LMFDB - Embedded newform 980.2.i.j.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [980,2,Mod(361,980)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(980, 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("980.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.i (of order $3$, degree $2$, not 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:	$7.82533939809$
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:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	980.361
Dual form			980.2.i.j.961.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 - 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-3.00000 - 5.19615i) q^{9} +O(q^{10})$	\(q+(1.50000 - 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-3.00000 - 5.19615i) q^{9} +(2.50000 - 4.33013i) q^{11} +3.00000 q^{13} -3.00000 q^{15} +(-0.500000 + 0.866025i) q^{17} +(3.00000 + 5.19615i) q^{19} +(-3.00000 - 5.19615i) q^{23} +(-0.500000 + 0.866025i) q^{25} -9.00000 q^{27} -9.00000 q^{29} +(-2.00000 + 3.46410i) q^{31} +(-7.50000 - 12.9904i) q^{33} +(-1.00000 - 1.73205i) q^{37} +(4.50000 - 7.79423i) q^{39} +4.00000 q^{41} +10.0000 q^{43} +(-3.00000 + 5.19615i) q^{45} +(-0.500000 - 0.866025i) q^{47} +(1.50000 + 2.59808i) q^{51} +(-2.00000 + 3.46410i) q^{53} -5.00000 q^{55} +18.0000 q^{57} +(-4.00000 + 6.92820i) q^{59} +(-4.00000 - 6.92820i) q^{61} +(-1.50000 - 2.59808i) q^{65} +(-6.00000 + 10.3923i) q^{67} -18.0000 q^{69} +8.00000 q^{71} +(1.00000 - 1.73205i) q^{73} +(1.50000 + 2.59808i) q^{75} +(-6.50000 - 11.2583i) q^{79} +(-4.50000 + 7.79423i) q^{81} +4.00000 q^{83} +1.00000 q^{85} +(-13.5000 + 23.3827i) q^{87} +(2.00000 + 3.46410i) q^{89} +(6.00000 + 10.3923i) q^{93} +(3.00000 - 5.19615i) q^{95} +13.0000 q^{97} -30.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{3} - q^{5} - 6 q^{9}+O(q^{10}) $ 2 * q + 3 * q^3 - q^5 - 6 * q^9	$ 2 q + 3 q^{3} - q^{5} - 6 q^{9} + 5 q^{11} + 6 q^{13} - 6 q^{15} - q^{17} + 6 q^{19} - 6 q^{23} - q^{25} - 18 q^{27} - 18 q^{29} - 4 q^{31} - 15 q^{33} - 2 q^{37} + 9 q^{39} + 8 q^{41} + 20 q^{43} - 6 q^{45} - q^{47} + 3 q^{51} - 4 q^{53} - 10 q^{55} + 36 q^{57} - 8 q^{59} - 8 q^{61} - 3 q^{65} - 12 q^{67} - 36 q^{69} + 16 q^{71} + 2 q^{73} + 3 q^{75} - 13 q^{79} - 9 q^{81} + 8 q^{83} + 2 q^{85} - 27 q^{87} + 4 q^{89} + 12 q^{93} + 6 q^{95} + 26 q^{97} - 60 q^{99}+O(q^{100}) $ 2 * q + 3 * q^3 - q^5 - 6 * q^9 + 5 * q^11 + 6 * q^13 - 6 * q^15 - q^17 + 6 * q^19 - 6 * q^23 - q^25 - 18 * q^27 - 18 * q^29 - 4 * q^31 - 15 * q^33 - 2 * q^37 + 9 * q^39 + 8 * q^41 + 20 * q^43 - 6 * q^45 - q^47 + 3 * q^51 - 4 * q^53 - 10 * q^55 + 36 * q^57 - 8 * q^59 - 8 * q^61 - 3 * q^65 - 12 * q^67 - 36 * q^69 + 16 * q^71 + 2 * q^73 + 3 * q^75 - 13 * q^79 - 9 * q^81 + 8 * q^83 + 2 * q^85 - 27 * q^87 + 4 * q^89 + 12 * q^93 + 6 * q^95 + 26 * q^97 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$3$	1.50000	−	2.59808i	0.866025	−	1.50000i		−	1.00000i	$-0.5\pi$
$3$	1.50000	−	2.59808i	0.866025	−	1.50000i	0.866025	−	0.500000i	$-0.166667\pi$
$4$		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			0
$7$		0			0
$8$		0			0
$9$	−3.00000	−	5.19615i	−1.00000	−	1.73205i
$10$		0			0
$11$	2.50000	−	4.33013i	0.753778	−	1.30558i	−0.192201	−	0.981356i	$-0.561563\pi$
$11$	2.50000	−	4.33013i	0.753778	−	1.30558i	0.945979	−	0.324227i	$-0.105104\pi$
$12$		0			0
$13$	3.00000			0.832050			0.416025	−	0.909353i	$-0.363423\pi$
$13$	3.00000			0.832050			0.416025	+	0.909353i	$0.363423\pi$
$14$		0			0
$15$	−3.00000			−0.774597
$16$		0			0
$17$	−0.500000	+	0.866025i	−0.121268	+	0.210042i	−0.920268	−	0.391289i	$-0.872029\pi$
$17$	−0.500000	+	0.866025i	−0.121268	+	0.210042i	0.799000	+	0.601331i	$0.205363\pi$
$18$		0			0
$19$	3.00000	+	5.19615i	0.688247	+	1.19208i	0.972404	+	0.233301i	$0.0749529\pi$
$19$	3.00000	+	5.19615i	0.688247	+	1.19208i	−0.284157	+	0.958778i	$0.591714\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	−0.988436	−	0.151642i	$-0.951544\pi$
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	0.362892	−	0.931831i	$-0.381789\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	−9.00000			−1.73205
$28$		0			0
$29$	−9.00000			−1.67126			−0.835629	−	0.549294i	$-0.814897\pi$
$29$	−9.00000			−1.67126			−0.835629	+	0.549294i	$0.814897\pi$
$30$		0			0
$31$	−2.00000	+	3.46410i	−0.359211	+	0.622171i	−0.987829	−	0.155543i	$-0.950287\pi$
$31$	−2.00000	+	3.46410i	−0.359211	+	0.622171i	0.628619	+	0.777714i	$0.283621\pi$
$32$		0			0
$33$	−7.50000	−	12.9904i	−1.30558	−	2.26134i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1.00000	−	1.73205i	−0.164399	−	0.284747i	0.772043	−	0.635571i	$-0.219235\pi$
$37$	−1.00000	−	1.73205i	−0.164399	−	0.284747i	−0.936442	+	0.350823i	$0.885902\pi$
$38$		0			0
$39$	4.50000	−	7.79423i	0.720577	−	1.24808i
$40$		0			0
$41$	4.00000			0.624695			0.312348	−	0.949968i	$-0.398885\pi$
$41$	4.00000			0.624695			0.312348	+	0.949968i	$0.398885\pi$
$42$		0			0
$43$	10.0000			1.52499			0.762493	−	0.646997i	$-0.223975\pi$
$43$	10.0000			1.52499			0.762493	+	0.646997i	$0.223975\pi$
$44$		0			0
$45$	−3.00000	+	5.19615i	−0.447214	+	0.774597i
$46$		0			0
$47$	−0.500000	−	0.866025i	−0.0729325	−	0.126323i	0.827253	−	0.561830i	$-0.189902\pi$
$47$	−0.500000	−	0.866025i	−0.0729325	−	0.126323i	−0.900185	+	0.435507i	$0.856569\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	1.50000	+	2.59808i	0.210042	+	0.363803i
$52$		0			0
$53$	−2.00000	+	3.46410i	−0.274721	+	0.475831i	−0.970065	−	0.242846i	$-0.921919\pi$
$53$	−2.00000	+	3.46410i	−0.274721	+	0.475831i	0.695344	+	0.718677i	$0.255252\pi$
$54$		0			0
$55$	−5.00000			−0.674200
$56$		0			0
$57$	18.0000			2.38416
$58$		0			0
$59$	−4.00000	+	6.92820i	−0.520756	+	0.901975i	0.478953	+	0.877841i	$0.341016\pi$
$59$	−4.00000	+	6.92820i	−0.520756	+	0.901975i	−0.999709	+	0.0241347i	$0.992317\pi$
$60$		0			0
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	−0.999901	−	0.0140840i	$-0.995517\pi$
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	0.487753	−	0.872982i	$-0.337817\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.50000	−	2.59808i	−0.186052	−	0.322252i
$66$		0			0
$67$	−6.00000	+	10.3923i	−0.733017	+	1.26962i	0.222571	+	0.974916i	$0.428555\pi$
$67$	−6.00000	+	10.3923i	−0.733017	+	1.26962i	−0.955588	+	0.294706i	$0.904778\pi$
$68$		0			0
$69$	−18.0000			−2.16695
