LMFDB - Embedded newform 140.2.i.b.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [140,2,Mod(81,140)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(140, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("140.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 140 = 2^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	140.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.11790562830$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	140.121
Dual form			140.2.i.b.81.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 + 2.59808i) q^{3} +(0.500000 - 0.866025i) q^{5} +(0.500000 - 2.59808i) q^{7} +(-3.00000 + 5.19615i) q^{9} +O(q^{10})$	\(q+(1.50000 + 2.59808i) q^{3} +(0.500000 - 0.866025i) q^{5} +(0.500000 - 2.59808i) q^{7} +(-3.00000 + 5.19615i) q^{9} +(1.00000 + 1.73205i) q^{11} -6.00000 q^{13} +3.00000 q^{15} +(-1.00000 - 1.73205i) q^{17} +(7.50000 - 2.59808i) q^{21} +(4.50000 - 7.79423i) q^{23} +(-0.500000 - 0.866025i) q^{25} -9.00000 q^{27} +3.00000 q^{29} +(-1.00000 - 1.73205i) q^{31} +(-3.00000 + 5.19615i) q^{33} +(-2.00000 - 1.73205i) q^{35} +(-4.00000 + 6.92820i) q^{37} +(-9.00000 - 15.5885i) q^{39} +5.00000 q^{41} +1.00000 q^{43} +(3.00000 + 5.19615i) q^{45} +(-4.00000 + 6.92820i) q^{47} +(-6.50000 - 2.59808i) q^{49} +(3.00000 - 5.19615i) q^{51} +(-2.00000 - 3.46410i) q^{53} +2.00000 q^{55} +(4.00000 + 6.92820i) q^{59} +(-3.50000 + 6.06218i) q^{61} +(12.0000 + 10.3923i) q^{63} +(-3.00000 + 5.19615i) q^{65} +(1.50000 + 2.59808i) q^{67} +27.0000 q^{69} +8.00000 q^{71} +(-7.00000 - 12.1244i) q^{73} +(1.50000 - 2.59808i) q^{75} +(5.00000 - 1.73205i) q^{77} +(-2.00000 + 3.46410i) q^{79} +(-4.50000 - 7.79423i) q^{81} -1.00000 q^{83} -2.00000 q^{85} +(4.50000 + 7.79423i) q^{87} +(-6.50000 + 11.2583i) q^{89} +(-3.00000 + 15.5885i) q^{91} +(3.00000 - 5.19615i) q^{93} -10.0000 q^{97} -12.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{3} + q^{5} + q^{7} - 6 q^{9}+O(q^{10}) $ 2 * q + 3 * q^3 + q^5 + q^7 - 6 * q^9	$ 2 q + 3 q^{3} + q^{5} + q^{7} - 6 q^{9} + 2 q^{11} - 12 q^{13} + 6 q^{15} - 2 q^{17} + 15 q^{21} + 9 q^{23} - q^{25} - 18 q^{27} + 6 q^{29} - 2 q^{31} - 6 q^{33} - 4 q^{35} - 8 q^{37} - 18 q^{39} + 10 q^{41} + 2 q^{43} + 6 q^{45} - 8 q^{47} - 13 q^{49} + 6 q^{51} - 4 q^{53} + 4 q^{55} + 8 q^{59} - 7 q^{61} + 24 q^{63} - 6 q^{65} + 3 q^{67} + 54 q^{69} + 16 q^{71} - 14 q^{73} + 3 q^{75} + 10 q^{77} - 4 q^{79} - 9 q^{81} - 2 q^{83} - 4 q^{85} + 9 q^{87} - 13 q^{89} - 6 q^{91} + 6 q^{93} - 20 q^{97} - 24 q^{99}+O(q^{100}) $ 2 * q + 3 * q^3 + q^5 + q^7 - 6 * q^9 + 2 * q^11 - 12 * q^13 + 6 * q^15 - 2 * q^17 + 15 * q^21 + 9 * q^23 - q^25 - 18 * q^27 + 6 * q^29 - 2 * q^31 - 6 * q^33 - 4 * q^35 - 8 * q^37 - 18 * q^39 + 10 * q^41 + 2 * q^43 + 6 * q^45 - 8 * q^47 - 13 * q^49 + 6 * q^51 - 4 * q^53 + 4 * q^55 + 8 * q^59 - 7 * q^61 + 24 * q^63 - 6 * q^65 + 3 * q^67 + 54 * q^69 + 16 * q^71 - 14 * q^73 + 3 * q^75 + 10 * q^77 - 4 * q^79 - 9 * q^81 - 2 * q^83 - 4 * q^85 + 9 * q^87 - 13 * q^89 - 6 * q^91 + 6 * q^93 - 20 * q^97 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$57$	$71$	$101$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.50000	+	2.59808i	0.866025	+	1.50000i	0.866025	+	0.500000i	$0.166667\pi$
$3$	1.50000	+	2.59808i	0.866025	+	1.50000i			1.00000i	$0.5\pi$
$4$		0			0
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	0.500000	−	2.59808i	0.188982	−	0.981981i
$7$	0.500000	−	2.59808i	0.188982	−	0.981981i
$8$		0			0
$9$	−3.00000	+	5.19615i	−1.00000	+	1.73205i
$10$		0			0
$11$	1.00000	+	1.73205i	0.301511	+	0.522233i	0.976478	−	0.215615i	$-0.0691756\pi$
$11$	1.00000	+	1.73205i	0.301511	+	0.522233i	−0.674967	+	0.737848i	$0.735842\pi$
$12$		0			0
$13$	−6.00000			−1.66410			−0.832050	−	0.554700i	$-0.812833\pi$
$13$	−6.00000			−1.66410			−0.832050	+	0.554700i	$0.812833\pi$
$14$		0			0
$15$	3.00000			0.774597
$16$		0			0
$17$	−1.00000	−	1.73205i	−0.242536	−	0.420084i	0.718900	−	0.695113i	$-0.244646\pi$
$17$	−1.00000	−	1.73205i	−0.242536	−	0.420084i	−0.961436	+	0.275029i	$0.911312\pi$
$18$		0			0
$19$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$19$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$20$		0			0
$21$	7.50000	−	2.59808i	1.63663	−	0.566947i
$22$		0			0
$23$	4.50000	−	7.79423i	0.938315	−	1.62521i	0.169701	−	0.985496i	$-0.445720\pi$
$23$	4.50000	−	7.79423i	0.938315	−	1.62521i	0.768613	−	0.639713i	$-0.220947\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	−9.00000			−1.73205
$28$		0			0
$29$	3.00000			0.557086			0.278543	−	0.960424i	$-0.410149\pi$
$29$	3.00000			0.557086			0.278543	+	0.960424i	$0.410149\pi$
$30$		0			0
$31$	−1.00000	−	1.73205i	−0.179605	−	0.311086i	0.762140	−	0.647412i	$-0.224149\pi$
$31$	−1.00000	−	1.73205i	−0.179605	−	0.311086i	−0.941745	+	0.336327i	$0.890815\pi$
$32$		0			0
$33$	−3.00000	+	5.19615i	−0.522233	+	0.904534i
$34$		0			0
$35$	−2.00000	−	1.73205i	−0.338062	−	0.292770i
$36$		0			0
$37$	−4.00000	+	6.92820i	−0.657596	+	1.13899i	0.323640	+	0.946180i	$0.395093\pi$
$37$	−4.00000	+	6.92820i	−0.657596	+	1.13899i	−0.981236	+	0.192809i	$0.938240\pi$
$38$		0			0
$39$	−9.00000	−	15.5885i	−1.44115	−	2.49615i
$40$		0			0
$41$	5.00000			0.780869			0.390434	−	0.920631i	$-0.372325\pi$
$41$	5.00000			0.780869			0.390434	+	0.920631i	$0.372325\pi$
$42$		0			0
$43$	1.00000			0.152499			0.0762493	−	0.997089i	$-0.475706\pi$
$43$	1.00000			0.152499			0.0762493	+	0.997089i	$0.475706\pi$
$44$		0			0
$45$	3.00000	+	5.19615i	0.447214	+	0.774597i
$46$		0			0
$47$	−4.00000	+	6.92820i	−0.583460	+	1.01058i	0.411606	+	0.911362i	$0.364968\pi$
$47$	−4.00000	+	6.92820i	−0.583460	+	1.01058i	−0.995066	+	0.0992202i	$0.968365\pi$
$48$		0			0
$49$	−6.50000	−	2.59808i	−0.928571	−	0.371154i
$50$		0			0
$51$	3.00000	−	5.19615i	0.420084	−	0.727607i
$52$		0			0
$53$	−2.00000	−	3.46410i	−0.274721	−	0.475831i	0.695344	−	0.718677i	$-0.255252\pi$
$53$	−2.00000	−	3.46410i	−0.274721	−	0.475831i	−0.970065	+	0.242846i	$0.921919\pi$
$54$		0			0
$55$	2.00000			0.269680
$56$		0			0
$57$		0			0
$58$		0			0
$59$	4.00000	+	6.92820i	0.520756	+	0.901975i	0.999709	+	0.0241347i	$0.00768307\pi$
$59$	4.00000	+	6.92820i	0.520756	+	0.901975i	−0.478953	+	0.877841i	$0.658984\pi$
$60$		0			0
$61$	−3.50000	+	6.06218i	−0.448129	+	0.776182i	−0.998264	−	0.0588933i	$-0.981243\pi$
$61$	−3.50000	+	6.06218i	−0.448129	+	0.776182i	0.550135	+	0.835076i	$0.314576\pi$
$62$		0			0
$63$	12.0000	+	10.3923i	1.51186	+	1.30931i
$64$		0			0
$65$	−3.00000	+	5.19615i	−0.372104	+	0.644503i
$66$		0			0
$67$	1.50000	+	2.59808i	0.183254	+	0.317406i	0.942987	−	0.332830i	$-0.108004\pi$
