LMFDB - Embedded newform 140.2.u.a.117.3

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			117.3
Root			$0.500000 + 0.617773i$ of defining polynomial
Character	$\chi$	$=$	140.117
Dual form			140.2.u.a.73.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.409133 - 1.52691i) q^{3} +(1.62046 + 1.54081i) q^{5} +(-0.512081 - 2.59572i) q^{7} +(0.434025 + 0.250584i) q^{9} +O(q^{10})$	\(q+(0.409133 - 1.52691i) q^{3} +(1.62046 + 1.54081i) q^{5} +(-0.512081 - 2.59572i) q^{7} +(0.434025 + 0.250584i) q^{9} +(-0.342727 - 0.593621i) q^{11} +(-1.04830 - 1.04830i) q^{13} +(3.01566 - 1.84390i) q^{15} +(-1.31940 - 0.353532i) q^{17} +(-1.55949 + 2.70111i) q^{19} +(-4.17293 - 0.280096i) q^{21} +(1.18980 + 4.44038i) q^{23} +(0.251796 + 4.99366i) q^{25} +(3.91351 - 3.91351i) q^{27} +7.90106i q^{29} +(-7.63715 + 4.40931i) q^{31} +(-1.04663 + 0.280442i) q^{33} +(3.16971 - 4.99529i) q^{35} +(-8.68572 + 2.32733i) q^{37} +(-2.02956 + 1.17176i) q^{39} -10.2469i q^{41} +(3.73689 - 3.73689i) q^{43} +(0.317217 + 1.07481i) q^{45} +(-1.80577 - 6.73924i) q^{47} +(-6.47555 + 2.65844i) q^{49} +(-1.07962 + 1.86996i) q^{51} +(8.94065 + 2.39564i) q^{53} +(0.359282 - 1.49002i) q^{55} +(3.48631 + 3.48631i) q^{57} +(2.10430 + 3.64475i) q^{59} +(3.57882 + 2.06623i) q^{61} +(0.428191 - 1.25493i) q^{63} +(-0.0834974 - 3.31397i) q^{65} +(-1.07466 + 4.01070i) q^{67} +7.26683 q^{69} +12.5889 q^{71} +(3.32399 - 12.4053i) q^{73} +(7.72786 + 1.65860i) q^{75} +(-1.36537 + 1.19361i) q^{77} +(-12.1515 - 7.01566i) q^{79} +(-3.62266 - 6.27464i) q^{81} +(-3.99595 - 3.99595i) q^{83} +(-1.59331 - 2.60583i) q^{85} +(12.0642 + 3.23259i) q^{87} +(5.79949 - 10.0450i) q^{89} +(-2.18429 + 3.25792i) q^{91} +(3.60799 + 13.4652i) q^{93} +(-6.68900 + 1.97417i) q^{95} +(2.60010 - 2.60010i) q^{97} -0.343528i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/140\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$101$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.409133	−	1.52691i	0.236213	−	0.881560i	−0.741385	−	0.671080i	$-0.765831\pi$
$3$	0.409133	−	1.52691i	0.236213	−	0.881560i	0.977598	−	0.210480i	$-0.0675026\pi$
$4$		0			0
$5$	1.62046	+	1.54081i	0.724693	+	0.689072i
$5$	1.62046	+	1.54081i	0.724693	+	0.689072i
$6$		0			0
$7$	−0.512081	−	2.59572i	−0.193549	−	0.981091i
$7$	−0.512081	−	2.59572i	−0.193549	−	0.981091i
$8$		0			0
$9$	0.434025	+	0.250584i	0.144675	+	0.0835281i
$10$		0			0
$11$	−0.342727	−	0.593621i	−0.103336	−	0.178984i	0.809721	−	0.586815i	$-0.199618\pi$
$11$	−0.342727	−	0.593621i	−0.103336	−	0.178984i	−0.913057	+	0.407831i	$0.866285\pi$
$12$		0			0
$13$	−1.04830	−	1.04830i	−0.290747	−	0.290747i	0.546628	−	0.837375i	$-0.315911\pi$
$13$	−1.04830	−	1.04830i	−0.290747	−	0.290747i	−0.837375	+	0.546628i	$0.815911\pi$
$14$		0			0
$15$	3.01566	−	1.84390i	0.778640	−	0.476092i
$16$		0			0
$17$	−1.31940	−	0.353532i	−0.320002	−	0.0857442i	0.0952428	−	0.995454i	$-0.469637\pi$
$17$	−1.31940	−	0.353532i	−0.320002	−	0.0857442i	−0.415244	+	0.909710i	$0.636304\pi$
$18$		0			0
$19$	−1.55949	+	2.70111i	−0.357771	+	0.619678i	−0.987588	−	0.157065i	$-0.949797\pi$
$19$	−1.55949	+	2.70111i	−0.357771	+	0.619678i	0.629817	+	0.776744i	$0.283130\pi$
$20$		0			0
$21$	−4.17293	−	0.280096i	−0.910609	−	0.0611220i
$22$		0			0
$23$	1.18980	+	4.44038i	0.248090	+	0.925883i	0.971805	+	0.235785i	$0.0757661\pi$
$23$	1.18980	+	4.44038i	0.248090	+	0.925883i	−0.723716	+	0.690098i	$0.757567\pi$
$24$		0			0
$25$	0.251796	+	4.99366i	0.0503591	+	0.998731i
$26$		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	−0.991139	−	0.132831i	$-0.957593\pi$
$31$	−7.63715	+	4.40931i	−1.37167	+	0.791936i	−0.380535	+	0.924767i	$0.624260\pi$
$32$		0			0
$33$	−1.04663	+	0.280442i	−0.182194	+	0.0488187i
$34$		0			0
$35$	3.16971	−	4.99529i	0.535779	−	0.844358i
$36$		0			0
$37$	−8.68572	+	2.32733i	−1.42792	+	0.382611i	−0.888288	−	0.459288i	$-0.848105\pi$
$37$	−8.68572	+	2.32733i	−1.42792	+	0.382611i	−0.539636	+	0.841899i	$0.681438\pi$
$38$		0			0
$39$	−2.02956	+	1.17176i	−0.324989	+	0.187632i
$40$		0			0
$41$		−	10.2469i		−	1.60029i	−0.599805	−	0.800146i	$-0.704755\pi$
$41$		−	10.2469i		−	1.60029i	0.599805	−	0.800146i	$-0.295245\pi$
$42$		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
$45$	0.317217	+	1.07481i	0.0472880	+	0.160224i
$46$		0			0
$47$	−1.80577	−	6.73924i	−0.263399	−	0.983019i	−0.963223	−	0.268703i	$-0.913405\pi$
$47$	−1.80577	−	6.73924i	−0.263399	−	0.983019i	0.699824	−	0.714315i	$-0.253262\pi$
$48$		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
$53$	8.94065	+	2.39564i	1.22809	+	0.329066i	0.813837	−	0.581094i	$-0.197375\pi$
$53$	8.94065	+	2.39564i	1.22809	+	0.329066i	0.414256	+	0.910160i	$0.364042\pi$
$54$		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	$-0.0783343\pi$
$59$	2.10430	+	3.64475i	0.273956	+	0.474506i	−0.695915	+	0.718124i	$0.745001\pi$
$60$		0			0
$61$	3.57882	+	2.06623i	0.458221	+	0.264554i	0.711296	−	0.702893i	$-0.248109\pi$
$61$	3.57882	+	2.06623i	0.458221	+	0.264554i	−0.253075	+	0.967447i	$0.581442\pi$
$62$		0			0
$63$	0.428191	−	1.25493i	0.0539470	−	0.158106i
$64$		0			0
$65$	−0.0834974	−	3.31397i	−0.0103566	−	0.411048i
$66$		0			0
$67$	−1.07466	+	4.01070i	−0.131291	+	0.489985i	−0.999986	−	0.00536291i	$-0.998293\pi$
$67$	−1.07466	+	4.01070i	−0.131291	+	0.489985i	0.868694	+	0.495348i	$0.164960\pi$
$68$		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
$73$	3.32399	−	12.4053i	0.389044	−	1.45193i	−0.442649	−	0.896695i	$-0.645961\pi$
$73$	3.32399	−	12.4053i	0.389044	−	1.45193i	0.831693	−	0.555236i	$-0.187372\pi$
$74$		0			0
$75$	7.72786	+	1.65860i	0.892336	+	0.191519i
$76$		0			0
