LMFDB - Embedded newform 1120.2.bq.b.719.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1120,2,Mod(719,1120)]

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, 3, 5]))

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

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

chi := DirichletCharacter("1120.719");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1120 = 2^{5} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1120.bq (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:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 280)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			719.10
Character	$\chi$	$=$	1120.719
Dual form			1120.2.bq.b.1039.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.929162 - 1.60936i) q^{3} +(0.698124 + 2.12429i) q^{5} +(-1.10610 + 2.40345i) q^{7} +(-0.226682 + 0.392626i) q^{9} +O(q^{10})$	\(q+(-0.929162 - 1.60936i) q^{3} +(0.698124 + 2.12429i) q^{5} +(-1.10610 + 2.40345i) q^{7} +(-0.226682 + 0.392626i) q^{9} +(-1.61069 - 2.78980i) q^{11} +0.668981i q^{13} +(2.77007 - 3.09734i) q^{15} +(-1.62295 - 2.81103i) q^{17} +(5.77054 + 3.33162i) q^{19} +(4.89574 - 0.453085i) q^{21} +(-4.41240 + 7.64251i) q^{23} +(-4.02524 + 2.96604i) q^{25} -4.73247 q^{27} +3.17360i q^{29} +(-2.58684 - 4.48053i) q^{31} +(-2.99319 + 5.18435i) q^{33} +(-5.87782 - 0.671772i) q^{35} +(-1.15890 + 2.00727i) q^{37} +(1.07663 - 0.621591i) q^{39} +9.34903i q^{41} +6.84531i q^{43} +(-0.992304 - 0.207439i) q^{45} +(-3.12812 - 1.80602i) q^{47} +(-4.55310 - 5.31689i) q^{49} +(-3.01597 + 5.22381i) q^{51} +(0.0130049 + 0.0225252i) q^{53} +(4.80189 - 5.36921i) q^{55} -12.3825i q^{57} +(-0.0160236 + 0.00925120i) q^{59} +(-0.897835 + 1.55510i) q^{61} +(-0.692921 - 0.979101i) q^{63} +(-1.42111 + 0.467032i) q^{65} +(-4.14522 + 2.39324i) q^{67} +16.3993 q^{69} +8.13591i q^{71} +(6.30342 + 10.9178i) q^{73} +(8.51352 + 3.72212i) q^{75} +(8.48672 - 0.785418i) q^{77} +(13.5306 + 7.81192i) q^{79} +(5.07728 + 8.79410i) q^{81} -6.60312 q^{83} +(4.83844 - 5.41008i) q^{85} +(5.10745 - 2.94879i) q^{87} +(-1.31681 - 0.760263i) q^{89} +(-1.60786 - 0.739958i) q^{91} +(-4.80718 + 8.32628i) q^{93} +(-3.04879 + 14.5842i) q^{95} -12.1700 q^{97} +1.46046 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 52 q^{9}+O(q^{10}) $ 80 * q - 52 * q^9	$ 80 q - 52 q^{9} + 48 q^{19} - 22 q^{25} + 22 q^{35} + 16 q^{49} - 20 q^{51} + 60 q^{59} - 12 q^{65} + 6 q^{75} - 36 q^{89} - 72 q^{91} - 104 q^{99}+O(q^{100}) $ 80 * q - 52 * q^9 + 48 * q^19 - 22 * q^25 + 22 * q^35 + 16 * q^49 - 20 * q^51 + 60 * q^59 - 12 * q^65 + 6 * q^75 - 36 * q^89 - 72 * q^91 - 104 * 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
$3$	−0.929162	−	1.60936i	−0.536452	−	0.929162i	−0.999092	−	0.0426153i	$-0.986431\pi$
$3$	−0.929162	−	1.60936i	−0.536452	−	0.929162i	0.462640	−	0.886546i	$-0.346902\pi$
$4$		0			0
$5$	0.698124	+	2.12429i	0.312211	+	0.950013i
$5$	0.698124	+	2.12429i	0.312211	+	0.950013i
$6$		0			0
$7$	−1.10610	+	2.40345i	−0.418066	+	0.908417i
$7$	−1.10610	+	2.40345i	−0.418066	+	0.908417i
$8$		0			0
$9$	−0.226682	+	0.392626i	−0.0755608	+	0.130875i
$10$		0			0
$11$	−1.61069	−	2.78980i	−0.485642	−	0.841157i	0.514222	−	0.857657i	$-0.328081\pi$
$11$	−1.61069	−	2.78980i	−0.485642	−	0.841157i	−0.999864	+	0.0165005i	$0.994747\pi$
$12$		0			0
$13$			0.668981i			0.185542i	0.995687	+	0.0927710i	$0.0295724\pi$
$13$			0.668981i			0.185542i	−0.995687	+	0.0927710i	$0.970428\pi$
$14$		0			0
$15$	2.77007	−	3.09734i	0.715230	−	0.799730i
$16$		0			0
$17$	−1.62295	−	2.81103i	−0.393624	−	0.681776i	0.599301	−	0.800524i	$-0.295445\pi$
$17$	−1.62295	−	2.81103i	−0.393624	−	0.681776i	−0.992924	+	0.118748i	$0.962112\pi$
$18$		0			0
$19$	5.77054	+	3.33162i	1.32385	+	0.764326i	0.984341	−	0.176276i	$-0.0564052\pi$
$19$	5.77054	+	3.33162i	1.32385	+	0.764326i	0.339511	+	0.940602i	$0.389738\pi$
$20$		0			0
$21$	4.89574	−	0.453085i	1.06834	−	0.0988712i
$22$		0			0
$23$	−4.41240	+	7.64251i	−0.920050	+	1.59357i	−0.120715	+	0.992687i	$0.538519\pi$
$23$	−4.41240	+	7.64251i	−0.920050	+	1.59357i	−0.799335	+	0.600886i	$0.794815\pi$
$24$		0			0
$25$	−4.02524	+	2.96604i	−0.805049	+	0.593208i
$26$		0			0
$27$	−4.73247			−0.910764
$28$		0			0
$29$			3.17360i			0.589322i	0.955602	+	0.294661i	$0.0952068\pi$
$29$			3.17360i			0.589322i	−0.955602	+	0.294661i	$0.904793\pi$
$30$		0			0
$31$	−2.58684	−	4.48053i	−0.464609	−	0.804727i	0.534574	−	0.845121i	$-0.320472\pi$
$31$	−2.58684	−	4.48053i	−0.464609	−	0.804727i	−0.999184	+	0.0403943i	$0.987139\pi$
$32$		0			0
$33$	−2.99319	+	5.18435i	−0.521047	+	0.902480i
$34$		0			0
$35$	−5.87782	−	0.671772i	−0.993532	−	0.113550i
$36$		0			0
$37$	−1.15890	+	2.00727i	−0.190522	+	0.329994i	−0.945423	−	0.325845i	$-0.894351\pi$
$37$	−1.15890	+	2.00727i	−0.190522	+	0.329994i	0.754901	+	0.655838i	$0.227685\pi$
$38$		0			0
$39$	1.07663	−	0.621591i	0.172398	−	0.0995343i
$40$		0			0
$41$			9.34903i			1.46007i	0.683408	+	0.730036i	$0.260497\pi$
$41$			9.34903i			1.46007i	−0.683408	+	0.730036i	$0.739503\pi$
$42$		0			0
$43$			6.84531i			1.04390i	0.852976	+	0.521950i	$0.174795\pi$
$43$			6.84531i			1.04390i	−0.852976	+	0.521950i	$0.825205\pi$
$44$		0			0
$45$	−0.992304	−	0.207439i	−0.147924	−	0.0309231i
$46$		0			0
$47$	−3.12812	−	1.80602i	−0.456284	−	0.263436i	0.254197	−	0.967153i	$-0.418189\pi$
$47$	−3.12812	−	1.80602i	−0.456284	−	0.263436i	−0.710480	+	0.703717i	$0.751522\pi$
$48$		0			0
$49$	−4.55310	−	5.31689i	−0.650442	−	0.759556i
$50$		0			0
$51$	−3.01597	+	5.22381i	−0.422320	+	0.731480i
$52$		0			0
$53$	0.0130049	+	0.0225252i	0.00178637	+	0.00309408i	0.866917	−	0.498452i	$-0.166098\pi$
$53$	0.0130049	+	0.0225252i	0.00178637	+	0.00309408i	−0.865131	+	0.501546i	$0.832765\pi$
$54$		0			0
$55$	4.80189	−	5.36921i	0.647487	−	0.723984i
$56$		0			0
$57$		−	12.3825i		−	1.64010i
$58$		0			0
$59$	−0.0160236	+	0.00925120i	−0.00208609	+	0.00120440i	−0.501043	−	0.865423i	$-0.667050\pi$
$59$	−0.0160236	+	0.00925120i	−0.00208609	+	0.00120440i	0.498957	+	0.866627i	$0.333717\pi$
$60$		0			0
$61$	−0.897835	+	1.55510i	−0.114956	+	0.199110i	−0.917762	−	0.397130i	$-0.870006\pi$
$61$	−0.897835	+	1.55510i	−0.114956	+	0.199110i	0.802806	+	0.596240i	$0.203339\pi$
$62$		0			0
$63$	−0.692921	−	0.979101i	−0.0872998	−	0.123355i
$64$		0			0
$65$	−1.42111	+	0.467032i	−0.176267	+	0.0579282i
$66$		0			0
$67$	−4.14522	+	2.39324i	−0.506419	+	0.292381i	−0.731360	−	0.681991i	$-0.761114\pi$
$67$	−4.14522	+	2.39324i	−0.506419	+	0.292381i	0.224942	+	0.974372i	$0.427781\pi$
$68$		0			0
$69$	16.3993			1.97425
$70$		0			0
$71$			8.13591i			0.965555i	0.875743	+	0.482778i	$0.160372\pi$
$71$			8.13591i			0.965555i	−0.875743	+	0.482778i	$0.839628\pi$
