LMFDB - Embedded newform 260.2.bk.c.193.2

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			193.2
Root			$-1.70974i$ of defining polynomial
Character	$\chi$	$=$	260.193
Dual form			260.2.bk.c.97.2

$q$-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 $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

$n$	$41$	$131$	$157$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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	0.589055	+	0.808093i	$0.299500\pi$
$3$	−0.563138	+	2.10166i	−0.325128	+	1.21339i	−0.914183	+	0.405301i	$0.867167\pi$
$4$		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	0.718105	−	0.695935i	$-0.245010\pi$
$7$	1.25530	+	0.724750i	0.474460	+	0.273930i	−0.243645	+	0.969865i	$0.578343\pi$
$8$		0			0
$9$	−1.50178	−	0.867051i	−0.500592	−	0.289017i
$10$		0			0
$11$	4.39230	+	1.17691i	1.32433	+	0.354852i	0.850597	−	0.525818i	$-0.176241\pi$
$11$	4.39230	+	1.17691i	1.32433	+	0.354852i	0.473730	+	0.880670i	$0.342907\pi$
$12$		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	−0.827024	−	0.562166i	$-0.809968\pi$
$17$	−5.20404	+	1.39442i	−1.26217	+	0.338196i	−0.435141	+	0.900362i	$0.643302\pi$
$18$		0			0
$19$	0.379384	+	1.41588i	0.0870366	+	0.324825i	0.995692	−	0.0927216i	$-0.0295567\pi$
$19$	0.379384	+	1.41588i	0.0870366	+	0.324825i	−0.908655	+	0.417547i	$0.862890\pi$
$20$		0			0
$21$	−2.23009	+	2.23009i	−0.486645	+	0.486645i
$22$		0			0
$23$	3.61547	+	0.968762i	0.753877	+	0.202001i	0.615237	−	0.788342i	$-0.289060\pi$
$23$	3.61547	+	0.968762i	0.753877	+	0.202001i	0.138640	+	0.990343i	$0.455727\pi$
$24$		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	−0.476458	−	0.879197i	$-0.658080\pi$
$29$	0.251591	−	0.145256i	0.0467193	−	0.0269734i	0.523178	+	0.852224i	$0.324746\pi$
$30$		0			0
$31$	−1.02636	−	1.02636i	−0.184340	−	0.184340i	0.608904	−	0.793244i	$-0.291609\pi$
$31$	−1.02636	−	1.02636i	−0.184340	−	0.184340i	−0.793244	+	0.608904i	$0.791609\pi$
$32$		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	0.107655	−	0.994188i	$-0.465666\pi$
$37$	6.21947	−	3.59081i	1.02247	−	0.590326i	0.914820	+	0.403862i	$0.132333\pi$
$38$		0			0
$39$	−1.43806	−	7.71202i	−0.230274	−	1.23491i
$40$		0			0
$41$	2.53542	−	9.46231i	0.395966	−	1.47776i	−0.424163	−	0.905586i	$-0.639432\pi$
$41$	2.53542	−	9.46231i	0.395966	−	1.47776i	0.820129	−	0.572179i	$-0.193902\pi$
$42$		0			0
$43$	−2.36558	−	8.82848i	−0.360748	−	1.34633i	−0.873094	−	0.487552i	$-0.837890\pi$
$43$	−2.36558	−	8.82848i	−0.360748	−	1.34633i	0.512346	−	0.858779i	$-0.328777\pi$
$44$		0			0
$45$	−3.83854	+	0.548808i	−0.572215	+	0.0818114i
$46$		0			0
$47$			4.46815i			0.651747i	0.945413	+	0.325874i	$0.105658\pi$
$47$			4.46815i			0.651747i	−0.945413	+	0.325874i	$0.894342\pi$
$48$		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	0.910023	−	0.414558i	$-0.136064\pi$
$53$	3.60704	+	3.60704i	0.495465	+	0.495465i	−0.414558	+	0.910023i	$0.636064\pi$
$54$		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	−0.593287	−	0.804991i	$-0.702170\pi$
$59$	−5.41208	+	1.45016i	−0.704593	+	0.188795i	−0.111306	+	0.993786i	$0.535503\pi$
$60$		0			0
$61$	6.00186	−	10.3955i	0.768459	−	1.33101i	−0.169939	−	0.985455i	$-0.554357\pi$
$61$	6.00186	−	10.3955i	0.768459	−	1.33101i	0.938398	−	0.345556i	$-0.112310\pi$
$62$		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	0.907680	−	0.419664i	$-0.137852\pi$
$67$	0.739961	+	1.28165i	0.0904006	+	0.156578i	−0.817279	+	0.576242i	$0.804519\pi$
$68$		0			0
$69$	−4.07202	+	7.05294i	−0.490213	+	0.849074i
$70$		0			0
$71$	−11.0787	+	2.96852i	−1.31480	+	0.352299i	−0.847026	−	0.531551i	$-0.821610\pi$
$71$	−11.0787	+	2.96852i	−1.31480	+	0.352299i	−0.467771	+	0.883850i	$0.654943\pi$
$72$		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	$0.0987876\pi$
$79$			5.42877i			0.610784i	−0.952227	+	0.305392i	$0.901212\pi$
