LMFDB - Embedded newform 2100.2.bi.n.1601.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2100,2,Mod(101,2100)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2100, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2100.101"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2100.bi (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,0,0,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$16.7685844245$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 420)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1601.8
Character	$\chi$	$=$	2100.1601
Dual form			2100.2.bi.n.101.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0597684 + 1.73102i) q^{3} +(-0.567546 - 2.58416i) q^{7} +(-2.99286 - 0.206921i) q^{9} +(-0.793196 + 0.457952i) q^{11} +4.31153i q^{13} +(-0.268531 - 0.465109i) q^{17} +(1.12887 + 0.651755i) q^{19} +(4.50715 - 0.827982i) q^{21} +(6.91920 + 3.99480i) q^{23} +(0.537062 - 5.16832i) q^{27} -3.46154i q^{29} +(-5.56113 + 3.21072i) q^{31} +(-0.745316 - 1.40041i) q^{33} +(-2.52172 + 4.36775i) q^{37} +(-7.46334 - 0.257693i) q^{39} -9.89809 q^{41} -8.22096 q^{43} +(-2.17066 + 3.75969i) q^{47} +(-6.35578 + 2.93326i) q^{49} +(0.821162 - 0.437033i) q^{51} +(-1.70594 + 0.984927i) q^{53} +(-1.19567 + 1.91514i) q^{57} +(-7.15363 - 12.3904i) q^{59} +(-8.38395 - 4.84048i) q^{61} +(1.16387 + 7.85146i) q^{63} +(6.05349 + 10.4850i) q^{67} +(-7.32863 + 11.7385i) q^{69} +0.943900i q^{71} +(8.85442 - 5.11210i) q^{73} +(1.63360 + 1.78984i) q^{77} +(-5.71817 + 9.90416i) q^{79} +(8.91437 + 1.23857i) q^{81} -9.35240 q^{83} +(5.99199 + 0.206891i) q^{87} +(0.874507 - 1.51469i) q^{89} +(11.1417 - 2.44699i) q^{91} +(-5.22544 - 9.81833i) q^{93} +10.7844i q^{97} +(2.46868 - 1.20646i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 12 q^{19} - 8 q^{21} - 12 q^{31} - 24 q^{39} + 44 q^{49} - 10 q^{51} - 24 q^{61} + 28 q^{79} - 20 q^{81} + 16 q^{91} + 28 q^{99}+O(q^{100}) $ 32 * q - 12 * q^19 - 8 * q^21 - 12 * q^31 - 24 * q^39 + 44 * q^49 - 10 * q^51 - 24 * q^61 + 28 * q^79 - 20 * q^81 + 16 * q^91 + 28 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times$.

$n$	$701$	$1051$	$1177$	$1501$
$\chi(n)$	$-1$	$1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.0597684	+	1.73102i	−0.0345073	+	0.999404i
$3$	−0.0597684	+	1.73102i	−0.0345073	+	0.999404i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.567546	−	2.58416i	−0.214512	−	0.976721i
$7$	−0.567546	−	2.58416i	−0.214512	−	0.976721i
$8$		0			0
$9$	−2.99286	−	0.206921i	−0.997618	−	0.0689735i
$10$		0			0
$11$	−0.793196	+	0.457952i	−0.239158	+	0.138078i	−0.614790	−	0.788691i	$-0.710759\pi$
$11$	−0.793196	+	0.457952i	−0.239158	+	0.138078i	0.375632	+	0.926769i	$0.377426\pi$
$12$		0			0
$13$			4.31153i			1.19580i	0.801569	+	0.597902i	$0.203999\pi$
$13$			4.31153i			1.19580i	−0.801569	+	0.597902i	$0.796001\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.268531	−	0.465109i	−0.0651283	−	0.112805i	0.831623	−	0.555341i	$-0.187412\pi$
$17$	−0.268531	−	0.465109i	−0.0651283	−	0.112805i	−0.896751	+	0.442536i	$0.854079\pi$
$18$		0			0
$19$	1.12887	+	0.651755i	0.258981	+	0.149523i	0.623870	−	0.781528i	$-0.285560\pi$
$19$	1.12887	+	0.651755i	0.258981	+	0.149523i	−0.364889	+	0.931051i	$0.618893\pi$
$20$		0			0
$21$	4.50715	−	0.827982i	0.983542	−	0.180681i
$22$		0			0
$23$	6.91920	+	3.99480i	1.44275	+	0.832974i	0.998033	−	0.0626950i	$-0.0199695\pi$
$23$	6.91920	+	3.99480i	1.44275	+	0.832974i	0.444721	+	0.895669i	$0.353303\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	0.537062	−	5.16832i	0.103358	−	0.994644i
$28$		0			0
$29$		−	3.46154i		−	0.642791i	−0.946945	−	0.321396i	$-0.895848\pi$
$29$		−	3.46154i		−	0.642791i	0.946945	−	0.321396i	$-0.104152\pi$
$30$		0			0
$31$	−5.56113	+	3.21072i	−0.998809	+	0.576663i	−0.907896	−	0.419196i	$-0.862312\pi$
$31$	−5.56113	+	3.21072i	−0.998809	+	0.576663i	−0.0909133	+	0.995859i	$0.528979\pi$
$32$		0			0
$33$	−0.745316	−	1.40041i	−0.129743	−	0.243780i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−2.52172	+	4.36775i	−0.414569	+	0.718054i	−0.995383	−	0.0959820i	$-0.969401\pi$
$37$	−2.52172	+	4.36775i	−0.414569	+	0.718054i	0.580814	+	0.814036i	$0.302734\pi$
$38$		0			0
$39$	−7.46334	−	0.257693i	−1.19509	−	0.0412640i
$40$		0			0
$41$	−9.89809			−1.54582			−0.772911	−	0.634515i	$-0.781200\pi$
$41$	−9.89809			−1.54582			−0.772911	+	0.634515i	$0.781200\pi$
$42$		0			0
$43$	−8.22096			−1.25369			−0.626843	−	0.779146i	$-0.715653\pi$
$43$	−8.22096			−1.25369			−0.626843	+	0.779146i	$0.715653\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2.17066	+	3.75969i	−0.316623	+	0.548407i	−0.979781	−	0.200072i	$-0.935882\pi$
$47$	−2.17066	+	3.75969i	−0.316623	+	0.548407i	0.663158	+	0.748479i	$0.269216\pi$
$48$		0			0
$49$	−6.35578	+	2.93326i	−0.907969	+	0.419038i
$50$		0			0
$51$	0.821162	−	0.437033i	0.114986	−	0.0611969i
$52$		0			0
$53$	−1.70594	+	0.984927i	−0.234329	+	0.135290i	−0.612568	−	0.790418i	$-0.709863\pi$
$53$	−1.70594	+	0.984927i	−0.234329	+	0.135290i	0.378238	+	0.925708i	$0.376530\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−1.19567	+	1.91514i	−0.158370	+	0.253667i
$58$		0			0
$59$	−7.15363	−	12.3904i	−0.931323	−	1.61310i	−0.781063	−	0.624452i	$-0.785322\pi$
$59$	−7.15363	−	12.3904i	−0.931323	−	1.61310i	−0.150260	−	0.988647i	$-0.548011\pi$
$60$		0			0
$61$	−8.38395	−	4.84048i	−1.07345	−	0.619759i	−0.144331	−	0.989529i	$-0.546103\pi$
$61$	−8.38395	−	4.84048i	−1.07345	−	0.619759i	−0.929123	+	0.369770i	$0.879436\pi$
$62$		0			0
$63$	1.16387	+	7.85146i	0.146634	+	0.989191i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	6.05349	+	10.4850i	0.739551	+	1.28094i	0.952697	+	0.303920i	$0.0982956\pi$
$67$	6.05349	+	10.4850i	0.739551	+	1.28094i	−0.213146	+	0.977020i	$0.568371\pi$
$68$		0			0
$69$	−7.32863	+	11.7385i	−0.882264	+	1.41315i
$70$		0			0
$71$			0.943900i			0.112020i	0.998430	+	0.0560102i	$0.0178379\pi$
$71$			0.943900i			0.112020i	−0.998430	+	0.0560102i	$0.982162\pi$
$72$		0			0
$73$	8.85442	−	5.11210i	1.03633	−	0.598326i	0.117540	−	0.993068i	$-0.462499\pi$
$73$	8.85442	−	5.11210i	1.03633	−	0.598326i	0.918792	+	0.394742i	$0.129166\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.63360	+	1.78984i	0.186166	+	0.203971i
$78$		0			0
$79$	−5.71817	+	9.90416i	−0.643345	+	1.11431i	0.341337	+	0.939941i	$0.389120\pi$
