LMFDB - Embedded newform 287.2.c.a.204.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,2,Mod(204,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("287.204");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	287.c (of order $2$, degree $1$, 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:	$2.29170653801$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 13x^{8} + 60x^{6} + 118x^{4} + 96x^{2} + 25 $ x^10 + 13x^8 + 60x^6 + 118x^4 + 96x^2 + 25
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			204.10
Root			$0.698160i$ of defining polynomial
Character	$\chi$	$=$	287.204
Dual form			287.2.c.a.204.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.51257 q^{2} +1.69816i q^{3} +4.31302 q^{4} -2.49861 q^{5} +4.26675i q^{6} +1.00000i q^{7} +5.81162 q^{8} +0.116251 q^{9} +O(q^{10})$	\(q+2.51257 q^{2} +1.69816i q^{3} +4.31302 q^{4} -2.49861 q^{5} +4.26675i q^{6} +1.00000i q^{7} +5.81162 q^{8} +0.116251 q^{9} -6.27793 q^{10} -0.348107i q^{11} +7.32420i q^{12} -3.06720i q^{13} +2.51257i q^{14} -4.24303i q^{15} +5.97609 q^{16} +1.01118i q^{17} +0.292089 q^{18} -7.16168i q^{19} -10.7765 q^{20} -1.69816 q^{21} -0.874645i q^{22} +1.09448 q^{23} +9.86907i q^{24} +1.24303 q^{25} -7.70655i q^{26} +5.29189i q^{27} +4.31302i q^{28} -3.45039i q^{29} -10.6609i q^{30} -0.619073 q^{31} +3.39211 q^{32} +0.591142 q^{33} +2.54066i q^{34} -2.49861i q^{35} +0.501393 q^{36} -9.80884 q^{37} -17.9942i q^{38} +5.20859 q^{39} -14.5210 q^{40} +(4.67704 + 4.37325i) q^{41} -4.26675 q^{42} -1.10371 q^{43} -1.50139i q^{44} -0.290466 q^{45} +2.74996 q^{46} +4.32841i q^{47} +10.1484i q^{48} -1.00000 q^{49} +3.12321 q^{50} -1.71714 q^{51} -13.2289i q^{52} +12.6330i q^{53} +13.2963i q^{54} +0.869783i q^{55} +5.81162i q^{56} +12.1617 q^{57} -8.66936i q^{58} +14.5405 q^{59} -18.3003i q^{60} -0.654679 q^{61} -1.55547 q^{62} +0.116251i q^{63} -3.42927 q^{64} +7.66372i q^{65} +1.48529 q^{66} -10.0293i q^{67} +4.36123i q^{68} +1.85860i q^{69} -6.27793i q^{70} -13.0244i q^{71} +0.675608 q^{72} -7.55378 q^{73} -24.6454 q^{74} +2.11087i q^{75} -30.8884i q^{76} +0.348107 q^{77} +13.0870 q^{78} +12.6400i q^{79} -14.9319 q^{80} -8.63773 q^{81} +(11.7514 + 10.9881i) q^{82} +6.60297 q^{83} -7.32420 q^{84} -2.52654i q^{85} -2.77316 q^{86} +5.85932 q^{87} -2.02307i q^{88} +10.4335i q^{89} -0.729817 q^{90} +3.06720 q^{91} +4.72052 q^{92} -1.05129i q^{93} +10.8754i q^{94} +17.8942i q^{95} +5.76034i q^{96} +1.81305i q^{97} -2.51257 q^{98} -0.0404679i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{2} + 12 q^{4} - 10 q^{5} + 12 q^{8} - 10 q^{9}+O(q^{10}) $ 10 * q + 4 * q^2 + 12 * q^4 - 10 * q^5 + 12 * q^8 - 10 * q^9	$ 10 q + 4 q^{2} + 12 q^{4} - 10 q^{5} + 12 q^{8} - 10 q^{9} + 8 q^{10} - 16 q^{16} + 20 q^{18} - 22 q^{20} - 12 q^{21} - 4 q^{23} - 4 q^{25} + 14 q^{31} + 18 q^{32} - 2 q^{33} + 20 q^{36} - 22 q^{37} - 46 q^{39} - 58 q^{40} - 4 q^{41} - 8 q^{42} + 18 q^{43} + 50 q^{45} + 8 q^{46} - 10 q^{49} - 22 q^{50} + 14 q^{51} + 62 q^{57} + 34 q^{59} - 28 q^{61} - 44 q^{62} + 8 q^{64} - 36 q^{66} - 20 q^{72} + 12 q^{74} + 12 q^{77} + 78 q^{78} - 4 q^{80} + 10 q^{81} + 74 q^{82} - 20 q^{83} - 6 q^{84} + 12 q^{86} - 8 q^{87} - 54 q^{90} - 14 q^{91} - 30 q^{92} - 4 q^{98}+O(q^{100}) $ 10 * q + 4 * q^2 + 12 * q^4 - 10 * q^5 + 12 * q^8 - 10 * q^9 + 8 * q^10 - 16 * q^16 + 20 * q^18 - 22 * q^20 - 12 * q^21 - 4 * q^23 - 4 * q^25 + 14 * q^31 + 18 * q^32 - 2 * q^33 + 20 * q^36 - 22 * q^37 - 46 * q^39 - 58 * q^40 - 4 * q^41 - 8 * q^42 + 18 * q^43 + 50 * q^45 + 8 * q^46 - 10 * q^49 - 22 * q^50 + 14 * q^51 + 62 * q^57 + 34 * q^59 - 28 * q^61 - 44 * q^62 + 8 * q^64 - 36 * q^66 - 20 * q^72 + 12 * q^74 + 12 * q^77 + 78 * q^78 - 4 * q^80 + 10 * q^81 + 74 * q^82 - 20 * q^83 - 6 * q^84 + 12 * q^86 - 8 * q^87 - 54 * q^90 - 14 * q^91 - 30 * q^92 - 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$1$	$-1$

Coefficient data

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

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

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

$2$	2.51257			1.77666			0.888328	−	0.459209i	$-0.151867\pi$
$2$	2.51257			1.77666			0.888328	+	0.459209i	$0.151867\pi$
$3$			1.69816i			0.980433i	0.871601	+	0.490217i	$0.163082\pi$
$3$			1.69816i			0.980433i	−0.871601	+	0.490217i	$0.836918\pi$
$4$	4.31302			2.15651
$5$	−2.49861			−1.11741			−0.558705	−	0.829366i	$-0.688702\pi$
$5$	−2.49861			−1.11741			−0.558705	+	0.829366i	$0.688702\pi$
$6$			4.26675i			1.74189i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	5.81162			2.05472
$9$	0.116251			0.0387504
$10$	−6.27793			−1.98526
$11$		−	0.348107i		−	0.104958i	−0.998622	−	0.0524792i	$-0.983288\pi$
$11$		−	0.348107i		−	0.104958i	0.998622	−	0.0524792i	$-0.0167123\pi$
$12$			7.32420i			2.11431i
$13$		−	3.06720i		−	0.850687i	−0.905032	−	0.425344i	$-0.860153\pi$
$13$		−	3.06720i		−	0.850687i	0.905032	−	0.425344i	$-0.139847\pi$
$14$			2.51257i			0.671513i
$15$		−	4.24303i		−	1.09555i
$16$	5.97609			1.49402
$17$			1.01118i			0.245247i	0.992453	+	0.122623i	$0.0391307\pi$
$17$			1.01118i			0.245247i	−0.992453	+	0.122623i	$0.960869\pi$
$18$	0.292089			0.0688461
$19$		−	7.16168i		−	1.64300i	−0.570207	−	0.821501i	$-0.693137\pi$
$19$		−	7.16168i		−	1.64300i	0.570207	−	0.821501i	$-0.306863\pi$
$20$	−10.7765			−2.40971
$21$	−1.69816			−0.370569
$22$		−	0.874645i		−	0.186475i
$23$	1.09448			0.228215			0.114108	−	0.993468i	$-0.463599\pi$
$23$	1.09448			0.228215			0.114108	+	0.993468i	$0.463599\pi$
$24$			9.86907i			2.01452i
$25$	1.24303			0.248607
$26$		−	7.70655i		−	1.51138i
$27$			5.29189i			1.01843i
$28$			4.31302i			0.815084i
$29$		−	3.45039i		−	0.640722i	−0.947296	−	0.320361i	$-0.896196\pi$
$29$		−	3.45039i		−	0.640722i	0.947296	−	0.320361i	$-0.103804\pi$
$30$		−	10.6609i		−	1.94641i
$31$	−0.619073			−0.111189			−0.0555944	−	0.998453i	$-0.517705\pi$
$31$	−0.619073			−0.111189			−0.0555944	+	0.998453i	$0.517705\pi$
$32$	3.39211			0.599645
$33$	0.591142			0.102905
$34$			2.54066i			0.435719i
$35$		−	2.49861i		−	0.422342i
$36$	0.501393			0.0835656
$37$	−9.80884			−1.61256			−0.806282	−	0.591532i	$-0.798523\pi$
$37$	−9.80884			−1.61256			−0.806282	+	0.591532i	$0.798523\pi$
$38$		−	17.9942i		−	2.91905i
$39$	5.20859			0.834042
$40$	−14.5210			−2.29597
$41$	4.67704	+	4.37325i	0.730430	+	0.682987i
$41$	4.67704	+	4.37325i	0.730430	+	0.682987i
$42$	−4.26675			−0.658374
$43$	−1.10371			−0.168315			−0.0841574	−	0.996452i	$-0.526820\pi$
$43$	−1.10371			−0.168315			−0.0841574	+	0.996452i	$0.526820\pi$
$44$		−	1.50139i		−	0.226344i
$45$	−0.290466			−0.0433001
$46$	2.74996			0.405460
$47$			4.32841i			0.631364i	0.948865	+	0.315682i	$0.102233\pi$
