LMFDB - Embedded newform 182.2.n.b.25.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [182,2,Mod(25,182)] 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("182.25"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(182, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 182 = 2 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	182.n (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12] 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:	$1.45327731679$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.17213603549184.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} + 19x^{8} - 28x^{6} + 31x^{4} - 6x^{2} + 1 $ x^12 - 5x^10 + 19x^8 - 28x^6 + 31x^4 - 6*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			25.1
Root			$-1.07992 - 0.623490i$ of defining polynomial
Character	$\chi$	$=$	182.25
Dual form			182.2.n.b.51.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.400969 + 0.694498i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.480608 + 0.277479i) q^{5} -0.801938i q^{6} +(-1.46533 + 2.20291i) q^{7} +1.00000i q^{8} +(1.17845 + 2.04113i) q^{9} +(0.277479 - 0.480608i) q^{10} +(-2.15983 - 1.24698i) q^{11} +(0.400969 + 0.694498i) q^{12} +(-0.890084 + 3.49396i) q^{13} +(0.167563 - 2.64044i) q^{14} -0.445042i q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.92543 + 5.06699i) q^{17} +(-2.04113 - 1.17845i) q^{18} +(2.50289 - 1.44504i) q^{19} +0.554958i q^{20} +(-0.942362 - 1.90097i) q^{21} +2.49396 q^{22} +(-3.04892 - 5.28088i) q^{23} +(-0.694498 - 0.400969i) q^{24} +(-2.34601 + 4.06341i) q^{25} +(-0.976144 - 3.47090i) q^{26} -4.29590 q^{27} +(1.17511 + 2.37047i) q^{28} +6.27413 q^{29} +(0.222521 + 0.385418i) q^{30} +(6.91774 + 3.99396i) q^{31} +(0.866025 + 0.500000i) q^{32} +(1.73205 - 1.00000i) q^{33} -5.85086i q^{34} +(0.0929903 - 1.46533i) q^{35} +2.35690 q^{36} +(7.89781 - 4.55980i) q^{37} +(-1.44504 + 2.50289i) q^{38} +(-2.06965 - 2.01913i) q^{39} +(-0.277479 - 0.480608i) q^{40} -4.71379i q^{41} +(1.76659 + 1.17511i) q^{42} +6.03684 q^{43} +(-2.15983 + 1.24698i) q^{44} +(-1.13274 - 0.653989i) q^{45} +(5.28088 + 3.04892i) q^{46} +(0.213891 - 0.123490i) q^{47} +0.801938 q^{48} +(-2.70560 - 6.45599i) q^{49} -4.69202i q^{50} +(-2.34601 - 4.06341i) q^{51} +(2.58082 + 2.51781i) q^{52} +(1.66487 - 2.88365i) q^{53} +(3.72036 - 2.14795i) q^{54} +1.38404 q^{55} +(-2.20291 - 1.46533i) q^{56} +2.31767i q^{57} +(-5.43355 + 3.13706i) q^{58} +(-5.66164 - 3.26875i) q^{59} +(-0.385418 - 0.222521i) q^{60} +(7.34481 + 12.7216i) q^{61} -7.98792 q^{62} +(-6.22324 - 0.394928i) q^{63} -1.00000 q^{64} +(-0.541719 - 1.92620i) q^{65} +(-1.00000 + 1.73205i) q^{66} +(-1.81678 - 1.04892i) q^{67} +(2.92543 + 5.06699i) q^{68} +4.89008 q^{69} +(0.652135 + 1.31551i) q^{70} +2.46681i q^{71} +(-2.04113 + 1.17845i) q^{72} +(3.03632 + 1.75302i) q^{73} +(-4.55980 + 7.89781i) q^{74} +(-1.88135 - 3.25860i) q^{75} -2.89008i q^{76} +(5.91185 - 2.93067i) q^{77} +(2.80194 + 0.713792i) q^{78} +(-7.54288 - 13.0646i) q^{79} +(0.480608 + 0.277479i) q^{80} +(-1.81282 + 3.13990i) q^{81} +(2.35690 + 4.08226i) q^{82} +11.6039i q^{83} +(-2.11747 - 0.134375i) q^{84} -3.24698i q^{85} +(-5.22805 + 3.01842i) q^{86} +(-2.51573 + 4.35737i) q^{87} +(1.24698 - 2.15983i) q^{88} +(-7.69904 + 4.44504i) q^{89} +1.30798 q^{90} +(-6.39260 - 7.08059i) q^{91} -6.09783 q^{92} +(-5.54760 + 3.20291i) q^{93} +(-0.123490 + 0.213891i) q^{94} +(-0.801938 + 1.38900i) q^{95} +(-0.694498 + 0.400969i) q^{96} +9.52542i q^{97} +(5.57111 + 4.23825i) q^{98} -5.87800i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{3} + 6 q^{4} + 6 q^{9} + 4 q^{10} - 4 q^{12} - 8 q^{13} - 6 q^{16} - 8 q^{17} - 8 q^{22} - 18 q^{25} - 2 q^{26} + 4 q^{27} + 32 q^{29} + 2 q^{30} - 28 q^{35} + 12 q^{36} - 16 q^{38} - 12 q^{39}+ \cdots + 8 q^{95}+O(q^{100}) $ 12 * q + 4 * q^3 + 6 * q^4 + 6 * q^9 + 4 * q^10 - 4 * q^12 - 8 * q^13 - 6 * q^16 - 8 * q^17 - 8 * q^22 - 18 * q^25 - 2 * q^26 + 4 * q^27 + 32 * q^29 + 2 * q^30 - 28 * q^35 + 12 * q^36 - 16 * q^38 - 12 * q^39 - 4 * q^40 + 28 * q^42 - 40 * q^43 - 8 * q^48 - 18 * q^51 - 4 * q^52 + 24 * q^53 - 24 * q^55 - 4 * q^61 - 20 * q^62 - 12 * q^64 + 8 * q^65 - 12 * q^66 + 8 * q^68 + 56 * q^69 - 12 * q^74 + 12 * q^75 + 56 * q^77 + 16 * q^78 - 16 * q^79 + 2 * q^81 + 12 * q^82 + 20 * q^87 - 4 * q^88 + 36 * q^90 - 28 * q^91 + 8 * q^94 + 8 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/182\mathbb{Z}\right)^\times$.

$n$	$15$	$157$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−0.400969	+	0.694498i	−0.231499	+	0.400969i	−0.958250	−	0.285933i	$-0.907696\pi$
$3$	−0.400969	+	0.694498i	−0.231499	+	0.400969i	0.726750	+	0.686902i	$0.241030\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−0.480608	+	0.277479i	−0.214934	+	0.124092i	−0.603603	−	0.797285i	$-0.706269\pi$
$5$	−0.480608	+	0.277479i	−0.214934	+	0.124092i	0.388668	+	0.921378i	$0.372935\pi$
$6$		−	0.801938i		−	0.327390i
$7$	−1.46533	+	2.20291i	−0.553844	+	0.832620i
$7$	−1.46533	+	2.20291i	−0.553844	+	0.832620i
$8$			1.00000i			0.353553i
$9$	1.17845	+	2.04113i	0.392816	+	0.680377i
$10$	0.277479	−	0.480608i	0.0877466	−	0.151982i
$11$	−2.15983	−	1.24698i	−0.651214	−	0.375978i	0.137707	−	0.990473i	$-0.456027\pi$
$11$	−2.15983	−	1.24698i	−0.651214	−	0.375978i	−0.788921	+	0.614494i	$0.789360\pi$
$12$	0.400969	+	0.694498i	0.115750	+	0.200484i
$13$	−0.890084	+	3.49396i	−0.246865	+	0.969050i
$13$	−0.890084	+	3.49396i	−0.246865	+	0.969050i
$14$	0.167563	−	2.64044i	0.0447830	−	0.705687i
$15$		−	0.445042i		−	0.114909i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.92543	+	5.06699i	−0.709520	+	1.22893i	0.255515	+	0.966805i	$0.417755\pi$
$17$	−2.92543	+	5.06699i	−0.709520	+	1.22893i	−0.965035	+	0.262120i	$0.915578\pi$
$18$	−2.04113	−	1.17845i	−0.481099	−	0.277763i
$19$	2.50289	−	1.44504i	0.574201	−	0.331515i	−0.184624	−	0.982809i	$-0.559107\pi$
$19$	2.50289	−	1.44504i	0.574201	−	0.331515i	0.758826	+	0.651294i	$0.225773\pi$
$20$			0.554958i			0.124092i
$21$	−0.942362	−	1.90097i	−0.205640	−	0.414825i
$22$	2.49396			0.531714
$23$	−3.04892	−	5.28088i	−0.635743	−	1.10114i	−0.986357	−	0.164619i	$-0.947360\pi$
$23$	−3.04892	−	5.28088i	−0.635743	−	1.10114i	0.350614	−	0.936520i	$-0.385973\pi$
$24$	−0.694498	−	0.400969i	−0.141764	−	0.0818474i
$25$	−2.34601	+	4.06341i	−0.469202	+	0.812682i
$26$	−0.976144	−	3.47090i	−0.191438	−	0.680699i
$27$	−4.29590			−0.826746
$28$	1.17511	+	2.37047i	0.222074	+	0.447977i
$29$	6.27413			1.16508			0.582538	−	0.812803i	$-0.302060\pi$
$29$	6.27413			1.16508			0.582538	+	0.812803i	$0.302060\pi$
$30$	0.222521	+	0.385418i	0.0406266	+	0.0703673i
$31$	6.91774	+	3.99396i	1.24246	+	0.717336i	0.969595	−	0.244715i	$-0.0786945\pi$
$31$	6.91774	+	3.99396i	1.24246	+	0.717336i	0.272868	+	0.962052i	$0.412028\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	1.73205	−	1.00000i	0.301511	−	0.174078i
$34$		−	5.85086i		−	1.00341i
$35$	0.0929903	−	1.46533i	0.0157182	−	0.247687i
$36$	2.35690			0.392816
$37$	7.89781	−	4.55980i	1.29839	−	0.749627i	0.318266	−	0.948002i	$-0.396900\pi$
$37$	7.89781	−	4.55980i	1.29839	−	0.749627i	0.980126	+	0.198375i	$0.0635663\pi$
$38$	−1.44504	+	2.50289i	−0.234417	+	0.406022i
$39$	−2.06965	−	2.01913i	−0.331410	−	0.323320i
$40$	−0.277479	−	0.480608i	−0.0438733	−	0.0759908i
$41$		−	4.71379i		−	0.736171i	−0.929792	−	0.368085i	$-0.880013\pi$
$41$		−	4.71379i		−	0.736171i	0.929792	−	0.368085i	$-0.119987\pi$
$42$	1.76659	+	1.17511i	0.272591	+	0.181323i
$43$	6.03684			0.920609			0.460304	−	0.887761i	$-0.347740\pi$
$43$	6.03684			0.920609			0.460304	+	0.887761i	$0.347740\pi$
$44$	−2.15983	+	1.24698i	−0.325607	+	0.187989i
$45$	−1.13274	−	0.653989i	−0.168859	−	0.0974910i
$46$	5.28088	+	3.04892i	0.778623	+	0.449538i
$47$	0.213891	−	0.123490i	0.0311992	−	0.0180128i	−0.484319	−	0.874891i	$-0.660933\pi$
$47$	0.213891	−	0.123490i	0.0311992	−	0.0180128i	0.515518	+	0.856878i	$0.327599\pi$
$48$	0.801938			0.115750
$49$	−2.70560	−	6.45599i	−0.386514	−	0.922284i
$50$		−	4.69202i		−	0.663552i
$51$	−2.34601	−	4.06341i	−0.328507	−	0.568991i
$52$	2.58082	+	2.51781i	0.357895	+	0.349158i
$53$	1.66487	−	2.88365i	0.228688	−	0.396099i	−0.728731	−	0.684800i	$-0.759890\pi$
$53$	1.66487	−	2.88365i	0.228688	−	0.396099i	0.957420	+	0.288700i	$0.0932231\pi$
$54$	3.72036	−	2.14795i	0.506276	−	0.292299i
$55$	1.38404			0.186624
$56$	−2.20291	−	1.46533i	−0.294376	−	0.195813i
$57$			2.31767i			0.306983i
$58$	−5.43355	+	3.13706i	−0.713460	+	0.411917i
$59$	−5.66164	−	3.26875i	−0.737083	−	0.425555i	0.0839249	−	0.996472i	$-0.473254\pi$
$59$	−5.66164	−	3.26875i	−0.737083	−	0.425555i	−0.821008	+	0.570917i	$0.806588\pi$
$60$	−0.385418	−	0.222521i	−0.0497572	−	0.0287273i
$61$	7.34481	+	12.7216i	0.940407	+	1.62883i	0.764696	+	0.644391i	$0.222889\pi$
$61$	7.34481	+	12.7216i	0.940407	+	1.62883i	0.175711	+	0.984442i	$0.443778\pi$
$62$	−7.98792			−1.01447
$63$	−6.22324	−	0.394928i	−0.784055	−	0.0497563i