$72$		0			0
$73$	6.30342	+	10.9178i	0.737760	+	1.27784i	0.953502	+	0.301387i	$0.0974495\pi$
$73$	6.30342	+	10.9178i	0.737760	+	1.27784i	−0.215742	+	0.976450i	$0.569217\pi$
$74$		0			0
$75$	8.51352	+	3.72212i	0.983056	+	0.429793i
$76$		0			0
$77$	8.48672	−	0.785418i	0.967151	−	0.0895067i
$78$		0			0
$79$	13.5306	+	7.81192i	1.52232	+	0.878910i	0.999652	+	0.0263718i	$0.00839538\pi$
$79$	13.5306	+	7.81192i	1.52232	+	0.878910i	0.522665	+	0.852538i	$0.324938\pi$
$80$		0			0
$81$	5.07728	+	8.79410i	0.564142	+	0.977123i
$82$		0			0
$83$	−6.60312			−0.724787			−0.362393	−	0.932025i	$-0.618040\pi$
$83$	−6.60312			−0.724787			−0.362393	+	0.932025i	$0.618040\pi$
$84$		0			0
$85$	4.83844	−	5.41008i	0.524802	−	0.586805i
$86$		0			0
$87$	5.10745	−	2.94879i	0.547576	−	0.316143i
$88$		0			0
$89$	−1.31681	−	0.760263i	−0.139582	−	0.0805877i	0.428583	−	0.903503i	$-0.359013\pi$
$89$	−1.31681	−	0.760263i	−0.139582	−	0.0805877i	−0.568165	+	0.822915i	$0.692346\pi$
$90$		0			0
$91$	−1.60786	−	0.739958i	−0.168549	−	0.0775687i
$92$		0			0
$93$	−4.80718	+	8.32628i	−0.498481	+	0.863395i
$94$		0			0
$95$	−3.04879	+	14.5842i	−0.312799	+	1.49631i
$96$		0			0
$97$	−12.1700			−1.23568			−0.617839	−	0.786305i	$-0.711992\pi$
$97$	−12.1700			−1.23568			−0.617839	+	0.786305i	$0.711992\pi$
$98$		0			0
$99$	1.46046			0.146782
$100$		0			0
$101$	−7.06658	−	12.2397i	−0.703151	−	1.21789i	−0.967355	−	0.253426i	$-0.918443\pi$
$101$	−7.06658	−	12.2397i	−0.703151	−	1.21789i	0.264204	−	0.964467i	$-0.414891\pi$
$102$		0			0
$103$	−0.433570	−	0.250322i	−0.0427209	−	0.0246649i	0.478487	−	0.878094i	$-0.341185\pi$
$103$	−0.433570	−	0.250322i	−0.0427209	−	0.0246649i	−0.521208	+	0.853429i	$0.674519\pi$
$104$		0			0
$105$	4.38032	+	10.0837i	0.427476	+	0.984066i
$106$		0			0
$107$	16.0652	+	9.27527i	1.55309	+	0.896674i	0.997888	+	0.0649558i	$0.0206907\pi$
$107$	16.0652	+	9.27527i	1.55309	+	0.896674i	0.555197	+	0.831719i	$0.312643\pi$
$108$		0			0
$109$	−3.92950	+	2.26870i	−0.376378	+	0.217302i	−0.676241	−	0.736680i	$-0.736392\pi$
$109$	−3.92950	+	2.26870i	−0.376378	+	0.217302i	0.299863	+	0.953982i	$0.403059\pi$
$110$		0			0
$111$	4.30722			0.408823
$112$		0			0
$113$		−	6.94668i		−	0.653489i	−0.945113	−	0.326744i	$-0.894048\pi$
$113$		−	6.94668i		−	0.653489i	0.945113	−	0.326744i	$-0.105952\pi$
$114$		0			0
$115$	−19.3153	−	4.03782i	−1.80116	−	0.376529i
$116$		0			0
$117$	−0.262659	−	0.151646i	−0.0242828	−	0.0140197i
$118$		0			0
$119$	8.55131	−	0.791396i	0.783897	−	0.0725471i
$120$		0			0
$121$	0.311339	−	0.539255i	0.0283036	−	0.0490232i
$122$		0			0
$123$	15.0459	−	8.68675i	1.35664	−	0.783258i
$124$		0			0
$125$	−9.11086	−	6.48013i	−0.814901	−	0.579601i
$126$		0			0
$127$	5.54642			0.492166			0.246083	−	0.969249i	$-0.420856\pi$
$127$	5.54642			0.492166			0.246083	+	0.969249i	$0.420856\pi$
$128$		0			0
$129$	11.0165	−	6.36040i	0.969951	−	0.560002i
$130$		0			0
$131$	−1.39758	−	0.806895i	−0.122107	−	0.0704987i	0.437702	−	0.899120i	$-0.355792\pi$
$131$	−1.39758	−	0.806895i	−0.122107	−	0.0704987i	−0.559810	+	0.828621i	$0.689126\pi$
$132$		0			0
$133$	−14.3901	+	10.1841i	−1.24778	+	0.883071i
$134$		0			0
$135$	−3.30385	−	10.0532i	−0.284350	−	0.865238i
$136$		0			0
$137$	7.25548	−	4.18895i	0.619877	−	0.357886i	−0.156944	−	0.987607i	$-0.550164\pi$
$137$	7.25548	−	4.18895i	0.619877	−	0.357886i	0.776821	+	0.629721i	$0.216831\pi$
$138$		0			0
$139$		−	10.1284i		−	0.859077i	−0.903048	−	0.429539i	$-0.858676\pi$
$139$		−	10.1284i		−	0.859077i	0.903048	−	0.429539i	$-0.141324\pi$
$140$		0			0
$141$			6.71235i			0.565282i
$142$		0			0
$143$	1.86632	−	1.07752i	0.156070	−	0.0901070i
$144$		0			0
$145$	−6.74165	+	2.21557i	−0.559864	+	0.183993i
$146$		0			0
$147$	−4.32620	+	12.2678i	−0.356819	+	1.01183i
$148$		0			0
$149$	2.14985	+	1.24122i	0.176123	+	0.101684i	0.585470	−	0.810694i	$-0.300910\pi$
$149$	2.14985	+	1.24122i	0.176123	+	0.101684i	−0.409347	+	0.912379i	$0.634243\pi$
$150$		0			0
$151$	−2.38942	+	1.37954i	−0.194449	+	0.112265i	−0.594063	−	0.804418i	$-0.702477\pi$
$151$	−2.38942	+	1.37954i	−0.194449	+	0.112265i	0.399615	+	0.916683i	$0.369144\pi$
$152$		0			0
$153$	1.47158			0.118970
$154$		0			0
$155$	7.71203	−	8.62317i	0.619445	−	0.692629i
$156$		0			0
$157$	−4.55831	+	2.63174i	−0.363793	+	0.210036i	−0.670743	−	0.741690i	$-0.734025\pi$
$157$	−4.55831	+	2.63174i	−0.363793	+	0.210036i	0.306951	+	0.951725i	$0.400691\pi$
$158$		0			0
$159$	0.0241674	−	0.0418591i	0.00191660	−	0.00331964i
$160$		0			0
$161$	−13.4878	−	19.0583i	−1.06299	−	1.50201i
$162$		0			0
$163$	3.72563	+	2.15099i	0.291814	+	0.168479i	0.638760	−	0.769406i	$-0.279448\pi$
$163$	3.72563	+	2.15099i	0.291814	+	0.168479i	−0.346946	+	0.937885i	$0.612781\pi$
$164$		0			0
$165$	−13.1027	−	2.73909i	−1.02004	−	0.213237i
$166$		0			0
$167$			3.88102i			0.300322i	0.988662	+	0.150161i	$0.0479792\pi$
$167$			3.88102i			0.300322i	−0.988662	+	0.150161i	$0.952021\pi$
$168$		0			0
$169$	12.5525			0.965574
$170$		0			0
$171$	−2.61616	+	1.51044i	−0.200063	+	0.115506i
$172$		0			0
$173$	−14.3964	−	8.31178i	−1.09454	−	0.631933i	−0.159758	−	0.987156i	$-0.551071\pi$
$173$	−14.3964	−	8.31178i	−1.09454	−	0.631933i	−0.934781	+	0.355223i	$0.884405\pi$
$174$		0			0
$175$	−2.67640	−	12.9552i	−0.202317	−	0.979320i
$176$		0			0
$177$	0.0297769	+	0.0171917i	0.00223817	+	0.00129221i
$178$		0			0
$179$	−7.95928	−	13.7859i	−0.594905	−	1.03040i	−0.993560	−	0.113304i	$-0.963856\pi$
$179$	−7.95928	−	13.7859i	−0.594905	−	1.03040i	0.398656	−	0.917101i	$-0.369477\pi$
$180$		0			0
$181$	−7.50289			−0.557685			−0.278843	−	0.960337i	$-0.589951\pi$
$181$	−7.50289			−0.557685			−0.278843	+	0.960337i	$0.589951\pi$
$182$		0			0
$183$	3.33693			0.246673
$184$		0			0
$185$	−5.07309	−	1.06052i	−0.372981	−	0.0779708i
$186$		0			0
$187$	−5.22815	+	9.05542i	−0.382320	+	0.662198i
$188$		0			0
$189$	5.23458	−	11.3742i	0.380759	−	0.827354i
$190$		0			0
$191$	−12.2310	−	7.06156i	−0.885002	−	0.510956i	−0.0126977	−	0.999919i	$-0.504042\pi$
$191$	−12.2310	−	7.06156i	−0.885002	−	0.510956i	−0.872304	+	0.488963i	$0.837375\pi$
$192$		0			0
$193$	−7.10077	+	4.09963i	−0.511124	+	0.295098i	−0.733296	−	0.679910i	$-0.762019\pi$
$193$	−7.10077	+	4.09963i	−0.511124	+	0.295098i	0.222171	+	0.975008i	$0.428686\pi$
$194$		0			0
$195$	2.07206	+	1.85313i	0.148383	+	0.132705i
$196$		0			0
$197$	6.63166			0.472486			0.236243	−	0.971694i	$-0.424084\pi$
$197$	6.63166			0.472486			0.236243	+	0.971694i	$0.424084\pi$
$198$		0			0
$199$	−1.78141	−	3.08549i	−0.126281	−	0.218725i	0.795952	−	0.605360i	$-0.206971\pi$
$199$	−1.78141	−	3.08549i	−0.126281	−	0.218725i	−0.922233	+	0.386635i	$0.873637\pi$
$200$		0			0
$201$	7.70315	+	4.44742i	0.543338	+	0.313697i
