LMFDB - Embedded newform 576.2.y.a.335.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,2,Mod(47,576)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(576, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 2]))

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

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

chi := DirichletCharacter("576.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	576.y (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.59938315643$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			335.11
Character	$\chi$	$=$	576.335
Dual form			576.2.y.a.239.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0841095 + 1.73001i) q^{3} +(-1.17929 - 0.315990i) q^{5} +(-1.93802 + 3.35676i) q^{7} +(-2.98585 - 0.291020i) q^{9} +O(q^{10})$	\(q+(-0.0841095 + 1.73001i) q^{3} +(-1.17929 - 0.315990i) q^{5} +(-1.93802 + 3.35676i) q^{7} +(-2.98585 - 0.291020i) q^{9} +(2.53144 - 0.678298i) q^{11} +(-2.21768 - 0.594225i) q^{13} +(0.645854 - 2.01360i) q^{15} -1.65347i q^{17} +(-2.32189 - 2.32189i) q^{19} +(-5.64421 - 3.63513i) q^{21} +(-6.27540 + 3.62310i) q^{23} +(-3.03925 - 1.75471i) q^{25} +(0.754605 - 5.14107i) q^{27} +(5.23808 - 1.40354i) q^{29} +(-6.44476 + 3.72088i) q^{31} +(0.960542 + 4.43646i) q^{33} +(3.34619 - 3.34619i) q^{35} +(0.499924 + 0.499924i) q^{37} +(1.21454 - 3.78662i) q^{39} +(5.22021 + 9.04166i) q^{41} +(-2.07069 - 7.72793i) q^{43} +(3.42922 + 1.28670i) q^{45} +(-1.91487 + 3.31665i) q^{47} +(-4.01188 - 6.94877i) q^{49} +(2.86051 + 0.139072i) q^{51} +(-4.69522 + 4.69522i) q^{53} -3.19964 q^{55} +(4.21219 - 3.82160i) q^{57} +(-1.60258 + 5.98090i) q^{59} +(-2.01670 - 7.52642i) q^{61} +(6.76354 - 9.45877i) q^{63} +(2.42752 + 1.40153i) q^{65} +(-3.58944 + 13.3960i) q^{67} +(-5.74017 - 11.1612i) q^{69} -10.9828i q^{71} +10.4967i q^{73} +(3.29130 - 5.11034i) q^{75} +(-2.62911 + 9.81199i) q^{77} +(7.83718 + 4.52480i) q^{79} +(8.83061 + 1.73789i) q^{81} +(-0.746054 - 2.78431i) q^{83} +(-0.522479 + 1.94992i) q^{85} +(1.98756 + 9.17996i) q^{87} +4.91926 q^{89} +(6.29259 - 6.29259i) q^{91} +(-5.89509 - 11.4624i) q^{93} +(2.00449 + 3.47188i) q^{95} +(-7.00277 + 12.1291i) q^{97} +(-7.75590 + 1.28860i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7}+O(q^{10}) $ 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7	$ 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7} + 6 q^{11} - 2 q^{13} + 8 q^{19} + 2 q^{21} + 12 q^{23} + 16 q^{27} - 6 q^{29} - 8 q^{33} - 8 q^{37} + 32 q^{39} + 2 q^{43} + 6 q^{45} - 24 q^{49} + 12 q^{51} + 16 q^{55} + 42 q^{59} - 2 q^{61} - 12 q^{65} + 2 q^{67} - 10 q^{69} + 56 q^{75} - 6 q^{77} - 8 q^{81} - 54 q^{83} + 8 q^{85} - 48 q^{87} - 20 q^{91} - 34 q^{93} - 4 q^{97} - 46 q^{99}+O(q^{100}) $ 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7 + 6 * q^11 - 2 * q^13 + 8 * q^19 + 2 * q^21 + 12 * q^23 + 16 * q^27 - 6 * q^29 - 8 * q^33 - 8 * q^37 + 32 * q^39 + 2 * q^43 + 6 * q^45 - 24 * q^49 + 12 * q^51 + 16 * q^55 + 42 * q^59 - 2 * q^61 - 12 * q^65 + 2 * q^67 - 10 * q^69 + 56 * q^75 - 6 * q^77 - 8 * q^81 - 54 * q^83 + 8 * q^85 - 48 * q^87 - 20 * q^91 - 34 * q^93 - 4 * q^97 - 46 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−0.0841095	+	1.73001i	−0.0485606	+	0.998820i
$3$	−0.0841095	+	1.73001i	−0.0485606	+	0.998820i
$4$		0			0
$5$	−1.17929	−	0.315990i	−0.527394	−	0.141315i	−0.0147097	−	0.999892i	$-0.504682\pi$
$5$	−1.17929	−	0.315990i	−0.527394	−	0.141315i	−0.512685	+	0.858577i	$0.671349\pi$
$6$		0			0
$7$	−1.93802	+	3.35676i	−0.732504	+	1.26873i	0.223305	+	0.974749i	$0.428315\pi$
$7$	−1.93802	+	3.35676i	−0.732504	+	1.26873i	−0.955810	+	0.293986i	$0.905018\pi$
$8$		0			0
$9$	−2.98585	−	0.291020i	−0.995284	−	0.0970067i
$10$		0			0
$11$	2.53144	−	0.678298i	0.763258	−	0.204514i	0.143867	−	0.989597i	$-0.454046\pi$
$11$	2.53144	−	0.678298i	0.763258	−	0.204514i	0.619391	+	0.785083i	$0.287380\pi$
$12$		0			0
$13$	−2.21768	−	0.594225i	−0.615074	−	0.164808i	−0.0621864	−	0.998065i	$-0.519807\pi$
$13$	−2.21768	−	0.594225i	−0.615074	−	0.164808i	−0.552887	+	0.833256i	$0.686474\pi$
$14$		0			0
$15$	0.645854	−	2.01360i	0.166759	−	0.519910i
$16$		0			0
$17$		−	1.65347i		−	0.401025i	−0.979691	−	0.200512i	$-0.935739\pi$
$17$		−	1.65347i		−	0.401025i	0.979691	−	0.200512i	$-0.0642607\pi$
$18$		0			0
$19$	−2.32189	−	2.32189i	−0.532679	−	0.532679i	0.388690	−	0.921369i	$-0.372928\pi$
$19$	−2.32189	−	2.32189i	−0.532679	−	0.532679i	−0.921369	+	0.388690i	$0.872928\pi$
$20$		0			0
$21$	−5.64421	−	3.63513i	−1.23167	−	0.793251i
$22$		0			0
$23$	−6.27540	+	3.62310i	−1.30851	+	0.755469i	−0.981848	−	0.189672i	$-0.939258\pi$
$23$	−6.27540	+	3.62310i	−1.30851	+	0.755469i	−0.326663	+	0.945141i	$0.605924\pi$
$24$		0			0
$25$	−3.03925	−	1.75471i	−0.607850	−	0.350943i
$26$		0			0
$27$	0.754605	−	5.14107i	0.145224	−	0.989399i
$28$		0			0
$29$	5.23808	−	1.40354i	0.972686	−	0.260631i	0.262725	−	0.964871i	$-0.415379\pi$
$29$	5.23808	−	1.40354i	0.972686	−	0.260631i	0.709962	+	0.704240i	$0.248712\pi$
$30$		0			0
$31$	−6.44476	+	3.72088i	−1.15751	+	0.668291i	−0.950707	−	0.310091i	$-0.899640\pi$
$31$	−6.44476	+	3.72088i	−1.15751	+	0.668291i	−0.206806	+	0.978382i	$0.566307\pi$
$32$		0			0
$33$	0.960542	+	4.43646i	0.167209	+	0.772289i
$34$		0			0
$35$	3.34619	−	3.34619i	0.565610	−	0.565610i
$36$		0			0
$37$	0.499924	+	0.499924i	0.0821870	+	0.0821870i	0.747005	−	0.664818i	$-0.231491\pi$
$37$	0.499924	+	0.499924i	0.0821870	+	0.0821870i	−0.664818	+	0.747005i	$0.731491\pi$
$38$		0			0
$39$	1.21454	−	3.78662i	0.194482	−	0.606345i
$40$		0			0
$41$	5.22021	+	9.04166i	0.815259	+	1.41207i	0.909142	+	0.416487i	$0.136739\pi$
$41$	5.22021	+	9.04166i	0.815259	+	1.41207i	−0.0938824	+	0.995583i	$0.529928\pi$
$42$		0			0
$43$	−2.07069	−	7.72793i	−0.315778	−	1.17850i	−0.923263	−	0.384168i	$-0.874488\pi$
$43$	−2.07069	−	7.72793i	−0.315778	−	1.17850i	0.607485	−	0.794331i	$-0.292178\pi$
$44$		0			0
$45$	3.42922	+	1.28670i	0.511199	+	0.191809i
$46$		0			0
$47$	−1.91487	+	3.31665i	−0.279312	+	0.483782i	−0.971214	−	0.238209i	$-0.923440\pi$
$47$	−1.91487	+	3.31665i	−0.279312	+	0.483782i	0.691902	+	0.721991i	$0.256773\pi$
$48$		0			0
$49$	−4.01188	−	6.94877i	−0.573125	−	0.992682i
$50$		0			0
$51$	2.86051	+	0.139072i	0.400552	+	0.0194740i
$52$		0			0
$53$	−4.69522	+	4.69522i	−0.644938	+	0.644938i	−0.951765	−	0.306827i	$-0.900733\pi$
$53$	−4.69522	+	4.69522i	−0.644938	+	0.644938i	0.306827	+	0.951765i	$0.400733\pi$
$54$		0			0
$55$	−3.19964			−0.431439
$56$		0			0
$57$	4.21219	−	3.82160i	0.557918	−	0.506183i
$58$		0			0
$59$	−1.60258	+	5.98090i	−0.208638	+	0.778647i	0.779672	+	0.626188i	$0.215386\pi$
$59$	−1.60258	+	5.98090i	−0.208638	+	0.778647i	−0.988310	+	0.152459i	$0.951281\pi$
$60$		0			0
$61$	−2.01670	−	7.52642i	−0.258212	−	0.963660i	−0.966275	−	0.257511i	$-0.917098\pi$
$61$	−2.01670	−	7.52642i	−0.258212	−	0.963660i	0.708064	−	0.706149i	$-0.249569\pi$
$62$		0			0
$63$	6.76354	−	9.45877i	0.852125	−	1.19169i
$64$		0			0
$65$	2.42752	+	1.40153i	0.301097	+	0.173838i
$66$		0			0
