LMFDB - Embedded newform 576.2.y.a.335.10

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			335.10
Character	$\chi$	$=$	576.335
Dual form			576.2.y.a.239.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.117756 - 1.72804i) q^{3} +(-3.58858 - 0.961558i) q^{5} +(1.29216 - 2.23809i) q^{7} +(-2.97227 + 0.406975i) q^{9} +O(q^{10})$	\(q+(-0.117756 - 1.72804i) q^{3} +(-3.58858 - 0.961558i) q^{5} +(1.29216 - 2.23809i) q^{7} +(-2.97227 + 0.406975i) q^{9} +(2.02011 - 0.541286i) q^{11} +(-0.998074 - 0.267433i) q^{13} +(-1.23904 + 6.31446i) q^{15} +4.13788i q^{17} +(-2.49279 - 2.49279i) q^{19} +(-4.01968 - 1.96936i) q^{21} +(-7.01915 + 4.05251i) q^{23} +(7.62322 + 4.40127i) q^{25} +(1.05327 + 5.08828i) q^{27} +(-7.02439 + 1.88218i) q^{29} +(2.03331 - 1.17393i) q^{31} +(-1.17324 - 3.42709i) q^{33} +(-6.78909 + 6.78909i) q^{35} +(-4.75590 - 4.75590i) q^{37} +(-0.344607 + 1.75621i) q^{39} +(0.636217 + 1.10196i) q^{41} +(-0.389880 - 1.45505i) q^{43} +(11.0576 + 1.39754i) q^{45} +(3.60814 - 6.24948i) q^{47} +(0.160635 + 0.278228i) q^{49} +(7.15044 - 0.487260i) q^{51} +(0.546616 - 0.546616i) q^{53} -7.76980 q^{55} +(-4.01411 + 4.60119i) q^{57} +(2.14469 - 8.00411i) q^{59} +(1.81511 + 6.77407i) q^{61} +(-2.92980 + 7.17808i) q^{63} +(3.32452 + 1.91941i) q^{65} +(-0.751980 + 2.80643i) q^{67} +(7.82945 + 11.6522i) q^{69} -6.59449i q^{71} -8.78699i q^{73} +(6.70790 - 13.6915i) q^{75} +(1.39886 - 5.22061i) q^{77} +(-5.64940 - 3.26168i) q^{79} +(8.66874 - 2.41928i) q^{81} +(-2.06791 - 7.71754i) q^{83} +(3.97882 - 14.8491i) q^{85} +(4.07965 + 11.9168i) q^{87} -14.1938 q^{89} +(-1.88821 + 1.88821i) q^{91} +(-2.26805 - 3.37542i) q^{93} +(6.54863 + 11.3426i) q^{95} +(6.54551 - 11.3372i) q^{97} +(-5.78401 + 2.43098i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.117756	−	1.72804i	−0.0679864	−	0.997686i
$3$	−0.117756	−	1.72804i	−0.0679864	−	0.997686i
$4$		0			0
$5$	−3.58858	−	0.961558i	−1.60486	−	0.430022i	−0.658357	−	0.752706i	$-0.728748\pi$
$5$	−3.58858	−	0.961558i	−1.60486	−	0.430022i	−0.946507	+	0.322684i	$0.895415\pi$
$6$		0			0
$7$	1.29216	−	2.23809i	0.488391	−	0.845919i	−0.511520	−	0.859272i	$-0.670917\pi$
$7$	1.29216	−	2.23809i	0.488391	−	0.845919i	0.999911	+	0.0133531i	$0.00425055\pi$
$8$		0			0
$9$	−2.97227	+	0.406975i	−0.990756	+	0.135658i
$10$		0			0
$11$	2.02011	−	0.541286i	0.609085	−	0.163204i	0.0589240	−	0.998262i	$-0.481233\pi$
$11$	2.02011	−	0.541286i	0.609085	−	0.163204i	0.550161	+	0.835059i	$0.314566\pi$
$12$		0			0
$13$	−0.998074	−	0.267433i	−0.276816	−	0.0741726i	0.117740	−	0.993044i	$-0.462435\pi$
$13$	−0.998074	−	0.267433i	−0.276816	−	0.0741726i	−0.394556	+	0.918872i	$0.629102\pi$
$14$		0			0
$15$	−1.23904	+	6.31446i	−0.319918	+	1.63039i
$16$		0			0
$17$			4.13788i			1.00358i	0.864988	+	0.501792i	$0.167326\pi$
$17$			4.13788i			1.00358i	−0.864988	+	0.501792i	$0.832674\pi$
$18$		0			0
$19$	−2.49279	−	2.49279i	−0.571886	−	0.571886i	0.360769	−	0.932655i	$-0.382514\pi$
$19$	−2.49279	−	2.49279i	−0.571886	−	0.571886i	−0.932655	+	0.360769i	$0.882514\pi$
$20$		0			0
$21$	−4.01968	−	1.96936i	−0.877165	−	0.429750i
$22$		0			0
$23$	−7.01915	+	4.05251i	−1.46359	+	0.845006i	−0.999175	−	0.0406102i	$-0.987070\pi$
$23$	−7.01915	+	4.05251i	−1.46359	+	0.845006i	−0.464418	+	0.885616i	$0.653736\pi$
$24$		0			0
$25$	7.62322	+	4.40127i	1.52464	+	0.880253i
$26$		0			0
$27$	1.05327	+	5.08828i	0.202702	+	0.979240i
$28$		0			0
$29$	−7.02439	+	1.88218i	−1.30440	+	0.349512i	−0.843111	−	0.537740i	$-0.819278\pi$
$29$	−7.02439	+	1.88218i	−1.30440	+	0.349512i	−0.461286	+	0.887252i	$0.652612\pi$
$30$		0			0
$31$	2.03331	−	1.17393i	0.365194	−	0.210845i	−0.306163	−	0.951979i	$-0.599045\pi$
$31$	2.03331	−	1.17393i	0.365194	−	0.210845i	0.671357	+	0.741134i	$0.265712\pi$
$32$		0			0
$33$	−1.17324	−	3.42709i	−0.204236	−	0.596580i
$34$		0			0
$35$	−6.78909	+	6.78909i	−1.14757	+	1.14757i
$36$		0			0
$37$	−4.75590	−	4.75590i	−0.781865	−	0.781865i	0.198280	−	0.980145i	$-0.436464\pi$
$37$	−4.75590	−	4.75590i	−0.781865	−	0.781865i	−0.980145	+	0.198280i	$0.936464\pi$
$38$		0			0
$39$	−0.344607	+	1.75621i	−0.0551813	+	0.281218i
$40$		0			0
$41$	0.636217	+	1.10196i	0.0993604	+	0.172097i	0.911420	−	0.411477i	$-0.134987\pi$
$41$	0.636217	+	1.10196i	0.0993604	+	0.172097i	−0.812060	+	0.583574i	$0.801654\pi$
$42$		0			0
$43$	−0.389880	−	1.45505i	−0.0594562	−	0.221894i	0.929805	−	0.368053i	$-0.119975\pi$
$43$	−0.389880	−	1.45505i	−0.0594562	−	0.221894i	−0.989261	+	0.146159i	$0.953309\pi$
$44$		0			0
$45$	11.0576	+	1.39754i	1.64836	+	0.208334i
$46$		0			0
$47$	3.60814	−	6.24948i	0.526301	−	0.911580i	−0.473230	−	0.880939i	$-0.656912\pi$
$47$	3.60814	−	6.24948i	0.526301	−	0.911580i	0.999530	−	0.0306407i	$-0.00975476\pi$
$48$		0			0
$49$	0.160635	+	0.278228i	0.0229479	+	0.0397469i
$50$		0			0
$51$	7.15044	−	0.487260i	1.00126	−	0.0682301i
$52$		0			0
$53$	0.546616	−	0.546616i	0.0750835	−	0.0750835i	−0.668568	−	0.743651i	$-0.733092\pi$
$53$	0.546616	−	0.546616i	0.0750835	−	0.0750835i	0.743651	+	0.668568i	$0.233092\pi$
$54$		0			0
$55$	−7.76980			−1.04768
$56$		0			0
$57$	−4.01411	+	4.60119i	−0.531682	+	0.609443i
$58$		0			0
$59$	2.14469	−	8.00411i	0.279215	−	1.04205i	−0.673748	−	0.738961i	$-0.735317\pi$
$59$	2.14469	−	8.00411i	0.279215	−	1.04205i	0.952963	−	0.303085i	$-0.0980167\pi$
$60$		0			0
$61$	1.81511	+	6.77407i	0.232401	+	0.867331i	0.979303	+	0.202398i	$0.0648734\pi$
$61$	1.81511	+	6.77407i	0.232401	+	0.867331i	−0.746903	+	0.664933i	$0.768460\pi$
$62$		0			0
$63$	−2.92980	+	7.17808i	−0.369121	+	0.904353i
$64$		0			0
$65$	3.32452	+	1.91941i	0.412356	+	0.238074i
$66$		0			0
$67$	−0.751980	+	2.80643i	−0.0918690	+	0.342860i	−0.996526	−	0.0832804i	$-0.973460\pi$
$67$	−0.751980	+	2.80643i	−0.0918690	+	0.342860i	0.904657	+	0.426140i	$0.140127\pi$
$68$		0			0
$69$	7.82945	+	11.6522i	0.942555	+	1.40276i
$70$		0			0
$71$		−	6.59449i		−	0.782622i	−0.920258	−	0.391311i	$-0.872022\pi$
$71$		−	6.59449i		−	0.782622i	0.920258	−	0.391311i	$-0.127978\pi$
$72$		0			0
$73$		−	8.78699i		−	1.02844i	−0.857658	−	0.514220i	$-0.828082\pi$
$73$		−	8.78699i		−	1.02844i	0.857658	−	0.514220i	$-0.171918\pi$
$74$		0			0
$75$	6.70790	−	13.6915i	0.774562	−	1.58096i
$76$		0			0
$77$	1.39886	−	5.22061i	0.159415	−	0.594944i
$78$		0			0
$79$	−5.64940	−	3.26168i	−0.635607	−	0.366968i	0.147313	−	0.989090i	$-0.452937\pi$
$79$	−5.64940	−	3.26168i	−0.635607	−	0.366968i	−0.782920	+	0.622122i	$0.786271\pi$
$80$		0			0
$81$	8.66874	−	2.41928i	0.963194	−	0.268808i
$82$		0			0
$83$	−2.06791	−	7.71754i	−0.226982	−	0.847110i	−0.981601	−	0.190946i	$-0.938845\pi$
$83$	−2.06791	−	7.71754i	−0.226982	−	0.847110i	0.754618	−	0.656164i	$-0.227822\pi$
$84$		0			0
$85$	3.97882	−	14.8491i	0.431563	−	1.61062i
