LMFDB - Embedded newform 592.2.be.e.399.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [592,2,Mod(319,592)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(592, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 5]))

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

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

chi := DirichletCharacter("592.319");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 592 = 2^{4} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	592.be (of order $12$, degree $4$, 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:	$4.72714379966$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 46 x^{18} + 885 x^{16} + 9292 x^{14} + 58264 x^{12} + 224256 x^{10} + 523884 x^{8} + 706272 x^{6} + \cdots + 144 $ x^20 + 46x^18 + 885x^16 + 9292x^14 + 58264x^12 + 224256x^10 + 523884x^8 + 706272x^6 + 490896x^4 + 133632*x^2 + 144
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			399.3
Root			$0.873351i$ of defining polynomial
Character	$\chi$	$=$	592.399
Dual form			592.2.be.e.319.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.436676 + 0.756344i) q^{3} +(-0.192218 - 0.717368i) q^{5} +(-1.90253 - 1.09843i) q^{7} +(1.11863 + 1.93752i) q^{9} +O(q^{10})$	\(q+(-0.436676 + 0.756344i) q^{3} +(-0.192218 - 0.717368i) q^{5} +(-1.90253 - 1.09843i) q^{7} +(1.11863 + 1.93752i) q^{9} -1.68860 q^{11} +(1.56403 + 5.83705i) q^{13} +(0.626514 + 0.167874i) q^{15} +(-4.60692 - 1.23442i) q^{17} +(-3.93040 + 1.05315i) q^{19} +(1.66158 - 0.959311i) q^{21} +(5.76297 + 5.76297i) q^{23} +(3.85246 - 2.22422i) q^{25} -4.57397 q^{27} +(5.98118 + 5.98118i) q^{29} +(-7.55406 + 7.55406i) q^{31} +(0.737369 - 1.27716i) q^{33} +(-0.422275 + 1.57595i) q^{35} +(-5.44496 + 2.71152i) q^{37} +(-5.09779 - 1.36595i) q^{39} +(-4.64651 - 2.68266i) q^{41} +(0.512617 + 0.512617i) q^{43} +(1.17490 - 1.17490i) q^{45} -10.8893i q^{47} +(-1.08692 - 1.88261i) q^{49} +(2.94538 - 2.94538i) q^{51} +(0.799717 + 1.38515i) q^{53} +(0.324579 + 1.21135i) q^{55} +(0.919768 - 3.43262i) q^{57} +(-3.25497 + 12.1477i) q^{59} +(-2.62960 + 0.704598i) q^{61} -4.91492i q^{63} +(3.88668 - 2.24397i) q^{65} +(0.515094 - 0.892169i) q^{67} +(-6.87534 + 1.84224i) q^{69} +(2.02351 + 1.16828i) q^{71} +6.19366i q^{73} +3.88505i q^{75} +(3.21260 + 1.85480i) q^{77} +(11.6758 - 3.12852i) q^{79} +(-1.35855 + 2.35307i) q^{81} +(5.53320 - 3.19459i) q^{83} +3.54213i q^{85} +(-7.13567 + 1.91200i) q^{87} +(1.03430 - 3.86007i) q^{89} +(3.43595 - 12.8231i) q^{91} +(-2.41480 - 9.01215i) q^{93} +(1.51099 + 2.61711i) q^{95} +(10.1153 - 10.1153i) q^{97} +(-1.88891 - 3.27169i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{3} - 4 q^{5} - 6 q^{7} - 16 q^{9}+O(q^{10}) $ 20 * q - 4 * q^3 - 4 * q^5 - 6 * q^7 - 16 * q^9	$ 20 q - 4 q^{3} - 4 q^{5} - 6 q^{7} - 16 q^{9} + 4 q^{11} + 4 q^{13} + 8 q^{15} - 4 q^{17} + 10 q^{19} - 18 q^{21} + 8 q^{23} + 42 q^{25} + 68 q^{27} - 8 q^{29} + 28 q^{31} - 20 q^{33} - 10 q^{35} - 24 q^{37} - 14 q^{39} - 6 q^{41} + 32 q^{43} + 8 q^{45} - 12 q^{49} - 58 q^{51} + 6 q^{53} + 26 q^{55} - 2 q^{57} - 56 q^{59} - 8 q^{61} + 6 q^{65} + 20 q^{67} + 26 q^{69} - 30 q^{71} + 60 q^{77} + 50 q^{79} - 22 q^{81} + 36 q^{83} - 32 q^{87} - 20 q^{89} - 50 q^{91} - 50 q^{93} - 72 q^{95} + 32 q^{97} - 14 q^{99}+O(q^{100}) $ 20 * q - 4 * q^3 - 4 * q^5 - 6 * q^7 - 16 * q^9 + 4 * q^11 + 4 * q^13 + 8 * q^15 - 4 * q^17 + 10 * q^19 - 18 * q^21 + 8 * q^23 + 42 * q^25 + 68 * q^27 - 8 * q^29 + 28 * q^31 - 20 * q^33 - 10 * q^35 - 24 * q^37 - 14 * q^39 - 6 * q^41 + 32 * q^43 + 8 * q^45 - 12 * q^49 - 58 * q^51 + 6 * q^53 + 26 * q^55 - 2 * q^57 - 56 * q^59 - 8 * q^61 + 6 * q^65 + 20 * q^67 + 26 * q^69 - 30 * q^71 + 60 * q^77 + 50 * q^79 - 22 * q^81 + 36 * q^83 - 32 * q^87 - 20 * q^89 - 50 * q^91 - 50 * q^93 - 72 * q^95 + 32 * q^97 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/592\mathbb{Z}\right)^\times$.

$n$	$113$	$149$	$223$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.436676	+	0.756344i	−0.252115	+	0.436676i	−0.964108	−	0.265511i	$-0.914459\pi$
$3$	−0.436676	+	0.756344i	−0.252115	+	0.436676i	0.711993	+	0.702186i	$0.247793\pi$
$4$		0			0
$5$	−0.192218	−	0.717368i	−0.0859626	−	0.320817i	0.909532	−	0.415634i	$-0.136440\pi$
$5$	−0.192218	−	0.717368i	−0.0859626	−	0.320817i	−0.995495	+	0.0948169i	$0.969773\pi$
$6$		0			0
$7$	−1.90253	−	1.09843i	−0.719088	−	0.415166i	0.0953288	−	0.995446i	$-0.469610\pi$
$7$	−1.90253	−	1.09843i	−0.719088	−	0.415166i	−0.814417	+	0.580280i	$0.802943\pi$
$8$		0			0
$9$	1.11863	+	1.93752i	0.372876	+	0.645841i
$10$		0			0
$11$	−1.68860			−0.509131			−0.254566	−	0.967056i	$-0.581932\pi$
$11$	−1.68860			−0.509131			−0.254566	+	0.967056i	$0.581932\pi$
$12$		0			0
$13$	1.56403	+	5.83705i	0.433785	+	1.61891i	0.743958	+	0.668226i	$0.232946\pi$
$13$	1.56403	+	5.83705i	0.433785	+	1.61891i	−0.310174	+	0.950680i	$0.600387\pi$
$14$		0			0
$15$	0.626514	+	0.167874i	0.161765	+	0.0433449i
$16$		0			0
$17$	−4.60692	−	1.23442i	−1.11734	−	0.299391i	−0.347535	−	0.937667i	$-0.612981\pi$
$17$	−4.60692	−	1.23442i	−1.11734	−	0.299391i	−0.769807	+	0.638276i	$0.779648\pi$
$18$		0			0
$19$	−3.93040	+	1.05315i	−0.901696	+	0.241609i	−0.679744	−	0.733449i	$-0.737909\pi$
$19$	−3.93040	+	1.05315i	−0.901696	+	0.241609i	−0.221951	+	0.975058i	$0.571243\pi$
$20$		0			0
$21$	1.66158	−	0.959311i	0.362586	−	0.209339i
$22$		0			0
$23$	5.76297	+	5.76297i	1.20166	+	1.20166i	0.973661	+	0.228002i	$0.0732192\pi$
$23$	5.76297	+	5.76297i	1.20166	+	1.20166i	0.228002	+	0.973661i	$0.426781\pi$
$24$		0			0
$25$	3.85246	−	2.22422i	0.770492	−	0.444844i
$26$		0			0
$27$	−4.57397			−0.880260
$28$		0			0
$29$	5.98118	+	5.98118i	1.11068	+	1.11068i	0.993059	+	0.117619i	$0.0375263\pi$
$29$	5.98118	+	5.98118i	1.11068	+	1.11068i	0.117619	+	0.993059i	$0.462474\pi$
$30$		0			0
$31$	−7.55406	+	7.55406i	−1.35675	+	1.35675i	−0.478856	+	0.877893i	$0.658948\pi$
$31$	−7.55406	+	7.55406i	−1.35675	+	1.35675i	−0.877893	+	0.478856i	$0.841052\pi$
$32$		0			0
$33$	0.737369	−	1.27716i	0.128359	−	0.222325i
$34$		0			0
$35$	−0.422275	+	1.57595i	−0.0713774	+	0.266384i
$36$		0			0
$37$	−5.44496	+	2.71152i	−0.895147	+	0.445772i
$37$	−5.44496	+	2.71152i	−0.895147	+	0.445772i
$38$		0			0
$39$	−5.09779	−	1.36595i	−0.816300	−	0.218727i
$40$		0			0
$41$	−4.64651	−	2.68266i	−0.725662	−	0.418961i	0.0911709	−	0.995835i	$-0.470939\pi$
$41$	−4.64651	−	2.68266i	−0.725662	−	0.418961i	−0.816833	+	0.576874i	$0.804272\pi$
$42$		0			0
$43$	0.512617	+	0.512617i	0.0781734	+	0.0781734i	0.745112	−	0.666939i	$-0.232396\pi$
$43$	0.512617	+	0.512617i	0.0781734	+	0.0781734i	−0.666939	+	0.745112i	$0.732396\pi$
$44$		0			0
$45$	1.17490	−	1.17490i	0.175143	−	0.175143i
$46$		0			0
$47$		−	10.8893i		−	1.58837i	−0.607675	−	0.794186i	$-0.707898\pi$
$47$		−	10.8893i		−	1.58837i	0.607675	−	0.794186i	$-0.292102\pi$
$48$		0			0
$49$	−1.08692	−	1.88261i	−0.155275	−	0.268944i
$50$		0			0
$51$	2.94538	−	2.94538i	0.412435	−	0.412435i
$52$		0			0
