LMFDB - Embedded newform 260.2.bk.c.97.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(33,260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(260, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 11]))

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

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

chi := DirichletCharacter("260.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.bk (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:	$2.07611045255$
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} + 30 x^{18} + 371 x^{16} + 2460 x^{14} + 9517 x^{12} + 21870 x^{10} + 29001 x^{8} + 20400 x^{6} + \cdots + 9 $ x^20 + 30x^18 + 371x^16 + 2460x^14 + 9517x^12 + 21870x^10 + 29001x^8 + 20400x^6 + 6399x^4 + 666*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			97.2
Root			$1.70974i$ of defining polynomial
Character	$\chi$	$=$	260.97
Dual form			260.2.bk.c.193.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.563138 - 2.10166i) q^{3} +(1.75876 + 1.38086i) q^{5} +(1.25530 - 0.724750i) q^{7} +(-1.50178 + 0.867051i) q^{9} +O(q^{10})$	\(q+(-0.563138 - 2.10166i) q^{3} +(1.75876 + 1.38086i) q^{5} +(1.25530 - 0.724750i) q^{7} +(-1.50178 + 0.867051i) q^{9} +(4.39230 - 1.17691i) q^{11} +(-3.25262 - 1.55579i) q^{13} +(1.91167 - 4.47393i) q^{15} +(-5.20404 - 1.39442i) q^{17} +(0.379384 - 1.41588i) q^{19} +(-2.23009 - 2.23009i) q^{21} +(3.61547 - 0.968762i) q^{23} +(1.18646 + 4.85719i) q^{25} +(-1.94761 - 1.94761i) q^{27} +(0.251591 + 0.145256i) q^{29} +(-1.02636 + 1.02636i) q^{31} +(-4.94694 - 8.56835i) q^{33} +(3.20855 + 0.458737i) q^{35} +(6.21947 + 3.59081i) q^{37} +(-1.43806 + 7.71202i) q^{39} +(2.53542 + 9.46231i) q^{41} +(-2.36558 + 8.82848i) q^{43} +(-3.83854 - 0.548808i) q^{45} -4.46815i q^{47} +(-2.44948 + 4.24262i) q^{49} +11.7224i q^{51} +(3.60704 - 3.60704i) q^{53} +(9.35013 + 3.99524i) q^{55} -3.18934 q^{57} +(-5.41208 - 1.45016i) q^{59} +(6.00186 + 10.3955i) q^{61} +(-1.25679 + 2.17682i) q^{63} +(-3.57225 - 7.22766i) q^{65} +(0.739961 - 1.28165i) q^{67} +(-4.07202 - 7.05294i) q^{69} +(-11.0787 - 2.96852i) q^{71} -11.7133 q^{73} +(9.54003 - 5.22881i) q^{75} +(4.66070 - 4.66070i) q^{77} -5.42877i q^{79} +(-5.59760 + 9.69532i) q^{81} +12.0274i q^{83} +(-7.22716 - 9.63849i) q^{85} +(0.163598 - 0.610558i) q^{87} +(-3.62430 - 13.5261i) q^{89} +(-5.21058 + 0.404351i) q^{91} +(2.73505 + 1.57908i) q^{93} +(2.62237 - 1.96631i) q^{95} +(5.38955 + 9.33497i) q^{97} +(-5.57580 + 5.57580i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{3} + 12 q^{5} + 6 q^{7} - 12 q^{9}+O(q^{10}) $ 20 * q - 2 * q^3 + 12 * q^5 + 6 * q^7 - 12 * q^9	$ 20 q - 2 q^{3} + 12 q^{5} + 6 q^{7} - 12 q^{9} + 8 q^{13} - 20 q^{15} + 20 q^{19} - 12 q^{21} + 6 q^{23} + 2 q^{25} - 20 q^{27} + 24 q^{29} + 8 q^{31} - 10 q^{33} - 36 q^{35} + 4 q^{39} + 6 q^{41} + 38 q^{43} - 16 q^{45} + 14 q^{49} + 30 q^{53} + 2 q^{55} - 76 q^{57} - 24 q^{59} - 32 q^{61} - 24 q^{63} - 30 q^{65} + 22 q^{67} - 16 q^{69} - 44 q^{73} - 2 q^{75} - 12 q^{77} + 2 q^{81} + 50 q^{85} + 38 q^{87} - 30 q^{89} - 72 q^{91} - 48 q^{93} - 30 q^{95} + 46 q^{97} + 20 q^{99}+O(q^{100}) $ 20 * q - 2 * q^3 + 12 * q^5 + 6 * q^7 - 12 * q^9 + 8 * q^13 - 20 * q^15 + 20 * q^19 - 12 * q^21 + 6 * q^23 + 2 * q^25 - 20 * q^27 + 24 * q^29 + 8 * q^31 - 10 * q^33 - 36 * q^35 + 4 * q^39 + 6 * q^41 + 38 * q^43 - 16 * q^45 + 14 * q^49 + 30 * q^53 + 2 * q^55 - 76 * q^57 - 24 * q^59 - 32 * q^61 - 24 * q^63 - 30 * q^65 + 22 * q^67 - 16 * q^69 - 44 * q^73 - 2 * q^75 - 12 * q^77 + 2 * q^81 + 50 * q^85 + 38 * q^87 - 30 * q^89 - 72 * q^91 - 48 * q^93 - 30 * q^95 + 46 * q^97 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

$n$	$41$	$131$	$157$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	−0.563138	−	2.10166i	−0.325128	−	1.21339i	−0.914183	−	0.405301i	$-0.867167\pi$
$3$	−0.563138	−	2.10166i	−0.325128	−	1.21339i	0.589055	−	0.808093i	$-0.299500\pi$
$4$		0			0
$5$	1.75876	+	1.38086i	0.786540	+	0.617539i
$5$	1.75876	+	1.38086i	0.786540	+	0.617539i
$6$		0			0
$7$	1.25530	−	0.724750i	0.474460	−	0.273930i	−0.243645	−	0.969865i	$-0.578343\pi$
$7$	1.25530	−	0.724750i	0.474460	−	0.273930i	0.718105	+	0.695935i	$0.245010\pi$
$8$		0			0
$9$	−1.50178	+	0.867051i	−0.500592	+	0.289017i
$10$		0			0
$11$	4.39230	−	1.17691i	1.32433	−	0.354852i	0.473730	−	0.880670i	$-0.342907\pi$
$11$	4.39230	−	1.17691i	1.32433	−	0.354852i	0.850597	+	0.525818i	$0.176241\pi$
$12$		0			0
$13$	−3.25262	−	1.55579i	−0.902114	−	0.431498i
$13$	−3.25262	−	1.55579i	−0.902114	−	0.431498i
$14$		0			0
$15$	1.91167	−	4.47393i	0.493592	−	1.15516i
$16$		0			0
$17$	−5.20404	−	1.39442i	−1.26217	−	0.338196i	−0.435141	−	0.900362i	$-0.643302\pi$
$17$	−5.20404	−	1.39442i	−1.26217	−	0.338196i	−0.827024	+	0.562166i	$0.809968\pi$
$18$		0			0
$19$	0.379384	−	1.41588i	0.0870366	−	0.324825i	−0.908655	−	0.417547i	$-0.862890\pi$
$19$	0.379384	−	1.41588i	0.0870366	−	0.324825i	0.995692	+	0.0927216i	$0.0295567\pi$
$20$		0			0
$21$	−2.23009	−	2.23009i	−0.486645	−	0.486645i
$22$		0			0
$23$	3.61547	−	0.968762i	0.753877	−	0.202001i	0.138640	−	0.990343i	$-0.455727\pi$
$23$	3.61547	−	0.968762i	0.753877	−	0.202001i	0.615237	+	0.788342i	$0.289060\pi$
$24$		0			0
$25$	1.18646	+	4.85719i	0.237292	+	0.971438i
$26$		0			0
$27$	−1.94761	−	1.94761i	−0.374818	−	0.374818i
$28$		0			0
$29$	0.251591	+	0.145256i	0.0467193	+	0.0269734i	0.523178	−	0.852224i	$-0.324746\pi$
$29$	0.251591	+	0.145256i	0.0467193	+	0.0269734i	−0.476458	+	0.879197i	$0.658080\pi$
$30$		0			0
$31$	−1.02636	+	1.02636i	−0.184340	+	0.184340i	−0.793244	−	0.608904i	$-0.791609\pi$
$31$	−1.02636	+	1.02636i	−0.184340	+	0.184340i	0.608904	+	0.793244i	$0.291609\pi$
$32$		0			0
$33$	−4.94694	−	8.56835i	−0.861152	−	1.49156i
$34$		0			0
$35$	3.20855	+	0.458737i	0.542344	+	0.0775407i
$36$		0			0
$37$	6.21947	+	3.59081i	1.02247	+	0.590326i	0.914820	−	0.403862i	$-0.132333\pi$
$37$	6.21947	+	3.59081i	1.02247	+	0.590326i	0.107655	+	0.994188i	$0.465666\pi$
$38$		0			0
$39$	−1.43806	+	7.71202i	−0.230274	+	1.23491i
$40$		0			0
$41$	2.53542	+	9.46231i	0.395966	+	1.47776i	0.820129	+	0.572179i	$0.193902\pi$
$41$	2.53542	+	9.46231i	0.395966	+	1.47776i	−0.424163	+	0.905586i	$0.639432\pi$
$42$		0			0
$43$	−2.36558	+	8.82848i	−0.360748	+	1.34633i	0.512346	+	0.858779i	$0.328777\pi$
$43$	−2.36558	+	8.82848i	−0.360748	+	1.34633i	−0.873094	+	0.487552i	$0.837890\pi$
$44$		0			0
$45$	−3.83854	−	0.548808i	−0.572215	−	0.0818114i
$46$		0			0
$47$		−	4.46815i		−	0.651747i	−0.945413	−	0.325874i	$-0.894342\pi$
$47$		−	4.46815i		−	0.651747i	0.945413	−	0.325874i	$-0.105658\pi$
$48$		0			0
$49$	−2.44948	+	4.24262i	−0.349925	+	0.606088i
$50$		0			0
$51$			11.7224i			1.64146i
$52$		0			0
$53$	3.60704	−	3.60704i	0.495465	−	0.495465i	−0.414558	−	0.910023i	$-0.636064\pi$
$53$	3.60704	−	3.60704i	0.495465	−	0.495465i	0.910023	+	0.414558i	$0.136064\pi$
$54$		0			0
$55$	9.35013	+	3.99524i	1.26077	+	0.538717i
$56$		0			0
$57$	−3.18934			−0.422439
$58$		0			0
