LMFDB - Embedded newform 208.2.i.e.113.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [208,2,Mod(81,208)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(208, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("208.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 208 = 2^{4} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	208.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.66088836204$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{17})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 5x^{2} + 4x + 16 $ x^4 - x^3 + 5x^2 + 4x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 104)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			113.2
Root			$1.28078 - 2.21837i$ of defining polynomial
Character	$\chi$	$=$	208.113
Dual form			208.2.i.e.81.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.28078 - 2.21837i) q^{3} -3.56155 q^{5} +(-1.28078 - 2.21837i) q^{7} +(-1.78078 - 3.08440i) q^{9} +O(q^{10})$	\(q+(1.28078 - 2.21837i) q^{3} -3.56155 q^{5} +(-1.28078 - 2.21837i) q^{7} +(-1.78078 - 3.08440i) q^{9} +(1.28078 - 2.21837i) q^{11} +(3.34233 - 1.35234i) q^{13} +(-4.56155 + 7.90084i) q^{15} +(2.50000 + 4.33013i) q^{17} +(-1.28078 - 2.21837i) q^{19} -6.56155 q^{21} +(-1.84233 + 3.19101i) q^{23} +7.68466 q^{25} -1.43845 q^{27} +(2.50000 - 4.33013i) q^{29} +8.00000 q^{31} +(-3.28078 - 5.68247i) q^{33} +(4.56155 + 7.90084i) q^{35} +(0.500000 - 0.866025i) q^{37} +(1.28078 - 9.14657i) q^{39} +(-4.62311 + 8.00745i) q^{41} +(-3.28078 - 5.68247i) q^{43} +(6.34233 + 10.9852i) q^{45} -4.00000 q^{47} +(0.219224 - 0.379706i) q^{49} +12.8078 q^{51} +4.43845 q^{53} +(-4.56155 + 7.90084i) q^{55} -6.56155 q^{57} +(-1.28078 - 2.21837i) q^{59} +(3.62311 + 6.27540i) q^{61} +(-4.56155 + 7.90084i) q^{63} +(-11.9039 + 4.81645i) q^{65} +(-4.71922 + 8.17394i) q^{67} +(4.71922 + 8.17394i) q^{69} +(3.84233 + 6.65511i) q^{71} -1.31534 q^{73} +(9.84233 - 17.0474i) q^{75} -6.56155 q^{77} +4.00000 q^{79} +(3.50000 - 6.06218i) q^{81} -2.24621 q^{83} +(-8.90388 - 15.4220i) q^{85} +(-6.40388 - 11.0918i) q^{87} +(4.84233 - 8.38716i) q^{89} +(-7.28078 - 5.68247i) q^{91} +(10.2462 - 17.7470i) q^{93} +(4.56155 + 7.90084i) q^{95} +(-1.40388 - 2.43160i) q^{97} -9.12311 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{3} - 6 q^{5} - q^{7} - 3 q^{9}+O(q^{10}) $ 4 * q + q^3 - 6 * q^5 - q^7 - 3 * q^9	$ 4 q + q^{3} - 6 q^{5} - q^{7} - 3 q^{9} + q^{11} + q^{13} - 10 q^{15} + 10 q^{17} - q^{19} - 18 q^{21} + 5 q^{23} + 6 q^{25} - 14 q^{27} + 10 q^{29} + 32 q^{31} - 9 q^{33} + 10 q^{35} + 2 q^{37} + q^{39} - 2 q^{41} - 9 q^{43} + 13 q^{45} - 16 q^{47} + 5 q^{49} + 10 q^{51} + 26 q^{53} - 10 q^{55} - 18 q^{57} - q^{59} - 2 q^{61} - 10 q^{63} - 27 q^{65} - 23 q^{67} + 23 q^{69} + 3 q^{71} - 30 q^{73} + 27 q^{75} - 18 q^{77} + 16 q^{79} + 14 q^{81} + 24 q^{83} - 15 q^{85} - 5 q^{87} + 7 q^{89} - 25 q^{91} + 8 q^{93} + 10 q^{95} + 15 q^{97} - 20 q^{99}+O(q^{100}) $ 4 * q + q^3 - 6 * q^5 - q^7 - 3 * q^9 + q^11 + q^13 - 10 * q^15 + 10 * q^17 - q^19 - 18 * q^21 + 5 * q^23 + 6 * q^25 - 14 * q^27 + 10 * q^29 + 32 * q^31 - 9 * q^33 + 10 * q^35 + 2 * q^37 + q^39 - 2 * q^41 - 9 * q^43 + 13 * q^45 - 16 * q^47 + 5 * q^49 + 10 * q^51 + 26 * q^53 - 10 * q^55 - 18 * q^57 - q^59 - 2 * q^61 - 10 * q^63 - 27 * q^65 - 23 * q^67 + 23 * q^69 + 3 * q^71 - 30 * q^73 + 27 * q^75 - 18 * q^77 + 16 * q^79 + 14 * q^81 + 24 * q^83 - 15 * q^85 - 5 * q^87 + 7 * q^89 - 25 * q^91 + 8 * q^93 + 10 * q^95 + 15 * q^97 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/208\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.28078	−	2.21837i	0.739457	−	1.28078i	−0.213284	−	0.976990i	$-0.568416\pi$
$3$	1.28078	−	2.21837i	0.739457	−	1.28078i	0.952740	−	0.303786i	$-0.0982508\pi$
$4$		0			0
$5$	−3.56155			−1.59277			−0.796387	−	0.604787i	$-0.793258\pi$
$5$	−3.56155			−1.59277			−0.796387	+	0.604787i	$0.793258\pi$
$6$		0			0
$7$	−1.28078	−	2.21837i	−0.484088	−	0.838465i	0.515745	−	0.856742i	$-0.327515\pi$
$7$	−1.28078	−	2.21837i	−0.484088	−	0.838465i	−0.999833	+	0.0182772i	$0.994182\pi$
$8$		0			0
$9$	−1.78078	−	3.08440i	−0.593592	−	1.02813i
$10$		0			0
$11$	1.28078	−	2.21837i	0.386169	−	0.668864i	−0.605762	−	0.795646i	$-0.707132\pi$
$11$	1.28078	−	2.21837i	0.386169	−	0.668864i	0.991931	+	0.126782i	$0.0404650\pi$
$12$		0			0
$13$	3.34233	−	1.35234i	0.926995	−	0.375073i
$13$	3.34233	−	1.35234i	0.926995	−	0.375073i
$14$		0			0
$15$	−4.56155	+	7.90084i	−1.17779	+	2.03999i
$16$		0			0
$17$	2.50000	+	4.33013i	0.606339	+	1.05021i	0.991838	+	0.127502i	$0.0406959\pi$
$17$	2.50000	+	4.33013i	0.606339	+	1.05021i	−0.385499	+	0.922708i	$0.625971\pi$
$18$		0			0
$19$	−1.28078	−	2.21837i	−0.293830	−	0.508929i	0.680882	−	0.732393i	$-0.261597\pi$
$19$	−1.28078	−	2.21837i	−0.293830	−	0.508929i	−0.974712	+	0.223464i	$0.928263\pi$
$20$		0			0
$21$	−6.56155			−1.43185
$22$		0			0
$23$	−1.84233	+	3.19101i	−0.384152	+	0.665371i	−0.991651	−	0.128949i	$-0.958840\pi$
$23$	−1.84233	+	3.19101i	−0.384152	+	0.665371i	0.607499	+	0.794320i	$0.292173\pi$
$24$		0			0
$25$	7.68466			1.53693
$26$		0			0
$27$	−1.43845			−0.276829
$28$		0			0
$29$	2.50000	−	4.33013i	0.464238	−	0.804084i	−0.534928	−	0.844897i	$-0.679661\pi$
$29$	2.50000	−	4.33013i	0.464238	−	0.804084i	0.999167	+	0.0408130i	$0.0129948\pi$
$30$		0			0
$31$	8.00000			1.43684			0.718421	−	0.695608i	$-0.244865\pi$
$31$	8.00000			1.43684			0.718421	+	0.695608i	$0.244865\pi$
$32$		0			0
$33$	−3.28078	−	5.68247i	−0.571110	−	0.989191i
$34$		0			0
$35$	4.56155	+	7.90084i	0.771043	+	1.33549i
$36$		0			0
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	0.904194	+	0.427121i	$0.140472\pi$
$38$		0			0
$39$	1.28078	−	9.14657i	0.205088	−	1.46462i
$40$		0			0
$41$	−4.62311	+	8.00745i	−0.722008	+	1.25055i	0.238186	+	0.971220i	$0.423447\pi$
$41$	−4.62311	+	8.00745i	−0.722008	+	1.25055i	−0.960194	+	0.279335i	$0.909886\pi$
$42$		0			0
$43$	−3.28078	−	5.68247i	−0.500314	−	0.866569i	−1.00000		0.000362281i	$-0.999885\pi$
$43$	−3.28078	−	5.68247i	−0.500314	−	0.866569i	0.499686	−	0.866206i	$-0.333449\pi$
$44$		0			0
$45$	6.34233	+	10.9852i	0.945459	+	1.63758i
$46$		0			0
$47$	−4.00000			−0.583460			−0.291730	−	0.956501i	$-0.594231\pi$
$47$	−4.00000			−0.583460			−0.291730	+	0.956501i	$0.594231\pi$
$48$		0			0
$49$	0.219224	−	0.379706i	0.0313177	−	0.0542438i
$50$		0			0
$51$	12.8078			1.79345
$52$		0			0
$53$	4.43845			0.609668			0.304834	−	0.952406i	$-0.401399\pi$
$53$	4.43845			0.609668			0.304834	+	0.952406i	$0.401399\pi$
$54$		0			0
$55$	−4.56155	+	7.90084i	−0.615080	+	1.06535i
$56$		0			0
$57$	−6.56155			−0.869099
$58$		0			0
$59$	−1.28078	−	2.21837i	−0.166743	−	0.288807i	0.770530	−	0.637404i	$-0.219992\pi$
$59$	−1.28078	−	2.21837i	−0.166743	−	0.288807i	−0.937273	+	0.348597i	$0.886658\pi$
$60$		0			0