$77$	−1.36537	+	1.19361i	−0.155599	+	0.136024i
$78$		0			0
$79$	−12.1515	−	7.01566i	−1.36715	−	0.789323i	−0.376585	−	0.926382i	$-0.622902\pi$
$79$	−12.1515	−	7.01566i	−1.36715	−	0.789323i	−0.990563	+	0.137059i	$0.956235\pi$
$80$		0			0
$81$	−3.62266	−	6.27464i	−0.402518	−	0.697182i
$82$		0			0
$83$	−3.99595	−	3.99595i	−0.438612	−	0.438612i	0.452933	−	0.891545i	$-0.350378\pi$
$83$	−3.99595	−	3.99595i	−0.438612	−	0.438612i	−0.891545	+	0.452933i	$0.850378\pi$
$84$		0			0
$85$	−1.59331	−	2.60583i	−0.172819	−	0.282642i
$86$		0			0
$87$	12.0642	+	3.23259i	1.29342	+	0.346570i
$88$		0			0
$89$	5.79949	−	10.0450i	0.614745	−	1.06477i	−0.375685	−	0.926748i	$-0.622592\pi$
$89$	5.79949	−	10.0450i	0.614745	−	1.06477i	0.990429	−	0.138021i	$-0.0440743\pi$
$90$		0			0
$91$	−2.18429	+	3.25792i	−0.228975	+	0.341523i
$92$		0			0
$93$	3.60799	+	13.4652i	0.374131	+	1.39628i
$94$		0			0
$95$	−6.68900	+	1.97417i	−0.686277	+	0.202546i
$96$		0			0
$97$	2.60010	−	2.60010i	0.264000	−	0.264000i	−0.562677	−	0.826677i	$-0.690228\pi$
$97$	2.60010	−	2.60010i	0.264000	−	0.264000i	0.826677	+	0.562677i	$0.190228\pi$
$98$		0			0
$99$		−	0.343528i		−	0.0345259i
$100$		0			0
$101$	−2.65764	+	1.53439i	−0.264445	+	0.152677i	−0.626361	−	0.779533i	$-0.715456\pi$
$101$	−2.65764	+	1.53439i	−0.264445	+	0.152677i	0.361915	+	0.932211i	$0.382123\pi$
$102$		0			0
$103$	−15.9958	+	4.28607i	−1.57612	+	0.422319i	−0.937721	−	0.347389i	$-0.887068\pi$
$103$	−15.9958	+	4.28607i	−1.57612	+	0.422319i	−0.638395	+	0.769709i	$0.720402\pi$
$104$		0			0
$105$	−6.33050	−	6.88359i	−0.617794	−	0.671770i
$106$		0			0
$107$	−5.12180	+	1.37238i	−0.495143	+	0.132673i	−0.497745	−	0.867323i	$-0.665838\pi$
$107$	−5.12180	+	1.37238i	−0.495143	+	0.132673i	0.00260205	+	0.999997i	$0.499172\pi$
$108$		0			0
$109$	14.3427	−	8.28074i	1.37378	−	0.793151i	0.382376	−	0.924007i	$-0.375106\pi$
$109$	14.3427	−	8.28074i	1.37378	−	0.793151i	0.991401	+	0.130856i	$0.0417726\pi$
$110$		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
$115$	−4.91377	+	9.02872i	−0.458212	+	0.841933i
$116$		0			0
$117$	−0.192301	−	0.717677i	−0.0177782	−	0.0663493i
$118$		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
$123$	−15.6460	−	4.19233i	−1.41075	−	0.378010i
$124$		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	0.853246	−	0.521509i	$-0.174631\pi$
$131$	9.47951	+	5.47300i	0.828229	+	0.478178i	−0.0250169	+	0.999687i	$0.507964\pi$
$132$		0			0
$133$	7.80993	+	2.66481i	0.677207	+	0.231068i
$134$		0			0
$135$	12.3717	−	0.311711i	1.06478	−	0.0268278i
$136$		0			0
$137$	0.349978	−	1.30614i	0.0299006	−	0.111591i	−0.949363	−	0.314182i	$-0.898270\pi$
$137$	0.349978	−	1.30614i	0.0299006	−	0.111591i	0.979263	+	0.202592i	$0.0649364\pi$
$138$		0			0
$139$	−0.703180			−0.0596429			−0.0298215	−	0.999555i	$-0.509494\pi$
$139$	−0.703180			−0.0596429			−0.0298215	+	0.999555i	$0.509494\pi$
$140$		0			0
$141$	−11.0290			−0.928808
$142$		0			0
$143$	−0.263013	+	0.981577i	−0.0219942	+	0.0820836i
$144$		0			0
$145$	−12.1741	+	12.8034i	−1.01100	+	1.06326i
$146$		0			0
$147$	1.40983	+	10.9752i	0.116281	+	0.905220i
$148$		0			0
$149$	9.78894	+	5.65165i	0.801941	+	0.463001i	0.844149	−	0.536108i	$-0.180106\pi$
$149$	9.78894	+	5.65165i	0.801941	+	0.463001i	−0.0422084	+	0.999109i	$0.513439\pi$
$150$		0			0
$151$	3.95170	+	6.84454i	0.321585	+	0.557001i	0.980815	−	0.194940i	$-0.0624512\pi$
$151$	3.95170	+	6.84454i	0.321585	+	0.557001i	−0.659230	+	0.751941i	$0.729118\pi$
$152$		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
$157$	2.25342	+	0.603801i	0.179842	+	0.0481886i	0.347616	−	0.937637i	$-0.386991\pi$
$157$	2.25342	+	0.603801i	0.179842	+	0.0481886i	−0.167774	+	0.985825i	$0.553658\pi$
$158$		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
$163$	0.292547	+	1.09180i	0.0229140	+	0.0855163i	0.976436	−	0.215807i	$-0.0692383\pi$
$163$	0.292547	+	1.09180i	0.0229140	+	0.0855163i	−0.953522	+	0.301324i	$0.902572\pi$
$164$		0			0
$165$	−2.12813	−	1.15821i	−0.165674	−	0.0901662i
$166$		0			0
$167$	−5.76281	+	5.76281i	−0.445940	+	0.445940i	−0.894002	−	0.448062i	$-0.852114\pi$
$167$	−5.76281	+	5.76281i	−0.445940	+	0.445940i	0.448062	+	0.894002i	$0.352114\pi$
$168$		0			0
$169$		−	10.8021i		−	0.830933i
$170$		0			0
$171$	−1.35371	+	0.781567i	−0.103521	+	0.0597679i
$172$		0			0
$173$	−16.8911	+	4.52596i	−1.28421	+	0.344103i	−0.835458	−	0.549554i	$-0.814798\pi$
$173$	−16.8911	+	4.52596i	−1.28421	+	0.344103i	−0.448751	+	0.893657i	$0.648131\pi$
$174$		0			0
$175$	12.8332	−	3.21075i	0.970099	−	0.242710i
$176$		0			0
$177$	6.42613	−	1.72188i	0.483017	−	0.129424i
$178$		0			0
$179$	−0.930020	+	0.536947i	−0.0695129	+	0.0401333i	−0.534354	−	0.845261i	$-0.679445\pi$
$179$	−0.930020	+	0.536947i	−0.0695129	+	0.0401333i	0.464841	+	0.885394i	$0.346112\pi$
$180$		0			0
$181$			8.93607i			0.664213i	0.943242	+	0.332106i	$0.107759\pi$
$181$			8.93607i			0.664213i	−0.943242	+	0.332106i	$0.892241\pi$
$182$		0			0
$183$	4.61916	−	4.61916i	0.341458	−	0.341458i
$184$		0			0
$185$	−17.6609	−	9.61171i	−1.29845	−	0.706667i
$186$		0			0
$187$	0.242330	+	0.904389i	0.0177210	+	0.0661355i
$188$		0			0
$189$	−12.1624	−	8.15435i	−0.884686	−	0.593142i
$190$		0			0
$191$	12.1898	−	21.1133i	0.882020	−	1.52770i	0.0329288	−	0.999458i	$-0.489517\pi$
$191$	12.1898	−	21.1133i	0.882020	−	1.52770i	0.849091	−	0.528246i	$-0.177150\pi$
$192$		0			0
$193$	8.72531	+	2.33794i	0.628062	+	0.168289i	0.558790	−	0.829309i	$-0.311266\pi$
$193$	8.72531	+	2.33794i	0.628062	+	0.168289i	0.0692717	+	0.997598i	$0.477932\pi$
$194$		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	$-0.0592168\pi$
$199$	4.67200	+	8.09214i	0.331189	+	0.573637i	−0.651556	+	0.758601i	$0.725883\pi$
