LMFDB - Embedded newform 576.2.y.a.47.1

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			47.1
Character	$\chi$	$=$	576.47
Dual form			576.2.y.a.527.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.72804 + 0.117756i) q^{3} +(-0.961558 + 3.58858i) q^{5} +(1.29216 - 2.23809i) q^{7} +(2.97227 - 0.406975i) q^{9} +O(q^{10})$	\(q+(-1.72804 + 0.117756i) q^{3} +(-0.961558 + 3.58858i) q^{5} +(1.29216 - 2.23809i) q^{7} +(2.97227 - 0.406975i) q^{9} +(0.541286 + 2.02011i) q^{11} +(0.267433 - 0.998074i) q^{13} +(1.23904 - 6.31446i) q^{15} +4.13788i q^{17} +(-2.49279 + 2.49279i) q^{19} +(-1.96936 + 4.01968i) q^{21} +(-7.01915 + 4.05251i) q^{23} +(-7.62322 - 4.40127i) q^{25} +(-5.08828 + 1.05327i) q^{27} +(-1.88218 - 7.02439i) q^{29} +(-2.03331 + 1.17393i) q^{31} +(-1.17324 - 3.42709i) q^{33} +(6.78909 + 6.78909i) q^{35} +(-4.75590 + 4.75590i) q^{37} +(-0.344607 + 1.75621i) q^{39} +(-0.636217 - 1.10196i) q^{41} +(1.45505 - 0.389880i) q^{43} +(-1.39754 + 11.0576i) q^{45} +(-3.60814 + 6.24948i) q^{47} +(0.160635 + 0.278228i) q^{49} +(-0.487260 - 7.15044i) q^{51} +(-0.546616 - 0.546616i) q^{53} -7.76980 q^{55} +(4.01411 - 4.60119i) q^{57} +(8.00411 + 2.14469i) q^{59} +(-6.77407 + 1.81511i) q^{61} +(2.92980 - 7.17808i) q^{63} +(3.32452 + 1.91941i) q^{65} +(2.80643 + 0.751980i) q^{67} +(11.6522 - 7.82945i) q^{69} -6.59449i q^{71} +8.78699i q^{73} +(13.6915 + 6.70790i) q^{75} +(5.22061 + 1.39886i) q^{77} +(5.64940 + 3.26168i) q^{79} +(8.66874 - 2.41928i) q^{81} +(-7.71754 + 2.06791i) q^{83} +(-14.8491 - 3.97882i) q^{85} +(4.07965 + 11.9168i) q^{87} +14.1938 q^{89} +(-1.88821 - 1.88821i) q^{91} +(3.37542 - 2.26805i) q^{93} +(-6.54863 - 11.3426i) q^{95} +(6.54551 - 11.3372i) q^{97} +(2.43098 + 5.78401i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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
$3$	−1.72804	+	0.117756i	−0.997686	+	0.0679864i
$3$	−1.72804	+	0.117756i	−0.997686	+	0.0679864i
$4$		0			0
$5$	−0.961558	+	3.58858i	−0.430022	+	1.60486i	0.322684	+	0.946507i	$0.395415\pi$
$5$	−0.961558	+	3.58858i	−0.430022	+	1.60486i	−0.752706	+	0.658357i	$0.771252\pi$
$6$		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
$11$	0.541286	+	2.02011i	0.163204	+	0.609085i	0.998262	+	0.0589240i	$0.0187670\pi$
$11$	0.541286	+	2.02011i	0.163204	+	0.609085i	−0.835059	+	0.550161i	$0.814566\pi$
$12$		0			0
$13$	0.267433	−	0.998074i	0.0741726	−	0.276816i	−0.918872	−	0.394556i	$-0.870898\pi$
$13$	0.267433	−	0.998074i	0.0741726	−	0.276816i	0.993044	+	0.117740i	$0.0375650\pi$
$14$		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	−0.932655	−	0.360769i	$-0.882514\pi$
$19$	−2.49279	+	2.49279i	−0.571886	+	0.571886i	0.360769	+	0.932655i	$0.382514\pi$
$20$		0			0
$21$	−1.96936	+	4.01968i	−0.429750	+	0.877165i
$22$		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
$27$	−5.08828	+	1.05327i	−0.979240	+	0.202702i
$28$		0			0
$29$	−1.88218	−	7.02439i	−0.349512	−	1.30440i	−0.887252	−	0.461286i	$-0.847388\pi$
$29$	−1.88218	−	7.02439i	−0.349512	−	1.30440i	0.537740	−	0.843111i	$-0.319278\pi$
$30$		0			0
$31$	−2.03331	+	1.17393i	−0.365194	+	0.210845i	−0.671357	−	0.741134i	$-0.734288\pi$
$31$	−2.03331	+	1.17393i	−0.365194	+	0.210845i	0.306163	+	0.951979i	$0.400955\pi$
$32$		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	−0.980145	−	0.198280i	$-0.936464\pi$
$37$	−4.75590	+	4.75590i	−0.781865	+	0.781865i	0.198280	+	0.980145i	$0.436464\pi$
$38$		0			0
$39$	−0.344607	+	1.75621i	−0.0551813	+	0.281218i
$40$		0			0
$41$	−0.636217	−	1.10196i	−0.0993604	−	0.172097i	0.812060	−	0.583574i	$-0.198346\pi$
$41$	−0.636217	−	1.10196i	−0.0993604	−	0.172097i	−0.911420	+	0.411477i	$0.865013\pi$
$42$		0			0
$43$	1.45505	−	0.389880i	0.221894	−	0.0594562i	−0.146159	−	0.989261i	$-0.546691\pi$
$43$	1.45505	−	0.389880i	0.221894	−	0.0594562i	0.368053	+	0.929805i	$0.380025\pi$
$44$		0			0
$45$	−1.39754	+	11.0576i	−0.208334	+	1.64836i
$46$		0			0
$47$	−3.60814	+	6.24948i	−0.526301	+	0.911580i	0.473230	+	0.880939i	$0.343088\pi$
$47$	−3.60814	+	6.24948i	−0.526301	+	0.911580i	−0.999530	+	0.0306407i	$0.990245\pi$
$48$		0			0
$49$	0.160635	+	0.278228i	0.0229479	+	0.0397469i
$50$		0			0
$51$	−0.487260	−	7.15044i	−0.0682301	−	1.00126i
$52$		0			0
$53$	−0.546616	−	0.546616i	−0.0750835	−	0.0750835i	0.668568	−	0.743651i	$-0.266908\pi$
$53$	−0.546616	−	0.546616i	−0.0750835	−	0.0750835i	−0.743651	+	0.668568i	$0.766908\pi$
$54$		0			0
$55$	−7.76980			−1.04768
$56$		0			0
$57$	4.01411	−	4.60119i	0.531682	−	0.609443i
$58$		0			0
$59$	8.00411	+	2.14469i	1.04205	+	0.279215i	0.738961	−	0.673748i	$-0.235317\pi$
$59$	8.00411	+	2.14469i	1.04205	+	0.279215i	0.303085	+	0.952963i	$0.401983\pi$
$60$		0			0
$61$	−6.77407	+	1.81511i	−0.867331	+	0.232401i	−0.664933	−	0.746903i	$-0.731540\pi$
$61$	−6.77407	+	1.81511i	−0.867331	+	0.232401i	−0.202398	+	0.979303i	$0.564873\pi$