$59$	−5.41208	−	1.45016i	−0.704593	−	0.188795i	−0.111306	−	0.993786i	$-0.535503\pi$
$59$	−5.41208	−	1.45016i	−0.704593	−	0.188795i	−0.593287	+	0.804991i	$0.702170\pi$
$60$		0			0
$61$	6.00186	+	10.3955i	0.768459	+	1.33101i	0.938398	+	0.345556i	$0.112310\pi$
$61$	6.00186	+	10.3955i	0.768459	+	1.33101i	−0.169939	+	0.985455i	$0.554357\pi$
$62$		0			0
$63$	−1.25679	+	2.17682i	−0.158341	+	0.274254i
$64$		0			0
$65$	−3.57225	−	7.22766i	−0.443083	−	0.896481i
$66$		0			0
$67$	0.739961	−	1.28165i	0.0904006	−	0.156578i	−0.817279	−	0.576242i	$-0.804519\pi$
$67$	0.739961	−	1.28165i	0.0904006	−	0.156578i	0.907680	+	0.419664i	$0.137852\pi$
$68$		0			0
$69$	−4.07202	−	7.05294i	−0.490213	−	0.849074i
$70$		0			0
$71$	−11.0787	−	2.96852i	−1.31480	−	0.352299i	−0.467771	−	0.883850i	$-0.654943\pi$
$71$	−11.0787	−	2.96852i	−1.31480	−	0.352299i	−0.847026	+	0.531551i	$0.821610\pi$
$72$		0			0
$73$	−11.7133			−1.37093			−0.685466	−	0.728104i	$-0.740402\pi$
$73$	−11.7133			−1.37093			−0.685466	+	0.728104i	$0.740402\pi$
$74$		0			0
$75$	9.54003	−	5.22881i	1.10159	−	0.603770i
$76$		0			0
$77$	4.66070	−	4.66070i	0.531136	−	0.531136i
$78$		0			0
$79$		−	5.42877i		−	0.610784i	−0.952227	−	0.305392i	$-0.901212\pi$
$79$		−	5.42877i		−	0.610784i	0.952227	−	0.305392i	$-0.0987876\pi$
$80$		0			0
$81$	−5.59760	+	9.69532i	−0.621955	+	1.07726i
$82$		0			0
$83$			12.0274i			1.32018i	0.751188	+	0.660088i	$0.229481\pi$
$83$			12.0274i			1.32018i	−0.751188	+	0.660088i	$0.770519\pi$
$84$		0			0
$85$	−7.22716	−	9.63849i	−0.783895	−	1.04544i
$86$		0			0
$87$	0.163598	−	0.610558i	0.0175396	−	0.0654587i
$88$		0			0
$89$	−3.62430	−	13.5261i	−0.384175	−	1.43376i	−0.839463	−	0.543416i	$-0.817131\pi$
$89$	−3.62430	−	13.5261i	−0.384175	−	1.43376i	0.455288	−	0.890344i	$-0.349536\pi$
$90$		0			0
$91$	−5.21058	+	0.404351i	−0.546217	+	0.0423874i
$92$		0			0
$93$	2.73505	+	1.57908i	0.283611	+	0.163743i
$94$		0			0
$95$	2.62237	−	1.96631i	0.269050	−	0.201740i
$96$		0			0
$97$	5.38955	+	9.33497i	0.547226	+	0.947823i	0.998463	+	0.0554189i	$0.0176494\pi$
$97$	5.38955	+	9.33497i	0.547226	+	0.947823i	−0.451237	+	0.892404i	$0.649017\pi$
$98$		0			0
$99$	−5.57580	+	5.57580i	−0.560389	+	0.560389i
$100$		0			0
$101$	2.04621	+	1.18138i	0.203605	+	0.117552i	0.598336	−	0.801245i	$-0.295829\pi$
$101$	2.04621	+	1.18138i	0.203605	+	0.117552i	−0.394731	+	0.918797i	$0.629162\pi$
$102$		0			0
$103$	1.28773	+	1.28773i	0.126883	+	0.126883i	0.767697	−	0.640813i	$-0.221403\pi$
$103$	1.28773	+	1.28773i	0.126883	+	0.126883i	−0.640813	+	0.767697i	$0.721403\pi$
$104$		0			0
$105$	−0.842749	−	7.00162i	−0.0822439	−	0.683288i
$106$		0			0
$107$	11.2891	−	3.02490i	1.09136	−	0.292428i	0.332115	−	0.943239i	$-0.392238\pi$
$107$	11.2891	−	3.02490i	1.09136	−	0.292428i	0.759240	+	0.650811i	$0.225571\pi$
$108$		0			0
$109$	9.52541	+	9.52541i	0.912369	+	0.912369i	0.996458	−	0.0840895i	$-0.0267982\pi$
$109$	9.52541	+	9.52541i	0.912369	+	0.912369i	−0.0840895	+	0.996458i	$0.526798\pi$
$110$		0			0
$111$	4.04425	−	15.0933i	0.383863	−	1.43260i
$112$		0			0
$113$	−13.3917	−	3.58830i	−1.25979	−	0.337559i	−0.433677	−	0.901069i	$-0.642784\pi$
$113$	−13.3917	−	3.58830i	−1.25979	−	0.337559i	−0.826109	+	0.563510i	$0.809451\pi$
$114$		0			0
$115$	7.69646	+	3.28863i	0.717698	+	0.306667i
$116$		0			0
$117$	6.23365	−	0.483743i	0.576301	−	0.0447220i
$118$		0			0
$119$	−7.54326	+	2.02121i	−0.691489	+	0.185284i
$120$		0			0
$121$	8.38086	−	4.83869i	0.761897	−	0.439881i
$122$		0			0
$123$	18.4588	−	10.6572i	1.66437	−	0.960925i
$124$		0			0
$125$	−4.62040	+	10.1810i	−0.413261	+	0.910613i
$126$		0			0
$127$	−1.12904	−	4.21363i	−0.100186	−	0.373899i	0.897569	−	0.440875i	$-0.145332\pi$
$127$	−1.12904	−	4.21363i	−0.100186	−	0.373899i	−0.997755	+	0.0669757i	$0.978665\pi$
$128$		0			0
$129$	19.8866			1.75092
$130$		0			0
$131$	14.6339			1.27857			0.639286	−	0.768969i	$-0.279230\pi$
$131$	14.6339			1.27857			0.639286	+	0.768969i	$0.279230\pi$
$132$		0			0
$133$	−0.549917	−	2.05232i	−0.0476838	−	0.177958i
$134$		0			0
$135$	−0.736002	−	6.11476i	−0.0633449	−	0.526274i
$136$		0			0
$137$	0.671485	−	0.387682i	0.0573689	−	0.0331219i	−0.471041	−	0.882111i	$-0.656122\pi$
$137$	0.671485	−	0.387682i	0.0573689	−	0.0331219i	0.528410	+	0.848989i	$0.322788\pi$
$138$		0			0
$139$	−19.7398	+	11.3968i	−1.67431	+	0.966664i	−0.709132	+	0.705076i	$0.750913\pi$
$139$	−19.7398	+	11.3968i	−1.67431	+	0.966664i	−0.965180	+	0.261588i	$0.915754\pi$
$140$		0			0
$141$	−9.39054	+	2.51619i	−0.790826	+	0.211901i
$142$		0			0
$143$	−16.1175	−	3.00543i	−1.34781	−	0.251327i
$144$		0			0
$145$	0.241909	+	0.602882i	0.0200895	+	0.0500666i
$146$		0			0
$147$	10.2959	+	2.75879i	0.849194	+	0.227541i
$148$		0			0
$149$	1.79239	−	6.68928i	0.146838	−	0.548007i	−0.852829	−	0.522191i	$-0.825115\pi$
$149$	1.79239	−	6.68928i	0.146838	−	0.548007i	0.999667	−	0.0258163i	$-0.00821850\pi$
$150$		0			0
$151$	−1.60288	−	1.60288i	−0.130440	−	0.130440i	0.638872	−	0.769313i	$-0.279401\pi$
$151$	−1.60288	−	1.60288i	−0.130440	−	0.130440i	−0.769313	+	0.638872i	$0.779401\pi$
$152$		0			0
$153$	9.02434	−	2.41806i	0.729575	−	0.195489i
$154$		0			0
$155$	−3.22238	+	0.387862i	−0.258828	+	0.0311538i
$156$		0			0
$157$	−3.08174	−	3.08174i	−0.245950	−	0.245950i	0.573356	−	0.819306i	$-0.305641\pi$
$157$	−3.08174	−	3.08174i	−0.245950	−	0.245950i	−0.819306	+	0.573356i	$0.805641\pi$
$158$		0			0
$159$	−9.61203	−	5.54951i	−0.762283	−	0.440104i
$160$		0			0
$161$	3.83640	−	3.83640i	0.302351	−	0.302351i
$162$		0			0
$163$	0.985666	+	1.70722i	0.0772033	+	0.133720i	0.902042	−	0.431648i	$-0.142068\pi$
$163$	0.985666	+	1.70722i	0.0772033	+	0.133720i	−0.824839	+	0.565368i	$0.808734\pi$
$164$		0			0
$165$	3.13121	−	21.9007i	0.243764	−	1.70497i
$166$		0			0
$167$	−13.2648	−	7.65842i	−1.02646	−	0.592626i	−0.110490	−	0.993877i	$-0.535242\pi$
$167$	−13.2648	−	7.65842i	−1.02646	−	0.592626i	−0.915968	+	0.401251i	$0.868575\pi$
$168$		0			0
$169$	8.15906	+	10.1208i	0.627620	+	0.778520i
$170$		0			0
$171$	0.657890	+	2.45528i	0.0503101	+	0.187760i
$172$		0			0
$173$	0.567617	−	2.11838i	0.0431552	−	0.161057i	−0.940986	−	0.338447i	$-0.890099\pi$
$173$	0.567617	−	2.11838i	0.0431552	−	0.161057i	0.984141	+	0.177389i	$0.0567652\pi$
$174$		0			0
$175$	5.00962	+	5.23736i	0.378691	+	0.395907i
$176$		0			0
$177$			12.1910i			0.916332i
$178$		0			0
$179$	12.3526	−	21.3953i	0.923275	−	1.59916i	0.128963	−	0.991649i	$-0.458835\pi$
$179$	12.3526	−	21.3953i	0.923275	−	1.59916i	0.794312	−	0.607510i	$-0.207831\pi$
$180$		0			0
$181$		−	10.9512i		−	0.813995i	−0.913429	−	0.406997i	$-0.866576\pi$
$181$		−	10.9512i		−	0.813995i	0.913429	−	0.406997i	$-0.133424\pi$
$182$		0			0
$183$	18.4680	−	18.4680i	1.36519	−	1.36519i
$184$		0			0
$185$	5.98014	+	14.9036i	0.439668	+	1.09573i
$186$		0			0
$187$	−24.4988			−1.79153
$188$		0			0
$189$	−3.85638	−	1.03331i	−0.280510	−	0.0751625i
$190$		0			0
$191$	−11.3738	−	19.7000i	−0.822977	−	1.42544i	−0.903455	−	0.428682i	$-0.858978\pi$
$191$	−11.3738	−	19.7000i	−0.822977	−	1.42544i	0.0804781	−	0.996756i	$-0.474355\pi$