$67$	−3.58944	+	13.3960i	−0.438520	+	1.63658i	0.293980	+	0.955812i	$0.405020\pi$
$67$	−3.58944	+	13.3960i	−0.438520	+	1.63658i	−0.732500	+	0.680767i	$0.761647\pi$
$68$		0			0
$69$	−5.74017	−	11.1612i	−0.691036	−	1.34365i
$70$		0			0
$71$		−	10.9828i		−	1.30341i	−0.758471	−	0.651706i	$-0.774053\pi$
$71$		−	10.9828i		−	1.30341i	0.758471	−	0.651706i	$-0.225947\pi$
$72$		0			0
$73$			10.4967i			1.22855i	0.789092	+	0.614276i	$0.210552\pi$
$73$			10.4967i			1.22855i	−0.789092	+	0.614276i	$0.789448\pi$
$74$		0			0
$75$	3.29130	−	5.11034i	0.380046	−	0.590091i
$76$		0			0
$77$	−2.62911	+	9.81199i	−0.299615	+	1.11818i
$78$		0			0
$79$	7.83718	+	4.52480i	0.881751	+	0.509079i	0.871235	−	0.490865i	$-0.163319\pi$
$79$	7.83718	+	4.52480i	0.881751	+	0.509079i	0.0105159	+	0.999945i	$0.496653\pi$
$80$		0			0
$81$	8.83061	+	1.73789i	0.981179	+	0.193098i
$82$		0			0
$83$	−0.746054	−	2.78431i	−0.0818900	−	0.305618i	0.912817	−	0.408369i	$-0.133902\pi$
$83$	−0.746054	−	2.78431i	−0.0818900	−	0.305618i	−0.994707	+	0.102751i	$0.967236\pi$
$84$		0			0
$85$	−0.522479	+	1.94992i	−0.0566708	+	0.211498i
$86$		0			0
$87$	1.98756	+	9.17996i	0.213089	+	0.984195i
$88$		0			0
$89$	4.91926			0.521441			0.260720	−	0.965414i	$-0.416040\pi$
$89$	4.91926			0.521441			0.260720	+	0.965414i	$0.416040\pi$
$90$		0			0
$91$	6.29259	−	6.29259i	0.659642	−	0.659642i
$92$		0			0
$93$	−5.89509	−	11.4624i	−0.611293	−	1.18860i
$94$		0			0
$95$	2.00449	+	3.47188i	0.205656	+	0.356207i
$96$		0			0
$97$	−7.00277	+	12.1291i	−0.711023	+	1.23153i	0.253450	+	0.967348i	$0.418435\pi$
$97$	−7.00277	+	12.1291i	−0.711023	+	1.23153i	−0.964473	+	0.264180i	$0.914899\pi$
$98$		0			0
$99$	−7.75590	+	1.28860i	−0.779498	+	0.129509i
$100$		0			0
$101$	1.05238	+	3.92753i	0.104716	+	0.390804i	0.998313	−	0.0580659i	$-0.0184933\pi$
$101$	1.05238	+	3.92753i	0.104716	+	0.390804i	−0.893597	+	0.448870i	$0.851827\pi$
$102$		0			0
$103$	−3.96541	−	6.86830i	−0.390724	−	0.676754i	0.601821	−	0.798631i	$-0.294442\pi$
$103$	−3.96541	−	6.86830i	−0.390724	−	0.676754i	−0.992545	+	0.121877i	$0.961109\pi$
$104$		0			0
$105$	5.50749	+	6.07039i	0.537476	+	0.592409i
$106$		0			0
$107$	10.7040	+	10.7040i	1.03479	+	1.03479i	0.999372	+	0.0354212i	$0.0112773\pi$
$107$	10.7040	+	10.7040i	1.03479	+	1.03479i	0.0354212	+	0.999372i	$0.488723\pi$
$108$		0			0
$109$	−0.225954	+	0.225954i	−0.0216424	+	0.0216424i	−0.717845	−	0.696203i	$-0.754871\pi$
$109$	−0.225954	+	0.225954i	−0.0216424	+	0.0216424i	0.696203	+	0.717845i	$0.254871\pi$
$110$		0			0
$111$	−0.906921	+	0.822824i	−0.0860811	+	0.0780990i
$112$		0			0
$113$	2.55128	−	1.47298i	0.240004	−	0.138567i	−0.375174	−	0.926954i	$-0.622417\pi$
$113$	2.55128	−	1.47298i	0.240004	−	0.138567i	0.615179	+	0.788388i	$0.289084\pi$
$114$		0			0
$115$	8.54538	−	2.28973i	0.796860	−	0.213518i
$116$		0			0
$117$	6.44873	+	2.41966i	0.596185	+	0.223697i
$118$		0			0
$119$	5.55029	+	3.20446i	0.508794	+	0.293752i
$120$		0			0
$121$	−3.57817	+	2.06586i	−0.325289	+	0.187805i
$122$		0			0
$123$	−16.0812	+	8.27051i	−1.44999	+	0.745726i
$124$		0			0
$125$	7.34619	+	7.34619i	0.657063	+	0.657063i
$126$		0			0
$127$			20.0270i			1.77711i	0.458770	+	0.888555i	$0.348290\pi$
$127$			20.0270i			1.77711i	−0.458770	+	0.888555i	$0.651710\pi$
$128$		0			0
$129$	13.5435	−	2.93232i	1.19244	−	0.258177i
$130$		0			0
$131$	8.78388	+	2.35363i	0.767451	+	0.205638i	0.621245	−	0.783616i	$-0.286627\pi$
$131$	8.78388	+	2.35363i	0.767451	+	0.205638i	0.146206	+	0.989254i	$0.453294\pi$
$132$		0			0
$133$	12.2939	−	3.29415i	1.06602	−	0.285639i
$134$		0			0
$135$	−2.51442	+	5.82436i	−0.216407	+	0.501281i
$136$		0			0
$137$	5.06820	−	8.77838i	0.433005	−	0.749987i	−0.564125	−	0.825689i	$-0.690786\pi$
$137$	5.06820	−	8.77838i	0.433005	−	0.749987i	0.997130	+	0.0757020i	$0.0241198\pi$
$138$		0			0
$139$	−6.98099	−	1.87055i	−0.592120	−	0.158658i	−0.0496980	−	0.998764i	$-0.515826\pi$
$139$	−6.98099	−	1.87055i	−0.592120	−	0.158658i	−0.542422	+	0.840106i	$0.682493\pi$
$140$		0			0
$141$	−5.57676	−	3.59169i	−0.469648	−	0.302475i
$142$		0			0
$143$	−6.01699			−0.503166
$144$		0			0
$145$	−6.62071			−0.549820
$146$		0			0
$147$	12.3589	−	6.35612i	1.01934	−	0.524244i
$148$		0			0
$149$	−3.33856	−	0.894564i	−0.273505	−	0.0732855i	0.119459	−	0.992839i	$-0.461884\pi$
$149$	−3.33856	−	0.894564i	−0.273505	−	0.0732855i	−0.392965	+	0.919554i	$0.628551\pi$
$150$		0			0
$151$	0.234448	−	0.406076i	0.0190791	−	0.0330460i	−0.856328	−	0.516432i	$-0.827260\pi$
$151$	0.234448	−	0.406076i	0.0190791	−	0.0330460i	0.875407	+	0.483386i	$0.160593\pi$
$152$		0			0
$153$	−0.481192	+	4.93701i	−0.0389021	+	0.399133i
$154$		0			0
$155$	8.77600	−	2.35152i	0.704906	−	0.188879i
$156$		0			0
$157$	6.27529	+	1.68146i	0.500823	+	0.134195i	0.500382	−	0.865805i	$-0.333193\pi$
$157$	6.27529	+	1.68146i	0.500823	+	0.134195i	0.000440823		1.00000i	$0.499860\pi$
$158$		0			0
$159$	−7.72785	−	8.51768i	−0.612859	−	0.675496i
$160$		0			0
$161$		−	28.0866i		−	2.21354i
$162$		0			0
$163$	−10.7957	−	10.7957i	−0.845583	−	0.845583i	0.143996	−	0.989578i	$-0.454005\pi$
$163$	−10.7957	−	10.7957i	−0.845583	−	0.845583i	−0.989578	+	0.143996i	$0.954005\pi$
$164$		0			0
$165$	0.269120	−	5.53540i	0.0209510	−	0.430930i
$166$		0			0
$167$	5.80942	−	3.35407i	0.449546	−	0.259546i	−0.258092	−	0.966120i	$-0.583094\pi$
$167$	5.80942	−	3.35407i	0.449546	−	0.259546i	0.707639	+	0.706575i	$0.249761\pi$
$168$		0			0
$169$	−6.69333	−	3.86440i	−0.514872	−	0.297261i
$170$		0			0
$171$	6.25711	+	7.60855i	0.478493	+	0.581840i
$172$		0			0
$173$	−7.96162	+	2.13331i	−0.605310	+	0.162192i	−0.548441	−	0.836189i	$-0.684779\pi$
$173$	−7.96162	+	2.13331i	−0.605310	+	0.162192i	−0.0568693	+	0.998382i	$0.518112\pi$
$174$		0			0
$175$	11.7803	−	6.80135i	0.890506	−	0.514134i
$176$		0			0
$177$	−10.2122	−	3.27552i	−0.767597	−	0.246203i
$178$		0			0
$179$	3.01712	−	3.01712i	0.225510	−	0.225510i	−0.585304	−	0.810814i	$-0.699025\pi$
$179$	3.01712	−	3.01712i	0.225510	−	0.225510i	0.810814	+	0.585304i	$0.199025\pi$
$180$		0			0
$181$	13.4602	+	13.4602i	1.00049	+	1.00049i	1.00000		0.000489717i	$0.000155882\pi$
$181$	13.4602	+	13.4602i	1.00049	+	1.00049i	0.000489717		1.00000i	$0.499844\pi$
$182$		0			0
$183$	13.1904	−	2.85586i	0.975062	−	0.211111i
$184$		0			0
$185$	−0.431585	−	0.747526i	−0.0317307	−	0.0549592i
$186$		0			0
$187$	−1.12154	−	4.18565i	−0.0820153	−	0.306085i
$188$		0			0
$189$	15.7949	+	12.4965i	1.14891	+	0.908989i
$190$		0			0
$191$	−0.130752	+	0.226469i	−0.00946088	+	0.0163867i	−0.870717	−	0.491784i	$-0.836345\pi$
$191$	−0.130752	+	0.226469i	−0.00946088	+	0.0163867i	0.861256	+	0.508171i	$0.169678\pi$
$192$		0			0
$193$	0.344850	+	0.597298i	0.0248229	+	0.0429944i	0.878170	−	0.478349i	$-0.158764\pi$
$193$	0.344850	+	0.597298i	0.0248229	+	0.0429944i	−0.853347	+	0.521343i	$0.825431\pi$
$194$		0			0
$195$	−2.62883	+	4.08174i	−0.188255	+	0.292300i
$196$		0			0
$197$	5.05530	−	5.05530i	0.360175	−	0.360175i	−0.503702	−	0.863877i	$-0.668029\pi$
$197$	5.05530	−	5.05530i	0.360175	−	0.360175i	0.863877	+	0.503702i	$0.168029\pi$