$202$		0			0
$203$	−7.62757	−	3.51031i	−0.535350	−	0.246375i
$204$		0			0
$205$	−19.8601	+	6.52678i	−1.38709	+	0.455850i
$206$		0			0
$207$	−2.00043	−	3.46485i	−0.139039	−	0.240823i
$208$		0			0
$209$		−	21.4649i		−	1.48476i
$210$		0			0
$211$	13.5590			0.933438			0.466719	−	0.884406i	$-0.345436\pi$
$211$	13.5590			0.933438			0.466719	+	0.884406i	$0.345436\pi$
$212$		0			0
$213$	13.0936	−	7.55958i	0.897157	−	0.517974i
$214$		0			0
$215$	−14.5414	+	4.77888i	−0.991718	+	0.325917i
$216$		0			0
$217$	13.6300	−	1.26141i	0.925265	−	0.0856303i
$218$		0			0
$219$	11.7138	−	20.2889i	0.791545	−	1.37100i
$220$		0			0
$221$	1.88053	−	1.08572i	0.126498	−	0.0730337i
$222$		0			0
$223$		−	17.5244i		−	1.17352i	−0.809760	−	0.586761i	$-0.800403\pi$
$223$		−	17.5244i		−	1.17352i	0.809760	−	0.586761i	$-0.199597\pi$
$224$		0			0
$225$	−0.252091	−	2.25276i	−0.0168061	−	0.150184i
$226$		0			0
$227$	−5.47563	−	9.48408i	−0.363431	−	0.629480i	0.625092	−	0.780551i	$-0.285061\pi$
$227$	−5.47563	−	9.48408i	−0.363431	−	0.629480i	−0.988523	+	0.151071i	$0.951728\pi$
$228$		0			0
$229$	−9.35182	+	16.1978i	−0.617985	+	1.07038i	0.371867	+	0.928286i	$0.378718\pi$
$229$	−9.35182	+	16.1978i	−0.617985	+	1.07038i	−0.989853	+	0.142096i	$0.954616\pi$
$230$		0			0
$231$	−9.14955	−	12.9284i	−0.601996	−	0.850624i
$232$		0			0
$233$	3.70368	+	2.13832i	0.242636	+	0.140086i	0.616388	−	0.787443i	$-0.288595\pi$
$233$	3.70368	+	2.13832i	0.242636	+	0.140086i	−0.373752	+	0.927529i	$0.621929\pi$
$234$		0			0
$235$	1.65270	−	7.90588i	0.107811	−	0.515723i
$236$		0			0
$237$		−	29.0342i		−	1.88597i
$238$		0			0
$239$			25.1064i			1.62400i	0.583658	+	0.812000i	$0.301621\pi$
$239$			25.1064i			1.62400i	−0.583658	+	0.812000i	$0.698379\pi$
$240$		0			0
$241$	1.69808	−	0.980389i	0.109383	−	0.0631524i	−0.444310	−	0.895873i	$-0.646551\pi$
$241$	1.69808	−	0.980389i	0.109383	−	0.0631524i	0.553694	+	0.832721i	$0.313218\pi$
$242$		0			0
$243$	2.33652	−	4.04696i	0.149888	−	0.259613i
$244$		0			0
$245$	8.11601	−	13.3840i	0.518513	−	0.855070i
$246$		0			0
$247$	−2.22879	+	3.86038i	−0.141815	+	0.245630i
$248$		0			0
$249$	6.13537	+	10.6268i	0.388813	+	0.673444i
$250$		0			0
$251$		−	10.2716i		−	0.648336i	−0.945999	−	0.324168i	$-0.894916\pi$
$251$		−	10.2716i		−	0.648336i	0.945999	−	0.324168i	$-0.105084\pi$
$252$		0			0
$253$	28.4281			1.78726
$254$		0			0
$255$	−13.2024	−	2.75993i	−0.826768	−	0.172834i
$256$		0			0
$257$	4.42809	−	7.66968i	0.276217	−	0.478422i	−0.694225	−	0.719759i	$-0.744253\pi$
$257$	4.42809	−	7.66968i	0.276217	−	0.478422i	0.970441	+	0.241337i	$0.0775859\pi$
$258$		0			0
$259$	−3.54252	−	5.00559i	−0.220121	−	0.311032i
$260$		0			0
$261$	−1.24604	−	0.719399i	−0.0771277	−	0.0445297i
$262$		0			0
$263$	−6.21178	−	10.7591i	−0.383035	−	0.663436i	0.608459	−	0.793585i	$-0.291788\pi$
$263$	−6.21178	−	10.7591i	−0.383035	−	0.663436i	−0.991494	+	0.130149i	$0.958454\pi$
$264$		0			0
$265$	−0.0387711	+	0.0433517i	−0.00238169	+	0.00266307i
$266$		0			0
$267$			2.82563i			0.172926i
$268$		0			0
$269$	13.6032	+	23.5615i	0.829403	+	1.43657i	0.898507	+	0.438959i	$0.144653\pi$
$269$	13.6032	+	23.5615i	0.829403	+	1.43657i	−0.0691035	+	0.997609i	$0.522014\pi$
$270$		0			0
$271$	−5.19784	+	9.00292i	−0.315746	+	0.546889i	−0.979596	−	0.200978i	$-0.935588\pi$
$271$	−5.19784	+	9.00292i	−0.315746	+	0.546889i	0.663850	+	0.747866i	$0.268922\pi$
$272$		0			0
$273$	0.303105	+	3.27516i	0.0183448	+	0.198221i
$274$		0			0
$275$	14.7581	+	6.45225i	0.889947	+	0.389085i
$276$		0			0
$277$	10.2142	+	17.6915i	0.613711	+	1.06298i	0.990609	+	0.136724i	$0.0436574\pi$
$277$	10.2142	+	17.6915i	0.613711	+	1.06298i	−0.376898	+	0.926255i	$0.623009\pi$
$278$		0			0
$279$	2.34556			0.140425
$280$		0			0
$281$	−31.1658			−1.85919			−0.929597	−	0.368578i	$-0.879845\pi$
$281$	−31.1658			−1.85919			−0.929597	+	0.368578i	$0.879845\pi$
$282$		0			0
$283$	7.09232	+	12.2843i	0.421594	+	0.730223i	0.996096	−	0.0882807i	$-0.0281373\pi$
$283$	7.09232	+	12.2843i	0.421594	+	0.730223i	−0.574501	+	0.818504i	$0.694804\pi$
$284$		0			0
$285$	26.3040	−	8.64449i	1.55811	−	0.512056i
$286$		0			0
$287$	−22.4699	−	10.3409i	−1.32635	−	0.610406i
$288$		0			0
$289$	3.23206	−	5.59809i	0.190121	−	0.329299i
$290$		0			0
$291$	11.3079	+	19.5859i	0.662881	+	1.14814i
$292$		0			0
$293$		−	13.3400i		−	0.779333i	−0.920956	−	0.389666i	$-0.872590\pi$
$293$		−	13.3400i		−	0.779333i	0.920956	−	0.389666i	$-0.127410\pi$
$294$		0			0
$295$	−0.0308387	−	0.0275802i	−0.00179550	−	0.00160578i
$296$		0			0
$297$	7.62256	+	13.2027i	0.442306	+	0.766096i
$298$		0			0
$299$	−5.11269	−	2.95181i	−0.295675	−	0.170708i
$300$		0			0
$301$	−16.4523	−	7.57158i	−0.948296	−	0.436418i
$302$		0			0
$303$	−13.1320	+	22.7453i	−0.754413	+	1.30668i
$304$		0			0
$305$	−3.93028	−	0.821615i	−0.225047	−	0.0470455i
$306$		0			0
$307$	15.5134			0.885395			0.442697	−	0.896671i	$-0.354022\pi$
$307$	15.5134			0.885395			0.442697	+	0.896671i	$0.354022\pi$
$308$		0			0
$309$			0.930357i			0.0529262i
$310$		0			0
$311$	−4.58870	−	7.94786i	−0.260201	−	0.450682i	0.706094	−	0.708118i	$-0.250456\pi$
$311$	−4.58870	−	7.94786i	−0.260201	−	0.450682i	−0.966295	+	0.257436i	$0.917122\pi$
$312$		0			0
$313$	16.2088	−	28.0744i	0.916175	−	1.58686i	0.111002	−	0.993820i	$-0.464594\pi$
$313$	16.2088	−	28.0744i	0.916175	−	1.58686i	0.805172	−	0.593041i	$-0.202073\pi$
$314$		0			0
$315$	1.59615	−	2.15550i	0.0899330	−	0.121449i
$316$		0			0
$317$	−0.205982	+	0.356772i	−0.0115691	+	0.0200383i	−0.871752	−	0.489947i	$-0.837016\pi$
$317$	−0.205982	+	0.356772i	−0.0115691	+	0.0200383i	0.860183	+	0.509986i	$0.170349\pi$
$318$		0			0
$319$	8.85371	−	5.11169i	0.495713	−	0.286200i
$320$		0			0
$321$		−	34.4729i		−	1.92409i
$322$		0			0
$323$		−	21.6282i		−	1.20343i
$324$		0			0
$325$	−1.98423	−	2.69281i	−0.110065	−	0.149370i
$326$		0			0
$327$	7.30229	+	4.21598i	0.403817	+	0.233144i
$328$		0			0
$329$	7.80069	−	5.52064i	0.430066	−	0.304363i
$330$		0			0
$331$	−14.7269	+	25.5078i	−0.809465	+	1.40203i	0.103770	+	0.994601i	$0.466909\pi$
$331$	−14.7269	+	25.5078i	−0.809465	+	1.40203i	−0.913235	+	0.407433i	$0.866424\pi$
$332$		0			0
$333$	−0.525405	−	0.910027i	−0.0287920	−	0.0498692i
$334$		0			0
$335$	−7.97783	−	7.13488i	−0.435875	−	0.389820i
$336$		0			0
$337$		−	0.726788i		−	0.0395906i	−0.999804	−	0.0197953i	$-0.993699\pi$
$337$		−	0.726788i		−	0.0395906i	0.999804	−	0.0197953i	$-0.00630146\pi$
$338$		0			0
$339$	−11.1797	+	6.45459i	−0.607197	+	0.350565i
$340$		0			0
$341$	−8.33319	+	14.4335i	−0.451268	+	0.781619i
$342$		0			0
$343$	17.8150	−	5.06212i	0.961921	−	0.273329i
$344$		0			0
$345$	11.4488	+	34.8370i	0.616382	+	1.87556i
$346$		0			0