$61$	3.62311	+	6.27540i	0.463891	+	0.803483i	0.999151	−	0.0412046i	$-0.0131195\pi$
$61$	3.62311	+	6.27540i	0.463891	+	0.803483i	−0.535260	+	0.844688i	$0.679786\pi$
$62$		0			0
$63$	−4.56155	+	7.90084i	−0.574702	+	0.995412i
$64$		0			0
$65$	−11.9039	+	4.81645i	−1.47649	+	0.597407i
$66$		0			0
$67$	−4.71922	+	8.17394i	−0.576545	+	0.998605i	0.419327	+	0.907835i	$0.362266\pi$
$67$	−4.71922	+	8.17394i	−0.576545	+	0.998605i	−0.995872	+	0.0907698i	$0.971067\pi$
$68$		0			0
$69$	4.71922	+	8.17394i	0.568128	+	0.984026i
$70$		0			0
$71$	3.84233	+	6.65511i	0.456001	+	0.789816i	0.998745	−	0.0500816i	$-0.0159482\pi$
$71$	3.84233	+	6.65511i	0.456001	+	0.789816i	−0.542745	+	0.839898i	$0.682615\pi$
$72$		0			0
$73$	−1.31534			−0.153949			−0.0769745	−	0.997033i	$-0.524526\pi$
$73$	−1.31534			−0.153949			−0.0769745	+	0.997033i	$0.524526\pi$
$74$		0			0
$75$	9.84233	−	17.0474i	1.13649	−	1.96847i
$76$		0			0
$77$	−6.56155			−0.747758
$78$		0			0
$79$	4.00000			0.450035			0.225018	−	0.974355i	$-0.427756\pi$
$79$	4.00000			0.450035			0.225018	+	0.974355i	$0.427756\pi$
$80$		0			0
$81$	3.50000	−	6.06218i	0.388889	−	0.673575i
$82$		0			0
$83$	−2.24621			−0.246554			−0.123277	−	0.992372i	$-0.539340\pi$
$83$	−2.24621			−0.246554			−0.123277	+	0.992372i	$0.539340\pi$
$84$		0			0
$85$	−8.90388	−	15.4220i	−0.965762	−	1.67275i
$86$		0			0
$87$	−6.40388	−	11.0918i	−0.686568	−	1.18917i
$88$		0			0
$89$	4.84233	−	8.38716i	0.513286	−	0.889037i	−0.486595	−	0.873627i	$-0.661761\pi$
$89$	4.84233	−	8.38716i	0.513286	−	0.889037i	0.999881	−	0.0154098i	$-0.00490527\pi$
$90$		0			0
$91$	−7.28078	−	5.68247i	−0.763233	−	0.595685i
$92$		0			0
$93$	10.2462	−	17.7470i	1.06248	−	1.84027i
$94$		0			0
$95$	4.56155	+	7.90084i	0.468005	+	0.810609i
$96$		0			0
$97$	−1.40388	−	2.43160i	−0.142543	−	0.246891i	0.785911	−	0.618340i	$-0.212194\pi$
$97$	−1.40388	−	2.43160i	−0.142543	−	0.246891i	−0.928453	+	0.371449i	$0.878861\pi$
$98$		0			0
$99$	−9.12311			−0.916907
$100$		0			0
$101$	−2.62311	+	4.54335i	−0.261009	+	0.452080i	−0.966510	−	0.256628i	$-0.917388\pi$
$101$	−2.62311	+	4.54335i	−0.261009	+	0.452080i	0.705501	+	0.708708i	$0.250722\pi$
$102$		0			0
$103$	−14.2462			−1.40372			−0.701860	−	0.712314i	$-0.747647\pi$
$103$	−14.2462			−1.40372			−0.701860	+	0.712314i	$0.747647\pi$
$104$		0			0
$105$	23.3693			2.28061
$106$		0			0
$107$	−1.84233	+	3.19101i	−0.178105	+	0.308486i	−0.941231	−	0.337763i	$-0.890330\pi$
$107$	−1.84233	+	3.19101i	−0.178105	+	0.308486i	0.763127	+	0.646249i	$0.223663\pi$
$108$		0			0
$109$	8.24621			0.789844			0.394922	−	0.918715i	$-0.370772\pi$
$109$	8.24621			0.789844			0.394922	+	0.918715i	$0.370772\pi$
$110$		0			0
$111$	−1.28078	−	2.21837i	−0.121566	−	0.210558i
$112$		0			0
$113$	−4.62311	−	8.00745i	−0.434905	−	0.753278i	0.562383	−	0.826877i	$-0.309885\pi$
$113$	−4.62311	−	8.00745i	−0.434905	−	0.753278i	−0.997288	+	0.0735992i	$0.976551\pi$
$114$		0			0
$115$	6.56155	−	11.3649i	0.611868	−	1.05979i
$116$		0			0
$117$	−10.1231	−	7.90084i	−0.935881	−	0.730433i
$118$		0			0
$119$	6.40388	−	11.0918i	0.587043	−	1.01679i
$120$		0			0
$121$	2.21922	+	3.84381i	0.201748	+	0.349437i
$122$		0			0
$123$	11.8423	+	20.5115i	1.06779	+	1.84946i
$124$		0			0
$125$	−9.56155			−0.855211
$126$		0			0
$127$	6.40388	−	11.0918i	0.568253	−	0.984242i	−0.428486	−	0.903548i	$-0.640953\pi$
$127$	6.40388	−	11.0918i	0.568253	−	0.984242i	0.996739	−	0.0806942i	$-0.0257137\pi$
$128$		0			0
$129$	−16.8078			−1.47984
$130$		0			0
$131$	−18.2462			−1.59418			−0.797089	−	0.603861i	$-0.793628\pi$
$131$	−18.2462			−1.59418			−0.797089	+	0.603861i	$0.793628\pi$
$132$		0			0
$133$	−3.28078	+	5.68247i	−0.284479	+	0.492733i
$134$		0			0
$135$	5.12311			0.440927
$136$		0			0
$137$	10.7462	+	18.6130i	0.918111	+	1.59021i	0.802282	+	0.596945i	$0.203619\pi$
$137$	10.7462	+	18.6130i	0.918111	+	1.59021i	0.115829	+	0.993269i	$0.463048\pi$
$138$		0			0
$139$	9.84233	+	17.0474i	0.834815	+	1.44594i	0.894181	+	0.447706i	$0.147759\pi$
$139$	9.84233	+	17.0474i	0.834815	+	1.44594i	−0.0593651	+	0.998236i	$0.518908\pi$
$140$		0			0
$141$	−5.12311	+	8.87348i	−0.431443	+	0.747282i
$142$		0			0
$143$	1.28078	−	9.14657i	0.107104	−	0.764875i
$144$		0			0
$145$	−8.90388	+	15.4220i	−0.739427	+	1.28073i
$146$		0			0
$147$	−0.561553	−	0.972638i	−0.0463161	−	0.0802218i
$148$		0			0
$149$	−6.62311	−	11.4716i	−0.542586	−	0.939786i	−0.998755	−	0.0498931i	$-0.984112\pi$
$149$	−6.62311	−	11.4716i	−0.542586	−	0.939786i	0.456169	−	0.889893i	$-0.349221\pi$
$150$		0			0
$151$	12.4924			1.01662			0.508309	−	0.861174i	$-0.330271\pi$
$151$	12.4924			1.01662			0.508309	+	0.861174i	$0.330271\pi$
$152$		0			0
$153$	8.90388	−	15.4220i	0.719836	−	1.24679i
$154$		0			0
$155$	−28.4924			−2.28857
$156$		0			0
$157$	−17.8078			−1.42121			−0.710607	−	0.703589i	$-0.751580\pi$
$157$	−17.8078			−1.42121			−0.710607	+	0.703589i	$0.751580\pi$
$158$		0			0
$159$	5.68466	−	9.84612i	0.450823	−	0.780848i
$160$		0			0
$161$	9.43845			0.743854
$162$		0			0
$163$	2.96543	+	5.13628i	0.232271	+	0.402305i	0.958476	−	0.285173i	$-0.0920511\pi$
$163$	2.96543	+	5.13628i	0.232271	+	0.402305i	−0.726205	+	0.687478i	$0.758718\pi$
$164$		0			0
$165$	11.6847	+	20.2384i	0.909649	+	1.57556i
$166$		0			0
$167$	−2.71922	+	4.70983i	−0.210420	+	0.364458i	−0.951846	−	0.306577i	$-0.900816\pi$
$167$	−2.71922	+	4.70983i	−0.210420	+	0.364458i	0.741426	+	0.671034i	$0.234150\pi$
$168$		0			0
$169$	9.34233	−	9.03996i	0.718641	−	0.695382i
$170$		0			0
$171$	−4.56155	+	7.90084i	−0.348831	+	0.604192i
$172$		0			0
$173$	7.96543	+	13.7965i	0.605601	+	1.04893i	0.991956	+	0.126581i	$0.0404005\pi$
$173$	7.96543	+	13.7965i	0.605601	+	1.04893i	−0.386355	+	0.922350i	$0.626266\pi$
$174$		0			0
$175$	−9.84233	−	17.0474i	−0.744010	−	1.28866i
$176$		0			0
$177$	−6.56155			−0.493197
$178$		0			0
$179$	2.15767	−	3.73720i	0.161272	−	0.279331i	−0.774053	−	0.633121i	$-0.781774\pi$
$179$	2.15767	−	3.73720i	0.161272	−	0.279331i	0.935325	+	0.353789i	$0.115107\pi$
$180$		0			0
$181$	−9.80776			−0.729005			−0.364503	−	0.931202i	$-0.618761\pi$
$181$	−9.80776			−0.729005			−0.364503	+	0.931202i	$0.618761\pi$
$182$		0			0
$183$	18.5616			1.37211
$184$		0			0
$185$	−1.78078	+	3.08440i	−0.130925	+	0.226769i
$186$		0			0
$187$	12.8078			0.936596
$188$		0			0
$189$	1.84233	+	3.19101i	0.134010	+	0.232112i
$190$		0			0
$191$	−2.15767	−	3.73720i	−0.156124	−	0.270414i	0.777344	−	0.629076i	$-0.216566\pi$
$191$	−2.15767	−	3.73720i	−0.156124	−	0.270414i	−0.933468	+	0.358662i	$0.883233\pi$
$192$		0			0
$193$	−1.50000	+	2.59808i	−0.107972	+	0.187014i	−0.914949	−	0.403570i	$-0.867769\pi$
$193$	−1.50000	+	2.59808i	−0.107972	+	0.187014i	0.806976	+	0.590584i	$0.201102\pi$
$194$		0			0
$195$	−4.56155	+	32.5760i	−0.326660	+	2.33282i
$196$		0			0
