LMFDB - Embedded newform 880.2.bo.d.641.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [880,2,Mod(81,880)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(880, 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("880.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 880 = 2^{4} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	880.bo (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.02683537787$
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:	no (minimal twist has level 440)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			641.1
Root			$-0.386111 + 0.280526i$ of defining polynomial
Character	$\chi$	$=$	880.641
Dual form			880.2.bo.d.81.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0911485 - 0.280526i) q^{3} +(-0.809017 - 0.587785i) q^{5} +(1.35666 - 4.17538i) q^{7} +(2.35666 - 1.71222i) q^{9} +(-3.31118 + 0.189896i) q^{11} +(-4.82402 + 3.50485i) q^{13} +(-0.0911485 + 0.280526i) q^{15} +(1.34932 + 0.980336i) q^{17} +(-2.37743 - 7.31696i) q^{19} -1.29496 q^{21} +0.904706 q^{23} +(0.309017 + 0.951057i) q^{25} +(-1.41102 - 1.02516i) q^{27} +(-1.46443 + 4.50705i) q^{29} +(-4.14709 + 3.01303i) q^{31} +(0.355081 + 0.911566i) q^{33} +(-3.55179 + 2.58053i) q^{35} +(-0.0571606 + 0.175922i) q^{37} +(1.42291 + 1.03380i) q^{39} +(-0.810356 - 2.49402i) q^{41} -3.59822 q^{43} -2.91300 q^{45} +(0.239853 + 0.738191i) q^{47} +(-9.93016 - 7.21469i) q^{49} +(0.152022 - 0.467875i) q^{51} +(7.76295 - 5.64012i) q^{53} +(2.79042 + 1.79264i) q^{55} +(-1.83590 + 1.33386i) q^{57} +(3.47762 - 10.7030i) q^{59} +(-10.6708 - 7.75277i) q^{61} +(-3.95196 - 12.1629i) q^{63} +5.96281 q^{65} +7.79954 q^{67} +(-0.0824626 - 0.253794i) q^{69} +(-5.63943 - 4.09729i) q^{71} +(3.94122 - 12.1298i) q^{73} +(0.238630 - 0.173375i) q^{75} +(-3.69927 + 14.0831i) q^{77} +(-8.11547 + 5.89624i) q^{79} +(2.54152 - 7.82200i) q^{81} +(3.31316 + 2.40715i) q^{83} +(-0.515393 - 1.58622i) q^{85} +1.39783 q^{87} -0.466291 q^{89} +(8.08953 + 24.8970i) q^{91} +(1.22324 + 0.888733i) q^{93} +(-2.37743 + 7.31696i) q^{95} +(-5.74372 + 4.17306i) q^{97} +(-7.47820 + 6.11699i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/880\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$321$	$661$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.0911485	−	0.280526i	−0.0526246	−	0.161962i	0.921290	−	0.388876i	$-0.127136\pi$
$3$	−0.0911485	−	0.280526i	−0.0526246	−	0.161962i	−0.973915	+	0.226914i	$0.927136\pi$
$4$		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	$-0.588523\pi$
$7$	1.35666	−	4.17538i	0.512771	−	1.57815i	0.787302	−	0.616568i	$-0.211477\pi$
$8$		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	$-0.755855\pi$
$19$	−2.37743	−	7.31696i	−0.545419	−	1.67863i	0.174573	−	0.984644i	$-0.444145\pi$
$20$		0			0
$21$	−1.29496			−0.282584
$22$		0			0
$23$	0.904706			0.188644			0.0943221	−	0.995542i	$-0.469932\pi$
$23$	0.904706			0.188644			0.0943221	+	0.995542i	$0.469932\pi$
$24$		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	−0.894223	−	0.447622i	$-0.852271\pi$
$31$	−4.14709	+	3.01303i	−0.744839	+	0.541157i	0.149384	+	0.988779i	$0.452271\pi$
$32$		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	$-0.588466\pi$
$43$	−3.59822			−0.548723			−0.274361	+	0.961627i	$0.588466\pi$
$44$		0			0
$45$	−2.91300			−0.434244
$46$		0			0
$47$	0.239853	+	0.738191i	0.0349861	+	0.107676i	0.967024	−	0.254683i	$-0.0819712\pi$
$47$	0.239853	+	0.738191i	0.0349861	+	0.107676i	−0.932038	+	0.362360i	$0.881971\pi$
$48$		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	$-0.638325\pi$
$59$	3.47762	−	10.7030i	0.452748	−	1.39341i	0.873759	−	0.486359i	$-0.161675\pi$
