LMFDB - Embedded newform 512.2.i.a.33.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [512,2,Mod(33,512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(512, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 15]))

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

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

chi := DirichletCharacter("512.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 512 = 2^{9} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	512.i (of order $16$, degree $8$, 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:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 64)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			33.1
Character	$\chi$	$=$	512.33
Dual form			512.2.i.a.481.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.03902 + 1.36243i) q^{3} +(1.53851 - 0.306028i) q^{5} +(-1.01301 - 2.44562i) q^{7} +(1.15334 - 2.78440i) q^{9} +O(q^{10})$	\(q+(-2.03902 + 1.36243i) q^{3} +(1.53851 - 0.306028i) q^{5} +(-1.01301 - 2.44562i) q^{7} +(1.15334 - 2.78440i) q^{9} +(-2.71620 + 4.06508i) q^{11} +(-4.23055 - 0.841509i) q^{13} +(-2.72010 + 2.72010i) q^{15} +(0.228271 + 0.228271i) q^{17} +(1.30758 - 6.57364i) q^{19} +(5.39754 + 3.60652i) q^{21} +(-2.81320 - 1.16527i) q^{23} +(-2.34605 + 0.971766i) q^{25} +(0.00660900 + 0.0332257i) q^{27} +(-1.67490 - 2.50666i) q^{29} +1.06551i q^{31} -11.9894i q^{33} +(-2.30695 - 3.45260i) q^{35} +(-2.13514 - 10.7341i) q^{37} +(9.77267 - 4.04797i) q^{39} +(-2.57626 - 1.06712i) q^{41} +(0.575838 + 0.384763i) q^{43} +(0.922311 - 4.63677i) q^{45} +(-2.61525 - 2.61525i) q^{47} +(-0.00513508 + 0.00513508i) q^{49} +(-0.776454 - 0.154446i) q^{51} +(-2.60438 + 3.89774i) q^{53} +(-2.93486 + 7.08539i) q^{55} +(6.28994 + 15.1853i) q^{57} +(8.66346 - 1.72327i) q^{59} +(-6.23588 + 4.16668i) q^{61} -7.97794 q^{63} -6.76625 q^{65} +(-6.91594 + 4.62108i) q^{67} +(7.32376 - 1.45679i) q^{69} +(0.606236 + 1.46358i) q^{71} +(-1.36883 + 3.30465i) q^{73} +(3.45968 - 5.17778i) q^{75} +(12.6932 + 2.52483i) q^{77} +(-4.69681 + 4.69681i) q^{79} +(6.33452 + 6.33452i) q^{81} +(0.803913 - 4.04154i) q^{83} +(0.421054 + 0.281340i) q^{85} +(6.83030 + 2.82920i) q^{87} +(-10.3334 + 4.28021i) q^{89} +(2.22758 + 11.1988i) q^{91} +(-1.45169 - 2.17261i) q^{93} -10.5137i q^{95} +7.30754i q^{97} +(8.18612 + 12.2514i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{3} + 8 q^{5} + 8 q^{7} - 8 q^{9}+O(q^{10}) $ 56 * q - 8 * q^3 + 8 * q^5 + 8 * q^7 - 8 * q^9	$ 56 q - 8 q^{3} + 8 q^{5} + 8 q^{7} - 8 q^{9} - 8 q^{11} + 8 q^{13} + 8 q^{15} - 8 q^{17} - 8 q^{19} + 8 q^{21} + 8 q^{23} - 8 q^{25} - 8 q^{27} + 8 q^{29} - 8 q^{35} + 8 q^{37} + 8 q^{39} - 8 q^{41} - 8 q^{43} + 8 q^{45} + 8 q^{47} - 8 q^{49} + 24 q^{51} + 8 q^{53} - 56 q^{55} - 8 q^{57} + 56 q^{59} + 8 q^{61} - 64 q^{63} - 16 q^{65} + 72 q^{67} + 8 q^{69} - 56 q^{71} - 8 q^{73} + 56 q^{75} + 8 q^{77} - 24 q^{79} - 8 q^{81} - 8 q^{83} + 8 q^{85} + 8 q^{87} - 8 q^{89} - 8 q^{91} - 16 q^{93} + 16 q^{99}+O(q^{100}) $ 56 * q - 8 * q^3 + 8 * q^5 + 8 * q^7 - 8 * q^9 - 8 * q^11 + 8 * q^13 + 8 * q^15 - 8 * q^17 - 8 * q^19 + 8 * q^21 + 8 * q^23 - 8 * q^25 - 8 * q^27 + 8 * q^29 - 8 * q^35 + 8 * q^37 + 8 * q^39 - 8 * q^41 - 8 * q^43 + 8 * q^45 + 8 * q^47 - 8 * q^49 + 24 * q^51 + 8 * q^53 - 56 * q^55 - 8 * q^57 + 56 * q^59 + 8 * q^61 - 64 * q^63 - 16 * q^65 + 72 * q^67 + 8 * q^69 - 56 * q^71 - 8 * q^73 + 56 * q^75 + 8 * q^77 - 24 * q^79 - 8 * q^81 - 8 * q^83 + 8 * q^85 + 8 * q^87 - 8 * q^89 - 8 * q^91 - 16 * q^93 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{15}{16}\right)$	$1$

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
$3$	−2.03902	+	1.36243i	−1.17723	+	0.786599i	−0.981009	−	0.193961i	$-0.937866\pi$
$3$	−2.03902	+	1.36243i	−1.17723	+	0.786599i	−0.196219	+	0.980560i	$0.562866\pi$
$4$		0			0
$5$	1.53851	−	0.306028i	0.688041	−	0.136860i	0.161325	−	0.986901i	$-0.448423\pi$
$5$	1.53851	−	0.306028i	0.688041	−	0.136860i	0.526716	+	0.850041i	$0.323423\pi$
$6$		0			0
$7$	−1.01301	−	2.44562i	−0.382882	−	0.924359i	−0.991406	−	0.130823i	$-0.958238\pi$
$7$	−1.01301	−	2.44562i	−0.382882	−	0.924359i	0.608524	−	0.793536i	$-0.291762\pi$
$8$		0			0
$9$	1.15334	−	2.78440i	0.384446	−	0.928134i
$10$		0			0
$11$	−2.71620	+	4.06508i	−0.818965	+	1.22567i	0.152457	+	0.988310i	$0.451281\pi$
$11$	−2.71620	+	4.06508i	−0.818965	+	1.22567i	−0.971422	+	0.237358i	$0.923719\pi$
$12$		0			0
$13$	−4.23055	−	0.841509i	−1.17334	−	0.233393i	−0.430332	−	0.902671i	$-0.641603\pi$
$13$	−4.23055	−	0.841509i	−1.17334	−	0.233393i	−0.743012	+	0.669278i	$0.766603\pi$
$14$		0			0
$15$	−2.72010	+	2.72010i	−0.702327	+	0.702327i
$16$		0			0
$17$	0.228271	+	0.228271i	0.0553640	+	0.0553640i	0.734247	−	0.678883i	$-0.237536\pi$
$17$	0.228271	+	0.228271i	0.0553640	+	0.0553640i	−0.678883	+	0.734247i	$0.737536\pi$
$18$		0			0
$19$	1.30758	−	6.57364i	0.299979	−	1.50810i	−0.477188	−	0.878801i	$-0.658344\pi$
$19$	1.30758	−	6.57364i	0.299979	−	1.50810i	0.777167	−	0.629295i	$-0.216656\pi$
$20$		0			0
$21$	5.39754	+	3.60652i	1.17784	+	0.787007i
$22$		0			0
$23$	−2.81320	−	1.16527i	−0.586593	−	0.242975i	0.0695913	−	0.997576i	$-0.477830\pi$
$23$	−2.81320	−	1.16527i	−0.586593	−	0.242975i	−0.656184	+	0.754601i	$0.727830\pi$
$24$		0			0
$25$	−2.34605	+	0.971766i	−0.469210	+	0.194353i
$26$		0			0
$27$	0.00660900	+	0.0332257i	0.00127190	+	0.00639428i
$28$		0			0
$29$	−1.67490	−	2.50666i	−0.311021	−	0.465476i	0.642722	−	0.766100i	$-0.277805\pi$
$29$	−1.67490	−	2.50666i	−0.311021	−	0.465476i	−0.953743	+	0.300624i	$0.902805\pi$
$30$		0			0
$31$			1.06551i			0.191372i	0.995412	+	0.0956860i	$0.0305045\pi$
$31$			1.06551i			0.191372i	−0.995412	+	0.0956860i	$0.969496\pi$
$32$		0			0
$33$		−	11.9894i		−	2.08709i
$34$		0			0
$35$	−2.30695	−	3.45260i	−0.389946	−	0.583595i
$36$		0			0
$37$	−2.13514	−	10.7341i	−0.351014	−	1.76467i	−0.603790	−	0.797144i	$-0.706343\pi$
$37$	−2.13514	−	10.7341i	−0.351014	−	1.76467i	0.252775	−	0.967525i	$-0.418657\pi$
$38$		0			0
$39$	9.77267	−	4.04797i	1.56488	−	0.648195i
$40$		0			0
$41$	−2.57626	−	1.06712i	−0.402344	−	0.166657i	0.172329	−	0.985039i	$-0.444871\pi$
$41$	−2.57626	−	1.06712i	−0.402344	−	0.166657i	−0.574673	+	0.818383i	$0.694871\pi$
$42$		0			0
$43$	0.575838	+	0.384763i	0.0878145	+	0.0586758i	0.598702	−	0.800972i	$-0.295683\pi$
$43$	0.575838	+	0.384763i	0.0878145	+	0.0586758i	−0.510888	+	0.859647i	$0.670683\pi$
$44$		0			0
$45$	0.922311	−	4.63677i	0.137490	−	0.691209i
$46$		0			0
$47$	−2.61525	−	2.61525i	−0.381474	−	0.381474i	0.490159	−	0.871633i	$-0.336939\pi$
$47$	−2.61525	−	2.61525i	−0.381474	−	0.381474i	−0.871633	+	0.490159i	$0.836939\pi$
$48$		0			0
$49$	−0.00513508	+	0.00513508i	−0.000733583	+	0.000733583i
$50$		0			0
$51$	−0.776454	−	0.154446i	−0.108725	−	0.0216268i
$52$		0			0
$53$	−2.60438	+	3.89774i	−0.357740	+	0.535395i	−0.966067	−	0.258291i	$-0.916841\pi$
$53$	−2.60438	+	3.89774i	−0.357740	+	0.535395i	0.608327	+	0.793686i	$0.291841\pi$
$54$		0			0
$55$	−2.93486	+	7.08539i	−0.395737	+	0.955393i
$56$		0			0
$57$	6.28994	+	15.1853i	0.833123	+	2.01134i
