LMFDB - Embedded newform 45.2.l.a.32.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [45,2,Mod(2,45)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(45, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([2, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("45.2"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$45 = 3^{2} \cdot 5$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	45.l (of order $12$ , degree $4$ , minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$0.359326809096$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{16} - 6 x^{15} + 18 x^{14} - 36 x^{13} + 34 x^{12} + 18 x^{11} - 72 x^{10} + 132 x^{9} - 93 x^{8} + \cdots + 1$ x^16 - 6x^15 + 18x^14 - 36x^13 + 34x^12 + 18x^11 - 72x^10 + 132x^9 - 93x^8 - 102x^7 + 144x^6 - 432x^5 + 502x^4 + 288x^3 + 72x^2 + 12*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$1$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			32.1
Root			$2.24352 - 0.601150i$ of defining polynomial
Character	$\chi$	$=$	45.32
Dual form			45.2.l.a.38.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.24352 - 0.601150i) q^{2} +(0.173261 + 1.72336i) q^{3} +(2.93996 + 1.69739i) q^{4} +(2.10323 + 0.759216i) q^{5} +(0.647285 - 3.97056i) q^{6} +(-0.201351 + 0.751454i) q^{7} +(-2.29074 - 2.29074i) q^{8} +(-2.93996 + 0.597183i) q^{9} +(-4.26225 - 2.96768i) q^{10} +(-0.220188 + 0.127126i) q^{11} +(-2.41583 + 5.36071i) q^{12} +(-0.992714 - 3.70486i) q^{13} +(0.903473 - 1.56486i) q^{14} +(-0.943998 + 3.75618i) q^{15} +(0.367473 + 0.636483i) q^{16} +(3.93311 - 3.93311i) q^{17} +(6.95487 + 0.427565i) q^{18} +0.440377i q^{19} +(4.89474 + 5.80207i) q^{20} +(-1.32991 - 0.216804i) q^{21} +(0.570419 - 0.152843i) q^{22} +(-3.42258 + 0.917076i) q^{23} +(3.55088 - 4.34467i) q^{24} +(3.84718 + 3.19362i) q^{25} +8.90871i q^{26} +(-1.53854 - 4.96315i) q^{27} +(-1.86747 + 1.86747i) q^{28} +(-2.76265 - 4.78505i) q^{29} +(4.37591 - 7.85958i) q^{30} +(-0.0971829 + 0.168326i) q^{31} +(1.23512 + 4.60955i) q^{32} +(-0.257234 - 0.357439i) q^{33} +(-11.1884 + 6.45964i) q^{34} +(-0.994005 + 1.42761i) q^{35} +(-9.65702 - 3.23456i) q^{36} +(-0.123005 - 0.123005i) q^{37} +(0.264732 - 0.987995i) q^{38} +(6.21282 - 2.35271i) q^{39} +(-3.07879 - 6.55713i) q^{40} +(-3.88223 - 2.24141i) q^{41} +(2.85336 + 1.28588i) q^{42} +(1.33488 + 0.357680i) q^{43} -0.863127 q^{44} +(-6.63682 - 0.976052i) q^{45} +8.22993 q^{46} +(4.17348 + 1.11828i) q^{47} +(-1.03322 + 0.743568i) q^{48} +(5.53804 + 3.19739i) q^{49} +(-6.71139 - 9.47769i) q^{50} +(7.45964 + 6.09673i) q^{51} +(3.37004 - 12.5772i) q^{52} +(0.938022 + 0.938022i) q^{53} +(0.468157 + 12.0598i) q^{54} +(-0.559623 + 0.100205i) q^{55} +(2.18263 - 1.26014i) q^{56} +(-0.758929 + 0.0763000i) q^{57} +(3.32153 + 12.3961i) q^{58} +(-4.02279 + 6.96768i) q^{59} +(-9.15100 + 9.44069i) q^{60} +(-1.44186 - 2.49737i) q^{61} +(0.319221 - 0.319221i) q^{62} +(0.143210 - 2.32949i) q^{63} -12.5540i q^{64} +(0.724881 - 8.54587i) q^{65} +(0.362236 + 0.956558i) q^{66} +(-12.9666 + 3.47438i) q^{67} +(18.2392 - 4.88718i) q^{68} +(-2.17345 - 5.73945i) q^{69} +(3.08828 - 2.60534i) q^{70} -2.15986i q^{71} +(8.10268 + 5.36670i) q^{72} +(-9.18432 + 9.18432i) q^{73} +(0.202021 + 0.349910i) q^{74} +(-4.83720 + 7.18342i) q^{75} +(-0.747490 + 1.29469i) q^{76} +(-0.0511939 - 0.191058i) q^{77} +(-15.3529 + 1.54353i) q^{78} +(11.9729 - 6.91256i) q^{79} +(0.289654 + 1.61766i) q^{80} +(8.28675 - 3.51139i) q^{81} +(7.36245 + 7.36245i) q^{82} +(-1.39384 + 5.20187i) q^{83} +(-3.54190 - 2.89477i) q^{84} +(11.2583 - 5.28617i) q^{85} +(-2.77981 - 1.60493i) q^{86} +(7.76772 - 5.59011i) q^{87} +(0.795606 + 0.213182i) q^{88} +0.285526 q^{89} +(14.3031 + 6.17952i) q^{90} +2.98392 q^{91} +(-11.6189 - 3.11327i) q^{92} +(-0.306924 - 0.138317i) q^{93} +(-8.69105 - 5.01778i) q^{94} +(-0.334341 + 0.926215i) q^{95} +(-7.72993 + 2.92722i) q^{96} +(-2.34065 + 8.73543i) q^{97} +(-10.5026 - 10.5026i) q^{98} +(0.571428 - 0.505238i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$16 q - 6 q^{2} - 6 q^{3} - 6 q^{5} - 2 q^{7} - 8 q^{10} - 6 q^{12} - 2 q^{13} - 6 q^{15} - 8 q^{16} + 36 q^{18} + 18 q^{20} - 12 q^{21} - 10 q^{22} + 18 q^{23} + 4 q^{25} + 18 q^{27} - 16 q^{28} + 30 q^{30}+ \cdots + 28 q^{97}+O(q^{100})$ 16 * q - 6 * q^2 - 6 * q^3 - 6 * q^5 - 2 * q^7 - 8 * q^10 - 6 * q^12 - 2 * q^13 - 6 * q^15 - 8 * q^16 + 36 * q^18 + 18 * q^20 - 12 * q^21 - 10 * q^22 + 18 * q^23 + 4 * q^25 + 18 * q^27 - 16 * q^28 + 30 * q^30 - 4 * q^31 + 30 * q^32 - 12 * q^33 - 48 * q^36 + 4 * q^37 - 30 * q^38 + 6 * q^40 - 24 * q^41 + 6 * q^42 - 2 * q^43 - 36 * q^45 + 32 * q^46 - 12 * q^47 - 30 * q^48 - 54 * q^50 + 36 * q^51 - 14 * q^52 - 16 * q^55 + 36 * q^56 - 6 * q^57 - 6 * q^58 + 18 * q^60 + 8 * q^61 + 36 * q^63 + 66 * q^65 + 36 * q^66 + 4 * q^67 + 42 * q^68 + 18 * q^70 + 18 * q^72 - 8 * q^73 + 42 * q^75 + 24 * q^76 - 6 * q^77 - 42 * q^78 - 48 * q^81 + 32 * q^82 - 66 * q^83 + 22 * q^85 - 48 * q^86 - 18 * q^87 + 18 * q^88 - 66 * q^90 - 40 * q^91 - 60 * q^92 - 18 * q^93 - 36 * q^95 - 24 * q^96 + 28 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$ .

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{4}\right)$

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

)

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

$2$	−2.24352	−	0.601150i	−1.58641	−	0.425077i	−0.645507	−	0.763754i	$-0.723354\pi$
$2$	−2.24352	−	0.601150i	−1.58641	−	0.425077i	−0.940903	+	0.338677i	$0.890021\pi$
$3$	0.173261	+	1.72336i	0.100032	+	0.994984i
$3$	0.173261	+	1.72336i	0.100032	+	0.994984i
$4$	2.93996	+	1.69739i	1.46998	+	0.848694i
$5$	2.10323	+	0.759216i	0.940595	+	0.339532i
$5$	2.10323	+	0.759216i	0.940595	+	0.339532i
$6$	0.647285	−	3.97056i	0.264253	−	1.62097i
$7$	−0.201351	+	0.751454i	−0.0761037	+	0.284023i	−0.993481	−	0.113995i	$-0.963635\pi$
$7$	−0.201351	+	0.751454i	−0.0761037	+	0.284023i	0.917378	+	0.398018i	$0.130302\pi$
$8$	−2.29074	−	2.29074i	−0.809899	−	0.809899i
$9$	−2.93996	+	0.597183i	−0.979987	+	0.199061i
$10$	−4.26225	−	2.96768i	−1.34784	−	0.938462i
$11$	−0.220188	+	0.127126i	−0.0663893	+	0.0383299i	−0.532827	−	0.846224i	$-0.678870\pi$
$11$	−0.220188	+	0.127126i	−0.0663893	+	0.0383299i	0.466438	+	0.884554i	$0.345537\pi$
$12$	−2.41583	+	5.36071i	−0.697391	+	1.54750i
$13$	−0.992714	−	3.70486i	−0.275329	−	1.02754i	−0.955620	−	0.294601i	$-0.904813\pi$
$13$	−0.992714	−	3.70486i	−0.275329	−	1.02754i	0.680291	−	0.732942i	$-0.261853\pi$
$14$	0.903473	−	1.56486i	0.241463	−	0.418227i
$15$	−0.943998	+	3.75618i	−0.243739	+	0.969841i
$16$	0.367473	+	0.636483i	0.0918684	+	0.159121i
$17$	3.93311	−	3.93311i	0.953920	−	0.953920i	−0.0450642	−	0.998984i	$-0.514349\pi$
$17$	3.93311	−	3.93311i	0.953920	−	0.953920i	0.998984	+	0.0450642i	$0.0143492\pi$
$18$	6.95487	+	0.427565i	1.63928	+	0.100778i
$19$			0.440377i			0.101029i	0.998723	+	0.0505147i	$0.0160862\pi$
$19$			0.440377i			0.101029i	−0.998723	+	0.0505147i	$0.983914\pi$
$20$	4.89474	+	5.80207i	1.09450	+	1.29738i
$21$	−1.32991	−	0.216804i	−0.290211	−	0.0473105i
$22$	0.570419	−	0.152843i	0.121614	−	0.0325863i
$23$	−3.42258	+	0.917076i	−0.713656	+	0.191224i	−0.597339	−	0.801989i	$-0.703775\pi$
$23$	−3.42258	+	0.917076i	−0.713656	+	0.191224i	−0.116317	+	0.993212i	$0.537109\pi$
$24$	3.55088	−	4.34467i	0.724821	−	0.886853i
$25$	3.84718	+	3.19362i	0.769436	+	0.638724i
$26$			8.90871i			1.74714i
$27$	−1.53854	−	4.96315i	−0.296093	−	0.955159i
$28$	−1.86747	+	1.86747i	−0.352919	+	0.352919i
$29$	−2.76265	−	4.78505i	−0.513011	−	0.888561i	−0.999886	−	0.0150897i	$-0.995197\pi$
$29$	−2.76265	−	4.78505i	−0.513011	−	0.888561i	0.486875	−	0.873472i	$-0.338137\pi$
$30$	4.37591	−	7.85958i	0.798928	−	1.43496i
$31$	−0.0971829	+	0.168326i	−0.0174546	+	0.0302322i	−0.874621	−	0.484808i	$-0.838890\pi$
$31$	−0.0971829	+	0.168326i	−0.0174546	+	0.0302322i	0.857166	+	0.515040i	$0.172223\pi$
$32$	1.23512	+	4.60955i	0.218341	+	0.814861i
$33$	−0.257234	−	0.357439i	−0.0447787	−	0.0622221i
$34$	−11.1884	+	6.45964i	−1.91880	+	1.10782i
$35$	−0.994005	+	1.42761i	−0.168018	+	0.241311i
$36$	−9.65702	−	3.23456i	−1.60950	−	0.539093i
$37$	−0.123005	−	0.123005i	−0.0202220	−	0.0202220i	0.696924	−	0.717145i	$-0.254552\pi$
$37$	−0.123005	−	0.123005i	−0.0202220	−	0.0202220i	−0.717145	+	0.696924i	$0.754552\pi$
$38$	0.264732	−	0.987995i	0.0429453	−	0.160274i
$39$	6.21282	−	2.35271i	0.994848	−	0.376736i
$40$	−3.07879	−	6.55713i	−0.486800	−	1.03677i
$41$	−3.88223	−	2.24141i	−0.606303	−	0.350049i	0.165214	−	0.986258i	$-0.447168\pi$
$41$	−3.88223	−	2.24141i	−0.606303	−	0.350049i	−0.771517	+	0.636209i	$0.780502\pi$
$42$	2.85336	+	1.28588i	0.440283	+	0.198416i
$43$	1.33488	+	0.357680i	0.203567	+	0.0545456i	0.359162	−	0.933275i	$-0.383063\pi$
$43$	1.33488	+	0.357680i	0.203567	+	0.0545456i	−0.155595	+	0.987821i	$0.549729\pi$
$44$	−0.863127			−0.130121
$45$	−6.63682	−	0.976052i	−0.989358	−	0.145501i
$46$	8.22993			1.21344
$47$	4.17348	+	1.11828i	0.608765	+	0.163118i	0.550015	−	0.835155i	$-0.314622\pi$
$47$	4.17348	+	1.11828i	0.608765	+	0.163118i	0.0587499	+	0.998273i	$0.481289\pi$
$48$	−1.03322	+	0.743568i	−0.149133	+	0.107325i
$49$	5.53804	+	3.19739i	0.791148	+	0.456770i