$198$		0			0
$199$	4.15845			0.294785			0.147392	−	0.989078i	$-0.452912\pi$
$199$	4.15845			0.294785			0.147392	+	0.989078i	$0.452912\pi$
$200$		0			0
$201$	−22.8732	−	7.33649i	−1.61335	−	0.517476i
$202$		0			0
$203$	−5.44018	+	20.3030i	−0.381826	+	1.42499i
$204$		0			0
$205$	−3.29906	−	12.3123i	−0.230417	−	0.859926i
$206$		0			0
$207$	19.7918	−	8.99178i	1.37563	−	0.624972i
$208$		0			0
$209$	−7.45267	−	4.30280i	−0.515512	−	0.297631i
$210$		0			0
$211$	2.22080	−	8.28816i	0.152887	−	0.570580i	−0.846391	−	0.532563i	$-0.821229\pi$
$211$	2.22080	−	8.28816i	0.152887	−	0.570580i	0.999277	−	0.0380175i	$-0.0121043\pi$
$212$		0			0
$213$	19.0002	+	0.923754i	1.30188	+	0.0632946i
$214$		0			0
$215$			9.76779i			0.666158i
$216$		0			0
$217$		−	28.8447i		−	1.95810i
$218$		0			0
$219$	−18.1594	−	0.882876i	−1.22710	−	0.0596592i
$220$		0			0
$221$	−0.982532	+	3.66686i	−0.0660923	+	0.246660i
$222$		0			0
$223$	−10.4773	−	6.04905i	−0.701610	−	0.405074i	0.106337	−	0.994330i	$-0.466088\pi$
$223$	−10.4773	−	6.04905i	−0.701610	−	0.405074i	−0.807947	+	0.589256i	$0.799421\pi$
$224$		0			0
$225$	8.56410	+	6.12379i	0.570940	+	0.408253i
$226$		0			0
$227$	3.35751	+	12.5304i	0.222846	+	0.831671i	0.983256	+	0.182229i	$0.0583311\pi$
$227$	3.35751	+	12.5304i	0.222846	+	0.831671i	−0.760411	+	0.649443i	$0.775002\pi$
$228$		0			0
$229$	−1.70767	+	6.37310i	−0.112846	+	0.421146i	−0.999117	−	0.0420210i	$-0.986620\pi$
$229$	−1.70767	+	6.37310i	−0.112846	+	0.421146i	0.886271	+	0.463167i	$0.153287\pi$
$230$		0			0
$231$	−16.7537	−	5.37367i	−1.10231	−	0.353561i
$232$		0			0
$233$	−7.09511			−0.464816			−0.232408	−	0.972618i	$-0.574660\pi$
$233$	−7.09511			−0.464816			−0.232408	+	0.972618i	$0.574660\pi$
$234$		0			0
$235$	3.30621	−	3.30621i	0.215673	−	0.215673i
$236$		0			0
$237$	−8.48711	+	13.1778i	−0.551297	+	0.855990i
$238$		0			0
$239$	−8.35740	−	14.4754i	−0.540595	−	0.936338i	−0.998870	−	0.0475275i	$-0.984866\pi$
$239$	−8.35740	−	14.4754i	−0.540595	−	0.936338i	0.458275	−	0.888810i	$-0.348468\pi$
$240$		0			0
$241$	−13.3143	+	23.0610i	−0.857647	+	1.48549i	0.0165212	+	0.999864i	$0.494741\pi$
$241$	−13.3143	+	23.0610i	−0.857647	+	1.48549i	−0.874168	+	0.485624i	$0.838592\pi$
$242$		0			0
$243$	−3.74929	+	15.1309i	−0.240517	+	0.970645i
$244$		0			0
$245$	2.53542	+	9.46233i	0.161982	+	0.604526i
$246$		0			0
$247$	3.76949	+	6.52894i	0.239847	+	0.415427i
$248$		0			0
$249$	4.87963	−	1.05649i	0.309234	−	0.0669524i
$250$		0			0
$251$	−12.5807	−	12.5807i	−0.794085	−	0.794085i	0.188070	−	0.982156i	$-0.439777\pi$
$251$	−12.5807	−	12.5807i	−0.794085	−	0.794085i	−0.982156	+	0.188070i	$0.939777\pi$
$252$		0			0
$253$	−13.4283	+	13.4283i	−0.844227	+	0.844227i
$254$		0			0
$255$	−3.32943	−	1.06790i	−0.208497	−	0.0668744i
$256$		0			0
$257$	−15.6784	+	9.05193i	−0.977992	+	0.564644i	−0.901663	−	0.432439i	$-0.857653\pi$
$257$	−15.6784	+	9.05193i	−0.977992	+	0.564644i	−0.0763288	+	0.997083i	$0.524320\pi$
$258$		0			0
$259$	−2.64699	+	0.709259i	−0.164476	+	0.0440712i
$260$		0			0
$261$	−16.0486	+	2.66637i	−0.993382	+	0.165044i
$262$		0			0
$263$	4.90611	+	2.83254i	0.302524	+	0.174662i	0.643576	−	0.765382i	$-0.277450\pi$
$263$	4.90611	+	2.83254i	0.302524	+	0.174662i	−0.341052	+	0.940044i	$0.610783\pi$
$264$		0			0
$265$	7.02067	−	4.05338i	0.431276	−	0.248997i
$266$		0			0
$267$	−0.413757	+	8.51036i	−0.0253215	+	0.520826i
$268$		0			0
$269$	−14.2691	−	14.2691i	−0.870000	−	0.870000i	0.122472	−	0.992472i	$-0.460918\pi$
$269$	−14.2691	−	14.2691i	−0.870000	−	0.870000i	−0.992472	+	0.122472i	$0.960918\pi$
$270$		0			0
$271$		−	0.189638i		−	0.0115197i	−0.999983	−	0.00575985i	$-0.998167\pi$
$271$		−	0.189638i		−	0.0115197i	0.999983	−	0.00575985i	$-0.00183343\pi$
$272$		0			0
$273$	10.3570	+	11.4155i	0.626831	+	0.690897i
$274$		0			0
$275$	−8.88390	−	2.38043i	−0.535720	−	0.143546i
$276$		0			0
$277$	−7.79717	+	2.08925i	−0.468487	+	0.125531i	−0.485337	−	0.874327i	$-0.661303\pi$
$277$	−7.79717	+	2.08925i	−0.468487	+	0.125531i	0.0168499	+	0.999858i	$0.494636\pi$
$278$		0			0
$279$	20.3259	−	9.23445i	1.21688	−	0.552852i
$280$		0			0
$281$	1.54002	−	2.66740i	0.0918700	−	0.159124i	−0.816428	−	0.577447i	$-0.804049\pi$
$281$	1.54002	−	2.66740i	0.0918700	−	0.159124i	0.908298	+	0.418324i	$0.137382\pi$
$282$		0			0
$283$	−7.94293	−	2.12830i	−0.472158	−	0.126514i	0.0148908	−	0.999889i	$-0.495260\pi$
$283$	−7.94293	−	2.12830i	−0.472158	−	0.126514i	−0.487049	+	0.873375i	$0.661927\pi$
$284$		0			0
$285$	−6.17498	+	3.17577i	−0.365774	+	0.188116i
$286$		0			0
$287$	−40.4675			−2.38872
$288$		0			0
$289$	14.2660			0.839179
$290$		0			0
$291$	−20.3945	−	13.1350i	−1.19555	−	0.769988i
$292$		0			0
$293$	−20.7143	−	5.55039i	−1.21014	−	0.324257i	−0.403326	−	0.915056i	$-0.632146\pi$
$293$	−20.7143	−	5.55039i	−1.21014	−	0.324257i	−0.806819	+	0.590799i	$0.798813\pi$
$294$		0			0
$295$	3.77981	−	6.54682i	0.220069	−	0.381171i
$296$		0			0
$297$	−1.57693	−	13.5262i	−0.0915030	−	0.784867i
$298$		0			0
$299$	16.0698	−	4.30588i	0.929338	−	0.249015i
$300$		0			0
$301$	29.9538	+	8.02611i	1.72651	+	0.462617i
$302$		0			0
$303$	−6.88317	+	1.49028i	−0.395428	+	0.0856144i
$304$		0			0
$305$			9.51309i			0.544718i
$306$		0			0
$307$	−14.6450	−	14.6450i	−0.835837	−	0.835837i	0.152471	−	0.988308i	$-0.451277\pi$
$307$	−14.6450	−	14.6450i	−0.835837	−	0.835837i	−0.988308	+	0.152471i	$0.951277\pi$
$308$		0			0
$309$	12.2157	−	6.28251i	0.694929	−	0.357399i
$310$		0			0
$311$	0.242062	−	0.139755i	0.0137261	−	0.00792475i	−0.493121	−	0.869961i	$-0.664144\pi$
$311$	0.242062	−	0.139755i	0.0137261	−	0.00792475i	0.506847	+	0.862036i	$0.330811\pi$
$312$		0			0
$313$	8.17606	+	4.72045i	0.462138	+	0.266816i	0.712943	−	0.701222i	$-0.247362\pi$
$313$	8.17606	+	4.72045i	0.462138	+	0.266816i	−0.250805	+	0.968038i	$0.580695\pi$
$314$		0			0
$315$	−10.9650	+	9.01743i	−0.617810	+	0.508074i
$316$		0			0
$317$	29.5930	−	7.92943i	1.66211	−	0.445361i	0.699144	−	0.714981i	$-0.253565\pi$
$317$	29.5930	−	7.92943i	1.66211	−	0.445361i	0.962967	+	0.269619i	$0.0868979\pi$
$318$		0			0
$319$	12.3079	−	7.10595i	0.689108	−	0.397857i
$320$		0			0
$321$	−19.4183	+	17.6177i	−1.08382	+	0.983323i
$322$		0			0
$323$	−3.83917	+	3.83917i	−0.213617	+	0.213617i
$324$		0			0
$325$	5.69739	+	5.69739i	0.316034	+	0.316034i
$326$		0			0
$327$	−0.371897	−	0.409906i	−0.0205659	−	0.0226679i
$328$		0			0
$329$	−7.42211	−	12.8555i	−0.409194	−	0.708745i
$330$		0			0
$331$	7.00136	+	26.1294i	0.384829	+	1.43620i	0.838436	+	0.545001i	$0.183471\pi$
$331$	7.00136	+	26.1294i	0.384829	+	1.43620i	−0.453606	+	0.891202i	$0.649863\pi$
$332$		0			0
$333$	−1.34721	−	1.63819i	−0.0738267	−	0.0897721i
$334$		0			0
$335$	8.46598	−	14.6635i	0.462546	−	0.801153i
$336$		0			0
$337$	−7.23274	−	12.5275i	−0.393993	−	0.682415i	0.598980	−	0.800764i	$-0.295573\pi$
$337$	−7.23274	−	12.5275i	−0.393993	−	0.682415i	−0.992972	+	0.118349i	$0.962240\pi$
$338$		0			0
$339$	2.33368	+	4.53763i	0.126748	+	0.246450i
$340$		0			0
$341$	−13.7907	+	13.7907i	−0.746806	+	0.746806i
