LMFDB - Embedded newform 440.2.y.a.201.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [440,2,Mod(81,440)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(440, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

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

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

chi := DirichletCharacter("440.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 440 = 2^{3} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	440.y (of order $5$, degree $4$, 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:	$3.51341768894$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.13140625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 $ x^8 - 3x^7 + 5x^6 - 3x^5 + 4x^4 + 3x^3 + 5x^2 + 3*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			201.2
Root			$-0.386111 + 0.280526i$ of defining polynomial
Character	$\chi$	$=$	440.201
Dual form			440.2.y.a.81.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0911485 + 0.280526i) q^{3} +(-0.809017 - 0.587785i) q^{5} +(-1.35666 + 4.17538i) q^{7} +(2.35666 - 1.71222i) q^{9} +(3.31118 - 0.189896i) q^{11} +(-4.82402 + 3.50485i) q^{13} +(0.0911485 - 0.280526i) q^{15} +(1.34932 + 0.980336i) q^{17} +(2.37743 + 7.31696i) q^{19} -1.29496 q^{21} -0.904706 q^{23} +(0.309017 + 0.951057i) q^{25} +(1.41102 + 1.02516i) q^{27} +(-1.46443 + 4.50705i) q^{29} +(4.14709 - 3.01303i) q^{31} +(0.355081 + 0.911566i) q^{33} +(3.55179 - 2.58053i) q^{35} +(-0.0571606 + 0.175922i) q^{37} +(-1.42291 - 1.03380i) q^{39} +(-0.810356 - 2.49402i) q^{41} +3.59822 q^{43} -2.91300 q^{45} +(-0.239853 - 0.738191i) q^{47} +(-9.93016 - 7.21469i) q^{49} +(-0.152022 + 0.467875i) q^{51} +(7.76295 - 5.64012i) q^{53} +(-2.79042 - 1.79264i) q^{55} +(-1.83590 + 1.33386i) q^{57} +(-3.47762 + 10.7030i) q^{59} +(-10.6708 - 7.75277i) q^{61} +(3.95196 + 12.1629i) q^{63} +5.96281 q^{65} -7.79954 q^{67} +(-0.0824626 - 0.253794i) q^{69} +(5.63943 + 4.09729i) q^{71} +(3.94122 - 12.1298i) q^{73} +(-0.238630 + 0.173375i) q^{75} +(-3.69927 + 14.0831i) q^{77} +(8.11547 - 5.89624i) q^{79} +(2.54152 - 7.82200i) q^{81} +(-3.31316 - 2.40715i) q^{83} +(-0.515393 - 1.58622i) q^{85} -1.39783 q^{87} -0.466291 q^{89} +(-8.08953 - 24.8970i) q^{91} +(1.22324 + 0.888733i) q^{93} +(2.37743 - 7.31696i) q^{95} +(-5.74372 + 4.17306i) q^{97} +(7.47820 - 6.11699i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{3} - 2 q^{5} + q^{7} + 7 q^{9} + 3 q^{11} - 4 q^{13} + q^{15} - 3 q^{17} + 9 q^{19} - 4 q^{21} - 22 q^{23} - 2 q^{25} - 8 q^{27} - 17 q^{29} - 4 q^{31} + 21 q^{33} + 6 q^{35} + 24 q^{37} - 13 q^{39}+ \cdots + 22 q^{99}+O(q^{100}) $ 8 * q + q^3 - 2 * q^5 + q^7 + 7 * q^9 + 3 * q^11 - 4 * q^13 + q^15 - 3 * q^17 + 9 * q^19 - 4 * q^21 - 22 * q^23 - 2 * q^25 - 8 * q^27 - 17 * q^29 - 4 * q^31 + 21 * q^33 + 6 * q^35 + 24 * q^37 - 13 * q^39 - 4 * q^41 - 14 * q^43 - 8 * q^45 - 12 * q^47 - 15 * q^49 - 17 * q^51 + 35 * q^53 + 3 * q^55 - q^57 + 21 * q^59 - 22 * q^61 + 5 * q^63 + 6 * q^65 + 14 * q^67 + 3 * q^69 + 40 * q^71 + 9 * q^73 + q^75 - 4 * q^77 + 41 * q^79 + 24 * q^81 - 7 * q^83 - 8 * q^85 - 46 * q^87 - 24 * q^89 - 18 * q^91 + 3 * q^93 + 9 * q^95 + 4 * q^97 + 22 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/440\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$221$	$321$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{4}{5}\right)$

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
$3$	0.0911485	+	0.280526i	0.0526246	+	0.161962i	0.973915	−	0.226914i	$-0.0728635\pi$
$3$	0.0911485	+	0.280526i	0.0526246	+	0.161962i	−0.921290	+	0.388876i	$0.872864\pi$
$4$		0			0
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$6$		0			0
$7$	−1.35666	+	4.17538i	−0.512771	+	1.57815i	0.274531	+	0.961578i	$0.411477\pi$
$7$	−1.35666	+	4.17538i	−0.512771	+	1.57815i	−0.787302	+	0.616568i	$0.788523\pi$
$8$		0			0
$9$	2.35666	−	1.71222i	0.785555	−	0.570739i
$10$		0			0
$11$	3.31118	−	0.189896i	0.998360	−	0.0572559i
$11$	3.31118	−	0.189896i	0.998360	−	0.0572559i
$12$		0			0
$13$	−4.82402	+	3.50485i	−1.33794	+	0.972071i	−0.338424	+	0.940994i	$0.609894\pi$
$13$	−4.82402	+	3.50485i	−1.33794	+	0.972071i	−0.999517	+	0.0310775i	$0.990106\pi$
$14$		0			0
$15$	0.0911485	−	0.280526i	0.0235345	−	0.0724316i
$16$		0			0
$17$	1.34932	+	0.980336i	0.327258	+	0.237767i	0.739266	−	0.673413i	$-0.235173\pi$
$17$	1.34932	+	0.980336i	0.327258	+	0.237767i	−0.412009	+	0.911180i	$0.635173\pi$
$18$		0			0
$19$	2.37743	+	7.31696i	0.545419	+	1.67863i	0.719992	+	0.693982i	$0.244145\pi$
$19$	2.37743	+	7.31696i	0.545419	+	1.67863i	−0.174573	+	0.984644i	$0.555855\pi$
$20$		0			0
$21$	−1.29496			−0.282584
$22$		0			0
$23$	−0.904706			−0.188644			−0.0943221	−	0.995542i	$-0.530068\pi$
$23$	−0.904706			−0.188644			−0.0943221	+	0.995542i	$0.530068\pi$
$24$		0			0
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$		0			0
$27$	1.41102	+	1.02516i	0.271551	+	0.197293i
$28$		0			0
$29$	−1.46443	+	4.50705i	−0.271938	+	0.836938i	0.718076	+	0.695965i	$0.245023\pi$
$29$	−1.46443	+	4.50705i	−0.271938	+	0.836938i	−0.990013	+	0.140973i	$0.954977\pi$
$30$		0			0
$31$	4.14709	−	3.01303i	0.744839	−	0.541157i	−0.149384	−	0.988779i	$-0.547729\pi$
$31$	4.14709	−	3.01303i	0.744839	−	0.541157i	0.894223	+	0.447622i	$0.147729\pi$
$32$		0			0
$33$	0.355081	+	0.911566i	0.0618116	+	0.158683i
$34$		0			0
$35$	3.55179	−	2.58053i	0.600362	−	0.436189i
$36$		0			0
$37$	−0.0571606	+	0.175922i	−0.00939715	+	0.0289214i	−0.955645	−	0.294521i	$-0.904840\pi$
$37$	−0.0571606	+	0.175922i	−0.00939715	+	0.0289214i	0.946248	+	0.323442i	$0.104840\pi$
$38$		0			0
$39$	−1.42291	−	1.03380i	−0.227847	−	0.165541i
$40$		0			0
$41$	−0.810356	−	2.49402i	−0.126556	−	0.389501i	0.867625	−	0.497219i	$-0.165645\pi$
$41$	−0.810356	−	2.49402i	−0.126556	−	0.389501i	−0.994181	+	0.107719i	$0.965645\pi$
$42$		0			0
$43$	3.59822			0.548723			0.274361	−	0.961627i	$-0.411534\pi$
$43$	3.59822			0.548723			0.274361	+	0.961627i	$0.411534\pi$
$44$		0			0
$45$	−2.91300			−0.434244
$46$		0			0
$47$	−0.239853	−	0.738191i	−0.0349861	−	0.107676i	0.932038	−	0.362360i	$-0.118029\pi$
$47$	−0.239853	−	0.738191i	−0.0349861	−	0.107676i	−0.967024	+	0.254683i	$0.918029\pi$
$48$		0			0
$49$	−9.93016	−	7.21469i	−1.41859	−	1.03067i
$50$		0			0
$51$	−0.152022	+	0.467875i	−0.0212873	+	0.0655157i
$52$		0			0
$53$	7.76295	−	5.64012i	1.06632	−	0.774729i	0.0910758	−	0.995844i	$-0.470969\pi$
$53$	7.76295	−	5.64012i	1.06632	−	0.774729i	0.975248	+	0.221114i	$0.0709694\pi$
$54$		0			0
$55$	−2.79042	−	1.79264i	−0.376260	−	0.241719i
$56$		0			0
$57$	−1.83590	+	1.33386i	−0.243171	+	0.176674i
$58$		0			0
$59$	−3.47762	+	10.7030i	−0.452748	+	1.39341i	0.421012	+	0.907055i	$0.361675\pi$
$59$	−3.47762	+	10.7030i	−0.452748	+	1.39341i	−0.873759	+	0.486359i	$0.838325\pi$
$60$		0			0