$67$	1.50000	+	2.59808i	0.183254	+	0.317406i	−0.759733	+	0.650236i	$0.774670\pi$
$68$		0			0
$69$	27.0000			3.25042
$70$		0			0
$71$	8.00000			0.949425			0.474713	−	0.880141i	$-0.342552\pi$
$71$	8.00000			0.949425			0.474713	+	0.880141i	$0.342552\pi$
$72$		0			0
$73$	−7.00000	−	12.1244i	−0.819288	−	1.41905i	−0.906208	−	0.422833i	$-0.861036\pi$
$73$	−7.00000	−	12.1244i	−0.819288	−	1.41905i	0.0869195	−	0.996215i	$-0.472298\pi$
$74$		0			0
$75$	1.50000	−	2.59808i	0.173205	−	0.300000i
$76$		0			0
$77$	5.00000	−	1.73205i	0.569803	−	0.197386i
$78$		0			0
$79$	−2.00000	+	3.46410i	−0.225018	+	0.389742i	−0.956325	−	0.292306i	$-0.905577\pi$
$79$	−2.00000	+	3.46410i	−0.225018	+	0.389742i	0.731307	+	0.682048i	$0.238911\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$		0			0
$83$	−1.00000			−0.109764			−0.0548821	−	0.998493i	$-0.517478\pi$
$83$	−1.00000			−0.109764			−0.0548821	+	0.998493i	$0.517478\pi$
$84$		0			0
$85$	−2.00000			−0.216930
$86$		0			0
$87$	4.50000	+	7.79423i	0.482451	+	0.835629i
$88$		0			0
$89$	−6.50000	+	11.2583i	−0.688999	+	1.19338i	0.283164	+	0.959072i	$0.408616\pi$
$89$	−6.50000	+	11.2583i	−0.688999	+	1.19338i	−0.972162	+	0.234309i	$0.924717\pi$
$90$		0			0
$91$	−3.00000	+	15.5885i	−0.314485	+	1.63411i
$92$		0			0
$93$	3.00000	−	5.19615i	0.311086	−	0.538816i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−10.0000			−1.01535			−0.507673	−	0.861550i	$-0.669494\pi$
$97$	−10.0000			−1.01535			−0.507673	+	0.861550i	$0.669494\pi$
$98$		0			0
$99$	−12.0000			−1.20605
$100$		0			0
$101$	1.50000	+	2.59808i	0.149256	+	0.258518i	0.930953	−	0.365140i	$-0.118979\pi$
$101$	1.50000	+	2.59808i	0.149256	+	0.258518i	−0.781697	+	0.623658i	$0.785646\pi$
$102$		0			0
$103$	−6.50000	+	11.2583i	−0.640464	+	1.10932i	0.344865	+	0.938652i	$0.387925\pi$
$103$	−6.50000	+	11.2583i	−0.640464	+	1.10932i	−0.985329	+	0.170664i	$0.945409\pi$
$104$		0			0
$105$	1.50000	−	7.79423i	0.146385	−	0.760639i
$106$		0			0
$107$	7.50000	−	12.9904i	0.725052	−	1.25583i	−0.233900	−	0.972261i	$-0.575149\pi$
$107$	7.50000	−	12.9904i	0.725052	−	1.25583i	0.958952	−	0.283567i	$-0.0915178\pi$
$108$		0			0
$109$	−4.50000	−	7.79423i	−0.431022	−	0.746552i	0.565940	−	0.824447i	$-0.308513\pi$
$109$	−4.50000	−	7.79423i	−0.431022	−	0.746552i	−0.996962	+	0.0778949i	$0.975180\pi$
$110$		0			0
$111$	−24.0000			−2.27798
$112$		0			0
$113$	−4.00000			−0.376288			−0.188144	−	0.982141i	$-0.560247\pi$
$113$	−4.00000			−0.376288			−0.188144	+	0.982141i	$0.560247\pi$
$114$		0			0
$115$	−4.50000	−	7.79423i	−0.419627	−	0.726816i
$116$		0			0
$117$	18.0000	−	31.1769i	1.66410	−	2.88231i
$118$		0			0
$119$	−5.00000	+	1.73205i	−0.458349	+	0.158777i
$120$		0			0
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$		0			0
$123$	7.50000	+	12.9904i	0.676252	+	1.17130i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	16.0000			1.41977			0.709885	−	0.704317i	$-0.248747\pi$
$127$	16.0000			1.41977			0.709885	+	0.704317i	$0.248747\pi$
$128$		0			0
$129$	1.50000	+	2.59808i	0.132068	+	0.228748i
$130$		0			0
$131$	2.00000	−	3.46410i	0.174741	−	0.302660i	−0.765331	−	0.643637i	$-0.777425\pi$
$131$	2.00000	−	3.46410i	0.174741	−	0.302660i	0.940072	+	0.340977i	$0.110758\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−4.50000	+	7.79423i	−0.387298	+	0.670820i
$136$		0			0
$137$	6.00000	+	10.3923i	0.512615	+	0.887875i	0.999893	+	0.0146279i	$0.00465636\pi$
$137$	6.00000	+	10.3923i	0.512615	+	0.887875i	−0.487278	+	0.873247i	$0.662010\pi$
$138$		0			0
$139$	10.0000			0.848189			0.424094	−	0.905618i	$-0.360592\pi$
$139$	10.0000			0.848189			0.424094	+	0.905618i	$0.360592\pi$
$140$		0			0
$141$	−24.0000			−2.02116
$142$		0			0
$143$	−6.00000	−	10.3923i	−0.501745	−	0.869048i
$144$		0			0
$145$	1.50000	−	2.59808i	0.124568	−	0.215758i
$146$		0			0
$147$	−3.00000	−	20.7846i	−0.247436	−	1.71429i
$148$		0			0
$149$	−4.50000	+	7.79423i	−0.368654	+	0.638528i	−0.989355	−	0.145519i	$-0.953515\pi$
$149$	−4.50000	+	7.79423i	−0.368654	+	0.638528i	0.620701	+	0.784047i	$0.286848\pi$
$150$		0			0
$151$	5.00000	+	8.66025i	0.406894	+	0.704761i	0.994540	−	0.104357i	$-0.0332784\pi$
$151$	5.00000	+	8.66025i	0.406894	+	0.704761i	−0.587646	+	0.809118i	$0.699945\pi$
$152$		0			0
$153$	12.0000			0.970143
$154$		0			0
$155$	−2.00000			−0.160644
$156$		0			0
$157$	1.00000	+	1.73205i	0.0798087	+	0.138233i	0.903167	−	0.429289i	$-0.141236\pi$
$157$	1.00000	+	1.73205i	0.0798087	+	0.138233i	−0.823359	+	0.567521i	$0.807902\pi$
$158$		0			0
$159$	6.00000	−	10.3923i	0.475831	−	0.824163i
$160$		0			0
$161$	−18.0000	−	15.5885i	−1.41860	−	1.22854i
$162$		0			0
$163$	−4.00000	+	6.92820i	−0.313304	+	0.542659i	−0.979076	−	0.203497i	$-0.934769\pi$
$163$	−4.00000	+	6.92820i	−0.313304	+	0.542659i	0.665771	+	0.746156i	$0.268103\pi$
$164$		0			0
$165$	3.00000	+	5.19615i	0.233550	+	0.404520i
$166$		0			0
$167$	−9.00000			−0.696441			−0.348220	−	0.937413i	$-0.613214\pi$
$167$	−9.00000			−0.696441			−0.348220	+	0.937413i	$0.613214\pi$
$168$		0			0
$169$	23.0000			1.76923
$170$		0			0
$171$		0			0
$172$		0			0
$173$	8.00000	−	13.8564i	0.608229	−	1.05348i	−0.383304	−	0.923622i	$-0.625214\pi$
$173$	8.00000	−	13.8564i	0.608229	−	1.05348i	0.991532	−	0.129861i	$-0.0414530\pi$
$174$		0			0
$175$	−2.50000	+	0.866025i	−0.188982	+	0.0654654i
$176$		0			0
$177$	−12.0000	+	20.7846i	−0.901975	+	1.56227i
$178$		0			0
$179$	3.00000	+	5.19615i	0.224231	+	0.388379i	0.956088	−	0.293079i	$-0.0946798\pi$
$179$	3.00000	+	5.19615i	0.224231	+	0.388379i	−0.731858	+	0.681457i	$0.761346\pi$
$180$		0			0
$181$	1.00000			0.0743294			0.0371647	−	0.999309i	$-0.488167\pi$
$181$	1.00000			0.0743294			0.0371647	+	0.999309i	$0.488167\pi$
$182$		0			0
$183$	−21.0000			−1.55236
$184$		0			0
$185$	4.00000	+	6.92820i	0.294086	+	0.509372i
$186$		0			0
$187$	2.00000	−	3.46410i	0.146254	−	0.253320i
$188$		0			0
$189$	−4.50000	+	23.3827i	−0.327327	+	1.70084i
$190$		0			0
$191$	−3.00000	+	5.19615i	−0.217072	+	0.375980i	−0.953912	−	0.300088i	$-0.902984\pi$
$191$	−3.00000	+	5.19615i	−0.217072	+	0.375980i	0.736839	+	0.676068i	$0.236317\pi$
$192$		0			0
$193$	−1.00000	−	1.73205i	−0.0719816	−	0.124676i	0.827788	−	0.561041i	$-0.189599\pi$
$193$	−1.00000	−	1.73205i	−0.0719816	−	0.124676i	−0.899770	+	0.436365i	$0.856266\pi$
$194$		0			0
$195$	−18.0000			−1.28901
$196$		0			0
$197$	14.0000			0.997459			0.498729	−	0.866758i	$-0.333800\pi$
$197$	14.0000			0.997459			0.498729	+	0.866758i	$0.333800\pi$
$198$		0			0
$199$	−10.0000	−	17.3205i	−0.708881	−	1.22782i	−0.965272	−	0.261245i	$-0.915867\pi$
$199$	−10.0000	−	17.3205i	−0.708881	−	1.22782i	0.256391	−	0.966573i	$-0.417466\pi$
$200$		0			0
