LMFDB - Embedded newform 512.2.k.a.17.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [512,2,Mod(17,512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(512, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 7]))

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

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

chi := DirichletCharacter("512.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 512 = 2^{9} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	512.k (of order $32$, degree $16$, 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:	$4.08834058349$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$15$ over $\Q(\zeta_{32})$
Twist minimal:	no (minimal twist has level 128)
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			17.8
Character	$\chi$	$=$	512.17
Dual form			512.2.k.a.241.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.169198 + 0.316547i) q^{3} +(-0.290696 - 0.238568i) q^{5} +(-3.87217 - 2.58730i) q^{7} +(1.59514 + 2.38729i) q^{9} +O(q^{10})$	\(q+(-0.169198 + 0.316547i) q^{3} +(-0.290696 - 0.238568i) q^{5} +(-3.87217 - 2.58730i) q^{7} +(1.59514 + 2.38729i) q^{9} +(0.0374510 - 0.123460i) q^{11} +(-2.75700 - 3.35941i) q^{13} +(0.124703 - 0.0516536i) q^{15} +(-1.63337 - 0.676562i) q^{17} +(-7.56032 - 0.744626i) q^{19} +(1.47416 - 0.787957i) q^{21} +(3.01688 + 0.600095i) q^{23} +(-0.947862 - 4.76523i) q^{25} +(-2.09718 + 0.206555i) q^{27} +(-7.48261 + 2.26982i) q^{29} +(2.44320 - 2.44320i) q^{31} +(0.0327441 + 0.0327441i) q^{33} +(0.508376 + 1.67589i) q^{35} +(-0.235812 - 2.39424i) q^{37} +(1.52989 - 0.304314i) q^{39} +(1.24216 - 6.24474i) q^{41} +(3.67876 + 6.88248i) q^{43} +(0.105831 - 1.07452i) q^{45} +(3.07637 - 7.42702i) q^{47} +(5.62078 + 13.5698i) q^{49} +(0.490525 - 0.402564i) q^{51} +(-5.20823 - 1.57990i) q^{53} +(-0.0403403 + 0.0269545i) q^{55} +(1.51490 - 2.26720i) q^{57} +(0.452339 - 0.551176i) q^{59} +(-1.09220 - 0.583792i) q^{61} -13.3711i q^{63} +1.63430i q^{65} +(-0.0559933 - 0.0299291i) q^{67} +(-0.700408 + 0.853450i) q^{69} +(-6.51783 + 9.75462i) q^{71} +(-7.60253 + 5.07985i) q^{73} +(1.66879 + 0.506223i) q^{75} +(-0.464443 + 0.381159i) q^{77} +(3.68039 + 8.88525i) q^{79} +(-3.00679 + 7.25904i) q^{81} +(0.820582 - 8.33151i) q^{83} +(0.313406 + 0.586342i) q^{85} +(0.547535 - 2.75264i) q^{87} +(11.4621 - 2.27994i) q^{89} +(1.98375 + 20.1414i) q^{91} +(0.360004 + 1.18677i) q^{93} +(2.02011 + 2.02011i) q^{95} +(0.983974 - 0.983974i) q^{97} +(0.354473 - 0.107528i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9}+O(q^{10}) $ 240 * q + 16 * q^3 - 16 * q^5 + 16 * q^7 - 16 * q^9	$ 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9} + 16 q^{11} - 16 q^{13} + 16 q^{15} - 16 q^{17} + 16 q^{19} - 16 q^{21} + 16 q^{23} - 16 q^{25} + 16 q^{27} - 16 q^{29} + 16 q^{31} - 16 q^{33} + 16 q^{35} - 16 q^{37} + 16 q^{39} - 16 q^{41} + 16 q^{43} - 16 q^{45} + 16 q^{47} - 16 q^{49} + 16 q^{51} - 16 q^{53} + 16 q^{55} - 16 q^{57} + 16 q^{59} - 16 q^{61} + 16 q^{67} - 16 q^{69} + 16 q^{71} - 16 q^{73} + 16 q^{75} - 16 q^{77} + 16 q^{79} - 16 q^{81} + 16 q^{83} - 16 q^{85} + 16 q^{87} - 16 q^{89} + 16 q^{91} - 16 q^{93} + 16 q^{95} - 16 q^{97} + 16 q^{99}+O(q^{100}) $ 240 * q + 16 * q^3 - 16 * q^5 + 16 * q^7 - 16 * q^9 + 16 * q^11 - 16 * q^13 + 16 * q^15 - 16 * q^17 + 16 * q^19 - 16 * q^21 + 16 * q^23 - 16 * q^25 + 16 * q^27 - 16 * q^29 + 16 * q^31 - 16 * q^33 + 16 * q^35 - 16 * q^37 + 16 * q^39 - 16 * q^41 + 16 * q^43 - 16 * q^45 + 16 * q^47 - 16 * q^49 + 16 * q^51 - 16 * q^53 + 16 * q^55 - 16 * q^57 + 16 * q^59 - 16 * q^61 + 16 * q^67 - 16 * q^69 + 16 * q^71 - 16 * q^73 + 16 * q^75 - 16 * q^77 + 16 * q^79 - 16 * q^81 + 16 * q^83 - 16 * q^85 + 16 * q^87 - 16 * q^89 + 16 * q^91 - 16 * q^93 + 16 * q^95 - 16 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/512\mathbb{Z}\right)^\times$.

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{7}{32}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.169198	+	0.316547i	−0.0976864	+	0.182758i	−0.926018	−	0.377480i	$-0.876791\pi$
$3$	−0.169198	+	0.316547i	−0.0976864	+	0.182758i	0.828331	+	0.560239i	$0.189291\pi$
$4$		0			0
$5$	−0.290696	−	0.238568i	−0.130003	−	0.106691i	0.567145	−	0.823618i	$-0.308048\pi$
$5$	−0.290696	−	0.238568i	−0.130003	−	0.106691i	−0.697148	+	0.716927i	$0.745548\pi$
$6$		0			0
$7$	−3.87217	−	2.58730i	−1.46354	−	0.977907i	−0.995556	−	0.0941715i	$-0.969980\pi$
$7$	−3.87217	−	2.58730i	−1.46354	−	0.977907i	−0.467986	−	0.883736i	$-0.655020\pi$
$8$		0			0
$9$	1.59514	+	2.38729i	0.531712	+	0.795764i
$10$		0			0
$11$	0.0374510	−	0.123460i	0.0112919	−	0.0372244i	−0.951113	−	0.308842i	$-0.900059\pi$
$11$	0.0374510	−	0.123460i	0.0112919	−	0.0372244i	0.962405	+	0.271618i	$0.0875586\pi$
$12$		0			0
$13$	−2.75700	−	3.35941i	−0.764654	−	0.931734i	0.234531	−	0.972109i	$-0.424645\pi$
$13$	−2.75700	−	3.35941i	−0.764654	−	0.931734i	−0.999185	+	0.0403751i	$0.987145\pi$
$14$		0			0
$15$	0.124703	−	0.0516536i	0.0321981	−	0.0133369i
$16$		0			0
$17$	−1.63337	−	0.676562i	−0.396149	−	0.164090i	0.175710	−	0.984442i	$-0.443778\pi$
$17$	−1.63337	−	0.676562i	−0.396149	−	0.164090i	−0.571860	+	0.820352i	$0.693778\pi$
$18$		0			0
$19$	−7.56032	−	0.744626i	−1.73446	−	0.170829i	−0.819148	−	0.573583i	$-0.805553\pi$
$19$	−7.56032	−	0.744626i	−1.73446	−	0.170829i	−0.915308	+	0.402754i	$0.868053\pi$
$20$		0			0
$21$	1.47416	−	0.787957i	0.321689	−	0.171946i
$22$		0			0
$23$	3.01688	+	0.600095i	0.629064	+	0.125129i	0.499318	−	0.866419i	$-0.333584\pi$
$23$	3.01688	+	0.600095i	0.629064	+	0.125129i	0.129746	+	0.991547i	$0.458584\pi$
$24$		0			0
$25$	−0.947862	−	4.76523i	−0.189572	−	0.953045i
$26$		0			0
$27$	−2.09718	+	0.206555i	−0.403603	+	0.0397514i
$28$		0			0
$29$	−7.48261	+	2.26982i	−1.38949	+	0.421496i	−0.894369	−	0.447330i	$-0.852375\pi$
$29$	−7.48261	+	2.26982i	−1.38949	+	0.421496i	−0.495117	+	0.868826i	$0.664875\pi$
$30$		0			0
$31$	2.44320	−	2.44320i	0.438812	−	0.438812i	−0.452800	−	0.891612i	$-0.649575\pi$
$31$	2.44320	−	2.44320i	0.438812	−	0.438812i	0.891612	+	0.452800i	$0.149575\pi$
$32$		0			0
$33$	0.0327441	+	0.0327441i	0.00570001	+	0.00570001i
$34$		0			0
$35$	0.508376	+	1.67589i	0.0859312	+	0.283277i
$36$		0			0
$37$	−0.235812	−	2.39424i	−0.0387672	−	0.393610i	−0.994914	−	0.100724i	$-0.967884\pi$
$37$	−0.235812	−	2.39424i	−0.0387672	−	0.393610i	0.956147	−	0.292887i	$-0.0946158\pi$
$38$		0			0
$39$	1.52989	−	0.304314i	0.244978	−	0.0487292i
$40$		0			0
$41$	1.24216	−	6.24474i	0.193992	−	0.975265i	−0.753976	−	0.656901i	$-0.771867\pi$
$41$	1.24216	−	6.24474i	0.193992	−	0.975265i	0.947969	−	0.318364i	$-0.103133\pi$
$42$		0			0
$43$	3.67876	+	6.88248i	0.561006	+	1.04957i	0.989295	+	0.145926i	$0.0466163\pi$
$43$	3.67876	+	6.88248i	0.561006	+	1.04957i	−0.428290	+	0.903641i	$0.640884\pi$
$44$		0			0
$45$	0.105831	−	1.07452i	0.0157764	−	0.160180i
$46$		0			0
$47$	3.07637	−	7.42702i	0.448735	−	1.08334i	−0.524061	−	0.851680i	$-0.675584\pi$
$47$	3.07637	−	7.42702i	0.448735	−	1.08334i	0.972796	−	0.231662i	$-0.0744162\pi$
$48$		0			0
$49$	5.62078	+	13.5698i	0.802968	+	1.93854i
$50$		0			0
$51$	0.490525	−	0.402564i	0.0686873	−	0.0563702i
$52$		0			0
$53$	−5.20823	−	1.57990i	−0.715405	−	0.217016i	−0.0884607	−	0.996080i	$-0.528195\pi$