$192$		0			0
$193$	−5.06182	+	8.76733i	−0.364358	+	0.631086i	−0.988673	−	0.150086i	$-0.952045\pi$
$193$	−5.06182	+	8.76733i	−0.364358	+	0.631086i	0.624315	+	0.781173i	$0.285378\pi$
$194$		0			0
$195$	−13.1784	+	11.5778i	−0.943726	+	0.829105i
$196$		0			0
$197$	2.68286	−	4.64685i	0.191146	−	0.331074i	−0.754484	−	0.656318i	$-0.772113\pi$
$197$	2.68286	−	4.64685i	0.191146	−	0.331074i	0.945630	+	0.325244i	$0.105446\pi$
$198$		0			0
$199$	7.93978	+	13.7521i	0.562836	+	0.974861i	0.997247	+	0.0741463i	$0.0236232\pi$
$199$	7.93978	+	13.7521i	0.562836	+	0.974861i	−0.434411	+	0.900715i	$0.643044\pi$
$200$		0			0
$201$	−3.11029	−	0.833400i	−0.219383	−	0.0587835i
$202$		0			0
$203$	0.421097			0.0295552
$204$		0			0
$205$	−8.60692	+	20.1430i	−0.601134	+	1.40685i
$206$		0			0
$207$	−4.58966	+	4.58966i	−0.319003	+	0.319003i
$208$		0			0
$209$		−	6.66546i		−	0.461060i
$210$		0			0
$211$	−9.83794	+	17.0398i	−0.677272	+	1.17307i	0.298528	+	0.954401i	$0.403504\pi$
$211$	−9.83794	+	17.0398i	−0.677272	+	1.17307i	−0.975799	+	0.218668i	$0.929829\pi$
$212$		0			0
$213$			24.9553i			1.70991i
$214$		0			0
$215$	−16.3514	+	12.2606i	−1.11515	+	0.836168i
$216$		0			0
$217$	−0.544540	+	2.03225i	−0.0369658	+	0.137958i
$218$		0			0
$219$	6.59618	+	24.6173i	0.445729	+	1.66348i
$220$		0			0
$221$	14.7573	+	12.6319i	0.992687	+	0.849713i
$222$		0			0
$223$	−18.8536	−	10.8851i	−1.26253	−	0.728921i	−0.288965	−	0.957340i	$-0.593311\pi$
$223$	−18.8536	−	10.8851i	−1.26253	−	0.728921i	−0.973563	+	0.228418i	$0.926645\pi$
$224$		0			0
$225$	−5.99323	−	6.26569i	−0.399549	−	0.417713i
$226$		0			0
$227$	2.47032	+	4.27872i	0.163961	+	0.283989i	0.936286	−	0.351239i	$-0.114240\pi$
$227$	2.47032	+	4.27872i	0.163961	+	0.283989i	−0.772325	+	0.635228i	$0.780906\pi$
$228$		0			0
$229$	12.3403	−	12.3403i	0.815468	−	0.815468i	−0.169980	−	0.985448i	$-0.554370\pi$
$229$	12.3403	−	12.3403i	0.815468	−	0.815468i	0.985448	+	0.169980i	$0.0543702\pi$
$230$		0			0
$231$	−12.4198	−	7.17059i	−0.817164	−	0.471790i
$232$		0			0
$233$	7.98171	+	7.98171i	0.522899	+	0.522899i	0.918446	−	0.395547i	$-0.129445\pi$
$233$	7.98171	+	7.98171i	0.522899	+	0.522899i	−0.395547	+	0.918446i	$0.629445\pi$
$234$		0			0
$235$	6.16989	−	7.85840i	0.402479	−	0.512626i
$236$		0			0
$237$	−11.4094	+	3.05715i	−0.741122	+	0.198583i
$238$		0			0
$239$	−4.23426	−	4.23426i	−0.273891	−	0.273891i	0.556773	−	0.830665i	$-0.312039\pi$
$239$	−4.23426	−	4.23426i	−0.273891	−	0.273891i	−0.830665	+	0.556773i	$0.812039\pi$
$240$		0			0
$241$	5.61985	−	20.9736i	0.362006	−	1.35103i	−0.509428	−	0.860513i	$-0.670143\pi$
$241$	5.61985	−	20.9736i	0.362006	−	1.35103i	0.871434	−	0.490512i	$-0.163190\pi$
$242$		0			0
$243$	15.5470	+	4.16582i	0.997343	+	0.267237i
$244$		0			0
$245$	−10.1665	+	4.07936i	−0.649513	+	0.260620i
$246$		0			0
$247$	−3.43680	+	4.01508i	−0.218678	+	0.255473i
$248$		0			0
$249$	25.2775	−	6.77308i	1.60189	−	0.429226i
$250$		0			0
$251$	21.8296	−	12.6033i	1.37787	−	0.795514i	0.385967	−	0.922513i	$-0.373868\pi$
$251$	21.8296	−	12.6033i	1.37787	−	0.795514i	0.991903	+	0.126999i	$0.0405345\pi$
$252$		0			0
$253$	14.7401	−	8.51018i	0.926700	−	0.535030i
$254$		0			0
$255$	−16.1869	+	20.6168i	−1.01367	+	1.29108i
$256$		0			0
$257$	3.26976	+	12.2029i	0.203962	+	0.761197i	0.989763	+	0.142718i	$0.0455841\pi$
$257$	3.26976	+	12.2029i	0.203962	+	0.761197i	−0.785801	+	0.618479i	$0.787749\pi$
$258$		0			0
$259$	10.4098			0.646831
$260$		0			0
$261$	−0.503778			−0.0311831
$262$		0			0
$263$	3.49468	+	13.0423i	0.215491	+	0.804223i	0.985993	+	0.166786i	$0.0533389\pi$
$263$	3.49468	+	13.0423i	0.215491	+	0.804223i	−0.770502	+	0.637437i	$0.779994\pi$
$264$		0			0
$265$	11.3247	−	1.36310i	0.695671	−	0.0837344i
$266$		0			0
$267$	−26.3862	+	15.2341i	−1.61481	+	0.932311i
$268$		0			0
$269$	−14.0205	+	8.09471i	−0.854842	+	0.493543i	−0.862282	−	0.506429i	$-0.830965\pi$
$269$	−14.0205	+	8.09471i	−0.854842	+	0.493543i	0.00743940	+	0.999972i	$0.497632\pi$
$270$		0			0
$271$	−11.1884	+	2.99792i	−0.679647	+	0.182111i	−0.582096	−	0.813120i	$-0.697767\pi$
$271$	−11.1884	+	2.99792i	−0.679647	+	0.182111i	−0.0975504	+	0.995231i	$0.531101\pi$
$272$		0			0
$273$	3.78408	+	10.7232i	0.229023	+	0.648995i
$274$		0			0
$275$	10.9278	+	19.9379i	0.658969	+	1.20230i
$276$		0			0
$277$	−24.9803	−	6.69346i	−1.50092	−	0.402171i	−0.587514	−	0.809214i	$-0.699893\pi$
$277$	−24.9803	−	6.69346i	−1.50092	−	0.402171i	−0.913409	+	0.407043i	$0.866560\pi$
$278$		0			0
$279$	0.651458	−	2.43127i	0.0390018	−	0.145557i
$280$		0			0
$281$	−14.6609	−	14.6609i	−0.874597	−	0.874597i	0.118372	−	0.992969i	$-0.462232\pi$
$281$	−14.6609	−	14.6609i	−0.874597	−	0.874597i	−0.992969	+	0.118372i	$0.962232\pi$
$282$		0			0
$283$	−3.27181	+	0.876680i	−0.194489	+	0.0521132i	−0.354749	−	0.934962i	$-0.615434\pi$
$283$	−3.27181	+	0.876680i	−0.194489	+	0.0521132i	0.160259	+	0.987075i	$0.448767\pi$
$284$		0			0
$285$	−5.60929	−	4.40403i	−0.332265	−	0.260872i
$286$		0			0
$287$	10.0405	+	10.0405i	0.592674	+	0.592674i
$288$		0			0
$289$	10.4152	+	6.01323i	0.612660	+	0.353719i
$290$		0			0
$291$	16.5839	−	16.5839i	0.972164	−	0.972164i
$292$		0			0
$293$	12.6537	+	21.9169i	0.739240	+	1.28040i	0.952838	+	0.303479i	$0.0981482\pi$
$293$	12.6537	+	21.9169i	0.739240	+	1.28040i	−0.213599	+	0.976922i	$0.568518\pi$
$294$		0			0
$295$	−7.51608	−	10.0238i	−0.437603	−	0.583609i
$296$		0			0
$297$	−10.8467	−	6.26232i	−0.629387	−	0.363377i
$298$		0			0
$299$	−13.2669	−	2.47388i	−0.767246	−	0.143068i
$300$		0			0
$301$	3.42891	+	12.7969i	0.197639	+	0.737600i
$302$		0			0
$303$	1.33056	−	4.96571i	0.0764386	−	0.285273i
$304$		0			0
$305$	−3.79893	+	26.5709i	−0.217526	+	1.52145i
$306$		0			0
$307$		−	12.8252i		−	0.731974i	−0.930620	−	0.365987i	$-0.880731\pi$
$307$		−	12.8252i		−	0.731974i	0.930620	−	0.365987i	$-0.119269\pi$
$308$		0			0
$309$	1.98119	−	3.43153i	0.112706	−	0.195213i
$310$		0			0
$311$			1.59622i			0.0905134i	0.998975	+	0.0452567i	$0.0144106\pi$
$311$			1.59622i			0.0905134i	−0.998975	+	0.0452567i	$0.985589\pi$
$312$		0			0
$313$	19.0754	−	19.0754i	1.07821	−	1.07821i	0.0815374	−	0.996670i	$-0.474017\pi$
$313$	19.0754	−	19.0754i	1.07821	−	1.07821i	0.996670	−	0.0815374i	$-0.0259830\pi$
$314$		0			0
$315$	−5.21628	+	2.09306i	−0.293904	+	0.117930i
$316$		0			0
$317$	15.6088			0.876680			0.438340	−	0.898809i	$-0.355567\pi$
$317$	15.6088			0.876680			0.438340	+	0.898809i	$0.355567\pi$
$318$		0			0
$319$	1.27602	+	0.341907i	0.0714431	+	0.0191431i
$320$		0			0
$321$	−12.7146	−	22.0224i	−0.709660	−	1.22917i
$322$		0			0
$323$	−3.94866	+	6.83928i	−0.219709	+	0.380548i
$324$		0			0
$325$	3.69765	−	17.6445i	0.205109	−	0.978739i
$326$		0			0
$327$	14.6551	−	25.3833i	0.810426	−	1.40370i
$328$		0			0
$329$	−3.23829	−	5.60889i	−0.178533	−	0.309228i
$330$		0			0
$331$	−25.7600	−	6.90237i	−1.41590	−	0.379388i	−0.531870	−	0.846826i	$-0.678511\pi$
$331$	−25.7600	−	6.90237i	−1.41590	−	0.379388i	−0.884026	+	0.467438i	$0.845177\pi$
$332$		0			0
$333$	−12.4537			−0.682457
