LMFDB - Embedded newform 864.2.y.c.97.3

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			97.3
Character	$\chi$	$=$	864.97
Dual form			864.2.y.c.481.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.11120 + 1.32862i) q^{3} +(-0.779464 - 0.283702i) q^{5} +(-0.260701 + 1.47851i) q^{7} +(-0.530450 - 2.95273i) q^{9} +O(q^{10})$	\(q+(-1.11120 + 1.32862i) q^{3} +(-0.779464 - 0.283702i) q^{5} +(-0.260701 + 1.47851i) q^{7} +(-0.530450 - 2.95273i) q^{9} +(-0.951862 + 0.346450i) q^{11} +(-0.300640 + 0.252267i) q^{13} +(1.24307 - 0.720359i) q^{15} +(-0.539319 - 0.934128i) q^{17} +(-2.72824 + 4.72544i) q^{19} +(-1.67468 - 1.98930i) q^{21} +(-0.702910 - 3.98640i) q^{23} +(-3.30314 - 2.77167i) q^{25} +(4.51249 + 2.57632i) q^{27} +(-4.12151 - 3.45836i) q^{29} +(-0.236948 - 1.34380i) q^{31} +(0.597415 - 1.64964i) q^{33} +(0.622663 - 1.07848i) q^{35} +(-3.69331 - 6.39701i) q^{37} +(-0.00109382 - 0.679756i) q^{39} +(5.32552 - 4.46864i) q^{41} +(-1.46500 + 0.533216i) q^{43} +(-0.424228 + 2.45204i) q^{45} +(1.71952 - 9.75189i) q^{47} +(4.45982 + 1.62324i) q^{49} +(1.84039 + 0.321458i) q^{51} -4.85192 q^{53} +0.840231 q^{55} +(-3.24668 - 8.87571i) q^{57} +(1.44533 + 0.526057i) q^{59} +(0.846702 - 4.80188i) q^{61} +(4.50393 - 0.0144950i) q^{63} +(0.305907 - 0.111341i) q^{65} +(-9.24848 + 7.76040i) q^{67} +(6.07748 + 3.49581i) q^{69} +(-3.94317 - 6.82978i) q^{71} +(-0.0975638 + 0.168985i) q^{73} +(7.35296 - 1.30873i) q^{75} +(-0.264078 - 1.49766i) q^{77} +(-1.32136 - 1.10875i) q^{79} +(-8.43725 + 3.13255i) q^{81} +(-7.05944 - 5.92358i) q^{83} +(0.155366 + 0.881125i) q^{85} +(9.17468 - 1.63297i) q^{87} +(-2.58462 + 4.47669i) q^{89} +(-0.294602 - 0.510266i) q^{91} +(2.04870 + 1.17842i) q^{93} +(3.46718 - 2.90931i) q^{95} +(-9.63792 + 3.50792i) q^{97} +(1.52789 + 2.62682i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.11120	+	1.32862i	−0.641554	+	0.767078i
$3$	−1.11120	+	1.32862i	−0.641554	+	0.767078i
$4$		0			0
$5$	−0.779464	−	0.283702i	−0.348587	−	0.126875i	0.161792	−	0.986825i	$-0.448273\pi$
$5$	−0.779464	−	0.283702i	−0.348587	−	0.126875i	−0.510379	+	0.859950i	$0.670495\pi$
$6$		0			0
$7$	−0.260701	+	1.47851i	−0.0985358	+	0.558824i	0.895071	+	0.445925i	$0.147125\pi$
$7$	−0.260701	+	1.47851i	−0.0985358	+	0.558824i	−0.993606	+	0.112900i	$0.963986\pi$
$8$		0			0
$9$	−0.530450	−	2.95273i	−0.176817	−	0.984244i
$10$		0			0
$11$	−0.951862	+	0.346450i	−0.286997	+	0.104458i	−0.481507	−	0.876442i	$-0.659911\pi$
$11$	−0.951862	+	0.346450i	−0.286997	+	0.104458i	0.194510	+	0.980901i	$0.437688\pi$
$12$		0			0
$13$	−0.300640	+	0.252267i	−0.0833825	+	0.0699663i	−0.683526	−	0.729926i	$-0.739555\pi$
$13$	−0.300640	+	0.252267i	−0.0833825	+	0.0699663i	0.600144	+	0.799892i	$0.295110\pi$
$14$		0			0
$15$	1.24307	−	0.720359i	0.320961	−	0.185996i
$16$		0			0
$17$	−0.539319	−	0.934128i	−0.130804	−	0.226559i	0.793183	−	0.608984i	$-0.208423\pi$
$17$	−0.539319	−	0.934128i	−0.130804	−	0.226559i	−0.923987	+	0.382424i	$0.875089\pi$
$18$		0			0
$19$	−2.72824	+	4.72544i	−0.625900	+	1.08409i	0.362466	+	0.931997i	$0.381935\pi$
$19$	−2.72824	+	4.72544i	−0.625900	+	1.08409i	−0.988366	+	0.152094i	$0.951398\pi$
$20$		0			0
$21$	−1.67468	−	1.98930i	−0.365446	−	0.434101i
$22$		0			0
$23$	−0.702910	−	3.98640i	−0.146567	−	0.831222i	−0.966096	−	0.258184i	$-0.916876\pi$
$23$	−0.702910	−	3.98640i	−0.146567	−	0.831222i	0.819529	−	0.573038i	$-0.194235\pi$
$24$		0			0
$25$	−3.30314	−	2.77167i	−0.660629	−	0.554334i
$26$		0			0
$27$	4.51249	+	2.57632i	0.868429	+	0.495814i
$28$		0			0
$29$	−4.12151	−	3.45836i	−0.765346	−	0.642201i	0.174167	−	0.984716i	$-0.444277\pi$
$29$	−4.12151	−	3.45836i	−0.765346	−	0.642201i	−0.939512	+	0.342515i	$0.888721\pi$
$30$		0			0
$31$	−0.236948	−	1.34380i	−0.0425572	−	0.241354i	0.956107	−	0.293016i	$-0.0946591\pi$
$31$	−0.236948	−	1.34380i	−0.0425572	−	0.241354i	−0.998665	+	0.0516626i	$0.983548\pi$
$32$		0			0
$33$	0.597415	−	1.64964i	0.103997	−	0.287165i
$34$		0			0
$35$	0.622663	−	1.07848i	0.105249	−	0.182297i
$36$		0			0
$37$	−3.69331	−	6.39701i	−0.607177	−	1.05166i	−0.991703	−	0.128547i	$-0.958969\pi$
$37$	−3.69331	−	6.39701i	−0.607177	−	1.05166i	0.384526	−	0.923114i	$-0.374365\pi$
$38$		0			0
$39$	−0.00109382	−	0.679756i	−0.000175152	−	0.108848i
$40$		0			0
$41$	5.32552	−	4.46864i	0.831707	−	0.697885i	−0.123975	−	0.992285i	$-0.539564\pi$
$41$	5.32552	−	4.46864i	0.831707	−	0.697885i	0.955682	+	0.294400i	$0.0951199\pi$
$42$		0			0
$43$	−1.46500	+	0.533216i	−0.223410	+	0.0813146i	−0.451300	−	0.892372i	$-0.649040\pi$
$43$	−1.46500	+	0.533216i	−0.223410	+	0.0813146i	0.227890	+	0.973687i	$0.426817\pi$
$44$		0			0
$45$	−0.424228	+	2.45204i	−0.0632402	+	0.365528i
$46$		0			0
$47$	1.71952	−	9.75189i	0.250818	−	1.42246i	−0.555765	−	0.831339i	$-0.687575\pi$
$47$	1.71952	−	9.75189i	0.250818	−	1.42246i	0.806583	−	0.591120i	$-0.201314\pi$
$48$		0			0
$49$	4.45982	+	1.62324i	0.637117	+	0.231892i
$50$		0			0
$51$	1.84039	+	0.321458i	0.257707	+	0.0450132i
$52$		0			0
$53$	−4.85192			−0.666462			−0.333231	−	0.942845i	$-0.608139\pi$
$53$	−4.85192			−0.666462			−0.333231	+	0.942845i	$0.608139\pi$
$54$		0			0
$55$	0.840231			0.113297
$56$		0			0
$57$	−3.24668	−	8.87571i	−0.430033	−	1.17562i
$58$		0			0
$59$	1.44533	+	0.526057i	0.188166	+	0.0684868i	0.434384	−	0.900728i	$-0.356966\pi$
$59$	1.44533	+	0.526057i	0.188166	+	0.0684868i	−0.246219	+	0.969214i	$0.579188\pi$
$60$		0			0
$61$	0.846702	−	4.80188i	0.108409	−	0.614818i	−0.881395	−	0.472380i	$-0.843395\pi$
$61$	0.846702	−	4.80188i	0.108409	−	0.614818i	0.989804	−	0.142438i	$-0.0454941\pi$
$62$		0			0
$63$	4.50393	−	0.0144950i	0.567442	−	0.00182620i
$64$		0			0
$65$	0.305907	−	0.111341i	0.0379430	−	0.0138101i
$66$		0			0
$67$	−9.24848	+	7.76040i	−1.12988	+	0.948083i	−0.999061	−	0.0433226i	$-0.986206\pi$
$67$	−9.24848	+	7.76040i	−1.12988	+	0.948083i	−0.130821	+	0.991406i	$0.541761\pi$
$68$		0			0
$69$	6.07748	+	3.49581i	0.731643	+	0.420846i
$70$		0			0
$71$	−3.94317	−	6.82978i	−0.467969	−	0.810546i	0.531361	−	0.847145i	$-0.321681\pi$
$71$	−3.94317	−	6.82978i	−0.467969	−	0.810546i	−0.999330	+	0.0365997i	$0.988347\pi$
$72$		0			0
$73$	−0.0975638	+	0.168985i	−0.0114190	+	0.0197782i	−0.871678	−	0.490078i	$-0.836968\pi$
$73$	−0.0975638	+	0.168985i	−0.0114190	+	0.0197782i	0.860259	+	0.509857i	$0.170302\pi$
$74$		0			0
$75$	7.35296	−	1.30873i	0.849046	−	0.151119i
$76$		0			0
$77$	−0.264078	−	1.49766i	−0.0300944	−	0.170674i
$78$		0			0
$79$	−1.32136	−	1.10875i	−0.148664	−	0.124744i	0.565422	−	0.824802i	$-0.308713\pi$
$79$	−1.32136	−	1.10875i	−0.148664	−	0.124744i	−0.714087	+	0.700057i	$0.753158\pi$
$80$		0			0
$81$	−8.43725	+	3.13255i	−0.937472	+	0.348061i
$82$		0			0
