LMFDB - Embedded newform 420.2.bh.a.341.2

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			341.2
Root			$1.72689 - 0.133595i$ of defining polynomial
Character	$\chi$	$=$	420.341
Dual form			420.2.bh.a.101.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.747749 - 1.56233i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-0.456468 + 2.60608i) q^{7} +(-1.88174 + 2.33646i) q^{9} +O(q^{10})$	\(q+(-0.747749 - 1.56233i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-0.456468 + 2.60608i) q^{7} +(-1.88174 + 2.33646i) q^{9} +(-0.698384 + 0.403212i) q^{11} +3.86649i q^{13} +(1.72689 + 0.133595i) q^{15} +(1.05989 + 1.83578i) q^{17} +(2.70603 + 1.56233i) q^{19} +(4.41287 - 1.23554i) q^{21} +(-4.21989 - 2.43635i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(5.05739 + 1.19282i) q^{27} +6.67701i q^{29} +(5.65010 - 3.26209i) q^{31} +(1.15217 + 0.789604i) q^{33} +(-2.02869 - 1.69835i) q^{35} +(-3.89991 + 6.75485i) q^{37} +(6.04074 - 2.89117i) q^{39} +8.44841 q^{41} -0.819076 q^{43} +(-1.08256 - 2.79787i) q^{45} +(-1.38776 + 2.40368i) q^{47} +(-6.58327 - 2.37918i) q^{49} +(2.07556 - 3.02860i) q^{51} +(-11.5565 + 6.67216i) q^{53} -0.806424i q^{55} +(0.417438 - 5.39594i) q^{57} +(-2.86351 - 4.95974i) q^{59} +(1.79397 + 1.03575i) q^{61} +(-5.23004 - 5.97049i) q^{63} +(-3.34848 - 1.93325i) q^{65} +(-5.45110 - 9.44157i) q^{67} +(-0.650969 + 8.41464i) q^{69} +10.3850i q^{71} +(2.67203 - 1.54270i) q^{73} +(-0.979142 + 1.42873i) q^{75} +(-0.732012 - 2.00410i) q^{77} +(6.76342 - 11.7146i) q^{79} +(-1.91809 - 8.79323i) q^{81} -12.8948 q^{83} -2.11978 q^{85} +(10.4317 - 4.99273i) q^{87} +(1.60530 - 2.78046i) q^{89} +(-10.0764 - 1.76493i) q^{91} +(-9.32131 - 6.38809i) q^{93} +(-2.70603 + 1.56233i) q^{95} -1.01388i q^{97} +(0.372090 - 2.39049i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 10 q^{21} + 24 q^{23} - 5 q^{25} + 8 q^{27} + 15 q^{31} - 20 q^{33} + q^{35} - q^{37} + 15 q^{39} - 8 q^{41} - 26 q^{43} + 3 q^{45} + 14 q^{47} - 13 q^{49} - 44 q^{51} - 24 q^{53} + 18 q^{57} + 42 q^{61} - q^{63} + 9 q^{65} + 7 q^{67} - 14 q^{69} - 3 q^{73} - q^{75} - 26 q^{77} + q^{79} + 41 q^{81} - 8 q^{83} - 12 q^{85} - 26 q^{87} + 28 q^{89} - 11 q^{91} - 47 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 + 10 * q^21 + 24 * q^23 - 5 * q^25 + 8 * q^27 + 15 * q^31 - 20 * q^33 + q^35 - q^37 + 15 * q^39 - 8 * q^41 - 26 * q^43 + 3 * q^45 + 14 * q^47 - 13 * q^49 - 44 * q^51 - 24 * q^53 + 18 * q^57 + 42 * q^61 - q^63 + 9 * q^65 + 7 * q^67 - 14 * q^69 - 3 * q^73 - q^75 - 26 * q^77 + q^79 + 41 * q^81 - 8 * q^83 - 12 * q^85 - 26 * q^87 + 28 * q^89 - 11 * q^91 - 47 * q^93 - 3 * q^95 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$211$	$241$	$281$	$337$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

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
$3$	−0.747749	−	1.56233i	−0.431713	−	0.902011i
$3$	−0.747749	−	1.56233i	−0.431713	−	0.902011i
$4$		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
$9$	−1.88174	+	2.33646i	−0.627248	+	0.778820i
$10$		0			0
$11$	−0.698384	+	0.403212i	−0.210571	+	0.121573i	−0.601577	−	0.798815i	$-0.705461\pi$
$11$	−0.698384	+	0.403212i	−0.210571	+	0.121573i	0.391006	+	0.920388i	$0.372127\pi$
$12$		0			0
$13$			3.86649i			1.07237i	0.844100	+	0.536186i	$0.180136\pi$
$13$			3.86649i			1.07237i	−0.844100	+	0.536186i	$0.819864\pi$
$14$		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	$-0.0839127\pi$
$17$	1.05989	+	1.83578i	0.257061	+	0.445242i	−0.708393	+	0.705819i	$0.750579\pi$
$18$		0			0
$19$	2.70603	+	1.56233i	0.620807	+	0.358423i	0.777183	−	0.629275i	$-0.216648\pi$
$19$	2.70603	+	1.56233i	0.620807	+	0.358423i	−0.156376	+	0.987698i	$0.549981\pi$
$20$		0			0
$21$	4.41287	−	1.23554i	0.962968	−	0.269617i
$22$		0			0
$23$	−4.21989	−	2.43635i	−0.879908	−	0.508015i	−0.00927994	−	0.999957i	$-0.502954\pi$
$23$	−4.21989	−	2.43635i	−0.879908	−	0.508015i	−0.870628	+	0.491942i	$0.836287\pi$
$24$		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	0.102198	−	0.994764i	$-0.467413\pi$
$31$	5.65010	−	3.26209i	1.01479	−	0.585888i	0.912590	+	0.408876i	$0.134079\pi$
$32$		0			0
$33$	1.15217	+	0.789604i	0.200566	+	0.137452i
$34$		0			0
$35$	−2.02869	−	1.69835i	−0.342912	−	0.287074i
$36$		0			0
$37$	−3.89991	+	6.75485i	−0.641142	+	1.11049i	0.344036	+	0.938956i	$0.388206\pi$
$37$	−3.89991	+	6.75485i	−0.641142	+	1.11049i	−0.985178	+	0.171534i	$0.945128\pi$
$38$		0			0
$39$	6.04074	−	2.89117i	0.967292	−	0.462957i
$40$		0			0
$41$	8.44841			1.31942			0.659710	−	0.751520i	$-0.270679\pi$
$41$	8.44841			1.31942			0.659710	+	0.751520i	$0.270679\pi$
$42$		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
$45$	−1.08256	−	2.79787i	−0.161379	−	0.417081i
$46$		0			0
$47$	−1.38776	+	2.40368i	−0.202426	+	0.350612i	−0.949310	−	0.314343i	$-0.898216\pi$
$47$	−1.38776	+	2.40368i	−0.202426	+	0.350612i	0.746883	+	0.664955i	$0.231549\pi$
$48$		0			0
$49$	−6.58327	−	2.37918i	−0.940468	−	0.339883i
$50$		0			0
$51$	2.07556	−	3.02860i	0.290637	−	0.424088i
$52$		0			0
$53$	−11.5565	+	6.67216i	−1.58741	+	0.916492i	−0.593678	+	0.804703i	$0.702325\pi$
$53$	−11.5565	+	6.67216i	−1.58741	+	0.916492i	−0.993732	+	0.111789i	$0.964342\pi$
$54$		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	$-0.288268\pi$
$59$	−2.86351	−	4.95974i	−0.372797	−	0.645703i	−0.989995	+	0.141105i	$0.954935\pi$
$60$		0			0
