LMFDB - Embedded newform 195.2.bb.a.166.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [195,2,Mod(121,195)] 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("195.121"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(195, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 195 = 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	195.bb (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$1.55708283941$
Analytic rank:	$1$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			166.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	195.166
Dual form			195.2.bb.a.121.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.36603 + 1.36603i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(2.73205 - 4.73205i) q^{4} -1.00000i q^{5} +(2.36603 + 1.36603i) q^{6} +(-2.13397 - 1.23205i) q^{7} +9.46410i q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.36603 + 2.36603i) q^{10} +(-3.00000 + 1.73205i) q^{11} -5.46410 q^{12} +(-0.866025 + 3.50000i) q^{13} +6.73205 q^{14} +(-0.866025 + 0.500000i) q^{15} +(-7.46410 - 12.9282i) q^{16} +(-1.63397 + 2.83013i) q^{17} -2.73205i q^{18} +(-1.26795 - 0.732051i) q^{19} +(-4.73205 - 2.73205i) q^{20} +2.46410i q^{21} +(4.73205 - 8.19615i) q^{22} +(-3.73205 - 6.46410i) q^{23} +(8.19615 - 4.73205i) q^{24} -1.00000 q^{25} +(-2.73205 - 9.46410i) q^{26} +1.00000 q^{27} +(-11.6603 + 6.73205i) q^{28} +(-0.366025 - 0.633975i) q^{29} +(1.36603 - 2.36603i) q^{30} +7.19615i q^{31} +(18.9282 + 10.9282i) q^{32} +(3.00000 + 1.73205i) q^{33} -8.92820i q^{34} +(-1.23205 + 2.13397i) q^{35} +(2.73205 + 4.73205i) q^{36} +(-3.46410 + 2.00000i) q^{37} +4.00000 q^{38} +(3.46410 - 1.00000i) q^{39} +9.46410 q^{40} +(-7.56218 + 4.36603i) q^{41} +(-3.36603 - 5.83013i) q^{42} +(-1.86603 + 3.23205i) q^{43} +18.9282i q^{44} +(0.866025 + 0.500000i) q^{45} +(17.6603 + 10.1962i) q^{46} -10.1962i q^{47} +(-7.46410 + 12.9282i) q^{48} +(-0.464102 - 0.803848i) q^{49} +(2.36603 - 1.36603i) q^{50} +3.26795 q^{51} +(14.1962 + 13.6603i) q^{52} +6.92820 q^{53} +(-2.36603 + 1.36603i) q^{54} +(1.73205 + 3.00000i) q^{55} +(11.6603 - 20.1962i) q^{56} +1.46410i q^{57} +(1.73205 + 1.00000i) q^{58} +(-9.29423 - 5.36603i) q^{59} +5.46410i q^{60} +(1.23205 - 2.13397i) q^{61} +(-9.83013 - 17.0263i) q^{62} +(2.13397 - 1.23205i) q^{63} -29.8564 q^{64} +(3.50000 + 0.866025i) q^{65} -9.46410 q^{66} +(4.79423 - 2.76795i) q^{67} +(8.92820 + 15.4641i) q^{68} +(-3.73205 + 6.46410i) q^{69} -6.73205i q^{70} +(8.02628 + 4.63397i) q^{71} +(-8.19615 - 4.73205i) q^{72} -5.39230i q^{73} +(5.46410 - 9.46410i) q^{74} +(0.500000 + 0.866025i) q^{75} +(-6.92820 + 4.00000i) q^{76} +8.53590 q^{77} +(-6.83013 + 7.09808i) q^{78} -11.9282 q^{79} +(-12.9282 + 7.46410i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(11.9282 - 20.6603i) q^{82} -9.46410i q^{83} +(11.6603 + 6.73205i) q^{84} +(2.83013 + 1.63397i) q^{85} -10.1962i q^{86} +(-0.366025 + 0.633975i) q^{87} +(-16.3923 - 28.3923i) q^{88} +(4.09808 - 2.36603i) q^{89} -2.73205 q^{90} +(6.16025 - 6.40192i) q^{91} -40.7846 q^{92} +(6.23205 - 3.59808i) q^{93} +(13.9282 + 24.1244i) q^{94} +(-0.732051 + 1.26795i) q^{95} -21.8564i q^{96} +(8.25833 + 4.76795i) q^{97} +(2.19615 + 1.26795i) q^{98} -3.46410i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{2} - 2 q^{3} + 4 q^{4} + 6 q^{6} - 12 q^{7} - 2 q^{9} + 2 q^{10} - 12 q^{11} - 8 q^{12} + 20 q^{14} - 16 q^{16} - 10 q^{17} - 12 q^{19} - 12 q^{20} + 12 q^{22} - 8 q^{23} + 12 q^{24} - 4 q^{25}+ \cdots - 12 q^{98}+O(q^{100}) $ 4 * q - 6 * q^2 - 2 * q^3 + 4 * q^4 + 6 * q^6 - 12 * q^7 - 2 * q^9 + 2 * q^10 - 12 * q^11 - 8 * q^12 + 20 * q^14 - 16 * q^16 - 10 * q^17 - 12 * q^19 - 12 * q^20 + 12 * q^22 - 8 * q^23 + 12 * q^24 - 4 * q^25 - 4 * q^26 + 4 * q^27 - 12 * q^28 + 2 * q^29 + 2 * q^30 + 48 * q^32 + 12 * q^33 + 2 * q^35 + 4 * q^36 + 16 * q^38 + 24 * q^40 - 6 * q^41 - 10 * q^42 - 4 * q^43 + 36 * q^46 - 16 * q^48 + 12 * q^49 + 6 * q^50 + 20 * q^51 + 36 * q^52 - 6 * q^54 + 12 * q^56 - 6 * q^59 - 2 * q^61 - 22 * q^62 + 12 * q^63 - 64 * q^64 + 14 * q^65 - 24 * q^66 - 12 * q^67 + 8 * q^68 - 8 * q^69 - 6 * q^71 - 12 * q^72 + 8 * q^74 + 2 * q^75 + 48 * q^77 - 10 * q^78 - 20 * q^79 - 24 * q^80 - 2 * q^81 + 20 * q^82 + 12 * q^84 - 6 * q^85 + 2 * q^87 - 24 * q^88 + 6 * q^89 - 4 * q^90 - 10 * q^91 - 80 * q^92 + 18 * q^93 + 28 * q^94 + 4 * q^95 - 12 * q^97 - 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/195\mathbb{Z}\right)^\times$.

$n$	$106$	$131$	$157$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−2.36603	+	1.36603i	−1.67303	+	0.965926i	−0.707107	+	0.707107i	$0.750000\pi$
$2$	−2.36603	+	1.36603i	−1.67303	+	0.965926i	−0.965926	+	0.258819i	$0.916667\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	2.73205	−	4.73205i	1.36603	−	2.36603i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	2.36603	+	1.36603i	0.965926	+	0.557678i
$7$	−2.13397	−	1.23205i	−0.806567	−	0.465671i	0.0391956	−	0.999232i	$-0.487520\pi$
$7$	−2.13397	−	1.23205i	−0.806567	−	0.465671i	−0.845762	+	0.533560i	$0.820854\pi$
$8$			9.46410i			3.34607i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.36603	+	2.36603i	0.431975	+	0.748203i
$11$	−3.00000	+	1.73205i	−0.904534	+	0.522233i	−0.878668	−	0.477432i	$-0.841568\pi$
$11$	−3.00000	+	1.73205i	−0.904534	+	0.522233i	−0.0258656	+	0.999665i	$0.508234\pi$
$12$	−5.46410			−1.57735
$13$	−0.866025	+	3.50000i	−0.240192	+	0.970725i
$13$	−0.866025	+	3.50000i	−0.240192	+	0.970725i
$14$	6.73205			1.79922
$15$	−0.866025	+	0.500000i	−0.223607	+	0.129099i
$16$	−7.46410	−	12.9282i	−1.86603	−	3.23205i
$17$	−1.63397	+	2.83013i	−0.396297	+	0.686407i	−0.993266	−	0.115858i	$-0.963038\pi$
$17$	−1.63397	+	2.83013i	−0.396297	+	0.686407i	0.596969	+	0.802264i	$0.296372\pi$
$18$		−	2.73205i		−	0.643951i
$19$	−1.26795	−	0.732051i	−0.290887	−	0.167944i	0.347455	−	0.937697i	$-0.387046\pi$
$19$	−1.26795	−	0.732051i	−0.290887	−	0.167944i	−0.638342	+	0.769753i	$0.720379\pi$
$20$	−4.73205	−	2.73205i	−1.05812	−	0.610905i
$21$			2.46410i			0.537711i
$22$	4.73205	−	8.19615i	1.00888	−	1.74743i
$23$	−3.73205	−	6.46410i	−0.778186	−	1.34786i	−0.932986	−	0.359912i	$-0.882807\pi$
$23$	−3.73205	−	6.46410i	−0.778186	−	1.34786i	0.154800	−	0.987946i	$-0.450527\pi$
$24$	8.19615	−	4.73205i	1.67303	−	0.965926i
$25$	−1.00000			−0.200000
$26$	−2.73205	−	9.46410i	−0.535799	−	1.85606i
$27$	1.00000			0.192450
$28$	−11.6603	+	6.73205i	−2.20358	+	1.27224i
$29$	−0.366025	−	0.633975i	−0.0679692	−	0.117726i	0.830038	−	0.557707i	$-0.188319\pi$
$29$	−0.366025	−	0.633975i	−0.0679692	−	0.117726i	−0.898007	+	0.439981i	$0.854985\pi$
$30$	1.36603	−	2.36603i	0.249401	−	0.431975i
$31$			7.19615i			1.29247i	0.763140	+	0.646234i	$0.223657\pi$
$31$			7.19615i			1.29247i	−0.763140	+	0.646234i	$0.776343\pi$
$32$	18.9282	+	10.9282i	3.34607	+	1.93185i
$33$	3.00000	+	1.73205i	0.522233	+	0.301511i
$34$		−	8.92820i		−	1.53117i
$35$	−1.23205	+	2.13397i	−0.208255	+	0.360708i
$36$	2.73205	+	4.73205i	0.455342	+	0.788675i
$37$	−3.46410	+	2.00000i	−0.569495	+	0.328798i	−0.756948	−	0.653476i	$-0.773310\pi$
$37$	−3.46410	+	2.00000i	−0.569495	+	0.328798i	0.187453	+	0.982274i	$0.439977\pi$
$38$	4.00000			0.648886
$39$	3.46410	−	1.00000i	0.554700	−	0.160128i
$40$	9.46410			1.49641
$41$	−7.56218	+	4.36603i	−1.18101	+	0.681859i	−0.956249	−	0.292554i	$-0.905495\pi$
$41$	−7.56218	+	4.36603i	−1.18101	+	0.681859i	−0.224765	+	0.974413i	$0.572161\pi$
$42$	−3.36603	−	5.83013i	−0.519389	−	0.899608i
$43$	−1.86603	+	3.23205i	−0.284566	+	0.492883i	−0.972504	−	0.232887i	$-0.925183\pi$
$43$	−1.86603	+	3.23205i	−0.284566	+	0.492883i	0.687938	+	0.725770i	$0.258516\pi$
$44$			18.9282i			2.85353i
$45$	0.866025	+	0.500000i	0.129099	+	0.0745356i
$46$	17.6603	+	10.1962i	2.60386	+	1.50334i
$47$		−	10.1962i		−	1.48726i	−0.668590	−	0.743631i	$-0.733102\pi$
$47$		−	10.1962i		−	1.48726i	0.668590	−	0.743631i	$-0.266898\pi$
$48$	−7.46410	+	12.9282i	−1.07735	+	1.86603i
$49$	−0.464102	−	0.803848i	−0.0663002	−	0.114835i
$50$	2.36603	−	1.36603i	0.334607	−	0.193185i
$51$	3.26795			0.457604
$52$	14.1962	+	13.6603i	1.96865	+	1.89434i
$53$	6.92820			0.951662			0.475831	−	0.879537i	$-0.342147\pi$
$53$	6.92820			0.951662			0.475831	+	0.879537i	$0.342147\pi$
$54$	−2.36603	+	1.36603i	−0.321975	+	0.185893i
$55$	1.73205	+	3.00000i	0.233550	+	0.404520i
$56$	11.6603	−	20.1962i	1.55817	−	2.69882i
$57$			1.46410i			0.193925i
$58$	1.73205	+	1.00000i	0.227429	+	0.131306i
$59$	−9.29423	−	5.36603i	−1.21001	−	0.698597i	−0.247245	−	0.968953i	$-0.579525\pi$
$59$	−9.29423	−	5.36603i	−1.21001	−	0.698597i	−0.962760	+	0.270356i	$0.912859\pi$
$60$			5.46410i			0.705412i
$61$	1.23205	−	2.13397i	0.157748	−	0.273227i	−0.776308	−	0.630353i	$-0.782910\pi$
$61$	1.23205	−	2.13397i	0.157748	−	0.273227i	0.934056	+	0.357126i	$0.116243\pi$