$80$		0			0
$81$	−5.59760	−	9.69532i	−0.621955	−	1.07726i
$82$		0			0
$83$		−	12.0274i		−	1.32018i	−0.751188	−	0.660088i	$-0.770519\pi$
$83$		−	12.0274i		−	1.32018i	0.751188	−	0.660088i	$-0.229481\pi$
$84$		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	0.455288	+	0.890344i	$0.349536\pi$
$89$	−3.62430	+	13.5261i	−0.384175	+	1.43376i	−0.839463	+	0.543416i	$0.817131\pi$
$90$		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	−0.451237	−	0.892404i	$-0.649017\pi$
$97$	5.38955	−	9.33497i	0.547226	−	0.947823i	0.998463	−	0.0554189i	$-0.0176494\pi$
$98$		0			0
$99$	−5.57580	−	5.57580i	−0.560389	−	0.560389i
$100$		0			0
$101$	2.04621	−	1.18138i	0.203605	−	0.117552i	−0.394731	−	0.918797i	$-0.629162\pi$
$101$	2.04621	−	1.18138i	0.203605	−	0.117552i	0.598336	+	0.801245i	$0.295829\pi$
$102$		0			0
$103$	1.28773	−	1.28773i	0.126883	−	0.126883i	−0.640813	−	0.767697i	$-0.721403\pi$
$103$	1.28773	−	1.28773i	0.126883	−	0.126883i	0.767697	+	0.640813i	$0.221403\pi$
$104$		0			0
$105$	−0.842749	+	7.00162i	−0.0822439	+	0.683288i
$106$		0			0
$107$	11.2891	+	3.02490i	1.09136	+	0.292428i	0.759240	−	0.650811i	$-0.225571\pi$
$107$	11.2891	+	3.02490i	1.09136	+	0.292428i	0.332115	+	0.943239i	$0.392238\pi$
$108$		0			0
$109$	9.52541	−	9.52541i	0.912369	−	0.912369i	−0.0840895	−	0.996458i	$-0.526798\pi$
$109$	9.52541	−	9.52541i	0.912369	−	0.912369i	0.996458	+	0.0840895i	$0.0267982\pi$
$110$		0			0
$111$	4.04425	+	15.0933i	0.383863	+	1.43260i
$112$		0			0
$113$	−13.3917	+	3.58830i	−1.25979	+	0.337559i	−0.826109	−	0.563510i	$-0.809451\pi$
$113$	−13.3917	+	3.58830i	−1.25979	+	0.337559i	−0.433677	+	0.901069i	$0.642784\pi$
$114$		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	−0.997755	−	0.0669757i	$-0.978665\pi$
$127$	−1.12904	+	4.21363i	−0.100186	+	0.373899i	0.897569	+	0.440875i	$0.145332\pi$
$128$		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	0.528410	−	0.848989i	$-0.322788\pi$
$137$	0.671485	+	0.387682i	0.0573689	+	0.0331219i	−0.471041	+	0.882111i	$0.656122\pi$
$138$		0			0
$139$	−19.7398	−	11.3968i	−1.67431	−	0.966664i	−0.965180	−	0.261588i	$-0.915754\pi$
$139$	−19.7398	−	11.3968i	−1.67431	−	0.966664i	−0.709132	−	0.705076i	$-0.750913\pi$
$140$		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	0.999667	+	0.0258163i	$0.00821850\pi$
$149$	1.79239	+	6.68928i	0.146838	+	0.548007i	−0.852829	+	0.522191i	$0.825115\pi$
$150$		0			0
$151$	−1.60288	+	1.60288i	−0.130440	+	0.130440i	−0.769313	−	0.638872i	$-0.779401\pi$
$151$	−1.60288	+	1.60288i	−0.130440	+	0.130440i	0.638872	+	0.769313i	$0.279401\pi$
$152$		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	−0.819306	−	0.573356i	$-0.805641\pi$
$157$	−3.08174	+	3.08174i	−0.245950	+	0.245950i	0.573356	+	0.819306i	$0.305641\pi$
$158$		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	−0.824839	−	0.565368i	$-0.808734\pi$
$163$	0.985666	−	1.70722i	0.0772033	−	0.133720i	0.902042	+	0.431648i	$0.142068\pi$
$164$		0			0
$165$	3.13121	+	21.9007i	0.243764	+	1.70497i
$166$		0			0
$167$	−13.2648	+	7.65842i	−1.02646	+	0.592626i	−0.915968	−	0.401251i	$-0.868575\pi$
$167$	−13.2648	+	7.65842i	−1.02646	+	0.592626i	−0.110490	+	0.993877i	$0.535242\pi$
$168$		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	0.984141	−	0.177389i	$-0.0567652\pi$
$173$	0.567617	+	2.11838i	0.0431552	+	0.161057i	−0.940986	+	0.338447i	$0.890099\pi$
$174$		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	0.794312	+	0.607510i	$0.207831\pi$
$179$	12.3526	+	21.3953i	0.923275	+	1.59916i	0.128963	+	0.991649i	$0.458835\pi$
$180$		0			0
$181$			10.9512i			0.813995i	0.913429	+	0.406997i	$0.133424\pi$
$181$			10.9512i			0.813995i	−0.913429	+	0.406997i	$0.866576\pi$
$182$		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	0.0804781	+	0.996756i	$0.474355\pi$
$191$	−11.3738	+	19.7000i	−0.822977	+	1.42544i	−0.903455	+	0.428682i	$0.858978\pi$