$53$	0.799717	+	1.38515i	0.109850	+	0.190265i	0.915709	−	0.401842i	$-0.131630\pi$
$53$	0.799717	+	1.38515i	0.109850	+	0.190265i	−0.805860	+	0.592107i	$0.798296\pi$
$54$		0			0
$55$	0.324579	+	1.21135i	0.0437662	+	0.163338i
$56$		0			0
$57$	0.919768	−	3.43262i	0.121826	−	0.454662i
$58$		0			0
$59$	−3.25497	+	12.1477i	−0.423761	+	1.58150i	0.342852	+	0.939390i	$0.388607\pi$
$59$	−3.25497	+	12.1477i	−0.423761	+	1.58150i	−0.766613	+	0.642109i	$0.778059\pi$
$60$		0			0
$61$	−2.62960	+	0.704598i	−0.336685	+	0.0902146i	−0.423201	−	0.906036i	$-0.639093\pi$
$61$	−2.62960	+	0.704598i	−0.336685	+	0.0902146i	0.0865154	+	0.996251i	$0.472427\pi$
$62$		0			0
$63$		−	4.91492i		−	0.619222i
$64$		0			0
$65$	3.88668	−	2.24397i	0.482083	−	0.278331i
$66$		0			0
$67$	0.515094	−	0.892169i	0.0629288	−	0.108996i	−0.832845	−	0.553507i	$-0.813289\pi$
$67$	0.515094	−	0.892169i	0.0629288	−	0.108996i	0.895773	+	0.444511i	$0.146623\pi$
$68$		0			0
$69$	−6.87534	+	1.84224i	−0.827694	+	0.221780i
$70$		0			0
$71$	2.02351	+	1.16828i	0.240147	+	0.138649i	0.615244	−	0.788336i	$-0.289057\pi$
$71$	2.02351	+	1.16828i	0.240147	+	0.138649i	−0.375097	+	0.926985i	$0.622391\pi$
$72$		0			0
$73$			6.19366i			0.724913i	0.932001	+	0.362456i	$0.118062\pi$
$73$			6.19366i			0.724913i	−0.932001	+	0.362456i	$0.881938\pi$
$74$		0			0
$75$			3.88505i			0.448607i
$76$		0			0
$77$	3.21260	+	1.85480i	0.366110	+	0.211374i
$78$		0			0
$79$	11.6758	−	3.12852i	1.31363	−	0.351987i	0.467043	−	0.884235i	$-0.345319\pi$
$79$	11.6758	−	3.12852i	1.31363	−	0.351987i	0.846589	+	0.532248i	$0.178653\pi$
$80$		0			0
$81$	−1.35855	+	2.35307i	−0.150950	+	0.261453i
$82$		0			0
$83$	5.53320	−	3.19459i	0.607347	−	0.350652i	−0.164579	−	0.986364i	$-0.552627\pi$
$83$	5.53320	−	3.19459i	0.607347	−	0.350652i	0.771926	+	0.635712i	$0.219293\pi$
$84$		0			0
$85$			3.54213i			0.384198i
$86$		0			0
$87$	−7.13567	+	1.91200i	−0.765024	+	0.204988i
$88$		0			0
$89$	1.03430	−	3.86007i	0.109636	−	0.409167i	−0.889194	−	0.457530i	$-0.848734\pi$
$89$	1.03430	−	3.86007i	0.109636	−	0.409167i	0.998830	+	0.0483639i	$0.0154007\pi$
$90$		0			0
$91$	3.43595	−	12.8231i	0.360185	−	1.34423i
$92$		0			0
$93$	−2.41480	−	9.01215i	−0.250403	−	0.934516i
$94$		0			0
$95$	1.51099	+	2.61711i	0.155024	+	0.268510i
$96$		0			0
$97$	10.1153	−	10.1153i	1.02706	−	1.02706i	0.0274339	−	0.999624i	$-0.491266\pi$
$97$	10.1153	−	10.1153i	1.02706	−	1.02706i	0.999624	−	0.0274339i	$-0.00873358\pi$
$98$		0			0
$99$	−1.88891	−	3.27169i	−0.189843	−	0.328818i
$100$		0			0
$101$			9.85174i			0.980285i	0.871642	+	0.490143i	$0.163055\pi$
$101$			9.85174i			0.980285i	−0.871642	+	0.490143i	$0.836945\pi$
$102$		0			0
$103$	7.50071	−	7.50071i	0.739067	−	0.739067i	−0.233330	−	0.972398i	$-0.574962\pi$
$103$	7.50071	−	7.50071i	0.739067	−	0.739067i	0.972398	+	0.233330i	$0.0749624\pi$
$104$		0			0
$105$	−1.00756	−	1.00756i	−0.0983282	−	0.0983282i
$106$		0			0
$107$	6.61288	+	3.81795i	0.639291	+	0.369095i	0.784341	−	0.620329i	$-0.213001\pi$
$107$	6.61288	+	3.81795i	0.639291	+	0.369095i	−0.145050	+	0.989424i	$0.546334\pi$
$108$		0			0
$109$	−0.890624	−	0.238642i	−0.0853063	−	0.0228578i	0.215913	−	0.976413i	$-0.430727\pi$
$109$	−0.890624	−	0.238642i	−0.0853063	−	0.0228578i	−0.301220	+	0.953555i	$0.597394\pi$
$110$		0			0
$111$	0.326838	−	5.30232i	0.0310221	−	0.503274i
$112$		0			0
$113$	4.98355	−	18.5989i	0.468813	−	1.74963i	−0.175114	−	0.984548i	$-0.556029\pi$
$113$	4.98355	−	18.5989i	0.468813	−	1.74963i	0.643927	−	0.765087i	$-0.277304\pi$
$114$		0			0
$115$	3.02642	−	5.24192i	0.282215	−	0.488811i
$116$		0			0
$117$	−9.55984	+	9.55984i	−0.883807	+	0.883807i
$118$		0			0
$119$	7.40888	+	7.40888i	0.679171	+	0.679171i
$120$		0			0
$121$	−8.14864			−0.740786
$122$		0			0
$123$	4.05803	−	2.34291i	0.365900	−	0.211253i
$124$		0			0
$125$	−4.96184	−	4.96184i	−0.443801	−	0.443801i
$126$		0			0
$127$	−9.18967	+	5.30566i	−0.815451	+	0.470801i	−0.848845	−	0.528641i	$-0.822702\pi$
$127$	−9.18967	+	5.30566i	−0.815451	+	0.470801i	0.0333941	+	0.999442i	$0.489368\pi$
$128$		0			0
$129$	−0.611562	+	0.163868i	−0.0538451	+	0.0144277i
$130$		0			0
$131$	14.0195	+	3.75651i	1.22489	+	0.328208i	0.812587	−	0.582840i	$-0.198059\pi$
$131$	14.0195	+	3.75651i	1.22489	+	0.328208i	0.412301	+	0.911048i	$0.364725\pi$
$132$		0			0
$133$	8.63450	+	2.31361i	0.748706	+	0.200615i
$134$		0			0
$135$	0.879199	+	3.28122i	0.0756694	+	0.282402i
$136$		0			0
$137$	−4.48288			−0.382998			−0.191499	−	0.981493i	$-0.561335\pi$
$137$	−4.48288			−0.382998			−0.191499	+	0.981493i	$0.561335\pi$
$138$		0			0
$139$	−3.46404	−	5.99990i	−0.293816	−	0.508905i	0.680893	−	0.732383i	$-0.261592\pi$
$139$	−3.46404	−	5.99990i	−0.293816	−	0.508905i	−0.974709	+	0.223479i	$0.928259\pi$
$140$		0			0
$141$	8.23608	+	4.75510i	0.693603	+	0.400452i
$142$		0			0
$143$	−2.64102	−	9.85642i	−0.220853	−	0.824235i
$144$		0			0
$145$	3.14102	−	5.44040i	0.260847	−	0.451801i
$146$		0			0
$147$	1.89853			0.156588
$148$		0			0
$149$	13.2506			1.08553			0.542765	−	0.839885i	$-0.317378\pi$
$149$	13.2506			1.08553			0.542765	+	0.839885i	$0.317378\pi$
$150$		0			0
$151$	5.02309	−	8.70025i	0.408773	−	0.708016i	−0.585979	−	0.810326i	$-0.699290\pi$
$151$	5.02309	−	8.70025i	0.408773	−	0.708016i	0.994753	+	0.102310i	$0.0326233\pi$
$152$		0			0
$153$	−2.76172	−	10.3069i	−0.223272	−	0.833261i
$154$		0			0
$155$	6.87107	+	3.96701i	0.551897	+	0.318638i
$156$		0			0
$157$	−5.71959	−	9.90663i	−0.456473	−	0.790635i	0.542298	−	0.840186i	$-0.317554\pi$
$157$	−5.71959	−	9.90663i	−0.456473	−	0.790635i	−0.998772	+	0.0495511i	$0.984221\pi$
$158$		0			0
$159$	−1.39687			−0.110779
$160$		0			0
$161$	−4.63402	−	17.2944i	−0.365212	−	1.36299i
$162$		0			0
$163$	−13.7505	−	3.68444i	−1.07702	−	0.288588i	−0.323648	−	0.946177i	$-0.604909\pi$
$163$	−13.7505	−	3.68444i	−1.07702	−	0.288588i	−0.753376	+	0.657589i	$0.771576\pi$
$164$		0			0
$165$	−1.05793	−	0.283471i	−0.0823597	−	0.0220682i
$166$		0			0
$167$	16.9856	−	4.55127i	1.31438	−	0.352188i	0.467512	−	0.883987i	$-0.345151\pi$
$167$	16.9856	−	4.55127i	1.31438	−	0.352188i	0.846871	+	0.531799i	$0.178484\pi$
$168$		0			0
$169$	−20.3666	+	11.7587i	−1.56666	+	0.904513i
$170$		0			0
$171$	−6.43716	−	6.43716i	−0.492262	−	0.492262i
$172$		0			0
$173$	−3.07038	+	1.77269i	−0.233437	+	0.134775i	−0.612157	−	0.790737i	$-0.709698\pi$
$173$	−3.07038	+	1.77269i	−0.233437	+	0.134775i	0.378720	+	0.925511i	$0.376364\pi$
$174$		0			0
$175$	−9.77255			−0.738735
$176$		0			0
$177$	−7.76650	−	7.76650i	−0.583766	−	0.583766i
$178$		0			0
$179$	9.71319	−	9.71319i	0.725998	−	0.725998i	−0.243822	−	0.969820i	$-0.578401\pi$
$179$	9.71319	−	9.71319i	0.725998	−	0.725998i	0.969820	+	0.243822i	$0.0784013\pi$
$180$		0			0
$181$	−10.0861	+	17.4697i	−0.749695	+	1.29851i	0.198273	+	0.980147i	$0.436467\pi$
$181$	−10.0861	+	17.4697i	−0.749695	+	1.29851i	−0.947969	+	0.318364i	$0.896867\pi$
$182$		0			0
$183$	0.615362	−	2.29656i	0.0454889	−	0.169767i
$184$		0			0
$185$	2.99178	+	3.38484i	0.219960	+	0.248858i
$186$		0			0
$187$	7.77923	+	2.08444i	0.568874	+	0.152429i
