LMFDB - Embedded newform 186.2.c.b.185.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [186,2,Mod(185,186)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("186.185"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(186, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 186 = 2 \cdot 3 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	186.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$1.48521747760$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.40282095616.8
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{6} + 8x^{4} - 36x^{2} + 81 $ x^8 - 4x^6 + 8x^4 - 36*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			185.8
Root			$-1.03179 - 1.39119i$ of defining polynomial
Character	$\chi$	$=$	186.185
Dual form			186.2.c.b.185.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} +(1.39119 + 1.03179i) q^{3} -1.00000 q^{4} +2.00000i q^{5} +(-1.03179 + 1.39119i) q^{6} -3.74166 q^{7} -1.00000i q^{8} +(0.870829 + 2.87083i) q^{9} -2.00000 q^{10} +3.50119 q^{11} +(-1.39119 - 1.03179i) q^{12} -2.78238i q^{13} -3.74166i q^{14} +(-2.06358 + 2.78238i) q^{15} +1.00000 q^{16} +5.56477 q^{17} +(-2.87083 + 0.870829i) q^{18} -2.00000i q^{20} +(-5.20536 - 3.86060i) q^{21} +3.50119i q^{22} -1.43762 q^{23} +(1.03179 - 1.39119i) q^{24} +1.00000 q^{25} +2.78238 q^{26} +(-1.75060 + 4.89238i) q^{27} +3.74166 q^{28} -4.22000 q^{29} +(-2.78238 - 2.06358i) q^{30} +(2.74166 - 4.84596i) q^{31} +1.00000i q^{32} +(4.87083 + 3.61249i) q^{33} +5.56477i q^{34} -7.48331i q^{35} +(-0.870829 - 2.87083i) q^{36} +6.19073i q^{37} +(2.87083 - 3.87083i) q^{39} +2.00000 q^{40} -1.74166i q^{41} +(3.86060 - 5.20536i) q^{42} -12.4743i q^{43} -3.50119 q^{44} +(-5.74166 + 1.74166i) q^{45} -1.43762i q^{46} -0.258343i q^{47} +(1.39119 + 1.03179i) q^{48} +7.00000 q^{49} +1.00000i q^{50} +(7.74166 + 5.74166i) q^{51} +2.78238i q^{52} +7.62834 q^{53} +(-4.89238 - 1.75060i) q^{54} +7.00238i q^{55} +3.74166i q^{56} -4.22000i q^{58} +7.48331i q^{59} +(2.06358 - 2.78238i) q^{60} -9.06596i q^{61} +(4.84596 + 2.74166i) q^{62} +(-3.25834 - 10.7417i) q^{63} -1.00000 q^{64} +5.56477 q^{65} +(-3.61249 + 4.87083i) q^{66} -15.4833 q^{67} -5.56477 q^{68} +(-2.00000 - 1.48331i) q^{69} +7.48331 q^{70} -13.4833i q^{71} +(2.87083 - 0.870829i) q^{72} +1.43762i q^{73} -6.19073 q^{74} +(1.39119 + 1.03179i) q^{75} -13.1003 q^{77} +(3.87083 + 2.87083i) q^{78} +7.00238i q^{79} +2.00000i q^{80} +(-7.48331 + 5.00000i) q^{81} +1.74166 q^{82} -16.6015 q^{83} +(5.20536 + 3.86060i) q^{84} +11.1295i q^{85} +12.4743 q^{86} +(-5.87083 - 4.35414i) q^{87} -3.50119i q^{88} +9.69192 q^{89} +(-1.74166 - 5.74166i) q^{90} +10.4107i q^{91} +1.43762 q^{92} +(8.81417 - 3.91285i) q^{93} +0.258343 q^{94} +(-1.03179 + 1.39119i) q^{96} -13.7417 q^{97} +7.00000i q^{98} +(3.04894 + 10.0513i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} - 8 q^{9} - 16 q^{10} + 8 q^{16} - 8 q^{18} + 8 q^{25} - 8 q^{31} + 24 q^{33} + 8 q^{36} + 8 q^{39} + 16 q^{40} - 16 q^{45} + 56 q^{49} + 32 q^{51} - 56 q^{63} - 8 q^{64} + 16 q^{66} - 64 q^{67}+ \cdots - 80 q^{97}+O(q^{100}) $ 8 * q - 8 * q^4 - 8 * q^9 - 16 * q^10 + 8 * q^16 - 8 * q^18 + 8 * q^25 - 8 * q^31 + 24 * q^33 + 8 * q^36 + 8 * q^39 + 16 * q^40 - 16 * q^45 + 56 * q^49 + 32 * q^51 - 56 * q^63 - 8 * q^64 + 16 * q^66 - 64 * q^67 - 16 * q^69 + 8 * q^72 + 16 * q^78 - 16 * q^82 - 32 * q^87 + 16 * q^90 + 40 * q^93 + 32 * q^94 - 80 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/186\mathbb{Z}\right)^\times$.

$n$	$125$	$127$
$\chi(n)$	$-1$	$-1$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	1.39119	+	1.03179i	0.803205	+	0.595703i
$3$	1.39119	+	1.03179i	0.803205	+	0.595703i
$4$	−1.00000			−0.500000
$5$			2.00000i			0.894427i	0.894427	+	0.447214i	$0.147584\pi$
$5$			2.00000i			0.894427i	−0.894427	+	0.447214i	$0.852416\pi$
$6$	−1.03179	+	1.39119i	−0.421226	+	0.567952i
$7$	−3.74166			−1.41421			−0.707107	−	0.707107i	$-0.750000\pi$
$7$	−3.74166			−1.41421			−0.707107	+	0.707107i	$0.750000\pi$
$8$		−	1.00000i		−	0.353553i
$9$	0.870829	+	2.87083i	0.290276	+	0.956943i
$10$	−2.00000			−0.632456
$11$	3.50119			1.05565			0.527824	−	0.849353i	$-0.323008\pi$
$11$	3.50119			1.05565			0.527824	+	0.849353i	$0.323008\pi$
$12$	−1.39119	−	1.03179i	−0.401602	−	0.297851i
$13$		−	2.78238i		−	0.771694i	−0.922563	−	0.385847i	$-0.873909\pi$
$13$		−	2.78238i		−	0.771694i	0.922563	−	0.385847i	$-0.126091\pi$
$14$		−	3.74166i		−	1.00000i
$15$	−2.06358	+	2.78238i	−0.532813	+	0.718408i
$16$	1.00000			0.250000
$17$	5.56477			1.34965			0.674827	−	0.737976i	$-0.264218\pi$
$17$	5.56477			1.34965			0.674827	+	0.737976i	$0.264218\pi$
$18$	−2.87083	+	0.870829i	−0.676661	+	0.205256i
$19$		0			0			−	1.00000i	$-0.5\pi$
$19$		0			0				1.00000i	$0.5\pi$
$20$		−	2.00000i		−	0.447214i
$21$	−5.20536	−	3.86060i	−1.13590	−	0.842451i
$22$			3.50119i			0.746457i
$23$	−1.43762			−0.299764			−0.149882	−	0.988704i	$-0.547889\pi$
$23$	−1.43762			−0.299764			−0.149882	+	0.988704i	$0.547889\pi$
$24$	1.03179	−	1.39119i	0.210613	−	0.283976i
$25$	1.00000			0.200000
$26$	2.78238			0.545670
$27$	−1.75060	+	4.89238i	−0.336902	+	0.941540i
$28$	3.74166			0.707107
$29$	−4.22000			−0.783634			−0.391817	−	0.920043i	$-0.628153\pi$
$29$	−4.22000			−0.783634			−0.391817	+	0.920043i	$0.628153\pi$
$30$	−2.78238	−	2.06358i	−0.507991	−	0.376756i
$31$	2.74166	−	4.84596i	0.492416	−	0.870360i
$31$	2.74166	−	4.84596i	0.492416	−	0.870360i
$32$			1.00000i			0.176777i
$33$	4.87083	+	3.61249i	0.847902	+	0.628853i
$34$			5.56477i			0.954350i
$35$		−	7.48331i		−	1.26491i
$36$	−0.870829	−	2.87083i	−0.145138	−	0.478471i
$37$			6.19073i			1.01775i	0.860841	+	0.508875i	$0.169938\pi$
$37$			6.19073i			1.01775i	−0.860841	+	0.508875i	$0.830062\pi$
$38$		0			0
$39$	2.87083	−	3.87083i	0.459700	−	0.619829i
$40$	2.00000			0.316228
$41$		−	1.74166i		−	0.272001i	−0.990709	−	0.136001i	$-0.956575\pi$
$41$		−	1.74166i		−	0.272001i	0.990709	−	0.136001i	$-0.0434249\pi$
$42$	3.86060	−	5.20536i	0.595703	−	0.803205i
$43$		−	12.4743i		−	1.90231i	−0.308709	−	0.951157i	$-0.599897\pi$
$43$		−	12.4743i		−	1.90231i	0.308709	−	0.951157i	$-0.400103\pi$
$44$	−3.50119			−0.527824
$45$	−5.74166	+	1.74166i	−0.855916	+	0.259631i
$46$		−	1.43762i		−	0.211965i
$47$		−	0.258343i		−	0.0376831i	−0.999822	−	0.0188416i	$-0.994002\pi$
$47$		−	0.258343i		−	0.0376831i	0.999822	−	0.0188416i	$-0.00599781\pi$
$48$	1.39119	+	1.03179i	0.200801	+	0.148926i
$49$	7.00000			1.00000
$50$			1.00000i			0.141421i
$51$	7.74166	+	5.74166i	1.08405	+	0.803993i
$52$			2.78238i			0.385847i
$53$	7.62834			1.04783			0.523917	−	0.851770i	$-0.324470\pi$
$53$	7.62834			1.04783			0.523917	+	0.851770i	$0.324470\pi$
$54$	−4.89238	−	1.75060i	−0.665769	−	0.238226i
$55$			7.00238i			0.944201i
$56$			3.74166i			0.500000i
$57$		0			0
$58$		−	4.22000i		−	0.554113i
$59$			7.48331i			0.974245i	0.873334	+	0.487122i	$0.161953\pi$
$59$			7.48331i			0.974245i	−0.873334	+	0.487122i	$0.838047\pi$
$60$	2.06358	−	2.78238i	0.266406	−	0.359204i
$61$		−	9.06596i		−	1.16078i	−0.814340	−	0.580389i	$-0.802901\pi$
$61$		−	9.06596i		−	1.16078i	0.814340	−	0.580389i	$-0.197099\pi$
$62$	4.84596	+	2.74166i	0.615437	+	0.348191i
$63$	−3.25834	−	10.7417i	−0.410513	−	1.35332i
$64$	−1.00000			−0.125000
$65$	5.56477			0.690224