$200$		0			0
$201$	5.68429	+	3.28182i	0.400939	+	0.231482i
$202$		0			0
$203$	20.5090	−	4.04599i	1.43945	−	0.283972i
$204$		0			0
$205$	15.7885	−	16.6047i	1.10272	−	1.15972i
$206$		0			0
$207$	−0.596288	+	2.22538i	−0.0414449	+	0.154675i
$208$		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
$213$	5.15052	−	19.2220i	0.352908	−	1.31707i
$214$		0			0
$215$	11.8133	−	0.297644i	0.805664	−	0.0202991i
$216$		0			0
$217$	15.3562	+	17.5660i	1.04245	+	1.19246i
$218$		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	0.695678	−	0.718354i	$-0.255104\pi$
$223$	−0.338625	−	0.338625i	−0.0226760	−	0.0226760i	−0.718354	+	0.695678i	$0.755104\pi$
$224$		0			0
$225$	−1.14205	+	2.23047i	−0.0761364	+	0.148698i
$226$		0			0
$227$	13.3958	+	3.58938i	0.889108	+	0.238236i	0.674333	−	0.738428i	$-0.264431\pi$
$227$	13.3958	+	3.58938i	0.889108	+	0.238236i	0.214775	+	0.976664i	$0.431098\pi$
$228$		0			0
$229$	1.33146	−	2.30615i	0.0879850	−	0.152395i	−0.818674	−	0.574258i	$-0.805291\pi$
$229$	1.33146	−	2.30615i	0.0879850	−	0.152395i	0.906659	+	0.421864i	$0.138624\pi$
$230$		0			0
$231$	1.26391	+	2.57314i	0.0831590	+	0.169300i
$232$		0			0
$233$	4.90012	+	18.2875i	0.321017	+	1.19805i	0.918255	+	0.395989i	$0.129598\pi$
$233$	4.90012	+	18.2875i	0.321017	+	1.19805i	−0.597238	+	0.802064i	$0.703735\pi$
$234$		0			0
$235$	7.45771	−	13.7030i	0.486487	−	0.893888i
$236$		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	−0.188207	−	0.982129i	$-0.560268\pi$
$241$	8.82144	−	5.09306i	0.568239	−	0.328073i	0.756446	+	0.654057i	$0.226934\pi$
$242$		0			0
$243$	4.97494	−	1.33303i	0.319142	−	0.0855139i
$244$		0			0
$245$	−14.5895	−	5.66970i	−0.932091	−	0.362224i
$246$		0			0
$247$	4.46640	−	1.19677i	0.284190	−	0.0761486i
$248$		0			0
$249$	−7.73631	+	4.46656i	−0.490268	+	0.283057i
$250$		0			0
$251$			7.28871i			0.460059i	0.973184	+	0.230030i	$0.0738823\pi$
$251$			7.28871i			0.460059i	−0.973184	+	0.230030i	$0.926118\pi$
$252$		0			0
$253$	2.22813	−	2.22813i	0.140081	−	0.140081i
$254$		0			0
$255$	−4.63074	+	1.36670i	−0.289988	+	0.0855863i
$256$		0			0
$257$	−3.16193	−	11.8005i	−0.197236	−	0.736095i	−0.991677	−	0.128753i	$-0.958903\pi$
$257$	−3.16193	−	11.8005i	−0.197236	−	0.736095i	0.794441	−	0.607342i	$-0.207764\pi$
$258$		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
$263$	−20.7745	−	5.56652i	−1.28101	−	0.343246i	−0.446772	−	0.894648i	$-0.647427\pi$
$263$	−20.7745	−	5.56652i	−1.28101	−	0.343246i	−0.834240	+	0.551402i	$0.814093\pi$
$264$		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	0.914855	+	0.403783i	$0.132305\pi$
$269$	13.2377	+	22.9283i	0.807114	+	1.39796i	−0.107741	+	0.994179i	$0.534362\pi$
$270$		0			0
$271$	−15.4571	−	8.92414i	−0.938949	−	0.542103i	−0.0493186	−	0.998783i	$-0.515705\pi$
$271$	−15.4571	−	8.92414i	−0.938949	−	0.542103i	−0.889631	+	0.456680i	$0.849038\pi$
$272$		0			0
$273$	4.08087	+	4.66812i	0.246986	+	0.282528i
$274$		0			0
$275$	2.87804	−	1.86093i	0.173553	−	0.112219i
$276$		0			0
$277$	6.86772	−	25.6307i	0.412641	−	1.54000i	−0.376873	−	0.926265i	$-0.623001\pi$
$277$	6.86772	−	25.6307i	0.412641	−	1.54000i	0.789514	−	0.613733i	$-0.210333\pi$
$278$		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
$283$	0.169240	−	0.631614i	0.0100603	−	0.0375456i	−0.960713	−	0.277543i	$-0.910480\pi$
$283$	0.169240	−	0.631614i	0.0100603	−	0.0375456i	0.970774	+	0.239997i	$0.0771466\pi$
$284$		0			0
$285$	0.277685	+	11.0212i	0.0164486	+	0.652838i
$286$		0			0
$287$	−26.5980	+	5.24723i	−1.57003	+	0.309734i
$288$		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	0.755712	−	0.654904i	$-0.227291\pi$
$293$	1.72555	+	1.72555i	0.100808	+	0.100808i	−0.654904	+	0.755712i	$0.727291\pi$
$294$		0			0
$295$	−2.20594	+	9.14851i	−0.128435	+	0.532647i
$296$		0			0
$297$	−3.66441	−	0.981876i	−0.212631	−	0.0569742i
$298$		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
$303$	1.25554	+	4.68574i	0.0721288	+	0.269188i
$304$		0			0
$305$	2.61567	+	8.86254i	0.149773	+	0.507468i
$306$		0			0
$307$	18.5555	−	18.5555i	1.05902	−	1.05902i	0.0608747	−	0.998145i	$-0.480611\pi$
$307$	18.5555	−	18.5555i	1.05902	−	1.05902i	0.998145	−	0.0608747i	$-0.0193890\pi$
$308$		0			0
$309$			26.1777i			1.48920i
$310$		0			0
$311$	4.30249	−	2.48404i	0.243972	−	0.140857i	−0.373029	−	0.927820i	$-0.621681\pi$
$311$	4.30249	−	2.48404i	0.243972	−	0.140857i	0.617001	+	0.786962i	$0.288347\pi$
$312$		0			0
$313$	−11.8215	+	3.16757i	−0.668192	+	0.179041i	−0.576940	−	0.816787i	$-0.695753\pi$
$313$	−11.8215	+	3.16757i	−0.668192	+	0.179041i	−0.0912515	+	0.995828i	$0.529087\pi$
$314$		0			0
$315$	2.62747	−	1.37380i	0.148041	−	0.0774048i
$316$		0			0
$317$	−25.0231	+	6.70491i	−1.40543	+	0.376585i	−0.880293	−	0.474430i	$-0.842654\pi$
$317$	−25.0231	+	6.70491i	−1.40543	+	0.376585i	−0.525142	+	0.851015i	$0.675988\pi$
$318$		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
$325$	4.97091	−	5.49882i	0.275736	−	0.305020i
$326$		0			0
$327$	−6.77585	−	25.2878i	−0.374705	−	1.39842i
$328$		0			0
$329$	−16.5685	+	8.13832i	−0.913450	+	0.448680i
$330$		0			0
$331$	−7.58313	+	13.1344i	−0.416806	+	0.721930i	−0.995616	−	0.0935328i	$-0.970184\pi$
$331$	−7.58313	+	13.1344i	−0.416806	+	0.721930i	0.578810	+	0.815463i	$0.303517\pi$
$332$		0			0
$333$	−4.35301	−	1.16639i	−0.238543	−	0.0639175i
$334$		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
$343$	10.2166	+	15.4474i	0.551643	+	0.834080i
$344$		0			0
$345$	11.7756	+	11.1968i	0.633978	+	0.602816i
$346$		0			0
$347$	1.56558	−	5.84281i	0.0840445	−	0.313658i	−0.911087	−	0.412214i	$-0.864756\pi$
$347$	1.56558	−	5.84281i	0.0840445	−	0.313658i	0.995132	+	0.0985557i	$0.0314223\pi$