$50$	−6.71139	−	9.47769i	−0.949134	−	1.34035i
$51$	7.45964	+	6.09673i	1.04456	+	0.853713i
$52$	3.37004	−	12.5772i	0.467341	−	1.74414i
$53$	0.938022	+	0.938022i	0.128847	+	0.128847i	0.768589	−	0.639742i	$-0.220959\pi$
$53$	0.938022	+	0.938022i	0.128847	+	0.128847i	−0.639742	+	0.768589i	$0.720959\pi$
$54$	0.468157	+	12.0598i	0.0637081	+	1.64114i
$55$	−0.559623	+	0.100205i	−0.0754596	+	0.0135116i
$56$	2.18263	−	1.26014i	0.291666	−	0.168393i
$57$	−0.758929	+	0.0763000i	−0.100523	+	0.0101062i
$58$	3.32153	+	12.3961i	0.436139	+	1.62769i
$59$	−4.02279	+	6.96768i	−0.523723	+	0.907114i	0.475896	+	0.879502i	$0.342124\pi$
$59$	−4.02279	+	6.96768i	−0.523723	+	0.907114i	−0.999619	+	0.0276128i	$0.991209\pi$
$60$	−9.15100	+	9.44069i	−1.18139	+	1.21879i
$61$	−1.44186	−	2.49737i	−0.184611	−	0.319755i	0.758835	−	0.651283i	$-0.225769\pi$
$61$	−1.44186	−	2.49737i	−0.184611	−	0.319755i	−0.943445	+	0.331528i	$0.892436\pi$
$62$	0.319221	−	0.319221i	0.0405411	−	0.0405411i
$63$	0.143210	−	2.32949i	0.0180428	−	0.293488i
$64$		−	12.5540i		−	1.56925i
$65$	0.724881	−	8.54587i	0.0899104	−	1.05998i
$66$	0.362236	+	0.956558i	0.0445882	+	0.117744i
$67$	−12.9666	+	3.47438i	−1.58412	+	0.424463i	−0.940197	−	0.340631i	$-0.889359\pi$
$67$	−12.9666	+	3.47438i	−1.58412	+	0.424463i	−0.643919	+	0.765093i	$0.722693\pi$
$68$	18.2392	−	4.88718i	2.21183	−	0.592658i
$69$	−2.17345	−	5.73945i	−0.261653	−	0.690948i
$70$	3.08828	−	2.60534i	0.369120	−	0.311397i
$71$		−	2.15986i		−	0.256328i	−0.991753	−	0.128164i	$-0.959092\pi$
$71$		−	2.15986i		−	0.256328i	0.991753	−	0.128164i	$-0.0409085\pi$
$72$	8.10268	+	5.36670i	0.954910	+	0.632471i
$73$	−9.18432	+	9.18432i	−1.07494	+	1.07494i	−0.0779897	+	0.996954i	$0.524850\pi$
$73$	−9.18432	+	9.18432i	−1.07494	+	1.07494i	−0.996954	+	0.0779897i	$0.975150\pi$
$74$	0.202021	+	0.349910i	0.0234844	+	0.0406762i
$75$	−4.83720	+	7.18342i	−0.558552	+	0.829470i
$76$	−0.747490	+	1.29469i	−0.0857430	+	0.148511i
$77$	−0.0511939	−	0.191058i	−0.00583409	−	0.0217731i
$78$	−15.3529	+	1.54353i	−1.73838	+	0.174770i
$79$	11.9729	−	6.91256i	1.34706	−	0.777723i	0.359225	−	0.933251i	$-0.383041\pi$
$79$	11.9729	−	6.91256i	1.34706	−	0.777723i	0.987832	+	0.155528i	$0.0497079\pi$
$80$	0.289654	+	1.61766i	0.0323843	+	0.180860i
$81$	8.28675	−	3.51139i	0.920749	−	0.390154i
$82$	7.36245	+	7.36245i	0.813047	+	0.813047i
$83$	−1.39384	+	5.20187i	−0.152993	+	0.570979i	0.846275	+	0.532746i	$0.178840\pi$
$83$	−1.39384	+	5.20187i	−0.152993	+	0.570979i	−0.999269	+	0.0382335i	$0.987827\pi$
$84$	−3.54190	−	2.89477i	−0.386452	−	0.315846i
$85$	11.2583	−	5.28617i	1.22114	−	0.573366i
$86$	−2.77981	−	1.60493i	−0.299755	−	0.173064i
$87$	7.76772	−	5.59011i	0.832787	−	0.599323i
$88$	0.795606	+	0.213182i	0.0848119	+	0.0227253i
$89$	0.285526			0.0302657			0.0151328	−	0.999885i	$-0.495183\pi$
$89$	0.285526			0.0302657			0.0151328	+	0.999885i	$0.495183\pi$
$90$	14.3031	+	6.17952i	1.50768	+	0.651378i
$91$	2.98392			0.312799
$92$	−11.6189	−	3.11327i	−1.21135	−	0.324581i
$93$	−0.306924	−	0.138317i	−0.0318266	−	0.0143428i
$94$	−8.69105	−	5.01778i	−0.896413	−	0.517545i
$95$	−0.334341	+	0.926215i	−0.0343027	+	0.0950276i
$96$	−7.72993	+	2.92722i	−0.788932	+	0.298758i
$97$	−2.34065	+	8.73543i	−0.237657	+	0.886948i	0.739276	+	0.673402i	$0.235168\pi$
$97$	−2.34065	+	8.73543i	−0.237657	+	0.886948i	−0.976933	+	0.213546i	$0.931499\pi$
$98$	−10.5026	−	10.5026i	−1.06092	−	1.06092i
$99$	0.571428	−	0.505238i	0.0574307	−	0.0507783i
$100$	5.88975	+	15.9193i	0.588975	+	1.59193i
$101$	−11.3943	+	6.57848i	−1.13377	+	0.654583i	−0.944881	−	0.327415i	$-0.893822\pi$
$101$	−11.3943	+	6.57848i	−1.13377	+	0.654583i	−0.188890	+	0.981998i	$0.560489\pi$
$102$	−13.0708	−	18.1625i	−1.29420	−	1.79836i
$103$	−4.23579	−	15.8082i	−0.417364	−	1.55763i	−0.780052	−	0.625714i	$-0.784808\pi$
$103$	−4.23579	−	15.8082i	−0.417364	−	1.55763i	0.362688	−	0.931911i	$-0.381859\pi$
$104$	−6.21282	+	10.7609i	−0.609217	+	1.05520i
$105$	−2.63252	−	1.46568i	−0.256907	−	0.143036i
$106$	−1.54058	−	2.66836i	−0.149634	−	0.259175i
$107$	−5.81401	+	5.81401i	−0.562062	+	0.562062i	−0.929893	−	0.367831i	$-0.880101\pi$
$107$	−5.81401	+	5.81401i	−0.562062	+	0.562062i	0.367831	+	0.929893i	$0.380101\pi$
$108$	3.90114	−	17.2030i	0.375387	−	1.65536i
$109$			8.81907i			0.844713i	0.906430	+	0.422357i	$0.138797\pi$
$109$			8.81907i			0.844713i	−0.906430	+	0.422357i	$0.861203\pi$
$110$	1.31577	+	0.111606i	0.125453	+	0.0106412i
$111$	0.190671	−	0.233295i	0.0180977	−	0.0221434i
$112$	−0.552279	+	0.147983i	−0.0521854	+	0.0139830i
$113$	13.0092	−	3.48580i	1.22380	−	0.327916i	0.411638	−	0.911347i	$-0.364957\pi$
$113$	13.0092	−	3.48580i	1.22380	−	0.327916i	0.812163	+	0.583431i	$0.198290\pi$
$114$	1.74854	+	0.285049i	0.163766	+	0.0266973i
$115$	−7.89473	−	0.669650i	−0.736188	−	0.0624452i
$116$		−	18.7571i		−	1.74156i
$117$	5.13102	+	10.2993i	0.474363	+	0.952172i
$118$	13.2138	−	13.2138i	1.21643	−	1.21643i
$119$	2.16361	+	3.74749i	0.198338	+	0.343532i
$120$	10.7669	−	6.44197i	0.982877	−	0.588069i
$121$	−5.46768	+	9.47030i	−0.497062	+	0.860936i
$122$	1.73354	+	6.46967i	0.156948	+	0.585736i
$123$	3.19012	−	7.07884i	0.287643	−	0.638278i
$124$	−0.571428	+	0.329914i	−0.0513157	+	0.0296272i
$125$	5.66687	+	9.63777i	0.506860	+	0.862028i
$126$	−1.72167	+	5.14017i	−0.153378	+	0.457923i
$127$	−6.72167	−	6.72167i	−0.596452	−	0.596452i	0.342915	−	0.939366i	$-0.388586\pi$
$127$	−6.72167	−	6.72167i	−0.596452	−	0.596452i	−0.939366	+	0.342915i	$0.888586\pi$
$128$	−5.07660	+	18.9461i	−0.448712	+	1.67462i
$129$	−0.385130	+	2.36245i	−0.0339088	+	0.208002i
$130$	−6.76364	+	18.7371i	−0.593210	+	1.64335i
$131$	11.6482	+	6.72508i	1.01771	+	0.587573i	0.913439	−	0.406977i	$-0.133417\pi$
$131$	11.6482	+	6.72508i	1.01771	+	0.587573i	0.104267	+	0.994549i	$0.466750\pi$
$132$	−0.149546	−	1.48748i	−0.0130163	−	0.129469i
$133$	−0.330923	−	0.0886705i	−0.0286946	−	0.00768870i
$134$	31.1794			2.69349
$135$	0.532192	−	11.6068i	0.0458038	−	0.998950i
$136$	−18.0195			−1.54516
$137$	9.45618	+	2.53378i	0.807896	+	0.216475i	0.639048	−	0.769167i	$-0.279329\pi$
$137$	9.45618	+	2.53378i	0.807896	+	0.216475i	0.168848	+	0.985642i	$0.445995\pi$
$138$	1.42592	+	14.1832i	0.121383	+	1.20735i
$139$	−6.84922	−	3.95440i	−0.580943	−	0.335408i	0.180565	−	0.983563i	$-0.442207\pi$
$139$	−6.84922	−	3.95440i	−0.580943	−	0.335408i	−0.761508	+	0.648155i	$0.775541\pi$
$140$	−5.34555	+	2.50992i	−0.451781	+	0.212127i
$141$	−1.20410	+	7.38618i	−0.101404	+	0.622029i
$142$	−1.29840	+	4.84570i	−0.108959	+	0.406642i
$143$	0.689567	+	0.689567i	0.0576645	+	0.0576645i
$144$	−1.46045	−	1.65179i	−0.121705	−	0.137649i
$145$	−2.17761	−	12.1615i	−0.180841	−	1.00996i
$146$	26.1264	−	15.0841i	2.16224	−	1.24837i
$147$	−4.55073	+	10.0980i	−0.375338	+	0.832872i
$148$	−0.152843	−	0.570419i	−0.0125636	−	0.0468882i
$149$	4.56755	−	7.91123i	0.374188	−	0.648113i	−0.616017	−	0.787733i	$-0.711255\pi$
$149$	4.56755	−	7.91123i	0.374188	−	0.648113i	0.990205	+	0.139620i	$0.0445880\pi$
$150$	15.1707	−	13.2083i	1.23868	−	1.07845i
$151$	−7.34991	−	12.7304i	−0.598127	−	1.03599i	−0.993097	−	0.117293i	$-0.962578\pi$
$151$	−7.34991	−	12.7304i	−0.598127	−	1.03599i	0.394970	−	0.918694i	$-0.370755\pi$
$152$	1.00879	−	1.00879i	0.0818235	−	0.0818235i
$153$	−9.21441	+	13.9120i	−0.744941	+	1.12472i
$154$			0.459419i			0.0370210i
$155$	−0.332194	+	0.280245i	−0.0266825	+	0.0225098i
$156$	22.2589	+	3.62867i	1.78214	+	0.290527i
$157$	16.3566	−	4.38274i	1.30540	−	0.349781i	0.461911	−	0.886926i	$-0.347164\pi$
$157$	16.3566	−	4.38274i	1.30540	−	0.349781i	0.843490	+	0.537146i	$0.180497\pi$
$158$	−31.0169	+	8.31097i	−2.46758	+	0.661185i
$159$	−1.45403	+	1.77907i	−0.115312	+	0.141090i
$160$	−0.901889	+	10.6327i	−0.0713006	+	0.840587i
$161$		−	2.75656i		−	0.217248i
$162$	−20.7024	+	2.89630i	−1.62653	+	0.227555i
$163$	9.74771	−	9.74771i	0.763499	−	0.763499i	−0.213454	−	0.976953i	$-0.568471\pi$
$163$	9.74771	−	9.74771i	0.763499	−	0.763499i	0.976953	+	0.213454i	$0.0684713\pi$
$164$	−7.60907	−	13.1793i	−0.594169	−	1.02913i
$165$	−0.269650	−	0.947073i	−0.0209922	−	0.0737295i
$166$	6.25421	−	10.8326i	0.485421	−	0.840773i
$167$	−5.10613	−	19.0563i	−0.395124	−	1.47462i	−0.821568	−	0.570110i	$-0.806900\pi$
$167$	−5.10613	−	19.0563i	−0.395124	−	1.47462i	0.426444	−	0.904514i	$-0.359766\pi$
$168$	2.54985	+	3.54313i	0.196725	+	0.273358i
$169$	−1.48218	+	0.855737i	−0.114014	+	0.0658259i
$170$	−28.4361	+	5.09169i	−2.18095	+	0.390515i
$171$	−0.262985	−	1.29469i	−0.0201110	−	0.0990074i
$172$	3.31737	+	3.31737i	0.252947	+	0.252947i
$173$	−2.68653	+	10.0263i	−0.204253	+	0.762284i	0.785422	+	0.618960i	$0.212446\pi$
$173$	−2.68653	+	10.0263i	−0.204253	+	0.762284i	−0.989676	+	0.143324i	$0.954221\pi$
$174$	−20.7875	+	7.87197i	−1.57590	+	0.596773i
$175$	−3.17449	+	2.24794i	−0.239969	+	0.169928i
$176$	−0.161827	−	0.0934307i	−0.0121981	−	0.00704260i
$177$	−12.7048	−	5.72550i	−0.954954	−	0.430355i
$178$	−0.640584	−	0.171644i	−0.0480138	−	0.0128653i
$179$	−15.1015			−1.12874			−0.564370	−	0.825522i	$-0.690881\pi$
$179$	−15.1015			−1.12874			−0.564370	+	0.825522i	$0.690881\pi$
$180$	−17.8552	−	14.1348i	−1.33085	−	1.05355i