$197$	−1.15767	+	2.00514i	−0.0824806	+	0.142861i	−0.904315	−	0.426866i	$-0.859618\pi$
$197$	−1.15767	+	2.00514i	−0.0824806	+	0.142861i	0.821834	+	0.569727i	$0.192951\pi$
$198$		0			0
$199$	4.71922	+	8.17394i	0.334537	+	0.579435i	0.983396	−	0.181474i	$-0.0580868\pi$
$199$	4.71922	+	8.17394i	0.334537	+	0.579435i	−0.648859	+	0.760909i	$0.724753\pi$
$200$		0			0
$201$	12.0885	+	20.9380i	0.852660	+	1.47685i
$202$		0			0
$203$	−12.8078			−0.898929
$204$		0			0
$205$	16.4654	−	28.5190i	1.15000	−	1.99185i
$206$		0			0
$207$	13.1231			0.912119
$208$		0			0
$209$	−6.56155			−0.453872
$210$		0			0
$211$	6.15767	−	10.6654i	0.423912	−	0.734236i	−0.572407	−	0.819970i	$-0.693990\pi$
$211$	6.15767	−	10.6654i	0.423912	−	0.734236i	0.996318	+	0.0857336i	$0.0273234\pi$
$212$		0			0
$213$	19.6847			1.34877
$214$		0			0
$215$	11.6847	+	20.2384i	0.796887	+	1.38025i
$216$		0			0
$217$	−10.2462	−	17.7470i	−0.695558	−	1.20474i
$218$		0			0
$219$	−1.68466	+	2.91791i	−0.113839	+	0.197174i
$220$		0			0
$221$	14.2116	+	11.0918i	0.955979	+	0.746119i
$222$		0			0
$223$	−1.84233	+	3.19101i	−0.123371	+	0.213686i	−0.921095	−	0.389337i	$-0.872704\pi$
$223$	−1.84233	+	3.19101i	−0.123371	+	0.213686i	0.797724	+	0.603023i	$0.206037\pi$
$224$		0			0
$225$	−13.6847	−	23.7025i	−0.912311	−	1.58017i
$226$		0			0
$227$	−3.52699	−	6.10892i	−0.234094	−	0.405463i	0.724915	−	0.688839i	$-0.241879\pi$
$227$	−3.52699	−	6.10892i	−0.234094	−	0.405463i	−0.959009	+	0.283375i	$0.908546\pi$
$228$		0			0
$229$	−4.24621			−0.280598			−0.140299	−	0.990109i	$-0.544806\pi$
$229$	−4.24621			−0.280598			−0.140299	+	0.990109i	$0.544806\pi$
$230$		0			0
$231$	−8.40388	+	14.5560i	−0.552935	+	0.957711i
$232$		0			0
$233$	4.24621			0.278179			0.139089	−	0.990280i	$-0.455583\pi$
$233$	4.24621			0.278179			0.139089	+	0.990280i	$0.455583\pi$
$234$		0			0
$235$	14.2462			0.929320
$236$		0			0
$237$	5.12311	−	8.87348i	0.332781	−	0.576394i
$238$		0			0
$239$	−1.75379			−0.113443			−0.0567216	−	0.998390i	$-0.518065\pi$
$239$	−1.75379			−0.113443			−0.0567216	+	0.998390i	$0.518065\pi$
$240$		0			0
$241$	12.7462	+	22.0771i	0.821056	+	1.42211i	0.904897	+	0.425631i	$0.139948\pi$
$241$	12.7462	+	22.0771i	0.821056	+	1.42211i	−0.0838412	+	0.996479i	$0.526719\pi$
$242$		0			0
$243$	−11.1231	−	19.2658i	−0.713548	−	1.23590i
$244$		0			0
$245$	−0.780776	+	1.35234i	−0.0498820	+	0.0863981i
$246$		0			0
$247$	−7.28078	−	5.68247i	−0.463265	−	0.361567i
$248$		0			0
$249$	−2.87689	+	4.98293i	−0.182316	+	0.315780i
$250$		0			0
$251$	14.9654	+	25.9209i	0.944610	+	1.63611i	0.756530	+	0.653958i	$0.226893\pi$
$251$	14.9654	+	25.9209i	0.944610	+	1.63611i	0.188079	+	0.982154i	$0.439774\pi$
$252$		0			0
$253$	4.71922	+	8.17394i	0.296695	+	0.513891i
$254$		0			0
$255$	−45.6155			−2.85656
$256$		0			0
$257$	5.62311	−	9.73950i	0.350760	−	0.607534i	−0.635623	−	0.772000i	$-0.719257\pi$
$257$	5.62311	−	9.73950i	0.350760	−	0.607534i	0.986383	+	0.164466i	$0.0525901\pi$
$258$		0			0
$259$	−2.56155			−0.159167
$260$		0			0
$261$	−17.8078			−1.10227
$262$		0			0
$263$	4.40388	−	7.62775i	0.271555	−	0.470347i	−0.697705	−	0.716385i	$-0.745795\pi$
$263$	4.40388	−	7.62775i	0.271555	−	0.470347i	0.969260	+	0.246038i	$0.0791288\pi$
$264$		0			0
$265$	−15.8078			−0.971063
$266$		0			0
$267$	−12.4039	−	21.4842i	−0.759105	−	1.31481i
$268$		0			0
$269$	−7.40388	−	12.8239i	−0.451423	−	0.781887i	0.547052	−	0.837099i	$-0.315750\pi$
$269$	−7.40388	−	12.8239i	−0.451423	−	0.781887i	−0.998475	+	0.0552116i	$0.982417\pi$
$270$		0			0
$271$	−2.71922	+	4.70983i	−0.165181	+	0.286102i	−0.936720	−	0.350081i	$-0.886154\pi$
$271$	−2.71922	+	4.70983i	−0.165181	+	0.286102i	0.771539	+	0.636183i	$0.219488\pi$
$272$		0			0
$273$	−21.9309	+	8.87348i	−1.32732	+	0.537047i
$274$		0			0
$275$	9.84233	−	17.0474i	0.593515	−	1.02800i
$276$		0			0
$277$	−5.50000	−	9.52628i	−0.330463	−	0.572379i	0.652140	−	0.758099i	$-0.273872\pi$
$277$	−5.50000	−	9.52628i	−0.330463	−	0.572379i	−0.982603	+	0.185720i	$0.940538\pi$
$278$		0			0
$279$	−14.2462	−	24.6752i	−0.852898	−	1.47726i
$280$		0			0
$281$	14.6847			0.876013			0.438007	−	0.898972i	$-0.355685\pi$
$281$	14.6847			0.876013			0.438007	+	0.898972i	$0.355685\pi$
$282$		0			0
$283$	−10.7192	+	18.5662i	−0.637192	+	1.10365i	0.348855	+	0.937177i	$0.386571\pi$
$283$	−10.7192	+	18.5662i	−0.637192	+	1.10365i	−0.986046	+	0.166472i	$0.946763\pi$
$284$		0			0
$285$	23.3693			1.38428
$286$		0			0
$287$	23.6847			1.39806
$288$		0			0
$289$	−4.00000	+	6.92820i	−0.235294	+	0.407541i
$290$		0			0
$291$	−7.19224			−0.421616
$292$		0			0
$293$	−5.74621	−	9.95273i	−0.335697	−	0.581445i	0.647921	−	0.761707i	$-0.275639\pi$
$293$	−5.74621	−	9.95273i	−0.335697	−	0.581445i	−0.983619	+	0.180263i	$0.942305\pi$
$294$		0			0
$295$	4.56155	+	7.90084i	0.265584	+	0.460005i
$296$		0			0
$297$	−1.84233	+	3.19101i	−0.106903	+	0.185161i
$298$		0			0
$299$	−1.84233	+	13.1569i	−0.106545	+	0.760881i
$300$		0			0
$301$	−8.40388	+	14.5560i	−0.484392	+	0.838991i
$302$		0			0
$303$	6.71922	+	11.6380i	0.386009	+	0.668588i
$304$		0			0
$305$	−12.9039	−	22.3502i	−0.738874	−	1.27977i
$306$		0			0
$307$	26.2462			1.49795			0.748975	−	0.662598i	$-0.230546\pi$
$307$	26.2462			1.49795			0.748975	+	0.662598i	$0.230546\pi$
$308$		0			0
$309$	−18.2462	+	31.6034i	−1.03799	+	1.79785i
$310$		0			0
$311$	14.2462			0.807829			0.403914	−	0.914797i	$-0.367649\pi$
$311$	14.2462			0.807829			0.403914	+	0.914797i	$0.367649\pi$
$312$		0			0
$313$	−32.2462			−1.82266			−0.911332	−	0.411673i	$-0.864945\pi$
$313$	−32.2462			−1.82266			−0.911332	+	0.411673i	$0.864945\pi$
$314$		0			0
$315$	16.2462	−	28.1393i	0.915370	−	1.58547i
$316$		0			0
$317$	16.4384			0.923275			0.461638	−	0.887069i	$-0.347262\pi$
$317$	16.4384			0.923275			0.461638	+	0.887069i	$0.347262\pi$
$318$		0			0
$319$	−6.40388	−	11.0918i	−0.358549	−	0.621024i
$320$		0			0
$321$	4.71922	+	8.17394i	0.263401	+	0.456225i
$322$		0			0
$323$	6.40388	−	11.0918i	0.356322	−	0.617167i
$324$		0			0
$325$	25.6847	−	10.3923i	1.42473	−	0.576461i
$326$		0			0
$327$	10.5616	−	18.2931i	0.584055	−	1.01161i
$328$		0			0
$329$	5.12311	+	8.87348i	0.282446	+	0.489211i
$330$		0			0
$331$	10.9654	+	18.9927i	0.602715	+	1.04393i	0.992408	+	0.122988i	$0.0392477\pi$
$331$	10.9654	+	18.9927i	0.602715	+	1.04393i	−0.389693	+	0.920945i	$0.627419\pi$
$332$		0			0
$333$	−3.56155			−0.195172
$334$		0			0
$335$	16.8078	−	29.1119i	0.918306	−	1.59055i
$336$		0			0
$337$	16.4384			0.895459			0.447730	−	0.894169i	$-0.352233\pi$
$337$	16.4384			0.895459			0.447730	+	0.894169i	$0.352233\pi$
$338$		0			0
$339$	−23.6847			−1.28637
$340$		0			0
$341$	10.2462	−	17.7470i	0.554863	−	0.961052i
$342$		0			0
$343$	−19.0540			−1.02882
$344$		0			0
$345$	−16.8078	−	29.1119i	−0.904900	−	1.56733i
$346$		0			0