$62$	−9.83013	−	17.0263i	−1.24843	−	2.16234i
$63$	2.13397	−	1.23205i	0.268856	−	0.155224i
$64$	−29.8564			−3.73205
$65$	3.50000	+	0.866025i	0.434122	+	0.107417i
$66$	−9.46410			−1.16495
$67$	4.79423	−	2.76795i	0.585708	−	0.338159i	−0.177690	−	0.984086i	$-0.556863\pi$
$67$	4.79423	−	2.76795i	0.585708	−	0.338159i	0.763399	+	0.645928i	$0.223529\pi$
$68$	8.92820	+	15.4641i	1.08270	+	1.87530i
$69$	−3.73205	+	6.46410i	−0.449286	+	0.778186i
$70$		−	6.73205i		−	0.804634i
$71$	8.02628	+	4.63397i	0.952544	+	0.549952i	0.893870	−	0.448326i	$-0.147979\pi$
$71$	8.02628	+	4.63397i	0.952544	+	0.549952i	0.0586738	+	0.998277i	$0.481313\pi$
$72$	−8.19615	−	4.73205i	−0.965926	−	0.557678i
$73$		−	5.39230i		−	0.631122i	−0.948905	−	0.315561i	$-0.897807\pi$
$73$		−	5.39230i		−	0.631122i	0.948905	−	0.315561i	$-0.102193\pi$
$74$	5.46410	−	9.46410i	0.635189	−	1.10018i
$75$	0.500000	+	0.866025i	0.0577350	+	0.100000i
$76$	−6.92820	+	4.00000i	−0.794719	+	0.458831i
$77$	8.53590			0.972756
$78$	−6.83013	+	7.09808i	−0.773360	+	0.803699i
$79$	−11.9282			−1.34203			−0.671014	−	0.741445i	$-0.734141\pi$
$79$	−11.9282			−1.34203			−0.671014	+	0.741445i	$0.734141\pi$
$80$	−12.9282	+	7.46410i	−1.44542	+	0.834512i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	11.9282	−	20.6603i	1.31725	−	2.28154i
$83$		−	9.46410i		−	1.03882i	−0.854525	−	0.519410i	$-0.826152\pi$
$83$		−	9.46410i		−	1.03882i	0.854525	−	0.519410i	$-0.173848\pi$
$84$	11.6603	+	6.73205i	1.27224	+	0.734527i
$85$	2.83013	+	1.63397i	0.306970	+	0.177229i
$86$		−	10.1962i		−	1.09948i
$87$	−0.366025	+	0.633975i	−0.0392420	+	0.0679692i
$88$	−16.3923	−	28.3923i	−1.74743	−	3.02663i
$89$	4.09808	−	2.36603i	0.434395	−	0.250798i	−0.266822	−	0.963746i	$-0.585974\pi$
$89$	4.09808	−	2.36603i	0.434395	−	0.250798i	0.701217	+	0.712948i	$0.252640\pi$
$90$	−2.73205			−0.287983
$91$	6.16025	−	6.40192i	0.645770	−	0.671104i
$92$	−40.7846			−4.25209
$93$	6.23205	−	3.59808i	0.646234	−	0.373103i
$94$	13.9282	+	24.1244i	1.43658	+	2.48824i
$95$	−0.732051	+	1.26795i	−0.0751068	+	0.130089i
$96$		−	21.8564i		−	2.23071i
$97$	8.25833	+	4.76795i	0.838506	+	0.484112i	0.856756	−	0.515722i	$-0.172476\pi$
$97$	8.25833	+	4.76795i	0.838506	+	0.484112i	−0.0182499	+	0.999833i	$0.505809\pi$
$98$	2.19615	+	1.26795i	0.221845	+	0.128082i
$99$		−	3.46410i		−	0.348155i
$100$	−2.73205	+	4.73205i	−0.273205	+	0.473205i
$101$	4.46410	+	7.73205i	0.444195	+	0.769368i	0.997996	−	0.0632812i	$-0.0201565\pi$
$101$	4.46410	+	7.73205i	0.444195	+	0.769368i	−0.553801	+	0.832649i	$0.686823\pi$
$102$	−7.73205	+	4.46410i	−0.765587	+	0.442012i
$103$	−7.19615			−0.709058			−0.354529	−	0.935045i	$-0.615359\pi$
$103$	−7.19615			−0.709058			−0.354529	+	0.935045i	$0.615359\pi$
$104$	−33.1244	−	8.19615i	−3.24811	−	0.803699i
$105$	2.46410			0.240472
$106$	−16.3923	+	9.46410i	−1.59216	+	0.919235i
$107$	3.56218	+	6.16987i	0.344369	+	0.596464i	0.985239	−	0.171185i	$-0.0547596\pi$
$107$	3.56218	+	6.16987i	0.344369	+	0.596464i	−0.640870	+	0.767649i	$0.721426\pi$
$108$	2.73205	−	4.73205i	0.262892	−	0.455342i
$109$		−	11.7321i		−	1.12373i	−0.827230	−	0.561863i	$-0.810085\pi$
$109$		−	11.7321i		−	1.12373i	0.827230	−	0.561863i	$-0.189915\pi$
$110$	−8.19615	−	4.73205i	−0.781472	−	0.451183i
$111$	3.46410	+	2.00000i	0.328798	+	0.189832i
$112$			36.7846i			3.47582i
$113$	−6.26795	+	10.8564i	−0.589639	+	1.02128i	0.404640	+	0.914476i	$0.367397\pi$
$113$	−6.26795	+	10.8564i	−0.589639	+	1.02128i	−0.994280	+	0.106809i	$0.965937\pi$
$114$	−2.00000	−	3.46410i	−0.187317	−	0.324443i
$115$	−6.46410	+	3.73205i	−0.602781	+	0.348016i
$116$	−4.00000			−0.371391
$117$	−2.59808	−	2.50000i	−0.240192	−	0.231125i
$118$	29.3205			2.69917
$119$	6.97372	−	4.02628i	0.639280	−	0.369088i
$120$	−4.73205	−	8.19615i	−0.431975	−	0.748203i
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$			6.73205i			0.609491i
$123$	7.56218	+	4.36603i	0.681859	+	0.393671i
$124$	34.0526	+	19.6603i	3.05801	+	1.76554i
$125$			1.00000i			0.0894427i
$126$	−3.36603	+	5.83013i	−0.299869	+	0.519389i
$127$	−1.33013	−	2.30385i	−0.118030	−	0.204433i	0.800957	−	0.598722i	$-0.204324\pi$
$127$	−1.33013	−	2.30385i	−0.118030	−	0.204433i	−0.918987	+	0.394288i	$0.870991\pi$
$128$	32.7846	−	18.9282i	2.89778	−	1.67303i
$129$	3.73205			0.328589
$130$	−9.46410	+	2.73205i	−0.830057	+	0.239617i
$131$	4.73205			0.413441			0.206721	−	0.978400i	$-0.433721\pi$
$131$	4.73205			0.413441			0.206721	+	0.978400i	$0.433721\pi$
$132$	16.3923	−	9.46410i	1.42677	−	0.823744i
$133$	1.80385	+	3.12436i	0.156413	+	0.270916i
$134$	−7.56218	+	13.0981i	−0.653273	+	1.13150i
$135$		−	1.00000i		−	0.0860663i
$136$	−26.7846	−	15.4641i	−2.29676	−	1.32604i
$137$	−13.0981	−	7.56218i	−1.11904	−	0.646080i	−0.177887	−	0.984051i	$-0.556926\pi$
$137$	−13.0981	−	7.56218i	−1.11904	−	0.646080i	−0.941157	+	0.337970i	$0.890260\pi$
$138$		−	20.3923i		−	1.73591i
$139$	2.03590	−	3.52628i	0.172683	−	0.299095i	−0.766674	−	0.642036i	$-0.778090\pi$
$139$	2.03590	−	3.52628i	0.172683	−	0.299095i	0.939357	+	0.342941i	$0.111423\pi$
$140$	6.73205	+	11.6603i	0.568962	+	0.985471i
$141$	−8.83013	+	5.09808i	−0.743631	+	0.429335i
$142$	−25.3205			−2.12485
$143$	−3.46410	−	12.0000i	−0.289683	−	1.00349i
$144$	14.9282			1.24402
$145$	−0.633975	+	0.366025i	−0.0526487	+	0.0303968i
$146$	7.36603	+	12.7583i	0.609617	+	1.05589i
$147$	−0.464102	+	0.803848i	−0.0382785	+	0.0663002i
$148$			21.8564i			1.79659i
$149$	3.46410	+	2.00000i	0.283790	+	0.163846i	0.635138	−	0.772399i	$-0.280943\pi$
$149$	3.46410	+	2.00000i	0.283790	+	0.163846i	−0.351348	+	0.936245i	$0.614277\pi$
$150$	−2.36603	−	1.36603i	−0.193185	−	0.111536i
$151$		−	9.85641i		−	0.802103i	−0.916056	−	0.401051i	$-0.868645\pi$
$151$		−	9.85641i		−	0.802103i	0.916056	−	0.401051i	$-0.131355\pi$
$152$	6.92820	−	12.0000i	0.561951	−	0.973329i
$153$	−1.63397	−	2.83013i	−0.132099	−	0.228802i
$154$	−20.1962	+	11.6603i	−1.62745	+	0.939610i
$155$	7.19615			0.578009
$156$	4.73205	−	19.1244i	0.378867	−	1.53117i
$157$	6.26795			0.500237			0.250118	−	0.968215i	$-0.419530\pi$
$157$	6.26795			0.500237			0.250118	+	0.968215i	$0.419530\pi$
$158$	28.2224	−	16.2942i	2.24526	−	1.29630i
$159$	−3.46410	−	6.00000i	−0.274721	−	0.475831i
$160$	10.9282	−	18.9282i	0.863950	−	1.49641i
$161$			18.3923i			1.44952i
$162$	2.36603	+	1.36603i	0.185893	+	0.107325i
$163$	−10.7942	−	6.23205i	−0.845469	−	0.488132i	0.0136503	−	0.999907i	$-0.495655\pi$
$163$	−10.7942	−	6.23205i	−0.845469	−	0.488132i	−0.859120	+	0.511775i	$0.828988\pi$
$164$			47.7128i			3.72574i
$165$	1.73205	−	3.00000i	0.134840	−	0.233550i
$166$	12.9282	+	22.3923i	1.00342	+	1.73798i
$167$	9.12436	−	5.26795i	0.706064	−	0.407646i	−0.103538	−	0.994625i	$-0.533016\pi$
$167$	9.12436	−	5.26795i	0.706064	−	0.407646i	0.809602	+	0.586979i	$0.199683\pi$
$168$	−23.3205			−1.79922
$169$	−11.5000	−	6.06218i	−0.884615	−	0.466321i
$170$	−8.92820			−0.684762
$171$	1.26795	−	0.732051i	0.0969625	−	0.0559813i
$172$	10.1962	+	17.6603i	0.777449	+	1.34658i
$173$	3.36603	−	5.83013i	0.255914	−	0.443256i	−0.709229	−	0.704978i	$-0.750957\pi$
$173$	3.36603	−	5.83013i	0.255914	−	0.443256i	0.965143	+	0.261722i	$0.0842902\pi$
$174$		−	2.00000i		−	0.151620i
$175$	2.13397	+	1.23205i	0.161313	+	0.0931343i
$176$	44.7846	+	25.8564i	3.37577	+	1.94900i
$177$			10.7321i			0.806670i
$178$	−6.46410	+	11.1962i	−0.484505	+	0.839187i
$179$	−7.56218	−	13.0981i	−0.565224	−	0.978996i	−0.997029	−	0.0770293i	$-0.975457\pi$
$179$	−7.56218	−	13.0981i	−0.565224	−	0.978996i	0.431805	−	0.901967i	$-0.357877\pi$
$180$	4.73205	−	2.73205i	0.352706	−	0.203635i
$181$	21.4641			1.59541			0.797707	−	0.603045i	$-0.206046\pi$
$181$	21.4641			1.59541			0.797707	+	0.603045i	$0.206046\pi$
$182$	−5.83013	+	23.5622i	−0.432158	+	1.74654i
$183$	−2.46410			−0.182152
$184$	61.1769	−	35.3205i	4.51002	−	2.60386i
$185$	2.00000	+	3.46410i	0.147043	+	0.254686i
$186$	−9.83013	+	17.0263i	−0.720780	+	1.24843i
$187$		−	11.3205i		−	0.827838i
$188$	−48.2487	−	27.8564i	−3.51890	−	2.03164i
$189$	−2.13397	−	1.23205i	−0.155224	−	0.0896185i
$190$		−	4.00000i		−	0.290191i
$191$	−8.75833	+	15.1699i	−0.633731	+	1.09765i	0.353052	+	0.935604i	$0.385144\pi$
$191$	−8.75833	+	15.1699i	−0.633731	+	1.09765i	−0.986783	+	0.162050i	$0.948189\pi$
$192$	14.9282	+	25.8564i	1.07735	+	1.86603i
$193$	−17.2583	+	9.96410i	−1.24228	+	0.717232i	−0.969558	−	0.244861i	$-0.921258\pi$
$193$	−17.2583	+	9.96410i	−1.24228	+	0.717232i	−0.272724	+	0.962092i	$0.587924\pi$
$194$	−26.0526			−1.87046
$195$	−1.00000	−	3.46410i	−0.0716115	−	0.248069i
$196$	−5.07180			−0.362271
$197$	−9.46410	+	5.46410i	−0.674289	+	0.389301i	−0.797700	−	0.603055i	$-0.793950\pi$
$197$	−9.46410	+	5.46410i	−0.674289	+	0.389301i	0.123411	+	0.992356i	$0.460617\pi$
