.7154i	0.120360	+	0.682597i	−0.863596	+	0.504185i	$0.831793\pi$
$348$		0			0
$349$	−1.85062	−	1.55286i	−0.0990615	−	0.0831225i	0.591912	−	0.806003i	$-0.298373\pi$
$349$	−1.85062	−	1.55286i	−0.0990615	−	0.0831225i	−0.690973	+	0.722880i	$0.742818\pi$
$350$		0			0
$351$	−9.84541	−	9.02464i	−0.525509	−	0.481699i
$352$		0			0
$353$	−11.3212	−	9.49965i	−0.602569	−	0.505615i	0.289701	−	0.957117i	$-0.406444\pi$
$353$	−11.3212	−	9.49965i	−0.602569	−	0.505615i	−0.892270	+	0.451502i	$0.850888\pi$
$354$		0			0
$355$	−2.96831	−	16.8341i	−0.157542	−	0.893463i
$356$		0			0
$357$	0.130652	+	0.0172080i	0.00691485	+	0.000910743i
$358$		0			0
$359$	11.6455	−	20.1707i	0.614628	−	1.06457i	−0.375822	−	0.926692i	$-0.622639\pi$
$359$	11.6455	−	20.1707i	0.614628	−	1.06457i	0.990450	−	0.137875i	$-0.0440272\pi$
$360$		0			0
$361$	1.99365	+	3.45311i	0.104929	+	0.181743i
$362$		0			0
$363$	−36.4782	+	8.08492i	−1.91461	+	0.424348i
$364$		0			0
$365$	−7.27510	+	6.10453i	−0.380796	+	0.319526i
$366$		0			0
$367$	−12.2708	+	4.46620i	−0.640529	+	0.233134i	−0.641808	−	0.766866i	$-0.721815\pi$
$367$	−12.2708	+	4.46620i	−0.640529	+	0.233134i	0.00127837	+	0.999999i	$0.499593\pi$
$368$		0			0
$369$	33.8994	+	9.08731i	1.76473	+	0.473066i
$370$		0			0
$371$	−0.0244309	+	0.138555i	−0.00126839	+	0.00719340i
$372$		0			0
$373$	35.5837	+	12.9514i	1.84246	+	0.670599i	0.988696	+	0.149932i	$0.0479056\pi$
$373$	35.5837	+	12.9514i	1.84246	+	0.670599i	0.853760	+	0.520667i	$0.174317\pi$
$374$		0			0
$375$	−0.897920	−	20.5916i	−0.0463684	−	1.06335i
$376$		0			0
$377$	20.9212			1.07750
$378$		0			0
$379$	2.57968			0.132509			0.0662545	−	0.997803i	$-0.478895\pi$
$379$	2.57968			0.132509			0.0662545	+	0.997803i	$0.478895\pi$
$380$		0			0
$381$	18.9999	−	12.1028i	0.973393	−	0.620045i
$382$		0			0
$383$	−23.3048	−	8.48226i	−1.19082	−	0.433423i	−0.330809	−	0.943698i	$-0.607322\pi$
$383$	−23.3048	−	8.48226i	−1.19082	−	0.433423i	−0.860012	+	0.510275i	$0.829544\pi$
$384$		0			0
$385$	−0.0772257	+	0.437969i	−0.00393579	+	0.0223210i
$386$		0			0
$387$	−0.261562	−	0.183190i	−0.0132959	−	0.00931209i
$388$		0			0
$389$	−20.5154	+	7.46700i	−1.04017	+	0.378592i	−0.804946	−	0.593348i	$-0.797806\pi$
$389$	−20.5154	+	7.46700i	−1.04017	+	0.378592i	−0.235227	+	0.971940i	$0.575583\pi$
$390$		0			0
$391$	−11.2052	+	9.40232i	−0.566674	+	0.475496i
$392$		0			0
$393$	−3.23200	+	10.2486i	−0.163033	+	0.516975i
$394$		0			0
$395$	−12.9985	−	22.5140i	−0.654023	−	1.13280i
$396$		0			0
$397$	5.51957	−	9.56018i	0.277019	−	0.479812i	−0.693623	−	0.720338i	$-0.743987\pi$
$397$	5.51957	−	9.56018i	0.277019	−	0.479812i	0.970643	+	0.240526i	$0.0773201\pi$
$398$		0			0
$399$	−0.0978874	−	0.236358i	−0.00490050	−	0.0118327i
$400$		0			0
$401$	−2.87214	−	16.2887i	−0.143428	−	0.813420i	−0.968616	−	0.248562i	$-0.920042\pi$
$401$	−2.87214	−	16.2887i	−0.143428	−	0.813420i	0.825188	−	0.564858i	$-0.191069\pi$
$402$		0			0
$403$	−7.85964	−	6.59502i	−0.391517	−	0.328522i
$404$		0			0
$405$	11.8288	−	14.0907i	0.587776	−	0.700173i
$406$		0			0
$407$	−21.9548	−	18.4223i	−1.08826	−	0.913157i
$408$		0			0
$409$	3.15671	+	17.9026i	0.156089	+	0.885227i	0.957783	+	0.287492i	$0.0928214\pi$
$409$	3.15671	+	17.9026i	0.156089	+	0.885227i	−0.801694	+	0.597735i	$0.796067\pi$
$410$		0			0
$411$	10.3156	+	24.9079i	0.508830	+	1.22861i
$412$		0			0
$413$	0.0156846	−	0.0271666i	0.000771791	−	0.00133678i
$414$		0			0
$415$	−12.0134	−	20.8079i	−0.589717	−	1.02142i
$416$		0			0
$417$	6.57348	−	20.8444i	0.321905	−	1.02076i
$418$		0			0
$419$	27.9860	−	23.4831i	1.36721	−	1.14722i	0.393524	−	0.919314i	$-0.371256\pi$
$419$	27.9860	−	23.4831i	1.36721	−	1.14722i	0.973683	−	0.227908i	$-0.0731887\pi$
$420$		0			0
$421$	−4.67413	+	1.70124i	−0.227803	+	0.0829135i	−0.453400	−	0.891307i	$-0.649789\pi$
$421$	−4.67413	+	1.70124i	−0.227803	+	0.0829135i	0.225597	+	0.974221i	$0.427567\pi$
$422$		0			0
$423$	0.864277	−	0.402904i	0.0420226	−	0.0195899i
$424$		0			0
$425$	0.284677	−	1.61449i	0.0138089	−	0.0783141i
$426$		0			0
$427$	−0.254840	−	0.0927543i	−0.0123326	−	0.00448870i
$428$		0			0
$429$	21.4295	−	13.6505i	1.03463	−	0.659050i
$430$		0			0
$431$	24.2877			1.16990			0.584949	−	0.811070i	$-0.301114\pi$
$431$	24.2877			1.16990			0.584949	+	0.811070i	$0.301114\pi$
$432$		0			0
$433$	−26.5015			−1.27358			−0.636790	−	0.771037i	$-0.719738\pi$