$188$		0			0
$189$	8.70210	+	5.02416i	0.632985	+	0.365454i
$190$		0			0
$191$	11.9133	+	11.9133i	0.862020	+	0.862020i	0.991573	−	0.129553i	$-0.0413542\pi$
$191$	11.9133	+	11.9133i	0.862020	+	0.862020i	−0.129553	+	0.991573i	$0.541354\pi$
$192$		0			0
$193$	−14.5013	+	14.5013i	−1.04382	+	1.04382i	−0.0448302	+	0.998995i	$0.514275\pi$
$193$	−14.5013	+	14.5013i	−1.04382	+	1.04382i	−0.998995	+	0.0448302i	$0.985725\pi$
$194$		0			0
$195$			3.91955i			0.280685i
$196$		0			0
$197$	−0.186018	−	0.322192i	−0.0132532	−	0.0229553i	0.859323	−	0.511434i	$-0.170885\pi$
$197$	−0.186018	−	0.322192i	−0.0132532	−	0.0229553i	−0.872576	+	0.488478i	$0.837552\pi$
$198$		0			0
$199$	−11.4592	+	11.4592i	−0.812320	+	0.812320i	−0.984981	−	0.172661i	$-0.944763\pi$
$199$	−11.4592	+	11.4592i	−0.812320	+	0.812320i	0.172661	+	0.984981i	$0.444763\pi$
$200$		0			0
$201$	0.449858	+	0.779177i	0.0317306	+	0.0549589i
$202$		0			0
$203$	−4.80949	−	17.9493i	−0.337560	−	1.25979i
$204$		0			0
$205$	−1.03131	+	3.84891i	−0.0720300	+	0.268820i
$206$		0			0
$207$	−4.71926	+	17.6125i	−0.328011	+	1.22415i
$208$		0			0
$209$	6.63686	−	1.77834i	0.459081	−	0.123011i
$210$		0			0
$211$			26.7975i			1.84481i	0.386220	+	0.922407i	$0.373781\pi$
$211$			26.7975i			1.84481i	−0.386220	+	0.922407i	$0.626219\pi$
$212$		0			0
$213$	−1.76724	+	1.02032i	−0.121089	+	0.0699109i
$214$		0			0
$215$	0.269201	−	0.466269i	0.0183593	−	0.0317993i
$216$		0			0
$217$	22.6694	−	6.07424i	1.53890	−	0.412347i
$218$		0			0
$219$	−4.68454	−	2.70462i	−0.316552	−	0.182761i
$220$		0			0
$221$		−	28.8215i		−	1.93874i
$222$		0			0
$223$			7.22652i			0.483924i	0.970286	+	0.241962i	$0.0777909\pi$
$223$			7.22652i			0.483924i	−0.970286	+	0.241962i	$0.922209\pi$
$224$		0			0
$225$	8.61894	+	4.97615i	0.574596	+	0.331743i
$226$		0			0
$227$	−2.10125	+	0.563028i	−0.139465	+	0.0373695i	−0.327876	−	0.944721i	$-0.606333\pi$
$227$	−2.10125	+	0.563028i	−0.139465	+	0.0373695i	0.188411	+	0.982090i	$0.439666\pi$
$228$		0			0
$229$	7.02169	−	12.1619i	0.464006	−	0.803682i	−0.535150	−	0.844757i	$-0.679745\pi$
$229$	7.02169	−	12.1619i	0.464006	−	0.803682i	0.999156	+	0.0410747i	$0.0130782\pi$
$230$		0			0
$231$	−2.80573	+	1.61989i	−0.184604	+	0.106581i
$232$		0			0
$233$			12.1654i			0.796980i	0.917173	+	0.398490i	$0.130466\pi$
$233$			12.1654i			0.796980i	−0.917173	+	0.398490i	$0.869534\pi$
$234$		0			0
$235$	−7.81165	+	2.09313i	−0.509576	+	0.136540i
$236$		0			0
$237$	−2.73230	+	10.1971i	−0.177482	+	0.662372i
$238$		0			0
$239$	−2.84019	+	10.5997i	−0.183717	+	0.685640i	0.811185	+	0.584790i	$0.198823\pi$
$239$	−2.84019	+	10.5997i	−0.183717	+	0.685640i	−0.994902	+	0.100850i	$0.967844\pi$
$240$		0			0
$241$	−1.87024	−	6.97984i	−0.120473	−	0.449611i	0.879165	−	0.476517i	$-0.158101\pi$
$241$	−1.87024	−	6.97984i	−0.120473	−	0.449611i	−0.999638	+	0.0269065i	$0.991434\pi$
$242$		0			0
$243$	−8.04744	−	13.9386i	−0.516243	−	0.894160i
$244$		0			0
$245$	−1.14160	+	1.14160i	−0.0729339	+	0.0729339i
$246$		0			0
$247$	−12.2945	−	21.2948i	−0.782283	−	1.35495i
$248$		0			0
$249$			5.58000i			0.353618i
$250$		0			0
$251$	−1.14918	+	1.14918i	−0.0725359	+	0.0725359i	−0.742444	−	0.669908i	$-0.766333\pi$
$251$	−1.14918	+	1.14918i	−0.0725359	+	0.0725359i	0.669908	+	0.742444i	$0.266333\pi$
$252$		0			0
$253$	−9.73133	−	9.73133i	−0.611804	−	0.611804i
$254$		0			0
$255$	−2.67907	−	1.54676i	−0.167770	−	0.0968621i
$256$		0			0
$257$	14.6024	+	3.91271i	0.910875	+	0.244068i	0.683681	−	0.729781i	$-0.260378\pi$
$257$	14.6024	+	3.91271i	0.910875	+	0.244068i	0.227194	+	0.973849i	$0.427045\pi$
$258$		0			0
$259$	13.3376	+	0.822136i	0.828759	+	0.0510850i
$260$		0			0
$261$	−4.89795	+	18.2794i	−0.303176	+	1.13147i
$262$		0			0
$263$	4.87275	−	8.43985i	0.300467	−	0.520423i	−0.675775	−	0.737108i	$-0.736191\pi$
$263$	4.87275	−	8.43985i	0.300467	−	0.520423i	0.976242	+	0.216684i	$0.0695243\pi$
$264$		0			0
$265$	0.839942	−	0.839942i	0.0515972	−	0.0515972i
$266$		0			0
$267$	2.46789	+	2.46789i	0.151032	+	0.151032i
$268$		0			0
$269$	18.0779			1.10223			0.551114	−	0.834430i	$-0.314203\pi$
$269$	18.0779			1.10223			0.551114	+	0.834430i	$0.314203\pi$
$270$		0			0
$271$	−0.939520	+	0.542432i	−0.0570718	+	0.0329504i	−0.528264	−	0.849080i	$-0.677157\pi$
$271$	−0.939520	+	0.542432i	−0.0570718	+	0.0329504i	0.471193	+	0.882030i	$0.343824\pi$
$272$		0			0
$273$	8.19830	+	8.19830i	0.496184	+	0.496184i
$274$		0			0
$275$	−6.50525	+	3.75581i	−0.392281	+	0.226484i
$276$		0			0
$277$	−10.4235	+	2.79296i	−0.626285	+	0.167813i	−0.557983	−	0.829852i	$-0.688425\pi$
$277$	−10.4235	+	2.79296i	−0.626285	+	0.167813i	−0.0683018	+	0.997665i	$0.521758\pi$
$278$		0			0
$279$	−23.0864	−	6.18597i	−1.38214	−	0.370344i
$280$		0			0
$281$	−4.87187	−	1.30541i	−0.290631	−	0.0778744i	0.110558	−	0.993870i	$-0.464736\pi$
$281$	−4.87187	−	1.30541i	−0.290631	−	0.0778744i	−0.401189	+	0.915995i	$0.631403\pi$
$282$		0			0
$283$	−3.81548	−	14.2396i	−0.226807	−	0.846454i	−0.981673	−	0.190575i	$-0.938965\pi$
$283$	−3.81548	−	14.2396i	−0.226807	−	0.846454i	0.754866	−	0.655879i	$-0.227702\pi$
$284$		0			0
$285$	−2.63925			−0.156336
$286$		0			0
$287$	5.89341	+	10.2077i	0.347877	+	0.602540i
$288$		0			0
$289$	4.97749	+	2.87375i	0.292793	+	0.169044i
$290$		0			0
$291$	3.23356	+	12.0678i	0.189555	+	0.707427i
$292$		0			0
$293$	−6.65410	+	11.5252i	−0.388736	+	0.673311i	−0.992280	−	0.124019i	$-0.960422\pi$
$293$	−6.65410	+	11.5252i	−0.388736	+	0.673311i	0.603543	+	0.797330i	$0.293755\pi$
$294$		0			0
$295$	9.34005			0.543799
$296$		0			0
$297$	7.72358			0.448168
$298$		0			0
$299$	−24.6253	+	42.6522i	−1.42412	+	2.46664i
$300$		0			0
$301$	−0.412197	−	1.53834i	−0.0237586	−	0.0886684i
$302$		0			0
$303$	−7.45131	−	4.30202i	−0.428067	−	0.247144i
$304$		0			0
$305$	1.01091	+	1.75095i	0.0578847	+	0.100259i
$306$		0			0
$307$	−13.4350			−0.766774			−0.383387	−	0.923588i	$-0.625242\pi$
$307$	−13.4350			−0.766774			−0.383387	+	0.923588i	$0.625242\pi$
$308$		0			0
$309$	2.39774	+	8.94850i	0.136403	+	0.509062i
$310$		0			0
$311$	−6.52982	−	1.74966i	−0.370272	−	0.0992141i	0.0688846	−	0.997625i	$-0.478056\pi$
$311$	−6.52982	−	1.74966i	−0.370272	−	0.0992141i	−0.439157	+	0.898411i	$0.644723\pi$
$312$		0			0
$313$	12.1552	+	3.25697i	0.687050	+	0.184095i	0.585423	−	0.810728i	$-0.300928\pi$
$313$	12.1552	+	3.25697i	0.687050	+	0.184095i	0.101627	+	0.994823i	$0.467595\pi$
$314$		0			0
$315$	−3.52581	+	0.944737i	−0.198657	+	0.0532299i
$316$		0			0
$317$	17.9989	−	10.3917i	1.01092	−	0.583653i	0.0994572	−	0.995042i	$-0.468289\pi$
$317$	17.9989	−	10.3917i	1.01092	−	0.583653i	0.911460	+	0.411388i	$0.134956\pi$
$318$		0			0
$319$	−10.0998	−	10.0998i	−0.565481	−	0.565481i
$320$		0			0
$321$	−5.77537	+	3.33441i	−0.322349	+	0.186109i
$322$		0			0
$323$	19.4071			1.07984
$324$		0			0
$325$	19.0082	+	19.0082i	1.05439	+	1.05439i
$326$		0			0
$327$	0.569409	−	0.569409i	0.0314884	−	0.0314884i
$328$		0			0
$329$	−11.9611	+	20.7173i	−0.659437	+	1.14218i
$330$		0			0
