LMFDB - Embedded newform 252.2.l.b.193.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(193,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 4]))

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

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

chi := DirichletCharacter("252.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.l (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 5x^{12} - 3x^{11} + 7x^{10} + 30x^{9} - 117x^{7} + 270x^{5} + 189x^{4} - 243x^{3} - 1215x^{2} + 2187 $ x^14 - 5x^12 - 3x^11 + 7x^10 + 30x^9 - 117x^7 + 270x^5 + 189x^4 - 243x^3 - 1215*x^2 + 2187
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			193.6
Root			$1.64515 + 0.541745i$ of defining polynomial
Character	$\chi$	$=$	252.193
Dual form			252.2.l.b.205.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.64515 + 0.541745i) q^{3} -0.763837 q^{5} +(-1.05641 + 2.42569i) q^{7} +(2.41302 + 1.78250i) q^{9} +O(q^{10})$	\(q+(1.64515 + 0.541745i) q^{3} -0.763837 q^{5} +(-1.05641 + 2.42569i) q^{7} +(2.41302 + 1.78250i) q^{9} +6.03389 q^{11} +(-1.26032 + 2.18294i) q^{13} +(-1.25662 - 0.413805i) q^{15} +(1.94444 - 3.36787i) q^{17} +(-2.13503 - 3.69798i) q^{19} +(-3.05206 + 3.41832i) q^{21} -1.46425 q^{23} -4.41655 q^{25} +(3.00412 + 4.23972i) q^{27} +(-3.00732 - 5.20884i) q^{29} +(-3.28482 - 5.68948i) q^{31} +(9.92665 + 3.26883i) q^{33} +(0.806926 - 1.85283i) q^{35} +(4.82492 + 8.35700i) q^{37} +(-3.25602 + 2.90849i) q^{39} +(-2.24844 + 3.89442i) q^{41} +(-2.13503 - 3.69798i) q^{43} +(-1.84316 - 1.36154i) q^{45} +(3.38924 - 5.87034i) q^{47} +(-4.76799 - 5.12507i) q^{49} +(5.02342 - 4.48725i) q^{51} +(-0.265581 + 0.460000i) q^{53} -4.60891 q^{55} +(-1.50908 - 7.24036i) q^{57} +(-5.59926 - 9.69821i) q^{59} +(-4.19144 + 7.25979i) q^{61} +(-6.87295 + 3.97020i) q^{63} +(0.962681 - 1.66741i) q^{65} +(0.961979 + 1.66620i) q^{67} +(-2.40890 - 0.793249i) q^{69} +9.90353 q^{71} +(-2.13099 + 3.69098i) q^{73} +(-7.26588 - 2.39265i) q^{75} +(-6.37428 + 14.6364i) q^{77} +(3.70372 - 6.41503i) q^{79} +(2.64537 + 8.60244i) q^{81} +(-8.05178 - 13.9461i) q^{83} +(-1.48523 + 2.57250i) q^{85} +(-2.12563 - 10.1985i) q^{87} +(1.76310 + 3.05377i) q^{89} +(-3.96373 - 5.36325i) q^{91} +(-2.32177 - 11.1396i) q^{93} +(1.63081 + 2.82465i) q^{95} +(2.33513 + 4.04456i) q^{97} +(14.5599 + 10.7554i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 4 q^{5} - 3 q^{7} + 10 q^{9}+O(q^{10}) $ 14 * q + 4 * q^5 - 3 * q^7 + 10 * q^9	$ 14 q + 4 q^{5} - 3 q^{7} + 10 q^{9} - 4 q^{11} + 2 q^{13} + 7 q^{15} + 2 q^{17} + 7 q^{19} - 2 q^{21} - 22 q^{23} + 18 q^{25} + 9 q^{27} + q^{29} - q^{31} + 5 q^{33} - 19 q^{35} + 10 q^{37} - 20 q^{39} - 33 q^{41} + 7 q^{43} + 5 q^{45} - 3 q^{47} - 13 q^{49} + 20 q^{51} - 15 q^{53} - 28 q^{55} - 18 q^{57} - 14 q^{59} - 10 q^{61} - 39 q^{63} + 15 q^{65} + 6 q^{67} - 43 q^{69} + 2 q^{71} + 21 q^{73} + q^{75} + 19 q^{77} - 10 q^{79} + 22 q^{81} - 25 q^{83} + 8 q^{85} - 2 q^{87} - 6 q^{89} + 2 q^{91} + 16 q^{93} - 28 q^{95} - 18 q^{97} + 7 q^{99}+O(q^{100}) $ 14 * q + 4 * q^5 - 3 * q^7 + 10 * q^9 - 4 * q^11 + 2 * q^13 + 7 * q^15 + 2 * q^17 + 7 * q^19 - 2 * q^21 - 22 * q^23 + 18 * q^25 + 9 * q^27 + q^29 - q^31 + 5 * q^33 - 19 * q^35 + 10 * q^37 - 20 * q^39 - 33 * q^41 + 7 * q^43 + 5 * q^45 - 3 * q^47 - 13 * q^49 + 20 * q^51 - 15 * q^53 - 28 * q^55 - 18 * q^57 - 14 * q^59 - 10 * q^61 - 39 * q^63 + 15 * q^65 + 6 * q^67 - 43 * q^69 + 2 * q^71 + 21 * q^73 + q^75 + 19 * q^77 - 10 * q^79 + 22 * q^81 - 25 * q^83 + 8 * q^85 - 2 * q^87 - 6 * q^89 + 2 * q^91 + 16 * q^93 - 28 * q^95 - 18 * q^97 + 7 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.64515	+	0.541745i	0.949827	+	0.312777i
$3$	1.64515	+	0.541745i	0.949827	+	0.312777i
$4$		0			0
$5$	−0.763837			−0.341598			−0.170799	−	0.985306i	$-0.554635\pi$
$5$	−0.763837			−0.341598			−0.170799	+	0.985306i	$0.554635\pi$
$6$		0			0
$7$	−1.05641	+	2.42569i	−0.399286	+	0.916826i
$7$	−1.05641	+	2.42569i	−0.399286	+	0.916826i
$8$		0			0
$9$	2.41302	+	1.78250i	0.804341	+	0.594167i
$10$		0			0
$11$	6.03389			1.81929			0.909644	−	0.415389i	$-0.136355\pi$
$11$	6.03389			1.81929			0.909644	+	0.415389i	$0.136355\pi$
$12$		0			0
$13$	−1.26032	+	2.18294i	−0.349551	+	0.605440i	−0.986170	−	0.165739i	$-0.946999\pi$
$13$	−1.26032	+	2.18294i	−0.349551	+	0.605440i	0.636619	+	0.771179i	$0.280332\pi$
$14$		0			0
$15$	−1.25662	−	0.413805i	−0.324459	−	0.106844i
$16$		0			0
$17$	1.94444	−	3.36787i	0.471596	−	0.816828i	−0.527876	−	0.849322i	$-0.677011\pi$
$17$	1.94444	−	3.36787i	0.471596	−	0.816828i	0.999472	+	0.0324932i	$0.0103447\pi$
$18$		0			0
$19$	−2.13503	−	3.69798i	−0.489809	−	0.848375i	0.510122	−	0.860102i	$-0.329600\pi$
$19$	−2.13503	−	3.69798i	−0.489809	−	0.848375i	−0.999931	+	0.0117275i	$0.996267\pi$
$20$		0			0
$21$	−3.05206	+	3.41832i	−0.666015	+	0.745939i
$22$		0			0
$23$	−1.46425			−0.305317			−0.152658	−	0.988279i	$-0.548783\pi$
$23$	−1.46425			−0.305317			−0.152658	+	0.988279i	$0.548783\pi$
$24$		0			0
$25$	−4.41655			−0.883311
$26$		0			0
$27$	3.00412	+	4.23972i	0.578143	+	0.815935i
$28$		0			0
$29$	−3.00732	−	5.20884i	−0.558446	−	0.967257i	−0.997626	−	0.0688580i	$-0.978064\pi$
$29$	−3.00732	−	5.20884i	−0.558446	−	0.967257i	0.439180	−	0.898399i	$-0.355269\pi$
$30$		0			0
$31$	−3.28482	−	5.68948i	−0.589972	−	1.02186i	−0.994235	−	0.107219i	$-0.965806\pi$
$31$	−3.28482	−	5.68948i	−0.589972	−	1.02186i	0.404264	−	0.914642i	$-0.367528\pi$
$32$		0			0
$33$	9.92665	+	3.26883i	1.72801	+	0.569031i
$34$		0			0
$35$	0.806926	−	1.85283i	0.136395	−	0.313186i
$36$		0			0
$37$	4.82492	+	8.35700i	0.793211	+	1.37388i	0.923969	+	0.382468i	$0.124926\pi$
$37$	4.82492	+	8.35700i	0.793211	+	1.37388i	−0.130758	+	0.991414i	$0.541741\pi$
$38$		0			0
$39$	−3.25602	+	2.90849i	−0.521380	+	0.465731i
$40$		0			0
$41$	−2.24844	+	3.89442i	−0.351148	+	0.608206i	−0.986451	−	0.164057i	$-0.947542\pi$
$41$	−2.24844	+	3.89442i	−0.351148	+	0.608206i	0.635303	+	0.772263i	$0.280875\pi$
$42$		0			0
$43$	−2.13503	−	3.69798i	−0.325589	−	0.563937i	0.656042	−	0.754724i	$-0.272229\pi$
$43$	−2.13503	−	3.69798i	−0.325589	−	0.563937i	−0.981631	+	0.190787i	$0.938896\pi$
$44$		0			0
$45$	−1.84316	−	1.36154i	−0.274762	−	0.202966i
$46$		0			0
$47$	3.38924	−	5.87034i	0.494372	−	0.856277i	−0.505607	−	0.862764i	$-0.668731\pi$
$47$	3.38924	−	5.87034i	0.494372	−	0.856277i	0.999979	+	0.00648676i	$0.00206481\pi$
$48$		0			0
$49$	−4.76799	−	5.12507i	−0.681141	−	0.732152i
$50$		0			0
$51$	5.02342	−	4.48725i	0.703419	−	0.628341i
$52$		0			0
$53$	−0.265581	+	0.460000i	−0.0364804	+	0.0631859i	−0.883689	−	0.468074i	$-0.844948\pi$
$53$	−0.265581	+	0.460000i	−0.0364804	+	0.0631859i	0.847209	+	0.531260i	$0.178281\pi$
$54$		0			0
$55$	−4.60891			−0.621465
$56$		0			0
$57$	−1.50908	−	7.24036i	−0.199882	−	0.959010i
$58$		0			0
$59$	−5.59926	−	9.69821i	−0.728962	−	1.26260i	−0.957322	−	0.289023i	$-0.906670\pi$
$59$	−5.59926	−	9.69821i	−0.728962	−	1.26260i	0.228360	−	0.973577i	$-0.426664\pi$
$60$		0			0
$61$	−4.19144	+	7.25979i	−0.536659	+	0.929521i	0.462422	+	0.886660i	$0.346981\pi$