$58$		0			0
$59$	8.66346	−	1.72327i	1.12789	−	0.224351i	0.404328	−	0.914614i	$-0.367505\pi$
$59$	8.66346	−	1.72327i	1.12789	−	0.224351i	0.723558	+	0.690263i	$0.242505\pi$
$60$		0			0
$61$	−6.23588	+	4.16668i	−0.798422	+	0.533489i	−0.886557	−	0.462620i	$-0.846909\pi$
$61$	−6.23588	+	4.16668i	−0.798422	+	0.533489i	0.0881344	+	0.996109i	$0.471909\pi$
$62$		0			0
$63$	−7.97794			−1.00513
$64$		0			0
$65$	−6.76625			−0.839251
$66$		0			0
$67$	−6.91594	+	4.62108i	−0.844917	+	0.564555i	−0.900974	−	0.433872i	$-0.857147\pi$
$67$	−6.91594	+	4.62108i	−0.844917	+	0.564555i	0.0560578	+	0.998428i	$0.482147\pi$
$68$		0			0
$69$	7.32376	−	1.45679i	0.881677	−	0.175376i
$70$		0			0
$71$	0.606236	+	1.46358i	0.0719470	+	0.173695i	0.955762	−	0.294141i	$-0.0950336\pi$
$71$	0.606236	+	1.46358i	0.0719470	+	0.173695i	−0.883815	+	0.467837i	$0.845034\pi$
$72$		0			0
$73$	−1.36883	+	3.30465i	−0.160210	+	0.386780i	−0.983517	−	0.180816i	$-0.942126\pi$
$73$	−1.36883	+	3.30465i	−0.160210	+	0.386780i	0.823307	+	0.567596i	$0.192126\pi$
$74$		0			0
$75$	3.45968	−	5.17778i	0.399489	−	0.597878i
$76$		0			0
$77$	12.6932	+	2.52483i	1.44652	+	0.287732i
$78$		0			0
$79$	−4.69681	+	4.69681i	−0.528433	+	0.528433i	−0.920105	−	0.391672i	$-0.871897\pi$
$79$	−4.69681	+	4.69681i	−0.528433	+	0.528433i	0.391672	+	0.920105i	$0.371897\pi$
$80$		0			0
$81$	6.33452	+	6.33452i	0.703836	+	0.703836i
$82$		0			0
$83$	0.803913	−	4.04154i	0.0882409	−	0.443617i	−0.911254	−	0.411844i	$-0.864885\pi$
$83$	0.803913	−	4.04154i	0.0882409	−	0.443617i	0.999495	−	0.0317726i	$-0.0101152\pi$
$84$		0			0
$85$	0.421054	+	0.281340i	0.0456698	+	0.0305156i
$86$		0			0
$87$	6.83030	+	2.82920i	0.732286	+	0.303323i
$88$		0			0
$89$	−10.3334	+	4.28021i	−1.09533	+	0.453702i	−0.855863	−	0.517202i	$-0.826974\pi$
$89$	−10.3334	+	4.28021i	−1.09533	+	0.453702i	−0.239470	+	0.970904i	$0.576974\pi$
$90$		0			0
$91$	2.22758	+	11.1988i	0.233514	+	1.17395i
$92$		0			0
$93$	−1.45169	−	2.17261i	−0.150533	−	0.225289i
$94$		0			0
$95$		−	10.5137i		−	1.07869i
$96$		0			0
$97$			7.30754i			0.741969i	0.928639	+	0.370984i	$0.120980\pi$
$97$			7.30754i			0.741969i	−0.928639	+	0.370984i	$0.879020\pi$
$98$		0			0
$99$	8.18612	+	12.2514i	0.822736	+	1.23131i
$100$		0			0
$101$	2.69620	+	13.5547i	0.268281	+	1.34874i	0.846295	+	0.532715i	$0.178828\pi$
$101$	2.69620	+	13.5547i	0.268281	+	1.34874i	−0.578013	+	0.816027i	$0.696172\pi$
$102$		0			0
$103$	8.88954	−	3.68217i	0.875913	−	0.362815i	0.101002	−	0.994886i	$-0.467795\pi$
$103$	8.88954	−	3.68217i	0.875913	−	0.362815i	0.774910	+	0.632071i	$0.217795\pi$
$104$		0			0
$105$	9.40784	+	3.89685i	0.918111	+	0.380294i
$106$		0			0
$107$	−3.97920	−	2.65882i	−0.384684	−	0.257037i	0.348159	−	0.937435i	$-0.386807\pi$
$107$	−3.97920	−	2.65882i	−0.384684	−	0.257037i	−0.732843	+	0.680398i	$0.761807\pi$
$108$		0			0
$109$	−1.26589	+	6.36406i	−0.121250	+	0.609566i	0.871602	+	0.490215i	$0.163082\pi$
$109$	−1.26589	+	6.36406i	−0.121250	+	0.609566i	−0.992852	+	0.119352i	$0.961918\pi$
$110$		0			0
$111$	18.9780	+	18.9780i	1.80131	+	1.80131i
$112$		0			0
$113$	10.3282	−	10.3282i	0.971595	−	0.971595i	−0.0280126	−	0.999608i	$-0.508918\pi$
$113$	10.3282	−	10.3282i	0.971595	−	0.971595i	0.999608	+	0.0280126i	$0.00891785\pi$
$114$		0			0
$115$	−4.68473	−	0.931850i	−0.436853	−	0.0868955i
$116$		0			0
$117$	−7.22235	+	10.8090i	−0.667706	+	0.999293i
$118$		0			0
$119$	0.327025	−	0.789507i	0.0299783	−	0.0723740i
$120$		0			0
$121$	−4.93762	−	11.9205i	−0.448875	−	1.08368i
$122$		0			0
$123$	6.70693	−	1.33409i	0.604743	−	0.120291i
$124$		0			0
$125$	−9.83344	+	6.57049i	−0.879529	+	0.587683i
$126$		0			0
$127$	−3.04637			−0.270322			−0.135161	−	0.990824i	$-0.543155\pi$
$127$	−3.04637			−0.270322			−0.135161	+	0.990824i	$0.543155\pi$
$128$		0			0
$129$	−1.69836			−0.149532
$130$		0			0
$131$	6.26153	−	4.18382i	0.547072	−	0.365542i	−0.251109	−	0.967959i	$-0.580795\pi$
$131$	6.26153	−	4.18382i	0.547072	−	0.365542i	0.798182	+	0.602417i	$0.205795\pi$
$132$		0			0
$133$	−17.4012	+	3.46132i	−1.50888	+	0.300134i
$134$		0			0
$135$	0.0203360	+	0.0490953i	0.00175024	+	0.00422545i
$136$		0			0
$137$	2.52012	−	6.08411i	0.215308	−	0.519800i	−0.778915	−	0.627129i	$-0.784230\pi$
$137$	2.52012	−	6.08411i	0.215308	−	0.519800i	0.994224	+	0.107329i	$0.0342298\pi$
$138$		0			0
$139$	−2.36467	+	3.53898i	−0.200569	+	0.300172i	−0.918096	−	0.396358i	$-0.870274\pi$
$139$	−2.36467	+	3.53898i	−0.200569	+	0.300172i	0.717527	+	0.696530i	$0.245274\pi$
$140$		0			0
$141$	8.89564	+	1.76945i	0.749148	+	0.149015i
$142$		0			0
$143$	14.9118	−	14.9118i	1.24699	−	1.24699i
$144$		0			0
$145$	−3.34395	−	3.34395i	−0.277700	−	0.277700i
$146$		0			0
$147$	0.00347435	−	0.0174667i	0.000286559	−	0.00144063i
$148$		0			0
$149$	2.62422	+	1.75345i	0.214985	+	0.143648i	0.658400	−	0.752668i	$-0.271233\pi$
$149$	2.62422	+	1.75345i	0.214985	+	0.143648i	−0.443416	+	0.896316i	$0.646233\pi$
$150$		0			0
$151$	−15.7824	−	6.53730i	−1.28436	−	0.531998i	−0.367058	−	0.930198i	$-0.619635\pi$
$151$	−15.7824	−	6.53730i	−1.28436	−	0.531998i	−0.917298	+	0.398200i	$0.869635\pi$
$152$		0			0
$153$	0.898873	−	0.372325i	0.0726696	−	0.0301007i
$154$		0			0
$155$	0.326077	+	1.63930i	0.0261912	+	0.131672i
$156$		0			0
$157$	−1.83146	−	2.74098i	−0.146167	−	0.218754i	0.751161	−	0.660119i	$-0.229494\pi$
$157$	−1.83146	−	2.74098i	−0.146167	−	0.218754i	−0.897328	+	0.441365i	$0.854494\pi$
$158$		0			0
$159$		−	11.4959i		−	0.911680i
$160$		0			0
$161$			8.06045i			0.635253i
$162$		0			0
$163$	−1.97712	−	2.95896i	−0.154860	−	0.231764i	0.745925	−	0.666030i	$-0.232008\pi$
$163$	−1.97712	−	2.95896i	−0.154860	−	0.231764i	−0.900785	+	0.434266i	$0.857008\pi$
$164$		0			0
$165$	−3.66909	−	18.4458i	−0.285639	−	1.43600i
$166$		0			0
$167$	−11.7493	+	4.86672i	−0.909189	+	0.376598i	−0.787746	−	0.616000i	$-0.788752\pi$
$167$	−11.7493	+	4.86672i	−0.909189	+	0.376598i	−0.121443	+	0.992598i	$0.538752\pi$
$168$		0			0
$169$	5.17899	+	2.14521i	0.398384	+	0.165016i
$170$		0			0
$171$	−16.7956	−	11.2224i	−1.28439	−	0.858201i
$172$		0			0
$173$	−0.119835	+	0.602450i	−0.00911086	+	0.0458034i	−0.985073	−	0.172135i	$-0.944933\pi$
$173$	−0.119835	+	0.602450i	−0.00911086	+	0.0458034i	0.975962	+	0.217939i	$0.0699333\pi$
$174$		0			0
$175$	4.75315	+	4.75315i	0.359304	+	0.359304i
$176$		0			0
$177$	−15.3171	+	15.3171i	−1.15131	+	1.15131i
$178$		0			0
$179$	17.8336	+	3.54732i	1.33294	+	0.265139i	0.809600	−	0.586983i	$-0.199684\pi$
$179$	17.8336	+	3.54732i	1.33294	+	0.265139i	0.523344	+	0.852122i	$0.324684\pi$
$180$		0			0
$181$	13.1144	−	19.6270i	0.974783	−	1.45887i	0.0883053	−	0.996093i	$-0.471855\pi$
$181$	13.1144	−	19.6270i	0.974783	−	1.45887i	0.886477	−	0.462772i	$-0.153145\pi$
$182$		0			0
$183$	7.03827	−	16.9919i	0.520284	−	1.25608i
$184$		0			0
$185$	−6.56984	−	15.8610i	−0.483024	−	1.16612i
$186$		0			0
$187$	−1.54797	+	0.307911i	−0.113199	+	0.0225167i
$188$		0			0
$189$	0.0745625	−	0.0498210i	0.00542362	−	0.00362395i
$190$		0			0
$191$	9.08320			0.657237			0.328619	−	0.944463i	$-0.393417\pi$
$191$	9.08320			0.657237			0.328619	+	0.944463i	$0.393417\pi$