$192$		0			0
$193$	−5.06182	−	8.76733i	−0.364358	−	0.631086i	0.624315	−	0.781173i	$-0.285378\pi$
$193$	−5.06182	−	8.76733i	−0.364358	−	0.631086i	−0.988673	+	0.150086i	$0.952045\pi$
$194$		0			0
$195$	−13.1784	−	11.5778i	−0.943726	−	0.829105i
$196$		0			0
$197$	2.68286	+	4.64685i	0.191146	+	0.331074i	0.945630	−	0.325244i	$-0.105446\pi$
$197$	2.68286	+	4.64685i	0.191146	+	0.331074i	−0.754484	+	0.656318i	$0.772113\pi$
$198$		0			0
$199$	7.93978	−	13.7521i	0.562836	−	0.974861i	−0.434411	−	0.900715i	$-0.643044\pi$
$199$	7.93978	−	13.7521i	0.562836	−	0.974861i	0.997247	−	0.0741463i	$-0.0236232\pi$
$200$		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	−0.975799	−	0.218668i	$-0.929829\pi$
$211$	−9.83794	−	17.0398i	−0.677272	−	1.17307i	0.298528	−	0.954401i	$-0.403504\pi$
$212$		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	−0.973563	−	0.228418i	$-0.926645\pi$
$223$	−18.8536	+	10.8851i	−1.26253	+	0.728921i	−0.288965	+	0.957340i	$0.593311\pi$
$224$		0			0
$225$	−5.99323	+	6.26569i	−0.399549	+	0.417713i
$226$		0			0
$227$	2.47032	−	4.27872i	0.163961	−	0.283989i	−0.772325	−	0.635228i	$-0.780906\pi$
$227$	2.47032	−	4.27872i	0.163961	−	0.283989i	0.936286	+	0.351239i	$0.114240\pi$
$228$		0			0
$229$	12.3403	+	12.3403i	0.815468	+	0.815468i	0.985448	−	0.169980i	$-0.0543702\pi$
$229$	12.3403	+	12.3403i	0.815468	+	0.815468i	−0.169980	+	0.985448i	$0.554370\pi$
$230$		0			0
$231$	−12.4198	+	7.17059i	−0.817164	+	0.471790i
$232$		0			0
$233$	7.98171	−	7.98171i	0.522899	−	0.522899i	−0.395547	−	0.918446i	$-0.629445\pi$
$233$	7.98171	−	7.98171i	0.522899	−	0.522899i	0.918446	+	0.395547i	$0.129445\pi$
$234$		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	−0.830665	−	0.556773i	$-0.812039\pi$
$239$	−4.23426	+	4.23426i	−0.273891	+	0.273891i	0.556773	+	0.830665i	$0.312039\pi$
$240$		0			0
$241$	5.61985	+	20.9736i	0.362006	+	1.35103i	0.871434	+	0.490512i	$0.163190\pi$
$241$	5.61985	+	20.9736i	0.362006	+	1.35103i	−0.509428	+	0.860513i	$0.670143\pi$
$242$		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	0.991903	−	0.126999i	$-0.0405345\pi$
$251$	21.8296	+	12.6033i	1.37787	+	0.795514i	0.385967	+	0.922513i	$0.373868\pi$
$252$		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	−0.785801	−	0.618479i	$-0.787749\pi$
$257$	3.26976	−	12.2029i	0.203962	−	0.761197i	0.989763	−	0.142718i	$-0.0455841\pi$
$258$		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	−0.770502	−	0.637437i	$-0.779994\pi$
$263$	3.49468	−	13.0423i	0.215491	−	0.804223i	0.985993	−	0.166786i	$-0.0533389\pi$
$264$		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	0.00743940	−	0.999972i	$-0.497632\pi$
$269$	−14.0205	−	8.09471i	−0.854842	−	0.493543i	−0.862282	+	0.506429i	$0.830965\pi$
$270$		0			0
$271$	−11.1884	−	2.99792i	−0.679647	−	0.182111i	−0.0975504	−	0.995231i	$-0.531101\pi$
$271$	−11.1884	−	2.99792i	−0.679647	−	0.182111i	−0.582096	+	0.813120i	$0.697767\pi$
$272$		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	−0.913409	−	0.407043i	$-0.866560\pi$
$277$	−24.9803	+	6.69346i	−1.50092	+	0.402171i	−0.587514	+	0.809214i	$0.699893\pi$
$278$		0			0
$279$	0.651458	+	2.43127i	0.0390018	+	0.145557i
$280$		0			0
$281$	−14.6609	+	14.6609i	−0.874597	+	0.874597i	−0.992969	−	0.118372i	$-0.962232\pi$
$281$	−14.6609	+	14.6609i	−0.874597	+	0.874597i	0.118372	+	0.992969i	$0.462232\pi$
$282$		0			0
$283$	−3.27181	−	0.876680i	−0.194489	−	0.0521132i	0.160259	−	0.987075i	$-0.448767\pi$
$283$	−3.27181	−	0.876680i	−0.194489	−	0.0521132i	−0.354749	+	0.934962i	$0.615434\pi$
$284$		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	−0.213599	−	0.976922i	$-0.568518\pi$
$293$	12.6537	−	21.9169i	0.739240	−	1.28040i	0.952838	−	0.303479i	$-0.0981482\pi$
$294$		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	$0.119269\pi$
