LMFDB - Embedded newform 55.2.b.a.34.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [55,2,Mod(34,55)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(55, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("55.34");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 55 = 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	55.b (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:	$0.439177211117$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			34.2
Root			$1.68614 + 0.396143i$ of defining polynomial
Character	$\chi$	$=$	55.34
Dual form			55.2.b.a.34.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.792287i q^{2} +2.52434i q^{3} +1.37228 q^{4} +(-2.18614 + 0.469882i) q^{5} +2.00000 q^{6} -3.46410i q^{7} -2.67181i q^{8} -3.37228 q^{9} +O(q^{10})$	\(q-0.792287i q^{2} +2.52434i q^{3} +1.37228 q^{4} +(-2.18614 + 0.469882i) q^{5} +2.00000 q^{6} -3.46410i q^{7} -2.67181i q^{8} -3.37228 q^{9} +(0.372281 + 1.73205i) q^{10} -1.00000 q^{11} +3.46410i q^{12} -2.74456 q^{14} +(-1.18614 - 5.51856i) q^{15} +0.627719 q^{16} +5.04868i q^{17} +2.67181i q^{18} -4.00000 q^{19} +(-3.00000 + 0.644810i) q^{20} +8.74456 q^{21} +0.792287i q^{22} -2.52434i q^{23} +6.74456 q^{24} +(4.55842 - 2.05446i) q^{25} -0.939764i q^{27} -4.75372i q^{28} +2.74456 q^{29} +(-4.37228 + 0.939764i) q^{30} -2.37228 q^{31} -5.84096i q^{32} -2.52434i q^{33} +4.00000 q^{34} +(1.62772 + 7.57301i) q^{35} -4.62772 q^{36} +11.0371i q^{37} +3.16915i q^{38} +(1.25544 + 5.84096i) q^{40} -2.74456 q^{41} -6.92820i q^{42} +3.46410i q^{43} -1.37228 q^{44} +(7.37228 - 1.58457i) q^{45} -2.00000 q^{46} -6.63325i q^{47} +1.58457i q^{48} -5.00000 q^{49} +(-1.62772 - 3.61158i) q^{50} -12.7446 q^{51} -3.16915i q^{53} -0.744563 q^{54} +(2.18614 - 0.469882i) q^{55} -9.25544 q^{56} -10.0974i q^{57} -2.17448i q^{58} +1.62772 q^{59} +(-1.62772 - 7.57301i) q^{60} +10.7446 q^{61} +1.87953i q^{62} +11.6819i q^{63} -3.37228 q^{64} -2.00000 q^{66} +0.644810i q^{67} +6.92820i q^{68} +6.37228 q^{69} +(6.00000 - 1.28962i) q^{70} +7.11684 q^{71} +9.01011i q^{72} -6.92820i q^{73} +8.74456 q^{74} +(5.18614 + 11.5070i) q^{75} -5.48913 q^{76} +3.46410i q^{77} -12.7446 q^{79} +(-1.37228 + 0.294954i) q^{80} -7.74456 q^{81} +2.17448i q^{82} -6.63325i q^{83} +12.0000 q^{84} +(-2.37228 - 11.0371i) q^{85} +2.74456 q^{86} +6.92820i q^{87} +2.67181i q^{88} +4.37228 q^{89} +(-1.25544 - 5.84096i) q^{90} -3.46410i q^{92} -5.98844i q^{93} -5.25544 q^{94} +(8.74456 - 1.87953i) q^{95} +14.7446 q^{96} +4.10891i q^{97} +3.96143i q^{98} +3.37228 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{4} - 3 q^{5} + 8 q^{6} - 2 q^{9}+O(q^{10}) $ 4 * q - 6 * q^4 - 3 * q^5 + 8 * q^6 - 2 * q^9	$ 4 q - 6 q^{4} - 3 q^{5} + 8 q^{6} - 2 q^{9} - 10 q^{10} - 4 q^{11} + 12 q^{14} + q^{15} + 14 q^{16} - 16 q^{19} - 12 q^{20} + 12 q^{21} + 4 q^{24} + q^{25} - 12 q^{29} - 6 q^{30} + 2 q^{31} + 16 q^{34} + 18 q^{35} - 30 q^{36} + 28 q^{40} + 12 q^{41} + 6 q^{44} + 18 q^{45} - 8 q^{46} - 20 q^{49} - 18 q^{50} - 28 q^{51} + 20 q^{54} + 3 q^{55} - 60 q^{56} + 18 q^{59} - 18 q^{60} + 20 q^{61} - 2 q^{64} - 8 q^{66} + 14 q^{69} + 24 q^{70} - 6 q^{71} + 12 q^{74} + 15 q^{75} + 24 q^{76} - 28 q^{79} + 6 q^{80} - 8 q^{81} + 48 q^{84} + 2 q^{85} - 12 q^{86} + 6 q^{89} - 28 q^{90} - 44 q^{94} + 12 q^{95} + 36 q^{96} + 2 q^{99}+O(q^{100}) $ 4 * q - 6 * q^4 - 3 * q^5 + 8 * q^6 - 2 * q^9 - 10 * q^10 - 4 * q^11 + 12 * q^14 + q^15 + 14 * q^16 - 16 * q^19 - 12 * q^20 + 12 * q^21 + 4 * q^24 + q^25 - 12 * q^29 - 6 * q^30 + 2 * q^31 + 16 * q^34 + 18 * q^35 - 30 * q^36 + 28 * q^40 + 12 * q^41 + 6 * q^44 + 18 * q^45 - 8 * q^46 - 20 * q^49 - 18 * q^50 - 28 * q^51 + 20 * q^54 + 3 * q^55 - 60 * q^56 + 18 * q^59 - 18 * q^60 + 20 * q^61 - 2 * q^64 - 8 * q^66 + 14 * q^69 + 24 * q^70 - 6 * q^71 + 12 * q^74 + 15 * q^75 + 24 * q^76 - 28 * q^79 + 6 * q^80 - 8 * q^81 + 48 * q^84 + 2 * q^85 - 12 * q^86 + 6 * q^89 - 28 * q^90 - 44 * q^94 + 12 * q^95 + 36 * q^96 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/55\mathbb{Z}\right)^\times$.

$n$	$12$	$46$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	0.792287i		−	0.560232i	−0.959966	−	0.280116i	$-0.909627\pi$
$2$		−	0.792287i		−	0.560232i	0.959966	−	0.280116i	$-0.0903729\pi$
$3$			2.52434i			1.45743i	0.684819	+	0.728714i	$0.259881\pi$
$3$			2.52434i			1.45743i	−0.684819	+	0.728714i	$0.740119\pi$
$4$	1.37228			0.686141
$5$	−2.18614	+	0.469882i	−0.977672	+	0.210138i
$5$	−2.18614	+	0.469882i	−0.977672	+	0.210138i
$6$	2.00000			0.816497
$7$		−	3.46410i		−	1.30931i	−0.755929	−	0.654654i	$-0.772814\pi$
$7$		−	3.46410i		−	1.30931i	0.755929	−	0.654654i	$-0.227186\pi$
$8$		−	2.67181i		−	0.944629i
$9$	−3.37228			−1.12409
$10$	0.372281	+	1.73205i	0.117726	+	0.547723i
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$			3.46410i			1.00000i
$13$		0			0		1.00000			$0$
$13$		0			0		−1.00000			$\pi$
$14$	−2.74456			−0.733515
$15$	−1.18614	−	5.51856i	−0.306260	−	1.42489i
$16$	0.627719			0.156930
$17$			5.04868i			1.22448i	0.790671	+	0.612242i	$0.209732\pi$
$17$			5.04868i			1.22448i	−0.790671	+	0.612242i	$0.790268\pi$
$18$			2.67181i			0.629753i
$19$	−4.00000			−0.917663			−0.458831	−	0.888523i	$-0.651732\pi$
$19$	−4.00000			−0.917663			−0.458831	+	0.888523i	$0.651732\pi$
$20$	−3.00000	+	0.644810i	−0.670820	+	0.144184i
$21$	8.74456			1.90822
$22$			0.792287i			0.168916i
$23$		−	2.52434i		−	0.526361i	−0.964747	−	0.263180i	$-0.915229\pi$
$23$		−	2.52434i		−	0.526361i	0.964747	−	0.263180i	$-0.0847714\pi$
$24$	6.74456			1.37673
$25$	4.55842	−	2.05446i	0.911684	−	0.410891i
$26$		0			0
$27$		−	0.939764i		−	0.180858i
$28$		−	4.75372i		−	0.898369i
$29$	2.74456			0.509652			0.254826	−	0.966987i	$-0.417982\pi$
$29$	2.74456			0.509652			0.254826	+	0.966987i	$0.417982\pi$
$30$	−4.37228	+	0.939764i	−0.798266	+	0.171577i
$31$	−2.37228			−0.426074			−0.213037	−	0.977044i	$-0.568336\pi$
$31$	−2.37228			−0.426074			−0.213037	+	0.977044i	$0.568336\pi$
$32$		−	5.84096i		−	1.03255i
$33$		−	2.52434i		−	0.439431i
$34$	4.00000			0.685994
$35$	1.62772	+	7.57301i	0.275135	+	1.28007i
$36$	−4.62772			−0.771286
$37$			11.0371i			1.81449i	0.420602	+	0.907245i	$0.361819\pi$
$37$			11.0371i			1.81449i	−0.420602	+	0.907245i	$0.638181\pi$
$38$			3.16915i			0.514104i
$39$		0			0
$40$	1.25544	+	5.84096i	0.198502	+	0.923537i
$41$	−2.74456			−0.428629			−0.214314	−	0.976765i	$-0.568752\pi$
$41$	−2.74456			−0.428629			−0.214314	+	0.976765i	$0.568752\pi$
$42$		−	6.92820i		−	1.06904i
$43$			3.46410i			0.528271i	0.964486	+	0.264135i	$0.0850865\pi$
$43$			3.46410i			0.528271i	−0.964486	+	0.264135i	$0.914913\pi$
$44$	−1.37228			−0.206879
$45$	7.37228	−	1.58457i	1.09899	−	0.236214i
$46$	−2.00000			−0.294884
$47$		−	6.63325i		−	0.967559i	−0.875190	−	0.483779i	$-0.839264\pi$
$47$		−	6.63325i		−	0.967559i	0.875190	−	0.483779i	$-0.160736\pi$
$48$			1.58457i			0.228714i
$49$	−5.00000			−0.714286
$50$	−1.62772	−	3.61158i	−0.230194	−	0.510754i
$51$	−12.7446			−1.78460
$52$		0			0
$53$		−	3.16915i		−	0.435316i	−0.976025	−	0.217658i	$-0.930158\pi$
$53$		−	3.16915i		−	0.435316i	0.976025	−	0.217658i	$-0.0698417\pi$
$54$	−0.744563			−0.101322
$55$	2.18614	−	0.469882i	0.294779	−	0.0633589i
