LMFDB - Embedded newform 2100.2.bi.n.1601.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2100,2,Mod(101,2100)]

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

lf = mfeigenbasis(mf)

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")

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

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			1601.3
Character	$\chi$	$=$	2100.1601
Dual form			2100.2.bi.n.101.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.52899 - 0.813749i) q^{3} +(-0.567546 - 2.58416i) q^{7} +(1.67563 + 2.48843i) q^{9} +O(q^{10})$	\(q+(-1.52899 - 0.813749i) q^{3} +(-0.567546 - 2.58416i) q^{7} +(1.67563 + 2.48843i) q^{9} +(0.793196 - 0.457952i) q^{11} +4.31153i q^{13} +(0.268531 + 0.465109i) q^{17} +(1.12887 + 0.651755i) q^{19} +(-1.23509 + 4.41300i) q^{21} +(-6.91920 - 3.99480i) q^{23} +(-0.537062 - 5.16832i) q^{27} +3.46154i q^{29} +(-5.56113 + 3.21072i) q^{31} +(-1.58545 + 0.0547421i) q^{33} +(-2.52172 + 4.36775i) q^{37} +(3.50850 - 6.59229i) q^{39} +9.89809 q^{41} -8.22096 q^{43} +(2.17066 - 3.75969i) q^{47} +(-6.35578 + 2.93326i) q^{49} +(-0.0320993 - 0.929664i) q^{51} +(1.70594 - 0.984927i) q^{53} +(-1.19567 - 1.91514i) q^{57} +(7.15363 + 12.3904i) q^{59} +(-8.38395 - 4.84048i) q^{61} +(5.47951 - 5.74239i) q^{63} +(6.05349 + 10.4850i) q^{67} +(7.32863 + 11.7385i) q^{69} -0.943900i q^{71} +(8.85442 - 5.11210i) q^{73} +(-1.63360 - 1.78984i) q^{77} +(-5.71817 + 9.90416i) q^{79} +(-3.38455 + 8.33935i) q^{81} +9.35240 q^{83} +(2.81682 - 5.29266i) q^{87} +(-0.874507 + 1.51469i) q^{89} +(11.1417 - 2.44699i) q^{91} +(11.1156 - 0.383799i) q^{93} +10.7844i q^{97} +(2.46868 + 1.20646i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * 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