$66$	−3.61249	+	4.87083i	−0.444666	+	0.599558i
$67$	−15.4833			−1.89159			−0.945794	−	0.324767i	$-0.894714\pi$
$67$	−15.4833			−1.89159			−0.945794	+	0.324767i	$0.894714\pi$
$68$	−5.56477			−0.674827
$69$	−2.00000	−	1.48331i	−0.240772	−	0.178570i
$70$	7.48331			0.894427
$71$		−	13.4833i		−	1.60018i	−0.599883	−	0.800088i	$-0.704786\pi$
$71$		−	13.4833i		−	1.60018i	0.599883	−	0.800088i	$-0.295214\pi$
$72$	2.87083	−	0.870829i	0.338330	−	0.102628i
$73$			1.43762i			0.168260i	0.996455	+	0.0841301i	$0.0268111\pi$
$73$			1.43762i			0.168260i	−0.996455	+	0.0841301i	$0.973189\pi$
$74$	−6.19073			−0.719657
$75$	1.39119	+	1.03179i	0.160641	+	0.119141i
$76$		0			0
$77$	−13.1003			−1.49291
$78$	3.87083	+	2.87083i	0.438285	+	0.325057i
$79$			7.00238i			0.787830i	0.919147	+	0.393915i	$0.128880\pi$
$79$			7.00238i			0.787830i	−0.919147	+	0.393915i	$0.871120\pi$
$80$			2.00000i			0.223607i
$81$	−7.48331	+	5.00000i	−0.831479	+	0.555556i
$82$	1.74166			0.192334
$83$	−16.6015			−1.82225			−0.911123	−	0.412135i	$-0.864783\pi$
$83$	−16.6015			−1.82225			−0.911123	+	0.412135i	$0.864783\pi$
$84$	5.20536	+	3.86060i	0.567952	+	0.421226i
$85$			11.1295i			1.20717i
$86$	12.4743			1.34514
$87$	−5.87083	−	4.35414i	−0.629419	−	0.466813i
$88$		−	3.50119i		−	0.373228i
$89$	9.69192			1.02734			0.513671	−	0.857987i	$-0.328285\pi$
$89$	9.69192			1.02734			0.513671	+	0.857987i	$0.328285\pi$
$90$	−1.74166	−	5.74166i	−0.183587	−	0.605224i
$91$			10.4107i			1.09134i
$92$	1.43762			0.149882
$93$	8.81417	−	3.91285i	0.913987	−	0.405744i
$94$	0.258343			0.0266460
$95$		0			0
$96$	−1.03179	+	1.39119i	−0.105306	+	0.141988i
$97$	−13.7417			−1.39525			−0.697627	−	0.716461i	$-0.745761\pi$
$97$	−13.7417			−1.39525			−0.697627	+	0.716461i	$0.745761\pi$
$98$			7.00000i			0.707107i
$99$	3.04894	+	10.0513i	0.306430	+	1.01020i
$100$	−1.00000			−0.100000
$101$			16.9666i			1.68824i	0.536152	+	0.844121i	$0.319877\pi$
$101$			16.9666i			1.68824i	−0.536152	+	0.844121i	$0.680123\pi$
$102$	−5.74166	+	7.74166i	−0.568509	+	0.766538i
$103$	−9.48331			−0.934419			−0.467209	−	0.884147i	$-0.654741\pi$
$103$	−9.48331			−0.934419			−0.467209	+	0.884147i	$0.654741\pi$
$104$	−2.78238			−0.272835
$105$	7.72119	−	10.4107i	0.753511	−	1.01598i
$106$			7.62834i			0.740930i
$107$			4.51669i			0.436644i	0.975877	+	0.218322i	$0.0700584\pi$
$107$			4.51669i			0.436644i	−0.975877	+	0.218322i	$0.929942\pi$
$108$	1.75060	−	4.89238i	0.168451	−	0.470770i
$109$	16.9666			1.62511			0.812554	−	0.582886i	$-0.198076\pi$
$109$	16.9666			1.62511			0.812554	+	0.582886i	$0.198076\pi$
$110$	−7.00238			−0.667651
$111$	−6.38751	+	8.61249i	−0.606276	+	0.817461i
$112$	−3.74166			−0.353553
$113$		−	2.25834i		−	0.212447i	−0.994342	−	0.106224i	$-0.966124\pi$
$113$		−	2.25834i		−	0.212447i	0.994342	−	0.106224i	$-0.0338759\pi$
$114$		0			0
$115$		−	2.87523i		−	0.268117i
$116$	4.22000			0.391817
$117$	7.98775	−	2.42298i	0.738467	−	0.224005i
$118$	−7.48331			−0.688895
$119$	−20.8215			−1.90870
$120$	2.78238	+	2.06358i	0.253996	+	0.188378i
$121$	1.25834			0.114395
$122$	9.06596			0.820793
$123$	1.79702	−	2.42298i	0.162032	−	0.218473i
$124$	−2.74166	+	4.84596i	−0.246208	+	0.435180i
$125$			12.0000i			1.07331i
$126$	10.7417	−	3.25834i	0.956943	−	0.290276i
$127$		−	13.8191i		−	1.22624i	−0.789988	−	0.613122i	$-0.789913\pi$
$127$		−	13.8191i		−	1.22624i	0.789988	−	0.613122i	$-0.210087\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	12.8708	−	17.3541i	1.13321	−	1.52795i
$130$			5.56477i			0.488062i
$131$			3.48331i			0.304339i	0.988354	+	0.152169i	$0.0486259\pi$
$131$			3.48331i			0.304339i	−0.988354	+	0.152169i	$0.951374\pi$
$132$	−4.87083	−	3.61249i	−0.423951	−	0.314427i
$133$		0			0
$134$		−	15.4833i		−	1.33755i
$135$	−9.78477	−	3.50119i	−0.842139	−	0.301335i
$136$		−	5.56477i		−	0.477175i
$137$	−4.12715			−0.352606			−0.176303	−	0.984336i	$-0.556414\pi$
$137$	−4.12715			−0.352606			−0.176303	+	0.984336i	$0.556414\pi$
$138$	1.48331	−	2.00000i	0.126268	−	0.170251i
$139$		−	20.1955i		−	1.71296i	−0.516181	−	0.856480i	$-0.672647\pi$
$139$		−	20.1955i		−	1.71296i	0.516181	−	0.856480i	$-0.327353\pi$
$140$			7.48331i			0.632456i
$141$	0.266555	−	0.359404i	0.0224480	−	0.0302673i
$142$	13.4833			1.13149
$143$		−	9.74166i		−	0.814638i
$144$	0.870829	+	2.87083i	0.0725691	+	0.239236i
$145$		−	8.44000i		−	0.700904i
$146$	−1.43762			−0.118978
$147$	9.73834	+	7.22251i	0.803205	+	0.595703i
$148$		−	6.19073i		−	0.508875i
$149$		−	2.51669i		−	0.206175i	−0.994672	−	0.103087i	$-0.967128\pi$
$149$		−	2.51669i		−	0.206175i	0.994672	−	0.103087i	$-0.0328722\pi$
$150$	−1.03179	+	1.39119i	−0.0842451	+	0.113590i
$151$			8.44000i			0.686837i	0.939182	+	0.343419i	$0.111585\pi$
$151$			8.44000i			0.686837i	−0.939182	+	0.343419i	$0.888415\pi$
$152$		0			0
$153$	4.84596	+	15.9755i	0.391773	+	1.29154i
$154$		−	13.1003i		−	1.05565i
$155$	9.69192	+	5.48331i	0.778474	+	0.440430i
$156$	−2.87083	+	3.87083i	−0.229850	+	0.309914i
$157$	1.48331			0.118381			0.0591907	−	0.998247i	$-0.481148\pi$
$157$	1.48331			0.118381			0.0591907	+	0.998247i	$0.481148\pi$
$158$	−7.00238			−0.557080
$159$	10.6125	+	7.87083i	0.841625	+	0.624197i
$160$	−2.00000			−0.158114
$161$	5.37907			0.423930
$162$	−5.00000	−	7.48331i	−0.392837	−	0.587945i
$163$	0.516685			0.0404699			0.0202350	−	0.999795i	$-0.493559\pi$
$163$	0.516685			0.0404699			0.0202350	+	0.999795i	$0.493559\pi$
$164$			1.74166i			0.136001i
$165$	−7.22497	+	9.74166i	−0.562463	+	0.758387i
$166$		−	16.6015i		−	1.28852i
$167$	4.31285			0.333738			0.166869	−	0.985979i	$-0.446634\pi$
$167$	4.31285			0.333738			0.166869	+	0.985979i	$0.446634\pi$
$168$	−3.86060	+	5.20536i	−0.297851	+	0.401602i
$169$	5.25834			0.404488
$170$	−11.1295			−0.853596
$171$		0			0
$172$			12.4743i			0.951157i
$173$		−	17.4833i		−	1.32923i	−0.747185	−	0.664616i	$-0.768595\pi$
$173$		−	17.4833i		−	1.32923i	0.747185	−	0.664616i	$-0.231405\pi$
$174$	4.35414	−	5.87083i	0.330087	−	0.445066i
$175$	−3.74166			−0.282843
$176$	3.50119			0.263912
$177$	−7.72119	+	10.4107i	−0.580360	+	0.782518i
$178$			9.69192i			0.726440i
$179$	5.47192			0.408990			0.204495	−	0.978868i	$-0.434445\pi$
$179$	5.47192			0.408990			0.204495	+	0.978868i	$0.434445\pi$
$180$	5.74166	−	1.74166i	0.427958	−	0.129815i
$181$			5.47192i			0.406724i	0.979104	+	0.203362i	$0.0651869\pi$
$181$			5.47192i			0.406724i	−0.979104	+	0.203362i	$0.934813\pi$
$182$	−10.4107			−0.771694
$183$	9.35414	−	12.6125i	0.691478	−	0.932342i
$184$			1.43762i			0.105982i
$185$	−12.3815			−0.910302
$186$	3.91285	+	8.81417i	0.286904	+	0.646286i
$187$	19.4833			1.42476
$188$			0.258343i			0.0188416i
$189$	6.55013	−	18.3056i	0.476452	−	1.33154i
$190$		0			0
$191$			8.25834i			0.597553i	0.954323	+	0.298776i	$0.0965785\pi$
$191$			8.25834i			0.597553i	−0.954323	+	0.298776i	$0.903422\pi$
$192$	−1.39119	−	1.03179i	−0.100401	−	0.0744629i
$193$	4.00000			0.287926			0.143963	−	0.989583i	$-0.454015\pi$
$193$	4.00000			0.287926			0.143963	+	0.989583i	$0.454015\pi$
$194$		−	13.7417i		−	0.986594i
$195$	7.74166	+	5.74166i	0.554392	+	0.411169i
$196$	−7.00000			−0.500000
$197$	−18.0391			−1.28523			−0.642615	−	0.766189i	$-0.722151\pi$
$197$	−18.0391			−1.28523			−0.642615	+	0.766189i	$0.722151\pi$
$198$	−10.0513	+	3.04894i	−0.714316	+	0.216679i