$61$	−10.6708	−	7.75277i	−1.36625	−	0.992640i	−0.998019	−	0.0629067i	$-0.979963\pi$
$61$	−10.6708	−	7.75277i	−1.36625	−	0.992640i	−0.368233	−	0.929734i	$-0.620037\pi$
$62$		0			0
$63$	3.95196	+	12.1629i	0.497900	+	1.53238i
$64$		0			0
$65$	5.96281			0.739596
$66$		0			0
$67$	−7.79954			−0.952866			−0.476433	−	0.879211i	$-0.658070\pi$
$67$	−7.79954			−0.952866			−0.476433	+	0.879211i	$0.658070\pi$
$68$		0			0
$69$	−0.0824626	−	0.253794i	−0.00992734	−	0.0305532i
$70$		0			0
$71$	5.63943	+	4.09729i	0.669278	+	0.486259i	0.869783	−	0.493434i	$-0.164258\pi$
$71$	5.63943	+	4.09729i	0.669278	+	0.486259i	−0.200506	+	0.979693i	$0.564258\pi$
$72$		0			0
$73$	3.94122	−	12.1298i	0.461285	−	1.41969i	−0.402310	−	0.915504i	$-0.631793\pi$
$73$	3.94122	−	12.1298i	0.461285	−	1.41969i	0.863595	−	0.504186i	$-0.168207\pi$
$74$		0			0
$75$	−0.238630	+	0.173375i	−0.0275546	+	0.0200196i
$76$		0			0
$77$	−3.69927	+	14.0831i	−0.421571	+	1.60492i
$78$		0			0
$79$	8.11547	−	5.89624i	0.913062	−	0.663378i	−0.0287255	−	0.999587i	$-0.509145\pi$
$79$	8.11547	−	5.89624i	0.913062	−	0.663378i	0.941787	+	0.336209i	$0.109145\pi$
$80$		0			0
$81$	2.54152	−	7.82200i	0.282391	−	0.869112i
$82$		0			0
$83$	−3.31316	−	2.40715i	−0.363667	−	0.264219i	0.390913	−	0.920428i	$-0.372159\pi$
$83$	−3.31316	−	2.40715i	−0.363667	−	0.264219i	−0.754580	+	0.656208i	$0.772159\pi$
$84$		0			0
$85$	−0.515393	−	1.58622i	−0.0559023	−	0.172049i
$86$		0			0
$87$	−1.39783			−0.149863
$88$		0			0
$89$	−0.466291			−0.0494267			−0.0247134	−	0.999695i	$-0.507867\pi$
$89$	−0.466291			−0.0494267			−0.0247134	+	0.999695i	$0.507867\pi$
$90$		0			0
$91$	−8.08953	−	24.8970i	−0.848013	−	2.60992i
$92$		0			0
$93$	1.22324	+	0.888733i	0.126844	+	0.0921574i
$94$		0			0
$95$	2.37743	−	7.31696i	0.243919	−	0.750705i
$96$		0			0
$97$	−5.74372	+	4.17306i	−0.583186	+	0.423710i	−0.839871	−	0.542785i	$-0.817370\pi$
$97$	−5.74372	+	4.17306i	−0.583186	+	0.423710i	0.256685	+	0.966495i	$0.417370\pi$
$98$		0			0
$99$	7.47820	−	6.11699i	0.751588	−	0.614780i
$100$		0			0
$101$	13.1749	−	9.57214i	1.31095	−	0.952463i	0.310955	−	0.950425i	$-0.399351\pi$
$101$	13.1749	−	9.57214i	1.31095	−	0.952463i	0.999998	−	0.00203865i	$-0.000648924\pi$
$102$		0			0
$103$	0.985946	−	3.03443i	0.0971481	−	0.298991i	−0.890659	−	0.454671i	$-0.849757\pi$
$103$	0.985946	−	3.03443i	0.0971481	−	0.298991i	0.987808	+	0.155680i	$0.0497568\pi$
$104$		0			0
$105$	1.04765	+	0.761160i	0.102240	+	0.0742816i
$106$		0			0
$107$	−4.06801	−	12.5201i	−0.393270	−	1.21036i	−0.930301	−	0.366797i	$-0.880454\pi$
$107$	−4.06801	−	12.5201i	−0.393270	−	1.21036i	0.537031	−	0.843562i	$-0.319546\pi$
$108$		0			0
$109$	1.33532			0.127900			0.0639502	−	0.997953i	$-0.479630\pi$
$109$	1.33532			0.127900			0.0639502	+	0.997953i	$0.479630\pi$
$110$		0			0
$111$	−0.0545610			−0.00517870
$112$		0			0
$113$	−0.517444	−	1.59253i	−0.0486770	−	0.149812i	0.923764	−	0.382963i	$-0.125096\pi$
$113$	−0.517444	−	1.59253i	−0.0486770	−	0.149812i	−0.972441	+	0.233151i	$0.925096\pi$
$114$		0			0
$115$	0.731923	+	0.531773i	0.0682521	+	0.0495881i
$116$		0			0
$117$	−5.36752	+	16.5195i	−0.496227	+	1.52723i
$118$		0			0
$119$	−5.92385	+	4.30393i	−0.543038	+	0.394541i
$120$		0			0
$121$	10.9279	−	1.25756i	0.993444	−	0.114324i
$122$		0			0
$123$	0.625776	−	0.454653i	0.0564243	−	0.0409946i
$124$		0			0
$125$	0.309017	−	0.951057i	0.0276393	−	0.0850651i
$126$		0			0
$127$	−0.729305	−	0.529871i	−0.0647153	−	0.0470185i	0.554957	−	0.831879i	$-0.312735\pi$
$127$	−0.729305	−	0.529871i	−0.0647153	−	0.0470185i	−0.619673	+	0.784860i	$0.712735\pi$
$128$		0			0
$129$	0.327972	+	1.00939i	0.0288763	+	0.0888722i
$130$		0			0
$131$	−14.5527			−1.27148			−0.635739	−	0.771904i	$-0.719305\pi$
$131$	−14.5527			−1.27148			−0.635739	+	0.771904i	$0.719305\pi$
$132$		0			0
$133$	−33.7765			−2.92879
$134$		0			0
$135$	−0.538961	−	1.65875i	−0.0463864	−	0.142763i
$136$		0			0
$137$	16.6573	+	12.1022i	1.42313	+	1.03396i	0.991246	+	0.132031i	$0.0421498\pi$
$137$	16.6573	+	12.1022i	1.42313	+	1.03396i	0.431881	+	0.901931i	$0.357850\pi$
$138$		0			0
$139$	−4.63035	+	14.2508i	−0.392741	+	1.20873i	0.537965	+	0.842967i	$0.319193\pi$
$139$	−4.63035	+	14.2508i	−0.392741	+	1.20873i	−0.930707	+	0.365767i	$0.880807\pi$
$140$		0			0
$141$	0.185220	−	0.134570i	0.0155983	−	0.0113328i
$142$		0			0
$143$	−15.3076	+	12.5213i	−1.28009	+	1.04708i
$144$		0			0
$145$	3.83392	−	2.78551i	0.318390	−	0.231324i
$146$		0			0
$147$	1.11879	−	3.44328i	0.0922762	−	0.283997i
$148$		0			0
$149$	−8.86891	−	6.44364i	−0.726570	−	0.527884i	0.161907	−	0.986806i	$-0.448236\pi$
$149$	−8.86891	−	6.44364i	−0.726570	−	0.527884i	−0.888476	+	0.458922i	$0.848236\pi$
$150$		0			0
$151$	−1.82682	−	5.62238i	−0.148665	−	0.457543i	0.848799	−	0.528715i	$-0.177326\pi$
$151$	−1.82682	−	5.62238i	−0.148665	−	0.457543i	−0.997464	+	0.0711723i	$0.977326\pi$
$152$		0			0
$153$	4.85844			0.392781
$154$		0			0
$155$	−5.12608			−0.411737
$156$		0			0
$157$	−1.36780	−	4.20964i	−0.109162	−	0.335966i	0.881523	−	0.472142i	$-0.156519\pi$
$157$	−1.36780	−	4.20964i	−0.109162	−	0.335966i	−0.990685	+	0.136176i	$0.956519\pi$
$158$		0			0
$159$	2.28978	+	1.66362i	0.181592	+	0.131934i
$160$		0			0
$161$	1.22738	−	3.77749i	0.0967313	−	0.297708i
$162$		0			0
$163$	5.97430	−	4.34059i	0.467944	−	0.339981i	−0.328696	−	0.944436i	$-0.606609\pi$
$163$	5.97430	−	4.34059i	0.467944	−	0.339981i	0.796639	+	0.604455i	$0.206609\pi$
$164$		0			0
$165$	0.248539	−	0.946183i	0.0193487	−	0.0736603i
$166$		0			0
$167$	15.7658	−	11.4545i	1.21999	−	0.886375i	0.223892	−	0.974614i	$-0.428124\pi$
$167$	15.7658	−	11.4545i	1.21999	−	0.886375i	0.996099	+	0.0882386i	$0.0281238\pi$
$168$		0			0
$169$	6.96991	−	21.4512i	0.536147	−	1.65009i
$170$		0			0
$171$	18.1310	+	13.1730i	1.38651	+	1.00736i
$172$		0			0
$173$	2.93815	+	9.04269i	0.223383	+	0.687503i	0.998452	+	0.0556257i	$0.0177153\pi$
$173$	2.93815	+	9.04269i	0.223383	+	0.687503i	−0.775068	+	0.631877i	$0.782285\pi$
$174$		0			0
$175$	−4.39026			−0.331872
$176$		0			0
$177$	−3.31946			−0.249506
$178$		0			0
$179$	2.22879	+	6.85952i	0.166588	+	0.512705i	0.999150	−	0.0412273i	$-0.0131268\pi$
$179$	2.22879	+	6.85952i	0.166588	+	0.512705i	−0.832562	+	0.553932i	$0.813127\pi$
$180$		0			0
$181$	18.9225	+	13.7480i	1.40650	+	1.02188i	0.993820	+	0.111002i	$0.0354060\pi$
$181$	18.9225	+	13.7480i	1.40650	+	1.02188i	0.412676	+	0.910878i	$0.364594\pi$
$182$		0			0
$183$	1.20223	−	3.70009i	0.0888715	−	0.273518i
$184$		0			0
$185$	0.149648	−	0.108726i	0.0110024	−	0.00799369i
$186$		0			0
$187$	4.65400	+	2.98984i	0.340334	+	0.218639i
$188$		0			0
$189$	−6.19473	+	4.50074i	−0.450601	+	0.327380i
$190$		0			0
$191$	−1.28728	+	3.96183i	−0.0931441	+	0.286668i	−0.986766	−	0.162153i	$-0.948156\pi$
$191$	−1.28728	+	3.96183i	−0.0931441	+	0.286668i	0.893621	+	0.448821i	$0.148156\pi$
$192$		0			0