$62$		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
$67$	2.80643	+	0.751980i	0.342860	+	0.0918690i	0.426140	−	0.904657i	$-0.359873\pi$
$67$	2.80643	+	0.751980i	0.342860	+	0.0918690i	−0.0832804	+	0.996526i	$0.526540\pi$
$68$		0			0
$69$	11.6522	−	7.82945i	1.40276	−	0.942555i
$70$		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	$0.171918\pi$
$73$			8.78699i			1.02844i	−0.857658	+	0.514220i	$0.828082\pi$
$74$		0			0
$75$	13.6915	+	6.70790i	1.58096	+	0.774562i
$76$		0			0
$77$	5.22061	+	1.39886i	0.594944	+	0.159415i
$78$		0			0
$79$	5.64940	+	3.26168i	0.635607	+	0.366968i	0.782920	−	0.622122i	$-0.213729\pi$
$79$	5.64940	+	3.26168i	0.635607	+	0.366968i	−0.147313	+	0.989090i	$0.547063\pi$
$80$		0			0
$81$	8.66874	−	2.41928i	0.963194	−	0.268808i
$82$		0			0
$83$	−7.71754	+	2.06791i	−0.847110	+	0.226982i	−0.656164	−	0.754618i	$-0.727822\pi$
$83$	−7.71754	+	2.06791i	−0.847110	+	0.226982i	−0.190946	+	0.981601i	$0.561155\pi$
$84$		0			0
$85$	−14.8491	−	3.97882i	−1.61062	−	0.431563i
$86$		0			0
$87$	4.07965	+	11.9168i	0.437385	+	1.27762i
$88$		0			0
$89$	14.1938			1.50454			0.752272	−	0.658852i	$-0.228958\pi$
$89$	14.1938			1.50454			0.752272	+	0.658852i	$0.228958\pi$
$90$		0			0
$91$	−1.88821	−	1.88821i	−0.197939	−	0.197939i
$92$		0			0
$93$	3.37542	−	2.26805i	0.350015	−	0.235185i
$94$		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
$99$	2.43098	+	5.78401i	0.244322	+	0.581314i
$100$		0			0
$101$	−3.94498	+	1.05705i	−0.392540	+	0.105181i	−0.449690	−	0.893185i	$-0.648465\pi$
$101$	−3.94498	+	1.05705i	−0.392540	+	0.105181i	0.0571499	+	0.998366i	$0.481799\pi$
$102$		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	$-0.661520\pi$
$107$	4.01417	−	4.01417i	0.388064	−	0.388064i	0.873996	+	0.485932i	$0.161520\pi$
$108$		0			0
$109$	−6.84996	−	6.84996i	−0.656107	−	0.656107i	0.298349	−	0.954457i	$-0.403564\pi$
$109$	−6.84996	−	6.84996i	−0.656107	−	0.656107i	−0.954457	+	0.298349i	$0.903564\pi$
$110$		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
$115$	−7.79344	−	29.0855i	−0.726742	−	2.71224i
$116$		0			0
$117$	0.388692	−	3.07538i	0.0359346	−	0.284319i
$118$		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
$123$	1.22917	+	1.82932i	0.110831	+	0.164944i
$124$		0			0
$125$	9.98936	−	9.98936i	0.893475	−	0.893475i
$126$		0			0
$127$			4.75792i			0.422197i	0.977465	+	0.211099i	$0.0677041\pi$
$127$			4.75792i			0.422197i	−0.977465	+	0.211099i	$0.932296\pi$
$128$		0			0
$129$	−2.46849	+	0.845072i	−0.217338	+	0.0744044i
$130$		0			0
$131$	−2.24125	+	8.36446i	−0.195819	+	0.730806i	0.796234	+	0.604988i	$0.206822\pi$
$131$	−2.24125	+	8.36446i	−0.195819	+	0.730806i	−0.992053	+	0.125818i	$0.959844\pi$
$132$		0			0
$133$	2.35800	+	8.80019i	0.204465	+	0.763073i
$134$		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	$0.417407\pi$
$137$	−8.29570	+	14.3686i	−0.708750	+	1.22759i	−0.965321	+	0.261065i	$0.915926\pi$
$138$		0			0
$139$	−1.84191	+	6.87408i	−0.156228	+	0.583052i	0.842769	+	0.538276i	$0.180924\pi$
$139$	−1.84191	+	6.87408i	−0.156228	+	0.583052i	−0.998997	+	0.0447763i	$0.985743\pi$
$140$		0			0
$141$	5.49910	−	11.2242i	0.463108	−	0.945252i
$142$		0			0
$143$	2.16097			0.180710
$144$		0			0
$145$	27.0175			2.24368
$146$		0			0
$147$	−0.310347	−	0.461874i	−0.0255970	−	0.0380948i
$148$		0			0
$149$	0.969882	−	3.61965i	0.0794558	−	0.296533i	−0.914751	−	0.404018i	$-0.867613\pi$
$149$	0.969882	−	3.61965i	0.0794558	−	0.296533i	0.994207	+	0.107485i	$0.0342798\pi$
$150$		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
$155$	−2.25761	−	8.42553i	−0.181336	−	0.676755i
$156$		0			0
$157$	−1.28460	+	4.79418i	−0.102522	+	0.382617i	−0.998052	−	0.0623832i	$-0.980130\pi$
$157$	−1.28460	+	4.79418i	−0.102522	+	0.382617i	0.895530	+	0.445001i	$0.146797\pi$
$158$		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	−0.296808	−	0.954937i	$-0.595922\pi$
$163$	8.40242	−	8.40242i	0.658129	−	0.658129i	0.954937	+	0.296808i	$0.0959223\pi$
$164$		0			0
$165$	13.4266	−	0.914940i	1.04526	−	0.0712280i
$166$		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
$171$	−6.39474	+	8.42375i	−0.489018	+	0.644180i
$172$		0			0
$173$	6.66438	+	24.8718i	0.506683	+	1.89097i	0.451012	+	0.892518i	$0.351063\pi$
$173$	6.66438	+	24.8718i	0.506683	+	1.89097i	0.0556715	+	0.998449i	$0.482270\pi$
$174$		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	0.995467	+	0.0951034i	$0.0303182\pi$
$179$	14.5908	+	14.5908i	1.09057	+	1.09057i	0.0951034	+	0.995467i	$0.469682\pi$
$180$		0			0
$181$	8.19403	−	8.19403i	0.609057	−	0.609057i	−0.333642	−	0.942700i	$-0.608278\pi$
$181$	8.19403	−	8.19403i	0.609057	−	0.609057i	0.942700	+	0.333642i	$0.108278\pi$
$182$		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
$187$	−8.35896	+	2.23978i	−0.611268	+	0.163789i
$188$		0			0
$189$	−4.21757	+	12.7490i	−0.306783	+	0.927356i
$190$		0			0
$191$	−2.80582	+	4.85981i	−0.203022	+	0.351644i	−0.949501	−	0.313765i	$-0.898410\pi$