$347$	−17.5270	−	30.3576i	−0.940898	−	1.62968i	−0.763763	−	0.645497i	$-0.776650\pi$
$347$	−17.5270	−	30.3576i	−0.940898	−	1.62968i	−0.177135	−	0.984187i	$-0.556683\pi$
$348$		0			0
$349$	−10.2808	+	17.8068i	−0.550317	+	0.953178i	0.447934	+	0.894067i	$0.352160\pi$
$349$	−10.2808	+	17.8068i	−0.550317	+	0.953178i	−0.998251	+	0.0591110i	$0.981173\pi$
$350$		0			0
$351$	−4.80776	+	1.94528i	−0.256619	+	0.103831i
$352$		0			0
$353$	4.50000	−	7.79423i	0.239511	−	0.414845i	−0.721063	−	0.692869i	$-0.756346\pi$
$353$	4.50000	−	7.79423i	0.239511	−	0.414845i	0.960574	+	0.278024i	$0.0896796\pi$
$354$		0			0
$355$	−13.6847	−	23.7025i	−0.726306	−	1.25800i
$356$		0			0
$357$	−16.4039	−	28.4124i	−0.868186	−	1.50374i
$358$		0			0
$359$	4.49242			0.237101			0.118550	−	0.992948i	$-0.462175\pi$
$359$	4.49242			0.237101			0.118550	+	0.992948i	$0.462175\pi$
$360$		0			0
$361$	6.21922	−	10.7720i	0.327328	−	0.566948i
$362$		0			0
$363$	11.3693			0.596734
$364$		0			0
$365$	4.68466			0.245206
$366$		0			0
$367$	−16.0885	+	27.8662i	−0.839815	+	1.45460i	0.0502341	+	0.998737i	$0.484003\pi$
$367$	−16.0885	+	27.8662i	−0.839815	+	1.45460i	−0.890049	+	0.455865i	$0.849330\pi$
$368$		0			0
$369$	32.9309			1.71431
$370$		0			0
$371$	−5.68466	−	9.84612i	−0.295133	−	0.511185i
$372$		0			0
$373$	5.62311	+	9.73950i	0.291153	+	0.504292i	0.974083	−	0.226192i	$-0.0726277\pi$
$373$	5.62311	+	9.73950i	0.291153	+	0.504292i	−0.682929	+	0.730484i	$0.739294\pi$
$374$		0			0
$375$	−12.2462	+	21.2111i	−0.632392	+	1.09533i
$376$		0			0
$377$	2.50000	−	17.8536i	0.128757	−	0.919506i
$378$		0			0
$379$	−12.9654	+	22.4568i	−0.665990	+	1.15353i	0.313026	+	0.949744i	$0.398657\pi$
$379$	−12.9654	+	22.4568i	−0.665990	+	1.15353i	−0.979016	+	0.203783i	$0.934676\pi$
$380$		0			0
$381$	−16.4039	−	28.4124i	−0.840396	−	1.45561i
$382$		0			0
$383$	8.08854	+	14.0098i	0.413305	+	0.715865i	0.995249	−	0.0973636i	$-0.0310410\pi$
$383$	8.08854	+	14.0098i	0.413305	+	0.715865i	−0.581944	+	0.813229i	$0.697708\pi$
$384$		0			0
$385$	23.3693			1.19101
$386$		0			0
$387$	−11.6847	+	20.2384i	−0.593965	+	1.02878i
$388$		0			0
$389$	−17.3153			−0.877923			−0.438961	−	0.898506i	$-0.644653\pi$
$389$	−17.3153			−0.877923			−0.438961	+	0.898506i	$0.644653\pi$
$390$		0			0
$391$	−18.4233			−0.931706
$392$		0			0
$393$	−23.3693	+	40.4768i	−1.17883	+	2.04179i
$394$		0			0
$395$	−14.2462			−0.716805
$396$		0			0
$397$	10.8423	+	18.7795i	0.544161	+	0.942514i	0.998659	+	0.0517667i	$0.0164852\pi$
$397$	10.8423	+	18.7795i	0.544161	+	0.942514i	−0.454498	+	0.890748i	$0.650181\pi$
$398$		0			0
$399$	8.40388	+	14.5560i	0.420720	+	0.728709i
$400$		0			0
$401$	4.74621	−	8.22068i	0.237014	−	0.410521i	−0.722842	−	0.691014i	$-0.757164\pi$
$401$	4.74621	−	8.22068i	0.237014	−	0.410521i	0.959856	+	0.280492i	$0.0904978\pi$
$402$		0			0
$403$	26.7386	−	10.8188i	1.33195	−	0.538921i
$404$		0			0
$405$	−12.4654	+	21.5908i	−0.619412	+	1.07285i
$406$		0			0
$407$	−1.28078	−	2.21837i	−0.0634857	−	0.109961i
$408$		0			0
$409$	−0.623106	−	1.07925i	−0.0308106	−	0.0533655i	0.850209	−	0.526445i	$-0.176476\pi$
$409$	−0.623106	−	1.07925i	−0.0308106	−	0.0533655i	−0.881020	+	0.473080i	$0.843142\pi$
$410$		0			0
$411$	55.0540			2.71561
$412$		0			0
$413$	−3.28078	+	5.68247i	−0.161436	+	0.279616i
$414$		0			0
$415$	8.00000			0.392705
$416$		0			0
$417$	50.4233			2.46924
$418$		0			0
$419$	−6.96543	+	12.0645i	−0.340284	+	0.589389i	−0.984485	−	0.175467i	$-0.943856\pi$
$419$	−6.96543	+	12.0645i	−0.340284	+	0.589389i	0.644202	+	0.764856i	$0.277190\pi$
$420$		0			0
$421$	−21.3153			−1.03885			−0.519423	−	0.854517i	$-0.673853\pi$
$421$	−21.3153			−1.03885			−0.519423	+	0.854517i	$0.673853\pi$
$422$		0			0
$423$	7.12311	+	12.3376i	0.346337	+	0.599874i
$424$		0			0
$425$	19.2116	+	33.2755i	0.931902	+	1.61410i
$426$		0			0
$427$	9.28078	−	16.0748i	0.449128	−	0.777913i
$428$		0			0
$429$	−18.6501	−	14.5560i	−0.900435	−	0.702768i
$430$		0			0
$431$	1.03457	−	1.79192i	0.0498333	−	0.0863137i	−0.840033	−	0.542536i	$-0.817464\pi$
$431$	1.03457	−	1.79192i	0.0498333	−	0.0863137i	0.889866	+	0.456222i	$0.150798\pi$
$432$		0			0
$433$	0.746211	+	1.29248i	0.0358606	+	0.0621124i	0.883399	−	0.468622i	$-0.155249\pi$
$433$	0.746211	+	1.29248i	0.0358606	+	0.0621124i	−0.847538	+	0.530735i	$0.821916\pi$
$434$		0			0
$435$	22.8078	+	39.5042i	1.09355	+	1.89408i
$436$		0			0
$437$	9.43845			0.451502
$438$		0			0
$439$	−18.9654	+	32.8491i	−0.905171	+	1.56780i	−0.0844831	+	0.996425i	$0.526924\pi$
$439$	−18.9654	+	32.8491i	−0.905171	+	1.56780i	−0.820688	+	0.571377i	$0.806409\pi$
$440$		0			0
$441$	−1.56155			−0.0743597
$442$		0			0
$443$	−21.7538			−1.03355			−0.516777	−	0.856120i	$-0.672868\pi$
$443$	−21.7538			−1.03355			−0.516777	+	0.856120i	$0.672868\pi$
$444$		0			0
$445$	−17.2462	+	29.8713i	−0.817549	+	1.41604i
$446$		0			0
$447$	−33.9309			−1.60488
$448$		0			0
$449$	−6.52699	−	11.3051i	−0.308028	−	0.533519i	0.669903	−	0.742448i	$-0.266336\pi$
$449$	−6.52699	−	11.3051i	−0.308028	−	0.533519i	−0.977931	+	0.208929i	$0.933002\pi$
$450$		0			0
$451$	11.8423	+	20.5115i	0.557634	+	0.965850i
$452$		0			0
$453$	16.0000	−	27.7128i	0.751746	−	1.30206i
$454$		0			0
$455$	25.9309	+	20.2384i	1.21566	+	0.948792i
$456$		0			0
$457$	4.50000	−	7.79423i	0.210501	−	0.364599i	−0.741370	−	0.671096i	$-0.765824\pi$
$457$	4.50000	−	7.79423i	0.210501	−	0.364599i	0.951871	+	0.306497i	$0.0991571\pi$
$458$		0			0
$459$	−3.59612	−	6.22866i	−0.167852	−	0.290729i
$460$		0			0
$461$	4.74621	+	8.22068i	0.221053	+	0.382875i	0.955128	−	0.296193i	$-0.0957173\pi$
$461$	4.74621	+	8.22068i	0.221053	+	0.382875i	−0.734075	+	0.679068i	$0.762384\pi$
$462$		0			0
$463$	−32.9848			−1.53294			−0.766468	−	0.642283i	$-0.777988\pi$
$463$	−32.9848			−1.53294			−0.766468	+	0.642283i	$0.777988\pi$
$464$		0			0
$465$	−36.4924	+	63.2067i	−1.69230	+	2.93114i
$466$		0			0
$467$	−9.75379			−0.451352			−0.225676	−	0.974202i	$-0.572459\pi$
$467$	−9.75379			−0.451352			−0.225676	+	0.974202i	$0.572459\pi$
$468$		0			0
$469$	24.1771			1.11639
$470$		0			0
$471$	−22.8078	+	39.5042i	−1.05093	+	1.82026i
$472$		0			0
$473$	−16.8078			−0.772822
$474$		0			0
$475$	−9.84233	−	17.0474i	−0.451597	−	0.782189i
$476$		0			0
$477$	−7.90388	−	13.6899i	−0.361894	−	0.626819i
$478$		0			0
$479$	16.6501	−	28.8388i	0.760762	−	1.31768i	−0.181696	−	0.983355i	$-0.558159\pi$
$479$	16.6501	−	28.8388i	0.760762	−	1.31768i	0.942458	−	0.334324i	$-0.108508\pi$
$480$		0			0
$481$	0.500000	−	3.57071i	0.0227980	−	0.162811i
$482$		0			0
$483$	12.0885	−	20.9380i	0.550048	−	0.952710i
$484$		0			0
$485$	5.00000	+	8.66025i	0.227038	+	0.393242i
$486$		0			0
$487$	−19.2808	−	33.3953i	−0.873695	−	1.51328i	−0.858146	−	0.513406i	$-0.828384\pi$
$487$	−19.2808	−	33.3953i	−0.873695	−	1.51328i	−0.0155493	−	0.999879i	$-0.504950\pi$
$488$		0			0
$489$	15.1922			0.687017