$193$	18.7417	+	13.6166i	1.34906	+	0.980148i	0.999058	+	0.0433979i	$0.0138183\pi$
$193$	18.7417	+	13.6166i	1.34906	+	0.980148i	0.350000	+	0.936750i	$0.386182\pi$
$194$		0			0
$195$	0.543502	+	1.67273i	0.0389210	+	0.119786i
$196$		0			0
$197$	10.1507			0.723209			0.361604	−	0.932332i	$-0.382229\pi$
$197$	10.1507			0.723209			0.361604	+	0.932332i	$0.382229\pi$
$198$		0			0
$199$	−17.0131			−1.20603			−0.603014	−	0.797731i	$-0.706034\pi$
$199$	−17.0131			−1.20603			−0.603014	+	0.797731i	$0.706034\pi$
$200$		0			0
$201$	−0.710917	−	2.18798i	−0.0501442	−	0.154328i
$202$		0			0
$203$	−16.8319	−	12.2291i	−1.18137	−	0.858315i
$204$		0			0
$205$	−0.810356	+	2.49402i	−0.0565977	+	0.174190i
$206$		0			0
$207$	−2.13209	+	1.54905i	−0.148190	+	0.107667i
$208$		0			0
$209$	9.26156	+	23.7763i	0.640635	+	1.64464i
$210$		0			0
$211$	4.86721	−	3.53624i	0.335073	−	0.243445i	−0.407507	−	0.913202i	$-0.633602\pi$
$211$	4.86721	−	3.53624i	0.335073	−	0.243445i	0.742580	+	0.669757i	$0.233602\pi$
$212$		0			0
$213$	−0.635371	+	1.95547i	−0.0435349	+	0.133987i
$214$		0			0
$215$	−2.91102	−	2.11498i	−0.198530	−	0.144240i
$216$		0			0
$217$	6.95437	+	21.4033i	0.472093	+	1.45295i
$218$		0			0
$219$	3.76197			0.254211
$220$		0			0
$221$	−9.94506			−0.668977
$222$		0			0
$223$	0.770711	+	2.37201i	0.0516107	+	0.158841i	0.973540	−	0.228517i	$-0.0733876\pi$
$223$	0.770711	+	2.37201i	0.0516107	+	0.158841i	−0.921929	+	0.387358i	$0.873388\pi$
$224$		0			0
$225$	2.35666	+	1.71222i	0.157111	+	0.114148i
$226$		0			0
$227$	−7.72396	+	23.7719i	−0.512657	+	1.57780i	0.274848	+	0.961488i	$0.411373\pi$
$227$	−7.72396	+	23.7719i	−0.512657	+	1.57780i	−0.787505	+	0.616309i	$0.788627\pi$
$228$		0			0
$229$	2.24164	−	1.62865i	0.148132	−	0.107624i	−0.511251	−	0.859432i	$-0.670818\pi$
$229$	2.24164	−	1.62865i	0.148132	−	0.107624i	0.659383	+	0.751807i	$0.270818\pi$
$230$		0			0
$231$	−4.28786	+	0.245909i	−0.282121	+	0.0161796i
$232$		0			0
$233$	7.76676	−	5.64288i	0.508818	−	0.369678i	−0.303557	−	0.952813i	$-0.598174\pi$
$233$	7.76676	−	5.64288i	0.508818	−	0.369678i	0.812375	+	0.583136i	$0.198174\pi$
$234$		0			0
$235$	−0.239853	+	0.738191i	−0.0156463	+	0.0481543i
$236$		0			0
$237$	2.39376	+	1.73917i	0.155492	+	0.112971i
$238$		0			0
$239$	4.56394	+	14.0464i	0.295217	+	0.908584i	0.983149	+	0.182808i	$0.0585188\pi$
$239$	4.56394	+	14.0464i	0.295217	+	0.908584i	−0.687932	+	0.725775i	$0.741481\pi$
$240$		0			0
$241$	−10.4338			−0.672099			−0.336049	−	0.941844i	$-0.609091\pi$
$241$	−10.4338			−0.672099			−0.336049	+	0.941844i	$0.609091\pi$
$242$		0			0
$243$	7.65828			0.491279
$244$		0			0
$245$	3.79298	+	11.6736i	0.242325	+	0.745799i
$246$		0			0
$247$	−37.1136	−	26.9646i	−2.36148	−	1.71572i
$248$		0			0
$249$	0.373280	−	1.14884i	0.0236557	−	0.0728047i
$250$		0			0
$251$	5.44787	−	3.95811i	0.343866	−	0.249834i	−0.402425	−	0.915453i	$-0.631833\pi$
$251$	5.44787	−	3.95811i	0.343866	−	0.249834i	0.746291	+	0.665619i	$0.231833\pi$
$252$		0			0
$253$	−2.99565	+	0.171800i	−0.188335	+	0.0108010i
$254$		0			0
$255$	0.397999	−	0.289163i	0.0249236	−	0.0181081i
$256$		0			0
$257$	2.39239	−	7.36301i	0.149233	−	0.459292i	−0.848298	−	0.529519i	$-0.822372\pi$
$257$	2.39239	−	7.36301i	0.149233	−	0.459292i	0.997531	+	0.0702272i	$0.0223724\pi$
$258$		0			0
$259$	−0.656995	−	0.477335i	−0.0408237	−	0.0296601i
$260$		0			0
$261$	4.26588	+	13.1290i	0.264051	+	0.812666i
$262$		0			0
$263$	18.1618			1.11990			0.559952	−	0.828525i	$-0.310819\pi$
$263$	18.1618			1.11990			0.559952	+	0.828525i	$0.310819\pi$
$264$		0			0
$265$	−9.59554			−0.589449
$266$		0			0
$267$	−0.0425017	−	0.130807i	−0.00260106	−	0.00800525i
$268$		0			0
$269$	8.67812	+	6.30502i	0.529114	+	0.384424i	0.820026	−	0.572326i	$-0.193959\pi$
$269$	8.67812	+	6.30502i	0.529114	+	0.384424i	−0.290912	+	0.956750i	$0.593959\pi$
$270$		0			0
$271$	−5.80566	+	17.8680i	−0.352669	+	1.08540i	0.604680	+	0.796469i	$0.293301\pi$
$271$	−5.80566	+	17.8680i	−0.352669	+	1.08540i	−0.957349	+	0.288935i	$0.906699\pi$
$272$		0			0
$273$	6.24692	−	4.53865i	0.378081	−	0.274692i
$274$		0			0
$275$	1.20381	+	3.09044i	0.0725927	+	0.186361i
$276$		0			0
$277$	−23.3375	+	16.9557i	−1.40221	+	1.01877i	−0.407814	+	0.913065i	$0.633709\pi$
$277$	−23.3375	+	16.9557i	−1.40221	+	1.01877i	−0.994398	+	0.105701i	$0.966291\pi$
$278$		0			0
$279$	4.61432	−	14.2014i	0.276252	−	0.850217i
$280$		0			0
$281$	−21.8873	−	15.9021i	−1.30569	−	0.948637i	−0.305693	−	0.952130i	$-0.598888\pi$
$281$	−21.8873	−	15.9021i	−1.30569	−	0.948637i	−0.999994	+	0.00349313i	$0.998888\pi$
$282$		0			0
$283$	3.97802	+	12.2431i	0.236468	+	0.727775i	0.996923	+	0.0783842i	$0.0249761\pi$
$283$	3.97802	+	12.2431i	0.236468	+	0.727775i	−0.760455	+	0.649391i	$0.775024\pi$
$284$		0			0
$285$	2.26930			0.134422
$286$		0			0
$287$	11.5129			0.679583
$288$		0			0
$289$	−4.39369	−	13.5224i	−0.258452	−	0.795435i
$290$		0			0
$291$	−1.69418	−	1.23090i	−0.0993148	−	0.0721565i
$292$		0			0
$293$	1.81972	−	5.60052i	0.106309	−	0.327186i	−0.883726	−	0.468004i	$-0.844973\pi$
$293$	1.81972	−	5.60052i	0.106309	−	0.327186i	0.990035	+	0.140818i	$0.0449733\pi$
$294$		0			0
$295$	9.10453	−	6.61483i	0.530086	−	0.385130i
$296$		0			0
$297$	4.86682	+	3.12656i	0.282401	+	0.181422i
$298$		0			0
$299$	4.36432	−	3.17086i	0.252395	−	0.183376i
$300$		0			0
$301$	−4.88157	+	15.0239i	−0.281369	+	0.865965i
$302$		0			0
$303$	3.88611	+	2.82343i	0.223251	+	0.162202i
$304$		0			0
$305$	4.07587	+	12.5442i	0.233384	+	0.718281i
$306$		0			0
$307$	6.85844			0.391432			0.195716	−	0.980661i	$-0.437297\pi$
$307$	6.85844			0.391432			0.195716	+	0.980661i	$0.437297\pi$
$308$		0			0
$309$	0.941105			0.0535376
$310$		0			0
$311$	−4.40946	−	13.5709i	−0.250037	−	0.769536i	−0.994767	−	0.102170i	$-0.967422\pi$
$311$	−4.40946	−	13.5709i	−0.250037	−	0.769536i	0.744730	−	0.667366i	$-0.232578\pi$
$312$		0			0
$313$	−1.29421	−	0.940297i	−0.0731529	−	0.0531487i	0.550608	−	0.834764i	$-0.314396\pi$
$313$	−1.29421	−	0.940297i	−0.0731529	−	0.0531487i	−0.623761	+	0.781615i	$0.714396\pi$
$314$		0			0
$315$	3.95196	−	12.1629i	0.222668	−	0.685300i
$316$		0			0
$317$	24.9627	−	18.1365i	1.40204	−	1.01864i	0.407624	−	0.913150i	$-0.366357\pi$
$317$	24.9627	−	18.1365i	1.40204	−	1.01864i	0.994420	−	0.105495i	$-0.0336427\pi$
$318$		0			0
$319$	−3.99312	+	15.2018i	−0.223572	+	0.851135i
$320$		0			0
$321$	3.14141	−	2.28237i	0.175337	−	0.127389i
$322$		0			0
$323$	−3.96518	+	12.2036i	−0.220629	+	0.679025i
$324$		0			0
$325$	−4.82402	−	3.50485i	−0.267588	−	0.194414i
$326$		0			0
$327$	0.121712	+	0.374592i	0.00673071	+	0.0207150i
$328$		0			0
$329$	3.40763			0.187869
$330$		0			0
$331$	−1.16816			−0.0642079			−0.0321040	−	0.999485i	$-0.510221\pi$
$331$	−1.16816			−0.0642079			−0.0321040	+	0.999485i	$0.510221\pi$
$332$		0			0
$333$	0.166509	+	0.512461i	0.00912462	+	0.0280827i
$334$		0			0
$335$	6.30996	+	4.58446i	0.344750	+	0.250476i
