LMFDB - Embedded newform 140.2.u.a.17.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [140,2,Mod(17,140)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(140, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("140.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 140 = 2^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	140.u (of order $12$, degree $4$, 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:	$1.11790562830$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 52 x^{14} - 224 x^{13} + 802 x^{12} - 2264 x^{11} + 5402 x^{10} - 10642 x^{9} + \cdots + 196 $ x^16 - 8x^15 + 52x^14 - 224x^13 + 802x^12 - 2264x^11 + 5402x^10 - 10642x^9 + 17766x^8 - 24680x^7 + 28682x^6 - 27248x^5 + 20861x^4 - 12338x^3 + 5322x^2 - 1484*x + 196
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			17.3
Root			$0.500000 - 1.61777i$ of defining polynomial
Character	$\chi$	$=$	140.17
Dual form			140.2.u.a.33.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.52691 - 0.409133i) q^{3} +(2.14461 - 0.632955i) q^{5} +(-2.59572 - 0.512081i) q^{7} +(-0.434025 + 0.250584i) q^{9} +O(q^{10})$	\(q+(1.52691 - 0.409133i) q^{3} +(2.14461 - 0.632955i) q^{5} +(-2.59572 - 0.512081i) q^{7} +(-0.434025 + 0.250584i) q^{9} +(-0.342727 + 0.593621i) q^{11} +(1.04830 + 1.04830i) q^{13} +(3.01566 - 1.84390i) q^{15} +(-0.353532 - 1.31940i) q^{17} +(1.55949 + 2.70111i) q^{19} +(-4.17293 + 0.280096i) q^{21} +(-4.44038 - 1.18980i) q^{23} +(4.19874 - 2.71489i) q^{25} +(-3.91351 + 3.91351i) q^{27} +7.90106i q^{29} +(-7.63715 - 4.40931i) q^{31} +(-0.280442 + 1.04663i) q^{33} +(-5.89095 + 0.544760i) q^{35} +(2.32733 - 8.68572i) q^{37} +(2.02956 + 1.17176i) q^{39} +10.2469i q^{41} +(3.73689 - 3.73689i) q^{43} +(-0.772206 + 0.812125i) q^{45} +(-6.73924 - 1.80577i) q^{47} +(6.47555 + 2.65844i) q^{49} +(-1.07962 - 1.86996i) q^{51} +(-2.39564 - 8.94065i) q^{53} +(-0.359282 + 1.49002i) q^{55} +(3.48631 + 3.48631i) q^{57} +(-2.10430 + 3.64475i) q^{59} +(3.57882 - 2.06623i) q^{61} +(1.25493 - 0.428191i) q^{63} +(2.91173 + 1.58468i) q^{65} +(4.01070 - 1.07466i) q^{67} -7.26683 q^{69} +12.5889 q^{71} +(12.4053 - 3.32399i) q^{73} +(5.30032 - 5.86322i) q^{75} +(1.19361 - 1.36537i) q^{77} +(12.1515 - 7.01566i) q^{79} +(-3.62266 + 6.27464i) q^{81} +(3.99595 + 3.99595i) q^{83} +(-1.59331 - 2.60583i) q^{85} +(3.23259 + 12.0642i) q^{87} +(-5.79949 - 10.0450i) q^{89} +(-2.18429 - 3.25792i) q^{91} +(-13.4652 - 3.60799i) q^{93} +(5.05419 + 4.80576i) q^{95} +(-2.60010 + 2.60010i) q^{97} -0.343528i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{5} + 2 q^{7}+O(q^{10}) $ 16 * q + 6 * q^5 + 2 * q^7	$ 16 q + 6 q^{5} + 2 q^{7} - 20 q^{15} + 18 q^{17} - 4 q^{21} - 16 q^{23} + 6 q^{25} - 12 q^{31} - 42 q^{33} - 40 q^{35} - 14 q^{37} + 28 q^{43} - 66 q^{45} - 6 q^{47} + 20 q^{51} - 10 q^{53} + 44 q^{57} + 60 q^{61} + 48 q^{63} + 34 q^{65} + 8 q^{67} - 8 q^{71} + 78 q^{73} + 96 q^{75} + 10 q^{77} + 24 q^{81} + 30 q^{87} - 64 q^{91} - 62 q^{93} + 2 q^{95}+O(q^{100}) $ 16 * q + 6 * q^5 + 2 * q^7 - 20 * q^15 + 18 * q^17 - 4 * q^21 - 16 * q^23 + 6 * q^25 - 12 * q^31 - 42 * q^33 - 40 * q^35 - 14 * q^37 + 28 * q^43 - 66 * q^45 - 6 * q^47 + 20 * q^51 - 10 * q^53 + 44 * q^57 + 60 * q^61 + 48 * q^63 + 34 * q^65 + 8 * q^67 - 8 * q^71 + 78 * q^73 + 96 * q^75 + 10 * q^77 + 24 * q^81 + 30 * q^87 - 64 * q^91 - 62 * q^93 + 2 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/140\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$101$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{1}{6}\right)$

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
$3$	1.52691	−	0.409133i	0.881560	−	0.236213i	0.210480	−	0.977598i	$-0.432497\pi$
$3$	1.52691	−	0.409133i	0.881560	−	0.236213i	0.671080	+	0.741385i	$0.265831\pi$
$4$		0			0
$5$	2.14461	−	0.632955i	0.959100	−	0.283066i
$5$	2.14461	−	0.632955i	0.959100	−	0.283066i
$6$		0			0
$7$	−2.59572	−	0.512081i	−0.981091	−	0.193549i
$7$	−2.59572	−	0.512081i	−0.981091	−	0.193549i
$8$		0			0
$9$	−0.434025	+	0.250584i	−0.144675	+	0.0835281i
$10$		0			0
$11$	−0.342727	+	0.593621i	−0.103336	+	0.178984i	−0.913057	−	0.407831i	$-0.866285\pi$
$11$	−0.342727	+	0.593621i	−0.103336	+	0.178984i	0.809721	+	0.586815i	$0.199618\pi$
$12$		0			0
$13$	1.04830	+	1.04830i	0.290747	+	0.290747i	0.837375	−	0.546628i	$-0.184089\pi$
$13$	1.04830	+	1.04830i	0.290747	+	0.290747i	−0.546628	+	0.837375i	$0.684089\pi$
$14$		0			0
$15$	3.01566	−	1.84390i	0.778640	−	0.476092i
$16$		0			0
$17$	−0.353532	−	1.31940i	−0.0857442	−	0.320002i	0.909710	−	0.415244i	$-0.136304\pi$
$17$	−0.353532	−	1.31940i	−0.0857442	−	0.320002i	−0.995454	+	0.0952428i	$0.969637\pi$
$18$		0			0
$19$	1.55949	+	2.70111i	0.357771	+	0.619678i	0.987588	−	0.157065i	$-0.0502034\pi$
$19$	1.55949	+	2.70111i	0.357771	+	0.619678i	−0.629817	+	0.776744i	$0.716870\pi$
$20$		0			0
$21$	−4.17293	+	0.280096i	−0.910609	+	0.0611220i
$22$		0			0
$23$	−4.44038	−	1.18980i	−0.925883	−	0.248090i	−0.235785	−	0.971805i	$-0.575766\pi$
$23$	−4.44038	−	1.18980i	−0.925883	−	0.248090i	−0.690098	+	0.723716i	$0.742433\pi$
$24$		0			0
$25$	4.19874	−	2.71489i	0.839747	−	0.542978i
$26$		0			0
$27$	−3.91351	+	3.91351i	−0.753155	+	0.753155i
$28$		0			0
$29$			7.90106i			1.46719i	0.679587	+	0.733595i	$0.262159\pi$
$29$			7.90106i			1.46719i	−0.679587	+	0.733595i	$0.737841\pi$
$30$		0			0
$31$	−7.63715	−	4.40931i	−1.37167	−	0.791936i	−0.380535	−	0.924767i	$-0.624260\pi$
$31$	−7.63715	−	4.40931i	−1.37167	−	0.791936i	−0.991139	+	0.132831i	$0.957593\pi$
$32$		0			0
$33$	−0.280442	+	1.04663i	−0.0488187	+	0.182194i
$34$		0			0
$35$	−5.89095	+	0.544760i	−0.995752	+	0.0920812i
$36$		0			0
$37$	2.32733	−	8.68572i	0.382611	−	1.42792i	−0.459288	−	0.888288i	$-0.651895\pi$
$37$	2.32733	−	8.68572i	0.382611	−	1.42792i	0.841899	−	0.539636i	$-0.181438\pi$
$38$		0			0
$39$	2.02956	+	1.17176i	0.324989	+	0.187632i
$40$		0			0
$41$			10.2469i			1.60029i	0.599805	+	0.800146i	$0.295245\pi$
$41$			10.2469i			1.60029i	−0.599805	+	0.800146i	$0.704755\pi$
$42$		0			0
$43$	3.73689	−	3.73689i	0.569871	−	0.569871i	−0.362221	−	0.932092i	$-0.617982\pi$
$43$	3.73689	−	3.73689i	0.569871	−	0.569871i	0.932092	+	0.362221i	$0.117982\pi$
$44$		0			0
$45$	−0.772206	+	0.812125i	−0.115114	+	0.121064i
$46$		0			0
$47$	−6.73924	−	1.80577i	−0.983019	−	0.263399i	−0.268703	−	0.963223i	$-0.586595\pi$
$47$	−6.73924	−	1.80577i	−0.983019	−	0.263399i	−0.714315	+	0.699824i	$0.753262\pi$
$48$		0			0
$49$	6.47555	+	2.65844i	0.925078	+	0.379777i
$50$		0			0
$51$	−1.07962	−	1.86996i	−0.151177	−	0.261847i
$52$		0			0
$53$	−2.39564	−	8.94065i	−0.329066	−	1.22809i	−0.910160	−	0.414256i	$-0.864042\pi$
$53$	−2.39564	−	8.94065i	−0.329066	−	1.22809i	0.581094	−	0.813837i	$-0.302625\pi$
$54$		0			0
$55$	−0.359282	+	1.49002i	−0.0484456	+	0.200914i
$56$		0			0
$57$	3.48631	+	3.48631i	0.461773	+	0.461773i
$58$		0			0
$59$	−2.10430	+	3.64475i	−0.273956	+	0.474506i	−0.969871	−	0.243618i	$-0.921666\pi$
$59$	−2.10430	+	3.64475i	−0.273956	+	0.474506i	0.695915	+	0.718124i	$0.254999\pi$
$60$		0			0
$61$	3.57882	−	2.06623i	0.458221	−	0.264554i	−0.253075	−	0.967447i	$-0.581442\pi$