$348$		0			0
$349$	5.80171			0.310558			0.155279	−	0.987871i	$-0.450372\pi$
$349$	5.80171			0.310558			0.155279	+	0.987871i	$0.450372\pi$
$350$		0			0
$351$	−8.20509			−0.437955
$352$		0			0
$353$	−3.06423	+	11.4359i	−0.163093	+	0.608670i	0.835183	+	0.549972i	$0.185362\pi$
$353$	−3.06423	+	11.4359i	−0.163093	+	0.608670i	−0.998276	+	0.0586980i	$0.981305\pi$
$354$		0			0
$355$	20.3998	+	19.3971i	1.08271	+	1.02949i
$356$		0			0
$357$	5.40675	+	1.84483i	0.286155	+	0.0976385i
$358$		0			0
$359$	4.22275	+	2.43801i	0.222868	+	0.128673i	0.607278	−	0.794490i	$-0.292262\pi$
$359$	4.22275	+	2.43801i	0.222868	+	0.128673i	−0.384409	+	0.923163i	$0.625595\pi$
$360$		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
$367$	−5.97731	−	1.60161i	−0.312013	−	0.0836036i	0.0994146	−	0.995046i	$-0.468303\pi$
$367$	−5.97731	−	1.60161i	−0.312013	−	0.0836036i	−0.411427	+	0.911443i	$0.634970\pi$
$368$		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
$373$	−8.49882	−	31.7180i	−0.440052	−	1.64230i	−0.728679	−	0.684856i	$-0.759865\pi$
$373$	−8.49882	−	31.7180i	−0.440052	−	1.64230i	0.288626	−	0.957442i	$-0.406801\pi$
$374$		0			0
$375$	9.96711	+	14.5949i	0.514699	+	0.753677i
$376$		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
$383$	0.830244	−	0.222463i	0.0424235	−	0.0113673i	−0.237545	−	0.971377i	$-0.576343\pi$
$383$	0.830244	−	0.222463i	0.0424235	−	0.0113673i	0.279968	+	0.960009i	$0.409676\pi$
$384$		0			0
$385$	−4.05166	−	0.169585i	−0.206492	−	0.00864287i
$386$		0			0
$387$	2.55831	−	0.685497i	0.130046	−	0.0348458i
$388$		0			0
$389$	−22.8241	+	13.1775i	−1.15723	+	0.668125i	−0.950638	−	0.310302i	$-0.899570\pi$
$389$	−22.8241	+	13.1775i	−1.15723	+	0.668125i	−0.206589	+	0.978428i	$0.566236\pi$
$390$		0			0
$391$		−	6.27927i		−	0.317556i
$392$		0			0
$393$	12.2351	−	12.2351i	0.617181	−	0.617181i
$394$		0			0
$395$	−8.88120	−	30.0918i	−0.446862	−	1.51408i
$396$		0			0
$397$	−2.80685	−	10.4753i	−0.140872	−	0.525741i	−0.999905	−	0.0138199i	$-0.995601\pi$
$397$	−2.80685	−	10.4753i	−0.140872	−	0.525741i	0.859033	−	0.511921i	$-0.171066\pi$
$398$		0			0
$399$	7.26422	−	10.8348i	0.363666	−	0.542417i
$400$		0			0
$401$	−1.50000	+	2.59808i	−0.0749064	+	0.129742i	−0.901046	−	0.433724i	$-0.857199\pi$
$401$	−1.50000	+	2.59808i	−0.0749064	+	0.129742i	0.826139	+	0.563466i	$0.190532\pi$
$402$		0			0
$403$	12.6283	+	3.38375i	0.629063	+	0.168557i
$404$		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	$-0.193382\pi$
$409$	−1.69537	−	2.93647i	−0.0838308	−	0.145199i	−0.904892	+	0.425640i	$0.860049\pi$
$410$		0			0
$411$	−1.85116	−	1.06877i	−0.0913109	−	0.0527184i
$412$		0			0
$413$	8.38319	−	7.32858i	0.412510	−	0.360616i
$414$		0			0
$415$	−0.318277	−	12.6323i	−0.0156236	−	0.620094i
$416$		0			0
$417$	−0.287694	+	1.07369i	−0.0140884	+	0.0525788i
$418$		0			0
$419$	1.03776			0.0506978			0.0253489	−	0.999679i	$-0.491930\pi$
$419$	1.03776			0.0506978			0.0253489	+	0.999679i	$0.491930\pi$
$420$		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
$423$	0.904997	−	3.37749i	0.0440024	−	0.164219i
$424$		0			0
$425$	1.43320	−	6.67765i	0.0695204	−	0.323914i
$426$		0			0
$427$	3.53072	−	10.3477i	0.170863	−	0.500760i
$428$		0			0
$429$	1.39117	+	0.803191i	0.0671662	+	0.0387784i
$430$		0			0
$431$	9.34273	+	16.1821i	0.450023	+	0.779463i	0.998387	−	0.0567767i	$-0.0180823\pi$
$431$	9.34273	+	16.1821i	0.450023	+	0.779463i	−0.548364	+	0.836240i	$0.684749\pi$
$432$		0			0
$433$	−7.43170	−	7.43170i	−0.357145	−	0.357145i	0.505615	−	0.862759i	$-0.331266\pi$
$433$	−7.43170	−	7.43170i	−0.357145	−	0.357145i	−0.862759	+	0.505615i	$0.831266\pi$
$434$		0			0
$435$	14.5687	+	23.8269i	0.698517	+	1.14241i
$436$		0			0
$437$	−13.8495	−	3.71095i	−0.662509	−	0.177519i
$438$		0			0
$439$	−13.5514	+	23.4717i	−0.646772	+	1.12024i	0.337118	+	0.941463i	$0.390548\pi$
$439$	−13.5514	+	23.4717i	−0.646772	+	1.12024i	−0.983889	+	0.178779i	$0.942785\pi$
$440$		0			0
$441$	−3.47671	−	0.468841i	−0.165558	−	0.0223258i
$442$		0			0
$443$	9.71108	+	36.2422i	0.461387	+	1.72192i	0.668597	+	0.743625i	$0.266895\pi$
$443$	9.71108	+	36.2422i	0.461387	+	1.72192i	−0.207210	+	0.978297i	$0.566438\pi$
$444$		0			0
$445$	24.8753	−	7.34164i	1.17920	−	0.348027i
$446$		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
$453$	12.0677	−	3.23354i	0.566992	−	0.151925i
$454$		0			0
$455$	−8.55939	+	1.91376i	−0.401271	+	0.0897184i
$456$		0			0
$457$	−14.3652	+	3.84913i	−0.671974	+	0.180055i	−0.578644	−	0.815580i	$-0.696418\pi$
$457$	−14.3652	+	3.84913i	−0.671974	+	0.180055i	−0.0933301	+	0.995635i	$0.529751\pi$
$458$		0			0
$459$	−6.54704	+	3.77993i	−0.305590	+	0.176432i
$460$		0			0
$461$		−	41.8860i		−	1.95082i	−0.220390	−	0.975412i	$-0.570733\pi$
$461$		−	41.8860i		−	1.95082i	0.220390	−	0.975412i	$-0.429267\pi$
$462$		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
$465$	−14.9007	+	27.3791i	−0.691006	+	1.26968i
$466$		0			0
$467$	10.5646	+	39.4275i	0.488870	+	1.82449i	0.561962	+	0.827163i	$0.310047\pi$
$467$	10.5646	+	39.4275i	0.488870	+	1.82449i	−0.0730918	+	0.997325i	$0.523287\pi$
$468$		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
$473$	−3.49904	−	0.937564i	−0.160886	−	0.0431092i
$474$		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	$-0.202235\pi$
$479$	−2.44050	−	4.22708i	−0.111509	−	0.193140i	−0.916379	+	0.400312i	$0.868902\pi$
$480$		0			0
$481$	11.5450	+	6.66552i	0.526407	+	0.303921i
$482$		0			0
$483$	−3.72121	−	18.8627i	−0.169321	−	0.858281i
$484$		0			0
$485$	8.21963	−	0.207098i	0.373234	−	0.00940384i
$486$		0			0
$487$	−9.16256	+	34.1952i	−0.415195	+	1.54953i	0.369249	+	0.929331i	$0.379615\pi$