$201$	−4.50000	+	7.79423i	−0.317406	+	0.549762i
$202$		0			0
$203$	1.50000	−	7.79423i	0.105279	−	0.547048i
$204$		0			0
$205$	2.50000	−	4.33013i	0.174608	−	0.302429i
$206$		0			0
$207$	27.0000	+	46.7654i	1.87663	+	3.25042i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	4.00000			0.275371			0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000			0.275371			0.137686	+	0.990476i	$0.456034\pi$
$212$		0			0
$213$	12.0000	+	20.7846i	0.822226	+	1.42414i
$214$		0			0
$215$	0.500000	−	0.866025i	0.0340997	−	0.0590624i
$216$		0			0
$217$	−5.00000	+	1.73205i	−0.339422	+	0.117579i
$218$		0			0
$219$	21.0000	−	36.3731i	1.41905	−	2.45786i
$220$		0			0
$221$	6.00000	+	10.3923i	0.403604	+	0.699062i
$222$		0			0
$223$	16.0000			1.07144			0.535720	−	0.844396i	$-0.320040\pi$
$223$	16.0000			1.07144			0.535720	+	0.844396i	$0.320040\pi$
$224$		0			0
$225$	6.00000			0.400000
$226$		0			0
$227$	2.00000	+	3.46410i	0.132745	+	0.229920i	0.924734	−	0.380615i	$-0.124288\pi$
$227$	2.00000	+	3.46410i	0.132745	+	0.229920i	−0.791989	+	0.610535i	$0.790954\pi$
$228$		0			0
$229$	7.00000	−	12.1244i	0.462573	−	0.801200i	−0.536515	−	0.843891i	$-0.680260\pi$
$229$	7.00000	−	12.1244i	0.462573	−	0.801200i	0.999088	+	0.0426906i	$0.0135930\pi$
$230$		0			0
$231$	12.0000	+	10.3923i	0.789542	+	0.683763i
$232$		0			0
$233$	9.00000	−	15.5885i	0.589610	−	1.02123i	−0.404674	−	0.914461i	$-0.632615\pi$
$233$	9.00000	−	15.5885i	0.589610	−	1.02123i	0.994283	−	0.106773i	$-0.0340517\pi$
$234$		0			0
$235$	4.00000	+	6.92820i	0.260931	+	0.451946i
$236$		0			0
$237$	−12.0000			−0.779484
$238$		0			0
$239$	−26.0000			−1.68180			−0.840900	−	0.541190i	$-0.817974\pi$
$239$	−26.0000			−1.68180			−0.840900	+	0.541190i	$0.817974\pi$
$240$		0			0
$241$	−5.00000	−	8.66025i	−0.322078	−	0.557856i	0.658838	−	0.752285i	$-0.271048\pi$
$241$	−5.00000	−	8.66025i	−0.322078	−	0.557856i	−0.980917	+	0.194429i	$0.937715\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−5.50000	+	4.33013i	−0.351382	+	0.276642i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	−1.50000	−	2.59808i	−0.0950586	−	0.164646i
$250$		0			0
$251$	30.0000			1.89358			0.946792	−	0.321847i	$-0.104304\pi$
$251$	30.0000			1.89358			0.946792	+	0.321847i	$0.104304\pi$
$252$		0			0
$253$	18.0000			1.13165
$254$		0			0
$255$	−3.00000	−	5.19615i	−0.187867	−	0.325396i
$256$		0			0
$257$	−4.00000	+	6.92820i	−0.249513	+	0.432169i	−0.963391	−	0.268101i	$-0.913604\pi$
$257$	−4.00000	+	6.92820i	−0.249513	+	0.432169i	0.713878	+	0.700270i	$0.246937\pi$
$258$		0			0
$259$	16.0000	+	13.8564i	0.994192	+	0.860995i
$260$		0			0
$261$	−9.00000	+	15.5885i	−0.557086	+	0.964901i
$262$		0			0
$263$	−8.50000	−	14.7224i	−0.524132	−	0.907824i	−0.999605	−	0.0280936i	$-0.991056\pi$
$263$	−8.50000	−	14.7224i	−0.524132	−	0.907824i	0.475473	−	0.879730i	$-0.342277\pi$
$264$		0			0
$265$	−4.00000			−0.245718
$266$		0			0
$267$	−39.0000			−2.38676
$268$		0			0
$269$	−4.50000	−	7.79423i	−0.274370	−	0.475223i	0.695606	−	0.718423i	$-0.255136\pi$
$269$	−4.50000	−	7.79423i	−0.274370	−	0.475223i	−0.969976	+	0.243201i	$0.921803\pi$
$270$		0			0
$271$	12.0000	−	20.7846i	0.728948	−	1.26258i	−0.228380	−	0.973572i	$-0.573343\pi$
$271$	12.0000	−	20.7846i	0.728948	−	1.26258i	0.957328	−	0.289003i	$-0.0933238\pi$
$272$		0			0
$273$	−45.0000	+	15.5885i	−2.72352	+	0.943456i
$274$		0			0
$275$	1.00000	−	1.73205i	0.0603023	−	0.104447i
$276$		0			0
$277$	−9.00000	−	15.5885i	−0.540758	−	0.936620i	−0.998861	−	0.0477206i	$-0.984804\pi$
$277$	−9.00000	−	15.5885i	−0.540758	−	0.936620i	0.458103	−	0.888899i	$-0.348529\pi$
$278$		0			0
$279$	12.0000			0.718421
$280$		0			0
$281$	−22.0000			−1.31241			−0.656205	−	0.754583i	$-0.727839\pi$
$281$	−22.0000			−1.31241			−0.656205	+	0.754583i	$0.727839\pi$
$282$		0			0
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	0.919327	−	0.393494i	$-0.128734\pi$
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	−0.800439	+	0.599414i	$0.795400\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	2.50000	−	12.9904i	0.147570	−	0.766798i
$288$		0			0
$289$	6.50000	−	11.2583i	0.382353	−	0.662255i
$290$		0			0
$291$	−15.0000	−	25.9808i	−0.879316	−	1.52302i
$292$		0			0
$293$	4.00000			0.233682			0.116841	−	0.993151i	$-0.462723\pi$
$293$	4.00000			0.233682			0.116841	+	0.993151i	$0.462723\pi$
$294$		0			0
$295$	8.00000			0.465778
$296$		0			0
$297$	−9.00000	−	15.5885i	−0.522233	−	0.904534i
$298$		0			0
$299$	−27.0000	+	46.7654i	−1.56145	+	2.70451i
$300$		0			0
$301$	0.500000	−	2.59808i	0.0288195	−	0.149751i
$302$		0			0
$303$	−4.50000	+	7.79423i	−0.258518	+	0.447767i
$304$		0			0
$305$	3.50000	+	6.06218i	0.200409	+	0.347119i
$306$		0			0
$307$	1.00000			0.0570730			0.0285365	−	0.999593i	$-0.490915\pi$
$307$	1.00000			0.0570730			0.0285365	+	0.999593i	$0.490915\pi$
$308$		0			0
$309$	−39.0000			−2.21863
$310$		0			0
$311$	−12.0000	−	20.7846i	−0.680458	−	1.17859i	−0.974841	−	0.222900i	$-0.928448\pi$
$311$	−12.0000	−	20.7846i	−0.680458	−	1.17859i	0.294384	−	0.955687i	$-0.404886\pi$
$312$		0			0
$313$	2.00000	−	3.46410i	0.113047	−	0.195803i	−0.803951	−	0.594696i	$-0.797272\pi$
$313$	2.00000	−	3.46410i	0.113047	−	0.195803i	0.916997	+	0.398894i	$0.130606\pi$
$314$		0			0
$315$	15.0000	−	5.19615i	0.845154	−	0.292770i
$316$		0			0
$317$	−5.00000	+	8.66025i	−0.280828	+	0.486408i	−0.971589	−	0.236675i	$-0.923942\pi$
$317$	−5.00000	+	8.66025i	−0.280828	+	0.486408i	0.690761	+	0.723083i	$0.257276\pi$
$318$		0			0
$319$	3.00000	+	5.19615i	0.167968	+	0.290929i
$320$		0			0
$321$	45.0000			2.51166
$322$		0			0
$323$		0			0
$324$		0			0
$325$	3.00000	+	5.19615i	0.166410	+	0.288231i
$326$		0			0
$327$	13.5000	−	23.3827i	0.746552	−	1.29307i
$328$		0			0
$329$	16.0000	+	13.8564i	0.882109	+	0.763928i
$330$		0			0
$331$	−5.00000	+	8.66025i	−0.274825	+	0.476011i	−0.970091	−	0.242742i	$-0.921953\pi$
$331$	−5.00000	+	8.66025i	−0.274825	+	0.476011i	0.695266	+	0.718752i	$0.255287\pi$
$332$		0			0
$333$	−24.0000	−	41.5692i	−1.31519	−	2.27798i
$334$		0			0
$335$	3.00000			0.163908
$336$		0			0
$337$	28.0000			1.52526			0.762629	−	0.646837i	$-0.223908\pi$
$337$	28.0000			1.52526			0.762629	+	0.646837i	$0.223908\pi$
$338$		0			0
$339$	−6.00000	−	10.3923i	−0.325875	−	0.564433i
$340$		0			0
$341$	2.00000	−	3.46410i	0.108306	−	0.187592i
$342$		0			0
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$		0			0
$345$	13.5000	−	23.3827i	0.726816	−	1.25888i
$346$		0			0
$347$	−12.5000	−	21.6506i	−0.671035	−	1.16227i	−0.977611	−	0.210421i	$-0.932517\pi$
$347$	−12.5000	−	21.6506i	−0.671035	−	1.16227i	0.306576	−	0.951846i	$-0.400817\pi$
$348$		0			0