$61$	3.57882	−	2.06623i	0.458221	−	0.264554i	0.711296	+	0.702893i	$0.248109\pi$
$62$		0			0
$63$	1.25493	−	0.428191i	0.158106	−	0.0539470i
$64$		0			0
$65$	2.91173	+	1.58468i	0.361156	+	0.196555i
$66$		0			0
$67$	4.01070	−	1.07466i	0.489985	−	0.131291i	−0.00536291	−	0.999986i	$-0.501707\pi$
$67$	4.01070	−	1.07466i	0.489985	−	0.131291i	0.495348	+	0.868694i	$0.335040\pi$
$68$		0			0
$69$	−7.26683			−0.874823
$70$		0			0
$71$	12.5889			1.49402			0.747011	−	0.664812i	$-0.231488\pi$
$71$	12.5889			1.49402			0.747011	+	0.664812i	$0.231488\pi$
$72$		0			0
$73$	12.4053	−	3.32399i	1.45193	−	0.389044i	0.555236	−	0.831693i	$-0.312628\pi$
$73$	12.4053	−	3.32399i	1.45193	−	0.389044i	0.896695	+	0.442649i	$0.145961\pi$
$74$		0			0
$75$	5.30032	−	5.86322i	0.612028	−	0.677027i
$76$		0			0
$77$	1.19361	−	1.36537i	0.136024	−	0.155599i
$78$		0			0
$79$	12.1515	−	7.01566i	1.36715	−	0.789323i	0.376585	−	0.926382i	$-0.377098\pi$
$79$	12.1515	−	7.01566i	1.36715	−	0.789323i	0.990563	+	0.137059i	$0.0437648\pi$
$80$		0			0
$81$	−3.62266	+	6.27464i	−0.402518	+	0.697182i
$82$		0			0
$83$	3.99595	+	3.99595i	0.438612	+	0.438612i	0.891545	−	0.452933i	$-0.149622\pi$
$83$	3.99595	+	3.99595i	0.438612	+	0.438612i	−0.452933	+	0.891545i	$0.649622\pi$
$84$		0			0
$85$	−1.59331	−	2.60583i	−0.172819	−	0.282642i
$86$		0			0
$87$	3.23259	+	12.0642i	0.346570	+	1.29342i
$88$		0			0
$89$	−5.79949	−	10.0450i	−0.614745	−	1.06477i	−0.990429	−	0.138021i	$-0.955926\pi$
$89$	−5.79949	−	10.0450i	−0.614745	−	1.06477i	0.375685	−	0.926748i	$-0.377408\pi$
$90$		0			0
$91$	−2.18429	−	3.25792i	−0.228975	−	0.341523i
$92$		0			0
$93$	−13.4652	−	3.60799i	−1.39628	−	0.374131i
$94$		0			0
$95$	5.05419	+	4.80576i	0.518549	+	0.493061i
$96$		0			0
$97$	−2.60010	+	2.60010i	−0.264000	+	0.264000i	−0.826677	−	0.562677i	$-0.809772\pi$
$97$	−2.60010	+	2.60010i	−0.264000	+	0.264000i	0.562677	+	0.826677i	$0.309772\pi$
$98$		0			0
$99$		−	0.343528i		−	0.0345259i
$100$		0			0
$101$	−2.65764	−	1.53439i	−0.264445	−	0.152677i	0.361915	−	0.932211i	$-0.382123\pi$
$101$	−2.65764	−	1.53439i	−0.264445	−	0.152677i	−0.626361	+	0.779533i	$0.715456\pi$
$102$		0			0
$103$	−4.28607	+	15.9958i	−0.422319	+	1.57612i	0.347389	+	0.937721i	$0.387068\pi$
$103$	−4.28607	+	15.9958i	−0.422319	+	1.57612i	−0.769709	+	0.638395i	$0.779598\pi$
$104$		0			0
$105$	−8.77204	+	3.24198i	−0.856063	+	0.316385i
$106$		0			0
$107$	1.37238	−	5.12180i	0.132673	−	0.495143i	−0.867323	−	0.497745i	$-0.834162\pi$
$107$	1.37238	−	5.12180i	0.132673	−	0.495143i	0.999997	+	0.00260205i	$0.000828258\pi$
$108$		0			0
$109$	−14.3427	−	8.28074i	−1.37378	−	0.793151i	−0.382376	−	0.924007i	$-0.624894\pi$
$109$	−14.3427	−	8.28074i	−1.37378	−	0.793151i	−0.991401	+	0.130856i	$0.958227\pi$
$110$		0			0
$111$		−	14.2145i		−	1.34918i
$112$		0			0
$113$	−7.21561	+	7.21561i	−0.678787	+	0.678787i	−0.959726	−	0.280939i	$-0.909354\pi$
$113$	−7.21561	+	7.21561i	−0.678787	+	0.678787i	0.280939	+	0.959726i	$0.409354\pi$
$114$		0			0
$115$	−10.2760	+	0.258909i	−0.958241	+	0.0241434i
$116$		0			0
$117$	−0.717677	−	0.192301i	−0.0663493	−	0.0177782i
$118$		0			0
$119$	0.242031	+	3.60583i	0.0221870	+	0.330546i
$120$		0			0
$121$	5.26508	+	9.11938i	0.478643	+	0.829034i
$122$		0			0
$123$	4.19233	+	15.6460i	0.378010	+	1.41075i
$124$		0			0
$125$	7.28626	−	8.48000i	0.651703	−	0.758474i
$126$		0			0
$127$	−2.13026	−	2.13026i	−0.189030	−	0.189030i	0.606247	−	0.795277i	$-0.292674\pi$
$127$	−2.13026	−	2.13026i	−0.189030	−	0.189030i	−0.795277	+	0.606247i	$0.792674\pi$
$128$		0			0
$129$	4.17700	−	7.23477i	0.367764	−	0.636986i
$130$		0			0
$131$	9.47951	−	5.47300i	0.828229	−	0.478178i	−0.0250169	−	0.999687i	$-0.507964\pi$
$131$	9.47951	−	5.47300i	0.828229	−	0.478178i	0.853246	+	0.521509i	$0.174631\pi$
$132$		0			0
$133$	−2.66481	−	7.80993i	−0.231068	−	0.677207i
$134$		0			0
$135$	−5.91589	+	10.8700i	−0.509159	+	0.935545i
$136$		0			0
$137$	−1.30614	+	0.349978i	−0.111591	+	0.0299006i	−0.314182	−	0.949363i	$-0.601730\pi$
$137$	−1.30614	+	0.349978i	−0.111591	+	0.0299006i	0.202592	+	0.979263i	$0.435064\pi$
$138$		0			0
$139$	0.703180			0.0596429			0.0298215	−	0.999555i	$-0.490506\pi$
$139$	0.703180			0.0596429			0.0298215	+	0.999555i	$0.490506\pi$
$140$		0			0
$141$	−11.0290			−0.928808
$142$		0			0
$143$	−0.981577	+	0.263013i	−0.0820836	+	0.0219942i
$144$		0			0
$145$	5.00102	+	16.9447i	0.415312	+	1.40718i
$146$		0			0
$147$	10.9752	+	1.40983i	0.905220	+	0.116281i
$148$		0			0
$149$	−9.78894	+	5.65165i	−0.801941	+	0.463001i	−0.844149	−	0.536108i	$-0.819894\pi$
$149$	−9.78894	+	5.65165i	−0.801941	+	0.463001i	0.0422084	+	0.999109i	$0.486561\pi$
$150$		0			0
$151$	3.95170	−	6.84454i	0.321585	−	0.557001i	−0.659230	−	0.751941i	$-0.729118\pi$
$151$	3.95170	−	6.84454i	0.321585	−	0.557001i	0.980815	+	0.194940i	$0.0624512\pi$
$152$		0			0
$153$	0.484063	+	0.484063i	0.0391341	+	0.0391341i
$154$		0			0
$155$	−19.1696	−	4.62229i	−1.53974	−	0.371272i
$156$		0			0
$157$	0.603801	+	2.25342i	0.0481886	+	0.179842i	0.985825	−	0.167774i	$-0.0536579\pi$
$157$	0.603801	+	2.25342i	0.0481886	+	0.179842i	−0.937637	+	0.347616i	$0.886991\pi$
$158$		0			0
$159$	−7.31583	−	12.6714i	−0.580183	−	1.00491i
$160$		0			0
$161$	10.9167	+	5.36222i	0.860358	+	0.422602i
$162$		0			0
$163$	−1.09180	−	0.292547i	−0.0855163	−	0.0229140i	0.215807	−	0.976436i	$-0.430762\pi$
$163$	−1.09180	−	0.292547i	−0.0855163	−	0.0229140i	−0.301324	+	0.953522i	$0.597428\pi$
$164$		0			0
$165$	0.0610265	+	2.42211i	0.00475091	+	0.188561i
$166$		0			0
$167$	5.76281	−	5.76281i	0.445940	−	0.445940i	−0.448062	−	0.894002i	$-0.647886\pi$
$167$	5.76281	−	5.76281i	0.445940	−	0.445940i	0.894002	+	0.448062i	$0.147886\pi$
$168$		0			0
$169$		−	10.8021i		−	0.830933i
$170$		0			0
$171$	−1.35371	−	0.781567i	−0.103521	−	0.0597679i
$172$		0			0
$173$	−4.52596	+	16.8911i	−0.344103	+	1.28421i	0.549554	+	0.835458i	$0.314798\pi$
$173$	−4.52596	+	16.8911i	−0.344103	+	1.28421i	−0.893657	+	0.448751i	$0.851869\pi$
$174$		0			0
$175$	−12.2890	+	4.89700i	−0.928961	+	0.370179i
$176$		0			0
$177$	−1.72188	+	6.42613i	−0.129424	+	0.483017i
$178$		0			0
$179$	0.930020	+	0.536947i	0.0695129	+	0.0401333i	0.534354	−	0.845261i	$-0.320555\pi$
$179$	0.930020	+	0.536947i	0.0695129	+	0.0401333i	−0.464841	+	0.885394i	$0.653888\pi$
$180$		0			0
$181$		−	8.93607i		−	0.664213i	−0.943242	−	0.332106i	$-0.892241\pi$
$181$		−	8.93607i		−	0.664213i	0.943242	−	0.332106i	$-0.107759\pi$
$182$		0			0
$183$	4.61916	−	4.61916i	0.341458	−	0.341458i
$184$		0			0
$185$	−0.506446	−	20.1006i	−0.0372346	−	1.47783i
$186$		0			0
$187$	0.904389	+	0.242330i	0.0661355	+	0.0177210i
$188$		0			0
$189$	12.1624	−	8.15435i	0.884686	−	0.593142i
$190$		0			0
$191$	12.1898	+	21.1133i	0.882020	+	1.52770i	0.849091	+	0.528246i	$0.177150\pi$
$191$	12.1898	+	21.1133i	0.882020	+	1.52770i	0.0329288	+	0.999458i	$0.489517\pi$
$192$		0			0
$193$	−2.33794	−	8.72531i	−0.168289	−	0.628062i	−0.997598	−	0.0692717i	$-0.977932\pi$
$193$	−2.33794	−	8.72531i	−0.168289	−	0.628062i	0.829309	−	0.558790i	$-0.188734\pi$
$194$		0			0
$195$	5.09429	+	1.22836i	0.364809	+	0.0879649i
$196$		0			0