$342$		0			0
$343$	3.96811			0.214258
$344$		0			0
$345$	3.24250	+	14.9762i	0.174570	+	0.806289i
$346$		0			0
$347$	2.74121	−	10.2303i	0.147156	−	0.549194i	−0.852494	−	0.522737i	$-0.824911\pi$
$347$	2.74121	−	10.2303i	0.147156	−	0.549194i	0.999650	−	0.0264566i	$-0.00842240\pi$
$348$		0			0
$349$	−0.171076	−	0.638465i	−0.00915749	−	0.0341762i	0.961196	−	0.275867i	$-0.0889648\pi$
$349$	−0.171076	−	0.638465i	−0.00915749	−	0.0341762i	−0.970353	+	0.241690i	$0.922298\pi$
$350$		0			0
$351$	−4.72843	+	10.9528i	−0.252385	+	0.584619i
$352$		0			0
$353$	8.55438	+	4.93888i	0.455304	+	0.262870i	0.710068	−	0.704133i	$-0.248664\pi$
$353$	8.55438	+	4.93888i	0.455304	+	0.262870i	−0.254764	+	0.967003i	$0.581998\pi$
$354$		0			0
$355$	−3.47044	+	12.9518i	−0.184192	+	0.687413i
$356$		0			0
$357$	−6.01057	+	9.33251i	−0.318113	+	0.493929i
$358$		0			0
$359$		−	31.4509i		−	1.65991i	−0.557828	−	0.829956i	$-0.688365\pi$
$359$		−	31.4509i		−	1.65991i	0.557828	−	0.829956i	$-0.311635\pi$
$360$		0			0
$361$		−	8.21762i		−	0.432506i
$362$		0			0
$363$	−3.27299	−	6.36403i	−0.171788	−	0.334025i
$364$		0			0
$365$	3.31686	−	12.3787i	0.173613	−	0.647931i
$366$		0			0
$367$	2.27957	+	1.31611i	0.118993	+	0.0687004i	0.558315	−	0.829629i	$-0.311448\pi$
$367$	2.27957	+	1.31611i	0.118993	+	0.0687004i	−0.439322	+	0.898329i	$0.644781\pi$
$368$		0			0
$369$	−12.9555	−	28.5162i	−0.674434	−	1.48450i
$370$		0			0
$371$	−6.66126	−	24.8602i	−0.345835	−	1.29068i
$372$		0			0
$373$	6.22536	−	23.2334i	0.322337	−	1.20298i	−0.594625	−	0.804003i	$-0.702699\pi$
$373$	6.22536	−	23.2334i	0.322337	−	1.20298i	0.916962	−	0.398975i	$-0.130634\pi$
$374$		0			0
$375$	−13.3268	+	12.0911i	−0.688195	+	0.624380i
$376$		0			0
$377$	−12.4504			−0.641228
$378$		0			0
$379$	8.59872	−	8.59872i	0.441687	−	0.441687i	−0.450892	−	0.892579i	$-0.648894\pi$
$379$	8.59872	−	8.59872i	0.441687	−	0.441687i	0.892579	+	0.450892i	$0.148894\pi$
$380$		0			0
$381$	−34.6469	−	1.68446i	−1.77501	−	0.0862976i
$382$		0			0
$383$	6.23486	+	10.7991i	0.318586	+	0.551808i	0.980193	−	0.198043i	$-0.0634585\pi$
$383$	6.23486	+	10.7991i	0.318586	+	0.551808i	−0.661607	+	0.749851i	$0.730125\pi$
$384$		0			0
$385$	6.20098	−	10.7404i	0.316031	−	0.547382i
$386$		0			0
$387$	3.93380	+	23.6771i	0.199966	+	1.20357i
$388$		0			0
$389$	3.38346	+	12.6272i	0.171548	+	0.640227i	0.997114	+	0.0759206i	$0.0241896\pi$
$389$	3.38346	+	12.6272i	0.171548	+	0.640227i	−0.825566	+	0.564306i	$0.809144\pi$
$390$		0			0
$391$	5.99068	+	10.3762i	0.302962	+	0.524745i
$392$		0			0
$393$	−4.81061	+	14.9982i	−0.242663	+	0.756560i
$394$		0			0
$395$	−7.81252	−	7.81252i	−0.393090	−	0.393090i
$396$		0			0
$397$	1.89653	−	1.89653i	0.0951839	−	0.0951839i	−0.657911	−	0.753095i	$-0.728560\pi$
$397$	1.89653	−	1.89653i	0.0951839	−	0.0951839i	0.753095	+	0.657911i	$0.228560\pi$
$398$		0			0
$399$	4.66486	+	21.5456i	0.233535	+	1.07863i
$400$		0			0
$401$	7.73867	−	4.46792i	0.386451	−	0.223118i	−0.294170	−	0.955753i	$-0.595043\pi$
$401$	7.73867	−	4.46792i	0.386451	−	0.223118i	0.680621	+	0.732635i	$0.261710\pi$
$402$		0			0
$403$	16.5035	−	4.42209i	0.822096	−	0.220280i
$404$		0			0
$405$	−9.86470	−	4.83985i	−0.490181	−	0.240494i
$406$		0			0
$407$	1.60463	+	0.926431i	0.0795384	+	0.0459215i
$408$		0			0
$409$	−5.14089	+	2.96810i	−0.254201	+	0.146763i	−0.621686	−	0.783266i	$-0.713552\pi$
$409$	−5.14089	+	2.96810i	−0.254201	+	0.146763i	0.367485	+	0.930029i	$0.380219\pi$
$410$		0			0
$411$	14.7604	+	9.50636i	0.728075	+	0.468914i
$412$		0			0
$413$	−16.9706	−	16.9706i	−0.835069	−	0.835069i
$414$		0			0
$415$			3.51925i			0.172753i
$416$		0			0
$417$	3.82323	−	11.9198i	0.187225	−	0.583717i
$418$		0			0
$419$	−30.6701	−	8.21802i	−1.49833	−	0.401476i	−0.585790	−	0.810463i	$-0.699216\pi$
$419$	−30.6701	−	8.21802i	−1.49833	−	0.401476i	−0.912540	+	0.408986i	$0.865882\pi$
$420$		0			0
$421$	17.0997	−	4.58184i	0.833387	−	0.223305i	0.183196	−	0.983076i	$-0.441356\pi$
$421$	17.0997	−	4.58184i	0.833387	−	0.223305i	0.650191	+	0.759771i	$0.274689\pi$
$422$		0			0
$423$	6.68272	−	9.34575i	0.324925	−	0.454406i
$424$		0			0
$425$	−2.90136	+	5.02530i	−0.140737	+	0.243763i
$426$		0			0
$427$	29.1728	+	7.81682i	1.41177	+	0.378283i
$428$		0			0
$429$	0.506086	−	10.4094i	0.0244340	−	0.502572i
$430$		0			0
$431$	20.7181			0.997956			0.498978	−	0.866615i	$-0.333709\pi$
$431$	20.7181			0.997956			0.498978	+	0.866615i	$0.333709\pi$
$432$		0			0
$433$	−9.78697			−0.470332			−0.235166	−	0.971955i	$-0.575563\pi$
$433$	−9.78697			−0.470332			−0.235166	+	0.971955i	$0.575563\pi$
$434$		0			0
$435$	0.556865	−	11.4539i	0.0266996	−	0.549172i
$436$		0			0
$437$	22.9833	+	6.15835i	1.09944	+	0.294594i
$438$		0			0
$439$	−10.6989	+	18.5310i	−0.510629	+	0.884435i	0.489295	+	0.872118i	$0.337254\pi$
$439$	−10.6989	+	18.5310i	−0.510629	+	0.884435i	−0.999924	+	0.0123167i	$0.996079\pi$
$440$		0			0
$441$	9.95663	+	21.9155i	0.474125	+	1.04360i
$442$		0			0
$443$	−23.0566	+	6.17801i	−1.09545	+	0.293526i	−0.760912	−	0.648855i	$-0.775248\pi$
$443$	−23.0566	+	6.17801i	−1.09545	+	0.293526i	−0.334542	+	0.942381i	$0.608581\pi$
$444$		0			0
$445$	−5.80124	−	1.55444i	−0.275005	−	0.0736874i
$446$		0			0
$447$	1.82841	−	5.70049i	0.0864806	−	0.269624i
$448$		0			0
$449$		−	17.2778i		−	0.815390i	−0.913118	−	0.407695i	$-0.866333\pi$
$449$		−	17.2778i		−	0.815390i	0.913118	−	0.407695i	$-0.133667\pi$
$450$		0			0
$451$	19.3476	+	19.3476i	0.911042	+	0.911042i
$452$		0			0
$453$	0.682795	+	0.439752i	0.0320805	+	0.0206613i
$454$		0			0
$455$	−9.40918	+	5.43239i	−0.441109	+	0.254674i
$456$		0			0
$457$	33.3114	+	19.2323i	1.55824	+	0.899651i	0.997426	+	0.0717098i	$0.0228455\pi$
$457$	33.3114	+	19.2323i	1.55824	+	0.899651i	0.560815	+	0.827941i	$0.310488\pi$
$458$		0			0
$459$	−8.50058	−	1.24772i	−0.396773	−	0.0582383i
$460$		0			0
$461$	−2.43896	+	0.653517i	−0.113594	+	0.0304373i	−0.315168	−	0.949036i	$-0.602061\pi$
$461$	−2.43896	+	0.653517i	−0.113594	+	0.0304373i	0.201574	+	0.979473i	$0.435394\pi$
$462$		0			0
$463$	24.3919	−	14.0827i	1.13359	−	0.654476i	0.188752	−	0.982025i	$-0.439556\pi$
$463$	24.3919	−	14.0827i	1.13359	−	0.654476i	0.944834	+	0.327549i	$0.106223\pi$
$464$		0			0
$465$	3.33001	+	15.3803i	0.154425	+	0.713246i
$466$		0			0
$467$	−2.16739	+	2.16739i	−0.100295	+	0.100295i	−0.755474	−	0.655179i	$-0.772593\pi$
$467$	−2.16739	+	2.16739i	−0.100295	+	0.100295i	0.655179	+	0.755474i	$0.272593\pi$
$468$		0			0
$469$	−38.0106	−	38.0106i	−1.75517	−	1.75517i
$470$		0			0
$471$	−3.43675	+	10.7149i	−0.158357	+	0.493715i
$472$		0			0
$473$	−10.4837	−	18.1583i	−0.482040	−	0.834918i
$474$		0			0
$475$	2.98256	+	11.1311i	0.136849	+	0.510729i
$476$		0			0
$477$	15.3856	−	12.6528i	0.704460	−	0.579333i
$478$		0			0
$479$	−0.298969	+	0.517829i	−0.0136602	+	0.0236602i	−0.872775	−	0.488123i	$-0.837682\pi$
$479$	−0.298969	+	0.517829i	−0.0136602	+	0.0236602i	0.859114	+	0.511783i	$0.171015\pi$
$480$		0			0
$481$	−0.811604	−	1.40574i	−0.0370060	−	0.0640962i
$482$		0			0
$483$	48.5901	+	2.36235i	2.21093	+	0.107491i