$181$	−7.82954			−0.581965			−0.290983	−	0.956728i	$-0.593982\pi$
$181$	−7.82954			−0.581965			−0.290983	+	0.956728i	$0.593982\pi$
$182$	−6.69448	−	1.79378i	−0.496228	−	0.132964i
$183$	4.05405	−	2.91754i	0.299684	−	0.215671i
$184$	9.94101	+	5.73945i	0.732861	+	0.423118i
$185$	−0.165321	−	0.352097i	−0.0121547	−	0.0258867i
$186$	0.605442	+	0.494825i	0.0443932	+	0.0362823i
$187$	−0.366025	+	1.36603i	−0.0267664	+	0.0998937i
$188$	10.3717	+	10.3717i	0.756436	+	0.756436i
$189$	4.03937	−	0.156806i	0.293821	−	0.0114060i
$190$	1.30690	−	1.87699i	0.0948122	−	0.136171i
$191$	9.93557	−	5.73631i	0.718913	−	0.415065i	−0.0954396	−	0.995435i	$-0.530426\pi$
$191$	9.93557	−	5.73631i	0.718913	−	0.415065i	0.814352	+	0.580371i	$0.197092\pi$
$192$	21.6351	−	2.17512i	1.56138	−	0.156976i
$193$	1.42826	+	5.33034i	0.102808	+	0.383686i	0.998087	−	0.0618198i	$-0.0196904\pi$
$193$	1.42826	+	5.33034i	0.102808	+	0.383686i	−0.895279	+	0.445506i	$0.853024\pi$
$194$	10.5026	−	18.1910i	0.754043	−	1.30604i
$195$	14.8532	−	0.231432i	1.06366	−	0.0165732i
$196$	10.8544	+	18.8004i	0.775315	+	1.34289i
$197$	−2.32295	+	2.32295i	−0.165504	+	0.165504i	−0.785000	−	0.619496i	$-0.787337\pi$
$197$	−2.32295	+	2.32295i	−0.165504	+	0.165504i	0.619496	+	0.785000i	$0.287337\pi$
$198$	−1.58573	+	0.789998i	−0.112693	+	0.0561427i
$199$			17.1978i			1.21912i	0.792741	+	0.609558i	$0.208653\pi$
$199$			17.1978i			1.21912i	−0.792741	+	0.609558i	$0.791347\pi$
$200$	−1.49714	−	16.1286i	−0.105864	−	1.14047i
$201$	−8.23421	−	21.7441i	−0.580796	−	1.53371i
$202$	29.5179	−	7.90930i	2.07687	−	0.556497i
$203$	4.15201	−	1.11253i	0.291414	−	0.0780841i
$204$	11.5825	+	30.5860i	0.810940	+	2.14145i
$205$	−6.46353	−	7.66166i	−0.451432	−	0.535113i
$206$			38.0123i			2.64844i
$207$	9.51458	−	4.74007i	0.661309	−	0.329458i
$208$	1.99328	−	1.99328i	0.138209	−	0.138209i
$209$	−0.0559832	−	0.0969658i	−0.00387244	−	0.00670726i
$210$	5.02502	+	4.87083i	0.346759	+	0.336119i
$211$	−2.27479	+	3.94005i	−0.156603	+	0.271245i	−0.933642	−	0.358209i	$-0.883388\pi$
$211$	−2.27479	+	3.94005i	−0.156603	+	0.271245i	0.777039	+	0.629453i	$0.216721\pi$
$212$	1.16556	+	4.34993i	0.0800511	+	0.298755i
$213$	3.72223	−	0.374220i	0.255043	−	0.0256411i
$214$	16.5390	−	9.54878i	1.13058	−	0.652741i
$215$	2.53601	+	1.76575i	0.172954	+	0.120423i
$216$	−7.84489	+	14.8937i	−0.533777	+	1.01339i
$217$	−0.106921	−	0.106921i	−0.00725827	−	0.00725827i
$218$	5.30158	−	19.7858i	0.359068	−	1.34006i
$219$	−17.4192	−	14.2366i	−1.17708	−	0.962023i
$220$	−1.81536	−	0.655300i	−0.122391	−	0.0441803i
$221$	−18.4761	−	10.6672i	−1.24284	−	0.717552i
$222$	−0.568020	+	0.408781i	−0.0381230	+	0.0274356i
$223$	17.6922	+	4.74061i	1.18476	+	0.317455i	0.796812	−	0.604227i	$-0.206518\pi$
$223$	17.6922	+	4.74061i	1.18476	+	0.317455i	0.387946	+	0.921682i	$0.373185\pi$
$224$	−3.71256			−0.248056
$225$	−13.2177	−	7.09164i	−0.881182	−	0.472776i
$226$	−31.2819			−2.08084
$227$	−10.8961	−	2.91961i	−0.723202	−	0.193781i	−0.121602	−	0.992579i	$-0.538803\pi$
$227$	−10.8961	−	2.91961i	−0.723202	−	0.193781i	−0.601600	+	0.798798i	$0.705470\pi$
$228$	−2.36073	−	1.06388i	−0.156343	−	0.0704570i
$229$	−4.22418	−	2.43883i	−0.279142	−	0.161163i	0.353893	−	0.935286i	$-0.384858\pi$
$229$	−4.22418	−	2.43883i	−0.279142	−	0.161163i	−0.633035	+	0.774123i	$0.718191\pi$
$230$	17.3095	+	6.24830i	1.14135	+	0.412000i
$231$	0.320393	−	0.121329i	0.0210803	−	0.00798284i
$232$	−4.63279	+	17.2898i	−0.304158	+	1.13513i
$233$	−7.90742	−	7.90742i	−0.518033	−	0.518033i	0.398943	−	0.916976i	$-0.369377\pi$
$233$	−7.90742	−	7.90742i	−0.518033	−	0.518033i	−0.916976	+	0.398943i	$0.869377\pi$
$234$	−5.32013	−	26.1913i	−0.347788	−	1.71218i
$235$	7.92879	+	5.52058i	0.517217	+	0.360123i
$236$	−23.6537	+	13.6565i	−1.53972	+	0.888960i
$237$	13.9873	+	19.4360i	0.908571	+	1.26250i
$238$	−2.60131	−	9.70823i	−0.168618	−	0.629291i
$239$	−11.1362	+	19.2884i	−0.720340	+	1.24767i	0.240523	+	0.970643i	$0.422681\pi$
$239$	−11.1362	+	19.2884i	−0.720340	+	1.24767i	−0.960864	+	0.277022i	$0.910652\pi$
$240$	−2.73764	+	0.779457i	−0.176714	+	0.0503138i
$241$	14.4746	+	25.0708i	0.932392	+	1.61495i	0.779220	+	0.626750i	$0.215615\pi$
$241$	14.4746	+	25.0708i	0.932392	+	1.61495i	0.153171	+	0.988200i	$0.451051\pi$
$242$	17.9599	−	17.9599i	1.15451	−	1.15451i
$243$	7.48717	+	13.6727i	0.480302	+	0.877103i
$244$		−	9.78955i		−	0.626712i
$245$	9.22028	+	10.9294i	0.589062	+	0.698255i
$246$	−11.4126	+	13.9638i	−0.727638	+	0.890300i
$247$	1.63153	−	0.437168i	0.103812	−	0.0278163i
$248$	0.608211	−	0.162970i	0.0386214	−	0.0103486i
$249$	−9.20620	−	1.50081i	−0.583420	−	0.0951097i
$250$	−6.92001	−	25.0292i	−0.437660	−	1.58298i
$251$		−	20.4218i		−	1.28901i	−0.764599	−	0.644507i	$-0.777063\pi$
$251$		−	20.4218i		−	1.28901i	0.764599	−	0.644507i	$-0.222937\pi$
$252$	4.37508	−	6.60552i	0.275604	−	0.416109i
$253$	0.637027	−	0.637027i	0.0400496	−	0.0400496i
$254$	11.0395	+	19.1209i	0.692679	+	1.19975i
$255$	11.0606	+	18.4863i	0.692643	+	1.15766i
$256$	10.2249	−	17.7101i	0.639057	−	1.10688i
$257$	1.90043	+	7.09249i	0.118545	+	0.442417i	0.999528	−	0.0307319i	$-0.00978380\pi$
$257$	1.90043	+	7.09249i	0.118545	+	0.442417i	−0.880982	+	0.473149i	$0.843117\pi$
$258$	2.28424	−	5.06870i	0.142210	−	0.315563i
$259$	0.117200	−	0.0676656i	0.00728247	−	0.00420453i
$260$	16.6368	−	23.8941i	1.03177	−	1.48185i
$261$	10.9796	+	12.4181i	0.679622	+	0.768658i
$262$	−22.0902	−	22.0902i	−1.36473	−	1.36473i
$263$	3.78069	−	14.1097i	0.233127	−	0.870044i	−0.745857	−	0.666107i	$-0.767960\pi$
$263$	3.78069	−	14.1097i	0.233127	−	0.870044i	0.978984	−	0.203937i	$-0.0653738\pi$
$264$	−0.229543	+	1.40805i	−0.0141274	+	0.0866598i
$265$	1.26072	+	2.68504i	0.0774452	+	0.164941i
$266$	0.689128	+	0.397868i	0.0422532	+	0.0243949i
$267$	0.0494705	+	0.492065i	0.00302754	+	0.0301139i
$268$	−44.0185	−	11.7947i	−2.68886	−	0.720478i
$269$	−3.76010			−0.229257			−0.114629	−	0.993408i	$-0.536568\pi$
$269$	−3.76010			−0.229257			−0.114629	+	0.993408i	$0.536568\pi$
$270$	−8.17139	+	25.7201i	−0.497295	+	1.56527i
$271$	14.0785			0.855209			0.427604	−	0.903966i	$-0.359358\pi$
$271$	14.0785			0.855209			0.427604	+	0.903966i	$0.359358\pi$
$272$	3.94867	+	1.05804i	0.239423	+	0.0641533i
$273$	0.516996	+	5.14237i	0.0312900	+	0.311230i
$274$	−19.6920	−	11.3692i	−1.18964	−	0.686837i
$275$	−1.25310	−	0.214122i	−0.0755645	−	0.0129120i
$276$	3.35219	−	20.5629i	0.201778	−	1.23774i
$277$	0.541447	−	2.02071i	0.0325324	−	0.121413i	−0.947750	−	0.319014i	$-0.896648\pi$
$277$	0.541447	−	2.02071i	0.0325324	−	0.121413i	0.980283	+	0.197601i	$0.0633151\pi$
$278$	12.9892	+	12.9892i	0.779040	+	0.779040i
$279$	0.185193	−	0.552907i	0.0110872	−	0.0331017i
$280$	5.54730	−	0.993284i	0.331514	−	0.0593600i
$281$	8.02672	−	4.63423i	0.478834	−	0.276455i	−0.241097	−	0.970501i	$-0.577507\pi$
$281$	8.02672	−	4.63423i	0.478834	−	0.276455i	0.719930	+	0.694046i	$0.244174\pi$
$282$	7.14164	−	15.8472i	0.425278	−	0.943688i
$283$	8.33602	+	31.1104i	0.495525	+	1.84932i	0.527071	+	0.849821i	$0.323290\pi$
$283$	8.33602	+	31.1104i	0.495525	+	1.84932i	−0.0315464	+	0.999502i	$0.510043\pi$
$284$	3.66612	−	6.34991i	0.217544	−	0.376798i
$285$	−1.65413	−	0.415714i	−0.0979824	−	0.0246248i
$286$	−1.13253	−	1.96159i	−0.0669677	−	0.115991i
$287$	2.46601	−	2.46601i	0.145564	−	0.145564i
$288$	−6.38396	−	12.8143i	−0.376179	−	0.755090i
$289$		−	13.9387i		−	0.819926i
$290$	−2.42539	+	28.5937i	−0.142424	+	1.67908i
$291$	−15.4599	−	2.52028i	−0.906273	−	0.147742i
$292$	−42.5909	+	11.4122i	−2.49244	+	0.667849i
$293$	6.37987	−	1.70948i	0.372716	−	0.0998690i	−0.0675984	−	0.997713i	$-0.521534\pi$
$293$	6.37987	−	1.70948i	0.372716	−	0.0998690i	0.440314	+	0.897844i	$0.354867\pi$
$294$	16.2801	−	19.9195i	0.949475	−	1.16173i
$295$	−13.7508	+	11.6005i	−0.800605	+	0.675406i
$296$			0.563547i			0.0327555i
$297$	0.969714	+	0.897240i	0.0562685	+	0.0520631i
$298$	−15.0032	+	15.0032i	−0.869114	+	0.869114i
$299$	6.79528	+	11.7698i	0.392981	+	0.680663i
$300$	−26.4142	+	12.9084i	−1.52503	+	0.745265i
$301$	−0.537559	+	0.931080i	−0.0309844	+	0.0536666i
$302$	8.83680	+	32.9794i	0.508501	+	1.89775i
$303$	−13.3113	−	18.4966i	−0.764713	−	1.06260i
$304$	−0.280292	+	0.161827i	−0.0160759	+	0.00928140i
$305$	−1.13652	−	6.34723i	−0.0650767	−	0.363441i
$306$	29.0359	−	25.6726i	1.65987	−	1.46761i
$307$	5.82120	+	5.82120i	0.332233	+	0.332233i	0.853434	−	0.521201i	$-0.174516\pi$
$307$	5.82120	+	5.82120i	0.332233	+	0.332233i	−0.521201	+	0.853434i	$0.674516\pi$
$308$	0.173792	−	0.648600i	0.00990271	−	0.0369574i
$309$	26.5093	−	10.0387i	1.50806	−	0.571084i
$310$	0.913754	−	0.429038i	0.0518977	−	0.0243677i
$311$	9.98678	+	5.76587i	0.566299	+	0.326953i	0.755670	−	0.654953i	$-0.227312\pi$
$311$	9.98678	+	5.76587i	0.566299	+	0.326953i	−0.189371	+	0.981906i	$0.560645\pi$
$312$	−19.6214	−	8.84250i	−1.11084	−	0.500608i
$313$	−6.43287	−	1.72368i	−0.363607	−	0.0974283i	0.0723896	−	0.997376i	$-0.476937\pi$
$313$	−6.43287	−	1.72368i	−0.363607	−	0.0974283i	−0.435997	+	0.899948i	$0.643604\pi$
$314$	−39.3311			−2.21958
$315$	2.06979	−	4.79073i	0.116619	−	0.269927i
$316$	46.9331			2.64020
$317$	1.93788	+	0.519254i	0.108842	+	0.0291642i	0.312829	−	0.949809i	$-0.398723\pi$