$433$	−26.5015			−1.27358			−0.636790	+	0.771037i	$0.719738\pi$
$434$		0			0
$435$	1.25549	+	28.7915i	0.0601959	+	1.38045i
$436$		0			0
$437$	26.6837	+	9.71209i	1.27646	+	0.464592i
$438$		0			0
$439$	−5.10368	+	28.9444i	−0.243585	+	1.38144i	0.580170	+	0.814496i	$0.302986\pi$
$439$	−5.10368	+	28.9444i	−0.243585	+	1.38144i	−0.823755	+	0.566946i	$0.808125\pi$
$440$		0			0
$441$	5.43185	+	20.2808i	0.258660	+	0.965754i
$442$		0			0
$443$	14.4391	−	5.25542i	0.686025	−	0.249693i	0.0245924	−	0.999698i	$-0.492171\pi$
$443$	14.4391	−	5.25542i	0.686025	−	0.249693i	0.661432	+	0.750005i	$0.269949\pi$
$444$		0			0
$445$	9.17306	−	7.69711i	0.434845	−	0.364878i
$446$		0			0
$447$	−29.9529	+	6.63868i	−1.41672	+	0.313999i
$448$		0			0
$449$	7.81175	+	13.5303i	0.368659	+	0.638536i	0.989356	−	0.145514i	$-0.0464836\pi$
$449$	7.81175	+	13.5303i	0.368659	+	0.638536i	−0.620697	+	0.784051i	$0.713150\pi$
$450$		0			0
$451$	−33.3834	+	57.8218i	−1.57196	+	2.72272i
$452$		0			0
$453$	−23.3616	−	3.07692i	−1.09763	−	0.144566i
$454$		0			0
$455$	−0.0347799	−	0.197246i	−0.00163051	−	0.00924705i
$456$		0			0
$457$	5.57252	+	4.67590i	0.260672	+	0.218729i	0.763751	−	0.645511i	$-0.223355\pi$
$457$	5.57252	+	4.67590i	0.260672	+	0.218729i	−0.503080	+	0.864240i	$0.667800\pi$
$458$		0			0
$459$	8.22885	−	6.31207i	0.384090	−	0.294622i
$460$		0			0
$461$	24.0778	+	20.2037i	1.12141	+	0.940978i	0.998675	−	0.0514612i	$-0.0163878\pi$
$461$	24.0778	+	20.2037i	1.12141	+	0.940978i	0.122739	+	0.992439i	$0.460832\pi$
$462$		0			0
$463$	2.81969	+	15.9913i	0.131042	+	0.743178i	0.977534	+	0.210776i	$0.0675991\pi$
$463$	2.81969	+	15.9913i	0.131042	+	0.743178i	−0.846492	+	0.532401i	$0.821290\pi$
$464$		0			0
$465$	8.60433	−	11.2121i	0.399016	−	0.519949i
$466$		0			0
$467$	13.2799	−	23.0015i	0.614523	−	1.06438i	−0.375945	−	0.926642i	$-0.622682\pi$
$467$	13.2799	−	23.0015i	0.614523	−	1.06438i	0.990468	−	0.137743i	$-0.0439847\pi$
$468$		0			0
$469$	0.141954	+	0.245871i	0.00655481	+	0.0113533i
$470$		0			0
$471$	−11.6599	−	12.7260i	−0.537261	−	0.586382i
$472$		0			0
$473$	0.465368	−	0.390490i	0.0213977	−	0.0179548i
$474$		0			0
$475$	−2.99063	+	1.08850i	−0.137219	+	0.0499437i
$476$		0			0
$477$	6.34979	+	9.07056i	0.290737	+	0.415312i
$478$		0			0
$479$	1.67683	−	9.50978i	0.0766164	−	0.434513i	−0.922236	−	0.386626i	$-0.873640\pi$
$479$	1.67683	−	9.50978i	0.0766164	−	0.434513i	0.998853	−	0.0478865i	$-0.0152486\pi$
$480$		0			0
$481$	12.1291	+	4.41462i	0.553037	+	0.201289i
$482$		0			0
$483$	0.429204	+	0.223459i	0.0195295	+	0.0101677i
$484$		0			0
$485$	18.6233			0.845641
$486$		0			0
$487$	8.59605			0.389524			0.194762	−	0.980851i	$-0.437607\pi$
$487$	8.59605			0.389524			0.194762	+	0.980851i	$0.437607\pi$
$488$		0			0
$489$	−1.19638	−	0.622877i	−0.0541020	−	0.0281675i
$490$		0			0
$491$	22.2984	+	8.11594i	1.00631	+	0.366267i	0.792015	−	0.610501i	$-0.209032\pi$
$491$	22.2984	+	8.11594i	1.00631	+	0.366267i	0.214296	+	0.976769i	$0.431254\pi$
$492$		0			0
$493$	−2.82102	+	15.9988i	−0.127053	+	0.720551i
$494$		0			0
$495$	20.0716	+	28.6719i	0.902150	+	1.28870i
$496$		0			0
$497$	−0.299546	+	0.109026i	−0.0134365	+	0.00489048i
$498$		0			0
$499$	−22.2988	+	18.7109i	−0.998231	+	0.837615i	−0.986738	−	0.162319i	$-0.948103\pi$
$499$	−22.2988	+	18.7109i	−0.998231	+	0.837615i	−0.0114924	+	0.999934i	$0.503658\pi$
$500$		0			0
$501$	−6.15772	−	6.72072i	−0.275107	−	0.300259i
$502$		0			0
$503$	−1.24365	−	2.15407i	−0.0554517	−	0.0960452i	0.836967	−	0.547253i	$-0.184327\pi$
$503$	−1.24365	−	2.15407i	−0.0554517	−	0.0960452i	−0.892419	+	0.451208i	$0.850993\pi$
$504$		0			0
$505$	3.54493	−	6.13999i	0.157747	−	0.273226i
$506$		0			0
$507$	6.74180	−	8.78508i	0.299414	−	0.390159i
$508$		0			0
$509$	−2.03659	−	11.5501i	−0.0902702	−	0.511948i	−0.996094	−	0.0882940i	$-0.971858\pi$
$509$	−2.03659	−	11.5501i	−0.0902702	−	0.511948i	0.905824	−	0.423654i	$-0.139253\pi$
$510$		0			0
$511$	0.135668	+	0.113839i	0.00600160	+	0.00503594i
$512$		0			0
$513$	−18.5993	−	7.70767i	−0.821180	−	0.340302i
$514$		0			0
$515$	−10.7548	−	9.02438i	−0.473915	−	0.397661i
$516$		0			0
$517$	0.315010	+	1.78651i	0.0138541	+	0.0785707i
$518$		0			0
$519$	17.3636	+	2.28693i	0.762178	+	0.100385i
$520$		0			0
$521$	3.34698	−	5.79714i	0.146634	−	0.253977i	−0.783347	−	0.621584i	$-0.786489\pi$