$56$	−9.25544			−1.23681
$57$		−	10.0974i		−	1.33743i
$58$		−	2.17448i		−	0.285523i
$59$	1.62772			0.211911			0.105955	−	0.994371i	$-0.466210\pi$
$59$	1.62772			0.211911			0.105955	+	0.994371i	$0.466210\pi$
$60$	−1.62772	−	7.57301i	−0.210138	−	0.977672i
$61$	10.7446			1.37570			0.687850	−	0.725853i	$-0.258555\pi$
$61$	10.7446			1.37570			0.687850	+	0.725853i	$0.258555\pi$
$62$			1.87953i			0.238700i
$63$			11.6819i			1.47178i
$64$	−3.37228			−0.421535
$65$		0			0
$66$	−2.00000			−0.246183
$67$			0.644810i			0.0787761i	0.999224	+	0.0393880i	$0.0125408\pi$
$67$			0.644810i			0.0787761i	−0.999224	+	0.0393880i	$0.987459\pi$
$68$			6.92820i			0.840168i
$69$	6.37228			0.767133
$70$	6.00000	−	1.28962i	0.717137	−	0.154139i
$71$	7.11684			0.844614			0.422307	−	0.906453i	$-0.361220\pi$
$71$	7.11684			0.844614			0.422307	+	0.906453i	$0.361220\pi$
$72$			9.01011i			1.06185i
$73$		−	6.92820i		−	0.810885i	−0.914121	−	0.405442i	$-0.867117\pi$
$73$		−	6.92820i		−	0.810885i	0.914121	−	0.405442i	$-0.132883\pi$
$74$	8.74456			1.01653
$75$	5.18614	+	11.5070i	0.598844	+	1.32871i
$76$	−5.48913			−0.629646
$77$			3.46410i			0.394771i
$78$		0			0
$79$	−12.7446			−1.43388			−0.716938	−	0.697137i	$-0.754457\pi$
$79$	−12.7446			−1.43388			−0.716938	+	0.697137i	$0.754457\pi$
$80$	−1.37228	+	0.294954i	−0.153426	+	0.0329768i
$81$	−7.74456			−0.860507
$82$			2.17448i			0.240131i
$83$		−	6.63325i		−	0.728094i	−0.931381	−	0.364047i	$-0.881395\pi$
$83$		−	6.63325i		−	0.728094i	0.931381	−	0.364047i	$-0.118605\pi$
$84$	12.0000			1.30931
$85$	−2.37228	−	11.0371i	−0.257310	−	1.19714i
$86$	2.74456			0.295954
$87$			6.92820i			0.742781i
$88$			2.67181i			0.284816i
$89$	4.37228			0.463461			0.231730	−	0.972780i	$-0.425561\pi$
$89$	4.37228			0.463461			0.231730	+	0.972780i	$0.425561\pi$
$90$	−1.25544	−	5.84096i	−0.132335	−	0.615692i
$91$		0			0
$92$		−	3.46410i		−	0.361158i
$93$		−	5.98844i		−	0.620972i
$94$	−5.25544			−0.542057
$95$	8.74456	−	1.87953i	0.897173	−	0.192835i
$96$	14.7446			1.50486
$97$			4.10891i			0.417197i	0.978001	+	0.208598i	$0.0668902\pi$
$97$			4.10891i			0.417197i	−0.978001	+	0.208598i	$0.933110\pi$
$98$			3.96143i			0.400165i
$99$	3.37228			0.338927
$100$	6.25544	−	2.81929i	0.625544	−	0.281929i
$101$	6.00000			0.597022			0.298511	−	0.954406i	$-0.403510\pi$
$101$	6.00000			0.597022			0.298511	+	0.954406i	$0.403510\pi$
$102$			10.0974i			0.999787i
$103$		−	10.3923i		−	1.02398i	−0.858990	−	0.511992i	$-0.828908\pi$
$103$		−	10.3923i		−	1.02398i	0.858990	−	0.511992i	$-0.171092\pi$
$104$		0			0
$105$	−19.1168	+	4.10891i	−1.86561	+	0.400989i
$106$	−2.51087			−0.243878
$107$		−	6.63325i		−	0.641260i	−0.947204	−	0.320630i	$-0.896105\pi$
$107$		−	6.63325i		−	0.641260i	0.947204	−	0.320630i	$-0.103895\pi$
$108$		−	1.28962i		−	0.124094i
$109$	−10.0000			−0.957826			−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000			−0.957826			−0.478913	+	0.877862i	$0.658969\pi$
$110$	−0.372281	−	1.73205i	−0.0354956	−	0.165145i
$111$	−27.8614			−2.64449
$112$		−	2.17448i		−	0.205469i
$113$			16.0858i			1.51322i	0.653864	+	0.756612i	$0.273147\pi$
$113$			16.0858i			1.51322i	−0.653864	+	0.756612i	$0.726853\pi$
$114$	−8.00000			−0.749269
$115$	1.18614	+	5.51856i	0.110608	+	0.514608i
$116$	3.76631			0.349693
$117$		0			0
$118$		−	1.28962i		−	0.118719i
$119$	17.4891			1.60323
$120$	−14.7446	+	3.16915i	−1.34599	+	0.289302i
$121$	1.00000			0.0909091
$122$		−	8.51278i		−	0.770711i
$123$		−	6.92820i		−	0.624695i
$124$	−3.25544			−0.292347
$125$	−9.00000	+	6.63325i	−0.804984	+	0.593296i
$126$	9.25544			0.824540
$127$		−	11.6819i		−	1.03660i	−0.855198	−	0.518302i	$-0.826564\pi$
$127$		−	11.6819i		−	1.03660i	0.855198	−	0.518302i	$-0.173436\pi$
$128$		−	9.01011i		−	0.796389i
$129$	−8.74456			−0.769916
$130$		0			0
$131$	8.74456			0.764016			0.382008	−	0.924159i	$-0.375233\pi$
$131$	8.74456			0.764016			0.382008	+	0.924159i	$0.375233\pi$
$132$		−	3.46410i		−	0.301511i
$133$			13.8564i			1.20150i
$134$	0.510875			0.0441329
$135$	0.441578	+	2.05446i	0.0380050	+	0.176819i
$136$	13.4891			1.15668
$137$			2.22938i			0.190469i	0.995455	+	0.0952346i	$0.0303601\pi$
$137$			2.22938i			0.190469i	−0.995455	+	0.0952346i	$0.969640\pi$
$138$		−	5.04868i		−	0.429772i
$139$	−18.2337			−1.54656			−0.773281	−	0.634064i	$-0.781386\pi$
$139$	−18.2337			−1.54656			−0.773281	+	0.634064i	$0.781386\pi$
$140$	2.23369	+	10.3923i	0.188781	+	0.878310i
$141$	16.7446			1.41015
$142$		−	5.63858i		−	0.473179i
$143$		0			0
$144$	−2.11684			−0.176404
$145$	−6.00000	+	1.28962i	−0.498273	+	0.107097i
$146$	−5.48913			−0.454283
$147$		−	12.6217i		−	1.04102i
$148$			15.1460i			1.24500i
$149$	−11.4891			−0.941226			−0.470613	−	0.882340i	$-0.655967\pi$
$149$	−11.4891			−0.941226			−0.470613	+	0.882340i	$0.655967\pi$
$150$	9.11684	−	4.10891i	0.744387	−	0.335491i
$151$	22.2337			1.80935			0.904676	−	0.426100i	$-0.140113\pi$
$151$	22.2337			1.80935			0.904676	+	0.426100i	$0.140113\pi$
$152$			10.6873i			0.866851i
$153$		−	17.0256i		−	1.37643i
$154$	2.74456			0.221163
$155$	5.18614	−	1.11469i	0.416561	−	0.0895342i
$156$		0			0
$157$		−	5.39853i		−	0.430850i	−0.976520	−	0.215425i	$-0.930886\pi$
$157$		−	5.39853i		−	0.430850i	0.976520	−	0.215425i	$-0.0691136\pi$
$158$			10.0974i			0.803302i
$159$	8.00000			0.634441
$160$	2.74456	+	12.7692i	0.216977	+	1.00949i
$161$	−8.74456			−0.689168
$162$			6.13592i			0.482083i
$163$		−	3.46410i		−	0.271329i	−0.990755	−	0.135665i	$-0.956683\pi$
$163$		−	3.46410i		−	0.271329i	0.990755	−	0.135665i	$-0.0433170\pi$
$164$	−3.76631			−0.294100
$165$	1.18614	+	5.51856i	0.0923409	+	0.429619i
$166$	−5.25544			−0.407901
$167$			22.3692i			1.73098i	0.500927	+	0.865490i	$0.332993\pi$
$167$			22.3692i			1.73098i	−0.500927	+	0.865490i	$0.667007\pi$
$168$		−	23.3639i		−	1.80256i
$169$	13.0000			1.00000
$170$	−8.74456	+	1.87953i	−0.670677	+	0.144153i
$171$	13.4891			1.03154
$172$			4.75372i			0.362468i
$173$		−	1.87953i		−	0.142898i	−0.997444	−	0.0714489i	$-0.977238\pi$
$173$		−	1.87953i		−	0.142898i	0.997444	−	0.0714489i	$-0.0227623\pi$
$174$	5.48913			0.416130
$175$	−7.11684	−	15.7908i	−0.537983	−	1.19368i
$176$	−0.627719			−0.0473161
$177$			4.10891i			0.308845i
$178$		−	3.46410i		−	0.259645i
$179$	15.8614			1.18554			0.592769	−	0.805373i	$-0.298035\pi$
$179$	15.8614			1.18554			0.592769	+	0.805373i	$0.298035\pi$
$180$	10.1168	−	2.17448i	0.754065	−	0.162076i
$181$	6.88316			0.511621			0.255810	−	0.966727i	$-0.417658\pi$
$181$	6.88316			0.511621			0.255810	+	0.966727i	$0.417658\pi$
$182$		0			0
$183$			27.1229i			2.00498i
$184$	−6.74456			−0.497216
$185$	−5.18614	−	24.1287i	−0.381293	−	1.77398i
$186$	−4.74456			−0.347888
$187$		−	5.04868i		−	0.369196i
$188$		−	9.10268i		−	0.663881i
$189$	−3.25544			−0.236798
$190$	−1.48913	−	6.92820i	−0.108033	−	0.502625i
$191$	−13.6277			−0.986067			−0.493034	−	0.870010i	$-0.664112\pi$
$191$	−13.6277			−0.986067			−0.493034	+	0.870010i	$0.664112\pi$
$192$		−	8.51278i		−	0.614357i
$193$			23.3639i			1.68177i	0.541216	+	0.840883i	$0.317964\pi$
$193$			23.3639i			1.68177i	−0.541216	+	0.840883i	$0.682036\pi$
$194$	3.25544			0.233727
$195$		0			0
$196$	−6.86141			−0.490100
$197$		−	1.87953i		−	0.133911i	−0.997756	−	0.0669554i	$-0.978671\pi$