$61$	1.79397	+	1.03575i	0.229694	+	0.132614i	0.610431	−	0.792070i	$-0.290996\pi$
$61$	1.79397	+	1.03575i	0.229694	+	0.132614i	−0.380737	+	0.924683i	$0.624330\pi$
$62$		0			0
$63$	−5.23004	−	5.97049i	−0.658923	−	0.752211i
$64$		0			0
$65$	−3.34848	−	1.93325i	−0.415328	−	0.239790i
$66$		0			0
$67$	−5.45110	−	9.44157i	−0.665957	−	1.15347i	−0.979025	−	0.203741i	$-0.934690\pi$
$67$	−5.45110	−	9.44157i	−0.665957	−	1.15347i	0.313067	−	0.949731i	$-0.398643\pi$
$68$		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	−0.335413	−	0.942071i	$-0.608876\pi$
$73$	2.67203	−	1.54270i	0.312737	−	0.180559i	0.648151	+	0.761512i	$0.275543\pi$
$74$		0			0
$75$	−0.979142	+	1.42873i	−0.113062	+	0.164976i
$76$		0			0
$77$	−0.732012	−	2.00410i	−0.0834205	−	0.228388i
$78$		0			0
$79$	6.76342	−	11.7146i	0.760944	−	1.31799i	−0.181420	−	0.983406i	$-0.558069\pi$
$79$	6.76342	−	11.7146i	0.760944	−	1.31799i	0.942364	−	0.334589i	$-0.108597\pi$
$80$		0			0
$81$	−1.91809	−	8.79323i	−0.213121	−	0.977026i
$82$		0			0
$83$	−12.8948			−1.41539			−0.707694	−	0.706519i	$-0.750265\pi$
$83$	−12.8948			−1.41539			−0.707694	+	0.706519i	$0.750265\pi$
$84$		0			0
$85$	−2.11978			−0.229922
$86$		0			0
$87$	10.4317	−	4.99273i	1.11839	−	0.535277i
$88$		0			0
$89$	1.60530	−	2.78046i	0.170161	−	0.294728i	−0.768315	−	0.640072i	$-0.778904\pi$
$89$	1.60530	−	2.78046i	0.170161	−	0.294728i	0.938476	+	0.345344i	$0.112238\pi$
$90$		0			0
$91$	−10.0764	−	1.76493i	−1.05629	−	0.185015i
$92$		0			0
$93$	−9.32131	−	6.38809i	−0.966574	−	0.662414i
$94$		0			0
$95$	−2.70603	+	1.56233i	−0.277633	+	0.160292i
$96$		0			0
$97$		−	1.01388i		−	0.102944i	−0.998674	−	0.0514721i	$-0.983609\pi$
$97$		−	1.01388i		−	0.102944i	0.998674	−	0.0514721i	$-0.0163913\pi$
$98$		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	$-0.0267040\pi$
$101$	4.27796	+	7.40965i	0.425673	+	0.737288i	−0.570810	+	0.821082i	$0.693371\pi$
$102$		0			0
$103$	8.46835	+	4.88921i	0.834411	+	0.481748i	0.855361	−	0.518033i	$-0.173336\pi$
$103$	8.46835	+	4.88921i	0.834411	+	0.481748i	−0.0209492	+	0.999781i	$0.506669\pi$
$104$		0			0
$105$	−1.13643	+	4.43943i	−0.110904	+	0.433244i
$106$		0			0
$107$	15.8336	+	9.14150i	1.53069	+	0.883743i	0.999330	+	0.0365946i	$0.0116510\pi$
$107$	15.8336	+	9.14150i	1.53069	+	0.883743i	0.531357	+	0.847148i	$0.321682\pi$
$108$		0			0
$109$	−8.74840	−	15.1527i	−0.837945	−	1.45136i	−0.891610	−	0.452804i	$-0.850424\pi$
$109$	−8.74840	−	15.1527i	−0.837945	−	1.45136i	0.0536658	−	0.998559i	$-0.482909\pi$
$110$		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
$117$	−9.03391	−	7.27575i	−0.835185	−	0.672643i
$118$		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
$123$	−6.31729	−	13.1992i	−0.569611	−	1.19013i
$124$		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
$129$	0.612463	+	1.27967i	0.0539244	+	0.112668i
$130$		0			0
$131$	5.93761	−	10.2842i	0.518772	−	0.898539i	−0.480990	−	0.876726i	$-0.659723\pi$
$131$	5.93761	−	10.2842i	0.518772	−	0.898539i	0.999762	−	0.0218131i	$-0.00694387\pi$
$132$		0			0
$133$	−5.30677	+	6.33898i	−0.460155	+	0.549659i
$134$		0			0
$135$	−3.56170	+	3.78342i	−0.306543	+	0.325625i
$136$		0			0
$137$	2.12894	−	1.22915i	0.181888	−	0.105013i	−0.406291	−	0.913744i	$-0.633178\pi$
$137$	2.12894	−	1.22915i	0.181888	−	0.105013i	0.588179	+	0.808730i	$0.299845\pi$
$138$		0			0
$139$			2.81335i			0.238625i	0.992857	+	0.119313i	$0.0380691\pi$
$139$			2.81335i			0.238625i	−0.992857	+	0.119313i	$0.961931\pi$
$140$		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
$147$	1.20557	+	12.0643i	0.0994339	+	0.995044i
$148$		0			0
$149$	12.8234	+	7.40357i	1.05053	+	0.606524i	0.922798	−	0.385285i	$-0.125897\pi$
$149$	12.8234	+	7.40357i	1.05053	+	0.606524i	0.127733	+	0.991809i	$0.459230\pi$
$150$		0			0
$151$	0.427898	+	0.741141i	0.0348218	+	0.0603132i	0.882911	−	0.469540i	$-0.155580\pi$
$151$	0.427898	+	0.741141i	0.0348218	+	0.0603132i	−0.848089	+	0.529853i	$0.822247\pi$
$152$		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	0.725547	−	0.688173i	$-0.241587\pi$
$157$	21.1042	−	12.1845i	1.68430	−	0.972428i	0.958748	−	0.284256i	$-0.0917465\pi$
$158$		0			0
$159$	19.0655	+	13.0660i	1.51199	+	1.03620i
$160$		0			0
$161$	8.27557	−	9.88524i	0.652207	−	0.779066i
$162$		0			0
$163$	−0.789402	+	1.36728i	−0.0618307	+	0.107094i	−0.895284	−	0.445496i	$-0.853027\pi$
$163$	−0.789402	+	1.36728i	−0.0618307	+	0.107094i	0.833453	+	0.552590i	$0.186361\pi$
$164$		0			0
$165$	−1.25990	+	0.603003i	−0.0980831	+	0.0469437i
$166$		0			0
$167$	−16.9264			−1.30980			−0.654902	−	0.755714i	$-0.727290\pi$
$167$	−16.9264			−1.30980			−0.654902	+	0.755714i	$0.727290\pi$
$168$		0			0
$169$	−1.94978			−0.149983
$170$		0			0
$171$	−8.74238	+	3.38264i	−0.668546	+	0.258677i
$172$		0			0
$173$	2.33037	−	4.03633i	0.177175	−	0.306876i	−0.763737	−	0.645528i	$-0.776637\pi$
$173$	2.33037	−	4.03633i	0.177175	−	0.306876i	0.940912	+	0.338652i	$0.109971\pi$
$174$		0			0
$175$	2.48516	−	0.907726i	0.187861	−	0.0686176i
$176$		0			0
$177$	−5.60756	+	8.18238i	−0.421490	+	0.615025i
$178$		0			0
$179$	−3.11674	+	1.79945i	−0.232956	+	0.134497i	−0.611935	−	0.790908i	$-0.709609\pi$
$179$	−3.11674	+	1.79945i	−0.232956	+	0.134497i	0.378979	+	0.925405i	$0.376275\pi$
$180$		0			0
$181$			22.5821i			1.67851i	0.543737	+	0.839256i	$0.317009\pi$
$181$			22.5821i			1.67851i	−0.543737	+	0.839256i	$0.682991\pi$