$86$		0			0
$87$	4.07965	+	11.9168i	0.437385	+	1.27762i
$88$		0			0
$89$	−14.1938			−1.50454			−0.752272	−	0.658852i	$-0.771042\pi$
$89$	−14.1938			−1.50454			−0.752272	+	0.658852i	$0.771042\pi$
$90$		0			0
$91$	−1.88821	+	1.88821i	−0.197939	+	0.197939i
$92$		0			0
$93$	−2.26805	−	3.37542i	−0.235185	−	0.350015i
$94$		0			0
$95$	6.54863	+	11.3426i	0.671875	+	1.16372i
$96$		0			0
$97$	6.54551	−	11.3372i	0.664596	−	1.15111i	−0.314799	−	0.949158i	$-0.601937\pi$
$97$	6.54551	−	11.3372i	0.664596	−	1.15111i	0.979395	−	0.201955i	$-0.0647295\pi$
$98$		0			0
$99$	−5.78401	+	2.43098i	−0.581314	+	0.244322i
$100$		0			0
$101$	−1.05705	−	3.94498i	−0.105181	−	0.392540i	0.893185	−	0.449690i	$-0.148465\pi$
$101$	−1.05705	−	3.94498i	−0.105181	−	0.392540i	−0.998366	+	0.0571499i	$0.981799\pi$
$102$		0			0
$103$	−2.22868	−	3.86019i	−0.219599	−	0.380356i	0.735087	−	0.677973i	$-0.237141\pi$
$103$	−2.22868	−	3.86019i	−0.219599	−	0.380356i	−0.954685	+	0.297617i	$0.903808\pi$
$104$		0			0
$105$	12.5313	+	10.9324i	1.22293	+	1.06689i
$106$		0			0
$107$	−4.01417	−	4.01417i	−0.388064	−	0.388064i	0.485932	−	0.873996i	$-0.338480\pi$
$107$	−4.01417	−	4.01417i	−0.388064	−	0.388064i	−0.873996	+	0.485932i	$0.838480\pi$
$108$		0			0
$109$	−6.84996	+	6.84996i	−0.656107	+	0.656107i	−0.954457	−	0.298349i	$-0.903564\pi$
$109$	−6.84996	+	6.84996i	−0.656107	+	0.656107i	0.298349	+	0.954457i	$0.403564\pi$
$110$		0			0
$111$	−7.65837	+	8.77844i	−0.726900	+	0.833212i
$112$		0			0
$113$	−7.97546	+	4.60464i	−0.750268	+	0.433168i	−0.825791	−	0.563976i	$-0.809271\pi$
$113$	−7.97546	+	4.60464i	−0.750268	+	0.433168i	0.0755225	+	0.997144i	$0.475938\pi$
$114$		0			0
$115$	29.0855	−	7.79344i	2.71224	−	0.726742i
$116$		0			0
$117$	3.07538	+	0.388692i	0.284319	+	0.0359346i
$118$		0			0
$119$	9.26095	+	5.34681i	0.848950	+	0.490142i
$120$		0			0
$121$	−5.73844	+	3.31309i	−0.521676	+	0.301190i
$122$		0			0
$123$	1.82932	−	1.22917i	0.164944	−	0.110831i
$124$		0			0
$125$	−9.98936	−	9.98936i	−0.893475	−	0.893475i
$126$		0			0
$127$		−	4.75792i		−	0.422197i	−0.977465	−	0.211099i	$-0.932296\pi$
$127$		−	4.75792i		−	0.422197i	0.977465	−	0.211099i	$-0.0677041\pi$
$128$		0			0
$129$	−2.46849	+	0.845072i	−0.217338	+	0.0744044i
$130$		0			0
$131$	−8.36446	−	2.24125i	−0.730806	−	0.195819i	−0.125818	−	0.992053i	$-0.540156\pi$
$131$	−8.36446	−	2.24125i	−0.730806	−	0.195819i	−0.604988	+	0.796234i	$0.706822\pi$
$132$		0			0
$133$	−8.80019	+	2.35800i	−0.763073	+	0.204465i
$134$		0			0
$135$	1.11292	−	19.2725i	0.0957853	−	1.65871i
$136$		0			0
$137$	8.29570	−	14.3686i	0.708750	−	1.22759i	−0.256571	−	0.966525i	$-0.582593\pi$
$137$	8.29570	−	14.3686i	0.708750	−	1.22759i	0.965321	−	0.261065i	$-0.0840738\pi$
$138$		0			0
$139$	6.87408	+	1.84191i	0.583052	+	0.156228i	0.538276	−	0.842769i	$-0.319076\pi$
$139$	6.87408	+	1.84191i	0.583052	+	0.156228i	0.0447763	+	0.998997i	$0.485743\pi$
$140$		0			0
$141$	−11.2242	−	5.49910i	−0.945252	−	0.463108i
$142$		0			0
$143$	−2.16097			−0.180710
$144$		0			0
$145$	27.0175			2.24368
$146$		0			0
$147$	0.461874	−	0.310347i	0.0380948	−	0.0255970i
$148$		0			0
$149$	3.61965	+	0.969882i	0.296533	+	0.0794558i	0.404018	−	0.914751i	$-0.367613\pi$
$149$	3.61965	+	0.969882i	0.296533	+	0.0794558i	−0.107485	+	0.994207i	$0.534280\pi$
$150$		0			0
$151$	−1.35324	+	2.34389i	−0.110125	+	0.190743i	−0.915821	−	0.401588i	$-0.868459\pi$
$151$	−1.35324	+	2.34389i	−0.110125	+	0.190743i	0.805695	+	0.592330i	$0.201792\pi$
$152$		0			0
$153$	−1.68401	−	12.2989i	−0.136144	−	0.994307i
$154$		0			0
$155$	−8.42553	+	2.25761i	−0.676755	+	0.181336i
$156$		0			0
$157$	4.79418	+	1.28460i	0.382617	+	0.102522i	0.445001	−	0.895530i	$-0.353203\pi$
$157$	4.79418	+	1.28460i	0.382617	+	0.102522i	−0.0623832	+	0.998052i	$0.519870\pi$
$158$		0			0
$159$	−1.00894	−	0.880209i	−0.0800144	−	0.0698051i
$160$		0			0
$161$			20.9460i			1.65077i
$162$		0			0
$163$	8.40242	+	8.40242i	0.658129	+	0.658129i	0.954937	−	0.296808i	$-0.0959223\pi$
$163$	8.40242	+	8.40242i	0.658129	+	0.658129i	−0.296808	+	0.954937i	$0.595922\pi$
$164$		0			0
$165$	0.914940	+	13.4266i	0.0712280	+	1.04526i
$166$		0			0
$167$	7.11596	−	4.10840i	0.550650	−	0.317918i	−0.198734	−	0.980053i	$-0.563683\pi$
$167$	7.11596	−	4.10840i	0.550650	−	0.317918i	0.749384	+	0.662136i	$0.230350\pi$
$168$		0			0
$169$	−10.3337	−	5.96616i	−0.794900	−	0.458936i
$170$		0			0
$171$	8.42375	+	6.39474i	0.644180	+	0.489018i
$172$		0			0
$173$	24.8718	−	6.66438i	1.89097	−	0.506683i	0.892518	−	0.451012i	$-0.148937\pi$
$173$	24.8718	−	6.66438i	1.89097	−	0.506683i	0.998449	−	0.0556715i	$-0.0177300\pi$
$174$		0			0
$175$	19.7009	−	11.3743i	1.48925	−	0.859816i
$176$		0			0
$177$	−14.0840	−	2.76359i	−1.05862	−	0.207724i
$178$		0			0
$179$	−14.5908	+	14.5908i	−1.09057	+	1.09057i	−0.0951034	+	0.995467i	$0.530318\pi$
$179$	−14.5908	+	14.5908i	−1.09057	+	1.09057i	−0.995467	+	0.0951034i	$0.969682\pi$
$180$		0			0
$181$	8.19403	+	8.19403i	0.609057	+	0.609057i	0.942700	−	0.333642i	$-0.108278\pi$
$181$	8.19403	+	8.19403i	0.609057	+	0.609057i	−0.333642	+	0.942700i	$0.608278\pi$
$182$		0			0
$183$	11.4922	−	3.93427i	0.849524	−	0.290830i
$184$		0			0
$185$	12.4939	+	21.6400i	0.918568	+	1.59101i
$186$		0			0
$187$	2.23978	+	8.35896i	0.163789	+	0.611268i
$188$		0			0
$189$	12.7490	+	4.21757i	0.927356	+	0.306783i
$190$		0			0
$191$	2.80582	−	4.85981i	0.203022	−	0.351644i	−0.746479	−	0.665409i	$-0.768257\pi$
$191$	2.80582	−	4.85981i	0.203022	−	0.351644i	0.949501	+	0.313765i	$0.101590\pi$
$192$		0			0
$193$	−12.5728	−	21.7767i	−0.905008	−	1.56752i	−0.820906	−	0.571063i	$-0.806531\pi$
$193$	−12.5728	−	21.7767i	−0.905008	−	1.56752i	−0.0841024	−	0.996457i	$-0.526802\pi$
$194$		0			0
$195$	2.92535	−	5.97094i	0.209488	−	0.427588i
$196$		0			0
$197$	4.31684	−	4.31684i	0.307562	−	0.307562i	−0.536401	−	0.843963i	$-0.680216\pi$
$197$	4.31684	−	4.31684i	0.307562	−	0.307562i	0.843963	+	0.536401i	$0.180216\pi$
$198$		0			0
$199$	14.6645			1.03954			0.519769	−	0.854307i	$-0.326018\pi$
$199$	14.6645			1.03954			0.519769	+	0.854307i	$0.326018\pi$
$200$		0			0
$201$	4.93818	+	0.968981i	0.348312	+	0.0683466i
$202$		0			0
$203$	−4.86416	+	18.1533i	−0.341397	+	1.27411i
$204$		0			0
$205$	−1.22352	−	4.56624i	−0.0854543	−	0.318920i
$206$		0			0
$207$	19.2135	−	14.9017i	1.33543	−	1.03574i
$208$		0			0
$209$	−6.38502	−	3.68639i	−0.441661	−	0.254993i
$210$		0			0
$211$	−0.604656	+	2.25661i	−0.0416263	+	0.155351i	−0.983611	−	0.180305i	$-0.942291\pi$
$211$	−0.604656	+	2.25661i	−0.0416263	+	0.155351i	0.941984	+	0.335656i	$0.108958\pi$
$212$		0			0
$213$	−11.3956	+	0.776541i	−0.780812	+	0.0532077i
$214$		0			0
$215$			5.59648i			0.381677i
$216$		0			0
$217$		−	6.06766i		−	0.411899i
$218$		0			0
