LMFDB - Embedded newform 1120.2.bz.e.271.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1120,2,Mod(271,1120)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1120, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 0, 5]))

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

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

chi := DirichletCharacter("1120.271");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1120 = 2^{5} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1120.bz (of order $6$, degree $2$, 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:	$8.94324502638$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 280)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			271.5
Character	$\chi$	$=$	1120.271
Dual form			1120.2.bz.e.591.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.75472 + 1.01309i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(1.63843 - 2.07739i) q^{7} +(0.552704 - 0.957311i) q^{9} +O(q^{10})$	\(q+(-1.75472 + 1.01309i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(1.63843 - 2.07739i) q^{7} +(0.552704 - 0.957311i) q^{9} +(0.572544 + 0.991675i) q^{11} -0.714654 q^{13} -2.02618i q^{15} +(-1.98251 + 1.14460i) q^{17} +(3.36692 + 1.94389i) q^{19} +(-0.770420 + 5.30512i) q^{21} +(4.00399 + 2.31171i) q^{23} +(-0.500000 - 0.866025i) q^{25} -3.83879i q^{27} -1.54366i q^{29} +(0.590584 + 1.02292i) q^{31} +(-2.00931 - 1.16008i) q^{33} +(0.979852 + 2.45762i) q^{35} +(5.72305 + 3.30420i) q^{37} +(1.25402 - 0.724009i) q^{39} +10.9848i q^{41} -10.8452 q^{43} +(0.552704 + 0.957311i) q^{45} +(-2.60440 + 4.51095i) q^{47} +(-1.63107 - 6.80732i) q^{49} +(2.31917 - 4.01692i) q^{51} +(2.25895 - 1.30420i) q^{53} -1.14509 q^{55} -7.87736 q^{57} +(-10.5249 + 6.07655i) q^{59} +(-7.13513 + 12.3584i) q^{61} +(-1.08314 - 2.71667i) q^{63} +(0.357327 - 0.618909i) q^{65} +(-4.08800 - 7.08062i) q^{67} -9.36787 q^{69} +15.8551i q^{71} +(-4.71396 + 2.72160i) q^{73} +(1.75472 + 1.01309i) q^{75} +(2.99817 + 0.435400i) q^{77} +(8.20023 + 4.73440i) q^{79} +(5.54715 + 9.60794i) q^{81} +2.78987i q^{83} -2.28920i q^{85} +(1.56386 + 2.70869i) q^{87} +(-11.0522 - 6.38097i) q^{89} +(-1.17091 + 1.48461i) q^{91} +(-2.07262 - 1.19663i) q^{93} +(-3.36692 + 1.94389i) q^{95} +5.18530i q^{97} +1.26579 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{3} - 12 q^{5} - 10 q^{7} + 12 q^{9}+O(q^{10}) $ 24 * q - 12 * q^3 - 12 * q^5 - 10 * q^7 + 12 * q^9	$ 24 q - 12 q^{3} - 12 q^{5} - 10 q^{7} + 12 q^{9} - 8 q^{11} + 20 q^{13} + 6 q^{17} - 18 q^{19} - 26 q^{21} - 18 q^{23} - 12 q^{25} + 6 q^{31} + 12 q^{33} + 8 q^{35} + 18 q^{39} - 32 q^{43} + 12 q^{45} + 8 q^{49} + 22 q^{51} + 30 q^{53} + 16 q^{55} - 44 q^{57} + 18 q^{59} + 22 q^{61} + 12 q^{63} - 10 q^{65} + 8 q^{67} - 12 q^{69} + 30 q^{73} + 12 q^{75} - 32 q^{77} - 6 q^{79} - 4 q^{81} - 14 q^{87} - 60 q^{89} - 18 q^{91} - 18 q^{93} + 18 q^{95} + 56 q^{99}+O(q^{100}) $ 24 * q - 12 * q^3 - 12 * q^5 - 10 * q^7 + 12 * q^9 - 8 * q^11 + 20 * q^13 + 6 * q^17 - 18 * q^19 - 26 * q^21 - 18 * q^23 - 12 * q^25 + 6 * q^31 + 12 * q^33 + 8 * q^35 + 18 * q^39 - 32 * q^43 + 12 * q^45 + 8 * q^49 + 22 * q^51 + 30 * q^53 + 16 * q^55 - 44 * q^57 + 18 * q^59 + 22 * q^61 + 12 * q^63 - 10 * q^65 + 8 * q^67 - 12 * q^69 + 30 * q^73 + 12 * q^75 - 32 * q^77 - 6 * q^79 - 4 * q^81 - 14 * q^87 - 60 * q^89 - 18 * q^91 - 18 * q^93 + 18 * q^95 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1120\mathbb{Z}\right)^\times$.

$n$	$351$	$421$	$801$	$897$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

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
$3$	−1.75472	+	1.01309i	−1.01309	+	0.584908i	−0.912095	−	0.409979i	$-0.865536\pi$
$3$	−1.75472	+	1.01309i	−1.01309	+	0.584908i	−0.100995	+	0.994887i	$0.532203\pi$
$4$		0			0
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$		0			0
$7$	1.63843	−	2.07739i	0.619270	−	0.785178i
$7$	1.63843	−	2.07739i	0.619270	−	0.785178i
$8$		0			0
$9$	0.552704	−	0.957311i	0.184235	−	0.319104i
$10$		0			0
$11$	0.572544	+	0.991675i	0.172628	+	0.299001i	0.939338	−	0.342993i	$-0.111441\pi$
$11$	0.572544	+	0.991675i	0.172628	+	0.299001i	−0.766710	+	0.641994i	$0.778107\pi$
$12$		0			0
$13$	−0.714654			−0.198209			−0.0991047	−	0.995077i	$-0.531598\pi$
$13$	−0.714654			−0.198209			−0.0991047	+	0.995077i	$0.531598\pi$
$14$		0			0
$15$		−	2.02618i		−	0.523158i
$16$		0			0
$17$	−1.98251	+	1.14460i	−0.480829	+	0.277607i	−0.720762	−	0.693183i	$-0.756208\pi$
$17$	−1.98251	+	1.14460i	−0.480829	+	0.277607i	0.239933	+	0.970789i	$0.422875\pi$
$18$		0			0
$19$	3.36692	+	1.94389i	0.772425	+	0.445960i	0.833739	−	0.552159i	$-0.186196\pi$
$19$	3.36692	+	1.94389i	0.772425	+	0.445960i	−0.0613139	+	0.998119i	$0.519529\pi$
$20$		0			0
$21$	−0.770420	+	5.30512i	−0.168119	+	1.15767i
$22$		0			0
$23$	4.00399	+	2.31171i	0.834891	+	0.482024i	0.855524	−	0.517763i	$-0.173235\pi$
$23$	4.00399	+	2.31171i	0.834891	+	0.482024i	−0.0206336	+	0.999787i	$0.506568\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$		−	3.83879i		−	0.738775i
$28$		0			0
$29$		−	1.54366i		−	0.286650i	−0.989676	−	0.143325i	$-0.954221\pi$
$29$		−	1.54366i		−	0.286650i	0.989676	−	0.143325i	$-0.0457794\pi$
$30$		0			0
$31$	0.590584	+	1.02292i	0.106072	+	0.183722i	0.914176	−	0.405318i	$-0.132839\pi$
$31$	0.590584	+	1.02292i	0.106072	+	0.183722i	−0.808104	+	0.589040i	$0.799506\pi$
$32$		0			0
$33$	−2.00931	−	1.16008i	−0.349776	−	0.201943i
$34$		0			0
$35$	0.979852	+	2.45762i	0.165625	+	0.415413i
$36$		0			0
$37$	5.72305	+	3.30420i	0.940864	+	0.543208i	0.890231	−	0.455510i	$-0.150543\pi$
$37$	5.72305	+	3.30420i	0.940864	+	0.543208i	0.0506326	+	0.998717i	$0.483876\pi$
$38$		0			0
$39$	1.25402	−	0.724009i	0.200804	−	0.115934i
$40$		0			0
$41$			10.9848i			1.71555i	0.514029	+	0.857773i	$0.328152\pi$
$41$			10.9848i			1.71555i	−0.514029	+	0.857773i	$0.671848\pi$
$42$		0			0
$43$	−10.8452			−1.65387			−0.826935	−	0.562297i	$-0.809918\pi$
$43$	−10.8452			−1.65387			−0.826935	+	0.562297i	$0.809918\pi$
$44$		0			0
$45$	0.552704	+	0.957311i	0.0823922	+	0.142708i
$46$		0			0
$47$	−2.60440	+	4.51095i	−0.379890	+	0.657989i	−0.991046	−	0.133521i	$-0.957372\pi$
$47$	−2.60440	+	4.51095i	−0.379890	+	0.657989i	0.611156	+	0.791510i	$0.290705\pi$
$48$		0			0
$49$	−1.63107	−	6.80732i	−0.233009	−	0.972474i
$50$		0			0
$51$	2.31917	−	4.01692i	0.324749	−	0.562481i
$52$		0			0
$53$	2.25895	−	1.30420i	0.310290	−	0.179146i	−0.336766	−	0.941588i	$-0.609333\pi$
$53$	2.25895	−	1.30420i	0.310290	−	0.179146i	0.647056	+	0.762442i	$0.276000\pi$
$54$		0			0
$55$	−1.14509			−0.154404
$56$		0			0
$57$	−7.87736			−1.04338
$58$		0			0
$59$	−10.5249	+	6.07655i	−1.37023	+	0.791100i	−0.990956	−	0.134187i	$-0.957158\pi$