$182$		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
$189$	−5.41711	+	12.6355i	−0.394037	+	0.919095i
$190$		0			0
$191$	2.92355	+	1.68791i	0.211541	+	0.122133i	0.602027	−	0.798475i	$-0.294360\pi$
$191$	2.92355	+	1.68791i	0.211541	+	0.122133i	−0.390486	+	0.920609i	$0.627693\pi$
$192$		0			0
$193$	5.54524	+	9.60463i	0.399155	+	0.691357i	0.993622	−	0.112763i	$-0.0359702\pi$
$193$	5.54524	+	9.60463i	0.399155	+	0.691357i	−0.594467	+	0.804120i	$0.702637\pi$
$194$		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	−0.537779	−	0.843086i	$-0.680736\pi$
$199$	−1.07964	+	0.623332i	−0.0765338	+	0.0441868i	0.461245	+	0.887273i	$0.347403\pi$
$200$		0			0
$201$	−10.6748	+	15.5763i	−0.752942	+	1.09867i
$202$		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
$207$	13.6332	−	5.27501i	0.947573	−	0.366639i
$208$		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
$213$	16.2249	−	7.76541i	1.11171	−	0.532077i
$214$		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
$219$	−4.40821	−	3.02104i	−0.297879	−	0.204143i
$220$		0			0
$221$	−7.09803	+	4.09805i	−0.477465	+	0.275665i
$222$		0			0
$223$			20.9369i			1.40204i	0.713143	+	0.701019i	$0.247271\pi$
$223$			20.9369i			1.40204i	−0.713143	+	0.701019i	$0.752729\pi$
$224$		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	$-0.118076\pi$
$227$	2.29103	+	3.96818i	0.152061	+	0.263377i	−0.779924	+	0.625874i	$0.784742\pi$
$228$		0			0
$229$	0.845272	+	0.488018i	0.0558572	+	0.0322492i	0.527669	−	0.849450i	$-0.323066\pi$
$229$	0.845272	+	0.488018i	0.0558572	+	0.0322492i	−0.471811	+	0.881700i	$0.656400\pi$
$230$		0			0
$231$	−2.58370	+	2.64220i	−0.169995	+	0.173844i
$232$		0			0
$233$	17.2382	+	9.95247i	1.12931	+	0.652008i	0.943762	−	0.330627i	$-0.107260\pi$
$233$	17.2382	+	9.95247i	1.12931	+	0.652008i	0.185550	+	0.982635i	$0.440593\pi$
$234$		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	−0.0981065	−	0.995176i	$-0.531279\pi$
$241$	11.0949	−	6.40567i	0.714688	−	0.412625i	0.812794	+	0.582551i	$0.197945\pi$
$242$		0			0
$243$	−12.3037	+	9.57181i	−0.789281	+	0.614032i
$244$		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
$249$	9.64207	+	20.1459i	0.611042	+	1.27670i
$250$		0			0
$251$	10.3349			0.652335			0.326167	−	0.945312i	$-0.394243\pi$
$251$	10.3349			0.652335			0.326167	+	0.945312i	$0.394243\pi$
$252$		0			0
$253$	3.92947			0.247044
$254$		0			0
$255$	1.58506	+	3.31179i	0.0992603	+	0.207392i
$256$		0			0
$257$	15.2527	−	26.4185i	0.951439	−	1.64794i	0.209124	−	0.977889i	$-0.432939\pi$
$257$	15.2527	−	26.4185i	0.951439	−	1.64794i	0.742315	−	0.670052i	$-0.233728\pi$
$258$		0			0
$259$	−15.8235	−	13.2469i	−0.983223	−	0.823119i
$260$		0			0
$261$	−15.6006	−	12.5644i	−0.965651	−	0.777718i
$262$		0			0
$263$	17.9054	−	10.3377i	1.10409	−	0.637447i	0.166799	−	0.985991i	$-0.446657\pi$
$263$	17.9054	−	10.3377i	1.10409	−	0.637447i	0.937293	+	0.348543i	$0.113324\pi$
$264$		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	0.944566	+	0.328322i	$0.106483\pi$
$269$	12.4095	+	21.4938i	0.756618	+	1.31050i	−0.187948	+	0.982179i	$0.560184\pi$
$270$		0			0
$271$	18.8571	+	10.8871i	1.14548	+	0.661346i	0.947783	−	0.318916i	$-0.103319\pi$
$271$	18.8571	+	10.8871i	1.14548	+	0.661346i	0.197702	+	0.980262i	$0.436652\pi$
$272$		0			0
$273$	4.77720	+	17.0623i	0.289129	+	1.03266i
$274$		0			0
$275$	0.698384	+	0.403212i	0.0421141	+	0.0243146i
$276$		0			0
$277$	−7.61126	−	13.1831i	−0.457316	−	0.792095i	0.541502	−	0.840699i	$-0.317856\pi$
$277$	−7.61126	−	13.1831i	−0.457316	−	0.792095i	−0.998818	+	0.0486048i	$0.984523\pi$
$278$		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	−0.993245	−	0.116033i	$-0.962982\pi$
$283$	−23.3730	+	13.4944i	−1.38938	+	0.802159i	−0.396135	+	0.918192i	$0.629649\pi$
$284$		0			0
$285$	4.46430	+	3.05948i	0.264443	+	0.181228i
$286$		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
$291$	−1.58402	+	0.758129i	−0.0928567	+	0.0444423i
$292$		0			0
$293$	14.4450			0.843887			0.421944	−	0.906622i	$-0.361348\pi$
$293$	14.4450			0.843887			0.421944	+	0.906622i	$0.361348\pi$
$294$		0			0
$295$	5.72702			0.333440
$296$		0			0
$297$	−4.01296	+	1.20616i	−0.232855	+	0.0699884i
$298$		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
$303$	8.37747	−	12.2241i	0.481273	−	0.702259i
$304$		0			0
$305$	−1.79397	+	1.03575i	−0.102722	+	0.0593067i
$306$		0			0
$307$			9.34543i			0.533372i	0.963783	+	0.266686i	$0.0859287\pi$
$307$			9.34543i			0.533372i	−0.963783	+	0.266686i	$0.914071\pi$
$308$		0			0
$309$	1.30635	−	16.8862i	0.0743154	−	0.960625i
$310$		0			0
$311$	−14.6664	−	25.4029i	−0.831654	−	1.44047i	−0.896726	−	0.442586i	$-0.854061\pi$
$311$	−14.6664	−	25.4029i	−0.831654	−	1.44047i	0.0650722	−	0.997881i	$-0.479272\pi$
$312$		0			0
$313$	9.55728	+	5.51790i	0.540209	+	0.311890i	0.745164	−	0.666881i	$-0.232371\pi$
$313$	9.55728	+	5.51790i	0.540209	+	0.311890i	−0.204954	+	0.978772i	$0.565705\pi$
$314$		0			0
$315$	7.78561	−	1.54410i	0.438670	−	0.0870003i
$316$		0			0
$317$	14.6987	+	8.48631i	0.825563	+	0.476639i	0.852331	−	0.523003i	$-0.175188\pi$
$317$	14.6987	+	8.48631i	0.825563	+	0.476639i	−0.0267682	+	0.999642i	$0.508522\pi$
$318$		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
$327$	−17.1318	+	24.9983i	−0.947393	+	1.38241i
$328$		0			0
$329$	−5.63070	−	4.71382i	−0.310430	−	0.259881i
$330$		0			0
$331$	5.82739	−	10.0933i	0.320302	−	0.554780i	−0.660248	−	0.751048i	$-0.729549\pi$