$307$			12.8252i			0.731974i	−0.930620	+	0.365987i	$0.880731\pi$
$308$		0			0
$309$	1.98119	+	3.43153i	0.112706	+	0.195213i
$310$		0			0
$311$		−	1.59622i		−	0.0905134i	−0.998975	−	0.0452567i	$-0.985589\pi$
$311$		−	1.59622i		−	0.0905134i	0.998975	−	0.0452567i	$-0.0144106\pi$
$312$		0			0
$313$	19.0754	+	19.0754i	1.07821	+	1.07821i	0.996670	+	0.0815374i	$0.0259830\pi$
$313$	19.0754	+	19.0754i	1.07821	+	1.07821i	0.0815374	+	0.996670i	$0.474017\pi$
$314$		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	−0.884026	−	0.467438i	$-0.845177\pi$
$331$	−25.7600	+	6.90237i	−1.41590	+	0.379388i	−0.531870	+	0.846826i	$0.678511\pi$
$332$		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	0.663861	−	0.747856i	$-0.268916\pi$
$337$	−1.54193	−	1.54193i	−0.0839941	−	0.0839941i	−0.747856	+	0.663861i	$0.768916\pi$
$338$		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	−0.999939	−	0.0110226i	$-0.996491\pi$
$347$	−2.59818	−	9.69655i	−0.139478	−	0.520538i	0.860461	−	0.509516i	$-0.170175\pi$
$348$		0			0
$349$	−5.70030	+	21.2738i	−0.305130	+	1.13876i	0.627703	+	0.778453i	$0.283995\pi$
$349$	−5.70030	+	21.2738i	−0.305130	+	1.13876i	−0.932833	+	0.360308i	$0.882671\pi$
$350$		0			0
$351$	3.30477	−	9.36491i	0.176396	−	0.499862i
$352$		0			0
$353$	−15.9958	+	9.23518i	−0.851371	+	0.491539i	−0.861113	−	0.508414i	$-0.830232\pi$
$353$	−15.9958	+	9.23518i	−0.851371	+	0.491539i	0.00974252	+	0.999953i	$0.496899\pi$
$354$		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	0.986755	−	0.162220i	$-0.0518655\pi$
$359$	15.6227	+	15.6227i	0.824534	+	0.824534i	−0.162220	+	0.986755i	$0.551865\pi$
$360$		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	0.999063	+	0.0432899i	$0.0137839\pi$
$367$	36.1290	+	9.68075i	1.88592	+	0.505331i	0.886858	+	0.462041i	$0.152883\pi$
$368$		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	0.154455	−	0.988000i	$-0.450638\pi$
$373$	15.1071	−	4.04794i	0.782218	−	0.209595i	0.627762	+	0.778405i	$0.283971\pi$
$374$		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	0.362362	−	0.932037i	$-0.381970\pi$
$379$	4.09134	+	1.09627i	0.210158	+	0.0563117i	−0.152204	+	0.988349i	$0.548637\pi$
$380$		0			0
$381$	−8.21981	−	4.74571i	−0.421114	−	0.243130i
$382$		0			0
$383$	12.5287	+	7.23343i	0.640185	+	0.369611i	0.784686	−	0.619894i	$-0.212824\pi$
$383$	12.5287	+	7.23343i	0.640185	+	0.369611i	−0.144501	+	0.989505i	$0.546158\pi$
$384$		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	0.476695	−	0.879069i	$-0.341834\pi$
$397$	−0.921577	−	0.532073i	−0.0462526	−	0.0267040i	−0.522948	+	0.852365i	$0.675168\pi$
$398$		0			0
$399$	−4.00359	−	2.31148i	−0.200430	−	0.115719i
$400$		0			0
$401$	19.6698	+	5.27051i	0.982263	+	0.263197i	0.713997	−	0.700148i	$-0.246883\pi$
$401$	19.6698	+	5.27051i	0.982263	+	0.263197i	0.268266	+	0.963345i	$0.413549\pi$
$402$		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	0.957928	+	0.287009i	$0.0926610\pi$
$409$	5.49767	+	20.5176i	0.271842	+	1.01453i	−0.686085	+	0.727521i	$0.740672\pi$
$410$		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	−0.584983	−	0.811045i	$-0.698899\pi$
$419$	−3.58399	+	2.06922i	−0.175089	+	0.101088i	0.409894	+	0.912133i	$0.365566\pi$
$420$		0			0
$421$	14.3449	+	14.3449i	0.699129	+	0.699129i	0.964223	−	0.265094i	$-0.0854029\pi$
$421$	14.3449	+	14.3449i	0.699129	+	0.699129i	−0.265094	+	0.964223i	$0.585403\pi$
$422$		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	0.576443	+	0.817137i	$0.304440\pi$
$431$	−6.87880	+	25.6720i	−0.331340	+	1.23658i	−0.907783	+	0.419440i	$0.862226\pi$
$432$		0			0
$433$	−3.86366	−	14.4194i	−0.185676	−	0.692951i	−0.994485	−	0.104880i	$-0.966554\pi$
$433$	−3.86366	−	14.4194i	−0.185676	−	0.692951i	0.808809	−	0.588071i	$-0.200112\pi$
$434$		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	0.842529	−	0.538651i	$-0.181066\pi$