Display 100 coefficients 10 coefficients

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
$3$	−1.52899	−	0.813749i	−0.882763	−	0.469818i
$3$	−1.52899	−	0.813749i	−0.882763	−	0.469818i
$4$		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
$9$	1.67563	+	2.48843i	0.558542	+	0.829476i
$10$		0			0
$11$	0.793196	−	0.457952i	0.239158	−	0.138078i	−0.375632	−	0.926769i	$-0.622574\pi$
$11$	0.793196	−	0.457952i	0.239158	−	0.138078i	0.614790	+	0.788691i	$0.289241\pi$
$12$		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	0.896751	−	0.442536i	$-0.145921\pi$
$17$	0.268531	+	0.465109i	0.0651283	+	0.112805i	−0.831623	+	0.555341i	$0.812588\pi$
$18$		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
$21$	−1.23509	+	4.41300i	−0.269518	+	0.962995i
$22$		0			0
$23$	−6.91920	−	3.99480i	−1.44275	−	0.832974i	−0.444721	−	0.895669i	$-0.646697\pi$
$23$	−6.91920	−	3.99480i	−1.44275	−	0.832974i	−0.998033	+	0.0626950i	$0.980030\pi$
$24$		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	$0.104152\pi$
$29$			3.46154i			0.642791i	−0.946945	+	0.321396i	$0.895848\pi$
$30$		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
$33$	−1.58545	+	0.0547421i	−0.275991	+	0.00952938i
$34$		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
$39$	3.50850	−	6.59229i	0.561810	−	1.05561i
$40$		0			0
$41$	9.89809			1.54582			0.772911	−	0.634515i	$-0.218800\pi$
$41$	9.89809			1.54582			0.772911	+	0.634515i	$0.218800\pi$
$42$		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	−0.663158	−	0.748479i	$-0.730784\pi$
$47$	2.17066	−	3.75969i	0.316623	−	0.548407i	0.979781	+	0.200072i	$0.0641176\pi$
$48$		0			0
$49$	−6.35578	+	2.93326i	−0.907969	+	0.419038i
$50$		0			0
$51$	−0.0320993	−	0.929664i	−0.00449480	−	0.130179i
$52$		0			0
$53$	1.70594	−	0.984927i	0.234329	−	0.135290i	−0.378238	−	0.925708i	$-0.623470\pi$
$53$	1.70594	−	0.984927i	0.234329	−	0.135290i	0.612568	+	0.790418i	$0.290137\pi$
$54$		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	$0.214678\pi$
$59$	7.15363	+	12.3904i	0.931323	+	1.61310i	0.150260	+	0.988647i	$0.451989\pi$
$60$		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
$63$	5.47951	−	5.74239i	0.690353	−	0.723473i
$64$		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	$-0.982162\pi$
$71$		−	0.943900i		−	0.112020i	0.998430	−	0.0560102i	$-0.0178379\pi$
$72$		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
$81$	−3.38455	+	8.33935i	−0.376062	+	0.926595i
$82$		0			0
$83$	9.35240			1.02656			0.513279	−	0.858222i	$-0.328430\pi$
$83$	9.35240			1.02656			0.513279	+	0.858222i	$0.328430\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	2.81682	−	5.29266i	0.301995	−	0.567433i
$88$		0			0
$89$	−0.874507	+	1.51469i	−0.0926976	+	0.160557i	−0.908645	−	0.417569i	$-0.862882\pi$
$89$	−0.874507	+	1.51469i	−0.0926976	+	0.160557i	0.815948	+	0.578126i	$0.196216\pi$
$90$		0			0
$91$	11.1417	−	2.44699i	1.16797	−	0.256515i
$92$		0			0
$93$	11.1156	−	0.383799i	1.15264	−	0.0397981i
$94$		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	0.999934	−	0.0114677i	$-0.00365037\pi$
$101$	4.92480	+	8.53000i	0.490036	+	0.848767i	−0.509898	+	0.860235i	$0.670317\pi$
$102$		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	0.561461	−	0.827504i	$-0.310240\pi$
$107$	1.29872	+	0.749815i	0.125552	+	0.0724873i	−0.435909	+	0.899991i	$0.643573\pi$
$108$		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	$0.158922\pi$
$113$			10.1791i			0.957567i	−0.877933	+	0.478783i	$0.841078\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−10.7289	+	7.22451i	−0.991891	+	0.667907i
$118$		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
$123$	−15.1341	−	8.05456i	−1.36459	−	0.726255i
$124$		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
$129$	12.5698	+	6.68980i	1.10671	+	0.589004i
$130$		0			0
$131$	8.80008	−	15.2422i	0.768867	−	1.33172i	−0.169311	−	0.985563i	$-0.554154\pi$
$131$	8.80008	−	15.2422i	0.768867	−	1.33172i	0.938178	−	0.346154i	$-0.112512\pi$
$132$		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	−0.833207	−	0.552962i	$-0.813497\pi$
$137$	−9.02351	+	5.20973i	−0.770931	+	0.445097i	0.0622758	+	0.998059i	$0.480164\pi$
$138$		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