$331$	5.82739	−	10.0933i	0.320302	−	0.554780i	0.980550	+	0.196268i	$0.0628822\pi$
$332$		0			0
$333$	−8.44380	−	21.8229i	−0.462717	−	1.19589i
$334$		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
$339$	−10.8741	+	5.20449i	−0.590602	+	0.282669i
$340$		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
$345$	−6.96181	−	4.77108i	−0.374811	−	0.256866i
$346$		0			0
$347$	−1.38025	+	0.796887i	−0.0740956	+	0.0427791i	−0.536590	−	0.843843i	$-0.680288\pi$
$347$	−1.38025	+	0.796887i	−0.0740956	+	0.0427791i	0.462494	+	0.886622i	$0.346955\pi$
$348$		0			0
$349$		−	15.4812i		−	0.828690i	−0.910120	−	0.414345i	$-0.864011\pi$
$349$		−	15.4812i		−	0.828690i	0.910120	−	0.414345i	$-0.135989\pi$
$350$		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	$-0.0560136\pi$
$353$	6.40056	+	11.0861i	0.340668	+	0.590054i	−0.643889	+	0.765119i	$0.722680\pi$
$354$		0			0
$355$	−8.99371	−	5.19252i	−0.477337	−	0.275590i
$356$		0			0
$357$	6.94533	+	6.79153i	0.367586	+	0.359446i
$358$		0			0
$359$	−5.66697	−	3.27183i	−0.299091	−	0.172680i	0.342943	−	0.939356i	$-0.388576\pi$
$359$	−5.66697	−	3.27183i	−0.299091	−	0.172680i	−0.642035	+	0.766676i	$0.721909\pi$
$360$		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	−0.837497	−	0.546442i	$-0.815982\pi$
$367$	−15.0004	+	8.66046i	−0.783012	+	0.452072i	0.0544847	+	0.998515i	$0.482648\pi$
$368$		0			0
$369$	−15.8977	+	19.7394i	−0.827603	+	1.02759i
$370$		0			0
$371$	−12.1130	−	33.1628i	−0.628875	−	1.72173i
$372$		0			0
$373$	0.497933	−	0.862445i	0.0257820	−	0.0446557i	−0.852847	−	0.522162i	$-0.825126\pi$
$373$	0.497933	−	0.862445i	0.0257820	−	0.0446557i	0.878629	+	0.477506i	$0.158459\pi$
$374$		0			0
$375$	−0.747749	−	1.56233i	−0.0386136	−	0.0806783i
$376$		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
$381$	−5.81105	−	12.1415i	−0.297709	−	0.622026i
$382$		0			0
$383$	9.93736	−	17.2120i	0.507776	−	0.879493i	−0.492184	−	0.870491i	$-0.663801\pi$
$383$	9.93736	−	17.2120i	0.507776	−	0.879493i	0.999959	−	0.00900178i	$-0.00286539\pi$
$384$		0			0
$385$	2.10160	+	0.368107i	0.107108	+	0.0187605i
$386$		0			0
$387$	1.54129	−	1.91374i	0.0783482	−	0.0972808i
$388$		0			0
$389$	1.56923	−	0.905994i	0.0795630	−	0.0459357i	−0.459691	−	0.888079i	$-0.652040\pi$
$389$	1.56923	−	0.905994i	0.0795630	−	0.0459357i	0.539254	+	0.842143i	$0.318706\pi$
$390$		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	−0.999897	−	0.0143590i	$-0.995429\pi$
$397$	−30.1320	−	17.3967i	−1.51228	−	0.873116i	−0.512384	−	0.858757i	$-0.671237\pi$
$398$		0			0
$399$	13.8717	+	3.55095i	0.694453	+	0.177770i
$400$		0			0
$401$	−32.5121	−	18.7709i	−1.62358	−	0.937374i	−0.985952	−	0.167029i	$-0.946583\pi$
$401$	−32.5121	−	18.7709i	−1.62358	−	0.937374i	−0.637627	−	0.770345i	$-0.720084\pi$
$402$		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	−0.417552	−	0.908653i	$-0.637112\pi$
$409$	3.24769	−	1.87505i	0.160588	−	0.0927154i	0.578140	+	0.815937i	$0.303779\pi$
$410$		0			0
$411$	−3.51225	−	2.40702i	−0.173246	−	0.118729i
$412$		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
$417$	4.39538	−	2.10368i	0.215242	−	0.103018i
$418$		0			0
$419$	−30.0547			−1.46827			−0.734134	−	0.679005i	$-0.762411\pi$
$419$	−30.0547			−1.46827			−0.734134	+	0.679005i	$0.762411\pi$
$420$		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
$423$	−3.00468	−	7.76556i	−0.146093	−	0.377574i
$424$		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
$429$	−3.05300	+	4.45484i	−0.147400	+	0.215082i
$430$		0			0
$431$	−31.7400	+	18.3251i	−1.52886	+	0.882688i	−0.529451	+	0.848340i	$0.677602\pi$
$431$	−31.7400	+	18.3251i	−1.52886	+	0.882688i	−0.999410	+	0.0343478i	$0.989065\pi$
$432$		0			0
$433$		−	36.4397i		−	1.75118i	−0.483057	−	0.875589i	$-0.660474\pi$
$433$		−	36.4397i		−	1.75118i	0.483057	−	0.875589i	$-0.339526\pi$
$434$		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	0.297833	−	0.954618i	$-0.403736\pi$
$439$	−7.96135	−	4.59649i	−0.379975	−	0.219378i	−0.677807	+	0.735240i	$0.737070\pi$
$440$		0			0
$441$	17.9469	−	10.9045i	0.854614	−	0.519264i
$442$		0			0
$443$	20.7332	+	11.9703i	0.985063	+	0.568727i	0.903795	−	0.427966i	$-0.140770\pi$
$443$	20.7332	+	11.9703i	0.985063	+	0.568727i	0.0812683	+	0.996692i	$0.474103\pi$
$444$		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
$453$	0.837945	−	1.22270i	0.0393701	−	0.0574476i
$454$		0			0
$455$	6.56667	−	7.84394i	0.307850	−	0.367729i
$456$		0			0
$457$	−3.33585	+	5.77786i	−0.156044	+	0.270277i	−0.933439	−	0.358737i	$-0.883208\pi$
$457$	−3.33585	+	5.77786i	−0.156044	+	0.270277i	0.777394	+	0.629013i	$0.216541\pi$
$458$		0			0
$459$	3.17052	+	10.5485i	0.147987	+	0.492362i
$460$		0			0
$461$	26.6895			1.24305			0.621527	−	0.783393i	$-0.286513\pi$
$461$	26.6895			1.24305			0.621527	+	0.783393i	$0.286513\pi$
$462$		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
$465$	10.1929	−	4.87844i	0.472685	−	0.226232i
$466$		0			0
$467$	0.549726	−	0.952153i	0.0254383	−	0.0440604i	−0.853026	−	0.521868i	$-0.825235\pi$
$467$	0.549726	−	0.952153i	0.0254383	−	0.0440604i	0.878464	+	0.477808i	$0.158569\pi$
$468$		0			0
$469$	27.0937	−	9.89620i	1.25107	−	0.456964i
$470$		0			0
$471$	−34.8168	−	23.8607i	−1.60427	−	1.09944i
$472$		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	$-0.0643180\pi$
$479$	6.91657	+	11.9798i	0.316026	+	0.547373i	−0.663629	+	0.748062i	$0.730985\pi$
$480$		0			0