$197$	1.78673	+	1.78673i	0.127299	+	0.127299i	0.767886	−	0.640587i	$-0.221309\pi$
$197$	1.78673	+	1.78673i	0.127299	+	0.127299i	−0.640587	+	0.767886i	$0.721309\pi$
$198$		0			0
$199$	−4.67200	+	8.09214i	−0.331189	+	0.573637i	−0.982745	−	0.184964i	$-0.940783\pi$
$199$	−4.67200	+	8.09214i	−0.331189	+	0.573637i	0.651556	+	0.758601i	$0.274117\pi$
$200$		0			0
$201$	5.68429	−	3.28182i	0.400939	−	0.231482i
$202$		0			0
$203$	4.04599	−	20.5090i	0.283972	−	1.43945i
$204$		0			0
$205$	6.48581	+	21.9756i	0.452989	+	1.53484i
$206$		0			0
$207$	2.22538	−	0.596288i	0.154675	−	0.0414449i
$208$		0			0
$209$	−2.13792			−0.147883
$210$		0			0
$211$	−9.84703			−0.677898			−0.338949	−	0.940805i	$-0.610071\pi$
$211$	−9.84703			−0.677898			−0.338949	+	0.940805i	$0.610071\pi$
$212$		0			0
$213$	19.2220	−	5.15052i	1.31707	−	0.352908i
$214$		0			0
$215$	5.64891	−	10.3795i	0.385252	−	0.707875i
$216$		0			0
$217$	17.5660	+	15.3562i	1.19246	+	1.04245i
$218$		0			0
$219$	17.5818	−	10.1508i	1.18807	−	0.685931i
$220$		0			0
$221$	1.01252	−	1.75374i	0.0681096	−	0.117969i
$222$		0			0
$223$	0.338625	+	0.338625i	0.0226760	+	0.0226760i	0.718354	−	0.695678i	$-0.244896\pi$
$223$	0.338625	+	0.338625i	0.0226760	+	0.0226760i	−0.695678	+	0.718354i	$0.744896\pi$
$224$		0			0
$225$	−1.14205	+	2.23047i	−0.0761364	+	0.148698i
$226$		0			0
$227$	3.58938	+	13.3958i	0.238236	+	0.889108i	0.976664	+	0.214775i	$0.0689019\pi$
$227$	3.58938	+	13.3958i	0.238236	+	0.889108i	−0.738428	+	0.674333i	$0.764431\pi$
$228$		0			0
$229$	−1.33146	−	2.30615i	−0.0879850	−	0.152395i	0.818674	−	0.574258i	$-0.194709\pi$
$229$	−1.33146	−	2.30615i	−0.0879850	−	0.152395i	−0.906659	+	0.421864i	$0.861376\pi$
$230$		0			0
$231$	1.26391	−	2.57314i	0.0831590	−	0.169300i
$232$		0			0
$233$	−18.2875	−	4.90012i	−1.19805	−	0.321017i	−0.395989	−	0.918255i	$-0.629598\pi$
$233$	−18.2875	−	4.90012i	−1.19805	−	0.321017i	−0.802064	+	0.597238i	$0.796265\pi$
$234$		0			0
$235$	−15.5960	+	0.392951i	−1.01737	+	0.0256333i
$236$		0			0
$237$	15.6838	−	15.6838i	1.01877	−	1.01877i
$238$		0			0
$239$		−	5.74416i		−	0.371559i	−0.982591	−	0.185779i	$-0.940519\pi$
$239$		−	5.74416i		−	0.371559i	0.982591	−	0.185779i	$-0.0594809\pi$
$240$		0			0
$241$	8.82144	+	5.09306i	0.568239	+	0.328073i	0.756446	−	0.654057i	$-0.226934\pi$
$241$	8.82144	+	5.09306i	0.568239	+	0.328073i	−0.188207	+	0.982129i	$0.560268\pi$
$242$		0			0
$243$	1.33303	−	4.97494i	0.0855139	−	0.319142i
$244$		0			0
$245$	15.5702	+	1.60260i	0.994745	+	0.102386i
$246$		0			0
$247$	−1.19677	+	4.46640i	−0.0761486	+	0.284190i
$248$		0			0
$249$	7.73631	+	4.46656i	0.490268	+	0.283057i
$250$		0			0
$251$		−	7.28871i		−	0.460059i	−0.973184	−	0.230030i	$-0.926118\pi$
$251$		−	7.28871i		−	0.460059i	0.973184	−	0.230030i	$-0.0738823\pi$
$252$		0			0
$253$	2.22813	−	2.22813i	0.140081	−	0.140081i
$254$		0			0
$255$	−3.49897	−	3.32699i	−0.219114	−	0.208344i
$256$		0			0
$257$	−11.8005	−	3.16193i	−0.736095	−	0.197236i	−0.128753	−	0.991677i	$-0.541097\pi$
$257$	−11.8005	−	3.16193i	−0.736095	−	0.197236i	−0.607342	+	0.794441i	$0.707764\pi$
$258$		0			0
$259$	−10.4889	+	21.3539i	−0.651748	+	1.32687i
$260$		0			0
$261$	−1.97988	−	3.42926i	−0.122552	−	0.212266i
$262$		0			0
$263$	5.56652	+	20.7745i	0.343246	+	1.28101i	0.894648	+	0.446772i	$0.147427\pi$
$263$	5.56652	+	20.7745i	0.343246	+	1.28101i	−0.551402	+	0.834240i	$0.685907\pi$
$264$		0			0
$265$	−10.7968	−	17.6579i	−0.663239	−	1.08472i
$266$		0			0
$267$	−12.9650	−	12.9650i	−0.793446	−	0.793446i
$268$		0			0
$269$	−13.2377	+	22.9283i	−0.807114	+	1.39796i	0.107741	+	0.994179i	$0.465638\pi$
$269$	−13.2377	+	22.9283i	−0.807114	+	1.39796i	−0.914855	+	0.403783i	$0.867695\pi$
$270$		0			0
$271$	−15.4571	+	8.92414i	−0.938949	+	0.542103i	−0.889631	−	0.456680i	$-0.849038\pi$
$271$	−15.4571	+	8.92414i	−0.938949	+	0.542103i	−0.0493186	+	0.998783i	$0.515705\pi$
$272$		0			0
$273$	−4.66812	−	4.08087i	−0.282528	−	0.246986i
$274$		0			0
$275$	0.172595	+	3.42293i	0.0104078	+	0.206410i
$276$		0			0
$277$	−25.6307	+	6.86772i	−1.54000	+	0.412641i	−0.926265	−	0.376873i	$-0.876999\pi$
$277$	−25.6307	+	6.86772i	−1.54000	+	0.412641i	−0.613733	+	0.789514i	$0.710333\pi$
$278$		0			0
$279$	4.41962			0.264596
$280$		0			0
$281$	−18.7465			−1.11832			−0.559161	−	0.829059i	$-0.688877\pi$
$281$	−18.7465			−1.11832			−0.559161	+	0.829059i	$0.688877\pi$
$282$		0			0
$283$	0.631614	−	0.169240i	0.0375456	−	0.0100603i	−0.239997	−	0.970774i	$-0.577147\pi$
$283$	0.631614	−	0.169240i	0.0375456	−	0.0100603i	0.277543	+	0.960713i	$0.410480\pi$
$284$		0			0
$285$	9.68346	+	5.27011i	0.573599	+	0.312174i
$286$		0			0
$287$	5.24723	−	26.5980i	0.309734	−	1.57003i
$288$		0			0
$289$	13.1066	−	7.56710i	0.770976	−	0.445123i
$290$		0			0
$291$	−2.90632	+	5.03390i	−0.170372	+	0.295092i
$292$		0			0
$293$	−1.72555	−	1.72555i	−0.100808	−	0.100808i	0.654904	−	0.755712i	$-0.272709\pi$
$293$	−1.72555	−	1.72555i	−0.100808	−	0.100808i	−0.755712	+	0.654904i	$0.772709\pi$
$294$		0			0
$295$	−2.20594	+	9.14851i	−0.128435	+	0.532647i
$296$		0			0
$297$	−0.981876	−	3.66441i	−0.0569742	−	0.212631i
$298$		0			0
$299$	−3.40760	−	5.90213i	−0.197066	−	0.341329i
$300$		0			0
$301$	−11.6135	+	7.78634i	−0.669393	+	0.448797i
$302$		0			0
$303$	−4.68574	−	1.25554i	−0.269188	−	0.0721288i
$304$		0			0
$305$	6.36735	−	6.69650i	0.364594	−	0.383441i
$306$		0			0
$307$	−18.5555	+	18.5555i	−1.05902	+	1.05902i	−0.0608747	+	0.998145i	$0.519389\pi$
$307$	−18.5555	+	18.5555i	−1.05902	+	1.05902i	−0.998145	+	0.0608747i	$0.980611\pi$
$308$		0			0
$309$			26.1777i			1.48920i
$310$		0			0
$311$	4.30249	+	2.48404i	0.243972	+	0.140857i	0.617001	−	0.786962i	$-0.288347\pi$
$311$	4.30249	+	2.48404i	0.243972	+	0.140857i	−0.373029	+	0.927820i	$0.621681\pi$
$312$		0			0
$313$	−3.16757	+	11.8215i	−0.179041	+	0.668192i	0.816787	+	0.576940i	$0.195753\pi$
$313$	−3.16757	+	11.8215i	−0.179041	+	0.668192i	−0.995828	+	0.0912515i	$0.970913\pi$
$314$		0			0
$315$	2.42031	−	1.71262i	0.136369	−	0.0964950i
$316$		0			0
$317$	6.70491	−	25.0231i	0.376585	−	1.40543i	−0.474430	−	0.880293i	$-0.657346\pi$
$317$	6.70491	−	25.0231i	0.376585	−	1.40543i	0.851015	−	0.525142i	$-0.175988\pi$
$318$		0			0
$319$	−4.69024	−	2.70791i	−0.262603	−	0.151614i
$320$		0			0
$321$		−	8.38199i		−	0.467837i
$322$		0			0
$323$	3.01252	−	3.01252i	0.167621	−	0.167621i
$324$		0			0
$325$	7.24757	+	1.55552i	0.402023	+	0.0862847i
$326$		0			0
$327$	−25.2878	−	6.77585i	−1.39842	−	0.374705i
$328$		0			0
$329$	16.5685	+	8.13832i	0.913450	+	0.448680i
$330$		0			0
$331$	−7.58313	−	13.1344i	−0.416806	−	0.721930i	0.578810	−	0.815463i	$-0.303517\pi$
$331$	−7.58313	−	13.1344i	−0.416806	−	0.721930i	−0.995616	+	0.0935328i	$0.970184\pi$
$332$		0			0
$333$	1.16639	+	4.35301i	0.0639175	+	0.238543i
$334$		0			0
$335$	7.92120	−	4.84334i	0.432781	−	0.264620i
$336$		0			0
$337$	12.7442	+	12.7442i	0.694218	+	0.694218i	0.963157	−	0.268939i	$-0.0866729\pi$
$337$	12.7442	+	12.7442i	0.694218	+	0.694218i	−0.268939	+	0.963157i	$0.586673\pi$
$338$		0			0
$339$	−8.06541	+	13.9697i	−0.438053	+	0.758730i
$340$		0			0
$341$	5.23492	−	3.02238i	0.283487	−	0.163671i
$342$		0			0