$147$	12.1049	+	0.687078i	0.998393	+	0.0566692i
$148$		0			0
$149$	5.42586	+	3.13262i	0.444504	+	0.256634i	0.705506	−	0.708704i	$-0.250720\pi$
$149$	5.42586	+	3.13262i	0.444504	+	0.256634i	−0.261003	+	0.965338i	$0.584053\pi$
$150$		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
$159$	−3.40985	+	0.117735i	−0.270419	+	0.00933699i
$160$		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	$-0.380230\pi$
$167$	9.49709			0.734907			0.367453	+	0.930042i	$0.380230\pi$
$168$		0			0
$169$	−5.58930			−0.429946
$170$		0			0
$171$	0.269723	+	3.90121i	0.0206262	+	0.298333i
$172$		0			0
$173$	−5.97492	+	10.3489i	−0.454264	+	0.786809i	−0.998646	−	0.0520289i	$-0.983431\pi$
$173$	−5.97492	+	10.3489i	−0.454264	+	0.786809i	0.544381	+	0.838838i	$0.316765\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−0.855122	−	24.7661i	−0.0642749	−	1.86154i
$178$		0			0
$179$	16.2343	−	9.37286i	1.21341	−	0.700561i	0.249907	−	0.968270i	$-0.419600\pi$
$179$	16.2343	−	9.37286i	1.21341	−	0.700561i	0.963500	+	0.267709i	$0.0862667\pi$
$180$		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
$189$	−13.0510	+	4.32112i	−0.949319	+	0.314315i
$190$		0			0
$191$	−14.9979	−	8.65904i	−1.08521	−	0.626546i	−0.152912	−	0.988240i	$-0.548865\pi$
$191$	−14.9979	−	8.65904i	−1.08521	−	0.626546i	−0.932297	+	0.361694i	$0.882199\pi$
$192$		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	$0.230980\pi$
$197$			18.6287i			1.32724i	−0.748071	+	0.663619i	$0.769020\pi$
$198$		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
$201$	−0.723615	−	20.9574i	−0.0510398	−	1.47822i
$202$		0			0
$203$	8.94517	−	1.96458i	0.627828	−	0.137887i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−1.65321	−	23.9117i	−0.114906	−	1.66198i
$208$		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
$213$	−0.768097	+	1.44321i	−0.0526292	+	0.0988874i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	11.4532	+	12.5486i	0.777495	+	0.851857i
$218$		0			0
$219$	−17.6983	+	0.611084i	−1.19594	+	0.0412933i
$220$		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	0.854491	−	0.519466i	$-0.173869\pi$
$227$	−0.340877	−	0.590416i	−0.0226248	−	0.0391873i	−0.877116	+	0.480278i	$0.840536\pi$
$228$		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
$231$	1.04128	+	4.06598i	0.0685110	+	0.267522i
$232$		0			0
$233$	−23.3282	−	13.4685i	−1.52828	−	0.882353i	−0.999434	−	0.0336360i	$-0.989291\pi$
$233$	−23.3282	−	13.4685i	−1.52828	−	0.882353i	−0.528847	−	0.848717i	$-0.677375\pi$
$234$		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	$0.189588\pi$
$239$			17.3461i			1.12202i	−0.827808	+	0.561012i	$0.810412\pi$
$240$		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
$243$	11.9611	−	9.99662i	0.767304	−	0.641283i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−2.81006	+	4.86717i	−0.178800	+	0.309690i
$248$		0			0
$249$	−14.2997	−	7.61050i	−0.906208	−	0.482296i
$250$		0			0
$251$	−6.56268			−0.414233			−0.207116	−	0.978316i	$-0.566408\pi$
$251$	−6.56268			−0.414233			−0.207116	+	0.978316i	$0.566408\pi$
$252$		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	$-0.655762\pi$
$257$	8.48645	−	14.6990i	0.529370	−	0.916896i	0.999413	−	0.0342527i	$-0.0109051\pi$
$258$		0			0
$259$	12.7182	+	4.03764i	0.790269	+	0.250887i
$260$		0			0
$261$	−8.61379	+	5.80024i	−0.533180	+	0.359026i
$262$		0			0
$263$	4.60699	−	2.65984i	0.284079	−	0.164013i	−0.351190	−	0.936304i	$-0.614223\pi$
$263$	4.60699	−	2.65984i	0.284079	−	0.164013i	0.635269	+	0.772291i	$0.280889\pi$
$264$		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	0.748607	−	0.663014i	$-0.230723\pi$
$269$	−3.27834	−	5.67825i	−0.199884	−	0.346209i	−0.948491	+	0.316805i	$0.897390\pi$
$270$		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
$273$	−19.0268	−	5.32511i	−1.15155	−	0.322290i
$274$		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	$0.233384\pi$
$281$			22.4373i			1.33850i	−0.743038	+	0.669250i	$0.766616\pi$
$282$		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
$291$	8.77578	−	16.4892i	0.514445	−	0.966616i
$292$		0			0
$293$	26.1686			1.52879			0.764393	−	0.644750i	$-0.223039\pi$