$83$	−7.05944	−	5.92358i	−0.774874	−	0.650197i	0.167078	−	0.985944i	$-0.446567\pi$
$83$	−7.05944	−	5.92358i	−0.774874	−	0.650197i	−0.941952	+	0.335747i	$0.891011\pi$
$84$		0			0
$85$	0.155366	+	0.881125i	0.0168518	+	0.0955714i
$86$		0			0
$87$	9.17468	−	1.63297i	0.983629	−	0.175073i
$88$		0			0
$89$	−2.58462	+	4.47669i	−0.273969	+	0.474528i	−0.969874	−	0.243605i	$-0.921670\pi$
$89$	−2.58462	+	4.47669i	−0.273969	+	0.474528i	0.695906	+	0.718133i	$0.255003\pi$
$90$		0			0
$91$	−0.294602	−	0.510266i	−0.0308827	−	0.0534904i
$92$		0			0
$93$	2.04870	+	1.17842i	0.212440	+	0.122197i
$94$		0			0
$95$	3.46718	−	2.90931i	0.355725	−	0.298489i
$96$		0			0
$97$	−9.63792	+	3.50792i	−0.978583	+	0.356175i	−0.781289	−	0.624169i	$-0.785438\pi$
$97$	−9.63792	+	3.50792i	−0.978583	+	0.356175i	−0.197294	+	0.980344i	$0.563215\pi$
$98$		0			0
$99$	1.52789	+	2.62682i	0.153559	+	0.264005i
$100$		0			0
$101$	0.576254	−	3.26810i	0.0573394	−	0.325188i	−0.942623	−	0.333859i	$-0.891649\pi$
$101$	0.576254	−	3.26810i	0.0573394	−	0.325188i	0.999962	+	0.00867115i	$0.00276015\pi$
$102$		0			0
$103$	−6.67539	−	2.42964i	−0.657746	−	0.239400i	−0.00848308	−	0.999964i	$-0.502700\pi$
$103$	−6.67539	−	2.42964i	−0.657746	−	0.239400i	−0.649263	+	0.760564i	$0.724923\pi$
$104$		0			0
$105$	0.740987	+	2.02570i	0.0723129	+	0.197688i
$106$		0			0
$107$	−3.46202			−0.334686			−0.167343	−	0.985899i	$-0.553519\pi$
$107$	−3.46202			−0.334686			−0.167343	+	0.985899i	$0.553519\pi$
$108$		0			0
$109$	8.88785			0.851302			0.425651	−	0.904887i	$-0.360045\pi$
$109$	8.88785			0.851302			0.425651	+	0.904887i	$0.360045\pi$
$110$		0			0
$111$	12.6032	+	2.20138i	1.19624	+	0.208946i
$112$		0			0
$113$	14.7713	+	5.37630i	1.38956	+	0.505760i	0.925063	−	0.379813i	$-0.124012\pi$
$113$	14.7713	+	5.37630i	1.38956	+	0.505760i	0.464501	+	0.885573i	$0.346234\pi$
$114$		0			0
$115$	−0.583056	+	3.30667i	−0.0543702	+	0.308349i
$116$		0			0
$117$	0.904351	+	0.753894i	0.0836073	+	0.0696976i
$118$		0			0
$119$	1.52172	−	0.553861i	0.139496	−	0.0507723i
$120$		0			0
$121$	−7.64047	+	6.41112i	−0.694589	+	0.582829i
$122$		0			0
$123$	0.0193760	+	12.0412i	0.00174707	+	1.08571i
$124$		0			0
$125$	3.86208	+	6.68931i	0.345435	+	0.598310i
$126$		0			0
$127$	−6.01031	+	10.4102i	−0.533329	+	0.923752i	0.465914	+	0.884830i	$0.345726\pi$
$127$	−6.01031	+	10.4102i	−0.533329	+	0.923752i	−0.999242	+	0.0389219i	$0.987608\pi$
$128$		0			0
$129$	0.919472	−	2.53893i	0.0809550	−	0.223541i
$130$		0			0
$131$	−0.523369	−	2.96817i	−0.0457270	−	0.259331i	0.953371	−	0.301802i	$-0.0975881\pi$
$131$	−0.523369	−	2.96817i	−0.0457270	−	0.259331i	−0.999098	+	0.0424711i	$0.986477\pi$
$132$		0			0
$133$	−6.27536	−	5.26565i	−0.544143	−	0.456590i
$134$		0			0
$135$	−2.78642	−	3.28835i	−0.239816	−	0.283016i
$136$		0			0
$137$	−5.39628	−	4.52801i	−0.461035	−	0.386854i	0.382477	−	0.923965i	$-0.375071\pi$
$137$	−5.39628	−	4.52801i	−0.461035	−	0.386854i	−0.843512	+	0.537111i	$0.819516\pi$
$138$		0			0
$139$	2.10611	+	11.9444i	0.178638	+	1.01311i	0.933860	+	0.357639i	$0.116418\pi$
$139$	2.10611	+	11.9444i	0.178638	+	1.01311i	−0.755222	+	0.655470i	$0.772471\pi$
$140$		0			0
$141$	11.0458	+	13.1209i	0.930224	+	1.10498i
$142$		0			0
$143$	0.198770	−	0.344280i	0.0166220	−	0.0287901i
$144$		0			0
$145$	2.23143	+	3.86495i	0.185310	+	0.320966i
$146$		0			0
$147$	−7.11244	+	4.12164i	−0.586624	+	0.339947i
$148$		0			0
$149$	5.10390	−	4.28268i	0.418128	−	0.350851i	−0.409323	−	0.912390i	$-0.634235\pi$
$149$	5.10390	−	4.28268i	0.418128	−	0.350851i	0.827450	+	0.561539i	$0.189790\pi$
$150$		0			0
$151$	−12.9043	+	4.69676i	−1.05013	+	0.382217i	−0.808713	−	0.588203i	$-0.799835\pi$
$151$	−12.9043	+	4.69676i	−1.05013	+	0.382217i	−0.241420	+	0.970421i	$0.577613\pi$
$152$		0			0
$153$	−2.47215	+	2.08797i	−0.199861	+	0.168803i
$154$		0			0
$155$	−0.196546	+	1.11467i	−0.0157869	+	0.0895322i
$156$		0			0
$157$	20.6981	+	7.53348i	1.65189	+	0.601237i	0.989057	−	0.147533i	$-0.0471333\pi$
$157$	20.6981	+	7.53348i	1.65189	+	0.601237i	0.662829	+	0.748771i	$0.269356\pi$
$158$		0			0
$159$	5.39147	−	6.44634i	0.427571	−	0.511228i
$160$		0			0
$161$	6.07719			0.478949
$162$		0			0
$163$	−8.21231			−0.643238			−0.321619	−	0.946869i	$-0.604227\pi$
$163$	−8.21231			−0.643238			−0.321619	+	0.946869i	$0.604227\pi$
$164$		0			0
$165$	−0.933668	+	1.11635i	−0.0726860	+	0.0869074i
$166$		0			0
$167$	−15.9328	−	5.79906i	−1.23292	−	0.448745i	−0.358321	−	0.933598i	$-0.616651\pi$
$167$	−15.9328	−	5.79906i	−1.23292	−	0.448745i	−0.874595	+	0.484854i	$0.838873\pi$
$168$		0			0
$169$	−2.23068	+	12.6508i	−0.171591	+	0.973140i
$170$		0			0
$171$	15.4002	+	5.54914i	1.17768	+	0.424353i
$172$		0			0
$173$	−17.7240	+	6.45100i	−1.34753	+	0.490460i	−0.912175	−	0.409800i	$-0.865599\pi$
$173$	−17.7240	+	6.45100i	−1.34753	+	0.490460i	−0.435353	+	0.900260i	$0.643376\pi$
$174$		0			0
$175$	4.95907	−	4.16116i	0.374871	−	0.314554i
$176$		0			0
$177$	−2.30498	+	1.33573i	−0.173253	+	0.100400i
$178$		0			0
$179$	−3.29178	−	5.70153i	−0.246039	−	0.426152i	0.716384	−	0.697706i	$-0.245796\pi$
$179$	−3.29178	−	5.70153i	−0.246039	−	0.426152i	−0.962423	+	0.271554i	$0.912463\pi$
$180$		0			0
$181$	11.2316	−	19.4537i	0.834838	−	1.44598i	−0.0593238	−	0.998239i	$-0.518894\pi$
$181$	11.2316	−	19.4537i	0.834838	−	1.44598i	0.894162	−	0.447744i	$-0.147772\pi$
$182$		0			0
$183$	5.43901	+	6.46082i	0.402063	+	0.477597i
$184$		0			0
$185$	1.06396	+	6.03403i	0.0782241	+	0.443631i
$186$		0			0
$187$	0.836986	+	0.702315i	0.0612065	+	0.0513583i
$188$		0			0
$189$	−4.98553	+	6.00011i	−0.362644	+	0.436444i
$190$		0			0
$191$	10.1550	+	8.52104i	0.734789	+	0.616561i	0.931432	−	0.363914i	$-0.118560\pi$
$191$	10.1550	+	8.52104i	0.734789	+	0.616561i	−0.196644	+	0.980475i	$0.563004\pi$
$192$		0			0
$193$	4.23883	+	24.0396i	0.305118	+	1.73041i	0.622951	+	0.782261i	$0.285934\pi$
$193$	4.23883	+	24.0396i	0.305118	+	1.73041i	−0.317833	+	0.948147i	$0.602955\pi$
$194$		0			0
$195$	−0.191995	+	0.530155i	−0.0137491	+	0.0379652i
$196$		0			0
$197$	−13.2050	+	22.8718i	−0.940821	+	1.62955i	−0.176910	+	0.984227i	$0.556610\pi$
$197$	−13.2050	+	22.8718i	−0.940821	+	1.62955i	−0.763910	+	0.645322i	$0.776723\pi$
$198$		0			0
$199$	−5.28951	−	9.16171i	−0.374964	−	0.649456i	0.615358	−	0.788248i	$-0.289011\pi$
$199$	−5.28951	−	9.16171i	−0.374964	−	0.649456i	−0.990322	+	0.138792i	$0.955678\pi$
$200$		0			0
$201$	−0.0336489	−	20.9111i	−0.00237341	−	1.47495i
$202$		0			0
$203$	6.18770	−	5.19210i	0.434292	−	0.364414i
$204$		0			0
$205$	−5.41881	+	1.97229i	−0.378466	+	0.137750i
$206$		0			0
$207$	−11.3979	+	4.19009i	−0.792210	+	0.291232i
$208$		0			0
$209$	0.959777	−	5.44317i	0.0663892	−	0.376512i
$210$		0			0
$211$	1.24445	+	0.452944i	0.0856718	+	0.0311820i	0.384500	−	0.923125i	$-0.374374\pi$
