LMFDB - Embedded newform 420.2.bh.b.101.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [420,2,Mod(101,420)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(420, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 0, 1]))

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

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

chi := DirichletCharacter("420.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	420.bh (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.35371688489$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	10.0.29471584693248.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 2x^{8} - 4x^{7} + 13x^{6} - 36x^{5} + 39x^{4} - 36x^{3} + 54x^{2} - 162x + 243 $ x^10 - 2x^9 + 2x^8 - 4x^7 + 13x^6 - 36x^5 + 39x^4 - 36x^3 + 54x^2 - 162*x + 243
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.4
Root			$1.72689 + 0.133595i$ of defining polynomial
Character	$\chi$	$=$	420.101
Dual form			420.2.bh.b.341.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.979142 - 1.42873i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-0.456468 - 2.60608i) q^{7} +(-1.08256 - 2.79787i) q^{9} +O(q^{10})$	\(q+(0.979142 - 1.42873i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-0.456468 - 2.60608i) q^{7} +(-1.08256 - 2.79787i) q^{9} +(0.698384 + 0.403212i) q^{11} -3.86649i q^{13} +(1.72689 + 0.133595i) q^{15} +(-1.05989 + 1.83578i) q^{17} +(2.70603 - 1.56233i) q^{19} +(-4.17034 - 1.89955i) q^{21} +(4.21989 - 2.43635i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-5.05739 - 1.19282i) q^{27} +6.67701i q^{29} +(5.65010 + 3.26209i) q^{31} +(1.25990 - 0.603003i) q^{33} +(2.02869 - 1.69835i) q^{35} +(-3.89991 - 6.75485i) q^{37} +(-5.52419 - 3.78585i) q^{39} -8.44841 q^{41} -0.819076 q^{43} +(1.88174 - 2.33646i) q^{45} +(1.38776 + 2.40368i) q^{47} +(-6.58327 + 2.37918i) q^{49} +(1.58506 + 3.31179i) q^{51} +(11.5565 + 6.67216i) q^{53} +0.806424i q^{55} +(0.417438 - 5.39594i) q^{57} +(2.86351 - 4.95974i) q^{59} +(1.79397 - 1.03575i) q^{61} +(-6.79730 + 4.09838i) q^{63} +(3.34848 - 1.93325i) q^{65} +(-5.45110 + 9.44157i) q^{67} +(0.650969 - 8.41464i) q^{69} +10.3850i q^{71} +(2.67203 + 1.54270i) q^{73} +(0.747749 + 1.56233i) q^{75} +(0.732012 - 2.00410i) q^{77} +(6.76342 + 11.7146i) q^{79} +(-6.65612 + 6.05773i) q^{81} +12.8948 q^{83} -2.11978 q^{85} +(9.53968 + 6.53775i) q^{87} +(-1.60530 - 2.78046i) q^{89} +(-10.0764 + 1.76493i) q^{91} +(10.1929 - 4.87844i) q^{93} +(2.70603 + 1.56233i) q^{95} +1.01388i q^{97} +(0.372090 - 2.39049i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{3} + 5 q^{5} - 5 q^{7} + 3 q^{9}+O(q^{10}) $ 10 * q + q^3 + 5 * q^5 - 5 * q^7 + 3 * q^9	$ 10 q + q^{3} + 5 q^{5} - 5 q^{7} + 3 q^{9} + 6 q^{11} + 2 q^{15} - 6 q^{17} + 3 q^{19} + 12 q^{21} - 24 q^{23} - 5 q^{25} - 8 q^{27} + 15 q^{31} - 4 q^{33} - q^{35} - q^{37} - 21 q^{39} + 8 q^{41} - 26 q^{43} + 3 q^{45} - 14 q^{47} - 13 q^{49} + 40 q^{51} + 24 q^{53} + 18 q^{57} + 42 q^{61} - 49 q^{63} - 9 q^{65} + 7 q^{67} + 14 q^{69} - 3 q^{73} + q^{75} + 26 q^{77} + q^{79} - 13 q^{81} + 8 q^{83} - 12 q^{85} + 8 q^{87} - 28 q^{89} - 11 q^{91} + 25 q^{93} + 3 q^{95} + 36 q^{99}+O(q^{100}) $ 10 * q + q^3 + 5 * q^5 - 5 * q^7 + 3 * q^9 + 6 * q^11 + 2 * q^15 - 6 * q^17 + 3 * q^19 + 12 * q^21 - 24 * q^23 - 5 * q^25 - 8 * q^27 + 15 * q^31 - 4 * q^33 - q^35 - q^37 - 21 * q^39 + 8 * q^41 - 26 * q^43 + 3 * q^45 - 14 * q^47 - 13 * q^49 + 40 * q^51 + 24 * q^53 + 18 * q^57 + 42 * q^61 - 49 * q^63 - 9 * q^65 + 7 * q^67 + 14 * q^69 - 3 * q^73 + q^75 + 26 * q^77 + q^79 - 13 * q^81 + 8 * q^83 - 12 * q^85 + 8 * q^87 - 28 * q^89 - 11 * q^91 + 25 * q^93 + 3 * q^95 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/420\mathbb{Z}\right)^\times$.

$n$	$211$	$241$	$281$	$337$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$	$1$

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
$3$	0.979142	−	1.42873i	0.565308	−	0.824880i
$3$	0.979142	−	1.42873i	0.565308	−	0.824880i
$4$		0			0
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	−0.456468	−	2.60608i	−0.172529	−	0.985004i
$7$	−0.456468	−	2.60608i	−0.172529	−	0.985004i
$8$		0			0
$9$	−1.08256	−	2.79787i	−0.360854	−	0.932622i
$10$		0			0
$11$	0.698384	+	0.403212i	0.210571	+	0.121573i	0.601577	−	0.798815i	$-0.294539\pi$
$11$	0.698384	+	0.403212i	0.210571	+	0.121573i	−0.391006	+	0.920388i	$0.627873\pi$
$12$		0			0
$13$		−	3.86649i		−	1.07237i	−0.844100	−	0.536186i	$-0.819864\pi$
$13$		−	3.86649i		−	1.07237i	0.844100	−	0.536186i	$-0.180136\pi$
$14$		0			0
$15$	1.72689	+	0.133595i	0.445881	+	0.0344940i
$16$		0			0
$17$	−1.05989	+	1.83578i	−0.257061	+	0.445242i	−0.965453	−	0.260577i	$-0.916087\pi$
$17$	−1.05989	+	1.83578i	−0.257061	+	0.445242i	0.708393	+	0.705819i	$0.249421\pi$
$18$		0			0
$19$	2.70603	−	1.56233i	0.620807	−	0.358423i	−0.156376	−	0.987698i	$-0.549981\pi$
$19$	2.70603	−	1.56233i	0.620807	−	0.358423i	0.777183	+	0.629275i	$0.216648\pi$
$20$		0			0
$21$	−4.17034	−	1.89955i	−0.910042	−	0.414515i
$22$		0			0
$23$	4.21989	−	2.43635i	0.879908	−	0.508015i	0.00927994	−	0.999957i	$-0.497046\pi$
$23$	4.21989	−	2.43635i	0.879908	−	0.508015i	0.870628	+	0.491942i	$0.163713\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	−5.05739	−	1.19282i	−0.973295	−	0.229558i
$28$		0			0
$29$			6.67701i			1.23989i	0.784645	+	0.619945i	$0.212845\pi$
$29$			6.67701i			1.23989i	−0.784645	+	0.619945i	$0.787155\pi$
$30$		0			0
$31$	5.65010	+	3.26209i	1.01479	+	0.585888i	0.912590	−	0.408876i	$-0.134079\pi$
$31$	5.65010	+	3.26209i	1.01479	+	0.585888i	0.102198	+	0.994764i	$0.467413\pi$
$32$		0			0
$33$	1.25990	−	0.603003i	0.219320	−	0.104969i
$34$		0			0
$35$	2.02869	−	1.69835i	0.342912	−	0.287074i
$36$		0			0
$37$	−3.89991	−	6.75485i	−0.641142	−	1.11049i	−0.985178	−	0.171534i	$-0.945128\pi$
$37$	−3.89991	−	6.75485i	−0.641142	−	1.11049i	0.344036	−	0.938956i	$-0.388206\pi$
$38$		0			0
$39$	−5.52419	−	3.78585i	−0.884579	−	0.606221i
$40$		0			0
$41$	−8.44841			−1.31942			−0.659710	−	0.751520i	$-0.729321\pi$
$41$	−8.44841			−1.31942			−0.659710	+	0.751520i	$0.729321\pi$
$42$		0			0
$43$	−0.819076			−0.124908			−0.0624540	−	0.998048i	$-0.519893\pi$
$43$	−0.819076			−0.124908			−0.0624540	+	0.998048i	$0.519893\pi$
$44$		0			0
$45$	1.88174	−	2.33646i	0.280514	−	0.348299i
$46$		0			0
$47$	1.38776	+	2.40368i	0.202426	+	0.350612i	0.949310	−	0.314343i	$-0.101784\pi$
$47$	1.38776	+	2.40368i	0.202426	+	0.350612i	−0.746883	+	0.664955i	$0.768451\pi$
$48$		0			0
$49$	−6.58327	+	2.37918i	−0.940468	+	0.339883i
$50$		0			0
$51$	1.58506	+	3.31179i	0.221953	+	0.463743i
$52$		0			0
$53$	11.5565	+	6.67216i	1.58741	+	0.916492i	0.993732	+	0.111789i	$0.0356581\pi$
$53$	11.5565	+	6.67216i	1.58741	+	0.916492i	0.593678	+	0.804703i	$0.297675\pi$
$54$		0			0
$55$			0.806424i			0.108738i
$56$		0			0
$57$	0.417438	−	5.39594i	0.0552910	−	0.714710i
$58$		0			0
$59$	2.86351	−	4.95974i	0.372797	−	0.645703i	−0.617198	−	0.786808i	$-0.711732\pi$