$198$	4.73205	+	8.19615i	0.336292	+	0.582475i
$199$	−7.50000	+	12.9904i	−0.531661	+	0.920864i	0.467656	+	0.883911i	$0.345099\pi$
$199$	−7.50000	+	12.9904i	−0.531661	+	0.920864i	−0.999317	+	0.0369532i	$0.988235\pi$
$200$		−	9.46410i		−	0.669213i
$201$	−4.79423	−	2.76795i	−0.338159	−	0.195236i
$202$	−21.1244	−	12.1962i	−1.48630	−	0.858118i
$203$			1.80385i			0.126605i
$204$	8.92820	−	15.4641i	0.625099	−	1.08270i
$205$	4.36603	+	7.56218i	0.304936	+	0.528165i
$206$	17.0263	−	9.83013i	1.18628	−	0.684897i
$207$	7.46410			0.518791
$208$	51.7128	−	14.9282i	3.58564	−	1.03508i
$209$	5.07180			0.350824
$210$	−5.83013	+	3.36603i	−0.402317	+	0.232278i
$211$	−9.23205	−	15.9904i	−0.635561	−	1.10082i	−0.986396	−	0.164386i	$-0.947436\pi$
$211$	−9.23205	−	15.9904i	−0.635561	−	1.10082i	0.350835	−	0.936437i	$-0.385898\pi$
$212$	18.9282	−	32.7846i	1.29999	−	2.25166i
$213$		−	9.26795i		−	0.635029i
$214$	−16.8564	−	9.73205i	−1.15228	−	0.665269i
$215$	3.23205	+	1.86603i	0.220424	+	0.127262i
$216$			9.46410i			0.643951i
$217$	8.86603	−	15.3564i	0.601865	−	1.04246i
$218$	16.0263	+	27.7583i	1.08544	+	1.88003i
$219$	−4.66987	+	2.69615i	−0.315561	+	0.182189i
$220$	18.9282			1.27614
$221$	−8.49038	−	8.16987i	−0.571125	−	0.549565i
$222$	−10.9282			−0.733453
$223$	−13.7321	+	7.92820i	−0.919566	+	0.530912i	−0.883497	−	0.468438i	$-0.844817\pi$
$223$	−13.7321	+	7.92820i	−0.919566	+	0.530912i	−0.0360695	+	0.999349i	$0.511484\pi$
$224$	−26.9282	−	46.6410i	−1.79922	−	3.11633i
$225$	0.500000	−	0.866025i	0.0333333	−	0.0577350i
$226$		−	34.2487i		−	2.27819i
$227$	4.90192	+	2.83013i	0.325352	+	0.187842i	0.653776	−	0.756688i	$-0.273184\pi$
$227$	4.90192	+	2.83013i	0.325352	+	0.187842i	−0.328424	+	0.944531i	$0.606517\pi$
$228$	6.92820	+	4.00000i	0.458831	+	0.264906i
$229$			2.39230i			0.158088i	0.996871	+	0.0790440i	$0.0251868\pi$
$229$			2.39230i			0.158088i	−0.996871	+	0.0790440i	$0.974813\pi$
$230$	10.1962	−	17.6603i	0.672314	−	1.16448i
$231$	−4.26795	−	7.39230i	−0.280810	−	0.486378i
$232$	6.00000	−	3.46410i	0.393919	−	0.227429i
$233$	3.85641			0.252642			0.126321	−	0.991989i	$-0.459683\pi$
$233$	3.85641			0.252642			0.126321	+	0.991989i	$0.459683\pi$
$234$	9.56218	+	2.36603i	0.625099	+	0.154672i
$235$	−10.1962			−0.665124
$236$	−50.7846	+	29.3205i	−3.30580	+	1.90860i
$237$	5.96410	+	10.3301i	0.387410	+	0.671014i
$238$	−11.0000	+	19.0526i	−0.713024	+	1.23499i
$239$			1.46410i			0.0947049i	0.998878	+	0.0473524i	$0.0150784\pi$
$239$			1.46410i			0.0947049i	−0.998878	+	0.0473524i	$0.984922\pi$
$240$	12.9282	+	7.46410i	0.834512	+	0.481806i
$241$	−19.3923	−	11.1962i	−1.24917	−	0.721208i	−0.278225	−	0.960516i	$-0.589746\pi$
$241$	−19.3923	−	11.1962i	−1.24917	−	0.721208i	−0.970944	+	0.239308i	$0.923079\pi$
$242$			2.73205i			0.175623i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−6.73205	−	11.6603i	−0.430975	−	0.746471i
$245$	−0.803848	+	0.464102i	−0.0513559	+	0.0296504i
$246$	−23.8564			−1.52103
$247$	3.66025	−	3.80385i	0.232896	−	0.242033i
$248$	−68.1051			−4.32468
$249$	−8.19615	+	4.73205i	−0.519410	+	0.299882i
$250$	−1.36603	−	2.36603i	−0.0863950	−	0.149641i
$251$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$251$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$252$		−	13.4641i		−	0.848159i
$253$	22.3923	+	12.9282i	1.40779	+	0.812789i
$254$	6.29423	+	3.63397i	0.394935	+	0.228016i
$255$		−	3.26795i		−	0.204647i
$256$	−21.8564	+	37.8564i	−1.36603	+	2.36603i
$257$	3.63397	+	6.29423i	0.226681	+	0.392623i	0.956822	−	0.290673i	$-0.0938791\pi$
$257$	3.63397	+	6.29423i	0.226681	+	0.392623i	−0.730141	+	0.683296i	$0.760546\pi$
$258$	−8.83013	+	5.09808i	−0.549740	+	0.317392i
$259$	9.85641			0.612447
$260$	13.6603	−	14.1962i	0.847173	−	0.880408i
$261$	0.732051			0.0453128
$262$	−11.1962	+	6.46410i	−0.691701	+	0.399354i
$263$	11.8301	+	20.4904i	0.729477	+	1.26349i	0.957105	+	0.289743i	$0.0935698\pi$
$263$	11.8301	+	20.4904i	0.729477	+	1.26349i	−0.227628	+	0.973748i	$0.573097\pi$
$264$	−16.3923	+	28.3923i	−1.00888	+	1.74743i
$265$		−	6.92820i		−	0.425596i
$266$	−8.53590	−	4.92820i	−0.523370	−	0.302168i
$267$	−4.09808	−	2.36603i	−0.250798	−	0.144798i
$268$		−	30.2487i		−	1.84773i
$269$	0.830127	−	1.43782i	0.0506137	−	0.0876656i	−0.839609	−	0.543192i	$-0.817216\pi$
$269$	0.830127	−	1.43782i	0.0506137	−	0.0876656i	0.890222	+	0.455526i	$0.150549\pi$
$270$	1.36603	+	2.36603i	0.0831337	+	0.143992i
$271$	0.232051	−	0.133975i	0.0140961	−	0.00813838i	−0.492935	−	0.870066i	$-0.664076\pi$
$271$	0.232051	−	0.133975i	0.0140961	−	0.00813838i	0.507031	+	0.861928i	$0.330743\pi$
$272$	48.7846			2.95800
$273$	−8.62436	−	2.13397i	−0.521970	−	0.129154i
$274$	41.3205			2.49626
$275$	3.00000	−	1.73205i	0.180907	−	0.104447i
$276$	20.3923	+	35.3205i	1.22747	+	2.12604i
$277$	−14.1244	+	24.4641i	−0.848650	+	1.46991i	0.0337628	+	0.999430i	$0.489251\pi$
$277$	−14.1244	+	24.4641i	−0.848650	+	1.46991i	−0.882413	+	0.470476i	$0.844082\pi$
$278$			11.1244i			0.667195i
$279$	−6.23205	−	3.59808i	−0.373103	−	0.215411i
$280$	−20.1962	−	11.6603i	−1.20695	−	0.696833i
$281$		−	3.12436i		−	0.186383i	−0.995648	−	0.0931917i	$-0.970293\pi$
$281$		−	3.12436i		−	0.186383i	0.995648	−	0.0931917i	$-0.0297070\pi$
$282$	13.9282	−	24.1244i	0.829412	−	1.43658i
$283$	−1.86603	−	3.23205i	−0.110924	−	0.192125i	0.805219	−	0.592977i	$-0.202048\pi$
$283$	−1.86603	−	3.23205i	−0.110924	−	0.192125i	−0.916143	+	0.400852i	$0.868714\pi$
$284$	43.8564	−	25.3205i	2.60240	−	1.50250i
$285$	1.46410			0.0867259
$286$	24.5885	+	23.6603i	1.45395	+	1.39906i
$287$	21.5167			1.27009
$288$	−18.9282	+	10.9282i	−1.11536	+	0.643951i
$289$	3.16025	+	5.47372i	0.185897	+	0.321984i
$290$	1.00000	−	1.73205i	0.0587220	−	0.101710i
$291$		−	9.53590i		−	0.559004i
$292$	−25.5167	−	14.7321i	−1.49325	−	0.862128i
$293$	5.70577	+	3.29423i	0.333335	+	0.192451i	0.657321	−	0.753611i	$-0.271690\pi$
$293$	5.70577	+	3.29423i	0.333335	+	0.192451i	−0.323986	+	0.946062i	$0.605023\pi$
$294$		−	2.53590i		−	0.147897i
$295$	−5.36603	+	9.29423i	−0.312422	+	0.541131i
$296$	−18.9282	−	32.7846i	−1.10018	−	1.90557i
$297$	−3.00000	+	1.73205i	−0.174078	+	0.100504i
$298$	−10.9282			−0.633054
$299$	25.8564	−	7.46410i	1.49531	−	0.431660i
$300$	5.46410			0.315470
$301$	7.96410	−	4.59808i	0.459043	−	0.265029i
$302$	13.4641	+	23.3205i	0.774772	+	1.34194i
$303$	4.46410	−	7.73205i	0.256456	−	0.444195i
$304$			21.8564i			1.25355i
$305$	−2.13397	−	1.23205i	−0.122191	−	0.0705470i
$306$	7.73205	+	4.46410i	0.442012	+	0.255196i
$307$			25.9282i			1.47980i	0.672716	+	0.739900i	$0.265127\pi$
$307$			25.9282i			1.47980i	−0.672716	+	0.739900i	$0.734873\pi$
$308$	23.3205	−	40.3923i	1.32881	−	2.30157i
$309$	3.59808	+	6.23205i	0.204687	+	0.354529i
$310$	−17.0263	+	9.83013i	−0.967028	+	0.558314i
$311$	0.196152			0.0111228			0.00556139	−	0.999985i	$-0.498230\pi$
$311$	0.196152			0.0111228			0.00556139	+	0.999985i	$0.498230\pi$
$312$	9.46410	+	32.7846i	0.535799	+	1.85606i
$313$	−21.1962			−1.19808			−0.599039	−	0.800720i	$-0.704450\pi$
$313$	−21.1962			−1.19808			−0.599039	+	0.800720i	$0.704450\pi$
$314$	−14.8301	+	8.56218i	−0.836912	+	0.483192i
$315$	−1.23205	−	2.13397i	−0.0694182	−	0.120236i
$316$	−32.5885	+	56.4449i	−1.83324	+	3.17527i
$317$			10.5359i			0.591755i	0.955226	+	0.295878i	$0.0956120\pi$
$317$			10.5359i			0.591755i	−0.955226	+	0.295878i	$0.904388\pi$
$318$	16.3923	+	9.46410i	0.919235	+	0.530720i
$319$	2.19615	+	1.26795i	0.122961	+	0.0709915i
$320$			29.8564i			1.66902i
$321$	3.56218	−	6.16987i	0.198821	−	0.344369i
$322$	−25.1244	−	43.5167i	−1.40013	−	2.42509i
$323$	4.14359	−	2.39230i	0.230556	−	0.133111i
$324$	−5.46410			−0.303561
$325$	0.866025	−	3.50000i	0.0480384	−	0.194145i
$326$	34.0526			1.88600
$327$	−10.1603	+	5.86603i	−0.561863	+	0.324392i
$328$	−41.3205	−	71.5692i	−2.28154	−	3.95175i
$329$	−12.5622	+	21.7583i	−0.692575	+	1.19958i
$330$			9.46410i			0.520982i
$331$	13.9641	+	8.06218i	0.767536	+	0.443137i	0.831995	−	0.554783i	$-0.187199\pi$
$331$	13.9641	+	8.06218i	0.767536	+	0.443137i	−0.0644586	+	0.997920i	$0.520532\pi$
$332$	−44.7846	−	25.8564i	−2.45787	−	1.41905i
$333$		−	4.00000i		−	0.219199i
$334$	−14.3923	+	24.9282i	−0.787512	+	1.36401i
$335$	−2.76795	−	4.79423i	−0.151229	−	0.261937i
$336$	31.8564	−	18.3923i	1.73791	−	1.00338i
$337$	7.05256			0.384177			0.192089	−	0.981378i	$-0.438474\pi$
$337$	7.05256			0.384177			0.192089	+	0.981378i	$0.438474\pi$
$338$	35.4904	−	1.36603i	1.93042	−	0.0743020i
$339$	12.5359			0.680857
$340$	15.4641	−	8.92820i	0.838659	−	0.484200i
$341$	−12.4641	−	21.5885i	−0.674969	−	1.16908i
$342$	−2.00000	+	3.46410i	−0.108148	+	0.187317i
$343$			19.5359i			1.05484i
$344$	−30.5885	−	17.6603i	−1.64922	−	0.952177i
$345$	6.46410	+	3.73205i	0.348016	+	0.200927i
$346$			18.3923i			0.988776i