$521$	3.34698	−	5.79714i	0.146634	−	0.253977i	0.929981	+	0.367607i	$0.119823\pi$
$522$		0			0
$523$	−16.7185	−	28.9573i	−0.731048	−	1.26621i	−0.956436	−	0.291943i	$-0.905698\pi$
$523$	−16.7185	−	28.9573i	−0.731048	−	1.26621i	0.225388	−	0.974269i	$-0.427635\pi$
$524$		0			0
$525$	−0.0529480	+	0.0117352i	−0.00231084	+	0.000512168i
$526$		0			0
$527$	6.10312	−	5.12113i	0.265856	−	0.223080i
$528$		0			0
$529$	−28.8589	+	10.5038i	−1.25473	+	0.456686i
$530$		0			0
$531$	−0.638689	−	2.38467i	−0.0277168	−	0.103486i
$532$		0			0
$533$	5.22152	−	29.6127i	0.226169	−	1.28267i
$534$		0			0
$535$	10.3638	+	3.77210i	0.448064	+	0.163082i
$536$		0			0
$537$	−0.0490939	−	1.12585i	−0.00211856	−	0.0485840i
$538$		0			0
$539$	−39.9419			−1.72042
$540$		0			0
$541$	2.45591			0.105588			0.0527939	−	0.998605i	$-0.483187\pi$
$541$	2.45591			0.105588			0.0527939	+	0.998605i	$0.483187\pi$
$542$		0			0
$543$	10.3984	−	6.62372i	0.446239	−	0.284251i
$544$		0			0
$545$	27.8202	+	10.1257i	1.19169	+	0.433739i
$546$		0			0
$547$	6.20864	−	35.2109i	0.265462	−	1.50551i	−0.502254	−	0.864720i	$-0.667496\pi$
$547$	6.20864	−	35.2109i	0.265462	−	1.50551i	0.767716	−	0.640790i	$-0.221393\pi$
$548$		0			0
$549$	−19.3440	+	9.01768i	−0.825583	+	0.384865i
$550$		0			0
$551$	29.6357	−	10.7865i	1.26252	−	0.459521i
$552$		0			0
$553$	−0.371376	+	0.311622i	−0.0157925	+	0.0132515i
$554$		0			0
$555$	−5.34747	+	16.9568i	−0.226988	+	0.719775i
$556$		0			0
$557$	6.36407	+	11.0229i	0.269654	+	0.467055i	0.968773	−	0.247951i	$-0.0797573\pi$
$557$	6.36407	+	11.0229i	0.269654	+	0.467055i	−0.699118	+	0.715006i	$0.746424\pi$
$558$		0			0
$559$	−0.136798	+	0.236941i	−0.00578593	+	0.0100215i
$560$		0			0
$561$	7.54918	+	18.2281i	0.318726	+	0.769593i
$562$		0			0
$563$	−3.57005	−	20.2468i	−0.150460	−	0.853300i	−0.962820	−	0.270144i	$-0.912929\pi$
$563$	−3.57005	−	20.2468i	−0.150460	−	0.853300i	0.812360	−	0.583156i	$-0.198182\pi$
$564$		0			0
$565$	33.0128	+	27.7010i	1.38886	+	1.16539i
$566$		0			0
$567$	−0.297080	−	0.171606i	−0.0124762	−	0.00720677i
$568$		0			0
$569$	−8.97725	−	7.53280i	−0.376346	−	0.315792i	0.434920	−	0.900469i	$-0.356777\pi$
$569$	−8.97725	−	7.53280i	−0.376346	−	0.315792i	−0.811266	+	0.584677i	$0.801221\pi$
$570$		0			0
$571$	3.26958	+	18.5427i	0.136828	+	0.775988i	0.973570	+	0.228391i	$0.0733464\pi$
$571$	3.26958	+	18.5427i	0.136828	+	0.775988i	−0.836742	+	0.547598i	$0.815542\pi$
$572$		0			0
$573$	−5.87300	−	14.1809i	−0.245348	−	0.592414i
$574$		0			0
$575$	3.00988	−	5.21326i	0.125520	−	0.217408i
$576$		0			0
$577$	−17.2881	−	29.9439i	−0.719713	−	1.24658i	−0.961113	−	0.276154i	$-0.910940\pi$
$577$	−17.2881	−	29.9439i	−0.719713	−	1.24658i	0.241400	−	0.970426i	$-0.422393\pi$
$578$		0			0
$579$	1.01177	−	3.20832i	0.0420479	−	0.133333i
$580$		0			0
$581$	−0.343234	+	0.288008i	−0.0142397	+	0.0119486i
$582$		0			0
$583$	−19.7934	+	7.20422i	−0.819761	+	0.298368i
$584$		0			0
$585$	−12.9109	−	9.04239i	−0.533798	−	0.373857i
$586$		0			0
$587$	−2.07356	+	11.7597i	−0.0855849	+	0.485376i	0.911644	+	0.410981i	$0.134814\pi$
$587$	−2.07356	+	11.7597i	−0.0855849	+	0.485376i	−0.997229	+	0.0743951i	$0.976297\pi$
$588$		0			0
$589$	−14.5337	−	5.28985i	−0.598852	−	0.217964i
$590$		0			0
$591$	−3.80355	+	2.42284i	−0.156457	+	0.0996622i
$592$		0			0
$593$	−0.264556			−0.0108640			−0.00543201	−	0.999985i	$-0.501729\pi$
$593$	−0.264556			−0.0108640			−0.00543201	+	0.999985i	$0.501729\pi$
$594$		0			0
$595$	0.155527			0.00637600
$596$		0			0
$597$	2.06008	+	47.2429i	0.0843134	+	1.93352i
$598$		0			0
$599$	−16.5692	−	6.03069i	−0.676999	−	0.246407i	−0.0194404	−	0.999811i	$-0.506188\pi$
$599$	−16.5692	−	6.03069i	−0.676999	−	0.246407i	−0.657558	+	0.753404i	$0.728411\pi$
$600$		0			0
$601$	−5.92209	+	33.5858i	−0.241567	+	1.36999i	0.586765	+	0.809757i	$0.300401\pi$
$601$	−5.92209	+	33.5858i	−0.241567	+	1.36999i	−0.828332	+	0.560237i	$0.810710\pi$
$602$		0			0
$603$	21.5811	+	5.78517i	0.878851	+	0.235590i
$604$		0			0
$605$	−41.4369	+	15.0818i	−1.68465	+	0.613163i
$606$		0			0
$607$	−6.47573	+	5.43379i	−0.262842	+	0.220551i	−0.764679	−	0.644412i	$-0.777102\pi$
$607$	−6.47573	+	5.43379i	−0.262842	+	0.220551i	0.501837	+	0.864962i	$0.332658\pi$
$608$		0			0
$609$	0.524690	−	0.116291i	0.0212615	−	0.00471234i
$610$		0			0