$191$	−2.80582	+	4.85981i	−0.203022	+	0.351644i	0.746479	+	0.665409i	$0.231743\pi$
$192$		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
$195$	−5.97094	−	2.92535i	−0.427588	−	0.209488i
$196$		0			0
$197$	−4.31684	−	4.31684i	−0.307562	−	0.307562i	0.536401	−	0.843963i	$-0.319784\pi$
$197$	−4.31684	−	4.31684i	−0.307562	−	0.307562i	−0.843963	+	0.536401i	$0.819784\pi$
$198$		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
$203$	−18.1533	−	4.86416i	−1.27411	−	0.341397i
$204$		0			0
$205$	4.56624	−	1.22352i	0.318920	−	0.0854543i
$206$		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
$211$	2.25661	+	0.604656i	0.155351	+	0.0416263i	0.335656	−	0.941984i	$-0.391042\pi$
$211$	2.25661	+	0.604656i	0.155351	+	0.0416263i	−0.180305	+	0.983611i	$0.557709\pi$
$212$		0			0
$213$	0.776541	+	11.3956i	0.0532077	+	0.780812i
$214$		0			0
$215$			5.59648i			0.381677i
$216$		0			0
$217$			6.06766i			0.411899i
$218$		0			0
$219$	−1.03472	−	15.1843i	−0.0699200	−	1.02606i
$220$		0			0
$221$	4.12991	+	1.10661i	0.277808	+	0.0744385i
$222$		0			0
$223$	24.9105	+	14.3821i	1.66813	+	0.963094i	0.968646	+	0.248445i	$0.0799195\pi$
$223$	24.9105	+	14.3821i	1.66813	+	0.963094i	0.699483	+	0.714650i	$0.253414\pi$
$224$		0			0
$225$	−24.4494	−	9.97928i	−1.62996	−	0.665286i
$226$		0			0
$227$	8.06995	−	2.16234i	0.535621	−	0.143519i	0.0191384	−	0.999817i	$-0.493908\pi$
$227$	8.06995	−	2.16234i	0.535621	−	0.143519i	0.516483	+	0.856298i	$0.327241\pi$
$228$		0			0
$229$	18.5393	+	4.96759i	1.22511	+	0.328268i	0.812674	−	0.582718i	$-0.198011\pi$
$229$	18.5393	+	4.96759i	1.22511	+	0.328268i	0.412438	+	0.910986i	$0.364677\pi$
$230$		0			0
$231$	−9.18616	−	1.80253i	−0.604405	−	0.118598i
$232$		0			0
$233$	−2.96265			−0.194090			−0.0970450	−	0.995280i	$-0.530939\pi$
$233$	−2.96265			−0.194090			−0.0970450	+	0.995280i	$0.530939\pi$
$234$		0			0
$235$	−18.9573	−	18.9573i	−1.23664	−	1.23664i
$236$		0			0
$237$	−10.1465	−	4.97108i	−0.659085	−	0.322906i
$238$		0			0
$239$	−5.14390	−	8.90950i	−0.332731	−	0.576307i	0.650315	−	0.759665i	$-0.274637\pi$
$239$	−5.14390	−	8.90950i	−0.332731	−	0.576307i	−0.983046	+	0.183357i	$0.941304\pi$
$240$		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
$243$	−14.6951	+	5.20141i	−0.942690	+	0.333671i
$244$		0			0
$245$	−1.15290	+	0.308920i	−0.0736564	+	0.0197362i
$246$		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	0.0601228	−	0.998191i	$-0.480851\pi$
$251$	16.7668	−	16.7668i	1.05831	−	1.05831i	0.998191	−	0.0601228i	$-0.0191492\pi$
$252$		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
$259$	4.49874	+	16.7895i	0.279538	+	1.04325i
$260$		0			0
$261$	−8.45309	−	20.1124i	−0.523233	−	1.24492i
$262$		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
$267$	−24.5276	+	1.67141i	−1.50106	+	0.102289i
$268$		0			0
$269$	1.70265	−	1.70265i	0.103812	−	0.103812i	−0.653293	−	0.757105i	$-0.726613\pi$
$269$	1.70265	−	1.70265i	0.103812	−	0.103812i	0.757105	+	0.653293i	$0.226613\pi$
$270$		0			0
$271$			9.55642i			0.580511i	0.956949	+	0.290256i	$0.0937403\pi$
$271$			9.55642i			0.580511i	−0.956949	+	0.290256i	$0.906260\pi$
$272$		0			0
$273$	3.48526	+	3.04057i	0.210938	+	0.184023i
$274$		0			0
$275$	4.76469	−	17.7821i	0.287321	−	1.07230i
$276$		0			0
$277$	0.571577	+	2.13315i	0.0343427	+	0.128169i	0.980969	−	0.194164i	$-0.0621995\pi$
$277$	0.571577	+	2.13315i	0.0343427	+	0.128169i	−0.946626	+	0.322333i	$0.895533\pi$
$278$		0			0
$279$	−5.56579	+	4.31676i	−0.333215	+	0.258437i
$280$		0			0
$281$	−8.26158	+	14.3095i	−0.492845	+	0.853632i	−0.999966	−	0.00824250i	$-0.997376\pi$
$281$	−8.26158	+	14.3095i	−0.492845	+	0.853632i	0.507121	+	0.861875i	$0.330710\pi$
$282$		0			0
$283$	1.95433	−	7.29366i	0.116173	−	0.433563i	−0.883199	−	0.468998i	$-0.844615\pi$
$283$	1.95433	−	7.29366i	0.116173	−	0.433563i	0.999372	+	0.0354353i	$0.0112818\pi$
$284$		0			0
$285$	12.6520	+	18.8293i	0.749438	+	1.11535i
$286$		0			0
$287$	−3.28838			−0.194107
$288$		0			0
$289$	−0.122073			−0.00718078
$290$		0			0
$291$	−9.97590	+	20.3619i	−0.584798	+	1.19363i
$292$		0			0
$293$	6.12613	−	22.8630i	0.357892	−	1.33567i	−0.518913	−	0.854827i	$-0.673663\pi$
$293$	6.12613	−	22.8630i	0.357892	−	1.33567i	0.876805	−	0.480845i	$-0.159670\pi$
$294$		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
$299$	2.16755	+	8.08940i	0.125353	+	0.467822i
$300$		0			0
$301$	1.00758	−	3.76033i	0.0580758	−	0.216742i
$302$		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	−0.972434	−	0.233179i	$-0.925087\pi$
$307$	−12.9528	+	12.9528i	−0.739255	+	0.739255i	0.233179	+	0.972434i	$0.425087\pi$
$308$		0			0
$309$	4.30582	+	6.40814i	0.244950	+	0.364546i
$310$		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	0.0569286	−	0.998378i	$-0.481869\pi$
$313$	−13.7859	−	7.95932i	−0.779228	−	0.449887i	−0.836157	+	0.548491i	$0.815203\pi$
$314$		0			0