$59$	2.86351	−	4.95974i	0.372797	−	0.645703i	0.989995	+	0.141105i	$0.0450655\pi$
$60$		0			0
$61$	1.79397	−	1.03575i	0.229694	−	0.132614i	−0.380737	−	0.924683i	$-0.624330\pi$
$61$	1.79397	−	1.03575i	0.229694	−	0.132614i	0.610431	+	0.792070i	$0.290996\pi$
$62$		0			0
$63$	−6.79730	+	4.09838i	−0.856380	+	0.516347i
$64$		0			0
$65$	3.34848	−	1.93325i	0.415328	−	0.239790i
$66$		0			0
$67$	−5.45110	+	9.44157i	−0.665957	+	1.15347i	0.313067	+	0.949731i	$0.398643\pi$
$67$	−5.45110	+	9.44157i	−0.665957	+	1.15347i	−0.979025	+	0.203741i	$0.934690\pi$
$68$		0			0
$69$	0.650969	−	8.41464i	0.0783674	−	1.01300i
$70$		0			0
$71$			10.3850i			1.23248i	0.787559	+	0.616239i	$0.211344\pi$
$71$			10.3850i			1.23248i	−0.787559	+	0.616239i	$0.788656\pi$
$72$		0			0
$73$	2.67203	+	1.54270i	0.312737	+	0.180559i	0.648151	−	0.761512i	$-0.275543\pi$
$73$	2.67203	+	1.54270i	0.312737	+	0.180559i	−0.335413	+	0.942071i	$0.608876\pi$
$74$		0			0
$75$	0.747749	+	1.56233i	0.0863426	+	0.180402i
$76$		0			0
$77$	0.732012	−	2.00410i	0.0834205	−	0.228388i
$78$		0			0
$79$	6.76342	+	11.7146i	0.760944	+	1.31799i	0.942364	+	0.334589i	$0.108597\pi$
$79$	6.76342	+	11.7146i	0.760944	+	1.31799i	−0.181420	+	0.983406i	$0.558069\pi$
$80$		0			0
$81$	−6.65612	+	6.05773i	−0.739569	+	0.673081i
$82$		0			0
$83$	12.8948			1.41539			0.707694	−	0.706519i	$-0.249735\pi$
$83$	12.8948			1.41539			0.707694	+	0.706519i	$0.249735\pi$
$84$		0			0
$85$	−2.11978			−0.229922
$86$		0			0
$87$	9.53968	+	6.53775i	1.02276	+	0.700920i
$88$		0			0
$89$	−1.60530	−	2.78046i	−0.170161	−	0.294728i	0.768315	−	0.640072i	$-0.221096\pi$
$89$	−1.60530	−	2.78046i	−0.170161	−	0.294728i	−0.938476	+	0.345344i	$0.887762\pi$
$90$		0			0
$91$	−10.0764	+	1.76493i	−1.05629	+	0.185015i
$92$		0			0
$93$	10.1929	−	4.87844i	1.05695	−	0.505871i
$94$		0			0
$95$	2.70603	+	1.56233i	0.277633	+	0.160292i
$96$		0			0
$97$			1.01388i			0.102944i	0.998674	+	0.0514721i	$0.0163913\pi$
$97$			1.01388i			0.102944i	−0.998674	+	0.0514721i	$0.983609\pi$
$98$		0			0
$99$	0.372090	−	2.39049i	0.0373965	−	0.240253i
$100$		0			0
$101$	−4.27796	+	7.40965i	−0.425673	+	0.737288i	−0.996483	−	0.0837947i	$-0.973296\pi$
$101$	−4.27796	+	7.40965i	−0.425673	+	0.737288i	0.570810	+	0.821082i	$0.306629\pi$
$102$		0			0
$103$	8.46835	−	4.88921i	0.834411	−	0.481748i	−0.0209492	−	0.999781i	$-0.506669\pi$
$103$	8.46835	−	4.88921i	0.834411	−	0.481748i	0.855361	+	0.518033i	$0.173336\pi$
$104$		0			0
$105$	−0.440112	−	4.56139i	−0.0429505	−	0.445146i
$106$		0			0
$107$	−15.8336	+	9.14150i	−1.53069	+	0.883743i	−0.531357	+	0.847148i	$0.678318\pi$
$107$	−15.8336	+	9.14150i	−1.53069	+	0.883743i	−0.999330	+	0.0365946i	$0.988349\pi$
$108$		0			0
$109$	−8.74840	+	15.1527i	−0.837945	+	1.45136i	0.0536658	+	0.998559i	$0.482909\pi$
$109$	−8.74840	+	15.1527i	−0.837945	+	1.45136i	−0.891610	+	0.452804i	$0.850424\pi$
$110$		0			0
$111$	−13.4695	−	1.04202i	−1.27846	−	0.0989039i
$112$		0			0
$113$		−	6.96021i		−	0.654761i	−0.944893	−	0.327381i	$-0.893834\pi$
$113$		−	6.96021i		−	0.654761i	0.944893	−	0.327381i	$-0.106166\pi$
$114$		0			0
$115$	4.21989	+	2.43635i	0.393507	+	0.227191i
$116$		0			0
$117$	−10.8179	+	4.18572i	−1.00012	+	0.386970i
$118$		0			0
$119$	5.26799	+	1.92417i	0.482916	+	0.176389i
$120$		0			0
$121$	−5.17484	−	8.96309i	−0.470440	−	0.814826i
$122$		0			0
$123$	−8.27219	+	12.0705i	−0.745879	+	1.08836i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	7.77139			0.689600			0.344800	−	0.938676i	$-0.387947\pi$
$127$	7.77139			0.689600			0.344800	+	0.938676i	$0.387947\pi$
$128$		0			0
$129$	−0.801992	+	1.17024i	−0.0706114	+	0.103034i
$130$		0			0
$131$	−5.93761	−	10.2842i	−0.518772	−	0.898539i	−0.999762	−	0.0218131i	$-0.993056\pi$
$131$	−5.93761	−	10.2842i	−0.518772	−	0.898539i	0.480990	−	0.876726i	$-0.340277\pi$
$132$		0			0
$133$	−5.30677	−	6.33898i	−0.460155	−	0.549659i
$134$		0			0
$135$	−1.49569	−	4.97624i	−0.128728	−	0.428286i
$136$		0			0
$137$	−2.12894	−	1.22915i	−0.181888	−	0.105013i	0.406291	−	0.913744i	$-0.366822\pi$
$137$	−2.12894	−	1.22915i	−0.181888	−	0.105013i	−0.588179	+	0.808730i	$0.700155\pi$
$138$		0			0
$139$		−	2.81335i		−	0.238625i	−0.992857	−	0.119313i	$-0.961931\pi$
$139$		−	2.81335i		−	0.238625i	0.992857	−	0.119313i	$-0.0380691\pi$
$140$		0			0
$141$	4.79303	+	0.370796i	0.403646	+	0.0312267i
$142$		0			0
$143$	1.55902	−	2.70030i	0.130372	−	0.225810i
$144$		0			0
$145$	−5.78246	+	3.33851i	−0.480208	+	0.277248i
$146$		0			0
$147$	−3.04674	+	11.7353i	−0.251291	+	0.967912i
$148$		0			0
$149$	−12.8234	+	7.40357i	−1.05053	+	0.606524i	−0.922798	−	0.385285i	$-0.874103\pi$
$149$	−12.8234	+	7.40357i	−1.05053	+	0.606524i	−0.127733	+	0.991809i	$0.540770\pi$
$150$		0			0
$151$	0.427898	−	0.741141i	0.0348218	−	0.0603132i	−0.848089	−	0.529853i	$-0.822247\pi$
$151$	0.427898	−	0.741141i	0.0348218	−	0.0603132i	0.882911	+	0.469540i	$0.155580\pi$
$152$		0			0
$153$	6.28366	+	0.978080i	0.508004	+	0.0790731i
$154$		0			0
$155$			6.52417i			0.524034i
$156$		0			0
$157$	21.1042	+	12.1845i	1.68430	+	0.972428i	0.958748	+	0.284256i	$0.0917465\pi$
$157$	21.1042	+	12.1845i	1.68430	+	0.972428i	0.725547	+	0.688173i	$0.241587\pi$
$158$		0			0
$159$	20.8482	−	9.97820i	1.65337	−	0.791323i
$160$		0			0
$161$	−8.27557	−	9.88524i	−0.652207	−	0.779066i
$162$		0			0
$163$	−0.789402	−	1.36728i	−0.0618307	−	0.107094i	0.833453	−	0.552590i	$-0.186361\pi$
$163$	−0.789402	−	1.36728i	−0.0618307	−	0.107094i	−0.895284	+	0.445496i	$0.853027\pi$
$164$		0			0
$165$	1.15217	+	0.789604i	0.0896960	+	0.0614706i
$166$		0			0
$167$	16.9264			1.30980			0.654902	−	0.755714i	$-0.272710\pi$
$167$	16.9264			1.30980			0.654902	+	0.755714i	$0.272710\pi$
$168$		0			0
$169$	−1.94978			−0.149983
$170$		0			0
$171$	−7.30064	−	5.87980i	−0.558294	−	0.449640i
$172$		0			0
$173$	−2.33037	−	4.03633i	−0.177175	−	0.306876i	0.763737	−	0.645528i	$-0.223363\pi$
$173$	−2.33037	−	4.03633i	−0.177175	−	0.306876i	−0.940912	+	0.338652i	$0.890029\pi$
$174$		0			0
$175$	2.48516	+	0.907726i	0.187861	+	0.0686176i
$176$		0			0
$177$	−4.28237	−	8.94748i	−0.321883	−	0.672534i
$178$		0			0
$179$	3.11674	+	1.79945i	0.232956	+	0.134497i	0.611935	−	0.790908i	$-0.290391\pi$
$179$	3.11674	+	1.79945i	0.232956	+	0.134497i	−0.378979	+	0.925405i	$0.623725\pi$
$180$		0			0
$181$		−	22.5821i		−	1.67851i	−0.543737	−	0.839256i	$-0.682991\pi$
$181$		−	22.5821i		−	1.67851i	0.543737	−	0.839256i	$-0.317009\pi$
$182$		0			0
$183$	0.276741	−	3.57725i	0.0204573	−	0.264438i
$184$		0			0
$185$	3.89991	−	6.75485i	0.286727	−	0.496627i
$186$		0			0
$187$	−1.48042	+	0.854719i	−0.108259	+	0.0625033i
$188$		0			0
$189$	−0.800034	+	13.7244i	−0.0581939	+	0.998305i
$190$		0			0
$191$	−2.92355	+	1.68791i	−0.211541	+	0.122133i	−0.602027	−	0.798475i	$-0.705640\pi$
$191$	−2.92355	+	1.68791i	−0.211541	+	0.122133i	0.390486	+	0.920609i	$0.372307\pi$
$192$		0			0
$193$	5.54524	−	9.60463i	0.399155	−	0.691357i	−0.594467	−	0.804120i	$-0.702637\pi$
$193$	5.54524	−	9.60463i	0.399155	−	0.691357i	0.993622	+	0.112763i	$0.0359702\pi$