$79$	−5.71817	+	9.90416i	−0.643345	+	1.11431i	−0.984681	+	0.174364i	$0.944213\pi$
$80$		0			0
$81$	8.91437	+	1.23857i	0.990485	+	0.137618i
$82$		0			0
$83$	−9.35240			−1.02656			−0.513279	−	0.858222i	$-0.671570\pi$
$83$	−9.35240			−1.02656			−0.513279	+	0.858222i	$0.671570\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	5.99199	+	0.206891i	0.642408	+	0.0221810i
$88$		0			0
$89$	0.874507	−	1.51469i	0.0926976	−	0.160557i	−0.815948	−	0.578126i	$-0.803784\pi$
$89$	0.874507	−	1.51469i	0.0926976	−	0.160557i	0.908645	+	0.417569i	$0.137118\pi$
$90$		0			0
$91$	11.1417	−	2.44699i	1.16797	−	0.256515i
$92$		0			0
$93$	−5.22544	−	9.81833i	−0.541853	−	1.01811i
$94$		0			0
$95$		0			0
$96$		0			0
$97$			10.7844i			1.09499i	0.836809	+	0.547494i	$0.184418\pi$
$97$			10.7844i			1.09499i	−0.836809	+	0.547494i	$0.815582\pi$
$98$		0			0
$99$	2.46868	−	1.20646i	0.248112	−	0.121253i
$100$		0			0
$101$	−4.92480	−	8.53000i	−0.490036	−	0.848767i	0.509898	−	0.860235i	$-0.329683\pi$
$101$	−4.92480	−	8.53000i	−0.490036	−	0.848767i	−0.999934	+	0.0114677i	$0.996350\pi$
$102$		0			0
$103$	2.12863	+	1.22897i	0.209741	+	0.121094i	0.601191	−	0.799106i	$-0.294693\pi$
$103$	2.12863	+	1.22897i	0.209741	+	0.121094i	−0.391450	+	0.920199i	$0.628026\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.29872	−	0.749815i	−0.125552	−	0.0724873i	0.435909	−	0.899991i	$-0.356427\pi$
$107$	−1.29872	−	0.749815i	−0.125552	−	0.0724873i	−0.561461	+	0.827504i	$0.689760\pi$
$108$		0			0
$109$	−1.93226	−	3.34677i	−0.185077	−	0.320563i	0.758525	−	0.651643i	$-0.225920\pi$
$109$	−1.93226	−	3.34677i	−0.185077	−	0.320563i	−0.943602	+	0.331081i	$0.892587\pi$
$110$		0			0
$111$	−7.40994	−	4.62620i	−0.703321	−	0.439100i
$112$		0			0
$113$		−	10.1791i		−	0.957567i	−0.877933	−	0.478783i	$-0.841078\pi$
$113$		−	10.1791i		−	0.957567i	0.877933	−	0.478783i	$-0.158922\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	0.892144	−	12.9038i	0.0824788	−	1.19296i
$118$		0			0
$119$	−1.04951	+	0.957898i	−0.0962087	+	0.0878104i
$120$		0			0
$121$	−5.08056	+	8.79979i	−0.461869	+	0.799981i
$122$		0			0
$123$	0.591593	−	17.1338i	0.0533421	−	1.54490i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−9.73798			−0.864106			−0.432053	−	0.901848i	$-0.642211\pi$
$127$	−9.73798			−0.864106			−0.432053	+	0.901848i	$0.642211\pi$
$128$		0			0
$129$	0.491354	−	14.2306i	0.0432613	−	1.25294i
$130$		0			0
$131$	−8.80008	+	15.2422i	−0.768867	+	1.33172i	0.169311	+	0.985563i	$0.445846\pi$
$131$	−8.80008	+	15.2422i	−0.768867	+	1.33172i	−0.938178	+	0.346154i	$0.887488\pi$
$132$		0			0
$133$	1.04355	−	3.28709i	0.0904874	−	0.285027i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	9.02351	−	5.20973i	0.770931	−	0.445097i	−0.0622758	−	0.998059i	$-0.519836\pi$
$137$	9.02351	−	5.20973i	0.770931	−	0.445097i	0.833207	+	0.552962i	$0.186503\pi$
$138$		0			0
$139$			7.09182i			0.601520i	0.953700	+	0.300760i	$0.0972403\pi$
$139$			7.09182i			0.601520i	−0.953700	+	0.300760i	$0.902760\pi$
$140$		0			0
$141$	−6.37836	−	3.98216i	−0.537155	−	0.335359i
$142$		0			0
$143$	−1.97447	−	3.41989i	−0.165114	−	0.285986i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−4.69766	−	11.1773i	−0.387456	−	0.921888i
$148$		0			0
$149$	−5.42586	−	3.13262i	−0.444504	−	0.256634i	0.261003	−	0.965338i	$-0.415947\pi$
$149$	−5.42586	−	3.13262i	−0.444504	−	0.256634i	−0.705506	+	0.708704i	$0.749280\pi$
$150$		0			0
$151$	8.85578	+	15.3387i	0.720673	+	1.24824i	0.960730	+	0.277484i	$0.0895006\pi$
$151$	8.85578	+	15.3387i	0.720673	+	1.24824i	−0.240057	+	0.970759i	$0.577166\pi$
$152$		0			0
$153$	0.707433	+	1.44757i	0.0571926	+	0.117029i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−0.670256	+	0.386973i	−0.0534923	+	0.0308838i	−0.526508	−	0.850170i	$-0.676499\pi$
$157$	−0.670256	+	0.386973i	−0.0534923	+	0.0308838i	0.473015	+	0.881054i	$0.343166\pi$
$158$		0			0
$159$	−1.60297	−	3.01189i	−0.127123	−	0.238858i
$160$		0			0
$161$	6.39625	−	20.1476i	0.504095	−	1.58785i
$162$		0			0
$163$	−3.44352	+	5.96435i	−0.269717	+	0.467164i	−0.968789	−	0.247888i	$-0.920264\pi$
$163$	−3.44352	+	5.96435i	−0.269717	+	0.467164i	0.699072	+	0.715052i	$0.253597\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−9.49709			−0.734907			−0.367453	−	0.930042i	$-0.619770\pi$
$167$	−9.49709			−0.734907			−0.367453	+	0.930042i	$0.619770\pi$
$168$		0			0
$169$	−5.58930			−0.429946
$170$		0			0
$171$	−3.24369	−	2.18419i	−0.248051	−	0.167029i
$172$		0			0
$173$	5.97492	−	10.3489i	0.454264	−	0.786809i	−0.544381	−	0.838838i	$-0.683235\pi$
$173$	5.97492	−	10.3489i	0.454264	−	0.786809i	0.998646	+	0.0520289i	$0.0165688\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	21.8757	−	11.6425i	1.64428	−	0.875105i
$178$		0			0
$179$	−16.2343	+	9.37286i	−1.21341	+	0.700561i	−0.963500	−	0.267709i	$-0.913733\pi$
$179$	−16.2343	+	9.37286i	−1.21341	+	0.700561i	−0.249907	+	0.968270i	$0.580400\pi$
$180$		0			0
$181$		−	16.1024i		−	1.19688i	−0.801167	−	0.598441i	$-0.795787\pi$
$181$		−	16.1024i		−	1.19688i	0.801167	−	0.598441i	$-0.204213\pi$
$182$		0			0
$183$	8.88005	−	14.2235i	0.656432	−	1.05143i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	0.425995	+	0.245948i	0.0311519	+	0.0179855i
$188$		0			0
$189$	−13.6606	+	1.54541i	−0.993662	+	0.112412i
$190$		0			0
$191$	14.9979	+	8.65904i	1.08521	+	0.626546i	0.932297	−	0.361694i	$-0.117801\pi$
$191$	14.9979	+	8.65904i	1.08521	+	0.626546i	0.152912	+	0.988240i	$0.451135\pi$
$192$		0			0
$193$	7.56517	+	13.1033i	0.544553	+	0.943193i	0.998635	+	0.0522332i	$0.0166339\pi$
$193$	7.56517	+	13.1033i	0.544553	+	0.943193i	−0.454082	+	0.890960i	$0.650033\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	18.6287i		−	1.32724i	−0.748071	−	0.663619i	$-0.769020\pi$
$197$		−	18.6287i		−	1.32724i	0.748071	−	0.663619i	$-0.230980\pi$
$198$		0			0
$199$	8.70283	−	5.02458i	0.616927	−	0.356183i	−0.158745	−	0.987320i	$-0.550745\pi$
$199$	8.70283	−	5.02458i	0.616927	−	0.356183i	0.775672	+	0.631137i	$0.217411\pi$
$200$		0			0
$201$	−18.5115	+	9.85204i	−1.30570	+	0.694909i
$202$		0			0
$203$	−8.94517	+	1.96458i	−0.627828	+	0.137887i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−19.8816	−	13.3876i	−1.38186	−	0.930502i
$208$		0			0
$209$	−1.19389			−0.0825830
$210$		0			0
$211$	−1.68592			−0.116064			−0.0580319	−	0.998315i	$-0.518483\pi$
$211$	−1.68592			−0.116064			−0.0580319	+	0.998315i	$0.518483\pi$
