LMFDB - Embedded newform 896.2.bh.a.81.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [896,2,Mod(81,896)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(896, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([0, 9, 16]))

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

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

chi := DirichletCharacter("896.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 896 = 2^{7} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	896.bh (of order $24$, 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:	$7.15459602111$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{24})$
Twist minimal:	no (minimal twist has level 224)
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			81.12
Character	$\chi$	$=$	896.81
Dual form			896.2.bh.a.177.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.653842 + 0.501711i) q^{3} +(-1.21118 + 1.57844i) q^{5} +(1.14530 - 2.38501i) q^{7} +(-0.600661 + 2.24170i) q^{9} +O(q^{10})$	\(q+(-0.653842 + 0.501711i) q^{3} +(-1.21118 + 1.57844i) q^{5} +(1.14530 - 2.38501i) q^{7} +(-0.600661 + 2.24170i) q^{9} +(-0.0369986 + 0.281032i) q^{11} +(-0.935223 + 2.25783i) q^{13} -1.63971i q^{15} +(-2.60609 - 1.50463i) q^{17} +(-4.78465 + 0.629911i) q^{19} +(0.447738 + 2.13403i) q^{21} +(1.19733 - 4.46850i) q^{23} +(0.269578 + 1.00608i) q^{25} +(-1.67811 - 4.05132i) q^{27} +(2.63582 + 1.09179i) q^{29} +(-0.920944 + 1.59512i) q^{31} +(-0.116806 - 0.202313i) q^{33} +(2.37743 + 4.69647i) q^{35} +(-3.70803 + 4.83240i) q^{37} +(-0.521288 - 1.94547i) q^{39} +(-5.86063 - 5.86063i) q^{41} +(-10.8743 + 4.50430i) q^{43} +(-2.81088 - 3.66321i) q^{45} +(-6.91568 + 3.99277i) q^{47} +(-4.37656 - 5.46312i) q^{49} +(2.45886 - 0.323715i) q^{51} +(0.380178 - 2.88774i) q^{53} +(-0.398780 - 0.398780i) q^{55} +(2.81237 - 2.81237i) q^{57} +(-1.50285 - 0.197854i) q^{59} +(-0.522701 - 3.97031i) q^{61} +(4.65854 + 4.00001i) q^{63} +(-2.43112 - 4.21083i) q^{65} +(-3.72219 + 2.85614i) q^{67} +(1.45903 + 3.52240i) q^{69} +(9.00400 - 9.00400i) q^{71} +(-9.38575 + 2.51490i) q^{73} +(-0.681021 - 0.522566i) q^{75} +(0.627890 + 0.410109i) q^{77} +(-9.86199 + 5.69382i) q^{79} +(-2.89975 - 1.67417i) q^{81} +(0.888813 - 2.14578i) q^{83} +(5.53141 - 2.29118i) q^{85} +(-2.27117 + 0.608558i) q^{87} +(10.9024 + 2.92129i) q^{89} +(4.31383 + 4.81641i) q^{91} +(-0.198138 - 1.50500i) q^{93} +(4.80079 - 8.31521i) q^{95} -17.3614 q^{97} +(-0.607766 - 0.251745i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 4 q^{3} - 4 q^{5} + 8 q^{7} - 4 q^{9}+O(q^{10}) $ 240 * q + 4 * q^3 - 4 * q^5 + 8 * q^7 - 4 * q^9	$ 240 q + 4 q^{3} - 4 q^{5} + 8 q^{7} - 4 q^{9} + 4 q^{11} - 16 q^{13} + 4 q^{19} - 8 q^{21} + 12 q^{23} - 4 q^{25} + 16 q^{27} - 16 q^{29} + 56 q^{31} - 8 q^{33} + 32 q^{35} - 4 q^{37} + 4 q^{39} - 16 q^{41} + 8 q^{45} + 28 q^{51} - 20 q^{53} + 16 q^{55} - 16 q^{57} + 36 q^{59} - 4 q^{61} + 16 q^{63} - 8 q^{65} - 36 q^{67} - 16 q^{69} - 48 q^{71} - 4 q^{73} - 16 q^{75} - 8 q^{77} + 96 q^{83} - 56 q^{85} + 4 q^{87} - 4 q^{89} + 56 q^{91} + 20 q^{93} + 8 q^{95} - 32 q^{97} - 8 q^{99}+O(q^{100}) $ 240 * q + 4 * q^3 - 4 * q^5 + 8 * q^7 - 4 * q^9 + 4 * q^11 - 16 * q^13 + 4 * q^19 - 8 * q^21 + 12 * q^23 - 4 * q^25 + 16 * q^27 - 16 * q^29 + 56 * q^31 - 8 * q^33 + 32 * q^35 - 4 * q^37 + 4 * q^39 - 16 * q^41 + 8 * q^45 + 28 * q^51 - 20 * q^53 + 16 * q^55 - 16 * q^57 + 36 * q^59 - 4 * q^61 + 16 * q^63 - 8 * q^65 - 36 * q^67 - 16 * q^69 - 48 * q^71 - 4 * q^73 - 16 * q^75 - 8 * q^77 + 96 * q^83 - 56 * q^85 + 4 * q^87 - 4 * q^89 + 56 * q^91 + 20 * q^93 + 8 * q^95 - 32 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/896\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$645$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{8}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.653842	+	0.501711i	−0.377496	+	0.289663i	−0.780030	−	0.625742i	$-0.784796\pi$
$3$	−0.653842	+	0.501711i	−0.377496	+	0.289663i	0.402534	+	0.915405i	$0.368129\pi$
$4$		0			0
$5$	−1.21118	+	1.57844i	−0.541656	+	0.705900i	−0.981346	−	0.192250i	$-0.938422\pi$
$5$	−1.21118	+	1.57844i	−0.541656	+	0.705900i	0.439690	+	0.898150i	$0.355088\pi$
$6$		0			0
$7$	1.14530	−	2.38501i	0.432884	−	0.901450i
$7$	1.14530	−	2.38501i	0.432884	−	0.901450i
$8$		0			0
$9$	−0.600661	+	2.24170i	−0.200220	+	0.747233i
$10$		0			0
$11$	−0.0369986	+	0.281032i	−0.0111555	+	0.0847343i	−0.996117	−	0.0880398i	$-0.971940\pi$
$11$	−0.0369986	+	0.281032i	−0.0111555	+	0.0847343i	0.984961	+	0.172774i	$0.0552731\pi$
$12$		0			0
$13$	−0.935223	+	2.25783i	−0.259384	+	0.626209i	−0.998898	−	0.0469326i	$-0.985055\pi$
$13$	−0.935223	+	2.25783i	−0.259384	+	0.626209i	0.739514	+	0.673141i	$0.235055\pi$
$14$		0			0
$15$		−	1.63971i		−	0.423372i
$16$		0			0
$17$	−2.60609	−	1.50463i	−0.632070	−	0.364926i	0.149483	−	0.988764i	$-0.452239\pi$
$17$	−2.60609	−	1.50463i	−0.632070	−	0.364926i	−0.781553	+	0.623839i	$0.785572\pi$
$18$		0			0
$19$	−4.78465	+	0.629911i	−1.09767	+	0.144511i	−0.657539	−	0.753421i	$-0.728402\pi$
$19$	−4.78465	+	0.629911i	−1.09767	+	0.144511i	−0.440134	+	0.897932i	$0.645069\pi$
$20$		0			0
$21$	0.447738	+	2.13403i	0.0977045	+	0.465684i
$22$		0			0
$23$	1.19733	−	4.46850i	0.249661	−	0.931746i	−0.721323	−	0.692599i	$-0.756465\pi$
$23$	1.19733	−	4.46850i	0.249661	−	0.931746i	0.970983	−	0.239147i	$-0.0768678\pi$
$24$		0			0
$25$	0.269578	+	1.00608i	0.0539156	+	0.201216i
$26$		0			0
$27$	−1.67811	−	4.05132i	−0.322953	−	0.779677i
$28$		0			0
$29$	2.63582	+	1.09179i	0.489459	+	0.202741i	0.613743	−	0.789506i	$-0.289663\pi$
$29$	2.63582	+	1.09179i	0.489459	+	0.202741i	−0.124284	+	0.992247i	$0.539663\pi$
$30$		0			0
$31$	−0.920944	+	1.59512i	−0.165406	+	0.286492i	−0.936800	−	0.349867i	$-0.886227\pi$
$31$	−0.920944	+	1.59512i	−0.165406	+	0.286492i	0.771393	+	0.636359i	$0.219560\pi$
$32$		0			0
$33$	−0.116806	−	0.202313i	−0.0203332	−	0.0352182i
$34$		0			0
$35$	2.37743	+	4.69647i	0.401859	+	0.793849i
$36$		0			0
$37$	−3.70803	+	4.83240i	−0.609596	+	0.794442i	−0.991548	−	0.129741i	$-0.958585\pi$
$37$	−3.70803	+	4.83240i	−0.609596	+	0.794442i	0.381951	+	0.924182i	$0.375252\pi$
$38$		0			0
$39$	−0.521288	−	1.94547i	−0.0834729	−	0.311525i
$40$		0			0
$41$	−5.86063	−	5.86063i	−0.915277	−	0.915277i	0.0814042	−	0.996681i	$-0.474060\pi$
$41$	−5.86063	−	5.86063i	−0.915277	−	0.915277i	−0.996681	+	0.0814042i	$0.974060\pi$
$42$		0			0
$43$	−10.8743	+	4.50430i	−1.65832	+	0.686899i	−0.997947	−	0.0640381i	$-0.979602\pi$
$43$	−10.8743	+	4.50430i	−1.65832	+	0.686899i	−0.660374	+	0.750937i	$0.729602\pi$
$44$		0			0
$45$	−2.81088	−	3.66321i	−0.419021	−	0.546079i
$46$		0			0
$47$	−6.91568	+	3.99277i	−1.00876	+	0.582405i	−0.910827	−	0.412788i	$-0.864555\pi$
$47$	−6.91568	+	3.99277i	−1.00876	+	0.582405i	−0.0979287	+	0.995193i	$0.531222\pi$
$48$		0			0
$49$	−4.37656	−	5.46312i	−0.625223	−	0.780446i
$50$		0			0
$51$	2.45886	−	0.323715i	0.344309	−	0.0453291i
$52$		0			0
$53$	0.380178	−	2.88774i	0.0522215	−	0.396661i	−0.945294	−	0.326219i	$-0.894225\pi$
$53$	0.380178	−	2.88774i	0.0522215	−	0.396661i	0.997516	−	0.0704428i	$-0.0224412\pi$
$54$		0			0
$55$	−0.398780	−	0.398780i	−0.0537715	−	0.0537715i