$197$		−	1.87953i		−	0.133911i	0.997756	−	0.0669554i	$-0.0213285\pi$
$198$		−	2.67181i		−	0.189878i
$199$	8.00000			0.567105			0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000			0.567105			0.283552	+	0.958957i	$0.408487\pi$
$200$	−5.48913	−	12.1793i	−0.388140	−	0.861204i
$201$	−1.62772			−0.114810
$202$		−	4.75372i		−	0.334471i
$203$		−	9.50744i		−	0.667292i
$204$	−17.4891			−1.22448
$205$	6.00000	−	1.28962i	0.419058	−	0.0900710i
$206$	−8.23369			−0.573668
$207$			8.51278i			0.591679i
$208$		0			0
$209$	4.00000			0.276686
$210$	3.25544	+	15.1460i	0.224647	+	1.04518i
$211$	−21.4891			−1.47937			−0.739686	−	0.672952i	$-0.765026\pi$
$211$	−21.4891			−1.47937			−0.739686	+	0.672952i	$0.765026\pi$
$212$		−	4.34896i		−	0.298688i
$213$			17.9653i			1.23096i
$214$	−5.25544			−0.359254
$215$	−1.62772	−	7.57301i	−0.111009	−	0.516475i
$216$	−2.51087			−0.170843
$217$			8.21782i			0.557862i
$218$			7.92287i			0.536604i
$219$	17.4891			1.18181
$220$	3.00000	−	0.644810i	0.202260	−	0.0434731i
$221$		0			0
$222$			22.0742i			1.48153i
$223$			7.57301i			0.507126i	0.967319	+	0.253563i	$0.0816026\pi$
$223$			7.57301i			0.507126i	−0.967319	+	0.253563i	$0.918397\pi$
$224$	−20.2337			−1.35192
$225$	−15.3723	+	6.92820i	−1.02482	+	0.461880i
$226$	12.7446			0.847756
$227$			9.80240i			0.650608i	0.945609	+	0.325304i	$0.105467\pi$
$227$			9.80240i			0.650608i	−0.945609	+	0.325304i	$0.894533\pi$
$228$		−	13.8564i		−	0.917663i
$229$	−20.3723			−1.34624			−0.673119	−	0.739534i	$-0.735046\pi$
$229$	−20.3723			−1.34624			−0.673119	+	0.739534i	$0.735046\pi$
$230$	4.37228	−	0.939764i	0.288300	−	0.0619662i
$231$	−8.74456			−0.575350
$232$		−	7.33296i		−	0.481433i
$233$		−	17.0256i		−	1.11538i	−0.830049	−	0.557691i	$-0.811688\pi$
$233$		−	17.0256i		−	1.11538i	0.830049	−	0.557691i	$-0.188312\pi$
$234$		0			0
$235$	3.11684	+	14.5012i	0.203320	+	0.945955i
$236$	2.23369			0.145401
$237$		−	32.1716i		−	2.08977i
$238$		−	13.8564i		−	0.898177i
$239$	3.25544			0.210577			0.105288	−	0.994442i	$-0.466423\pi$
$239$	3.25544			0.210577			0.105288	+	0.994442i	$0.466423\pi$
$240$	−0.744563	−	3.46410i	−0.0480613	−	0.223607i
$241$	5.25544			0.338532			0.169266	−	0.985570i	$-0.445860\pi$
$241$	5.25544			0.338532			0.169266	+	0.985570i	$0.445860\pi$
$242$		−	0.792287i		−	0.0509301i
$243$		−	22.3692i		−	1.43498i
$244$	14.7446			0.943924
$245$	10.9307	−	2.34941i	0.698337	−	0.150098i
$246$	−5.48913			−0.349974
$247$		0			0
$248$			6.33830i			0.402482i
$249$	16.7446			1.06114
$250$	5.25544	+	7.13058i	0.332383	+	0.450978i
$251$	−4.88316			−0.308222			−0.154111	−	0.988054i	$-0.549251\pi$
$251$	−4.88316			−0.308222			−0.154111	+	0.988054i	$0.549251\pi$
$252$			16.0309i			1.00985i
$253$			2.52434i			0.158704i
$254$	−9.25544			−0.580738
$255$	27.8614	−	5.98844i	1.74475	−	0.375011i
$256$	−13.8832			−0.867697
$257$		−	23.9538i		−	1.49419i	−0.664715	−	0.747097i	$-0.731447\pi$
$257$		−	23.9538i		−	1.49419i	0.664715	−	0.747097i	$-0.268553\pi$
$258$			6.92820i			0.431331i
$259$	38.2337			2.37573
$260$		0			0
$261$	−9.25544			−0.572897
$262$		−	6.92820i		−	0.428026i
$263$			14.1514i			0.872610i	0.899799	+	0.436305i	$0.143713\pi$
$263$			14.1514i			0.872610i	−0.899799	+	0.436305i	$0.856287\pi$
$264$	−6.74456			−0.415099
$265$	1.48913	+	6.92820i	0.0914762	+	0.425596i
$266$	10.9783			0.673120
$267$			11.0371i			0.675460i
$268$			0.884861i			0.0540515i
$269$	−11.4891			−0.700504			−0.350252	−	0.936655i	$-0.613904\pi$
$269$	−11.4891			−0.700504			−0.350252	+	0.936655i	$0.613904\pi$
$270$	1.62772	−	0.349857i	0.0990598	−	0.0212916i
$271$	−9.48913			−0.576423			−0.288212	−	0.957567i	$-0.593061\pi$
$271$	−9.48913			−0.576423			−0.288212	+	0.957567i	$0.593061\pi$
$272$			3.16915i			0.192158i
$273$		0			0
$274$	1.76631			0.106707
$275$	−4.55842	+	2.05446i	−0.274883	+	0.123888i
$276$	8.74456			0.526361
$277$		−	8.21782i		−	0.493761i	−0.969046	−	0.246881i	$-0.920594\pi$
$277$		−	8.21782i		−	0.493761i	0.969046	−	0.246881i	$-0.0794055\pi$
$278$			14.4463i			0.866432i
$279$	8.00000			0.478947
$280$	20.2337	−	4.34896i	1.20919	−	0.259900i
$281$	−23.4891			−1.40124			−0.700622	−	0.713533i	$-0.747094\pi$
$281$	−23.4891			−1.40124			−0.700622	+	0.713533i	$0.747094\pi$
$282$		−	13.2665i		−	0.790009i
$283$		−	4.75372i		−	0.282579i	−0.989968	−	0.141290i	$-0.954875\pi$
$283$		−	4.75372i		−	0.282579i	0.989968	−	0.141290i	$-0.0451249\pi$
$284$	9.76631			0.579524
$285$	4.74456	+	22.0742i	0.281044	+	1.30756i
$286$		0			0
$287$			9.50744i			0.561207i
$288$			19.6974i			1.16068i
$289$	−8.48913			−0.499360
$290$	1.02175	+	4.75372i	0.0599992	+	0.279148i
$291$	−10.3723			−0.608034
$292$		−	9.50744i		−	0.556381i
$293$		−	10.0974i		−	0.589894i	−0.955514	−	0.294947i	$-0.904698\pi$
$293$		−	10.0974i		−	0.589894i	0.955514	−	0.294947i	$-0.0953019\pi$
$294$	−10.0000			−0.583212
$295$	−3.55842	+	0.764836i	−0.207179	+	0.0445304i
$296$	29.4891			1.71402
$297$			0.939764i			0.0545306i
$298$			9.10268i			0.527304i
$299$		0			0
$300$	7.11684	+	15.7908i	0.410891	+	0.911684i
$301$	12.0000			0.691669
$302$		−	17.6155i		−	1.01366i
$303$			15.1460i			0.870117i
$304$	−2.51087			−0.144009
$305$	−23.4891	+	5.04868i	−1.34498	+	0.289086i
$306$	−13.4891			−0.771122
$307$			28.1176i			1.60475i	0.596817	+	0.802377i	$0.296432\pi$
$307$			28.1176i			1.60475i	−0.596817	+	0.802377i	$0.703568\pi$
$308$			4.75372i			0.270868i
$309$	26.2337			1.49238
$310$	−0.883156	−	4.10891i	−0.0501599	−	0.233371i
$311$	−17.4891			−0.991717			−0.495859	−	0.868403i	$-0.665147\pi$
$311$	−17.4891			−0.991717			−0.495859	+	0.868403i	$0.665147\pi$
$312$		0			0
$313$		−	31.8217i		−	1.79867i	−0.437260	−	0.899335i	$-0.644051\pi$
$313$		−	31.8217i		−	1.79867i	0.437260	−	0.899335i	$-0.355949\pi$
$314$	−4.27719			−0.241376
$315$	−5.48913	−	25.5383i	−0.309277	−	1.43892i
$316$	−17.4891			−0.983840
$317$			3.51900i			0.197647i	0.995105	+	0.0988235i	$0.0315079\pi$
$317$			3.51900i			0.197647i	−0.995105	+	0.0988235i	$0.968492\pi$
$318$		−	6.33830i		−	0.355434i
$319$	−2.74456			−0.153666
$320$	7.37228	−	1.58457i	0.412123	−	0.0885804i
$321$	16.7446			0.934590
$322$			6.92820i			0.386094i
$323$		−	20.1947i		−	1.12366i
$324$	−10.6277			−0.590429
$325$		0			0
$326$	−2.74456			−0.152007
$327$		−	25.2434i		−	1.39596i
$328$			7.33296i			0.404895i
$329$	−22.9783			−1.26683
$330$	4.37228	−	0.939764i	0.240686	−	0.0517323i
$331$	3.11684			0.171317			0.0856586	−	0.996325i	$-0.472701\pi$
$331$	3.11684			0.171317			0.0856586	+	0.996325i	$0.472701\pi$
$332$		−	9.10268i		−	0.499575i
$333$		−	37.2203i		−	2.03966i
$334$	17.7228			0.969749
$335$	−0.302985	−	1.40965i	−0.0165538	−	0.0770172i
$336$	5.48913			0.299456
$337$			12.5668i			0.684556i	0.939599	+	0.342278i	$0.111199\pi$
$337$			12.5668i			0.684556i	−0.939599	+	0.342278i	$0.888801\pi$
$338$		−	10.2997i		−	0.560232i
$339$	−40.6060			−2.20541
$340$	−3.25544	−	15.1460i	−0.176551	−	0.821409i
$341$	2.37228			0.128466
$342$		−	10.6873i		−	0.577901i
$343$		−	6.92820i		−	0.374088i
$344$	9.25544			0.499020
$345$	−13.9307	+	2.99422i	−0.750004	+	0.161203i
$346$	−1.48913			−0.0800559
$347$			29.2974i			1.57277i	0.617739	+	0.786383i	$0.288049\pi$
$347$			29.2974i			1.57277i	−0.617739	+	0.786383i	$0.711951\pi$