$331$	−1.95916	+	7.31167i	−0.107685	+	0.401886i	−0.998636	−	0.0522137i	$-0.983372\pi$
$331$	−1.95916	+	7.31167i	−0.107685	+	0.401886i	0.890951	+	0.454100i	$0.150039\pi$
$332$		0			0
$333$	−11.3445	−	7.51655i	−0.621676	−	0.411904i
$334$		0			0
$335$	−0.739024	−	0.198021i	−0.0403772	−	0.0108190i
$336$		0			0
$337$	−8.16381	−	4.71338i	−0.444711	−	0.256754i	0.260883	−	0.965370i	$-0.415986\pi$
$337$	−8.16381	−	4.71338i	−0.444711	−	0.256754i	−0.705594	+	0.708616i	$0.749320\pi$
$338$		0			0
$339$	11.8910	+	11.8910i	0.645828	+	0.645828i
$340$		0			0
$341$	12.7558	−	12.7558i	0.690763	−	0.690763i
$342$		0			0
$343$			20.1536i			1.08819i
$344$		0			0
$345$	2.64313	+	4.57804i	0.142301	+	0.246473i
$346$		0			0
$347$	−6.88014	+	6.88014i	−0.369345	+	0.369345i	−0.867238	−	0.497893i	$-0.834107\pi$
$347$	−6.88014	+	6.88014i	−0.369345	+	0.369345i	0.497893	+	0.867238i	$0.334107\pi$
$348$		0			0
$349$	13.1388	+	22.7570i	0.703303	+	1.21816i	0.967301	+	0.253633i	$0.0816255\pi$
$349$	13.1388	+	22.7570i	0.703303	+	1.21816i	−0.263998	+	0.964523i	$0.585041\pi$
$350$		0			0
$351$	−7.15383	−	26.6985i	−0.381843	−	1.42506i
$352$		0			0
$353$	1.31348	−	4.90196i	0.0699093	−	0.260905i	−0.922122	−	0.386900i	$-0.873546\pi$
$353$	1.31348	−	4.90196i	0.0699093	−	0.260905i	0.992031	+	0.125995i	$0.0402124\pi$
$354$		0			0
$355$	0.449128	−	1.67617i	0.0238372	−	0.0889618i
$356$		0			0
$357$	−8.83894	+	2.36839i	−0.467806	+	0.125348i
$358$		0			0
$359$			35.0629i			1.85055i	0.379300	+	0.925274i	$0.376165\pi$
$359$			35.0629i			1.85055i	−0.379300	+	0.925274i	$0.623835\pi$
$360$		0			0
$361$	−2.11555	+	1.22141i	−0.111345	+	0.0642849i
$362$		0			0
$363$	3.55831	−	6.16318i	0.186763	−	0.323483i
$364$		0			0
$365$	4.44313	−	1.19053i	0.232564	−	0.0623154i
$366$		0			0
$367$	10.4831	+	6.05244i	0.547216	+	0.315935i	0.747998	−	0.663701i	$-0.231015\pi$
$367$	10.4831	+	6.05244i	0.547216	+	0.315935i	−0.200783	+	0.979636i	$0.564349\pi$
$368$		0			0
$369$		−	12.0036i		−	0.624883i
$370$		0			0
$371$		−	3.51372i		−	0.182423i
$372$		0			0
$373$	−12.8222	−	7.40290i	−0.663909	−	0.383308i	0.129856	−	0.991533i	$-0.458548\pi$
$373$	−12.8222	−	7.40290i	−0.663909	−	0.383308i	−0.793765	+	0.608225i	$0.791882\pi$
$374$		0			0
$375$	5.91958	−	1.58615i	0.305686	−	0.0819082i
$376$		0			0
$377$	−25.5577	+	44.2672i	−1.31629	+	2.27988i
$378$		0			0
$379$	1.73210	−	1.00003i	0.0889720	−	0.0513680i	−0.454854	−	0.890566i	$-0.650309\pi$
$379$	1.73210	−	1.00003i	0.0889720	−	0.0513680i	0.543826	+	0.839198i	$0.316975\pi$
$380$		0			0
$381$		−	9.26741i		−	0.474784i
$382$		0			0
$383$	8.75712	−	2.34646i	0.447468	−	0.119899i	−0.0280463	−	0.999607i	$-0.508929\pi$
$383$	8.75712	−	2.34646i	0.447468	−	0.119899i	0.475514	+	0.879708i	$0.342262\pi$
$384$		0			0
$385$	0.713051	−	2.66114i	0.0363405	−	0.135624i
$386$		0			0
$387$	−0.419779	+	1.56664i	−0.0213385	+	0.0796365i
$388$		0			0
$389$	−8.39208	−	31.3197i	−0.425495	−	1.58797i	−0.762839	−	0.646588i	$-0.776195\pi$
$389$	−8.39208	−	31.3197i	−0.425495	−	1.58797i	0.337344	−	0.941382i	$-0.390472\pi$
$390$		0			0
$391$	−19.4356	−	33.6635i	−0.982901	−	1.70244i
$392$		0			0
$393$	−8.96318	+	8.96318i	−0.452132	+	0.452132i
$394$		0			0
$395$	−4.48861	−	7.77449i	−0.225846	−	0.391177i
$396$		0			0
$397$		−	18.9882i		−	0.952990i	−0.879177	−	0.476495i	$-0.841907\pi$
$397$		−	18.9882i		−	0.952990i	0.879177	−	0.476495i	$-0.158093\pi$
$398$		0			0
$399$	−5.52036	+	5.52036i	−0.276364	+	0.276364i
$400$		0			0
$401$	0.651005	+	0.651005i	0.0325096	+	0.0325096i	0.723175	−	0.690665i	$-0.242682\pi$
$401$	0.651005	+	0.651005i	0.0325096	+	0.0325096i	−0.690665	+	0.723175i	$0.742682\pi$
$402$		0			0
$403$	−55.9082	−	32.2786i	−2.78499	−	1.60791i
$404$		0			0
$405$	1.94916	+	0.522275i	0.0968543	+	0.0259520i
$406$		0			0
$407$	9.19435	−	4.57867i	0.455747	−	0.226956i
$408$		0			0
$409$	1.57949	−	5.89475i	0.0781010	−	0.291477i	−0.915818	−	0.401595i	$-0.868456\pi$
$409$	1.57949	−	5.89475i	0.0781010	−	0.291477i	0.993919	+	0.110118i	$0.0351228\pi$
$410$		0			0
$411$	1.95756	−	3.39060i	0.0965596	−	0.167246i
$412$		0			0
$413$	19.5360	−	19.5360i	0.961306	−	0.961306i
$414$		0			0
$415$	−3.35528	−	3.35528i	−0.164704	−	0.164704i
$416$		0			0
$417$	6.05065			0.296302
$418$		0			0
$419$	−28.1119	+	16.2304i	−1.37336	+	0.792909i	−0.991349	−	0.131250i	$-0.958101\pi$
$419$	−28.1119	+	16.2304i	−1.37336	+	0.792909i	−0.382009	+	0.924159i	$0.624768\pi$
$420$		0			0
$421$	−0.367099	−	0.367099i	−0.0178913	−	0.0178913i	0.698105	−	0.715996i	$-0.254027\pi$
$421$	−0.367099	−	0.367099i	−0.0178913	−	0.0178913i	−0.715996	+	0.698105i	$0.754027\pi$
$422$		0			0
$423$	21.0983	−	12.1811i	1.02583	−	0.592266i
$424$		0			0
$425$	−20.4936	+	5.49124i	−0.994085	+	0.266364i
$426$		0			0
$427$	5.77683	+	1.54790i	0.279560	+	0.0749080i
$428$		0			0
$429$	8.60812	+	2.30654i	0.415604	+	0.111361i
$430$		0			0
$431$	−1.11449	−	4.15932i	−0.0536829	−	0.200347i	0.933876	−	0.357597i	$-0.116404\pi$
$431$	−1.11449	−	4.15932i	−0.0536829	−	0.200347i	−0.987559	+	0.157250i	$0.949737\pi$
$432$		0			0
$433$	31.0318			1.49129			0.745647	−	0.666341i	$-0.232141\pi$
$433$	31.0318			1.49129			0.745647	+	0.666341i	$0.232141\pi$
$434$		0			0
$435$	2.74321	+	4.75138i	0.131527	+	0.227811i
$436$		0			0
$437$	−28.7200	−	16.5815i	−1.37387	−	0.793202i
$438$		0			0
$439$	7.71636	+	28.7978i	0.368282	+	1.37445i	0.862917	+	0.505345i	$0.168635\pi$
$439$	7.71636	+	28.7978i	0.368282	+	1.37445i	−0.494636	+	0.869100i	$0.664699\pi$
$440$		0			0
$441$	2.43173	−	4.21188i	0.115797	−	0.200566i
$442$		0			0
$443$	36.4750			1.73298			0.866491	−	0.499193i	$-0.166370\pi$
$443$	36.4750			1.73298			0.866491	+	0.499193i	$0.166370\pi$
$444$		0			0
$445$	−2.96790			−0.140692
$446$		0			0
$447$	−5.78620	+	10.0220i	−0.273678	+	0.474024i
$448$		0			0
$449$	−1.92423	−	7.18134i	−0.0908103	−	0.338908i	0.905541	−	0.424259i	$-0.139466\pi$
$449$	−1.92423	−	7.18134i	−0.0908103	−	0.338908i	−0.996351	+	0.0853509i	$0.972799\pi$
$450$		0			0
$451$	7.84607	+	4.52993i	0.369457	+	0.213306i
$452$		0			0
$453$	4.38692	+	7.59837i	0.206116	+	0.357003i
$454$		0			0
$455$	−9.85935			−0.462213
$456$		0			0
$457$	7.48095	+	27.9193i	0.349944	+	1.30601i	0.886729	+	0.462290i	$0.152972\pi$
$457$	7.48095	+	27.9193i	0.349944	+	1.30601i	−0.536785	+	0.843719i	$0.680361\pi$
$458$		0			0
$459$	21.0719	+	5.64620i	0.983552	+	0.263542i
$460$		0			0
$461$	2.89938	+	0.776887i	0.135038	+	0.0361832i	0.325705	−	0.945472i	$-0.394398\pi$
$461$	2.89938	+	0.776887i	0.135038	+	0.0361832i	−0.190667	+	0.981655i	$0.561065\pi$
$462$		0			0
$463$	19.7886	−	5.30234i	0.919654	−	0.246420i	0.232216	−	0.972664i	$-0.425402\pi$
$463$	19.7886	−	5.30234i	0.919654	−	0.246420i	0.687437	+	0.726244i	$0.258736\pi$
$464$		0			0
$465$	−6.00086	+	3.46460i	−0.278283	+	0.160667i
$466$		0			0
$467$	6.35148	+	6.35148i	0.293912	+	0.293912i	0.838623	−	0.544712i	$-0.183361\pi$
$467$	6.35148	+	6.35148i	0.293912	+	0.293912i	−0.544712	+	0.838623i	$0.683361\pi$
$468$		0			0
$469$	−1.95996	+	1.13159i	−0.0905027	+	0.0522517i