$481$	−26.1176	−	15.0790i	−1.19086	−	0.687543i
$482$		0			0
$483$	−21.6320	−	5.53749i	−0.984292	−	0.251964i
$484$		0			0
$485$	0.878048	+	0.506941i	0.0398701	+	0.0230190i
$486$		0			0
$487$	15.8416	+	27.4385i	0.717854	+	1.24336i	0.961849	+	0.273582i	$0.0882086\pi$
$487$	15.8416	+	27.4385i	0.717854	+	1.24336i	−0.243995	+	0.969776i	$0.578458\pi$
$488$		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
$495$	1.88418	+	1.51748i	0.0846875	+	0.0682058i
$496$		0			0
$497$	−27.0642	−	4.74044i	−1.21400	−	0.212638i
$498$		0			0
$499$	5.50065	−	9.52740i	0.246243	−	0.426505i	−0.716237	−	0.697857i	$-0.754137\pi$
$499$	5.50065	−	9.52740i	0.246243	−	0.426505i	0.962480	+	0.271352i	$0.0874706\pi$
$500$		0			0
$501$	12.6567	+	26.4446i	0.565460	+	1.18146i
$502$		0			0
$503$	20.2246			0.901772			0.450886	−	0.892582i	$-0.351108\pi$
$503$	20.2246			0.901772			0.450886	+	0.892582i	$0.351108\pi$
$504$		0			0
$505$	−8.55593			−0.380734
$506$		0			0
$507$	1.45795	+	3.04620i	0.0647497	+	0.135287i
$508$		0			0
$509$	5.24557	−	9.08560i	0.232506	−	0.402712i	−0.726039	−	0.687654i	$-0.758641\pi$
$509$	5.24557	−	9.08560i	0.232506	−	0.402712i	0.958545	+	0.284941i	$0.0919742\pi$
$510$		0			0
$511$	2.80069	+	7.66771i	0.123895	+	0.339199i
$512$		0			0
$513$	11.8219	+	11.1291i	0.521949	+	0.491362i
$514$		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	$-0.251353\pi$
$521$	−6.00130	−	10.3946i	−0.262922	−	0.455394i	−0.967017	+	0.254712i	$0.918019\pi$
$522$		0			0
$523$	−7.74038	−	4.46891i	−0.338463	−	0.195412i	0.321129	−	0.947035i	$-0.395938\pi$
$523$	−7.74038	−	4.46891i	−0.338463	−	0.195412i	−0.659592	+	0.751624i	$0.729271\pi$
$524$		0			0
$525$	−3.27644	−	3.20389i	−0.142996	−	0.139829i
$526$		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
$537$	5.14187	+	3.52383i	0.221888	+	0.152065i
$538$		0			0
$539$	5.55697	−	0.992874i	0.239356	−	0.0427661i
$540$		0			0
$541$	−15.9695	+	27.6599i	−0.686581	+	1.18919i	0.286357	+	0.958123i	$0.407556\pi$
$541$	−15.9695	+	27.6599i	−0.686581	+	1.18919i	−0.972937	+	0.231069i	$0.925778\pi$
$542$		0			0
$543$	35.2806	−	16.8857i	1.51404	−	0.724635i
$544$		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
$549$	−5.79577	+	2.24252i	−0.247357	+	0.0957085i
$550$		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
$555$	−7.63714	+	11.1439i	−0.324179	+	0.473031i
$556$		0			0
$557$	−9.17988	+	5.30000i	−0.388964	+	0.224568i	−0.681711	−	0.731621i	$-0.738764\pi$
$557$	−9.17988	+	5.30000i	−0.388964	+	0.224568i	0.292747	+	0.956190i	$0.405431\pi$
$558$		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	$-0.151261\pi$
$563$	1.14796	+	1.98833i	0.0483808	+	0.0837980i	−0.840821	+	0.541313i	$0.817927\pi$
$564$		0			0
$565$	6.02772	+	3.48010i	0.253588	+	0.146409i
$566$		0			0
$567$	23.7914	−	0.984852i	0.999144	−	0.0413599i
$568$		0			0
$569$	24.1648	+	13.9515i	1.01304	+	0.584878i	0.912080	−	0.410012i	$-0.134476\pi$
$569$	24.1648	+	13.9515i	1.01304	+	0.584878i	0.100959	+	0.994891i	$0.467809\pi$
$570$		0			0
$571$	3.11649	+	5.39791i	0.130421	+	0.225896i	0.923839	−	0.382782i	$-0.125034\pi$
$571$	3.11649	+	5.39791i	0.130421	+	0.225896i	−0.793418	+	0.608677i	$0.791700\pi$
$572$		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	−0.241687	−	0.970354i	$-0.577701\pi$
$577$	11.4776	−	6.62662i	0.477820	−	0.275870i	0.719508	+	0.694484i	$0.244368\pi$
$578$		0			0
$579$	10.8592	−	15.8453i	0.451291	−	0.658510i
$580$		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
$585$	10.8179	−	4.18572i	0.447267	−	0.173058i
$586$		0			0
$587$	−18.6209			−0.768568			−0.384284	−	0.923215i	$-0.625552\pi$
$587$	−18.6209			−0.768568			−0.384284	+	0.923215i	$0.625552\pi$
$588$		0			0
$589$	20.3858			0.839982
$590$		0			0
$591$	−25.4011	+	12.1572i	−1.04486	+	0.500082i
$592$		0			0
$593$	1.37822	−	2.38715i	0.0565967	−	0.0980284i	−0.836339	−	0.548213i	$-0.815308\pi$
$593$	1.37822	−	2.38715i	0.0565967	−	0.0980284i	0.892936	+	0.450184i	$0.148642\pi$
$594$		0			0
$595$	0.967610	−	5.52430i	0.0396681	−	0.226474i
$596$		0			0
$597$	1.78115	+	1.22066i	0.0728976	+	0.0499583i
$598$		0			0
$599$	−16.2530	+	9.38368i	−0.664080	+	0.383407i	−0.793830	−	0.608140i	$-0.791916\pi$
$599$	−16.2530	+	9.38368i	−0.664080	+	0.383407i	0.129750	+	0.991547i	$0.458583\pi$
$600$		0			0
$601$			16.5669i			0.675779i	0.941186	+	0.337890i	$0.109713\pi$
$601$			16.5669i			0.675779i	−0.941186	+	0.337890i	$0.890287\pi$
$602$		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	0.955122	−	0.296213i	$-0.0957240\pi$
$607$	28.9773	+	16.7301i	1.17615	+	0.679053i	0.221032	+	0.975266i	$0.429057\pi$
$608$		0			0
$609$	8.24971	+	29.4648i	0.334295	+	1.19397i
$610$		0			0
$611$	−9.29381	−	5.36578i	−0.375987	−	0.217076i
$612$		0			0
$613$	18.7772	+	32.5231i	0.758404	+	1.31359i	0.943664	+	0.330905i	$0.107354\pi$
$613$	18.7772	+	32.5231i	0.758404	+	1.31359i	−0.185260	+	0.982690i	$0.559313\pi$
$614$		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	−0.889888	−	0.456179i	$-0.849218\pi$
$619$	−23.3812	+	13.4991i	−0.939770	+	0.542576i	−0.0498816	+	0.998755i	$0.515884\pi$
$620$		0			0
$621$	−18.4355	−	17.3551i	−0.739791	−	0.696438i
$622$		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
$627$	1.88418	+	3.93676i	0.0752468	+	0.157219i
$628$		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
$633$	5.72376	+	11.9591i	0.227499	+	0.475331i
$634$		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