$315$	22.9420	+	17.4160i	1.29263	+	0.981280i
$316$		0			0
$317$	−7.69292	−	28.7104i	−0.432077	−	1.61253i	−0.747965	−	0.663738i	$-0.768969\pi$
$317$	−7.69292	−	28.7104i	−0.432077	−	1.61253i	0.315888	−	0.948797i	$-0.397698\pi$
$318$		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
$331$	1.90112	−	0.509403i	0.104495	−	0.0279993i	−0.206193	−	0.978511i	$-0.566107\pi$
$331$	1.90112	−	0.509403i	0.104495	−	0.0279993i	0.310688	+	0.950512i	$0.399441\pi$
$332$		0			0
$333$	−12.2003	+	16.0713i	−0.668571	+	0.880704i
$334$		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
$339$	13.2397	−	8.89617i	0.719083	−	0.483173i
$340$		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
$347$	3.06413	+	0.821032i	0.164491	+	0.0440753i	0.340125	−	0.940380i	$-0.389531\pi$
$347$	3.06413	+	0.821032i	0.164491	+	0.0440753i	−0.175634	+	0.984456i	$0.556197\pi$
$348$		0			0
$349$	15.9915	−	4.28490i	0.856003	−	0.229365i	0.195978	−	0.980608i	$-0.437212\pi$
$349$	15.9915	−	4.28490i	0.856003	−	0.229365i	0.660026	+	0.751243i	$0.270545\pi$
$350$		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
$355$	23.6649	+	6.34099i	1.25600	+	0.336545i
$356$		0			0
$357$	−16.6329	−	8.14899i	−0.880309	−	0.431291i
$358$		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
$363$	−9.52614	+	6.40090i	−0.499993	+	0.335960i
$364$		0			0
$365$	−31.5329	−	8.44921i	−1.65051	−	0.442252i
$366$		0			0
$367$	−20.6334	−	11.9127i	−1.07706	−	0.621839i	−0.146955	−	0.989143i	$-0.546947\pi$
$367$	−20.6334	−	11.9127i	−1.07706	−	0.621839i	−0.930101	+	0.367304i	$0.880281\pi$
$368$		0			0
$369$	−2.33948	−	3.01639i	−0.121788	−	0.157027i
$370$		0			0
$371$	−1.92969	+	0.517059i	−0.100185	+	0.0268444i
$372$		0			0
$373$	8.84822	+	2.37087i	0.458143	+	0.122759i	0.480507	−	0.876991i	$-0.340453\pi$
$373$	8.84822	+	2.37087i	0.458143	+	0.122759i	−0.0223639	+	0.999750i	$0.507119\pi$
$374$		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	0.690583	−	0.723253i	$-0.257354\pi$
$379$	−0.636018	−	0.636018i	−0.0326701	−	0.0326701i	−0.723253	+	0.690583i	$0.757354\pi$
$380$		0			0
$381$	−0.560274	−	8.22190i	−0.0287037	−	0.421220i
$382$		0			0
$383$	6.80598	+	11.7883i	0.347769	+	0.602354i	0.985853	−	0.167613i	$-0.0536060\pi$
$383$	6.80598	+	11.7883i	0.347769	+	0.602354i	−0.638084	+	0.769967i	$0.720273\pi$
$384$		0			0
$385$	−10.0398	+	17.3895i	−0.511678	+	0.886252i
$386$		0			0
$387$	4.16614	−	1.75100i	0.211777	−	0.0890083i
$388$		0			0
$389$	−8.00251	+	2.14427i	−0.405744	+	0.108719i	−0.455918	−	0.890022i	$-0.650689\pi$
$389$	−8.00251	+	2.14427i	−0.405744	+	0.108719i	0.0501744	+	0.998740i	$0.484022\pi$
$390$		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	0.515798	−	0.856710i	$-0.327496\pi$
$397$	−6.79264	−	6.79264i	−0.340913	−	0.340913i	−0.856710	+	0.515798i	$0.827496\pi$
$398$		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
$403$	0.627898	+	2.34335i	0.0312778	+	0.116731i
$404$		0			0
$405$	0.346272	+	33.4348i	0.0172064	+	1.66139i
$406$		0			0
$407$	−12.1817	−	7.03312i	−0.603826	−	0.348619i
$408$		0			0
$409$	11.5152	−	6.64832i	0.569392	−	0.328738i	−0.187515	−	0.982262i	$-0.560043\pi$
$409$	11.5152	−	6.64832i	0.569392	−	0.328738i	0.756906	+	0.653523i	$0.226710\pi$
$410$		0			0
$411$	12.6434	−	25.8064i	0.623650	−	1.27294i
$412$		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
$419$	3.29438	−	12.2948i	0.160941	−	0.600639i	−0.837582	−	0.546311i	$-0.816032\pi$
$419$	3.29438	−	12.2948i	0.160941	−	0.600639i	0.998523	−	0.0543282i	$-0.0173017\pi$
$420$		0			0
$421$	1.72149	+	6.42470i	0.0839004	+	0.313121i	0.995104	−	0.0988365i	$-0.0315121\pi$
$421$	1.72149	+	6.42470i	0.0839004	+	0.313121i	−0.911203	+	0.411957i	$0.864845\pi$
$422$		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
$427$	−4.69083	+	17.5064i	−0.227005	+	0.847194i
$428$		0			0
$429$	−3.73426	+	0.254468i	−0.180292	+	0.0122858i
$430$		0			0
$431$	−37.3843			−1.80074			−0.900370	−	0.435126i	$-0.856704\pi$
$431$	−37.3843			−1.80074			−0.900370	+	0.435126i	$0.856704\pi$
$432$		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
$435$	−46.6873	+	3.18147i	−2.23849	+	0.152540i
$436$		0			0
$437$	7.39522	−	27.5993i	0.353761	−	1.32026i
$438$		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
$443$	2.46777	+	9.20983i	0.117247	+	0.437572i	0.999445	−	0.0333063i	$-0.0106037\pi$
$443$	2.46777	+	9.20983i	0.117247	+	0.437572i	−0.882198	+	0.470879i	$0.843937\pi$
$444$		0			0
$445$	−13.6482	+	50.9358i	−0.646987	+	2.41459i
$446$		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
$453$	2.06246	−	4.20969i	0.0969026	−	0.197788i
$454$		0			0
$455$	8.59164	−	4.96039i	0.402782	−	0.232546i
$456$		0			0
$457$	−5.15261	−	2.97486i	−0.241029	−	0.139158i	0.374621	−	0.927178i	$-0.377773\pi$
$457$	−5.15261	−	2.97486i	−0.241029	−	0.139158i	−0.615649	+	0.788020i	$0.711106\pi$
$458$		0			0
$459$	−4.35832	−	21.0547i	−0.203429	−	0.982750i
$460$		0			0