$439$	−0.947472	−	1.64107i	−0.0452204	−	0.0783240i	−0.887750	+	0.460327i	$0.847732\pi$
$440$		0			0
$441$			8.49528i			0.404537i
$442$		0			0
$443$	−9.19043	−	9.19043i	−0.436651	−	0.436651i	0.454232	−	0.890883i	$-0.349914\pi$
$443$	−9.19043	−	9.19043i	−0.436651	−	0.436651i	−0.890883	+	0.454232i	$0.849914\pi$
$444$		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	−0.148820	−	0.988864i	$-0.547548\pi$
$449$	4.59242	−	1.23053i	0.216730	−	0.0580725i	0.365550	+	0.930792i	$0.380881\pi$
$450$		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	−0.994618	−	0.103610i	$-0.966961\pi$
$457$	−12.5494	−	21.7363i	−0.587038	−	1.01678i	0.407580	−	0.913169i	$-0.366373\pi$
$458$		0			0
$459$	7.41967	−	12.8512i	0.346321	−	0.599845i
$460$		0			0
$461$	1.24463	−	0.333498i	0.0579683	−	0.0155326i	−0.229718	−	0.973257i	$-0.573780\pi$
$461$	1.24463	−	0.333498i	0.0579683	−	0.0155326i	0.287687	+	0.957725i	$0.407114\pi$
$462$		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	0.866773	−	0.498702i	$-0.166190\pi$
$467$	7.95409	+	7.95409i	0.368071	+	0.368071i	−0.498702	+	0.866773i	$0.666190\pi$
$468$		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	0.717687	+	0.696366i	$0.245201\pi$
$479$	−5.51597	+	20.5859i	−0.252031	+	0.940592i	−0.969718	+	0.244227i	$0.921466\pi$
$480$		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	0.287171	+	0.957879i	$0.407285\pi$
$487$	−15.1379	+	26.2196i	−0.685963	+	1.18812i	−0.973133	+	0.230243i	$0.926048\pi$
$488$		0			0
$489$	3.03294	+	3.03294i	0.137154	+	0.137154i
$490$		0			0
$491$	7.93926	−	4.58373i	0.358294	−	0.206861i	−0.310038	−	0.950724i	$-0.600342\pi$
$491$	7.93926	−	4.58373i	0.358294	−	0.206861i	0.668332	+	0.743863i	$0.267009\pi$
$492$		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	−0.958289	−	0.285800i	$-0.907741\pi$
$499$	−15.0223	+	15.0223i	−0.672489	+	0.672489i	0.285800	+	0.958289i	$0.407741\pi$
$500$		0			0
$501$	−8.62550	−	32.1908i	−0.385359	−	1.43818i
$502$		0			0
$503$	27.2502	−	7.30167i	1.21503	−	0.325565i	0.406294	−	0.913742i	$-0.366821\pi$
$503$	27.2502	−	7.30167i	1.21503	−	0.325565i	0.808732	+	0.588177i	$0.200154\pi$
$504$		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	0.00666482	−	0.999978i	$-0.497879\pi$
$509$	−10.9997	−	2.94735i	−0.487552	−	0.130639i	−0.494217	+	0.869339i	$0.664545\pi$
$510$		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	0.690515	+	0.723318i	$0.257384\pi$
$523$	−6.15518	+	22.9715i	−0.269147	+	1.00447i	−0.959663	+	0.281154i	$0.909283\pi$
$524$		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	−0.365933	−	0.930641i	$-0.619250\pi$
$541$	13.1348	−	13.1348i	0.564708	−	0.564708i	0.930641	+	0.365933i	$0.119250\pi$
$542$		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	−0.986777	−	0.162081i	$-0.948179\pi$
$547$	−19.2880	+	19.2880i	−0.824696	+	0.824696i	0.162081	+	0.986777i	$0.448179\pi$
$548$		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	−0.462910	−	0.886405i	$-0.653195\pi$
$557$	1.72959	−	0.998577i	0.0732849	−	0.0423111i	0.536195	+	0.844094i	$0.319861\pi$
$558$		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	0.900906	−	0.434013i	$-0.142903\pi$
$563$	−2.28516	−	8.52834i	−0.0963081	−	0.359427i	−0.997215	+	0.0745867i	$0.976236\pi$
$564$		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	−0.999099	−	0.0424461i	$-0.986485\pi$
$569$	−12.7930	−	22.1581i	−0.536309	−	0.928914i	0.462790	−	0.886468i	$-0.346848\pi$
$570$		0			0
$571$		−	17.2404i		−	0.721487i	−0.932665	−	0.360744i	$-0.882523\pi$
$571$		−	17.2404i		−	0.721487i	0.932665	−	0.360744i	$-0.117477\pi$
$572$		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	0.999726	−	0.0234240i	$-0.00745678\pi$
$587$	11.6192	+	20.1251i	0.479577	+	0.830652i	−0.520149	+	0.854076i	$0.674123\pi$
$588$		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	$-0.737058\pi$