$59$	−10.5249	+	6.07655i	−1.37023	+	0.791100i	−0.379269	+	0.925286i	$0.623824\pi$
$60$		0			0
$61$	−7.13513	+	12.3584i	−0.913559	+	1.58233i	−0.104563	+	0.994518i	$0.533344\pi$
$61$	−7.13513	+	12.3584i	−0.913559	+	1.58233i	−0.808997	+	0.587813i	$0.799989\pi$
$62$		0			0
$63$	−1.08314	−	2.71667i	−0.136462	−	0.342268i
$64$		0			0
$65$	0.357327	−	0.618909i	0.0443210	−	0.0767662i
$66$		0			0
$67$	−4.08800	−	7.08062i	−0.499429	−	0.865036i	0.500571	−	0.865695i	$-0.333123\pi$
$67$	−4.08800	−	7.08062i	−0.499429	−	0.865036i	−1.00000		0.000659524i	$0.999790\pi$
$68$		0			0
$69$	−9.36787			−1.12776
$70$		0			0
$71$			15.8551i			1.88166i	0.338881	+	0.940829i	$0.389952\pi$
$71$			15.8551i			1.88166i	−0.338881	+	0.940829i	$0.610048\pi$
$72$		0			0
$73$	−4.71396	+	2.72160i	−0.551727	+	0.318540i	−0.749818	−	0.661644i	$-0.769859\pi$
$73$	−4.71396	+	2.72160i	−0.551727	+	0.318540i	0.198091	+	0.980184i	$0.436526\pi$
$74$		0			0
$75$	1.75472	+	1.01309i	0.202618	+	0.116982i
$76$		0			0
$77$	2.99817	+	0.435400i	0.341673	+	0.0496184i
$78$		0			0
$79$	8.20023	+	4.73440i	0.922598	+	0.532662i	0.884463	−	0.466611i	$-0.154525\pi$
$79$	8.20023	+	4.73440i	0.922598	+	0.532662i	0.0381347	+	0.999273i	$0.487858\pi$
$80$		0			0
$81$	5.54715	+	9.60794i	0.616350	+	1.06755i
$82$		0			0
$83$			2.78987i			0.306229i	0.988208	+	0.153114i	$0.0489303\pi$
$83$			2.78987i			0.306229i	−0.988208	+	0.153114i	$0.951070\pi$
$84$		0			0
$85$		−	2.28920i		−	0.248299i
$86$		0			0
$87$	1.56386	+	2.70869i	0.167664	+	0.290402i
$88$		0			0
$89$	−11.0522	−	6.38097i	−1.17153	−	0.676382i	−0.217488	−	0.976063i	$-0.569786\pi$
$89$	−11.0522	−	6.38097i	−1.17153	−	0.676382i	−0.954039	+	0.299681i	$0.903120\pi$
$90$		0			0
$91$	−1.17091	+	1.48461i	−0.122745	+	0.155630i
$92$		0			0
$93$	−2.07262	−	1.19663i	−0.214921	−	0.124085i
$94$		0			0
$95$	−3.36692	+	1.94389i	−0.345439	+	0.199439i
$96$		0			0
$97$			5.18530i			0.526487i	0.964729	+	0.263244i	$0.0847923\pi$
$97$			5.18530i			0.526487i	−0.964729	+	0.263244i	$0.915208\pi$
$98$		0			0
$99$	1.26579			0.127216
$100$		0			0
$101$	0.506008	+	0.876431i	0.0503497	+	0.0872082i	0.890102	−	0.455762i	$-0.150633\pi$
$101$	0.506008	+	0.876431i	0.0503497	+	0.0872082i	−0.839752	+	0.542970i	$0.817300\pi$
$102$		0			0
$103$	1.22006	−	2.11321i	0.120217	−	0.208221i	−0.799636	−	0.600484i	$-0.794974\pi$
$103$	1.22006	−	2.11321i	0.120217	−	0.208221i	0.919853	+	0.392263i	$0.128308\pi$
$104$		0			0
$105$	−4.20916	−	3.31976i	−0.410772	−	0.323976i
$106$		0			0
$107$	0.680251	−	1.17823i	0.0657623	−	0.113904i	−0.831270	−	0.555869i	$-0.812385\pi$
$107$	0.680251	−	1.17823i	0.0657623	−	0.113904i	0.897032	+	0.441966i	$0.145719\pi$
$108$		0			0
$109$	9.05255	−	5.22649i	0.867077	−	0.500607i	0.000700983	−	1.00000i	$-0.499777\pi$
$109$	9.05255	−	5.22649i	0.867077	−	0.500607i	0.866376	+	0.499393i	$0.166444\pi$
$110$		0			0
$111$	−13.3898			−1.27091
$112$		0			0
$113$	−7.83586			−0.737135			−0.368568	−	0.929601i	$-0.620152\pi$
$113$	−7.83586			−0.737135			−0.368568	+	0.929601i	$0.620152\pi$
$114$		0			0
$115$	−4.00399	+	2.31171i	−0.373374	+	0.215568i
$116$		0			0
$117$	−0.394992	+	0.684146i	−0.0365170	+	0.0632494i
$118$		0			0
$119$	−0.870430	+	5.99379i	−0.0797922	+	0.549450i
$120$		0			0
$121$	4.84439	−	8.39073i	0.440399	−	0.762793i
$122$		0			0
$123$	−11.1286	−	19.2754i	−1.00344	−	1.73800i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$		−	12.0344i		−	1.06788i	−0.845522	−	0.533940i	$-0.820711\pi$
$127$		−	12.0344i		−	1.06788i	0.845522	−	0.533940i	$-0.179289\pi$
$128$		0			0
$129$	19.0302	−	10.9871i	1.67552	−	0.967362i
$130$		0			0
$131$	17.9090	+	10.3397i	1.56471	+	0.903387i	0.996769	+	0.0803195i	$0.0255941\pi$
$131$	17.9090	+	10.3397i	1.56471	+	0.903387i	0.567943	+	0.823068i	$0.307739\pi$
$132$		0			0
$133$	9.55470	−	3.80946i	0.828498	−	0.330322i
$134$		0			0
$135$	3.32449	+	1.91939i	0.286126	+	0.165195i
$136$		0			0
$137$	2.37459	+	4.11290i	0.202875	+	0.351389i	0.949453	−	0.313908i	$-0.101638\pi$
$137$	2.37459	+	4.11290i	0.202875	+	0.351389i	−0.746579	+	0.665297i	$0.768305\pi$
$138$		0			0
$139$			10.9812i			0.931416i	0.884938	+	0.465708i	$0.154200\pi$
$139$			10.9812i			0.931416i	−0.884938	+	0.465708i	$0.845800\pi$
$140$		0			0
$141$		−	10.5540i		−	0.888803i
$142$		0			0
$143$	−0.409171	−	0.708704i	−0.0342166	−	0.0592648i
$144$		0			0
$145$	1.33685	+	0.771829i	0.111019	+	0.0640969i
$146$		0			0
$147$	9.75850	+	10.2926i	0.804868	+	0.848915i
$148$		0			0
$149$	13.4757	+	7.78020i	1.10397	+	0.637379i	0.937261	−	0.348627i	$-0.113352\pi$
$149$	13.4757	+	7.78020i	1.10397	+	0.637379i	0.166711	+	0.986006i	$0.446685\pi$
$150$		0			0
$151$	−10.8679	+	6.27460i	−0.884419	+	0.510620i	−0.872113	−	0.489305i	$-0.837251\pi$
$151$	−10.8679	+	6.27460i	−0.884419	+	0.510620i	−0.0123061	+	0.999924i	$0.503917\pi$
$152$		0			0
$153$			2.53050i			0.204579i
$154$		0			0
$155$	−1.18117			−0.0948737
$156$		0			0
$157$	3.83150	+	6.63634i	0.305787	+	0.529638i	0.977436	−	0.211231i	$-0.0677473\pi$
$157$	3.83150	+	6.63634i	0.305787	+	0.529638i	−0.671650	+	0.740869i	$0.734414\pi$
$158$		0			0
$159$	−2.64255	+	4.57704i	−0.209568	+	0.362983i
$160$		0			0
$161$	11.3626	−	4.53026i	0.895498	−	0.357035i
$162$		0			0
$163$	10.0482	−	17.4040i	0.787037	−	1.36319i	−0.140738	−	0.990047i	$-0.544947\pi$
$163$	10.0482	−	17.4040i	0.787037	−	1.36319i	0.927775	−	0.373141i	$-0.121719\pi$
$164$		0			0
$165$	2.00931	−	1.16008i	0.156425	−	0.0903118i
$166$		0			0
$167$	−6.77446			−0.524224			−0.262112	−	0.965037i	$-0.584419\pi$
$167$	−6.77446			−0.524224			−0.262112	+	0.965037i	$0.584419\pi$
$168$		0			0
$169$	−12.4893			−0.960713
$170$		0			0
$171$	3.72182	−	2.14880i	0.284615	−	0.164322i
$172$		0			0
$173$	8.70160	−	15.0716i	0.661570	−	1.14587i	−0.318633	−	0.947878i	$-0.603224\pi$
$173$	8.70160	−	15.0716i	0.661570	−	1.14587i	0.980203	−	0.197995i	$-0.0634429\pi$
$174$		0			0
$175$	−2.61829	−	0.380233i	−0.197924	−	0.0287429i
$176$		0			0
$177$	12.3122	−	21.3253i	0.925441	−	1.60291i
$178$		0			0
$179$	7.66373	+	13.2740i	0.572814	+	0.992143i	0.996275	+	0.0862291i	$0.0274817\pi$
$179$	7.66373	+	13.2740i	0.572814	+	0.992143i	−0.423461	+	0.905914i	$0.639185\pi$
$180$		0			0
$181$	3.10021			0.230437			0.115218	−	0.993340i	$-0.463243\pi$
$181$	3.10021			0.230437			0.115218	+	0.993340i	$0.463243\pi$
$182$		0			0
$183$		−	28.9141i		−	2.13739i
$184$		0			0
$185$	−5.72305	+	3.30420i	−0.420767	+	0.242930i
$186$		0			0
$187$	−2.27014	−	1.31067i	−0.166009	−	0.0958456i
$188$		0			0
$189$	−7.97464	−	6.28960i	−0.580070	−	0.457501i
$190$		0			0
$191$	12.6460	+	7.30118i	0.915034	+	0.528295i	0.882047	−	0.471161i	$-0.156165\pi$
$191$	12.6460	+	7.30118i	0.915034	+	0.528295i	0.0329865	+	0.999456i	$0.489498\pi$
$192$		0			0