$192$		0			0
$193$	−23.8071			−1.71367			−0.856836	−	0.515589i	$-0.827573\pi$
$193$	−23.8071			−1.71367			−0.856836	+	0.515589i	$0.827573\pi$
$194$		0			0
$195$	13.7965	−	9.21854i	0.987990	−	0.660154i
$196$		0			0
$197$	7.77466	−	1.54648i	0.553922	−	0.110182i	0.0898105	−	0.995959i	$-0.471374\pi$
$197$	7.77466	−	1.54648i	0.553922	−	0.110182i	0.464111	+	0.885777i	$0.346374\pi$
$198$		0			0
$199$	3.63779	+	8.78239i	0.257876	+	0.622567i	0.998798	−	0.0490240i	$-0.0156111\pi$
$199$	3.63779	+	8.78239i	0.257876	+	0.622567i	−0.740922	+	0.671591i	$0.765611\pi$
$200$		0			0
$201$	7.80584	−	18.8450i	0.550581	−	1.32922i
$202$		0			0
$203$	−4.43367	+	6.63545i	−0.311182	+	0.465717i
$204$		0			0
$205$	−4.29016	−	0.853366i	−0.299638	−	0.0596017i
$206$		0			0
$207$	−6.48913	+	6.48913i	−0.451026	+	0.451026i
$208$		0			0
$209$	23.1707	+	23.1707i	1.60275	+	1.60275i
$210$		0			0
$211$	−1.94225	+	9.76436i	−0.133710	+	0.672206i	0.854543	+	0.519380i	$0.173837\pi$
$211$	−1.94225	+	9.76436i	−0.133710	+	0.672206i	−0.988253	+	0.152825i	$0.951163\pi$
$212$		0			0
$213$	−3.23016	−	2.15832i	−0.221327	−	0.147886i
$214$		0			0
$215$	1.00368	+	0.415738i	0.0684503	+	0.0283531i
$216$		0			0
$217$	2.60585	−	1.07938i	0.176896	−	0.0732729i
$218$		0			0
$219$	−1.71128	−	8.60318i	−0.115638	−	0.581349i
$220$		0			0
$221$	−0.773622	−	1.15781i	−0.0520394	−	0.0778825i
$222$		0			0
$223$			12.2329i			0.819179i	0.912270	+	0.409589i	$0.134328\pi$
$223$			12.2329i			0.819179i	−0.912270	+	0.409589i	$0.865672\pi$
$224$		0			0
$225$			7.65312i			0.510208i
$226$		0			0
$227$	9.90466	+	14.8234i	0.657395	+	0.983861i	0.999030	+	0.0440287i	$0.0140193\pi$
$227$	9.90466	+	14.8234i	0.657395	+	0.983861i	−0.341635	+	0.939833i	$0.610981\pi$
$228$		0			0
$229$	3.25861	+	16.3821i	0.215335	+	1.08256i	0.925564	+	0.378591i	$0.123591\pi$
$229$	3.25861	+	16.3821i	0.215335	+	1.08256i	−0.710229	+	0.703971i	$0.751409\pi$
$230$		0			0
$231$	−29.3216	+	12.1454i	−1.92922	+	0.799108i
$232$		0			0
$233$	−9.60560	−	3.97877i	−0.629283	−	0.260658i	0.0451652	−	0.998980i	$-0.485619\pi$
$233$	−9.60560	−	3.97877i	−0.629283	−	0.260658i	−0.674449	+	0.738322i	$0.735619\pi$
$234$		0			0
$235$	−4.82392	−	3.22324i	−0.314678	−	0.210261i
$236$		0			0
$237$	3.17782	−	15.9760i	0.206421	−	1.03775i
$238$		0			0
$239$	−14.7694	−	14.7694i	−0.955353	−	0.955353i	0.0436917	−	0.999045i	$-0.486088\pi$
$239$	−14.7694	−	14.7694i	−0.955353	−	0.955353i	−0.999045	+	0.0436917i	$0.986088\pi$
$240$		0			0
$241$	7.07909	−	7.07909i	0.456004	−	0.456004i	−0.441337	−	0.897341i	$-0.645496\pi$
$241$	7.07909	−	7.07909i	0.456004	−	0.456004i	0.897341	+	0.441337i	$0.145496\pi$
$242$		0			0
$243$	−21.6462	−	4.30570i	−1.38861	−	0.276211i
$244$		0			0
$245$	−0.00632887	+	0.00947183i	−0.000404337	+	0.000605133i
$246$		0			0
$247$	−11.0635	+	26.7098i	−0.703957	+	1.69950i
$248$		0			0
$249$	3.86712	+	9.33606i	0.245069	+	0.591649i
$250$		0			0
$251$	−17.5456	+	3.49003i	−1.10747	+	0.220289i	−0.714756	−	0.699374i	$-0.753462\pi$
$251$	−17.5456	+	3.49003i	−1.10747	+	0.220289i	−0.392710	+	0.919662i	$0.628462\pi$
$252$		0			0
$253$	12.3781	−	8.27079i	0.778205	−	0.519980i
$254$		0			0
$255$	−1.24184			−0.0777672
$256$		0			0
$257$	26.9095			1.67857			0.839284	−	0.543694i	$-0.182975\pi$
$257$	26.9095			1.67857			0.839284	+	0.543694i	$0.182975\pi$
$258$		0			0
$259$	−24.0885	+	16.0955i	−1.49679	+	1.00012i
$260$		0			0
$261$	−8.91128	+	1.77256i	−0.551594	+	0.109719i
$262$		0			0
$263$	−1.36380	−	3.29251i	−0.0840956	−	0.203025i	0.876238	−	0.481879i	$-0.160045\pi$
$263$	−1.36380	−	3.29251i	−0.0840956	−	0.203025i	−0.960334	+	0.278854i	$0.910045\pi$
$264$		0			0
$265$	−2.81405	+	6.79371i	−0.172865	+	0.417334i
$266$		0			0
$267$	15.2384	−	22.8059i	0.932576	−	1.39570i
$268$		0			0
$269$	19.9604	+	3.97036i	1.21700	+	0.242077i	0.761505	−	0.648159i	$-0.224461\pi$
$269$	19.9604	+	3.97036i	1.21700	+	0.242077i	0.455499	+	0.890236i	$0.349461\pi$
$270$		0			0
$271$	1.83438	−	1.83438i	0.111431	−	0.111431i	−0.649193	−	0.760624i	$-0.724893\pi$
$271$	1.83438	−	1.83438i	0.111431	−	0.111431i	0.760624	+	0.649193i	$0.224893\pi$
$272$		0			0
$273$	−19.7996	−	19.7996i	−1.19833	−	1.19833i
$274$		0			0
$275$	2.42204	−	12.1764i	0.146054	−	0.734264i
$276$		0			0
$277$	−20.9494	−	13.9979i	−1.25873	−	0.841055i	−0.266300	−	0.963890i	$-0.585801\pi$
$277$	−20.9494	−	13.9979i	−1.25873	−	0.841055i	−0.992427	+	0.122835i	$0.960801\pi$
$278$		0			0
$279$	2.96682	+	1.22890i	0.177619	+	0.0735722i
$280$		0			0
$281$	11.8565	−	4.91114i	0.707302	−	0.292974i	0.000114440	−	1.00000i	$-0.499964\pi$
$281$	11.8565	−	4.91114i	0.707302	−	0.292974i	0.707188	+	0.707026i	$0.249964\pi$
$282$		0			0
$283$	−2.20386	−	11.0795i	−0.131006	−	0.658610i	−0.989352	−	0.145540i	$-0.953508\pi$
$283$	−2.20386	−	11.0795i	−0.131006	−	0.658610i	0.858347	−	0.513070i	$-0.171492\pi$
$284$		0			0
$285$	14.3242	+	21.4377i	0.848494	+	1.26986i
$286$		0			0
$287$			7.38157i			0.435720i
$288$		0			0
$289$		−	16.8958i		−	0.993870i
$290$		0			0
$291$	−9.95601	−	14.9002i	−0.583632	−	0.873467i
$292$		0			0
$293$	−3.55830	−	17.8888i	−0.207878	−	1.04507i	−0.933936	−	0.357440i	$-0.883650\pi$
$293$	−3.55830	−	17.8888i	−0.207878	−	1.04507i	0.726058	−	0.687633i	$-0.241350\pi$
$294$		0			0
$295$	12.8014	−	5.30252i	0.745327	−	0.308725i
$296$		0			0
$297$	−0.153016	−	0.0633815i	−0.00887891	−	0.00367777i
$298$		0			0
$299$	10.9208	+	7.29705i	0.631566	+	0.421999i
$300$		0			0
$301$	0.357655	−	1.79805i	0.0206149	−	0.103638i
$302$		0			0
$303$	−23.9649	−	23.9649i	−1.37675	−	1.37675i
$304$		0			0
$305$	−8.31881	+	8.31881i	−0.476334	+	0.476334i
$306$		0			0
$307$	6.20347	+	1.23395i	0.354051	+	0.0704251i	0.368912	−	0.929464i	$-0.379730\pi$
$307$	6.20347	+	1.23395i	0.354051	+	0.0704251i	−0.0148607	+	0.999890i	$0.504730\pi$
$308$		0			0
$309$	−13.1093	+	19.6194i	−0.745759	+	1.11611i
$310$		0			0
$311$	−6.82557	+	16.4784i	−0.387042	+	0.934403i	0.603521	+	0.797347i	$0.293764\pi$
$311$	−6.82557	+	16.4784i	−0.387042	+	0.934403i	−0.990563	+	0.137056i	$0.956236\pi$
$312$		0			0
$313$	−2.69923	−	6.51651i	−0.152569	−	0.368335i	0.829053	−	0.559170i	$-0.188880\pi$
$313$	−2.69923	−	6.51651i	−0.152569	−	0.368335i	−0.981622	+	0.190836i	$0.938880\pi$
$314$		0			0
$315$	−12.2741	+	2.44147i	−0.691567	+	0.137561i
$316$		0			0
$317$	27.9024	−	18.6438i	1.56716	−	1.04714i	0.597748	−	0.801684i	$-0.296062\pi$
$317$	27.9024	−	18.6438i	1.56716	−	1.04714i	0.969408	−	0.245456i	$-0.0789378\pi$
$318$		0			0
$319$	14.7392			0.825234
$320$		0			0
$321$	11.7361			0.655046
$322$		0			0
$323$	1.79906	−	1.20209i	0.100102	−	0.0668861i
$324$		0			0
$325$	10.7428	−	2.13688i	0.595905	−	0.118533i
$326$		0			0
$327$	−6.08941	−	14.7011i	−0.336745	−	0.812974i
$328$		0			0
$329$	−3.74664	+	9.04519i	−0.206559	+	0.498678i
$330$		0			0
$331$	−6.61521	+	9.90037i	−0.363605	+	0.544173i	−0.967494	−	0.252895i	$-0.918617\pi$
$331$	−6.61521	+	9.90037i	−0.363605	+	0.544173i	0.603889	+	0.797069i	$0.293617\pi$
$332$		0			0
$333$	−32.3505	−	6.43491i	−1.77279	−	0.352631i
$334$		0			0
$335$	−9.22604	+	9.22604i	−0.504072	+	0.504072i