$293$	26.1686			1.52879			0.764393	+	0.644750i	$0.223039\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−2.79284	−	3.85355i	−0.162057	−	0.223605i
$298$		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
$303$	−0.588695	−	17.0498i	−0.0338196	−	0.979488i
$304$		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	$-0.978815\pi$
$311$	−9.81378	−	16.9980i	−0.556488	−	0.963866i	0.441298	−	0.897361i	$-0.354518\pi$
$312$		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	0.835275	−	0.549832i	$-0.185308\pi$
$317$	13.8295	+	7.98449i	0.776745	+	0.448454i	−0.0585306	+	0.998286i	$0.518642\pi$
$318$		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
$327$	0.230976	+	6.68956i	0.0127730	+	0.369934i
$328$		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
$333$	−15.0943	+	1.04359i	−0.827163	+	0.0571885i
$334$		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
$339$	8.28321	−	15.5637i	0.449882	−	0.845305i
$340$		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	−0.984130	−	0.177451i	$-0.943215\pi$
$347$	−24.6358	+	14.2235i	−1.32252	+	0.763556i	−0.338388	+	0.941007i	$0.609882\pi$
$348$		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	$-0.794138\pi$
$353$	−17.3018	−	29.9676i	−0.920881	−	1.59501i	−0.122826	−	0.992428i	$-0.539196\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−2.38418	+	0.610577i	−0.126184	+	0.0323152i
$358$		0			0
$359$	−19.8260	−	11.4465i	−1.04638	−	0.604126i	−0.124743	−	0.992189i	$-0.539811\pi$
$359$	−19.8260	−	11.4465i	−1.04638	−	0.604126i	−0.921633	+	0.388064i	$0.873144\pi$
$360$		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
$369$	16.5855	+	24.6307i	0.863406	+	1.28222i
$370$		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
$381$	14.8893	+	7.92427i	0.762801	+	0.405972i
$382$		0			0
$383$	−14.7015	+	25.4637i	−0.751211	+	1.30114i	0.196025	+	0.980599i	$0.437197\pi$
$383$	−14.7015	+	25.4637i	−0.751211	+	1.30114i	−0.947236	+	0.320537i	$0.896137\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−13.7753	−	20.4573i	−0.700236	−	1.03990i
$388$		0			0
$389$	−20.2730	+	11.7046i	−1.02788	+	0.593448i	−0.916377	−	0.400316i	$-0.868900\pi$
$389$	−20.2730	+	11.7046i	−1.02788	+	0.593448i	−0.111504	+	0.993764i	$0.535567\pi$
$390$		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
$399$	−4.27045	+	4.17674i	−0.213790	+	0.209099i
$400$		0			0
$401$	−21.6844	−	12.5195i	−1.08287	−	0.625193i	−0.151198	−	0.988504i	$-0.548313\pi$
$401$	−21.6844	−	12.5195i	−1.08287	−	0.625193i	−0.931668	+	0.363311i	$0.881646\pi$
$402$		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
$411$	18.0363	−	0.622754i	0.889664	−	0.0307182i
$412$		0			0
$413$	27.9589	−	25.5183i	1.37577	−	1.25567i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	5.77096	−	10.8433i	0.282605	−	0.531000i
$418$		0			0
$419$	−9.85560			−0.481477			−0.240739	−	0.970590i	$-0.577390\pi$
$419$	−9.85560			−0.481477			−0.240739	+	0.970590i	$0.577390\pi$
$420$		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
$423$	12.9929	−	0.898308i	0.631738	−	0.0436772i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−7.75029	+	24.4127i	−0.375063	+	1.18141i
$428$		0			0
$429$	−0.236022	−	6.83571i	−0.0113953	−	0.330031i
$430$		0			0
$431$	2.84702	−	1.64373i	0.137136	−	0.0791755i	−0.429862	−	0.902894i	$-0.641438\pi$
$431$	2.84702	−	1.64373i	0.137136	−	0.0791755i	0.566998	+	0.823719i	$0.308105\pi$
$432$		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
$441$	−17.9491	−	10.9009i	−0.854720	−	0.519089i
$442$		0			0
$443$	−16.4179	−	9.47885i	−0.780036	−	0.450354i	0.0564073	−	0.998408i	$-0.482035\pi$
$443$	−16.4179	−	9.47885i	−0.780036	−	0.450354i	−0.836443	+	0.548054i	$0.815369\pi$
$444$		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	$-0.606960\pi$
$449$		−	40.0091i		−	1.88815i	0.329737	−	0.944073i	$-0.393040\pi$
$450$		0			0
$451$	7.85112	−	4.53285i	0.369695	−	0.213444i
$452$		0			0
$453$	−1.05859	−	30.6591i	−0.0497370	−	1.44049i
$454$		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
$459$	2.25962	−	1.63765i	0.105470	−	0.0764388i
$460$		0			0
$461$	8.71020			0.405674			0.202837	−	0.979212i	$-0.434984\pi$
$461$	8.71020			0.405674			0.202837	+	0.979212i	$0.434984\pi$
$462$		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	−0.951921	−	0.306345i	$-0.900894\pi$