$211$	1.24445	+	0.452944i	0.0856718	+	0.0311820i	−0.298829	+	0.954307i	$0.596596\pi$
$212$		0			0
$213$	13.4558	+	2.35031i	0.921979	+	0.161040i
$214$		0			0
$215$	1.29319			0.0881946
$216$		0			0
$217$	2.04860			0.139068
$218$		0			0
$219$	−0.116104	−	0.317402i	−0.00784556	−	0.0214481i
$220$		0			0
$221$	0.397791	+	0.144784i	0.0267583	+	0.00973922i
$222$		0			0
$223$	−2.96965	+	16.8417i	−0.198862	+	1.12780i	0.707948	+	0.706265i	$0.249621\pi$
$223$	−2.96965	+	16.8417i	−0.198862	+	1.12780i	−0.906810	+	0.421539i	$0.861490\pi$
$224$		0			0
$225$	−6.43184	+	11.2235i	−0.428789	+	0.748235i
$226$		0			0
$227$	−12.2979	+	4.47608i	−0.816242	+	0.297088i	−0.716200	−	0.697895i	$-0.754120\pi$
$227$	−12.2979	+	4.47608i	−0.816242	+	0.297088i	−0.100042	+	0.994983i	$0.531898\pi$
$228$		0			0
$229$	−5.90431	+	4.95431i	−0.390168	+	0.327390i	−0.816679	−	0.577093i	$-0.804187\pi$
$229$	−5.90431	+	4.95431i	−0.390168	+	0.327390i	0.426511	+	0.904483i	$0.359743\pi$
$230$		0			0
$231$	2.28326	+	1.31335i	0.150227	+	0.0864118i
$232$		0			0
$233$	11.2215	+	19.4362i	0.735145	+	1.27331i	0.954660	+	0.297700i	$0.0962194\pi$
$233$	11.2215	+	19.4362i	0.735145	+	1.27331i	−0.219514	+	0.975609i	$0.570447\pi$
$234$		0			0
$235$	−4.10693	+	7.11342i	−0.267907	+	0.464028i
$236$		0			0
$237$	2.94140	−	0.523530i	0.191065	−	0.0340070i
$238$		0			0
$239$	−1.95650	−	11.0958i	−0.126555	−	0.717731i	−0.980372	−	0.197157i	$-0.936829\pi$
$239$	−1.95650	−	11.0958i	−0.126555	−	0.717731i	0.853817	−	0.520574i	$-0.174282\pi$
$240$		0			0
$241$	−2.32807	−	1.95348i	−0.149964	−	0.125835i	0.564719	−	0.825283i	$-0.308985\pi$
$241$	−2.32807	−	1.95348i	−0.149964	−	0.125835i	−0.714683	+	0.699449i	$0.753429\pi$
$242$		0			0
$243$	5.21354	−	14.6908i	0.334449	−	0.942414i
$244$		0			0
$245$	−3.01575	−	2.53052i	−0.192669	−	0.161669i
$246$		0			0
$247$	−0.371856	−	2.10890i	−0.0236606	−	0.134186i
$248$		0			0
$249$	15.7146	−	2.79700i	0.995875	−	0.177253i
$250$		0			0
$251$	15.0190	−	26.0136i	0.947988	−	1.64196i	0.198333	−	0.980135i	$-0.436447\pi$
$251$	15.0190	−	26.0136i	0.947988	−	1.64196i	0.749655	−	0.661829i	$-0.230219\pi$
$252$		0			0
$253$	2.05016	+	3.55098i	0.128893	+	0.223248i
$254$		0			0
$255$	−1.34332	−	0.772688i	−0.0841221	−	0.0483876i
$256$		0			0
$257$	15.4773	−	12.9870i	0.965448	−	0.810107i	−0.0163828	−	0.999866i	$-0.505215\pi$
$257$	15.4773	−	12.9870i	0.965448	−	0.810107i	0.981831	+	0.189759i	$0.0607706\pi$
$258$		0			0
$259$	10.4209	−	3.79289i	0.647523	−	0.235679i
$260$		0			0
$261$	−8.02535	+	14.0042i	−0.496757	+	0.866839i
$262$		0			0
$263$	1.46602	−	8.31420i	0.0903985	−	0.512675i	−0.905662	−	0.424000i	$-0.860626\pi$
$263$	1.46602	−	8.31420i	0.0903985	−	0.512675i	0.996061	−	0.0886752i	$-0.0282633\pi$
$264$		0			0
$265$	3.78189	+	1.37650i	0.232320	+	0.0845575i
$266$		0			0
$267$	−3.07577	−	8.40848i	−0.188234	−	0.514591i
$268$		0			0
$269$	−15.2422			−0.929332			−0.464666	−	0.885486i	$-0.653826\pi$
$269$	−15.2422			−0.929332			−0.464666	+	0.885486i	$0.653826\pi$
$270$		0			0
$271$	31.4057			1.90776			0.953881	−	0.300185i	$-0.0970484\pi$
$271$	31.4057			1.90776			0.953881	+	0.300185i	$0.0970484\pi$
$272$		0			0
$273$	1.00531	+	0.175596i	0.0608442	+	0.0106276i
$274$		0			0
$275$	4.10438	+	1.49387i	0.247504	+	0.0900839i
$276$		0			0
$277$	0.965349	−	5.47476i	0.0580022	−	0.328947i	−0.941975	−	0.335683i	$-0.891033\pi$
$277$	0.965349	−	5.47476i	0.0580022	−	0.328947i	0.999977	+	0.00673594i	$0.00214413\pi$
$278$		0			0
$279$	−3.84219	+	1.41246i	−0.230026	+	0.0845620i
$280$		0			0
$281$	14.6977	−	5.34953i	0.876791	−	0.319126i	0.135877	−	0.990726i	$-0.456615\pi$
$281$	14.6977	−	5.34953i	0.876791	−	0.319126i	0.740914	+	0.671600i	$0.234393\pi$
$282$		0			0
$283$	3.69367	−	3.09936i	0.219566	−	0.184238i	−0.526370	−	0.850256i	$-0.676447\pi$
$283$	3.69367	−	3.09936i	0.219566	−	0.184238i	0.745935	+	0.666018i	$0.232003\pi$
$284$		0			0
$285$	0.0126147	+	7.83939i	0.000747230	+	0.464365i
$286$		0			0
$287$	5.21856	+	9.03882i	0.308042	+	0.533545i
$288$		0			0
$289$	7.91827	−	13.7148i	0.465781	−	0.806756i
$290$		0			0
$291$	6.04902	−	16.7031i	0.354600	−	0.979155i
$292$		0			0
$293$	1.43209	+	8.12181i	0.0836638	+	0.474481i	0.997637	+	0.0687064i	$0.0218872\pi$
$293$	1.43209	+	8.12181i	0.0836638	+	0.474481i	−0.913973	+	0.405775i	$0.867002\pi$
$294$		0			0
$295$	−0.977339	−	0.820085i	−0.0569029	−	0.0477472i
$296$		0			0
$297$	−5.18783	−	0.888954i	−0.301029	−	0.0515824i
$298$		0			0
$299$	1.21696	+	1.02115i	0.0703787	+	0.0590547i
$300$		0			0
$301$	−0.406438	−	2.30502i	−0.0234267	−	0.132859i
$302$		0			0
$303$	3.70172	+	4.39715i	0.212658	+	0.252609i
$304$		0			0
$305$	−2.02228	+	3.50268i	−0.115795	+	0.200563i
$306$		0			0
$307$	−17.3393	−	30.0325i	−0.989603	−	1.71404i	−0.619356	−	0.785110i	$-0.712606\pi$
$307$	−17.3393	−	30.0325i	−0.989603	−	1.71404i	−0.370247	−	0.928933i	$-0.620727\pi$
$308$		0			0
$309$	10.6458	−	6.16921i	0.605618	−	0.350954i
$310$		0			0
$311$	−11.3323	+	9.50891i	−0.642594	+	0.539201i	−0.904814	−	0.425808i	$-0.859990\pi$
$311$	−11.3323	+	9.50891i	−0.642594	+	0.539201i	0.262219	+	0.965008i	$0.415546\pi$
$312$		0			0
$313$	−21.6326	+	7.87362i	−1.22275	+	0.445043i	−0.871107	−	0.491093i	$-0.836598\pi$
$313$	−21.6326	+	7.87362i	−1.22275	+	0.445043i	−0.351639	+	0.936136i	$0.614375\pi$
$314$		0			0
$315$	−3.51477	−	1.26647i	−0.198035	−	0.0713578i
$316$		0			0
$317$	5.59393	−	31.7248i	0.314186	−	1.78184i	−0.262559	−	0.964916i	$-0.584566\pi$
$317$	5.59393	−	31.7248i	0.314186	−	1.78184i	0.576745	−	0.816924i	$-0.304323\pi$
$318$		0			0
$319$	5.12126	+	1.86399i	0.286736	+	0.104363i
$320$		0			0
$321$	3.84701	−	4.59970i	0.214719	−	0.256730i
$322$		0			0
$323$	5.88556			0.327481
$324$		0			0
$325$	1.69226			0.0938696
$326$		0			0
$327$	−9.87622	+	11.8086i	−0.546156	+	0.653015i
$328$		0			0
$329$	13.9700	+	5.08466i	0.770190	+	0.280326i
$330$		0			0
$331$	3.78935	−	21.4904i	0.208281	−	1.18122i	−0.683911	−	0.729566i	$-0.739722\pi$
$331$	3.78935	−	21.4904i	0.208281	−	1.18122i	0.892192	−	0.451656i	$-0.149167\pi$
$332$		0			0
$333$	−16.9295	+	14.2987i	−0.927732	+	0.783561i
$334$		0			0
$335$	9.41050	−	3.42514i	0.514150	−	0.187135i
$336$		0			0
$337$	−2.74881	+	2.30653i	−0.149737	+	0.125645i	−0.714579	−	0.699555i	$-0.753382\pi$
$337$	−2.74881	+	2.30653i	−0.149737	+	0.125645i	0.564842	+	0.825199i	$0.308937\pi$
$338$		0			0
$339$	−23.5569	+	13.6512i	−1.27944	+	0.741431i
$340$		0			0
$341$	0.691102	+	1.19702i	0.0374252	+	0.0648224i
$342$		0			0
$343$	−8.81728	+	15.2720i	−0.476088	+	0.824609i
$344$		0			0
$345$	−3.74541	−	4.44905i	−0.201646	−	0.239529i
$346$		0			0
$347$	3.73695	+	21.1933i	0.200610	+	1.13771i	0.904200	+	0.427109i	$0.140468\pi$