$336$		0			0
$337$	−21.7272	−	21.7272i	−1.18356	−	1.18356i	−0.978816	−	0.204740i	$-0.934365\pi$
$337$	−21.7272	−	21.7272i	−1.18356	−	1.18356i	−0.204740	−	0.978816i	$-0.565635\pi$
$338$		0			0
$339$	−6.98796	+	35.1308i	−0.379534	+	1.90804i
$340$		0			0
$341$	−4.33140	−	2.89415i	−0.234559	−	0.156727i
$342$		0			0
$343$	−17.1016	−	7.08372i	−0.923400	−	0.382485i
$344$		0			0
$345$	10.8218	−	4.48255i	0.582628	−	0.241332i
$346$		0			0
$347$	−6.17477	−	31.0427i	−0.331479	−	1.66646i	−0.683107	−	0.730318i	$-0.739372\pi$
$347$	−6.17477	−	31.0427i	−0.331479	−	1.66646i	0.351628	−	0.936140i	$-0.385628\pi$
$348$		0			0
$349$	3.28116	+	4.91061i	0.175637	+	0.262859i	0.908835	−	0.417156i	$-0.136973\pi$
$349$	3.28116	+	4.91061i	0.175637	+	0.262859i	−0.733198	+	0.680015i	$0.761973\pi$
$350$		0			0
$351$		−	0.146124i		−	0.00779954i
$352$		0			0
$353$			0.529453i			0.0281800i	0.999901	+	0.0140900i	$0.00448513\pi$
$353$			0.529453i			0.0281800i	−0.999901	+	0.0140900i	$0.995515\pi$
$354$		0			0
$355$	1.38060	+	2.06621i	0.0732744	+	0.109663i
$356$		0			0
$357$	0.408838	+	2.05537i	0.0216380	+	0.108782i
$358$		0			0
$359$	20.4053	−	8.45215i	1.07695	−	0.446087i	0.227512	−	0.973775i	$-0.426941\pi$
$359$	20.4053	−	8.45215i	1.07695	−	0.446087i	0.849438	+	0.527688i	$0.176941\pi$
$360$		0			0
$361$	−23.9492	−	9.92010i	−1.26049	−	0.522110i
$362$		0			0
$363$	26.3087	+	17.5789i	1.38085	+	0.922654i
$364$		0			0
$365$	−1.09464	+	5.50312i	−0.0572960	+	0.288047i
$366$		0			0
$367$	14.5467	+	14.5467i	0.759333	+	0.759333i	0.976201	−	0.216868i	$-0.0695840\pi$
$367$	14.5467	+	14.5467i	0.759333	+	0.759333i	−0.216868	+	0.976201i	$0.569584\pi$
$368$		0			0
$369$	−5.94259	+	5.94259i	−0.309359	+	0.309359i
$370$		0			0
$371$	12.1707	+	2.42090i	0.631869	+	0.125687i
$372$		0			0
$373$	10.8226	−	16.1972i	0.560375	−	0.838660i	−0.437799	−	0.899073i	$-0.644242\pi$
$373$	10.8226	−	16.1972i	0.560375	−	0.838660i	0.998173	+	0.0604127i	$0.0192417\pi$
$374$		0			0
$375$	11.0987	−	26.7947i	0.573136	−	1.38367i
$376$		0			0
$377$	4.97637	+	12.0140i	0.256296	+	0.618753i
$378$		0			0
$379$	21.0139	−	4.17992i	1.07941	−	0.214708i	0.376808	−	0.926291i	$-0.377022\pi$
$379$	21.0139	−	4.17992i	1.07941	−	0.214708i	0.702602	+	0.711583i	$0.252022\pi$
$380$		0			0
$381$	6.21161	−	4.15047i	0.318231	−	0.212635i
$382$		0			0
$383$	6.11960			0.312697			0.156348	−	0.987702i	$-0.450028\pi$
$383$	6.11960			0.312697			0.156348	+	0.987702i	$0.450028\pi$
$384$		0			0
$385$	20.3012			1.03465
$386$		0			0
$387$	1.73547	−	1.15960i	0.0882189	−	0.0589460i
$388$		0			0
$389$	−30.1172	+	5.99068i	−1.52700	+	0.303740i	−0.885959	−	0.463764i	$-0.846498\pi$
$389$	−30.1172	+	5.99068i	−1.52700	+	0.303740i	−0.641044	+	0.767504i	$0.721498\pi$
$390$		0			0
$391$	−0.376176	−	0.908170i	−0.0190241	−	0.0459281i
$392$		0			0
$393$	−7.06722	+	17.0618i	−0.356494	+	0.860653i
$394$		0			0
$395$	−5.78872	+	8.66343i	−0.291262	+	0.435905i
$396$		0			0
$397$	−28.0202	−	5.57357i	−1.40630	−	0.279730i	−0.567140	−	0.823621i	$-0.691950\pi$
$397$	−28.0202	−	5.57357i	−1.40630	−	0.279730i	−0.839155	+	0.543892i	$0.816950\pi$
$398$		0			0
$399$	30.7656	−	30.7656i	1.54021	−	1.54021i
$400$		0			0
$401$	3.48263	+	3.48263i	0.173914	+	0.173914i	0.788697	−	0.614782i	$-0.210756\pi$
$401$	3.48263	+	3.48263i	0.173914	+	0.173914i	−0.614782	+	0.788697i	$0.710756\pi$
$402$		0			0
$403$	0.896640	−	4.50771i	0.0446648	−	0.224545i
$404$		0			0
$405$	11.6842	+	7.80716i	0.580595	+	0.387941i
$406$		0			0
$407$	49.4343	+	20.4764i	2.45037	+	1.01498i
$408$		0			0
$409$	18.5077	−	7.66613i	0.915145	−	0.379065i	0.125121	−	0.992141i	$-0.460068\pi$
$409$	18.5077	−	7.66613i	0.915145	−	0.379065i	0.790024	+	0.613076i	$0.210068\pi$
$410$		0			0
$411$	3.15059	+	15.8391i	0.155407	+	0.781285i
$412$		0			0
$413$	−12.9906	−	19.4419i	−0.639228	−	0.956672i
$414$		0			0
$415$		−	6.46396i		−	0.317303i
$416$		0			0
$417$		−	10.4377i		−	0.511138i
$418$		0			0
$419$	−17.7369	−	26.5451i	−0.866503	−	1.29681i	−0.953742	−	0.300626i	$-0.902804\pi$
$419$	−17.7369	−	26.5451i	−0.866503	−	1.29681i	0.0872386	−	0.996187i	$-0.472196\pi$
$420$		0			0
$421$	4.00504	+	20.1347i	0.195194	+	0.981304i	0.946832	+	0.321729i	$0.104264\pi$
$421$	4.00504	+	20.1347i	0.195194	+	0.981304i	−0.751638	+	0.659576i	$0.770736\pi$
$422$		0			0
$423$	−10.2982	+	4.26564i	−0.500714	+	0.207403i
$424$		0			0
$425$	−0.757362	−	0.313710i	−0.0367375	−	0.0152172i
$426$		0			0
$427$	16.5071	+	11.0297i	0.798836	+	0.533765i
$428$		0			0
$429$	−10.0892	+	50.7218i	−0.487111	+	2.44887i
$430$		0			0
$431$	−27.4402	−	27.4402i	−1.32175	−	1.32175i	−0.912360	−	0.409388i	$-0.865742\pi$
$431$	−27.4402	−	27.4402i	−1.32175	−	1.32175i	−0.409388	−	0.912360i	$-0.634258\pi$
$432$		0			0
$433$	5.45442	−	5.45442i	0.262123	−	0.262123i	−0.563793	−	0.825916i	$-0.690659\pi$
$433$	5.45442	−	5.45442i	0.262123	−	0.262123i	0.825916	+	0.563793i	$0.190659\pi$
$434$		0			0
$435$	11.3743	+	2.26249i	0.545355	+	0.108478i
$436$		0			0
$437$	−11.3385	+	16.9693i	−0.542394	+	0.811751i
$438$		0			0
$439$	8.42495	−	20.3396i	0.402101	−	0.970757i	−0.585055	−	0.810994i	$-0.698927\pi$
$439$	8.42495	−	20.3396i	0.402101	−	0.970757i	0.987155	−	0.159763i	$-0.0510731\pi$
$440$		0			0
$441$	0.00837565	+	0.0202206i	0.000398840	+	0.000962886i
$442$		0			0
$443$	−28.7291	+	5.71458i	−1.36496	+	0.271508i	−0.822592	−	0.568632i	$-0.807473\pi$
$443$	−28.7291	+	5.71458i	−1.36496	+	0.271508i	−0.542370	+	0.840139i	$0.682473\pi$
$444$		0			0
$445$	−14.5881	+	9.74743i	−0.691540	+	0.462072i
$446$		0			0
$447$	−7.73980			−0.366080
$448$		0			0
$449$	−6.13112			−0.289345			−0.144673	−	0.989480i	$-0.546213\pi$
$449$	−6.13112			−0.289345			−0.144673	+	0.989480i	$0.546213\pi$
$450$		0			0
$451$	11.3356	−	7.57419i	0.533772	−	0.356655i
$452$		0			0
$453$	41.0873	−	8.17277i	1.93045	−	0.383990i
$454$		0			0
$455$	6.85428	+	16.5477i	0.321334	+	0.775768i
$456$		0			0
$457$	−6.01802	+	14.5288i	−0.281511	+	0.679628i	−0.999871	−	0.0160431i	$-0.994893\pi$
$457$	−6.01802	+	14.5288i	−0.281511	+	0.679628i	0.718360	+	0.695672i	$0.244893\pi$
$458$		0			0
$459$	−0.00607582	+	0.00909311i	−0.000283595	+	0.000424430i
$460$		0			0
$461$	−8.71608	−	1.73374i	−0.405949	−	0.0807482i	−0.0121074	−	0.999927i	$-0.503854\pi$
$461$	−8.71608	−	1.73374i	−0.405949	−	0.0807482i	−0.393841	+	0.919179i	$0.628854\pi$
$462$		0			0
$463$	−28.3923	+	28.3923i	−1.31950	+	1.31950i	−0.405329	+	0.914171i	$0.632843\pi$
$463$	−28.3923	+	28.3923i	−1.31950	+	1.31950i	−0.914171	+	0.405329i	$0.867157\pi$
$464$		0			0
$465$	−2.89831	−	2.89831i	−0.134406	−	0.134406i
$466$		0			0
$467$	−1.97602	+	9.93412i	−0.0914392	+	0.459696i	0.907753	+	0.419505i	$0.137796\pi$
$467$	−1.97602	+	9.93412i	−0.0914392	+	0.459696i	−0.999192	+	0.0401906i	$0.987204\pi$
$468$		0			0
$469$	18.3073	+	12.2326i	0.845355	+	0.564848i
$470$		0			0
$471$	7.46878	+	3.09367i	0.344143	+	0.142549i
$472$		0			0
$473$	−3.12819	+	1.29574i	−0.143834	+	0.0595780i
$474$		0			0
$475$	3.32039	+	16.6927i	0.152350	+	0.765915i
$476$		0			0
$477$	7.84913	+	11.7471i	0.359387	+	0.537861i