$347$	−6.73205	+	11.6603i	−0.361395	+	0.625955i	−0.988191	−	0.153229i	$-0.951033\pi$
$347$	−6.73205	+	11.6603i	−0.361395	+	0.625955i	0.626795	+	0.779184i	$0.284366\pi$
$348$	2.00000	+	3.46410i	0.107211	+	0.185695i
$349$	19.0359	−	10.9904i	1.01897	−	0.588302i	0.105163	−	0.994455i	$-0.466463\pi$
$349$	19.0359	−	10.9904i	1.01897	−	0.588302i	0.913805	+	0.406153i	$0.133130\pi$
$350$	−6.73205			−0.359843
$351$	−0.866025	+	3.50000i	−0.0462250	+	0.186816i
$352$	−75.7128			−4.03551
$353$	19.9808	−	11.5359i	1.06347	−	0.613994i	0.137079	−	0.990560i	$-0.456229\pi$
$353$	19.9808	−	11.5359i	1.06347	−	0.613994i	0.926390	+	0.376566i	$0.122895\pi$
$354$	−14.6603	−	25.3923i	−0.779184	−	1.34959i
$355$	4.63397	−	8.02628i	0.245946	−	0.425991i
$356$		−	25.8564i		−	1.37039i
$357$	−6.97372	−	4.02628i	−0.369088	−	0.213093i
$358$	35.7846	+	20.6603i	1.89128	+	1.09193i
$359$		−	16.3397i		−	0.862379i	−0.902261	−	0.431189i	$-0.858094\pi$
$359$		−	16.3397i		−	0.862379i	0.902261	−	0.431189i	$-0.141906\pi$
$360$	−4.73205	+	8.19615i	−0.249401	+	0.431975i
$361$	−8.42820	−	14.5981i	−0.443590	−	0.768320i
$362$	−50.7846	+	29.3205i	−2.66918	+	1.54105i
$363$	−1.00000			−0.0524864
$364$	−13.4641	−	46.6410i	−0.705711	−	2.44465i
$365$	−5.39230			−0.282246
$366$	5.83013	−	3.36603i	0.304746	−	0.175945i
$367$	−3.06218	−	5.30385i	−0.159844	−	0.276859i	0.774968	−	0.632000i	$-0.217766\pi$
$367$	−3.06218	−	5.30385i	−0.159844	−	0.276859i	−0.934812	+	0.355142i	$0.884433\pi$
$368$	−55.7128	+	96.4974i	−2.90423	+	5.03028i
$369$		−	8.73205i		−	0.454572i
$370$	−9.46410	−	5.46410i	−0.492015	−	0.284065i
$371$	−14.7846	−	8.53590i	−0.767579	−	0.443162i
$372$		−	39.3205i		−	2.03867i
$373$	13.0622	−	22.6244i	0.676334	−	1.17144i	−0.299743	−	0.954020i	$-0.596901\pi$
$373$	13.0622	−	22.6244i	0.676334	−	1.17144i	0.976077	−	0.217425i	$-0.0697657\pi$
$374$	15.4641	+	26.7846i	0.799630	+	1.38500i
$375$	0.866025	−	0.500000i	0.0447214	−	0.0258199i
$376$	96.4974			4.97647
$377$	2.53590	−	0.732051i	0.130605	−	0.0377025i
$378$	6.73205			0.346259
$379$	14.0885	−	8.13397i	0.723675	−	0.417814i	−0.0924285	−	0.995719i	$-0.529463\pi$
$379$	14.0885	−	8.13397i	0.723675	−	0.417814i	0.816104	+	0.577905i	$0.196130\pi$
$380$	4.00000	+	6.92820i	0.205196	+	0.355409i
$381$	−1.33013	+	2.30385i	−0.0681445	+	0.118030i
$382$		−	47.8564i		−	2.44855i
$383$	−22.2224	−	12.8301i	−1.13551	−	0.655589i	−0.190198	−	0.981746i	$-0.560913\pi$
$383$	−22.2224	−	12.8301i	−1.13551	−	0.655589i	−0.945316	+	0.326157i	$0.894246\pi$
$384$	−32.7846	−	18.9282i	−1.67303	−	0.965926i
$385$		−	8.53590i		−	0.435030i
$386$	27.2224	−	47.1506i	1.38559	−	2.39990i
$387$	−1.86603	−	3.23205i	−0.0948554	−	0.164294i
$388$	45.1244	−	26.0526i	2.29084	−	1.32262i
$389$	−10.5359			−0.534191			−0.267096	−	0.963670i	$-0.586064\pi$
$389$	−10.5359			−0.534191			−0.267096	+	0.963670i	$0.586064\pi$
$390$	7.09808	+	6.83013i	0.359425	+	0.345857i
$391$	24.3923			1.23357
$392$	7.60770	−	4.39230i	0.384247	−	0.221845i
$393$	−2.36603	−	4.09808i	−0.119350	−	0.206721i
$394$	14.9282	−	25.8564i	0.752072	−	1.30263i
$395$			11.9282i			0.600173i
$396$	−16.3923	−	9.46410i	−0.823744	−	0.475589i
$397$	8.93782	+	5.16025i	0.448576	+	0.258986i	0.707229	−	0.706985i	$-0.249945\pi$
$397$	8.93782	+	5.16025i	0.448576	+	0.258986i	−0.258652	+	0.965970i	$0.583278\pi$
$398$		−	40.9808i		−	2.05418i
$399$	1.80385	−	3.12436i	0.0903053	−	0.156413i
$400$	7.46410	+	12.9282i	0.373205	+	0.646410i
$401$	−16.7321	+	9.66025i	−0.835559	+	0.482410i	−0.855752	−	0.517386i	$-0.826905\pi$
$401$	−16.7321	+	9.66025i	−0.835559	+	0.482410i	0.0201934	+	0.999796i	$0.493572\pi$
$402$	15.1244			0.754334
$403$	−25.1865	−	6.23205i	−1.25463	−	0.310441i
$404$	48.7846			2.42713
$405$	−0.866025	+	0.500000i	−0.0430331	+	0.0248452i
$406$	−2.46410	−	4.26795i	−0.122291	−	0.211815i
$407$	6.92820	−	12.0000i	0.343418	−	0.594818i
$408$			30.9282i			1.53117i
$409$	12.6962	+	7.33013i	0.627784	+	0.362451i	0.779893	−	0.625912i	$-0.215273\pi$
$409$	12.6962	+	7.33013i	0.627784	+	0.362451i	−0.152109	+	0.988364i	$0.548607\pi$
$410$	−20.6603	−	11.9282i	−1.02034	−	0.589092i
$411$			15.1244i			0.746029i
$412$	−19.6603	+	34.0526i	−0.968591	+	1.67765i
$413$	13.2224	+	22.9019i	0.650633	+	1.12693i
$414$	−17.6603	+	10.1962i	−0.867954	+	0.501114i
$415$	−9.46410			−0.464574
$416$	−54.6410	+	56.7846i	−2.67900	+	2.78409i
$417$	−4.07180			−0.199397
$418$	−12.0000	+	6.92820i	−0.586939	+	0.338869i
$419$	19.2224	+	33.2942i	0.939077	+	1.62653i	0.767197	+	0.641412i	$0.221651\pi$
$419$	19.2224	+	33.2942i	0.939077	+	1.62653i	0.171880	+	0.985118i	$0.445016\pi$
$420$	6.73205	−	11.6603i	0.328490	−	0.568962i
$421$			7.58846i			0.369839i	0.982754	+	0.184919i	$0.0592024\pi$
$421$			7.58846i			0.369839i	−0.982754	+	0.184919i	$0.940798\pi$
$422$	43.6865	+	25.2224i	2.12663	+	1.22781i
$423$	8.83013	+	5.09808i	0.429335	+	0.247877i
$424$			65.5692i			3.18432i
$425$	1.63397	−	2.83013i	0.0792594	−	0.137281i
$426$	12.6603	+	21.9282i	0.613391	+	1.06242i
$427$	−5.25833	+	3.03590i	−0.254468	+	0.146917i
$428$	38.9282			1.88167
$429$	−8.66025	+	9.00000i	−0.418121	+	0.434524i
$430$	−10.1962			−0.491702
$431$	−9.80385	+	5.66025i	−0.472235	+	0.272645i	−0.717175	−	0.696893i	$-0.754565\pi$
$431$	−9.80385	+	5.66025i	−0.472235	+	0.272645i	0.244940	+	0.969538i	$0.421232\pi$
$432$	−7.46410	−	12.9282i	−0.359117	−	0.622008i
$433$	7.59808	−	13.1603i	0.365140	−	0.632441i	−0.623658	−	0.781697i	$-0.714354\pi$
$433$	7.59808	−	13.1603i	0.365140	−	0.632441i	0.988799	+	0.149256i	$0.0476877\pi$
$434$			48.4449i			2.32543i
$435$	0.633975	+	0.366025i	0.0303968	+	0.0175496i
$436$	−55.5167	−	32.0526i	−2.65877	−	1.53504i
$437$			10.9282i			0.522767i
$438$	7.36603	−	12.7583i	0.351962	−	0.609617i
$439$	−2.69615	−	4.66987i	−0.128680	−	0.222881i	0.794485	−	0.607284i	$-0.207741\pi$
$439$	−2.69615	−	4.66987i	−0.128680	−	0.222881i	−0.923166	+	0.384403i	$0.874407\pi$
$440$	−28.3923	+	16.3923i	−1.35355	+	0.781472i
$441$	0.928203			0.0442002
$442$	31.2487	+	7.73205i	1.48635	+	0.367776i
$443$	−21.1244			−1.00365			−0.501824	−	0.864970i	$-0.667338\pi$
$443$	−21.1244			−1.00365			−0.501824	+	0.864970i	$0.667338\pi$
$444$	18.9282	−	10.9282i	0.898293	−	0.518630i
$445$	−2.36603	−	4.09808i	−0.112160	−	0.194267i
$446$	21.6603	−	37.5167i	1.02564	−	1.77647i
$447$		−	4.00000i		−	0.189194i
$448$	63.7128	+	36.7846i	3.01015	+	1.73791i
$449$	−21.5885	−	12.4641i	−1.01882	−	0.588217i	−0.105060	−	0.994466i	$-0.533503\pi$
$449$	−21.5885	−	12.4641i	−1.01882	−	0.588217i	−0.913763	+	0.406249i	$0.866837\pi$
$450$			2.73205i			0.128790i
$451$	15.1244	−	26.1962i	0.712178	−	1.23353i
$452$	34.2487	+	59.3205i	1.61092	+	2.79020i
$453$	−8.53590	+	4.92820i	−0.401051	+	0.231547i
$454$	−15.4641			−0.725766
$455$	−6.40192	−	6.16025i	−0.300127	−	0.288797i
$456$	−13.8564			−0.648886
$457$	−13.3301	+	7.69615i	−0.623557	+	0.360011i	−0.778253	−	0.627951i	$-0.783894\pi$
$457$	−13.3301	+	7.69615i	−0.623557	+	0.360011i	0.154696	+	0.987962i	$0.450560\pi$
$458$	−3.26795	−	5.66025i	−0.152701	−	0.264486i
$459$	−1.63397	+	2.83013i	−0.0762674	+	0.132099i
$460$			40.7846i			1.90159i
$461$	29.0263	+	16.7583i	1.35189	+	0.780513i	0.988514	−	0.151130i	$-0.0482912\pi$
$461$	29.0263	+	16.7583i	1.35189	+	0.780513i	0.363375	+	0.931643i	$0.381624\pi$
$462$	20.1962	+	11.6603i	0.939610	+	0.542484i
$463$			39.7846i			1.84895i	0.381246	+	0.924474i	$0.375495\pi$
$463$			39.7846i			1.84895i	−0.381246	+	0.924474i	$0.624505\pi$
$464$	−5.46410	+	9.46410i	−0.253665	+	0.439360i
$465$	−3.59808	−	6.23205i	−0.166857	−	0.289004i
$466$	−9.12436	+	5.26795i	−0.422678	+	0.244033i
$467$	6.33975			0.293368			0.146684	−	0.989183i	$-0.453140\pi$
$467$	6.33975			0.293368			0.146684	+	0.989183i	$0.453140\pi$
$468$	−18.9282	+	5.46410i	−0.874957	+	0.252578i
$469$	−13.6410			−0.629884
$470$	24.1244	−	13.9282i	1.11277	−	0.642460i
$471$	−3.13397	−	5.42820i	−0.144406	−	0.250118i
$472$	50.7846	−	87.9615i	2.33755	−	4.04876i
$473$		−	12.9282i		−	0.594439i
$474$	−28.2224	−	16.2942i	−1.29630	−	0.748419i
$475$	1.26795	+	0.732051i	0.0581775	+	0.0335888i
$476$		−	44.0000i		−	2.01674i
$477$	−3.46410	+	6.00000i	−0.158610	+	0.274721i
$478$	−2.00000	−	3.46410i	−0.0914779	−	0.158444i
$479$	−25.9019	+	14.9545i	−1.18349	+	0.683288i	−0.956819	−	0.290684i	$-0.906117\pi$
$479$	−25.9019	+	14.9545i	−1.18349	+	0.683288i	−0.226670	+	0.973972i	$0.572784\pi$
$480$	−21.8564			−0.997604
$481$	−4.00000	−	13.8564i	−0.182384	−	0.631798i
$482$	61.1769			2.78653
$483$	15.9282	−	9.19615i	0.724758	−	0.418439i
$484$	−2.73205	−	4.73205i	−0.124184	−	0.215093i
$485$	4.76795	−	8.25833i	0.216501	−	0.374991i
$486$		−	2.73205i		−	0.123928i
$487$	18.0000	+	10.3923i	0.815658	+	0.470920i	0.848917	−	0.528526i	$-0.177255\pi$