$47$			4.32841i			0.631364i	−0.948865	+	0.315682i	$0.897767\pi$
$48$			10.1484i			1.46479i
$49$	−1.00000			−0.142857
$50$	3.12321			0.441689
$51$	−1.71714			−0.240448
$52$		−	13.2289i		−	1.83451i
$53$			12.6330i			1.73528i	0.497196	+	0.867638i	$0.334363\pi$
$53$			12.6330i			1.73528i	−0.497196	+	0.867638i	$0.665637\pi$
$54$			13.2963i			1.80939i
$55$			0.869783i			0.117282i
$56$			5.81162i			0.776611i
$57$	12.1617			1.61085
$58$		−	8.66936i		−	1.13834i
$59$	14.5405			1.89301			0.946504	−	0.322693i	$-0.104588\pi$
$59$	14.5405			1.89301			0.946504	+	0.322693i	$0.104588\pi$
$60$		−	18.3003i		−	2.36256i
$61$	−0.654679			−0.0838231			−0.0419116	−	0.999121i	$-0.513345\pi$
$61$	−0.654679			−0.0838231			−0.0419116	+	0.999121i	$0.513345\pi$
$62$	−1.55547			−0.197544
$63$			0.116251i			0.0146463i
$64$	−3.42927			−0.428659
$65$			7.66372i			0.950567i
$66$	1.48529			0.182826
$67$		−	10.0293i		−	1.22528i	−0.790363	−	0.612638i	$-0.790108\pi$
$67$		−	10.0293i		−	1.22528i	0.790363	−	0.612638i	$-0.209892\pi$
$68$			4.36123i			0.528877i
$69$			1.85860i			0.223750i
$70$		−	6.27793i		−	0.750356i
$71$		−	13.0244i		−	1.54572i	−0.634579	−	0.772858i	$-0.718827\pi$
$71$		−	13.0244i		−	1.54572i	0.634579	−	0.772858i	$-0.281173\pi$
$72$	0.675608			0.0796212
$73$	−7.55378			−0.884103			−0.442052	−	0.896990i	$-0.645749\pi$
$73$	−7.55378			−0.884103			−0.442052	+	0.896990i	$0.645749\pi$
$74$	−24.6454			−2.86497
$75$			2.11087i			0.243743i
$76$		−	30.8884i		−	3.54315i
$77$	0.348107			0.0396705
$78$	13.0870			1.48181
$79$			12.6400i			1.42211i	0.703138	+	0.711053i	$0.251782\pi$
$79$			12.6400i			1.42211i	−0.703138	+	0.711053i	$0.748218\pi$
$80$	−14.9319			−1.66944
$81$	−8.63773			−0.959748
$82$	11.7514	+	10.9881i	1.29772	+	1.21343i
$83$	6.60297			0.724770			0.362385	−	0.932029i	$-0.381963\pi$
$83$	6.60297			0.724770			0.362385	+	0.932029i	$0.381963\pi$
$84$	−7.32420			−0.799135
$85$		−	2.52654i		−	0.274041i
$86$	−2.77316			−0.299038
$87$	5.85932			0.628185
$88$		−	2.02307i		−	0.215660i
$89$			10.4335i			1.10595i	0.833199	+	0.552974i	$0.186507\pi$
$89$			10.4335i			1.10595i	−0.833199	+	0.552974i	$0.813493\pi$
$90$	−0.729817			−0.0769294
$91$	3.06720			0.321530
$92$	4.72052			0.492148
$93$		−	1.05129i		−	0.109013i
$94$			10.8754i			1.12172i
$95$			17.8942i			1.83591i
$96$			5.76034i			0.587912i
$97$			1.81305i			0.184088i	0.995755	+	0.0920438i	$0.0293400\pi$
$97$			1.81305i			0.184088i	−0.995755	+	0.0920438i	$0.970660\pi$
$98$	−2.51257			−0.253808
$99$		−	0.0404679i		−	0.00406718i
$100$	5.36123			0.536123
$101$		−	1.66813i		−	0.165985i	−0.996550	−	0.0829925i	$-0.973552\pi$
$101$		−	1.66813i		−	0.165985i	0.996550	−	0.0829925i	$-0.0264477\pi$
$102$	−4.31445			−0.427194
$103$	−18.3072			−1.80387			−0.901933	−	0.431875i	$-0.857852\pi$
$103$	−18.3072			−1.80387			−0.901933	+	0.431875i	$0.857852\pi$
$104$		−	17.8254i		−	1.74792i
$105$	4.24303			0.414078
$106$			31.7413i			3.08299i
$107$	−13.0566			−1.26223			−0.631115	−	0.775689i	$-0.717402\pi$
$107$	−13.0566			−1.26223			−0.631115	+	0.775689i	$0.717402\pi$
$108$			22.8240i			2.19624i
$109$			17.3725i			1.66399i	0.554785	+	0.831994i	$0.312801\pi$
$109$			17.3725i			1.66399i	−0.554785	+	0.831994i	$0.687199\pi$
$110$			2.18539i			0.208369i
$111$		−	16.6570i		−	1.58101i
$112$			5.97609i			0.564687i
$113$	9.31931			0.876687			0.438343	−	0.898808i	$-0.355565\pi$
$113$	9.31931			0.876687			0.438343	+	0.898808i	$0.355565\pi$
$114$	30.5571			2.86193
$115$	−2.73468			−0.255010
$116$		−	14.8816i		−	1.38172i
$117$		−	0.356565i		−	0.0329645i
$118$	36.5340			3.36322
$119$	−1.01118			−0.0926946
$120$		−	24.6589i		−	2.25104i
$121$	10.8788			0.988984
$122$	−1.64493			−0.148925
$123$	−7.42648	+	7.94236i	−0.669623	+	0.716138i
$124$	−2.67007			−0.239780
$125$	9.38718			0.839615
$126$			0.292089i			0.0260214i
$127$	0.834694			0.0740671			0.0370336	−	0.999314i	$-0.488209\pi$
$127$	0.834694			0.0740671			0.0370336	+	0.999314i	$0.488209\pi$
$128$	−15.4005			−1.36122
$129$		−	1.87428i		−	0.165021i
$130$			19.2556i			1.68883i
$131$	−13.6386			−1.19161			−0.595807	−	0.803128i	$-0.703168\pi$
$131$	−13.6386			−1.19161			−0.595807	+	0.803128i	$0.703168\pi$
$132$	2.54961			0.221915
$133$	7.16168			0.620996
$134$		−	25.1994i		−	2.17690i
$135$		−	13.2224i		−	1.13800i
$136$			5.87659i			0.503913i
$137$		−	9.67246i		−	0.826374i	−0.910646	−	0.413187i	$-0.864416\pi$
$137$		−	9.67246i		−	0.826374i	0.910646	−	0.413187i	$-0.135584\pi$
$138$			4.66988i			0.397526i
$139$	6.42218			0.544722			0.272361	−	0.962195i	$-0.412196\pi$
$139$	6.42218			0.544722			0.272361	+	0.962195i	$0.412196\pi$
$140$		−	10.7765i		−	0.910783i
$141$	−7.35034			−0.619010
$142$		−	32.7248i		−	2.74621i
$143$	−1.06771			−0.0892867
$144$	0.694727			0.0578940
$145$			8.62117i			0.715950i
$146$	−18.9794			−1.57075
$147$		−	1.69816i		−	0.140062i
$148$	−42.3057			−3.47751
$149$		−	1.74372i		−	0.142851i	−0.997446	−	0.0714254i	$-0.977245\pi$
$149$		−	1.74372i		−	0.142851i	0.997446	−	0.0714254i	$-0.0227548\pi$
$150$			5.30372i			0.433047i
$151$		−	9.37714i		−	0.763101i	−0.924348	−	0.381551i	$-0.875390\pi$
$151$		−	9.37714i		−	0.763101i	0.924348	−	0.381551i	$-0.124610\pi$
$152$		−	41.6210i		−	3.37591i
$153$			0.117551i			0.00950341i
$154$	0.874645			0.0704809
$155$	1.54682			0.124244
$156$	22.4648			1.79862
$157$		−	13.6882i		−	1.09244i	−0.837642	−	0.546219i	$-0.816067\pi$
$157$		−	13.6882i		−	1.09244i	0.837642	−	0.546219i	$-0.183933\pi$
$158$			31.7588i			2.52660i
$159$	−21.4529			−1.70132
$160$	−8.47554			−0.670050
$161$			1.09448i			0.0862572i
$162$	−21.7029			−1.70514
$163$	24.8870			1.94930			0.974651	−	0.223731i	$-0.0718238\pi$
$163$	24.8870			1.94930			0.974651	+	0.223731i	$0.0718238\pi$
$164$	20.1721	+	18.8619i	1.57518	+	1.47287i
$165$	−1.47703			−0.114987
$166$	16.5904			1.28767
$167$			9.84179i			0.761580i	0.924661	+	0.380790i	$0.124348\pi$
$167$			9.84179i			0.761580i	−0.924661	+	0.380790i	$0.875652\pi$
$168$	−9.86907			−0.761415
$169$	3.59231			0.276331
$170$		−	6.34811i		−	0.486878i
$171$		−	0.832553i		−	0.0636670i
$172$	−4.76034			−0.362972
$173$	6.18150			0.469971			0.234985	−	0.971999i	$-0.424496\pi$
$173$	6.18150			0.469971			0.234985	+	0.971999i	$0.424496\pi$
$174$	14.7220			1.11607
$175$			1.24303i			0.0939646i
$176$		−	2.08032i		−	0.156810i
$177$			24.6920i			1.85597i
$178$			26.2149i			1.96489i
$179$		−	10.4046i		−	0.777680i	−0.921305	−	0.388840i	$-0.872876\pi$
$179$		−	10.4046i		−	0.777680i	0.921305	−	0.388840i	$-0.127124\pi$
$180$	−1.25278			−0.0933771
$181$		−	13.1378i		−	0.976525i	−0.872697	−	0.488263i	$-0.837631\pi$
$181$		−	13.1378i		−	0.976525i	0.872697	−	0.488263i	$-0.162369\pi$
$182$	7.70655			0.571248