$478$		0			0
$479$			35.2640i			1.61125i	0.592424	+	0.805627i	$0.298171\pi$
$479$			35.2640i			1.61125i	−0.592424	+	0.805627i	$0.701829\pi$
$480$		0			0
$481$			47.2077i			2.15249i
$482$		0			0
$483$	−10.9818	−	16.4354i	−0.499689	−	0.747837i
$484$		0			0
$485$	2.23631	+	11.2427i	0.101546	+	0.510505i
$486$		0			0
$487$	−13.0372	+	5.40020i	−0.590774	+	0.244707i	−0.657984	−	0.753032i	$-0.728590\pi$
$487$	−13.0372	+	5.40020i	−0.590774	+	0.244707i	0.0672097	+	0.997739i	$0.478590\pi$
$488$		0			0
$489$	8.06276	+	3.33970i	0.364611	+	0.151027i
$490$		0			0
$491$	1.51681	+	1.01350i	0.0684528	+	0.0457387i	0.589326	−	0.807896i	$-0.299393\pi$
$491$	1.51681	+	1.01350i	0.0684528	+	0.0457387i	−0.520873	+	0.853634i	$0.674393\pi$
$492$		0			0
$493$	0.189868	−	0.954531i	0.00855123	−	0.0429899i
$494$		0			0
$495$	16.3437	+	16.3437i	0.734593	+	0.734593i
$496$		0			0
$497$	2.96525	−	2.96525i	0.133010	−	0.133010i
$498$		0			0
$499$	6.00903	+	1.19527i	0.269001	+	0.0535076i	0.327748	−	0.944765i	$-0.393710\pi$
$499$	6.00903	+	1.19527i	0.269001	+	0.0535076i	−0.0587467	+	0.998273i	$0.518710\pi$
$500$		0			0
$501$	17.3265	−	25.9309i	0.774091	−	1.15851i
$502$		0			0
$503$	−0.252675	+	0.610011i	−0.0112662	+	0.0271990i	−0.929413	−	0.369042i	$-0.879686\pi$
$503$	−0.252675	+	0.610011i	−0.0112662	+	0.0271990i	0.918146	+	0.396241i	$0.129686\pi$
$504$		0			0
$505$	8.29623	+	20.0289i	0.369177	+	0.891273i
$506$		0			0
$507$	−13.4828	+	2.68189i	−0.598791	+	0.119107i
$508$		0			0
$509$	−0.523675	+	0.349909i	−0.0232115	+	0.0155094i	−0.567122	−	0.823634i	$-0.691943\pi$
$509$	−0.523675	+	0.349909i	−0.0232115	+	0.0155094i	0.543910	+	0.839143i	$0.316943\pi$
$510$		0			0
$511$	9.46857			0.418865
$512$		0			0
$513$	0.227055			0.0100247
$514$		0			0
$515$	12.5498	−	8.38549i	0.553009	−	0.369509i
$516$		0			0
$517$	17.7348	−	3.52766i	0.779974	−	0.155146i
$518$		0			0
$519$	−0.576450	−	1.39167i	−0.0253033	−	0.0610877i
$520$		0			0
$521$	0.0504944	−	0.121904i	0.00221220	−	0.00534072i	−0.922770	−	0.385352i	$-0.874080\pi$
$521$	0.0504944	−	0.121904i	0.00221220	−	0.00534072i	0.924982	+	0.380011i	$0.124080\pi$
$522$		0			0
$523$	2.15403	−	3.22374i	0.0941892	−	0.140964i	−0.781382	−	0.624053i	$-0.785485\pi$
$523$	2.15403	−	3.22374i	0.0941892	−	0.140964i	0.875572	+	0.483088i	$0.160485\pi$
$524$		0			0
$525$	−16.1676	−	3.21593i	−0.705611	−	0.140355i
$526$		0			0
$527$	−0.243227	+	0.243227i	−0.0105951	+	0.0105951i
$528$		0			0
$529$	−9.70721	−	9.70721i	−0.422053	−	0.422053i
$530$		0			0
$531$	5.19361	−	26.1101i	0.225384	−	1.13308i
$532$		0			0
$533$	10.0010	+	6.68246i	0.433192	+	0.289450i
$534$		0			0
$535$	−6.93569	−	2.87286i	−0.299856	−	0.124204i
$536$		0			0
$537$	−41.1960	+	17.0639i	−1.77774	+	0.736363i
$538$		0			0
$539$	−0.00692661	−	0.0348224i	−0.000298350	−	0.00149991i
$540$		0			0
$541$	6.56680	+	9.82791i	0.282329	+	0.422535i	0.945346	−	0.326070i	$-0.105724\pi$
$541$	6.56680	+	9.82791i	0.282329	+	0.422535i	−0.663017	+	0.748604i	$0.730724\pi$
$542$		0			0
$543$			57.8873i			2.48418i
$544$		0			0
$545$			10.1785i			0.436001i
$546$		0			0
$547$	3.90437	+	5.84330i	0.166939	+	0.249841i	0.905501	−	0.424343i	$-0.139495\pi$
$547$	3.90437	+	5.84330i	0.166939	+	0.249841i	−0.738563	+	0.674185i	$0.764495\pi$
$548$		0			0
$549$	4.40964	+	22.1688i	0.188199	+	0.946140i
$550$		0			0
$551$	−18.6680	+	7.73252i	−0.795282	+	0.329417i
$552$		0			0
$553$	16.2446	+	6.72872i	0.690789	+	0.286134i
$554$		0			0
$555$	35.0055	+	23.3900i	1.48590	+	0.992848i
$556$		0			0
$557$	8.38778	−	42.1682i	0.355402	−	1.78672i	−0.227076	−	0.973877i	$-0.572916\pi$
$557$	8.38778	−	42.1682i	0.355402	−	1.78672i	0.582477	−	0.812847i	$-0.302084\pi$
$558$		0			0
$559$	−2.11233	−	2.11233i	−0.0893422	−	0.0893422i
$560$		0			0
$561$	2.73684	−	2.73684i	0.115549	−	0.115549i
$562$		0			0
$563$	−10.4779	−	2.08419i	−0.441592	−	0.0878381i	−0.0307136	−	0.999528i	$-0.509778\pi$
$563$	−10.4779	−	2.08419i	−0.441592	−	0.0878381i	−0.410879	+	0.911690i	$0.634778\pi$
$564$		0			0
$565$	12.7293	−	19.0507i	0.535525	−	0.801469i
$566$		0			0
$567$	9.07492	−	21.9088i	0.381111	−	0.920083i
$568$		0			0
$569$	−9.56257	−	23.0861i	−0.400884	−	0.967819i	−0.987452	−	0.157919i	$-0.949521\pi$
$569$	−9.56257	−	23.0861i	−0.400884	−	0.967819i	0.586568	−	0.809900i	$-0.300479\pi$
$570$		0			0
$571$	20.9430	−	4.16583i	0.876439	−	0.174335i	0.263685	−	0.964609i	$-0.415062\pi$
$571$	20.9430	−	4.16583i	0.876439	−	0.174335i	0.612753	+	0.790274i	$0.290062\pi$
$572$		0			0
$573$	−18.5208	+	12.3752i	−0.773718	+	0.516982i
$574$		0			0
$575$	7.73227			0.322458
$576$		0			0
$577$	13.5096			0.562413			0.281207	−	0.959647i	$-0.409265\pi$
$577$	13.5096			0.562413			0.281207	+	0.959647i	$0.409265\pi$
$578$		0			0
$579$	48.5431	−	32.4355i	2.01738	−	1.34797i
$580$		0			0
$581$	−10.6985	+	2.12806i	−0.443847	+	0.0882866i
$582$		0			0
$583$	−8.77059	−	21.1741i	−0.363241	−	0.876941i
$584$		0			0
$585$	−7.80377	+	18.8400i	−0.322646	+	0.778937i
$586$		0			0
$587$	7.71852	−	11.5516i	0.318577	−	0.476785i	−0.637273	−	0.770638i	$-0.719938\pi$
$587$	7.71852	−	11.5516i	0.318577	−	0.476785i	0.955851	+	0.293853i	$0.0949377\pi$
$588$		0			0
$589$	7.00431	+	1.39324i	0.288607	+	0.0574076i
$590$		0			0
$591$	−13.7457	+	13.7457i	−0.565423	+	0.565423i
$592$		0			0
$593$	3.80843	+	3.80843i	0.156393	+	0.156393i	0.780966	−	0.624573i	$-0.214727\pi$
$593$	3.80843	+	3.80843i	0.156393	+	0.156393i	−0.624573	+	0.780966i	$0.714727\pi$
$594$		0			0
$595$	0.261518	−	1.31474i	0.0107212	−	0.0538991i
$596$		0			0
$597$	−19.3829	−	12.9512i	−0.793290	−	0.530059i
$598$		0			0
$599$	−9.18975	−	3.80652i	−0.375483	−	0.155530i	0.186957	−	0.982368i	$-0.440137\pi$
$599$	−9.18975	−	3.80652i	−0.375483	−	0.155530i	−0.562440	+	0.826838i	$0.690137\pi$
$600$		0			0
$601$	28.7287	−	11.8998i	1.17187	−	0.485404i	0.290059	−	0.957009i	$-0.406325\pi$
$601$	28.7287	−	11.8998i	1.17187	−	0.485404i	0.881810	+	0.471605i	$0.156325\pi$
$602$		0			0
$603$	4.89054	+	24.5864i	0.199158	+	1.00124i
$604$		0			0
$605$	−11.2446	−	16.8287i	−0.457157	−	0.684183i
$606$		0			0
$607$		−	38.5851i		−	1.56612i	−0.621946	−	0.783060i	$-0.713657\pi$
$607$		−	38.5851i		−	1.56612i	0.621946	−	0.783060i	$-0.286343\pi$
$608$		0			0
$609$		−	19.5704i		−	0.793031i
$610$		0			0
$611$	8.86320	+	13.2647i	0.358567	+	0.536633i
$612$		0			0
$613$	6.11185	+	30.7263i	0.246855	+	1.24102i	0.882970	+	0.469430i	$0.155541\pi$
$613$	6.11185	+	30.7263i	0.246855	+	1.24102i	−0.636114	+	0.771595i	$0.719459\pi$
$614$		0			0
$615$	9.91038	−	4.10501i	0.399625	−	0.165530i
$616$		0			0
$617$	29.6969	+	12.3009i	1.19555	+	0.495214i	0.889559	−	0.456820i	$-0.151012\pi$
$617$	29.6969	+	12.3009i	1.19555	+	0.495214i	0.305992	+	0.952034i	$0.401012\pi$
$618$		0			0
$619$	−29.9290	−	19.9979i	−1.20295	−	0.803784i	−0.217884	−	0.975975i	$-0.569915\pi$
$619$	−29.9290	−	19.9979i	−1.20295	−	0.803784i	−0.985064	+	0.172191i	$0.944915\pi$
$620$		0			0
$621$	0.0201243	−	0.101172i	0.000807560	−	0.00405988i
$622$		0			0
$623$	20.9356	+	20.9356i	0.838766	+	0.838766i
$624$		0			0
$625$	−4.14010	+	4.14010i	−0.165604	+	0.165604i