$639$	−24.2642	−	19.5420i	−0.959878	−	0.773069i
$640$		0			0
$641$	−26.6664	+	15.3959i	−1.05326	+	0.608100i	−0.923560	−	0.383453i	$-0.874735\pi$
$641$	−26.6664	+	15.3959i	−1.05326	+	0.608100i	−0.129700	+	0.991553i	$0.541401\pi$
$642$		0			0
$643$		−	3.42929i		−	0.135238i	−0.997711	−	0.0676189i	$-0.978460\pi$
$643$		−	3.42929i		−	0.135238i	0.997711	−	0.0676189i	$-0.0215402\pi$
$644$		0			0
$645$	−1.41445	−	0.109424i	−0.0556941	−	0.00430858i
$646$		0			0
$647$	25.2967	+	43.8152i	0.994516	+	1.72255i	0.587828	+	0.808986i	$0.299983\pi$
$647$	25.2967	+	43.8152i	0.994516	+	1.72255i	0.406689	+	0.913567i	$0.366683\pi$
$648$		0			0
$649$	3.99966	+	2.30920i	0.157000	+	0.0906441i
$650$		0			0
$651$	20.9027	−	21.3761i	0.819243	−	0.837795i
$652$		0			0
$653$	−4.57643	−	2.64220i	−0.179090	−	0.103397i	0.407775	−	0.913082i	$-0.366305\pi$
$653$	−4.57643	−	2.64220i	−0.179090	−	0.103397i	−0.586865	+	0.809685i	$0.699638\pi$
$654$		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	−0.937180	−	0.348845i	$-0.886574\pi$
$661$	−28.3751	+	16.3823i	−1.10366	+	0.637199i	−0.166481	+	0.986045i	$0.553241\pi$
$662$		0			0
$663$	11.7101	+	8.02515i	0.454781	+	0.311671i
$664$		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
$669$	32.7103	−	15.6555i	1.26465	−	0.605278i
$670$		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
$675$	−1.49569	−	4.97624i	−0.0575690	−	0.191535i
$676$		0			0
$677$	−9.58044	+	16.5938i	−0.368206	+	0.637752i	−0.989285	−	0.145996i	$-0.953361\pi$
$677$	−9.58044	+	16.5938i	−0.368206	+	0.637752i	0.621079	+	0.783748i	$0.286695\pi$
$678$		0			0
$679$	2.64225	+	0.462805i	0.101400	+	0.0177608i
$680$		0			0
$681$	4.48649	−	6.54654i	0.171923	−	0.250864i
$682$		0			0
$683$	−25.0821	+	14.4812i	−0.959741	+	0.554107i	−0.896093	−	0.443866i	$-0.853607\pi$
$683$	−25.0821	+	14.4812i	−0.959741	+	0.554107i	−0.0636479	+	0.997972i	$0.520273\pi$
$684$		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	0.999999	+	0.00118303i	$0.000376571\pi$
$691$	39.4572	+	22.7806i	1.50102	+	0.866616i	0.501024	+	0.865433i	$0.332957\pi$
$692$		0			0
$693$	6.05995	+	2.06088i	0.230198	+	0.0782862i
$694$		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
$705$	−2.71764	+	3.96549i	−0.102352	+	0.149349i
$706$		0			0
$707$	−21.2629	+	7.76643i	−0.799672	+	0.292087i
$708$		0			0
$709$	−9.88537	+	17.1220i	−0.371253	+	0.643029i	−0.989759	−	0.142752i	$-0.954405\pi$
$709$	−9.88537	+	17.1220i	−0.371253	+	0.643029i	0.618506	+	0.785780i	$0.287738\pi$
$710$		0			0
$711$	14.6436	+	37.8463i	0.549180	+	1.41935i
$712$		0			0
$713$	−31.7904			−1.19056
$714$		0			0
$715$	3.11804			0.116608
$716$		0			0
$717$	−44.1675	+	21.1391i	−1.64947	+	0.789454i
$718$		0			0
$719$	0.740641	−	1.28283i	0.0276212	−	0.0478414i	−0.851884	−	0.523730i	$-0.824540\pi$
$719$	0.740641	−	1.28283i	0.0276212	−	0.0478414i	0.879506	+	0.475889i	$0.157873\pi$
$720$		0			0
$721$	−16.6072	+	19.8374i	−0.618484	+	0.738784i
$722$		0			0
$723$	−18.3040	−	12.5441i	−0.680733	−	0.466521i
$724$		0			0
$725$	5.78246	−	3.33851i	0.214755	−	0.123989i
$726$		0			0
$727$		−	6.35193i		−	0.235580i	−0.993039	−	0.117790i	$-0.962419\pi$
$727$		−	6.35193i		−	0.235580i	0.993039	−	0.117790i	$-0.0375810\pi$
$728$		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	−0.283857	−	0.958866i	$-0.591614\pi$
$733$	−34.0100	−	19.6357i	−1.25619	−	0.725261i	−0.972331	+	0.233605i	$0.924948\pi$
$734$		0			0
$735$	−11.0507	−	4.98808i	−0.407613	−	0.183988i
$736$		0			0
$737$	7.61392	+	4.39590i	0.280462	+	0.161925i
$738$		0			0
$739$	11.2904	+	19.5555i	0.415324	+	0.719362i	0.995462	−	0.0951558i	$-0.0303349\pi$
$739$	11.2904	+	19.5555i	0.415324	+	0.719362i	−0.580139	+	0.814518i	$0.697002\pi$
$740$		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
$747$	24.2647	−	30.1282i	0.887799	−	1.10233i
$748$		0			0
$749$	−31.0510	+	37.0906i	−1.13458	+	1.35526i
$750$		0			0
$751$	8.62709	−	14.9426i	0.314807	−	0.545262i	−0.664589	−	0.747209i	$-0.731393\pi$
$751$	8.62709	−	14.9426i	0.314807	−	0.545262i	0.979396	+	0.201947i	$0.0647268\pi$
$752$		0			0
$753$	−7.72793	−	16.1466i	−0.281621	−	0.588413i
$754$		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
$759$	−2.93826	−	6.13913i	−0.106652	−	0.222836i
$760$		0			0
$761$	0.00796126	−	0.0137893i	0.000288596	−	0.000499862i	−0.865881	−	0.500250i	$-0.833241\pi$
$761$	0.00796126	−	0.0137893i	0.000288596	−	0.000499862i	0.866170	+	0.499750i	$0.166575\pi$
$762$		0			0
$763$	43.4824	−	15.8823i	1.57417	−	0.574977i
$764$		0			0
$765$	3.98887	−	4.95277i	0.144218	−	0.179068i
$766$		0			0
$767$	19.1768	−	11.0717i	0.692435	−	0.399777i
$768$		0			0
$769$		−	13.0356i		−	0.470075i	−0.971986	−	0.235037i	$-0.924479\pi$
$769$		−	13.0356i		−	0.470075i	0.971986	−	0.235037i	$-0.0755213\pi$
$770$		0			0
$771$	−52.6796	−	4.07537i	−1.89721	−	0.146771i
$772$		0			0
$773$	14.7085	+	25.4758i	0.529027	+	0.916301i	0.999427	+	0.0338481i	$0.0107762\pi$
$773$	14.7085	+	25.4758i	0.529027	+	0.916301i	−0.470400	+	0.882453i	$0.655890\pi$
$774$		0			0
$775$	−5.65010	−	3.26209i	−0.202958	−	0.117178i
$776$		0			0
$777$	−8.86395	+	34.6268i	−0.317993	+	1.24223i
$778$		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	−0.464664	−	0.885487i	$-0.653825\pi$
$787$	1.95977	−	1.13148i	0.0698584	−	0.0403327i	0.534522	+	0.845154i	$0.320492\pi$
$788$		0			0
$789$	−29.5395	−	20.2441i	−1.05164	−	0.720708i