$334$		0			0
$335$	3.07119	−	1.23233i	0.167797	−	0.0673294i
$336$		0			0
$337$	−1.54193	+	1.54193i	−0.0839941	+	0.0839941i	−0.747856	−	0.663861i	$-0.768916\pi$
$337$	−1.54193	+	1.54193i	−0.0839941	+	0.0839941i	0.663861	+	0.747856i	$0.268916\pi$
$338$		0			0
$339$			30.1655i			1.63837i
$340$		0			0
$341$	−3.30015	+	5.71602i	−0.178713	+	0.309540i
$342$		0			0
$343$			17.2475i			0.931279i
$344$		0			0
$345$	2.57742	−	18.0273i	0.138764	−	0.970557i
$346$		0			0
$347$	−2.59818	+	9.69655i	−0.139478	+	0.520538i	0.860461	+	0.509516i	$0.170175\pi$
$347$	−2.59818	+	9.69655i	−0.139478	+	0.520538i	−0.999939	+	0.0110226i	$0.996491\pi$
$348$		0			0
$349$	−5.70030	−	21.2738i	−0.305130	−	1.13876i	−0.932833	−	0.360308i	$-0.882671\pi$
$349$	−5.70030	−	21.2738i	−0.305130	−	1.13876i	0.627703	−	0.778453i	$-0.283995\pi$
$350$		0			0
$351$	3.30477	+	9.36491i	0.176396	+	0.499862i
$352$		0			0
$353$	−15.9958	−	9.23518i	−0.851371	−	0.491539i	0.00974252	−	0.999953i	$-0.496899\pi$
$353$	−15.9958	−	9.23518i	−0.851371	−	0.491539i	−0.861113	+	0.508414i	$0.830232\pi$
$354$		0			0
$355$	−15.3856	−	20.5190i	−0.816583	−	1.08904i
$356$		0			0
$357$	8.49579	+	14.7151i	0.449645	+	0.778808i
$358$		0			0
$359$	15.6227	−	15.6227i	0.824534	−	0.824534i	−0.162220	−	0.986755i	$-0.551865\pi$
$359$	15.6227	−	15.6227i	0.824534	−	0.824534i	0.986755	+	0.162220i	$0.0518655\pi$
$360$		0			0
$361$	14.5937	+	8.42568i	0.768089	+	0.443457i
$362$		0			0
$363$	−14.8889	−	14.8889i	−0.781463	−	0.781463i
$364$		0			0
$365$	−20.6008	−	16.1743i	−1.07829	−	0.846604i
$366$		0			0
$367$	36.1290	−	9.68075i	1.88592	−	0.505331i	0.886858	−	0.462041i	$-0.152883\pi$
$367$	36.1290	−	9.68075i	1.88592	−	0.505331i	0.999063	−	0.0432899i	$-0.0137839\pi$
$368$		0			0
$369$	−12.0119	−	12.0119i	−0.625316	−	0.625316i
$370$		0			0
$371$	1.91373	−	7.14212i	0.0993557	−	0.370801i
$372$		0			0
$373$	15.1071	+	4.04794i	0.782218	+	0.209595i	0.627762	−	0.778405i	$-0.283971\pi$
$373$	15.1071	+	4.04794i	0.782218	+	0.209595i	0.154455	+	0.988000i	$0.450638\pi$
$374$		0			0
$375$	23.9988	+	3.97723i	1.23929	+	0.205383i
$376$		0			0
$377$	−0.592342	−	0.863884i	−0.0305072	−	0.0444923i
$378$		0			0
$379$	4.09134	−	1.09627i	0.210158	−	0.0563117i	−0.152204	−	0.988349i	$-0.548637\pi$
$379$	4.09134	−	1.09627i	0.210158	−	0.0563117i	0.362362	+	0.932037i	$0.381970\pi$
$380$		0			0
$381$	−8.21981	+	4.74571i	−0.421114	+	0.243130i
$382$		0			0
$383$	12.5287	−	7.23343i	0.640185	−	0.369611i	−0.144501	−	0.989505i	$-0.546158\pi$
$383$	12.5287	−	7.23343i	0.640185	−	0.369611i	0.784686	+	0.619894i	$0.212824\pi$
$384$		0			0
$385$	14.6328	−	1.76128i	0.745757	−	0.0897629i
$386$		0			0
$387$	−4.10216	−	15.3095i	−0.208525	−	0.778225i
$388$		0			0
$389$	−3.89275			−0.197370			−0.0986852	−	0.995119i	$-0.531464\pi$
$389$	−3.89275			−0.197370			−0.0986852	+	0.995119i	$0.531464\pi$
$390$		0			0
$391$	−20.1659			−1.01983
$392$		0			0
$393$	−8.24093	−	30.7556i	−0.415700	−	1.55141i
$394$		0			0
$395$	7.49636	−	9.54789i	0.377183	−	0.480407i
$396$		0			0
$397$	−0.921577	+	0.532073i	−0.0462526	+	0.0267040i	−0.522948	−	0.852365i	$-0.675168\pi$
$397$	−0.921577	+	0.532073i	−0.0462526	+	0.0267040i	0.476695	+	0.879069i	$0.341834\pi$
$398$		0			0
$399$	−4.00359	+	2.31148i	−0.200430	+	0.115719i
$400$		0			0
$401$	19.6698	−	5.27051i	0.982263	−	0.263197i	0.268266	−	0.963345i	$-0.413549\pi$
$401$	19.6698	−	5.27051i	0.982263	−	0.263197i	0.713997	+	0.700148i	$0.246883\pi$
$402$		0			0
$403$	4.93516	−	1.74156i	0.245838	−	0.0867535i
$404$		0			0
$405$	−23.2327	+	9.32224i	−1.15444	+	0.463226i
$406$		0			0
$407$	31.5438	+	8.45214i	1.56357	+	0.418957i
$408$		0			0
$409$	5.49767	−	20.5176i	0.271842	−	1.01453i	−0.686085	−	0.727521i	$-0.740672\pi$
$409$	5.49767	−	20.5176i	0.271842	−	1.01453i	0.957928	−	0.287009i	$-0.0926610\pi$
$410$		0			0
$411$	−1.19292	−	1.19292i	−0.0588422	−	0.0588422i
$412$		0			0
$413$	−7.84481	+	2.10201i	−0.386018	+	0.103433i
$414$		0			0
$415$	−16.6081	+	21.1533i	−0.815260	+	1.03837i
$416$		0			0
$417$	35.0685	+	35.0685i	1.71731	+	1.71731i
$418$		0			0
$419$	−3.58399	−	2.06922i	−0.175089	−	0.101088i	0.409894	−	0.912133i	$-0.365566\pi$
$419$	−3.58399	−	2.06922i	−0.175089	−	0.101088i	−0.584983	+	0.811045i	$0.698899\pi$
$420$		0			0
$421$	14.3449	−	14.3449i	0.699129	−	0.699129i	−0.265094	−	0.964223i	$-0.585403\pi$
$421$	14.3449	−	14.3449i	0.699129	−	0.699129i	0.964223	+	0.265094i	$0.0854029\pi$
$422$		0			0
$423$	3.87412	+	6.71017i	0.188366	+	0.326260i
$424$		0			0
$425$	0.598575	−	26.9315i	0.0290352	−	1.30637i
$426$		0			0
$427$	15.0683	+	8.69969i	0.729207	+	0.421008i
$428$		0			0
$429$	2.75998	+	35.5660i	0.133253	+	1.71714i
$430$		0			0
$431$	−6.87880	−	25.6720i	−0.331340	−	1.23658i	−0.907783	−	0.419440i	$-0.862226\pi$
$431$	−6.87880	−	25.6720i	−0.331340	−	1.23658i	0.576443	−	0.817137i	$-0.304440\pi$
$432$		0			0
$433$	−3.86366	+	14.4194i	−0.185676	+	0.692951i	0.808809	+	0.588071i	$0.200112\pi$
$433$	−3.86366	+	14.4194i	−0.185676	+	0.692951i	−0.994485	+	0.104880i	$0.966554\pi$
$434$		0			0
$435$	1.13082	−	0.847917i	0.0542189	−	0.0406545i
$436$		0			0
$437$		−	5.48660i		−	0.262460i
$438$		0			0
$439$	−0.947472	+	1.64107i	−0.0452204	+	0.0783240i	−0.887750	−	0.460327i	$-0.847732\pi$
$439$	−0.947472	+	1.64107i	−0.0452204	+	0.0783240i	0.842529	+	0.538651i	$0.181066\pi$
$440$		0			0
$441$		−	8.49528i		−	0.404537i
$442$		0			0
$443$	−9.19043	+	9.19043i	−0.436651	+	0.436651i	−0.890883	−	0.454232i	$-0.849914\pi$
$443$	−9.19043	+	9.19043i	−0.436651	+	0.436651i	0.454232	+	0.890883i	$0.349914\pi$
$444$		0			0
$445$	12.3033	−	28.7937i	0.583233	−	1.36495i
$446$		0			0
$447$	−15.0680			−0.712690
$448$		0			0
$449$	4.59242	+	1.23053i	0.216730	+	0.0580725i	0.365550	−	0.930792i	$-0.380881\pi$
$449$	4.59242	+	1.23053i	0.216730	+	0.0580725i	−0.148820	+	0.988864i	$0.547548\pi$
$450$		0			0
$451$	22.2726	+	38.5773i	1.04878	+	1.81653i
$452$		0			0
$453$	−2.46606	+	4.27135i	−0.115866	+	0.200686i
$454$		0			0
$455$	−9.72250	−	6.48392i	−0.455798	−	0.303971i
$456$		0			0
$457$	−12.5494	+	21.7363i	−0.587038	+	1.01678i	0.407580	+	0.913169i	$0.366373\pi$
$457$	−12.5494	+	21.7363i	−0.587038	+	1.01678i	−0.994618	+	0.103610i	$0.966961\pi$
$458$		0			0
$459$	7.41967	+	12.8512i	0.346321	+	0.599845i
$460$		0			0
$461$	1.24463	+	0.333498i	0.0579683	+	0.0155326i	0.287687	−	0.957725i	$-0.407114\pi$
$461$	1.24463	+	0.333498i	0.0579683	+	0.0155326i	−0.229718	+	0.973257i	$0.573780\pi$
$462$		0			0
$463$	21.0066			0.976260			0.488130	−	0.872771i	$-0.337679\pi$
$463$	21.0066			0.976260			0.488130	+	0.872771i	$0.337679\pi$
$464$		0			0
$465$	2.62980	+	6.55393i	0.121954	+	0.303931i
$466$		0			0
$467$	7.95409	−	7.95409i	0.368071	−	0.368071i	−0.498702	−	0.866773i	$-0.666190\pi$
$467$	7.95409	−	7.95409i	0.368071	−	0.368071i	0.866773	+	0.498702i	$0.166190\pi$
$468$		0			0
$469$		−	2.14514i		−	0.0990536i
$470$		0			0
$471$	−4.74133	+	8.21222i	−0.218469	+	0.378399i
$472$		0			0
$473$			41.5614i			1.91099i
$474$		0			0