$343$	−15.4474	−	10.2166i	−0.834080	−	0.551643i
$344$		0			0
$345$	−15.5845	+	4.59958i	−0.839043	+	0.247633i
$346$		0			0
$347$	−5.84281	+	1.56558i	−0.313658	+	0.0840445i	−0.412214	−	0.911087i	$-0.635244\pi$
$347$	−5.84281	+	1.56558i	−0.313658	+	0.0840445i	0.0985557	+	0.995132i	$0.468578\pi$
$348$		0			0
$349$	−5.80171			−0.310558			−0.155279	−	0.987871i	$-0.549628\pi$
$349$	−5.80171			−0.310558			−0.155279	+	0.987871i	$0.549628\pi$
$350$		0			0
$351$	−8.20509			−0.437955
$352$		0			0
$353$	−11.4359	+	3.06423i	−0.608670	+	0.163093i	−0.549972	−	0.835183i	$-0.685362\pi$
$353$	−11.4359	+	3.06423i	−0.608670	+	0.163093i	−0.0586980	+	0.998276i	$0.518695\pi$
$354$		0			0
$355$	26.9982	−	7.96818i	1.43292	−	0.422907i
$356$		0			0
$357$	1.84483	+	5.40675i	0.0976385	+	0.286155i
$358$		0			0
$359$	−4.22275	+	2.43801i	−0.222868	+	0.128673i	−0.607278	−	0.794490i	$-0.707738\pi$
$359$	−4.22275	+	2.43801i	−0.222868	+	0.128673i	0.384409	+	0.923163i	$0.374405\pi$
$360$		0			0
$361$	4.63599	−	8.02976i	0.243999	−	0.422619i
$362$		0			0
$363$	11.7703	+	11.7703i	0.617781	+	0.617781i
$364$		0			0
$365$	24.5006	−	14.9807i	1.28242	−	0.784125i
$366$		0			0
$367$	−1.60161	−	5.97731i	−0.0836036	−	0.312013i	0.911443	−	0.411427i	$-0.134970\pi$
$367$	−1.60161	−	5.97731i	−0.0836036	−	0.312013i	−0.995046	+	0.0994146i	$0.968303\pi$
$368$		0			0
$369$	−2.56770	−	4.44739i	−0.133669	−	0.231522i
$370$		0			0
$371$	1.64008	+	24.4342i	0.0851485	+	1.26856i
$372$		0			0
$373$	31.7180	+	8.49882i	1.64230	+	0.440052i	0.957442	−	0.288626i	$-0.0931986\pi$
$373$	31.7180	+	8.49882i	1.64230	+	0.440052i	0.684856	+	0.728679i	$0.259865\pi$
$374$		0			0
$375$	7.65598	−	15.9292i	0.395353	−	0.822581i
$376$		0			0
$377$	−8.28270	+	8.28270i	−0.426581	+	0.426581i
$378$		0			0
$379$		−	6.53089i		−	0.335469i	−0.985832	−	0.167735i	$-0.946355\pi$
$379$		−	6.53089i		−	0.335469i	0.985832	−	0.167735i	$-0.0536452\pi$
$380$		0			0
$381$	−4.12426	−	2.38115i	−0.211292	−	0.121990i
$382$		0			0
$383$	0.222463	−	0.830244i	0.0113673	−	0.0424235i	−0.960009	−	0.279968i	$-0.909676\pi$
$383$	0.222463	−	0.830244i	0.0113673	−	0.0424235i	0.971377	+	0.237545i	$0.0763427\pi$
$384$		0			0
$385$	1.69561	−	3.68369i	0.0864162	−	0.187738i
$386$		0			0
$387$	−0.685497	+	2.55831i	−0.0348458	+	0.130046i
$388$		0			0
$389$	22.8241	+	13.1775i	1.15723	+	0.668125i	0.950638	−	0.310302i	$-0.100430\pi$
$389$	22.8241	+	13.1775i	1.15723	+	0.668125i	0.206589	+	0.978428i	$0.433764\pi$
$390$		0			0
$391$			6.27927i			0.317556i
$392$		0			0
$393$	12.2351	−	12.2351i	0.617181	−	0.617181i
$394$		0			0
$395$	21.6196	−	22.7372i	1.08780	−	1.14403i
$396$		0			0
$397$	−10.4753	−	2.80685i	−0.525741	−	0.140872i	−0.0138199	−	0.999905i	$-0.504399\pi$
$397$	−10.4753	−	2.80685i	−0.525741	−	0.140872i	−0.511921	+	0.859033i	$0.671066\pi$
$398$		0			0
$399$	−7.26422	−	10.8348i	−0.363666	−	0.542417i
$400$		0			0
$401$	−1.50000	−	2.59808i	−0.0749064	−	0.129742i	0.826139	−	0.563466i	$-0.190532\pi$
$401$	−1.50000	−	2.59808i	−0.0749064	−	0.129742i	−0.901046	+	0.433724i	$0.857199\pi$
$402$		0			0
$403$	−3.38375	−	12.6283i	−0.168557	−	0.629063i
$404$		0			0
$405$	−3.79765	+	15.7497i	−0.188707	+	0.782606i
$406$		0			0
$407$	4.35839	+	4.35839i	0.216037	+	0.216037i
$408$		0			0
$409$	1.69537	−	2.93647i	0.0838308	−	0.145199i	−0.821062	−	0.570840i	$-0.806618\pi$
$409$	1.69537	−	2.93647i	0.0838308	−	0.145199i	0.904892	+	0.425640i	$0.139951\pi$
$410$		0			0
$411$	−1.85116	+	1.06877i	−0.0913109	+	0.0527184i
$412$		0			0
$413$	7.32858	−	8.38319i	0.360616	−	0.412510i
$414$		0			0
$415$	11.0990	+	6.04050i	0.544829	+	0.296517i
$416$		0			0
$417$	1.07369	−	0.287694i	0.0525788	−	0.0140884i
$418$		0			0
$419$	−1.03776			−0.0506978			−0.0253489	−	0.999679i	$-0.508070\pi$
$419$	−1.03776			−0.0506978			−0.0253489	+	0.999679i	$0.508070\pi$
$420$		0			0
$421$	−0.683118			−0.0332931			−0.0166466	−	0.999861i	$-0.505299\pi$
$421$	−0.683118			−0.0332931			−0.0166466	+	0.999861i	$0.505299\pi$
$422$		0			0
$423$	3.37749	−	0.904997i	0.164219	−	0.0440024i
$424$		0			0
$425$	−5.06641	−	4.58001i	−0.245757	−	0.222163i
$426$		0			0
$427$	−10.3477	+	3.53072i	−0.500760	+	0.170863i
$428$		0			0
$429$	−1.39117	+	0.803191i	−0.0671662	+	0.0387784i
$430$		0			0
$431$	9.34273	−	16.1821i	0.450023	−	0.779463i	−0.548364	−	0.836240i	$-0.684749\pi$
$431$	9.34273	−	16.1821i	0.450023	−	0.779463i	0.998387	+	0.0567767i	$0.0180823\pi$
$432$		0			0
$433$	7.43170	+	7.43170i	0.357145	+	0.357145i	0.862759	−	0.505615i	$-0.168734\pi$
$433$	7.43170	+	7.43170i	0.357145	+	0.357145i	−0.505615	+	0.862759i	$0.668734\pi$
$434$		0			0
$435$	14.5687	+	23.8269i	0.698517	+	1.14241i
$436$		0			0
$437$	−3.71095	−	13.8495i	−0.177519	−	0.662509i
$438$		0			0
$439$	13.5514	+	23.4717i	0.646772	+	1.12024i	0.983889	+	0.178779i	$0.0572147\pi$
$439$	13.5514	+	23.4717i	0.646772	+	1.12024i	−0.337118	+	0.941463i	$0.609452\pi$
$440$		0			0
$441$	−3.47671	+	0.468841i	−0.165558	+	0.0223258i
$442$		0			0
$443$	−36.2422	−	9.71108i	−1.72192	−	0.461387i	−0.743625	−	0.668597i	$-0.766895\pi$
$443$	−36.2422	−	9.71108i	−1.72192	−	0.461387i	−0.978297	+	0.207210i	$0.933562\pi$
$444$		0			0
$445$	−18.7957	−	17.8718i	−0.891002	−	0.847207i
$446$		0			0
$447$	−12.6345	+	12.6345i	−0.597592	+	0.597592i
$448$		0			0
$449$		−	6.36931i		−	0.300586i	−0.988641	−	0.150293i	$-0.951978\pi$
$449$		−	6.36931i		−	0.300586i	0.988641	−	0.150293i	$-0.0480217\pi$
$450$		0			0
$451$	−6.08276	−	3.51188i	−0.286426	−	0.165368i
$452$		0			0
$453$	3.23354	−	12.0677i	0.151925	−	0.566992i
$454$		0			0
$455$	−6.74657	−	5.60442i	−0.316284	−	0.262739i
$456$		0			0
$457$	3.84913	−	14.3652i	0.180055	−	0.671974i	−0.815580	−	0.578644i	$-0.803582\pi$
$457$	3.84913	−	14.3652i	0.180055	−	0.671974i	0.995635	−	0.0933301i	$-0.0297512\pi$
$458$		0			0
$459$	6.54704	+	3.77993i	0.305590	+	0.176432i
$460$		0			0
$461$			41.8860i			1.95082i	0.220390	+	0.975412i	$0.429267\pi$
$461$			41.8860i			1.95082i	−0.220390	+	0.975412i	$0.570733\pi$
$462$		0			0
$463$	17.8985	−	17.8985i	0.831813	−	0.831813i	−0.155952	−	0.987765i	$-0.549845\pi$
$463$	17.8985	−	17.8985i	0.831813	−	0.831813i	0.987765	+	0.155952i	$0.0498445\pi$
$464$		0			0
$465$	−31.1614	+	0.785128i	−1.44507	+	0.0364094i
$466$		0			0
$467$	39.4275	+	10.5646i	1.82449	+	0.488870i	0.997325	−	0.0730918i	$-0.0232866\pi$
$467$	39.4275	+	10.5646i	1.82449	+	0.488870i	0.827163	+	0.561962i	$0.189953\pi$
$468$		0			0
$469$	−10.9610	+	0.735725i	−0.506131	+	0.0339726i
$470$		0			0
$471$	1.84390	+	3.19372i	0.0849622	+	0.147159i
$472$		0			0
$473$	0.937564	+	3.49904i	0.0431092	+	0.160886i
$474$		0			0
$475$	13.8811	+	7.10742i	0.636909	+	0.326111i
$476$		0			0
$477$	3.28015	+	3.28015i	0.150188	+	0.150188i
$478$		0			0
$479$	2.44050	−	4.22708i	0.111509	−	0.193140i	−0.804870	−	0.593452i	$-0.797765\pi$
$479$	2.44050	−	4.22708i	0.111509	−	0.193140i	0.916379	+	0.400312i	$0.131098\pi$
$480$		0			0
$481$	11.5450	−	6.66552i	0.526407	−	0.303921i
$482$		0			0
$483$	18.8627	+	3.72121i	0.858281	+	0.169321i
$484$		0			0
$485$	−3.93046	+	7.22196i	−0.178473	+	0.327932i
$486$		0			0
$487$	34.1952	−	9.16256i	1.54953	−	0.415195i	0.620200	−	0.784444i	$-0.287052\pi$