$194$		0			0
$195$	0.516544	−	6.67701i	0.0369905	−	0.478151i
$196$		0			0
$197$		−	16.2585i		−	1.15837i	−0.815197	−	0.579184i	$-0.803371\pi$
$197$		−	16.2585i		−	1.15837i	0.815197	−	0.579184i	$-0.196629\pi$
$198$		0			0
$199$	−1.07964	−	0.623332i	−0.0765338	−	0.0441868i	0.461245	−	0.887273i	$-0.347403\pi$
$199$	−1.07964	−	0.623332i	−0.0765338	−	0.0441868i	−0.537779	+	0.843086i	$0.680736\pi$
$200$		0			0
$201$	8.15210	+	17.0328i	0.575005	+	1.20140i
$202$		0			0
$203$	17.4008	−	3.04784i	1.22130	−	0.213917i
$204$		0			0
$205$	−4.22420	−	7.31654i	−0.295031	−	0.511009i
$206$		0			0
$207$	−11.3849	−	9.16919i	−0.791305	−	0.637303i
$208$		0			0
$209$	2.51980			0.174298
$210$		0			0
$211$	−7.65466			−0.526968			−0.263484	−	0.964664i	$-0.584872\pi$
$211$	−7.65466			−0.526968			−0.263484	+	0.964664i	$0.584872\pi$
$212$		0			0
$213$	14.8375	+	10.1684i	1.01665	+	0.696730i
$214$		0			0
$215$	−0.409538	−	0.709341i	−0.0279303	−	0.0483766i
$216$		0			0
$217$	5.92216	−	16.2136i	0.402022	−	1.10065i
$218$		0			0
$219$	4.82040	−	2.30710i	0.325732	−	0.155899i
$220$		0			0
$221$	7.09803	+	4.09805i	0.477465	+	0.275665i
$222$		0			0
$223$		−	20.9369i		−	1.40204i	−0.713143	−	0.701019i	$-0.752729\pi$
$223$		−	20.9369i		−	1.40204i	0.713143	−	0.701019i	$-0.247271\pi$
$224$		0			0
$225$	2.96430	+	0.461407i	0.197620	+	0.0307605i
$226$		0			0
$227$	−2.29103	+	3.96818i	−0.152061	+	0.263377i	−0.931985	−	0.362497i	$-0.881924\pi$
$227$	−2.29103	+	3.96818i	−0.152061	+	0.263377i	0.779924	+	0.625874i	$0.215258\pi$
$228$		0			0
$229$	0.845272	−	0.488018i	0.0558572	−	0.0322492i	−0.471811	−	0.881700i	$-0.656400\pi$
$229$	0.845272	−	0.488018i	0.0558572	−	0.0322492i	0.527669	+	0.849450i	$0.323066\pi$
$230$		0			0
$231$	−2.14658	−	3.00814i	−0.141234	−	0.197921i
$232$		0			0
$233$	−17.2382	+	9.95247i	−1.12931	+	0.652008i	−0.943762	−	0.330627i	$-0.892740\pi$
$233$	−17.2382	+	9.95247i	−1.12931	+	0.652008i	−0.185550	+	0.982635i	$0.559407\pi$
$234$		0			0
$235$	−1.38776	+	2.40368i	−0.0905277	+	0.156799i
$236$		0			0
$237$	23.3594	+	1.80712i	1.51736	+	0.117385i
$238$		0			0
$239$		−	28.2703i		−	1.82865i	−0.404977	−	0.914327i	$-0.632721\pi$
$239$		−	28.2703i		−	1.82865i	0.404977	−	0.914327i	$-0.367279\pi$
$240$		0			0
$241$	11.0949	+	6.40567i	0.714688	+	0.412625i	0.812794	−	0.582551i	$-0.197945\pi$
$241$	11.0949	+	6.40567i	0.714688	+	0.412625i	−0.0981065	+	0.995176i	$0.531279\pi$
$242$		0			0
$243$	2.13760	+	15.4412i	0.137127	+	0.990553i
$244$		0			0
$245$	−5.35207	−	4.51169i	−0.341931	−	0.288241i
$246$		0			0
$247$	−6.04074	−	10.4629i	−0.384363	−	0.665736i
$248$		0			0
$249$	12.6258	−	18.4232i	0.800130	−	1.16753i
$250$		0			0
$251$	−10.3349			−0.652335			−0.326167	−	0.945312i	$-0.605757\pi$
$251$	−10.3349			−0.652335			−0.326167	+	0.945312i	$0.605757\pi$
$252$		0			0
$253$	3.92947			0.247044
$254$		0			0
$255$	−2.07556	+	3.02860i	−0.129977	+	0.189658i
$256$		0			0
$257$	−15.2527	−	26.4185i	−0.951439	−	1.64794i	−0.742315	−	0.670052i	$-0.766272\pi$
$257$	−15.2527	−	26.4185i	−0.951439	−	1.64794i	−0.209124	−	0.977889i	$-0.567061\pi$
$258$		0			0
$259$	−15.8235	+	13.2469i	−0.983223	+	0.823119i
$260$		0			0
$261$	18.6814	−	7.22828i	1.15635	−	0.447419i
$262$		0			0
$263$	−17.9054	−	10.3377i	−1.10409	−	0.637447i	−0.166799	−	0.985991i	$-0.553343\pi$
$263$	−17.9054	−	10.3377i	−1.10409	−	0.637447i	−0.937293	+	0.348543i	$0.886676\pi$
$264$		0			0
$265$			13.3443i			0.819735i
$266$		0			0
$267$	−5.54435	−	0.428919i	−0.339309	−	0.0262494i
$268$		0			0
$269$	−12.4095	+	21.4938i	−0.756618	+	1.31050i	0.187948	+	0.982179i	$0.439816\pi$
$269$	−12.4095	+	21.4938i	−0.756618	+	1.31050i	−0.944566	+	0.328322i	$0.893517\pi$
$270$		0			0
$271$	18.8571	−	10.8871i	1.14548	−	0.661346i	0.197702	−	0.980262i	$-0.436652\pi$
$271$	18.8571	−	10.8871i	1.14548	−	0.661346i	0.947783	+	0.318916i	$0.103319\pi$
$272$		0			0
$273$	−7.34459	+	16.1246i	−0.444515	+	0.975905i
$274$		0			0
$275$	−0.698384	+	0.403212i	−0.0421141	+	0.0243146i
$276$		0			0
$277$	−7.61126	+	13.1831i	−0.457316	+	0.792095i	−0.998818	−	0.0486048i	$-0.984523\pi$
$277$	−7.61126	+	13.1831i	−0.457316	+	0.792095i	0.541502	+	0.840699i	$0.317856\pi$
$278$		0			0
$279$	3.01030	−	19.3396i	0.180222	−	1.15783i
$280$		0			0
$281$			17.9488i			1.07073i	0.844619	+	0.535367i	$0.179827\pi$
$281$			17.9488i			1.07073i	−0.844619	+	0.535367i	$0.820173\pi$
$282$		0			0
$283$	−23.3730	−	13.4944i	−1.38938	−	0.802159i	−0.396135	−	0.918192i	$-0.629649\pi$
$283$	−23.3730	−	13.4944i	−1.38938	−	0.802159i	−0.993245	+	0.116033i	$0.962982\pi$
$284$		0			0
$285$	4.88174	−	2.33646i	0.289169	−	0.138400i
$286$		0			0
$287$	3.85643	+	22.0172i	0.227638	+	1.29963i
$288$		0			0
$289$	6.25328	+	10.8310i	0.367840	+	0.637117i
$290$		0			0
$291$	1.44857	+	0.992735i	0.0849166	+	0.0581951i
$292$		0			0
$293$	−14.4450			−0.843887			−0.421944	−	0.906622i	$-0.638652\pi$
$293$	−14.4450			−0.843887			−0.421944	+	0.906622i	$0.638652\pi$
$294$		0			0
$295$	5.72702			0.333440
$296$		0			0
$297$	−3.05104	−	2.87224i	−0.177039	−	0.166665i
$298$		0			0
$299$	−9.42015	−	16.3162i	−0.544782	−	0.943589i
$300$		0			0
$301$	0.373882	+	2.13457i	0.0215502	+	0.123035i
$302$		0			0
$303$	6.39768	+	13.3672i	0.367537	+	0.767924i
$304$		0			0
$305$	1.79397	+	1.03575i	0.102722	+	0.0593067i
$306$		0			0
$307$		−	9.34543i		−	0.533372i	−0.963783	−	0.266686i	$-0.914071\pi$
$307$		−	9.34543i		−	0.533372i	0.963783	−	0.266686i	$-0.0859287\pi$
$308$		0			0
$309$	1.30635	−	16.8862i	0.0743154	−	0.960625i
$310$		0			0
$311$	14.6664	−	25.4029i	0.831654	−	1.44047i	−0.0650722	−	0.997881i	$-0.520728\pi$
$311$	14.6664	−	25.4029i	0.831654	−	1.44047i	0.896726	−	0.442586i	$-0.145939\pi$
$312$		0			0
$313$	9.55728	−	5.51790i	0.540209	−	0.311890i	−0.204954	−	0.978772i	$-0.565705\pi$
$313$	9.55728	−	5.51790i	0.540209	−	0.311890i	0.745164	+	0.666881i	$0.232371\pi$
$314$		0			0
$315$	−6.94795	−	3.83745i	−0.391473	−	0.216216i
$316$		0			0
$317$	−14.6987	+	8.48631i	−0.825563	+	0.476639i	−0.852331	−	0.523003i	$-0.824812\pi$
$317$	−14.6987	+	8.48631i	−0.825563	+	0.476639i	0.0267682	+	0.999642i	$0.491478\pi$
$318$		0			0
$319$	−2.69225	+	4.66312i	−0.150737	+	0.261085i
$320$		0			0
$321$	−2.44252	+	31.5728i	−0.136328	+	1.76222i
$322$		0			0
$323$			6.62357i			0.368546i
$324$		0			0
$325$	3.34848	+	1.93325i	0.185740	+	0.107237i
$326$		0			0
$327$	13.0832	+	27.3357i	0.723503	+	1.51167i
$328$		0			0
$329$	5.63070	−	4.71382i	0.310430	−	0.259881i
$330$		0			0
$331$	5.82739	+	10.0933i	0.320302	+	0.554780i	0.980550	−	0.196268i	$-0.0628822\pi$
$331$	5.82739	+	10.0933i	0.320302	+	0.554780i	−0.660248	+	0.751048i	$0.729549\pi$
$332$		0			0
$333$	−14.6773	+	18.2240i	−0.804310	+	0.998668i
$334$		0			0
$335$	−10.9022			−0.595650
$336$		0			0
$337$	10.1753			0.554286			0.277143	−	0.960829i	$-0.410612\pi$
$337$	10.1753			0.554286			0.277143	+	0.960829i	$0.410612\pi$
$338$		0			0
$339$	−9.94428	−	6.81503i	−0.540099	−	0.370142i
$340$		0			0
