LMFDB - Embedded newform 980.2.k.g.687.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [980,2,Mod(687,980)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(980, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("980.687");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.k (of order $4$, 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:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{14})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 49 $ x^4 + 49
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			687.1
Root			$-1.87083 - 1.87083i$ of defining polynomial
Character	$\chi$	$=$	980.687
Dual form			980.2.k.g.883.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 + 1.00000i) q^{2} +(-1.87083 - 1.87083i) q^{3} +2.00000i q^{4} +(1.00000 + 2.00000i) q^{5} -3.74166i q^{6} +(-2.00000 + 2.00000i) q^{8} +4.00000i q^{9} +(-1.00000 + 3.00000i) q^{10} +3.74166i q^{11} +(3.74166 - 3.74166i) q^{12} +(2.00000 - 2.00000i) q^{13} +(1.87083 - 5.61249i) q^{15} -4.00000 q^{16} +(-2.00000 - 2.00000i) q^{17} +(-4.00000 + 4.00000i) q^{18} -3.74166 q^{19} +(-4.00000 + 2.00000i) q^{20} +(-3.74166 + 3.74166i) q^{22} +(-1.87083 - 1.87083i) q^{23} +7.48331 q^{24} +(-3.00000 + 4.00000i) q^{25} +4.00000 q^{26} +(1.87083 - 1.87083i) q^{27} +3.00000i q^{29} +(7.48331 - 3.74166i) q^{30} +7.48331i q^{31} +(-4.00000 - 4.00000i) q^{32} +(7.00000 - 7.00000i) q^{33} -4.00000i q^{34} -8.00000 q^{36} +(-3.74166 - 3.74166i) q^{38} -7.48331 q^{39} +(-6.00000 - 2.00000i) q^{40} -3.00000 q^{41} +(5.61249 + 5.61249i) q^{43} -7.48331 q^{44} +(-8.00000 + 4.00000i) q^{45} -3.74166i q^{46} +(-7.48331 + 7.48331i) q^{47} +(7.48331 + 7.48331i) q^{48} +(-7.00000 + 1.00000i) q^{50} +7.48331i q^{51} +(4.00000 + 4.00000i) q^{52} +(-5.00000 + 5.00000i) q^{53} +3.74166 q^{54} +(-7.48331 + 3.74166i) q^{55} +(7.00000 + 7.00000i) q^{57} +(-3.00000 + 3.00000i) q^{58} -3.74166 q^{59} +(11.2250 + 3.74166i) q^{60} +3.00000 q^{61} +(-7.48331 + 7.48331i) q^{62} -8.00000i q^{64} +(6.00000 + 2.00000i) q^{65} +14.0000 q^{66} +(9.35414 - 9.35414i) q^{67} +(4.00000 - 4.00000i) q^{68} +7.00000i q^{69} +3.74166i q^{71} +(-8.00000 - 8.00000i) q^{72} +(-2.00000 + 2.00000i) q^{73} +(13.0958 - 1.87083i) q^{75} -7.48331i q^{76} +(-7.48331 - 7.48331i) q^{78} -3.74166 q^{79} +(-4.00000 - 8.00000i) q^{80} +5.00000 q^{81} +(-3.00000 - 3.00000i) q^{82} +(1.87083 + 1.87083i) q^{83} +(2.00000 - 6.00000i) q^{85} +11.2250i q^{86} +(5.61249 - 5.61249i) q^{87} +(-7.48331 - 7.48331i) q^{88} +3.00000i q^{89} +(-12.0000 - 4.00000i) q^{90} +(3.74166 - 3.74166i) q^{92} +(14.0000 - 14.0000i) q^{93} -14.9666 q^{94} +(-3.74166 - 7.48331i) q^{95} +14.9666i q^{96} +(9.00000 + 9.00000i) q^{97} -14.9666 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{5} - 8 q^{8} - 4 q^{10} + 8 q^{13} - 16 q^{16} - 8 q^{17} - 16 q^{18} - 16 q^{20} - 12 q^{25} + 16 q^{26} - 16 q^{32} + 28 q^{33} - 32 q^{36} - 24 q^{40} - 12 q^{41} - 32 q^{45} - 28 q^{50}+ \cdots + 36 q^{97}+O(q^{100}) $ 4 * q + 4 * q^2 + 4 * q^5 - 8 * q^8 - 4 * q^10 + 8 * q^13 - 16 * q^16 - 8 * q^17 - 16 * q^18 - 16 * q^20 - 12 * q^25 + 16 * q^26 - 16 * q^32 + 28 * q^33 - 32 * q^36 - 24 * q^40 - 12 * q^41 - 32 * q^45 - 28 * q^50 + 16 * q^52 - 20 * q^53 + 28 * q^57 - 12 * q^58 + 12 * q^61 + 24 * q^65 + 56 * q^66 + 16 * q^68 - 32 * q^72 - 8 * q^73 - 16 * q^80 + 20 * q^81 - 12 * q^82 + 8 * q^85 - 48 * q^90 + 56 * q^93 + 36 * q^97

Character values

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

$n$	$101$	$197$	$491$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.00000	+	1.00000i	0.707107	+	0.707107i
$2$	1.00000	+	1.00000i	0.707107	+	0.707107i
$3$	−1.87083	−	1.87083i	−1.08012	−	1.08012i	−0.996497	−	0.0836263i	$-0.973350\pi$
$3$	−1.87083	−	1.87083i	−1.08012	−	1.08012i	−0.0836263	−	0.996497i	$-0.526650\pi$
$4$			2.00000i			1.00000i
$5$	1.00000	+	2.00000i	0.447214	+	0.894427i
$5$	1.00000	+	2.00000i	0.447214	+	0.894427i
$6$		−	3.74166i		−	1.52753i
$7$		0			0
$7$		0			0
$8$	−2.00000	+	2.00000i	−0.707107	+	0.707107i
$9$			4.00000i			1.33333i
$10$	−1.00000	+	3.00000i	−0.316228	+	0.948683i
$11$			3.74166i			1.12815i	0.825723	+	0.564076i	$0.190768\pi$
$11$			3.74166i			1.12815i	−0.825723	+	0.564076i	$0.809232\pi$
$12$	3.74166	−	3.74166i	1.08012	−	1.08012i
$13$	2.00000	−	2.00000i	0.554700	−	0.554700i	−0.373094	−	0.927794i	$-0.621703\pi$
$13$	2.00000	−	2.00000i	0.554700	−	0.554700i	0.927794	+	0.373094i	$0.121703\pi$
$14$		0			0
$15$	1.87083	−	5.61249i	0.483046	−	1.44914i
$16$	−4.00000			−1.00000
$17$	−2.00000	−	2.00000i	−0.485071	−	0.485071i	0.421676	−	0.906747i	$-0.361442\pi$
$17$	−2.00000	−	2.00000i	−0.485071	−	0.485071i	−0.906747	+	0.421676i	$0.861442\pi$
$18$	−4.00000	+	4.00000i	−0.942809	+	0.942809i
$19$	−3.74166			−0.858395			−0.429198	−	0.903211i	$-0.641204\pi$
$19$	−3.74166			−0.858395			−0.429198	+	0.903211i	$0.641204\pi$
$20$	−4.00000	+	2.00000i	−0.894427	+	0.447214i
$21$		0			0
$22$	−3.74166	+	3.74166i	−0.797724	+	0.797724i
$23$	−1.87083	−	1.87083i	−0.390095	−	0.390095i	0.484626	−	0.874721i	$-0.338956\pi$
$23$	−1.87083	−	1.87083i	−0.390095	−	0.390095i	−0.874721	+	0.484626i	$0.838956\pi$
$24$	7.48331			1.52753
$25$	−3.00000	+	4.00000i	−0.600000	+	0.800000i
$26$	4.00000			0.784465
$27$	1.87083	−	1.87083i	0.360041	−	0.360041i
$28$		0			0
$29$			3.00000i			0.557086i	0.960424	+	0.278543i	$0.0898515\pi$
$29$			3.00000i			0.557086i	−0.960424	+	0.278543i	$0.910149\pi$
$30$	7.48331	−	3.74166i	1.36626	−	0.683130i
$31$			7.48331i			1.34404i	0.740532	+	0.672022i	$0.234574\pi$
$31$			7.48331i			1.34404i	−0.740532	+	0.672022i	$0.765426\pi$
$32$	−4.00000	−	4.00000i	−0.707107	−	0.707107i
$33$	7.00000	−	7.00000i	1.21854	−	1.21854i
$34$		−	4.00000i		−	0.685994i
$35$		0			0
$36$	−8.00000			−1.33333
$37$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$37$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$38$	−3.74166	−	3.74166i	−0.606977	−	0.606977i
$39$	−7.48331			−1.19829
$40$	−6.00000	−	2.00000i	−0.948683	−	0.316228i
$41$	−3.00000			−0.468521			−0.234261	−	0.972174i	$-0.575267\pi$
$41$	−3.00000			−0.468521			−0.234261	+	0.972174i	$0.575267\pi$
$42$		0			0
$43$	5.61249	+	5.61249i	0.855896	+	0.855896i	0.990852	−	0.134956i	$-0.0430892\pi$
$43$	5.61249	+	5.61249i	0.855896	+	0.855896i	−0.134956	+	0.990852i	$0.543089\pi$
$44$	−7.48331			−1.12815
$45$	−8.00000	+	4.00000i	−1.19257	+	0.596285i
$46$		−	3.74166i		−	0.551677i
$47$	−7.48331	+	7.48331i	−1.09155	+	1.09155i	−0.0961907	+	0.995363i	$0.530666\pi$
$47$	−7.48331	+	7.48331i	−1.09155	+	1.09155i	−0.995363	+	0.0961907i	$0.969334\pi$
$48$	7.48331	+	7.48331i	1.08012	+	1.08012i
$49$		0			0
$50$	−7.00000	+	1.00000i	−0.989949	+	0.141421i
$51$			7.48331i			1.04787i
$52$	4.00000	+	4.00000i	0.554700	+	0.554700i
$53$	−5.00000	+	5.00000i	−0.686803	+	0.686803i	−0.961524	−	0.274721i	$-0.911414\pi$
$53$	−5.00000	+	5.00000i	−0.686803	+	0.686803i	0.274721	+	0.961524i	$0.411414\pi$
$54$	3.74166			0.509175
$55$	−7.48331	+	3.74166i	−1.00905	+	0.504525i
$56$		0			0
$57$	7.00000	+	7.00000i	0.927173	+	0.927173i
$58$	−3.00000	+	3.00000i	−0.393919	+	0.393919i
$59$	−3.74166			−0.487122			−0.243561	−	0.969886i	$-0.578316\pi$
$59$	−3.74166			−0.487122			−0.243561	+	0.969886i	$0.578316\pi$
$60$	11.2250	+	3.74166i	1.44914	+	0.483046i
$61$	3.00000			0.384111			0.192055	−	0.981384i	$-0.438485\pi$
$61$	3.00000			0.384111			0.192055	+	0.981384i	$0.438485\pi$
$62$	−7.48331	+	7.48331i	−0.950382	+	0.950382i
$63$		0			0
$64$		−	8.00000i		−	1.00000i
$65$	6.00000	+	2.00000i	0.744208	+	0.248069i
$66$	14.0000			1.72328
$67$	9.35414	−	9.35414i	1.14279	−	1.14279i	0.154853	−	0.987938i	$-0.450510\pi$
$67$	9.35414	−	9.35414i	1.14279	−	1.14279i	0.987938	−	0.154853i	$-0.0494904\pi$