$64$	−1.00000			−0.125000
$65$	−0.541719	−	1.92620i	−0.0671920	−	0.238916i
$66$	−1.00000	+	1.73205i	−0.123091	+	0.213201i
$67$	−1.81678	−	1.04892i	−0.221955	−	0.128146i	0.384900	−	0.922958i	$-0.374236\pi$
$67$	−1.81678	−	1.04892i	−0.221955	−	0.128146i	−0.606855	+	0.794813i	$0.707569\pi$
$68$	2.92543	+	5.06699i	0.354760	+	0.614463i
$69$	4.89008			0.588697
$70$	0.652135	+	1.31551i	0.0779450	+	0.157234i
$71$			2.46681i			0.292757i	0.989229	+	0.146378i	$0.0467617\pi$
$71$			2.46681i			0.292757i	−0.989229	+	0.146378i	$0.953238\pi$
$72$	−2.04113	+	1.17845i	−0.240550	+	0.138881i
$73$	3.03632	+	1.75302i	0.355374	+	0.205176i	0.667050	−	0.745013i	$-0.267557\pi$
$73$	3.03632	+	1.75302i	0.355374	+	0.205176i	−0.311675	+	0.950189i	$0.600890\pi$
$74$	−4.55980	+	7.89781i	−0.530066	+	0.918102i
$75$	−1.88135	−	3.25860i	−0.217240	−	0.376271i
$76$		−	2.89008i		−	0.331515i
$77$	5.91185	−	2.93067i	0.673718	−	0.333981i
$78$	2.80194	+	0.713792i	0.317257	+	0.0808210i
$79$	−7.54288	−	13.0646i	−0.848640	−	1.46989i	−0.882422	−	0.470458i	$-0.844089\pi$
$79$	−7.54288	−	13.0646i	−0.848640	−	1.46989i	0.0337823	−	0.999429i	$-0.489245\pi$
$80$	0.480608	+	0.277479i	0.0537336	+	0.0310231i
$81$	−1.81282	+	3.13990i	−0.201425	+	0.348878i
$82$	2.35690	+	4.08226i	0.260276	+	0.450811i
$83$			11.6039i			1.27369i	0.770992	+	0.636845i	$0.219761\pi$
$83$			11.6039i			1.27369i	−0.770992	+	0.636845i	$0.780239\pi$
$84$	−2.11747	−	0.134375i	−0.231035	−	0.0146615i
$85$		−	3.24698i		−	0.352184i
$86$	−5.22805	+	3.01842i	−0.563755	+	0.325484i
$87$	−2.51573	+	4.35737i	−0.269715	+	0.467159i
$88$	1.24698	−	2.15983i	0.132928	−	0.230239i
$89$	−7.69904	+	4.44504i	−0.816096	+	0.471173i	−0.849068	−	0.528283i	$-0.822836\pi$
$89$	−7.69904	+	4.44504i	−0.816096	+	0.471173i	0.0329721	+	0.999456i	$0.489503\pi$
$90$	1.30798			0.137873
$91$	−6.39260	−	7.08059i	−0.670126	−	0.742247i
$92$	−6.09783			−0.635743
$93$	−5.54760	+	3.20291i	−0.575259	+	0.332126i
$94$	−0.123490	+	0.213891i	−0.0127370	+	0.0220611i
$95$	−0.801938	+	1.38900i	−0.0822771	+	0.142508i
$96$	−0.694498	+	0.400969i	−0.0708820	+	0.0409237i
$97$			9.52542i			0.967160i	0.875300	+	0.483580i	$0.160664\pi$
$97$			9.52542i			0.967160i	−0.875300	+	0.483580i	$0.839336\pi$
$98$	5.57111	+	4.23825i	0.562767	+	0.428128i
$99$		−	5.87800i		−	0.590761i
$100$	2.34601	+	4.06341i	0.234601	+	0.406341i
$101$	1.41789	−	2.45587i	0.141086	−	0.244368i	−0.786820	−	0.617183i	$-0.788274\pi$
$101$	1.41789	−	2.45587i	0.141086	−	0.244368i	0.927906	+	0.372815i	$0.121607\pi$
$102$	4.06341	+	2.34601i	0.402338	+	0.232290i
$103$	−2.10992	−	3.65448i	−0.207896	−	0.360087i	0.743155	−	0.669119i	$-0.233328\pi$
$103$	−2.10992	−	3.65448i	−0.207896	−	0.360087i	−0.951052	+	0.309032i	$0.899995\pi$
$104$	−3.49396	−	0.890084i	−0.342611	−	0.0872799i
$105$	0.980386	+	0.652135i	0.0956758	+	0.0636418i
$106$			3.32975i			0.323414i
$107$	6.95473	+	12.0459i	0.672339	+	1.16453i	0.977239	+	0.212141i	$0.0680437\pi$
$107$	6.95473	+	12.0459i	0.672339	+	1.16453i	−0.304900	+	0.952384i	$0.598623\pi$
$108$	−2.14795	+	3.72036i	−0.206686	+	0.357991i
$109$	−2.12793	−	1.22856i	−0.203819	−	0.117675i	0.394617	−	0.918846i	$-0.370877\pi$
$109$	−2.12793	−	1.22856i	−0.203819	−	0.117675i	−0.598436	+	0.801171i	$0.704211\pi$
$110$	−1.19862	+	0.692021i	−0.114284	+	0.0659817i
$111$			7.31336i			0.694153i
$112$	2.64044	+	0.167563i	0.249498	+	0.0158332i
$113$	11.7681			1.10705			0.553524	−	0.832833i	$-0.313283\pi$
$113$	11.7681			1.10705			0.553524	+	0.832833i	$0.313283\pi$
$114$	−1.15883	−	2.00716i	−0.108535	−	0.187988i
$115$	2.93067	+	1.69202i	0.273286	+	0.157782i
$116$	3.13706	−	5.43355i	0.291269	−	0.504493i
$117$	−8.18055	+	2.30067i	−0.756292	+	0.212697i
$118$	6.53750			0.601826
$119$	−6.87538	−	13.8693i	−0.630265	−	1.27139i
$120$	0.445042			0.0406266
$121$	−2.39008	−	4.13975i	−0.217280	−	0.376341i
$122$	−12.7216	−	7.34481i	−1.15176	−	0.664968i
$123$	3.27372	+	1.89008i	0.295181	+	0.170423i
$124$	6.91774	−	3.99396i	0.621231	−	0.358668i
$125$		−	5.37867i		−	0.481083i
$126$	5.58695	−	2.76960i	0.497725	−	0.246736i
$127$	−2.45042			−0.217439			−0.108720	−	0.994072i	$-0.534675\pi$
$127$	−2.45042			−0.217439			−0.108720	+	0.994072i	$0.534675\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−2.42058	+	4.19257i	−0.213120	+	0.369135i
$130$	1.43224	+	1.39728i	0.125616	+	0.122550i
$131$	2.03050	+	3.51693i	0.177406	+	0.307275i	0.940991	−	0.338431i	$-0.109896\pi$
$131$	2.03050	+	3.51693i	0.177406	+	0.307275i	−0.763586	+	0.645707i	$0.776563\pi$
$132$		−	2.00000i		−	0.174078i
$133$	−0.484271	+	7.63109i	−0.0419916	+	0.661700i
$134$	2.09783			0.181225
$135$	2.06464	−	1.19202i	0.177696	−	0.102593i
$136$	−5.06699	−	2.92543i	−0.434491	−	0.250853i
$137$	−8.89765	−	5.13706i	−0.760178	−	0.438889i	0.0691817	−	0.997604i	$-0.477961\pi$
$137$	−8.89765	−	5.13706i	−0.760178	−	0.438889i	−0.829360	+	0.558715i	$0.811295\pi$
$138$	−4.23494	+	2.44504i	−0.360502	+	0.208136i
$139$	3.19136			0.270687			0.135344	−	0.990799i	$-0.456786\pi$
$139$	3.19136			0.270687			0.135344	+	0.990799i	$0.456786\pi$
$140$	−1.22252	−	0.813199i	−0.103322	−	0.0687278i
$141$			0.198062i			0.0166799i
$142$	−1.23341	−	2.13632i	−0.103505	−	0.179276i
$143$	6.27933	−	6.43645i	0.525104	−	0.538243i
$144$	1.17845	−	2.04113i	0.0982040	−	0.170094i
$145$	−3.01539	+	1.74094i	−0.250415	+	0.144577i
$146$	−3.50604			−0.290162
$147$	5.56853	+	0.709618i	0.459285	+	0.0585283i
$148$		−	9.11960i		−	0.749627i
$149$	20.6853	−	11.9426i	1.69460	−	0.978380i	0.743894	−	0.668298i	$-0.232977\pi$
$149$	20.6853	−	11.9426i	1.69460	−	0.978380i	0.950710	−	0.310082i	$-0.100357\pi$
$150$	3.25860	+	1.88135i	0.266064	+	0.153612i
$151$	12.6981	+	7.33124i	1.03336	+	0.596608i	0.917944	−	0.396710i	$-0.129848\pi$
$151$	12.6981	+	7.33124i	1.03336	+	0.596608i	0.115411	+	0.993318i	$0.463181\pi$
$152$	1.44504	+	2.50289i	0.117208	+	0.203011i
$153$	−13.7899			−1.11484
$154$	−3.65448	+	5.49396i	−0.294487	+	0.442716i
$155$	−4.43296			−0.356064
$156$	−2.78345	+	0.782807i	−0.222854	+	0.0626747i
$157$	3.20775	−	5.55599i	0.256006	−	0.443416i	−0.709162	−	0.705046i	$-0.750927\pi$
$157$	3.20775	−	5.55599i	0.256006	−	0.443416i	0.965168	+	0.261630i	$0.0842599\pi$
$158$	13.0646	+	7.54288i	1.03937	+	0.600079i
$159$	1.33513	+	2.31251i	0.105882	+	0.183394i
$160$	−0.554958			−0.0438733
$161$	16.1010	+	1.02177i	1.26893	+	0.0805268i
$162$		−	3.62565i		−	0.284858i
$163$	−8.63933	+	4.98792i	−0.676684	+	0.390684i	−0.798605	−	0.601856i	$-0.794428\pi$
$163$	−8.63933	+	4.98792i	−0.676684	+	0.390684i	0.121920	+	0.992540i	$0.461095\pi$
$164$	−4.08226	−	2.35690i	−0.318771	−	0.184043i
$165$	−0.554958	+	0.961216i	−0.0432034	+	0.0748305i
$166$	−5.80194	−	10.0493i	−0.450318	−	0.779973i
$167$		−	6.80433i		−	0.526535i	−0.964723	−	0.263267i	$-0.915200\pi$
$167$		−	6.80433i		−	0.526535i	0.964723	−	0.263267i	$-0.0848002\pi$
$168$	1.90097	−	0.942362i	0.146663	−	0.0727048i
$169$	−11.4155	−	6.21983i	−0.878116	−	0.478449i
$170$	1.62349	+	2.81197i	0.124516	+	0.215668i
$171$	5.89904	+	3.40581i	0.451111	+	0.260449i
$172$	3.01842	−	5.22805i	0.230152	−	0.398635i
$173$	−1.64310	−	2.84594i	−0.124923	−	0.216373i	0.796780	−	0.604270i	$-0.206535\pi$
$173$	−1.64310	−	2.84594i	−0.124923	−	0.216373i	−0.921703	+	0.387897i	$0.873202\pi$
$174$		−	5.03146i		−	0.381434i
$175$	−5.51362	−	11.1223i	−0.416791	−	0.840766i
$176$			2.49396i			0.187989i
$177$	4.54028	−	2.62133i	0.341269	−	0.197032i
$178$	4.44504	−	7.69904i	0.333170	−	0.577067i
$179$	−2.92058	+	5.05860i	−0.218295	+	0.378097i	−0.954287	−	0.298893i	$-0.903383\pi$
$179$	−2.92058	+	5.05860i	−0.218295	+	0.378097i	0.735992	+	0.676990i	$0.236716\pi$
$180$	−1.13274	+	0.653989i	−0.0844297	+	0.0487455i
$181$	10.6703			0.793114			0.396557	−	0.918010i	$-0.370205\pi$
$181$	10.6703			0.793114			0.396557	+	0.918010i	$0.370205\pi$
$182$	9.07644	+	2.93567i	0.672791	+	0.217606i
$183$	−11.7802			−0.870815
$184$	5.28088	−	3.04892i	0.389312	−	0.224769i
$185$	−2.53050	+	4.38295i	−0.186046	+	0.322241i
$186$	3.20291	−	5.54760i	0.234849	−	0.406770i
$187$	12.6369	−	7.29590i	0.924099	−	0.533529i
$188$		−	0.246980i		−	0.0180128i
$189$	6.29492	−	9.46346i	0.457888	−	0.688365i
$190$		−	1.60388i		−	0.116357i
$191$	11.5429	+	19.9928i	0.835213	+	1.44663i	0.893857	+	0.448353i	$0.147989\pi$
$191$	11.5429	+	19.9928i	0.835213	+	1.44663i	−0.0586435	+	0.998279i	$0.518678\pi$
$192$	0.400969	−	0.694498i	0.0289374	−	0.0501211i
$193$	11.5062	+	6.64310i	0.828234	+	0.478181i	0.853248	−	0.521506i	$-0.174630\pi$
$193$	11.5062	+	6.64310i	0.828234	+	0.478181i	−0.0250136	+	0.999687i	$0.507963\pi$
$194$	−4.76271	−	8.24925i	−0.341943	−	0.592262i
$195$	1.55496	+	0.396125i	0.111353	+	0.0283671i
$196$	−6.94385	−	0.884879i	−0.495989	−	0.0632056i
$197$			14.8834i			1.06040i	0.847874	+	0.530198i	$0.177883\pi$
$197$			14.8834i			1.06040i	−0.847874	+	0.530198i	$0.822117\pi$
$198$	2.93900	+	5.09050i	0.208866	+	0.361766i
$199$	−3.77479	+	6.53813i	−0.267588	+	0.463476i	−0.968238	−	0.250029i	$-0.919560\pi$