$461$	6.37780	+	23.8023i	0.297044	+	1.10858i	0.939581	+	0.342328i	$0.111215\pi$
$461$	6.37780	+	23.8023i	0.297044	+	1.10858i	−0.642537	+	0.766255i	$0.722118\pi$
$462$		0			0
$463$	20.8183	−	12.0194i	0.967507	−	0.558590i	0.0690315	−	0.997614i	$-0.478009\pi$
$463$	20.8183	−	12.0194i	0.967507	−	0.558590i	0.898475	+	0.439024i	$0.144676\pi$
$464$		0			0
$465$	4.89341	+	14.2938i	0.226926	+	0.662861i
$466$		0			0
$467$	−25.3702	−	25.3702i	−1.17399	−	1.17399i	−0.981249	−	0.192744i	$-0.938261\pi$
$467$	−25.3702	−	25.3702i	−1.17399	−	1.17399i	−0.192744	−	0.981249i	$-0.561739\pi$
$468$		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
$475$	29.9745	−	8.03166i	1.37533	−	0.368518i
$476$		0			0
$477$	−1.84715	−	1.40223i	−0.0845751	−	0.0642037i
$478$		0			0
$479$	−0.498647	+	0.863682i	−0.0227838	+	0.0394626i	−0.877192	−	0.480139i	$-0.840586\pi$
$479$	−0.498647	+	0.863682i	−0.0227838	+	0.0394626i	0.854409	+	0.519602i	$0.173920\pi$
$480$		0			0
$481$	3.47486	+	6.01863i	0.158440	+	0.274426i
$482$		0			0
$483$	−2.46651	−	36.1956i	−0.112230	−	1.64695i
$484$		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
$491$	−0.535020	−	0.143358i	−0.0241451	−	0.00646966i	0.246726	−	0.969085i	$-0.420645\pi$
$491$	−0.535020	−	0.143358i	−0.0241451	−	0.00646966i	−0.270871	+	0.962616i	$0.587312\pi$
$492$		0			0
$493$	29.0661	−	7.78824i	1.30907	−	0.350765i
$494$		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
$499$	42.1874	+	11.3041i	1.88857	+	0.506041i	0.998764	+	0.0497007i	$0.0158267\pi$
$499$	42.1874	+	11.3041i	1.88857	+	0.506041i	0.889805	+	0.456340i	$0.150840\pi$
$500$		0			0
$501$	−11.8129	+	7.93744i	−0.527761	+	0.354619i
$502$		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
$507$	−18.5596	−	9.09293i	−0.824262	−	0.403831i
$508$		0			0
$509$	−9.69736	−	2.59840i	−0.429828	−	0.115172i	0.0374174	−	0.999300i	$-0.488087\pi$
$509$	−9.69736	−	2.59840i	−0.429828	−	0.115172i	−0.467245	+	0.884128i	$0.654754\pi$
$510$		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
$515$	15.9956	−	4.28602i	0.704852	−	0.188865i
$516$		0			0
$517$	−14.5776	−	3.90607i	−0.641124	−	0.171789i
$518$		0			0
$519$	−14.4451	−	42.1948i	−0.634071	−	1.85214i
$520$		0			0
$521$	−3.20573			−0.140445			−0.0702227	−	0.997531i	$-0.522371\pi$
$521$	−3.20573			−0.140445			−0.0702227	+	0.997531i	$0.522371\pi$
$522$		0			0
$523$	28.1479	+	28.1479i	1.23082	+	1.23082i	0.963648	+	0.267175i	$0.0860902\pi$
$523$	28.1479	+	28.1479i	1.23082	+	1.23082i	0.267175	+	0.963648i	$0.413910\pi$
$524$		0			0
$525$	32.7046	−	21.9752i	1.42734	−	0.959075i
$526$		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
$531$	24.6632	+	3.11714i	1.07029	+	0.135272i
$532$		0			0
$533$	−1.26998	+	0.340291i	−0.0550091	+	0.0147396i
$534$		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	0.947894	−	0.318586i	$-0.103208\pi$
$541$	14.6373	+	14.6373i	0.629307	+	0.629307i	−0.318586	+	0.947894i	$0.603208\pi$
$542$		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
$547$	−4.55558	−	17.0017i	−0.194783	−	0.726938i	−0.992323	−	0.123673i	$-0.960533\pi$
$547$	−4.55558	−	17.0017i	−0.194783	−	0.726938i	0.797541	−	0.603265i	$-0.206134\pi$
$548$		0			0
$549$	−19.3957	+	8.15186i	−0.827786	+	0.347913i
$550$		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
$555$	24.1382	+	35.9237i	1.02461	+	1.52487i
$556$		0			0
$557$	−8.32037	+	8.32037i	−0.352546	+	0.352546i	−0.861056	−	0.508510i	$-0.830196\pi$
$557$	−8.32037	+	8.32037i	−0.352546	+	0.352546i	0.508510	+	0.861056i	$0.330196\pi$
$558$		0			0
$559$		−	1.55652i		−	0.0658337i
$560$		0			0
$561$	14.1809	−	4.85475i	0.598718	−	0.204968i
$562$		0			0
$563$	−5.81439	+	21.6996i	−0.245047	+	0.914529i	0.728312	+	0.685245i	$0.240305\pi$
$563$	−5.81439	+	21.6996i	−0.245047	+	0.914529i	−0.973360	+	0.229284i	$0.926362\pi$
$564$		0			0
$565$	−8.85525	−	33.0482i	−0.372543	−	1.39035i
$566$		0			0
$567$	5.78686	−	22.5275i	0.243025	−	0.946067i
$568$		0			0
$569$	7.57037	−	13.1123i	0.317367	−	0.549695i	−0.662571	−	0.748999i	$-0.730535\pi$
$569$	7.57037	−	13.1123i	0.317367	−	0.549695i	0.979938	+	0.199304i	$0.0638681\pi$
$570$		0			0
$571$	8.82715	−	32.9434i	0.369405	−	1.37864i	−0.491945	−	0.870626i	$-0.663714\pi$
$571$	8.82715	−	32.9434i	0.369405	−	1.37864i	0.861350	−	0.508012i	$-0.169619\pi$
$572$		0			0
$573$	4.27630	−	8.72837i	0.178645	−	0.364633i
$574$		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
$579$	24.2906	+	36.1505i	1.00948	+	1.50237i
$580$		0			0
$581$	−5.34414	+	19.9446i	−0.221712	+	0.827442i
$582$		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
$587$	8.04265	+	30.0156i	0.331955	+	1.23887i	0.907132	+	0.420846i	$0.138267\pi$
$587$	8.04265	+	30.0156i	0.331955	+	1.23887i	−0.575177	+	0.818029i	$0.695067\pi$
$588$		0			0
$589$	2.14226	−	7.99501i	0.0882701	−	0.329429i
$590$		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
$597$	−25.3409	+	1.72683i	−1.03713	+	0.0706745i