$60$		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	$-0.341930\pi$
$67$	7.79954			0.952866			0.476433	+	0.879211i	$0.341930\pi$
$68$		0			0
$69$	−0.0824626	−	0.253794i	−0.00992734	−	0.0305532i
$70$		0			0
$71$	−5.63943	−	4.09729i	−0.669278	−	0.486259i	0.200506	−	0.979693i	$-0.435742\pi$
$71$	−5.63943	−	4.09729i	−0.669278	−	0.486259i	−0.869783	+	0.493434i	$0.835742\pi$
$72$		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	−0.941787	−	0.336209i	$-0.890855\pi$
$79$	−8.11547	+	5.89624i	−0.913062	+	0.663378i	0.0287255	+	0.999587i	$0.490855\pi$
$80$		0			0
$81$	2.54152	−	7.82200i	0.282391	−	0.869112i
$82$		0			0
$83$	3.31316	+	2.40715i	0.363667	+	0.264219i	0.754580	−	0.656208i	$-0.227841\pi$
$83$	3.31316	+	2.40715i	0.363667	+	0.264219i	−0.390913	+	0.920428i	$0.627841\pi$
$84$		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	−0.987808	−	0.155680i	$-0.950243\pi$
$103$	−0.985946	+	3.03443i	−0.0971481	+	0.298991i	0.890659	+	0.454671i	$0.150243\pi$
$104$		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	$0.119546\pi$
$107$	4.06801	+	12.5201i	0.393270	+	1.21036i	−0.537031	+	0.843562i	$0.680454\pi$
$108$		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	0.619673	−	0.784860i	$-0.287265\pi$
$127$	0.729305	+	0.529871i	0.0647153	+	0.0470185i	−0.554957	+	0.831879i	$0.687265\pi$
$128$		0			0
$129$	0.327972	+	1.00939i	0.0288763	+	0.0888722i
$130$		0			0
$131$	14.5527			1.27148			0.635739	−	0.771904i	$-0.280695\pi$
$131$	14.5527			1.27148			0.635739	+	0.771904i	$0.280695\pi$
$132$		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	$-0.680807\pi$
$139$	4.63035	−	14.2508i	0.392741	−	1.20873i	0.930707	−	0.365767i	$-0.119193\pi$
$140$		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	0.997464	−	0.0711723i	$-0.0226740\pi$
$151$	1.82682	+	5.62238i	0.148665	+	0.457543i	−0.848799	+	0.528715i	$0.822674\pi$
$152$		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	−0.796639	−	0.604455i	$-0.793391\pi$
$163$	−5.97430	+	4.34059i	−0.467944	+	0.339981i	0.328696	+	0.944436i	$0.393391\pi$
$164$		0			0
$165$	0.248539	−	0.946183i	0.0193487	−	0.0736603i
$166$		0			0
$167$	−15.7658	+	11.4545i	−1.21999	+	0.886375i	−0.996099	−	0.0882386i	$-0.971876\pi$
$167$	−15.7658	+	11.4545i	−1.21999	+	0.886375i	−0.223892	+	0.974614i	$0.571876\pi$
$168$		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	0.832562	−	0.553932i	$-0.186873\pi$
$179$	−2.22879	−	6.85952i	−0.166588	−	0.512705i	−0.999150	+	0.0412273i	$0.986873\pi$
$180$		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	−0.893621	−	0.448821i	$-0.851844\pi$
$191$	1.28728	−	3.96183i	0.0931441	−	0.286668i	0.986766	+	0.162153i	$0.0518439\pi$
$192$		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	$-0.293966\pi$
$199$	17.0131			1.20603			0.603014	+	0.797731i	$0.293966\pi$
$200$		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	−0.742580	−	0.669757i	$-0.766398\pi$
$211$	−4.86721	+	3.53624i	−0.335073	+	0.243445i	0.407507	+	0.913202i	$0.366398\pi$
$212$		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	0.921929	−	0.387358i	$-0.126612\pi$
$223$	−0.770711	−	2.37201i	−0.0516107	−	0.158841i	−0.973540	+	0.228517i	$0.926612\pi$
$224$		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	$-0.588627\pi$
$227$	7.72396	−	23.7719i	0.512657	−	1.57780i	0.787505	−	0.616309i	$-0.211373\pi$
$228$		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	$-0.941481\pi$
$239$	−4.56394	−	14.0464i	−0.295217	−	0.908584i	0.687932	−	0.725775i	$-0.258519\pi$
$240$		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	−0.746291	−	0.665619i	$-0.768167\pi$
$251$	−5.44787	+	3.95811i	−0.343866	+	0.249834i	0.402425	+	0.915453i	$0.368167\pi$