$53$	−5.20823	−	1.57990i	−0.715405	−	0.217016i	−0.626945	+	0.779064i	$0.715695\pi$
$54$		0			0
$55$	−0.0403403	+	0.0269545i	−0.00543948	+	0.00363455i
$56$		0			0
$57$	1.51490	−	2.26720i	0.200653	−	0.300299i
$58$		0			0
$59$	0.452339	−	0.551176i	0.0588895	−	0.0717570i	−0.742733	−	0.669588i	$-0.766471\pi$
$59$	0.452339	−	0.551176i	0.0588895	−	0.0717570i	0.801622	+	0.597831i	$0.203971\pi$
$60$		0			0
$61$	−1.09220	−	0.583792i	−0.139842	−	0.0747470i	0.399992	−	0.916519i	$-0.369013\pi$
$61$	−1.09220	−	0.583792i	−0.139842	−	0.0747470i	−0.539834	+	0.841772i	$0.681513\pi$
$62$		0			0
$63$		−	13.3711i		−	1.68460i
$64$		0			0
$65$			1.63430i			0.202710i
$66$		0			0
$67$	−0.0559933	−	0.0299291i	−0.00684067	−	0.00365642i	0.467973	−	0.883743i	$-0.344984\pi$
$67$	−0.0559933	−	0.0299291i	−0.00684067	−	0.00365642i	−0.474814	+	0.880086i	$0.657484\pi$
$68$		0			0
$69$	−0.700408	+	0.853450i	−0.0843192	+	0.102743i
$70$		0			0
$71$	−6.51783	+	9.75462i	−0.773524	+	1.15766i	0.210144	+	0.977670i	$0.432607\pi$
$71$	−6.51783	+	9.75462i	−0.773524	+	1.15766i	−0.983668	+	0.179990i	$0.942393\pi$
$72$		0			0
$73$	−7.60253	+	5.07985i	−0.889809	+	0.594552i	−0.914250	−	0.405150i	$-0.867219\pi$
$73$	−7.60253	+	5.07985i	−0.889809	+	0.594552i	0.0244410	+	0.999701i	$0.492219\pi$
$74$		0			0
$75$	1.66879	+	0.506223i	0.192696	+	0.0584536i
$76$		0			0
$77$	−0.464443	+	0.381159i	−0.0529282	+	0.0434371i
$78$		0			0
$79$	3.68039	+	8.88525i	0.414076	+	0.999669i	0.984032	+	0.177993i	$0.0569605\pi$
$79$	3.68039	+	8.88525i	0.414076	+	0.999669i	−0.569955	+	0.821676i	$0.693039\pi$
$80$		0			0
$81$	−3.00679	+	7.25904i	−0.334088	+	0.806560i
$82$		0			0
$83$	0.820582	−	8.33151i	0.0900706	−	0.914502i	−0.838884	−	0.544310i	$-0.816792\pi$
$83$	0.820582	−	8.33151i	0.0900706	−	0.914502i	0.928955	−	0.370193i	$-0.120708\pi$
$84$		0			0
$85$	0.313406	+	0.586342i	0.0339937	+	0.0635977i
$86$		0			0
$87$	0.547535	−	2.75264i	0.0587019	−	0.295114i
$88$		0			0
$89$	11.4621	−	2.27994i	1.21498	−	0.241674i	0.454325	−	0.890836i	$-0.349880\pi$
$89$	11.4621	−	2.27994i	1.21498	−	0.241674i	0.760650	+	0.649162i	$0.224880\pi$
$90$		0			0
$91$	1.98375	+	20.1414i	0.207954	+	2.11139i
$92$		0			0
$93$	0.360004	+	1.18677i	0.0373306	+	0.123063i
$94$		0			0
$95$	2.02011	+	2.02011i	0.207259	+	0.207259i
$96$		0			0
$97$	0.983974	−	0.983974i	0.0999074	−	0.0999074i	−0.655386	−	0.755294i	$-0.727494\pi$
$97$	0.983974	−	0.983974i	0.0999074	−	0.0999074i	0.755294	+	0.655386i	$0.227494\pi$
$98$		0			0
$99$	0.354473	−	0.107528i	0.0356259	−	0.0108070i
$100$		0			0
$101$	11.7696	−	1.15920i	1.17112	−	0.115345i	0.506305	−	0.862355i	$-0.331011\pi$
$101$	11.7696	−	1.15920i	1.17112	−	0.115345i	0.664813	+	0.747009i	$0.268511\pi$
$102$		0			0
$103$	−0.0984998	−	0.495192i	−0.00970547	−	0.0487927i	0.975629	−	0.219426i	$-0.0704186\pi$
$103$	−0.0984998	−	0.495192i	−0.00970547	−	0.0487927i	−0.985335	+	0.170634i	$0.945419\pi$
$104$		0			0
$105$	−0.616514	−	0.122632i	−0.0601656	−	0.0119677i
$106$		0			0
$107$	3.73443	−	1.99610i	0.361021	−	0.192970i	−0.280906	−	0.959735i	$-0.590635\pi$
$107$	3.73443	−	1.99610i	0.361021	−	0.192970i	0.641928	+	0.766765i	$0.278135\pi$
$108$		0			0
$109$	−1.12948	−	0.111244i	−0.108185	−	0.0106553i	0.0437798	−	0.999041i	$-0.486060\pi$
$109$	−1.12948	−	0.111244i	−0.108185	−	0.0106553i	−0.151965	+	0.988386i	$0.548560\pi$
$110$		0			0
$111$	0.797787	+	0.330454i	0.0757226	+	0.0313653i
$112$		0			0
$113$	9.26419	−	3.83735i	0.871501	−	0.360988i	0.0983064	−	0.995156i	$-0.468657\pi$
$113$	9.26419	−	3.83735i	0.871501	−	0.360988i	0.773195	+	0.634169i	$0.218657\pi$
$114$		0			0
$115$	−0.733831	−	0.894176i	−0.0684301	−	0.0833824i
$116$		0			0
$117$	3.62211	−	11.9405i	0.334864	−	1.10390i
$118$		0			0
$119$	4.57420	+	6.84577i	0.419316	+	0.627551i
$120$		0			0
$121$	9.13233	+	6.10203i	0.830211	+	0.554730i
$122$		0			0
$123$	1.76658	+	1.44980i	0.159287	+	0.130724i
$124$		0			0
$125$	−1.74765	+	3.26962i	−0.156314	+	0.292444i
$126$		0			0
$127$	9.31156			0.826267			0.413133	−	0.910670i	$-0.364434\pi$
$127$	9.31156			0.826267			0.413133	+	0.910670i	$0.364434\pi$
$128$		0			0
$129$	−2.80106			−0.246620
$130$		0			0
$131$	−3.76681	+	7.04721i	−0.329108	+	0.615718i	−0.990997	−	0.133884i	$-0.957255\pi$
$131$	−3.76681	+	7.04721i	−0.329108	+	0.615718i	0.661889	+	0.749602i	$0.269755\pi$
$132$		0			0
$133$	27.3482	+	22.4441i	2.37139	+	1.94615i
$134$		0			0
$135$	0.658919	+	0.440276i	0.0567107	+	0.0378929i
$136$		0			0
$137$	−8.06477	−	12.0698i	−0.689020	−	1.03119i	−0.996816	−	0.0797389i	$-0.974591\pi$
$137$	−8.06477	−	12.0698i	−0.689020	−	1.03119i	0.307796	−	0.951452i	$-0.400409\pi$
$138$		0			0
$139$	3.22072	−	10.6173i	0.273178	−	0.900546i	−0.707798	−	0.706415i	$-0.750311\pi$
$139$	3.22072	−	10.6173i	0.273178	−	0.900546i	0.980976	−	0.194131i	$-0.0621887\pi$
$140$		0			0
$141$	1.83048	+	2.23045i	0.154155	+	0.187838i
$142$		0			0
$143$	−0.518004	+	0.214564i	−0.0433177	+	0.0179428i
$144$		0			0
$145$	2.71667	+	1.12528i	0.225607	+	0.0934495i
$146$		0			0
$147$	−5.24649	−	0.516734i	−0.432723	−	0.0426195i
$148$		0			0
$149$	−17.4822	+	9.34441i	−1.43219	+	0.765524i	−0.991248	−	0.132010i	$-0.957857\pi$
$149$	−17.4822	+	9.34441i	−1.43219	+	0.765524i	−0.440945	+	0.897534i	$0.645357\pi$
$150$		0			0
$151$	−8.69199	−	1.72894i	−0.707344	−	0.140699i	−0.171707	−	0.985148i	$-0.554928\pi$
$151$	−8.69199	−	1.72894i	−0.707344	−	0.140699i	−0.535637	+	0.844449i	$0.679928\pi$
$152$		0			0
$153$	−0.990291	−	4.97853i	−0.0800603	−	0.402490i
$154$		0			0
$155$	−1.29310	+	0.127359i	−0.103864	+	0.0102297i
$156$		0			0
$157$	−12.9411	+	3.92564i	−1.03281	+	0.313301i	−0.760796	−	0.648992i	$-0.775191\pi$
$157$	−12.9411	+	3.92564i	−1.03281	+	0.313301i	−0.272018	+	0.962292i	$0.587691\pi$
$158$		0			0
$159$	1.38133	−	1.38133i	0.109547	−	0.109547i
$160$		0			0
$161$	−10.1293	−	10.1293i	−0.798297	−	0.798297i
$162$		0			0
$163$	−0.763931	−	2.51834i	−0.0598357	−	0.197252i	0.921927	−	0.387365i	$-0.126615\pi$
$163$	−0.763931	−	2.51834i	−0.0598357	−	0.197252i	−0.981762	+	0.190113i	$0.939115\pi$
$164$		0			0
$165$	−0.00170688	−	0.0173302i	−0.000132880	−	0.00134916i
$166$		0			0
$167$	−8.86170	+	1.76270i	−0.685739	+	0.136402i	−0.525650	−	0.850701i	$-0.676178\pi$
$167$	−8.86170	+	1.76270i	−0.685739	+	0.136402i	−0.160089	+	0.987103i	$0.551178\pi$
$168$		0			0
$169$	−1.14844	+	5.77359i	−0.0883415	+	0.444123i
$170$		0			0
$171$	−10.2821	−	19.2365i	−0.786292	−	1.47105i
$172$		0			0
$173$	1.51763	−	15.4087i	0.115383	−	1.17150i	−0.746851	−	0.664992i	$-0.768435\pi$
$173$	1.51763	−	15.4087i	0.115383	−	1.17150i	0.862233	−	0.506511i	$-0.169065\pi$
$174$		0			0
$175$	−8.65878	+	20.9042i	−0.654543	+	1.58021i
$176$		0			0
$177$	0.0979384	+	0.236444i	0.00736150	+	0.0177722i
$178$		0			0
$179$	−4.13352	+	3.39230i	−0.308954	+	0.253552i	−0.776074	−	0.630642i	$-0.782792\pi$
$179$	−4.13352	+	3.39230i	−0.308954	+	0.253552i	0.467120	+	0.884194i	$0.345292\pi$
$180$		0			0
$181$	13.7386	+	4.16756i	1.02118	+	0.309772i	0.756101	−	0.654454i	$-0.227102\pi$
$181$	13.7386	+	4.16756i	1.02118	+	0.309772i	0.265080	+	0.964226i	$0.414602\pi$
$182$		0			0
$183$	0.369595	−	0.246956i	0.0273213	−	0.0182555i
$184$		0			0
$185$	−0.502638	+	0.752251i	−0.0369547	+	0.0553066i
$186$		0			0