$68$	4.00000	−	4.00000i	0.485071	−	0.485071i
$69$			7.00000i			0.842701i
$70$		0			0
$71$			3.74166i			0.444053i	0.975041	+	0.222027i	$0.0712672\pi$
$71$			3.74166i			0.444053i	−0.975041	+	0.222027i	$0.928733\pi$
$72$	−8.00000	−	8.00000i	−0.942809	−	0.942809i
$73$	−2.00000	+	2.00000i	−0.234082	+	0.234082i	−0.814394	−	0.580312i	$-0.802931\pi$
$73$	−2.00000	+	2.00000i	−0.234082	+	0.234082i	0.580312	+	0.814394i	$0.302931\pi$
$74$		0			0
$75$	13.0958	−	1.87083i	1.51217	−	0.216025i
$76$		−	7.48331i		−	0.858395i
$77$		0			0
$78$	−7.48331	−	7.48331i	−0.847319	−	0.847319i
$79$	−3.74166			−0.420969			−0.210485	−	0.977597i	$-0.567504\pi$
$79$	−3.74166			−0.420969			−0.210485	+	0.977597i	$0.567504\pi$
$80$	−4.00000	−	8.00000i	−0.447214	−	0.894427i
$81$	5.00000			0.555556
$82$	−3.00000	−	3.00000i	−0.331295	−	0.331295i
$83$	1.87083	+	1.87083i	0.205350	+	0.205350i	0.802288	−	0.596938i	$-0.203616\pi$
$83$	1.87083	+	1.87083i	0.205350	+	0.205350i	−0.596938	+	0.802288i	$0.703616\pi$
$84$		0			0
$85$	2.00000	−	6.00000i	0.216930	−	0.650791i
$86$			11.2250i			1.21042i
$87$	5.61249	−	5.61249i	0.601722	−	0.601722i
$88$	−7.48331	−	7.48331i	−0.797724	−	0.797724i
$89$			3.00000i			0.317999i	0.987279	+	0.159000i	$0.0508269\pi$
$89$			3.00000i			0.317999i	−0.987279	+	0.159000i	$0.949173\pi$
$90$	−12.0000	−	4.00000i	−1.26491	−	0.421637i
$91$		0			0
$92$	3.74166	−	3.74166i	0.390095	−	0.390095i
$93$	14.0000	−	14.0000i	1.45173	−	1.45173i
$94$	−14.9666			−1.54369
$95$	−3.74166	−	7.48331i	−0.383886	−	0.767772i
$96$			14.9666i			1.52753i
$97$	9.00000	+	9.00000i	0.913812	+	0.913812i	0.996570	−	0.0827581i	$-0.0263729\pi$
$97$	9.00000	+	9.00000i	0.913812	+	0.913812i	−0.0827581	+	0.996570i	$0.526373\pi$
$98$		0			0
$99$	−14.9666			−1.50420
$100$	−8.00000	−	6.00000i	−0.800000	−	0.600000i
$101$	−15.0000			−1.49256			−0.746278	−	0.665635i	$-0.768161\pi$
$101$	−15.0000			−1.49256			−0.746278	+	0.665635i	$0.768161\pi$
$102$	−7.48331	+	7.48331i	−0.740959	+	0.740959i
$103$	−1.87083	−	1.87083i	−0.184338	−	0.184338i	0.608905	−	0.793243i	$-0.291609\pi$
$103$	−1.87083	−	1.87083i	−0.184338	−	0.184338i	−0.793243	+	0.608905i	$0.791609\pi$
$104$			8.00000i			0.784465i
$105$		0			0
$106$	−10.0000			−0.971286
$107$	9.35414	−	9.35414i	0.904299	−	0.904299i	−0.0915054	−	0.995805i	$-0.529168\pi$
$107$	9.35414	−	9.35414i	0.904299	−	0.904299i	0.995805	+	0.0915054i	$0.0291679\pi$
$108$	3.74166	+	3.74166i	0.360041	+	0.360041i
$109$		−	15.0000i		−	1.43674i	−0.695662	−	0.718370i	$-0.744889\pi$
$109$		−	15.0000i		−	1.43674i	0.695662	−	0.718370i	$-0.255111\pi$
$110$	−11.2250	−	3.74166i	−1.07026	−	0.356753i
$111$		0			0
$112$		0			0
$113$	−1.00000	+	1.00000i	−0.0940721	+	0.0940721i	−0.752577	−	0.658505i	$-0.771189\pi$
$113$	−1.00000	+	1.00000i	−0.0940721	+	0.0940721i	0.658505	+	0.752577i	$0.271189\pi$
$114$			14.0000i			1.31122i
$115$	1.87083	−	5.61249i	0.174456	−	0.523367i
$116$	−6.00000			−0.557086
$117$	8.00000	+	8.00000i	0.739600	+	0.739600i
$118$	−3.74166	−	3.74166i	−0.344447	−	0.344447i
$119$		0			0
$120$	7.48331	+	14.9666i	0.683130	+	1.36626i
$121$	−3.00000			−0.272727
$122$	3.00000	+	3.00000i	0.271607	+	0.271607i
$123$	5.61249	+	5.61249i	0.506061	+	0.506061i
$124$	−14.9666			−1.34404
$125$	−11.0000	−	2.00000i	−0.983870	−	0.178885i
$126$		0			0
$127$	7.48331	−	7.48331i	0.664037	−	0.664037i	−0.292292	−	0.956329i	$-0.594418\pi$
$127$	7.48331	−	7.48331i	0.664037	−	0.664037i	0.956329	+	0.292292i	$0.0944180\pi$
$128$	8.00000	−	8.00000i	0.707107	−	0.707107i
$129$		−	21.0000i		−	1.84895i
$130$	4.00000	+	8.00000i	0.350823	+	0.701646i
$131$		−	14.9666i		−	1.30764i	−0.756650	−	0.653820i	$-0.773165\pi$
$131$		−	14.9666i		−	1.30764i	0.756650	−	0.653820i	$-0.226835\pi$
$132$	14.0000	+	14.0000i	1.21854	+	1.21854i
$133$		0			0
$134$	18.7083			1.61615
$135$	5.61249	+	1.87083i	0.483046	+	0.161015i
$136$	8.00000			0.685994
$137$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$137$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$138$	−7.00000	+	7.00000i	−0.595880	+	0.595880i
$139$	11.2250			0.952090			0.476045	−	0.879421i	$-0.342070\pi$
$139$	11.2250			0.952090			0.476045	+	0.879421i	$0.342070\pi$
$140$		0			0
$141$	28.0000			2.35803
$142$	−3.74166	+	3.74166i	−0.313993	+	0.313993i
$143$	7.48331	+	7.48331i	0.625786	+	0.625786i
$144$		−	16.0000i		−	1.33333i
$145$	−6.00000	+	3.00000i	−0.498273	+	0.249136i
$146$	−4.00000			−0.331042
$147$		0			0
$148$		0			0
$149$			7.00000i			0.573462i	0.958011	+	0.286731i	$0.0925686\pi$
$149$			7.00000i			0.573462i	−0.958011	+	0.286731i	$0.907431\pi$
$150$	14.9666	+	11.2250i	1.22202	+	0.916515i
$151$			22.4499i			1.82695i	0.406894	+	0.913475i	$0.366612\pi$
$151$			22.4499i			1.82695i	−0.406894	+	0.913475i	$0.633388\pi$
$152$	7.48331	−	7.48331i	0.606977	−	0.606977i
$153$	8.00000	−	8.00000i	0.646762	−	0.646762i
$154$		0			0
$155$	−14.9666	+	7.48331i	−1.20215	+	0.601074i
$156$		−	14.9666i		−	1.19829i
$157$	9.00000	+	9.00000i	0.718278	+	0.718278i	0.968252	−	0.249974i	$-0.0804222\pi$
$157$	9.00000	+	9.00000i	0.718278	+	0.718278i	−0.249974	+	0.968252i	$0.580422\pi$
$158$	−3.74166	−	3.74166i	−0.297670	−	0.297670i
$159$	18.7083			1.48366
$160$	4.00000	−	12.0000i	0.316228	−	0.948683i
$161$		0			0
$162$	5.00000	+	5.00000i	0.392837	+	0.392837i
$163$	−7.48331	−	7.48331i	−0.586138	−	0.586138i	0.350445	−	0.936583i	$-0.386030\pi$
$163$	−7.48331	−	7.48331i	−0.586138	−	0.586138i	−0.936583	+	0.350445i	$0.886030\pi$
$164$		−	6.00000i		−	0.468521i
$165$	21.0000	+	7.00000i	1.63485	+	0.544949i
$166$			3.74166i			0.290409i
$167$	5.61249	−	5.61249i	0.434307	−	0.434307i	−0.455783	−	0.890091i	$-0.650641\pi$
$167$	5.61249	−	5.61249i	0.434307	−	0.434307i	0.890091	+	0.455783i	$0.150641\pi$
$168$		0			0
$169$			5.00000i			0.384615i
$170$	8.00000	−	4.00000i	0.613572	−	0.306786i
$171$		−	14.9666i		−	1.14453i
$172$	−11.2250	+	11.2250i	−0.855896	+	0.855896i
$173$	8.00000	−	8.00000i	0.608229	−	0.608229i	−0.334254	−	0.942483i	$-0.608484\pi$
$173$	8.00000	−	8.00000i	0.608229	−	0.608229i	0.942483	+	0.334254i	$0.108484\pi$
$174$	11.2250			0.850963
$175$		0			0
$176$		−	14.9666i		−	1.12815i
$177$	7.00000	+	7.00000i	0.526152	+	0.526152i
$178$	−3.00000	+	3.00000i	−0.224860	+	0.224860i
$179$	7.48331			0.559329			0.279665	−	0.960098i	$-0.409777\pi$
$179$	7.48331			0.559329			0.279665	+	0.960098i	$0.409777\pi$
$180$	−8.00000	−	16.0000i	−0.596285	−	1.19257i
$181$	13.0000			0.966282			0.483141	−	0.875542i	$-0.339496\pi$
$181$	13.0000			0.966282			0.483141	+	0.875542i	$0.339496\pi$
$182$		0			0
$183$	−5.61249	−	5.61249i	−0.414887	−	0.414887i
$184$	7.48331			0.551677
$185$		0			0
$186$	28.0000			2.05306
$187$	7.48331	−	7.48331i	0.547234	−	0.547234i
$188$	−14.9666	−	14.9666i	−1.09155	−	1.09155i
$189$		0			0
$190$	3.74166	−	11.2250i	0.271448	−	0.814345i
$191$			3.74166i			0.270737i	0.990795	+	0.135368i	$0.0432218\pi$
$191$			3.74166i			0.270737i	−0.990795	+	0.135368i	$0.956778\pi$
$192$	−14.9666	+	14.9666i	−1.08012	+	1.08012i
$193$	5.00000	−	5.00000i	0.359908	−	0.359908i	−0.503871	−	0.863779i	$-0.668091\pi$
$193$	5.00000	−	5.00000i	0.359908	−	0.359908i	0.863779	+	0.503871i	$0.168091\pi$
$194$			18.0000i			1.29232i
$195$	−7.48331	−	14.9666i	−0.535891	−	1.07178i
$196$		0			0
$197$	−1.00000	−	1.00000i	−0.0712470	−	0.0712470i	0.670585	−	0.741832i	$-0.266043\pi$
$197$	−1.00000	−	1.00000i	−0.0712470	−	0.0712470i	−0.741832	+	0.670585i	$0.766043\pi$
$198$	−14.9666	−	14.9666i	−1.06363	−	1.06363i
$199$		0			0			−	1.00000i	$-0.5\pi$
$199$		0			0				1.00000i	$0.5\pi$
$200$	−2.00000	−	14.0000i	−0.141421	−	0.989949i
$201$	−35.0000			−2.46871
$202$	−15.0000	−	15.0000i	−1.05540	−	1.05540i
$203$		0			0
$204$	−14.9666			−1.04787