$212$		0			0
$213$	−1.63391	−	0.0564154i	−0.111954	−	0.00386552i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	11.4532	+	12.5486i	0.777495	+	0.851857i
$218$		0			0
$219$	8.31993	+	15.6327i	0.562209	+	1.05636i
$220$		0			0
$221$	2.00533	−	1.15778i	0.134893	−	0.0778806i
$222$		0			0
$223$			14.2095i			0.951541i	0.879570	+	0.475770i	$0.157831\pi$
$223$			14.2095i			0.951541i	−0.879570	+	0.475770i	$0.842169\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	0.340877	+	0.590416i	0.0226248	+	0.0391873i	0.877116	−	0.480278i	$-0.159464\pi$
$227$	0.340877	+	0.590416i	0.0226248	+	0.0391873i	−0.854491	+	0.519466i	$0.826131\pi$
$228$		0			0
$229$	2.56113	+	1.47867i	0.169244	+	0.0977133i	0.582230	−	0.813024i	$-0.302181\pi$
$229$	2.56113	+	1.47867i	0.169244	+	0.0977133i	−0.412985	+	0.910738i	$0.635514\pi$
$230$		0			0
$231$	−3.19588	+	2.72081i	−0.210274	+	0.179016i
$232$		0			0
$233$	23.3282	+	13.4685i	1.52828	+	0.882353i	0.999434	+	0.0336360i	$0.0107087\pi$
$233$	23.3282	+	13.4685i	1.52828	+	0.882353i	0.528847	+	0.848717i	$0.322625\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−16.8025	−	10.4902i	−1.09144	−	0.681413i
$238$		0			0
$239$		−	17.3461i		−	1.12202i	−0.827808	−	0.561012i	$-0.810412\pi$
$239$		−	17.3461i		−	1.12202i	0.827808	−	0.561012i	$-0.189588\pi$
$240$		0			0
$241$	1.32282	−	0.763728i	0.0852101	−	0.0491961i	−0.456790	−	0.889575i	$-0.651001\pi$
$241$	1.32282	−	0.763728i	0.0852101	−	0.0491961i	0.542000	+	0.840379i	$0.317667\pi$
$242$		0			0
$243$	−2.67678	+	15.3569i	−0.171716	+	0.985147i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−2.81006	+	4.86717i	−0.178800	+	0.309690i
$248$		0			0
$249$	0.558978	−	16.1892i	0.0354238	−	1.02595i
$250$		0			0
$251$	6.56268			0.414233			0.207116	−	0.978316i	$-0.433592\pi$
$251$	6.56268			0.414233			0.207116	+	0.978316i	$0.433592\pi$
$252$		0			0
$253$	−7.31771			−0.460061
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−8.48645	+	14.6990i	−0.529370	+	0.916896i	0.470043	+	0.882644i	$0.344238\pi$
$257$	−8.48645	+	14.6990i	−0.529370	+	0.916896i	−0.999413	+	0.0342527i	$0.989095\pi$
$258$		0			0
$259$	12.7182	+	4.03764i	0.790269	+	0.250887i
$260$		0			0
$261$	−0.716263	+	10.3599i	−0.0443356	+	0.641260i
$262$		0			0
$263$	−4.60699	+	2.65984i	−0.284079	+	0.164013i	−0.635269	−	0.772291i	$-0.719111\pi$
$263$	−4.60699	+	2.65984i	−0.284079	+	0.164013i	0.351190	+	0.936304i	$0.385777\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	2.56969	+	1.60432i	0.157263	+	0.0981828i
$268$		0			0
$269$	3.27834	+	5.67825i	0.199884	+	0.346209i	0.948491	−	0.316805i	$-0.102610\pi$
$269$	3.27834	+	5.67825i	0.199884	+	0.346209i	−0.748607	+	0.663014i	$0.769277\pi$
$270$		0			0
$271$	4.54171	+	2.62216i	0.275889	+	0.159285i	0.631561	−	0.775326i	$-0.282415\pi$
$271$	4.54171	+	2.62216i	0.275889	+	0.159285i	−0.355672	+	0.934611i	$0.615748\pi$
$272$		0			0
$273$	3.56987	+	19.4327i	0.216058	+	1.17612i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	1.38663	+	2.40171i	0.0833145	+	0.144305i	0.904672	−	0.426109i	$-0.140116\pi$
$277$	1.38663	+	2.40171i	0.0833145	+	0.144305i	−0.821357	+	0.570414i	$0.806783\pi$
$278$		0			0
$279$	17.3080	−	8.45851i	1.03620	−	0.506398i
$280$		0			0
$281$		−	22.4373i		−	1.33850i	−0.743038	−	0.669250i	$-0.766616\pi$
$281$		−	22.4373i		−	1.33850i	0.743038	−	0.669250i	$-0.233384\pi$
$282$		0			0
$283$	−6.27592	+	3.62340i	−0.373064	+	0.215389i	−0.674796	−	0.738004i	$-0.735769\pi$
$283$	−6.27592	+	3.62340i	−0.373064	+	0.215389i	0.301732	+	0.953393i	$0.402435\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	5.61762	+	25.5783i	0.331598	+	1.50984i
$288$		0			0
$289$	8.35578	−	14.4726i	0.491517	−	0.851332i
$290$		0			0
$291$	−18.6680	−	0.644566i	−1.09434	−	0.0377851i
$292$		0			0
$293$	−26.1686			−1.52879			−0.764393	−	0.644750i	$-0.776961\pi$
$293$	−26.1686			−1.52879			−0.764393	+	0.644750i	$0.776961\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	1.94085	+	4.34544i	0.112619	+	0.252148i
$298$		0			0
$299$	−17.2237	+	29.8324i	−0.996073	+	1.72525i
$300$		0			0
$301$	4.66578	+	21.2443i	0.268931	+	1.22450i
$302$		0			0
$303$	15.0599	−	8.01510i	0.865171	−	0.460455i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			22.4144i			1.27926i	0.768683	+	0.639630i	$0.220912\pi$
$307$			22.4144i			1.27926i	−0.768683	+	0.639630i	$0.779088\pi$
$308$		0			0
$309$	−2.25459	+	3.61125i	−0.128259	+	0.205437i
$310$		0			0
$311$	9.81378	+	16.9980i	0.556488	+	0.963866i	0.997786	+	0.0665052i	$0.0211849\pi$
$311$	9.81378	+	16.9980i	0.556488	+	0.963866i	−0.441298	+	0.897361i	$0.645482\pi$
$312$		0			0
$313$	−11.1139	−	6.41664i	−0.628197	−	0.362690i	0.151856	−	0.988403i	$-0.451475\pi$
$313$	−11.1139	−	6.41664i	−0.628197	−	0.362690i	−0.780054	+	0.625713i	$0.784808\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−13.8295	−	7.98449i	−0.776745	−	0.448454i	0.0585306	−	0.998286i	$-0.481358\pi$
$317$	−13.8295	−	7.98449i	−0.776745	−	0.448454i	−0.835275	+	0.549832i	$0.814692\pi$
$318$		0			0
$319$	1.58522	+	2.74568i	0.0887552	+	0.153728i
$320$		0			0
$321$	1.37557	−	2.20329i	0.0767766	−	0.122976i
$322$		0			0
$323$		−	0.700065i		−	0.0389526i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	5.90882	−	3.14475i	0.326758	−	0.173905i
$328$		0			0
$329$	10.9476	+	3.47553i	0.603561	+	0.191612i
$330$		0			0
$331$	9.81888	−	17.0068i	0.539694	−	0.934778i	−0.459226	−	0.888319i	$-0.651873\pi$
$331$	9.81888	−	17.0068i	0.539694	−	0.934778i	0.998920	−	0.0464584i	$-0.0147935\pi$
$332$		0			0
$333$	8.45093	−	12.5503i	0.463108	−	0.687750i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.304237			0.0165729			0.00828643	−	0.999966i	$-0.497362\pi$
$337$	0.304237			0.0165729			0.00828643	+	0.999966i	$0.497362\pi$
$338$		0			0
$339$	17.6202	+	0.608387i	0.956996	+	0.0330430i
$340$		0			0
$341$	2.94071	−	5.09346i	0.159249	−	0.275827i
$342$		0			0
$343$	11.1872	+	14.7596i	0.604053	+	0.796944i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	24.6358	−	14.2235i	1.32252	−	0.763556i	0.338388	−	0.941007i	$-0.390118\pi$
$347$	24.6358	−	14.2235i	1.32252	−	0.763556i	0.984130	+	0.177451i	$0.0567851\pi$
$348$		0			0
$349$		−	13.9719i		−	0.747897i	−0.927450	−	0.373948i	$-0.878004\pi$
$349$		−	13.9719i		−	0.747897i	0.927450	−	0.373948i	$-0.121996\pi$
$350$		0			0
$351$	22.2834	+	2.31556i	1.18940	+	0.123595i
$352$		0			0