$252$		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	$-0.689181\pi$
$263$	−18.1618			−1.11990			−0.559952	+	0.828525i	$0.689181\pi$
$264$		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	$-0.706699\pi$
$271$	5.80566	−	17.8680i	0.352669	−	1.08540i	0.957349	−	0.288935i	$-0.0933011\pi$
$272$		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	$-0.975024\pi$
$283$	−3.97802	−	12.2431i	−0.236468	−	0.727775i	0.760455	−	0.649391i	$-0.224976\pi$
$284$		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	$-0.562703\pi$
$307$	−6.85844			−0.391432			−0.195716	+	0.980661i	$0.562703\pi$
$308$		0			0
$309$	0.941105			0.0535376
$310$		0			0
$311$	4.40946	+	13.5709i	0.250037	+	0.769536i	0.994767	+	0.102170i	$0.0325784\pi$
$311$	4.40946	+	13.5709i	0.250037	+	0.769536i	−0.744730	+	0.667366i	$0.767422\pi$
$312$		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	$-0.489779\pi$
$331$	1.16816			0.0642079			0.0321040	+	0.999485i	$0.489779\pi$
$332$		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	$0.0529659\pi$
$347$	26.9818	+	19.6034i	1.44846	+	1.05237i	0.462273	+	0.886738i	$0.347034\pi$
$348$		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	−0.926413	−	0.376510i	$-0.877124\pi$
$359$	0.840838	−	2.58783i	0.0443777	−	0.136581i	0.970790	+	0.239929i	$0.0771242\pi$
$360$		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	−0.972962	−	0.230963i	$-0.925812\pi$
$367$	−0.959060	+	2.95168i	−0.0500625	+	0.154077i	0.922900	+	0.385040i	$0.125812\pi$
$368$		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	0.838523	−	0.544867i	$-0.183420\pi$
$379$	11.2805	+	8.19577i	0.579441	+	0.420989i	−0.259081	+	0.965855i	$0.583420\pi$
$380$		0			0
$381$	0.0821677	−	0.252886i	0.00420958	−	0.0129558i
$382$		0			0
$383$	6.59841	−	4.79402i	0.337163	−	0.244963i	−0.406301	−	0.913739i	$-0.633182\pi$
$383$	6.59841	−	4.79402i	0.337163	−	0.244963i	0.743464	+	0.668776i	$0.233182\pi$
$384$		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	$-0.584453\pi$
$419$	−10.7348			−0.524429			−0.262215	+	0.965010i	$0.584453\pi$
$420$		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	−0.748825	−	0.662768i	$-0.769381\pi$
$431$	−7.26399	+	5.27760i	−0.349894	+	0.254213i	0.398931	+	0.916981i	$0.369381\pi$
$432$		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	$-0.727607\pi$
$439$	−27.4750			−1.31131			−0.655655	+	0.755060i	$0.727607\pi$
$440$		0			0
$441$	−35.7552			−1.70263
$442$		0			0
$443$	9.33108	+	28.7181i	0.443333	+	1.36444i	0.884301	+	0.466916i	$0.154635\pi$
$443$	9.33108	+	28.7181i	0.443333	+	1.36444i	−0.440968	+	0.897523i	$0.645365\pi$
$444$		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	$-0.395784\pi$
$463$	13.8394			0.643172			0.321586	+	0.946880i	$0.395784\pi$
$464$		0			0
$465$	−0.467235	−	1.43800i	−0.0216675	−	0.0666857i
$466$		0			0
$467$	20.1359	+	14.6296i	0.931778	+	0.676976i	0.946428	−	0.322916i	$-0.104663\pi$
$467$	20.1359	+	14.6296i	0.931778	+	0.676976i	−0.0146495	+	0.999893i	$0.504663\pi$
$468$		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	−0.0833469	−	0.996521i	$-0.526561\pi$
$479$	−23.1303	−	16.8051i	−1.05685	−	0.767846i	−0.973503	+	0.228674i	$0.926561\pi$
$480$		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	0.913172	−	0.407574i	$-0.133625\pi$
$487$	−1.43808	−	4.42594i	−0.0651654	−	0.200559i	−0.978338	+	0.207015i	$0.933625\pi$
$488$		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	$0.290227\pi$
$491$	−7.70564	+	23.7155i	−0.347751	+	1.07027i	−0.960095	+	0.279675i	$0.909773\pi$
$492$		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	$0.211904\pi$