$347$	3.73695	+	21.1933i	0.200610	+	1.13771i	−0.703590	+	0.710606i	$0.748421\pi$
$348$		0			0
$349$	−11.2561	−	9.44496i	−0.602523	−	0.505577i	0.289732	−	0.957108i	$-0.406434\pi$
$349$	−11.2561	−	9.44496i	−0.602523	−	0.505577i	−0.892256	+	0.451531i	$0.850878\pi$
$350$		0			0
$351$	−2.00656	+	0.363806i	−0.107102	+	0.0194185i
$352$		0			0
$353$	−20.3227	−	17.0528i	−1.08167	−	0.907628i	−0.0856111	−	0.996329i	$-0.527284\pi$
$353$	−20.3227	−	17.0528i	−1.08167	−	0.907628i	−0.996058	+	0.0887001i	$0.971729\pi$
$354$		0			0
$355$	1.13594	+	6.44225i	0.0602896	+	0.341919i
$356$		0			0
$357$	−0.955072	+	2.63724i	−0.0505478	+	0.139577i
$358$		0			0
$359$	−18.4484	+	31.9536i	−0.973669	+	1.68644i	−0.289410	+	0.957205i	$0.593459\pi$
$359$	−18.4484	+	31.9536i	−0.973669	+	1.68644i	−0.684259	+	0.729239i	$0.739874\pi$
$360$		0			0
$361$	−5.38654	−	9.32976i	−0.283502	−	0.491040i
$362$		0			0
$363$	−0.0277985	−	17.2753i	−0.00145904	−	0.906720i
$364$		0			0
$365$	0.123989	−	0.104039i	0.00648987	−	0.00544565i
$366$		0			0
$367$	−9.91731	+	3.60960i	−0.517679	+	0.188420i	−0.587629	−	0.809131i	$-0.699938\pi$
$367$	−9.91731	+	3.60960i	−0.517679	+	0.188420i	0.0699495	+	0.997551i	$0.477716\pi$
$368$		0			0
$369$	−16.0196	−	13.3544i	−0.833948	−	0.695205i
$370$		0			0
$371$	1.26490	−	7.17361i	0.0656704	−	0.372435i
$372$		0			0
$373$	−2.87708	−	1.04717i	−0.148969	−	0.0542204i	0.266459	−	0.963846i	$-0.414146\pi$
$373$	−2.87708	−	1.04717i	−0.148969	−	0.0542204i	−0.415429	+	0.909626i	$0.636368\pi$
$374$		0			0
$375$	−13.1791	−	2.30197i	−0.680565	−	0.118873i
$376$		0			0
$377$	2.11152			0.108749
$378$		0			0
$379$	23.9970			1.23264			0.616322	−	0.787494i	$-0.288622\pi$
$379$	23.9970			1.23264			0.616322	+	0.787494i	$0.288622\pi$
$380$		0			0
$381$	−7.15244	−	19.5532i	−0.366431	−	1.00174i
$382$		0			0
$383$	8.84393	+	3.21893i	0.451904	+	0.164480i	0.557937	−	0.829883i	$-0.311593\pi$
$383$	8.84393	+	3.21893i	0.451904	+	0.164480i	−0.106034	+	0.994363i	$0.533815\pi$
$384$		0			0
$385$	−0.219049	+	1.24229i	−0.0111638	+	0.0633129i
$386$		0			0
$387$	2.35155	+	4.04290i	0.119536	+	0.205512i
$388$		0			0
$389$	−24.2184	+	8.81477i	−1.22792	+	0.446927i	−0.872885	−	0.487926i	$-0.837754\pi$
$389$	−24.2184	+	8.81477i	−1.22792	+	0.446927i	−0.355036	+	0.934853i	$0.615531\pi$
$390$		0			0
$391$	−3.34472	+	2.80655i	−0.169150	+	0.141933i
$392$		0			0
$393$	4.52514	+	2.60289i	0.228263	+	0.131298i
$394$		0			0
$395$	0.715396	+	1.23910i	0.0359955	+	0.0623460i
$396$		0			0
$397$	18.2272	−	31.5705i	0.914799	−	1.58448i	0.107605	−	0.994194i	$-0.465682\pi$
$397$	18.2272	−	31.5705i	0.914799	−	1.58448i	0.807195	−	0.590285i	$-0.200985\pi$
$398$		0			0
$399$	13.9692	−	2.48634i	0.699337	−	0.124473i
$400$		0			0
$401$	−4.43515	−	25.1530i	−0.221481	−	1.25608i	−0.869300	−	0.494285i	$-0.835430\pi$
$401$	−4.43515	−	25.1530i	−0.221481	−	1.25608i	0.647819	−	0.761794i	$-0.275681\pi$
$402$		0			0
$403$	0.410233	+	0.344226i	0.0204352	+	0.0171471i
$404$		0			0
$405$	7.46524	−	0.0480512i	0.370951	−	0.00238768i
$406$		0			0
$407$	5.73177	+	4.80952i	0.284113	+	0.238399i
$408$		0			0
$409$	2.27933	+	12.9267i	0.112706	+	0.639185i	0.987861	+	0.155343i	$0.0496482\pi$
$409$	2.27933	+	12.9267i	0.112706	+	0.639185i	−0.875155	+	0.483843i	$0.839241\pi$
$410$		0			0
$411$	12.0124	−	2.13804i	0.592526	−	0.105462i
$412$		0			0
$413$	−1.15458	+	1.99979i	−0.0568131	+	0.0984032i
$414$		0			0
$415$	3.82205	+	6.61999i	0.187617	+	0.324962i
$416$		0			0
$417$	−18.2098	−	10.4744i	−0.891739	−	0.512934i
$418$		0			0
$419$	−8.68497	+	7.28755i	−0.424288	+	0.356020i	−0.829792	−	0.558073i	$-0.811541\pi$
$419$	−8.68497	+	7.28755i	−0.424288	+	0.356020i	0.405503	+	0.914094i	$0.367096\pi$
$420$		0			0
$421$	−13.9221	+	5.06724i	−0.678523	+	0.246962i	−0.658213	−	0.752831i	$-0.728688\pi$
$421$	−13.9221	+	5.06724i	−0.678523	+	0.246962i	−0.0203099	+	0.999794i	$0.506465\pi$
$422$		0			0
$423$	−29.7068	+	0.0956054i	−1.44440	+	0.00464849i
$424$		0			0
$425$	−0.807644	+	4.58038i	−0.0391765	+	0.222181i
$426$		0			0
$427$	6.87890	+	2.50371i	0.332893	+	0.121163i
$428$		0			0
$429$	0.236542	+	0.646655i	0.0114204	+	0.0312208i
$430$		0			0
$431$	−5.45758			−0.262883			−0.131441	−	0.991324i	$-0.541960\pi$
$431$	−5.45758			−0.262883			−0.131441	+	0.991324i	$0.541960\pi$
$432$		0			0
$433$	12.7172			0.611148			0.305574	−	0.952168i	$-0.401152\pi$
$433$	12.7172			0.611148			0.305574	+	0.952168i	$0.401152\pi$
$434$		0			0
$435$	−7.61461	−	1.33003i	−0.365093	−	0.0637701i
$436$		0			0
$437$	20.7552	+	7.55428i	0.992857	+	0.361370i
$438$		0			0
$439$	1.04485	−	5.92562i	0.0498678	−	0.282815i	−0.949669	−	0.313256i	$-0.898580\pi$
$439$	1.04485	−	5.92562i	0.0498678	−	0.282815i	0.999537	+	0.0304414i	$0.00969131\pi$
$440$		0			0
$441$	2.42729	−	14.0297i	0.115585	−	0.668081i
$442$		0			0
$443$	−18.4808	+	6.72647i	−0.878050	+	0.319584i	−0.741423	−	0.671038i	$-0.765849\pi$
$443$	−18.4808	+	6.72647i	−0.878050	+	0.319584i	−0.136627	+	0.990623i	$0.543626\pi$
$444$		0			0
$445$	3.28466	−	2.75616i	0.155708	−	0.130654i
$446$		0			0
$447$	0.0185696	+	11.5401i	0.000878313	+	0.545826i
$448$		0			0
$449$	3.49576	+	6.05483i	0.164975	+	0.285745i	0.936646	−	0.350276i	$-0.113912\pi$
$449$	3.49576	+	6.05483i	0.164975	+	0.285745i	−0.771671	+	0.636021i	$0.780579\pi$
$450$		0			0
$451$	−3.52100	+	6.09856i	−0.165798	+	0.287170i
$452$		0			0
$453$	8.09906	−	22.3639i	0.380527	−	1.05075i
$454$		0			0
$455$	0.0848684	+	0.481313i	0.00397869	+	0.0225643i
$456$		0			0
$457$	−21.4678	−	18.0136i	−1.00422	−	0.842642i	−0.0166580	−	0.999861i	$-0.505303\pi$
$457$	−21.4678	−	18.0136i	−1.00422	−	0.842642i	−0.987564	+	0.157219i	$0.949747\pi$
$458$		0			0
$459$	−0.0270565	−	5.60471i	−0.00126289	−	0.261605i
$460$		0			0
$461$	−20.9135	−	17.5485i	−0.974037	−	0.817314i	0.00914223	−	0.999958i	$-0.497090\pi$
$461$	−20.9135	−	17.5485i	−0.974037	−	0.817314i	−0.983179	+	0.182644i	$0.941534\pi$
$462$		0			0
$463$	−6.40963	−	36.3508i	−0.297881	−	1.68937i	−0.655257	−	0.755406i	$-0.727440\pi$
$463$	−6.40963	−	36.3508i	−0.297881	−	1.68937i	0.357377	−	0.933960i	$-0.383671\pi$
$464$		0			0
$465$	−1.26256	−	1.49976i	−0.0585500	−	0.0695496i
$466$		0			0
$467$	−2.78853	+	4.82988i	−0.129038	+	0.223500i	−0.923304	−	0.384070i	$-0.874522\pi$
$467$	−2.78853	+	4.82988i	−0.129038	+	0.223500i	0.794266	+	0.607570i	$0.207856\pi$
$468$		0			0
$469$	−9.06274	−	15.6971i	−0.418478	−	0.724826i
$470$		0			0
$471$	−33.0089	+	19.1286i	−1.52097	+	0.881399i
$472$		0			0
$473$	1.20974	−	1.01510i	0.0556241	−	0.0466742i
$474$		0			0
$475$	22.1091	−	8.04706i	1.01444	−	0.369224i
$476$		0			0
$477$	2.57370	+	14.3264i	0.117842	+	0.655961i
$478$		0			0
$479$	−5.52675	+	31.3438i	−0.252524	+	1.43213i	0.549826	+	0.835279i	$0.314694\pi$