$490$		0			0
$491$	17.5270	−	30.3576i	0.790982	−	1.37002i	−0.134378	−	0.990930i	$-0.542904\pi$
$491$	17.5270	−	30.3576i	0.790982	−	1.37002i	0.925360	−	0.379091i	$-0.123763\pi$
$492$		0			0
$493$	25.0000			1.12594
$494$		0			0
$495$	32.4924			1.46043
$496$		0			0
$497$	9.84233	−	17.0474i	0.441489	−	0.764681i
$498$		0			0
$499$	−16.4924			−0.738302			−0.369151	−	0.929369i	$-0.620352\pi$
$499$	−16.4924			−0.738302			−0.369151	+	0.929369i	$0.620352\pi$
$500$		0			0
$501$	6.96543	+	12.0645i	0.311193	+	0.539002i
$502$		0			0
$503$	−10.1577	−	17.5936i	−0.452908	−	0.784460i	0.545657	−	0.838009i	$-0.316280\pi$
$503$	−10.1577	−	17.5936i	−0.452908	−	0.784460i	−0.998565	+	0.0535486i	$0.982947\pi$
$504$		0			0
$505$	9.34233	−	16.1814i	0.415728	−	0.720062i
$506$		0			0
$507$	−8.08854	−	32.3029i	−0.359225	−	1.43462i
$508$		0			0
$509$	16.5000	−	28.5788i	0.731350	−	1.26673i	−0.224957	−	0.974369i	$-0.572224\pi$
$509$	16.5000	−	28.5788i	0.731350	−	1.26673i	0.956306	−	0.292366i	$-0.0944425\pi$
$510$		0			0
$511$	1.68466	+	2.91791i	0.0745249	+	0.129081i
$512$		0			0
$513$	1.84233	+	3.19101i	0.0813408	+	0.140886i
$514$		0			0
$515$	50.7386			2.23581
$516$		0			0
$517$	−5.12311	+	8.87348i	−0.225314	+	0.390255i
$518$		0			0
$519$	40.8078			1.79126
$520$		0			0
$521$	−28.0540			−1.22907			−0.614533	−	0.788891i	$-0.710656\pi$
$521$	−28.0540			−1.22907			−0.614533	+	0.788891i	$0.710656\pi$
$522$		0			0
$523$	20.6501	−	35.7670i	0.902966	−	1.56398i	0.0793404	−	0.996848i	$-0.474719\pi$
$523$	20.6501	−	35.7670i	0.902966	−	1.56398i	0.823625	−	0.567135i	$-0.191948\pi$
$524$		0			0
$525$	−50.4233			−2.20065
$526$		0			0
$527$	20.0000	+	34.6410i	0.871214	+	1.50899i
$528$		0			0
$529$	4.71165	+	8.16081i	0.204854	+	0.354818i
$530$		0			0
$531$	−4.56155	+	7.90084i	−0.197955	+	0.342867i
$532$		0			0
$533$	−4.62311	+	33.0156i	−0.200249	+	1.43006i
$534$		0			0
$535$	6.56155	−	11.3649i	0.283681	−	0.491349i
$536$		0			0
$537$	−5.52699	−	9.57302i	−0.238507	−	0.413106i
$538$		0			0
$539$	−0.561553	−	0.972638i	−0.0241878	−	0.0418945i
$540$		0			0
$541$	6.68466			0.287396			0.143698	−	0.989622i	$-0.454101\pi$
$541$	6.68466			0.287396			0.143698	+	0.989622i	$0.454101\pi$
$542$		0			0
$543$	−12.5616	+	21.7572i	−0.539068	+	0.933693i
$544$		0			0
$545$	−29.3693			−1.25804
$546$		0			0
$547$	16.4924			0.705165			0.352583	−	0.935781i	$-0.385304\pi$
$547$	16.4924			0.705165			0.352583	+	0.935781i	$0.385304\pi$
$548$		0			0
$549$	12.9039	−	22.3502i	0.550724	−	0.953882i
$550$		0			0
$551$	−12.8078			−0.545629
$552$		0			0
$553$	−5.12311	−	8.87348i	−0.217857	−	0.377339i
$554$		0			0
$555$	4.56155	+	7.90084i	0.193627	+	0.335372i
$556$		0			0
$557$	0.746211	−	1.29248i	0.0316180	−	0.0547640i	−0.849783	−	0.527132i	$-0.823267\pi$
$557$	0.746211	−	1.29248i	0.0316180	−	0.0547640i	0.881401	+	0.472368i	$0.156601\pi$
$558$		0			0
$559$	−18.6501	−	14.5560i	−0.788815	−	0.615651i
$560$		0			0
$561$	16.4039	−	28.4124i	0.692572	−	1.19957i
$562$		0			0
$563$	−15.5270	−	26.8935i	−0.654385	−	1.13343i	−0.982048	−	0.188633i	$-0.939594\pi$
$563$	−15.5270	−	26.8935i	−0.654385	−	1.13343i	0.327663	−	0.944795i	$-0.393739\pi$
$564$		0			0
$565$	16.4654	+	28.5190i	0.692706	+	1.19980i
$566$		0			0
$567$	−17.9309			−0.753026
$568$		0			0
$569$	−3.15767	+	5.46925i	−0.132376	+	0.229283i	−0.924592	−	0.380958i	$-0.875594\pi$
$569$	−3.15767	+	5.46925i	−0.132376	+	0.229283i	0.792216	+	0.610241i	$0.208927\pi$
$570$		0			0
$571$	−24.4924			−1.02498			−0.512488	−	0.858694i	$-0.671276\pi$
$571$	−24.4924			−1.02498			−0.512488	+	0.858694i	$0.671276\pi$
$572$		0			0
$573$	−11.0540			−0.461786
$574$		0			0
$575$	−14.1577	+	24.5218i	−0.590416	+	1.02263i
$576$		0			0
$577$	−31.5616			−1.31392			−0.656962	−	0.753923i	$-0.728159\pi$
$577$	−31.5616			−1.31392			−0.656962	+	0.753923i	$0.728159\pi$
$578$		0			0
$579$	3.84233	+	6.65511i	0.159682	+	0.276577i
$580$		0			0
$581$	2.87689	+	4.98293i	0.119354	+	0.206727i
$582$		0			0
$583$	5.68466	−	9.84612i	0.235434	−	0.407785i
$584$		0			0
$585$	36.0540	+	28.1393i	1.49065	+	1.16342i
$586$		0			0
$587$	−6.96543	+	12.0645i	−0.287494	+	0.497955i	−0.973211	−	0.229914i	$-0.926156\pi$
$587$	−6.96543	+	12.0645i	−0.287494	+	0.497955i	0.685717	+	0.727869i	$0.259489\pi$
$588$		0			0
$589$	−10.2462	−	17.7470i	−0.422188	−	0.731251i
$590$		0			0
$591$	2.96543	+	5.13628i	0.121982	+	0.211278i
$592$		0			0
$593$	−23.5616			−0.967557			−0.483779	−	0.875190i	$-0.660736\pi$
$593$	−23.5616			−0.967557			−0.483779	+	0.875190i	$0.660736\pi$
$594$		0			0
$595$	−22.8078	+	39.5042i	−0.935027	+	1.61951i
$596$		0			0
$597$	24.1771			0.989502
$598$		0			0
$599$	22.7386			0.929075			0.464538	−	0.885553i	$-0.346221\pi$
$599$	22.7386			0.929075			0.464538	+	0.885553i	$0.346221\pi$
$600$		0			0
$601$	18.9924	−	32.8958i	0.774717	−	1.34185i	−0.160236	−	0.987079i	$-0.551226\pi$
$601$	18.9924	−	32.8958i	0.774717	−	1.34185i	0.934953	−	0.354771i	$-0.115441\pi$
$602$		0			0
$603$	33.6155			1.36893
$604$		0			0
$605$	−7.90388	−	13.6899i	−0.321339	−	0.556575i
$606$		0			0
$607$	15.8423	+	27.4397i	0.643020	+	1.11374i	0.984755	+	0.173947i	$0.0556523\pi$
$607$	15.8423	+	27.4397i	0.643020	+	1.11374i	−0.341735	+	0.939796i	$0.611014\pi$
$608$		0			0
$609$	−16.4039	+	28.4124i	−0.664719	+	1.15133i
$610$		0			0
$611$	−13.3693	+	5.40938i	−0.540865	+	0.218840i
$612$		0			0
$613$	4.50000	−	7.79423i	0.181753	−	0.314806i	−0.760724	−	0.649075i	$-0.775156\pi$
$613$	4.50000	−	7.79423i	0.181753	−	0.314806i	0.942478	+	0.334269i	$0.108489\pi$
$614$		0			0
$615$	−42.1771	−	73.0528i	−1.70074	−	2.94578i
$616$		0			0
$617$	−4.37689	−	7.58100i	−0.176207	−	0.305200i	0.764371	−	0.644776i	$-0.223050\pi$
$617$	−4.37689	−	7.58100i	−0.176207	−	0.305200i	−0.940578	+	0.339577i	$0.889716\pi$
$618$		0			0
$619$	−36.9848			−1.48655			−0.743273	−	0.668988i	$-0.766728\pi$
$619$	−36.9848			−1.48655			−0.743273	+	0.668988i	$0.766728\pi$
$620$		0			0
$621$	2.65009	−	4.59010i	0.106345	−	0.184194i
$622$		0			0
$623$	−24.8078			−0.993902
$624$		0			0
$625$	−4.36932			−0.174773
$626$		0			0
$627$	−8.40388	+	14.5560i	−0.335619	+	0.581309i
$628$		0			0
$629$	5.00000			0.199363
$630$		0			0
$631$	−13.5270	−	23.4294i	−0.538501	−	0.932711i	−0.998985	−	0.0450430i	$-0.985658\pi$
$631$	−13.5270	−	23.4294i	−0.538501	−	0.932711i	0.460484	−	0.887668i	$-0.347676\pi$
$632$		0			0
$633$	−15.7732	−	27.3200i	−0.626928	−	1.08587i
$634$		0			0
$635$	−22.8078	+	39.5042i	−0.905099	+	1.56768i
$636$		0			0
$637$	0.219224	−	1.56557i	0.00868596	−	0.0620301i
$638$		0			0
$639$	13.6847	−	23.7025i	0.541357	−	0.937657i
$640$		0			0
$641$	−15.7462	−	27.2732i	−0.621938	−	1.07723i	−0.989124	−	0.147081i	$-0.953012\pi$
$641$	−15.7462	−	27.2732i	−0.621938	−	1.07723i	0.367187	−	0.930147i	$-0.380321\pi$
$642$		0			0