$611$	−0.408499	−	0.707540i	−0.0165261	−	0.0286240i
$612$		0			0
$613$	0.983845	−	1.70407i	0.0397371	−	0.0688267i	−0.845473	−	0.534018i	$-0.820681\pi$
$613$	0.983845	−	1.70407i	0.0397371	−	0.0688267i	0.885210	+	0.465192i	$0.154015\pi$
$614$		0			0
$615$	41.0660	+	5.40873i	1.65594	+	0.218101i
$616$		0			0
$617$	−6.83634	−	38.7708i	−0.275221	−	1.56085i	−0.738260	−	0.674516i	$-0.764352\pi$
$617$	−6.83634	−	38.7708i	−0.275221	−	1.56085i	0.463039	−	0.886338i	$-0.346759\pi$
$618$		0			0
$619$	−7.18784	−	6.03132i	−0.288904	−	0.242419i	0.486804	−	0.873511i	$-0.338163\pi$
$619$	−7.18784	−	6.03132i	−0.288904	−	0.242419i	−0.775708	+	0.631092i	$0.782607\pi$
$620$		0			0
$621$	36.3208	−	11.4453i	1.45750	−	0.459286i
$622$		0			0
$623$	−0.171062	−	0.143538i	−0.00685345	−	0.00575073i
$624$		0			0
$625$	−3.51089	−	19.9112i	−0.140436	−	0.796449i
$626$		0			0
$627$	23.3179	−	30.3850i	0.931226	−	1.21346i
$628$		0			0
$629$	−5.01142	+	8.68003i	−0.199818	+	0.346095i
$630$		0			0
$631$	−10.5400	−	18.2558i	−0.419590	−	0.726751i	0.576308	−	0.817232i	$-0.304493\pi$
$631$	−10.5400	−	18.2558i	−0.419590	−	0.726751i	−0.995898	+	0.0904812i	$0.971159\pi$
$632$		0			0
$633$	−24.9269	−	27.2059i	−0.990756	−	1.08134i
$634$		0			0
$635$	20.3665	−	17.0895i	0.808219	−	0.678176i
$636$		0			0
$637$	16.9036	−	6.15242i	0.669747	−	0.243768i
$638$		0			0
$639$	−10.6046	+	22.7351i	−0.419512	+	0.899389i
$640$		0			0
$641$	−5.90976	+	33.5159i	−0.233421	+	1.32380i	0.612491	+	0.790477i	$0.290167\pi$
$641$	−5.90976	+	33.5159i	−0.233421	+	1.32380i	−0.845913	+	0.533321i	$0.820944\pi$
$642$		0			0
$643$	27.1317	+	9.87514i	1.06997	+	0.389437i	0.816166	−	0.577818i	$-0.196096\pi$
$643$	27.1317	+	9.87514i	1.06997	+	0.389437i	0.253805	+	0.967255i	$0.418318\pi$
$644$		0			0
$645$	−0.334284	−	0.174040i	−0.0131624	−	0.00685284i
$646$		0			0
$647$	27.8771			1.09596			0.547981	−	0.836491i	$-0.315397\pi$
$647$	27.8771			1.09596			0.547981	+	0.836491i	$0.315397\pi$
$648$		0			0
$649$	4.69646			0.184352
$650$		0			0
$651$	−0.233773	−	0.121711i	−0.00916228	−	0.00477022i
$652$		0			0
$653$	−21.1370	−	7.69326i	−0.827157	−	0.301060i	−0.106465	−	0.994316i	$-0.533953\pi$
$653$	−21.1370	−	7.69326i	−0.827157	−	0.301060i	−0.720691	+	0.693256i	$0.756175\pi$
$654$		0			0
$655$	−2.20232	+	12.4900i	−0.0860516	+	0.488023i
$656$		0			0
$657$	13.8848	−	1.21323i	0.541696	−	0.0473325i
$658$		0			0
$659$	25.6899	−	9.35037i	1.00074	−	0.364239i	0.210869	−	0.977514i	$-0.432371\pi$
$659$	25.6899	−	9.35037i	1.00074	−	0.364239i	0.789869	+	0.613276i	$0.210149\pi$
$660$		0			0
$661$	19.9463	−	16.7369i	0.775820	−	0.650990i	−0.166373	−	0.986063i	$-0.553205\pi$
$661$	19.9463	−	16.7369i	0.775820	−	0.650990i	0.942192	+	0.335073i	$0.108761\pi$
$662$		0			0
$663$	−6.00262	−	6.55143i	−0.233122	−	0.254436i
$664$		0			0
$665$	−0.150963	−	0.261475i	−0.00585409	−	0.0101396i
$666$		0			0
$667$	−29.8265	+	51.6610i	−1.15489	+	2.00032i
$668$		0			0
$669$	3.55810	−	4.63648i	0.137564	−	0.179257i
$670$		0			0
$671$	−7.05048	−	39.9852i	−0.272181	−	1.54361i
$672$		0			0
$673$	−24.9038	−	20.8968i	−0.959972	−	0.805512i	0.0209763	−	0.999780i	$-0.493323\pi$
$673$	−24.9038	−	20.8968i	−0.959972	−	0.805512i	−0.980949	+	0.194268i	$0.937767\pi$
$674$		0			0
$675$	−2.29381	+	3.59925i	−0.0882888	+	0.138535i
$676$		0			0
$677$	16.6158	+	13.9423i	0.638597	+	0.535846i	0.903587	−	0.428405i	$-0.140924\pi$
$677$	16.6158	+	13.9423i	0.638597	+	0.535846i	−0.264990	+	0.964251i	$0.585369\pi$
$678$		0			0
$679$	−0.0603067	−	0.342017i	−0.00231436	−	0.0131254i
$680$		0			0
$681$	36.0515	+	4.74828i	1.38150	+	0.181955i
$682$		0			0
$683$	−17.9847	+	31.1503i	−0.688164	+	1.19193i	0.284268	+	0.958745i	$0.408250\pi$
$683$	−17.9847	+	31.1503i	−0.688164	+	1.19193i	−0.972431	+	0.233189i	$0.925084\pi$
$684$		0			0
$685$	15.9088	+	27.5548i	0.607843	+	1.05281i
$686$		0			0
$687$	32.5101	−	7.20544i	1.24034	−	0.274905i
$688$		0			0
$689$	7.26700	−	6.09774i	0.276851	−	0.232305i
$690$		0			0
$691$	13.9558	−	5.07948i	0.530902	−	0.193232i	−0.0626392	−	0.998036i	$-0.519952\pi$
$691$	13.9558	−	5.07948i	0.530902	−	0.193232i	0.593541	+	0.804804i	$0.297730\pi$
$692$		0			0
$693$	0.461561	−	0.461460i	0.0175333	−	0.0175294i
$694$		0			0
$695$	4.47924	−	25.4030i	0.169907	−	0.963591i
$696$		0			0
$697$	21.9413	+	7.98598i	0.831086	+	0.302490i
$698$		0			0