$187$	−0.144699	+	0.176317i	−0.0105815	+	0.0128935i
$188$		0			0
$189$	8.65506	+	4.62623i	0.629563	+	0.336509i
$190$		0			0
$191$		−	10.5910i		−	0.766339i	−0.923678	−	0.383170i	$-0.874832\pi$
$191$		−	10.5910i		−	0.766339i	0.923678	−	0.383170i	$-0.125168\pi$
$192$		0			0
$193$			6.71985i			0.483705i	0.970313	+	0.241853i	$0.0777551\pi$
$193$			6.71985i			0.483705i	−0.970313	+	0.241853i	$0.922245\pi$
$194$		0			0
$195$	−0.517332	−	0.276519i	−0.0370469	−	0.0198020i
$196$		0			0
$197$	13.7966	−	16.8112i	0.982964	−	1.19775i	0.00271120	−	0.999996i	$-0.499137\pi$
$197$	13.7966	−	16.8112i	0.982964	−	1.19775i	0.980253	−	0.197749i	$-0.0633630\pi$
$198$		0			0
$199$	−4.27949	+	6.40471i	−0.303365	+	0.454018i	−0.951563	−	0.307454i	$-0.900523\pi$
$199$	−4.27949	+	6.40471i	−0.303365	+	0.454018i	0.648198	+	0.761472i	$0.275523\pi$
$200$		0			0
$201$	0.0189479	−	0.0126606i	0.00133648	−	0.000893008i
$202$		0			0
$203$	34.8466	+	10.5706i	2.44575	+	0.741912i
$204$		0			0
$205$	−1.85088	+	1.51898i	−0.129271	+	0.106090i
$206$		0			0
$207$	3.37974	+	8.15941i	0.234908	+	0.567118i
$208$		0			0
$209$	−0.375073	+	0.905506i	−0.0259443	+	0.0626352i
$210$		0			0
$211$	2.17178	−	22.0505i	0.149512	−	1.51802i	−0.568903	−	0.822404i	$-0.692632\pi$
$211$	2.17178	−	22.0505i	0.149512	−	1.51802i	0.718415	−	0.695615i	$-0.244868\pi$
$212$		0			0
$213$	−1.98499	−	3.71366i	−0.136009	−	0.254456i
$214$		0			0
$215$	0.572537	−	2.87834i	0.0390467	−	0.196301i
$216$		0			0
$217$	−15.7818	+	3.13919i	−1.07134	+	0.213102i
$218$		0			0
$219$	−0.321679	−	3.26606i	−0.0217370	−	0.220700i
$220$		0			0
$221$	2.23034	+	7.35243i	0.150029	+	0.494578i
$222$		0			0
$223$	−10.4639	−	10.4639i	−0.700714	−	0.700714i	0.263850	−	0.964564i	$-0.415008\pi$
$223$	−10.4639	−	10.4639i	−0.700714	−	0.700714i	−0.964564	+	0.263850i	$0.915008\pi$
$224$		0			0
$225$	9.86401	−	9.86401i	0.657601	−	0.657601i
$226$		0			0
$227$	27.9477	−	8.47785i	1.85496	−	0.562694i	0.856001	−	0.516974i	$-0.172942\pi$
$227$	27.9477	−	8.47785i	1.85496	−	0.562694i	0.998954	−	0.0457200i	$-0.0145582\pi$
$228$		0			0
$229$	−20.8861	+	2.05710i	−1.38019	+	0.135937i	−0.760719	−	0.649081i	$-0.775154\pi$
$229$	−20.8861	+	2.05710i	−1.38019	+	0.135937i	−0.619473	+	0.785018i	$0.712654\pi$
$230$		0			0
$231$	−0.0420718	−	0.211509i	−0.00276812	−	0.0139163i
$232$		0			0
$233$	−13.7285	−	2.73077i	−0.899384	−	0.178899i	−0.276317	−	0.961067i	$-0.589114\pi$
$233$	−13.7285	−	2.73077i	−0.899384	−	0.178899i	−0.623068	+	0.782168i	$0.714114\pi$
$234$		0			0
$235$	−2.66613	+	1.42508i	−0.173919	+	0.0929619i
$236$		0			0
$237$	−3.43531	−	0.338349i	−0.223147	−	0.0219781i
$238$		0			0
$239$	−18.0025	−	7.45689i	−1.16449	−	0.482346i	−0.285121	−	0.958492i	$-0.592034\pi$
$239$	−18.0025	−	7.45689i	−1.16449	−	0.482346i	−0.879367	+	0.476145i	$0.842034\pi$
$240$		0			0
$241$	−16.4376	+	6.80868i	−1.05884	+	0.438585i	−0.843039	−	0.537852i	$-0.819236\pi$
$241$	−16.4376	+	6.80868i	−1.05884	+	0.438585i	−0.215800	+	0.976438i	$0.569236\pi$
$242$		0			0
$243$	−5.79971	−	7.06697i	−0.372052	−	0.453346i
$244$		0			0
$245$	1.60337	−	5.28561i	0.102436	−	0.337685i
$246$		0			0
$247$	18.3423	+	27.4512i	1.16709	+	1.74668i
$248$		0			0
$249$	2.49847	+	1.66943i	0.158334	+	0.105796i
$250$		0			0
$251$	−14.5868	−	11.9711i	−0.920713	−	0.755609i	0.0492694	−	0.998786i	$-0.484311\pi$
$251$	−14.5868	−	11.9711i	−0.920713	−	0.755609i	−0.969982	+	0.243176i	$0.921811\pi$
$252$		0			0
$253$	0.187073	−	0.349989i	0.0117612	−	0.0220036i
$254$		0			0
$255$	−0.238632			−0.0149437
$256$		0			0
$257$	−16.7317			−1.04370			−0.521848	−	0.853039i	$-0.674757\pi$
$257$	−16.7317			−1.04370			−0.521848	+	0.853039i	$0.674757\pi$
$258$		0			0
$259$	−5.28151	+	9.88100i	−0.328177	+	0.613976i
$260$		0			0
$261$	−17.3545	−	14.2425i	−1.07422	−	0.881588i
$262$		0			0
$263$	−17.4594	−	11.6660i	−1.07659	−	0.719355i	−0.114869	−	0.993381i	$-0.536645\pi$
$263$	−17.4594	−	11.6660i	−1.07659	−	0.719355i	−0.961723	+	0.274025i	$0.911645\pi$
$264$		0			0
$265$	1.13710	+	1.70179i	0.0698513	+	0.104540i
$266$		0			0
$267$	−1.21764	+	4.01404i	−0.0745187	+	0.245655i
$268$		0			0
$269$	14.7006	+	17.9127i	0.896309	+	1.09216i	0.995278	+	0.0970653i	$0.0309456\pi$
$269$	14.7006	+	17.9127i	0.896309	+	1.09216i	−0.0989689	+	0.995091i	$0.531554\pi$
$270$		0			0
$271$	20.9689	−	8.68559i	1.27377	−	0.527612i	0.359660	−	0.933083i	$-0.382893\pi$
$271$	20.9689	−	8.68559i	1.27377	−	0.527612i	0.914108	+	0.405472i	$0.132893\pi$
$272$		0			0
$273$	−6.71134	−	2.77993i	−0.406189	−	0.168249i
$274$		0			0
$275$	−0.623811	−	0.0614400i	−0.0376172	−	0.00370497i
$276$		0			0
$277$	−9.58056	+	5.12092i	−0.575640	+	0.307686i	−0.733406	−	0.679790i	$-0.762071\pi$
$277$	−9.58056	+	5.12092i	−0.575640	+	0.307686i	0.157766	+	0.987476i	$0.449571\pi$
$278$		0			0
$279$	9.72988	+	1.93539i	0.582513	+	0.115869i
$280$		0			0
$281$	−5.82714	−	29.2950i	−0.347618	−	1.74760i	−0.619250	−	0.785194i	$-0.712563\pi$
$281$	−5.82714	−	29.2950i	−0.347618	−	1.74760i	0.271632	−	0.962401i	$-0.412437\pi$
$282$		0			0
$283$	−12.9430	+	1.27477i	−0.769379	+	0.0757773i	−0.475088	−	0.879938i	$-0.657584\pi$
$283$	−12.9430	+	1.27477i	−0.769379	+	0.0757773i	−0.294292	+	0.955716i	$0.595084\pi$
$284$		0			0
$285$	−0.981256	+	0.297661i	−0.0581246	+	0.0176319i
$286$		0			0
$287$	−20.9669	+	20.9669i	−1.23763	+	1.23763i
$288$		0			0
$289$	−9.81067	−	9.81067i	−0.577098	−	0.577098i
$290$		0			0
$291$	0.144988	+	0.477960i	0.00849932	+	0.0280185i
$292$		0			0
$293$	1.32160	+	13.4185i	0.0772090	+	0.783916i	0.953351	+	0.301863i	$0.0976086\pi$
$293$	1.32160	+	13.4185i	0.0772090	+	0.783916i	−0.876142	+	0.482053i	$0.839891\pi$
$294$		0			0
$295$	−0.262986	+	0.0523111i	−0.0153116	+	0.00304567i
$296$		0			0
$297$	−0.0530406	+	0.266653i	−0.00307773	+	0.0154728i
$298$		0			0
$299$	−6.30158	−	11.7894i	−0.364430	−	0.681800i
$300$		0			0
$301$	3.56225	−	36.1682i	0.205325	−	2.08470i
$302$		0			0
$303$	−1.62445	+	3.92176i	−0.0933220	+	0.225299i
$304$		0			0
$305$	0.178223	+	0.430269i	0.0102050	+	0.0246371i
$306$		0			0
$307$	−0.328760	+	0.269806i	−0.0187633	+	0.0153987i	−0.643728	−	0.765254i	$-0.722613\pi$
$307$	−0.328760	+	0.269806i	−0.0187633	+	0.0153987i	0.624965	+	0.780653i	$0.285113\pi$
$308$		0			0
$309$	0.173417	+	0.0526056i	0.00986537	+	0.00299263i
$310$		0			0
$311$	2.91420	−	1.94721i	0.165249	−	0.110416i	−0.470196	−	0.882562i	$-0.655817\pi$
$311$	2.91420	−	1.94721i	0.165249	−	0.110416i	0.635445	+	0.772146i	$0.280817\pi$
$312$		0			0
$313$	10.3272	−	15.4557i	0.583727	−	0.873609i	−0.415628	−	0.909535i	$-0.636438\pi$
$313$	10.3272	−	15.4557i	0.583727	−	0.873609i	0.999354	+	0.0359260i	$0.0114381\pi$
$314$		0			0
$315$	−3.18991	+	3.88692i	−0.179731	+	0.219003i
$316$		0			0
$317$	19.0697	+	10.1929i	1.07106	+	0.572493i	0.910066	−	0.414463i	$-0.136030\pi$
$317$	19.0697	+	10.1929i	1.07106	+	0.572493i	0.160993	+	0.986956i	$0.448530\pi$
$318$		0			0
$319$			1.00881i			0.0564823i
$320$		0			0
$321$			1.51986i			0.0848302i
$322$		0			0
$323$	11.8450	+	6.33127i	0.659072	+	0.352281i
$324$		0			0
$325$	−13.3951	+	16.3220i	−0.743027	+	0.905381i
$326$		0			0
$327$	0.226320	−	0.338712i	0.0125155	−	0.0187308i
$328$		0			0
$329$	−31.1282	+	20.7992i	−1.71615	+	1.14670i
$330$		0			0