$317$	1.93788	+	0.519254i	0.108842	+	0.0291642i	−0.203987	+	0.978974i	$0.565390\pi$
$318$	4.33164	−	3.11730i	0.242906	−	0.174810i
$319$	1.21661	+	0.702408i	0.0681169	+	0.0393273i
$320$	9.53121	−	26.4040i	0.532811	−	1.47603i
$321$	−11.0270	−	9.01232i	−0.615467	−	0.503018i
$322$	−1.65711	+	6.18441i	−0.0923470	+	0.344644i
$323$	1.73205	+	1.73205i	0.0963739	+	0.0963739i
$324$	30.3229	+	3.74247i	1.68461	+	0.207915i
$325$	8.01276	−	17.4236i	0.444468	−	0.966488i
$326$	−27.7290	+	16.0094i	−1.53577	+	0.886677i
$327$	−15.1985	+	1.52800i	−0.840477	+	0.0844986i
$328$	3.75870	+	14.0277i	0.207540	+	0.774548i
$329$	−1.68067	+	2.91101i	−0.0926585	+	0.160489i
$330$	0.0356324	+	2.28688i	0.00196150	+	0.125889i
$331$	−11.7700	−	20.3862i	−0.646937	−	1.12053i	−0.983850	−	0.178992i	$-0.942716\pi$
$331$	−11.7700	−	20.3862i	−0.646937	−	1.12053i	0.336913	−	0.941536i	$-0.390617\pi$
$332$	−12.9274	+	12.9274i	−0.709484	+	0.709484i
$333$	0.435088	+	0.288174i	0.0238427	+	0.0157919i
$334$			45.8229i			2.50732i
$335$	−29.9095	−	2.53699i	−1.63413	−	0.138611i
$336$	−0.350716	−	0.926137i	−0.0191331	−	0.0505249i
$337$	11.0048	−	2.94873i	0.599470	−	0.160627i	0.0536923	−	0.998558i	$-0.482901\pi$
$337$	11.0048	−	2.94873i	0.599470	−	0.160627i	0.545778	+	0.837930i	$0.316234\pi$
$338$	3.83973	−	1.02885i	0.208854	−	0.0559622i
$339$	8.26128	+	21.8156i	0.448691	+	1.18486i
$340$	42.0718	+	3.56863i	2.28166	+	0.193536i
$341$		−	0.0494178i		−	0.00267612i
$342$	−0.188289	+	3.06276i	−0.0101815	+	0.165615i
$343$	−7.36850	+	7.36850i	−0.397861	+	0.397861i
$344$	−2.23851	−	3.87721i	−0.120692	−	0.209045i
$345$	−0.213798	−	13.7215i	−0.0115105	−	0.738742i
$346$	12.0546	−	20.8792i	0.648059	−	1.12247i
$347$	−3.69845	−	13.8028i	−0.198543	−	0.740974i	−0.991321	−	0.131463i	$-0.958033\pi$
$347$	−3.69845	−	13.8028i	−0.198543	−	0.740974i	0.792778	−	0.609511i	$-0.208634\pi$
$348$	32.3254	−	3.24988i	1.73282	−	0.174212i
$349$	−15.2113	+	8.78224i	−0.814242	+	0.470103i	−0.848427	−	0.529313i	$-0.822450\pi$
$349$	−15.2113	+	8.78224i	−0.814242	+	0.470103i	0.0341849	+	0.999416i	$0.489116\pi$
$350$	8.47339	−	3.13496i	0.452922	−	0.167570i
$351$	−16.8605	+	10.6271i	−0.899944	+	0.567232i
$352$	−0.857952	−	0.857952i	−0.0457290	−	0.0457290i
$353$	4.51136	−	16.8366i	0.240116	−	0.896124i	−0.735660	−	0.677351i	$-0.763128\pi$
$353$	4.51136	−	16.8366i	0.240116	−	0.896124i	0.975776	−	0.218773i	$-0.0702054\pi$
$354$	25.0617	+	20.4828i	1.33201	+	1.08865i
$355$	1.63980	−	4.54269i	0.0870317	−	0.241101i
$356$	0.839435	+	0.484648i	0.0444900	+	0.0256863i
$357$	−6.08342	+	4.37799i	−0.321969	+	0.231708i
$358$	33.8806	+	9.07828i	1.79064	+	0.479802i
$359$	34.0577			1.79750			0.898748	−	0.438465i	$-0.144478\pi$
$359$	34.0577			1.79750			0.898748	+	0.438465i	$0.144478\pi$
$360$	12.9673	+	17.4391i	0.683439	+	0.919121i
$361$	18.8061			0.989793
$362$	17.5658	+	4.70673i	0.923236	+	0.247380i
$363$	−17.2681	−	7.78196i	−0.906340	−	0.408447i
$364$	8.77260	+	5.06486i	0.459809	+	0.265471i
$365$	−26.2897	+	12.3439i	−1.37606	+	0.646109i
$366$	−10.8492	+	4.10847i	−0.567099	+	0.214753i
$367$	3.65315	−	13.6337i	0.190693	−	0.711675i	−0.802647	−	0.596454i	$-0.796576\pi$
$367$	3.65315	−	13.6337i	0.190693	−	0.711675i	0.993340	−	0.115221i	$-0.0367577\pi$
$368$	−1.84141	−	1.84141i	−0.0959901	−	0.0959901i
$369$	12.7521	+	4.27125i	0.663850	+	0.222352i
$370$	0.159239	+	0.889320i	0.00827845	+	0.0462336i
$371$	−0.893752	+	0.516008i	−0.0464013	+	0.0267898i
$372$	−0.667568	−	0.927616i	−0.0346118	−	0.0480947i
$373$	−5.57233	−	20.7962i	−0.288524	−	1.07679i	−0.946225	−	0.323508i	$-0.895138\pi$
$373$	−5.57233	−	20.7962i	−0.288524	−	1.07679i	0.657701	−	0.753279i	$-0.271529\pi$
$374$	1.64237	−	2.84467i	0.0849251	−	0.147095i
$375$	−15.6275	+	11.4359i	−0.807002	+	0.590549i
$376$	−6.99867	−	12.1221i	−0.360929	−	0.625147i
$377$	−14.9854	+	14.9854i	−0.771788	+	0.771788i
$378$	−9.15668	−	2.07647i	−0.470969	−	0.106802i
$379$		−	9.52893i		−	0.489468i	−0.969590	−	0.244734i	$-0.921299\pi$
$379$		−	9.52893i		−	0.489468i	0.969590	−	0.244734i	$-0.0787007\pi$
$380$	−2.55510	+	2.15553i	−0.131074	+	0.110576i
$381$	10.4193	−	12.7485i	0.533795	−	0.653124i
$382$	−25.7391	+	6.89676i	−1.31693	+	0.352869i
$383$	−9.61802	+	2.57714i	−0.491458	+	0.131686i	−0.496033	−	0.868304i	$-0.665210\pi$
$383$	−9.61802	+	2.57714i	−0.491458	+	0.131686i	0.00457478	+	0.999990i	$0.498544\pi$
$384$	−33.5306	−	5.46620i	−1.71110	−	0.278946i
$385$	0.0373818	−	0.440707i	0.00190516	−	0.0224605i
$386$		−	12.8173i		−	0.652385i
$387$	−4.13809	−	0.254398i	−0.210351	−	0.0129318i
$388$	−21.7088	+	21.7088i	−1.10210	+	1.10210i
$389$	−14.5672	−	25.2312i	−0.738587	−	1.27927i	−0.953131	−	0.302557i	$-0.902160\pi$
$389$	−14.5672	−	25.2312i	−0.738587	−	1.27927i	0.214544	−	0.976714i	$-0.431173\pi$
$390$	−33.4627	−	8.40980i	−1.69445	−	0.425847i
$391$	−9.85441	+	17.0683i	−0.498359	+	0.863183i
$392$	−5.36182	−	20.0106i	−0.270813	−	1.01069i
$393$	−9.57158	+	21.2392i	−0.482822	+	1.07138i
$394$	6.60804	−	3.81516i	0.332908	−	0.192205i
$395$	30.4299	−	5.44870i	1.53110	−	0.274154i
$396$	2.53756	−	0.515445i	0.127517	−	0.0259021i
$397$	−18.9354	−	18.9354i	−0.950338	−	0.950338i	0.0484856	−	0.998824i	$-0.484561\pi$
$397$	−18.9354	−	18.9354i	−0.950338	−	0.950338i	−0.998824	+	0.0484856i	$0.984561\pi$
$398$	10.3384	−	38.5836i	0.518219	−	1.93402i
$399$	0.0954754	−	0.585663i	0.00477975	−	0.0293198i
$400$	−0.618946	+	3.62223i	−0.0309473	+	0.181112i
$401$	21.2096	+	12.2453i	1.05916	+	0.611503i	0.925198	−	0.379484i	$-0.123898\pi$
$401$	21.2096	+	12.2453i	1.05916	+	0.611503i	0.133957	+	0.990987i	$0.457232\pi$
$402$	5.40217	+	53.7334i	0.269436	+	2.67998i
$403$	0.720098	+	0.192950i	0.0358706	+	0.00961151i
$404$	−44.6649			−2.22216
$405$	20.0949	−	1.09384i	0.998522	−	0.0543532i
$406$	−9.98392			−0.495493
$407$	0.0427215	+	0.0114472i	0.00211763	+	0.000567417i
$408$	−3.12207	−	31.0541i	−0.154566	−	1.53741i
$409$	−12.2649	−	7.08116i	−0.606462	−	0.350141i	0.165118	−	0.986274i	$-0.447200\pi$
$409$	−12.2649	−	7.08116i	−0.606462	−	0.350141i	−0.771579	+	0.636133i	$0.780533\pi$
$410$	9.89526	+	21.0747i	0.488692	+	1.04080i
$411$	−2.72823	+	16.7354i	−0.134574	+	0.825498i
$412$	14.3795	−	53.6652i	0.708429	−	2.64389i
$413$	−4.42589	−	4.42589i	−0.217784	−	0.217784i
$414$	−24.1957	+	4.91477i	−1.18915	+	0.241548i
$415$	−6.88091	+	9.88252i	−0.337770	+	0.485114i
$416$	15.8516	−	9.15193i	0.777189	−	0.448710i
$417$	5.62816	−	12.4888i	0.275612	−	0.611581i
$418$	0.0673086	+	0.251199i	0.00329217	+	0.0122866i
$419$	13.8808	−	24.0422i	0.678120	−	1.17454i	−0.297426	−	0.954745i	$-0.596128\pi$
$419$	13.8808	−	24.0422i	0.678120	−	1.17454i	0.975546	−	0.219794i	$-0.0705385\pi$
$420$	−5.25167	−	8.77745i	−0.256255	−	0.428296i
$421$	−0.429901	−	0.744611i	−0.0209521	−	0.0362901i	0.855359	−	0.518035i	$-0.173336\pi$
$421$	−0.429901	−	0.744611i	−0.0209521	−	0.0362901i	−0.876311	+	0.481745i	$0.840003\pi$
$422$	7.47211	−	7.47211i	0.363737	−	0.363737i
$423$	−12.9377	−	0.795372i	−0.629053	−	0.0386723i
$424$		−	4.29753i		−	0.208706i
$425$	27.6923	−	2.57053i	1.34327	−	0.124689i
$426$	−8.57586	−	1.39805i	−0.415502	−	0.0677356i
$427$	2.16698	−	0.580639i	0.104867	−	0.0280991i
$428$	−26.9616	+	7.22434i	−1.30324	+	0.349202i
$429$	−1.06890	+	1.30785i	−0.0516070	+	0.0631436i
$430$	−4.62811	−	5.48601i	−0.223187	−	0.264559i
$431$			25.5770i			1.23200i	0.787746	+	0.616000i	$0.211248\pi$
$431$			25.5770i			1.23200i	−0.787746	+	0.616000i	$0.788752\pi$
$432$	2.59359	−	2.80308i	0.124784	−	0.134863i
$433$	6.30733	−	6.30733i	0.303111	−	0.303111i	−0.539119	−	0.842230i	$-0.681243\pi$
$433$	6.30733	−	6.30733i	0.303111	−	0.303111i	0.842230	+	0.539119i	$0.181243\pi$
$434$	0.175604	+	0.304155i	0.00842927	+	0.0145999i
$435$	20.5814	−	5.85993i	0.986804	−	0.280962i
$436$	−14.9694	+	25.9277i	−0.716903	+	1.24171i
$437$	−0.403859	−	1.50722i	−0.0193192	−	0.0721002i
$438$	30.5220	+	42.4118i	1.45840	+	2.02651i
$439$	12.4666	−	7.19760i	0.594999	−	0.343523i	−0.172073	−	0.985084i	$-0.555046\pi$
$439$	12.4666	−	7.19760i	0.594999	−	0.343523i	0.767072	+	0.641561i	$0.221713\pi$
$440$	1.51149	+	1.05241i	0.0720577	+	0.0501716i
$441$	−18.1910	−	6.09297i	−0.866240	−	0.290142i
$442$	35.0390	+	35.0390i	1.66663	+	1.66663i
$443$	−5.67359	+	21.1741i	−0.269560	+	1.00601i	0.689839	+	0.723962i	$0.257681\pi$
$443$	−5.67359	+	21.1741i	−0.269560	+	1.00601i	−0.959400	+	0.282050i	$0.908986\pi$
$444$	0.956558	−	0.362236i	0.0453962	−	0.0171910i
$445$	0.600528	+	0.216776i	0.0284677	+	0.0102762i
$446$	−36.8430	−	21.2713i	−1.74457	−	1.00723i
$447$	14.4253	+	6.50084i	0.682293	+	0.307479i
$448$	9.43376	+	2.52777i	0.445703	+	0.119426i
$449$	23.6447			1.11586			0.557931	−	0.829888i	$-0.311596\pi$
$449$	23.6447			1.11586			0.557931	+	0.829888i	$0.311596\pi$
$450$	25.3911	+	23.8561i	1.19695	+	1.12459i
$451$	1.13976			0.0536693
$452$	44.1632	+	11.8335i	2.07726	+	0.556601i
$453$	20.6657	−	14.8722i	0.970958	−	0.698759i
$454$	22.6906	+	13.1004i	1.06492	+	0.614833i
$455$	6.27587	+	2.26544i	0.294217	+	0.106205i
$456$	1.91329	+	1.56373i	0.0895981	+	0.0732281i
$457$	−1.47628	+	5.50956i	−0.0690575	+	0.257726i	−0.991820	−	0.127642i	$-0.959259\pi$