$199$		−	1.43762i		−	0.101910i	−0.998701	−	0.0509550i	$-0.983774\pi$
$199$		−	1.43762i		−	0.101910i	0.998701	−	0.0509550i	$-0.0162265\pi$
$200$		−	1.00000i		−	0.0707107i
$201$	−21.5403	−	15.9755i	−1.51933	−	1.12682i
$202$	−16.9666			−1.19377
$203$	15.7898			1.10823
$204$	−7.74166	−	5.74166i	−0.542024	−	0.401996i
$205$	3.48331			0.243285
$206$		−	9.48331i		−	0.660734i
$207$	−1.25192	−	4.12715i	−0.0870143	−	0.286857i
$208$		−	2.78238i		−	0.192924i
$209$		0			0
$210$	10.4107	+	7.72119i	0.718408	+	0.532813i
$211$	18.9666			1.30572			0.652858	−	0.757480i	$-0.273570\pi$
$211$	18.9666			1.30572			0.652858	+	0.757480i	$0.273570\pi$
$212$	−7.62834			−0.523917
$213$	13.9119	−	18.7579i	0.953229	−	1.28527i
$214$	−4.51669			−0.308754
$215$	24.9486			1.70148
$216$	4.89238	+	1.75060i	0.332885	+	0.119113i
$217$	−10.2583	+	18.1319i	−0.696382	+	1.23087i
$218$			16.9666i			1.14913i
$219$	−1.48331	+	2.00000i	−0.100233	+	0.135147i
$220$		−	7.00238i		−	0.472101i
$221$		−	15.4833i		−	1.04152i
$222$	−8.61249	−	6.38751i	−0.578032	−	0.428702i
$223$			19.5695i			1.31047i	0.755424	+	0.655236i	$0.227431\pi$
$223$			19.5695i			1.31047i	−0.755424	+	0.655236i	$0.772569\pi$
$224$		−	3.74166i		−	0.250000i
$225$	0.870829	+	2.87083i	0.0580552	+	0.191389i
$226$	2.25834			0.150223
$227$			14.9666i			0.993370i	0.867931	+	0.496685i	$0.165450\pi$
$227$			14.9666i			0.993370i	−0.867931	+	0.496685i	$0.834550\pi$
$228$		0			0
$229$		−	2.06358i		−	0.136365i	−0.997673	−	0.0681824i	$-0.978280\pi$
$229$		−	2.06358i		−	0.136365i	0.997673	−	0.0681824i	$-0.0217200\pi$
$230$	2.87523			0.189587
$231$	−18.2250	−	13.5167i	−1.19912	−	0.889333i
$232$			4.22000i			0.277057i
$233$		−	9.22497i		−	0.604348i	−0.953253	−	0.302174i	$-0.902288\pi$
$233$		−	9.22497i		−	0.604348i	0.953253	−	0.302174i	$-0.0977124\pi$
$234$	2.42298	+	7.98775i	0.158395	+	0.522175i
$235$	0.516685			0.0337048
$236$		−	7.48331i		−	0.487122i
$237$	−7.22497	+	9.74166i	−0.469312	+	0.632789i
$238$		−	20.8215i		−	1.34965i
$239$	−18.1319			−1.17286			−0.586428	−	0.810001i	$-0.699466\pi$
$239$	−18.1319			−1.17286			−0.586428	+	0.810001i	$0.699466\pi$
$240$	−2.06358	+	2.78238i	−0.133203	+	0.179602i
$241$			1.25192i			0.0806431i	0.999187	+	0.0403216i	$0.0128382\pi$
$241$			1.25192i			0.0806431i	−0.999187	+	0.0403216i	$0.987162\pi$
$242$			1.25834i			0.0808893i
$243$	−15.5697	−	0.765233i	−0.998794	−	0.0490897i
$244$			9.06596i			0.580389i
$245$			14.0000i			0.894427i
$246$	2.42298	+	1.79702i	0.154484	+	0.114574i
$247$		0			0
$248$	−4.84596	−	2.74166i	−0.307719	−	0.174095i
$249$	−23.0958	−	17.1292i	−1.46364	−	1.08552i
$250$	−12.0000			−0.758947
$251$	21.6331			1.36547			0.682735	−	0.730666i	$-0.260790\pi$
$251$	21.6331			1.36547			0.682735	+	0.730666i	$0.260790\pi$
$252$	3.25834	+	10.7417i	0.205256	+	0.676661i
$253$	−5.03337			−0.316445
$254$	13.8191			0.867085
$255$	−11.4833	+	15.4833i	−0.719113	+	0.969603i
$256$	1.00000			0.0625000
$257$			8.00000i			0.499026i	0.968371	+	0.249513i	$0.0802706\pi$
$257$			8.00000i			0.499026i	−0.968371	+	0.249513i	$0.919729\pi$
$258$	17.3541	+	12.8708i	1.08042	+	0.801303i
$259$		−	23.1636i		−	1.43931i
$260$	−5.56477			−0.345112
$261$	−3.67490	−	12.1149i	−0.227470	−	0.749893i
$262$	−3.48331			−0.215200
$263$	7.00238			0.431785			0.215893	−	0.976417i	$-0.430734\pi$
$263$	7.00238			0.431785			0.215893	+	0.976417i	$0.430734\pi$
$264$	3.61249	−	4.87083i	0.222333	−	0.299779i
$265$			15.2567i			0.937211i
$266$		0			0
$267$	13.4833	+	10.0000i	0.825165	+	0.611990i
$268$	15.4833			0.945794
$269$	−0.625959			−0.0381654			−0.0190827	−	0.999818i	$-0.506075\pi$
$269$	−0.625959			−0.0381654			−0.0190827	+	0.999818i	$0.506075\pi$
$270$	3.50119	−	9.78477i	0.213076	−	0.595482i
$271$			1.25192i			0.0760486i	0.999277	+	0.0380243i	$0.0121064\pi$
$271$			1.25192i			0.0760486i	−0.999277	+	0.0380243i	$0.987894\pi$
$272$	5.56477			0.337414
$273$	−10.7417	+	14.4833i	−0.650115	+	0.876570i
$274$		−	4.12715i		−	0.249330i
$275$	3.50119			0.211130
$276$	2.00000	+	1.48331i	0.120386	+	0.0892851i
$277$			19.4767i			1.17024i	0.810947	+	0.585120i	$0.198953\pi$
$277$			19.4767i			1.17024i	−0.810947	+	0.585120i	$0.801047\pi$
$278$	20.1955			1.21125
$279$	16.2994	+	3.65083i	0.975821	+	0.218569i
$280$	−7.48331			−0.447214
$281$		−	16.9666i		−	1.01214i	−0.862491	−	0.506072i	$-0.831097\pi$
$281$		−	16.9666i		−	1.01214i	0.862491	−	0.506072i	$-0.168903\pi$
$282$	0.359404	+	0.266555i	0.0214022	+	0.0158731i
$283$	0.516685			0.0307137			0.0153569	−	0.999882i	$-0.495112\pi$
$283$	0.516685			0.0307137			0.0153569	+	0.999882i	$0.495112\pi$
$284$			13.4833i			0.800088i
$285$		0			0
$286$	9.74166			0.576036
$287$			6.51669i			0.384668i
$288$	−2.87083	+	0.870829i	−0.169165	+	0.0513141i
$289$	13.9666			0.821566
$290$	8.44000			0.495614
$291$	−19.1173	−	14.1785i	−1.12067	−	0.831157i
$292$		−	1.43762i		−	0.0841301i
$293$			29.4833i			1.72243i	0.508238	+	0.861217i	$0.330297\pi$
$293$			29.4833i			1.72243i	−0.508238	+	0.861217i	$0.669703\pi$
$294$	−7.22251	+	9.73834i	−0.421226	+	0.567952i
$295$	−14.9666			−0.871391
$296$	6.19073			0.359829
$297$	−6.12917	+	17.1292i	−0.355651	+	0.993935i
$298$	2.51669			0.145788
$299$			4.00000i			0.231326i
$300$	−1.39119	−	1.03179i	−0.0803205	−	0.0595703i
$301$			46.6746i			2.69028i
$302$	−8.44000			−0.485667
$303$	−17.5060	+	23.6038i	−1.00569	+	1.35600i
$304$		0			0
$305$	18.1319			1.03823
$306$	−15.9755	+	4.84596i	−0.913258	+	0.277025i
$307$	−18.9666			−1.08248			−0.541241	−	0.840867i	$-0.682045\pi$
$307$	−18.9666			−1.08248			−0.541241	+	0.840867i	$0.682045\pi$
$308$	13.1003			0.746457
$309$	−13.1931	−	9.78477i	−0.750530	−	0.556636i
$310$	−5.48331	+	9.69192i	−0.311431	+	0.550464i
$311$		−	6.96663i		−	0.395041i	−0.980299	−	0.197521i	$-0.936711\pi$
$311$		−	6.96663i		−	0.395041i	0.980299	−	0.197521i	$-0.0632890\pi$
$312$	−3.87083	−	2.87083i	−0.219143	−	0.162529i
$313$			0.185699i			0.0104963i	0.999986	+	0.00524816i	$0.00167055\pi$
$313$			0.185699i			0.0104963i	−0.999986	+	0.00524816i	$0.998329\pi$
$314$			1.48331i			0.0837083i
$315$	21.4833	−	6.51669i	1.21045	−	0.367174i
$316$		−	7.00238i		−	0.393915i
$317$		−	25.4833i		−	1.43129i	−0.698466	−	0.715643i	$-0.746134\pi$
$317$		−	25.4833i		−	1.43129i	0.698466	−	0.715643i	$-0.253866\pi$
$318$	−7.87083	+	10.6125i	−0.441374	+	0.595119i
$319$	−14.7750			−0.827243
$320$		−	2.00000i		−	0.111803i
$321$	−4.66026	+	6.28357i	−0.260110	+	0.350715i
$322$			5.37907i			0.299764i
$323$		0			0
$324$	7.48331	−	5.00000i	0.415740	−	0.277778i
$325$		−	2.78238i		−	0.154339i
$326$			0.516685i			0.0286165i
$327$	23.6038	+	17.5060i	1.30530	+	0.968082i
$328$	−1.74166			−0.0961669
$329$			0.966630i			0.0532920i
$330$	−9.74166	−	7.22497i	−0.536261	−	0.397722i
$331$		−	10.3179i		−	0.567122i	−0.958954	−	0.283561i	$-0.908484\pi$
$331$		−	10.3179i		−	0.567122i	0.958954	−	0.283561i	$-0.0915158\pi$
$332$	16.6015			0.911123
$333$	−17.7725	+	5.39106i	−0.973928	+	0.295428i
$334$			4.31285i			0.235989i
$335$		−	30.9666i		−	1.69189i
$336$	−5.20536	−	3.86060i	−0.283976	−	0.210613i
$337$		−	31.9510i		−	1.74048i	−0.492627	−	0.870241i	$-0.663963\pi$
$337$		−	31.9510i		−	1.74048i	0.492627	−	0.870241i	$-0.336037\pi$
$338$			5.25834i			0.286016i
$339$	2.33013	−	3.14179i	0.126555	−	0.170638i
$340$		−	11.1295i		−	0.603584i