$349$	−17.0000			−0.909989			−0.454995	−	0.890494i	$-0.650359\pi$
$349$	−17.0000			−0.909989			−0.454995	+	0.890494i	$0.650359\pi$
$350$		0			0
$351$	54.0000			2.88231
$352$		0			0
$353$	18.0000	+	31.1769i	0.958043	+	1.65938i	0.727245	+	0.686378i	$0.240800\pi$
$353$	18.0000	+	31.1769i	0.958043	+	1.65938i	0.230799	+	0.973002i	$0.425866\pi$
$354$		0			0
$355$	4.00000	−	6.92820i	0.212298	−	0.367711i
$356$		0			0
$357$	−12.0000	−	10.3923i	−0.635107	−	0.550019i
$358$		0			0
$359$	5.00000	−	8.66025i	0.263890	−	0.457071i	−0.703382	−	0.710812i	$-0.748328\pi$
$359$	5.00000	−	8.66025i	0.263890	−	0.457071i	0.967272	+	0.253741i	$0.0816611\pi$
$360$		0			0
$361$	9.50000	+	16.4545i	0.500000	+	0.866025i
$362$		0			0
$363$	21.0000			1.10221
$364$		0			0
$365$	−14.0000			−0.732793
$366$		0			0
$367$	−0.500000	−	0.866025i	−0.0260998	−	0.0452062i	0.852680	−	0.522433i	$-0.174975\pi$
$367$	−0.500000	−	0.866025i	−0.0260998	−	0.0452062i	−0.878780	+	0.477227i	$0.841642\pi$
$368$		0			0
$369$	−15.0000	+	25.9808i	−0.780869	+	1.35250i
$370$		0			0
$371$	−10.0000	+	3.46410i	−0.519174	+	0.179847i
$372$		0			0
$373$	−16.0000	+	27.7128i	−0.828449	+	1.43492i	0.0708063	+	0.997490i	$0.477443\pi$
$373$	−16.0000	+	27.7128i	−0.828449	+	1.43492i	−0.899255	+	0.437425i	$0.855891\pi$
$374$		0			0
$375$	−1.50000	−	2.59808i	−0.0774597	−	0.134164i
$376$		0			0
$377$	−18.0000			−0.927047
$378$		0			0
$379$		0			0			−	1.00000i	$-0.5\pi$
$379$		0			0				1.00000i	$0.5\pi$
$380$		0			0
$381$	24.0000	+	41.5692i	1.22956	+	2.12966i
$382$		0			0
$383$	4.50000	−	7.79423i	0.229939	−	0.398266i	−0.727851	−	0.685736i	$-0.759481\pi$
$383$	4.50000	−	7.79423i	0.229939	−	0.398266i	0.957790	+	0.287469i	$0.0928139\pi$
$384$		0			0
$385$	1.00000	−	5.19615i	0.0509647	−	0.264820i
$386$		0			0
$387$	−3.00000	+	5.19615i	−0.152499	+	0.264135i
$388$		0			0
$389$	5.00000	+	8.66025i	0.253510	+	0.439092i	0.964490	−	0.264120i	$-0.0850816\pi$
$389$	5.00000	+	8.66025i	0.253510	+	0.439092i	−0.710980	+	0.703213i	$0.751748\pi$
$390$		0			0
$391$	−18.0000			−0.910299
$392$		0			0
$393$	12.0000			0.605320
$394$		0			0
$395$	2.00000	+	3.46410i	0.100631	+	0.174298i
$396$		0			0
$397$	−5.00000	+	8.66025i	−0.250943	+	0.434646i	−0.963786	−	0.266678i	$-0.914074\pi$
$397$	−5.00000	+	8.66025i	−0.250943	+	0.434646i	0.712843	+	0.701324i	$0.247407\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	14.5000	−	25.1147i	0.724095	−	1.25417i	−0.235250	−	0.971935i	$-0.575591\pi$
$401$	14.5000	−	25.1147i	0.724095	−	1.25417i	0.959345	−	0.282235i	$-0.0910758\pi$
$402$		0			0
$403$	6.00000	+	10.3923i	0.298881	+	0.517678i
$404$		0			0
$405$	−9.00000			−0.447214
$406$		0			0
$407$	−16.0000			−0.793091
$408$		0			0
$409$	−1.50000	−	2.59808i	−0.0741702	−	0.128467i	0.826555	−	0.562856i	$-0.190297\pi$
$409$	−1.50000	−	2.59808i	−0.0741702	−	0.128467i	−0.900725	+	0.434389i	$0.856964\pi$
$410$		0			0
$411$	−18.0000	+	31.1769i	−0.887875	+	1.53784i
$412$		0			0
$413$	20.0000	−	6.92820i	0.984136	−	0.340915i
$414$		0			0
$415$	−0.500000	+	0.866025i	−0.0245440	+	0.0425115i
$416$		0			0
$417$	15.0000	+	25.9808i	0.734553	+	1.27228i
$418$		0			0
$419$	−24.0000			−1.17248			−0.586238	−	0.810139i	$-0.699392\pi$
$419$	−24.0000			−1.17248			−0.586238	+	0.810139i	$0.699392\pi$
$420$		0			0
$421$	−1.00000			−0.0487370			−0.0243685	−	0.999703i	$-0.507758\pi$
$421$	−1.00000			−0.0487370			−0.0243685	+	0.999703i	$0.507758\pi$
$422$		0			0
$423$	−24.0000	−	41.5692i	−1.16692	−	2.02116i
$424$		0			0
$425$	−1.00000	+	1.73205i	−0.0485071	+	0.0840168i
$426$		0			0
$427$	14.0000	+	12.1244i	0.677507	+	0.586739i
$428$		0			0
$429$	18.0000	−	31.1769i	0.869048	−	1.50524i
$430$		0			0
$431$	−3.00000	−	5.19615i	−0.144505	−	0.250290i	0.784683	−	0.619897i	$-0.212826\pi$
$431$	−3.00000	−	5.19615i	−0.144505	−	0.250290i	−0.929188	+	0.369607i	$0.879492\pi$
$432$		0			0
$433$	−4.00000			−0.192228			−0.0961139	−	0.995370i	$-0.530641\pi$
$433$	−4.00000			−0.192228			−0.0961139	+	0.995370i	$0.530641\pi$
$434$		0			0
$435$	9.00000			0.431517
$436$		0			0
$437$		0			0
$438$		0			0
$439$	−2.00000	+	3.46410i	−0.0954548	+	0.165333i	−0.909798	−	0.415051i	$-0.863764\pi$
$439$	−2.00000	+	3.46410i	−0.0954548	+	0.165333i	0.814344	+	0.580383i	$0.197097\pi$
$440$		0			0
$441$	33.0000	−	25.9808i	1.57143	−	1.23718i
$442$		0			0
$443$	−18.5000	+	32.0429i	−0.878962	+	1.52241i	−0.0264796	+	0.999649i	$0.508430\pi$
$443$	−18.5000	+	32.0429i	−0.878962	+	1.52241i	−0.852482	+	0.522757i	$0.824904\pi$
$444$		0			0
$445$	6.50000	+	11.2583i	0.308130	+	0.533696i
$446$		0			0
$447$	−27.0000			−1.27706
$448$		0			0
$449$	15.0000			0.707894			0.353947	−	0.935266i	$-0.384839\pi$
$449$	15.0000			0.707894			0.353947	+	0.935266i	$0.384839\pi$
$450$		0			0
$451$	5.00000	+	8.66025i	0.235441	+	0.407795i
$452$		0			0
$453$	−15.0000	+	25.9808i	−0.704761	+	1.22068i
$454$		0			0
$455$	12.0000	+	10.3923i	0.562569	+	0.487199i
$456$		0			0
$457$	−14.0000	+	24.2487i	−0.654892	+	1.13431i	0.327028	+	0.945015i	$0.393953\pi$
$457$	−14.0000	+	24.2487i	−0.654892	+	1.13431i	−0.981921	+	0.189292i	$0.939381\pi$
$458$		0			0
$459$	9.00000	+	15.5885i	0.420084	+	0.727607i
$460$		0			0
$461$	−2.00000			−0.0931493			−0.0465746	−	0.998915i	$-0.514831\pi$
$461$	−2.00000			−0.0931493			−0.0465746	+	0.998915i	$0.514831\pi$
$462$		0			0
$463$	17.0000			0.790057			0.395029	−	0.918669i	$-0.370735\pi$
$463$	17.0000			0.790057			0.395029	+	0.918669i	$0.370735\pi$
$464$		0			0
$465$	−3.00000	−	5.19615i	−0.139122	−	0.240966i
$466$		0			0
$467$	−2.50000	+	4.33013i	−0.115686	+	0.200374i	−0.918054	−	0.396456i	$-0.870240\pi$
$467$	−2.50000	+	4.33013i	−0.115686	+	0.200374i	0.802368	+	0.596830i	$0.203573\pi$
$468$		0			0
$469$	7.50000	−	2.59808i	0.346318	−	0.119968i
$470$		0			0
$471$	−3.00000	+	5.19615i	−0.138233	+	0.239426i
$472$		0			0
$473$	1.00000	+	1.73205i	0.0459800	+	0.0796398i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	24.0000			1.09888
$478$		0			0
$479$	15.0000	+	25.9808i	0.685367	+	1.18709i	0.973321	+	0.229447i	$0.0736918\pi$
$479$	15.0000	+	25.9808i	0.685367	+	1.18709i	−0.287954	+	0.957644i	$0.592975\pi$
$480$		0			0
$481$	24.0000	−	41.5692i	1.09431	−	1.89539i
$482$		0			0
$483$	13.5000	−	70.1481i	0.614271	−	3.19185i
$484$		0			0
$485$	−5.00000	+	8.66025i	−0.227038	+	0.393242i
$486$		0			0
$487$	−16.0000	−	27.7128i	−0.725029	−	1.25579i	−0.958962	−	0.283535i	$-0.908493\pi$
$487$	−16.0000	−	27.7128i	−0.725029	−	1.25579i	0.233933	−	0.972253i	$-0.424840\pi$
$488$		0			0
$489$	−24.0000			−1.08532
$490$		0			0
$491$	6.00000			0.270776			0.135388	−	0.990793i	$-0.456772\pi$
$491$	6.00000			0.270776			0.135388	+	0.990793i	$0.456772\pi$