$499$	−4.75417	+	14.6318i	−0.212826	+	0.655010i	−0.999301	+	0.0373883i	$0.988096\pi$
$500$		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	$0.160549\pi$
$503$	10.1206	+	31.1481i	0.451257	+	1.38883i	−0.424217	+	0.905560i	$0.639451\pi$
$504$		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	0.102313	−	0.994752i	$-0.467376\pi$
$523$	−18.5729	−	13.4940i	−0.812136	−	0.590051i	−0.914449	+	0.404701i	$0.867376\pi$
$524$		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	$-0.964780\pi$
$547$	−5.95740	−	18.3350i	−0.254720	−	0.783947i	0.739165	−	0.673525i	$-0.235220\pi$
$548$		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	−0.618262	−	0.785972i	$-0.712163\pi$
$563$	−1.46665	+	1.06558i	−0.0618120	+	0.0449090i	0.556450	+	0.830881i	$0.312163\pi$
$564$		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	$-0.264233\pi$
$571$	32.2491			1.34958			0.674792	+	0.738008i	$0.264233\pi$
$572$		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	−0.993908	−	0.110214i	$-0.964846\pi$
$587$	−3.02941	+	9.32357i	−0.125037	+	0.384825i	0.868871	+	0.495039i	$0.164846\pi$
$588$		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	0.583178	−	0.812344i	$-0.301809\pi$
$599$	−0.225061	−	0.163516i	−0.00919574	−	0.00668110i	−0.592374	+	0.805663i	$0.701809\pi$
$600$		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	−0.890249	−	0.455474i	$-0.849470\pi$
$607$	−18.0387	+	13.1059i	−0.732169	+	0.531952i	0.158080	+	0.987426i	$0.449470\pi$
$608$		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	$0.102187\pi$
$619$	9.12336	+	28.0788i	0.366699	+	1.12858i	−0.582212	+	0.813037i	$0.697813\pi$
$620$		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	$-0.536516\pi$
$631$	14.1188	−	43.4532i	0.562061	−	1.72985i	0.676527	−	0.736418i	$-0.263484\pi$
$632$		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	−0.0930318	−	0.995663i	$-0.529656\pi$
$643$	−27.0998	−	19.6892i	−1.06871	−	0.776465i	−0.975680	+	0.219198i	$0.929656\pi$
$644$		0			0
$645$	0.327972	−	1.00939i	0.0129139	−	0.0397449i
$646$		0			0
$647$	31.7188	−	23.0451i	1.24700	−	0.905996i	0.248953	−	0.968516i	$-0.419914\pi$
$647$	31.7188	−	23.0451i	1.24700	−	0.905996i	0.998044	+	0.0625198i	$0.0199136\pi$
$648$		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	$-0.661042\pi$
$659$	−24.8813			−0.969238			−0.484619	+	0.874725i	$0.661042\pi$
$660$		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	$-0.645559\pi$
$683$	−23.0773			−0.883030			−0.441515	+	0.897254i	$0.645559\pi$
$684$		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	$-0.351795\pi$
$691$	37.7877	−	27.4544i	1.43751	−	1.04441i	0.988555	−	0.150862i	$-0.0482049\pi$
$692$		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	−0.899305	−	0.437321i	$-0.855927\pi$
$719$	2.28722	−	7.03934i	0.0852990	−	0.262523i	0.984604	+	0.174798i	$0.0559273\pi$
$720$		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	$-0.608445\pi$
$727$	−18.0187			−0.668275			−0.334137	+	0.942524i	$0.608445\pi$
$728$		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	−0.757200	−	0.653183i	$-0.773433\pi$
$739$	−10.0576	+	7.30726i	−0.369974	+	0.268802i	0.387226	+	0.921985i	$0.373433\pi$
$740$		0			0
$741$	4.18144	−	12.8691i	0.153609	−	0.472759i
$742$		0			0
$743$	30.2327	+	21.9653i	1.10913	+	0.805829i	0.982526	−	0.186125i	$-0.0595928\pi$
$743$	30.2327	+	21.9653i	1.10913	+	0.805829i	0.126602	+	0.991954i	$0.459593\pi$
$744$		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	0.985665	−	0.168715i	$-0.0539617\pi$
$751$	2.44111	+	7.51295i	0.0890772	+	0.274151i	−0.896588	+	0.442866i	$0.853962\pi$
$752$		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	0.549784	−	0.835307i	$-0.314710\pi$