$61$	−4.19144	+	7.25979i	−0.536659	+	0.929521i	−0.999081	+	0.0428608i	$0.986353\pi$
$62$		0			0
$63$	−6.87295	+	3.97020i	−0.865911	+	0.500199i
$64$		0			0
$65$	0.962681	−	1.66741i	0.119406	−	0.206817i
$66$		0			0
$67$	0.961979	+	1.66620i	0.117524	+	0.203558i	0.918786	−	0.394756i	$-0.129171\pi$
$67$	0.961979	+	1.66620i	0.117524	+	0.203558i	−0.801262	+	0.598314i	$0.795838\pi$
$68$		0			0
$69$	−2.40890	−	0.793249i	−0.289998	−	0.0954960i
$70$		0			0
$71$	9.90353			1.17533			0.587666	−	0.809103i	$-0.300047\pi$
$71$	9.90353			1.17533			0.587666	+	0.809103i	$0.300047\pi$
$72$		0			0
$73$	−2.13099	+	3.69098i	−0.249413	+	0.431997i	−0.963363	−	0.268200i	$-0.913571\pi$
$73$	−2.13099	+	3.69098i	−0.249413	+	0.431997i	0.713950	+	0.700197i	$0.246904\pi$
$74$		0			0
$75$	−7.26588	−	2.39265i	−0.838992	−	0.276279i
$76$		0			0
$77$	−6.37428	+	14.6364i	−0.726416	+	1.66797i
$78$		0			0
$79$	3.70372	−	6.41503i	0.416701	−	0.721748i	−0.578904	−	0.815396i	$-0.696519\pi$
$79$	3.70372	−	6.41503i	0.416701	−	0.721748i	0.995605	+	0.0936479i	$0.0298528\pi$
$80$		0			0
$81$	2.64537	+	8.60244i	0.293930	+	0.955827i
$82$		0			0
$83$	−8.05178	−	13.9461i	−0.883798	−	1.53078i	−0.847085	−	0.531457i	$-0.821645\pi$
$83$	−8.05178	−	13.9461i	−0.883798	−	1.53078i	−0.0367125	−	0.999326i	$-0.511689\pi$
$84$		0			0
$85$	−1.48523	+	2.57250i	−0.161096	+	0.279027i
$86$		0			0
$87$	−2.12563	−	10.1985i	−0.227891	−	1.09340i
$88$		0			0
$89$	1.76310	+	3.05377i	0.186888	+	0.323699i	0.944211	−	0.329341i	$-0.106827\pi$
$89$	1.76310	+	3.05377i	0.186888	+	0.323699i	−0.757323	+	0.653040i	$0.773493\pi$
$90$		0			0
$91$	−3.96373	−	5.36325i	−0.415512	−	0.562221i
$92$		0			0
$93$	−2.32177	−	11.1396i	−0.240757	−	1.15512i
$94$		0			0
$95$	1.63081	+	2.82465i	0.167318	+	0.289803i
$96$		0			0
$97$	2.33513	+	4.04456i	0.237096	+	0.410662i	0.959880	−	0.280412i	$-0.0904710\pi$
$97$	2.33513	+	4.04456i	0.237096	+	0.410662i	−0.722784	+	0.691074i	$0.757138\pi$
$98$		0			0
$99$	14.5599	+	10.7554i	1.46333	+	1.08096i
$100$		0			0
$101$	−4.71965			−0.469623			−0.234811	−	0.972041i	$-0.575447\pi$
$101$	−4.71965			−0.469623			−0.234811	+	0.972041i	$0.575447\pi$
$102$		0			0
$103$	3.16531			0.311888			0.155944	−	0.987766i	$-0.450158\pi$
$103$	3.16531			0.311888			0.155944	+	0.987766i	$0.450158\pi$
$104$		0			0
$105$	2.33128	−	2.61104i	0.227509	−	0.254811i
$106$		0			0
$107$	7.65537	+	13.2595i	0.740073	+	1.28184i	0.952462	+	0.304659i	$0.0985424\pi$
$107$	7.65537	+	13.2595i	0.740073	+	1.28184i	−0.212389	+	0.977185i	$0.568124\pi$
$108$		0			0
$109$	7.65371	−	13.2566i	0.733092	−	1.26975i	−0.222463	−	0.974941i	$-0.571410\pi$
$109$	7.65371	−	13.2566i	0.733092	−	1.26975i	0.955555	−	0.294812i	$-0.0952569\pi$
$110$		0			0
$111$	3.41034	+	16.3624i	0.323695	+	1.55305i
$112$		0			0
$113$	−1.56114	+	2.70397i	−0.146860	+	0.254368i	−0.930065	−	0.367395i	$-0.880250\pi$
$113$	−1.56114	+	2.70397i	−0.146860	+	0.254368i	0.783206	+	0.621763i	$0.213583\pi$
$114$		0			0
$115$	1.11845			0.104296
$116$		0			0
$117$	−6.93229	+	3.02097i	−0.640891	+	0.279289i
$118$		0			0
$119$	6.11529	+	8.27448i	0.560588	+	0.758520i
$120$		0			0
$121$	25.4079			2.30981
$122$		0			0
$123$	−5.80881	+	5.18881i	−0.523762	+	0.467859i
$124$		0			0
$125$	7.19271			0.643335
$126$		0			0
$127$	1.27814			0.113416			0.0567082	−	0.998391i	$-0.481940\pi$
$127$	1.27814			0.113416			0.0567082	+	0.998391i	$0.481940\pi$
$128$		0			0
$129$	−1.50908	−	7.24036i	−0.132867	−	0.637479i
$130$		0			0
$131$	7.77465			0.679274			0.339637	−	0.940557i	$-0.389696\pi$
$131$	7.77465			0.679274			0.339637	+	0.940557i	$0.389696\pi$
$132$		0			0
$133$	11.2256	−	1.27234i	0.973386	−	0.110326i
$134$		0			0
$135$	−2.29466	−	3.23846i	−0.197493	−	0.278722i
$136$		0			0
$137$	2.82307			0.241191			0.120596	−	0.992702i	$-0.461520\pi$
$137$	2.82307			0.241191			0.120596	+	0.992702i	$0.461520\pi$
$138$		0			0
$139$	−11.2206	+	19.4346i	−0.951718	+	1.64842i	−0.210013	+	0.977699i	$0.567351\pi$
$139$	−11.2206	+	19.4346i	−0.951718	+	1.64842i	−0.741705	+	0.670726i	$0.765983\pi$
$140$		0			0
$141$	8.75603	−	7.82147i	0.737391	−	0.658687i
$142$		0			0
$143$	−7.60466	+	13.1717i	−0.635933	+	1.10147i
$144$		0			0
$145$	2.29710	+	3.97870i	0.190764	+	0.330413i
$146$		0			0
$147$	−5.06757	−	11.0145i	−0.417966	−	0.908463i
$148$		0			0
$149$	−20.1703			−1.65241			−0.826206	−	0.563369i	$-0.809505\pi$
$149$	−20.1703			−1.65241			−0.826206	+	0.563369i	$0.809505\pi$
$150$		0			0
$151$	8.29450			0.674997			0.337498	−	0.941326i	$-0.390419\pi$
$151$	8.29450			0.674997			0.337498	+	0.941326i	$0.390419\pi$
$152$		0			0
$153$	10.6952	−	4.66078i	0.864657	−	0.376802i
$154$		0			0
$155$	2.50907	+	4.34583i	0.201533	+	0.349066i
$156$		0			0
$157$	3.33332	+	5.77348i	0.266028	+	0.460774i	0.967832	−	0.251596i	$-0.0809553\pi$
$157$	3.33332	+	5.77348i	0.266028	+	0.460774i	−0.701804	+	0.712370i	$0.747622\pi$
$158$		0			0
$159$	−0.686123	+	0.612891i	−0.0544131	+	0.0486054i
$160$		0			0
$161$	1.54685	−	3.55182i	0.121909	−	0.279922i
$162$		0			0
$163$	3.69751	+	6.40428i	0.289611	+	0.501622i	0.973717	−	0.227761i	$-0.0731406\pi$
$163$	3.69751	+	6.40428i	0.289611	+	0.501622i	−0.684106	+	0.729383i	$0.739807\pi$
$164$		0			0
$165$	−7.58234	−	2.49685i	−0.590284	−	0.194380i
$166$		0			0
$167$	−0.475526	+	0.823635i	−0.0367973	+	0.0637348i	−0.883838	−	0.467794i	$-0.845049\pi$
$167$	−0.475526	+	0.823635i	−0.0367973	+	0.0637348i	0.847040	+	0.531529i	$0.178382\pi$
$168$		0			0
$169$	3.32317	+	5.75590i	0.255629	+	0.442762i
$170$		0			0
$171$	1.43978	−	12.7290i	0.110103	−	0.973411i
$172$		0			0
$173$	−2.33554	+	4.04527i	−0.177568	+	0.307557i	−0.941047	−	0.338276i	$-0.890156\pi$
$173$	−2.33554	+	4.04527i	−0.177568	+	0.307557i	0.763479	+	0.645833i	$0.223490\pi$
$174$		0			0
$175$	4.66570	−	10.7132i	0.352694	−	0.809843i
$176$		0			0
$177$	−3.95766	−	18.9884i	−0.297476	−	1.42725i
$178$		0			0
$179$	−7.49486	+	12.9815i	−0.560192	+	0.970281i	0.437287	+	0.899322i	$0.355939\pi$
$179$	−7.49486	+	12.9815i	−0.560192	+	0.970281i	−0.997479	+	0.0709591i	$0.977394\pi$
$180$		0			0
$181$	−13.6525			−1.01478			−0.507391	−	0.861716i	$-0.669390\pi$
$181$	−13.6525			−1.01478			−0.507391	+	0.861716i	$0.669390\pi$
$182$		0			0
$183$	−10.8285	+	9.67273i	−0.800466	+	0.715029i
$184$		0			0
$185$	−3.68545	−	6.38338i	−0.270959	−	0.469316i
$186$		0			0
$187$	11.7325	−	20.3214i	0.857969	−	1.48605i
$188$		0			0
$189$	−13.4579	+	2.80818i	−0.978916	+	0.204265i
$190$		0			0
$191$	−6.14528	+	10.6439i	−0.444657	+	0.770168i	−0.998028	−	0.0627667i	$-0.980008\pi$
$191$	−6.14528	+	10.6439i	−0.444657	+	0.770168i	0.553372	+	0.832934i	$0.313341\pi$
$192$		0			0
$193$	−3.58578	−	6.21075i	−0.258110	−	0.447060i	0.707626	−	0.706588i	$-0.249766\pi$
$193$	−3.58578	−	6.21075i	−0.258110	−	0.447060i	−0.965736	+	0.259528i	$0.916433\pi$
$194$		0			0
$195$	2.48707	−	2.22161i	0.178102	−	0.159093i
$196$		0			0
$197$	−13.0286			−0.928247			−0.464124	−	0.885770i	$-0.653631\pi$
$197$	−13.0286			−0.928247			−0.464124	+	0.885770i	$0.653631\pi$
$198$		0			0
$199$	−2.48087	+	4.29699i	−0.175864	+	0.304606i	−0.940460	−	0.339904i	$-0.889605\pi$