$56$		0			0
$57$	2.81237	−	2.81237i	0.372507	−	0.372507i
$58$		0			0
$59$	−1.50285	−	0.197854i	−0.195655	−	0.0257584i	0.0320619	−	0.999486i	$-0.489793\pi$
$59$	−1.50285	−	0.197854i	−0.195655	−	0.0257584i	−0.227717	+	0.973727i	$0.573126\pi$
$60$		0			0
$61$	−0.522701	−	3.97031i	−0.0669250	−	0.508346i	−0.991773	−	0.128009i	$-0.959141\pi$
$61$	−0.522701	−	3.97031i	−0.0669250	−	0.508346i	0.924848	−	0.380337i	$-0.124192\pi$
$62$		0			0
$63$	4.65854	+	4.00001i	0.586921	+	0.503954i
$64$		0			0
$65$	−2.43112	−	4.21083i	−0.301544	−	0.522289i
$66$		0			0
$67$	−3.72219	+	2.85614i	−0.454738	+	0.348933i	−0.810594	−	0.585608i	$-0.800856\pi$
$67$	−3.72219	+	2.85614i	−0.454738	+	0.348933i	0.355856	+	0.934541i	$0.384189\pi$
$68$		0			0
$69$	1.45903	+	3.52240i	0.175646	+	0.424048i
$70$		0			0
$71$	9.00400	−	9.00400i	1.06858	−	1.06858i	0.0711094	−	0.997469i	$-0.477346\pi$
$71$	9.00400	−	9.00400i	1.06858	−	1.06858i	0.997469	−	0.0711094i	$-0.0226539\pi$
$72$		0			0
$73$	−9.38575	+	2.51490i	−1.09852	+	0.294347i	−0.762161	−	0.647387i	$-0.775862\pi$
$73$	−9.38575	+	2.51490i	−1.09852	+	0.294347i	−0.336358	+	0.941734i	$0.609195\pi$
$74$		0			0
$75$	−0.681021	−	0.522566i	−0.0786376	−	0.0603407i
$76$		0			0
$77$	0.627890	+	0.410109i	0.0715547	+	0.0467363i
$78$		0			0
$79$	−9.86199	+	5.69382i	−1.10956	+	0.640605i	−0.938716	−	0.344693i	$-0.887983\pi$
$79$	−9.86199	+	5.69382i	−1.10956	+	0.640605i	−0.170845	+	0.985298i	$0.554650\pi$
$80$		0			0
$81$	−2.89975	−	1.67417i	−0.322194	−	0.186019i
$82$		0			0
$83$	0.888813	−	2.14578i	0.0975599	−	0.235530i	−0.867563	−	0.497327i	$-0.834315\pi$
$83$	0.888813	−	2.14578i	0.0975599	−	0.235530i	0.965123	+	0.261797i	$0.0843149\pi$
$84$		0			0
$85$	5.53141	−	2.29118i	0.599966	−	0.248514i
$86$		0			0
$87$	−2.27117	+	0.608558i	−0.243495	+	0.0652443i
$88$		0			0
$89$	10.9024	+	2.92129i	1.15565	+	0.309656i	0.785228	−	0.619207i	$-0.212546\pi$
$89$	10.9024	+	2.92129i	1.15565	+	0.309656i	0.370424	+	0.928863i	$0.379212\pi$
$90$		0			0
$91$	4.31383	+	4.81641i	0.452212	+	0.504897i
$92$		0			0
$93$	−0.198138	−	1.50500i	−0.0205459	−	0.156062i
$94$		0			0
$95$	4.80079	−	8.31521i	0.492551	−	0.853123i
$96$		0			0
$97$	−17.3614			−1.76278			−0.881389	−	0.472391i	$-0.843391\pi$
$97$	−17.3614			−1.76278			−0.881389	+	0.472391i	$0.843391\pi$
$98$		0			0
$99$	−0.607766	−	0.251745i	−0.0610827	−	0.0253013i
$100$		0			0
$101$	15.2923	+	2.01327i	1.52164	+	0.200328i	0.844512	−	0.535537i	$-0.179891\pi$
$101$	15.2923	+	2.01327i	1.52164	+	0.200328i	0.677128	+	0.735865i	$0.263224\pi$
$102$		0			0
$103$	5.43286	+	1.45573i	0.535315	+	0.143437i	0.516342	−	0.856383i	$-0.327293\pi$
$103$	5.43286	+	1.45573i	0.535315	+	0.143437i	0.0189737	+	0.999820i	$0.493960\pi$
$104$		0			0
$105$	−3.91073	−	1.87797i	−0.381648	−	0.183271i
$106$		0			0
$107$	−3.87119	−	2.97047i	−0.374242	−	0.287166i	0.404465	−	0.914553i	$-0.367458\pi$
$107$	−3.87119	−	2.97047i	−0.374242	−	0.287166i	−0.778707	+	0.627387i	$0.784124\pi$
$108$		0			0
$109$	6.79312	+	8.85297i	0.650663	+	0.847961i	0.995891	−	0.0905582i	$-0.0288651\pi$
$109$	6.79312	+	8.85297i	0.650663	+	0.847961i	−0.345228	+	0.938519i	$0.612198\pi$
$110$		0			0
$111$		−	5.01998i		−	0.476476i
$112$		0			0
$113$			13.0340i			1.22614i	0.790030	+	0.613069i	$0.210065\pi$
$113$			13.0340i			1.22614i	−0.790030	+	0.613069i	$0.789935\pi$
$114$		0			0
$115$	5.60308	+	7.30207i	0.522490	+	0.680922i
$116$		0			0
$117$	−4.49962	−	3.45268i	−0.415990	−	0.319200i
$118$		0			0
$119$	−6.57332	+	4.49230i	−0.602575	+	0.411809i
$120$		0			0
$121$	10.5476	+	2.82621i	0.958870	+	0.256929i
$122$		0			0
$123$	6.77227	+	0.891586i	0.610635	+	0.0803916i
$124$		0			0
$125$	−11.1052	−	4.59993i	−0.993280	−	0.411430i
$126$		0			0
$127$	3.75239			0.332971			0.166485	−	0.986044i	$-0.446758\pi$
$127$	3.75239			0.332971			0.166485	+	0.986044i	$0.446758\pi$
$128$		0			0
$129$	4.85024	−	8.40087i	0.427040	−	0.739655i
$130$		0			0
$131$	2.05085	+	15.5777i	0.179183	+	1.36103i	0.810605	+	0.585593i	$0.199138\pi$
$131$	2.05085	+	15.5777i	0.179183	+	1.36103i	−0.631422	+	0.775440i	$0.717528\pi$
$132$		0			0
$133$	−3.97753	+	12.1329i	−0.344895	+	1.05205i
$134$		0			0
$135$	8.42726	+	2.25808i	0.725303	+	0.194344i
$136$		0			0
$137$	17.3679	−	4.65371i	1.48384	−	0.397593i	0.576186	−	0.817319i	$-0.304540\pi$
$137$	17.3679	−	4.65371i	1.48384	−	0.397593i	0.907651	+	0.419726i	$0.137874\pi$
$138$		0			0
$139$	−15.2428	+	6.31377i	−1.29288	+	0.535527i	−0.919841	−	0.392291i	$-0.871683\pi$
$139$	−15.2428	+	6.31377i	−1.29288	+	0.535527i	−0.373035	+	0.927817i	$0.621683\pi$
$140$		0			0
$141$	2.51855	−	6.08031i	0.212100	−	0.512055i
$142$		0			0
$143$	−0.599920	−	0.346364i	−0.0501678	−	0.0289644i
$144$		0			0
$145$	−4.91578	+	2.83812i	−0.408233	+	0.235693i
$146$		0			0
$147$	5.60248	+	1.37625i	0.462085	+	0.113511i
$148$		0			0
$149$	12.0869	+	9.27460i	0.990197	+	0.759805i	0.970771	−	0.240006i	$-0.0771495\pi$
$149$	12.0869	+	9.27460i	0.990197	+	0.759805i	0.0194259	+	0.999811i	$0.493816\pi$
$150$		0			0
$151$	17.4352	−	4.67175i	1.41886	−	0.380182i	0.533780	−	0.845623i	$-0.320771\pi$
$151$	17.4352	−	4.67175i	1.41886	−	0.380182i	0.885079	+	0.465441i	$0.154104\pi$
$152$		0			0
$153$	4.93830	−	4.93830i	0.399238	−	0.399238i
$154$		0			0
$155$	−1.40238	−	3.38563i	−0.112641	−	0.271941i
$156$		0			0
$157$	14.8947	−	11.4291i	1.18872	−	0.912140i	0.191136	−	0.981564i	$-0.438783\pi$
$157$	14.8947	−	11.4291i	1.18872	−	0.912140i	0.997587	+	0.0694239i	$0.0221161\pi$
$158$		0			0
$159$	1.20023	+	2.07886i	0.0951846	+	0.164865i
$160$		0			0
$161$	−9.28611	−	7.97343i	−0.731848	−	0.628395i
$162$		0			0
$163$	−2.13600	−	16.2245i	−0.167304	−	1.27080i	−0.844723	−	0.535204i	$-0.820235\pi$
$163$	−2.13600	−	16.2245i	−0.167304	−	1.27080i	0.677418	−	0.735598i	$-0.263099\pi$
$164$		0			0
$165$	0.460812	+	0.0606670i	0.0358741	+	0.00472292i
$166$		0			0
$167$	−3.94741	+	3.94741i	−0.305460	+	0.305460i	−0.843145	−	0.537685i	$-0.819299\pi$
$167$	−3.94741	+	3.94741i	−0.305460	+	0.305460i	0.537685	+	0.843145i	$0.319299\pi$
$168$		0			0
$169$	4.96924	+	4.96924i	0.382250	+	0.382250i
$170$		0			0
$171$	1.46188	−	11.1041i	0.111793	−	0.849152i
$172$		0			0
$173$	−0.438836	+	0.0577739i	−0.0333641	+	0.00439247i	−0.147190	−	0.989108i	$-0.547023\pi$
$173$	−0.438836	+	0.0577739i	−0.0333641	+	0.00439247i	0.113826	+	0.993501i	$0.463689\pi$
$174$		0			0
$175$	2.70826	+	0.509319i	0.204725	+	0.0385009i
$176$		0			0
$177$	1.08189	−	0.624631i	0.0813201	−	0.0469502i
$178$		0			0
$179$	−1.93510	−	2.52188i	−0.144636	−	0.188494i	0.715417	−	0.698698i	$-0.246237\pi$
$179$	−1.93510	−	2.52188i	−0.144636	−	0.188494i	−0.860054	+	0.510204i	$0.829570\pi$
$180$		0			0
$181$	−10.0500	+	4.16286i	−0.747014	+	0.309423i	−0.723522	−	0.690301i	$-0.757478\pi$
$181$	−10.0500	+	4.16286i	−0.747014	+	0.309423i	−0.0234913	+	0.999724i	$0.507478\pi$
$182$		0			0
$183$	2.33371	+	2.33371i	0.172513	+	0.172513i
$184$		0			0
$185$	−3.13656	−	11.7058i	−0.230605	−	0.860628i
$186$		0			0
$187$	0.519270	−	0.676726i	0.0379728	−	0.0494871i
$188$		0			0
$189$	−11.5844	−	0.637675i	−0.842640	−	0.0463840i
$190$		0			0
$191$	−5.86417	−	10.1570i	−0.424317	−	0.734938i	0.572040	−	0.820226i	$-0.306152\pi$