$341$	2.63063	+	4.55638i	0.142456	+	0.246742i
$342$		0			0
$343$	9.20538	+	16.0705i	0.497044	+	0.867725i
$344$		0			0
$345$	7.61278	−	3.64356i	0.409858	−	0.196163i
$346$		0			0
$347$	1.38025	+	0.796887i	0.0740956	+	0.0427791i	0.536590	−	0.843843i	$-0.319712\pi$
$347$	1.38025	+	0.796887i	0.0740956	+	0.0427791i	−0.462494	+	0.886622i	$0.653045\pi$
$348$		0			0
$349$			15.4812i			0.828690i	0.910120	+	0.414345i	$0.135989\pi$
$349$			15.4812i			0.828690i	−0.910120	+	0.414345i	$0.864011\pi$
$350$		0			0
$351$	−4.61202	+	19.5544i	−0.246171	+	1.04374i
$352$		0			0
$353$	−6.40056	+	11.0861i	−0.340668	+	0.590054i	−0.984557	−	0.175065i	$-0.943986\pi$
$353$	−6.40056	+	11.0861i	−0.340668	+	0.590054i	0.643889	+	0.765119i	$0.277320\pi$
$354$		0			0
$355$	−8.99371	+	5.19252i	−0.477337	+	0.275590i
$356$		0			0
$357$	7.90724	−	5.64251i	0.418496	−	0.298633i
$358$		0			0
$359$	5.66697	−	3.27183i	0.299091	−	0.172680i	−0.342943	−	0.939356i	$-0.611424\pi$
$359$	5.66697	−	3.27183i	0.299091	−	0.172680i	0.642035	+	0.766676i	$0.278091\pi$
$360$		0			0
$361$	−4.61826	+	7.99906i	−0.243066	+	0.421003i
$362$		0			0
$363$	−17.8728	−	1.38266i	−0.938077	−	0.0725710i
$364$		0			0
$365$			3.08539i			0.161497i
$366$		0			0
$367$	−15.0004	−	8.66046i	−0.783012	−	0.452072i	0.0544847	−	0.998515i	$-0.482648\pi$
$367$	−15.0004	−	8.66046i	−0.783012	−	0.452072i	−0.837497	+	0.546442i	$0.815982\pi$
$368$		0			0
$369$	9.14593	+	23.6375i	0.476118	+	1.23052i
$370$		0			0
$371$	12.1130	−	33.1628i	0.628875	−	1.72173i
$372$		0			0
$373$	0.497933	+	0.862445i	0.0257820	+	0.0446557i	0.878629	−	0.477506i	$-0.158459\pi$
$373$	0.497933	+	0.862445i	0.0257820	+	0.0446557i	−0.852847	+	0.522162i	$0.825126\pi$
$374$		0			0
$375$	−0.979142	+	1.42873i	−0.0505627	+	0.0737795i
$376$		0			0
$377$	25.8166			1.32962
$378$		0			0
$379$	−20.2985			−1.04266			−0.521331	−	0.853355i	$-0.674564\pi$
$379$	−20.2985			−1.04266			−0.521331	+	0.853355i	$0.674564\pi$
$380$		0			0
$381$	7.60930	−	11.1033i	0.389836	−	0.568837i
$382$		0			0
$383$	−9.93736	−	17.2120i	−0.507776	−	0.879493i	−0.999959	−	0.00900178i	$-0.997135\pi$
$383$	−9.93736	−	17.2120i	−0.507776	−	0.879493i	0.492184	−	0.870491i	$-0.336199\pi$
$384$		0			0
$385$	2.10160	−	0.368107i	0.107108	−	0.0187605i
$386$		0			0
$387$	0.886700	+	2.29167i	0.0450735	+	0.116492i
$388$		0			0
$389$	−1.56923	−	0.905994i	−0.0795630	−	0.0459357i	0.459691	−	0.888079i	$-0.347960\pi$
$389$	−1.56923	−	0.905994i	−0.0795630	−	0.0459357i	−0.539254	+	0.842143i	$0.681294\pi$
$390$		0			0
$391$			10.3291i			0.522363i
$392$		0			0
$393$	−20.5072	−	1.58647i	−1.03445	−	0.0800268i
$394$		0			0
$395$	−6.76342	+	11.7146i	−0.340305	+	0.589425i
$396$		0			0
$397$	−30.1320	+	17.3967i	−1.51228	+	0.873116i	−0.512384	+	0.858757i	$0.671237\pi$
$397$	−30.1320	+	17.3967i	−1.51228	+	0.873116i	−0.999897	+	0.0143590i	$0.995429\pi$
$398$		0			0
$399$	−14.2528	+	1.37520i	−0.713532	+	0.0688461i
$400$		0			0
$401$	32.5121	−	18.7709i	1.62358	−	0.937374i	0.637627	−	0.770345i	$-0.279916\pi$
$401$	32.5121	−	18.7709i	1.62358	−	0.937374i	0.985952	−	0.167029i	$-0.0534173\pi$
$402$		0			0
$403$	12.6128	−	21.8461i	0.628290	−	1.08823i
$404$		0			0
$405$	−8.57421	−	2.73550i	−0.426056	−	0.135928i
$406$		0			0
$407$		−	6.28997i		−	0.311782i
$408$		0			0
$409$	3.24769	+	1.87505i	0.160588	+	0.0927154i	0.578140	−	0.815937i	$-0.303779\pi$
$409$	3.24769	+	1.87505i	0.160588	+	0.0927154i	−0.417552	+	0.908653i	$0.637112\pi$
$410$		0			0
$411$	−3.84066	+	1.83819i	−0.189446	+	0.0906710i
$412$		0			0
$413$	−14.2326	−	5.19856i	−0.700339	−	0.255804i
$414$		0			0
$415$	6.44740	+	11.1672i	0.316490	+	0.548178i
$416$		0			0
$417$	−4.01953	−	2.75467i	−0.196837	−	0.134897i
$418$		0			0
$419$	30.0547			1.46827			0.734134	−	0.679005i	$-0.237589\pi$
$419$	30.0547			1.46827			0.734134	+	0.679005i	$0.237589\pi$
$420$		0			0
$421$	20.5447			1.00129			0.500643	−	0.865654i	$-0.333097\pi$
$421$	20.5447			1.00129			0.500643	+	0.865654i	$0.333097\pi$
$422$		0			0
$423$	5.22283	−	6.48491i	0.253943	−	0.315307i
$424$		0			0
$425$	−1.05989	−	1.83578i	−0.0514121	−	0.0890484i
$426$		0			0
$427$	−3.51813	−	4.20243i	−0.170254	−	0.203370i
$428$		0			0
$429$	−2.33151	−	4.87140i	−0.112566	−	0.235193i
$430$		0			0
$431$	31.7400	+	18.3251i	1.52886	+	0.882688i	0.999410	+	0.0343478i	$0.0109354\pi$
$431$	31.7400	+	18.3251i	1.52886	+	0.882688i	0.529451	+	0.848340i	$0.322398\pi$
$432$		0			0
$433$			36.4397i			1.75118i	0.483057	+	0.875589i	$0.339526\pi$
$433$			36.4397i			1.75118i	−0.483057	+	0.875589i	$0.660474\pi$
$434$		0			0
$435$	−0.892015	+	11.5305i	−0.0427688	+	0.552844i
$436$		0			0
$437$	7.61278	−	13.1857i	0.364168	−	0.630758i
$438$		0			0
$439$	−7.96135	+	4.59649i	−0.379975	+	0.219378i	−0.677807	−	0.735240i	$-0.737070\pi$
$439$	−7.96135	+	4.59649i	−0.379975	+	0.219378i	0.297833	+	0.954618i	$0.403736\pi$
$440$		0			0
$441$	13.7834	+	15.8435i	0.656354	+	0.754453i
$442$		0			0
$443$	−20.7332	+	11.9703i	−0.985063	+	0.568727i	−0.903795	−	0.427966i	$-0.859230\pi$
$443$	−20.7332	+	11.9703i	−0.985063	+	0.568727i	−0.0812683	+	0.996692i	$0.525897\pi$
$444$		0			0
$445$	1.60530	−	2.78046i	0.0760985	−	0.131806i
$446$		0			0
$447$	−1.97816	+	25.5703i	−0.0935636	+	1.20943i
$448$		0			0
$449$			24.0126i			1.13322i	0.823985	+	0.566611i	$0.191746\pi$
$449$			24.0126i			1.13322i	−0.823985	+	0.566611i	$0.808254\pi$
$450$		0			0
$451$	−5.90023	−	3.40650i	−0.277831	−	0.160406i
$452$		0			0
$453$	−0.639920	−	1.33703i	−0.0300661	−	0.0628193i
$454$		0			0
$455$	−6.56667	−	7.84394i	−0.307850	−	0.367729i
$456$		0			0
$457$	−3.33585	−	5.77786i	−0.156044	−	0.270277i	0.777394	−	0.629013i	$-0.216541\pi$
$457$	−3.33585	−	5.77786i	−0.156044	−	0.270277i	−0.933439	+	0.358737i	$0.883208\pi$
$458$		0			0
$459$	7.55001	−	8.02000i	0.352404	−	0.374342i
$460$		0			0
$461$	−26.6895			−1.24305			−0.621527	−	0.783393i	$-0.713487\pi$
$461$	−26.6895			−1.24305			−0.621527	+	0.783393i	$0.713487\pi$
$462$		0			0
$463$	10.9550			0.509123			0.254562	−	0.967057i	$-0.418069\pi$
$463$	10.9550			0.509123			0.254562	+	0.967057i	$0.418069\pi$
$464$		0			0
$465$	9.32131	+	6.38809i	0.432265	+	0.296241i
$466$		0			0
$467$	−0.549726	−	0.952153i	−0.0254383	−	0.0440604i	0.853026	−	0.521868i	$-0.174765\pi$
$467$	−0.549726	−	0.952153i	−0.0254383	−	0.0440604i	−0.878464	+	0.477808i	$0.841431\pi$
$468$		0			0
$469$	27.0937	+	9.89620i	1.25107	+	0.456964i
$470$		0			0
$471$	38.0724	−	18.2219i	1.75428	−	0.839620i
$472$		0			0
$473$	−0.572029	−	0.330261i	−0.0263019	−	0.0151854i
$474$		0			0
$475$			3.12466i			0.143369i
$476$		0			0
$477$	6.15717	−	39.5566i	0.281917	−	1.81117i
$478$		0			0
$479$	−6.91657	+	11.9798i	−0.316026	+	0.547373i	−0.979655	−	0.200689i	$-0.935682\pi$
$479$	−6.91657	+	11.9798i	−0.316026	+	0.547373i	0.663629	+	0.748062i	$0.269015\pi$
$480$		0			0
$481$	−26.1176	+	15.0790i	−1.19086	+	0.687543i
$482$		0			0
$483$	−22.2263	+	2.14454i	−1.01133	+	0.0975799i
$484$		0			0
$485$	−0.878048	+	0.506941i	−0.0398701	+	0.0230190i
$486$		0			0