$199$	−3.77479	+	6.53813i	−0.267588	+	0.463476i	0.700651	+	0.713505i	$0.252893\pi$
$200$	−4.06341	−	2.34601i	−0.287326	−	0.165888i
$201$	1.45694	−	0.841166i	0.102765	−	0.0593313i
$202$			2.83579i			0.199525i
$203$	−9.19369	+	13.8213i	−0.645270	+	0.970066i
$204$	−4.69202			−0.328507
$205$	1.30798	+	2.26549i	0.0913532	+	0.158228i
$206$	3.65448	+	2.10992i	0.254620	+	0.147005i
$207$	7.18598	−	12.4465i	0.499460	−	0.865090i
$208$	3.47090	−	0.976144i	0.240664	−	0.0676834i
$209$	−7.20775			−0.498571
$210$	−1.17511	−	0.0745725i	−0.0810900	−	0.00514599i
$211$	−2.69740			−0.185697			−0.0928483	−	0.995680i	$-0.529597\pi$
$211$	−2.69740			−0.185697			−0.0928483	+	0.995680i	$0.529597\pi$
$212$	−1.66487	−	2.88365i	−0.114344	−	0.198050i
$213$	−1.71320	−	0.989115i	−0.117386	−	0.0677730i
$214$	−12.0459	−	6.95473i	−0.823444	−	0.475416i
$215$	−2.90135	+	1.67510i	−0.197870	+	0.114241i
$216$		−	4.29590i		−	0.292299i
$217$	−18.9351	+	9.38665i	−1.28540	+	0.637208i
$218$	2.45712			0.166417
$219$	−2.43494	+	1.40581i	−0.164538	+	0.0949961i
$220$	0.692021	−	1.19862i	0.0466561	−	0.0808107i
$221$	−15.1000	−	14.7314i	−1.01573	−	0.990939i
$222$	−3.65668	−	6.33355i	−0.245420	−	0.425080i
$223$			2.62565i			0.175826i	0.996128	+	0.0879131i	$0.0280198\pi$
$223$			2.62565i			0.175826i	−0.996128	+	0.0879131i	$0.971980\pi$
$224$	−2.37047	+	1.17511i	−0.158384	+	0.0785151i
$225$	−11.0586			−0.737240
$226$	−10.1915	+	5.88404i	−0.677926	+	0.391401i
$227$	7.90620	+	4.56465i	0.524753	+	0.302966i	0.738877	−	0.673840i	$-0.235356\pi$
$227$	7.90620	+	4.56465i	0.524753	+	0.302966i	−0.214124	+	0.976806i	$0.568690\pi$
$228$	2.00716	+	1.15883i	0.132927	+	0.0767456i
$229$	−9.27003	+	5.35205i	−0.612581	+	0.353674i	−0.773975	−	0.633216i	$-0.781734\pi$
$229$	−9.27003	+	5.35205i	−0.612581	+	0.353674i	0.161394	+	0.986890i	$0.448401\pi$
$230$	−3.38404			−0.223137
$231$	−0.335126	+	5.28088i	−0.0220496	+	0.347456i
$232$			6.27413i			0.411917i
$233$	−3.55011	−	6.14898i	−0.232576	−	0.402833i	0.725990	−	0.687706i	$-0.241382\pi$
$233$	−3.55011	−	6.14898i	−0.232576	−	0.402833i	−0.958565	+	0.284873i	$0.908049\pi$
$234$	5.93423	−	6.08271i	0.387933	−	0.397639i
$235$	−0.0685317	+	0.118700i	−0.00447051	+	0.00774316i
$236$	−5.66164	+	3.26875i	−0.368541	+	0.212777i
$237$	12.0978			0.785839
$238$	12.8889	+	8.57345i	0.835462	+	0.555735i
$239$		−	15.6136i		−	1.00996i	−0.863132	−	0.504979i	$-0.831500\pi$
$239$		−	15.6136i		−	1.00996i	0.863132	−	0.504979i	$-0.168500\pi$
$240$	−0.385418	+	0.222521i	−0.0248786	+	0.0143637i
$241$	−14.4159	−	8.32304i	−0.928612	−	0.536134i	−0.0422397	−	0.999108i	$-0.513449\pi$
$241$	−14.4159	−	8.32304i	−0.928612	−	0.536134i	−0.886372	+	0.462973i	$0.846783\pi$
$242$	4.13975	+	2.39008i	0.266113	+	0.153640i
$243$	−7.89762	−	13.6791i	−0.506632	−	0.877513i
$244$	14.6896			0.940407
$245$	3.09173	+	2.35205i	0.197523	+	0.150267i
$246$	−3.78017			−0.241015
$247$	2.82114	+	10.0312i	0.179505	+	0.638269i
$248$	−3.99396	+	6.91774i	−0.253617	+	0.439277i
$249$	−8.05887	−	4.65279i	−0.510710	−	0.294859i
$250$	2.68933	+	4.65806i	0.170088	+	0.294602i
$251$	11.9336			0.753244			0.376622	−	0.926367i	$-0.377086\pi$
$251$	11.9336			0.753244			0.376622	+	0.926367i	$0.377086\pi$
$252$	−3.45364	+	5.19202i	−0.217559	+	0.327067i
$253$			15.2078i			0.956103i
$254$	2.12212	−	1.22521i	0.133154	−	0.0768765i
$255$	2.25502	+	1.30194i	0.141215	+	0.0815305i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−0.634375	−	1.09877i	−0.0395712	−	0.0685394i	0.845561	−	0.533878i	$-0.179266\pi$
$257$	−0.634375	−	1.09877i	−0.0395712	−	0.0685394i	−0.885133	+	0.465339i	$0.845933\pi$
$258$		−	4.84117i		−	0.301398i
$259$	−1.52811	+	24.0798i	−0.0949519	+	1.49624i
$260$	−1.93900	−	0.493959i	−0.120252	−	0.0306340i
$261$	7.39373	+	12.8063i	0.457660	+	0.792691i
$262$	−3.51693	−	2.03050i	−0.217277	−	0.125445i
$263$	−2.65279	+	4.59477i	−0.163578	+	0.283326i	−0.936149	−	0.351602i	$-0.885637\pi$
$263$	−2.65279	+	4.59477i	−0.163578	+	0.283326i	0.772571	+	0.634928i	$0.218970\pi$
$264$	1.00000	+	1.73205i	0.0615457	+	0.106600i
$265$			1.84787i			0.113514i
$266$	−3.39616	−	6.85086i	−0.208232	−	0.420053i
$267$		−	7.12929i		−	0.436306i
$268$	−1.81678	+	1.04892i	−0.110977	+	0.0640728i
$269$	13.0097	−	22.5334i	0.793215	−	1.37389i	−0.130752	−	0.991415i	$-0.541739\pi$
$269$	13.0097	−	22.5334i	0.793215	−	1.37389i	0.923967	−	0.382473i	$-0.124928\pi$
$270$	−1.19202	+	2.06464i	−0.0725441	+	0.125650i
$271$	−21.0446	+	12.1501i	−1.27837	+	0.738066i	−0.976548	−	0.215299i	$-0.930928\pi$
$271$	−21.0446	+	12.1501i	−1.27837	+	0.738066i	−0.301820	+	0.953365i	$0.597594\pi$
$272$	5.85086			0.354760
$273$	7.48069	−	1.60055i	0.452752	−	0.0968699i
$274$	10.2741			0.620683
$275$	10.1340	−	5.85086i	0.611102	−	0.352820i
$276$	2.44504	−	4.23494i	0.147174	−	0.254913i
$277$	−0.939001	+	1.62640i	−0.0564191	+	0.0977208i	−0.892856	−	0.450343i	$-0.851302\pi$
$277$	−0.939001	+	1.62640i	−0.0564191	+	0.0977208i	0.836436	+	0.548064i	$0.184635\pi$
$278$	−2.76380	+	1.59568i	−0.165762	+	0.0957025i
$279$			18.8267i			1.12712i
$280$	1.46533	+	0.0929903i	0.0875704	+	0.00555724i
$281$			31.9081i			1.90348i	0.306906	+	0.951740i	$0.400706\pi$
$281$			31.9081i			1.90348i	−0.306906	+	0.951740i	$0.599294\pi$
$282$	−0.0990311	−	0.171527i	−0.00589722	−	0.0102143i
$283$	14.7681	−	25.5791i	0.877872	−	1.52052i	0.0241996	−	0.999707i	$-0.492296\pi$
$283$	14.7681	−	25.5791i	0.877872	−	1.52052i	0.853672	−	0.520811i	$-0.174370\pi$
$284$	2.13632	+	1.23341i	0.126767	+	0.0731892i
$285$	−0.643104	−	1.11389i	−0.0380942	−	0.0659811i
$286$	−2.21983	+	8.71379i	−0.131261	+	0.515257i
$287$	10.3840	+	6.90728i	0.612951	+	0.407724i
$288$			2.35690i			0.138881i
$289$	−8.61625	−	14.9238i	−0.506838	−	0.877870i
$290$	1.74094	−	3.01539i	0.102231	−	0.177070i
$291$	−6.61539	−	3.81940i	−0.387801	−	0.223897i
$292$	3.03632	−	1.75302i	0.177687	−	0.102588i
$293$		−	8.69932i		−	0.508220i	−0.967175	−	0.254110i	$-0.918218\pi$
$293$		−	8.69932i		−	0.508220i	0.967175	−	0.254110i	$-0.0817825\pi$
$294$	−5.17730	+	2.16972i	−0.301946	+	0.126541i
$295$	3.62804			0.211233
$296$	4.55980	+	7.89781i	0.265033	+	0.459051i
$297$	9.27842	+	5.35690i	0.538388	+	0.310839i
$298$	−11.9426	+	20.6853i	−0.691819	+	1.19827i
$299$	21.1650	−	5.95237i	1.22400	−	0.344234i
$300$	−3.76271			−0.217240
$301$	−8.84598	+	13.2986i	−0.509874	+	0.766518i
$302$	−14.6625			−0.843731
$303$	1.13706	+	1.96945i	0.0653226	+	0.113142i
$304$	−2.50289	−	1.44504i	−0.143550	−	0.0828788i
$305$	−7.05995	−	4.07606i	−0.404252	−	0.233395i
$306$	11.9424	−	6.89493i	0.682700	−	0.394157i
$307$		−	26.1521i		−	1.49258i	−0.665620	−	0.746290i	$-0.731833\pi$
$307$		−	26.1521i		−	1.49258i	0.665620	−	0.746290i	$-0.268167\pi$
$308$	0.417895	−	6.58515i	0.0238118	−	0.375224i
$309$	3.38404			0.192511
$310$	3.83906	−	2.21648i	0.218044	−	0.125888i
$311$	−5.55496	+	9.62147i	−0.314993	+	0.545583i	−0.979436	−	0.201755i	$-0.935335\pi$
$311$	−5.55496	+	9.62147i	−0.314993	+	0.545583i	0.664443	+	0.747339i	$0.268669\pi$
$312$	2.01913	−	2.06965i	0.114311	−	0.117171i
$313$	−3.91335	−	6.77811i	−0.221195	−	0.383122i	0.733976	−	0.679176i	$-0.237663\pi$
$313$	−3.91335	−	6.77811i	−0.221195	−	0.383122i	−0.955171	+	0.296054i	$0.904329\pi$
$314$			6.41550i			0.362048i
$315$	3.10052	−	1.53701i	0.174695	−	0.0866009i
$316$	−15.0858			−0.848640
$317$	−9.83909	+	5.68060i	−0.552619	+	0.319054i	−0.750177	−	0.661237i	$-0.770032\pi$
$317$	−9.83909	+	5.68060i	−0.552619	+	0.319054i	0.197559	+	0.980291i	$0.436699\pi$
$318$	−2.31251	−	1.33513i	−0.129679	−	0.0748701i
$319$	−13.5511	−	7.82371i	−0.758714	−	0.438044i
$320$	0.480608	−	0.277479i	0.0268668	−	0.0155116i
$321$	−11.1545			−0.622585
$322$	−14.4547	+	7.16560i	−0.805531	+	0.399323i
$323$			16.9095i			0.940868i
$324$	1.81282	+	3.13990i	0.100712	+	0.174439i
$325$	−12.1092	−	11.8136i	−0.671700	−	0.655303i
$326$	4.98792	−	8.63933i	0.276255	−	0.478488i
$327$	1.70647	−	0.985230i	0.0943679	−	0.0544833i
$328$	4.71379			0.260276
$329$	−0.0413846	+	0.652135i	−0.00228161	+	0.0359534i
$330$		−	1.10992i		−	0.0610989i
$331$	−17.5579	+	10.1371i	−0.965070	+	0.557183i	−0.897730	−	0.440547i	$-0.854785\pi$
$331$	−17.5579	+	10.1371i	−0.965070	+	0.557183i	−0.0673402	+	0.997730i	$0.521451\pi$
$332$	10.0493	+	5.80194i	0.551524	+	0.318423i
$333$	18.6143	+	10.7470i	1.02006	+	0.588931i
$334$	3.40217	+	5.89272i	0.186158	+	0.322435i
$335$	1.16421			0.0636076
$336$	−1.17511	+	1.76659i	−0.0641073	+	0.0963756i
$337$	−18.6963			−1.01845			−0.509227	−	0.860632i	$-0.670069\pi$
$337$	−18.6963			−1.01845			−0.509227	+	0.860632i	$0.670069\pi$
$338$	12.9960	−	0.321218i	0.706891	−	0.0174720i
$339$	−4.71864	+	8.17292i	−0.256281	+	0.443892i
$340$	−2.81197	−	1.62349i	−0.152500	−	0.0880461i
$341$	−9.96077	−	17.2526i	−0.539406	−	0.934279i
$342$	−6.81163			−0.368331
$343$	18.1865	+	3.50000i	0.981981	+	0.188982i
$344$			6.03684i			0.325484i
$345$	−2.35021	+	1.35690i	−0.126531	+	0.0730528i