$183$		−	1.11175i		−	0.0821830i
$184$	6.36071			0.468918
$185$	24.5084			1.80190
$186$		−	2.64143i		−	0.193679i
$187$	0.351999			0.0257407
$188$			18.6685i			1.36154i
$189$	−5.29189			−0.384929
$190$			44.9605i			3.26178i
$191$		−	4.01393i		−	0.290438i	−0.989400	−	0.145219i	$-0.953611\pi$
$191$		−	4.01393i		−	0.290438i	0.989400	−	0.145219i	$-0.0463886\pi$
$192$		−	5.82345i		−	0.420271i
$193$			12.8565i			0.925434i	0.886506	+	0.462717i	$0.153125\pi$
$193$			12.8565i			0.925434i	−0.886506	+	0.462717i	$0.846875\pi$
$194$			4.55543i			0.327061i
$195$	−13.0142			−0.931968
$196$	−4.31302			−0.308073
$197$	9.30450			0.662918			0.331459	−	0.943470i	$-0.392459\pi$
$197$	9.30450			0.662918			0.331459	+	0.943470i	$0.392459\pi$
$198$		−	0.101678i		−	0.00722598i
$199$			9.08955i			0.644341i	0.946682	+	0.322171i	$0.104412\pi$
$199$			9.08955i			0.644341i	−0.946682	+	0.322171i	$0.895588\pi$
$200$	7.22405			0.510818
$201$	17.0314			1.20130
$202$		−	4.19129i		−	0.294898i
$203$	3.45039			0.242170
$204$	−7.40607			−0.518529
$205$	−11.6861	−	10.9270i	−0.816191	−	0.763177i
$206$	−45.9983			−3.20485
$207$	0.127235			0.00884343
$208$		−	18.3298i		−	1.27095i
$209$	−2.49303			−0.172447
$210$	10.6609			0.735674
$211$		−	9.57921i		−	0.659460i	−0.944075	−	0.329730i	$-0.893042\pi$
$211$		−	9.57921i		−	0.659460i	0.944075	−	0.329730i	$-0.106958\pi$
$212$			54.4864i			3.74214i
$213$	22.1176			1.51547
$214$	−32.8057			−2.24255
$215$	2.75775			0.188077
$216$			30.7545i			2.09258i
$217$		−	0.619073i		−	0.0420254i
$218$			43.6498i			2.95633i
$219$		−	12.8275i		−	0.866805i
$220$			3.75139i			0.252919i
$221$	3.10148			0.208628
$222$		−	41.8519i		−	2.80891i
$223$	−4.92007			−0.329472			−0.164736	−	0.986338i	$-0.552677\pi$
$223$	−4.92007			−0.329472			−0.164736	+	0.986338i	$0.552677\pi$
$224$			3.39211i			0.226645i
$225$	0.144504			0.00963362
$226$	23.4154			1.55757
$227$		−	22.7023i		−	1.50680i	−0.657562	−	0.753401i	$-0.728412\pi$
$227$		−	22.7023i		−	1.50680i	0.657562	−	0.753401i	$-0.271588\pi$
$228$	52.4535			3.47382
$229$		−	11.6126i		−	0.767381i	−0.923462	−	0.383691i	$-0.874653\pi$
$229$		−	11.6126i		−	0.767381i	0.923462	−	0.383691i	$-0.125347\pi$
$230$	−6.87108			−0.453065
$231$			0.591142i			0.0388943i
$232$		−	20.0524i		−	1.31650i
$233$			25.7932i			1.68977i	0.534946	+	0.844886i	$0.320332\pi$
$233$			25.7932i			1.68977i	−0.534946	+	0.844886i	$0.679668\pi$
$234$		−	0.895896i		−	0.0585665i
$235$		−	10.8150i		−	0.705493i
$236$	62.7133			4.08229
$237$	−21.4647			−1.39428
$238$	−2.54066			−0.164686
$239$		−	1.18965i		−	0.0769519i	−0.999260	−	0.0384760i	$-0.987750\pi$
$239$		−	1.18965i		−	0.0769519i	0.999260	−	0.0384760i	$-0.0122503\pi$
$240$		−	25.3568i		−	1.63677i
$241$	−18.2230			−1.17385			−0.586925	−	0.809642i	$-0.699661\pi$
$241$	−18.2230			−1.17385			−0.586925	+	0.809642i	$0.699661\pi$
$242$	27.3338			1.75708
$243$			1.20743i			0.0774566i
$244$	−2.82364			−0.180765
$245$	2.49861			0.159630
$246$	−18.6596	+	19.9557i	−1.18969	+	1.27233i
$247$	−21.9663			−1.39768
$248$	−3.59782			−0.228462
$249$			11.2129i			0.710588i
$250$	23.5860			1.49171
$251$	−5.26122			−0.332085			−0.166042	−	0.986119i	$-0.553099\pi$
$251$	−5.26122			−0.332085			−0.166042	+	0.986119i	$0.553099\pi$
$252$			0.501393i			0.0315848i
$253$		−	0.380997i		−	0.0239531i
$254$	2.09723			0.131592
$255$	4.29047			0.268679
$256$	−31.8363			−1.98977
$257$			16.2646i			1.01455i	0.861783	+	0.507277i	$0.169348\pi$
$257$			16.2646i			1.01455i	−0.861783	+	0.507277i	$0.830652\pi$
$258$		−	4.70927i		−	0.293187i
$259$		−	9.80884i		−	0.609492i
$260$			33.0538i			2.04991i
$261$		−	0.401112i		−	0.0248282i
$262$	−34.2681			−2.11709
$263$		−	22.0719i		−	1.36101i	−0.732742	−	0.680507i	$-0.761760\pi$
$263$		−	22.0719i		−	1.36101i	0.732742	−	0.680507i	$-0.238240\pi$
$264$	3.43550			0.211440
$265$		−	31.5649i		−	1.93902i
$266$	17.9942			1.10330
$267$	−17.7177			−1.08431
$268$		−	43.2566i		−	2.64232i
$269$	−6.61836			−0.403529			−0.201764	−	0.979434i	$-0.564667\pi$
$269$	−6.61836			−0.403529			−0.201764	+	0.979434i	$0.564667\pi$
$270$		−	33.2221i		−	2.02183i
$271$	18.8438			1.14468			0.572340	−	0.820016i	$-0.306036\pi$
$271$	18.8438			1.14468			0.572340	+	0.820016i	$0.306036\pi$
$272$			6.04289i			0.366404i
$273$			5.20859i			0.315238i
$274$		−	24.3028i		−	1.46818i
$275$		−	0.432710i		−	0.0260934i
$276$			8.01620i			0.482518i
$277$	−16.4286			−0.987096			−0.493548	−	0.869718i	$-0.664300\pi$
$277$	−16.4286			−0.987096			−0.493548	+	0.869718i	$0.664300\pi$
$278$	16.1362			0.967784
$279$	−0.0719680			−0.00430861
$280$		−	14.5210i		−	0.867794i
$281$			27.1851i			1.62173i	0.585236	+	0.810863i	$0.301002\pi$
$281$			27.1851i			1.62173i	−0.585236	+	0.810863i	$0.698998\pi$
$282$	−18.4683			−1.09977
$283$	−15.1641			−0.901411			−0.450705	−	0.892673i	$-0.648827\pi$
$283$	−15.1641			−0.901411			−0.450705	+	0.892673i	$0.648827\pi$
$284$		−	56.1746i		−	3.33335i
$285$	−30.3872			−1.79999
$286$	−2.68271			−0.158632
$287$	−4.37325	+	4.67704i	−0.258145	+	0.276077i
$288$	0.394336			0.0232365
$289$	15.9775			0.939854
$290$			21.6613i			1.27200i
$291$	−3.07886			−0.180486
$292$	−32.5796			−1.90658
$293$			0.643610i			0.0376001i	0.999823	+	0.0188000i	$0.00598459\pi$
$293$			0.643610i			0.0376001i	−0.999823	+	0.0188000i	$0.994015\pi$
$294$		−	4.26675i		−	0.248842i
$295$	−36.3309			−2.11527
$296$	−57.0053			−3.31336
$297$	1.84215			0.106892
$298$		−	4.38121i		−	0.253797i
$299$		−	3.35699i		−	0.194140i
$300$			9.10423i			0.525633i
$301$		−	1.10371i		−	0.0636170i
$302$		−	23.5607i		−	1.35577i
$303$	2.83275			0.162737
$304$		−	42.7988i		−	2.45468i
$305$	1.63579			0.0936649
$306$			0.295355i			0.0168843i
$307$	−12.7588			−0.728185			−0.364092	−	0.931363i	$-0.618621\pi$
$307$	−12.7588			−0.728185			−0.364092	+	0.931363i	$0.618621\pi$
$308$	1.50139			0.0855498
$309$		−	31.0886i		−	1.76857i
$310$	3.88650			0.220738
$311$		−	14.6006i		−	0.827922i	−0.910295	−	0.413961i	$-0.864145\pi$
$311$		−	14.6006i		−	0.827922i	0.910295	−	0.413961i	$-0.135855\pi$
$312$	30.2704			1.71372
$313$		−	26.0531i		−	1.47261i	−0.676651	−	0.736304i	$-0.736569\pi$
$313$		−	26.0531i		−	1.47261i	0.676651	−	0.736304i	$-0.263431\pi$
$314$		−	34.3926i		−	1.94089i
$315$		−	0.290466i		−	0.0163659i
$316$			54.5164i			3.06679i
$317$			13.3722i			0.751059i	0.926811	+	0.375529i	$0.122539\pi$
$317$			13.3722i			0.751059i	−0.926811	+	0.375529i	$0.877461\pi$
$318$	−53.9019			−3.02267
$319$	−1.20111			−0.0672491
$320$	8.56839			0.478988
$321$		−	22.1722i		−	1.23753i
$322$			2.74996i			0.153249i
$323$	7.24174			0.402941
$324$	−37.2547			−2.06971
$325$		−	3.81263i		−	0.211487i
$326$	62.5304			3.46324
$327$	−29.5014			−1.63143
$328$	27.1812	+	25.4157i	1.50083	+	1.40335i