$193$	8.50498	+	14.7311i	0.612202	+	1.06037i	0.990868	+	0.134832i	$0.0430494\pi$
$193$	8.50498	+	14.7311i	0.612202	+	1.06037i	−0.378666	+	0.925533i	$0.623617\pi$
$194$		0			0
$195$			1.44802i			0.103695i
$196$		0			0
$197$		−	15.2341i		−	1.08538i	−0.839932	−	0.542692i	$-0.817405\pi$
$197$		−	15.2341i		−	1.08538i	0.839932	−	0.542692i	$-0.182595\pi$
$198$		0			0
$199$	−8.02143	−	13.8935i	−0.568624	−	0.984886i	−0.996702	−	0.0811444i	$-0.974142\pi$
$199$	−8.02143	−	13.8935i	−0.568624	−	0.984886i	0.428078	−	0.903742i	$-0.359191\pi$
$200$		0			0
$201$	14.3466	+	8.28303i	1.01193	+	0.584240i
$202$		0			0
$203$	−3.20677	−	2.52918i	−0.225071	−	0.177514i
$204$		0			0
$205$	−9.51316	−	5.49242i	−0.664428	−	0.383608i
$206$		0			0
$207$	4.42605	−	2.55538i	0.307632	−	0.177611i
$208$		0			0
$209$			4.45186i			0.307941i
$210$		0			0
$211$	5.85788			0.403273			0.201637	−	0.979460i	$-0.435374\pi$
$211$	5.85788			0.403273			0.201637	+	0.979460i	$0.435374\pi$
$212$		0			0
$213$	−16.0627	−	27.8214i	−1.10060	−	1.90629i
$214$		0			0
$215$	5.42258	−	9.39218i	0.369817	−	0.640541i
$216$		0			0
$217$	3.09263	+	0.449119i	0.209942	+	0.0304882i
$218$		0			0
$219$	5.51446	−	9.55132i	0.372633	−	0.645419i
$220$		0			0
$221$	1.41681	−	0.817994i	0.0953048	−	0.0550243i
$222$		0			0
$223$	−12.3268			−0.825465			−0.412732	−	0.910852i	$-0.635426\pi$
$223$	−12.3268			−0.825465			−0.412732	+	0.910852i	$0.635426\pi$
$224$		0			0
$225$	−1.10541			−0.0736938
$226$		0			0
$227$	−6.79256	+	3.92168i	−0.450838	+	0.260291i	−0.708184	−	0.706028i	$-0.750485\pi$
$227$	−6.79256	+	3.92168i	−0.450838	+	0.260291i	0.257346	+	0.966319i	$0.417152\pi$
$228$		0			0
$229$	−7.70634	+	13.3478i	−0.509249	+	0.882046i	0.490693	+	0.871332i	$0.336744\pi$
$229$	−7.70634	+	13.3478i	−0.509249	+	0.882046i	−0.999943	+	0.0107133i	$0.996590\pi$
$230$		0			0
$231$	−5.70205	+	2.27341i	−0.375168	+	0.149579i
$232$		0			0
$233$	−5.62905	+	9.74980i	−0.368771	+	0.638731i	−0.989374	−	0.145395i	$-0.953555\pi$
$233$	−5.62905	+	9.74980i	−0.368771	+	0.638731i	0.620602	+	0.784126i	$0.286888\pi$
$234$		0			0
$235$	−2.60440	−	4.51095i	−0.169892	−	0.294262i
$236$		0			0
$237$	−19.1855			−1.24623
$238$		0			0
$239$		−	14.1518i		−	0.915404i	−0.889106	−	0.457702i	$-0.848673\pi$
$239$		−	14.1518i		−	0.915404i	0.889106	−	0.457702i	$-0.151327\pi$
$240$		0			0
$241$	17.9056	−	10.3378i	1.15340	−	0.665915i	0.203685	−	0.979036i	$-0.434708\pi$
$241$	17.9056	−	10.3378i	1.15340	−	0.665915i	0.949713	+	0.313121i	$0.101375\pi$
$242$		0			0
$243$	−9.49397	−	5.48135i	−0.609038	−	0.351628i
$244$		0			0
$245$	6.71085	+	1.99112i	0.428740	+	0.127208i
$246$		0			0
$247$	−2.40619	−	1.38921i	−0.153102	−	0.0883935i
$248$		0			0
$249$	−2.82640	−	4.89546i	−0.179116	−	0.310237i
$250$		0			0
$251$			13.1277i			0.828616i	0.910137	+	0.414308i	$0.135976\pi$
$251$			13.1277i			0.828616i	−0.910137	+	0.414308i	$0.864024\pi$
$252$		0			0
$253$			5.29421i			0.332844i
$254$		0			0
$255$	2.31917	+	4.01692i	0.145232	+	0.251549i
$256$		0			0
$257$	17.6932	+	10.2152i	1.10367	+	0.637205i	0.937183	−	0.348839i	$-0.113424\pi$
$257$	17.6932	+	10.2152i	1.10367	+	0.637205i	0.166488	+	0.986043i	$0.446757\pi$
$258$		0			0
$259$	16.2409	−	6.47526i	1.00916	−	0.402353i
$260$		0			0
$261$	−1.47776	−	0.853186i	−0.0914711	−	0.0528109i
$262$		0			0
$263$	27.1210	−	15.6583i	1.67235	−	0.965532i	0.706034	−	0.708178i	$-0.250483\pi$
$263$	27.1210	−	15.6583i	1.67235	−	0.965532i	0.966317	−	0.257355i	$-0.0828508\pi$
$264$		0			0
$265$			2.60841i			0.160233i
$266$		0			0
$267$	25.8580			1.58248
$268$		0			0
$269$	−0.435079	−	0.753580i	−0.0265273	−	0.0459466i	0.852457	−	0.522797i	$-0.175112\pi$
$269$	−0.435079	−	0.753580i	−0.0265273	−	0.0459466i	−0.878984	+	0.476851i	$0.841778\pi$
$270$		0			0
$271$	15.6655	−	27.1335i	0.951614	−	1.64824i	0.209682	−	0.977770i	$-0.432757\pi$
$271$	15.6655	−	27.1335i	0.951614	−	1.64824i	0.741932	−	0.670475i	$-0.233910\pi$
$272$		0			0
$273$	0.550584	−	3.79133i	0.0333229	−	0.229462i
$274$		0			0
$275$	0.572544	−	0.991675i	0.0345257	−	0.0598002i
$276$		0			0
$277$	−24.3707	+	14.0705i	−1.46430	+	0.845412i	−0.999206	−	0.0398511i	$-0.987312\pi$
$277$	−24.3707	+	14.0705i	−1.46430	+	0.845412i	−0.465091	+	0.885263i	$0.653978\pi$
$278$		0			0
$279$	1.30567			0.0781685
$280$		0			0
$281$	−22.1338			−1.32039			−0.660195	−	0.751094i	$-0.729527\pi$
$281$	−22.1338			−1.32039			−0.660195	+	0.751094i	$0.729527\pi$
$282$		0			0
$283$	2.28363	−	1.31845i	0.135748	−	0.0783739i	−0.430588	−	0.902548i	$-0.641694\pi$
$283$	2.28363	−	1.31845i	0.135748	−	0.0783739i	0.566336	+	0.824175i	$0.308361\pi$
$284$		0			0
$285$	3.93868	−	6.82199i	0.233307	−	0.404100i
$286$		0			0
$287$	22.8198	+	17.9980i	1.34701	+	1.06239i
$288$		0			0
$289$	−5.87977	+	10.1841i	−0.345869	+	0.599063i
$290$		0			0
$291$	−5.25318	−	9.09877i	−0.307947	−	0.533379i
$292$		0			0
$293$	−9.78791			−0.571816			−0.285908	−	0.958257i	$-0.592295\pi$
$293$	−9.78791			−0.571816			−0.285908	+	0.958257i	$0.592295\pi$
$294$		0			0
$295$		−	12.1531i		−	0.707581i
$296$		0			0
$297$	3.80683	−	2.19787i	0.220894	−	0.127533i
$298$		0			0
$299$	−2.86147	−	1.65207i	−0.165483	−	0.0955418i
$300$		0			0
$301$	−17.7691	+	22.5296i	−1.02419	+	1.29858i
$302$		0			0
$303$	−1.77581	−	1.02526i	−0.102017	−	0.0588998i
$304$		0			0
$305$	−7.13513	−	12.3584i	−0.408556	−	0.707640i
$306$		0			0
$307$			10.6770i			0.609367i	0.952454	+	0.304683i	$0.0985506\pi$
$307$			10.6770i			0.609367i	−0.952454	+	0.304683i	$0.901449\pi$
$308$		0			0
$309$			4.94414i			0.281262i
$310$		0			0
$311$	4.23321	+	7.33214i	0.240043	+	0.415767i	0.960726	−	0.277497i	$-0.0895050\pi$
$311$	4.23321	+	7.33214i	0.240043	+	0.415767i	−0.720683	+	0.693265i	$0.756172\pi$
$312$		0			0
$313$	−20.2436	−	11.6877i	−1.14424	−	0.660626i	−0.196761	−	0.980452i	$-0.563042\pi$
$313$	−20.2436	−	11.6877i	−1.14424	−	0.660626i	−0.947476	+	0.319826i	$0.896376\pi$
$314$		0			0
$315$	2.89427	+	0.420312i	0.163074	+	0.0236819i
$316$		0			0
$317$	11.0950	+	6.40571i	0.623158	+	0.359780i	0.778097	−	0.628144i	$-0.216185\pi$
$317$	11.0950	+	6.40571i	0.623158	+	0.359780i	−0.154940	+	0.987924i	$0.549518\pi$
$318$		0			0
$319$	1.53081	−	0.883811i	0.0857087	−	0.0494839i
$320$		0			0
$321$			2.75662i			0.153860i
$322$		0			0
$323$	−8.89994			−0.495206
$324$		0			0
$325$	0.357327	+	0.618909i	0.0198209	+	0.0343309i
$326$		0			0
$327$	−10.5898	+	18.3421i	−0.585618	+	1.01432i
$328$		0			0
$329$	5.10384	+	12.8012i	0.281384	+	0.705754i
$330$		0			0
$331$	11.1099	−	19.2429i	0.610656	−	1.05769i	−0.380474	−	0.924792i	$-0.624239\pi$
$331$	11.1099	−	19.2429i	0.610656	−	1.05769i	0.991130	−	0.132896i	$-0.0424275\pi$
$332$		0			0
$333$	6.32630	−	3.65249i	0.346679	−	0.200155i
$334$		0			0
$335$	8.17600			0.446703