$347$	14.4004	−	8.31409i	0.773056	−	0.446324i	−0.0609078	−	0.998143i	$-0.519400\pi$
$347$	14.4004	−	8.31409i	0.773056	−	0.446324i	0.833964	+	0.551819i	$0.186066\pi$
$348$		0			0
$349$	33.3428			1.78480			0.892401	−	0.451244i	$-0.149020\pi$
$349$	33.3428			1.78480			0.892401	+	0.451244i	$0.149020\pi$
$350$		0			0
$351$		−	3.16593i		−	0.168985i
$352$		0			0
$353$	4.25151	+	7.36384i	0.226285	+	0.391938i	0.956704	−	0.291062i	$-0.0940085\pi$
$353$	4.25151	+	7.36384i	0.226285	+	0.391938i	−0.730419	+	0.682999i	$0.760675\pi$
$354$		0			0
$355$	−17.2831	+	5.67988i	−0.917290	+	0.301457i
$356$		0			0
$357$	−9.21918	−	13.0268i	−0.487931	−	0.689449i
$358$		0			0
$359$	−28.2304	−	16.2989i	−1.48995	−	0.860220i	−0.490012	−	0.871716i	$-0.663007\pi$
$359$	−28.2304	−	16.2989i	−1.48995	−	0.860220i	−0.999934	+	0.0114955i	$0.996341\pi$
$360$		0			0
$361$	12.6994	+	21.9960i	0.668389	+	1.15768i
$362$		0			0
$363$	−1.15714			−0.0607340
$364$		0			0
$365$	−18.7921	+	21.0123i	−0.983625	+	1.09984i
$366$		0			0
$367$	3.02375	−	1.74576i	0.157838	−	0.0911280i	−0.419000	−	0.907986i	$-0.637619\pi$
$367$	3.02375	−	1.74576i	0.157838	−	0.0911280i	0.576839	+	0.816858i	$0.304286\pi$
$368$		0			0
$369$	−3.67067	−	2.11926i	−0.191087	−	0.110324i
$370$		0			0
$371$	−0.0685228	+	0.00634157i	−0.00355753	+	0.000329238i
$372$		0			0
$373$	12.1896	−	21.1129i	0.631151	−	1.09319i	−0.356165	−	0.934423i	$-0.615916\pi$
$373$	12.1896	−	21.1129i	0.631151	−	1.09319i	0.987317	−	0.158763i	$-0.0507507\pi$
$374$		0			0
$375$	−1.96337	+	20.6837i	−0.101388	+	1.06810i
$376$		0			0
$377$	−2.12308			−0.109344
$378$		0			0
$379$	33.6902			1.73055			0.865274	−	0.501299i	$-0.167144\pi$
$379$	33.6902			1.73055			0.865274	+	0.501299i	$0.167144\pi$
$380$		0			0
$381$	−5.15352	−	8.92617i	−0.264023	−	0.457301i
$382$		0			0
$383$	12.7966	+	7.38811i	0.653875	+	0.377515i	0.789939	−	0.613185i	$-0.210112\pi$
$383$	12.7966	+	7.38811i	0.653875	+	0.377515i	−0.136064	+	0.990700i	$0.543445\pi$
$384$		0			0
$385$	7.59324	+	17.4800i	0.386987	+	0.890861i
$386$		0			0
$387$	−2.68764	−	1.55171i	−0.136621	−	0.0788779i
$388$		0			0
$389$	−0.178263	+	0.102920i	−0.00903829	+	0.00521826i	−0.504512	−	0.863404i	$-0.668328\pi$
$389$	−0.178263	+	0.102920i	−0.00903829	+	0.00521826i	0.495474	+	0.868623i	$0.334994\pi$
$390$		0			0
$391$	28.6445			1.44861
$392$		0			0
$393$			2.99894i			0.151277i
$394$		0			0
$395$	−7.14874	+	34.1968i	−0.359692	+	1.72063i
$396$		0			0
$397$	4.39175	+	2.53558i	0.220416	+	0.127257i	0.606143	−	0.795356i	$-0.292716\pi$
$397$	4.39175	+	2.53558i	0.220416	+	0.127257i	−0.385727	+	0.922613i	$0.626049\pi$
$398$		0			0
$399$	29.7605	+	13.6962i	1.48989	+	0.685668i
$400$		0			0
$401$	−9.62688	+	16.6743i	−0.480744	+	0.832672i	−0.999756	−	0.0220944i	$-0.992967\pi$
$401$	−9.62688	+	16.6743i	−0.480744	+	0.832672i	0.519012	+	0.854767i	$0.326300\pi$
$402$		0			0
$403$	2.99739	−	1.73054i	0.149311	−	0.0862045i
$404$		0			0
$405$	−15.1367	+	16.9250i	−0.752148	+	0.841010i
$406$		0			0
$407$	7.46653			0.370102
$408$		0			0
$409$	−18.9967	+	10.9678i	−0.939327	+	0.542321i	−0.889749	−	0.456450i	$-0.849121\pi$
$409$	−18.9967	+	10.9678i	−0.939327	+	0.542321i	−0.0495776	+	0.998770i	$0.515788\pi$
$410$		0			0
$411$	−13.4830	−	7.78442i	−0.665068	−	0.383977i
$412$		0			0
$413$	−0.00451114	−	0.0487445i	−0.000221979	−	0.00239856i
$414$		0			0
$415$	−4.60980	−	14.0270i	−0.226286	−	0.688557i
$416$		0			0
$417$	−16.3001	+	9.41089i	−0.798222	+	0.460853i
$418$		0			0
$419$		−	20.3822i		−	0.995734i	−0.867253	−	0.497867i	$-0.834117\pi$
$419$		−	20.3822i		−	0.995734i	0.867253	−	0.497867i	$-0.165883\pi$
$420$		0			0
$421$			21.2887i			1.03755i	0.854912	+	0.518774i	$0.173611\pi$
$421$			21.2887i			1.03755i	−0.854912	+	0.518774i	$0.826389\pi$
$422$		0			0
$423$	1.41818	−	0.818788i	0.0689544	−	0.0398108i
$424$		0			0
$425$	14.8704	+	6.50136i	0.721321	+	0.315362i
$426$		0			0
$427$	−2.74449	−	3.87798i	−0.132815	−	0.187669i
$428$		0			0
$429$	−3.46823	−	2.00239i	−0.167448	−	0.0966761i
$430$		0			0
$431$	18.7227	−	10.8096i	0.901842	−	0.520679i	0.0240450	−	0.999711i	$-0.492346\pi$
$431$	18.7227	−	10.8096i	0.901842	−	0.520679i	0.877797	+	0.479032i	$0.159012\pi$
$432$		0			0
$433$	−29.8068			−1.43243			−0.716213	−	0.697882i	$-0.754126\pi$
$433$	−29.8068			−1.43243			−0.716213	+	0.697882i	$0.754126\pi$
$434$		0			0
$435$	9.82972	+	8.79110i	0.471299	+	0.421501i
$436$		0			0
$437$	−50.9239	+	29.4009i	−2.43602	+	1.40644i
$438$		0			0
$439$	14.9755	−	25.9383i	0.714740	−	1.23797i	−0.248320	−	0.968678i	$-0.579878\pi$
$439$	14.9755	−	25.9383i	0.714740	−	1.23797i	0.963060	−	0.269288i	$-0.0867883\pi$
$440$		0			0
$441$	3.11965	−	0.582416i	0.148555	−	0.0277341i
$442$		0			0
$443$	−32.1133	−	18.5406i	−1.52575	−	0.880893i	−0.999533	−	0.0305429i	$-0.990276\pi$
$443$	−32.1133	−	18.5406i	−1.52575	−	0.880893i	−0.526218	−	0.850350i	$-0.676390\pi$
$444$		0			0
$445$	0.695721	−	3.32806i	0.0329803	−	0.157765i
$446$		0			0
$447$		−	4.61317i		−	0.218195i
$448$		0			0
$449$	17.1980			0.811625			0.405813	−	0.913956i	$-0.366989\pi$
$449$	17.1980			0.811625			0.405813	+	0.913956i	$0.366989\pi$
$450$		0			0
$451$	26.0819	−	15.0584i	1.22815	−	0.709073i
$452$		0			0
$453$	4.44032	+	2.56362i	0.208625	+	0.120449i
$454$		0			0
$455$	0.449403	−	3.93215i	0.0210683	−	0.184342i
$456$		0			0
$457$	8.54674	+	4.93447i	0.399800	+	0.230825i	0.686398	−	0.727226i	$-0.259191\pi$
$457$	8.54674	+	4.93447i	0.399800	+	0.230825i	−0.286598	+	0.958051i	$0.592524\pi$
$458$		0			0
$459$	7.68057	+	13.3031i	0.358498	+	0.620937i
$460$		0			0
$461$	19.0434			0.886938			0.443469	−	0.896290i	$-0.353748\pi$
$461$	19.0434			0.886938			0.443469	+	0.896290i	$0.353748\pi$
$462$		0			0
$463$	15.5965			0.724831			0.362415	−	0.932017i	$-0.381952\pi$
$463$	15.5965			0.724831			0.362415	+	0.932017i	$0.381952\pi$
$464$		0			0
$465$	−21.0435	−	4.39908i	−0.975867	−	0.204002i
$466$		0			0
$467$	11.3528	−	19.6636i	0.525343	−	0.909921i	−0.474221	−	0.880406i	$-0.657270\pi$
$467$	11.3528	−	19.6636i	0.525343	−	0.909921i	0.999564	−	0.0295151i	$-0.00939632\pi$
$468$		0			0
$469$	−1.16701	−	12.6100i	−0.0538876	−	0.582274i
$470$		0			0
$471$	8.47081	+	4.89062i	0.390314	+	0.225348i
$472$		0			0
$473$	19.0970	−	11.0257i	0.878083	−	0.506961i
$474$		0			0
$475$	−33.1095	+	3.70506i	−1.51917	+	0.170000i
$476$		0			0
$477$	−0.0117920			−0.000539917
$478$		0			0
$479$	17.2162	+	29.8193i	0.786626	+	1.36248i	0.928023	+	0.372523i	$0.121507\pi$
$479$	17.2162	+	29.8193i	0.786626	+	1.36248i	−0.141397	+	0.989953i	$0.545159\pi$
$480$		0			0
$481$	−1.34283	−	0.775282i	−0.0612277	−	0.0353498i
$482$		0			0
$483$	−18.1393	+	39.4149i	−0.825366	+	1.79344i
$484$		0			0
$485$	−8.49618	−	25.8527i	−0.385792	−	1.17391i