$348$			9.50744i			0.509652i
$349$	7.48913			0.400884			0.200442	−	0.979706i	$-0.435762\pi$
$349$	7.48913			0.400884			0.200442	+	0.979706i	$0.435762\pi$
$350$	−12.5109	+	5.63858i	−0.668734	+	0.301395i
$351$		0			0
$352$			5.84096i			0.311324i
$353$			21.7244i			1.15627i	0.815941	+	0.578136i	$0.196220\pi$
$353$			21.7244i			1.15627i	−0.815941	+	0.578136i	$0.803780\pi$
$354$	3.25544			0.173025
$355$	−15.5584	+	3.34408i	−0.825755	+	0.177485i
$356$	6.00000			0.317999
$357$			44.1485i			2.33658i
$358$		−	12.5668i		−	0.664175i
$359$	−6.51087			−0.343631			−0.171815	−	0.985129i	$-0.554963\pi$
$359$	−6.51087			−0.343631			−0.171815	+	0.985129i	$0.554963\pi$
$360$	−4.23369	−	19.6974i	−0.223135	−	1.03814i
$361$	−3.00000			−0.157895
$362$		−	5.45343i		−	0.286626i
$363$			2.52434i			0.132493i
$364$		0			0
$365$	3.25544	+	15.1460i	0.170397	+	0.792779i
$366$	21.4891			1.12325
$367$			24.0087i			1.25324i	0.779324	+	0.626621i	$0.215563\pi$
$367$			24.0087i			1.25324i	−0.779324	+	0.626621i	$0.784437\pi$
$368$		−	1.58457i		−	0.0826016i
$369$	9.25544			0.481819
$370$	−19.1168	+	4.10891i	−0.993837	+	0.213612i
$371$	−10.9783			−0.569962
$372$		−	8.21782i		−	0.426074i
$373$			8.21782i			0.425503i	0.977106	+	0.212751i	$0.0682424\pi$
$373$			8.21782i			0.425503i	−0.977106	+	0.212751i	$0.931758\pi$
$374$	−4.00000			−0.206835
$375$	−16.7446	−	22.7190i	−0.864685	−	1.17321i
$376$	−17.7228			−0.913984
$377$		0			0
$378$			2.57924i			0.132662i
$379$	6.37228			0.327322			0.163661	−	0.986517i	$-0.447670\pi$
$379$	6.37228			0.327322			0.163661	+	0.986517i	$0.447670\pi$
$380$	12.0000	−	2.57924i	0.615587	−	0.132312i
$381$	29.4891			1.51077
$382$			10.7971i			0.552426i
$383$			5.69349i			0.290924i	0.989364	+	0.145462i	$0.0464668\pi$
$383$			5.69349i			0.290924i	−0.989364	+	0.145462i	$0.953533\pi$
$384$	22.7446			1.16068
$385$	−1.62772	−	7.57301i	−0.0829562	−	0.385957i
$386$	18.5109			0.942179
$387$		−	11.6819i		−	0.593826i
$388$			5.63858i			0.286256i
$389$	9.86141			0.499993			0.249997	−	0.968247i	$-0.419571\pi$
$389$	9.86141			0.499993			0.249997	+	0.968247i	$0.419571\pi$
$390$		0			0
$391$	12.7446			0.644520
$392$			13.3591i			0.674735i
$393$			22.0742i			1.11350i
$394$	−1.48913			−0.0750210
$395$	27.8614	−	5.98844i	1.40186	−	0.301311i
$396$	4.62772			0.232552
$397$		−	23.3639i		−	1.17260i	−0.810095	−	0.586299i	$-0.800584\pi$
$397$		−	23.3639i		−	1.17260i	0.810095	−	0.586299i	$-0.199416\pi$
$398$		−	6.33830i		−	0.317710i
$399$	−34.9783			−1.75110
$400$	2.86141	−	1.28962i	0.143070	−	0.0644810i
$401$	11.4891			0.573740			0.286870	−	0.957970i	$-0.407385\pi$
$401$	11.4891			0.573740			0.286870	+	0.957970i	$0.407385\pi$
$402$			1.28962i			0.0643204i
$403$		0			0
$404$	8.23369			0.409641
$405$	16.9307	−	3.63903i	0.841293	−	0.180825i
$406$	−7.53262			−0.373838
$407$		−	11.0371i		−	0.547089i
$408$			34.0511i			1.68578i
$409$	−4.51087			−0.223048			−0.111524	−	0.993762i	$-0.535573\pi$
$409$	−4.51087			−0.223048			−0.111524	+	0.993762i	$0.535573\pi$
$410$	−1.02175	−	4.75372i	−0.0504606	−	0.234770i
$411$	−5.62772			−0.277595
$412$		−	14.2612i		−	0.702597i
$413$		−	5.63858i		−	0.277457i
$414$	6.74456			0.331477
$415$	3.11684	+	14.5012i	0.153000	+	0.711837i
$416$		0			0
$417$		−	46.0280i		−	2.25400i
$418$		−	3.16915i		−	0.155008i
$419$	−22.9783			−1.12256			−0.561280	−	0.827626i	$-0.689691\pi$
$419$	−22.9783			−1.12256			−0.561280	+	0.827626i	$0.689691\pi$
$420$	−26.2337	+	5.63858i	−1.28007	+	0.275135i
$421$	31.4891			1.53469			0.767343	−	0.641237i	$-0.221578\pi$
$421$	31.4891			1.53469			0.767343	+	0.641237i	$0.221578\pi$
$422$			17.0256i			0.828791i
$423$			22.3692i			1.08763i
$424$	−8.46738			−0.411212
$425$	10.3723	+	23.0140i	0.503130	+	1.11634i
$426$	14.2337			0.689624
$427$		−	37.2203i		−	1.80121i
$428$		−	9.10268i		−	0.439995i
$429$		0			0
$430$	−6.00000	+	1.28962i	−0.289346	+	0.0621910i
$431$	31.7228			1.52803			0.764017	−	0.645196i	$-0.223224\pi$
$431$	31.7228			1.52803			0.764017	+	0.645196i	$0.223224\pi$
$432$		−	0.589907i		−	0.0283819i
$433$		−	20.5446i		−	0.987308i	−0.869658	−	0.493654i	$-0.835661\pi$
$433$		−	20.5446i		−	0.987308i	0.869658	−	0.493654i	$-0.164339\pi$
$434$	6.51087			0.312532
$435$	−3.25544	−	15.1460i	−0.156086	−	0.726196i
$436$	−13.7228			−0.657204
$437$			10.0974i			0.483022i
$438$		−	13.8564i		−	0.662085i
$439$	1.48913			0.0710721			0.0355360	−	0.999368i	$-0.488686\pi$
$439$	1.48913			0.0710721			0.0355360	+	0.999368i	$0.488686\pi$
$440$	−1.25544	−	5.84096i	−0.0598506	−	0.278457i
$441$	16.8614			0.802924
$442$		0			0
$443$		−	15.0911i		−	0.717001i	−0.933530	−	0.358500i	$-0.883288\pi$
$443$		−	15.0911i		−	0.717001i	0.933530	−	0.358500i	$-0.116712\pi$
$444$	−38.2337			−1.81449
$445$	−9.55842	+	2.05446i	−0.453113	+	0.0973905i
$446$	6.00000			0.284108
$447$		−	29.0024i		−	1.37177i
$448$			11.6819i			0.551919i
$449$	21.8614			1.03170			0.515852	−	0.856678i	$-0.327476\pi$
$449$	21.8614			1.03170			0.515852	+	0.856678i	$0.327476\pi$
$450$	5.48913	+	12.1793i	0.258760	+	0.574136i
$451$	2.74456			0.129236
$452$			22.0742i			1.03828i
$453$			56.1253i			2.63700i
$454$	7.76631			0.364491
$455$		0			0
$456$	−26.9783			−1.26337
$457$			20.7846i			0.972263i	0.873886	+	0.486132i	$0.161592\pi$
$457$			20.7846i			0.972263i	−0.873886	+	0.486132i	$0.838408\pi$
$458$			16.1407i			0.754205i
$459$	4.74456			0.221457
$460$	1.62772	+	7.57301i	0.0758928	+	0.353094i
$461$	−32.2337			−1.50127			−0.750636	−	0.660716i	$-0.770253\pi$
$461$	−32.2337			−1.50127			−0.750636	+	0.660716i	$0.770253\pi$
$462$			6.92820i			0.322329i
$463$		−	20.1398i		−	0.935976i	−0.883735	−	0.467988i	$-0.844979\pi$
$463$		−	20.1398i		−	0.935976i	0.883735	−	0.467988i	$-0.155021\pi$
$464$	1.72281			0.0799796
$465$	2.81386	+	13.0916i	0.130490	+	0.607107i
$466$	−13.4891			−0.624872
$467$			4.40387i			0.203787i	0.994795	+	0.101893i	$0.0324900\pi$
$467$			4.40387i			0.203787i	−0.994795	+	0.101893i	$0.967510\pi$
$468$		0			0
$469$	2.23369			0.103142
$470$	11.4891	−	2.46943i	0.529954	−	0.113907i
$471$	13.6277			0.627932
$472$		−	4.34896i		−	0.200177i
$473$		−	3.46410i		−	0.159280i
$474$	−25.4891			−1.17075
$475$	−18.2337	+	8.21782i	−0.836619	+	0.377060i
$476$	24.0000			1.10004
$477$			10.6873i			0.489336i
$478$		−	2.57924i		−	0.117972i
$479$	−17.4891			−0.799099			−0.399549	−	0.916712i	$-0.630833\pi$
$479$	−17.4891			−0.799099			−0.399549	+	0.916712i	$0.630833\pi$
$480$	−32.2337	+	6.92820i	−1.47126	+	0.316228i
$481$		0			0
$482$		−	4.16381i		−	0.189657i
$483$		−	22.0742i		−	1.00441i
$484$	1.37228			0.0623764
$485$	−1.93070	−	8.98266i	−0.0876687	−	0.407882i
$486$	−17.7228			−0.803923
$487$		−	22.7190i		−	1.02950i	−0.857341	−	0.514749i	$-0.827885\pi$
$487$		−	22.7190i		−	1.02950i	0.857341	−	0.514749i	$-0.172115\pi$
$488$		−	28.7075i		−	1.29953i
$489$	8.74456			0.395443
$490$	−1.86141	−	8.66025i	−0.0840898	−	0.391230i
$491$	29.4891			1.33083			0.665413	−	0.746476i	$-0.268256\pi$
$491$	29.4891			1.33083			0.665413	+	0.746476i	$0.268256\pi$
$492$		−	9.50744i		−	0.428629i
$493$			13.8564i			0.624061i
$494$		0			0
$495$	−7.37228	+	1.58457i	−0.331359	+	0.0712213i
$496$	−1.48913			−0.0668637
$497$		−	24.6535i		−	1.10586i