$487$	−9.16256	+	34.1952i	−0.415195	+	1.54953i	−0.784444	+	0.620200i	$0.787052\pi$
$488$		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
$493$	2.79328	−	10.4247i	0.125803	−	0.469503i
$494$		0			0
$495$	0.529313	−	0.556675i	0.0237908	−	0.0250207i
$496$		0			0
$497$	−6.44652	−	32.6772i	−0.289166	−	1.46577i
$498$		0			0
$499$	−11.3336	−	6.54347i	−0.507363	−	0.292926i	0.224386	−	0.974500i	$-0.427962\pi$
$499$	−11.3336	−	6.54347i	−0.507363	−	0.292926i	−0.731749	+	0.681574i	$0.761296\pi$
$500$		0			0
$501$	6.44151	+	11.1570i	0.287786	+	0.498459i
$502$		0			0
$503$	15.2498	+	15.2498i	0.679955	+	0.679955i	0.959990	−	0.280035i	$-0.0903460\pi$
$503$	15.2498	+	15.2498i	0.679955	+	0.679955i	−0.280035	+	0.959990i	$0.590346\pi$
$504$		0			0
$505$	−6.67081	−	1.60850i	−0.296847	−	0.0715775i
$506$		0			0
$507$	−16.4938	−	4.41951i	−0.732516	−	0.196277i
$508$		0			0
$509$	0.264712	−	0.458495i	0.0117332	−	0.0203224i	−0.860099	−	0.510127i	$-0.829598\pi$
$509$	0.264712	−	0.458495i	0.0117332	−	0.0203224i	0.871832	+	0.489804i	$0.162932\pi$
$510$		0			0
$511$	−33.9029	−	2.27563i	−1.49978	−	0.100668i
$512$		0			0
$513$	4.46776	+	16.6739i	0.197257	+	0.736172i
$514$		0			0
$515$	−32.5247	−	17.7012i	−1.43321	−	0.780006i
$516$		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	−0.429622	−	0.903009i	$-0.641353\pi$
$521$	3.14066	−	1.81326i	0.137595	−	0.0794404i	0.567217	+	0.823568i	$0.308020\pi$
$522$		0			0
$523$	−19.9361	+	5.34185i	−0.871743	+	0.233583i	−0.666841	−	0.745200i	$-0.732354\pi$
$523$	−19.9361	+	5.34185i	−0.871743	+	0.233583i	−0.204902	+	0.978783i	$0.565687\pi$
$524$		0			0
$525$	0.347978	−	20.9087i	0.0151870	−	0.912531i
$526$		0			0
$527$	11.6353	−	3.11767i	0.506842	−	0.135808i
$528$		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
$535$	−10.4143	−	5.66784i	−0.450248	−	0.245042i
$536$		0			0
$537$	0.439366	+	1.63974i	0.0189600	+	0.0707598i
$538$		0			0
$539$	3.79745	+	2.93290i	0.163568	+	0.126329i
$540$		0			0
$541$	−13.7743	+	23.8578i	−0.592204	+	1.02573i	0.401731	+	0.915758i	$0.368409\pi$
$541$	−13.7743	+	23.8578i	−0.592204	+	1.02573i	−0.993935	+	0.109969i	$0.964925\pi$
$542$		0			0
$543$	13.6445	+	3.65604i	0.585543	+	0.156896i
$544$		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
$553$	−11.9882	+	35.1345i	−0.509788	+	1.49407i
$554$		0			0
$555$	−21.9018	+	23.0340i	−0.929680	+	0.977739i
$556$		0			0
$557$	2.70252	−	10.0860i	0.114510	−	0.427356i	−0.884740	−	0.466085i	$-0.845664\pi$
$557$	2.70252	−	10.0860i	0.114510	−	0.427356i	0.999250	+	0.0387290i	$0.0123309\pi$
$558$		0			0
$559$	−7.83479			−0.331376
$560$		0			0
$561$	1.48006			0.0624883
$562$		0			0
$563$	−7.15482	+	26.7021i	−0.301540	+	1.12536i	0.634344	+	0.773051i	$0.281270\pi$
$563$	−7.15482	+	26.7021i	−0.301540	+	1.12536i	−0.935883	+	0.352310i	$0.885396\pi$
$564$		0			0
$565$	−22.8105	+	0.574723i	−0.959645	+	0.0241788i
$566$		0			0
$567$	−14.4321	+	12.6165i	−0.606092	+	0.529845i
$568$		0			0
$569$	9.63770	+	5.56433i	0.404033	+	0.233269i	0.688223	−	0.725499i	$-0.258391\pi$
$569$	9.63770	+	5.56433i	0.404033	+	0.233269i	−0.284189	+	0.958768i	$0.591724\pi$
$570$		0			0
$571$	−10.3474	−	17.9222i	−0.433025	−	0.750022i	0.564107	−	0.825702i	$-0.309221\pi$
$571$	−10.3474	−	17.9222i	−0.433025	−	0.750022i	−0.997132	+	0.0756800i	$0.975887\pi$
$572$		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
$577$	7.00314	+	1.87648i	0.291544	+	0.0781191i	0.401627	−	0.915803i	$-0.368445\pi$
$577$	7.00314	+	1.87648i	0.291544	+	0.0781191i	−0.110083	+	0.993922i	$0.535112\pi$
$578$		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
$583$	−1.64210	−	6.12841i	−0.0680090	−	0.253813i
$584$		0			0
$585$	0.794189	−	1.45927i	0.0328357	−	0.0603333i
$586$		0			0
$587$	−5.87340	+	5.87340i	−0.242421	+	0.242421i	−0.817851	−	0.575430i	$-0.804835\pi$
$587$	−5.87340	+	5.87340i	−0.242421	+	0.242421i	0.575430	+	0.817851i	$0.304835\pi$
$588$		0			0
$589$		−	27.5051i		−	1.13333i
$590$		0			0
$591$	3.45918	−	1.99716i	0.142292	−	0.0821521i
$592$		0			0
$593$	26.3818	−	7.06897i	1.08337	−	0.290288i	0.327394	−	0.944888i	$-0.393830\pi$
$593$	26.3818	−	7.06897i	1.08337	−	0.290288i	0.755975	+	0.654600i	$0.227163\pi$
$594$		0			0
$595$	−5.94812	+	5.47019i	−0.243849	+	0.224256i
$596$		0			0
$597$	14.2674	−	3.82294i	0.583926	−	0.156463i
$598$		0			0
$599$	21.9641	−	12.6810i	0.897430	−	0.518131i	0.0210645	−	0.999778i	$-0.493294\pi$
$599$	21.9641	−	12.6810i	0.897430	−	0.518131i	0.876366	+	0.481647i	$0.159961\pi$
$600$		0			0
$601$			13.8045i			0.563099i	0.959547	+	0.281550i	$0.0908484\pi$
$601$			13.8045i			0.563099i	−0.959547	+	0.281550i	$0.909152\pi$
$602$		0			0
$603$	−1.47145	+	1.47145i	−0.0599221	+	0.0599221i
$604$		0			0
$605$	22.5831	−	6.66512i	0.918134	−	0.270975i
$606$		0			0
$607$	5.79866	+	21.6409i	0.235360	+	0.878376i	0.977986	+	0.208670i	$0.0669134\pi$
$607$	5.79866	+	21.6409i	0.235360	+	0.878376i	−0.742626	+	0.669707i	$0.766420\pi$
$608$		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
$613$	−32.1509	−	8.61481i	−1.29856	−	0.347949i	−0.457656	−	0.889129i	$-0.651311\pi$
$613$	−32.1509	−	8.61481i	−1.29856	−	0.347949i	−0.840907	+	0.541180i	$0.817978\pi$
$614$		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	−0.955696	−	0.294357i	$-0.904895\pi$
$619$	−18.2311	−	31.5771i	−0.732768	−	1.26919i	0.222927	−	0.974835i	$-0.428439\pi$
$620$		0			0
$621$	22.0338	+	12.7212i	0.884184	+	0.510484i
$622$		0			0
$623$	−29.0439	−	9.91000i	−1.16362	−	0.397036i
$624$		0			0
$625$	−24.8732	+	2.51476i	−0.994928	+	0.100590i
$626$		0			0
$627$	0.874694	−	3.26440i	0.0349319	−	0.130368i
$628$		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