$205$	−3.00000	−	6.00000i	−0.209529	−	0.419058i
$206$		−	3.74166i		−	0.260694i
$207$	7.48331	−	7.48331i	0.520126	−	0.520126i
$208$	−8.00000	+	8.00000i	−0.554700	+	0.554700i
$209$		−	14.0000i		−	0.968400i
$210$		0			0
$211$			11.2250i			0.772759i	0.922340	+	0.386379i	$0.126274\pi$
$211$			11.2250i			0.772759i	−0.922340	+	0.386379i	$0.873726\pi$
$212$	−10.0000	−	10.0000i	−0.686803	−	0.686803i
$213$	7.00000	−	7.00000i	0.479632	−	0.479632i
$214$	18.7083			1.27887
$215$	−5.61249	+	16.8375i	−0.382768	+	1.14831i
$216$			7.48331i			0.509175i
$217$		0			0
$218$	15.0000	−	15.0000i	1.01593	−	1.01593i
$219$	7.48331			0.505676
$220$	−7.48331	−	14.9666i	−0.504525	−	1.00905i
$221$	−8.00000			−0.538138
$222$		0			0
$223$	3.74166	+	3.74166i	0.250560	+	0.250560i	0.821200	−	0.570640i	$-0.193305\pi$
$223$	3.74166	+	3.74166i	0.250560	+	0.250560i	−0.570640	+	0.821200i	$0.693305\pi$
$224$		0			0
$225$	−16.0000	−	12.0000i	−1.06667	−	0.800000i
$226$	−2.00000			−0.133038
$227$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$227$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$228$	−14.0000	+	14.0000i	−0.927173	+	0.927173i
$229$		−	16.0000i		−	1.05731i	−0.848837	−	0.528655i	$-0.822697\pi$
$229$		−	16.0000i		−	1.05731i	0.848837	−	0.528655i	$-0.177303\pi$
$230$	7.48331	−	3.74166i	0.493435	−	0.246718i
$231$		0			0
$232$	−6.00000	−	6.00000i	−0.393919	−	0.393919i
$233$	−14.0000	+	14.0000i	−0.917170	+	0.917170i	−0.996823	−	0.0796522i	$-0.974619\pi$
$233$	−14.0000	+	14.0000i	−0.917170	+	0.917170i	0.0796522	+	0.996823i	$0.474619\pi$
$234$			16.0000i			1.04595i
$235$	−22.4499	−	7.48331i	−1.46447	−	0.488158i
$236$		−	7.48331i		−	0.487122i
$237$	7.00000	+	7.00000i	0.454699	+	0.454699i
$238$		0			0
$239$	22.4499			1.45217			0.726083	−	0.687607i	$-0.241339\pi$
$239$	22.4499			1.45217			0.726083	+	0.687607i	$0.241339\pi$
$240$	−7.48331	+	22.4499i	−0.483046	+	1.44914i
$241$	12.0000			0.772988			0.386494	−	0.922292i	$-0.373686\pi$
$241$	12.0000			0.772988			0.386494	+	0.922292i	$0.373686\pi$
$242$	−3.00000	−	3.00000i	−0.192847	−	0.192847i
$243$	−14.9666	−	14.9666i	−0.960110	−	0.960110i
$244$			6.00000i			0.384111i
$245$		0			0
$246$			11.2250i			0.715678i
$247$	−7.48331	+	7.48331i	−0.476152	+	0.476152i
$248$	−14.9666	−	14.9666i	−0.950382	−	0.950382i
$249$		−	7.00000i		−	0.443607i
$250$	−9.00000	−	13.0000i	−0.569210	−	0.822192i
$251$			7.48331i			0.472343i	0.971711	+	0.236171i	$0.0758927\pi$
$251$			7.48331i			0.472343i	−0.971711	+	0.236171i	$0.924107\pi$
$252$		0			0
$253$	7.00000	−	7.00000i	0.440086	−	0.440086i
$254$	14.9666			0.939090
$255$	−14.9666	+	7.48331i	−0.937247	+	0.468623i
$256$	16.0000			1.00000
$257$	20.0000	+	20.0000i	1.24757	+	1.24757i	0.956792	+	0.290774i	$0.0939128\pi$
$257$	20.0000	+	20.0000i	1.24757	+	1.24757i	0.290774	+	0.956792i	$0.406087\pi$
$258$	21.0000	−	21.0000i	1.30740	−	1.30740i
$259$		0			0
$260$	−4.00000	+	12.0000i	−0.248069	+	0.744208i
$261$	−12.0000			−0.742781
$262$	14.9666	−	14.9666i	0.924641	−	0.924641i
$263$	1.87083	+	1.87083i	0.115360	+	0.115360i	0.762430	−	0.647070i	$-0.224006\pi$
$263$	1.87083	+	1.87083i	0.115360	+	0.115360i	−0.647070	+	0.762430i	$0.724006\pi$
$264$			28.0000i			1.72328i
$265$	−15.0000	−	5.00000i	−0.921443	−	0.307148i
$266$		0			0
$267$	5.61249	−	5.61249i	0.343479	−	0.343479i
$268$	18.7083	+	18.7083i	1.14279	+	1.14279i
$269$			13.0000i			0.792624i	0.918116	+	0.396312i	$0.129710\pi$
$269$			13.0000i			0.792624i	−0.918116	+	0.396312i	$0.870290\pi$
$270$	3.74166	+	7.48331i	0.227710	+	0.455420i
$271$			11.2250i			0.681868i	0.940087	+	0.340934i	$0.110743\pi$
$271$			11.2250i			0.681868i	−0.940087	+	0.340934i	$0.889257\pi$
$272$	8.00000	+	8.00000i	0.485071	+	0.485071i
$273$		0			0
$274$		0			0
$275$	−14.9666	−	11.2250i	−0.902522	−	0.676891i
$276$	−14.0000			−0.842701
$277$	2.00000	+	2.00000i	0.120168	+	0.120168i	0.764634	−	0.644465i	$-0.222920\pi$
$277$	2.00000	+	2.00000i	0.120168	+	0.120168i	−0.644465	+	0.764634i	$0.722920\pi$
$278$	11.2250	+	11.2250i	0.673229	+	0.673229i
$279$	−29.9333			−1.79206
$280$		0			0
$281$	−4.00000			−0.238620			−0.119310	−	0.992857i	$-0.538068\pi$
$281$	−4.00000			−0.238620			−0.119310	+	0.992857i	$0.538068\pi$
$282$	28.0000	+	28.0000i	1.66738	+	1.66738i
$283$	7.48331	+	7.48331i	0.444837	+	0.444837i	0.893634	−	0.448797i	$-0.148147\pi$
$283$	7.48331	+	7.48331i	0.444837	+	0.444837i	−0.448797	+	0.893634i	$0.648147\pi$
$284$	−7.48331			−0.444053
$285$	−7.00000	+	21.0000i	−0.414644	+	1.24393i
$286$			14.9666i			0.884995i
$287$		0			0
$288$	16.0000	−	16.0000i	0.942809	−	0.942809i
$289$		−	9.00000i		−	0.529412i
$290$	−9.00000	−	3.00000i	−0.528498	−	0.176166i
$291$		−	33.6749i		−	1.97406i
$292$	−4.00000	−	4.00000i	−0.234082	−	0.234082i
$293$	20.0000	−	20.0000i	1.16841	−	1.16841i	0.185831	−	0.982582i	$-0.440502\pi$
$293$	20.0000	−	20.0000i	1.16841	−	1.16841i	0.982582	−	0.185831i	$-0.0594976\pi$
$294$		0			0
$295$	−3.74166	−	7.48331i	−0.217848	−	0.435695i
$296$		0			0
$297$	7.00000	+	7.00000i	0.406181	+	0.406181i
$298$	−7.00000	+	7.00000i	−0.405499	+	0.405499i
$299$	−7.48331			−0.432771
$300$	3.74166	+	26.1916i	0.216025	+	1.51217i
$301$		0			0
$302$	−22.4499	+	22.4499i	−1.29185	+	1.29185i
$303$	28.0624	+	28.0624i	1.61214	+	1.61214i
$304$	14.9666			0.858395
$305$	3.00000	+	6.00000i	0.171780	+	0.343559i
$306$	16.0000			0.914659
$307$	−9.35414	+	9.35414i	−0.533869	+	0.533869i	−0.921722	−	0.387852i	$-0.873217\pi$
$307$	−9.35414	+	9.35414i	−0.533869	+	0.533869i	0.387852	+	0.921722i	$0.373217\pi$
$308$		0			0
$309$			7.00000i			0.398216i
$310$	−22.4499	−	7.48331i	−1.27507	−	0.425024i
$311$			18.7083i			1.06085i	0.847732	+	0.530425i	$0.177968\pi$
$311$			18.7083i			1.06085i	−0.847732	+	0.530425i	$0.822032\pi$
$312$	14.9666	−	14.9666i	0.847319	−	0.847319i
$313$	−4.00000	+	4.00000i	−0.226093	+	0.226093i	−0.811058	−	0.584965i	$-0.801108\pi$
$313$	−4.00000	+	4.00000i	−0.226093	+	0.226093i	0.584965	+	0.811058i	$0.301108\pi$
$314$			18.0000i			1.01580i
$315$		0			0
$316$		−	7.48331i		−	0.420969i
$317$	10.0000	+	10.0000i	0.561656	+	0.561656i	0.929778	−	0.368122i	$-0.119999\pi$
$317$	10.0000	+	10.0000i	0.561656	+	0.561656i	−0.368122	+	0.929778i	$0.619999\pi$
$318$	18.7083	+	18.7083i	1.04911	+	1.04911i
$319$	−11.2250			−0.628478
$320$	16.0000	−	8.00000i	0.894427	−	0.447214i
$321$	−35.0000			−1.95351
$322$		0			0
$323$	7.48331	+	7.48331i	0.416383	+	0.416383i
$324$			10.0000i			0.555556i
$325$	2.00000	+	14.0000i	0.110940	+	0.776580i
$326$		−	14.9666i		−	0.828925i
$327$	−28.0624	+	28.0624i	−1.55186	+	1.55186i
$328$	6.00000	−	6.00000i	0.331295	−	0.331295i
$329$		0			0
$330$	14.0000	+	28.0000i	0.770675	+	1.54135i
$331$		−	22.4499i		−	1.23396i	−0.786979	−	0.616980i	$-0.788356\pi$
$331$		−	22.4499i		−	1.23396i	0.786979	−	0.616980i	$-0.211644\pi$
$332$	−3.74166	+	3.74166i	−0.205350	+	0.205350i
$333$		0			0
$334$	11.2250			0.614203
$335$	28.0624	+	9.35414i	1.53321	+	0.511071i
$336$		0			0
$337$	−21.0000	−	21.0000i	−1.14394	−	1.14394i	−0.987722	−	0.156221i	$-0.950069\pi$
$337$	−21.0000	−	21.0000i	−1.14394	−	1.14394i	−0.156221	−	0.987722i	$-0.549931\pi$
$338$	−5.00000	+	5.00000i	−0.271964	+	0.271964i
$339$	3.74166			0.203219
$340$	12.0000	+	4.00000i	0.650791	+	0.216930i
$341$	−28.0000			−1.51629
$342$	14.9666	−	14.9666i	0.809303	−	0.809303i
$343$		0			0
$344$	−22.4499			−1.21042
$345$	−14.0000	+	7.00000i	−0.753735	+	0.376867i
$346$	16.0000			0.860165
$347$	−13.0958	+	13.0958i	−0.703019	+	0.703019i	−0.965058	−	0.262038i	$-0.915605\pi$
$347$	−13.0958	+	13.0958i	−0.703019	+	0.703019i	0.262038	+	0.965058i	$0.415605\pi$
$348$	11.2250	+	11.2250i	0.601722	+	0.601722i
$349$			11.0000i			0.588817i	0.955680	+	0.294408i	$0.0951225\pi$
$349$			11.0000i			0.588817i	−0.955680	+	0.294408i	$0.904877\pi$