$487$	15.8416	−	27.4385i	0.717854	−	1.24336i	−0.243995	−	0.969776i	$-0.578458\pi$
$487$	15.8416	−	27.4385i	0.717854	−	1.24336i	0.961849	−	0.273582i	$-0.0882086\pi$
$488$		0			0
$489$	−2.72642	−	0.210920i	−0.123293	−	0.00953813i
$490$		0			0
$491$			37.3388i			1.68508i	0.538636	+	0.842538i	$0.318940\pi$
$491$			37.3388i			1.68508i	−0.538636	+	0.842538i	$0.681060\pi$
$492$		0			0
$493$	−12.2575	−	7.07689i	−0.552051	−	0.318727i
$494$		0			0
$495$	2.25627	−	0.873004i	0.101412	−	0.0392386i
$496$		0			0
$497$	27.0642	−	4.74044i	1.21400	−	0.212638i
$498$		0			0
$499$	5.50065	+	9.52740i	0.246243	+	0.426505i	0.962480	−	0.271352i	$-0.0874706\pi$
$499$	5.50065	+	9.52740i	0.246243	+	0.426505i	−0.716237	+	0.697857i	$0.754137\pi$
$500$		0			0
$501$	16.5734	−	24.1833i	0.740443	−	1.08043i
$502$		0			0
$503$	−20.2246			−0.901772			−0.450886	−	0.892582i	$-0.648892\pi$
$503$	−20.2246			−0.901772			−0.450886	+	0.892582i	$0.648892\pi$
$504$		0			0
$505$	−8.55593			−0.380734
$506$		0			0
$507$	−1.90911	+	2.78572i	−0.0847867	+	0.123718i
$508$		0			0
$509$	−5.24557	−	9.08560i	−0.232506	−	0.402712i	0.726039	−	0.687654i	$-0.241359\pi$
$509$	−5.24557	−	9.08560i	−0.232506	−	0.402712i	−0.958545	+	0.284941i	$0.908026\pi$
$510$		0			0
$511$	2.80069	−	7.66771i	0.123895	−	0.339199i
$512$		0			0
$513$	−15.5490	+	4.67351i	−0.686507	+	0.206340i
$514$		0			0
$515$	8.46835	+	4.88921i	0.373160	+	0.215444i
$516$		0			0
$517$			2.23825i			0.0984383i
$518$		0			0
$519$	−8.04860	−	0.622652i	−0.353295	−	0.0273314i
$520$		0			0
$521$	6.00130	−	10.3946i	0.262922	−	0.455394i	−0.704095	−	0.710105i	$-0.748647\pi$
$521$	6.00130	−	10.3946i	0.262922	−	0.455394i	0.967017	+	0.254712i	$0.0819806\pi$
$522$		0			0
$523$	−7.74038	+	4.46891i	−0.338463	+	0.195412i	−0.659592	−	0.751624i	$-0.729271\pi$
$523$	−7.74038	+	4.46891i	−0.338463	+	0.195412i	0.321129	+	0.947035i	$0.395938\pi$
$524$		0			0
$525$	3.73023	−	2.66184i	0.162800	−	0.116172i
$526$		0			0
$527$	−11.9769	+	6.91489i	−0.521724	+	0.301217i
$528$		0			0
$529$	0.371651	−	0.643719i	0.0161587	−	0.0279878i
$530$		0			0
$531$	−16.9766	−	2.64249i	−0.736723	−	0.114674i
$532$		0			0
$533$			32.6657i			1.41491i
$534$		0			0
$535$	−15.8336	−	9.14150i	−0.684544	−	0.395222i
$536$		0			0
$537$	5.62266	−	2.69107i	0.242636	−	0.116128i
$538$		0			0
$539$	−5.55697	−	0.992874i	−0.239356	−	0.0427661i
$540$		0			0
$541$	−15.9695	−	27.6599i	−0.686581	−	1.18919i	−0.972937	−	0.231069i	$-0.925778\pi$
$541$	−15.9695	−	27.6599i	−0.686581	−	1.18919i	0.286357	−	0.958123i	$-0.407556\pi$
$542$		0			0
$543$	−32.2638	−	22.1110i	−1.38457	−	0.948876i
$544$		0			0
$545$	−17.4968			−0.749480
$546$		0			0
$547$	−33.6313			−1.43797			−0.718984	−	0.695026i	$-0.755393\pi$
$547$	−33.6313			−1.43797			−0.718984	+	0.695026i	$0.755393\pi$
$548$		0			0
$549$	−4.83996	−	3.89802i	−0.206565	−	0.166363i
$550$		0			0
$551$	10.4317	+	18.0682i	0.444405	+	0.769732i
$552$		0			0
$553$	27.4418	−	22.9733i	1.16695	−	0.976926i
$554$		0			0
$555$	−5.83231	−	12.1859i	−0.247568	−	0.517263i
$556$		0			0
$557$	9.17988	+	5.30000i	0.388964	+	0.224568i	0.681711	−	0.731621i	$-0.261236\pi$
$557$	9.17988	+	5.30000i	0.388964	+	0.224568i	−0.292747	+	0.956190i	$0.594569\pi$
$558$		0			0
$559$			3.16695i			0.133948i
$560$		0			0
$561$	−0.228372	+	2.95201i	−0.00964188	+	0.124634i
$562$		0			0
$563$	−1.14796	+	1.98833i	−0.0483808	+	0.0837980i	−0.889202	−	0.457515i	$-0.848739\pi$
$563$	−1.14796	+	1.98833i	−0.0483808	+	0.0837980i	0.840821	+	0.541313i	$0.182073\pi$
$564$		0			0
$565$	6.02772	−	3.48010i	0.253588	−	0.146409i
$566$		0			0
$567$	18.8252	+	14.5812i	0.790585	+	0.612353i
$568$		0			0
$569$	−24.1648	+	13.9515i	−1.01304	+	0.584878i	−0.912080	−	0.410012i	$-0.865524\pi$
$569$	−24.1648	+	13.9515i	−1.01304	+	0.584878i	−0.100959	+	0.994891i	$0.532191\pi$
$570$		0			0
$571$	3.11649	−	5.39791i	0.130421	−	0.225896i	−0.793418	−	0.608677i	$-0.791700\pi$
$571$	3.11649	−	5.39791i	0.130421	−	0.225896i	0.923839	+	0.382782i	$0.125034\pi$
$572$		0			0
$573$	−0.450993	+	5.82969i	−0.0188405	+	0.243539i
$574$		0			0
$575$			4.87271i			0.203206i
$576$		0			0
$577$	11.4776	+	6.62662i	0.477820	+	0.275870i	0.719508	−	0.694484i	$-0.244368\pi$
$577$	11.4776	+	6.62662i	0.477820	+	0.275870i	−0.241687	+	0.970354i	$0.577701\pi$
$578$		0			0
$579$	−8.29289	−	17.3270i	−0.344641	−	0.720084i
$580$		0			0
$581$	−5.88606	−	33.6048i	−0.244195	−	1.39416i
$582$		0			0
$583$	5.38059	+	9.31946i	0.222841	+	0.385973i
$584$		0			0
$585$	−9.03391	−	7.27575i	−0.373506	−	0.300815i
$586$		0			0
$587$	18.6209			0.768568			0.384284	−	0.923215i	$-0.374448\pi$
$587$	18.6209			0.768568			0.384284	+	0.923215i	$0.374448\pi$
$588$		0			0
$589$	20.3858			0.839982
$590$		0			0
$591$	−23.2290	−	15.9193i	−0.955514	−	0.654834i
$592$		0			0
$593$	−1.37822	−	2.38715i	−0.0565967	−	0.0980284i	0.836339	−	0.548213i	$-0.184692\pi$
$593$	−1.37822	−	2.38715i	−0.0565967	−	0.0980284i	−0.892936	+	0.450184i	$0.851358\pi$
$594$		0			0
$595$	0.967610	+	5.52430i	0.0396681	+	0.226474i
$596$		0			0
$597$	−1.94770	+	0.932191i	−0.0797140	+	0.0381520i
$598$		0			0
$599$	16.2530	+	9.38368i	0.664080	+	0.383407i	0.793830	−	0.608140i	$-0.208084\pi$
$599$	16.2530	+	9.38368i	0.664080	+	0.383407i	−0.129750	+	0.991547i	$0.541417\pi$
$600$		0			0
$601$		−	16.5669i		−	0.675779i	−0.941186	−	0.337890i	$-0.890287\pi$
$601$		−	16.5669i		−	0.675779i	0.941186	−	0.337890i	$-0.109713\pi$
$602$		0			0
$603$	32.3174	+	5.03035i	1.31607	+	0.204852i
$604$		0			0
$605$	5.17484	−	8.96309i	0.210387	−	0.364401i
$606$		0			0
$607$	28.9773	−	16.7301i	1.17615	−	0.679053i	0.221032	−	0.975266i	$-0.429057\pi$
$607$	28.9773	−	16.7301i	1.17615	−	0.679053i	0.955122	+	0.296213i	$0.0957240\pi$
$608$		0			0
$609$	12.6833	−	27.8454i	0.513954	−	1.12835i
$610$		0			0
$611$	9.29381	−	5.36578i	0.375987	−	0.217076i
$612$		0			0
$613$	18.7772	−	32.5231i	0.758404	−	1.31359i	−0.185260	−	0.982690i	$-0.559313\pi$
$613$	18.7772	−	32.5231i	0.758404	−	1.31359i	0.943664	−	0.330905i	$-0.107354\pi$
$614$		0			0
$615$	−14.5895	−	1.12866i	−0.588305	−	0.0455121i
$616$		0			0
$617$		−	22.5088i		−	0.906172i	−0.891467	−	0.453086i	$-0.850323\pi$
$617$		−	22.5088i		−	0.906172i	0.891467	−	0.453086i	$-0.149677\pi$
$618$		0			0
$619$	−23.3812	−	13.4991i	−0.939770	−	0.542576i	−0.0498816	−	0.998755i	$-0.515884\pi$
$619$	−23.3812	−	13.4991i	−0.939770	−	0.542576i	−0.889888	+	0.456179i	$0.849218\pi$
$620$		0			0
$621$	−24.2478	+	7.28804i	−0.973029	+	0.292459i
$622$		0			0
$623$	−6.51332	+	5.45272i	−0.260951	+	0.218459i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	2.46724	−	3.60012i	0.0985322	−	0.143775i
$628$		0			0
$629$	16.5339			0.659249
$630$		0			0
$631$	9.17965			0.365436			0.182718	−	0.983165i	$-0.441510\pi$
$631$	9.17965			0.365436			0.182718	+	0.983165i	$0.441510\pi$
$632$		0			0
$633$	−7.49499	+	10.9365i	−0.297899	+	0.434686i
$634$		0			0
$635$	3.88570	+	6.73022i	0.154199	+	0.267081i
$636$		0			0
$637$	9.19909	+	25.4542i	0.364481	+	1.00853i
$638$		0			0