$479$	−5.52675	+	31.3438i	−0.252524	+	1.43213i	−0.802349	+	0.596855i	$0.796417\pi$
$480$		0			0
$481$	2.72411	+	0.991495i	0.124209	+	0.0452083i
$482$		0			0
$483$	−6.75300	+	8.07426i	−0.307272	+	0.367391i
$484$		0			0
$485$	8.50762			0.386311
$486$		0			0
$487$	29.5020			1.33687			0.668433	−	0.743773i	$-0.266966\pi$
$487$	29.5020			1.33687			0.668433	+	0.743773i	$0.266966\pi$
$488$		0			0
$489$	9.12556	−	10.9110i	0.412672	−	0.493414i
$490$		0			0
$491$	31.7205	+	11.5453i	1.43152	+	0.521032i	0.937368	−	0.348341i	$-0.113255\pi$
$491$	31.7205	+	11.5453i	1.43152	+	0.521032i	0.494156	+	0.869373i	$0.335477\pi$
$492$		0			0
$493$	−1.00774	+	5.71518i	−0.0453864	+	0.257399i
$494$		0			0
$495$	−0.445700	−	2.48098i	−0.0200327	−	0.111512i
$496$		0			0
$497$	11.1259	−	4.04949i	0.499064	−	0.181645i
$498$		0			0
$499$	3.42361	−	2.87275i	0.153262	−	0.128602i	−0.562932	−	0.826503i	$-0.690327\pi$
$499$	3.42361	−	2.87275i	0.153262	−	0.128602i	0.716194	+	0.697901i	$0.245882\pi$
$500$		0			0
$501$	25.4093	−	14.7246i	1.13520	−	0.657849i
$502$		0			0
$503$	11.5052	+	19.9276i	0.512992	+	0.888529i	0.999886	+	0.0150678i	$0.00479640\pi$
$503$	11.5052	+	19.9276i	0.512992	+	0.888529i	−0.486894	+	0.873461i	$0.661870\pi$
$504$		0			0
$505$	−1.37633	+	2.38388i	−0.0612461	+	0.106081i
$506$		0			0
$507$	−14.3294	−	17.0214i	−0.636389	−	0.755945i
$508$		0			0
$509$	−4.79427	−	27.1897i	−0.212502	−	1.20516i	−0.885188	−	0.465233i	$-0.845971\pi$
$509$	−4.79427	−	27.1897i	−0.212502	−	1.20516i	0.672686	−	0.739928i	$-0.265141\pi$
$510$		0			0
$511$	−0.224412	−	0.188304i	−0.00992738	−	0.00833007i
$512$		0			0
$513$	−24.4854	+	14.2947i	−1.08106	+	0.631126i
$514$		0			0
$515$	4.51393	+	3.78764i	0.198908	+	0.166903i
$516$		0			0
$517$	1.74179	+	9.87819i	0.0766039	+	0.434442i
$518$		0			0
$519$	11.1240	−	30.7167i	0.488291	−	1.34832i
$520$		0			0
$521$	−11.8912	+	20.5961i	−0.520962	+	0.902333i	0.478741	+	0.877956i	$0.341093\pi$
$521$	−11.8912	+	20.5961i	−0.520962	+	0.902333i	−0.999703	+	0.0243763i	$0.992240\pi$
$522$		0			0
$523$	−16.3583	−	28.3334i	−0.715298	−	1.23893i	−0.962845	−	0.270056i	$-0.912958\pi$
$523$	−16.3583	−	28.3334i	−0.715298	−	1.23893i	0.247547	−	0.968876i	$-0.420376\pi$
$524$		0			0
$525$	0.0180427	+	11.2126i	0.000787448	+	0.489358i
$526$		0			0
$527$	−1.12749	+	0.946078i	−0.0491143	+	0.0412118i
$528$		0			0
$529$	6.21561	−	2.26230i	0.270244	−	0.0983607i
$530$		0			0
$531$	0.786630	−	4.54672i	0.0341368	−	0.197311i
$532$		0			0
$533$	−0.473774	+	2.68691i	−0.0205214	+	0.116383i
$534$		0			0
$535$	2.69852	+	0.982181i	0.116667	+	0.0424634i
$536$		0			0
$537$	11.2330	+	1.96205i	0.484739	+	0.0846686i
$538$		0			0
$539$	−4.80751			−0.207074
$540$		0			0
$541$	23.4398			1.00776			0.503878	−	0.863775i	$-0.331906\pi$
$541$	23.4398			1.00776			0.503878	+	0.863775i	$0.331906\pi$
$542$		0			0
$543$	13.3659	+	36.5395i	0.573587	+	1.56806i
$544$		0			0
$545$	−6.92776	−	2.52150i	−0.296753	−	0.108009i
$546$		0			0
$547$	4.08388	−	23.1608i	0.174614	−	0.990285i	−0.763975	−	0.645246i	$-0.776755\pi$
$547$	4.08388	−	23.1608i	0.174614	−	0.990285i	0.938589	−	0.345038i	$-0.112134\pi$
$548$		0			0
$549$	−14.6278	+	0.0470766i	−0.624300	+	0.00200918i
$550$		0			0
$551$	27.5867	−	10.0408i	1.17523	−	0.427750i
$552$		0			0
$553$	1.98378	−	1.66459i	0.0843588	−	0.0707855i
$554$		0			0
$555$	−9.19920	−	5.29144i	−0.390484	−	0.224609i
$556$		0			0
$557$	−3.25007	−	5.62928i	−0.137710	−	0.238520i	0.788920	−	0.614496i	$-0.210641\pi$
$557$	−3.25007	−	5.62928i	−0.137710	−	0.238520i	−0.926629	+	0.375976i	$0.877307\pi$
$558$		0			0
$559$	0.305924	−	0.529877i	0.0129392	−	0.0224114i
$560$		0			0
$561$	−1.86317	+	0.331619i	−0.0786631	+	0.0140010i
$562$		0			0
$563$	1.81419	+	10.2888i	0.0764589	+	0.433620i	0.998875	+	0.0474222i	$0.0151006\pi$
$563$	1.81419	+	10.2888i	0.0764589	+	0.433620i	−0.922416	+	0.386198i	$0.873788\pi$
$564$		0			0
$565$	−9.98841	−	8.38127i	−0.420215	−	0.352603i
$566$		0			0
$567$	−2.43191	−	13.2912i	−0.102131	−	0.558179i
$568$		0			0
$569$	−14.5235	−	12.1867i	−0.608858	−	0.510892i	0.285421	−	0.958402i	$-0.407867\pi$
$569$	−14.5235	−	12.1867i	−0.608858	−	0.510892i	−0.894279	+	0.447510i	$0.852311\pi$
$570$		0			0
$571$	−0.124228	−	0.704529i	−0.00519876	−	0.0294836i	0.982098	−	0.188371i	$-0.0603206\pi$
$571$	−0.124228	−	0.704529i	−0.00519876	−	0.0294836i	−0.987297	+	0.158887i	$0.949209\pi$
$572$		0			0
$573$	−22.6055	+	4.02347i	−0.944357	+	0.168083i
$574$		0			0
$575$	−8.72717	+	15.1159i	−0.363948	+	0.630377i
$576$		0			0
$577$	−8.04548	−	13.9352i	−0.334938	−	0.580129i	0.648535	−	0.761185i	$-0.275382\pi$
$577$	−8.04548	−	13.9352i	−0.334938	−	0.580129i	−0.983473	+	0.181056i	$0.942049\pi$
$578$		0			0
$579$	−36.6496	−	21.0811i	−1.52311	−	0.876101i
$580$		0			0
$581$	10.5985	−	8.89317i	0.439699	−	0.368951i
$582$		0			0
$583$	4.61836	−	1.68094i	0.191273	−	0.0696176i
$584$		0			0
$585$	−0.491028	−	0.844199i	−0.0203015	−	0.0349033i
$586$		0			0
$587$	−4.15996	+	23.5923i	−0.171700	+	0.973759i	0.770184	+	0.637821i	$0.220164\pi$
$587$	−4.15996	+	23.5923i	−0.171700	+	0.973759i	−0.941884	+	0.335937i	$0.890947\pi$
$588$		0			0
$589$	6.99651	+	2.54652i	0.288286	+	0.104928i
$590$		0			0
$591$	−15.7144	−	42.9597i	−0.646404	−	1.76713i
$592$		0			0
$593$	−27.4887			−1.12883			−0.564413	−	0.825492i	$-0.690898\pi$
$593$	−27.4887			−1.12883			−0.564413	+	0.825492i	$0.690898\pi$
$594$		0			0
$595$	−1.34326			−0.0550682
$596$		0			0
$597$	18.0501	+	3.15279i	0.738743	+	0.129035i
$598$		0			0
$599$	−22.6599	−	8.24753i	−0.925858	−	0.336985i	−0.165292	−	0.986245i	$-0.552857\pi$
$599$	−22.6599	−	8.24753i	−0.925858	−	0.336985i	−0.760567	+	0.649260i	$0.775079\pi$
$600$		0			0
$601$	1.96581	−	11.1487i	0.0801870	−	0.454763i	−0.918105	−	0.396338i	$-0.870281\pi$
$601$	1.96581	−	11.1487i	0.0801870	−	0.454763i	0.998292	−	0.0584253i	$-0.0186080\pi$
$602$		0			0
$603$	27.8202	+	23.1918i	1.13293	+	0.944442i
$604$		0			0
$605$	7.77432	−	2.82962i	0.316071	−	0.115040i
$606$		0			0
$607$	25.4334	−	21.3411i	1.03231	−	0.866209i	0.0411841	−	0.999152i	$-0.486887\pi$
$607$	25.4334	−	21.3411i	1.03231	−	0.866209i	0.991124	+	0.132942i	$0.0424425\pi$
$608$		0			0
$609$	0.0225128	+	13.9906i	0.000912267	+	0.566927i
$610$		0			0
$611$	1.94312	+	3.36559i	0.0786103	+	0.136157i
$612$		0			0
$613$	−15.8323	+	27.4223i	−0.639459	+	1.10757i	0.346093	+	0.938200i	$0.387508\pi$
$613$	−15.8323	+	27.4223i	−0.639459	+	1.10757i	−0.985552	+	0.169375i	$0.945825\pi$
$614$		0			0
$615$	3.40099	−	9.39115i	0.137141	−	0.378688i
$616$		0			0
$617$	5.30996	+	30.1143i	0.213771	+	1.21236i	0.883026	+	0.469323i	$0.155502\pi$
$617$	5.30996	+	30.1143i	0.213771	+	1.21236i	−0.669255	+	0.743032i	$0.733387\pi$
$618$		0			0