$70$		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
$73$	1.00000	−	1.73205i	0.117041	−	0.202721i	−0.801553	−	0.597924i	$-0.795992\pi$
$73$	1.00000	−	1.73205i	0.117041	−	0.202721i	0.918594	+	0.395203i	$0.129326\pi$
$74$		0			0
$75$	1.50000	+	2.59808i	0.173205	+	0.300000i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−6.50000	−	11.2583i	−0.731307	−	1.26666i	−0.956325	−	0.292306i	$-0.905577\pi$
$79$	−6.50000	−	11.2583i	−0.731307	−	1.26666i	0.225018	−	0.974355i	$-0.427756\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$		0			0
$83$	4.00000			0.439057			0.219529	−	0.975606i	$-0.429548\pi$
$83$	4.00000			0.439057			0.219529	+	0.975606i	$0.429548\pi$
$84$		0			0
$85$	1.00000			0.108465
$86$		0			0
$87$	−13.5000	+	23.3827i	−1.44735	+	2.50689i
$88$		0			0
$89$	2.00000	+	3.46410i	0.212000	+	0.367194i	0.952340	−	0.305038i	$-0.0986691\pi$
$89$	2.00000	+	3.46410i	0.212000	+	0.367194i	−0.740341	+	0.672232i	$0.765336\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	6.00000	+	10.3923i	0.622171	+	1.07763i
$94$		0			0
$95$	3.00000	−	5.19615i	0.307794	−	0.533114i
$96$		0			0
$97$	13.0000			1.31995			0.659975	−	0.751288i	$-0.270567\pi$
$97$	13.0000			1.31995			0.659975	+	0.751288i	$0.270567\pi$
$98$		0			0
$99$	−30.0000			−3.01511
$100$		0			0
$101$	3.00000	−	5.19615i	0.298511	−	0.517036i	−0.677284	−	0.735721i	$-0.736843\pi$
$101$	3.00000	−	5.19615i	0.298511	−	0.517036i	0.975796	+	0.218685i	$0.0701767\pi$
$102$		0			0
$103$	9.50000	+	16.4545i	0.936063	+	1.62131i	0.772728	+	0.634738i	$0.218892\pi$
$103$	9.50000	+	16.4545i	0.936063	+	1.62131i	0.163335	+	0.986571i	$0.447775\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.00000	+	5.19615i	0.290021	+	0.502331i	0.973814	−	0.227345i	$-0.0730044\pi$
$107$	3.00000	+	5.19615i	0.290021	+	0.502331i	−0.683793	+	0.729676i	$0.739671\pi$
$108$		0			0
$109$	1.50000	−	2.59808i	0.143674	−	0.248851i	−0.785203	−	0.619238i	$-0.787442\pi$
$109$	1.50000	−	2.59808i	0.143674	−	0.248851i	0.928877	+	0.370387i	$0.120775\pi$
$110$		0			0
$111$	−6.00000			−0.569495
$112$		0			0
$113$	14.0000			1.31701			0.658505	−	0.752577i	$-0.271189\pi$
$113$	14.0000			1.31701			0.658505	+	0.752577i	$0.271189\pi$
$114$		0			0
$115$	−3.00000	+	5.19615i	−0.279751	+	0.484544i
$116$		0			0
$117$	−9.00000	−	15.5885i	−0.832050	−	1.44115i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−7.00000	−	12.1244i	−0.636364	−	1.10221i
$122$		0			0
$123$	6.00000	−	10.3923i	0.541002	−	0.937043i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	−8.00000			−0.709885			−0.354943	−	0.934888i	$-0.615500\pi$
$127$	−8.00000			−0.709885			−0.354943	+	0.934888i	$0.615500\pi$
$128$		0			0
$129$	15.0000	−	25.9808i	1.32068	−	2.28748i
$130$		0			0
$131$	−5.00000	−	8.66025i	−0.436852	−	0.756650i	0.560593	−	0.828092i	$-0.310573\pi$
$131$	−5.00000	−	8.66025i	−0.436852	−	0.756650i	−0.997445	+	0.0714417i	$0.977240\pi$
$132$		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	−0.487278	−	0.873247i	$-0.662010\pi$
$137$	6.00000	−	10.3923i	0.512615	−	0.887875i	0.999893	−	0.0146279i	$-0.00465636\pi$
$138$		0			0
$139$	14.0000			1.18746			0.593732	−	0.804663i	$-0.297654\pi$
$139$	14.0000			1.18746			0.593732	+	0.804663i	$0.297654\pi$
$140$		0			0
$141$	−3.00000			−0.252646
$142$		0			0
$143$	7.50000	−	12.9904i	0.627182	−	1.08631i
$144$		0			0
$145$	4.50000	+	7.79423i	0.373705	+	0.647275i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	0.962348	−	0.271821i	$-0.0876260\pi$
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	−0.716578	+	0.697507i	$0.754293\pi$
$150$		0			0
$151$	−2.50000	+	4.33013i	−0.203447	+	0.352381i	−0.949637	−	0.313353i	$-0.898548\pi$
$151$	−2.50000	+	4.33013i	−0.203447	+	0.352381i	0.746190	+	0.665733i	$0.231881\pi$
$152$		0			0
$153$	6.00000			0.485071
$154$		0			0
$155$	4.00000			0.321288
$156$		0			0
$157$	−1.00000	+	1.73205i	−0.0798087	+	0.138233i	−0.903167	−	0.429289i	$-0.858764\pi$
$157$	−1.00000	+	1.73205i	−0.0798087	+	0.138233i	0.823359	+	0.567521i	$0.192098\pi$
$158$		0			0
$159$	6.00000	+	10.3923i	0.475831	+	0.824163i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	5.00000	+	8.66025i	0.391630	+	0.678323i	0.992665	−	0.120900i	$-0.0385779\pi$
$163$	5.00000	+	8.66025i	0.391630	+	0.678323i	−0.601035	+	0.799223i	$0.705245\pi$
$164$		0			0
$165$	−7.50000	+	12.9904i	−0.583874	+	1.01130i
$166$		0			0
$167$	−3.00000			−0.232147			−0.116073	−	0.993241i	$-0.537031\pi$
$167$	−3.00000			−0.232147			−0.116073	+	0.993241i	$0.537031\pi$
$168$		0			0
$169$	−4.00000			−0.307692
$170$		0			0
$171$	18.0000	−	31.1769i	1.37649	−	2.38416i
$172$		0			0
$173$	−0.500000	−	0.866025i	−0.0380143	−	0.0658427i	0.846392	−	0.532560i	$-0.178770\pi$
$173$	−0.500000	−	0.866025i	−0.0380143	−	0.0658427i	−0.884407	+	0.466717i	$0.845437\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	12.0000	+	20.7846i	0.901975	+	1.56227i
$178$		0			0
$179$	6.00000	−	10.3923i	0.448461	−	0.776757i	−0.549825	−	0.835280i	$-0.685306\pi$
$179$	6.00000	−	10.3923i	0.448461	−	0.776757i	0.998286	+	0.0585225i	$0.0186389\pi$
$180$		0			0
$181$	20.0000			1.48659			0.743294	−	0.668965i	$-0.233262\pi$
$181$	20.0000			1.48659			0.743294	+	0.668965i	$0.233262\pi$
$182$		0			0
$183$	−24.0000			−1.77413
$184$		0			0
$185$	−1.00000	+	1.73205i	−0.0735215	+	0.127343i
$186$		0			0
$187$	2.50000	+	4.33013i	0.182818	+	0.316650i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1.50000	−	2.59808i	−0.108536	−	0.187990i	0.806641	−	0.591041i	$-0.201283\pi$
$191$	−1.50000	−	2.59808i	−0.108536	−	0.187990i	−0.915177	+	0.403051i	$0.867950\pi$
$192$		0			0
$193$	2.00000	−	3.46410i	0.143963	−	0.249351i	−0.785022	−	0.619467i	$-0.787349\pi$
$193$	2.00000	−	3.46410i	0.143963	−	0.249351i	0.928986	+	0.370116i	$0.120682\pi$
$194$		0			0
$195$	−9.00000			−0.644503
$196$		0			0
$197$	8.00000			0.569976			0.284988	−	0.958531i	$-0.408010\pi$
$197$	8.00000			0.569976			0.284988	+	0.958531i	$0.408010\pi$
$198$		0			0
$199$	4.00000	−	6.92820i	0.283552	−	0.491127i	−0.688705	−	0.725042i	$-0.741820\pi$
$199$	4.00000	−	6.92820i	0.283552	−	0.491127i	0.972257	+	0.233915i	$0.0751537\pi$
$200$		0			0
$201$	18.0000	+	31.1769i	1.26962	+	2.19905i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−2.00000	−	3.46410i	−0.139686	−	0.241943i
$206$		0			0