$790$		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
$795$	−20.8482	+	9.97820i	−0.739410	+	0.353890i
$796$		0			0
$797$	−19.6277			−0.695250			−0.347625	−	0.937634i	$-0.613012\pi$
$797$	−19.6277			−0.695250			−0.347625	+	0.937634i	$0.613012\pi$
$798$		0			0
$799$	−5.88350			−0.208143
$800$		0			0
$801$	3.47567	+	8.98283i	0.122807	+	0.317393i
$802$		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
$807$	24.3012	−	35.4596i	0.855444	−	1.24824i
$808$		0			0
$809$	21.2506	−	12.2690i	0.747130	−	0.431356i	−0.0775260	−	0.996990i	$-0.524702\pi$
$809$	21.2506	−	12.2690i	0.747130	−	0.431356i	0.824656	+	0.565635i	$0.191369\pi$
$810$		0			0
$811$		−	38.7927i		−	1.36220i	−0.732192	−	0.681098i	$-0.761503\pi$
$811$		−	38.7927i		−	1.36220i	0.732192	−	0.681098i	$-0.238497\pi$
$812$		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
$819$	23.0849	−	20.2219i	0.806650	−	0.706611i
$820$		0			0
$821$	−11.8734	−	6.85513i	−0.414386	−	0.239246i	0.278287	−	0.960498i	$-0.410233\pi$
$821$	−11.8734	−	6.85513i	−0.414386	−	0.239246i	−0.692672	+	0.721252i	$0.743567\pi$
$822$		0			0
$823$	−4.04168	−	7.00040i	−0.140884	−	0.244019i	0.786946	−	0.617022i	$-0.211661\pi$
$823$	−4.04168	−	7.00040i	−0.140884	−	0.244019i	−0.927830	+	0.373004i	$0.878328\pi$
$824$		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	−0.207150	−	0.978309i	$-0.566419\pi$
$829$	15.4475	−	8.91864i	0.536515	−	0.309757i	0.743665	+	0.668552i	$0.233086\pi$
$830$		0			0
$831$	−14.9050	+	21.7489i	−0.517049	+	0.754462i
$832$		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
$837$	32.4658	−	9.75811i	1.12218	−	0.337290i
$838$		0			0
$839$	−4.49497			−0.155183			−0.0775917	−	0.996985i	$-0.524723\pi$
$839$	−4.49497			−0.155183			−0.0775917	+	0.996985i	$0.524723\pi$
$840$		0			0
$841$	−15.5825			−0.537329
$842$		0			0
$843$	28.0419	−	13.4212i	0.965814	−	0.462250i
$844$		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
$849$	38.5598	+	26.4259i	1.32337	+	0.906934i
$850$		0			0
$851$	32.9144	−	19.0032i	1.12829	−	0.651420i
$852$		0			0
$853$		−	33.0503i		−	1.13162i	−0.824535	−	0.565811i	$-0.808563\pi$
$853$		−	33.0503i		−	1.13162i	0.824535	−	0.565811i	$-0.191437\pi$
$854$		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	$-0.164375\pi$
$857$	0.210762	+	0.365051i	0.00719949	+	0.0124699i	−0.862403	+	0.506222i	$0.831042\pi$
$858$		0			0
$859$	−17.0294	−	9.83192i	−0.581035	−	0.335461i	0.180509	−	0.983573i	$-0.442225\pi$
$859$	−17.0294	−	9.83192i	−0.581035	−	0.335461i	−0.761545	+	0.648112i	$0.775559\pi$
$860$		0			0
$861$	37.2818	−	10.4383i	1.27056	−	0.355737i
$862$		0			0
$863$	0.782575	+	0.451820i	0.0266392	+	0.0153801i	0.513260	−	0.858233i	$-0.328437\pi$
$863$	0.782575	+	0.451820i	0.0266392	+	0.0153801i	−0.486621	+	0.873613i	$0.661771\pi$
$864$		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
$873$	2.36889	+	1.90787i	0.0801749	+	0.0645715i
$874$		0			0
$875$	−0.456468	+	2.60608i	−0.0154314	+	0.0881015i
$876$		0			0
$877$	7.65916	−	13.2661i	0.258632	−	0.447963i	−0.707244	−	0.706970i	$-0.750062\pi$
$877$	7.65916	−	13.2661i	0.258632	−	0.447963i	0.965876	+	0.259006i	$0.0833951\pi$
$878$		0			0
$879$	−10.8013	−	22.5679i	−0.364317	−	0.761196i
$880$		0			0
$881$	43.8614			1.47773			0.738863	−	0.673855i	$-0.235363\pi$
$881$	43.8614			1.47773			0.738863	+	0.673855i	$0.235363\pi$
$882$		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
$885$	−4.28237	−	8.94748i	−0.143950	−	0.300766i
$886$		0			0
$887$	7.44790	−	12.9001i	0.250076	−	0.433145i	−0.713470	−	0.700685i	$-0.752878\pi$
$887$	7.44790	−	12.9001i	0.250076	−	0.433145i	0.963547	+	0.267541i	$0.0862110\pi$
$888$		0			0
$889$	−3.54739	+	20.2528i	−0.118976	+	0.679259i
$890$		0			0
$891$	4.88510	+	5.36766i	0.163657	+	0.179823i
$892$		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
$903$	−3.61448	+	1.01200i	−0.120282	+	0.0336772i
$904$		0			0
$905$	−19.5566	−	11.2910i	−0.650085	−	0.375327i
$906$		0			0
$907$	−9.54899	−	16.5393i	−0.317069	−	0.549180i	0.662806	−	0.748791i	$-0.269365\pi$
$907$	−9.54899	−	16.5393i	−0.317069	−	0.549180i	−0.979875	+	0.199611i	$0.936032\pi$
$908$		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
$915$	2.95961	+	2.02829i	0.0978419	+	0.0670531i
$916$		0			0
$917$	24.0912	+	20.1683i	0.795562	+	0.666016i
$918$		0			0
$919$	−14.8318	+	25.6894i	−0.489255	+	0.847415i	−0.999924	−	0.0123630i	$-0.996065\pi$
$919$	−14.8318	+	25.6894i	−0.489255	+	0.847415i	0.510668	+	0.859778i	$0.329398\pi$
$920$		0			0
$921$	14.6006	−	6.98804i	0.481107	−	0.230264i
$922$		0			0
$923$	−40.1537			−1.32168
$924$		0			0
$925$	7.79983			0.256457
$926$		0			0
$927$	−27.3587	+	10.5857i	−0.898577	+	0.347681i
$928$		0			0
$929$	−16.8256	+	29.1428i	−0.552030	+	0.956144i	0.446098	+	0.894984i	$0.352813\pi$
$929$	−16.8256	+	29.1428i	−0.552030	+	0.956144i	−0.998128	+	0.0611601i	$0.980520\pi$
$930$		0			0
$931$	−14.0975	−	16.7234i	−0.462027	−	0.548087i
$932$		0			0
$933$	−28.7209	+	41.9087i	−0.940281	+	1.37203i
$934$		0			0
$935$	1.48042	−	0.854719i	0.0484148	−	0.0279523i
$936$		0			0
$937$			7.99276i			0.261112i	0.991441	+	0.130556i	$0.0416762\pi$
$937$			7.99276i			0.261112i	−0.991441	+	0.130556i	$0.958324\pi$
$938$		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	$-0.0751955\pi$
$941$	8.69431	+	15.0590i	0.283426	+	0.490909i	−0.688800	+	0.724951i	$0.741862\pi$
$942$		0			0
$943$	−35.6514	−	20.5833i	−1.16097	−	0.670285i