$475$	7.32732	+	0.162856i	0.336201	+	0.00747235i
$476$		0			0
$477$	−2.28948	+	8.54445i	−0.104828	+	0.391223i
$478$		0			0
$479$	−5.51597	−	20.5859i	−0.252031	−	0.940592i	−0.969718	−	0.244227i	$-0.921466\pi$
$479$	−5.51597	−	20.5859i	−0.252031	−	0.940592i	0.717687	−	0.696366i	$-0.245201\pi$
$480$		0			0
$481$	−14.6430	−	21.3557i	−0.667664	−	0.973736i
$482$		0			0
$483$	−10.2232	−	5.90239i	−0.465173	−	0.268568i
$484$		0			0
$485$	−3.41136	+	23.8602i	−0.154902	+	1.08343i
$486$		0			0
$487$	−15.1379	−	26.2196i	−0.685963	−	1.18812i	−0.973133	−	0.230243i	$-0.926048\pi$
$487$	−15.1379	−	26.2196i	−0.685963	−	1.18812i	0.287171	−	0.957879i	$-0.407285\pi$
$488$		0			0
$489$	3.03294	−	3.03294i	0.137154	−	0.137154i
$490$		0			0
$491$	7.93926	+	4.58373i	0.358294	+	0.206861i	0.668332	−	0.743863i	$-0.267009\pi$
$491$	7.93926	+	4.58373i	0.358294	+	0.206861i	−0.310038	+	0.950724i	$0.600342\pi$
$492$		0			0
$493$	−1.10674	−	1.10674i	−0.0498451	−	0.0498451i
$494$		0			0
$495$	−17.5059	+	2.10709i	−0.786831	+	0.0947068i
$496$		0			0
$497$	−16.0585	+	4.30287i	−0.720324	+	0.193010i
$498$		0			0
$499$	−15.0223	−	15.0223i	−0.672489	−	0.672489i	0.285800	−	0.958289i	$-0.407741\pi$
$499$	−15.0223	−	15.0223i	−0.672489	−	0.672489i	−0.958289	+	0.285800i	$0.907741\pi$
$500$		0			0
$501$	−8.62550	+	32.1908i	−0.385359	+	1.43818i
$502$		0			0
$503$	27.2502	+	7.30167i	1.21503	+	0.325565i	0.808732	−	0.588177i	$-0.200154\pi$
$503$	27.2502	+	7.30167i	1.21503	+	0.325565i	0.406294	+	0.913742i	$0.366821\pi$
$504$		0			0
$505$	1.96747	+	4.90328i	0.0875512	+	0.218193i
$506$		0			0
$507$	16.6757	−	22.8470i	0.740595	−	1.01467i
$508$		0			0
$509$	−10.9997	+	2.94735i	−0.487552	+	0.130639i	−0.494217	−	0.869339i	$-0.664545\pi$
$509$	−10.9997	+	2.94735i	−0.487552	+	0.130639i	0.00666482	+	0.999978i	$0.497879\pi$
$510$		0			0
$511$	−14.7037	+	8.48918i	−0.650453	+	0.375539i
$512$		0			0
$513$	−3.49648	+	2.01869i	−0.154373	+	0.0891275i
$514$		0			0
$515$	0.486631	+	4.04296i	0.0214435	+	0.178154i
$516$		0			0
$517$	−5.25863	−	19.6255i	−0.231274	−	0.863127i
$518$		0			0
$519$	−4.77176			−0.209457
$520$		0			0
$521$	−26.2904			−1.15180			−0.575902	−	0.817519i	$-0.695349\pi$
$521$	−26.2904			−1.15180			−0.575902	+	0.817519i	$0.695349\pi$
$522$		0			0
$523$	−6.15518	−	22.9715i	−0.269147	−	1.00447i	−0.959663	−	0.281154i	$-0.909283\pi$
$523$	−6.15518	−	22.9715i	−0.269147	−	1.00447i	0.690515	−	0.723318i	$-0.257384\pi$
$524$		0			0
$525$	8.18605	−	13.4779i	0.357269	−	0.588222i
$526$		0			0
$527$	6.77241	−	3.91005i	0.295011	−	0.170324i
$528$		0			0
$529$	−7.78547	+	4.49495i	−0.338499	+	0.195432i
$530$		0			0
$531$	9.38511	−	2.51473i	0.407279	−	0.109130i
$532$		0			0
$533$	6.47459	−	34.7219i	0.280445	−	1.50397i
$534$		0			0
$535$	24.0317	+	10.2685i	1.03898	+	0.443948i
$536$		0			0
$537$	−51.9218	−	13.9124i	−2.24059	−	0.600365i
$538$		0			0
$539$	−5.76564	+	21.5176i	−0.248343	+	0.926831i
$540$		0			0
$541$	13.1348	+	13.1348i	0.564708	+	0.564708i	0.930641	−	0.365933i	$-0.119250\pi$
$541$	13.1348	+	13.1348i	0.564708	+	0.564708i	−0.365933	+	0.930641i	$0.619250\pi$
$542$		0			0
$543$	−23.0157	+	6.16703i	−0.987697	+	0.264653i
$544$		0			0
$545$	3.59965	+	29.9061i	0.154192	+	1.28104i
$546$		0			0
$547$	−19.2880	−	19.2880i	−0.824696	−	0.824696i	0.162081	−	0.986777i	$-0.448179\pi$
$547$	−19.2880	−	19.2880i	−0.824696	−	0.824696i	−0.986777	+	0.162081i	$0.948179\pi$
$548$		0			0
$549$	−18.0269	−	10.4078i	−0.769369	−	0.444196i
$550$		0			0
$551$	0.301115	−	0.301115i	0.0128279	−	0.0128279i
$552$		0			0
$553$	−3.93450	−	6.81475i	−0.167312	−	0.289793i
$554$		0			0
$555$	27.9546	−	20.9610i	1.18661	−	0.889745i
$556$		0			0
$557$	1.72959	+	0.998577i	0.0732849	+	0.0423111i	0.536195	−	0.844094i	$-0.319861\pi$
$557$	1.72959	+	0.998577i	0.0732849	+	0.0423111i	−0.462910	+	0.886405i	$0.653195\pi$
$558$		0			0
$559$	21.4296	−	25.0353i	0.906375	−	1.05888i
$560$		0			0
$561$	13.7962	+	51.4882i	0.582477	+	2.17383i
$562$		0			0
$563$	−2.28516	+	8.52834i	−0.0963081	+	0.359427i	−0.997215	−	0.0745867i	$-0.976236\pi$
$563$	−2.28516	+	8.52834i	−0.0963081	+	0.359427i	0.900906	+	0.434013i	$0.142903\pi$
$564$		0			0
$565$	−18.5978	−	24.8030i	−0.782417	−	1.04347i
$566$		0			0
$567$			16.2274i			0.681488i
$568$		0			0
$569$	−12.7930	+	22.1581i	−0.536309	+	0.928914i	0.462790	+	0.886468i	$0.346848\pi$
$569$	−12.7930	+	22.1581i	−0.536309	+	0.928914i	−0.999099	+	0.0424461i	$0.986485\pi$
$570$		0			0
$571$			17.2404i			0.721487i	0.932665	+	0.360744i	$0.117477\pi$
$571$			17.2404i			0.721487i	−0.932665	+	0.360744i	$0.882523\pi$
$572$		0			0
$573$	−34.9976	+	34.9976i	−1.46205	+	1.46205i
$574$		0			0
$575$	8.99507	+	16.4116i	0.375120	+	0.684412i
$576$		0			0
$577$	−35.8547			−1.49265			−0.746325	−	0.665581i	$-0.768184\pi$
$577$	−35.8547			−1.49265			−0.746325	+	0.665581i	$0.768184\pi$
$578$		0			0
$579$	21.2765	+	5.70101i	0.884219	+	0.236926i
$580$		0			0
$581$	8.71684	+	15.0980i	0.361636	+	0.626371i
$582$		0			0
$583$	11.5980	−	20.0883i	0.480340	−	0.831974i
$584$		0			0
$585$	11.6315	+	7.75700i	0.480902	+	0.320713i
$586$		0			0
$587$	11.6192	−	20.1251i	0.479577	−	0.830652i	−0.520149	−	0.854076i	$-0.674123\pi$
$587$	11.6192	−	20.1251i	0.479577	−	0.830652i	0.999726	+	0.0234240i	$0.00745678\pi$
$588$		0			0
$589$	1.06382	+	1.84259i	0.0438339	+	0.0759226i
$590$		0			0
$591$	−11.2769	−	3.02164i	−0.463871	−	0.124294i
$592$		0			0
$593$	−18.9013			−0.776182			−0.388091	−	0.921621i	$-0.626865\pi$
$593$	−18.9013			−0.776182			−0.388091	+	0.921621i	$0.626865\pi$
$594$		0			0
$595$	−16.0578	−	6.86135i	−0.658304	−	0.281288i
$596$		0			0
$597$	24.4311	−	24.4311i	0.999897	−	0.999897i
$598$		0			0
$599$			35.9904i			1.47053i	0.677781	+	0.735264i	$0.262942\pi$
$599$			35.9904i			1.47053i	−0.677781	+	0.735264i	$0.737058\pi$
$600$		0			0
$601$	−4.79547	+	8.30599i	−0.195611	+	0.338808i	−0.947101	−	0.320937i	$-0.896002\pi$
$601$	−4.79547	+	8.30599i	−0.195611	+	0.338808i	0.751490	+	0.659745i	$0.229336\pi$
$602$		0			0
$603$			2.56633i			0.104509i
$604$		0			0
$605$	21.4215	+	3.06269i	0.870906	+	0.124516i
$606$		0			0
$607$	−12.4598	+	46.5006i	−0.505728	+	1.88740i	−0.0468517	+	0.998902i	$0.514919\pi$
$607$	−12.4598	+	46.5006i	−0.505728	+	1.88740i	−0.458876	+	0.888500i	$0.651748\pi$
$608$		0			0
$609$	−0.237136	−	0.885003i	−0.00960923	−	0.0358621i
$610$		0			0
$611$	−6.95149	+	14.5332i	−0.281227	+	0.587950i
$612$		0			0
$613$	−21.4121	−	12.3623i	−0.864825	−	0.499307i	0.000800300	−	1.00000i	$-0.499745\pi$
$613$	−21.4121	−	12.3623i	−0.864825	−	0.499307i	−0.865625	+	0.500693i	$0.833079\pi$
$614$		0			0
$615$	47.1806	+	6.74556i	1.90250	+	0.272007i
$616$		0			0
$617$	19.9719	+	34.5924i	0.804040	+	1.39264i	0.916937	+	0.399031i	$0.130654\pi$
$617$	19.9719	+	34.5924i	0.804040	+	1.39264i	−0.112897	+	0.993607i	$0.536013\pi$
$618$		0			0
$619$	−3.50369	+	3.50369i	−0.140825	+	0.140825i	−0.774005	−	0.633180i	$-0.781749\pi$
$619$	−3.50369	+	3.50369i	−0.140825	+	0.140825i	0.633180	+	0.774005i	$0.281749\pi$
$620$		0			0
$621$	−8.92830	−	5.15476i	−0.358280	−	0.206853i