$598$		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	0.0366348	−	0.999329i	$-0.488336\pi$
$601$	−19.8695	−	11.4716i	−0.810492	−	0.467938i	−0.847127	+	0.531391i	$0.821670\pi$
$602$		0			0
$603$	8.64749	+	1.09294i	0.352153	+	0.0445080i
$604$		0			0
$605$	6.37146	+	23.7786i	0.259037	+	0.966738i
$606$		0			0
$607$	−16.8592	+	9.73364i	−0.684292	+	0.395076i	−0.801470	−	0.598035i	$-0.795949\pi$
$607$	−16.8592	+	9.73364i	−0.684292	+	0.395076i	0.117178	+	0.993111i	$0.462615\pi$
$608$		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	−0.887877	−	0.460080i	$-0.847821\pi$
$613$	−10.5918	+	10.5918i	−0.427797	+	0.427797i	0.460080	+	0.887877i	$0.347821\pi$
$614$		0			0
$615$	−7.74658	+	2.65200i	−0.312372	+	0.106939i
$616$		0			0
$617$	−9.33080	−	16.1614i	−0.375644	−	0.650634i	0.614779	−	0.788699i	$-0.289245\pi$
$617$	−9.33080	−	16.1614i	−0.375644	−	0.650634i	−0.990423	+	0.138065i	$0.955912\pi$
$618$		0			0
$619$	−21.0028	+	5.62767i	−0.844172	+	0.226195i	−0.654887	−	0.755727i	$-0.727284\pi$
$619$	−21.0028	+	5.62767i	−0.844172	+	0.226195i	−0.189285	+	0.981922i	$0.560617\pi$
$620$		0			0
$621$	31.4470	−	28.0134i	1.26192	−	1.12414i
$622$		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
$627$	11.4677	+	5.61837i	0.457975	+	0.224376i
$628$		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
$635$	−17.0742	−	4.57502i	−0.677569	−	0.181554i
$636$		0			0
$637$	0.320651	−	0.0859183i	0.0127047	−	0.00340421i
$638$		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
$643$	−33.6691	−	9.02160i	−1.32778	−	0.355777i	−0.475892	−	0.879503i	$-0.657875\pi$
$643$	−33.6691	−	9.02160i	−1.32778	−	0.355777i	−0.851887	+	0.523726i	$0.824542\pi$
$644$		0			0
$645$	−0.659018	−	9.67095i	−0.0259488	−	0.380793i
$646$		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
$651$	−0.714503	−	10.4852i	−0.0280036	−	0.410946i
$652$		0			0
$653$	14.2429	+	3.81636i	0.557366	+	0.149346i	0.526496	−	0.850178i	$-0.323505\pi$
$653$	14.2429	+	3.81636i	0.557366	+	0.149346i	0.0308703	+	0.999523i	$0.490172\pi$
$654$		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
$659$	−33.8013	+	9.05703i	−1.31671	+	0.352812i	−0.847745	−	0.530404i	$-0.822040\pi$
$659$	−33.8013	+	9.05703i	−1.31671	+	0.352812i	−0.468967	+	0.883216i	$0.655374\pi$
$660$		0			0
$661$	35.8049	+	9.59389i	1.39265	+	0.373159i	0.875699	−	0.482857i	$-0.160401\pi$
$661$	35.8049	+	9.59389i	1.39265	+	0.373159i	0.516949	+	0.856016i	$0.327068\pi$
$662$		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
$669$	−44.7399	−	21.9195i	−1.72975	−	0.847456i
$670$		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
$675$	43.4248	+	14.3656i	1.67142	+	0.552931i
$676$		0			0
$677$	−20.8441	+	5.58517i	−0.801105	+	0.214655i	−0.636069	−	0.771632i	$-0.719441\pi$
$677$	−20.8441	+	5.58517i	−0.801105	+	0.214655i	−0.165036	+	0.986288i	$0.552774\pi$
$678$		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	$-0.576640\pi$
$683$	19.1487	−	19.1487i	0.732704	−	0.732704i	0.971155	+	0.238451i	$0.0766395\pi$
$684$		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
$691$	−8.78531	−	32.7872i	−0.334209	−	1.24728i	−0.904724	−	0.425997i	$-0.859923\pi$
$691$	−8.78531	−	32.7872i	−0.334209	−	1.24728i	0.570516	−	0.821287i	$-0.306743\pi$
$692$		0			0
$693$	16.0863	+	2.03312i	0.611070	+	0.0772320i
$694$		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
$699$	5.11960	−	0.348870i	0.193641	−	0.0131955i
$700$		0			0
$701$	−28.6582	+	28.6582i	−1.08240	+	1.08240i	−0.0861190	+	0.996285i	$0.527447\pi$
$701$	−28.6582	+	28.6582i	−1.08240	+	1.08240i	−0.996285	+	0.0861190i	$0.972553\pi$
$702$		0			0
$703$		−	23.7109i		−	0.894275i
$704$		0			0
$705$	34.9914	+	30.5268i	1.31785	+	1.14970i
$706$		0			0
$707$	−2.73177	+	10.1951i	−0.102739	+	0.383426i
$708$		0			0
$709$	2.14398	+	8.00146i	0.0805190	+	0.300501i	0.994428	−	0.105418i	$-0.0336181\pi$
$709$	2.14398	+	8.00146i	0.0805190	+	0.300501i	−0.913909	+	0.405919i	$0.866951\pi$
$710$		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
$715$	−2.07790	+	7.75484i	−0.0777091	+	0.290014i
$716$		0			0
$717$	9.93803	+	14.7903i	0.371142	+	0.552353i
$718$		0			0
$719$	17.3387			0.646625			0.323312	−	0.946292i	$-0.395204\pi$
$719$	17.3387			0.646625			0.323312	+	0.946292i	$0.395204\pi$
$720$		0			0
$721$	−11.5193			−0.429001
$722$		0			0
$723$	19.6184	−	40.0431i	0.729615	−	1.48922i
$724$		0			0
$725$	−16.5680	+	61.8325i	−0.615318	+	2.29640i
$726$		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
$731$	1.61328	+	6.02084i	0.0596693	+	0.222689i
$732$		0			0
$733$	−0.123620	+	0.461357i	−0.00456602	+	0.0170406i	−0.968171	−	0.250289i	$-0.919474\pi$
$733$	−0.123620	+	0.461357i	−0.00456602	+	0.0170406i	0.963605	+	0.267329i	$0.0861411\pi$
$734$		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	−0.400038	+	0.916499i	$0.631003\pi$
$739$	−35.7895	+	35.7895i	−1.31654	+	1.31654i	−0.916499	+	0.400038i	$0.868997\pi$
$740$		0			0