$467$	−4.55236	+	7.88492i	−0.210658	+	0.364870i	0.741263	+	0.671215i	$0.234227\pi$
$468$		0			0
$469$	23.6592	−	21.5939i	1.09248	−	0.997113i
$470$		0			0
$471$	1.33971	−	0.0462575i	0.0617308	−	0.00213143i
$472$		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	$-0.960421\pi$
$479$	−13.2092	−	22.8791i	−0.603546	−	1.04537i	0.388733	−	0.921350i	$-0.372913\pi$
$480$		0			0
$481$	−18.8317	−	10.8725i	−0.858652	−	0.495743i
$482$		0			0
$483$	26.1749	−	25.6005i	1.19100	−	1.16486i
$484$		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	$-0.731761\pi$
$491$		−	33.0800i		−	1.49288i	0.665453	−	0.746440i	$-0.268239\pi$
$492$		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
$501$	−14.5210	−	7.72824i	−0.648749	−	0.345272i
$502$		0			0
$503$	21.1753			0.944158			0.472079	−	0.881556i	$-0.343504\pi$
$503$	21.1753			0.944158			0.472079	+	0.881556i	$0.343504\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	8.54599	+	4.54828i	0.379541	+	0.201996i
$508$		0			0
$509$	−15.5918	+	27.0059i	−0.691096	+	1.19701i	0.280383	+	0.959888i	$0.409539\pi$
$509$	−15.5918	+	27.0059i	−0.691096	+	1.19701i	−0.971479	+	0.237125i	$0.923795\pi$
$510$		0			0
$511$	−18.2358	−	19.9799i	−0.806704	−	0.883859i
$512$		0			0
$513$	2.76220	−	6.18441i	0.121954	−	0.273048i
$514$		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	$0.158165\pi$
$521$	19.4555	+	33.6980i	0.852363	+	1.47634i	−0.0267070	+	0.999643i	$0.508502\pi$
$522$		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
$537$	−32.4492	+	1.12040i	−1.40029	+	0.0483489i
$538$		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
$543$	−13.1033	+	24.6204i	−0.562316	+	1.05656i
$544$		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
$549$	−2.00319	−	28.9737i	−0.0854939	−	1.23657i
$550$		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	0.388156	−	0.921594i	$-0.373112\pi$
$557$	32.5776	−	18.8087i	1.38036	−	0.796950i	0.992202	+	0.124644i	$0.0397789\pi$
$558$		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	0.738622	−	0.674120i	$-0.235477\pi$
$563$	−5.08942	−	8.81514i	−0.214494	−	0.371514i	−0.953116	+	0.302606i	$0.902143\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	23.4711	+	4.01327i	0.985695	+	0.168541i
$568$		0			0
$569$	−0.744706	−	0.429956i	−0.0312197	−	0.0180247i	0.484309	−	0.874897i	$-0.339071\pi$
$569$	−0.744706	−	0.429956i	−0.0312197	−	0.0180247i	−0.515529	+	0.856872i	$0.672404\pi$
$570$		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
$579$	−0.904316	−	26.1909i	−0.0375821	−	1.08846i
$580$		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	$-0.346225\pi$
$587$	22.5090			0.929048			0.464524	+	0.885561i	$0.346225\pi$
$588$		0			0
$589$	−8.37041			−0.344897
$590$		0			0
$591$	15.1591	−	28.4831i	0.623560	−	1.17164i
$592$		0			0
$593$	−11.8863	+	20.5878i	−0.488114	+	0.845438i	−0.999907	−	0.0136712i	$-0.995648\pi$
$593$	−11.8863	+	20.5878i	−0.488114	+	0.845438i	0.511793	+	0.859109i	$0.328982\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−17.3953	+	0.600622i	−0.711942	+	0.0245818i
$598$		0			0
$599$	−37.6990	+	21.7655i	−1.54034	+	0.889314i	−0.541521	+	0.840687i	$0.682151\pi$
$599$	−37.6990	+	21.7655i	−1.54034	+	0.889314i	−0.998817	+	0.0486270i	$0.984515\pi$
$600$		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
$609$	−15.2758	−	4.27529i	−0.619005	−	0.173244i
$610$		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	$0.0475826\pi$
$617$			7.39865i			0.297858i	−0.988848	+	0.148929i	$0.952417\pi$
$618$		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
$621$	−16.9304	+	37.9061i	−0.679394	+	1.52112i
$622$		0			0
$623$	4.41053	+	1.40021i	0.176704	+	0.0560983i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−1.82545	−	0.971526i	−0.0729013	−	0.0387990i
$628$		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
$633$	2.57776	+	1.37192i	0.102457	+	0.0545288i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−12.6469	−	27.4032i	−0.501087	−	1.08575i
$638$		0			0
$639$	2.34883	−	1.58162i	0.0929182	−	0.0625681i
$640$		0			0
$641$	12.2389	−	7.06611i	0.483406	−	0.279094i	−0.238429	−	0.971160i	$-0.576632\pi$
$641$	12.2389	−	7.06611i	0.483406	−	0.279094i	0.721835	+	0.692065i	$0.243299\pi$