$331$	−13.0526	−	3.95946i	−0.717436	−	0.217632i	−0.0896003	−	0.995978i	$-0.528559\pi$
$331$	−13.0526	−	3.95946i	−0.717436	−	0.217632i	−0.627836	+	0.778346i	$0.716059\pi$
$332$		0			0
$333$	5.33959	−	4.38209i	0.292608	−	0.240137i
$334$		0			0
$335$	0.00913691	+	0.0220584i	0.000499203	+	0.00120518i
$336$		0			0
$337$	−1.10573	+	2.66946i	−0.0602327	+	0.145415i	−0.951130	−	0.308789i	$-0.900076\pi$
$337$	−1.10573	+	2.66946i	−0.0602327	+	0.145415i	0.890898	+	0.454204i	$0.150076\pi$
$338$		0			0
$339$	−0.352778	+	3.58182i	−0.0191603	+	0.194538i
$340$		0			0
$341$	−0.210136	−	0.393137i	−0.0113795	−	0.0212896i
$342$		0			0
$343$	6.98467	−	35.1143i	0.377137	−	1.89599i
$344$		0			0
$345$	0.407211	−	0.0809993i	0.0219235	−	0.00436086i
$346$		0			0
$347$	−0.546202	−	5.54568i	−0.0293217	−	0.297708i	−0.998650	−	0.0519395i	$-0.983460\pi$
$347$	−0.546202	−	5.54568i	−0.0293217	−	0.297708i	0.969329	−	0.245768i	$-0.0790403\pi$
$348$		0			0
$349$	0.942120	+	3.10575i	0.0504306	+	0.166247i	0.978539	−	0.206064i	$-0.0660655\pi$
$349$	0.942120	+	3.10575i	0.0504306	+	0.166247i	−0.928108	+	0.372311i	$0.878565\pi$
$350$		0			0
$351$	6.47584	+	6.47584i	0.345655	+	0.345655i
$352$		0			0
$353$	22.8258	−	22.8258i	1.21489	−	1.21489i	0.245494	−	0.969398i	$-0.421050\pi$
$353$	22.8258	−	22.8258i	1.21489	−	1.21489i	0.969398	−	0.245494i	$-0.0789502\pi$
$354$		0			0
$355$	4.22184	−	1.28068i	0.224072	−	0.0679715i
$356$		0			0
$357$	−2.94095	+	0.289658i	−0.155652	+	0.0153303i
$358$		0			0
$359$	−2.82307	−	14.1925i	−0.148996	−	0.749054i	−0.980958	−	0.194221i	$-0.937782\pi$
$359$	−2.82307	−	14.1925i	−0.148996	−	0.749054i	0.831962	−	0.554833i	$-0.187218\pi$
$360$		0			0
$361$	37.9690	+	7.55251i	1.99837	+	0.397500i
$362$		0			0
$363$	−3.47675	+	1.85836i	−0.182482	+	0.0975386i
$364$		0			0
$365$	3.42191	+	0.337029i	0.179111	+	0.0176409i
$366$		0			0
$367$	1.26026	+	0.522016i	0.0657850	+	0.0272490i	0.415333	−	0.909669i	$-0.363665\pi$
$367$	1.26026	+	0.522016i	0.0657850	+	0.0272490i	−0.349548	+	0.936918i	$0.613665\pi$
$368$		0			0
$369$	16.8894	−	6.99583i	0.879228	−	0.364188i
$370$		0			0
$371$	16.0795	+	19.5929i	0.834804	+	1.01721i
$372$		0			0
$373$	1.53332	−	5.05467i	0.0793922	−	0.261721i	−0.908255	−	0.418418i	$-0.862585\pi$
$373$	1.53332	−	5.05467i	0.0793922	−	0.261721i	0.987647	+	0.156697i	$0.0500847\pi$
$374$		0			0
$375$	−0.739289	−	1.10642i	−0.0381767	−	0.0571355i
$376$		0			0
$377$	28.2548	+	18.8793i	1.45520	+	0.972332i
$378$		0			0
$379$	−5.53334	−	4.54110i	−0.284229	−	0.233260i	0.481466	−	0.876465i	$-0.340105\pi$
$379$	−5.53334	−	4.54110i	−0.284229	−	0.233260i	−0.765694	+	0.643204i	$0.777605\pi$
$380$		0			0
$381$	−1.57549	+	2.94754i	−0.0807150	+	0.151007i
$382$		0			0
$383$	−13.5439			−0.692062			−0.346031	−	0.938223i	$-0.612471\pi$
$383$	−13.5439			−0.692062			−0.346031	+	0.938223i	$0.612471\pi$
$384$		0			0
$385$	0.225944			0.0115152
$386$		0			0
$387$	−10.5623	+	19.7608i	−0.536914	+	1.00450i
$388$		0			0
$389$	17.7527	+	14.5693i	0.900100	+	0.738693i	0.965839	−	0.259144i	$-0.0834404\pi$
$389$	17.7527	+	14.5693i	0.900100	+	0.738693i	−0.0657387	+	0.997837i	$0.520940\pi$
$390$		0			0
$391$	−4.52167	−	3.02128i	−0.228671	−	0.152793i
$392$		0			0
$393$	−1.59344	−	2.38474i	−0.0803782	−	0.120294i
$394$		0			0
$395$	1.04986	−	3.46093i	0.0528242	−	0.174138i
$396$		0			0
$397$	6.04850	+	7.37012i	0.303566	+	0.369896i	0.902342	−	0.431020i	$-0.141846\pi$
$397$	6.04850	+	7.37012i	0.303566	+	0.369896i	−0.598777	+	0.800916i	$0.704346\pi$
$398$		0			0
$399$	−11.7319	+	4.85950i	−0.587329	+	0.243279i
$400$		0			0
$401$	−11.9716	−	4.95878i	−0.597831	−	0.247630i	0.0631846	−	0.998002i	$-0.479874\pi$
$401$	−11.9716	−	4.95878i	−0.597831	−	0.247630i	−0.661016	+	0.750372i	$0.729874\pi$
$402$		0			0
$403$	−14.9436	−	1.47182i	−0.744396	−	0.0733166i
$404$		0			0
$405$	2.60583	−	1.39285i	0.129485	−	0.0692111i
$406$		0			0
$407$	−0.304423	−	0.0605535i	−0.0150897	−	0.00300152i
$408$		0			0
$409$	5.22956	+	26.2908i	0.258585	+	1.29999i	0.863761	+	0.503902i	$0.168103\pi$
$409$	5.22956	+	26.2908i	0.258585	+	1.29999i	−0.605176	+	0.796092i	$0.706897\pi$
$410$		0			0
$411$	5.18519	−	0.510697i	0.255767	−	0.0251908i
$412$		0			0
$413$	−3.17759	+	0.963911i	−0.156359	+	0.0474310i
$414$		0			0
$415$	−2.22617	+	2.22617i	−0.109278	+	0.109278i
$416$		0			0
$417$	2.81593	+	2.81593i	0.137897	+	0.137897i
$418$		0			0
$419$	−5.38764	−	17.7607i	−0.263203	−	0.867665i	−0.984552	−	0.175093i	$-0.943977\pi$
$419$	−5.38764	−	17.7607i	−0.263203	−	0.867665i	0.721349	−	0.692572i	$-0.243523\pi$
$420$		0			0
$421$	−2.93626	−	29.8123i	−0.143104	−	1.45296i	−0.751712	−	0.659492i	$-0.770772\pi$
$421$	−2.93626	−	29.8123i	−0.143104	−	1.45296i	0.608607	−	0.793472i	$-0.291728\pi$
$422$		0			0
$423$	22.6377	−	4.50292i	1.10068	−	0.218939i
$424$		0			0
$425$	−1.67577	+	8.42464i	−0.0812866	+	0.408655i
$426$		0			0
$427$	2.71873	+	5.08639i	0.131569	+	0.246148i
$428$		0			0
$429$	0.0197255	−	0.200276i	0.000952356	−	0.00966943i
$430$		0			0
$431$	−2.04983	+	4.94873i	−0.0987369	+	0.238372i	−0.965528	−	0.260300i	$-0.916179\pi$
$431$	−2.04983	+	4.94873i	−0.0987369	+	0.238372i	0.866791	+	0.498672i	$0.166179\pi$
$432$		0			0
$433$	2.73282	+	6.59761i	0.131331	+	0.317061i	0.975842	−	0.218477i	$-0.0701089\pi$
$433$	2.73282	+	6.59761i	0.131331	+	0.317061i	−0.844511	+	0.535538i	$0.820109\pi$
$434$		0			0
$435$	−0.815858	+	0.669557i	−0.0391174	+	0.0321028i
$436$		0			0
$437$	−22.3618	−	6.78336i	−1.06971	−	0.324492i
$438$		0			0
$439$	−13.0418	+	8.71427i	−0.622452	+	0.415909i	−0.826409	−	0.563071i	$-0.809620\pi$
$439$	−13.0418	+	8.71427i	−0.622452	+	0.415909i	0.203957	+	0.978980i	$0.434620\pi$
$440$		0			0
$441$	−23.4291	+	35.0641i	−1.11567	+	1.66972i
$442$		0			0
$443$	18.1309	−	22.0925i	0.861424	−	1.04965i	−0.136831	−	0.990594i	$-0.543692\pi$
$443$	18.1309	−	22.0925i	0.861424	−	1.04965i	0.998255	−	0.0590537i	$-0.0188083\pi$
$444$		0			0
$445$	−3.87589	−	2.07171i	−0.183735	−	0.0982083i
$446$		0			0
$447$		−	7.11497i		−	0.336527i
$448$		0			0
$449$		−	4.22940i		−	0.199598i	−0.995008	−	0.0997988i	$-0.968180\pi$
$449$		−	4.22940i		−	0.199598i	0.995008	−	0.0997988i	$-0.0318199\pi$
$450$		0			0
$451$	−0.724453	−	0.387228i	−0.0341132	−	0.0182339i
$452$		0			0
$453$	2.01796	−	2.45889i	0.0948119	−	0.115529i
$454$		0			0
$455$	4.22842	−	6.32828i	0.198231	−	0.296674i
$456$		0			0
$457$	−1.04106	+	0.695613i	−0.0486986	+	0.0325394i	−0.579681	−	0.814843i	$-0.696823\pi$
$457$	−1.04106	+	0.695613i	−0.0486986	+	0.0325394i	0.530983	+	0.847383i	$0.321823\pi$
$458$		0			0
$459$	3.56521	+	1.08150i	0.166410	+	0.0504799i
$460$		0			0
$461$	0.107896	−	0.0885481i	0.00502522	−	0.00412409i	−0.631877	−	0.775068i	$-0.717715\pi$
$461$	0.107896	−	0.0885481i	0.00502522	−	0.00412409i	0.636903	+	0.770944i	$0.280215\pi$
$462$		0			0
$463$	9.15289	+	22.0970i	0.425371	+	1.02694i	0.980737	+	0.195330i	$0.0625779\pi$
$463$	9.15289	+	22.0970i	0.425371	+	1.02694i	−0.555367	+	0.831606i	$0.687422\pi$
$464$		0			0
$465$	0.178474	−	0.430875i	0.00827654	−	0.0199813i
$466$		0			0
$467$	−2.14973	+	21.8266i	−0.0994777	+	1.01001i	0.807793	+	0.589466i	$0.200662\pi$
$467$	−2.14973	+	21.8266i	−0.0994777	+	1.01001i	−0.907271	+	0.420547i	$0.861838\pi$
$468$		0			0
$469$	0.139380	+	0.260762i	0.00643598	+	0.0120409i