$199$	−2.48087	+	4.29699i	−0.175864	+	0.304606i	0.764596	+	0.644510i	$0.222939\pi$
$200$		0			0
$201$	0.679944	+	3.26229i	0.0479595	+	0.230104i
$202$		0			0
$203$	15.8120	−	1.79217i	1.10979	−	0.125786i
$204$		0			0
$205$	1.71744	−	2.97470i	0.119951	−	0.207762i
$206$		0			0
$207$	−3.53326	−	2.61002i	−0.245579	−	0.181409i
$208$		0			0
$209$	−12.8825	−	22.3132i	−0.891104	−	1.54344i
$210$		0			0
$211$	2.07384	−	3.59199i	0.142769	−	0.247283i	−0.785769	−	0.618519i	$-0.787733\pi$
$211$	2.07384	−	3.59199i	0.142769	−	0.247283i	0.928538	+	0.371237i	$0.121066\pi$
$212$		0			0
$213$	16.2928	+	5.36519i	1.11636	+	0.367617i
$214$		0			0
$215$	1.63081	+	2.82465i	0.111221	+	0.192640i
$216$		0			0
$217$	17.2711	−	1.95754i	1.17244	−	0.132887i
$218$		0			0
$219$	−5.50536	+	4.91776i	−0.372018	+	0.332311i
$220$		0			0
$221$	4.90125	+	8.48921i	0.329694	+	0.571046i
$222$		0			0
$223$	−4.63830	−	8.03378i	−0.310604	−	0.537982i	0.667889	−	0.744261i	$-0.267198\pi$
$223$	−4.63830	−	8.03378i	−0.310604	−	0.537982i	−0.978493	+	0.206279i	$0.933865\pi$
$224$		0			0
$225$	−10.6573	−	7.87252i	−0.710483	−	0.524834i
$226$		0			0
$227$	−21.3602			−1.41773			−0.708863	−	0.705346i	$-0.750792\pi$
$227$	−21.3602			−1.41773			−0.708863	+	0.705346i	$0.750792\pi$
$228$		0			0
$229$	−20.0071			−1.32210			−0.661052	−	0.750340i	$-0.729890\pi$
$229$	−20.0071			−1.32210			−0.661052	+	0.750340i	$0.729890\pi$
$230$		0			0
$231$	−18.4158	+	20.6258i	−1.21167	+	1.35708i
$232$		0			0
$233$	7.63657	+	13.2269i	0.500288	+	0.866525i	1.00000		0.000332882i	$0.000105960\pi$
$233$	7.63657	+	13.2269i	0.500288	+	0.866525i	−0.499712	+	0.866192i	$0.666561\pi$
$234$		0			0
$235$	−2.58883	+	4.48398i	−0.168876	+	0.292503i
$236$		0			0
$237$	9.56848	−	8.54721i	0.621540	−	0.555201i
$238$		0			0
$239$	9.03828	−	15.6548i	0.584638	−	1.01262i	−0.410283	−	0.911958i	$-0.634570\pi$
$239$	9.03828	−	15.6548i	0.584638	−	1.01262i	0.994920	−	0.100664i	$-0.0320967\pi$
$240$		0			0
$241$	4.31045			0.277660			0.138830	−	0.990316i	$-0.455666\pi$
$241$	4.31045			0.277660			0.138830	+	0.990316i	$0.455666\pi$
$242$		0			0
$243$	−0.308301	+	15.5854i	−0.0197775	+	0.999804i
$244$		0			0
$245$	3.64196	+	3.91471i	0.232677	+	0.250102i
$246$		0			0
$247$	10.7633			0.684853
$248$		0			0
$249$	−5.69114	−	27.3054i	−0.360662	−	1.73041i
$250$		0			0
$251$	16.3348			1.03104			0.515521	−	0.856877i	$-0.327599\pi$
$251$	16.3348			1.03104			0.515521	+	0.856877i	$0.327599\pi$
$252$		0			0
$253$	−8.83512			−0.555459
$254$		0			0
$255$	−3.83707	+	3.42753i	−0.240287	+	0.214640i
$256$		0			0
$257$	1.29540			0.0808046			0.0404023	−	0.999183i	$-0.487136\pi$
$257$	1.29540			0.0808046			0.0404023	+	0.999183i	$0.487136\pi$
$258$		0			0
$259$	−25.3686	+	2.87534i	−1.57633	+	0.178665i
$260$		0			0
$261$	2.02802	−	17.9296i	0.125531	−	1.10982i
$262$		0			0
$263$	28.2728			1.74337			0.871687	−	0.490062i	$-0.163026\pi$
$263$	28.2728			1.74337			0.871687	+	0.490062i	$0.163026\pi$
$264$		0			0
$265$	0.202861	−	0.351365i	0.0124616	−	0.0215842i
$266$		0			0
$267$	1.24619	+	5.97906i	0.0762655	+	0.365912i
$268$		0			0
$269$	7.10969	−	12.3143i	0.433485	−	0.750818i	−0.563685	−	0.825990i	$-0.690617\pi$
$269$	7.10969	−	12.3143i	0.433485	−	0.750818i	0.997171	+	0.0751711i	$0.0239503\pi$
$270$		0			0
$271$	−7.18914	−	12.4520i	−0.436709	−	0.756403i	0.560724	−	0.828003i	$-0.310523\pi$
$271$	−7.18914	−	12.4520i	−0.436709	−	0.756403i	−0.997433	+	0.0716001i	$0.977189\pi$
$272$		0			0
$273$	−3.61542	−	10.9707i	−0.218815	−	0.663975i
$274$		0			0
$275$	−26.6490			−1.60700
$276$		0			0
$277$	−15.4361			−0.927468			−0.463734	−	0.885974i	$-0.653491\pi$
$277$	−15.4361			−0.927468			−0.463734	+	0.885974i	$0.653491\pi$
$278$		0			0
$279$	2.21515	−	19.5841i	0.132618	−	1.17247i
$280$		0			0
$281$	−9.39609	−	16.2745i	−0.560524	−	0.970856i	−0.997451	−	0.0713587i	$-0.977266\pi$
$281$	−9.39609	−	16.2745i	−0.560524	−	0.970856i	0.436927	−	0.899497i	$-0.356067\pi$
$282$		0			0
$283$	16.2864	+	28.2089i	0.968128	+	1.67685i	0.700965	+	0.713196i	$0.252753\pi$
$283$	16.2864	+	28.2089i	0.968128	+	1.67685i	0.267163	+	0.963651i	$0.413914\pi$
$284$		0			0
$285$	1.15269	+	5.53046i	0.0682793	+	0.327596i
$286$		0			0
$287$	−7.07139	−	9.56815i	−0.417411	−	0.564790i
$288$		0			0
$289$	0.938304	+	1.62519i	0.0551944	+	0.0955994i
$290$		0			0
$291$	1.65051	+	7.91894i	0.0967545	+	0.464216i
$292$		0			0
$293$	−1.69821	+	2.94138i	−0.0992103	+	0.171837i	−0.911358	−	0.411615i	$-0.864965\pi$
$293$	−1.69821	+	2.94138i	−0.0992103	+	0.171837i	0.812148	+	0.583452i	$0.198298\pi$
$294$		0			0
$295$	4.27692	+	7.40785i	0.249012	+	0.431302i
$296$		0			0
$297$	18.1265	+	25.5820i	1.05181	+	1.48442i
$298$		0			0
$299$	1.84543	−	3.19637i	0.106724	−	0.184851i
$300$		0			0
$301$	11.2256	−	1.27234i	0.647035	−	0.0733364i
$302$		0			0
$303$	−7.76452	−	2.55685i	−0.446060	−	0.146887i
$304$		0			0
$305$	3.20158	−	5.54529i	0.183322	−	0.317523i
$306$		0			0
$307$	3.69564			0.210921			0.105461	−	0.994423i	$-0.466368\pi$
$307$	3.69564			0.210921			0.105461	+	0.994423i	$0.466368\pi$
$308$		0			0
$309$	5.20741	+	1.71479i	0.296239	+	0.0975512i
$310$		0			0
$311$	8.58119	+	14.8631i	0.486594	+	0.842806i	0.999881	−	0.0154108i	$-0.00490561\pi$
$311$	8.58119	+	14.8631i	0.486594	+	0.842806i	−0.513287	+	0.858217i	$0.671572\pi$
$312$		0			0
$313$	−2.64824	+	4.58688i	−0.149687	+	0.259266i	−0.931112	−	0.364734i	$-0.881160\pi$
$313$	−2.64824	+	4.58688i	−0.149687	+	0.259266i	0.781425	+	0.624000i	$0.214493\pi$
$314$		0			0
$315$	5.24981	−	3.03259i	0.295793	−	0.170867i
$316$		0			0
$317$	−14.0890	+	24.4028i	−0.791315	+	1.37060i	0.133838	+	0.991003i	$0.457270\pi$
$317$	−14.0890	+	24.4028i	−0.791315	+	1.37060i	−0.925153	+	0.379594i	$0.876064\pi$
$318$		0			0
$319$	−18.1459	−	31.4296i	−1.01597	−	1.75972i
$320$		0			0
$321$	5.41096	+	25.9611i	0.302010	+	1.44901i
$322$		0			0
$323$	−16.6057			−0.923968
$324$		0			0
$325$	5.56628	−	9.64109i	0.308762	−	0.534791i
$326$		0			0
$327$	19.7732	−	17.6627i	1.09346	−	0.976751i
$328$		0			0
$329$	10.6592	+	14.4228i	0.587662	+	0.795153i
$330$		0			0
$331$	−14.5860	+	25.2637i	−0.801720	+	1.38862i	0.116762	+	0.993160i	$0.462748\pi$
$331$	−14.5860	+	25.2637i	−0.801720	+	1.38862i	−0.918483	+	0.395461i	$0.870585\pi$
$332$		0			0
$333$	−3.25373	+	28.7661i	−0.178303	+	1.57637i
$334$		0			0
$335$	−0.734794	−	1.27270i	−0.0401461	−	0.0695351i
$336$		0			0
$337$	−0.447174	+	0.774528i	−0.0243591	+	0.0421912i	−0.877948	−	0.478756i	$-0.841088\pi$
$337$	−0.447174	+	0.774528i	−0.0243591	+	0.0421912i	0.853589	+	0.520947i	$0.174421\pi$
$338$		0			0
$339$	−4.03317	+	3.60270i	−0.219052	+	0.195672i
$340$		0			0
$341$	−19.8203	−	34.3297i	−1.07333	−	1.85906i
$342$		0			0
$343$	17.4688	−	6.15150i	0.943227	−	0.332150i
$344$		0			0
$345$	1.84001	+	0.605913i	0.0990627	+	0.0326212i
$346$		0			0
$347$	−9.98982	−	17.3029i	−0.536282	−	0.928867i	−0.999100	−	0.0424143i	$-0.986495\pi$
$347$	−9.98982	−	17.3029i	−0.536282	−	0.928867i	0.462818	−	0.886453i	$-0.346838\pi$
$348$		0			0
$349$	2.58530	+	4.47788i	0.138388	+	0.239695i	0.926887	−	0.375341i	$-0.122475\pi$