$643$	−16.6501	−	28.8388i	−0.656616	−	1.13729i	−0.981486	−	0.191533i	$-0.938654\pi$
$643$	−16.6501	−	28.8388i	−0.656616	−	1.13729i	0.324871	−	0.945758i	$-0.394679\pi$
$644$		0			0
$645$	59.8617			2.35705
$646$		0			0
$647$	−2.96543	+	5.13628i	−0.116583	+	0.201928i	−0.918412	−	0.395626i	$-0.870528\pi$
$647$	−2.96543	+	5.13628i	−0.116583	+	0.201928i	0.801828	+	0.597555i	$0.203861\pi$
$648$		0			0
$649$	−6.56155			−0.257563
$650$		0			0
$651$	−52.4924			−2.05734
$652$		0			0
$653$	−22.7732	+	39.4443i	−0.891184	+	1.54358i	−0.0527268	+	0.998609i	$0.516791\pi$
$653$	−22.7732	+	39.4443i	−0.891184	+	1.54358i	−0.838457	+	0.544967i	$0.816542\pi$
$654$		0			0
$655$	64.9848			2.53917
$656$		0			0
$657$	2.34233	+	4.05703i	0.0913830	+	0.158280i
$658$		0			0
$659$	8.71922	+	15.1021i	0.339653	+	0.588296i	0.984367	−	0.176128i	$-0.0563571\pi$
$659$	8.71922	+	15.1021i	0.339653	+	0.588296i	−0.644715	+	0.764423i	$0.723024\pi$
$660$		0			0
$661$	21.8693	−	37.8788i	0.850618	−	1.47331i	−0.0300338	−	0.999549i	$-0.509561\pi$
$661$	21.8693	−	37.8788i	0.850618	−	1.47331i	0.880652	−	0.473764i	$-0.157105\pi$
$662$		0			0
$663$	42.8078	−	17.3205i	1.66252	−	0.672673i
$664$		0			0
$665$	11.6847	−	20.2384i	0.453112	−	0.784812i
$666$		0			0
$667$	9.21165	+	15.9550i	0.356676	+	0.617782i
$668$		0			0
$669$	4.71922	+	8.17394i	0.182456	+	0.316023i
$670$		0			0
$671$	18.5616			0.716561
$672$		0			0
$673$	−0.376894	+	0.652800i	−0.0145282	+	0.0251636i	−0.873198	−	0.487365i	$-0.837958\pi$
$673$	−0.376894	+	0.652800i	−0.0145282	+	0.0251636i	0.858670	+	0.512529i	$0.171291\pi$
$674$		0			0
$675$	−11.0540			−0.425468
$676$		0			0
$677$	20.7386			0.797050			0.398525	−	0.917157i	$-0.369522\pi$
$677$	20.7386			0.797050			0.398525	+	0.917157i	$0.369522\pi$
$678$		0			0
$679$	−3.59612	+	6.22866i	−0.138006	+	0.239034i
$680$		0			0
$681$	−18.0691			−0.692411
$682$		0			0
$683$	9.84233	+	17.0474i	0.376606	+	0.652301i	0.990566	−	0.137036i	$-0.0437576\pi$
$683$	9.84233	+	17.0474i	0.376606	+	0.652301i	−0.613960	+	0.789337i	$0.710424\pi$
$684$		0			0
$685$	−38.2732	−	66.2911i	−1.46234	−	2.53285i
$686$		0			0
$687$	−5.43845	+	9.41967i	−0.207490	+	0.359383i
$688$		0			0
$689$	14.8348	−	6.00231i	0.565159	−	0.228670i
$690$		0			0
$691$	−10.7192	+	18.5662i	−0.407778	+	0.706293i	−0.994640	−	0.103394i	$-0.967030\pi$
$691$	−10.7192	+	18.5662i	−0.407778	+	0.706293i	0.586862	+	0.809687i	$0.300363\pi$
$692$		0			0
$693$	11.6847	+	20.2384i	0.443863	+	0.768794i
$694$		0			0
$695$	−35.0540	−	60.7153i	−1.32967	−	2.30306i
$696$		0			0
$697$	−46.2311			−1.75113
$698$		0			0
$699$	5.43845	−	9.41967i	0.205701	−	0.356285i
$700$		0			0
$701$	−16.7386			−0.632209			−0.316105	−	0.948724i	$-0.602375\pi$
$701$	−16.7386			−0.632209			−0.316105	+	0.948724i	$0.602375\pi$
$702$		0			0
$703$	−2.56155			−0.0966108
$704$		0			0
$705$	18.2462	−	31.6034i	0.687192	−	1.19025i
$706$		0			0
$707$	13.4384			0.505405
$708$		0			0
$709$	7.86932	+	13.6301i	0.295538	+	0.511888i	0.975110	−	0.221722i	$-0.0711676\pi$
$709$	7.86932	+	13.6301i	0.295538	+	0.511888i	−0.679572	+	0.733609i	$0.737834\pi$
$710$		0			0
$711$	−7.12311	−	12.3376i	−0.267137	−	0.462695i
$712$		0			0
$713$	−14.7386	+	25.5281i	−0.551966	+	0.956033i
$714$		0			0
$715$	−4.56155	+	32.5760i	−0.170592	+	1.21827i
$716$		0			0
$717$	−2.24621	+	3.89055i	−0.0838863	+	0.145295i
$718$		0			0
$719$	−7.03457	−	12.1842i	−0.262345	−	0.454395i	0.704520	−	0.709685i	$-0.251163\pi$
$719$	−7.03457	−	12.1842i	−0.262345	−	0.454395i	−0.966865	+	0.255290i	$0.917829\pi$
$720$		0			0
$721$	18.2462	+	31.6034i	0.679524	+	1.17697i
$722$		0			0
$723$	65.3002			2.42854
$724$		0			0
$725$	19.2116	−	33.2755i	0.713503	−	1.23582i
$726$		0			0
$727$	42.7386			1.58509			0.792544	−	0.609815i	$-0.208756\pi$
$727$	42.7386			1.58509			0.792544	+	0.609815i	$0.208756\pi$
$728$		0			0
$729$	−35.9848			−1.33277
$730$		0			0
$731$	16.4039	−	28.4124i	0.606719	−	1.05087i
$732$		0			0
$733$	−21.8078			−0.805488			−0.402744	−	0.915313i	$-0.631944\pi$
$733$	−21.8078			−0.805488			−0.402744	+	0.915313i	$0.631944\pi$
$734$		0			0
$735$	2.00000	+	3.46410i	0.0737711	+	0.127775i
$736$		0			0
$737$	12.0885	+	20.9380i	0.445287	+	0.771260i
$738$		0			0
$739$	9.03457	−	15.6483i	0.332342	−	0.575633i	−0.650629	−	0.759396i	$-0.725495\pi$
$739$	9.03457	−	15.6483i	0.332342	−	0.575633i	0.982971	+	0.183763i	$0.0588279\pi$
$740$		0			0
$741$	−21.9309	+	8.87348i	−0.805651	+	0.325975i
$742$		0			0
$743$	−18.9654	+	32.8491i	−0.695774	+	1.20512i	0.274145	+	0.961688i	$0.411605\pi$
$743$	−18.9654	+	32.8491i	−0.695774	+	1.20512i	−0.969919	+	0.243428i	$0.921728\pi$
$744$		0			0
$745$	23.5885	+	40.8566i	0.864217	+	1.49687i
$746$		0			0
$747$	4.00000	+	6.92820i	0.146352	+	0.253490i
$748$		0			0
$749$	9.43845			0.344873
$750$		0			0
$751$	2.65009	−	4.59010i	0.0967033	−	0.167495i	−0.813615	−	0.581404i	$-0.802504\pi$
$751$	2.65009	−	4.59010i	0.0967033	−	0.167495i	0.910318	+	0.413909i	$0.135837\pi$
$752$		0			0
$753$	76.6695			2.79399
$754$		0			0
$755$	−44.4924			−1.61925
$756$		0			0
$757$	−26.7732	+	46.3725i	−0.973088	+	1.68544i	−0.286984	+	0.957935i	$0.592653\pi$
$757$	−26.7732	+	46.3725i	−0.973088	+	1.68544i	−0.686104	+	0.727503i	$0.740681\pi$
$758$		0			0
$759$	24.1771			0.877572
$760$		0			0
$761$	25.9654	+	44.9735i	0.941246	+	1.63029i	0.763098	+	0.646283i	$0.223677\pi$
$761$	25.9654	+	44.9735i	0.941246	+	1.63029i	0.178148	+	0.984004i	$0.442989\pi$
$762$		0			0
$763$	−10.5616	−	18.2931i	−0.382354	−	0.662256i
$764$		0			0
$765$	−31.7116	+	54.9262i	−1.14654	+	1.98586i
$766$		0			0
$767$	−7.28078	−	5.68247i	−0.262894	−	0.205182i
$768$		0			0
$769$	13.9654	−	24.1888i	0.503606	−	0.872272i	−0.496385	−	0.868103i	$-0.665340\pi$
$769$	13.9654	−	24.1888i	0.503606	−	0.872272i	0.999991	−	0.00416940i	$-0.00132717\pi$
$770$		0			0
$771$	−14.4039	−	24.9483i	−0.518743	−	0.898489i
$772$		0			0
$773$	−27.4039	−	47.4649i	−0.985649	−	1.70719i	−0.639016	−	0.769194i	$-0.720658\pi$
$773$	−27.4039	−	47.4649i	−0.985649	−	1.70719i	−0.346633	−	0.938001i	$-0.612675\pi$
$774$		0			0
$775$	61.4773			2.20833
$776$		0			0
$777$	−3.28078	+	5.68247i	−0.117697	+	0.203858i
$778$		0			0
$779$	23.6847			0.848591
$780$		0			0
$781$	19.6847			0.704372
$782$		0			0
$783$	−3.59612	+	6.22866i	−0.128515	+	0.222594i
$784$		0			0
$785$	63.4233			2.26367
$786$		0			0
$787$	17.2116	+	29.8114i	0.613529	+	1.06266i	0.990641	+	0.136496i	$0.0435839\pi$
$787$	17.2116	+	29.8114i	0.613529	+	1.06266i	−0.377112	+	0.926168i	$0.623083\pi$
$788$		0			0
$789$	−11.2808	−	19.5389i	−0.401606	−	0.695602i
$790$		0			0
$791$	−11.8423	+	20.5115i	−0.421065	+	0.729306i
$792$		0			0
$793$	20.5961	+	16.0748i	0.731390	+	0.570832i
$794$		0			0
$795$	−20.2462	+	35.0675i	−0.718059	+	1.24371i
$796$		0			0
$797$	7.96543	+	13.7965i	0.282150	+	0.488698i	0.971914	−	0.235336i	$-0.0756190\pi$