$470$		0			0
$471$	0.946958	−	4.76068i	0.0436335	−	0.219360i
$472$		0			0
$473$	0.987481	−	0.196422i	0.0454044	−	0.00903150i
$474$		0			0
$475$	3.61783	+	36.7324i	0.165997	+	1.68540i
$476$		0			0
$477$	−4.53616	−	14.9537i	−0.207696	−	0.684684i
$478$		0			0
$479$	8.93487	+	8.93487i	0.408245	+	0.408245i	0.881126	−	0.472881i	$-0.156786\pi$
$479$	8.93487	+	8.93487i	0.408245	+	0.408245i	−0.472881	+	0.881126i	$0.656786\pi$
$480$		0			0
$481$	−7.39310	+	7.39310i	−0.337096	+	0.337096i
$482$		0			0
$483$	4.92023	−	1.49254i	0.223878	−	0.0679127i
$484$		0			0
$485$	−0.520781	+	0.0512925i	−0.0236475	+	0.00232907i
$486$		0			0
$487$	2.44910	+	12.3125i	0.110979	+	0.557931i	0.995765	+	0.0919331i	$0.0293046\pi$
$487$	2.44910	+	12.3125i	0.110979	+	0.557931i	−0.884786	+	0.465998i	$0.845695\pi$
$488$		0			0
$489$	0.926429	+	0.184278i	0.0418946	+	0.00833335i
$490$		0			0
$491$	−16.6140	+	8.88037i	−0.749779	+	0.400765i	−0.801576	−	0.597892i	$-0.796005\pi$
$491$	−16.6140	+	8.88037i	−0.749779	+	0.400765i	0.0517973	+	0.998658i	$0.483505\pi$
$492$		0			0
$493$	13.7575	+	1.35500i	0.619607	+	0.0610260i
$494$		0			0
$495$	−0.128697	−	0.0533079i	−0.00578448	−	0.00239601i
$496$		0			0
$497$	50.4763	−	20.9080i	2.26417	−	0.937850i
$498$		0			0
$499$	23.4285	+	28.5477i	1.04880	+	1.27797i	0.959422	+	0.281975i	$0.0909895\pi$
$499$	23.4285	+	28.5477i	1.04880	+	1.27797i	0.0893830	+	0.995997i	$0.471510\pi$
$500$		0			0
$501$	0.941402	−	3.10339i	0.0420587	−	0.138649i
$502$		0			0
$503$	−7.33000	−	10.9701i	−0.326828	−	0.489133i	0.631274	−	0.775560i	$-0.282532\pi$
$503$	−7.33000	−	10.9701i	−0.326828	−	0.489133i	−0.958102	+	0.286427i	$0.907532\pi$
$504$		0			0
$505$	−3.69792	−	2.47087i	−0.164555	−	0.109952i
$506$		0			0
$507$	−1.63330	−	1.34041i	−0.0725374	−	0.0595299i
$508$		0			0
$509$	3.68184	−	6.88824i	0.163195	−	0.305316i	−0.787011	−	0.616939i	$-0.788373\pi$
$509$	3.68184	−	6.88824i	0.163195	−	0.305316i	0.950206	+	0.311623i	$0.100873\pi$
$510$		0			0
$511$	42.5814			1.88369
$512$		0			0
$513$	16.0092			0.706823
$514$		0			0
$515$	−0.0895033	+	0.167449i	−0.00394399	+	0.00737868i
$516$		0			0
$517$	−0.801723	−	0.657957i	−0.0352597	−	0.0289369i
$518$		0			0
$519$	4.62080	+	3.08752i	0.202831	+	0.135527i
$520$		0			0
$521$	17.1010	+	25.5935i	0.749210	+	1.12127i	0.988632	+	0.150357i	$0.0480422\pi$
$521$	17.1010	+	25.5935i	0.749210	+	1.12127i	−0.239422	+	0.970916i	$0.576958\pi$
$522$		0			0
$523$	5.58974	−	18.4269i	0.244422	−	0.805752i	−0.745790	−	0.666181i	$-0.767928\pi$
$523$	5.58974	−	18.4269i	0.244422	−	0.805752i	0.990212	−	0.139571i	$-0.0445723\pi$
$524$		0			0
$525$	−5.15210	−	6.27785i	−0.224856	−	0.273988i
$526$		0			0
$527$	−5.64362	+	2.33767i	−0.245840	+	0.101830i
$528$		0			0
$529$	−12.5078	−	5.18088i	−0.543815	−	0.225256i
$530$		0			0
$531$	2.03736	+	0.200662i	0.0884139	+	0.00870801i
$532$		0			0
$533$	−24.4033	+	13.0438i	−1.05702	+	0.564991i
$534$		0			0
$535$	−1.56179	−	0.310659i	−0.0675220	−	0.0134310i
$536$		0			0
$537$	−0.374437	−	1.88242i	−0.0161582	−	0.0812325i
$538$		0			0
$539$	1.88582	−	0.185737i	0.0812280	−	0.00800026i
$540$		0			0
$541$	−5.92382	+	1.79697i	−0.254685	+	0.0772578i	−0.415045	−	0.909801i	$-0.636234\pi$
$541$	−5.92382	+	1.79697i	−0.254685	+	0.0772578i	0.160361	+	0.987059i	$0.448734\pi$
$542$		0			0
$543$	−3.64377	+	3.64377i	−0.156369	+	0.156369i
$544$		0			0
$545$	0.301797	+	0.301797i	0.0129275	+	0.0129275i
$546$		0			0
$547$	9.80424	+	32.3203i	0.419199	+	1.38191i	0.871652	+	0.490126i	$0.163049\pi$
$547$	9.80424	+	32.3203i	0.419199	+	1.38191i	−0.452452	+	0.891789i	$0.649451\pi$
$548$		0			0
$549$	−0.348524	−	3.53863i	−0.0148746	−	0.151025i
$550$		0			0
$551$	58.2611	−	11.5888i	2.48201	−	0.493702i
$552$		0			0
$553$	8.73772	−	43.9275i	0.371566	−	1.86799i
$554$		0			0
$555$	−0.153077	−	0.286388i	−0.00649777	−	0.0121565i
$556$		0			0
$557$	−3.55510	+	36.0956i	−0.150635	+	1.52942i	0.561560	+	0.827436i	$0.310201\pi$
$557$	−3.55510	+	36.0956i	−0.150635	+	1.52942i	−0.712195	+	0.701982i	$0.752299\pi$
$558$		0			0
$559$	12.9787	−	31.3335i	0.548942	−	1.32526i
$560$		0			0
$561$	−0.0313296	−	0.0756364i	−0.00132274	−	0.00319337i
$562$		0			0
$563$	11.5131	−	9.44860i	0.485221	−	0.398211i	−0.359728	−	0.933057i	$-0.617131\pi$
$563$	11.5131	−	9.44860i	0.485221	−	0.398211i	0.844949	+	0.534846i	$0.179631\pi$
$564$		0			0
$565$	−3.60853	−	1.09463i	−0.151812	−	0.0460516i
$566$		0			0
$567$	30.4241	−	20.3288i	1.27769	−	0.853727i
$568$		0			0
$569$	−5.71722	+	8.55642i	−0.239678	+	0.358704i	−0.931735	−	0.363139i	$-0.881705\pi$
$569$	−5.71722	+	8.55642i	−0.239678	+	0.358704i	0.692057	+	0.721843i	$0.256705\pi$
$570$		0			0
$571$	−3.52558	+	4.29593i	−0.147541	+	0.179779i	−0.841537	−	0.540200i	$-0.818349\pi$
$571$	−3.52558	+	4.29593i	−0.147541	+	0.179779i	0.693996	+	0.719979i	$0.255849\pi$
$572$		0			0
$573$	3.35255	+	1.79198i	0.140055	+	0.0748609i
$574$		0			0
$575$		−	14.9449i		−	0.623247i
$576$		0			0
$577$			32.1848i			1.33987i	0.742419	+	0.669936i	$0.233678\pi$
$577$			32.1848i			1.33987i	−0.742419	+	0.669936i	$0.766322\pi$
$578$		0			0
$579$	−2.12715	−	1.13698i	−0.0884012	−	0.0472514i
$580$		0			0
$581$	−24.7336	+	30.1379i	−1.02612	+	1.25033i
$582$		0			0
$583$	−0.390107	+	0.583837i	−0.0161566	+	0.0241800i
$584$		0			0
$585$	−3.90154	+	2.60693i	−0.161309	+	0.107783i
$586$		0			0
$587$	−7.29998	−	2.21442i	−0.301302	−	0.0913991i	0.136014	−	0.990707i	$-0.456571\pi$
$587$	−7.29998	−	2.21442i	−0.301302	−	0.0913991i	−0.437316	+	0.899308i	$0.644071\pi$
$588$		0			0
$589$	−20.2907	+	16.6521i	−0.836063	+	0.686139i
$590$		0			0
$591$	2.98717	+	7.21166i	0.122876	+	0.296648i
$592$		0			0
$593$	8.92437	−	21.5453i	0.366480	−	0.884761i	−0.627842	−	0.778341i	$-0.716061\pi$
$593$	8.92437	−	21.5453i	0.366480	−	0.884761i	0.994321	−	0.106419i	$-0.0339386\pi$
$594$		0			0
$595$	0.303481	−	3.08129i	0.0124415	−	0.126321i
$596$		0			0
$597$	−1.30331	−	2.43832i	−0.0533409	−	0.0997939i
$598$		0			0
$599$	−4.51458	+	22.6963i	−0.184461	+	0.927346i	0.772031	+	0.635585i	$0.219241\pi$
$599$	−4.51458	+	22.6963i	−0.184461	+	0.927346i	−0.956491	+	0.291761i	$0.905759\pi$
$600$		0			0
$601$	24.8283	−	4.93867i	1.01277	−	0.201452i	0.339308	−	0.940675i	$-0.389807\pi$
$601$	24.8283	−	4.93867i	1.01277	−	0.201452i	0.673461	+	0.739223i	$0.264807\pi$
$602$		0			0
$603$	−0.0178677	−	0.181413i	−0.000727627	−	0.00738772i
$604$		0			0
$605$	−1.19898	−	3.95251i	−0.0487455	−	0.160692i
$606$		0			0
$607$	−3.69678	−	3.69678i	−0.150048	−	0.150048i	0.628092	−	0.778139i	$-0.283836\pi$
$607$	−3.69678	−	3.69678i	−0.150048	−	0.150048i	−0.778139	+	0.628092i	$0.783836\pi$
$608$		0			0
$609$	−9.24207	+	9.24207i	−0.374507	+	0.374507i
$610$		0			0
$611$	−33.4320	+	10.1415i	−1.35251	+	0.410280i
$612$		0			0
$613$	−23.5566	+	2.32013i	−0.951444	+	0.0937090i	−0.561815	−	0.827263i	$-0.689897\pi$
$613$	−23.5566	+	2.32013i	−0.951444	+	0.0937090i	−0.389629	+	0.920972i	$0.627397\pi$
$614$		0			0
$615$	−0.167663	−	0.842899i	−0.00676083	−	0.0339890i
$616$		0			0
$617$	7.67201	+	1.52606i	0.308863	+	0.0614367i	0.347088	−	0.937832i	$-0.387170\pi$
$617$	7.67201	+	1.52606i	0.308863	+	0.0614367i	−0.0382250	+	0.999269i	$0.512170\pi$
$618$		0			0
$619$	−42.7018	+	22.8246i	−1.71633	+	0.917398i	−0.749493	+	0.662013i	$0.769702\pi$