$639$	29.0560	−	11.2425i	1.14944	−	0.444745i
$640$		0			0
$641$	26.6664	+	15.3959i	1.05326	+	0.608100i	0.923560	−	0.383453i	$-0.125265\pi$
$641$	26.6664	+	15.3959i	1.05326	+	0.608100i	0.129700	+	0.991553i	$0.458599\pi$
$642$		0			0
$643$			3.42929i			0.135238i	0.997711	+	0.0676189i	$0.0215402\pi$
$643$			3.42929i			0.135238i	−0.997711	+	0.0676189i	$0.978460\pi$
$644$		0			0
$645$	−1.41445	−	0.109424i	−0.0556941	−	0.00430858i
$646$		0			0
$647$	−25.2967	+	43.8152i	−0.994516	+	1.72255i	−0.406689	+	0.913567i	$0.633317\pi$
$647$	−25.2967	+	43.8152i	−0.994516	+	1.72255i	−0.587828	+	0.808986i	$0.700017\pi$
$648$		0			0
$649$	3.99966	−	2.30920i	0.157000	−	0.0906441i
$650$		0			0
$651$	−17.3663	−	24.3366i	−0.680640	−	0.953828i
$652$		0			0
$653$	4.57643	−	2.64220i	0.179090	−	0.103397i	−0.407775	−	0.913082i	$-0.633695\pi$
$653$	4.57643	−	2.64220i	0.179090	−	0.103397i	0.586865	+	0.809685i	$0.300362\pi$
$654$		0			0
$655$	5.93761	−	10.2842i	0.232002	−	0.401839i
$656$		0			0
$657$	1.42362	−	9.14605i	0.0555408	−	0.356821i
$658$		0			0
$659$		−	26.0502i		−	1.01477i	−0.861719	−	0.507385i	$-0.830612\pi$
$659$		−	26.0502i		−	1.01477i	0.861719	−	0.507385i	$-0.169388\pi$
$660$		0			0
$661$	−28.3751	−	16.3823i	−1.10366	−	0.637199i	−0.166481	−	0.986045i	$-0.553241\pi$
$661$	−28.3751	−	16.3823i	−1.10366	−	0.637199i	−0.937180	+	0.348845i	$0.886574\pi$
$662$		0			0
$663$	12.8050	−	6.12863i	0.497305	−	0.238016i
$664$		0			0
$665$	2.83633	−	7.76528i	0.109988	−	0.301125i
$666$		0			0
$667$	16.2676	+	28.1763i	0.629883	+	1.09099i
$668$		0			0
$669$	−29.9132	−	20.5002i	−1.15651	−	0.792583i
$670$		0			0
$671$	1.67050			0.0644891
$672$		0			0
$673$	−38.5194			−1.48481			−0.742406	−	0.669950i	$-0.766315\pi$
$673$	−38.5194			−1.48481			−0.742406	+	0.669950i	$0.766315\pi$
$674$		0			0
$675$	3.56170	−	3.78342i	0.137090	−	0.145624i
$676$		0			0
$677$	9.58044	+	16.5938i	0.368206	+	0.637752i	0.989285	−	0.145996i	$-0.0466387\pi$
$677$	9.58044	+	16.5938i	0.368206	+	0.637752i	−0.621079	+	0.783748i	$0.713305\pi$
$678$		0			0
$679$	2.64225	−	0.462805i	0.101400	−	0.0177608i
$680$		0			0
$681$	3.42623	+	7.15868i	0.131293	+	0.274321i
$682$		0			0
$683$	25.0821	+	14.4812i	0.959741	+	0.554107i	0.896093	−	0.443866i	$-0.146393\pi$
$683$	25.0821	+	14.4812i	0.959741	+	0.554107i	0.0636479	+	0.997972i	$0.479727\pi$
$684$		0			0
$685$		−	2.45829i		−	0.0939265i
$686$		0			0
$687$	0.130393	−	1.68551i	0.00497482	−	0.0643062i
$688$		0			0
$689$	25.7979	−	44.6832i	0.982821	−	1.70230i
$690$		0			0
$691$	39.4572	−	22.7806i	1.50102	−	0.866616i	0.501024	−	0.865433i	$-0.332957\pi$
$691$	39.4572	−	22.7806i	1.50102	−	0.866616i	0.999999	−	0.00118303i	$-0.000376571\pi$
$692$		0			0
$693$	−6.39964	+	0.121486i	−0.243102	+	0.00461485i
$694$		0			0
$695$	2.43643	−	1.40667i	0.0924191	−	0.0533582i
$696$		0			0
$697$	8.95437	−	15.5094i	0.339171	−	0.587461i
$698$		0			0
$699$	−2.65920	+	34.3737i	−0.100580	+	1.30013i
$700$		0			0
$701$			39.2878i			1.48388i	0.670466	+	0.741940i	$0.266094\pi$
$701$			39.2878i			1.48388i	−0.670466	+	0.741940i	$0.733906\pi$
$702$		0			0
$703$	−21.1066	−	12.1859i	−0.796050	−	0.459600i
$704$		0			0
$705$	2.07540	+	4.33629i	0.0781640	+	0.163314i
$706$		0			0
$707$	21.2629	+	7.76643i	0.799672	+	0.292087i
$708$		0			0
$709$	−9.88537	−	17.1220i	−0.371253	−	0.643029i	0.618506	−	0.785780i	$-0.287738\pi$
$709$	−9.88537	−	17.1220i	−0.371253	−	0.643029i	−0.989759	+	0.142752i	$0.954405\pi$
$710$		0			0
$711$	25.4540	−	31.6049i	0.954601	−	1.18528i
$712$		0			0
$713$	31.7904			1.19056
$714$		0			0
$715$	3.11804			0.116608
$716$		0			0
$717$	−40.3907	−	27.6806i	−1.50842	−	1.03375i
$718$		0			0
$719$	−0.740641	−	1.28283i	−0.0276212	−	0.0478414i	0.851884	−	0.523730i	$-0.175460\pi$
$719$	−0.740641	−	1.28283i	−0.0276212	−	0.0478414i	−0.879506	+	0.475889i	$0.842127\pi$
$720$		0			0
$721$	−16.6072	−	19.8374i	−0.618484	−	0.738784i
$722$		0			0
$723$	20.0155	−	9.57966i	0.744385	−	0.356271i
$724$		0			0
$725$	−5.78246	−	3.33851i	−0.214755	−	0.123989i
$726$		0			0
$727$			6.35193i			0.235580i	0.993039	+	0.117790i	$0.0375810\pi$
$727$			6.35193i			0.235580i	−0.993039	+	0.117790i	$0.962419\pi$
$728$		0			0
$729$	24.1544	+	12.0651i	0.894607	+	0.446855i
$730$		0			0
$731$	0.868129	−	1.50364i	0.0321089	−	0.0556142i
$732$		0			0
$733$	−34.0100	+	19.6357i	−1.25619	+	0.725261i	−0.972331	−	0.233605i	$-0.924948\pi$
$733$	−34.0100	+	19.6357i	−1.25619	+	0.725261i	−0.283857	+	0.958866i	$0.591614\pi$
$734$		0			0
$735$	−11.6864	+	3.22910i	−0.431061	+	0.119107i
$736$		0			0
$737$	−7.61392	+	4.39590i	−0.280462	+	0.161925i
$738$		0			0
$739$	11.2904	−	19.5555i	0.415324	−	0.719362i	−0.580139	−	0.814518i	$-0.697002\pi$
$739$	11.2904	−	19.5555i	0.415324	−	0.719362i	0.995462	+	0.0951558i	$0.0303349\pi$
$740$		0			0
$741$	−20.8634	−	1.61402i	−0.766436	−	0.0592926i
$742$		0			0
$743$		−	26.6330i		−	0.977070i	−0.872544	−	0.488535i	$-0.837532\pi$
$743$		−	26.6330i		−	0.977070i	0.872544	−	0.488535i	$-0.162468\pi$
$744$		0			0
$745$	−12.8234	−	7.40357i	−0.469811	−	0.271246i
$746$		0			0
$747$	−13.9594	−	36.0779i	−0.510748	−	1.32002i
$748$		0			0
$749$	31.0510	+	37.0906i	1.13458	+	1.35526i
$750$		0			0
$751$	8.62709	+	14.9426i	0.314807	+	0.545262i	0.979396	−	0.201947i	$-0.0647268\pi$
$751$	8.62709	+	14.9426i	0.314807	+	0.545262i	−0.664589	+	0.747209i	$0.731393\pi$
$752$		0			0
$753$	−10.1194	+	14.7659i	−0.368770	+	0.538098i
$754$		0			0
$755$	0.855795			0.0311456
$756$		0			0
$757$	25.1712			0.914863			0.457431	−	0.889245i	$-0.348770\pi$
$757$	25.1712			0.914863			0.457431	+	0.889245i	$0.348770\pi$
$758$		0			0
$759$	3.84751	−	5.61417i	0.139656	−	0.203781i
$760$		0			0
$761$	−0.00796126	−	0.0137893i	−0.000288596	−	0.000499862i	0.865881	−	0.500250i	$-0.166759\pi$
$761$	−0.00796126	−	0.0137893i	−0.000288596	−	0.000499862i	−0.866170	+	0.499750i	$0.833425\pi$
$762$		0			0
$763$	43.4824	+	15.8823i	1.57417	+	0.574977i
$764$		0			0
$765$	2.29479	+	5.93085i	0.0829683	+	0.214430i
$766$		0			0
$767$	−19.1768	−	11.0717i	−0.692435	−	0.399777i
$768$		0			0
$769$			13.0356i			0.470075i	0.971986	+	0.235037i	$0.0755213\pi$
$769$			13.0356i			0.470075i	−0.971986	+	0.235037i	$0.924479\pi$
$770$		0			0
$771$	−52.6796	−	4.07537i	−1.89721	−	0.146771i
$772$		0			0
$773$	−14.7085	+	25.4758i	−0.529027	+	0.916301i	0.470400	+	0.882453i	$0.344110\pi$
$773$	−14.7085	+	25.4758i	−0.529027	+	0.916301i	−0.999427	+	0.0338481i	$0.989224\pi$
$774$		0			0
$775$	−5.65010	+	3.26209i	−0.202958	+	0.117178i
$776$		0			0
$777$	3.43280	+	35.5781i	0.123151	+	1.27636i
$778$		0			0
$779$	−22.8617	+	13.1992i	−0.819105	+	0.472910i
$780$		0			0
$781$	−4.18738	+	7.25275i	−0.149836	+	0.259524i
$782$		0			0
$783$	7.96445	−	33.7683i	0.284626	−	1.20678i
$784$		0			0
$785$			24.3690i			0.869766i
$786$		0			0
$787$	1.95977	+	1.13148i	0.0698584	+	0.0403327i	0.534522	−	0.845154i	$-0.320492\pi$
$787$	1.95977	+	1.13148i	0.0698584	+	0.0403327i	−0.464664	+	0.885487i	$0.653825\pi$
$788$		0			0