$353$	17.3018	+	29.9676i	0.920881	+	1.59501i	0.798055	+	0.602585i	$0.205862\pi$
$353$	17.3018	+	29.9676i	0.920881	+	1.59501i	0.122826	+	0.992428i	$0.460804\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−1.59541	−	1.87398i	−0.0844382	−	0.0991815i
$358$		0			0
$359$	19.8260	+	11.4465i	1.04638	+	0.604126i	0.921633	−	0.388064i	$-0.126856\pi$
$359$	19.8260	+	11.4465i	1.04638	+	0.604126i	0.124743	+	0.992189i	$0.460189\pi$
$360$		0			0
$361$	−8.65043	−	14.9830i	−0.455286	−	0.788578i
$362$		0			0
$363$	−14.9289	−	9.32050i	−0.783566	−	0.489199i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−25.1145	+	14.4999i	−1.31097	+	0.756887i	−0.982256	−	0.187543i	$-0.939947\pi$
$367$	−25.1145	+	14.4999i	−1.31097	+	0.756887i	−0.328711	+	0.944431i	$0.606614\pi$
$368$		0			0
$369$	29.6235	+	2.04812i	1.54214	+	0.106621i
$370$		0			0
$371$	3.51341	+	3.84944i	0.182407	+	0.199853i
$372$		0			0
$373$	12.0154	−	20.8113i	0.622136	−	1.07757i	−0.366952	−	0.930240i	$-0.619599\pi$
$373$	12.0154	−	20.8113i	0.622136	−	1.07757i	0.989087	−	0.147331i	$-0.0470682\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	14.9245			0.768652
$378$		0			0
$379$	14.0820			0.723342			0.361671	−	0.932306i	$-0.382206\pi$
$379$	14.0820			0.723342			0.361671	+	0.932306i	$0.382206\pi$
$380$		0			0
$381$	0.582023	−	16.8566i	0.0298180	−	0.863591i
$382$		0			0
$383$	14.7015	−	25.4637i	0.751211	−	1.30114i	−0.196025	−	0.980599i	$-0.562803\pi$
$383$	14.7015	−	25.4637i	0.751211	−	1.30114i	0.947236	−	0.320537i	$-0.103863\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	24.6042	+	1.70109i	1.25070	+	0.0864711i
$388$		0			0
$389$	20.2730	−	11.7046i	1.02788	−	0.593448i	0.111504	−	0.993764i	$-0.464433\pi$
$389$	20.2730	−	11.7046i	1.02788	−	0.593448i	0.916377	+	0.400316i	$0.131100\pi$
$390$		0			0
$391$		−	4.29091i		−	0.217001i
$392$		0			0
$393$	−25.8586	−	16.1441i	−1.30439	−	0.814363i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	10.3384	+	5.96889i	0.518871	+	0.299570i	0.736473	−	0.676467i	$-0.236490\pi$
$397$	10.3384	+	5.96889i	0.518871	+	0.299570i	−0.217602	+	0.976038i	$0.569823\pi$
$398$		0			0
$399$	5.62764	+	2.00287i	0.281734	+	0.100269i
$400$		0			0
$401$	21.6844	+	12.5195i	1.08287	+	0.625193i	0.931668	−	0.363311i	$-0.118354\pi$
$401$	21.6844	+	12.5195i	1.08287	+	0.625193i	0.151198	+	0.988504i	$0.451687\pi$
$402$		0			0
$403$	−13.8431	−	23.9770i	−0.689575	−	1.19438i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	4.61931i		−	0.228971i
$408$		0			0
$409$	−26.1378	+	15.0906i	−1.29243	+	0.746184i	−0.979084	−	0.203455i	$-0.934783\pi$
$409$	−26.1378	+	15.0906i	−1.29243	+	0.746184i	−0.313345	+	0.949640i	$0.601449\pi$
$410$		0			0
$411$	8.47882	+	15.9313i	0.418229	+	0.785831i
$412$		0			0
$413$	−27.9589	+	25.5183i	−1.37577	+	1.25567i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−12.2761	−	0.423867i	−0.601162	−	0.0207568i
$418$		0			0
$419$	9.85560			0.481477			0.240739	−	0.970590i	$-0.422610\pi$
$419$	9.85560			0.481477			0.240739	+	0.970590i	$0.422610\pi$
$420$		0			0
$421$	−8.16112			−0.397749			−0.198874	−	0.980025i	$-0.563729\pi$
$421$	−8.16112			−0.397749			−0.198874	+	0.980025i	$0.563729\pi$
$422$		0			0
$423$	7.27443	−	10.8031i	0.353695	−	0.525263i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−7.75029	+	24.4127i	−0.375063	+	1.18141i
$428$		0			0
$429$	6.03791	−	3.21345i	0.291513	−	0.155147i
$430$		0			0
$431$	−2.84702	+	1.64373i	−0.137136	+	0.0791755i	−0.566998	−	0.823719i	$-0.691895\pi$
$431$	−2.84702	+	1.64373i	−0.137136	+	0.0791755i	0.429862	+	0.902894i	$0.358562\pi$
$432$		0			0
$433$			31.9717i			1.53646i	0.640173	+	0.768231i	$0.278863\pi$
$433$			31.9717i			1.53646i	−0.640173	+	0.768231i	$0.721137\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	5.20726	+	9.01924i	0.249097	+	0.431449i
$438$		0			0
$439$	−36.1217	−	20.8549i	−1.72399	−	0.995349i	−0.910167	−	0.414242i	$-0.864047\pi$
$439$	−36.1217	−	20.8549i	−1.72399	−	0.995349i	−0.813827	−	0.581107i	$-0.802620\pi$
$440$		0			0
$441$	19.6289	−	7.46369i	0.934709	−	0.355414i
$442$		0			0
$443$	16.4179	+	9.47885i	0.780036	+	0.450354i	0.836443	−	0.548054i	$-0.184631\pi$
$443$	16.4179	+	9.47885i	0.780036	+	0.450354i	−0.0564073	+	0.998408i	$0.517965\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	5.74692	−	9.20503i	0.271820	−	0.435383i
$448$		0			0
$449$			40.0091i			1.88815i	0.329737	+	0.944073i	$0.393040\pi$
$449$			40.0091i			1.88815i	−0.329737	+	0.944073i	$0.606960\pi$
$450$		0			0
$451$	7.85112	−	4.53285i	0.369695	−	0.213444i
$452$		0			0
$453$	−27.0808	+	14.4128i	−1.27237	+	0.677171i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−5.69340	+	9.86127i	−0.266326	+	0.461291i	−0.967910	−	0.251296i	$-0.919143\pi$
$457$	−5.69340	+	9.86127i	−0.266326	+	0.461291i	0.701584	+	0.712587i	$0.252477\pi$
$458$		0			0
$459$	−2.54805	+	1.13806i	−0.118933	+	0.0531202i
$460$		0			0
$461$	−8.71020			−0.405674			−0.202837	−	0.979212i	$-0.565016\pi$
$461$	−8.71020			−0.405674			−0.202837	+	0.979212i	$0.565016\pi$
$462$		0			0
$463$	−16.1154			−0.748944			−0.374472	−	0.927238i	$-0.622176\pi$
$463$	−16.1154			−0.748944			−0.374472	+	0.927238i	$0.622176\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	4.55236	−	7.88492i	0.210658	−	0.364870i	−0.741263	−	0.671215i	$-0.765773\pi$
$467$	4.55236	−	7.88492i	0.210658	−	0.364870i	0.951921	+	0.306345i	$0.0991060\pi$
$468$		0			0
$469$	23.6592	−	21.5939i	1.09248	−	0.997113i
$470$		0			0
$471$	−0.629797	−	1.18336i	−0.0290195	−	0.0545261i
$472$		0			0
$473$	6.52084	−	3.76481i	0.299828	−	0.173106i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	5.30944	−	2.59475i	0.243103	−	0.118805i
$478$		0			0
$479$	13.2092	+	22.8791i	0.603546	+	1.04537i	0.992279	+	0.124022i	$0.0395794\pi$
$479$	13.2092	+	22.8791i	0.603546	+	1.04537i	−0.388733	+	0.921350i	$0.627087\pi$
$480$		0			0
$481$	−18.8317	−	10.8725i	−0.858652	−	0.495743i
$482$		0			0
$483$	34.4935	+	12.2762i	1.56951	+	0.558587i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−4.58065	−	7.93392i	−0.207569	−	0.359520i	0.743379	−	0.668870i	$-0.233222\pi$
$487$	−4.58065	−	7.93392i	−0.207569	−	0.359520i	−0.950948	+	0.309350i	$0.899889\pi$
$488$		0			0
$489$	−10.1186	−	6.31727i	−0.457578	−	0.285677i
$490$		0			0
$491$			33.0800i			1.49288i	0.665453	+	0.746440i	$0.268239\pi$
$491$			33.0800i			1.49288i	−0.665453	+	0.746440i	$0.731761\pi$