$346$	2.84594	+	1.64310i	0.152999	+	0.0883338i
$347$	6.59999	−	11.4315i	0.354306	−	0.613676i	−0.632693	−	0.774403i	$-0.718050\pi$
$347$	6.59999	−	11.4315i	0.354306	−	0.613676i	0.986999	+	0.160727i	$0.0513838\pi$
$348$	2.51573	+	4.35737i	0.134857	+	0.233580i
$349$		−	33.2349i		−	1.77902i	−0.456912	−	0.889512i	$-0.651045\pi$
$349$		−	33.2349i		−	1.77902i	0.456912	−	0.889512i	$-0.348955\pi$
$350$	10.3361	+	6.87538i	0.552487	+	0.367504i
$351$	3.82371	−	15.0097i	0.204094	−	0.801158i
$352$	−1.24698	−	2.15983i	−0.0664642	−	0.115119i
$353$	−16.8886	−	9.75063i	−0.898889	−	0.518974i	−0.0220491	−	0.999757i	$-0.507019\pi$
$353$	−16.8886	−	9.75063i	−0.898889	−	0.518974i	−0.876839	+	0.480783i	$0.840352\pi$
$354$	−2.62133	+	4.54028i	−0.139322	+	0.241313i
$355$	−0.684489	−	1.18557i	−0.0363289	−	0.0629235i
$356$			8.89008i			0.471173i
$357$	12.3890	+	0.786208i	0.655695	+	0.0416106i
$358$		−	5.84117i		−	0.308715i
$359$	3.77991	−	2.18233i	0.199496	−	0.115179i	−0.396924	−	0.917851i	$-0.629922\pi$
$359$	3.77991	−	2.18233i	0.199496	−	0.115179i	0.596420	+	0.802672i	$0.296589\pi$
$360$	0.653989	−	1.13274i	0.0344683	−	0.0597008i
$361$	−5.32371	+	9.22093i	−0.280195	+	0.485312i
$362$	−9.24071	+	5.33513i	−0.485681	+	0.280408i
$363$	3.83340			0.201201
$364$	−9.32827	+	1.99586i	−0.488934	+	0.104611i
$365$	−1.94571			−0.101843
$366$	10.2019	−	5.89008i	0.533263	−	0.307880i
$367$	14.7506	−	25.5488i	0.769976	−	1.33364i	−0.167599	−	0.985855i	$-0.553601\pi$
$367$	14.7506	−	25.5488i	0.769976	−	1.33364i	0.937575	−	0.347783i	$-0.113065\pi$
$368$	−3.04892	+	5.28088i	−0.158936	+	0.275285i
$369$	9.62147	−	5.55496i	0.500874	−	0.289180i
$370$		−	5.06100i		−	0.263109i
$371$	3.91281	+	7.89307i	0.203143	+	0.409788i
$372$			6.40581i			0.332126i
$373$	−4.94869	−	8.57138i	−0.256233	−	0.443809i	0.708996	−	0.705212i	$-0.249148\pi$
$373$	−4.94869	−	8.57138i	−0.256233	−	0.443809i	−0.965230	+	0.261403i	$0.915815\pi$
$374$	−7.29590	+	12.6369i	−0.377262	+	0.653437i
$375$	3.73548	+	2.15668i	0.192899	+	0.111370i
$376$	0.123490	+	0.213891i	0.00636850	+	0.0110306i
$377$	−5.58450	+	21.9215i	−0.287616	+	1.12902i
$378$	−0.719833	+	11.3431i	−0.0370242	+	0.583424i
$379$		−	20.2935i		−	1.04241i	−0.853432	−	0.521204i	$-0.825483\pi$
$379$		−	20.2935i		−	1.04241i	0.853432	−	0.521204i	$-0.174517\pi$
$380$	0.801938	+	1.38900i	0.0411385	+	0.0712540i
$381$	0.982542	−	1.70181i	0.0503371	−	0.0871865i
$382$	−19.9928	−	11.5429i	−1.02292	−	0.590585i
$383$	14.3773	−	8.30074i	0.734646	−	0.424148i	−0.0854734	−	0.996340i	$-0.527240\pi$
$383$	14.3773	−	8.30074i	0.734646	−	0.424148i	0.820119	+	0.572192i	$0.193907\pi$
$384$			0.801938i			0.0409237i
$385$	−2.02808	+	3.04892i	−0.103361	+	0.155387i
$386$	−13.2862			−0.676250
$387$	7.11410	+	12.3220i	0.361630	+	0.626361i
$388$	8.24925	+	4.76271i	0.418792	+	0.241790i
$389$	11.2174	−	19.4292i	0.568747	−	0.985098i	−0.427943	−	0.903805i	$-0.640762\pi$
$389$	11.2174	−	19.4292i	0.568747	−	0.985098i	0.996690	−	0.0812928i	$-0.0259049\pi$
$390$	−1.54470	+	0.434425i	−0.0782187	+	0.0219980i
$391$	35.6775			1.80429
$392$	6.45599	−	2.70560i	0.326077	−	0.136653i
$393$	−3.25667			−0.164277
$394$	−7.44169	−	12.8894i	−0.374907	−	0.649358i
$395$	7.25033	+	4.18598i	0.364804	+	0.210620i
$396$	−5.09050	−	2.93900i	−0.255807	−	0.147690i
$397$	17.9073	−	10.3388i	0.898741	−	0.518888i	0.0219493	−	0.999759i	$-0.493013\pi$
$397$	17.9073	−	10.3388i	0.898741	−	0.518888i	0.876791	+	0.480871i	$0.159679\pi$
$398$		−	7.54958i		−	0.378426i
$399$	−5.10560	−	3.39616i	−0.255600	−	0.170020i
$400$	4.69202			0.234601
$401$	27.4336	−	15.8388i	1.36997	−	0.790951i	0.379043	−	0.925379i	$-0.376253\pi$
$401$	27.4336	−	15.8388i	1.36997	−	0.790951i	0.990923	+	0.134428i	$0.0429198\pi$
$402$	−0.841166	+	1.45694i	−0.0419536	+	0.0726657i
$403$	−20.1121	+	20.6153i	−1.00185	+	1.02692i
$404$	−1.41789	−	2.45587i	−0.0705429	−	0.122184i
$405$		−	2.01208i		−	0.0999811i
$406$	1.05131	−	16.5665i	0.0521757	−	0.822179i
$407$	−22.7439			−1.12737
$408$	4.06341	−	2.34601i	0.201169	−	0.116145i
$409$	6.32682	+	3.65279i	0.312841	+	0.180619i	0.648197	−	0.761473i	$-0.275523\pi$
$409$	6.32682	+	3.65279i	0.312841	+	0.180619i	−0.335356	+	0.942091i	$0.608857\pi$
$410$	−2.26549	−	1.30798i	−0.111884	−	0.0645965i
$411$	7.13537	−	4.11960i	0.351962	−	0.203205i
$412$	−4.21983			−0.207896
$413$	15.4969	−	7.68226i	0.762555	−	0.378019i
$414$			14.3720i			0.706343i
$415$	−3.21983	−	5.57691i	−0.158055	−	0.273760i
$416$	−2.51781	+	2.58082i	−0.123446	+	0.126535i
$417$	−1.27963	+	2.21639i	−0.0626640	+	0.108537i
$418$	6.24210	−	3.60388i	0.305311	−	0.176271i
$419$	−31.5381			−1.54074			−0.770368	−	0.637599i	$-0.779928\pi$
$419$	−31.5381			−1.54074			−0.770368	+	0.637599i	$0.779928\pi$
$420$	1.05496	−	0.522971i	0.0514767	−	0.0255184i
$421$		−	0.359289i		−	0.0175107i	−0.999962	−	0.00875533i	$-0.997213\pi$
$421$		−	0.359289i		−	0.0175107i	0.999962	−	0.00875533i	$-0.00278694\pi$
$422$	2.33602	−	1.34870i	0.113715	−	0.0656536i
$423$	0.504118	+	0.291053i	0.0245111	+	0.0141515i
$424$	2.88365	+	1.66487i	0.140042	+	0.0808534i
$425$	−13.7262	−	23.7744i	−0.665817	−	1.15323i
$426$	1.97823			0.0958455
$427$	−38.7871	−	2.46144i	−1.87704	−	0.119117i
$428$	13.9095			0.672339
$429$	1.95229	+	6.94180i	0.0942574	+	0.335153i
$430$	1.67510	−	2.90135i	0.0807803	−	0.139916i
$431$	31.0259	+	17.9128i	1.49447	+	0.862830i	0.999980	−	0.00635609i	$-0.00202322\pi$
$431$	31.0259	+	17.9128i	1.49447	+	0.862830i	0.494485	+	0.869186i	$0.335357\pi$
$432$	2.14795	+	3.72036i	0.103343	+	0.178996i
$433$	4.89977			0.235468			0.117734	−	0.993045i	$-0.462437\pi$
$433$	4.89977			0.235468			0.117734	+	0.993045i	$0.462437\pi$
$434$	11.7050	−	17.5966i	0.561856	−	0.844666i
$435$		−	2.79225i		−	0.133878i
$436$	−2.12793	+	1.22856i	−0.101909	+	0.0588374i
$437$	−15.2622	−	8.81163i	−0.730089	−	0.421517i
$438$	1.40581	−	2.43494i	0.0671724	−	0.116346i
$439$	19.5646	+	33.8870i	0.933770	+	1.61734i	0.776813	+	0.629731i	$0.216835\pi$
$439$	19.5646	+	33.8870i	0.933770	+	1.61734i	0.156956	+	0.987606i	$0.449832\pi$
$440$			1.38404i			0.0659817i
$441$	9.98911	−	13.1305i	0.475672	−	0.625263i
$442$	20.4426	+	5.20775i	0.972358	+	0.247707i
$443$	0.269282	+	0.466411i	0.0127940	+	0.0221598i	0.872352	−	0.488879i	$-0.162594\pi$
$443$	0.269282	+	0.466411i	0.0127940	+	0.0221598i	−0.859558	+	0.511039i	$0.829261\pi$
$444$	6.33355	+	3.65668i	0.300577	+	0.173538i
$445$	2.46681	−	4.27264i	0.116938	−	0.202543i
$446$	−1.31282	−	2.27388i	−0.0621640	−	0.107671i
$447$			19.1545i			0.905978i
$448$	1.46533	−	2.20291i	0.0692305	−	0.104078i
$449$			14.0194i			0.661615i	0.943698	+	0.330808i	$0.107321\pi$
$449$			14.0194i			0.661615i	−0.943698	+	0.330808i	$0.892679\pi$
$450$	9.57703	−	5.52930i	0.451466	−	0.260654i
$451$	−5.87800	+	10.1810i	−0.276784	+	0.479404i
$452$	5.88404	−	10.1915i	0.276762	−	0.479366i
$453$	−10.1831	+	5.87920i	−0.478442	+	0.276229i
$454$	−9.12929			−0.428459
$455$	5.03705	+	1.62917i	0.236140	+	0.0763769i
$456$	−2.31767			−0.108535
$457$	−1.67342	+	0.966148i	−0.0782792	+	0.0451945i	−0.538629	−	0.842543i	$-0.681057\pi$
$457$	−1.67342	+	0.966148i	−0.0782792	+	0.0451945i	0.460350	+	0.887738i	$0.347724\pi$
$458$	5.35205	−	9.27003i	0.250085	−	0.433160i
$459$	12.5673	−	21.7673i	0.586593	−	1.01601i
$460$	2.93067	−	1.69202i	0.136643	−	0.0788909i
$461$		−	28.6926i		−	1.33635i	−0.744005	−	0.668174i	$-0.767076\pi$
$461$		−	28.6926i		−	1.33635i	0.744005	−	0.668174i	$-0.232924\pi$
$462$	−2.35021	−	4.74094i	−0.109342	−	0.220568i
$463$		−	27.7198i		−	1.28825i	−0.764922	−	0.644123i	$-0.777222\pi$
$463$		−	27.7198i		−	1.28825i	0.764922	−	0.644123i	$-0.222778\pi$
$464$	−3.13706	−	5.43355i	−0.145635	−	0.252246i
$465$	1.77748	−	3.07868i	0.0824286	−	0.142771i
$466$	6.14898	+	3.55011i	0.284846	+	0.164456i
$467$	11.2513	+	19.4878i	0.520648	+	0.901788i	0.999712	+	0.0240083i	$0.00764281\pi$
$467$	11.2513	+	19.4878i	0.520648	+	0.901788i	−0.479064	+	0.877780i	$0.659024\pi$
$468$	−2.09783	+	8.23490i	−0.0969724	+	0.380658i
$469$	4.97285	−	2.46518i	0.229625	−	0.113831i
$470$		−	0.137063i		−	0.00632226i
$471$	2.57242	+	4.45556i	0.118531	+	0.205301i
$472$	3.26875	−	5.66164i	0.150456	−	0.260598i
$473$	−13.0386	−	7.52781i	−0.599513	−	0.346129i
$474$	−10.4770	+	6.04892i	−0.481226	+	0.277836i
$475$			13.5603i			0.622191i
$476$	−15.4488	−	0.980386i	−0.708096	−	0.0449359i
$477$	7.84787			0.359329
$478$	7.80678	+	13.5217i	0.357074	+	0.618470i
$479$	7.43232	+	4.29105i	0.339591	+	0.196063i	0.660091	−	0.751185i	$-0.270518\pi$
$479$	7.43232	+	4.29105i	0.339591	+	0.196063i	−0.320500	+	0.947249i	$0.603851\pi$
$480$	0.222521	−	0.385418i	0.0101566	−	0.0175918i
$481$	8.90205	+	31.6532i	0.405899	+	1.44326i
$482$	16.6461			0.758209
$483$	−7.16560	+	10.7724i	−0.326046	+	0.490161i
$484$	−4.78017			−0.217280
$485$	−2.64310	−	4.57799i	−0.120017	−	0.207876i
$486$	13.6791	+	7.89762i	0.620495	+	0.358243i
$487$	13.9400	+	8.04825i	0.631681	+	0.364701i	0.781403	−	0.624027i	$-0.214504\pi$