$492$		0			0
$493$	−3.00000	−	5.19615i	−0.135113	−	0.234023i
$494$		0			0
$495$	−6.00000	+	10.3923i	−0.269680	+	0.467099i
$496$		0			0
$497$	4.00000	−	20.7846i	0.179425	−	0.932317i
$498$		0			0
$499$	3.00000	−	5.19615i	0.134298	−	0.232612i	−0.791031	−	0.611776i	$-0.790455\pi$
$499$	3.00000	−	5.19615i	0.134298	−	0.232612i	0.925329	+	0.379165i	$0.123789\pi$
$500$		0			0
$501$	−13.5000	−	23.3827i	−0.603136	−	1.04466i
$502$		0			0
$503$	27.0000			1.20387			0.601935	−	0.798545i	$-0.294397\pi$
$503$	27.0000			1.20387			0.601935	+	0.798545i	$0.294397\pi$
$504$		0			0
$505$	3.00000			0.133498
$506$		0			0
$507$	34.5000	+	59.7558i	1.53220	+	2.65385i
$508$		0			0
$509$	20.5000	−	35.5070i	0.908647	−	1.57382i	0.0927004	−	0.995694i	$-0.470450\pi$
$509$	20.5000	−	35.5070i	0.908647	−	1.57382i	0.815946	−	0.578128i	$-0.196217\pi$
$510$		0			0
$511$	−35.0000	+	12.1244i	−1.54831	+	0.536350i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	6.50000	+	11.2583i	0.286424	+	0.496101i
$516$		0			0
$517$	−16.0000			−0.703679
$518$		0			0
$519$	48.0000			2.10697
$520$		0			0
$521$	−7.00000	−	12.1244i	−0.306676	−	0.531178i	0.670957	−	0.741496i	$-0.265883\pi$
$521$	−7.00000	−	12.1244i	−0.306676	−	0.531178i	−0.977633	+	0.210318i	$0.932550\pi$
$522$		0			0
$523$	−2.00000	+	3.46410i	−0.0874539	+	0.151475i	−0.906434	−	0.422347i	$-0.861206\pi$
$523$	−2.00000	+	3.46410i	−0.0874539	+	0.151475i	0.818980	+	0.573822i	$0.194540\pi$
$524$		0			0
$525$	−6.00000	−	5.19615i	−0.261861	−	0.226779i
$526$		0			0
$527$	−2.00000	+	3.46410i	−0.0871214	+	0.150899i
$528$		0			0
$529$	−29.0000	−	50.2295i	−1.26087	−	2.18389i
$530$		0			0
$531$	−48.0000			−2.08302
$532$		0			0
$533$	−30.0000			−1.29944
$534$		0			0
$535$	−7.50000	−	12.9904i	−0.324253	−	0.561623i
$536$		0			0
$537$	−9.00000	+	15.5885i	−0.388379	+	0.672692i
$538$		0			0
$539$	−2.00000	−	13.8564i	−0.0861461	−	0.596838i
$540$		0			0
$541$	−16.5000	+	28.5788i	−0.709390	+	1.22870i	0.255693	+	0.966758i	$0.417696\pi$
$541$	−16.5000	+	28.5788i	−0.709390	+	1.22870i	−0.965084	+	0.261942i	$0.915637\pi$
$542$		0			0
$543$	1.50000	+	2.59808i	0.0643712	+	0.111494i
$544$		0			0
$545$	−9.00000			−0.385518
$546$		0			0
$547$	−15.0000			−0.641354			−0.320677	−	0.947189i	$-0.603910\pi$
$547$	−15.0000			−0.641354			−0.320677	+	0.947189i	$0.603910\pi$
$548$		0			0
$549$	−21.0000	−	36.3731i	−0.896258	−	1.55236i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	8.00000	+	6.92820i	0.340195	+	0.294617i
$554$		0			0
$555$	−12.0000	+	20.7846i	−0.509372	+	0.882258i
$556$		0			0
$557$	1.00000	+	1.73205i	0.0423714	+	0.0733893i	0.886433	−	0.462856i	$-0.153175\pi$
$557$	1.00000	+	1.73205i	0.0423714	+	0.0733893i	−0.844062	+	0.536246i	$0.819842\pi$
$558$		0			0
$559$	−6.00000			−0.253773
$560$		0			0
$561$	12.0000			0.506640
$562$		0			0
$563$	6.50000	+	11.2583i	0.273942	+	0.474482i	0.969868	−	0.243632i	$-0.0783389\pi$
$563$	6.50000	+	11.2583i	0.273942	+	0.474482i	−0.695925	+	0.718114i	$0.745006\pi$
$564$		0			0
$565$	−2.00000	+	3.46410i	−0.0841406	+	0.145736i
$566$		0			0
$567$	−22.5000	+	7.79423i	−0.944911	+	0.327327i
$568$		0			0
$569$	−15.0000	+	25.9808i	−0.628833	+	1.08917i	0.358954	+	0.933355i	$0.383134\pi$
$569$	−15.0000	+	25.9808i	−0.628833	+	1.08917i	−0.987786	+	0.155815i	$0.950200\pi$
$570$		0			0
$571$	−12.0000	−	20.7846i	−0.502184	−	0.869809i	−0.999997	−	0.00252413i	$-0.999197\pi$
$571$	−12.0000	−	20.7846i	−0.502184	−	0.869809i	0.497812	−	0.867285i	$-0.334137\pi$
$572$		0			0
$573$	−18.0000			−0.751961
$574$		0			0
$575$	−9.00000			−0.375326
$576$		0			0
$577$	−11.0000	−	19.0526i	−0.457936	−	0.793168i	0.540916	−	0.841077i	$-0.318078\pi$
$577$	−11.0000	−	19.0526i	−0.457936	−	0.793168i	−0.998852	+	0.0479084i	$0.984744\pi$
$578$		0			0
$579$	3.00000	−	5.19615i	0.124676	−	0.215945i
$580$		0			0
$581$	−0.500000	+	2.59808i	−0.0207435	+	0.107786i
$582$		0			0
$583$	4.00000	−	6.92820i	0.165663	−	0.286937i
$584$		0			0
$585$	−18.0000	−	31.1769i	−0.744208	−	1.28901i
$586$		0			0
$587$	20.0000			0.825488			0.412744	−	0.910847i	$-0.364570\pi$
$587$	20.0000			0.825488			0.412744	+	0.910847i	$0.364570\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$	21.0000	+	36.3731i	0.863825	+	1.49619i
$592$		0			0
$593$	18.0000	−	31.1769i	0.739171	−	1.28028i	−0.213697	−	0.976900i	$-0.568551\pi$
$593$	18.0000	−	31.1769i	0.739171	−	1.28028i	0.952869	−	0.303383i	$-0.0981160\pi$
$594$		0			0
$595$	−1.00000	+	5.19615i	−0.0409960	+	0.213021i
$596$		0			0
$597$	30.0000	−	51.9615i	1.22782	−	2.12664i
$598$		0			0
$599$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$599$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$600$		0			0
$601$	−6.00000			−0.244745			−0.122373	−	0.992484i	$-0.539050\pi$
$601$	−6.00000			−0.244745			−0.122373	+	0.992484i	$0.539050\pi$
$602$		0			0
$603$	−18.0000			−0.733017
$604$		0			0
$605$	−3.50000	−	6.06218i	−0.142295	−	0.246463i
$606$		0			0
$607$	−0.500000	+	0.866025i	−0.0202944	+	0.0351509i	−0.875994	−	0.482322i	$-0.839794\pi$
$607$	−0.500000	+	0.866025i	−0.0202944	+	0.0351509i	0.855700	+	0.517472i	$0.173127\pi$
$608$		0			0
$609$	22.5000	−	7.79423i	0.911746	−	0.315838i
$610$		0			0
$611$	24.0000	−	41.5692i	0.970936	−	1.68171i
$612$		0			0
$613$	3.00000	+	5.19615i	0.121169	+	0.209871i	0.920229	−	0.391381i	$-0.128002\pi$
$613$	3.00000	+	5.19615i	0.121169	+	0.209871i	−0.799060	+	0.601251i	$0.794669\pi$
$614$		0			0
$615$	15.0000			0.604858
$616$		0			0
$617$	20.0000			0.805170			0.402585	−	0.915383i	$-0.368112\pi$
$617$	20.0000			0.805170			0.402585	+	0.915383i	$0.368112\pi$
$618$		0			0
$619$	5.00000	+	8.66025i	0.200967	+	0.348085i	0.948840	−	0.315757i	$-0.102258\pi$
$619$	5.00000	+	8.66025i	0.200967	+	0.348085i	−0.747873	+	0.663842i	$0.768925\pi$
$620$		0			0
$621$	−40.5000	+	70.1481i	−1.62521	+	2.81494i
$622$		0			0
$623$	26.0000	+	22.5167i	1.04167	+	0.902111i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	16.0000			0.637962
$630$		0			0
$631$	−34.0000			−1.35352			−0.676759	−	0.736204i	$-0.736616\pi$
$631$	−34.0000			−1.35352			−0.676759	+	0.736204i	$0.736616\pi$
$632$		0			0
$633$	6.00000	+	10.3923i	0.238479	+	0.413057i
$634$		0			0
$635$	8.00000	−	13.8564i	0.317470	−	0.549875i
$636$		0			0
$637$	39.0000	+	15.5885i	1.54524	+	0.617637i
$638$		0			0
$639$	−24.0000	+	41.5692i	−0.949425	+	1.64445i
$640$		0			0
$641$	15.5000	+	26.8468i	0.612213	+	1.06038i	0.990867	+	0.134846i	$0.0430539\pi$
$641$	15.5000	+	26.8468i	0.612213	+	1.06038i	−0.378653	+	0.925539i	$0.623613\pi$
$642$		0			0
$643$	−20.0000			−0.788723			−0.394362	−	0.918955i	$-0.629034\pi$
$643$	−20.0000			−0.788723			−0.394362	+	0.918955i	$0.629034\pi$