$470$		0			0
$471$	9.99043			0.460335
$472$		0			0
$473$	−0.865604	−	0.865604i	−0.0398005	−	0.0398005i
$474$		0			0
$475$	−12.7993	+	12.7993i	−0.587271	+	0.587271i
$476$		0			0
$477$	−1.78917	+	3.09894i	−0.0819206	+	0.141891i
$478$		0			0
$479$	−3.32574	+	12.4118i	−0.151957	+	0.567111i	0.847390	+	0.530971i	$0.178173\pi$
$479$	−3.32574	+	12.4118i	−0.151957	+	0.567111i	−0.999347	+	0.0361397i	$0.988494\pi$
$480$		0			0
$481$	−24.3434	−	27.5416i	−1.10996	−	1.25579i
$482$		0			0
$483$	15.1041	+	4.04713i	0.687260	+	0.184151i
$484$		0			0
$485$	−9.20077	−	5.31207i	−0.417786	−	0.241209i
$486$		0			0
$487$	17.3539	+	17.3539i	0.786382	+	0.786382i	0.980899	−	0.194517i	$-0.0623140\pi$
$487$	17.3539	+	17.3539i	0.786382	+	0.786382i	−0.194517	+	0.980899i	$0.562314\pi$
$488$		0			0
$489$	8.79123	−	8.79123i	0.397553	−	0.397553i
$490$		0			0
$491$		−	33.3114i		−	1.50332i	−0.659549	−	0.751661i	$-0.729253\pi$
$491$		−	33.3114i		−	1.50332i	0.659549	−	0.751661i	$-0.270747\pi$
$492$		0			0
$493$	−20.1715	−	34.9381i	−0.908481	−	1.57353i
$494$		0			0
$495$	−1.98392	+	1.98392i	−0.0891708	+	0.0891708i
$496$		0			0
$497$	−2.56653	−	4.44536i	−0.115125	−	0.199402i
$498$		0			0
$499$	−0.237832	−	0.887600i	−0.0106468	−	0.0397344i	0.960398	−	0.278632i	$-0.0898808\pi$
$499$	−0.237832	−	0.887600i	−0.0106468	−	0.0397344i	−0.971045	+	0.238897i	$0.923214\pi$
$500$		0			0
$501$	−3.97486	+	14.8344i	−0.177583	+	0.662750i
$502$		0			0
$503$	−3.08613	+	11.5176i	−0.137604	+	0.513544i	0.862370	+	0.506279i	$0.168979\pi$
$503$	−3.08613	+	11.5176i	−0.137604	+	0.513544i	−0.999974	+	0.00726514i	$0.997687\pi$
$504$		0			0
$505$	7.06732	−	1.89368i	0.314492	−	0.0842678i
$506$		0			0
$507$		−	20.5389i		−	0.912164i
$508$		0			0
$509$	0.720332	−	0.415884i	0.0319281	−	0.0184337i	−0.483951	−	0.875095i	$-0.660799\pi$
$509$	0.720332	−	0.415884i	0.0319281	−	0.0184337i	0.515879	+	0.856661i	$0.327465\pi$
$510$		0			0
$511$	6.80327	−	11.7836i	0.300959	−	0.521276i
$512$		0			0
$513$	17.9775	−	4.81706i	0.793727	−	0.212678i
$514$		0			0
$515$	−6.82254	−	3.93900i	−0.300637	−	0.173573i
$516$		0			0
$517$			18.3877i			0.808689i
$518$		0			0
$519$		−	3.09635i		−	0.135915i
$520$		0			0
$521$	8.21862	+	4.74502i	0.360064	+	0.207883i	0.669109	−	0.743164i	$-0.266676\pi$
$521$	8.21862	+	4.74502i	0.360064	+	0.207883i	−0.309045	+	0.951048i	$0.600009\pi$
$522$		0			0
$523$	28.5757	−	7.65684i	1.24953	−	0.334810i	0.427375	−	0.904075i	$-0.359439\pi$
$523$	28.5757	−	7.65684i	1.24953	−	0.334810i	0.822155	+	0.569264i	$0.192772\pi$
$524$		0			0
$525$	4.26743	−	7.39141i	0.186246	−	0.322588i
$526$		0			0
$527$	44.1258	−	25.4761i	1.92215	−	1.10976i
$528$		0			0
$529$			43.4237i			1.88799i
$530$		0			0
$531$	−27.1776	+	7.28221i	−1.17941	+	0.316021i
$532$		0			0
$533$	8.39154	−	31.3176i	0.363478	−	1.35652i
$534$		0			0
$535$	1.46776	−	5.47774i	0.0634567	−	0.236824i
$536$		0			0
$537$	3.10500	+	11.5880i	0.133991	+	0.500061i
$538$		0			0
$539$	1.83538	+	3.17896i	0.0790552	+	0.136928i
$540$		0			0
$541$	−18.7379	+	18.7379i	−0.805605	+	0.805605i	−0.983965	−	0.178361i	$-0.942921\pi$
$541$	−18.7379	+	18.7379i	−0.805605	+	0.805605i	0.178361	+	0.983965i	$0.442921\pi$
$542$		0			0
$543$	−8.80873	−	15.2572i	−0.378019	−	0.654747i
$544$		0			0
$545$			0.684776i			0.0293326i
$546$		0			0
$547$	12.4764	−	12.4764i	0.533453	−	0.533453i	−0.388145	−	0.921598i	$-0.626884\pi$
$547$	12.4764	−	12.4764i	0.533453	−	0.533453i	0.921598	+	0.388145i	$0.126884\pi$
$548$		0			0
$549$	−4.30672	−	4.30672i	−0.183806	−	0.183806i
$550$		0			0
$551$	−29.8075	−	17.2094i	−1.26984	−	0.733144i
$552$		0			0
$553$	−25.6500	−	6.87290i	−1.09075	−	0.292266i
$554$		0			0
$555$	−3.86654	+	0.784740i	−0.164126	+	0.0333104i
$556$		0			0
$557$	8.21821	−	30.6708i	0.348217	−	1.29956i	−0.540592	−	0.841285i	$-0.681800\pi$
$557$	8.21821	−	30.6708i	0.348217	−	1.29956i	0.888809	−	0.458278i	$-0.151533\pi$
$558$		0			0
$559$	−2.19042	+	3.79392i	−0.0926449	+	0.160466i
$560$		0			0
$561$	−4.97355	+	4.97355i	−0.209984	+	0.209984i
$562$		0			0
$563$	14.8876	+	14.8876i	0.627440	+	0.627440i	0.947423	−	0.319984i	$-0.103677\pi$
$563$	14.8876	+	14.8876i	0.627440	+	0.627440i	−0.319984	+	0.947423i	$0.603677\pi$
$564$		0			0
$565$	−14.3002			−0.601612
$566$		0			0
$567$	5.16935	−	2.98453i	0.217092	−	0.125338i
$568$		0			0
$569$	7.98876	+	7.98876i	0.334906	+	0.334906i	0.854446	−	0.519540i	$-0.173897\pi$
$569$	7.98876	+	7.98876i	0.334906	+	0.334906i	−0.519540	+	0.854446i	$0.673897\pi$
$570$		0			0
$571$	18.6332	−	10.7579i	0.779777	−	0.450204i	−0.0565743	−	0.998398i	$-0.518018\pi$
$571$	18.6332	−	10.7579i	0.779777	−	0.450204i	0.836351	+	0.548194i	$0.184684\pi$
$572$		0			0
$573$	−14.2129	+	3.80833i	−0.593751	+	0.159095i
$574$		0			0
$575$	35.0197	+	9.38350i	1.46042	+	0.391319i
$576$		0			0
$577$	15.0396	+	4.02986i	0.626109	+	0.167765i	0.557903	−	0.829906i	$-0.311606\pi$
$577$	15.0396	+	4.02986i	0.626109	+	0.167765i	0.0682054	+	0.997671i	$0.478273\pi$
$578$		0			0
$579$	−4.63561	−	17.3003i	−0.192649	−	0.718977i
$580$		0			0
$581$	−14.0361			−0.582315
$582$		0			0
$583$	−1.35040	−	2.33896i	−0.0559278	−	0.0968698i
$584$		0			0
$585$	8.69549	+	5.02035i	0.359514	+	0.207566i
$586$		0			0
$587$	−11.4597	−	42.7680i	−0.472991	−	1.76523i	−0.628933	−	0.777459i	$-0.716508\pi$
$587$	−11.4597	−	42.7680i	−0.472991	−	1.76523i	0.155942	−	0.987766i	$-0.450159\pi$
$588$		0			0
$589$	21.7349	−	37.6460i	0.895573	−	1.55118i
$590$		0			0
$591$	0.324918			0.0133653
$592$		0			0
$593$	−2.06956			−0.0849867			−0.0424934	−	0.999097i	$-0.513530\pi$
$593$	−2.06956			−0.0849867			−0.0424934	+	0.999097i	$0.513530\pi$
$594$		0			0
$595$	3.89077	−	6.73901i	0.159506	−	0.276273i
$596$		0			0
$597$	−3.66314	−	13.6710i	−0.149922	−	0.559518i
$598$		0			0
$599$	−14.2598	−	8.23291i	−0.582641	−	0.336388i	0.179541	−	0.983750i	$-0.442539\pi$
$599$	−14.2598	−	8.23291i	−0.582641	−	0.336388i	−0.762182	+	0.647363i	$0.775872\pi$
$600$		0			0
$601$	4.55713	+	7.89318i	0.185889	+	0.321969i	0.943876	−	0.330301i	$-0.107150\pi$
$601$	4.55713	+	7.89318i	0.185889	+	0.321969i	−0.757987	+	0.652270i	$0.773817\pi$
$602$		0			0
$603$	2.30480			0.0938586
$604$		0			0
$605$	1.56632	+	5.84557i	0.0636798	+	0.237656i
$606$		0			0
$607$	7.35962	+	1.97200i	0.298718	+	0.0800412i	0.405065	−	0.914288i	$-0.367249\pi$
$607$	7.35962	+	1.97200i	0.298718	+	0.0800412i	−0.106347	+	0.994329i	$0.533916\pi$
$608$		0			0
$609$	15.6760	+	4.20037i	0.635224	+	0.170208i
$610$		0			0
$611$	63.5615	−	17.0313i	2.57142	−	0.689011i
$612$		0			0
$613$	4.01775	−	2.31965i	0.162275	−	0.0936897i	−0.416663	−	0.909061i	$-0.636800\pi$
$613$	4.01775	−	2.31965i	0.162275	−	0.0936897i	0.578938	+	0.815371i	$0.303467\pi$
$614$		0			0
$615$	−2.46075	−	2.46075i	−0.0992271	−	0.0992271i
$616$		0			0
$617$	−18.0550	+	10.4241i	−0.726866	+	0.419656i	−0.817275	−	0.576248i	$-0.804516\pi$
$617$	−18.0550	+	10.4241i	−0.726866	+	0.419656i	0.0904083	+	0.995905i	$0.471183\pi$
$618$		0			0
$619$	−22.5640			−0.906922			−0.453461	−	0.891276i	$-0.649811\pi$