$341$	9.59907	−	16.9666i	0.519819	−	0.918795i
$342$		0			0
$343$		0			0
$344$	−12.4743			−0.672569
$345$	2.96663	−	4.00000i	0.159718	−	0.215353i
$346$	17.4833			0.939909
$347$	19.4767			1.04556			0.522782	−	0.852467i	$-0.324894\pi$
$347$	19.4767			1.04556			0.522782	+	0.852467i	$0.324894\pi$
$348$	5.87083	+	4.35414i	0.314709	+	0.233407i
$349$	−16.9666			−0.908203			−0.454101	−	0.890950i	$-0.650040\pi$
$349$	−16.9666			−0.908203			−0.454101	+	0.890950i	$0.650040\pi$
$350$		−	3.74166i		−	0.200000i
$351$	13.6125	+	4.87083i	0.726581	+	0.259986i
$352$			3.50119i			0.186614i
$353$	−20.8215			−1.10821			−0.554107	−	0.832445i	$-0.686940\pi$
$353$	−20.8215			−1.10821			−0.554107	+	0.832445i	$0.686940\pi$
$354$	−10.4107	−	7.72119i	−0.553324	−	0.410377i
$355$	26.9666			1.43124
$356$	−9.69192			−0.513671
$357$	−28.9666	−	21.4833i	−1.53308	−	1.13702i
$358$			5.47192i			0.289200i
$359$		−	24.2583i		−	1.28031i	−0.768247	−	0.640153i	$-0.778871\pi$
$359$		−	24.2583i		−	1.28031i	0.768247	−	0.640153i	$-0.221129\pi$
$360$	1.74166	+	5.74166i	0.0917934	+	0.302612i
$361$	−19.0000			−1.00000
$362$	−5.47192			−0.287598
$363$	1.75060	+	1.29834i	0.0918825	+	0.0681453i
$364$		−	10.4107i		−	0.545670i
$365$	−2.87523			−0.150497
$366$	12.6125	+	9.35414i	0.659265	+	0.488949i
$367$		−	12.5671i		−	0.656000i	−0.944678	−	0.328000i	$-0.893625\pi$
$367$		−	12.5671i		−	0.656000i	0.944678	−	0.328000i	$-0.106375\pi$
$368$	−1.43762			−0.0749409
$369$	5.00000	−	1.51669i	0.260290	−	0.0789555i
$370$		−	12.3815i		−	0.643681i
$371$	−28.5426			−1.48186
$372$	−8.81417	+	3.91285i	−0.456993	+	0.202872i
$373$	17.4833			0.905252			0.452626	−	0.891701i	$-0.350487\pi$
$373$	17.4833			0.905252			0.452626	+	0.891701i	$0.350487\pi$
$374$			19.4833i			1.00746i
$375$	−12.3815	+	16.6943i	−0.639375	+	0.862090i
$376$	−0.258343			−0.0133230
$377$			11.7417i			0.604726i
$378$	18.3056	+	6.55013i	0.941540	+	0.336902i
$379$	26.9666			1.38518			0.692591	−	0.721330i	$-0.256469\pi$
$379$	26.9666			1.38518			0.692591	+	0.721330i	$0.256469\pi$
$380$		0			0
$381$	14.2583	−	19.2250i	0.730477	−	0.984925i
$382$	−8.25834			−0.422534
$383$	−12.3815			−0.632663			−0.316331	−	0.948649i	$-0.602451\pi$
$383$	−12.3815			−0.632663			−0.316331	+	0.948649i	$0.602451\pi$
$384$	1.03179	−	1.39119i	0.0526532	−	0.0709940i
$385$		−	26.2005i		−	1.33530i
$386$			4.00000i			0.203595i
$387$	35.8116	−	10.8630i	1.82040	−	0.552196i
$388$	13.7417			0.697627
$389$	18.7579			0.951062			0.475531	−	0.879699i	$-0.342256\pi$
$389$	18.7579			0.951062			0.475531	+	0.879699i	$0.342256\pi$
$390$	−5.74166	+	7.74166i	−0.290740	+	0.392014i
$391$	−8.00000			−0.404577
$392$		−	7.00000i		−	0.353553i
$393$	−3.59404	+	4.84596i	−0.181295	+	0.244446i
$394$		−	18.0391i		−	0.908795i
$395$	−14.0048			−0.704656
$396$	−3.04894	−	10.0513i	−0.153215	−	0.505098i
$397$	−8.96663			−0.450022			−0.225011	−	0.974356i	$-0.572242\pi$
$397$	−8.96663			−0.450022			−0.225011	+	0.974356i	$0.572242\pi$
$398$	1.43762			0.0720612
$399$		0			0
$400$	1.00000			0.0500000
$401$	−22.4448			−1.12084			−0.560419	−	0.828209i	$-0.689360\pi$
$401$	−22.4448			−1.12084			−0.560419	+	0.828209i	$0.689360\pi$
$402$	15.9755	−	21.5403i	0.796785	−	1.07433i
$403$	−13.4833	−	7.62834i	−0.671652	−	0.379995i
$404$		−	16.9666i		−	0.844121i
$405$	−10.0000	−	14.9666i	−0.496904	−	0.743698i
$406$			15.7898i			0.783634i
$407$			21.6749i			1.07439i
$408$	5.74166	−	7.74166i	0.284254	−	0.383269i
$409$			26.3862i			1.30471i	0.757912	+	0.652357i	$0.226220\pi$
$409$			26.3862i			1.30471i	−0.757912	+	0.652357i	$0.773780\pi$
$410$			3.48331i			0.172029i
$411$	−5.74166	−	4.25834i	−0.283215	−	0.210049i
$412$	9.48331			0.467209
$413$		−	28.0000i		−	1.37779i
$414$	4.12715	−	1.25192i	0.202838	−	0.0615284i
$415$		−	33.2029i		−	1.62987i
$416$	2.78238			0.136418
$417$	20.8375	−	28.0958i	1.02041	−	1.37586i
$418$		0			0
$419$			24.0000i			1.17248i	0.810139	+	0.586238i	$0.199392\pi$
$419$			24.0000i			1.17248i	−0.810139	+	0.586238i	$0.800608\pi$
$420$	−7.72119	+	10.4107i	−0.376756	+	0.507991i
$421$	−1.48331			−0.0722923			−0.0361462	−	0.999347i	$-0.511508\pi$
$421$	−1.48331			−0.0722923			−0.0361462	+	0.999347i	$0.511508\pi$
$422$			18.9666i			0.923281i
$423$	0.741657	−	0.224972i	0.0360606	−	0.0109385i
$424$		−	7.62834i		−	0.370465i
$425$	5.56477			0.269931
$426$	18.7579	+	13.9119i	0.908822	+	0.674035i
$427$			33.9217i			1.64159i
$428$		−	4.51669i		−	0.218322i
$429$	10.0513	−	13.5525i	0.485282	−	0.654321i
$430$			24.9486i			1.20313i
$431$			1.29171i			0.0622196i	0.999516	+	0.0311098i	$0.00990416\pi$
$431$			1.29171i			0.0622196i	−0.999516	+	0.0311098i	$0.990096\pi$
$432$	−1.75060	+	4.89238i	−0.0842256	+	0.235385i
$433$			2.68953i			0.129251i	0.997910	+	0.0646254i	$0.0205852\pi$
$433$			2.68953i			0.129251i	−0.997910	+	0.0646254i	$0.979415\pi$
$434$	−18.1319	−	10.2583i	−0.870360	−	0.492416i
$435$	8.70829	−	11.7417i	0.417530	−	0.562969i
$436$	−16.9666			−0.812554
$437$		0			0
$438$	−2.00000	−	1.48331i	−0.0955637	−	0.0708755i
$439$	4.77503			0.227900			0.113950	−	0.993487i	$-0.463650\pi$
$439$	4.77503			0.227900			0.113950	+	0.993487i	$0.463650\pi$
$440$	7.00238			0.333826
$441$	6.09580	+	20.0958i	0.290276	+	0.956943i
$442$	15.4833			0.736466
$443$		−	0.516685i		−	0.0245485i	−0.999925	−	0.0122742i	$-0.996093\pi$
$443$		−	0.516685i		−	0.0245485i	0.999925	−	0.0122742i	$-0.00390711\pi$
$444$	6.38751	−	8.61249i	0.303138	−	0.408731i
$445$			19.3838i			0.918882i
$446$	−19.5695			−0.926644
$447$	2.59668	−	3.50119i	0.122819	−	0.165601i
$448$	3.74166			0.176777
$449$	−1.25192			−0.0590816			−0.0295408	−	0.999564i	$-0.509405\pi$
$449$	−1.25192			−0.0590816			−0.0295408	+	0.999564i	$0.509405\pi$
$450$	−2.87083	+	0.870829i	−0.135332	+	0.0410513i
$451$		−	6.09788i		−	0.287138i
$452$			2.25834i			0.106224i
$453$	−8.70829	+	11.7417i	−0.409151	+	0.551671i
$454$	−14.9666			−0.702419
$455$	−20.8215			−0.976125
$456$		0			0
$457$		−	33.2029i		−	1.55317i	−0.630015	−	0.776583i	$-0.716951\pi$
$457$		−	33.2029i		−	1.55317i	0.630015	−	0.776583i	$-0.283049\pi$
$458$	2.06358			0.0964245
$459$	−9.74166	+	27.2250i	−0.454702	+	1.27075i
$460$			2.87523i			0.134058i
$461$	21.6331			1.00755			0.503777	−	0.863834i	$-0.331943\pi$
$461$	21.6331			1.00755			0.503777	+	0.863834i	$0.331943\pi$
$462$	13.5167	−	18.2250i	0.628853	−	0.847902i
$463$		−	5.75047i		−	0.267247i	−0.991032	−	0.133623i	$-0.957339\pi$
$463$		−	5.75047i		−	0.267247i	0.991032	−	0.133623i	$-0.0426613\pi$
$464$	−4.22000			−0.195909
$465$	7.82570	+	17.6283i	0.362908	+	0.817495i
$466$	9.22497			0.427339
$467$			38.4499i			1.77925i	0.456691	+	0.889626i	$0.349035\pi$
$467$			38.4499i			1.77925i	−0.456691	+	0.889626i	$0.650965\pi$
$468$	−7.98775	+	2.42298i	−0.369234	+	0.112002i
$469$	57.9333			2.67511
$470$			0.516685i			0.0238329i
$471$	2.06358	+	1.53047i	0.0950845	+	0.0705201i
$472$	7.48331			0.344447
$473$		−	43.6749i		−	2.00817i
$474$	−9.74166	−	7.22497i	−0.447449	−	0.331854i
$475$		0			0
$476$	20.8215			0.954350
$477$	6.64298	+	21.8997i	0.304161	+	1.00272i
$478$		−	18.1319i		−	0.829335i
$479$			37.9333i			1.73321i	0.498991	+	0.866607i	$0.333704\pi$
$479$			37.9333i			1.73321i	−0.498991	+	0.866607i	$0.666296\pi$
$480$	−2.78238	−	2.06358i	−0.126998	−	0.0941889i
$481$	17.2250			0.785391
$482$	−1.25192			−0.0570233