$619$	−42.7018	+	22.8246i	−1.71633	+	0.917398i	−0.966839	+	0.255386i	$0.917798\pi$
$620$		0			0
$621$	−6.45091	−	0.635359i	−0.258866	−	0.0254961i
$622$		0			0
$623$	−50.2819	−	20.8274i	−2.01450	−	0.834434i
$624$		0			0
$625$	−21.1557	+	8.76296i	−0.846226	+	0.350518i
$626$		0			0
$627$	−0.223174	−	0.271938i	−0.00891269	−	0.0108601i
$628$		0			0
$629$	−1.23468	+	4.07021i	−0.0492301	+	0.162290i
$630$		0			0
$631$	−12.1499	−	18.1836i	−0.483679	−	0.723876i	0.506721	−	0.862110i	$-0.330857\pi$
$631$	−12.1499	−	18.1836i	−0.483679	−	0.723876i	−0.990400	+	0.138234i	$0.955857\pi$
$632$		0			0
$633$	6.61255	+	4.41837i	0.262825	+	0.175614i
$634$		0			0
$635$	−2.70683	−	2.22144i	−0.107417	−	0.0881550i
$636$		0			0
$637$	30.0900	−	56.2943i	1.19221	−	2.23046i
$638$		0			0
$639$	−33.6840			−1.33252
$640$		0			0
$641$	−1.17029			−0.0462237			−0.0231119	−	0.999733i	$-0.507357\pi$
$641$	−1.17029			−0.0462237			−0.0231119	+	0.999733i	$0.507357\pi$
$642$		0			0
$643$	10.5190	−	19.6797i	0.414830	−	0.776092i	−0.584548	−	0.811359i	$-0.698728\pi$
$643$	10.5190	−	19.6797i	0.414830	−	0.776092i	0.999378	+	0.0352672i	$0.0112282\pi$
$644$		0			0
$645$	0.814257	+	0.668243i	0.0320613	+	0.0263121i
$646$		0			0
$647$	4.24214	+	2.83450i	0.166776	+	0.111436i	0.636157	−	0.771560i	$-0.280523\pi$
$647$	4.24214	+	2.83450i	0.166776	+	0.111436i	−0.469381	+	0.882996i	$0.655523\pi$
$648$		0			0
$649$	−0.0511074	−	0.0764876i	−0.00200614	−	0.00300240i
$650$		0			0
$651$	1.67654	−	5.52682i	0.0657089	−	0.216613i
$652$		0			0
$653$	−4.04579	−	4.92981i	−0.158324	−	0.192918i	0.687807	−	0.725894i	$-0.258574\pi$
$653$	−4.04579	−	4.92981i	−0.158324	−	0.192918i	−0.846131	+	0.532976i	$0.821074\pi$
$654$		0			0
$655$	2.77623	−	1.14995i	0.108476	−	0.0449324i
$656$		0			0
$657$	−24.2542	−	10.0464i	−0.946245	−	0.391948i
$658$		0			0
$659$	23.4653	+	2.31113i	0.914076	+	0.0900287i	0.544108	−	0.839015i	$-0.316868\pi$
$659$	23.4653	+	2.31113i	0.914076	+	0.0900287i	0.369969	+	0.929044i	$0.379368\pi$
$660$		0			0
$661$	14.2906	−	7.63849i	0.555840	−	0.297103i	−0.169458	−	0.985537i	$-0.554202\pi$
$661$	14.2906	−	7.63849i	0.555840	−	0.297103i	0.725298	+	0.688435i	$0.241702\pi$
$662$		0			0
$663$	−2.70476	−	0.538009i	−0.105044	−	0.0208946i
$664$		0			0
$665$	−2.59557	−	13.0488i	−0.100652	−	0.506011i
$666$		0			0
$667$	−23.9363	+	2.35752i	−0.926816	+	0.0912834i
$668$		0			0
$669$	5.08278	−	1.54184i	0.196511	−	0.0596111i
$670$		0			0
$671$	−0.112979	+	0.112979i	−0.00436149	+	0.00436149i
$672$		0			0
$673$	−6.41513	−	6.41513i	−0.247285	−	0.247285i	0.572570	−	0.819856i	$-0.305946\pi$
$673$	−6.41513	−	6.41513i	−0.247285	−	0.247285i	−0.819856	+	0.572570i	$0.805946\pi$
$674$		0			0
$675$	2.97212	+	9.79777i	0.114397	+	0.377116i
$676$		0			0
$677$	−3.45206	−	35.0494i	−0.132673	−	1.34706i	−0.798971	−	0.601370i	$-0.794622\pi$
$677$	−3.45206	−	35.0494i	−0.132673	−	1.34706i	0.666297	−	0.745686i	$-0.267878\pi$
$678$		0			0
$679$	−6.35595	+	1.26428i	−0.243919	+	0.0485185i
$680$		0			0
$681$	−2.04506	+	10.2812i	−0.0783667	+	0.393976i
$682$		0			0
$683$	0.766540	+	1.43409i	0.0293308	+	0.0548741i	0.896160	−	0.443732i	$-0.146346\pi$
$683$	0.766540	+	1.43409i	0.0293308	+	0.0548741i	−0.866829	+	0.498606i	$0.833846\pi$
$684$		0			0
$685$	−0.535067	+	5.43263i	−0.0204439	+	0.207570i
$686$		0			0
$687$	2.88271	−	6.95948i	0.109982	−	0.265521i
$688$		0			0
$689$	9.05155	+	21.8524i	0.344837	+	0.832509i
$690$		0			0
$691$	29.6592	−	24.3407i	1.12829	−	0.925963i	0.130436	−	0.991457i	$-0.458362\pi$
$691$	29.6592	−	24.3407i	1.12829	−	0.925963i	0.997853	+	0.0654936i	$0.0208622\pi$
$692$		0			0
$693$	−1.65079	−	0.500761i	−0.0627082	−	0.0190223i
$694$		0			0
$695$	−3.46919	+	2.31804i	−0.131594	+	0.0879282i
$696$		0			0
$697$	−6.25385	+	9.35955i	−0.236882	+	0.354518i
$698$		0			0
$699$	3.18725	−	3.88367i	0.120553	−	0.146894i
$700$		0			0
$701$	15.7454	+	8.41608i	0.594695	+	0.317871i	0.741143	−	0.671347i	$-0.234284\pi$
$701$	15.7454	+	8.41608i	0.594695	+	0.317871i	−0.146448	+	0.989218i	$0.546784\pi$
$702$		0			0
$703$			18.2768i			0.689322i
$704$		0			0
$705$		−	1.08508i		−	0.0408663i
$706$		0			0
$707$	−48.5730	−	25.9628i	−1.82678	−	0.976433i
$708$		0			0
$709$	20.9493	−	25.5268i	0.786767	−	0.958679i	−0.213064	−	0.977038i	$-0.568344\pi$
$709$	20.9493	−	25.5268i	0.786767	−	0.958679i	0.999831	+	0.0183593i	$0.00584428\pi$
$710$		0			0
$711$	−15.3410	+	22.9594i	−0.575331	+	0.861043i
$712$		0			0
$713$	8.83702	−	5.90471i	0.330949	−	0.221133i
$714$		0			0
$715$	0.201770	+	0.0612061i	0.00754575	+	0.00228898i
$716$		0			0
$717$	5.40644	−	4.43695i	0.201907	−	0.165701i
$718$		0			0
$719$	−2.14045	−	5.16750i	−0.0798253	−	0.192715i	0.878928	−	0.476954i	$-0.158259\pi$
$719$	−2.14045	−	5.16750i	−0.0798253	−	0.192715i	−0.958754	+	0.284239i	$0.908259\pi$
$720$		0			0
$721$	−0.899802	+	2.17231i	−0.0335104	+	0.0809012i
$722$		0			0
$723$	0.625941	−	6.35528i	0.0232790	−	0.236355i
$724$		0			0
$725$	17.9087	+	33.5048i	0.665113	+	1.24434i
$726$		0			0
$727$	1.35886	−	6.83144i	0.0503972	−	0.253364i	−0.947371	−	0.320138i	$-0.896271\pi$
$727$	1.35886	−	6.83144i	0.0503972	−	0.253364i	0.997768	+	0.0667741i	$0.0212707\pi$
$728$		0			0
$729$	−19.9001	+	3.95839i	−0.737042	+	0.146607i
$730$		0			0
$731$	−1.35234	−	13.7305i	−0.0500180	−	0.507841i
$732$		0			0
$733$	−2.58694	−	8.52799i	−0.0955507	−	0.314989i	0.896116	−	0.443821i	$-0.146377\pi$
$733$	−2.58694	−	8.52799i	−0.0955507	−	0.314989i	−0.991666	+	0.128832i	$0.958877\pi$
$734$		0			0
$735$	1.40185	+	1.40185i	0.0517082	+	0.0517082i
$736$		0			0
$737$	−0.00579203	+	0.00579203i	−0.000213352	+	0.000213352i
$738$		0			0
$739$	32.1860	−	9.76351i	1.18398	−	0.359157i	0.363919	−	0.931431i	$-0.381439\pi$
$739$	32.1860	−	9.76351i	1.18398	−	0.359157i	0.820062	+	0.572274i	$0.193939\pi$
$740$		0			0
$741$	−11.7931	+	1.16151i	−0.433229	+	0.0426693i
$742$		0			0
$743$	−1.71980	−	8.64601i	−0.0630933	−	0.317191i	0.936331	−	0.351118i	$-0.114199\pi$
$743$	−1.71980	−	8.64601i	−0.0630933	−	0.317191i	−0.999424	+	0.0339272i	$0.989199\pi$
$744$		0			0
$745$	7.31126	+	1.45430i	0.267864	+	0.0532814i
$746$		0			0
$747$	21.1987	−	11.3309i	0.775619	−	0.414577i
$748$		0			0
$749$	−19.6249	−	1.93288i	−0.717077	−	0.0706259i
$750$		0			0
$751$	25.7504	+	10.6662i	0.939647	+	0.389214i	0.799330	−	0.600892i	$-0.205188\pi$
$751$	25.7504	+	10.6662i	0.939647	+	0.389214i	0.140317	+	0.990107i	$0.455188\pi$
$752$		0			0
$753$	6.25747	−	2.59193i	0.228035	−	0.0944552i
$754$		0			0
$755$	2.11425	+	2.57622i	0.0769455	+	0.0937584i
$756$		0			0
$757$	4.53676	−	14.9557i	0.164892	−	0.543574i	−0.835087	−	0.550118i	$-0.814583\pi$
$757$	4.53676	−	14.9557i	0.164892	−	0.543574i	0.999979	+	0.00654331i	$0.00208281\pi$
$758$		0			0
$759$	0.0791355	+	0.118435i	0.00287244	+	0.00429890i
$760$		0			0
$761$	−34.4234	−	23.0010i	−1.24785	−	0.833785i	−0.256692	−	0.966493i	$-0.582633\pi$
$761$	−34.4234	−	23.0010i	−1.24785	−	0.833785i	−0.991155	+	0.132709i	$0.957633\pi$
$762$		0			0
$763$	4.08573	+	3.35307i	0.147913	+	0.121389i
$764$		0			0
$765$	−0.899843	+	1.68349i	−0.0325339	+	0.0608666i
$766$		0			0
$767$	−3.09873			−0.111889
$768$		0			0
$769$	6.84793			0.246943			0.123471	−	0.992348i	$-0.460597\pi$