$642$		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	0.999482	−	0.0321804i	$-0.0102451\pi$
$647$	12.0026	+	20.7892i	0.471872	+	0.817306i	−0.527610	+	0.849487i	$0.676912\pi$
$648$		0			0
$649$	11.3485	+	6.55204i	0.445466	+	0.257190i
$650$		0			0
$651$	−7.30044	−	28.5068i	−0.286127	−	1.11727i
$652$		0			0
$653$	−25.0705	−	14.4745i	−0.981085	−	0.566430i	−0.0784876	−	0.996915i	$-0.525009\pi$
$653$	−25.0705	−	14.4745i	−0.981085	−	0.566430i	−0.902598	+	0.430485i	$0.858342\pi$
$654$		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	$0.0316168\pi$
$659$			5.09127i			0.198328i	−0.995071	+	0.0991638i	$0.968383\pi$
$660$		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
$663$	4.00827	−	0.138397i	0.155669	−	0.00537490i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	13.8282	−	23.9511i	0.535429	−	0.927389i
$668$		0			0
$669$	11.5630	−	21.7262i	0.447051	−	0.839985i
$670$		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	−0.624060	−	0.781377i	$-0.714518\pi$
$677$	9.48823	−	16.4341i	0.364662	−	0.631614i	0.988722	+	0.149763i	$0.0478511\pi$
$678$		0			0
$679$	27.8686	−	6.12064i	1.06950	−	0.234889i
$680$		0			0
$681$	0.0407473	+	1.18013i	0.00156144	+	0.0452226i
$682$		0			0
$683$	−18.1149	+	10.4587i	−0.693149	+	0.400190i	−0.804791	−	0.593559i	$-0.797722\pi$
$683$	−18.1149	+	10.4587i	−0.693149	+	0.400190i	0.111642	+	0.993749i	$0.464389\pi$
$684$		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
$693$	1.71659	−	7.06419i	0.0652077	−	0.268346i
$694$		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	$-0.883338\pi$
$701$		−	18.9758i		−	0.716706i	0.933586	−	0.358353i	$-0.116662\pi$
$702$		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
$711$	−34.2273	+	2.36641i	−1.28362	+	0.0887475i
$712$		0			0
$713$	51.3048			1.92138
$714$		0			0
$715$		0			0
$716$		0			0
$717$	14.1153	−	26.5220i	0.527147	−	0.990482i
$718$		0			0
$719$	6.70106	−	11.6066i	0.249907	−	0.432852i	−0.713593	−	0.700561i	$-0.752933\pi$
$719$	6.70106	−	11.6066i	0.249907	−	0.432852i	0.963500	+	0.267709i	$0.0862665\pi$
$720$		0			0
$721$	1.96775	−	6.19823i	0.0732829	−	0.230834i
$722$		0			0
$723$	−2.64406	+	0.0912936i	−0.0983335	+	0.00339525i
$724$		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	$0.0832003\pi$
$743$			14.0878i			0.516830i	−0.966034	+	0.258415i	$0.916800\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	15.6711	+	23.2728i	0.573376	+	0.851506i
$748$		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
$753$	10.0343	+	5.34037i	0.365669	+	0.194614i
$754$		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
$759$	11.1887	+	5.95478i	0.406125	+	0.216145i
$760$		0			0
$761$	−9.76529	+	16.9140i	−0.353991	+	0.613131i	−0.986945	−	0.161059i	$-0.948509\pi$
$761$	−9.76529	+	16.9140i	−0.353991	+	0.613131i	0.632953	+	0.774190i	$0.281842\pi$
$762$		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	0.991048	−	0.133509i	$-0.0426246\pi$
$773$	10.5624	+	18.2945i	0.379901	+	0.658009i	−0.611146	+	0.791518i	$0.709291\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−16.1603	−	16.5229i	−0.579749	−	0.592756i
$778$		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
$789$	−9.20848	+	0.317949i	−0.327831	+	0.0113193i
$790$		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	$-0.463233\pi$
$797$	6.50728			0.230500			0.115250	+	0.993337i	$0.463233\pi$
$798$		0			0
$799$	2.33156			0.0824845
$800$		0			0
$801$	−5.23455	+	0.361907i	−0.184954	+	0.0127874i
$802$		0			0
$803$	4.68219	−	8.10980i	0.165231	−	0.286189i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	0.391882	+	11.3497i	0.0137949	+	0.399530i
$808$		0			0
$809$	1.41519	−	0.817063i	0.0497556	−	0.0287264i	−0.474916	−	0.880031i	$-0.657522\pi$
$809$	1.41519	−	0.817063i	0.0497556	−	0.0287264i	0.524671	+	0.851305i	$0.324188\pi$
$810$		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
$819$	24.7585	+	23.6251i	0.865131	+	0.825526i
$820$		0			0
$821$	19.6357	+	11.3367i	0.685292	+	0.395654i	0.801846	−	0.597531i	$-0.203851\pi$
$821$	19.6357	+	11.3367i	0.685292	+	0.395654i	−0.116554	+	0.993184i	$0.537185\pi$
$822$		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	$0.191200\pi$