$349$	2.58530	+	4.47788i	0.138388	+	0.239695i	−0.788499	+	0.615037i	$0.789141\pi$
$350$		0			0
$351$	−13.0412	+	1.21440i	−0.696090	+	0.0648201i
$352$		0			0
$353$	33.1222			1.76292			0.881459	−	0.472261i	$-0.156562\pi$
$353$	33.1222			1.76292			0.881459	+	0.472261i	$0.156562\pi$
$354$		0			0
$355$	−7.56468			−0.401491
$356$		0			0
$357$	5.57790	+	16.9257i	0.295214	+	0.895801i
$358$		0			0
$359$	−17.2965	−	29.9584i	−0.912874	−	1.58114i	−0.809985	−	0.586451i	$-0.800525\pi$
$359$	−17.2965	−	29.9584i	−0.912874	−	1.58114i	−0.102889	−	0.994693i	$-0.532809\pi$
$360$		0			0
$361$	0.383301	−	0.663897i	0.0201737	−	0.0349420i
$362$		0			0
$363$	41.7997	+	13.7646i	2.19392	+	0.722454i
$364$		0			0
$365$	1.62773	−	2.81931i	0.0851992	−	0.147569i
$366$		0			0
$367$	−3.29611			−0.172055			−0.0860277	−	0.996293i	$-0.527417\pi$
$367$	−3.29611			−0.172055			−0.0860277	+	0.996293i	$0.527417\pi$
$368$		0			0
$369$	−12.3674	+	5.38947i	−0.643819	+	0.280565i
$370$		0			0
$371$	−0.835256	−	1.13017i	−0.0433644	−	0.0586754i
$372$		0			0
$373$	−23.6754			−1.22587			−0.612933	−	0.790135i	$-0.710010\pi$
$373$	−23.6754			−1.22587			−0.612933	+	0.790135i	$0.710010\pi$
$374$		0			0
$375$	11.8331	+	3.89661i	0.611057	+	0.201220i
$376$		0			0
$377$	15.1608			0.780821
$378$		0			0
$379$	−25.4415			−1.30684			−0.653421	−	0.756995i	$-0.726667\pi$
$379$	−25.4415			−1.30684			−0.653421	+	0.756995i	$0.726667\pi$
$380$		0			0
$381$	2.10273	+	0.692425i	0.107726	+	0.0354740i
$382$		0			0
$383$	23.7278			1.21244			0.606218	−	0.795299i	$-0.292686\pi$
$383$	23.7278			1.21244			0.606218	+	0.795299i	$0.292686\pi$
$384$		0			0
$385$	4.86891	−	11.1798i	0.248142	−	0.569776i
$386$		0			0
$387$	1.43978	−	12.7290i	0.0731880	−	0.647052i
$388$		0			0
$389$	19.5275			0.990082			0.495041	−	0.868870i	$-0.335153\pi$
$389$	19.5275			0.990082			0.495041	+	0.868870i	$0.335153\pi$
$390$		0			0
$391$	−2.84714	+	4.93139i	−0.143986	+	0.249391i
$392$		0			0
$393$	12.7905	+	4.21188i	0.645193	+	0.212461i
$394$		0			0
$395$	−2.82904	+	4.90004i	−0.142344	+	0.246548i
$396$		0			0
$397$	14.4468	+	25.0226i	0.725064	+	1.25585i	0.958948	+	0.283583i	$0.0915231\pi$
$397$	14.4468	+	25.0226i	0.725064	+	1.25585i	−0.233884	+	0.972265i	$0.575144\pi$
$398$		0			0
$399$	19.1571	+	3.98825i	0.959056	+	0.199662i
$400$		0			0
$401$	5.50584			0.274949			0.137474	−	0.990505i	$-0.456102\pi$
$401$	5.50584			0.274949			0.137474	+	0.990505i	$0.456102\pi$
$402$		0			0
$403$	16.5598			0.824900
$404$		0			0
$405$	−2.02063	−	6.57086i	−0.100406	−	0.326509i
$406$		0			0
$407$	29.1130	+	50.4253i	1.44308	+	2.49949i
$408$		0			0
$409$	0.511954	+	0.886731i	0.0253145	+	0.0438460i	0.878405	−	0.477917i	$-0.158608\pi$
$409$	0.511954	+	0.886731i	0.0253145	+	0.0438460i	−0.853091	+	0.521763i	$0.825275\pi$
$410$		0			0
$411$	4.64437	+	1.52938i	0.229090	+	0.0754390i
$412$		0			0
$413$	29.4400	−	3.33680i	1.44865	−	0.164193i
$414$		0			0
$415$	6.15025	+	10.6525i	0.301904	+	0.522912i
$416$		0			0
$417$	−28.9882	+	25.8942i	−1.41956	+	1.26804i
$418$		0			0
$419$	16.9398	−	29.3405i	0.827562	−	1.43338i	−0.0723837	−	0.997377i	$-0.523061\pi$
$419$	16.9398	−	29.3405i	0.827562	−	1.43338i	0.899946	−	0.436002i	$-0.143606\pi$
$420$		0			0
$421$	0.563823	+	0.976570i	0.0274790	+	0.0475951i	0.879438	−	0.476014i	$-0.157919\pi$
$421$	0.563823	+	0.976570i	0.0274790	+	0.0475951i	−0.851959	+	0.523609i	$0.824585\pi$
$422$		0			0
$423$	18.6422	−	8.12394i	0.906416	−	0.395000i
$424$		0			0
$425$	−8.58772	+	14.8744i	−0.416566	+	0.721513i
$426$		0			0
$427$	−13.1821	−	17.8365i	−0.637929	−	0.863168i
$428$		0			0
$429$	−19.6465	+	17.5495i	−0.948540	+	0.847299i
$430$		0			0
$431$	−1.44172	+	2.49713i	−0.0694450	+	0.120282i	−0.898657	−	0.438652i	$-0.855456\pi$
$431$	−1.44172	+	2.49713i	−0.0694450	+	0.120282i	0.829212	+	0.558934i	$0.188790\pi$
$432$		0			0
$433$	−14.3808			−0.691097			−0.345548	−	0.938401i	$-0.612307\pi$
$433$	−14.3808			−0.691097			−0.345548	+	0.938401i	$0.612307\pi$
$434$		0			0
$435$	1.62363	+	7.79000i	0.0778473	+	0.373502i
$436$		0			0
$437$	3.12621	+	5.41476i	0.149547	+	0.259023i
$438$		0			0
$439$	−10.4958	+	18.1792i	−0.500936	+	0.867646i	0.499064	+	0.866565i	$0.333677\pi$
$439$	−10.4958	+	18.1792i	−0.500936	+	0.867646i	−0.999999	+	0.00108089i	$0.999656\pi$
$440$		0			0
$441$	−2.36983	−	20.8659i	−0.112849	−	0.993612i
$442$		0			0
$443$	10.0293	−	17.3713i	0.476507	−	0.825335i	−0.523130	−	0.852253i	$-0.675236\pi$
$443$	10.0293	−	17.3713i	0.476507	−	0.825335i	0.999638	+	0.0269179i	$0.00856926\pi$
$444$		0			0
$445$	−1.34672	−	2.33258i	−0.0638405	−	0.110575i
$446$		0			0
$447$	−33.1830	−	10.9271i	−1.56950	−	0.516836i
$448$		0			0
$449$	−11.4192			−0.538903			−0.269452	−	0.963014i	$-0.586842\pi$
$449$	−11.4192			−0.538903			−0.269452	+	0.963014i	$0.586842\pi$
$450$		0			0
$451$	−13.5669	+	23.4985i	−0.638839	+	1.10650i
$452$		0			0
$453$	13.6457	+	4.49350i	0.641130	+	0.211123i
$454$		0			0
$455$	3.02765	+	4.09664i	0.141938	+	0.192054i
$456$		0			0
$457$	9.10294	−	15.7667i	0.425817	−	0.737537i	−0.570679	−	0.821173i	$-0.693320\pi$
$457$	9.10294	−	15.7667i	0.425817	−	0.737537i	0.996496	+	0.0836359i	$0.0266533\pi$
$458$		0			0
$459$	20.1202	−	1.87359i	0.939129	−	0.0874519i
$460$		0			0
$461$	−18.6430	−	32.2906i	−0.868289	−	1.50392i	−0.863744	−	0.503931i	$-0.831887\pi$
$461$	−18.6430	−	32.2906i	−0.868289	−	1.50392i	−0.00454533	−	0.999990i	$-0.501447\pi$
$462$		0			0
$463$	−0.530345	+	0.918584i	−0.0246472	+	0.0426902i	−0.878086	−	0.478503i	$-0.841180\pi$
$463$	−0.530345	+	0.918584i	−0.0246472	+	0.0426902i	0.853439	+	0.521193i	$0.174513\pi$
$464$		0			0
$465$	1.77345	+	8.50882i	0.0822420	+	0.394587i
$466$		0			0
$467$	−14.0374	−	24.3134i	−0.649571	−	1.12509i	−0.983225	−	0.182395i	$-0.941615\pi$
$467$	−14.0374	−	24.3134i	−0.649571	−	1.12509i	0.333654	−	0.942696i	$-0.391718\pi$
$468$		0			0
$469$	−5.05793	+	0.573277i	−0.233553	+	0.0264715i
$470$		0			0
$471$	2.35605	+	11.3040i	0.108561	+	0.520863i
$472$		0			0
$473$	−12.8825	−	22.3132i	−0.592340	−	1.02596i
$474$		0			0
$475$	9.42947	+	16.3323i	0.432654	+	0.749378i
$476$		0			0
$477$	−1.46080	+	0.636592i	−0.0668856	+	0.0291476i
$478$		0			0
$479$	7.23410			0.330535			0.165267	−	0.986249i	$-0.447151\pi$
$479$	7.23410			0.330535			0.165267	+	0.986249i	$0.447151\pi$
$480$		0			0
$481$	−24.3238			−1.10907
$482$		0			0
$483$	4.46897	−	5.00527i	0.203345	−	0.227748i
$484$		0			0
$485$	−1.78365	−	3.08938i	−0.0809916	−	0.140282i
$486$		0			0
$487$	16.9145	−	29.2968i	0.766470	−	1.32756i	−0.172996	−	0.984922i	$-0.555345\pi$
$487$	16.9145	−	29.2968i	0.766470	−	1.32756i	0.939466	−	0.342642i	$-0.111322\pi$
$488$		0			0
$489$	2.61347	+	12.5391i	0.118185	+	0.567038i
$490$		0			0
$491$	−0.300406	+	0.520319i	−0.0135572	+	0.0234817i	−0.872724	−	0.488213i	$-0.837649\pi$
$491$	−0.300406	+	0.520319i	−0.0135572	+	0.0234817i	0.859167	+	0.511695i	$0.170982\pi$
$492$		0			0
$493$	−23.3902			−1.05344
$494$		0			0
$495$	−11.1214	−	8.21539i	−0.499870	−	0.369254i
$496$		0			0
$497$	−10.4622	+	24.0229i	−0.469294	+	1.07758i