$350$		0			0
$351$		−	7.48331i		−	0.399430i
$352$	14.9666	−	14.9666i	0.797724	−	0.797724i
$353$	17.0000	−	17.0000i	0.904819	−	0.904819i	−0.0910295	−	0.995848i	$-0.529016\pi$
$353$	17.0000	−	17.0000i	0.904819	−	0.904819i	0.995848	+	0.0910295i	$0.0290158\pi$
$354$			14.0000i			0.744092i
$355$	−7.48331	+	3.74166i	−0.397173	+	0.198587i
$356$	−6.00000			−0.317999
$357$		0			0
$358$	7.48331	+	7.48331i	0.395505	+	0.395505i
$359$	−22.4499			−1.18486			−0.592431	−	0.805621i	$-0.701832\pi$
$359$	−22.4499			−1.18486			−0.592431	+	0.805621i	$0.701832\pi$
$360$	8.00000	−	24.0000i	0.421637	−	1.26491i
$361$	−5.00000			−0.263158
$362$	13.0000	+	13.0000i	0.683265	+	0.683265i
$363$	5.61249	+	5.61249i	0.294579	+	0.294579i
$364$		0			0
$365$	−6.00000	−	2.00000i	−0.314054	−	0.104685i
$366$		−	11.2250i		−	0.586739i
$367$	−13.0958	+	13.0958i	−0.683595	+	0.683595i	−0.960808	−	0.277213i	$-0.910589\pi$
$367$	−13.0958	+	13.0958i	−0.683595	+	0.683595i	0.277213	+	0.960808i	$0.410589\pi$
$368$	7.48331	+	7.48331i	0.390095	+	0.390095i
$369$		−	12.0000i		−	0.624695i
$370$		0			0
$371$		0			0
$372$	28.0000	+	28.0000i	1.45173	+	1.45173i
$373$	24.0000	−	24.0000i	1.24267	−	1.24267i	0.283785	−	0.958888i	$-0.408410\pi$
$373$	24.0000	−	24.0000i	1.24267	−	1.24267i	0.958888	−	0.283785i	$-0.0915902\pi$
$374$	14.9666			0.773906
$375$	16.8375	+	24.3208i	0.869483	+	1.25592i
$376$		−	29.9333i		−	1.54369i
$377$	6.00000	+	6.00000i	0.309016	+	0.309016i
$378$		0			0
$379$	11.2250			0.576588			0.288294	−	0.957542i	$-0.406912\pi$
$379$	11.2250			0.576588			0.288294	+	0.957542i	$0.406912\pi$
$380$	14.9666	−	7.48331i	0.767772	−	0.383886i
$381$	−28.0000			−1.43448
$382$	−3.74166	+	3.74166i	−0.191440	+	0.191440i
$383$	9.35414	+	9.35414i	0.477974	+	0.477974i	0.904483	−	0.426509i	$-0.140257\pi$
$383$	9.35414	+	9.35414i	0.477974	+	0.477974i	−0.426509	+	0.904483i	$0.640257\pi$
$384$	−29.9333			−1.52753
$385$		0			0
$386$	10.0000			0.508987
$387$	−22.4499	+	22.4499i	−1.14119	+	1.14119i
$388$	−18.0000	+	18.0000i	−0.913812	+	0.913812i
$389$			8.00000i			0.405616i	0.979219	+	0.202808i	$0.0650067\pi$
$389$			8.00000i			0.405616i	−0.979219	+	0.202808i	$0.934993\pi$
$390$	7.48331	−	22.4499i	0.378932	−	1.13680i
$391$			7.48331i			0.378447i
$392$		0			0
$393$	−28.0000	+	28.0000i	−1.41241	+	1.41241i
$394$		−	2.00000i		−	0.100759i
$395$	−3.74166	−	7.48331i	−0.188263	−	0.376526i
$396$		−	29.9333i		−	1.50420i
$397$	−11.0000	−	11.0000i	−0.552074	−	0.552074i	0.374965	−	0.927039i	$-0.377655\pi$
$397$	−11.0000	−	11.0000i	−0.552074	−	0.552074i	−0.927039	+	0.374965i	$0.877655\pi$
$398$		0			0
$399$		0			0
$400$	12.0000	−	16.0000i	0.600000	−	0.800000i
$401$	−23.0000			−1.14857			−0.574283	−	0.818657i	$-0.694719\pi$
$401$	−23.0000			−1.14857			−0.574283	+	0.818657i	$0.694719\pi$
$402$	−35.0000	−	35.0000i	−1.74564	−	1.74564i
$403$	14.9666	+	14.9666i	0.745541	+	0.745541i
$404$		−	30.0000i		−	1.49256i
$405$	5.00000	+	10.0000i	0.248452	+	0.496904i
$406$		0			0
$407$		0			0
$408$	−14.9666	−	14.9666i	−0.740959	−	0.740959i
$409$		−	5.00000i		−	0.247234i	−0.992330	−	0.123617i	$-0.960551\pi$
$409$		−	5.00000i		−	0.247234i	0.992330	−	0.123617i	$-0.0394494\pi$
$410$	3.00000	−	9.00000i	0.148159	−	0.444478i
$411$		0			0
$412$	3.74166	−	3.74166i	0.184338	−	0.184338i
$413$		0			0
$414$	14.9666			0.735570
$415$	−1.87083	+	5.61249i	−0.0918354	+	0.275506i
$416$	−16.0000			−0.784465
$417$	−21.0000	−	21.0000i	−1.02837	−	1.02837i
$418$	14.0000	−	14.0000i	0.684762	−	0.684762i
$419$	−14.9666			−0.731168			−0.365584	−	0.930778i	$-0.619131\pi$
$419$	−14.9666			−0.731168			−0.365584	+	0.930778i	$0.619131\pi$
$420$		0			0
$421$	−7.00000			−0.341159			−0.170580	−	0.985344i	$-0.554564\pi$
$421$	−7.00000			−0.341159			−0.170580	+	0.985344i	$0.554564\pi$
$422$	−11.2250	+	11.2250i	−0.546423	+	0.546423i
$423$	−29.9333	−	29.9333i	−1.45540	−	1.45540i
$424$		−	20.0000i		−	0.971286i
$425$	14.0000	−	2.00000i	0.679100	−	0.0970143i
$426$	14.0000			0.678302
$427$		0			0
$428$	18.7083	+	18.7083i	0.904299	+	0.904299i
$429$		−	28.0000i		−	1.35185i
$430$	−22.4499	+	11.2250i	−1.08263	+	0.541316i
$431$			11.2250i			0.540688i	0.962764	+	0.270344i	$0.0871374\pi$
$431$			11.2250i			0.540688i	−0.962764	+	0.270344i	$0.912863\pi$
$432$	−7.48331	+	7.48331i	−0.360041	+	0.360041i
$433$	−23.0000	+	23.0000i	−1.10531	+	1.10531i	−0.111551	+	0.993759i	$0.535582\pi$
$433$	−23.0000	+	23.0000i	−1.10531	+	1.10531i	−0.993759	+	0.111551i	$0.964418\pi$
$434$		0			0
$435$	16.8375	+	5.61249i	0.807294	+	0.269098i
$436$	30.0000			1.43674
$437$	7.00000	+	7.00000i	0.334855	+	0.334855i
$438$	7.48331	+	7.48331i	0.357567	+	0.357567i
$439$		0			0			−	1.00000i	$-0.5\pi$
$439$		0			0				1.00000i	$0.5\pi$
$440$	7.48331	−	22.4499i	0.356753	−	1.07026i
$441$		0			0
$442$	−8.00000	−	8.00000i	−0.380521	−	0.380521i
$443$	5.61249	+	5.61249i	0.266657	+	0.266657i	0.827752	−	0.561094i	$-0.189620\pi$
$443$	5.61249	+	5.61249i	0.266657	+	0.266657i	−0.561094	+	0.827752i	$0.689620\pi$
$444$		0			0
$445$	−6.00000	+	3.00000i	−0.284427	+	0.142214i
$446$			7.48331i			0.354345i
$447$	13.0958	−	13.0958i	0.619410	−	0.619410i
$448$		0			0
$449$			35.0000i			1.65175i	0.563852	+	0.825876i	$0.309319\pi$
$449$			35.0000i			1.65175i	−0.563852	+	0.825876i	$0.690681\pi$
$450$	−4.00000	−	28.0000i	−0.188562	−	1.31993i
$451$		−	11.2250i		−	0.528563i
$452$	−2.00000	−	2.00000i	−0.0940721	−	0.0940721i
$453$	42.0000	−	42.0000i	1.97333	−	1.97333i
$454$		0			0
$455$		0			0
$456$	−28.0000			−1.31122
$457$	−24.0000	−	24.0000i	−1.12267	−	1.12267i	−0.991338	−	0.131335i	$-0.958074\pi$
$457$	−24.0000	−	24.0000i	−1.12267	−	1.12267i	−0.131335	−	0.991338i	$-0.541926\pi$
$458$	16.0000	−	16.0000i	0.747631	−	0.747631i
$459$	−7.48331			−0.349291
$460$	11.2250	+	3.74166i	0.523367	+	0.174456i
$461$	−20.0000			−0.931493			−0.465746	−	0.884918i	$-0.654214\pi$
$461$	−20.0000			−0.931493			−0.465746	+	0.884918i	$0.654214\pi$
$462$		0			0
$463$	−24.3208	−	24.3208i	−1.13028	−	1.13028i	−0.990130	−	0.140152i	$-0.955241\pi$
$463$	−24.3208	−	24.3208i	−1.13028	−	1.13028i	−0.140152	−	0.990130i	$-0.544759\pi$
$464$		−	12.0000i		−	0.557086i
$465$	42.0000	+	14.0000i	1.94770	+	0.649234i
$466$	−28.0000			−1.29707
$467$	28.0624	−	28.0624i	1.29857	−	1.29857i	0.369241	−	0.929334i	$-0.379618\pi$
$467$	28.0624	−	28.0624i	1.29857	−	1.29857i	0.929334	−	0.369241i	$-0.120382\pi$
$468$	−16.0000	+	16.0000i	−0.739600	+	0.739600i
$469$		0			0
$470$	−14.9666	−	29.9333i	−0.690359	−	1.38072i
$471$		−	33.6749i		−	1.55166i
$472$	7.48331	−	7.48331i	0.344447	−	0.344447i
$473$	−21.0000	+	21.0000i	−0.965581	+	0.965581i
$474$			14.0000i			0.643041i
$475$	11.2250	−	14.9666i	0.515037	−	0.686716i
$476$		0			0
$477$	−20.0000	−	20.0000i	−0.915737	−	0.915737i
$478$	22.4499	+	22.4499i	1.02684	+	1.02684i
$479$	7.48331			0.341921			0.170961	−	0.985278i	$-0.445313\pi$
$479$	7.48331			0.341921			0.170961	+	0.985278i	$0.445313\pi$
$480$	−29.9333	+	14.9666i	−1.36626	+	0.683130i
$481$		0			0
$482$	12.0000	+	12.0000i	0.546585	+	0.546585i
$483$		0			0
$484$		−	6.00000i		−	0.272727i
$485$	−9.00000	+	27.0000i	−0.408669	+	1.22601i
$486$		−	29.9333i		−	1.35780i
$487$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$487$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$488$	−6.00000	+	6.00000i	−0.271607	+	0.271607i
$489$			28.0000i			1.26620i
$490$		0			0
$491$		−	22.4499i		−	1.01315i	−0.862195	−	0.506576i	$-0.830911\pi$
$491$		−	22.4499i		−	1.01315i	0.862195	−	0.506576i	$-0.169089\pi$
$492$	−11.2250	+	11.2250i	−0.506061	+	0.506061i
$493$	6.00000	−	6.00000i	0.270226	−	0.270226i
$494$	−14.9666			−0.673380
$495$	−14.9666	−	29.9333i	−0.672700	−	1.34540i
$496$		−	29.9333i		−	1.34404i
$497$		0			0