$492$		0			0
$493$	−1.60999	+	0.929529i	−0.0725104	+	0.0418639i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	2.43919	−	0.535707i	0.109413	−	0.0240297i
$498$		0			0
$499$	8.54365	−	14.7980i	0.382466	−	0.662451i	−0.608948	−	0.793210i	$-0.708408\pi$
$499$	8.54365	−	14.7980i	0.382466	−	0.662451i	0.991414	+	0.130759i	$0.0417414\pi$
$500$		0			0
$501$	0.567626	−	16.4396i	0.0253597	−	0.734469i
$502$		0			0
$503$	−21.1753			−0.944158			−0.472079	−	0.881556i	$-0.656496\pi$
$503$	−21.1753			−0.944158			−0.472079	+	0.881556i	$0.656496\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.334063	−	9.67518i	0.0148363	−	0.429690i
$508$		0			0
$509$	15.5918	−	27.0059i	0.691096	−	1.19701i	−0.280383	−	0.959888i	$-0.590461\pi$
$509$	15.5918	−	27.0059i	0.691096	−	1.19701i	0.971479	−	0.237125i	$-0.0762052\pi$
$510$		0			0
$511$	−18.2358	−	19.9799i	−0.806704	−	0.883859i
$512$		0			0
$513$	3.97475	−	5.48434i	0.175490	−	0.242140i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		−	3.97623i		−	0.174874i
$518$		0			0
$519$	17.5570	+	10.9612i	0.770665	+	0.481145i
$520$		0			0
$521$	−19.4555	−	33.6980i	−0.852363	−	1.47634i	−0.879070	−	0.476693i	$-0.841835\pi$
$521$	−19.4555	−	33.6980i	−0.852363	−	1.47634i	0.0267070	−	0.999643i	$-0.491498\pi$
$522$		0			0
$523$	3.25839	+	1.88123i	0.142480	+	0.0822606i	0.569545	−	0.821960i	$-0.307119\pi$
$523$	3.25839	+	1.88123i	0.142480	+	0.0822606i	−0.427066	+	0.904221i	$0.640453\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	2.98667	+	1.72436i	0.130101	+	0.0751141i
$528$		0			0
$529$	20.4169	+	35.3631i	0.887692	+	1.53753i
$530$		0			0
$531$	18.8459	+	38.5630i	0.817844	+	1.67349i
$532$		0			0
$533$		−	42.6759i		−	1.84850i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−15.2543	−	28.6620i	−0.658272	−	1.23686i
$538$		0			0
$539$	3.69809	−	5.23730i	0.159288	−	0.225586i
$540$		0			0
$541$	−13.6223	+	23.5945i	−0.585667	+	1.01440i	0.409125	+	0.912478i	$0.365834\pi$
$541$	−13.6223	+	23.5945i	−0.585667	+	1.01440i	−0.994792	+	0.101927i	$0.967499\pi$
$542$		0			0
$543$	27.8736	+	0.962414i	1.19617	+	0.0413012i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	13.4516			0.575148			0.287574	−	0.957758i	$-0.407151\pi$
$547$	13.4516			0.575148			0.287574	+	0.957758i	$0.407151\pi$
$548$		0			0
$549$	24.0904	+	16.2217i	1.02815	+	0.692323i
$550$		0			0
$551$	2.25607	−	3.90763i	0.0961119	−	0.166471i
$552$		0			0
$553$	28.8393	+	9.15561i	1.22637	+	0.389336i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−32.5776	+	18.8087i	−1.38036	+	0.796950i	−0.992202	−	0.124644i	$-0.960221\pi$
$557$	−32.5776	+	18.8087i	−1.38036	+	0.796950i	−0.388156	+	0.921594i	$0.626888\pi$
$558$		0			0
$559$		−	35.4449i		−	1.49916i
$560$		0			0
$561$	−0.451203	+	0.722706i	−0.0190498	+	0.0305127i
$562$		0			0
$563$	5.08942	+	8.81514i	0.214494	+	0.371514i	0.953116	−	0.302606i	$-0.0978566\pi$
$563$	5.08942	+	8.81514i	0.214494	+	0.371514i	−0.738622	+	0.674120i	$0.764523\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−1.85866	−	23.7391i	−0.0780564	−	0.996949i
$568$		0			0
$569$	0.744706	+	0.429956i	0.0312197	+	0.0180247i	0.515529	−	0.856872i	$-0.327596\pi$
$569$	0.744706	+	0.429956i	0.0312197	+	0.0180247i	−0.484309	+	0.874897i	$0.660929\pi$
$570$		0			0
$571$	−1.71817	−	2.97596i	−0.0719032	−	0.124540i	0.827832	−	0.560976i	$-0.189574\pi$
$571$	−1.71817	−	2.97596i	−0.0719032	−	0.124540i	−0.899735	+	0.436436i	$0.856241\pi$
$572$		0			0
$573$	−15.8854	+	25.4441i	−0.663620	+	1.06294i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	22.2565	−	12.8498i	0.926550	−	0.534944i	0.0408310	−	0.999166i	$-0.486999\pi$
$577$	22.2565	−	12.8498i	0.926550	−	0.534944i	0.885719	+	0.464222i	$0.153666\pi$
$578$		0			0
$579$	−23.1341	+	12.3123i	−0.961422	+	0.511681i
$580$		0			0
$581$	5.30792	+	24.1681i	0.220210	+	1.00266i
$582$		0			0
$583$	0.902098	−	1.56248i	0.0373611	−	0.0647113i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−22.5090			−0.929048			−0.464524	−	0.885561i	$-0.653775\pi$
$587$	−22.5090			−0.929048			−0.464524	+	0.885561i	$0.653775\pi$
$588$		0			0
$589$	−8.37041			−0.344897
$590$		0			0
$591$	32.2466	+	1.11341i	1.32645	+	0.0457994i
$592$		0			0
$593$	11.8863	−	20.5878i	0.488114	−	0.845438i	−0.511793	−	0.859109i	$-0.671018\pi$
$593$	11.8863	−	20.5878i	0.488114	−	0.845438i	0.999907	+	0.0136712i	$0.00435181\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	8.17749	+	15.3651i	0.334682	+	0.628850i
$598$		0			0
$599$	37.6990	−	21.7655i	1.54034	−	0.889314i	0.541521	−	0.840687i	$-0.317849\pi$
$599$	37.6990	−	21.7655i	1.54034	−	0.889314i	0.998817	−	0.0486270i	$-0.0154846\pi$
$600$		0			0
$601$			19.9347i			0.813153i	0.913617	+	0.406577i	$0.133278\pi$
$601$			19.9347i			0.813153i	−0.913617	+	0.406577i	$0.866722\pi$
$602$		0			0
$603$	−15.9477	−	32.6325i	−0.649439	−	1.32890i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	9.20867	+	5.31663i	0.373768	+	0.215795i	0.675103	−	0.737723i	$-0.264099\pi$
$607$	9.20867	+	5.31663i	0.373768	+	0.215795i	−0.301335	+	0.953518i	$0.597432\pi$
$608$		0			0
$609$	−2.86609	−	15.6017i	−0.116140	−	0.632212i
$610$		0			0
$611$	−16.2100	−	9.35886i	−0.655788	−	0.378619i
$612$		0			0
$613$	−7.56721	−	13.1068i	−0.305637	−	0.529378i	0.671766	−	0.740763i	$-0.265536\pi$
$613$	−7.56721	−	13.1068i	−0.305637	−	0.529378i	−0.977403	+	0.211385i	$0.932203\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	7.39865i		−	0.297858i	−0.988848	−	0.148929i	$-0.952417\pi$
$617$		−	7.39865i		−	0.297858i	0.988848	−	0.148929i	$-0.0475826\pi$
$618$		0			0
$619$	−16.0456	+	9.26396i	−0.644929	+	0.372350i	−0.786511	−	0.617577i	$-0.788115\pi$
$619$	−16.0456	+	9.26396i	−0.644929	+	0.372350i	0.141582	+	0.989927i	$0.454781\pi$
$620$		0			0
$621$	24.3625	−	33.6152i	0.977632	−	1.34893i
$622$		0			0
$623$	−4.41053	−	1.40021i	−0.176704	−	0.0560983i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	0.0713568	−	2.06665i	0.00284972	−	0.0825339i
$628$		0			0
$629$	2.70864			0.108001
$630$		0			0
$631$	13.1786			0.524632			0.262316	−	0.964982i	$-0.415514\pi$
$631$	13.1786			0.524632			0.262316	+	0.964982i	$0.415514\pi$
$632$		0			0
$633$	0.100765	−	2.91837i	0.00400505	−	0.115995i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−12.6469	−	27.4032i	−0.501087	−	1.08575i
$638$		0			0
$639$	0.195312	−	2.82496i	0.00772643	−	0.111754i
$640$		0			0