$599$		−	35.9904i		−	1.47053i	0.677781	−	0.735264i	$-0.262942\pi$
$600$		0			0
$601$	−4.79547	−	8.30599i	−0.195611	−	0.338808i	0.751490	−	0.659745i	$-0.229336\pi$
$601$	−4.79547	−	8.30599i	−0.195611	−	0.338808i	−0.947101	+	0.320937i	$0.896002\pi$
$602$		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	−0.458876	−	0.888500i	$-0.651748\pi$
$607$	−12.4598	−	46.5006i	−0.505728	−	1.88740i	−0.0468517	−	0.998902i	$-0.514919\pi$
$608$		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	−0.865625	−	0.500693i	$-0.833079\pi$
$613$	−21.4121	+	12.3623i	−0.864825	+	0.499307i	0.000800300		1.00000i	$0.499745\pi$
$614$		0			0
$615$	47.1806	−	6.74556i	1.90250	−	0.272007i
$616$		0			0
$617$	19.9719	−	34.5924i	0.804040	−	1.39264i	−0.112897	−	0.993607i	$-0.536013\pi$
$617$	19.9719	−	34.5924i	0.804040	−	1.39264i	0.916937	−	0.399031i	$-0.130654\pi$
$618$		0			0
$619$	−3.50369	−	3.50369i	−0.140825	−	0.140825i	0.633180	−	0.774005i	$-0.281749\pi$
$619$	−3.50369	−	3.50369i	−0.140825	−	0.140825i	−0.774005	+	0.633180i	$0.781749\pi$
$620$		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	0.993349	+	0.115144i	$0.0367330\pi$
$631$	4.78921	+	17.8736i	0.190656	+	0.711536i	−0.802693	+	0.596392i	$0.796600\pi$
$632$		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	0.360719	−	0.932675i	$-0.382531\pi$
$641$	−6.75083	−	3.89760i	−0.266642	−	0.153946i	−0.627361	+	0.778729i	$0.715865\pi$
$642$		0			0
$643$	−23.4142	−	13.5182i	−0.923367	−	0.533106i	−0.0386590	−	0.999252i	$-0.512309\pi$
$643$	−23.4142	−	13.5182i	−0.923367	−	0.533106i	−0.884708	+	0.466147i	$0.845642\pi$
$644$		0			0
$645$	34.9758	−	27.4606i	1.37717	−	1.08126i
$646$		0			0
$647$	9.97989	−	37.2455i	0.392350	−	1.46427i	−0.433897	−	0.900962i	$-0.642862\pi$
$647$	9.97989	−	37.2455i	0.392350	−	1.46427i	0.826247	−	0.563308i	$-0.190471\pi$
$648$		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	0.748993	+	0.662578i	$0.230538\pi$
$653$	−5.90149	+	22.0247i	−0.230943	+	0.861891i	−0.979936	+	0.199313i	$0.936129\pi$
$654$		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	0.307078	−	0.951684i	$-0.400649\pi$
$659$	−9.33308	−	5.38846i	−0.363565	−	0.209905i	−0.670644	+	0.741780i	$0.733982\pi$
$660$		0			0
$661$	41.0956	+	11.0115i	1.59843	+	0.428299i	0.944569	−	0.328312i	$-0.106480\pi$
$661$	41.0956	+	11.0115i	1.59843	+	0.428299i	0.653865	+	0.756611i	$0.273146\pi$
$662$		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	0.578320	−	0.815810i	$-0.303709\pi$
$673$	17.4138	+	4.66602i	0.671254	+	0.179862i	0.0929342	+	0.995672i	$0.470375\pi$
$674$		0			0
$675$	7.14916	+	11.7707i	0.275171	+	0.453054i
$676$		0			0
$677$	−17.4931	+	17.4931i	−0.672315	+	0.672315i	−0.958249	−	0.285934i	$-0.907696\pi$
$677$	−17.4931	+	17.4931i	−0.672315	+	0.672315i	0.285934	+	0.958249i	$0.407696\pi$
$678$		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	−0.845679	−	0.533692i	$-0.820804\pi$
$683$	1.02842	−	1.78127i	0.0393514	−	0.0681586i	0.885030	+	0.465533i	$0.154138\pi$
$684$		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	−0.975889	−	0.218266i	$-0.929960\pi$
$691$	−0.568099	+	2.12017i	−0.0216115	+	0.0806552i	0.954278	+	0.298921i	$0.0966267\pi$
$692$		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	$0.163363\pi$
$701$			25.9991i			0.981972i	−0.871168	+	0.490986i	$0.836637\pi$
$702$		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	0.558603	−	0.829435i	$-0.311337\pi$
$709$	38.7979	−	10.3959i	1.45709	−	0.390425i	0.898482	+	0.439010i	$0.144671\pi$
$710$		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	−0.997369	−	0.0724910i	$-0.976905\pi$
$719$	−11.6884	+	20.2450i	−0.435905	+	0.755010i	0.561464	+	0.827501i	$0.310238\pi$
$720$		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	0.262034	−	0.965059i	$-0.415607\pi$
$727$	−18.9556	−	18.9556i	−0.703024	−	0.703024i	−0.965059	+	0.262034i	$0.915607\pi$