$644$		0			0
$645$	3.00000			0.118125
$646$		0			0
$647$	−0.500000	−	0.866025i	−0.0196570	−	0.0340470i	0.856030	−	0.516927i	$-0.172924\pi$
$647$	−0.500000	−	0.866025i	−0.0196570	−	0.0340470i	−0.875687	+	0.482880i	$0.839591\pi$
$648$		0			0
$649$	−8.00000	+	13.8564i	−0.314027	+	0.543912i
$650$		0			0
$651$	−12.0000	−	10.3923i	−0.470317	−	0.407307i
$652$		0			0
$653$	17.0000	−	29.4449i	0.665261	−	1.15227i	−0.313953	−	0.949439i	$-0.601653\pi$
$653$	17.0000	−	29.4449i	0.665261	−	1.15227i	0.979214	−	0.202828i	$-0.0650132\pi$
$654$		0			0
$655$	−2.00000	−	3.46410i	−0.0781465	−	0.135354i
$656$		0			0
$657$	84.0000			3.27715
$658$		0			0
$659$	4.00000			0.155818			0.0779089	−	0.996960i	$-0.475176\pi$
$659$	4.00000			0.155818			0.0779089	+	0.996960i	$0.475176\pi$
$660$		0			0
$661$	−15.5000	−	26.8468i	−0.602880	−	1.04422i	−0.992383	−	0.123194i	$-0.960686\pi$
$661$	−15.5000	−	26.8468i	−0.602880	−	1.04422i	0.389503	−	0.921025i	$-0.372647\pi$
$662$		0			0
$663$	−18.0000	+	31.1769i	−0.699062	+	1.21081i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	13.5000	−	23.3827i	0.522722	−	0.905381i
$668$		0			0
$669$	24.0000	+	41.5692i	0.927894	+	1.60716i
$670$		0			0
$671$	−14.0000			−0.540464
$672$		0			0
$673$	16.0000			0.616755			0.308377	−	0.951264i	$-0.400214\pi$
$673$	16.0000			0.616755			0.308377	+	0.951264i	$0.400214\pi$
$674$		0			0
$675$	4.50000	+	7.79423i	0.173205	+	0.300000i
$676$		0			0
$677$	−3.00000	+	5.19615i	−0.115299	+	0.199704i	−0.917899	−	0.396813i	$-0.870116\pi$
$677$	−3.00000	+	5.19615i	−0.115299	+	0.199704i	0.802600	+	0.596518i	$0.203449\pi$
$678$		0			0
$679$	−5.00000	+	25.9808i	−0.191882	+	0.997050i
$680$		0			0
$681$	−6.00000	+	10.3923i	−0.229920	+	0.398234i
$682$		0			0
$683$	−14.5000	−	25.1147i	−0.554827	−	0.960989i	−0.997917	−	0.0645115i	$-0.979451\pi$
$683$	−14.5000	−	25.1147i	−0.554827	−	0.960989i	0.443090	−	0.896477i	$-0.353882\pi$
$684$		0			0
$685$	12.0000			0.458496
$686$		0			0
$687$	42.0000			1.60240
$688$		0			0
$689$	12.0000	+	20.7846i	0.457164	+	0.791831i
$690$		0			0
$691$	13.0000	−	22.5167i	0.494543	−	0.856574i	−0.505437	−	0.862864i	$-0.668669\pi$
$691$	13.0000	−	22.5167i	0.494543	−	0.856574i	0.999980	+	0.00628943i	$0.00200200\pi$
$692$		0			0
$693$	−6.00000	+	31.1769i	−0.227921	+	1.18431i
$694$		0			0
$695$	5.00000	−	8.66025i	0.189661	−	0.328502i
$696$		0			0
$697$	−5.00000	−	8.66025i	−0.189389	−	0.328031i
$698$		0			0
$699$	54.0000			2.04247
$700$		0			0
$701$	−29.0000			−1.09531			−0.547657	−	0.836703i	$-0.684480\pi$
$701$	−29.0000			−1.09531			−0.547657	+	0.836703i	$0.684480\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	−12.0000	+	20.7846i	−0.451946	+	0.782794i
$706$		0			0
$707$	7.50000	−	2.59808i	0.282067	−	0.0977107i
$708$		0			0
$709$	−15.5000	+	26.8468i	−0.582115	+	1.00825i	0.413114	+	0.910679i	$0.364441\pi$
$709$	−15.5000	+	26.8468i	−0.582115	+	1.00825i	−0.995228	+	0.0975728i	$0.968892\pi$
$710$		0			0
$711$	−12.0000	−	20.7846i	−0.450035	−	0.779484i
$712$		0			0
$713$	−18.0000			−0.674105
$714$		0			0
$715$	−12.0000			−0.448775
$716$		0			0
$717$	−39.0000	−	67.5500i	−1.45648	−	2.52270i
$718$		0			0
$719$	3.00000	−	5.19615i	0.111881	−	0.193784i	−0.804648	−	0.593753i	$-0.797646\pi$
$719$	3.00000	−	5.19615i	0.111881	−	0.193784i	0.916529	+	0.399969i	$0.130979\pi$
$720$		0			0
$721$	26.0000	+	22.5167i	0.968291	+	0.838564i
$722$		0			0
$723$	15.0000	−	25.9808i	0.557856	−	0.966235i
$724$		0			0
$725$	−1.50000	−	2.59808i	−0.0557086	−	0.0964901i
$726$		0			0
$727$	3.00000			0.111264			0.0556319	−	0.998451i	$-0.482283\pi$
$727$	3.00000			0.111264			0.0556319	+	0.998451i	$0.482283\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	−1.00000	−	1.73205i	−0.0369863	−	0.0640622i
$732$		0			0
$733$	−17.0000	+	29.4449i	−0.627909	+	1.08757i	0.360061	+	0.932929i	$0.382756\pi$
$733$	−17.0000	+	29.4449i	−0.627909	+	1.08757i	−0.987971	+	0.154642i	$0.950578\pi$
$734$		0			0
$735$	−19.5000	−	7.79423i	−0.719268	−	0.287494i
$736$		0			0
$737$	−3.00000	+	5.19615i	−0.110506	+	0.191403i
$738$		0			0
$739$	−5.00000	−	8.66025i	−0.183928	−	0.318573i	0.759287	−	0.650756i	$-0.225548\pi$
$739$	−5.00000	−	8.66025i	−0.183928	−	0.318573i	−0.943215	+	0.332184i	$0.892215\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−3.00000			−0.110059			−0.0550297	−	0.998485i	$-0.517525\pi$
$743$	−3.00000			−0.110059			−0.0550297	+	0.998485i	$0.517525\pi$
$744$		0			0
$745$	4.50000	+	7.79423i	0.164867	+	0.285558i
$746$		0			0
$747$	3.00000	−	5.19615i	0.109764	−	0.190117i
$748$		0			0
$749$	−30.0000	−	25.9808i	−1.09618	−	0.949316i
$750$		0			0
$751$	−10.0000	+	17.3205i	−0.364905	+	0.632034i	−0.988761	−	0.149505i	$-0.952232\pi$
$751$	−10.0000	+	17.3205i	−0.364905	+	0.632034i	0.623856	+	0.781540i	$0.285565\pi$
$752$		0			0
$753$	45.0000	+	77.9423i	1.63989	+	2.84037i
$754$		0			0
$755$	10.0000			0.363937
$756$		0			0
$757$	−38.0000			−1.38113			−0.690567	−	0.723269i	$-0.742639\pi$
$757$	−38.0000			−1.38113			−0.690567	+	0.723269i	$0.742639\pi$
$758$		0			0
$759$	27.0000	+	46.7654i	0.980038	+	1.69748i
$760$		0			0
$761$	−15.0000	+	25.9808i	−0.543750	+	0.941802i	0.454935	+	0.890525i	$0.349663\pi$
$761$	−15.0000	+	25.9808i	−0.543750	+	0.941802i	−0.998684	+	0.0512772i	$0.983671\pi$
$762$		0			0
$763$	−22.5000	+	7.79423i	−0.814555	+	0.282170i
$764$		0			0
$765$	6.00000	−	10.3923i	0.216930	−	0.375735i
$766$		0			0
$767$	−24.0000	−	41.5692i	−0.866590	−	1.50098i
$768$		0			0
$769$	−2.00000			−0.0721218			−0.0360609	−	0.999350i	$-0.511481\pi$
$769$	−2.00000			−0.0721218			−0.0360609	+	0.999350i	$0.511481\pi$
$770$		0			0
$771$	−24.0000			−0.864339
$772$		0			0
$773$	9.00000	+	15.5885i	0.323708	+	0.560678i	0.981250	−	0.192740i	$-0.0617373\pi$
$773$	9.00000	+	15.5885i	0.323708	+	0.560678i	−0.657542	+	0.753418i	$0.728404\pi$
$774$		0			0
$775$	−1.00000	+	1.73205i	−0.0359211	+	0.0622171i
$776$		0			0
$777$	−12.0000	+	62.3538i	−0.430498	+	2.23693i
$778$		0			0
$779$		0			0
$780$		0			0
$781$	8.00000	+	13.8564i	0.286263	+	0.495821i
$782$		0			0
$783$	−27.0000			−0.964901
$784$		0			0
$785$	2.00000			0.0713831
$786$		0			0
$787$	5.50000	+	9.52628i	0.196054	+	0.339575i	0.947245	−	0.320509i	$-0.103854\pi$
$787$	5.50000	+	9.52628i	0.196054	+	0.339575i	−0.751192	+	0.660084i	$0.770521\pi$
$788$		0			0
$789$	25.5000	−	44.1673i	0.907824	−	1.57240i
$790$		0			0
$791$	−2.00000	+	10.3923i	−0.0711118	+	0.369508i
$792$		0			0
$793$	21.0000	−	36.3731i	0.745732	−	1.29165i
$794$		0			0
$795$	−6.00000	−	10.3923i	−0.212798	−	0.368577i
$796$		0			0
$797$	36.0000			1.27519			0.637593	−	0.770374i	$-0.279930\pi$