$487$	18.0000	+	10.3923i	0.815658	+	0.470920i	−0.0332590	+	0.999447i	$0.510589\pi$
$488$	20.1962	+	11.6603i	0.914237	+	0.527835i
$489$			12.4641i			0.563646i
$490$	1.26795	−	2.19615i	0.0572801	−	0.0992121i
$491$	−8.56218	−	14.8301i	−0.386406	−	0.669274i	0.605557	−	0.795802i	$-0.292950\pi$
$491$	−8.56218	−	14.8301i	−0.386406	−	0.669274i	−0.991963	+	0.126527i	$0.959617\pi$
$492$	41.3205	−	23.8564i	1.86287	−	1.07553i
$493$	2.39230			0.107744
$494$	−3.46410	+	14.0000i	−0.155857	+	0.629890i
$495$	−3.46410			−0.155700
$496$	93.0333	−	53.7128i	4.17732	−	2.41178i
$497$	−11.4186	−	19.7776i	−0.512194	−	0.887145i
$498$	12.9282	−	22.3923i	0.579327	−	1.00342i
$499$			20.3923i			0.912885i	0.889753	+	0.456442i	$0.150877\pi$
$499$			20.3923i			0.912885i	−0.889753	+	0.456442i	$0.849123\pi$
$500$	4.73205	+	2.73205i	0.211624	+	0.122181i
$501$	−9.12436	−	5.26795i	−0.407646	−	0.235355i
$502$		0			0
$503$	−5.39230	+	9.33975i	−0.240431	+	0.416439i	−0.960837	−	0.277114i	$-0.910622\pi$
$503$	−5.39230	+	9.33975i	−0.240431	+	0.416439i	0.720406	+	0.693552i	$0.243955\pi$
$504$	11.6603	+	20.1962i	0.519389	+	0.899608i
$505$	7.73205	−	4.46410i	0.344072	−	0.198650i
$506$	−70.6410			−3.14038
$507$	0.500000	+	12.9904i	0.0222058	+	0.576923i
$508$	−14.5359			−0.644926
$509$	0.803848	−	0.464102i	0.0356299	−	0.0205709i	−0.482079	−	0.876128i	$-0.660118\pi$
$509$	0.803848	−	0.464102i	0.0356299	−	0.0205709i	0.517709	+	0.855557i	$0.326785\pi$
$510$	4.46410	+	7.73205i	0.197674	+	0.342381i
$511$	−6.64359	+	11.5070i	−0.293895	+	0.509042i
$512$		−	43.7128i		−	1.93185i
$513$	−1.26795	−	0.732051i	−0.0559813	−	0.0323208i
$514$	−17.1962	−	9.92820i	−0.758490	−	0.437914i
$515$			7.19615i			0.317100i
$516$	10.1962	−	17.6603i	0.448861	−	0.777449i
$517$	17.6603	+	30.5885i	0.776697	+	1.34528i
$518$	−23.3205	+	13.4641i	−1.02464	+	0.591579i
$519$	−6.73205			−0.295504
$520$	−8.19615	+	33.1244i	−0.359425	+	1.45260i
$521$	−9.26795			−0.406036			−0.203018	−	0.979175i	$-0.565075\pi$
$521$	−9.26795			−0.406036			−0.203018	+	0.979175i	$0.565075\pi$
$522$	−1.73205	+	1.00000i	−0.0758098	+	0.0437688i
$523$	15.2679	+	26.4449i	0.667621	+	1.15635i	0.978568	+	0.205926i	$0.0660206\pi$
$523$	15.2679	+	26.4449i	0.667621	+	1.15635i	−0.310947	+	0.950427i	$0.600646\pi$
$524$	12.9282	−	22.3923i	0.564771	−	0.978212i
$525$		−	2.46410i		−	0.107542i
$526$	−55.9808	−	32.3205i	−2.44088	−	1.40924i
$527$	−20.3660	−	11.7583i	−0.887158	−	0.512201i
$528$		−	51.7128i		−	2.25051i
$529$	−16.3564	+	28.3301i	−0.711148	+	1.23174i
$530$	9.46410	+	16.3923i	0.411094	+	0.712036i
$531$	9.29423	−	5.36603i	0.403335	−	0.232866i
$532$	19.7128			0.854659
$533$	−8.73205	−	30.2487i	−0.378227	−	1.31022i
$534$	12.9282			0.559458
$535$	6.16987	−	3.56218i	0.266747	−	0.154006i
$536$	26.1962	+	45.3731i	1.13150	+	1.95982i
$537$	−7.56218	+	13.0981i	−0.326332	+	0.565224i
$538$			4.53590i			0.195556i
$539$	2.78461	+	1.60770i	0.119942	+	0.0692483i
$540$	−4.73205	−	2.73205i	−0.203635	−	0.117569i
$541$		−	13.5885i		−	0.584213i	−0.956386	−	0.292107i	$-0.905644\pi$
$541$		−	13.5885i		−	0.584213i	0.956386	−	0.292107i	$-0.0943562\pi$
$542$	−0.366025	+	0.633975i	−0.0157221	+	0.0272315i
$543$	−10.7321	−	18.5885i	−0.460556	−	0.797707i
$544$	−61.8564	+	35.7128i	−2.65207	+	1.53117i
$545$	−11.7321			−0.502546
$546$	23.3205	−	6.73205i	0.998026	−	0.288105i
$547$	−7.33975			−0.313825			−0.156912	−	0.987613i	$-0.550154\pi$
$547$	−7.33975			−0.313825			−0.156912	+	0.987613i	$0.550154\pi$
$548$	−71.5692	+	41.3205i	−3.05729	+	1.76512i
$549$	1.23205	+	2.13397i	0.0525826	+	0.0910758i
$550$	−4.73205	+	8.19615i	−0.201775	+	0.349485i
$551$			1.07180i			0.0456601i
$552$	−61.1769	−	35.3205i	−2.60386	−	1.50334i
$553$	25.4545	+	14.6962i	1.08243	+	0.624944i
$554$		−	77.1769i		−	3.27893i
$555$	2.00000	−	3.46410i	0.0848953	−	0.147043i
$556$	−11.1244	−	19.2679i	−0.471778	−	0.817143i
$557$	12.5885	−	7.26795i	0.533390	−	0.307953i	−0.209006	−	0.977914i	$-0.567023\pi$
$557$	12.5885	−	7.26795i	0.533390	−	0.307953i	0.742396	+	0.669962i	$0.233689\pi$
$558$	19.6603			0.832285
$559$	−9.69615	−	9.33013i	−0.410104	−	0.394622i
$560$	36.7846			1.55443
$561$	−9.80385	+	5.66025i	−0.413919	+	0.238976i
$562$	4.26795	+	7.39230i	0.180033	+	0.311826i
$563$	1.73205	−	3.00000i	0.0729972	−	0.126435i	−0.827216	−	0.561884i	$-0.810077\pi$
$563$	1.73205	−	3.00000i	0.0729972	−	0.126435i	0.900214	+	0.435449i	$0.143410\pi$
$564$			55.7128i			2.34593i
$565$	10.8564	+	6.26795i	0.456732	+	0.263695i
$566$	8.83013	+	5.09808i	0.371158	+	0.214288i
$567$			2.46410i			0.103483i
$568$	−43.8564	+	75.9615i	−1.84017	+	3.18727i
$569$	−16.9019	−	29.2750i	−0.708566	−	1.22727i	−0.965389	−	0.260813i	$-0.916009\pi$
$569$	−16.9019	−	29.2750i	−0.708566	−	1.22727i	0.256824	−	0.966458i	$-0.417324\pi$
$570$	−3.46410	+	2.00000i	−0.145095	+	0.0837708i
$571$	−23.8564			−0.998360			−0.499180	−	0.866498i	$-0.666365\pi$
$571$	−23.8564			−0.998360			−0.499180	+	0.866498i	$0.666365\pi$
$572$	−66.2487	−	16.3923i	−2.77000	−	0.685397i
$573$	17.5167			0.731769
$574$	−50.9090	+	29.3923i	−2.12490	+	1.22681i
$575$	3.73205	+	6.46410i	0.155637	+	0.269572i
$576$	14.9282	−	25.8564i	0.622008	−	1.07735i
$577$		−	43.7128i		−	1.81979i	−0.414841	−	0.909894i	$-0.636163\pi$
$577$		−	43.7128i		−	1.81979i	0.414841	−	0.909894i	$-0.363837\pi$
$578$	−14.9545	−	8.63397i	−0.622024	−	0.359126i
$579$	17.2583	+	9.96410i	0.717232	+	0.414094i
$580$			4.00000i			0.166091i
$581$	−11.6603	+	20.1962i	−0.483749	+	0.837878i
$582$	13.0263	+	22.5622i	0.539957	+	0.935232i
$583$	−20.7846	+	12.0000i	−0.860811	+	0.496989i
$584$	51.0333			2.11177
$585$	−2.50000	+	2.59808i	−0.103362	+	0.107417i
$586$	−18.0000			−0.743573
$587$	7.22243	−	4.16987i	0.298102	−	0.172109i	−0.343488	−	0.939157i	$-0.611609\pi$
$587$	7.22243	−	4.16987i	0.298102	−	0.172109i	0.641590	+	0.767048i	$0.278275\pi$
$588$	2.53590	+	4.39230i	0.104579	+	0.181136i
$589$	5.26795	−	9.12436i	0.217062	−	0.375963i
$590$		−	29.3205i		−	1.20711i
$591$	9.46410	+	5.46410i	0.389301	+	0.224763i
$592$	51.7128	+	29.8564i	2.12538	+	1.22709i
$593$		−	13.3205i		−	0.547008i	−0.961871	−	0.273504i	$-0.911817\pi$
$593$		−	13.3205i		−	0.547008i	0.961871	−	0.273504i	$-0.0881826\pi$
$594$	4.73205	−	8.19615i	0.194158	−	0.336292i
$595$	−4.02628	−	6.97372i	−0.165061	−	0.285895i
$596$	18.9282	−	10.9282i	0.775329	−	0.447637i
$597$	15.0000			0.613909
$598$	−50.9808	+	52.9808i	−2.08476	+	2.16654i
$599$	1.12436			0.0459399			0.0229700	−	0.999736i	$-0.492688\pi$
$599$	1.12436			0.0459399			0.0229700	+	0.999736i	$0.492688\pi$
$600$	−8.19615	+	4.73205i	−0.334607	+	0.193185i
$601$	−13.1244	−	22.7321i	−0.535354	−	0.927260i	−0.999146	−	0.0413158i	$-0.986845\pi$
$601$	−13.1244	−	22.7321i	−0.535354	−	0.927260i	0.463793	−	0.885944i	$-0.346488\pi$
$602$	−12.5622	+	21.7583i	−0.511996	+	0.886803i
$603$			5.53590i			0.225439i
$604$	−46.6410	−	26.9282i	−1.89780	−	1.09569i
$605$	−0.866025	−	0.500000i	−0.0352089	−	0.0203279i
$606$			24.3923i			0.990870i
$607$	−19.1962	+	33.2487i	−0.779148	+	1.34952i	0.153286	+	0.988182i	$0.451015\pi$
$607$	−19.1962	+	33.2487i	−0.779148	+	1.34952i	−0.932433	+	0.361342i	$0.882319\pi$
$608$	−16.0000	−	27.7128i	−0.648886	−	1.12390i
$609$	1.56218	−	0.901924i	0.0633026	−	0.0365478i
$610$	6.73205			0.272573
$611$	35.6865	+	8.83013i	1.44372	+	0.357229i
$612$	−17.8564			−0.721802
$613$	37.9186	−	21.8923i	1.53152	−	0.884222i	0.532225	−	0.846603i	$-0.321356\pi$
$613$	37.9186	−	21.8923i	1.53152	−	0.884222i	0.999292	−	0.0376189i	$-0.0119773\pi$
$614$	−35.4186	−	61.3468i	−1.42938	−	2.47575i
$615$	4.36603	−	7.56218i	0.176055	−	0.304936i
$616$			80.7846i			3.25490i
$617$	−38.6603	−	22.3205i	−1.55640	−	0.898590i	−0.997596	−	0.0692919i	$-0.977926\pi$
$617$	−38.6603	−	22.3205i	−1.55640	−	0.898590i	−0.558807	−	0.829298i	$-0.688741\pi$
$618$	−17.0263	−	9.83013i	−0.684897	−	0.395426i
$619$			19.5885i			0.787327i	0.919255	+	0.393663i	$0.128792\pi$
$619$			19.5885i			0.787327i	−0.919255	+	0.393663i	$0.871208\pi$
$620$	19.6603	−	34.0526i	0.789575	−	1.36758i
$621$	−3.73205	−	6.46410i	−0.149762	−	0.259395i
$622$	−0.464102	+	0.267949i	−0.0186088	+	0.0107438i
$623$	−11.6603			−0.467158
$624$	−38.7846	−	37.3205i	−1.55263	−	1.49402i
$625$	1.00000			0.0400000
$626$	50.1506	−	28.9545i	2.00442	−	1.15725i
$627$	−2.53590	−	4.39230i	−0.101274	−	0.175412i
$628$	17.1244	−	29.6603i	0.683336	−	1.18357i
$629$		−	13.0718i		−	0.521207i
$630$	5.83013	+	3.36603i	0.232278	+	0.134106i
$631$	36.0167	+	20.7942i	1.43380	+	0.827805i	0.997408	−	0.0719512i	$-0.0229226\pi$
$631$	36.0167	+	20.7942i	1.43380	+	0.827805i	0.436392	+	0.899756i	$0.356256\pi$
$632$		−	112.890i		−	4.49051i
$633$	−9.23205	+	15.9904i	−0.366941	+	0.635561i
$634$	−14.3923	−	24.9282i	−0.571591	−	0.990025i
$635$	−2.30385	+	1.33013i	−0.0914254	+	0.0527845i
$636$	−37.8564			−1.50110