$633$	−4.02875	+	15.0355i	−0.160128	+	0.597607i
$634$		0			0
$635$	−0.169675	−	6.73433i	−0.00673336	−	0.267244i
$636$		0			0
$637$	9.57518	+	4.00148i	0.379383	+	0.158544i
$638$		0			0
$639$	5.46387	+	3.15457i	0.216147	+	0.124793i
$640$		0			0
$641$	8.05261	+	13.9475i	0.318059	+	0.550894i	0.980083	−	0.198588i	$-0.0636357\pi$
$641$	8.05261	+	13.9475i	0.318059	+	0.550894i	−0.662024	+	0.749483i	$0.730302\pi$
$642$		0			0
$643$	29.1021	+	29.1021i	1.14768	+	1.14768i	0.987009	+	0.160667i	$0.0513646\pi$
$643$	29.1021	+	29.1021i	1.14768	+	1.14768i	0.160667	+	0.987009i	$0.448635\pi$
$644$		0			0
$645$	4.37876	−	18.1596i	0.172413	−	0.715035i
$646$		0			0
$647$	41.2480	+	11.0524i	1.62163	+	0.434513i	0.951479	−	0.307715i	$-0.0995642\pi$
$647$	41.2480	+	11.0524i	1.62163	+	0.434513i	0.670147	+	0.742228i	$0.266231\pi$
$648$		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
$653$	−8.62895	−	32.2037i	−0.337677	−	1.26023i	−0.900938	−	0.433948i	$-0.857120\pi$
$653$	−8.62895	−	32.2037i	−0.337677	−	1.26023i	0.563261	−	0.826279i	$-0.309547\pi$
$654$		0			0
$655$	6.92833	+	23.4749i	0.270712	+	0.917242i
$656$		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	−0.492011	−	0.870589i	$-0.663738\pi$
$661$	0.409726	−	0.236556i	0.0159365	−	0.00920095i	0.507947	+	0.861388i	$0.330405\pi$
$662$		0			0
$663$	3.09205	−	0.828513i	0.120085	−	0.0321768i
$664$		0			0
$665$	8.54972	+	16.3519i	0.331544	+	0.634098i
$666$		0			0
$667$	−35.0837	+	9.40065i	−1.35845	+	0.363995i
$668$		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
$675$	20.5281	+	18.5573i	0.790128	+	0.714272i
$676$		0			0
$677$	−3.67670	−	13.7216i	−0.141307	−	0.527365i	−0.999892	−	0.0146937i	$-0.995323\pi$
$677$	−3.67670	−	13.7216i	−0.141307	−	0.527365i	0.858585	−	0.512671i	$-0.171344\pi$
$678$		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
$683$	20.2251	+	5.41929i	0.773891	+	0.207363i	0.624090	−	0.781353i	$-0.285470\pi$
$683$	20.2251	+	5.41929i	0.773891	+	0.207363i	0.149801	+	0.988716i	$0.452137\pi$
$684$		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	0.602778	−	0.797909i	$-0.294060\pi$
$691$	5.60324	+	3.23504i	0.213157	+	0.123067i	−0.389620	+	0.920976i	$0.627394\pi$
$692$		0			0
$693$	−0.891704	+	0.175914i	−0.0338730	+	0.00668244i
$694$		0			0
$695$	−1.13948	−	1.08347i	−0.0432228	−	0.0410983i
$696$		0			0
$697$	−3.62260	+	13.5197i	−0.137216	+	0.512096i
$698$		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
$703$	7.25890	−	27.0906i	0.273774	−	1.02174i
$704$		0			0
$705$	−17.8721	−	16.9936i	−0.673100	−	0.640016i
$706$		0			0
$707$	5.34378	+	6.11276i	0.200973	+	0.229894i
$708$		0			0
$709$	−7.77659	−	4.48981i	−0.292056	−	0.168619i	0.346813	−	0.937934i	$-0.387264\pi$
$709$	−7.77659	−	4.48981i	−0.292056	−	0.168619i	−0.638869	+	0.769316i	$0.720597\pi$
$710$		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
$717$	−8.77079	−	2.35013i	−0.327551	−	0.0877670i
$718$		0			0
$719$	20.2758	−	35.1187i	0.756160	−	1.30971i	−0.188635	−	0.982047i	$-0.560406\pi$
$719$	20.2758	−	35.1187i	0.756160	−	1.30971i	0.944795	−	0.327661i	$-0.106260\pi$
$720$		0			0
$721$	19.3166	+	39.3259i	0.719388	+	1.46457i
$722$		0			0
$723$	−4.16748	−	15.5532i	−0.154990	−	0.578432i
$724$		0			0
$725$	−39.4552	+	1.98945i	−1.46533	+	0.0738864i
$726$		0			0
$727$	11.9052	−	11.9052i	0.441540	−	0.441540i	−0.450990	−	0.892529i	$-0.648929\pi$
$727$	11.9052	−	11.9052i	0.441540	−	0.441540i	0.892529	+	0.450990i	$0.148929\pi$
$728$		0			0
$729$		−	29.8776i		−	1.10658i
$730$		0			0
$731$	−6.25157	+	3.60935i	−0.231223	+	0.133496i
$732$		0			0
$733$	5.98288	−	1.60311i	0.220983	−	0.0592121i	−0.146629	−	0.989192i	$-0.546842\pi$
$733$	5.98288	−	1.60311i	0.220983	−	0.0592121i	0.367611	+	0.929979i	$0.380176\pi$
$734$		0			0
$735$	−14.6262	+	19.9572i	−0.539494	+	0.736132i
$736$		0			0
$737$	2.74916	−	0.736634i	0.101266	−	0.0271343i
$738$		0			0
$739$	34.3295	−	19.8201i	1.26283	−	0.729095i	0.289208	−	0.957266i	$-0.406608\pi$
$739$	34.3295	−	19.8201i	1.26283	−	0.729095i	0.973621	+	0.228171i	$0.0732746\pi$
$740$		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
$745$	7.15448	+	24.2412i	0.262120	+	0.888129i
$746$		0			0
$747$	−0.733018	−	2.73566i	−0.0268197	−	0.100093i
$748$		0			0
$749$	6.18510	+	12.5920i	0.225999	+	0.460101i
$750$		0			0
$751$	9.16731	−	15.8782i	0.334520	−	0.579405i	−0.648873	−	0.760897i	$-0.724759\pi$
$751$	9.16731	−	15.8782i	0.334520	−	0.579405i	0.983392	+	0.181492i	$0.0580926\pi$
$752$		0			0
$753$	11.1292	+	2.98205i	0.405570	+	0.108672i
$754$		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	0.671515	−	0.740991i	$-0.265644\pi$
$761$	10.0843	+	5.82217i	0.365555	+	0.211054i	−0.305960	+	0.952045i	$0.598977\pi$
$762$		0			0
$763$	−28.8391	−	32.9891i	−1.04405	−	1.19429i
$764$		0			0
$765$	−0.0385556	−	1.53025i	−0.00139398	−	0.0553265i
$766$		0			0
$767$	1.61486	−	6.02674i	0.0583092	−	0.217613i
$768$		0			0
$769$	−45.3371			−1.63490			−0.817448	−	0.576002i	$-0.804612\pi$
$769$	−45.3371			−1.63490			−0.817448	+	0.576002i	$0.804612\pi$
$770$		0			0
$771$	−19.3119			−0.695501
$772$		0			0
$773$	−1.88925	+	7.05078i	−0.0679516	+	0.253599i	−0.991543	−	0.129780i	$-0.958573\pi$
$773$	−1.88925	+	7.05078i	−0.0679516	+	0.253599i	0.923591	+	0.383379i	$0.125240\pi$
$774$		0			0
$775$	−23.9416	−	37.0271i	−0.860007	−	1.33005i
$776$		0			0
$777$	36.8968	−	7.27896i	1.32367	−	0.261131i
$778$		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
$787$	−29.5872	−	7.92786i	−1.05467	−	0.282598i	−0.310489	−	0.950577i	$-0.600493\pi$
$787$	−29.5872	−	7.92786i	−1.05467	−	0.282598i	−0.744180	+	0.667979i	$0.767159\pi$
$788$		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