$797$	36.0000			1.27519			0.637593	+	0.770374i	$0.279930\pi$
$798$		0			0
$799$	16.0000			0.566039
$800$		0			0
$801$	−39.0000	−	67.5500i	−1.37800	−	2.38676i
$802$		0			0
$803$	14.0000	−	24.2487i	0.494049	−	0.855718i
$804$		0			0
$805$	−22.5000	+	7.79423i	−0.793021	+	0.274710i
$806$		0			0
$807$	13.5000	−	23.3827i	0.475223	−	0.823110i
$808$		0			0
$809$	−22.5000	−	38.9711i	−0.791058	−	1.37015i	−0.925312	−	0.379206i	$-0.876197\pi$
$809$	−22.5000	−	38.9711i	−0.791058	−	1.37015i	0.134255	−	0.990947i	$-0.457136\pi$
$810$		0			0
$811$	50.0000			1.75574			0.877869	−	0.478901i	$-0.158965\pi$
$811$	50.0000			1.75574			0.877869	+	0.478901i	$0.158965\pi$
$812$		0			0
$813$	72.0000			2.52515
$814$		0			0
$815$	4.00000	+	6.92820i	0.140114	+	0.242684i
$816$		0			0
$817$		0			0
$818$		0			0
$819$	−72.0000	−	62.3538i	−2.51588	−	2.17882i
$820$		0			0
$821$	−9.00000	+	15.5885i	−0.314102	+	0.544041i	−0.979246	−	0.202674i	$-0.935037\pi$
$821$	−9.00000	+	15.5885i	−0.314102	+	0.544041i	0.665144	+	0.746715i	$0.268370\pi$
$822$		0			0
$823$	−9.50000	−	16.4545i	−0.331149	−	0.573567i	0.651588	−	0.758573i	$-0.274103\pi$
$823$	−9.50000	−	16.4545i	−0.331149	−	0.573567i	−0.982737	+	0.185006i	$0.940770\pi$
$824$		0			0
$825$	6.00000			0.208893
$826$		0			0
$827$	23.0000			0.799788			0.399894	−	0.916561i	$-0.369047\pi$
$827$	23.0000			0.799788			0.399894	+	0.916561i	$0.369047\pi$
$828$		0			0
$829$	5.00000	+	8.66025i	0.173657	+	0.300783i	0.939696	−	0.342012i	$-0.111108\pi$
$829$	5.00000	+	8.66025i	0.173657	+	0.300783i	−0.766039	+	0.642795i	$0.777775\pi$
$830$		0			0
$831$	27.0000	−	46.7654i	0.936620	−	1.62227i
$832$		0			0
$833$	2.00000	+	13.8564i	0.0692959	+	0.480096i
$834$		0			0
$835$	−4.50000	+	7.79423i	−0.155729	+	0.269730i
$836$		0			0
$837$	9.00000	+	15.5885i	0.311086	+	0.538816i
$838$		0			0
$839$	14.0000			0.483334			0.241667	−	0.970359i	$-0.422306\pi$
$839$	14.0000			0.483334			0.241667	+	0.970359i	$0.422306\pi$
$840$		0			0
$841$	−20.0000			−0.689655
$842$		0			0
$843$	−33.0000	−	57.1577i	−1.13658	−	1.96861i
$844$		0			0
$845$	11.5000	−	19.9186i	0.395612	−	0.685220i
$846$		0			0
$847$	−14.0000	−	12.1244i	−0.481046	−	0.416598i
$848$		0			0
$849$	−6.00000	+	10.3923i	−0.205919	+	0.356663i
$850$		0			0
$851$	36.0000	+	62.3538i	1.23406	+	2.13746i
$852$		0			0
$853$	−40.0000			−1.36957			−0.684787	−	0.728743i	$-0.740105\pi$
$853$	−40.0000			−1.36957			−0.684787	+	0.728743i	$0.740105\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	27.0000	+	46.7654i	0.922302	+	1.59747i	0.795843	+	0.605503i	$0.207028\pi$
$857$	27.0000	+	46.7654i	0.922302	+	1.59747i	0.126459	+	0.991972i	$0.459639\pi$
$858$		0			0
$859$	18.0000	−	31.1769i	0.614152	−	1.06374i	−0.376381	−	0.926465i	$-0.622831\pi$
$859$	18.0000	−	31.1769i	0.614152	−	1.06374i	0.990533	−	0.137277i	$-0.0438352\pi$
$860$		0			0
$861$	37.5000	−	12.9904i	1.27800	−	0.442711i
$862$		0			0
$863$	−18.5000	+	32.0429i	−0.629747	+	1.09075i	0.357855	+	0.933777i	$0.383508\pi$
$863$	−18.5000	+	32.0429i	−0.629747	+	1.09075i	−0.987602	+	0.156977i	$0.949825\pi$
$864$		0			0
$865$	−8.00000	−	13.8564i	−0.272008	−	0.471132i
$866$		0			0
$867$	39.0000			1.32451
$868$		0			0
$869$	−8.00000			−0.271381
$870$		0			0
$871$	−9.00000	−	15.5885i	−0.304953	−	0.528195i
$872$		0			0
$873$	30.0000	−	51.9615i	1.01535	−	1.75863i
$874$		0			0
$875$	−0.500000	+	2.59808i	−0.0169031	+	0.0878310i
$876$		0			0
$877$	−16.0000	+	27.7128i	−0.540282	+	0.935795i	0.458606	+	0.888640i	$0.348349\pi$
$877$	−16.0000	+	27.7128i	−0.540282	+	0.935795i	−0.998888	+	0.0471555i	$0.984984\pi$
$878$		0			0
$879$	6.00000	+	10.3923i	0.202375	+	0.350524i
$880$		0			0
$881$	−31.0000			−1.04442			−0.522208	−	0.852818i	$-0.674892\pi$
$881$	−31.0000			−1.04442			−0.522208	+	0.852818i	$0.674892\pi$
$882$		0			0
$883$	−36.0000			−1.21150			−0.605748	−	0.795656i	$-0.707126\pi$
$883$	−36.0000			−1.21150			−0.605748	+	0.795656i	$0.707126\pi$
$884$		0			0
$885$	12.0000	+	20.7846i	0.403376	+	0.698667i
$886$		0			0
$887$	−26.5000	+	45.8993i	−0.889783	+	1.54115i	−0.0496513	+	0.998767i	$0.515811\pi$
$887$	−26.5000	+	45.8993i	−0.889783	+	1.54115i	−0.840132	+	0.542383i	$0.817522\pi$
$888$		0			0
$889$	8.00000	−	41.5692i	0.268311	−	1.39419i
$890$		0			0
$891$	9.00000	−	15.5885i	0.301511	−	0.522233i
$892$		0			0
$893$		0			0
$894$		0			0
$895$	6.00000			0.200558
$896$		0			0
$897$	−162.000			−5.40902
$898$		0			0
$899$	−3.00000	−	5.19615i	−0.100056	−	0.173301i
$900$		0			0
$901$	−4.00000	+	6.92820i	−0.133259	+	0.230812i
$902$		0			0
$903$	7.50000	−	2.59808i	0.249584	−	0.0864586i
$904$		0			0
$905$	0.500000	−	0.866025i	0.0166206	−	0.0287877i
$906$		0			0
$907$	18.5000	+	32.0429i	0.614282	+	1.06397i	0.990510	+	0.137441i	$0.0438878\pi$
$907$	18.5000	+	32.0429i	0.614282	+	1.06397i	−0.376228	+	0.926527i	$0.622779\pi$
$908$		0			0
$909$	−18.0000			−0.597022
$910$		0			0
$911$	54.0000			1.78910			0.894550	−	0.446968i	$-0.147496\pi$
$911$	54.0000			1.78910			0.894550	+	0.446968i	$0.147496\pi$
$912$		0			0
$913$	−1.00000	−	1.73205i	−0.0330952	−	0.0573225i
$914$		0			0
$915$	−10.5000	+	18.1865i	−0.347119	+	0.601228i
$916$		0			0
$917$	−8.00000	−	6.92820i	−0.264183	−	0.228789i
$918$		0			0
$919$	−16.0000	+	27.7128i	−0.527791	+	0.914161i	0.471684	+	0.881768i	$0.343646\pi$
$919$	−16.0000	+	27.7128i	−0.527791	+	0.914161i	−0.999475	+	0.0323936i	$0.989687\pi$
$920$		0			0
$921$	1.50000	+	2.59808i	0.0494267	+	0.0856095i
$922$		0			0
$923$	−48.0000			−1.57994
$924$		0			0
$925$	8.00000			0.263038
$926$		0			0
$927$	−39.0000	−	67.5500i	−1.28093	−	2.21863i
$928$		0			0
$929$	2.50000	−	4.33013i	0.0820223	−	0.142067i	−0.822096	−	0.569349i	$-0.807195\pi$
$929$	2.50000	−	4.33013i	0.0820223	−	0.142067i	0.904118	+	0.427282i	$0.140529\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	36.0000	−	62.3538i	1.17859	−	2.04137i
$934$		0			0
$935$	−2.00000	−	3.46410i	−0.0654070	−	0.113288i
$936$		0			0
$937$	−52.0000			−1.69877			−0.849383	−	0.527777i	$-0.823026\pi$
$937$	−52.0000			−1.69877			−0.849383	+	0.527777i	$0.823026\pi$
$938$		0			0
$939$	12.0000			0.391605
$940$		0			0
$941$	−19.0000	−	32.9090i	−0.619382	−	1.07280i	−0.989599	−	0.143856i	$-0.954050\pi$
$941$	−19.0000	−	32.9090i	−0.619382	−	1.07280i	0.370216	−	0.928946i	$-0.379284\pi$
$942$		0			0
$943$	22.5000	−	38.9711i	0.732701	−	1.26908i
$944$		0			0
$945$	18.0000	+	15.5885i	0.585540	+	0.507093i
$946$		0			0
$947$	−14.5000	+	25.1147i	−0.471187	+	0.816119i	−0.999457	−	0.0329571i	$-0.989508\pi$
$947$	−14.5000	+	25.1147i	−0.471187	+	0.816119i	0.528270	+	0.849076i	$0.322841\pi$
$948$		0			0
$949$	42.0000	+	72.7461i	1.36338	+	2.36144i
$950$		0			0