$498$	7.00000	−	7.00000i	0.313678	−	0.313678i
$499$	41.1582			1.84250			0.921248	−	0.388976i	$-0.127171\pi$
$499$	41.1582			1.84250			0.921248	+	0.388976i	$0.127171\pi$
$500$	4.00000	−	22.0000i	0.178885	−	0.983870i
$501$	−21.0000			−0.938211
$502$	−7.48331	+	7.48331i	−0.333997	+	0.333997i
$503$	−16.8375	−	16.8375i	−0.750745	−	0.750745i	0.223873	−	0.974618i	$-0.428130\pi$
$503$	−16.8375	−	16.8375i	−0.750745	−	0.750745i	−0.974618	+	0.223873i	$0.928130\pi$
$504$		0			0
$505$	−15.0000	−	30.0000i	−0.667491	−	1.33498i
$506$	14.0000			0.622376
$507$	9.35414	−	9.35414i	0.415432	−	0.415432i
$508$	14.9666	+	14.9666i	0.664037	+	0.664037i
$509$			11.0000i			0.487566i	0.969830	+	0.243783i	$0.0783885\pi$
$509$			11.0000i			0.487566i	−0.969830	+	0.243783i	$0.921611\pi$
$510$	−22.4499	−	7.48331i	−0.994100	−	0.331367i
$511$		0			0
$512$	16.0000	+	16.0000i	0.707107	+	0.707107i
$513$	−7.00000	+	7.00000i	−0.309058	+	0.309058i
$514$			40.0000i			1.76432i
$515$	1.87083	−	5.61249i	0.0824386	−	0.247316i
$516$	42.0000			1.84895
$517$	−28.0000	−	28.0000i	−1.23144	−	1.23144i
$518$		0			0
$519$	−29.9333			−1.31392
$520$	−16.0000	+	8.00000i	−0.701646	+	0.350823i
$521$	−12.0000			−0.525730			−0.262865	−	0.964833i	$-0.584667\pi$
$521$	−12.0000			−0.525730			−0.262865	+	0.964833i	$0.584667\pi$
$522$	−12.0000	−	12.0000i	−0.525226	−	0.525226i
$523$	14.9666	+	14.9666i	0.654445	+	0.654445i	0.954060	−	0.299615i	$-0.0968583\pi$
$523$	14.9666	+	14.9666i	0.654445	+	0.654445i	−0.299615	+	0.954060i	$0.596858\pi$
$524$	29.9333			1.30764
$525$		0			0
$526$			3.74166i			0.163144i
$527$	14.9666	−	14.9666i	0.651957	−	0.651957i
$528$	−28.0000	+	28.0000i	−1.21854	+	1.21854i
$529$		−	16.0000i		−	0.695652i
$530$	−10.0000	−	20.0000i	−0.434372	−	0.868744i
$531$		−	14.9666i		−	0.649496i
$532$		0			0
$533$	−6.00000	+	6.00000i	−0.259889	+	0.259889i
$534$	11.2250			0.485752
$535$	28.0624	+	9.35414i	1.21324	+	0.404415i
$536$			37.4166i			1.61615i
$537$	−14.0000	−	14.0000i	−0.604145	−	0.604145i
$538$	−13.0000	+	13.0000i	−0.560470	+	0.560470i
$539$		0			0
$540$	−3.74166	+	11.2250i	−0.161015	+	0.483046i
$541$	7.00000			0.300954			0.150477	−	0.988614i	$-0.451919\pi$
$541$	7.00000			0.300954			0.150477	+	0.988614i	$0.451919\pi$
$542$	−11.2250	+	11.2250i	−0.482154	+	0.482154i
$543$	−24.3208	−	24.3208i	−1.04370	−	1.04370i
$544$			16.0000i			0.685994i
$545$	30.0000	−	15.0000i	1.28506	−	0.642529i
$546$		0			0
$547$	−20.5791	+	20.5791i	−0.879899	+	0.879899i	−0.993524	−	0.113624i	$-0.963754\pi$
$547$	−20.5791	+	20.5791i	−0.879899	+	0.879899i	0.113624	+	0.993524i	$0.463754\pi$
$548$		0			0
$549$			12.0000i			0.512148i
$550$	−3.74166	−	26.1916i	−0.159545	−	1.11681i
$551$		−	11.2250i		−	0.478200i
$552$	−14.0000	−	14.0000i	−0.595880	−	0.595880i
$553$		0			0
$554$			4.00000i			0.169944i
$555$		0			0
$556$			22.4499i			0.952090i
$557$	19.0000	+	19.0000i	0.805056	+	0.805056i	0.983881	−	0.178825i	$-0.0572296\pi$
$557$	19.0000	+	19.0000i	0.805056	+	0.805056i	−0.178825	+	0.983881i	$0.557230\pi$
$558$	−29.9333	−	29.9333i	−1.26718	−	1.26718i
$559$	22.4499			0.949531
$560$		0			0
$561$	−28.0000			−1.18216
$562$	−4.00000	−	4.00000i	−0.168730	−	0.168730i
$563$	16.8375	+	16.8375i	0.709614	+	0.709614i	0.966454	−	0.256840i	$-0.0826813\pi$
$563$	16.8375	+	16.8375i	0.709614	+	0.709614i	−0.256840	+	0.966454i	$0.582681\pi$
$564$			56.0000i			2.35803i
$565$	−3.00000	−	1.00000i	−0.126211	−	0.0420703i
$566$			14.9666i			0.629094i
$567$		0			0
$568$	−7.48331	−	7.48331i	−0.313993	−	0.313993i
$569$			12.0000i			0.503066i	0.967849	+	0.251533i	$0.0809347\pi$
$569$			12.0000i			0.503066i	−0.967849	+	0.251533i	$0.919065\pi$
$570$	−28.0000	+	14.0000i	−1.17279	+	0.586395i
$571$		−	18.7083i		−	0.782917i	−0.920196	−	0.391459i	$-0.871971\pi$
$571$		−	18.7083i		−	0.782917i	0.920196	−	0.391459i	$-0.128029\pi$
$572$	−14.9666	+	14.9666i	−0.625786	+	0.625786i
$573$	7.00000	−	7.00000i	0.292429	−	0.292429i
$574$		0			0
$575$	13.0958	−	1.87083i	0.546133	−	0.0780189i
$576$	32.0000			1.33333
$577$	3.00000	+	3.00000i	0.124892	+	0.124892i	0.766790	−	0.641898i	$-0.221853\pi$
$577$	3.00000	+	3.00000i	0.124892	+	0.124892i	−0.641898	+	0.766790i	$0.721853\pi$
$578$	9.00000	−	9.00000i	0.374351	−	0.374351i
$579$	−18.7083			−0.777490
$580$	−6.00000	−	12.0000i	−0.249136	−	0.498273i
$581$		0			0
$582$	33.6749	−	33.6749i	1.39587	−	1.39587i
$583$	−18.7083	−	18.7083i	−0.774818	−	0.774818i
$584$		−	8.00000i		−	0.331042i
$585$	−8.00000	+	24.0000i	−0.330759	+	0.992278i
$586$	40.0000			1.65238
$587$	−14.9666	+	14.9666i	−0.617739	+	0.617739i	−0.944951	−	0.327212i	$-0.893891\pi$
$587$	−14.9666	+	14.9666i	−0.617739	+	0.617739i	0.327212	+	0.944951i	$0.393891\pi$
$588$		0			0
$589$		−	28.0000i		−	1.15372i
$590$	3.74166	−	11.2250i	0.154042	−	0.462125i
$591$			3.74166i			0.153911i
$592$		0			0
$593$	−15.0000	+	15.0000i	−0.615976	+	0.615976i	−0.944497	−	0.328521i	$-0.893450\pi$
$593$	−15.0000	+	15.0000i	−0.615976	+	0.615976i	0.328521	+	0.944497i	$0.393450\pi$
$594$			14.0000i			0.574427i
$595$		0			0
$596$	−14.0000			−0.573462
$597$		0			0
$598$	−7.48331	−	7.48331i	−0.306015	−	0.306015i
$599$	44.8999			1.83456			0.917280	−	0.398243i	$-0.130380\pi$
$599$	44.8999			1.83456			0.917280	+	0.398243i	$0.130380\pi$
$600$	−22.4499	+	29.9333i	−0.916515	+	1.22202i
$601$	−4.00000			−0.163163			−0.0815817	−	0.996667i	$-0.525997\pi$
$601$	−4.00000			−0.163163			−0.0815817	+	0.996667i	$0.525997\pi$
$602$		0			0
$603$	37.4166	+	37.4166i	1.52372	+	1.52372i
$604$	−44.8999			−1.82695
$605$	−3.00000	−	6.00000i	−0.121967	−	0.243935i
$606$			56.1249i			2.27992i
$607$	31.8041	−	31.8041i	1.29089	−	1.29089i	0.356650	−	0.934238i	$-0.383919\pi$
$607$	31.8041	−	31.8041i	1.29089	−	1.29089i	0.934238	−	0.356650i	$-0.116081\pi$
$608$	14.9666	+	14.9666i	0.606977	+	0.606977i
$609$		0			0
$610$	−3.00000	+	9.00000i	−0.121466	+	0.364399i
$611$			29.9333i			1.21097i
$612$	16.0000	+	16.0000i	0.646762	+	0.646762i
$613$	22.0000	−	22.0000i	0.888572	−	0.888572i	−0.105814	−	0.994386i	$-0.533745\pi$
$613$	22.0000	−	22.0000i	0.888572	−	0.888572i	0.994386	+	0.105814i	$0.0337449\pi$
$614$	−18.7083			−0.755005
$615$	−5.61249	+	16.8375i	−0.226317	+	0.678952i
$616$		0			0
$617$	4.00000	+	4.00000i	0.161034	+	0.161034i	0.783025	−	0.621991i	$-0.213676\pi$
$617$	4.00000	+	4.00000i	0.161034	+	0.161034i	−0.621991	+	0.783025i	$0.713676\pi$
$618$	−7.00000	+	7.00000i	−0.281581	+	0.281581i
$619$	11.2250			0.451170			0.225585	−	0.974224i	$-0.427571\pi$
$619$	11.2250			0.451170			0.225585	+	0.974224i	$0.427571\pi$
$620$	−14.9666	−	29.9333i	−0.601074	−	1.20215i
$621$	−7.00000			−0.280900
$622$	−18.7083	+	18.7083i	−0.750134	+	0.750134i
$623$		0			0
$624$	29.9333			1.19829
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$	−8.00000			−0.319744
$627$	−26.1916	+	26.1916i	−1.04599	+	1.04599i
$628$	−18.0000	+	18.0000i	−0.718278	+	0.718278i
$629$		0			0
$630$		0			0
$631$			33.6749i			1.34058i	0.742101	+	0.670289i	$0.233830\pi$
$631$			33.6749i			1.34058i	−0.742101	+	0.670289i	$0.766170\pi$
$632$	7.48331	−	7.48331i	0.297670	−	0.297670i
$633$	21.0000	−	21.0000i	0.834675	−	0.834675i
$634$			20.0000i			0.794301i
$635$	22.4499	+	7.48331i	0.890899	+	0.296966i
$636$			37.4166i			1.48366i
$637$		0			0
$638$	−11.2250	−	11.2250i	−0.444401	−	0.444401i
$639$	−14.9666			−0.592071
$640$	24.0000	+	8.00000i	0.948683	+	0.316228i
$641$	−13.0000			−0.513469			−0.256735	−	0.966482i	$-0.582647\pi$
$641$	−13.0000			−0.513469			−0.256735	+	0.966482i	$0.582647\pi$
$642$	−35.0000	−	35.0000i	−1.38134	−	1.38134i
$643$	−14.9666	−	14.9666i	−0.590226	−	0.590226i	0.347466	−	0.937692i	$-0.387042\pi$
$643$	−14.9666	−	14.9666i	−0.590226	−	0.590226i	−0.937692	+	0.347466i	$0.887042\pi$
$644$		0			0