$219$	−15.1843	+	1.03472i	−1.02606	+	0.0699200i
$220$		0			0
$221$	1.10661	−	4.12991i	0.0744385	−	0.277808i
$222$		0			0
$223$	−24.9105	−	14.3821i	−1.66813	−	0.963094i	−0.968646	−	0.248445i	$-0.920081\pi$
$223$	−24.9105	−	14.3821i	−1.66813	−	0.963094i	−0.699483	−	0.714650i	$-0.746586\pi$
$224$		0			0
$225$	−24.4494	−	9.97928i	−1.62996	−	0.665286i
$226$		0			0
$227$	2.16234	+	8.06995i	0.143519	+	0.535621i	0.999817	+	0.0191384i	$0.00609231\pi$
$227$	2.16234	+	8.06995i	0.143519	+	0.535621i	−0.856298	+	0.516483i	$0.827241\pi$
$228$		0			0
$229$	−4.96759	+	18.5393i	−0.328268	+	1.22511i	0.582718	+	0.812674i	$0.301989\pi$
$229$	−4.96759	+	18.5393i	−0.328268	+	1.22511i	−0.910986	+	0.412438i	$0.864677\pi$
$230$		0			0
$231$	−9.18616	−	1.80253i	−0.604405	−	0.118598i
$232$		0			0
$233$	2.96265			0.194090			0.0970450	−	0.995280i	$-0.469061\pi$
$233$	2.96265			0.194090			0.0970450	+	0.995280i	$0.469061\pi$
$234$		0			0
$235$	−18.9573	+	18.9573i	−1.23664	+	1.23664i
$236$		0			0
$237$	−4.97108	+	10.1465i	−0.322906	+	0.659085i
$238$		0			0
$239$	5.14390	+	8.90950i	0.332731	+	0.576307i	0.983046	−	0.183357i	$-0.0586965\pi$
$239$	5.14390	+	8.90950i	0.332731	+	0.576307i	−0.650315	+	0.759665i	$0.725363\pi$
$240$		0			0
$241$	−12.8722	+	22.2954i	−0.829173	+	1.43617i	0.0695144	+	0.997581i	$0.477855\pi$
$241$	−12.8722	+	22.2954i	−0.829173	+	1.43617i	−0.898688	+	0.438589i	$0.855478\pi$
$242$		0			0
$243$	−5.20141	−	14.6951i	−0.333671	−	0.942690i
$244$		0			0
$245$	−0.308920	−	1.15290i	−0.0197362	−	0.0736564i
$246$		0			0
$247$	1.82134	+	3.15465i	0.115889	+	0.200725i
$248$		0			0
$249$	−13.0927	+	4.48222i	−0.829718	+	0.284049i
$250$		0			0
$251$	−16.7668	−	16.7668i	−1.05831	−	1.05831i	−0.998191	−	0.0601228i	$-0.980851\pi$
$251$	−16.7668	−	16.7668i	−1.05831	−	1.05831i	−0.0601228	−	0.998191i	$-0.519149\pi$
$252$		0			0
$253$	−11.9859	+	11.9859i	−0.753544	+	0.753544i
$254$		0			0
$255$	−26.1285	−	5.12699i	−1.63623	−	0.321065i
$256$		0			0
$257$	−6.74821	+	3.89608i	−0.420942	+	0.243031i	−0.695480	−	0.718545i	$-0.744808\pi$
$257$	−6.74821	+	3.89608i	−0.420942	+	0.243031i	0.274538	+	0.961576i	$0.411475\pi$
$258$		0			0
$259$	−16.7895	+	4.49874i	−1.04325	+	0.279538i
$260$		0			0
$261$	20.1124	−	8.45309i	1.24492	−	0.523233i
$262$		0			0
$263$	−12.3513	−	7.13103i	−0.761615	−	0.439718i	0.0682606	−	0.997668i	$-0.478255\pi$
$263$	−12.3513	−	7.13103i	−0.761615	−	0.439718i	−0.829875	+	0.557949i	$0.811588\pi$
$264$		0			0
$265$	−2.48718	+	1.43597i	−0.152786	+	0.0882112i
$266$		0			0
$267$	1.67141	+	24.5276i	0.102289	+	1.50106i
$268$		0			0
$269$	−1.70265	−	1.70265i	−0.103812	−	0.103812i	0.653293	−	0.757105i	$-0.273387\pi$
$269$	−1.70265	−	1.70265i	−0.103812	−	0.103812i	−0.757105	+	0.653293i	$0.773387\pi$
$270$		0			0
$271$		−	9.55642i		−	0.580511i	−0.956949	−	0.290256i	$-0.906260\pi$
$271$		−	9.55642i		−	0.580511i	0.956949	−	0.290256i	$-0.0937403\pi$
$272$		0			0
$273$	3.48526	+	3.04057i	0.210938	+	0.184023i
$274$		0			0
$275$	17.7821	+	4.76469i	1.07230	+	0.287321i
$276$		0			0
$277$	−2.13315	+	0.571577i	−0.128169	+	0.0343427i	−0.322333	−	0.946626i	$-0.604467\pi$
$277$	−2.13315	+	0.571577i	−0.128169	+	0.0343427i	0.194164	+	0.980969i	$0.437800\pi$
$278$		0			0
$279$	−5.56579	+	4.31676i	−0.333215	+	0.258437i
$280$		0			0
$281$	8.26158	−	14.3095i	0.492845	−	0.853632i	−0.507121	−	0.861875i	$-0.669290\pi$
$281$	8.26158	−	14.3095i	0.492845	−	0.853632i	0.999966	+	0.00824250i	$0.00262370\pi$
$282$		0			0
$283$	−7.29366	−	1.95433i	−0.433563	−	0.116173i	0.0354353	−	0.999372i	$-0.488718\pi$
$283$	−7.29366	−	1.95433i	−0.433563	−	0.116173i	−0.468998	+	0.883199i	$0.655385\pi$
$284$		0			0
$285$	18.8293	−	12.6520i	1.11535	−	0.749438i
$286$		0			0
$287$	3.28838			0.194107
$288$		0			0
$289$	−0.122073			−0.00718078
$290$		0			0
$291$	−20.3619	−	9.97590i	−1.19363	−	0.584798i
$292$		0			0
$293$	22.8630	+	6.12613i	1.33567	+	0.357892i	0.854827	−	0.518913i	$-0.173663\pi$
$293$	22.8630	+	6.12613i	1.33567	+	0.357892i	0.480845	+	0.876805i	$0.340330\pi$
$294$		0			0
$295$	−15.3928	+	26.6612i	−0.896206	+	1.55227i
$296$		0			0
$297$	4.88194	+	9.70875i	0.283279	+	0.563359i
$298$		0			0
$299$	8.08940	−	2.16755i	0.467822	−	0.125353i
$300$		0			0
$301$	−3.76033	−	1.00758i	−0.216742	−	0.0580758i
$302$		0			0
$303$	−6.69261	+	2.29118i	−0.384481	+	0.131625i
$304$		0			0
$305$		−	26.0547i		−	1.49189i
$306$		0			0
$307$	−12.9528	−	12.9528i	−0.739255	−	0.739255i	0.233179	−	0.972434i	$-0.425087\pi$
$307$	−12.9528	−	12.9528i	−0.739255	−	0.739255i	−0.972434	+	0.233179i	$0.925087\pi$
$308$		0			0
$309$	−6.40814	+	4.30582i	−0.364546	+	0.244950i
$310$		0			0
$311$	3.74301	−	2.16103i	0.212247	−	0.122541i	−0.390108	−	0.920769i	$-0.627562\pi$
$311$	3.74301	−	2.16103i	0.212247	−	0.122541i	0.602355	+	0.798228i	$0.294229\pi$
$312$		0			0
$313$	13.7859	+	7.95932i	0.779228	+	0.449887i	0.836157	−	0.548491i	$-0.184797\pi$
$313$	13.7859	+	7.95932i	0.779228	+	0.449887i	−0.0569286	+	0.998378i	$0.518131\pi$
$314$		0			0
$315$	17.4160	−	22.9420i	0.981280	−	1.29263i
$316$		0			0
$317$	−28.7104	+	7.69292i	−1.61253	+	0.432077i	−0.948797	−	0.315888i	$-0.897698\pi$
$317$	−28.7104	+	7.69292i	−1.61253	+	0.432077i	−0.663738	+	0.747965i	$0.731031\pi$
$318$		0			0
$319$	−13.1712	+	7.60441i	−0.737447	+	0.425765i
$320$		0			0
$321$	−6.46396	+	7.40934i	−0.360783	+	0.413549i
$322$		0			0
$323$	10.3149	−	10.3149i	0.573935	−	0.573935i
$324$		0			0
$325$	−6.43149	−	6.43149i	−0.356755	−	0.356755i
$326$		0			0
$327$	12.6437	+	11.0304i	0.699196	+	0.609983i
$328$		0			0
$329$	−9.32459	−	16.1507i	−0.514082	−	0.890415i
$330$		0			0
$331$	−0.509403	−	1.90112i	−0.0279993	−	0.104495i	0.950512	−	0.310688i	$-0.100559\pi$
$331$	−0.509403	−	1.90112i	−0.0279993	−	0.104495i	−0.978511	+	0.206193i	$0.933893\pi$
$332$		0			0
$333$	16.0713	+	12.2003i	0.880704	+	0.668571i
$334$		0			0
$335$	5.39709	−	9.34803i	0.294874	−	0.510738i
$336$		0			0
$337$	9.46585	+	16.3953i	0.515638	+	0.893111i	0.999835	+	0.0181522i	$0.00577834\pi$
$337$	9.46585	+	16.3953i	0.515638	+	0.893111i	−0.484197	+	0.874959i	$0.660888\pi$
$338$		0			0
$339$	8.89617	+	13.2397i	0.483173	+	0.719083i
$340$		0			0
$341$	3.47208	−	3.47208i	0.188024	−	0.188024i
$342$		0			0
$343$	18.9205			1.02161
$344$		0			0
$345$	−16.8924	−	49.3433i	−0.909456	−	2.65655i
$346$		0			0
$347$	0.821032	−	3.06413i	0.0440753	−	0.164491i	−0.940380	−	0.340125i	$-0.889531\pi$
$347$	0.821032	−	3.06413i	0.0440753	−	0.164491i	0.984456	+	0.175634i	$0.0561974\pi$
$348$		0			0
$349$	−4.28490	−	15.9915i	−0.229365	−	0.856003i	−0.980608	−	0.195978i	$-0.937212\pi$
$349$	−4.28490	−	15.9915i	−0.229365	−	0.856003i	0.751243	−	0.660026i	$-0.229455\pi$
$350$		0			0
$351$	0.309532	−	5.36016i	0.0165216	−	0.286104i