$498$		0			0
$499$	5.64134			0.252541			0.126271	−	0.991996i	$-0.459699\pi$
$499$	5.64134			0.252541			0.126271	+	0.991996i	$0.459699\pi$
$500$		0			0
$501$	−1.22851	+	1.09739i	−0.0548858	+	0.0490276i
$502$		0			0
$503$	−31.0034			−1.38237			−0.691186	−	0.722677i	$-0.742911\pi$
$503$	−31.0034			−1.38237			−0.691186	+	0.722677i	$0.742911\pi$
$504$		0			0
$505$	3.60504			0.160422
$506$		0			0
$507$	2.34888	+	11.2696i	0.104317	+	0.500501i
$508$		0			0
$509$	34.6959			1.53787			0.768935	−	0.639327i	$-0.220787\pi$
$509$	34.6959			1.53787			0.768935	+	0.639327i	$0.220787\pi$
$510$		0			0
$511$	−6.70199	−	9.06833i	−0.296479	−	0.401159i
$512$		0			0
$513$	9.26453	−	20.1611i	0.409039	−	0.890135i
$514$		0			0
$515$	−2.41778			−0.106540
$516$		0			0
$517$	20.4503	−	35.4210i	0.899405	−	1.55781i
$518$		0			0
$519$	−6.03382	+	5.38981i	−0.264855	+	0.236586i
$520$		0			0
$521$	−12.5083	+	21.6650i	−0.547998	+	0.949161i	0.450413	+	0.892820i	$0.351277\pi$
$521$	−12.5083	+	21.6650i	−0.547998	+	0.949161i	−0.998412	+	0.0563408i	$0.982057\pi$
$522$		0			0
$523$	−1.59320	−	2.75950i	−0.0696656	−	0.120664i	0.829088	−	0.559117i	$-0.188860\pi$
$523$	−1.59320	−	2.75950i	−0.0696656	−	0.120664i	−0.898754	+	0.438453i	$0.855527\pi$
$524$		0			0
$525$	13.4796	−	15.0972i	0.588298	−	0.658896i
$526$		0			0
$527$	−25.5486			−1.11291
$528$		0			0
$529$	−20.8560			−0.906782
$530$		0			0
$531$	3.77592	−	33.3827i	0.163861	−	1.44869i
$532$		0			0
$533$	−5.66753	−	9.81645i	−0.245488	−	0.425198i
$534$		0			0
$535$	−5.84745	−	10.1281i	−0.252808	−	0.437875i
$536$		0			0
$537$	−19.3628	+	17.2961i	−0.835567	+	0.746384i
$538$		0			0
$539$	−28.7695	−	30.9241i	−1.23919	−	1.33200i
$540$		0			0
$541$	−6.80693	−	11.7900i	−0.292653	−	0.506890i	0.681783	−	0.731554i	$-0.261205\pi$
$541$	−6.80693	−	11.7900i	−0.292653	−	0.506890i	−0.974436	+	0.224664i	$0.927871\pi$
$542$		0			0
$543$	−22.4604	−	7.39617i	−0.963867	−	0.317400i
$544$		0			0
$545$	−5.84618	+	10.1259i	−0.250423	+	0.433745i
$546$		0			0
$547$	−5.91254	−	10.2408i	−0.252802	−	0.437866i	0.711494	−	0.702692i	$-0.248019\pi$
$547$	−5.91254	−	10.2408i	−0.252802	−	0.437866i	−0.964296	+	0.264826i	$0.914685\pi$
$548$		0			0
$549$	−23.0546	+	10.0468i	−0.983948	+	0.428787i
$550$		0			0
$551$	−12.8414	+	22.2420i	−0.547064	+	0.947543i
$552$		0			0
$553$	11.6483	+	15.7610i	0.495334	+	0.670226i
$554$		0			0
$555$	−2.60494	−	12.4982i	−0.110574	−	0.530518i
$556$		0			0
$557$	−9.32911	+	16.1585i	−0.395287	+	0.684657i	−0.993138	−	0.116950i	$-0.962688\pi$
$557$	−9.32911	+	16.1585i	−0.395287	+	0.684657i	0.597851	+	0.801607i	$0.296021\pi$
$558$		0			0
$559$	10.7633			0.455239
$560$		0			0
$561$	30.3108	−	27.0756i	1.27972	−	1.14313i
$562$		0			0
$563$	−11.3196	−	19.6060i	−0.477062	−	0.826296i	0.522592	−	0.852583i	$-0.324965\pi$
$563$	−11.3196	−	19.6060i	−0.477062	−	0.826296i	−0.999654	+	0.0262866i	$0.991632\pi$
$564$		0			0
$565$	1.19246	−	2.06539i	0.0501670	−	0.0868917i
$566$		0			0
$567$	−23.6615	−	2.67086i	−0.993690	−	0.112165i
$568$		0			0
$569$	−5.45277	+	9.44447i	−0.228592	+	0.395933i	−0.957391	−	0.288795i	$-0.906745\pi$
$569$	−5.45277	+	9.44447i	−0.228592	+	0.395933i	0.728799	+	0.684728i	$0.240079\pi$
$570$		0			0
$571$	13.8055	+	23.9119i	0.577743	+	1.00068i	0.995738	+	0.0922313i	$0.0293999\pi$
$571$	13.8055	+	23.9119i	0.577743	+	1.00068i	−0.417994	+	0.908450i	$0.637267\pi$
$572$		0			0
$573$	−15.8762	+	14.1817i	−0.663237	+	0.592448i
$574$		0			0
$575$	6.46693			0.269690
$576$		0			0
$577$	−10.2592	+	17.7695i	−0.427096	+	0.739753i	−0.996614	−	0.0822267i	$-0.973797\pi$
$577$	−10.2592	+	17.7695i	−0.427096	+	0.739753i	0.569517	+	0.821979i	$0.307130\pi$
$578$		0			0
$579$	−2.53449	−	12.1602i	−0.105330	−	0.505360i
$580$		0			0
$581$	42.3350	−	4.79834i	1.75635	−	0.199069i
$582$		0			0
$583$	−1.60249	+	2.77559i	−0.0663683	+	0.114953i
$584$		0			0
$585$	5.29514	−	2.30753i	0.218927	−	0.0954044i
$586$		0			0
$587$	7.59632	+	13.1572i	0.313534	+	0.543056i	0.979125	−	0.203260i	$-0.0651538\pi$
$587$	7.59632	+	13.1572i	0.313534	+	0.543056i	−0.665591	+	0.746317i	$0.731820\pi$
$588$		0			0
$589$	−14.0264	+	24.2944i	−0.577947	+	1.00103i
$590$		0			0
$591$	−21.4339	−	7.05817i	−0.881674	−	0.290334i
$592$		0			0
$593$	3.39373	+	5.87812i	0.139364	+	0.241385i	0.927256	−	0.374428i	$-0.122161\pi$
$593$	3.39373	+	5.87812i	0.139364	+	0.241385i	−0.787892	+	0.615813i	$0.788828\pi$
$594$		0			0
$595$	−4.67108	−	6.32035i	−0.191496	−	0.259109i
$596$		0			0
$597$	−6.40927	+	5.72519i	−0.262314	+	0.234316i
$598$		0			0
$599$	−6.32519	−	10.9555i	−0.258440	−	0.447632i	0.707384	−	0.706829i	$-0.249875\pi$
$599$	−6.32519	−	10.9555i	−0.258440	−	0.447632i	−0.965824	+	0.259198i	$0.916542\pi$
$600$		0			0
$601$	−11.3699	−	19.6932i	−0.463787	−	0.803303i	0.535359	−	0.844625i	$-0.320176\pi$
$601$	−11.3699	−	19.6932i	−0.463787	−	0.803303i	−0.999146	+	0.0413219i	$0.986843\pi$
$602$		0			0
$603$	−0.648720	+	5.73530i	−0.0264179	+	0.233559i
$604$		0			0
$605$	−19.4075			−0.789026
$606$		0			0
$607$	41.9226			1.70159			0.850794	−	0.525500i	$-0.176122\pi$
$607$	41.9226			1.70159			0.850794	+	0.525500i	$0.176122\pi$
$608$		0			0
$609$	26.9840	+	5.61770i	1.09345	+	0.227641i
$610$		0			0
$611$	8.54308	+	14.7971i	0.345616	+	0.598625i
$612$		0			0
$613$	−13.7038	+	23.7356i	−0.553490	+	0.958673i	0.444529	+	0.895764i	$0.353371\pi$
$613$	−13.7038	+	23.7356i	−0.553490	+	0.958673i	−0.998019	+	0.0629086i	$0.979962\pi$
$614$		0			0
$615$	4.43698	−	3.96340i	0.178916	−	0.159820i
$616$		0			0
$617$	5.75420	−	9.96656i	0.231655	−	0.401239i	−0.726640	−	0.687018i	$-0.758919\pi$
$617$	5.75420	−	9.96656i	0.231655	−	0.401239i	0.958295	+	0.285780i	$0.0922526\pi$
$618$		0			0
$619$	37.7559			1.51754			0.758770	−	0.651359i	$-0.225801\pi$
$619$	37.7559			1.51754			0.758770	+	0.651359i	$0.225801\pi$
$620$		0			0
$621$	−4.39878	−	6.20801i	−0.176517	−	0.249119i
$622$		0			0
$623$	−9.27007	+	1.05069i	−0.371398	+	0.0420951i
$624$		0			0
$625$	16.5887			0.663549
$626$		0			0
$627$	−9.10561	−	43.6876i	−0.363643	−	1.74471i
$628$		0			0
$629$	37.5270			1.49630
$630$		0			0
$631$	45.4466			1.80920			0.904600	−	0.426262i	$-0.140170\pi$
$631$	45.4466			1.80920			0.904600	+	0.426262i	$0.140170\pi$
$632$		0			0
$633$	5.35771	−	4.78587i	0.212950	−	0.190221i
$634$		0			0
$635$	−0.976288			−0.0387428
$636$		0			0
$637$	17.1969	−	3.94901i	0.681367	−	0.156466i
$638$		0			0
$639$	23.8975	+	17.6531i	0.945369	+	0.698344i
$640$		0			0
$641$	−0.299606			−0.0118337			−0.00591687	−	0.999982i	$-0.501883\pi$
$641$	−0.299606			−0.0118337			−0.00591687	+	0.999982i	$0.501883\pi$
$642$		0			0
$643$	−3.61580	+	6.26275i	−0.142593	+	0.246979i	−0.928472	−	0.371401i	$-0.878877\pi$
$643$	−3.61580	+	6.26275i	−0.142593	+	0.246979i	0.785879	+	0.618380i	$0.212211\pi$
$644$		0			0
$645$	1.15269	+	5.53046i	0.0453870	+	0.217761i
$646$		0			0
$647$	−4.78298	+	8.28437i	−0.188039	+	0.325692i	−0.944596	−	0.328235i	$-0.893546\pi$
$647$	−4.78298	+	8.28437i	−0.188039	+	0.325692i	0.756558	+	0.653927i	$0.226880\pi$
$648$		0			0
$649$	−33.7854	−	58.5180i	−1.32619	−	2.29703i