$619$	12.3451	+	10.3588i	0.496193	+	0.416355i	0.856240	−	0.516579i	$-0.172795\pi$
$619$	12.3451	+	10.3588i	0.496193	+	0.416355i	−0.360047	+	0.932934i	$0.617239\pi$
$620$		0			0
$621$	7.09838	−	19.7995i	0.284848	−	0.794528i
$622$		0			0
$623$	−5.94502	−	4.98846i	−0.238182	−	0.199858i
$624$		0			0
$625$	2.63123	+	14.9225i	0.105249	+	0.596898i
$626$		0			0
$627$	6.16538	+	7.32365i	0.246222	+	0.292478i
$628$		0			0
$629$	−3.98375	+	6.90006i	−0.158843	+	0.275123i
$630$		0			0
$631$	−3.32509	−	5.75923i	−0.132370	−	0.229271i	0.792220	−	0.610236i	$-0.208925\pi$
$631$	−3.32509	−	5.75923i	−0.132370	−	0.229271i	−0.924590	+	0.380964i	$0.875592\pi$
$632$		0			0
$633$	−1.98463	+	1.15009i	−0.0788821	+	0.0457120i
$634$		0			0
$635$	7.63820	−	6.40921i	0.303113	−	0.254342i
$636$		0			0
$637$	−1.75029	+	0.637054i	−0.0693491	+	0.0252410i
$638$		0			0
$639$	−18.0748	+	15.2660i	−0.715030	+	0.603913i
$640$		0			0
$641$	−0.0338793	+	0.192139i	−0.00133815	+	0.00758904i	−0.985470	−	0.169852i	$-0.945671\pi$
$641$	−0.0338793	+	0.192139i	−0.00133815	+	0.00758904i	0.984131	+	0.177441i	$0.0567820\pi$
$642$		0			0
$643$	8.11856	+	2.95492i	0.320165	+	0.116530i	0.497103	−	0.867691i	$-0.334397\pi$
$643$	8.11856	+	2.95492i	0.320165	+	0.116530i	−0.176938	+	0.984222i	$0.556619\pi$
$644$		0			0
$645$	−1.43700	+	1.71815i	−0.0565816	+	0.0676521i
$646$		0			0
$647$	14.3569			0.564429			0.282215	−	0.959351i	$-0.408931\pi$
$647$	14.3569			0.564429			0.282215	+	0.959351i	$0.408931\pi$
$648$		0			0
$649$	−1.55801			−0.0611571
$650$		0			0
$651$	−2.27641	+	2.72180i	−0.0892195	+	0.106676i
$652$		0			0
$653$	4.89387	+	1.78122i	0.191512	+	0.0697047i	0.435996	−	0.899949i	$-0.356396\pi$
$653$	4.89387	+	1.78122i	0.191512	+	0.0697047i	−0.244484	+	0.969653i	$0.578618\pi$
$654$		0			0
$655$	−0.434129	+	2.46207i	−0.0169628	+	0.0962009i
$656$		0			0
$657$	0.550721	+	0.198441i	0.0214857	+	0.00774193i
$658$		0			0
$659$	−12.3022	+	4.47765i	−0.479227	+	0.174424i	−0.570328	−	0.821417i	$-0.693184\pi$
$659$	−12.3022	+	4.47765i	−0.479227	+	0.174424i	0.0911007	+	0.995842i	$0.470961\pi$
$660$		0			0
$661$	3.71289	−	3.11548i	0.144415	−	0.121178i	−0.567718	−	0.823223i	$-0.692174\pi$
$661$	3.71289	−	3.11548i	0.144415	−	0.121178i	0.712133	+	0.702045i	$0.247729\pi$
$662$		0			0
$663$	−0.634389	+	0.367627i	−0.0246376	+	0.0142775i
$664$		0			0
$665$	3.39754	+	5.88472i	0.131751	+	0.228200i
$666$		0			0
$667$	−10.8894	+	18.8609i	−0.421638	+	0.730298i
$668$		0			0
$669$	−19.0763	−	22.6601i	−0.737532	−	0.876090i
$670$		0			0
$671$	0.857667	+	4.86407i	0.0331099	+	0.187775i
$672$		0			0
$673$	24.9836	+	20.9637i	0.963047	+	0.808092i	0.981446	−	0.191738i	$-0.0614125\pi$
$673$	24.9836	+	20.9637i	0.963047	+	0.808092i	−0.0183991	+	0.999831i	$0.505857\pi$
$674$		0			0
$675$	−7.76470	−	21.0171i	−0.298863	−	0.808948i
$676$		0			0
$677$	26.0566	+	21.8641i	1.00144	+	0.840304i	0.987183	−	0.159594i	$-0.0510186\pi$
$677$	26.0566	+	21.8641i	1.00144	+	0.840304i	0.0142529	+	0.999898i	$0.495463\pi$
$678$		0			0
$679$	−2.67387	−	15.1643i	−0.102614	−	0.581952i
$680$		0			0
$681$	7.71851	−	21.3131i	0.295774	−	0.816719i
$682$		0			0
$683$	9.81564	−	17.0012i	0.375585	−	0.650532i	−0.614829	−	0.788660i	$-0.710775\pi$
$683$	9.81564	−	17.0012i	0.375585	−	0.650532i	0.990414	+	0.138128i	$0.0441085\pi$
$684$		0			0
$685$	2.92160	+	5.06036i	0.111629	+	0.193346i
$686$		0			0
$687$	−0.0214818	−	13.3498i	−0.000819581	−	0.509328i
$688$		0			0
$689$	1.45868	−	1.22398i	0.0555713	−	0.0466298i
$690$		0			0
$691$	42.7595	−	15.5632i	1.62665	−	0.592052i	0.642017	−	0.766690i	$-0.278098\pi$
$691$	42.7595	−	15.5632i	1.62665	−	0.592052i	0.984633	+	0.174638i	$0.0558755\pi$
$692$		0			0
$693$	−4.28210	+	1.57418i	−0.162664	+	0.0597983i
$694$		0			0
$695$	1.74700	−	9.90771i	0.0662674	−	0.375821i
$696$		0			0
$697$	−7.04644	−	2.56470i	−0.266903	−	0.0971448i
$698$		0			0
$699$	−38.2927	−	6.68852i	−1.44836	−	0.252983i
$700$		0			0
$701$	0.0811953			0.00306671			0.00153335	−	0.999999i	$-0.499512\pi$
$701$	0.0811953			0.00306671			0.00153335	+	0.999999i	$0.499512\pi$
$702$		0			0
$703$	40.3049			1.52013
$704$		0			0
$705$	−4.88737	−	13.3610i	−0.184069	−	0.503204i
$706$		0			0
$707$	4.68169	+	1.70399i	0.176073	+	0.0640853i
$708$		0			0
$709$	0.0289701	−	0.164297i	0.00108799	−	0.00617032i	−0.984259	−	0.176732i	$-0.943447\pi$
$709$	0.0289701	−	0.164297i	0.00108799	−	0.00617032i	0.985347	+	0.170562i	$0.0545584\pi$
$710$		0			0
$711$	−2.57293	+	4.48975i	−0.0964923	+	0.168379i
$712$		0			0
$713$	−5.19038	+	1.88914i	−0.194381	+	0.0707490i
$714$		0			0
$715$	−0.252607	+	0.211962i	−0.00944697	+	0.00792695i
$716$		0			0
$717$	16.9162	+	9.73032i	0.631747	+	0.363385i
$718$		0			0
$719$	9.15023	+	15.8487i	0.341246	+	0.591056i	0.984664	−	0.174459i	$-0.0558177\pi$
$719$	9.15023	+	15.8487i	0.341246	+	0.591056i	−0.643418	+	0.765515i	$0.722484\pi$
$720$		0			0
$721$	5.33254	−	9.23622i	0.198594	−	0.343975i
$722$		0			0
$723$	5.18239	−	0.922395i	0.192735	−	0.0343043i
$724$		0			0
$725$	4.02853	+	22.8469i	0.149616	+	0.848514i
$726$		0			0
$727$	−6.32399	−	5.30645i	−0.234544	−	0.196805i	0.517939	−	0.855418i	$-0.326699\pi$
$727$	−6.32399	−	5.30645i	−0.234544	−	0.196805i	−0.752483	+	0.658612i	$0.771144\pi$
$728$		0			0
$729$	13.7251	+	23.2513i	0.508338	+	0.861158i
$730$		0			0
$731$	1.28819	+	1.08092i	0.0476456	+	0.0399794i
$732$		0			0
$733$	4.94664	+	28.0538i	0.182708	+	1.03619i	0.928864	+	0.370420i	$0.120786\pi$
$733$	4.94664	+	28.0538i	0.182708	+	1.03619i	−0.746156	+	0.665771i	$0.768103\pi$
$734$		0			0
$735$	6.71321	−	1.19486i	0.247620	−	0.0440731i
$736$		0			0
$737$	6.11470	−	10.5910i	0.225238	−	0.390123i
$738$		0			0
$739$	−21.4894	−	37.2207i	−0.790499	−	1.36918i	−0.925658	−	0.378361i	$-0.876488\pi$
$739$	−21.4894	−	37.2207i	−0.790499	−	1.36918i	0.135159	−	0.990824i	$-0.456845\pi$
$740$		0			0
$741$	3.21513	+	1.84937i	0.118111	+	0.0679381i
$742$		0			0
$743$	16.3479	−	13.7175i	0.599747	−	0.503247i	−0.291617	−	0.956535i	$-0.594193\pi$
$743$	16.3479	−	13.7175i	0.599747	−	0.503247i	0.891364	+	0.453288i	$0.149749\pi$
$744$		0			0
$745$	−5.19331	+	1.89021i	−0.190268	+	0.0692519i
$746$		0			0
$747$	−13.7460	+	23.9868i	−0.502942	+	0.877631i
$748$		0			0
$749$	0.902553	−	5.11863i	0.0329786	−	0.187031i
$750$		0			0
$751$	−24.1893	−	8.80418i	−0.882679	−	0.321269i	−0.139389	−	0.990238i	$-0.544514\pi$
$751$	−24.1893	−	8.80418i	−0.882679	−	0.321269i	−0.743291	+	0.668969i	$0.766736\pi$
$752$		0			0
$753$	17.8730	+	48.8609i	0.651328	+	1.78059i
$754$		0			0
$755$	11.3909			0.414557
$756$		0			0
$757$	−6.42508			−0.233523			−0.116762	−	0.993160i	$-0.537251\pi$
$757$	−6.42508			−0.233523			−0.116762	+	0.993160i	$0.537251\pi$
$758$		0			0
$759$	−6.99605	−	1.22199i	−0.253940	−	0.0443553i
$760$		0			0