$336$		0			0
$337$	14.9570			0.814761			0.407381	−	0.913258i	$-0.366442\pi$
$337$	14.9570			0.814761			0.407381	+	0.913258i	$0.366442\pi$
$338$		0			0
$339$	13.7498	−	7.93843i	0.746785	−	0.431156i
$340$		0			0
$341$	−0.676270	+	1.17133i	−0.0366221	+	0.0634313i
$342$		0			0
$343$	−16.8138	−	7.76500i	−0.907861	−	0.419270i
$344$		0			0
$345$	4.68394	−	8.11282i	0.252175	−	0.436779i
$346$		0			0
$347$	−8.51734	−	14.7525i	−0.457235	−	0.791954i	0.541579	−	0.840650i	$-0.317827\pi$
$347$	−8.51734	−	14.7525i	−0.457235	−	0.791954i	−0.998814	+	0.0486962i	$0.984493\pi$
$348$		0			0
$349$	1.40440			0.0751760			0.0375880	−	0.999293i	$-0.488033\pi$
$349$	1.40440			0.0751760			0.0375880	+	0.999293i	$0.488033\pi$
$350$		0			0
$351$			2.74340i			0.146432i
$352$		0			0
$353$	11.0830	−	6.39876i	0.589887	−	0.340572i	−0.175166	−	0.984539i	$-0.556046\pi$
$353$	11.0830	−	6.39876i	0.589887	−	0.340572i	0.765053	+	0.643967i	$0.222713\pi$
$354$		0			0
$355$	−13.7310	−	7.92757i	−0.728763	−	0.420752i
$356$		0			0
$357$	−4.54489	−	11.3993i	−0.240541	−	0.603313i
$358$		0			0
$359$	−5.28987	−	3.05411i	−0.279189	−	0.161190i	0.353867	−	0.935296i	$-0.384866\pi$
$359$	−5.28987	−	3.05411i	−0.279189	−	0.161190i	−0.633056	+	0.774106i	$0.718200\pi$
$360$		0			0
$361$	−1.94255	−	3.36460i	−0.102240	−	0.177084i
$362$		0			0
$363$			19.6312i			1.03037i
$364$		0			0
$365$		−	5.44321i		−	0.284910i
$366$		0			0
$367$	4.55727	+	7.89342i	0.237888	+	0.412033i	0.960108	−	0.279630i	$-0.0902117\pi$
$367$	4.55727	+	7.89342i	0.237888	+	0.412033i	−0.722220	+	0.691663i	$0.756878\pi$
$368$		0			0
$369$	10.5159	+	6.07137i	0.547437	+	0.316063i
$370$		0			0
$371$	0.991802	−	6.82956i	0.0514918	−	0.354573i
$372$		0			0
$373$	19.9065	+	11.4930i	1.03072	+	0.595086i	0.917191	−	0.398448i	$-0.130451\pi$
$373$	19.9065	+	11.4930i	1.03072	+	0.595086i	0.113529	+	0.993535i	$0.463785\pi$
$374$		0			0
$375$	−1.75472	+	1.01309i	−0.0906135	+	0.0523158i
$376$		0			0
$377$			1.10318i			0.0568167i
$378$		0			0
$379$	−18.0966			−0.929562			−0.464781	−	0.885426i	$-0.653867\pi$
$379$	−18.0966			−0.929562			−0.464781	+	0.885426i	$0.653867\pi$
$380$		0			0
$381$	12.1919	+	21.1170i	0.624612	+	1.08186i
$382$		0			0
$383$	−10.7474	+	18.6150i	−0.549165	+	0.951182i	0.449167	+	0.893448i	$0.351721\pi$
$383$	−10.7474	+	18.6150i	−0.549165	+	0.951182i	−0.998332	+	0.0577341i	$0.981612\pi$
$384$		0			0
$385$	−1.87615	+	2.37879i	−0.0956175	+	0.121234i
$386$		0			0
$387$	−5.99416	+	10.3822i	−0.304700	+	0.527756i
$388$		0			0
$389$	2.38186	−	1.37517i	0.120765	−	0.0697238i	−0.438401	−	0.898780i	$-0.644455\pi$
$389$	2.38186	−	1.37517i	0.120765	−	0.0697238i	0.559166	+	0.829056i	$0.311122\pi$
$390$		0			0
$391$	−10.5839			−0.535253
$392$		0			0
$393$	−41.9004			−2.11359
$394$		0			0
$395$	−8.20023	+	4.73440i	−0.412598	+	0.238214i
$396$		0			0
$397$	7.62990	−	13.2154i	0.382934	−	0.663260i	−0.608547	−	0.793518i	$-0.708247\pi$
$397$	7.62990	−	13.2154i	0.382934	−	0.663260i	0.991480	+	0.130258i	$0.0415805\pi$
$398$		0			0
$399$	−12.9065	+	16.3643i	−0.646135	+	0.819241i
$400$		0			0
$401$	4.15899	−	7.20358i	0.207690	−	0.359729i	−0.743297	−	0.668962i	$-0.766739\pi$
$401$	4.15899	−	7.20358i	0.207690	−	0.359729i	0.950986	+	0.309233i	$0.100072\pi$
$402$		0			0
$403$	−0.422063	−	0.731035i	−0.0210245	−	0.0364154i
$404$		0			0
$405$	−11.0943			−0.551280
$406$		0			0
$407$			7.56720i			0.375092i
$408$		0			0
$409$	23.3269	−	13.4678i	1.15344	−	0.665941i	0.203719	−	0.979029i	$-0.434697\pi$
$409$	23.3269	−	13.4678i	1.15344	−	0.665941i	0.949724	+	0.313089i	$0.101364\pi$
$410$		0			0
$411$	−8.33349	−	4.81134i	−0.411061	−	0.237326i
$412$		0			0
$413$	−4.62101	+	31.8203i	−0.227385	+	1.56578i
$414$		0			0
$415$	−2.41610	−	1.39494i	−0.118602	−	0.0684748i
$416$		0			0
$417$	−11.1250	−	19.2690i	−0.544793	−	0.943608i
$418$		0			0
$419$		−	8.97603i		−	0.438508i	−0.975668	−	0.219254i	$-0.929638\pi$
$419$		−	8.97603i		−	0.438508i	0.975668	−	0.219254i	$-0.0703623\pi$
$420$		0			0
$421$		−	13.4720i		−	0.656583i	−0.944576	−	0.328292i	$-0.893527\pi$
$421$		−	13.4720i		−	0.656583i	0.944576	−	0.328292i	$-0.106473\pi$
$422$		0			0
$423$	2.87892	+	4.98643i	0.139978	+	0.242449i
$424$		0			0
$425$	1.98251	+	1.14460i	0.0961658	+	0.0555213i
$426$		0			0
$427$	13.9827	+	35.0708i	0.676672	+	1.69720i
$428$		0			0
$429$	1.43596	+	0.829054i	0.0693290	+	0.0400271i
$430$		0			0
$431$	20.5363	−	11.8567i	0.989200	−	0.571115i	0.0841648	−	0.996452i	$-0.473178\pi$
$431$	20.5363	−	11.8567i	0.989200	−	0.571115i	0.905035	+	0.425337i	$0.139844\pi$
$432$		0			0
$433$		−	18.5650i		−	0.892178i	−0.894989	−	0.446089i	$-0.852817\pi$
$433$		−	18.5650i		−	0.892178i	0.894989	−	0.446089i	$-0.147183\pi$
$434$		0			0
$435$	−3.12773			−0.149963
$436$		0			0
$437$	8.98743	+	15.5667i	0.429927	+	0.744656i
$438$		0			0
$439$	−3.44704	+	5.97045i	−0.164518	+	0.284954i	−0.936484	−	0.350710i	$-0.885940\pi$
$439$	−3.44704	+	5.97045i	−0.164518	+	0.284954i	0.771966	+	0.635664i	$0.219274\pi$
$440$		0			0
$441$	−7.41822	−	2.20100i	−0.353249	−	0.104809i
$442$		0			0
$443$	−14.1129	+	24.4443i	−0.670525	+	1.16138i	0.307230	+	0.951635i	$0.400598\pi$
$443$	−14.1129	+	24.4443i	−0.670525	+	1.16138i	−0.977755	+	0.209749i	$0.932735\pi$
$444$		0			0
$445$	11.0522	−	6.38097i	0.523923	−	0.302487i
$446$		0			0
$447$	−31.5282			−1.49123
$448$		0			0
$449$	1.93651			0.0913896			0.0456948	−	0.998955i	$-0.485450\pi$
$449$	1.93651			0.0913896			0.0456948	+	0.998955i	$0.485450\pi$
$450$		0			0
$451$	−10.8934	+	6.28930i	−0.512950	+	0.296152i
$452$		0			0
$453$	12.7135	−	22.0204i	0.597331	−	1.03461i
$454$		0			0
$455$	−0.700255	−	1.75635i	−0.0328285	−	0.0823389i
$456$		0			0
$457$	−17.3752	+	30.0948i	−0.812779	+	1.40777i	0.0981335	+	0.995173i	$0.468713\pi$
$457$	−17.3752	+	30.0948i	−0.812779	+	1.40777i	−0.910912	+	0.412601i	$0.864621\pi$
$458$		0			0
$459$	4.39388	+	7.61043i	0.205089	+	0.355224i
$460$		0			0
$461$	29.3117			1.36518			0.682590	−	0.730802i	$-0.260854\pi$
$461$	29.3117			1.36518			0.682590	+	0.730802i	$0.260854\pi$
$462$		0			0
$463$		−	9.47208i		−	0.440205i	−0.975477	−	0.220102i	$-0.929361\pi$
$463$		−	9.47208i		−	0.440205i	0.975477	−	0.220102i	$-0.0706391\pi$
$464$		0			0
$465$	2.07262	−	1.19663i	0.0961156	−	0.0554924i
$466$		0			0
$467$	−11.2422	−	6.49066i	−0.520225	−	0.300352i	0.216802	−	0.976216i	$-0.430437\pi$
$467$	−11.2422	−	6.49066i	−0.520225	−	0.300352i	−0.737027	+	0.675864i	$0.763771\pi$
$468$		0			0
$469$	−21.4071	−	3.10878i	−0.988489	−	0.143550i
$470$		0			0
$471$	−13.4464	−	7.76330i	−0.619579	−	0.357714i
$472$		0			0
$473$	−6.20932	−	10.7549i	−0.285505	−	0.494509i
$474$		0			0
$475$		−	3.88779i		−	0.178384i
$476$		0			0
$477$		−	2.88335i		−	0.132020i
$478$		0			0