$336$		0			0
$337$	4.33522	−	13.3424i	0.236154	−	0.726809i	−0.760812	−	0.648973i	$-0.775199\pi$
$337$	4.33522	−	13.3424i	0.236154	−	0.726809i	0.996966	−	0.0778359i	$-0.0248010\pi$
$338$		0			0
$339$	0.399582	−	0.290313i	0.0217023	−	0.0157677i
$340$		0			0
$341$	13.1596	−	10.7642i	0.712632	−	0.582916i
$342$		0			0
$343$	18.7334	−	13.6106i	1.01151	−	0.734905i
$344$		0			0
$345$	−0.0824626	+	0.253794i	−0.00443964	+	0.0136638i
$346$		0			0
$347$	−26.9818	−	19.6034i	−1.44846	−	1.05237i	−0.986188	−	0.165630i	$-0.947034\pi$
$347$	−26.9818	−	19.6034i	−1.44846	−	1.05237i	−0.462273	−	0.886738i	$-0.652966\pi$
$348$		0			0
$349$	−10.9166	−	33.5978i	−0.584351	−	1.79845i	−0.601862	−	0.798600i	$-0.705574\pi$
$349$	−10.9166	−	33.5978i	−0.584351	−	1.79845i	0.0175108	−	0.999847i	$-0.494426\pi$
$350$		0			0
$351$	−10.3998			−0.555102
$352$		0			0
$353$	11.7558			0.625698			0.312849	−	0.949803i	$-0.398717\pi$
$353$	11.7558			0.625698			0.312849	+	0.949803i	$0.398717\pi$
$354$		0			0
$355$	−2.15407	−	6.62955i	−0.114326	−	0.351860i
$356$		0			0
$357$	−1.74732	−	1.26950i	−0.0924778	−	0.0671890i
$358$		0			0
$359$	−0.840838	+	2.58783i	−0.0443777	+	0.136581i	−0.970790	−	0.239929i	$-0.922876\pi$
$359$	−0.840838	+	2.58783i	−0.0443777	+	0.136581i	0.926413	+	0.376510i	$0.122876\pi$
$360$		0			0
$361$	−32.5145	+	23.6232i	−1.71129	+	1.24332i
$362$		0			0
$363$	1.34884	+	2.95093i	0.0707957	+	0.154884i
$364$		0			0
$365$	−10.3183	+	7.49665i	−0.540082	+	0.392393i
$366$		0			0
$367$	0.959060	−	2.95168i	0.0500625	−	0.154077i	−0.922900	−	0.385040i	$-0.874188\pi$
$367$	0.959060	−	2.95168i	0.0500625	−	0.154077i	0.972962	+	0.230963i	$0.0741877\pi$
$368$		0			0
$369$	−6.18004	−	4.49006i	−0.321720	−	0.233743i
$370$		0			0
$371$	13.0179	+	40.0650i	0.675857	+	2.08007i
$372$		0			0
$373$	−27.4604			−1.42185			−0.710924	−	0.703269i	$-0.751723\pi$
$373$	−27.4604			−1.42185			−0.710924	+	0.703269i	$0.751723\pi$
$374$		0			0
$375$	0.294963			0.0152318
$376$		0			0
$377$	−8.73211	−	26.8747i	−0.449727	−	1.38412i
$378$		0			0
$379$	−11.2805	−	8.19577i	−0.579441	−	0.420989i	0.259081	−	0.965855i	$-0.416580\pi$
$379$	−11.2805	−	8.19577i	−0.579441	−	0.420989i	−0.838523	+	0.544867i	$0.816580\pi$
$380$		0			0
$381$	0.0821677	−	0.252886i	0.00420958	−	0.0129558i
$382$		0			0
$383$	−6.59841	+	4.79402i	−0.337163	+	0.244963i	−0.743464	−	0.668776i	$-0.766818\pi$
$383$	−6.59841	+	4.79402i	−0.337163	+	0.244963i	0.406301	+	0.913739i	$0.366818\pi$
$384$		0			0
$385$	11.2706	−	9.21908i	0.574403	−	0.469848i
$386$		0			0
$387$	8.47979	−	6.16093i	0.431052	−	0.313177i
$388$		0			0
$389$	−0.958326	+	2.94942i	−0.0485891	+	0.149542i	−0.972407	−	0.233290i	$-0.925051\pi$
$389$	−0.958326	+	2.94942i	−0.0485891	+	0.149542i	0.923818	+	0.382831i	$0.125051\pi$
$390$		0			0
$391$	−1.22074	−	0.886916i	−0.0617352	−	0.0448533i
$392$		0			0
$393$	−1.32646	−	4.08243i	−0.0669111	−	0.205931i
$394$		0			0
$395$	−10.0313			−0.504728
$396$		0			0
$397$	23.1546			1.16209			0.581047	−	0.813870i	$-0.302643\pi$
$397$	23.1546			1.16209			0.581047	+	0.813870i	$0.302643\pi$
$398$		0			0
$399$	−3.07868	−	9.47520i	−0.154127	−	0.474353i
$400$		0			0
$401$	6.66933	+	4.84555i	0.333051	+	0.241975i	0.741724	−	0.670705i	$-0.234008\pi$
$401$	6.66933	+	4.84555i	0.333051	+	0.241975i	−0.408673	+	0.912681i	$0.634008\pi$
$402$		0			0
$403$	−9.44537	+	29.0699i	−0.470507	+	1.44807i
$404$		0			0
$405$	−6.65379	+	4.83426i	−0.330630	+	0.240217i
$406$		0			0
$407$	−0.155862	+	0.593366i	−0.00772581	+	0.0294120i
$408$		0			0
$409$	−1.76891	+	1.28518i	−0.0874667	+	0.0635483i	−0.630659	−	0.776060i	$-0.717215\pi$
$409$	−1.76891	+	1.28518i	−0.0874667	+	0.0635483i	0.543192	+	0.839608i	$0.317215\pi$
$410$		0			0
$411$	−1.87670	+	5.77590i	−0.0925710	+	0.284904i
$412$		0			0
$413$	−39.9712	−	29.0408i	−1.96686	−	1.42900i
$414$		0			0
$415$	1.26552	+	3.89486i	0.0621217	+	0.191191i
$416$		0			0
$417$	−4.41977			−0.216437
$418$		0			0
$419$	10.7348			0.524429			0.262215	−	0.965010i	$-0.415547\pi$
$419$	10.7348			0.524429			0.262215	+	0.965010i	$0.415547\pi$
$420$		0			0
$421$	5.80597	+	17.8689i	0.282966	+	0.870878i	0.987001	+	0.160714i	$0.0513795\pi$
$421$	5.80597	+	17.8689i	0.282966	+	0.870878i	−0.704036	+	0.710165i	$0.748620\pi$
$422$		0			0
$423$	−1.82919	−	1.32899i	−0.0889385	−	0.0646176i
$424$		0			0
$425$	−0.515393	+	1.58622i	−0.0250003	+	0.0769429i
$426$		0			0
$427$	46.8474	−	34.0366i	2.26711	−	1.64715i
$428$		0			0
$429$	−4.90782	−	3.15290i	−0.236952	−	0.152224i
$430$		0			0
$431$	7.26399	−	5.27760i	0.349894	−	0.254213i	−0.398931	−	0.916981i	$-0.630619\pi$
$431$	7.26399	−	5.27760i	0.349894	−	0.254213i	0.748825	+	0.662768i	$0.230619\pi$
$432$		0			0
$433$	9.73586	−	29.9639i	0.467876	−	1.43997i	−0.387454	−	0.921889i	$-0.626645\pi$
$433$	9.73586	−	29.9639i	0.467876	−	1.43997i	0.855330	−	0.518084i	$-0.173355\pi$
$434$		0			0
$435$	1.13087	+	0.821622i	0.0542208	+	0.0393937i
$436$		0			0
$437$	−2.15087	−	6.61970i	−0.102890	−	0.316663i
$438$		0			0
$439$	27.4750			1.31131			0.655655	−	0.755060i	$-0.272393\pi$
$439$	27.4750			1.31131			0.655655	+	0.755060i	$0.272393\pi$
$440$		0			0
$441$	−35.7552			−1.70263
$442$		0			0
$443$	−9.33108	−	28.7181i	−0.443333	−	1.36444i	−0.884301	−	0.466916i	$-0.845365\pi$
$443$	−9.33108	−	28.7181i	−0.443333	−	1.36444i	0.440968	−	0.897523i	$-0.354635\pi$
$444$		0			0
$445$	0.377237	+	0.274079i	0.0178827	+	0.0129926i
$446$		0			0
$447$	0.999223	−	3.07529i	0.0472616	−	0.145456i
$448$		0			0
$449$	22.1525	−	16.0947i	1.04544	−	0.759558i	0.0741012	−	0.997251i	$-0.476391\pi$
$449$	22.1525	−	16.0947i	1.04544	−	0.759558i	0.971340	+	0.237693i	$0.0763912\pi$
$450$		0			0
$451$	−3.15684	−	8.10428i	−0.148650	−	0.381615i
$452$		0			0
$453$	1.41071	−	1.02494i	0.0662811	−	0.0481560i
$454$		0			0
$455$	−8.08953	+	24.8970i	−0.379243	+	1.16719i
$456$		0			0
$457$	−11.5596	−	8.39854i	−0.540735	−	0.392867i	0.283623	−	0.958936i	$-0.408464\pi$
$457$	−11.5596	−	8.39854i	−0.540735	−	0.392867i	−0.824358	+	0.566069i	$0.808464\pi$
$458$		0			0
$459$	0.898905	+	2.76655i	0.0419573	+	0.129131i
$460$		0			0
$461$	8.78738			0.409269			0.204635	−	0.978838i	$-0.434399\pi$
$461$	8.78738			0.409269			0.204635	+	0.978838i	$0.434399\pi$
$462$		0			0
$463$	−13.8394			−0.643172			−0.321586	−	0.946880i	$-0.604216\pi$
$463$	−13.8394			−0.643172			−0.321586	+	0.946880i	$0.604216\pi$
$464$		0			0
$465$	−0.467235	−	1.43800i	−0.0216675	−	0.0666857i
$466$		0			0
$467$	−20.1359	−	14.6296i	−0.931778	−	0.676976i	0.0146495	−	0.999893i	$-0.495337\pi$
$467$	−20.1359	−	14.6296i	−0.931778	−	0.676976i	−0.946428	+	0.322916i	$0.895337\pi$
$468$		0			0
$469$	10.5814	−	32.5661i	0.488602	−	1.50376i
$470$		0			0
$471$	1.05624	−	0.767405i	0.0486691	−	0.0353602i
$472$		0			0
$473$	11.9144	−	0.683288i	0.547823	−	0.0314176i
$474$		0			0
$475$	−6.22418	+	4.52213i	−0.285585	+	0.207490i