$207$	−18.0000	+	31.1769i	−1.25109	+	2.16695i
$208$		0			0
$209$	30.0000			2.07514
$210$		0			0
$211$	−11.0000			−0.757271			−0.378636	−	0.925546i	$-0.623607\pi$
$211$	−11.0000			−0.757271			−0.378636	+	0.925546i	$0.623607\pi$
$212$		0			0
$213$	12.0000	−	20.7846i	0.822226	−	1.42414i
$214$		0			0
$215$	−5.00000	−	8.66025i	−0.340997	−	0.590624i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−3.00000	−	5.19615i	−0.202721	−	0.351123i
$220$		0			0
$221$	−1.50000	+	2.59808i	−0.100901	+	0.174766i
$222$		0			0
$223$	5.00000			0.334825			0.167412	−	0.985887i	$-0.446459\pi$
$223$	5.00000			0.334825			0.167412	+	0.985887i	$0.446459\pi$
$224$		0			0
$225$	6.00000			0.400000
$226$		0			0
$227$	−0.500000	+	0.866025i	−0.0331862	+	0.0574801i	−0.882141	−	0.470985i	$-0.843899\pi$
$227$	−0.500000	+	0.866025i	−0.0331862	+	0.0574801i	0.848955	+	0.528465i	$0.177232\pi$
$228$		0			0
$229$	2.00000	+	3.46410i	0.132164	+	0.228914i	0.924510	−	0.381157i	$-0.124474\pi$
$229$	2.00000	+	3.46410i	0.132164	+	0.228914i	−0.792347	+	0.610071i	$0.791141\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−12.0000	−	20.7846i	−0.786146	−	1.36165i	−0.928312	−	0.371802i	$-0.878740\pi$
$233$	−12.0000	−	20.7846i	−0.786146	−	1.36165i	0.142166	−	0.989843i	$-0.454593\pi$
$234$		0			0
$235$	−0.500000	+	0.866025i	−0.0326164	+	0.0564933i
$236$		0			0
$237$	−39.0000			−2.53332
$238$		0			0
$239$	1.00000			0.0646846			0.0323423	−	0.999477i	$-0.489703\pi$
$239$	1.00000			0.0646846			0.0323423	+	0.999477i	$0.489703\pi$
$240$		0			0
$241$	−13.0000	+	22.5167i	−0.837404	+	1.45043i	0.0546547	+	0.998505i	$0.482594\pi$
$241$	−13.0000	+	22.5167i	−0.837404	+	1.45043i	−0.892058	+	0.451920i	$0.850739\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$	9.00000	+	15.5885i	0.572656	+	0.991870i
$248$		0			0
$249$	6.00000	−	10.3923i	0.380235	−	0.658586i
$250$		0			0
$251$	−30.0000			−1.89358			−0.946792	−	0.321847i	$-0.895696\pi$
$251$	−30.0000			−1.89358			−0.946792	+	0.321847i	$0.895696\pi$
$252$		0			0
$253$	−30.0000			−1.88608
$254$		0			0
$255$	1.50000	−	2.59808i	0.0939336	−	0.162698i
$256$		0			0
$257$	7.00000	+	12.1244i	0.436648	+	0.756297i	0.997429	−	0.0716680i	$-0.0228322\pi$
$257$	7.00000	+	12.1244i	0.436648	+	0.756297i	−0.560781	+	0.827964i	$0.689499\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	27.0000	+	46.7654i	1.67126	+	2.89470i
$262$		0			0
$263$	−1.00000	+	1.73205i	−0.0616626	+	0.106803i	−0.895209	−	0.445647i	$-0.852974\pi$
$263$	−1.00000	+	1.73205i	−0.0616626	+	0.106803i	0.833546	+	0.552450i	$0.186307\pi$
$264$		0			0
$265$	4.00000			0.245718
$266$		0			0
$267$	12.0000			0.734388
$268$		0			0
$269$	9.00000	−	15.5885i	0.548740	−	0.950445i	−0.449622	−	0.893219i	$-0.648441\pi$
$269$	9.00000	−	15.5885i	0.548740	−	0.950445i	0.998361	−	0.0572259i	$-0.0182255\pi$
$270$		0			0
$271$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$271$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	2.50000	+	4.33013i	0.150756	+	0.261116i
$276$		0			0
$277$	−3.00000	+	5.19615i	−0.180253	+	0.312207i	−0.941966	−	0.335707i	$-0.891025\pi$
$277$	−3.00000	+	5.19615i	−0.180253	+	0.312207i	0.761714	+	0.647913i	$0.224358\pi$
$278$		0			0
$279$	24.0000			1.43684
$280$		0			0
$281$	11.0000			0.656205			0.328102	−	0.944642i	$-0.393591\pi$
$281$	11.0000			0.656205			0.328102	+	0.944642i	$0.393591\pi$
$282$		0			0
$283$	−15.5000	+	26.8468i	−0.921379	+	1.59588i	−0.124096	+	0.992270i	$0.539603\pi$
$283$	−15.5000	+	26.8468i	−0.921379	+	1.59588i	−0.797283	+	0.603606i	$0.793730\pi$
$284$		0			0
$285$	−9.00000	−	15.5885i	−0.533114	−	0.923381i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	8.00000	+	13.8564i	0.470588	+	0.815083i
$290$		0			0
$291$	19.5000	−	33.7750i	1.14311	−	1.97993i
$292$		0			0
$293$	5.00000			0.292103			0.146052	−	0.989277i	$-0.453343\pi$
$293$	5.00000			0.292103			0.146052	+	0.989277i	$0.453343\pi$
$294$		0			0
$295$	8.00000			0.465778
$296$		0			0
$297$	−22.5000	+	38.9711i	−1.30558	+	2.26134i
$298$		0			0
$299$	−9.00000	−	15.5885i	−0.520483	−	0.901504i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−9.00000	−	15.5885i	−0.517036	−	0.895533i
$304$		0			0
$305$	−4.00000	+	6.92820i	−0.229039	+	0.396708i
$306$		0			0
$307$	23.0000			1.31268			0.656340	−	0.754466i	$-0.272104\pi$
$307$	23.0000			1.31268			0.656340	+	0.754466i	$0.272104\pi$
$308$		0			0
$309$	57.0000			3.24262
$310$		0			0
$311$	−9.00000	+	15.5885i	−0.510343	+	0.883940i	0.489585	+	0.871956i	$0.337148\pi$
$311$	−9.00000	+	15.5885i	−0.510343	+	0.883940i	−0.999928	+	0.0119847i	$0.996185\pi$
$312$		0			0
$313$	−3.50000	−	6.06218i	−0.197832	−	0.342655i	0.749993	−	0.661445i	$-0.230057\pi$
$313$	−3.50000	−	6.06218i	−0.197832	−	0.342655i	−0.947825	+	0.318791i	$0.896723\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	13.0000	+	22.5167i	0.730153	+	1.26466i	0.956818	+	0.290689i	$0.0938844\pi$
$317$	13.0000	+	22.5167i	0.730153	+	1.26466i	−0.226665	+	0.973973i	$0.572782\pi$
$318$		0			0
$319$	−22.5000	+	38.9711i	−1.25976	+	2.18197i
$320$		0			0
$321$	18.0000			1.00466
$322$		0			0
$323$	−6.00000			−0.333849
$324$		0			0
$325$	−1.50000	+	2.59808i	−0.0832050	+	0.144115i
$326$		0			0
$327$	−4.50000	−	7.79423i	−0.248851	−	0.431022i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−14.0000	−	24.2487i	−0.769510	−	1.33283i	−0.937829	−	0.347097i	$-0.887167\pi$
$331$	−14.0000	−	24.2487i	−0.769510	−	1.33283i	0.168320	−	0.985732i	$-0.446166\pi$
$332$		0			0
$333$	−6.00000	+	10.3923i	−0.328798	+	0.569495i
$334$		0			0
$335$	12.0000			0.655630
$336$		0			0
$337$	22.0000			1.19842			0.599208	−	0.800593i	$-0.295482\pi$
$337$	22.0000			1.19842			0.599208	+	0.800593i	$0.295482\pi$
$338$		0			0
$339$	21.0000	−	36.3731i	1.14056	−	1.97551i
$340$		0			0
$341$	10.0000	+	17.3205i	0.541530	+	0.937958i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	9.00000	+	15.5885i	0.484544	+	0.839254i
$346$		0			0
$347$	−5.00000	+	8.66025i	−0.268414	+	0.464907i	−0.968452	−	0.249198i	$-0.919833\pi$
$347$	−5.00000	+	8.66025i	−0.268414	+	0.464907i	0.700038	+	0.714105i	$0.253166\pi$
$348$		0			0
$349$	−10.0000			−0.535288			−0.267644	−	0.963518i	$-0.586245\pi$
$349$	−10.0000			−0.535288			−0.267644	+	0.963518i	$0.586245\pi$
$350$		0			0
$351$	−27.0000			−1.44115
$352$		0			0