$483$	7.48331	+	5.55006i	0.340503	+	0.252536i
$484$	−1.25834			−0.0571974
$485$		−	27.4833i		−	1.24795i
$486$	0.765233	−	15.5697i	0.0347117	−	0.706254i
$487$			5.56477i			0.252164i	0.992020	+	0.126082i	$0.0402402\pi$
$487$			5.56477i			0.252164i	−0.992020	+	0.126082i	$0.959760\pi$
$488$	−9.06596			−0.410397
$489$	0.718808	+	0.533109i	0.0325056	+	0.0241080i
$490$	−14.0000			−0.632456
$491$	−11.0367			−0.498079			−0.249039	−	0.968493i	$-0.580115\pi$
$491$	−11.0367			−0.498079			−0.249039	+	0.968493i	$0.580115\pi$
$492$	−1.79702	+	2.42298i	−0.0810159	+	0.109236i
$493$	−23.4833			−1.05764
$494$		0			0
$495$	−20.1026	+	6.09788i	−0.903547	+	0.274079i
$496$	2.74166	−	4.84596i	0.123104	−	0.217590i
$497$			50.4499i			2.26299i
$498$	17.1292	−	23.0958i	0.767577	−	1.03495i
$499$		−	4.40570i		−	0.197226i	−0.995126	−	0.0986131i	$-0.968559\pi$
$499$		−	4.40570i		−	0.197226i	0.995126	−	0.0986131i	$-0.0314406\pi$
$500$		−	12.0000i		−	0.536656i
$501$	6.00000	+	4.44994i	0.268060	+	0.198809i
$502$			21.6331i			0.965533i
$503$			9.48331i			0.422840i	0.977395	+	0.211420i	$0.0678088\pi$
$503$			9.48331i			0.422840i	−0.977395	+	0.211420i	$0.932191\pi$
$504$	−10.7417	+	3.25834i	−0.478471	+	0.145138i
$505$	−33.9333			−1.51001
$506$		−	5.03337i		−	0.223761i
$507$	7.31536	+	5.42549i	0.324887	+	0.240955i
$508$			13.8191i			0.613122i
$509$	0.625959			0.0277451			0.0138726	−	0.999904i	$-0.495584\pi$
$509$	0.625959			0.0277451			0.0138726	+	0.999904i	$0.495584\pi$
$510$	−15.4833	−	11.4833i	−0.685613	−	0.508490i
$511$		−	5.37907i		−	0.237956i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−8.00000			−0.352865
$515$		−	18.9666i		−	0.835770i
$516$	−12.8708	+	17.3541i	−0.566607	+	0.763974i
$517$		−	0.904507i		−	0.0397802i
$518$	23.1636			1.01775
$519$	18.0391	−	24.3226i	0.791827	−	1.06765i
$520$		−	5.56477i		−	0.244031i
$521$			10.0000i			0.438108i	0.975713	+	0.219054i	$0.0702971\pi$
$521$			10.0000i			0.438108i	−0.975713	+	0.219054i	$0.929703\pi$
$522$	12.1149	−	3.67490i	0.530255	−	0.160846i
$523$			6.90953i			0.302133i	0.988524	+	0.151066i	$0.0482707\pi$
$523$			6.90953i			0.302133i	−0.988524	+	0.151066i	$0.951729\pi$
$524$		−	3.48331i		−	0.152169i
$525$	−5.20536	−	3.86060i	−0.227181	−	0.168490i
$526$			7.00238i			0.305318i
$527$	15.2567	−	26.9666i	0.664592	−	1.17468i
$528$	4.87083	+	3.61249i	0.211976	+	0.157213i
$529$	−20.9333			−0.910142
$530$	−15.2567			−0.662708
$531$	−21.4833	+	6.51669i	−0.932296	+	0.282800i
$532$		0			0
$533$	−4.84596			−0.209902
$534$	−10.0000	+	13.4833i	−0.432742	+	0.583480i
$535$	−9.03337			−0.390547
$536$			15.4833i			0.668777i
$537$	7.61249	+	5.64586i	0.328503	+	0.243637i
$538$		−	0.625959i		−	0.0269870i
$539$	24.5083			1.05565
$540$	9.78477	+	3.50119i	0.421069	+	0.150667i
$541$	−18.0000			−0.773880			−0.386940	−	0.922105i	$-0.626468\pi$
$541$	−18.0000			−0.773880			−0.386940	+	0.922105i	$0.626468\pi$
$542$	−1.25192			−0.0537745
$543$	−5.64586	+	7.61249i	−0.242287	+	0.326683i
$544$			5.56477i			0.238587i
$545$			33.9333i			1.45354i
$546$	−14.4833	−	10.7417i	−0.619829	−	0.459700i
$547$	−2.44994			−0.104752			−0.0523760	−	0.998627i	$-0.516679\pi$
$547$	−2.44994			−0.104752			−0.0523760	+	0.998627i	$0.516679\pi$
$548$	4.12715			0.176303
$549$	26.0268	−	7.89490i	1.11080	−	0.336946i
$550$			3.50119i			0.149291i
$551$		0			0
$552$	−1.48331	+	2.00000i	−0.0631341	+	0.0851257i
$553$		−	26.2005i		−	1.11416i
$554$	−19.4767			−0.827485
$555$	−17.2250	−	12.7750i	−0.731159	−	0.542270i
$556$			20.1955i			0.856480i
$557$	−37.4229			−1.58566			−0.792830	−	0.609443i	$-0.791393\pi$
$557$	−37.4229			−1.58566			−0.792830	+	0.609443i	$0.791393\pi$
$558$	−3.65083	+	16.2994i	−0.154552	+	0.690010i
$559$	−34.7083			−1.46800
$560$		−	7.48331i		−	0.316228i
$561$	27.1050	+	20.1026i	1.14438	+	0.848734i
$562$	16.9666			0.715694
$563$			26.4499i			1.11473i	0.830267	+	0.557366i	$0.188188\pi$
$563$			26.4499i			1.11473i	−0.830267	+	0.557366i	$0.811812\pi$
$564$	−0.266555	+	0.359404i	−0.0112240	+	0.0151336i
$565$	4.51669			0.190018
$566$			0.516685i			0.0217179i
$567$	28.0000	−	18.7083i	1.17589	−	0.785674i
$568$	−13.4833			−0.565747
$569$	−27.8238			−1.16644			−0.583218	−	0.812316i	$-0.698207\pi$
$569$	−27.8238			−1.16644			−0.583218	+	0.812316i	$0.698207\pi$
$570$		0			0
$571$			32.0438i			1.34099i	0.741913	+	0.670496i	$0.233919\pi$
$571$			32.0438i			1.34099i	−0.741913	+	0.670496i	$0.766081\pi$
$572$			9.74166i			0.407319i
$573$	−8.52086	+	11.4889i	−0.355964	+	0.479957i
$574$	−6.51669			−0.272001
$575$	−1.43762			−0.0599527
$576$	−0.870829	−	2.87083i	−0.0362845	−	0.119618i
$577$	9.74166			0.405551			0.202775	−	0.979225i	$-0.435004\pi$
$577$	9.74166			0.405551			0.202775	+	0.979225i	$0.435004\pi$
$578$			13.9666i			0.580935i
$579$	5.56477	+	4.12715i	0.231264	+	0.171519i
$580$			8.44000i			0.350452i
$581$	62.1169			2.57704
$582$	14.1785	−	19.1173i	0.587717	−	0.792437i
$583$	26.7083			1.10614
$584$	1.43762			0.0594890
$585$	4.84596	+	15.9755i	0.200356	+	0.660505i
$586$	−29.4833			−1.21794
$587$	−24.1369			−0.996238			−0.498119	−	0.867109i	$-0.665976\pi$
$587$	−24.1369			−0.996238			−0.498119	+	0.867109i	$0.665976\pi$
$588$	−9.73834	−	7.22251i	−0.401602	−	0.297851i
$589$		0			0
$590$		−	14.9666i		−	0.616166i
$591$	−25.0958	−	18.6125i	−1.03230	−	0.765615i
$592$			6.19073i			0.254437i
$593$		−	5.74166i		−	0.235782i	−0.993027	−	0.117891i	$-0.962387\pi$
$593$		−	5.74166i		−	0.235782i	0.993027	−	0.117891i	$-0.0376133\pi$
$594$	−17.1292	−	6.12917i	−0.702818	−	0.251483i
$595$		−	41.6429i		−	1.70719i
$596$			2.51669i			0.103087i
$597$	1.48331	−	2.00000i	0.0607080	−	0.0818546i
$598$	−4.00000			−0.163572
$599$		−	14.7083i		−	0.600964i	−0.953787	−	0.300482i	$-0.902852\pi$
$599$		−	14.7083i		−	0.600964i	0.953787	−	0.300482i	$-0.0971476\pi$
$600$	1.03179	−	1.39119i	0.0421226	−	0.0567952i
$601$		−	36.2638i		−	1.47923i	−0.673029	−	0.739616i	$-0.735007\pi$
$601$		−	36.2638i		−	1.47923i	0.673029	−	0.739616i	$-0.264993\pi$
$602$	−46.6746			−1.90231
$603$	−13.4833	−	44.4499i	−0.549083	−	1.81014i
$604$		−	8.44000i		−	0.343419i
$605$			2.51669i			0.102318i
$606$	−23.6038	−	17.5060i	−0.958840	−	0.711131i
$607$	14.9666			0.607477			0.303738	−	0.952755i	$-0.401765\pi$
$607$	14.9666			0.607477			0.303738	+	0.952755i	$0.401765\pi$
$608$		0			0
$609$	21.9666	+	16.2917i	0.890133	+	0.660174i
$610$			18.1319i			0.734140i
$611$	−0.718808			−0.0290799
$612$	−4.84596	−	15.9755i	−0.195886	−	0.645771i
$613$			21.4474i			0.866253i	0.901333	+	0.433126i	$0.142590\pi$
$613$			21.4474i			0.866253i	−0.901333	+	0.433126i	$0.857410\pi$
$614$		−	18.9666i		−	0.765431i
$615$	4.84596	+	3.59404i	0.195408	+	0.144926i
$616$			13.1003i			0.527824i
$617$		−	2.00000i		−	0.0805170i	−0.999189	−	0.0402585i	$-0.987182\pi$
$617$		−	2.00000i		−	0.0805170i	0.999189	−	0.0402585i	$-0.0128181\pi$
$618$	9.78477	−	13.1931i	0.393601	−	0.530705i
$619$			31.8581i			1.28049i	0.768172	+	0.640243i	$0.221166\pi$
$619$			31.8581i			1.28049i	−0.768172	+	0.640243i	$0.778834\pi$
$620$	−9.69192	−	5.48331i	−0.389237	−	0.220215i
$621$	2.51669	−	7.03337i	0.100991	−	0.282239i
$622$	6.96663			0.279336
$623$	−36.2638			−1.45288
$624$	2.87083	−	3.87083i	0.114925	−	0.154957i
$625$	−19.0000			−0.760000
$626$	−0.185699			−0.00742202
$627$		0			0
$628$	−1.48331			−0.0591907