$329$	−4.32841			−0.238633
$330$	−3.71115			−0.204292
$331$		−	29.4856i		−	1.62068i	−0.585963	−	0.810338i	$-0.699284\pi$
$331$		−	29.4856i		−	1.62068i	0.585963	−	0.810338i	$-0.300716\pi$
$332$	28.4787			1.56297
$333$	−1.14029			−0.0624874
$334$			24.7282i			1.35307i
$335$			25.0593i			1.36914i
$336$	−10.1484			−0.553638
$337$	28.0414			1.52751			0.763755	−	0.645506i	$-0.223353\pi$
$337$	28.0414			1.52751			0.763755	+	0.645506i	$0.223353\pi$
$338$	9.02593			0.490946
$339$			15.8257i			0.859533i
$340$		−	10.8970i		−	0.590973i
$341$			0.215504i			0.0116702i
$342$		−	2.09185i		−	0.113114i
$343$		−	1.00000i		−	0.0539949i
$344$	−6.41437			−0.345840
$345$		−	4.64392i		−	0.250020i
$346$	15.5315			0.834977
$347$			13.7213i			0.736597i	0.929708	+	0.368298i	$0.120060\pi$
$347$			13.7213i			0.736597i	−0.929708	+	0.368298i	$0.879940\pi$
$348$	25.2714			1.35469
$349$	14.4149			0.771613			0.385807	−	0.922580i	$-0.373923\pi$
$349$	14.4149			0.771613			0.385807	+	0.922580i	$0.373923\pi$
$350$			3.12321i			0.166943i
$351$	16.2313			0.866362
$352$		−	1.18082i		−	0.0629378i
$353$	26.4494			1.40776			0.703880	−	0.710319i	$-0.251449\pi$
$353$	26.4494			1.40776			0.703880	+	0.710319i	$0.251449\pi$
$354$			62.0405i			3.29742i
$355$			32.5429i			1.72720i
$356$			44.9998i			2.38499i
$357$		−	1.71714i		−	0.0908809i
$358$		−	26.1424i		−	1.38167i
$359$	−5.41115			−0.285590			−0.142795	−	0.989752i	$-0.545609\pi$
$359$	−5.41115			−0.285590			−0.142795	+	0.989752i	$0.545609\pi$
$360$	−1.68808			−0.0889696
$361$	−32.2896			−1.69945
$362$		−	33.0097i		−	1.73495i
$363$			18.4740i			0.969633i
$364$	13.2289			0.693381
$365$	18.8739			0.987907
$366$		−	2.79335i		−	0.146011i
$367$	−15.8355			−0.826606			−0.413303	−	0.910594i	$-0.635625\pi$
$367$	−15.8355			−0.826606			−0.413303	+	0.910594i	$0.635625\pi$
$368$	6.54072			0.340958
$369$	0.543711	+	0.508396i	0.0283045	+	0.0264660i
$370$	61.5792			3.20135
$371$	−12.6330			−0.655873
$372$		−	4.53421i		−	0.235088i
$373$	−6.36186			−0.329405			−0.164702	−	0.986343i	$-0.552666\pi$
$373$	−6.36186			−0.329405			−0.164702	+	0.986343i	$0.552666\pi$
$374$	0.884422			0.0457324
$375$			15.9409i			0.823186i
$376$			25.1551i			1.29728i
$377$	−10.5830			−0.545054
$378$	−13.2963			−0.683886
$379$	29.8798			1.53482			0.767410	−	0.641156i	$-0.221545\pi$
$379$	29.8798			1.53482			0.767410	+	0.641156i	$0.221545\pi$
$380$			77.1781i			3.95915i
$381$			1.41744i			0.0726179i
$382$		−	10.0853i		−	0.516008i
$383$			1.31230i			0.0670555i	0.999438	+	0.0335277i	$0.0106742\pi$
$383$			1.31230i			0.0670555i	−0.999438	+	0.0335277i	$0.989326\pi$
$384$		−	26.1525i		−	1.33459i
$385$	−0.869783			−0.0443283
$386$			32.3030i			1.64418i
$387$	−0.128308			−0.00652227
$388$			7.81973i			0.396987i
$389$	−17.2911			−0.876691			−0.438346	−	0.898807i	$-0.644435\pi$
$389$	−17.2911			−0.876691			−0.438346	+	0.898807i	$0.644435\pi$
$390$	−32.6992			−1.65579
$391$			1.10672i			0.0559690i
$392$	−5.81162			−0.293531
$393$		−	23.1606i		−	1.16830i
$394$	23.3782			1.17778
$395$		−	31.5823i		−	1.58908i
$396$		−	0.174539i		−	0.00877090i
$397$		−	11.2964i		−	0.566952i	−0.958979	−	0.283476i	$-0.908512\pi$
$397$		−	11.2964i		−	0.566952i	0.958979	−	0.283476i	$-0.0914876\pi$
$398$			22.8382i			1.14477i
$399$			12.1617i			0.608845i
$400$	7.42849			0.371424
$401$	−1.16991			−0.0584225			−0.0292112	−	0.999573i	$-0.509300\pi$
$401$	−1.16991			−0.0584225			−0.0292112	+	0.999573i	$0.509300\pi$
$402$	42.7926			2.13430
$403$			1.89882i			0.0945869i
$404$		−	7.19467i		−	0.357948i
$405$	21.5823			1.07243
$406$	8.66936			0.430253
$407$			3.41453i			0.169252i
$408$	−9.97939			−0.494054
$409$	6.51601			0.322196			0.161098	−	0.986938i	$-0.448497\pi$
$409$	6.51601			0.322196			0.161098	+	0.986938i	$0.448497\pi$
$410$	−29.3621	−	27.4550i	−1.45009	−	1.35590i
$411$	16.4254			0.810205
$412$	−78.9595			−3.89006
$413$			14.5405i			0.715489i
$414$	0.319686			0.0157117
$415$	−16.4982			−0.809866
$416$		−	10.4043i		−	0.510111i
$417$			10.9059i			0.534064i
$418$	−6.26392			−0.306379
$419$	11.4389			0.558828			0.279414	−	0.960171i	$-0.409860\pi$
$419$	11.4389			0.558828			0.279414	+	0.960171i	$0.409860\pi$
$420$	18.3003			0.892963
$421$		−	12.2159i		−	0.595365i	−0.954665	−	0.297682i	$-0.903786\pi$
$421$		−	12.2159i		−	0.595365i	0.954665	−	0.297682i	$-0.0962136\pi$
$422$		−	24.0685i		−	1.17163i
$423$			0.503183i			0.0244656i
$424$			73.4183i			3.56551i
$425$			1.25693i			0.0609701i
$426$	55.5720			2.69247
$427$		−	0.654679i		−	0.0316822i
$428$	−56.3134			−2.72201
$429$		−	1.81315i		−	0.0875397i
$430$	6.92904			0.334148
$431$	4.23711			0.204094			0.102047	−	0.994780i	$-0.467461\pi$
$431$	4.23711			0.204094			0.102047	+	0.994780i	$0.467461\pi$
$432$			31.6248i			1.52155i
$433$	−14.1624			−0.680603			−0.340301	−	0.940316i	$-0.610529\pi$
$433$	−14.1624			−0.680603			−0.340301	+	0.940316i	$0.610529\pi$
$434$		−	1.55547i		−	0.0746647i
$435$	−14.6401			−0.701941
$436$			74.9281i			3.58840i
$437$		−	7.83832i		−	0.374958i
$438$		−	32.2301i		−	1.54001i
$439$			2.59684i			0.123941i	0.998078	+	0.0619703i	$0.0197384\pi$
$439$			2.59684i			0.123941i	−0.998078	+	0.0619703i	$0.980262\pi$
$440$			5.05485i			0.240981i
$441$	−0.116251			−0.00553577
$442$	7.79270			0.370661
$443$	−27.9936			−1.33002			−0.665008	−	0.746836i	$-0.731572\pi$
$443$	−27.9936			−1.33002			−0.665008	+	0.746836i	$0.731572\pi$
$444$		−	71.8419i		−	3.40946i
$445$		−	26.0692i		−	1.23580i
$446$	−12.3620			−0.585359
$447$	2.96111			0.140056
$448$		−	3.42927i		−	0.162018i
$449$	15.8227			0.746721			0.373360	−	0.927686i	$-0.378205\pi$
$449$	15.8227			0.746721			0.373360	+	0.927686i	$0.378205\pi$
$450$	0.363077			0.0171156
$451$	1.52236	−	1.62811i	0.0716852	−	0.0766648i
$452$	40.1943			1.89058
$453$	15.9239			0.748170
$454$		−	57.0410i		−	2.67707i
$455$	−7.66372			−0.359281
$456$	70.6791			3.30985
$457$			20.8952i			0.977437i	0.872441	+	0.488719i	$0.162536\pi$
$457$			20.8952i			0.977437i	−0.872441	+	0.488719i	$0.837464\pi$
$458$		−	29.1775i		−	1.36337i
$459$	−5.35105			−0.249766
$460$	−11.7947			−0.549931
$461$	−17.2930			−0.805417			−0.402709	−	0.915328i	$-0.631931\pi$
$461$	−17.2930			−0.805417			−0.402709	+	0.915328i	$0.631931\pi$
$462$			1.48529i			0.0691018i
$463$			26.4260i			1.22812i	0.789259	+	0.614061i	$0.210465\pi$
$463$			26.4260i			1.22812i	−0.789259	+	0.614061i	$0.789535\pi$
$464$		−	20.6199i		−	0.957253i
$465$			2.62675i			0.121813i
$466$			64.8074i			3.00214i
$467$	28.7444			1.33013			0.665067	−	0.746784i	$-0.268403\pi$
$467$	28.7444			1.33013			0.665067	+	0.746784i	$0.268403\pi$
$468$		−	1.53787i		−	0.0710882i
$469$	10.0293			0.463111
$470$		−	27.1735i		−	1.25342i