$352$		0			0
$353$	19.7145	+	11.3822i	1.04930	+	0.605813i	0.922453	−	0.386109i	$-0.126181\pi$
$353$	19.7145	+	11.3822i	1.04930	+	0.605813i	0.126846	+	0.991922i	$0.459514\pi$
$354$		0			0
$355$	−6.34099	+	23.6649i	−0.336545	+	1.25600i
$356$		0			0
$357$	8.14899	−	16.6329i	0.431291	−	0.880309i
$358$		0			0
$359$		−	7.54182i		−	0.398042i	−0.979995	−	0.199021i	$-0.936224\pi$
$359$		−	7.54182i		−	0.398042i	0.979995	−	0.199021i	$-0.0637762\pi$
$360$		0			0
$361$		−	6.57197i		−	0.345893i
$362$		0			0
$363$	6.40090	+	9.52614i	0.335960	+	0.499993i
$364$		0			0
$365$	−8.44921	+	31.5329i	−0.442252	+	1.65051i
$366$		0			0
$367$	20.6334	+	11.9127i	1.07706	+	0.621839i	0.930101	−	0.367304i	$-0.119719\pi$
$367$	20.6334	+	11.9127i	1.07706	+	0.621839i	0.146955	+	0.989143i	$0.453053\pi$
$368$		0			0
$369$	−2.33948	−	3.01639i	−0.121788	−	0.157027i
$370$		0			0
$371$	−0.517059	−	1.92969i	−0.0268444	−	0.100185i
$372$		0			0
$373$	−2.37087	+	8.84822i	−0.122759	+	0.458143i	−0.999750	−	0.0223639i	$-0.992881\pi$
$373$	−2.37087	+	8.84822i	−0.122759	+	0.458143i	0.876991	+	0.480507i	$0.159547\pi$
$374$		0			0
$375$	−16.0857	+	18.4383i	−0.830664	+	0.952152i
$376$		0			0
$377$	7.51422			0.387002
$378$		0			0
$379$	−0.636018	+	0.636018i	−0.0326701	+	0.0326701i	−0.723253	−	0.690583i	$-0.757354\pi$
$379$	−0.636018	+	0.636018i	−0.0326701	+	0.0326701i	0.690583	+	0.723253i	$0.257354\pi$
$380$		0			0
$381$	−8.22190	+	0.560274i	−0.421220	+	0.0287037i
$382$		0			0
$383$	−6.80598	−	11.7883i	−0.347769	−	0.602354i	0.638084	−	0.769967i	$-0.279727\pi$
$383$	−6.80598	−	11.7883i	−0.347769	−	0.602354i	−0.985853	+	0.167613i	$0.946394\pi$
$384$		0			0
$385$	−10.0398	+	17.3895i	−0.511678	+	0.886252i
$386$		0			0
$387$	1.75100	+	4.16614i	0.0890083	+	0.211777i
$388$		0			0
$389$	−2.14427	−	8.00251i	−0.108719	−	0.405744i	0.890022	−	0.455918i	$-0.150689\pi$
$389$	−2.14427	−	8.00251i	−0.108719	−	0.405744i	−0.998740	+	0.0501744i	$0.984022\pi$
$390$		0			0
$391$	−16.7688	−	29.0444i	−0.848034	−	1.46884i
$392$		0			0
$393$	−2.88801	+	14.7181i	−0.145681	+	0.742428i
$394$		0			0
$395$	17.1370	+	17.1370i	0.862258	+	0.862258i
$396$		0			0
$397$	−6.79264	+	6.79264i	−0.340913	+	0.340913i	−0.856710	−	0.515798i	$-0.827496\pi$
$397$	−6.79264	+	6.79264i	−0.340913	+	0.340913i	0.515798	+	0.856710i	$0.327496\pi$
$398$		0			0
$399$	5.11101	+	14.9294i	0.255870	+	0.747407i
$400$		0			0
$401$	5.01378	−	2.89471i	0.250376	−	0.144555i	−0.369560	−	0.929207i	$-0.620492\pi$
$401$	5.01378	−	2.89471i	0.250376	−	0.144555i	0.619936	+	0.784652i	$0.287158\pi$
$402$		0			0
$403$	−2.34335	+	0.627898i	−0.116731	+	0.0312778i
$404$		0			0
$405$	−33.4348	+	0.346272i	−1.66139	+	0.0172064i
$406$		0			0
$407$	−12.1817	−	7.03312i	−0.603826	−	0.348619i
$408$		0			0
$409$	−11.5152	+	6.64832i	−0.569392	+	0.328738i	−0.756906	−	0.653523i	$-0.773290\pi$
$409$	−11.5152	+	6.64832i	−0.569392	+	0.328738i	0.187515	+	0.982262i	$0.439957\pi$
$410$		0			0
$411$	−25.8064	−	12.6434i	−1.27294	−	0.623650i
$412$		0			0
$413$	−15.1426	−	15.1426i	−0.745120	−	0.745120i
$414$		0			0
$415$			29.6834i			1.45710i
$416$		0			0
$417$	2.37343	−	12.0956i	0.116227	−	0.592325i
$418$		0			0
$419$	12.2948	+	3.29438i	0.600639	+	0.160941i	0.546311	−	0.837582i	$-0.316032\pi$
$419$	12.2948	+	3.29438i	0.600639	+	0.160941i	0.0543282	+	0.998523i	$0.482698\pi$
$420$		0			0
$421$	−6.42470	+	1.72149i	−0.313121	+	0.0839004i	−0.411957	−	0.911203i	$-0.635155\pi$
$421$	−6.42470	+	1.72149i	−0.313121	+	0.0839004i	0.0988365	+	0.995104i	$0.468488\pi$
$422$		0			0
$423$	−8.18097	+	20.0435i	−0.397772	+	0.974550i
$424$		0			0
$425$	−18.2119	+	31.5440i	−0.883408	+	1.53011i
$426$		0			0
$427$	17.5064	+	4.69083i	0.847194	+	0.227005i
$428$		0			0
$429$	0.254468	+	3.73426i	0.0122858	+	0.180292i
$430$		0			0
$431$	37.3843			1.80074			0.900370	−	0.435126i	$-0.143296\pi$
$431$	37.3843			1.80074			0.900370	+	0.435126i	$0.143296\pi$
$432$		0			0
$433$	−18.8561			−0.906166			−0.453083	−	0.891468i	$-0.649676\pi$
$433$	−18.8561			−0.906166			−0.453083	+	0.891468i	$0.649676\pi$
$434$		0			0
$435$	−3.18147	−	46.6873i	−0.152540	−	2.23849i
$436$		0			0
$437$	27.5993	+	7.39522i	1.32026	+	0.353761i
$438$		0			0
$439$	4.21577	−	7.30192i	0.201208	−	0.348502i	−0.747710	−	0.664025i	$-0.768847\pi$
$439$	4.21577	−	7.30192i	0.201208	−	0.348502i	0.948918	+	0.315523i	$0.102180\pi$
$440$		0			0
$441$	−0.590682	−	0.761594i	−0.0281277	−	0.0362664i
$442$		0			0
$443$	9.20983	−	2.46777i	0.437572	−	0.117247i	−0.0333063	−	0.999445i	$-0.510604\pi$
$443$	9.20983	−	2.46777i	0.437572	−	0.117247i	0.470879	+	0.882198i	$0.343937\pi$
$444$		0			0
$445$	50.9358	+	13.6482i	2.41459	+	0.646987i
$446$		0			0
$447$	1.24976	−	6.36912i	0.0591117	−	0.301249i
$448$		0			0
$449$			7.54348i			0.355999i	0.984031	+	0.177999i	$0.0569625\pi$
$449$			7.54348i			0.355999i	−0.984031	+	0.177999i	$0.943038\pi$
$450$		0			0
$451$	1.88170	+	1.88170i	0.0886058	+	0.0886058i
$452$		0			0
$453$	4.20969	+	2.06246i	0.197788	+	0.0969026i
$454$		0			0
$455$	8.59164	−	4.96039i	0.402782	−	0.232546i
$456$		0			0
$457$	5.15261	+	2.97486i	0.241029	+	0.139158i	0.615649	−	0.788020i	$-0.288894\pi$
$457$	5.15261	+	2.97486i	0.241029	+	0.139158i	−0.374621	+	0.927178i	$0.622227\pi$
$458$		0			0
$459$	−21.0547	+	4.35832i	−0.982750	+	0.203429i
$460$		0			0
$461$	23.8023	−	6.37780i	1.10858	−	0.297044i	0.342328	−	0.939581i	$-0.388785\pi$
$461$	23.8023	−	6.37780i	1.10858	−	0.297044i	0.766255	+	0.642537i	$0.222118\pi$
$462$		0			0
$463$	−20.8183	+	12.0194i	−0.967507	+	0.558590i	−0.898475	−	0.439024i	$-0.855324\pi$
$463$	−20.8183	+	12.0194i	−0.967507	+	0.558590i	−0.0690315	+	0.997614i	$0.521991\pi$
$464$		0			0
$465$	4.89341	+	14.2938i	0.226926	+	0.662861i
$466$		0			0
$467$	25.3702	−	25.3702i	1.17399	−	1.17399i	0.192744	−	0.981249i	$-0.438261\pi$
$467$	25.3702	−	25.3702i	1.17399	−	1.17399i	0.981249	−	0.192744i	$-0.0617388\pi$
$468$		0			0
$469$	5.30936	+	5.30936i	0.245163	+	0.245163i
$470$		0			0
$471$	1.65530	−	8.43582i	0.0762720	−	0.388702i
$472$		0			0
$473$	−1.57520	−	2.72833i	−0.0724278	−	0.125449i
$474$		0			0
$475$	−8.03166	−	29.9745i	−0.368518	−	1.37533i
$476$		0			0
$477$	−1.40223	+	1.84715i	−0.0642037	+	0.0845751i
$478$		0			0
$479$	0.498647	−	0.863682i	0.0227838	−	0.0394626i	−0.854409	−	0.519602i	$-0.826080\pi$
$479$	0.498647	−	0.863682i	0.0227838	−	0.0394626i	0.877192	+	0.480139i	$0.159414\pi$
$480$		0			0
$481$	3.47486	+	6.01863i	0.158440	+	0.274426i
$482$		0			0
$483$	36.1956	−	2.46651i	1.64695	−	0.112230i
$484$		0			0
$485$	−34.3904	+	34.3904i	−1.56159	+	1.56159i
$486$		0			0
$487$	18.8397			0.853709			0.426855	−	0.904320i	$-0.359622\pi$
$487$	18.8397			0.853709			0.426855	+	0.904320i	$0.359622\pi$
$488$		0			0