$487$	34.1952	−	9.16256i	1.54953	−	0.415195i	0.929331	+	0.369249i	$0.120385\pi$
$488$		0			0
$489$	−1.78677			−0.0808003
$490$		0			0
$491$	25.8068			1.16464			0.582322	−	0.812958i	$-0.302144\pi$
$491$	25.8068			1.16464			0.582322	+	0.812958i	$0.302144\pi$
$492$		0			0
$493$	10.4247	−	2.79328i	0.469503	−	0.125803i
$494$		0			0
$495$	−0.217438	−	0.736736i	−0.00977312	−	0.0331138i
$496$		0			0
$497$	−32.6772	−	6.44652i	−1.46577	−	0.289166i
$498$		0			0
$499$	11.3336	−	6.54347i	0.507363	−	0.292926i	−0.224386	−	0.974500i	$-0.572038\pi$
$499$	11.3336	−	6.54347i	0.507363	−	0.292926i	0.731749	+	0.681574i	$0.238704\pi$
$500$		0			0
$501$	6.44151	−	11.1570i	0.287786	−	0.498459i
$502$		0			0
$503$	−15.2498	−	15.2498i	−0.679955	−	0.679955i	0.280035	−	0.959990i	$-0.409654\pi$
$503$	−15.2498	−	15.2498i	−0.679955	−	0.679955i	−0.959990	+	0.280035i	$0.909654\pi$
$504$		0			0
$505$	−6.67081	−	1.60850i	−0.296847	−	0.0715775i
$506$		0			0
$507$	−4.41951	−	16.4938i	−0.196277	−	0.732516i
$508$		0			0
$509$	−0.264712	−	0.458495i	−0.0117332	−	0.0203224i	0.860099	−	0.510127i	$-0.170402\pi$
$509$	−0.264712	−	0.458495i	−0.0117332	−	0.0203224i	−0.871832	+	0.489804i	$0.837068\pi$
$510$		0			0
$511$	−33.9029	+	2.27563i	−1.49978	+	0.100668i
$512$		0			0
$513$	−16.6739	−	4.46776i	−0.736172	−	0.197257i
$514$		0			0
$515$	0.932683	+	37.0178i	0.0410989	+	1.63120i
$516$		0			0
$517$	3.38167	−	3.38167i	0.148726	−	0.148726i
$518$		0			0
$519$			27.6429i			1.21339i
$520$		0			0
$521$	3.14066	+	1.81326i	0.137595	+	0.0794404i	0.567217	−	0.823568i	$-0.308020\pi$
$521$	3.14066	+	1.81326i	0.137595	+	0.0794404i	−0.429622	+	0.903009i	$0.641353\pi$
$522$		0			0
$523$	−5.34185	+	19.9361i	−0.233583	+	0.871743i	0.745200	+	0.666841i	$0.232354\pi$
$523$	−5.34185	+	19.9361i	−0.233583	+	0.871743i	−0.978783	+	0.204902i	$0.934313\pi$
$524$		0			0
$525$	−16.7606	+	12.5051i	−0.731493	+	0.545767i
$526$		0			0
$527$	−3.11767	+	11.6353i	−0.135808	+	0.506842i
$528$		0			0
$529$	−1.61722	−	0.933702i	−0.0703139	−	0.0405957i
$530$		0			0
$531$		−	2.10922i		−	0.0915321i
$532$		0			0
$533$	−10.7418	+	10.7418i	−0.465280	+	0.465280i
$534$		0			0
$535$	−0.298641	−	11.8529i	−0.0129114	−	0.512447i
$536$		0			0
$537$	1.63974	+	0.439366i	0.0707598	+	0.0189600i
$538$		0			0
$539$	−3.79745	+	2.93290i	−0.163568	+	0.126329i
$540$		0			0
$541$	−13.7743	−	23.8578i	−0.592204	−	1.02573i	−0.993935	−	0.109969i	$-0.964925\pi$
$541$	−13.7743	−	23.8578i	−0.592204	−	1.02573i	0.401731	−	0.915758i	$-0.368409\pi$
$542$		0			0
$543$	−3.65604	−	13.6445i	−0.156896	−	0.585543i
$544$		0			0
$545$	−36.0008	−	8.68072i	−1.54210	−	0.371841i
$546$		0			0
$547$	5.00886	+	5.00886i	0.214164	+	0.214164i	0.806034	−	0.591870i	$-0.201610\pi$
$547$	5.00886	+	5.00886i	0.214164	+	0.214164i	−0.591870	+	0.806034i	$0.701610\pi$
$548$		0			0
$549$	−1.03553	+	1.79359i	−0.0441954	+	0.0765486i
$550$		0			0
$551$	−21.3417	+	12.3216i	−0.909186	+	0.524919i
$552$		0			0
$553$	−35.1345	+	11.9882i	−1.49407	+	0.509788i
$554$		0			0
$555$	−8.99712	−	30.4845i	−0.381907	−	1.29400i
$556$		0			0
$557$	−10.0860	+	2.70252i	−0.427356	+	0.114510i	−0.466085	−	0.884740i	$-0.654336\pi$
$557$	−10.0860	+	2.70252i	−0.427356	+	0.114510i	0.0387290	+	0.999250i	$0.487669\pi$
$558$		0			0
$559$	7.83479			0.331376
$560$		0			0
$561$	1.48006			0.0624883
$562$		0			0
$563$	−26.7021	+	7.15482i	−1.12536	+	0.301540i	−0.773051	−	0.634344i	$-0.781270\pi$
$563$	−26.7021	+	7.15482i	−1.12536	+	0.301540i	−0.352310	+	0.935883i	$0.614604\pi$
$564$		0			0
$565$	−10.9075	+	20.0418i	−0.458883	+	0.843167i
$566$		0			0
$567$	12.6165	−	14.4321i	0.529845	−	0.606092i
$568$		0			0
$569$	−9.63770	+	5.56433i	−0.404033	+	0.233269i	−0.688223	−	0.725499i	$-0.741609\pi$
$569$	−9.63770	+	5.56433i	−0.404033	+	0.233269i	0.284189	+	0.958768i	$0.408276\pi$
$570$		0			0
$571$	−10.3474	+	17.9222i	−0.433025	+	0.750022i	−0.997132	−	0.0756800i	$-0.975887\pi$
$571$	−10.3474	+	17.9222i	−0.433025	+	0.750022i	0.564107	+	0.825702i	$0.309221\pi$
$572$		0			0
$573$	27.2508	+	27.2508i	1.13842	+	1.13842i
$574$		0			0
$575$	−21.8741	+	7.05950i	−0.912215	+	0.294402i
$576$		0			0
$577$	1.87648	+	7.00314i	0.0781191	+	0.291544i	0.993922	−	0.110083i	$-0.0351115\pi$
$577$	1.87648	+	7.00314i	0.0781191	+	0.291544i	−0.915803	+	0.401627i	$0.868445\pi$
$578$		0			0
$579$	−7.13963	−	12.3662i	−0.296713	−	0.513922i
$580$		0			0
$581$	−8.32611	−	12.4186i	−0.345425	−	0.515211i
$582$		0			0
$583$	6.12841	+	1.64210i	0.253813	+	0.0680090i
$584$		0			0
$585$	−1.66086	+	0.0418462i	−0.0686681	+	0.00173013i
$586$		0			0
$587$	5.87340	−	5.87340i	0.242421	−	0.242421i	−0.575430	−	0.817851i	$-0.695165\pi$
$587$	5.87340	−	5.87340i	0.242421	−	0.242421i	0.817851	+	0.575430i	$0.195165\pi$
$588$		0			0
$589$		−	27.5051i		−	1.13333i
$590$		0			0
$591$	3.45918	+	1.99716i	0.142292	+	0.0821521i
$592$		0			0
$593$	7.06897	−	26.3818i	0.290288	−	1.08337i	−0.654600	−	0.755975i	$-0.727163\pi$
$593$	7.06897	−	26.3818i	0.290288	−	1.08337i	0.944888	−	0.327394i	$-0.106170\pi$
$594$		0			0
$595$	2.80140	+	7.57993i	0.114846	+	0.310747i
$596$		0			0
$597$	−3.82294	+	14.2674i	−0.156463	+	0.583926i
$598$		0			0
$599$	−21.9641	−	12.6810i	−0.897430	−	0.518131i	−0.0210645	−	0.999778i	$-0.506706\pi$
$599$	−21.9641	−	12.6810i	−0.897430	−	0.518131i	−0.876366	+	0.481647i	$0.840039\pi$
$600$		0			0
$601$		−	13.8045i		−	0.563099i	−0.959547	−	0.281550i	$-0.909152\pi$
$601$		−	13.8045i		−	0.563099i	0.959547	−	0.281550i	$-0.0908484\pi$
$602$		0			0
$603$	−1.47145	+	1.47145i	−0.0599221	+	0.0599221i
$604$		0			0
$605$	17.0637	+	16.2250i	0.693739	+	0.659639i
$606$		0			0
$607$	21.6409	+	5.79866i	0.878376	+	0.235360i	0.669707	−	0.742626i	$-0.266420\pi$
$607$	21.6409	+	5.79866i	0.878376	+	0.235360i	0.208670	+	0.977986i	$0.433087\pi$
$608$		0			0
$609$	−2.21306	−	32.9706i	−0.0896776	−	1.33604i
$610$		0			0
$611$	−5.17176	−	8.95776i	−0.209227	−	0.362392i
$612$		0			0
$613$	8.61481	+	32.1509i	0.347949	+	1.29856i	0.889129	+	0.457656i	$0.151311\pi$
$613$	8.61481	+	32.1509i	0.347949	+	1.29856i	−0.541180	+	0.840907i	$0.682022\pi$
$614$		0			0
$615$	18.8942	+	30.9011i	0.761886	+	1.24605i
$616$		0			0
$617$	21.1167	+	21.1167i	0.850125	+	0.850125i	0.990148	−	0.140023i	$-0.0447177\pi$
$617$	21.1167	+	21.1167i	0.850125	+	0.850125i	−0.140023	+	0.990148i	$0.544718\pi$
$618$		0			0
$619$	18.2311	−	31.5771i	0.732768	−	1.26919i	−0.222927	−	0.974835i	$-0.571561\pi$
$619$	18.2311	−	31.5771i	0.732768	−	1.26919i	0.955696	−	0.294357i	$-0.0951055\pi$
$620$		0			0
$621$	22.0338	−	12.7212i	0.884184	−	0.510484i
$622$		0			0
$623$	9.91000	+	29.0439i	0.397036	+	1.16362i
$624$		0			0
$625$	10.2588	−	22.7982i	0.410350	−	0.911928i
$626$		0			0
$627$	−3.26440	+	0.874694i	−0.130368	+	0.0349319i
$628$		0			0
$629$	−12.2827			−0.489744
$630$		0			0
$631$	47.0247			1.87203			0.936013	−	0.351966i	$-0.114487\pi$
$631$	47.0247			1.87203			0.936013	+	0.351966i	$0.114487\pi$
$632$		0			0
$633$	−15.0355	+	4.02875i	−0.597607	+	0.160128i
$634$		0			0
$635$	−5.91694	−	3.22022i	−0.234807	−	0.127791i
$636$		0			0
$637$	4.00148	+	9.57518i	0.158544	+	0.379383i
$638$		0			0