$353$	1.50000	−	2.59808i	0.0798369	−	0.138282i	−0.823343	−	0.567545i	$-0.807893\pi$
$353$	1.50000	−	2.59808i	0.0798369	−	0.138282i	0.903179	+	0.429263i	$0.141227\pi$
$354$		0			0
$355$	−4.00000	−	6.92820i	−0.212298	−	0.367711i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	8.00000	+	13.8564i	0.422224	+	0.731313i	0.996157	−	0.0875892i	$-0.0279163\pi$
$359$	8.00000	+	13.8564i	0.422224	+	0.731313i	−0.573933	+	0.818902i	$0.694583\pi$
$360$		0			0
$361$	−8.50000	+	14.7224i	−0.447368	+	0.774865i
$362$		0			0
$363$	−42.0000			−2.20443
$364$		0			0
$365$	−2.00000			−0.104685
$366$		0			0
$367$	−8.50000	+	14.7224i	−0.443696	+	0.768505i	−0.997960	−	0.0638362i	$-0.979666\pi$
$367$	−8.50000	+	14.7224i	−0.443696	+	0.768505i	0.554264	+	0.832341i	$0.313000\pi$
$368$		0			0
$369$	−12.0000	−	20.7846i	−0.624695	−	1.08200i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	2.00000	+	3.46410i	0.103556	+	0.179364i	0.913147	−	0.407630i	$-0.133645\pi$
$373$	2.00000	+	3.46410i	0.103556	+	0.179364i	−0.809591	+	0.586994i	$0.800311\pi$
$374$		0			0
$375$	1.50000	−	2.59808i	0.0774597	−	0.134164i
$376$		0			0
$377$	−27.0000			−1.39057
$378$		0			0
$379$	12.0000			0.616399			0.308199	−	0.951322i	$-0.400274\pi$
$379$	12.0000			0.616399			0.308199	+	0.951322i	$0.400274\pi$
$380$		0			0
$381$	−12.0000	+	20.7846i	−0.614779	+	1.06483i
$382$		0			0
$383$	18.0000	+	31.1769i	0.919757	+	1.59307i	0.799783	+	0.600289i	$0.204948\pi$
$383$	18.0000	+	31.1769i	0.919757	+	1.59307i	0.119974	+	0.992777i	$0.461719\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−30.0000	−	51.9615i	−1.52499	−	2.64135i
$388$		0			0
$389$	15.5000	−	26.8468i	0.785881	−	1.36119i	−0.142590	−	0.989782i	$-0.545543\pi$
$389$	15.5000	−	26.8468i	0.785881	−	1.36119i	0.928471	−	0.371404i	$-0.121124\pi$
$390$		0			0
$391$	6.00000			0.303433
$392$		0			0
$393$	−30.0000			−1.51330
$394$		0			0
$395$	−6.50000	+	11.2583i	−0.327050	+	0.566468i
$396$		0			0
$397$	3.50000	+	6.06218i	0.175660	+	0.304252i	0.940389	−	0.340099i	$-0.110461\pi$
$397$	3.50000	+	6.06218i	0.175660	+	0.304252i	−0.764730	+	0.644351i	$0.777127\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−12.5000	−	21.6506i	−0.624220	−	1.08118i	−0.988691	−	0.149966i	$-0.952083\pi$
$401$	−12.5000	−	21.6506i	−0.624220	−	1.08118i	0.364471	−	0.931215i	$-0.381250\pi$
$402$		0			0
$403$	−6.00000	+	10.3923i	−0.298881	+	0.517678i
$404$		0			0
$405$	9.00000			0.447214
$406$		0			0
$407$	−10.0000			−0.495682
$408$		0			0
$409$	3.00000	−	5.19615i	0.148340	−	0.256933i	−0.782274	−	0.622935i	$-0.785940\pi$
$409$	3.00000	−	5.19615i	0.148340	−	0.256933i	0.930614	+	0.366002i	$0.119274\pi$
$410$		0			0
$411$	−18.0000	−	31.1769i	−0.887875	−	1.53784i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−2.00000	−	3.46410i	−0.0981761	−	0.170046i
$416$		0			0
$417$	21.0000	−	36.3731i	1.02837	−	1.78120i
$418$		0			0
$419$	−36.0000			−1.75872			−0.879358	−	0.476162i	$-0.842028\pi$
$419$	−36.0000			−1.75872			−0.879358	+	0.476162i	$0.842028\pi$
$420$		0			0
$421$	−19.0000			−0.926003			−0.463002	−	0.886357i	$-0.653228\pi$
$421$	−19.0000			−0.926003			−0.463002	+	0.886357i	$0.653228\pi$
$422$		0			0
$423$	−3.00000	+	5.19615i	−0.145865	+	0.252646i
$424$		0			0
$425$	−0.500000	−	0.866025i	−0.0242536	−	0.0420084i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−22.5000	−	38.9711i	−1.08631	−	1.88154i
$430$		0			0
$431$	4.50000	−	7.79423i	0.216757	−	0.375435i	−0.737057	−	0.675830i	$-0.763785\pi$
$431$	4.50000	−	7.79423i	0.216757	−	0.375435i	0.953815	+	0.300395i	$0.0971186\pi$
$432$		0			0
$433$	−2.00000			−0.0961139			−0.0480569	−	0.998845i	$-0.515303\pi$
$433$	−2.00000			−0.0961139			−0.0480569	+	0.998845i	$0.515303\pi$
$434$		0			0
$435$	27.0000			1.29455
$436$		0			0
$437$	18.0000	−	31.1769i	0.861057	−	1.49139i
$438$		0			0
$439$	−1.00000	−	1.73205i	−0.0477274	−	0.0826663i	0.841175	−	0.540763i	$-0.181865\pi$
$439$	−1.00000	−	1.73205i	−0.0477274	−	0.0826663i	−0.888902	+	0.458097i	$0.848531\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	7.00000	+	12.1244i	0.332580	+	0.576046i	0.983017	−	0.183515i	$-0.0587475\pi$
$443$	7.00000	+	12.1244i	0.332580	+	0.576046i	−0.650437	+	0.759560i	$0.725414\pi$
$444$		0			0
$445$	2.00000	−	3.46410i	0.0948091	−	0.164214i
$446$		0			0
$447$	18.0000			0.851371
$448$		0			0
$449$	−9.00000			−0.424736			−0.212368	−	0.977190i	$-0.568118\pi$
$449$	−9.00000			−0.424736			−0.212368	+	0.977190i	$0.568118\pi$
$450$		0			0
$451$	10.0000	−	17.3205i	0.470882	−	0.815591i
$452$		0			0
$453$	7.50000	+	12.9904i	0.352381	+	0.610341i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−8.00000	−	13.8564i	−0.374224	−	0.648175i	0.615986	−	0.787757i	$-0.288758\pi$
$457$	−8.00000	−	13.8564i	−0.374224	−	0.648175i	−0.990211	+	0.139581i	$0.955424\pi$
$458$		0			0
$459$	4.50000	−	7.79423i	0.210042	−	0.363803i
$460$		0			0
$461$	−40.0000			−1.86299			−0.931493	−	0.363760i	$-0.881493\pi$
$461$	−40.0000			−1.86299			−0.931493	+	0.363760i	$0.881493\pi$
$462$		0			0
$463$	−16.0000			−0.743583			−0.371792	−	0.928316i	$-0.621256\pi$
$463$	−16.0000			−0.743583			−0.371792	+	0.928316i	$0.621256\pi$
$464$		0			0
$465$	6.00000	−	10.3923i	0.278243	−	0.481932i
$466$		0			0
$467$	2.50000	+	4.33013i	0.115686	+	0.200374i	0.918054	−	0.396456i	$-0.129760\pi$
$467$	2.50000	+	4.33013i	0.115686	+	0.200374i	−0.802368	+	0.596830i	$0.796427\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	3.00000	+	5.19615i	0.138233	+	0.239426i
$472$		0			0
$473$	25.0000	−	43.3013i	1.14950	−	1.99099i
$474$		0			0
$475$	−6.00000			−0.275299
$476$		0			0
$477$	24.0000			1.09888
$478$		0			0
$479$	3.00000	−	5.19615i	0.137073	−	0.237418i	−0.789314	−	0.613990i	$-0.789564\pi$
$479$	3.00000	−	5.19615i	0.137073	−	0.237418i	0.926388	+	0.376571i	$0.122897\pi$
$480$		0			0
$481$	−3.00000	−	5.19615i	−0.136788	−	0.236924i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−6.50000	−	11.2583i	−0.295150	−	0.511214i
$486$		0			0
$487$	−13.0000	+	22.5167i	−0.589086	+	1.02033i	0.405266	+	0.914199i	$0.367179\pi$
$487$	−13.0000	+	22.5167i	−0.589086	+	1.02033i	−0.994352	+	0.106129i	$0.966154\pi$
$488$		0			0
$489$	30.0000			1.35665
$490$		0			0
$491$	−15.0000			−0.676941			−0.338470	−	0.940977i	$-0.609909\pi$
$491$	−15.0000			−0.676941			−0.338470	+	0.940977i	$0.609909\pi$
$492$		0			0
$493$	4.50000	−	7.79423i	0.202670	−	0.351034i