$641$	−12.2389	+	7.06611i	−0.483406	+	0.279094i	−0.721835	−	0.692065i	$-0.756701\pi$
$641$	−12.2389	+	7.06611i	−0.483406	+	0.279094i	0.238429	+	0.971160i	$0.423368\pi$
$642$		0			0
$643$			17.9278i			0.707005i	0.935434	+	0.353503i	$0.115009\pi$
$643$			17.9278i			0.707005i	−0.935434	+	0.353503i	$0.884991\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−12.0026	−	20.7892i	−0.471872	−	0.817306i	0.527610	−	0.849487i	$-0.323088\pi$
$647$	−12.0026	−	20.7892i	−0.471872	−	0.817306i	−0.999482	+	0.0321804i	$0.989755\pi$
$648$		0			0
$649$	11.3485	+	6.55204i	0.445466	+	0.257190i
$650$		0			0
$651$	−22.4065	+	19.0757i	−0.878179	+	0.747637i
$652$		0			0
$653$	25.0705	+	14.4745i	0.981085	+	0.566430i	0.902598	−	0.430485i	$-0.141658\pi$
$653$	25.0705	+	14.4745i	0.981085	+	0.566430i	0.0784876	+	0.996915i	$0.474991\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−27.5578	+	13.4676i	−1.07513	+	0.525422i
$658$		0			0
$659$		−	5.09127i		−	0.198328i	−0.995071	−	0.0991638i	$-0.968383\pi$
$659$		−	5.09127i		−	0.198328i	0.995071	−	0.0991638i	$-0.0316168\pi$
$660$		0			0
$661$	25.1768	−	14.5358i	0.979264	−	0.565378i	0.0772160	−	0.997014i	$-0.475397\pi$
$661$	25.1768	−	14.5358i	0.979264	−	0.565378i	0.902048	+	0.431636i	$0.142064\pi$
$662$		0			0
$663$	1.88428	+	3.54047i	0.0731794	+	0.137500i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	13.8282	−	23.9511i	0.535429	−	0.927389i
$668$		0			0
$669$	−24.5970	−	0.849281i	−0.950974	−	0.0328351i
$670$		0			0
$671$	8.86682			0.342300
$672$		0			0
$673$	−8.51862			−0.328369			−0.164184	−	0.986430i	$-0.552499\pi$
$673$	−8.51862			−0.328369			−0.164184	+	0.986430i	$0.552499\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−9.48823	+	16.4341i	−0.364662	+	0.631614i	−0.988722	−	0.149763i	$-0.952149\pi$
$677$	−9.48823	+	16.4341i	−0.364662	+	0.631614i	0.624060	+	0.781377i	$0.285482\pi$
$678$		0			0
$679$	27.8686	−	6.12064i	1.06950	−	0.234889i
$680$		0			0
$681$	−1.04239	+	0.554776i	−0.0399447	+	0.0212591i
$682$		0			0
$683$	18.1149	−	10.4587i	0.693149	−	0.400190i	−0.111642	−	0.993749i	$-0.535611\pi$
$683$	18.1149	−	10.4587i	0.693149	−	0.400190i	0.804791	+	0.593559i	$0.202278\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−2.71268	+	4.34499i	−0.103495	+	0.165772i
$688$		0			0
$689$	−4.24654	−	7.35523i	−0.161780	−	0.280212i
$690$		0			0
$691$	29.4902	+	17.0261i	1.12186	+	0.647705i	0.941875	−	0.335964i	$-0.109062\pi$
$691$	29.4902	+	17.0261i	1.12186	+	0.647705i	0.179984	+	0.983670i	$0.442396\pi$
$692$		0			0
$693$	−4.51877	−	5.69475i	−0.171654	−	0.216326i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	2.65794	+	4.60369i	0.100677	+	0.174377i
$698$		0			0
$699$	−24.7086	+	39.5766i	−0.934565	+	1.49692i
$700$		0			0
$701$			18.9758i			0.716706i	0.933586	+	0.358353i	$0.116662\pi$
$701$			18.9758i			0.716706i	−0.933586	+	0.358353i	$0.883338\pi$
$702$		0			0
$703$	−5.69340	+	3.28709i	−0.214731	+	0.123975i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−19.2479	+	17.5676i	−0.723890	+	0.660699i
$708$		0			0
$709$	1.53691	−	2.66200i	0.0577197	−	0.0999735i	−0.835722	−	0.549153i	$-0.814950\pi$
$709$	1.53691	−	2.66200i	0.0577197	−	0.0999735i	0.893441	+	0.449180i	$0.148284\pi$
$710$		0			0
$711$	19.1630	−	28.4585i	0.718670	−	1.06728i
$712$		0			0
$713$	−51.3048			−1.92138
$714$		0			0
$715$		0			0
$716$		0			0
$717$	30.0264	+	1.03675i	1.12136	+	0.0387180i
$718$		0			0
$719$	−6.70106	+	11.6066i	−0.249907	+	0.432852i	−0.963500	−	0.267709i	$-0.913733\pi$
$719$	−6.70106	+	11.6066i	−0.249907	+	0.432852i	0.713593	+	0.700561i	$0.247067\pi$
$720$		0			0
$721$	1.96775	−	6.19823i	0.0732829	−	0.230834i
$722$		0			0
$723$	1.24297	+	2.33547i	0.0462264	+	0.0868569i
$724$		0			0
$725$		0			0
$726$		0			0
$727$			4.88627i			0.181222i	0.995886	+	0.0906109i	$0.0288820\pi$
$727$			4.88627i			0.181222i	−0.995886	+	0.0906109i	$0.971118\pi$
$728$		0			0
$729$	−26.4231	−	5.55142i	−0.978634	−	0.205608i
$730$		0			0
$731$	2.20758	+	3.82364i	0.0816504	+	0.141423i
$732$		0			0
$733$	32.0351	+	18.4955i	1.18324	+	0.683145i	0.956762	−	0.290871i	$-0.0939450\pi$
$733$	32.0351	+	18.4955i	1.18324	+	0.683145i	0.226480	+	0.974016i	$0.427278\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−9.60321	−	5.54441i	−0.353739	−	0.204231i
$738$		0			0
$739$	18.9759	+	32.8672i	0.698040	+	1.20904i	0.969145	+	0.246491i	$0.0792777\pi$
$739$	18.9759	+	32.8672i	0.698040	+	1.20904i	−0.271105	+	0.962550i	$0.587389\pi$
$740$		0			0
$741$	−8.25721	−	5.15517i	−0.303336	−	0.189380i
$742$		0			0
$743$		−	14.0878i		−	0.516830i	−0.966034	−	0.258415i	$-0.916800\pi$
$743$		−	14.0878i		−	0.516830i	0.966034	−	0.258415i	$-0.0832003\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	27.9904	+	1.93520i	1.02411	+	0.0708054i
$748$		0			0
$749$	−1.20056	+	3.78165i	−0.0438675	+	0.138178i
$750$		0			0
$751$	12.8752	−	22.3005i	0.469823	−	0.813757i	−0.529582	−	0.848259i	$-0.677651\pi$
$751$	12.8752	−	22.3005i	0.469823	−	0.813757i	0.999405	+	0.0345016i	$0.0109844\pi$
$752$		0			0
$753$	−0.392241	+	11.3601i	−0.0142941	+	0.413986i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−40.3111			−1.46513			−0.732565	−	0.680697i	$-0.761677\pi$
$757$	−40.3111			−1.46513			−0.732565	+	0.680697i	$0.761677\pi$
$758$		0			0
$759$	0.437368	−	12.6671i	0.0158755	−	0.459787i
$760$		0			0
$761$	9.76529	−	16.9140i	0.353991	−	0.613131i	−0.632953	−	0.774190i	$-0.718158\pi$
$761$	9.76529	−	16.9140i	0.353991	−	0.613131i	0.986945	+	0.161059i	$0.0514909\pi$
$762$		0			0
$763$	−7.55196	+	6.89272i	−0.273399	+	0.249533i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	53.4218	−	30.8431i	1.92895	−	1.11368i
$768$		0			0
$769$		−	47.6475i		−	1.71821i	−0.511797	−	0.859107i	$-0.671020\pi$
$769$		−	47.6475i		−	1.71821i	0.511797	−	0.859107i	$-0.328980\pi$
$770$		0			0
$771$	−24.9370	−	15.5687i	−0.898083	−	0.560695i
$772$		0			0
$773$	−10.5624	−	18.2945i	−0.379901	−	0.658009i	0.611146	−	0.791518i	$-0.290709\pi$
$773$	−10.5624	−	18.2945i	−0.379901	−	0.658009i	−0.991048	+	0.133509i	$0.957375\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−7.74937	+	21.7741i	−0.278007	+	0.781141i
$778$		0			0
$779$	−11.1737	−	6.45112i	−0.400338	−	0.231135i
$780$		0			0
$781$	−0.432261	−	0.748698i	−0.0154675	−	0.0267905i
$782$		0			0
$783$	−17.8903	−	1.85906i	−0.639349	−	0.0664373i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	5.66953	−	3.27330i	0.202097	−	0.116681i	−0.395536	−	0.918450i	$-0.629441\pi$