$489$	13.5303	−	15.5092i	0.611862	−	0.701350i
$490$		0			0
$491$	−0.143358	+	0.535020i	−0.00646966	+	0.0241451i	−0.969085	−	0.246726i	$-0.920645\pi$
$491$	−0.143358	+	0.535020i	−0.00646966	+	0.0241451i	0.962616	+	0.270871i	$0.0873118\pi$
$492$		0			0
$493$	−7.78824	−	29.0661i	−0.350765	−	1.30907i
$494$		0			0
$495$	23.0939	−	3.16211i	1.03799	−	0.142126i
$496$		0			0
$497$	−14.7591	−	8.52115i	−0.662035	−	0.382226i
$498$		0			0
$499$	−11.3041	+	42.1874i	−0.506041	+	1.88857i	−0.0497007	+	0.998764i	$0.515827\pi$
$499$	−11.3041	+	42.1874i	−0.506041	+	1.88857i	−0.456340	+	0.889805i	$0.650840\pi$
$500$		0			0
$501$	−7.93744	−	11.8129i	−0.354619	−	0.527761i
$502$		0			0
$503$			20.7324i			0.924412i	0.886773	+	0.462206i	$0.152942\pi$
$503$			20.7324i			0.924412i	−0.886773	+	0.462206i	$0.847058\pi$
$504$		0			0
$505$			15.1733i			0.675203i
$506$		0			0
$507$	−9.09293	+	18.5596i	−0.403831	+	0.824262i
$508$		0			0
$509$	−2.59840	+	9.69736i	−0.115172	+	0.429828i	−0.999300	−	0.0374174i	$-0.988087\pi$
$509$	−2.59840	+	9.69736i	−0.115172	+	0.429828i	0.884128	+	0.467245i	$0.154754\pi$
$510$		0			0
$511$	−19.6661	−	11.3542i	−0.869976	−	0.502281i
$512$		0			0
$513$	10.0584	−	15.3096i	0.444091	−	0.675936i
$514$		0			0
$515$	4.28602	+	15.9956i	0.188865	+	0.704852i
$516$		0			0
$517$	3.90607	−	14.5776i	0.171789	−	0.641124i
$518$		0			0
$519$	−14.4451	−	42.1948i	−0.634071	−	1.85214i
$520$		0			0
$521$	3.20573			0.140445			0.0702227	−	0.997531i	$-0.477629\pi$
$521$	3.20573			0.140445			0.0702227	+	0.997531i	$0.477629\pi$
$522$		0			0
$523$	28.1479	−	28.1479i	1.23082	−	1.23082i	0.267175	−	0.963648i	$-0.413910\pi$
$523$	28.1479	−	28.1479i	1.23082	−	1.23082i	0.963648	−	0.267175i	$-0.0860902\pi$
$524$		0			0
$525$	−21.9752	−	32.7046i	−0.959075	−	1.42734i
$526$		0			0
$527$	4.85760	+	8.41362i	0.211601	+	0.366503i
$528$		0			0
$529$	21.3456	−	36.9717i	0.928070	−	1.60746i
$530$		0			0
$531$	−3.11714	+	24.6632i	−0.135272	+	1.07029i
$532$		0			0
$533$	−0.340291	−	1.26998i	−0.0147396	−	0.0550091i
$534$		0			0
$535$	10.5453	+	18.2650i	0.455914	+	0.789666i
$536$		0			0
$537$	26.9318	+	23.4954i	1.16219	+	1.01390i
$538$		0			0
$539$	0.475101	+	0.475101i	0.0204640	+	0.0204640i
$540$		0			0
$541$	14.6373	−	14.6373i	0.629307	−	0.629307i	−0.318586	−	0.947894i	$-0.603208\pi$
$541$	14.6373	−	14.6373i	0.629307	−	0.629307i	0.947894	+	0.318586i	$0.103208\pi$
$542$		0			0
$543$	13.1947	−	15.1245i	0.566241	−	0.649056i
$544$		0			0
$545$	31.1683	−	17.9950i	1.33510	−	0.770822i
$546$		0			0
$547$	17.0017	−	4.55558i	0.726938	−	0.194783i	0.123673	−	0.992323i	$-0.460533\pi$
$547$	17.0017	−	4.55558i	0.726938	−	0.194783i	0.603265	+	0.797541i	$0.293866\pi$
$548$		0			0
$549$	−8.15186	−	19.3957i	−0.347913	−	0.827786i
$550$		0			0
$551$	22.2022	+	12.8185i	0.945847	+	0.546085i
$552$		0			0
$553$	−14.5999	+	8.42924i	−0.620850	+	0.358448i
$554$		0			0
$555$	35.9237	−	24.1382i	1.52487	−	1.02461i
$556$		0			0
$557$	8.32037	+	8.32037i	0.352546	+	0.352546i	0.861056	−	0.508510i	$-0.169804\pi$
$557$	8.32037	+	8.32037i	0.352546	+	0.352546i	−0.508510	+	0.861056i	$0.669804\pi$
$558$		0			0
$559$			1.55652i			0.0658337i
$560$		0			0
$561$	14.1809	−	4.85475i	0.598718	−	0.204968i
$562$		0			0
$563$	−21.6996	−	5.81439i	−0.914529	−	0.245047i	−0.229284	−	0.973360i	$-0.573638\pi$
$563$	−21.6996	−	5.81439i	−0.914529	−	0.245047i	−0.685245	+	0.728312i	$0.740305\pi$
$564$		0			0
$565$	33.0482	−	8.85525i	1.39035	−	0.372543i
$566$		0			0
$567$	5.78686	−	22.5275i	0.243025	−	0.946067i
$568$		0			0
$569$	−7.57037	+	13.1123i	−0.317367	+	0.549695i	−0.979938	−	0.199304i	$-0.936132\pi$
$569$	−7.57037	+	13.1123i	−0.317367	+	0.549695i	0.662571	+	0.748999i	$0.269465\pi$
$570$		0			0
$571$	−32.9434	−	8.82715i	−1.37864	−	0.369405i	−0.508012	−	0.861350i	$-0.669619\pi$
$571$	−32.9434	−	8.82715i	−1.37864	−	0.369405i	−0.870626	+	0.491945i	$0.836286\pi$
$572$		0			0
$573$	−8.72837	−	4.27630i	−0.364633	−	0.178645i
$574$		0			0
$575$	−71.3446			−2.97528
$576$		0			0
$577$	19.9524			0.830629			0.415315	−	0.909678i	$-0.363671\pi$
$577$	19.9524			0.830629			0.415315	+	0.909678i	$0.363671\pi$
$578$		0			0
$579$	−36.1505	+	24.2906i	−1.50237	+	1.00948i
$580$		0			0
$581$	−19.9446	−	5.34414i	−0.827442	−	0.221712i
$582$		0			0
$583$	0.808347	−	1.40010i	0.0334783	−	0.0579861i
$584$		0			0
$585$	−10.6625	−	4.35201i	−0.440841	−	0.179934i
$586$		0			0
$587$	30.0156	−	8.04265i	1.23887	−	0.331955i	0.420846	−	0.907132i	$-0.361733\pi$
$587$	30.0156	−	8.04265i	1.23887	−	0.331955i	0.818029	+	0.575177i	$0.195067\pi$
$588$		0			0
$589$	−7.99501	−	2.14226i	−0.329429	−	0.0882701i
$590$		0			0
$591$	−7.96803	−	6.95136i	−0.327761	−	0.285941i
$592$		0			0
$593$		−	38.3863i		−	1.57634i	−0.615460	−	0.788168i	$-0.711030\pi$
$593$		−	38.3863i		−	1.57634i	0.615460	−	0.788168i	$-0.288970\pi$
$594$		0			0
$595$	−28.0924	−	28.0924i	−1.15168	−	1.15168i
$596$		0			0
$597$	−1.72683	−	25.3409i	−0.0706745	−	1.03713i
$598$		0			0
$599$	24.9602	−	14.4108i	1.01985	−	0.588809i	0.105787	−	0.994389i	$-0.466264\pi$
$599$	24.9602	−	14.4108i	1.01985	−	0.588809i	0.914060	+	0.405580i	$0.132930\pi$
$600$		0			0
$601$	19.8695	+	11.4716i	0.810492	+	0.467938i	0.847127	−	0.531391i	$-0.178330\pi$
$601$	19.8695	+	11.4716i	0.810492	+	0.467938i	−0.0366348	+	0.999329i	$0.511664\pi$
$602$		0			0
$603$	1.09294	−	8.64749i	0.0445080	−	0.352153i
$604$		0			0
$605$	23.7786	−	6.37146i	0.966738	−	0.259037i
$606$		0			0
$607$	16.8592	−	9.73364i	0.684292	−	0.395076i	−0.117178	−	0.993111i	$-0.537385\pi$
$607$	16.8592	−	9.73364i	0.684292	−	0.395076i	0.801470	+	0.598035i	$0.204051\pi$
$608$		0			0
$609$	31.9425	+	6.26782i	1.29437	+	0.253985i
$610$		0			0
$611$	−5.27251	+	5.27251i	−0.213303	+	0.213303i
$612$		0			0
$613$	−10.5918	−	10.5918i	−0.427797	−	0.427797i	0.460080	−	0.887877i	$-0.347821\pi$
$613$	−10.5918	−	10.5918i	−0.427797	−	0.427797i	−0.887877	+	0.460080i	$0.847821\pi$
$614$		0			0
$615$	−7.74658	+	2.65200i	−0.312372	+	0.106939i
$616$		0			0
$617$	9.33080	+	16.1614i	0.375644	+	0.650634i	0.990423	−	0.138065i	$-0.0440882\pi$
$617$	9.33080	+	16.1614i	0.375644	+	0.650634i	−0.614779	+	0.788699i	$0.710755\pi$
$618$		0			0
$619$	5.62767	+	21.0028i	0.226195	+	0.844172i	0.981922	+	0.189285i	$0.0606170\pi$
$619$	5.62767	+	21.0028i	0.226195	+	0.844172i	−0.755727	+	0.654887i	$0.772716\pi$
$620$		0			0
$621$	−28.0134	−	31.4470i	−1.12414	−	1.26192i
$622$		0			0
$623$	−18.3407	+	31.7671i	−0.734807	+	1.27272i
$624$		0			0
$625$	4.23597	+	7.33691i	0.169439	+	0.293477i
$626$		0			0
$627$	−5.61837	+	11.4677i	−0.224376	+	0.457975i
$628$		0			0
$629$	19.6794	−	19.6794i	0.784667	−	0.784667i
$630$		0			0
$631$	−26.5211			−1.05579			−0.527894	−	0.849310i	$-0.677018\pi$