$494$		0			0
$495$	15.0000	+	25.9808i	0.674200	+	1.16775i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	4.50000	+	7.79423i	0.201448	+	0.348918i	0.948995	−	0.315291i	$-0.102102\pi$
$499$	4.50000	+	7.79423i	0.201448	+	0.348918i	−0.747547	+	0.664208i	$0.768769\pi$
$500$		0			0
$501$	−4.50000	+	7.79423i	−0.201045	+	0.348220i
$502$		0			0
$503$	3.00000			0.133763			0.0668817	−	0.997761i	$-0.478695\pi$
$503$	3.00000			0.133763			0.0668817	+	0.997761i	$0.478695\pi$
$504$		0			0
$505$	−6.00000			−0.266996
$506$		0			0
$507$	−6.00000	+	10.3923i	−0.266469	+	0.461538i
$508$		0			0
$509$	−7.00000	−	12.1244i	−0.310270	−	0.537403i	0.668151	−	0.744026i	$-0.267086\pi$
$509$	−7.00000	−	12.1244i	−0.310270	−	0.537403i	−0.978421	+	0.206623i	$0.933753\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−27.0000	−	46.7654i	−1.19208	−	2.06474i
$514$		0			0
$515$	9.50000	−	16.4545i	0.418620	−	0.725071i
$516$		0			0
$517$	−5.00000			−0.219900
$518$		0			0
$519$	−3.00000			−0.131685
$520$		0			0
$521$	7.00000	−	12.1244i	0.306676	−	0.531178i	−0.670957	−	0.741496i	$-0.734117\pi$
$521$	7.00000	−	12.1244i	0.306676	−	0.531178i	0.977633	+	0.210318i	$0.0674500\pi$
$522$		0			0
$523$	2.00000	+	3.46410i	0.0874539	+	0.151475i	0.906434	−	0.422347i	$-0.138794\pi$
$523$	2.00000	+	3.46410i	0.0874539	+	0.151475i	−0.818980	+	0.573822i	$0.805460\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−2.00000	−	3.46410i	−0.0871214	−	0.150899i
$528$		0			0
$529$	−6.50000	+	11.2583i	−0.282609	+	0.489493i
$530$		0			0
$531$	48.0000			2.08302
$532$		0			0
$533$	12.0000			0.519778
$534$		0			0
$535$	3.00000	−	5.19615i	0.129701	−	0.224649i
$536$		0			0
$537$	−18.0000	−	31.1769i	−0.776757	−	1.34538i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−19.5000	−	33.7750i	−0.838370	−	1.45210i	−0.891256	−	0.453500i	$-0.850175\pi$
$541$	−19.5000	−	33.7750i	−0.838370	−	1.45210i	0.0528859	−	0.998601i	$-0.483158\pi$
$542$		0			0
$543$	30.0000	−	51.9615i	1.28742	−	2.22988i
$544$		0			0
$545$	−3.00000			−0.128506
$546$		0			0
$547$	−24.0000			−1.02617			−0.513083	−	0.858339i	$-0.671497\pi$
$547$	−24.0000			−1.02617			−0.513083	+	0.858339i	$0.671497\pi$
$548$		0			0
$549$	−24.0000	+	41.5692i	−1.02430	+	1.77413i
$550$		0			0
$551$	−27.0000	−	46.7654i	−1.15024	−	1.99227i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	3.00000	+	5.19615i	0.127343	+	0.220564i
$556$		0			0
$557$	−20.0000	+	34.6410i	−0.847427	+	1.46779i	0.0360693	+	0.999349i	$0.488516\pi$
$557$	−20.0000	+	34.6410i	−0.847427	+	1.46779i	−0.883497	+	0.468438i	$0.844817\pi$
$558$		0			0
$559$	30.0000			1.26886
$560$		0			0
$561$	15.0000			0.633300
$562$		0			0
$563$	−14.0000	+	24.2487i	−0.590030	+	1.02196i	0.404198	+	0.914671i	$0.367551\pi$
$563$	−14.0000	+	24.2487i	−0.590030	+	1.02196i	−0.994228	+	0.107290i	$0.965783\pi$
$564$		0			0
$565$	−7.00000	−	12.1244i	−0.294492	−	0.510075i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	15.0000	+	25.9808i	0.628833	+	1.08917i	0.987786	+	0.155815i	$0.0498003\pi$
$569$	15.0000	+	25.9808i	0.628833	+	1.08917i	−0.358954	+	0.933355i	$0.616866\pi$
$570$		0			0
$571$	6.00000	−	10.3923i	0.251092	−	0.434904i	−0.712735	−	0.701434i	$-0.752544\pi$
$571$	6.00000	−	10.3923i	0.251092	−	0.434904i	0.963827	+	0.266529i	$0.0858769\pi$
$572$		0			0
$573$	−9.00000			−0.375980
$574$		0			0
$575$	6.00000			0.250217
$576$		0			0
$577$	6.50000	−	11.2583i	0.270599	−	0.468690i	−0.698417	−	0.715691i	$-0.746112\pi$
$577$	6.50000	−	11.2583i	0.270599	−	0.468690i	0.969015	+	0.247001i	$0.0794451\pi$
$578$		0			0
$579$	−6.00000	−	10.3923i	−0.249351	−	0.431889i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	10.0000	+	17.3205i	0.414158	+	0.717342i
$584$		0			0
$585$	−9.00000	+	15.5885i	−0.372104	+	0.644503i
$586$		0			0
$587$	16.0000			0.660391			0.330195	−	0.943913i	$-0.392885\pi$
$587$	16.0000			0.660391			0.330195	+	0.943913i	$0.392885\pi$
$588$		0			0
$589$	−24.0000			−0.988903
$590$		0			0
$591$	12.0000	−	20.7846i	0.493614	−	0.854965i
$592$		0			0
$593$	−13.5000	−	23.3827i	−0.554379	−	0.960212i	−0.997952	−	0.0639736i	$-0.979623\pi$
$593$	−13.5000	−	23.3827i	−0.554379	−	0.960212i	0.443573	−	0.896238i	$-0.353711\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−12.0000	−	20.7846i	−0.491127	−	0.850657i
$598$		0			0
$599$	−7.50000	+	12.9904i	−0.306442	+	0.530773i	−0.977581	−	0.210558i	$-0.932472\pi$
$599$	−7.50000	+	12.9904i	−0.306442	+	0.530773i	0.671140	+	0.741331i	$0.265805\pi$
$600$		0			0
$601$	−30.0000			−1.22373			−0.611863	−	0.790964i	$-0.709580\pi$
$601$	−30.0000			−1.22373			−0.611863	+	0.790964i	$0.709580\pi$
$602$		0			0
$603$	72.0000			2.93207
$604$		0			0
$605$	−7.00000	+	12.1244i	−0.284590	+	0.492925i
$606$		0			0
$607$	6.50000	+	11.2583i	0.263827	+	0.456962i	0.967256	−	0.253804i	$-0.0816819\pi$
$607$	6.50000	+	11.2583i	0.263827	+	0.456962i	−0.703429	+	0.710766i	$0.748349\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−1.50000	−	2.59808i	−0.0606835	−	0.105107i
$612$		0			0
$613$	−21.0000	+	36.3731i	−0.848182	+	1.46909i	0.0346469	+	0.999400i	$0.488969\pi$
$613$	−21.0000	+	36.3731i	−0.848182	+	1.46909i	−0.882829	+	0.469695i	$0.844364\pi$
$614$		0			0
$615$	−12.0000			−0.483887
$616$		0			0
$617$	−46.0000			−1.85189			−0.925945	−	0.377658i	$-0.876729\pi$
$617$	−46.0000			−1.85189			−0.925945	+	0.377658i	$0.876729\pi$
$618$		0			0
$619$	−5.00000	+	8.66025i	−0.200967	+	0.348085i	−0.948840	−	0.315757i	$-0.897742\pi$
$619$	−5.00000	+	8.66025i	−0.200967	+	0.348085i	0.747873	+	0.663842i	$0.231075\pi$
$620$		0			0
$621$	27.0000	+	46.7654i	1.08347	+	1.87663i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	45.0000	−	77.9423i	1.79713	−	3.11272i
$628$		0			0
$629$	2.00000			0.0797452
$630$		0			0
$631$	47.0000			1.87104			0.935520	−	0.353273i	$-0.114931\pi$
$631$	47.0000			1.87104			0.935520	+	0.353273i	$0.114931\pi$
$632$		0			0
$633$	−16.5000	+	28.5788i	−0.655816	+	1.13591i
$634$		0			0
$635$	4.00000	+	6.92820i	0.158735	+	0.274937i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−24.0000	−	41.5692i	−0.949425	−	1.64445i
$640$		0			0
$641$	−1.00000	+	1.73205i	−0.0394976	+	0.0684119i	−0.885098	−	0.465404i	$-0.845909\pi$
$641$	−1.00000	+	1.73205i	−0.0394976	+	0.0684119i	0.845601	+	0.533816i	$0.179242\pi$
$642$		0			0