$486$		0			0
$487$	−0.417834	−	0.723709i	−0.0189338	−	0.0327944i	0.856403	−	0.516308i	$-0.172694\pi$
$487$	−0.417834	−	0.723709i	−0.0189338	−	0.0327944i	−0.875337	+	0.483513i	$0.839361\pi$
$488$		0			0
$489$		−	7.99448i		−	0.361523i
$490$		0			0
$491$	−28.3101			−1.27762			−0.638809	−	0.769365i	$-0.720573\pi$
$491$	−28.3101			−1.27762			−0.638809	+	0.769365i	$0.720573\pi$
$492$		0			0
$493$	8.92109	−	5.15060i	0.401786	−	0.231971i
$494$		0			0
$495$	1.01958	+	3.10245i	0.0458269	+	0.139445i
$496$		0			0
$497$	−19.5542	−	8.99911i	−0.877127	−	0.403665i
$498$		0			0
$499$	−2.19914	+	3.80903i	−0.0984472	+	0.170516i	−0.911042	−	0.412313i	$-0.864721\pi$
$499$	−2.19914	+	3.80903i	−0.0984472	+	0.170516i	0.812595	+	0.582829i	$0.198054\pi$
$500$		0			0
$501$	6.24594	−	3.60609i	0.279048	−	0.161108i
$502$		0			0
$503$		−	21.2435i		−	0.947200i	−0.880740	−	0.473600i	$-0.842954\pi$
$503$		−	21.2435i		−	0.947200i	0.880740	−	0.473600i	$-0.157046\pi$
$504$		0			0
$505$	21.0673	−	23.5563i	0.937482	−	1.04824i
$506$		0			0
$507$	−11.6633	−	20.2014i	−0.517984	−	0.897174i
$508$		0			0
$509$	4.64622	−	8.04750i	0.205940	−	0.356699i	−0.744492	−	0.667632i	$-0.767308\pi$
$509$	4.64622	−	8.04750i	0.205940	−	0.356699i	0.950432	+	0.310933i	$0.100641\pi$
$510$		0			0
$511$	−33.2126	+	3.07372i	−1.46924	+	0.135973i
$512$		0			0
$513$	−27.3089	−	15.7668i	−1.20572	−	0.696121i
$514$		0			0
$515$	0.229071	−	1.09579i	0.0100941	−	0.0482861i
$516$		0			0
$517$			11.6358i			0.511742i
$518$		0			0
$519$			30.8919i			1.35601i
$520$		0			0
$521$	19.2972	−	11.1412i	0.845425	−	0.488106i	−0.0136798	−	0.999906i	$-0.504355\pi$
$521$	19.2972	−	11.1412i	0.845425	−	0.488106i	0.859104	+	0.511800i	$0.171021\pi$
$522$		0			0
$523$	1.18906	−	2.05951i	0.0519939	−	0.0900560i	−0.838857	−	0.544352i	$-0.816776\pi$
$523$	1.18906	−	2.05951i	0.0519939	−	0.0900560i	0.890851	+	0.454296i	$0.150109\pi$
$524$		0			0
$525$	−18.3627	+	16.3447i	−0.801413	+	0.713343i
$526$		0			0
$527$	−8.39662	+	14.5434i	−0.365762	+	0.633519i
$528$		0			0
$529$	−27.4386	−	47.5251i	−1.19298	−	2.06631i
$530$		0			0
$531$		−	0.00838834i		−	0.000364023i
$532$		0			0
$533$	−6.25432			−0.270905
$534$		0			0
$535$	−8.48786	+	40.6026i	−0.366962	+	1.75540i
$536$		0			0
$537$	−14.7909	+	25.6186i	−0.638275	+	1.10552i
$538$		0			0
$539$	−7.49943	+	21.2661i	−0.323023	+	0.915996i
$540$		0			0
$541$	−18.1918	−	10.5031i	−0.782128	−	0.451562i	0.0550562	−	0.998483i	$-0.482466\pi$
$541$	−18.1918	−	10.5031i	−0.782128	−	0.451562i	−0.837184	+	0.546922i	$0.815800\pi$
$542$		0			0
$543$	6.97140	+	12.0748i	0.299171	+	0.518180i
$544$		0			0
$545$	−7.56266	−	6.76358i	−0.323949	−	0.289720i
$546$		0			0
$547$		−	14.9270i		−	0.638234i	−0.947715	−	0.319117i	$-0.896614\pi$
$547$		−	14.9270i		−	0.638234i	0.947715	−	0.319117i	$-0.103386\pi$
$548$		0			0
$549$	−0.407047	−	0.705026i	−0.0173723	−	0.0300898i
$550$		0			0
$551$	−10.5732	+	18.3134i	−0.450434	+	0.780175i
$552$		0			0
$553$	−33.7417	+	23.8794i	−1.43485	+	1.01546i
$554$		0			0
$555$	3.00698	+	9.14980i	0.127639	+	0.388387i
$556$		0			0
$557$	1.63827	+	2.83757i	0.0694157	+	0.120232i	0.898644	−	0.438678i	$-0.144553\pi$
$557$	1.63827	+	2.83757i	0.0694157	+	0.120232i	−0.829229	+	0.558910i	$0.811220\pi$
$558$		0			0
$559$	−4.57938			−0.193687
$560$		0			0
$561$	19.4312			0.820385
$562$		0			0
$563$	4.29192	+	7.43383i	0.180883	+	0.313299i	0.942181	−	0.335103i	$-0.108771\pi$
$563$	4.29192	+	7.43383i	0.180883	+	0.313299i	−0.761298	+	0.648402i	$0.775438\pi$
$564$		0			0
$565$	14.7568	−	4.84965i	0.620823	−	0.204026i
$566$		0			0
$567$	−26.7521	+	2.47582i	−1.12348	+	0.103975i
$568$		0			0
$569$	−12.8908	+	22.3275i	−0.540411	+	0.936019i	0.458470	+	0.888710i	$0.348398\pi$
$569$	−12.8908	+	22.3275i	−0.540411	+	0.936019i	−0.998880	+	0.0473086i	$0.984936\pi$
$570$		0			0
$571$	15.5532	+	26.9389i	0.650881	+	1.12736i	0.982909	+	0.184089i	$0.0589336\pi$
$571$	15.5532	+	26.9389i	0.650881	+	1.12736i	−0.332029	+	0.943269i	$0.607733\pi$
$572$		0			0
$573$			26.2453i			1.09641i
$574$		0			0
$575$	−4.90699	−	43.8503i	−0.204636	−	1.82869i
$576$		0			0
$577$	10.1101	+	17.5112i	0.420889	+	0.729001i	0.996027	−	0.0890553i	$-0.0283848\pi$
$577$	10.1101	+	17.5112i	0.420889	+	0.729001i	−0.575137	+	0.818057i	$0.695051\pi$
$578$		0			0
$579$	13.1955	+	7.61844i	0.548387	+	0.316611i
$580$		0			0
$581$	7.30370	−	15.8702i	0.303008	−	0.658409i
$582$		0			0
$583$	0.0418939	−	0.0725624i	0.00173507	−	0.00300523i
$584$		0			0
$585$	0.138772	−	0.663833i	0.00573753	−	0.0274461i
$586$		0			0
$587$	−21.6836			−0.894976			−0.447488	−	0.894290i	$-0.647681\pi$
$587$	−21.6836			−0.894976			−0.447488	+	0.894290i	$0.647681\pi$
$588$		0			0
$589$		−	34.4734i		−	1.42045i
$590$		0			0
$591$	−6.16188	−	10.6727i	−0.253466	−	0.439016i
$592$		0			0
$593$	14.9180	−	25.8387i	0.612609	−	1.06107i	−0.378190	−	0.925728i	$-0.623453\pi$
$593$	14.9180	−	25.8387i	0.612609	−	1.06107i	0.990799	−	0.135342i	$-0.0432133\pi$
$594$		0			0
$595$	7.65103	+	17.6130i	0.313662	+	0.722062i
$596$		0			0
$597$	−3.31044	+	5.73384i	−0.135487	+	0.234671i
$598$		0			0
$599$	−6.90813	+	3.98841i	−0.282259	+	0.162962i	−0.634445	−	0.772968i	$-0.718771\pi$
$599$	−6.90813	+	3.98841i	−0.282259	+	0.162962i	0.352187	+	0.935930i	$0.385438\pi$
$600$		0			0
$601$			42.8990i			1.74989i	0.484224	+	0.874944i	$0.339102\pi$
$601$			42.8990i			1.74989i	−0.484224	+	0.874944i	$0.660898\pi$
$602$		0			0
$603$		−	2.17002i		−	0.0883702i
$604$		0			0
$605$	1.36289	+	0.284909i	0.0554094	+	0.0115832i
$606$		0			0
$607$	24.6567	+	14.2355i	1.00078	+	0.577802i	0.908480	−	0.417929i	$-0.137244\pi$
$607$	24.6567	+	14.2355i	1.00078	+	0.577802i	0.0923032	+	0.995731i	$0.470577\pi$
$608$		0			0
$609$	1.43791	+	15.5371i	0.0582670	+	0.629596i
$610$		0			0
$611$	1.20820	−	2.09266i	0.0488783	−	0.0846598i
$612$		0			0
$613$	13.6922	+	23.7156i	0.553022	+	0.957863i	0.998054	+	0.0623483i	$0.0198589\pi$
$613$	13.6922	+	23.7156i	0.553022	+	0.957863i	−0.445032	+	0.895515i	$0.646808\pi$
$614$		0			0
$615$	28.9571	+	25.8975i	1.16766	+	1.04429i
$616$		0			0
$617$			26.4349i			1.06423i	0.846673	+	0.532114i	$0.178602\pi$
$617$			26.4349i			1.06423i	−0.846673	+	0.532114i	$0.821398\pi$
$618$		0			0
$619$	6.44010	−	3.71819i	0.258850	−	0.149447i	−0.364960	−	0.931023i	$-0.618917\pi$
$619$	6.44010	−	3.71819i	0.258850	−	0.149447i	0.623810	+	0.781576i	$0.285584\pi$
$620$		0			0
$621$	20.8816	−	36.1679i	0.837949	−	1.45137i
$622$		0			0
$623$	3.28377	−	2.32396i	0.131562	−	0.0931076i
$624$		0			0
$625$	7.40519	−	23.8781i	0.296208	−	0.955124i
$626$		0			0
$627$	−34.5446	+	19.9443i	−1.37958	+	0.796500i
$628$		0			0
$629$	7.52335			0.299976
$630$		0			0