$476$		0			0
$477$	8.63757	−	26.5837i	0.395487	−	1.21718i
$478$		0			0
$479$	23.1303	+	16.8051i	1.05685	+	0.767846i	0.973503	−	0.228674i	$-0.0734390\pi$
$479$	23.1303	+	16.8051i	1.05685	+	0.767846i	0.0833469	+	0.996521i	$0.473439\pi$
$480$		0			0
$481$	−0.340838	−	1.04899i	−0.0155409	−	0.0478299i
$482$		0			0
$483$	1.17156			0.0533079
$484$		0			0
$485$	7.09963			0.322377
$486$		0			0
$487$	1.43808	+	4.42594i	0.0651654	+	0.200559i	0.978338	−	0.207015i	$-0.0663749\pi$
$487$	1.43808	+	4.42594i	0.0651654	+	0.200559i	−0.913172	+	0.407574i	$0.866375\pi$
$488$		0			0
$489$	1.76220	+	1.28031i	0.0796893	+	0.0578977i
$490$		0			0
$491$	7.70564	−	23.7155i	0.347751	−	1.07027i	−0.612344	−	0.790592i	$-0.709773\pi$
$491$	7.70564	−	23.7155i	0.347751	−	1.07027i	0.960095	−	0.279675i	$-0.0902268\pi$
$492$		0			0
$493$	−6.39440	+	4.64581i	−0.287989	+	0.209237i
$494$		0			0
$495$	−9.64547	+	0.553168i	−0.433532	+	0.0248630i
$496$		0			0
$497$	−24.7586	+	17.9882i	−1.11057	+	0.806879i
$498$		0			0
$499$	4.75417	−	14.6318i	0.212826	−	0.655010i	−0.786475	−	0.617622i	$-0.788096\pi$
$499$	4.75417	−	14.6318i	0.212826	−	0.655010i	0.999301	−	0.0373883i	$-0.0119038\pi$
$500$		0			0
$501$	4.65031	+	3.37865i	0.207761	+	0.150947i
$502$		0			0
$503$	−10.1206	−	31.1481i	−0.451257	−	1.38883i	−0.875474	−	0.483265i	$-0.839451\pi$
$503$	−10.1206	−	31.1481i	−0.451257	−	1.38883i	0.424217	−	0.905560i	$-0.360549\pi$
$504$		0			0
$505$	−16.2851			−0.724677
$506$		0			0
$507$	6.65292			0.295467
$508$		0			0
$509$	4.85208	+	14.9332i	0.215065	+	0.661901i	0.999149	+	0.0412466i	$0.0131329\pi$
$509$	4.85208	+	14.9332i	0.215065	+	0.661901i	−0.784084	+	0.620654i	$0.786867\pi$
$510$		0			0
$511$	45.2998	+	32.9122i	2.00394	+	1.45595i
$512$		0			0
$513$	−4.14650	+	12.7616i	−0.183073	+	0.563439i
$514$		0			0
$515$	−2.58124	+	1.87538i	−0.113743	+	0.0826391i
$516$		0			0
$517$	−0.934376	−	2.39874i	−0.0410938	−	0.105496i
$518$		0			0
$519$	−2.26891	+	1.64846i	−0.0995939	+	0.0723592i
$520$		0			0
$521$	−10.3905	+	31.9786i	−0.455215	+	1.40101i	0.415668	+	0.909516i	$0.363548\pi$
$521$	−10.3905	+	31.9786i	−0.455215	+	1.40101i	−0.870883	+	0.491490i	$0.836452\pi$
$522$		0			0
$523$	18.5729	+	13.4940i	0.812136	+	0.590051i	0.914449	−	0.404701i	$-0.132624\pi$
$523$	18.5729	+	13.4940i	0.812136	+	0.590051i	−0.102313	+	0.994752i	$0.532624\pi$
$524$		0			0
$525$	−0.400166	−	1.23158i	−0.0174647	−	0.0537507i
$526$		0			0
$527$	8.54952			0.372423
$528$		0			0
$529$	−22.1815			−0.964413
$530$		0			0
$531$	10.1303	+	31.1779i	0.439617	+	1.35300i
$532$		0			0
$533$	12.6503	+	9.19101i	0.547947	+	0.398107i
$534$		0			0
$535$	−4.06801	+	12.5201i	−0.175876	+	0.541289i
$536$		0			0
$537$	−1.72113	+	1.25047i	−0.0742720	+	0.0539618i
$538$		0			0
$539$	−34.2506	−	22.0034i	−1.47528	−	0.947756i
$540$		0			0
$541$	15.1914	−	11.0372i	0.653131	−	0.474528i	−0.211205	−	0.977442i	$-0.567739\pi$
$541$	15.1914	−	11.0372i	0.653131	−	0.474528i	0.864336	+	0.502914i	$0.167739\pi$
$542$		0			0
$543$	−2.13192	+	6.56136i	−0.0914893	+	0.281575i
$544$		0			0
$545$	−1.08030	−	0.784881i	−0.0462748	−	0.0336206i
$546$		0			0
$547$	5.95740	+	18.3350i	0.254720	+	0.783947i	0.993885	+	0.110423i	$0.0352205\pi$
$547$	5.95740	+	18.3350i	0.254720	+	0.783947i	−0.739165	+	0.673525i	$0.764780\pi$
$548$		0			0
$549$	−38.4218			−1.63980
$550$		0			0
$551$	−36.4595			−1.55323
$552$		0			0
$553$	13.6091	+	41.8844i	0.578717	+	1.78111i
$554$		0			0
$555$	0.0441407	+	0.0320701i	0.00187367	+	0.00136130i
$556$		0			0
$557$	−5.54314	+	17.0600i	−0.234870	+	0.722857i	0.762268	+	0.647261i	$0.224086\pi$
$557$	−5.54314	+	17.0600i	−0.234870	+	0.722857i	−0.997139	+	0.0755955i	$0.975914\pi$
$558$		0			0
$559$	−17.3579	+	12.6112i	−0.734159	+	0.533398i
$560$		0			0
$561$	−0.414525	+	1.57809i	−0.0175012	+	0.0666270i
$562$		0			0
$563$	1.46665	−	1.06558i	0.0618120	−	0.0449090i	−0.556450	−	0.830881i	$-0.687837\pi$
$563$	1.46665	−	1.06558i	0.0618120	−	0.0449090i	0.618262	+	0.785972i	$0.287837\pi$
$564$		0			0
$565$	−0.517444	+	1.59253i	−0.0217690	+	0.0669982i
$566$		0			0
$567$	29.2119	+	21.2237i	1.22678	+	0.891310i
$568$		0			0
$569$	2.63761	+	8.11773i	0.110574	+	0.340313i	0.990998	−	0.133874i	$-0.0427419\pi$
$569$	2.63761	+	8.11773i	0.110574	+	0.340313i	−0.880424	+	0.474187i	$0.842742\pi$
$570$		0			0
$571$	−32.2491			−1.34958			−0.674792	−	0.738008i	$-0.735767\pi$
$571$	−32.2491			−1.34958			−0.674792	+	0.738008i	$0.735767\pi$
$572$		0			0
$573$	−1.22873			−0.0513310
$574$		0			0
$575$	−0.279570	−	0.860427i	−0.0116589	−	0.0358823i
$576$		0			0
$577$	−24.2423	−	17.6131i	−1.00922	−	0.733243i	−0.0451763	−	0.998979i	$-0.514385\pi$
$577$	−24.2423	−	17.6131i	−1.00922	−	0.733243i	−0.964046	+	0.265736i	$0.914385\pi$
$578$		0			0
$579$	−2.11155	+	6.49868i	−0.0877530	+	0.270076i
$580$		0			0
$581$	14.5456	−	10.5680i	0.603455	−	0.438435i
$582$		0			0
$583$	24.6335	−	20.1496i	1.02022	−	0.834512i
$584$		0			0
$585$	14.0523	−	10.2096i	0.580993	−	0.422116i
$586$		0			0
$587$	3.02941	−	9.32357i	0.125037	−	0.384825i	−0.868871	−	0.495039i	$-0.835154\pi$
$587$	3.02941	−	9.32357i	0.125037	−	0.384825i	0.993908	+	0.110214i	$0.0351537\pi$
$588$		0			0
$589$	31.9057	+	23.1808i	1.31465	+	0.955149i
$590$		0			0
$591$	0.925223	+	2.84754i	0.0380586	+	0.117132i
$592$		0			0
$593$	15.4666			0.635136			0.317568	−	0.948235i	$-0.397134\pi$
$593$	15.4666			0.635136			0.317568	+	0.948235i	$0.397134\pi$
$594$		0			0
$595$	7.32228			0.300184
$596$		0			0
$597$	−1.55072	−	4.77263i	−0.0634668	−	0.195331i
$598$		0			0
$599$	0.225061	+	0.163516i	0.00919574	+	0.00668110i	0.592374	−	0.805663i	$-0.298191\pi$
$599$	0.225061	+	0.163516i	0.00919574	+	0.00668110i	−0.583178	+	0.812344i	$0.698191\pi$
$600$		0			0
$601$	9.27220	−	28.5369i	0.378221	−	1.16404i	−0.563059	−	0.826417i	$-0.690376\pi$
$601$	9.27220	−	28.5369i	0.378221	−	1.16404i	0.941280	−	0.337628i	$-0.109624\pi$
$602$		0			0
$603$	−18.3809	+	13.3545i	−0.748528	+	0.543837i
$604$		0			0
$605$	−9.58002	−	5.40586i	−0.389483	−	0.219779i
$606$		0			0
$607$	18.0387	−	13.1059i	0.732169	−	0.531952i	−0.158080	−	0.987426i	$-0.550530\pi$
$607$	18.0387	−	13.1059i	0.732169	−	0.531952i	0.890249	+	0.455474i	$0.150530\pi$
$608$		0			0
$609$	1.89638	−	5.83646i	0.0768452	−	0.236505i
$610$		0			0
$611$	3.74430	+	2.72040i	0.151478	+	0.110055i
$612$		0			0
$613$	−8.76829	−	26.9860i	−0.354148	−	1.08996i	−0.956502	−	0.291726i	$-0.905770\pi$
$613$	−8.76829	−	26.9860i	−0.354148	−	1.08996i	0.602354	−	0.798229i	$-0.294230\pi$
$614$		0			0
$615$	−0.773501			−0.0311906
$616$		0			0
$617$	−15.1603			−0.610332			−0.305166	−	0.952299i	$-0.598712\pi$
$617$	−15.1603			−0.610332			−0.305166	+	0.952299i	$0.598712\pi$
$618$		0			0
$619$	−9.12336	−	28.0788i	−0.366699	−	1.12858i	−0.948910	−	0.315545i	$-0.897813\pi$
$619$	−9.12336	−	28.0788i	−0.366699	−	1.12858i	0.582212	−	0.813037i	$-0.302187\pi$