$479$	−9.96246	−	17.2555i	−0.455197	−	0.788424i	0.543503	−	0.839407i	$-0.317098\pi$
$479$	−9.96246	−	17.2555i	−0.455197	−	0.788424i	−0.998699	+	0.0509837i	$0.983764\pi$
$480$		0			0
$481$	−4.09000	−	2.36136i	−0.186488	−	0.107669i
$482$		0			0
$483$	−15.3486	+	19.4607i	−0.698388	+	0.885492i
$484$		0			0
$485$	−4.49060	−	2.59265i	−0.203908	−	0.117726i
$486$		0			0
$487$	−23.4025	+	13.5114i	−1.06047	+	0.612261i	−0.925562	−	0.378597i	$-0.876407\pi$
$487$	−23.4025	+	13.5114i	−1.06047	+	0.612261i	−0.134906	+	0.990858i	$0.543073\pi$
$488$		0			0
$489$			40.7190i			1.84138i
$490$		0			0
$491$	−0.454409			−0.0205072			−0.0102536	−	0.999947i	$-0.503264\pi$
$491$	−0.454409			−0.0205072			−0.0102536	+	0.999947i	$0.503264\pi$
$492$		0			0
$493$	1.76687	+	3.06031i	0.0795760	+	0.137830i
$494$		0			0
$495$	−0.632894	+	1.09620i	−0.0284465	+	0.0492707i
$496$		0			0
$497$	32.9372	+	25.9776i	1.47744	+	1.16525i
$498$		0			0
$499$	4.29223	−	7.43436i	0.192147	−	0.332808i	−0.753815	−	0.657087i	$-0.771788\pi$
$499$	4.29223	−	7.43436i	0.192147	−	0.332808i	0.945961	+	0.324279i	$0.105122\pi$
$500$		0			0
$501$	11.8873	−	6.86314i	0.531086	−	0.306623i
$502$		0			0
$503$	43.3946			1.93487			0.967434	−	0.253123i	$-0.0814578\pi$
$503$	43.3946			1.93487			0.967434	+	0.253123i	$0.0814578\pi$
$504$		0			0
$505$	−1.01202			−0.0450341
$506$		0			0
$507$	21.9152	−	12.6528i	0.973289	−	0.561929i
$508$		0			0
$509$	11.5209	−	19.9548i	0.510654	−	0.884479i	−0.489270	−	0.872133i	$-0.662737\pi$
$509$	11.5209	−	19.9548i	0.510654	−	0.884479i	0.999924	−	0.0123465i	$-0.00393010\pi$
$510$		0			0
$511$	−2.06969	+	14.2519i	−0.0915575	+	0.630466i
$512$		0			0
$513$	7.46219	−	12.9249i	0.329464	−	0.570648i
$514$		0			0
$515$	1.22006	+	2.11321i	0.0537625	+	0.0931193i
$516$		0			0
$517$	−5.96452			−0.262319
$518$		0			0
$519$			35.2620i			1.54783i
$520$		0			0
$521$	−36.5041	+	21.0756i	−1.59927	+	0.923340i	−0.607644	+	0.794209i	$0.707885\pi$
$521$	−36.5041	+	21.0756i	−1.59927	+	0.923340i	−0.991628	+	0.129130i	$0.958781\pi$
$522$		0			0
$523$	9.61525	+	5.55137i	0.420445	+	0.242744i	0.695268	−	0.718751i	$-0.255286\pi$
$523$	9.61525	+	5.55137i	0.420445	+	0.242744i	−0.274822	+	0.961495i	$0.588619\pi$
$524$		0			0
$525$	4.97958	−	1.98536i	0.217327	−	0.0866481i
$526$		0			0
$527$	−2.34167	−	1.35197i	−0.102005	−	0.0588926i
$528$		0			0
$529$	−0.812016	−	1.40645i	−0.0353051	−	0.0611501i
$530$		0			0
$531$			13.4341i			0.582992i
$532$		0			0
$533$		−	7.85037i		−	0.340037i
$534$		0			0
$535$	0.680251	+	1.17823i	0.0294098	+	0.0509393i
$536$		0			0
$537$	−26.8955	−	15.5281i	−1.16063	−	0.670087i
$538$		0			0
$539$	5.81679	−	5.51497i	0.250547	−	0.237547i
$540$		0			0
$541$	−21.7744	−	12.5715i	−0.936156	−	0.540490i	−0.0474025	−	0.998876i	$-0.515094\pi$
$541$	−21.7744	−	12.5715i	−0.936156	−	0.540490i	−0.888753	+	0.458386i	$0.848428\pi$
$542$		0			0
$543$	−5.44001	+	3.14079i	−0.233453	+	0.134784i
$544$		0			0
$545$			10.4530i			0.447756i
$546$		0			0
$547$	−4.35086			−0.186030			−0.0930148	−	0.995665i	$-0.529650\pi$
$547$	−4.35086			−0.186030			−0.0930148	+	0.995665i	$0.529650\pi$
$548$		0			0
$549$	7.88722	+	13.6611i	0.336619	+	0.583040i
$550$		0			0
$551$	3.00071	−	5.19738i	0.127834	−	0.221416i
$552$		0			0
$553$	23.2707	−	9.27803i	0.989571	−	0.394542i
$554$		0			0
$555$	6.69491	−	11.5959i	0.284183	−	0.492220i
$556$		0			0
$557$	−22.5821	+	13.0378i	−0.956833	+	0.552428i	−0.895197	−	0.445671i	$-0.852965\pi$
$557$	−22.5821	+	13.0378i	−0.956833	+	0.552428i	−0.0616365	+	0.998099i	$0.519632\pi$
$558$		0			0
$559$	7.75053			0.327813
$560$		0			0
$561$	5.31130			0.224243
$562$		0			0
$563$	15.6768	−	9.05099i	0.660697	−	0.381454i	−0.131845	−	0.991270i	$-0.542090\pi$
$563$	15.6768	−	9.05099i	0.660697	−	0.381454i	0.792542	+	0.609817i	$0.208757\pi$
$564$		0			0
$565$	3.91793	−	6.78605i	0.164828	−	0.285491i
$566$		0			0
$567$	29.0480	+	4.21842i	1.21990	+	0.177157i
$568$		0			0
$569$	−12.4224	+	21.5163i	−0.520776	+	0.902010i	0.478932	+	0.877852i	$0.341024\pi$
$569$	−12.4224	+	21.5163i	−0.520776	+	0.902010i	−0.999708	+	0.0241585i	$0.992309\pi$
$570$		0			0
$571$	2.25668	+	3.90869i	0.0944392	+	0.163574i	0.909374	−	0.415979i	$-0.136561\pi$
$571$	2.25668	+	3.90869i	0.0944392	+	0.163574i	−0.814935	+	0.579552i	$0.803228\pi$
$572$		0			0
$573$	−29.5870			−1.23602
$574$		0			0
$575$		−	4.62342i		−	0.192810i
$576$		0			0
$577$	−20.3993	+	11.7776i	−0.849235	+	0.490306i	−0.860393	−	0.509632i	$-0.829782\pi$
$577$	−20.3993	+	11.7776i	−0.849235	+	0.490306i	0.0111579	+	0.999938i	$0.496448\pi$
$578$		0			0
$579$	−29.8478	−	17.2326i	−1.24043	−	0.716164i
$580$		0			0
$581$	5.79565	+	4.57103i	0.240444	+	0.189638i
$582$		0			0
$583$	2.58669	+	1.49343i	0.107130	+	0.0618514i
$584$		0			0
$585$	−0.394992	−	0.684146i	−0.0163309	−	0.0282860i
$586$		0			0
$587$		−	3.48482i		−	0.143834i	−0.997411	−	0.0719170i	$-0.977088\pi$
$587$		−	3.48482i		−	0.143834i	0.997411	−	0.0719170i	$-0.0229117\pi$
$588$		0			0
$589$			4.59213i			0.189215i
$590$		0			0
$591$	15.4335	+	26.7316i	0.634850	+	1.09959i
$592$		0			0
$593$	−11.4527	−	6.61223i	−0.470307	−	0.271532i	0.246061	−	0.969254i	$-0.420864\pi$
$593$	−11.4527	−	6.61223i	−0.470307	−	0.271532i	−0.716368	+	0.697722i	$0.754197\pi$
$594$		0			0
$595$	−4.75556	−	3.75071i	−0.194959	−	0.153764i
$596$		0			0
$597$	28.1508	+	16.2529i	1.15214	+	0.665186i
$598$		0			0
$599$	12.0329	−	6.94719i	0.491650	−	0.283855i	−0.233608	−	0.972331i	$-0.575053\pi$
$599$	12.0329	−	6.94719i	0.491650	−	0.283855i	0.725259	+	0.688476i	$0.241720\pi$
$600$		0			0
$601$		−	18.8327i		−	0.768200i	−0.923291	−	0.384100i	$-0.874512\pi$
$601$		−	18.8327i		−	0.768200i	0.923291	−	0.384100i	$-0.125488\pi$
$602$		0			0
$603$	−9.03781			−0.368048
$604$		0			0
$605$	4.84439	+	8.39073i	0.196952	+	0.341132i
$606$		0			0
$607$	12.1505	−	21.0453i	0.493175	−	0.854204i	−0.506794	−	0.862067i	$-0.669170\pi$
$607$	12.1505	−	21.0453i	0.493175	−	0.854204i	0.999969	+	0.00786319i	$0.00250296\pi$
$608$		0			0
$609$	8.18929	+	1.18927i	0.331847	+	0.0481915i
$610$		0			0
$611$	1.86124	−	3.22377i	0.0752978	−	0.130420i
$612$		0			0
$613$	16.2648	−	9.39048i	0.656929	−	0.379278i	−0.134177	−	0.990957i	$-0.542839\pi$
$613$	16.2648	−	9.39048i	0.656929	−	0.379278i	0.791106	+	0.611679i	$0.209506\pi$
$614$		0			0
$615$	22.2573			0.897500
$616$		0			0
$617$	26.0641			1.04930			0.524651	−	0.851317i	$-0.324196\pi$
$617$	26.0641			1.04930			0.524651	+	0.851317i	$0.324196\pi$
$618$		0			0
$619$	20.7007	−	11.9515i	0.832030	−	0.480373i	−0.0225171	−	0.999746i	$-0.507168\pi$
$619$	20.7007	−	11.9515i	0.832030	−	0.480373i	0.854547	+	0.519374i	$0.173835\pi$
$620$		0			0
$621$	8.87415	−	15.3705i	0.356107	−	0.616796i
$622$		0			0