$484$		0			0
$485$	12.0910	−	12.0910i	0.549023	−	0.549023i
$486$		0			0
$487$	−2.90101			−0.131457			−0.0657287	−	0.997838i	$-0.520937\pi$
$487$	−2.90101			−0.131457			−0.0657287	+	0.997838i	$0.520937\pi$
$488$		0			0
$489$	19.5846	−	17.7686i	0.885647	−	0.803523i
$490$		0			0
$491$	0.760458	−	2.83807i	0.0343190	−	0.128080i	−0.946641	−	0.322290i	$-0.895547\pi$
$491$	0.760458	−	2.83807i	0.0343190	−	0.128080i	0.980960	+	0.194210i	$0.0622142\pi$
$492$		0			0
$493$	−2.32070	−	8.66099i	−0.104519	−	0.390071i
$494$		0			0
$495$	9.55364	+	0.931159i	0.429404	+	0.0418525i
$496$		0			0
$497$	36.8664	+	21.2848i	1.65368	+	0.954755i
$498$		0			0
$499$	−3.32662	+	12.4151i	−0.148920	+	0.555777i	0.850630	+	0.525765i	$0.176221\pi$
$499$	−3.32662	+	12.4151i	−0.148920	+	0.555777i	−0.999550	+	0.0300115i	$0.990446\pi$
$500$		0			0
$501$	5.31394	+	10.3324i	0.237409	+	0.461620i
$502$		0			0
$503$			2.78327i			0.124100i	0.998073	+	0.0620500i	$0.0197638\pi$
$503$			2.78327i			0.124100i	−0.998073	+	0.0620500i	$0.980236\pi$
$504$		0			0
$505$		−	4.96424i		−	0.220906i
$506$		0			0
$507$	7.24841	−	11.2545i	0.321913	−	0.499829i
$508$		0			0
$509$	−8.72439	+	32.5599i	−0.386702	+	1.44319i	0.448765	+	0.893650i	$0.351864\pi$
$509$	−8.72439	+	32.5599i	−0.386702	+	1.44319i	−0.835467	+	0.549541i	$0.814803\pi$
$510$		0			0
$511$	−35.2350	−	20.3429i	−1.55871	−	0.899919i
$512$		0			0
$513$	−13.6891	+	10.1849i	−0.604390	+	0.449674i
$514$		0			0
$515$	2.50606	+	9.35275i	0.110430	+	0.412131i
$516$		0			0
$517$	−2.59770	+	9.69474i	−0.114247	+	0.426374i
$518$		0			0
$519$	−3.02099	−	13.9531i	−0.132607	−	0.612473i
$520$		0			0
$521$	12.7253			0.557504			0.278752	−	0.960363i	$-0.410079\pi$
$521$	12.7253			0.557504			0.278752	+	0.960363i	$0.410079\pi$
$522$		0			0
$523$	7.32974	−	7.32974i	0.320507	−	0.320507i	−0.528454	−	0.848962i	$-0.677228\pi$
$523$	7.32974	−	7.32974i	0.320507	−	0.320507i	0.848962	+	0.528454i	$0.177228\pi$
$524$		0			0
$525$	10.7756	+	20.9520i	0.470284	+	0.914422i
$526$		0			0
$527$	6.15236	+	10.6562i	0.268001	+	0.464191i
$528$		0			0
$529$	14.7537	−	25.5542i	0.641467	−	1.11105i
$530$		0			0
$531$	6.52562	−	17.3917i	0.283188	−	0.754736i
$532$		0			0
$533$	−6.20396	−	23.1535i	−0.268723	−	1.00289i
$534$		0			0
$535$	−9.24076	−	16.0055i	−0.399513	−	0.691976i
$536$		0			0
$537$	4.96588	+	5.47342i	0.214294	+	0.236195i
$538$		0			0
$539$	−14.8692	−	14.8692i	−0.640460	−	0.640460i
$540$		0			0
$541$	0.283076	−	0.283076i	0.0121704	−	0.0121704i	−0.700995	−	0.713166i	$-0.747261\pi$
$541$	0.283076	−	0.283076i	0.0121704	−	0.0121704i	0.713166	+	0.700995i	$0.247261\pi$
$542$		0			0
$543$	−24.4184	+	22.1541i	−1.04789	+	0.950725i
$544$		0			0
$545$	0.337864	−	0.195066i	0.0144725	−	0.00835570i
$546$		0			0
$547$	−0.947844	+	0.253974i	−0.0405269	+	0.0108591i	−0.279026	−	0.960284i	$-0.590011\pi$
$547$	−0.947844	+	0.253974i	−0.0405269	+	0.0108591i	0.238499	+	0.971143i	$0.423345\pi$
$548$		0			0
$549$	3.83122	+	23.0597i	0.163513	+	0.984163i
$550$		0			0
$551$	−15.4211	−	8.90339i	−0.656962	−	0.379297i
$552$		0			0
$553$	−30.3773	+	17.5383i	−1.29177	+	0.745806i
$554$		0			0
$555$	1.32953	−	0.683771i	0.0564353	−	0.0290244i
$556$		0			0
$557$	10.5939	+	10.5939i	0.448877	+	0.448877i	0.894981	−	0.446104i	$-0.147189\pi$
$557$	10.5939	+	10.5939i	0.448877	+	0.448877i	−0.446104	+	0.894981i	$0.647189\pi$
$558$		0			0
$559$			18.3685i			0.776906i
$560$		0			0
$561$	7.33554	−	1.58822i	0.309707	−	0.0670549i
$562$		0			0
$563$	40.4774	+	10.8459i	1.70592	+	0.457099i	0.974418	−	0.224742i	$-0.0721540\pi$
$563$	40.4774	+	10.8459i	1.70592	+	0.457099i	0.731500	+	0.681842i	$0.238821\pi$
$564$		0			0
$565$	−3.47415	+	0.930895i	−0.146158	+	0.0391630i
$566$		0			0
$567$	−22.9476	+	26.2742i	−0.963709	+	1.10341i
$568$		0			0
$569$	−18.6572	+	32.3152i	−0.782151	+	1.35473i	0.148535	+	0.988907i	$0.452544\pi$
$569$	−18.6572	+	32.3152i	−0.782151	+	1.35473i	−0.930686	+	0.365818i	$0.880789\pi$
$570$		0			0
$571$	−22.6439	−	6.06741i	−0.947616	−	0.253913i	−0.248266	−	0.968692i	$-0.579861\pi$
$571$	−22.6439	−	6.06741i	−0.947616	−	0.253913i	−0.699350	+	0.714779i	$0.746527\pi$
$572$		0			0
$573$	−0.380796	−	0.245250i	−0.0159080	−	0.0102455i
$574$		0			0
$575$	25.4300			1.06051
$576$		0			0
$577$	44.5543			1.85482			0.927410	−	0.374047i	$-0.122030\pi$
$577$	44.5543			1.85482			0.927410	+	0.374047i	$0.122030\pi$
$578$		0			0
$579$	−1.06234	+	0.546355i	−0.0441491	+	0.0227057i
$580$		0			0
$581$	10.7921	+	2.89174i	0.447733	+	0.119970i
$582$		0			0
$583$	−8.70092	+	15.0704i	−0.360355	+	0.624153i
$584$		0			0
$585$	−6.84033	−	4.89121i	−0.282813	−	0.202227i
$586$		0			0
$587$	16.0531	−	4.30142i	0.662584	−	0.177539i	0.0881720	−	0.996105i	$-0.471897\pi$
$587$	16.0531	−	4.30142i	0.662584	−	0.177539i	0.574412	+	0.818566i	$0.305231\pi$
$588$		0			0
$589$	23.6035	+	6.32455i	0.972567	+	0.260599i
$590$		0			0
$591$	8.32051	+	9.17090i	0.342260	+	0.377241i
$592$		0			0
$593$			38.8079i			1.59365i	0.604211	+	0.796824i	$0.293488\pi$
$593$			38.8079i			1.59365i	−0.604211	+	0.796824i	$0.706512\pi$
$594$		0			0
$595$	−5.53282	−	5.53282i	−0.226824	−	0.226824i
$596$		0			0
$597$	−0.349765	+	7.19415i	−0.0143149	+	0.294437i
$598$		0			0
$599$	1.76012	−	1.01621i	0.0719165	−	0.0415210i	−0.463611	−	0.886039i	$-0.653446\pi$
$599$	1.76012	−	1.01621i	0.0719165	−	0.0415210i	0.535527	+	0.844518i	$0.320113\pi$
$600$		0			0
$601$	14.9323	+	8.62115i	0.609100	+	0.351664i	0.772613	−	0.634877i	$-0.218949\pi$
$601$	14.9323	+	8.62115i	0.609100	+	0.351664i	−0.163513	+	0.986541i	$0.552283\pi$
$602$		0			0
$603$	14.6160	−	38.9538i	0.595211	−	1.58632i
$604$		0			0
$605$	4.87249	−	1.30558i	0.198095	−	0.0530794i
$606$		0			0
$607$	10.3001	−	5.94674i	0.418066	−	0.241371i	−0.276183	−	0.961105i	$-0.589070\pi$
$607$	10.3001	−	5.94674i	0.418066	−	0.241371i	0.694250	+	0.719734i	$0.255736\pi$
$608$		0			0
$609$	−34.6668	−	11.1192i	−1.40477	−	0.450574i
$610$		0			0
$611$	6.21739	−	6.21739i	0.251529	−	0.251529i
$612$		0			0
$613$	−3.45525	−	3.45525i	−0.139556	−	0.139556i	0.633877	−	0.773434i	$-0.281462\pi$
$613$	−3.45525	−	3.45525i	−0.139556	−	0.139556i	−0.773434	+	0.633877i	$0.781462\pi$
$614$		0			0
$615$	21.5778	−	4.67183i	0.870101	−	0.188386i
$616$		0			0
$617$	20.6596	+	35.7835i	0.831725	+	1.44059i	0.896669	+	0.442701i	$0.145980\pi$
$617$	20.6596	+	35.7835i	0.831725	+	1.44059i	−0.0649443	+	0.997889i	$0.520687\pi$
$618$		0			0
$619$	−3.19640	−	11.9291i	−0.128474	−	0.479471i	0.871466	−	0.490456i	$-0.163170\pi$
$619$	−3.19640	−	11.9291i	−0.128474	−	0.479471i	−0.999940	+	0.0109851i	$0.996503\pi$
$620$		0			0
$621$	13.8912	+	34.9963i	0.557433	+	1.40435i
$622$		0			0
$623$	−9.53365	+	16.5128i	−0.381958	+	0.661570i
$624$		0			0
$625$	2.43160	+	4.21165i	0.0972639	+	0.168466i
$626$		0			0
$627$	8.07072	−	12.5313i	0.322313	−	0.500451i
$628$		0			0
$629$	0.826608	−	0.826608i	0.0329590	−	0.0329590i
$630$		0			0
$631$	21.4353			0.853326			0.426663	−	0.904411i	$-0.359689\pi$
$631$	21.4353			0.853326			0.426663	+	0.904411i	$0.359689\pi$