$637$	3.21539	−	0.928203i	0.127398	−	0.0367768i
$638$	−6.92820			−0.274290
$639$	−8.02628	+	4.63397i	−0.317515	+	0.183317i
$640$	−18.9282	−	32.7846i	−0.748203	−	1.29593i
$641$	−1.39230	+	2.41154i	−0.0549927	+	0.0952502i	−0.892211	−	0.451618i	$-0.850847\pi$
$641$	−1.39230	+	2.41154i	−0.0549927	+	0.0952502i	0.837219	+	0.546868i	$0.184180\pi$
$642$			19.4641i			0.768187i
$643$	−32.7224	−	18.8923i	−1.29045	−	0.745040i	−0.311713	−	0.950176i	$-0.600903\pi$
$643$	−32.7224	−	18.8923i	−1.29045	−	0.745040i	−0.978733	+	0.205136i	$0.934236\pi$
$644$	87.0333	+	50.2487i	3.42959	+	1.98008i
$645$		−	3.73205i		−	0.146949i
$646$	−6.53590	+	11.3205i	−0.257151	+	0.445399i
$647$	1.00000	+	1.73205i	0.0393141	+	0.0680939i	0.885013	−	0.465566i	$-0.154149\pi$
$647$	1.00000	+	1.73205i	0.0393141	+	0.0680939i	−0.845699	+	0.533660i	$0.820816\pi$
$648$	8.19615	−	4.73205i	0.321975	−	0.185893i
$649$	37.1769			1.45932
$650$	2.73205	+	9.46410i	0.107160	+	0.371213i
$651$	−17.7321			−0.694974
$652$	−58.9808	+	34.0526i	−2.30986	+	1.33360i
$653$	22.7583	+	39.4186i	0.890602	+	1.54257i	0.839155	+	0.543893i	$0.183050\pi$
$653$	22.7583	+	39.4186i	0.890602	+	1.54257i	0.0514475	+	0.998676i	$0.483617\pi$
$654$	16.0263	−	27.7583i	0.626677	−	1.08544i
$655$		−	4.73205i		−	0.184897i
$656$	112.890	+	65.1769i	4.40760	+	2.54473i
$657$	4.66987	+	2.69615i	0.182189	+	0.105187i
$658$		−	68.6410i		−	2.67591i
$659$	−12.5885	+	21.8038i	−0.490377	+	0.849357i	−0.999939	−	0.0110766i	$-0.996474\pi$
$659$	−12.5885	+	21.8038i	−0.490377	+	0.849357i	0.509562	+	0.860434i	$0.329807\pi$
$660$	−9.46410	−	16.3923i	−0.368390	−	0.638070i
$661$	14.7679	−	8.52628i	0.574407	−	0.331634i	−0.184501	−	0.982832i	$-0.559067\pi$
$661$	14.7679	−	8.52628i	0.574407	−	0.331634i	0.758907	+	0.651199i	$0.225733\pi$
$662$	−44.0526			−1.71215
$663$	−2.83013	+	11.4378i	−0.109913	+	0.444208i
$664$	89.5692			3.47596
$665$	3.12436	−	1.80385i	0.121157	−	0.0699502i
$666$	5.46410	+	9.46410i	0.211730	+	0.366726i
$667$	−2.73205	+	4.73205i	−0.105785	+	0.183226i
$668$		−	57.5692i		−	2.22742i
$669$	13.7321	+	7.92820i	0.530912	+	0.306522i
$670$	13.0981	+	7.56218i	0.506023	+	0.292152i
$671$			8.53590i			0.329525i
$672$	−26.9282	+	46.6410i	−1.03878	+	1.79922i
$673$	−0.669873	−	1.16025i	−0.0258217	−	0.0447245i	0.852826	−	0.522196i	$-0.174887\pi$
$673$	−0.669873	−	1.16025i	−0.0258217	−	0.0447245i	−0.878647	+	0.477471i	$0.841554\pi$
$674$	−16.6865	+	9.63397i	−0.642741	+	0.371087i
$675$	−1.00000			−0.0384900
$676$	−60.1051	+	37.8564i	−2.31174	+	1.45602i
$677$	−8.78461			−0.337620			−0.168810	−	0.985649i	$-0.553992\pi$
$677$	−8.78461			−0.337620			−0.168810	+	0.985649i	$0.553992\pi$
$678$	−29.6603	+	17.1244i	−1.13910	+	0.657657i
$679$	−11.7487	−	20.3494i	−0.450874	−	0.780937i
$680$	−15.4641	+	26.7846i	−0.593021	+	1.02714i
$681$		−	5.66025i		−	0.216901i
$682$	58.9808	+	34.0526i	2.25849	+	1.30394i
$683$	−38.7391	−	22.3660i	−1.48231	−	0.855812i	−0.482512	−	0.875890i	$-0.660275\pi$
$683$	−38.7391	−	22.3660i	−1.48231	−	0.855812i	−0.999798	+	0.0200773i	$0.993609\pi$
$684$		−	8.00000i		−	0.305888i
$685$	−7.56218	+	13.0981i	−0.288936	+	0.500452i
$686$	−26.6865	−	46.2224i	−1.01890	−	1.76478i
$687$	2.07180	−	1.19615i	0.0790440	−	0.0456361i
$688$	55.7128			2.12403
$689$	−6.00000	+	24.2487i	−0.228582	+	0.923802i
$690$	−20.3923			−0.776322
$691$	10.7487	−	6.20577i	0.408900	−	0.236079i	−0.281417	−	0.959586i	$-0.590804\pi$
$691$	10.7487	−	6.20577i	0.408900	−	0.236079i	0.690317	+	0.723507i	$0.257471\pi$
$692$	−18.3923	−	31.8564i	−0.699171	−	1.21100i
$693$	−4.26795	+	7.39230i	−0.162126	+	0.280810i
$694$		−	36.7846i		−	1.39632i
$695$	−3.52628	−	2.03590i	−0.133759	−	0.0772260i
$696$	−6.00000	−	3.46410i	−0.227429	−	0.131306i
$697$		−	28.5359i		−	1.08087i
$698$	−30.0263	+	52.0070i	−1.13651	+	1.96850i
$699$	−1.92820	−	3.33975i	−0.0729313	−	0.126321i
$700$	11.6603	−	6.73205i	0.440716	−	0.254448i
$701$	−32.7846			−1.23826			−0.619129	−	0.785289i	$-0.712514\pi$
$701$	−32.7846			−1.23826			−0.619129	+	0.785289i	$0.712514\pi$
$702$	−2.73205	−	9.46410i	−0.103115	−	0.357199i
$703$	5.85641			0.220879
$704$	89.5692	−	51.7128i	3.37577	−	1.94900i
$705$	5.09808	+	8.83013i	0.192005	+	0.332562i
$706$	−31.5167	+	54.5885i	−1.18615	+	2.05446i
$707$		−	22.0000i		−	0.827395i
$708$	50.7846	+	29.3205i	1.90860	+	1.10193i
$709$	11.5526	+	6.66987i	0.433865	+	0.250492i	0.700992	−	0.713169i	$-0.252741\pi$
$709$	11.5526	+	6.66987i	0.433865	+	0.250492i	−0.267127	+	0.963661i	$0.586074\pi$
$710$			25.3205i			0.950262i
$711$	5.96410	−	10.3301i	0.223671	−	0.387410i
$712$	22.3923	+	38.7846i	0.839187	+	1.45351i
$713$	46.5167	−	26.8564i	1.74206	−	1.00578i
$714$	22.0000			0.823329
$715$	−12.0000	+	3.46410i	−0.448775	+	0.129550i
$716$	−82.6410			−3.08844
$717$	1.26795	−	0.732051i	0.0473524	−	0.0273389i
$718$	22.3205	+	38.6603i	0.832994	+	1.44279i
$719$	15.6340	−	27.0788i	0.583049	−	1.00987i	−0.412067	−	0.911154i	$-0.635193\pi$
$719$	15.6340	−	27.0788i	0.583049	−	1.00987i	0.995116	−	0.0987166i	$-0.0314737\pi$
$720$		−	14.9282i		−	0.556341i
$721$	15.3564	+	8.86603i	0.571902	+	0.330188i
$722$	39.8827	+	23.0263i	1.48428	+	0.856949i
$723$			22.3923i			0.832779i
$724$	58.6410	−	101.569i	2.17938	−	3.77479i
$725$	0.366025	+	0.633975i	0.0135938	+	0.0235452i
$726$	2.36603	−	1.36603i	0.0878114	−	0.0506980i
$727$	9.73205			0.360942			0.180471	−	0.983580i	$-0.442238\pi$
$727$	9.73205			0.360942			0.180471	+	0.983580i	$0.442238\pi$
$728$	60.5885	+	58.3013i	2.24556	+	2.16079i
$729$	1.00000			0.0370370
$730$	12.7583	−	7.36603i	0.472207	−	0.272629i
$731$	−6.09808	−	10.5622i	−0.225545	−	0.390656i
$732$	−6.73205	+	11.6603i	−0.248824	+	0.430975i
$733$		−	32.3205i		−	1.19379i	−0.802321	−	0.596893i	$-0.796402\pi$
$733$		−	32.3205i		−	1.19379i	0.802321	−	0.596893i	$-0.203598\pi$
$734$	14.4904	+	8.36603i	0.534850	+	0.308796i
$735$	0.803848	+	0.464102i	0.0296504	+	0.0171186i
$736$		−	163.138i		−	6.01336i
$737$	−9.58846	+	16.6077i	−0.353195	+	0.611752i
$738$	11.9282	+	20.6603i	0.439083	+	0.760514i
$739$	9.00000	−	5.19615i	0.331070	−	0.191144i	−0.325246	−	0.945629i	$-0.605447\pi$
$739$	9.00000	−	5.19615i	0.331070	−	0.191144i	0.656316	+	0.754486i	$0.272114\pi$
$740$	21.8564			0.803457
$741$	−5.12436	−	1.26795i	−0.188248	−	0.0465793i
$742$	46.6410			1.71225
$743$	22.4378	−	12.9545i	0.823164	−	0.475254i	−0.0283424	−	0.999598i	$-0.509023\pi$
$743$	22.4378	−	12.9545i	0.823164	−	0.475254i	0.851506	+	0.524344i	$0.175690\pi$
$744$	34.0526	+	58.9808i	1.24843	+	2.16234i
$745$	2.00000	−	3.46410i	0.0732743	−	0.126915i
$746$			71.3731i			2.61315i
$747$	8.19615	+	4.73205i	0.299882	+	0.173137i
$748$	−53.5692	−	30.9282i	−1.95868	−	1.13085i
$749$		−	17.5551i		−	0.641451i
$750$	−1.36603	+	2.36603i	−0.0498802	+	0.0863950i
$751$	6.66025	+	11.5359i	0.243036	+	0.420951i	0.961578	−	0.274533i	$-0.0885233\pi$
$751$	6.66025	+	11.5359i	0.243036	+	0.420951i	−0.718542	+	0.695484i	$0.755190\pi$
$752$	−131.818	+	76.1051i	−4.80691	+	2.77527i
$753$		0			0
$754$	−5.00000	+	5.19615i	−0.182089	+	0.189233i
$755$	−9.85641			−0.358711
$756$	−11.6603	+	6.73205i	−0.424079	+	0.244842i
$757$	−6.53590	−	11.3205i	−0.237551	−	0.411451i	0.722460	−	0.691413i	$-0.243011\pi$
$757$	−6.53590	−	11.3205i	−0.237551	−	0.411451i	−0.960011	+	0.279962i	$0.909678\pi$
$758$	−22.2224	+	38.4904i	−0.807155	+	1.39803i
$759$		−	25.8564i		−	0.938528i
$760$	−12.0000	−	6.92820i	−0.435286	−	0.251312i
$761$	−18.9282	−	10.9282i	−0.686147	−	0.396147i	0.116020	−	0.993247i	$-0.462986\pi$
$761$	−18.9282	−	10.9282i	−0.686147	−	0.396147i	−0.802167	+	0.597100i	$0.796320\pi$
$762$		−	7.26795i		−	0.263290i
$763$	−14.4545	+	25.0359i	−0.523287	+	0.906360i
$764$	47.8564	+	82.8897i	1.73138	+	2.99885i
$765$	−2.83013	+	1.63397i	−0.102323	+	0.0590765i
$766$	70.1051			2.53300
$767$	26.8301	−	27.8827i	0.968780	−	1.00679i
$768$	43.7128			1.57735
$769$	−25.6410	+	14.8038i	−0.924639	+	0.533840i	−0.885112	−	0.465378i	$-0.845918\pi$
$769$	−25.6410	+	14.8038i	−0.924639	+	0.533840i	−0.0395267	+	0.999219i	$0.512585\pi$
$770$	11.6603	+	20.1962i	0.420206	+	0.727819i
$771$	3.63397	−	6.29423i	0.130874	−	0.226681i
$772$			108.890i			3.91903i
$773$	17.1962	+	9.92820i	0.618503	+	0.357093i	0.776286	−	0.630381i	$-0.217101\pi$
$773$	17.1962	+	9.92820i	0.618503	+	0.357093i	−0.157783	+	0.987474i	$0.550435\pi$
$774$	8.83013	+	5.09808i	0.317392	+	0.183247i
$775$		−	7.19615i		−	0.258493i
$776$	−45.1244	+	78.1577i	−1.61987	+	2.80570i
$777$	−4.92820	−	8.53590i	−0.176798	−	0.306224i
$778$	24.9282	−	14.3923i	0.893719	−	0.515989i
$779$	12.7846			0.458056
$780$	−19.1244	−	4.73205i	−0.684762	−	0.169435i
$781$	−32.1051			−1.14881
$782$	−57.7128	+	33.3205i	−2.06381	+	1.19154i
$783$	−0.366025	−	0.633975i	−0.0130807	−	0.0226564i
$784$	−6.92820	+	12.0000i	−0.247436	+	0.428571i