$699$	−0.0271682	−	0.623038i	−0.00102760	−	0.0235655i
$700$		0			0
$701$	−44.1162			−1.66625			−0.833123	−	0.553088i	$-0.813450\pi$
$701$	−44.1162			−1.66625			−0.833123	+	0.553088i	$0.813450\pi$
$702$		0			0
$703$	19.4574			0.733848
$704$		0			0
$705$	0.949194	−	0.604630i	0.0357487	−	0.0227717i
$706$		0			0
$707$	−0.124240	−	0.0452197i	−0.00467253	−	0.00170066i
$708$		0			0
$709$	7.36082	−	41.7453i	0.276441	−	1.56778i	−0.457905	−	0.889001i	$-0.651400\pi$
$709$	7.36082	−	41.7453i	0.276441	−	1.56778i	0.734346	−	0.678775i	$-0.237489\pi$
$710$		0			0
$711$	−3.32940	+	38.0073i	−0.124862	+	1.42538i
$712$		0			0
$713$	27.4903	−	10.0057i	1.02952	−	0.374715i
$714$		0			0
$715$	22.9709	−	19.2748i	0.859062	−	0.720838i
$716$		0			0
$717$	0.673624	−	2.13605i	0.0251569	−	0.0797724i
$718$		0			0
$719$	19.3665	+	33.5437i	0.722248	+	1.25097i	0.960097	+	0.279668i	$0.0902243\pi$
$719$	19.3665	+	33.5437i	0.722248	+	1.25097i	−0.237849	+	0.971302i	$0.576442\pi$
$720$		0			0
$721$	−0.130906	+	0.226735i	−0.00487518	+	0.00844406i
$722$		0			0
$723$	−11.2950	−	27.2727i	−0.420064	−	1.01428i
$724$		0			0
$725$	−1.16096	−	6.58414i	−0.0431170	−	0.244529i
$726$		0			0
$727$	−17.8664	−	14.9917i	−0.662630	−	0.556013i	0.248244	−	0.968698i	$-0.420147\pi$
$727$	−17.8664	−	14.9917i	−0.662630	−	0.556013i	−0.910874	+	0.412685i	$0.864591\pi$
$728$		0			0
$729$	−26.0823	+	6.97954i	−0.966011	+	0.258502i
$730$		0			0
$731$	−0.162747	−	0.136561i	−0.00601940	−	0.00505088i
$732$		0			0
$733$	−5.65364	−	32.0634i	−0.208822	−	1.18429i	−0.891311	−	0.453392i	$-0.850214\pi$
$733$	−5.65364	−	32.0634i	−0.208822	−	1.18429i	0.682489	−	0.730895i	$-0.260897\pi$
$734$		0			0
$735$	9.48128	+	22.8934i	0.349722	+	0.844435i
$736$		0			0
$737$	−21.2526	+	36.8106i	−0.782850	+	1.35594i
$738$		0			0
$739$	−23.3808	−	40.4967i	−0.860076	−	1.48969i	−0.871855	−	0.489764i	$-0.837083\pi$
$739$	−23.3808	−	40.4967i	−0.860076	−	1.48969i	0.0117795	−	0.999931i	$-0.496250\pi$
$740$		0			0
$741$	−5.18793	+	16.4509i	−0.190583	+	0.604337i
$742$		0			0
$743$	−27.5657	+	23.1303i	−1.01129	+	0.848570i	−0.988508	−	0.151171i	$-0.951696\pi$
$743$	−27.5657	+	23.1303i	−1.01129	+	0.848570i	−0.0227782	+	0.999741i	$0.507251\pi$
$744$		0			0
$745$	−34.0247	+	12.3840i	−1.24657	+	0.453713i
$746$		0			0
$747$	−3.07710	+	35.1271i	−0.112585	+	1.28523i
$748$		0			0
$749$	0.0357141	−	0.202545i	0.00130497	−	0.00740083i
$750$		0			0
$751$	−44.1794	−	16.0800i	−1.61213	−	0.586767i	−0.630269	−	0.776377i	$-0.717055\pi$
$751$	−44.1794	−	16.0800i	−1.61213	−	0.586767i	−0.981860	+	0.189610i	$0.939278\pi$
$752$		0			0
$753$	11.1393	−	7.09569i	0.405940	−	0.258581i
$754$		0			0
$755$	−27.8095			−1.01209
$756$		0			0
$757$	−29.5232			−1.07304			−0.536519	−	0.843888i	$-0.680261\pi$
$757$	−29.5232			−1.07304			−0.536519	+	0.843888i	$0.680261\pi$
$758$		0			0
$759$	3.15608	+	72.3770i	0.114558	+	2.62712i
$760$		0			0
$761$	−17.7293	−	6.45293i	−0.642686	−	0.233918i	5.76650e−5	−	1.00000i	$-0.499982\pi$
$761$	−17.7293	−	6.45293i	−0.642686	−	0.233918i	−0.642743	+	0.766082i	$0.722204\pi$
$762$		0			0
$763$	0.0958702	−	0.543707i	0.00347073	−	0.0196835i
$764$		0			0
$765$	8.65578	−	8.65388i	0.312950	−	0.312882i
$766$		0			0
$767$	−1.98757	+	0.723416i	−0.0717669	+	0.0261210i
$768$		0			0
$769$	3.52220	−	2.95548i	0.127014	−	0.106577i	−0.577068	−	0.816696i	$-0.695803\pi$
$769$	3.52220	−	2.95548i	0.127014	−	0.106577i	0.704082	+	0.710119i	$0.251359\pi$
$770$		0			0
$771$	19.8911	−	4.40861i	0.716360	−	0.158772i
$772$		0			0
$773$	−23.5818	−	40.8449i	−0.848179	−	1.46909i	−0.882832	−	0.469689i	$-0.844366\pi$
$773$	−23.5818	−	40.8449i	−0.848179	−	1.46909i	0.0346529	−	0.999399i	$-0.488967\pi$
$774$		0			0
$775$	−1.63938	+	2.83949i	−0.0588882	+	0.101997i
$776$		0			0
$777$	0.328727	+	0.0432961i	0.0117930	+	0.00155324i
$778$		0			0
$779$	−7.87118	−	44.6397i	−0.282014	−	1.59938i
$780$		0			0
$781$	−36.5593	−	30.6769i	−1.30819	−	1.09770i
$782$		0			0
$783$	22.7306	−	35.6670i	0.812325	−	1.27463i
$784$		0			0
$785$	−15.6044	−	13.0937i	−0.556946	−	0.467333i
$786$		0			0
$787$	−2.09630	−	11.8887i	−0.0747251	−	0.423787i	−0.999104	−	0.0423126i	$-0.986527\pi$
$787$	−2.09630	−	11.8887i	−0.0747251	−	0.423787i	0.924379	−	0.381475i	$-0.124584\pi$
$788$		0			0
$789$	−32.2958	+	42.0839i	−1.14976	+	1.49823i
$790$		0			0