$632$		0			0
$633$	14.1518	+	4.53912i	0.562483	+	0.180414i
$634$		0			0
$635$	6.32833	−	23.6177i	0.251132	−	0.937238i
$636$		0			0
$637$	4.76792	+	17.7941i	0.188912	+	0.705028i
$638$		0			0
$639$	−3.19620	+	32.7929i	−0.126440	+	1.29727i
$640$		0			0
$641$	−40.1623	−	23.1877i	−1.58631	−	0.915859i	−0.993907	−	0.110220i	$-0.964844\pi$
$641$	−40.1623	−	23.1877i	−1.58631	−	0.915859i	−0.592407	−	0.805639i	$-0.701822\pi$
$642$		0			0
$643$	4.94288	−	18.4471i	0.194928	−	0.727482i	−0.797357	−	0.603508i	$-0.793769\pi$
$643$	4.94288	−	18.4471i	0.194928	−	0.727482i	0.992285	−	0.123974i	$-0.0395641\pi$
$644$		0			0
$645$	−16.8984	−	0.821564i	−0.665372	−	0.0323491i
$646$		0			0
$647$			45.8797i			1.80372i	0.432033	+	0.901858i	$0.357797\pi$
$647$			45.8797i			1.80372i	−0.432033	+	0.901858i	$0.642203\pi$
$648$		0			0
$649$			16.2273i			0.636978i
$650$		0			0
$651$	49.9015	+	2.42611i	1.95579	+	0.0950867i
$652$		0			0
$653$	9.78101	−	36.5032i	0.382761	−	1.42848i	−0.458906	−	0.888485i	$-0.651759\pi$
$653$	9.78101	−	36.5032i	0.382761	−	1.42848i	0.841667	−	0.539997i	$-0.181575\pi$
$654$		0			0
$655$	−9.61502	−	5.55123i	−0.375690	−	0.216905i
$656$		0			0
$657$	3.05476	−	31.3417i	0.119178	−	1.22276i
$658$		0			0
$659$	8.01748	+	29.9216i	0.312317	+	1.16558i	0.926462	+	0.376388i	$0.122834\pi$
$659$	8.01748	+	29.9216i	0.312317	+	1.16558i	−0.614145	+	0.789193i	$0.710499\pi$
$660$		0			0
$661$	−9.93628	+	37.0827i	−0.386476	+	1.44235i	0.449350	+	0.893356i	$0.351656\pi$
$661$	−9.93628	+	37.0827i	−0.386476	+	1.44235i	−0.835827	+	0.548994i	$0.815011\pi$
$662$		0			0
$663$	−6.26105	−	2.00821i	−0.243159	−	0.0779922i
$664$		0			0
$665$	−15.5390			−0.602577
$666$		0			0
$667$	−27.7858	+	27.7858i	−1.07587	+	1.07587i
$668$		0			0
$669$	11.3461	−	17.6170i	0.438667	−	0.681111i
$670$		0			0
$671$	−10.2103	−	17.6848i	−0.394165	−	0.682713i
$672$		0			0
$673$	−8.24767	+	14.2854i	−0.317924	+	0.550661i	−0.980055	−	0.198728i	$-0.936319\pi$
$673$	−8.24767	+	14.2854i	−0.317924	+	0.550661i	0.662131	+	0.749389i	$0.269652\pi$
$674$		0			0
$675$	−11.3145	+	14.3009i	−0.435497	+	0.550441i
$676$		0			0
$677$	−10.7252	−	40.0270i	−0.412203	−	1.53836i	−0.790372	−	0.612627i	$-0.790113\pi$
$677$	−10.7252	−	40.0270i	−0.412203	−	1.53836i	0.378169	−	0.925737i	$-0.376554\pi$
$678$		0			0
$679$	−27.1431	−	47.0132i	−1.04166	−	1.80420i
$680$		0			0
$681$	−21.9601	+	4.75459i	−0.841512	+	0.182196i
$682$		0			0
$683$	−6.62321	−	6.62321i	−0.253430	−	0.253430i	0.568945	−	0.822375i	$-0.307352\pi$
$683$	−6.62321	−	6.62321i	−0.253430	−	0.253430i	−0.822375	+	0.568945i	$0.807352\pi$
$684$		0			0
$685$	−8.75075	+	8.75075i	−0.334349	+	0.334349i
$686$		0			0
$687$	−10.8819	−	3.49031i	−0.415169	−	0.133164i
$688$		0			0
$689$	13.2025	−	7.62248i	0.502976	−	0.290393i
$690$		0			0
$691$	22.8153	−	6.11334i	0.867935	−	0.232562i	0.202740	−	0.979233i	$-0.435015\pi$
$691$	22.8153	−	6.11334i	0.867935	−	0.232562i	0.665194	+	0.746670i	$0.268349\pi$
$692$		0			0
$693$	10.7056	−	28.5320i	0.406673	−	1.08384i
$694$		0			0
$695$	7.64154	+	4.41184i	0.289860	+	0.167351i
$696$		0			0
$697$	14.9501	−	8.63144i	0.566275	−	0.326939i
$698$		0			0
$699$	0.596766	−	12.2746i	0.0225718	−	0.464267i
$700$		0			0
$701$	−5.24880	−	5.24880i	−0.198245	−	0.198245i	0.601003	−	0.799247i	$-0.294768\pi$
$701$	−5.24880	−	5.24880i	−0.198245	−	0.198245i	−0.799247	+	0.601003i	$0.794768\pi$
$702$		0			0
$703$		−	2.32154i		−	0.0875586i
$704$		0			0
$705$	5.44168	+	5.99785i	0.204946	+	0.225892i
$706$		0			0
$707$	−15.2233	−	4.07907i	−0.572531	−	0.153409i
$708$		0			0
$709$	5.03953	−	1.35034i	0.189263	−	0.0507130i	−0.162942	−	0.986636i	$-0.552098\pi$
$709$	5.03953	−	1.35034i	0.189263	−	0.0507130i	0.352206	+	0.935923i	$0.385432\pi$
$710$		0			0
$711$	−22.0838	−	15.7911i	−0.828209	−	0.592214i
$712$		0			0
$713$	26.9623	−	46.7001i	1.00975	−	1.74893i
$714$		0			0
$715$	7.09577	+	1.90131i	0.265367	+	0.0711048i
$716$		0			0
$717$	25.7455	−	13.2408i	0.961485	−	0.494488i
$718$		0			0
$719$	37.6412			1.40378			0.701889	−	0.712286i	$-0.252340\pi$
$719$	37.6412			1.40378			0.701889	+	0.712286i	$0.252340\pi$
$720$		0			0
$721$	30.7403			1.14483
$722$		0			0
$723$	−38.7758	−	24.9734i	−1.44209	−	0.928771i
$724$		0			0
$725$	−18.3826	−	4.92561i	−0.682714	−	0.182933i
$726$		0			0
$727$	−3.14610	+	5.44920i	−0.116682	+	0.202100i	−0.918451	−	0.395535i	$-0.870559\pi$
$727$	−3.14610	+	5.44920i	−0.116682	+	0.202100i	0.801769	+	0.597634i	$0.203893\pi$
$728$		0			0
$729$	−25.8611	−	7.75895i	−0.957820	−	0.287369i
$730$		0			0
$731$	−12.7779	+	3.42382i	−0.472607	+	0.126635i
$732$		0			0
$733$	−31.5136	−	8.44405i	−1.16398	−	0.311888i	−0.375427	−	0.926852i	$-0.622504\pi$
$733$	−31.5136	−	8.44405i	−1.16398	−	0.311888i	−0.788555	+	0.614964i	$0.789171\pi$
$734$		0			0
$735$	−16.5832	+	3.59043i	−0.611679	+	0.132435i
$736$		0			0
$737$			36.3458i			1.33882i
$738$		0			0
$739$	−0.850912	−	0.850912i	−0.0313013	−	0.0313013i	0.691283	−	0.722584i	$-0.257046\pi$
$739$	−0.850912	−	0.850912i	−0.0313013	−	0.0313013i	−0.722584	+	0.691283i	$0.757046\pi$
$740$		0			0
$741$	−11.6122	+	5.97209i	−0.426584	+	0.219390i
$742$		0			0
$743$	−25.4064	+	14.6684i	−0.932070	+	0.538131i	−0.887466	−	0.460874i	$-0.847536\pi$
$743$	−25.4064	+	14.6684i	−0.932070	+	0.538131i	−0.0446046	+	0.999005i	$0.514203\pi$
$744$		0			0
$745$	3.65445	+	2.10990i	0.133889	+	0.0773007i
$746$		0			0
$747$	1.41732	+	8.53065i	0.0518568	+	0.312120i
$748$		0			0
$749$	−56.6753	+	15.1861i	−2.07087	+	0.554888i
$750$		0			0
$751$	−17.8715	+	10.3181i	−0.652141	+	0.376514i	−0.789276	−	0.614038i	$-0.789544\pi$
$751$	−17.8715	+	10.3181i	−0.652141	+	0.376514i	0.137135	+	0.990552i	$0.456211\pi$
$752$		0			0
$753$	22.8228	−	20.7065i	0.831710	−	0.754587i
$754$		0			0
$755$	−0.404798	+	0.404798i	−0.0147321	+	0.0147321i
$756$		0			0
$757$	−38.7488	−	38.7488i	−1.40835	−	1.40835i	−0.768502	−	0.639847i	$-0.778998\pi$
$757$	−38.7488	−	38.7488i	−1.40835	−	1.40835i	−0.639847	−	0.768502i	$-0.721002\pi$
$758$		0			0
$759$	−22.1015	−	24.3604i	−0.802235	−	0.884228i
$760$		0			0
$761$	6.22122	+	10.7755i	0.225519	+	0.390611i	0.956475	−	0.291814i	$-0.0942588\pi$
$761$	6.22122	+	10.7755i	0.225519	+	0.390611i	−0.730956	+	0.682425i	$0.760925\pi$
$762$		0			0
$763$	−0.320568	−	1.19638i	−0.0116053	−	0.0433117i
$764$		0			0
$765$	2.12751	−	5.67011i	0.0769202	−	0.205003i
$766$		0			0
$767$	7.10801	−	12.3114i	0.256655	−	0.444540i
$768$		0			0
$769$	−9.70125	−	16.8031i	−0.349836	−	0.605934i	0.636384	−	0.771372i	$-0.280429\pi$
$769$	−9.70125	−	16.8031i	−0.349836	−	0.605934i	−0.986220	+	0.165438i	$0.947096\pi$
$770$		0			0
$771$	−14.3412	−	27.8851i	−0.516486	−	1.00426i
$772$		0			0
$773$	29.9097	−	29.9097i	1.07578	−	1.07578i	0.0788954	−	0.996883i	$-0.474861\pi$
$773$	29.9097	−	29.9097i	1.07578	−	1.07578i	0.996883	−	0.0788954i	$-0.0251393\pi$
$774$		0			0
$775$	26.1163			0.938126
$776$		0			0
$777$	−1.00439	−	4.63897i	−0.0360321	−	0.166422i
$778$		0			0
$779$	8.87301	−	33.1145i	0.317909	−	1.18645i
$780$		0			0
$781$	−7.44957	−	27.8022i	−0.266567	−	0.994840i