$191$	−5.86417	−	10.1570i	−0.424317	−	0.734938i	−0.996356	+	0.0852879i	$0.972819\pi$
$192$		0			0
$193$	−0.0203294	+	0.0352116i	−0.00146334	+	0.00253458i	−0.866756	−	0.498732i	$-0.833799\pi$
$193$	−0.0203294	+	0.0352116i	−0.00146334	+	0.00253458i	0.865293	+	0.501267i	$0.167132\pi$
$194$		0			0
$195$	3.70219	+	1.53350i	0.265119	+	0.109816i
$196$		0			0
$197$	1.06593	+	2.57339i	0.0759445	+	0.183346i	0.957292	−	0.289122i	$-0.0933633\pi$
$197$	1.06593	+	2.57339i	0.0759445	+	0.183346i	−0.881348	+	0.472468i	$0.843363\pi$
$198$		0			0
$199$	4.60717	+	17.1942i	0.326594	+	1.21886i	0.912700	+	0.408630i	$0.133993\pi$
$199$	4.60717	+	17.1942i	0.326594	+	1.21886i	−0.586106	+	0.810234i	$0.699340\pi$
$200$		0			0
$201$	1.00077	−	3.73492i	0.0705889	−	0.263441i
$202$		0			0
$203$	5.62275	−	5.03602i	0.394639	−	0.353459i
$204$		0			0
$205$	16.3489	−	2.15238i	1.14186	−	0.150329i
$206$		0			0
$207$	9.29784	+	5.36811i	0.646244	+	0.373109i
$208$		0			0
$209$		−	1.36794i		−	0.0946227i
$210$		0			0
$211$	−3.34033	+	8.06427i	−0.229958	+	0.555167i	−0.996172	−	0.0874185i	$-0.972138\pi$
$211$	−3.34033	+	8.06427i	−0.229958	+	0.555167i	0.766214	+	0.642586i	$0.222138\pi$
$212$		0			0
$213$	−1.36979	+	10.4046i	−0.0938565	+	0.712911i
$214$		0			0
$215$	6.06101	−	22.6200i	0.413358	−	1.54267i
$216$		0			0
$217$	2.74962	+	4.02336i	0.186657	+	0.273123i
$218$		0			0
$219$	4.87504	−	6.35328i	0.329425	−	0.429315i
$220$		0			0
$221$	5.83446	−	4.47694i	0.392469	−	0.301152i
$222$		0			0
$223$	3.00411			0.201170			0.100585	−	0.994928i	$-0.467929\pi$
$223$	3.00411			0.201170			0.100585	+	0.994928i	$0.467929\pi$
$224$		0			0
$225$	−2.41725			−0.161150
$226$		0			0
$227$	−7.93583	+	6.08938i	−0.526720	+	0.404166i	−0.837601	−	0.546282i	$-0.816043\pi$
$227$	−7.93583	+	6.08938i	−0.526720	+	0.404166i	0.310881	+	0.950449i	$0.399376\pi$
$228$		0			0
$229$	−14.6561	+	19.1002i	−0.968504	+	1.26218i	−0.00348584	+	0.999994i	$0.501110\pi$
$229$	−14.6561	+	19.1002i	−0.968504	+	1.26218i	−0.965018	+	0.262185i	$0.915557\pi$
$230$		0			0
$231$	−0.616297	+	0.0468726i	−0.0405494	+	0.00308399i
$232$		0			0
$233$	0.148628	−	0.554687i	0.00973693	−	0.0363387i	−0.960886	−	0.276943i	$-0.910679\pi$
$233$	0.148628	−	0.554687i	0.00973693	−	0.0363387i	0.970623	+	0.240604i	$0.0773455\pi$
$234$		0			0
$235$	2.07378	−	15.7520i	0.135279	−	1.02754i
$236$		0			0
$237$	3.59153	−	8.67072i	0.233295	−	0.563224i
$238$		0			0
$239$			15.0082i			0.970802i	0.874292	+	0.485401i	$0.161326\pi$
$239$			15.0082i			0.970802i	−0.874292	+	0.485401i	$0.838674\pi$
$240$		0			0
$241$	11.4802	+	6.62812i	0.739508	+	0.426955i	0.821890	−	0.569646i	$-0.192920\pi$
$241$	11.4802	+	6.62812i	0.739508	+	0.426955i	−0.0823825	+	0.996601i	$0.526253\pi$
$242$		0			0
$243$	15.7787	−	2.07731i	1.01221	−	0.133259i
$244$		0			0
$245$	13.9240	−	0.291314i	0.889573	−	0.0186114i
$246$		0			0
$247$	3.05248	−	11.3920i	0.194225	−	0.724857i
$248$		0			0
$249$	0.495419	+	1.84893i	0.0313959	+	0.117171i
$250$		0			0
$251$	−6.81376	−	16.4499i	−0.430081	−	1.03831i	−0.979261	−	0.202603i	$-0.935060\pi$
$251$	−6.81376	−	16.4499i	−0.430081	−	1.03831i	0.549180	−	0.835704i	$-0.314940\pi$
$252$		0			0
$253$	1.21149	+	0.501816i	0.0761658	+	0.0315489i
$254$		0			0
$255$	−2.46716	+	4.27324i	−0.154499	+	0.267601i
$256$		0			0
$257$	14.9320	+	25.8630i	0.931434	+	1.61329i	0.780873	+	0.624689i	$0.214774\pi$
$257$	14.9320	+	25.8630i	0.931434	+	1.61329i	0.150560	+	0.988601i	$0.451892\pi$
$258$		0			0
$259$	7.27851	+	14.3783i	0.452265	+	0.893422i
$260$		0			0
$261$	−4.03070	+	5.25291i	−0.249494	+	0.325147i
$262$		0			0
$263$	−1.62289	−	6.05671i	−0.100072	−	0.373473i	0.897668	−	0.440673i	$-0.145260\pi$
$263$	−1.62289	−	6.05671i	−0.100072	−	0.373473i	−0.997740	+	0.0672001i	$0.978593\pi$
$264$		0			0
$265$	4.09766	+	4.09766i	0.251717	+	0.251717i
$266$		0			0
$267$	−8.59408	+	3.55979i	−0.525949	+	0.217855i
$268$		0			0
$269$	−1.29550	−	1.68832i	−0.0789879	−	0.102939i	0.752188	−	0.658948i	$-0.228998\pi$
$269$	−1.29550	−	1.68832i	−0.0789879	−	0.102939i	−0.831176	+	0.556009i	$0.812332\pi$
$270$		0			0
$271$	−4.24269	+	2.44952i	−0.257725	+	0.148798i	−0.623296	−	0.781986i	$-0.714207\pi$
$271$	−4.24269	+	2.44952i	−0.257725	+	0.148798i	0.365571	+	0.930783i	$0.380874\pi$
$272$		0			0
$273$	−5.23701	−	0.984879i	−0.316958	−	0.0596076i
$274$		0			0
$275$	−0.292714	+	0.0385366i	−0.0176513	+	0.00232384i
$276$		0			0
$277$	2.13296	−	16.2015i	0.128157	−	0.973451i	−0.799670	−	0.600440i	$-0.794992\pi$
$277$	2.13296	−	16.2015i	0.128157	−	0.973451i	0.927827	−	0.373011i	$-0.121675\pi$
$278$		0			0
$279$	−3.02261	−	3.02261i	−0.180959	−	0.180959i
$280$		0			0
$281$	−9.70406	+	9.70406i	−0.578896	+	0.578896i	−0.934599	−	0.355703i	$-0.884241\pi$
$281$	−9.70406	+	9.70406i	−0.578896	+	0.578896i	0.355703	+	0.934599i	$0.384241\pi$
$282$		0			0
$283$	26.2599	+	3.45718i	1.56099	+	0.205508i	0.860985	−	0.508630i	$-0.169848\pi$
$283$	26.2599	+	3.45718i	1.56099	+	0.205508i	0.700004	+	0.714139i	$0.253181\pi$
$284$		0			0
$285$	1.03287	+	7.84544i	0.0611821	+	0.464724i
$286$		0			0
$287$	−20.6899	+	7.26547i	−1.22128	+	0.428867i
$288$		0			0
$289$	−3.97219	−	6.88004i	−0.233659	−	0.404708i
$290$		0			0
$291$	11.3516	−	8.71037i	0.665441	−	0.510611i
$292$		0			0
$293$	−9.73563	−	23.5039i	−0.568761	−	1.37311i	−0.902600	−	0.430481i	$-0.858344\pi$
$293$	−9.73563	−	23.5039i	−0.568761	−	1.37311i	0.333838	−	0.942630i	$-0.391656\pi$
$294$		0			0
$295$	2.13253	−	2.13253i	0.124160	−	0.124160i
$296$		0			0
$297$	1.20064	−	0.321710i	0.0696681	−	0.0186675i
$298$		0			0
$299$	8.96933	+	6.88241i	0.518710	+	0.398020i
$300$		0			0
$301$	−1.71161	+	31.0942i	−0.0986557	+	1.79224i
$302$		0			0
$303$	−11.0088	+	6.35594i	−0.632440	+	0.365139i
$304$		0			0
$305$	6.89998	+	3.98370i	0.395091	+	0.228106i
$306$		0			0
$307$	4.83508	−	11.6729i	0.275952	−	0.666208i	−0.723763	−	0.690048i	$-0.757589\pi$
$307$	4.83508	−	11.6729i	0.275952	−	0.666208i	0.999716	+	0.0238401i	$0.00758925\pi$
$308$		0			0
$309$	−4.28259	+	1.77390i	−0.243628	+	0.100914i
$310$		0			0
$311$	−26.7705	+	7.17315i	−1.51802	+	0.406752i	−0.919089	−	0.394050i	$-0.871074\pi$
$311$	−26.7705	+	7.17315i	−1.51802	+	0.406752i	−0.598929	+	0.800802i	$0.704407\pi$
$312$		0			0
$313$	13.0015	+	3.48375i	0.734890	+	0.196913i	0.606806	−	0.794850i	$-0.292451\pi$
$313$	13.0015	+	3.48375i	0.734890	+	0.196913i	0.128084	+	0.991763i	$0.459117\pi$
$314$		0			0
$315$	−11.9561	+	2.50849i	−0.673650	+	0.141338i
$316$		0			0
$317$	−3.61482	−	27.4573i	−0.203028	−	1.54215i	−0.724735	−	0.689028i	$-0.758038\pi$
$317$	−3.61482	−	27.4573i	−0.203028	−	1.54215i	0.521707	−	0.853125i	$-0.325296\pi$
$318$		0			0
$319$	−0.404350	+	0.700354i	−0.0226392	+	0.0392123i
$320$		0			0
$321$	4.02146			0.224456
$322$		0			0
$323$	13.4170	+	5.55750i	0.746542	+	0.309228i
$324$		0			0
$325$	−2.52367	−	0.332247i	−0.139988	−	0.0184298i
$326$		0			0
$327$	−8.88326	−	2.38026i	−0.491245	−	0.131629i
$328$		0			0
$329$	1.60225	+	21.0669i	0.0883349	+	1.16146i
$330$		0			0
$331$	9.59145	+	7.35978i	0.527194	+	0.404530i	0.837774	−	0.546017i	$-0.183857\pi$
$331$	9.59145	+	7.35978i	0.527194	+	0.404530i	−0.310580	+	0.950547i	$0.600523\pi$
$332$		0			0