$643$	−19.0000			−0.749287			−0.374643	−	0.927169i	$-0.622235\pi$
$643$	−19.0000			−0.749287			−0.374643	+	0.927169i	$0.622235\pi$
$644$		0			0
$645$	−30.0000			−1.18125
$646$		0			0
$647$	−4.00000	+	6.92820i	−0.157256	+	0.272376i	−0.933878	−	0.357591i	$-0.883598\pi$
$647$	−4.00000	+	6.92820i	−0.157256	+	0.272376i	0.776622	+	0.629967i	$0.216932\pi$
$648$		0			0
$649$	20.0000	+	34.6410i	0.785069	+	1.35978i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−1.00000	−	1.73205i	−0.0391330	−	0.0677804i	0.845796	−	0.533507i	$-0.179126\pi$
$653$	−1.00000	−	1.73205i	−0.0391330	−	0.0677804i	−0.884929	+	0.465727i	$0.845793\pi$
$654$		0			0
$655$	−5.00000	+	8.66025i	−0.195366	+	0.338384i
$656$		0			0
$657$	−12.0000			−0.468165
$658$		0			0
$659$	31.0000			1.20759			0.603794	−	0.797140i	$-0.293655\pi$
$659$	31.0000			1.20759			0.603794	+	0.797140i	$0.293655\pi$
$660$		0			0
$661$	−16.0000	+	27.7128i	−0.622328	+	1.07790i	0.366723	+	0.930330i	$0.380480\pi$
$661$	−16.0000	+	27.7128i	−0.622328	+	1.07790i	−0.989051	+	0.147573i	$0.952854\pi$
$662$		0			0
$663$	4.50000	+	7.79423i	0.174766	+	0.302703i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	27.0000	+	46.7654i	1.04544	+	1.81076i
$668$		0			0
$669$	7.50000	−	12.9904i	0.289967	−	0.502237i
$670$		0			0
$671$	−40.0000			−1.54418
$672$		0			0
$673$	4.00000			0.154189			0.0770943	−	0.997024i	$-0.475436\pi$
$673$	4.00000			0.154189			0.0770943	+	0.997024i	$0.475436\pi$
$674$		0			0
$675$	4.50000	−	7.79423i	0.173205	−	0.300000i
$676$		0			0
$677$	−13.5000	−	23.3827i	−0.518847	−	0.898670i	−0.999760	−	0.0219013i	$-0.993028\pi$
$677$	−13.5000	−	23.3827i	−0.518847	−	0.898670i	0.480913	−	0.876768i	$-0.340305\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	1.50000	+	2.59808i	0.0574801	+	0.0995585i
$682$		0			0
$683$	−4.00000	+	6.92820i	−0.153056	+	0.265100i	−0.932349	−	0.361559i	$-0.882245\pi$
$683$	−4.00000	+	6.92820i	−0.153056	+	0.265100i	0.779294	+	0.626659i	$0.215578\pi$
$684$		0			0
$685$	−12.0000			−0.458496
$686$		0			0
$687$	12.0000			0.457829
$688$		0			0
$689$	−6.00000	+	10.3923i	−0.228582	+	0.395915i
$690$		0			0
$691$	14.0000	+	24.2487i	0.532585	+	0.922464i	0.999276	+	0.0380440i	$0.0121127\pi$
$691$	14.0000	+	24.2487i	0.532585	+	0.922464i	−0.466691	+	0.884420i	$0.654554\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−7.00000	−	12.1244i	−0.265525	−	0.459903i
$696$		0			0
$697$	−2.00000	+	3.46410i	−0.0757554	+	0.131212i
$698$		0			0
$699$	−72.0000			−2.72329
$700$		0			0
$701$	−5.00000			−0.188847			−0.0944237	−	0.995532i	$-0.530101\pi$
$701$	−5.00000			−0.188847			−0.0944237	+	0.995532i	$0.530101\pi$
$702$		0			0
$703$	6.00000	−	10.3923i	0.226294	−	0.391953i
$704$		0			0
$705$	1.50000	+	2.59808i	0.0564933	+	0.0978492i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−15.5000	−	26.8468i	−0.582115	−	1.00825i	−0.995228	−	0.0975728i	$-0.968892\pi$
$709$	−15.5000	−	26.8468i	−0.582115	−	1.00825i	0.413114	−	0.910679i	$-0.364441\pi$
$710$		0			0
$711$	−39.0000	+	67.5500i	−1.46261	+	2.53332i
$712$		0			0
$713$	24.0000			0.898807
$714$		0			0
$715$	−15.0000			−0.560968
$716$		0			0
$717$	1.50000	−	2.59808i	0.0560185	−	0.0970269i
$718$		0			0
$719$	3.00000	+	5.19615i	0.111881	+	0.193784i	0.916529	−	0.399969i	$-0.130979\pi$
$719$	3.00000	+	5.19615i	0.111881	+	0.193784i	−0.804648	+	0.593753i	$0.797646\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	39.0000	+	67.5500i	1.45043	+	2.51221i
$724$		0			0
$725$	4.50000	−	7.79423i	0.167126	−	0.289470i
$726$		0			0
$727$	−24.0000			−0.890111			−0.445055	−	0.895503i	$-0.646816\pi$
$727$	−24.0000			−0.890111			−0.445055	+	0.895503i	$0.646816\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	−5.00000	+	8.66025i	−0.184932	+	0.320311i
$732$		0			0
$733$	−23.5000	−	40.7032i	−0.867992	−	1.50341i	−0.864045	−	0.503415i	$-0.832077\pi$
$733$	−23.5000	−	40.7032i	−0.867992	−	1.50341i	−0.00394730	−	0.999992i	$-0.501256\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	30.0000	+	51.9615i	1.10506	+	1.91403i
$738$		0			0
$739$	2.50000	−	4.33013i	0.0919640	−	0.159286i	−0.816373	−	0.577524i	$-0.804019\pi$
$739$	2.50000	−	4.33013i	0.0919640	−	0.159286i	0.908337	+	0.418238i	$0.137352\pi$
$740$		0			0
$741$	54.0000			1.98374
$742$		0			0
$743$	36.0000			1.32071			0.660356	−	0.750953i	$-0.270405\pi$
$743$	36.0000			1.32071			0.660356	+	0.750953i	$0.270405\pi$
$744$		0			0
$745$	3.00000	−	5.19615i	0.109911	−	0.190372i
$746$		0			0
$747$	−12.0000	−	20.7846i	−0.439057	−	0.760469i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	9.50000	+	16.4545i	0.346660	+	0.600433i	0.985654	−	0.168779i	$-0.0539825\pi$
$751$	9.50000	+	16.4545i	0.346660	+	0.600433i	−0.638994	+	0.769212i	$0.720649\pi$
$752$		0			0
$753$	−45.0000	+	77.9423i	−1.63989	+	2.84037i
$754$		0			0
$755$	5.00000			0.181969
$756$		0			0
$757$	−32.0000			−1.16306			−0.581530	−	0.813525i	$-0.697546\pi$
$757$	−32.0000			−1.16306			−0.581530	+	0.813525i	$0.697546\pi$
$758$		0			0
$759$	−45.0000	+	77.9423i	−1.63340	+	2.82913i
$760$		0			0
$761$	−9.00000	−	15.5885i	−0.326250	−	0.565081i	0.655515	−	0.755182i	$-0.272452\pi$
$761$	−9.00000	−	15.5885i	−0.326250	−	0.565081i	−0.981764	+	0.190101i	$0.939118\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−3.00000	−	5.19615i	−0.108465	−	0.187867i
$766$		0			0
$767$	−12.0000	+	20.7846i	−0.433295	+	0.750489i
$768$		0			0
$769$	−22.0000			−0.793340			−0.396670	−	0.917961i	$-0.629834\pi$
$769$	−22.0000			−0.793340			−0.396670	+	0.917961i	$0.629834\pi$
$770$		0			0
$771$	42.0000			1.51259
$772$		0			0
$773$	22.5000	−	38.9711i	0.809269	−	1.40169i	−0.104102	−	0.994567i	$-0.533197\pi$
$773$	22.5000	−	38.9711i	0.809269	−	1.40169i	0.913371	−	0.407128i	$-0.133470\pi$
$774$		0			0
$775$	−2.00000	−	3.46410i	−0.0718421	−	0.124434i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	12.0000	+	20.7846i	0.429945	+	0.744686i
$780$		0			0
$781$	20.0000	−	34.6410i	0.715656	−	1.23955i
$782$		0			0
$783$	81.0000			2.89470
$784$		0			0
$785$	2.00000			0.0713831
$786$		0			0
$787$	15.5000	−	26.8468i	0.552515	−	0.956985i	−0.445577	−	0.895244i	$-0.647001\pi$
$787$	15.5000	−	26.8468i	0.552515	−	0.956985i	0.998092	−	0.0617409i	$-0.0196653\pi$
$788$		0			0
$789$	3.00000	+	5.19615i	0.106803	+	0.184988i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−12.0000	−	20.7846i	−0.426132	−	0.738083i