$626$		0			0
$627$	−78.8140	−	15.6771i	−3.14753	−	0.626083i
$628$		0			0
$629$	1.96289	−	2.93767i	0.0782655	−	0.117133i
$630$		0			0
$631$	15.0722	−	36.3874i	0.600013	−	1.44856i	−0.273554	−	0.961857i	$-0.588199\pi$
$631$	15.0722	−	36.3874i	0.600013	−	1.44856i	0.873567	−	0.486703i	$-0.161801\pi$
$632$		0			0
$633$	−9.34296	−	22.5559i	−0.371349	−	0.896516i
$634$		0			0
$635$	−4.68686	+	0.932275i	−0.185992	+	0.0369962i
$636$		0			0
$637$	0.0260454	−	0.0174030i	0.00103196	−	0.000689532i
$638$		0			0
$639$	4.77440			0.188872
$640$		0			0
$641$	−26.2384			−1.03636			−0.518178	−	0.855273i	$-0.673390\pi$
$641$	−26.2384			−1.03636			−0.518178	+	0.855273i	$0.673390\pi$
$642$		0			0
$643$	−38.6415	+	25.8194i	−1.52387	+	1.01822i	−0.539527	+	0.841968i	$0.681397\pi$
$643$	−38.6415	+	25.8194i	−1.52387	+	1.01822i	−0.984345	+	0.176251i	$0.943603\pi$
$644$		0			0
$645$	−2.61293	+	0.519745i	−0.102884	+	0.0204649i
$646$		0			0
$647$	12.2347	+	29.5371i	0.480994	+	1.16122i	0.959137	+	0.282941i	$0.0913100\pi$
$647$	12.2347	+	29.5371i	0.480994	+	1.16122i	−0.478143	+	0.878282i	$0.658690\pi$
$648$		0			0
$649$	−16.5265	+	39.8984i	−0.648721	+	1.56615i
$650$		0			0
$651$	−3.84280	+	5.75115i	−0.150611	+	0.225406i
$652$		0			0
$653$	−7.27084	−	1.44626i	−0.284530	−	0.0565965i	0.0507621	−	0.998711i	$-0.483835\pi$
$653$	−7.27084	−	1.44626i	−0.284530	−	0.0565965i	−0.335292	+	0.942114i	$0.608835\pi$
$654$		0			0
$655$	8.35304	−	8.35304i	0.326380	−	0.326380i
$656$		0			0
$657$	7.62275	+	7.62275i	0.297392	+	0.297392i
$658$		0			0
$659$	−3.26994	+	16.4391i	−0.127379	+	0.640376i	0.863359	+	0.504589i	$0.168356\pi$
$659$	−3.26994	+	16.4391i	−0.127379	+	0.640376i	−0.990738	+	0.135786i	$0.956644\pi$
$660$		0			0
$661$	−33.5942	−	22.4469i	−1.30666	−	0.873084i	−0.309690	−	0.950838i	$-0.600225\pi$
$661$	−33.5942	−	22.4469i	−1.30666	−	0.873084i	−0.996973	+	0.0777539i	$0.975225\pi$
$662$		0			0
$663$	3.15486	+	1.30679i	0.122525	+	0.0507513i
$664$		0			0
$665$	−25.7126	+	10.6505i	−0.997093	+	0.413010i
$666$		0			0
$667$	1.79090	+	9.00345i	0.0693438	+	0.348615i
$668$		0			0
$669$	−16.6665	−	24.9432i	−0.644365	−	0.964360i
$670$		0			0
$671$		−	36.6669i		−	1.41551i
$672$		0			0
$673$		−	23.6438i		−	0.911401i	−0.890133	−	0.455701i	$-0.849389\pi$
$673$		−	23.6438i		−	0.911401i	0.890133	−	0.455701i	$-0.150611\pi$
$674$		0			0
$675$	−0.0477926	−	0.0715267i	−0.00183954	−	0.00275306i
$676$		0			0
$677$	4.38350	+	22.0374i	0.168472	+	0.846964i	0.968884	+	0.247515i	$0.0796139\pi$
$677$	4.38350	+	22.0374i	0.168472	+	0.846964i	−0.800412	+	0.599450i	$0.795386\pi$
$678$		0			0
$679$	17.8715	−	7.40262i	0.685845	−	0.284086i
$680$		0			0
$681$	−40.3916	−	16.7307i	−1.54781	−	0.641123i
$682$		0			0
$683$	−18.4573	−	12.3328i	−0.706251	−	0.471902i	0.149851	−	0.988709i	$-0.452121\pi$
$683$	−18.4573	−	12.3328i	−0.706251	−	0.471902i	−0.856102	+	0.516807i	$0.827121\pi$
$684$		0			0
$685$	2.01531	−	10.1317i	0.0770011	−	0.387111i
$686$		0			0
$687$	−28.9639	−	28.9639i	−1.10504	−	1.10504i
$688$		0			0
$689$	14.2980	−	14.2980i	0.544709	−	0.544709i
$690$		0			0
$691$	31.1924	+	6.20456i	1.18662	+	0.236033i	0.748654	−	0.662961i	$-0.230700\pi$
$691$	31.1924	+	6.20456i	1.18662	+	0.236033i	0.437962	+	0.898993i	$0.355700\pi$
$692$		0			0
$693$	21.6697	−	32.4310i	0.823163	−	1.23195i
$694$		0			0
$695$	−2.55503	+	6.16839i	−0.0969179	+	0.233980i
$696$		0			0
$697$	−0.344493	−	0.831680i	−0.0130486	−	0.0315021i
$698$		0			0
$699$	25.0068	−	4.97416i	0.945844	−	0.188140i
$700$		0			0
$701$	0.645283	−	0.431165i	0.0243720	−	0.0162849i	−0.543325	−	0.839523i	$-0.682835\pi$
$701$	0.645283	−	0.431165i	0.0243720	−	0.0162849i	0.567697	+	0.823238i	$0.307835\pi$
$702$		0			0
$703$	−73.3537			−2.76659
$704$		0			0
$705$	14.2275			0.535839
$706$		0			0
$707$	30.4184	−	20.3249i	1.14400	−	0.764397i
$708$		0			0
$709$	−37.8179	+	7.52244i	−1.42028	+	0.282511i	−0.844703	−	0.535236i	$-0.820223\pi$
$709$	−37.8179	+	7.52244i	−1.42028	+	0.282511i	−0.575578	+	0.817747i	$0.695223\pi$
$710$		0			0
$711$	7.66081	+	18.4948i	0.287303	+	0.693610i
$712$		0			0
$713$	1.24161	−	2.99751i	0.0464986	−	0.112257i
$714$		0			0
$715$	18.3785	−	27.5054i	0.687317	−	1.02864i
$716$		0			0
$717$	50.2374	+	9.99283i	1.87615	+	0.373189i
$718$		0			0
$719$	23.5486	−	23.5486i	0.878215	−	0.878215i	−0.115135	−	0.993350i	$-0.536730\pi$
$719$	23.5486	−	23.5486i	0.878215	−	0.878215i	0.993350	+	0.115135i	$0.0367300\pi$
$720$		0			0
$721$	−18.0104	−	18.0104i	−0.670742	−	0.670742i
$722$		0			0
$723$	−4.78964	+	24.0792i	−0.178129	+	0.895514i
$724$		0			0
$725$	6.36529	+	4.25315i	0.236401	+	0.157958i
$726$		0			0
$727$	30.1679	+	12.4960i	1.11887	+	0.463449i	0.863982	−	0.503522i	$-0.167963\pi$
$727$	30.1679	+	12.4960i	1.11887	+	0.463449i	0.254884	+	0.966972i	$0.417963\pi$
$728$		0			0
$729$	25.1739	−	10.4274i	0.932368	−	0.386200i
$730$		0			0
$731$	0.0436171	+	0.219278i	0.00161324	+	0.00811028i
$732$		0			0
$733$	8.07259	+	12.0815i	0.298168	+	0.446240i	0.950058	−	0.312074i	$-0.101024\pi$
$733$	8.07259	+	12.0815i	0.298168	+	0.446240i	−0.651890	+	0.758313i	$0.726024\pi$
$734$		0			0
$735$		−	0.0279359i		−	0.00103043i
$736$		0			0
$737$		−	40.6657i		−	1.49794i
$738$		0			0
$739$	−0.511163	−	0.765010i	−0.0188034	−	0.0281414i	0.821949	−	0.569561i	$-0.192887\pi$
$739$	−0.511163	−	0.765010i	−0.0188034	−	0.0281414i	−0.840752	+	0.541420i	$0.817887\pi$
$740$		0			0
$741$	−13.8314	−	69.5351i	−0.508109	−	2.55443i
$742$		0			0
$743$	−1.25045	+	0.517953i	−0.0458745	+	0.0190019i	−0.405503	−	0.914094i	$-0.632904\pi$
$743$	−1.25045	+	0.517953i	−0.0458745	+	0.0190019i	0.359628	+	0.933096i	$0.382904\pi$
$744$		0			0
$745$	4.57399	+	1.89461i	0.167578	+	0.0694131i
$746$		0			0
$747$	−10.3261	−	6.89967i	−0.377812	−	0.252446i
$748$		0			0
$749$	−2.47149	+	12.4250i	−0.0903063	+	0.454001i
$750$		0			0
$751$	0.132681	+	0.132681i	0.00484161	+	0.00484161i	0.709523	−	0.704682i	$-0.248910\pi$
$751$	0.132681	+	0.132681i	0.00484161	+	0.00484161i	−0.704682	+	0.709523i	$0.748910\pi$
$752$		0			0
$753$	31.0208	−	31.0208i	1.13046	−	1.13046i
$754$		0			0
$755$	−26.2820	−	5.22781i	−0.956499	−	0.190259i
$756$		0			0
$757$	−13.3592	+	19.9934i	−0.485547	+	0.726673i	−0.990656	−	0.136383i	$-0.956452\pi$
$757$	−13.3592	+	19.9934i	−0.485547	+	0.726673i	0.505109	+	0.863056i	$0.331452\pi$
$758$		0			0
$759$	−13.9708	+	33.7286i	−0.507110	+	1.22427i
$760$		0			0
$761$	−5.79279	−	13.9850i	−0.209988	−	0.506957i	0.783433	−	0.621477i	$-0.213467\pi$
$761$	−5.79279	−	13.9850i	−0.209988	−	0.506957i	−0.993421	+	0.114520i	$0.963467\pi$
$762$		0			0
$763$	16.8464	−	3.35097i	0.609882	−	0.121313i
$764$		0			0
$765$	1.26898	−	0.847905i	0.0458801	−	0.0306561i
$766$		0			0
$767$	−38.1014			−1.37576
$768$		0			0
$769$	−19.9780			−0.720424			−0.360212	−	0.932870i	$-0.617296\pi$
$769$	−19.9780			−0.720424			−0.360212	+	0.932870i	$0.617296\pi$
$770$		0			0
$771$	−54.8690	+	36.6623i	−1.97606	+	1.32036i
$772$		0			0
$773$	22.0912	−	4.39422i	0.794566	−	0.158049i	0.218914	−	0.975744i	$-0.429748\pi$
$773$	22.0912	−	4.39422i	0.794566	−	0.158049i	0.575652	+	0.817695i	$0.304748\pi$