$741$	−3.51883	−	5.23689i	−0.129267	−	0.192382i
$742$		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
$747$	−22.0970	+	9.28722i	−0.808487	+	0.339801i
$748$		0			0
$749$	−3.79711	−	14.1710i	−0.138743	−	0.517798i
$750$		0			0
$751$	12.6419	−	7.29878i	0.461308	−	0.266336i	−0.251286	−	0.967913i	$-0.580853\pi$
$751$	12.6419	−	7.29878i	0.461308	−	0.266336i	0.712594	+	0.701577i	$0.247520\pi$
$752$		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	−0.179440	−	0.983769i	$-0.557429\pi$
$757$	22.1300	−	22.1300i	0.804329	−	0.804329i	0.983769	+	0.179440i	$0.0574286\pi$
$758$		0			0
$759$	22.1235	+	19.3007i	0.803032	+	0.700570i
$760$		0			0
$761$	13.0131	+	22.5393i	0.471724	+	0.817050i	0.999477	−	0.0323484i	$-0.0102986\pi$
$761$	13.0131	+	22.5393i	0.471724	+	0.817050i	−0.527753	+	0.849398i	$0.676965\pi$
$762$		0			0
$763$	−24.1821	+	6.47957i	−0.875451	+	0.234576i
$764$		0			0
$765$	−45.7549	−	5.78288i	−1.65427	−	0.209080i
$766$		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
$771$	11.2024	−	7.52724i	0.403445	−	0.271087i
$772$		0			0
$773$	3.23556	+	3.23556i	0.116375	+	0.116375i	0.762896	−	0.646521i	$-0.223777\pi$
$773$	3.23556	+	3.23556i	0.116375	+	0.116375i	−0.646521	+	0.762896i	$0.723777\pi$
$774$		0			0
$775$	20.6672			0.742388
$776$		0			0
$777$	−9.75108	−	28.4833i	−0.349818	−	1.02183i
$778$		0			0
$779$	4.33291	+	1.16100i	0.155243	+	0.0415972i
$780$		0			0
$781$	13.3216	−	3.56951i	0.476683	−	0.127727i
$782$		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
$787$	−24.4646	−	6.55528i	−0.872070	−	0.233671i	−0.205087	−	0.978744i	$-0.565748\pi$
$787$	−24.4646	−	6.55528i	−0.872070	−	0.233671i	−0.666983	+	0.745073i	$0.732415\pi$
$788$		0			0
$789$	22.1833	+	10.8683i	0.789747	+	0.386922i
$790$		0			0
$791$			23.7997i			0.846221i
$792$		0			0
$793$			7.24645i			0.257329i
$794$		0			0
$795$	−4.12886	+	2.77431i	−0.146436	+	0.0983945i
$796$		0			0
$797$	30.4414	+	8.15674i	1.07829	+	0.288927i	0.753895	−	0.656995i	$-0.228173\pi$
$797$	30.4414	+	8.15674i	1.07829	+	0.288927i	0.324394	+	0.945922i	$0.394840\pi$
$798$		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
$803$	−17.7507	+	4.75628i	−0.626407	+	0.167845i
$804$		0			0
$805$	−75.1664	−	20.1408i	−2.64927	−	0.709869i
$806$		0			0
$807$	−2.74175	+	3.14275i	−0.0965143	+	0.110630i
$808$		0			0
$809$	46.7989			1.64536			0.822681	−	0.568503i	$-0.192477\pi$
$809$	46.7989			1.64536			0.822681	+	0.568503i	$0.192477\pi$
$810$		0			0
$811$	−32.5365	−	32.5365i	−1.14251	−	1.14251i	−0.987989	−	0.154522i	$-0.950616\pi$
$811$	−32.5365	−	32.5365i	−1.14251	−	1.14251i	−0.154522	−	0.987989i	$-0.549384\pi$
$812$		0			0
$813$	−1.12533	−	16.5139i	−0.0394669	−	0.579168i
$814$		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
$819$	−6.38073	−	4.84382i	−0.222961	−	0.169257i
$820$		0			0
$821$	10.3044	−	2.76106i	0.359627	−	0.0963618i	−0.0744814	−	0.997222i	$-0.523730\pi$
$821$	10.3044	−	2.76106i	0.359627	−	0.0963618i	0.434108	+	0.900861i	$0.357063\pi$
$822$		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	$-0.842713\pi$
$827$	−11.6788	+	11.6788i	−0.406113	+	0.406113i	0.474268	+	0.880381i	$0.342713\pi$
$828$		0			0
$829$	29.2209	+	29.2209i	1.01488	+	1.01488i	0.999888	+	0.0149948i	$0.00477317\pi$
$829$	29.2209	+	29.2209i	1.01488	+	1.01488i	0.0149948	+	0.999888i	$0.495227\pi$
$830$		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
$835$	7.90094	+	29.4867i	0.273423	+	1.02043i
$836$		0			0
$837$	9.10961	−	8.11495i	0.314874	−	0.280494i
$838$		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
$843$	12.5913	−	25.7003i	0.433669	−	0.885164i
$844$		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
$851$	14.1090	−	52.6557i	0.483652	−	1.80501i
$852$		0			0
$853$	5.89168	+	21.9880i	0.201727	+	0.752856i	0.990422	+	0.138072i	$0.0440904\pi$
$853$	5.89168	+	21.9880i	0.201727	+	0.752856i	−0.788695	+	0.614785i	$0.789243\pi$
$854$		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	$0.433032\pi$
$857$	−21.7367	+	37.6490i	−0.742510	+	1.28607i	−0.951349	+	0.308115i	$0.900302\pi$
$858$		0			0
$859$	−0.490831	+	1.83181i	−0.0167469	+	0.0625005i	−0.973794	−	0.227433i	$-0.926967\pi$
$859$	−0.490831	+	1.83181i	−0.0167469	+	0.0625005i	0.957047	+	0.289934i	$0.0936333\pi$
$860$		0			0
$861$	5.68246	−	0.387226i	0.193658	−	0.0131966i
$862$		0			0
$863$	−5.75112			−0.195770			−0.0978852	−	0.995198i	$-0.531208\pi$
$863$	−5.75112			−0.195770			−0.0978852	+	0.995198i	$0.531208\pi$
$864$		0			0
$865$	−95.6627			−3.25263
$866$		0			0
$867$	0.210948	−	0.0143748i	0.00716416	−	0.000488195i
$868$		0			0
$869$	−3.53100	+	13.1779i	−0.119781	+	0.447029i
$870$		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
$875$	−9.44921	−	35.2649i	−0.319442	−	1.19217i
$876$		0			0
$877$	−10.6306	+	39.6739i	−0.358969	+	1.33969i	0.516446	+	0.856320i	$0.327255\pi$
$877$	−10.6306	+	39.6739i	−0.358969	+	1.33969i	−0.875415	+	0.483372i	$0.839412\pi$