$951$	−30.0000			−0.972817
$952$		0			0
$953$	−60.0000			−1.94359			−0.971795	−	0.235826i	$-0.924220\pi$
$953$	−60.0000			−1.94359			−0.971795	+	0.235826i	$0.924220\pi$
$954$		0			0
$955$	3.00000	+	5.19615i	0.0970777	+	0.168144i
$956$		0			0
$957$	−9.00000	+	15.5885i	−0.290929	+	0.503903i
$958$		0			0
$959$	30.0000	−	10.3923i	0.968751	−	0.335585i
$960$		0			0
$961$	13.5000	−	23.3827i	0.435484	−	0.754280i
$962$		0			0
$963$	45.0000	+	77.9423i	1.45010	+	2.51166i
$964$		0			0
$965$	−2.00000			−0.0643823
$966$		0			0
$967$	37.0000			1.18984			0.594920	−	0.803785i	$-0.297184\pi$
$967$	37.0000			1.18984			0.594920	+	0.803785i	$0.297184\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	6.00000	−	10.3923i	0.192549	−	0.333505i	−0.753545	−	0.657396i	$-0.771658\pi$
$971$	6.00000	−	10.3923i	0.192549	−	0.333505i	0.946094	+	0.323891i	$0.104991\pi$
$972$		0			0
$973$	5.00000	−	25.9808i	0.160293	−	0.832905i
$974$		0			0
$975$	−9.00000	+	15.5885i	−0.288231	+	0.499230i
$976$		0			0
$977$	3.00000	+	5.19615i	0.0959785	+	0.166240i	0.910017	−	0.414572i	$-0.136069\pi$
$977$	3.00000	+	5.19615i	0.0959785	+	0.166240i	−0.814038	+	0.580812i	$0.802735\pi$
$978$		0			0
$979$	−26.0000			−0.830964
$980$		0			0
$981$	54.0000			1.72409
$982$		0			0
$983$	9.50000	+	16.4545i	0.303003	+	0.524816i	0.976815	−	0.214087i	$-0.0686775\pi$
$983$	9.50000	+	16.4545i	0.303003	+	0.524816i	−0.673812	+	0.738903i	$0.735344\pi$
$984$		0			0
$985$	7.00000	−	12.1244i	0.223039	−	0.386314i
$986$		0			0
$987$	−12.0000	+	62.3538i	−0.381964	+	1.98474i
$988$		0			0
$989$	4.50000	−	7.79423i	0.143092	−	0.247842i
$990$		0			0
$991$	19.0000	+	32.9090i	0.603555	+	1.04539i	0.992278	+	0.124033i	$0.0395829\pi$
$991$	19.0000	+	32.9090i	0.603555	+	1.04539i	−0.388723	+	0.921355i	$0.627084\pi$
$992$		0			0
$993$	−30.0000			−0.952021
$994$		0			0
$995$	−20.0000			−0.634043
$996$		0			0
$997$	20.0000	+	34.6410i	0.633406	+	1.09709i	0.986850	+	0.161636i	$0.0516771\pi$
$997$	20.0000	+	34.6410i	0.633406	+	1.09709i	−0.353444	+	0.935456i	$0.614990\pi$
$998$		0			0
$999$	36.0000	−	62.3538i	1.13899	−	1.97279i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	140.2.i.b.121.1	yes	2
3.2	odd	2		1260.2.s.b.541.1		2
4.3	odd	2		560.2.q.a.401.1		2
5.2	odd	4		700.2.r.c.149.2		4
5.3	odd	4		700.2.r.c.149.1		4
5.4	even	2		700.2.i.a.401.1		2
7.2	even	3		980.2.a.a.1.1		1
7.3	odd	6		980.2.i.a.361.1		2
7.4	even	3	inner	140.2.i.b.81.1	✓	2
7.5	odd	6		980.2.a.i.1.1		1
7.6	odd	2		980.2.i.a.961.1		2
21.2	odd	6		8820.2.a.w.1.1		1
21.5	even	6		8820.2.a.k.1.1		1
21.11	odd	6		1260.2.s.b.361.1		2
28.11	odd	6		560.2.q.a.81.1		2
28.19	even	6		3920.2.a.d.1.1		1
28.23	odd	6		3920.2.a.bi.1.1		1
35.2	odd	12		4900.2.e.c.2549.2		2
35.4	even	6		700.2.i.a.501.1		2
35.9	even	6		4900.2.a.v.1.1		1
35.12	even	12		4900.2.e.b.2549.1		2
35.18	odd	12		700.2.r.c.249.2		4
35.19	odd	6		4900.2.a.a.1.1		1
35.23	odd	12		4900.2.e.c.2549.1		2
35.32	odd	12		700.2.r.c.249.1		4
35.33	even	12		4900.2.e.b.2549.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.i.b.81.1	✓	2	7.4	even	3	inner
140.2.i.b.121.1	yes	2	1.1	even	1	trivial
560.2.q.a.81.1		2	28.11	odd	6
560.2.q.a.401.1		2	4.3	odd	2
700.2.i.a.401.1		2	5.4	even	2
700.2.i.a.501.1		2	35.4	even	6
700.2.r.c.149.1		4	5.3	odd	4
700.2.r.c.149.2		4	5.2	odd	4
700.2.r.c.249.1		4	35.32	odd	12
700.2.r.c.249.2		4	35.18	odd	12
980.2.a.a.1.1		1	7.2	even	3
980.2.a.i.1.1		1	7.5	odd	6
980.2.i.a.361.1		2	7.3	odd	6
980.2.i.a.961.1		2	7.6	odd	2
1260.2.s.b.361.1		2	21.11	odd	6
1260.2.s.b.541.1		2	3.2	odd	2
3920.2.a.d.1.1		1	28.19	even	6
3920.2.a.bi.1.1		1	28.23	odd	6
4900.2.a.a.1.1		1	35.19	odd	6
4900.2.a.v.1.1		1	35.9	even	6
4900.2.e.b.2549.1		2	35.12	even	12
4900.2.e.b.2549.2		2	35.33	even	12
4900.2.e.c.2549.1		2	35.23	odd	12
4900.2.e.c.2549.2		2	35.2	odd	12
8820.2.a.k.1.1		1	21.5	even	6
8820.2.a.w.1.1		1	21.2	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:	\( N \)	\(=\)	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	140.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 + 2.59808i) q^{3} +(0.500000 - 0.866025i) q^{5} +(0.500000 - 2.59808i) q^{7} +(-3.00000 + 5.19615i) q^{9} +O(q^{10})\)	\(q+(1.50000 + 2.59808i) q^{3} +(0.500000 - 0.866025i) q^{5} +(0.500000 - 2.59808i) q^{7} +(-3.00000 + 5.19615i) q^{9} +(1.00000 + 1.73205i) q^{11} -6.00000 q^{13} +3.00000 q^{15} +(-1.00000 - 1.73205i) q^{17} +(7.50000 - 2.59808i) q^{21} +(4.50000 - 7.79423i) q^{23} +(-0.500000 - 0.866025i) q^{25} -9.00000 q^{27} +3.00000 q^{29} +(-1.00000 - 1.73205i) q^{31} +(-3.00000 + 5.19615i) q^{33} +(-2.00000 - 1.73205i) q^{35} +(-4.00000 + 6.92820i) q^{37} +(-9.00000 - 15.5885i) q^{39} +5.00000 q^{41} +1.00000 q^{43} +(3.00000 + 5.19615i) q^{45} +(-4.00000 + 6.92820i) q^{47} +(-6.50000 - 2.59808i) q^{49} +(3.00000 - 5.19615i) q^{51} +(-2.00000 - 3.46410i) q^{53} +2.00000 q^{55} +(4.00000 + 6.92820i) q^{59} +(-3.50000 + 6.06218i) q^{61} +(12.0000 + 10.3923i) q^{63} +(-3.00000 + 5.19615i) q^{65} +(1.50000 + 2.59808i) q^{67} +27.0000 q^{69} +8.00000 q^{71} +(-7.00000 - 12.1244i) q^{73} +(1.50000 - 2.59808i) q^{75} +(5.00000 - 1.73205i) q^{77} +(-2.00000 + 3.46410i) q^{79} +(-4.50000 - 7.79423i) q^{81} -1.00000 q^{83} -2.00000 q^{85} +(4.50000 + 7.79423i) q^{87} +(-6.50000 + 11.2583i) q^{89} +(-3.00000 + 15.5885i) q^{91} +(3.00000 - 5.19615i) q^{93} -10.0000 q^{97} -12.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{3} + q^{5} + q^{7} - 6 q^{9}+O(q^{10}) \) 2 * q + 3 * q^3 + q^5 + q^7 - 6 * q^9	\( 2 q + 3 q^{3} + q^{5} + q^{7} - 6 q^{9} + 2 q^{11} - 12 q^{13} + 6 q^{15} - 2 q^{17} + 15 q^{21} + 9 q^{23} - q^{25} - 18 q^{27} + 6 q^{29} - 2 q^{31} - 6 q^{33} - 4 q^{35} - 8 q^{37} - 18 q^{39} + 10 q^{41} + 2 q^{43} + 6 q^{45} - 8 q^{47} - 13 q^{49} + 6 q^{51} - 4 q^{53} + 4 q^{55} + 8 q^{59} - 7 q^{61} + 24 q^{63} - 6 q^{65} + 3 q^{67} + 54 q^{69} + 16 q^{71} - 14 q^{73} + 3 q^{75} + 10 q^{77} - 4 q^{79} - 9 q^{81} - 2 q^{83} - 4 q^{85} + 9 q^{87} - 13 q^{89} - 6 q^{91} + 6 q^{93} - 20 q^{97} - 24 q^{99}+O(q^{100}) \) 2 * q + 3 * q^3 + q^5 + q^7 - 6 * q^9 + 2 * q^11 - 12 * q^13 + 6 * q^15 - 2 * q^17 + 15 * q^21 + 9 * q^23 - q^25 - 18 * q^27 + 6 * q^29 - 2 * q^31 - 6 * q^33 - 4 * q^35 - 8 * q^37 - 18 * q^39 + 10 * q^41 + 2 * q^43 + 6 * q^45 - 8 * q^47 - 13 * q^49 + 6 * q^51 - 4 * q^53 + 4 * q^55 + 8 * q^59 - 7 * q^61 + 24 * q^63 - 6 * q^65 + 3 * q^67 + 54 * q^69 + 16 * q^71 - 14 * q^73 + 3 * q^75 + 10 * q^77 - 4 * q^79 - 9 * q^81 - 2 * q^83 - 4 * q^85 + 9 * q^87 - 13 * q^89 - 6 * q^91 + 6 * q^93 - 20 * q^97 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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