$769$	6.84793			0.246943			0.123471	+	0.992348i	$0.460597\pi$
$770$		0			0
$771$	2.83097	−	5.29637i	0.101955	−	0.190744i
$772$		0			0
$773$	−16.4694	−	13.5161i	−0.592362	−	0.486139i	0.289799	−	0.957088i	$-0.406412\pi$
$773$	−16.4694	−	13.5161i	−0.592362	−	0.486139i	−0.882160	+	0.470949i	$0.843912\pi$
$774$		0			0
$775$	−13.9582	−	9.32660i	−0.501395	−	0.335021i
$776$		0			0
$777$	−2.23418	−	3.34369i	−0.0801508	−	0.119954i
$778$		0			0
$779$	−14.0411	+	46.2873i	−0.503075	+	1.65841i
$780$		0			0
$781$	0.960201	+	1.17001i	0.0343587	+	0.0418662i
$782$		0			0
$783$	15.2236	−	6.30581i	0.544046	−	0.225351i
$784$		0			0
$785$	4.69846	+	1.94616i	0.167695	+	0.0694616i
$786$		0			0
$787$	−50.3252	−	4.95660i	−1.79390	−	0.176684i	−0.854487	−	0.519473i	$-0.826128\pi$
$787$	−50.3252	−	4.95660i	−1.79390	−	0.176684i	−0.939412	+	0.342790i	$0.888628\pi$
$788$		0			0
$789$	6.64692	−	3.55285i	0.236637	−	0.126485i
$790$		0			0
$791$	−45.8009	−	9.11036i	−1.62849	−	0.323927i
$792$		0			0
$793$	1.04999	+	5.27866i	0.0372863	+	0.187451i
$794$		0			0
$795$	−0.731089	+	0.0720059i	−0.0259290	+	0.00255379i
$796$		0			0
$797$	−7.34470	+	2.22799i	−0.260163	+	0.0789195i	−0.417672	−	0.908598i	$-0.637154\pi$
$797$	−7.34470	+	2.22799i	−0.260163	+	0.0789195i	0.157509	+	0.987518i	$0.449654\pi$
$798$		0			0
$799$	−10.0497	+	10.0497i	−0.355532	+	0.355532i
$800$		0			0
$801$	23.7264	+	23.7264i	0.838332	+	0.838332i
$802$		0			0
$803$	0.342433	+	1.12885i	0.0120842	+	0.0398363i
$804$		0			0
$805$	0.528017	+	5.36104i	0.0186101	+	0.188952i
$806$		0			0
$807$	−8.15750	+	1.62263i	−0.287158	+	0.0571192i
$808$		0			0
$809$	0.571512	−	2.87319i	0.0200933	−	0.101016i	−0.969437	−	0.245339i	$-0.921101\pi$
$809$	0.571512	−	2.87319i	0.0200933	−	0.101016i	0.989531	+	0.144324i	$0.0461006\pi$
$810$		0			0
$811$	5.14446	+	9.62460i	0.180646	+	0.337966i	0.955904	−	0.293680i	$-0.0948799\pi$
$811$	5.14446	+	9.62460i	0.180646	+	0.337966i	−0.775258	+	0.631645i	$0.782380\pi$
$812$		0			0
$813$	−0.798490	+	8.10721i	−0.0280043	+	0.284332i
$814$		0			0
$815$	−0.378724	+	0.914321i	−0.0132661	+	0.0320273i
$816$		0			0
$817$	−22.6877	−	54.7730i	−0.793743	−	1.91627i
$818$		0			0
$819$	−44.9190	+	36.8641i	−1.56960	+	1.28814i
$820$		0			0
$821$	36.9919	+	11.2214i	1.29103	+	0.391628i	0.859807	−	0.510619i	$-0.170584\pi$
$821$	36.9919	+	11.2214i	1.29103	+	0.391628i	0.431219	+	0.902247i	$0.358084\pi$
$822$		0			0
$823$	−38.5367	+	25.7494i	−1.34330	+	0.897567i	−0.999145	−	0.0413437i	$-0.986836\pi$
$823$	−38.5367	+	25.7494i	−1.34330	+	0.897567i	−0.344160	+	0.938911i	$0.611836\pi$
$824$		0			0
$825$	0.124996	−	0.187070i	0.00435180	−	0.00651293i
$826$		0			0
$827$	34.8921	−	42.5162i	1.21332	−	1.47843i	0.380597	−	0.924741i	$-0.375719\pi$
$827$	34.8921	−	42.5162i	1.21332	−	1.47843i	0.832722	−	0.553692i	$-0.186781\pi$
$828$		0			0
$829$	−20.5059	−	10.9606i	−0.712200	−	0.380679i	0.0751605	−	0.997171i	$-0.476053\pi$
$829$	−20.5059	−	10.9606i	−0.712200	−	0.380679i	−0.787361	+	0.616492i	$0.788553\pi$
$830$		0			0
$831$		−	3.89914i		−	0.135260i
$832$		0			0
$833$		−	25.9672i		−	0.899710i
$834$		0			0
$835$	2.99658	+	1.60171i	0.103701	+	0.0554293i
$836$		0			0
$837$	−4.61919	+	5.62850i	−0.159663	+	0.194549i
$838$		0			0
$839$	1.72866	−	2.58713i	0.0596801	−	0.0893175i	−0.800429	−	0.599427i	$-0.795395\pi$
$839$	1.72866	−	2.58713i	0.0596801	−	0.0893175i	0.860109	+	0.510110i	$0.170395\pi$
$840$		0			0
$841$	26.7247	−	17.8569i	0.921542	−	0.615755i
$842$		0			0
$843$	10.2592	+	3.11209i	0.353345	+	0.107186i
$844$		0			0
$845$	1.71124	−	1.40438i	0.0588684	−	0.0483121i
$846$		0			0
$847$	−19.5741	−	47.2561i	−0.672575	−	1.62374i
$848$		0			0
$849$	1.78640	−	4.31274i	0.0613089	−	0.148013i
$850$		0			0
$851$	0.725354	−	7.36465i	0.0248648	−	0.252457i
$852$		0			0
$853$	13.0066	+	24.3337i	0.445338	+	0.833169i	0.999999	+	0.00109256i	$0.000347772\pi$
$853$	13.0066	+	24.3337i	0.445338	+	0.833169i	−0.554661	+	0.832076i	$0.687152\pi$
$854$		0			0
$855$	−1.60024	+	8.04493i	−0.0547269	+	0.275131i
$856$		0			0
$857$	−46.4102	+	9.23157i	−1.58534	+	0.315344i	−0.907562	−	0.419919i	$-0.862059\pi$
$857$	−46.4102	+	9.23157i	−1.58534	+	0.315344i	−0.677782	+	0.735263i	$0.737059\pi$
$858$		0			0
$859$	−3.03008	−	30.7649i	−0.103385	−	1.04969i	−0.897229	−	0.441565i	$-0.854424\pi$
$859$	−3.03008	−	30.7649i	−0.103385	−	1.04969i	0.793844	−	0.608121i	$-0.208076\pi$
$860$		0			0
$861$	−3.08945	−	10.1845i	−0.105288	−	0.347088i
$862$		0			0
$863$	30.6853	+	30.6853i	1.04454	+	1.04454i	0.998961	+	0.0455796i	$0.0145135\pi$
$863$	30.6853	+	30.6853i	1.04454	+	1.04454i	0.0455796	+	0.998961i	$0.485487\pi$
$864$		0			0
$865$	−4.11719	+	4.11719i	−0.139989	+	0.139989i
$866$		0			0
$867$	4.76548	−	1.44559i	0.161844	−	0.0490949i
$868$		0			0
$869$	1.23480	−	0.121618i	0.0418878	−	0.00412559i
$870$		0			0
$871$	0.0538295	+	0.270619i	0.00182394	+	0.00916958i
$872$		0			0
$873$	3.91861	+	0.779459i	0.132625	+	0.0263807i
$874$		0			0
$875$	15.2267	−	8.13883i	0.514756	−	0.275143i
$876$		0			0
$877$	−5.42796	−	0.534608i	−0.183289	−	0.0180524i	0.00595603	−	0.999982i	$-0.498104\pi$
$877$	−5.42796	−	0.534608i	−0.183289	−	0.0180524i	−0.189245	+	0.981930i	$0.560604\pi$
$878$		0			0
$879$	−4.47119	−	1.85203i	−0.150809	−	0.0624673i
$880$		0			0
$881$	−34.5822	+	14.3244i	−1.16510	+	0.482601i	−0.879571	−	0.475768i	$-0.842170\pi$
$881$	−34.5822	+	14.3244i	−1.16510	+	0.482601i	−0.285532	+	0.958369i	$0.592170\pi$
$882$		0			0
$883$	−4.07951	−	4.97090i	−0.137287	−	0.167284i	0.699829	−	0.714311i	$-0.253260\pi$
$883$	−4.07951	−	4.97090i	−0.137287	−	0.167284i	−0.837115	+	0.547027i	$0.815760\pi$
$884$		0			0
$885$	0.0279377	−	0.0920982i	0.000939115	−	0.00309585i
$886$		0			0
$887$	14.0664	+	21.0518i	0.472303	+	0.706851i	0.988768	−	0.149457i	$-0.0477526\pi$
$887$	14.0664	+	21.0518i	0.472303	+	0.706851i	−0.516465	+	0.856308i	$0.672753\pi$
$888$		0			0
$889$	−36.0559	−	24.0918i	−1.20928	−	0.808013i
$890$		0			0
$891$	0.783590	+	0.643076i	0.0262513	+	0.0215438i
$892$		0			0
$893$	−28.7887	+	53.8599i	−0.963377	+	1.80235i
$894$		0			0
$895$	2.01089			0.0672166
$896$		0			0
$897$	4.79812			0.160204
$898$		0			0
$899$	−12.7359	+	23.8272i	−0.424766	+	0.794681i
$900$		0			0
$901$	7.43804	+	6.10424i	0.247797	+	0.203362i
$902$		0			0
$903$	10.8462	+	7.24719i	0.360939	+	0.241171i
$904$		0			0
$905$	−2.99950	−	4.48907i	−0.0997069	−	0.149222i
$906$		0			0
$907$	−5.00064	+	16.4849i	−0.166044	+	0.547372i	−0.999990	−	0.00447315i	$-0.998576\pi$
$907$	−5.00064	+	16.4849i	−0.166044	+	0.547372i	0.833946	+	0.551845i	$0.186076\pi$
$908$		0			0
$909$	21.5415	+	26.2484i	0.714485	+	0.870603i
$910$		0			0
$911$	3.61155	−	1.49595i	0.119656	−	0.0495632i	−0.322052	−	0.946722i	$-0.604373\pi$
$911$	3.61155	−	1.49595i	0.119656	−	0.0495632i	0.441708	+	0.897159i	$0.354373\pi$
$912$		0			0
$913$	−0.997873	−	0.413332i	−0.0330248	−	0.0136793i
$914$		0			0
$915$	−0.166355	−	0.0163846i	−0.00549954	−	0.000541657i
$916$		0			0
$917$	32.8190	−	17.5421i	1.08378	−	0.579292i
$918$		0			0
$919$	8.92639	+	1.77557i	0.294454	+	0.0585706i	0.340107	−	0.940387i	$-0.389537\pi$
$919$	8.92639	+	1.77557i	0.294454	+	0.0585706i	−0.0456526	+	0.998957i	$0.514537\pi$
$920$		0			0
$921$	−0.0297809	−	0.149719i	−0.000981313	−	0.00493340i
$922$		0			0