$791$	0.401825	−	0.695981i	0.0142872	−	0.0247462i
$792$		0			0
$793$	9.14290	+	15.8360i	0.324674	+	0.562352i
$794$		0			0
$795$	8.82773	+	9.63484i	0.313087	+	0.341712i
$796$		0			0
$797$	4.01169	−	3.36621i	0.142101	−	0.119237i	−0.568966	−	0.822361i	$-0.692656\pi$
$797$	4.01169	−	3.36621i	0.142101	−	0.119237i	0.711068	+	0.703124i	$0.248212\pi$
$798$		0			0
$799$	0.596150	−	0.216981i	0.0210903	−	0.00767623i
$800$		0			0
$801$	−17.5071	+	1.52974i	−0.618583	+	0.0540507i
$802$		0			0
$803$	−4.60426	+	26.1120i	−0.162481	+	0.921474i
$804$		0			0
$805$	0.536647	+	0.195323i	0.0189143	+	0.00688425i
$806$		0			0
$807$	−45.7556	−	23.8220i	−1.61067	−	0.838575i
$808$		0			0
$809$	0.733326			0.0257824			0.0128912	−	0.999917i	$-0.495896\pi$
$809$	0.733326			0.0257824			0.0128912	+	0.999917i	$0.495896\pi$
$810$		0			0
$811$	17.0555			0.598898			0.299449	−	0.954112i	$-0.403197\pi$
$811$	17.0555			0.598898			0.299449	+	0.954112i	$0.403197\pi$
$812$		0			0
$813$	−45.3747	−	23.6237i	−1.59136	−	0.828520i
$814$		0			0
$815$	−1.49587	−	0.544450i	−0.0523979	−	0.0190713i
$816$		0			0
$817$	−0.0716179	+	0.406165i	−0.00250559	+	0.0142099i
$818$		0			0
$819$	−0.124255	+	0.266389i	−0.00434181	+	0.00930838i
$820$		0			0
$821$	15.9756	−	5.81465i	0.557553	−	0.202933i	−0.0478460	−	0.998855i	$-0.515236\pi$
$821$	15.9756	−	5.81465i	0.557553	−	0.202933i	0.605399	+	0.795922i	$0.293013\pi$
$822$		0			0
$823$	−22.8843	+	19.2022i	−0.797698	+	0.669348i	−0.947638	−	0.319347i	$-0.896536\pi$
$823$	−22.8843	+	19.2022i	−0.797698	+	0.669348i	0.149940	+	0.988695i	$0.452092\pi$
$824$		0			0
$825$	−5.48511	−	5.98661i	−0.190967	−	0.208427i
$826$		0			0
$827$	−24.3312	−	42.1428i	−0.846077	−	1.46545i	−0.884683	−	0.466194i	$-0.845625\pi$
$827$	−24.3312	−	42.1428i	−0.846077	−	1.46545i	0.0386055	−	0.999255i	$-0.487708\pi$
$828$		0			0
$829$	−6.85609	+	11.8751i	−0.238122	+	0.412439i	−0.960175	−	0.279398i	$-0.909865\pi$
$829$	−6.85609	+	11.8751i	−0.238122	+	0.412439i	0.722054	+	0.691837i	$0.243198\pi$
$830$		0			0
$831$	27.2542	−	35.5144i	0.945439	−	1.23198i
$832$		0			0
$833$	2.42557	+	13.7561i	0.0840411	+	0.476621i
$834$		0			0
$835$	−8.24086	−	6.91490i	−0.285187	−	0.239300i
$836$		0			0
$837$	−19.7827	+	6.23390i	−0.683791	+	0.215475i
$838$		0			0
$839$	4.04645	+	3.39537i	0.139699	+	0.117221i	0.709959	−	0.704243i	$-0.248713\pi$
$839$	4.04645	+	3.39537i	0.139699	+	0.117221i	−0.570260	+	0.821464i	$0.693158\pi$
$840$		0			0
$841$	6.46880	+	36.6864i	0.223062	+	1.26505i
$842$		0			0
$843$	27.7511	+	3.65504i	0.955798	+	0.125886i
$844$		0			0
$845$	6.53466	−	11.3184i	0.224799	−	0.389364i
$846$		0			0
$847$	0.411160	+	0.712150i	0.0141276	+	0.0244697i
$848$		0			0
$849$	−16.1017	+	3.56874i	−0.552610	+	0.122479i
$850$		0			0
$851$	−28.1929	+	23.6567i	−0.966441	+	0.810940i
$852$		0			0
$853$	−25.3986	+	9.24432i	−0.869630	+	0.316520i	−0.738018	−	0.674782i	$-0.764238\pi$
$853$	−25.3986	+	9.24432i	−0.869630	+	0.316520i	−0.131613	+	0.991301i	$0.542016\pi$
$854$		0			0
$855$	−22.9508	−	6.15234i	−0.784901	−	0.210406i
$856$		0			0
$857$	−1.96401	+	11.1385i	−0.0670893	+	0.380482i	0.932713	+	0.360619i	$0.117434\pi$
$857$	−1.96401	+	11.1385i	−0.0670893	+	0.380482i	−0.999803	+	0.0198638i	$0.993677\pi$
$858$		0			0
$859$	−30.3651	−	11.0520i	−1.03604	−	0.377089i	−0.232664	−	0.972557i	$-0.574744\pi$
$859$	−30.3651	−	11.0520i	−1.03604	−	0.377089i	−0.803379	+	0.595468i	$0.796967\pi$
$860$		0			0
$861$	−0.0336504	−	0.771691i	−0.00114680	−	0.0262992i
$862$		0			0
$863$	−6.64145			−0.226078			−0.113039	−	0.993591i	$-0.536058\pi$
$863$	−6.64145			−0.226078			−0.113039	+	0.993591i	$0.536058\pi$
$864$		0			0
$865$	20.6695			0.702784
$866$		0			0
$867$	−19.0150	+	12.1124i	−0.645784	+	0.411360i
$868$		0			0
$869$	−68.2043	−	24.8243i	−2.31367	−	0.842108i
$870$		0			0
$871$	3.32413	−	18.8521i	0.112634	−	0.638779i
$872$		0			0
$873$	−22.3869	−	15.6791i	−0.757680	−	0.530657i
$874$		0			0
$875$	−0.426268	+	0.155149i	−0.0144105	+	0.00524499i
$876$		0			0
$877$	−20.6401	+	17.3191i	−0.696967	+	0.584825i	−0.920909	−	0.389778i	$-0.872552\pi$
$877$	−20.6401	+	17.3191i	−0.696967	+	0.584825i	0.223942	+	0.974602i	$0.428107\pi$
$878$		0			0
$879$	−11.7458	+	37.2458i	−0.396176	+	1.25627i
$880$		0			0
$881$	16.1772	+	28.0197i	0.545024	+	0.944009i	0.998605	+	0.0527940i	$0.0168127\pi$