$645$	42.0000	−	21.0000i	1.65375	−	0.826874i
$646$			14.9666i			0.588854i
$647$	9.35414	−	9.35414i	0.367749	−	0.367749i	−0.498906	−	0.866656i	$-0.666265\pi$
$647$	9.35414	−	9.35414i	0.367749	−	0.367749i	0.866656	+	0.498906i	$0.166265\pi$
$648$	−10.0000	+	10.0000i	−0.392837	+	0.392837i
$649$		−	14.0000i		−	0.549548i
$650$	−12.0000	+	16.0000i	−0.470679	+	0.627572i
$651$		0			0
$652$	14.9666	−	14.9666i	0.586138	−	0.586138i
$653$	−30.0000	+	30.0000i	−1.17399	+	1.17399i	−0.192741	+	0.981250i	$0.561738\pi$
$653$	−30.0000	+	30.0000i	−1.17399	+	1.17399i	−0.981250	+	0.192741i	$0.938262\pi$
$654$	−56.1249			−2.19466
$655$	29.9333	−	14.9666i	1.16959	−	0.584795i
$656$	12.0000			0.468521
$657$	−8.00000	−	8.00000i	−0.312110	−	0.312110i
$658$		0			0
$659$	−11.2250			−0.437263			−0.218631	−	0.975808i	$-0.570159\pi$
$659$	−11.2250			−0.437263			−0.218631	+	0.975808i	$0.570159\pi$
$660$	−14.0000	+	42.0000i	−0.544949	+	1.63485i
$661$	15.0000			0.583432			0.291716	−	0.956505i	$-0.405774\pi$
$661$	15.0000			0.583432			0.291716	+	0.956505i	$0.405774\pi$
$662$	22.4499	−	22.4499i	0.872542	−	0.872542i
$663$	14.9666	+	14.9666i	0.581256	+	0.581256i
$664$	−7.48331			−0.290409
$665$		0			0
$666$		0			0
$667$	5.61249	−	5.61249i	0.217316	−	0.217316i
$668$	11.2250	+	11.2250i	0.434307	+	0.434307i
$669$		−	14.0000i		−	0.541271i
$670$	18.7083	+	37.4166i	0.722764	+	1.44553i
$671$			11.2250i			0.433335i
$672$		0			0
$673$	−24.0000	+	24.0000i	−0.925132	+	0.925132i	−0.997386	−	0.0722542i	$-0.976981\pi$
$673$	−24.0000	+	24.0000i	−0.925132	+	0.925132i	0.0722542	+	0.997386i	$0.476981\pi$
$674$		−	42.0000i		−	1.61778i
$675$	1.87083	+	13.0958i	0.0720082	+	0.504058i
$676$	−10.0000			−0.384615
$677$	18.0000	+	18.0000i	0.691796	+	0.691796i	0.962627	−	0.270831i	$-0.0872984\pi$
$677$	18.0000	+	18.0000i	0.691796	+	0.691796i	−0.270831	+	0.962627i	$0.587298\pi$
$678$	3.74166	+	3.74166i	0.143697	+	0.143697i
$679$		0			0
$680$	8.00000	+	16.0000i	0.306786	+	0.613572i
$681$		0			0
$682$	−28.0000	−	28.0000i	−1.07218	−	1.07218i
$683$	−24.3208	−	24.3208i	−0.930609	−	0.930609i	0.0671354	−	0.997744i	$-0.478614\pi$
$683$	−24.3208	−	24.3208i	−0.930609	−	0.930609i	−0.997744	+	0.0671354i	$0.978614\pi$
$684$	29.9333			1.14453
$685$		0			0
$686$		0			0
$687$	−29.9333	+	29.9333i	−1.14203	+	1.14203i
$688$	−22.4499	−	22.4499i	−0.855896	−	0.855896i
$689$			20.0000i			0.761939i
$690$	−21.0000	−	7.00000i	−0.799456	−	0.266485i
$691$			41.1582i			1.56573i	0.622190	+	0.782866i	$0.286243\pi$
$691$			41.1582i			1.56573i	−0.622190	+	0.782866i	$0.713757\pi$
$692$	16.0000	+	16.0000i	0.608229	+	0.608229i
$693$		0			0
$694$	−26.1916			−0.994220
$695$	11.2250	+	22.4499i	0.425787	+	0.851575i
$696$			22.4499i			0.850963i
$697$	6.00000	+	6.00000i	0.227266	+	0.227266i
$698$	−11.0000	+	11.0000i	−0.416356	+	0.416356i
$699$	52.3832			1.98131
$700$		0			0
$701$	39.0000			1.47301			0.736505	−	0.676432i	$-0.236475\pi$
$701$	39.0000			1.47301			0.736505	+	0.676432i	$0.236475\pi$
$702$	7.48331	−	7.48331i	0.282440	−	0.282440i
$703$		0			0
$704$	29.9333			1.12815
$705$	28.0000	+	56.0000i	1.05454	+	2.10908i
$706$	34.0000			1.27961
$707$		0			0
$708$	−14.0000	+	14.0000i	−0.526152	+	0.526152i
$709$			5.00000i			0.187779i	0.995583	+	0.0938895i	$0.0299300\pi$
$709$			5.00000i			0.187779i	−0.995583	+	0.0938895i	$0.970070\pi$
$710$	−11.2250	−	3.74166i	−0.421266	−	0.140422i
$711$		−	14.9666i		−	0.561292i
$712$	−6.00000	−	6.00000i	−0.224860	−	0.224860i
$713$	14.0000	−	14.0000i	0.524304	−	0.524304i
$714$		0			0
$715$	−7.48331	+	22.4499i	−0.279860	+	0.839580i
$716$			14.9666i			0.559329i
$717$	−42.0000	−	42.0000i	−1.56852	−	1.56852i
$718$	−22.4499	−	22.4499i	−0.837824	−	0.837824i
$719$	18.7083			0.697701			0.348851	−	0.937178i	$-0.386572\pi$
$719$	18.7083			0.697701			0.348851	+	0.937178i	$0.386572\pi$
$720$	32.0000	−	16.0000i	1.19257	−	0.596285i
$721$		0			0
$722$	−5.00000	−	5.00000i	−0.186081	−	0.186081i
$723$	−22.4499	−	22.4499i	−0.834922	−	0.834922i
$724$			26.0000i			0.966282i
$725$	−12.0000	−	9.00000i	−0.445669	−	0.334252i
$726$			11.2250i			0.416598i
$727$	−5.61249	+	5.61249i	−0.208156	+	0.208156i	−0.803483	−	0.595328i	$-0.797022\pi$
$727$	−5.61249	+	5.61249i	−0.208156	+	0.208156i	0.595328	+	0.803483i	$0.297022\pi$
$728$		0			0
$729$			41.0000i			1.51852i
$730$	−4.00000	−	8.00000i	−0.148047	−	0.296093i
$731$		−	22.4499i		−	0.830341i
$732$	11.2250	−	11.2250i	0.414887	−	0.414887i
$733$	25.0000	−	25.0000i	0.923396	−	0.923396i	−0.0738717	−	0.997268i	$-0.523536\pi$
$733$	25.0000	−	25.0000i	0.923396	−	0.923396i	0.997268	+	0.0738717i	$0.0235355\pi$
$734$	−26.1916			−0.966750
$735$		0			0
$736$			14.9666i			0.551677i
$737$	35.0000	+	35.0000i	1.28924	+	1.28924i
$738$	12.0000	−	12.0000i	0.441726	−	0.441726i
$739$	41.1582			1.51403			0.757015	−	0.653397i	$-0.226657\pi$
$739$	41.1582			1.51403			0.757015	+	0.653397i	$0.226657\pi$
$740$		0			0
$741$	28.0000			1.02861
$742$		0			0
$743$	−28.0624	−	28.0624i	−1.02951	−	1.02951i	−0.999551	−	0.0299596i	$-0.990462\pi$
$743$	−28.0624	−	28.0624i	−1.02951	−	1.02951i	−0.0299596	−	0.999551i	$-0.509538\pi$
$744$			56.0000i			2.05306i
$745$	−14.0000	+	7.00000i	−0.512920	+	0.256460i
$746$	48.0000			1.75740
$747$	−7.48331	+	7.48331i	−0.273800	+	0.273800i
$748$	14.9666	+	14.9666i	0.547234	+	0.547234i
$749$		0			0
$750$	−7.48331	+	41.1582i	−0.273252	+	1.50289i
$751$			44.8999i			1.63842i	0.573494	+	0.819210i	$0.305588\pi$
$751$			44.8999i			1.63842i	−0.573494	+	0.819210i	$0.694412\pi$
$752$	29.9333	−	29.9333i	1.09155	−	1.09155i
$753$	14.0000	−	14.0000i	0.510188	−	0.510188i
$754$			12.0000i			0.437014i
$755$	−44.8999	+	22.4499i	−1.63407	+	0.817037i
$756$		0			0
$757$	10.0000	+	10.0000i	0.363456	+	0.363456i	0.865084	−	0.501628i	$-0.167265\pi$
$757$	10.0000	+	10.0000i	0.363456	+	0.363456i	−0.501628	+	0.865084i	$0.667265\pi$
$758$	11.2250	+	11.2250i	0.407709	+	0.407709i
$759$	−26.1916			−0.950695
$760$	22.4499	+	7.48331i	0.814345	+	0.271448i
$761$	−30.0000			−1.08750			−0.543750	−	0.839248i	$-0.682996\pi$
$761$	−30.0000			−1.08750			−0.543750	+	0.839248i	$0.682996\pi$
$762$	−28.0000	−	28.0000i	−1.01433	−	1.01433i
$763$		0			0
$764$	−7.48331			−0.270737
$765$	24.0000	+	8.00000i	0.867722	+	0.289241i
$766$			18.7083i			0.675958i
$767$	−7.48331	+	7.48331i	−0.270207	+	0.270207i
$768$	−29.9333	−	29.9333i	−1.08012	−	1.08012i
$769$		−	8.00000i		−	0.288487i	−0.989542	−	0.144244i	$-0.953925\pi$
$769$		−	8.00000i		−	0.288487i	0.989542	−	0.144244i	$-0.0460749\pi$
$770$		0			0
$771$		−	74.8331i		−	2.69505i
$772$	10.0000	+	10.0000i	0.359908	+	0.359908i
$773$	−26.0000	+	26.0000i	−0.935155	+	0.935155i	−0.998022	−	0.0628669i	$-0.979976\pi$
$773$	−26.0000	+	26.0000i	−0.935155	+	0.935155i	0.0628669	+	0.998022i	$0.479976\pi$
$774$	−44.8999			−1.61389
$775$	−29.9333	−	22.4499i	−1.07523	−	0.806426i
$776$	−36.0000			−1.29232
$777$		0			0
$778$	−8.00000	+	8.00000i	−0.286814	+	0.286814i
$779$	11.2250			0.402176
$780$	29.9333	−	14.9666i	1.07178	−	0.535891i
$781$	−14.0000			−0.500959
$782$	−7.48331	+	7.48331i	−0.267603	+	0.267603i
$783$	5.61249	+	5.61249i	0.200574	+	0.200574i
$784$		0			0
$785$	−9.00000	+	27.0000i	−0.321224	+	0.963671i
$786$	−56.0000			−1.99745
$787$	−28.0624	+	28.0624i	−1.00032	+	1.00032i	−0.000317662		1.00000i	$0.500101\pi$
$787$	−28.0624	+	28.0624i	−1.00032	+	1.00032i	−1.00000		0.000317662i	$0.999899\pi$
$788$	2.00000	−	2.00000i	0.0712470	−	0.0712470i
$789$		−	7.00000i		−	0.249207i
$790$	3.74166	−	11.2250i	0.133122	−	0.399367i
$791$		0			0
$792$	29.9333	−	29.9333i	1.06363	−	1.06363i
$793$	6.00000	−	6.00000i	0.213066	−	0.213066i
$794$		−	22.0000i		−	0.780751i
$795$	18.7083	+	37.4166i	0.663515	+	1.32703i
$796$		0			0
$797$	−8.00000	−	8.00000i	−0.283375	−	0.283375i	0.551079	−	0.834453i	$-0.314216\pi$