$498$		−	13.2665i		−	0.594486i
$499$	20.0000			0.895323			0.447661	−	0.894203i	$-0.352257\pi$
$499$	20.0000			0.895323			0.447661	+	0.894203i	$0.352257\pi$
$500$	−12.3505	+	9.10268i	−0.552333	+	0.407084i
$501$	−56.4674			−2.52278
$502$			3.86886i			0.172676i
$503$			0.294954i			0.0131513i	0.999978	+	0.00657567i	$0.00209311\pi$
$503$			0.294954i			0.0131513i	−0.999978	+	0.00657567i	$0.997907\pi$
$504$	31.2119			1.39029
$505$	−13.1168	+	2.81929i	−0.583692	+	0.125457i
$506$	2.00000			0.0889108
$507$			32.8164i			1.45743i
$508$		−	16.0309i		−	0.711256i
$509$	−28.3723			−1.25758			−0.628790	−	0.777575i	$-0.716449\pi$
$509$	−28.3723			−1.25758			−0.628790	+	0.777575i	$0.716449\pi$
$510$	−4.74456	−	22.0742i	−0.210093	−	0.977463i
$511$	−24.0000			−1.06170
$512$		−	7.02078i		−	0.310277i
$513$			3.75906i			0.165966i
$514$	−18.9783			−0.837095
$515$	4.88316	+	22.7190i	0.215178	+	1.00112i
$516$	−12.0000			−0.528271
$517$			6.63325i			0.291730i
$518$		−	30.2921i		−	1.33096i
$519$	4.74456			0.208263
$520$		0			0
$521$	18.6060			0.815142			0.407571	−	0.913173i	$-0.366376\pi$
$521$	18.6060			0.815142			0.407571	+	0.913173i	$0.366376\pi$
$522$			7.33296i			0.320955i
$523$			9.10268i			0.398033i	0.979996	+	0.199016i	$0.0637747\pi$
$523$			9.10268i			0.398033i	−0.979996	+	0.199016i	$0.936225\pi$
$524$	12.0000			0.524222
$525$	39.8614	−	17.9653i	1.73969	−	0.784071i
$526$	11.2119			0.488864
$527$		−	11.9769i		−	0.521721i
$528$		−	1.58457i		−	0.0689597i
$529$	16.6277			0.722944
$530$	5.48913	−	1.17981i	0.238432	−	0.0512479i
$531$	−5.48913			−0.238208
$532$			19.0149i			0.824400i
$533$		0			0
$534$	8.74456			0.378414
$535$	3.11684	+	14.5012i	0.134753	+	0.626942i
$536$	1.72281			0.0744142
$537$			40.0395i			1.72783i
$538$			9.10268i			0.392445i
$539$	5.00000			0.215365
$540$	0.605969	+	2.81929i	0.0260768	+	0.121323i
$541$	−0.233688			−0.0100470			−0.00502351	−	0.999987i	$-0.501599\pi$
$541$	−0.233688			−0.0100470			−0.00502351	+	0.999987i	$0.501599\pi$
$542$			7.51811i			0.322930i
$543$			17.3754i			0.745650i
$544$	29.4891			1.26434
$545$	21.8614	−	4.69882i	0.936440	−	0.201275i
$546$		0			0
$547$			9.10268i			0.389203i	0.980882	+	0.194601i	$0.0623413\pi$
$547$			9.10268i			0.389203i	−0.980882	+	0.194601i	$0.937659\pi$
$548$			3.05934i			0.130689i
$549$	−36.2337			−1.54642
$550$	1.62772	+	3.61158i	0.0694062	+	0.153998i
$551$	−10.9783			−0.467689
$552$		−	17.0256i		−	0.724656i
$553$			44.1485i			1.87738i
$554$	−6.51087			−0.276621
$555$	60.9090	−	13.0916i	2.58544	−	0.555706i
$556$	−25.0217			−1.06116
$557$		−	32.1716i		−	1.36315i	−0.731747	−	0.681577i	$-0.761295\pi$
$557$		−	32.1716i		−	1.36315i	0.731747	−	0.681577i	$-0.238705\pi$
$558$		−	6.33830i		−	0.268321i
$559$		0			0
$560$	1.02175	+	4.75372i	0.0431768	+	0.200881i
$561$	12.7446			0.538076
$562$			18.6101i			0.785021i
$563$		−	12.2718i		−	0.517196i	−0.965985	−	0.258598i	$-0.916739\pi$
$563$		−	12.2718i		−	0.517196i	0.965985	−	0.258598i	$-0.0832605\pi$
$564$	22.9783			0.967559
$565$	−7.55842	−	35.1658i	−0.317985	−	1.47944i
$566$	−3.76631			−0.158310
$567$			26.8280i			1.12667i
$568$		−	19.0149i		−	0.797847i
$569$	38.7446			1.62426			0.812128	−	0.583479i	$-0.198309\pi$
$569$	38.7446			1.62426			0.812128	+	0.583479i	$0.198309\pi$
$570$	17.4891	−	3.75906i	0.732539	−	0.157449i
$571$	−21.4891			−0.899292			−0.449646	−	0.893207i	$-0.648450\pi$
$571$	−21.4891			−0.899292			−0.449646	+	0.893207i	$0.648450\pi$
$572$		0			0
$573$		−	34.4010i		−	1.43712i
$574$	7.53262			0.314406
$575$	−5.18614	−	11.5070i	−0.216277	−	0.479875i
$576$	11.3723			0.473845
$577$		−	31.8217i		−	1.32476i	−0.749170	−	0.662378i	$-0.769547\pi$
$577$		−	31.8217i		−	1.32476i	0.749170	−	0.662378i	$-0.230453\pi$
$578$			6.72582i			0.279757i
$579$	−58.9783			−2.45105
$580$	−8.23369	+	1.76972i	−0.341885	+	0.0734837i
$581$	−22.9783			−0.953298
$582$			8.21782i			0.340640i
$583$			3.16915i			0.131253i
$584$	−18.5109			−0.765985
$585$		0			0
$586$	−8.00000			−0.330477
$587$			28.0078i			1.15600i	0.816035	+	0.578002i	$0.196167\pi$
$587$			28.0078i			1.15600i	−0.816035	+	0.578002i	$0.803833\pi$
$588$		−	17.3205i		−	0.714286i
$589$	9.48913			0.390993
$590$	0.605969	+	2.81929i	0.0249474	+	0.116068i
$591$	4.74456			0.195165
$592$			6.92820i			0.284747i
$593$			43.5586i			1.78874i	0.447333	+	0.894368i	$0.352374\pi$
$593$			43.5586i			1.78874i	−0.447333	+	0.894368i	$0.647626\pi$
$594$	0.744563			0.0305498
$595$	−38.2337	+	8.21782i	−1.56743	+	0.336898i
$596$	−15.7663			−0.645813
$597$			20.1947i			0.826514i
$598$		0			0
$599$	34.9783			1.42917			0.714586	−	0.699547i	$-0.246615\pi$
$599$	34.9783			1.42917			0.714586	+	0.699547i	$0.246615\pi$
$600$	30.7446	−	13.8564i	1.25514	−	0.565685i
$601$	30.4674			1.24279			0.621395	−	0.783497i	$-0.286566\pi$
$601$	30.4674			1.24279			0.621395	+	0.783497i	$0.286566\pi$
$602$		−	9.50744i		−	0.387494i
$603$		−	2.17448i		−	0.0885517i
$604$	30.5109			1.24147
$605$	−2.18614	+	0.469882i	−0.0888793	+	0.0191034i
$606$	12.0000			0.487467
$607$		−	3.46410i		−	0.140604i	−0.997526	−	0.0703018i	$-0.977604\pi$
$607$		−	3.46410i		−	0.140604i	0.997526	−	0.0703018i	$-0.0223962\pi$
$608$			23.3639i			0.947529i
$609$	24.0000			0.972529
$610$	4.00000	+	18.6101i	0.161955	+	0.753502i
$611$		0			0
$612$		−	23.3639i		−	0.944428i
$613$		−	44.1485i		−	1.78314i	−0.452883	−	0.891570i	$-0.649605\pi$
$613$		−	44.1485i		−	1.78314i	0.452883	−	0.891570i	$-0.350395\pi$
$614$	22.2772			0.899034
$615$	3.25544	+	15.1460i	0.131272	+	0.610747i
$616$	9.25544			0.372912
$617$			3.75906i			0.151334i	0.997133	+	0.0756669i	$0.0241086\pi$
$617$			3.75906i			0.151334i	−0.997133	+	0.0756669i	$0.975891\pi$
$618$		−	20.7846i		−	0.836080i
$619$	3.11684			0.125277			0.0626383	−	0.998036i	$-0.480049\pi$
$619$	3.11684			0.125277			0.0626383	+	0.998036i	$0.480049\pi$
$620$	7.11684	−	1.52967i	0.285819	−	0.0614331i
$621$	−2.37228			−0.0951964
$622$			13.8564i			0.555591i
$623$		−	15.1460i		−	0.606813i
$624$		0			0
$625$	16.5584	−	18.7302i	0.662337	−	0.749206i
$626$	−25.2119			−1.00767
$627$			10.0974i			0.403249i
$628$		−	7.40830i		−	0.295624i
$629$	−55.7228			−2.22181
$630$	−20.2337	+	4.34896i	−0.806129	+	0.173267i
$631$	−16.6060			−0.661073			−0.330537	−	0.943793i	$-0.607230\pi$
$631$	−16.6060			−0.661073			−0.330537	+	0.943793i	$0.607230\pi$
$632$			34.0511i			1.35448i
$633$		−	54.2458i		−	2.15608i
$634$	2.78806			0.110728
$635$	5.48913	+	25.5383i	0.217829	+	1.01346i
$636$	10.9783			0.435316
$637$		0			0
$638$			2.17448i			0.0860885i
$639$	−24.0000			−0.949425
$640$	4.23369	+	19.6974i	0.167351	+	0.778607i
$641$	−19.6277			−0.775248			−0.387624	−	0.921818i	$-0.626704\pi$
$641$	−19.6277			−0.775248			−0.387624	+	0.921818i	$0.626704\pi$
$642$		−	13.2665i		−	0.523587i
$643$			39.1547i			1.54411i	0.635556	+	0.772055i	$0.280771\pi$
$643$			39.1547i			1.54411i	−0.635556	+	0.772055i	$0.719229\pi$
$644$	−12.0000			−0.472866
$645$	19.1168	−	4.10891i	0.752725	−	0.161788i
$646$	−16.0000			−0.629512
$647$		−	41.0342i		−	1.61322i	−0.591083	−	0.806611i	$-0.701299\pi$
$647$		−	41.0342i		−	1.61322i	0.591083	−	0.806611i	$-0.298701\pi$
$648$			20.6920i			0.812860i
$649$	−1.62772			−0.0638935
$650$		0			0
$651$	−20.7446			−0.813044