$333$	−8.60551	−	11.2149i	−0.471579	−	0.614574i
$334$		0			0
$335$		−	9.33455i		−	0.510001i
$336$		0			0
$337$			10.0032i			0.544907i	0.962169	+	0.272454i	$0.0878351\pi$
$337$			10.0032i			0.544907i	−0.962169	+	0.272454i	$0.912165\pi$
$338$		0			0
$339$	−6.53931	−	8.52219i	−0.355166	−	0.462862i
$340$		0			0
$341$	−0.414207	−	0.317832i	−0.0224305	−	0.0172116i
$342$		0			0
$343$	−18.0421	+	4.18121i	−0.974182	+	0.225764i
$344$		0			0
$345$	−7.32705	−	1.96328i	−0.394475	−	0.105699i
$346$		0			0
$347$	−12.4376	−	1.63744i	−0.667686	−	0.0879025i	−0.210939	−	0.977499i	$-0.567652\pi$
$347$	−12.4376	−	1.63744i	−0.667686	−	0.0879025i	−0.456747	+	0.889597i	$0.650986\pi$
$348$		0			0
$349$	−15.1869	−	6.29062i	−0.812937	−	0.336729i	−0.0628116	−	0.998025i	$-0.520007\pi$
$349$	−15.1869	−	6.29062i	−0.812937	−	0.336729i	−0.750125	+	0.661296i	$0.770007\pi$
$350$		0			0
$351$	10.7166			0.572009
$352$		0			0
$353$	2.25354	−	3.90325i	0.119944	−	0.207749i	−0.799801	−	0.600265i	$-0.795062\pi$
$353$	2.25354	−	3.90325i	0.119944	−	0.207749i	0.919745	+	0.392516i	$0.128395\pi$
$354$		0			0
$355$	3.30681	+	25.1177i	0.175507	+	1.33311i
$356$		0			0
$357$	2.04408	−	6.23516i	0.108184	−	0.330000i
$358$		0			0
$359$	12.3833	+	3.31810i	0.653567	+	0.175123i	0.570341	−	0.821408i	$-0.306811\pi$
$359$	12.3833	+	3.31810i	0.653567	+	0.175123i	0.0832261	+	0.996531i	$0.473478\pi$
$360$		0			0
$361$	4.14347	−	1.11024i	0.218077	−	0.0584336i
$362$		0			0
$363$	−8.31439	+	3.44393i	−0.436392	+	0.180760i
$364$		0			0
$365$	7.39821	−	17.8609i	0.387240	−	0.934880i
$366$		0			0
$367$	7.26582	+	4.19492i	0.379273	+	0.218973i	0.677502	−	0.735521i	$-0.263063\pi$
$367$	7.26582	+	4.19492i	0.379273	+	0.218973i	−0.298229	+	0.954494i	$0.596396\pi$
$368$		0			0
$369$	16.6580	−	9.61752i	0.867182	−	0.500668i
$370$		0			0
$371$	−6.45187	−	4.21407i	−0.334964	−	0.218783i
$372$		0			0
$373$	−19.3138	−	14.8200i	−1.00003	−	0.767350i	−0.0273800	−	0.999625i	$-0.508716\pi$
$373$	−19.3138	−	14.8200i	−1.00003	−	0.767350i	−0.972650	+	0.232275i	$0.925383\pi$
$374$		0			0
$375$	9.56888	−	2.56397i	0.494135	−	0.132403i
$376$		0			0
$377$	−4.93015	+	4.93015i	−0.253916	+	0.253916i
$378$		0			0
$379$	−2.25759	−	5.45030i	−0.115964	−	0.279963i	0.855231	−	0.518247i	$-0.173415\pi$
$379$	−2.25759	−	5.45030i	−0.115964	−	0.279963i	−0.971196	+	0.238284i	$0.923415\pi$
$380$		0			0
$381$	−2.45347	+	1.88261i	−0.125695	+	0.0964492i
$382$		0			0
$383$	−8.80019	−	15.2424i	−0.449669	−	0.778849i	0.548696	−	0.836022i	$-0.315125\pi$
$383$	−8.80019	−	15.2424i	−0.449669	−	0.778849i	−0.998364	+	0.0571732i	$0.981791\pi$
$384$		0			0
$385$	−1.40782	+	0.494371i	−0.0717492	+	0.0251955i
$386$		0			0
$387$	−3.56549	−	27.0825i	−0.181244	−	1.37668i
$388$		0			0
$389$	−10.9212	−	1.43780i	−0.553726	−	0.0728994i	−0.151530	−	0.988453i	$-0.548420\pi$
$389$	−10.9212	−	1.43780i	−0.553726	−	0.0728994i	−0.402197	+	0.915553i	$0.631753\pi$
$390$		0			0
$391$	−9.84378	+	9.84378i	−0.497821	+	0.497821i
$392$		0			0
$393$	−9.15644	−	9.15644i	−0.461881	−	0.461881i
$394$		0			0
$395$	2.95728	−	22.4628i	0.148797	−	1.13023i
$396$		0			0
$397$	−18.9762	+	2.49827i	−0.952390	+	0.125385i	−0.590680	−	0.806906i	$-0.701140\pi$
$397$	−18.9762	+	2.49827i	−0.952390	+	0.125385i	−0.361710	+	0.932290i	$0.617807\pi$
$398$		0			0
$399$	−3.48652	−	9.92855i	−0.174544	−	0.497049i
$400$		0			0
$401$	−29.0696	+	16.7833i	−1.45166	+	0.838119i	−0.998576	−	0.0533470i	$-0.983011\pi$
$401$	−29.0696	+	16.7833i	−1.45166	+	0.838119i	−0.453088	+	0.891466i	$0.649678\pi$
$402$		0			0
$403$	−2.74022	−	3.57113i	−0.136500	−	0.177890i
$404$		0			0
$405$	6.15469	−	2.54936i	0.305829	−	0.126679i
$406$		0			0
$407$	−1.22087	−	1.22087i	−0.0605161	−	0.0605161i
$408$		0			0
$409$	−1.84937	−	6.90193i	−0.0914453	−	0.341278i	0.905011	−	0.425388i	$-0.139862\pi$
$409$	−1.84937	−	6.90193i	−0.0914453	−	0.341278i	−0.996457	+	0.0841092i	$0.973196\pi$
$410$		0			0
$411$	−9.02103	+	11.7564i	−0.444974	+	0.579902i
$412$		0			0
$413$	−2.19311	+	3.35772i	−0.107916	+	0.165222i
$414$		0			0
$415$	2.31048	+	4.00187i	0.113417	+	0.196444i
$416$		0			0
$417$	6.79869	−	11.7757i	0.332933	−	0.576657i
$418$		0			0
$419$	14.6354	+	6.06218i	0.714986	+	0.296157i	0.710366	−	0.703832i	$-0.248529\pi$
$419$	14.6354	+	6.06218i	0.714986	+	0.296157i	0.00462018	+	0.999989i	$0.498529\pi$
$420$		0			0
$421$	−13.7810	−	33.2703i	−0.671646	−	1.62150i	−0.778814	−	0.627255i	$-0.784178\pi$
$421$	−13.7810	−	33.2703i	−0.671646	−	1.62150i	0.107169	−	0.994241i	$-0.465822\pi$
$422$		0			0
$423$	−4.79661	−	17.9012i	−0.233219	−	0.870385i
$424$		0			0
$425$	0.811228	−	3.02755i	0.0393504	−	0.146858i
$426$		0			0
$427$	−10.0679	−	3.30056i	−0.487219	−	0.159725i
$428$		0			0
$429$	0.566027	−	0.0745189i	0.0273281	−	0.00359781i
$430$		0			0
$431$	−1.94052	−	1.12036i	−0.0934714	−	0.0539657i	0.452536	−	0.891746i	$-0.350520\pi$
$431$	−1.94052	−	1.12036i	−0.0934714	−	0.0539657i	−0.546007	+	0.837781i	$0.683853\pi$
$432$		0			0
$433$			13.5666i			0.651970i	0.945375	+	0.325985i	$0.105696\pi$
$433$			13.5666i			0.651970i	−0.945375	+	0.325985i	$0.894304\pi$
$434$		0			0
$435$	1.79022	−	4.32198i	0.0858346	−	0.207223i
$436$		0			0
$437$	−2.91405	+	22.1344i	−0.139398	+	1.05883i
$438$		0			0
$439$	−4.99168	+	18.6292i	−0.238240	+	0.889123i	0.738422	+	0.674339i	$0.235571\pi$
$439$	−4.99168	+	18.6292i	−0.238240	+	0.889123i	−0.976662	+	0.214784i	$0.931095\pi$
$440$		0			0
$441$	14.8755	−	6.52944i	0.708358	−	0.310926i
$442$		0			0
$443$	−19.9623	+	26.0154i	−0.948437	+	1.23603i	0.0232434	+	0.999730i	$0.492601\pi$
$443$	−19.9623	+	26.0154i	−0.948437	+	1.23603i	−0.971681	+	0.236298i	$0.924066\pi$
$444$		0			0
$445$	−17.8158	+	13.6706i	−0.844552	+	0.648048i
$446$		0			0
$447$	−12.5561			−0.593882
$448$		0			0
$449$	21.9115			1.03407			0.517035	−	0.855965i	$-0.327036\pi$
$449$	21.9115			1.03407			0.517035	+	0.855965i	$0.327036\pi$
$450$		0			0
$451$	1.86386	−	1.43019i	0.0877658	−	0.0673450i
$452$		0			0
$453$	−9.05601	+	11.8020i	−0.425489	+	0.554508i
$454$		0			0
$455$	−12.8272	+	0.975580i	−0.601351	+	0.0457359i
$456$		0			0
$457$	4.93544	−	18.4193i	0.230870	−	0.861620i	−0.749097	−	0.662460i	$-0.769512\pi$
$457$	4.93544	−	18.4193i	0.230870	−	0.861620i	0.979967	−	0.199159i	$-0.0638211\pi$
$458$		0			0
$459$	−1.72241	+	13.0830i	−0.0803954	+	0.610664i
$460$		0			0
$461$	4.04090	−	9.75561i	0.188204	−	0.454364i	−0.801410	−	0.598115i	$-0.795917\pi$
$461$	4.04090	−	9.75561i	0.188204	−	0.454364i	0.989614	+	0.143751i	$0.0459165\pi$
$462$		0			0
$463$			39.8744i			1.85312i	0.376145	+	0.926561i	$0.377250\pi$
$463$			39.8744i			1.85312i	−0.376145	+	0.926561i	$0.622750\pi$
$464$		0			0
$465$	2.61554	+	1.51008i	0.121293	+	0.0700284i
$466$		0			0
$467$	−0.773879	+	0.101883i	−0.0358108	+	0.00471459i	−0.148410	−	0.988926i	$-0.547416\pi$
$467$	−0.773879	+	0.101883i	−0.0358108	+	0.00471459i	0.112599	+	0.993640i	$0.464082\pi$
$468$		0			0
$469$	2.54888	+	12.1486i	0.117697	+	0.560971i
$470$		0			0
$471$	−4.00467	+	14.9456i	−0.184525	+	0.688658i
$472$		0			0
$473$	−0.863517	−	3.22269i	−0.0397046	−	0.148179i
$474$		0			0
$475$	−1.92357	−	4.64392i	−0.0882597	−	0.213078i
$476$		0			0
$477$	6.24508	+	2.58680i	0.285943	+	0.118441i
$478$		0			0