$881$	16.1772	+	28.0197i	0.545024	+	0.944009i	−0.453582	+	0.891215i	$0.649854\pi$
$882$		0			0
$883$	−22.1349	+	38.3388i	−0.744900	+	1.29020i	0.205342	+	0.978690i	$0.434169\pi$
$883$	−22.1349	+	38.3388i	−0.744900	+	1.29020i	−0.950242	+	0.311514i	$0.899164\pi$
$884$		0			0
$885$	−1.11483	−	2.69186i	−0.0374746	−	0.0904857i
$886$		0			0
$887$	8.68742	+	49.2688i	0.291695	+	1.65428i	0.680340	+	0.732897i	$0.261832\pi$
$887$	8.68742	+	49.2688i	0.291695	+	1.65428i	−0.388645	+	0.921388i	$0.627057\pi$
$888$		0			0
$889$	−0.379800	−	0.318690i	−0.0127381	−	0.0106885i
$890$		0			0
$891$	0.0112518	−	51.3645i	0.000376948	−	1.72078i
$892$		0			0
$893$	−0.943446	−	0.791645i	−0.0315712	−	0.0264914i
$894$		0			0
$895$	−0.230951	−	1.30979i	−0.00771983	−	0.0437813i
$896$		0			0
$897$	−12.4842	−	30.1442i	−0.416836	−	1.00649i
$898$		0			0
$899$	16.2455	−	28.1380i	0.541817	−	0.938455i
$900$		0			0
$901$	3.68316	+	6.37942i	0.122704	+	0.212529i
$902$		0			0
$903$	−0.00211376	+	0.00670270i	−7.03414e−5	+	0.000223052i
$904$		0			0
$905$	11.1463	−	9.35289i	0.370517	−	0.310901i
$906$		0			0
$907$	−31.0867	+	11.3146i	−1.03222	+	0.375697i	−0.801925	−	0.597425i	$-0.796191\pi$
$907$	−31.0867	+	11.3146i	−1.03222	+	0.375697i	−0.230293	+	0.973121i	$0.573969\pi$
$908$		0			0
$909$	−9.43062	+	4.39631i	−0.312794	+	0.145816i
$910$		0			0
$911$	−3.41970	+	19.3941i	−0.113300	+	0.642555i	0.874278	+	0.485425i	$0.161335\pi$
$911$	−3.41970	+	19.3941i	−0.113300	+	0.642555i	−0.987578	+	0.157130i	$0.949776\pi$
$912$		0			0
$913$	−63.0359	−	22.9432i	−2.08618	−	0.759309i
$914$		0			0
$915$	−21.2446	+	13.5327i	−0.702325	+	0.447376i
$916$		0			0
$917$	0.236509			0.00781022
$918$		0			0
$919$	20.9795			0.692050			0.346025	−	0.938225i	$-0.387531\pi$
$919$	20.9795			0.692050			0.346025	+	0.938225i	$0.387531\pi$
$920$		0			0
$921$	−0.874194	−	20.0475i	−0.0288057	−	0.660588i
$922$		0			0
$923$	20.1974	+	7.35125i	0.664805	+	0.241969i
$924$		0			0
$925$	0.716262	−	4.06212i	0.0235505	−	0.133562i
$926$		0			0
$927$	5.33057	+	19.9027i	0.175079	+	0.653689i
$928$		0			0
$929$	36.3907	−	13.2451i	1.19394	−	0.434559i	0.332835	−	0.942985i	$-0.391995\pi$
$929$	36.3907	−	13.2451i	1.19394	−	0.434559i	0.861105	+	0.508427i	$0.169773\pi$
$930$		0			0
$931$	20.7726	−	17.4303i	0.680795	−	0.571255i
$932$		0			0
$933$	22.6302	−	5.01570i	0.740880	−	0.164207i
$934$		0			0
$935$	11.6424	+	20.1652i	0.380747	+	0.659474i
$936$		0			0
$937$	−16.2104	+	28.0773i	−0.529572	+	0.917245i	0.469833	+	0.882755i	$0.344314\pi$
$937$	−16.2104	+	28.0773i	−0.529572	+	0.917245i	−0.999405	+	0.0344899i	$0.989019\pi$
$938$		0			0
$939$	−50.8705	−	6.70006i	−1.66010	−	0.218648i
$940$		0			0
$941$	5.94574	+	33.7200i	0.193826	+	1.09924i	0.914081	+	0.405531i	$0.132913\pi$
$941$	5.94574	+	33.7200i	0.193826	+	1.09924i	−0.720256	+	0.693709i	$0.755975\pi$
$942$		0			0
$943$	65.6789	+	55.1111i	2.13880	+	1.79467i
$944$		0			0
$945$	−0.374058	−	0.155012i	−0.0121681	−	0.00504253i
$946$		0			0
$947$	−16.7018	−	14.0144i	−0.542734	−	0.455408i	0.329738	−	0.944073i	$-0.393040\pi$
$947$	−16.7018	−	14.0144i	−0.542734	−	0.455408i	−0.872472	+	0.488665i	$0.837484\pi$
$948$		0			0
$949$	−2.07360	−	11.7600i	−0.0673120	−	0.381745i
$950$		0			0
$951$	9.26882	−	12.0780i	0.300562	−	0.391656i
$952$		0			0
$953$	5.72831	−	9.92172i	0.185558	−	0.321396i	−0.758206	−	0.652015i	$-0.773924\pi$
$953$	5.72831	−	9.92172i	0.185558	−	0.321396i	0.943764	+	0.330619i	$0.107257\pi$
$954$		0			0
$955$	−9.05739	−	15.6879i	−0.293090	−	0.507647i
$956$		0			0
$957$	54.3550	+	59.3246i	1.75705	+	1.91769i
$958$		0			0
$959$	0.454527	−	0.381393i	0.0146774	−	0.0123158i
$960$		0			0
$961$	14.1574	−	5.15288i	0.456691	−	0.166222i
$962$		0			0
$963$	−9.28239	−	13.2597i	−0.299121	−	0.427288i
$964$		0			0
$965$	0.689433	−	3.90997i	0.0221936	−	0.125866i
$966$		0			0
$967$	49.7554	+	18.1095i	1.60003	+	0.582362i	0.979433	−	0.201771i	$-0.0646696\pi$
$967$	49.7554	+	18.1095i	1.60003	+	0.582362i	0.620593	+	0.784133i	$0.286892\pi$
$968$		0			0
$969$	−11.8807	−	6.18553i	−0.381663	−	0.198708i
$970$		0			0
$971$	−0.467925			−0.0150164			−0.00750821	−	0.999972i	$-0.502390\pi$
$971$	−0.467925			−0.0150164			−0.00750821	+	0.999972i	$0.502390\pi$
$972$		0			0
$973$	−0.481030			−0.0154211
$974$		0			0
$975$	3.24348	+	1.68867i	0.103874	+	0.0540808i
$976$		0			0