$471$	23.2448			1.07106
$472$	84.5037			3.88960
$473$			0.384211i			0.0176660i
$474$	−53.9316			−2.47716
$475$		−	8.90221i		−	0.408462i
$476$	−4.36123			−0.199897
$477$			1.46860i			0.0672426i
$478$		−	2.98908i		−	0.136717i
$479$		−	24.7598i		−	1.13131i	−0.824643	−	0.565653i	$-0.808624\pi$
$479$		−	24.7598i		−	1.13131i	0.824643	−	0.565653i	$-0.191376\pi$
$480$		−	14.3928i		−	0.656939i
$481$			30.0856i			1.37179i
$482$	−45.7867			−2.08553
$483$	−1.85860			−0.0845694
$484$	46.9206			2.13275
$485$		−	4.53011i		−	0.205702i
$486$			3.03375i			0.137614i
$487$	16.5935			0.751925			0.375963	−	0.926635i	$-0.377312\pi$
$487$	16.5935			0.751925			0.375963	+	0.926635i	$0.377312\pi$
$488$	−3.80475			−0.172233
$489$			42.2621i			1.91116i
$490$	6.27793			0.283608
$491$	19.6968			0.888904			0.444452	−	0.895803i	$-0.353398\pi$
$491$	19.6968			0.888904			0.444452	+	0.895803i	$0.353398\pi$
$492$	−32.0306	+	34.2555i	−1.44405	+	1.54436i
$493$	3.48896			0.157135
$494$	−55.1918			−2.48320
$495$			0.101113i			0.00454471i
$496$	−3.69964			−0.166119
$497$	13.0244			0.584226
$498$			28.1732i			1.26247i
$499$			6.57544i			0.294357i	0.989110	+	0.147178i	$0.0470192\pi$
$499$			6.57544i			0.294357i	−0.989110	+	0.147178i	$0.952981\pi$
$500$	40.4871			1.81064
$501$	−16.7129			−0.746679
$502$	−13.2192			−0.590001
$503$			8.81266i			0.392937i	0.980510	+	0.196469i	$0.0629474\pi$
$503$			8.81266i			0.392937i	−0.980510	+	0.196469i	$0.937053\pi$
$504$			0.675608i			0.0300940i
$505$			4.16799i			0.185473i
$506$		−	0.957282i		−	0.0425564i
$507$			6.10031i			0.270924i
$508$	3.60005			0.159726
$509$			18.5113i			0.820499i	0.911973	+	0.410250i	$0.134558\pi$
$509$			18.5113i			0.820499i	−0.911973	+	0.410250i	$0.865442\pi$
$510$	10.7801			0.477351
$511$		−	7.55378i		−	0.334160i
$512$	−49.1901			−2.17391
$513$	37.8988			1.67327
$514$			40.8659i			1.80252i
$515$	45.7426			2.01566
$516$		−	8.08382i		−	0.355870i
$517$	1.50675			0.0662669
$518$		−	24.6454i		−	1.08286i
$519$			10.4972i			0.460775i
$520$			44.5386i			1.95315i
$521$			17.0858i			0.748541i	0.927320	+	0.374271i	$0.122107\pi$
$521$			17.0858i			0.748541i	−0.927320	+	0.374271i	$0.877893\pi$
$522$		−	1.00782i		−	0.0441112i
$523$	19.5384			0.854356			0.427178	−	0.904168i	$-0.359508\pi$
$523$	19.5384			0.854356			0.427178	+	0.904168i	$0.359508\pi$
$524$	−58.8237			−2.56973
$525$	−2.11087			−0.0921260
$526$		−	55.4573i		−	2.41805i
$527$		−	0.625993i		−	0.0272687i
$528$	3.53272			0.153742
$529$	−21.8021			−0.947918
$530$		−	79.3091i		−	3.44497i
$531$	1.69035			0.0733548
$532$	30.8884			1.33918
$533$	13.4136	−	14.3454i	0.581008	−	0.621368i
$534$	−44.5171			−1.92644
$535$	32.6233			1.41043
$536$		−	58.2866i		−	2.51760i
$537$	17.6688			0.762463
$538$	−16.6291			−0.716932
$539$			0.348107i			0.0149940i
$540$		−	57.0283i		−	2.45411i
$541$	−7.98328			−0.343228			−0.171614	−	0.985164i	$-0.554898\pi$
$541$	−7.98328			−0.343228			−0.171614	+	0.985164i	$0.554898\pi$
$542$	47.3465			2.03370
$543$	22.3101			0.957418
$544$			3.43002i			0.147061i
$545$		−	43.4071i		−	1.85936i
$546$			13.0870i			0.560070i
$547$		−	17.7133i		−	0.757364i	−0.925527	−	0.378682i	$-0.876377\pi$
$547$		−	17.7133i		−	0.757364i	0.925527	−	0.378682i	$-0.123623\pi$
$548$		−	41.7175i		−	1.78208i
$549$	−0.0761073			−0.00324818
$550$		−	1.08721i		−	0.0463590i
$551$	−24.7106			−1.05271
$552$			10.8015i			0.459743i
$553$	−12.6400			−0.537506
$554$	−41.2779			−1.75373
$555$			41.6192i			1.76664i
$556$	27.6990			1.17470
$557$			22.6435i			0.959436i	0.877423	+	0.479718i	$0.159261\pi$
$557$			22.6435i			0.959436i	−0.877423	+	0.479718i	$0.840739\pi$
$558$	−0.180825			−0.00765492
$559$			3.38531i			0.143183i
$560$		−	14.9319i		−	0.630988i
$561$			0.597750i			0.0252370i
$562$			68.3045i			2.88125i
$563$			21.9021i			0.923063i	0.887124	+	0.461531i	$0.152700\pi$
$563$			21.9021i			0.923063i	−0.887124	+	0.461531i	$0.847300\pi$
$564$	−31.7021			−1.33490
$565$	−23.2853			−0.979619
$566$	−38.1008			−1.60150
$567$		−	8.63773i		−	0.362751i
$568$		−	75.6931i		−	3.17601i
$569$	−13.8239			−0.579530			−0.289765	−	0.957098i	$-0.593577\pi$
$569$	−13.8239			−0.579530			−0.289765	+	0.957098i	$0.593577\pi$
$570$	−76.3501			−3.19796
$571$			0.110611i			0.00462894i	0.999997	+	0.00231447i	$0.000736720\pi$
$571$			0.110611i			0.00462894i	−0.999997	+	0.00231447i	$0.999263\pi$
$572$	−4.60507			−0.192548
$573$	6.81629			0.284755
$574$	−10.9881	+	11.7514i	−0.458635	+	0.490494i
$575$	1.36048			0.0567359
$576$	−0.398657			−0.0166107
$577$		−	26.7103i		−	1.11196i	−0.831194	−	0.555982i	$-0.812342\pi$
$577$		−	26.7103i		−	1.11196i	0.831194	−	0.555982i	$-0.187658\pi$
$578$	40.1447			1.66980
$579$	−21.8325			−0.907326
$580$			37.1833i			1.54395i
$581$			6.60297i			0.273937i
$582$	−7.73585			−0.320661
$583$	4.39764			0.182132
$584$	−43.8998			−1.81658
$585$			0.890916i			0.0368348i
$586$			1.61712i			0.0668025i
$587$			44.2028i			1.82444i	0.409696	+	0.912222i	$0.365635\pi$
$587$			44.2028i			1.82444i	−0.409696	+	0.912222i	$0.634365\pi$
$588$		−	7.32420i		−	0.302045i
$589$			4.43360i			0.182683i
$590$	−91.2840			−3.75810
$591$			15.8005i			0.649947i
$592$	−58.6185			−2.40921
$593$			18.6657i			0.766508i	0.923643	+	0.383254i	$0.125197\pi$
$593$			18.6657i			0.766508i	−0.923643	+	0.383254i	$0.874803\pi$
$594$	4.62853			0.189911
$595$	2.52654			0.103578
$596$		−	7.52068i		−	0.308059i
$597$	−15.4355			−0.631734
$598$		−	8.43468i		−	0.344920i
$599$	9.40359			0.384220			0.192110	−	0.981373i	$-0.438467\pi$
$599$	9.40359			0.384220			0.192110	+	0.981373i	$0.438467\pi$
$600$			12.2676i			0.500823i
$601$			40.6428i			1.65786i	0.559356	+	0.828928i	$0.311049\pi$
$601$			40.6428i			1.65786i	−0.559356	+	0.828928i	$0.688951\pi$
$602$		−	2.77316i		−	0.113026i
$603$		−	1.16592i		−	0.0474799i
$604$		−	40.4438i		−	1.64563i
$605$	−27.1819			−1.10510
$606$	7.11748			0.289128
$607$	21.6043			0.876893			0.438446	−	0.898757i	$-0.355529\pi$
$607$	21.6043			0.876893			0.438446	+	0.898757i	$0.355529\pi$
$608$		−	24.2932i		−	0.985218i
$609$			5.85932i			0.237432i
$610$	4.11003			0.166410
$611$	13.2761			0.537093
$612$			0.506998i			0.0204942i
$613$	36.1939			1.46186			0.730928	−	0.682454i	$-0.239087\pi$
$613$	36.1939			1.46186			0.730928	+	0.682454i	$0.239087\pi$
$614$	−32.0575			−1.29373
$615$	18.5559	−	19.8448i	0.748244	−	0.800221i
$616$	2.02307			0.0815118
$617$	0.0490347			0.00197406			0.000987032	−	1.00000i	$-0.499686\pi$
$617$	0.0490347			0.00197406			0.000987032		1.00000i	$0.499686\pi$
$618$		−	78.1125i		−	3.14214i
$619$	−2.66710			−0.107200			−0.0535999	−	0.998562i	$-0.517070\pi$
$619$	−2.66710			−0.107200			−0.0535999	+	0.998562i	$0.517070\pi$
$620$	6.67146			0.267932