$631$	−26.5211			−1.05579			−0.527894	+	0.849310i	$0.677018\pi$
$632$		0			0
$633$	3.97072	+	0.779143i	0.157822	+	0.0309682i
$634$		0			0
$635$	−4.57502	+	17.0742i	−0.181554	+	0.677569i
$636$		0			0
$637$	−0.0859183	−	0.320651i	−0.00340421	−	0.0127047i
$638$		0			0
$639$	2.68379	+	19.6006i	0.106169	+	0.775388i
$640$		0			0
$641$	1.35222	+	0.780702i	0.0534093	+	0.0308359i	0.526467	−	0.850196i	$-0.323516\pi$
$641$	1.35222	+	0.780702i	0.0534093	+	0.0308359i	−0.473058	+	0.881032i	$0.656850\pi$
$642$		0			0
$643$	9.02160	−	33.6691i	0.355777	−	1.32778i	−0.523726	−	0.851887i	$-0.675458\pi$
$643$	9.02160	−	33.6691i	0.355777	−	1.32778i	0.879503	−	0.475892i	$-0.157875\pi$
$644$		0			0
$645$	9.67095	−	0.659018i	0.380793	−	0.0259488i
$646$		0			0
$647$		−	7.73678i		−	0.304164i	−0.988368	−	0.152082i	$-0.951402\pi$
$647$		−	7.73678i		−	0.304164i	0.988368	−	0.152082i	$-0.0485978\pi$
$648$		0			0
$649$		−	17.3300i		−	0.680264i
$650$		0			0
$651$	−10.4852	+	0.714503i	−0.410946	+	0.0280036i
$652$		0			0
$653$	3.81636	−	14.2429i	0.149346	−	0.557366i	−0.850178	−	0.526496i	$-0.823505\pi$
$653$	3.81636	−	14.2429i	0.149346	−	0.557366i	0.999523	−	0.0308703i	$-0.00982788\pi$
$654$		0			0
$655$	27.8615	+	16.0858i	1.08864	+	0.628526i
$656$		0			0
$657$	3.57608	+	26.1173i	0.139516	+	1.01893i
$658$		0			0
$659$	−9.05703	−	33.8013i	−0.352812	−	1.31671i	−0.883216	−	0.468967i	$-0.844626\pi$
$659$	−9.05703	−	33.8013i	−0.352812	−	1.31671i	0.530404	−	0.847745i	$-0.322040\pi$
$660$		0			0
$661$	−9.59389	+	35.8049i	−0.373159	+	1.39265i	0.482857	+	0.875699i	$0.339599\pi$
$661$	−9.59389	+	35.8049i	−0.373159	+	1.39265i	−0.856016	+	0.516949i	$0.827068\pi$
$662$		0			0
$663$	−7.26698	−	1.42594i	−0.282226	−	0.0553790i
$664$		0			0
$665$	33.8476			1.31255
$666$		0			0
$667$	41.6777	−	41.6777i	1.61377	−	1.61377i
$668$		0			0
$669$	−21.9195	+	44.7399i	−0.847456	+	1.72975i
$670$		0			0
$671$	7.33342	+	12.7019i	0.283103	+	0.490350i
$672$		0			0
$673$	−14.5046	+	25.1226i	−0.559109	+	0.968406i	0.438462	+	0.898750i	$0.355523\pi$
$673$	−14.5046	+	25.1226i	−0.559109	+	0.968406i	−0.997571	+	0.0696559i	$0.977810\pi$
$674$		0			0
$675$	−14.3656	+	43.4248i	−0.552931	+	1.67142i
$676$		0			0
$677$	−5.58517	−	20.8441i	−0.214655	−	0.801105i	−0.986288	−	0.165036i	$-0.947226\pi$
$677$	−5.58517	−	20.8441i	−0.214655	−	0.801105i	0.771632	−	0.636069i	$-0.219441\pi$
$678$		0			0
$679$	−16.9157	−	29.2989i	−0.649165	−	1.12439i
$680$		0			0
$681$	13.6906	−	4.68689i	0.524624	−	0.179602i
$682$		0			0
$683$	−19.1487	−	19.1487i	−0.732704	−	0.732704i	0.238451	−	0.971155i	$-0.423360\pi$
$683$	−19.1487	−	19.1487i	−0.732704	−	0.732704i	−0.971155	+	0.238451i	$0.923360\pi$
$684$		0			0
$685$	−43.5861	+	43.5861i	−1.66534	+	1.66534i
$686$		0			0
$687$	32.6217	+	6.40110i	1.24460	+	0.244217i
$688$		0			0
$689$	−0.691747	+	0.399380i	−0.0263534	+	0.0152152i
$690$		0			0
$691$	32.7872	−	8.78531i	1.24728	−	0.334209i	0.425997	−	0.904724i	$-0.359923\pi$
$691$	32.7872	−	8.78531i	1.24728	−	0.334209i	0.821287	+	0.570516i	$0.193257\pi$
$692$		0			0
$693$	−2.03312	+	16.0863i	−0.0772320	+	0.611070i
$694$		0			0
$695$	−22.8971	−	13.2197i	−0.868538	−	0.501450i
$696$		0			0
$697$	−4.55978	+	2.63259i	−0.172714	+	0.0997165i
$698$		0			0
$699$	−0.348870	−	5.11960i	−0.0131955	−	0.193641i
$700$		0			0
$701$	28.6582	+	28.6582i	1.08240	+	1.08240i	0.996285	+	0.0861190i	$0.0274465\pi$
$701$	28.6582	+	28.6582i	1.08240	+	1.08240i	0.0861190	+	0.996285i	$0.472553\pi$
$702$		0			0
$703$			23.7109i			0.894275i
$704$		0			0
$705$	34.9914	+	30.5268i	1.31785	+	1.14970i
$706$		0			0
$707$	−10.1951	−	2.73177i	−0.383426	−	0.102739i
$708$		0			0
$709$	−8.00146	+	2.14398i	−0.300501	+	0.0805190i	−0.405919	−	0.913909i	$-0.633049\pi$
$709$	−8.00146	+	2.14398i	−0.300501	+	0.0805190i	0.105418	+	0.994428i	$0.466382\pi$
$710$		0			0
$711$	18.1189	+	7.39543i	0.679513	+	0.277350i
$712$		0			0
$713$	−9.51476	+	16.4800i	−0.356330	+	0.617182i
$714$		0			0
$715$	7.75484	+	2.07790i	0.290014	+	0.0777091i
$716$		0			0
$717$	14.7903	−	9.93803i	0.552353	−	0.371142i
$718$		0			0
$719$	−17.3387			−0.646625			−0.323312	−	0.946292i	$-0.604796\pi$
$719$	−17.3387			−0.646625			−0.323312	+	0.946292i	$0.604796\pi$
$720$		0			0
$721$	−11.5193			−0.429001
$722$		0			0
$723$	40.0431	+	19.6184i	1.48922	+	0.729615i
$724$		0			0
$725$	−61.8325	−	16.5680i	−2.29640	−	0.615318i
$726$		0			0
$727$	−25.1782	+	43.6100i	−0.933809	+	1.61741i	−0.157066	+	0.987588i	$0.550204\pi$
$727$	−25.1782	+	43.6100i	−0.933809	+	1.61741i	−0.776743	+	0.629817i	$0.783130\pi$
$728$		0			0
$729$	−24.7812	+	10.7187i	−0.917824	+	0.396989i
$730$		0			0
$731$	6.02084	−	1.61328i	0.222689	−	0.0596693i
$732$		0			0
$733$	0.461357	+	0.123620i	0.0170406	+	0.00456602i	0.267329	−	0.963605i	$-0.413859\pi$
$733$	0.461357	+	0.123620i	0.0170406	+	0.00456602i	−0.250289	+	0.968171i	$0.580526\pi$
$734$		0			0
$735$	−1.95589	+	0.669588i	−0.0721442	+	0.0246981i
$736$		0			0
$737$			6.07632i			0.223824i
$738$		0			0
$739$	−35.7895	−	35.7895i	−1.31654	−	1.31654i	−0.916499	−	0.400038i	$-0.868997\pi$
$739$	−35.7895	−	35.7895i	−1.31654	−	1.31654i	−0.400038	−	0.916499i	$-0.631003\pi$
$740$		0			0
$741$	5.23689	−	3.51883i	0.192382	−	0.129267i
$742$		0			0
$743$	−40.8564	+	23.5884i	−1.49888	+	0.865376i	−0.999999	−	0.00129681i	$-0.999587\pi$
$743$	−40.8564	+	23.5884i	−1.49888	+	0.865376i	−0.498877	+	0.866673i	$0.666254\pi$
$744$		0			0
$745$	−12.0568	−	6.96101i	−0.441728	−	0.255032i
$746$		0			0
$747$	9.28722	+	22.0970i	0.339801	+	0.808487i
$748$		0			0
$749$	−14.1710	+	3.79711i	−0.517798	+	0.138743i
$750$		0			0
$751$	−12.6419	+	7.29878i	−0.461308	+	0.266336i	−0.712594	−	0.701577i	$-0.752480\pi$
$751$	−12.6419	+	7.29878i	−0.461308	+	0.266336i	0.251286	+	0.967913i	$0.419147\pi$
$752$		0			0
$753$	−26.9994	+	30.9482i	−0.983914	+	1.12782i
$754$		0			0
$755$	7.11001	−	7.11001i	0.258760	−	0.258760i
$756$		0			0
$757$	22.1300	+	22.1300i	0.804329	+	0.804329i	0.983769	−	0.179440i	$-0.0574286\pi$
$757$	22.1300	+	22.1300i	0.804329	+	0.804329i	−0.179440	+	0.983769i	$0.557429\pi$
$758$		0			0
$759$	22.1235	+	19.3007i	0.803032	+	0.700570i
$760$		0			0
$761$	−13.0131	−	22.5393i	−0.471724	−	0.817050i	0.527753	−	0.849398i	$-0.323035\pi$
$761$	−13.0131	−	22.5393i	−0.471724	−	0.817050i	−0.999477	+	0.0323484i	$0.989701\pi$
$762$		0			0
$763$	6.47957	+	24.1821i	0.234576	+	0.875451i
$764$		0			0
$765$	−5.78288	+	45.7549i	−0.209080	+	1.65427i
$766$		0			0
$767$	−4.28113	+	7.41513i	−0.154583	+	0.267745i
$768$		0			0
$769$	−17.7312	−	30.7114i	−0.639404	−	1.10748i	−0.985564	−	0.169305i	$-0.945848\pi$
$769$	−17.7312	−	30.7114i	−0.639404	−	1.10748i	0.346159	−	0.938176i	$-0.387486\pi$
$770$		0			0
$771$	7.52724	+	11.2024i	0.271087	+	0.403445i
$772$		0			0