$793$	−1.58565	−	5.91772i	−0.0563081	−	0.210145i
$794$		0			0
$795$	31.3793	−	9.26119i	1.11291	−	0.328461i
$796$		0			0
$797$	−30.7751	+	30.7751i	−1.09011	+	1.09011i	−0.0945938	+	0.995516i	$0.530155\pi$
$797$	−30.7751	+	30.7751i	−1.09011	+	1.09011i	−0.995516	+	0.0945938i	$0.969845\pi$
$798$		0			0
$799$			9.53015i			0.337153i
$800$		0			0
$801$	5.03424	−	2.90652i	0.177876	−	0.102697i
$802$		0			0
$803$	−8.50328	+	2.27845i	−0.300074	+	0.0804046i
$804$		0			0
$805$	25.9523	+	8.13135i	0.914698	+	0.286592i
$806$		0			0
$807$	40.4253	−	10.8319i	1.42304	−	0.381302i
$808$		0			0
$809$	−12.6957	+	7.32984i	−0.446355	+	0.257703i	−0.706290	−	0.707923i	$-0.749632\pi$
$809$	−12.6957	+	7.32984i	−0.446355	+	0.257703i	0.259934	+	0.965626i	$0.416299\pi$
$810$		0			0
$811$			0.360507i			0.0126591i	0.999980	+	0.00632956i	$0.00201477\pi$
$811$			0.360507i			0.0126591i	−0.999980	+	0.00632956i	$0.997985\pi$
$812$		0			0
$813$	−19.9503	+	19.9503i	−0.699688	+	0.699688i
$814$		0			0
$815$	−1.20820	+	2.21998i	−0.0423213	+	0.0777625i
$816$		0			0
$817$	4.26613	+	15.9214i	0.149253	+	0.557020i
$818$		0			0
$819$	−1.76442	+	0.866669i	−0.0616537	+	0.0302839i
$820$		0			0
$821$	−11.1407	+	19.2962i	−0.388812	+	0.673442i	−0.992290	−	0.123938i	$-0.960448\pi$
$821$	−11.1407	+	19.2962i	−0.388812	+	0.673442i	0.603478	+	0.797379i	$0.293781\pi$
$822$		0			0
$823$	11.1760	+	2.99459i	0.389569	+	0.104385i	0.448287	−	0.893890i	$-0.352034\pi$
$823$	11.1760	+	2.99459i	0.389569	+	0.104385i	−0.0587174	+	0.998275i	$0.518701\pi$
$824$		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	$-0.0212748\pi$
$829$	12.6987	+	21.9948i	0.441044	+	0.763911i	−0.556723	+	0.830698i	$0.687941\pi$
$830$		0			0
$831$	−36.3258	−	20.9727i	−1.26013	−	0.727536i
$832$		0			0
$833$	9.48368	−	1.21823i	0.328590	−	0.0422093i
$834$		0			0
$835$	−18.2178	+	0.459008i	−0.630454	+	0.0158846i
$836$		0			0
$837$	−12.6322	+	47.1440i	−0.436632	+	1.62953i
$838$		0			0
$839$	−4.36253			−0.150611			−0.0753057	−	0.997160i	$-0.523993\pi$
$839$	−4.36253			−0.150611			−0.0753057	+	0.997160i	$0.523993\pi$
$840$		0			0
$841$	−33.4268			−1.15265
$842$		0			0
$843$	−7.66981	+	28.6241i	−0.264162	+	0.985867i
$844$		0			0
$845$	16.6440	−	17.5044i	0.572572	−	0.602171i
$846$		0			0
$847$	−26.3675	−	8.99681i	−0.905999	−	0.309134i
$848$		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	$0.101563\pi$
$853$	36.8935	+	36.8935i	1.26321	+	1.26321i	0.313683	+	0.949528i	$0.398437\pi$
$854$		0			0
$855$	−3.39789	−	0.819319i	−0.116205	−	0.0280201i
$856$		0			0
$857$	24.6686	+	6.60994i	0.842665	+	0.225791i	0.654231	−	0.756295i	$-0.272992\pi$
$857$	24.6686	+	6.60994i	0.842665	+	0.225791i	0.188433	+	0.982086i	$0.439659\pi$
$858$		0			0
$859$	−16.3819	+	28.3743i	−0.558944	+	0.968120i	0.438641	+	0.898662i	$0.355460\pi$
$859$	−16.3819	+	28.3743i	−0.558944	+	0.968120i	−0.997585	+	0.0694571i	$0.977873\pi$
$860$		0			0
$861$	−2.87011	+	42.7595i	−0.0978130	+	1.45724i
$862$		0			0
$863$	−6.22751	−	23.2414i	−0.211987	−	0.791146i	−0.987206	−	0.159453i	$-0.949027\pi$
$863$	−6.22751	−	23.2414i	−0.211987	−	0.791146i	0.775219	−	0.631693i	$-0.217640\pi$
$864$		0			0
$865$	−34.3451	−	18.6919i	−1.16777	−	0.635544i
$866$		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
$873$	1.78005	−	0.476963i	0.0602456	−	0.0161428i
$874$		0			0
$875$	25.7429	+	14.5707i	0.870268	+	0.492578i
$876$		0			0
$877$	46.7037	−	12.5142i	1.57707	−	0.422575i	0.639054	−	0.769162i	$-0.279326\pi$
$877$	46.7037	−	12.5142i	1.57707	−	0.422575i	0.938018	+	0.346586i	$0.112659\pi$
$878$		0			0
$879$	3.34074	−	1.92878i	0.112680	−	0.0650560i
$880$		0			0
$881$			3.63541i			0.122480i	0.998123	+	0.0612400i	$0.0195055\pi$
$881$			3.63541i			0.122480i	−0.998123	+	0.0612400i	$0.980494\pi$
$882$		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
$885$	13.0664	+	7.11122i	0.439222	+	0.239041i
$886$		0			0
$887$	2.92442	+	10.9141i	0.0981924	+	0.366459i	0.997484	−	0.0708903i	$-0.0225840\pi$
$887$	2.92442	+	10.9141i	0.0981924	+	0.366459i	−0.899292	+	0.437349i	$0.855917\pi$
$888$		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
$893$	21.0195	+	5.63217i	0.703392	+	0.188473i
$894$		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
$903$	−16.6405	+	14.5471i	−0.553761	+	0.484098i
$904$		0			0
$905$	−13.7688	+	14.4806i	−0.457691	+	0.481350i
$906$		0			0
$907$	4.17302	−	15.5739i	0.138563	−	0.517124i	−0.861395	−	0.507936i	$-0.830409\pi$
$907$	4.17302	−	15.5739i	0.138563	−	0.517124i	0.999958	−	0.00918798i	$-0.00292467\pi$
$908$		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
$913$	−1.00256	+	3.74160i	−0.0331798	+	0.123829i
$914$		0			0
$915$	14.6024	−	0.367916i	0.482741	−	0.0121629i
$916$		0			0
$917$	9.35211	−	27.4088i	0.308834	−	0.905118i
$918$		0			0
$919$	42.7681	+	24.6922i	1.41079	+	0.814520i	0.995463	−	0.0951513i	$-0.0303335\pi$
$919$	42.7681	+	24.6922i	1.41079	+	0.814520i	0.415328	+	0.909672i	$0.363667\pi$
$920$		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
$927$	−8.01661	−	2.14804i	−0.263300	−	0.0705510i
$928$		0			0
$929$	−26.4711	+	45.8492i	−0.868487	+	1.50426i	−0.00494489	+	0.999988i	$0.501574\pi$
$929$	−26.4711	+	45.8492i	−0.868487	+	1.50426i	−0.863542	+	0.504276i	$0.831759\pi$
$930$		0			0
$931$	2.91779	−	21.6370i	0.0956267	−	0.709124i
$932$		0			0
$933$	−2.03261	−	7.58580i	−0.0665447	−	0.248348i
$934$		0			0
$935$	−1.00081	+	1.83891i	−0.0327299	+	0.0601389i
$936$		0			0
$937$	−28.9004	+	28.9004i	−0.944134	+	0.944134i	−0.998520	−	0.0543857i	$-0.982680\pi$
$937$	−28.9004	+	28.9004i	−0.944134	+	0.944134i	0.0543857	+	0.998520i	$0.482680\pi$
$938$		0			0
$939$			19.3463i			0.631343i