$787$	5.66953	−	3.27330i	0.202097	−	0.116681i	0.597633	+	0.801770i	$0.296108\pi$
$788$		0			0
$789$	−4.32889	−	8.13376i	−0.154113	−	0.289569i
$790$		0			0
$791$	−26.3044	+	5.77709i	−0.935276	+	0.205410i
$792$		0			0
$793$	20.8699	−	36.1477i	0.741110	−	1.28364i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−6.50728			−0.230500			−0.115250	−	0.993337i	$-0.536767\pi$
$797$	−6.50728			−0.230500			−0.115250	+	0.993337i	$0.536767\pi$
$798$		0			0
$799$	2.33156			0.0824845
$800$		0			0
$801$	−2.93069	+	4.35230i	−0.103551	+	0.153781i
$802$		0			0
$803$	−4.68219	+	8.10980i	−0.165231	+	0.286189i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−10.0251	+	5.33549i	−0.352900	+	0.187818i
$808$		0			0
$809$	−1.41519	+	0.817063i	−0.0497556	+	0.0287264i	−0.524671	−	0.851305i	$-0.675812\pi$
$809$	−1.41519	+	0.817063i	−0.0497556	+	0.0287264i	0.474916	+	0.880031i	$0.342478\pi$
$810$		0			0
$811$			29.4411i			1.03382i	0.856041	+	0.516909i	$0.172917\pi$
$811$			29.4411i			1.03382i	−0.856041	+	0.516909i	$0.827083\pi$
$812$		0			0
$813$	−4.81045	+	7.70506i	−0.168710	+	0.270228i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−9.28042	−	5.35805i	−0.324681	−	0.187454i
$818$		0			0
$819$	−33.8518	+	5.01805i	−1.18288	+	0.175345i
$820$		0			0
$821$	−19.6357	−	11.3367i	−0.685292	−	0.395654i	0.116554	−	0.993184i	$-0.462815\pi$
$821$	−19.6357	−	11.3367i	−0.685292	−	0.395654i	−0.801846	+	0.597531i	$0.796149\pi$
$822$		0			0
$823$	9.59438	+	16.6180i	0.334439	+	0.579266i	0.983377	−	0.181576i	$-0.0581198\pi$
$823$	9.59438	+	16.6180i	0.334439	+	0.579266i	−0.648938	+	0.760841i	$0.724786\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	32.5074i		−	1.13039i	−0.824957	−	0.565196i	$-0.808800\pi$
$827$		−	32.5074i		−	1.13039i	0.824957	−	0.565196i	$-0.191200\pi$
$828$		0			0
$829$	−44.7613	+	25.8429i	−1.55462	+	0.897563i	−0.556868	+	0.830601i	$0.687997\pi$
$829$	−44.7613	+	25.8429i	−1.55462	+	0.897563i	−0.997756	+	0.0669618i	$0.978669\pi$
$830$		0			0
$831$	−4.24029	+	2.25674i	−0.147094	+	0.0782853i
$832$		0			0
$833$	3.07101	+	2.16846i	0.106404	+	0.0751327i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	13.6074	+	30.4661i	0.470340	+	1.05306i
$838$		0			0
$839$	2.88841			0.0997192			0.0498596	−	0.998756i	$-0.484123\pi$
$839$	2.88841			0.0997192			0.0498596	+	0.998756i	$0.484123\pi$
$840$		0			0
$841$	17.0178			0.586819
$842$		0			0
$843$	38.8395	+	1.34104i	1.33770	+	0.0461880i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	25.6235	+	8.13470i	0.880435	+	0.279512i
$848$		0			0
$849$	−5.89708	−	11.0803i	−0.202387	−	0.380275i
$850$		0			0
$851$	−34.8966	+	20.1476i	−1.19624	+	0.690650i
$852$		0			0
$853$		−	49.3673i		−	1.69031i	−0.534525	−	0.845153i	$-0.679509\pi$
$853$		−	49.3673i		−	1.69031i	0.534525	−	0.845153i	$-0.320491\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	8.75185	+	15.1586i	0.298957	+	0.517809i	0.975898	−	0.218228i	$-0.0700278\pi$
$857$	8.75185	+	15.1586i	0.298957	+	0.517809i	−0.676940	+	0.736038i	$0.736694\pi$
$858$		0			0
$859$	5.23153	+	3.02042i	0.178497	+	0.103056i	0.586586	−	0.809887i	$-0.300471\pi$
$859$	5.23153	+	3.02042i	0.178497	+	0.103056i	−0.408089	+	0.912942i	$0.633805\pi$
$860$		0			0
$861$	−44.6122	+	8.19544i	−1.52038	+	0.279300i
$862$		0			0
$863$	29.4595	+	17.0085i	1.00281	+	0.578975i	0.909080	−	0.416622i	$-0.136786\pi$
$863$	29.4595	+	17.0085i	1.00281	+	0.578975i	0.0937342	+	0.995597i	$0.470120\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	24.5530	+	15.3290i	0.833864	+	0.520601i
$868$		0			0
$869$		−	10.4746i		−	0.355326i
$870$		0			0
$871$	−45.2062	+	26.0998i	−1.53175	+	0.884358i
$872$		0			0
$873$	2.23151	−	32.2761i	0.0755252	−	1.09238i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−3.62002	+	6.27005i	−0.122239	+	0.211725i	−0.920650	−	0.390388i	$-0.872341\pi$
$877$	−3.62002	+	6.27005i	−0.122239	+	0.211725i	0.798411	+	0.602113i	$0.205674\pi$
$878$		0			0
$879$	1.56406	−	45.2984i	0.0527543	−	1.52788i
$880$		0			0
$881$	25.9119			0.872993			0.436496	−	0.899706i	$-0.356219\pi$
$881$	25.9119			0.872993			0.436496	+	0.899706i	$0.356219\pi$
$882$		0			0
$883$	−17.5664			−0.591155			−0.295577	−	0.955319i	$-0.595512\pi$
$883$	−17.5664			−0.591155			−0.295577	+	0.955319i	$0.595512\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−7.38392	+	12.7893i	−0.247928	+	0.429423i	−0.962951	−	0.269678i	$-0.913083\pi$
$887$	−7.38392	+	12.7893i	−0.247928	+	0.429423i	0.715023	+	0.699101i	$0.246416\pi$
$888$		0			0
$889$	5.52675	+	25.1645i	0.185361	+	0.843990i
$890$		0			0
$891$	−7.63805	+	3.09993i	−0.255884	+	0.103851i
$892$		0			0
$893$	−4.90079	+	2.82947i	−0.163999	+	0.0946847i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−50.6110	−	31.5976i	−1.68985	−	1.05501i
$898$		0			0
$899$	11.1140	+	19.2501i	0.370674	+	0.642026i
$900$		0			0
$901$	0.916197	+	0.528966i	0.0305229	+	0.0176224i
$902$		0			0
$903$	−37.0532	+	6.80681i	−1.23305	+	0.226517i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−14.6622	−	25.3957i	−0.486851	−	0.843250i	0.513035	−	0.858368i	$-0.328521\pi$
$907$	−14.6622	−	25.3957i	−0.486851	−	0.843250i	−0.999886	+	0.0151176i	$0.995188\pi$
$908$		0			0
$909$	12.9742	+	26.5481i	0.430326	+	0.880545i
$910$		0			0
$911$		−	30.3043i		−	1.00403i	−0.864860	−	0.502013i	$-0.832593\pi$
$911$		−	30.3043i		−	1.00403i	0.864860	−	0.502013i	$-0.167407\pi$
$912$		0			0
$913$	7.41828	−	4.28295i	0.245509	−	0.141745i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	44.3827	+	14.0902i	1.46565	+	0.465299i
$918$		0			0
$919$	−3.81888	+	6.61449i	−0.125973	+	0.218192i	−0.922113	−	0.386921i	$-0.873539\pi$
$919$	−3.81888	+	6.61449i	−0.125973	+	0.218192i	0.796140	+	0.605113i	$0.206872\pi$
$920$		0			0
$921$	−38.7998	−	1.33968i	−1.27850	−	0.0441438i
$922$		0			0
$923$	−4.06965			−0.133954
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−6.11640	−	4.11858i	−0.200889	−	0.135272i
$928$		0			0
$929$	8.62508	−	14.9391i	0.282980	−	0.490135i	−0.689138	−	0.724631i	$-0.742010\pi$
$929$	8.62508	−	14.9391i	0.282980	−	0.490135i	0.972117	+	0.234495i	$0.0753438\pi$
$930$		0			0
$931$	−9.08663	−	0.831132i	−0.297802	−	0.0272393i
$932$		0			0
$933$	−30.0104	+	15.9719i	−0.982495	+	0.522896i
$934$		0			0
$935$		0			0
$936$		0			0
$937$			36.0492i			1.17768i	0.808251	+	0.588839i	$0.200415\pi$