$487$	13.9400	+	8.04825i	0.631681	+	0.364701i	−0.149722	+	0.988728i	$0.547838\pi$
$488$	−12.7216	+	7.34481i	−0.575879	+	0.332484i
$489$		−	8.00000i		−	0.361773i
$490$	−3.85354	−	0.491071i	−0.174085	−	0.0221843i
$491$	−11.0382			−0.498145			−0.249073	−	0.968485i	$-0.580126\pi$
$491$	−11.0382			−0.498145			−0.249073	+	0.968485i	$0.580126\pi$
$492$	3.27372	−	1.89008i	0.147591	−	0.0852116i
$493$	−18.3545	+	31.7909i	−0.826645	+	1.43179i
$494$	−7.45877	−	7.27670i	−0.335586	−	0.327394i
$495$	1.63102	+	2.82501i	0.0733090	+	0.126975i
$496$		−	7.98792i		−	0.358668i
$497$	−5.43416	−	3.61470i	−0.243755	−	0.162142i
$498$	9.30559			0.416993
$499$	−11.9340	+	6.89008i	−0.534238	+	0.308443i	−0.742741	−	0.669579i	$-0.766474\pi$
$499$	−11.9340	+	6.89008i	−0.534238	+	0.308443i	0.208502	+	0.978022i	$0.433141\pi$
$500$	−4.65806	−	2.68933i	−0.208315	−	0.120271i
$501$	4.72560	+	2.72832i	0.211124	+	0.121893i
$502$	−10.3348	+	5.96681i	−0.461266	+	0.266312i
$503$	−28.1823			−1.25658			−0.628292	−	0.777977i	$-0.716246\pi$
$503$	−28.1823			−1.25658			−0.628292	+	0.777977i	$0.716246\pi$
$504$	0.394928	−	6.22324i	0.0175915	−	0.277205i
$505$			1.57374i			0.0700307i
$506$	−7.60388	−	13.1703i	−0.338033	−	0.585491i
$507$	8.89692	−	5.43409i	0.395126	−	0.241336i
$508$	−1.22521	+	2.12212i	−0.0543599	+	0.0941541i
$509$	−20.0776	+	11.5918i	−0.889923	+	0.513797i	−0.873917	−	0.486075i	$-0.838428\pi$
$509$	−20.0776	+	11.5918i	−0.889923	+	0.513797i	−0.0160056	+	0.999872i	$0.505095\pi$
$510$	−2.60388			−0.115302
$511$	−8.31096	+	4.11997i	−0.367655	+	0.182257i
$512$		−	1.00000i		−	0.0441942i
$513$	−10.7521	+	6.20775i	−0.474719	+	0.274079i
$514$	1.09877	+	0.634375i	0.0484647	+	0.0279811i
$515$	2.02808	+	1.17092i	0.0893681	+	0.0515967i
$516$	2.42058	+	4.19257i	0.106560	+	0.184568i
$517$	−0.615957			−0.0270898
$518$	−10.7165	−	21.6177i	−0.470856	−	0.949829i
$519$	2.63533			0.115678
$520$	1.92620	−	0.541719i	0.0844696	−	0.0237560i
$521$	−7.74578	+	13.4161i	−0.339349	+	0.587770i	−0.984310	−	0.176445i	$-0.943540\pi$
$521$	−7.74578	+	13.4161i	−0.339349	+	0.587770i	0.644961	+	0.764215i	$0.276873\pi$
$522$	−12.8063	−	7.39373i	−0.560517	−	0.323615i
$523$	−20.6129	−	35.7026i	−0.901339	−	1.56117i	−0.825757	−	0.564026i	$-0.809252\pi$
$523$	−20.6129	−	35.7026i	−0.901339	−	1.56117i	−0.0755819	−	0.997140i	$-0.524081\pi$
$524$	4.06100			0.177406
$525$	9.93521	+	0.630490i	0.433608	+	0.0275168i
$526$		−	5.30559i		−	0.231335i
$527$	−40.4747	+	23.3681i	−1.76311	+	1.01793i
$528$	−1.73205	−	1.00000i	−0.0753778	−	0.0435194i
$529$	−7.09179	+	12.2833i	−0.308339	+	0.534059i
$530$	−0.923936	−	1.60030i	−0.0401332	−	0.0695127i
$531$		−	15.4082i		−	0.668659i
$532$	6.36658	+	4.23494i	0.276026	+	0.183608i
$533$	16.4698	+	4.19567i	0.713386	+	0.181735i
$534$	3.56465	+	6.17415i	0.154257	+	0.267182i
$535$	−6.68500	−	3.85958i	−0.289018	−	0.166864i
$536$	1.04892	−	1.81678i	0.0453063	−	0.0784729i
$537$	−2.34213	−	4.05668i	−0.101070	−	0.175059i
$538$			26.0194i			1.12178i
$539$	−2.20685	+	17.3177i	−0.0950559	+	0.745925i
$540$		−	2.38404i		−	0.102593i
$541$	−7.66392	+	4.42476i	−0.329497	+	0.190235i	−0.655618	−	0.755093i	$-0.727592\pi$
$541$	−7.66392	+	4.42476i	−0.329497	+	0.190235i	0.326121	+	0.945328i	$0.394258\pi$
$542$	12.1501	−	21.0446i	0.521892	−	0.903943i
$543$	−4.27844	+	7.41047i	−0.183605	+	0.318014i
$544$	−5.06699	+	2.92543i	−0.217245	+	0.125427i
$545$	1.36360			0.0584102
$546$	−5.67819	+	5.12646i	−0.243004	+	0.219392i
$547$	21.6329			0.924958			0.462479	−	0.886630i	$-0.346960\pi$
$547$	21.6329			0.924958			0.462479	+	0.886630i	$0.346960\pi$
$548$	−8.89765	+	5.13706i	−0.380089	+	0.219444i
$549$	−17.3110	+	29.9835i	−0.738814	+	1.27966i
$550$	−5.85086	+	10.1340i	−0.249481	+	0.432114i
$551$	15.7034	−	9.06638i	0.668988	−	0.386241i
$552$			4.89008i			0.208136i
$553$	39.8330	+	2.52781i	1.69387	+	0.107493i
$554$		−	1.87800i		−	0.0797887i
$555$	−2.02930	−	3.51486i	−0.0861391	−	0.149197i
$556$	1.59568	−	2.76380i	0.0676719	−	0.117211i
$557$	21.5848	+	12.4620i	0.914576	+	0.528031i	0.881901	−	0.471436i	$-0.156264\pi$
$557$	21.5848	+	12.4620i	0.914576	+	0.528031i	0.0326751	+	0.999466i	$0.489597\pi$
$558$	−9.41335	−	16.3044i	−0.398499	−	0.690220i
$559$	−5.37329	+	21.0925i	−0.227266	+	0.892116i
$560$	−1.31551	+	0.652135i	−0.0555905	+	0.0275577i
$561$			11.7017i			0.494047i
$562$	−15.9541	−	27.6333i	−0.672982	−	1.16564i
$563$	−12.0305	+	20.8374i	−0.507025	+	0.878193i	0.492942	+	0.870062i	$0.335922\pi$
$563$	−12.0305	+	20.8374i	−0.507025	+	0.878193i	−0.999967	+	0.00813097i	$0.997412\pi$
$564$	0.171527	+	0.0990311i	0.00722259	+	0.00416996i
$565$	−5.65583	+	3.26540i	−0.237943	+	0.137376i
$566$			29.5362i			1.24150i
$567$	−4.26052	−	8.59448i	−0.178925	−	0.360934i
$568$	−2.46681			−0.103505
$569$	16.8470	+	29.1798i	0.706262	+	1.22328i	0.966234	+	0.257665i	$0.0829532\pi$
$569$	16.8470	+	29.1798i	0.706262	+	1.22328i	−0.259973	+	0.965616i	$0.583714\pi$
$570$	1.11389	+	0.643104i	0.0466557	+	0.0269367i
$571$	−2.19083	+	3.79462i	−0.0916832	+	0.158800i	−0.908219	−	0.418494i	$-0.862558\pi$
$571$	−2.19083	+	3.79462i	−0.0916832	+	0.158800i	0.816536	+	0.577294i	$0.195891\pi$
$572$	−2.43446	−	8.65628i	−0.101790	−	0.361937i
$573$	−18.5133			−0.773406
$574$	−12.4465	−	0.789856i	−0.519506	−	0.0329680i
$575$	28.6112			1.19317
$576$	−1.17845	−	2.04113i	−0.0491020	−	0.0850472i
$577$	−31.3254	−	18.0858i	−1.30410	−	0.752920i	−0.322991	−	0.946402i	$-0.604689\pi$
$577$	−31.3254	−	18.0858i	−1.30410	−	0.752920i	−0.981104	+	0.193482i	$0.938022\pi$
$578$	14.9238	+	8.61625i	0.620748	+	0.358389i
$579$	−9.22725	+	5.32736i	−0.383471	+	0.221397i
$580$			3.48188i			0.144577i
$581$	−25.5623	−	17.0035i	−1.06050	−	0.705426i
$582$	7.63879			0.316638
$583$	−7.19170	+	4.15213i	−0.297850	+	0.171964i
$584$	−1.75302	+	3.03632i	−0.0725405	+	0.125644i
$585$	3.29325	−	3.37565i	0.136159	−	0.139566i
$586$	4.34966	+	7.53383i	0.179683	+	0.311220i
$587$		−	35.0616i		−	1.44715i	−0.690248	−	0.723573i	$-0.742498\pi$
$587$		−	35.0616i		−	1.44715i	0.690248	−	0.723573i	$-0.257502\pi$
$588$	3.39881	−	4.46768i	0.140165	−	0.184244i
$589$	23.0858			0.951232
$590$	−3.14197	+	1.81402i	−0.129353	+	0.0746820i
$591$	−10.3365	−	5.96777i	−0.425186	−	0.245481i
$592$	−7.89781	−	4.55980i	−0.324598	−	0.187407i
$593$	−21.1444	+	12.2078i	−0.868298	+	0.501312i	−0.866782	−	0.498687i	$-0.833816\pi$
$593$	−21.1444	+	12.2078i	−0.868298	+	0.501312i	−0.00151591	+	0.999999i	$0.500483\pi$
$594$	−10.7138			−0.439592
$595$	7.15279	+	4.75791i	0.293236	+	0.195055i
$596$		−	23.8853i		−	0.978380i
$597$	−3.02715	−	5.24317i	−0.123893	−	0.214589i
$598$	−15.3532	+	15.7374i	−0.627840	+	0.643550i
$599$	−16.3002	+	28.2328i	−0.666008	+	1.15356i	0.313002	+	0.949752i	$0.398665\pi$
$599$	−16.3002	+	28.2328i	−0.666008	+	1.15356i	−0.979011	+	0.203808i	$0.934668\pi$
$600$	3.25860	−	1.88135i	0.133032	−	0.0768060i
$601$	15.9989			0.652610			0.326305	−	0.945265i	$-0.394196\pi$
$601$	15.9989			0.652610			0.326305	+	0.945265i	$0.394196\pi$
$602$	1.01155	−	15.9399i	0.0412277	−	0.649662i
$603$		−	4.94438i		−	0.201351i
$604$	12.6981	−	7.33124i	0.516678	−	0.298304i
$605$	2.29739	+	1.32640i	0.0934020	+	0.0539257i
$606$	−1.96945	−	1.13706i	−0.0800035	−	0.0461900i
$607$	−8.79656	−	15.2361i	−0.357041	−	0.618414i	0.630424	−	0.776251i	$-0.282881\pi$
$607$	−8.79656	−	15.2361i	−0.357041	−	0.618414i	−0.987465	+	0.157837i	$0.949548\pi$
$608$	2.89008			0.117208
$609$	−5.91250	−	11.9269i	−0.239587	−	0.483303i
$610$	8.15213			0.330070
$611$	0.241088	+	0.857241i	0.00975337	+	0.0346803i
$612$	−6.89493	+	11.9424i	−0.278711	+	0.482742i
$613$	14.8635	+	8.58144i	0.600331	+	0.346601i	0.769172	−	0.639042i	$-0.220669\pi$
$613$	14.8635	+	8.58144i	0.600331	+	0.346601i	−0.168841	+	0.985643i	$0.554002\pi$
$614$	13.0761	+	22.6484i	0.527707	+	0.914015i
$615$	−2.09783			−0.0845929
$616$	2.93067	+	5.91185i	0.118080	+	0.238195i
$617$		−	29.5797i		−	1.19083i	−0.803417	−	0.595417i	$-0.796987\pi$
$617$		−	29.5797i		−	1.19083i	0.803417	−	0.595417i	$-0.203013\pi$
$618$	−2.93067	+	1.69202i	−0.117889	+	0.0680631i
$619$	30.5076	+	17.6136i	1.22620	+	0.707949i	0.966234	−	0.257668i	$-0.0829540\pi$
$619$	30.5076	+	17.6136i	1.22620	+	0.707949i	0.259970	+	0.965617i	$0.416287\pi$
$620$	−2.21648	+	3.83906i	−0.0890160	+	0.154180i
$621$	13.0978	+	22.6861i	0.525598	+	0.910362i
$622$		−	11.1099i		−	0.445467i
$623$	1.48965	−	23.4737i	0.0596815	−	0.940455i
$624$	−0.713792	+	2.80194i	−0.0285745	+	0.112167i
$625$	−10.2376	−	17.7320i	−0.409503	−	0.709281i
$626$	6.77811	+	3.91335i	0.270908	+	0.156409i
$627$	2.89008	−	5.00577i	0.115419	−	0.199911i
$628$	−3.20775	−	5.55599i	−0.128003	−	0.221708i
$629$			53.3575i			2.12750i
$630$	−1.91662	+	2.88135i	−0.0763602	+	0.114796i
$631$		−	9.55065i		−	0.380205i	−0.981764	−	0.190103i	$-0.939118\pi$
$631$		−	9.55065i		−	0.380205i	0.981764	−	0.190103i	$-0.0608821\pi$
$632$	13.0646	−	7.54288i	0.519684	−	0.300040i
$633$	1.08157	−	1.87334i	0.0429887	−	0.0744585i