$789$	−32.3017	+	15.4600i	−1.14997	+	0.550389i
$790$		0			0
$791$	−18.1388	+	3.17711i	−0.644943	+	0.112965i
$792$		0			0
$793$	−4.00471	−	6.93636i	−0.142211	−	0.246318i
$794$		0			0
$795$	19.0655	+	13.0660i	0.676183	+	0.463403i
$796$		0			0
$797$	19.6277			0.695250			0.347625	−	0.937634i	$-0.386988\pi$
$797$	19.6277			0.695250			0.347625	+	0.937634i	$0.386988\pi$
$798$		0			0
$799$	−5.88350			−0.208143
$800$		0			0
$801$	−6.04152	+	7.50143i	−0.213467	+	0.265050i
$802$		0			0
$803$	1.24407	+	2.15479i	0.0439022	+	0.0760409i
$804$		0			0
$805$	4.42308	−	12.1095i	0.155893	−	0.426803i
$806$		0			0
$807$	18.5583	+	38.7753i	0.653284	+	1.36496i
$808$		0			0
$809$	−21.2506	−	12.2690i	−0.747130	−	0.431356i	0.0775260	−	0.996990i	$-0.475298\pi$
$809$	−21.2506	−	12.2690i	−0.747130	−	0.431356i	−0.824656	+	0.565635i	$0.808631\pi$
$810$		0			0
$811$			38.7927i			1.36220i	0.732192	+	0.681098i	$0.238497\pi$
$811$			38.7927i			1.36220i	−0.732192	+	0.681098i	$0.761503\pi$
$812$		0			0
$813$	2.90893	−	37.6018i	0.102021	−	1.31875i
$814$		0			0
$815$	0.789402	−	1.36728i	0.0276515	−	0.0478939i
$816$		0			0
$817$	−2.21645	+	1.27967i	−0.0775436	+	0.0447698i
$818$		0			0
$819$	15.8464	+	26.2817i	0.553716	+	0.918358i
$820$		0			0
$821$	11.8734	−	6.85513i	0.414386	−	0.239246i	−0.278287	−	0.960498i	$-0.589767\pi$
$821$	11.8734	−	6.85513i	0.414386	−	0.239246i	0.692672	+	0.721252i	$0.256433\pi$
$822$		0			0
$823$	−4.04168	+	7.00040i	−0.140884	+	0.244019i	−0.927830	−	0.373004i	$-0.878328\pi$
$823$	−4.04168	+	7.00040i	−0.140884	+	0.244019i	0.786946	+	0.617022i	$0.211661\pi$
$824$		0			0
$825$	−0.107734	+	1.39261i	−0.00375082	+	0.0484843i
$826$		0			0
$827$		−	37.6581i		−	1.30950i	−0.755845	−	0.654751i	$-0.772774\pi$
$827$		−	37.6581i		−	1.30950i	0.755845	−	0.654751i	$-0.227226\pi$
$828$		0			0
$829$	15.4475	+	8.91864i	0.536515	+	0.309757i	0.743665	−	0.668552i	$-0.233086\pi$
$829$	15.4475	+	8.91864i	0.536515	+	0.309757i	−0.207150	+	0.978309i	$0.566419\pi$
$830$		0			0
$831$	11.3826	+	23.7826i	0.394859	+	0.825008i
$832$		0			0
$833$	2.60988	−	14.6071i	0.0904269	−	0.506106i
$834$		0			0
$835$	8.46320	+	14.6587i	0.292881	+	0.507285i
$836$		0			0
$837$	−24.6837	−	23.2372i	−0.853193	−	0.803194i
$838$		0			0
$839$	4.49497			0.155183			0.0775917	−	0.996985i	$-0.475277\pi$
$839$	4.49497			0.155183			0.0775917	+	0.996985i	$0.475277\pi$
$840$		0			0
$841$	−15.5825			−0.537329
$842$		0			0
$843$	25.6440	+	17.5744i	0.883228	+	0.605295i
$844$		0			0
$845$	−0.974891	−	1.68856i	−0.0335373	−	0.0580883i
$846$		0			0
$847$	−20.9963	+	17.5774i	−0.721443	+	0.603966i
$848$		0			0
$849$	−42.1654	+	20.1809i	−1.44711	+	0.692605i
$850$		0			0
$851$	−32.9144	−	19.0032i	−1.12829	−	0.651420i
$852$		0			0
$853$			33.0503i			1.13162i	0.824535	+	0.565811i	$0.191437\pi$
$853$			33.0503i			1.13162i	−0.824535	+	0.565811i	$0.808563\pi$
$854$		0			0
$855$	1.44174	−	9.26244i	0.0493065	−	0.316769i
$856$		0			0
$857$	−0.210762	+	0.365051i	−0.00719949	+	0.0124699i	−0.869603	−	0.493752i	$-0.835625\pi$
$857$	−0.210762	+	0.365051i	−0.00719949	+	0.0124699i	0.862403	+	0.506222i	$0.168958\pi$
$858$		0			0
$859$	−17.0294	+	9.83192i	−0.581035	+	0.335461i	−0.761545	−	0.648112i	$-0.775559\pi$
$859$	−17.0294	+	9.83192i	−0.581035	+	0.335461i	0.180509	+	0.983573i	$0.442225\pi$
$860$		0			0
$861$	35.2327	+	16.0482i	1.20073	+	0.546920i
$862$		0			0
$863$	−0.782575	+	0.451820i	−0.0266392	+	0.0153801i	−0.513260	−	0.858233i	$-0.671563\pi$
$863$	−0.782575	+	0.451820i	−0.0266392	+	0.0153801i	0.486621	+	0.873613i	$0.338229\pi$
$864$		0			0
$865$	2.33037	−	4.03633i	0.0792351	−	0.137239i
$866$		0			0
$867$	21.5974	+	1.67081i	0.733488	+	0.0567437i
$868$		0			0
$869$			10.9084i			0.370041i
$870$		0			0
$871$	36.5058	+	21.0766i	1.23695	+	0.714154i
$872$		0			0
$873$	2.83671	−	1.09759i	0.0960080	−	0.0371478i
$874$		0			0
$875$	0.456468	+	2.60608i	0.0154314	+	0.0881015i
$876$		0			0
$877$	7.65916	+	13.2661i	0.258632	+	0.447963i	0.965876	−	0.259006i	$-0.0833951\pi$
$877$	7.65916	+	13.2661i	0.258632	+	0.447963i	−0.707244	+	0.706970i	$0.750062\pi$
$878$		0			0
$879$	−14.1437	+	20.6381i	−0.477056	+	0.696106i
$880$		0			0
$881$	−43.8614			−1.47773			−0.738863	−	0.673855i	$-0.764637\pi$
$881$	−43.8614			−1.47773			−0.738863	+	0.673855i	$0.764637\pi$
$882$		0			0
$883$	−2.91300			−0.0980304			−0.0490152	−	0.998798i	$-0.515608\pi$
$883$	−2.91300			−0.0980304			−0.0490152	+	0.998798i	$0.515608\pi$
$884$		0			0
$885$	5.60756	−	8.18238i	0.188496	−	0.275048i
$886$		0			0
$887$	−7.44790	−	12.9001i	−0.250076	−	0.433145i	0.713470	−	0.700685i	$-0.247122\pi$
$887$	−7.44790	−	12.9001i	−0.250076	−	0.433145i	−0.963547	+	0.267541i	$0.913789\pi$
$888$		0			0
$889$	−3.54739	−	20.2528i	−0.118976	−	0.679259i
$890$		0			0
$891$	−7.09108	+	1.54679i	−0.237560	+	0.0518195i
$892$		0			0
$893$	7.51067	+	4.33629i	0.251335	+	0.145108i
$894$		0			0
$895$			3.59890i			0.120298i
$896$		0			0
$897$	−32.5352	−	2.51697i	−1.08632	−	0.0840391i
$898$		0			0
$899$	−21.7810	+	37.7258i	−0.726437	+	1.25823i
$900$		0			0
$901$	−24.4972	+	14.1435i	−0.816121	+	0.471188i
$902$		0			0
$903$	3.41582	+	1.55587i	0.113671	+	0.0517762i
$904$		0			0
$905$	19.5566	−	11.2910i	0.650085	−	0.375327i
$906$		0			0
$907$	−9.54899	+	16.5393i	−0.317069	+	0.549180i	−0.979875	−	0.199611i	$-0.936032\pi$
$907$	−9.54899	+	16.5393i	−0.317069	+	0.549180i	0.662806	+	0.748791i	$0.269365\pi$
$908$		0			0
$909$	25.3624	+	3.94777i	0.841217	+	0.130939i
$910$		0			0
$911$			6.16915i			0.204393i	0.994764	+	0.102197i	$0.0325871\pi$
$911$			6.16915i			0.204393i	−0.994764	+	0.102197i	$0.967413\pi$
$912$		0			0
$913$	9.00552	+	5.19934i	0.298039	+	0.172073i
$914$		0			0
$915$	3.23636	−	1.54896i	0.106991	−	0.0512070i
$916$		0			0
$917$	−24.0912	+	20.1683i	−0.795562	+	0.666016i
$918$		0			0
$919$	−14.8318	−	25.6894i	−0.489255	−	0.847415i	0.510668	−	0.859778i	$-0.329398\pi$
$919$	−14.8318	−	25.6894i	−0.489255	−	0.847415i	−0.999924	+	0.0123630i	$0.996065\pi$
$920$		0			0
$921$	−13.3521	−	9.15051i	−0.439968	−	0.301519i
$922$		0			0
$923$	40.1537			1.32168
$924$		0			0
$925$	7.79983			0.256457
$926$		0			0
$927$	−22.8469	−	18.4005i	−0.750389	−	0.604350i
$928$		0			0
$929$	16.8256	+	29.1428i	0.552030	+	0.956144i	0.998128	+	0.0611601i	$0.0194800\pi$
$929$	16.8256	+	29.1428i	0.552030	+	0.956144i	−0.446098	+	0.894984i	$0.647187\pi$
$930$		0			0
$931$	−14.0975	+	16.7234i	−0.462027	+	0.548087i
$932$		0			0
$933$	−21.9335	−	45.8274i	−0.718072	−	1.50032i
$934$		0			0
$935$	−1.48042	−	0.854719i	−0.0484148	−	0.0279523i
$936$		0			0
$937$		−	7.99276i		−	0.261112i	−0.991441	−	0.130556i	$-0.958324\pi$
$937$		−	7.99276i		−	0.261112i	0.991441	−	0.130556i	$-0.0416762\pi$
$938$		0			0
$939$	1.47433	−	19.0576i	0.0481128	−	0.621922i
$940$		0			0
$941$	−8.69431	+	15.0590i	−0.283426	+	0.490909i	−0.972226	−	0.234043i	$-0.924804\pi$
$941$	−8.69431	+	15.0590i	−0.283426	+	0.490909i	0.688800	+	0.724951i	$0.258138\pi$
$942$		0			0
$943$	−35.6514	+	20.5833i	−1.16097	+	0.670285i