$782$		0			0
$783$	−3.26300	−	27.9884i	−0.116610	−	1.00022i
$784$		0			0
$785$	−6.86906	−	3.96585i	−0.245167	−	0.141547i
$786$		0			0
$787$	−3.02137	+	11.2759i	−0.107700	+	0.401942i	−0.998637	−	0.0521839i	$-0.983382\pi$
$787$	−3.02137	+	11.2759i	−0.107700	+	0.401942i	0.890937	+	0.454126i	$0.150048\pi$
$788$		0			0
$789$	−5.31297	+	8.24937i	−0.189147	+	0.293685i
$790$		0			0
$791$			11.4187i			0.406002i
$792$		0			0
$793$			17.8896i			0.635277i
$794$		0			0
$795$	6.42188	+	12.4867i	0.227761	+	0.442859i
$796$		0			0
$797$	7.63006	−	28.4758i	0.270271	−	1.00866i	−0.688674	−	0.725071i	$-0.741807\pi$
$797$	7.63006	−	28.4758i	0.270271	−	1.00866i	0.958945	−	0.283593i	$-0.0915264\pi$
$798$		0			0
$799$	5.48396	+	3.16617i	0.194009	+	0.112011i
$800$		0			0
$801$	−14.6882	−	1.43160i	−0.518982	−	0.0505833i
$802$		0			0
$803$	7.11992	+	26.5719i	0.251256	+	0.937702i
$804$		0			0
$805$	−8.87509	+	33.1223i	−0.312806	+	1.16741i
$806$		0			0
$807$	25.8857	−	23.4854i	0.911222	−	0.826726i
$808$		0			0
$809$	20.9519			0.736631			0.368316	−	0.929701i	$-0.379935\pi$
$809$	20.9519			0.736631			0.368316	+	0.929701i	$0.379935\pi$
$810$		0			0
$811$	−20.4725	+	20.4725i	−0.718886	+	0.718886i	−0.968377	−	0.249491i	$-0.919737\pi$
$811$	−20.4725	+	20.4725i	−0.718886	+	0.718886i	0.249491	+	0.968377i	$0.419737\pi$
$812$		0			0
$813$	0.328075	+	0.0159504i	0.0115061	+	0.000559404i
$814$		0			0
$815$	9.31991	+	16.1426i	0.326462	+	0.565449i
$816$		0			0
$817$	−13.1355	+	22.7514i	−0.459553	+	0.795970i
$818$		0			0
$819$	−20.6200	+	16.9575i	−0.720521	+	0.592542i
$820$		0			0
$821$	0.747963	+	2.79144i	0.0261041	+	0.0974218i	0.977749	−	0.209779i	$-0.0672744\pi$
$821$	0.747963	+	2.79144i	0.0261041	+	0.0974218i	−0.951645	+	0.307201i	$0.900608\pi$
$822$		0			0
$823$	19.7347	+	34.1816i	0.687909	+	1.19149i	0.972513	+	0.232849i	$0.0748047\pi$
$823$	19.7347	+	34.1816i	0.687909	+	1.19149i	−0.284604	+	0.958645i	$0.591862\pi$
$824$		0			0
$825$	4.86539	−	15.1690i	0.169391	−	0.528117i
$826$		0			0
$827$	39.7044	+	39.7044i	1.38066	+	1.38066i	0.843448	+	0.537211i	$0.180522\pi$
$827$	39.7044	+	39.7044i	1.38066	+	1.38066i	0.537211	+	0.843448i	$0.319478\pi$
$828$		0			0
$829$	−34.2723	+	34.2723i	−1.19033	+	1.19033i	−0.213352	+	0.976975i	$0.568438\pi$
$829$	−34.2723	+	34.2723i	−1.19033	+	1.19033i	−0.976975	+	0.213352i	$0.931562\pi$
$830$		0			0
$831$	−2.95860	−	13.6649i	−0.102633	−	0.474030i
$832$		0			0
$833$	−11.4896	+	6.63350i	−0.398090	+	0.229837i
$834$		0			0
$835$	−7.91084	+	2.11970i	−0.273766	+	0.0733554i
$836$		0			0
$837$	14.2661	+	35.9407i	0.493107	+	1.24229i
$838$		0			0
$839$	−7.72719	−	4.46130i	−0.266772	−	0.154021i	0.360648	−	0.932702i	$-0.382556\pi$
$839$	−7.72719	−	4.46130i	−0.266772	−	0.154021i	−0.627420	+	0.778681i	$0.715889\pi$
$840$		0			0
$841$	0.352787	−	0.203682i	0.0121651	−	0.00702351i
$842$		0			0
$843$	4.48508	+	2.88860i	0.154475	+	0.0994888i
$844$		0			0
$845$	6.67227	+	6.67227i	0.229533	+	0.229533i
$846$		0			0
$847$		−	16.0147i		−	0.550273i
$848$		0			0
$849$	4.35005	−	13.5623i	0.149293	−	0.465457i
$850$		0			0
$851$	−4.94850	−	1.32595i	−0.169632	−	0.0454529i
$852$		0			0
$853$	−26.1333	+	7.00239i	−0.894786	+	0.239757i	−0.676776	−	0.736189i	$-0.736623\pi$
$853$	−26.1333	+	7.00239i	−0.894786	+	0.239757i	−0.218010	+	0.975946i	$0.569957\pi$
$854$		0			0
$855$	−4.97472	−	10.9499i	−0.170132	−	0.374477i
$856$		0			0
$857$	−24.0832	+	41.7133i	−0.822666	+	1.42490i	0.0810244	+	0.996712i	$0.474181\pi$
$857$	−24.0832	+	41.7133i	−0.822666	+	1.42490i	−0.903690	+	0.428187i	$0.859153\pi$
$858$		0			0
$859$	−28.0522	−	7.51656i	−0.957128	−	0.256462i	−0.253744	−	0.967271i	$-0.581662\pi$
$859$	−28.0522	−	7.51656i	−0.957128	−	0.256462i	−0.703384	+	0.710810i	$0.748329\pi$
$860$		0			0
$861$	3.40370	−	70.0091i	0.115998	−	2.38591i
$862$		0			0
$863$	10.5561			0.359334			0.179667	−	0.983728i	$-0.442498\pi$
$863$	10.5561			0.359334			0.179667	+	0.983728i	$0.442498\pi$
$864$		0			0
$865$	10.0632			0.342158
$866$		0			0
$867$	−1.19991	+	24.6804i	−0.0407511	+	0.838189i
$868$		0			0
$869$	22.9085	+	6.13832i	0.777118	+	0.208228i
$870$		0			0
$871$	15.9205	−	27.5750i	0.539444	−	0.934344i
$872$		0			0
$873$	24.4390	−	34.1779i	0.827136	−	1.15675i
$874$		0			0
$875$	−38.8965	+	10.4223i	−1.31494	+	0.352337i
$876$		0			0
$877$	−6.20335	−	1.66218i	−0.209472	−	0.0561279i	0.152557	−	0.988295i	$-0.451249\pi$
$877$	−6.20335	−	1.66218i	−0.209472	−	0.0561279i	−0.362029	+	0.932167i	$0.617916\pi$
$878$		0			0
$879$	11.3445	−	35.3691i	0.382640	−	1.19297i
$880$		0			0
$881$			30.8423i			1.03910i	0.854439	+	0.519552i	$0.173901\pi$
$881$			30.8423i			1.03910i	−0.854439	+	0.519552i	$0.826099\pi$
$882$		0			0
$883$	0.0570127	+	0.0570127i	0.00191863	+	0.00191863i	0.708065	−	0.706147i	$-0.249568\pi$
$883$	0.0570127	+	0.0570127i	0.00191863	+	0.00191863i	−0.706147	+	0.708065i	$0.749568\pi$
$884$		0			0
$885$	11.0081	+	7.08975i	0.370034	+	0.238319i
$886$		0			0
$887$	29.6650	−	17.1271i	0.996055	−	0.575072i	0.0889760	−	0.996034i	$-0.471641\pi$
$887$	29.6650	−	17.1271i	0.996055	−	0.575072i	0.907079	+	0.420961i	$0.138307\pi$
$888$		0			0
$889$	−67.2258	−	38.8128i	−2.25468	−	1.30174i
$890$		0			0
$891$	23.5330	−	1.59043i	0.788385	−	0.0532814i
$892$		0			0
$893$	12.1470	−	3.25478i	0.406484	−	0.108917i
$894$		0			0
$895$	−4.51145	+	2.60468i	−0.150801	+	0.0870650i
$896$		0			0
$897$	6.09758	+	28.1630i	0.203592	+	0.940334i
$898$		0			0
$899$	−28.5357	+	28.5357i	−0.951720	+	0.951720i
$900$		0			0
$901$	7.76339	+	7.76339i	0.258636	+	0.258636i
$902$		0			0
$903$	−16.4046	+	51.1453i	−0.545912	+	1.70201i
$904$		0			0
$905$	−11.6202	−	20.1268i	−0.386269	−	0.669037i
$906$		0			0
$907$	1.17997	+	4.40372i	0.0391804	+	0.146223i	0.982745	−	0.184965i	$-0.0592172\pi$
$907$	1.17997	+	4.40372i	0.0391804	+	0.146223i	−0.943565	+	0.331188i	$0.892551\pi$
$908$		0			0
$909$	−1.99926	−	12.0333i	−0.0663111	−	0.399119i
$910$		0			0
$911$	4.58628	−	7.94367i	0.151950	−	0.263185i	−0.779994	−	0.625787i	$-0.784778\pi$
$911$	4.58628	−	7.94367i	0.151950	−	0.263185i	0.931944	+	0.362601i	$0.118111\pi$
$912$		0			0
$913$	−3.77718	−	6.54227i	−0.125006	−	0.216518i
$914$		0			0
$915$	−16.4577	−	0.800141i	−0.544075	−	0.0264519i
$916$		0			0
$917$	−24.9240	+	24.9240i	−0.823061	+	0.823061i
$918$		0			0
$919$	−2.72325			−0.0898318			−0.0449159	−	0.998991i	$-0.514302\pi$
$919$	−2.72325			−0.0898318			−0.0449159	+	0.998991i	$0.514302\pi$
$920$		0			0
$921$	26.5678	−	24.1043i	0.875440	−	0.794262i
$922$		0			0
$923$	−6.52623	+	24.3562i	−0.214813	+	0.801695i
$924$		0			0
$925$	−0.642172	−	2.39662i	−0.0211145	−	0.0788003i
$926$		0			0
$927$	9.84132	+	21.6617i	0.323232	+	0.711465i
$928$		0			0
$929$	3.93105	+	2.26959i	0.128973	+	0.0744629i	0.563099	−	0.826390i	$-0.309609\pi$
$929$	3.93105	+	2.26959i	0.128973	+	0.0744629i	−0.434125	+	0.900853i	$0.642942\pi$
$930$		0			0
$931$	−6.81916	+	25.4495i	−0.223489	+	0.834072i
$932$		0			0
$933$	0.221417	+	0.430524i	0.00724885	+	0.0140947i
$934$		0			0
$935$			5.29050i			0.173018i