$621$			5.79188i			0.232420i
$622$		−	36.6850i		−	1.47093i
$623$	−10.4335			−0.418009
$624$	31.1270			1.24608
$625$	−29.6700			−1.18680
$626$		−	65.4603i		−	2.61632i
$627$		−	4.23357i		−	0.169072i
$628$		−	59.0375i		−	2.35585i
$629$		−	9.91849i		−	0.395476i
$630$		−	0.729817i		−	0.0290766i
$631$	−16.9255			−0.673795			−0.336898	−	0.941541i	$-0.609378\pi$
$631$	−16.9255			−0.673795			−0.336898	+	0.941541i	$0.609378\pi$
$632$			73.4587i			2.92203i
$633$	16.2670			0.646557
$634$			33.5987i			1.33437i
$635$	−2.08557			−0.0827634
$636$	−92.5266			−3.66892
$637$			3.06720i			0.121527i
$638$	−3.01787			−0.119479
$639$		−	1.51411i		−	0.0598971i
$640$	38.4798			1.52105
$641$		−	43.4693i		−	1.71693i	−0.512869	−	0.858467i	$-0.671417\pi$
$641$		−	43.4693i		−	1.71693i	0.512869	−	0.858467i	$-0.328583\pi$
$642$		−	55.7093i		−	2.19867i
$643$			36.2558i			1.42979i	0.699232	+	0.714895i	$0.253525\pi$
$643$			36.2558i			1.42979i	−0.699232	+	0.714895i	$0.746475\pi$
$644$			4.72052i			0.186014i
$645$			4.68310i			0.184397i
$646$	18.1954			0.715888
$647$	−5.73725			−0.225555			−0.112777	−	0.993620i	$-0.535975\pi$
$647$	−5.73725			−0.225555			−0.112777	+	0.993620i	$0.535975\pi$
$648$	−50.1993			−1.97201
$649$		−	5.06164i		−	0.198687i
$650$		−	9.57951i		−	0.375739i
$651$	1.05129			0.0412031
$652$	107.338			4.20369
$653$			3.03768i			0.118874i	0.998232	+	0.0594368i	$0.0189305\pi$
$653$			3.03768i			0.118874i	−0.998232	+	0.0594368i	$0.981070\pi$
$654$	−74.1243			−2.89849
$655$	34.0776			1.33152
$656$	27.9504	+	26.1349i	1.09128	+	1.02040i
$657$	−0.878136			−0.0342594
$658$	−10.8754			−0.423969
$659$		−	38.2178i		−	1.48875i	−0.667760	−	0.744377i	$-0.732747\pi$
$659$		−	38.2178i		−	1.48875i	0.667760	−	0.744377i	$-0.267253\pi$
$660$	−6.37046			−0.247970
$661$	−32.3113			−1.25676			−0.628382	−	0.777905i	$-0.716282\pi$
$661$	−32.3113			−1.25676			−0.628382	+	0.777905i	$0.716282\pi$
$662$		−	74.0847i		−	2.87938i
$663$			5.26682i			0.204546i
$664$	38.3740			1.48920
$665$	−17.8942			−0.693908
$666$	−2.86506			−0.111019
$667$		−	3.77639i		−	0.146222i
$668$			42.4478i			1.64235i
$669$		−	8.35507i		−	0.323026i
$670$			62.9634i			2.43249i
$671$			0.227899i			0.00879793i
$672$	−5.76034			−0.222210
$673$		−	29.9219i		−	1.15340i	−0.816955	−	0.576701i	$-0.804340\pi$
$673$		−	29.9219i		−	1.15340i	0.816955	−	0.576701i	$-0.195660\pi$
$674$	70.4560			2.71386
$675$			6.57801i			0.253188i
$676$	15.4937			0.595911
$677$	20.3416			0.781791			0.390896	−	0.920435i	$-0.372165\pi$
$677$	20.3416			0.781791			0.390896	+	0.920435i	$0.372165\pi$
$678$			39.7632i			1.52710i
$679$	−1.81305			−0.0695786
$680$		−	14.6833i		−	0.563078i
$681$	38.5521			1.47732
$682$			0.541469i			0.0207339i
$683$		−	29.7966i		−	1.14013i	−0.821598	−	0.570067i	$-0.806917\pi$
$683$		−	29.7966i		−	1.14013i	0.821598	−	0.570067i	$-0.193083\pi$
$684$		−	3.59082i		−	0.137298i
$685$			24.1677i			0.923399i
$686$		−	2.51257i		−	0.0959304i
$687$	19.7200			0.752366
$688$	−6.59589			−0.251466
$689$	38.7479			1.47618
$690$		−	11.6682i		−	0.444200i
$691$		−	42.4609i		−	1.61529i	−0.589670	−	0.807644i	$-0.700742\pi$
$691$		−	42.4609i		−	1.61529i	0.589670	−	0.807644i	$-0.299258\pi$
$692$	26.6609			1.01350
$693$	0.0404679			0.00153725
$694$			34.4757i			1.30868i
$695$	−16.0465			−0.608678
$696$	34.0522			1.29074
$697$	−4.42214	+	4.72932i	−0.167500	+	0.179136i
$698$	36.2185			1.37089
$699$	−43.8011			−1.65671
$700$			5.36123i			0.202636i
$701$	−8.54106			−0.322591			−0.161296	−	0.986906i	$-0.551567\pi$
$701$	−8.54106			−0.322591			−0.161296	+	0.986906i	$0.551567\pi$
$702$	40.7823			1.53923
$703$			70.2477i			2.64944i
$704$			1.19375i			0.0449913i
$705$	18.3656			0.691689
$706$	66.4560			2.50111
$707$	1.66813			0.0627364
$708$			106.497i			4.00241i
$709$		−	32.7615i		−	1.23038i	−0.788378	−	0.615191i	$-0.789079\pi$
$709$		−	32.7615i		−	1.23038i	0.788378	−	0.615191i	$-0.210921\pi$
$710$			81.7665i			3.06864i
$711$			1.46941i			0.0551072i
$712$			60.6355i			2.27241i
$713$	−0.677564			−0.0253750
$714$		−	4.31445i		−	0.161464i
$715$	2.66780			0.0997699
$716$		−	44.8754i		−	1.67707i
$717$	2.02021			0.0754462
$718$	−13.5959			−0.507395
$719$			38.9438i			1.45236i	0.687505	+	0.726180i	$0.258706\pi$
$719$			38.9438i			1.45236i	−0.687505	+	0.726180i	$0.741294\pi$
$720$	−1.73585			−0.0646913
$721$		−	18.3072i		−	0.681798i
$722$	−81.1300			−3.01935
$723$		−	30.9456i		−	1.15088i
$724$		−	56.6636i		−	2.10589i
$725$		−	4.28896i		−	0.159288i
$726$			46.4172i			1.72270i
$727$			14.0329i			0.520453i	0.965548	+	0.260226i	$0.0837972\pi$
$727$			14.0329i			0.520453i	−0.965548	+	0.260226i	$0.916203\pi$
$728$	17.8254			0.660653
$729$	−27.9636			−1.03569
$730$	47.4221			1.75517
$731$		−	1.11605i		−	0.0412787i
$732$		−	4.79500i		−	0.177228i
$733$	−24.6194			−0.909340			−0.454670	−	0.890660i	$-0.650243\pi$
$733$	−24.6194			−0.909340			−0.454670	+	0.890660i	$0.650243\pi$
$734$	−39.7878			−1.46860
$735$			4.24303i			0.156507i
$736$	3.71260			0.136848
$737$	−3.49128			−0.128603
$738$	1.36611	+	1.27738i	0.0502873	+	0.0470210i
$739$	5.02913			0.185000			0.0924998	−	0.995713i	$-0.470514\pi$
$739$	5.02913			0.185000			0.0924998	+	0.995713i	$0.470514\pi$
$740$	105.705			3.88580
$741$		−	37.3023i		−	1.37033i
$742$	−31.7413			−1.16526
$743$	−6.91129			−0.253551			−0.126775	−	0.991931i	$-0.540463\pi$
$743$	−6.91129			−0.253551			−0.126775	+	0.991931i	$0.540463\pi$
$744$		−	6.10968i		−	0.223992i
$745$			4.35686i			0.159623i
$746$	−15.9846			−0.585239
$747$	0.767603			0.0280851
$748$	1.51818			0.0555100
$749$		−	13.0566i		−	0.477078i
$750$			40.0527i			1.46252i
$751$		−	21.7219i		−	0.792645i	−0.918111	−	0.396322i	$-0.870286\pi$
$751$		−	21.7219i		−	0.792645i	0.918111	−	0.396322i	$-0.129714\pi$
$752$			25.8670i			0.943272i
$753$		−	8.93439i		−	0.325587i
$754$	−26.5906			−0.968374
$755$			23.4298i			0.852697i
$756$	−22.8240			−0.830102
$757$			38.7559i			1.40861i	0.709899	+	0.704303i	$0.248741\pi$
$757$			38.7559i			1.40861i	−0.709899	+	0.704303i	$0.751259\pi$
$758$	75.0751			2.72685
$759$	0.646994			0.0234844
$760$			103.994i			3.77228i
$761$	−43.2783			−1.56884			−0.784419	−	0.620231i	$-0.787039\pi$
$761$	−43.2783			−1.56884			−0.784419	+	0.620231i	$0.787039\pi$
$762$			3.56143i			0.129017i
$763$	−17.3725			−0.628928
$764$		−	17.3121i		−	0.626331i
$765$		−	0.293713i		−	0.0106192i
$766$			3.29725i			0.119135i
$767$		−	44.5985i		−	1.61036i
$768$		−	54.0632i		−	1.95084i
$769$	37.4776			1.35148			0.675739	−	0.737141i	$-0.263825\pi$
$769$	37.4776			1.35148			0.675739	+	0.737141i	$0.263825\pi$
$770$	−2.18539			−0.0787561
$771$	−27.6198			−0.994703
$772$			55.4505i			1.99571i
$773$			26.4720i			0.952131i	0.879410	+	0.476065i	$0.157937\pi$