$977$	23.4179	+	8.52341i	0.749205	+	0.272688i	0.688271	−	0.725454i	$-0.258370\pi$
$977$	23.4179	+	8.52341i	0.749205	+	0.272688i	0.0609335	+	0.998142i	$0.480592\pi$
$978$		0			0
$979$	5.80544	−	32.9243i	0.185543	−	1.05226i
$980$		0			0
$981$	−24.9174	−	35.5941i	−0.795552	−	1.13643i
$982$		0			0
$983$	−14.4328	+	5.25312i	−0.460335	+	0.167548i	−0.561769	−	0.827294i	$-0.689879\pi$
$983$	−14.4328	+	5.25312i	−0.460335	+	0.167548i	0.101434	+	0.994842i	$0.467657\pi$
$984$		0			0
$985$	−4.07713	+	3.42112i	−0.129908	+	0.109006i
$986$		0			0
$987$	−0.0141777	−	0.0154740i	−0.000451282	−	0.000492542i
$988$		0			0
$989$	−0.390053	−	0.675592i	−0.0124030	−	0.0214826i
$990$		0			0
$991$	16.6147	−	28.7775i	0.527783	−	0.914147i	−0.471693	−	0.881763i	$-0.656357\pi$
$991$	16.6147	−	28.7775i	0.527783	−	0.914147i	0.999476	−	0.0323838i	$-0.0103099\pi$
$992$		0			0
$993$	20.4513	−	26.6497i	0.649004	−	0.845702i
$994$		0			0
$995$	9.69114	+	54.9612i	0.307230	+	1.74239i
$996$		0			0
$997$	13.6461	+	11.4504i	0.432176	+	0.362638i	0.832772	−	0.553616i	$-0.186753\pi$
$997$	13.6461	+	11.4504i	0.432176	+	0.362638i	−0.400596	+	0.916255i	$0.631197\pi$
$998$		0			0
$999$	20.7042	−	15.8815i	0.655051	−	0.502467i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.y.c.97.2	yes	54
4.3	odd	2		864.2.y.b.97.8	✓	54
27.22	even	9	inner	864.2.y.c.481.2	yes	54
108.103	odd	18		864.2.y.b.481.8	yes	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.y.b.97.8	✓	54	4.3	odd	2
864.2.y.b.481.8	yes	54	108.103	odd	18
864.2.y.c.97.2	yes	54	1.1	even	1	trivial
864.2.y.c.481.2	yes	54	27.22	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.y (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.53630 - 0.799856i) q^{3} +(-1.92089 - 0.699146i) q^{5} +(-0.00661950 + 0.0375410i) q^{7} +(1.72046 + 2.45764i) q^{9} +O(q^{10})\)	\(q+(-1.53630 - 0.799856i) q^{3} +(-1.92089 - 0.699146i) q^{5} +(-0.00661950 + 0.0375410i) q^{7} +(1.72046 + 2.45764i) q^{9} +(-5.36298 + 1.95197i) q^{11} +(1.96898 - 1.65217i) q^{13} +(2.39185 + 2.61053i) q^{15} +(0.997944 + 1.72849i) q^{17} +(1.93731 - 3.35552i) q^{19} +(0.0401970 - 0.0523798i) q^{21} +(1.27263 + 7.21744i) q^{23} +(-0.629218 - 0.527976i) q^{25} +(-0.677388 - 5.15181i) q^{27} +(6.23526 + 5.23200i) q^{29} +(-0.693158 - 3.93110i) q^{31} +(9.80047 + 1.29080i) q^{33} +(0.0389620 - 0.0674841i) q^{35} +(2.51087 + 4.34896i) q^{37} +(-4.34644 + 0.963334i) q^{39} +(8.96178 - 7.51983i) q^{41} +(-0.100025 + 0.0364061i) q^{43} +(-1.58656 - 5.92371i) q^{45} +(0.0551956 - 0.313030i) q^{47} +(6.57648 + 2.39364i) q^{49} +(-0.150602 - 3.45370i) q^{51} +3.69075 q^{53} +11.6664 q^{55} +(-5.66023 + 3.60553i) q^{57} +(-0.773278 - 0.281450i) q^{59} +(-1.23537 + 7.00614i) q^{61} +(-0.103651 + 0.0483195i) q^{63} +(-4.93729 + 1.79703i) q^{65} +(5.70526 - 4.78728i) q^{67} +(3.81777 - 12.1061i) q^{69} +(4.18112 + 7.24192i) q^{71} +(2.32294 - 4.02346i) q^{73} +(0.544364 + 1.31442i) q^{75} +(-0.0377786 - 0.214253i) q^{77} +(9.74225 + 8.17472i) q^{79} +(-3.08003 + 8.45656i) q^{81} +(9.00400 + 7.55525i) q^{83} +(-0.708471 - 4.01794i) q^{85} +(-5.39440 - 13.0253i) q^{87} +(-2.92897 + 5.07312i) q^{89} +(0.0489905 + 0.0848540i) q^{91} +(-2.07941 + 6.59379i) q^{93} +(-6.06736 + 5.09112i) q^{95} +(-8.56104 + 3.11596i) q^{97} +(-14.0240 - 9.82203i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q+O(q^{10}) \) 54 * q	\( 54 q + 9 q^{11} + 12 q^{17} - 18 q^{19} + 12 q^{21} + 21 q^{27} + 6 q^{29} - 36 q^{31} - 9 q^{33} - 24 q^{39} + 3 q^{41} + 21 q^{43} + 42 q^{45} - 18 q^{49} - 24 q^{51} + 36 q^{53} + 72 q^{55} + 39 q^{57} - 18 q^{59} - 18 q^{61} + 30 q^{63} + 48 q^{65} + 27 q^{67} + 24 q^{69} + 84 q^{75} + 36 q^{77} - 72 q^{79} + 36 q^{81} - 6 q^{87} + 33 q^{89} - 36 q^{91} + 72 q^{93} - 36 q^{95} + 9 q^{97} - 120 q^{99}+O(q^{100}) \) 54 * q + 9 * q^11 + 12 * q^17 - 18 * q^19 + 12 * q^21 + 21 * q^27 + 6 * q^29 - 36 * q^31 - 9 * q^33 - 24 * q^39 + 3 * q^41 + 21 * q^43 + 42 * q^45 - 18 * q^49 - 24 * q^51 + 36 * q^53 + 72 * q^55 + 39 * q^57 - 18 * q^59 - 18 * q^61 + 30 * q^63 + 48 * q^65 + 27 * q^67 + 24 * q^69 + 84 * q^75 + 36 * q^77 - 72 * q^79 + 36 * q^81 - 6 * q^87 + 33 * q^89 - 36 * q^91 + 72 * q^93 - 36 * q^95 + 9 * q^97 - 120 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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