$631$			23.0524i			0.917701i	0.888514	+	0.458850i	$0.151739\pi$
$631$			23.0524i			0.917701i	−0.888514	+	0.458850i	$0.848261\pi$
$632$		0			0
$633$	−12.5985	−	21.8212i	−0.500744	−	0.867315i
$634$		0			0
$635$	3.87209	+	11.7822i	0.153659	+	0.467564i
$636$		0			0
$637$	3.55690	−	3.04593i	0.140929	−	0.120684i
$638$		0			0
$639$	−3.19437	−	1.84427i	−0.126367	−	0.0729581i
$640$		0			0
$641$	4.04336	+	7.00330i	0.159703	+	0.276614i	0.934762	−	0.355276i	$-0.115613\pi$
$641$	4.04336	+	7.00330i	0.159703	+	0.276614i	−0.775059	+	0.631889i	$0.782280\pi$
$642$		0			0
$643$	22.3144			0.879995			0.439998	−	0.897999i	$-0.354979\pi$
$643$	22.3144			0.879995			0.439998	+	0.897999i	$0.354979\pi$
$644$		0			0
$645$	21.2023	+	18.9620i	0.834838	+	0.746628i
$646$		0			0
$647$	−1.37529	+	0.794021i	−0.0540681	+	0.0312162i	−0.526790	−	0.849995i	$-0.676605\pi$
$647$	−1.37529	+	0.794021i	−0.0540681	+	0.0312162i	0.472722	+	0.881211i	$0.343271\pi$
$648$		0			0
$649$	0.0516180	+	0.0298017i	0.00202618	+	0.00116982i
$650$		0			0
$651$	−14.6945	−	20.7635i	−0.575924	−	0.813784i
$652$		0			0
$653$	−22.2296	+	38.5028i	−0.869912	+	1.50673i	−0.00782554	+	0.999969i	$0.502491\pi$
$653$	−22.2296	+	38.5028i	−0.869912	+	1.50673i	−0.862086	+	0.506762i	$0.830842\pi$
$654$		0			0
$655$	0.738395	−	3.53219i	0.0288515	−	0.138014i
$656$		0			0
$657$	−5.71550			−0.222983
$658$		0			0
$659$	−6.14200			−0.239259			−0.119629	−	0.992819i	$-0.538171\pi$
$659$	−6.14200			−0.239259			−0.119629	+	0.992819i	$0.538171\pi$
$660$		0			0
$661$	−4.19173	−	7.26029i	−0.163039	−	0.282393i	0.772918	−	0.634506i	$-0.218796\pi$
$661$	−4.19173	−	7.26029i	−0.163039	−	0.282393i	−0.935957	+	0.352114i	$0.885463\pi$
$662$		0			0
$663$	−3.49463	−	2.01762i	−0.135720	−	0.0783581i
$664$		0			0
$665$	−31.6801	−	23.4591i	−1.22850	−	0.909706i
$666$		0			0
$667$	−24.2543	−	14.0032i	−0.939128	−	0.542206i
$668$		0			0
$669$	−28.2030	+	16.2830i	−1.09039	+	0.629538i
$670$		0			0
$671$	5.78454			0.223310
$672$		0			0
$673$		−	5.56001i		−	0.214323i	−0.994242	−	0.107161i	$-0.965824\pi$
$673$		−	5.56001i		−	0.214323i	0.994242	−	0.107161i	$-0.0341761\pi$
$674$		0			0
$675$	19.0494	−	14.0367i	0.733210	−	0.540273i
$676$		0			0
$677$	13.5074	+	7.79851i	0.519132	+	0.299721i	0.736579	−	0.676351i	$-0.236440\pi$
$677$	13.5074	+	7.79851i	0.519132	+	0.299721i	−0.217447	+	0.976072i	$0.569773\pi$
$678$		0			0
$679$	13.4612	−	29.2500i	0.516594	−	1.12251i
$680$		0			0
$681$	−10.1755	+	17.6245i	−0.389926	+	0.675371i
$682$		0			0
$683$	−13.9790	+	8.07076i	−0.534890	+	0.308819i	−0.743006	−	0.669285i	$-0.766600\pi$
$683$	−13.9790	+	8.07076i	−0.534890	+	0.308819i	0.208115	+	0.978104i	$0.433267\pi$
$684$		0			0
$685$	13.9638	+	12.4883i	0.533529	+	0.477155i
$686$		0			0
$687$	34.7574			1.32608
$688$		0			0
$689$	−0.0150689	+	0.00870005i	−0.000574081	+	0.000331446i
$690$		0			0
$691$	−12.5750	−	7.26020i	−0.478377	−	0.276191i	0.241363	−	0.970435i	$-0.422406\pi$
$691$	−12.5750	−	7.26020i	−0.478377	−	0.276191i	−0.719740	+	0.694244i	$0.755739\pi$
$692$		0			0
$693$	−1.61541	+	3.51014i	−0.0613645	+	0.133339i
$694$		0			0
$695$	21.5156	−	7.07086i	0.816135	−	0.268213i
$696$		0			0
$697$	26.2804	−	15.1730i	0.995442	−	0.574719i
$698$		0			0
$699$		−	7.94737i		−	0.300597i
$700$		0			0
$701$			50.0391i			1.88995i	0.327140	+	0.944976i	$0.393915\pi$
$701$			50.0391i			1.88995i	−0.327140	+	0.944976i	$0.606085\pi$
$702$		0			0
$703$	−13.3749	+	7.72203i	−0.504446	+	0.291242i
$704$		0			0
$705$	−14.2590	+	4.68606i	−0.537025	+	0.176487i
$706$		0			0
$707$	37.2337	−	3.44586i	1.40032	−	0.129595i
$708$		0			0
$709$	24.6072	+	14.2069i	0.924141	+	0.533553i	0.884954	−	0.465679i	$-0.154190\pi$
$709$	24.6072	+	14.2069i	0.924141	+	0.533553i	0.0391872	+	0.999232i	$0.487523\pi$
$710$		0			0
$711$	−6.13432	+	3.54165i	−0.230055	+	0.132822i
$712$		0			0
$713$	45.6567			1.70986
$714$		0			0
$715$	3.59190	+	3.21237i	0.134329	+	0.120136i
$716$		0			0
$717$	40.4051	−	23.3279i	1.50896	−	0.871197i
$718$		0			0
$719$	6.99938	−	12.1233i	0.261033	−	0.452122i	−0.705484	−	0.708726i	$-0.749270\pi$
$719$	6.99938	−	12.1233i	0.261033	−	0.452122i	0.966517	+	0.256604i	$0.0826036\pi$
$720$		0			0
$721$	1.08121	−	0.765181i	0.0402662	−	0.0284968i
$722$		0			0
$723$	−3.15559	−	1.82188i	−0.117358	−	0.0677564i
$724$		0			0
$725$	−9.41303	−	12.7745i	−0.349591	−	0.474433i
$726$		0			0
$727$			27.8172i			1.03168i	0.856684	+	0.515842i	$0.172521\pi$
$727$			27.8172i			1.03168i	−0.856684	+	0.515842i	$0.827479\pi$
$728$		0			0
$729$	21.7797			0.806654
$730$		0			0
$731$	19.2424	−	11.1096i	0.711705	−	0.410903i
$732$		0			0
$733$	−40.1317	−	23.1700i	−1.48230	−	0.855804i	−0.482498	−	0.875897i	$-0.660271\pi$
$733$	−40.1317	−	23.1700i	−1.48230	−	0.855804i	−0.999798	+	0.0200925i	$0.993604\pi$
$734$		0			0
$735$	−29.0806	−	0.625674i	−1.07266	−	0.0230783i
$736$		0			0
$737$	13.3533	+	7.70955i	0.491877	+	0.283985i
$738$		0			0
$739$	4.81690	+	8.34311i	0.177192	+	0.306906i	0.940918	−	0.338635i	$-0.109965\pi$
$739$	4.81690	+	8.34311i	0.177192	+	0.306906i	−0.763725	+	0.645541i	$0.776632\pi$
$740$		0			0
$741$	8.28362			0.304307
$742$		0			0
$743$	−32.6002			−1.19599			−0.597993	−	0.801501i	$-0.704035\pi$
$743$	−32.6002			−1.19599			−0.597993	+	0.801501i	$0.704035\pi$
$744$		0			0
$745$	−1.13585	+	5.43344i	−0.0416142	+	0.199066i
$746$		0			0
$747$	1.49681	−	2.59255i	0.0547655	−	0.0948566i
$748$		0			0
$749$	−40.0623	+	28.3526i	−1.46385	+	1.03598i
$750$		0			0
$751$	4.64496	+	2.68177i	0.169497	+	0.0978591i	0.582349	−	0.812939i	$-0.302134\pi$
$751$	4.64496	+	2.68177i	0.169497	+	0.0978591i	−0.412852	+	0.910798i	$0.635467\pi$
$752$		0			0
$753$	−16.5306	+	9.54396i	−0.602409	+	0.347801i
$754$		0			0
$755$	−4.59865	−	4.11275i	−0.167362	−	0.149678i
$756$		0			0
$757$	−14.4301			−0.524470			−0.262235	−	0.965004i	$-0.584460\pi$
$757$	−14.4301			−0.524470			−0.262235	+	0.965004i	$0.584460\pi$
$758$		0			0
$759$	−26.4143	−	45.7509i	−0.958778	−	1.66065i
$760$		0			0
$761$	−14.5866	−	8.42159i	−0.528765	−	0.305283i	0.211748	−	0.977324i	$-0.432084\pi$
$761$	−14.5866	−	8.42159i	−0.528765	−	0.305283i	−0.740513	+	0.672042i	$0.765418\pi$
$762$		0			0
$763$	−1.10628	−	11.9537i	−0.0400500	−	0.432755i
$764$		0			0
$765$	1.02734	+	3.12606i	0.0371437	+	0.113023i
$766$		0			0
$767$	−0.00618888	−	0.0107195i	−0.000223467	−	0.000387057i
$768$		0			0
$769$			53.2864i			1.92156i	0.277315	+	0.960779i	$0.410555\pi$
$769$			53.2864i			1.92156i	−0.277315	+	0.960779i	$0.589445\pi$
$770$		0			0
$771$	−16.4577			−0.592708
$772$		0			0
$773$	−0.228998	+	0.132212i	−0.00823647	+	0.00475533i	−0.504113	−	0.863638i	$-0.668180\pi$
$773$	−0.228998	+	0.132212i	−0.00823647	+	0.00475533i	0.495876	+	0.868393i	$0.334847\pi$