$773$			26.4720i			0.952131i	−0.879410	+	0.476065i	$0.842063\pi$
$774$	−0.322383			−0.0115878
$775$	−0.769529			−0.0276423
$776$			10.5368i			0.378249i
$777$	16.6570			0.597566
$778$	−43.4450			−1.55758
$779$	31.3198	−	33.4954i	1.12215	−	1.20010i
$780$	−56.1306			−2.00980
$781$	−4.53390			−0.162236
$782$			2.78070i			0.0994378i
$783$	18.2591			0.652528
$784$	−5.97609			−0.213432
$785$			34.2015i			1.22070i
$786$		−	58.1927i		−	2.07566i
$787$	44.0294			1.56948			0.784739	−	0.619827i	$-0.212797\pi$
$787$	44.0294			1.56948			0.784739	+	0.619827i	$0.212797\pi$
$788$	40.1305			1.42959
$789$	37.4817			1.33438
$790$		−	79.3528i		−	2.82325i
$791$			9.31931i			0.331356i
$792$		−	0.235184i		−	0.00835691i
$793$			2.00803i			0.0713073i
$794$		−	28.3831i		−	1.00728i
$795$	53.6023			1.90108
$796$			39.2034i			1.38953i
$797$	−14.5052			−0.513802			−0.256901	−	0.966438i	$-0.582701\pi$
$797$	−14.5052			−0.513802			−0.256901	+	0.966438i	$0.582701\pi$
$798$			30.5571i			1.08171i
$799$	−4.37680			−0.154840
$800$	4.21651			0.149076
$801$			1.21290i			0.0428559i
$802$	−2.93948			−0.103797
$803$			2.62953i			0.0927940i
$804$	73.4567			2.59062
$805$		−	2.73468i		−	0.0963847i
$806$			4.77092i			0.168048i
$807$		−	11.2390i		−	0.395633i
$808$		−	9.69453i		−	0.341052i
$809$			7.89790i			0.277675i	0.990315	+	0.138838i	$0.0443366\pi$
$809$			7.89790i			0.277675i	−0.990315	+	0.138838i	$0.955663\pi$
$810$	54.2271			1.90534
$811$	−4.33807			−0.152330			−0.0761652	−	0.997095i	$-0.524268\pi$
$811$	−4.33807			−0.152330			−0.0761652	+	0.997095i	$0.524268\pi$
$812$	14.8816			0.522242
$813$			31.9998i			1.12228i
$814$			8.57925i			0.300703i
$815$	−62.1829			−2.17817
$816$	−10.2618			−0.359235
$817$			7.90445i			0.276542i
$818$	16.3719			0.572431
$819$	0.356565			0.0124594
$820$	−50.4023	−	47.1285i	−1.76012	−	1.64580i
$821$	−32.5083			−1.13455			−0.567274	−	0.823529i	$-0.692002\pi$
$821$	−32.5083			−1.13455			−0.567274	+	0.823529i	$0.692002\pi$
$822$	41.2700			1.43946
$823$		−	46.3504i		−	1.61567i	−0.589407	−	0.807836i	$-0.700639\pi$
$823$		−	46.3504i		−	1.61567i	0.589407	−	0.807836i	$-0.299361\pi$
$824$	−106.395			−3.70644
$825$	0.734810			0.0255828
$826$			36.5340i			1.27118i
$827$			36.2175i			1.25940i	0.776836	+	0.629702i	$0.216823\pi$
$827$			36.2175i			1.25940i	−0.776836	+	0.629702i	$0.783177\pi$
$828$	0.548766			0.0190709
$829$	−23.0666			−0.801136			−0.400568	−	0.916267i	$-0.631187\pi$
$829$	−23.0666			−0.801136			−0.400568	+	0.916267i	$0.631187\pi$
$830$	−41.4530			−1.43885
$831$		−	27.8983i		−	0.967782i
$832$			10.5182i			0.364654i
$833$		−	1.01118i		−	0.0350353i
$834$			27.4018i			0.948848i
$835$		−	24.5908i		−	0.850998i
$836$	−10.7525			−0.371883
$837$		−	3.27607i		−	0.113238i
$838$	28.7411			0.992846
$839$		−	18.4896i		−	0.638332i	−0.947699	−	0.319166i	$-0.896597\pi$
$839$		−	18.4896i		−	0.638332i	0.947699	−	0.319166i	$-0.103403\pi$
$840$	24.6589			0.850814
$841$	17.0948			0.589475
$842$		−	30.6932i		−	1.05776i
$843$	−46.1646			−1.58999
$844$		−	41.3153i		−	1.42213i
$845$	−8.97576			−0.308775
$846$			1.26428i			0.0434670i
$847$			10.8788i			0.373801i
$848$			75.4959i			2.59254i
$849$		−	25.7510i		−	0.883773i
$850$			3.15813i			0.108323i
$851$	−10.7356			−0.368011
$852$	95.3935			3.26813
$853$	−40.5233			−1.38749			−0.693746	−	0.720220i	$-0.744041\pi$
$853$	−40.5233			−1.38749			−0.693746	+	0.720220i	$0.744041\pi$
$854$		−	1.64493i		−	0.0562883i
$855$			2.08022i			0.0711421i
$856$	−75.8801			−2.59353
$857$	−45.6585			−1.55966			−0.779832	−	0.625989i	$-0.784695\pi$
$857$	−45.6585			−1.55966			−0.779832	+	0.625989i	$0.784695\pi$
$858$		−	4.55567i		−	0.155528i
$859$	18.3803			0.627129			0.313565	−	0.949567i	$-0.398477\pi$
$859$	18.3803			0.627129			0.313565	+	0.949567i	$0.398477\pi$
$860$	11.8942			0.405589
$861$	−7.94236	−	7.42648i	−0.270675	−	0.253094i
$862$	10.6460			0.362605
$863$	35.4482			1.20667			0.603335	−	0.797488i	$-0.293838\pi$
$863$	35.4482			1.20667			0.603335	+	0.797488i	$0.293838\pi$
$864$			17.9507i			0.610694i
$865$	−15.4451			−0.525151
$866$	−35.5841			−1.20920
$867$			27.1324i			0.921464i
$868$		−	2.67007i		−	0.0906282i
$869$	4.40006			0.149262
$870$	−36.7844			−1.24711
$871$	−30.7619			−1.04233
$872$			100.963i			3.41903i
$873$			0.210770i			0.00713347i
$874$		−	19.6943i		−	0.666171i
$875$			9.38718i			0.317345i
$876$		−	55.3254i		−	1.86927i
$877$	−37.3158			−1.26007			−0.630033	−	0.776568i	$-0.716959\pi$
$877$	−37.3158			−1.26007			−0.630033	+	0.776568i	$0.716959\pi$
$878$			6.52476i			0.220200i
$879$	−1.09295			−0.0368644
$880$			5.19790i			0.175221i
$881$	−16.1498			−0.544101			−0.272051	−	0.962283i	$-0.587702\pi$
$881$	−16.1498			−0.544101			−0.272051	+	0.962283i	$0.587702\pi$
$882$	−0.292089			−0.00983516
$883$			1.66579i			0.0560583i	0.999607	+	0.0280291i	$0.00892312\pi$
$883$			1.66579i			0.0560583i	−0.999607	+	0.0280291i	$0.991077\pi$
$884$	13.3768			0.449909
$885$		−	61.6957i		−	2.07388i
$886$	−70.3360			−2.36298
$887$		−	31.9823i		−	1.07386i	−0.843627	−	0.536930i	$-0.819584\pi$
$887$		−	31.9823i		−	1.07386i	0.843627	−	0.536930i	$-0.180416\pi$
$888$		−	96.8041i		−	3.24853i
$889$			0.834694i			0.0279947i
$890$		−	65.5007i		−	2.19559i
$891$			3.00686i			0.100734i
$892$	−21.2204			−0.710510
$893$	30.9987			1.03733
$894$	7.44000			0.248831
$895$			25.9971i			0.868988i
$896$		−	15.4005i		−	0.514495i
$897$	5.70071			0.190341
$898$	39.7558			1.32667
$899$			2.13605i			0.0712411i
$900$	0.623249			0.0207750
$901$	−12.7742			−0.425571
$902$	3.82504	−	4.09075i	0.127360	−	0.136207i
$903$	1.87428			0.0623723
$904$	54.1603			1.80135
$905$			32.8262i			1.09118i
$906$	40.0099			1.32924
$907$	48.8937			1.62349			0.811744	−	0.584013i	$-0.198518\pi$
$907$	48.8937			1.62349			0.811744	+	0.584013i	$0.198518\pi$
$908$		−	97.9152i		−	3.24943i
$909$		−	0.193922i		−	0.00643198i
$910$	−19.2556			−0.638318
$911$	−56.1753			−1.86117			−0.930586	−	0.366074i	$-0.880702\pi$
$911$	−56.1753			−1.86117			−0.930586	+	0.366074i	$0.880702\pi$
$912$	72.6793			2.40665
$913$		−	2.29854i		−	0.0760706i
$914$			52.5008i			1.73657i
$915$			2.77783i			0.0918322i
$916$		−	50.0853i		−	1.65487i
$917$		−	13.6386i		−	0.450388i
$918$	−13.4449			−0.443748
$919$			45.2075i			1.49126i	0.666361	+	0.745629i	$0.267851\pi$
$919$			45.2075i			1.49126i	−0.666361	+	0.745629i	$0.732149\pi$
$920$	−15.8929			−0.523974
$921$		−	21.6665i		−	0.713936i
$922$	−43.4500			−1.43095
$923$	−39.9485			−1.31492
$924$			2.54961i			0.0838759i
$925$	−12.1927			−0.400894
$926$			66.3973i			2.18195i
$927$	−2.12824			−0.0699005
$928$		−	11.7041i		−	0.384206i
$929$		−	25.9988i		−	0.852992i	−0.904490	−	0.426496i	$-0.859748\pi$