$629$			34.4499i			1.37361i
$630$	6.51669	+	21.4833i	0.259631	+	0.855916i
$631$			18.1319i			0.721820i	0.932601	+	0.360910i	$0.117534\pi$
$631$			18.1319i			0.721820i	−0.932601	+	0.360910i	$0.882466\pi$
$632$	7.00238			0.278540
$633$	26.3862	+	19.5695i	1.04876	+	0.777819i
$634$	25.4833			1.01207
$635$	27.6381			1.09679
$636$	−10.6125	−	7.87083i	−0.420812	−	0.312099i
$637$		−	19.4767i		−	0.771694i
$638$		−	14.7750i		−	0.584949i
$639$	38.7083	−	11.7417i	1.53128	−	0.464493i
$640$	2.00000			0.0790569
$641$	23.5110			0.928628			0.464314	−	0.885671i	$-0.346301\pi$
$641$	23.5110			0.928628			0.464314	+	0.885671i	$0.346301\pi$
$642$	−6.28357	−	4.66026i	−0.247993	−	0.183926i
$643$			18.9436i			0.747062i	0.927618	+	0.373531i	$0.121853\pi$
$643$			18.9436i			0.747062i	−0.927618	+	0.373531i	$0.878147\pi$
$644$	−5.37907			−0.211965
$645$	34.7083	+	25.7417i	1.36664	+	1.01358i
$646$		0			0
$647$	−40.3910			−1.58793			−0.793967	−	0.607961i	$-0.791988\pi$
$647$	−40.3910			−1.58793			−0.793967	+	0.607961i	$0.791988\pi$
$648$	5.00000	+	7.48331i	0.196419	+	0.293972i
$649$			26.2005i			1.02846i
$650$	2.78238			0.109134
$651$	−32.9796	+	14.6405i	−1.29257	+	0.573808i
$652$	−0.516685			−0.0202350
$653$			36.4499i			1.42640i	0.700962	+	0.713198i	$0.252754\pi$
$653$			36.4499i			1.42640i	−0.700962	+	0.713198i	$0.747246\pi$
$654$	−17.5060	+	23.6038i	−0.684537	+	0.922983i
$655$	−6.96663			−0.272209
$656$		−	1.74166i		−	0.0680003i
$657$	−4.12715	+	1.25192i	−0.161015	+	0.0488420i
$658$	−0.966630			−0.0376831
$659$			30.9666i			1.20629i	0.797632	+	0.603144i	$0.206086\pi$
$659$			30.9666i			1.20629i	−0.797632	+	0.603144i	$0.793914\pi$
$660$	7.22497	−	9.74166i	0.281232	−	0.379193i
$661$	5.48331			0.213276			0.106638	−	0.994298i	$-0.465991\pi$
$661$	5.48331			0.213276			0.106638	+	0.994298i	$0.465991\pi$
$662$	10.3179			0.401016
$663$	15.9755	−	21.5403i	0.620437	−	0.836554i
$664$			16.6015i			0.644261i
$665$		0			0
$666$	−5.39106	−	17.7725i	−0.208899	−	0.688671i
$667$	6.06674			0.234905
$668$	−4.31285			−0.166869
$669$	−20.1916	+	27.2250i	−0.780652	+	1.05258i
$670$	30.9666			1.19635
$671$		−	31.7417i		−	1.22537i
$672$	3.86060	−	5.20536i	0.148926	−	0.200801i
$673$		−	43.2662i		−	1.66779i	−0.551923	−	0.833895i	$-0.686106\pi$
$673$		−	43.2662i		−	1.66779i	0.551923	−	0.833895i	$-0.313894\pi$
$674$	31.9510			1.23071
$675$	−1.75060	+	4.89238i	−0.0673805	+	0.188308i
$676$	−5.25834			−0.202244
$677$	17.1346			0.658535			0.329267	−	0.944237i	$-0.393198\pi$
$677$	17.1346			0.658535			0.329267	+	0.944237i	$0.393198\pi$
$678$	3.14179	+	2.33013i	0.120660	+	0.0894881i
$679$	51.4166			1.97319
$680$	11.1295			0.426798
$681$	−15.4424	+	20.8215i	−0.591753	+	0.797880i
$682$	16.9666	+	9.59907i	0.649686	+	0.367567i
$683$		−	7.48331i		−	0.286341i	−0.989698	−	0.143171i	$-0.954270\pi$
$683$		−	7.48331i		−	0.286341i	0.989698	−	0.143171i	$-0.0457297\pi$
$684$		0			0
$685$		−	8.25430i		−	0.315381i
$686$		0			0
$687$	2.12917	−	2.87083i	0.0812330	−	0.109529i
$688$		−	12.4743i		−	0.475578i
$689$		−	21.2250i		−	0.808607i
$690$	4.00000	+	2.96663i	0.152277	+	0.112938i
$691$	−21.0334			−0.800147			−0.400074	−	0.916483i	$-0.631015\pi$
$691$	−21.0334			−0.800147			−0.400074	+	0.916483i	$0.631015\pi$
$692$			17.4833i			0.664616i
$693$	−11.4081	−	37.6086i	−0.433357	−	1.42863i
$694$			19.4767i			0.739325i
$695$	40.3910			1.53212
$696$	−4.35414	+	5.87083i	−0.165043	+	0.222533i
$697$		−	9.69192i		−	0.367108i
$698$		−	16.9666i		−	0.642196i
$699$	9.51821	−	12.8337i	0.360012	−	0.485415i
$700$	3.74166			0.141421
$701$			13.4833i			0.509258i	0.967039	+	0.254629i	$0.0819533\pi$
$701$			13.4833i			0.509258i	−0.967039	+	0.254629i	$0.918047\pi$
$702$	−4.87083	+	13.6125i	−0.183838	+	0.513770i
$703$		0			0
$704$	−3.50119			−0.131956
$705$	0.718808	+	0.533109i	0.0270719	+	0.0200781i
$706$		−	20.8215i		−	0.783626i
$707$		−	63.4833i		−	2.38754i
$708$	7.72119	−	10.4107i	0.290180	−	0.391259i
$709$		−	8.16145i		−	0.306510i	−0.988187	−	0.153255i	$-0.951024\pi$
$709$		−	8.16145i		−	0.306510i	0.988187	−	0.153255i	$-0.0489755\pi$
$710$			26.9666i			1.01204i
$711$	−20.1026	+	6.09788i	−0.753908	+	0.228688i
$712$		−	9.69192i		−	0.363220i
$713$	−3.94145	+	6.96663i	−0.147609	+	0.260902i
$714$	21.4833	−	28.9666i	0.803993	−	1.08405i
$715$	19.4833			0.728635
$716$	−5.47192			−0.204495
$717$	−25.2250	−	18.7083i	−0.942044	−	0.698674i
$718$	24.2583			0.905313
$719$	−9.69192			−0.361448			−0.180724	−	0.983534i	$-0.557844\pi$
$719$	−9.69192			−0.361448			−0.180724	+	0.983534i	$0.557844\pi$
$720$	−5.74166	+	1.74166i	−0.213979	+	0.0649077i
$721$	35.4833			1.32147
$722$		−	19.0000i		−	0.707107i
$723$	−1.29171	+	1.74166i	−0.0480393	+	0.0647729i
$724$		−	5.47192i		−	0.203362i
$725$	−4.22000			−0.156727
$726$	−1.29834	+	1.75060i	−0.0481860	+	0.0649707i
$727$	14.9666			0.555082			0.277541	−	0.960714i	$-0.410481\pi$
$727$	14.9666			0.555082			0.277541	+	0.960714i	$0.410481\pi$
$728$	10.4107			0.385847
$729$	−20.8708	−	17.1292i	−0.772994	−	0.634414i
$730$		−	2.87523i		−	0.106417i
$731$		−	69.4166i		−	2.56746i
$732$	−9.35414	+	12.6125i	−0.345739	+	0.466171i
$733$	31.4166			1.16040			0.580199	−	0.814475i	$-0.302975\pi$
$733$	31.4166			1.16040			0.580199	+	0.814475i	$0.302975\pi$
$734$	12.5671			0.463862
$735$	−14.4450	+	19.4767i	−0.532813	+	0.718408i
$736$		−	1.43762i		−	0.0529912i
$737$	−54.2101			−1.99685
$738$	1.51669	+	5.00000i	0.0558300	+	0.184053i
$739$			16.0683i			0.591084i	0.955330	+	0.295542i	$0.0955001\pi$
$739$			16.0683i			0.591084i	−0.955330	+	0.295542i	$0.904500\pi$
$740$	12.3815			0.455151
$741$		0			0
$742$		−	28.5426i		−	1.04783i
$743$	36.0781			1.32358			0.661789	−	0.749690i	$-0.269797\pi$
$743$	36.0781			1.32358			0.661789	+	0.749690i	$0.269797\pi$
$744$	−3.91285	−	8.81417i	−0.143452	−	0.323143i
$745$	5.03337			0.184408
$746$			17.4833i			0.640110i
$747$	−14.4570	−	47.6599i	−0.528955	−	1.74379i
$748$	−19.4833			−0.712381
$749$		−	16.8999i		−	0.617508i
$750$	−16.6943	−	12.3815i	−0.609590	−	0.452107i
$751$	−26.7083			−0.974599			−0.487300	−	0.873235i	$-0.662018\pi$
$751$	−26.7083			−0.974599			−0.487300	+	0.873235i	$0.662018\pi$
$752$		−	0.258343i		−	0.00942079i
$753$	30.0958	+	22.3208i	1.09675	+	0.813414i
$754$	−11.7417			−0.427606
$755$	−16.8800			−0.614326
$756$	−6.55013	+	18.3056i	−0.238226	+	0.665769i
$757$		−	13.1931i		−	0.479512i	−0.970833	−	0.239756i	$-0.922933\pi$
$757$		−	13.1931i		−	0.479512i	0.970833	−	0.239756i	$-0.0770674\pi$
$758$			26.9666i			0.979472i
$759$	−7.00238	−	5.19337i	−0.254170	−	0.188507i
$760$		0			0
$761$	−34.6405			−1.25572			−0.627859	−	0.778327i	$-0.716069\pi$
$761$	−34.6405			−1.25572			−0.627859	+	0.778327i	$0.716069\pi$
$762$	19.2250	+	14.2583i	0.696447	+	0.516525i
$763$	−63.4833			−2.29825
$764$		−	8.25834i		−	0.298776i
$765$	−31.9510	+	9.69192i	−1.15519	+	0.350412i
$766$		−	12.3815i		−	0.447360i
$767$	20.8215			0.751819
$768$	1.39119	+	1.03179i	0.0502003	+	0.0372314i
$769$	−35.6749			−1.28647			−0.643235	−	0.765669i	$-0.722408\pi$
$769$	−35.6749			−1.28647			−0.643235	+	0.765669i	$0.722408\pi$
$770$	26.2005			0.944201
$771$	−8.25430	+	11.1295i	−0.297271	+	0.400820i
$772$	−4.00000			−0.143963
$773$	−13.0074			−0.467844			−0.233922	−	0.972255i	$-0.575156\pi$
$773$	−13.0074			−0.467844			−0.233922	+	0.972255i	$0.575156\pi$