$937$			36.0492i			1.17768i	−0.808251	+	0.588839i	$0.799585\pi$
$938$		0			0
$939$	11.7716	−	18.8549i	0.384151	−	0.615308i
$940$		0			0
$941$	15.8153	+	27.3930i	0.515565	+	0.892985i	0.999837	+	0.0180673i	$0.00575131\pi$
$941$	15.8153	+	27.3930i	0.515565	+	0.892985i	−0.484272	+	0.874918i	$0.660915\pi$
$942$		0			0
$943$	−68.4869	−	39.5409i	−2.23024	−	1.28763i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	35.1757	+	20.3087i	1.14306	+	0.659944i	0.947186	−	0.320685i	$-0.103913\pi$
$947$	35.1757	+	20.3087i	1.14306	+	0.659944i	0.195871	+	0.980630i	$0.437247\pi$
$948$		0			0
$949$	22.0410	+	38.1761i	0.715481	+	1.23925i
$950$		0			0
$951$	14.6479	−	23.4620i	0.474990	−	0.760807i
$952$		0			0
$953$		−	5.31938i		−	0.172312i	−0.996282	−	0.0861558i	$-0.972542\pi$
$953$		−	5.31938i		−	0.172312i	0.996282	−	0.0861558i	$-0.0274583\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−4.84757	+	2.57994i	−0.156700	+	0.0833975i
$958$		0			0
$959$	−18.5840	−	20.3615i	−0.600110	−	0.657506i
$960$		0			0
$961$	5.11747	−	8.86371i	0.165080	−	0.285926i
$962$		0			0
$963$	3.73172	+	2.51282i	0.120253	+	0.0809745i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	6.75930			0.217364			0.108682	−	0.994077i	$-0.465337\pi$
$967$	6.75930			0.217364			0.108682	+	0.994077i	$0.465337\pi$
$968$		0			0
$969$	1.21183	+	0.0418417i	0.0389294	+	0.00134415i
$970$		0			0
$971$	21.9851	−	38.0793i	0.705535	−	1.22202i	−0.260963	−	0.965349i	$-0.584040\pi$
$971$	21.9851	−	38.0793i	0.705535	−	1.22202i	0.966498	−	0.256674i	$-0.0826266\pi$
$972$		0			0
$973$	18.3264	−	4.02493i	0.587517	−	0.129033i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−8.00974	+	4.62443i	−0.256254	+	0.147949i	−0.622625	−	0.782521i	$-0.713934\pi$
$977$	−8.00974	+	4.62443i	−0.256254	+	0.147949i	0.366370	+	0.930469i	$0.380600\pi$
$978$		0			0
$979$			1.60193i			0.0511979i
$980$		0			0
$981$	5.09046	+	10.4162i	0.162526	+	0.332565i
$982$		0			0
$983$	6.56947	+	11.3787i	0.209533	+	0.362923i	0.951568	−	0.307439i	$-0.0994722\pi$
$983$	6.56947	+	11.3787i	0.209533	+	0.362923i	−0.742034	+	0.670362i	$0.766139\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−6.67054	+	18.7428i	−0.212326	+	0.596589i
$988$		0			0
$989$	−56.8825	−	32.8411i	−1.80876	−	1.04429i
$990$		0			0
$991$	3.18520	+	5.51694i	0.101181	+	0.175251i	0.912172	−	0.409808i	$-0.134404\pi$
$991$	3.18520	+	5.51694i	0.101181	+	0.175251i	−0.810990	+	0.585060i	$0.801071\pi$
$992$		0			0
$993$	28.8522	+	18.0131i	0.915598	+	0.571630i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	20.3595	−	11.7546i	0.644792	−	0.372271i	−0.141666	−	0.989915i	$-0.545246\pi$
$997$	20.3595	−	11.7546i	0.644792	−	0.372271i	0.786458	+	0.617644i	$0.211913\pi$
$998$		0			0
$999$	21.2196	+	15.3788i	0.671359	+	0.486565i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.bi.n.1601.8		32
3.2	odd	2	inner	2100.2.bi.n.1601.3		32
5.2	odd	4		420.2.bn.a.89.16	yes	32
5.3	odd	4		420.2.bn.a.89.1	✓	32
5.4	even	2	inner	2100.2.bi.n.1601.9		32
7.3	odd	6	inner	2100.2.bi.n.101.3		32
15.2	even	4		420.2.bn.a.89.6	yes	32
15.8	even	4		420.2.bn.a.89.11	yes	32
15.14	odd	2	inner	2100.2.bi.n.1601.14		32
21.17	even	6	inner	2100.2.bi.n.101.8		32
35.2	odd	12		2940.2.f.a.1469.12		32
35.3	even	12		420.2.bn.a.269.6	yes	32
35.12	even	12		2940.2.f.a.1469.21		32
35.17	even	12		420.2.bn.a.269.11	yes	32
35.23	odd	12		2940.2.f.a.1469.22		32
35.24	odd	6	inner	2100.2.bi.n.101.14		32
35.33	even	12		2940.2.f.a.1469.11		32
105.2	even	12		2940.2.f.a.1469.9		32
105.17	odd	12		420.2.bn.a.269.1	yes	32
105.23	even	12		2940.2.f.a.1469.23		32
105.38	odd	12		420.2.bn.a.269.16	yes	32
105.47	odd	12		2940.2.f.a.1469.24		32
105.59	even	6	inner	2100.2.bi.n.101.9		32
105.68	odd	12		2940.2.f.a.1469.10		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bn.a.89.1	✓	32	5.3	odd	4
420.2.bn.a.89.6	yes	32	15.2	even	4
420.2.bn.a.89.11	yes	32	15.8	even	4
420.2.bn.a.89.16	yes	32	5.2	odd	4
420.2.bn.a.269.1	yes	32	105.17	odd	12
420.2.bn.a.269.6	yes	32	35.3	even	12
420.2.bn.a.269.11	yes	32	35.17	even	12
420.2.bn.a.269.16	yes	32	105.38	odd	12
2100.2.bi.n.101.3		32	7.3	odd	6	inner
2100.2.bi.n.101.8		32	21.17	even	6	inner
2100.2.bi.n.101.9		32	105.59	even	6	inner
2100.2.bi.n.101.14		32	35.24	odd	6	inner
2100.2.bi.n.1601.3		32	3.2	odd	2	inner
2100.2.bi.n.1601.8		32	1.1	even	1	trivial
2100.2.bi.n.1601.9		32	5.4	even	2	inner
2100.2.bi.n.1601.14		32	15.14	odd	2	inner
2940.2.f.a.1469.9		32	105.2	even	12
2940.2.f.a.1469.10		32	105.68	odd	12
2940.2.f.a.1469.11		32	35.33	even	12
2940.2.f.a.1469.12		32	35.2	odd	12
2940.2.f.a.1469.21		32	35.12	even	12
2940.2.f.a.1469.22		32	35.23	odd	12
2940.2.f.a.1469.23		32	105.23	even	12
2940.2.f.a.1469.24		32	105.47	odd	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2100.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0597684 + 1.73102i) q^{3} +(-0.567546 - 2.58416i) q^{7} +(-2.99286 - 0.206921i) q^{9} +(-0.793196 + 0.457952i) q^{11} +4.31153i q^{13} +(-0.268531 - 0.465109i) q^{17} +(1.12887 + 0.651755i) q^{19} +(4.50715 - 0.827982i) q^{21} +(6.91920 + 3.99480i) q^{23} +(0.537062 - 5.16832i) q^{27} -3.46154i q^{29} +(-5.56113 + 3.21072i) q^{31} +(-0.745316 - 1.40041i) q^{33} +(-2.52172 + 4.36775i) q^{37} +(-7.46334 - 0.257693i) q^{39} -9.89809 q^{41} -8.22096 q^{43} +(-2.17066 + 3.75969i) q^{47} +(-6.35578 + 2.93326i) q^{49} +(0.821162 - 0.437033i) q^{51} +(-1.70594 + 0.984927i) q^{53} +(-1.19567 + 1.91514i) q^{57} +(-7.15363 - 12.3904i) q^{59} +(-8.38395 - 4.84048i) q^{61} +(1.16387 + 7.85146i) q^{63} +(6.05349 + 10.4850i) q^{67} +(-7.32863 + 11.7385i) q^{69} +0.943900i q^{71} +(8.85442 - 5.11210i) q^{73} +(1.63360 + 1.78984i) q^{77} +(-5.71817 + 9.90416i) q^{79} +(8.91437 + 1.23857i) q^{81} -9.35240 q^{83} +(5.99199 + 0.206891i) q^{87} +(0.874507 - 1.51469i) q^{89} +(11.1417 - 2.44699i) q^{91} +(-5.22544 - 9.81833i) q^{93} +10.7844i q^{97} +(2.46868 - 1.20646i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 12 q^{19} - 8 q^{21} - 12 q^{31} - 24 q^{39} + 44 q^{49} - 10 q^{51} - 24 q^{61} + 28 q^{79} - 20 q^{81} + 16 q^{91} + 28 q^{99}+O(q^{100}) \) 32 * q - 12 * q^19 - 8 * q^21 - 12 * q^31 - 24 * q^39 + 44 * q^49 - 10 * q^51 - 24 * q^61 + 28 * q^79 - 20 * q^81 + 16 * q^91 + 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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