$619$	−22.5640			−0.906922			−0.453461	+	0.891276i	$0.649811\pi$
$620$		0			0
$621$	−26.3596	−	26.3596i	−1.05778	−	1.05778i
$622$		0			0
$623$	−6.20779	+	6.20779i	−0.248710	+	0.248710i
$624$		0			0
$625$	8.51538	−	14.7491i	0.340615	−	0.589963i
$626$		0			0
$627$	−1.55312	+	5.79631i	−0.0620255	+	0.231482i
$628$		0			0
$629$	28.4317	−	5.77040i	1.13365	−	0.230081i
$630$		0			0
$631$	13.9238	+	3.73087i	0.554297	+	0.148524i	0.525085	−	0.851050i	$-0.324033\pi$
$631$	13.9238	+	3.73087i	0.554297	+	0.148524i	0.0292122	+	0.999573i	$0.490700\pi$
$632$		0			0
$633$	−20.2681	−	11.7018i	−0.805585	−	0.465105i
$634$		0			0
$635$	5.57253	+	5.57253i	0.221139	+	0.221139i
$636$		0			0
$637$	9.28889	−	9.28889i	0.368039	−	0.368039i
$638$		0			0
$639$			5.22747i			0.206796i
$640$		0			0
$641$	14.8083	+	25.6488i	0.584893	+	1.01306i	0.994889	+	0.100977i	$0.0321969\pi$
$641$	14.8083	+	25.6488i	0.584893	+	1.01306i	−0.409995	+	0.912088i	$0.634470\pi$
$642$		0			0
$643$	−16.2246	+	16.2246i	−0.639837	+	0.639837i	−0.950515	−	0.310678i	$-0.899444\pi$
$643$	−16.2246	+	16.2246i	−0.639837	+	0.639837i	0.310678	+	0.950515i	$0.399444\pi$
$644$		0			0
$645$	0.235107	+	0.407217i	0.00925732	+	0.0160341i
$646$		0			0
$647$	−9.24061	−	34.4864i	−0.363286	−	1.35580i	−0.869730	−	0.493528i	$-0.835707\pi$
$647$	−9.24061	−	34.4864i	−0.363286	−	1.35580i	0.506444	−	0.862273i	$-0.330960\pi$
$648$		0			0
$649$	5.49634	−	20.5126i	0.215750	−	0.805190i
$650$		0			0
$651$	−5.30495	+	19.7983i	−0.207917	+	0.775958i
$652$		0			0
$653$	1.14887	−	0.307838i	0.0449586	−	0.0120466i	−0.236270	−	0.971688i	$-0.575925\pi$
$653$	1.14887	−	0.307838i	0.0449586	−	0.0120466i	0.281228	+	0.959641i	$0.409258\pi$
$654$		0			0
$655$		−	10.7792i		−	0.421178i
$656$		0			0
$657$	−12.0003	+	6.92840i	−0.468178	+	0.270303i
$658$		0			0
$659$	5.47329	−	9.48002i	0.213209	−	0.369289i	−0.739508	−	0.673148i	$-0.764942\pi$
$659$	5.47329	−	9.48002i	0.213209	−	0.369289i	0.952717	+	0.303859i	$0.0982751\pi$
$660$		0			0
$661$	−9.30592	+	2.49351i	−0.361958	+	0.0969865i	−0.435215	−	0.900327i	$-0.643328\pi$
$661$	−9.30592	+	2.49351i	−0.361958	+	0.0969865i	0.0732563	+	0.997313i	$0.476661\pi$
$662$		0			0
$663$	21.7990	+	12.5856i	0.846602	+	0.488786i
$664$		0			0
$665$		−	6.63883i		−	0.257443i
$666$		0			0
$667$			68.9388i			2.66932i
$668$		0			0
$669$	−5.46574	−	3.15565i	−0.211318	−	0.122004i
$670$		0			0
$671$	4.44033	−	1.18978i	0.171417	−	0.0459310i
$672$		0			0
$673$	12.4828	−	21.6209i	0.481178	−	0.833424i	−0.518589	−	0.855024i	$-0.673543\pi$
$673$	12.4828	−	21.6209i	0.481178	−	0.833424i	0.999767	+	0.0215994i	$0.00687584\pi$
$674$		0			0
$675$	−17.6210	+	10.1735i	−0.678233	+	0.391578i
$676$		0			0
$677$			35.6331i			1.36949i	0.728782	+	0.684746i	$0.240087\pi$
$677$			35.6331i			1.36949i	−0.728782	+	0.684746i	$0.759913\pi$
$678$		0			0
$679$	−30.3557	+	8.13378i	−1.16494	+	0.312146i
$680$		0			0
$681$	0.491721	−	1.83513i	0.0188428	−	0.0703223i
$682$		0			0
$683$	0.0806302	−	0.300916i	0.00308523	−	0.0115142i	−0.964366	−	0.264572i	$-0.914769\pi$
$683$	0.0806302	−	0.300916i	0.00308523	−	0.0115142i	0.967451	+	0.253057i	$0.0814361\pi$
$684$		0			0
$685$	0.861691	+	3.21587i	0.0329235	+	0.122872i
$686$		0			0
$687$	6.13240	+	10.6216i	0.233966	+	0.405240i
$688$		0			0
$689$	−6.83440	+	6.83440i	−0.260370	+	0.260370i
$690$		0			0
$691$	−5.83287	−	10.1028i	−0.221893	−	0.384330i	0.733490	−	0.679700i	$-0.237890\pi$
$691$	−5.83287	−	10.1028i	−0.221893	−	0.384330i	−0.955383	+	0.295371i	$0.904557\pi$
$692$		0			0
$693$			8.29932i			0.315265i
$694$		0			0
$695$	−3.63828	+	3.63828i	−0.138008	+	0.138008i
$696$		0			0
$697$	18.0945	+	18.0945i	0.685380	+	0.685380i
$698$		0			0
$699$	−9.20120	−	5.31232i	−0.348022	−	0.200930i
$700$		0			0
$701$	46.8050	+	12.5414i	1.76780	+	0.473681i	0.988274	−	0.152689i	$-0.0487932\pi$
$701$	46.8050	+	12.5414i	1.76780	+	0.473681i	0.779526	+	0.626370i	$0.215460\pi$
$702$		0			0
$703$	18.5453	−	16.3917i	0.699448	−	0.618226i
$704$		0			0
$705$	1.82803	−	6.82232i	0.0688478	−	0.256943i
$706$		0			0
$707$	10.8214	−	18.7432i	0.406981	−	0.704911i
$708$		0			0
$709$	1.15646	−	1.15646i	0.0434318	−	0.0434318i	−0.685057	−	0.728489i	$-0.740223\pi$
$709$	1.15646	−	1.15646i	0.0434318	−	0.0434318i	0.728489	+	0.685057i	$0.240223\pi$
$710$		0			0
$711$	19.1225	+	19.1225i	0.717149	+	0.717149i
$712$		0			0
$713$	−87.0677			−3.26071
$714$		0			0
$715$	−6.56303	+	3.78917i	−0.245443	+	0.141707i
$716$		0			0
$717$	−6.77681	−	6.77681i	−0.253085	−	0.253085i
$718$		0			0
$719$	−20.7967	+	12.0070i	−0.775587	+	0.447785i	−0.834864	−	0.550456i	$-0.814454\pi$
$719$	−20.7967	+	12.0070i	−0.775587	+	0.447785i	0.0592771	+	0.998242i	$0.481120\pi$
$720$		0			0
$721$	−22.5093	+	6.03135i	−0.838290	+	0.224619i
$722$		0			0
$723$	6.09585	+	1.63338i	0.226707	+	0.0607460i
$724$		0			0
$725$	36.3457	+	9.73881i	1.34985	+	0.361690i
$726$		0			0
$727$	−13.2315	−	49.3805i	−0.490728	−	1.83142i	−0.552749	−	0.833348i	$-0.686421\pi$
$727$	−13.2315	−	49.3805i	−0.490728	−	1.83142i	0.0620202	−	0.998075i	$-0.480246\pi$
$728$		0			0
$729$	5.90520			0.218711
$730$		0			0
$731$	−1.72880	−	2.99437i	−0.0639420	−	0.110751i
$732$		0			0
$733$	−6.27069	−	3.62039i	−0.231613	−	0.133722i	0.379703	−	0.925109i	$-0.376026\pi$
$733$	−6.27069	−	3.62039i	−0.231613	−	0.133722i	−0.611316	+	0.791386i	$0.709360\pi$
$734$		0			0
$735$	−0.364932	−	1.36195i	−0.0134607	−	0.0502361i
$736$		0			0
$737$	−0.869787	+	1.50651i	−0.0320390	+	0.0554932i
$738$		0			0
$739$	21.2591			0.782028			0.391014	−	0.920385i	$-0.372124\pi$
$739$	21.2591			0.782028			0.391014	+	0.920385i	$0.372124\pi$
$740$		0			0
$741$	21.4749			0.788901
$742$		0			0
$743$	−2.34947	+	4.06939i	−0.0861936	+	0.149292i	−0.905899	−	0.423493i	$-0.860804\pi$
$743$	−2.34947	+	4.06939i	−0.0861936	+	0.149292i	0.819706	+	0.572785i	$0.194137\pi$
$744$		0			0
$745$	−2.54700	−	9.50553i	−0.0933149	−	0.348256i
$746$		0			0
$747$	12.3792	+	7.14713i	0.452931	+	0.261500i
$748$		0			0
$749$	−8.38746	−	14.5275i	−0.306471	−	0.530823i
$750$		0			0
$751$	4.08878			0.149202			0.0746009	−	0.997213i	$-0.476232\pi$
$751$	4.08878			0.149202			0.0746009	+	0.997213i	$0.476232\pi$
$752$		0			0
$753$	−0.367358	−	1.37100i	−0.0133873	−	0.0499620i
$754$		0			0
$755$	−7.20681	−	1.93106i	−0.262283	−	0.0702784i
$756$		0			0
$757$	−6.95516	−	1.86363i	−0.252789	−	0.0677347i	0.130199	−	0.991488i	$-0.458438\pi$
$757$	−6.95516	−	1.86363i	−0.252789	−	0.0677347i	−0.382988	+	0.923753i	$0.625105\pi$
$758$		0			0
$759$	11.6097	−	3.11080i	0.421405	−	0.112915i
$760$		0			0
$761$	9.70867	−	5.60530i	0.351939	−	0.203192i	−0.313600	−	0.949555i	$-0.601535\pi$
$761$	9.70867	−	5.60530i	0.351939	−	0.203192i	0.665539	+	0.746363i	$0.268202\pi$
$762$		0			0
$763$	1.43231	+	1.43231i	0.0518530	+	0.0518530i
$764$		0			0
$765$	−6.86296	+	3.96233i	−0.248131	+	0.143258i
$766$		0			0
$767$	−75.9977			−2.74412
$768$		0			0
$769$	8.25592	+	8.25592i	0.297716	+	0.297716i	0.840119	−	0.542403i	$-0.182485\pi$