$878$		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	0.0388519	−	0.999245i	$-0.487630\pi$
$883$	30.8474	−	30.8474i	1.03810	−	1.03810i	0.999245	−	0.0388519i	$-0.0123701\pi$
$884$		0			0
$885$	23.4600	−	47.8843i	0.788599	−	1.60961i
$886$		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
$891$	9.57946	+	16.2023i	0.320924	+	0.542796i
$892$		0			0
$893$	−6.58431	−	24.5730i	−0.220336	−	0.822304i
$894$		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
$907$	43.5725	−	11.6752i	1.44680	−	0.387670i	0.551892	−	0.833916i	$-0.313906\pi$
$907$	43.5725	−	11.6752i	1.44680	−	0.387670i	0.894910	+	0.446246i	$0.147239\pi$
$908$		0			0
$909$	−11.2953	+	4.74735i	−0.374642	+	0.157460i
$910$		0			0
$911$	0.452588	−	0.783905i	0.0149949	−	0.0259719i	−0.858431	−	0.512930i	$-0.828560\pi$
$911$	0.452588	−	0.783905i	0.0149949	−	0.0259719i	0.873425	+	0.486958i	$0.161893\pi$
$912$		0			0
$913$	−8.35479	−	14.4709i	−0.276503	−	0.478917i
$914$		0			0
$915$	3.06809	+	45.0236i	0.101428	+	1.48843i
$916$		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
$923$	−6.58179	−	1.76359i	−0.216642	−	0.0580492i
$924$		0			0
$925$	57.1873	−	15.3233i	1.88031	−	0.503826i
$926$		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
$931$	−1.09399	−	0.293135i	−0.0358542	−	0.00960711i
$932$		0			0
$933$	−6.21362	+	4.17512i	−0.203425	+	0.136687i
$934$		0			0
$935$		−	32.1505i		−	1.05143i
$936$		0			0
$937$			40.0398i			1.30804i	0.756476	+	0.654021i	$0.226919\pi$
$937$			40.0398i			1.30804i	−0.756476	+	0.654021i	$0.773081\pi$
$938$		0			0
$939$	24.7600	+	12.1307i	0.808011	+	0.395870i
$940$		0			0
$941$	−10.3853	−	2.78273i	−0.338551	−	0.0907146i	0.0855380	−	0.996335i	$-0.472739\pi$
$941$	−10.3853	−	2.78273i	−0.338551	−	0.0907146i	−0.424089	+	0.905620i	$0.639406\pi$
$942$		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
$947$	37.6297	−	10.0828i	1.22280	−	0.327648i	0.411028	−	0.911623i	$-0.365170\pi$
$947$	37.6297	−	10.0828i	1.22280	−	0.327648i	0.811772	+	0.583975i	$0.198503\pi$
$948$		0			0
$949$	8.77007	+	2.34993i	0.284689	+	0.0762821i
$950$		0			0
$951$	16.6745	+	48.7069i	0.540708	+	1.57943i
$952$		0			0
$953$	−7.83389			−0.253765			−0.126882	−	0.991918i	$-0.540497\pi$
$953$	−7.83389			−0.253765			−0.126882	+	0.991918i	$0.540497\pi$
$954$		0			0
$955$	−14.7419	−	14.7419i	−0.477037	−	0.477037i
$956$		0			0
$957$	−21.8650	+	14.6917i	−0.706794	+	0.474916i
$958$		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
$963$	10.2975	−	13.5648i	0.331833	−	0.437121i
$964$		0			0
$965$	90.2370	−	24.1789i	2.90483	−	0.778347i
$966$		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	$-0.969846\pi$
$971$	−28.0737	+	28.0737i	−0.900928	+	0.900928i	0.0945888	+	0.995516i	$0.469846\pi$
$972$		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
$979$	7.68293	+	28.6731i	0.245547	+	0.916396i
$980$		0			0
$981$	−23.1477	−	17.5722i	−0.739048	−	0.561036i
$982$		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
$987$	−18.0151	−	26.8110i	−0.573428	−	0.853405i
$988$		0			0
$989$	−8.63324	+	8.63324i	−0.274521	+	0.274521i
$990$		0			0
$991$		−	37.2374i		−	1.18289i	−0.806347	−	0.591443i	$-0.798558\pi$
$991$		−	37.2374i		−	1.18289i	0.806347	−	0.591443i	$-0.201442\pi$
$992$		0			0
$993$	−3.22523	+	1.10414i	−0.102349	+	0.0350387i
$994$		0			0
$995$	−14.1008	+	52.6247i	−0.447024	+	1.66832i
$996$		0			0
$997$	−3.73234	−	13.9293i	−0.118204	−	0.441145i	0.881302	−	0.472553i	$-0.156667\pi$
$997$	−3.73234	−	13.9293i	−0.118204	−	0.441145i	−0.999507	+	0.0314082i	$0.990001\pi$
$998$		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.47.1		88
3.2	odd	2		1728.2.z.a.1007.21		88
4.3	odd	2		144.2.u.a.83.2	yes	88
9.4	even	3		1728.2.z.a.1583.21		88
9.5	odd	6	inner	576.2.y.a.239.10		88
12.11	even	2		432.2.v.a.35.21		88
16.5	even	4		144.2.u.a.11.9	✓	88
16.11	odd	4	inner	576.2.y.a.335.10		88
36.23	even	6		144.2.u.a.131.9	yes	88
36.31	odd	6		432.2.v.a.179.14		88
48.5	odd	4		432.2.v.a.251.14		88
48.11	even	4		1728.2.z.a.143.21		88
144.5	odd	12		144.2.u.a.59.2	yes	88
144.59	even	12	inner	576.2.y.a.527.1		88
144.85	even	12		432.2.v.a.395.21		88
144.139	odd	12		1728.2.z.a.719.21		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.9	✓	88	16.5	even	4
144.2.u.a.59.2	yes	88	144.5	odd	12
144.2.u.a.83.2	yes	88	4.3	odd	2
144.2.u.a.131.9	yes	88	36.23	even	6
432.2.v.a.35.21		88	12.11	even	2
432.2.v.a.179.14		88	36.31	odd	6
432.2.v.a.251.14		88	48.5	odd	4
432.2.v.a.395.21		88	144.85	even	12
576.2.y.a.47.1		88	1.1	even	1	trivial
576.2.y.a.239.10		88	9.5	odd	6	inner
576.2.y.a.335.10		88	16.11	odd	4	inner
576.2.y.a.527.1		88	144.59	even	12	inner
1728.2.z.a.143.21		88	48.11	even	4
1728.2.z.a.719.21		88	144.139	odd	12
1728.2.z.a.1007.21		88	3.2	odd	2
1728.2.z.a.1583.21		88	9.4	even	3

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)

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