$457$	−1.47628	+	5.50956i	−0.0690575	+	0.257726i	0.922763	+	0.385369i	$0.125926\pi$
$458$	8.01095	+	8.01095i	0.374327	+	0.374327i
$459$	−25.5719	−	13.4694i	−1.19359	−	0.628697i
$460$	−22.0736	−	15.3692i	−1.02919	−	0.716591i
$461$	−27.8943	+	16.1048i	−1.29916	+	0.750073i	−0.980260	−	0.197713i	$-0.936648\pi$
$461$	−27.8943	+	16.1048i	−1.29916	+	0.750073i	−0.318905	+	0.947787i	$0.603315\pi$
$462$	−0.791745	+	0.0795993i	−0.0368353	+	0.00370329i
$463$	−1.65471	−	6.17544i	−0.0769007	−	0.286997i	0.916757	−	0.399446i	$-0.130797\pi$
$463$	−1.65471	−	6.17544i	−0.0769007	−	0.286997i	−0.993658	+	0.112448i	$0.964131\pi$
$464$	2.03040	−	3.51676i	0.0942590	−	0.163261i
$465$	−0.540521	−	0.523935i	−0.0250660	−	0.0242969i
$466$	12.9869	+	22.4940i	0.601608	+	1.04202i
$467$	−12.7982	+	12.7982i	−0.592230	+	0.592230i	−0.938233	−	0.346003i	$-0.887539\pi$
$467$	−12.7982	+	12.7982i	−0.592230	+	0.592230i	0.346003	+	0.938233i	$0.387539\pi$
$468$	−2.39692	+	38.9889i	−0.110798	+	1.80226i
$469$		−	10.4433i		−	0.482228i
$470$	−14.4697	−	17.1520i	−0.667439	−	0.791161i
$471$	10.3870	+	27.4290i	0.478609	+	1.26386i
$472$	25.1763	−	6.74597i	1.15883	−	0.310508i
$473$	−0.339395	+	0.0909406i	−0.0156054	+	0.00418145i
$474$	−19.6968	−	52.0135i	−0.904706	−	2.38906i
$475$	−1.40639	+	1.69421i	−0.0645298	+	0.0777356i
$476$			14.6900i			0.673314i
$477$	−3.31792	−	2.19758i	−0.151917	−	0.100620i
$478$	36.5795	−	36.5795i	1.67311	−	1.67311i
$479$	−1.76166	−	3.05128i	−0.0804921	−	0.139416i	0.822969	−	0.568086i	$-0.192316\pi$
$479$	−1.76166	−	3.05128i	−0.0804921	−	0.139416i	−0.903461	+	0.428669i	$0.858983\pi$
$480$	−18.4802	+	0.287945i	−0.843503	+	0.0131428i
$481$	−0.333609	+	0.577827i	−0.0152112	+	0.0263467i
$482$	−17.4028	−	64.9482i	−0.792677	−	2.95831i
$483$	4.75056	−	0.477604i	0.216158	−	0.0217318i
$484$	−32.1495	+	18.5615i	−1.46134	+	0.843706i
$485$	−11.5550	+	16.5956i	−0.524686	+	0.753566i
$486$	−8.57829	−	35.1759i	−0.389119	−	1.59561i
$487$	29.3442	+	29.3442i	1.32971	+	1.32971i	0.905616	+	0.424098i	$0.139409\pi$
$487$	29.3442	+	29.3442i	1.32971	+	1.32971i	0.424098	+	0.905616i	$0.360591\pi$
$488$	−2.41790	+	9.02373i	−0.109453	+	0.408485i
$489$	18.4877	+	15.1099i	0.836044	+	0.683295i
$490$	−14.1157	−	30.0632i	−0.637681	−	1.35812i
$491$	17.9001	+	10.3346i	0.807819	+	0.466395i	0.846198	−	0.532869i	$-0.178886\pi$
$491$	17.9001	+	10.3346i	0.807819	+	0.466395i	−0.0383788	+	0.999263i	$0.512219\pi$
$492$	21.3944	−	15.3967i	0.964533	−	0.694135i
$493$	−29.6859	−	7.95433i	−1.33699	−	0.358245i
$494$	−3.92319			−0.176513
$495$	1.58543	−	0.628795i	0.0712598	−	0.0282622i
$496$	−0.142849			−0.00641409
$497$	1.62304	+	0.434891i	0.0728031	+	0.0195075i
$498$	19.7521	+	8.90140i	0.885114	+	0.398881i
$499$	22.6691	+	13.0880i	1.01481	+	0.585901i	0.912596	−	0.408862i	$-0.134074\pi$
$499$	22.6691	+	13.0880i	1.01481	+	0.585901i	0.102214	+	0.994762i	$0.467407\pi$
$500$	0.301355	+	37.9535i	0.0134770	+	1.69733i
$501$	31.9563	−	12.1014i	1.42770	−	0.540652i
$502$	−12.2766	+	45.8168i	−0.547930	+	2.04490i
$503$	−6.72022	−	6.72022i	−0.299640	−	0.299640i	0.541233	−	0.840873i	$-0.317958\pi$
$503$	−6.72022	−	6.72022i	−0.299640	−	0.299640i	−0.840873	+	0.541233i	$0.817958\pi$
$504$	−5.66431	+	5.00820i	−0.252308	+	0.223083i
$505$	−28.9593	+	5.18536i	−1.28867	+	0.230746i
$506$	−1.81213	+	1.04624i	−0.0805592	+	0.0465109i
$507$	−1.73155	−	2.40607i	−0.0769008	−	0.106857i
$508$	−8.35217	−	31.1707i	−0.370568	−	1.38298i
$509$	−11.9676	+	20.7285i	−0.530454	+	0.918773i	0.468915	+	0.883243i	$0.344645\pi$
$509$	−11.9676	+	20.7285i	−0.530454	+	0.918773i	−0.999369	+	0.0355293i	$0.988688\pi$
$510$	−13.7017	−	48.1236i	−0.606721	−	2.13095i
$511$	−5.05232	−	8.75087i	−0.223501	−	0.387116i
$512$	−5.84717	+	5.84717i	−0.258411	+	0.258411i
$513$	2.18566	−	0.677538i	0.0964991	−	0.0299141i
$514$		−	17.0546i		−	0.752246i
$515$	3.09298	−	36.4641i	0.136293	−	1.60680i
$516$	−5.14226	+	6.29181i	−0.226376	+	0.276981i
$517$	−1.06111	+	0.284325i	−0.0466678	+	0.0125046i
$518$	−0.303618	+	0.0813543i	−0.0133402	+	0.00357450i
$519$	−17.7444	−	2.89271i	−0.778893	−	0.126976i
$520$	−21.2369	+	17.9159i	−0.931299	+	0.785662i
$521$		−	3.23141i		−	0.141571i	−0.997492	−	0.0707853i	$-0.977449\pi$
$521$		−	3.23141i		−	0.141571i	0.997492	−	0.0707853i	$-0.0225505\pi$
$522$	−17.1679	−	34.4606i	−0.751420	−	1.50830i
$523$	−8.67002	+	8.67002i	−0.379114	+	0.379114i	−0.870782	−	0.491669i	$-0.836387\pi$
$523$	−8.67002	+	8.67002i	−0.379114	+	0.379114i	0.491669	+	0.870782i	$0.336387\pi$
$524$	22.8301	+	39.5429i	0.997339	+	1.72744i
$525$	−4.42403	−	5.08132i	−0.193080	−	0.221767i
$526$	−16.9641	+	29.3827i	−0.739672	+	1.28115i
$527$	0.279813	+	1.04427i	0.0121888	+	0.0454893i
$528$	0.132977	−	0.295074i	0.00578707	−	0.0128415i
$529$	−9.04559	+	5.22247i	−0.393286	+	0.227064i
$530$	−1.21434	−	6.78183i	−0.0527474	−	0.294584i
$531$	7.66587	−	22.8870i	0.332670	−	0.993213i
$532$	−0.822392	−	0.822392i	−0.0356552	−	0.0356552i
$533$	−4.45016	+	16.6082i	−0.192758	+	0.719381i
$534$	0.184817	−	1.13370i	0.00799780	−	0.0490599i
$535$	−16.6423	+	7.81413i	−0.719510	+	0.337834i
$536$	37.6619	+	21.7441i	1.62675	+	0.939202i
$537$	−2.61650	−	26.0254i	−0.112910	−	1.12308i
$538$	8.43586	+	2.26038i	0.363696	+	0.0974520i
$539$	−1.62588			−0.0700317
$540$	21.2658	−	33.2201i	0.915134	−	1.42956i
$541$	−11.1502			−0.479386			−0.239693	−	0.970849i	$-0.577047\pi$
$541$	−11.1502			−0.479386			−0.239693	+	0.970849i	$0.577047\pi$
$542$	−31.5855	−	8.46330i	−1.35671	−	0.363530i
$543$	−1.35655	−	13.4931i	−0.0582153	−	0.579046i
$544$	22.9878	+	13.2720i	0.985592	+	0.569032i
$545$	−6.69558	+	18.5486i	−0.286807	+	0.794533i
$546$	1.93144	−	11.8478i	0.0826582	−	0.507040i
$547$	3.54511	−	13.2305i	0.151578	−	0.565697i	−0.847796	−	0.530323i	$-0.822071\pi$
$547$	3.54511	−	13.2305i	0.151578	−	0.565697i	0.999374	−	0.0353748i	$-0.0112625\pi$
$548$	23.5000	+	23.5000i	1.00387	+	1.00387i
$549$	5.73038	+	6.48111i	0.244567	+	0.276607i
$550$	2.68263	+	1.23369i	0.114388	+	0.0526045i
$551$	2.10722	−	1.21661i	0.0897708	−	0.0518292i
$552$	−8.16876	+	18.1264i	−0.347686	+	0.771511i
$553$	2.78371	+	10.3889i	0.118375	+	0.441782i
$554$	−2.42950	+	4.20802i	−0.103220	+	0.178781i
$555$	0.578147	−	0.345913i	0.0245410	−	0.0146832i
$556$	−13.4243	−	23.2516i	−0.569317	−	0.986086i
$557$	11.8934	−	11.8934i	0.503938	−	0.503938i	−0.408721	−	0.912659i	$-0.634025\pi$
$557$	11.8934	−	11.8934i	0.503938	−	0.503938i	0.912659	+	0.408721i	$0.134025\pi$
$558$	−0.747864	+	1.12913i	−0.0316596	+	0.0477999i
$559$		−	5.30061i		−	0.224192i
$560$	−1.27392	−	0.108057i	−0.0538330	−	0.00456624i
$561$	−2.41758	−	0.394116i	−0.102070	−	0.0166396i
$562$	−20.7940	+	5.57173i	−0.877141	+	0.235029i
$563$	−23.7986	+	6.37683i	−1.00299	+	0.268751i	−0.722699	−	0.691163i	$-0.757099\pi$
$563$	−23.7986	+	6.37683i	−1.00299	+	0.268751i	−0.280294	+	0.959914i	$0.590432\pi$
$564$	−16.0772	+	19.6713i	−0.676974	+	0.828310i
$565$	30.0078	+	2.54533i	1.26244	+	0.107083i
$566$		−	74.8082i		−	3.14442i
$567$	0.970098	+	6.93413i	0.0407403	+	0.291206i
$568$	−4.94768	+	4.94768i	−0.207600	+	0.207600i
$569$	6.24856	+	10.8228i	0.261953	+	0.453716i	0.966761	−	0.255682i	$-0.0823000\pi$
$569$	6.24856	+	10.8228i	0.261953	+	0.453716i	−0.704808	+	0.709399i	$0.748967\pi$
$570$	3.46118	+	1.92705i	0.144973	+	0.0807151i
$571$	13.7065	−	23.7404i	0.573601	−	0.993506i	−0.422591	−	0.906320i	$-0.638879\pi$
$571$	13.7065	−	23.7404i	0.573601	−	0.993506i	0.996192	−	0.0871853i	$-0.0277872\pi$
$572$	0.856838	+	3.19776i	0.0358262	+	0.133705i
$573$	11.6072	+	16.1287i	0.484897	+	0.673787i
$574$	−7.01498	+	4.05010i	−0.292800	+	0.169048i
$575$	−16.0961	−	7.40224i	−0.671252	−	0.308695i
$576$	7.49704	+	36.9083i	0.312377	+	1.53785i
$577$	−11.1638	−	11.1638i	−0.464755	−	0.464755i	0.435455	−	0.900210i	$-0.356587\pi$
$577$	−11.1638	−	11.1638i	−0.464755	−	0.464755i	−0.900210	+	0.435455i	$0.856587\pi$
$578$	−8.37928	+	31.2719i	−0.348532	+	1.30074i
$579$	−8.93865	+	3.38495i	−0.371478	+	0.140674i
$580$	14.2407	−	39.4507i	0.591314	−	1.63810i
$581$	−3.62831	−	2.09481i	−0.150528	−	0.0869072i
$582$	33.1695	+	14.9480i	1.37492	+	0.619615i
$583$	−0.325788	−	0.0872947i	−0.0134928	−	0.00361538i
$584$	42.0778			1.74119
$585$	2.97233	+	25.5574i	0.122891	+	1.05667i
$586$	−15.3410			−0.633733
$587$	17.7860	+	4.76574i	0.734106	+	0.196703i	0.606457	−	0.795116i	$-0.292590\pi$
$587$	17.7860	+	4.76574i	0.734106	+	0.196703i	0.127649	+	0.991819i	$0.459257\pi$
$588$	−30.5193	+	21.9635i	−1.25859	+	0.905758i
$589$	−0.0741267	−	0.0427971i	−0.00305434	−	0.00176342i
$590$	37.8240	−	17.7596i	1.55719	−	0.731152i
$591$	−4.40577	−	3.60082i	−0.181229	−	0.148118i
$592$	0.0330896	−	0.123492i	0.00135997	−	0.00507549i
$593$	−14.5424	−	14.5424i	−0.597186	−	0.597186i	0.342377	−	0.939563i	$-0.388768\pi$
$593$	−14.5424	−	14.5424i	−0.597186	−	0.597186i	−0.939563	+	0.342377i	$0.888768\pi$
$594$	−1.63620	−	2.59592i	−0.0671341	−	0.106512i
$595$	1.70543	+	9.52450i	0.0699158	+	0.390466i
$596$	26.8568	−	15.5058i	1.10010	−	0.635143i
$597$	−29.6380	+	2.97970i	−1.21300	+	0.121951i
$598$	−8.16997	−	30.4907i	−0.334095	−	1.24686i
$599$	17.6972	−	30.6525i	0.723089	−	1.25243i	−0.236666	−	0.971591i	$-0.576055\pi$