$797$	7.96543	+	13.7965i	0.282150	+	0.488698i	−0.689764	+	0.724034i	$0.742286\pi$
$798$		0			0
$799$	−10.0000	−	17.3205i	−0.353775	−	0.612756i
$800$		0			0
$801$	−34.4924			−1.21873
$802$		0			0
$803$	−1.68466	+	2.91791i	−0.0594503	+	0.102971i
$804$		0			0
$805$	−33.6155			−1.18479
$806$		0			0
$807$	−37.9309			−1.33523
$808$		0			0
$809$	3.37689	−	5.84895i	0.118725	−	0.205638i	−0.800537	−	0.599283i	$-0.795453\pi$
$809$	3.37689	−	5.84895i	0.118725	−	0.205638i	0.919263	+	0.393644i	$0.128786\pi$
$810$		0			0
$811$	−8.00000			−0.280918			−0.140459	−	0.990086i	$-0.544858\pi$
$811$	−8.00000			−0.280918			−0.140459	+	0.990086i	$0.544858\pi$
$812$		0			0
$813$	6.96543	+	12.0645i	0.244288	+	0.423120i
$814$		0			0
$815$	−10.5616	−	18.2931i	−0.369955	−	0.640781i
$816$		0			0
$817$	−8.40388	+	14.5560i	−0.294015	+	0.509248i
$818$		0			0
$819$	−4.56155	+	32.5760i	−0.159394	+	1.13830i
$820$		0			0
$821$	−3.40388	+	5.89570i	−0.118796	+	0.205761i	−0.919291	−	0.393579i	$-0.871237\pi$
$821$	−3.40388	+	5.89570i	−0.118796	+	0.205761i	0.800495	+	0.599340i	$0.204570\pi$
$822$		0			0
$823$	22.0885	+	38.2585i	0.769958	+	1.33361i	0.937585	+	0.347756i	$0.113056\pi$
$823$	22.0885	+	38.2585i	0.769958	+	1.33361i	−0.167627	+	0.985851i	$0.553610\pi$
$824$		0			0
$825$	−25.2116	−	43.6679i	−0.877757	−	1.52032i
$826$		0			0
$827$	−28.9848			−1.00790			−0.503951	−	0.863732i	$-0.668121\pi$
$827$	−28.9848			−1.00790			−0.503951	+	0.863732i	$0.668121\pi$
$828$		0			0
$829$	−19.7462	+	34.2014i	−0.685814	+	1.18787i	0.287366	+	0.957821i	$0.407220\pi$
$829$	−19.7462	+	34.2014i	−0.685814	+	1.18787i	−0.973180	+	0.230044i	$0.926113\pi$
$830$		0			0
$831$	−28.1771			−0.977452
$832$		0			0
$833$	2.19224			0.0759565
$834$		0			0
$835$	9.68466	−	16.7743i	0.335151	−	0.580499i
$836$		0			0
$837$	−11.5076			−0.397760
$838$		0			0
$839$	19.8423	+	34.3679i	0.685033	+	1.18651i	0.973426	+	0.229000i	$0.0735457\pi$
$839$	19.8423	+	34.3679i	0.685033	+	1.18651i	−0.288393	+	0.957512i	$0.593121\pi$
$840$		0			0
$841$	2.00000	+	3.46410i	0.0689655	+	0.119452i
$842$		0			0
$843$	18.8078	−	32.5760i	0.647774	−	1.12198i
$844$		0			0
$845$	−33.2732	+	32.1963i	−1.14463	+	1.10759i
$846$		0			0
$847$	5.68466	−	9.84612i	0.195327	−	0.338317i
$848$		0			0
$849$	27.4579	+	47.5584i	0.942351	+	1.63220i
$850$		0			0
$851$	1.84233	+	3.19101i	0.0631542	+	0.109386i
$852$		0			0
$853$	13.4233			0.459605			0.229802	−	0.973237i	$-0.426192\pi$
$853$	13.4233			0.459605			0.229802	+	0.973237i	$0.426192\pi$
$854$		0			0
$855$	16.2462	−	28.1393i	0.555609	−	0.962343i
$856$		0			0
$857$	−52.0540			−1.77813			−0.889065	−	0.457781i	$-0.848644\pi$
$857$	−52.0540			−1.77813			−0.889065	+	0.457781i	$0.848644\pi$
$858$		0			0
$859$	5.75379			0.196317			0.0981584	−	0.995171i	$-0.468705\pi$
$859$	5.75379			0.196317			0.0981584	+	0.995171i	$0.468705\pi$
$860$		0			0
$861$	30.3348	−	52.5413i	1.03381	−	1.79060i
$862$		0			0
$863$	38.2462			1.30192			0.650958	−	0.759114i	$-0.274367\pi$
$863$	38.2462			1.30192			0.650958	+	0.759114i	$0.274367\pi$
$864$		0			0
$865$	−28.3693	−	49.1371i	−0.964586	−	1.67071i
$866$		0			0
$867$	10.2462	+	17.7470i	0.347980	+	0.602718i
$868$		0			0
$869$	5.12311	−	8.87348i	0.173789	−	0.301012i
$870$		0			0
$871$	−4.71922	+	33.7020i	−0.159905	+	1.14195i
$872$		0			0
$873$	−5.00000	+	8.66025i	−0.169224	+	0.293105i
$874$		0			0
$875$	12.2462	+	21.2111i	0.413998	+	0.717065i
$876$		0			0
$877$	−4.86932	−	8.43390i	−0.164425	−	0.284793i	0.772026	−	0.635591i	$-0.219244\pi$
$877$	−4.86932	−	8.43390i	−0.164425	−	0.284793i	−0.936451	+	0.350798i	$0.885910\pi$
$878$		0			0
$879$	−29.4384			−0.992934
$880$		0			0
$881$	−0.623106	+	1.07925i	−0.0209930	+	0.0363609i	−0.876331	−	0.481709i	$-0.840016\pi$
$881$	−0.623106	+	1.07925i	−0.0209930	+	0.0363609i	0.855338	+	0.518070i	$0.173349\pi$
$882$		0			0
$883$	−20.0000			−0.673054			−0.336527	−	0.941674i	$-0.609252\pi$
$883$	−20.0000			−0.673054			−0.336527	+	0.941674i	$0.609252\pi$
$884$		0			0
$885$	23.3693			0.785551
$886$		0			0
$887$	4.15767	−	7.20130i	0.139601	−	0.241796i	−0.787745	−	0.616002i	$-0.788751\pi$
$887$	4.15767	−	7.20130i	0.139601	−	0.241796i	0.927346	+	0.374206i	$0.122085\pi$
$888$		0			0
$889$	−32.8078			−1.10034
$890$		0			0
$891$	−8.96543	−	15.5286i	−0.300353	−	0.520227i
$892$		0			0
$893$	5.12311	+	8.87348i	0.171438	+	0.296940i
$894$		0			0
$895$	−7.68466	+	13.3102i	−0.256870	+	0.444912i
$896$		0			0
$897$	26.8272	+	20.9380i	0.895733	+	0.699098i
$898$		0			0
$899$	20.0000	−	34.6410i	0.667037	−	1.15534i
$900$		0			0
$901$	11.0961	+	19.2190i	0.369665	+	0.640279i
$902$		0			0
$903$	21.5270	+	37.2858i	0.716373	+	1.24079i
$904$		0			0
$905$	34.9309			1.16114
$906$		0			0
$907$	6.65009	−	11.5183i	0.220813	−	0.382459i	−0.734242	−	0.678888i	$-0.762462\pi$
$907$	6.65009	−	11.5183i	0.220813	−	0.382459i	0.955055	+	0.296429i	$0.0957957\pi$
$908$		0			0
$909$	18.6847			0.619731
$910$		0			0
$911$	−18.7386			−0.620839			−0.310419	−	0.950600i	$-0.600469\pi$
$911$	−18.7386			−0.620839			−0.310419	+	0.950600i	$0.600469\pi$
$912$		0			0
$913$	−2.87689	+	4.98293i	−0.0952113	+	0.164911i
$914$		0			0
$915$	−66.1080			−2.18546
$916$		0			0
$917$	23.3693	+	40.4768i	0.771723	+	1.33666i
$918$		0			0
$919$	−5.77320	−	9.99947i	−0.190440	−	0.329852i	0.754956	−	0.655775i	$-0.227658\pi$
$919$	−5.77320	−	9.99947i	−0.190440	−	0.329852i	−0.945396	+	0.325923i	$0.894325\pi$
$920$		0			0
$921$	33.6155	−	58.2238i	1.10767	−	1.91854i
$922$		0			0
$923$	21.8423	+	17.0474i	0.718949	+	0.561122i
$924$		0			0
$925$	3.84233	−	6.65511i	0.126335	−	0.218819i
$926$		0			0
$927$	25.3693	+	43.9409i	0.833238	+	1.44321i
$928$		0			0
$929$	−13.9924	−	24.2356i	−0.459076	−	0.795144i	0.539836	−	0.841770i	$-0.318486\pi$
$929$	−13.9924	−	24.2356i	−0.459076	−	0.795144i	−0.998912	+	0.0466265i	$0.985153\pi$
$930$		0			0
$931$	−1.12311			−0.0368083
$932$		0			0
$933$	18.2462	−	31.6034i	0.597354	−	1.03465i
$934$		0			0
$935$	−45.6155			−1.49179
$936$		0			0
$937$	−1.31534			−0.0429703			−0.0214852	−	0.999769i	$-0.506839\pi$
$937$	−1.31534			−0.0429703			−0.0214852	+	0.999769i	$0.506839\pi$
$938$		0			0
$939$	−41.3002	+	71.5340i	−1.34778	+	2.33442i
$940$		0			0
$941$	14.0000			0.456387			0.228193	−	0.973616i	$-0.426718\pi$
$941$	14.0000			0.456387			0.228193	+	0.973616i	$0.426718\pi$
$942$		0			0
$943$	−17.0346	−	29.5047i	−0.554722	−	0.960806i
$944$		0			0
$945$	−6.56155	−	11.3649i	−0.213447	−	0.369702i
$946$		0			0
$947$	−23.2116	+	40.2038i	−0.754277	+	1.30645i	0.191456	+	0.981501i	$0.438679\pi$
$947$	−23.2116	+	40.2038i	−0.754277	+	1.30645i	−0.945733	+	0.324945i	$0.894654\pi$
$948$		0			0
$949$	−4.39630	+	1.77879i	−0.142710	+	0.0577421i
$950$		0			0
$951$	21.0540	−	36.4666i	0.682722	−	1.18251i
$952$		0			0