$622$		0			0
$623$	−14.3526	−	14.3526i	−0.575025	−	0.575025i
$624$		0			0
$625$	−22.1846	+	11.5257i	−0.887385	+	0.461029i
$626$		0			0
$627$	−14.0085	+	3.75358i	−0.559447	+	0.149903i
$628$		0			0
$629$	−27.3593	−	27.3593i	−1.09089	−	1.09089i
$630$		0			0
$631$	4.78921	−	17.8736i	0.190656	−	0.711536i	−0.802693	−	0.596392i	$-0.796600\pi$
$631$	4.78921	−	17.8736i	0.190656	−	0.711536i	0.993349	−	0.115144i	$-0.0367330\pi$
$632$		0			0
$633$	41.3520	+	11.0802i	1.64360	+	0.440400i
$634$		0			0
$635$	3.83272	−	8.96979i	0.152097	−	0.355955i
$636$		0			0
$637$	14.5678	−	9.98875i	0.577198	−	0.395769i
$638$		0			0
$639$	19.2116	−	5.14772i	0.759998	−	0.203641i
$640$		0			0
$641$	−6.75083	+	3.89760i	−0.266642	+	0.153946i	−0.627361	−	0.778729i	$-0.715865\pi$
$641$	−6.75083	+	3.89760i	−0.266642	+	0.153946i	0.360719	+	0.932675i	$0.382531\pi$
$642$		0			0
$643$	−23.4142	+	13.5182i	−0.923367	+	0.533106i	−0.884708	−	0.466147i	$-0.845642\pi$
$643$	−23.4142	+	13.5182i	−0.923367	+	0.533106i	−0.0386590	+	0.999252i	$0.512309\pi$
$644$		0			0
$645$	34.9758	+	27.4606i	1.37717	+	1.08126i
$646$		0			0
$647$	9.97989	+	37.2455i	0.392350	+	1.46427i	0.826247	+	0.563308i	$0.190471\pi$
$647$	9.97989	+	37.2455i	0.392350	+	1.46427i	−0.433897	+	0.900962i	$0.642862\pi$
$648$		0			0
$649$	−25.4782			−1.00011
$650$		0			0
$651$	4.57775			0.179416
$652$		0			0
$653$	−5.90149	−	22.0247i	−0.230943	−	0.861891i	−0.979936	−	0.199313i	$-0.936129\pi$
$653$	−5.90149	−	22.0247i	−0.230943	−	0.861891i	0.748993	−	0.662578i	$-0.230538\pi$
$654$		0			0
$655$	25.7375	+	20.2074i	1.00565	+	0.789568i
$656$		0			0
$657$	17.5907	−	10.1560i	0.686278	−	0.396223i
$658$		0			0
$659$	−9.33308	+	5.38846i	−0.363565	+	0.209905i	−0.670644	−	0.741780i	$-0.733982\pi$
$659$	−9.33308	+	5.38846i	−0.363565	+	0.209905i	0.307078	+	0.951684i	$0.400649\pi$
$660$		0			0
$661$	41.0956	−	11.0115i	1.59843	−	0.428299i	0.653865	−	0.756611i	$-0.273146\pi$
$661$	41.0956	−	11.0115i	1.59843	−	0.428299i	0.944569	+	0.328312i	$0.106480\pi$
$662$		0			0
$663$	18.2375	−	38.1284i	0.708287	−	1.48079i
$664$		0			0
$665$	1.86679	−	4.36889i	0.0723910	−	0.169418i
$666$		0			0
$667$	1.05034	+	0.281437i	0.0406692	+	0.0108973i
$668$		0			0
$669$	−12.2596	+	45.7536i	−0.473985	+	1.76894i
$670$		0			0
$671$	38.5966	+	38.5966i	1.49000	+	1.49000i
$672$		0			0
$673$	17.4138	−	4.66602i	0.671254	−	0.179862i	0.0929342	−	0.995672i	$-0.470375\pi$
$673$	17.4138	−	4.66602i	0.671254	−	0.179862i	0.578320	+	0.815810i	$0.303709\pi$
$674$		0			0
$675$	7.14916	−	11.7707i	0.275171	−	0.453054i
$676$		0			0
$677$	−17.4931	−	17.4931i	−0.672315	−	0.672315i	0.285934	−	0.958249i	$-0.407696\pi$
$677$	−17.4931	−	17.4931i	−0.672315	−	0.672315i	−0.958249	+	0.285934i	$0.907696\pi$
$678$		0			0
$679$	13.5310	+	7.81215i	0.519274	+	0.299803i
$680$		0			0
$681$	7.60129	−	7.60129i	0.291282	−	0.291282i
$682$		0			0
$683$	1.02842	+	1.78127i	0.0393514	+	0.0681586i	0.885030	−	0.465533i	$-0.154138\pi$
$683$	1.02842	+	1.78127i	0.0393514	+	0.0681586i	−0.845679	+	0.533692i	$0.820804\pi$
$684$		0			0
$685$	1.71631	+	0.245387i	0.0655770	+	0.00937576i
$686$		0			0
$687$	−32.8843	−	18.9858i	−1.25462	−	0.724353i
$688$		0			0
$689$	−17.3441	+	6.12054i	−0.660757	+	0.233174i
$690$		0			0
$691$	−0.568099	−	2.12017i	−0.0216115	−	0.0806552i	0.954278	−	0.298921i	$-0.0966267\pi$
$691$	−0.568099	−	2.12017i	−0.0216115	−	0.0806552i	−0.975889	+	0.218266i	$0.929960\pi$
$692$		0			0
$693$	−2.95826	+	11.0404i	−0.112375	+	0.419390i
$694$		0			0
$695$	−50.4550	−	7.21371i	−1.91387	−	0.273632i
$696$		0			0
$697$		−	52.7777i		−	1.99910i
$698$		0			0
$699$	12.2800	−	21.2696i	0.464474	−	0.804492i
$700$		0			0
$701$		−	25.9991i		−	0.981972i	−0.871168	−	0.490986i	$-0.836637\pi$
$701$		−	25.9991i		−	0.981972i	0.871168	−	0.490986i	$-0.163363\pi$
$702$		0			0
$703$	7.44372	−	7.44372i	0.280745	−	0.280745i
$704$		0			0
$705$	−19.9902	−	8.54165i	−0.752874	−	0.321697i
$706$		0			0
$707$	3.42482			0.128803
$708$		0			0
$709$	38.7979	+	10.3959i	1.45709	+	0.390425i	0.898482	−	0.439010i	$-0.144671\pi$
$709$	38.7979	+	10.3959i	1.45709	+	0.390425i	0.558603	+	0.829435i	$0.311337\pi$
$710$		0			0
$711$	4.70702	+	8.15280i	0.176527	+	0.305754i
$712$		0			0
$713$	−2.71648	+	4.70508i	−0.101733	+	0.176207i
$714$		0			0
$715$	−24.1967	−	27.5418i	−0.904905	−	1.03000i
$716$		0			0
$717$	−6.51450	+	11.2834i	−0.243288	+	0.421388i
$718$		0			0
$719$	−11.6884	−	20.2450i	−0.435905	−	0.755010i	0.561464	−	0.827501i	$-0.310238\pi$
$719$	−11.6884	−	20.2450i	−0.435905	−	0.755010i	−0.997369	+	0.0724910i	$0.976905\pi$
$720$		0			0
$721$	2.54976	+	0.683207i	0.0949582	+	0.0254440i
$722$		0			0
$723$	−47.2440			−1.75702
$724$		0			0
$725$	−0.407034	+	1.39437i	−0.0151169	+	0.0517854i
$726$		0			0
$727$	−18.9556	+	18.9556i	−0.703024	+	0.703024i	−0.965059	−	0.262034i	$-0.915607\pi$
$727$	−18.9556	+	18.9556i	−0.703024	+	0.703024i	0.262034	+	0.965059i	$0.415607\pi$
$728$		0			0
$729$		−	1.43494i		−	0.0531459i
$730$		0			0
$731$	24.6212	−	42.6452i	0.910648	−	1.57729i
$732$		0			0
$733$		−	48.4953i		−	1.79122i	−0.444845	−	0.895608i	$-0.646741\pi$
$733$		−	48.4953i		−	1.79122i	0.444845	−	0.895608i	$-0.353259\pi$
$734$		0			0
$735$	14.2986	+	19.0693i	0.527410	+	0.703380i
$736$		0			0
$737$	1.74174	−	6.50025i	0.0641577	−	0.239440i
$738$		0			0
$739$	1.74097	+	6.49738i	0.0640425	+	0.239010i	0.990526	−	0.137326i	$-0.0438507\pi$
$739$	1.74097	+	6.49738i	0.0640425	+	0.239010i	−0.926483	+	0.376335i	$0.877184\pi$
$740$		0			0
$741$	10.3737	+	4.96194i	0.381088	+	0.182281i
$742$		0			0
$743$	19.9313	+	11.5074i	0.731209	+	0.422164i	0.818864	−	0.573987i	$-0.194604\pi$
$743$	19.9313	+	11.5074i	0.731209	+	0.422164i	−0.0876550	+	0.996151i	$0.527937\pi$
$744$		0			0
$745$	12.3893	−	9.28979i	0.453910	−	0.340352i
$746$		0			0
$747$	−10.4284	−	18.0624i	−0.381553	−	0.660870i
$748$		0			0
$749$	11.9789	−	11.9789i	0.437700	−	0.437700i
$750$		0			0
$751$	−14.0748	−	8.12611i	−0.513598	−	0.296526i	0.220713	−	0.975339i	$-0.429161\pi$
$751$	−14.0748	−	8.12611i	−0.513598	−	0.296526i	−0.734311	+	0.678813i	$0.762495\pi$
$752$		0			0
$753$	−38.7809	−	38.7809i	−1.41326	−	1.41326i
$754$		0			0
$755$	−0.605727	−	5.03242i	−0.0220447	−	0.183149i
$756$		0			0
$757$	23.9153	−	6.40809i	0.869218	−	0.232906i	0.203468	−	0.979082i	$-0.434779\pi$
$757$	23.9153	−	6.40809i	0.869218	−	0.232906i	0.665749	+	0.746175i	$0.268112\pi$
$758$		0			0
$759$	−26.1862	−	26.1862i	−0.950499	−	0.950499i
$760$		0			0
$761$	−4.77474	+	17.8196i	−0.173084	+	0.645960i	0.823786	+	0.566901i	$0.191858\pi$
$761$	−4.77474	+	17.8196i	−0.173084	+	0.645960i	−0.996870	+	0.0790582i	$0.974809\pi$
$762$		0			0
$763$	18.8608	+	5.05374i	0.682807	+	0.182958i
$764$		0			0
$765$	19.2106	+	8.20855i	0.694562	+	0.296781i
$766$		0			0
$767$	15.3473	+	13.1369i	0.554159	+	0.474345i
$768$		0			0
$769$	−38.7050	+	10.3710i	−1.39574	+	0.373987i	−0.876812	−	0.480833i	$-0.840335\pi$
$769$	−38.7050	+	10.3710i	−1.39574	+	0.373987i	−0.518926	+	0.854819i	$0.673668\pi$