$940$		0			0
$941$	−31.1600	+	17.9902i	−1.01579	+	0.586465i	−0.912881	−	0.408226i	$-0.866147\pi$
$941$	−31.1600	+	17.9902i	−1.01579	+	0.586465i	−0.102906	+	0.994691i	$0.532814\pi$
$942$		0			0
$943$	45.5000	−	12.1917i	1.48168	−	0.397016i
$944$		0			0
$945$	−7.14442	−	31.9538i	−0.232408	−	1.03946i
$946$		0			0
$947$	18.6929	−	5.00874i	0.607437	−	0.162762i	0.0580267	−	0.998315i	$-0.481519\pi$
$947$	18.6929	−	5.00874i	0.607437	−	0.162762i	0.549410	+	0.835553i	$0.314852\pi$
$948$		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
$955$	52.2847	−	15.4311i	1.69189	−	0.499340i
$956$		0			0
$957$	−2.21579	−	8.26945i	−0.0716264	−	0.267313i
$958$		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
$963$	−2.56688	−	0.687794i	−0.0827167	−	0.0221639i
$964$		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	0.530357	−	0.847774i	$-0.322058\pi$
$971$	1.91146	+	1.10358i	0.0613417	+	0.0354157i	−0.469015	+	0.883190i	$0.655391\pi$
$972$		0			0
$973$	0.360085	+	1.82526i	0.0115438	+	0.0585151i
$974$		0			0
$975$	−6.36242	−	9.83985i	−0.203761	−	0.315128i
$976$		0			0
$977$	14.0366	−	52.3853i	0.449071	−	1.67596i	−0.255887	−	0.966707i	$-0.582368\pi$
$977$	14.0366	−	52.3853i	0.449071	−	1.67596i	0.704958	−	0.709249i	$-0.250966\pi$
$978$		0			0
$979$	−7.95058			−0.254102
$980$		0			0
$981$	8.30009			0.265001
$982$		0			0
$983$	9.12508	−	34.0552i	0.291045	−	1.08619i	−0.653263	−	0.757131i	$-0.726601\pi$
$983$	9.12508	−	34.0552i	0.291045	−	1.08619i	0.944308	−	0.329063i	$-0.106733\pi$
$984$		0			0
$985$	0.142313	+	5.64835i	0.00453447	+	0.179971i
$986$		0			0
$987$	5.64774	+	28.6282i	0.179769	+	0.911245i
$988$		0			0
$989$	21.0394	+	12.1471i	0.669013	+	0.386255i
$990$		0			0
$991$	−4.16103	−	7.20712i	−0.132179	−	0.228942i	0.792337	−	0.610084i	$-0.208864\pi$
$991$	−4.16103	−	7.20712i	−0.132179	−	0.228942i	−0.924516	+	0.381142i	$0.875531\pi$
$992$		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
$997$	−30.5090	−	8.17487i	−0.966230	−	0.258901i	−0.258995	−	0.965879i	$-0.583391\pi$
$997$	−30.5090	−	8.17487i	−0.966230	−	0.258901i	−0.707235	+	0.706978i	$0.750058\pi$
$998$		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.117.3	yes	16
3.2	odd	2		1260.2.dq.a.397.2		16
4.3	odd	2		560.2.ci.d.257.2		16
5.2	odd	4		700.2.bc.b.593.2		16
5.3	odd	4	inner	140.2.u.a.33.3	yes	16
5.4	even	2		700.2.bc.b.257.2		16
7.2	even	3		980.2.m.a.97.6		16
7.3	odd	6	inner	140.2.u.a.17.3	✓	16
7.4	even	3		980.2.v.a.717.2		16
7.5	odd	6		980.2.m.a.97.3		16
7.6	odd	2		980.2.v.a.117.2		16
15.8	even	4		1260.2.dq.a.1153.1		16
20.3	even	4		560.2.ci.d.33.2		16
21.17	even	6		1260.2.dq.a.577.1		16
28.3	even	6		560.2.ci.d.17.2		16
35.3	even	12	inner	140.2.u.a.73.3	yes	16
35.13	even	4		980.2.v.a.313.2		16
35.17	even	12		700.2.bc.b.493.2		16
35.18	odd	12		980.2.v.a.913.2		16
35.23	odd	12		980.2.m.a.293.3		16
35.24	odd	6		700.2.bc.b.157.2		16
35.33	even	12		980.2.m.a.293.6		16
105.38	odd	12		1260.2.dq.a.73.2		16
140.3	odd	12		560.2.ci.d.353.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.u.a.17.3	✓	16	7.3	odd	6	inner
140.2.u.a.33.3	yes	16	5.3	odd	4	inner
140.2.u.a.73.3	yes	16	35.3	even	12	inner
140.2.u.a.117.3	yes	16	1.1	even	1	trivial
560.2.ci.d.17.2		16	28.3	even	6
560.2.ci.d.33.2		16	20.3	even	4
560.2.ci.d.257.2		16	4.3	odd	2
560.2.ci.d.353.2		16	140.3	odd	12
700.2.bc.b.157.2		16	35.24	odd	6
700.2.bc.b.257.2		16	5.4	even	2
700.2.bc.b.493.2		16	35.17	even	12
700.2.bc.b.593.2		16	5.2	odd	4
980.2.m.a.97.3		16	7.5	odd	6
980.2.m.a.97.6		16	7.2	even	3
980.2.m.a.293.3		16	35.23	odd	12
980.2.m.a.293.6		16	35.33	even	12
980.2.v.a.117.2		16	7.6	odd	2
980.2.v.a.313.2		16	35.13	even	4
980.2.v.a.717.2		16	7.4	even	3
980.2.v.a.913.2		16	35.18	odd	12
1260.2.dq.a.73.2		16	105.38	odd	12
1260.2.dq.a.397.2		16	3.2	odd	2
1260.2.dq.a.577.1		16	21.17	even	6
1260.2.dq.a.1153.1		16	15.8	even	4

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)

\(f(q)\)	\(=\)	\(q+(0.409133 - 1.52691i) q^{3} +(1.62046 + 1.54081i) q^{5} +(-0.512081 - 2.59572i) q^{7} +(0.434025 + 0.250584i) q^{9} +O(q^{10})\)	\(q+(0.409133 - 1.52691i) q^{3} +(1.62046 + 1.54081i) q^{5} +(-0.512081 - 2.59572i) q^{7} +(0.434025 + 0.250584i) q^{9} +(-0.342727 - 0.593621i) q^{11} +(-1.04830 - 1.04830i) q^{13} +(3.01566 - 1.84390i) q^{15} +(-1.31940 - 0.353532i) q^{17} +(-1.55949 + 2.70111i) q^{19} +(-4.17293 - 0.280096i) q^{21} +(1.18980 + 4.44038i) q^{23} +(0.251796 + 4.99366i) q^{25} +(3.91351 - 3.91351i) q^{27} +7.90106i q^{29} +(-7.63715 + 4.40931i) q^{31} +(-1.04663 + 0.280442i) q^{33} +(3.16971 - 4.99529i) q^{35} +(-8.68572 + 2.32733i) q^{37} +(-2.02956 + 1.17176i) q^{39} -10.2469i q^{41} +(3.73689 - 3.73689i) q^{43} +(0.317217 + 1.07481i) q^{45} +(-1.80577 - 6.73924i) q^{47} +(-6.47555 + 2.65844i) q^{49} +(-1.07962 + 1.86996i) q^{51} +(8.94065 + 2.39564i) q^{53} +(0.359282 - 1.49002i) q^{55} +(3.48631 + 3.48631i) q^{57} +(2.10430 + 3.64475i) q^{59} +(3.57882 + 2.06623i) q^{61} +(0.428191 - 1.25493i) q^{63} +(-0.0834974 - 3.31397i) q^{65} +(-1.07466 + 4.01070i) q^{67} +7.26683 q^{69} +12.5889 q^{71} +(3.32399 - 12.4053i) q^{73} +(7.72786 + 1.65860i) q^{75} +(-1.36537 + 1.19361i) q^{77} +(-12.1515 - 7.01566i) q^{79} +(-3.62266 - 6.27464i) q^{81} +(-3.99595 - 3.99595i) q^{83} +(-1.59331 - 2.60583i) q^{85} +(12.0642 + 3.23259i) q^{87} +(5.79949 - 10.0450i) q^{89} +(-2.18429 + 3.25792i) q^{91} +(3.60799 + 13.4652i) q^{93} +(-6.68900 + 1.97417i) q^{95} +(2.60010 - 2.60010i) q^{97} -0.343528i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{5} + 2 q^{7}+O(q^{10}) \) 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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