$797$	−8.00000	−	8.00000i	−0.283375	−	0.283375i	−0.834453	+	0.551079i	$0.814216\pi$
$798$		0			0
$799$	29.9333			1.05896
$800$	28.0000	−	4.00000i	0.989949	−	0.141421i
$801$	−12.0000			−0.423999
$802$	−23.0000	−	23.0000i	−0.812158	−	0.812158i
$803$	−7.48331	−	7.48331i	−0.264080	−	0.264080i
$804$		−	70.0000i		−	2.46871i
$805$		0			0
$806$			29.9333i			1.05435i
$807$	24.3208	−	24.3208i	0.856132	−	0.856132i
$808$	30.0000	−	30.0000i	1.05540	−	1.05540i
$809$			49.0000i			1.72275i	0.507971	+	0.861374i	$0.330396\pi$
$809$			49.0000i			1.72275i	−0.507971	+	0.861374i	$0.669604\pi$
$810$	−5.00000	+	15.0000i	−0.175682	+	0.527046i
$811$		−	22.4499i		−	0.788324i	−0.919041	−	0.394162i	$-0.871035\pi$
$811$		−	22.4499i		−	0.788324i	0.919041	−	0.394162i	$-0.128965\pi$
$812$		0			0
$813$	21.0000	−	21.0000i	0.736502	−	0.736502i
$814$		0			0
$815$	7.48331	−	22.4499i	0.262129	−	0.786387i
$816$		−	29.9333i		−	1.04787i
$817$	−21.0000	−	21.0000i	−0.734697	−	0.734697i
$818$	5.00000	−	5.00000i	0.174821	−	0.174821i
$819$		0			0
$820$	12.0000	−	6.00000i	0.419058	−	0.209529i
$821$	28.0000			0.977207			0.488603	−	0.872506i	$-0.337507\pi$
$821$	28.0000			0.977207			0.488603	+	0.872506i	$0.337507\pi$
$822$		0			0
$823$	−16.8375	−	16.8375i	−0.586917	−	0.586917i	0.349878	−	0.936795i	$-0.386223\pi$
$823$	−16.8375	−	16.8375i	−0.586917	−	0.586917i	−0.936795	+	0.349878i	$0.886223\pi$
$824$	7.48331			0.260694
$825$	7.00000	+	49.0000i	0.243709	+	1.70596i
$826$		0			0
$827$	9.35414	−	9.35414i	0.325275	−	0.325275i	−0.525511	−	0.850787i	$-0.676126\pi$
$827$	9.35414	−	9.35414i	0.325275	−	0.325275i	0.850787	+	0.525511i	$0.176126\pi$
$828$	14.9666	+	14.9666i	0.520126	+	0.520126i
$829$		−	20.0000i		−	0.694629i	−0.937749	−	0.347314i	$-0.887094\pi$
$829$		−	20.0000i		−	0.694629i	0.937749	−	0.347314i	$-0.112906\pi$
$830$	−7.48331	+	3.74166i	−0.259750	+	0.129875i
$831$		−	7.48331i		−	0.259593i
$832$	−16.0000	−	16.0000i	−0.554700	−	0.554700i
$833$		0			0
$834$		−	42.0000i		−	1.45434i
$835$	16.8375	+	5.61249i	0.582684	+	0.194228i
$836$	28.0000			0.968400
$837$	14.0000	+	14.0000i	0.483911	+	0.483911i
$838$	−14.9666	−	14.9666i	−0.517014	−	0.517014i
$839$	18.7083			0.645882			0.322941	−	0.946419i	$-0.395328\pi$
$839$	18.7083			0.645882			0.322941	+	0.946419i	$0.395328\pi$
$840$		0			0
$841$	20.0000			0.689655
$842$	−7.00000	−	7.00000i	−0.241236	−	0.241236i
$843$	7.48331	+	7.48331i	0.257739	+	0.257739i
$844$	−22.4499			−0.772759
$845$	−10.0000	+	5.00000i	−0.344010	+	0.172005i
$846$		−	59.8665i		−	2.05825i
$847$		0			0
$848$	20.0000	−	20.0000i	0.686803	−	0.686803i
$849$		−	28.0000i		−	0.960958i
$850$	16.0000	+	12.0000i	0.548795	+	0.411597i
$851$		0			0
$852$	14.0000	+	14.0000i	0.479632	+	0.479632i
$853$	−9.00000	+	9.00000i	−0.308154	+	0.308154i	−0.844193	−	0.536039i	$-0.819920\pi$
$853$	−9.00000	+	9.00000i	−0.308154	+	0.308154i	0.536039	+	0.844193i	$0.319920\pi$
$854$		0			0
$855$	29.9333	−	14.9666i	1.02370	−	0.511848i
$856$			37.4166i			1.27887i
$857$	25.0000	+	25.0000i	0.853984	+	0.853984i	0.990621	−	0.136637i	$-0.0436295\pi$
$857$	25.0000	+	25.0000i	0.853984	+	0.853984i	−0.136637	+	0.990621i	$0.543630\pi$
$858$	28.0000	−	28.0000i	0.955904	−	0.955904i
$859$	−44.8999			−1.53196			−0.765982	−	0.642862i	$-0.777747\pi$
$859$	−44.8999			−1.53196			−0.765982	+	0.642862i	$0.777747\pi$
$860$	−33.6749	−	11.2250i	−1.14831	−	0.382768i
$861$		0			0
$862$	−11.2250	+	11.2250i	−0.382324	+	0.382324i
$863$	−35.5457	−	35.5457i	−1.20999	−	1.20999i	−0.971029	−	0.238962i	$-0.923193\pi$
$863$	−35.5457	−	35.5457i	−1.20999	−	1.20999i	−0.238962	−	0.971029i	$-0.576807\pi$
$864$	−14.9666			−0.509175
$865$	24.0000	+	8.00000i	0.816024	+	0.272008i
$866$	−46.0000			−1.56314
$867$	−16.8375	+	16.8375i	−0.571830	+	0.571830i
$868$		0			0
$869$		−	14.0000i		−	0.474917i
$870$	11.2250	+	22.4499i	0.380562	+	0.761124i
$871$		−	37.4166i		−	1.26781i
$872$	30.0000	+	30.0000i	1.01593	+	1.01593i
$873$	−36.0000	+	36.0000i	−1.21842	+	1.21842i
$874$			14.0000i			0.473557i
$875$		0			0
$876$			14.9666i			0.505676i
$877$	−9.00000	−	9.00000i	−0.303908	−	0.303908i	0.538632	−	0.842541i	$-0.318941\pi$
$877$	−9.00000	−	9.00000i	−0.303908	−	0.303908i	−0.842541	+	0.538632i	$0.818941\pi$
$878$		0			0
$879$	−74.8331			−2.52406
$880$	29.9333	−	14.9666i	1.00905	−	0.504525i
$881$	15.0000			0.505363			0.252681	−	0.967550i	$-0.418688\pi$
$881$	15.0000			0.505363			0.252681	+	0.967550i	$0.418688\pi$
$882$		0			0
$883$	−29.9333	−	29.9333i	−1.00733	−	1.00733i	−0.999973	−	0.00736147i	$-0.997657\pi$
$883$	−29.9333	−	29.9333i	−1.00733	−	1.00733i	−0.00736147	−	0.999973i	$-0.502343\pi$
$884$		−	16.0000i		−	0.538138i
$885$	−7.00000	+	21.0000i	−0.235302	+	0.705907i
$886$			11.2250i			0.377110i
$887$	−9.35414	+	9.35414i	−0.314081	+	0.314081i	−0.846488	−	0.532407i	$-0.821288\pi$
$887$	−9.35414	+	9.35414i	−0.314081	+	0.314081i	0.532407	+	0.846488i	$0.321288\pi$
$888$		0			0
$889$		0			0
$890$	−9.00000	−	3.00000i	−0.301681	−	0.100560i
$891$			18.7083i			0.626751i
$892$	−7.48331	+	7.48331i	−0.250560	+	0.250560i
$893$	28.0000	−	28.0000i	0.936984	−	0.936984i
$894$	26.1916			0.875978
$895$	7.48331	+	14.9666i	0.250140	+	0.500279i
$896$		0			0
$897$	14.0000	+	14.0000i	0.467446	+	0.467446i
$898$	−35.0000	+	35.0000i	−1.16797	+	1.16797i
$899$	−22.4499			−0.748748
$900$	24.0000	−	32.0000i	0.800000	−	1.06667i
$901$	20.0000			0.666297
$902$	11.2250	−	11.2250i	0.373751	−	0.373751i
$903$		0			0
$904$		−	4.00000i		−	0.133038i
$905$	13.0000	+	26.0000i	0.432135	+	0.864269i
$906$	84.0000			2.79071
$907$	−9.35414	+	9.35414i	−0.310599	+	0.310599i	−0.845142	−	0.534542i	$-0.820484\pi$
$907$	−9.35414	+	9.35414i	−0.310599	+	0.310599i	0.534542	+	0.845142i	$0.320484\pi$
$908$		0			0
$909$		−	60.0000i		−	1.99007i
$910$		0			0
$911$			48.6415i			1.61157i	0.592211	+	0.805783i	$0.298255\pi$
$911$			48.6415i			1.61157i	−0.592211	+	0.805783i	$0.701745\pi$
$912$	−28.0000	−	28.0000i	−0.927173	−	0.927173i
$913$	−7.00000	+	7.00000i	−0.231666	+	0.231666i
$914$		−	48.0000i		−	1.58770i
$915$	5.61249	−	16.8375i	0.185543	−	0.556629i
$916$	32.0000			1.05731
$917$		0			0
$918$	−7.48331	−	7.48331i	−0.246986	−	0.246986i
$919$	−11.2250			−0.370278			−0.185139	−	0.982712i	$-0.559273\pi$
$919$	−11.2250			−0.370278			−0.185139	+	0.982712i	$0.559273\pi$
$920$	7.48331	+	14.9666i	0.246718	+	0.493435i
$921$	35.0000			1.15329
$922$	−20.0000	−	20.0000i	−0.658665	−	0.658665i
$923$	7.48331	+	7.48331i	0.246316	+	0.246316i
$924$		0			0
$925$		0			0
$926$		−	48.6415i		−	1.59846i
$927$	7.48331	−	7.48331i	0.245784	−	0.245784i
$928$	12.0000	−	12.0000i	0.393919	−	0.393919i
$929$		−	33.0000i		−	1.08269i	−0.840799	−	0.541347i	$-0.817914\pi$
$929$		−	33.0000i		−	1.08269i	0.840799	−	0.541347i	$-0.182086\pi$
$930$	28.0000	+	56.0000i	0.918156	+	1.83631i
$931$		0			0
$932$	−28.0000	−	28.0000i	−0.917170	−	0.917170i
$933$	35.0000	−	35.0000i	1.14585	−	1.14585i
$934$	56.1249			1.83646
$935$	22.4499	+	7.48331i	0.734192	+	0.244731i
$936$	−32.0000			−1.04595
$937$	12.0000	+	12.0000i	0.392023	+	0.392023i	0.875408	−	0.483385i	$-0.160593\pi$
$937$	12.0000	+	12.0000i	0.392023	+	0.392023i	−0.483385	+	0.875408i	$0.660593\pi$
$938$		0			0
$939$	14.9666			0.488417
$940$	14.9666	−	44.8999i	0.488158	−	1.46447i
$941$	−48.0000			−1.56476			−0.782378	−	0.622804i	$-0.785993\pi$
$941$	−48.0000			−1.56476			−0.782378	+	0.622804i	$0.785993\pi$
$942$	33.6749	−	33.6749i	1.09719	−	1.09719i
$943$	5.61249	+	5.61249i	0.182768	+	0.182768i
$944$	14.9666			0.487122
$945$		0			0
$946$	−42.0000			−1.36554
$947$	−13.0958	+	13.0958i	−0.425556	+	0.425556i	−0.887112	−	0.461555i	$-0.847292\pi$
$947$	−13.0958	+	13.0958i	−0.425556	+	0.425556i	0.461555	+	0.887112i	$0.347292\pi$