$623$	−31.3640	+	12.5048i	−1.25657	+	0.500995i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	−4.51013	−	7.81178i	−0.180117	−	0.311972i
$628$		0			0
$629$	−15.1280			−0.603192
$630$		0			0
$631$			29.3239i			1.16736i	0.811982	+	0.583682i	$0.198389\pi$
$631$			29.3239i			1.16736i	−0.811982	+	0.583682i	$0.801611\pi$
$632$		0			0
$633$	−10.2790	+	5.93457i	−0.408552	+	0.235878i
$634$		0			0
$635$	10.4221	+	6.01720i	0.413588	+	0.238785i
$636$		0			0
$637$	1.16565	+	4.86488i	0.0461847	+	0.192754i
$638$		0			0
$639$	15.1783	+	8.76320i	0.600444	+	0.346667i
$640$		0			0
$641$	2.35512	+	4.07919i	0.0930217	+	0.161118i	0.908781	−	0.417273i	$-0.137014\pi$
$641$	2.35512	+	4.07919i	0.0930217	+	0.161118i	−0.815760	+	0.578391i	$0.803681\pi$
$642$		0			0
$643$		−	3.22266i		−	0.127089i	−0.997979	−	0.0635446i	$-0.979759\pi$
$643$		−	3.22266i		−	0.127089i	0.997979	−	0.0635446i	$-0.0202405\pi$
$644$		0			0
$645$			21.9742i			0.865235i
$646$		0			0
$647$	−0.242759	−	0.420471i	−0.00954385	−	0.0165304i	0.861214	−	0.508242i	$-0.169705\pi$
$647$	−0.242759	−	0.420471i	−0.00954385	−	0.0165304i	−0.870758	+	0.491712i	$0.836371\pi$
$648$		0			0
$649$	−12.0519	−	6.95818i	−0.473079	−	0.273133i
$650$		0			0
$651$	−5.88172	+	2.34504i	−0.230523	+	0.0919093i
$652$		0			0
$653$	−4.25225	−	2.45504i	−0.166403	−	0.0960730i	0.414485	−	0.910056i	$-0.363962\pi$
$653$	−4.25225	−	2.45504i	−0.166403	−	0.0960730i	−0.580889	+	0.813983i	$0.697295\pi$
$654$		0			0
$655$	−17.9090	+	10.3397i	−0.699761	+	0.404007i
$656$		0			0
$657$			6.01696i			0.234744i
$658$		0			0
$659$	−50.3794			−1.96250			−0.981252	−	0.192729i	$-0.938266\pi$
$659$	−50.3794			−1.96250			−0.981252	+	0.192729i	$0.938266\pi$
$660$		0			0
$661$	−2.39100	−	4.14133i	−0.0929991	−	0.161079i	0.815773	−	0.578373i	$-0.196312\pi$
$661$	−2.39100	−	4.14133i	−0.0929991	−	0.161079i	−0.908772	+	0.417294i	$0.862979\pi$
$662$		0			0
$663$	−1.65740	+	2.87071i	−0.0643683	+	0.111489i
$664$		0			0
$665$	−1.47826	+	10.1793i	−0.0573246	+	0.394738i
$666$		0			0
$667$	3.56849	−	6.18080i	0.138172	−	0.239321i
$668$		0			0
$669$	21.6302	−	12.4882i	0.836270	−	0.482821i
$670$		0			0
$671$	−16.3407			−0.630825
$672$		0			0
$673$	27.2854			1.05177			0.525887	−	0.850555i	$-0.323734\pi$
$673$	27.2854			1.05177			0.525887	+	0.850555i	$0.323734\pi$
$674$		0			0
$675$	−3.32449	+	1.91939i	−0.127960	+	0.0738775i
$676$		0			0
$677$	−21.2029	+	36.7245i	−0.814893	+	1.41144i	0.0945112	+	0.995524i	$0.469871\pi$
$677$	−21.2029	+	36.7245i	−0.814893	+	1.41144i	−0.909405	+	0.415913i	$0.863462\pi$
$678$		0			0
$679$	10.7719	+	8.49577i	0.413386	+	0.326038i
$680$		0			0
$681$	7.94604	−	13.7629i	0.304493	−	0.527397i
$682$		0			0
$683$	22.2969	+	38.6193i	0.853165	+	1.47773i	0.878337	+	0.478042i	$0.158653\pi$
$683$	22.2969	+	38.6193i	0.853165	+	1.47773i	−0.0251714	+	0.999683i	$0.508013\pi$
$684$		0			0
$685$	−4.74917			−0.181457
$686$		0			0
$687$		−	31.2289i		−	1.19146i
$688$		0			0
$689$	−1.61437	+	0.932055i	−0.0615025	+	0.0355085i
$690$		0			0
$691$	−2.71156	−	1.56552i	−0.103152	−	0.0595551i	0.447536	−	0.894266i	$-0.352302\pi$
$691$	−2.71156	−	1.56552i	−0.103152	−	0.0595551i	−0.550689	+	0.834711i	$0.685635\pi$
$692$		0			0
$693$	2.07391	−	2.62953i	0.0787814	−	0.0998876i
$694$		0			0
$695$	−9.51003	−	5.49062i	−0.360736	−	0.208271i
$696$		0			0
$697$	−12.5733	−	21.7776i	−0.476247	−	0.824884i
$698$		0			0
$699$		−	22.8110i		−	0.862789i
$700$		0			0
$701$			0.816220i			0.0308282i	0.999881	+	0.0154141i	$0.00490665\pi$
$701$			0.816220i			0.0308282i	−0.999881	+	0.0154141i	$0.995093\pi$
$702$		0			0
$703$	12.8460	+	22.2500i	0.484498	+	0.839175i
$704$		0			0
$705$	9.13999	+	5.27698i	0.344232	+	0.198742i
$706$		0			0
$707$	2.64975	+	0.384801i	0.0996540	+	0.0144719i
$708$		0			0
$709$	25.7963	+	14.8935i	0.968799	+	0.559336i	0.898870	−	0.438216i	$-0.144389\pi$
$709$	25.7963	+	14.8935i	0.968799	+	0.559336i	0.0699290	+	0.997552i	$0.477723\pi$
$710$		0			0
$711$	9.06459	−	5.23345i	0.339949	−	0.196270i
$712$		0			0
$713$			5.46103i			0.204517i
$714$		0			0
$715$	0.818341			0.0306042
$716$		0			0
$717$	14.3370	+	24.8325i	0.535427	+	0.927386i
$718$		0			0
$719$	−2.37920	+	4.12090i	−0.0887293	+	0.153684i	−0.906974	−	0.421186i	$-0.861614\pi$
$719$	−2.37920	+	4.12090i	−0.0887293	+	0.153684i	0.818245	+	0.574870i	$0.194947\pi$
$720$		0			0
$721$	−2.39096	−	5.99691i	−0.0890442	−	0.223336i
$722$		0			0
$723$	−20.9462	+	36.2799i	−0.778998	+	1.34926i
$724$		0			0
$725$	−1.33685	+	0.771829i	−0.0496492	+	0.0286650i
$726$		0			0
$727$	−14.0543			−0.521246			−0.260623	−	0.965441i	$-0.583928\pi$
$727$	−14.0543			−0.521246			−0.260623	+	0.965441i	$0.583928\pi$
$728$		0			0
$729$	−11.0705			−0.410019
$730$		0			0
$731$	21.5006	−	12.4134i	0.795229	−	0.459125i
$732$		0			0
$733$	0.785118	−	1.35986i	0.0289990	−	0.0502277i	−0.851162	−	0.524904i	$-0.824101\pi$
$733$	0.785118	−	1.35986i	0.0289990	−	0.0502277i	0.880161	+	0.474676i	$0.157435\pi$
$734$		0			0
$735$	−13.7929	+	3.30483i	−0.508757	+	0.121901i
$736$		0			0
$737$	4.68112	−	8.10793i	0.172431	−	0.298660i
$738$		0			0
$739$	3.63252	+	6.29171i	0.133625	+	0.231444i	0.925071	−	0.379794i	$-0.124005\pi$
$739$	3.63252	+	6.29171i	0.133625	+	0.231444i	−0.791447	+	0.611238i	$0.790672\pi$
$740$		0			0
$741$	5.62959			0.206808
$742$		0			0
$743$			0.694046i			0.0254621i	0.999919	+	0.0127310i	$0.00405253\pi$
$743$			0.694046i			0.0254621i	−0.999919	+	0.0127310i	$0.995947\pi$
$744$		0			0
$745$	−13.4757	+	7.78020i	−0.493711	+	0.285044i
$746$		0			0
$747$	2.67078	+	1.54197i	0.0977187	+	0.0564179i
$748$		0			0
$749$	−1.33309	−	3.34359i	−0.0487100	−	0.122172i
$750$		0			0
$751$	−14.2883	−	8.24935i	−0.521387	−	0.301023i	0.216115	−	0.976368i	$-0.430661\pi$
$751$	−14.2883	−	8.24935i	−0.521387	−	0.301023i	−0.737502	+	0.675345i	$0.763995\pi$
$752$		0			0
$753$	−13.2996	−	23.0356i	−0.484664	−	0.839463i
$754$		0			0
$755$		−	12.5492i		−	0.456712i
$756$		0			0
$757$		−	45.3048i		−	1.64663i	−0.567583	−	0.823316i	$-0.692121\pi$
$757$		−	45.3048i		−	1.64663i	0.567583	−	0.823316i	$-0.307879\pi$
$758$		0			0
$759$	−5.36352	−	9.28988i	−0.194683	−	0.337201i
$760$		0			0
$761$	4.16297	+	2.40349i	0.150907	+	0.0871265i	0.573552	−	0.819169i	$-0.305565\pi$
$761$	4.16297	+	2.40349i	0.150907	+	0.0871265i	−0.422645	+	0.906295i	$0.638898\pi$
$762$		0			0
$763$	3.97457	−	27.3689i	0.143889	−	0.990820i
$764$		0			0
$765$	−2.19148	−	1.26525i	−0.0792331	−	0.0457453i
$766$		0			0
$767$	7.52166	−	4.34263i	0.271592	−	0.156803i
$768$		0			0
$769$		−	5.47427i		−	0.197407i	−0.995117	−	0.0987035i	$-0.968530\pi$
$769$		−	5.47427i		−	0.197407i	0.995117	−	0.0987035i	$-0.0314695\pi$
$770$		0			0
$771$	−41.3955			−1.49082
$772$		0			0
$773$	−7.14164	−	12.3697i	−0.256867	−	0.444906i	0.708534	−	0.705677i	$-0.249357\pi$