$479$	−7.19859	+	12.4683i	−0.328912	+	0.569692i	−0.982296	−	0.187334i	$-0.940015\pi$
$479$	−7.19859	+	12.4683i	−0.328912	+	0.569692i	0.653384	+	0.757026i	$0.273349\pi$
$480$		0			0
$481$	−7.44289	−	12.8915i	−0.339367	−	0.587800i
$482$		0			0
$483$	10.0720	+	0.554424i	0.458292	+	0.0252272i
$484$		0			0
$485$	21.0277	−	27.4039i	0.954820	−	1.24435i
$486$		0			0
$487$	6.93237	+	25.8720i	0.314136	+	1.17237i	0.924791	+	0.380474i	$0.124239\pi$
$487$	6.93237	+	25.8720i	0.314136	+	1.17237i	−0.610656	+	0.791896i	$0.709094\pi$
$488$		0			0
$489$	9.53662	+	9.53662i	0.431261	+	0.431261i
$490$		0			0
$491$	35.5529	−	14.7265i	1.60448	−	0.664598i	0.612441	−	0.790517i	$-0.290188\pi$
$491$	35.5529	−	14.7265i	1.60448	−	0.664598i	0.992041	+	0.125919i	$0.0401878\pi$
$492$		0			0
$493$	−5.22644	−	6.81123i	−0.235387	−	0.306762i
$494$		0			0
$495$	1.13348	−	0.654414i	0.0509460	−	0.0294137i
$496$		0			0
$497$	−11.1623	−	31.7869i	−0.500699	−	1.42584i
$498$		0			0
$499$	−14.4127	+	1.89747i	−0.645203	+	0.0849426i	−0.446025	−	0.895021i	$-0.647161\pi$
$499$	−14.4127	+	1.89747i	−0.645203	+	0.0849426i	−0.199178	+	0.979963i	$0.563827\pi$
$500$		0			0
$501$	0.600525	−	4.56144i	0.0268295	−	0.203790i
$502$		0			0
$503$	11.3509	+	11.3509i	0.506113	+	0.506113i	0.913331	−	0.407218i	$-0.133501\pi$
$503$	11.3509	+	11.3509i	0.506113	+	0.506113i	−0.407218	+	0.913331i	$0.633501\pi$
$504$		0			0
$505$	−21.6995	+	21.6995i	−0.965617	+	0.965617i
$506$		0			0
$507$	−5.74222	−	0.755978i	−0.255021	−	0.0335742i
$508$		0			0
$509$	4.35143	+	33.0524i	0.192874	+	1.46502i	0.764562	+	0.644551i	$0.222956\pi$
$509$	4.35143	+	33.0524i	0.192874	+	1.46502i	−0.571688	+	0.820471i	$0.693711\pi$
$510$		0			0
$511$	−4.75146	+	25.2655i	−0.210192	+	1.11768i
$512$		0			0
$513$	10.5811	+	18.3271i	0.467169	+	0.809160i
$514$		0			0
$515$	−8.87795	+	6.81229i	−0.391209	+	0.300185i
$516$		0			0
$517$	−0.866226	−	2.09125i	−0.0380966	−	0.0919733i
$518$		0			0
$519$	0.257944	−	0.257944i	0.0113225	−	0.0113225i
$520$		0			0
$521$	−19.0562	+	5.10609i	−0.834867	+	0.223702i	−0.650836	−	0.759218i	$-0.725581\pi$
$521$	−19.0562	+	5.10609i	−0.834867	+	0.223702i	−0.184031	+	0.982920i	$0.558915\pi$
$522$		0			0
$523$	18.1737	+	13.9452i	0.794680	+	0.609780i	0.924249	−	0.381791i	$-0.124693\pi$
$523$	18.1737	+	13.9452i	0.794680	+	0.609780i	−0.129568	+	0.991570i	$0.541359\pi$
$524$		0			0
$525$	−2.02630	+	1.02575i	−0.0884351	+	0.0447673i
$526$		0			0
$527$	4.80012	−	2.77135i	0.209097	−	0.120722i
$528$		0			0
$529$	1.38471	+	0.799461i	0.0602046	+	0.0347592i
$530$		0			0
$531$	1.34623	−	3.25010i	0.0584216	−	0.141042i
$532$		0			0
$533$	18.7133	−	7.75130i	0.810563	−	0.335746i
$534$		0			0
$535$	9.37742	−	2.51267i	0.405421	−	0.108632i
$536$		0			0
$537$	2.53050	+	0.678046i	0.109199	+	0.0292599i
$538$		0			0
$539$	1.69724	−	1.02783i	0.0731053	−	0.0442716i
$540$		0			0
$541$	2.34115	+	17.7828i	0.100654	+	0.764542i	0.965112	+	0.261837i	$0.0843284\pi$
$541$	2.34115	+	17.7828i	0.100654	+	0.764542i	−0.864458	+	0.502705i	$0.832338\pi$
$542$		0			0
$543$	4.48259	−	7.76407i	0.192366	−	0.333188i
$544$		0			0
$545$	−22.2016			−0.951011
$546$		0			0
$547$	−36.8707	−	15.2723i	−1.57648	−	0.652998i	−0.588625	−	0.808406i	$-0.700331\pi$
$547$	−36.8707	−	15.2723i	−1.57648	−	0.652998i	−0.987850	+	0.155408i	$0.950331\pi$
$548$		0			0
$549$	9.21420	+	1.21307i	0.393252	+	0.0517726i
$550$		0			0
$551$	−13.2992	−	3.56351i	−0.566564	−	0.151810i
$552$		0			0
$553$	2.28486	+	30.0421i	0.0971622	+	1.27752i
$554$		0			0
$555$	7.92374	+	6.08010i	0.336344	+	0.258086i
$556$		0			0
$557$	−5.41524	−	7.05727i	−0.229451	−	0.299026i	0.664412	−	0.747366i	$-0.268682\pi$
$557$	−5.41524	−	7.05727i	−0.229451	−	0.299026i	−0.893863	+	0.448340i	$0.852015\pi$
$558$		0			0
$559$		−	28.7649i		−	1.21663i
$560$		0			0
$561$			0.702995i			0.0296805i
$562$		0			0
$563$	0.211448	+	0.275565i	0.00891148	+	0.0116137i	0.797788	−	0.602938i	$-0.206003\pi$
$563$	0.211448	+	0.275565i	0.00891148	+	0.0116137i	−0.788876	+	0.614552i	$0.789337\pi$
$564$		0			0
$565$	−20.5734	−	15.7865i	−0.865531	−	0.664145i
$566$		0			0
$567$	−7.31401	+	4.99850i	−0.307159	+	0.209917i
$568$		0			0
$569$	−29.8453	−	7.99703i	−1.25118	−	0.335253i	−0.428389	−	0.903595i	$-0.640919\pi$
$569$	−29.8453	−	7.99703i	−1.25118	−	0.335253i	−0.822793	+	0.568342i	$0.807585\pi$
$570$		0			0
$571$	13.1448	+	1.73055i	0.550093	+	0.0724211i	0.400449	−	0.916319i	$-0.368854\pi$
$571$	13.1448	+	1.73055i	0.550093	+	0.0724211i	0.149643	+	0.988740i	$0.452187\pi$
$572$		0			0
$573$	8.93014	+	3.69898i	0.373062	+	0.154527i
$574$		0			0
$575$	4.81843			0.200943
$576$		0			0
$577$	9.50239	−	16.4586i	0.395589	−	0.685181i	−0.597587	−	0.801804i	$-0.703874\pi$
$577$	9.50239	−	16.4586i	0.395589	−	0.685181i	0.993176	+	0.116623i	$0.0372070\pi$
$578$		0			0
$579$	−0.00437379	−	0.0332223i	−0.000181769	−	0.00138067i
$580$		0			0
$581$	−4.09976	−	4.57740i	−0.170087	−	0.189903i
$582$		0			0
$583$	0.797481	+	0.213684i	0.0330283	+	0.00884990i
$584$		0			0
$585$	10.8997	−	2.92056i	0.450647	−	0.120750i
$586$		0			0
$587$	−3.98106	+	1.64901i	−0.164316	+	0.0680619i	−0.463325	−	0.886188i	$-0.653344\pi$
$587$	−3.98106	+	1.64901i	−0.164316	+	0.0680619i	0.299009	+	0.954250i	$0.403344\pi$
$588$		0			0
$589$	3.40161	−	8.21220i	0.140161	−	0.338378i
$590$		0			0
$591$	−1.98804	−	1.14780i	−0.0817772	−	0.0472141i
$592$		0			0
$593$	−8.40850	+	4.85465i	−0.345296	+	0.199357i	−0.662611	−	0.748963i	$-0.730552\pi$
$593$	−8.40850	+	4.85465i	−0.345296	+	0.199357i	0.317316	+	0.948320i	$0.397219\pi$
$594$		0			0
$595$	0.870640	−	15.8166i	0.0356927	−	0.648416i
$596$		0			0
$597$	−11.6389	−	8.93082i	−0.476347	−	0.365514i
$598$		0			0
$599$	4.16938	−	1.11718i	0.170356	−	0.0456468i	−0.172633	−	0.984986i	$-0.555227\pi$
$599$	4.16938	−	1.11718i	0.170356	−	0.0456468i	0.342989	+	0.939339i	$0.388561\pi$
$600$		0			0
$601$	−5.39715	+	5.39715i	−0.220155	+	0.220155i	−0.808563	−	0.588409i	$-0.799755\pi$
$601$	−5.39715	+	5.39715i	−0.220155	+	0.220155i	0.588409	+	0.808563i	$0.299755\pi$
$602$		0			0
$603$	−4.16682	−	10.0596i	−0.169686	−	0.409659i
$604$		0			0
$605$	−17.2360	+	13.2257i	−0.700744	+	0.537700i
$606$		0			0
$607$	−14.3426	−	24.8421i	−0.582149	−	1.00831i	−0.995224	−	0.0976147i	$-0.968879\pi$
$607$	−14.3426	−	24.8421i	−0.582149	−	1.00831i	0.413075	−	0.910697i	$-0.364455\pi$
$608$		0			0
$609$	−1.14976	+	6.11375i	−0.0465907	+	0.247742i
$610$		0			0
$611$	−2.54728	−	19.3485i	−0.103052	−	0.782758i
$612$		0			0
$613$	10.9285	+	1.43876i	0.441398	+	0.0581112i	0.347950	−	0.937513i	$-0.386878\pi$
$613$	10.9285	+	1.43876i	0.441398	+	0.0581112i	0.0934479	+	0.995624i	$0.470211\pi$
$614$		0			0
$615$	−9.60975	+	9.60975i	−0.387503	+	0.387503i
$616$		0			0
$617$	−0.387683	−	0.387683i	−0.0156075	−	0.0156075i	0.699260	−	0.714867i	$-0.253513\pi$
$617$	−0.387683	−	0.387683i	−0.0156075	−	0.0156075i	−0.714867	+	0.699260i	$0.753513\pi$
$618$		0			0
$619$	4.36182	−	33.1313i	0.175316	−	1.33166i	−0.646939	−	0.762542i	$-0.723951\pi$
$619$	4.36182	−	33.1313i	0.175316	−	1.33166i	0.822255	−	0.569119i	$-0.192715\pi$
$620$		0			0
$621$	−20.1126	+	2.64787i	−0.807090	+	0.106255i
$622$		0			0
$623$	19.4539	−	22.6566i	0.779402	−	0.907717i