$953$	2.59612	+	4.49661i	0.0840965	+	0.145659i	0.905006	−	0.425399i	$-0.139866\pi$
$953$	2.59612	+	4.49661i	0.0840965	+	0.145659i	−0.820909	+	0.571059i	$0.806533\pi$
$954$		0			0
$955$	7.68466	+	13.3102i	0.248670	+	0.430709i
$956$		0			0
$957$	−32.8078			−1.06052
$958$		0			0
$959$	27.5270	−	47.6781i	0.888893	−	1.53961i
$960$		0			0
$961$	33.0000			1.06452
$962$		0			0
$963$	13.1231			0.422886
$964$		0			0
$965$	5.34233	−	9.25319i	0.171976	−	0.297871i
$966$		0			0
$967$	−22.2462			−0.715390			−0.357695	−	0.933838i	$-0.616437\pi$
$967$	−22.2462			−0.715390			−0.357695	+	0.933838i	$0.616437\pi$
$968$		0			0
$969$	−16.4039	−	28.4124i	−0.526969	−	0.912736i
$970$		0			0
$971$	15.8423	+	27.4397i	0.508405	+	0.880582i	0.999953	+	0.00973207i	$0.00309786\pi$
$971$	15.8423	+	27.4397i	0.508405	+	0.880582i	−0.491548	+	0.870850i	$0.663569\pi$
$972$		0			0
$973$	25.2116	−	43.6679i	0.808248	−	1.39993i
$974$		0			0
$975$	9.84233	−	70.2883i	0.315207	−	2.25103i
$976$		0			0
$977$	7.62311	−	13.2036i	0.243885	−	0.422421i	−0.717933	−	0.696113i	$-0.754911\pi$
$977$	7.62311	−	13.2036i	0.243885	−	0.422421i	0.961817	+	0.273692i	$0.0882448\pi$
$978$		0			0
$979$	−12.4039	−	21.4842i	−0.396430	−	0.686637i
$980$		0			0
$981$	−14.6847	−	25.4346i	−0.468845	−	0.812063i
$982$		0			0
$983$	−40.9848			−1.30721			−0.653607	−	0.756834i	$-0.726745\pi$
$983$	−40.9848			−1.30721			−0.653607	+	0.756834i	$0.726745\pi$
$984$		0			0
$985$	4.12311	−	7.14143i	0.131373	−	0.227545i
$986$		0			0
$987$	26.2462			0.835426
$988$		0			0
$989$	24.1771			0.768786
$990$		0			0
$991$	28.6501	−	49.6234i	0.910100	−	1.57634i	0.0961794	−	0.995364i	$-0.469338\pi$
$991$	28.6501	−	49.6234i	0.910100	−	1.57634i	0.813921	−	0.580976i	$-0.197329\pi$
$992$		0			0
$993$	56.1771			1.78273
$994$		0			0
$995$	−16.8078	−	29.1119i	−0.532842	−	0.922909i
$996$		0			0
$997$	13.3769	+	23.1695i	0.423650	+	0.733784i	0.996293	−	0.0860208i	$-0.0274151\pi$
$997$	13.3769	+	23.1695i	0.423650	+	0.733784i	−0.572643	+	0.819805i	$0.694082\pi$
$998$		0			0
$999$	−0.719224	+	1.24573i	−0.0227552	+	0.0394132i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	208.2.i.e.113.2		4
3.2	odd	2		1872.2.t.s.1153.2		4
4.3	odd	2		104.2.i.b.9.1	✓	4
8.3	odd	2		832.2.i.o.321.2		4
8.5	even	2		832.2.i.l.321.1		4
12.11	even	2		936.2.t.f.217.2		4
13.3	even	3	inner	208.2.i.e.81.2		4
13.4	even	6		2704.2.a.r.1.1		2
13.6	odd	12		2704.2.f.l.337.2		4
13.7	odd	12		2704.2.f.l.337.1		4
13.9	even	3		2704.2.a.q.1.1		2
39.29	odd	6		1872.2.t.s.289.2		4
52.3	odd	6		104.2.i.b.81.1	yes	4
52.7	even	12		1352.2.f.d.337.3		4
52.11	even	12		1352.2.o.c.361.1		8
52.15	even	12		1352.2.o.c.361.2		8
52.19	even	12		1352.2.f.d.337.4		4
52.23	odd	6		1352.2.i.e.1329.1		4
52.31	even	4		1352.2.o.c.1161.2		8
52.35	odd	6		1352.2.a.f.1.2		2
52.43	odd	6		1352.2.a.h.1.2		2
52.47	even	4		1352.2.o.c.1161.1		8
52.51	odd	2		1352.2.i.e.529.1		4
104.3	odd	6		832.2.i.o.705.2		4
104.29	even	6		832.2.i.l.705.1		4
156.107	even	6		936.2.t.f.289.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.i.b.9.1	✓	4	4.3	odd	2
104.2.i.b.81.1	yes	4	52.3	odd	6
208.2.i.e.81.2		4	13.3	even	3	inner
208.2.i.e.113.2		4	1.1	even	1	trivial
832.2.i.l.321.1		4	8.5	even	2
832.2.i.l.705.1		4	104.29	even	6
832.2.i.o.321.2		4	8.3	odd	2
832.2.i.o.705.2		4	104.3	odd	6
936.2.t.f.217.2		4	12.11	even	2
936.2.t.f.289.2		4	156.107	even	6
1352.2.a.f.1.2		2	52.35	odd	6
1352.2.a.h.1.2		2	52.43	odd	6
1352.2.f.d.337.3		4	52.7	even	12
1352.2.f.d.337.4		4	52.19	even	12
1352.2.i.e.529.1		4	52.51	odd	2
1352.2.i.e.1329.1		4	52.23	odd	6
1352.2.o.c.361.1		8	52.11	even	12
1352.2.o.c.361.2		8	52.15	even	12
1352.2.o.c.1161.1		8	52.47	even	4
1352.2.o.c.1161.2		8	52.31	even	4
1872.2.t.s.289.2		4	39.29	odd	6
1872.2.t.s.1153.2		4	3.2	odd	2
2704.2.a.q.1.1		2	13.9	even	3
2704.2.a.r.1.1		2	13.4	even	6
2704.2.f.l.337.1		4	13.7	odd	12
2704.2.f.l.337.2		4	13.6	odd	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:	\( N \)	\(=\)	\( 208 = 2^{4} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	208.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.28078 - 2.21837i) q^{3} -3.56155 q^{5} +(-1.28078 - 2.21837i) q^{7} +(-1.78078 - 3.08440i) q^{9} +O(q^{10})\)	\(q+(1.28078 - 2.21837i) q^{3} -3.56155 q^{5} +(-1.28078 - 2.21837i) q^{7} +(-1.78078 - 3.08440i) q^{9} +(1.28078 - 2.21837i) q^{11} +(3.34233 - 1.35234i) q^{13} +(-4.56155 + 7.90084i) q^{15} +(2.50000 + 4.33013i) q^{17} +(-1.28078 - 2.21837i) q^{19} -6.56155 q^{21} +(-1.84233 + 3.19101i) q^{23} +7.68466 q^{25} -1.43845 q^{27} +(2.50000 - 4.33013i) q^{29} +8.00000 q^{31} +(-3.28078 - 5.68247i) q^{33} +(4.56155 + 7.90084i) q^{35} +(0.500000 - 0.866025i) q^{37} +(1.28078 - 9.14657i) q^{39} +(-4.62311 + 8.00745i) q^{41} +(-3.28078 - 5.68247i) q^{43} +(6.34233 + 10.9852i) q^{45} -4.00000 q^{47} +(0.219224 - 0.379706i) q^{49} +12.8078 q^{51} +4.43845 q^{53} +(-4.56155 + 7.90084i) q^{55} -6.56155 q^{57} +(-1.28078 - 2.21837i) q^{59} +(3.62311 + 6.27540i) q^{61} +(-4.56155 + 7.90084i) q^{63} +(-11.9039 + 4.81645i) q^{65} +(-4.71922 + 8.17394i) q^{67} +(4.71922 + 8.17394i) q^{69} +(3.84233 + 6.65511i) q^{71} -1.31534 q^{73} +(9.84233 - 17.0474i) q^{75} -6.56155 q^{77} +4.00000 q^{79} +(3.50000 - 6.06218i) q^{81} -2.24621 q^{83} +(-8.90388 - 15.4220i) q^{85} +(-6.40388 - 11.0918i) q^{87} +(4.84233 - 8.38716i) q^{89} +(-7.28078 - 5.68247i) q^{91} +(10.2462 - 17.7470i) q^{93} +(4.56155 + 7.90084i) q^{95} +(-1.40388 - 2.43160i) q^{97} -9.12311 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{3} - 6 q^{5} - q^{7} - 3 q^{9}+O(q^{10}) \) 4 * q + q^3 - 6 * q^5 - q^7 - 3 * q^9	\( 4 q + q^{3} - 6 q^{5} - q^{7} - 3 q^{9} + q^{11} + q^{13} - 10 q^{15} + 10 q^{17} - q^{19} - 18 q^{21} + 5 q^{23} + 6 q^{25} - 14 q^{27} + 10 q^{29} + 32 q^{31} - 9 q^{33} + 10 q^{35} + 2 q^{37} + q^{39} - 2 q^{41} - 9 q^{43} + 13 q^{45} - 16 q^{47} + 5 q^{49} + 10 q^{51} + 26 q^{53} - 10 q^{55} - 18 q^{57} - q^{59} - 2 q^{61} - 10 q^{63} - 27 q^{65} - 23 q^{67} + 23 q^{69} + 3 q^{71} - 30 q^{73} + 27 q^{75} - 18 q^{77} + 16 q^{79} + 14 q^{81} + 24 q^{83} - 15 q^{85} - 5 q^{87} + 7 q^{89} - 25 q^{91} + 8 q^{93} + 10 q^{95} + 15 q^{97} - 20 q^{99}+O(q^{100}) \) 4 * q + q^3 - 6 * q^5 - q^7 - 3 * q^9 + q^11 + q^13 - 10 * q^15 + 10 * q^17 - q^19 - 18 * q^21 + 5 * q^23 + 6 * q^25 - 14 * q^27 + 10 * q^29 + 32 * q^31 - 9 * q^33 + 10 * q^35 + 2 * q^37 + q^39 - 2 * q^41 - 9 * q^43 + 13 * q^45 - 16 * q^47 + 5 * q^49 + 10 * q^51 + 26 * q^53 - 10 * q^55 - 18 * q^57 - q^59 - 2 * q^61 - 10 * q^63 - 27 * q^65 - 23 * q^67 + 23 * q^69 + 3 * q^71 - 30 * q^73 + 27 * q^75 - 18 * q^77 + 16 * q^79 + 14 * q^81 + 24 * q^83 - 15 * q^85 - 5 * q^87 + 7 * q^89 - 25 * q^91 + 8 * q^93 + 10 * q^95 + 15 * q^97 - 20 * q^99

Introduction

L-functions

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