$794$		0			0
$795$	6.00000	−	10.3923i	0.212798	−	0.368577i
$796$		0			0
$797$	33.0000			1.16892			0.584460	−	0.811423i	$-0.301306\pi$
$797$	33.0000			1.16892			0.584460	+	0.811423i	$0.301306\pi$
$798$		0			0
$799$	1.00000			0.0353775
$800$		0			0
$801$	12.0000	−	20.7846i	0.423999	−	0.734388i
$802$		0			0
$803$	−5.00000	−	8.66025i	−0.176446	−	0.305614i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−27.0000	−	46.7654i	−0.950445	−	1.64622i
$808$		0			0
$809$	−4.50000	+	7.79423i	−0.158212	+	0.274030i	−0.934224	−	0.356687i	$-0.883906\pi$
$809$	−4.50000	+	7.79423i	−0.158212	+	0.274030i	0.776012	+	0.630718i	$0.217239\pi$
$810$		0			0
$811$	−14.0000			−0.491606			−0.245803	−	0.969320i	$-0.579052\pi$
$811$	−14.0000			−0.491606			−0.245803	+	0.969320i	$0.579052\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	5.00000	−	8.66025i	0.175142	−	0.303355i
$816$		0			0
$817$	30.0000	+	51.9615i	1.04957	+	1.81790i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	19.5000	+	33.7750i	0.680555	+	1.17876i	0.974812	+	0.223029i	$0.0715945\pi$
$821$	19.5000	+	33.7750i	0.680555	+	1.17876i	−0.294257	+	0.955726i	$0.595072\pi$
$822$		0			0
$823$	−14.0000	+	24.2487i	−0.488009	+	0.845257i	−0.999905	−	0.0137907i	$-0.995610\pi$
$823$	−14.0000	+	24.2487i	−0.488009	+	0.845257i	0.511896	+	0.859048i	$0.328943\pi$
$824$		0			0
$825$	15.0000			0.522233
$826$		0			0
$827$	50.0000			1.73867			0.869335	−	0.494223i	$-0.164547\pi$
$827$	50.0000			1.73867			0.869335	+	0.494223i	$0.164547\pi$
$828$		0			0
$829$	−14.0000	+	24.2487i	−0.486240	+	0.842193i	−0.999875	−	0.0158163i	$-0.994965\pi$
$829$	−14.0000	+	24.2487i	−0.486240	+	0.842193i	0.513635	+	0.858009i	$0.328299\pi$
$830$		0			0
$831$	9.00000	+	15.5885i	0.312207	+	0.540758i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	1.50000	+	2.59808i	0.0519096	+	0.0899101i
$836$		0			0
$837$	18.0000	−	31.1769i	0.622171	−	1.07763i
$838$		0			0
$839$	−2.00000			−0.0690477			−0.0345238	−	0.999404i	$-0.510991\pi$
$839$	−2.00000			−0.0690477			−0.0345238	+	0.999404i	$0.510991\pi$
$840$		0			0
$841$	52.0000			1.79310
$842$		0			0
$843$	16.5000	−	28.5788i	0.568290	−	0.984307i
$844$		0			0
$845$	2.00000	+	3.46410i	0.0688021	+	0.119169i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	46.5000	+	80.5404i	1.59588	+	2.76414i
$850$		0			0
$851$	−6.00000	+	10.3923i	−0.205677	+	0.356244i
$852$		0			0
$853$	10.0000			0.342393			0.171197	−	0.985237i	$-0.445237\pi$
$853$	10.0000			0.342393			0.171197	+	0.985237i	$0.445237\pi$
$854$		0			0
$855$	−36.0000			−1.23117
$856$		0			0
$857$	9.00000	−	15.5885i	0.307434	−	0.532492i	−0.670366	−	0.742030i	$-0.733863\pi$
$857$	9.00000	−	15.5885i	0.307434	−	0.532492i	0.977800	+	0.209539i	$0.0671963\pi$
$858$		0			0
$859$	18.0000	+	31.1769i	0.614152	+	1.06374i	0.990533	+	0.137277i	$0.0438352\pi$
$859$	18.0000	+	31.1769i	0.614152	+	1.06374i	−0.376381	+	0.926465i	$0.622831\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−8.00000	−	13.8564i	−0.272323	−	0.471678i	0.697133	−	0.716942i	$-0.254459\pi$
$863$	−8.00000	−	13.8564i	−0.272323	−	0.471678i	−0.969456	+	0.245264i	$0.921125\pi$
$864$		0			0
$865$	−0.500000	+	0.866025i	−0.0170005	+	0.0294457i
$866$		0			0
$867$	48.0000			1.63017
$868$		0			0
$869$	−65.0000			−2.20497
$870$		0			0
$871$	−18.0000	+	31.1769i	−0.609907	+	1.05639i
$872$		0			0
$873$	−39.0000	−	67.5500i	−1.31995	−	2.28622i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−13.0000	−	22.5167i	−0.438979	−	0.760334i	0.558632	−	0.829416i	$-0.311326\pi$
$877$	−13.0000	−	22.5167i	−0.438979	−	0.760334i	−0.997611	+	0.0690819i	$0.977993\pi$
$878$		0			0
$879$	7.50000	−	12.9904i	0.252969	−	0.438155i
$880$		0			0
$881$	−32.0000			−1.07811			−0.539054	−	0.842271i	$-0.681218\pi$
$881$	−32.0000			−1.07811			−0.539054	+	0.842271i	$0.681218\pi$
$882$		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
$887$	4.00000	+	6.92820i	0.134307	+	0.232626i	0.925332	−	0.379157i	$-0.123786\pi$
$887$	4.00000	+	6.92820i	0.134307	+	0.232626i	−0.791026	+	0.611783i	$0.790453\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	22.5000	+	38.9711i	0.753778	+	1.30558i
$892$		0			0
$893$	3.00000	−	5.19615i	0.100391	−	0.173883i
$894$		0			0
$895$	−12.0000			−0.401116
$896$		0			0
$897$	−54.0000			−1.80301
$898$		0			0
$899$	18.0000	−	31.1769i	0.600334	−	1.03981i
$900$		0			0
$901$	−2.00000	−	3.46410i	−0.0666297	−	0.115406i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−10.0000	−	17.3205i	−0.332411	−	0.575753i
$906$		0			0
$907$	−7.00000	+	12.1244i	−0.232431	+	0.402583i	−0.958523	−	0.285015i	$-0.908001\pi$
$907$	−7.00000	+	12.1244i	−0.232431	+	0.402583i	0.726092	+	0.687598i	$0.241335\pi$
$908$		0			0
$909$	−36.0000			−1.19404
$910$		0			0
$911$	−48.0000			−1.59031			−0.795155	−	0.606406i	$-0.792611\pi$
$911$	−48.0000			−1.59031			−0.795155	+	0.606406i	$0.792611\pi$
$912$		0			0
$913$	10.0000	−	17.3205i	0.330952	−	0.573225i
$914$		0			0
$915$	12.0000	+	20.7846i	0.396708	+	0.687118i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	15.5000	+	26.8468i	0.511298	+	0.885594i	0.999914	+	0.0130951i	$0.00416842\pi$
$919$	15.5000	+	26.8468i	0.511298	+	0.885594i	−0.488616	+	0.872499i	$0.662498\pi$
$920$		0			0
$921$	34.5000	−	59.7558i	1.13681	−	1.96902i
$922$		0			0
$923$	24.0000			0.789970
$924$		0			0
$925$	2.00000			0.0657596
$926$		0			0
$927$	57.0000	−	98.7269i	1.87213	−	3.24262i
$928$		0			0
$929$	14.0000	+	24.2487i	0.459325	+	0.795574i	0.998925	−	0.0463469i	$-0.0147580\pi$
$929$	14.0000	+	24.2487i	0.459325	+	0.795574i	−0.539600	+	0.841921i	$0.681425\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	27.0000	+	46.7654i	0.883940	+	1.53103i
$934$		0			0
$935$	2.50000	−	4.33013i	0.0817587	−	0.141610i
$936$		0			0
$937$	37.0000			1.20874			0.604369	−	0.796705i	$-0.293425\pi$
$937$	37.0000			1.20874			0.604369	+	0.796705i	$0.293425\pi$
$938$		0			0
$939$	−21.0000			−0.685309
$940$		0			0
$941$	16.0000	−	27.7128i	0.521585	−	0.903412i	−0.478100	−	0.878306i	$-0.658674\pi$
$941$	16.0000	−	27.7128i	0.521585	−	0.903412i	0.999685	−	0.0251063i	$-0.00799243\pi$
$942$		0			0
$943$	−12.0000	−	20.7846i	−0.390774	−	0.676840i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−4.00000	−	6.92820i	−0.129983	−	0.225136i	0.793687	−	0.608326i	$-0.208159\pi$