$620$		0			0
$621$	−1.27656	−	0.927473i	−0.0512265	−	0.0372182i
$622$		0			0
$623$	0.632600	−	1.94694i	0.0253446	−	0.0780026i
$624$		0			0
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$		0			0
$627$	−5.82572	+	4.76529i	−0.232657	+	0.190307i
$628$		0			0
$629$	−0.249591	+	0.181338i	−0.00995184	+	0.00723043i
$630$		0			0
$631$	−14.1188	+	43.4532i	−0.562061	+	1.72985i	0.114466	+	0.993427i	$0.463484\pi$
$631$	−14.1188	+	43.4532i	−0.562061	+	1.72985i	−0.676527	+	0.736418i	$0.736516\pi$
$632$		0			0
$633$	1.43565	+	1.04306i	0.0570618	+	0.0414579i
$634$		0			0
$635$	0.278570	+	0.857349i	0.0110547	+	0.0340229i
$636$		0			0
$637$	73.1897			2.89988
$638$		0			0
$639$	20.3057			0.803281
$640$		0			0
$641$	11.1602	+	34.3475i	0.440801	+	1.35665i	0.887024	+	0.461724i	$0.152769\pi$
$641$	11.1602	+	34.3475i	0.440801	+	1.35665i	−0.446223	+	0.894922i	$0.647231\pi$
$642$		0			0
$643$	27.0998	+	19.6892i	1.06871	+	0.776465i	0.975680	−	0.219198i	$-0.0703442\pi$
$643$	27.0998	+	19.6892i	1.06871	+	0.776465i	0.0930318	+	0.995663i	$0.470344\pi$
$644$		0			0
$645$	0.327972	−	1.00939i	0.0129139	−	0.0397449i
$646$		0			0
$647$	−31.7188	+	23.0451i	−1.24700	+	0.905996i	−0.998044	−	0.0625198i	$-0.980086\pi$
$647$	−31.7188	+	23.0451i	−1.24700	+	0.905996i	−0.248953	+	0.968516i	$0.580086\pi$
$648$		0			0
$649$	−9.48258	+	36.1000i	−0.372224	+	1.41705i
$650$		0			0
$651$	−5.37032	+	3.90177i	−0.210480	+	0.152922i
$652$		0			0
$653$	7.65109	−	23.5476i	0.299410	−	0.921491i	−0.682294	−	0.731078i	$-0.739017\pi$
$653$	7.65109	−	23.5476i	0.299410	−	0.921491i	0.981704	−	0.190412i	$-0.0609825\pi$
$654$		0			0
$655$	11.7734	+	8.55388i	0.460025	+	0.334228i
$656$		0			0
$657$	−11.4808	−	35.3342i	−0.447907	−	1.37852i
$658$		0			0
$659$	24.8813			0.969238			0.484619	−	0.874725i	$-0.338958\pi$
$659$	24.8813			0.969238			0.484619	+	0.874725i	$0.338958\pi$
$660$		0			0
$661$	−5.94396			−0.231193			−0.115597	−	0.993296i	$-0.536878\pi$
$661$	−5.94396			−0.231193			−0.115597	+	0.993296i	$0.536878\pi$
$662$		0			0
$663$	−0.906478	−	2.78985i	−0.0352047	−	0.108349i
$664$		0			0
$665$	27.3258	+	19.8533i	1.05965	+	0.769879i
$666$		0			0
$667$	1.32488	−	4.07755i	0.0512995	−	0.157883i
$668$		0			0
$669$	−0.595161	+	0.432410i	−0.0230103	+	0.0167179i
$670$		0			0
$671$	−36.8051	−	23.6445i	−1.42085	−	0.912786i
$672$		0			0
$673$	−30.6213	+	22.2477i	−1.18036	+	0.857585i	−0.992213	−	0.124555i	$-0.960250\pi$
$673$	−30.6213	+	22.2477i	−1.18036	+	0.857585i	−0.188152	+	0.982140i	$0.560250\pi$
$674$		0			0
$675$	−0.538961	+	1.65875i	−0.0207446	+	0.0638454i
$676$		0			0
$677$	−0.153794	−	0.111738i	−0.00591078	−	0.00429443i	0.584826	−	0.811159i	$-0.301163\pi$
$677$	−0.153794	−	0.111738i	−0.00591078	−	0.00429443i	−0.590737	+	0.806864i	$0.701163\pi$
$678$		0			0
$679$	−9.63181	−	29.6437i	−0.369635	−	1.13762i
$680$		0			0
$681$	−7.37267			−0.282521
$682$		0			0
$683$	23.0773			0.883030			0.441515	−	0.897254i	$-0.354441\pi$
$683$	23.0773			0.883030			0.441515	+	0.897254i	$0.354441\pi$
$684$		0			0
$685$	−6.36251	−	19.5818i	−0.243099	−	0.748182i
$686$		0			0
$687$	0.661201	+	0.480391i	0.0252264	+	0.0183281i
$688$		0			0
$689$	−17.6808	+	54.4160i	−0.673586	+	2.07308i
$690$		0			0
$691$	−37.7877	+	27.4544i	−1.43751	+	1.04441i	−0.448958	+	0.893553i	$0.648205\pi$
$691$	−37.7877	+	27.4544i	−1.43751	+	1.04441i	−0.988555	+	0.150862i	$0.951795\pi$
$692$		0			0
$693$	15.3953	+	39.5231i	0.584821	+	1.50136i
$694$		0			0
$695$	12.1224	−	8.80746i	0.459830	−	0.334086i
$696$		0			0
$697$	1.35155	−	4.15965i	0.0511936	−	0.157558i
$698$		0			0
$699$	2.29091	+	1.66444i	0.0866501	+	0.0629550i
$700$		0			0
$701$	1.28934	+	3.96818i	0.0486977	+	0.149876i	0.972448	−	0.233118i	$-0.0748929\pi$
$701$	1.28934	+	3.96818i	0.0486977	+	0.149876i	−0.923751	+	0.382994i	$0.874893\pi$
$702$		0			0
$703$	−1.42311			−0.0536737
$704$		0			0
$705$	−0.228944			−0.00862254
$706$		0			0
$707$	22.0934	+	67.9965i	0.830908	+	2.55727i
$708$		0			0
$709$	7.07305	+	5.13887i	0.265634	+	0.192994i	0.712627	−	0.701543i	$-0.247505\pi$
$709$	7.07305	+	5.13887i	0.265634	+	0.192994i	−0.446993	+	0.894537i	$0.647505\pi$
$710$		0			0
$711$	9.02981	−	27.7909i	0.338644	−	1.04224i
$712$		0			0
$713$	−3.75189	+	2.72591i	−0.140510	+	0.102086i
$714$		0			0
$715$	19.7440	−	1.13232i	0.738382	−	0.0423462i
$716$		0			0
$717$	−3.52438	+	2.56061i	−0.131620	+	0.0956278i
$718$		0			0
$719$	−2.28722	+	7.03934i	−0.0852990	+	0.262523i	−0.984604	−	0.174798i	$-0.944073\pi$
$719$	−2.28722	+	7.03934i	−0.0852990	+	0.262523i	0.899305	+	0.437321i	$0.144073\pi$
$720$		0			0
$721$	11.3323	+	8.23340i	0.422037	+	0.306628i
$722$		0			0
$723$	−0.951024	−	2.92695i	−0.0353690	−	0.108854i
$724$		0			0
$725$	−4.73899			−0.176002
$726$		0			0
$727$	18.0187			0.668275			0.334137	−	0.942524i	$-0.391555\pi$
$727$	18.0187			0.668275			0.334137	+	0.942524i	$0.391555\pi$
$728$		0			0
$729$	−6.92653	−	21.3177i	−0.256538	−	0.789543i
$730$		0			0
$731$	4.85514	+	3.52746i	0.179574	+	0.130468i
$732$		0			0
$733$	−11.2463	+	34.6127i	−0.415393	+	1.27845i	0.496506	+	0.868033i	$0.334616\pi$
$733$	−11.2463	+	34.6127i	−0.415393	+	1.27845i	−0.911899	+	0.410415i	$0.865384\pi$
$734$		0			0
$735$	−2.92903	+	2.12806i	−0.108039	+	0.0784948i
$736$		0			0
$737$	−25.8257	+	1.48110i	−0.951302	+	0.0545572i
$738$		0			0
$739$	10.0576	−	7.30726i	0.369974	−	0.268802i	−0.387226	−	0.921985i	$-0.626567\pi$
$739$	10.0576	−	7.30726i	0.369974	−	0.268802i	0.757200	+	0.653183i	$0.226567\pi$
$740$		0			0
$741$	4.18144	−	12.8691i	0.153609	−	0.472759i
$742$		0			0
$743$	−30.2327	−	21.9653i	−1.10913	−	0.805829i	−0.126602	−	0.991954i	$-0.540407\pi$
$743$	−30.2327	−	21.9653i	−1.10913	−	0.805829i	−0.982526	+	0.186125i	$0.940407\pi$
$744$		0			0
$745$	3.38762	+	10.4260i	0.124113	+	0.381980i
$746$		0			0
$747$	−11.9296			−0.436480
$748$		0			0
$749$	57.7950			2.11178
$750$		0			0
$751$	−2.44111	−	7.51295i	−0.0890772	−	0.274151i	0.896588	−	0.442866i	$-0.146038\pi$
$751$	−2.44111	−	7.51295i	−0.0890772	−	0.274151i	−0.985665	+	0.168715i	$0.946038\pi$
$752$		0			0
$753$	1.60692	+	1.16749i	0.0585594	+	0.0425459i
$754$		0			0
$755$	−1.82682	+	5.62238i	−0.0664848	+	0.204619i
$756$		0			0
$757$	2.56487	−	1.86349i	0.0932219	−	0.0677297i	−0.540198	−	0.841538i	$-0.681651\pi$
$757$	2.56487	−	1.86349i	0.0932219	−	0.0677297i	0.633420	+	0.773808i	$0.281651\pi$
$758$		0			0
$759$	−0.321244	−	0.824699i	−0.0116604	−	0.0299347i
$760$		0			0
$761$	−37.8368	+	27.4901i	−1.37158	+	0.996514i	−0.373972	+	0.927440i	$0.622004\pi$
$761$	−37.8368	+	27.4901i	−1.37158	+	0.996514i	−0.997612	+	0.0690739i	$0.977996\pi$
$762$		0			0
$763$	−1.81158	+	5.57547i	−0.0655836	+	0.201845i
$764$		0			0
$765$	−3.93056	−	2.85572i	−0.142110	−	0.103249i
$766$		0			0
$767$	−20.7364	−	63.8201i	−0.748748	−	2.30441i
$768$		0			0