$639$	−5.46387	+	3.15457i	−0.216147	+	0.124793i
$640$		0			0
$641$	8.05261	−	13.9475i	0.318059	−	0.550894i	−0.662024	−	0.749483i	$-0.730302\pi$
$641$	8.05261	−	13.9475i	0.318059	−	0.550894i	0.980083	+	0.198588i	$0.0636357\pi$
$642$		0			0
$643$	−29.1021	−	29.1021i	−1.14768	−	1.14768i	−0.987009	−	0.160667i	$-0.948635\pi$
$643$	−29.1021	−	29.1021i	−1.14768	−	1.14768i	−0.160667	−	0.987009i	$-0.551365\pi$
$644$		0			0
$645$	4.37876	−	18.1596i	0.172413	−	0.715035i
$646$		0			0
$647$	11.0524	+	41.2480i	0.434513	+	1.62163i	0.742228	+	0.670147i	$0.233769\pi$
$647$	11.0524	+	41.2480i	0.434513	+	1.62163i	−0.307715	+	0.951479i	$0.599564\pi$
$648$		0			0
$649$	−1.44240	−	2.49831i	−0.0566192	−	0.0980673i
$650$		0			0
$651$	33.1044	+	16.2606i	1.29746	+	0.637304i
$652$		0			0
$653$	32.2037	+	8.62895i	1.26023	+	0.337677i	0.826279	−	0.563261i	$-0.190453\pi$
$653$	32.2037	+	8.62895i	1.26023	+	0.337677i	0.433948	+	0.900938i	$0.357120\pi$
$654$		0			0
$655$	16.8657	−	17.7376i	0.658999	−	0.693065i
$656$		0			0
$657$	−4.55127	+	4.55127i	−0.177562	+	0.177562i
$658$		0			0
$659$		−	2.01773i		−	0.0785996i	−0.999227	−	0.0392998i	$-0.987487\pi$
$659$		−	2.01773i		−	0.0785996i	0.999227	−	0.0392998i	$-0.0125127\pi$
$660$		0			0
$661$	0.409726	+	0.236556i	0.0159365	+	0.00920095i	0.507947	−	0.861388i	$-0.330405\pi$
$661$	0.409726	+	0.236556i	0.0159365	+	0.00920095i	−0.492011	+	0.870589i	$0.663738\pi$
$662$		0			0
$663$	0.828513	−	3.09205i	0.0321768	−	0.120085i
$664$		0			0
$665$	−10.6583	−	15.0626i	−0.413312	−	0.584102i
$666$		0			0
$667$	9.40065	−	35.0837i	0.363995	−	1.35845i
$668$		0			0
$669$	0.655592	+	0.378506i	0.0253466	+	0.0146339i
$670$		0			0
$671$			2.83262i			0.109352i
$672$		0			0
$673$	−15.1663	+	15.1663i	−0.584616	+	0.584616i	−0.936168	−	0.351552i	$-0.885654\pi$
$673$	−15.1663	+	15.1663i	−0.584616	+	0.584616i	0.351552	+	0.936168i	$0.385654\pi$
$674$		0			0
$675$	−5.80705	+	27.0565i	−0.223513	+	1.04141i
$676$		0			0
$677$	−13.7216	−	3.67670i	−0.527365	−	0.141307i	−0.0146937	−	0.999892i	$-0.504677\pi$
$677$	−13.7216	−	3.67670i	−0.527365	−	0.141307i	−0.512671	+	0.858585i	$0.671344\pi$
$678$		0			0
$679$	8.08060	−	5.41767i	0.310105	−	0.207911i
$680$		0			0
$681$	10.9613	+	18.9855i	0.420038	+	0.727527i
$682$		0			0
$683$	−5.41929	−	20.2251i	−0.207363	−	0.773891i	−0.988716	−	0.149801i	$-0.952137\pi$
$683$	−5.41929	−	20.2251i	−0.207363	−	0.773891i	0.781353	−	0.624090i	$-0.214530\pi$
$684$		0			0
$685$	−2.57964	+	1.57729i	−0.0985628	+	0.0602653i
$686$		0			0
$687$	−2.97653	−	2.97653i	−0.113562	−	0.113562i
$688$		0			0
$689$	6.86115	−	11.8839i	0.261389	−	0.452739i
$690$		0			0
$691$	5.60324	−	3.23504i	0.213157	−	0.123067i	−0.389620	−	0.920976i	$-0.627394\pi$
$691$	5.60324	−	3.23504i	0.213157	−	0.123067i	0.602778	+	0.797909i	$0.294060\pi$
$692$		0			0
$693$	−0.175914	+	0.891704i	−0.00668244	+	0.0338730i
$694$		0			0
$695$	1.50805	−	0.445082i	0.0572036	−	0.0168829i
$696$		0			0
$697$	13.5197	−	3.62260i	0.512096	−	0.137216i
$698$		0			0
$699$	−29.9281			−1.13198
$700$		0			0
$701$	15.5423			0.587026			0.293513	−	0.955955i	$-0.405176\pi$
$701$	15.5423			0.587026			0.293513	+	0.955955i	$0.405176\pi$
$702$		0			0
$703$	27.0906	−	7.25890i	1.02174	−	0.273774i
$704$		0			0
$705$	−23.6529	+	6.98085i	−0.890820	+	0.262914i
$706$		0			0
$707$	6.11276	+	5.34378i	0.229894	+	0.200973i
$708$		0			0
$709$	7.77659	−	4.48981i	0.292056	−	0.168619i	−0.346813	−	0.937934i	$-0.612736\pi$
$709$	7.77659	−	4.48981i	0.292056	−	0.168619i	0.638869	+	0.769316i	$0.279403\pi$
$710$		0			0
$711$	−3.51603	+	6.08994i	−0.131861	+	0.228391i
$712$		0			0
$713$	28.6657	+	28.6657i	1.07354	+	1.07354i
$714$		0			0
$715$	−1.93863	+	1.18536i	−0.0725006	+	0.0443298i
$716$		0			0
$717$	−2.35013	−	8.77079i	−0.0877670	−	0.327551i
$718$		0			0
$719$	−20.2758	−	35.1187i	−0.756160	−	1.30971i	−0.944795	−	0.327661i	$-0.893740\pi$
$719$	−20.2758	−	35.1187i	−0.756160	−	1.30971i	0.188635	−	0.982047i	$-0.439594\pi$
$720$		0			0
$721$	19.3166	−	39.3259i	0.719388	−	1.46457i
$722$		0			0
$723$	15.5532	+	4.16748i	0.578432	+	0.154990i
$724$		0			0
$725$	21.4505	+	33.1745i	0.796652	+	1.23207i
$726$		0			0
$727$	−11.9052	+	11.9052i	−0.441540	+	0.441540i	−0.892529	−	0.450990i	$-0.851071\pi$
$727$	−11.9052	+	11.9052i	−0.441540	+	0.441540i	0.450990	+	0.892529i	$0.351071\pi$
$728$		0			0
$729$		−	29.8776i		−	1.10658i
$730$		0			0
$731$	−6.25157	−	3.60935i	−0.231223	−	0.133496i
$732$		0			0
$733$	1.60311	−	5.98288i	0.0592121	−	0.220983i	−0.929979	−	0.367611i	$-0.880176\pi$
$733$	1.60311	−	5.98288i	0.0592121	−	0.220983i	0.989192	+	0.146629i	$0.0468423\pi$
$734$		0			0
$735$	24.4299	−	3.92328i	0.901112	−	0.144712i
$736$		0			0
$737$	−0.736634	+	2.74916i	−0.0271343	+	0.101266i
$738$		0			0
$739$	−34.3295	−	19.8201i	−1.26283	−	0.729095i	−0.289208	−	0.957266i	$-0.593392\pi$
$739$	−34.3295	−	19.8201i	−1.26283	−	0.729095i	−0.973621	+	0.228171i	$0.926725\pi$
$740$		0			0
$741$			7.30942i			0.268518i
$742$		0			0
$743$	−15.7507	+	15.7507i	−0.577837	+	0.577837i	−0.934307	−	0.356470i	$-0.883980\pi$
$743$	−15.7507	+	15.7507i	−0.577837	+	0.577837i	0.356470	+	0.934307i	$0.383980\pi$
$744$		0			0
$745$	−17.4162	+	18.3166i	−0.638082	+	0.671067i
$746$		0			0
$747$	−2.73566	−	0.733018i	−0.100093	−	0.0268197i
$748$		0			0
$749$	−6.18510	+	12.5920i	−0.225999	+	0.460101i
$750$		0			0
$751$	9.16731	+	15.8782i	0.334520	+	0.579405i	0.983392	−	0.181492i	$-0.0580926\pi$
$751$	9.16731	+	15.8782i	0.334520	+	0.579405i	−0.648873	+	0.760897i	$0.724759\pi$
$752$		0			0
$753$	−2.98205	−	11.1292i	−0.108672	−	0.405570i
$754$		0			0
$755$	4.14258	−	17.1802i	0.150764	−	0.625250i
$756$		0			0
$757$	−14.1143	−	14.1143i	−0.512994	−	0.512994i	0.402449	−	0.915443i	$-0.368159\pi$
$757$	−14.1143	−	14.1143i	−0.512994	−	0.512994i	−0.915443	+	0.402449i	$0.868159\pi$
$758$		0			0
$759$	2.49054	−	4.31374i	0.0904009	−	0.156579i
$760$		0			0
$761$	10.0843	−	5.82217i	0.365555	−	0.211054i	−0.305960	−	0.952045i	$-0.598977\pi$
$761$	10.0843	−	5.82217i	0.365555	−	0.211054i	0.671515	+	0.740991i	$0.265644\pi$
$762$		0			0
$763$	32.9891	+	28.8391i	1.19429	+	1.04405i
$764$		0			0
$765$	1.34452	+	0.731737i	0.0486111	+	0.0264560i
$766$		0			0
$767$	−6.02674	+	1.61486i	−0.217613	+	0.0583092i
$768$		0			0
$769$	45.3371			1.63490			0.817448	−	0.576002i	$-0.195388\pi$
$769$	45.3371			1.63490			0.817448	+	0.576002i	$0.195388\pi$
$770$		0			0
$771$	−19.3119			−0.695501
$772$		0			0
$773$	−7.05078	+	1.88925i	−0.253599	+	0.0679516i	−0.383379	−	0.923591i	$-0.625240\pi$
$773$	−7.05078	+	1.88925i	−0.253599	+	0.0679516i	0.129780	+	0.991543i	$0.458573\pi$
$774$		0			0
$775$	−44.0372	+	2.22049i	−1.58186	+	0.0797624i
$776$		0			0
$777$	−7.27896	+	36.8968i	−0.261131	+	1.32367i
$778$		0			0
$779$	−27.6780	+	15.9799i	−0.991666	+	0.572539i
$780$		0			0
$781$	−4.31455	+	7.47301i	−0.154387	+	0.267405i
$782$		0			0
$783$	−30.9209	−	30.9209i	−1.10502	−	1.10502i
$784$		0			0
$785$	2.72123	+	4.45053i	0.0971250	+	0.158846i
$786$		0			0
$787$	−7.92786	−	29.5872i	−0.282598	−	1.05467i	−0.950577	−	0.310489i	$-0.899507\pi$
$787$	−7.92786	−	29.5872i	−0.282598	−	1.05467i	0.667979	−	0.744180i	$-0.267159\pi$