$761$	13.1716	+	4.79406i	0.477469	+	0.173784i	0.569533	−	0.821969i	$-0.307124\pi$
$761$	13.1716	+	4.79406i	0.477469	+	0.173784i	−0.0920639	+	0.995753i	$0.529346\pi$
$762$		0			0
$763$	−2.31707	+	13.1408i	−0.0838837	+	0.475728i
$764$		0			0
$765$	2.51931	−	0.926147i	0.0910859	−	0.0334849i
$766$		0			0
$767$	−0.567231	+	0.206455i	−0.0204815	+	0.00745466i
$768$		0			0
$769$	8.81132	−	7.39357i	0.317744	−	0.266619i	−0.469940	−	0.882698i	$-0.655724\pi$
$769$	8.81132	−	7.39357i	0.317744	−	0.266619i	0.787684	+	0.616079i	$0.211280\pi$
$770$		0			0
$771$	0.0563114	+	34.9946i	0.00202801	+	1.26030i
$772$		0			0
$773$	9.37732	+	16.2420i	0.337279	+	0.584184i	0.983920	−	0.178610i	$-0.0571601\pi$
$773$	9.37732	+	16.2420i	0.337279	+	0.584184i	−0.646641	+	0.762794i	$0.723827\pi$
$774$		0			0
$775$	−2.94190	+	5.09551i	−0.105676	+	0.183036i
$776$		0			0
$777$	−6.54043	+	18.0601i	−0.234637	+	0.647901i
$778$		0			0
$779$	6.58704	+	37.3570i	0.236005	+	1.33845i
$780$		0			0
$781$	6.11953	+	5.13490i	0.218974	+	0.183741i
$782$		0			0
$783$	−9.68843	−	26.2242i	−0.346236	−	0.937175i
$784$		0			0
$785$	−13.9961	−	11.7442i	−0.499544	−	0.419167i
$786$		0			0
$787$	6.47085	+	36.6980i	0.230661	+	1.30814i	0.851562	+	0.524254i	$0.175656\pi$
$787$	6.47085	+	36.6980i	0.230661	+	1.30814i	−0.620901	+	0.783889i	$0.713233\pi$
$788$		0			0
$789$	9.41734	+	11.1865i	0.335266	+	0.398252i
$790$		0			0
$791$	−11.7998	+	20.4379i	−0.419553	+	0.726687i
$792$		0			0
$793$	0.956804	+	1.65723i	0.0339771	+	0.0588501i
$794$		0			0
$795$	−6.03129	+	3.49512i	−0.213908	+	0.123959i
$796$		0			0
$797$	17.1517	−	14.3920i	0.607546	−	0.509791i	−0.286315	−	0.958135i	$-0.592430\pi$
$797$	17.1517	−	14.3920i	0.607546	−	0.509791i	0.893861	+	0.448344i	$0.147986\pi$
$798$		0			0
$799$	−10.0369	+	3.65313i	−0.355080	+	0.129238i
$800$		0			0
$801$	14.5895	+	5.25702i	0.515493	+	0.185748i
$802$		0			0
$803$	0.0343224	−	0.194652i	0.00121121	−	0.00686911i
$804$		0			0
$805$	−4.73695	−	1.72411i	−0.166955	−	0.0607668i
$806$		0			0
$807$	16.9372	−	20.2510i	0.596217	−	0.712870i
$808$		0			0
$809$	28.1008			0.987972			0.493986	−	0.869470i	$-0.335539\pi$
$809$	28.1008			0.987972			0.493986	+	0.869470i	$0.335539\pi$
$810$		0			0
$811$	22.9244			0.804984			0.402492	−	0.915423i	$-0.368144\pi$
$811$	22.9244			0.804984			0.402492	+	0.915423i	$0.368144\pi$
$812$		0			0
$813$	−34.8982	+	41.7262i	−1.22393	+	1.46340i
$814$		0			0
$815$	6.40120	+	2.32985i	0.224224	+	0.0816110i
$816$		0			0
$817$	1.47718	−	8.37750i	0.0516800	−	0.293092i
$818$		0			0
$819$	−1.35041	+	1.14055i	−0.0471870	+	0.0398541i
$820$		0			0
$821$	−23.4803	+	8.54612i	−0.819467	+	0.298262i	−0.717529	−	0.696529i	$-0.754727\pi$
$821$	−23.4803	+	8.54612i	−0.819467	+	0.298262i	−0.101939	+	0.994791i	$0.532505\pi$
$822$		0			0
$823$	−9.38214	+	7.87255i	−0.327041	+	0.274420i	−0.791493	−	0.611179i	$-0.790696\pi$
$823$	−9.38214	+	7.87255i	−0.327041	+	0.274420i	0.464452	+	0.885598i	$0.346251\pi$
$824$		0			0
$825$	−6.54559	+	3.79316i	−0.227888	+	0.132061i
$826$		0			0
$827$	−16.9273	−	29.3189i	−0.588618	−	1.01952i	−0.994414	−	0.105553i	$-0.966339\pi$
$827$	−16.9273	−	29.3189i	−0.588618	−	1.01952i	0.405795	−	0.913964i	$-0.366995\pi$
$828$		0			0
$829$	−16.2045	+	28.0670i	−0.562806	+	0.974808i	0.434445	+	0.900699i	$0.356945\pi$
$829$	−16.2045	+	28.0670i	−0.562806	+	0.974808i	−0.997250	+	0.0741093i	$0.976389\pi$
$830$		0			0
$831$	6.20117	+	7.36616i	0.215116	+	0.255529i
$832$		0			0
$833$	−0.888951	−	5.04149i	−0.0308003	−	0.174677i
$834$		0			0
$835$	10.7738	+	9.04032i	0.372844	+	0.312853i
$836$		0			0
$837$	2.39284	−	6.67434i	0.0827086	−	0.230699i
$838$		0			0
$839$	13.7445	+	11.5330i	0.474514	+	0.398165i	0.848438	−	0.529295i	$-0.177543\pi$
$839$	13.7445	+	11.5330i	0.474514	+	0.398165i	−0.373924	+	0.927459i	$0.621988\pi$
$840$		0			0
$841$	−0.00918107	−	0.0520685i	−0.000316589	−	0.00179546i
$842$		0			0
$843$	−9.22467	+	25.4720i	−0.317715	+	0.877304i
$844$		0			0
$845$	5.32779	−	9.22801i	0.183282	−	0.317453i
$846$		0			0
$847$	−7.48702	−	12.9679i	−0.257257	−	0.445583i
$848$		0			0
$849$	0.0134387	+	8.35149i	0.000461217	+	0.286622i
$850$		0			0
$851$	−22.9050	+	19.2196i	−0.785172	+	0.658838i
$852$		0			0
$853$	−21.1902	+	7.71261i	−0.725540	+	0.264075i	−0.678276	−	0.734808i	$-0.737272\pi$
$853$	−21.1902	+	7.71261i	−0.725540	+	0.264075i	−0.0472640	+	0.998882i	$0.515050\pi$
$854$		0			0
$855$	−10.4296	−	8.69440i	−0.356684	−	0.297342i
$856$		0			0
$857$	−5.53617	+	31.3972i	−0.189112	+	1.07251i	0.731446	+	0.681900i	$0.238846\pi$
$857$	−5.53617	+	31.3972i	−0.189112	+	1.07251i	−0.920557	+	0.390607i	$0.872265\pi$
$858$		0			0
$859$	13.0497	+	4.74970i	0.445250	+	0.162058i	0.554908	−	0.831912i	$-0.312753\pi$
$859$	13.0497	+	4.74970i	0.445250	+	0.162058i	−0.109658	+	0.993969i	$0.534976\pi$
$860$		0			0
$861$	−17.8080	−	3.11050i	−0.606896	−	0.106005i
$862$		0			0
$863$	−23.0837			−0.785778			−0.392889	−	0.919586i	$-0.628524\pi$
$863$	−23.0837			−0.785778			−0.392889	+	0.919586i	$0.628524\pi$
$864$		0			0
$865$	15.6454			0.531958
$866$		0			0
$867$	9.42297	+	25.7603i	0.320021	+	0.874867i
$868$		0			0
$869$	1.64188	+	0.597594i	0.0556968	+	0.0202720i
$870$		0			0
$871$	0.822772	−	4.66617i	0.0278786	−	0.158107i
$872$		0			0
$873$	15.4704	+	26.5974i	0.523593	+	0.900187i
$874$		0			0
$875$	−10.8971	+	3.96621i	−0.368388	+	0.134082i
$876$		0			0
$877$	0.355716	−	0.298481i	0.0120117	−	0.0100790i	−0.636762	−	0.771060i	$-0.719727\pi$
$877$	0.355716	−	0.298481i	0.0120117	−	0.0100790i	0.648774	+	0.760981i	$0.275282\pi$
$878$		0			0
$879$	−12.3821	−	7.12228i	−0.417639	−	0.240229i
$880$		0			0
$881$	−8.52830	−	14.7714i	−0.287326	−	0.497663i	0.685845	−	0.727748i	$-0.259433\pi$
$881$	−8.52830	−	14.7714i	−0.287326	−	0.497663i	−0.973171	+	0.230085i	$0.926100\pi$
$882$		0			0
$883$	−20.2075	+	35.0004i	−0.680037	+	1.17786i	0.294933	+	0.955518i	$0.404703\pi$
$883$	−20.2075	+	35.0004i	−0.680037	+	1.17786i	−0.974969	+	0.222340i	$0.928631\pi$
$884$		0			0
$885$	2.17560	−	0.387228i	0.0731321	−	0.0130165i
$886$		0			0
$887$	−4.20784	−	23.8638i	−0.141285	−	0.801270i	−0.970275	−	0.242005i	$-0.922195\pi$
$887$	−4.20784	−	23.8638i	−0.141285	−	0.801270i	0.828989	−	0.559264i	$-0.188916\pi$
$888$		0			0
$889$	−13.8246	−	11.6002i	−0.463663	−	0.389060i
$890$		0			0
$891$	6.94582	−	5.90484i	0.232694	−	0.197820i
$892$		0			0
$893$	41.3907	+	34.7310i	1.38509	+	1.16223i
$894$		0			0
$895$	0.948290	+	5.37802i	0.0316978	+	0.179767i
$896$		0			0
$897$	−2.70901	+	0.482168i	−0.0904513	+	0.0160991i
$898$		0			0
$899$	−3.67076	+	6.35795i	−0.122427	+	0.212049i
$900$		0			0
$901$	2.61673	+	4.53231i	0.0871760	+	0.150993i
$902$		0			0
$903$	3.51413	+	2.02135i	0.116943	+	0.0672664i
$904$		0			0