$769$	−1.95610			−0.0705388			−0.0352694	−	0.999378i	$-0.511229\pi$
$769$	−1.95610			−0.0705388			−0.0352694	+	0.999378i	$0.511229\pi$
$770$		0			0
$771$	2.28358			0.0822411
$772$		0			0
$773$	−6.31718	−	19.4423i	−0.227213	−	0.699290i	−0.998059	−	0.0622690i	$-0.980166\pi$
$773$	−6.31718	−	19.4423i	−0.227213	−	0.699290i	0.770846	−	0.637021i	$-0.219834\pi$
$774$		0			0
$775$	4.14709	+	3.01303i	0.148968	+	0.108231i
$776$		0			0
$777$	0.0740209	−	0.227813i	0.00265548	−	0.00817274i
$778$		0			0
$779$	16.3221	−	11.8587i	0.584800	−	0.424882i
$780$		0			0
$781$	19.4513	+	12.4960i	0.696021	+	0.447141i
$782$		0			0
$783$	−6.68680	+	4.85825i	−0.238967	+	0.173620i
$784$		0			0
$785$	−1.36780	+	4.20964i	−0.0488187	+	0.150249i
$786$		0			0
$787$	2.09694	+	1.52351i	0.0747478	+	0.0543074i	0.624532	−	0.781000i	$-0.285290\pi$
$787$	2.09694	+	1.52351i	0.0747478	+	0.0543074i	−0.549784	+	0.835307i	$0.685290\pi$
$788$		0			0
$789$	1.65542	+	5.09486i	0.0589346	+	0.181382i
$790$		0			0
$791$	7.35141			0.261386
$792$		0			0
$793$	78.6483			2.79288
$794$		0			0
$795$	−0.874619	−	2.69180i	−0.0310196	−	0.0954684i
$796$		0			0
$797$	−18.1112	−	13.1586i	−0.641532	−	0.466100i	0.218844	−	0.975760i	$-0.429771\pi$
$797$	−18.1112	−	13.1586i	−0.641532	−	0.466100i	−0.860376	+	0.509660i	$0.829771\pi$
$798$		0			0
$799$	0.400038	−	1.23119i	0.0141523	−	0.0435564i
$800$		0			0
$801$	−1.09889	+	0.798390i	−0.0388274	+	0.0282097i
$802$		0			0
$803$	10.7467	−	40.9125i	0.379243	−	1.44377i
$804$		0			0
$805$	−3.21333	+	2.33462i	−0.113255	+	0.0822845i
$806$		0			0
$807$	−0.977727	+	3.00913i	−0.0344176	+	0.105927i
$808$		0			0
$809$	−9.67269	−	7.02762i	−0.340074	−	0.247078i	0.404619	−	0.914485i	$-0.367404\pi$
$809$	−9.67269	−	7.02762i	−0.340074	−	0.247078i	−0.744693	+	0.667407i	$0.767404\pi$
$810$		0			0
$811$	5.70741	+	17.5656i	0.200414	+	0.616812i	0.999871	+	0.0160875i	$0.00512103\pi$
$811$	5.70741	+	17.5656i	0.200414	+	0.616812i	−0.799456	+	0.600724i	$0.794879\pi$
$812$		0			0
$813$	−5.54162			−0.194353
$814$		0			0
$815$	−7.38464			−0.258673
$816$		0			0
$817$	8.55449	+	26.3280i	0.299284	+	0.921101i
$818$		0			0
$819$	−61.6934	−	44.8229i	−2.15574	−	1.56624i
$820$		0			0
$821$	17.1422	−	52.7584i	0.598268	−	1.84128i	0.0605325	−	0.998166i	$-0.480720\pi$
$821$	17.1422	−	52.7584i	0.598268	−	1.84128i	0.537736	−	0.843114i	$-0.319280\pi$
$822$		0			0
$823$	−35.3648	+	25.6940i	−1.23274	+	0.895637i	−0.997092	−	0.0762021i	$-0.975721\pi$
$823$	−35.3648	+	25.6940i	−1.23274	+	0.895637i	−0.235646	+	0.971839i	$0.575721\pi$
$824$		0			0
$825$	−0.757225	+	0.619391i	−0.0263632	+	0.0215644i
$826$		0			0
$827$	−25.6778	+	18.6560i	−0.892906	+	0.648734i	−0.936634	−	0.350309i	$-0.886076\pi$
$827$	−25.6778	+	18.6560i	−0.892906	+	0.648734i	0.0437281	+	0.999043i	$0.486076\pi$
$828$		0			0
$829$	−10.8249	+	33.3157i	−0.375966	+	1.15710i	0.566859	+	0.823815i	$0.308158\pi$
$829$	−10.8249	+	33.3157i	−0.375966	+	1.15710i	−0.942825	+	0.333289i	$0.891842\pi$
$830$		0			0
$831$	−6.88368	−	5.00129i	−0.238792	−	0.173493i
$832$		0			0
$833$	−6.32612	−	19.4698i	−0.219187	−	0.674589i
$834$		0			0
$835$	−19.4876			−0.674394
$836$		0			0
$837$	8.94047			0.309028
$838$		0			0
$839$	−4.89922	−	15.0783i	−0.169140	−	0.520559i	0.830177	−	0.557499i	$-0.188239\pi$
$839$	−4.89922	−	15.0783i	−0.169140	−	0.520559i	−0.999317	+	0.0369398i	$0.988239\pi$
$840$		0			0
$841$	5.29256	+	3.84527i	0.182502	+	0.132596i
$842$		0			0
$843$	2.46595	−	7.58941i	0.0849318	−	0.261393i
$844$		0			0
$845$	−18.2475	+	13.2576i	−0.627732	+	0.456074i
$846$		0			0
$847$	−9.57465	+	47.3342i	−0.328989	+	1.62642i
$848$		0			0
$849$	−3.07191	+	2.23188i	−0.105428	+	0.0765978i
$850$		0			0
$851$	0.0517136	−	0.159158i	0.00177272	−	0.00545586i
$852$		0			0
$853$	18.2728	+	13.2760i	0.625650	+	0.454561i	0.854890	−	0.518809i	$-0.173624\pi$
$853$	18.2728	+	13.2760i	0.625650	+	0.454561i	−0.229241	+	0.973370i	$0.573624\pi$
$854$		0			0
$855$	−6.92543	−	21.3143i	−0.236845	−	0.728933i
$856$		0			0
$857$	40.9108			1.39749			0.698744	−	0.715372i	$-0.253743\pi$
$857$	40.9108			1.39749			0.698744	+	0.715372i	$0.253743\pi$
$858$		0			0
$859$	15.9523			0.544284			0.272142	−	0.962257i	$-0.412268\pi$
$859$	15.9523			0.544284			0.272142	+	0.962257i	$0.412268\pi$
$860$		0			0
$861$	1.04938	+	3.22966i	0.0357628	+	0.110067i
$862$		0			0
$863$	−5.89687	−	4.28433i	−0.200732	−	0.145840i	0.482879	−	0.875687i	$-0.339591\pi$
$863$	−5.89687	−	4.28433i	−0.200732	−	0.145840i	−0.683610	+	0.729847i	$0.739591\pi$
$864$		0			0
$865$	2.93815	−	9.04269i	0.0999000	−	0.307461i
$866$		0			0
$867$	3.39291	−	2.46509i	0.115229	−	0.0837189i
$868$		0			0
$869$	25.7521	−	21.0646i	0.873582	−	0.714568i
$870$		0			0
$871$	37.6251	−	27.3362i	1.27488	−	0.926253i
$872$		0			0
$873$	−6.39084	+	19.6690i	−0.216297	+	0.665694i
$874$		0			0
$875$	3.55179	+	2.58053i	0.120072	+	0.0872378i
$876$		0			0
$877$	2.20860	+	6.79737i	0.0745791	+	0.229531i	0.981396	−	0.191993i	$-0.0614952\pi$
$877$	2.20860	+	6.79737i	0.0745791	+	0.229531i	−0.906817	+	0.421524i	$0.861495\pi$
$878$		0			0
$879$	1.73696			0.0585861
$880$		0			0
$881$	−17.5763			−0.592160			−0.296080	−	0.955163i	$-0.595680\pi$
$881$	−17.5763			−0.592160			−0.296080	+	0.955163i	$0.595680\pi$
$882$		0			0
$883$	−1.93709	−	5.96175i	−0.0651882	−	0.200629i	0.913157	−	0.407608i	$-0.133637\pi$
$883$	−1.93709	−	5.96175i	−0.0651882	−	0.200629i	−0.978345	+	0.206979i	$0.933637\pi$
$884$		0			0
$885$	2.68550	+	1.95113i	0.0902720	+	0.0655865i
$886$		0			0
$887$	−7.62945	+	23.4810i	−0.256172	+	0.788416i	0.737425	+	0.675429i	$0.236042\pi$
$887$	−7.62945	+	23.4810i	−0.256172	+	0.788416i	−0.993597	+	0.112986i	$0.963958\pi$
$888$		0			0
$889$	3.20184	−	2.32627i	0.107386	−	0.0780206i
$890$		0			0
$891$	6.93008	−	26.3827i	0.232166	−	0.883854i
$892$		0			0
$893$	4.83108	−	3.50999i	0.161666	−	0.117457i
$894$		0			0
$895$	2.22879	−	6.85952i	0.0745003	−	0.229288i
$896$		0			0
$897$	1.28731	+	0.935286i	0.0429821	+	0.0312283i
$898$		0			0
$899$	7.50678	+	23.1035i	0.250365	+	0.770545i
$900$		0			0
$901$	16.0039			0.533167
$902$		0			0
$903$	−4.65956			−0.155060
$904$		0			0
$905$	−7.22774	−	22.2447i	−0.240258	−	0.739439i
$906$		0			0
$907$	−20.5798	−	14.9521i	−0.683340	−	0.496476i	0.191124	−	0.981566i	$-0.438787\pi$
$907$	−20.5798	−	14.9521i	−0.683340	−	0.496476i	−0.874464	+	0.485090i	$0.838787\pi$
$908$		0			0
$909$	14.6593	−	45.1166i	0.486218	−	1.49642i
$910$		0			0
$911$	19.8448	−	14.4181i	0.657489	−	0.477694i	−0.208325	−	0.978060i	$-0.566801\pi$
$911$	19.8448	−	14.4181i	0.657489	−	0.477694i	0.865814	+	0.500366i	$0.166801\pi$
$912$		0			0
$913$	−11.4276	−	7.34137i	−0.378198	−	0.242964i
$914$		0			0
$915$	−3.14748	+	2.28678i	−0.104053	+	0.0755986i
$916$		0			0
$917$	19.7432	−	60.7632i	0.651977	−	2.00658i
$918$		0			0
$919$	−17.1714	−	12.4757i	−0.566432	−	0.411537i	0.267376	−	0.963592i	$-0.413844\pi$