$652$		−	4.75372i		−	0.186170i
$653$			25.5932i			1.00154i	0.865580	+	0.500770i	$0.166950\pi$
$653$			25.5932i			1.00154i	−0.865580	+	0.500770i	$0.833050\pi$
$654$	−20.0000			−0.782062
$655$	−19.1168	+	4.10891i	−0.746957	+	0.160548i
$656$	−1.72281			−0.0672646
$657$			23.3639i			0.911511i
$658$			18.2054i			0.709719i
$659$	−32.7446			−1.27555			−0.637774	−	0.770224i	$-0.720144\pi$
$659$	−32.7446			−1.27555			−0.637774	+	0.770224i	$0.720144\pi$
$660$	1.62772	+	7.57301i	0.0633589	+	0.294779i
$661$	35.3505			1.37498			0.687488	−	0.726196i	$-0.258713\pi$
$661$	35.3505			1.37498			0.687488	+	0.726196i	$0.258713\pi$
$662$		−	2.46943i		−	0.0959773i
$663$		0			0
$664$	−17.7228			−0.687779
$665$	−6.51087	−	30.2921i	−0.252481	−	1.17468i
$666$	−29.4891			−1.14268
$667$		−	6.92820i		−	0.268261i
$668$			30.6968i			1.18770i
$669$	−19.1168			−0.739100
$670$	−1.11684	+	0.240051i	−0.0431474	+	0.00927397i
$671$	−10.7446			−0.414789
$672$		−	51.0767i		−	1.97033i
$673$		−	1.28962i		−	0.0497112i	−0.999691	−	0.0248556i	$-0.992087\pi$
$673$		−	1.28962i		−	0.0497112i	0.999691	−	0.0248556i	$-0.00791260\pi$
$674$	9.95650			0.383510
$675$	−1.93070	−	4.28384i	−0.0743128	−	0.164885i
$676$	17.8397			0.686141
$677$		−	43.4487i		−	1.66987i	−0.550348	−	0.834935i	$-0.685505\pi$
$677$		−	43.4487i		−	1.66987i	0.550348	−	0.834935i	$-0.314495\pi$
$678$			32.1716i			1.23554i
$679$	14.2337			0.546239
$680$	−29.4891	+	6.33830i	−1.13086	+	0.243063i
$681$	−24.7446			−0.948214
$682$		−	1.87953i		−	0.0719708i
$683$			44.4434i			1.70058i	0.526314	+	0.850290i	$0.323573\pi$
$683$			44.4434i			1.70058i	−0.526314	+	0.850290i	$0.676427\pi$
$684$	18.5109			0.707781
$685$	−1.04755	−	4.87375i	−0.0400247	−	0.186216i
$686$	−5.48913			−0.209576
$687$		−	51.4265i		−	1.96204i
$688$			2.17448i			0.0829013i
$689$		0			0
$690$	2.37228	+	11.0371i	0.0903112	+	0.420176i
$691$	16.1386			0.613941			0.306971	−	0.951719i	$-0.400685\pi$
$691$	16.1386			0.613941			0.306971	+	0.951719i	$0.400685\pi$
$692$		−	2.57924i		−	0.0980480i
$693$		−	11.6819i		−	0.443760i
$694$	23.2119			0.881113
$695$	39.8614	−	8.56768i	1.51203	−	0.324991i
$696$	18.5109			0.701653
$697$		−	13.8564i		−	0.524849i
$698$		−	5.93354i		−	0.224588i
$699$	42.9783			1.62559
$700$	−9.76631	−	21.6695i	−0.369132	−	0.819029i
$701$	−35.4891			−1.34041			−0.670203	−	0.742178i	$-0.733793\pi$
$701$	−35.4891			−1.34041			−0.670203	+	0.742178i	$0.733793\pi$
$702$		0			0
$703$		−	44.1485i		−	1.66509i
$704$	3.37228			0.127098
$705$	−36.6060	+	7.86797i	−1.37866	+	0.296325i
$706$	17.2119			0.647780
$707$		−	20.7846i		−	0.781686i
$708$			5.63858i			0.211911i
$709$	−41.1168			−1.54418			−0.772088	−	0.635516i	$-0.780787\pi$
$709$	−41.1168			−1.54418			−0.772088	+	0.635516i	$0.780787\pi$
$710$	2.64947	+	12.3267i	0.0994328	+	0.462614i
$711$	42.9783			1.61181
$712$		−	11.6819i		−	0.437799i
$713$			5.98844i			0.224269i
$714$	34.9783			1.30903
$715$		0			0
$716$	21.7663			0.813445
$717$			8.21782i			0.306900i
$718$			5.15848i			0.192513i
$719$	−21.3505			−0.796240			−0.398120	−	0.917333i	$-0.630337\pi$
$719$	−21.3505			−0.796240			−0.398120	+	0.917333i	$0.630337\pi$
$720$	4.62772	−	0.994667i	0.172465	−	0.0370690i
$721$	−36.0000			−1.34071
$722$			2.37686i			0.0884576i
$723$			13.2665i			0.493386i
$724$	9.44563			0.351044
$725$	12.5109	−	5.63858i	0.464642	−	0.209412i
$726$	2.00000			0.0742270
$727$			15.7908i			0.585650i	0.956166	+	0.292825i	$0.0945953\pi$
$727$			15.7908i			0.585650i	−0.956166	+	0.292825i	$0.905405\pi$
$728$		0			0
$729$	33.2337			1.23088
$730$	12.0000	−	2.57924i	0.444140	−	0.0954620i
$731$	−17.4891			−0.646859
$732$			37.2203i			1.37570i
$733$			30.2921i			1.11886i	0.828877	+	0.559431i	$0.188980\pi$
$733$			30.2921i			1.11886i	−0.828877	+	0.559431i	$0.811020\pi$
$734$	19.0217			0.702106
$735$	5.93070	+	27.5928i	0.218757	+	1.01778i
$736$	−14.7446			−0.543492
$737$		−	0.644810i		−	0.0237519i
$738$		−	7.33296i		−	0.269930i
$739$	−0.744563			−0.0273892			−0.0136946	−	0.999906i	$-0.504359\pi$
$739$	−0.744563			−0.0273892			−0.0136946	+	0.999906i	$0.504359\pi$
$740$	−7.11684	−	33.1113i	−0.261620	−	1.21720i
$741$		0			0
$742$			8.69793i			0.319311i
$743$		−	21.7793i		−	0.799004i	−0.916732	−	0.399502i	$-0.869183\pi$
$743$		−	21.7793i		−	0.799004i	0.916732	−	0.399502i	$-0.130817\pi$
$744$	−16.0000			−0.586588
$745$	25.1168	−	5.39853i	0.920210	−	0.197787i
$746$	6.51087			0.238380
$747$			22.3692i			0.818446i
$748$		−	6.92820i		−	0.253320i
$749$	−22.9783			−0.839607
$750$	−18.0000	+	13.2665i	−0.657267	+	0.484424i
$751$	21.6277			0.789207			0.394603	−	0.918852i	$-0.370882\pi$
$751$	21.6277			0.789207			0.394603	+	0.918852i	$0.370882\pi$
$752$		−	4.16381i		−	0.151839i
$753$		−	12.3267i		−	0.449211i
$754$		0			0
$755$	−48.6060	+	10.4472i	−1.76895	+	0.380213i
$756$	−4.46738			−0.162477
$757$			39.7995i			1.44654i	0.690567	+	0.723269i	$0.257361\pi$
$757$			39.7995i			1.44654i	−0.690567	+	0.723269i	$0.742639\pi$
$758$		−	5.04868i		−	0.183376i
$759$	−6.37228			−0.231299
$760$	−5.02175	−	23.3639i	−0.182158	−	0.847496i
$761$	21.2554			0.770509			0.385255	−	0.922810i	$-0.374114\pi$
$761$	21.2554			0.770509			0.385255	+	0.922810i	$0.374114\pi$
$762$		−	23.3639i		−	0.846383i
$763$			34.6410i			1.25409i
$764$	−18.7011			−0.676581
$765$	8.00000	+	37.2203i	0.289241	+	1.34570i
$766$	4.51087			0.162985
$767$		0			0
$768$		−	35.0458i		−	1.26461i
$769$	51.2119			1.84675			0.923375	−	0.383900i	$-0.125419\pi$
$769$	51.2119			1.84675			0.923375	+	0.383900i	$0.125419\pi$
$770$	−6.00000	+	1.28962i	−0.216225	+	0.0464747i
$771$	60.4674			2.17768
$772$			32.0618i			1.15393i
$773$		−	30.8820i		−	1.11075i	−0.831601	−	0.555373i	$-0.812575\pi$
$773$		−	30.8820i		−	1.11075i	0.831601	−	0.555373i	$-0.187425\pi$
$774$	−9.25544			−0.332680
$775$	−10.8139	+	4.87375i	−0.388445	+	0.175070i
$776$	10.9783			0.394096
$777$			96.5147i			3.46245i
$778$		−	7.81306i		−	0.280112i
$779$	10.9783			0.393337
$780$		0			0
$781$	−7.11684			−0.254661
$782$		−	10.0974i		−	0.361081i
$783$		−	2.57924i		−	0.0921745i
$784$	−3.13859			−0.112093
$785$	2.53667	+	11.8020i	0.0905377	+	0.421230i
$786$	17.4891			0.623816
$787$		−	4.75372i		−	0.169452i	−0.996404	−	0.0847259i	$-0.972999\pi$
$787$		−	4.75372i		−	0.169452i	0.996404	−	0.0847259i	$-0.0270015\pi$
$788$		−	2.57924i		−	0.0918816i
$789$	−35.7228			−1.27177
$790$	−4.74456	−	22.0742i	−0.168804	−	0.785366i
$791$	55.7228			1.98128
$792$		−	9.01011i		−	0.320160i
$793$		0			0
$794$	−18.5109			−0.656926
$795$	−17.4891	+	3.75906i	−0.620275	+	0.133320i
$796$	10.9783			0.389114
$797$			31.2318i			1.10629i	0.833086	+	0.553144i	$0.186572\pi$
$797$			31.2318i			1.10629i	−0.833086	+	0.553144i	$0.813428\pi$
$798$			27.7128i			0.981023i
$799$	33.4891			1.18476
$800$	−12.0000	−	26.6256i	−0.424264	−	0.941356i
$801$	−14.7446			−0.520974
$802$		−	9.10268i		−	0.321427i
$803$			6.92820i			0.244491i
$804$	−2.23369			−0.0787761
$805$	19.1168	−	4.10891i	0.673780	−	0.144820i
$806$		0			0
$807$		−	29.0024i		−	1.02093i
$808$		−	16.0309i		−	0.563965i
$809$	21.2554			0.747301			0.373651	−	0.927569i	$-0.378106\pi$
$809$	21.2554			0.747301			0.373651	+	0.927569i	$0.378106\pi$
$810$	−2.88316	−	13.4140i	−0.101304	−	0.471319i