$785$		−	6.26795i		−	0.223713i
$786$	11.1962	+	6.46410i	0.399354	+	0.230567i
$787$	24.6506	+	14.2321i	0.878700	+	0.507318i	0.870230	−	0.492646i	$-0.163970\pi$
$787$	24.6506	+	14.2321i	0.878700	+	0.507318i	0.00847061	+	0.999964i	$0.497304\pi$
$788$			59.7128i			2.12718i
$789$	11.8301	−	20.4904i	0.421164	−	0.729477i
$790$	−16.2942	−	28.2224i	−0.579723	−	1.00411i
$791$	26.7513	−	15.4449i	0.951166	−	0.549156i
$792$	32.7846			1.16495
$793$	6.40192	+	6.16025i	0.227339	+	0.218757i
$794$	−28.1962			−1.00064
$795$	−6.00000	+	3.46410i	−0.212798	+	0.122859i
$796$	40.9808	+	70.9808i	1.45252	+	2.51585i
$797$	14.2224	−	24.6340i	0.503784	−	0.872580i	−0.496206	−	0.868205i	$-0.665274\pi$
$797$	14.2224	−	24.6340i	0.503784	−	0.872580i	0.999990	−	0.00437536i	$-0.00139272\pi$
$798$			9.85641i			0.348913i
$799$	28.8564	+	16.6603i	1.02087	+	0.589397i
$800$	−18.9282	−	10.9282i	−0.669213	−	0.386370i
$801$			4.73205i			0.167199i
$802$	26.3923	−	45.7128i	0.931945	−	1.61418i
$803$	9.33975	+	16.1769i	0.329592	+	0.570871i
$804$	−26.1962	+	15.1244i	−0.923867	+	0.533395i
$805$	18.3923			0.648244
$806$	68.1051	−	19.6603i	2.39890	−	0.692503i
$807$	−1.66025			−0.0584437
$808$	−73.1769	+	42.2487i	−2.57435	+	1.48630i
$809$	−18.0000	−	31.1769i	−0.632846	−	1.09612i	−0.986967	−	0.160922i	$-0.948553\pi$
$809$	−18.0000	−	31.1769i	−0.632846	−	1.09612i	0.354121	−	0.935200i	$-0.384780\pi$
$810$	1.36603	−	2.36603i	0.0479972	−	0.0831337i
$811$			39.0526i			1.37132i	0.727922	+	0.685660i	$0.240486\pi$
$811$			39.0526i			1.37132i	−0.727922	+	0.685660i	$0.759514\pi$
$812$	8.53590	+	4.92820i	0.299551	+	0.172946i
$813$	−0.232051	−	0.133975i	−0.00813838	−	0.00469869i
$814$			37.8564i			1.32687i
$815$	−6.23205	+	10.7942i	−0.218299	+	0.378105i
$816$	−24.3923	−	42.2487i	−0.853901	−	1.47900i
$817$	4.73205	−	2.73205i	0.165554	−	0.0955824i
$818$	−40.0526			−1.40040
$819$	2.46410	+	8.53590i	0.0861027	+	0.298268i
$820$	47.7128			1.66620
$821$	−11.1962	+	6.46410i	−0.390748	+	0.225599i	−0.682484	−	0.730900i	$-0.739100\pi$
$821$	−11.1962	+	6.46410i	−0.390748	+	0.225599i	0.291736	+	0.956499i	$0.405767\pi$
$822$	−20.6603	−	35.7846i	−0.720609	−	1.24813i
$823$	24.5885	−	42.5885i	0.857100	−	1.48454i	−0.0175835	−	0.999845i	$-0.505597\pi$
$823$	24.5885	−	42.5885i	0.857100	−	1.48454i	0.874683	−	0.484695i	$-0.161069\pi$
$824$		−	68.1051i		−	2.37255i
$825$	−3.00000	−	1.73205i	−0.104447	−	0.0603023i
$826$	−62.5692	−	36.1244i	−2.17706	−	1.25693i
$827$			28.5885i			0.994118i	0.867717	+	0.497059i	$0.165587\pi$
$827$			28.5885i			0.994118i	−0.867717	+	0.497059i	$0.834413\pi$
$828$	20.3923	−	35.3205i	0.708682	−	1.22747i
$829$	12.0885	+	20.9378i	0.419849	+	0.727201i	0.995924	−	0.0901966i	$-0.0287495\pi$
$829$	12.0885	+	20.9378i	0.419849	+	0.727201i	−0.576075	+	0.817397i	$0.695416\pi$
$830$	22.3923	−	12.9282i	0.777248	−	0.448744i
$831$	28.2487			0.979937
$832$	25.8564	−	104.497i	0.896410	−	3.62280i
$833$	3.03332			0.105098
$834$	9.63397	−	5.56218i	0.333597	−	0.192602i
$835$	−5.26795	−	9.12436i	−0.182305	−	0.315761i
$836$	13.8564	−	24.0000i	0.479234	−	0.830057i
$837$			7.19615i			0.248735i
$838$	−90.9615	−	52.5167i	−3.14221	−	1.81416i
$839$	23.7846	+	13.7321i	0.821136	+	0.474083i	0.850808	−	0.525477i	$-0.176113\pi$
$839$	23.7846	+	13.7321i	0.821136	+	0.474083i	−0.0296721	+	0.999560i	$0.509446\pi$
$840$			23.3205i			0.804634i
$841$	14.2321	−	24.6506i	0.490760	−	0.850022i
$842$	−10.3660	−	17.9545i	−0.357237	−	0.618752i
$843$	−2.70577	+	1.56218i	−0.0931917	+	0.0538043i
$844$	−100.890			−3.47277
$845$	−6.06218	+	11.5000i	−0.208545	+	0.395612i
$846$	−27.8564			−0.957723
$847$	−2.13397	+	1.23205i	−0.0733242	+	0.0423338i
$848$	−51.7128	−	89.5692i	−1.77583	−	3.07582i
$849$	−1.86603	+	3.23205i	−0.0640418	+	0.110924i
$850$			8.92820i			0.306235i
$851$	25.8564	+	14.9282i	0.886346	+	0.511732i
$852$	−43.8564	−	25.3205i	−1.50250	−	0.867466i
$853$		−	37.3923i		−	1.28029i	−0.768255	−	0.640144i	$-0.778875\pi$
$853$		−	37.3923i		−	1.28029i	0.768255	−	0.640144i	$-0.221125\pi$
$854$	8.29423	−	14.3660i	0.283823	−	0.491595i
$855$	−0.732051	−	1.26795i	−0.0250356	−	0.0433629i
$856$	−58.3923	+	33.7128i	−1.99581	+	1.15228i
$857$	−7.12436			−0.243363			−0.121682	−	0.992569i	$-0.538829\pi$
$857$	−7.12436			−0.243363			−0.121682	+	0.992569i	$0.538829\pi$
$858$	8.19615	−	33.1244i	0.279812	−	1.13085i
$859$	−33.7846			−1.15272			−0.576358	−	0.817197i	$-0.695527\pi$
$859$	−33.7846			−1.15272			−0.576358	+	0.817197i	$0.695527\pi$
$860$	17.6603	−	10.1962i	0.602210	−	0.347686i
$861$	−10.7583	−	18.6340i	−0.366643	−	0.635044i
$862$	15.4641	−	26.7846i	0.526709	−	0.912287i
$863$		−	13.6077i		−	0.463211i	−0.972810	−	0.231606i	$-0.925602\pi$
$863$		−	13.6077i		−	0.463211i	0.972810	−	0.231606i	$-0.0743979\pi$
$864$	18.9282	+	10.9282i	0.643951	+	0.371785i
$865$	−5.83013	−	3.36603i	−0.198230	−	0.114448i
$866$			41.5167i			1.41079i
$867$	3.16025	−	5.47372i	0.107328	−	0.185897i
$868$	−48.4449	−	83.9090i	−1.64433	−	2.84806i
$869$	35.7846	−	20.6603i	1.21391	−	0.700851i
$870$	−2.00000			−0.0678064
$871$	5.53590	+	19.1769i	0.187577	+	0.649785i
$872$	111.033			3.76006
$873$	−8.25833	+	4.76795i	−0.279502	+	0.161371i
$874$	−14.9282	−	25.8564i	−0.504954	−	0.874606i
$875$	1.23205	−	2.13397i	0.0416509	−	0.0721415i
$876$			29.4641i			0.995500i
$877$	−43.8564	−	25.3205i	−1.48093	−	0.855013i	−0.481159	−	0.876633i	$-0.659784\pi$
$877$	−43.8564	−	25.3205i	−1.48093	−	0.855013i	−0.999766	+	0.0216203i	$0.993117\pi$
$878$	12.7583	+	7.36603i	0.430573	+	0.248591i
$879$		−	6.58846i		−	0.222223i
$880$	25.8564	−	44.7846i	0.871619	−	1.50969i
$881$	18.5885	+	32.1962i	0.626261	+	1.08472i	0.988296	+	0.152551i	$0.0487489\pi$
$881$	18.5885	+	32.1962i	0.626261	+	1.08472i	−0.362035	+	0.932165i	$0.617918\pi$
$882$	−2.19615	+	1.26795i	−0.0739483	+	0.0426941i
$883$	−16.6603			−0.560662			−0.280331	−	0.959903i	$-0.590444\pi$
$883$	−16.6603			−0.560662			−0.280331	+	0.959903i	$0.590444\pi$
$884$	−61.8564	+	17.8564i	−2.08046	+	0.600576i
$885$	10.7321			0.360754
$886$	49.9808	−	28.8564i	1.67914	−	0.969450i
$887$	−24.4904	−	42.4186i	−0.822307	−	1.42428i	−0.903961	−	0.427616i	$-0.859354\pi$
$887$	−24.4904	−	42.4186i	−0.822307	−	1.42428i	0.0816540	−	0.996661i	$-0.473980\pi$
$888$	−18.9282	+	32.7846i	−0.635189	+	1.10018i
$889$			6.55514i			0.219852i
$890$	11.1962	+	6.46410i	0.375296	+	0.216677i
$891$	3.00000	+	1.73205i	0.100504	+	0.0580259i
$892$			86.6410i			2.90096i
$893$	−7.46410	+	12.9282i	−0.249777	+	0.432626i
$894$	5.46410	+	9.46410i	0.182747	+	0.316527i
$895$	−13.0981	+	7.56218i	−0.437820	+	0.252776i
$896$	−93.2820			−3.11633
$897$	−19.3923	−	18.6603i	−0.647490	−	0.623048i
$898$	68.1051			2.27270
$899$	4.56218	−	2.63397i	0.152157	−	0.0878480i
$900$	−2.73205	−	4.73205i	−0.0910684	−	0.157735i
$901$	−11.3205	+	19.6077i	−0.377141	+	0.653227i
$902$			82.6410i			2.75164i
$903$	−7.96410	−	4.59808i	−0.265029	−	0.153014i
$904$	−102.746	−	59.3205i	−3.41729	−	1.97297i
$905$		−	21.4641i		−	0.713491i
$906$	13.4641	−	23.3205i	0.447315	−	0.774772i
$907$	−15.7321	−	27.2487i	−0.522374	−	0.904779i	−0.999661	−	0.0260311i	$-0.991713\pi$
$907$	−15.7321	−	27.2487i	−0.522374	−	0.904779i	0.477287	−	0.878747i	$-0.341620\pi$
$908$	26.7846	−	15.4641i	0.888878	−	0.513194i
$909$	−8.92820			−0.296130
$910$	23.5622	+	5.83013i	0.781079	+	0.193267i
$911$	47.7128			1.58080			0.790398	−	0.612594i	$-0.209874\pi$
$911$	47.7128			1.58080			0.790398	+	0.612594i	$0.209874\pi$
$912$	18.9282	−	10.9282i	0.626775	−	0.361869i
$913$	16.3923	+	28.3923i	0.542506	+	0.939648i
$914$	21.0263	−	36.4186i	0.695488	−	1.20462i
$915$			2.46410i			0.0814607i
$916$	11.3205	+	6.53590i	0.374040	+	0.215952i
$917$	−10.0981	−	5.83013i	−0.333468	−	0.192528i
$918$		−	8.92820i		−	0.294675i
$919$	16.4641	−	28.5167i	0.543101	−	0.940678i	−0.455623	−	0.890173i	$-0.650584\pi$
$919$	16.4641	−	28.5167i	0.543101	−	0.940678i	0.998724	−	0.0505051i	$-0.0160831\pi$
$920$	−35.3205	−	61.1769i	−1.16448	−	2.01694i
$921$	22.4545	−	12.9641i	0.739900	−	0.427182i
$922$	−91.5692			−3.01567
$923$	−23.1699	+	24.0788i	−0.762646	+	0.792565i
$924$	−46.6410			−1.53438
$925$	3.46410	−	2.00000i	0.113899	−	0.0657596i
$926$	−54.3468	−	94.1314i	−1.78595	−	3.09335i
$927$	3.59808	−	6.23205i	0.118176	−	0.204687i
$928$		−	16.0000i		−	0.525226i
$929$	−16.7321	−	9.66025i	−0.548961	−	0.316943i	0.199742	−	0.979849i	$-0.435990\pi$
$929$	−16.7321	−	9.66025i	−0.548961	−	0.316943i	−0.748703	+	0.662906i	$0.769323\pi$
$930$	17.0263	+	9.83013i	0.558314	+	0.322343i
$931$			1.35898i			0.0445389i
$932$	10.5359	−	18.2487i	0.345115	−	0.597756i
$933$	−0.0980762	−	0.169873i	−0.00321087	−	0.00556139i
$934$	−15.0000	+	8.66025i	−0.490815	+	0.283372i
$935$	−11.3205			−0.370220
$936$	23.6603	−	24.5885i	0.773360	−	0.803699i