$769$	8.25592	+	8.25592i	0.297716	+	0.297716i	−0.542403	+	0.840119i	$0.682485\pi$
$770$		0			0
$771$	−9.33589	+	9.33589i	−0.336224	+	0.336224i
$772$		0			0
$773$	−23.5967	+	40.8706i	−0.848713	+	1.47001i	0.0336448	+	0.999434i	$0.489289\pi$
$773$	−23.5967	+	40.8706i	−0.848713	+	1.47001i	−0.882357	+	0.470580i	$0.844045\pi$
$774$		0			0
$775$	−12.2998	+	45.9036i	−0.441823	+	1.64891i
$776$		0			0
$777$	−6.44603	+	9.72882i	−0.231250	+	0.349019i
$778$		0			0
$779$	21.0879	+	5.65048i	0.755551	+	0.202449i
$780$		0			0
$781$	−3.41690	−	1.97275i	−0.122266	−	0.0705905i
$782$		0			0
$783$	−27.3577	−	27.3577i	−0.977686	−	0.977686i
$784$		0			0
$785$	−6.00729	+	6.00729i	−0.214409	+	0.214409i
$786$		0			0
$787$		−	13.5085i		−	0.481526i	−0.970584	−	0.240763i	$-0.922602\pi$
$787$		−	13.5085i		−	0.481526i	0.970584	−	0.240763i	$-0.0773976\pi$
$788$		0			0
$789$	4.25562	+	7.37095i	0.151504	+	0.262413i
$790$		0			0
$791$	−29.9108	+	29.9108i	−1.06351	+	1.06351i
$792$		0			0
$793$	−8.22555	−	14.2471i	−0.292098	−	0.505928i
$794$		0			0
$795$	0.268503	+	1.00207i	0.00952283	+	0.0355397i
$796$		0			0
$797$	5.88509	−	21.9635i	0.208461	−	0.777986i	−0.779906	−	0.625897i	$-0.784733\pi$
$797$	5.88509	−	21.9635i	0.208461	−	0.777986i	0.988367	−	0.152089i	$-0.0486001\pi$
$798$		0			0
$799$	−13.4420	+	50.1663i	−0.475544	+	1.77475i
$800$		0			0
$801$	8.63597	−	2.31400i	0.305137	−	0.0817612i
$802$		0			0
$803$		−	10.4586i		−	0.369076i
$804$		0			0
$805$	−11.5157	+	6.64860i	−0.405875	+	0.234332i
$806$		0			0
$807$	−7.89417	+	13.6731i	−0.277888	+	0.481316i
$808$		0			0
$809$	1.03240	−	0.276630i	0.0362972	−	0.00972581i	−0.240625	−	0.970618i	$-0.577352\pi$
$809$	1.03240	−	0.276630i	0.0362972	−	0.00972581i	0.276922	+	0.960892i	$0.410686\pi$
$810$		0			0
$811$	42.6563	+	24.6276i	1.49787	+	0.864793i	0.999997	−	0.00245912i	$-0.000782762\pi$
$811$	42.6563	+	24.6276i	1.49787	+	0.864793i	0.497869	+	0.867252i	$0.334116\pi$
$812$		0			0
$813$		−	0.947468i		−	0.0332291i
$814$		0			0
$815$			10.5724i			0.370335i
$816$		0			0
$817$	−2.55465	−	1.47493i	−0.0893760	−	0.0516012i
$818$		0			0
$819$	28.6886	−	7.68709i	1.00246	−	0.268609i
$820$		0			0
$821$	6.97661	−	12.0838i	0.243485	−	0.421729i	−0.718219	−	0.695817i	$-0.755043\pi$
$821$	6.97661	−	12.0838i	0.243485	−	0.421729i	0.961705	+	0.274088i	$0.0883759\pi$
$822$		0			0
$823$	21.4991	−	12.4125i	0.749413	−	0.432674i	−0.0760690	−	0.997103i	$-0.524237\pi$
$823$	21.4991	−	12.4125i	0.749413	−	0.432674i	0.825482	+	0.564429i	$0.190904\pi$
$824$		0			0
$825$		−	6.56028i		−	0.228400i
$826$		0			0
$827$	−54.0877	+	14.4928i	−1.88082	+	0.503963i	−0.881309	+	0.472541i	$0.843337\pi$
$827$	−54.0877	+	14.4928i	−1.88082	+	0.503963i	−0.999506	+	0.0314223i	$0.989996\pi$
$828$		0			0
$829$	−7.05602	+	26.3334i	−0.245066	+	0.914597i	0.728285	+	0.685274i	$0.240318\pi$
$829$	−7.05602	+	26.3334i	−0.245066	+	0.914597i	−0.973350	+	0.229323i	$0.926349\pi$
$830$		0			0
$831$	2.43923	−	9.10335i	0.0846161	−	0.315792i
$832$		0			0
$833$	2.68344	+	10.0147i	0.0929758	+	0.346990i
$834$		0			0
$835$	−6.52987	−	11.3101i	−0.225975	−	0.391401i
$836$		0			0
$837$	34.5520	−	34.5520i	1.19429	−	1.19429i
$838$		0			0
$839$	−0.965907	−	1.67300i	−0.0333468	−	0.0577584i	0.848870	−	0.528601i	$-0.177283\pi$
$839$	−0.965907	−	1.67300i	−0.0333468	−	0.0577584i	−0.882217	+	0.470843i	$0.843950\pi$
$840$		0			0
$841$			42.5491i			1.46721i
$842$		0			0
$843$	3.11477	−	3.11477i	0.107278	−	0.107278i
$844$		0			0
$845$	12.3501	+	12.3501i	0.424857	+	0.424857i
$846$		0			0
$847$	15.5030	+	8.95067i	0.532690	+	0.307549i
$848$		0			0
$849$	12.4361	+	3.33225i	0.426807	+	0.114363i
$850$		0			0
$851$	−47.0056	−	15.7527i	−1.61133	−	0.539997i
$852$		0			0
$853$	−2.89375	+	10.7996i	−0.0990802	+	0.369772i	−0.997606	−	0.0691475i	$-0.977972\pi$
$853$	−2.89375	+	10.7996i	−0.0990802	+	0.369772i	0.898526	+	0.438920i	$0.144639\pi$
$854$		0			0
$855$	−3.38047	+	5.85515i	−0.115610	+	0.200242i
$856$		0			0
$857$	18.2726	−	18.2726i	0.624181	−	0.624181i	−0.322417	−	0.946598i	$-0.604495\pi$
$857$	18.2726	−	18.2726i	0.624181	−	0.624181i	0.946598	+	0.322417i	$0.104495\pi$
$858$		0			0
$859$	−2.97354	−	2.97354i	−0.101456	−	0.101456i	0.654557	−	0.756013i	$-0.272855\pi$
$859$	−2.97354	−	2.97354i	−0.101456	−	0.101456i	−0.756013	+	0.654557i	$0.772855\pi$
$860$		0			0
$861$	−10.2940			−0.350819
$862$		0			0
$863$	7.70750	−	4.44993i	0.262366	−	0.151477i	−0.363047	−	0.931771i	$-0.618264\pi$
$863$	7.70750	−	4.44993i	0.262366	−	0.151477i	0.625414	+	0.780293i	$0.284930\pi$
$864$		0			0
$865$	1.86185	+	1.86185i	0.0633048	+	0.0633048i
$866$		0			0
$867$	−4.34709	+	2.50980i	−0.147635	+	0.0852372i
$868$		0			0
$869$	−19.7157	+	5.28282i	−0.668811	+	0.179207i
$870$		0			0
$871$	6.01326	+	1.61125i	0.203752	+	0.0545951i
$872$		0			0
$873$	30.9140	+	8.28339i	1.04628	+	0.280350i
$874$		0			0
$875$	3.98983	+	14.8903i	0.134881	+	0.503383i
$876$		0			0
$877$	19.6575			0.663788			0.331894	−	0.943317i	$-0.392312\pi$
$877$	19.6575			0.663788			0.331894	+	0.943317i	$0.392312\pi$
$878$		0			0
$879$	−5.81136	−	10.0656i	−0.196012	−	0.339503i
$880$		0			0
$881$	−14.5473	−	8.39887i	−0.490110	−	0.282965i	0.234510	−	0.972114i	$-0.424651\pi$
$881$	−14.5473	−	8.39887i	−0.490110	−	0.282965i	−0.724620	+	0.689148i	$0.757985\pi$
$882$		0			0
$883$	−1.74719	−	6.52059i	−0.0587975	−	0.219435i	0.930276	−	0.366862i	$-0.119568\pi$
$883$	−1.74719	−	6.52059i	−0.0587975	−	0.219435i	−0.989073	+	0.147426i	$0.952901\pi$
$884$		0			0
$885$	−4.07857	+	7.06430i	−0.137100	+	0.237464i
$886$		0			0
$887$	−25.5877			−0.859149			−0.429575	−	0.903031i	$-0.641337\pi$
$887$	−25.5877			−0.859149			−0.429575	+	0.903031i	$0.641337\pi$
$888$		0			0
$889$	23.3115			0.781842
$890$		0			0
$891$	2.29404	−	3.97339i	0.0768532	−	0.133114i
$892$		0			0
$893$	11.4681	+	42.7994i	0.383764	+	1.43223i
$894$		0			0
$895$	−8.83498	−	5.10088i	−0.295321	−	0.170504i
$896$		0			0
$897$	−21.5065	−	37.2504i	−0.718081	−	1.24375i
$898$		0			0
$899$	−90.3645			−3.01382
$900$		0			0
$901$	−1.97437	−	7.36846i	−0.0657759	−	0.245479i
$902$		0			0
$903$	1.34351	+	0.359993i	0.0447093	+	0.0119798i
$904$		0			0
$905$	14.4709	+	3.87747i	0.481030	+	0.128891i
$906$		0			0
$907$	−37.9004	+	10.1554i	−1.25846	+	0.337204i	−0.825599	−	0.564257i	$-0.809163\pi$
$907$	−37.9004	+	10.1554i	−1.25846	+	0.337204i	−0.432862	+	0.901460i	$0.642496\pi$
$908$		0			0
$909$	−19.0880	+	11.0204i	−0.633108	+	0.365525i
$910$		0			0
$911$	10.5316	+	10.5316i	0.348927	+	0.348927i	0.859710	−	0.510783i	$-0.170644\pi$
$911$	10.5316	+	10.5316i	0.348927	+	0.348927i	−0.510783	+	0.859710i	$0.670644\pi$
$912$		0			0
$913$	−9.34334	+	5.39438i	−0.309219	+	0.178528i
$914$		0			0
$915$	−1.76576			−0.0583743
$916$		0			0
$917$	−22.5462	−	22.5462i	−0.744541	−	0.744541i
$918$		0			0
$919$	−2.54674	+	2.54674i	−0.0840093	+	0.0840093i	−0.747863	−	0.663853i	$-0.768920\pi$
$919$	−2.54674	+	2.54674i	−0.0840093	+	0.0840093i	0.663853	+	0.747863i	$0.268920\pi$
$920$		0			0
$921$	5.86672	−	10.1615i	0.193315	−	0.334831i
$922$		0			0