$774$		0			0
$775$	−1.03543	−	2.49975i	−0.0371938	−	0.0897937i
$776$		0			0
$777$	27.1881	−	65.6379i	0.975368	−	2.35475i
$778$		0			0
$779$	−10.3835	+	15.5401i	−0.372029	+	0.556781i
$780$		0			0
$781$	−7.59625	−	1.51099i	−0.271815	−	0.0540674i
$782$		0			0
$783$	0.0722162	−	0.0722162i	0.00258080	−	0.00258080i
$784$		0			0
$785$	−3.65654	−	3.65654i	−0.130507	−	0.130507i
$786$		0			0
$787$	4.09490	−	20.5865i	0.145968	−	0.733828i	−0.836584	−	0.547838i	$-0.815451\pi$
$787$	4.09490	−	20.5865i	0.145968	−	0.733828i	0.982552	−	0.185990i	$-0.0595491\pi$
$788$		0			0
$789$	7.26663	+	4.85541i	0.258699	+	0.172857i
$790$		0			0
$791$	−35.7214	−	14.7963i	−1.27011	−	0.526096i
$792$		0			0
$793$	29.8875	−	12.3798i	1.06134	−	0.439620i
$794$		0			0
$795$	−3.51805	−	17.6864i	−0.124772	−	0.627273i
$796$		0			0
$797$	8.04761	+	12.0441i	0.285061	+	0.426624i	0.946172	−	0.323664i	$-0.104915\pi$
$797$	8.04761	+	12.0441i	0.285061	+	0.426624i	−0.661111	+	0.750288i	$0.729915\pi$
$798$		0			0
$799$		−	1.19397i		−	0.0422398i
$800$		0			0
$801$			33.7087i			1.19104i
$802$		0			0
$803$	−9.71565	−	14.5405i	−0.342858	−	0.513123i
$804$		0			0
$805$	2.46672	+	12.4011i	0.0869406	+	0.437080i
$806$		0			0
$807$	−46.1089	+	19.0989i	−1.62311	+	0.672314i
$808$		0			0
$809$	22.9681	+	9.51370i	0.807516	+	0.334484i	0.747962	−	0.663741i	$-0.231032\pi$
$809$	22.9681	+	9.51370i	0.807516	+	0.334484i	0.0595534	+	0.998225i	$0.481032\pi$
$810$		0			0
$811$	−42.7853	−	28.5882i	−1.50240	−	1.00387i	−0.989358	−	0.145502i	$-0.953520\pi$
$811$	−42.7853	−	28.5882i	−1.50240	−	1.00387i	−0.513037	−	0.858366i	$-0.671480\pi$
$812$		0			0
$813$	−1.24112	+	6.23955i	−0.0435281	+	0.218831i
$814$		0			0
$815$	−3.94733	−	3.94733i	−0.138269	−	0.138269i
$816$		0			0
$817$	3.28225	−	3.28225i	0.114831	−	0.114831i
$818$		0			0
$819$	33.7511	+	6.71351i	1.17936	+	0.234589i
$820$		0			0
$821$	−23.3191	+	34.8995i	−0.813842	+	1.21800i	0.159171	+	0.987251i	$0.449118\pi$
$821$	−23.3191	+	34.8995i	−0.813842	+	1.21800i	−0.973013	+	0.230750i	$0.925882\pi$
$822$		0			0
$823$	−9.73452	+	23.5012i	−0.339324	+	0.819201i	0.658457	+	0.752618i	$0.271209\pi$
$823$	−9.73452	+	23.5012i	−0.339324	+	0.819201i	−0.997781	+	0.0665823i	$0.978791\pi$
$824$		0			0
$825$	11.6509	+	28.1278i	0.405632	+	0.979283i
$826$		0			0
$827$	−32.4157	+	6.44788i	−1.12720	+	0.224215i	−0.723265	−	0.690571i	$-0.757359\pi$
$827$	−32.4157	+	6.44788i	−1.12720	+	0.224215i	−0.403939	+	0.914786i	$0.632359\pi$
$828$		0			0
$829$	35.9504	−	24.0213i	1.24861	−	0.834295i	0.257363	−	0.966315i	$-0.417146\pi$
$829$	35.9504	−	24.0213i	1.24861	−	0.834295i	0.991247	+	0.132020i	$0.0421464\pi$
$830$		0			0
$831$	61.7874			2.14338
$832$		0			0
$833$	−0.00234438			−8.12281e−5
$834$		0			0
$835$	−16.5870	+	11.0831i	−0.574018	+	0.383546i
$836$		0			0
$837$	−0.0354024	+	0.00704198i	−0.00122369	+	0.000243406i
$838$		0			0
$839$	−10.8934	−	26.2990i	−0.376083	−	0.907943i	−0.992692	−	0.120674i	$-0.961494\pi$
$839$	−10.8934	−	26.2990i	−0.376083	−	0.907943i	0.616610	−	0.787269i	$-0.288506\pi$
$840$		0			0
$841$	7.61974	−	18.3957i	0.262750	−	0.634334i
$842$		0			0
$843$	−17.4846	+	26.1676i	−0.602203	+	0.901261i
$844$		0			0
$845$	8.62441	+	1.71550i	0.296689	+	0.0590150i
$846$		0			0
$847$	−24.1511	+	24.1511i	−0.829843	+	0.829843i
$848$		0			0
$849$	19.5888	+	19.5888i	0.672286	+	0.672286i
$850$		0			0
$851$	−6.50146	+	32.6851i	−0.222867	+	1.12043i
$852$		0			0
$853$	17.6610	+	11.8007i	0.604702	+	0.404049i	0.819888	−	0.572524i	$-0.194036\pi$
$853$	17.6610	+	11.8007i	0.604702	+	0.404049i	−0.215186	+	0.976573i	$0.569036\pi$
$854$		0			0
$855$	−29.2745	−	12.1259i	−1.00117	−	0.414696i
$856$		0			0
$857$	−49.6011	+	20.5455i	−1.69434	+	0.701820i	−0.999844	−	0.0176747i	$-0.994374\pi$
$857$	−49.6011	+	20.5455i	−1.69434	+	0.701820i	−0.694498	+	0.719494i	$0.744374\pi$
$858$		0			0
$859$	−2.87816	−	14.4695i	−0.0982015	−	0.493693i	−0.998314	−	0.0580359i	$-0.981516\pi$
$859$	−2.87816	−	14.4695i	−0.0982015	−	0.493693i	0.900113	−	0.435657i	$-0.143484\pi$
$860$		0			0
$861$	−10.0569	−	15.0512i	−0.342737	−	0.512942i
$862$		0			0
$863$		−	8.61085i		−	0.293117i	−0.989202	−	0.146558i	$-0.953180\pi$
$863$		−	8.61085i		−	0.293117i	0.989202	−	0.146558i	$-0.0468196\pi$
$864$		0			0
$865$			0.963545i			0.0327615i
$866$		0			0
$867$	23.0193	+	34.4508i	0.781777	+	1.17001i
$868$		0			0
$869$	−6.33544	−	31.8504i	−0.214915	−	1.08045i
$870$		0			0
$871$	33.1469	−	13.7299i	1.12314	−	0.465220i
$872$		0			0
$873$	20.3471	+	8.42806i	0.688646	+	0.285247i
$874$		0			0
$875$	26.0303	+	17.3929i	0.879985	+	0.587987i
$876$		0			0
$877$	−5.30612	+	26.6757i	−0.179175	+	0.900774i	0.781671	+	0.623691i	$0.214368\pi$
$877$	−5.30612	+	26.6757i	−0.179175	+	0.900774i	−0.960846	+	0.277083i	$0.910632\pi$
$878$		0			0
$879$	31.6276	+	31.6276i	1.06677	+	1.06677i
$880$		0			0
$881$	−29.5442	+	29.5442i	−0.995371	+	0.995371i	−0.999989	−	0.00461881i	$-0.998530\pi$
$881$	−29.5442	+	29.5442i	−0.995371	+	0.995371i	0.00461881	+	0.999989i	$0.498530\pi$
$882$		0			0
$883$	7.22231	+	1.43661i	0.243050	+	0.0483457i	0.315112	−	0.949054i	$-0.397958\pi$
$883$	7.22231	+	1.43661i	0.243050	+	0.0483457i	−0.0720619	+	0.997400i	$0.522958\pi$
$884$		0			0
$885$	−18.8780	+	28.2530i	−0.634578	+	0.949713i
$886$		0			0
$887$	7.30913	−	17.6458i	0.245417	−	0.592488i	−0.752388	−	0.658721i	$-0.771098\pi$
$887$	7.30913	−	17.6458i	0.245417	−	0.592488i	0.997804	+	0.0662325i	$0.0210979\pi$
$888$		0			0
$889$	3.08601	+	7.45028i	0.103501	+	0.249874i
$890$		0			0
$891$	−42.9562	+	8.54452i	−1.43909	+	0.286252i
$892$		0			0
$893$	−20.6114	+	13.7721i	−0.689733	+	0.460865i
$894$		0			0
$895$	28.5226			0.953406
$896$		0			0
$897$	−32.2094			−1.07544
$898$		0			0
$899$	2.67089	−	1.78463i	0.0890791	−	0.0595207i
$900$		0			0
$901$	−1.48425	+	0.295235i	−0.0494475	+	0.00983572i
$902$		0			0
$903$	1.72045	+	4.15354i	0.0572531	+	0.138221i
$904$		0			0
$905$	14.1701	−	34.2097i	0.471030	−	1.13717i
$906$		0			0
$907$	−0.812920	+	1.21662i	−0.0269926	+	0.0403973i	−0.844721	−	0.535208i	$-0.820233\pi$
$907$	−0.812920	+	1.21662i	−0.0269926	+	0.0403973i	0.817728	+	0.575605i	$0.195233\pi$
$908$		0			0
$909$	40.8513	+	8.12583i	1.35495	+	0.269517i
$910$		0			0
$911$	14.4917	−	14.4917i	0.480130	−	0.480130i	−0.425043	−	0.905173i	$-0.639741\pi$
$911$	14.4917	−	14.4917i	0.480130	−	0.480130i	0.905173	+	0.425043i	$0.139741\pi$
$912$		0			0
$913$	14.2456	+	14.2456i	0.471461	+	0.471461i
$914$		0			0
$915$	5.62843	−	28.2960i	0.186070	−	0.935438i
$916$		0			0
$917$	−16.5750	−	11.0751i	−0.547356	−	0.365732i
$918$		0			0
$919$	−5.31718	−	2.20245i	−0.175397	−	0.0726520i	0.293257	−	0.956034i	$-0.405261\pi$
$919$	−5.31718	−	2.20245i	−0.175397	−	0.0726520i	−0.468654	+	0.883382i	$0.655261\pi$
$920$		0			0
$921$	−14.3302	+	5.93575i	−0.472195	+	0.195590i
$922$		0			0
$923$	−1.33309	−	6.70192i	−0.0438793	−	0.220596i
$924$		0			0
$925$	15.4401	+	23.1078i	0.507668	+	0.759779i
$926$		0			0
$927$		−	28.9988i		−	0.952447i
$928$		0			0
$929$			45.4656i			1.49168i	0.666126	+	0.745839i	$0.267951\pi$