$773$	−3.23556	+	3.23556i	−0.116375	+	0.116375i	−0.762896	−	0.646521i	$-0.776223\pi$
$773$	−3.23556	+	3.23556i	−0.116375	+	0.116375i	0.646521	+	0.762896i	$0.276223\pi$
$774$		0			0
$775$	20.6672			0.742388
$776$		0			0
$777$	9.75108	+	28.4833i	0.349818	+	1.02183i
$778$		0			0
$779$	1.16100	−	4.33291i	0.0415972	−	0.155243i
$780$		0			0
$781$	−3.56951	−	13.3216i	−0.127727	−	0.476683i
$782$		0			0
$783$	−16.9757	−	33.7596i	−0.606661	−	1.20647i
$784$		0			0
$785$	−15.9691	−	9.21977i	−0.569962	−	0.329068i
$786$		0			0
$787$	6.55528	−	24.4646i	0.233671	−	0.872070i	−0.745073	−	0.666983i	$-0.767585\pi$
$787$	6.55528	−	24.4646i	0.233671	−	0.872070i	0.978744	−	0.205087i	$-0.0657479\pi$
$788$		0			0
$789$	−10.8683	+	22.1833i	−0.386922	+	0.789747i
$790$		0			0
$791$			23.7997i			0.846221i
$792$		0			0
$793$		−	7.24645i		−	0.257329i
$794$		0			0
$795$	2.77431	+	4.12886i	0.0983945	+	0.146436i
$796$		0			0
$797$	8.15674	−	30.4414i	0.288927	−	1.07829i	−0.656995	−	0.753895i	$-0.728173\pi$
$797$	8.15674	−	30.4414i	0.288927	−	1.07829i	0.945922	−	0.324394i	$-0.105160\pi$
$798$		0			0
$799$	25.8596	+	14.9300i	0.914847	+	0.528187i
$800$		0			0
$801$	42.1879	−	5.77654i	1.49064	−	0.204104i
$802$		0			0
$803$	−4.75628	−	17.7507i	−0.167845	−	0.626407i
$804$		0			0
$805$	20.1408	−	75.1664i	0.709869	−	2.64927i
$806$		0			0
$807$	−2.74175	+	3.14275i	−0.0965143	+	0.110630i
$808$		0			0
$809$	−46.7989			−1.64536			−0.822681	−	0.568503i	$-0.807523\pi$
$809$	−46.7989			−1.64536			−0.822681	+	0.568503i	$0.807523\pi$
$810$		0			0
$811$	−32.5365	+	32.5365i	−1.14251	+	1.14251i	−0.154522	+	0.987989i	$0.549384\pi$
$811$	−32.5365	+	32.5365i	−1.14251	+	1.14251i	−0.987989	+	0.154522i	$0.950616\pi$
$812$		0			0
$813$	−16.5139	+	1.12533i	−0.579168	+	0.0394669i
$814$		0			0
$815$	−22.0734	−	38.2322i	−0.773197	−	1.33922i
$816$		0			0
$817$	−2.65526	+	4.59904i	−0.0928956	+	0.160900i
$818$		0			0
$819$	4.84382	−	6.38073i	0.169257	−	0.222961i
$820$		0			0
$821$	2.76106	+	10.3044i	0.0963618	+	0.359627i	0.997222	−	0.0744814i	$-0.0237301\pi$
$821$	2.76106	+	10.3044i	0.0963618	+	0.359627i	−0.900861	+	0.434108i	$0.857063\pi$
$822$		0			0
$823$	9.53960	+	16.5231i	0.332530	+	0.575958i	0.983007	−	0.183567i	$-0.0587645\pi$
$823$	9.53960	+	16.5231i	0.332530	+	0.575958i	−0.650478	+	0.759526i	$0.725431\pi$
$824$		0			0
$825$	6.13964	−	31.2892i	0.213755	−	1.08935i
$826$		0			0
$827$	11.6788	+	11.6788i	0.406113	+	0.406113i	0.880381	−	0.474268i	$-0.157287\pi$
$827$	11.6788	+	11.6788i	0.406113	+	0.406113i	−0.474268	+	0.880381i	$0.657287\pi$
$828$		0			0
$829$	29.2209	−	29.2209i	1.01488	−	1.01488i	0.0149948	−	0.999888i	$-0.495227\pi$
$829$	29.2209	−	29.2209i	1.01488	−	1.01488i	0.999888	−	0.0149948i	$-0.00477317\pi$
$830$		0			0
$831$	1.23890	+	3.61887i	0.0429770	+	0.125537i
$832$		0			0
$833$	−1.15127	+	0.664689i	−0.0398893	+	0.0230301i
$834$		0			0
$835$	−29.4867	+	7.90094i	−1.02043	+	0.273423i
$836$		0			0
$837$	8.11495	+	9.10961i	0.280494	+	0.314874i
$838$		0			0
$839$	4.64393	+	2.68117i	0.160326	+	0.0925643i	0.578016	−	0.816025i	$-0.303827\pi$
$839$	4.64393	+	2.68117i	0.160326	+	0.0925643i	−0.417690	+	0.908589i	$0.637160\pi$
$840$		0			0
$841$	20.6847	−	11.9423i	0.713267	−	0.411805i
$842$		0			0
$843$	−25.7003	−	12.5913i	−0.885164	−	0.433669i
$844$		0			0
$845$	31.3465	+	31.3465i	1.07835	+	1.07835i
$846$		0			0
$847$			17.1242i			0.588394i
$848$		0			0
$849$	−2.51829	+	12.8339i	−0.0864276	+	0.440458i
$850$		0			0
$851$	52.6557	+	14.1090i	1.80501	+	0.483652i
$852$		0			0
$853$	−21.9880	+	5.89168i	−0.752856	+	0.201727i	−0.614785	−	0.788695i	$-0.710757\pi$
$853$	−21.9880	+	5.89168i	−0.752856	+	0.201727i	−0.138072	+	0.990422i	$0.544090\pi$
$854$		0			0
$855$	−24.0804	−	31.0480i	−0.823533	−	1.06182i
$856$		0			0
$857$	21.7367	−	37.6490i	0.742510	−	1.28607i	−0.208839	−	0.977950i	$-0.566968\pi$
$857$	21.7367	−	37.6490i	0.742510	−	1.28607i	0.951349	−	0.308115i	$-0.0996983\pi$
$858$		0			0
$859$	1.83181	+	0.490831i	0.0625005	+	0.0167469i	0.289934	−	0.957047i	$-0.406367\pi$
$859$	1.83181	+	0.490831i	0.0625005	+	0.0167469i	−0.227433	+	0.973794i	$0.573033\pi$
$860$		0			0
$861$	−0.387226	−	5.68246i	−0.0131966	−	0.193658i
$862$		0			0
$863$	5.75112			0.195770			0.0978852	−	0.995198i	$-0.468792\pi$
$863$	5.75112			0.195770			0.0978852	+	0.995198i	$0.468792\pi$
$864$		0			0
$865$	−95.6627			−3.25263
$866$		0			0
$867$	0.0143748	+	0.210948i	0.000488195	+	0.00716416i
$868$		0			0
$869$	−13.1779	−	3.53100i	−0.447029	−	0.119781i
$870$		0			0
$871$	1.50106	−	2.59992i	0.0508616	−	0.0880949i
$872$		0			0
$873$	−14.8411	+	36.3609i	−0.502294	+	1.23063i
$874$		0			0
$875$	−35.2649	+	9.44921i	−1.19217	+	0.319442i
$876$		0			0
$877$	39.6739	+	10.6306i	1.33969	+	0.358969i	0.856320	−	0.516446i	$-0.172745\pi$
$877$	39.6739	+	10.6306i	1.33969	+	0.358969i	0.483372	+	0.875415i	$0.339412\pi$
$878$		0			0
$879$	7.89396	−	40.2297i	0.266257	−	1.35691i
$880$		0			0
$881$			7.20282i			0.242669i	0.992612	+	0.121335i	$0.0387174\pi$
$881$			7.20282i			0.242669i	−0.992612	+	0.121335i	$0.961283\pi$
$882$		0			0
$883$	30.8474	+	30.8474i	1.03810	+	1.03810i	0.999245	+	0.0388519i	$0.0123701\pi$
$883$	30.8474	+	30.8474i	1.03810	+	1.03810i	0.0388519	+	0.999245i	$0.487630\pi$
$884$		0			0
$885$	47.8843	+	23.4600i	1.60961	+	0.788599i
$886$		0			0
$887$	−34.5994	+	19.9760i	−1.16173	+	0.670728i	−0.951719	−	0.306970i	$-0.900685\pi$
$887$	−34.5994	+	19.9760i	−1.16173	+	0.670728i	−0.210016	+	0.977698i	$0.567351\pi$
$888$		0			0
$889$	−10.6487	−	6.14801i	−0.357145	−	0.206198i
$890$		0			0
$891$	16.2023	−	9.57946i	0.542796	−	0.320924i
$892$		0			0
$893$	−24.5730	+	6.58431i	−0.822304	+	0.220336i
$894$		0			0
$895$	66.3904	−	38.3305i	2.21919	−	1.28125i
$896$		0			0
$897$	−4.69819	−	13.7236i	−0.156868	−	0.458218i
$898$		0			0
$899$	−12.0732	+	12.0732i	−0.402665	+	0.402665i
$900$		0			0
$901$	2.26183	+	2.26183i	0.0753526	+	0.0753526i
$902$		0			0
$903$	−1.29834	+	6.61666i	−0.0432059	+	0.220189i
$904$		0			0
$905$	−21.5259	−	37.2840i	−0.715546	−	1.23936i
$906$		0			0
$907$	−11.6752	−	43.5725i	−0.387670	−	1.44680i	−0.833916	−	0.551892i	$-0.813906\pi$
$907$	−11.6752	−	43.5725i	−0.387670	−	1.44680i	0.446246	−	0.894910i	$-0.352761\pi$
$908$		0			0
$909$	4.74735	+	11.2953i	0.157460	+	0.374642i
$910$		0			0
$911$	−0.452588	+	0.783905i	−0.0149949	+	0.0259719i	−0.873425	−	0.486958i	$-0.838107\pi$
$911$	−0.452588	+	0.783905i	−0.0149949	+	0.0259719i	0.858431	+	0.512930i	$0.171440\pi$
$912$		0			0
$913$	−8.35479	−	14.4709i	−0.276503	−	0.478917i
$914$		0			0
$915$	−45.0236	+	3.06809i	−1.48843	+	0.101428i
$916$		0			0
$917$	−15.8244	+	15.8244i	−0.522566	+	0.522566i
$918$		0			0
$919$	0.631829			0.0208421			0.0104211	−	0.999946i	$-0.496683\pi$