$773$	−7.14164	−	12.3697i	−0.256867	−	0.444906i	−0.965401	+	0.260770i	$0.916024\pi$
$774$		0			0
$775$	0.590584	−	1.02292i	0.0212144	−	0.0367444i
$776$		0			0
$777$	−21.9384	+	27.8158i	−0.787034	+	0.997888i
$778$		0			0
$779$	−21.3534	+	36.9851i	−0.765064	+	1.32513i
$780$		0			0
$781$	−15.7231	+	9.07776i	−0.562618	+	0.324828i
$782$		0			0
$783$	−5.92577			−0.211770
$784$		0			0
$785$	−7.66299			−0.273504
$786$		0			0
$787$	−10.3383	+	5.96882i	−0.368521	+	0.212765i	−0.672812	−	0.739814i	$-0.734914\pi$
$787$	−10.3383	+	5.96882i	−0.368521	+	0.212765i	0.304291	+	0.952579i	$0.401580\pi$
$788$		0			0
$789$	−31.7266	+	54.9520i	−1.12950	+	1.95634i
$790$		0			0
$791$	−12.8385	+	16.2781i	−0.456486	+	0.578783i
$792$		0			0
$793$	5.09915	−	8.83199i	0.181076	−	0.313633i
$794$		0			0
$795$	−2.64255	−	4.57704i	−0.0937217	−	0.162331i
$796$		0			0
$797$	44.5344			1.57749			0.788745	−	0.614720i	$-0.210731\pi$
$797$	44.5344			1.57749			0.788745	+	0.614720i	$0.210731\pi$
$798$		0			0
$799$		−	11.9240i		−	0.421840i
$800$		0			0
$801$	−12.2172	+	7.05358i	−0.431672	+	0.249226i
$802$		0			0
$803$	−5.39789	−	3.11647i	−0.190487	−	0.109978i
$804$		0			0
$805$	−1.75797	+	12.1054i	−0.0619604	+	0.426660i
$806$		0			0
$807$	1.52689	+	0.881550i	0.0537490	+	0.0310320i
$808$		0			0
$809$	8.90901	+	15.4309i	0.313224	+	0.542520i	0.979058	−	0.203579i	$-0.0652575\pi$
$809$	8.90901	+	15.4309i	0.313224	+	0.542520i	−0.665834	+	0.746100i	$0.731924\pi$
$810$		0			0
$811$			38.8733i			1.36503i	0.730873	+	0.682513i	$0.239113\pi$
$811$			38.8733i			1.36503i	−0.730873	+	0.682513i	$0.760887\pi$
$812$		0			0
$813$			63.4825i			2.22643i
$814$		0			0
$815$	10.0482	+	17.4040i	0.351974	+	0.609636i
$816$		0			0
$817$	−36.5148	−	21.0818i	−1.27749	−	0.737560i
$818$		0			0
$819$	0.774068	+	1.94148i	0.0270481	+	0.0678408i
$820$		0			0
$821$	−12.4121	−	7.16612i	−0.433185	−	0.250099i	0.267518	−	0.963553i	$-0.413797\pi$
$821$	−12.4121	−	7.16612i	−0.433185	−	0.250099i	−0.700703	+	0.713454i	$0.747130\pi$
$822$		0			0
$823$	−8.71650	+	5.03248i	−0.303838	+	0.175421i	−0.644166	−	0.764886i	$-0.722795\pi$
$823$	−8.71650	+	5.03248i	−0.303838	+	0.175421i	0.340328	+	0.940307i	$0.389462\pi$
$824$		0			0
$825$			2.32015i			0.0807774i
$826$		0			0
$827$	−33.0985			−1.15095			−0.575475	−	0.817820i	$-0.695183\pi$
$827$	−33.0985			−1.15095			−0.575475	+	0.817820i	$0.695183\pi$
$828$		0			0
$829$	−19.9412	−	34.5392i	−0.692586	−	1.19959i	−0.970988	−	0.239130i	$-0.923138\pi$
$829$	−19.9412	−	34.5392i	−0.692586	−	1.19959i	0.278401	−	0.960465i	$-0.410196\pi$
$830$		0			0
$831$	28.5093	−	49.3795i	0.988976	−	1.71296i
$832$		0			0
$833$	11.0253	+	11.6287i	0.382003	+	0.402909i
$834$		0			0
$835$	3.38723	−	5.86686i	0.117220	−	0.203031i
$836$		0			0
$837$	3.92678	−	2.26712i	0.135729	−	0.0783633i
$838$		0			0
$839$	−9.19183			−0.317337			−0.158669	−	0.987332i	$-0.550720\pi$
$839$	−9.19183			−0.317337			−0.158669	+	0.987332i	$0.550720\pi$
$840$		0			0
$841$	26.6171			0.917832
$842$		0			0
$843$	38.8387	−	22.4235i	1.33768	−	0.772307i
$844$		0			0
$845$	6.24463	−	10.8160i	0.214822	−	0.372083i
$846$		0			0
$847$	−9.49356	−	23.8113i	−0.326203	−	0.818167i
$848$		0			0
$849$	−2.67142	+	4.62704i	−0.0916830	+	0.158800i
$850$		0			0
$851$	15.2767	+	26.4600i	0.523679	+	0.907038i
$852$		0			0
$853$	−22.3596			−0.765577			−0.382788	−	0.923836i	$-0.625036\pi$
$853$	−22.3596			−0.765577			−0.382788	+	0.923836i	$0.625036\pi$
$854$		0			0
$855$			4.29759i			0.146975i
$856$		0			0
$857$	2.08869	−	1.20591i	0.0713485	−	0.0411930i	−0.463901	−	0.885887i	$-0.653551\pi$
$857$	2.08869	−	1.20591i	0.0713485	−	0.0411930i	0.535250	+	0.844694i	$0.320217\pi$
$858$		0			0
$859$	−30.5635	−	17.6459i	−1.04281	−	0.602069i	−0.122185	−	0.992507i	$-0.538990\pi$
$859$	−30.5635	−	17.6459i	−1.04281	−	0.602069i	−0.920629	+	0.390438i	$0.872324\pi$
$860$		0			0
$861$	−58.2759	−	8.46295i	−1.98604	−	0.288417i
$862$		0			0
$863$	19.8260	+	11.4466i	0.674886	+	0.389645i	0.797925	−	0.602756i	$-0.205931\pi$
$863$	19.8260	+	11.4466i	0.674886	+	0.389645i	−0.123040	+	0.992402i	$0.539264\pi$
$864$		0			0
$865$	8.70160	+	15.0716i	0.295863	+	0.512450i
$866$		0			0
$867$		−	23.8270i		−	0.809206i
$868$		0			0
$869$			10.8426i			0.367810i
$870$		0			0
$871$	2.92151	+	5.06020i	0.0989915	+	0.171458i
$872$		0			0
$873$	4.96395	+	2.86594i	0.168004	+	0.0969972i
$874$		0			0
$875$	1.63843	−	2.07739i	0.0553892	−	0.0702285i
$876$		0			0
$877$	−37.7590	−	21.8002i	−1.27503	−	0.736140i	−0.299101	−	0.954221i	$-0.596687\pi$
$877$	−37.7590	−	21.8002i	−1.27503	−	0.736140i	−0.975931	+	0.218082i	$0.930020\pi$
$878$		0			0
$879$	17.1751	−	9.91604i	0.579301	−	0.334460i
$880$		0			0
$881$		−	5.79085i		−	0.195099i	−0.995231	−	0.0975494i	$-0.968900\pi$
$881$		−	5.79085i		−	0.195099i	0.995231	−	0.0975494i	$-0.0311004\pi$
$882$		0			0
$883$	20.0070			0.673288			0.336644	−	0.941632i	$-0.390708\pi$
$883$	20.0070			0.673288			0.336644	+	0.941632i	$0.390708\pi$
$884$		0			0
$885$	12.3122	+	21.3253i	0.413870	+	0.716844i
$886$		0			0
$887$	6.86765	−	11.8951i	0.230593	−	0.399399i	−0.727390	−	0.686225i	$-0.759267\pi$
$887$	6.86765	−	11.8951i	0.230593	−	0.399399i	0.957983	+	0.286826i	$0.0926001\pi$
$888$		0			0
$889$	−25.0001	−	19.7176i	−0.838476	−	0.661306i
$890$		0			0
$891$	−6.35197	+	11.0019i	−0.212799	+	0.368579i
$892$		0			0
$893$	−17.5376	+	10.1253i	−0.586873	+	0.338832i
$894$		0			0
$895$	−15.3275			−0.512341
$896$		0			0
$897$	6.69479			0.223533
$898$		0			0
$899$	1.57904	−	0.911659i	0.0526639	−	0.0304055i
$900$		0			0
$901$	−2.98559	+	5.17119i	−0.0994644	+	0.172277i
$902$		0			0
$903$	8.35533	−	57.5348i	0.278048	−	1.91464i
$904$		0			0
$905$	−1.55010	+	2.68486i	−0.0515272	+	0.0892478i
$906$		0			0
$907$	3.55400	+	6.15571i	0.118009	+	0.204397i	0.918978	−	0.394308i	$-0.129016\pi$
$907$	3.55400	+	6.15571i	0.118009	+	0.204397i	−0.800970	+	0.598705i	$0.795682\pi$
$908$		0			0
$909$	1.11869			0.0371046
$910$		0			0
$911$		−	13.1201i		−	0.434690i	−0.976095	−	0.217345i	$-0.930260\pi$
$911$		−	13.1201i		−	0.434690i	0.976095	−	0.217345i	$-0.0697397\pi$
$912$		0			0
$913$	−2.76665	+	1.59732i	−0.0915627	+	0.0528637i
$914$		0			0
$915$	25.0404	+	14.4571i	0.827809	+	0.477936i
$916$		0			0
$917$	50.8223	−	20.2628i	1.67830	−	0.669137i
$918$		0			0
$919$	23.7519	+	13.7132i	0.783502	+	0.452355i	0.837670	−	0.546176i	$-0.183917\pi$
$919$	23.7519	+	13.7132i	0.783502	+	0.452355i	−0.0541677	+	0.998532i	$0.517251\pi$
$920$		0			0
$921$	−10.8167	−	18.7351i	−0.356423	−	0.617343i
$922$		0			0
$923$		−	11.3309i		−	0.372963i
$924$		0			0
$925$		−	6.60841i		−	0.217283i
$926$		0			0
$927$	−1.34867	−	2.33596i	−0.0442961	−	0.0767231i
$928$		0			0
$929$	10.4779	+	6.04939i	0.343767	+	0.198474i	0.661937	−	0.749560i	$-0.269735\pi$