$599$	17.6972	−	30.6525i	0.723089	−	1.25243i	0.959756	−	0.280836i	$-0.0906118\pi$
$600$	27.5361	−	5.37458i	1.12416	−	0.219416i
$601$	7.31737	+	12.6741i	0.298482	+	0.516986i	0.975789	−	0.218715i	$-0.0701864\pi$
$601$	7.31737	+	12.6741i	0.298482	+	0.516986i	−0.677307	+	0.735700i	$0.736853\pi$
$602$	1.76575	−	1.76575i	0.0719664	−	0.0719664i
$603$	36.0463	−	17.9579i	1.46792	−	0.731304i
$604$		−	49.9026i		−	2.03051i
$605$	−18.6898	+	15.7671i	−0.759849	+	0.641023i
$606$	18.7449	+	49.4997i	0.761460	+	2.01079i
$607$	−7.54883	+	2.02270i	−0.306397	+	0.0820989i	−0.408742	−	0.912650i	$-0.634032\pi$
$607$	−7.54883	+	2.02270i	−0.306397	+	0.0820989i	0.102344	+	0.994749i	$0.467366\pi$
$608$	−2.02994	+	0.543920i	−0.0823248	+	0.0220589i
$609$	2.63667	+	6.96266i	0.106843	+	0.282141i
$610$	−1.26583	+	14.9234i	−0.0512522	+	0.604229i
$611$		−	16.5723i		−	0.670444i
$612$	−50.7040	+	25.2603i	−2.04959	+	1.02109i
$613$	3.49830	−	3.49830i	0.141295	−	0.141295i	−0.632921	−	0.774216i	$-0.718144\pi$
$613$	3.49830	−	3.49830i	0.141295	−	0.141295i	0.774216	+	0.632921i	$0.218144\pi$
$614$	−9.56058	−	16.5594i	−0.385833	−	0.668283i
$615$	12.0839	−	12.4665i	0.487272	−	0.502697i
$616$	−0.320393	+	0.554937i	−0.0129090	+	0.0223590i
$617$	6.40561	+	23.9061i	0.257880	+	0.962421i	0.966466	+	0.256796i	$0.0826670\pi$
$617$	6.40561	+	23.9061i	0.257880	+	0.962421i	−0.708585	+	0.705625i	$0.750666\pi$
$618$	−65.5090	+	6.58605i	−2.63516	+	0.264930i
$619$	−15.4357	+	8.91182i	−0.620414	+	0.358196i	−0.777030	−	0.629463i	$-0.783275\pi$
$619$	−15.4357	+	8.91182i	−0.620414	+	0.358196i	0.156616	+	0.987660i	$0.449941\pi$
$620$	−1.45232	+	0.260049i	−0.0583267	+	0.0104438i
$621$	9.81737	+	15.5758i	0.393958	+	0.625035i
$622$	−18.9394	−	18.9394i	−0.759402	−	0.759402i
$623$	−0.0574910	+	0.214559i	−0.00230333	+	0.00859614i
$624$	3.78051	+	3.08979i	0.151342	+	0.123691i
$625$	4.60160	+	24.5729i	0.184064	+	0.982914i
$626$	13.3961	+	7.73424i	0.535416	+	0.309122i
$627$	0.157408	−	0.113280i	0.00628625	−	0.00452396i
$628$	55.5270	+	14.8784i	2.21577	+	0.593714i
$629$	−0.967588			−0.0385803
$630$	−7.52357	+	9.50386i	−0.299746	+	0.378643i
$631$	−29.9153			−1.19091			−0.595454	−	0.803389i	$-0.703028\pi$
$631$	−29.9153			−1.19091			−0.595454	+	0.803389i	$0.703028\pi$
$632$	−43.2617	−	11.5919i	−1.72086	−	0.461102i
$633$	−7.18428	−	3.23763i	−0.285549	−	0.128684i
$634$	−4.03553	−	2.32991i	−0.160271	−	0.0925327i
$635$	−9.03403	−	19.2404i	−0.358505	−	0.763533i
$636$	−7.29457	+	2.76236i	−0.289249	+	0.109535i
$637$	6.34819	−	23.6917i	0.251524	−	0.938701i
$638$	−2.30723	−	2.30723i	−0.0913441	−	0.0913441i
$639$	1.28983	+	6.34991i	0.0510250	+	0.251199i
$640$	−25.0615	+	35.9939i	−0.990642	+	1.42278i
$641$	−13.7403	+	7.93299i	−0.542711	+	0.313334i	−0.746177	−	0.665748i	$-0.768113\pi$
$641$	−13.7403	+	7.93299i	−0.542711	+	0.313334i	0.203466	+	0.979082i	$0.434779\pi$
$642$	19.3216	+	26.8482i	0.762561	+	1.05961i
$643$	6.01727	+	22.4568i	0.237298	+	0.885608i	0.977099	+	0.212783i	$0.0682527\pi$
$643$	6.01727	+	22.4568i	0.237298	+	0.885608i	−0.739801	+	0.672825i	$0.765081\pi$
$644$	4.67895	−	8.10419i	0.184377	−	0.319350i
$645$	−2.60363	+	4.67639i	−0.102518	+	0.184133i
$646$	−2.84467	−	4.92712i	−0.111922	−	0.193855i
$647$	−8.90965	+	8.90965i	−0.350274	+	0.350274i	−0.860212	−	0.509937i	$-0.829669\pi$
$647$	−8.90965	+	8.90965i	−0.350274	+	0.350274i	0.509937	+	0.860212i	$0.329669\pi$
$648$	−27.0265	−	10.9391i	−1.06170	−	0.429728i
$649$		−	2.04560i		−	0.0802969i
$650$	−28.4510	+	34.2734i	−1.11594	+	1.34431i
$651$	0.165739	−	0.202789i	0.00649581	−	0.00794793i
$652$	45.2035	−	12.1122i	1.77031	−	0.474352i
$653$	14.0422	−	3.76260i	0.549515	−	0.147242i	0.0266300	−	0.999645i	$-0.491522\pi$
$653$	14.0422	−	3.76260i	0.549515	−	0.147242i	0.522885	+	0.852403i	$0.324856\pi$
$654$	35.0166	+	5.70845i	1.36926	+	0.223218i
$655$	19.3930	+	22.9879i	0.757749	+	0.898211i
$656$		−	3.29463i		−	0.128634i
$657$	21.5168	−	32.4863i	0.839452	−	1.26741i
$658$	5.52058	−	5.52058i	0.215215	−	0.215215i
$659$	−4.50735	−	7.80696i	−0.175582	−	0.304116i	0.764781	−	0.644291i	$-0.222847\pi$
$659$	−4.50735	−	7.80696i	−0.175582	−	0.304116i	−0.940362	+	0.340174i	$0.889514\pi$
$660$	0.814790	−	3.24206i	0.0317156	−	0.126197i
$661$	15.0034	−	25.9866i	0.583564	−	1.01076i	−0.411488	−	0.911415i	$-0.634991\pi$
$661$	15.0034	−	25.9866i	0.583564	−	1.01076i	0.995053	−	0.0993481i	$-0.0316757\pi$
$662$	14.1511	+	52.8125i	0.549996	+	2.05261i
$663$	15.1822	−	33.6892i	0.589629	−	1.30838i
$664$	15.1090	−	8.72321i	0.586345	−	0.338526i
$665$	−0.628687	−	0.437737i	−0.0243795	−	0.0169747i
$666$	−0.802894	−	0.908079i	−0.0311115	−	0.0351874i
$667$	13.8436	+	13.8436i	0.536028	+	0.536028i
$668$	17.3342	−	64.6920i	0.670679	−	2.50301i
$669$	−5.10443	+	31.3115i	−0.197349	+	1.21057i
$670$	65.5775	+	23.6719i	2.53348	+	0.914525i
$671$	0.634959	+	0.366594i	0.0245123	+	0.0141522i
$672$	−0.643241	−	6.39808i	−0.0248136	−	0.246811i
$673$	26.2818	+	7.04218i	1.01309	+	0.271456i	0.726919	−	0.686723i	$-0.240951\pi$
$673$	26.2818	+	7.04218i	1.01309	+	0.271456i	0.286169	+	0.958179i	$0.407618\pi$
$674$	−26.4622			−1.01928
$675$	9.93136	−	24.0077i	0.382258	−	0.924056i
$676$	−5.81007			−0.223464
$677$	16.7622	+	4.49141i	0.644223	+	0.172619i	0.566116	−	0.824326i	$-0.308446\pi$
$677$	16.7622	+	4.49141i	0.644223	+	0.172619i	0.0781075	+	0.996945i	$0.475112\pi$
$678$	−5.41993	−	53.9100i	−0.208151	−	2.07040i
$679$	−6.09297	−	3.51778i	−0.233827	−	0.135000i
$680$	−37.8992	−	13.6807i	−1.45337	−	0.524630i
$681$	3.14367	−	19.2838i	0.120466	−	0.738959i
$682$	−0.0297075	+	0.110870i	−0.00113756	+	0.00424543i
$683$	27.4945	+	27.4945i	1.05205	+	1.05205i	0.998569	+	0.0534806i	$0.0170315\pi$
$683$	27.4945	+	27.4945i	1.05205	+	1.05205i	0.0534806	+	0.998569i	$0.482968\pi$
$684$	1.42442	−	4.25273i	0.0544642	−	0.162607i
$685$	17.9649	+	12.5084i	0.686403	+	0.477922i
$686$	20.9610	−	12.1018i	0.800293	−	0.462049i
$687$	3.47111	−	7.70236i	0.132431	−	0.293863i
$688$	0.262876	+	0.981065i	0.0100220	+	0.0374028i
$689$	2.54405	−	4.40643i	0.0969207	−	0.167872i
$690$	−7.76903	+	30.9131i	−0.295762	+	1.17684i
$691$	−9.07512	−	15.7186i	−0.345234	−	0.597962i	0.640162	−	0.768240i	$-0.278867\pi$
$691$	−9.07512	−	15.7186i	−0.345234	−	0.597962i	−0.985396	+	0.170277i	$0.945534\pi$
$692$	−24.9168	+	24.9168i	−0.947195	+	0.947195i
$693$	0.264605	+	0.531132i	0.0100515	+	0.0201760i
$694$			33.1902i			1.25988i
$695$	−11.4033	−	13.5171i	−0.432550	−	0.512731i
$696$	−30.5993	−	4.98833i	−1.15986	−	0.189082i
$697$	−24.0850	+	6.45355i	−0.912283	+	0.244446i
$698$	39.4063	−	10.5589i	1.49155	−	0.399660i
$699$	12.2573	−	14.9974i	0.463614	−	0.567254i
$700$	−13.1485	+	1.22051i	−0.496967	+	0.0461309i
$701$			5.23510i			0.197727i	0.995101	+	0.0988635i	$0.0315207\pi$
$701$			5.23510i			0.197727i	−0.995101	+	0.0988635i	$0.968479\pi$
$702$	44.2153	−	13.7064i	1.66880	−	0.517316i
$703$	0.0541687	−	0.0541687i	0.00204301	−	0.00204301i
$704$	1.59594	+	2.76425i	0.0601492	+	0.104181i
$705$	−8.14022	+	14.6207i	−0.306579	+	0.550647i
$706$	−20.2427	+	35.0614i	−0.761844	+	1.31955i
$707$	−2.64917	−	9.88684i	−0.0996323	−	0.371833i
$708$	−27.6333	−	38.3978i	−1.03852	−	1.44308i
$709$	−14.7176	+	8.49720i	−0.552730	+	0.319119i	−0.750222	−	0.661186i	$-0.770054\pi$
$709$	−14.7176	+	8.49720i	−0.552730	+	0.319119i	0.197492	+	0.980304i	$0.436720\pi$
$710$	−6.40977	+	9.20587i	−0.240555	+	0.345490i
$711$	−31.0718	+	27.4727i	−1.16528	+	1.03031i
$712$	−0.654066	−	0.654066i	−0.0245121	−	0.0245121i
$713$	0.178248	−	0.665231i	0.00667545	−	0.0249131i
$714$	16.2801	−	6.16507i	0.609268	−	0.230722i
$715$	0.926790	+	1.97385i	0.0346600	+	0.0738179i
$716$	−44.3979	−	25.6331i	−1.65923	−	0.957955i
$717$	−35.1705	−	15.8498i	−1.31346	−	0.591920i
$718$	−76.4092	−	20.4738i	−2.85157	−	0.764075i
$719$	−49.3502			−1.84045			−0.920225	−	0.391389i	$-0.871995\pi$
$719$	−49.3502			−1.84045			−0.920225	+	0.391389i	$0.871995\pi$
$720$	−1.81761	−	4.58289i	−0.0677385	−	0.170794i
$721$	12.7320			0.474164
$722$	−42.1918	−	11.3053i	−1.57022	−	0.420739i
$723$	−40.6981	+	29.2888i	−1.51358	+	1.08926i
$724$	−23.0186	−	13.2898i	−0.855478	−	0.493910i
$725$	4.65321	−	27.2318i	0.172816	−	1.01136i
$726$	34.0632	+	27.8397i	1.26421	+	1.03323i
$727$	−10.1550	+	37.8991i	−0.376630	+	1.40560i	0.474319	+	0.880353i	$0.342694\pi$
$727$	−10.1550	+	37.8991i	−0.376630	+	1.40560i	−0.850949	+	0.525249i	$0.823972\pi$
$728$	−6.83537	−	6.83537i	−0.253336	−	0.253336i
$729$	−22.2658	+	15.2721i	−0.824658	+	0.565632i
$730$	66.4020	−	11.8898i	2.45765	−	0.440060i
$731$	6.65702	−	3.84343i	0.246219	−	0.142155i
$732$	16.8709	−	1.69615i	0.623568	−	0.0626914i
$733$	−1.96236	−	7.32362i	−0.0724813	−	0.270504i	0.920169	−	0.391521i	$-0.128051\pi$
$733$	−1.96236	−	7.32362i	−0.0724813	−	0.270504i	−0.992650	+	0.121017i	$0.961384\pi$
$734$	−16.3918	+	28.3915i	−0.605034	+	1.04795i
$735$	−17.2378	+	17.7835i	−0.635828	+	0.655955i
$736$	−8.45462	−	14.6438i	−0.311641	−	0.539778i
$737$	2.41340	−	2.41340i	0.0888987	−	0.0888987i
$738$	−26.0421	−	17.2486i	−0.958621	−	0.634930i
$739$		−	43.8329i		−	1.61242i	−0.591629	−	0.806210i	$-0.701515\pi$
$739$		−	43.8329i		−	1.61242i	0.591629	−	0.806210i	$-0.298485\pi$