$948$	−14.0000	+	14.0000i	−0.454699	+	0.454699i
$949$			8.00000i			0.259691i
$950$	26.1916	−	3.74166i	0.849768	−	0.121395i
$951$		−	37.4166i		−	1.21332i
$952$		0			0
$953$	36.0000	−	36.0000i	1.16615	−	1.16615i	0.183051	−	0.983103i	$-0.441403\pi$
$953$	36.0000	−	36.0000i	1.16615	−	1.16615i	0.983103	−	0.183051i	$-0.0585973\pi$
$954$		−	40.0000i		−	1.29505i
$955$	−7.48331	+	3.74166i	−0.242154	+	0.121077i
$956$			44.8999i			1.45217i
$957$	21.0000	+	21.0000i	0.678834	+	0.678834i
$958$	7.48331	+	7.48331i	0.241775	+	0.241775i
$959$		0			0
$960$	−44.8999	−	14.9666i	−1.44914	−	0.483046i
$961$	−25.0000			−0.806452
$962$		0			0
$963$	37.4166	+	37.4166i	1.20573	+	1.20573i
$964$			24.0000i			0.772988i
$965$	15.0000	+	5.00000i	0.482867	+	0.160956i
$966$		0			0
$967$	24.3208	−	24.3208i	0.782103	−	0.782103i	−0.198082	−	0.980185i	$-0.563471\pi$
$967$	24.3208	−	24.3208i	0.782103	−	0.782103i	0.980185	+	0.198082i	$0.0634713\pi$
$968$	6.00000	−	6.00000i	0.192847	−	0.192847i
$969$		−	28.0000i		−	0.899490i
$970$	−36.0000	+	18.0000i	−1.15589	+	0.577945i
$971$			44.8999i			1.44091i	0.693504	+	0.720453i	$0.256066\pi$
$971$			44.8999i			1.44091i	−0.693504	+	0.720453i	$0.743934\pi$
$972$	29.9333	−	29.9333i	0.960110	−	0.960110i
$973$		0			0
$974$		0			0
$975$	22.4499	−	29.9333i	0.718974	−	0.958632i
$976$	−12.0000			−0.384111
$977$	−1.00000	−	1.00000i	−0.0319928	−	0.0319928i	0.690929	−	0.722922i	$-0.257202\pi$
$977$	−1.00000	−	1.00000i	−0.0319928	−	0.0319928i	−0.722922	+	0.690929i	$0.757202\pi$
$978$	−28.0000	+	28.0000i	−0.895341	+	0.895341i
$979$	−11.2250			−0.358752
$980$		0			0
$981$	60.0000			1.91565
$982$	22.4499	−	22.4499i	0.716407	−	0.716407i
$983$	−5.61249	−	5.61249i	−0.179011	−	0.179011i	0.611914	−	0.790924i	$-0.290400\pi$
$983$	−5.61249	−	5.61249i	−0.179011	−	0.179011i	−0.790924	+	0.611914i	$0.790400\pi$
$984$	−22.4499			−0.715678
$985$	1.00000	−	3.00000i	0.0318626	−	0.0955879i
$986$	12.0000			0.382158
$987$		0			0
$988$	−14.9666	−	14.9666i	−0.476152	−	0.476152i
$989$		−	21.0000i		−	0.667761i
$990$	14.9666	−	44.8999i	0.475671	−	1.42701i
$991$			37.4166i			1.18858i	0.804252	+	0.594288i	$0.202566\pi$
$991$			37.4166i			1.18858i	−0.804252	+	0.594288i	$0.797434\pi$
$992$	29.9333	−	29.9333i	0.950382	−	0.950382i
$993$	−42.0000	+	42.0000i	−1.33283	+	1.33283i
$994$		0			0
$995$		0			0
$996$	14.0000			0.443607
$997$	−3.00000	−	3.00000i	−0.0950110	−	0.0950110i	0.658004	−	0.753015i	$-0.271401\pi$
$997$	−3.00000	−	3.00000i	−0.0950110	−	0.0950110i	−0.753015	+	0.658004i	$0.771401\pi$
$998$	41.1582	+	41.1582i	1.30284	+	1.30284i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.k.g.687.1		4
4.3	odd	2	inner	980.2.k.g.687.2		4
5.3	odd	4	inner	980.2.k.g.883.2		4
7.2	even	3		980.2.x.f.67.2		8
7.3	odd	6		140.2.w.a.107.2	yes	8
7.4	even	3		980.2.x.f.667.1		8
7.5	odd	6		140.2.w.a.67.1	yes	8
7.6	odd	2		980.2.k.e.687.2		4
20.3	even	4	inner	980.2.k.g.883.1		4
28.3	even	6		140.2.w.a.107.1	yes	8
28.11	odd	6		980.2.x.f.667.2		8
28.19	even	6		140.2.w.a.67.2	yes	8
28.23	odd	6		980.2.x.f.67.1		8
28.27	even	2		980.2.k.e.687.1		4
35.3	even	12		140.2.w.a.23.2	yes	8
35.12	even	12		700.2.be.c.543.2		8
35.13	even	4		980.2.k.e.883.1		4
35.17	even	12		700.2.be.c.443.1		8
35.18	odd	12		980.2.x.f.863.1		8
35.19	odd	6		700.2.be.c.207.2		8
35.23	odd	12		980.2.x.f.263.2		8
35.24	odd	6		700.2.be.c.107.1		8
35.33	even	12		140.2.w.a.123.1	yes	8
140.3	odd	12		140.2.w.a.23.1	✓	8
140.19	even	6		700.2.be.c.207.1		8
140.23	even	12		980.2.x.f.263.1		8
140.47	odd	12		700.2.be.c.543.1		8
140.59	even	6		700.2.be.c.107.2		8
140.83	odd	4		980.2.k.e.883.2		4
140.87	odd	12		700.2.be.c.443.2		8
140.103	odd	12		140.2.w.a.123.2	yes	8
140.123	even	12		980.2.x.f.863.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.w.a.23.1	✓	8	140.3	odd	12
140.2.w.a.23.2	yes	8	35.3	even	12
140.2.w.a.67.1	yes	8	7.5	odd	6
140.2.w.a.67.2	yes	8	28.19	even	6
140.2.w.a.107.1	yes	8	28.3	even	6
140.2.w.a.107.2	yes	8	7.3	odd	6
140.2.w.a.123.1	yes	8	35.33	even	12
140.2.w.a.123.2	yes	8	140.103	odd	12
700.2.be.c.107.1		8	35.24	odd	6
700.2.be.c.107.2		8	140.59	even	6
700.2.be.c.207.1		8	140.19	even	6
700.2.be.c.207.2		8	35.19	odd	6
700.2.be.c.443.1		8	35.17	even	12
700.2.be.c.443.2		8	140.87	odd	12
700.2.be.c.543.1		8	140.47	odd	12
700.2.be.c.543.2		8	35.12	even	12
980.2.k.e.687.1		4	28.27	even	2
980.2.k.e.687.2		4	7.6	odd	2
980.2.k.e.883.1		4	35.13	even	4
980.2.k.e.883.2		4	140.83	odd	4
980.2.k.g.687.1		4	1.1	even	1	trivial
980.2.k.g.687.2		4	4.3	odd	2	inner
980.2.k.g.883.1		4	20.3	even	4	inner
980.2.k.g.883.2		4	5.3	odd	4	inner
980.2.x.f.67.1		8	28.23	odd	6
980.2.x.f.67.2		8	7.2	even	3
980.2.x.f.263.1		8	140.23	even	12
980.2.x.f.263.2		8	35.23	odd	12
980.2.x.f.667.1		8	7.4	even	3
980.2.x.f.667.2		8	28.11	odd	6
980.2.x.f.863.1		8	35.18	odd	12
980.2.x.f.863.2		8	140.123	even	12

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.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +(-1.87083 - 1.87083i) q^{3} +2.00000i q^{4} +(1.00000 + 2.00000i) q^{5} -3.74166i q^{6} +(-2.00000 + 2.00000i) q^{8} +4.00000i q^{9} +(-1.00000 + 3.00000i) q^{10} +3.74166i q^{11} +(3.74166 - 3.74166i) q^{12} +(2.00000 - 2.00000i) q^{13} +(1.87083 - 5.61249i) q^{15} -4.00000 q^{16} +(-2.00000 - 2.00000i) q^{17} +(-4.00000 + 4.00000i) q^{18} -3.74166 q^{19} +(-4.00000 + 2.00000i) q^{20} +(-3.74166 + 3.74166i) q^{22} +(-1.87083 - 1.87083i) q^{23} +7.48331 q^{24} +(-3.00000 + 4.00000i) q^{25} +4.00000 q^{26} +(1.87083 - 1.87083i) q^{27} +3.00000i q^{29} +(7.48331 - 3.74166i) q^{30} +7.48331i q^{31} +(-4.00000 - 4.00000i) q^{32} +(7.00000 - 7.00000i) q^{33} -4.00000i q^{34} -8.00000 q^{36} +(-3.74166 - 3.74166i) q^{38} -7.48331 q^{39} +(-6.00000 - 2.00000i) q^{40} -3.00000 q^{41} +(5.61249 + 5.61249i) q^{43} -7.48331 q^{44} +(-8.00000 + 4.00000i) q^{45} -3.74166i q^{46} +(-7.48331 + 7.48331i) q^{47} +(7.48331 + 7.48331i) q^{48} +(-7.00000 + 1.00000i) q^{50} +7.48331i q^{51} +(4.00000 + 4.00000i) q^{52} +(-5.00000 + 5.00000i) q^{53} +3.74166 q^{54} +(-7.48331 + 3.74166i) q^{55} +(7.00000 + 7.00000i) q^{57} +(-3.00000 + 3.00000i) q^{58} -3.74166 q^{59} +(11.2250 + 3.74166i) q^{60} +3.00000 q^{61} +(-7.48331 + 7.48331i) q^{62} -8.00000i q^{64} +(6.00000 + 2.00000i) q^{65} +14.0000 q^{66} +(9.35414 - 9.35414i) q^{67} +(4.00000 - 4.00000i) q^{68} +7.00000i q^{69} +3.74166i q^{71} +(-8.00000 - 8.00000i) q^{72} +(-2.00000 + 2.00000i) q^{73} +(13.0958 - 1.87083i) q^{75} -7.48331i q^{76} +(-7.48331 - 7.48331i) q^{78} -3.74166 q^{79} +(-4.00000 - 8.00000i) q^{80} +5.00000 q^{81} +(-3.00000 - 3.00000i) q^{82} +(1.87083 + 1.87083i) q^{83} +(2.00000 - 6.00000i) q^{85} +11.2250i q^{86} +(5.61249 - 5.61249i) q^{87} +(-7.48331 - 7.48331i) q^{88} +3.00000i q^{89} +(-12.0000 - 4.00000i) q^{90} +(3.74166 - 3.74166i) q^{92} +(14.0000 - 14.0000i) q^{93} -14.9666 q^{94} +(-3.74166 - 7.48331i) q^{95} +14.9666i q^{96} +(9.00000 + 9.00000i) q^{97} -14.9666 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{5} - 8 q^{8} - 4 q^{10} + 8 q^{13} - 16 q^{16} - 8 q^{17} - 16 q^{18} - 16 q^{20} - 12 q^{25} + 16 q^{26} - 16 q^{32} + 28 q^{33} - 32 q^{36} - 24 q^{40} - 12 q^{41} - 32 q^{45} - 28 q^{50}+ \cdots + 36 q^{97}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^5 - 8 * q^8 - 4 * q^10 + 8 * q^13 - 16 * q^16 - 8 * q^17 - 16 * q^18 - 16 * q^20 - 12 * q^25 + 16 * q^26 - 16 * q^32 + 28 * q^33 - 32 * q^36 - 24 * q^40 - 12 * q^41 - 32 * q^45 - 28 * q^50 + 16 * q^52 - 20 * q^53 + 28 * q^57 - 12 * q^58 + 12 * q^61 + 24 * q^65 + 56 * q^66 + 16 * q^68 - 32 * q^72 - 8 * q^73 - 16 * q^80 + 20 * q^81 - 12 * q^82 + 8 * q^85 - 48 * q^90 + 56 * q^93 + 36 * q^97

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