$788$		0			0
$789$	16.9991	+	29.4433i	0.605184	+	1.04821i
$790$		0			0
$791$	22.4247	−	15.0347i	0.797330	−	0.534574i
$792$		0			0
$793$	5.91772	+	1.58565i	0.210145	+	0.0563081i
$794$		0			0
$795$	−23.7101	−	22.5447i	−0.840909	−	0.799576i
$796$		0			0
$797$	30.7751	−	30.7751i	1.09011	−	1.09011i	0.0945938	−	0.995516i	$-0.469845\pi$
$797$	30.7751	−	30.7751i	1.09011	−	1.09011i	0.995516	−	0.0945938i	$-0.0301552\pi$
$798$		0			0
$799$			9.53015i			0.337153i
$800$		0			0
$801$	5.03424	+	2.90652i	0.177876	+	0.102697i
$802$		0			0
$803$	−2.27845	+	8.50328i	−0.0804046	+	0.300074i
$804$		0			0
$805$	26.8062	+	4.59008i	0.944794	+	0.161779i
$806$		0			0
$807$	−10.8319	+	40.4253i	−0.381302	+	1.42304i
$808$		0			0
$809$	12.6957	+	7.32984i	0.446355	+	0.257703i	0.706290	−	0.707923i	$-0.250368\pi$
$809$	12.6957	+	7.32984i	0.446355	+	0.257703i	−0.259934	+	0.965626i	$0.583701\pi$
$810$		0			0
$811$		−	0.360507i		−	0.0126591i	−0.999980	−	0.00632956i	$-0.997985\pi$
$811$		−	0.360507i		−	0.0126591i	0.999980	−	0.00632956i	$-0.00201477\pi$
$812$		0			0
$813$	−19.9503	+	19.9503i	−0.699688	+	0.699688i
$814$		0			0
$815$	−2.52666	+	0.0636605i	−0.0885049	+	0.00222993i
$816$		0			0
$817$	15.9214	+	4.26613i	0.557020	+	0.149253i
$818$		0			0
$819$	1.76442	+	0.866669i	0.0616537	+	0.0302839i
$820$		0			0
$821$	−11.1407	−	19.2962i	−0.388812	−	0.673442i	0.603478	−	0.797379i	$-0.293781\pi$
$821$	−11.1407	−	19.2962i	−0.388812	−	0.673442i	−0.992290	+	0.123938i	$0.960448\pi$
$822$		0			0
$823$	−2.99459	−	11.1760i	−0.104385	−	0.389569i	0.893890	−	0.448287i	$-0.147966\pi$
$823$	−2.99459	−	11.1760i	−0.104385	−	0.389569i	−0.998275	+	0.0587174i	$0.981299\pi$
$824$		0			0
$825$	1.66397	+	5.15587i	0.0579319	+	0.179504i
$826$		0			0
$827$	−24.7972	−	24.7972i	−0.862283	−	0.862283i	0.129320	−	0.991603i	$-0.458721\pi$
$827$	−24.7972	−	24.7972i	−0.862283	−	0.862283i	−0.991603	+	0.129320i	$0.958721\pi$
$828$		0			0
$829$	−12.6987	+	21.9948i	−0.441044	+	0.763911i	−0.997767	−	0.0667871i	$-0.978725\pi$
$829$	−12.6987	+	21.9948i	−0.441044	+	0.763911i	0.556723	+	0.830698i	$0.312059\pi$
$830$		0			0
$831$	−36.3258	+	20.9727i	−1.26013	+	0.727536i
$832$		0			0
$833$	1.21823	−	9.48368i	0.0422093	−	0.328590i
$834$		0			0
$835$	8.71140	−	16.0066i	0.301471	−	0.553932i
$836$		0			0
$837$	47.1440	−	12.6322i	1.62953	−	0.436632i
$838$		0			0
$839$	4.36253			0.150611			0.0753057	−	0.997160i	$-0.476007\pi$
$839$	4.36253			0.150611			0.0753057	+	0.997160i	$0.476007\pi$
$840$		0			0
$841$	−33.4268			−1.15265
$842$		0			0
$843$	−28.6241	+	7.66981i	−0.985867	+	0.264162i
$844$		0			0
$845$	−6.83726	−	23.1664i	−0.235209	−	0.796948i
$846$		0			0
$847$	−8.99681	−	26.3675i	−0.309134	−	0.905999i
$848$		0			0
$849$	0.895173	−	0.516829i	0.0307223	−	0.0177375i
$850$		0			0
$851$	−20.6685	+	35.7988i	−0.708506	+	1.22717i
$852$		0			0
$853$	−36.8935	−	36.8935i	−1.26321	−	1.26321i	−0.949528	−	0.313683i	$-0.898437\pi$
$853$	−36.8935	−	36.8935i	−1.26321	−	1.26321i	−0.313683	−	0.949528i	$-0.601563\pi$
$854$		0			0
$855$	−3.39789	−	0.819319i	−0.116205	−	0.0280201i
$856$		0			0
$857$	6.60994	+	24.6686i	0.225791	+	0.842665i	0.982086	+	0.188433i	$0.0603410\pi$
$857$	6.60994	+	24.6686i	0.225791	+	0.842665i	−0.756295	+	0.654231i	$0.772992\pi$
$858$		0			0
$859$	16.3819	+	28.3743i	0.558944	+	0.968120i	0.997585	+	0.0694571i	$0.0221267\pi$
$859$	16.3819	+	28.3743i	0.558944	+	0.968120i	−0.438641	+	0.898662i	$0.644540\pi$
$860$		0			0
$861$	−2.87011	−	42.7595i	−0.0978130	−	1.45724i
$862$		0			0
$863$	23.2414	+	6.22751i	0.791146	+	0.211987i	0.631693	−	0.775219i	$-0.282360\pi$
$863$	23.2414	+	6.22751i	0.791146	+	0.211987i	0.159453	+	0.987206i	$0.449027\pi$
$864$		0			0
$865$	0.984886	+	39.0897i	0.0334871	+	1.32909i
$866$		0			0
$867$	16.9166	−	16.9166i	0.574518	−	0.574518i
$868$		0			0
$869$			9.61784i			0.326263i
$870$		0			0
$871$	5.33101	+	3.07786i	0.180634	+	0.104289i
$872$		0			0
$873$	0.476963	−	1.78005i	0.0161428	−	0.0602456i
$874$		0			0
$875$	−23.2556	+	18.2806i	−0.786181	+	0.617996i
$876$		0			0
$877$	−12.5142	+	46.7037i	−0.422575	+	1.57707i	0.346586	+	0.938018i	$0.387341\pi$
$877$	−12.5142	+	46.7037i	−0.422575	+	1.57707i	−0.769162	+	0.639054i	$0.779326\pi$
$878$		0			0
$879$	−3.34074	−	1.92878i	−0.112680	−	0.0650560i
$880$		0			0
$881$		−	3.63541i		−	0.122480i	−0.998123	−	0.0612400i	$-0.980494\pi$
$881$		−	3.63541i		−	0.122480i	0.998123	−	0.0612400i	$-0.0195055\pi$
$882$		0			0
$883$	−7.50117	+	7.50117i	−0.252434	+	0.252434i	−0.821968	−	0.569534i	$-0.807124\pi$
$883$	−7.50117	+	7.50117i	−0.252434	+	0.252434i	0.569534	+	0.821968i	$0.307124\pi$
$884$		0			0
$885$	0.374694	+	14.8714i	0.0125952	+	0.499898i
$886$		0			0
$887$	10.9141	+	2.92442i	0.366459	+	0.0981924i	0.437349	−	0.899292i	$-0.355917\pi$
$887$	10.9141	+	2.92442i	0.366459	+	0.0981924i	−0.0708903	+	0.997484i	$0.522584\pi$
$888$		0			0
$889$	4.43869	+	6.62043i	0.148869	+	0.222042i
$890$		0			0
$891$	−2.48317	−	4.30098i	−0.0831894	−	0.144088i
$892$		0			0
$893$	−5.63217	−	21.0195i	−0.188473	−	0.703392i
$894$		0			0
$895$	2.33440	+	0.562883i	0.0780303	+	0.0188151i
$896$		0			0
$897$	−7.61784	−	7.61784i	−0.254352	−	0.254352i
$898$		0			0
$899$	34.8383	−	60.3416i	1.16192	−	2.01251i
$900$		0			0
$901$	−10.9494	+	6.32162i	−0.364776	+	0.210604i
$902$		0			0
$903$	−14.5471	+	16.6405i	−0.484098	+	0.553761i
$904$		0			0
$905$	−5.65613	−	19.1644i	−0.188016	−	0.637047i
$906$		0			0
$907$	−15.5739	+	4.17302i	−0.517124	+	0.138563i	−0.507936	−	0.861395i	$-0.669591\pi$
$907$	−15.5739	+	4.17302i	−0.517124	+	0.138563i	−0.00918798	+	0.999958i	$0.502925\pi$
$908$		0			0
$909$	1.53798			0.0510114
$910$		0			0
$911$	−31.2211			−1.03440			−0.517201	−	0.855864i	$-0.673026\pi$
$911$	−31.2211			−1.03440			−0.517201	+	0.855864i	$0.673026\pi$
$912$		0			0
$913$	−3.74160	+	1.00256i	−0.123829	+	0.0331798i
$914$		0			0
$915$	6.98259	−	12.8300i	0.230837	−	0.424148i
$916$		0			0
$917$	−27.4088	+	9.35211i	−0.905118	+	0.308834i
$918$		0			0
$919$	−42.7681	+	24.6922i	−1.41079	+	0.814520i	−0.995463	−	0.0951513i	$-0.969667\pi$
$919$	−42.7681	+	24.6922i	−1.41079	+	0.814520i	−0.415328	+	0.909672i	$0.636333\pi$
$920$		0			0
$921$	−20.7409	+	35.9242i	−0.683435	+	1.18374i
$922$		0			0
$923$	13.1969	+	13.1969i	0.434382	+	0.434382i
$924$		0			0
$925$	−13.8089	−	42.7875i	−0.454034	−	1.40684i
$926$		0			0
$927$	−2.14804	−	8.01661i	−0.0705510	−	0.263300i
$928$		0			0
$929$	26.4711	+	45.8492i	0.868487	+	1.50426i	0.863542	+	0.504276i	$0.168241\pi$
$929$	26.4711	+	45.8492i	0.868487	+	1.50426i	0.00494489	+	0.999988i	$0.498426\pi$
$930$		0			0
$931$	2.91779	+	21.6370i	0.0956267	+	0.709124i
$932$		0			0
$933$	7.58580	+	2.03261i	0.248348	+	0.0665447i
$934$		0			0
$935$	2.09295	−	0.0527330i	0.0684468	−	0.00172455i
$936$		0			0
$937$	28.9004	−	28.9004i	0.944134	−	0.944134i	−0.0543857	−	0.998520i	$-0.517320\pi$
$937$	28.9004	−	28.9004i	0.944134	−	0.944134i	0.998520	+	0.0543857i	$0.0173201\pi$
$938$		0			0
$939$			19.3463i			0.631343i
$940$		0			0
$941$	−31.1600	−	17.9902i	−1.01579	−	0.586465i	−0.102906	−	0.994691i	$-0.532814\pi$