$650$		0			0
$651$	29.4740	+	6.13607i	1.15518	+	0.240492i
$652$		0			0
$653$	39.0070			1.52646			0.763232	−	0.646125i	$-0.223612\pi$
$653$	39.0070			1.52646			0.763232	+	0.646125i	$0.223612\pi$
$654$		0			0
$655$	−5.93856			−0.232039
$656$		0			0
$657$	−11.7213	+	5.10794i	−0.457292	+	0.199280i
$658$		0			0
$659$	−0.251281	−	0.435231i	−0.00978851	−	0.0169542i	0.861090	−	0.508453i	$-0.169782\pi$
$659$	−0.251281	−	0.435231i	−0.00978851	−	0.0169542i	−0.870878	+	0.491499i	$0.836449\pi$
$660$		0			0
$661$	1.09910	+	1.90370i	0.0427501	+	0.0740453i	0.886609	−	0.462520i	$-0.153055\pi$
$661$	1.09910	+	1.90370i	0.0427501	+	0.0740453i	−0.843859	+	0.536566i	$0.819721\pi$
$662$		0			0
$663$	3.46429	+	16.6212i	0.134542	+	0.645515i
$664$		0			0
$665$	−8.57455	+	0.971859i	−0.332507	+	0.0376871i
$666$		0			0
$667$	4.40347	+	7.62703i	0.170503	+	0.295320i
$668$		0			0
$669$	−3.27844	−	15.7295i	−0.126752	−	0.608139i
$670$		0			0
$671$	−25.2907	+	43.8048i	−0.976337	+	1.69107i
$672$		0			0
$673$	7.50630	+	13.0013i	0.289346	+	0.501163i	0.973654	−	0.228031i	$-0.0732287\pi$
$673$	7.50630	+	13.0013i	0.289346	+	0.501163i	−0.684307	+	0.729194i	$0.739895\pi$
$674$		0			0
$675$	−13.2679	−	18.7250i	−0.510680	−	0.720724i
$676$		0			0
$677$	−14.8304	+	25.6869i	−0.569977	+	0.987229i	0.426591	+	0.904445i	$0.359715\pi$
$677$	−14.8304	+	25.6869i	−0.569977	+	0.987229i	−0.996568	+	0.0827841i	$0.973619\pi$
$678$		0			0
$679$	−12.2777	+	1.39158i	−0.471175	+	0.0534041i
$680$		0			0
$681$	−35.1407	−	11.5718i	−1.34659	−	0.443432i
$682$		0			0
$683$	−12.7295	+	22.0482i	−0.487083	+	0.843652i	−0.999890	−	0.0148520i	$-0.995272\pi$
$683$	−12.7295	+	22.0482i	−0.487083	+	0.843652i	0.512807	+	0.858504i	$0.328606\pi$
$684$		0			0
$685$	−2.15636			−0.0823904
$686$		0			0
$687$	−32.9146	−	10.8387i	−1.25577	−	0.413524i
$688$		0			0
$689$	−0.669436	−	1.15950i	−0.0255035	−	0.0441733i
$690$		0			0
$691$	5.95499	−	10.3143i	0.226538	−	0.392376i	−0.730241	−	0.683189i	$-0.760592\pi$
$691$	5.95499	−	10.3143i	0.226538	−	0.392376i	0.956780	+	0.290813i	$0.0939258\pi$
$692$		0			0
$693$	−41.4707	+	23.9558i	−1.57534	+	0.910005i
$694$		0			0
$695$	8.57070	−	14.8449i	0.325105	−	0.563099i
$696$		0			0
$697$	8.74393	+	15.1449i	0.331200	+	0.573655i
$698$		0			0
$699$	5.39766	+	25.8973i	0.204158	+	0.979527i
$700$		0			0
$701$	−3.84543			−0.145240			−0.0726199	−	0.997360i	$-0.523136\pi$
$701$	−3.84543			−0.145240			−0.0726199	+	0.997360i	$0.523136\pi$
$702$		0			0
$703$	20.6027	−	35.6849i	0.777044	−	1.34588i
$704$		0			0
$705$	−6.68818	+	5.97433i	−0.251891	+	0.225006i
$706$		0			0
$707$	4.98589	−	11.4484i	0.187514	−	0.430562i
$708$		0			0
$709$	13.3533	−	23.1286i	0.501494	−	0.868614i	−0.498504	−	0.866887i	$-0.666117\pi$
$709$	13.3533	−	23.1286i	0.501494	−	0.868614i	0.999999	−	0.00172652i	$-0.000549569\pi$
$710$		0			0
$711$	20.3720	−	8.87774i	0.764009	−	0.332941i
$712$		0			0
$713$	4.80979	+	8.33081i	0.180128	+	0.311991i
$714$		0			0
$715$	5.80872	−	10.0610i	0.217234	−	0.376260i
$716$		0			0
$717$	23.3502	−	20.8580i	0.872029	−	0.778955i
$718$		0			0
$719$	13.3611	+	23.1420i	0.498284	+	0.863052i	0.999998	−	0.00198088i	$-0.000630534\pi$
$719$	13.3611	+	23.1420i	0.498284	+	0.863052i	−0.501715	+	0.865033i	$0.667297\pi$
$720$		0			0
$721$	−3.34388	+	7.67808i	−0.124532	+	0.285947i
$722$		0			0
$723$	7.09133	+	2.33516i	0.263729	+	0.0868457i
$724$		0			0
$725$	13.2820	+	23.0051i	0.493281	+	0.854388i
$726$		0			0
$727$	−1.13012	−	1.95743i	−0.0419139	−	0.0725970i	0.844307	−	0.535859i	$-0.180012\pi$
$727$	−1.13012	−	1.95743i	−0.0419139	−	0.0725970i	−0.886221	+	0.463262i	$0.846679\pi$
$728$		0			0
$729$	−8.95052	+	25.4733i	−0.331501	+	0.943455i
$730$		0			0
$731$	−16.6057			−0.614186
$732$		0			0
$733$	36.7404			1.35704			0.678519	−	0.734583i	$-0.262622\pi$
$733$	36.7404			1.35704			0.678519	+	0.734583i	$0.262622\pi$
$734$		0			0
$735$	3.87079	+	8.41330i	0.142776	+	0.310329i
$736$		0			0
$737$	5.80448	+	10.0536i	0.213811	+	0.370331i
$738$		0			0
$739$	−17.0909	+	29.6022i	−0.628697	+	1.08894i	0.359116	+	0.933293i	$0.383078\pi$
$739$	−17.0909	+	29.6022i	−0.628697	+	1.08894i	−0.987813	+	0.155643i	$0.950255\pi$
$740$		0			0
$741$	17.7072	+	5.83097i	0.650491	+	0.214206i
$742$		0			0
$743$	−4.56487	+	7.90658i	−0.167469	+	0.290064i	−0.937529	−	0.347907i	$-0.886893\pi$
$743$	−4.56487	+	7.90658i	−0.167469	+	0.290064i	0.770061	+	0.637971i	$0.220226\pi$
$744$		0			0
$745$	15.4068			0.564461
$746$		0			0
$747$	5.42980	−	48.0046i	0.198666	−	1.75640i
$748$		0			0
$749$	−40.2507	+	4.56211i	−1.47073	+	0.166696i
$750$		0			0
$751$	−38.1295			−1.39137			−0.695683	−	0.718349i	$-0.744898\pi$
$751$	−38.1295			−1.39137			−0.695683	+	0.718349i	$0.744898\pi$
$752$		0			0
$753$	26.8731	+	8.84928i	0.979311	+	0.322486i
$754$		0			0
$755$	−6.33564			−0.230578
$756$		0			0
$757$	18.6952			0.679488			0.339744	−	0.940518i	$-0.389660\pi$
$757$	18.6952			0.679488			0.339744	+	0.940518i	$0.389660\pi$
$758$		0			0
$759$	−14.5351	−	4.78638i	−0.527590	−	0.173735i
$760$		0			0
$761$	−16.1572			−0.585697			−0.292849	−	0.956159i	$-0.594603\pi$
$761$	−16.1572			−0.585697			−0.292849	+	0.956159i	$0.594603\pi$
$762$		0			0
$763$	24.0710	+	32.5700i	0.871429	+	1.17911i
$764$		0			0
$765$	−8.16940	+	3.56008i	−0.295365	+	0.128715i
$766$		0			0
$767$	28.2275			1.01924
$768$		0			0
$769$	−16.9628	+	29.3804i	−0.611694	+	1.05949i	0.379261	+	0.925290i	$0.376178\pi$
$769$	−16.9628	+	29.3804i	−0.611694	+	1.05949i	−0.990955	+	0.134195i	$0.957155\pi$
$770$		0			0
$771$	2.13112	+	0.701774i	0.0767503	+	0.0252738i
$772$		0			0
$773$	19.8452	−	34.3728i	0.713781	−	1.23630i	−0.249647	−	0.968337i	$-0.580315\pi$
$773$	19.8452	−	34.3728i	0.713781	−	1.23630i	0.963428	−	0.267968i	$-0.0863522\pi$
$774$		0			0
$775$	14.5076	+	25.1279i	0.521128	+	0.902621i
$776$		0			0
$777$	−43.2928	−	9.01297i	−1.55312	−	0.323339i
$778$		0			0
$779$	19.2020			0.687982
$780$		0			0
$781$	59.7568			2.13827
$782$		0			0
$783$	13.0497	−	28.3982i	0.466357	−	1.01487i
$784$		0			0
$785$	−2.54611	−	4.41000i	−0.0908746	−	0.157400i
$786$		0			0
$787$	0.158840	+	0.275119i	0.00566204	+	0.00980695i	0.868843	−	0.495089i	$-0.164864\pi$
$787$	0.158840	+	0.275119i	0.00566204	+	0.00980695i	−0.863180	+	0.504895i	$0.831531\pi$
$788$		0			0
$789$	46.5129	+	15.3166i	1.65590	+	0.545287i
$790$		0			0
$791$	−4.90980	−	6.64335i	−0.174573	−	0.236211i
$792$		0			0
$793$	−10.5651	−	18.2994i	−0.375179	−	0.649829i
$794$		0			0
$795$	0.524086	−	0.468148i	0.0185874	−	0.0166035i
$796$		0			0
$797$	−21.0702	+	36.4946i	−0.746344	+	1.29271i	0.203221	+	0.979133i	$0.434859\pi$
$797$	−21.0702	+	36.4946i	−0.746344	+	1.29271i	−0.949564	+	0.313572i	$0.898474\pi$
$798$		0			0
$799$	−13.1804	−	22.8290i	−0.466288	−	0.807634i
$800$		0			0
$801$	−1.18896	+	10.5115i	−0.0420099	+	0.371407i
$802$		0			0
$803$	−12.8582	+	22.2710i	−0.453755	+	0.785926i
$804$		0			0
$805$	−1.18154	+	2.71301i	−0.0416438	+	0.0956210i
$806$		0			0
$807$	18.3677	−	16.4073i	0.646574	−	0.577563i
$808$		0			0
$809$	−6.40052	+	11.0860i	−0.225030	+	0.389764i	−0.956329	−	0.292294i	$-0.905581\pi$