$811$	34.2337			1.20211			0.601054	−	0.799209i	$-0.294748\pi$
$811$	34.2337			1.20211			0.601054	+	0.799209i	$0.294748\pi$
$812$		−	13.0469i		−	0.457856i
$813$		−	23.9538i		−	0.840095i
$814$	−8.74456			−0.306497
$815$	1.62772	+	7.57301i	0.0570165	+	0.265271i
$816$	−8.00000			−0.280056
$817$		−	13.8564i		−	0.484774i
$818$			3.57391i			0.124959i
$819$		0			0
$820$	8.23369	−	1.76972i	0.287533	−	0.0618014i
$821$	−18.0000			−0.628204			−0.314102	−	0.949389i	$-0.601703\pi$
$821$	−18.0000			−0.628204			−0.314102	+	0.949389i	$0.601703\pi$
$822$			4.45877i			0.155517i
$823$		−	33.5161i		−	1.16830i	−0.811646	−	0.584149i	$-0.801428\pi$
$823$		−	33.5161i		−	1.16830i	0.811646	−	0.584149i	$-0.198572\pi$
$824$	−27.7663			−0.967285
$825$	−5.18614	−	11.5070i	−0.180558	−	0.400622i
$826$	−4.46738			−0.155440
$827$			18.0202i			0.626624i	0.949650	+	0.313312i	$0.101439\pi$
$827$			18.0202i			0.626624i	−0.949650	+	0.313312i	$0.898561\pi$
$828$			11.6819i			0.405975i
$829$	−31.3505			−1.08885			−0.544424	−	0.838810i	$-0.683252\pi$
$829$	−31.3505			−1.08885			−0.544424	+	0.838810i	$0.683252\pi$
$830$	11.4891	−	2.46943i	0.398793	−	0.0857153i
$831$	20.7446			0.719621
$832$		0			0
$833$		−	25.2434i		−	0.874631i
$834$	−36.4674			−1.26276
$835$	−10.5109	−	48.9022i	−0.363744	−	1.69233i
$836$	5.48913			0.189845
$837$			2.22938i			0.0770588i
$838$			18.2054i			0.628894i
$839$	−7.11684			−0.245701			−0.122850	−	0.992425i	$-0.539204\pi$
$839$	−7.11684			−0.245701			−0.122850	+	0.992425i	$0.539204\pi$
$840$	10.9783	+	51.0767i	0.378786	+	1.76231i
$841$	−21.4674			−0.740254
$842$		−	24.9484i		−	0.859779i
$843$		−	59.2945i		−	2.04221i
$844$	−29.4891			−1.01506
$845$	−28.4198	+	6.10846i	−0.977672	+	0.210138i
$846$	17.7228			0.609323
$847$		−	3.46410i		−	0.119028i
$848$		−	1.98933i		−	0.0683140i
$849$	12.0000			0.411839
$850$	18.2337	−	8.21782i	0.625410	−	0.281869i
$851$	27.8614			0.955077
$852$			24.6535i			0.844614i
$853$		−	24.6535i		−	0.844119i	−0.906568	−	0.422059i	$-0.861307\pi$
$853$		−	24.6535i		−	0.844119i	0.906568	−	0.422059i	$-0.138693\pi$
$854$	−29.4891			−1.00910
$855$	−29.4891	+	6.33830i	−1.00851	+	0.216765i
$856$	−17.7228			−0.605753
$857$			10.6873i			0.365070i	0.983199	+	0.182535i	$0.0584303\pi$
$857$			10.6873i			0.365070i	−0.983199	+	0.182535i	$0.941570\pi$
$858$		0			0
$859$	−11.1168			−0.379302			−0.189651	−	0.981852i	$-0.560736\pi$
$859$	−11.1168			−0.379302			−0.189651	+	0.981852i	$0.560736\pi$
$860$	−2.23369	−	10.3923i	−0.0761681	−	0.354375i
$861$	−24.0000			−0.817918
$862$		−	25.1336i		−	0.856053i
$863$			23.6588i			0.805355i	0.915342	+	0.402678i	$0.131920\pi$
$863$			23.6588i			0.805355i	−0.915342	+	0.402678i	$0.868080\pi$
$864$	−5.48913			−0.186744
$865$	0.883156	+	4.10891i	0.0300282	+	0.139707i
$866$	−16.2772			−0.553121
$867$		−	21.4294i		−	0.727781i
$868$			11.2772i			0.382772i
$869$	12.7446			0.432330
$870$	−12.0000	+	2.57924i	−0.406838	+	0.0874444i
$871$		0			0
$872$			26.7181i			0.904791i
$873$		−	13.8564i		−	0.468968i
$874$	8.00000			0.270604
$875$	22.9783	+	31.1769i	0.776807	+	1.05397i
$876$	24.0000			0.810885
$877$		0			0		1.00000			$0$
$877$		0			0		−1.00000			$\pi$
$878$		−	1.17981i		−	0.0398168i
$879$	25.4891			0.859727
$880$	1.37228	−	0.294954i	0.0462596	−	0.00994289i
$881$	21.8614			0.736530			0.368265	−	0.929721i	$-0.379952\pi$
$881$	21.8614			0.736530			0.368265	+	0.929721i	$0.379952\pi$
$882$		−	13.3591i		−	0.449823i
$883$			24.2487i			0.816034i	0.912974	+	0.408017i	$0.133780\pi$
$883$			24.2487i			0.816034i	−0.912974	+	0.408017i	$0.866220\pi$
$884$		0			0
$885$	−1.93070	−	8.98266i	−0.0648999	−	0.301949i
$886$	−11.9565			−0.401687
$887$			14.1514i			0.475156i	0.971368	+	0.237578i	$0.0763536\pi$
$887$			14.1514i			0.475156i	−0.971368	+	0.237578i	$0.923646\pi$
$888$			74.4405i			2.49806i
$889$	−40.4674			−1.35723
$890$	1.62772	+	7.57301i	0.0545613	+	0.253848i
$891$	7.74456			0.259453
$892$			10.3923i			0.347960i
$893$			26.5330i			0.887893i
$894$	−22.9783			−0.768508
$895$	−34.6753	+	7.45299i	−1.15907	+	0.249126i
$896$	−31.2119			−1.04272
$897$		0			0
$898$		−	17.3205i		−	0.577993i
$899$	−6.51087			−0.217150
$900$	−21.0951	+	9.50744i	−0.703170	+	0.316915i
$901$	16.0000			0.533037
$902$		−	2.17448i		−	0.0724023i
$903$			30.2921i			1.00806i
$904$	42.9783			1.42944
$905$	−15.0475	+	3.23427i	−0.500197	+	0.107511i
$906$	44.4674			1.47733
$907$		−	19.8997i		−	0.660760i	−0.943848	−	0.330380i	$-0.892823\pi$
$907$		−	19.8997i		−	0.660760i	0.943848	−	0.330380i	$-0.107177\pi$
$908$			13.4516i			0.446409i
$909$	−20.2337			−0.671109
$910$		0			0
$911$	−30.5109			−1.01087			−0.505435	−	0.862865i	$-0.668668\pi$
$911$	−30.5109			−1.01087			−0.505435	+	0.862865i	$0.668668\pi$
$912$		−	6.33830i		−	0.209882i
$913$			6.63325i			0.219529i
$914$	16.4674			0.544692
$915$	−12.7446	−	59.2945i	−0.421322	−	1.96022i
$916$	−27.9565			−0.923709
$917$		−	30.2921i		−	1.00033i
$918$		−	3.75906i		−	0.124067i
$919$	−6.23369			−0.205630			−0.102815	−	0.994700i	$-0.532785\pi$
$919$	−6.23369			−0.205630			−0.102815	+	0.994700i	$0.532785\pi$
$920$	14.7446	−	3.16915i	0.486114	−	0.104484i
$921$	−70.9783			−2.33881
$922$			25.5383i			0.841060i
$923$		0			0
$924$	−12.0000			−0.394771
$925$	22.6753	+	50.3118i	0.745558	+	1.65424i
$926$	−15.9565			−0.524363
$927$			35.0458i			1.15105i
$928$		−	16.0309i		−	0.526240i
$929$	52.9783			1.73816			0.869080	−	0.494672i	$-0.164712\pi$
$929$	52.9783			1.73816			0.869080	+	0.494672i	$0.164712\pi$
$930$	10.3723	−	2.22938i	0.340121	−	0.0731044i
$931$	20.0000			0.655474
$932$		−	23.3639i		−	0.765308i
$933$		−	44.1485i		−	1.44536i
$934$	3.48913			0.114168
$935$	2.37228	+	11.0371i	0.0775819	+	0.360952i
$936$		0			0
$937$			25.9431i			0.847524i	0.905774	+	0.423762i	$0.139291\pi$
$937$			25.9431i			0.847524i	−0.905774	+	0.423762i	$0.860709\pi$
$938$		−	1.76972i		−	0.0577835i
$939$	80.3288			2.62143
$940$	4.27719	+	19.8997i	0.139506	+	0.649058i
$941$	10.4674			0.341227			0.170613	−	0.985338i	$-0.445425\pi$
$941$	10.4674			0.341227			0.170613	+	0.985338i	$0.445425\pi$
$942$		−	10.7971i		−	0.351787i
$943$			6.92820i			0.225613i
$944$	1.02175			0.0332551
$945$	7.11684	−	1.52967i	0.231511	−	0.0497602i
$946$	−2.74456			−0.0892334
$947$		−	56.1802i		−	1.82561i	−0.408393	−	0.912806i	$-0.633911\pi$
$947$		−	56.1802i		−	1.82561i	0.408393	−	0.912806i	$-0.366089\pi$
$948$		−	44.1485i		−	1.43388i
$949$		0			0
$950$	6.51087	+	14.4463i	0.211241	+	0.468700i
$951$	−8.88316			−0.288056
$952$		−	46.7277i		−	1.51445i
$953$		−	41.6790i		−	1.35012i	−0.737765	−	0.675058i	$-0.764119\pi$
$953$		−	41.6790i		−	1.35012i	0.737765	−	0.675058i	$-0.235881\pi$
$954$	8.46738			0.274141
$955$	29.7921	−	6.40342i	0.964050	−	0.207210i
$956$	4.46738			0.144485
$957$		−	6.92820i		−	0.223957i
$958$			13.8564i			0.447680i
$959$	7.72281			0.249383
$960$	4.00000	+	18.6101i	0.129099	+	0.600639i
$961$	−25.3723			−0.818461
$962$		0			0
$963$			22.3692i			0.720837i
$964$	7.21194			0.232281
$965$	−10.9783	−	51.0767i	−0.353402	−	1.64422i
$966$	−17.4891			−0.562703
$967$			46.3229i			1.48965i	0.667262	+	0.744823i	$0.267466\pi$
$967$			46.3229i			1.48965i	−0.667262	+	0.744823i	$0.732534\pi$
$968$		−	2.67181i		−	0.0858754i
$969$	50.9783			1.63766