$941$	−31.1600	−	17.9902i	−1.01579	−	0.586465i	−0.912881	+	0.408226i	$0.866147\pi$
$942$		0			0
$943$	12.1917	−	45.5000i	0.397016	−	1.48168i
$944$		0			0
$945$	20.9224	−	25.1862i	0.680604	−	0.819307i
$946$		0			0
$947$	−5.00874	+	18.6929i	−0.162762	+	0.607437i	0.835553	+	0.549410i	$0.185148\pi$
$947$	−5.00874	+	18.6929i	−0.162762	+	0.607437i	−0.998315	+	0.0580267i	$0.981519\pi$
$948$		0			0
$949$	16.4891	+	9.51997i	0.535258	+	0.309031i
$950$		0			0
$951$		−	40.9511i		−	1.32793i
$952$		0			0
$953$	13.7055	−	13.7055i	0.443965	−	0.443965i	−0.449377	−	0.893342i	$-0.648354\pi$
$953$	13.7055	−	13.7055i	0.443965	−	0.443965i	0.893342	+	0.449377i	$0.148354\pi$
$954$		0			0
$955$	39.5061	+	37.5643i	1.27839	+	1.21555i
$956$		0			0
$957$	−8.26945	−	2.21579i	−0.267313	−	0.0716264i
$958$		0			0
$959$	3.56958	−	0.239598i	0.115268	−	0.00773702i
$960$		0			0
$961$	23.3841	+	40.5024i	0.754325	+	1.30653i
$962$		0			0
$963$	0.687794	+	2.56688i	0.0221639	+	0.0827167i
$964$		0			0
$965$	−10.5367	−	17.2326i	−0.339189	−	0.554737i
$966$		0			0
$967$	−26.8117	−	26.8117i	−0.862207	−	0.862207i	0.129387	−	0.991594i	$-0.458699\pi$
$967$	−26.8117	−	26.8117i	−0.862207	−	0.862207i	−0.991594	+	0.129387i	$0.958699\pi$
$968$		0			0
$969$	3.36732	−	5.83236i	0.108174	−	0.187362i
$970$		0			0
$971$	1.91146	−	1.10358i	0.0613417	−	0.0354157i	−0.469015	−	0.883190i	$-0.655391\pi$
$971$	1.91146	−	1.10358i	0.0613417	−	0.0354157i	0.530357	+	0.847774i	$0.322058\pi$
$972$		0			0
$973$	−1.82526	−	0.360085i	−0.0585151	−	0.0115438i
$974$		0			0
$975$	11.7028	−	0.590090i	0.374789	−	0.0188980i
$976$		0			0
$977$	−52.3853	+	14.0366i	−1.67596	+	0.449071i	−0.966707	−	0.255887i	$-0.917632\pi$
$977$	−52.3853	+	14.0366i	−1.67596	+	0.449071i	−0.709249	+	0.704958i	$0.750966\pi$
$978$		0			0
$979$	7.95058			0.254102
$980$		0			0
$981$	8.30009			0.265001
$982$		0			0
$983$	34.0552	−	9.12508i	1.08619	−	0.291045i	0.329063	−	0.944308i	$-0.393267\pi$
$983$	34.0552	−	9.12508i	1.08619	−	0.291045i	0.757131	+	0.653263i	$0.226601\pi$
$984$		0			0
$985$	4.96277	+	2.70093i	0.158127	+	0.0860587i
$986$		0			0
$987$	28.6282	+	5.64774i	0.911245	+	0.179769i
$988$		0			0
$989$	−21.0394	+	12.1471i	−0.669013	+	0.386255i
$990$		0			0
$991$	−4.16103	+	7.20712i	−0.132179	+	0.228942i	−0.924516	−	0.381142i	$-0.875531\pi$
$991$	−4.16103	+	7.20712i	−0.132179	+	0.228942i	0.792337	+	0.610084i	$0.208864\pi$
$992$		0			0
$993$	−16.9524	−	16.9524i	−0.537969	−	0.537969i
$994$		0			0
$995$	−4.89767	+	20.3117i	−0.155267	+	0.643924i
$996$		0			0
$997$	−8.17487	−	30.5090i	−0.258901	−	0.966230i	−0.965879	−	0.258995i	$-0.916609\pi$
$997$	−8.17487	−	30.5090i	−0.258901	−	0.966230i	0.706978	−	0.707235i	$-0.250058\pi$
$998$		0			0
$999$	24.8836	+	43.0997i	0.787283	+	1.36361i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	140.2.u.a.17.3	✓	16
3.2	odd	2		1260.2.dq.a.577.1		16
4.3	odd	2		560.2.ci.d.17.2		16
5.2	odd	4		700.2.bc.b.493.2		16
5.3	odd	4	inner	140.2.u.a.73.3	yes	16
5.4	even	2		700.2.bc.b.157.2		16
7.2	even	3		980.2.v.a.117.2		16
7.3	odd	6		980.2.m.a.97.6		16
7.4	even	3		980.2.m.a.97.3		16
7.5	odd	6	inner	140.2.u.a.117.3	yes	16
7.6	odd	2		980.2.v.a.717.2		16
15.8	even	4		1260.2.dq.a.73.2		16
20.3	even	4		560.2.ci.d.353.2		16
21.5	even	6		1260.2.dq.a.397.2		16
28.19	even	6		560.2.ci.d.257.2		16
35.3	even	12		980.2.m.a.293.3		16
35.12	even	12		700.2.bc.b.593.2		16
35.13	even	4		980.2.v.a.913.2		16
35.18	odd	12		980.2.m.a.293.6		16
35.19	odd	6		700.2.bc.b.257.2		16
35.23	odd	12		980.2.v.a.313.2		16
35.33	even	12	inner	140.2.u.a.33.3	yes	16
105.68	odd	12		1260.2.dq.a.1153.1		16
140.103	odd	12		560.2.ci.d.33.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.u.a.17.3	✓	16	1.1	even	1	trivial
140.2.u.a.33.3	yes	16	35.33	even	12	inner
140.2.u.a.73.3	yes	16	5.3	odd	4	inner
140.2.u.a.117.3	yes	16	7.5	odd	6	inner
560.2.ci.d.17.2		16	4.3	odd	2
560.2.ci.d.33.2		16	140.103	odd	12
560.2.ci.d.257.2		16	28.19	even	6
560.2.ci.d.353.2		16	20.3	even	4
700.2.bc.b.157.2		16	5.4	even	2
700.2.bc.b.257.2		16	35.19	odd	6
700.2.bc.b.493.2		16	5.2	odd	4
700.2.bc.b.593.2		16	35.12	even	12
980.2.m.a.97.3		16	7.4	even	3
980.2.m.a.97.6		16	7.3	odd	6
980.2.m.a.293.3		16	35.3	even	12
980.2.m.a.293.6		16	35.18	odd	12
980.2.v.a.117.2		16	7.2	even	3
980.2.v.a.313.2		16	35.23	odd	12
980.2.v.a.717.2		16	7.6	odd	2
980.2.v.a.913.2		16	35.13	even	4
1260.2.dq.a.73.2		16	15.8	even	4
1260.2.dq.a.397.2		16	21.5	even	6
1260.2.dq.a.577.1		16	3.2	odd	2
1260.2.dq.a.1153.1		16	105.68	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	140.u (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.52691 - 0.409133i) q^{3} +(2.14461 - 0.632955i) q^{5} +(-2.59572 - 0.512081i) q^{7} +(-0.434025 + 0.250584i) q^{9} +O(q^{10})\)	\(q+(1.52691 - 0.409133i) q^{3} +(2.14461 - 0.632955i) q^{5} +(-2.59572 - 0.512081i) q^{7} +(-0.434025 + 0.250584i) q^{9} +(-0.342727 + 0.593621i) q^{11} +(1.04830 + 1.04830i) q^{13} +(3.01566 - 1.84390i) q^{15} +(-0.353532 - 1.31940i) q^{17} +(1.55949 + 2.70111i) q^{19} +(-4.17293 + 0.280096i) q^{21} +(-4.44038 - 1.18980i) q^{23} +(4.19874 - 2.71489i) q^{25} +(-3.91351 + 3.91351i) q^{27} +7.90106i q^{29} +(-7.63715 - 4.40931i) q^{31} +(-0.280442 + 1.04663i) q^{33} +(-5.89095 + 0.544760i) q^{35} +(2.32733 - 8.68572i) q^{37} +(2.02956 + 1.17176i) q^{39} +10.2469i q^{41} +(3.73689 - 3.73689i) q^{43} +(-0.772206 + 0.812125i) q^{45} +(-6.73924 - 1.80577i) q^{47} +(6.47555 + 2.65844i) q^{49} +(-1.07962 - 1.86996i) q^{51} +(-2.39564 - 8.94065i) q^{53} +(-0.359282 + 1.49002i) q^{55} +(3.48631 + 3.48631i) q^{57} +(-2.10430 + 3.64475i) q^{59} +(3.57882 - 2.06623i) q^{61} +(1.25493 - 0.428191i) q^{63} +(2.91173 + 1.58468i) q^{65} +(4.01070 - 1.07466i) q^{67} -7.26683 q^{69} +12.5889 q^{71} +(12.4053 - 3.32399i) q^{73} +(5.30032 - 5.86322i) q^{75} +(1.19361 - 1.36537i) q^{77} +(12.1515 - 7.01566i) q^{79} +(-3.62266 + 6.27464i) q^{81} +(3.99595 + 3.99595i) q^{83} +(-1.59331 - 2.60583i) q^{85} +(3.23259 + 12.0642i) q^{87} +(-5.79949 - 10.0450i) q^{89} +(-2.18429 - 3.25792i) q^{91} +(-13.4652 - 3.60799i) q^{93} +(5.05419 + 4.80576i) q^{95} +(-2.60010 + 2.60010i) q^{97} -0.343528i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{5} + 2 q^{7}+O(q^{10}) \) 16 * q + 6 * q^5 + 2 * q^7	\( 16 q + 6 q^{5} + 2 q^{7} - 20 q^{15} + 18 q^{17} - 4 q^{21} - 16 q^{23} + 6 q^{25} - 12 q^{31} - 42 q^{33} - 40 q^{35} - 14 q^{37} + 28 q^{43} - 66 q^{45} - 6 q^{47} + 20 q^{51} - 10 q^{53} + 44 q^{57} + 60 q^{61} + 48 q^{63} + 34 q^{65} + 8 q^{67} - 8 q^{71} + 78 q^{73} + 96 q^{75} + 10 q^{77} + 24 q^{81} + 30 q^{87} - 64 q^{91} - 62 q^{93} + 2 q^{95}+O(q^{100}) \) 16 * q + 6 * q^5 + 2 * q^7 - 20 * q^15 + 18 * q^17 - 4 * q^21 - 16 * q^23 + 6 * q^25 - 12 * q^31 - 42 * q^33 - 40 * q^35 - 14 * q^37 + 28 * q^43 - 66 * q^45 - 6 * q^47 + 20 * q^51 - 10 * q^53 + 44 * q^57 + 60 * q^61 + 48 * q^63 + 34 * q^65 + 8 * q^67 - 8 * q^71 + 78 * q^73 + 96 * q^75 + 10 * q^77 + 24 * q^81 + 30 * q^87 - 64 * q^91 - 62 * q^93 + 2 * q^95

Introduction

L-functions

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Database

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