$634$	5.68060	−	9.83909i	0.225606	−	0.390760i
$635$	1.17769	−	0.679940i	0.0467352	−	0.0269826i
$636$	2.67025			0.105882
$637$	24.9652	−	3.70687i	0.989156	−	0.146872i
$638$	15.6474			0.619487
$639$	−5.03509	+	2.90701i	−0.199185	+	0.115000i
$640$	−0.277479	+	0.480608i	−0.0109683	+	0.0189977i
$641$	10.6957	−	18.5254i	0.422454	−	0.731711i	−0.573725	−	0.819048i	$-0.694502\pi$
$641$	10.6957	−	18.5254i	0.422454	−	0.731711i	0.996179	+	0.0873368i	$0.0278356\pi$
$642$	9.66010	−	5.57726i	0.381254	−	0.220117i
$643$			4.05429i			0.159886i	0.996799	+	0.0799429i	$0.0254738\pi$
$643$			4.05429i			0.159886i	−0.996799	+	0.0799429i	$0.974526\pi$
$644$	8.93536	−	13.4330i	0.352103	−	0.529333i
$645$		−	2.68664i		−	0.105787i
$646$	−8.45473	−	14.6440i	−0.332647	−	0.576161i
$647$	−13.9366	+	24.1389i	−0.547905	+	0.948999i	0.450513	+	0.892770i	$0.351241\pi$
$647$	−13.9366	+	24.1389i	−0.547905	+	0.948999i	−0.998418	+	0.0562289i	$0.982092\pi$
$648$	−3.13990	−	1.81282i	−0.123347	−	0.0712144i
$649$	8.15213	+	14.1199i	0.319999	+	0.554255i
$650$	16.3937	+	4.17629i	0.643015	+	0.163808i
$651$	1.07338	−	16.9142i	0.0420689	−	0.662918i
$652$			9.97584i			0.390684i
$653$	−4.73556	−	8.20223i	−0.185317	−	0.320978i	0.758366	−	0.651829i	$-0.225998\pi$
$653$	−4.73556	−	8.20223i	−0.185317	−	0.320978i	−0.943683	+	0.330850i	$0.892664\pi$
$654$	−0.985230	+	1.70647i	−0.0385255	+	0.0667282i
$655$	−1.95175	−	1.12684i	−0.0762611	−	0.0440294i
$656$	−4.08226	+	2.35690i	−0.159386	+	0.0920213i
$657$			8.26337i			0.322385i
$658$	−0.290227	−	0.585458i	−0.0113142	−	0.0228235i
$659$	1.29829			0.0505742			0.0252871	−	0.999680i	$-0.491950\pi$
$659$	1.29829			0.0505742			0.0252871	+	0.999680i	$0.491950\pi$
$660$	0.554958	+	0.961216i	0.0216017	+	0.0374153i
$661$	−9.38292	−	5.41723i	−0.364953	−	0.210706i	0.306298	−	0.951936i	$-0.400910\pi$
$661$	−9.38292	−	5.41723i	−0.364953	−	0.210706i	−0.671251	+	0.741230i	$0.734243\pi$
$662$	10.1371	−	17.5579i	0.393988	−	0.682408i
$663$	16.2855	−	4.58009i	0.632478	−	0.177876i
$664$	−11.6039			−0.450318
$665$	−1.88472	−	3.80194i	−0.0730865	−	0.147433i
$666$	−21.4940			−0.832874
$667$	−19.1293	−	33.1329i	−0.740689	−	1.28291i
$668$	−5.89272	−	3.40217i	−0.227996	−	0.131634i
$669$	−1.82351	−	1.05280i	−0.0705008	−	0.0407037i
$670$	−1.00824	+	0.582105i	−0.0389515	+	0.0224887i
$671$		−	36.6353i		−	1.41429i
$672$	0.134375	−	2.11747i	0.00518363	−	0.0816831i
$673$	17.8025			0.686237			0.343119	−	0.939292i	$-0.388517\pi$
$673$	17.8025			0.686237			0.343119	+	0.939292i	$0.388517\pi$
$674$	16.1915	−	9.34817i	0.623673	−	0.360078i
$675$	10.0782	−	17.4560i	0.387911	−	0.671881i
$676$	−11.0943	+	6.77620i	−0.426703	+	0.260623i
$677$	17.0640	+	29.5557i	0.655822	+	1.13592i	0.981687	+	0.190501i	$0.0610112\pi$
$677$	17.0640	+	29.5557i	0.655822	+	1.13592i	−0.325865	+	0.945416i	$0.605655\pi$
$678$		−	9.43727i		−	0.362436i
$679$	−20.9836	−	13.9579i	−0.805277	−	0.535656i
$680$	3.24698			0.124516
$681$	−6.34028	+	3.66056i	−0.242960	+	0.140273i
$682$	17.2526	+	9.96077i	0.660635	+	0.381418i
$683$	−20.3434	−	11.7453i	−0.778417	−	0.449420i	0.0574517	−	0.998348i	$-0.481702\pi$
$683$	−20.3434	−	11.7453i	−0.778417	−	0.449420i	−0.835869	+	0.548929i	$0.815036\pi$
$684$	5.89904	−	3.40581i	0.225555	−	0.130225i
$685$	5.70171			0.217851
$686$	−17.5000	+	6.06218i	−0.668153	+	0.231455i
$687$		−	8.58402i		−	0.327501i
$688$	−3.01842	−	5.22805i	−0.115076	−	0.199318i
$689$	8.59347	+	8.38369i	0.327385	+	0.319393i
$690$	1.35690	−	2.35021i	0.0516561	−	0.0894711i
$691$	20.7898	−	12.0030i	0.790880	−	0.456615i	−0.0493920	−	0.998779i	$-0.515728\pi$
$691$	20.7898	−	12.0030i	0.790880	−	0.456615i	0.840272	+	0.542164i	$0.182395\pi$
$692$	−3.28621			−0.124923
$693$	12.9487	+	8.61323i	0.491880	+	0.327190i
$694$			13.2000i			0.501064i
$695$	−1.53379	+	0.885535i	−0.0581800	+	0.0335903i
$696$	−4.35737	−	2.51573i	−0.165166	−	0.0953585i
$697$	23.8847	+	13.7899i	0.904699	+	0.522328i
$698$	16.6174	+	28.7823i	0.628980	+	1.08942i
$699$	5.69394			0.215365
$700$	−12.3890	−	0.786208i	−0.468260	−	0.0297159i
$701$	3.28621			0.124118			0.0620592	−	0.998072i	$-0.480233\pi$
$701$	3.28621			0.124118			0.0620592	+	0.998072i	$0.480233\pi$
$702$	4.19342	+	14.9106i	0.158270	+	0.562765i
$703$	13.1782	−	22.8253i	0.497026	−	0.860874i
$704$	2.15983	+	1.24698i	0.0814017	+	0.0469973i
$705$	−0.0549581	−	0.0951903i	−0.00206984	−	0.00358507i
$706$	19.5013			0.733939
$707$	3.33235	+	6.72215i	0.125326	+	0.252813i
$708$		−	5.24267i		−	0.197032i
$709$	20.6278	−	11.9095i	0.774693	−	0.447269i	−0.0598532	−	0.998207i	$-0.519063\pi$
$709$	20.6278	−	11.9095i	0.774693	−	0.447269i	0.834546	+	0.550938i	$0.185730\pi$
$710$	1.18557	+	0.684489i	0.0444936	+	0.0256884i
$711$	17.7778	−	30.7920i	0.666719	−	1.15479i
$712$	−4.44504	−	7.69904i	−0.166585	−	0.288534i
$713$		−	48.7090i		−	1.82417i
$714$	−11.1223	+	5.51362i	−0.416241	+	0.206342i
$715$	−1.23191	+	4.83579i	−0.0460710	+	0.180848i
$716$	2.92058	+	5.05860i	0.109147	+	0.189049i
$717$	10.8436	+	6.26055i	0.404962	+	0.233805i
$718$	−2.18233	+	3.77991i	−0.0814439	+	0.141065i
$719$	−16.9172	−	29.3015i	−0.630906	−	1.09276i	−0.987367	−	0.158451i	$-0.949350\pi$
$719$	−16.9172	−	29.3015i	−0.630906	−	1.09276i	0.356461	−	0.934310i	$-0.383983\pi$
$720$			1.30798i			0.0487455i
$721$	11.1422	+	0.707087i	0.414958	+	0.0263333i
$722$		−	10.6474i		−	0.396256i
$723$	11.5607	−	6.67456i	0.429946	−	0.248230i
$724$	5.33513	−	9.24071i	0.198278	−	0.343428i
$725$	−14.7192	+	25.4943i	−0.546656	+	0.946836i
$726$	−3.31982	+	1.91670i	−0.123210	+	0.0711353i
$727$	19.3163			0.716403			0.358202	−	0.933644i	$-0.383390\pi$
$727$	19.3163			0.716403			0.358202	+	0.933644i	$0.383390\pi$
$728$	7.08059	−	6.39260i	0.262424	−	0.236925i
$729$	1.78986			0.0662910
$730$	1.68503	−	0.972853i	0.0623658	−	0.0360069i
$731$	−17.6603	+	30.5886i	−0.653191	+	1.13136i
$732$	−5.89008	+	10.2019i	−0.217704	+	0.377074i
$733$	14.0233	−	8.09634i	0.517962	−	0.299045i	−0.218139	−	0.975918i	$-0.569999\pi$
$733$	14.0233	−	8.09634i	0.517962	−	0.299045i	0.736100	+	0.676873i	$0.236665\pi$
$734$			29.5013i			1.08891i
$735$	−2.87318	+	1.20410i	−0.105979	+	0.0444140i
$736$		−	6.09783i		−	0.224769i
$737$	2.61596	+	4.53097i	0.0963600	+	0.166900i
$738$	−5.55496	+	9.62147i	−0.204481	+	0.354171i
$739$	29.2075	+	16.8629i	1.07441	+	0.620313i	0.929384	−	0.369114i	$-0.120339\pi$
$739$	29.2075	+	16.8629i	1.07441	+	0.620313i	0.145030	+	0.989427i	$0.453672\pi$
$740$	2.53050	+	4.38295i	0.0930230	+	0.161121i
$741$	−8.09783	−	2.06292i	−0.297481	−	0.0757832i
$742$	−7.33513	−	4.87919i	−0.269281	−	0.179121i
$743$		−	32.5512i		−	1.19419i	−0.802171	−	0.597095i	$-0.796322\pi$
$743$		−	32.5512i		−	1.19419i	0.802171	−	0.597095i	$-0.203678\pi$
$744$	−3.20291	−	5.54760i	−0.117424	−	0.203385i
$745$	−6.62767	+	11.4795i	−0.242819	+	0.420575i
$746$	8.57138	+	4.94869i	0.313821	+	0.181184i
$747$	−23.6850	+	13.6746i	−0.866590	+	0.500326i
$748$		−	14.5918i		−	0.533529i
$749$	−36.7271	−	2.33071i	−1.34198	−	0.0851622i
$750$	−4.31336			−0.157501
$751$	−20.8780	−	36.1618i	−0.761849	−	1.31956i	−0.941896	−	0.335903i	$-0.890958\pi$
$751$	−20.8780	−	36.1618i	−0.761849	−	1.31956i	0.180047	−	0.983658i	$-0.442375\pi$
$752$	−0.213891	−	0.123490i	−0.00779979	−	0.00450321i
$753$	−4.78501	+	8.28788i	−0.174376	+	0.302027i
$754$	−6.12445	−	21.7769i	−0.223039	−	0.793067i
$755$	−8.13706			−0.296138
$756$	−5.04814	−	10.1833i	−0.183599	−	0.370363i
$757$	29.9603			1.08893			0.544463	−	0.838785i	$-0.316734\pi$
$757$	29.9603			1.08893			0.544463	+	0.838785i	$0.316734\pi$
$758$	10.1468	+	17.5747i	0.368547	+	0.638341i
$759$	−10.5618	−	6.09783i	−0.383368	−	0.221337i
$760$	−1.38900	−	0.801938i	−0.0503842	−	0.0290893i
$761$	45.5040	−	26.2717i	1.64952	−	0.952350i	0.672255	−	0.740320i	$-0.265326\pi$
$761$	45.5040	−	26.2717i	1.64952	−	0.952350i	0.977263	−	0.212030i	$-0.0680073\pi$
$762$			1.96508i			0.0711875i
$763$	5.82454	−	2.88738i	0.210862	−	0.104530i
$764$	23.0858			0.835213
$765$	6.62751	−	3.82640i	0.239618	−	0.138344i
$766$	−8.30074	+	14.3773i	−0.299918	+	0.519473i
$767$	16.4602	−	16.8721i	0.594344	−	0.609216i
$768$	−0.400969	−	0.694498i	−0.0144687	−	0.0250606i
$769$			2.92021i			0.105306i	0.998613	+	0.0526528i	$0.0167677\pi$
$769$			2.92021i			0.105306i	−0.998613	+	0.0526528i	$0.983232\pi$
$770$	0.231914	−	3.65448i	0.00835760	−	0.131698i
$771$	1.01746			0.0366429
$772$	11.5062	−	6.64310i	0.414117	−	0.239091i
$773$	−5.06118	−	2.92208i	−0.182038	−	0.105100i	0.406212	−	0.913779i	$-0.366850\pi$
$773$	−5.06118	−	2.92208i	−0.182038	−	0.105100i	−0.588250	+	0.808679i	$0.700183\pi$
$774$	−12.3220	−	7.11410i	−0.442904	−	0.255711i
$775$	−32.4582	+	18.7397i	−1.16593	+	0.673151i
$776$	−9.52542			−0.341943
$777$	−16.1106	−	10.7165i	−0.577966	−	0.384452i
$778$			22.4349i			0.804329i
$779$	−6.81163	−	11.7981i	−0.244052	−	0.422710i
$780$	1.12053	−	1.14857i	0.0401215	−	0.0411254i
$781$	3.07606	−	5.32790i	0.110070	−	0.190647i
$782$	−30.8977	+	17.8388i	−1.10490	+	0.637913i