$905$	−14.2737	+	11.9770i	−0.474473	+	0.398130i
$906$		0			0
$907$	−42.3106	+	15.3998i	−1.40490	+	0.511342i	−0.929629	−	0.368497i	$-0.879872\pi$
$907$	−42.3106	+	15.3998i	−1.40490	+	0.511342i	−0.475272	+	0.879839i	$0.657650\pi$
$908$		0			0
$909$	−9.95549	+	0.0320397i	−0.330203	+	0.00106269i
$910$		0			0
$911$	2.90151	−	16.4553i	0.0961314	−	0.545188i	−0.898263	−	0.439458i	$-0.855171\pi$
$911$	2.90151	−	16.4553i	0.0961314	−	0.545188i	0.994395	−	0.105731i	$-0.0337182\pi$
$912$		0			0
$913$	8.77184	+	3.19269i	0.290305	+	0.105663i
$914$		0			0
$915$	−2.40657	−	6.57903i	−0.0795586	−	0.217496i
$916$		0			0
$917$	4.52492			0.149426
$918$		0			0
$919$	53.4206			1.76218			0.881092	−	0.472945i	$-0.156809\pi$
$919$	53.4206			1.76218			0.881092	+	0.472945i	$0.156809\pi$
$920$		0			0
$921$	59.1691	+	10.3350i	1.94969	+	0.340549i
$922$		0			0
$923$	2.90840	+	1.05857i	0.0957313	+	0.0348433i
$924$		0			0
$925$	−5.53083	+	31.3669i	−0.181852	+	1.03134i
$926$		0			0
$927$	−3.63312	+	20.9994i	−0.119327	+	0.689712i
$928$		0			0
$929$	10.9844	−	3.99800i	0.360387	−	0.131170i	−0.155479	−	0.987839i	$-0.549692\pi$
$929$	10.9844	−	3.99800i	0.360387	−	0.131170i	0.515867	+	0.856669i	$0.327470\pi$
$930$		0			0
$931$	−19.8380	+	16.6460i	−0.650164	+	0.545552i
$932$		0			0
$933$	−0.0412304	−	25.6226i	−0.00134982	−	0.838846i
$934$		0			0
$935$	−0.453153	−	0.784883i	−0.0148197	−	0.0256684i
$936$		0			0
$937$	8.77516	−	15.1990i	0.286672	−	0.496530i	−0.686341	−	0.727280i	$-0.740784\pi$
$937$	8.77516	−	15.1990i	0.286672	−	0.496530i	0.973013	+	0.230749i	$0.0741177\pi$
$938$		0			0
$939$	13.5772	−	37.4906i	0.443075	−	1.22346i
$940$		0			0
$941$	0.647386	+	3.67151i	0.0211042	+	0.119688i	0.993540	−	0.113483i	$-0.0362009\pi$
$941$	0.647386	+	3.67151i	0.0211042	+	0.119688i	−0.972436	+	0.233171i	$0.925090\pi$
$942$		0			0
$943$	−21.5572	−	18.0886i	−0.701998	−	0.589046i
$944$		0			0
$945$	5.58828	−	3.26247i	0.181787	−	0.106128i
$946$		0			0
$947$	−17.6238	−	14.7881i	−0.572697	−	0.480550i	0.309843	−	0.950788i	$-0.399724\pi$
$947$	−17.6238	−	14.7881i	−0.572697	−	0.480550i	−0.882540	+	0.470238i	$0.844168\pi$
$948$		0			0
$949$	−0.0132979	−	0.0754159i	−0.000431667	−	0.00244810i
$950$		0			0
$951$	35.9341	+	42.6849i	1.16524	+	1.38415i
$952$		0			0
$953$	−8.39152	+	14.5345i	−0.271828	+	0.470820i	−0.969330	−	0.245763i	$-0.920961\pi$
$953$	−8.39152	+	14.5345i	−0.271828	+	0.470820i	0.697502	+	0.716583i	$0.254295\pi$
$954$		0			0
$955$	−5.49801	−	9.52283i	−0.177911	−	0.308151i
$956$		0			0
$957$	−8.16729	+	4.73293i	−0.264011	+	0.152994i
$958$		0			0
$959$	8.10153	−	6.79799i	0.261612	−	0.219519i
$960$		0			0
$961$	27.3808	−	9.96580i	0.883252	−	0.321477i
$962$		0			0
$963$	1.83643	+	10.2224i	0.0591781	+	0.329413i
$964$		0			0
$965$	3.51606	−	19.9406i	0.113186	−	0.641909i
$966$		0			0
$967$	−0.828305	−	0.301478i	−0.0266365	−	0.00969489i	0.328668	−	0.944446i	$-0.393400\pi$
$967$	−0.828305	−	0.301478i	−0.0266365	−	0.00969489i	−0.355304	+	0.934751i	$0.615623\pi$
$968$		0			0
$969$	−6.54006	+	7.81966i	−0.210097	+	0.251204i
$970$		0			0
$971$	4.31839			0.138584			0.0692918	−	0.997596i	$-0.477926\pi$
$971$	4.31839			0.138584			0.0692918	+	0.997596i	$0.477926\pi$
$972$		0			0
$973$	−18.2089			−0.583752
$974$		0			0
$975$	−1.88044	+	2.24836i	−0.0602224	+	0.0720053i
$976$		0			0
$977$	−21.1834	−	7.71013i	−0.677717	−	0.246669i	−0.0198503	−	0.999803i	$-0.506319\pi$
$977$	−21.1834	−	7.71013i	−0.677717	−	0.246669i	−0.657867	+	0.753134i	$0.728541\pi$
$978$		0			0
$979$	0.909253	−	5.15663i	0.0290599	−	0.164807i
$980$		0			0
$981$	−4.71456	−	26.2434i	−0.150524	−	0.837889i
$982$		0			0
$983$	36.0745	−	13.1301i	1.15060	−	0.418784i	0.304868	−	0.952394i	$-0.401387\pi$
$983$	36.0745	−	13.1301i	1.15060	−	0.418784i	0.845730	+	0.533611i	$0.179165\pi$
$984$		0			0
$985$	16.7816	−	14.0815i	0.534707	−	0.448673i
$986$		0			0
$987$	−22.2791	+	12.9107i	−0.709151	+	0.410951i
$988$		0			0
$989$	3.15537	+	5.46527i	0.100335	+	0.173785i
$990$		0			0
$991$	−23.0944	+	40.0007i	−0.733617	+	1.27066i	0.221710	+	0.975113i	$0.428836\pi$
$991$	−23.0944	+	40.0007i	−0.733617	+	1.27066i	−0.955327	+	0.295550i	$0.904497\pi$
$992$		0			0
$993$	24.3418	+	28.9149i	0.772465	+	0.917586i
$994$		0			0
$995$	1.52379	+	8.64186i	0.0483075	+	0.273965i
$996$		0			0
$997$	5.95722	+	4.99870i	0.188667	+	0.158310i	0.732229	−	0.681059i	$-0.238480\pi$
$997$	5.95722	+	4.99870i	0.188667	+	0.158310i	−0.543562	+	0.839369i	$0.682925\pi$
$998$		0			0
$999$	−0.185286	−	38.3816i	−0.00586218	−	1.21434i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.y.c.97.3	yes	54
4.3	odd	2		864.2.y.b.97.7	✓	54
27.22	even	9	inner	864.2.y.c.481.3	yes	54
108.103	odd	18		864.2.y.b.481.7	yes	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.y.b.97.7	✓	54	4.3	odd	2
864.2.y.b.481.7	yes	54	108.103	odd	18
864.2.y.c.97.3	yes	54	1.1	even	1	trivial
864.2.y.c.481.3	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)

\(f(q)\)	\(=\)	\(q+(-1.11120 + 1.32862i) q^{3} +(-0.779464 - 0.283702i) q^{5} +(-0.260701 + 1.47851i) q^{7} +(-0.530450 - 2.95273i) q^{9} +O(q^{10})\)	\(q+(-1.11120 + 1.32862i) q^{3} +(-0.779464 - 0.283702i) q^{5} +(-0.260701 + 1.47851i) q^{7} +(-0.530450 - 2.95273i) q^{9} +(-0.951862 + 0.346450i) q^{11} +(-0.300640 + 0.252267i) q^{13} +(1.24307 - 0.720359i) q^{15} +(-0.539319 - 0.934128i) q^{17} +(-2.72824 + 4.72544i) q^{19} +(-1.67468 - 1.98930i) q^{21} +(-0.702910 - 3.98640i) q^{23} +(-3.30314 - 2.77167i) q^{25} +(4.51249 + 2.57632i) q^{27} +(-4.12151 - 3.45836i) q^{29} +(-0.236948 - 1.34380i) q^{31} +(0.597415 - 1.64964i) q^{33} +(0.622663 - 1.07848i) q^{35} +(-3.69331 - 6.39701i) q^{37} +(-0.00109382 - 0.679756i) q^{39} +(5.32552 - 4.46864i) q^{41} +(-1.46500 + 0.533216i) q^{43} +(-0.424228 + 2.45204i) q^{45} +(1.71952 - 9.75189i) q^{47} +(4.45982 + 1.62324i) q^{49} +(1.84039 + 0.321458i) q^{51} -4.85192 q^{53} +0.840231 q^{55} +(-3.24668 - 8.87571i) q^{57} +(1.44533 + 0.526057i) q^{59} +(0.846702 - 4.80188i) q^{61} +(4.50393 - 0.0144950i) q^{63} +(0.305907 - 0.111341i) q^{65} +(-9.24848 + 7.76040i) q^{67} +(6.07748 + 3.49581i) q^{69} +(-3.94317 - 6.82978i) q^{71} +(-0.0975638 + 0.168985i) q^{73} +(7.35296 - 1.30873i) q^{75} +(-0.264078 - 1.49766i) q^{77} +(-1.32136 - 1.10875i) q^{79} +(-8.43725 + 3.13255i) q^{81} +(-7.05944 - 5.92358i) q^{83} +(0.155366 + 0.881125i) q^{85} +(9.17468 - 1.63297i) q^{87} +(-2.58462 + 4.47669i) q^{89} +(-0.294602 - 0.510266i) q^{91} +(2.04870 + 1.17842i) q^{93} +(3.46718 - 2.90931i) q^{95} +(-9.63792 + 3.50792i) q^{97} +(1.52789 + 2.62682i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q+O(q^{10}) \) 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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