$929$	10.4779	+	6.04939i	0.343767	+	0.198474i	−0.318169	+	0.948034i	$0.603068\pi$
$930$		0			0
$931$	7.74104	−	26.0903i	0.253702	−	0.855077i
$932$		0			0
$933$	−14.8562	−	8.57725i	−0.486371	−	0.280807i
$934$		0			0
$935$	2.27014	−	1.31067i	0.0742417	−	0.0428634i
$936$		0			0
$937$		−	50.1666i		−	1.63887i	−0.573171	−	0.819435i	$-0.694287\pi$
$937$		−	50.1666i		−	1.63887i	0.573171	−	0.819435i	$-0.305713\pi$
$938$		0			0
$939$	47.3626			1.54562
$940$		0			0
$941$	21.2678	+	36.8369i	0.693311	+	1.20085i	0.970747	+	0.240106i	$0.0771820\pi$
$941$	21.2678	+	36.8369i	0.693311	+	1.20085i	−0.277436	+	0.960744i	$0.589485\pi$
$942$		0			0
$943$	−25.3938	+	43.9833i	−0.826935	+	1.43229i
$944$		0			0
$945$	9.43427	−	3.76144i	0.306897	−	0.122360i
$946$		0			0
$947$	7.96280	−	13.7920i	0.258756	−	0.448179i	−0.707153	−	0.707061i	$-0.750021\pi$
$947$	7.96280	−	13.7920i	0.258756	−	0.448179i	0.965909	+	0.258882i	$0.0833540\pi$
$948$		0			0
$949$	3.36885	−	1.94501i	0.109357	−	0.0631375i
$950$		0			0
$951$	−25.9582			−0.841754
$952$		0			0
$953$	31.6348			1.02475			0.512375	−	0.858762i	$-0.328766\pi$
$953$	31.6348			1.02475			0.512375	+	0.858762i	$0.328766\pi$
$954$		0			0
$955$	−12.6460	+	7.30118i	−0.409216	+	0.236261i
$956$		0			0
$957$	−1.79076	+	3.10169i	−0.0578871	+	0.100263i
$958$		0			0
$959$	12.4347	+	1.80579i	0.401537	+	0.0583120i
$960$		0			0
$961$	14.8024	−	25.6385i	0.477497	−	0.827050i
$962$		0			0
$963$	−0.751954	−	1.30242i	−0.0242314	−	0.0419700i
$964$		0			0
$965$	−17.0100			−0.547570
$966$		0			0
$967$		−	9.06338i		−	0.291459i	−0.989324	−	0.145729i	$-0.953447\pi$
$967$		−	9.06338i		−	0.291459i	0.989324	−	0.145729i	$-0.0465529\pi$
$968$		0			0
$969$	15.6169	−	9.01644i	0.501688	−	0.289650i
$970$		0			0
$971$	42.3233	+	24.4354i	1.35822	+	0.784168i	0.989384	−	0.145327i	$-0.0464234\pi$
$971$	42.3233	+	24.4354i	1.35822	+	0.784168i	0.368835	+	0.929495i	$0.379757\pi$
$972$		0			0
$973$	22.8123	+	17.9920i	0.731327	+	0.576798i
$974$		0			0
$975$	−1.25402	−	0.724009i	−0.0401608	−	0.0231869i
$976$		0			0
$977$	−15.3107	−	26.5188i	−0.489831	−	0.848413i	0.510100	−	0.860115i	$-0.329608\pi$
$977$	−15.3107	−	26.5188i	−0.489831	−	0.848413i	−0.999932	+	0.0117023i	$0.996275\pi$
$978$		0			0
$979$		−	14.6135i		−	0.467051i
$980$		0			0
$981$		−	11.5548i		−	0.368917i
$982$		0			0
$983$	−9.15271	−	15.8530i	−0.291926	−	0.505631i	0.682339	−	0.731036i	$-0.260963\pi$
$983$	−9.15271	−	15.8530i	−0.291926	−	0.505631i	−0.974265	+	0.225405i	$0.927630\pi$
$984$		0			0
$985$	13.1931	+	7.61705i	0.420367	+	0.242699i
$986$		0			0
$987$	−21.9246	−	17.2920i	−0.697869	−	0.550409i
$988$		0			0
$989$	−43.4239	−	25.0708i	−1.38080	−	0.797206i
$990$		0			0
$991$	33.4098	−	19.2891i	1.06130	−	0.612740i	0.135506	−	0.990777i	$-0.456734\pi$
$991$	33.4098	−	19.2891i	1.06130	−	0.612740i	0.925791	+	0.378037i	$0.123401\pi$
$992$		0			0
$993$			45.0214i			1.42871i
$994$		0			0
$995$	16.0429			0.508593
$996$		0			0
$997$	−27.5501	−	47.7182i	−0.872522	−	1.51125i	−0.859379	−	0.511338i	$-0.829150\pi$
$997$	−27.5501	−	47.7182i	−0.872522	−	1.51125i	−0.0131423	−	0.999914i	$-0.504183\pi$
$998$		0			0
$999$	12.6841	−	21.9696i	0.401308	−	0.695086i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1120.2.bz.e.271.5		24
4.3	odd	2		280.2.bj.f.131.11	yes	24
7.3	odd	6		1120.2.bz.f.591.5		24
8.3	odd	2		1120.2.bz.f.271.5		24
8.5	even	2		280.2.bj.e.131.7	✓	24
28.3	even	6		280.2.bj.e.171.7	yes	24
56.3	even	6	inner	1120.2.bz.e.591.5		24
56.45	odd	6		280.2.bj.f.171.11	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bj.e.131.7	✓	24	8.5	even	2
280.2.bj.e.171.7	yes	24	28.3	even	6
280.2.bj.f.131.11	yes	24	4.3	odd	2
280.2.bj.f.171.11	yes	24	56.45	odd	6
1120.2.bz.e.271.5		24	1.1	even	1	trivial
1120.2.bz.e.591.5		24	56.3	even	6	inner
1120.2.bz.f.271.5		24	8.3	odd	2
1120.2.bz.f.591.5		24	7.3	odd	6

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:	\( N \)	\(=\)	\( 1120 = 2^{5} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1120.bz (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.75472 + 1.01309i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(1.63843 - 2.07739i) q^{7} +(0.552704 - 0.957311i) q^{9} +O(q^{10})\)	\(q+(-1.75472 + 1.01309i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(1.63843 - 2.07739i) q^{7} +(0.552704 - 0.957311i) q^{9} +(0.572544 + 0.991675i) q^{11} -0.714654 q^{13} -2.02618i q^{15} +(-1.98251 + 1.14460i) q^{17} +(3.36692 + 1.94389i) q^{19} +(-0.770420 + 5.30512i) q^{21} +(4.00399 + 2.31171i) q^{23} +(-0.500000 - 0.866025i) q^{25} -3.83879i q^{27} -1.54366i q^{29} +(0.590584 + 1.02292i) q^{31} +(-2.00931 - 1.16008i) q^{33} +(0.979852 + 2.45762i) q^{35} +(5.72305 + 3.30420i) q^{37} +(1.25402 - 0.724009i) q^{39} +10.9848i q^{41} -10.8452 q^{43} +(0.552704 + 0.957311i) q^{45} +(-2.60440 + 4.51095i) q^{47} +(-1.63107 - 6.80732i) q^{49} +(2.31917 - 4.01692i) q^{51} +(2.25895 - 1.30420i) q^{53} -1.14509 q^{55} -7.87736 q^{57} +(-10.5249 + 6.07655i) q^{59} +(-7.13513 + 12.3584i) q^{61} +(-1.08314 - 2.71667i) q^{63} +(0.357327 - 0.618909i) q^{65} +(-4.08800 - 7.08062i) q^{67} -9.36787 q^{69} +15.8551i q^{71} +(-4.71396 + 2.72160i) q^{73} +(1.75472 + 1.01309i) q^{75} +(2.99817 + 0.435400i) q^{77} +(8.20023 + 4.73440i) q^{79} +(5.54715 + 9.60794i) q^{81} +2.78987i q^{83} -2.28920i q^{85} +(1.56386 + 2.70869i) q^{87} +(-11.0522 - 6.38097i) q^{89} +(-1.17091 + 1.48461i) q^{91} +(-2.07262 - 1.19663i) q^{93} +(-3.36692 + 1.94389i) q^{95} +5.18530i q^{97} +1.26579 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{3} - 12 q^{5} - 10 q^{7} + 12 q^{9}+O(q^{10}) \) 24 * q - 12 * q^3 - 12 * q^5 - 10 * q^7 + 12 * q^9	\( 24 q - 12 q^{3} - 12 q^{5} - 10 q^{7} + 12 q^{9} - 8 q^{11} + 20 q^{13} + 6 q^{17} - 18 q^{19} - 26 q^{21} - 18 q^{23} - 12 q^{25} + 6 q^{31} + 12 q^{33} + 8 q^{35} + 18 q^{39} - 32 q^{43} + 12 q^{45} + 8 q^{49} + 22 q^{51} + 30 q^{53} + 16 q^{55} - 44 q^{57} + 18 q^{59} + 22 q^{61} + 12 q^{63} - 10 q^{65} + 8 q^{67} - 12 q^{69} + 30 q^{73} + 12 q^{75} - 32 q^{77} - 6 q^{79} - 4 q^{81} - 14 q^{87} - 60 q^{89} - 18 q^{91} - 18 q^{93} + 18 q^{95} + 56 q^{99}+O(q^{100}) \) 24 * q - 12 * q^3 - 12 * q^5 - 10 * q^7 + 12 * q^9 - 8 * q^11 + 20 * q^13 + 6 * q^17 - 18 * q^19 - 26 * q^21 - 18 * q^23 - 12 * q^25 + 6 * q^31 + 12 * q^33 + 8 * q^35 + 18 * q^39 - 32 * q^43 + 12 * q^45 + 8 * q^49 + 22 * q^51 + 30 * q^53 + 16 * q^55 - 44 * q^57 + 18 * q^59 + 22 * q^61 + 12 * q^63 - 10 * q^65 + 8 * q^67 - 12 * q^69 + 30 * q^73 + 12 * q^75 - 32 * q^77 - 6 * q^79 - 4 * q^81 - 14 * q^87 - 60 * q^89 - 18 * q^91 - 18 * q^93 + 18 * q^95 + 56 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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