$937$	−16.2487			−0.530822			−0.265411	−	0.964135i	$-0.585508\pi$
$937$	−16.2487			−0.530822			−0.265411	+	0.964135i	$0.585508\pi$
$938$	32.2750	−	18.6340i	1.05382	−	0.608421i
$939$	10.5981	+	18.3564i	0.345855	+	0.599039i
$940$	−27.8564	+	48.2487i	−0.908576	+	1.57370i
$941$			40.5885i			1.32315i	0.749881	+	0.661573i	$0.230111\pi$
$941$			40.5885i			1.32315i	−0.749881	+	0.661573i	$0.769889\pi$
$942$	14.8301	+	8.56218i	0.483192	+	0.278971i
$943$	56.4449	+	32.5885i	1.83810	+	1.06123i
$944$			160.210i			5.21440i
$945$	−1.23205	+	2.13397i	−0.0400786	+	0.0694182i
$946$	17.6603	+	30.5885i	0.574184	+	0.994517i
$947$	31.6865	−	18.2942i	1.02967	−	0.594483i	0.112783	−	0.993620i	$-0.464024\pi$
$947$	31.6865	−	18.2942i	1.02967	−	0.594483i	0.916891	+	0.399137i	$0.130690\pi$
$948$	65.1769			2.11685
$949$	18.8731	+	4.66987i	0.612646	+	0.151590i
$950$	−4.00000			−0.129777
$951$	9.12436	−	5.26795i	0.295878	−	0.170825i
$952$	38.1051	+	66.0000i	1.23499	+	2.13907i
$953$	−12.1244	+	21.0000i	−0.392746	+	0.680257i	−0.992811	−	0.119695i	$-0.961808\pi$
$953$	−12.1244	+	21.0000i	−0.392746	+	0.680257i	0.600064	+	0.799952i	$0.295142\pi$
$954$		−	18.9282i		−	0.612823i
$955$	15.1699	+	8.75833i	0.490886	+	0.283413i
$956$	6.92820	+	4.00000i	0.224074	+	0.129369i
$957$		−	2.53590i		−	0.0819740i
$958$	40.8564	−	70.7654i	1.32001	−	2.28633i
$959$	18.6340	+	32.2750i	0.601722	+	1.04221i
$960$	25.8564	−	14.9282i	0.834512	−	0.481806i
$961$	−20.7846			−0.670471
$962$	28.3923	+	27.3205i	0.915405	+	0.880849i
$963$	−7.12436			−0.229579
$964$	−105.962	+	61.1769i	−3.41279	+	1.97038i
$965$	9.96410	+	17.2583i	0.320756	+	0.555565i
$966$	−25.1244	+	43.5167i	−0.808363	+	1.40013i
$967$			32.2487i			1.03705i	0.855063	+	0.518524i	$0.173518\pi$
$967$			32.2487i			1.03705i	−0.855063	+	0.518524i	$0.826482\pi$
$968$	8.19615	+	4.73205i	0.263434	+	0.152094i
$969$	−4.14359	−	2.39230i	−0.133111	−	0.0768519i
$970$			26.0526i			0.836497i
$971$	0.588457	−	1.01924i	0.0188845	−	0.0327089i	−0.856429	−	0.516265i	$-0.827322\pi$
$971$	0.588457	−	1.01924i	0.0188845	−	0.0327089i	0.875313	+	0.483556i	$0.160655\pi$
$972$	2.73205	+	4.73205i	0.0876306	+	0.151781i
$973$	−8.68911	+	5.01666i	−0.278560	+	0.160827i
$974$	−56.7846			−1.81950
$975$	−3.46410	+	1.00000i	−0.110940	+	0.0320256i
$976$	−36.7846			−1.17745
$977$	0.928203	−	0.535898i	0.0296959	−	0.0171449i	−0.485079	−	0.874471i	$-0.661209\pi$
$977$	0.928203	−	0.535898i	0.0296959	−	0.0171449i	0.514774	+	0.857326i	$0.327876\pi$
$978$	−17.0263	−	29.4904i	−0.544440	−	0.942998i
$979$	−8.19615	+	14.1962i	−0.261950	+	0.453711i
$980$			5.07180i			0.162013i
$981$	10.1603	+	5.86603i	0.324392	+	0.187288i
$982$	40.5167	+	23.3923i	1.29294	+	0.746478i
$983$			23.8564i			0.760901i	0.924801	+	0.380451i	$0.124231\pi$
$983$			23.8564i			0.760901i	−0.924801	+	0.380451i	$0.875769\pi$
$984$	−41.3205	+	71.5692i	−1.31725	+	2.28154i
$985$	5.46410	+	9.46410i	0.174101	+	0.301551i
$986$	−5.66025	+	3.26795i	−0.180259	+	0.104073i
$987$	25.1244			0.799717
$988$	−8.00000	−	27.7128i	−0.254514	−	0.881662i
$989$	27.8564			0.885782
$990$	8.19615	−	4.73205i	0.260491	−	0.150394i
$991$	−14.4641	−	25.0526i	−0.459467	−	0.795821i	0.539465	−	0.842008i	$-0.318626\pi$
$991$	−14.4641	−	25.0526i	−0.459467	−	0.795821i	−0.998933	+	0.0461870i	$0.985293\pi$
$992$	−78.6410	+	136.210i	−2.49685	+	4.32468i
$993$		−	16.1244i		−	0.511691i
$994$	54.0333	+	31.1962i	1.71383	+	0.989482i
$995$	12.9904	+	7.50000i	0.411823	+	0.237766i
$996$			51.7128i			1.63858i
$997$	28.7942	−	49.8731i	0.911922	−	1.57950i	0.100577	−	0.994929i	$-0.467931\pi$
$997$	28.7942	−	49.8731i	0.911922	−	1.57950i	0.811346	−	0.584567i	$-0.198735\pi$
$998$	−27.8564	−	48.2487i	−0.881779	−	1.52729i
$999$	−3.46410	+	2.00000i	−0.109599	+	0.0632772i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	195.2.bb.a.166.1	yes	4
3.2	odd	2		585.2.bu.a.361.2		4
5.2	odd	4		975.2.w.a.49.1		4
5.3	odd	4		975.2.w.f.49.2		4
5.4	even	2		975.2.bc.h.751.2		4
13.2	odd	12		2535.2.a.n.1.1		2
13.4	even	6	inner	195.2.bb.a.121.1	✓	4
13.11	odd	12		2535.2.a.s.1.2		2
39.2	even	12		7605.2.a.bk.1.2		2
39.11	even	12		7605.2.a.y.1.1		2
39.17	odd	6		585.2.bu.a.316.2		4
65.4	even	6		975.2.bc.h.901.2		4
65.17	odd	12		975.2.w.f.199.2		4
65.43	odd	12		975.2.w.a.199.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bb.a.121.1	✓	4	13.4	even	6	inner
195.2.bb.a.166.1	yes	4	1.1	even	1	trivial
585.2.bu.a.316.2		4	39.17	odd	6
585.2.bu.a.361.2		4	3.2	odd	2
975.2.w.a.49.1		4	5.2	odd	4
975.2.w.a.199.1		4	65.43	odd	12
975.2.w.f.49.2		4	5.3	odd	4
975.2.w.f.199.2		4	65.17	odd	12
975.2.bc.h.751.2		4	5.4	even	2
975.2.bc.h.901.2		4	65.4	even	6
2535.2.a.n.1.1		2	13.2	odd	12
2535.2.a.s.1.2		2	13.11	odd	12
7605.2.a.y.1.1		2	39.11	even	12
7605.2.a.bk.1.2		2	39.2	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 195 = 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	195.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.36603 + 1.36603i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(2.73205 - 4.73205i) q^{4} -1.00000i q^{5} +(2.36603 + 1.36603i) q^{6} +(-2.13397 - 1.23205i) q^{7} +9.46410i q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.36603 + 2.36603i) q^{10} +(-3.00000 + 1.73205i) q^{11} -5.46410 q^{12} +(-0.866025 + 3.50000i) q^{13} +6.73205 q^{14} +(-0.866025 + 0.500000i) q^{15} +(-7.46410 - 12.9282i) q^{16} +(-1.63397 + 2.83013i) q^{17} -2.73205i q^{18} +(-1.26795 - 0.732051i) q^{19} +(-4.73205 - 2.73205i) q^{20} +2.46410i q^{21} +(4.73205 - 8.19615i) q^{22} +(-3.73205 - 6.46410i) q^{23} +(8.19615 - 4.73205i) q^{24} -1.00000 q^{25} +(-2.73205 - 9.46410i) q^{26} +1.00000 q^{27} +(-11.6603 + 6.73205i) q^{28} +(-0.366025 - 0.633975i) q^{29} +(1.36603 - 2.36603i) q^{30} +7.19615i q^{31} +(18.9282 + 10.9282i) q^{32} +(3.00000 + 1.73205i) q^{33} -8.92820i q^{34} +(-1.23205 + 2.13397i) q^{35} +(2.73205 + 4.73205i) q^{36} +(-3.46410 + 2.00000i) q^{37} +4.00000 q^{38} +(3.46410 - 1.00000i) q^{39} +9.46410 q^{40} +(-7.56218 + 4.36603i) q^{41} +(-3.36603 - 5.83013i) q^{42} +(-1.86603 + 3.23205i) q^{43} +18.9282i q^{44} +(0.866025 + 0.500000i) q^{45} +(17.6603 + 10.1962i) q^{46} -10.1962i q^{47} +(-7.46410 + 12.9282i) q^{48} +(-0.464102 - 0.803848i) q^{49} +(2.36603 - 1.36603i) q^{50} +3.26795 q^{51} +(14.1962 + 13.6603i) q^{52} +6.92820 q^{53} +(-2.36603 + 1.36603i) q^{54} +(1.73205 + 3.00000i) q^{55} +(11.6603 - 20.1962i) q^{56} +1.46410i q^{57} +(1.73205 + 1.00000i) q^{58} +(-9.29423 - 5.36603i) q^{59} +5.46410i q^{60} +(1.23205 - 2.13397i) q^{61} +(-9.83013 - 17.0263i) q^{62} +(2.13397 - 1.23205i) q^{63} -29.8564 q^{64} +(3.50000 + 0.866025i) q^{65} -9.46410 q^{66} +(4.79423 - 2.76795i) q^{67} +(8.92820 + 15.4641i) q^{68} +(-3.73205 + 6.46410i) q^{69} -6.73205i q^{70} +(8.02628 + 4.63397i) q^{71} +(-8.19615 - 4.73205i) q^{72} -5.39230i q^{73} +(5.46410 - 9.46410i) q^{74} +(0.500000 + 0.866025i) q^{75} +(-6.92820 + 4.00000i) q^{76} +8.53590 q^{77} +(-6.83013 + 7.09808i) q^{78} -11.9282 q^{79} +(-12.9282 + 7.46410i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(11.9282 - 20.6603i) q^{82} -9.46410i q^{83} +(11.6603 + 6.73205i) q^{84} +(2.83013 + 1.63397i) q^{85} -10.1962i q^{86} +(-0.366025 + 0.633975i) q^{87} +(-16.3923 - 28.3923i) q^{88} +(4.09808 - 2.36603i) q^{89} -2.73205 q^{90} +(6.16025 - 6.40192i) q^{91} -40.7846 q^{92} +(6.23205 - 3.59808i) q^{93} +(13.9282 + 24.1244i) q^{94} +(-0.732051 + 1.26795i) q^{95} -21.8564i q^{96} +(8.25833 + 4.76795i) q^{97} +(2.19615 + 1.26795i) q^{98} -3.46410i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{2} - 2 q^{3} + 4 q^{4} + 6 q^{6} - 12 q^{7} - 2 q^{9} + 2 q^{10} - 12 q^{11} - 8 q^{12} + 20 q^{14} - 16 q^{16} - 10 q^{17} - 12 q^{19} - 12 q^{20} + 12 q^{22} - 8 q^{23} + 12 q^{24} - 4 q^{25}+ \cdots - 12 q^{98}+O(q^{100}) \) 4 * q - 6 * q^2 - 2 * q^3 + 4 * q^4 + 6 * q^6 - 12 * q^7 - 2 * q^9 + 2 * q^10 - 12 * q^11 - 8 * q^12 + 20 * q^14 - 16 * q^16 - 10 * q^17 - 12 * q^19 - 12 * q^20 + 12 * q^22 - 8 * q^23 + 12 * q^24 - 4 * q^25 - 4 * q^26 + 4 * q^27 - 12 * q^28 + 2 * q^29 + 2 * q^30 + 48 * q^32 + 12 * q^33 + 2 * q^35 + 4 * q^36 + 16 * q^38 + 24 * q^40 - 6 * q^41 - 10 * q^42 - 4 * q^43 + 36 * q^46 - 16 * q^48 + 12 * q^49 + 6 * q^50 + 20 * q^51 + 36 * q^52 - 6 * q^54 + 12 * q^56 - 6 * q^59 - 2 * q^61 - 22 * q^62 + 12 * q^63 - 64 * q^64 + 14 * q^65 - 24 * q^66 - 12 * q^67 + 8 * q^68 - 8 * q^69 - 6 * q^71 - 12 * q^72 + 8 * q^74 + 2 * q^75 + 48 * q^77 - 10 * q^78 - 20 * q^79 - 24 * q^80 - 2 * q^81 + 20 * q^82 + 12 * q^84 - 6 * q^85 + 2 * q^87 - 24 * q^88 + 6 * q^89 - 4 * q^90 - 10 * q^91 - 80 * q^92 + 18 * q^93 + 28 * q^94 + 4 * q^95 - 12 * q^97 - 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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