$809$	−6.40052	+	11.0860i	−0.225030	+	0.389764i	0.731298	+	0.682058i	$0.238915\pi$
$810$		0			0
$811$	27.1410			0.953051			0.476526	−	0.879161i	$-0.341896\pi$
$811$	27.1410			0.953051			0.476526	+	0.879161i	$0.341896\pi$
$812$		0			0
$813$	−5.08141	−	24.3800i	−0.178213	−	0.855044i
$814$		0			0
$815$	−2.82429	−	4.89182i	−0.0989307	−	0.171353i
$816$		0			0
$817$	−9.11670	+	15.7906i	−0.318953	+	0.552443i
$818$		0			0
$819$	−0.00458903	−	20.0070i	−0.000160354	−	0.699101i
$820$		0			0
$821$	5.95924	−	10.3217i	0.207979	−	0.360230i	−0.743099	−	0.669182i	$-0.766645\pi$
$821$	5.95924	−	10.3217i	0.207979	−	0.360230i	0.951078	+	0.308952i	$0.0999781\pi$
$822$		0			0
$823$	9.26505	+	16.0475i	0.322959	+	0.559382i	0.981097	−	0.193515i	$-0.0619890\pi$
$823$	9.26505	+	16.0475i	0.322959	+	0.559382i	−0.658138	+	0.752897i	$0.728656\pi$
$824$		0			0
$825$	−43.8416	−	14.4370i	−1.52637	−	0.502631i
$826$		0			0
$827$	9.64616			0.335430			0.167715	−	0.985836i	$-0.446361\pi$
$827$	9.64616			0.335430			0.167715	+	0.985836i	$0.446361\pi$
$828$		0			0
$829$	10.2155	−	17.6938i	0.354800	−	0.614531i	−0.632284	−	0.774737i	$-0.717882\pi$
$829$	10.2155	−	17.6938i	0.354800	−	0.614531i	0.987084	+	0.160206i	$0.0512158\pi$
$830$		0			0
$831$	−25.3947	−	8.36246i	−0.880934	−	0.290090i
$832$		0			0
$833$	−26.5316	+	6.09258i	−0.919266	+	0.211095i
$834$		0			0
$835$	0.363224	−	0.629122i	0.0125699	−	0.0217717i
$836$		0			0
$837$	14.2538	−	31.0186i	0.492684	−	1.07216i
$838$		0			0
$839$	−7.18866	−	12.4511i	−0.248180	−	0.429861i	0.714841	−	0.699287i	$-0.246499\pi$
$839$	−7.18866	−	12.4511i	−0.248180	−	0.429861i	−0.963021	+	0.269427i	$0.913166\pi$
$840$		0			0
$841$	−3.58799	+	6.21459i	−0.123724	+	0.214296i
$842$		0			0
$843$	−6.64133	−	31.8643i	−0.228739	−	1.09746i
$844$		0			0
$845$	−2.53836	−	4.39657i	−0.0873222	−	0.151247i
$846$		0			0
$847$	−26.8412	+	61.6318i	−0.922274	+	2.11769i
$848$		0			0
$849$	11.5115	+	55.2310i	0.395075	+	1.89552i
$850$		0			0
$851$	−7.06487	−	12.2367i	−0.242181	−	0.419469i
$852$		0			0
$853$	−2.05636	−	3.56173i	−0.0704085	−	0.121951i	0.828672	−	0.559735i	$-0.189097\pi$
$853$	−2.05636	−	3.56173i	−0.0704085	−	0.121951i	−0.899080	+	0.437784i	$0.855764\pi$
$854$		0			0
$855$	−1.09975	+	9.72288i	−0.0376108	+	0.332516i
$856$		0			0
$857$	51.1084			1.74583			0.872915	−	0.487873i	$-0.162227\pi$
$857$	51.1084			1.74583			0.872915	+	0.487873i	$0.162227\pi$
$858$		0			0
$859$	15.3165			0.522592			0.261296	−	0.965259i	$-0.415850\pi$
$859$	15.3165			0.522592			0.261296	+	0.965259i	$0.415850\pi$
$860$		0			0
$861$	−6.44998	−	19.5719i	−0.219815	−	0.667009i
$862$		0			0
$863$	12.4865	+	21.6272i	0.425045	+	0.736199i	0.996425	−	0.0844866i	$-0.0269250\pi$
$863$	12.4865	+	21.6272i	0.425045	+	0.736199i	−0.571380	+	0.820686i	$0.693592\pi$
$864$		0			0
$865$	1.78397	−	3.08993i	0.0606568	−	0.105061i
$866$		0			0
$867$	0.663210	+	3.18200i	0.0225238	+	0.108066i
$868$		0			0
$869$	22.3479	−	38.7076i	0.758099	−	1.31307i
$870$		0			0
$871$	−4.84962			−0.164323
$872$		0			0
$873$	−1.57471	+	13.9220i	−0.0532960	+	0.471188i
$874$		0			0
$875$	−7.59846	+	17.4473i	−0.256875	+	0.589827i
$876$		0			0
$877$	36.3918			1.22886			0.614432	−	0.788970i	$-0.289385\pi$
$877$	36.3918			1.22886			0.614432	+	0.788970i	$0.289385\pi$
$878$		0			0
$879$	−4.38728	+	3.91901i	−0.147979	+	0.132185i
$880$		0			0
$881$	56.1807			1.89277			0.946387	−	0.323035i	$-0.104703\pi$
$881$	56.1807			1.89277			0.946387	+	0.323035i	$0.104703\pi$
$882$		0			0
$883$	−22.7585			−0.765884			−0.382942	−	0.923772i	$-0.625089\pi$
$883$	−22.7585			−0.765884			−0.382942	+	0.923772i	$0.625089\pi$
$884$		0			0
$885$	3.02301	+	14.5040i	0.101617	+	0.487547i
$886$		0			0
$887$	−10.0314			−0.336820			−0.168410	−	0.985717i	$-0.553863\pi$
$887$	−10.0314			−0.336820			−0.168410	+	0.985717i	$0.553863\pi$
$888$		0			0
$889$	−1.35024	+	3.10037i	−0.0452856	+	0.103983i
$890$		0			0
$891$	15.9619	+	51.9062i	0.534744	+	1.73892i
$892$		0			0
$893$	−28.9445			−0.968592
$894$		0			0
$895$	5.72485	−	9.91573i	0.191361	−	0.331446i
$896$		0			0
$897$	4.76762	−	4.25875i	0.159186	−	0.142196i
$898$		0			0
$899$	−19.7571	+	34.2202i	−0.658935	+	1.14131i
$900$		0			0
$901$	1.03281	+	1.78888i	0.0344080	+	0.0595964i
$902$		0			0
$903$	19.1571	+	3.98825i	0.637509	+	0.132721i
$904$		0			0
$905$	10.4283			0.346647
$906$		0			0
$907$	−20.5712			−0.683054			−0.341527	−	0.939872i	$-0.610944\pi$
$907$	−20.5712			−0.683054			−0.341527	+	0.939872i	$0.610944\pi$
$908$		0			0
$909$	−11.3886	−	8.41278i	−0.377737	−	0.279034i
$910$		0			0
$911$	−1.19047	−	2.06196i	−0.0394421	−	0.0683157i	0.845630	−	0.533769i	$-0.179225\pi$
$911$	−1.19047	−	2.06196i	−0.0394421	−	0.0683157i	−0.885073	+	0.465453i	$0.845891\pi$
$912$		0			0
$913$	−48.5836	−	84.1493i	−1.60788	−	2.78493i
$914$		0			0
$915$	8.27120	−	7.38839i	0.273437	−	0.244253i
$916$		0			0
$917$	−8.21323	+	18.8589i	−0.271225	+	0.622777i
$918$		0			0
$919$	−11.8130	−	20.4608i	−0.389676	−	0.674939i	0.602730	−	0.797945i	$-0.294080\pi$
$919$	−11.8130	−	20.4608i	−0.389676	−	0.674939i	−0.992406	+	0.123007i	$0.960746\pi$
$920$		0			0
$921$	6.07988	+	2.00210i	0.200339	+	0.0659713i
$922$		0			0
$923$	−12.4816	+	21.6188i	−0.410838	+	0.711593i
$924$		0			0
$925$	−21.3095	−	36.9091i	−0.700652	−	1.21356i
$926$		0			0
$927$	7.63798	+	5.64218i	0.250864	+	0.185313i
$928$		0			0
$929$	29.6884	−	51.4219i	0.974046	−	1.68710i	0.290999	−	0.956723i	$-0.406012\pi$
$929$	29.6884	−	51.4219i	0.974046	−	1.68710i	0.683047	−	0.730374i	$-0.260654\pi$
$930$		0			0
$931$	−8.77259	+	28.5741i	−0.287510	+	0.936478i
$932$		0			0
$933$	6.06534	+	29.1007i	0.198570	+	0.952715i
$934$		0			0
$935$	−8.96175	+	15.5222i	−0.293081	+	0.507630i
$936$		0			0
$937$	16.1455			0.527451			0.263725	−	0.964598i	$-0.415049\pi$
$937$	16.1455			0.527451			0.263725	+	0.964598i	$0.415049\pi$
$938$		0			0
$939$	−6.84166	+	6.11143i	−0.223269	+	0.199439i
$940$		0			0
$941$	−9.88063	−	17.1137i	−0.322099	−	0.557892i	0.658822	−	0.752299i	$-0.271055\pi$
$941$	−9.88063	−	17.1137i	−0.322099	−	0.557892i	−0.980921	+	0.194407i	$0.937722\pi$
$942$		0			0
$943$	3.29228	−	5.70239i	0.107211	−	0.185695i
$944$		0			0
$945$	10.2796	−	2.14499i	0.334396	−	0.0697766i
$946$		0			0
$947$	24.4618	−	42.3691i	0.794902	−	1.37681i	−0.128000	−	0.991774i	$-0.540856\pi$
$947$	24.4618	−	42.3691i	0.794902	−	1.37681i	0.922902	−	0.385036i	$-0.125811\pi$
$948$		0			0
$949$	−5.37147	−	9.30366i	−0.174365	−	0.302010i
$950$		0			0
$951$	−36.3985	+	32.5136i	−1.18030	+	1.05433i
$952$		0			0
$953$	−48.6464			−1.57581			−0.787905	−	0.615797i	$-0.788834\pi$
$953$	−48.6464			−1.57581			−0.787905	+	0.615797i	$0.788834\pi$
$954$		0			0
$955$	4.69399	−	8.13022i	0.151894	−	0.263088i
$956$		0			0
$957$	−12.8258	−	61.5368i	−0.414600	−	1.98920i
$958$		0			0
$959$	−2.98232	+	6.84790i	−0.0963043	+	0.221130i
$960$		0			0
$961$	−6.08013	+	10.5311i	−0.196133	+	0.339713i
$962$		0			0
$963$	−5.16248	+	45.6412i	−0.166358	+	1.47077i
$964$		0			0
$965$	2.73895	+	4.74400i	0.0881699	+	0.152715i
$966$		0			0