$827$			32.5074i			1.13039i	−0.824957	+	0.565196i	$0.808800\pi$
$828$		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
$831$	−0.165753	−	4.80057i	−0.00574992	−	0.166530i
$832$		0			0
$833$	−3.07101	−	2.16846i	−0.106404	−	0.0751327i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	19.5807	+	27.0174i	0.676809	+	0.933857i
$838$		0			0
$839$	−2.88841			−0.0997192			−0.0498596	−	0.998756i	$-0.515877\pi$
$839$	−2.88841			−0.0997192			−0.0498596	+	0.998756i	$0.515877\pi$
$840$		0			0
$841$	17.0178			0.586819
$842$		0			0
$843$	18.2584	−	34.3065i	0.628851	−	1.18158i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	25.6235	+	8.13470i	0.880435	+	0.279512i
$848$		0			0
$849$	12.5444	−	0.433130i	0.430521	−	0.0148650i
$850$		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	0.676940	−	0.736038i	$-0.263306\pi$
$857$	−8.75185	−	15.1586i	−0.298957	−	0.517809i	−0.975898	+	0.218228i	$0.929972\pi$
$858$		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
$861$	−12.2250	+	43.6803i	−0.416626	+	1.48862i
$862$		0			0
$863$	−29.4595	−	17.0085i	−1.00281	−	0.578975i	−0.0937342	−	0.995597i	$-0.529880\pi$
$863$	−29.4595	−	17.0085i	−1.00281	−	0.578975i	−0.909080	+	0.416622i	$0.863214\pi$
$864$		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
$873$	−26.8362	+	18.0706i	−0.908267	+	0.611597i
$874$		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
$879$	−40.0116	−	21.2947i	−1.34956	−	0.718252i
$880$		0			0
$881$	−25.9119			−0.872993			−0.436496	−	0.899706i	$-0.643781\pi$
$881$	−25.9119			−0.872993			−0.436496	+	0.899706i	$0.643781\pi$
$882$		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	−0.715023	−	0.699101i	$-0.753584\pi$
$887$	7.38392	−	12.7893i	0.247928	−	0.429423i	0.962951	+	0.269678i	$0.0869171\pi$
$888$		0			0
$889$	5.52675	+	25.1645i	0.185361	+	0.843990i
$890$		0			0
$891$	1.13441	+	8.16471i	0.0380041	+	0.273528i
$892$		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
$903$	10.1536	−	36.2791i	0.337890	−	1.20729i
$904$		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	$0.167407\pi$
$911$			30.3043i			1.00403i	−0.864860	+	0.502013i	$0.832593\pi$
$912$		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
$921$	18.2397	−	34.2715i	0.601019	−	1.12928i
$922$		0			0
$923$	4.06965			0.133954
$924$		0			0
$925$		0			0
$926$		0			0
$927$	0.508597	+	7.35624i	0.0167045	+	0.241611i
$928$		0			0
$929$	−8.62508	+	14.9391i	−0.282980	+	0.490135i	−0.972117	−	0.234495i	$-0.924656\pi$
$929$	−8.62508	+	14.9391i	−0.282980	+	0.490135i	0.689138	+	0.724631i	$0.257990\pi$
$930$		0			0
$931$	−9.08663	−	0.831132i	−0.297802	−	0.0272393i
$932$		0			0
$933$	1.17311	+	33.9757i	0.0384058	+	1.11231i
$934$		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	$-0.994249\pi$
$941$	−15.8153	−	27.3930i	−0.515565	−	0.892985i	0.484272	−	0.874918i	$-0.339085\pi$
$942$		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	−0.195871	−	0.980630i	$-0.562753\pi$
$947$	−35.1757	−	20.3087i	−1.14306	−	0.659944i	−0.947186	+	0.320685i	$0.896087\pi$
$948$		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	$0.0274583\pi$
$953$			5.31938i			0.172312i	−0.996282	+	0.0861558i	$0.972542\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−0.189492	−	5.48808i	−0.00612540	−	0.177405i
$958$		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
$963$	0.310304	+	4.48817i	0.00999941	+	0.144629i
$964$		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
$969$	0.569677	−	1.07039i	0.0183007	−	0.0343860i
$970$		0			0
$971$	−21.9851	+	38.0793i	−0.705535	+	1.22202i	0.260963	+	0.965349i	$0.415960\pi$
$971$	−21.9851	+	38.0793i	−0.705535	+	1.22202i	−0.966498	+	0.256674i	$0.917373\pi$
$972$		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	−0.366370	−	0.930469i	$-0.619400\pi$
$977$	8.00974	−	4.62443i	0.256254	−	0.147949i	0.622625	+	0.782521i	$0.286066\pi$
$978$		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	0.742034	−	0.670362i	$-0.233861\pi$
$983$	−6.56947	−	11.3787i	−0.209533	−	0.362923i	−0.951568	+	0.307439i	$0.900528\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	13.9106	+	14.2227i	0.442778	+	0.452712i
$988$		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
$999$	23.9283	+	10.6873i	0.757057	+	0.338132i