$944$		0			0
$945$	−8.23408	−	11.0091i	−0.267855	−	0.358126i
$946$		0			0
$947$	36.6302	+	21.1485i	1.19032	+	0.687233i	0.958380	−	0.285496i	$-0.0921583\pi$
$947$	36.6302	+	21.1485i	1.19032	+	0.687233i	0.231943	+	0.972729i	$0.425492\pi$
$948$		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
$957$	−5.27220	+	7.69303i	−0.170426	+	0.248680i
$958$		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
$963$	−51.1534	+	19.7925i	−1.64840	+	0.637804i
$964$		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
$969$	10.3482	−	4.95277i	0.332432	−	0.159106i
$970$		0			0
$971$	21.5452	−	37.3173i	0.691418	−	1.19757i	−0.279956	−	0.960013i	$-0.590320\pi$
$971$	21.5452	−	37.3173i	0.691418	−	1.19757i	0.971373	−	0.237558i	$-0.0763469\pi$
$972$		0			0
$973$	−7.33180	−	1.28420i	−0.235047	−	0.0411697i
$974$		0			0
$975$	−5.52419	−	3.78585i	−0.176916	−	0.121244i
$976$		0			0
$977$	19.7402	−	11.3970i	0.631545	−	0.364622i	−0.149805	−	0.988716i	$-0.547865\pi$
$977$	19.7402	−	11.3970i	0.631545	−	0.364622i	0.781350	+	0.624093i	$0.214531\pi$
$978$		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	−0.960759	−	0.277385i	$-0.910532\pi$
$983$	−22.5929	−	39.1321i	−0.720602	−	1.24812i	0.240157	−	0.970734i	$-0.422801\pi$
$984$		0			0
$985$	14.0802	+	8.12923i	0.448634	+	0.259019i
$986$		0			0
$987$	−3.15419	+	12.3218i	−0.100399	+	0.392206i
$988$		0			0
$989$	3.45641	+	1.99556i	0.109907	+	0.0634551i
$990$		0			0
$991$	−25.2760	−	43.7793i	−0.802919	−	1.39070i	−0.917687	−	0.397304i	$-0.869946\pi$
$991$	−25.2760	−	43.7793i	−0.802919	−	1.39070i	0.114768	−	0.993392i	$-0.463388\pi$
$992$		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	−0.812760	−	0.582599i	$-0.802036\pi$
$997$	−22.5635	+	13.0271i	−0.714595	+	0.412571i	0.0981654	+	0.995170i	$0.468703\pi$
$998$		0			0
$999$	−27.7807	+	29.5100i	−0.878942	+	0.933656i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bh.a.101.2	✓	10	21.17	even	6	inner
420.2.bh.a.341.2	yes	10	1.1	even	1	trivial
420.2.bh.b.101.4	yes	10	7.3	odd	6
420.2.bh.b.341.4	yes	10	3.2	odd	2
2100.2.bi.j.101.2		10	35.24	odd	6
2100.2.bi.j.1601.2		10	15.14	odd	2
2100.2.bi.k.101.4		10	105.59	even	6
2100.2.bi.k.1601.4		10	5.4	even	2
2100.2.bo.g.1349.2		20	15.8	even	4
2100.2.bo.g.1349.9		20	15.2	even	4
2100.2.bo.g.1949.2		20	35.17	even	12
2100.2.bo.g.1949.9		20	35.3	even	12
2100.2.bo.h.1349.3		20	5.2	odd	4
2100.2.bo.h.1349.8		20	5.3	odd	4
2100.2.bo.h.1949.3		20	105.38	odd	12
2100.2.bo.h.1949.8		20	105.17	odd	12
2940.2.d.a.881.1		10	7.5	odd	6
2940.2.d.a.881.2		10	21.2	odd	6
2940.2.d.b.881.9		10	21.5	even	6
2940.2.d.b.881.10		10	7.2	even	3

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)

\(f(q)\)	\(=\)	\(q+(-0.747749 - 1.56233i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-0.456468 + 2.60608i) q^{7} +(-1.88174 + 2.33646i) q^{9} +O(q^{10})\)	\(q+(-0.747749 - 1.56233i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-0.456468 + 2.60608i) q^{7} +(-1.88174 + 2.33646i) q^{9} +(-0.698384 + 0.403212i) q^{11} +3.86649i q^{13} +(1.72689 + 0.133595i) q^{15} +(1.05989 + 1.83578i) q^{17} +(2.70603 + 1.56233i) q^{19} +(4.41287 - 1.23554i) q^{21} +(-4.21989 - 2.43635i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(5.05739 + 1.19282i) q^{27} +6.67701i q^{29} +(5.65010 - 3.26209i) q^{31} +(1.15217 + 0.789604i) q^{33} +(-2.02869 - 1.69835i) q^{35} +(-3.89991 + 6.75485i) q^{37} +(6.04074 - 2.89117i) q^{39} +8.44841 q^{41} -0.819076 q^{43} +(-1.08256 - 2.79787i) q^{45} +(-1.38776 + 2.40368i) q^{47} +(-6.58327 - 2.37918i) q^{49} +(2.07556 - 3.02860i) q^{51} +(-11.5565 + 6.67216i) q^{53} -0.806424i q^{55} +(0.417438 - 5.39594i) q^{57} +(-2.86351 - 4.95974i) q^{59} +(1.79397 + 1.03575i) q^{61} +(-5.23004 - 5.97049i) q^{63} +(-3.34848 - 1.93325i) q^{65} +(-5.45110 - 9.44157i) q^{67} +(-0.650969 + 8.41464i) q^{69} +10.3850i q^{71} +(2.67203 - 1.54270i) q^{73} +(-0.979142 + 1.42873i) q^{75} +(-0.732012 - 2.00410i) q^{77} +(6.76342 - 11.7146i) q^{79} +(-1.91809 - 8.79323i) q^{81} -12.8948 q^{83} -2.11978 q^{85} +(10.4317 - 4.99273i) q^{87} +(1.60530 - 2.78046i) q^{89} +(-10.0764 - 1.76493i) q^{91} +(-9.32131 - 6.38809i) q^{93} +(-2.70603 + 1.56233i) q^{95} -1.01388i q^{97} +(0.372090 - 2.39049i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{3} - 5 q^{5} - 5 q^{7} - 3 q^{9}+O(q^{10}) \) 10 * q - q^3 - 5 * q^5 - 5 * q^7 - 3 * q^9	\( 10 q - q^{3} - 5 q^{5} - 5 q^{7} - 3 q^{9} - 6 q^{11} + 2 q^{15} + 6 q^{17} + 3 q^{19} + 10 q^{21} + 24 q^{23} - 5 q^{25} + 8 q^{27} + 15 q^{31} - 20 q^{33} + q^{35} - q^{37} + 15 q^{39} - 8 q^{41} - 26 q^{43} + 3 q^{45} + 14 q^{47} - 13 q^{49} - 44 q^{51} - 24 q^{53} + 18 q^{57} + 42 q^{61} - q^{63} + 9 q^{65} + 7 q^{67} - 14 q^{69} - 3 q^{73} - q^{75} - 26 q^{77} + q^{79} + 41 q^{81} - 8 q^{83} - 12 q^{85} - 26 q^{87} + 28 q^{89} - 11 q^{91} - 47 q^{93} - 3 q^{95} + 36 q^{99}+O(q^{100}) \) 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 + 10 * q^21 + 24 * q^23 - 5 * q^25 + 8 * q^27 + 15 * q^31 - 20 * q^33 + q^35 - q^37 + 15 * q^39 - 8 * q^41 - 26 * q^43 + 3 * q^45 + 14 * q^47 - 13 * q^49 - 44 * q^51 - 24 * q^53 + 18 * q^57 + 42 * q^61 - q^63 + 9 * q^65 + 7 * q^67 - 14 * q^69 - 3 * q^73 - q^75 - 26 * q^77 + q^79 + 41 * q^81 - 8 * q^83 - 12 * q^85 - 26 * q^87 + 28 * q^89 - 11 * q^91 - 47 * q^93 - 3 * q^95 + 36 * q^99

Introduction

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