$923$	50.7395	−	4.99740i	1.67011	−	0.164491i
$924$		0			0
$925$	−11.1856	+	3.39310i	−0.367779	+	0.111565i
$926$		0			0
$927$	1.02505	−	1.02505i	0.0336669	−	0.0336669i
$928$		0			0
$929$	8.14581	+	8.14581i	0.267255	+	0.267255i	0.827993	−	0.560738i	$-0.189483\pi$
$929$	8.14581	+	8.14581i	0.267255	+	0.267255i	−0.560738	+	0.827993i	$0.689483\pi$
$930$		0			0
$931$	−32.3905	−	106.777i	−1.06156	−	3.49948i
$932$		0			0
$933$	0.123306	+	1.25194i	0.00403684	+	0.0409868i
$934$		0			0
$935$	0.0841269	−	0.0167339i	0.00275124	−	0.000547256i
$936$		0			0
$937$	2.79659	−	14.0594i	0.0913607	−	0.459301i	−0.907840	−	0.419318i	$-0.862269\pi$
$937$	2.79659	−	14.0594i	0.0913607	−	0.459301i	0.999200	−	0.0399837i	$-0.0127306\pi$
$938$		0			0
$939$	3.14512	+	5.88411i	0.102637	+	0.192021i
$940$		0			0
$941$	3.70748	−	37.6427i	0.120860	−	1.22712i	−0.723112	−	0.690731i	$-0.757289\pi$
$941$	3.70748	−	37.6427i	0.120860	−	1.22712i	0.843973	−	0.536386i	$-0.180211\pi$
$942$		0			0
$943$	7.49488	−	18.0943i	0.244067	−	0.589230i
$944$		0			0
$945$	−1.41232	−	3.40964i	−0.0459428	−	0.110916i
$946$		0			0
$947$	−18.2310	+	14.9618i	−0.592428	+	0.486193i	−0.882183	−	0.470908i	$-0.843926\pi$
$947$	−18.2310	+	14.9618i	−0.592428	+	0.486193i	0.289754	+	0.957101i	$0.406426\pi$
$948$		0			0
$949$	38.0255	+	11.5349i	1.23436	+	0.374439i
$950$		0			0
$951$	−6.45309	+	4.31182i	−0.209256	+	0.139820i
$952$		0			0
$953$	16.6556	−	24.9268i	0.539526	−	0.807458i	−0.457110	−	0.889410i	$-0.651115\pi$
$953$	16.6556	−	24.9268i	0.539526	−	0.807458i	0.996636	+	0.0819520i	$0.0261154\pi$
$954$		0			0
$955$	−2.52667	+	3.07876i	−0.0817613	+	0.0996264i
$956$		0			0
$957$	−0.319334	−	0.170688i	−0.0103226	−	0.00551755i
$958$		0			0
$959$			67.6022i			2.18299i
$960$		0			0
$961$			19.0615i			0.614887i
$962$		0			0
$963$	10.7222	+	5.73113i	0.345518	+	0.184683i
$964$		0			0
$965$	1.60314	−	1.95343i	0.0516069	−	0.0628831i
$966$		0			0
$967$	11.3660	−	17.0104i	0.365505	−	0.547017i	−0.602445	−	0.798161i	$-0.705807\pi$
$967$	11.3660	−	17.0104i	0.365505	−	0.547017i	0.967950	+	0.251143i	$0.0808066\pi$
$968$		0			0
$969$	−4.00829	+	2.67825i	−0.128765	+	0.0860378i
$970$		0			0
$971$	−42.2809	−	12.8258i	−1.35686	−	0.411599i	−0.473706	−	0.880683i	$-0.657084\pi$
$971$	−42.2809	−	12.8258i	−1.35686	−	0.411599i	−0.883153	+	0.469085i	$0.844584\pi$
$972$		0			0
$973$	−39.9412	+	32.7789i	−1.28046	+	1.05084i
$974$		0			0
$975$	−2.90025	−	7.00182i	−0.0928823	−	0.224238i
$976$		0			0
$977$	−9.56833	+	23.1000i	−0.306118	+	0.739034i	0.693706	+	0.720258i	$0.255977\pi$
$977$	−9.56833	+	23.1000i	−0.306118	+	0.739034i	−0.999824	+	0.0187755i	$0.994023\pi$
$978$		0			0
$979$	0.147785	−	1.50049i	0.00472323	−	0.0479557i
$980$		0			0
$981$	−1.53611	−	2.87386i	−0.0490442	−	0.0917552i
$982$		0			0
$983$	−4.26269	+	21.4300i	−0.135959	+	0.683511i	0.851337	+	0.524619i	$0.175792\pi$
$983$	−4.26269	+	21.4300i	−0.135959	+	0.683511i	−0.987296	+	0.158892i	$0.949208\pi$
$984$		0			0
$985$	−8.02120	+	1.59552i	−0.255577	+	0.0508373i
$986$		0			0
$987$	−1.31709	−	13.3727i	−0.0419236	−	0.425657i
$988$		0			0
$989$	6.96825	+	22.9712i	0.221577	+	0.730443i
$990$		0			0
$991$	−7.50476	−	7.50476i	−0.238397	−	0.238397i	0.577789	−	0.816186i	$-0.303916\pi$
$991$	−7.50476	−	7.50476i	−0.238397	−	0.238397i	−0.816186	+	0.577789i	$0.803916\pi$
$992$		0			0
$993$	3.46183	−	3.46183i	0.109858	−	0.109858i
$994$		0			0
$995$	2.77199	−	0.840873i	0.0878779	−	0.0266575i
$996$		0			0
$997$	22.0570	−	2.17242i	0.698551	−	0.0688013i	0.257494	−	0.966280i	$-0.417103\pi$
$997$	22.0570	−	2.17242i	0.698551	−	0.0688013i	0.441058	+	0.897479i	$0.354603\pi$
$998$		0			0
$999$	0.989081	+	4.97245i	0.0312931	+	0.157321i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.k.a.17.8		240
4.3	odd	2		128.2.k.a.45.4	yes	240
128.37	even	32	inner	512.2.k.a.241.8		240
128.91	odd	32		128.2.k.a.37.4	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
128.2.k.a.37.4	✓	240	128.91	odd	32
128.2.k.a.45.4	yes	240	4.3	odd	2
512.2.k.a.17.8		240	1.1	even	1	trivial
512.2.k.a.241.8		240	128.37	even	32	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 512 = 2^{9} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	512.k (of order \(32\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.169198 + 0.316547i) q^{3} +(-0.290696 - 0.238568i) q^{5} +(-3.87217 - 2.58730i) q^{7} +(1.59514 + 2.38729i) q^{9} +O(q^{10})\)	\(q+(-0.169198 + 0.316547i) q^{3} +(-0.290696 - 0.238568i) q^{5} +(-3.87217 - 2.58730i) q^{7} +(1.59514 + 2.38729i) q^{9} +(0.0374510 - 0.123460i) q^{11} +(-2.75700 - 3.35941i) q^{13} +(0.124703 - 0.0516536i) q^{15} +(-1.63337 - 0.676562i) q^{17} +(-7.56032 - 0.744626i) q^{19} +(1.47416 - 0.787957i) q^{21} +(3.01688 + 0.600095i) q^{23} +(-0.947862 - 4.76523i) q^{25} +(-2.09718 + 0.206555i) q^{27} +(-7.48261 + 2.26982i) q^{29} +(2.44320 - 2.44320i) q^{31} +(0.0327441 + 0.0327441i) q^{33} +(0.508376 + 1.67589i) q^{35} +(-0.235812 - 2.39424i) q^{37} +(1.52989 - 0.304314i) q^{39} +(1.24216 - 6.24474i) q^{41} +(3.67876 + 6.88248i) q^{43} +(0.105831 - 1.07452i) q^{45} +(3.07637 - 7.42702i) q^{47} +(5.62078 + 13.5698i) q^{49} +(0.490525 - 0.402564i) q^{51} +(-5.20823 - 1.57990i) q^{53} +(-0.0403403 + 0.0269545i) q^{55} +(1.51490 - 2.26720i) q^{57} +(0.452339 - 0.551176i) q^{59} +(-1.09220 - 0.583792i) q^{61} -13.3711i q^{63} +1.63430i q^{65} +(-0.0559933 - 0.0299291i) q^{67} +(-0.700408 + 0.853450i) q^{69} +(-6.51783 + 9.75462i) q^{71} +(-7.60253 + 5.07985i) q^{73} +(1.66879 + 0.506223i) q^{75} +(-0.464443 + 0.381159i) q^{77} +(3.68039 + 8.88525i) q^{79} +(-3.00679 + 7.25904i) q^{81} +(0.820582 - 8.33151i) q^{83} +(0.313406 + 0.586342i) q^{85} +(0.547535 - 2.75264i) q^{87} +(11.4621 - 2.27994i) q^{89} +(1.98375 + 20.1414i) q^{91} +(0.360004 + 1.18677i) q^{93} +(2.02011 + 2.02011i) q^{95} +(0.983974 - 0.983974i) q^{97} +(0.354473 - 0.107528i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9}+O(q^{10}) \) 240 * q + 16 * q^3 - 16 * q^5 + 16 * q^7 - 16 * q^9	\( 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9} + 16 q^{11} - 16 q^{13} + 16 q^{15} - 16 q^{17} + 16 q^{19} - 16 q^{21} + 16 q^{23} - 16 q^{25} + 16 q^{27} - 16 q^{29} + 16 q^{31} - 16 q^{33} + 16 q^{35} - 16 q^{37} + 16 q^{39} - 16 q^{41} + 16 q^{43} - 16 q^{45} + 16 q^{47} - 16 q^{49} + 16 q^{51} - 16 q^{53} + 16 q^{55} - 16 q^{57} + 16 q^{59} - 16 q^{61} + 16 q^{67} - 16 q^{69} + 16 q^{71} - 16 q^{73} + 16 q^{75} - 16 q^{77} + 16 q^{79} - 16 q^{81} + 16 q^{83} - 16 q^{85} + 16 q^{87} - 16 q^{89} + 16 q^{91} - 16 q^{93} + 16 q^{95} - 16 q^{97} + 16 q^{99}+O(q^{100}) \) 240 * q + 16 * q^3 - 16 * q^5 + 16 * q^7 - 16 * q^9 + 16 * q^11 - 16 * q^13 + 16 * q^15 - 16 * q^17 + 16 * q^19 - 16 * q^21 + 16 * q^23 - 16 * q^25 + 16 * q^27 - 16 * q^29 + 16 * q^31 - 16 * q^33 + 16 * q^35 - 16 * q^37 + 16 * q^39 - 16 * q^41 + 16 * q^43 - 16 * q^45 + 16 * q^47 - 16 * q^49 + 16 * q^51 - 16 * q^53 + 16 * q^55 - 16 * q^57 + 16 * q^59 - 16 * q^61 + 16 * q^67 - 16 * q^69 + 16 * q^71 - 16 * q^73 + 16 * q^75 - 16 * q^77 + 16 * q^79 - 16 * q^81 + 16 * q^83 - 16 * q^85 + 16 * q^87 - 16 * q^89 + 16 * q^91 - 16 * q^93 + 16 * q^95 - 16 * q^97 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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