$774$	10.8630	+	35.8116i	0.390462	+	1.28722i
$775$	2.74166	−	4.84596i	0.0984832	−	0.174072i
$776$			13.7417i			0.493297i
$777$	23.8999	−	32.2250i	0.857404	−	1.15606i
$778$			18.7579i			0.672502i
$779$		0			0
$780$	−7.74166	−	5.74166i	−0.277196	−	0.205584i
$781$		−	47.2077i		−	1.68922i
$782$		−	8.00000i		−	0.286079i
$783$	7.38751	−	20.6459i	0.264008	−	0.737823i
$784$	7.00000			0.250000
$785$			2.96663i			0.105884i
$786$	−4.84596	−	3.59404i	−0.172850	−	0.128195i
$787$			41.2026i			1.46872i	0.678763	+	0.734358i	$0.262517\pi$
$787$			41.2026i			1.46872i	−0.678763	+	0.734358i	$0.737483\pi$
$788$	18.0391			0.642615
$789$	9.74166	+	7.22497i	0.346812	+	0.257216i
$790$		−	14.0048i		−	0.498267i
$791$			8.44994i			0.300445i
$792$	10.0513	−	3.04894i	0.357158	−	0.108339i
$793$	−25.2250			−0.895765
$794$		−	8.96663i		−	0.318214i
$795$	−15.7417	+	21.2250i	−0.558299	+	0.752772i
$796$			1.43762i			0.0509550i
$797$	3.84860			0.136324			0.0681622	−	0.997674i	$-0.478286\pi$
$797$	3.84860			0.136324			0.0681622	+	0.997674i	$0.478286\pi$
$798$		0			0
$799$		−	1.43762i		−	0.0508592i
$800$			1.00000i			0.0353553i
$801$	8.44000	+	27.8238i	0.298213	+	0.983107i
$802$		−	22.4448i		−	0.792552i
$803$			5.03337i			0.177624i
$804$	21.5403	+	15.9755i	0.759666	+	0.563412i
$805$			10.7581i			0.379174i
$806$	7.62834	−	13.4833i	0.268697	−	0.474930i
$807$	−0.870829	−	0.645857i	−0.0306546	−	0.0227352i
$808$	16.9666			0.596884
$809$	30.3277			1.06626			0.533132	−	0.846032i	$-0.321015\pi$
$809$	30.3277			1.06626			0.533132	+	0.846032i	$0.321015\pi$
$810$	14.9666	−	10.0000i	0.525874	−	0.351364i
$811$	−4.51669			−0.158602			−0.0793011	−	0.996851i	$-0.525269\pi$
$811$	−4.51669			−0.158602			−0.0793011	+	0.996851i	$0.525269\pi$
$812$	−15.7898			−0.554113
$813$	−1.29171	+	1.74166i	−0.0453024	+	0.0610826i
$814$	−21.6749			−0.759705
$815$			1.03337i			0.0361974i
$816$	7.74166	+	5.74166i	0.271012	+	0.200998i
$817$		0			0
$818$	−26.3862			−0.922572
$819$	−29.8874	+	9.06596i	−1.04435	+	0.316790i
$820$	−3.48331			−0.121643
$821$	−26.6648			−0.930607			−0.465303	−	0.885151i	$-0.654055\pi$
$821$	−26.6648			−0.930607			−0.465303	+	0.885151i	$0.654055\pi$
$822$	4.25834	−	5.74166i	0.148527	−	0.200263i
$823$		−	19.1981i		−	0.669205i	−0.942359	−	0.334602i	$-0.891398\pi$
$823$		−	19.1981i		−	0.669205i	0.942359	−	0.334602i	$-0.108602\pi$
$824$			9.48331i			0.330367i
$825$	4.87083	+	3.61249i	0.169580	+	0.125771i
$826$	28.0000			0.974245
$827$	14.6307			0.508760			0.254380	−	0.967104i	$-0.418129\pi$
$827$	14.6307			0.508760			0.254380	+	0.967104i	$0.418129\pi$
$828$	1.25192	+	4.12715i	0.0435071	+	0.143428i
$829$			0.278548i			0.00967438i	0.999988	+	0.00483719i	$0.00153973\pi$
$829$			0.278548i			0.00967438i	−0.999988	+	0.00483719i	$0.998460\pi$
$830$	33.2029			1.15249
$831$	−20.0958	+	27.0958i	−0.697116	+	0.939943i
$832$			2.78238i			0.0964618i
$833$	38.9534			1.34965
$834$	28.0958	+	20.8375i	0.972878	+	0.721542i
$835$			8.62570i			0.298505i
$836$		0			0
$837$	18.9088	+	21.8966i	0.653582	+	0.756856i
$838$	−24.0000			−0.829066
$839$		−	21.6749i		−	0.748301i	−0.927368	−	0.374151i	$-0.877934\pi$
$839$		−	21.6749i		−	0.748301i	0.927368	−	0.374151i	$-0.122066\pi$
$840$	−10.4107	−	7.72119i	−0.359204	−	0.266406i
$841$	−11.1916			−0.385917
$842$		−	1.48331i		−	0.0511184i
$843$	17.5060	−	23.6038i	0.602937	−	0.812959i
$844$	−18.9666			−0.652858
$845$			10.5167i			0.361785i
$846$	0.224972	+	0.741657i	0.00773470	+	0.0254987i
$847$	−4.70829			−0.161779
$848$	7.62834			0.261958
$849$	0.718808	+	0.533109i	0.0246694	+	0.0182963i
$850$			5.56477i			0.190870i
$851$		−	8.89989i		−	0.305084i
$852$	−13.9119	+	18.7579i	−0.476614	+	0.642634i
$853$	17.4833			0.598617			0.299309	−	0.954156i	$-0.403244\pi$
$853$	17.4833			0.598617			0.299309	+	0.954156i	$0.403244\pi$
$854$	−33.9217			−1.16078
$855$		0			0
$856$	4.51669			0.154377
$857$		−	42.0000i		−	1.43469i	−0.696717	−	0.717346i	$-0.745357\pi$
$857$		−	42.0000i		−	1.43469i	0.696717	−	0.717346i	$-0.254643\pi$
$858$	13.5525	+	10.0513i	0.462675	+	0.343146i
$859$		−	23.7895i		−	0.811688i	−0.913942	−	0.405844i	$-0.866978\pi$
$859$		−	23.7895i		−	0.811688i	0.913942	−	0.405844i	$-0.133022\pi$
$860$	−24.9486			−0.850740
$861$	−6.72384	+	9.06596i	−0.229148	+	0.308967i
$862$	−1.29171			−0.0439959
$863$	7.00238			0.238364			0.119182	−	0.992872i	$-0.461973\pi$
$863$	7.00238			0.238364			0.119182	+	0.992872i	$0.461973\pi$
$864$	−4.89238	−	1.75060i	−0.166442	−	0.0595565i
$865$	34.9666			1.18890
$866$	−2.68953			−0.0913941
$867$	19.4303	+	14.4106i	0.659886	+	0.489409i
$868$	10.2583	−	18.1319i	0.348191	−	0.615437i
$869$			24.5167i			0.831672i
$870$	11.7417	+	8.70829i	0.398079	+	0.295239i
$871$			43.0805i			1.45973i
$872$		−	16.9666i		−	0.574563i
$873$	−11.9666	−	39.4499i	−0.405009	−	1.33518i
$874$		0			0
$875$		−	44.8999i		−	1.51789i
$876$	1.48331	−	2.00000i	0.0501166	−	0.0675737i
$877$	−25.4833			−0.860510			−0.430255	−	0.902707i	$-0.641576\pi$
$877$	−25.4833			−0.860510			−0.430255	+	0.902707i	$0.641576\pi$
$878$			4.77503i			0.161149i
$879$	−30.4205	+	41.0169i	−1.02606	+	1.38347i
$880$			7.00238i			0.236050i
$881$	48.8310			1.64516			0.822579	−	0.568651i	$-0.192535\pi$
$881$	48.8310			1.64516			0.822579	+	0.568651i	$0.192535\pi$
$882$	−20.0958	+	6.09580i	−0.676661	+	0.205256i
$883$			0.811658i			0.0273145i	0.999907	+	0.0136572i	$0.00434737\pi$
$883$			0.811658i			0.0273145i	−0.999907	+	0.0136572i	$0.995653\pi$
$884$			15.4833i			0.520760i
$885$	−20.8215	−	15.4424i	−0.699905	−	0.519090i
$886$	0.516685			0.0173584
$887$			23.2250i			0.779818i	0.920853	+	0.389909i	$0.127494\pi$
$887$			23.2250i			0.779818i	−0.920853	+	0.389909i	$0.872506\pi$
$888$	8.61249	+	6.38751i	0.289016	+	0.214351i
$889$			51.7062i			1.73417i
$890$	−19.3838			−0.649748
$891$	−26.2005	+	17.5060i	−0.877750	+	0.586472i
$892$		−	19.5695i		−	0.655236i
$893$		0			0
$894$	3.50119	+	2.59668i	0.117097	+	0.0868461i
$895$			10.9438i			0.365812i
$896$			3.74166i			0.125000i
$897$	−4.12715	+	5.56477i	−0.137802	+	0.185802i
$898$		−	1.25192i		−	0.0417770i
$899$	−11.5698	+	20.4499i	−0.385874	+	0.682044i
$900$	−0.870829	−	2.87083i	−0.0290276	−	0.0956943i
$901$	42.4499			1.41421
$902$	6.09788			0.203037
$903$	−48.1582	+	64.9333i	−1.60261	+	2.16084i
$904$	−2.25834			−0.0751114
$905$	−10.9438			−0.363785
$906$	−11.7417	−	8.70829i	−0.390090	−	0.289313i
$907$	−1.55006			−0.0514688			−0.0257344	−	0.999669i	$-0.508192\pi$
$907$	−1.55006			−0.0514688			−0.0257344	+	0.999669i	$0.508192\pi$
$908$		−	14.9666i		−	0.496685i
$909$	−48.7083	+	14.7750i	−1.61555	+	0.490057i
$910$		−	20.8215i		−	0.690224i
$911$	34.4548			1.14154			0.570770	−	0.821110i	$-0.306645\pi$
$911$	34.4548			1.14154			0.570770	+	0.821110i	$0.306645\pi$
$912$		0			0
$913$	−58.1249			−1.92365
$914$	33.2029			1.09825
$915$	25.2250	+	18.7083i	0.833912	+	0.618477i
$916$			2.06358i			0.0681824i
$917$		−	13.0334i		−	0.430400i
$918$	−27.2250	−	9.74166i	−0.898558	−	0.321523i
$919$	−40.0000			−1.31948			−0.659739	−	0.751495i	$-0.729333\pi$
$919$	−40.0000			−1.31948			−0.659739	+	0.751495i	$0.729333\pi$
$920$	−2.87523			−0.0947936
$921$	−26.3862	−	19.5695i	−0.869455	−	0.644838i
$922$			21.6331i			0.712448i
$923$	−37.5158			−1.23485
$924$	18.2250	+	13.5167i	0.599558	+	0.444666i