$919$	0.631829			0.0208421			0.0104211	+	0.999946i	$0.496683\pi$
$920$		0			0
$921$	−20.8577	+	23.9082i	−0.687285	+	0.787803i
$922$		0			0
$923$	−1.76359	+	6.58179i	−0.0580492	+	0.216642i
$924$		0			0
$925$	−15.3233	−	57.1873i	−0.503826	−	1.88031i
$926$		0			0
$927$	8.19525	+	10.5665i	0.269167	+	0.347050i
$928$		0			0
$929$	−21.7169	−	12.5383i	−0.712509	−	0.411367i	0.0994805	−	0.995040i	$-0.468282\pi$
$929$	−21.7169	−	12.5383i	−0.712509	−	0.411367i	−0.811989	+	0.583672i	$0.801615\pi$
$930$		0			0
$931$	0.293135	−	1.09399i	0.00960711	−	0.0358542i
$932$		0			0
$933$	−4.17512	−	6.21362i	−0.136687	−	0.203425i
$934$		0			0
$935$		−	32.1505i		−	1.05143i
$936$		0			0
$937$		−	40.0398i		−	1.30804i	−0.756476	−	0.654021i	$-0.773081\pi$
$937$		−	40.0398i		−	1.30804i	0.756476	−	0.654021i	$-0.226919\pi$
$938$		0			0
$939$	12.1307	−	24.7600i	0.395870	−	0.808011i
$940$		0			0
$941$	−2.78273	+	10.3853i	−0.0907146	+	0.338551i	−0.996335	−	0.0855380i	$-0.972739\pi$
$941$	−2.78273	+	10.3853i	−0.0907146	+	0.338551i	0.905620	+	0.424089i	$0.139406\pi$
$942$		0			0
$943$	−8.93140	−	5.15654i	−0.290846	−	0.167920i
$944$		0			0
$945$	−41.6955	−	27.3940i	−1.35636	−	0.891128i
$946$		0			0
$947$	10.0828	+	37.6297i	0.327648	+	1.22280i	0.911623	+	0.411028i	$0.134830\pi$
$947$	10.0828	+	37.6297i	0.327648	+	1.22280i	−0.583975	+	0.811772i	$0.698503\pi$
$948$		0			0
$949$	−2.34993	+	8.77007i	−0.0762821	+	0.284689i
$950$		0			0
$951$	16.6745	+	48.7069i	0.540708	+	1.57943i
$952$		0			0
$953$	7.83389			0.253765			0.126882	−	0.991918i	$-0.459503\pi$
$953$	7.83389			0.253765			0.126882	+	0.991918i	$0.459503\pi$
$954$		0			0
$955$	−14.7419	+	14.7419i	−0.477037	+	0.477037i
$956$		0			0
$957$	14.6917	+	21.8650i	0.474916	+	0.706794i
$958$		0			0
$959$	−21.4388	−	37.1331i	−0.692295	−	1.19909i
$960$		0			0
$961$	−12.7438	+	22.0728i	−0.411089	+	0.712027i
$962$		0			0
$963$	13.5648	+	10.2975i	0.437121	+	0.331833i
$964$		0			0
$965$	24.1789	+	90.2370i	0.778347	+	2.90483i
$966$		0			0
$967$	−22.1358	−	38.3403i	−0.711839	−	1.23294i	−0.964166	−	0.265299i	$-0.914529\pi$
$967$	−22.1358	−	38.3403i	−0.711839	−	1.23294i	0.252328	−	0.967642i	$-0.418804\pi$
$968$		0			0
$969$	−19.0392	−	16.6099i	−0.611627	−	0.533588i
$970$		0			0
$971$	28.0737	+	28.0737i	0.900928	+	0.900928i	0.995516	−	0.0945888i	$-0.0301536\pi$
$971$	28.0737	+	28.0737i	0.900928	+	0.900928i	−0.0945888	+	0.995516i	$0.530154\pi$
$972$		0			0
$973$	13.0048	−	13.0048i	0.416914	−	0.416914i
$974$		0			0
$975$	−10.3566	+	11.8712i	−0.331675	+	0.380184i
$976$		0			0
$977$	−14.8614	+	8.58022i	−0.475458	+	0.274506i	−0.718522	−	0.695505i	$-0.755181\pi$
$977$	−14.8614	+	8.58022i	−0.475458	+	0.274506i	0.243064	+	0.970010i	$0.421848\pi$
$978$		0			0
$979$	−28.6731	+	7.68293i	−0.916396	+	0.245547i
$980$		0			0
$981$	17.5722	−	23.1477i	0.561036	−	0.739048i
$982$		0			0
$983$	26.8455	+	15.4993i	0.856240	+	0.494350i	0.862751	−	0.505629i	$-0.168739\pi$
$983$	26.8455	+	15.4993i	0.856240	+	0.494350i	−0.00651160	+	0.999979i	$0.502073\pi$
$984$		0			0
$985$	−19.6423	+	11.3405i	−0.625854	+	0.361337i
$986$		0			0
$987$	−26.8110	+	18.0151i	−0.853405	+	0.573428i
$988$		0			0
$989$	8.63324	+	8.63324i	0.274521	+	0.274521i
$990$		0			0
$991$			37.2374i			1.18289i	0.806347	+	0.591443i	$0.201442\pi$
$991$			37.2374i			1.18289i	−0.806347	+	0.591443i	$0.798558\pi$
$992$		0			0
$993$	−3.22523	+	1.10414i	−0.102349	+	0.0350387i
$994$		0			0
$995$	−52.6247	−	14.1008i	−1.66832	−	0.447024i
$996$		0			0
$997$	13.9293	−	3.73234i	0.441145	−	0.118204i	−0.0314082	−	0.999507i	$-0.509999\pi$
$997$	13.9293	−	3.73234i	0.441145	−	0.118204i	0.472553	+	0.881302i	$0.343333\pi$
$998$		0			0
$999$	19.1901	−	29.2086i	0.607148	−	0.924120i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.y.a.335.10		88
3.2	odd	2		1728.2.z.a.143.21		88
4.3	odd	2		144.2.u.a.11.9	✓	88
9.4	even	3		1728.2.z.a.719.21		88
9.5	odd	6	inner	576.2.y.a.527.1		88
12.11	even	2		432.2.v.a.251.14		88
16.3	odd	4	inner	576.2.y.a.47.1		88
16.13	even	4		144.2.u.a.83.2	yes	88
36.23	even	6		144.2.u.a.59.2	yes	88
36.31	odd	6		432.2.v.a.395.21		88
48.29	odd	4		432.2.v.a.35.21		88
48.35	even	4		1728.2.z.a.1007.21		88
144.13	even	12		432.2.v.a.179.14		88
144.67	odd	12		1728.2.z.a.1583.21		88
144.77	odd	12		144.2.u.a.131.9	yes	88
144.131	even	12	inner	576.2.y.a.239.10		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.9	✓	88	4.3	odd	2
144.2.u.a.59.2	yes	88	36.23	even	6
144.2.u.a.83.2	yes	88	16.13	even	4
144.2.u.a.131.9	yes	88	144.77	odd	12
432.2.v.a.35.21		88	48.29	odd	4
432.2.v.a.179.14		88	144.13	even	12
432.2.v.a.251.14		88	12.11	even	2
432.2.v.a.395.21		88	36.31	odd	6
576.2.y.a.47.1		88	16.3	odd	4	inner
576.2.y.a.239.10		88	144.131	even	12	inner
576.2.y.a.335.10		88	1.1	even	1	trivial
576.2.y.a.527.1		88	9.5	odd	6	inner
1728.2.z.a.143.21		88	3.2	odd	2
1728.2.z.a.719.21		88	9.4	even	3
1728.2.z.a.1007.21		88	48.35	even	4
1728.2.z.a.1583.21		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)

\(f(q)\)	\(=\)	\(q+(-0.117756 - 1.72804i) q^{3} +(-3.58858 - 0.961558i) q^{5} +(1.29216 - 2.23809i) q^{7} +(-2.97227 + 0.406975i) q^{9} +O(q^{10})\)	\(q+(-0.117756 - 1.72804i) q^{3} +(-3.58858 - 0.961558i) q^{5} +(1.29216 - 2.23809i) q^{7} +(-2.97227 + 0.406975i) q^{9} +(2.02011 - 0.541286i) q^{11} +(-0.998074 - 0.267433i) q^{13} +(-1.23904 + 6.31446i) q^{15} +4.13788i q^{17} +(-2.49279 - 2.49279i) q^{19} +(-4.01968 - 1.96936i) q^{21} +(-7.01915 + 4.05251i) q^{23} +(7.62322 + 4.40127i) q^{25} +(1.05327 + 5.08828i) q^{27} +(-7.02439 + 1.88218i) q^{29} +(2.03331 - 1.17393i) q^{31} +(-1.17324 - 3.42709i) q^{33} +(-6.78909 + 6.78909i) q^{35} +(-4.75590 - 4.75590i) q^{37} +(-0.344607 + 1.75621i) q^{39} +(0.636217 + 1.10196i) q^{41} +(-0.389880 - 1.45505i) q^{43} +(11.0576 + 1.39754i) q^{45} +(3.60814 - 6.24948i) q^{47} +(0.160635 + 0.278228i) q^{49} +(7.15044 - 0.487260i) q^{51} +(0.546616 - 0.546616i) q^{53} -7.76980 q^{55} +(-4.01411 + 4.60119i) q^{57} +(2.14469 - 8.00411i) q^{59} +(1.81511 + 6.77407i) q^{61} +(-2.92980 + 7.17808i) q^{63} +(3.32452 + 1.91941i) q^{65} +(-0.751980 + 2.80643i) q^{67} +(7.82945 + 11.6522i) q^{69} -6.59449i q^{71} -8.78699i q^{73} +(6.70790 - 13.6915i) q^{75} +(1.39886 - 5.22061i) q^{77} +(-5.64940 - 3.26168i) q^{79} +(8.66874 - 2.41928i) q^{81} +(-2.06791 - 7.71754i) q^{83} +(3.97882 - 14.8491i) q^{85} +(4.07965 + 11.9168i) q^{87} -14.1938 q^{89} +(-1.88821 + 1.88821i) q^{91} +(-2.26805 - 3.37542i) q^{93} +(6.54863 + 11.3426i) q^{95} +(6.54551 - 11.3372i) q^{97} +(-5.78401 + 2.43098i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7}+O(q^{10}) \) 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

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