$770$		0			0
$771$	23.8050	−	13.7439i	0.857318	−	0.494973i
$772$		0			0
$773$	20.6228	−	11.9066i	0.741750	−	0.428250i	−0.0809550	−	0.996718i	$-0.525797\pi$
$773$	20.6228	−	11.9066i	0.741750	−	0.428250i	0.822705	+	0.568468i	$0.192464\pi$
$774$		0			0
$775$	−6.20297	−	3.76750i	−0.222817	−	0.135333i
$776$		0			0
$777$	−5.86213	−	21.8778i	−0.210303	−	0.784861i
$778$		0			0
$779$	14.3594			0.514479
$780$		0			0
$781$	−52.1545			−1.86624
$782$		0			0
$783$	−0.207099	−	0.772904i	−0.00740112	−	0.0276213i
$784$		0			0
$785$	−1.16459	−	9.67548i	−0.0415659	−	0.345333i
$786$		0			0
$787$	5.78665	−	3.34092i	0.206272	−	0.119091i	−0.393306	−	0.919408i	$-0.628669\pi$
$787$	5.78665	−	3.34092i	0.206272	−	0.119091i	0.599577	+	0.800317i	$0.295335\pi$
$788$		0			0
$789$	25.4425	−	14.6892i	0.905778	−	0.522951i
$790$		0			0
$791$	−19.4113	+	5.20123i	−0.690185	+	0.184935i
$792$		0			0
$793$	−3.34854	−	43.1503i	−0.118910	−	1.53231i
$794$		0			0
$795$	−9.24215	−	23.0331i	−0.327785	−	0.816899i
$796$		0			0
$797$	25.8557	+	6.92801i	0.915856	+	0.245403i	0.685813	−	0.727778i	$-0.259447\pi$
$797$	25.8557	+	6.92801i	0.915856	+	0.245403i	0.230043	+	0.973181i	$0.426113\pi$
$798$		0			0
$799$	−6.23048	+	23.2525i	−0.220418	+	0.822613i
$800$		0			0
$801$	17.1707	+	17.1707i	0.606696	+	0.606696i
$802$		0			0
$803$	−51.4481	+	13.7855i	−1.81556	+	0.486479i
$804$		0			0
$805$	12.0448	−	1.44977i	0.424524	−	0.0510978i
$806$		0			0
$807$	24.9078	+	24.9078i	0.876796	+	0.876796i
$808$		0			0
$809$	9.00929	+	5.20152i	0.316750	+	0.182876i	0.649943	−	0.759983i	$-0.274793\pi$
$809$	9.00929	+	5.20152i	0.316750	+	0.182876i	−0.333193	+	0.942859i	$0.608126\pi$
$810$		0			0
$811$	−2.88418	+	2.88418i	−0.101277	+	0.101277i	−0.755930	−	0.654653i	$-0.772815\pi$
$811$	−2.88418	+	2.88418i	−0.101277	+	0.101277i	0.654653	+	0.755930i	$0.272815\pi$
$812$		0			0
$813$	12.6012	+	21.8260i	0.441944	+	0.765470i
$814$		0			0
$815$	−0.623886	+	4.36366i	−0.0218538	+	0.152852i
$816$		0			0
$817$	11.6026	+	6.69877i	0.405924	+	0.234360i
$818$		0			0
$819$	7.47453	−	5.12508i	0.261181	−	0.179085i
$820$		0			0
$821$	−3.80641	−	14.2057i	−0.132845	−	0.495783i	0.867153	−	0.498042i	$-0.165948\pi$
$821$	−3.80641	−	14.2057i	−0.132845	−	0.495783i	−0.999997	+	0.00225931i	$0.999281\pi$
$822$		0			0
$823$	−6.90567	+	25.7723i	−0.240717	+	0.898366i	0.734772	+	0.678315i	$0.237289\pi$
$823$	−6.90567	+	25.7723i	−0.240717	+	0.898366i	−0.975488	+	0.220052i	$0.929377\pi$
$824$		0			0
$825$	35.7488	−	34.1942i	1.24461	−	1.19049i
$826$		0			0
$827$		−	15.9935i		−	0.556148i	−0.960560	−	0.278074i	$-0.910304\pi$
$827$		−	15.9935i		−	0.556148i	0.960560	−	0.278074i	$-0.0896961\pi$
$828$		0			0
$829$	−10.7937	+	18.6953i	−0.374882	+	0.649314i	−0.990309	−	0.138879i	$-0.955650\pi$
$829$	−10.7937	+	18.6953i	−0.374882	+	0.649314i	0.615428	+	0.788193i	$0.288983\pi$
$830$		0			0
$831$			56.2695i			1.95197i
$832$		0			0
$833$	18.6632	−	18.6632i	0.646640	−	0.646640i
$834$		0			0
$835$	−12.7543	−	31.7861i	−0.441382	−	1.10000i
$836$		0			0
$837$	3.99791			0.138188
$838$		0			0
$839$	−52.3906	−	14.0380i	−1.80872	−	0.484646i	−0.813439	−	0.581650i	$-0.802407\pi$
$839$	−52.3906	−	14.0380i	−1.80872	−	0.484646i	−0.995284	+	0.0970040i	$0.969074\pi$
$840$		0			0
$841$	−14.4578	−	25.0416i	−0.498545	−	0.863505i
$842$		0			0
$843$	−22.5562	+	39.0684i	−0.776875	+	1.34559i
$844$		0			0
$845$	0.374468	+	29.0665i	0.0128821	+	0.999917i
$846$		0			0
$847$	7.01368	−	12.1481i	0.240993	−	0.417412i
$848$		0			0
$849$	3.68497	+	6.38255i	0.126468	+	0.219049i
$850$		0			0
$851$	25.9649	+	6.95728i	0.890066	+	0.238493i
$852$		0			0
$853$	17.9281			0.613848			0.306924	−	0.951734i	$-0.400700\pi$
$853$	17.9281			0.613848			0.306924	+	0.951734i	$0.400700\pi$
$854$		0			0
$855$	−2.23332	+	5.22670i	−0.0763781	+	0.178749i
$856$		0			0
$857$	35.9470	−	35.9470i	1.22793	−	1.22793i	0.263179	−	0.964747i	$-0.415229\pi$
$857$	35.9470	−	35.9470i	1.22793	−	1.22793i	0.964747	−	0.263179i	$-0.0847708\pi$
$858$		0			0
$859$			40.8361i			1.39331i	0.717406	+	0.696655i	$0.245329\pi$
$859$			40.8361i			1.39331i	−0.717406	+	0.696655i	$0.754671\pi$
$860$		0			0
$861$	15.4476	−	26.7560i	0.526452	−	0.911841i
$862$		0			0
$863$			1.61377i			0.0549334i	0.999623	+	0.0274667i	$0.00874403\pi$
$863$			1.61377i			0.0549334i	−0.999623	+	0.0274667i	$0.991256\pi$
$864$		0			0
$865$	3.92348	−	2.94191i	0.133402	−	0.100028i
$866$		0			0
$867$	6.77256	−	25.2755i	0.230008	−	0.858402i
$868$		0			0
$869$	−6.38919	−	23.8448i	−0.216738	−	0.808878i
$870$		0			0
$871$	−4.40078	+	3.01750i	−0.149115	+	0.102244i
$872$		0			0
$873$	−16.1878	−	9.34603i	−0.547874	−	0.316315i
$874$		0			0
$875$	1.57864	+	16.1288i	0.0533679	+	0.545254i
$876$		0			0
$877$	17.7214	+	30.6943i	0.598409	+	1.03647i	0.993056	+	0.117642i	$0.0375334\pi$
$877$	17.7214	+	30.6943i	0.598409	+	1.03647i	−0.394647	+	0.918833i	$0.629133\pi$
$878$		0			0
$879$	38.9361	−	38.9361i	1.31328	−	1.31328i
$880$		0			0
$881$	12.1387	+	7.00829i	0.408964	+	0.236115i	0.690344	−	0.723481i	$-0.257459\pi$
$881$	12.1387	+	7.00829i	0.408964	+	0.236115i	−0.281381	+	0.959596i	$0.590792\pi$
$882$		0			0
$883$	−34.3985	−	34.3985i	−1.15760	−	1.15760i	−0.984990	−	0.172612i	$-0.944779\pi$
$883$	−34.3985	−	34.3985i	−1.15760	−	1.15760i	−0.172612	−	0.984990i	$-0.555221\pi$
$884$		0			0
$885$	−16.8341	+	21.4410i	−0.565871	+	0.720732i
$886$		0			0
$887$	−44.1266	+	11.8237i	−1.48163	+	0.397000i	−0.906900	−	0.421346i	$-0.861558\pi$
$887$	−44.1266	+	11.8237i	−1.48163	+	0.397000i	−0.574725	+	0.818346i	$0.694891\pi$
$888$		0			0
$889$	−4.47111	−	4.47111i	−0.149956	−	0.149956i
$890$		0			0
$891$	−13.1758	+	49.1726i	−0.441405	+	1.64734i
$892$		0			0
$893$	−6.32637	−	1.69515i	−0.211704	−	0.0567259i
$894$		0			0
$895$	51.2691	−	20.5720i	1.71374	−	0.687645i
$896$		0			0
$897$	2.27185	+	29.2757i	0.0758548	+	0.977488i
$898$		0			0
$899$	−0.407308	+	0.109138i	−0.0135845	+	0.00363996i
$900$		0			0
$901$	−23.8009	+	13.7415i	−0.792923	+	0.457794i
$902$		0			0
$903$	24.9637	−	14.4128i	0.830741	−	0.479629i
$904$		0			0
$905$	15.1220	−	19.2605i	0.502673	−	0.640240i
$906$		0			0
$907$	13.5412	+	50.5364i	0.449628	+	1.67804i	0.703419	+	0.710776i	$0.251656\pi$
$907$	13.5412	+	50.5364i	0.449628	+	1.67804i	−0.253790	+	0.967259i	$0.581677\pi$
$908$		0			0
$909$	−4.09726			−0.135898
$910$		0			0
$911$	18.3525			0.608044			0.304022	−	0.952665i	$-0.401670\pi$
$911$	18.3525			0.608044			0.304022	+	0.952665i	$0.401670\pi$
$912$		0			0
$913$	14.1552	+	52.8278i	0.468468	+	1.74835i
$914$		0			0
$915$	57.9824	−	6.97904i	1.91684	−	0.230720i
$916$		0			0
$917$	18.3700	−	10.6059i	0.606632	−	0.350239i
$918$		0			0
$919$	−38.0739	+	21.9820i	−1.25594	+	0.725118i	−0.972283	−	0.233807i	$-0.924882\pi$
$919$	−38.0739	+	21.9820i	−1.25594	+	0.725118i	−0.283659	+	0.958925i	$0.591548\pi$
$920$		0			0
$921$	−26.9543	+	7.22238i	−0.888174	+	0.237985i
$922$		0			0
$923$	31.4163	+	26.8915i	1.03408	+	0.885146i
$924$		0			0
$925$	−10.0621	+	34.4695i	−0.330840	+	1.13335i
$926$		0			0