$624$		0			0
$625$	16.2010	−	9.35364i	0.648039	−	0.374146i
$626$		0			0
$627$	0.686312	+	0.894420i	0.0274087	+	0.0357197i
$628$		0			0
$629$	16.9344	−	7.01447i	0.675220	−	0.279685i
$630$		0			0
$631$	5.66210	+	5.66210i	0.225405	+	0.225405i	0.810770	−	0.585365i	$-0.199049\pi$
$631$	5.66210	+	5.66210i	0.225405	+	0.225405i	−0.585365	+	0.810770i	$0.699049\pi$
$632$		0			0
$633$	−1.86188	−	6.94863i	−0.0740031	−	0.276183i
$634$		0			0
$635$	−4.54482	+	5.92292i	−0.180356	+	0.235044i
$636$		0			0
$637$	16.4279	−	4.77228i	0.650895	−	0.189085i
$638$		0			0
$639$	14.7759	+	25.5926i	0.584525	+	1.01243i
$640$		0			0
$641$	−12.9563	+	22.4411i	−0.511745	+	0.886368i	0.488162	+	0.872753i	$0.337667\pi$
$641$	−12.9563	+	22.4411i	−0.511745	+	0.886368i	−0.999907	+	0.0136154i	$0.995666\pi$
$642$		0			0
$643$	−39.2743	−	16.2679i	−1.54883	−	0.641545i	−0.565722	−	0.824596i	$-0.691403\pi$
$643$	−39.2743	−	16.2679i	−1.54883	−	0.641545i	−0.983103	+	0.183051i	$0.941403\pi$
$644$		0			0
$645$	7.38575	+	17.8308i	0.290814	+	0.702086i
$646$		0			0
$647$	−8.56657	−	31.9709i	−0.336787	−	1.25690i	−0.901919	−	0.431904i	$-0.857842\pi$
$647$	−8.56657	−	31.9709i	−0.336787	−	1.25690i	0.565133	−	0.825000i	$-0.308825\pi$
$648$		0			0
$649$	0.111207	−	0.415029i	0.00436525	−	0.0162913i
$650$		0			0
$651$	−3.81638	−	1.25113i	−0.149576	−	0.0490355i
$652$		0			0
$653$	25.2963	−	3.33032i	0.989922	−	0.130326i	0.381864	−	0.924218i	$-0.375282\pi$
$653$	25.2963	−	3.33032i	0.989922	−	0.130326i	0.608058	+	0.793893i	$0.291949\pi$
$654$		0			0
$655$	−27.0725	−	15.6303i	−1.05781	−	0.610726i
$656$		0			0
$657$		−	22.5506i		−	0.879784i
$658$		0			0
$659$	2.67764	−	6.46439i	0.104306	−	0.251817i	−0.863107	−	0.505022i	$-0.831485\pi$
$659$	2.67764	−	6.46439i	0.104306	−	0.251817i	0.967413	+	0.253205i	$0.0814846\pi$
$660$		0			0
$661$	−4.64599	+	35.2898i	−0.180708	+	1.37261i	0.625150	+	0.780504i	$0.285038\pi$
$661$	−4.64599	+	35.2898i	−0.180708	+	1.37261i	−0.805858	+	0.592109i	$0.798296\pi$
$662$		0			0
$663$	−1.56869	+	5.85442i	−0.0609228	+	0.227367i
$664$		0			0
$665$	−14.3335	−	20.9734i	−0.555830	−	0.813313i
$666$		0			0
$667$	8.03461	−	10.4709i	0.311101	−	0.405435i
$668$		0			0
$669$	−1.96422	+	1.50720i	−0.0759410	+	0.0582715i
$670$		0			0
$671$	1.13512			0.0438209
$672$		0			0
$673$	6.85257			0.264147			0.132074	−	0.991240i	$-0.457836\pi$
$673$	6.85257			0.264147			0.132074	+	0.991240i	$0.457836\pi$
$674$		0			0
$675$	3.62356	−	2.78046i	0.139471	−	0.107020i
$676$		0			0
$677$	24.7809	−	32.2951i	0.952407	−	1.24120i	−0.0180282	−	0.999837i	$-0.505739\pi$
$677$	24.7809	−	32.2951i	0.952407	−	1.24120i	0.970435	−	0.241363i	$-0.0775945\pi$
$678$		0			0
$679$	−19.8840	+	41.4070i	−0.763079	+	1.58906i
$680$		0			0
$681$	2.13367	−	7.96298i	0.0817626	−	0.305142i
$682$		0			0
$683$	−6.56860	+	49.8935i	−0.251341	+	1.90912i	0.142242	+	0.989832i	$0.454569\pi$
$683$	−6.56860	+	49.8935i	−0.251341	+	1.90912i	−0.393583	+	0.919289i	$0.628765\pi$
$684$		0			0
$685$	−13.6900	+	33.0506i	−0.523069	+	1.26280i
$686$		0			0
$687$		−	19.8417i		−	0.757006i
$688$		0			0
$689$	6.16446	+	3.55906i	0.234847	+	0.135589i
$690$		0			0
$691$	−16.8761	+	2.22178i	−0.641996	+	0.0845204i	−0.444494	−	0.895782i	$-0.646616\pi$
$691$	−16.8761	+	2.22178i	−0.641996	+	0.0845204i	−0.197502	+	0.980302i	$0.563283\pi$
$692$		0			0
$693$	−1.29649	+	1.16120i	−0.0492496	+	0.0441105i
$694$		0			0
$695$	8.49585	−	31.7069i	0.322266	−	1.20271i
$696$		0			0
$697$	6.45527	+	24.0914i	0.244511	+	0.912527i
$698$		0			0
$699$	0.181113	+	0.437245i	0.00685032	+	0.0165381i
$700$		0			0
$701$	20.3176	+	8.41582i	0.767384	+	0.317861i	0.731812	−	0.681506i	$-0.238675\pi$
$701$	20.3176	+	8.41582i	0.767384	+	0.317861i	0.0355720	+	0.999367i	$0.488675\pi$
$702$		0			0
$703$	14.6976	−	25.4571i	0.554332	−	0.960131i
$704$		0			0
$705$	6.54699	+	11.3397i	0.246574	+	0.427079i
$706$		0			0
$707$	22.3160	−	34.1665i	0.839279	−	1.28496i
$708$		0			0
$709$	−17.4040	+	22.6814i	−0.653622	+	0.851817i	−0.996148	−	0.0876919i	$-0.972051\pi$
$709$	−17.4040	+	22.6814i	−0.653622	+	0.851817i	0.342526	+	0.939508i	$0.388718\pi$
$710$		0			0
$711$	−6.84012	−	25.5277i	−0.256525	−	0.957363i
$712$		0			0
$713$	6.02512	+	6.02512i	0.225643	+	0.225643i
$714$		0			0
$715$	1.27333	−	0.527429i	0.0476197	−	0.0197247i
$716$		0			0
$717$	−7.52979	−	9.81301i	−0.281205	−	0.366474i
$718$		0			0
$719$	42.5600	−	24.5720i	1.58722	−	0.916382i	0.593457	−	0.804866i	$-0.297763\pi$
$719$	42.5600	−	24.5720i	1.58722	−	0.916382i	0.993763	−	0.111516i	$-0.0355707\pi$
$720$		0			0
$721$	9.69420	−	11.2902i	0.361031	−	0.420468i
$722$		0			0
$723$	−10.8317	+	1.42602i	−0.402834	+	0.0530341i
$724$		0			0
$725$	−0.387870	+	2.94616i	−0.0144051	+	0.109418i
$726$		0			0
$727$	4.95398	+	4.95398i	0.183733	+	0.183733i	0.792980	−	0.609247i	$-0.208528\pi$
$727$	4.95398	+	4.95398i	0.183733	+	0.183733i	−0.609247	+	0.792980i	$0.708528\pi$
$728$		0			0
$729$	−2.17168	+	2.17168i	−0.0804327	+	0.0804327i
$730$		0			0
$731$	35.1168	+	4.62321i	1.29884	+	0.170996i
$732$		0			0
$733$	−1.44739	−	10.9940i	−0.0534607	−	0.406074i	−0.997163	−	0.0752773i	$-0.976016\pi$
$733$	−1.44739	−	10.9940i	−0.0534607	−	0.406074i	0.943702	−	0.330797i	$-0.107318\pi$
$734$		0			0
$735$	−8.95795	+	7.17630i	−0.330419	+	0.264702i
$736$		0			0
$737$	−0.664950	−	1.15173i	−0.0244938	−	0.0424244i
$738$		0			0
$739$	−3.89430	+	2.98820i	−0.143254	+	0.109923i	−0.677902	−	0.735152i	$-0.737111\pi$
$739$	−3.89430	+	2.98820i	−0.143254	+	0.109923i	0.534648	+	0.845075i	$0.320444\pi$
$740$		0			0
$741$	3.71965	+	8.98004i	0.136645	+	0.329890i
$742$		0			0
$743$	13.7474	−	13.7474i	0.504343	−	0.504343i	−0.408441	−	0.912785i	$-0.633928\pi$
$743$	13.7474	−	13.7474i	0.504343	−	0.504343i	0.912785	+	0.408441i	$0.133928\pi$
$744$		0			0
$745$	−29.2788	+	7.84524i	−1.07269	+	0.287427i
$746$		0			0
$747$	4.27633	+	3.28134i	0.156463	+	0.120058i
$748$		0			0
$749$	−11.5183	+	5.83075i	−0.420869	+	0.213051i
$750$		0			0
$751$	−2.28593	+	1.31978i	−0.0834149	+	0.0481596i	−0.541127	−	0.840941i	$-0.682002\pi$
$751$	−2.28593	+	1.31978i	−0.0834149	+	0.0481596i	0.457712	+	0.889100i	$0.348669\pi$
$752$		0			0
$753$	12.7082	+	7.33708i	0.463112	+	0.267378i
$754$		0			0
$755$	−13.7431	+	33.1788i	−0.500163	+	1.20750i
$756$		0			0
$757$	−25.8003	+	10.6868i	−0.937729	+	0.388420i	−0.798605	−	0.601855i	$-0.794429\pi$
$757$	−25.8003	+	10.6868i	−0.937729	+	0.388420i	−0.139124	+	0.990275i	$0.544429\pi$
$758$		0			0
$759$	−1.04389	+	0.279710i	−0.0378908	+	0.0101528i
$760$		0			0
$761$	−11.5546	−	3.09604i	−0.418853	−	0.112231i	0.0432362	−	0.999065i	$-0.486233\pi$
$761$	−11.5546	−	3.09604i	−0.418853	−	0.112231i	−0.462089	+	0.886834i	$0.652900\pi$
$762$		0			0
$763$	28.8946	−	6.06234i	1.04606	−	0.219471i
$764$		0			0
$765$	1.81364	+	13.7760i	0.0655724	+	0.498072i
$766$		0			0
$767$	1.85222	−	3.20814i	0.0668799	−	0.115839i
$768$		0			0
$769$	36.0231			1.29903			0.649513	−	0.760351i	$-0.274973\pi$
$769$	36.0231			1.29903			0.649513	+	0.760351i	$0.274973\pi$
$770$		0			0
$771$	−22.7389	−	9.41877i	−0.818922	−	0.339209i
$772$		0			0
$773$	31.8055	+	4.18727i	1.14396	+	0.150606i	0.678595	−	0.734512i	$-0.262589\pi$