$783$	−26.9530			−0.963222
$784$	−4.23825	+	5.57111i	−0.151366	+	0.198968i
$785$			3.56033i			0.127074i
$786$	2.82036	−	1.62833i	0.100599	−	0.0580808i
$787$	30.5639	+	17.6461i	1.08949	+	0.629015i	0.933440	−	0.358735i	$-0.116792\pi$
$787$	30.5639	+	17.6461i	1.08949	+	0.629015i	0.156047	+	0.987750i	$0.450125\pi$
$788$	12.8894	+	7.44169i	0.459165	+	0.265099i
$789$	−2.12737	−	3.68472i	−0.0757365	−	0.131180i
$790$	−8.37196			−0.297861
$791$	−17.2442	+	25.9240i	−0.613132	+	0.921751i
$792$	5.87800			0.208866
$793$	−50.9862	+	14.3392i	−1.81057	+	0.509200i
$794$	−10.3388	+	17.9073i	−0.366909	+	0.635506i
$795$	−1.28334	−	0.740939i	−0.0455155	−	0.0262784i
$796$	3.77479	+	6.53813i	0.133794	+	0.231738i
$797$	−35.4228			−1.25474			−0.627370	−	0.778721i	$-0.715869\pi$
$797$	−35.4228			−1.25474			−0.627370	+	0.778721i	$0.715869\pi$
$798$	6.11966	+	0.388355i	0.216634	+	0.0137476i
$799$			1.44504i			0.0511219i
$800$	−4.06341	+	2.34601i	−0.143663	+	0.0829440i
$801$	−18.1458	−	10.4765i	−0.641151	−	0.370169i
$802$	−15.8388	+	27.4336i	−0.559287	+	0.968713i
$803$	−4.37196	−	7.57246i	−0.154283	−	0.267226i
$804$		−	1.68233i		−	0.0593313i
$805$	−8.02177	+	3.97661i	−0.282730	+	0.140157i
$806$	7.10992	−	27.9095i	0.250436	−	0.983069i
$807$	10.4330	+	18.0704i	0.367258	+	0.636109i
$808$	2.45587	+	1.41789i	0.0863971	+	0.0498814i
$809$	−0.0199098	+	0.0344848i	−0.000699992	+	0.00121242i	−0.866375	−	0.499394i	$-0.833556\pi$
$809$	−0.0199098	+	0.0344848i	−0.000699992	+	0.00121242i	0.865675	+	0.500606i	$0.166889\pi$
$810$	1.00604	+	1.74251i	0.0353487	+	0.0612257i
$811$			16.4638i			0.578123i	0.957310	+	0.289062i	$0.0933432\pi$
$811$			16.4638i			0.578123i	−0.957310	+	0.289062i	$0.906657\pi$
$812$	7.37277	+	14.8726i	0.258733	+	0.521927i
$813$		−	19.4873i		−	0.683448i
$814$	19.6968	−	11.3720i	0.690373	−	0.398587i
$815$	2.76809	−	4.79447i	0.0969618	−	0.167943i
$816$	−2.34601	+	4.06341i	−0.0821268	+	0.142248i
$817$	15.1095	−	8.72348i	0.528615	−	0.305196i
$818$	−7.30559			−0.255434
$819$	6.91907	−	21.3922i	0.241772	−	0.747505i
$820$	2.61596			0.0913532
$821$	11.0584	−	6.38458i	0.385941	−	0.222823i	−0.294459	−	0.955664i	$-0.595139\pi$
$821$	11.0584	−	6.38458i	0.385941	−	0.222823i	0.680400	+	0.732841i	$0.261806\pi$
$822$	−4.11960	+	7.13537i	−0.143688	+	0.248874i
$823$	−10.1468	+	17.5747i	−0.353694	+	0.612615i	−0.986893	−	0.161373i	$-0.948408\pi$
$823$	−10.1468	+	17.5747i	−0.353694	+	0.612615i	0.633200	+	0.773988i	$0.281741\pi$
$824$	3.65448	−	2.10992i	0.127310	−	0.0735024i
$825$			9.38404i			0.326710i
$826$	−9.57962	+	14.4015i	−0.333318	+	0.501092i
$827$			27.4711i			0.955265i	0.878560	+	0.477632i	$0.158505\pi$
$827$			27.4711i			0.955265i	−0.878560	+	0.477632i	$0.841495\pi$
$828$	−7.18598	−	12.4465i	−0.249730	−	0.432545i
$829$	15.3545	−	26.5948i	0.533284	−	0.923675i	−0.465960	−	0.884806i	$-0.654291\pi$
$829$	15.3545	−	26.5948i	0.533284	−	0.923675i	0.999244	−	0.0388693i	$-0.0123756\pi$
$830$	5.57691	+	3.21983i	0.193577	+	0.111762i
$831$	−0.753020	−	1.30427i	−0.0261220	−	0.0452446i
$832$	0.890084	−	3.49396i	0.0308581	−	0.121131i
$833$	40.6274	+	5.17730i	1.40766	+	0.179383i
$834$		−	2.55927i		−	0.0886203i
$835$	1.88806	+	3.27021i	0.0653390	+	0.113170i
$836$	−3.60388	+	6.24210i	−0.124643	+	0.215887i
$837$	−29.7179	−	17.1576i	−1.02720	−	0.593055i
$838$	27.3128	−	15.7690i	0.943505	−	0.544733i
$839$			42.5991i			1.47068i	0.677696	+	0.735342i	$0.262978\pi$
$839$			42.5991i			1.47068i	−0.677696	+	0.735342i	$0.737022\pi$
$840$	−0.652135	+	0.980386i	−0.0225008	+	0.0338265i
$841$	10.3647			0.357402
$842$	0.179644	+	0.311153i	0.00619095	+	0.0107230i
$843$	−22.1601	−	12.7942i	−0.763236	−	0.440655i
$844$	−1.34870	+	2.33602i	−0.0464241	+	0.0804090i
$845$	7.21225	−	0.178263i	0.248109	−	0.00613242i
$846$	−0.582105			−0.0200132
$847$	12.6217	+	0.800978i	0.433688	+	0.0275219i
$848$	−3.32975			−0.114344
$849$	11.8431	+	20.5128i	0.406454	+	0.703998i
$850$	23.7744	+	13.7262i	0.815456	+	0.470804i
$851$	−48.1595	−	27.8049i	−1.65089	−	0.953140i
$852$	−1.71320	+	0.989115i	−0.0586932	+	0.0338865i
$853$		−	39.2524i		−	1.34398i	−0.740562	−	0.671988i	$-0.765441\pi$
$853$		−	39.2524i		−	1.34398i	0.740562	−	0.671988i	$-0.234559\pi$
$854$	34.8213	−	17.2619i	1.19156	−	0.590689i
$855$	−3.78017			−0.129279
$856$	−12.0459	+	6.95473i	−0.411722	+	0.237708i
$857$	2.56033	−	4.43463i	0.0874594	−	0.151484i	−0.818977	−	0.573826i	$-0.805459\pi$
$857$	2.56033	−	4.43463i	0.0874594	−	0.151484i	0.906437	+	0.422342i	$0.138792\pi$
$858$	−5.16163	−	5.03563i	−0.176215	−	0.171914i
$859$	−1.14310	−	1.97991i	−0.0390022	−	0.0675538i	0.845865	−	0.533396i	$-0.179085\pi$
$859$	−1.14310	−	1.97991i	−0.0390022	−	0.0675538i	−0.884868	+	0.465843i	$0.845751\pi$
$860$			3.35019i			0.114241i
$861$	−8.96077	+	4.44210i	−0.305382	+	0.151386i
$862$	−35.8256			−1.22023
$863$	−32.1726	+	18.5749i	−1.09517	+	0.632296i	−0.934948	−	0.354785i	$-0.884554\pi$
$863$	−32.1726	+	18.5749i	−1.09517	+	0.632296i	−0.160221	+	0.987081i	$0.551221\pi$
$864$	−3.72036	−	2.14795i	−0.126569	−	0.0730747i
$865$	1.57938	+	0.911854i	0.0537004	+	0.0310040i
$866$	−4.24333	+	2.44989i	−0.144194	+	0.0832505i
$867$	13.8194			0.469331
$868$	−1.33848	+	21.0916i	−0.0454309	+	0.715896i
$869$			37.6233i			1.27628i
$870$	1.39612	+	2.41816i	0.0473331	+	0.0819833i
$871$	5.28196	−	5.41412i	0.178972	−	0.183451i
$872$	1.22856	−	2.12793i	0.0416043	−	0.0720608i
$873$	−19.4426	+	11.2252i	−0.658033	+	0.379916i
$874$	17.6233			0.596115
$875$	11.8487	+	7.88154i	0.400559	+	0.266445i
$876$			2.81163i			0.0949961i
$877$	1.16672	−	0.673604i	0.0393972	−	0.0227460i	−0.480172	−	0.877174i	$-0.659426\pi$
$877$	1.16672	−	0.673604i	0.0393972	−	0.0227460i	0.519569	+	0.854428i	$0.326092\pi$
$878$	−33.8870	−	19.5646i	−1.14363	−	0.660275i
$879$	6.04166	+	3.48816i	0.203780	+	0.117653i
$880$	−0.692021	−	1.19862i	−0.0233280	−	0.0404053i
$881$	29.5157			0.994410			0.497205	−	0.867633i	$-0.334360\pi$
$881$	29.5157			0.994410			0.497205	+	0.867633i	$0.334360\pi$
$882$	−2.08557	+	16.3659i	−0.0702247	+	0.551069i
$883$	−16.0968			−0.541699			−0.270850	−	0.962622i	$-0.587305\pi$
$883$	−16.0968			−0.541699			−0.270850	+	0.962622i	$0.587305\pi$
$884$	−20.3077	+	5.71128i	−0.683023	+	0.192091i
$885$	−1.45473	+	2.51967i	−0.0489002	+	0.0846977i
$886$	−0.466411	−	0.269282i	−0.0156694	−	0.00904672i
$887$	11.8116	+	20.4583i	0.396596	+	0.686924i	0.993303	−	0.115535i	$-0.0368582\pi$
$887$	11.8116	+	20.4583i	0.396596	+	0.686924i	−0.596708	+	0.802459i	$0.703525\pi$
$888$	−7.31336			−0.245420
$889$	3.59068	−	5.39804i	0.120428	−	0.181045i
$890$			4.93362i			0.165375i
$891$	7.83079	−	4.52111i	0.262341	−	0.151463i
$892$	2.27388	+	1.31282i	0.0761350	+	0.0439566i
$893$	0.356896	−	0.618162i	0.0119431	−	0.0206860i
$894$	−9.57726	−	16.5883i	−0.320312	−	0.554796i
$895$		−	3.24160i		−	0.108355i
$896$	−0.167563	+	2.64044i	−0.00559788	+	0.0882109i
$897$	−4.35258	+	17.0858i	−0.145329	+	0.570477i
$898$	−7.00969	−	12.1411i	−0.233916	−	0.405155i
$899$	43.4028	+	25.0586i	1.44756	+	0.835751i
$900$	−5.52930	+	9.57703i	−0.184310	+	0.319234i
$901$	9.74094	+	16.8718i	0.324518	+	0.562081i
$902$		−	11.7560i		−	0.391432i
$903$	−5.68889	−	11.4758i	−0.189314	−	0.381892i
$904$			11.7681i			0.391401i
$905$	−5.12821	+	2.96077i	−0.170467	+	0.0984194i
$906$	5.87920	−	10.1831i	0.195323	−	0.338310i
$907$	12.7927	−	22.1576i	0.424774	−	0.735730i	−0.571625	−	0.820515i	$-0.693687\pi$
$907$	12.7927	−	22.1576i	0.424774	−	0.735730i	0.996399	+	0.0847848i	$0.0270203\pi$
$908$	7.90620	−	4.56465i	0.262376	−	0.151483i
$909$	6.68366			0.221683
$910$	−5.17680	+	1.10762i	−0.171609	+	0.0367172i
$911$	−51.8732			−1.71864			−0.859318	−	0.511441i	$-0.829112\pi$
$911$	−51.8732			−1.71864			−0.859318	+	0.511441i	$0.829112\pi$
$912$	2.00716	−	1.15883i	0.0664637	−	0.0383728i
$913$	14.4698	−	25.0624i	0.478880	−	0.829445i
$914$	0.966148	−	1.67342i	0.0319573	−	0.0553517i
$915$	5.66164	−	3.26875i	0.187168	−	0.108062i
$916$			10.7041i			0.353674i
$917$	−10.7228	−	0.680472i	−0.354099	−	0.0224712i
$918$			25.1347i			0.829568i
$919$	9.79954	+	16.9733i	0.323257	+	0.559898i	0.981158	−	0.193207i	$-0.0618888\pi$
$919$	9.79954	+	16.9733i	0.323257	+	0.559898i	−0.657901	+	0.753104i	$0.728555\pi$
$920$	−1.69202	+	2.93067i	−0.0557843	+	0.0966212i
$921$	18.1626	+	10.4862i	0.598478	+	0.345532i
$922$	14.3463	+	24.8485i	0.472470	+	0.818343i
$923$	−8.61894	−	2.19567i	−0.283696	−	0.0722713i
$924$	4.40581	+	2.93067i	0.144941	+	0.0964119i
$925$			42.7894i			1.40691i
$926$	13.8599	+	24.0060i	0.455464	+	0.788887i
$927$	4.97285	−	8.61323i	0.163330	−	0.282896i
$928$	5.43355	+	3.13706i	0.178365	+	0.102979i
$929$	3.03218	−	1.75063i	0.0994825	−	0.0574362i	−0.449433	−	0.893314i	$-0.648374\pi$
$929$	3.03218	−	1.75063i	0.0994825	−	0.0574362i	0.548916	+	0.835878i	$0.315041\pi$
$930$			3.55496i			0.116572i
$931$	−16.1010	−	12.2489i	−0.527688	−	0.401441i
$932$	−7.10023			−0.232576
$933$	−4.45473	−	7.71582i	−0.145841	−	0.252605i