$787$	−2.09694	−	1.52351i	−0.0747478	−	0.0543074i	−0.624532	+	0.781000i	$0.714710\pi$
$788$		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	$-0.994879\pi$
$811$	−5.70741	−	17.5656i	−0.200414	−	0.616812i	0.799456	−	0.600724i	$-0.205121\pi$
$812$		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	0.235646	−	0.971839i	$-0.424279\pi$
$823$	35.3648	−	25.6940i	1.23274	−	0.895637i	0.997092	+	0.0762021i	$0.0242794\pi$
$824$		0			0
$825$	−0.757225	+	0.619391i	−0.0263632	+	0.0215644i
$826$		0			0
$827$	25.6778	−	18.6560i	0.892906	−	0.648734i	−0.0437281	−	0.999043i	$-0.513924\pi$
$827$	25.6778	−	18.6560i	0.892906	−	0.648734i	0.936634	+	0.350309i	$0.113924\pi$
$828$		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	0.999317	−	0.0369398i	$-0.0117610\pi$
$839$	4.89922	+	15.0783i	0.169140	+	0.520559i	−0.830177	+	0.557499i	$0.811761\pi$
$840$		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	$-0.587732\pi$
$859$	−15.9523			−0.544284			−0.272142	+	0.962257i	$0.587732\pi$
$860$		0			0
$861$	1.04938	+	3.22966i	0.0357628	+	0.110067i
$862$		0			0
$863$	5.89687	+	4.28433i	0.200732	+	0.145840i	0.683610	−	0.729847i	$-0.260409\pi$
$863$	5.89687	+	4.28433i	0.200732	+	0.145840i	−0.482879	+	0.875687i	$0.660409\pi$
$864$		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	0.978345	−	0.206979i	$-0.0663631\pi$
$883$	1.93709	+	5.96175i	0.0651882	+	0.200629i	−0.913157	+	0.407608i	$0.866363\pi$
$884$		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	$-0.763958\pi$
$887$	7.62945	−	23.4810i	0.256172	−	0.788416i	0.993597	−	0.112986i	$-0.0360416\pi$
$888$		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	0.874464	−	0.485090i	$-0.161213\pi$
$907$	20.5798	+	14.9521i	0.683340	+	0.496476i	−0.191124	+	0.981566i	$0.561213\pi$
$908$		0			0
$909$	14.6593	−	45.1166i	0.486218	−	1.49642i
$910$		0			0
$911$	−19.8448	+	14.4181i	−0.657489	+	0.477694i	−0.865814	−	0.500366i	$-0.833199\pi$
$911$	−19.8448	+	14.4181i	−0.657489	+	0.477694i	0.208325	+	0.978060i	$0.433199\pi$
$912$		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	0.833807	−	0.552056i	$-0.186156\pi$
$919$	17.1714	+	12.4757i	0.566432	+	0.411537i	−0.267376	+	0.963592i	$0.586156\pi$
$920$		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	$-0.566379\pi$
$947$	−12.7418			−0.414052			−0.207026	+	0.978335i	$0.566379\pi$
$948$		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	$-0.301681\pi$
$967$	36.2900			1.16701			0.583504	+	0.812110i	$0.301681\pi$
$968$		0			0
$969$	−3.78485			−0.121587
$970$		0			0
$971$	2.15967	+	6.64677i	0.0693070	+	0.213305i	0.979711	−	0.200415i	$-0.0642291\pi$
$971$	2.15967	+	6.64677i	0.0693070	+	0.213305i	−0.910404	+	0.413720i	$0.864229\pi$
$972$		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	$0.251017\pi$
$983$	−8.85213	+	27.2441i	−0.282339	+	0.868951i	−0.987184	+	0.159589i	$0.948983\pi$
$984$		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	$-0.646514\pi$
$991$	−27.9673			−0.888409			−0.444205	+	0.895925i	$0.646514\pi$
$992$		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	880.2.bo.d.641.1		8
4.3	odd	2		440.2.y.a.201.2	yes	8
11.2	odd	10		9680.2.a.ct.1.2		4
11.4	even	5	inner	880.2.bo.d.81.1		8
11.9	even	5		9680.2.a.cu.1.2		4
44.15	odd	10		440.2.y.a.81.2	✓	8
44.31	odd	10		4840.2.a.y.1.3		4
44.35	even	10		4840.2.a.z.1.3		4

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

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:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	880.bo (of order \(5\), degree \(4\), not 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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