$929$		−	25.9988i		−	0.852992i	0.904490	−	0.426496i	$-0.140252\pi$
$930$			6.59989i			0.216419i
$931$			7.16168i			0.234715i
$932$			111.247i			3.64401i
$933$	24.7941			0.811723
$934$	72.2224			2.36319
$935$	−0.879506			−0.0287629
$936$		−	2.07222i		−	0.0677327i
$937$			8.69362i			0.284008i	0.989866	+	0.142004i	$0.0453546\pi$
$937$			8.69362i			0.284008i	−0.989866	+	0.142004i	$0.954645\pi$
$938$	25.1994			0.822789
$939$	44.2424			1.44379
$940$		−	46.6453i		−	1.52140i
$941$	4.07935			0.132983			0.0664915	−	0.997787i	$-0.478819\pi$
$941$	4.07935			0.132983			0.0664915	+	0.997787i	$0.478819\pi$
$942$	58.4042			1.90291
$943$	5.11893	+	4.78644i	0.166695	+	0.155868i
$944$	86.8951			2.82820
$945$	13.2224			0.430123
$946$			0.965358i			0.0313865i
$947$	−60.2359			−1.95740			−0.978702	−	0.205288i	$-0.934187\pi$
$947$	−60.2359			−1.95740			−0.978702	+	0.205288i	$0.934187\pi$
$948$	−92.5776			−3.00678
$949$			23.1689i			0.752096i
$950$		−	22.3675i		−	0.725696i
$951$	−22.7082			−0.736363
$952$	−5.87659			−0.190461
$953$	10.9792			0.355653			0.177826	−	0.984062i	$-0.443093\pi$
$953$	10.9792			0.355653			0.177826	+	0.984062i	$0.443093\pi$
$954$			3.68997i			0.119467i
$955$			10.0292i			0.324538i
$956$		−	5.13097i		−	0.165947i
$957$		−	2.03967i		−	0.0659333i
$958$		−	62.2109i		−	2.00994i
$959$	9.67246			0.312340
$960$			14.5505i			0.469616i
$961$	−30.6167			−0.987637
$962$			75.5923i			2.43719i
$963$	−1.51785			−0.0489119
$964$	−78.5963			−2.53142
$965$		−	32.1234i		−	1.03409i
$966$	−4.66988			−0.150251
$967$		−	9.64543i		−	0.310176i	−0.987901	−	0.155088i	$-0.950434\pi$
$967$		−	9.64543i		−	0.310176i	0.987901	−	0.155088i	$-0.0495661\pi$
$968$	63.2236			2.03208
$969$			12.2976i			0.395057i
$970$		−	11.3822i		−	0.365461i
$971$		−	36.9139i		−	1.18462i	−0.805709	−	0.592311i	$-0.798216\pi$
$971$		−	36.9139i		−	1.18462i	0.805709	−	0.592311i	$-0.201784\pi$
$972$			5.20766i			0.167036i
$973$			6.42218i			0.205886i
$974$	41.6925			1.33591
$975$	6.47446			0.207349
$976$	−3.91242			−0.125234
$977$			10.1908i			0.326031i	0.986624	+	0.163016i	$0.0521221\pi$
$977$			10.1908i			0.326031i	−0.986624	+	0.163016i	$0.947878\pi$
$978$			106.187i			3.39548i
$979$	3.63197			0.116078
$980$	10.7765			0.344244
$981$			2.01958i			0.0644802i
$982$	49.4896			1.57928
$983$	21.8735			0.697656			0.348828	−	0.937187i	$-0.386580\pi$
$983$	21.8735			0.697656			0.348828	+	0.937187i	$0.386580\pi$
$984$	−43.1599	+	46.1580i	−1.37589	+	1.47146i
$985$	−23.2483			−0.740752
$986$	8.76627			0.279175
$987$		−	7.35034i		−	0.233964i
$988$	−94.7409			−3.01411
$989$	−1.20799			−0.0384120
$990$			0.254055i			0.00807438i
$991$			8.90379i			0.282838i	0.989950	+	0.141419i	$0.0451665\pi$
$991$			8.90379i			0.282838i	−0.989950	+	0.141419i	$0.954834\pi$
$992$	−2.09996			−0.0666738
$993$	50.0713			1.58896
$994$	32.7248			1.03797
$995$		−	22.7112i		−	0.719994i
$996$			48.3614i			1.53239i
$997$		−	42.1571i		−	1.33513i	−0.744552	−	0.667564i	$-0.767337\pi$
$997$		−	42.1571i		−	1.33513i	0.744552	−	0.667564i	$-0.232663\pi$
$998$			16.5213i			0.522971i
$999$		−	51.9073i		−	1.64228i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.c.a.204.10	yes	10
41.40	even	2	inner	287.2.c.a.204.9	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.c.a.204.9	✓	10	41.40	even	2	inner
287.2.c.a.204.10	yes	10	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	287.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.51257 q^{2} +1.69816i q^{3} +4.31302 q^{4} -2.49861 q^{5} +4.26675i q^{6} +1.00000i q^{7} +5.81162 q^{8} +0.116251 q^{9} +O(q^{10})\)	\(q+2.51257 q^{2} +1.69816i q^{3} +4.31302 q^{4} -2.49861 q^{5} +4.26675i q^{6} +1.00000i q^{7} +5.81162 q^{8} +0.116251 q^{9} -6.27793 q^{10} -0.348107i q^{11} +7.32420i q^{12} -3.06720i q^{13} +2.51257i q^{14} -4.24303i q^{15} +5.97609 q^{16} +1.01118i q^{17} +0.292089 q^{18} -7.16168i q^{19} -10.7765 q^{20} -1.69816 q^{21} -0.874645i q^{22} +1.09448 q^{23} +9.86907i q^{24} +1.24303 q^{25} -7.70655i q^{26} +5.29189i q^{27} +4.31302i q^{28} -3.45039i q^{29} -10.6609i q^{30} -0.619073 q^{31} +3.39211 q^{32} +0.591142 q^{33} +2.54066i q^{34} -2.49861i q^{35} +0.501393 q^{36} -9.80884 q^{37} -17.9942i q^{38} +5.20859 q^{39} -14.5210 q^{40} +(4.67704 + 4.37325i) q^{41} -4.26675 q^{42} -1.10371 q^{43} -1.50139i q^{44} -0.290466 q^{45} +2.74996 q^{46} +4.32841i q^{47} +10.1484i q^{48} -1.00000 q^{49} +3.12321 q^{50} -1.71714 q^{51} -13.2289i q^{52} +12.6330i q^{53} +13.2963i q^{54} +0.869783i q^{55} +5.81162i q^{56} +12.1617 q^{57} -8.66936i q^{58} +14.5405 q^{59} -18.3003i q^{60} -0.654679 q^{61} -1.55547 q^{62} +0.116251i q^{63} -3.42927 q^{64} +7.66372i q^{65} +1.48529 q^{66} -10.0293i q^{67} +4.36123i q^{68} +1.85860i q^{69} -6.27793i q^{70} -13.0244i q^{71} +0.675608 q^{72} -7.55378 q^{73} -24.6454 q^{74} +2.11087i q^{75} -30.8884i q^{76} +0.348107 q^{77} +13.0870 q^{78} +12.6400i q^{79} -14.9319 q^{80} -8.63773 q^{81} +(11.7514 + 10.9881i) q^{82} +6.60297 q^{83} -7.32420 q^{84} -2.52654i q^{85} -2.77316 q^{86} +5.85932 q^{87} -2.02307i q^{88} +10.4335i q^{89} -0.729817 q^{90} +3.06720 q^{91} +4.72052 q^{92} -1.05129i q^{93} +10.8754i q^{94} +17.8942i q^{95} +5.76034i q^{96} +1.81305i q^{97} -2.51257 q^{98} -0.0404679i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{2} + 12 q^{4} - 10 q^{5} + 12 q^{8} - 10 q^{9}+O(q^{10}) \) 10 * q + 4 * q^2 + 12 * q^4 - 10 * q^5 + 12 * q^8 - 10 * q^9	\( 10 q + 4 q^{2} + 12 q^{4} - 10 q^{5} + 12 q^{8} - 10 q^{9} + 8 q^{10} - 16 q^{16} + 20 q^{18} - 22 q^{20} - 12 q^{21} - 4 q^{23} - 4 q^{25} + 14 q^{31} + 18 q^{32} - 2 q^{33} + 20 q^{36} - 22 q^{37} - 46 q^{39} - 58 q^{40} - 4 q^{41} - 8 q^{42} + 18 q^{43} + 50 q^{45} + 8 q^{46} - 10 q^{49} - 22 q^{50} + 14 q^{51} + 62 q^{57} + 34 q^{59} - 28 q^{61} - 44 q^{62} + 8 q^{64} - 36 q^{66} - 20 q^{72} + 12 q^{74} + 12 q^{77} + 78 q^{78} - 4 q^{80} + 10 q^{81} + 74 q^{82} - 20 q^{83} - 6 q^{84} + 12 q^{86} - 8 q^{87} - 54 q^{90} - 14 q^{91} - 30 q^{92} - 4 q^{98}+O(q^{100}) \) 10 * q + 4 * q^2 + 12 * q^4 - 10 * q^5 + 12 * q^8 - 10 * q^9 + 8 * q^10 - 16 * q^16 + 20 * q^18 - 22 * q^20 - 12 * q^21 - 4 * q^23 - 4 * q^25 + 14 * q^31 + 18 * q^32 - 2 * q^33 + 20 * q^36 - 22 * q^37 - 46 * q^39 - 58 * q^40 - 4 * q^41 - 8 * q^42 + 18 * q^43 + 50 * q^45 + 8 * q^46 - 10 * q^49 - 22 * q^50 + 14 * q^51 + 62 * q^57 + 34 * q^59 - 28 * q^61 - 44 * q^62 + 8 * q^64 - 36 * q^66 - 20 * q^72 + 12 * q^74 + 12 * q^77 + 78 * q^78 - 4 * q^80 + 10 * q^81 + 74 * q^82 - 20 * q^83 - 6 * q^84 + 12 * q^86 - 8 * q^87 - 54 * q^90 - 14 * q^91 - 30 * q^92 - 4 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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