$919$	−17.1714	−	12.4757i	−0.566432	−	0.411537i	−0.833807	+	0.552056i	$0.813844\pi$
$920$		0			0
$921$	0.625136	+	1.92397i	0.0205989	+	0.0633970i
$922$		0			0
$923$	−41.5651			−1.36813
$924$		0			0
$925$	−0.184976			−0.00608196
$926$		0			0
$927$	−2.87206	−	8.83928i	−0.0943307	−	0.290320i
$928$		0			0
$929$	−27.7116	−	20.1337i	−0.909190	−	0.660565i	0.0316201	−	0.999500i	$-0.489933\pi$
$929$	−27.7116	−	20.1337i	−0.909190	−	0.660565i	−0.940810	+	0.338935i	$0.889933\pi$
$930$		0			0
$931$	29.1814	−	89.8110i	0.956381	−	2.94344i
$932$		0			0
$933$	3.40508	−	2.47394i	0.111477	−	0.0809931i
$934$		0			0
$935$	−2.00778	−	5.15439i	−0.0656614	−	0.168566i
$936$		0			0
$937$	−28.2608	+	20.5326i	−0.923239	+	0.670772i	−0.944328	−	0.329005i	$-0.893287\pi$
$937$	−28.2608	+	20.5326i	−0.923239	+	0.670772i	0.0210892	+	0.999778i	$0.493287\pi$
$938$		0			0
$939$	0.145813	−	0.448766i	0.00475842	−	0.0146449i
$940$		0			0
$941$	15.1298	+	10.9924i	0.493216	+	0.358343i	0.806420	−	0.591343i	$-0.201402\pi$
$941$	15.1298	+	10.9924i	0.493216	+	0.358343i	−0.313203	+	0.949686i	$0.601402\pi$
$942$		0			0
$943$	0.733134	+	2.25636i	0.0238741	+	0.0734770i
$944$		0			0
$945$	7.65711			0.249086
$946$		0			0
$947$	12.7418			0.414052			0.207026	−	0.978335i	$-0.433621\pi$
$947$	12.7418			0.414052			0.207026	+	0.978335i	$0.433621\pi$
$948$		0			0
$949$	23.5008	+	72.3279i	0.762867	+	2.34786i
$950$		0			0
$951$	7.36307	+	5.34958i	0.238764	+	0.173472i
$952$		0			0
$953$	1.78515	−	5.49412i	0.0578266	−	0.177972i	−0.917971	−	0.396647i	$-0.870174\pi$
$953$	1.78515	−	5.49412i	0.0578266	−	0.177972i	0.975798	+	0.218675i	$0.0701736\pi$
$954$		0			0
$955$	3.37013	−	2.44855i	0.109055	−	0.0792331i
$956$		0			0
$957$	−4.62846	+	0.265442i	−0.149617	+	0.00858053i
$958$		0			0
$959$	−73.1297	+	53.1318i	−2.36148	+	1.71572i
$960$		0			0
$961$	−1.45958	+	4.49212i	−0.0470832	+	0.144907i
$962$		0			0
$963$	−31.0240	−	22.5402i	−0.999734	−	0.726349i
$964$		0			0
$965$	−7.15870	−	22.0322i	−0.230447	−	0.709242i
$966$		0			0
$967$	−36.2900			−1.16701			−0.583504	−	0.812110i	$-0.698319\pi$
$967$	−36.2900			−1.16701			−0.583504	+	0.812110i	$0.698319\pi$
$968$		0			0
$969$	−3.78485			−0.121587
$970$		0			0
$971$	−2.15967	−	6.64677i	−0.0693070	−	0.213305i	0.910404	−	0.413720i	$-0.135771\pi$
$971$	−2.15967	−	6.64677i	−0.0693070	−	0.213305i	−0.979711	+	0.200415i	$0.935771\pi$
$972$		0			0
$973$	−53.2206	−	38.6670i	−1.70617	−	1.23961i
$974$		0			0
$975$	0.543502	−	1.67273i	0.0174060	−	0.0535701i
$976$		0			0
$977$	−21.0340	+	15.2821i	−0.672936	+	0.488917i	−0.871007	−	0.491271i	$-0.836532\pi$
$977$	−21.0340	+	15.2821i	−0.672936	+	0.488917i	0.198071	+	0.980188i	$0.436532\pi$
$978$		0			0
$979$	−1.54397	+	0.0885469i	−0.0493456	+	0.00282997i
$980$		0			0
$981$	3.14690	−	2.28636i	0.100473	−	0.0729977i
$982$		0			0
$983$	8.85213	−	27.2441i	0.282339	−	0.868951i	−0.704844	−	0.709362i	$-0.748983\pi$
$983$	8.85213	−	27.2441i	0.282339	−	0.868951i	0.987184	−	0.159589i	$-0.0510168\pi$
$984$		0			0
$985$	−8.21211	−	5.96644i	−0.261659	−	0.190107i
$986$		0			0
$987$	0.310600	+	0.955930i	0.00988652	+	0.0304276i
$988$		0			0
$989$	−3.25533			−0.103513
$990$		0			0
$991$	27.9673			0.888409			0.444205	−	0.895925i	$-0.353486\pi$
$991$	27.9673			0.888409			0.444205	+	0.895925i	$0.353486\pi$
$992$		0			0
$993$	−0.106476	−	0.327700i	−0.00337892	−	0.0103992i
$994$		0			0
$995$	13.7639	+	10.0001i	0.436345	+	0.317023i
$996$		0			0
$997$	4.03510	−	12.4188i	0.127793	−	0.393307i	−0.866607	−	0.498992i	$-0.833704\pi$
$997$	4.03510	−	12.4188i	0.127793	−	0.393307i	0.994400	+	0.105686i	$0.0337037\pi$
$998$		0			0
$999$	−0.261004	+	0.189631i	−0.00825780	+	0.00599964i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	440.2.y.a.201.2	yes	8
4.3	odd	2		880.2.bo.d.641.1		8
11.2	odd	10		4840.2.a.z.1.3		4
11.4	even	5	inner	440.2.y.a.81.2	✓	8
11.9	even	5		4840.2.a.y.1.3		4
44.15	odd	10		880.2.bo.d.81.1		8
44.31	odd	10		9680.2.a.cu.1.2		4
44.35	even	10		9680.2.a.ct.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
440.2.y.a.81.2	✓	8	11.4	even	5	inner
440.2.y.a.201.2	yes	8	1.1	even	1	trivial
880.2.bo.d.81.1		8	44.15	odd	10
880.2.bo.d.641.1		8	4.3	odd	2
4840.2.a.y.1.3		4	11.9	even	5
4840.2.a.z.1.3		4	11.2	odd	10
9680.2.a.ct.1.2		4	44.35	even	10
9680.2.a.cu.1.2		4	44.31	odd	10

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:	\( N \)	\(=\)	\( 440 = 2^{3} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	440.y (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0911485 + 0.280526i) q^{3} +(-0.809017 - 0.587785i) q^{5} +(-1.35666 + 4.17538i) q^{7} +(2.35666 - 1.71222i) q^{9} +(3.31118 - 0.189896i) q^{11} +(-4.82402 + 3.50485i) q^{13} +(0.0911485 - 0.280526i) q^{15} +(1.34932 + 0.980336i) q^{17} +(2.37743 + 7.31696i) q^{19} -1.29496 q^{21} -0.904706 q^{23} +(0.309017 + 0.951057i) q^{25} +(1.41102 + 1.02516i) q^{27} +(-1.46443 + 4.50705i) q^{29} +(4.14709 - 3.01303i) q^{31} +(0.355081 + 0.911566i) q^{33} +(3.55179 - 2.58053i) q^{35} +(-0.0571606 + 0.175922i) q^{37} +(-1.42291 - 1.03380i) q^{39} +(-0.810356 - 2.49402i) q^{41} +3.59822 q^{43} -2.91300 q^{45} +(-0.239853 - 0.738191i) q^{47} +(-9.93016 - 7.21469i) q^{49} +(-0.152022 + 0.467875i) q^{51} +(7.76295 - 5.64012i) q^{53} +(-2.79042 - 1.79264i) q^{55} +(-1.83590 + 1.33386i) q^{57} +(-3.47762 + 10.7030i) q^{59} +(-10.6708 - 7.75277i) q^{61} +(3.95196 + 12.1629i) q^{63} +5.96281 q^{65} -7.79954 q^{67} +(-0.0824626 - 0.253794i) q^{69} +(5.63943 + 4.09729i) q^{71} +(3.94122 - 12.1298i) q^{73} +(-0.238630 + 0.173375i) q^{75} +(-3.69927 + 14.0831i) q^{77} +(8.11547 - 5.89624i) q^{79} +(2.54152 - 7.82200i) q^{81} +(-3.31316 - 2.40715i) q^{83} +(-0.515393 - 1.58622i) q^{85} -1.39783 q^{87} -0.466291 q^{89} +(-8.08953 - 24.8970i) q^{91} +(1.22324 + 0.888733i) q^{93} +(2.37743 - 7.31696i) q^{95} +(-5.74372 + 4.17306i) q^{97} +(7.47820 - 6.11699i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{3} - 2 q^{5} + q^{7} + 7 q^{9} + 3 q^{11} - 4 q^{13} + q^{15} - 3 q^{17} + 9 q^{19} - 4 q^{21} - 22 q^{23} - 2 q^{25} - 8 q^{27} - 17 q^{29} - 4 q^{31} + 21 q^{33} + 6 q^{35} + 24 q^{37} - 13 q^{39}+ \cdots + 22 q^{99}+O(q^{100}) \) 8 * q + q^3 - 2 * q^5 + q^7 + 7 * q^9 + 3 * q^11 - 4 * q^13 + q^15 - 3 * q^17 + 9 * q^19 - 4 * q^21 - 22 * q^23 - 2 * q^25 - 8 * q^27 - 17 * q^29 - 4 * q^31 + 21 * q^33 + 6 * q^35 + 24 * q^37 - 13 * q^39 - 4 * q^41 - 14 * q^43 - 8 * q^45 - 12 * q^47 - 15 * q^49 - 17 * q^51 + 35 * q^53 + 3 * q^55 - q^57 + 21 * q^59 - 22 * q^61 + 5 * q^63 + 6 * q^65 + 14 * q^67 + 3 * q^69 + 40 * q^71 + 9 * q^73 + q^75 - 4 * q^77 + 41 * q^79 + 24 * q^81 - 7 * q^83 - 8 * q^85 - 46 * q^87 - 24 * q^89 - 18 * q^91 + 3 * q^93 + 9 * q^95 + 4 * q^97 + 22 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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