$967$	22.1435	−	38.3537i	0.712087	−	1.23337i	−0.251986	−	0.967731i	$-0.581084\pi$
$967$	22.1435	−	38.3537i	0.712087	−	1.23337i	0.964072	−	0.265639i	$-0.0855831\pi$
$968$		0			0
$969$	−27.3189	−	8.99608i	−0.877610	−	0.288996i
$970$		0			0
$971$	−18.6355	−	32.2776i	−0.598040	−	1.03584i	−0.993110	−	0.117185i	$-0.962613\pi$
$971$	−18.6355	−	32.2776i	−0.598040	−	1.03584i	0.395070	−	0.918651i	$-0.370720\pi$
$972$		0			0
$973$	−35.2889	−	47.7487i	−1.13131	−	1.53075i
$974$		0			0
$975$	14.3804	−	12.8455i	0.460541	−	0.411386i
$976$		0			0
$977$	−30.9312	−	53.5744i	−0.989577	−	1.71400i	−0.619499	−	0.784997i	$-0.712664\pi$
$977$	−30.9312	−	53.5744i	−0.989577	−	1.71400i	−0.370078	−	0.929001i	$-0.620669\pi$
$978$		0			0
$979$	10.6383	+	18.4261i	0.340003	+	0.588902i
$980$		0			0
$981$	42.0985	−	18.3458i	1.34410	−	0.585735i
$982$		0			0
$983$	−10.9765			−0.350096			−0.175048	−	0.984560i	$-0.556008\pi$
$983$	−10.9765			−0.350096			−0.175048	+	0.984560i	$0.556008\pi$
$984$		0			0
$985$	9.95170			0.317088
$986$		0			0
$987$	9.72252	+	29.5022i	0.309471	+	0.939064i
$988$		0			0
$989$	3.12621	+	5.41476i	0.0994077	+	0.172179i
$990$		0			0
$991$	−5.43169	+	9.40796i	−0.172543	+	0.298854i	−0.939308	−	0.343074i	$-0.888532\pi$
$991$	−5.43169	+	9.40796i	−0.172543	+	0.298854i	0.766765	+	0.641928i	$0.221865\pi$
$992$		0			0
$993$	−37.6827	+	33.6607i	−1.19582	+	1.06819i
$994$		0			0
$995$	1.89498	−	3.28220i	0.0600749	−	0.104053i
$996$		0			0
$997$	−40.9291			−1.29624			−0.648119	−	0.761539i	$-0.724444\pi$
$997$	−40.9291			−1.29624			−0.648119	+	0.761539i	$0.724444\pi$
$998$		0			0
$999$	−20.9367	+	45.5617i	−0.662409	+	1.44151i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.l.b.193.6	yes	14
3.2	odd	2		756.2.l.b.361.4		14
4.3	odd	2		1008.2.t.j.193.2		14
7.2	even	3		252.2.i.b.121.1	yes	14
7.3	odd	6		1764.2.j.h.589.4		14
7.4	even	3		1764.2.j.g.589.4		14
7.5	odd	6		1764.2.i.i.373.7		14
7.6	odd	2		1764.2.l.i.949.2		14
9.2	odd	6		756.2.i.b.613.4		14
9.4	even	3		2268.2.k.e.1621.4		14
9.5	odd	6		2268.2.k.f.1621.4		14
9.7	even	3		252.2.i.b.25.1	✓	14
12.11	even	2		3024.2.t.j.1873.4		14
21.2	odd	6		756.2.i.b.37.4		14
21.5	even	6		5292.2.i.i.1549.4		14
21.11	odd	6		5292.2.j.h.1765.4		14
21.17	even	6		5292.2.j.g.1765.4		14
21.20	even	2		5292.2.l.i.361.4		14
28.23	odd	6		1008.2.q.j.625.7		14
36.7	odd	6		1008.2.q.j.529.7		14
36.11	even	6		3024.2.q.j.2881.4		14
63.2	odd	6		756.2.l.b.289.4		14
63.11	odd	6		5292.2.j.h.3529.4		14
63.16	even	3	inner	252.2.l.b.205.6	yes	14
63.20	even	6		5292.2.i.i.2125.4		14
63.23	odd	6		2268.2.k.f.1297.4		14
63.25	even	3		1764.2.j.g.1177.4		14
63.34	odd	6		1764.2.i.i.1537.7		14
63.38	even	6		5292.2.j.g.3529.4		14
63.47	even	6		5292.2.l.i.3313.4		14
63.52	odd	6		1764.2.j.h.1177.4		14
63.58	even	3		2268.2.k.e.1297.4		14
63.61	odd	6		1764.2.l.i.961.2		14
84.23	even	6		3024.2.q.j.2305.4		14
252.79	odd	6		1008.2.t.j.961.2		14
252.191	even	6		3024.2.t.j.289.4		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.i.b.25.1	✓	14	9.7	even	3
252.2.i.b.121.1	yes	14	7.2	even	3
252.2.l.b.193.6	yes	14	1.1	even	1	trivial
252.2.l.b.205.6	yes	14	63.16	even	3	inner
756.2.i.b.37.4		14	21.2	odd	6
756.2.i.b.613.4		14	9.2	odd	6
756.2.l.b.289.4		14	63.2	odd	6
756.2.l.b.361.4		14	3.2	odd	2
1008.2.q.j.529.7		14	36.7	odd	6
1008.2.q.j.625.7		14	28.23	odd	6
1008.2.t.j.193.2		14	4.3	odd	2
1008.2.t.j.961.2		14	252.79	odd	6
1764.2.i.i.373.7		14	7.5	odd	6
1764.2.i.i.1537.7		14	63.34	odd	6
1764.2.j.g.589.4		14	7.4	even	3
1764.2.j.g.1177.4		14	63.25	even	3
1764.2.j.h.589.4		14	7.3	odd	6
1764.2.j.h.1177.4		14	63.52	odd	6
1764.2.l.i.949.2		14	7.6	odd	2
1764.2.l.i.961.2		14	63.61	odd	6
2268.2.k.e.1297.4		14	63.58	even	3
2268.2.k.e.1621.4		14	9.4	even	3
2268.2.k.f.1297.4		14	63.23	odd	6
2268.2.k.f.1621.4		14	9.5	odd	6
3024.2.q.j.2305.4		14	84.23	even	6
3024.2.q.j.2881.4		14	36.11	even	6
3024.2.t.j.289.4		14	252.191	even	6
3024.2.t.j.1873.4		14	12.11	even	2
5292.2.i.i.1549.4		14	21.5	even	6
5292.2.i.i.2125.4		14	63.20	even	6
5292.2.j.g.1765.4		14	21.17	even	6
5292.2.j.g.3529.4		14	63.38	even	6
5292.2.j.h.1765.4		14	21.11	odd	6
5292.2.j.h.3529.4		14	63.11	odd	6
5292.2.l.i.361.4		14	21.20	even	2
5292.2.l.i.3313.4		14	63.47	even	6

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.64515 + 0.541745i) q^{3} -0.763837 q^{5} +(-1.05641 + 2.42569i) q^{7} +(2.41302 + 1.78250i) q^{9} +O(q^{10})\)	\(q+(1.64515 + 0.541745i) q^{3} -0.763837 q^{5} +(-1.05641 + 2.42569i) q^{7} +(2.41302 + 1.78250i) q^{9} +6.03389 q^{11} +(-1.26032 + 2.18294i) q^{13} +(-1.25662 - 0.413805i) q^{15} +(1.94444 - 3.36787i) q^{17} +(-2.13503 - 3.69798i) q^{19} +(-3.05206 + 3.41832i) q^{21} -1.46425 q^{23} -4.41655 q^{25} +(3.00412 + 4.23972i) q^{27} +(-3.00732 - 5.20884i) q^{29} +(-3.28482 - 5.68948i) q^{31} +(9.92665 + 3.26883i) q^{33} +(0.806926 - 1.85283i) q^{35} +(4.82492 + 8.35700i) q^{37} +(-3.25602 + 2.90849i) q^{39} +(-2.24844 + 3.89442i) q^{41} +(-2.13503 - 3.69798i) q^{43} +(-1.84316 - 1.36154i) q^{45} +(3.38924 - 5.87034i) q^{47} +(-4.76799 - 5.12507i) q^{49} +(5.02342 - 4.48725i) q^{51} +(-0.265581 + 0.460000i) q^{53} -4.60891 q^{55} +(-1.50908 - 7.24036i) q^{57} +(-5.59926 - 9.69821i) q^{59} +(-4.19144 + 7.25979i) q^{61} +(-6.87295 + 3.97020i) q^{63} +(0.962681 - 1.66741i) q^{65} +(0.961979 + 1.66620i) q^{67} +(-2.40890 - 0.793249i) q^{69} +9.90353 q^{71} +(-2.13099 + 3.69098i) q^{73} +(-7.26588 - 2.39265i) q^{75} +(-6.37428 + 14.6364i) q^{77} +(3.70372 - 6.41503i) q^{79} +(2.64537 + 8.60244i) q^{81} +(-8.05178 - 13.9461i) q^{83} +(-1.48523 + 2.57250i) q^{85} +(-2.12563 - 10.1985i) q^{87} +(1.76310 + 3.05377i) q^{89} +(-3.96373 - 5.36325i) q^{91} +(-2.32177 - 11.1396i) q^{93} +(1.63081 + 2.82465i) q^{95} +(2.33513 + 4.04456i) q^{97} +(14.5599 + 10.7554i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 4 q^{5} - 3 q^{7} + 10 q^{9}+O(q^{10}) \) 14 * q + 4 * q^5 - 3 * q^7 + 10 * q^9	\( 14 q + 4 q^{5} - 3 q^{7} + 10 q^{9} - 4 q^{11} + 2 q^{13} + 7 q^{15} + 2 q^{17} + 7 q^{19} - 2 q^{21} - 22 q^{23} + 18 q^{25} + 9 q^{27} + q^{29} - q^{31} + 5 q^{33} - 19 q^{35} + 10 q^{37} - 20 q^{39} - 33 q^{41} + 7 q^{43} + 5 q^{45} - 3 q^{47} - 13 q^{49} + 20 q^{51} - 15 q^{53} - 28 q^{55} - 18 q^{57} - 14 q^{59} - 10 q^{61} - 39 q^{63} + 15 q^{65} + 6 q^{67} - 43 q^{69} + 2 q^{71} + 21 q^{73} + q^{75} + 19 q^{77} - 10 q^{79} + 22 q^{81} - 25 q^{83} + 8 q^{85} - 2 q^{87} - 6 q^{89} + 2 q^{91} + 16 q^{93} - 28 q^{95} - 18 q^{97} + 7 q^{99}+O(q^{100}) \) 14 * q + 4 * q^5 - 3 * q^7 + 10 * q^9 - 4 * q^11 + 2 * q^13 + 7 * q^15 + 2 * q^17 + 7 * q^19 - 2 * q^21 - 22 * q^23 + 18 * q^25 + 9 * q^27 + q^29 - q^31 + 5 * q^33 - 19 * q^35 + 10 * q^37 - 20 * q^39 - 33 * q^41 + 7 * q^43 + 5 * q^45 - 3 * q^47 - 13 * q^49 + 20 * q^51 - 15 * q^53 - 28 * q^55 - 18 * q^57 - 14 * q^59 - 10 * q^61 - 39 * q^63 + 15 * q^65 + 6 * q^67 - 43 * q^69 + 2 * q^71 + 21 * q^73 + q^75 + 19 * q^77 - 10 * q^79 + 22 * q^81 - 25 * q^83 + 8 * q^85 - 2 * q^87 - 6 * q^89 + 2 * q^91 + 16 * q^93 - 28 * q^95 - 18 * q^97 + 7 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more