$728$		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	$0.353259\pi$
$733$			48.4953i			1.79122i	−0.444845	+	0.895608i	$0.646741\pi$
$734$		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	−0.926483	−	0.376335i	$-0.877184\pi$
$739$	1.74097	−	6.49738i	0.0640425	−	0.239010i	0.990526	+	0.137326i	$0.0438507\pi$
$740$		0			0
$741$	10.3737	−	4.96194i	0.381088	−	0.182281i
$742$		0			0
$743$	19.9313	−	11.5074i	0.731209	−	0.422164i	−0.0876550	−	0.996151i	$-0.527937\pi$
$743$	19.9313	−	11.5074i	0.731209	−	0.422164i	0.818864	+	0.573987i	$0.194604\pi$
$744$		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	−0.734311	−	0.678813i	$-0.762495\pi$
$751$	−14.0748	+	8.12611i	−0.513598	+	0.296526i	0.220713	+	0.975339i	$0.429161\pi$
$752$		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	0.665749	−	0.746175i	$-0.268112\pi$
$757$	23.9153	+	6.40809i	0.869218	+	0.232906i	0.203468	+	0.979082i	$0.434779\pi$
$758$		0			0
$759$	−26.1862	+	26.1862i	−0.950499	+	0.950499i
$760$		0			0
$761$	−4.77474	−	17.8196i	−0.173084	−	0.645960i	−0.996870	−	0.0790582i	$-0.974809\pi$
$761$	−4.77474	−	17.8196i	−0.173084	−	0.645960i	0.823786	−	0.566901i	$-0.191858\pi$
$762$		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	−0.518926	−	0.854819i	$-0.673668\pi$
$769$	−38.7050	−	10.3710i	−1.39574	−	0.373987i	−0.876812	+	0.480833i	$0.840335\pi$
$770$		0			0
$771$	23.8050	+	13.7439i	0.857318	+	0.494973i
$772$		0			0
$773$	20.6228	+	11.9066i	0.741750	+	0.428250i	0.822705	−	0.568468i	$-0.192464\pi$
$773$	20.6228	+	11.9066i	0.741750	+	0.428250i	−0.0809550	+	0.996718i	$0.525797\pi$
$774$		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	0.599577	−	0.800317i	$-0.295335\pi$
$787$	5.78665	+	3.34092i	0.206272	+	0.119091i	−0.393306	+	0.919408i	$0.628669\pi$
$788$		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	0.230043	−	0.973181i	$-0.426113\pi$
$797$	25.8557	−	6.92801i	0.915856	−	0.245403i	0.685813	+	0.727778i	$0.259447\pi$
$798$		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	−0.333193	−	0.942859i	$-0.608126\pi$
$809$	9.00929	−	5.20152i	0.316750	−	0.182876i	0.649943	+	0.759983i	$0.274793\pi$
$810$		0			0
$811$	−2.88418	−	2.88418i	−0.101277	−	0.101277i	0.654653	−	0.755930i	$-0.272815\pi$
$811$	−2.88418	−	2.88418i	−0.101277	−	0.101277i	−0.755930	+	0.654653i	$0.772815\pi$
$812$		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	−0.999997	−	0.00225931i	$-0.999281\pi$
$821$	−3.80641	+	14.2057i	−0.132845	+	0.495783i	0.867153	+	0.498042i	$0.165948\pi$
$822$		0			0
$823$	−6.90567	−	25.7723i	−0.240717	−	0.898366i	−0.975488	−	0.220052i	$-0.929377\pi$
$823$	−6.90567	−	25.7723i	−0.240717	−	0.898366i	0.734772	−	0.678315i	$-0.237289\pi$
$824$		0			0
$825$	35.7488	+	34.1942i	1.24461	+	1.19049i
$826$		0			0
$827$			15.9935i			0.556148i	0.960560	+	0.278074i	$0.0896961\pi$
$827$			15.9935i			0.556148i	−0.960560	+	0.278074i	$0.910304\pi$
$828$		0			0
$829$	−10.7937	−	18.6953i	−0.374882	−	0.649314i	0.615428	−	0.788193i	$-0.288983\pi$
$829$	−10.7937	−	18.6953i	−0.374882	−	0.649314i	−0.990309	+	0.138879i	$0.955650\pi$
$830$		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	−0.995284	−	0.0970040i	$-0.969074\pi$
$839$	−52.3906	+	14.0380i	−1.80872	+	0.484646i	−0.813439	+	0.581650i	$0.802407\pi$
$840$		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	0.964747	+	0.263179i	$0.0847708\pi$
$857$	35.9470	+	35.9470i	1.22793	+	1.22793i	0.263179	+	0.964747i	$0.415229\pi$
$858$		0			0
$859$		−	40.8361i		−	1.39331i	−0.717406	−	0.696655i	$-0.754671\pi$
$859$		−	40.8361i		−	1.39331i	0.717406	−	0.696655i	$-0.245329\pi$
$860$		0			0
$861$	15.4476	+	26.7560i	0.526452	+	0.911841i
$862$		0			0
$863$		−	1.61377i		−	0.0549334i	−0.999623	−	0.0274667i	$-0.991256\pi$
$863$		−	1.61377i		−	0.0549334i	0.999623	−	0.0274667i	$-0.00874403\pi$