$934$	−19.4878	−	11.2513i	−0.637661	−	0.368154i
$935$	−4.04892	+	7.01293i	−0.132414	+	0.229347i
$936$	−2.30067	−	8.18055i	−0.0751998	−	0.267390i
$937$	−12.9129			−0.421847			−0.210923	−	0.977503i	$-0.567647\pi$
$937$	−12.9129			−0.421847			−0.210923	+	0.977503i	$0.567647\pi$
$938$	−3.07403	+	4.62133i	−0.100371	+	0.150892i
$939$	6.27652			0.204826
$940$	0.0685317	+	0.118700i	0.00223526	+	0.00387158i
$941$	6.76133	+	3.90366i	0.220413	+	0.127256i	0.606142	−	0.795357i	$-0.292716\pi$
$941$	6.76133	+	3.90366i	0.220413	+	0.127256i	−0.385728	+	0.922612i	$0.626050\pi$
$942$	−4.45556	−	2.57242i	−0.145170	−	0.0838139i
$943$	−24.8930	+	14.3720i	−0.810627	+	0.468015i
$944$			6.53750i			0.212777i
$945$	−0.399477	+	6.29492i	−0.0129950	+	0.204774i
$946$	15.0556			0.489500
$947$	−16.6889	+	9.63533i	−0.542316	+	0.313106i	−0.746017	−	0.665927i	$-0.768036\pi$
$947$	−16.6889	+	9.63533i	−0.542316	+	0.313106i	0.203701	+	0.979033i	$0.434703\pi$
$948$	6.04892	−	10.4770i	0.196460	−	0.340278i
$949$	−8.82756	+	9.04844i	−0.286555	+	0.293725i
$950$	−6.78017	−	11.7436i	−0.219978	−	0.381013i
$951$		−	9.11098i		−	0.295444i
$952$	13.8693	−	6.87538i	0.449506	−	0.222832i
$953$	45.7482			1.48193			0.740965	−	0.671543i	$-0.234368\pi$
$953$	45.7482			1.48193			0.740965	+	0.671543i	$0.234368\pi$
$954$	−6.79646	+	3.92394i	−0.220043	+	0.127042i
$955$	−11.0952	−	6.40581i	−0.359032	−	0.207287i
$956$	−13.5217	−	7.80678i	−0.437324	−	0.252489i
$957$	10.8671	−	6.27413i	0.351284	−	0.202814i
$958$	−8.58211			−0.277275
$959$	24.3545	−	12.0732i	0.786448	−	0.389864i
$960$			0.445042i			0.0143637i
$961$	16.4034	+	28.4116i	0.529143	+	0.916502i
$962$	−23.5360	−	22.9615i	−0.758832	−	0.740308i
$963$	−16.3916	+	28.3910i	−0.528211	+	0.914889i
$964$	−14.4159	+	8.32304i	−0.464306	+	0.268067i
$965$	−7.37329			−0.237355
$966$	0.819396	−	12.9120i	0.0263636	−	0.415436i
$967$		−	49.4838i		−	1.59129i	−0.605762	−	0.795646i	$-0.707132\pi$
$967$		−	49.4838i		−	1.59129i	0.605762	−	0.795646i	$-0.292868\pi$
$968$	4.13975	−	2.39008i	0.133056	−	0.0768202i
$969$	−11.7436	−	6.78017i	−0.377259	−	0.217810i
$970$	4.57799	+	2.64310i	0.146990	+	0.0848650i
$971$	1.34093	+	2.32256i	0.0430325	+	0.0745344i	0.886739	−	0.462270i	$-0.152965\pi$
$971$	1.34093	+	2.32256i	0.0430325	+	0.0745344i	−0.843707	+	0.536804i	$0.819631\pi$
$972$	−15.7952			−0.506632
$973$	−4.67640	+	7.03026i	−0.149919	+	0.225380i
$974$	−16.0965			−0.515765
$975$	13.0600	−	3.67295i	0.418254	−	0.117628i
$976$	7.34481	−	12.7216i	0.235102	−	0.407208i
$977$	−46.8930	−	27.0737i	−1.50024	−	0.866163i	−1.00000		0.000276237i	$-0.999912\pi$
$977$	−46.8930	−	27.0737i	−1.50024	−	0.866163i	−0.500239	−	0.865887i	$-0.666755\pi$
$978$	4.00000	+	6.92820i	0.127906	+	0.221540i
$979$	22.1715			0.708604
$980$	3.58280	−	1.50149i	0.114448	−	0.0479634i
$981$		−	5.79118i		−	0.184898i
$982$	9.55933	−	5.51908i	0.305050	−	0.176121i
$983$	29.1061	+	16.8044i	0.928339	+	0.535977i	0.886286	−	0.463139i	$-0.153277\pi$
$983$	29.1061	+	16.8044i	0.928339	+	0.535977i	0.0420531	+	0.999115i	$0.486610\pi$
$984$	−1.89008	+	3.27372i	−0.0602537	+	0.104362i
$985$	−4.12983	−	7.15307i	−0.131587	−	0.227916i
$986$		−	36.7090i		−	1.16905i
$987$	−0.436313	−	0.290227i	−0.0138880	−	0.00923804i
$988$	10.0978	+	2.57242i	0.321255	+	0.0818395i
$989$	−18.4058	−	31.8798i	−0.585271	−	1.01372i
$990$	−2.82501	−	1.63102i	−0.0897848	−	0.0518373i
$991$	17.7560	−	30.7543i	0.564038	−	0.976943i	−0.433100	−	0.901346i	$-0.642580\pi$
$991$	17.7560	−	30.7543i	0.564038	−	0.976943i	0.997138	−	0.0755969i	$-0.0240862\pi$
$992$	3.99396	+	6.91774i	0.126808	+	0.219638i
$993$		−	16.2586i		−	0.515951i
$994$	6.51347	+	0.413346i	0.206595	+	0.0131105i
$995$		−	4.18970i		−	0.132822i
$996$	−8.05887	+	4.65279i	−0.255355	+	0.147429i
$997$	−30.5743	+	52.9563i	−0.968299	+	1.67714i	−0.267821	+	0.963469i	$0.586304\pi$
$997$	−30.5743	+	52.9563i	−0.968299	+	1.67714i	−0.700478	+	0.713674i	$0.747030\pi$
$998$	6.89008	−	11.9340i	0.218102	−	0.377763i
$999$	−33.9282	+	19.5884i	−1.07344	+	0.619751i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	182.2.n.b.25.1	✓	12
3.2	odd	2		1638.2.dm.d.1117.5		12
7.2	even	3	inner	182.2.n.b.51.4	yes	12
7.3	odd	6		1274.2.d.m.883.1		6
7.4	even	3		1274.2.d.k.883.3		6
7.5	odd	6		1274.2.n.l.961.6		12
7.6	odd	2		1274.2.n.l.753.3		12
13.12	even	2	inner	182.2.n.b.25.4	yes	12
21.2	odd	6		1638.2.dm.d.415.2		12
39.38	odd	2		1638.2.dm.d.1117.2		12
91.12	odd	6		1274.2.n.l.961.3		12
91.25	even	6		1274.2.d.k.883.6		6
91.38	odd	6		1274.2.d.m.883.4		6
91.51	even	6	inner	182.2.n.b.51.1	yes	12
91.90	odd	2		1274.2.n.l.753.6		12
273.233	odd	6		1638.2.dm.d.415.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.n.b.25.1	✓	12	1.1	even	1	trivial
182.2.n.b.25.4	yes	12	13.12	even	2	inner
182.2.n.b.51.1	yes	12	91.51	even	6	inner
182.2.n.b.51.4	yes	12	7.2	even	3	inner
1274.2.d.k.883.3		6	7.4	even	3
1274.2.d.k.883.6		6	91.25	even	6
1274.2.d.m.883.1		6	7.3	odd	6
1274.2.d.m.883.4		6	91.38	odd	6
1274.2.n.l.753.3		12	7.6	odd	2
1274.2.n.l.753.6		12	91.90	odd	2
1274.2.n.l.961.3		12	91.12	odd	6
1274.2.n.l.961.6		12	7.5	odd	6
1638.2.dm.d.415.2		12	21.2	odd	6
1638.2.dm.d.415.5		12	273.233	odd	6
1638.2.dm.d.1117.2		12	39.38	odd	2
1638.2.dm.d.1117.5		12	3.2	odd	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:	\( N \)	\(=\)	\( 182 = 2 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	182.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.400969 + 0.694498i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.480608 + 0.277479i) q^{5} -0.801938i q^{6} +(-1.46533 + 2.20291i) q^{7} +1.00000i q^{8} +(1.17845 + 2.04113i) q^{9} +(0.277479 - 0.480608i) q^{10} +(-2.15983 - 1.24698i) q^{11} +(0.400969 + 0.694498i) q^{12} +(-0.890084 + 3.49396i) q^{13} +(0.167563 - 2.64044i) q^{14} -0.445042i q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.92543 + 5.06699i) q^{17} +(-2.04113 - 1.17845i) q^{18} +(2.50289 - 1.44504i) q^{19} +0.554958i q^{20} +(-0.942362 - 1.90097i) q^{21} +2.49396 q^{22} +(-3.04892 - 5.28088i) q^{23} +(-0.694498 - 0.400969i) q^{24} +(-2.34601 + 4.06341i) q^{25} +(-0.976144 - 3.47090i) q^{26} -4.29590 q^{27} +(1.17511 + 2.37047i) q^{28} +6.27413 q^{29} +(0.222521 + 0.385418i) q^{30} +(6.91774 + 3.99396i) q^{31} +(0.866025 + 0.500000i) q^{32} +(1.73205 - 1.00000i) q^{33} -5.85086i q^{34} +(0.0929903 - 1.46533i) q^{35} +2.35690 q^{36} +(7.89781 - 4.55980i) q^{37} +(-1.44504 + 2.50289i) q^{38} +(-2.06965 - 2.01913i) q^{39} +(-0.277479 - 0.480608i) q^{40} -4.71379i q^{41} +(1.76659 + 1.17511i) q^{42} +6.03684 q^{43} +(-2.15983 + 1.24698i) q^{44} +(-1.13274 - 0.653989i) q^{45} +(5.28088 + 3.04892i) q^{46} +(0.213891 - 0.123490i) q^{47} +0.801938 q^{48} +(-2.70560 - 6.45599i) q^{49} -4.69202i q^{50} +(-2.34601 - 4.06341i) q^{51} +(2.58082 + 2.51781i) q^{52} +(1.66487 - 2.88365i) q^{53} +(3.72036 - 2.14795i) q^{54} +1.38404 q^{55} +(-2.20291 - 1.46533i) q^{56} +2.31767i q^{57} +(-5.43355 + 3.13706i) q^{58} +(-5.66164 - 3.26875i) q^{59} +(-0.385418 - 0.222521i) q^{60} +(7.34481 + 12.7216i) q^{61} -7.98792 q^{62} +(-6.22324 - 0.394928i) q^{63} -1.00000 q^{64} +(-0.541719 - 1.92620i) q^{65} +(-1.00000 + 1.73205i) q^{66} +(-1.81678 - 1.04892i) q^{67} +(2.92543 + 5.06699i) q^{68} +4.89008 q^{69} +(0.652135 + 1.31551i) q^{70} +2.46681i q^{71} +(-2.04113 + 1.17845i) q^{72} +(3.03632 + 1.75302i) q^{73} +(-4.55980 + 7.89781i) q^{74} +(-1.88135 - 3.25860i) q^{75} -2.89008i q^{76} +(5.91185 - 2.93067i) q^{77} +(2.80194 + 0.713792i) q^{78} +(-7.54288 - 13.0646i) q^{79} +(0.480608 + 0.277479i) q^{80} +(-1.81282 + 3.13990i) q^{81} +(2.35690 + 4.08226i) q^{82} +11.6039i q^{83} +(-2.11747 - 0.134375i) q^{84} -3.24698i q^{85} +(-5.22805 + 3.01842i) q^{86} +(-2.51573 + 4.35737i) q^{87} +(1.24698 - 2.15983i) q^{88} +(-7.69904 + 4.44504i) q^{89} +1.30798 q^{90} +(-6.39260 - 7.08059i) q^{91} -6.09783 q^{92} +(-5.54760 + 3.20291i) q^{93} +(-0.123490 + 0.213891i) q^{94} +(-0.801938 + 1.38900i) q^{95} +(-0.694498 + 0.400969i) q^{96} +9.52542i q^{97} +(5.57111 + 4.23825i) q^{98} -5.87800i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{3} + 6 q^{4} + 6 q^{9} + 4 q^{10} - 4 q^{12} - 8 q^{13} - 6 q^{16} - 8 q^{17} - 8 q^{22} - 18 q^{25} - 2 q^{26} + 4 q^{27} + 32 q^{29} + 2 q^{30} - 28 q^{35} + 12 q^{36} - 16 q^{38} - 12 q^{39}+ \cdots + 8 q^{95}+O(q^{100}) \) 12 * q + 4 * q^3 + 6 * q^4 + 6 * q^9 + 4 * q^10 - 4 * q^12 - 8 * q^13 - 6 * q^16 - 8 * q^17 - 8 * q^22 - 18 * q^25 - 2 * q^26 + 4 * q^27 + 32 * q^29 + 2 * q^30 - 28 * q^35 + 12 * q^36 - 16 * q^38 - 12 * q^39 - 4 * q^40 + 28 * q^42 - 40 * q^43 - 8 * q^48 - 18 * q^51 - 4 * q^52 + 24 * q^53 - 24 * q^55 - 4 * q^61 - 20 * q^62 - 12 * q^64 + 8 * q^65 - 12 * q^66 + 8 * q^68 + 56 * q^69 - 12 * q^74 + 12 * q^75 + 56 * q^77 + 16 * q^78 - 16 * q^79 + 2 * q^81 + 12 * q^82 + 20 * q^87 - 4 * q^88 + 36 * q^90 - 28 * q^91 + 8 * q^94 + 8 * q^95

Introduction

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