$970$	−7.11684	+	1.52967i	−0.228508	+	0.0491148i
$971$	54.0951			1.73599			0.867997	−	0.496569i	$-0.165407\pi$
$971$	54.0951			1.73599			0.867997	+	0.496569i	$0.165407\pi$
$972$		−	30.6968i		−	0.984601i
$973$			63.1633i			2.02492i
$974$	−18.0000			−0.576757
$975$		0			0
$976$	6.74456			0.215888
$977$			27.3630i			0.875419i	0.899117	+	0.437709i	$0.144210\pi$
$977$			27.3630i			0.875419i	−0.899117	+	0.437709i	$0.855790\pi$
$978$		−	6.92820i		−	0.221540i
$979$	−4.37228			−0.139739
$980$	15.0000	−	3.22405i	0.479157	−	0.102989i
$981$	33.7228			1.07669
$982$		−	23.3639i		−	0.745570i
$983$		−	8.16292i		−	0.260357i	−0.991491	−	0.130178i	$-0.958445\pi$
$983$		−	8.16292i		−	0.260357i	0.991491	−	0.130178i	$-0.0415550\pi$
$984$	−18.5109			−0.590105
$985$	0.883156	+	4.10891i	0.0281397	+	0.130921i
$986$	10.9783			0.349619
$987$		−	58.0049i		−	1.84632i
$988$		0			0
$989$	8.74456			0.278061
$990$	1.25544	+	5.84096i	0.0399004	+	0.185638i
$991$	−26.9783			−0.856992			−0.428496	−	0.903544i	$-0.640956\pi$
$991$	−26.9783			−0.856992			−0.428496	+	0.903544i	$0.640956\pi$
$992$			13.8564i			0.439941i
$993$			7.86797i			0.249682i
$994$	−19.5326			−0.619537
$995$	−17.4891	+	3.75906i	−0.554443	+	0.119170i
$996$	22.9783			0.728094
$997$		−	22.0742i		−	0.699098i	−0.936918	−	0.349549i	$-0.886335\pi$
$997$		−	22.0742i		−	0.699098i	0.936918	−	0.349549i	$-0.113665\pi$
$998$		−	15.8457i		−	0.501588i
$999$	10.3723			0.328164

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	55.2.b.a.34.2	✓	4
3.2	odd	2		495.2.c.a.199.3		4
4.3	odd	2		880.2.b.h.529.1		4
5.2	odd	4		275.2.a.h.1.3		4
5.3	odd	4		275.2.a.h.1.2		4
5.4	even	2	inner	55.2.b.a.34.3	yes	4
11.2	odd	10		605.2.j.j.444.3		16
11.3	even	5		605.2.j.i.9.2		16
11.4	even	5		605.2.j.i.269.3		16
11.5	even	5		605.2.j.i.124.3		16
11.6	odd	10		605.2.j.j.124.2		16
11.7	odd	10		605.2.j.j.269.2		16
11.8	odd	10		605.2.j.j.9.3		16
11.9	even	5		605.2.j.i.444.2		16
11.10	odd	2		605.2.b.c.364.3		4
15.2	even	4		2475.2.a.bi.1.2		4
15.8	even	4		2475.2.a.bi.1.3		4
15.14	odd	2		495.2.c.a.199.2		4
20.3	even	4		4400.2.a.cc.1.4		4
20.7	even	4		4400.2.a.cc.1.1		4
20.19	odd	2		880.2.b.h.529.4		4
55.4	even	10		605.2.j.i.269.2		16
55.9	even	10		605.2.j.i.444.3		16
55.14	even	10		605.2.j.i.9.3		16
55.19	odd	10		605.2.j.j.9.2		16
55.24	odd	10		605.2.j.j.444.2		16
55.29	odd	10		605.2.j.j.269.3		16
55.32	even	4		3025.2.a.ba.1.2		4
55.39	odd	10		605.2.j.j.124.3		16
55.43	even	4		3025.2.a.ba.1.3		4
55.49	even	10		605.2.j.i.124.2		16
55.54	odd	2		605.2.b.c.364.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.b.a.34.2	✓	4	1.1	even	1	trivial
55.2.b.a.34.3	yes	4	5.4	even	2	inner
275.2.a.h.1.2		4	5.3	odd	4
275.2.a.h.1.3		4	5.2	odd	4
495.2.c.a.199.2		4	15.14	odd	2
495.2.c.a.199.3		4	3.2	odd	2
605.2.b.c.364.2		4	55.54	odd	2
605.2.b.c.364.3		4	11.10	odd	2
605.2.j.i.9.2		16	11.3	even	5
605.2.j.i.9.3		16	55.14	even	10
605.2.j.i.124.2		16	55.49	even	10
605.2.j.i.124.3		16	11.5	even	5
605.2.j.i.269.2		16	55.4	even	10
605.2.j.i.269.3		16	11.4	even	5
605.2.j.i.444.2		16	11.9	even	5
605.2.j.i.444.3		16	55.9	even	10
605.2.j.j.9.2		16	55.19	odd	10
605.2.j.j.9.3		16	11.8	odd	10
605.2.j.j.124.2		16	11.6	odd	10
605.2.j.j.124.3		16	55.39	odd	10
605.2.j.j.269.2		16	11.7	odd	10
605.2.j.j.269.3		16	55.29	odd	10
605.2.j.j.444.2		16	55.24	odd	10
605.2.j.j.444.3		16	11.2	odd	10
880.2.b.h.529.1		4	4.3	odd	2
880.2.b.h.529.4		4	20.19	odd	2
2475.2.a.bi.1.2		4	15.2	even	4
2475.2.a.bi.1.3		4	15.8	even	4
3025.2.a.ba.1.2		4	55.32	even	4
3025.2.a.ba.1.3		4	55.43	even	4
4400.2.a.cc.1.1		4	20.7	even	4
4400.2.a.cc.1.4		4	20.3	even	4

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:	\( N \)	\(=\)	\( 55 = 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	55.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.792287i q^{2} +2.52434i q^{3} +1.37228 q^{4} +(-2.18614 + 0.469882i) q^{5} +2.00000 q^{6} -3.46410i q^{7} -2.67181i q^{8} -3.37228 q^{9} +O(q^{10})\)	\(q-0.792287i q^{2} +2.52434i q^{3} +1.37228 q^{4} +(-2.18614 + 0.469882i) q^{5} +2.00000 q^{6} -3.46410i q^{7} -2.67181i q^{8} -3.37228 q^{9} +(0.372281 + 1.73205i) q^{10} -1.00000 q^{11} +3.46410i q^{12} -2.74456 q^{14} +(-1.18614 - 5.51856i) q^{15} +0.627719 q^{16} +5.04868i q^{17} +2.67181i q^{18} -4.00000 q^{19} +(-3.00000 + 0.644810i) q^{20} +8.74456 q^{21} +0.792287i q^{22} -2.52434i q^{23} +6.74456 q^{24} +(4.55842 - 2.05446i) q^{25} -0.939764i q^{27} -4.75372i q^{28} +2.74456 q^{29} +(-4.37228 + 0.939764i) q^{30} -2.37228 q^{31} -5.84096i q^{32} -2.52434i q^{33} +4.00000 q^{34} +(1.62772 + 7.57301i) q^{35} -4.62772 q^{36} +11.0371i q^{37} +3.16915i q^{38} +(1.25544 + 5.84096i) q^{40} -2.74456 q^{41} -6.92820i q^{42} +3.46410i q^{43} -1.37228 q^{44} +(7.37228 - 1.58457i) q^{45} -2.00000 q^{46} -6.63325i q^{47} +1.58457i q^{48} -5.00000 q^{49} +(-1.62772 - 3.61158i) q^{50} -12.7446 q^{51} -3.16915i q^{53} -0.744563 q^{54} +(2.18614 - 0.469882i) q^{55} -9.25544 q^{56} -10.0974i q^{57} -2.17448i q^{58} +1.62772 q^{59} +(-1.62772 - 7.57301i) q^{60} +10.7446 q^{61} +1.87953i q^{62} +11.6819i q^{63} -3.37228 q^{64} -2.00000 q^{66} +0.644810i q^{67} +6.92820i q^{68} +6.37228 q^{69} +(6.00000 - 1.28962i) q^{70} +7.11684 q^{71} +9.01011i q^{72} -6.92820i q^{73} +8.74456 q^{74} +(5.18614 + 11.5070i) q^{75} -5.48913 q^{76} +3.46410i q^{77} -12.7446 q^{79} +(-1.37228 + 0.294954i) q^{80} -7.74456 q^{81} +2.17448i q^{82} -6.63325i q^{83} +12.0000 q^{84} +(-2.37228 - 11.0371i) q^{85} +2.74456 q^{86} +6.92820i q^{87} +2.67181i q^{88} +4.37228 q^{89} +(-1.25544 - 5.84096i) q^{90} -3.46410i q^{92} -5.98844i q^{93} -5.25544 q^{94} +(8.74456 - 1.87953i) q^{95} +14.7446 q^{96} +4.10891i q^{97} +3.96143i q^{98} +3.37228 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{4} - 3 q^{5} + 8 q^{6} - 2 q^{9}+O(q^{10}) \) 4 * q - 6 * q^4 - 3 * q^5 + 8 * q^6 - 2 * q^9	\( 4 q - 6 q^{4} - 3 q^{5} + 8 q^{6} - 2 q^{9} - 10 q^{10} - 4 q^{11} + 12 q^{14} + q^{15} + 14 q^{16} - 16 q^{19} - 12 q^{20} + 12 q^{21} + 4 q^{24} + q^{25} - 12 q^{29} - 6 q^{30} + 2 q^{31} + 16 q^{34} + 18 q^{35} - 30 q^{36} + 28 q^{40} + 12 q^{41} + 6 q^{44} + 18 q^{45} - 8 q^{46} - 20 q^{49} - 18 q^{50} - 28 q^{51} + 20 q^{54} + 3 q^{55} - 60 q^{56} + 18 q^{59} - 18 q^{60} + 20 q^{61} - 2 q^{64} - 8 q^{66} + 14 q^{69} + 24 q^{70} - 6 q^{71} + 12 q^{74} + 15 q^{75} + 24 q^{76} - 28 q^{79} + 6 q^{80} - 8 q^{81} + 48 q^{84} + 2 q^{85} - 12 q^{86} + 6 q^{89} - 28 q^{90} - 44 q^{94} + 12 q^{95} + 36 q^{96} + 2 q^{99}+O(q^{100}) \) 4 * q - 6 * q^4 - 3 * q^5 + 8 * q^6 - 2 * q^9 - 10 * q^10 - 4 * q^11 + 12 * q^14 + q^15 + 14 * q^16 - 16 * q^19 - 12 * q^20 + 12 * q^21 + 4 * q^24 + q^25 - 12 * q^29 - 6 * q^30 + 2 * q^31 + 16 * q^34 + 18 * q^35 - 30 * q^36 + 28 * q^40 + 12 * q^41 + 6 * q^44 + 18 * q^45 - 8 * q^46 - 20 * q^49 - 18 * q^50 - 28 * q^51 + 20 * q^54 + 3 * q^55 - 60 * q^56 + 18 * q^59 - 18 * q^60 + 20 * q^61 - 2 * q^64 - 8 * q^66 + 14 * q^69 + 24 * q^70 - 6 * q^71 + 12 * q^74 + 15 * q^75 + 24 * q^76 - 28 * q^79 + 6 * q^80 - 8 * q^81 + 48 * q^84 + 2 * q^85 - 12 * q^86 + 6 * q^89 - 28 * q^90 - 44 * q^94 + 12 * q^95 + 36 * q^96 + 2 * q^99

Introduction

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