$864$		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	−0.394647	−	0.918833i	$-0.629133\pi$
$877$	17.7214	−	30.6943i	0.598409	−	1.03647i	0.993056	−	0.117642i	$-0.0375334\pi$
$878$		0			0
$879$	38.9361	+	38.9361i	1.31328	+	1.31328i
$880$		0			0
$881$	12.1387	−	7.00829i	0.408964	−	0.236115i	−0.281381	−	0.959596i	$-0.590792\pi$
$881$	12.1387	−	7.00829i	0.408964	−	0.236115i	0.690344	+	0.723481i	$0.257459\pi$
$882$		0			0
$883$	−34.3985	+	34.3985i	−1.15760	+	1.15760i	−0.172612	+	0.984990i	$0.555221\pi$
$883$	−34.3985	+	34.3985i	−1.15760	+	1.15760i	−0.984990	+	0.172612i	$0.944779\pi$
$884$		0			0
$885$	−16.8341	−	21.4410i	−0.565871	−	0.720732i
$886$		0			0
$887$	−44.1266	−	11.8237i	−1.48163	−	0.397000i	−0.574725	−	0.818346i	$-0.694891\pi$
$887$	−44.1266	−	11.8237i	−1.48163	−	0.397000i	−0.906900	+	0.421346i	$0.861558\pi$
$888$		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	−0.253790	−	0.967259i	$-0.581677\pi$
$907$	13.5412	−	50.5364i	0.449628	−	1.67804i	0.703419	−	0.710776i	$-0.251656\pi$
$908$		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	−0.283659	−	0.958925i	$-0.591548\pi$
$919$	−38.0739	−	21.9820i	−1.25594	−	0.725118i	−0.972283	+	0.233807i	$0.924882\pi$
$920$		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	0.963469	−	0.267821i	$-0.0863035\pi$
$929$	−0.147215	−	0.549414i	−0.00482997	−	0.0180257i	−0.968299	+	0.249795i	$0.919637\pi$
$930$		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	−0.810990	−	0.585059i	$-0.801071\pi$
$937$	−6.91585	+	6.91585i	−0.225931	+	0.225931i	0.585059	+	0.810990i	$0.301071\pi$
$938$		0			0
$939$	−50.8322	+	29.3480i	−1.65885	+	0.957736i
$940$		0			0
$941$	−4.12906	−	4.12906i	−0.134604	−	0.134604i	0.636595	−	0.771198i	$-0.280342\pi$
$941$	−4.12906	−	4.12906i	−0.134604	−	0.134604i	−0.771198	+	0.636595i	$0.780342\pi$
$942$		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	−0.700317	−	0.713832i	$-0.746958\pi$
$947$	−13.3027	+	7.68029i	−0.432278	+	0.249576i	0.268039	+	0.963408i	$0.413625\pi$
$948$		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	0.932808	−	0.360373i	$-0.117351\pi$
$953$	−1.70449	−	6.36124i	−0.0552138	−	0.206061i	−0.988022	+	0.154312i	$0.950684\pi$
$954$		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	0.173193	+	0.984888i	$0.444592\pi$
$971$	−23.8799	+	41.3611i	−0.766341	+	1.32734i	−0.939534	+	0.342454i	$0.888742\pi$
$972$		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	0.931279	−	0.364307i	$-0.118694\pi$
$977$	4.69292	+	8.12838i	0.150140	+	0.260050i	−0.781139	+	0.624357i	$0.785361\pi$
$978$		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	0.913763	−	0.406248i	$-0.133163\pi$
$991$	3.30731	+	5.72843i	0.105060	+	0.181970i	−0.808703	+	0.588218i	$0.799830\pi$
$992$		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	−0.996647	−	0.0818241i	$-0.973925\pi$
$997$	−5.50791	−	20.5558i	−0.174437	−	0.651009i	0.822209	−	0.569185i	$-0.192741\pi$
$998$		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.193.2	yes	20
5.2	odd	4		260.2.bf.c.37.4	✓	20
5.3	odd	4		1300.2.bn.d.557.2		20
5.4	even	2		1300.2.bs.d.193.4		20
13.6	odd	12		260.2.bf.c.253.4	yes	20
65.19	odd	12		1300.2.bn.d.1293.2		20
65.32	even	12	inner	260.2.bk.c.97.2	yes	20
65.58	even	12		1300.2.bs.d.357.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.bf.c.37.4	✓	20	5.2	odd	4
260.2.bf.c.253.4	yes	20	13.6	odd	12
260.2.bk.c.97.2	yes	20	65.32	even	12	inner
260.2.bk.c.193.2	yes	20	1.1	even	1	trivial
1300.2.bn.d.557.2		20	5.3	odd	4
1300.2.bn.d.1293.2		20	65.19	odd	12
1300.2.bs.d.193.4		20	5.4	even	2
1300.2.bs.d.357.4		20	65.58	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
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

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Representations

Groups

Database

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