$936$		0			0
$937$			15.3808i			0.502470i	0.967926	+	0.251235i	$0.0808367\pi$
$937$			15.3808i			0.502470i	−0.967926	+	0.251235i	$0.919163\pi$
$938$		0			0
$939$	−8.85409	+	13.7476i	−0.288942	+	0.448636i
$940$		0			0
$941$	−5.88269	+	21.9545i	−0.191770	+	0.715696i	0.801309	+	0.598251i	$0.204137\pi$
$941$	−5.88269	+	21.9545i	−0.191770	+	0.715696i	−0.993079	+	0.117446i	$0.962529\pi$
$942$		0			0
$943$	−65.5177	−	37.8267i	−2.13355	−	1.23181i
$944$		0			0
$945$	−14.6779	−	19.7281i	−0.477474	−	0.641754i
$946$		0			0
$947$	−10.6876	−	39.8867i	−0.347301	−	1.29614i	−0.889901	−	0.456153i	$-0.849227\pi$
$947$	−10.6876	−	39.8867i	−0.347301	−	1.29614i	0.542600	−	0.839991i	$-0.317440\pi$
$948$		0			0
$949$	6.23743	−	23.2784i	0.202476	−	0.755649i
$950$		0			0
$951$	11.2289	+	51.8631i	0.364123	+	1.68178i
$952$		0			0
$953$	−3.63707			−0.117816			−0.0589081	−	0.998263i	$-0.518762\pi$
$953$	−3.63707			−0.117816			−0.0589081	+	0.998263i	$0.518762\pi$
$954$		0			0
$955$	0.225756	−	0.225756i	0.00730531	−	0.00730531i
$956$		0			0
$957$	11.2581	+	21.8904i	0.363924	+	0.707615i
$958$		0			0
$959$	19.6446	+	34.0254i	0.634357	+	1.09874i
$960$		0			0
$961$	12.1900	−	21.1136i	0.393224	−	0.681085i
$962$		0			0
$963$	−28.8454	−	35.0756i	−0.929531	−	1.13030i
$964$		0			0
$965$	−0.217938	−	0.813357i	−0.00701568	−	0.0261829i
$966$		0			0
$967$	−13.2430	−	22.9375i	−0.425865	−	0.737619i	0.570636	−	0.821203i	$-0.306697\pi$
$967$	−13.2430	−	22.9375i	−0.425865	−	0.737619i	−0.996501	+	0.0835839i	$0.973363\pi$
$968$		0			0
$969$	−6.31889	−	6.96471i	−0.202992	−	0.223739i
$970$		0			0
$971$	−19.1926	−	19.1926i	−0.615920	−	0.615920i	0.328562	−	0.944482i	$-0.393436\pi$
$971$	−19.1926	−	19.1926i	−0.615920	−	0.615920i	−0.944482	+	0.328562i	$0.893436\pi$
$972$		0			0
$973$	19.8083	−	19.8083i	0.635025	−	0.635025i
$974$		0			0
$975$	−10.3357	+	9.37732i	−0.331008	+	0.300315i
$976$		0			0
$977$	−39.5474	+	22.8327i	−1.26523	+	0.730482i	−0.974082	−	0.226195i	$-0.927371\pi$
$977$	−39.5474	+	22.8327i	−1.26523	+	0.730482i	−0.291151	+	0.956677i	$0.594038\pi$
$978$		0			0
$979$	12.4528	−	3.33672i	0.397994	−	0.106642i
$980$		0			0
$981$	0.740421	−	0.608907i	0.0236398	−	0.0194409i
$982$		0			0
$983$	−4.07756	−	2.35418i	−0.130054	−	0.0750868i	0.433561	−	0.901124i	$-0.357257\pi$
$983$	−4.07756	−	2.35418i	−0.130054	−	0.0750868i	−0.563616	+	0.826037i	$0.690590\pi$
$984$		0			0
$985$	−7.55909	+	4.36424i	−0.240852	+	0.139056i
$986$		0			0
$987$	22.8643	−	11.7590i	0.727780	−	0.374295i
$988$		0			0
$989$	40.9935	+	40.9935i	1.30352	+	1.30352i
$990$		0			0
$991$		−	18.1880i		−	0.577760i	−0.957365	−	0.288880i	$-0.906717\pi$
$991$		−	18.1880i		−	0.577760i	0.957365	−	0.288880i	$-0.0932829\pi$
$992$		0			0
$993$	−45.7930	+	9.91467i	−1.45320	+	0.314633i
$994$		0			0
$995$	−4.90402	−	1.31403i	−0.155468	−	0.0416575i
$996$		0			0
$997$	−51.8412	+	13.8908i	−1.64183	+	0.439926i	−0.957308	−	0.289069i	$-0.906654\pi$
$997$	−51.8412	+	13.8908i	−1.64183	+	0.439926i	−0.684519	+	0.728995i	$0.739988\pi$
$998$		0			0
$999$	2.94739	−	2.19290i	0.0932513	−	0.0693802i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.y.a.335.11		88
3.2	odd	2		1728.2.z.a.143.15		88
4.3	odd	2		144.2.u.a.11.4	✓	88
9.4	even	3		1728.2.z.a.719.15		88
9.5	odd	6	inner	576.2.y.a.527.22		88
12.11	even	2		432.2.v.a.251.19		88
16.3	odd	4	inner	576.2.y.a.47.22		88
16.13	even	4		144.2.u.a.83.5	yes	88
36.23	even	6		144.2.u.a.59.5	yes	88
36.31	odd	6		432.2.v.a.395.18		88
48.29	odd	4		432.2.v.a.35.18		88
48.35	even	4		1728.2.z.a.1007.15		88
144.13	even	12		432.2.v.a.179.19		88
144.67	odd	12		1728.2.z.a.1583.15		88
144.77	odd	12		144.2.u.a.131.4	yes	88
144.131	even	12	inner	576.2.y.a.239.11		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.4	✓	88	4.3	odd	2
144.2.u.a.59.5	yes	88	36.23	even	6
144.2.u.a.83.5	yes	88	16.13	even	4
144.2.u.a.131.4	yes	88	144.77	odd	12
432.2.v.a.35.18		88	48.29	odd	4
432.2.v.a.179.19		88	144.13	even	12
432.2.v.a.251.19		88	12.11	even	2
432.2.v.a.395.18		88	36.31	odd	6
576.2.y.a.47.22		88	16.3	odd	4	inner
576.2.y.a.239.11		88	144.131	even	12	inner
576.2.y.a.335.11		88	1.1	even	1	trivial
576.2.y.a.527.22		88	9.5	odd	6	inner
1728.2.z.a.143.15		88	3.2	odd	2
1728.2.z.a.719.15		88	9.4	even	3
1728.2.z.a.1007.15		88	48.35	even	4
1728.2.z.a.1583.15		88	144.67	odd	12

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:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.y (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0841095 + 1.73001i) q^{3} +(-1.17929 - 0.315990i) q^{5} +(-1.93802 + 3.35676i) q^{7} +(-2.98585 - 0.291020i) q^{9} +O(q^{10})\)	\(q+(-0.0841095 + 1.73001i) q^{3} +(-1.17929 - 0.315990i) q^{5} +(-1.93802 + 3.35676i) q^{7} +(-2.98585 - 0.291020i) q^{9} +(2.53144 - 0.678298i) q^{11} +(-2.21768 - 0.594225i) q^{13} +(0.645854 - 2.01360i) q^{15} -1.65347i q^{17} +(-2.32189 - 2.32189i) q^{19} +(-5.64421 - 3.63513i) q^{21} +(-6.27540 + 3.62310i) q^{23} +(-3.03925 - 1.75471i) q^{25} +(0.754605 - 5.14107i) q^{27} +(5.23808 - 1.40354i) q^{29} +(-6.44476 + 3.72088i) q^{31} +(0.960542 + 4.43646i) q^{33} +(3.34619 - 3.34619i) q^{35} +(0.499924 + 0.499924i) q^{37} +(1.21454 - 3.78662i) q^{39} +(5.22021 + 9.04166i) q^{41} +(-2.07069 - 7.72793i) q^{43} +(3.42922 + 1.28670i) q^{45} +(-1.91487 + 3.31665i) q^{47} +(-4.01188 - 6.94877i) q^{49} +(2.86051 + 0.139072i) q^{51} +(-4.69522 + 4.69522i) q^{53} -3.19964 q^{55} +(4.21219 - 3.82160i) q^{57} +(-1.60258 + 5.98090i) q^{59} +(-2.01670 - 7.52642i) q^{61} +(6.76354 - 9.45877i) q^{63} +(2.42752 + 1.40153i) q^{65} +(-3.58944 + 13.3960i) q^{67} +(-5.74017 - 11.1612i) q^{69} -10.9828i q^{71} +10.4967i q^{73} +(3.29130 - 5.11034i) q^{75} +(-2.62911 + 9.81199i) q^{77} +(7.83718 + 4.52480i) q^{79} +(8.83061 + 1.73789i) q^{81} +(-0.746054 - 2.78431i) q^{83} +(-0.522479 + 1.94992i) q^{85} +(1.98756 + 9.17996i) q^{87} +4.91926 q^{89} +(6.29259 - 6.29259i) q^{91} +(-5.89509 - 11.4624i) q^{93} +(2.00449 + 3.47188i) q^{95} +(-7.00277 + 12.1291i) q^{97} +(-7.75590 + 1.28860i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7}+O(q^{10}) \) 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7	\( 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7} + 6 q^{11} - 2 q^{13} + 8 q^{19} + 2 q^{21} + 12 q^{23} + 16 q^{27} - 6 q^{29} - 8 q^{33} - 8 q^{37} + 32 q^{39} + 2 q^{43} + 6 q^{45} - 24 q^{49} + 12 q^{51} + 16 q^{55} + 42 q^{59} - 2 q^{61} - 12 q^{65} + 2 q^{67} - 10 q^{69} + 56 q^{75} - 6 q^{77} - 8 q^{81} - 54 q^{83} + 8 q^{85} - 48 q^{87} - 20 q^{91} - 34 q^{93} - 4 q^{97} - 46 q^{99}+O(q^{100}) \) 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7 + 6 * q^11 - 2 * q^13 + 8 * q^19 + 2 * q^21 + 12 * q^23 + 16 * q^27 - 6 * q^29 - 8 * q^33 - 8 * q^37 + 32 * q^39 + 2 * q^43 + 6 * q^45 - 24 * q^49 + 12 * q^51 + 16 * q^55 + 42 * q^59 - 2 * q^61 - 12 * q^65 + 2 * q^67 - 10 * q^69 + 56 * q^75 - 6 * q^77 - 8 * q^81 - 54 * q^83 + 8 * q^85 - 48 * q^87 - 20 * q^91 - 34 * q^93 - 4 * q^97 - 46 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more