$774$		0			0
$775$	23.7021	+	10.3626i	0.851404	+	0.372235i
$776$		0			0
$777$	−4.76421	+	10.3522i	−0.170915	+	0.371382i
$778$		0			0
$779$	−31.1474	+	53.9489i	−1.11597	+	1.93292i
$780$		0			0
$781$	22.6976	−	13.1045i	0.812183	−	0.468914i
$782$		0			0
$783$		−	15.0190i		−	0.536734i
$784$		0			0
$785$	−8.77286	−	7.84590i	−0.313117	−	0.280032i
$786$		0			0
$787$	7.22171	+	12.5084i	0.257426	+	0.445875i	0.965552	−	0.260211i	$-0.0837922\pi$
$787$	7.22171	+	12.5084i	0.257426	+	0.445875i	−0.708126	+	0.706087i	$0.750459\pi$
$788$		0			0
$789$	−11.5435	+	19.9939i	−0.410960	+	0.711803i
$790$		0			0
$791$	16.6960	+	7.68371i	0.593640	+	0.273201i
$792$		0			0
$793$	−1.04033	−	0.600634i	−0.0369432	−	0.0213292i
$794$		0			0
$795$	0.105793	+	0.0221157i	0.00375209	+	0.000784364i
$796$		0			0
$797$		−	34.3379i		−	1.21631i	−0.793818	−	0.608156i	$-0.791909\pi$
$797$		−	34.3379i		−	1.21631i	0.793818	−	0.608156i	$-0.208091\pi$
$798$		0			0
$799$			11.7244i			0.414778i
$800$		0			0
$801$	0.596997	−	0.344676i	0.0210938	−	0.0121785i
$802$		0			0
$803$	20.3057	−	35.1706i	0.716574	−	1.24114i
$804$		0			0
$805$	31.0693	−	41.9571i	1.09505	−	1.47879i
$806$		0			0
$807$	25.2792	−	43.7848i	0.889870	−	1.54130i
$808$		0			0
$809$	8.65907	+	14.9980i	0.304437	+	0.527300i	0.977136	−	0.212616i	$-0.0681984\pi$
$809$	8.65907	+	14.9980i	0.304437	+	0.527300i	−0.672699	+	0.739916i	$0.734865\pi$
$810$		0			0
$811$			25.3807i			0.891236i	0.895223	+	0.445618i	$0.147016\pi$
$811$			25.3807i			0.891236i	−0.895223	+	0.445618i	$0.852984\pi$
$812$		0			0
$813$	19.3185			0.677530
$814$		0			0
$815$	−1.96839	+	9.41600i	−0.0689497	+	0.329828i
$816$		0			0
$817$	−22.8060	+	39.5011i	−0.797880	+	1.38197i
$818$		0			0
$819$	0.655000	−	0.463551i	0.0228875	−	0.0161978i
$820$		0			0
$821$	20.2636	+	11.6992i	0.707206	+	0.408306i	0.810026	−	0.586394i	$-0.199453\pi$
$821$	20.2636	+	11.6992i	0.707206	+	0.408306i	−0.102820	+	0.994700i	$0.532786\pi$
$822$		0			0
$823$	9.67683	+	16.7608i	0.337313	+	0.584243i	0.983926	−	0.178575i	$-0.0571486\pi$
$823$	9.67683	+	16.7608i	0.337313	+	0.584243i	−0.646613	+	0.762818i	$0.723815\pi$
$824$		0			0
$825$	−3.32870	−	29.7462i	−0.115890	−	1.03563i
$826$		0			0
$827$		−	29.0919i		−	1.01162i	−0.862644	−	0.505812i	$-0.831193\pi$
$827$		−	29.0919i		−	1.01162i	0.862644	−	0.505812i	$-0.168807\pi$
$828$		0			0
$829$	13.3551	+	23.1317i	0.463841	+	0.803397i	0.999148	−	0.0412606i	$-0.0131374\pi$
$829$	13.3551	+	23.1317i	0.463841	+	0.803397i	−0.535307	+	0.844658i	$0.679804\pi$
$830$		0			0
$831$	18.9813	−	32.8765i	0.658453	−	1.14047i
$832$		0			0
$833$	−7.55651	+	21.4280i	−0.261817	+	0.742435i
$834$		0			0
$835$	−8.24442	+	2.70943i	−0.285310	+	0.0937638i
$836$		0			0
$837$	12.2421	+	21.2040i	0.423150	+	0.732917i
$838$		0			0
$839$	−24.7914			−0.855896			−0.427948	−	0.903803i	$-0.640763\pi$
$839$	−24.7914			−0.855896			−0.427948	+	0.903803i	$0.640763\pi$
$840$		0			0
$841$	18.9283			0.652699
$842$		0			0
$843$	28.9580	+	50.1568i	0.997367	+	1.72749i
$844$		0			0
$845$	8.76318	+	26.6651i	0.301463	+	0.917308i
$846$		0			0
$847$	0.951699	+	1.34476i	0.0327008	+	0.0462064i
$848$		0			0
$849$	13.1798	−	22.8281i	0.452330	−	0.783459i
$850$		0			0
$851$	−10.2271	−	17.7138i	−0.350579	−	0.607221i
$852$		0			0
$853$		−	50.6858i		−	1.73545i	−0.497047	−	0.867724i	$-0.665582\pi$
$853$		−	50.6858i		−	1.73545i	0.497047	−	0.867724i	$-0.334418\pi$
$854$		0			0
$855$	−5.03502	−	4.50301i	−0.172194	−	0.154000i
$856$		0			0
$857$	−10.5812	−	18.3272i	−0.361448	−	0.626047i	0.626751	−	0.779219i	$-0.284384\pi$
$857$	−10.5812	−	18.3272i	−0.361448	−	0.626047i	−0.988199	+	0.153173i	$0.951051\pi$
$858$		0			0
$859$	−2.47660	−	1.42986i	−0.0845003	−	0.0487863i	0.457154	−	0.889387i	$-0.348869\pi$
$859$	−2.47660	−	1.42986i	−0.0845003	−	0.0487863i	−0.541655	+	0.840601i	$0.682202\pi$
$860$		0			0
$861$	4.23590	+	45.7704i	0.144359	+	1.55985i
$862$		0			0
$863$	−6.07596	+	10.5239i	−0.206828	+	0.358237i	−0.950714	−	0.310070i	$-0.899647\pi$
$863$	−6.07596	+	10.5239i	−0.206828	+	0.358237i	0.743886	+	0.668307i	$0.232981\pi$
$864$		0			0
$865$	7.60616	−	36.3849i	0.258617	−	1.23712i
$866$		0			0
$867$	−12.0124			−0.407963
$868$		0			0
$869$		−	50.3304i		−	1.70734i
$870$		0			0
$871$	−1.60103	−	2.77307i	−0.0542489	−	0.0939619i
$872$		0			0
$873$	2.75873	−	4.77826i	0.0933688	−	0.161720i
$874$		0			0
$875$	25.6522	−	14.7298i	0.867201	−	0.497958i
$876$		0			0
$877$	16.6594	−	28.8550i	0.562549	−	0.974363i	−0.434725	−	0.900563i	$-0.643154\pi$
$877$	16.6594	−	28.8550i	0.562549	−	0.974363i	0.997273	−	0.0737992i	$-0.0235124\pi$
$878$		0			0
$879$	−21.4688	+	12.3950i	−0.724126	+	0.418074i
$880$		0			0
$881$		−	19.5712i		−	0.659372i	−0.944091	−	0.329686i	$-0.893057\pi$
$881$		−	19.5712i		−	0.659372i	0.944091	−	0.329686i	$-0.106943\pi$
$882$		0			0
$883$			42.7210i			1.43768i	0.695178	+	0.718838i	$0.255325\pi$
$883$			42.7210i			1.43768i	−0.695178	+	0.718838i	$0.744675\pi$
$884$		0			0
$885$	−0.0157323	+	0.0752569i	−0.000528834	+	0.00252973i
$886$		0			0
$887$	3.02603	+	1.74708i	0.101604	+	0.0586613i	0.549941	−	0.835203i	$-0.314650\pi$
$887$	3.02603	+	1.74708i	0.101604	+	0.0586613i	−0.448337	+	0.893865i	$0.647983\pi$
$888$		0			0
$889$	−6.13489	+	13.3305i	−0.205757	+	0.447091i
$890$		0			0
$891$	16.3559	−	28.3292i	0.547942	−	0.949064i
$892$		0			0
$893$	−12.0340	−	20.8434i	−0.402701	−	0.697499i
$894$		0			0
$895$	23.7287	−	26.5321i	0.793162	−	0.886870i
$896$		0			0
$897$			10.9708i			0.366306i
$898$		0			0
$899$	14.2194	−	8.20958i	0.474244	−	0.273805i
$900$		0			0
$901$	0.0422128	−	0.0731146i	0.00140631	−	0.00243580i
$902$		0			0
$903$	3.10150	+	33.5128i	0.103212	+	1.11524i
$904$		0			0
$905$	−5.23795	−	15.9383i	−0.174115	−	0.529808i
$906$		0			0
$907$	18.3487	−	10.5936i	0.609258	−	0.351755i	−0.163417	−	0.986557i	$-0.552252\pi$
$907$	18.3487	−	10.5936i	0.609258	−	0.351755i	0.772675	+	0.634802i	$0.218918\pi$
$908$		0			0
$909$	6.40748			0.212523
$910$		0			0
$911$		−	14.1566i		−	0.469030i	−0.972112	−	0.234515i	$-0.924650\pi$
$911$		−	14.1566i		−	0.469030i	0.972112	−	0.234515i	$-0.0753502\pi$
$912$		0			0
$913$	10.6356	+	18.4214i	0.351987	+	0.609659i
$914$		0			0
$915$	2.32960	+	7.08863i	0.0770140	+	0.234343i
$916$		0			0
$917$	3.48519	−	2.46651i	0.115091	−	0.0814513i
$918$		0			0
$919$	−25.4716	−	14.7060i	−0.840230	−	0.485107i	0.0171122	−	0.999854i	$-0.494553\pi$
$919$	−25.4716	−	14.7060i	−0.840230	−	0.485107i	−0.857342	+	0.514746i	$0.827886\pi$
$920$		0			0
$921$	−14.4144	−	24.9665i	−0.474972	−	0.822675i
$922$		0			0
$923$	−5.44277			−0.179151
$924$		0			0
$925$	−1.28880	−	11.5171i	−0.0423755	−	0.378680i
$926$		0			0
$927$	0.196565	−	0.113487i	0.00645606	−	0.00372741i