$925$			6.19073i			0.203550i
$926$	5.75047			0.188972
$927$	−8.25834	−	27.2250i	−0.271240	−	0.894185i
$928$		−	4.22000i		−	0.138528i
$929$	56.8996			1.86681			0.933407	−	0.358818i	$-0.116820\pi$
$929$	56.8996			1.86681			0.933407	+	0.358818i	$0.116820\pi$
$930$	−17.6283	+	7.82570i	−0.578056	+	0.256615i
$931$		0			0
$932$			9.22497i			0.302174i
$933$	7.18808	−	9.69192i	0.235327	−	0.317299i
$934$	−38.4499			−1.25812
$935$			38.9666i			1.27435i
$936$	−2.42298	−	7.98775i	−0.0791976	−	0.261088i
$937$	14.9666			0.488938			0.244469	−	0.969657i	$-0.421386\pi$
$937$	14.9666			0.488938			0.244469	+	0.969657i	$0.421386\pi$
$938$			57.9333i			1.89159i
$939$	−0.191602	+	0.258343i	−0.00625269	+	0.00843069i
$940$	−0.516685			−0.0168524
$941$	41.0169			1.33711			0.668557	−	0.743661i	$-0.266912\pi$
$941$	41.0169			1.33711			0.668557	+	0.743661i	$0.266912\pi$
$942$	−1.53047	+	2.06358i	−0.0498653	+	0.0672349i
$943$			2.50384i			0.0815361i
$944$			7.48331i			0.243561i
$945$	36.6112	+	13.1003i	1.19096	+	0.426151i
$946$	43.6749			1.41999
$947$	44.7967			1.45570			0.727848	−	0.685738i	$-0.240520\pi$
$947$	44.7967			1.45570			0.727848	+	0.685738i	$0.240520\pi$
$948$	7.22497	−	9.74166i	0.234656	−	0.316394i
$949$	4.00000			0.129845
$950$		0			0
$951$	26.2934	−	35.4522i	0.852621	−	1.14962i
$952$			20.8215i			0.674827i
$953$	−29.2615			−0.947871			−0.473936	−	0.880559i	$-0.657167\pi$
$953$	−29.2615			−0.947871			−0.473936	+	0.880559i	$0.657167\pi$
$954$	−21.8997	+	6.64298i	−0.709028	+	0.215074i
$955$	−16.5167			−0.534467
$956$	18.1319			0.586428
$957$	−20.5549	−	15.2447i	−0.664445	−	0.492791i
$958$	−37.9333			−1.22557
$959$	15.4424			0.498661
$960$	2.06358	−	2.78238i	0.0666016	−	0.0898010i
$961$	−15.9666	−	26.5719i	−0.515053	−	0.857159i
$962$			17.2250i			0.555355i
$963$	−12.9666	+	3.93326i	−0.417844	+	0.126748i
$964$		−	1.25192i		−	0.0403216i
$965$			8.00000i			0.257529i
$966$	−5.55006	+	7.48331i	−0.178570	+	0.240772i
$967$		−	30.6991i		−	0.987215i	−0.869685	−	0.493608i	$-0.835678\pi$
$967$		−	30.6991i		−	0.987215i	0.869685	−	0.493608i	$-0.164322\pi$
$968$		−	1.25834i		−	0.0404447i
$969$		0			0
$970$	27.4833			0.882436
$971$		−	50.4499i		−	1.61902i	−0.587109	−	0.809508i	$-0.699734\pi$
$971$		−	50.4499i		−	1.61902i	0.587109	−	0.809508i	$-0.300266\pi$
$972$	15.5697	+	0.765233i	0.499397	+	0.0245449i
$973$			75.5646i			2.42249i
$974$	−5.56477			−0.178307
$975$	2.87083	−	3.87083i	0.0919401	−	0.123966i
$976$		−	9.06596i		−	0.290194i
$977$			34.9666i			1.11868i	0.828938	+	0.559341i	$0.188946\pi$
$977$			34.9666i			1.11868i	−0.828938	+	0.559341i	$0.811054\pi$
$978$	−0.533109	+	0.718808i	−0.0170470	+	0.0229850i
$979$	33.9333			1.08451
$980$		−	14.0000i		−	0.447214i
$981$	14.7750	+	48.7083i	0.471730	+	1.55514i
$982$		−	11.0367i		−	0.352195i
$983$	−31.7653			−1.01316			−0.506578	−	0.862194i	$-0.669090\pi$
$983$	−31.7653			−1.01316			−0.506578	+	0.862194i	$0.669090\pi$
$984$	−2.42298	−	1.79702i	−0.0772418	−	0.0572869i
$985$		−	36.0781i		−	1.14954i
$986$		−	23.4833i		−	0.747861i
$987$	−0.997356	+	1.34477i	−0.0317462	+	0.0428044i
$988$		0			0
$989$			17.9333i			0.570244i
$990$	−6.09788	−	20.1026i	−0.193803	−	0.638904i
$991$		−	16.8800i		−	0.536211i	−0.963390	−	0.268105i	$-0.913602\pi$
$991$		−	16.8800i		−	0.536211i	0.963390	−	0.268105i	$-0.0863976\pi$
$992$	4.84596	+	2.74166i	0.153859	+	0.0870477i
$993$	10.6459	−	14.3541i	0.337836	−	0.455515i
$994$	−50.4499			−1.60018
$995$	2.87523			0.0911510
$996$	23.0958	+	17.1292i	0.731818	+	0.542759i
$997$	−2.00000			−0.0633406			−0.0316703	−	0.999498i	$-0.510083\pi$
$997$	−2.00000			−0.0633406			−0.0316703	+	0.999498i	$0.510083\pi$
$998$	4.40570			0.139460
$999$	−30.2874	−	10.8375i	−0.958251	−	0.342882i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	186.2.c.b.185.8	yes	8
3.2	odd	2	inner	186.2.c.b.185.1	✓	8
4.3	odd	2		1488.2.h.c.929.1		8
12.11	even	2		1488.2.h.c.929.7		8
31.30	odd	2	inner	186.2.c.b.185.5	yes	8
93.92	even	2	inner	186.2.c.b.185.4	yes	8
124.123	even	2		1488.2.h.c.929.8		8
372.371	odd	2		1488.2.h.c.929.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
186.2.c.b.185.1	✓	8	3.2	odd	2	inner
186.2.c.b.185.4	yes	8	93.92	even	2	inner
186.2.c.b.185.5	yes	8	31.30	odd	2	inner
186.2.c.b.185.8	yes	8	1.1	even	1	trivial
1488.2.h.c.929.1		8	4.3	odd	2
1488.2.h.c.929.2		8	372.371	odd	2
1488.2.h.c.929.7		8	12.11	even	2
1488.2.h.c.929.8		8	124.123	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 186 = 2 \cdot 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	186.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(1.39119 + 1.03179i) q^{3} -1.00000 q^{4} +2.00000i q^{5} +(-1.03179 + 1.39119i) q^{6} -3.74166 q^{7} -1.00000i q^{8} +(0.870829 + 2.87083i) q^{9} -2.00000 q^{10} +3.50119 q^{11} +(-1.39119 - 1.03179i) q^{12} -2.78238i q^{13} -3.74166i q^{14} +(-2.06358 + 2.78238i) q^{15} +1.00000 q^{16} +5.56477 q^{17} +(-2.87083 + 0.870829i) q^{18} -2.00000i q^{20} +(-5.20536 - 3.86060i) q^{21} +3.50119i q^{22} -1.43762 q^{23} +(1.03179 - 1.39119i) q^{24} +1.00000 q^{25} +2.78238 q^{26} +(-1.75060 + 4.89238i) q^{27} +3.74166 q^{28} -4.22000 q^{29} +(-2.78238 - 2.06358i) q^{30} +(2.74166 - 4.84596i) q^{31} +1.00000i q^{32} +(4.87083 + 3.61249i) q^{33} +5.56477i q^{34} -7.48331i q^{35} +(-0.870829 - 2.87083i) q^{36} +6.19073i q^{37} +(2.87083 - 3.87083i) q^{39} +2.00000 q^{40} -1.74166i q^{41} +(3.86060 - 5.20536i) q^{42} -12.4743i q^{43} -3.50119 q^{44} +(-5.74166 + 1.74166i) q^{45} -1.43762i q^{46} -0.258343i q^{47} +(1.39119 + 1.03179i) q^{48} +7.00000 q^{49} +1.00000i q^{50} +(7.74166 + 5.74166i) q^{51} +2.78238i q^{52} +7.62834 q^{53} +(-4.89238 - 1.75060i) q^{54} +7.00238i q^{55} +3.74166i q^{56} -4.22000i q^{58} +7.48331i q^{59} +(2.06358 - 2.78238i) q^{60} -9.06596i q^{61} +(4.84596 + 2.74166i) q^{62} +(-3.25834 - 10.7417i) q^{63} -1.00000 q^{64} +5.56477 q^{65} +(-3.61249 + 4.87083i) q^{66} -15.4833 q^{67} -5.56477 q^{68} +(-2.00000 - 1.48331i) q^{69} +7.48331 q^{70} -13.4833i q^{71} +(2.87083 - 0.870829i) q^{72} +1.43762i q^{73} -6.19073 q^{74} +(1.39119 + 1.03179i) q^{75} -13.1003 q^{77} +(3.87083 + 2.87083i) q^{78} +7.00238i q^{79} +2.00000i q^{80} +(-7.48331 + 5.00000i) q^{81} +1.74166 q^{82} -16.6015 q^{83} +(5.20536 + 3.86060i) q^{84} +11.1295i q^{85} +12.4743 q^{86} +(-5.87083 - 4.35414i) q^{87} -3.50119i q^{88} +9.69192 q^{89} +(-1.74166 - 5.74166i) q^{90} +10.4107i q^{91} +1.43762 q^{92} +(8.81417 - 3.91285i) q^{93} +0.258343 q^{94} +(-1.03179 + 1.39119i) q^{96} -13.7417 q^{97} +7.00000i q^{98} +(3.04894 + 10.0513i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} - 8 q^{9} - 16 q^{10} + 8 q^{16} - 8 q^{18} + 8 q^{25} - 8 q^{31} + 24 q^{33} + 8 q^{36} + 8 q^{39} + 16 q^{40} - 16 q^{45} + 56 q^{49} + 32 q^{51} - 56 q^{63} - 8 q^{64} + 16 q^{66} - 64 q^{67}+ \cdots - 80 q^{97}+O(q^{100}) \) 8 * q - 8 * q^4 - 8 * q^9 - 16 * q^10 + 8 * q^16 - 8 * q^18 + 8 * q^25 - 8 * q^31 + 24 * q^33 + 8 * q^36 + 8 * q^39 + 16 * q^40 - 16 * q^45 + 56 * q^49 + 32 * q^51 - 56 * q^63 - 8 * q^64 + 16 * q^66 - 64 * q^67 - 16 * q^69 + 8 * q^72 + 16 * q^78 - 16 * q^82 - 32 * q^87 + 16 * q^90 + 40 * q^93 + 32 * q^94 - 80 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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