$740$	0.111606	−	1.31577i	0.00410273	−	0.0483685i
$741$	1.03608	+	2.73598i	0.0380614	+	0.100509i
$742$	2.31535	−	0.620396i	0.0849992	−	0.0227755i
$743$	−9.01884	+	2.41659i	−0.330869	+	0.0886561i	−0.420429	−	0.907325i	$-0.638121\pi$
$743$	−9.01884	+	2.41659i	−0.330869	+	0.0886561i	0.0895603	+	0.995981i	$0.471454\pi$
$744$	0.386235	+	1.01993i	0.0141601	+	0.0373925i
$745$	15.6130	−	13.1714i	0.572015	−	0.482563i
$746$			50.0066i			1.83087i
$747$	0.991358	−	16.1257i	0.0362719	−	0.590007i
$748$	−3.39477	+	3.39477i	−0.124125	+	0.124125i
$749$	−3.19830	−	5.53962i	−0.116863	−	0.202413i
$750$	41.9354	−	16.2623i	1.53126	−	0.593814i
$751$	23.6963	−	41.0432i	0.864689	−	1.49769i	−0.00266566	−	0.999996i	$-0.500849\pi$
$751$	23.6963	−	41.0432i	0.864689	−	1.49769i	0.867355	−	0.497690i	$-0.165818\pi$
$752$	0.821878	+	3.06729i	0.0299708	+	0.111853i
$753$	35.1942	−	3.53830i	1.28255	−	0.128943i
$754$	42.6286	−	24.6116i	1.55244	−	0.896303i
$755$	−5.79343	−	32.3552i	−0.210845	−	1.17753i
$756$	12.1417	+	6.39537i	0.441591	+	0.232597i
$757$	1.37906	+	1.37906i	0.0501227	+	0.0501227i	0.731724	−	0.681601i	$-0.238716\pi$
$757$	1.37906	+	1.37906i	0.0501227	+	0.0501227i	−0.681601	+	0.731724i	$0.738716\pi$
$758$	−5.72832	+	21.3784i	−0.208062	+	0.776497i
$759$	1.20820	+	0.987457i	0.0438549	+	0.0358424i
$760$	2.88761	−	1.35583i	0.104744	−	0.0491811i
$761$	−41.8540	−	24.1644i	−1.51720	−	0.875958i	−0.999796	−	0.0202203i	$-0.993563\pi$
$761$	−41.8540	−	24.1644i	−1.51720	−	0.875958i	−0.517409	−	0.855738i	$-0.673103\pi$
$762$	−31.0396	+	22.3379i	−1.12445	+	0.809218i
$763$	−6.62712	−	1.77573i	−0.239918	−	0.0642858i
$764$	38.9469			1.40905
$765$	−29.9423	+	22.2644i	−1.08256	+	0.804972i
$766$	23.1275			0.835631
$767$	29.8078	+	7.98696i	1.07630	+	0.288393i
$768$	32.2924	+	14.5528i	1.16525	+	0.525128i
$769$	−25.7542	−	14.8692i	−0.928719	−	0.536196i	−0.0423126	−	0.999104i	$-0.513473\pi$
$769$	−25.7542	−	14.8692i	−0.928719	−	0.536196i	−0.886406	+	0.462908i	$0.846806\pi$
$770$	−0.348798	+	0.966265i	−0.0125698	+	0.0348218i
$771$	−11.8937	+	4.50398i	−0.428340	+	0.162207i
$772$	−4.84862	+	18.0953i	−0.174506	+	0.651264i
$773$	14.1444	+	14.1444i	0.508738	+	0.508738i	0.914139	−	0.405401i	$-0.132868\pi$
$773$	14.1444	+	14.1444i	0.508738	+	0.508738i	−0.405401	+	0.914139i	$0.632868\pi$
$774$	9.13097	+	3.05836i	0.328206	+	0.109931i
$775$	−0.911448	+	0.337214i	−0.0327402	+	0.0121131i
$776$	25.3724	−	14.6488i	0.910816	−	0.525860i
$777$	0.136919	+	0.190255i	0.00491193	+	0.00682535i
$778$	17.5142	+	65.3638i	0.627913	+	2.34340i
$779$	0.987064	−	1.70964i	0.0353652	−	0.0612544i
$780$	44.0608	+	24.5313i	1.57763	+	0.878361i
$781$	0.274574	+	0.475576i	0.00982503	+	0.0170175i
$782$	32.3692	−	32.3692i	1.15752	−	1.15752i
$783$	−19.4985	+	21.0735i	−0.696819	+	0.753104i
$784$			4.69982i			0.167851i
$785$	37.7292	+	3.20028i	1.34661	+	0.114223i
$786$	34.2420	−	41.8967i	1.22137	−	1.49441i
$787$	−1.74131	+	0.466583i	−0.0620710	+	0.0166319i	−0.289721	−	0.957111i	$-0.593562\pi$
$787$	−1.74131	+	0.466583i	−0.0620710	+	0.0166319i	0.227650	+	0.973743i	$0.426896\pi$
$788$	−10.7723	+	2.88644i	−0.383749	+	0.102825i
$789$	24.9712	+	4.07084i	0.889000	+	0.144926i
$790$	−71.5457	−	6.06868i	−2.54548	−	0.215914i
$791$			10.4777i			0.372543i
$792$	−2.46636	−	0.151625i	−0.0876383	−	0.00538774i
$793$	−7.82105	+	7.82105i	−0.277733	+	0.277733i
$794$	31.0989	+	53.8649i	1.10366	+	1.91159i
$795$	−4.40887	+	2.63789i	−0.156366	+	0.0935562i
$796$	−29.1913	+	50.5607i	−1.03466	+	1.79208i
$797$	1.83545	+	6.85000i	0.0650150	+	0.242639i	0.990784	−	0.135450i	$-0.0432479\pi$
$797$	1.83545	+	6.85000i	0.0650150	+	0.242639i	−0.925769	+	0.378089i	$0.876581\pi$
$798$	−0.566273	+	1.25655i	−0.0200458	+	0.0444815i
$799$	20.8131	−	12.0165i	0.736315	−	0.425112i
$800$	−9.96939	+	21.6783i	−0.352471	+	0.766443i
$801$	−0.839435	+	0.170511i	−0.0296600	+	0.00602472i
$802$	−40.2228	−	40.2228i	−1.42032	−	1.42032i
$803$	0.854717	−	3.18985i	0.0301623	−	0.112567i
$804$	12.6999	−	77.9035i	0.447891	−	2.74744i
$805$	2.09283	−	5.79769i	0.0737625	−	0.204342i
$806$	−1.49956	−	0.865774i	−0.0528199	−	0.0304956i
$807$	−0.651477	−	6.48001i	−0.0229331	−	0.228107i
$808$	41.1709	+	11.0317i	1.44839	+	0.388094i
$809$	24.7868			0.871457			0.435728	−	0.900078i	$-0.356491\pi$
$809$	24.7868			0.871457			0.435728	+	0.900078i	$0.356491\pi$
$810$	−45.7408	−	9.62598i	−1.60717	−	0.338222i
$811$	−5.24853			−0.184301			−0.0921505	−	0.995745i	$-0.529374\pi$
$811$	−5.24853			−0.184301			−0.0921505	+	0.995745i	$0.529374\pi$
$812$	14.0951	+	3.77678i	0.494642	+	0.132539i
$813$	2.43926	+	24.2624i	0.0855484	+	0.850919i
$814$	−0.0889652	−	0.0513641i	−0.00311823	−	0.00180031i
$815$	27.9023	−	13.1011i	0.977376	−	0.458911i
$816$	−1.13924	+	6.98831i	−0.0398815	+	0.244640i
$817$	−0.157514	+	0.587849i	−0.00551071	+	0.0205662i
$818$	23.2598	+	23.2598i	0.813260	+	0.813260i
$819$	−8.77260	+	1.78194i	−0.306539	+	0.0622661i
$820$	−5.99772	−	33.4961i	−0.209449	−	1.16973i
$821$	23.5611	−	13.6030i	0.822288	−	0.474748i	−0.0289167	−	0.999582i	$-0.509206\pi$
$821$	23.5611	−	13.6030i	0.822288	−	0.474748i	0.851205	+	0.524834i	$0.175872\pi$
$822$	16.1814	−	35.9063i	0.564390	−	1.25237i
$823$	−8.71001	−	32.5062i	−0.303612	−	1.13309i	−0.934134	−	0.356923i	$-0.883826\pi$
$823$	−8.71001	−	32.5062i	−0.303612	−	1.13309i	0.630522	−	0.776171i	$-0.282841\pi$
$824$	−26.5093	+	45.9155i	−0.923496	+	1.59954i
$825$	0.151897	−	2.19664i	0.00528837	−	0.0764771i
$826$	7.26896	+	12.5902i	0.252920	+	0.438070i
$827$	9.12836	−	9.12836i	0.317424	−	0.317424i	−0.530353	−	0.847777i	$-0.677941\pi$
$827$	9.12836	−	9.12836i	0.317424	−	0.317424i	0.847777	+	0.530353i	$0.177941\pi$
$828$	36.0182	+	2.21429i	1.25172	+	0.0769521i
$829$			44.3456i			1.54019i	0.637931	+	0.770093i	$0.279790\pi$
$829$			44.3456i			1.54019i	−0.637931	+	0.770093i	$0.720210\pi$
$830$	21.3783	−	18.0352i	0.742053	−	0.626011i
$831$	3.57623	+	0.583001i	0.124058	+	0.0202241i
$832$	−46.5109	+	12.4626i	−1.61247	+	0.432061i
$833$	34.3574	−	9.20604i	1.19041	−	0.318970i
$834$	−20.1346	+	24.6356i	−0.697203	+	0.853061i
$835$	3.72850	−	43.9566i	0.129030	−	1.52118i
$836$		−	0.380101i		−	0.0131461i
$837$	0.984946	+	0.223357i	0.0340447	+	0.00772035i
$838$	−45.5948	+	45.5948i	−1.57505	+	1.57505i
$839$	23.9660	+	41.5104i	0.827399	+	1.43310i	0.900072	+	0.435742i	$0.143514\pi$
$839$	23.9660	+	41.5104i	0.827399	+	1.43310i	−0.0726721	+	0.997356i	$0.523153\pi$
$840$	2.67292	+	9.38791i	0.0922244	+	0.323914i
$841$	−0.764464	+	1.32409i	−0.0263608	+	0.0456583i
$842$	0.516871	+	1.92899i	0.0178125	+	0.0664773i
$843$	9.37717	+	13.0300i	0.322967	+	0.448778i
$844$	−13.3756	+	7.72240i	−0.460407	+	0.265816i
$845$	−3.76706	+	0.674519i	−0.129591	+	0.0232042i
$846$	28.5479	+	9.56193i	0.981497	+	0.328746i
$847$	−6.01556	−	6.01556i	−0.206697	−	0.206697i
$848$	−0.252337	+	0.941733i	−0.00866527	+	0.0323392i
$849$	−52.1703	+	19.7562i	−1.79048	+	0.678031i
$850$	−63.6735	−	10.8802i	−2.18398	−	0.373186i
$851$	0.533801	+	0.308190i	0.0182985	+	0.0105646i
$852$	11.5784	+	5.21787i	0.396669	+	0.178761i
$853$	−5.60190	−	1.50103i	−0.191806	−	0.0513941i	0.161637	−	0.986850i	$-0.448322\pi$
$853$	−5.60190	−	1.50103i	−0.191806	−	0.0513941i	−0.353443	+	0.935456i	$0.614989\pi$
$854$	−5.21071			−0.178307
$855$	0.429831	−	2.92270i	0.0146999	−	0.0999542i
$856$	26.6368			0.910427
$857$	−30.7371	−	8.23598i	−1.04996	−	0.281336i	−0.307724	−	0.951476i	$-0.599567\pi$
$857$	−30.7371	−	8.23598i	−1.04996	−	0.281336i	−0.742235	+	0.670140i	$0.766234\pi$
$858$	3.18432	−	2.29162i	0.108711	−	0.0782347i
$859$	−10.3188	−	5.95757i	−0.352074	−	0.203270i	0.313525	−	0.949580i	$-0.398490\pi$
$859$	−10.3188	−	5.95757i	−0.352074	−	0.203270i	−0.665598	+	0.746310i	$0.731824\pi$
$860$	4.45860	+	9.49581i	0.152037	+	0.323804i
$861$	4.67709	+	3.82256i	0.159395	+	0.130273i
$862$	15.3756	−	57.3825i	0.523695	−	1.95446i
$863$	−13.3552	−	13.3552i	−0.454617	−	0.454617i	0.442267	−	0.896884i	$-0.354174\pi$
$863$	−13.3552	−	13.3552i	−0.454617	−	0.454617i	−0.896884	+	0.442267i	$0.854174\pi$
$864$	20.9776	−	13.2221i	0.713672	−	0.449825i
$865$	−13.2625	+	19.0480i	−0.450940	+	0.647650i
$866$	−17.9423	+	10.3590i	−0.609704	+	0.352013i
$867$	24.0215	−	2.41504i	0.815814	−	0.0820191i
$868$	−0.132857	−	0.495830i	−0.00450947	−	0.0168296i
$869$	−1.75753	+	3.04413i	−0.0596201	+	0.103265i
$870$	−49.6976	+	0.774350i	−1.68491	+	0.0262529i
$871$	25.7442	+	44.5902i	0.872308	+	1.51088i
$872$	20.2022	−	20.2022i	0.684132	−	0.684132i
$873$	1.66477	−	27.0796i	0.0563441	−	0.916506i
$874$			3.62427i			0.122593i
$875$	−8.38337	+	2.31781i	−0.283410	+	0.0783564i
$876$	−27.0467	−	71.4223i	−0.913824	−	2.41314i
$877$	−6.46168	+	1.73140i	−0.218195	+	0.0584653i	−0.366261	−	0.930512i	$-0.619362\pi$
$877$	−6.46168	+	1.73140i	−0.218195	+	0.0584653i	0.148065	+	0.988978i	$0.452695\pi$
$878$	−32.2960	+	8.65368i	−1.08994	+	0.292048i
$879$	4.05144	+	10.6986i	0.136652	+	0.360856i
$880$	−0.269425	−	0.319368i	−0.00908232	−	0.0107659i
$881$			13.4495i			0.453126i	0.973996	+	0.226563i	$0.0727490\pi$
$881$			13.4495i			0.453126i	−0.973996	+	0.226563i	$0.927251\pi$
$882$	37.1492	+	24.6053i	1.25088	+	0.828503i