$944$		0			0
$945$	−12.2857	+	6.16936i	−0.399655	+	0.200689i
$946$		0			0
$947$	−36.6302	+	21.1485i	−1.19032	+	0.687233i	−0.958380	−	0.285496i	$-0.907842\pi$
$947$	−36.6302	+	21.1485i	−1.19032	+	0.687233i	−0.231943	+	0.972729i	$0.574508\pi$
$948$		0			0
$949$	5.96483	−	10.3314i	0.193627	−	0.335371i
$950$		0			0
$951$	−2.26746	+	29.3099i	−0.0735273	+	0.950438i
$952$		0			0
$953$		−	40.5612i		−	1.31391i	−0.753932	−	0.656953i	$-0.771845\pi$
$953$		−	40.5612i		−	1.31391i	0.753932	−	0.656953i	$-0.228155\pi$
$954$		0			0
$955$	−2.92355	−	1.68791i	−0.0946040	−	0.0546196i
$956$		0			0
$957$	4.02626	+	8.41237i	0.130150	+	0.271933i
$958$		0			0
$959$	−2.23145	+	6.10926i	−0.0720574	+	0.197278i
$960$		0			0
$961$	5.78241	+	10.0154i	0.186529	+	0.323078i
$962$		0			0
$963$	42.7175	+	34.4039i	1.37655	+	1.10865i
$964$		0			0
$965$	11.0905			0.357015
$966$		0			0
$967$	−37.6713			−1.21143			−0.605714	−	0.795682i	$-0.707112\pi$
$967$	−37.6713			−1.21143			−0.605714	+	0.795682i	$0.707112\pi$
$968$		0			0
$969$	9.46333	+	6.48542i	0.304006	+	0.208342i
$970$		0			0
$971$	−21.5452	−	37.3173i	−0.691418	−	1.19757i	−0.971373	−	0.237558i	$-0.923653\pi$
$971$	−21.5452	−	37.3173i	−0.691418	−	1.19757i	0.279956	−	0.960013i	$-0.409680\pi$
$972$		0			0
$973$	−7.33180	+	1.28420i	−0.235047	+	0.0411697i
$974$		0			0
$975$	6.04074	−	2.89117i	0.193458	−	0.0925915i
$976$		0			0
$977$	−19.7402	−	11.3970i	−0.631545	−	0.364622i	0.149805	−	0.988716i	$-0.452135\pi$
$977$	−19.7402	−	11.3970i	−0.631545	−	0.364622i	−0.781350	+	0.624093i	$0.785469\pi$
$978$		0			0
$979$		−	2.58910i		−	0.0827481i
$980$		0			0
$981$	51.8658	+	8.07315i	1.65595	+	0.257756i
$982$		0			0
$983$	22.5929	−	39.1321i	0.720602	−	1.24812i	−0.240157	−	0.970734i	$-0.577199\pi$
$983$	22.5929	−	39.1321i	0.720602	−	1.24812i	0.960759	−	0.277385i	$-0.0894677\pi$
$984$		0			0
$985$	14.0802	−	8.12923i	0.448634	−	0.259019i
$986$		0			0
$987$	−1.22154	−	12.6603i	−0.0388822	−	0.402981i
$988$		0			0
$989$	−3.45641	+	1.99556i	−0.109907	+	0.0634551i
$990$		0			0
$991$	−25.2760	+	43.7793i	−0.802919	+	1.39070i	0.114768	+	0.993392i	$0.463388\pi$
$991$	−25.2760	+	43.7793i	−0.802919	+	1.39070i	−0.917687	+	0.397304i	$0.869946\pi$
$992$		0			0
$993$	20.1265	+	1.55702i	0.638696	+	0.0494105i
$994$		0			0
$995$		−	1.24666i		−	0.0395219i
$996$		0			0
$997$	−22.5635	−	13.0271i	−0.714595	−	0.412571i	0.0981654	−	0.995170i	$-0.468703\pi$
$997$	−22.5635	−	13.0271i	−0.714595	−	0.412571i	−0.812760	+	0.582599i	$0.802036\pi$
$998$		0			0
$999$	11.6661	+	38.8138i	0.369099	+	1.22801i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	420.2.bh.b.101.4	yes	10
3.2	odd	2		420.2.bh.a.101.2	✓	10
5.2	odd	4		2100.2.bo.g.1949.2		20
5.3	odd	4		2100.2.bo.g.1949.9		20
5.4	even	2		2100.2.bi.j.101.2		10
7.3	odd	6		2940.2.d.b.881.10		10
7.4	even	3		2940.2.d.a.881.1		10
7.5	odd	6		420.2.bh.a.341.2	yes	10
15.2	even	4		2100.2.bo.h.1949.8		20
15.8	even	4		2100.2.bo.h.1949.3		20
15.14	odd	2		2100.2.bi.k.101.4		10
21.5	even	6	inner	420.2.bh.b.341.4	yes	10
21.11	odd	6		2940.2.d.b.881.9		10
21.17	even	6		2940.2.d.a.881.2		10
35.12	even	12		2100.2.bo.h.1349.3		20
35.19	odd	6		2100.2.bi.k.1601.4		10
35.33	even	12		2100.2.bo.h.1349.8		20
105.47	odd	12		2100.2.bo.g.1349.9		20
105.68	odd	12		2100.2.bo.g.1349.2		20
105.89	even	6		2100.2.bi.j.1601.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bh.a.101.2	✓	10	3.2	odd	2
420.2.bh.a.341.2	yes	10	7.5	odd	6
420.2.bh.b.101.4	yes	10	1.1	even	1	trivial
420.2.bh.b.341.4	yes	10	21.5	even	6	inner
2100.2.bi.j.101.2		10	5.4	even	2
2100.2.bi.j.1601.2		10	105.89	even	6
2100.2.bi.k.101.4		10	15.14	odd	2
2100.2.bi.k.1601.4		10	35.19	odd	6
2100.2.bo.g.1349.2		20	105.68	odd	12
2100.2.bo.g.1349.9		20	105.47	odd	12
2100.2.bo.g.1949.2		20	5.2	odd	4
2100.2.bo.g.1949.9		20	5.3	odd	4
2100.2.bo.h.1349.3		20	35.12	even	12
2100.2.bo.h.1349.8		20	35.33	even	12
2100.2.bo.h.1949.3		20	15.8	even	4
2100.2.bo.h.1949.8		20	15.2	even	4
2940.2.d.a.881.1		10	7.4	even	3
2940.2.d.a.881.2		10	21.17	even	6
2940.2.d.b.881.9		10	21.11	odd	6
2940.2.d.b.881.10		10	7.3	odd	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:	\( N \)	\(=\)	\( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	420.bh (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.979142 - 1.42873i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-0.456468 - 2.60608i) q^{7} +(-1.08256 - 2.79787i) q^{9} +O(q^{10})\)	\(q+(0.979142 - 1.42873i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-0.456468 - 2.60608i) q^{7} +(-1.08256 - 2.79787i) q^{9} +(0.698384 + 0.403212i) q^{11} -3.86649i q^{13} +(1.72689 + 0.133595i) q^{15} +(-1.05989 + 1.83578i) q^{17} +(2.70603 - 1.56233i) q^{19} +(-4.17034 - 1.89955i) q^{21} +(4.21989 - 2.43635i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-5.05739 - 1.19282i) q^{27} +6.67701i q^{29} +(5.65010 + 3.26209i) q^{31} +(1.25990 - 0.603003i) q^{33} +(2.02869 - 1.69835i) q^{35} +(-3.89991 - 6.75485i) q^{37} +(-5.52419 - 3.78585i) q^{39} -8.44841 q^{41} -0.819076 q^{43} +(1.88174 - 2.33646i) q^{45} +(1.38776 + 2.40368i) q^{47} +(-6.58327 + 2.37918i) q^{49} +(1.58506 + 3.31179i) q^{51} +(11.5565 + 6.67216i) q^{53} +0.806424i q^{55} +(0.417438 - 5.39594i) q^{57} +(2.86351 - 4.95974i) q^{59} +(1.79397 - 1.03575i) q^{61} +(-6.79730 + 4.09838i) q^{63} +(3.34848 - 1.93325i) q^{65} +(-5.45110 + 9.44157i) q^{67} +(0.650969 - 8.41464i) q^{69} +10.3850i q^{71} +(2.67203 + 1.54270i) q^{73} +(0.747749 + 1.56233i) q^{75} +(0.732012 - 2.00410i) q^{77} +(6.76342 + 11.7146i) q^{79} +(-6.65612 + 6.05773i) q^{81} +12.8948 q^{83} -2.11978 q^{85} +(9.53968 + 6.53775i) q^{87} +(-1.60530 - 2.78046i) q^{89} +(-10.0764 + 1.76493i) q^{91} +(10.1929 - 4.87844i) q^{93} +(2.70603 + 1.56233i) q^{95} +1.01388i q^{97} +(0.372090 - 2.39049i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{3} + 5 q^{5} - 5 q^{7} + 3 q^{9}+O(q^{10}) \) 10 * q + q^3 + 5 * q^5 - 5 * q^7 + 3 * q^9	\( 10 q + q^{3} + 5 q^{5} - 5 q^{7} + 3 q^{9} + 6 q^{11} + 2 q^{15} - 6 q^{17} + 3 q^{19} + 12 q^{21} - 24 q^{23} - 5 q^{25} - 8 q^{27} + 15 q^{31} - 4 q^{33} - q^{35} - q^{37} - 21 q^{39} + 8 q^{41} - 26 q^{43} + 3 q^{45} - 14 q^{47} - 13 q^{49} + 40 q^{51} + 24 q^{53} + 18 q^{57} + 42 q^{61} - 49 q^{63} - 9 q^{65} + 7 q^{67} + 14 q^{69} - 3 q^{73} + q^{75} + 26 q^{77} + q^{79} - 13 q^{81} + 8 q^{83} - 12 q^{85} + 8 q^{87} - 28 q^{89} - 11 q^{91} + 25 q^{93} + 3 q^{95} + 36 q^{99}+O(q^{100}) \) 10 * q + q^3 + 5 * q^5 - 5 * q^7 + 3 * q^9 + 6 * q^11 + 2 * q^15 - 6 * q^17 + 3 * q^19 + 12 * q^21 - 24 * q^23 - 5 * q^25 - 8 * q^27 + 15 * q^31 - 4 * q^33 - q^35 - q^37 - 21 * q^39 + 8 * q^41 - 26 * q^43 + 3 * q^45 - 14 * q^47 - 13 * q^49 + 40 * q^51 + 24 * q^53 + 18 * q^57 + 42 * q^61 - 49 * q^63 - 9 * q^65 + 7 * q^67 + 14 * q^69 - 3 * q^73 + q^75 + 26 * q^77 + q^79 - 13 * q^81 + 8 * q^83 - 12 * q^85 + 8 * q^87 - 28 * q^89 - 11 * q^91 + 25 * q^93 + 3 * q^95 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more