Twists

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

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

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)

\(f(q)\)	\(=\)	\(q+(-1.52899 - 0.813749i) q^{3} +(-0.567546 - 2.58416i) q^{7} +(1.67563 + 2.48843i) q^{9} +O(q^{10})\)	\(q+(-1.52899 - 0.813749i) q^{3} +(-0.567546 - 2.58416i) q^{7} +(1.67563 + 2.48843i) q^{9} +(0.793196 - 0.457952i) q^{11} +4.31153i q^{13} +(0.268531 + 0.465109i) q^{17} +(1.12887 + 0.651755i) q^{19} +(-1.23509 + 4.41300i) q^{21} +(-6.91920 - 3.99480i) q^{23} +(-0.537062 - 5.16832i) q^{27} +3.46154i q^{29} +(-5.56113 + 3.21072i) q^{31} +(-1.58545 + 0.0547421i) q^{33} +(-2.52172 + 4.36775i) q^{37} +(3.50850 - 6.59229i) q^{39} +9.89809 q^{41} -8.22096 q^{43} +(2.17066 - 3.75969i) q^{47} +(-6.35578 + 2.93326i) q^{49} +(-0.0320993 - 0.929664i) q^{51} +(1.70594 - 0.984927i) q^{53} +(-1.19567 - 1.91514i) q^{57} +(7.15363 + 12.3904i) q^{59} +(-8.38395 - 4.84048i) q^{61} +(5.47951 - 5.74239i) q^{63} +(6.05349 + 10.4850i) q^{67} +(7.32863 + 11.7385i) q^{69} -0.943900i q^{71} +(8.85442 - 5.11210i) q^{73} +(-1.63360 - 1.78984i) q^{77} +(-5.71817 + 9.90416i) q^{79} +(-3.38455 + 8.33935i) q^{81} +9.35240 q^{83} +(2.81682 - 5.29266i) q^{87} +(-0.874507 + 1.51469i) q^{89} +(11.1417 - 2.44699i) q^{91} +(11.1156 - 0.383799i) q^{93} +10.7844i q^{97} +(2.46868 + 1.20646i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * 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

Related objects

Downloads

Learn more