$773$	31.8055	+	4.18727i	1.14396	+	0.150606i	0.465367	+	0.885118i	$0.345922\pi$
$774$		0			0
$775$	−1.85308	−	0.496532i	−0.0665647	−	0.0178360i
$776$		0			0
$777$	−11.9727	−	5.74940i	−0.429519	−	0.206259i
$778$		0			0
$779$	31.7327	+	24.3494i	1.13694	+	0.872407i
$780$		0			0
$781$	2.19728	+	2.86355i	0.0786247	+	0.102466i
$782$		0			0
$783$		−	12.5107i		−	0.447095i
$784$		0			0
$785$			37.3530i			1.33319i
$786$		0			0
$787$	16.7610	+	21.8433i	0.597465	+	0.778631i	0.989994	−	0.141108i	$-0.0450665\pi$
$787$	16.7610	+	21.8433i	0.597465	+	0.778631i	−0.392529	+	0.919739i	$0.628400\pi$
$788$		0			0
$789$	4.09983	+	3.14591i	0.145958	+	0.111997i
$790$		0			0
$791$	31.0863	+	14.9279i	1.10530	+	0.530775i
$792$		0			0
$793$	9.45311	+	2.53295i	0.335690	+	0.0899478i
$794$		0			0
$795$	−4.73506	−	0.623382i	−0.167935	−	0.0221091i
$796$		0			0
$797$	0.0323599	+	0.0134039i	0.00114625	+	0.000474791i	0.383256	−	0.923642i	$-0.374803\pi$
$797$	0.0323599	+	0.0134039i	0.00114625	+	0.000474791i	−0.382110	+	0.924117i	$0.624803\pi$
$798$		0			0
$799$	24.0305			0.850139
$800$		0			0
$801$	−13.0973	+	22.6852i	−0.462770	+	0.801542i
$802$		0			0
$803$	−0.359509	−	2.73074i	−0.0126868	−	0.0963659i
$804$		0			0
$805$	23.8327	−	5.00031i	0.839994	−	0.176238i
$806$		0			0
$807$	1.69410	+	0.453933i	0.0596352	+	0.0159792i
$808$		0			0
$809$	20.7380	−	5.55674i	0.729110	−	0.195365i	0.124877	−	0.992172i	$-0.460146\pi$
$809$	20.7380	−	5.55674i	0.729110	−	0.195365i	0.604233	+	0.796808i	$0.293480\pi$
$810$		0			0
$811$	0.440880	−	0.182619i	0.0154814	−	0.00641261i	−0.374929	−	0.927053i	$-0.622333\pi$
$811$	0.440880	−	0.182619i	0.0154814	−	0.00641261i	0.390411	+	0.920641i	$0.372333\pi$
$812$		0			0
$813$	1.54510	−	3.73020i	0.0541890	−	0.130824i
$814$		0			0
$815$	28.1965	+	16.2793i	0.987681	+	0.570238i
$816$		0			0
$817$	49.1926	−	28.4013i	1.72103	−	0.993637i
$818$		0			0
$819$	−13.3881	+	6.77728i	−0.467818	+	0.236817i
$820$		0			0
$821$	−42.9801	−	32.9798i	−1.50002	−	1.15100i	−0.948474	−	0.316856i	$-0.897373\pi$
$821$	−42.9801	−	32.9798i	−1.50002	−	1.15100i	−0.551542	−	0.834147i	$-0.685960\pi$
$822$		0			0
$823$	−27.0214	+	7.24038i	−0.941908	+	0.252384i	−0.696925	−	0.717144i	$-0.745449\pi$
$823$	−27.0214	+	7.24038i	−0.941908	+	0.252384i	−0.244983	+	0.969527i	$0.578782\pi$
$824$		0			0
$825$	0.172055	−	0.172055i	0.00599017	−	0.00599017i
$826$		0			0
$827$	5.87779	+	14.1902i	0.204391	+	0.493443i	0.992522	−	0.122064i	$-0.0389513\pi$
$827$	5.87779	+	14.1902i	0.204391	+	0.493443i	−0.788131	+	0.615507i	$0.788951\pi$
$828$		0			0
$829$	2.79965	−	2.14825i	0.0972358	−	0.0746117i	−0.558999	−	0.829168i	$-0.688815\pi$
$829$	2.79965	−	2.14825i	0.0972358	−	0.0746117i	0.656235	+	0.754556i	$0.272148\pi$
$830$		0			0
$831$	6.73382	+	11.6633i	0.233594	+	0.404596i
$832$		0			0
$833$	3.18575	+	20.8225i	0.110380	+	0.721456i
$834$		0			0
$835$	−1.44973	−	11.0118i	−0.0501699	−	0.381079i
$836$		0			0
$837$	8.00779	+	1.05425i	0.276790	+	0.0364401i
$838$		0			0
$839$	−15.9078	+	15.9078i	−0.549199	+	0.549199i	−0.926209	−	0.377010i	$-0.876952\pi$
$839$	−15.9078	+	15.9078i	−0.549199	+	0.549199i	0.377010	+	0.926209i	$0.376952\pi$
$840$		0			0
$841$	−14.7506	−	14.7506i	−0.508640	−	0.508640i
$842$		0			0
$843$	1.47629	−	11.2136i	0.0508462	−	0.386215i
$844$		0			0
$845$	−13.8623	+	1.82501i	−0.476878	+	0.0627822i
$846$		0			0
$847$	18.8207	−	21.9192i	0.646688	−	0.753153i
$848$		0			0
$849$	−18.9043	+	10.9144i	−0.648795	+	0.374582i
$850$		0			0
$851$	17.1538	+	22.3553i	0.588026	+	0.766330i
$852$		0			0
$853$	51.4854	−	21.3260i	1.76283	−	0.730187i	0.766726	−	0.641975i	$-0.221885\pi$
$853$	51.4854	−	21.3260i	1.76283	−	0.730187i	0.996102	−	0.0882126i	$-0.0281155\pi$
$854$		0			0
$855$	15.7566	+	15.7566i	0.538863	+	0.538863i
$856$		0			0
$857$	−6.72540	−	25.0995i	−0.229735	−	0.857383i	−0.980452	−	0.196759i	$-0.936958\pi$
$857$	−6.72540	−	25.0995i	−0.229735	−	0.857383i	0.750717	−	0.660624i	$-0.229708\pi$
$858$		0			0
$859$	−26.3295	+	34.3133i	−0.898351	+	1.17075i	0.0863089	+	0.996268i	$0.472493\pi$
$859$	−26.3295	+	34.3133i	−0.898351	+	1.17075i	−0.984660	+	0.174485i	$0.944174\pi$
$860$		0			0
$861$	9.88274	−	15.1308i	0.336803	−	0.515656i
$862$		0			0
$863$	16.3101	+	28.2499i	0.555201	+	0.961637i	0.997888	+	0.0649602i	$0.0206921\pi$
$863$	16.3101	+	28.2499i	0.555201	+	0.961637i	−0.442687	+	0.896676i	$0.645975\pi$
$864$		0			0
$865$	0.440317	−	0.762651i	0.0149712	−	0.0259309i
$866$		0			0
$867$	6.04898	+	2.50557i	0.205434	+	0.0850936i
$868$		0			0
$869$	−1.23527	−	2.98220i	−0.0419036	−	0.101164i
$870$		0			0
$871$	−2.96759	−	11.0752i	−0.100553	−	0.375269i
$872$		0			0
$873$	10.4283	−	38.9189i	0.352944	−	1.31721i
$874$		0			0
$875$	−23.6897	+	21.2177i	−0.800858	+	0.717290i
$876$		0			0
$877$	34.5051	−	4.54268i	1.16515	−	0.153395i	0.476962	−	0.878924i	$-0.341738\pi$
$877$	34.5051	−	4.54268i	1.16515	−	0.153395i	0.688192	+	0.725529i	$0.258405\pi$
$878$		0			0
$879$	18.1577	+	10.4834i	0.612444	+	0.353595i
$880$		0			0
$881$		−	53.3341i		−	1.79687i	−0.439105	−	0.898436i	$-0.644704\pi$
$881$		−	53.3341i		−	1.79687i	0.439105	−	0.898436i	$-0.355296\pi$
$882$		0			0
$883$	−3.47989	+	8.40119i	−0.117107	+	0.282722i	−0.971554	−	0.236816i	$-0.923896\pi$
$883$	−3.47989	+	8.40119i	−0.117107	+	0.282722i	0.854447	+	0.519539i	$0.173896\pi$
$884$		0			0
$885$	−0.324424	+	2.46424i	−0.0109054	+	0.0828347i
$886$		0			0
$887$	12.8996	−	48.1421i	0.433127	−	1.61645i	−0.312382	−	0.949957i	$-0.601127\pi$
$887$	12.8996	−	48.1421i	0.433127	−	1.61645i	0.745509	−	0.666496i	$-0.232207\pi$
$888$		0			0
$889$	4.29763	−	8.94949i	0.144138	−	0.300156i
$890$		0			0
$891$	0.577782	−	0.752980i	0.0193564	−	0.0252258i
$892$		0			0
$893$	30.5740	−	23.4603i	1.02312	−	0.785068i
$894$		0			0
$895$	6.32439			0.211401
$896$		0			0
$897$	−9.31750			−0.311102
$898$		0			0
$899$	−4.16898	+	3.19897i	−0.139043	+	0.106692i
$900$		0			0
$901$	−5.33575	+	6.95368i	−0.177760	+	0.231661i
$902$		0			0
$903$	−14.4812	−	21.1894i	−0.481903	−	0.705140i
$904$		0			0
$905$	5.60158	−	20.9054i	0.186203	−	0.694918i
$906$		0			0
$907$	−1.15321	+	8.75952i	−0.0382918	+	0.290855i	0.961575	+	0.274542i	$0.0885262\pi$
$907$	−1.15321	+	8.75952i	−0.0382918	+	0.290855i	−0.999867	+	0.0163132i	$0.994807\pi$
$908$		0			0
$909$	−13.6986	+	33.0714i	−0.454355	+	1.09691i
$910$		0			0
$911$		−	0.641243i		−	0.0212453i	−0.999944	−	0.0106227i	$-0.996619\pi$
$911$		−	0.641243i		−	0.0212453i	0.999944	−	0.0106227i	$-0.00338136\pi$
$912$		0			0
$913$	0.570149	+	0.329176i	0.0188692	+	0.0108941i
$914$		0			0
$915$	−6.51016	+	0.857079i	−0.215219	+	0.0283341i
$916$		0			0
$917$	39.5019	+	12.9499i	1.30447	+	0.427645i
$918$		0			0
$919$	−8.67008	+	32.3572i	−0.286000	+	1.06737i	0.662106	+	0.749410i	$0.269663\pi$
$919$	−8.67008	+	32.3572i	−0.286000	+	1.06737i	−0.948106	+	0.317955i	$0.897004\pi$
$920$		0			0
$921$	2.69505	+	10.0580i	0.0888048	+	0.331424i
$922$		0			0
$923$	11.9087	+	28.7502i	0.391981	+	0.946325i
$924$		0			0
$925$	−5.86138	−	2.42786i	−0.192721	−	0.0798276i
$926$		0			0
$927$	−6.52662	+	11.3044i	−0.214362	+	0.371286i
$928$		0			0
$929$	−11.9332	−	20.6689i	−0.391516	−	0.678126i	0.601134	−	0.799148i	$-0.294716\pi$