$929$			45.4656i			1.49168i	−0.666126	+	0.745839i	$0.732049\pi$
$930$		0			0
$931$	0.0270416	+	0.0404707i	0.000886254	+	0.00132637i
$932$		0			0
$933$	−8.53316	−	42.8991i	−0.279363	−	1.40445i
$934$		0			0
$935$	−2.28734	+	0.947446i	−0.0748039	+	0.0309848i
$936$		0			0
$937$	−23.3888	−	9.68796i	−0.764079	−	0.316492i	−0.0336074	−	0.999435i	$-0.510700\pi$
$937$	−23.3888	−	9.68796i	−0.764079	−	0.316492i	−0.730471	+	0.682943i	$0.760700\pi$
$938$		0			0
$939$	14.3821	+	9.60978i	0.469341	+	0.313603i
$940$		0			0
$941$	9.35177	−	47.0145i	0.304859	−	1.53263i	−0.459698	−	0.888075i	$-0.652043\pi$
$941$	9.35177	−	47.0145i	0.304859	−	1.53263i	0.764558	−	0.644555i	$-0.222957\pi$
$942$		0			0
$943$	6.00406	+	6.00406i	0.195519	+	0.195519i
$944$		0			0
$945$	0.0994682	−	0.0994682i	0.00323570	−	0.00323570i
$946$		0			0
$947$	19.0706	+	3.79337i	0.619711	+	0.123268i	0.494954	−	0.868919i	$-0.335185\pi$
$947$	19.0706	+	3.79337i	0.619711	+	0.123268i	0.124757	+	0.992187i	$0.460185\pi$
$948$		0			0
$949$	8.57180	−	12.8286i	0.278252	−	0.416434i
$950$		0			0
$951$	−31.4927	+	76.0301i	−1.02122	+	2.46545i
$952$		0			0
$953$	11.3085	+	27.3010i	0.366317	+	0.884367i	0.994347	+	0.106178i	$0.0338614\pi$
$953$	11.3085	+	27.3010i	0.366317	+	0.884367i	−0.628030	+	0.778189i	$0.716139\pi$
$954$		0			0
$955$	13.9746	−	2.77971i	0.452206	−	0.0899493i
$956$		0			0
$957$	−30.0534	+	20.0811i	−0.971489	+	0.649128i
$958$		0			0
$959$	−17.4323			−0.562920
$960$		0			0
$961$	29.8647			0.963377
$962$		0			0
$963$	−11.9926	+	8.01318i	−0.386455	+	0.258221i
$964$		0			0
$965$	−36.6274	+	7.28563i	−1.17908	+	0.234533i
$966$		0			0
$967$	−7.94230	−	19.1744i	−0.255407	−	0.616607i	0.743217	−	0.669051i	$-0.233299\pi$
$967$	−7.94230	−	19.1744i	−0.255407	−	0.616607i	−0.998624	+	0.0524434i	$0.983299\pi$
$968$		0			0
$969$	−2.03055	+	4.90217i	−0.0652306	+	0.157481i
$970$		0			0
$971$	13.5493	−	20.2780i	0.434819	−	0.650753i	−0.547752	−	0.836641i	$-0.684516\pi$
$971$	13.5493	−	20.2780i	0.434819	−	0.650753i	0.982571	+	0.185888i	$0.0595161\pi$
$972$		0			0
$973$	11.0504	+	2.19807i	0.354261	+	0.0704668i
$974$		0			0
$975$	−18.9935	+	18.9935i	−0.608279	+	0.608279i
$976$		0			0
$977$	−2.62269	−	2.62269i	−0.0839073	−	0.0839073i	0.663907	−	0.747815i	$-0.268897\pi$
$977$	−2.62269	−	2.62269i	−0.0839073	−	0.0839073i	−0.747815	+	0.663907i	$0.768897\pi$
$978$		0			0
$979$	10.6680	−	53.6318i	0.340952	−	1.71408i
$980$		0			0
$981$	16.2601	+	10.8646i	0.519145	+	0.346882i
$982$		0			0
$983$	15.6197	+	6.46990i	0.498191	+	0.206358i	0.617607	−	0.786487i	$-0.288102\pi$
$983$	15.6197	+	6.46990i	0.498191	+	0.206358i	−0.119416	+	0.992844i	$0.538102\pi$
$984$		0			0
$985$	11.4881	−	4.75853i	0.366041	−	0.151619i
$986$		0			0
$987$	−4.68396	−	23.5479i	−0.149092	−	0.749537i
$988$		0			0
$989$	−1.17160	−	1.75342i	−0.0372546	−	0.0557555i
$990$		0			0
$991$		−	26.6890i		−	0.847803i	−0.905708	−	0.423902i	$-0.860660\pi$
$991$		−	26.6890i		−	0.847803i	0.905708	−	0.423902i	$-0.139340\pi$
$992$		0			0
$993$		−	29.1998i		−	0.926628i
$994$		0			0
$995$	8.28441	+	12.3985i	0.262634	+	0.393059i
$996$		0			0
$997$	−9.09171	−	45.7071i	−0.287937	−	1.44756i	−0.805847	−	0.592124i	$-0.798290\pi$
$997$	−9.09171	−	45.7071i	−0.287937	−	1.44756i	0.517910	−	0.855435i	$-0.326710\pi$
$998$		0			0
$999$	0.342535	−	0.141883i	0.0108373	−	0.00448897i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.i.a.33.1		56
4.3	odd	2		512.2.i.b.33.7		56
8.3	odd	2		64.2.i.a.13.3	yes	56
8.5	even	2		256.2.i.a.145.7		56
24.11	even	2		576.2.bd.a.397.5		56
64.5	even	16	inner	512.2.i.a.481.1		56
64.27	odd	16		64.2.i.a.5.3	✓	56
64.37	even	16		256.2.i.a.113.7		56
64.59	odd	16		512.2.i.b.481.7		56
192.155	even	16		576.2.bd.a.325.5		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.5.3	✓	56	64.27	odd	16
64.2.i.a.13.3	yes	56	8.3	odd	2
256.2.i.a.113.7		56	64.37	even	16
256.2.i.a.145.7		56	8.5	even	2
512.2.i.a.33.1		56	1.1	even	1	trivial
512.2.i.a.481.1		56	64.5	even	16	inner
512.2.i.b.33.7		56	4.3	odd	2
512.2.i.b.481.7		56	64.59	odd	16
576.2.bd.a.325.5		56	192.155	even	16
576.2.bd.a.397.5		56	24.11	even	2

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.i (of order \(16\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.03902 + 1.36243i) q^{3} +(1.53851 - 0.306028i) q^{5} +(-1.01301 - 2.44562i) q^{7} +(1.15334 - 2.78440i) q^{9} +O(q^{10})\)	\(q+(-2.03902 + 1.36243i) q^{3} +(1.53851 - 0.306028i) q^{5} +(-1.01301 - 2.44562i) q^{7} +(1.15334 - 2.78440i) q^{9} +(-2.71620 + 4.06508i) q^{11} +(-4.23055 - 0.841509i) q^{13} +(-2.72010 + 2.72010i) q^{15} +(0.228271 + 0.228271i) q^{17} +(1.30758 - 6.57364i) q^{19} +(5.39754 + 3.60652i) q^{21} +(-2.81320 - 1.16527i) q^{23} +(-2.34605 + 0.971766i) q^{25} +(0.00660900 + 0.0332257i) q^{27} +(-1.67490 - 2.50666i) q^{29} +1.06551i q^{31} -11.9894i q^{33} +(-2.30695 - 3.45260i) q^{35} +(-2.13514 - 10.7341i) q^{37} +(9.77267 - 4.04797i) q^{39} +(-2.57626 - 1.06712i) q^{41} +(0.575838 + 0.384763i) q^{43} +(0.922311 - 4.63677i) q^{45} +(-2.61525 - 2.61525i) q^{47} +(-0.00513508 + 0.00513508i) q^{49} +(-0.776454 - 0.154446i) q^{51} +(-2.60438 + 3.89774i) q^{53} +(-2.93486 + 7.08539i) q^{55} +(6.28994 + 15.1853i) q^{57} +(8.66346 - 1.72327i) q^{59} +(-6.23588 + 4.16668i) q^{61} -7.97794 q^{63} -6.76625 q^{65} +(-6.91594 + 4.62108i) q^{67} +(7.32376 - 1.45679i) q^{69} +(0.606236 + 1.46358i) q^{71} +(-1.36883 + 3.30465i) q^{73} +(3.45968 - 5.17778i) q^{75} +(12.6932 + 2.52483i) q^{77} +(-4.69681 + 4.69681i) q^{79} +(6.33452 + 6.33452i) q^{81} +(0.803913 - 4.04154i) q^{83} +(0.421054 + 0.281340i) q^{85} +(6.83030 + 2.82920i) q^{87} +(-10.3334 + 4.28021i) q^{89} +(2.22758 + 11.1988i) q^{91} +(-1.45169 - 2.17261i) q^{93} -10.5137i q^{95} +7.30754i q^{97} +(8.18612 + 12.2514i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{3} + 8 q^{5} + 8 q^{7} - 8 q^{9}+O(q^{10}) \) 56 * q - 8 * q^3 + 8 * q^5 + 8 * q^7 - 8 * q^9	\( 56 q - 8 q^{3} + 8 q^{5} + 8 q^{7} - 8 q^{9} - 8 q^{11} + 8 q^{13} + 8 q^{15} - 8 q^{17} - 8 q^{19} + 8 q^{21} + 8 q^{23} - 8 q^{25} - 8 q^{27} + 8 q^{29} - 8 q^{35} + 8 q^{37} + 8 q^{39} - 8 q^{41} - 8 q^{43} + 8 q^{45} + 8 q^{47} - 8 q^{49} + 24 q^{51} + 8 q^{53} - 56 q^{55} - 8 q^{57} + 56 q^{59} + 8 q^{61} - 64 q^{63} - 16 q^{65} + 72 q^{67} + 8 q^{69} - 56 q^{71} - 8 q^{73} + 56 q^{75} + 8 q^{77} - 24 q^{79} - 8 q^{81} - 8 q^{83} + 8 q^{85} + 8 q^{87} - 8 q^{89} - 8 q^{91} - 16 q^{93} + 16 q^{99}+O(q^{100}) \) 56 * q - 8 * q^3 + 8 * q^5 + 8 * q^7 - 8 * q^9 - 8 * q^11 + 8 * q^13 + 8 * q^15 - 8 * q^17 - 8 * q^19 + 8 * q^21 + 8 * q^23 - 8 * q^25 - 8 * q^27 + 8 * q^29 - 8 * q^35 + 8 * q^37 + 8 * q^39 - 8 * q^41 - 8 * q^43 + 8 * q^45 + 8 * q^47 - 8 * q^49 + 24 * q^51 + 8 * q^53 - 56 * q^55 - 8 * q^57 + 56 * q^59 + 8 * q^61 - 64 * q^63 - 16 * q^65 + 72 * q^67 + 8 * q^69 - 56 * q^71 - 8 * q^73 + 56 * q^75 + 8 * q^77 - 24 * q^79 - 8 * q^81 - 8 * q^83 + 8 * q^85 + 8 * q^87 - 8 * q^89 - 8 * q^91 - 16 * q^93 + 16 * q^99

Introduction

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Database

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