$927$	−3.05040	−	0.817352i	−0.100188	−	0.0268454i
$928$		0			0
$929$	−0.147215	+	0.549414i	−0.00482997	+	0.0180257i	−0.968299	−	0.249795i	$-0.919637\pi$
$929$	−0.147215	+	0.549414i	−0.00482997	+	0.0180257i	0.963469	+	0.267821i	$0.0863035\pi$
$930$		0			0
$931$	5.07774	+	5.07774i	0.166416	+	0.166416i
$932$		0			0
$933$	3.35471	−	0.898893i	0.109828	−	0.0294284i
$934$		0			0
$935$	−43.0875	−	33.8294i	−1.40911	−	1.10634i
$936$		0			0
$937$	−6.91585	−	6.91585i	−0.225931	−	0.225931i	0.585059	−	0.810990i	$-0.301071\pi$
$937$	−6.91585	−	6.91585i	−0.225931	−	0.225931i	−0.810990	+	0.585059i	$0.801071\pi$
$938$		0			0
$939$	−50.8322	−	29.3480i	−1.65885	−	0.957736i
$940$		0			0
$941$	−4.12906	+	4.12906i	−0.134604	+	0.134604i	−0.771198	−	0.636595i	$-0.780342\pi$
$941$	−4.12906	+	4.12906i	−0.134604	+	0.134604i	0.636595	+	0.771198i	$0.280342\pi$
$942$		0			0
$943$	18.3334	+	31.7545i	0.597019	+	1.03407i
$944$		0			0
$945$	−5.35557	−	7.14246i	−0.174217	−	0.232344i
$946$		0			0
$947$	−13.3027	−	7.68029i	−0.432278	−	0.249576i	0.268039	−	0.963408i	$-0.413625\pi$
$947$	−13.3027	−	7.68029i	−0.432278	−	0.249576i	−0.700317	+	0.713832i	$0.746958\pi$
$948$		0			0
$949$	38.0987	+	18.2233i	1.23674	+	0.591554i
$950$		0			0
$951$	−8.78994	−	32.8045i	−0.285033	−	1.06376i
$952$		0			0
$953$	−1.70449	+	6.36124i	−0.0552138	+	0.206061i	−0.988022	−	0.154312i	$-0.950684\pi$
$953$	−1.70449	+	6.36124i	−0.0552138	+	0.206061i	0.932808	+	0.360373i	$0.117351\pi$
$954$		0			0
$955$	7.19913	−	50.3530i	0.232958	−	1.62939i
$956$		0			0
$957$		−	2.87429i		−	0.0929127i
$958$		0			0
$959$	0.561945	−	0.973318i	0.0181462	−	0.0314301i
$960$		0			0
$961$			28.8932i			0.932038i
$962$		0			0
$963$	−14.3309	+	14.3309i	−0.461807	+	0.461807i
$964$		0			0
$965$	−21.0090	+	8.42995i	−0.676302	+	0.271370i
$966$		0			0
$967$	−0.220203			−0.00708125			−0.00354063	−	0.999994i	$-0.501127\pi$
$967$	−0.220203			−0.00708125			−0.00354063	+	0.999994i	$0.501127\pi$
$968$		0			0
$969$	16.5975	+	4.44728i	0.533188	+	0.142867i
$970$		0			0
$971$	−23.8799	−	41.3611i	−0.766341	−	1.32734i	−0.939534	−	0.342454i	$-0.888742\pi$
$971$	−23.8799	−	41.3611i	−0.766341	−	1.32734i	0.173193	−	0.984888i	$-0.444592\pi$
$972$		0			0
$973$	−16.5197	+	28.6129i	−0.529596	+	0.917287i
$974$		0			0
$975$	−39.1650	+	2.16506i	−1.25428	+	0.0693375i
$976$		0			0
$977$	4.69292	−	8.12838i	0.150140	−	0.260050i	−0.781139	−	0.624357i	$-0.785361\pi$
$977$	4.69292	−	8.12838i	0.150140	−	0.260050i	0.931279	+	0.364307i	$0.118694\pi$
$978$		0			0
$979$	−31.8380	−	55.1450i	−1.01755	−	1.76244i
$980$		0			0
$981$	−22.5640	−	6.04602i	−0.720415	−	0.193035i
$982$		0			0
$983$	18.2960			0.583553			0.291776	−	0.956487i	$-0.405754\pi$
$983$	18.2960			0.583553			0.291776	+	0.956487i	$0.405754\pi$
$984$		0			0
$985$	11.1351	−	4.46803i	0.354795	−	0.142363i
$986$		0			0
$987$	−9.96437	+	9.96437i	−0.317170	+	0.317170i
$988$		0			0
$989$			34.2108i			1.08784i
$990$		0			0
$991$	3.30731	−	5.72843i	0.105060	−	0.181970i	−0.808703	−	0.588218i	$-0.799830\pi$
$991$	3.30731	−	5.72843i	0.105060	−	0.181970i	0.913763	+	0.406248i	$0.133163\pi$
$992$		0			0
$993$			58.0257i			1.84139i
$994$		0			0
$995$	−5.02556	+	35.1503i	−0.159321	+	1.11434i
$996$		0			0
$997$	−5.50791	+	20.5558i	−0.174437	+	0.651009i	0.822209	+	0.569185i	$0.192741\pi$
$997$	−5.50791	+	20.5558i	−0.174437	+	0.651009i	−0.996647	+	0.0818241i	$0.973925\pi$
$998$		0			0
$999$	−5.11960	−	19.1066i	−0.161977	−	0.604507i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	260.2.bk.c.97.2	yes	20
5.2	odd	4		1300.2.bn.d.1293.2		20
5.3	odd	4		260.2.bf.c.253.4	yes	20
5.4	even	2		1300.2.bs.d.357.4		20
13.11	odd	12		260.2.bf.c.37.4	✓	20
65.24	odd	12		1300.2.bn.d.557.2		20
65.37	even	12		1300.2.bs.d.193.4		20
65.63	even	12	inner	260.2.bk.c.193.2	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.bf.c.37.4	✓	20	13.11	odd	12
260.2.bf.c.253.4	yes	20	5.3	odd	4
260.2.bk.c.97.2	yes	20	1.1	even	1	trivial
260.2.bk.c.193.2	yes	20	65.63	even	12	inner
1300.2.bn.d.557.2		20	65.24	odd	12
1300.2.bn.d.1293.2		20	5.2	odd	4
1300.2.bs.d.193.4		20	65.37	even	12
1300.2.bs.d.357.4		20	5.4	even	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:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.bk (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.563138 - 2.10166i) q^{3} +(1.75876 + 1.38086i) q^{5} +(1.25530 - 0.724750i) q^{7} +(-1.50178 + 0.867051i) q^{9} +O(q^{10})\)	\(q+(-0.563138 - 2.10166i) q^{3} +(1.75876 + 1.38086i) q^{5} +(1.25530 - 0.724750i) q^{7} +(-1.50178 + 0.867051i) q^{9} +(4.39230 - 1.17691i) q^{11} +(-3.25262 - 1.55579i) q^{13} +(1.91167 - 4.47393i) q^{15} +(-5.20404 - 1.39442i) q^{17} +(0.379384 - 1.41588i) q^{19} +(-2.23009 - 2.23009i) q^{21} +(3.61547 - 0.968762i) q^{23} +(1.18646 + 4.85719i) q^{25} +(-1.94761 - 1.94761i) q^{27} +(0.251591 + 0.145256i) q^{29} +(-1.02636 + 1.02636i) q^{31} +(-4.94694 - 8.56835i) q^{33} +(3.20855 + 0.458737i) q^{35} +(6.21947 + 3.59081i) q^{37} +(-1.43806 + 7.71202i) q^{39} +(2.53542 + 9.46231i) q^{41} +(-2.36558 + 8.82848i) q^{43} +(-3.83854 - 0.548808i) q^{45} -4.46815i q^{47} +(-2.44948 + 4.24262i) q^{49} +11.7224i q^{51} +(3.60704 - 3.60704i) q^{53} +(9.35013 + 3.99524i) q^{55} -3.18934 q^{57} +(-5.41208 - 1.45016i) q^{59} +(6.00186 + 10.3955i) q^{61} +(-1.25679 + 2.17682i) q^{63} +(-3.57225 - 7.22766i) q^{65} +(0.739961 - 1.28165i) q^{67} +(-4.07202 - 7.05294i) q^{69} +(-11.0787 - 2.96852i) q^{71} -11.7133 q^{73} +(9.54003 - 5.22881i) q^{75} +(4.66070 - 4.66070i) q^{77} -5.42877i q^{79} +(-5.59760 + 9.69532i) q^{81} +12.0274i q^{83} +(-7.22716 - 9.63849i) q^{85} +(0.163598 - 0.610558i) q^{87} +(-3.62430 - 13.5261i) q^{89} +(-5.21058 + 0.404351i) q^{91} +(2.73505 + 1.57908i) q^{93} +(2.62237 - 1.96631i) q^{95} +(5.38955 + 9.33497i) q^{97} +(-5.57580 + 5.57580i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{3} + 12 q^{5} + 6 q^{7} - 12 q^{9}+O(q^{10}) \) 20 * q - 2 * q^3 + 12 * q^5 + 6 * q^7 - 12 * q^9	\( 20 q - 2 q^{3} + 12 q^{5} + 6 q^{7} - 12 q^{9} + 8 q^{13} - 20 q^{15} + 20 q^{19} - 12 q^{21} + 6 q^{23} + 2 q^{25} - 20 q^{27} + 24 q^{29} + 8 q^{31} - 10 q^{33} - 36 q^{35} + 4 q^{39} + 6 q^{41} + 38 q^{43} - 16 q^{45} + 14 q^{49} + 30 q^{53} + 2 q^{55} - 76 q^{57} - 24 q^{59} - 32 q^{61} - 24 q^{63} - 30 q^{65} + 22 q^{67} - 16 q^{69} - 44 q^{73} - 2 q^{75} - 12 q^{77} + 2 q^{81} + 50 q^{85} + 38 q^{87} - 30 q^{89} - 72 q^{91} - 48 q^{93} - 30 q^{95} + 46 q^{97} + 20 q^{99}+O(q^{100}) \) 20 * q - 2 * q^3 + 12 * q^5 + 6 * q^7 - 12 * q^9 + 8 * q^13 - 20 * q^15 + 20 * q^19 - 12 * q^21 + 6 * q^23 + 2 * q^25 - 20 * q^27 + 24 * q^29 + 8 * q^31 - 10 * q^33 - 36 * q^35 + 4 * q^39 + 6 * q^41 + 38 * q^43 - 16 * q^45 + 14 * q^49 + 30 * q^53 + 2 * q^55 - 76 * q^57 - 24 * q^59 - 32 * q^61 - 24 * q^63 - 30 * q^65 + 22 * q^67 - 16 * q^69 - 44 * q^73 - 2 * q^75 - 12 * q^77 + 2 * q^81 + 50 * q^85 + 38 * q^87 - 30 * q^89 - 72 * q^91 - 48 * q^93 - 30 * q^95 + 46 * q^97 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more