$929$	−11.9332	−	20.6689i	−0.391516	−	0.678126i	−0.992650	+	0.121023i	$0.961383\pi$
$930$		0			0
$931$	24.3816	+	23.3823i	0.799074	+	0.766323i
$932$		0			0
$933$	13.9049	−	18.1212i	0.455225	−	0.593260i
$934$		0			0
$935$	0.439242	+	1.63927i	0.0143648	+	0.0536100i
$936$		0			0
$937$	11.8504	+	11.8504i	0.387136	+	0.387136i	0.873665	−	0.486529i	$-0.161737\pi$
$937$	11.8504	+	11.8504i	0.387136	+	0.387136i	−0.486529	+	0.873665i	$0.661737\pi$
$938$		0			0
$939$	−10.2488	+	4.24518i	−0.334456	+	0.138536i
$940$		0			0
$941$	1.44088	+	1.87779i	0.0469712	+	0.0612141i	0.816248	−	0.577701i	$-0.196050\pi$
$941$	1.44088	+	1.87779i	0.0469712	+	0.0612141i	−0.769277	+	0.638915i	$0.779383\pi$
$942$		0			0
$943$	−33.2053	+	19.1711i	−1.08131	+	0.624297i
$944$		0			0
$945$	15.0373	−	17.5129i	0.489164	−	0.569696i
$946$		0			0
$947$	1.15521	−	0.152087i	0.0375394	−	0.00494215i	−0.111733	−	0.993738i	$-0.535640\pi$
$947$	1.15521	−	0.152087i	0.0375394	−	0.00494215i	0.149272	+	0.988796i	$0.452307\pi$
$948$		0			0
$949$	3.09955	−	23.5434i	0.100616	−	0.764251i
$950$		0			0
$951$	16.1391	+	16.1391i	0.523346	+	0.523346i
$952$		0			0
$953$	−3.07326	+	3.07326i	−0.0995525	+	0.0995525i	−0.755129	−	0.655576i	$-0.772426\pi$
$953$	−3.07326	+	3.07326i	−0.0995525	+	0.0995525i	0.655576	+	0.755129i	$0.272426\pi$
$954$		0			0
$955$	23.1349	+	3.04576i	0.748626	+	0.0985585i
$956$		0			0
$957$	−0.0869943	−	0.660788i	−0.00281213	−	0.0213602i
$958$		0			0
$959$	8.79234	−	46.7525i	0.283919	−	1.50972i
$960$		0			0
$961$	13.8037	+	23.9088i	0.445281	+	0.771250i
$962$		0			0
$963$	8.98418	−	6.89380i	0.289511	−	0.222150i
$964$		0			0
$965$	−0.0309568	−	0.0747363i	−0.000996534	−	0.00240585i
$966$		0			0
$967$	15.4680	−	15.4680i	0.497417	−	0.497417i	−0.413216	−	0.910633i	$-0.635594\pi$
$967$	15.4680	−	15.4680i	0.497417	−	0.497417i	0.910633	+	0.413216i	$0.135594\pi$
$968$		0			0
$969$	−11.5609	+	3.09772i	−0.371388	+	0.0995132i
$970$		0			0
$971$	31.4267	+	24.1146i	1.00853	+	0.773874i	0.974234	−	0.225538i	$-0.0724139\pi$
$971$	31.4267	+	24.1146i	1.00853	+	0.773874i	0.0342976	+	0.999412i	$0.489081\pi$
$972$		0			0
$973$	−2.39920	+	43.5854i	−0.0769149	+	1.39728i
$974$		0			0
$975$	1.81677	−	1.04891i	0.0581832	−	0.0335921i
$976$		0			0
$977$	3.13552	+	1.81030i	0.100314	+	0.0579165i	0.549318	−	0.835613i	$-0.314888\pi$
$977$	3.13552	+	1.81030i	0.100314	+	0.0579165i	−0.449004	+	0.893530i	$0.648221\pi$
$978$		0			0
$979$	−1.22435	+	2.95584i	−0.0391304	+	0.0944690i
$980$		0			0
$981$	−23.9261	+	9.91050i	−0.763900	+	0.316418i
$982$		0			0
$983$	−40.3577	+	10.8138i	−1.28721	+	0.344907i	−0.836600	−	0.547814i	$-0.815460\pi$
$983$	−40.3577	+	10.8138i	−1.28721	+	0.344907i	−0.450610	+	0.892721i	$0.648793\pi$
$984$		0			0
$985$	−5.35297	−	1.43432i	−0.170560	−	0.0457014i
$986$		0			0
$987$	−11.6171	−	12.9706i	−0.369777	−	0.412858i
$988$		0			0
$989$	7.10727	+	53.9851i	0.225998	+	1.71663i
$990$		0			0
$991$	14.2547	−	24.6898i	0.452815	−	0.784298i	−0.545745	−	0.837951i	$-0.683753\pi$
$991$	14.2547	−	24.6898i	0.452815	−	0.784298i	0.998560	+	0.0536534i	$0.0170866\pi$
$992$		0			0
$993$	−9.96377			−0.316191
$994$		0			0
$995$	−32.7201	−	13.5531i	−1.03730	−	0.429663i
$996$		0			0
$997$	0.0970311	+	0.0127744i	0.00307301	+	0.000404569i	0.132063	−	0.991241i	$-0.457840\pi$
$997$	0.0970311	+	0.0127744i	0.00307301	+	0.000404569i	−0.128990	+	0.991646i	$0.541173\pi$
$998$		0			0
$999$	25.8001	+	6.91311i	0.816279	+	0.218721i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.bh.a.81.12		240
4.3	odd	2		224.2.bd.a.221.1	yes	240
7.2	even	3	inner	896.2.bh.a.849.12		240
28.23	odd	6		224.2.bd.a.93.21	yes	240
32.11	odd	8		224.2.bd.a.53.21	✓	240
32.21	even	8	inner	896.2.bh.a.305.12		240
224.107	odd	24		224.2.bd.a.149.1	yes	240
224.149	even	24	inner	896.2.bh.a.177.12		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.bd.a.53.21	✓	240	32.11	odd	8
224.2.bd.a.93.21	yes	240	28.23	odd	6
224.2.bd.a.149.1	yes	240	224.107	odd	24
224.2.bd.a.221.1	yes	240	4.3	odd	2
896.2.bh.a.81.12		240	1.1	even	1	trivial
896.2.bh.a.177.12		240	224.149	even	24	inner
896.2.bh.a.305.12		240	32.21	even	8	inner
896.2.bh.a.849.12		240	7.2	even	3	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:	\( N \)	\(=\)	\( 896 = 2^{7} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	896.bh (of order \(24\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.653842 + 0.501711i) q^{3} +(-1.21118 + 1.57844i) q^{5} +(1.14530 - 2.38501i) q^{7} +(-0.600661 + 2.24170i) q^{9} +O(q^{10})\)	\(q+(-0.653842 + 0.501711i) q^{3} +(-1.21118 + 1.57844i) q^{5} +(1.14530 - 2.38501i) q^{7} +(-0.600661 + 2.24170i) q^{9} +(-0.0369986 + 0.281032i) q^{11} +(-0.935223 + 2.25783i) q^{13} -1.63971i q^{15} +(-2.60609 - 1.50463i) q^{17} +(-4.78465 + 0.629911i) q^{19} +(0.447738 + 2.13403i) q^{21} +(1.19733 - 4.46850i) q^{23} +(0.269578 + 1.00608i) q^{25} +(-1.67811 - 4.05132i) q^{27} +(2.63582 + 1.09179i) q^{29} +(-0.920944 + 1.59512i) q^{31} +(-0.116806 - 0.202313i) q^{33} +(2.37743 + 4.69647i) q^{35} +(-3.70803 + 4.83240i) q^{37} +(-0.521288 - 1.94547i) q^{39} +(-5.86063 - 5.86063i) q^{41} +(-10.8743 + 4.50430i) q^{43} +(-2.81088 - 3.66321i) q^{45} +(-6.91568 + 3.99277i) q^{47} +(-4.37656 - 5.46312i) q^{49} +(2.45886 - 0.323715i) q^{51} +(0.380178 - 2.88774i) q^{53} +(-0.398780 - 0.398780i) q^{55} +(2.81237 - 2.81237i) q^{57} +(-1.50285 - 0.197854i) q^{59} +(-0.522701 - 3.97031i) q^{61} +(4.65854 + 4.00001i) q^{63} +(-2.43112 - 4.21083i) q^{65} +(-3.72219 + 2.85614i) q^{67} +(1.45903 + 3.52240i) q^{69} +(9.00400 - 9.00400i) q^{71} +(-9.38575 + 2.51490i) q^{73} +(-0.681021 - 0.522566i) q^{75} +(0.627890 + 0.410109i) q^{77} +(-9.86199 + 5.69382i) q^{79} +(-2.89975 - 1.67417i) q^{81} +(0.888813 - 2.14578i) q^{83} +(5.53141 - 2.29118i) q^{85} +(-2.27117 + 0.608558i) q^{87} +(10.9024 + 2.92129i) q^{89} +(4.31383 + 4.81641i) q^{91} +(-0.198138 - 1.50500i) q^{93} +(4.80079 - 8.31521i) q^{95} -17.3614 q^{97} +(-0.607766 - 0.251745i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 4 q^{3} - 4 q^{5} + 8 q^{7} - 4 q^{9}+O(q^{10}) \) 240 * q + 4 * q^3 - 4 * q^5 + 8 * q^7 - 4 * q^9	\( 240 q + 4 q^{3} - 4 q^{5} + 8 q^{7} - 4 q^{9} + 4 q^{11} - 16 q^{13} + 4 q^{19} - 8 q^{21} + 12 q^{23} - 4 q^{25} + 16 q^{27} - 16 q^{29} + 56 q^{31} - 8 q^{33} + 32 q^{35} - 4 q^{37} + 4 q^{39} - 16 q^{41} + 8 q^{45} + 28 q^{51} - 20 q^{53} + 16 q^{55} - 16 q^{57} + 36 q^{59} - 4 q^{61} + 16 q^{63} - 8 q^{65} - 36 q^{67} - 16 q^{69} - 48 q^{71} - 4 q^{73} - 16 q^{75} - 8 q^{77} + 96 q^{83} - 56 q^{85} + 4 q^{87} - 4 q^{89} + 56 q^{91} + 20 q^{93} + 8 q^{95} - 32 q^{97} - 8 q^{99}+O(q^{100}) \) 240 * q + 4 * q^3 - 4 * q^5 + 8 * q^7 - 4 * q^9 + 4 * q^11 - 16 * q^13 + 4 * q^19 - 8 * q^21 + 12 * q^23 - 4 * q^25 + 16 * q^27 - 16 * q^29 + 56 * q^31 - 8 * q^33 + 32 * q^35 - 4 * q^37 + 4 * q^39 - 16 * q^41 + 8 * q^45 + 28 * q^51 - 20 * q^53 + 16 * q^55 - 16 * q^57 + 36 * q^59 - 4 * q^61 + 16 * q^63 - 8 * q^65 - 36 * q^67 - 16 * q^69 - 48 * q^71 - 4 * q^73 - 16 * q^75 - 8 * q^77 + 96 * q^83 - 56 * q^85 + 4 * q^87 - 4 * q^89 + 56 * q^91 + 20 * q^93 + 8 * q^95 - 32 * q^97 - 8 * q^99

Introduction

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