$883$	32.5618	−	32.5618i	1.09579	−	1.09579i	0.100896	−	0.994897i	$-0.467829\pi$
$883$	32.5618	−	32.5618i	1.09579	−	1.09579i	0.994897	−	0.100896i	$-0.0321708\pi$
$884$	−36.2127	−	62.7222i	−1.21796	−	2.10957i
$885$	−22.3743	−	21.6878i	−0.752105	−	0.729027i
$886$	25.4576	−	44.0939i	0.855266	−	1.48136i
$887$	6.81864	+	25.4475i	0.228948	+	0.854444i	0.980784	+	0.195095i	$0.0625015\pi$
$887$	6.81864	+	25.4475i	0.228948	+	0.854444i	−0.751837	+	0.659349i	$0.770832\pi$
$888$	−0.971196	+	0.0976406i	−0.0325912	+	0.00327661i
$889$	6.40444	−	3.69760i	0.214798	−	0.124014i
$890$	−1.21698	−	0.847349i	−0.0407933	−	0.0284032i
$891$	−1.37826	+	1.82663i	−0.0461733	+	0.0611943i
$892$	43.9677	+	43.9677i	1.47215	+	1.47215i
$893$	−0.492465	+	1.83790i	−0.0164797	+	0.0615031i
$894$	−28.4555	−	23.2566i	−0.951694	−	0.777816i
$895$	−31.7620	−	11.4653i	−1.06169	−	0.383243i
$896$	−13.2150	−	7.62966i	−0.441481	−	0.254889i
$897$	−19.1062	+	13.7500i	−0.637939	+	0.459098i
$898$	−53.0474	−	14.2140i	−1.77021	−	0.474327i
$899$	1.07393			0.0358175
$900$	−26.8224	−	43.2848i	−0.894079	−	1.44283i
$901$	7.37869			0.245820
$902$	−2.55708	−	0.685169i	−0.0851416	−	0.0228136i
$903$	−1.69773	−	0.765090i	−0.0564968	−	0.0254606i
$904$	−37.7857	−	21.8156i	−1.25673	−	0.725576i
$905$	−16.4674	−	5.94432i	−0.547393	−	0.197596i
$906$	−55.3044	+	20.9430i	−1.83736	+	0.695786i
$907$	−12.1728	+	45.4294i	−0.404190	+	1.50846i	0.401354	+	0.915923i	$0.368540\pi$
$907$	−12.1728	+	45.4294i	−0.404190	+	1.50846i	−0.805544	+	0.592536i	$0.798127\pi$
$908$	−27.0785	−	27.0785i	−0.898632	−	0.898632i
$909$	29.5701	−	26.1449i	0.980779	−	0.867172i
$910$	−12.7182	−	8.85530i	−0.421604	−	0.293550i
$911$	−19.0663	+	11.0079i	−0.631694	+	0.364709i	−0.781408	−	0.624021i	$-0.785498\pi$
$911$	−19.0663	+	11.0079i	−0.631694	+	0.364709i	0.149714	+	0.988729i	$0.452165\pi$
$912$	−0.327450	−	0.455007i	−0.0108429	−	0.0150668i
$913$	−0.354385	−	1.32258i	−0.0117284	−	0.0437711i
$914$	6.62414	−	11.4733i	0.219107	−	0.379505i
$915$	10.7417	−	3.05836i	0.355108	−	0.101106i
$916$	−8.27929	−	14.3402i	−0.273556	−	0.473812i
$917$	−7.39896	+	7.39896i	−0.244335	+	0.244335i
$918$	49.2740	+	45.5914i	1.62629	+	1.50474i
$919$			28.3896i			0.936486i	0.883600	+	0.468243i	$0.155113\pi$
$919$			28.3896i			0.936486i	−0.883600	+	0.468243i	$0.844887\pi$
$920$	16.5508	+	19.6188i	0.545663	+	0.646812i
$921$	−9.02345	+	11.0406i	−0.297333	+	0.363801i
$922$	72.2628	−	19.3627i	2.37985	−	0.637678i
$923$	−8.00199	+	2.14413i	−0.263389	+	0.0705748i
$924$	1.14788	+	0.187129i	0.0377626	+	0.00615611i
$925$	−0.0803917	−	0.866057i	−0.00264326	−	0.0284758i
$926$			14.8495i			0.487984i
$927$	21.8934	+	43.9459i	0.719074	+	1.44337i
$928$	18.6447	−	18.6447i	0.612042	−	0.612042i
$929$	−18.9202	−	32.7708i	−0.620753	−	1.07518i	−0.989346	−	0.145585i	$-0.953494\pi$
$929$	−18.9202	−	32.7708i	−0.620753	−	1.07518i	0.368593	−	0.929591i	$-0.379840\pi$
$930$	0.897707	+	1.50039i	0.0294370	+	0.0491999i
$931$	−1.40805	+	2.43882i	−0.0461471	+	0.0799292i
$932$	−9.82556	−	36.6695i	−0.321847	−	1.20115i
$933$	−8.20637	+	18.2099i	−0.268665	+	0.596164i
$934$	36.4067	−	21.0194i	1.19126	−	0.687776i
$935$	−1.80695	+	2.59518i	−0.0590934	+	0.0848714i
$936$	11.8392	−	35.3469i	0.386977	−	1.15535i
$937$	36.4371	+	36.4371i	1.19035	+	1.19035i	0.976969	+	0.213379i	$0.0684470\pi$
$937$	36.4371	+	36.4371i	1.19035	+	1.19035i	0.213379	+	0.976969i	$0.431553\pi$
$938$	−6.27801	+	23.4299i	−0.204984	+	0.765012i
$939$	1.85597	−	11.3848i	0.0605672	−	0.371530i
$940$	13.9398	+	29.6885i	0.454665	+	0.968333i
$941$	27.0690	+	15.6283i	0.882423	+	0.509467i	0.871457	−	0.490473i	$-0.163176\pi$
$941$	27.0690	+	15.6283i	0.882423	+	0.509467i	0.0109667	+	0.999940i	$0.496509\pi$
$942$	−6.81455	−	67.7818i	−0.222030	−	2.20845i
$943$	15.3428	+	4.11108i	0.499630	+	0.133875i
$944$	−5.91308			−0.192454
$945$	8.61478	+	2.73695i	0.280239	+	0.0890331i
$946$	0.816109			0.0265340
$947$	14.5266	+	3.89239i	0.472050	+	0.126486i	0.486999	−	0.873403i	$-0.338092\pi$
$947$	14.5266	+	3.89239i	0.472050	+	0.126486i	−0.0149482	+	0.999888i	$0.504758\pi$
$948$	8.13168	+	80.8828i	0.264105	+	2.62695i
$949$	43.1441	+	24.9092i	1.40052	+	0.808588i
$950$	4.17375	−	2.95554i	0.135414	−	0.0958904i
$951$	−0.559103	+	3.42964i	−0.0181302	+	0.111214i
$952$	3.62825	−	13.5408i	0.117592	−	0.438860i
$953$	−37.2073	−	37.2073i	−1.20526	−	1.20526i	−0.972544	−	0.232720i	$-0.925237\pi$
$953$	−37.2073	−	37.2073i	−1.20526	−	1.20526i	−0.232720	−	0.972544i	$-0.574763\pi$
$954$	6.12275	+	6.92488i	0.198231	+	0.224201i
$955$	25.2519	−	4.52154i	0.817133	−	0.146314i
$956$	−65.4799	+	37.8048i	−2.11777	+	1.22270i
$957$	−0.999714	+	2.21835i	−0.0323162	+	0.0717092i
$958$	2.11804	+	7.90463i	0.0684308	+	0.255387i
$959$	−3.80803	+	6.59570i	−0.122968	+	0.212986i
$960$	47.1551	+	11.8510i	1.52192	+	0.382488i
$961$	15.4811	+	26.8141i	0.499391	+	0.864970i
$962$	1.09582	−	1.09582i	0.0353306	−	0.0353306i
$963$	13.6209	−	20.5650i	0.438929	−	0.662698i
$964$			98.2761i			3.16526i
$965$	−1.04292	+	12.2953i	−0.0335727	+	0.395800i
$966$	−10.9451	−	1.78428i	−0.352153	−	0.0574083i
$967$	19.0216	−	5.09683i	0.611694	−	0.163903i	0.0603451	−	0.998178i	$-0.480780\pi$
$967$	19.0216	−	5.09683i	0.611694	−	0.163903i	0.551349	+	0.834275i	$0.314113\pi$
$968$	34.2190	−	9.16896i	1.09984	−	0.294701i
$969$	−2.68486	+	3.28505i	−0.0862500	+	0.105531i
$970$	35.9004	−	30.2863i	1.15269	−	0.972433i
$971$			6.75294i			0.216712i	0.994112	+	0.108356i	$0.0345586\pi$
$971$			6.75294i			0.216712i	−0.994112	+	0.108356i	$0.965441\pi$
$972$	−1.19586	+	52.9058i	−0.0383573	+	1.69695i
$973$	4.35065	−	4.35065i	0.139475	−	0.139475i
$974$	−48.1942	−	83.4747i	−1.54424	−	2.67470i
$975$	31.4155	+	10.7901i	1.00610	+	0.345559i
$976$	1.05969	−	1.83543i	0.0339198	−	0.0587508i
$977$	−7.67249	−	28.6341i	−0.245465	−	0.916086i	−0.973149	−	0.230175i	$-0.926070\pi$
$977$	−7.67249	−	28.6341i	−0.245465	−	0.916086i	0.727685	−	0.685912i	$-0.240596\pi$
$978$	−32.3943	−	45.0134i	−1.03586	−	1.43937i
$979$	−0.0628695	+	0.0362977i	−0.00200932	+	0.00116008i
$980$	8.55579	+	47.7825i	0.273305	+	1.52635i
$981$	−5.26660	−	25.9277i	−0.168149	−	0.827808i
$982$	−33.9466	−	33.9466i	−1.08328	−	1.08328i
$983$	−4.57606	+	17.0781i	−0.145954	+	0.544706i	0.853758	+	0.520671i	$0.174318\pi$
$983$	−4.57606	+	17.0781i	−0.145954	+	0.544706i	−0.999711	+	0.0240353i	$0.992349\pi$
$984$	−23.5235	+	8.90805i	−0.749903	+	0.283978i
$985$	−6.64934	+	3.12209i	−0.211866	+	0.0994780i
$986$	61.8194	+	35.6914i	1.96873	+	1.13665i
$987$	−5.30793	−	2.39205i	−0.168953	−	0.0761397i
$988$	5.53869	+	1.48409i	0.176209	+	0.0472151i
$989$	−4.89674			−0.155707
$990$	−3.93495	+	0.457634i	−0.125061	+	0.0145446i
$991$	−61.9280			−1.96721			−0.983603	−	0.180345i	$-0.942279\pi$
$991$	−61.9280			−1.96721			−0.983603	+	0.180345i	$0.942279\pi$
$992$	−0.895938	−	0.240066i	−0.0284461	−	0.00762210i
$993$	33.0936	−	23.8161i	1.05019	−	0.755781i
$994$	−3.37988	−	1.95138i	−0.107203	−	0.0618939i
$995$	−13.0568	+	36.1709i	−0.413929	+	1.14669i
$996$	−24.5184	−	20.0388i	−0.776896	−	0.634954i
$997$	6.50403	−	24.2734i	0.205985	−	0.768745i	−0.783163	−	0.621817i	$-0.786395\pi$
$997$	6.50403	−	24.2734i	0.205985	−	0.768745i	0.989147	−	0.146928i	$-0.0469386\pi$
$998$	−42.9908	−	42.9908i	−1.36085	−	1.36085i
$999$	−0.421246	+	0.799744i	−0.0133276	+	0.0253028i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.2.l.a.32.1	yes	16
3.2	odd	2		135.2.m.a.17.4		16
4.3	odd	2		720.2.cu.c.257.2		16
5.2	odd	4		225.2.p.b.68.4		16
5.3	odd	4	inner	45.2.l.a.23.1	yes	16
5.4	even	2		225.2.p.b.32.4		16
9.2	odd	6	inner	45.2.l.a.2.1	✓	16
9.4	even	3		405.2.f.a.242.8		16
9.5	odd	6		405.2.f.a.242.1		16
9.7	even	3		135.2.m.a.62.4		16
15.2	even	4		675.2.q.a.368.1		16
15.8	even	4		135.2.m.a.98.4		16
15.14	odd	2		675.2.q.a.557.1		16
20.3	even	4		720.2.cu.c.113.4		16
36.11	even	6		720.2.cu.c.497.4		16
45.2	even	12		225.2.p.b.218.4		16
45.7	odd	12		675.2.q.a.143.1		16
45.13	odd	12		405.2.f.a.323.1		16
45.23	even	12		405.2.f.a.323.8		16
45.29	odd	6		225.2.p.b.182.4		16
45.34	even	6		675.2.q.a.332.1		16
45.38	even	12	inner	45.2.l.a.38.1	yes	16
45.43	odd	12		135.2.m.a.8.4		16
180.83	odd	12		720.2.cu.c.353.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.2.l.a.2.1	✓	16	9.2	odd	6	inner
45.2.l.a.23.1	yes	16	5.3	odd	4	inner
45.2.l.a.32.1	yes	16	1.1	even	1	trivial
45.2.l.a.38.1	yes	16	45.38	even	12	inner
135.2.m.a.8.4		16	45.43	odd	12
135.2.m.a.17.4		16	3.2	odd	2
135.2.m.a.62.4		16	9.7	even	3
135.2.m.a.98.4		16	15.8	even	4
225.2.p.b.32.4		16	5.4	even	2
225.2.p.b.68.4		16	5.2	odd	4
225.2.p.b.182.4		16	45.29	odd	6
225.2.p.b.218.4		16	45.2	even	12
405.2.f.a.242.1		16	9.5	odd	6
405.2.f.a.242.8		16	9.4	even	3
405.2.f.a.323.1		16	45.13	odd	12
405.2.f.a.323.8		16	45.23	even	12
675.2.q.a.143.1		16	45.7	odd	12
675.2.q.a.332.1		16	45.34	even	6
675.2.q.a.368.1		16	15.2	even	4
675.2.q.a.557.1		16	15.14	odd	2
720.2.cu.c.113.4		16	20.3	even	4
720.2.cu.c.257.2		16	4.3	odd	2
720.2.cu.c.353.2		16	180.83	odd	12
720.2.cu.c.497.4		16	36.11	even	6

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	45.2.l.a.32.1

Level	$45$
Weight	$2$
Character	45.32
Analytic conductor	$0.359$
Analytic rank	$0$
Dimension	$16$
Inner twists	$4$