$923$	−3.65445	+	13.6386i	−0.120288	+	0.448919i
$924$		0			0
$925$	−14.9455	+	22.5568i	−0.491404	+	0.741664i
$926$		0			0
$927$	22.9233	+	6.14228i	0.752900	+	0.201739i
$928$		0			0
$929$	45.6725	+	26.3690i	1.49846	+	0.865139i	0.999998	−	0.00177018i	$-0.000563465\pi$
$929$	45.6725	+	26.3690i	1.49846	+	0.865139i	0.498466	+	0.866909i	$0.333897\pi$
$930$		0			0
$931$	6.25471	+	6.25471i	0.204990	+	0.204990i
$932$		0			0
$933$	4.17476	−	4.17476i	0.136675	−	0.136675i
$934$		0			0
$935$		−	5.98124i		−	0.195607i
$936$		0			0
$937$	2.28361	+	3.95533i	0.0746023	+	0.129215i	0.900913	−	0.433999i	$-0.142898\pi$
$937$	2.28361	+	3.95533i	0.0746023	+	0.129215i	−0.826311	+	0.563214i	$0.809565\pi$
$938$		0			0
$939$	−7.77125	+	7.77125i	−0.253605	+	0.253605i
$940$		0			0
$941$	12.9917	+	22.5022i	0.423517	+	0.733552i	0.996281	−	0.0861680i	$-0.0274622\pi$
$941$	12.9917	+	22.5022i	0.423517	+	0.733552i	−0.572764	+	0.819720i	$0.694129\pi$
$942$		0			0
$943$	−11.3176	−	42.2378i	−0.368551	−	1.37545i
$944$		0			0
$945$	1.93147	−	7.20834i	0.0628307	−	0.234487i
$946$		0			0
$947$	−4.50351	+	16.8073i	−0.146344	+	0.546165i	0.853348	+	0.521343i	$0.174569\pi$
$947$	−4.50351	+	16.8073i	−0.146344	+	0.546165i	−0.999692	+	0.0248221i	$0.992098\pi$
$948$		0			0
$949$	−36.1527	+	9.68708i	−1.17357	+	0.314456i
$950$		0			0
$951$			18.1511i			0.588591i
$952$		0			0
$953$	6.95601	−	4.01605i	0.225327	−	0.130093i	−0.383087	−	0.923712i	$-0.625139\pi$
$953$	6.95601	−	4.01605i	0.225327	−	0.130093i	0.608415	+	0.793619i	$0.291806\pi$
$954$		0			0
$955$	6.25629	−	10.8362i	0.202449	−	0.350652i
$956$		0			0
$957$	12.0493	−	3.22859i	0.389498	−	0.104366i
$958$		0			0
$959$	8.52881	+	4.92411i	0.275410	+	0.159008i
$960$		0			0
$961$		−	83.1277i		−	2.68154i
$962$		0			0
$963$			17.0835i			0.550507i
$964$		0			0
$965$	13.1902	+	7.61534i	0.424606	+	0.245147i
$966$		0			0
$967$	32.3452	−	8.66688i	1.04015	−	0.278708i	0.301976	−	0.953316i	$-0.402354\pi$
$967$	32.3452	−	8.66688i	1.04015	−	0.278708i	0.738176	+	0.674608i	$0.235687\pi$
$968$		0			0
$969$	−8.47460	+	14.6784i	−0.272243	+	0.471539i
$970$		0			0
$971$	24.7113	−	14.2671i	0.793023	−	0.457852i	−0.0480029	−	0.998847i	$-0.515286\pi$
$971$	24.7113	−	14.2671i	0.793023	−	0.457852i	0.841026	+	0.540995i	$0.181952\pi$
$972$		0			0
$973$			15.2200i			0.487930i
$974$		0			0
$975$	−22.6772	+	6.07634i	−0.726252	+	0.194599i
$976$		0			0
$977$	−10.0612	+	37.5487i	−0.321885	+	1.20129i	0.595522	+	0.803339i	$0.296945\pi$
$977$	−10.0612	+	37.5487i	−0.321885	+	1.20129i	−0.917407	+	0.397951i	$0.869721\pi$
$978$		0			0
$979$	−1.74652	+	6.51810i	−0.0558190	+	0.208319i
$980$		0			0
$981$	−0.533904	−	1.99256i	−0.0170462	−	0.0636174i
$982$		0			0
$983$	−2.75962	−	4.77980i	−0.0880181	−	0.152452i	0.818655	−	0.574285i	$-0.194720\pi$
$983$	−2.75962	−	4.77980i	−0.0880181	−	0.152452i	−0.906673	+	0.421834i	$0.861387\pi$
$984$		0			0
$985$	−0.195374	+	0.195374i	−0.00622515	+	0.00622515i
$986$		0			0
$987$	−10.4463	−	18.0934i	−0.332508	−	0.575921i
$988$		0			0
$989$			5.90839i			0.187876i
$990$		0			0
$991$	−6.72488	+	6.72488i	−0.213623	+	0.213623i	−0.805805	−	0.592182i	$-0.798267\pi$
$991$	−6.72488	+	6.72488i	−0.213623	+	0.213623i	0.592182	+	0.805805i	$0.298267\pi$
$992$		0			0
$993$	−4.67463	−	4.67463i	−0.148345	−	0.148345i
$994$		0			0
$995$	10.4231	+	6.01779i	0.330435	+	0.190777i
$996$		0			0
$997$	20.0217	+	5.36480i	0.634094	+	0.169905i	0.561527	−	0.827459i	$-0.310214\pi$
$997$	20.0217	+	5.36480i	0.634094	+	0.169905i	0.0725669	+	0.997364i	$0.476881\pi$
$998$		0			0
$999$	24.9051	−	12.4024i	0.787962	−	0.392395i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	592.2.be.e.399.3	yes	20
4.3	odd	2		592.2.be.f.399.3	yes	20
37.23	odd	12		592.2.be.f.319.3	yes	20
148.23	even	12	inner	592.2.be.e.319.3	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
592.2.be.e.319.3	✓	20	148.23	even	12	inner
592.2.be.e.399.3	yes	20	1.1	even	1	trivial
592.2.be.f.319.3	yes	20	37.23	odd	12
592.2.be.f.399.3	yes	20	4.3	odd	2

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:	\( N \)	\(=\)	\( 592 = 2^{4} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	592.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.436676 + 0.756344i) q^{3} +(-0.192218 - 0.717368i) q^{5} +(-1.90253 - 1.09843i) q^{7} +(1.11863 + 1.93752i) q^{9} +O(q^{10})\)	\(q+(-0.436676 + 0.756344i) q^{3} +(-0.192218 - 0.717368i) q^{5} +(-1.90253 - 1.09843i) q^{7} +(1.11863 + 1.93752i) q^{9} -1.68860 q^{11} +(1.56403 + 5.83705i) q^{13} +(0.626514 + 0.167874i) q^{15} +(-4.60692 - 1.23442i) q^{17} +(-3.93040 + 1.05315i) q^{19} +(1.66158 - 0.959311i) q^{21} +(5.76297 + 5.76297i) q^{23} +(3.85246 - 2.22422i) q^{25} -4.57397 q^{27} +(5.98118 + 5.98118i) q^{29} +(-7.55406 + 7.55406i) q^{31} +(0.737369 - 1.27716i) q^{33} +(-0.422275 + 1.57595i) q^{35} +(-5.44496 + 2.71152i) q^{37} +(-5.09779 - 1.36595i) q^{39} +(-4.64651 - 2.68266i) q^{41} +(0.512617 + 0.512617i) q^{43} +(1.17490 - 1.17490i) q^{45} -10.8893i q^{47} +(-1.08692 - 1.88261i) q^{49} +(2.94538 - 2.94538i) q^{51} +(0.799717 + 1.38515i) q^{53} +(0.324579 + 1.21135i) q^{55} +(0.919768 - 3.43262i) q^{57} +(-3.25497 + 12.1477i) q^{59} +(-2.62960 + 0.704598i) q^{61} -4.91492i q^{63} +(3.88668 - 2.24397i) q^{65} +(0.515094 - 0.892169i) q^{67} +(-6.87534 + 1.84224i) q^{69} +(2.02351 + 1.16828i) q^{71} +6.19366i q^{73} +3.88505i q^{75} +(3.21260 + 1.85480i) q^{77} +(11.6758 - 3.12852i) q^{79} +(-1.35855 + 2.35307i) q^{81} +(5.53320 - 3.19459i) q^{83} +3.54213i q^{85} +(-7.13567 + 1.91200i) q^{87} +(1.03430 - 3.86007i) q^{89} +(3.43595 - 12.8231i) q^{91} +(-2.41480 - 9.01215i) q^{93} +(1.51099 + 2.61711i) q^{95} +(10.1153 - 10.1153i) q^{97} +(-1.88891 - 3.27169i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{3} - 4 q^{5} - 6 q^{7} - 16 q^{9}+O(q^{10}) \) 20 * q - 4 * q^3 - 4 * q^5 - 6 * q^7 - 16 * q^9	\( 20 q - 4 q^{3} - 4 q^{5} - 6 q^{7} - 16 q^{9} + 4 q^{11} + 4 q^{13} + 8 q^{15} - 4 q^{17} + 10 q^{19} - 18 q^{21} + 8 q^{23} + 42 q^{25} + 68 q^{27} - 8 q^{29} + 28 q^{31} - 20 q^{33} - 10 q^{35} - 24 q^{37} - 14 q^{39} - 6 q^{41} + 32 q^{43} + 8 q^{45} - 12 q^{49} - 58 q^{51} + 6 q^{53} + 26 q^{55} - 2 q^{57} - 56 q^{59} - 8 q^{61} + 6 q^{65} + 20 q^{67} + 26 q^{69} - 30 q^{71} + 60 q^{77} + 50 q^{79} - 22 q^{81} + 36 q^{83} - 32 q^{87} - 20 q^{89} - 50 q^{91} - 50 q^{93} - 72 q^{95} + 32 q^{97} - 14 q^{99}+O(q^{100}) \) 20 * q - 4 * q^3 - 4 * q^5 - 6 * q^7 - 16 * q^9 + 4 * q^11 + 4 * q^13 + 8 * q^15 - 4 * q^17 + 10 * q^19 - 18 * q^21 + 8 * q^23 + 42 * q^25 + 68 * q^27 - 8 * q^29 + 28 * q^31 - 20 * q^33 - 10 * q^35 - 24 * q^37 - 14 * q^39 - 6 * q^41 + 32 * q^43 + 8 * q^45 - 12 * q^49 - 58 * q^51 + 6 * q^53 + 26 * q^55 - 2 * q^57 - 56 * q^59 - 8 * q^61 + 6 * q^65 + 20 * q^67 + 26 * q^69 - 30 * q^71 + 60 * q^77 + 50 * q^79 - 22 * q^81 + 36 * q^83 - 32 * q^87 - 20 * q^89 - 50 * q^91 - 50 * q^93 - 72 * q^95 + 32 * q^97 - 14 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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