$947$	−4.00000	−	6.92820i	−0.129983	−	0.225136i	−0.923670	+	0.383190i	$0.874825\pi$
$948$		0			0
$949$	3.00000	−	5.19615i	0.0973841	−	0.168674i
$950$		0			0
$951$	78.0000			2.52932
$952$		0			0
$953$	24.0000			0.777436			0.388718	−	0.921357i	$-0.372918\pi$
$953$	24.0000			0.777436			0.388718	+	0.921357i	$0.372918\pi$
$954$		0			0
$955$	−1.50000	+	2.59808i	−0.0485389	+	0.0840718i
$956$		0			0
$957$	67.5000	+	116.913i	2.18197	+	3.77927i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$		0			0
$963$	18.0000	−	31.1769i	0.580042	−	1.00466i
$964$		0			0
$965$	−4.00000			−0.128765
$966$		0			0
$967$	−2.00000			−0.0643157			−0.0321578	−	0.999483i	$-0.510238\pi$
$967$	−2.00000			−0.0643157			−0.0321578	+	0.999483i	$0.510238\pi$
$968$		0			0
$969$	−9.00000	+	15.5885i	−0.289122	+	0.500773i
$970$		0			0
$971$	−12.0000	−	20.7846i	−0.385098	−	0.667010i	0.606685	−	0.794943i	$-0.292499\pi$
$971$	−12.0000	−	20.7846i	−0.385098	−	0.667010i	−0.991783	+	0.127933i	$0.959166\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	4.50000	+	7.79423i	0.144115	+	0.249615i
$976$		0			0
$977$	21.0000	−	36.3731i	0.671850	−	1.16368i	−0.305530	−	0.952183i	$-0.598833\pi$
$977$	21.0000	−	36.3731i	0.671850	−	1.16368i	0.977379	−	0.211495i	$-0.0678332\pi$
$978$		0			0
$979$	20.0000			0.639203
$980$		0			0
$981$	−18.0000			−0.574696
$982$		0			0
$983$	−21.5000	+	37.2391i	−0.685744	+	1.18774i	0.287459	+	0.957793i	$0.407189\pi$
$983$	−21.5000	+	37.2391i	−0.685744	+	1.18774i	−0.973203	+	0.229950i	$0.926144\pi$
$984$		0			0
$985$	−4.00000	−	6.92820i	−0.127451	−	0.220751i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−30.0000	−	51.9615i	−0.953945	−	1.65228i
$990$		0			0
$991$	−8.00000	+	13.8564i	−0.254128	+	0.440163i	−0.964658	−	0.263504i	$-0.915122\pi$
$991$	−8.00000	+	13.8564i	−0.254128	+	0.440163i	0.710530	+	0.703667i	$0.248455\pi$
$992$		0			0
$993$	−84.0000			−2.66566
$994$		0			0
$995$	−8.00000			−0.253617
$996$		0			0
$997$	5.50000	−	9.52628i	0.174187	−	0.301700i	−0.765693	−	0.643206i	$-0.777604\pi$
$997$	5.50000	−	9.52628i	0.174187	−	0.301700i	0.939880	+	0.341506i	$0.110937\pi$
$998$		0			0
$999$	9.00000	+	15.5885i	0.284747	+	0.493197i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.i.j.361.1		2
7.2	even	3	inner	980.2.i.j.961.1		2
7.3	odd	6		140.2.a.b.1.1	✓	1
7.4	even	3		980.2.a.b.1.1		1
7.5	odd	6		980.2.i.b.961.1		2
7.6	odd	2		980.2.i.b.361.1		2
21.11	odd	6		8820.2.a.n.1.1		1
21.17	even	6		1260.2.a.h.1.1		1
28.3	even	6		560.2.a.a.1.1		1
28.11	odd	6		3920.2.a.bl.1.1		1
35.3	even	12		700.2.e.a.449.2		2
35.4	even	6		4900.2.a.u.1.1		1
35.17	even	12		700.2.e.a.449.1		2
35.18	odd	12		4900.2.e.a.2549.1		2
35.24	odd	6		700.2.a.b.1.1		1
35.32	odd	12		4900.2.e.a.2549.2		2
56.3	even	6		2240.2.a.bb.1.1		1
56.45	odd	6		2240.2.a.c.1.1		1
84.59	odd	6		5040.2.a.bd.1.1		1
105.17	odd	12		6300.2.k.p.6049.1		2
105.38	odd	12		6300.2.k.p.6049.2		2
105.59	even	6		6300.2.a.bf.1.1		1
140.3	odd	12		2800.2.g.c.449.1		2
140.59	even	6		2800.2.a.be.1.1		1
140.87	odd	12		2800.2.g.c.449.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.a.b.1.1	✓	1	7.3	odd	6
560.2.a.a.1.1		1	28.3	even	6
700.2.a.b.1.1		1	35.24	odd	6
700.2.e.a.449.1		2	35.17	even	12
700.2.e.a.449.2		2	35.3	even	12
980.2.a.b.1.1		1	7.4	even	3
980.2.i.b.361.1		2	7.6	odd	2
980.2.i.b.961.1		2	7.5	odd	6
980.2.i.j.361.1		2	1.1	even	1	trivial
980.2.i.j.961.1		2	7.2	even	3	inner
1260.2.a.h.1.1		1	21.17	even	6
2240.2.a.c.1.1		1	56.45	odd	6
2240.2.a.bb.1.1		1	56.3	even	6
2800.2.a.be.1.1		1	140.59	even	6
2800.2.g.c.449.1		2	140.3	odd	12
2800.2.g.c.449.2		2	140.87	odd	12
3920.2.a.bl.1.1		1	28.11	odd	6
4900.2.a.u.1.1		1	35.4	even	6
4900.2.e.a.2549.1		2	35.18	odd	12
4900.2.e.a.2549.2		2	35.32	odd	12
5040.2.a.bd.1.1		1	84.59	odd	6
6300.2.a.bf.1.1		1	105.59	even	6
6300.2.k.p.6049.1		2	105.17	odd	12
6300.2.k.p.6049.2		2	105.38	odd	12
8820.2.a.n.1.1		1	21.11	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:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 - 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-3.00000 - 5.19615i) q^{9} +O(q^{10})\)	\(q+(1.50000 - 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-3.00000 - 5.19615i) q^{9} +(2.50000 - 4.33013i) q^{11} +3.00000 q^{13} -3.00000 q^{15} +(-0.500000 + 0.866025i) q^{17} +(3.00000 + 5.19615i) q^{19} +(-3.00000 - 5.19615i) q^{23} +(-0.500000 + 0.866025i) q^{25} -9.00000 q^{27} -9.00000 q^{29} +(-2.00000 + 3.46410i) q^{31} +(-7.50000 - 12.9904i) q^{33} +(-1.00000 - 1.73205i) q^{37} +(4.50000 - 7.79423i) q^{39} +4.00000 q^{41} +10.0000 q^{43} +(-3.00000 + 5.19615i) q^{45} +(-0.500000 - 0.866025i) q^{47} +(1.50000 + 2.59808i) q^{51} +(-2.00000 + 3.46410i) q^{53} -5.00000 q^{55} +18.0000 q^{57} +(-4.00000 + 6.92820i) q^{59} +(-4.00000 - 6.92820i) q^{61} +(-1.50000 - 2.59808i) q^{65} +(-6.00000 + 10.3923i) q^{67} -18.0000 q^{69} +8.00000 q^{71} +(1.00000 - 1.73205i) q^{73} +(1.50000 + 2.59808i) q^{75} +(-6.50000 - 11.2583i) q^{79} +(-4.50000 + 7.79423i) q^{81} +4.00000 q^{83} +1.00000 q^{85} +(-13.5000 + 23.3827i) q^{87} +(2.00000 + 3.46410i) q^{89} +(6.00000 + 10.3923i) q^{93} +(3.00000 - 5.19615i) q^{95} +13.0000 q^{97} -30.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{3} - q^{5} - 6 q^{9}+O(q^{10}) \) 2 * q + 3 * q^3 - q^5 - 6 * q^9	\( 2 q + 3 q^{3} - q^{5} - 6 q^{9} + 5 q^{11} + 6 q^{13} - 6 q^{15} - q^{17} + 6 q^{19} - 6 q^{23} - q^{25} - 18 q^{27} - 18 q^{29} - 4 q^{31} - 15 q^{33} - 2 q^{37} + 9 q^{39} + 8 q^{41} + 20 q^{43} - 6 q^{45} - q^{47} + 3 q^{51} - 4 q^{53} - 10 q^{55} + 36 q^{57} - 8 q^{59} - 8 q^{61} - 3 q^{65} - 12 q^{67} - 36 q^{69} + 16 q^{71} + 2 q^{73} + 3 q^{75} - 13 q^{79} - 9 q^{81} + 8 q^{83} + 2 q^{85} - 27 q^{87} + 4 q^{89} + 12 q^{93} + 6 q^{95} + 26 q^{97} - 60 q^{99}+O(q^{100}) \) 2 * q + 3 * q^3 - q^5 - 6 * q^9 + 5 * q^11 + 6 * q^13 - 6 * q^15 - q^17 + 6 * q^19 - 6 * q^23 - q^25 - 18 * q^27 - 18 * q^29 - 4 * q^31 - 15 * q^33 - 2 * q^37 + 9 * q^39 + 8 * q^41 + 20 * q^43 - 6 * q^45 - q^47 + 3 * q^51 - 4 * q^53 - 10 * q^55 + 36 * q^57 - 8 * q^59 - 8 * q^61 - 3 * q^65 - 12 * q^67 - 36 * q^69 + 16 * q^71 + 2 * q^73 + 3 * q^75 - 13 * q^79 - 9 * q^81 + 8 * q^83 + 2 * q^85 - 27 * q^87 + 4 * q^89 + 12 * q^93 + 6 * q^95 + 26 * q^97 - 60 * q^99

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