$928$		0			0
$929$	16.8894	+	9.75112i	0.554125	+	0.319924i	0.750784	−	0.660548i	$-0.229676\pi$
$929$	16.8894	+	9.75112i	0.554125	+	0.319924i	−0.196659	+	0.980472i	$0.563009\pi$
$930$		0			0
$931$	−8.55994	−	45.8505i	−0.280541	−	1.50269i
$932$		0			0
$933$	−8.52728	+	14.7697i	−0.279171	+	0.483538i
$934$		0			0
$935$	−22.8863	−	4.78431i	−0.748461	−	0.156464i
$936$		0			0
$937$	−2.05387			−0.0670971			−0.0335485	−	0.999437i	$-0.510681\pi$
$937$	−2.05387			−0.0670971			−0.0335485	+	0.999437i	$0.510681\pi$
$938$		0			0
$939$	−60.2423			−1.96593
$940$		0			0
$941$	−15.1289	−	26.2040i	−0.493187	−	0.854226i	0.506782	−	0.862074i	$-0.330835\pi$
$941$	−15.1289	−	26.2040i	−0.493187	−	0.854226i	−0.999969	+	0.00784879i	$0.997502\pi$
$942$		0			0
$943$	−71.4500	−	41.2517i	−2.32673	−	1.34334i
$944$		0			0
$945$	27.8166	+	3.17914i	0.904874	+	0.103418i
$946$		0			0
$947$	34.8806	+	20.1383i	1.13347	+	0.654407i	0.944804	−	0.327635i	$-0.106252\pi$
$947$	34.8806	+	20.1383i	1.13347	+	0.654407i	0.188662	+	0.982042i	$0.439585\pi$
$948$		0			0
$949$	−7.30383	+	4.21687i	−0.237092	+	0.136885i
$950$		0			0
$951$	0.765564			0.0248251
$952$		0			0
$953$			45.4230i			1.47140i	0.677309	+	0.735698i	$0.263146\pi$
$953$			45.4230i			1.47140i	−0.677309	+	0.735698i	$0.736854\pi$
$954$		0			0
$955$	6.46208	−	30.9120i	0.209108	−	1.00029i
$956$		0			0
$957$	−16.4531	−	9.49917i	−0.531852	−	0.307065i
$958$		0			0
$959$	2.04265	+	22.0715i	0.0659605	+	0.712727i
$960$		0			0
$961$	2.11656	−	3.66599i	0.0682761	−	0.118258i
$962$		0			0
$963$	−7.28342	+	4.20508i	−0.234705	+	0.135507i
$964$		0			0
$965$	−13.6660	−	12.2221i	−0.439925	−	0.393442i
$966$		0			0
$967$	−52.7807			−1.69731			−0.848656	−	0.528945i	$-0.822588\pi$
$967$	−52.7807			−1.69731			−0.848656	+	0.528945i	$0.822588\pi$
$968$		0			0
$969$	−34.8075	+	20.0961i	−1.11818	+	0.645580i
$970$		0			0
$971$	26.0287	+	15.0277i	0.835300	+	0.482261i	0.855664	−	0.517532i	$-0.173149\pi$
$971$	26.0287	+	15.0277i	0.835300	+	0.482261i	−0.0203639	+	0.999793i	$0.506482\pi$
$972$		0			0
$973$	24.3430	+	11.2030i	0.780400	+	0.359151i
$974$		0			0
$975$	−2.49002	+	5.69538i	−0.0797446	+	0.182398i
$976$		0			0
$977$	36.9900	−	21.3562i	1.18341	−	0.683245i	0.226613	−	0.973985i	$-0.427235\pi$
$977$	36.9900	−	21.3562i	1.18341	−	0.683245i	0.956802	+	0.290740i	$0.0939015\pi$
$978$		0			0
$979$			4.89820i			0.156547i
$980$		0			0
$981$		−	2.05710i		−	0.0656781i
$982$		0			0
$983$	10.5472	−	6.08944i	0.336404	−	0.194223i	−0.322277	−	0.946646i	$-0.604448\pi$
$983$	10.5472	−	6.08944i	0.336404	−	0.194223i	0.658681	+	0.752423i	$0.271115\pi$
$984$		0			0
$985$	4.62972	+	14.0876i	0.147515	+	0.448868i
$986$		0			0
$987$	−16.1328	−	7.42451i	−0.513512	−	0.236325i
$988$		0			0
$989$	−52.3153	−	30.2043i	−1.66353	−	0.960440i
$990$		0			0
$991$	−16.8998	+	9.75712i	−0.536841	+	0.309945i	−0.743798	−	0.668405i	$-0.766977\pi$
$991$	−16.8998	+	9.75712i	−0.536841	+	0.309945i	0.206957	+	0.978350i	$0.433644\pi$
$992$		0			0
$993$	54.7348			1.73696
$994$		0			0
$995$	5.31085	−	5.93830i	0.168365	−	0.188257i
$996$		0			0
$997$	−25.7749	+	14.8811i	−0.816298	+	0.471290i	−0.849138	−	0.528171i	$-0.822878\pi$
$997$	−25.7749	+	14.8811i	−0.816298	+	0.471290i	0.0328401	+	0.999461i	$0.489545\pi$
$998$		0			0
$999$	5.48446	−	9.49936i	0.173521	−	0.300547i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1120.2.bq.b.719.10		80
4.3	odd	2		280.2.ba.b.19.25	yes	80
5.4	even	2	inner	1120.2.bq.b.719.32		80
7.3	odd	6	inner	1120.2.bq.b.1039.31		80
8.3	odd	2	inner	1120.2.bq.b.719.9		80
8.5	even	2		280.2.ba.b.19.39	yes	80
20.19	odd	2		280.2.ba.b.19.16	yes	80
28.3	even	6		280.2.ba.b.59.2	yes	80
35.24	odd	6	inner	1120.2.bq.b.1039.9		80
40.19	odd	2	inner	1120.2.bq.b.719.31		80
40.29	even	2		280.2.ba.b.19.2	✓	80
56.3	even	6	inner	1120.2.bq.b.1039.32		80
56.45	odd	6		280.2.ba.b.59.16	yes	80
140.59	even	6		280.2.ba.b.59.39	yes	80
280.59	even	6	inner	1120.2.bq.b.1039.10		80
280.269	odd	6		280.2.ba.b.59.25	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.ba.b.19.2	✓	80	40.29	even	2
280.2.ba.b.19.16	yes	80	20.19	odd	2
280.2.ba.b.19.25	yes	80	4.3	odd	2
280.2.ba.b.19.39	yes	80	8.5	even	2
280.2.ba.b.59.2	yes	80	28.3	even	6
280.2.ba.b.59.16	yes	80	56.45	odd	6
280.2.ba.b.59.25	yes	80	280.269	odd	6
280.2.ba.b.59.39	yes	80	140.59	even	6
1120.2.bq.b.719.9		80	8.3	odd	2	inner
1120.2.bq.b.719.10		80	1.1	even	1	trivial
1120.2.bq.b.719.31		80	40.19	odd	2	inner
1120.2.bq.b.719.32		80	5.4	even	2	inner
1120.2.bq.b.1039.9		80	35.24	odd	6	inner
1120.2.bq.b.1039.10		80	280.59	even	6	inner
1120.2.bq.b.1039.31		80	7.3	odd	6	inner
1120.2.bq.b.1039.32		80	56.3	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.929162 - 1.60936i) q^{3} +(0.698124 + 2.12429i) q^{5} +(-1.10610 + 2.40345i) q^{7} +(-0.226682 + 0.392626i) q^{9} +O(q^{10})\)	\(q+(-0.929162 - 1.60936i) q^{3} +(0.698124 + 2.12429i) q^{5} +(-1.10610 + 2.40345i) q^{7} +(-0.226682 + 0.392626i) q^{9} +(-1.61069 - 2.78980i) q^{11} +0.668981i q^{13} +(2.77007 - 3.09734i) q^{15} +(-1.62295 - 2.81103i) q^{17} +(5.77054 + 3.33162i) q^{19} +(4.89574 - 0.453085i) q^{21} +(-4.41240 + 7.64251i) q^{23} +(-4.02524 + 2.96604i) q^{25} -4.73247 q^{27} +3.17360i q^{29} +(-2.58684 - 4.48053i) q^{31} +(-2.99319 + 5.18435i) q^{33} +(-5.87782 - 0.671772i) q^{35} +(-1.15890 + 2.00727i) q^{37} +(1.07663 - 0.621591i) q^{39} +9.34903i q^{41} +6.84531i q^{43} +(-0.992304 - 0.207439i) q^{45} +(-3.12812 - 1.80602i) q^{47} +(-4.55310 - 5.31689i) q^{49} +(-3.01597 + 5.22381i) q^{51} +(0.0130049 + 0.0225252i) q^{53} +(4.80189 - 5.36921i) q^{55} -12.3825i q^{57} +(-0.0160236 + 0.00925120i) q^{59} +(-0.897835 + 1.55510i) q^{61} +(-0.692921 - 0.979101i) q^{63} +(-1.42111 + 0.467032i) q^{65} +(-4.14522 + 2.39324i) q^{67} +16.3993 q^{69} +8.13591i q^{71} +(6.30342 + 10.9178i) q^{73} +(8.51352 + 3.72212i) q^{75} +(8.48672 - 0.785418i) q^{77} +(13.5306 + 7.81192i) q^{79} +(5.07728 + 8.79410i) q^{81} -6.60312 q^{83} +(4.83844 - 5.41008i) q^{85} +(5.10745 - 2.94879i) q^{87} +(-1.31681 - 0.760263i) q^{89} +(-1.60786 - 0.739958i) q^{91} +(-4.80718 + 8.32628i) q^{93} +(-3.04879 + 14.5842i) q^{95} -12.1700 q^{97} +1.46046 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 52 q^{9}+O(q^{10}) \) 80 * q - 52 * q^9	\( 80 q - 52 q^{9} + 48 q^{19} - 22 q^{25} + 22 q^{35} + 16 q^{49} - 20 q^{51} + 60 q^{59} - 12 q^{65} + 6 q^{75} - 36 q^{89} - 72 q^{91} - 104 q^{99}+O(q^{100}) \) 80 * q - 52 * q^9 + 48 * q^19 - 22 * q^25 + 22 * q^35 + 16 * q^49 - 20 * q^51 + 60 * q^59 - 12 * q^65 + 6 * q^75 - 36 * q^89 - 72 * q^91 - 104 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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